Properties

Label 280.2.h.b.251.13
Level $280$
Weight $2$
Character 280.251
Analytic conductor $2.236$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - x^{15} - 2 x^{12} + 6 x^{11} - 12 x^{9} + 8 x^{8} - 24 x^{7} + 48 x^{5} - 32 x^{4} - 128 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.13
Root \(1.14218 + 0.833926i\) of defining polynomial
Character \(\chi\) \(=\) 280.251
Dual form 280.2.h.b.251.14

$q$-expansion

\(f(q)\) \(=\) \(q+(1.14218 - 0.833926i) q^{2} -0.586834i q^{3} +(0.609136 - 1.90498i) q^{4} +1.00000 q^{5} +(-0.489376 - 0.670268i) q^{6} +(-2.52442 - 0.792014i) q^{7} +(-0.892871 - 2.68380i) q^{8} +2.65563 q^{9} +O(q^{10})\) \(q+(1.14218 - 0.833926i) q^{2} -0.586834i q^{3} +(0.609136 - 1.90498i) q^{4} +1.00000 q^{5} +(-0.489376 - 0.670268i) q^{6} +(-2.52442 - 0.792014i) q^{7} +(-0.892871 - 2.68380i) q^{8} +2.65563 q^{9} +(1.14218 - 0.833926i) q^{10} -0.580189 q^{11} +(-1.11791 - 0.357462i) q^{12} +1.14766 q^{13} +(-3.54382 + 1.20056i) q^{14} -0.586834i q^{15} +(-3.25791 - 2.32079i) q^{16} -1.82880i q^{17} +(3.03319 - 2.21459i) q^{18} +4.72462i q^{19} +(0.609136 - 1.90498i) q^{20} +(-0.464781 + 1.48142i) q^{21} +(-0.662679 + 0.483835i) q^{22} +2.79961i q^{23} +(-1.57494 + 0.523967i) q^{24} +1.00000 q^{25} +(1.31083 - 0.957061i) q^{26} -3.31891i q^{27} +(-3.04649 + 4.32653i) q^{28} +7.40518i q^{29} +(-0.489376 - 0.670268i) q^{30} +4.73007 q^{31} +(-5.65647 + 0.0661016i) q^{32} +0.340475i q^{33} +(-1.52509 - 2.08882i) q^{34} +(-2.52442 - 0.792014i) q^{35} +(1.61764 - 5.05892i) q^{36} +4.35175i q^{37} +(3.93998 + 5.39635i) q^{38} -0.673485i q^{39} +(-0.892871 - 2.68380i) q^{40} -8.46264i q^{41} +(0.704530 + 2.07963i) q^{42} -4.32314 q^{43} +(-0.353414 + 1.10525i) q^{44} +2.65563 q^{45} +(2.33466 + 3.19765i) q^{46} +3.56830 q^{47} +(-1.36192 + 1.91185i) q^{48} +(5.74543 + 3.99876i) q^{49} +(1.14218 - 0.833926i) q^{50} -1.07320 q^{51} +(0.699080 - 2.18627i) q^{52} +5.48977i q^{53} +(-2.76773 - 3.79079i) q^{54} -0.580189 q^{55} +(0.128378 + 7.48221i) q^{56} +2.77257 q^{57} +(6.17537 + 8.45803i) q^{58} +13.2957i q^{59} +(-1.11791 - 0.357462i) q^{60} +0.275184 q^{61} +(5.40258 - 3.94453i) q^{62} +(-6.70392 - 2.10329i) q^{63} +(-6.40556 + 4.79257i) q^{64} +1.14766 q^{65} +(0.283931 + 0.388882i) q^{66} -7.71818 q^{67} +(-3.48384 - 1.11399i) q^{68} +1.64291 q^{69} +(-3.54382 + 1.20056i) q^{70} -1.13454i q^{71} +(-2.37113 - 7.12717i) q^{72} +1.78121i q^{73} +(3.62904 + 4.97047i) q^{74} -0.586834i q^{75} +(9.00031 + 2.87794i) q^{76} +(1.46464 + 0.459518i) q^{77} +(-0.561636 - 0.769239i) q^{78} -10.0108i q^{79} +(-3.25791 - 2.32079i) q^{80} +6.01923 q^{81} +(-7.05721 - 9.66583i) q^{82} -15.6230i q^{83} +(2.53896 + 1.78778i) q^{84} -1.82880i q^{85} +(-4.93780 + 3.60518i) q^{86} +4.34561 q^{87} +(0.518034 + 1.55711i) q^{88} +15.3393i q^{89} +(3.03319 - 2.21459i) q^{90} +(-2.89717 - 0.908961i) q^{91} +(5.33320 + 1.70534i) q^{92} -2.77577i q^{93} +(4.07563 - 2.97569i) q^{94} +4.72462i q^{95} +(0.0387907 + 3.31941i) q^{96} -14.9759i q^{97} +(9.89696 - 0.223972i) q^{98} -1.54077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + q^{2} + q^{4} + 16q^{5} + q^{8} - 16q^{9} + O(q^{10}) \) \( 16q + q^{2} + q^{4} + 16q^{5} + q^{8} - 16q^{9} + q^{10} - 4q^{11} + 14q^{12} - q^{14} + 9q^{16} - 15q^{18} + q^{20} - 4q^{21} + 6q^{22} + 22q^{24} + 16q^{25} - 20q^{26} + q^{28} - 16q^{31} - 19q^{32} - 14q^{34} + 15q^{36} - 30q^{38} + q^{40} + 44q^{42} - 4q^{43} - 20q^{44} - 16q^{45} + 6q^{46} - 34q^{48} - 8q^{49} + q^{50} - 40q^{51} - 38q^{52} + 26q^{54} - 4q^{55} + 33q^{56} - 16q^{57} + 18q^{58} + 14q^{60} - 8q^{61} + 28q^{62} + 28q^{63} - 23q^{64} + 46q^{66} + 20q^{67} + 12q^{68} - 40q^{69} - q^{70} - 13q^{72} - 28q^{74} + 34q^{76} - 4q^{77} - 6q^{78} + 9q^{80} + 24q^{81} - 16q^{82} - 42q^{84} - 24q^{86} + 72q^{87} - 44q^{88} - 15q^{90} - 32q^{91} - 30q^{92} - 58q^{94} - 30q^{96} + 5q^{98} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.14218 0.833926i 0.807641 0.589674i
\(3\) 0.586834i 0.338809i −0.985547 0.169404i \(-0.945816\pi\)
0.985547 0.169404i \(-0.0541844\pi\)
\(4\) 0.609136 1.90498i 0.304568 0.952491i
\(5\) 1.00000 0.447214
\(6\) −0.489376 0.670268i −0.199787 0.273636i
\(7\) −2.52442 0.792014i −0.954142 0.299353i
\(8\) −0.892871 2.68380i −0.315677 0.948867i
\(9\) 2.65563 0.885209
\(10\) 1.14218 0.833926i 0.361188 0.263710i
\(11\) −0.580189 −0.174934 −0.0874668 0.996167i \(-0.527877\pi\)
−0.0874668 + 0.996167i \(0.527877\pi\)
\(12\) −1.11791 0.357462i −0.322712 0.103190i
\(13\) 1.14766 0.318303 0.159152 0.987254i \(-0.449124\pi\)
0.159152 + 0.987254i \(0.449124\pi\)
\(14\) −3.54382 + 1.20056i −0.947125 + 0.320864i
\(15\) 0.586834i 0.151520i
\(16\) −3.25791 2.32079i −0.814476 0.580197i
\(17\) 1.82880i 0.443550i −0.975098 0.221775i \(-0.928815\pi\)
0.975098 0.221775i \(-0.0711851\pi\)
\(18\) 3.03319 2.21459i 0.714931 0.521985i
\(19\) 4.72462i 1.08390i 0.840410 + 0.541951i \(0.182314\pi\)
−0.840410 + 0.541951i \(0.817686\pi\)
\(20\) 0.609136 1.90498i 0.136207 0.425967i
\(21\) −0.464781 + 1.48142i −0.101423 + 0.323272i
\(22\) −0.662679 + 0.483835i −0.141284 + 0.103154i
\(23\) 2.79961i 0.583759i 0.956455 + 0.291879i \(0.0942806\pi\)
−0.956455 + 0.291879i \(0.905719\pi\)
\(24\) −1.57494 + 0.523967i −0.321484 + 0.106954i
\(25\) 1.00000 0.200000
\(26\) 1.31083 0.957061i 0.257075 0.187695i
\(27\) 3.31891i 0.638725i
\(28\) −3.04649 + 4.32653i −0.575732 + 0.817638i
\(29\) 7.40518i 1.37511i 0.726133 + 0.687554i \(0.241316\pi\)
−0.726133 + 0.687554i \(0.758684\pi\)
