Properties

Label 390.2.t.a.343.1
Level $390$
Weight $2$
Character 390.343
Analytic conductor $3.114$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.t (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \( x^{12} + 6x^{10} - 24x^{9} + 18x^{8} + 40x^{7} - 82x^{6} + 12x^{5} + 228x^{4} - 284x^{3} + 124x^{2} - 16x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 343.1
Root \(0.0572576 + 0.138232i\) of defining polynomial
Character \(\chi\) \(=\) 390.343
Dual form 390.2.t.a.307.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.20289 - 0.383740i) q^{5} +(0.707107 - 0.707107i) q^{6} +1.52873 q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.20289 - 0.383740i) q^{5} +(0.707107 - 0.707107i) q^{6} +1.52873 q^{7} -1.00000i q^{8} +1.00000i q^{9} +(0.383740 - 2.20289i) q^{10} +(2.70115 + 2.70115i) q^{11} +(0.707107 + 0.707107i) q^{12} +(3.17182 - 1.71451i) q^{13} +1.52873i q^{14} +(1.28634 + 1.82903i) q^{15} +1.00000 q^{16} +(4.03439 + 4.03439i) q^{17} -1.00000 q^{18} +(1.06701 + 1.06701i) q^{19} +(2.20289 + 0.383740i) q^{20} +(-1.08097 - 1.08097i) q^{21} +(-2.70115 + 2.70115i) q^{22} +(-0.485915 + 0.485915i) q^{23} +(-0.707107 + 0.707107i) q^{24} +(4.70549 + 1.69068i) q^{25} +(1.71451 + 3.17182i) q^{26} +(0.707107 - 0.707107i) q^{27} -1.52873 q^{28} -2.28429i q^{29} +(-1.82903 + 1.28634i) q^{30} +(1.00000 - 1.00000i) q^{31} +1.00000i q^{32} -3.82000i q^{33} +(-4.03439 + 4.03439i) q^{34} +(-3.36763 - 0.586634i) q^{35} -1.00000i q^{36} +7.96284 q^{37} +(-1.06701 + 1.06701i) q^{38} +(-3.45516 - 1.03047i) q^{39} +(-0.383740 + 2.20289i) q^{40} +(-8.22579 + 8.22579i) q^{41} +(1.08097 - 1.08097i) q^{42} +(5.76210 - 5.76210i) q^{43} +(-2.70115 - 2.70115i) q^{44} +(0.383740 - 2.20289i) q^{45} +(-0.485915 - 0.485915i) q^{46} +2.92343 q^{47} +(-0.707107 - 0.707107i) q^{48} -4.66299 q^{49} +(-1.69068 + 4.70549i) q^{50} -5.70549i q^{51} +(-3.17182 + 1.71451i) q^{52} +(-3.69068 - 3.69068i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-4.91381 - 6.98689i) q^{55} -1.52873i q^{56} -1.50898i q^{57} +2.28429 q^{58} +(-4.50044 + 4.50044i) q^{59} +(-1.28634 - 1.82903i) q^{60} -2.43047 q^{61} +(1.00000 + 1.00000i) q^{62} +1.52873i q^{63} -1.00000 q^{64} +(-7.64511 + 2.55973i) q^{65} +3.82000 q^{66} -3.79906i q^{67} +(-4.03439 - 4.03439i) q^{68} +0.687188 q^{69} +(0.586634 - 3.36763i) q^{70} +(10.7079 - 10.7079i) q^{71} +1.00000 q^{72} +10.3127i q^{73} +7.96284i q^{74} +(-2.13179 - 4.52277i) q^{75} +(-1.06701 - 1.06701i) q^{76} +(4.12932 + 4.12932i) q^{77} +(1.03047 - 3.45516i) q^{78} +1.53731i q^{79} +(-2.20289 - 0.383740i) q^{80} -1.00000 q^{81} +(-8.22579 - 8.22579i) q^{82} +7.72020 q^{83} +(1.08097 + 1.08097i) q^{84} +(-7.33918 - 10.4355i) q^{85} +(5.76210 + 5.76210i) q^{86} +(-1.61524 + 1.61524i) q^{87} +(2.70115 - 2.70115i) q^{88} +(-7.21676 + 7.21676i) q^{89} +(2.20289 + 0.383740i) q^{90} +(4.84885 - 2.62102i) q^{91} +(0.485915 - 0.485915i) q^{92} -1.41421 q^{93} +2.92343i q^{94} +(-1.94106 - 2.75997i) q^{95} +(0.707107 - 0.707107i) q^{96} -6.36597i q^{97} -4.66299i q^{98} +(-2.70115 + 2.70115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 12 q^{4} - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 12 q^{4} - 4 q^{5} + 4 q^{11} + 20 q^{13} - 4 q^{15} + 12 q^{16} + 8 q^{17} - 12 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{25} - 4 q^{26} + 4 q^{30} + 12 q^{31} - 8 q^{34} + 12 q^{35} - 16 q^{37} + 4 q^{38} - 12 q^{39} + 8 q^{41} + 8 q^{42} + 16 q^{43} - 4 q^{44} + 32 q^{47} - 20 q^{49} + 8 q^{50} - 20 q^{52} - 16 q^{53} - 12 q^{55} - 40 q^{58} + 20 q^{59} + 4 q^{60} + 16 q^{61} + 12 q^{62} - 12 q^{64} - 32 q^{65} - 16 q^{66} - 8 q^{68} - 32 q^{69} - 20 q^{70} - 32 q^{71} + 12 q^{72} + 4 q^{76} + 16 q^{77} - 4 q^{80} - 12 q^{81} + 8 q^{82} + 32 q^{83} + 8 q^{84} + 12 q^{85} + 16 q^{86} + 20 q^{87} + 4 q^{88} + 16 q^{89} + 4 q^{90} - 28 q^{91} - 8 q^{95} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) −1.00000 −0.500000
\(5\) −2.20289 0.383740i −0.985164 0.171614i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) 1.52873 0.577805 0.288903 0.957359i \(-0.406710\pi\)
0.288903 + 0.957359i \(0.406710\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) 0.383740 2.20289i 0.121349 0.696616i
\(11\) 2.70115 + 2.70115i 0.814427 + 0.814427i 0.985294 0.170867i \(-0.0546568\pi\)
−0.170867 + 0.985294i \(0.554657\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) 3.17182 1.71451i 0.879705 0.475520i
\(14\) 1.52873i 0.408570i
\(15\) 1.28634 + 1.82903i 0.332131 + 0.472253i
\(16\) 1.00000 0.250000
\(17\) 4.03439 + 4.03439i 0.978483 + 0.978483i 0.999773 0.0212904i \(-0.00677744\pi\)
−0.0212904 + 0.999773i \(0.506777\pi\)
\(18\) −1.00000 −0.235702
\(19\) 1.06701 + 1.06701i 0.244790 + 0.244790i 0.818828 0.574039i \(-0.194624\pi\)
−0.574039 + 0.818828i \(0.694624\pi\)
\(20\) 2.20289 + 0.383740i 0.492582 + 0.0858069i
\(21\) −1.08097 1.08097i −0.235888 0.235888i
\(22\) −2.70115 + 2.70115i −0.575887 + 0.575887i
\(23\) −0.485915 + 0.485915i −0.101320 + 0.101320i −0.755950 0.654630i \(-0.772825\pi\)
0.654630 + 0.755950i \(0.272825\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) 4.70549 + 1.69068i 0.941097 + 0.338136i
\(26\) 1.71451 + 3.17182i 0.336243 + 0.622045i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −1.52873 −0.288903
\(29\) 2.28429i 0.424183i −0.977250 0.212091i \(-0.931973\pi\)
0.977250 0.212091i \(-0.0680275\pi\)
\(30\) −1.82903 + 1.28634i −0.333933 + 0.234852i
\(31\) 1.00000 1.00000i 0.179605 0.179605i −0.611578 0.791184i \(-0.709465\pi\)
0.791184 + 0.611578i \(0.209465\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 3.82000i 0.664977i
