Properties

Label 690.2.j.b.367.4
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 367.4
Character \(\chi\) \(=\) 690.367
Dual form 690.2.j.b.643.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(0.597287 + 2.15482i) q^{5} +1.00000 q^{6} +(-1.47923 + 1.47923i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(0.597287 + 2.15482i) q^{5} +1.00000 q^{6} +(-1.47923 + 1.47923i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(1.10134 - 1.94603i) q^{10} +0.912381i q^{11} +(-0.707107 - 0.707107i) q^{12} +(-1.90626 + 1.90626i) q^{13} +2.09194 q^{14} +(-1.94603 - 1.10134i) q^{15} -1.00000 q^{16} +(-2.19207 + 2.19207i) q^{17} +(-0.707107 + 0.707107i) q^{18} +5.16113 q^{19} +(-2.15482 + 0.597287i) q^{20} -2.09194i q^{21} +(0.645151 - 0.645151i) q^{22} +(-1.50490 - 4.55360i) q^{23} +1.00000i q^{24} +(-4.28650 + 2.57409i) q^{25} +2.69587 q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.47923 - 1.47923i) q^{28} -8.27544i q^{29} +(0.597287 + 2.15482i) q^{30} -5.45970 q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.645151 - 0.645151i) q^{33} +3.10005 q^{34} +(-4.07099 - 2.30394i) q^{35} +1.00000 q^{36} +(-3.73458 + 3.73458i) q^{37} +(-3.64947 - 3.64947i) q^{38} -2.69587i q^{39} +(1.94603 + 1.10134i) q^{40} -12.1968 q^{41} +(-1.47923 + 1.47923i) q^{42} +(0.0783063 + 0.0783063i) q^{43} -0.912381 q^{44} +(2.15482 - 0.597287i) q^{45} +(-2.15576 + 4.28401i) q^{46} +(-4.92197 - 4.92197i) q^{47} +(0.707107 - 0.707107i) q^{48} +2.62378i q^{49} +(4.85117 + 1.21085i) q^{50} -3.10005i q^{51} +(-1.90626 - 1.90626i) q^{52} +(8.84686 + 8.84686i) q^{53} -1.00000i q^{54} +(-1.96602 + 0.544954i) q^{55} +2.09194i q^{56} +(-3.64947 + 3.64947i) q^{57} +(-5.85162 + 5.85162i) q^{58} -5.65776i q^{59} +(1.10134 - 1.94603i) q^{60} +9.70810i q^{61} +(3.86059 + 3.86059i) q^{62} +(1.47923 + 1.47923i) q^{63} -1.00000i q^{64} +(-5.24624 - 2.96907i) q^{65} +0.912381i q^{66} +(-5.22443 + 5.22443i) q^{67} +(-2.19207 - 2.19207i) q^{68} +(4.28401 + 2.15576i) q^{69} +(1.24949 + 4.50776i) q^{70} +10.3196 q^{71} +(-0.707107 - 0.707107i) q^{72} +(-8.97067 + 8.97067i) q^{73} +5.28150 q^{74} +(1.21085 - 4.85117i) q^{75} +5.16113i q^{76} +(-1.34962 - 1.34962i) q^{77} +(-1.90626 + 1.90626i) q^{78} +13.2521 q^{79} +(-0.597287 - 2.15482i) q^{80} -1.00000 q^{81} +(8.62442 + 8.62442i) q^{82} +(-8.86710 - 8.86710i) q^{83} +2.09194 q^{84} +(-6.03280 - 3.41421i) q^{85} -0.110742i q^{86} +(5.85162 + 5.85162i) q^{87} +(0.645151 + 0.645151i) q^{88} -0.837888 q^{89} +(-1.94603 - 1.10134i) q^{90} -5.63959i q^{91} +(4.55360 - 1.50490i) q^{92} +(3.86059 - 3.86059i) q^{93} +6.96072i q^{94} +(3.08268 + 11.1213i) q^{95} -1.00000 q^{96} +(-0.302433 + 0.302433i) q^{97} +(1.85529 - 1.85529i) q^{98} +0.912381 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
\(5\) 0.597287 + 2.15482i 0.267115 + 0.963665i
\(6\) 1.00000 0.408248
\(7\) −1.47923 + 1.47923i −0.559095 + 0.559095i −0.929050 0.369955i \(-0.879373\pi\)
0.369955 + 0.929050i \(0.379373\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 1.10134 1.94603i 0.348275 0.615390i
\(11\) 0.912381i 0.275093i 0.990495 + 0.137547i \(0.0439217\pi\)
−0.990495 + 0.137547i \(0.956078\pi\)
\(12\) −0.707107 0.707107i −0.204124 0.204124i
\(13\) −1.90626 + 1.90626i −0.528703 + 0.528703i −0.920185 0.391483i \(-0.871962\pi\)
0.391483 + 0.920185i \(0.371962\pi\)
\(14\) 2.09194 0.559095
\(15\) −1.94603 1.10134i −0.502464 0.284365i
\(16\) −1.00000 −0.250000
\(17\) −2.19207 + 2.19207i −0.531654 + 0.531654i −0.921064 0.389410i \(-0.872679\pi\)
0.389410 + 0.921064i \(0.372679\pi\)
\(18\) −0.707107 + 0.707107i −0.166667 + 0.166667i
\(19\) 5.16113 1.18405 0.592023 0.805921i \(-0.298330\pi\)
0.592023 + 0.805921i \(0.298330\pi\)
\(20\) −2.15482 + 0.597287i −0.481832 + 0.133558i
\(21\) 2.09194i 0.456499i
\(22\) 0.645151 0.645151i 0.137547 0.137547i
\(23\) −1.50490 4.55360i −0.313794 0.949491i
\(24\) 1.00000i 0.204124i
\(25\) −4.28650 + 2.57409i −0.857299 + 0.514819i
\(26\) 2.69587 0.528703
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) −1.47923 1.47923i −0.279547 0.279547i
\(29\) 8.27544i 1.53671i −0.640023 0.768355i \(-0.721075\pi\)
0.640023 0.768355i \(-0.278925\pi\)
\(30\) 0.597287 + 2.15482i 0.109049 + 0.393414i
\(31\) −5.45970 −0.980591 −0.490295 0.871556i \(-0.663111\pi\)
−0.490295 + 0.871556i \(0.663111\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) −0.645151 0.645151i −0.112306 0.112306i
\(34\) 3.10005 0.531654
\(35\) −4.07099 2.30394i −0.688123 0.389437i
\(36\) 1.00000 0.166667
\(37\) −3.73458 + 3.73458i −0.613962 + 0.613962i −0.943976 0.330014i \(-0.892946\pi\)
0.330014 + 0.943976i \(0.392946\pi\)
\(38\) −3.64947 3.64947i −0.592023 0.592023i
\(39\) 2.69587i 0.431684i
\(40\) 1.94603 + 1.10134i 0.307695 + 0.174137i
\(41\) −12.1968 −1.90482 −0.952408 0.304826i \(-0.901402\pi\)
−0.952408 + 0.304826i \(0.901402\pi\)
\(42\) −1.47923 + 1.47923i −0.228250 + 0.228250i
\(43\) 0.0783063 + 0.0783063i 0.0119416 + 0.0119416i 0.713052 0.701111i \(-0.247312\pi\)
−0.701111 + 0.713052i \(0.747312\pi\)
\(44\) −0.912381 −0.137547
\(45\) 2.15482 0.597287i 0.321222 0.0890384i
\(46\) −2.15576 + 4.28401i −0.317849 + 0.631642i
\(47\) −4.92197 4.92197i −0.717943 0.717943i 0.250241 0.968184i \(-0.419490\pi\)
−0.968184 + 0.250241i \(0.919490\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 2.62378i 0.374826i
\(50\) 4.85117 + 1.21085i 0.686059 + 0.171240i
\(51\) 3.10005i 0.434094i
\(52\) −1.90626 1.90626i −0.264351 0.264351i