\(30\) −0.489376 0.670268i −0.0893474 0.122374i
\(31\) 4.73007 0.849546 0.424773 0.905300i \(-0.360354\pi\)
0.424773 + 0.905300i \(0.360354\pi\)
\(32\) −5.65647 + 0.0661016i −0.999932 + 0.0116852i
\(33\) 0.340475i 0.0592691i
\(34\) −1.52509 2.08882i −0.261550 0.358229i
\(35\) −2.52442 0.792014i −0.426705 0.133875i
\(36\) 1.61764 5.05892i 0.269606 0.843153i
\(37\) 4.35175i 0.715423i 0.933832 + 0.357712i \(0.116443\pi\)
−0.933832 + 0.357712i \(0.883557\pi\)
\(38\) 3.93998 + 5.39635i 0.639149 + 0.875404i
\(39\) 0.673485i 0.107844i
\(40\) −0.892871 2.68380i −0.141175 0.424346i
\(41\) 8.46264i 1.32164i −0.750544 0.660821i \(-0.770208\pi\)
0.750544 0.660821i \(-0.229792\pi\)
\(42\) 0.704530 + 2.07963i 0.108711 + 0.320894i
\(43\) −4.32314 −0.659273 −0.329637 0.944108i \(-0.606926\pi\)
−0.329637 + 0.944108i \(0.606926\pi\)
\(44\) −0.353414 + 1.10525i −0.0532792 + 0.166623i
\(45\) 2.65563 0.395877
\(46\) 2.33466 + 3.19765i 0.344228 + 0.471468i
\(47\) 3.56830 0.520490 0.260245 0.965543i \(-0.416197\pi\)
0.260245 + 0.965543i \(0.416197\pi\)
\(48\) −1.36192 + 1.91185i −0.196576 + 0.275952i
\(49\) 5.74543 + 3.99876i 0.820775 + 0.571251i
\(50\) 1.14218 0.833926i 0.161528 0.117935i
\(51\) −1.07320 −0.150279
\(52\) 0.699080 2.18627i 0.0969450 0.303181i
\(53\) 5.48977i 0.754079i 0.926197 + 0.377039i \(0.123058\pi\)
−0.926197 + 0.377039i \(0.876942\pi\)
\(54\) −2.76773 3.79079i −0.376640 0.515861i
\(55\) −0.580189 −0.0782327
\(56\) 0.128378 + 7.48221i 0.0171552 + 0.999853i
\(57\) 2.77257 0.367235
\(58\) 6.17537 + 8.45803i 0.810866 + 1.11059i
\(59\) 13.2957i 1.73095i 0.500948 + 0.865477i \(0.332985\pi\)
−0.500948 + 0.865477i \(0.667015\pi\)
\(60\) −1.11791 0.357462i −0.144321 0.0461481i
\(61\) 0.275184 0.0352337 0.0176168 0.999845i \(-0.494392\pi\)
0.0176168 + 0.999845i \(0.494392\pi\)
\(62\) 5.40258 3.94453i 0.686128 0.500955i
\(63\) −6.70392 2.10329i −0.844615 0.264990i
\(64\) −6.40556 + 4.79257i −0.800695 + 0.599072i
\(65\) 1.14766 0.142349
\(66\) 0.283931 + 0.388882i 0.0349494 + 0.0478681i
\(67\) −7.71818 −0.942925 −0.471463 0.881886i \(-0.656274\pi\)
−0.471463 + 0.881886i \(0.656274\pi\)
\(68\) −3.48384 1.11399i −0.422477 0.135091i
\(69\) 1.64291 0.197783
\(70\) −3.54382 + 1.20056i −0.423567 + 0.143495i
\(71\) 1.13454i 0.134645i −0.997731 0.0673224i \(-0.978554\pi\)
0.997731 0.0673224i \(-0.0214456\pi\)
\(72\) −2.37113 7.12717i −0.279440 0.839945i
\(73\) 1.78121i 0.208474i 0.994552 + 0.104237i \(0.0332401\pi\)
−0.994552 + 0.104237i \(0.966760\pi\)
\(74\) 3.62904 + 4.97047i 0.421867 + 0.577805i
\(75\) 0.586834i 0.0677617i
\(76\) 9.00031 + 2.87794i 1.03241 + 0.330122i
\(77\) 1.46464 + 0.459518i 0.166912 + 0.0523669i
\(78\) −0.561636 0.769239i −0.0635928 0.0870991i
\(79\) 10.0108i 1.12630i −0.826355 0.563149i \(-0.809590\pi\)
0.826355 0.563149i \(-0.190410\pi\)
\(80\) −3.25791 2.32079i −0.364245 0.259472i
\(81\) 6.01923 0.668803
\(82\) −7.05721 9.66583i −0.779338 1.06741i
\(83\) 15.6230i 1.71485i −0.514607 0.857426i \(-0.672062\pi\)
0.514607 0.857426i \(-0.327938\pi\)
\(84\) 2.53896 + 1.78778i 0.277023 + 0.195063i
\(85\) 1.82880i 0.198362i
\(86\) −4.93780 + 3.60518i −0.532456 + 0.388757i
\(87\) 4.34561 0.465899
\(88\) 0.518034 + 1.55711i 0.0552226 + 0.165989i
\(89\) 15.3393i 1.62596i 0.582293 + 0.812979i \(0.302156\pi\)
−0.582293 + 0.812979i \(0.697844\pi\)
\(90\) 3.03319 2.21459i 0.319727 0.233439i
\(91\) −2.89717 0.908961i −0.303706 0.0952850i
\(92\) 5.33320 + 1.70534i 0.556025 + 0.177794i
\(93\) 2.77577i 0.287833i
\(94\) 4.07563 2.97569i 0.420369 0.306919i
\(95\) 4.72462i 0.484736i
\(96\) 0.0387907 + 3.31941i 0.00395906 + 0.338786i
\(97\) 14.9759i 1.52058i −0.649585 0.760289i \(-0.725057\pi\)
0.649585 0.760289i \(-0.274943\pi\)
\(98\) 9.89696 0.223972i 0.999744 0.0226246i
\(99\) −1.54077 −0.154853
\(100\) 0.609136 1.90498i 0.0609136 0.190498i
\(101\) −12.7803 −1.27169 −0.635845 0.771817i \(-0.719348\pi\)
−0.635845 + 0.771817i \(0.719348\pi\)
\(102\) −1.22579 + 0.894973i −0.121371 + 0.0886155i
\(103\) −15.1439 −1.49217 −0.746085 0.665851i \(-0.768069\pi\)
−0.746085 + 0.665851i \(0.768069\pi\)
\(104\) −1.02471 3.08008i −0.100481 0.302027i
\(105\) −0.464781 + 1.48142i −0.0453579 + 0.144572i
\(106\) 4.57806 + 6.27029i 0.444661 + 0.609025i
\(107\) 6.70224 0.647930 0.323965 0.946069i \(-0.394984\pi\)
0.323965 + 0.946069i \(0.394984\pi\)
\(108\) −6.32247 2.02167i −0.608380 0.194535i
\(109\) 11.2152i 1.07422i −0.843511 0.537112i \(-0.819515\pi\)
0.843511 0.537112i \(-0.180485\pi\)
\(110\) −0.662679 + 0.483835i −0.0631839 + 0.0461318i
\(111\) 2.55376 0.242392
\(112\) 6.38624 + 8.43895i 0.603443 + 0.797406i
\(113\) 1.41012 0.132653 0.0663265 0.997798i \(-0.478872\pi\)
0.0663265 + 0.997798i \(0.478872\pi\)
\(114\) 3.16676 2.31211i 0.296594 0.216549i
\(115\) 2.79961i 0.261065i
\(116\) 14.1067 + 4.51077i 1.30978 + 0.418814i
\(117\) 3.04775 0.281765
\(118\) 11.0876 + 15.1861i 1.02070 + 1.39799i
\(119\) −1.44844 + 4.61668i −0.132778 + 0.423210i
\(120\) −1.57494 + 0.523967i −0.143772 + 0.0478314i
\(121\) −10.6634 −0.969398
\(122\) 0.314309 0.229483i 0.0284562 0.0207764i
\(123\) −4.96616 −0.447784
\(124\) 2.88126 9.01069i 0.258745 0.809184i
\(125\) 1.00000 0.0894427
\(126\) −9.41106 + 3.18824i −0.838404 + 0.284031i
\(127\) 15.7103i 1.39406i −0.717041 0.697031i \(-0.754504\pi\)
0.717041 0.697031i \(-0.245496\pi\)
\(128\) −3.31964 + 10.8157i −0.293417 + 0.955984i
\(129\) 2.53697i 0.223368i
\(130\) 1.31083 0.957061i 0.114967 0.0839398i
\(131\) 5.01749i 0.438380i 0.975682 + 0.219190i \(0.0703415\pi\)
