Properties

Label 390.2.t.b.307.1
Level $390$
Weight $2$
Character 390.307
Analytic conductor $3.114$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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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: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 32x^{14} + 396x^{12} + 2412x^{10} + 7716x^{8} + 12984x^{6} + 10756x^{4} + 3648x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 307.1
Root \(-1.09662i\) of defining polynomial
Character \(\chi\) \(=\) 390.307
Dual form 390.2.t.b.343.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.09731 - 0.775429i) q^{5} +(-0.707107 - 0.707107i) q^{6} -0.946681 q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.09731 - 0.775429i) q^{5} +(-0.707107 - 0.707107i) q^{6} -0.946681 q^{7} -1.00000i q^{8} -1.00000i q^{9} +(0.775429 - 2.09731i) q^{10} +(3.13105 - 3.13105i) q^{11} +(0.707107 - 0.707107i) q^{12} +(-3.59681 - 0.250975i) q^{13} -0.946681i q^{14} +(2.03133 - 0.934711i) q^{15} +1.00000 q^{16} +(3.42154 - 3.42154i) q^{17} +1.00000 q^{18} +(1.00303 - 1.00303i) q^{19} +(2.09731 + 0.775429i) q^{20} +(0.669405 - 0.669405i) q^{21} +(3.13105 + 3.13105i) q^{22} +(-4.25224 - 4.25224i) q^{23} +(0.707107 + 0.707107i) q^{24} +(3.79742 + 3.25263i) q^{25} +(0.250975 - 3.59681i) q^{26} +(0.707107 + 0.707107i) q^{27} +0.946681 q^{28} -5.39250i q^{29} +(0.934711 + 2.03133i) q^{30} +(-2.43972 - 2.43972i) q^{31} +1.00000i q^{32} +4.42797i q^{33} +(3.42154 + 3.42154i) q^{34} +(1.98548 + 0.734084i) q^{35} +1.00000i q^{36} -11.9002 q^{37} +(1.00303 + 1.00303i) q^{38} +(2.72079 - 2.36586i) q^{39} +(-0.775429 + 2.09731i) q^{40} +(6.03479 + 6.03479i) q^{41} +(0.669405 + 0.669405i) q^{42} +(-0.242187 - 0.242187i) q^{43} +(-3.13105 + 3.13105i) q^{44} +(-0.775429 + 2.09731i) q^{45} +(4.25224 - 4.25224i) q^{46} +0.854435 q^{47} +(-0.707107 + 0.707107i) q^{48} -6.10380 q^{49} +(-3.25263 + 3.79742i) q^{50} +4.83878i q^{51} +(3.59681 + 0.250975i) q^{52} +(3.90244 - 3.90244i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-8.99469 + 4.13888i) q^{55} +0.946681i q^{56} +1.41850i q^{57} +5.39250 q^{58} +(-9.38267 - 9.38267i) q^{59} +(-2.03133 + 0.934711i) q^{60} +9.79944 q^{61} +(2.43972 - 2.43972i) q^{62} +0.946681i q^{63} -1.00000 q^{64} +(7.34900 + 3.31544i) q^{65} -4.42797 q^{66} -3.51092i q^{67} +(-3.42154 + 3.42154i) q^{68} +6.01358 q^{69} +(-0.734084 + 1.98548i) q^{70} +(-6.99770 - 6.99770i) q^{71} -1.00000 q^{72} +16.4476i q^{73} -11.9002i q^{74} +(-4.98514 + 0.385225i) q^{75} +(-1.00303 + 1.00303i) q^{76} +(-2.96410 + 2.96410i) q^{77} +(2.36586 + 2.72079i) q^{78} -8.09997i q^{79} +(-2.09731 - 0.775429i) q^{80} -1.00000 q^{81} +(-6.03479 + 6.03479i) q^{82} -15.2370 q^{83} +(-0.669405 + 0.669405i) q^{84} +(-9.82918 + 4.52287i) q^{85} +(0.242187 - 0.242187i) q^{86} +(3.81307 + 3.81307i) q^{87} +(-3.13105 - 3.13105i) q^{88} +(0.244613 + 0.244613i) q^{89} +(-2.09731 - 0.775429i) q^{90} +(3.40503 + 0.237593i) q^{91} +(4.25224 + 4.25224i) q^{92} +3.45028 q^{93} +0.854435i q^{94} +(-2.88145 + 1.32589i) q^{95} +(-0.707107 - 0.707107i) q^{96} -2.67283i q^{97} -6.10380i q^{98} +(-3.13105 - 3.13105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{4} + 4 q^{11} - 8 q^{13} - 4 q^{15} + 16 q^{16} - 4 q^{17} + 16 q^{18} - 4 q^{19} - 8 q^{21} + 4 q^{22} - 16 q^{23} + 16 q^{25} + 4 q^{26} - 4 q^{30} + 12 q^{31} - 4 q^{34} - 12 q^{35} - 32 q^{37} - 4 q^{38} + 4 q^{39} + 4 q^{41} - 8 q^{42} + 16 q^{43} - 4 q^{44} + 16 q^{46} + 16 q^{47} + 80 q^{49} + 8 q^{50} + 8 q^{52} - 44 q^{53} - 20 q^{55} - 12 q^{59} + 4 q^{60} - 32 q^{61} - 12 q^{62} - 16 q^{64} - 28 q^{65} + 4 q^{68} + 16 q^{69} - 36 q^{70} + 16 q^{71} - 16 q^{72} + 4 q^{76} + 32 q^{77} + 16 q^{78} - 16 q^{81} - 4 q^{82} + 16 q^{83} + 8 q^{84} - 40 q^{85} - 16 q^{86} + 28 q^{87} - 4 q^{88} - 4 q^{89} + 76 q^{91} + 16 q^{92} - 40 q^{95} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(5\) −2.09731 0.775429i −0.937946 0.346782i
\(6\) −0.707107 0.707107i −0.288675 0.288675i
\(7\) −0.946681 −0.357812 −0.178906 0.983866i \(-0.557256\pi\)
−0.178906 + 0.983866i \(0.557256\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) 0.775429 2.09731i 0.245212 0.663228i
\(11\) 3.13105 3.13105i 0.944047 0.944047i −0.0544686 0.998515i \(-0.517346\pi\)
0.998515 + 0.0544686i \(0.0173465\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) −3.59681 0.250975i −0.997574 0.0696079i
\(14\) 0.946681i 0.253011i
\(15\) 2.03133 0.934711i 0.524488 0.241341i
\(16\) 1.00000 0.250000
\(17\) 3.42154 3.42154i 0.829845 0.829845i −0.157650 0.987495i \(-0.550392\pi\)
0.987495 + 0.157650i \(0.0503919\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.00303 1.00303i 0.230112 0.230112i −0.582628 0.812739i \(-0.697975\pi\)
0.812739 + 0.582628i \(0.197975\pi\)
\(20\) 2.09731 + 0.775429i 0.468973 + 0.173391i
\(21\) 0.669405 0.669405i 0.146076 0.146076i
\(22\) 3.13105 + 3.13105i 0.667542 + 0.667542i
\(23\) −4.25224 4.25224i −0.886654 0.886654i 0.107546 0.994200i \(-0.465701\pi\)
−0.994200 + 0.107546i \(0.965701\pi\)
\(24\) 0.707107 + 0.707107i 0.144338 + 0.144338i
\(25\) 3.79742 + 3.25263i 0.759484 + 0.650526i
\(26\) 0.250975 3.59681i 0.0492202 0.705392i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 0.946681 0.178906
\(29\) 5.39250i 1.00136i −0.865632 0.500681i \(-0.833083\pi\)
0.865632 0.500681i \(-0.166917\pi\)
\(30\) 0.934711 + 2.03133i 0.170654 + 0.370869i
\(31\) −2.43972 2.43972i −0.438187 0.438187i 0.453215 0.891401i \(-0.350277\pi\)
−0.891401 + 0.453215i \(0.850277\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 4.42797i 0.770811i