\(53\) 8.84686 + 8.84686i 1.21521 + 1.21521i 0.969290 + 0.245919i \(0.0790897\pi\)
0.245919 + 0.969290i \(0.420910\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −1.96602 + 0.544954i −0.265098 + 0.0734816i
\(56\) 2.09194i 0.279547i
\(57\) −3.64947 + 3.64947i −0.483385 + 0.483385i
\(58\) −5.85162 + 5.85162i −0.768355 + 0.768355i
\(59\) 5.65776i 0.736577i −0.929711 0.368289i \(-0.879944\pi\)
0.929711 0.368289i \(-0.120056\pi\)
\(60\) 1.10134 1.94603i 0.142183 0.251232i
\(61\) 9.70810i 1.24299i 0.783416 + 0.621497i \(0.213475\pi\)
−0.783416 + 0.621497i \(0.786525\pi\)
\(62\) 3.86059 + 3.86059i 0.490295 + 0.490295i
\(63\) 1.47923 + 1.47923i 0.186365 + 0.186365i
\(64\) 1.00000i 0.125000i
\(65\) −5.24624 2.96907i −0.650717 0.368268i
\(66\) 0.912381i 0.112306i
\(67\) −5.22443 + 5.22443i −0.638265 + 0.638265i −0.950127 0.311862i \(-0.899047\pi\)
0.311862 + 0.950127i \(0.399047\pi\)
\(68\) −2.19207 2.19207i −0.265827 0.265827i
\(69\) 4.28401 + 2.15576i 0.515734 + 0.259522i
\(70\) 1.24949 + 4.50776i 0.149343 + 0.538780i
\(71\) 10.3196 1.22472 0.612358 0.790580i \(-0.290221\pi\)
0.612358 + 0.790580i \(0.290221\pi\)
\(72\) −0.707107 0.707107i −0.0833333 0.0833333i
\(73\) −8.97067 + 8.97067i −1.04994 + 1.04994i −0.0512515 + 0.998686i \(0.516321\pi\)
−0.998686 + 0.0512515i \(0.983679\pi\)
\(74\) 5.28150 0.613962
\(75\) 1.21085 4.85117i 0.139817 0.560165i
\(76\) 5.16113i 0.592023i
\(77\) −1.34962 1.34962i −0.153803 0.153803i
\(78\) −1.90626 + 1.90626i −0.215842 + 0.215842i
\(79\) 13.2521 1.49098 0.745489 0.666518i \(-0.232216\pi\)
0.745489 + 0.666518i \(0.232216\pi\)
\(80\) −0.597287 2.15482i −0.0667788 0.240916i
\(81\) −1.00000 −0.111111
\(82\) 8.62442 + 8.62442i 0.952408 + 0.952408i
\(83\) −8.86710 8.86710i −0.973290 0.973290i 0.0263622 0.999652i \(-0.491608\pi\)
−0.999652 + 0.0263622i \(0.991608\pi\)
\(84\) 2.09194 0.228250
\(85\) −6.03280 3.41421i −0.654349 0.370323i
\(86\) 0.110742i 0.0119416i
\(87\) 5.85162 + 5.85162i 0.627360 + 0.627360i
\(88\) 0.645151 + 0.645151i 0.0687733 + 0.0687733i
\(89\) −0.837888 −0.0888160 −0.0444080 0.999013i \(-0.514140\pi\)
−0.0444080 + 0.999013i \(0.514140\pi\)
\(90\) −1.94603 1.10134i −0.205130 0.116092i
\(91\) 5.63959i 0.591190i
\(92\) 4.55360 1.50490i 0.474746 0.156897i
\(93\) 3.86059 3.86059i 0.400324 0.400324i
\(94\) 6.96072i 0.717943i
\(95\) 3.08268 + 11.1213i 0.316276 + 1.14102i
\(96\) −1.00000 −0.102062
\(97\) −0.302433 + 0.302433i −0.0307074 + 0.0307074i −0.722294 0.691586i \(-0.756912\pi\)
0.691586 + 0.722294i \(0.256912\pi\)
\(98\) 1.85529 1.85529i 0.187413 0.187413i
\(99\) 0.912381 0.0916978
\(100\) −2.57409 4.28650i −0.257409 0.428650i
\(101\) −7.34962 −0.731314 −0.365657 0.930750i \(-0.619156\pi\)
−0.365657 + 0.930750i \(0.619156\pi\)
\(102\) −2.19207 + 2.19207i −0.217047 + 0.217047i
\(103\) −7.10380 7.10380i −0.699959 0.699959i 0.264443 0.964401i \(-0.414812\pi\)
−0.964401 + 0.264443i \(0.914812\pi\)
\(104\) 2.69587i 0.264351i
\(105\) 4.50776 1.24949i 0.439912 0.121938i
\(106\) 12.5113i 1.21521i
\(107\) −8.43368 + 8.43368i −0.815315 + 0.815315i −0.985425 0.170110i \(-0.945588\pi\)
0.170110 + 0.985425i \(0.445588\pi\)
\(108\) −0.707107 + 0.707107i −0.0680414 + 0.0680414i
\(109\) 1.62328 0.155482 0.0777411 0.996974i \(-0.475229\pi\)
0.0777411 + 0.996974i \(0.475229\pi\)
\(110\) 1.77552 + 1.00484i 0.169290 + 0.0958081i
\(111\) 5.28150i 0.501298i
\(112\) 1.47923 1.47923i 0.139774 0.139774i
\(113\) 0.871735 + 0.871735i 0.0820059 + 0.0820059i 0.746920 0.664914i \(-0.231532\pi\)
−0.664914 + 0.746920i \(0.731532\pi\)
\(114\) 5.16113 0.483385
\(115\) 8.91333 5.96260i 0.831172 0.556015i
\(116\) 8.27544 0.768355
\(117\) 1.90626 + 1.90626i 0.176234 + 0.176234i
\(118\) −4.00064 + 4.00064i −0.368289 + 0.368289i
\(119\) 6.48512i 0.594490i
\(120\) −2.15482 + 0.597287i −0.196707 + 0.0545246i
\(121\) 10.1676 0.924324
\(122\) 6.86466 6.86466i 0.621497 0.621497i
\(123\) 8.62442 8.62442i 0.777638 0.777638i
\(124\) 5.45970i 0.490295i
\(125\) −8.10698 7.69915i −0.725110 0.688633i
\(126\) 2.09194i 0.186365i
\(127\) 8.50911 + 8.50911i 0.755062 + 0.755062i 0.975419 0.220357i \(-0.0707224\pi\)
−0.220357 + 0.975419i \(0.570722\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −0.110742 −0.00975027
\(130\) 1.61021 + 5.80910i 0.141224 + 0.509492i
\(131\) −0.782944 −0.0684061 −0.0342030 0.999415i \(-0.510889\pi\)
−0.0342030 + 0.999415i \(0.510889\pi\)
\(132\) 0.645151 0.645151i 0.0561532 0.0561532i
\(133\) −7.63448 + 7.63448i −0.661994 + 0.661994i
\(134\) 7.38845 0.638265
\(135\) −1.10134 + 1.94603i −0.0947884 + 0.167488i
\(136\) 3.10005i 0.265827i
\(137\) 7.97847 7.97847i 0.681647 0.681647i −0.278724 0.960371i \(-0.589912\pi\)
0.960371 + 0.278724i \(0.0899115\pi\)
\(138\) −1.50490 4.55360i −0.128106 0.387628i
\(139\) 5.31355i 0.450689i −0.974279 0.225345i \(-0.927649\pi\)
0.974279 0.225345i \(-0.0723508\pi\)
\(140\) 2.30394 4.07099i 0.194719 0.344061i
\(141\) 6.96072 0.586198
\(142\) −7.29709 7.29709i −0.612358 0.612358i
\(143\) −1.73924 1.73924i −0.145443 0.145443i
\(144\) 1.00000i 0.0833333i
\(145\) 17.8321 4.94282i 1.48087 0.410479i
\(146\) 12.6864 1.04994
\(147\) −1.85529 1.85529i −0.153022 0.153022i
\(148\) −3.73458 3.73458i −0.306981 0.306981i
\(149\) 8.12233 0.665407 0.332704 0.943031i \(-0.392039\pi\)
0.332704 + 0.943031i \(0.392039\pi\)
\(150\) −4.28650 + 2.57409i −0.349991 + 0.210174i
\(151\) 2.41716 0.196705 0.0983527 0.995152i \(-0.468643\pi\)
0.0983527 + 0.995152i \(0.468643\pi\)
