Properties

Label 690.2.j.b.643.3
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 643.3
Character \(\chi\) \(=\) 690.643
Dual form 690.2.j.b.367.3

$q$-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} +(4.55360 - 1.50490i) 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} +(-1.50490 - 4.55360i) 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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

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

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
\(5\) −0.597287 + 2.15482i −0.267115 + 0.963665i
\(6\) 1.00000 0.408248
\(7\) 1.47923 + 1.47923i 0.559095 + 0.559095i 0.929050 0.369955i \(-0.120627\pi\)
−0.369955 + 0.929050i \(0.620627\pi\)
\(8\) 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 0.391483 0.920185i \(-0.371962\pi\)
−0.920185 + 0.391483i \(0.871962\pi\)
\(14\) −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 \(-0.127321\pi\)
−0.389410 + 0.921064i \(0.627321\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) −5.16113 −1.18405 −0.592023 0.805921i \(-0.701670\pi\)
−0.592023 + 0.805921i \(0.701670\pi\)
\(20\) 2.15482 + 0.597287i 0.481832 + 0.133558i
\(21\) 2.09194i 0.456499i
\(22\) −0.645151 0.645151i −0.137547 0.137547i
\(23\) 4.55360 1.50490i 0.949491 0.313794i
\(24\) 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 \(0.278925\pi\)
−0.640023 + 0.768355i \(0.721075\pi\)
\(30\) −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 \(-0.107054\pi\)
−0.330014 + 0.943976i \(0.607054\pi\)
\(38\) 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 \(-0.752688\pi\)
0.701111 + 0.713052i \(0.252688\pi\)
\(44\) 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 −0.968184 0.250241i \(-0.919490\pi\)
0.250241 + 0.968184i \(0.419490\pi\)
\(48\) 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 −0.245919 + 0.969290i \(0.579090\pi\)
−0.969290 + 0.245919i \(0.920910\pi\)
\(54\) 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 \(0.120056\pi\)
−0.929711 + 0.368289i \(0.879944\pi\)
\(60\) −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 \(-0.100953\pi\)
−0.311862 + 0.950127i \(0.600953\pi\)
\(68\) 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 −0.998686 0.0512515i \(-0.983679\pi\)
−0.0512515 0.998686i \(-0.516321\pi\)
\(74\) −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 \(-0.767784\pi\)
−0.745489 + 0.666518i \(0.767784\pi\)
\(80\) 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 \(-0.508392\pi\)
0.999652 + 0.0263622i \(0.00839232\pi\)
\(84\) −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 \(-0.485860\pi\)
0.0444080 + 0.999013i \(0.485860\pi\)
\(90\) 1.94603 1.10134i 0.205130 0.116092i
\(91\) 5.63959i 0.591190i
\(92\) −1.50490 4.55360i −0.156897 0.474746i
\(93\) 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 \(-0.243088\pi\)
−0.691586 + 0.722294i \(0.743088\pi\)
\(98\) 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 \(-0.585188\pi\)
0.964401 + 0.264443i \(0.0851880\pi\)
\(104\) 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 \(-0.0544124\pi\)
−0.170110 + 0.985425i \(0.554412\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) −1.62328 −0.155482 −0.0777411 0.996974i \(-0.524771\pi\)
−0.0777411 + 0.996974i \(0.524771\pi\)
\(110\) 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 \(-0.768468\pi\)
0.664914 + 0.746920i \(0.268468\pi\)
\(114\) −5.16113 −0.483385
\(115\) 0.522984 + 10.7110i 0.0487685 + 0.998810i
\(116\) 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 −0.220357 0.975419i \(-0.570722\pi\)
0.975419 + 0.220357i \(0.0707224\pi\)
\(128\) −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 \(-0.410088\pi\)
−0.960371 + 0.278724i \(0.910088\pi\)
\(138\) 4.55360 1.50490i 0.387628 0.128106i
\(139\) 5.31355i 0.450689i 0.974279 + 0.225345i \(0.0723508\pi\)
−0.974279 + 0.225345i \(0.927649\pi\)