\(34\) 3.42154 + 3.42154i 0.586789 + 0.586789i
\(35\) 1.98548 + 0.734084i 0.335608 + 0.124083i
\(36\) 1.00000i 0.166667i
\(37\) −11.9002 −1.95637 −0.978187 0.207725i \(-0.933394\pi\)
−0.978187 + 0.207725i \(0.933394\pi\)
\(38\) 1.00303 + 1.00303i 0.162713 + 0.162713i
\(39\) 2.72079 2.36586i 0.435675 0.378841i
\(40\) −0.775429 + 2.09731i −0.122606 + 0.331614i
\(41\) 6.03479 + 6.03479i 0.942477 + 0.942477i 0.998433 0.0559566i \(-0.0178208\pi\)
−0.0559566 + 0.998433i \(0.517821\pi\)
\(42\) 0.669405 + 0.669405i 0.103291 + 0.103291i
\(43\) −0.242187 0.242187i −0.0369332 0.0369332i 0.688399 0.725332i \(-0.258314\pi\)
−0.725332 + 0.688399i \(0.758314\pi\)
\(44\) −3.13105 + 3.13105i −0.472023 + 0.472023i
\(45\) −0.775429 + 2.09731i −0.115594 + 0.312649i
\(46\) 4.25224 4.25224i 0.626959 0.626959i
\(47\) 0.854435 0.124632 0.0623161 0.998056i \(-0.480151\pi\)
0.0623161 + 0.998056i \(0.480151\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) −6.10380 −0.871971
\(50\) −3.25263 + 3.79742i −0.459991 + 0.537036i
\(51\) 4.83878i 0.677565i
\(52\) 3.59681 + 0.250975i 0.498787 + 0.0348039i
\(53\) 3.90244 3.90244i 0.536041 0.536041i −0.386322 0.922364i \(-0.626255\pi\)
0.922364 + 0.386322i \(0.126255\pi\)
\(54\) −0.707107 + 0.707107i −0.0962250 + 0.0962250i
\(55\) −8.99469 + 4.13888i −1.21284 + 0.558086i
\(56\) 0.946681i 0.126506i
\(57\) 1.41850i 0.187885i
\(58\) 5.39250 0.708069
\(59\) −9.38267 9.38267i −1.22152 1.22152i −0.967092 0.254428i \(-0.918113\pi\)
−0.254428 0.967092i \(-0.581887\pi\)
\(60\) −2.03133 + 0.934711i −0.262244 + 0.120671i
\(61\) 9.79944 1.25469 0.627345 0.778741i \(-0.284142\pi\)
0.627345 + 0.778741i \(0.284142\pi\)
\(62\) 2.43972 2.43972i 0.309845 0.309845i
\(63\) 0.946681i 0.119271i
\(64\) −1.00000 −0.125000
\(65\) 7.34900 + 3.31544i 0.911532 + 0.411230i
\(66\) −4.42797 −0.545046
\(67\) 3.51092i 0.428927i −0.976732 0.214464i \(-0.931200\pi\)
0.976732 0.214464i \(-0.0688003\pi\)
\(68\) −3.42154 + 3.42154i −0.414922 + 0.414922i
\(69\) 6.01358 0.723950
\(70\) −0.734084 + 1.98548i −0.0877398 + 0.237311i
\(71\) −6.99770 6.99770i −0.830475 0.830475i 0.157107 0.987582i \(-0.449783\pi\)
−0.987582 + 0.157107i \(0.949783\pi\)
\(72\) −1.00000 −0.117851
\(73\) 16.4476i 1.92505i 0.271199 + 0.962523i \(0.412580\pi\)
−0.271199 + 0.962523i \(0.587420\pi\)
\(74\) 11.9002i 1.38337i
\(75\) −4.98514 + 0.385225i −0.575634 + 0.0444820i
\(76\) −1.00303 + 1.00303i −0.115056 + 0.115056i
\(77\) −2.96410 + 2.96410i −0.337791 + 0.337791i
\(78\) 2.36586 + 2.72079i 0.267881 + 0.308069i
\(79\) 8.09997i 0.911317i −0.890155 0.455659i \(-0.849404\pi\)
0.890155 0.455659i \(-0.150596\pi\)
\(80\) −2.09731 0.775429i −0.234486 0.0866956i
\(81\) −1.00000 −0.111111
\(82\) −6.03479 + 6.03479i −0.666432 + 0.666432i
\(83\) −15.2370 −1.67248 −0.836239 0.548365i \(-0.815251\pi\)
−0.836239 + 0.548365i \(0.815251\pi\)
\(84\) −0.669405 + 0.669405i −0.0730380 + 0.0730380i
\(85\) −9.82918 + 4.52287i −1.06612 + 0.490574i
\(86\) 0.242187 0.242187i 0.0261157 0.0261157i
\(87\) 3.81307 + 3.81307i 0.408804 + 0.408804i
\(88\) −3.13105 3.13105i −0.333771 0.333771i
\(89\) 0.244613 + 0.244613i 0.0259289 + 0.0259289i 0.719952 0.694023i \(-0.244164\pi\)
−0.694023 + 0.719952i \(0.744164\pi\)
\(90\) −2.09731 0.775429i −0.221076 0.0817374i
\(91\) 3.40503 + 0.237593i 0.356944 + 0.0249065i
\(92\) 4.25224 + 4.25224i 0.443327 + 0.443327i
\(93\) 3.45028 0.357778
\(94\) 0.854435i 0.0881282i
\(95\) −2.88145 + 1.32589i −0.295631 + 0.136034i
\(96\) −0.707107 0.707107i −0.0721688 0.0721688i
\(97\) 2.67283i 0.271384i −0.990751 0.135692i \(-0.956674\pi\)
0.990751 0.135692i \(-0.0433258\pi\)
\(98\) 6.10380i 0.616576i
\(99\) −3.13105 3.13105i −0.314682 0.314682i
\(100\) −3.79742 3.25263i −0.379742 0.325263i
\(101\) 7.16455i 0.712899i 0.934315 + 0.356450i \(0.116013\pi\)
−0.934315 + 0.356450i \(0.883987\pi\)
\(102\) −4.83878 −0.479111
\(103\) 8.00473 + 8.00473i 0.788729 + 0.788729i 0.981286 0.192557i \(-0.0616779\pi\)
−0.192557 + 0.981286i \(0.561678\pi\)
\(104\) −0.250975 + 3.59681i −0.0246101 + 0.352696i
\(105\) −1.92302 + 0.884873i −0.187668 + 0.0863548i
\(106\) 3.90244 + 3.90244i 0.379039 + 0.379039i
\(107\) 5.33595 + 5.33595i 0.515845 + 0.515845i 0.916312 0.400466i \(-0.131152\pi\)
−0.400466 + 0.916312i \(0.631152\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) 3.93054 3.93054i 0.376478 0.376478i −0.493352 0.869830i \(-0.664229\pi\)
0.869830 + 0.493352i \(0.164229\pi\)
\(110\) −4.13888 8.99469i −0.394626 0.857610i
\(111\) 8.41469 8.41469i 0.798687 0.798687i
\(112\) −0.946681 −0.0894529
\(113\) 3.32488 3.32488i 0.312778 0.312778i −0.533207 0.845985i \(-0.679013\pi\)
0.845985 + 0.533207i \(0.179013\pi\)
\(114\) −1.41850 −0.132855
\(115\) 5.62096 + 12.2156i 0.524157 + 1.13911i
\(116\) 5.39250i 0.500681i
\(117\) −0.250975 + 3.59681i −0.0232026 + 0.332525i
\(118\) 9.38267 9.38267i 0.863745 0.863745i
\(119\) −3.23910 + 3.23910i −0.296928 + 0.296928i
\(120\) −0.934711 2.03133i −0.0853271 0.185435i
\(121\) 8.60694i 0.782449i
\(122\) 9.79944i 0.887200i
\(123\) −8.53449 −0.769529
\(124\) 2.43972 + 2.43972i 0.219093 + 0.219093i
\(125\) −5.44219 9.76640i −0.486764 0.873534i
\(126\) −0.946681 −0.0843370
\(127\) −3.09330 + 3.09330i −0.274486 + 0.274486i −0.830903 0.556417i \(-0.812176\pi\)
0.556417 + 0.830903i \(0.312176\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0.342504 0.0301558
\(130\) −3.31544 + 7.34900i −0.290783 + 0.644550i
\(131\) −2.99792 −0.261930 −0.130965 0.991387i \(-0.541808\pi\)
−0.130965 + 0.991387i \(0.541808\pi\)
\(132\) 4.42797i 0.385406i
\(133\) −0.949553 + 0.949553i −0.0823367 + 0.0823367i
\(134\) 3.51092 0.303297
