Properties

Label 625.2.e.a.249.2
Level $625$
Weight $2$
Character 625.249
Analytic conductor $4.991$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 625 = 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 625.e (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.99065012633\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: 8.0.58140625.2
Defining polynomial: \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 25)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 249.2
Root \(1.17421 - 0.0566033i\) of defining polynomial
Character \(\chi\) \(=\) 625.249
Dual form 625.2.e.a.374.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.107666 - 0.148189i) q^{2} +(1.39991 - 0.454857i) q^{3} +(0.607666 + 1.87020i) q^{4} +(0.0833172 - 0.256424i) q^{6} +3.26086i q^{7} +(0.690983 + 0.224514i) q^{8} +(-0.674207 + 0.489840i) q^{9} +O(q^{10})\) \(q+(0.107666 - 0.148189i) q^{2} +(1.39991 - 0.454857i) q^{3} +(0.607666 + 1.87020i) q^{4} +(0.0833172 - 0.256424i) q^{6} +3.26086i q^{7} +(0.690983 + 0.224514i) q^{8} +(-0.674207 + 0.489840i) q^{9} +(-1.61803 - 1.17557i) q^{11} +(1.70135 + 2.34171i) q^{12} +(0.174207 + 0.239775i) q^{13} +(0.483224 + 0.351083i) q^{14} +(-3.07411 + 2.23347i) q^{16} +(4.91027 + 1.59545i) q^{17} +0.152649i q^{18} +(-0.534717 + 1.64569i) q^{19} +(1.48322 + 4.56489i) q^{21} +(-0.348414 + 0.113207i) q^{22} +(0.516776 - 0.711281i) q^{23} +1.06943 q^{24} +0.0542883 q^{26} +(-3.31659 + 4.56489i) q^{27} +(-6.09846 + 1.98151i) q^{28} +(-1.82696 - 5.62280i) q^{29} +(1.88486 - 5.80100i) q^{31} +2.14910i q^{32} +(-2.79981 - 0.909715i) q^{33} +(0.765097 - 0.555875i) q^{34} +(-1.32579 - 0.963245i) q^{36} +(4.75401 + 6.54333i) q^{37} +(0.186303 + 0.256424i) q^{38} +(0.352937 + 0.256424i) q^{39} +(0.821270 - 0.596687i) q^{41} +(0.836161 + 0.271685i) q^{42} -3.24199i q^{43} +(1.21533 - 3.74041i) q^{44} +(-0.0497651 - 0.153161i) q^{46} +(4.01342 - 1.30404i) q^{47} +(-3.28756 + 4.52494i) q^{48} -3.63318 q^{49} +7.59963 q^{51} +(-0.342569 + 0.471506i) q^{52} +(7.70424 - 2.50326i) q^{53} +(0.319385 + 0.982966i) q^{54} +(-0.732108 + 2.25320i) q^{56} +2.54703i q^{57} +(-1.02994 - 0.334648i) q^{58} +(4.80261 - 3.48930i) q^{59} +(-0.740748 - 0.538185i) q^{61} +(-0.656711 - 0.903885i) q^{62} +(-1.59730 - 2.19849i) q^{63} +(-5.82975 - 4.23556i) q^{64} +(-0.436254 + 0.316957i) q^{66} +(-6.55093 - 2.12853i) q^{67} +10.1527i q^{68} +(0.399907 - 1.23079i) q^{69} +(-1.84445 - 5.67664i) q^{71} +(-0.575842 + 0.187102i) q^{72} +(5.19215 - 7.14638i) q^{73} +1.48150 q^{74} -3.40270 q^{76} +(3.83337 - 5.27618i) q^{77} +(0.0759986 - 0.0246934i) q^{78} +(2.39818 + 7.38084i) q^{79} +(-1.79397 + 5.52127i) q^{81} -0.185946i q^{82} +(13.8049 + 4.48550i) q^{83} +(-7.63597 + 