\(140\) 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 \(-0.607961\pi\)
−0.332704 + 0.943031i \(0.607961\pi\)
\(150\) −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 \(-0.0595783\pi\)
−0.186080 + 0.982535i \(0.559578\pi\)
\(158\) 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 0.993284 0.115699i \(-0.0369108\pi\)
−0.115699 + 0.993284i \(0.536911\pi\)
\(164\) 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 0.0792276 0.996857i \(-0.474755\pi\)
0.996857 0.0792276i \(-0.0252454\pi\)
\(168\) 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 0.868327 0.495992i \(-0.165196\pi\)
−0.495992 + 0.868327i \(0.665196\pi\)
\(174\) 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 \(0.0210205\pi\)
−0.997820 + 0.0659899i \(0.978980\pi\)
\(180\) −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 0.683902 0.729574i \(-0.260281\pi\)
−0.729574 + 0.683902i \(0.760281\pi\)
\(194\) −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 −0.467580 0.883951i \(-0.654874\pi\)
0.883951 + 0.467580i \(0.154874\pi\)
\(198\) 0.645151 0.645151i 0.0458489 0.0458489i
\(199\) 17.5085 1.24114 0.620572 0.784150i \(-0.286901\pi\)
0.620572 + 0.784150i \(0.286901\pi\)
\(200\) −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
\(207\) 1.50490 + 4.55360i 0.104598 + 0.316497i
\(208\) 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 0.929062 0.369925i \(-0.120617\pi\)
−0.369925 + 0.929062i \(0.620617\pi\)
\(224\) 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 \(-0.178698\pi\)
−0.532368 + 0.846513i \(0.678698\pi\)
\(228\) 3.64947 3.64947i 0.241692 0.241692i
\(229\) −5.56644 −0.367840 −0.183920 0.982941i \(-0.558879\pi\)
−0.183920 + 0.982941i \(0.558879\pi\)
\(230\) −7.94366 7.20405i −0.523789 0.475021i
\(231\) 1.90865 0.125580
\(232\) −5.85162 + 5.85162i −0.384178 + 0.384178i
\(233\) 1.86513 + 1.86513i 0.122189 + 0.122189i 0.765557 0.643368i \(-0.222463\pi\)
−0.643368 + 0.765557i \(0.722463\pi\)
\(234\) 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 \(-0.788960\pi\)
0.788148 0.615486i \(-0.211040\pi\)
\(240\) −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
\(253\) 1.37304 + 4.15462i 0.0863225 + 0.261199i
\(254\) 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 −0.998080 0.0619452i \(-0.980270\pi\)
0.0619452 + 0.998080i \(0.480270\pi\)
\(258\) −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 −0.568469 + 0.822705i \(0.692464\pi\)
−0.822705 + 0.568469i \(0.807536\pi\)
\(264\) 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 \(-0.705113\pi\)
0.600705 0.799471i \(-0.294887\pi\)
\(270\) −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 −0.260749 0.965407i \(-0.583970\pi\)
0.965407 + 0.260749i \(0.0839696\pi\)
\(278\) −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 \(-0.851292\pi\)
0.450370 + 0.892842i \(0.351292\pi\)
\(284\) 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 \(-0.895072\pi\)
0.323705 + 0.946158i \(0.395072\pi\)
\(294\) 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 −0.561692 0.827347i \(-0.689849\pi\)
0.827347 + 0.561692i \(0.189849\pi\)
\(308\) 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 \(-0.612067\pi\)
0.938661 + 0.344841i \(0.112067\pi\)
\(314\) −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 −0.993861 0.110638i \(-0.964711\pi\)
0.110638 + 0.993861i \(0.464711\pi\)
\(318\) −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
\(322\) −9.52586 + 3.14817i −0.530856 + 0.175440i
\(323\) −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 \(-0.124055\pi\)
−0.379938 + 0.925012i \(0.624055\pi\)
\(338\) 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
\(345\) 7.20405 7.94366i 0.387853 0.427672i
\(346\) −6.92582 −0.372335
\(347\) −7.67093 + 7.67093i −0.411797 + 0.411797i −0.882364 0.470567i \(-0.844049\pi\)
0.470567 + 0.882364i \(0.344049\pi\)
\(348\) −5.85162 5.85162i −0.313680 0.313680i
\(349\) 24.2192i 1.29643i −0.761459 0.648213i \(-0.775517\pi\)