\(34\) −4.03439 + 4.03439i −0.691892 + 0.691892i
\(35\) −3.36763 0.586634i −0.569233 0.0991593i
\(36\) 1.00000i 0.166667i
\(37\) 7.96284 1.30908 0.654541 0.756026i \(-0.272862\pi\)
0.654541 + 0.756026i \(0.272862\pi\)
\(38\) −1.06701 + 1.06701i −0.173092 + 0.173092i
\(39\) −3.45516 1.03047i −0.553268 0.165008i
\(40\) −0.383740 + 2.20289i −0.0606746 + 0.348308i
\(41\) −8.22579 + 8.22579i −1.28465 + 1.28465i −0.346663 + 0.937990i \(0.612685\pi\)
−0.937990 + 0.346663i \(0.887315\pi\)
\(42\) 1.08097 1.08097i 0.166798 0.166798i
\(43\) 5.76210 5.76210i 0.878711 0.878711i −0.114690 0.993401i \(-0.536587\pi\)
0.993401 + 0.114690i \(0.0365874\pi\)
\(44\) −2.70115 2.70115i −0.407214 0.407214i
\(45\) 0.383740 2.20289i 0.0572046 0.328388i
\(46\) −0.485915 0.485915i −0.0716443 0.0716443i
\(47\) 2.92343 0.426426 0.213213 0.977006i \(-0.431607\pi\)
0.213213 + 0.977006i \(0.431607\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) −4.66299 −0.666141
\(50\) −1.69068 + 4.70549i −0.239098 + 0.665456i
\(51\) 5.70549i 0.798928i
\(52\) −3.17182 + 1.71451i −0.439852 + 0.237760i
\(53\) −3.69068 3.69068i −0.506954 0.506954i 0.406636 0.913590i \(-0.366702\pi\)
−0.913590 + 0.406636i \(0.866702\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) −4.91381 6.98689i −0.662578 0.942112i
\(56\) 1.52873i 0.204285i
\(57\) 1.50898i 0.199870i
\(58\) 2.28429 0.299943
\(59\) −4.50044 + 4.50044i −0.585908 + 0.585908i −0.936521 0.350613i \(-0.885973\pi\)
0.350613 + 0.936521i \(0.385973\pi\)
\(60\) −1.28634 1.82903i −0.166065 0.236126i
\(61\) −2.43047 −0.311190 −0.155595 0.987821i \(-0.549729\pi\)
−0.155595 + 0.987821i \(0.549729\pi\)
\(62\) 1.00000 + 1.00000i 0.127000 + 0.127000i
\(63\) 1.52873i 0.192602i
\(64\) −1.00000 −0.125000
\(65\) −7.64511 + 2.55973i −0.948260 + 0.317496i
\(66\) 3.82000 0.470210
\(67\) 3.79906i 0.464129i −0.972700 0.232064i \(-0.925452\pi\)
0.972700 0.232064i \(-0.0745480\pi\)
\(68\) −4.03439 4.03439i −0.489241 0.489241i
\(69\) 0.687188 0.0827277
\(70\) 0.586634 3.36763i 0.0701162 0.402509i
\(71\) 10.7079 10.7079i 1.27080 1.27080i 0.325128 0.945670i \(-0.394593\pi\)
0.945670 0.325128i \(-0.105407\pi\)
\(72\) 1.00000 0.117851
\(73\) 10.3127i 1.20701i 0.797358 + 0.603506i \(0.206230\pi\)
−0.797358 + 0.603506i \(0.793770\pi\)
\(74\) 7.96284i 0.925661i
\(75\) −2.13179 4.52277i −0.246158 0.522245i
\(76\) −1.06701 1.06701i −0.122395 0.122395i
\(77\) 4.12932 + 4.12932i 0.470580 + 0.470580i
\(78\) 1.03047 3.45516i 0.116678 0.391220i
\(79\) 1.53731i 0.172961i 0.996254 + 0.0864803i \(0.0275620\pi\)
−0.996254 + 0.0864803i \(0.972438\pi\)
\(80\) −2.20289 0.383740i −0.246291 0.0429034i
\(81\) −1.00000 −0.111111
\(82\) −8.22579 8.22579i −0.908387 0.908387i
\(83\) 7.72020 0.847402 0.423701 0.905802i \(-0.360731\pi\)
0.423701 + 0.905802i \(0.360731\pi\)
\(84\) 1.08097 + 1.08097i 0.117944 + 0.117944i
\(85\) −7.33918 10.4355i −0.796045 1.13189i
\(86\) 5.76210 + 5.76210i 0.621343 + 0.621343i
\(87\) −1.61524 + 1.61524i −0.173172 + 0.173172i
\(88\) 2.70115 2.70115i 0.287944 0.287944i
\(89\) −7.21676 + 7.21676i −0.764976 + 0.764976i −0.977217 0.212242i \(-0.931924\pi\)
0.212242 + 0.977217i \(0.431924\pi\)
\(90\) 2.20289 + 0.383740i 0.232205 + 0.0404498i
\(91\) 4.84885 2.62102i 0.508298 0.274758i
\(92\) 0.485915 0.485915i 0.0506602 0.0506602i
\(93\) −1.41421 −0.146647
\(94\) 2.92343i 0.301529i
\(95\) −1.94106 2.75997i −0.199149 0.283167i
\(96\) 0.707107 0.707107i 0.0721688 0.0721688i
\(97\) 6.36597i 0.646366i −0.946336 0.323183i \(-0.895247\pi\)
0.946336 0.323183i \(-0.104753\pi\)
\(98\) 4.66299i 0.471033i
\(99\) −2.70115 + 2.70115i −0.271476 + 0.271476i
\(100\) −4.70549 1.69068i −0.470549 0.169068i
\(101\) 10.5668i 1.05143i 0.850660 + 0.525717i \(0.176203\pi\)
−0.850660 + 0.525717i \(0.823797\pi\)
\(102\) 5.70549 0.564927
\(103\) −4.86744 + 4.86744i −0.479603 + 0.479603i −0.905005 0.425402i \(-0.860133\pi\)
0.425402 + 0.905005i \(0.360133\pi\)
\(104\) −1.71451 3.17182i −0.168122 0.311023i
\(105\) 1.96646 + 2.79609i 0.191907 + 0.272870i
\(106\) 3.69068 3.69068i 0.358470 0.358470i
\(107\) 13.0918 13.0918i 1.26563 1.26563i 0.317307 0.948323i \(-0.397221\pi\)
0.948323 0.317307i \(-0.102779\pi\)
\(108\) −0.707107 + 0.707107i −0.0680414 + 0.0680414i
\(109\) −0.124070 0.124070i −0.0118838 0.0118838i 0.701140 0.713024i \(-0.252675\pi\)
−0.713024 + 0.701140i \(0.752675\pi\)
\(110\) 6.98689 4.91381i 0.666173 0.468513i
\(111\) −5.63058 5.63058i −0.534431 0.534431i
\(112\) 1.52873 0.144451
\(113\) −3.69674 3.69674i −0.347760 0.347760i 0.511514 0.859275i \(-0.329085\pi\)
−0.859275 + 0.511514i \(0.829085\pi\)
\(114\) 1.50898 0.141329
\(115\) 1.25688 0.883955i 0.117205 0.0824292i
\(116\) 2.28429i 0.212091i
\(117\) 1.71451 + 3.17182i 0.158507 + 0.293235i
\(118\) −4.50044 4.50044i −0.414299 0.414299i
\(119\) 6.16749 + 6.16749i 0.565372 + 0.565372i
\(120\) 1.82903 1.28634i 0.166967 0.117426i
\(121\) 3.59242i 0.326583i
\(122\) 2.43047i 0.220044i
\(123\) 11.6330 1.04891
\(124\) −1.00000 + 1.00000i −0.0898027 + 0.0898027i
\(125\) −9.71691 5.53007i −0.869107 0.494624i
\(126\) −1.52873 −0.136190
\(127\) −10.2359 10.2359i −0.908290 0.908290i 0.0878440 0.996134i \(-0.472002\pi\)
−0.996134 + 0.0878440i \(0.972002\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −8.14884 −0.717465
\(130\) −2.55973 7.64511i −0.224503 0.670521i
\(131\) −11.8485 −1.03521 −0.517606 0.855619i \(-0.673177\pi\)
−0.517606 + 0.855619i \(0.673177\pi\)
\(132\) 3.82000i 0.332489i
\(133\) 1.63117 + 1.63117i 0.141441 + 0.141441i
\(134\) 3.79906 0.328189
\(135\) −1.82903 + 1.28634i −0.157418 + 0.110710i