5.54786i) q^{84} +(-0.480429 - 0.349052i) q^{86} +(-5.11514 - 7.04039i) q^{87} +(-0.854102 - 1.17557i) q^{88} +(6.08901 + 4.42392i) q^{89} +(-0.781873 + 0.568064i) q^{91} +(1.64427 + 0.534255i) q^{92} -8.97820i q^{93} +(0.238863 - 0.735146i) q^{94} +(0.977536 + 3.00855i) q^{96} +(-6.39727 + 2.07860i) q^{97} +(-0.391169 + 0.538398i) q^{98} +1.66673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 5 q^{3} + 4 q^{4} + 6 q^{6} + 10 q^{8} + q^{9} - 4 q^{11} + 10 q^{12} - 5 q^{13} - 7 q^{14} - 2 q^{16} + 15 q^{17} + 10 q^{19} + q^{21} + 10 q^{22} + 15 q^{23} - 20 q^{24} + 6 q^{26} - 5 q^{27} - 20 q^{28} + 15 q^{29} + q^{31} + 10 q^{33} - 12 q^{34} - 17 q^{36} - 5 q^{37} + 12 q^{39} - 9 q^{41} + 5 q^{42} + 8 q^{44} + 16 q^{46} - 15 q^{47} - 5 q^{48} + 14 q^{49} - 4 q^{51} - 20 q^{52} + 35 q^{53} - 10 q^{54} - 15 q^{56} - 20 q^{58} + 15 q^{59} + 6 q^{61} + 45 q^{62} - 20 q^{63} - 26 q^{64} - 18 q^{66} - 13 q^{69} - 29 q^{71} + 5 q^{72} + 10 q^{73} - 12 q^{74} - 20 q^{76} + 20 q^{77} - 25 q^{78} - 10 q^{79} - 12 q^{81} + 15 q^{83} - 27 q^{84} + 16 q^{86} - 55 q^{87} + 20 q^{88} + 40 q^{89} + q^{91} - 5 q^{92} - 7 q^{94} + 11 q^{96} - 10 q^{97} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{10}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.107666 0.148189i 0.0761313 0.104786i −0.769253 0.638944i \(-0.779371\pi\)
0.845384 + 0.534159i \(0.179371\pi\)
\(3\) 1.39991 0.454857i 0.808237 0.262612i 0.124386 0.992234i \(-0.460304\pi\)
0.683851 + 0.729622i \(0.260304\pi\)
\(4\) 0.607666 + 1.87020i 0.303833 + 0.935102i
\(5\) 0 0
\(6\) 0.0833172 0.256424i 0.0340141 0.104685i
\(7\) 3.26086i 1.23249i 0.787555 + 0.616244i \(0.211346\pi\)
−0.787555 + 0.616244i \(0.788654\pi\)
\(8\) 0.690983 + 0.224514i 0.244299 + 0.0793777i
\(9\) −0.674207 + 0.489840i −0.224736 + 0.163280i
\(10\) 0 0
\(11\) −1.61803 1.17557i −0.487856 0.354448i 0.316503 0.948591i \(-0.397491\pi\)
−0.804359 + 0.594144i \(0.797491\pi\)
\(12\) 1.70135 + 2.34171i 0.491138 + 0.675993i
\(13\) 0.174207 + 0.239775i 0.0483163 + 0.0665017i 0.832492 0.554038i \(-0.186914\pi\)
−0.784175 + 0.620539i \(0.786914\pi\)
\(14\) 0.483224 + 0.351083i 0.129147 + 0.0938308i
\(15\) 0 0
\(16\) −3.07411 + 2.23347i −0.768528 + 0.558369i
\(17\) 4.91027 + 1.59545i 1.19092 + 0.386952i 0.836412 0.548102i \(-0.184649\pi\)
0.354505 + 0.935054i \(0.384649\pi\)
\(18\) 0.152649i 0.0359798i
\(19\) −0.534717 + 1.64569i −0.122672 + 0.377547i −0.993470 0.114095i \(-0.963603\pi\)
0.870797 + 0.491642i \(0.163603\pi\)
\(20\) 0 0
\(21\) 1.48322 + 4.56489i 0.323666 + 0.996142i
\(22\) −0.348414 + 0.113207i −0.0742821 + 0.0241357i
\(23\) 0.516776 0.711281i 0.107755 0.148312i −0.751734 0.659467i \(-0.770782\pi\)
0.859489 + 0.511155i \(0.170782\pi\)
\(24\) 1.06943 0.218297
