Properties

Label 825.2.m.b.361.1
Level $825$
Weight $2$
Character 825.361
Analytic conductor $6.588$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.m (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \(x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 361.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 825.361
Dual form 825.2.m.b.16.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.309017 + 0.951057i) q^{3} +(1.61803 - 1.17557i) q^{4} +(0.690983 + 2.12663i) q^{5} +(3.73607 + 2.71441i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(0.309017 + 0.951057i) q^{3} +(1.61803 - 1.17557i) q^{4} +(0.690983 + 2.12663i) q^{5} +(3.73607 + 2.71441i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(2.19098 - 2.48990i) q^{11} +(1.61803 + 1.17557i) q^{12} +(3.73607 - 2.71441i) q^{13} +(-1.80902 + 1.31433i) q^{15} +(1.23607 - 3.80423i) q^{16} +(-1.42705 + 1.03681i) q^{17} +(-6.04508 - 4.39201i) q^{19} +(3.61803 + 2.62866i) q^{20} +(-1.42705 + 4.39201i) q^{21} +(-1.92705 + 1.40008i) q^{23} +(-4.04508 + 2.93893i) q^{25} +(-0.809017 - 0.587785i) q^{27} +9.23607 q^{28} +(-4.61803 + 3.35520i) q^{29} -2.00000 q^{31} +(3.04508 + 1.31433i) q^{33} +(-3.19098 + 9.82084i) q^{35} +(-0.618034 + 1.90211i) q^{36} +(-1.78115 - 5.48183i) q^{37} +(3.73607 + 2.71441i) q^{39} +1.76393 q^{41} +1.76393 q^{43} +(0.618034 - 6.60440i) q^{44} +(-1.80902 - 1.31433i) q^{45} +(1.11803 + 3.44095i) q^{47} +4.00000 q^{48} +(4.42705 + 13.6251i) q^{49} +(-1.42705 - 1.03681i) q^{51} +(2.85410 - 8.78402i) q^{52} +(-7.28115 - 5.29007i) q^{53} +(6.80902 + 2.93893i) q^{55} +(2.30902 - 7.10642i) q^{57} +(-2.39919 - 7.38394i) q^{59} +(-1.38197 + 4.25325i) q^{60} +(3.19098 + 2.31838i) q^{61} -4.61803 q^{63} +(-2.47214 - 7.60845i) q^{64} +(8.35410 + 6.06961i) q^{65} +(-0.690983 - 2.12663i) q^{67} +(-1.09017 + 3.35520i) q^{68} +(-1.92705 - 1.40008i) q^{69} -2.52786 q^{71} +5.70820 q^{73} +(-4.04508 - 2.93893i) q^{75} -14.9443 q^{76} +(14.9443 - 3.35520i) q^{77} +(9.78115 + 7.10642i) q^{79} +8.94427 q^{80} +(0.309017 - 0.951057i) q^{81} +(-9.78115 + 7.10642i) q^{83} +(2.85410 + 8.78402i) q^{84} +(-3.19098 - 2.31838i) q^{85} +(-4.61803 - 3.35520i) q^{87} +(-10.2812 + 7.46969i) q^{89} +21.3262 q^{91} +(-1.47214 + 4.53077i) q^{92} +(-0.618034 - 1.90211i) q^{93} +(5.16312 - 15.8904i) q^{95} +(5.35410 + 3.88998i) q^{97} +(-0.309017 + 3.30220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{3} + 2 q^{4} + 5 q^{5} + 6 q^{7} - q^{9} + O(q^{10}) \) \( 4 q - q^{3} + 2 q^{4} + 5 q^{5} + 6 q^{7} - q^{9} + 11 q^{11} + 2 q^{12} + 6 q^{13} - 5 q^{15} - 4 q^{16} + q^{17} - 13 q^{19} + 10 q^{20} + q^{21} - q^{23} - 5 q^{25} - q^{27} + 28 q^{28} - 14 q^{29} - 8 q^{31} + q^{33} - 15 q^{35} + 2 q^{36} + 13 q^{37} + 6 q^{39} + 16 q^{41} + 16 q^{43} - 2 q^{44} - 5 q^{45} + 16 q^{48} + 11 q^{49} + q^{51} - 2 q^{52} - 9 q^{53} + 25 q^{55} + 7 q^{57} + 15 q^{59} - 10 q^{60} + 15 q^{61} - 14 q^{63} + 8 q^{64} + 20 q^{65} - 5 q^{67} + 18 q^{68} - q^{69} - 28 q^{71} - 4 q^{73} - 5 q^{75} - 24 q^{76} + 24 q^{77} + 19 q^{79} - q^{81} - 19 q^{83} - 2 q^{84} - 15 q^{85} - 14 q^{87} - 21 q^{89} + 54 q^{91} + 12 q^{92} + 2 q^{93} + 5 q^{95} + 8 q^{97} + q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(3\) 0.309017 + 0.951057i 0.178411 + 0.549093i
\(4\) 1.61803 1.17557i 0.809017 0.587785i
\(5\) 0.690983 + 2.12663i 0.309017 + 0.951057i
\(6\) 0 0
\(7\) 3.73607 + 2.71441i 1.41210 + 1.02595i 0.993013 + 0.118006i \(0.0376501\pi\)
0.419088 + 0.907946i \(0.362350\pi\)
\(8\) 0 0
\(9\) −0.809017 + 0.587785i −0.269672 + 0.195928i
\(10\) 0 0
\(11\) 2.19098 2.48990i 0.660606 0.750733i
\(12\) 1.61803 + 1.17557i 0.467086 + 0.339358i
\(13\) 3.73607 2.71441i 1.03620 0.752843i 0.0666589 0.997776i \(-0.478766\pi\)
0.969540 + 0.244933i \(0.0787661\pi\)
\(14\) 0 0
\(15\) −1.80902 + 1.31433i −0.467086 + 0.339358i
\(16\) 1.23607 3.80423i 0.309017 0.951057i
\(17\) −1.42705 + 1.03681i −0.346111 + 0.251464i −0.747236 0.664559i \(-0.768619\pi\)
0.401125 + 0.916023i \(0.368619\pi\)
\(18\) 0 0
\(19\) −6.04508 4.39201i −1.38684 1.00760i −0.996204 0.0870503i \(-0.972256\pi\)
−0.390634 0.920546i \(-0.627744\pi\)
\(20\) 3.61803 + 2.62866i 0.809017 + 0.587785i
\(21\) −1.42705 + 4.39201i −0.311408 + 0.958415i
\(22\) 0 0
\(23\) −1.92705 + 1.40008i −0.401818 + 0.291938i −0.770281 0.637705i \(-0.779884\pi\)
0.368463 + 0.929642i \(0.379884\pi\)
\(24\) 0 0
\(25\) −4.04508 + 2.93893i −0.809017 + 0.587785i
\(26\) 0 0
\(27\) −0.809017 0.587785i −0.155695 0.113119i
\(28\) 9.23607 1.74545
\(29\) −4.61803 + 3.35520i −0.857547 + 0.623045i −0.927217 0.374526i \(-0.877806\pi\)
0.0696692 + 0.997570i \(0.477806\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 0 0
\(33\) 3.04508 + 1.31433i 0.530081 + 0.228795i
\(34\) 0 0
\(35\) −3.19098 + 9.82084i −0.539375 + 1.66002i
\(36\) −0.618034 + 1.90211i −0.103006 + 0.317019i