\(136\) 4.03439 4.03439i 0.345946 0.345946i
\(137\) −11.9361 −1.01977 −0.509886 0.860242i \(-0.670312\pi\)
−0.509886 + 0.860242i \(0.670312\pi\)
\(138\) 0.687188i 0.0584973i
\(139\) 20.0448i 1.70018i −0.526639 0.850089i \(-0.676548\pi\)
0.526639 0.850089i \(-0.323452\pi\)
\(140\) 3.36763 + 0.586634i 0.284616 + 0.0495797i
\(141\) −2.06718 2.06718i −0.174088 0.174088i
\(142\) 10.7079 + 10.7079i 0.898590 + 0.898590i
\(143\) 13.1987 + 3.93641i 1.10373 + 0.329179i
\(144\) 1.00000i 0.0833333i
\(145\) −0.876575 + 5.03206i −0.0727956 + 0.417890i
\(146\) −10.3127 −0.853486
\(147\) 3.29723 + 3.29723i 0.271951 + 0.271951i
\(148\) −7.96284 −0.654541
\(149\) 3.91078 + 3.91078i 0.320383 + 0.320383i 0.848914 0.528531i \(-0.177257\pi\)
−0.528531 + 0.848914i \(0.677257\pi\)
\(150\) 4.52277 2.13179i 0.369283 0.174060i
\(151\) 16.6941 + 16.6941i 1.35854 + 1.35854i 0.875714 + 0.482830i \(0.160391\pi\)
0.482830 + 0.875714i \(0.339609\pi\)
\(152\) 1.06701 1.06701i 0.0865462 0.0865462i
\(153\) −4.03439 + 4.03439i −0.326161 + 0.326161i
\(154\) −4.12932 + 4.12932i −0.332750 + 0.332750i
\(155\) −2.58663 + 1.81915i −0.207763 + 0.146118i
\(156\) 3.45516 + 1.03047i 0.276634 + 0.0825039i
\(157\) −9.39497 + 9.39497i −0.749800 + 0.749800i −0.974441 0.224642i \(-0.927879\pi\)
0.224642 + 0.974441i \(0.427879\pi\)
\(158\) −1.53731 −0.122302
\(159\) 5.21941i 0.413926i
\(160\) 0.383740 2.20289i 0.0303373 0.174154i
\(161\) −0.742832 + 0.742832i −0.0585434 + 0.0585434i
\(162\) 1.00000i 0.0785674i
\(163\) 14.0308i 1.09898i 0.835501 + 0.549489i \(0.185178\pi\)
−0.835501 + 0.549489i \(0.814822\pi\)
\(164\) 8.22579 8.22579i 0.642326 0.642326i
\(165\) −1.46589 + 8.41506i −0.114119 + 0.655112i
\(166\) 7.72020i 0.599204i
\(167\) 14.4217 1.11599 0.557993 0.829845i \(-0.311571\pi\)
0.557993 + 0.829845i \(0.311571\pi\)
\(168\) −1.08097 + 1.08097i −0.0833990 + 0.0833990i
\(169\) 7.12090 10.8762i 0.547762 0.836635i
\(170\) 10.4355 7.33918i 0.800365 0.562889i
\(171\) −1.06701 + 1.06701i −0.0815965 + 0.0815965i
\(172\) −5.76210 + 5.76210i −0.439356 + 0.439356i
\(173\) 12.0153 12.0153i 0.913507 0.913507i −0.0830394 0.996546i \(-0.526463\pi\)
0.996546 + 0.0830394i \(0.0264627\pi\)
\(174\) −1.61524 1.61524i −0.122451 0.122451i
\(175\) 7.19341 + 2.58459i 0.543771 + 0.195376i
\(176\) 2.70115 + 2.70115i 0.203607 + 0.203607i
\(177\) 6.36459 0.478392
\(178\) −7.21676 7.21676i −0.540919 0.540919i
\(179\) −10.2606 −0.766913 −0.383456 0.923559i \(-0.625266\pi\)
−0.383456 + 0.923559i \(0.625266\pi\)
\(180\) −0.383740 + 2.20289i −0.0286023 + 0.164194i
\(181\) 22.4534i 1.66895i 0.551046 + 0.834475i \(0.314229\pi\)
−0.551046 + 0.834475i \(0.685771\pi\)
\(182\) 2.62102 + 4.84885i 0.194283 + 0.359421i
\(183\) 1.71860 + 1.71860i 0.127043 + 0.127043i
\(184\) 0.485915 + 0.485915i 0.0358221 + 0.0358221i
\(185\) −17.5413 3.05566i −1.28966 0.224657i
\(186\) 1.41421i 0.103695i
\(187\) 21.7950i 1.59381i
\(188\) −2.92343 −0.213213
\(189\) 1.08097 1.08097i 0.0786293 0.0786293i
\(190\) 2.75997 1.94106i 0.200229 0.140819i
\(191\) −12.2203 −0.884229 −0.442115 0.896959i \(-0.645772\pi\)
−0.442115 + 0.896959i \(0.645772\pi\)
\(192\) 0.707107 + 0.707107i 0.0510310 + 0.0510310i
\(193\) 24.1428i 1.73783i 0.494958 + 0.868917i \(0.335183\pi\)
−0.494958 + 0.868917i \(0.664817\pi\)
\(194\) 6.36597 0.457050
\(195\) 7.21592 + 3.59591i 0.516743 + 0.257508i
\(196\) 4.66299 0.333071
\(197\) 3.53326i 0.251735i −0.992047 0.125867i \(-0.959829\pi\)
0.992047 0.125867i \(-0.0401714\pi\)
\(198\) −2.70115 2.70115i −0.191962 0.191962i
\(199\) −12.1781 −0.863284 −0.431642 0.902045i \(-0.642066\pi\)
−0.431642 + 0.902045i \(0.642066\pi\)
\(200\) 1.69068 4.70549i 0.119549 0.332728i
\(201\) −2.68634 + 2.68634i −0.189480 + 0.189480i
\(202\) −10.5668 −0.743476
\(203\) 3.49207i 0.245095i
\(204\) 5.70549i 0.399464i
\(205\) 21.2771 14.9640i 1.48606 1.04513i
\(206\) −4.86744 4.86744i −0.339130 0.339130i
\(207\) −0.485915 0.485915i −0.0337734 0.0337734i
\(208\) 3.17182 1.71451i 0.219926 0.118880i
\(209\) 5.76432i 0.398726i
\(210\) −2.79609 + 1.96646i −0.192948 + 0.135699i
\(211\) −14.2670 −0.982180 −0.491090 0.871109i \(-0.663401\pi\)
−0.491090 + 0.871109i \(0.663401\pi\)
\(212\) 3.69068 + 3.69068i 0.253477 + 0.253477i
\(213\) −15.1433 −1.03760
\(214\) 13.0918 + 13.0918i 0.894935 + 0.894935i
\(215\) −14.9044 + 10.4821i −1.01647 + 0.714876i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) 1.52873 1.52873i 0.103777 0.103777i
\(218\) 0.124070 0.124070i 0.00840311 0.00840311i
\(219\) 7.29219 7.29219i 0.492761 0.492761i
\(220\) 4.91381 + 6.98689i 0.331289 + 0.471056i
\(221\) 19.7134 + 5.87935i 1.32606 + 0.395488i
\(222\) 5.63058 5.63058i 0.377900 0.377900i
\(223\) −11.9632 −0.801112 −0.400556 0.916272i \(-0.631183\pi\)
−0.400556 + 0.916272i \(0.631183\pi\)
\(224\) 1.52873i 0.102142i
\(225\) −1.69068 + 4.70549i −0.112712 + 0.313699i
\(226\) 3.69674 3.69674i 0.245904 0.245904i
\(227\) 22.2944i 1.47973i −0.672756 0.739864i \(-0.734890\pi\)
0.672756 0.739864i \(-0.265110\pi\)
\(228\) 1.50898i 0.0999349i
\(229\) 5.97023 5.97023i 0.394524 0.394524i −0.481772 0.876296i \(-0.660007\pi\)
0.876296 + 0.481772i \(0.160007\pi\)
\(230\) 0.883955 + 1.25688i 0.0582862 + 0.0828765i
\(231\) 5.83975i 0.384227i
\(232\) −2.28429 −0.149971
\(233\) −13.3554 + 13.3554i −0.874943 + 0.874943i −0.993006 0.118063i \(-0.962332\pi\)
0.118063 + 0.993006i \(0.462332\pi\)
\(234\) −3.17182 + 1.71451i −0.207348 + 0.112081i
\(235\) −6.44001 1.12184i −0.420100 0.0731806i
\(236\) 4.50044 4.50044i 0.292954 0.292954i
\(237\) 1.08704 1.08704i 0.0706108 0.0706108i
\(238\) −6.16749 + 6.16749i −0.399779 + 0.399779i