\(25\) 0 0
\(26\) 0.0542883 0.0106468
\(27\) −3.31659 + 4.56489i −0.638278 + 0.878514i
\(28\) −6.09846 + 1.98151i −1.15250 + 0.374470i
\(29\) −1.82696 5.62280i −0.339258 1.04413i −0.964587 0.263766i \(-0.915035\pi\)
0.625329 0.780361i \(-0.284965\pi\)
\(30\) 0 0
\(31\) 1.88486 5.80100i 0.338531 1.04189i −0.626426 0.779481i \(-0.715483\pi\)
0.964957 0.262409i \(-0.0845170\pi\)
\(32\) 2.14910i 0.379912i
\(33\) −2.79981 0.909715i −0.487385 0.158361i
\(34\) 0.765097 0.555875i 0.131213 0.0953318i
\(35\) 0 0
\(36\) −1.32579 0.963245i −0.220965 0.160541i
\(37\) 4.75401 + 6.54333i 0.781554 + 1.07572i 0.995109 + 0.0987860i \(0.0314959\pi\)
−0.213554 + 0.976931i \(0.568504\pi\)
\(38\) 0.186303 + 0.256424i 0.0302223 + 0.0415974i
\(39\) 0.352937 + 0.256424i 0.0565152 + 0.0410607i
\(40\) 0 0
\(41\) 0.821270 0.596687i 0.128261 0.0931869i −0.521805 0.853065i \(-0.674741\pi\)
0.650066 + 0.759878i \(0.274741\pi\)
\(42\) 0.836161 + 0.271685i 0.129022 + 0.0419219i
\(43\) 3.24199i 0.494399i −0.968965 0.247200i \(-0.920490\pi\)
0.968965 0.247200i \(-0.0795103\pi\)
\(44\) 1.21533 3.74041i 0.183218 0.563887i
\(45\) 0 0
\(46\) −0.0497651 0.153161i −0.00733747 0.0225824i
\(47\) 4.01342 1.30404i 0.585417 0.190214i −0.00130878 0.999999i \(-0.500417\pi\)
0.586726 + 0.809786i \(0.300417\pi\)
\(48\) −3.28756 + 4.52494i −0.474519 + 0.653119i
\(49\) −3.63318 −0.519026
\(50\) 0 0
\(51\) 7.59963 1.06416
\(52\) −0.342569 + 0.471506i −0.0475058 + 0.0653861i
\(53\) 7.70424 2.50326i 1.05826 0.343849i 0.272355 0.962197i \(-0.412198\pi\)
0.785905 + 0.618348i \(0.212198\pi\)
\(54\) 0.319385 + 0.982966i 0.0434628 + 0.133765i
\(55\) 0 0
\(56\) −0.732108 + 2.25320i −0.0978320 + 0.301096i
\(57\) 2.54703i 0.337363i
\(58\) −1.02994 0.334648i −0.135238 0.0439414i
\(59\) 4.80261 3.48930i 0.625246 0.454268i −0.229504 0.973308i \(-0.573710\pi\)
0.854750 + 0.519040i \(0.173710\pi\)
\(60\) 0 0
\(61\) −0.740748 0.538185i −0.0948431 0.0689075i 0.539353 0.842080i \(-0.318669\pi\)
−0.634196 + 0.773172i \(0.718669\pi\)
\(62\) −0.656711 0.903885i −0.0834024 0.114794i
\(63\) −1.59730 2.19849i −0.201241 0.276984i
\(64\) −5.82975 4.23556i −0.728719 0.529445i
\(65\) 0 0
\(66\) −0.436254 + 0.316957i −0.0536992 + 0.0390147i
\(67\) −6.55093 2.12853i −0.800323 0.260041i −0.119829 0.992794i \(-0.538235\pi\)
−0.680494 + 0.732754i \(0.738235\pi\)
\(68\) 10.1527i 1.23120i
\(69\) 0.399907 1.23079i 0.0481431 0.148169i
\(70\) 0 0
\(71\) −1.84445 5.67664i −0.218896 0.673694i −0.998854 0.0478614i \(-0.984759\pi\)
0.779958 0.625832i \(-0.215241\pi\)
\(72\) −0.575842 + 0.187102i −0.0678636 + 0.0220502i
\(73\) 5.19215 7.14638i 0.607695 0.836420i −0.388690 0.921368i \(-0.627072\pi\)
0.996385 + 0.0849481i \(0.0270724\pi\)
\(74\) 1.48150 0.172220
\(75\) 0 0