\(152\) 3.64947 3.64947i 0.296011 0.296011i
\(153\) 2.19207 + 2.19207i 0.177218 + 0.177218i
\(154\) 1.90865i 0.153803i
\(155\) −3.26101 11.7647i −0.261931 0.944960i
\(156\) 2.69587 0.215842
\(157\) −9.97955 + 9.97955i −0.796455 + 0.796455i −0.982535 0.186080i \(-0.940422\pi\)
0.186080 + 0.982535i \(0.440422\pi\)
\(158\) −9.37065 9.37065i −0.745489 0.745489i
\(159\) −12.5113 −0.992214
\(160\) −1.10134 + 1.94603i −0.0870687 + 0.153847i
\(161\) 8.96189 + 4.50971i 0.706296 + 0.355415i
\(162\) 0.707107 + 0.707107i 0.0555556 + 0.0555556i
\(163\) 11.2043 11.2043i 0.877585 0.877585i −0.115699 0.993284i \(-0.536911\pi\)
0.993284 + 0.115699i \(0.0369108\pi\)
\(164\) 12.1968i 0.952408i
\(165\) 1.00484 1.77552i 0.0782270 0.138224i
\(166\) 12.5400i 0.973290i
\(167\) 13.9061 + 13.9061i 1.07608 + 1.07608i 0.996857 + 0.0792276i \(0.0252454\pi\)
0.0792276 + 0.996857i \(0.474755\pi\)
\(168\) −1.47923 1.47923i −0.114125 0.114125i
\(169\) 5.73231i 0.440947i
\(170\) 1.85162 + 6.68005i 0.142013 + 0.512336i
\(171\) 5.16113i 0.394682i
\(172\) −0.0783063 + 0.0783063i −0.00597080 + 0.00597080i
\(173\) 4.89730 4.89730i 0.372335 0.372335i −0.495992 0.868327i \(-0.665196\pi\)
0.868327 + 0.495992i \(0.165196\pi\)
\(174\) 8.27544i 0.627360i
\(175\) 2.53303 10.1484i 0.191479 0.767144i
\(176\) 0.912381i 0.0687733i
\(177\) 4.00064 + 4.00064i 0.300706 + 0.300706i
\(178\) 0.592477 + 0.592477i 0.0444080 + 0.0444080i
\(179\) 1.76577i 0.131980i −0.997820 0.0659899i \(-0.978980\pi\)
0.997820 0.0659899i \(-0.0210205\pi\)
\(180\) 0.597287 + 2.15482i 0.0445192 + 0.160611i
\(181\) 4.71006i 0.350096i 0.984560 + 0.175048i \(0.0560080\pi\)
−0.984560 + 0.175048i \(0.943992\pi\)
\(182\) −3.98779 + 3.98779i −0.295595 + 0.295595i
\(183\) −6.86466 6.86466i −0.507450 0.507450i
\(184\) −4.28401 2.15576i −0.315821 0.158924i
\(185\) −10.2780 5.81673i −0.755652 0.427655i
\(186\) −5.45970 −0.400324
\(187\) −2.00000 2.00000i −0.146254 0.146254i
\(188\) 4.92197 4.92197i 0.358972 0.358972i
\(189\) −2.09194 −0.152166
\(190\) 5.68417 10.0437i 0.412373 0.728650i
\(191\) 22.1289i 1.60119i 0.599207 + 0.800594i \(0.295483\pi\)
−0.599207 + 0.800594i \(0.704517\pi\)
\(192\) 0.707107 + 0.707107i 0.0510310 + 0.0510310i
\(193\) −0.634485 + 0.634485i −0.0456712 + 0.0456712i −0.729574 0.683902i \(-0.760281\pi\)
0.683902 + 0.729574i \(0.260281\pi\)
\(194\) 0.427704 0.0307074
\(195\) 5.80910 1.61021i 0.415999 0.115309i
\(196\) −2.62378 −0.187413
\(197\) 5.84405 + 5.84405i 0.416371 + 0.416371i 0.883951 0.467580i \(-0.154874\pi\)
−0.467580 + 0.883951i \(0.654874\pi\)
\(198\) −0.645151 0.645151i −0.0458489 0.0458489i
\(199\) −17.5085 −1.24114 −0.620572 0.784150i \(-0.713099\pi\)
−0.620572 + 0.784150i \(0.713099\pi\)
\(200\) −1.21085 + 4.85117i −0.0856201 + 0.343029i
\(201\) 7.38845i 0.521141i
\(202\) 5.19696 + 5.19696i 0.365657 + 0.365657i
\(203\) 12.2412 + 12.2412i 0.859167 + 0.859167i
\(204\) 3.10005 0.217047
\(205\) −7.28498 26.2818i −0.508805 1.83560i
\(206\) 10.0463i 0.699959i
\(207\) −4.55360 + 1.50490i −0.316497 + 0.104598i
\(208\) 1.90626 1.90626i 0.132176 0.132176i
\(209\) 4.70892i 0.325723i
\(210\) −4.07099 2.30394i −0.280925 0.158987i
\(211\) 3.92363 0.270113 0.135057 0.990838i \(-0.456878\pi\)
0.135057 + 0.990838i \(0.456878\pi\)
\(212\) −8.84686 + 8.84686i −0.607605 + 0.607605i
\(213\) −7.29709 + 7.29709i −0.499989 + 0.499989i
\(214\) 11.9270 0.815315
\(215\) −0.121965 + 0.215507i −0.00831792 + 0.0146975i
\(216\) 1.00000 0.0680414
\(217\) 8.07613 8.07613i 0.548243 0.548243i
\(218\) −1.14783 1.14783i −0.0777411 0.0777411i
\(219\) 12.6864i 0.857270i
\(220\) −0.544954 1.96602i −0.0367408 0.132549i
\(221\) 8.35732i 0.562174i
\(222\) −3.73458 + 3.73458i −0.250649 + 0.250649i
\(223\) 8.34970 8.34970i 0.559137 0.559137i −0.369925 0.929062i \(-0.620617\pi\)
0.929062 + 0.369925i \(0.120617\pi\)
\(224\) −2.09194 −0.139774
\(225\) 2.57409 + 4.28650i 0.171606 + 0.285766i
\(226\) 1.23282i 0.0820059i
\(227\) −4.73307 + 4.73307i −0.314145 + 0.314145i −0.846513 0.532368i \(-0.821302\pi\)
0.532368 + 0.846513i \(0.321302\pi\)
\(228\) −3.64947 3.64947i −0.241692 0.241692i
\(229\) 5.56644 0.367840 0.183920 0.982941i \(-0.441121\pi\)
0.183920 + 0.982941i \(0.441121\pi\)
\(230\) −10.5189 2.08648i −0.693594 0.137578i
\(231\) 1.90865 0.125580
\(232\) −5.85162 5.85162i −0.384178 0.384178i
\(233\) 1.86513 1.86513i 0.122189 0.122189i −0.643368 0.765557i \(-0.722463\pi\)
0.765557 + 0.643368i \(0.222463\pi\)
\(234\) 2.69587i 0.176234i
\(235\) 7.66613 13.5458i 0.500083 0.883630i
\(236\) 5.65776 0.368289
\(237\) −9.37065 + 9.37065i −0.608689 + 0.608689i
\(238\) −4.58567 + 4.58567i −0.297245 + 0.297245i
\(239\) 19.0304i 1.23097i 0.788148 + 0.615486i \(0.211040\pi\)
−0.788148 + 0.615486i \(0.788960\pi\)
\(240\) 1.94603 + 1.10134i 0.125616 + 0.0710913i
\(241\) 0.615651i 0.0396576i −0.999803 0.0198288i \(-0.993688\pi\)
0.999803 0.0198288i \(-0.00631211\pi\)
\(242\) −7.18955 7.18955i −0.462162 0.462162i
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) −9.70810 −0.621497
\(245\) −5.65378 + 1.56715i −0.361206 + 0.100122i
\(246\) −12.1968 −0.777638
\(247\) −9.83849 + 9.83849i −0.626008 + 0.626008i
\(248\) −3.86059 + 3.86059i −0.245148 + 0.245148i
\(249\) 12.5400 0.794688
\(250\) 0.288377 + 11.1766i 0.0182385 + 0.706872i
\(251\) 18.8785i 1.19160i −0.803133 0.595800i \(-0.796835\pi\)
0.803133 0.595800i \(-0.203165\pi\)
\(252\) −1.47923 + 1.47923i −0.0931825 + 0.0931825i
\(253\) 4.15462 1.37304i 0.261199 0.0863225i