\(239\) 9.78834 + 9.78834i 0.633155 + 0.633155i 0.948858 0.315703i \(-0.102240\pi\)
−0.315703 + 0.948858i \(0.602240\pi\)
\(240\) 1.28634 + 1.82903i 0.0830327 + 0.118063i
\(241\) −4.18100 4.18100i −0.269322 0.269322i 0.559505 0.828827i \(-0.310991\pi\)
−0.828827 + 0.559505i \(0.810991\pi\)
\(242\) −3.59242 −0.230929
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 2.43047 0.155595
\(245\) 10.2721 + 1.78938i 0.656259 + 0.114319i
\(246\) 11.6330i 0.741695i
\(247\) 5.21378 + 1.55497i 0.331745 + 0.0989402i
\(248\) −1.00000 1.00000i −0.0635001 0.0635001i
\(249\) −5.45901 5.45901i −0.345950 0.345950i
\(250\) 5.53007 9.71691i 0.349752 0.614551i
\(251\) 16.6015i 1.04788i −0.851755 0.523940i \(-0.824462\pi\)
0.851755 0.523940i \(-0.175538\pi\)
\(252\) 1.52873i 0.0963009i
\(253\) −2.62506 −0.165036
\(254\) 10.2359 10.2359i 0.642258 0.642258i
\(255\) −2.18942 + 12.5686i −0.137107 + 0.787075i
\(256\) 1.00000 0.0625000
\(257\) −11.6326 11.6326i −0.725624 0.725624i 0.244121 0.969745i \(-0.421501\pi\)
−0.969745 + 0.244121i \(0.921501\pi\)
\(258\) 8.14884i 0.507324i
\(259\) 12.1730 0.756395
\(260\) 7.64511 2.55973i 0.474130 0.158748i
\(261\) 2.28429 0.141394
\(262\) 11.8485i 0.732005i
\(263\) 1.07114 + 1.07114i 0.0660491 + 0.0660491i 0.739360 0.673311i \(-0.235128\pi\)
−0.673311 + 0.739360i \(0.735128\pi\)
\(264\) −3.82000 −0.235105
\(265\) 6.71391 + 9.54643i 0.412432 + 0.586433i
\(266\) −1.63117 + 1.63117i −0.100014 + 0.100014i
\(267\) 10.2060 0.624600
\(268\) 3.79906i 0.232064i
\(269\) 16.8729i 1.02876i −0.857562 0.514380i \(-0.828022\pi\)
0.857562 0.514380i \(-0.171978\pi\)
\(270\) −1.28634 1.82903i −0.0782839 0.111311i
\(271\) 4.55193 + 4.55193i 0.276510 + 0.276510i 0.831714 0.555204i \(-0.187360\pi\)
−0.555204 + 0.831714i \(0.687360\pi\)
\(272\) 4.03439 + 4.03439i 0.244621 + 0.244621i
\(273\) −5.28200 1.57531i −0.319681 0.0953424i
\(274\) 11.9361i 0.721087i
\(275\) 8.14345 + 17.2770i 0.491069 + 1.04184i
\(276\) −0.687188 −0.0413638
\(277\) 3.22540 + 3.22540i 0.193796 + 0.193796i 0.797334 0.603538i \(-0.206243\pi\)
−0.603538 + 0.797334i \(0.706243\pi\)
\(278\) 20.0448 1.20221
\(279\) 1.00000 + 1.00000i 0.0598684 + 0.0598684i
\(280\) −0.586634 + 3.36763i −0.0350581 + 0.201254i
\(281\) 4.05048 + 4.05048i 0.241631 + 0.241631i 0.817525 0.575894i \(-0.195346\pi\)
−0.575894 + 0.817525i \(0.695346\pi\)
\(282\) 2.06718 2.06718i 0.123099 0.123099i
\(283\) 14.1280 14.1280i 0.839825 0.839825i −0.149010 0.988836i \(-0.547609\pi\)
0.988836 + 0.149010i \(0.0476088\pi\)
\(284\) −10.7079 + 10.7079i −0.635399 + 0.635399i
\(285\) −0.579058 + 3.32413i −0.0343004 + 0.196905i
\(286\) −3.93641 + 13.1987i −0.232765 + 0.780456i
\(287\) −12.5750 + 12.5750i −0.742279 + 0.742279i
\(288\) −1.00000 −0.0589256
\(289\) 15.5526i 0.914858i
\(290\) −5.03206 0.876575i −0.295493 0.0514743i
\(291\) −4.50142 + 4.50142i −0.263878 + 0.263878i
\(292\) 10.3127i 0.603506i
\(293\) 29.4674i 1.72150i −0.509027 0.860751i \(-0.669995\pi\)
0.509027 0.860751i \(-0.330005\pi\)
\(294\) −3.29723 + 3.29723i −0.192298 + 0.192298i
\(295\) 11.6410 8.18700i 0.677765 0.476666i
\(296\) 7.96284i 0.462831i
\(297\) 3.82000 0.221659
\(298\) −3.91078 + 3.91078i −0.226545 + 0.226545i
\(299\) −0.708129 + 2.37434i −0.0409522 + 0.137312i
\(300\) 2.13179 + 4.52277i 0.123079 + 0.261122i
\(301\) 8.80868 8.80868i 0.507724 0.507724i
\(302\) −16.6941 + 16.6941i −0.960636 + 0.960636i
\(303\) 7.47184 7.47184i 0.429246 0.429246i
\(304\) 1.06701 + 1.06701i 0.0611974 + 0.0611974i
\(305\) 5.35407 + 0.932668i 0.306573 + 0.0534044i
\(306\) −4.03439 4.03439i −0.230631 0.230631i
\(307\) −20.8097 −1.18767 −0.593835 0.804587i \(-0.702387\pi\)
−0.593835 + 0.804587i \(0.702387\pi\)
\(308\) −4.12932 4.12932i −0.235290 0.235290i
\(309\) 6.88359 0.391594
\(310\) −1.81915 2.58663i −0.103321 0.146911i
\(311\) 31.1763i 1.76785i −0.467631 0.883924i \(-0.654892\pi\)
0.467631 0.883924i \(-0.345108\pi\)
\(312\) −1.03047 + 3.45516i −0.0583391 + 0.195610i
\(313\) 10.7473 + 10.7473i 0.607475 + 0.607475i 0.942285 0.334811i \(-0.108672\pi\)
−0.334811 + 0.942285i \(0.608672\pi\)
\(314\) −9.39497 9.39497i −0.530189 0.530189i
\(315\) 0.586634 3.36763i 0.0330531 0.189744i
\(316\) 1.53731i 0.0864803i
\(317\) 19.2205i 1.07953i −0.841816 0.539764i \(-0.818513\pi\)
0.841816 0.539764i \(-0.181487\pi\)
\(318\) −5.21941 −0.292690
\(319\) 6.17022 6.17022i 0.345466 0.345466i
\(320\) 2.20289 + 0.383740i 0.123146 + 0.0214517i
\(321\) −18.5146 −1.03338
\(322\) −0.742832 0.742832i −0.0413964 0.0413964i
\(323\) 8.60949i 0.479045i
\(324\) 1.00000 0.0555556
\(325\) 17.8237 2.70509i 0.988678 0.150051i
\(326\) −14.0308 −0.777095
\(327\) 0.175462i 0.00970308i
\(328\) 8.22579 + 8.22579i 0.454193 + 0.454193i
\(329\) 4.46913 0.246391
\(330\) −8.41506 1.46589i −0.463234 0.0806945i
\(331\) 12.9738 12.9738i 0.713107 0.713107i −0.254077 0.967184i \(-0.581772\pi\)
0.967184 + 0.254077i \(0.0817717\pi\)
\(332\) −7.72020 −0.423701
\(333\) 7.96284i 0.436361i
\(334\) 14.4217i 0.789122i
\(335\) −1.45785 + 8.36892i −0.0796509 + 0.457243i
\(336\) −1.08097 1.08097i −0.0589720 0.0589720i
\(337\) −19.7453 19.7453i −1.07560 1.07560i −0.996898 0.0786992i \(-0.974923\pi\)
−0.0786992 0.996898i \(-0.525077\pi\)
\(338\) 10.8762 + 7.12090i 0.591590 + 0.387326i
\(339\) 5.22798i 0.283945i
\(340\) 7.33918 + 10.4355i 0.398023 + 0.565944i
\(341\) 5.40230 0.292551
\(342\) −1.06701 1.06701i −0.0576974 0.0576974i
\(343\) −17.8295 −0.962705
\(344\) −5.76210 5.76210i −0.310671 0.310671i
\(345\) −1.51380 0.263701i −0.0815004 0.0141972i
\(346\) 12.0153 + 12.0153i 0.645947 + 0.645947i