−0.975682 + 0.219190i \(0.929658\pi\)
\(132\) 0.648598 + 0.207396i 0.0564532 + 0.0180515i
\(133\) 3.74196 11.9269i 0.324469 1.03420i
\(134\) −8.81552 + 6.43638i −0.761545 + 0.556019i
\(135\) 3.31891i 0.285647i
\(136\) −4.90815 + 1.63289i −0.420870 + 0.140019i
\(137\) −14.8703 −1.27045 −0.635226 0.772326i \(-0.719093\pi\)
−0.635226 + 0.772326i \(0.719093\pi\)
\(138\) 1.87649 1.37006i 0.159737 0.116627i
\(139\) 0.148572i 0.0126017i 0.999980 + 0.00630086i \(0.00200564\pi\)
−0.999980 + 0.00630086i \(0.997994\pi\)
\(140\) −3.04649 + 4.32653i −0.257475 + 0.365659i
\(141\) 2.09400i 0.176346i
\(142\) −0.946120 1.29584i −0.0793966 0.108745i
\(143\) −0.665859 −0.0556819
\(144\) −8.65178 6.16314i −0.720982 0.513595i
\(145\) 7.40518i 0.614967i
\(146\) 1.48539 + 2.03445i 0.122932 + 0.168372i
\(147\) 2.34661 3.37161i 0.193545 0.278086i
\(148\) 8.29000 + 2.65081i 0.681434 + 0.217895i
\(149\) 8.85493i 0.725424i −0.931901 0.362712i \(-0.881851\pi\)
0.931901 0.362712i \(-0.118149\pi\)
\(150\) −0.489376 0.670268i −0.0399574 0.0547272i
\(151\) 12.3932i 1.00855i −0.863544 0.504273i \(-0.831761\pi\)
0.863544 0.504273i \(-0.168239\pi\)
\(152\) 12.6799 4.21847i 1.02848 0.342163i
\(153\) 4.85662i 0.392635i
\(154\) 2.05609 0.696553i 0.165684 0.0561298i
\(155\) 4.73007 0.379928
\(156\) −1.28298 0.410244i −0.102720 0.0328458i
\(157\) −15.6090 −1.24574 −0.622869 0.782326i \(-0.714033\pi\)
−0.622869 + 0.782326i \(0.714033\pi\)
\(158\) −8.34822 11.4341i −0.664149 0.909644i
\(159\) 3.22159 0.255488
\(160\) −5.65647 + 0.0661016i −0.447183 + 0.00522579i
\(161\) 2.21733 7.06740i 0.174750 0.556989i
\(162\) 6.87502 5.01959i 0.540153 0.394376i
\(163\) −5.60110 −0.438712 −0.219356 0.975645i \(-0.570396\pi\)
−0.219356 + 0.975645i \(0.570396\pi\)
\(164\) −16.1212 5.15490i −1.25885 0.402530i
\(165\) 0.340475i 0.0265059i
\(166\) −13.0285 17.8443i −1.01120 1.38498i
\(167\) 9.34952 0.723488 0.361744 0.932278i \(-0.382181\pi\)
0.361744 + 0.932278i \(0.382181\pi\)
\(168\) 4.39082 0.0753363i 0.338759 0.00581232i
\(169\) −11.6829 −0.898683
\(170\) −1.52509 2.08882i −0.116969 0.160205i
\(171\) 12.5468i 0.959479i
\(172\) −2.63338 + 8.23551i −0.200794 + 0.627952i
\(173\) 23.5706 1.79204 0.896018 0.444018i \(-0.146447\pi\)
0.896018 + 0.444018i \(0.146447\pi\)
\(174\) 4.96346 3.62392i 0.376279 0.274729i
\(175\) −2.52442 0.792014i −0.190828 0.0598706i
\(176\) 1.89020 + 1.34650i 0.142479 + 0.101496i
\(177\) 7.80238 0.586463
\(178\) 12.7918 + 17.5202i 0.958786 + 1.31319i
\(179\) 19.7086 1.47309 0.736546 0.676387i \(-0.236455\pi\)
0.736546 + 0.676387i \(0.236455\pi\)
\(180\) 1.61764 5.05892i 0.120572 0.377069i
\(181\) −21.0102 −1.56168 −0.780839 0.624732i \(-0.785208\pi\)
−0.780839 + 0.624732i \(0.785208\pi\)
\(182\) −4.06709 + 1.37783i −0.301473 + 0.102132i
\(183\) 0.161487i 0.0119375i
\(184\) 7.51359 2.49969i 0.553909 0.184279i
\(185\) 4.35175i 0.319947i
\(186\) −2.31478 3.17042i −0.169728 0.232466i
\(187\) 1.06105i 0.0775919i
\(188\) 2.17358 6.79754i 0.158525 0.495761i
\(189\) −2.62862 + 8.37834i −0.191204 + 0.609435i
\(190\) 3.93998 + 5.39635i 0.285836 + 0.391492i
\(191\) 16.9750i 1.22827i 0.789201 + 0.614135i \(0.210495\pi\)
−0.789201 + 0.614135i \(0.789505\pi\)
\(192\) 2.81244 + 3.75900i 0.202971 + 0.271283i
\(193\) 14.8445 1.06853 0.534266 0.845317i \(-0.320588\pi\)
0.534266 + 0.845317i \(0.320588\pi\)
\(194\) −12.4888 17.1052i −0.896645 1.22808i
\(195\) 0.673485i 0.0482292i
\(196\) 11.1173 8.50914i 0.794093 0.607796i
\(197\) 6.30785i 0.449416i −0.974426 0.224708i \(-0.927857\pi\)
0.974426 0.224708i \(-0.0721428\pi\)
\(198\) −1.75983 + 1.28488i −0.125065 + 0.0913127i
\(199\) 11.9770 0.849030 0.424515 0.905421i \(-0.360445\pi\)
0.424515 + 0.905421i \(0.360445\pi\)
\(200\) −0.892871 2.68380i −0.0631355 0.189773i
\(201\) 4.52929i 0.319471i
\(202\) −14.5974 + 10.6578i −1.02707 + 0.749883i
\(203\) 5.86501 18.6938i 0.411643 1.31205i
\(204\) −0.653728 + 2.04443i −0.0457701 + 0.143139i
\(205\) 8.46264i 0.591056i
\(206\) −17.2970 + 12.6289i −1.20514 + 0.879895i
\(207\) 7.43471i 0.516748i
\(208\) −3.73896 2.66347i −0.259250 0.184678i
\(209\) 2.74117i 0.189611i
\(210\) 0.704530 + 2.07963i 0.0486172 + 0.143508i
\(211\) 10.8525 0.747120 0.373560 0.927606i \(-0.378137\pi\)
0.373560 + 0.927606i \(0.378137\pi\)
\(212\) 10.4579 + 3.34402i 0.718253 + 0.229668i
\(213\) −0.665785 −0.0456189
\(214\) 7.65515 5.58917i 0.523295 0.382068i
\(215\) −4.32314 −0.294836
\(216\) −8.90730 + 2.96336i −0.606065 + 0.201631i
\(217\) −11.9407 3.74628i −0.810588 0.254314i
\(218\) −9.35267 12.8098i −0.633443 0.867588i
\(219\) 1.04527 0.0706329
\(220\) −0.353414 + 1.10525i −0.0238272 + 0.0745159i
\(221\) 2.09884i 0.141183i
\(222\) 2.91684 2.12964i 0.195766 0.142932i
\(223\) −14.0737 −0.942445 −0.471223 0.882014i \(-0.656187\pi\)
−0.471223 + 0.882014i \(0.656187\pi\)
\(224\) 14.3317 + 4.31313i 0.957575 + 0.288183i
\(225\) 2.65563 0.177042
\(226\) 1.61061 1.17594i 0.107136 0.0782221i
\(227\) 14.9683i 0.993478i 0.867900 + 0.496739i \(0.165469\pi\)
−0.867900 + 0.496739i \(0.834531\pi\)
\(228\) 1.68887 5.28169i 0.111848 0.349788i
\(229\) 21.5684 1.42528 0.712641 0.701529i \(-0.247499\pi\)
0.712641 + 0.701529i \(0.247499\pi\)
\(230\) 2.33466 + 3.19765i 0.153943 + 0.210847i
\(231\) 0.269661 0.859503i 0.0177424 0.0565511i
\(232\) 19.8740 6.61187i 1.30479 0.434091i
\(233\) −19.5888 −1.28331 −0.641653 0.766995i \(-0.721751\pi\)
−0.641653 + 0.766995i \(0.721751\pi\)
\(234\) 3.48107 2.54160i 0.227565 0.166149i
\(235\) 3.56830 0.232770
\(236\) 25.3281 + 8.09891i 1.64872 + 0.527194i