\(135\) −0.934711 2.03133i −0.0804471 0.174829i
\(136\) −3.42154 3.42154i −0.293394 0.293394i
\(137\) 17.3517 1.48245 0.741227 0.671255i \(-0.234244\pi\)
0.741227 + 0.671255i \(0.234244\pi\)
\(138\) 6.01358i 0.511910i
\(139\) 2.49588i 0.211698i 0.994382 + 0.105849i \(0.0337560\pi\)
−0.994382 + 0.105849i \(0.966244\pi\)
\(140\) −1.98548 0.734084i −0.167804 0.0620414i
\(141\) −0.604177 + 0.604177i −0.0508808 + 0.0508808i
\(142\) 6.99770 6.99770i 0.587234 0.587234i
\(143\) −12.0476 + 10.4760i −1.00747 + 0.876044i
\(144\) 1.00000i 0.0833333i
\(145\) −4.18150 + 11.3097i −0.347254 + 0.939223i
\(146\) −16.4476 −1.36121
\(147\) 4.31603 4.31603i 0.355981 0.355981i
\(148\) 11.9002 0.978187
\(149\) −1.72580 + 1.72580i −0.141383 + 0.141383i −0.774256 0.632873i \(-0.781876\pi\)
0.632873 + 0.774256i \(0.281876\pi\)
\(150\) −0.385225 4.98514i −0.0314535 0.407035i
\(151\) 1.86471 1.86471i 0.151748 0.151748i −0.627150 0.778898i \(-0.715779\pi\)
0.778898 + 0.627150i \(0.215779\pi\)
\(152\) −1.00303 1.00303i −0.0813567 0.0813567i
\(153\) −3.42154 3.42154i −0.276615 0.276615i
\(154\) −2.96410 2.96410i −0.238854 0.238854i
\(155\) 3.22502 + 7.00868i 0.259040 + 0.562951i
\(156\) −2.72079 + 2.36586i −0.217838 + 0.189420i
\(157\) 2.33729 + 2.33729i 0.186536 + 0.186536i 0.794197 0.607661i \(-0.207892\pi\)
−0.607661 + 0.794197i \(0.707892\pi\)
\(158\) 8.09997 0.644399
\(159\) 5.51888i 0.437676i
\(160\) 0.775429 2.09731i 0.0613030 0.165807i
\(161\) 4.02552 + 4.02552i 0.317255 + 0.317255i
\(162\) 1.00000i 0.0785674i
\(163\) 23.5470i 1.84434i −0.386779 0.922172i \(-0.626412\pi\)
0.386779 0.922172i \(-0.373588\pi\)
\(164\) −6.03479 6.03479i −0.471238 0.471238i
\(165\) 3.43358 9.28683i 0.267304 0.722979i
\(166\) 15.2370i 1.18262i
\(167\) 9.77190 0.756172 0.378086 0.925770i \(-0.376582\pi\)
0.378086 + 0.925770i \(0.376582\pi\)
\(168\) −0.669405 0.669405i −0.0516457 0.0516457i
\(169\) 12.8740 + 1.80542i 0.990309 + 0.138878i
\(170\) −4.52287 9.82918i −0.346888 0.753864i
\(171\) −1.00303 1.00303i −0.0767039 0.0767039i
\(172\) 0.242187 + 0.242187i 0.0184666 + 0.0184666i
\(173\) 5.96615 + 5.96615i 0.453598 + 0.453598i 0.896547 0.442949i \(-0.146068\pi\)
−0.442949 + 0.896547i \(0.646068\pi\)
\(174\) −3.81307 + 3.81307i −0.289068 + 0.289068i
\(175\) −3.59495 3.07920i −0.271752 0.232766i
\(176\) 3.13105 3.13105i 0.236012 0.236012i
\(177\) 13.2691 0.997367
\(178\) −0.244613 + 0.244613i −0.0183345 + 0.0183345i
\(179\) 7.96800 0.595557 0.297778 0.954635i \(-0.403754\pi\)
0.297778 + 0.954635i \(0.403754\pi\)
\(180\) 0.775429 2.09731i 0.0577970 0.156324i
\(181\) 17.3575i 1.29017i 0.764109 + 0.645087i \(0.223179\pi\)
−0.764109 + 0.645087i \(0.776821\pi\)
\(182\) −0.237593 + 3.40503i −0.0176116 + 0.252397i
\(183\) −6.92925 + 6.92925i −0.512225 + 0.512225i
\(184\) −4.25224 + 4.25224i −0.313479 + 0.313479i
\(185\) 24.9583 + 9.22773i 1.83497 + 0.678436i
\(186\) 3.45028i 0.252987i
\(187\) 21.4260i 1.56682i
\(188\) −0.854435 −0.0623161
\(189\) −0.669405 0.669405i −0.0486920 0.0486920i
\(190\) −1.32589 2.88145i −0.0961903 0.209043i
\(191\) 6.75356 0.488671 0.244335 0.969691i \(-0.421430\pi\)
0.244335 + 0.969691i \(0.421430\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) 7.55869i 0.544086i −0.962285 0.272043i \(-0.912301\pi\)
0.962285 0.272043i \(-0.0876994\pi\)
\(194\) 2.67283 0.191898
\(195\) −7.54090 + 2.85216i −0.540015 + 0.204248i
\(196\) 6.10380 0.435985
\(197\) 17.8690i 1.27312i −0.771229 0.636558i \(-0.780358\pi\)
0.771229 0.636558i \(-0.219642\pi\)
\(198\) 3.13105 3.13105i 0.222514 0.222514i
\(199\) 6.41529 0.454768 0.227384 0.973805i \(-0.426983\pi\)
0.227384 + 0.973805i \(0.426983\pi\)
\(200\) 3.25263 3.79742i 0.229996 0.268518i
\(201\) 2.48260 + 2.48260i 0.175109 + 0.175109i
\(202\) −7.16455 −0.504096
\(203\) 5.10497i 0.358299i
\(204\) 4.83878i 0.338783i
\(205\) −7.97728 17.3364i −0.557158 1.21083i
\(206\) −8.00473 + 8.00473i −0.557716 + 0.557716i
\(207\) −4.25224 + 4.25224i −0.295551 + 0.295551i
\(208\) −3.59681 0.250975i −0.249394 0.0174020i
\(209\) 6.28109i 0.434472i
\(210\) −0.884873 1.92302i −0.0610621 0.132701i
\(211\) 8.36808 0.576082 0.288041 0.957618i \(-0.406996\pi\)
0.288041 + 0.957618i \(0.406996\pi\)
\(212\) −3.90244 + 3.90244i −0.268021 + 0.268021i
\(213\) 9.89625 0.678080
\(214\) −5.33595 + 5.33595i −0.364758 + 0.364758i
\(215\) 0.320143 + 0.695741i 0.0218336 + 0.0474491i
\(216\) 0.707107 0.707107i 0.0481125 0.0481125i
\(217\) 2.30964 + 2.30964i 0.156788 + 0.156788i
\(218\) 3.93054 + 3.93054i 0.266210 + 0.266210i
\(219\) −11.6302 11.6302i −0.785897 0.785897i
\(220\) 8.99469 4.13888i 0.606422 0.279043i
\(221\) −13.1653 + 11.4479i −0.885595 + 0.770068i
\(222\) 8.41469 + 8.41469i 0.564757 + 0.564757i
\(223\) −6.31913 −0.423160 −0.211580 0.977361i \(-0.567861\pi\)
−0.211580 + 0.977361i \(0.567861\pi\)
\(224\) 0.946681i 0.0632528i
\(225\) 3.25263 3.79742i 0.216842 0.253161i
\(226\) 3.32488 + 3.32488i 0.221168 + 0.221168i
\(227\) 2.06238i 0.136885i 0.997655 + 0.0684423i \(0.0218029\pi\)
−0.997655 + 0.0684423i \(0.978197\pi\)
\(228\) 1.41850i 0.0939427i
\(229\) 1.31652 + 1.31652i 0.0869979 + 0.0869979i 0.749266 0.662269i \(-0.230406\pi\)
−0.662269 + 0.749266i \(0.730406\pi\)
\(230\) −12.2156 + 5.62096i −0.805472 + 0.370635i
\(231\) 4.19188i 0.275805i
\(232\) −5.39250 −0.354035
\(233\) 10.4414 + 10.4414i 0.684040 + 0.684040i 0.960908 0.276868i \(-0.0892966\pi\)
−0.276868 + 0.960908i \(0.589297\pi\)
\(234\) −3.59681 0.250975i −0.235131 0.0164067i
\(235\) −1.79201 0.662553i −0.116898 0.0432202i
\(236\) 9.38267 + 9.38267i 0.610760 + 0.610760i
\(237\) 5.72754 + 5.72754i 0.372044 + 0.372044i