\(347\) −0.843939 + 0.843939i −0.0453050 + 0.0453050i −0.729396 0.684091i \(-0.760199\pi\)
0.684091 + 0.729396i \(0.260199\pi\)
\(348\) 1.61524 1.61524i 0.0865859 0.0865859i
\(349\) 17.0343 17.0343i 0.911828 0.911828i −0.0845883 0.996416i \(-0.526958\pi\)
0.996416 + 0.0845883i \(0.0269575\pi\)
\(350\) −2.58459 + 7.19341i −0.138152 + 0.384504i
\(351\) 1.03047 3.45516i 0.0550026 0.184423i
\(352\) −2.70115 + 2.70115i −0.143972 + 0.143972i
\(353\) −6.51257 −0.346629 −0.173314 0.984867i \(-0.555448\pi\)
−0.173314 + 0.984867i \(0.555448\pi\)
\(354\) 6.36459i 0.338274i
\(355\) −27.6975 + 19.4794i −1.47003 + 1.03386i
\(356\) 7.21676 7.21676i 0.382488 0.382488i
\(357\) 8.72214i 0.461625i
\(358\) 10.2606i 0.542289i
\(359\) 17.5895 17.5895i 0.928337 0.928337i −0.0692614 0.997599i \(-0.522064\pi\)
0.997599 + 0.0692614i \(0.0220643\pi\)
\(360\) −2.20289 0.383740i −0.116103 0.0202249i
\(361\) 16.7230i 0.880156i
\(362\) −22.4534 −1.18013
\(363\) 2.54022 2.54022i 0.133327 0.133327i
\(364\) −4.84885 + 2.62102i −0.254149 + 0.137379i
\(365\) 3.95740 22.7178i 0.207140 1.18911i
\(366\) −1.71860 + 1.71860i −0.0898327 + 0.0898327i
\(367\) −10.9276 + 10.9276i −0.570418 + 0.570418i −0.932245 0.361827i \(-0.882153\pi\)
0.361827 + 0.932245i \(0.382153\pi\)
\(368\) −0.485915 + 0.485915i −0.0253301 + 0.0253301i
\(369\) −8.22579 8.22579i −0.428218 0.428218i
\(370\) 3.05566 17.5413i 0.158856 0.911929i
\(371\) −5.64204 5.64204i −0.292920 0.292920i
\(372\) 1.41421 0.0733236
\(373\) 6.56604 + 6.56604i 0.339977 + 0.339977i 0.856359 0.516382i \(-0.172721\pi\)
−0.516382 + 0.856359i \(0.672721\pi\)
\(374\) −21.7950 −1.12699
\(375\) 2.96054 + 10.7812i 0.152882 + 0.556741i
\(376\) 2.92343i 0.150764i
\(377\) −3.91645 7.24537i −0.201707 0.373156i
\(378\) 1.08097 + 1.08097i 0.0555993 + 0.0555993i
\(379\) −23.1557 23.1557i −1.18943 1.18943i −0.977226 0.212203i \(-0.931936\pi\)
−0.212203 0.977226i \(-0.568064\pi\)
\(380\) 1.94106 + 2.75997i 0.0995743 + 0.141584i
\(381\) 14.4758i 0.741616i
\(382\) 12.2203i 0.625244i
\(383\) 1.38206 0.0706198 0.0353099 0.999376i \(-0.488758\pi\)
0.0353099 + 0.999376i \(0.488758\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) −7.51188 10.6811i −0.382841 0.544357i
\(386\) −24.1428 −1.22883
\(387\) 5.76210 + 5.76210i 0.292904 + 0.292904i
\(388\) 6.36597i 0.323183i
\(389\) −19.6760 −0.997614 −0.498807 0.866713i \(-0.666228\pi\)
−0.498807 + 0.866713i \(0.666228\pi\)
\(390\) −3.59591 + 7.21592i −0.182086 + 0.365392i
\(391\) −3.92074 −0.198280
\(392\) 4.66299i 0.235516i
\(393\) 8.37818 + 8.37818i 0.422624 + 0.422624i
\(394\) 3.53326 0.178003
\(395\) 0.589926 3.38652i 0.0296824 0.170395i
\(396\) 2.70115 2.70115i 0.135738 0.135738i
\(397\) −35.9373 −1.80364 −0.901819 0.432113i \(-0.857768\pi\)
−0.901819 + 0.432113i \(0.857768\pi\)
\(398\) 12.1781i 0.610434i
\(399\) 2.30683i 0.115486i
\(400\) 4.70549 + 1.69068i 0.235274 + 0.0845339i
\(401\) −1.64796 1.64796i −0.0822953 0.0822953i 0.664761 0.747056i \(-0.268533\pi\)
−0.747056 + 0.664761i \(0.768533\pi\)
\(402\) −2.68634 2.68634i −0.133982 0.133982i
\(403\) 1.45731 4.88633i 0.0725938 0.243406i
\(404\) 10.5668i 0.525717i
\(405\) 2.20289 + 0.383740i 0.109463 + 0.0190682i
\(406\) 3.49207 0.173308
\(407\) 21.5088 + 21.5088i 1.06615 + 1.06615i
\(408\) −5.70549 −0.282464
\(409\) 12.3833 + 12.3833i 0.612314 + 0.612314i 0.943548 0.331234i \(-0.107465\pi\)
−0.331234 + 0.943548i \(0.607465\pi\)
\(410\) 14.9640 + 21.2771i 0.739018 + 1.05080i
\(411\) 8.44011 + 8.44011i 0.416320 + 0.416320i
\(412\) 4.86744 4.86744i 0.239801 0.239801i
\(413\) −6.87996 + 6.87996i −0.338540 + 0.338540i
\(414\) 0.485915 0.485915i 0.0238814 0.0238814i
\(415\) −17.0068 2.96255i −0.834830 0.145426i
\(416\) 1.71451 + 3.17182i 0.0840608 + 0.155511i
\(417\) −14.1738 + 14.1738i −0.694095 + 0.694095i
\(418\) −5.76432 −0.281942
\(419\) 8.21451i 0.401305i 0.979662 + 0.200652i \(0.0643062\pi\)
−0.979662 + 0.200652i \(0.935694\pi\)
\(420\) −1.96646 2.79609i −0.0959534 0.136435i
\(421\) −10.9922 + 10.9922i −0.535725 + 0.535725i −0.922270 0.386545i \(-0.873668\pi\)
0.386545 + 0.922270i \(0.373668\pi\)
\(422\) 14.2670i 0.694506i
\(423\) 2.92343i 0.142142i
\(424\) −3.69068 + 3.69068i −0.179235 + 0.179235i
\(425\) 12.1629 + 25.8046i 0.589988 + 1.25171i
\(426\) 15.1433i 0.733696i
\(427\) −3.71553 −0.179807
\(428\) −13.0918 + 13.0918i −0.632815 + 0.632815i
\(429\) −6.54944 12.1164i −0.316210 0.584984i
\(430\) −10.4821 14.9044i −0.505494 0.718756i
\(431\) 15.4246 15.4246i 0.742976 0.742976i −0.230174 0.973150i \(-0.573929\pi\)
0.973150 + 0.230174i \(0.0739294\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) −3.28016 + 3.28016i −0.157634 + 0.157634i −0.781518 0.623883i \(-0.785554\pi\)
0.623883 + 0.781518i \(0.285554\pi\)
\(434\) 1.52873 + 1.52873i 0.0733813 + 0.0733813i
\(435\) 4.17804 2.93837i 0.200321 0.140884i
\(436\) 0.124070 + 0.124070i 0.00594190 + 0.00594190i
\(437\) −1.03696 −0.0496043
\(438\) 7.29219 + 7.29219i 0.348434 + 0.348434i
\(439\) 12.4347 0.593477 0.296739 0.954959i \(-0.404101\pi\)
0.296739 + 0.954959i \(0.404101\pi\)
\(440\) −6.98689 + 4.91381i −0.333087 + 0.234257i
\(441\) 4.66299i 0.222047i
\(442\) −5.87935 + 19.7134i −0.279652 + 0.937669i
\(443\) −12.5904 12.5904i −0.598187 0.598187i 0.341643 0.939830i \(-0.389017\pi\)
−0.939830 + 0.341643i \(0.889017\pi\)
\(444\) 5.63058 + 5.63058i 0.267215 + 0.267215i
\(445\) 18.6671 13.1284i 0.884907 0.622346i
\(446\) 11.9632i 0.566472i
\(447\) 5.53068i 0.261592i
\(448\) −1.52873 −0.0722256
\(449\) 15.4853 15.4853i 0.730796 0.730796i −0.239982 0.970777i \(-0.577141\pi\)
0.970777 + 0.239982i \(0.0771414\pi\)