\(37\) −1.78115 5.48183i −0.292820 0.901206i −0.983945 0.178472i \(-0.942885\pi\)
0.691125 0.722735i \(-0.257115\pi\)
\(38\) 0 0
\(39\) 3.73607 + 2.71441i 0.598250 + 0.434654i
\(40\) 0 0
\(41\) 1.76393 0.275480 0.137740 0.990468i \(-0.456016\pi\)
0.137740 + 0.990468i \(0.456016\pi\)
\(42\) 0 0
\(43\) 1.76393 0.268997 0.134499 0.990914i \(-0.457058\pi\)
0.134499 + 0.990914i \(0.457058\pi\)
\(44\) 0.618034 6.60440i 0.0931721 0.995650i
\(45\) −1.80902 1.31433i −0.269672 0.195928i
\(46\) 0 0
\(47\) 1.11803 + 3.44095i 0.163082 + 0.501915i 0.998890 0.0471073i \(-0.0150003\pi\)
−0.835808 + 0.549022i \(0.815000\pi\)
\(48\) 4.00000 0.577350
\(49\) 4.42705 + 13.6251i 0.632436 + 1.94644i
\(50\) 0 0
\(51\) −1.42705 1.03681i −0.199827 0.145183i
\(52\) 2.85410 8.78402i 0.395793 1.21812i
\(53\) −7.28115 5.29007i −1.00014 0.726647i −0.0380244 0.999277i \(-0.512106\pi\)
−0.962119 + 0.272630i \(0.912106\pi\)
\(54\) 0 0
\(55\) 6.80902 + 2.93893i 0.918128 + 0.396285i
\(56\) 0 0
\(57\) 2.30902 7.10642i 0.305837 0.941269i
\(58\) 0 0
\(59\) −2.39919 7.38394i −0.312348 0.961307i −0.976833 0.214005i \(-0.931349\pi\)
0.664485 0.747302i \(-0.268651\pi\)
\(60\) −1.38197 + 4.25325i −0.178411 + 0.549093i
\(61\) 3.19098 + 2.31838i 0.408564 + 0.296839i 0.773020 0.634382i \(-0.218745\pi\)
−0.364456 + 0.931220i \(0.618745\pi\)
\(62\) 0 0
\(63\) −4.61803 −0.581818
\(64\) −2.47214 7.60845i −0.309017 0.951057i
\(65\) 8.35410 + 6.06961i 1.03620 + 0.752843i
\(66\) 0 0
\(67\) −0.690983 2.12663i −0.0844170 0.259809i 0.899934 0.436025i \(-0.143614\pi\)
−0.984351 + 0.176216i \(0.943614\pi\)
\(68\) −1.09017 + 3.35520i −0.132203 + 0.406878i
\(69\) −1.92705 1.40008i −0.231990 0.168550i
\(70\) 0 0
\(71\) −2.52786 −0.300002 −0.150001 0.988686i \(-0.547928\pi\)
−0.150001 + 0.988686i \(0.547928\pi\)
\(72\) 0 0
\(73\) 5.70820 0.668095 0.334047 0.942556i \(-0.391585\pi\)
0.334047 + 0.942556i \(0.391585\pi\)
\(74\) 0 0
\(75\) −4.04508 2.93893i −0.467086 0.339358i
\(76\) −14.9443 −1.71423
\(77\) 14.9443 3.35520i 1.70306 0.382360i
\(78\) 0 0
\(79\) 9.78115 + 7.10642i 1.10047 + 0.799535i 0.981136 0.193320i \(-0.0619254\pi\)
0.119330 + 0.992855i \(0.461925\pi\)
\(80\) 8.94427 1.00000
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 0 0
\(83\) −9.78115 + 7.10642i −1.07362 + 0.780031i −0.976560 0.215247i \(-0.930944\pi\)
−0.0970614 + 0.995278i \(0.530944\pi\)
\(84\) 2.85410 + 8.78402i 0.311408 + 0.958415i
\(85\) −3.19098 2.31838i −0.346111 0.251464i
\(86\) 0 0
\(87\) −4.61803 3.35520i −0.495105 0.359715i
\(88\) 0 0
\(89\) −10.2812 + 7.46969i −1.08980 + 0.791786i −0.979365 0.202097i \(-0.935224\pi\)
−0.110435 + 0.993883i \(0.535224\pi\)
\(90\) 0 0
\(91\) 21.3262 2.23560
\(92\) −1.47214 + 4.53077i −0.153481 + 0.472365i
\(93\) −0.618034 1.90211i −0.0640871 0.197240i
\(94\) 0 0
\(95\) 5.16312 15.8904i 0.529725 1.63033i
\(96\) 0 0
\(97\) 5.35410 + 3.88998i 0.543627 + 0.394968i 0.825430 0.564504i \(-0.190933\pi\)
−0.281803 + 0.959472i \(0.590933\pi\)
\(98\) 0 0
\(99\) −0.309017 + 3.30220i −0.0310574 + 0.331883i
\(100\) −3.09017 + 9.51057i −0.309017 + 0.951057i
\(101\) −3.19098 + 9.82084i −0.317515 + 0.977210i 0.657192 + 0.753723i \(0.271744\pi\)
−0.974707 + 0.223487i \(0.928256\pi\)
\(102\) 0 0
\(103\) −11.6353 + 8.45351i −1.14646 + 0.832949i −0.988006 0.154418i \(-0.950650\pi\)
−0.158450 + 0.987367i \(0.550650\pi\)
\(104\) 0 0
\(105\) −10.3262 −1.00774
\(106\) 0 0
\(107\) 8.89919 6.46564i 0.860317 0.625057i −0.0676543 0.997709i \(-0.521551\pi\)
0.927971 + 0.372652i \(0.121551\pi\)
\(108\) −2.00000 −0.192450
\(109\) −12.0902 8.78402i −1.15803 0.841357i −0.168501 0.985702i \(-0.553893\pi\)
−0.989527 + 0.144345i \(0.953893\pi\)
\(110\) 0 0
\(111\) 4.66312 3.38795i 0.442604 0.321570i
\(112\) 14.9443 10.8576i 1.41210 1.02595i
\(113\) 8.38197 0.788509 0.394255 0.919001i \(-0.371003\pi\)
0.394255 + 0.919001i \(0.371003\pi\)
\(114\) 0 0
\(115\) −4.30902 3.13068i −0.401818 0.291938i
\(116\) −3.52786 + 10.8576i −0.327554 + 1.00811i
\(117\) −1.42705 + 4.39201i −0.131931 + 0.406042i
\(118\) 0 0
\(119\) −8.14590 −0.746733
\(120\) 0 0
\(121\) −1.39919 10.9106i −0.127199 0.991877i
\(122\) 0 0
\(123\) 0.545085 + 1.67760i 0.0491487 + 0.151264i
\(124\) −3.23607 + 2.35114i −0.290607 + 0.211139i
\(125\) −9.04508 6.57164i −0.809017 0.587785i
\(126\) 0 0
\(127\) −9.23607 6.71040i −0.819569 0.595451i 0.0970204 0.995282i \(-0.469069\pi\)
−0.916589 + 0.399831i \(0.869069\pi\)
\(128\) 0 0
\(129\) 0.545085 + 1.67760i 0.0479921 + 0.147704i
\(130\) 0 0
\(131\) 6.25329 + 19.2456i 0.546352 + 1.68150i 0.717753 + 0.696298i \(0.245171\pi\)
−0.171400 + 0.985201i \(0.554829\pi\)
\(132\) 6.47214 1.45309i 0.563327 0.126475i
\(133\) −10.6631 32.8177i −0.924610 2.84566i
\(134\) 0 0
\(135\) 0.690983 2.12663i 0.0594703 0.183031i
\(136\) 0 0
\(137\) −0.791796 + 2.43690i −0.0676477 + 0.208198i −0.979166 0.203061i \(-0.934911\pi\)
0.911518 + 0.411259i \(0.134911\pi\)
\(138\) 0 0