\(237\) −5.87465 −0.381600
\(238\) 2.19559 + 6.48095i 0.142319 + 0.420098i
\(239\) 23.2562i 1.50432i 0.658981 + 0.752160i \(0.270988\pi\)
−0.658981 + 0.752160i \(0.729012\pi\)
\(240\) −1.36192 + 1.91185i −0.0879113 + 0.123409i
\(241\) 20.9056i 1.34665i −0.739347 0.673324i \(-0.764866\pi\)
0.739347 0.673324i \(-0.235134\pi\)
\(242\) −12.1795 + 8.89247i −0.782926 + 0.571629i
\(243\) 13.4890i 0.865321i
\(244\) 0.167624 0.524220i 0.0107311 0.0335597i
\(245\) 5.74543 + 3.99876i 0.367062 + 0.255471i
\(246\) −5.67224 + 4.14141i −0.361649 + 0.264047i
\(247\) 5.42225i 0.345009i
\(248\) −4.22334 12.6946i −0.268182 0.806105i
\(249\) −9.16813 −0.581007
\(250\) 1.14218 0.833926i 0.0722376 0.0527421i
\(251\) 3.33668i 0.210610i −0.994440 0.105305i \(-0.966418\pi\)
0.994440 0.105305i \(-0.0335818\pi\)
\(252\) −8.09034 + 11.4897i −0.509643 + 0.723780i
\(253\) 1.62430i 0.102119i
\(254\) −13.1012 17.9439i −0.822043 1.12590i
\(255\) −1.07320 −0.0672067
\(256\) 5.22790 + 15.1218i 0.326744 + 0.945113i
\(257\) 24.4200i 1.52328i 0.648002 + 0.761639i \(0.275605\pi\)
−0.648002 + 0.761639i \(0.724395\pi\)
\(258\) 2.11564 + 2.89767i 0.131714 + 0.180401i
\(259\) 3.44665 10.9857i 0.214164 0.682616i
\(260\) 0.699080 2.18627i 0.0433551 0.135587i
\(261\) 19.6654i 1.21726i
\(262\) 4.18422 + 5.73087i 0.258502 + 0.354054i
\(263\) 27.1113i 1.67176i 0.548915 + 0.835878i \(0.315041\pi\)
−0.548915 + 0.835878i \(0.684959\pi\)
\(264\) 0.913766 0.304000i 0.0562384 0.0187099i
\(265\) 5.48977i 0.337234i
\(266\) −5.67219 16.7432i −0.347785 1.02659i
\(267\) 9.00160 0.550889
\(268\) −4.70142 + 14.7030i −0.287185 + 0.898128i
\(269\) −18.5701 −1.13224 −0.566121 0.824322i \(-0.691556\pi\)
−0.566121 + 0.824322i \(0.691556\pi\)
\(270\) −2.76773 3.79079i −0.168438 0.230700i
\(271\) 12.9119 0.784344 0.392172 0.919892i \(-0.371724\pi\)
0.392172 + 0.919892i \(0.371724\pi\)
\(272\) −4.24427 + 5.95807i −0.257346 + 0.361261i
\(273\) −0.533409 + 1.70016i −0.0322834 + 0.102898i
\(274\) −16.9845 + 12.4007i −1.02607 + 0.749153i
\(275\) −0.580189 −0.0349867
\(276\) 1.00075 3.12970i 0.0602383 0.188386i
\(277\) 0.557017i 0.0334679i −0.999860 0.0167340i \(-0.994673\pi\)
0.999860 0.0167340i \(-0.00532683\pi\)
\(278\) 0.123898 + 0.169696i 0.00743091 + 0.0101777i
\(279\) 12.5613 0.752025
\(280\) 0.128378 + 7.48221i 0.00767203 + 0.447148i
\(281\) −27.3862 −1.63372 −0.816860 0.576835i \(-0.804287\pi\)
−0.816860 + 0.576835i \(0.804287\pi\)
\(282\) −1.74624 2.39172i −0.103987 0.142425i
\(283\) 5.24149i 0.311574i −0.987791 0.155787i \(-0.950209\pi\)
0.987791 0.155787i \(-0.0497914\pi\)
\(284\) −2.16127 0.691088i −0.128248 0.0410085i
\(285\) 2.77257 0.164233
\(286\) −0.760529 + 0.555277i −0.0449710 + 0.0328342i
\(287\) −6.70253 + 21.3633i −0.395638 + 1.26103i
\(288\) −15.0215 + 0.175541i −0.885148 + 0.0103439i
\(289\) 13.6555 0.803263
\(290\) 6.17537 + 8.45803i 0.362630 + 0.496673i
\(291\) −8.78840 −0.515185
\(292\) 3.39316 + 1.08500i 0.198570 + 0.0634947i
\(293\) 6.66098 0.389138 0.194569 0.980889i \(-0.437669\pi\)
0.194569 + 0.980889i \(0.437669\pi\)
\(294\) −0.131435 5.80787i −0.00766542 0.338722i
\(295\) 13.2957i 0.774107i
\(296\) 11.6792 3.88555i 0.678841 0.225843i
\(297\) 1.92560i 0.111735i
\(298\) −7.38435 10.1139i −0.427764 0.585882i
\(299\) 3.21299i 0.185812i
\(300\) −1.11791 0.357462i −0.0645424 0.0206381i
\(301\) 10.9134 + 3.42399i 0.629041 + 0.197355i
\(302\) −10.3350 14.1552i −0.594714 0.814543i
\(303\) 7.49993i 0.430860i
\(304\) 10.9648 15.3924i 0.628876 0.882812i
\(305\) 0.275184 0.0157570
\(306\) −4.05006 5.54712i −0.231527 0.317108i
\(307\) 17.0826i 0.974957i 0.873135 + 0.487479i \(0.162083\pi\)
−0.873135 + 0.487479i \(0.837917\pi\)
\(308\) 1.76754 2.51021i 0.100715 0.143032i
\(309\) 8.88694i 0.505560i
\(310\) 5.40258 3.94453i 0.306846 0.224034i
\(311\) 29.4721 1.67121 0.835604 0.549332i \(-0.185118\pi\)
0.835604 + 0.549332i \(0.185118\pi\)
\(312\) −1.80750 + 0.601335i −0.102329 + 0.0340439i
\(313\) 26.1624i 1.47879i 0.673275 + 0.739393i \(0.264887\pi\)
−0.673275 + 0.739393i \(0.735113\pi\)
\(314\) −17.8283 + 13.0168i −1.00611 + 0.734580i
\(315\) −6.70392 2.10329i −0.377723 0.118507i
\(316\) −19.0703 6.09792i −1.07279 0.343035i
\(317\) 5.72675i 0.321646i 0.986983 + 0.160823i \(0.0514149\pi\)
−0.986983 + 0.160823i \(0.948585\pi\)
\(318\) 3.67962 2.68656i 0.206343 0.150655i
\(319\) 4.29641i 0.240553i
\(320\) −6.40556 + 4.79257i −0.358082 + 0.267913i
\(321\) 3.93310i 0.219524i
\(322\) −3.36110 9.92131i −0.187307 0.552893i
\(323\) 8.64040 0.480765
\(324\) 3.66653 11.4665i 0.203696 0.637028i
\(325\) 1.14766 0.0636606
\(326\) −6.39745 + 4.67090i −0.354322 + 0.258697i
\(327\) −6.58148 −0.363957
\(328\) −22.7120 + 7.55604i −1.25406 + 0.417213i
\(329\) −9.00789 2.82614i −0.496621 0.155810i
\(330\) 0.283931 + 0.388882i 0.0156299 + 0.0214073i
\(331\) 17.6047 0.967641 0.483820 0.875167i \(-0.339249\pi\)
0.483820 + 0.875167i \(0.339249\pi\)
\(332\) −29.7616 9.51657i −1.63338 0.522289i
\(333\) 11.5566i 0.633299i
\(334\) 10.6788 7.79681i 0.584318 0.426622i
\(335\) −7.71818 −0.421689
\(336\) 4.95227 3.74766i 0.270168 0.204452i
\(337\) 24.3443 1.32612 0.663059 0.748567i \(-0.269258\pi\)
0.663059 + 0.748567i \(0.269258\pi\)
\(338\) −13.3439 + 9.74265i −0.725813 + 0.529930i
\(339\) 0.827507i 0.0449440i
\(340\) −3.48384 1.11399i −0.188938 0.0604147i
\(341\) −2.74434 −0.148614
\(342\) 10.4631 + 14.3307i 0.565780 + 0.774915i
\(343\) −11.3368 14.6450i −0.612131 0.790756i
\(344\) 3.86001 + 11.6025i 0.208118 + 0.625562i
\(345\) 1.64291 0.0884510