\(450\) −4.70549 1.69068i −0.221819 0.0796993i
\(451\) −44.4382 −2.09251
\(452\) 3.69674 + 3.69674i 0.173880 + 0.173880i
\(453\) 23.6090i 1.10925i
\(454\) 22.2944 1.04633
\(455\) −11.6873 + 3.91314i −0.547909 + 0.183451i
\(456\) −1.50898 −0.0706646
\(457\) 15.3846i 0.719660i 0.933018 + 0.359830i \(0.117165\pi\)
−0.933018 + 0.359830i \(0.882835\pi\)
\(458\) 5.97023 + 5.97023i 0.278971 + 0.278971i
\(459\) 5.70549 0.266309
\(460\) −1.25688 + 0.883955i −0.0586026 + 0.0412146i
\(461\) −26.1557 + 26.1557i −1.21819 + 1.21819i −0.249925 + 0.968265i \(0.580406\pi\)
−0.968265 + 0.249925i \(0.919594\pi\)
\(462\) 5.83975 0.271690
\(463\) 5.65611i 0.262862i 0.991325 + 0.131431i \(0.0419571\pi\)
−0.991325 + 0.131431i \(0.958043\pi\)
\(464\) 2.28429i 0.106046i
\(465\) 3.11536 + 0.542690i 0.144472 + 0.0251667i
\(466\) −13.3554 13.3554i −0.618678 0.618678i
\(467\) 23.4369 + 23.4369i 1.08453 + 1.08453i 0.996081 + 0.0884497i \(0.0281913\pi\)
0.0884497 + 0.996081i \(0.471809\pi\)
\(468\) −1.71451 3.17182i −0.0792533 0.146617i
\(469\) 5.80773i 0.268176i
\(470\) 1.12184 6.44001i 0.0517465 0.297056i
\(471\) 13.2865 0.612209
\(472\) 4.50044 + 4.50044i 0.207150 + 0.207150i
\(473\) 31.1286 1.43129
\(474\) 1.08704 + 1.08704i 0.0499294 + 0.0499294i
\(475\) 3.21684 + 6.82479i 0.147599 + 0.313143i
\(476\) −6.16749 6.16749i −0.282686 0.282686i
\(477\) 3.69068 3.69068i 0.168985 0.168985i
\(478\) −9.78834 + 9.78834i −0.447708 + 0.447708i
\(479\) −3.55522 + 3.55522i −0.162442 + 0.162442i −0.783648 0.621206i \(-0.786643\pi\)
0.621206 + 0.783648i \(0.286643\pi\)
\(480\) −1.82903 + 1.28634i −0.0834833 + 0.0587130i
\(481\) 25.2567 13.6524i 1.15161 0.622495i
\(482\) 4.18100 4.18100i 0.190439 0.190439i
\(483\) 1.05052 0.0478005
\(484\) 3.59242i 0.163292i
\(485\) −2.44288 + 14.0236i −0.110925 + 0.636777i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) 6.62780i 0.300334i −0.988661 0.150167i \(-0.952019\pi\)
0.988661 0.150167i \(-0.0479812\pi\)
\(488\) 2.43047i 0.110022i
\(489\) 9.92129 9.92129i 0.448656 0.448656i
\(490\) −1.78938 + 10.2721i −0.0808357 + 0.464045i
\(491\) 15.5268i 0.700713i 0.936616 + 0.350357i \(0.113940\pi\)
−0.936616 + 0.350357i \(0.886060\pi\)
\(492\) −11.6330 −0.524457
\(493\) 9.21573 9.21573i 0.415056 0.415056i
\(494\) −1.55497 + 5.21378i −0.0699613 + 0.234579i
\(495\) 6.98689 4.91381i 0.314037 0.220859i
\(496\) 1.00000 1.00000i 0.0449013 0.0449013i
\(497\) 16.3695 16.3695i 0.734274 0.734274i
\(498\) 5.45901 5.45901i 0.244624 0.244624i
\(499\) 3.06206 + 3.06206i 0.137077 + 0.137077i 0.772316 0.635239i \(-0.219098\pi\)
−0.635239 + 0.772316i \(0.719098\pi\)
\(500\) 9.71691 + 5.53007i 0.434553 + 0.247312i
\(501\) −10.1977 10.1977i −0.455600 0.455600i
\(502\) 16.6015 0.740963
\(503\) −21.0989 21.0989i −0.940753 0.940753i 0.0575878 0.998340i \(-0.481659\pi\)
−0.998340 + 0.0575878i \(0.981659\pi\)
\(504\) 1.52873 0.0680950
\(505\) 4.05489 23.2775i 0.180440 1.03583i
\(506\) 2.62506i 0.116698i
\(507\) −12.7259 + 2.65543i −0.565177 + 0.117932i
\(508\) 10.2359 + 10.2359i 0.454145 + 0.454145i
\(509\) 23.9745 + 23.9745i 1.06265 + 1.06265i 0.997901 + 0.0647506i \(0.0206252\pi\)
0.0647506 + 0.997901i \(0.479375\pi\)
\(510\) −12.5686 2.18942i −0.556546 0.0969493i
\(511\) 15.7653i 0.697418i
\(512\) 1.00000i 0.0441942i
\(513\) 1.50898 0.0666233
\(514\) 11.6326 11.6326i 0.513094 0.513094i
\(515\) 12.5903 8.85462i 0.554794 0.390181i
\(516\) 8.14884 0.358732
\(517\) 7.89663 + 7.89663i 0.347293 + 0.347293i
\(518\) 12.1730i 0.534852i
\(519\) −16.9922 −0.745875
\(520\) 2.55973 + 7.64511i 0.112252 + 0.335260i
\(521\) −17.4440 −0.764238 −0.382119 0.924113i \(-0.624806\pi\)
−0.382119 + 0.924113i \(0.624806\pi\)
\(522\) 2.28429i 0.0999808i
\(523\) 20.2159 + 20.2159i 0.883980 + 0.883980i 0.993936 0.109957i \(-0.0350712\pi\)
−0.109957 + 0.993936i \(0.535071\pi\)
\(524\) 11.8485 0.517606
\(525\) −3.25893 6.91409i −0.142231 0.301756i
\(526\) −1.07114 + 1.07114i −0.0467038 + 0.0467038i
\(527\) 8.06878 0.351481
\(528\) 3.82000i 0.166244i
\(529\) 22.5278i 0.979468i
\(530\) −9.54643 + 6.71391i −0.414671 + 0.291634i
\(531\) −4.50044 4.50044i −0.195303 0.195303i
\(532\) −1.63117 1.63117i −0.0707203 0.0707203i
\(533\) −11.9875 + 40.1940i −0.519237 + 1.74099i
\(534\) 10.2060i 0.441659i
\(535\) −33.8636 + 23.8160i −1.46405 + 1.02965i
\(536\) −3.79906 −0.164094
\(537\) 7.25534 + 7.25534i 0.313091 + 0.313091i
\(538\) 16.8729 0.727443
\(539\) −12.5954 12.5954i −0.542524 0.542524i
\(540\) 1.82903 1.28634i 0.0787088 0.0553551i
\(541\) −0.554543 0.554543i −0.0238417 0.0238417i 0.695085 0.718927i \(-0.255367\pi\)
−0.718927 + 0.695085i \(0.755367\pi\)
\(542\) −4.55193 + 4.55193i −0.195522 + 0.195522i
\(543\) 15.8770 15.8770i 0.681346 0.681346i
\(544\) −4.03439 + 4.03439i −0.172973 + 0.172973i
\(545\) 0.225703 + 0.320925i 0.00966807 + 0.0137469i
\(546\) 1.57531 5.28200i 0.0674172 0.226049i
\(547\) −9.17919 + 9.17919i −0.392474 + 0.392474i −0.875568 0.483095i \(-0.839513\pi\)
0.483095 + 0.875568i \(0.339513\pi\)
\(548\) 11.9361 0.509886
\(549\) 2.43047i 0.103730i
\(550\) −17.2770 + 8.14345i −0.736694 + 0.347238i
\(551\) 2.43737 2.43737i 0.103835 0.103835i
\(552\) 0.687188i 0.0292487i
\(553\) 2.35013i 0.0999375i
\(554\) −3.22540 + 3.22540i −0.137034 + 0.137034i
\(555\) 10.2429 + 14.5642i 0.434787 + 0.618218i
\(556\) 20.0448i 0.850089i
\(557\) 37.1733 1.57508 0.787541 0.616262i \(-0.211354\pi\)
0.787541 + 0.616262i \(0.211354\pi\)
\(558\) −1.00000 + 1.00000i −0.0423334 + 0.0423334i
\(559\) 8.39716 28.1555i 0.355162 1.19085i
\(560\) −3.36763 0.586634i −0.142308 0.0247898i
\(561\) 15.4114 15.4114i 0.650669 0.650669i