\(139\) −1.76393 −0.149615 −0.0748074 0.997198i \(-0.523834\pi\)
−0.0748074 + 0.997198i \(0.523834\pi\)
\(140\) 6.38197 + 19.6417i 0.539375 + 1.66002i
\(141\) −2.92705 + 2.12663i −0.246502 + 0.179094i
\(142\) 0 0
\(143\) 1.42705 15.2497i 0.119336 1.27524i
\(144\) 1.23607 + 3.80423i 0.103006 + 0.317019i
\(145\) −10.3262 7.50245i −0.857547 0.623045i
\(146\) 0 0
\(147\) −11.5902 + 8.42075i −0.955941 + 0.694532i
\(148\) −9.32624 6.77591i −0.766612 0.556976i
\(149\) −0.673762 2.07363i −0.0551967 0.169878i 0.919658 0.392721i \(-0.128466\pi\)
−0.974854 + 0.222843i \(0.928466\pi\)
\(150\) 0 0
\(151\) −11.2082 + 8.14324i −0.912111 + 0.662687i −0.941548 0.336879i \(-0.890629\pi\)
0.0294371 + 0.999567i \(0.490629\pi\)
\(152\) 0 0
\(153\) 0.545085 1.67760i 0.0440675 0.135626i
\(154\) 0 0
\(155\) −1.38197 4.25325i −0.111002 0.341630i
\(156\) 9.23607 0.739477
\(157\) 3.00000 2.17963i 0.239426 0.173953i −0.461601 0.887087i \(-0.652725\pi\)
0.701028 + 0.713134i \(0.252725\pi\)
\(158\) 0 0
\(159\) 2.78115 8.55951i 0.220560 0.678813i
\(160\) 0 0
\(161\) −11.0000 −0.866921
\(162\) 0 0
\(163\) −8.16312 + 5.93085i −0.639385 + 0.464540i −0.859639 0.510902i \(-0.829311\pi\)
0.220254 + 0.975443i \(0.429311\pi\)
\(164\) 2.85410 2.07363i 0.222868 0.161923i
\(165\) −0.690983 + 7.38394i −0.0537930 + 0.574839i
\(166\) 0 0
\(167\) 20.6525 1.59814 0.799068 0.601240i \(-0.205327\pi\)
0.799068 + 0.601240i \(0.205327\pi\)
\(168\) 0 0
\(169\) 2.57295 7.91872i 0.197919 0.609133i
\(170\) 0 0
\(171\) 7.47214 0.571409
\(172\) 2.85410 2.07363i 0.217623 0.158113i
\(173\) 5.83688 17.9641i 0.443770 1.36578i −0.440057 0.897970i \(-0.645042\pi\)
0.883827 0.467813i \(-0.154958\pi\)
\(174\) 0 0
\(175\) −23.0902 −1.74545
\(176\) −6.76393 11.4127i −0.509851 0.860263i
\(177\) 6.28115 4.56352i 0.472120 0.343016i
\(178\) 0 0
\(179\) −6.30902 19.4172i −0.471558 1.45131i −0.850544 0.525904i \(-0.823727\pi\)
0.378986 0.925402i \(-0.376273\pi\)
\(180\) −4.47214 −0.333333
\(181\) 15.0623 10.9434i 1.11957 0.813417i 0.135428 0.990787i \(-0.456759\pi\)
0.984144 + 0.177370i \(0.0567590\pi\)
\(182\) 0 0
\(183\) −1.21885 + 3.75123i −0.0900998 + 0.277299i
\(184\) 0 0
\(185\) 10.4271 7.57570i 0.766612 0.556976i
\(186\) 0 0
\(187\) −0.545085 + 5.82485i −0.0398606 + 0.425955i
\(188\) 5.85410 + 4.25325i 0.426954 + 0.310200i
\(189\) −1.42705 4.39201i −0.103803 0.319472i
\(190\) 0 0
\(191\) −0.718847 2.21238i −0.0520139 0.160082i 0.921675 0.387962i \(-0.126821\pi\)
−0.973689 + 0.227879i \(0.926821\pi\)
\(192\) 6.47214 4.70228i 0.467086 0.339358i
\(193\) 2.30902 + 7.10642i 0.166207 + 0.511532i 0.999123 0.0418671i \(-0.0133306\pi\)
−0.832917 + 0.553399i \(0.813331\pi\)
\(194\) 0 0
\(195\) −3.19098 + 9.82084i −0.228511 + 0.703285i
\(196\) 23.1803 + 16.8415i 1.65574 + 1.20296i
\(197\) −5.37132 + 16.5312i −0.382691 + 1.17780i 0.555451 + 0.831550i \(0.312546\pi\)
−0.938142 + 0.346252i \(0.887454\pi\)
\(198\) 0 0
\(199\) 10.2705 0.728057 0.364029 0.931388i \(-0.381401\pi\)
0.364029 + 0.931388i \(0.381401\pi\)
\(200\) 0 0
\(201\) 1.80902 1.31433i 0.127598 0.0927055i
\(202\) 0 0
\(203\) −26.3607 −1.85016
\(204\) −3.52786 −0.247000
\(205\) 1.21885 + 3.75123i 0.0851280 + 0.261997i
\(206\) 0 0
\(207\) 0.736068 2.26538i 0.0511603 0.157455i
\(208\) −5.70820 17.5680i −0.395793 1.21812i
\(209\) −24.1803 + 5.42882i −1.67259 + 0.375520i
\(210\) 0 0
\(211\) 3.19098 + 9.82084i 0.219676 + 0.676094i 0.998788 + 0.0492096i \(0.0156702\pi\)
−0.779112 + 0.626885i \(0.784330\pi\)
\(212\) −18.0000 −1.23625
\(213\) −0.781153 2.40414i −0.0535237 0.164729i
\(214\) 0 0
\(215\) 1.21885 + 3.75123i 0.0831247 + 0.255831i
\(216\) 0 0
\(217\) −7.47214 5.42882i −0.507242 0.368533i
\(218\) 0 0
\(219\) 1.76393 + 5.42882i 0.119195 + 0.366846i
\(220\) 14.4721 3.24920i 0.975711 0.219061i
\(221\) −2.51722 + 7.74721i −0.169327 + 0.521134i
\(222\) 0 0
\(223\) 9.04508 27.8379i 0.605704 1.86416i 0.113824 0.993501i \(-0.463690\pi\)
0.491879 0.870663i \(-0.336310\pi\)
\(224\) 0 0
\(225\) 1.54508 4.75528i 0.103006 0.317019i
\(226\) 0 0
\(227\) 21.3262 1.41547 0.707736 0.706477i \(-0.249717\pi\)
0.707736 + 0.706477i \(0.249717\pi\)
\(228\) −4.61803 14.2128i −0.305837 0.941269i
\(229\) −15.5623 11.3067i −1.02839 0.747166i −0.0604011 0.998174i \(-0.519238\pi\)
−0.967985 + 0.251008i \(0.919238\pi\)
\(230\) 0 0
\(231\) 7.80902 + 13.1760i 0.513796 + 0.866919i
\(232\) 0 0
\(233\) −7.47214 −0.489516 −0.244758 0.969584i \(-0.578708\pi\)
−0.244758 + 0.969584i \(0.578708\pi\)
\(234\) 0 0
\(235\) −6.54508 + 4.75528i −0.426954 + 0.310200i
\(236\) −12.5623 9.12705i −0.817736 0.594120i
\(237\) −3.73607 + 11.4984i −0.242684 + 0.746904i
\(238\) 0 0
\(239\) 4.40983 13.5721i 0.285248 0.877904i −0.701076 0.713087i \(-0.747297\pi\)
0.986324 0.164817i \(-0.0527034\pi\)
\(240\) 2.76393 + 8.50651i 0.178411 + 0.549093i
\(241\) 22.7533 + 16.5312i 1.46567 + 1.06487i 0.981841 + 0.189707i \(0.0607538\pi\)