\(254\) 12.0337i 0.755062i
\(255\) 6.68005 1.85162i 0.418321 0.115953i
\(256\) 1.00000 0.0625000
\(257\) −15.0074 15.0074i −0.936134 0.936134i 0.0619452 0.998080i \(-0.480270\pi\)
−0.998080 + 0.0619452i \(0.980270\pi\)
\(258\) 0.0783063 + 0.0783063i 0.00487514 + 0.00487514i
\(259\) 11.0486i 0.686526i
\(260\) 2.96907 5.24624i 0.184134 0.325358i
\(261\) −8.27544 −0.512237
\(262\) 0.553625 + 0.553625i 0.0342030 + 0.0342030i
\(263\) 22.5610 + 22.5610i 1.39117 + 1.39117i 0.822705 + 0.568469i \(0.192464\pi\)
0.568469 + 0.822705i \(0.307536\pi\)
\(264\) −0.912381 −0.0561532
\(265\) −13.7793 + 24.3475i −0.846454 + 1.49565i
\(266\) 10.7968 0.661994
\(267\) 0.592477 0.592477i 0.0362590 0.0362590i
\(268\) −5.22443 5.22443i −0.319133 0.319133i
\(269\) 26.2246i 1.59894i 0.600705 + 0.799471i \(0.294887\pi\)
−0.600705 + 0.799471i \(0.705113\pi\)
\(270\) 2.15482 0.597287i 0.131138 0.0363498i
\(271\) 8.26950 0.502337 0.251168 0.967943i \(-0.419185\pi\)
0.251168 + 0.967943i \(0.419185\pi\)
\(272\) 2.19207 2.19207i 0.132914 0.132914i
\(273\) 3.98779 + 3.98779i 0.241352 + 0.241352i
\(274\) −11.2833 −0.681647
\(275\) −2.34855 3.91092i −0.141623 0.235837i
\(276\) −2.15576 + 4.28401i −0.129761 + 0.257867i
\(277\) 11.7278 + 11.7278i 0.704657 + 0.704657i 0.965407 0.260749i \(-0.0839696\pi\)
−0.260749 + 0.965407i \(0.583970\pi\)
\(278\) −3.75725 + 3.75725i −0.225345 + 0.225345i
\(279\) 5.45970i 0.326864i
\(280\) −4.50776 + 1.24949i −0.269390 + 0.0746713i
\(281\) 29.2523i 1.74504i 0.488574 + 0.872522i \(0.337517\pi\)
−0.488574 + 0.872522i \(0.662483\pi\)
\(282\) −4.92197 4.92197i −0.293099 0.293099i
\(283\) 7.44353 + 7.44353i 0.442472 + 0.442472i 0.892842 0.450370i \(-0.148708\pi\)
−0.450370 + 0.892842i \(0.648708\pi\)
\(284\) 10.3196i 0.612358i
\(285\) −10.0437 5.68417i −0.594940 0.336701i
\(286\) 2.45966i 0.145443i
\(287\) 18.0418 18.0418i 1.06497 1.06497i
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) 7.38969i 0.434688i
\(290\) −16.1043 9.11409i −0.945676 0.535198i
\(291\) 0.427704i 0.0250725i
\(292\) −8.97067 8.97067i −0.524969 0.524969i
\(293\) 10.6547 + 10.6547i 0.622453 + 0.622453i 0.946158 0.323705i \(-0.104928\pi\)
−0.323705 + 0.946158i \(0.604928\pi\)
\(294\) 2.62378i 0.153022i
\(295\) 12.1914 3.37931i 0.709814 0.196751i
\(296\) 5.28150i 0.306981i
\(297\) −0.645151 + 0.645151i −0.0374355 + 0.0374355i
\(298\) −5.74336 5.74336i −0.332704 0.332704i
\(299\) 11.5491 + 5.81163i 0.667902 + 0.336095i
\(300\) 4.85117 + 1.21085i 0.280082 + 0.0699085i
\(301\) −0.231665 −0.0133530
\(302\) −1.70919 1.70919i −0.0983527 0.0983527i
\(303\) 5.19696 5.19696i 0.298558 0.298558i
\(304\) −5.16113 −0.296011
\(305\) −20.9192 + 5.79853i −1.19783 + 0.332023i
\(306\) 3.10005i 0.177218i
\(307\) 4.65466 + 4.65466i 0.265655 + 0.265655i 0.827347 0.561692i \(-0.189849\pi\)
−0.561692 + 0.827347i \(0.689849\pi\)
\(308\) 1.34962 1.34962i 0.0769016 0.0769016i
\(309\) 10.0463 0.571514
\(310\) −6.01299 + 10.6248i −0.341515 + 0.603445i
\(311\) 10.2005 0.578419 0.289209 0.957266i \(-0.406608\pi\)
0.289209 + 0.957266i \(0.406608\pi\)
\(312\) −1.90626 1.90626i −0.107921 0.107921i
\(313\) −10.5057 10.5057i −0.593820 0.593820i 0.344841 0.938661i \(-0.387933\pi\)
−0.938661 + 0.344841i \(0.887933\pi\)
\(314\) 14.1132 0.796455
\(315\) −2.30394 + 4.07099i −0.129812 + 0.229374i
\(316\) 13.2521i 0.745489i
\(317\) −15.7253 15.7253i −0.883223 0.883223i 0.110638 0.993861i \(-0.464711\pi\)
−0.993861 + 0.110638i \(0.964711\pi\)
\(318\) 8.84686 + 8.84686i 0.496107 + 0.496107i
\(319\) 7.55036 0.422739
\(320\) 2.15482 0.597287i 0.120458 0.0333894i
\(321\) 11.9270i 0.665702i
\(322\) −3.14817 9.52586i −0.175440 0.530856i
\(323\) −11.3135 + 11.3135i −0.629503 + 0.629503i
\(324\) 1.00000i 0.0555556i
\(325\) 3.26429 13.0781i 0.181070 0.725442i
\(326\) −15.8452 −0.877585
\(327\) −1.14783 + 1.14783i −0.0634753 + 0.0634753i
\(328\) −8.62442 + 8.62442i −0.476204 + 0.476204i
\(329\) 14.5614 0.802797
\(330\) −1.96602 + 0.544954i −0.108226 + 0.0299987i
\(331\) −20.0508 −1.10209 −0.551045 0.834475i \(-0.685771\pi\)
−0.551045 + 0.834475i \(0.685771\pi\)
\(332\) 8.86710 8.86710i 0.486645 0.486645i
\(333\) 3.73458 + 3.73458i 0.204654 + 0.204654i
\(334\) 19.6662i 1.07608i
\(335\) −14.3782 8.13721i −0.785564 0.444583i
\(336\) 2.09194i 0.114125i
\(337\) −10.0062 + 10.0062i −0.545074 + 0.545074i −0.925012 0.379938i \(-0.875945\pi\)
0.379938 + 0.925012i \(0.375945\pi\)
\(338\) 4.05335 4.05335i 0.220473 0.220473i
\(339\) −1.23282 −0.0669575
\(340\) 3.41421 6.03280i 0.185162 0.327175i
\(341\) 4.98133i 0.269754i
\(342\) −3.64947 + 3.64947i −0.197341 + 0.197341i
\(343\) −14.2357 14.2357i −0.768658 0.768658i
\(344\) 0.110742 0.00597080
\(345\) −2.08648 + 10.5189i −0.112332 + 0.566317i
\(346\) −6.92582 −0.372335
\(347\) −7.67093 7.67093i −0.411797 0.411797i 0.470567 0.882364i \(-0.344049\pi\)
−0.882364 + 0.470567i \(0.844049\pi\)
\(348\) −5.85162 + 5.85162i −0.313680 + 0.313680i
\(349\) 24.2192i 1.29643i 0.761459 + 0.648213i \(0.224483\pi\)
−0.761459 + 0.648213i \(0.775517\pi\)
\(350\) −8.96710 + 5.38485i −0.479311 + 0.287832i
\(351\) −2.69587 −0.143895
\(352\) −0.645151 + 0.645151i −0.0343867 + 0.0343867i
\(353\) −4.31291 + 4.31291i −0.229553 + 0.229553i −0.812506 0.582953i \(-0.801897\pi\)
0.582953 + 0.812506i \(0.301897\pi\)
\(354\) 5.65776i 0.300706i
\(355\) 6.16380 + 22.2370i 0.327140 + 1.18022i
\(356\) 0.837888i 0.0444080i
\(357\) 4.58567 + 4.58567i 0.242700 + 0.242700i