\(76\) −3.40270 −0.390317
\(77\) 3.83337 5.27618i 0.436853 0.601276i
\(78\) 0.0759986 0.0246934i 0.00860514 0.00279598i
\(79\) 2.39818 + 7.38084i 0.269816 + 0.830409i 0.990545 + 0.137191i \(0.0438075\pi\)
−0.720728 + 0.693218i \(0.756192\pi\)
\(80\) 0 0
\(81\) −1.79397 + 5.52127i −0.199330 + 0.613474i
\(82\) 0.185946i 0.0205343i
\(83\) 13.8049 + 4.48550i 1.51529 + 0.492347i 0.944433 0.328703i \(-0.106612\pi\)
0.570856 + 0.821050i \(0.306612\pi\)
\(84\) −7.63597 + 5.54786i −0.833153 + 0.605321i
\(85\) 0 0
\(86\) −0.480429 0.349052i −0.0518059 0.0376392i
\(87\) −5.11514 7.04039i −0.548401 0.754809i
\(88\) −0.854102 1.17557i −0.0910476 0.125316i
\(89\) 6.08901 + 4.42392i 0.645433 + 0.468935i 0.861713 0.507397i \(-0.169392\pi\)
−0.216279 + 0.976332i \(0.569392\pi\)
\(90\) 0 0
\(91\) −0.781873 + 0.568064i −0.0819625 + 0.0595493i
\(92\) 1.64427 + 0.534255i 0.171427 + 0.0556999i
\(93\) 8.97820i 0.930996i
\(94\) 0.238863 0.735146i 0.0246369 0.0758245i
\(95\) 0 0
\(96\) 0.977536 + 3.00855i 0.0997694 + 0.307058i
\(97\) −6.39727 + 2.07860i −0.649544 + 0.211050i −0.615213 0.788361i \(-0.710930\pi\)
−0.0343310 + 0.999411i \(0.510930\pi\)
\(98\) −0.391169 + 0.538398i −0.0395141 + 0.0543865i
\(99\) 1.66673 0.167513
\(100\) 0 0
\(101\) −12.1955 −1.21350 −0.606748 0.794894i \(-0.707526\pi\)
−0.606748 + 0.794894i \(0.707526\pi\)
\(102\) 0.818220 1.12618i 0.0810159 0.111509i
\(103\) −1.31379 + 0.426878i −0.129452 + 0.0420615i −0.373027 0.927821i \(-0.621680\pi\)
0.243575 + 0.969882i \(0.421680\pi\)
\(104\) 0.0665412 + 0.204793i 0.00652490 + 0.0200816i
\(105\) 0 0
\(106\) 0.458527 1.41120i 0.0445361 0.137068i
\(107\) 15.8285i 1.53020i −0.643911 0.765101i \(-0.722689\pi\)
0.643911 0.765101i \(-0.277311\pi\)
\(108\) −10.5527 3.42877i −1.01543 0.329933i
\(109\) −1.62108 + 1.17779i −0.155272 + 0.112811i −0.662708 0.748878i \(-0.730593\pi\)
0.507437 + 0.861689i \(0.330593\pi\)
\(110\) 0 0
\(111\) 9.63145 + 6.99766i 0.914177 + 0.664188i
\(112\) −7.28304 10.0242i −0.688182 0.947202i
\(113\) 6.12912 + 8.43601i 0.576579 + 0.793593i 0.993315 0.115434i \(-0.0368260\pi\)
−0.416736 + 0.909028i \(0.636826\pi\)
\(114\) 0.377443 + 0.274228i 0.0353508 + 0.0256838i
\(115\) 0 0
\(116\) 9.40559 6.83356i 0.873288 0.634481i
\(117\) −0.234903 0.0763247i −0.0217168 0.00705622i
\(118\) 1.08737i 0.100101i
\(119\) −5.20252 + 16.0117i −0.476914 + 1.46779i
\(120\) 0 0
\(121\) −2.16312 6.65740i −0.196647 0.605218i
\(122\) −0.159507 + 0.0518268i −0.0144410 + 0.00469218i
\(123\) 0.878294 1.20887i 0.0791931 0.109000i
\(124\) 11.9944 1.07713
\(125\) 0 0
\(126\) −0.497767 −0.0443446
\(127\) 3.43858 4.73280i 0.305125 0.419969i −0.628728 0.777625i \(-0.716424\pi\)
0.933853 + 0.357657i \(0.116424\pi\)
\(128\) −5.34317 + 1.73610i −0.472274 + 0.153451i