0.483827 + 0.875163i \(0.339246\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 7.88854 0.505012
\(245\) −25.9164 + 18.8294i −1.65574 + 1.20296i
\(246\) 0 0
\(247\) −34.5066 −2.19560
\(248\) 0 0
\(249\) −9.78115 7.10642i −0.619855 0.450351i
\(250\) 0 0
\(251\) 5.09017 15.6659i 0.321289 0.988825i −0.651799 0.758391i \(-0.725986\pi\)
0.973088 0.230433i \(-0.0740144\pi\)
\(252\) −7.47214 + 5.42882i −0.470700 + 0.341984i
\(253\) −0.736068 + 7.86572i −0.0462762 + 0.494514i
\(254\) 0 0
\(255\) 1.21885 3.75123i 0.0763272 0.234911i
\(256\) −12.9443 9.40456i −0.809017 0.587785i
\(257\) −18.5623 13.4863i −1.15788 0.841253i −0.168376 0.985723i \(-0.553852\pi\)
−0.989509 + 0.144470i \(0.953852\pi\)
\(258\) 0 0
\(259\) 8.22542 25.3153i 0.511103 1.57301i
\(260\) 20.6525 1.28081
\(261\) 1.76393 5.42882i 0.109185 0.336036i
\(262\) 0 0
\(263\) −4.28115 3.11044i −0.263987 0.191798i 0.447916 0.894076i \(-0.352166\pi\)
−0.711903 + 0.702278i \(0.752166\pi\)
\(264\) 0 0
\(265\) 6.21885 19.1396i 0.382021 1.17574i
\(266\) 0 0
\(267\) −10.2812 7.46969i −0.629196 0.457138i
\(268\) −3.61803 2.62866i −0.221007 0.160571i
\(269\) −22.6525 + 16.4580i −1.38115 + 1.00346i −0.384374 + 0.923178i \(0.625583\pi\)
−0.996772 + 0.0802836i \(0.974417\pi\)
\(270\) 0 0
\(271\) −4.61803 + 3.35520i −0.280526 + 0.203814i −0.719147 0.694858i \(-0.755467\pi\)
0.438621 + 0.898672i \(0.355467\pi\)
\(272\) 2.18034 + 6.71040i 0.132203 + 0.406878i
\(273\) 6.59017 + 20.2825i 0.398855 + 1.22755i
\(274\) 0 0
\(275\) −1.54508 + 16.5110i −0.0931721 + 0.995650i
\(276\) −4.76393 −0.286755
\(277\) −0.336881 1.03681i −0.0202412 0.0622961i 0.940426 0.339999i \(-0.110427\pi\)
−0.960667 + 0.277703i \(0.910427\pi\)
\(278\) 0 0
\(279\) 1.61803 1.17557i 0.0968692 0.0703796i
\(280\) 0 0
\(281\) 9.23607 6.71040i 0.550978 0.400309i −0.277168 0.960821i \(-0.589396\pi\)
0.828146 + 0.560513i \(0.189396\pi\)
\(282\) 0 0
\(283\) 19.2254 + 13.9681i 1.14283 + 0.830317i 0.987511 0.157547i \(-0.0503587\pi\)
0.155321 + 0.987864i \(0.450359\pi\)
\(284\) −4.09017 + 2.97168i −0.242707 + 0.176337i
\(285\) 16.7082 0.989709
\(286\) 0 0
\(287\) 6.59017 + 4.78804i 0.389005 + 0.282629i
\(288\) 0 0
\(289\) −4.29180 + 13.2088i −0.252459 + 0.776988i
\(290\) 0 0
\(291\) −2.04508 + 6.29412i −0.119885 + 0.368968i
\(292\) 9.23607 6.71040i 0.540500 0.392696i
\(293\) 7.47214 + 5.42882i 0.436527 + 0.317155i 0.784253 0.620441i \(-0.213046\pi\)
−0.347727 + 0.937596i \(0.613046\pi\)
\(294\) 0 0
\(295\) 14.0451 10.2044i 0.817736 0.594120i
\(296\) 0 0
\(297\) −3.23607 + 0.726543i −0.187776 + 0.0421583i
\(298\) 0 0
\(299\) −3.39919 + 10.4616i −0.196580 + 0.605011i
\(300\) −10.0000 −0.577350
\(301\) 6.59017 + 4.78804i 0.379851 + 0.275978i
\(302\) 0 0
\(303\) −10.3262 −0.593227
\(304\) −24.1803 + 17.5680i −1.38684 + 1.00760i
\(305\) −2.72542 + 8.38800i −0.156057 + 0.480295i
\(306\) 0 0
\(307\) 24.5967 1.40381 0.701905 0.712270i \(-0.252333\pi\)
0.701905 + 0.712270i \(0.252333\pi\)
\(308\) 20.2361 22.9969i 1.15306 1.31037i
\(309\) −11.6353 8.45351i −0.661907 0.480903i
\(310\) 0 0
\(311\) 10.3992 32.0054i 0.589684 1.81486i 0.0100978 0.999949i \(-0.496786\pi\)
0.579586 0.814911i \(-0.303214\pi\)
\(312\) 0 0
\(313\) −6.29180 + 19.3642i −0.355633 + 1.09453i 0.600008 + 0.799994i \(0.295164\pi\)
−0.955641 + 0.294533i \(0.904836\pi\)
\(314\) 0 0
\(315\) −3.19098 9.82084i −0.179792 0.553341i
\(316\) 24.1803 1.36025
\(317\) −9.47214 −0.532008 −0.266004 0.963972i \(-0.585703\pi\)
−0.266004 + 0.963972i \(0.585703\pi\)
\(318\) 0 0
\(319\) −1.76393 + 18.8496i −0.0987612 + 1.05538i
\(320\) 14.4721 10.5146i 0.809017 0.587785i
\(321\) 8.89919 + 6.46564i 0.496704 + 0.360877i
\(322\) 0 0
\(323\) 13.1803 0.733374
\(324\) −0.618034 1.90211i −0.0343352 0.105673i
\(325\) −7.13525 + 21.9601i −0.395793 + 1.21812i
\(326\) 0 0
\(327\) 4.61803 14.2128i 0.255378 0.785972i
\(328\) 0 0
\(329\) −5.16312 + 15.8904i −0.284652 + 0.876069i
\(330\) 0 0
\(331\) 3.92705 + 12.0862i 0.215850 + 0.664319i 0.999092 + 0.0426017i \(0.0135646\pi\)
−0.783242 + 0.621717i \(0.786435\pi\)
\(332\) −7.47214 + 22.9969i −0.410087 + 1.26212i
\(333\) 4.66312 + 3.38795i 0.255537 + 0.185659i
\(334\) 0 0
\(335\) 4.04508 2.93893i 0.221007 0.160571i
\(336\) 14.9443 + 10.8576i 0.815277 + 0.592333i
\(337\) 2.85410 + 8.78402i 0.155473 + 0.478496i 0.998208 0.0598314i \(-0.0190563\pi\)
−0.842736 + 0.538328i \(0.819056\pi\)
\(338\) 0 0
\(339\) 2.59017 + 7.97172i 0.140679 + 0.432965i
\(340\) −7.88854 −0.427816
\(341\) −4.38197 + 4.97980i −0.237297 + 0.269671i
\(342\) 0 0
\(343\) −10.4549 + 32.1769i −0.564512 + 1.73739i
\(344\) 0 0
\(345\) 1.64590 5.06555i 0.0886122 0.272720i
\(346\) 0 0
\(347\) 22.4164 1.20338 0.601688 0.798731i \(-0.294495\pi\)
0.601688 + 0.798731i \(0.294495\pi\)
\(348\) −11.4164 −0.611984
\(349\) −16.7082 + 12.1392i −0.894370 + 0.649798i −0.937014 0.349293i \(-0.886422\pi\)