\(346\) 26.9217 19.6561i 1.44732 1.05672i
\(347\) 16.7400 0.898650 0.449325 0.893368i \(-0.351664\pi\)
0.449325 + 0.893368i \(0.351664\pi\)
\(348\) 2.64707 8.27831i 0.141898 0.443764i
\(349\) −14.2317 −0.761807 −0.380903 0.924615i \(-0.624387\pi\)
−0.380903 + 0.924615i \(0.624387\pi\)
\(350\) −3.54382 + 1.20056i −0.189425 + 0.0641727i
\(351\) 3.80898i 0.203308i
\(352\) 3.28182 0.0383515i 0.174922 0.00204414i
\(353\) 6.08004i 0.323608i −0.986823 0.161804i \(-0.948269\pi\)
0.986823 0.161804i \(-0.0517312\pi\)
\(354\) 8.91170 6.50660i 0.473651 0.345822i
\(355\) 1.13454i 0.0602150i
\(356\) 29.2210 + 9.34370i 1.54871 + 0.495215i
\(357\) 2.70922 + 0.849993i 0.143387 + 0.0449864i
\(358\) 22.5107 16.4355i 1.18973 0.868645i
\(359\) 16.3854i 0.864787i −0.901685 0.432394i \(-0.857669\pi\)
0.901685 0.432394i \(-0.142331\pi\)
\(360\) −2.37113 7.12717i −0.124970 0.375635i
\(361\) −3.32202 −0.174843
\(362\) −23.9974 + 17.5210i −1.26128 + 0.920882i
\(363\) 6.25763i 0.328441i
\(364\) −3.49633 + 4.96538i −0.183257 + 0.260257i
\(365\) 1.78121i 0.0932326i
\(366\) −0.134668 0.184447i −0.00703922 0.00964119i
\(367\) 13.1245 0.685092 0.342546 0.939501i \(-0.388711\pi\)
0.342546 + 0.939501i \(0.388711\pi\)
\(368\) 6.49729 9.12086i 0.338695 0.475458i
\(369\) 22.4736i 1.16993i
\(370\) 3.62904 + 4.97047i 0.188665 + 0.258402i
\(371\) 4.34798 13.8585i 0.225736 0.719498i
\(372\) −5.28778 1.69082i −0.274159 0.0876649i
\(373\) 0.552362i 0.0286002i −0.999898 0.0143001i \(-0.995448\pi\)
0.999898 0.0143001i \(-0.00455202\pi\)
\(374\) 0.884839 + 1.21191i 0.0457539 + 0.0626664i
\(375\) 0.586834i 0.0303040i
\(376\) −3.18603 9.57659i −0.164307 0.493875i
\(377\) 8.49862i 0.437701i
\(378\) 3.98456 + 11.7616i 0.204944 + 0.604953i
\(379\) −29.1600 −1.49785 −0.748925 0.662655i \(-0.769430\pi\)
−0.748925 + 0.662655i \(0.769430\pi\)
\(380\) 9.00031 + 2.87794i 0.461706 + 0.147635i
\(381\) −9.21933 −0.472320
\(382\) 14.1559 + 19.3885i 0.724280 + 0.992002i
\(383\) −5.89451 −0.301195 −0.150598 0.988595i \(-0.548120\pi\)
−0.150598 + 0.988595i \(0.548120\pi\)
\(384\) 6.34704 + 1.94808i 0.323896 + 0.0994124i
\(385\) 1.46464 + 0.459518i 0.0746451 + 0.0234192i
\(386\) 16.9551 12.3792i 0.862990 0.630085i
\(387\) −11.4807 −0.583594
\(388\) −28.5289 9.12240i −1.44834 0.463120i
\(389\) 13.5376i 0.686385i −0.939265 0.343192i \(-0.888492\pi\)
0.939265 0.343192i \(-0.111508\pi\)
\(390\) −0.561636 0.769239i −0.0284395 0.0389519i
\(391\) 5.11994 0.258926
\(392\) 5.60194 18.9900i 0.282941 0.959137i
\(393\) 2.94444 0.148527
\(394\) −5.26028 7.20468i −0.265009 0.362967i
\(395\) 10.0108i 0.503696i
\(396\) −0.938536 + 2.93513i −0.0471632 + 0.147496i
\(397\) −4.22501 −0.212047 −0.106024 0.994364i \(-0.533812\pi\)
−0.106024 + 0.994364i \(0.533812\pi\)
\(398\) 13.6799 9.98796i 0.685711 0.500651i
\(399\) −6.99913 2.19591i −0.350395 0.109933i
\(400\) −3.25791 2.32079i −0.162895 0.116039i
\(401\) 8.09225 0.404108 0.202054 0.979374i \(-0.435238\pi\)
0.202054 + 0.979374i \(0.435238\pi\)
\(402\) 3.77709 + 5.17325i 0.188384 + 0.258018i
\(403\) 5.42850 0.270413
\(404\) −7.78496 + 24.3463i −0.387316 + 1.21127i
\(405\) 6.01923 0.299098
\(406\) −8.89038 26.2426i −0.441222 1.30240i
\(407\) 2.52484i 0.125152i
\(408\) 0.958233 + 2.88027i 0.0474396 + 0.142594i
\(409\) 27.6608i 1.36774i −0.729605 0.683868i \(-0.760296\pi\)
0.729605 0.683868i \(-0.239704\pi\)
\(410\) −7.05721 9.66583i −0.348531 0.477361i
\(411\) 8.72637i 0.430440i
\(412\) −9.22468 + 28.8488i −0.454468 + 1.42128i
\(413\) 10.5304 33.5640i 0.518167 1.65158i
\(414\) 6.20000 + 8.49176i 0.304713 + 0.417347i
\(415\) 15.6230i 0.766905i
\(416\) −6.49169 + 0.0758621i −0.318281 + 0.00371944i
\(417\) 0.0871872 0.00426957
\(418\) −2.28593 3.13090i −0.111809 0.153138i
\(419\) 10.5982i 0.517755i −0.965910 0.258877i \(-0.916647\pi\)
0.965910 0.258877i \(-0.0833526\pi\)
\(420\) 2.53896 + 1.78778i 0.123888 + 0.0872349i
\(421\) 25.5951i 1.24743i −0.781652 0.623715i \(-0.785623\pi\)
0.781652 0.623715i \(-0.214377\pi\)
\(422\) 12.3955 9.05021i 0.603405 0.440557i
\(423\) 9.47606 0.460742
\(424\) 14.7335 4.90166i 0.715520 0.238046i
\(425\) 1.82880i 0.0887101i
\(426\) −0.760445 + 0.555215i −0.0368437 + 0.0269003i
\(427\) −0.694680 0.217949i −0.0336179 0.0105473i
\(428\) 4.08258 12.7676i 0.197339 0.617147i
\(429\) 0.390749i 0.0188655i
\(430\) −4.93780 + 3.60518i −0.238122 + 0.173857i
\(431\) 32.7406i 1.57706i −0.614997 0.788529i \(-0.710843\pi\)
0.614997 0.788529i \(-0.289157\pi\)
\(432\) −7.70249 + 10.8127i −0.370586 + 0.520227i
\(433\) 16.8933i 0.811840i 0.913909 + 0.405920i \(0.133049\pi\)
−0.913909 + 0.405920i \(0.866951\pi\)
\(434\) −16.7625 + 5.67874i −0.804626 + 0.272588i
\(435\) 4.34561 0.208356
\(436\) −21.3648 6.83161i −1.02319 0.327175i
\(437\) −13.2271 −0.632737
\(438\) 1.19389 0.871679i 0.0570461 0.0416504i
\(439\) −31.6749 −1.51176 −0.755881 0.654709i \(-0.772791\pi\)
−0.755881 + 0.654709i \(0.772791\pi\)
\(440\) 0.518034 + 1.55711i 0.0246963 + 0.0742324i
\(441\) 15.2577 + 10.6192i 0.726558 + 0.505676i
\(442\) −1.75028 2.39725i −0.0832522 0.114026i
\(443\) −12.8303 −0.609587 −0.304794 0.952418i \(-0.598587\pi\)
−0.304794 + 0.952418i \(0.598587\pi\)
\(444\) 1.55559 4.86486i 0.0738248 0.230876i
\(445\) 15.3393i 0.727151i
\(446\) −16.0747 + 11.7364i −0.761157 + 0.555736i
\(447\) −5.19637 −0.245780
\(448\) 19.9661 7.02519i 0.943311 0.331909i
\(449\) 9.10148 0.429525 0.214763 0.976666i \(-0.431102\pi\)
0.214763 + 0.976666i \(0.431102\pi\)
\(450\) 3.03319 2.21459i 0.142986 0.104397i
\(451\) 4.90993i 0.231200i