\(129\) −1.47464 4.53849i −0.129835 0.399591i
\(130\) 0 0
\(131\) −0.462488 + 1.42339i −0.0404077 + 0.124362i −0.969225 0.246175i \(-0.920826\pi\)
0.928818 + 0.370537i \(0.120826\pi\)
\(132\) 5.78902i 0.503870i
\(133\) −5.36635 1.74363i −0.465322 0.151192i
\(134\) −1.02074 + 0.741608i −0.0881782 + 0.0640652i
\(135\) 0 0
\(136\) 3.03472 + 2.20485i 0.260225 + 0.189064i
\(137\) −4.61345 6.34987i −0.394154 0.542506i 0.565111 0.825015i \(-0.308833\pi\)
−0.959265 + 0.282509i \(0.908833\pi\)
\(138\) −0.139333 0.191776i −0.0118608 0.0163250i
\(139\) 4.36183 + 3.16906i 0.369966 + 0.268796i 0.757197 0.653187i \(-0.226568\pi\)
−0.387231 + 0.921983i \(0.626568\pi\)
\(140\) 0 0
\(141\) 5.02526 3.65106i 0.423203 0.307475i
\(142\) −1.03980 0.337852i −0.0872583 0.0283519i
\(143\) 0.592757i 0.0495689i
\(144\) 0.978544 3.01165i 0.0815453 0.250971i
\(145\) 0 0
\(146\) −0.500000 1.53884i −0.0413803 0.127355i
\(147\) −5.08611 + 1.65258i −0.419495 + 0.136302i
\(148\) −9.34851 + 12.8671i −0.768443 + 1.05767i
\(149\) −18.8229 −1.54203 −0.771015 0.636817i \(-0.780251\pi\)
−0.771015 + 0.636817i \(0.780251\pi\)
\(150\) 0 0
\(151\) −3.88797 −0.316398 −0.158199 0.987407i \(-0.550569\pi\)
−0.158199 + 0.987407i \(0.550569\pi\)
\(152\) −0.738960 + 1.01709i −0.0599376 + 0.0824970i
\(153\) −4.09205 + 1.32959i −0.330823 + 0.107491i
\(154\) −0.369150 1.13613i −0.0297470 0.0915518i
\(155\) 0 0
\(156\) −0.265097 + 0.815884i −0.0212247 + 0.0653230i
\(157\) 4.28378i 0.341883i −0.985281 0.170941i \(-0.945319\pi\)
0.985281 0.170941i \(-0.0546808\pi\)
\(158\) 1.35196 + 0.439279i 0.107556 + 0.0349472i
\(159\) 9.64660 7.00866i 0.765025 0.555823i
\(160\) 0 0
\(161\) 2.31939 + 1.68513i 0.182793 + 0.132807i
\(162\) 0.625044 + 0.860299i 0.0491081 + 0.0675915i
\(163\) −9.24370 12.7229i −0.724023 0.996531i −0.999381 0.0351898i \(-0.988796\pi\)
0.275358 0.961342i \(-0.411204\pi\)
\(164\) 1.61498 + 1.17335i 0.126109 + 0.0916236i
\(165\) 0 0
\(166\) 2.15102 1.56281i 0.166952 0.121298i
\(167\) −20.0036 6.49956i −1.54792 0.502951i −0.594375 0.804188i \(-0.702601\pi\)
−0.953549 + 0.301237i \(0.902601\pi\)
\(168\) 3.48727i 0.269049i
\(169\) 3.99008 12.2802i 0.306929 0.944630i
\(170\) 0 0
\(171\) −0.445615 1.37146i −0.0340770 0.104878i
\(172\) 6.06318 1.97005i 0.462313 0.150215i
\(173\) 4.21244 5.79793i 0.320266 0.440808i −0.618283 0.785956i \(-0.712171\pi\)
0.938548 + 0.345148i \(0.112171\pi\)
\(174\) −1.59404 −0.120844
\(175\) 0 0
\(176\) 7.59963 0.572843
\(177\) 5.13607 7.06920i 0.386051 0.531353i
\(178\) 1.31116 0.426020i 0.0982753 0.0319316i
\(179\) −2.48429 7.64586i −0.185685 0.571479i 0.814275 0.580480i \(-0.197135\pi\)
−0.999959 + 0.00900088i \(0.997135\pi\)
\(180\) 0 0