\(238\) −3.23910 3.23910i −0.209960 0.209960i
\(239\) −16.6032 + 16.6032i −1.07397 + 1.07397i −0.0769369 + 0.997036i \(0.524514\pi\)
−0.997036 + 0.0769369i \(0.975486\pi\)
\(240\) 2.03133 0.934711i 0.131122 0.0603354i
\(241\) 12.3249 12.3249i 0.793917 0.793917i −0.188212 0.982128i \(-0.560269\pi\)
0.982128 + 0.188212i \(0.0602691\pi\)
\(242\) 8.60694 0.553275
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) −9.79944 −0.627345
\(245\) 12.8016 + 4.73306i 0.817861 + 0.302384i
\(246\) 8.53449i 0.544139i
\(247\) −3.85945 + 3.35598i −0.245571 + 0.213536i
\(248\) −2.43972 + 2.43972i −0.154922 + 0.154922i
\(249\) 10.7742 10.7742i 0.682786 0.682786i
\(250\) 9.76640 5.44219i 0.617682 0.344194i
\(251\) 20.9264i 1.32086i −0.750886 0.660431i \(-0.770373\pi\)
0.750886 0.660431i \(-0.229627\pi\)
\(252\) 0.946681i 0.0596353i
\(253\) −26.6280 −1.67409
\(254\) −3.09330 3.09330i −0.194091 0.194091i
\(255\) 3.75213 10.1484i 0.234968 0.635519i
\(256\) 1.00000 0.0625000
\(257\) 5.26288 5.26288i 0.328290 0.328290i −0.523646 0.851936i \(-0.675429\pi\)
0.851936 + 0.523646i \(0.175429\pi\)
\(258\) 0.342504i 0.0213234i
\(259\) 11.2657 0.700014
\(260\) −7.34900 3.31544i −0.455766 0.205615i
\(261\) −5.39250 −0.333787
\(262\) 2.99792i 0.185212i
\(263\) 12.1431 12.1431i 0.748773 0.748773i −0.225476 0.974249i \(-0.572394\pi\)
0.974249 + 0.225476i \(0.0723938\pi\)
\(264\) 4.42797 0.272523
\(265\) −11.2107 + 5.15856i −0.688667 + 0.316888i
\(266\) −0.949553 0.949553i −0.0582208 0.0582208i
\(267\) −0.345935 −0.0211709
\(268\) 3.51092i 0.214464i
\(269\) 11.3324i 0.690950i −0.938428 0.345475i \(-0.887718\pi\)
0.938428 0.345475i \(-0.112282\pi\)
\(270\) 2.03133 0.934711i 0.123623 0.0568847i
\(271\) 8.07401 8.07401i 0.490461 0.490461i −0.417990 0.908452i \(-0.637265\pi\)
0.908452 + 0.417990i \(0.137265\pi\)
\(272\) 3.42154 3.42154i 0.207461 0.207461i
\(273\) −2.57572 + 2.23971i −0.155890 + 0.135554i
\(274\) 17.3517i 1.04825i
\(275\) 22.0741 1.70577i 1.33112 0.102862i
\(276\) −6.01358 −0.361975
\(277\) −3.26424 + 3.26424i −0.196129 + 0.196129i −0.798338 0.602209i \(-0.794287\pi\)
0.602209 + 0.798338i \(0.294287\pi\)
\(278\) −2.49588 −0.149693
\(279\) −2.43972 + 2.43972i −0.146062 + 0.146062i
\(280\) 0.734084 1.98548i 0.0438699 0.118655i
\(281\) −22.2236 + 22.2236i −1.32575 + 1.32575i −0.416709 + 0.909040i \(0.636816\pi\)
−0.909040 + 0.416709i \(0.863184\pi\)
\(282\) −0.604177 0.604177i −0.0359782 0.0359782i
\(283\) −10.4468 10.4468i −0.620997 0.620997i 0.324789 0.945786i \(-0.394707\pi\)
−0.945786 + 0.324789i \(0.894707\pi\)
\(284\) 6.99770 + 6.99770i 0.415237 + 0.415237i
\(285\) 1.09995 2.97504i 0.0651553 0.176226i
\(286\) −10.4760 12.0476i −0.619457 0.712389i
\(287\) −5.71303 5.71303i −0.337229 0.337229i
\(288\) 1.00000 0.0589256
\(289\) 6.41383i 0.377284i
\(290\) −11.3097 4.18150i −0.664131 0.245546i
\(291\) 1.88997 + 1.88997i 0.110792 + 0.110792i
\(292\) 16.4476i 0.962523i
\(293\) 24.5333i 1.43325i 0.697458 + 0.716625i \(0.254314\pi\)
−0.697458 + 0.716625i \(0.745686\pi\)
\(294\) 4.31603 + 4.31603i 0.251716 + 0.251716i
\(295\) 12.4028 + 26.9540i 0.722118 + 1.56932i
\(296\) 11.9002i 0.691683i
\(297\) 4.42797 0.256937
\(298\) −1.72580 1.72580i −0.0999727 0.0999727i
\(299\) 14.2273 + 16.3617i 0.822785 + 0.946221i
\(300\) 4.98514 0.385225i 0.287817 0.0222410i
\(301\) 0.229274 + 0.229274i 0.0132151 + 0.0132151i
\(302\) 1.86471 + 1.86471i 0.107302 + 0.107302i
\(303\) −5.06610 5.06610i −0.291040 0.291040i
\(304\) 1.00303 1.00303i 0.0575279 0.0575279i
\(305\) −20.5525 7.59877i −1.17683 0.435104i
\(306\) 3.42154 3.42154i 0.195596 0.195596i
\(307\) −26.9486 −1.53804 −0.769019 0.639226i \(-0.779255\pi\)
−0.769019 + 0.639226i \(0.779255\pi\)
\(308\) 2.96410 2.96410i 0.168896 0.168896i
\(309\) −11.3204 −0.643995
\(310\) −7.00868 + 3.22502i −0.398066 + 0.183169i
\(311\) 16.4762i 0.934281i 0.884183 + 0.467140i \(0.154716\pi\)
−0.884183 + 0.467140i \(0.845284\pi\)
\(312\) −2.36586 2.72079i −0.133940 0.154035i
\(313\) 2.89698 2.89698i 0.163747 0.163747i −0.620477 0.784224i \(-0.713061\pi\)
0.784224 + 0.620477i \(0.213061\pi\)
\(314\) −2.33729 + 2.33729i −0.131901 + 0.131901i
\(315\) 0.734084 1.98548i 0.0413609 0.111869i
\(316\) 8.09997i 0.455659i
\(317\) 13.4323i 0.754434i −0.926125 0.377217i \(-0.876881\pi\)
0.926125 0.377217i \(-0.123119\pi\)
\(318\) −5.51888 −0.309484
\(319\) −16.8842 16.8842i −0.945332 0.945332i
\(320\) 2.09731 + 0.775429i 0.117243 + 0.0433478i
\(321\) −7.54617 −0.421186
\(322\) −4.02552 + 4.02552i −0.224333 + 0.224333i
\(323\) 6.86383i 0.381914i
\(324\) 1.00000 0.0555556
\(325\) −12.8423 12.6521i −0.712360 0.701814i
\(326\) 23.5470 1.30415
\(327\) 5.55863i 0.307393i
\(328\) 6.03479 6.03479i 0.333216 0.333216i
\(329\) −0.808877 −0.0445948
\(330\) 9.28683 + 3.43358i 0.511223 + 0.189012i
\(331\) 4.34332 + 4.34332i 0.238730 + 0.238730i 0.816324 0.577594i \(-0.196008\pi\)
−0.577594 + 0.816324i \(0.696008\pi\)
\(332\) 15.2370 0.836239
\(333\) 11.9002i 0.652125i
\(334\) 9.77190i 0.534695i
\(335\) −2.72247 + 7.36349i −0.148744 + 0.402310i
\(336\) 0.669405 0.669405i 0.0365190 0.0365190i
\(337\) −2.98172 + 2.98172i −0.162425 + 0.162425i −0.783640 0.621215i \(-0.786639\pi\)
0.621215 + 0.783640i \(0.286639\pi\)
\(338\) −1.80542 + 12.8740i −0.0982017 + 0.700255i
\(339\) 4.70209i 0.255382i
\(340\) 9.82918 4.52287i 0.533062 0.245287i
\(341\) −15.2778 −0.827337
\(342\) 1.00303 1.00303i 0.0542378 0.0542378i
\(343\) 12.4051 0.669813
\(344\) −0.242187 + 0.242187i −0.0130579 + 0.0130579i
\(345\) −12.6123 4.66310i −0.679026 0.251053i
\(346\) −5.96615 + 5.96615i −0.320742 + 0.320742i