\(358\) −1.24859 + 1.24859i −0.0659899 + 0.0659899i
\(359\) −24.1751 −1.27591 −0.637957 0.770072i \(-0.720220\pi\)
−0.637957 + 0.770072i \(0.720220\pi\)
\(360\) 1.10134 1.94603i 0.0580458 0.102565i
\(361\) 7.63731 0.401964
\(362\) 3.33051 3.33051i 0.175048 0.175048i
\(363\) −7.18955 + 7.18955i −0.377354 + 0.377354i
\(364\) 5.63959 0.295595
\(365\) −24.6882 13.9721i −1.29224 0.731333i
\(366\) 9.70810i 0.507450i
\(367\) −9.65448 + 9.65448i −0.503960 + 0.503960i −0.912666 0.408706i \(-0.865980\pi\)
0.408706 + 0.912666i \(0.365980\pi\)
\(368\) 1.50490 + 4.55360i 0.0784484 + 0.237373i
\(369\) 12.1968i 0.634939i
\(370\) 3.15457 + 11.3807i 0.163998 + 0.591653i
\(371\) −26.1730 −1.35883
\(372\) 3.86059 + 3.86059i 0.200162 + 0.200162i
\(373\) −11.1907 11.1907i −0.579430 0.579430i 0.355316 0.934746i \(-0.384373\pi\)
−0.934746 + 0.355316i \(0.884373\pi\)
\(374\) 2.82843i 0.146254i
\(375\) 11.1766 0.288377i 0.577158 0.0148917i
\(376\) −6.96072 −0.358972
\(377\) 15.7752 + 15.7752i 0.812463 + 0.812463i
\(378\) 1.47923 + 1.47923i 0.0760832 + 0.0760832i
\(379\) −2.09559 −0.107643 −0.0538217 0.998551i \(-0.517140\pi\)
−0.0538217 + 0.998551i \(0.517140\pi\)
\(380\) −11.1213 + 3.08268i −0.570511 + 0.158138i
\(381\) −12.0337 −0.616505
\(382\) 15.6475 15.6475i 0.800594 0.800594i
\(383\) 14.3286 + 14.3286i 0.732155 + 0.732155i 0.971046 0.238891i \(-0.0767840\pi\)
−0.238891 + 0.971046i \(0.576784\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 2.10207 3.71429i 0.107132 0.189298i
\(386\) 0.897297 0.0456712
\(387\) 0.0783063 0.0783063i 0.00398053 0.00398053i
\(388\) −0.302433 0.302433i −0.0153537 0.0153537i
\(389\) −31.8387 −1.61429 −0.807143 0.590356i \(-0.798987\pi\)
−0.807143 + 0.590356i \(0.798987\pi\)
\(390\) −5.24624 2.96907i −0.265654 0.150345i
\(391\) 13.2806 + 6.68295i 0.671631 + 0.337971i
\(392\) 1.85529 + 1.85529i 0.0937065 + 0.0937065i
\(393\) 0.553625 0.553625i 0.0279267 0.0279267i
\(394\) 8.26474i 0.416371i
\(395\) 7.91531 + 28.5559i 0.398263 + 1.43680i
\(396\) 0.912381i 0.0458489i
\(397\) 4.21350 + 4.21350i 0.211470 + 0.211470i 0.804892 0.593422i \(-0.202223\pi\)
−0.593422 + 0.804892i \(0.702223\pi\)
\(398\) 12.3804 + 12.3804i 0.620572 + 0.620572i
\(399\) 10.7968i 0.540516i
\(400\) 4.28650 2.57409i 0.214325 0.128705i
\(401\) 10.3648i 0.517594i 0.965932 + 0.258797i \(0.0833260\pi\)
−0.965932 + 0.258797i \(0.916674\pi\)
\(402\) −5.22443 + 5.22443i −0.260571 + 0.260571i
\(403\) 10.4076 10.4076i 0.518441 0.518441i
\(404\) 7.34962i 0.365657i
\(405\) −0.597287 2.15482i −0.0296795 0.107074i
\(406\) 17.3117i 0.859167i
\(407\) −3.40736 3.40736i −0.168897 0.168897i
\(408\) −2.19207 2.19207i −0.108523 0.108523i
\(409\) 37.4377i 1.85118i −0.378531 0.925589i \(-0.623571\pi\)
0.378531 0.925589i \(-0.376429\pi\)
\(410\) −13.4328 + 23.7353i −0.663399 + 1.17220i
\(411\) 11.2833i 0.556562i
\(412\) 7.10380 7.10380i 0.349979 0.349979i
\(413\) 8.36910 + 8.36910i 0.411817 + 0.411817i
\(414\) 4.28401 + 2.15576i 0.210547 + 0.105950i
\(415\) 13.8108 24.4032i 0.677945 1.19791i
\(416\) −2.69587 −0.132176
\(417\) 3.75725 + 3.75725i 0.183993 + 0.183993i
\(418\) 3.32971 3.32971i 0.162861 0.162861i
\(419\) −15.3885 −0.751778 −0.375889 0.926665i \(-0.622663\pi\)
−0.375889 + 0.926665i \(0.622663\pi\)
\(420\) 1.24949 + 4.50776i 0.0609689 + 0.219956i
\(421\) 29.0436i 1.41550i 0.706465 + 0.707748i \(0.250289\pi\)
−0.706465 + 0.707748i \(0.749711\pi\)
\(422\) −2.77442 2.77442i −0.135057 0.135057i
\(423\) −4.92197 + 4.92197i −0.239314 + 0.239314i
\(424\) 12.5113 0.607605
\(425\) 3.75370 15.0389i 0.182081 0.729492i
\(426\) 10.3196 0.499989
\(427\) −14.3605 14.3605i −0.694952 0.694952i
\(428\) −8.43368 8.43368i −0.407657 0.407657i
\(429\) 2.45966 0.118753
\(430\) 0.238629 0.0661447i 0.0115077 0.00318978i
\(431\) 6.36434i 0.306559i −0.988183 0.153280i \(-0.951016\pi\)
0.988183 0.153280i \(-0.0489835\pi\)
\(432\) −0.707107 0.707107i −0.0340207 0.0340207i
\(433\) 19.6731 + 19.6731i 0.945429 + 0.945429i 0.998586 0.0531576i \(-0.0169286\pi\)
−0.0531576 + 0.998586i \(0.516929\pi\)
\(434\) −11.4214 −0.548243
\(435\) −9.11409 + 16.1043i −0.436987 + 0.772141i
\(436\) 1.62328i 0.0777411i
\(437\) −7.76700 23.5017i −0.371546 1.12424i
\(438\) −8.97067 + 8.97067i −0.428635 + 0.428635i
\(439\) 7.59434i 0.362458i 0.983441 + 0.181229i \(0.0580075\pi\)
−0.983441 + 0.181229i \(0.941992\pi\)
\(440\) −1.00484 + 1.77552i −0.0479040 + 0.0846448i
\(441\) 2.62378 0.124942
\(442\) −5.90952 + 5.90952i −0.281087 + 0.281087i
\(443\) −4.89201 + 4.89201i −0.232426 + 0.232426i −0.813705 0.581278i \(-0.802553\pi\)
0.581278 + 0.813705i \(0.302553\pi\)
\(444\) 5.28150 0.250649
\(445\) −0.500460 1.80550i −0.0237241 0.0855888i
\(446\) −11.8083 −0.559137
\(447\) −5.74336 + 5.74336i −0.271651 + 0.271651i
\(448\) 1.47923 + 1.47923i 0.0698869 + 0.0698869i
\(449\) 6.82441i 0.322064i −0.986949 0.161032i \(-0.948518\pi\)
0.986949 0.161032i \(-0.0514822\pi\)
\(450\) 1.21085 4.85117i 0.0570801 0.228686i
\(451\) 11.1281i 0.524002i
\(452\) −0.871735 + 0.871735i −0.0410029 + 0.0410029i
\(453\) −1.70919 + 1.70919i −0.0803046 + 0.0803046i
\(454\) 6.69357 0.314145
\(455\) 12.1523 3.36846i 0.569709 0.157916i
\(456\) 5.16113i 0.241692i
\(457\) 12.7153 12.7153i 0.594797 0.594797i −0.344126 0.938923i \(-0.611825\pi\)
0.938923 + 0.344126i \(0.111825\pi\)
\(458\) −3.93606 3.93606i −0.183920 0.183920i
\(459\) −3.10005 −0.144698
\(460\) 5.96260 + 8.91333i 0.278008 + 0.415586i
\(461\) 3.97264 0.185024 0.0925121 0.995712i \(-0.470510\pi\)