\(181\) −6.37104 + 19.6080i −0.473555 + 1.45745i 0.374341 + 0.927291i \(0.377869\pi\)
−0.847896 + 0.530162i \(0.822131\pi\)
\(182\) 0.177026i 0.0131221i
\(183\) −1.28178 0.416474i −0.0947516 0.0307867i
\(184\) 0.516776 0.375460i 0.0380972 0.0276793i
\(185\) 0 0
\(186\) −1.33047 0.966645i −0.0975550 0.0708779i
\(187\) −6.06943 8.35386i −0.443841 0.610895i
\(188\) 4.87763 + 6.71349i 0.355738 + 0.489631i
\(189\) −14.8855 10.8149i −1.08276 0.786670i
\(190\) 0 0
\(191\) −14.5868 + 10.5979i −1.05546 + 0.766840i −0.973244 0.229774i \(-0.926201\pi\)
−0.0822207 + 0.996614i \(0.526201\pi\)
\(192\) −10.0877 3.27769i −0.728016 0.236547i
\(193\) 6.78859i 0.488653i 0.969693 + 0.244327i \(0.0785669\pi\)
−0.969693 + 0.244327i \(0.921433\pi\)
\(194\) −0.380741 + 1.17180i −0.0273356 + 0.0841304i
\(195\) 0 0
\(196\) −2.20776 6.79478i −0.157697 0.485342i
\(197\) 7.60405 2.47071i 0.541766 0.176031i −0.0253343 0.999679i \(-0.508065\pi\)
0.567101 + 0.823648i \(0.308065\pi\)
\(198\) 0.179450 0.246992i 0.0127530 0.0175529i
\(199\) 5.20485 0.368962 0.184481 0.982836i \(-0.440940\pi\)
0.184481 + 0.982836i \(0.440940\pi\)
\(200\) 0 0
\(201\) −10.1389 −0.715141
\(202\) −1.31304 + 1.80724i −0.0923850 + 0.127157i
\(203\) 18.3351 5.95745i 1.28687 0.418131i
\(204\) 4.61803 + 14.2128i 0.323327 + 0.995098i
\(205\) 0 0
\(206\) −0.0781921 + 0.240650i −0.00544790 + 0.0167669i
\(207\) 0.732688i 0.0509254i
\(208\) −1.07106 0.348010i −0.0742649 0.0241301i
\(209\) 2.79981 2.03418i 0.193667 0.140707i
\(210\) 0 0
\(211\) −13.4313 9.75839i −0.924646 0.671795i 0.0200297 0.999799i \(-0.493624\pi\)
−0.944676 + 0.328004i \(0.893624\pi\)
\(212\) 9.36321 + 12.8874i 0.643068 + 0.885107i
\(213\) −5.16413 7.10781i −0.353840 0.487019i
\(214\) −2.34562 1.70419i −0.160343 0.116496i
\(215\) 0 0
\(216\) −3.31659 + 2.40964i −0.225665 + 0.163955i
\(217\) 18.9162 + 6.14625i 1.28412 + 0.417235i
\(218\) 0.367035i 0.0248587i
\(219\) 4.01794 12.3660i 0.271507 0.835613i
\(220\) 0 0
\(221\) 0.472856 + 1.45530i 0.0318077 + 0.0978941i
\(222\) 2.07396 0.673869i 0.139195 0.0452272i
\(223\) 3.89589 5.36223i 0.260888 0.359082i −0.658399 0.752669i \(-0.728766\pi\)
0.919287 + 0.393587i \(0.128766\pi\)
\(224\) −7.00792 −0.468236
\(225\) 0 0
\(226\) 1.91002 0.127053
\(227\) −7.87158 + 10.8343i −0.522455 + 0.719097i −0.985957 0.166998i \(-0.946593\pi\)
0.463502 + 0.886096i \(0.346593\pi\)
\(228\) −4.76347 + 1.54774i −0.315468 + 0.102502i
\(229\) −3.11697 9.59304i −0.205975 0.633926i −0.999672 0.0256124i \(-0.991846\pi\)
0.793697 0.608313i \(-0.208154\pi\)
\(230\) 0 0
\(231\) 2.96645 9.12979i 0.195178 0.600696i
\(232\) 4.29544i 0.282009i
\(233\) 20.9285 + 6.80007i 1.37107 + 0.445488i 0.899723 0.436461i \(-0.143768\pi\)
0.471346 + 0.881948i \(0.343768\pi\)