\(347\) −25.3043 25.3043i −1.35841 1.35841i −0.875884 0.482521i \(-0.839721\pi\)
−0.482521 0.875884i \(-0.660279\pi\)
\(348\) −3.81307 3.81307i −0.204402 0.204402i
\(349\) 10.5348 + 10.5348i 0.563915 + 0.563915i 0.930417 0.366502i \(-0.119445\pi\)
−0.366502 + 0.930417i \(0.619445\pi\)
\(350\) 3.07920 3.59495i 0.164590 0.192158i
\(351\) −2.36586 2.72079i −0.126280 0.145225i
\(352\) 3.13105 + 3.13105i 0.166885 + 0.166885i
\(353\) −24.7214 −1.31579 −0.657893 0.753111i \(-0.728552\pi\)
−0.657893 + 0.753111i \(0.728552\pi\)
\(354\) 13.2691i 0.705245i
\(355\) 9.25014 + 20.1026i 0.490946 + 1.06693i
\(356\) −0.244613 0.244613i −0.0129645 0.0129645i
\(357\) 4.58078i 0.242441i
\(358\) 7.96800i 0.421122i
\(359\) 1.44201 + 1.44201i 0.0761066 + 0.0761066i 0.744135 0.668029i \(-0.232862\pi\)
−0.668029 + 0.744135i \(0.732862\pi\)
\(360\) 2.09731 + 0.775429i 0.110538 + 0.0408687i
\(361\) 16.9878i 0.894097i
\(362\) −17.3575 −0.912291
\(363\) 6.08602 + 6.08602i 0.319433 + 0.319433i
\(364\) −3.40503 0.237593i −0.178472 0.0124533i
\(365\) 12.7539 34.4957i 0.667572 1.80559i
\(366\) −6.92925 6.92925i −0.362198 0.362198i
\(367\) 0.992346 + 0.992346i 0.0518000 + 0.0518000i 0.732532 0.680732i \(-0.238338\pi\)
−0.680732 + 0.732532i \(0.738338\pi\)
\(368\) −4.25224 4.25224i −0.221663 0.221663i
\(369\) 6.03479 6.03479i 0.314159 0.314159i
\(370\) −9.22773 + 24.9583i −0.479727 + 1.29752i
\(371\) −3.69437 + 3.69437i −0.191802 + 0.191802i
\(372\) −3.45028 −0.178889
\(373\) 20.8743 20.8743i 1.08083 1.08083i 0.0843970 0.996432i \(-0.473104\pi\)
0.996432 0.0843970i \(-0.0268964\pi\)
\(374\) 21.4260 1.10791
\(375\) 10.7541 + 3.05768i 0.555339 + 0.157898i
\(376\) 0.854435i 0.0440641i
\(377\) −1.35338 + 19.3958i −0.0697027 + 0.998932i
\(378\) 0.669405 0.669405i 0.0344305 0.0344305i
\(379\) −17.6422 + 17.6422i −0.906221 + 0.906221i −0.995965 0.0897438i \(-0.971395\pi\)
0.0897438 + 0.995965i \(0.471395\pi\)
\(380\) 2.88145 1.32589i 0.147815 0.0680168i
\(381\) 4.37458i 0.224117i
\(382\) 6.75356i 0.345542i
\(383\) 29.6580 1.51545 0.757725 0.652574i \(-0.226311\pi\)
0.757725 + 0.652574i \(0.226311\pi\)
\(384\) 0.707107 + 0.707107i 0.0360844 + 0.0360844i
\(385\) 8.51510 3.91820i 0.433970 0.199690i
\(386\) 7.55869 0.384727
\(387\) −0.242187 + 0.242187i −0.0123111 + 0.0123111i
\(388\) 2.67283i 0.135692i
\(389\) −16.8263 −0.853127 −0.426564 0.904458i \(-0.640276\pi\)
−0.426564 + 0.904458i \(0.640276\pi\)
\(390\) −2.85216 7.54090i −0.144425 0.381848i
\(391\) −29.0984 −1.47157
\(392\) 6.10380i 0.308288i
\(393\) 2.11985 2.11985i 0.106932 0.106932i
\(394\) 17.8690 0.900229
\(395\) −6.28095 + 16.9881i −0.316029 + 0.854766i
\(396\) 3.13105 + 3.13105i 0.157341 + 0.157341i
\(397\) −28.3338 −1.42203 −0.711016 0.703176i \(-0.751765\pi\)
−0.711016 + 0.703176i \(0.751765\pi\)
\(398\) 6.41529i 0.321569i
\(399\) 1.34287i 0.0672276i
\(400\) 3.79742 + 3.25263i 0.189871 + 0.162631i
\(401\) −8.47925 + 8.47925i −0.423433 + 0.423433i −0.886384 0.462951i \(-0.846791\pi\)
0.462951 + 0.886384i \(0.346791\pi\)
\(402\) −2.48260 + 2.48260i −0.123821 + 0.123821i
\(403\) 8.16289 + 9.38751i 0.406622 + 0.467625i
\(404\) 7.16455i 0.356450i
\(405\) 2.09731 + 0.775429i 0.104216 + 0.0385314i
\(406\) −5.10497 −0.253356
\(407\) −37.2600 + 37.2600i −1.84691 + 1.84691i
\(408\) 4.83878 0.239555
\(409\) −24.9472 + 24.9472i −1.23356 + 1.23356i −0.270971 + 0.962588i \(0.587345\pi\)
−0.962588 + 0.270971i \(0.912655\pi\)
\(410\) 17.3364 7.97728i 0.856183 0.393970i
\(411\) −12.2695 + 12.2695i −0.605209 + 0.605209i
\(412\) −8.00473 8.00473i −0.394365 0.394365i
\(413\) 8.88240 + 8.88240i 0.437074 + 0.437074i
\(414\) −4.25224 4.25224i −0.208986 0.208986i
\(415\) 31.9567 + 11.8152i 1.56869 + 0.579986i
\(416\) 0.250975 3.59681i 0.0123051 0.176348i
\(417\) −1.76485 1.76485i −0.0864252 0.0864252i
\(418\) 6.28109 0.307218
\(419\) 12.4367i 0.607574i −0.952740 0.303787i \(-0.901749\pi\)
0.952740 0.303787i \(-0.0982511\pi\)
\(420\) 1.92302 0.884873i 0.0938340 0.0431774i
\(421\) −14.7295 14.7295i −0.717871 0.717871i 0.250298 0.968169i \(-0.419471\pi\)
−0.968169 + 0.250298i \(0.919471\pi\)
\(422\) 8.36808i 0.407352i
\(423\) 0.854435i 0.0415440i
\(424\) −3.90244 3.90244i −0.189519 0.189519i
\(425\) 24.1220 1.86402i 1.17009 0.0904184i
\(426\) 9.89625i 0.479475i
\(427\) −9.27695 −0.448943
\(428\) −5.33595 5.33595i −0.257923 0.257923i
\(429\) 1.11131 15.9266i 0.0536545 0.768941i
\(430\) −0.695741 + 0.320143i −0.0335516 + 0.0154387i
\(431\) −8.50842 8.50842i −0.409836 0.409836i 0.471845 0.881681i \(-0.343588\pi\)
−0.881681 + 0.471845i \(0.843588\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) −6.47843 6.47843i −0.311333 0.311333i 0.534093 0.845426i \(-0.320653\pi\)
−0.845426 + 0.534093i \(0.820653\pi\)
\(434\) −2.30964 + 2.30964i −0.110866 + 0.110866i
\(435\) −5.04043 10.9540i −0.241670 0.525202i
\(436\) −3.93054 + 3.93054i −0.188239 + 0.188239i
\(437\) −8.53028 −0.408059
\(438\) 11.6302 11.6302i 0.555713 0.555713i
\(439\) 40.8316 1.94879 0.974393 0.224854i \(-0.0721904\pi\)
0.974393 + 0.224854i \(0.0721904\pi\)
\(440\) 4.13888 + 8.99469i 0.197313 + 0.428805i
\(441\) 6.10380i 0.290657i
\(442\) −11.4479 13.1653i −0.544520 0.626211i
\(443\) −8.09147 + 8.09147i −0.384437 + 0.384437i −0.872698 0.488261i \(-0.837632\pi\)
0.488261 + 0.872698i \(0.337632\pi\)
\(444\) −8.41469 + 8.41469i −0.399343 + 0.399343i
\(445\) −0.323349 0.702709i −0.0153282 0.0333116i
\(446\) 6.31913i 0.299219i
\(447\) 2.44065i 0.115439i
\(448\) 0.946681 0.0447265
\(449\) 22.0410 + 22.0410i 1.04018 + 1.04018i 0.999158 + 0.0410213i \(0.0130611\pi\)
0.0410213 + 0.999158i \(0.486939\pi\)
\(450\) 3.79742 + 3.25263i 0.179012 + 0.153330i