0.0426440 + 0.999090i \(0.486422\pi\)
\(350\) 0 0
\(351\) −4.61803 −0.246492
\(352\) 0 0
\(353\) 9.43769 29.0462i 0.502318 1.54598i −0.302916 0.953017i \(-0.597960\pi\)
0.805234 0.592958i \(-0.202040\pi\)
\(354\) 0 0
\(355\) −1.74671 5.37582i −0.0927058 0.285319i
\(356\) −7.85410 + 24.1724i −0.416267 + 1.28114i
\(357\) −2.51722 7.74721i −0.133225 0.410026i
\(358\) 0 0
\(359\) −0.545085 1.67760i −0.0287685 0.0885403i 0.935641 0.352952i \(-0.114822\pi\)
−0.964410 + 0.264412i \(0.914822\pi\)
\(360\) 0 0
\(361\) 11.3820 + 35.0301i 0.599051 + 1.84369i
\(362\) 0 0
\(363\) 9.94427 4.70228i 0.521939 0.246806i
\(364\) 34.5066 25.0705i 1.80864 1.31405i
\(365\) 3.94427 + 12.1392i 0.206453 + 0.635396i
\(366\) 0 0
\(367\) 3.69098 11.3597i 0.192668 0.592970i −0.807328 0.590103i \(-0.799087\pi\)
0.999996 0.00286759i \(-0.000912782\pi\)
\(368\) 2.94427 + 9.06154i 0.153481 + 0.472365i
\(369\) −1.42705 + 1.03681i −0.0742893 + 0.0539743i
\(370\) 0 0
\(371\) −12.8435 39.5281i −0.666799 2.05220i
\(372\) −3.23607 2.35114i −0.167782 0.121901i
\(373\) −11.0000 + 7.99197i −0.569558 + 0.413808i −0.834945 0.550334i \(-0.814500\pi\)
0.265386 + 0.964142i \(0.414500\pi\)
\(374\) 0 0
\(375\) 3.45492 10.6331i 0.178411 0.549093i
\(376\) 0 0
\(377\) −8.14590 + 25.0705i −0.419535 + 1.29120i
\(378\) 0 0
\(379\) −5.18034 −0.266096 −0.133048 0.991110i \(-0.542476\pi\)
−0.133048 + 0.991110i \(0.542476\pi\)
\(380\) −10.3262 31.7809i −0.529725 1.63033i
\(381\) 3.52786 10.8576i 0.180738 0.556254i
\(382\) 0 0
\(383\) 33.5967 1.71671 0.858357 0.513053i \(-0.171486\pi\)
0.858357 + 0.513053i \(0.171486\pi\)
\(384\) 0 0
\(385\) 17.4615 + 29.4625i 0.889920 + 1.50155i
\(386\) 0 0
\(387\) −1.42705 + 1.03681i −0.0725411 + 0.0527042i
\(388\) 13.2361 0.671960
\(389\) 17.7639 0.900667 0.450334 0.892860i \(-0.351305\pi\)
0.450334 + 0.892860i \(0.351305\pi\)
\(390\) 0 0
\(391\) 1.29837 3.99598i 0.0656616 0.202086i
\(392\) 0 0
\(393\) −16.3713 + 11.8945i −0.825824 + 0.599996i
\(394\) 0 0
\(395\) −8.35410 + 25.7113i −0.420340 + 1.29367i
\(396\) 3.38197 + 5.70634i 0.169950 + 0.286754i
\(397\) 0.527864 1.62460i 0.0264927 0.0815363i −0.936936 0.349501i \(-0.886351\pi\)
0.963429 + 0.267965i \(0.0863511\pi\)
\(398\) 0 0
\(399\) 27.9164 20.2825i 1.39757 1.01539i
\(400\) 6.18034 + 19.0211i 0.309017 + 0.951057i
\(401\) −2.20820 6.79615i −0.110272 0.339384i 0.880659 0.473750i \(-0.157100\pi\)
−0.990932 + 0.134367i \(0.957100\pi\)
\(402\) 0 0
\(403\) −7.47214 + 5.42882i −0.372214 + 0.270429i
\(404\) 6.38197 + 19.6417i 0.317515 + 0.977210i
\(405\) 2.23607 0.111111
\(406\) 0 0
\(407\) −17.5517 7.57570i −0.870004 0.375513i
\(408\) 0 0
\(409\) 25.9443 18.8496i 1.28286 0.932054i 0.283226 0.959053i \(-0.408595\pi\)
0.999635 + 0.0269996i \(0.00859527\pi\)
\(410\) 0 0
\(411\) −2.56231 −0.126389
\(412\) −8.88854 + 27.3561i −0.437907 + 1.34774i
\(413\) 11.0795 34.0993i 0.545188 1.67792i
\(414\) 0 0
\(415\) −21.8713 15.8904i −1.07362 0.780031i
\(416\) 0 0
\(417\) −0.545085 1.67760i −0.0266929 0.0821524i
\(418\) 0 0
\(419\) −2.80902 8.64527i −0.137229 0.422349i 0.858701 0.512477i \(-0.171272\pi\)
−0.995930 + 0.0901286i \(0.971272\pi\)
\(420\) −16.7082 + 12.1392i −0.815277 + 0.592333i
\(421\) −7.86475 24.2052i −0.383304 1.17969i −0.937703 0.347438i \(-0.887052\pi\)
0.554399 0.832251i \(-0.312948\pi\)
\(422\) 0 0
\(423\) −2.92705 2.12663i −0.142318 0.103400i
\(424\) 0 0
\(425\) 2.72542 8.38800i 0.132203 0.406878i
\(426\) 0 0
\(427\) 5.62868 + 17.3233i 0.272391 + 0.838333i
\(428\) 6.79837 20.9232i 0.328612 1.01136i
\(429\) 14.9443 3.35520i 0.721516 0.161990i
\(430\) 0 0
\(431\) 19.1459 0.922225 0.461113 0.887342i \(-0.347450\pi\)
0.461113 + 0.887342i \(0.347450\pi\)
\(432\) −3.23607 + 2.35114i −0.155695 + 0.113119i
\(433\) −6.39919 + 19.6947i −0.307525 + 0.946466i 0.671197 + 0.741279i \(0.265780\pi\)
−0.978723 + 0.205187i \(0.934220\pi\)
\(434\) 0 0
\(435\) 3.94427 12.1392i 0.189113 0.582031i
\(436\) −29.8885 −1.43140
\(437\) 17.7984 0.851412
\(438\) 0 0
\(439\) −7.13525 + 5.18407i −0.340547 + 0.247422i −0.744893 0.667184i \(-0.767499\pi\)
0.404346 + 0.914606i \(0.367499\pi\)
\(440\) 0 0
\(441\) −11.5902 8.42075i −0.551913 0.400988i
\(442\) 0 0
\(443\) −3.02786 + 2.19987i −0.143858 + 0.104519i −0.657387 0.753554i \(-0.728338\pi\)
0.513528 + 0.858073i \(0.328338\pi\)
\(444\) 3.56231 10.9637i 0.169060 0.520312i
\(445\) −22.9894 16.7027i −1.08980 0.791786i
\(446\) 0 0
\(447\) 1.76393 1.28157i 0.0834311 0.0606163i
\(448\) 11.4164 35.1361i 0.539375 1.66002i
\(449\) −9.41641 + 28.9807i −0.444388 + 1.36768i 0.438766 + 0.898601i \(0.355416\pi\)
−0.883154 + 0.469084i \(0.844584\pi\)
\(450\) 0 0
\(451\) 3.86475 4.39201i 0.181984 0.206812i
\(452\) 13.5623 9.85359i 0.637917 0.463474i
\(453\) −11.2082 8.14324i −0.526607 0.382603i
\(454\) 0 0
\(455\) 14.7361 + 45.3530i 0.690838 + 2.12618i
\(456\) 0 0
\(457\) −1.01064 3.11044i −0.0472759 0.145500i 0.924632 0.380862i \(-0.124373\pi\)