\(234\) −0.0366015 + 0.0265926i −0.00239272 + 0.00173841i
\(235\) 0 0
\(236\) 9.44408 + 6.86153i 0.614757 + 0.446647i
\(237\) 6.71445 + 9.24165i 0.436151 + 0.600310i
\(238\) 1.81263 + 2.49487i 0.117495 + 0.161718i
\(239\) 6.11640 + 4.44383i 0.395637 + 0.287447i 0.767762 0.640736i \(-0.221371\pi\)
−0.372124 + 0.928183i \(0.621371\pi\)
\(240\) 0 0
\(241\) 16.4995 11.9876i 1.06283 0.772190i 0.0882188 0.996101i \(-0.471883\pi\)
0.974610 + 0.223911i \(0.0718825\pi\)
\(242\) −1.21945 0.396223i −0.0783892 0.0254702i
\(243\) 8.38230i 0.537725i
\(244\) 0.556388 1.71239i 0.0356191 0.109624i
\(245\) 0 0
\(246\) −0.0845790 0.260307i −0.00539256 0.0165966i
\(247\) −0.487747 + 0.158479i −0.0310346 + 0.0100838i
\(248\) 2.60481 3.58521i 0.165406 0.227661i
\(249\) 21.3659 1.35401
\(250\) 0 0
\(251\) 10.5717 0.667278 0.333639 0.942701i \(-0.391723\pi\)
0.333639 + 0.942701i \(0.391723\pi\)
\(252\) 3.14100 4.32322i 0.197865 0.272337i
\(253\) −1.67232 + 0.543370i −0.105138 + 0.0341614i
\(254\) −0.331133 1.01912i −0.0207771 0.0639455i
\(255\) 0 0
\(256\) 4.13553 12.7279i 0.258471 0.795491i
\(257\) 20.2700i 1.26441i 0.774801 + 0.632205i \(0.217850\pi\)
−0.774801 + 0.632205i \(0.782150\pi\)
\(258\) −0.831324 0.270114i −0.0517560 0.0168165i
\(259\) −21.3369 + 15.5021i −1.32581 + 0.963256i
\(260\) 0 0
\(261\) 3.98602 + 2.89601i 0.246728 + 0.179259i
\(262\) 0.161137 + 0.221786i 0.00995509 + 0.0137020i
\(263\) 16.5114 + 22.7260i 1.01814 + 1.40135i 0.913501 + 0.406835i \(0.133368\pi\)
0.104636 + 0.994511i \(0.466632\pi\)
\(264\) −1.73038 1.25719i −0.106498 0.0773750i
\(265\) 0 0
\(266\) −0.836161 + 0.607507i −0.0512683 + 0.0372486i
\(267\) 10.5363 + 3.42345i 0.644811 + 0.209512i
\(268\) 13.5450i 0.827393i
\(269\) −6.28015 + 19.3283i −0.382907 + 1.17847i 0.555080 + 0.831797i \(0.312688\pi\)
−0.937987 + 0.346670i \(0.887312\pi\)
\(270\) 0 0
\(271\) 9.71756 + 29.9076i 0.590300 + 1.81676i 0.576854 + 0.816847i \(0.304280\pi\)
0.0134456 + 0.999910i \(0.495720\pi\)
\(272\) −18.6581 + 6.06239i −1.13132 + 0.367587i
\(273\) −0.836161 + 1.15088i −0.0506068 + 0.0696542i
\(274\) −1.43769 −0.0868543
\(275\) 0 0
\(276\) 2.54483 0.153181
\(277\) −8.18813 + 11.2700i −0.491977 + 0.677148i −0.980751 0.195262i \(-0.937444\pi\)
0.488774 + 0.872410i \(0.337444\pi\)
\(278\) 0.939241 0.305178i 0.0563319 0.0183033i
\(279\) 1.57078 + 4.83435i 0.0940399 + 0.289425i
\(280\) 0 0
\(281\) 7.99664 24.6111i 0.477040 1.46818i −0.366147 0.930557i \(-0.619323\pi\)
0.843187 0.537620i \(-0.180677\pi\)
\(282\) 1.13778i 0.0677541i
\(283\) −22.5701 7.33348i −1.34166 0.435930i −0.451778 0.892130i \(-0.649210\pi\)
−0.889877 + 0.456200i \(0.849210\pi\)
\(284\) 9.49567 6.89901i 0.563464 0.409381i
\(285\) 0 0
\(286\) −0.0878403 0.0638197i −0.00519411 0.00377374i