0.761459 0.648213i \(-0.224483\pi\)
\(350\) 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 0.582953 0.812506i \(-0.301897\pi\)
−0.812506 + 0.582953i \(0.801897\pi\)
\(354\) 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 \(-0.279780\pi\)
0.637957 + 0.770072i \(0.279780\pi\)
\(360\) −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 \(-0.134020\pi\)
−0.408706 + 0.912666i \(0.634020\pi\)
\(368\) −4.55360 + 1.50490i −0.237373 + 0.0784484i
\(369\) 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 \(-0.615627\pi\)
0.934746 + 0.355316i \(0.115627\pi\)
\(374\) 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 \(-0.482860\pi\)
0.0538217 + 0.998551i \(0.482860\pi\)
\(380\) −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 \(-0.923216\pi\)
0.238891 + 0.971046i \(0.423216\pi\)
\(384\) 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 \(-0.201013\pi\)
0.807143 + 0.590356i \(0.201013\pi\)
\(390\) 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 −0.593422 0.804892i \(-0.702223\pi\)
0.804892 + 0.593422i \(0.202223\pi\)
\(398\) −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 \(0.376429\pi\)
−0.378531 + 0.925589i \(0.623571\pi\)
\(410\) 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 \(-0.377337\pi\)
0.375889 + 0.926665i \(0.377337\pi\)
\(420\) 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 \(-0.983071\pi\)
0.0531576 + 0.998586i \(0.483071\pi\)
\(434\) 11.4214 0.548243
\(435\) 9.11409 + 16.1043i 0.436987 + 0.772141i
\(436\) 1.62328i 0.0777411i
\(437\) −23.5017 + 7.76700i −1.12424 + 0.371546i
\(438\) −8.97067 8.97067i −0.428635 0.428635i
\(439\) 7.59434i 0.362458i −0.983441 0.181229i \(-0.941992\pi\)
0.983441 0.181229i \(-0.0580075\pi\)
\(440\) −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 0.581278 0.813705i \(-0.302553\pi\)
−0.813705 + 0.581278i \(0.802553\pi\)
\(444\) −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 \(0.0514822\pi\)
−0.986949 + 0.161032i \(0.948518\pi\)
\(450\) 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 \(-0.388175\pi\)
−0.938923 + 0.344126i \(0.888175\pi\)
\(458\) 3.93606 3.93606i 0.183920 0.183920i
\(459\) 3.10005 0.144698
\(460\) 10.7110 0.522984i 0.499405 0.0243842i
\(461\) 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 0.973923 0.226879i \(-0.0728524\pi\)
−0.226879 + 0.973923i \(0.572852\pi\)
\(464\) 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 \(-0.430930\pi\)
−0.976550 + 0.215292i \(0.930930\pi\)
\(468\) −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 \(-0.380653\pi\)
0.366218 + 0.930529i \(0.380653\pi\)
\(480\) 0.597287 2.15482i 0.0272623 0.0983536i
\(481\) 14.2382i 0.649207i
\(482\) 0.435331 + 0.435331i 0.0198288 + 0.0198288i
\(483\) −3.14817 9.52586i −0.143247 0.433442i
\(484\) 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 0.0804367 0.996760i \(-0.474368\pi\)
0.996760 0.0804367i \(-0.0256315\pi\)
\(488\) −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 \(0.223092\pi\)
−0.764285 + 0.644879i \(0.776908\pi\)
\(500\) −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 \(-0.626888\pi\)
0.921594 + 0.388155i \(0.126888\pi\)
\(504\) −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 \(0.00276536\pi\)
−0.999962 + 0.00868754i \(0.997235\pi\)
\(510\) −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 0.00905061 0.999959i \(-0.497119\pi\)
0.999959 0.00905061i \(-0.00288094\pi\)
\(524\) 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 −0.578194 0.815899i \(-0.696242\pi\)
0.815899 + 0.578194i \(0.196242\pi\)
\(548\) −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
\(552\) −1.50490 4.55360i −0.0640529 0.193814i
\(553\) −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 −0.972578 0.232575i \(-0.925285\pi\)
−0.232575 0.972578i \(-0.574715\pi\)
\(558\) 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 \(-0.949846\pi\)