−0.971908 + 0.235361i \(0.924373\pi\)
\(458\) 0 0
\(459\) 1.76393 0.0823333
\(460\) −10.6525 −0.496674
\(461\) −4.95492 + 3.59996i −0.230773 + 0.167667i −0.697163 0.716913i \(-0.745555\pi\)
0.466389 + 0.884580i \(0.345555\pi\)
\(462\) 0 0
\(463\) −12.2533 8.90254i −0.569459 0.413736i 0.265450 0.964125i \(-0.414480\pi\)
−0.834909 + 0.550389i \(0.814480\pi\)
\(464\) 7.05573 + 21.7153i 0.327554 + 1.00811i
\(465\) 3.61803 2.62866i 0.167782 0.121901i
\(466\) 0 0
\(467\) 27.4894 19.9722i 1.27206 0.924203i 0.272773 0.962078i \(-0.412059\pi\)
0.999282 + 0.0378758i \(0.0120591\pi\)
\(468\) 2.85410 + 8.78402i 0.131931 + 0.406042i
\(469\) 3.19098 9.82084i 0.147346 0.453484i
\(470\) 0 0
\(471\) 3.00000 + 2.17963i 0.138233 + 0.100432i
\(472\) 0 0
\(473\) 3.86475 4.39201i 0.177701 0.201945i
\(474\) 0 0
\(475\) 37.3607 1.71423
\(476\) −13.1803 + 9.57608i −0.604120 + 0.438919i
\(477\) 9.00000 0.412082
\(478\) 0 0
\(479\) −14.9443 −0.682821 −0.341411 0.939914i \(-0.610905\pi\)
−0.341411 + 0.939914i \(0.610905\pi\)
\(480\) 0 0
\(481\) −21.5344 15.6457i −0.981886 0.713382i
\(482\) 0 0
\(483\) −3.39919 10.4616i −0.154668 0.476020i
\(484\) −15.0902 16.0090i −0.685917 0.727680i
\(485\) −4.57295 + 14.0741i −0.207647 + 0.639072i
\(486\) 0 0
\(487\) 29.5623 1.33960 0.669798 0.742543i \(-0.266381\pi\)
0.669798 + 0.742543i \(0.266381\pi\)
\(488\) 0 0
\(489\) −8.16312 5.93085i −0.369149 0.268202i
\(490\) 0 0
\(491\) −9.70163 29.8585i −0.437828 1.34750i −0.890160 0.455647i \(-0.849408\pi\)
0.452332 0.891850i \(-0.350592\pi\)
\(492\) 2.85410 + 2.07363i 0.128673 + 0.0934863i
\(493\) 3.11146 9.57608i 0.140133 0.431285i
\(494\) 0 0
\(495\) −7.23607 + 1.62460i −0.325237 + 0.0730203i
\(496\) −2.47214 + 7.60845i −0.111002 + 0.341630i
\(497\) −9.44427 6.86167i −0.423633 0.307788i
\(498\) 0 0
\(499\) 35.4164 + 25.7315i 1.58546 + 1.15190i 0.910084 + 0.414425i \(0.136017\pi\)
0.675372 + 0.737477i \(0.263983\pi\)
\(500\) −22.3607 −1.00000
\(501\) 6.38197 + 19.6417i 0.285125 + 0.877525i
\(502\) 0 0
\(503\) 11.7533 + 36.1729i 0.524053 + 1.61287i 0.766180 + 0.642626i \(0.222155\pi\)
−0.242127 + 0.970245i \(0.577845\pi\)
\(504\) 0 0
\(505\) −23.0902 −1.02750
\(506\) 0 0
\(507\) 8.32624 0.369781
\(508\) −22.8328 −1.01304
\(509\) −23.2705 −1.03145 −0.515724 0.856755i \(-0.672477\pi\)
−0.515724 + 0.856755i \(0.672477\pi\)
\(510\) 0 0
\(511\) 21.3262 + 15.4944i 0.943417 + 0.685433i
\(512\) 0 0
\(513\) 2.30902 + 7.10642i 0.101946 + 0.313756i
\(514\) 0 0
\(515\) −26.0172 18.9026i −1.14646 0.832949i
\(516\) 2.85410 + 2.07363i 0.125645 + 0.0912863i
\(517\) 11.0172 + 4.75528i 0.484537 + 0.209137i
\(518\) 0 0
\(519\) 18.8885 0.829115
\(520\) 0 0
\(521\) 0.663119 0.481784i 0.0290518 0.0211073i −0.573165 0.819440i \(-0.694284\pi\)
0.602216 + 0.798333i \(0.294284\pi\)
\(522\) 0 0
\(523\) 18.3435 + 13.3273i 0.802103 + 0.582762i 0.911530 0.411233i \(-0.134902\pi\)
−0.109427 + 0.993995i \(0.534902\pi\)
\(524\) 32.7426 + 23.7889i 1.43037 + 1.03922i
\(525\) −7.13525 21.9601i −0.311408 0.958415i
\(526\) 0 0
\(527\) 2.85410 2.07363i 0.124327 0.0903286i
\(528\) 8.76393 9.95959i 0.381401 0.433436i
\(529\) −5.35410 + 16.4782i −0.232787 + 0.716445i
\(530\) 0 0
\(531\) 6.28115 + 4.56352i 0.272579 + 0.198040i
\(532\) −55.8328 40.5649i −2.42066 1.75871i
\(533\) 6.59017 4.78804i 0.285452 0.207393i
\(534\) 0 0
\(535\) 19.8992 + 14.4576i 0.860317 + 0.625057i
\(536\) 0 0
\(537\) 16.5172 12.0005i 0.712771 0.517858i
\(538\) 0 0
\(539\) 43.6246 + 18.8294i 1.87905 + 0.811038i
\(540\) −1.38197 4.25325i −0.0594703 0.183031i
\(541\) −19.5623 + 14.2128i −0.841049 + 0.611058i −0.922664 0.385606i \(-0.873992\pi\)
0.0816143 + 0.996664i \(0.473992\pi\)
\(542\) 0 0
\(543\) 15.0623 + 10.9434i 0.646385 + 0.469626i
\(544\) 0 0
\(545\) 10.3262 31.7809i 0.442327 1.36134i
\(546\) 0 0
\(547\) −7.47214 22.9969i −0.319485 0.983275i −0.973869 0.227112i \(-0.927072\pi\)
0.654383 0.756163i \(-0.272928\pi\)
\(548\) 1.58359 + 4.87380i 0.0676477 + 0.208198i
\(549\) −3.94427 −0.168337
\(550\) 0 0
\(551\) 42.6525 1.81706
\(552\) 0 0
\(553\) 17.2533 + 53.1002i 0.733684 + 2.25805i
\(554\) 0 0
\(555\) 10.4271 + 7.57570i 0.442604 + 0.321570i
\(556\) −2.85410 + 2.07363i −0.121041 + 0.0879414i
\(557\) 2.30902 + 1.67760i 0.0978362 + 0.0710822i 0.635628 0.771996i \(-0.280741\pi\)
−0.537792 + 0.843078i \(0.680741\pi\)
\(558\) 0 0
\(559\) 6.59017 4.78804i 0.278734 0.202512i
\(560\) 33.4164 + 24.2784i 1.41210 + 1.02595i
\(561\) −5.70820 + 1.28157i −0.241001 + 0.0541080i
\(562\) 0 0
\(563\) 13.5172 9.82084i 0.569683 0.413899i −0.265307 0.964164i \(-0.585473\pi\)
0.834990 + 0.550265i \(0.185473\pi\)
\(564\) −2.23607 + 6.88191i −0.0941554 + 0.289781i
\(565\) 5.79180 + 17.8253i 0.243663 + 0.749917i
\(566\) 0 0
\(567\) 3.73607 2.71441i 0.156900 0.113995i
\(568\) 0 0
\(569\) 6.38197 + 4.63677i 0.267546 + 0.194383i 0.713467 0.700689i \(-0.247124\pi\)