\(452\) 0.858956 2.68625i 0.0404019 0.126351i
\(453\) −7.27276 −0.341704
\(454\) 12.4824 + 17.0964i 0.585828 + 0.802373i
\(455\) −2.89717 0.908961i −0.135822 0.0426127i
\(456\) −2.47554 7.44101i −0.115928 0.348457i
\(457\) −5.29969 −0.247909 −0.123954 0.992288i \(-0.539558\pi\)
−0.123954 + 0.992288i \(0.539558\pi\)
\(458\) 24.6350 17.9865i 1.15112 0.840452i
\(459\) −6.06964 −0.283307
\(460\) 5.33320 + 1.70534i 0.248662 + 0.0795120i
\(461\) 0.755725 0.0351976 0.0175988 0.999845i \(-0.494398\pi\)
0.0175988 + 0.999845i \(0.494398\pi\)
\(462\) −0.408761 1.20658i −0.0190173 0.0561352i
\(463\) 3.99447i 0.185639i −0.995683 0.0928193i \(-0.970412\pi\)
0.995683 0.0928193i \(-0.0295879\pi\)
\(464\) 17.1859 24.1254i 0.797833 1.11999i
\(465\) 2.77577i 0.128723i
\(466\) −22.3739 + 16.3356i −1.03645 + 0.756733i
\(467\) 3.90589i 0.180743i −0.995908 0.0903716i \(-0.971195\pi\)
0.995908 0.0903716i \(-0.0288055\pi\)
\(468\) 1.85650 5.80591i 0.0858165 0.268378i
\(469\) 19.4839 + 6.11290i 0.899685 + 0.282268i
\(470\) 4.07563 2.97569i 0.187995 0.137259i
\(471\) 9.15992i 0.422067i
\(472\) 35.6830 11.8714i 1.64245 0.546423i
\(473\) 2.50824 0.115329
\(474\) −6.70989 + 4.89902i −0.308196 + 0.225020i
\(475\) 4.72462i 0.216780i
\(476\) 7.91239 + 5.57143i 0.362664 + 0.255366i
\(477\) 14.5788i 0.667517i
\(478\) 19.3940 + 26.5627i 0.887059 + 1.21495i
\(479\) 9.21055 0.420841 0.210420 0.977611i \(-0.432517\pi\)
0.210420 + 0.977611i \(0.432517\pi\)
\(480\) 0.0387907 + 3.31941i 0.00177054 + 0.151510i
\(481\) 4.99432i 0.227721i
\(482\) −17.4337 23.8779i −0.794084 1.08761i
\(483\) −4.14739 1.30120i −0.188713 0.0592068i
\(484\) −6.49545 + 20.3135i −0.295248 + 0.923343i
\(485\) 14.9759i 0.680023i
\(486\) −11.2488 15.4069i −0.510258 0.698869i
\(487\) 21.4403i 0.971552i −0.874083 0.485776i \(-0.838537\pi\)
0.874083 0.485776i \(-0.161463\pi\)
\(488\) −0.245703 0.738538i −0.0111225 0.0334320i
\(489\) 3.28692i 0.148640i
\(490\) 9.89696 0.223972i 0.447099 0.0101180i
\(491\) 19.6672 0.887570 0.443785 0.896133i \(-0.353635\pi\)
0.443785 + 0.896133i \(0.353635\pi\)
\(492\) −3.02507 + 9.46045i −0.136381 + 0.426510i
\(493\) 13.5426 0.609930
\(494\) 4.52175 + 6.19316i 0.203443 + 0.278644i
\(495\) −1.54077 −0.0692523
\(496\) −15.4101 10.9775i −0.691935 0.492904i
\(497\) −0.898570 + 2.86405i −0.0403064 + 0.128470i
\(498\) −10.4716 + 7.64554i −0.469245 + 0.342605i
\(499\) −12.2344 −0.547686 −0.273843 0.961774i \(-0.588295\pi\)
−0.273843 + 0.961774i \(0.588295\pi\)
\(500\) 0.609136 1.90498i 0.0272414 0.0851933i
\(501\) 5.48662i 0.245124i
\(502\) −2.78255 3.81108i −0.124191 0.170097i
\(503\) 5.42742 0.241997 0.120998 0.992653i \(-0.461390\pi\)
0.120998 + 0.992653i \(0.461390\pi\)
\(504\) 0.340923 + 19.8700i 0.0151859 + 0.885078i
\(505\) −12.7803 −0.568717
\(506\) −1.35455 1.85524i −0.0602170 0.0824755i
\(507\) 6.85591i 0.304482i
\(508\) −29.9278 9.56970i −1.32783 0.424587i
\(509\) −17.3838 −0.770522 −0.385261 0.922808i \(-0.625889\pi\)
−0.385261 + 0.922808i \(0.625889\pi\)
\(510\) −1.22579 + 0.894973i −0.0542789 + 0.0396301i
\(511\) 1.41074 4.49652i 0.0624074 0.198914i
\(512\) 18.5816 + 12.9121i 0.821201 + 0.570640i
\(513\) 15.6806 0.692315
\(514\) 20.3645 + 27.8920i 0.898238 + 1.23026i
\(515\) −15.1439 −0.667319
\(516\) 4.83288 + 1.54536i 0.212756 + 0.0680307i
\(517\) −2.07029 −0.0910511
\(518\) −5.22454 15.4218i −0.229553 0.677596i
\(519\) 13.8320i 0.607157i
\(520\) −1.02471 3.08008i −0.0449365 0.135071i
\(521\) 12.8139i 0.561388i −0.959797 0.280694i \(-0.909435\pi\)
0.959797 0.280694i \(-0.0905646\pi\)
\(522\) 16.3995 + 22.4614i 0.717786 + 0.983107i
\(523\) 8.05393i 0.352174i 0.984375 + 0.176087i \(0.0563439\pi\)
−0.984375 + 0.176087i \(0.943656\pi\)
\(524\) 9.55823 + 3.05634i 0.417553 + 0.133517i
\(525\) −0.464781 + 1.48142i −0.0202847 + 0.0646544i
\(526\) 22.6088 + 30.9659i 0.985792 + 1.35018i
\(527\) 8.65037i 0.376816i
\(528\) 0.790169 1.10923i 0.0343877 0.0482732i
\(529\) 15.1622 0.659226
\(530\) 4.57806 + 6.27029i 0.198858 + 0.272364i
\(531\) 35.3085i 1.53226i
\(532\) −20.4412 14.3935i −0.886239 0.624037i
\(533\) 9.71221i 0.420683i
\(534\) 10.2814 7.50666i 0.444921 0.324845i
\(535\) 6.70224 0.289763
\(536\) 6.89133 + 20.7140i 0.297660 + 0.894710i
\(537\) 11.5657i 0.499096i
\(538\) −21.2104 + 15.4861i −0.914445 + 0.667654i
\(539\) −3.33344 2.32004i −0.143581 0.0999310i
\(540\) −6.32247 2.02167i −0.272076 0.0869989i
\(541\) 15.9099i 0.684018i 0.939697 + 0.342009i \(0.111107\pi\)
−0.939697 + 0.342009i \(0.888893\pi\)
\(542\) 14.7477 10.7676i 0.633469 0.462508i
\(543\) 12.3295i 0.529110i
\(544\) 0.120887 + 10.3446i 0.00518299 + 0.443520i
\(545\) 11.2152i 0.480408i
\(546\) 0.808560 + 2.38671i 0.0346032 + 0.102142i
\(547\) −28.6893 −1.22667 −0.613333 0.789825i \(-0.710172\pi\)
−0.613333 + 0.789825i \(0.710172\pi\)
\(548\) −9.05802 + 28.3276i −0.386939 + 1.21009i
\(549\) 0.730785 0.0311891
\(550\) −0.662679 + 0.483835i −0.0282567 + 0.0206308i
\(551\) −34.9867 −1.49048
\(552\) −1.46690 4.40923i −0.0624355 0.187669i
\(553\) −7.92866 + 25.2714i −0.337161 + 1.07465i
\(554\) −0.464511 0.636212i −0.0197352 0.0270301i
\(555\) 2.55376 0.108401
\(556\) 0.283027 + 0.0905007i 0.0120030 + 0.00383808i
\(557\) 29.6910i 1.25805i −0.777386 0.629024i \(-0.783455\pi\)
0.777386 0.629024i \(-0.216545\pi\)
\(558\) 14.3472 10.4752i 0.607366 0.443450i
\(559\) −4.96149 −0.209849
\(560\) 6.38624 + 8.43895i 0.269868 + 0.356611i
\(561\) 0.622662 0.0262888
\(562\) −31.2798 + 22.8380i −1.31946 + 0.963363i
\(563\) 25.7978i 1.08725i 0.839329 + 0.543624i \(0.182948\pi\)