0.0925121 + 0.995712i \(0.470510\pi\)
\(462\) −1.34962 1.34962i −0.0627899 0.0627899i
\(463\) 16.0745 16.0745i 0.747043 0.747043i −0.226879 0.973923i \(-0.572852\pi\)
0.973923 + 0.226879i \(0.0728524\pi\)
\(464\) 8.27544i 0.384178i
\(465\) 10.6248 + 6.01299i 0.492711 + 0.278846i
\(466\) −2.63770 −0.122189
\(467\) 16.4509 16.4509i 0.761258 0.761258i −0.215292 0.976550i \(-0.569070\pi\)
0.976550 + 0.215292i \(0.0690703\pi\)
\(468\) −1.90626 + 1.90626i −0.0881171 + 0.0881171i
\(469\) 15.4562i 0.713702i
\(470\) −14.9991 + 4.15755i −0.691856 + 0.191773i
\(471\) 14.1132i 0.650303i
\(472\) −4.00064 4.00064i −0.184144 0.184144i
\(473\) −0.0714452 + 0.0714452i −0.00328505 + 0.00328505i
\(474\) 13.2521 0.608689
\(475\) −22.1232 + 13.2852i −1.01508 + 0.609569i
\(476\) 6.48512 0.297245
\(477\) 8.84686 8.84686i 0.405070 0.405070i
\(478\) 13.4565 13.4565i 0.615486 0.615486i
\(479\) −16.0301 −0.732435 −0.366218 0.930529i \(-0.619347\pi\)
−0.366218 + 0.930529i \(0.619347\pi\)
\(480\) −0.597287 2.15482i −0.0272623 0.0983536i
\(481\) 14.2382i 0.649207i
\(482\) −0.435331 + 0.435331i −0.0198288 + 0.0198288i
\(483\) −9.52586 + 3.14817i −0.433442 + 0.143247i
\(484\) 10.1676i 0.462162i
\(485\) −0.832327 0.471048i −0.0377940 0.0213892i
\(486\) −1.00000 −0.0453609
\(487\) 23.7717 + 23.7717i 1.07720 + 1.07720i 0.996760 + 0.0804367i \(0.0256315\pi\)
0.0804367 + 0.996760i \(0.474368\pi\)
\(488\) 6.86466 + 6.86466i 0.310749 + 0.310749i
\(489\) 15.8452i 0.716546i
\(490\) 5.10597 + 2.88968i 0.230664 + 0.130542i
\(491\) −6.01407 −0.271411 −0.135706 0.990749i \(-0.543330\pi\)
−0.135706 + 0.990749i \(0.543330\pi\)
\(492\) 8.62442 + 8.62442i 0.388819 + 0.388819i
\(493\) 18.1403 + 18.1403i 0.816999 + 0.816999i
\(494\) 13.9137 0.626008
\(495\) 0.544954 + 1.96602i 0.0244939 + 0.0883659i
\(496\) 5.45970 0.245148
\(497\) −15.2651 + 15.2651i −0.684733 + 0.684733i
\(498\) −8.86710 8.86710i −0.397344 0.397344i
\(499\) 28.8110i 1.28976i −0.764285 0.644879i \(-0.776908\pi\)
0.764285 0.644879i \(-0.223092\pi\)
\(500\) 7.69915 8.10698i 0.344316 0.362555i
\(501\) −19.6662 −0.878619
\(502\) −13.3491 + 13.3491i −0.595800 + 0.595800i
\(503\) −11.9638 11.9638i −0.533439 0.533439i 0.388155 0.921594i \(-0.373112\pi\)
−0.921594 + 0.388155i \(0.873112\pi\)
\(504\) 2.09194 0.0931825
\(505\) −4.38983 15.8371i −0.195345 0.704742i
\(506\) −3.90865 1.96687i −0.173761 0.0874381i
\(507\) −4.05335 4.05335i −0.180016 0.180016i
\(508\) −8.50911 + 8.50911i −0.377531 + 0.377531i
\(509\) 0.392000i 0.0173751i −0.999962 0.00868754i \(-0.997235\pi\)
0.999962 0.00868754i \(-0.00276536\pi\)
\(510\) −6.03280 3.41421i −0.267137 0.151184i
\(511\) 26.5393i 1.17403i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 3.64947 + 3.64947i 0.161128 + 0.161128i
\(514\) 21.2236i 0.936134i
\(515\) 11.0644 19.5504i 0.487556 0.861495i
\(516\) 0.110742i 0.00487514i
\(517\) 4.49071 4.49071i 0.197501 0.197501i
\(518\) −7.81253 + 7.81253i −0.343263 + 0.343263i
\(519\) 6.92582i 0.304010i
\(520\) −5.80910 + 1.61021i −0.254746 + 0.0706122i
\(521\) 34.1983i 1.49826i 0.662426 + 0.749128i \(0.269527\pi\)
−0.662426 + 0.749128i \(0.730473\pi\)
\(522\) 5.85162 + 5.85162i 0.256118 + 0.256118i
\(523\) −23.0752 23.0752i −1.00901 1.00901i −0.999959 0.00905061i \(-0.997119\pi\)
−0.00905061 0.999959i \(-0.502881\pi\)
\(524\) 0.782944i 0.0342030i
\(525\) 5.38485 + 8.96710i 0.235014 + 0.391356i
\(526\) 31.9061i 1.39117i
\(527\) 11.9680 11.9680i 0.521335 0.521335i
\(528\) 0.645151 + 0.645151i 0.0280766 + 0.0280766i
\(529\) −18.4705 + 13.7054i −0.803067 + 0.595889i
\(530\) 26.9597 7.47287i 1.17105 0.324601i
\(531\) −5.65776 −0.245526
\(532\) −7.63448 7.63448i −0.330997 0.330997i
\(533\) 23.2503 23.2503i 1.00708 1.00708i
\(534\) −0.837888 −0.0362590
\(535\) −23.2104 13.1357i −1.00347 0.567907i
\(536\) 7.38845i 0.319133i
\(537\) 1.24859 + 1.24859i 0.0538805 + 0.0538805i
\(538\) 18.5436 18.5436i 0.799471 0.799471i
\(539\) −2.39389 −0.103112
\(540\) −1.94603 1.10134i −0.0837440 0.0473942i
\(541\) 10.0462 0.431921 0.215961 0.976402i \(-0.430712\pi\)
0.215961 + 0.976402i \(0.430712\pi\)
\(542\) −5.84742 5.84742i −0.251168 0.251168i
\(543\) −3.33051 3.33051i −0.142926 0.142926i
\(544\) −3.10005 −0.132914
\(545\) 0.969565 + 3.49788i 0.0415316 + 0.149833i
\(546\) 5.63959i 0.241352i
\(547\) 5.55946 + 5.55946i 0.237705 + 0.237705i 0.815899 0.578194i \(-0.196242\pi\)
−0.578194 + 0.815899i \(0.696242\pi\)
\(548\) 7.97847 + 7.97847i 0.340824 + 0.340824i
\(549\) 9.70810 0.414332
\(550\) −1.10476 + 4.42612i −0.0471070 + 0.188730i
\(551\) 42.7107i 1.81954i
\(552\) 4.55360 1.50490i 0.193814 0.0640529i
\(553\) −19.6028 + 19.6028i −0.833598 + 0.833598i
\(554\) 16.5857i 0.704657i
\(555\) 11.3807 3.15457i 0.483083 0.133904i
\(556\) 5.31355 0.225345
\(557\) 28.4426 28.4426i 1.20515 1.20515i 0.232575 0.972578i \(-0.425285\pi\)
0.972578 0.232575i \(-0.0747152\pi\)
\(558\) 3.86059 3.86059i 0.163432 0.163432i
\(559\) −0.298545 −0.0126271
\(560\) 4.07099 + 2.30394i 0.172031 + 0.0973593i
\(561\) 2.82843 0.119416
\(562\) 20.6845 20.6845i 0.872522 0.872522i
\(563\) 19.7106 + 19.7106i 0.830701 + 0.830701i 0.987613 0.156912i \(-0.0501538\pi\)
−0.156912 + 0.987613i \(0.550154\pi\)
\(564\) 6.96072i 0.293099i
\(565\) −1.35775 + 2.39911i −0.0571212 + 0.100931i
\(566\) 10.5267i 0.442472i
\(567\) 1.47923 1.47923i 0.0621216 0.0621216i
\(568\) 7.29709 7.29709i 0.306179 0.306179i
\(569\) −36.0611 −1.51176 −0.755880 0.654710i \(-0.772791\pi\)