−0.445921 + 0.895072i \(0.647124\pi\)
\(570\) 0 0
\(571\) 1.29837 3.99598i 0.0543353 0.167227i −0.920206 0.391434i \(-0.871979\pi\)
0.974542 + 0.224207i \(0.0719792\pi\)
\(572\) −15.6180 26.3521i −0.653023 1.10184i
\(573\) 1.88197 1.36733i 0.0786203 0.0571210i
\(574\) 0 0
\(575\) 3.68034 11.3269i 0.153481 0.472365i
\(576\) 6.47214 + 4.70228i 0.269672 + 0.195928i
\(577\) −8.07295 5.86534i −0.336081 0.244177i 0.406925 0.913461i \(-0.366601\pi\)
−0.743007 + 0.669284i \(0.766601\pi\)
\(578\) 0 0
\(579\) −6.04508 + 4.39201i −0.251225 + 0.182526i
\(580\) −25.5279 −1.05999
\(581\) −55.8328 −2.31634
\(582\) 0 0
\(583\) −29.1246 + 6.53888i −1.20622 + 0.270813i
\(584\) 0 0
\(585\) −10.3262 −0.426937
\(586\) 0 0
\(587\) 5.61803 + 17.2905i 0.231881 + 0.713657i 0.997520 + 0.0703858i \(0.0224230\pi\)
−0.765639 + 0.643271i \(0.777577\pi\)
\(588\) −8.85410 + 27.2501i −0.365137 + 1.12378i
\(589\) 12.0902 + 8.78402i 0.498167 + 0.361939i
\(590\) 0 0
\(591\) −17.3820 −0.714999
\(592\) −23.0557 −0.947585
\(593\) −18.4721 −0.758560 −0.379280 0.925282i \(-0.623828\pi\)
−0.379280 + 0.925282i \(0.623828\pi\)
\(594\) 0 0
\(595\) −5.62868 17.3233i −0.230753 0.710186i
\(596\) −3.52786 2.56314i −0.144507 0.104990i
\(597\) 3.17376 + 9.76784i 0.129893 + 0.399771i
\(598\) 0 0
\(599\) −0.236068 0.726543i −0.00964548 0.0296857i 0.946118 0.323822i \(-0.104968\pi\)
−0.955763 + 0.294136i \(0.904968\pi\)
\(600\) 0 0
\(601\) −10.6631 7.74721i −0.434958 0.316015i 0.348671 0.937245i \(-0.386633\pi\)
−0.783628 + 0.621230i \(0.786633\pi\)
\(602\) 0 0
\(603\) 1.80902 + 1.31433i 0.0736689 + 0.0535236i
\(604\) −8.56231 + 26.3521i −0.348395 + 1.07225i
\(605\) 22.2361 10.5146i 0.904025 0.427480i
\(606\) 0 0
\(607\) −4.69756 + 14.4576i −0.190668 + 0.586816i −1.00000 0.000535683i \(-0.999829\pi\)
0.809332 + 0.587352i \(0.199829\pi\)
\(608\) 0 0
\(609\) −8.14590 25.0705i −0.330088 1.01591i
\(610\) 0 0
\(611\) 13.5172 + 9.82084i 0.546848 + 0.397308i
\(612\) −1.09017 3.35520i −0.0440675 0.135626i
\(613\) 9.65248 0.389860 0.194930 0.980817i \(-0.437552\pi\)
0.194930 + 0.980817i \(0.437552\pi\)
\(614\) 0 0
\(615\) −3.19098 + 2.31838i −0.128673 + 0.0934863i
\(616\) 0 0
\(617\) 6.63525 + 20.4212i 0.267125 + 0.822127i 0.991196 + 0.132402i \(0.0422688\pi\)
−0.724071 + 0.689726i \(0.757731\pi\)
\(618\) 0 0
\(619\) −17.6353 12.8128i −0.708821 0.514988i 0.173972 0.984751i \(-0.444340\pi\)
−0.882793 + 0.469762i \(0.844340\pi\)
\(620\) −7.23607 5.25731i −0.290607 0.211139i
\(621\) 2.38197 0.0955850
\(622\) 0 0
\(623\) −58.6869 −2.35124
\(624\) 14.9443 10.8576i 0.598250 0.434654i
\(625\) 7.72542 23.7764i 0.309017 0.951057i
\(626\) 0 0
\(627\) −12.6353 21.3193i −0.504603 0.851410i
\(628\) 2.29180 7.05342i 0.0914526 0.281462i
\(629\) 8.22542 + 5.97612i 0.327969 + 0.238284i
\(630\) 0 0
\(631\) −10.2426 + 31.5236i −0.407753 + 1.25494i 0.510821 + 0.859687i \(0.329342\pi\)
−0.918574 + 0.395248i \(0.870658\pi\)
\(632\) 0 0
\(633\) −8.35410 + 6.06961i −0.332046 + 0.241245i
\(634\) 0 0
\(635\) 7.88854 24.2784i 0.313047 0.963461i
\(636\) −5.56231 17.1190i −0.220560 0.678813i
\(637\) 53.5238 + 38.8873i 2.12069 + 1.54077i
\(638\) 0 0
\(639\) 2.04508 1.48584i 0.0809023 0.0587790i
\(640\) 0 0
\(641\) −41.0902 −1.62296 −0.811482 0.584377i \(-0.801339\pi\)
−0.811482 + 0.584377i \(0.801339\pi\)
\(642\) 0 0
\(643\) 1.27051 + 3.91023i 0.0501040 + 0.154204i 0.972978 0.230898i \(-0.0741663\pi\)
−0.922874 + 0.385102i \(0.874166\pi\)
\(644\) −17.7984 + 12.9313i −0.701354 + 0.509564i
\(645\) −3.19098 + 2.31838i −0.125645 + 0.0912863i
\(646\) 0 0
\(647\) 20.3713 + 14.8006i 0.800879 + 0.581873i 0.911172 0.412026i \(-0.135179\pi\)
−0.110293 + 0.993899i \(0.535179\pi\)
\(648\) 0 0
\(649\) −23.6418 10.2044i −0.928023 0.400556i
\(650\) 0 0
\(651\) 2.85410 8.78402i 0.111861 0.344273i
\(652\) −6.23607 + 19.1926i −0.244223 + 0.751642i
\(653\) −12.9443 + 9.40456i −0.506549 + 0.368029i −0.811513 0.584335i \(-0.801356\pi\)
0.304964 + 0.952364i \(0.401356\pi\)
\(654\) 0 0
\(655\) −36.6074 + 26.5968i −1.43037 + 1.03922i
\(656\) 2.18034 6.71040i 0.0851280 0.261997i
\(657\) −4.61803 + 3.35520i −0.180167 + 0.130899i
\(658\) 0 0
\(659\) −32.7426 23.7889i −1.27547 0.926685i −0.276066 0.961139i \(-0.589031\pi\)
−0.999406 + 0.0344537i \(0.989031\pi\)
\(660\) 7.56231 + 12.7598i 0.294362 + 0.496673i
\(661\) 1.26393 0.918300i 0.0491613 0.0357177i −0.562933 0.826502i \(-0.690327\pi\)
0.612095 + 0.790785i \(0.290327\pi\)
\(662\) 0 0
\(663\) −8.14590 −0.316360
\(664\) 0 0
\(665\) 62.4230 45.3530i 2.42066 1.75871i
\(666\) 0 0
\(667\) 4.20163 12.9313i 0.162688 0.500701i
\(668\) 33.4164 24.2784i 1.29292 0.939361i
\(669\) 29.2705 1.13166
\(670\) 0 0
\(671\) 12.7639 2.86568i 0.492746 0.110628i
\(672\) 0 0
\(673\) 8.22542 + 25.3153i 0.317067 + 0.975831i 0.974895 + 0.222664i \(0.0714752\pi\)
−0.657829 + 0.753168i \(0.728525\pi\)
\(674\) 0 0
\(675\) 5.00000 0.192450