−0.839329 + 0.543624i \(0.817052\pi\)
\(564\) −3.98903 1.27553i −0.167968 0.0537095i
\(565\) 1.41012 0.0593242
\(566\) −4.37101 5.98671i −0.183727 0.251640i
\(567\) −15.1951 4.76731i −0.638133 0.200208i
\(568\) −3.04487 + 1.01300i −0.127760 + 0.0425044i
\(569\) −6.17604 −0.258913 −0.129457 0.991585i \(-0.541323\pi\)
−0.129457 + 0.991585i \(0.541323\pi\)
\(570\) 3.16676 2.31211i 0.132641 0.0968438i
\(571\) −44.7626 −1.87326 −0.936628 0.350325i \(-0.886071\pi\)
−0.936628 + 0.350325i \(0.886071\pi\)
\(572\) −0.405599 + 1.26845i −0.0169589 + 0.0530365i
\(573\) 9.96153 0.416149
\(574\) 10.1599 + 29.9901i 0.424067 + 1.25176i
\(575\) 2.79961i 0.116752i
\(576\) −17.0108 + 12.7273i −0.708783 + 0.530303i
\(577\) 45.0609i 1.87591i −0.346760 0.937954i \(-0.612718\pi\)
0.346760 0.937954i \(-0.387282\pi\)
\(578\) 15.5970 11.3876i 0.648748 0.473664i
\(579\) 8.71126i 0.362028i
\(580\) 14.1067 + 4.51077i 0.585750 + 0.187299i
\(581\) −12.3737 + 39.4392i −0.513346 + 1.63621i
\(582\) −10.0379 + 7.32887i −0.416084 + 0.303791i
\(583\) 3.18511i 0.131914i
\(584\) 4.78040 1.59039i 0.197814 0.0658107i
\(585\) 3.04775 0.126009
\(586\) 7.60801 5.55476i 0.314284 0.229465i
\(587\) 0.738708i 0.0304897i 0.999884 + 0.0152449i \(0.00485278\pi\)
−0.999884 + 0.0152449i \(0.995147\pi\)
\(588\) −4.99345 6.52401i −0.205927 0.269046i
\(589\) 22.3478i 0.920824i
\(590\) 11.0876 + 15.1861i 0.456471 + 0.625200i
\(591\) −3.70166 −0.152266
\(592\) 10.0995 14.1776i 0.415086 0.582696i
\(593\) 5.51961i 0.226663i 0.993557 + 0.113332i \(0.0361522\pi\)
−0.993557 + 0.113332i \(0.963848\pi\)
\(594\) 1.60581 + 2.19937i 0.0658870 + 0.0902414i
\(595\) −1.44844 + 4.61668i −0.0593802 + 0.189265i
\(596\) −16.8685 5.39386i −0.690959 0.220941i
\(597\) 7.02853i 0.287659i
\(598\) 2.67940 + 3.66981i 0.109569 + 0.150070i
\(599\) 0.145815i 0.00595785i −0.999996 0.00297893i \(-0.999052\pi\)
0.999996 0.00297893i \(-0.000948223\pi\)
\(600\) −1.57494 + 0.523967i −0.0642969 + 0.0213909i
\(601\) 21.7269i 0.886257i 0.896458 + 0.443128i \(0.146131\pi\)
−0.896458 + 0.443128i \(0.853869\pi\)
\(602\) 15.3204 5.19020i 0.624415 0.211537i
\(603\) −20.4966 −0.834686
\(604\) −23.6088 7.54916i −0.960630 0.307171i
\(605\) −10.6634 −0.433528
\(606\) 6.25438 + 8.56624i 0.254067 + 0.347980i
\(607\) 18.6456 0.756804 0.378402 0.925641i \(-0.376474\pi\)
0.378402 + 0.925641i \(0.376474\pi\)
\(608\) −0.312305 26.7247i −0.0126656 1.08383i
\(609\) −10.9702 3.44179i −0.444534 0.139468i
\(610\) 0.314309 0.229483i 0.0127260 0.00929148i
\(611\) 4.09518 0.165673
\(612\) −9.25177 2.95834i −0.373981 0.119584i
\(613\) 47.1735i 1.90532i 0.304041 + 0.952659i \(0.401664\pi\)
−0.304041 + 0.952659i \(0.598336\pi\)
\(614\) 14.2456 + 19.5114i 0.574907 + 0.787415i
\(615\) −4.96616 −0.200255
\(616\) −0.0744833 4.34110i −0.00300102 0.174908i
\(617\) 16.2076 0.652493 0.326246 0.945285i \(-0.394216\pi\)
0.326246 + 0.945285i \(0.394216\pi\)
\(618\) 7.41105 + 10.1505i 0.298116 + 0.408311i
\(619\) 30.2319i 1.21512i −0.794273 0.607561i \(-0.792148\pi\)
0.794273 0.607561i \(-0.207852\pi\)
\(620\) 2.88126 9.01069i 0.115714 0.361878i
\(621\) 9.29166 0.372861
\(622\) 33.6623 24.5775i 1.34974 0.985469i
\(623\) 12.1489 38.7228i 0.486736 1.55140i
\(624\) −1.56301 + 2.19415i −0.0625706 + 0.0878363i
\(625\) 1.00000 0.0400000
\(626\) 21.8175 + 29.8821i 0.872002 + 1.19433i
\(627\) −1.60861 −0.0642418
\(628\) −9.50804 + 29.7349i −0.379412 + 1.18655i
\(629\) 7.95850 0.317326
\(630\) −9.41106 + 3.18824i −0.374945 + 0.127023i
\(631\) 6.27504i 0.249806i 0.992169 + 0.124903i \(0.0398619\pi\)
−0.992169 + 0.124903i \(0.960138\pi\)
\(632\) −26.8669 + 8.93831i −1.06871 + 0.355547i
\(633\) 6.36864i 0.253131i
\(634\) 4.77569 + 6.54096i 0.189667 + 0.259775i
\(635\) 15.7103i 0.623443i
\(636\) 1.96239 6.13706i 0.0778136 0.243350i
\(637\) 6.59379 + 4.58920i 0.261255 + 0.181831i
\(638\) −3.58288 4.90726i −0.141848 0.194280i
\(639\) 3.01291i 0.119189i
\(640\) −3.31964 + 10.8157i −0.131220 + 0.427529i
\(641\) −0.954180 −0.0376878 −0.0188439 0.999822i \(-0.505999\pi\)
−0.0188439 + 0.999822i \(0.505999\pi\)
\(642\) −3.27991 4.49230i −0.129448 0.177297i
\(643\) 29.7150i 1.17184i 0.810367 + 0.585922i \(0.199268\pi\)
−0.810367 + 0.585922i \(0.800732\pi\)
\(644\) −12.1126 8.52898i −0.477303 0.336089i
\(645\) 2.53697i 0.0998930i
\(646\) 9.86887 7.20545i 0.388286 0.283495i
\(647\) 22.3760 0.879693 0.439846 0.898073i \(-0.355033\pi\)
0.439846 + 0.898073i \(0.355033\pi\)
\(648\) −5.37439 16.1544i −0.211126 0.634605i
\(649\) 7.71403i 0.302802i
\(650\) 1.31083 0.957061i 0.0514149 0.0375390i
\(651\) −2.19844 + 7.00721i −0.0861638 + 0.274634i
\(652\) −3.41184 + 10.6700i −0.133618 + 0.417869i
\(653\) 3.18538i 0.124653i 0.998056 + 0.0623267i \(0.0198521\pi\)
−0.998056 + 0.0623267i \(0.980148\pi\)
\(654\) −7.51721 + 5.48846i −0.293946 + 0.214616i
\(655\) 5.01749i 0.196050i
\(656\) −19.6400 + 27.5705i −0.766812 + 1.07645i
\(657\) 4.73022i 0.184543i
\(658\) −12.6454 + 4.28396i −0.492969 + 0.167006i
\(659\) −1.50751 −0.0587242 −0.0293621 0.999569i \(-0.509348\pi\)
−0.0293621 + 0.999569i \(0.509348\pi\)
\(660\) 0.648598 + 0.207396i 0.0252466 + 0.00807286i
\(661\) 11.0607 0.430210 0.215105 0.976591i \(-0.430991\pi\)
0.215105 + 0.976591i \(0.430991\pi\)
\(662\) 20.1077 14.6810i 0.781506 0.570593i
\(663\) −1.23167 −0.0478342
\(664\) −41.9291 + 13.9494i −1.62717 + 0.541340i
\(665\) 3.74196 11.9269i 0.145107 0.462507i
\(666\) 9.63736 + 13.1997i 0.373440 + 0.511478i
\(667\) −20.7316 −0.802731
\(668\) 5.69513 17.8107i 0.220351 0.689115i