−0.755880 + 0.654710i \(0.772791\pi\)
\(570\) 3.08268 + 11.1213i 0.129119 + 0.465821i
\(571\) 26.1960i 1.09627i 0.836390 + 0.548134i \(0.184662\pi\)
−0.836390 + 0.548134i \(0.815338\pi\)
\(572\) 1.73924 1.73924i 0.0727213 0.0727213i
\(573\) −15.6475 15.6475i −0.653682 0.653682i
\(574\) −25.5149 −1.06497
\(575\) 18.1721 + 15.6452i 0.757831 + 0.652451i
\(576\) −1.00000 −0.0416667
\(577\) −12.1729 12.1729i −0.506763 0.506763i 0.406768 0.913531i \(-0.366656\pi\)
−0.913531 + 0.406768i \(0.866656\pi\)
\(578\) 5.22530 5.22530i 0.217344 0.217344i
\(579\) 0.897297i 0.0372904i
\(580\) 4.94282 + 17.8321i 0.205239 + 0.740437i
\(581\) 26.2329 1.08832
\(582\) −0.302433 + 0.302433i −0.0125362 + 0.0125362i
\(583\) −8.07171 + 8.07171i −0.334296 + 0.334296i
\(584\) 12.6864i 0.524969i
\(585\) −2.96907 + 5.24624i −0.122756 + 0.216906i
\(586\) 15.0680i 0.622453i
\(587\) −21.6269 21.6269i −0.892636 0.892636i 0.102134 0.994771i \(-0.467433\pi\)
−0.994771 + 0.102134i \(0.967433\pi\)
\(588\) 1.85529 1.85529i 0.0765110 0.0765110i
\(589\) −28.1782 −1.16106
\(590\) −11.0102 6.23112i −0.453282 0.256531i
\(591\) −8.26474 −0.339966
\(592\) 3.73458 3.73458i 0.153490 0.153490i
\(593\) 10.4088 10.4088i 0.427438 0.427438i −0.460317 0.887755i \(-0.652264\pi\)
0.887755 + 0.460317i \(0.152264\pi\)
\(594\) 0.912381 0.0374355
\(595\) 13.9743 3.87348i 0.572889 0.158797i
\(596\) 8.12233i 0.332704i
\(597\) 12.3804 12.3804i 0.506695 0.506695i
\(598\) −4.05701 12.2759i −0.165904 0.501999i
\(599\) 20.6812i 0.845013i 0.906360 + 0.422506i \(0.138850\pi\)
−0.906360 + 0.422506i \(0.861150\pi\)
\(600\) −2.57409 4.28650i −0.105087 0.174995i
\(601\) 34.8691 1.42234 0.711171 0.703019i \(-0.248165\pi\)
0.711171 + 0.703019i \(0.248165\pi\)
\(602\) 0.163812 + 0.163812i 0.00667649 + 0.00667649i
\(603\) 5.22443 + 5.22443i 0.212755 + 0.212755i
\(604\) 2.41716i 0.0983527i
\(605\) 6.07296 + 21.9093i 0.246901 + 0.890738i
\(606\) −7.34962 −0.298558
\(607\) 15.1745 + 15.1745i 0.615913 + 0.615913i 0.944481 0.328567i \(-0.106566\pi\)
−0.328567 + 0.944481i \(0.606566\pi\)
\(608\) 3.64947 + 3.64947i 0.148006 + 0.148006i
\(609\) −17.3117 −0.701507
\(610\) 18.8923 + 10.6919i 0.764926 + 0.432904i
\(611\) 18.7652 0.759157
\(612\) −2.19207 + 2.19207i −0.0886090 + 0.0886090i
\(613\) 20.4989 + 20.4989i 0.827943 + 0.827943i 0.987232 0.159289i \(-0.0509201\pi\)
−0.159289 + 0.987232i \(0.550920\pi\)
\(614\) 6.58268i 0.265655i
\(615\) 23.7353 + 13.4328i 0.957101 + 0.541663i
\(616\) −1.90865 −0.0769016
\(617\) 17.4461 17.4461i 0.702354 0.702354i −0.262561 0.964915i \(-0.584567\pi\)
0.964915 + 0.262561i \(0.0845671\pi\)
\(618\) −7.10380 7.10380i −0.285757 0.285757i
\(619\) −1.36779 −0.0549760 −0.0274880 0.999622i \(-0.508751\pi\)
−0.0274880 + 0.999622i \(0.508751\pi\)
\(620\) 11.7647 3.26101i 0.472480 0.130965i
\(621\) 2.15576 4.28401i 0.0865075 0.171911i
\(622\) −7.21286 7.21286i −0.289209 0.289209i
\(623\) 1.23943 1.23943i 0.0496566 0.0496566i
\(624\) 2.69587i 0.107921i
\(625\) 11.7481 22.0677i 0.469923 0.882707i
\(626\) 14.8574i 0.593820i
\(627\) −3.32971 3.32971i −0.132976 0.132976i
\(628\) −9.97955 9.97955i −0.398227 0.398227i
\(629\) 16.3729i 0.652831i
\(630\) 4.50776 1.24949i 0.179593 0.0497809i
\(631\) 29.9727i 1.19320i −0.802540 0.596598i \(-0.796519\pi\)
0.802540 0.596598i \(-0.203481\pi\)
\(632\) 9.37065 9.37065i 0.372744 0.372744i
\(633\) −2.77442 + 2.77442i −0.110273 + 0.110273i
\(634\) 22.2390i 0.883223i
\(635\) −13.2532 + 23.4180i −0.525938 + 0.929315i
\(636\) 12.5113i 0.496107i
\(637\) −5.00162 5.00162i −0.198171 0.198171i
\(638\) −5.33891 5.33891i −0.211369 0.211369i
\(639\) 10.3196i 0.408239i
\(640\) −1.94603 1.10134i −0.0769237 0.0435343i
\(641\) 6.35878i 0.251157i 0.992084 + 0.125578i \(0.0400786\pi\)
−0.992084 + 0.125578i \(0.959921\pi\)
\(642\) −8.43368 + 8.43368i −0.332851 + 0.332851i
\(643\) −31.9508 31.9508i −1.26002 1.26002i −0.951083 0.308934i \(-0.900028\pi\)
−0.308934 0.951083i \(-0.599972\pi\)
\(644\) −4.50971 + 8.96189i −0.177708 + 0.353148i
\(645\) −0.0661447 0.238629i −0.00260445 0.00939599i
\(646\) 15.9998 0.629503
\(647\) 6.63244 + 6.63244i 0.260748 + 0.260748i 0.825358 0.564610i \(-0.190973\pi\)
−0.564610 + 0.825358i \(0.690973\pi\)
\(648\) −0.707107 + 0.707107i −0.0277778 + 0.0277778i
\(649\) 5.16203 0.202627
\(650\) −11.5558 + 6.93941i −0.453256 + 0.272186i
\(651\) 11.4214i 0.447639i
\(652\) 11.2043 + 11.2043i 0.438793 + 0.438793i
\(653\) 33.4213 33.4213i 1.30788 1.30788i 0.384932 0.922945i \(-0.374225\pi\)
0.922945 0.384932i \(-0.125775\pi\)
\(654\) 1.62328 0.0634753
\(655\) −0.467642 1.68710i −0.0182723 0.0659205i
\(656\) 12.1968 0.476204
\(657\) 8.97067 + 8.97067i 0.349979 + 0.349979i
\(658\) −10.2965 10.2965i −0.401398 0.401398i
\(659\) 17.4038 0.677955 0.338978 0.940794i \(-0.389919\pi\)
0.338978 + 0.940794i \(0.389919\pi\)
\(660\) 1.77552 + 1.00484i 0.0691122 + 0.0391135i
\(661\) 13.4061i 0.521436i 0.965415 + 0.260718i \(0.0839592\pi\)
−0.965415 + 0.260718i \(0.916041\pi\)
\(662\) 14.1780 + 14.1780i 0.551045 + 0.551045i
\(663\) 5.90952 + 5.90952i 0.229507 + 0.229507i
\(664\) −12.5400 −0.486645
\(665\) −21.0109 11.8910i −0.814768 0.461111i
\(666\) 5.28150i 0.204654i
\(667\) −37.6830 + 12.4537i −1.45909 + 0.482210i
\(668\) −13.9061 + 13.9061i −0.538042 + 0.538042i
\(669\) 11.8083i 0.456534i
\(670\) 4.41303 + 15.9208i 0.170490 + 0.615074i
\(671\) −8.85749 −0.341940
\(672\) 1.47923 1.47923i 0.0570624 0.0570624i
\(673\) 10.3552 10.3552i 0.399163 0.399163i −0.478775 0.877938i \(-0.658919\pi\)