\(676\) −5.14590 15.8374i −0.197919 0.609133i
\(677\) 1.21885 + 0.885544i 0.0468441 + 0.0340342i 0.610961 0.791661i \(-0.290783\pi\)
−0.564117 + 0.825695i \(0.690783\pi\)
\(678\) 0 0
\(679\) 9.44427 + 29.0665i 0.362438 + 1.11547i
\(680\) 0 0
\(681\) 6.59017 + 20.2825i 0.252536 + 0.777225i
\(682\) 0 0
\(683\) 5.69098 + 17.5150i 0.217759 + 0.670195i 0.998946 + 0.0458972i \(0.0146147\pi\)
−0.781187 + 0.624297i \(0.785385\pi\)
\(684\) 12.0902 8.78402i 0.462279 0.335865i
\(685\) −5.72949 −0.218913
\(686\) 0 0
\(687\) 5.94427 18.2946i 0.226788 0.697982i
\(688\) 2.18034 6.71040i 0.0831247 0.255831i
\(689\) −41.5623 −1.58340
\(690\) 0 0
\(691\) 28.7254 20.8702i 1.09277 0.793941i 0.112902 0.993606i \(-0.463985\pi\)
0.979864 + 0.199665i \(0.0639853\pi\)
\(692\) −11.6738 35.9281i −0.443770 1.36578i
\(693\) −10.1180 + 11.4984i −0.384352 + 0.436789i
\(694\) 0 0
\(695\) −1.21885 3.75123i −0.0462335 0.142292i
\(696\) 0 0
\(697\) −2.51722 + 1.82887i −0.0953465 + 0.0692733i
\(698\) 0 0
\(699\) −2.30902 7.10642i −0.0873350 0.268790i
\(700\) −37.3607 + 27.1441i −1.41210 + 1.02595i
\(701\) 1.76393 1.28157i 0.0666228 0.0484043i −0.553975 0.832533i \(-0.686890\pi\)
0.620598 + 0.784129i \(0.286890\pi\)
\(702\) 0 0
\(703\) −13.3090 + 40.9609i −0.501959 + 1.54487i
\(704\) −24.3607 10.5146i −0.918128 0.396285i
\(705\) −6.54508 4.75528i −0.246502 0.179094i
\(706\) 0 0
\(707\) −38.5795 + 28.0297i −1.45093 + 1.05416i
\(708\) 4.79837 14.7679i 0.180334 0.555011i
\(709\) 2.20163 6.77591i 0.0826838 0.254475i −0.901165 0.433476i \(-0.857287\pi\)
0.983849 + 0.179002i \(0.0572868\pi\)
\(710\) 0 0
\(711\) −12.0902 −0.453417
\(712\) 0 0
\(713\) 3.85410 2.80017i 0.144337 0.104867i
\(714\) 0 0
\(715\) 33.4164 7.50245i 1.24970 0.280576i
\(716\) −33.0344 24.0009i −1.23456 0.896957i
\(717\) 14.2705 0.532942
\(718\) 0 0
\(719\) −4.74265 + 14.5964i −0.176871 + 0.544352i −0.999714 0.0239161i \(-0.992387\pi\)
0.822843 + 0.568269i \(0.192387\pi\)
\(720\) −7.23607 + 5.25731i −0.269672 + 0.195928i
\(721\) −66.4164 −2.47348
\(722\) 0 0
\(723\) −8.69098 + 26.7481i −0.323221 + 0.994772i
\(724\) 11.5066 35.4136i 0.427639 1.31614i
\(725\) 8.81966 27.1441i 0.327554 1.00811i
\(726\) 0 0
\(727\) −26.6074 + 19.3314i −0.986814 + 0.716962i −0.959221 0.282657i \(-0.908784\pi\)
−0.0275925 + 0.999619i \(0.508784\pi\)
\(728\) 0 0
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) 0 0
\(731\) −2.51722 + 1.82887i −0.0931028 + 0.0676431i
\(732\) 2.43769 + 7.50245i 0.0900998 + 0.277299i
\(733\) −10.2467 + 31.5361i −0.378471 + 1.16481i 0.562636 + 0.826705i \(0.309787\pi\)
−0.941107 + 0.338109i \(0.890213\pi\)
\(734\) 0 0
\(735\) −25.9164 18.8294i −0.955941 0.694532i
\(736\) 0 0
\(737\) −6.80902 2.93893i −0.250813 0.108257i
\(738\) 0 0
\(739\) −5.96556 18.3601i −0.219447 0.675387i −0.998808 0.0488125i \(-0.984456\pi\)
0.779361 0.626575i \(-0.215544\pi\)
\(740\) 7.96556 24.5155i 0.292820 0.901206i
\(741\) −10.6631 32.8177i −0.391719 1.20559i
\(742\) 0 0
\(743\) −12.2188 37.6057i −0.448266 1.37962i −0.878862 0.477076i \(-0.841697\pi\)
0.430596 0.902545i \(-0.358303\pi\)
\(744\) 0 0
\(745\) 3.94427 2.86568i 0.144507 0.104990i
\(746\) 0 0
\(747\) 3.73607 11.4984i 0.136696 0.420706i
\(748\) 5.96556 + 10.0656i 0.218122 + 0.368035i
\(749\) 50.7984 1.85613
\(750\) 0 0
\(751\) −22.2705 + 16.1805i −0.812662 + 0.590434i −0.914601 0.404357i \(-0.867495\pi\)
0.101939 + 0.994791i \(0.467495\pi\)
\(752\) 14.4721 0.527744
\(753\) 16.4721 0.600278
\(754\) 0 0
\(755\) −25.0623 18.2088i −0.912111 0.662687i
\(756\) −7.47214 5.42882i −0.271759 0.197444i
\(757\) 0.343459 1.05706i 0.0124832 0.0384194i −0.944621 0.328164i \(-0.893570\pi\)
0.957104 + 0.289744i \(0.0935703\pi\)
\(758\) 0 0
\(759\) −7.70820 + 1.73060i −0.279790 + 0.0628168i
\(760\) 0 0
\(761\) −5.16312 15.8904i −0.187163 0.576028i 0.812816 0.582521i \(-0.197933\pi\)
−0.999979 + 0.00649228i \(0.997933\pi\)
\(762\) 0 0
\(763\) −21.3262 65.6354i −0.772062 2.37616i
\(764\) −3.76393 2.73466i −0.136174 0.0989364i
\(765\) 3.94427 0.142605
\(766\) 0 0
\(767\) −29.0066 21.0745i −1.04737 0.760957i
\(768\) 4.94427 15.2169i 0.178411 0.549093i
\(769\) −9.31559 28.6705i −0.335929 1.03388i −0.966263 0.257559i \(-0.917082\pi\)
0.630334 0.776324i \(-0.282918\pi\)
\(770\) 0 0
\(771\) 7.09017 21.8213i 0.255346 0.785875i
\(772\) 12.0902 + 8.78402i 0.435135 + 0.316144i
\(773\) −3.12461 + 9.61657i −0.112384 + 0.345884i −0.991393 0.130923i \(-0.958206\pi\)
0.879008 + 0.476807i \(0.158206\pi\)
\(774\) 0 0
\(775\) 8.09017 5.87785i 0.290607 0.211139i
\(776\) 0 0
\(777\) 26.6180 0.954917
\(778\) 0 0
\(779\) −10.6631 7.74721i −0.382046 0.277573i
\(780\) 6.38197 + 19.6417i 0.228511 + 0.703285i
\(781\) −5.53851 + 6.29412i −0.198183 + 0.225221i
\(782\) 0 0
\(783\) 5.70820 0.203995
\(784\) 57.3050 2.04661
\(785\) 6.70820 + 4.87380i 0.239426 + 0.173953i
\(786\) 0 0
\(787\) −5.91641 + 18.2088i −0.210897 + 0.649075i