0.156912 + 0.987613i \(0.449846\pi\)
\(564\) 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 \(-0.227209\pi\)
0.755880 + 0.654710i \(0.227209\pi\)
\(570\) 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
\(575\) −23.3927 5.27064i −0.975545 0.219801i
\(576\) −1.00000 −0.0416667
\(577\) −12.1729 + 12.1729i −0.506763 + 0.506763i −0.913531 0.406768i \(-0.866656\pi\)
0.406768 + 0.913531i \(0.366656\pi\)
\(578\) 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 −0.994771 0.102134i \(-0.967433\pi\)
0.102134 + 0.994771i \(0.467433\pi\)
\(588\) 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 0.887755 0.460317i \(-0.152264\pi\)
−0.460317 + 0.887755i \(0.652264\pi\)
\(594\) −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
\(598\) 12.2759 4.05701i 0.501999 0.165904i
\(599\) 20.6812i 0.845013i −0.906360 0.422506i \(-0.861150\pi\)
0.906360 0.422506i \(-0.138850\pi\)
\(600\) −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 −0.328567 0.944481i \(-0.606566\pi\)
0.944481 + 0.328567i \(0.106566\pi\)
\(608\) −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 \(-0.949080\pi\)
0.159289 + 0.987232i \(0.449080\pi\)
\(614\) 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 \(-0.415433\pi\)
−0.964915 + 0.262561i \(0.915433\pi\)
\(618\) 7.10380 7.10380i 0.285757 0.285757i
\(619\) 1.36779 0.0549760 0.0274880 0.999622i \(-0.491249\pi\)
0.0274880 + 0.999622i \(0.491249\pi\)
\(620\) −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 0.308934 0.951083i \(-0.400028\pi\)
0.951083 0.308934i \(-0.0999724\pi\)
\(644\) 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 −0.564610 0.825358i \(-0.690973\pi\)
0.825358 + 0.564610i \(0.190973\pi\)
\(648\) −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 0.922945 + 0.384932i \(0.125775\pi\)
0.384932 + 0.922945i \(0.374225\pi\)
\(654\) −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 \(-0.610081\pi\)
−0.338978 + 0.940794i \(0.610081\pi\)
\(660\) 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
\(667\) 12.4537 + 37.6830i 0.482210 + 1.45909i
\(668\) −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 0.877938 0.478775i \(-0.158919\pi\)
−0.478775 + 0.877938i \(0.658919\pi\)
\(674\) −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 0.964221 + 0.265099i \(0.0854047\pi\)
0.265099 + 0.964221i \(0.414595\pi\)
\(678\) −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 0.872670 0.488310i \(-0.162387\pi\)
−0.488310 + 0.872670i \(0.662387\pi\)
\(684\) −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
\(690\) 0.522984 + 10.7110i 0.0199096 + 0.407763i
\(691\) −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 \(-0.911194\pi\)
−0.961333 + 0.275388i \(0.911194\pi\)
\(710\) −11.3655 20.0824i −0.426538 0.753678i
\(711\) 13.2521i 0.496993i
\(712\) 0.592477 + 0.592477i 0.0222040 + 0.0222040i
\(713\) −24.8613 + 8.21631i −0.931062 + 0.307703i
\(714\) 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 \(-0.713837\pi\)
0.622387 0.782709i \(-0.286163\pi\)
\(720\) 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 \(-0.135546\pi\)
−0.413079 + 0.910695i \(0.635546\pi\)
\(728\) 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 \(-0.681366\pi\)
0.842020 + 0.539446i \(0.181366\pi\)
\(734\) −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 \(-0.825076\pi\)
0.852766 0.522294i \(-0.174924\pi\)
\(740\) 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 \(-0.926050\pi\)
0.230237 + 0.973135i \(0.426050\pi\)
\(744\) 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 \(-0.152107\pi\)
−0.459878 + 0.887982i \(0.652107\pi\)
\(758\) −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 \(-0.806990\pi\)
−0.821729 + 0.569879i \(0.806990\pi\)
\(770\) 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 \(-0.531363\pi\)
0.995150 + 0.0983701i \(0.0313629\pi\)
\(774\) 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 +