\(451\) 37.7905 1.77948
\(452\) −3.32488 + 3.32488i −0.156389 + 0.156389i
\(453\) 2.63710i 0.123902i
\(454\) −2.06238 −0.0967921
\(455\) −6.95716 3.13866i −0.326157 0.147143i
\(456\) 1.41850 0.0664275
\(457\) 17.5342i 0.820213i −0.912038 0.410107i \(-0.865491\pi\)
0.912038 0.410107i \(-0.134509\pi\)
\(458\) −1.31652 + 1.31652i −0.0615168 + 0.0615168i
\(459\) 4.83878 0.225855
\(460\) −5.62096 12.2156i −0.262079 0.569554i
\(461\) −17.5242 17.5242i −0.816184 0.816184i 0.169368 0.985553i \(-0.445827\pi\)
−0.985553 + 0.169368i \(0.945827\pi\)
\(462\) 4.19188 0.195024
\(463\) 12.6976i 0.590106i 0.955481 + 0.295053i \(0.0953372\pi\)
−0.955481 + 0.295053i \(0.904663\pi\)
\(464\) 5.39250i 0.250340i
\(465\) −7.23632 2.67545i −0.335576 0.124071i
\(466\) −10.4414 + 10.4414i −0.483689 + 0.483689i
\(467\) −1.17459 + 1.17459i −0.0543535 + 0.0543535i −0.733761 0.679408i \(-0.762237\pi\)
0.679408 + 0.733761i \(0.262237\pi\)
\(468\) 0.250975 3.59681i 0.0116013 0.166262i
\(469\) 3.32372i 0.153475i
\(470\) 0.662553 1.79201i 0.0305613 0.0826595i
\(471\) −3.30542 −0.152306
\(472\) −9.38267 + 9.38267i −0.431872 + 0.431872i
\(473\) −1.51660 −0.0697334
\(474\) −5.72754 + 5.72754i −0.263075 + 0.263075i
\(475\) 7.07144 0.546443i 0.324460 0.0250725i
\(476\) 3.23910 3.23910i 0.148464 0.148464i
\(477\) −3.90244 3.90244i −0.178680 0.178680i
\(478\) −16.6032 16.6032i −0.759414 0.759414i
\(479\) 22.2742 + 22.2742i 1.01773 + 1.01773i 0.999840 + 0.0178921i \(0.00569553\pi\)
0.0178921 + 0.999840i \(0.494304\pi\)
\(480\) 0.934711 + 2.03133i 0.0426635 + 0.0927173i
\(481\) 42.8026 + 2.98664i 1.95163 + 0.136179i
\(482\) 12.3249 + 12.3249i 0.561384 + 0.561384i
\(483\) −5.69294 −0.259038
\(484\) 8.60694i 0.391224i
\(485\) −2.07259 + 5.60575i −0.0941113 + 0.254544i
\(486\) 0.707107 + 0.707107i 0.0320750 + 0.0320750i
\(487\) 33.0320i 1.49682i −0.663234 0.748412i \(-0.730817\pi\)
0.663234 0.748412i \(-0.269183\pi\)
\(488\) 9.79944i 0.443600i
\(489\) 16.6503 + 16.6503i 0.752951 + 0.752951i
\(490\) −4.73306 + 12.8016i −0.213818 + 0.578315i
\(491\) 36.4206i 1.64364i −0.569747 0.821820i \(-0.692959\pi\)
0.569747 0.821820i \(-0.307041\pi\)
\(492\) 8.53449 0.384764
\(493\) −18.4506 18.4506i −0.830974 0.830974i
\(494\) −3.35598 3.85945i −0.150993 0.173645i
\(495\) 4.13888 + 8.99469i 0.186029 + 0.404281i
\(496\) −2.43972 2.43972i −0.109547 0.109547i
\(497\) 6.62459 + 6.62459i 0.297154 + 0.297154i
\(498\) 10.7742 + 10.7742i 0.482803 + 0.482803i
\(499\) 26.4644 26.4644i 1.18471 1.18471i 0.206199 0.978510i \(-0.433891\pi\)
0.978510 0.206199i \(-0.0661094\pi\)
\(500\) 5.44219 + 9.76640i 0.243382 + 0.436767i
\(501\) −6.90978 + 6.90978i −0.308706 + 0.308706i
\(502\) 20.9264 0.933991
\(503\) 18.3270 18.3270i 0.817161 0.817161i −0.168535 0.985696i \(-0.553903\pi\)
0.985696 + 0.168535i \(0.0539035\pi\)
\(504\) 0.946681 0.0421685
\(505\) 5.55560 15.0263i 0.247221 0.668661i
\(506\) 26.6280i 1.18376i
\(507\) −10.3799 + 7.82669i −0.460989 + 0.347595i
\(508\) 3.09330 3.09330i 0.137243 0.137243i
\(509\) 4.50027 4.50027i 0.199471 0.199471i −0.600302 0.799773i \(-0.704953\pi\)
0.799773 + 0.600302i \(0.204953\pi\)
\(510\) 10.1484 + 3.75213i 0.449380 + 0.166147i
\(511\) 15.5706i 0.688804i
\(512\) 1.00000i 0.0441942i
\(513\) 1.41850 0.0626285
\(514\) 5.26288 + 5.26288i 0.232136 + 0.232136i
\(515\) −10.5813 22.9955i −0.466268 1.01330i
\(516\) −0.342504 −0.0150779
\(517\) 2.67528 2.67528i 0.117659 0.117659i
\(518\) 11.2657i 0.494985i
\(519\) −8.43741 −0.370361
\(520\) 3.31544 7.34900i 0.145392 0.322275i
\(521\) −2.48916 −0.109052 −0.0545260 0.998512i \(-0.517365\pi\)
−0.0545260 + 0.998512i \(0.517365\pi\)
\(522\) 5.39250i 0.236023i
\(523\) 8.64710 8.64710i 0.378111 0.378111i −0.492309 0.870420i \(-0.663847\pi\)
0.870420 + 0.492309i \(0.163847\pi\)
\(524\) 2.99792 0.130965
\(525\) 4.71934 0.364686i 0.205969 0.0159162i
\(526\) 12.1431 + 12.1431i 0.529462 + 0.529462i
\(527\) −16.6952 −0.727253
\(528\) 4.42797i 0.192703i
\(529\) 13.1631i 0.572310i
\(530\) −5.15856 11.2107i −0.224074 0.486961i
\(531\) −9.38267 + 9.38267i −0.407173 + 0.407173i
\(532\) 0.949553 0.949553i 0.0411683 0.0411683i
\(533\) −20.1914 23.2206i −0.874587 1.00579i
\(534\) 0.345935i 0.0149701i
\(535\) −7.05349 15.3288i −0.304949 0.662721i
\(536\) −3.51092 −0.151649
\(537\) −5.63423 + 5.63423i −0.243135 + 0.243135i
\(538\) 11.3324 0.488576
\(539\) −19.1113 + 19.1113i −0.823181 + 0.823181i
\(540\) 0.934711 + 2.03133i 0.0402236 + 0.0874147i
\(541\) −14.9033 + 14.9033i −0.640743 + 0.640743i −0.950738 0.309995i \(-0.899673\pi\)
0.309995 + 0.950738i \(0.399673\pi\)
\(542\) 8.07401 + 8.07401i 0.346809 + 0.346809i
\(543\) −12.2736 12.2736i −0.526712 0.526712i
\(544\) 3.42154 + 3.42154i 0.146697 + 0.146697i
\(545\) −11.2914 + 5.19571i −0.483672 + 0.222560i
\(546\) −2.23971 2.57572i −0.0958509 0.110231i
\(547\) 32.1953 + 32.1953i 1.37657 + 1.37657i 0.850341 + 0.526232i \(0.176396\pi\)
0.526232 + 0.850341i \(0.323604\pi\)
\(548\) −17.3517 −0.741227
\(549\) 9.79944i 0.418230i
\(550\) 1.70577 + 22.0741i 0.0727342 + 0.941241i
\(551\) −5.40885 5.40885i −0.230425 0.230425i
\(552\) 6.01358i 0.255955i
\(553\) 7.66808i 0.326080i
\(554\) −3.26424 3.26424i −0.138684 0.138684i
\(555\) −24.1732 + 11.1232i −1.02609 + 0.472154i
\(556\) 2.49588i 0.105849i
\(557\) 38.6878 1.63925 0.819627 0.572897i \(-0.194180\pi\)
0.819627 + 0.572897i \(0.194180\pi\)
\(558\) −2.43972 2.43972i −0.103282 0.103282i
\(559\) 0.810318 + 0.931883i 0.0342728 + 0.0394145i
\(560\) 1.98548 + 0.734084i 0.0839020 + 0.0310207i
\(561\) 15.1505 + 15.1505i 0.639653 + 0.639653i
\(562\) −22.2236 22.2236i −0.937446 0.937446i