\(562\) −4.05048 + 4.05048i −0.170859 + 0.170859i
\(563\) 19.8005 19.8005i 0.834493 0.834493i −0.153635 0.988128i \(-0.549098\pi\)
0.988128 + 0.153635i \(0.0490979\pi\)
\(564\) 2.06718 + 2.06718i 0.0870439 + 0.0870439i
\(565\) 6.72495 + 9.56212i 0.282921 + 0.402282i
\(566\) 14.1280 + 14.1280i 0.593846 + 0.593846i
\(567\) −1.52873 −0.0642006
\(568\) −10.7079 10.7079i −0.449295 0.449295i
\(569\) −22.5105 −0.943689 −0.471844 0.881682i \(-0.656412\pi\)
−0.471844 + 0.881682i \(0.656412\pi\)
\(570\) −3.32413 0.579058i −0.139233 0.0242541i
\(571\) 17.9308i 0.750379i −0.926948 0.375190i \(-0.877578\pi\)
0.926948 0.375190i \(-0.122422\pi\)
\(572\) −13.1987 3.93641i −0.551866 0.164590i
\(573\) 8.64105 + 8.64105i 0.360985 + 0.360985i
\(574\) −12.5750 12.5750i −0.524870 0.524870i
\(575\) −3.10799 + 1.46494i −0.129612 + 0.0610923i
\(576\) 1.00000i 0.0416667i
\(577\) 12.5758i 0.523535i −0.965131 0.261768i \(-0.915695\pi\)
0.965131 0.261768i \(-0.0843054\pi\)
\(578\) −15.5526 −0.646902
\(579\) 17.0715 17.0715i 0.709467 0.709467i
\(580\) 0.876575 5.03206i 0.0363978 0.208945i
\(581\) 11.8021 0.489633
\(582\) −4.50142 4.50142i −0.186590 0.186590i
\(583\) 19.9381i 0.825754i
\(584\) 10.3127 0.426743
\(585\) −2.55973 7.64511i −0.105832 0.316087i
\(586\) 29.4674 1.21729
\(587\) 9.73305i 0.401726i 0.979619 + 0.200863i \(0.0643746\pi\)
−0.979619 + 0.200863i \(0.935625\pi\)
\(588\) −3.29723 3.29723i −0.135976 0.135976i
\(589\) 2.13403 0.0879310
\(590\) 8.18700 + 11.6410i 0.337053 + 0.479252i
\(591\) −2.49840 + 2.49840i −0.102770 + 0.102770i
\(592\) 7.96284 0.327271
\(593\) 29.3940i 1.20707i 0.797337 + 0.603534i \(0.206241\pi\)
−0.797337 + 0.603534i \(0.793759\pi\)
\(594\) 3.82000i 0.156737i
\(595\) −11.2196 15.9530i −0.459959 0.654010i
\(596\) −3.91078 3.91078i −0.160192 0.160192i
\(597\) 8.61123 + 8.61123i 0.352434 + 0.352434i
\(598\) −2.37434 0.708129i −0.0970941 0.0289575i
\(599\) 7.65108i 0.312615i −0.987708 0.156307i \(-0.950041\pi\)
0.987708 0.156307i \(-0.0499590\pi\)
\(600\) −4.52277 + 2.13179i −0.184641 + 0.0870301i
\(601\) −8.65440 −0.353020 −0.176510 0.984299i \(-0.556481\pi\)
−0.176510 + 0.984299i \(0.556481\pi\)
\(602\) 8.80868 + 8.80868i 0.359015 + 0.359015i
\(603\) 3.79906 0.154710
\(604\) −16.6941 16.6941i −0.679272 0.679272i
\(605\) 1.37855 7.91372i 0.0560462 0.321738i
\(606\) 7.47184 + 7.47184i 0.303523 + 0.303523i
\(607\) 19.6391 19.6391i 0.797125 0.797125i −0.185516 0.982641i \(-0.559396\pi\)
0.982641 + 0.185516i \(0.0593958\pi\)
\(608\) −1.06701 + 1.06701i −0.0432731 + 0.0432731i
\(609\) −2.46926 + 2.46926i −0.100060 + 0.100060i
\(610\) −0.932668 + 5.35407i −0.0377626 + 0.216780i
\(611\) 9.27260 5.01226i 0.375129 0.202774i
\(612\) 4.03439 4.03439i 0.163080 0.163080i
\(613\) 5.05853 0.204312 0.102156 0.994768i \(-0.467426\pi\)
0.102156 + 0.994768i \(0.467426\pi\)
\(614\) 20.8097i 0.839810i
\(615\) −25.6263 4.46406i −1.03335 0.180008i
\(616\) 4.12932 4.12932i 0.166375 0.166375i
\(617\) 3.30694i 0.133132i 0.997782 + 0.0665662i \(0.0212044\pi\)
−0.997782 + 0.0665662i \(0.978796\pi\)
\(618\) 6.88359i 0.276899i
\(619\) −2.89470 + 2.89470i −0.116348 + 0.116348i −0.762884 0.646536i \(-0.776217\pi\)
0.646536 + 0.762884i \(0.276217\pi\)
\(620\) 2.58663 1.81915i 0.103882 0.0730590i
\(621\) 0.687188i 0.0275759i
\(622\) 31.1763 1.25006
\(623\) −11.0325 + 11.0325i −0.442007 + 0.442007i
\(624\) −3.45516 1.03047i −0.138317 0.0412520i
\(625\) 19.2832 + 15.9109i 0.771329 + 0.636437i
\(626\) −10.7473 + 10.7473i −0.429549 + 0.429549i
\(627\) 4.07599 4.07599i 0.162779 0.162779i
\(628\) 9.39497 9.39497i 0.374900 0.374900i
\(629\) 32.1252 + 32.1252i 1.28092 + 1.28092i
\(630\) 3.36763 + 0.586634i 0.134170 + 0.0233721i
\(631\) 6.05694 + 6.05694i 0.241123 + 0.241123i 0.817315 0.576192i \(-0.195462\pi\)
−0.576192 + 0.817315i \(0.695462\pi\)
\(632\) 1.53731 0.0611508
\(633\) 10.0883 + 10.0883i 0.400973 + 0.400973i
\(634\) 19.2205 0.763342
\(635\) 18.6207 + 26.4766i 0.738940 + 1.05069i
\(636\) 5.21941i 0.206963i
\(637\) −14.7902 + 7.99475i −0.586008 + 0.316763i
\(638\) 6.17022 + 6.17022i 0.244281 + 0.244281i
\(639\) 10.7079 + 10.7079i 0.423599 + 0.423599i
\(640\) −0.383740 + 2.20289i −0.0151687 + 0.0870770i
\(641\) 6.88364i 0.271887i 0.990717 + 0.135944i \(0.0434066\pi\)
−0.990717 + 0.135944i \(0.956593\pi\)
\(642\) 18.5146i 0.730712i
\(643\) −44.0145 −1.73576 −0.867882 0.496771i \(-0.834519\pi\)
−0.867882 + 0.496771i \(0.834519\pi\)
\(644\) 0.742832 0.742832i 0.0292717 0.0292717i
\(645\) 17.9510 + 3.12703i 0.706821 + 0.123127i
\(646\) −8.60949 −0.338736
\(647\) 6.25687 + 6.25687i 0.245983 + 0.245983i 0.819320 0.573337i \(-0.194351\pi\)
−0.573337 + 0.819320i \(0.694351\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −24.3127 −0.954358
\(650\) 2.70509 + 17.8237i 0.106102 + 0.699101i
\(651\) −2.16195 −0.0847335
\(652\) 14.0308i 0.549489i
\(653\) −29.1179 29.1179i −1.13947 1.13947i −0.988545 0.150926i \(-0.951774\pi\)
−0.150926 0.988545i \(-0.548226\pi\)
\(654\) −0.175462 −0.00686111
\(655\) 26.1011 + 4.54676i 1.01985 + 0.177657i
\(656\) −8.22579 + 8.22579i −0.321163 + 0.321163i
\(657\) −10.3127 −0.402337
\(658\) 4.46913i 0.174225i
\(659\) 41.2913i 1.60848i 0.594304 + 0.804241i \(0.297428\pi\)
−0.594304 + 0.804241i \(0.702572\pi\)
\(660\) 1.46589 8.41506i 0.0570596 0.327556i
\(661\) −27.4575 27.4575i −1.06797 1.06797i −0.997515 0.0704594i \(-0.977553\pi\)
−0.0704594 0.997515i \(-0.522447\pi\)
\(662\) 12.9738 + 12.9738i 0.504243 + 0.504243i
\(663\) −9.78212 18.0968i −0.379906 0.702821i
\(664\) 7.72020i 0.299602i
\(665\) −2.96736 4.21925i −0.115069 0.163615i
\(666\) −7.96284 −0.308554