\(669\) 8.25893i 0.319309i
\(670\) −8.81552 + 6.43638i −0.340573 + 0.248659i
\(671\) −0.159659 −0.00616355
\(672\) 2.53109 8.41031i 0.0976390 0.324435i
\(673\) 31.5781 1.21725 0.608624 0.793459i \(-0.291722\pi\)
0.608624 + 0.793459i \(0.291722\pi\)
\(674\) 27.8055 20.3013i 1.07103 0.781977i
\(675\) 3.31891i 0.127745i
\(676\) −7.11647 + 22.2557i −0.273710 + 0.855987i
\(677\) 5.96254 0.229159 0.114580 0.993414i \(-0.463448\pi\)
0.114580 + 0.993414i \(0.463448\pi\)
\(678\) −0.690079 0.945159i −0.0265023 0.0362986i
\(679\) −11.8612 + 37.8056i −0.455189 + 1.45085i
\(680\) −4.90815 + 1.63289i −0.188219 + 0.0626183i
\(681\) 8.78388 0.336599
\(682\) −3.13452 + 2.28857i −0.120027 + 0.0876339i
\(683\) 32.0466 1.22623 0.613114 0.789994i \(-0.289916\pi\)
0.613114 + 0.789994i \(0.289916\pi\)
\(684\) 23.9015 + 7.64272i 0.913895 + 0.292227i
\(685\) −14.8703 −0.568163
\(686\) −25.1615 7.27313i −0.960671 0.277689i
\(687\) 12.6571i 0.482898i
\(688\) 14.0844 + 10.0331i 0.536963 + 0.382508i
\(689\) 6.30038i 0.240026i
\(690\) 1.87649 1.37006i 0.0714367 0.0521573i
\(691\) 17.0740i 0.649526i −0.945795 0.324763i \(-0.894715\pi\)
0.945795 0.324763i \(-0.105285\pi\)
\(692\) 14.3577 44.9015i 0.545797 1.70690i
\(693\) 3.88955 + 1.22031i 0.147752 + 0.0463557i
\(694\) 19.1200 13.9599i 0.725787 0.529911i
\(695\) 0.148572i 0.00563566i
\(696\) −3.88007 11.6628i −0.147074 0.442076i
\(697\) −15.4765 −0.586215
\(698\) −16.2551 + 11.8682i −0.615266 + 0.449218i
\(699\) 11.4954i 0.434796i
\(700\) −3.04649 + 4.32653i −0.115146 + 0.163528i
\(701\) 32.7289i 1.23615i −0.786118 0.618076i \(-0.787912\pi\)
0.786118 0.618076i \(-0.212088\pi\)
\(702\) −3.17640 4.35053i −0.119886 0.164200i
\(703\) −20.5604 −0.775449
\(704\) 3.71644 2.78060i 0.140069 0.104798i
\(705\) 2.09400i 0.0788645i
\(706\) −5.07030 6.94448i −0.190823 0.261359i
\(707\) 32.2629 + 10.1222i 1.21337 + 0.380684i
\(708\) 4.75271 14.8634i 0.178618 0.558600i
\(709\) 20.9447i 0.786594i −0.919412 0.393297i \(-0.871334\pi\)
0.919412 0.393297i \(-0.128666\pi\)
\(710\) −0.946120 1.29584i −0.0355073 0.0486321i
\(711\) 26.5848i 0.997009i
\(712\) 41.1675 13.6960i 1.54282 0.513279i
\(713\) 13.2423i 0.495930i
\(714\) 3.80324 1.28845i 0.142333 0.0482190i
\(715\) −0.665859 −0.0249017
\(716\) 12.0052 37.5446i 0.448657 1.40311i
\(717\) 13.6475 0.509677
\(718\) −13.6642 18.7150i −0.509943 0.698438i
\(719\) −0.417030 −0.0155526 −0.00777630 0.999970i \(-0.502475\pi\)
−0.00777630 + 0.999970i \(0.502475\pi\)
\(720\) −8.65178 6.16314i −0.322433 0.229687i
\(721\) 38.2295 + 11.9942i 1.42374 + 0.446686i
\(722\) −3.79433 + 2.77032i −0.141210 + 0.103100i
\(723\) −12.2681 −0.456256
\(724\) −12.7981 + 40.0241i −0.475638 + 1.48748i
\(725\) 7.40518i 0.275022i
\(726\) 5.21840 + 7.14733i 0.193673 + 0.265262i
\(727\) 4.48987 0.166520 0.0832601 0.996528i \(-0.473467\pi\)
0.0832601 + 0.996528i \(0.473467\pi\)
\(728\) 0.147334 + 8.58702i 0.00546055 + 0.318256i
\(729\) 10.1419 0.375624
\(730\) 1.48539 + 2.03445i 0.0549769 + 0.0752984i
\(731\) 7.90619i 0.292421i
\(732\) −0.307630 0.0983677i −0.0113703 0.00363578i
\(733\) 22.8948 0.845640 0.422820 0.906214i \(-0.361040\pi\)
0.422820 + 0.906214i \(0.361040\pi\)
\(734\) 14.9905 10.9448i 0.553308 0.403981i
\(735\) 2.34661 3.37161i 0.0865559 0.124364i
\(736\) −0.185059 15.8359i −0.00682135 0.583719i
\(737\) 4.47800 0.164949
\(738\) −18.7413 25.6688i −0.689877 0.944883i
\(739\) −0.354985 −0.0130583 −0.00652917 0.999979i \(-0.502078\pi\)
−0.00652917 + 0.999979i \(0.502078\pi\)
\(740\) 8.29000 + 2.65081i 0.304747 + 0.0974457i
\(741\) 3.18196 0.116892
\(742\) −6.59081 19.4548i −0.241956 0.714207i
\(743\) 6.75171i 0.247696i −0.992301 0.123848i \(-0.960476\pi\)
0.992301 0.123848i \(-0.0395235\pi\)
\(744\) −7.44960 + 2.47840i −0.273116 + 0.0908626i
\(745\) 8.85493i 0.324419i
\(746\) −0.460629 0.630896i −0.0168648 0.0230987i
\(747\) 41.4890i 1.51800i
\(748\) 2.02129 + 0.646326i 0.0739055 + 0.0236320i
\(749\) −16.9193 5.30827i −0.618218 0.193960i
\(750\) −0.489376 0.670268i −0.0178695 0.0244747i
\(751\) 27.4120i 1.00028i 0.865945 + 0.500139i \(0.166718\pi\)
−0.865945 + 0.500139i \(0.833282\pi\)
\(752\) −11.6252 8.28125i −0.423926 0.301986i
\(753\) −1.95808 −0.0713564
\(754\) 7.08721 + 9.70693i 0.258101 + 0.353505i
\(755\) 12.3932i 0.451035i
\(756\) 14.3594 + 10.1110i 0.522246 + 0.367735i
\(757\) 27.6550i 1.00514i 0.864537 + 0.502570i \(0.167612\pi\)
−0.864537 + 0.502570i \(0.832388\pi\)
\(758\) −33.3059 + 24.3173i −1.20973 + 0.883244i
\(759\) −0.953196 −0.0345988
\(760\) 12.6799 4.21847i 0.459949 0.153020i
\(761\) 14.1083i 0.511424i −0.966753 0.255712i \(-0.917690\pi\)
0.966753 0.255712i \(-0.0823099\pi\)
\(762\) −10.5301 + 7.68823i −0.381465 + 0.278515i
\(763\) −8.88262 + 28.3120i −0.321572 + 1.02496i
\(764\) 32.3371 + 10.3401i 1.16992 + 0.374092i
\(765\) 4.85662i 0.175592i
\(766\) −6.73258 + 4.91558i −0.243258 + 0.177607i
\(767\) 15.2589i 0.550968i
\(768\) 8.87399 3.06791i 0.320213 0.110704i
\(769\) 2.82610i 0.101912i −0.998701 0.0509558i \(-0.983773\pi\)
0.998701 0.0509558i \(-0.0162268\pi\)
\(770\) 2.05609 0.696553i 0.0740962 0.0251020i
\(771\) 14.3305 0.516100
\(772\) 9.04233 28.2785i 0.325441 1.01777i
\(773\) −44.5587 −1.60266 −0.801332 0.598220i \(-0.795875\pi\)
−0.801332 + 0.598220i \(0.795875\pi\)
\(774\) −13.1129 + 9.57401i −0.471335 + 0.344131i
\(775\) 4.73007 0.169909
\(776\) −40.1925 + 13.3716i −1.44282 + 0.480012i
\(777\) −6.44676 2.02261i −0.231276 0.0725607i
\(778\) −11.2894 15.4624i −0.404743 0.554352i
\(779\) 39.9827