\(563\) −17.2310 17.2310i −0.726198 0.726198i 0.243662 0.969860i \(-0.421651\pi\)
−0.969860 + 0.243662i \(0.921651\pi\)
\(564\) 0.604177 0.604177i 0.0254404 0.0254404i
\(565\) −9.55151 + 4.39510i −0.401835 + 0.184903i
\(566\) 10.4468 10.4468i 0.439111 0.439111i
\(567\) 0.946681 0.0397569
\(568\) −6.99770 + 6.99770i −0.293617 + 0.293617i
\(569\) 7.21162 0.302327 0.151163 0.988509i \(-0.451698\pi\)
0.151163 + 0.988509i \(0.451698\pi\)
\(570\) 2.97504 + 1.09995i 0.124611 + 0.0460718i
\(571\) 20.5745i 0.861017i −0.902587 0.430508i \(-0.858334\pi\)
0.902587 0.430508i \(-0.141666\pi\)
\(572\) 12.0476 10.4760i 0.503735 0.438022i
\(573\) −4.77549 + 4.77549i −0.199499 + 0.199499i
\(574\) 5.71303 5.71303i 0.238457 0.238457i
\(575\) −2.31658 29.9785i −0.0966082 1.25019i
\(576\) 1.00000i 0.0416667i
\(577\) 4.77462i 0.198770i −0.995049 0.0993850i \(-0.968312\pi\)
0.995049 0.0993850i \(-0.0316875\pi\)
\(578\) 6.41383 0.266780
\(579\) 5.34480 + 5.34480i 0.222122 + 0.222122i
\(580\) 4.18150 11.3097i 0.173627 0.469611i
\(581\) 14.4246 0.598433
\(582\) −1.88997 + 1.88997i −0.0783419 + 0.0783419i
\(583\) 24.4375i 1.01210i
\(584\) 16.4476 0.680607
\(585\) 3.31544 7.34900i 0.137077 0.303844i
\(586\) −24.5333 −1.01346
\(587\) 10.7668i 0.444393i −0.975002 0.222196i \(-0.928677\pi\)
0.975002 0.222196i \(-0.0713226\pi\)
\(588\) −4.31603 + 4.31603i −0.177990 + 0.177990i
\(589\) −4.89424 −0.201664
\(590\) −26.9540 + 12.4028i −1.10968 + 0.510614i
\(591\) 12.6353 + 12.6353i 0.519747 + 0.519747i
\(592\) −11.9002 −0.489094
\(593\) 41.5640i 1.70683i −0.521233 0.853414i \(-0.674528\pi\)
0.521233 0.853414i \(-0.325472\pi\)
\(594\) 4.42797i 0.181682i
\(595\) 9.30510 4.28171i 0.381472 0.175533i
\(596\) 1.72580 1.72580i 0.0706914 0.0706914i
\(597\) −4.53630 + 4.53630i −0.185658 + 0.185658i
\(598\) −16.3617 + 14.2273i −0.669079 + 0.581797i
\(599\) 34.5955i 1.41353i −0.707446 0.706767i \(-0.750153\pi\)
0.707446 0.706767i \(-0.249847\pi\)
\(600\) 0.385225 + 4.98514i 0.0157268 + 0.203517i
\(601\) −10.8465 −0.442436 −0.221218 0.975224i \(-0.571003\pi\)
−0.221218 + 0.975224i \(0.571003\pi\)
\(602\) −0.229274 + 0.229274i −0.00934451 + 0.00934451i
\(603\) −3.51092 −0.142976
\(604\) −1.86471 + 1.86471i −0.0758739 + 0.0758739i
\(605\) −6.67407 + 18.0514i −0.271339 + 0.733894i
\(606\) 5.06610 5.06610i 0.205796 0.205796i
\(607\) −2.08924 2.08924i −0.0847995 0.0847995i 0.663435 0.748234i \(-0.269098\pi\)
−0.748234 + 0.663435i \(0.769098\pi\)
\(608\) 1.00303 + 1.00303i 0.0406784 + 0.0406784i
\(609\) −3.60976 3.60976i −0.146275 0.146275i
\(610\) 7.59877 20.5525i 0.307665 0.832145i
\(611\) −3.07324 0.214442i −0.124330 0.00867538i
\(612\) 3.42154 + 3.42154i 0.138307 + 0.138307i
\(613\) 39.8520 1.60961 0.804804 0.593541i \(-0.202270\pi\)
0.804804 + 0.593541i \(0.202270\pi\)
\(614\) 26.9486i 1.08756i
\(615\) 17.8995 + 6.61789i 0.721776 + 0.266859i
\(616\) 2.96410 + 2.96410i 0.119427 + 0.119427i
\(617\) 35.2269i 1.41818i −0.705118 0.709090i \(-0.749106\pi\)
0.705118 0.709090i \(-0.250894\pi\)
\(618\) 11.3204i 0.455373i
\(619\) 29.3560 + 29.3560i 1.17992 + 1.17992i 0.979765 + 0.200150i \(0.0641431\pi\)
0.200150 + 0.979765i \(0.435857\pi\)
\(620\) −3.22502 7.00868i −0.129520 0.281475i
\(621\) 6.01358i 0.241317i
\(622\) −16.4762 −0.660636
\(623\) −0.231570 0.231570i −0.00927768 0.00927768i
\(624\) 2.72079 2.36586i 0.108919 0.0947102i
\(625\) 3.84080 + 24.7032i 0.153632 + 0.988128i
\(626\) 2.89698 + 2.89698i 0.115787 + 0.115787i
\(627\) 4.44140 + 4.44140i 0.177373 + 0.177373i
\(628\) −2.33729 2.33729i −0.0932679 0.0932679i
\(629\) −40.7168 + 40.7168i −1.62349 + 1.62349i
\(630\) 1.98548 + 0.734084i 0.0791036 + 0.0292466i
\(631\) −10.8434 + 10.8434i −0.431670 + 0.431670i −0.889196 0.457526i \(-0.848736\pi\)
0.457526 + 0.889196i \(0.348736\pi\)
\(632\) −8.09997 −0.322199
\(633\) −5.91713 + 5.91713i −0.235185 + 0.235185i
\(634\) 13.4323 0.533465
\(635\) 8.88623 4.08897i 0.352639 0.162266i
\(636\) 5.51888i 0.218838i
\(637\) 21.9542 + 1.53190i 0.869856 + 0.0606960i
\(638\) 16.8842 16.8842i 0.668451 0.668451i
\(639\) −6.99770 + 6.99770i −0.276825 + 0.276825i
\(640\) −0.775429 + 2.09731i −0.0306515 + 0.0829035i
\(641\) 45.5504i 1.79913i −0.436784 0.899566i \(-0.643883\pi\)
0.436784 0.899566i \(-0.356117\pi\)
\(642\) 7.54617i 0.297823i
\(643\) 13.2934 0.524241 0.262120 0.965035i \(-0.415578\pi\)
0.262120 + 0.965035i \(0.415578\pi\)
\(644\) −4.02552 4.02552i −0.158628 0.158628i
\(645\) −0.718338 0.265588i −0.0282845 0.0104575i
\(646\) 6.86383 0.270054
\(647\) 0.168076 0.168076i 0.00660775 0.00660775i −0.703795 0.710403i \(-0.748513\pi\)
0.710403 + 0.703795i \(0.248513\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −58.7552 −2.30634
\(650\) 12.6521 12.8423i 0.496258 0.503715i
\(651\) −3.26632 −0.128017
\(652\) 23.5470i 0.922172i
\(653\) 16.2763 16.2763i 0.636941 0.636941i −0.312859 0.949800i \(-0.601287\pi\)
0.949800 + 0.312859i \(0.101287\pi\)
\(654\) −5.55863 −0.217360
\(655\) 6.28758 + 2.32468i 0.245676 + 0.0908326i
\(656\) 6.03479 + 6.03479i 0.235619 + 0.235619i
\(657\) 16.4476 0.641682
\(658\) 0.808877i 0.0315333i
\(659\) 36.6617i 1.42814i 0.700077 + 0.714068i \(0.253149\pi\)
−0.700077 + 0.714068i \(0.746851\pi\)
\(660\) −3.43358 + 9.28683i −0.133652 + 0.361489i
\(661\) 1.76972 1.76972i 0.0688341 0.0688341i −0.671852 0.740686i \(-0.734501\pi\)
0.740686 + 0.671852i \(0.234501\pi\)
\(662\) −4.34332 + 4.34332i −0.168808 + 0.168808i
\(663\) 1.21441 17.4042i 0.0471639 0.675922i
\(664\) 15.2370i 0.591310i
\(665\) 2.72782 1.25520i 0.105780 0.0486744i
\(666\) −11.9002 −0.461122
\(667\) −22.9302 + 22.9302i −0.887861 + 0.887861i