\(667\) 1.10997 + 1.10997i 0.0429783 + 0.0429783i
\(668\) −14.4217 −0.557993
\(669\) 8.45923 + 8.45923i 0.327053 + 0.327053i
\(670\) −8.36892 1.45785i −0.323320 0.0563217i
\(671\) −6.56506 6.56506i −0.253441 0.253441i
\(672\) 1.08097 1.08097i 0.0416995 0.0416995i
\(673\) 27.6552 27.6552i 1.06603 1.06603i 0.0683689 0.997660i \(-0.478221\pi\)
0.997660 0.0683689i \(-0.0217795\pi\)
\(674\) 19.7453 19.7453i 0.760562 0.760562i
\(675\) 4.52277 2.13179i 0.174082 0.0820527i
\(676\) −7.12090 + 10.8762i −0.273881 + 0.418317i
\(677\) −16.1493 + 16.1493i −0.620669 + 0.620669i −0.945703 0.325033i \(-0.894624\pi\)
0.325033 + 0.945703i \(0.394624\pi\)
\(678\) −5.22798 −0.200780
\(679\) 9.73184i 0.373474i
\(680\) −10.4355 + 7.33918i −0.400183 + 0.281445i
\(681\) −15.7645 + 15.7645i −0.604096 + 0.604096i
\(682\) 5.40230i 0.206865i
\(683\) 45.8440i 1.75417i 0.480333 + 0.877086i \(0.340516\pi\)
−0.480333 + 0.877086i \(0.659484\pi\)
\(684\) 1.06701 1.06701i 0.0407983 0.0407983i
\(685\) 26.2940 + 4.58037i 1.00464 + 0.175007i
\(686\) 17.8295i 0.680735i
\(687\) −8.44318 −0.322128
\(688\) 5.76210 5.76210i 0.219678 0.219678i
\(689\) −18.0339 5.37846i −0.687036 0.204903i
\(690\) 0.263701 1.51380i 0.0100389 0.0576295i
\(691\) −17.8144 + 17.8144i −0.677692 + 0.677692i −0.959477 0.281786i \(-0.909073\pi\)
0.281786 + 0.959477i \(0.409073\pi\)
\(692\) −12.0153 + 12.0153i −0.456753 + 0.456753i
\(693\) −4.12932 + 4.12932i −0.156860 + 0.156860i
\(694\) −0.843939 0.843939i −0.0320355 0.0320355i
\(695\) −7.69200 + 44.1566i −0.291774 + 1.67496i
\(696\) 1.61524 + 1.61524i 0.0612255 + 0.0612255i
\(697\) −66.3721 −2.51402
\(698\) 17.0343 + 17.0343i 0.644760 + 0.644760i
\(699\) 18.8874 0.714388
\(700\) −7.19341 2.58459i −0.271885 0.0976882i
\(701\) 21.1219i 0.797763i −0.917003 0.398881i \(-0.869399\pi\)
0.917003 0.398881i \(-0.130601\pi\)
\(702\) 3.45516 + 1.03047i 0.130407 + 0.0388927i
\(703\) 8.49645 + 8.49645i 0.320450 + 0.320450i
\(704\) −2.70115 2.70115i −0.101803 0.101803i
\(705\) 3.76052 + 5.34704i 0.141629 + 0.201381i
\(706\) 6.51257i 0.245104i
\(707\) 16.1537i 0.607523i
\(708\) −6.36459 −0.239196
\(709\) 9.51410 9.51410i 0.357310 0.357310i −0.505511 0.862820i \(-0.668696\pi\)
0.862820 + 0.505511i \(0.168696\pi\)
\(710\) −19.4794 27.6975i −0.731048 1.03947i
\(711\) −1.53731 −0.0576535
\(712\) 7.21676 + 7.21676i 0.270460 + 0.270460i
\(713\) 0.971830i 0.0363953i
\(714\) 8.72214 0.326418
\(715\) −27.5648 13.7364i −1.03087 0.513711i
\(716\) 10.2606 0.383456
\(717\) 13.8428i 0.516969i
\(718\) 17.5895 + 17.5895i 0.656433 + 0.656433i
\(719\) −33.0993 −1.23440 −0.617198 0.786808i \(-0.711732\pi\)
−0.617198 + 0.786808i \(0.711732\pi\)
\(720\) 0.383740 2.20289i 0.0143011 0.0820970i
\(721\) −7.44099 + 7.44099i −0.277117 + 0.277117i
\(722\) 16.7230 0.622364
\(723\) 5.91283i 0.219901i
\(724\) 22.4534i 0.834475i
\(725\) 3.86200 10.7487i 0.143431 0.399197i
\(726\) 2.54022 + 2.54022i 0.0942765 + 0.0942765i
\(727\) 3.32729 + 3.32729i 0.123402 + 0.123402i 0.766111 0.642708i \(-0.222189\pi\)
−0.642708 + 0.766111i \(0.722189\pi\)
\(728\) −2.62102 4.84885i −0.0971416 0.179710i
\(729\) 1.00000i 0.0370370i
\(730\) 22.7178 + 3.95740i 0.840824 + 0.146470i
\(731\) 46.4931 1.71961
\(732\) −1.71860 1.71860i −0.0635213 0.0635213i
\(733\) −33.4623 −1.23596 −0.617980 0.786194i \(-0.712049\pi\)
−0.617980 + 0.786194i \(0.712049\pi\)
\(734\) −10.9276 10.9276i −0.403346 0.403346i
\(735\) −5.99817 8.52873i −0.221246 0.314587i
\(736\) −0.485915 0.485915i −0.0179111 0.0179111i
\(737\) 10.2618 10.2618i 0.377999 0.377999i
\(738\) 8.22579 8.22579i 0.302796 0.302796i
\(739\) −34.2147 + 34.2147i −1.25861 + 1.25861i −0.306850 + 0.951758i \(0.599275\pi\)
−0.951758 + 0.306850i \(0.900725\pi\)
\(740\) 17.5413 + 3.05566i 0.644831 + 0.112328i
\(741\) −2.58717 4.78623i −0.0950421 0.175826i
\(742\) 5.64204 5.64204i 0.207126 0.207126i
\(743\) −39.0384 −1.43218 −0.716091 0.698007i \(-0.754070\pi\)
−0.716091 + 0.698007i \(0.754070\pi\)
\(744\) 1.41421i 0.0518476i
\(745\) −7.11431 10.1158i −0.260648 0.370613i
\(746\) −6.56604 + 6.56604i −0.240400 + 0.240400i
\(747\) 7.72020i 0.282467i
\(748\) 21.7950i 0.796903i
\(749\) 20.0138 20.0138i 0.731287 0.731287i
\(750\) −10.7812 + 2.96054i −0.393675 + 0.108104i
\(751\) 4.17727i 0.152431i 0.997091 + 0.0762154i \(0.0242837\pi\)
−0.997091 + 0.0762154i \(0.975716\pi\)
\(752\) 2.92343 0.106607
\(753\) −11.7391 + 11.7391i −0.427795 + 0.427795i
\(754\) 7.24537 3.91645i 0.263861 0.142629i
\(755\) −30.3691 43.1815i −1.10524 1.57153i
\(756\) −1.08097 + 1.08097i −0.0393147 + 0.0393147i
\(757\) 12.0444 12.0444i 0.437763 0.437763i −0.453496 0.891258i \(-0.649823\pi\)
0.891258 + 0.453496i \(0.149823\pi\)
\(758\) 23.1557 23.1557i 0.841053 0.841053i
\(759\) 1.85620 + 1.85620i 0.0673757 + 0.0673757i
\(760\) −2.75997 + 1.94106i −0.100115 + 0.0704097i
\(761\) 15.0242 + 15.0242i 0.544628 + 0.544628i 0.924882 0.380254i \(-0.124163\pi\)
−0.380254 + 0.924882i \(0.624163\pi\)
\(762\) −14.4758 −0.524402
\(763\) −0.189670 0.189670i −0.00686652 0.00686652i
\(764\) 12.2203 0.442115
\(765\) 10.4355 7.33918i 0.377296 0.265348i
\(766\) 1.38206i 0.0499358i
\(767\) −6.55854 + 21.9907i −0.236815 + 0.794037i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) 17.0100 + 17.0100i 0.613397 + 0.613397i 0.943830 0.330432i \(-0.107195\pi\)
−0.330432 + 0.943830i \(0.607195\pi\)
\(770\) 10.6811 7.51188i 0.384918 0.270709i
\(771\) 16.4510i 0.592470i
\(772\) 24.1428i 0.868917i
\(773\) −20.2751 −0.729246 −0.364623 0.931155i \(-0.618802\pi\)
−0.364623 + 0.931155i \(0.618802\pi\)
\(774\) −5.76210 + 5.76210i −0.207114 + 0.207114i
\(775\) 6.39616 3