0.877938 + 0.478775i \(0.158919\pi\)
\(674\) 14.1509 0.545074
\(675\) −4.85117 1.21085i −0.186722 0.0466057i
\(676\) −5.73231 −0.220473
\(677\) −31.9860 + 31.9860i −1.22932 + 1.22932i −0.265099 + 0.964221i \(0.585405\pi\)
−0.964221 + 0.265099i \(0.914595\pi\)
\(678\) 0.871735 + 0.871735i 0.0334788 + 0.0334788i
\(679\) 0.894732i 0.0343367i
\(680\) −6.68005 + 1.85162i −0.256168 + 0.0710064i
\(681\) 6.69357i 0.256498i
\(682\) −3.52233 + 3.52233i −0.134877 + 0.134877i
\(683\) 10.0450 10.0450i 0.384360 0.384360i −0.488310 0.872670i \(-0.662387\pi\)
0.872670 + 0.488310i \(0.162387\pi\)
\(684\) 5.16113 0.197341
\(685\) 21.9576 + 12.4267i 0.838957 + 0.474801i
\(686\) 20.1324i 0.768658i
\(687\) −3.93606 + 3.93606i −0.150170 + 0.150170i
\(688\) −0.0783063 0.0783063i −0.00298540 0.00298540i
\(689\) −33.7289 −1.28497
\(690\) 8.91333 5.96260i 0.339325 0.226992i
\(691\) −38.3889 −1.46038 −0.730192 0.683242i \(-0.760569\pi\)
−0.730192 + 0.683242i \(0.760569\pi\)
\(692\) 4.89730 + 4.89730i 0.186167 + 0.186167i
\(693\) −1.34962 + 1.34962i −0.0512677 + 0.0512677i
\(694\) 10.8483i 0.411797i
\(695\) 11.4497 3.17372i 0.434313 0.120386i
\(696\) 8.27544 0.313680
\(697\) 26.7361 26.7361i 1.01270 1.01270i
\(698\) 17.1256 17.1256i 0.648213 0.648213i
\(699\) 2.63770i 0.0997669i
\(700\) 10.1484 + 2.53303i 0.383572 + 0.0957395i
\(701\) 30.4867i 1.15147i −0.817638 0.575733i \(-0.804717\pi\)
0.817638 0.575733i \(-0.195283\pi\)
\(702\) 1.90626 + 1.90626i 0.0719473 + 0.0719473i
\(703\) −19.2747 + 19.2747i −0.726959 + 0.726959i
\(704\) 0.912381 0.0343867
\(705\) 4.15755 + 14.9991i 0.156582 + 0.564898i
\(706\) 6.09938 0.229553
\(707\) 10.8717 10.8717i 0.408874 0.408874i
\(708\) −4.00064 + 4.00064i −0.150353 + 0.150353i
\(709\) 51.1949 1.92267 0.961333 0.275388i \(-0.0888062\pi\)
0.961333 + 0.275388i \(0.0888062\pi\)
\(710\) 11.3655 20.0824i 0.426538 0.753678i
\(711\) 13.2521i 0.496993i
\(712\) −0.592477 + 0.592477i −0.0222040 + 0.0222040i
\(713\) 8.21631 + 24.8613i 0.307703 + 0.931062i
\(714\) 6.48512i 0.242700i
\(715\) 2.70892 4.78658i 0.101308 0.179008i
\(716\) 1.76577 0.0659899
\(717\) −13.4565 13.4565i −0.502543 0.502543i
\(718\) 17.0944 + 17.0944i 0.637957 + 0.637957i
\(719\) 41.9754i 1.56542i 0.622387 + 0.782709i \(0.286163\pi\)
−0.622387 + 0.782709i \(0.713837\pi\)
\(720\) −2.15482 + 0.597287i −0.0803054 + 0.0222596i
\(721\) 21.0163 0.782686
\(722\) −5.40040 5.40040i −0.200982 0.200982i
\(723\) 0.435331 + 0.435331i 0.0161901 + 0.0161901i
\(724\) −4.71006 −0.175048
\(725\) 21.3018 + 35.4726i 0.791127 + 1.31742i
\(726\) 10.1676 0.377354
\(727\) −13.4172 + 13.4172i −0.497617 + 0.497617i −0.910695 0.413079i \(-0.864454\pi\)
0.413079 + 0.910695i \(0.364454\pi\)
\(728\) −3.98779 3.98779i −0.147797 0.147797i
\(729\) 1.00000i 0.0370370i
\(730\) 7.57745 + 27.3370i 0.280454 + 1.01179i
\(731\) −0.343305 −0.0126976
\(732\) 6.86466 6.86466i 0.253725 0.253725i
\(733\) −8.19187 8.19187i −0.302574 0.302574i 0.539446 0.842020i \(-0.318634\pi\)
−0.842020 + 0.539446i \(0.818634\pi\)
\(734\) 13.6535 0.503960
\(735\) 2.88968 5.10597i 0.106587 0.188336i
\(736\) 2.15576 4.28401i 0.0794622 0.157911i
\(737\) −4.76667 4.76667i −0.175582 0.175582i
\(738\) 8.62442 8.62442i 0.317469 0.317469i
\(739\) 28.3966i 1.04459i 0.852766 + 0.522294i \(0.174924\pi\)
−0.852766 + 0.522294i \(0.825076\pi\)
\(740\) 5.81673 10.2780i 0.213827 0.377826i
\(741\) 13.9137i 0.511134i
\(742\) 18.5071 + 18.5071i 0.679417 + 0.679417i
\(743\) 20.2499 + 20.2499i 0.742898 + 0.742898i 0.973135 0.230237i \(-0.0739501\pi\)
−0.230237 + 0.973135i \(0.573950\pi\)
\(744\) 5.45970i 0.200162i
\(745\) 4.85137 + 17.5022i 0.177740 + 0.641229i
\(746\) 15.8260i 0.579430i
\(747\) −8.86710 + 8.86710i −0.324430 + 0.324430i
\(748\) 2.00000 2.00000i 0.0731272 0.0731272i
\(749\) 24.9506i 0.911677i
\(750\) −8.10698 7.69915i −0.296025 0.281133i
\(751\) 24.6848i 0.900762i −0.892836 0.450381i \(-0.851288\pi\)
0.892836 0.450381i \(-0.148712\pi\)
\(752\) 4.92197 + 4.92197i 0.179486 + 0.179486i
\(753\) 13.3491 + 13.3491i 0.486469 + 0.486469i
\(754\) 22.3095i 0.812463i
\(755\) 1.44374 + 5.20854i 0.0525430 + 0.189558i
\(756\) 2.09194i 0.0760832i
\(757\) −11.7787 + 11.7787i −0.428104 + 0.428104i −0.887982 0.459878i \(-0.847893\pi\)
0.459878 + 0.887982i \(0.347893\pi\)
\(758\) 1.48181 + 1.48181i 0.0538217 + 0.0538217i
\(759\) −1.96687 + 3.90865i −0.0713929 + 0.141875i
\(760\) 10.0437 + 5.68417i 0.364325 + 0.206187i
\(761\) −0.392492 −0.0142278 −0.00711391 0.999975i \(-0.502264\pi\)
−0.00711391 + 0.999975i \(0.502264\pi\)
\(762\) 8.50911 + 8.50911i 0.308253 + 0.308253i
\(763\) −2.40120 + 2.40120i −0.0869293 + 0.0869293i
\(764\) −22.1289 −0.800594
\(765\) −3.41421 + 6.03280i −0.123441 + 0.218116i
\(766\) 20.2636i 0.732155i
\(767\) 10.7852 + 10.7852i 0.389430 + 0.389430i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 45.5745 1.64346 0.821729 0.569879i \(-0.193010\pi\)
0.821729 + 0.569879i \(0.193010\pi\)
\(770\) −4.11279 + 1.14001i −0.148215 + 0.0410832i
\(771\) 21.2236 0.764351
\(772\) −0.634485 0.634485i −0.0228356 0.0228356i
\(773\) −24.9331 24.9331i −0.896780 0.896780i 0.0983701 0.995150i \(-0.468637\pi\)
−0.995150 + 0.0983701i \(0.968637\pi\)
\(774\) −0.110742 −0.00398053
\(775\) 23.4030 14.0538i 0.840659 0.504826i
\(776\) 0.427704i 0.0153537i
\(777\) 7.81253 + 7.81253i 0.280273 + 0.280273i
\(778\) 22.5134 + 22.5134i 0.807143 + 0.807143i
\(779\) −62.9492 −2.25539
\(780\) 1.61021 + 5.80910i