\(668\) −9.77190 −0.378086
\(669\) 4.46830 4.46830i 0.172754 0.172754i
\(670\) −7.36349 2.72247i −0.284476 0.105178i
\(671\) 30.6825 30.6825i 1.18449 1.18449i
\(672\) 0.669405 + 0.669405i 0.0258228 + 0.0258228i
\(673\) 16.5684 + 16.5684i 0.638667 + 0.638667i 0.950227 0.311560i \(-0.100851\pi\)
−0.311560 + 0.950227i \(0.600851\pi\)
\(674\) −2.98172 2.98172i −0.114852 0.114852i
\(675\) 0.385225 + 4.98514i 0.0148273 + 0.191878i
\(676\) −12.8740 1.80542i −0.495155 0.0694391i
\(677\) −11.4370 11.4370i −0.439558 0.439558i 0.452305 0.891863i \(-0.350602\pi\)
−0.891863 + 0.452305i \(0.850602\pi\)
\(678\) −4.70209 −0.180583
\(679\) 2.53031i 0.0971046i
\(680\) 4.52287 + 9.82918i 0.173444 + 0.376932i
\(681\) −1.45832 1.45832i −0.0558829 0.0558829i
\(682\) 15.2778i 0.585016i
\(683\) 9.80987i 0.375364i 0.982230 + 0.187682i \(0.0600975\pi\)
−0.982230 + 0.187682i \(0.939902\pi\)
\(684\) 1.00303 + 1.00303i 0.0383519 + 0.0383519i
\(685\) −36.3919 13.4550i −1.39046 0.514089i
\(686\) 12.4051i 0.473629i
\(687\) −1.86184 −0.0710334
\(688\) −0.242187 0.242187i −0.00923330 0.00923330i
\(689\) −15.0157 + 13.0569i −0.572054 + 0.497429i
\(690\) 4.66310 12.6123i 0.177521 0.480144i
\(691\) 27.4993 + 27.4993i 1.04612 + 1.04612i 0.998884 + 0.0472402i \(0.0150426\pi\)
0.0472402 + 0.998884i \(0.484957\pi\)
\(692\) −5.96615 5.96615i −0.226799 0.226799i
\(693\) 2.96410 + 2.96410i 0.112597 + 0.112597i
\(694\) 25.3043 25.3043i 0.960538 0.960538i
\(695\) 1.93538 5.23463i 0.0734130 0.198561i
\(696\) 3.81307 3.81307i 0.144534 0.144534i
\(697\) 41.2965 1.56422
\(698\) −10.5348 + 10.5348i −0.398748 + 0.398748i
\(699\) −14.7664 −0.558516
\(700\) 3.59495 + 3.07920i 0.135876 + 0.116383i
\(701\) 6.79306i 0.256570i 0.991737 + 0.128285i \(0.0409473\pi\)
−0.991737 + 0.128285i \(0.959053\pi\)
\(702\) 2.72079 2.36586i 0.102690 0.0892936i
\(703\) −11.9363 + 11.9363i −0.450185 + 0.450185i
\(704\) −3.13105 + 3.13105i −0.118006 + 0.118006i
\(705\) 1.73564 0.798650i 0.0653680 0.0300789i
\(706\) 24.7214i 0.930401i
\(707\) 6.78254i 0.255084i
\(708\) −13.2691 −0.498683
\(709\) 1.32520 + 1.32520i 0.0497688 + 0.0497688i 0.731553 0.681784i \(-0.238796\pi\)
−0.681784 + 0.731553i \(0.738796\pi\)
\(710\) −20.1026 + 9.25014i −0.754436 + 0.347151i
\(711\) −8.09997 −0.303772
\(712\) 0.244613 0.244613i 0.00916726 0.00916726i
\(713\) 20.7486i 0.777040i
\(714\) 4.58078 0.171432
\(715\) 33.3909 12.6293i 1.24875 0.472309i
\(716\) −7.96800 −0.297778
\(717\) 23.4805i 0.876895i
\(718\) −1.44201 + 1.44201i −0.0538155 + 0.0538155i
\(719\) 22.5002 0.839117 0.419558 0.907728i \(-0.362185\pi\)
0.419558 + 0.907728i \(0.362185\pi\)
\(720\) −0.775429 + 2.09731i −0.0288985 + 0.0781621i
\(721\) −7.57792 7.57792i −0.282217 0.282217i
\(722\) −16.9878 −0.632222
\(723\) 17.4300i 0.648230i
\(724\) 17.3575i 0.645087i
\(725\) 17.5398 20.4776i 0.651411 0.760518i
\(726\) −6.08602 + 6.08602i −0.225874 + 0.225874i
\(727\) −19.5890 + 19.5890i −0.726516 + 0.726516i −0.969924 0.243408i \(-0.921735\pi\)
0.243408 + 0.969924i \(0.421735\pi\)
\(728\) 0.237593 3.40503i 0.00880579 0.126199i
\(729\) 1.00000i 0.0370370i
\(730\) 34.4957 + 12.7539i 1.27674 + 0.472045i
\(731\) −1.65731 −0.0612976
\(732\) 6.92925 6.92925i 0.256113 0.256113i
\(733\) 8.60108 0.317688 0.158844 0.987304i \(-0.449223\pi\)
0.158844 + 0.987304i \(0.449223\pi\)
\(734\) −0.992346 + 0.992346i −0.0366281 + 0.0366281i
\(735\) −12.3988 + 5.70529i −0.457338 + 0.210443i
\(736\) 4.25224 4.25224i 0.156740 0.156740i
\(737\) −10.9929 10.9929i −0.404927 0.404927i
\(738\) 6.03479 + 6.03479i 0.222144 + 0.222144i
\(739\) −1.33478 1.33478i −0.0491006 0.0491006i 0.682130 0.731231i \(-0.261054\pi\)
−0.731231 + 0.682130i \(0.761054\pi\)
\(740\) −24.9583 9.22773i −0.917487 0.339218i
\(741\) 0.356009 5.10208i 0.0130783 0.187430i
\(742\) −3.69437 3.69437i −0.135624 0.135624i
\(743\) −36.1540 −1.32636 −0.663181 0.748459i \(-0.730794\pi\)
−0.663181 + 0.748459i \(0.730794\pi\)
\(744\) 3.45028i 0.126494i
\(745\) 4.95776 2.28130i 0.181638 0.0835803i
\(746\) 20.8743 + 20.8743i 0.764262 + 0.764262i
\(747\) 15.2370i 0.557493i
\(748\) 21.4260i 0.783412i
\(749\) −5.05144 5.05144i −0.184576 0.184576i
\(750\) −3.05768 + 10.7541i −0.111651 + 0.392684i
\(751\) 46.2231i 1.68670i 0.537361 + 0.843352i \(0.319421\pi\)
−0.537361 + 0.843352i \(0.680579\pi\)
\(752\) 0.854435 0.0311580
\(753\) 14.7972 + 14.7972i 0.539240 + 0.539240i
\(754\) −19.3958 1.35338i −0.706352 0.0492872i
\(755\) −5.35682 + 2.46492i −0.194955 + 0.0897077i
\(756\) 0.669405 + 0.669405i 0.0243460 + 0.0243460i
\(757\) 35.7855 + 35.7855i 1.30065 + 1.30065i 0.927956 + 0.372689i \(0.121564\pi\)
0.372689 + 0.927956i \(0.378436\pi\)
\(758\) −17.6422 17.6422i −0.640795 0.640795i
\(759\) 18.8288 18.8288i 0.683443 0.683443i
\(760\) 1.32589 + 2.88145i 0.0480951 + 0.104521i
\(761\) 4.25598 4.25598i 0.154279 0.154279i −0.625747 0.780026i \(-0.715206\pi\)
0.780026 + 0.625747i \(0.215206\pi\)
\(762\) 4.37458 0.158474
\(763\) −3.72097 + 3.72097i −0.134708 + 0.134708i
\(764\) −6.75356 −0.244335
\(765\) 4.52287 + 9.82918i 0.163525 + 0.355375i
\(766\) 29.6580i 1.07159i
\(767\) 31.3928 + 36.1025i 1.13353 + 1.30358i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 6.64731 6.64731i 0.239708 0.239708i −0.577021 0.816729i \(-0.695785\pi\)
0.816729 + 0.577021i \(0.195785\pi\)
\(770\) 3.91820 + 8.51510i 0.141202 + 0.306863i
\(771\) 7.44284i 0.268047i
\(772\) 7.55869i 0.272043i
\(773\) 47.1882 1.69724 0.848620 0.529002i \(-0.177434\pi\)
0.848620 + 0.529002i \(0.177434\pi\)
\(774\) −0.242187 0.242187i −0.00870524 0.00870524i
\(775\) −1.32914 17.2001i −0.0477440 0.617847i