\(287\) 1.94571 + 2.67804i 0.114852 + 0.158080i
\(288\) −1.05272 1.44894i −0.0620320 0.0853797i
\(289\) 7.81207 + 5.67580i 0.459533 + 0.333871i
\(290\) 0 0
\(291\) −8.01011 + 5.81969i −0.469561 + 0.341156i
\(292\) 16.5203 + 5.36776i 0.966776 + 0.314124i
\(293\) 12.3029i 0.718742i 0.933195 + 0.359371i \(0.117009\pi\)
−0.933195 + 0.359371i \(0.882991\pi\)
\(294\) −0.302706 + 0.931634i −0.0176542 + 0.0543340i
\(295\) 0 0
\(296\) 1.81587 + 5.58867i 0.105545 + 0.324835i
\(297\) 10.7327 3.48727i 0.622775 0.202352i
\(298\) −2.02658 + 2.78935i −0.117397 + 0.161583i
\(299\) 0.260574 0.0150694
\(300\) 0 0
\(301\) 10.5717 0.609341
\(302\) −0.418601 + 0.576155i −0.0240878 + 0.0331540i
\(303\) −17.0725 + 5.54721i −0.980792 + 0.318679i
\(304\) −2.03182 6.25331i −0.116533 0.358652i
\(305\) 0 0
\(306\) −0.243544 + 0.749550i −0.0139225 + 0.0428489i
\(307\) 4.28249i 0.244415i 0.992505 + 0.122207i \(0.0389973\pi\)
−0.992505 + 0.122207i \(0.961003\pi\)
\(308\) 12.1969 + 3.96302i 0.694984 + 0.225814i
\(309\) −1.64502 + 1.19518i −0.0935820 + 0.0679913i
\(310\) 0 0
\(311\) −20.7486 15.0747i −1.17655 0.854810i −0.184768 0.982782i \(-0.559153\pi\)
−0.991778 + 0.127972i \(0.959153\pi\)
\(312\) 0.186303 + 0.256424i 0.0105473 + 0.0145171i
\(313\) −13.1377 18.0825i −0.742589 1.02209i −0.998466 0.0553767i \(-0.982364\pi\)
0.255876 0.966709i \(-0.417636\pi\)
\(314\) −0.634810 0.461216i −0.0358244 0.0260280i
\(315\) 0 0
\(316\) −12.3464 + 8.97016i −0.694538 + 0.504611i
\(317\) 20.8499 + 6.77453i 1.17105 + 0.380496i 0.829033 0.559200i \(-0.188892\pi\)
0.342012 + 0.939695i \(0.388892\pi\)
\(318\) 2.18412i 0.122479i
\(319\) −3.65392 + 11.2456i −0.204580 + 0.629632i
\(320\) 0 0
\(321\) −7.19972 22.1585i −0.401849 1.23676i
\(322\) 0.499437 0.162277i 0.0278325 0.00904334i
\(323\) −5.25121 + 7.22768i −0.292185 + 0.402159i
\(324\) −11.4160 −0.634224
\(325\) 0 0
\(326\) −2.88062 −0.159543
\(327\) −1.73364 + 2.38615i −0.0958706 + 0.131955i
\(328\) 0.701448 0.227914i 0.0387310 0.0125845i
\(329\) 4.25228 + 13.0872i 0.234436 + 0.721519i
\(330\) 0 0
\(331\) −2.76972 + 8.52431i −0.152237 + 0.468539i −0.997871 0.0652260i \(-0.979223\pi\)
0.845633 + 0.533765i \(0.179223\pi\)
\(332\) 28.5437i 1.56654i
\(333\) −6.41037 2.08286i −0.351286 0.114140i
\(334\) −3.11687 + 2.26454i −0.170547 + 0.123910i
\(335\) 0 0
\(336\) −14.7552 10.7203i −0.804961 0.584838i
\(337\) 17.0949 + 23.5291i 0.931218 + 1.28171i 0.959383 + 0.282108i \(0.0910337\pi\)
−0.0281648 + 0.999603i \(0.508966\pi\)
\(338\) −1.39020 1.91344i −0.0756168 0.104078i
\(339\) 12.4174 + 9.02176i 0.674420 + 0.489995i
\(340\) 0 0
\(341\) −9.86925 + 7.17043i −0.534450 + 0.388300i
\(342\) −0.251213 0.0816242i −0.0135841 0.00441373i
\(343\) 10.9787i 0.592795i
\(344\) 0.727872 2.24016i 0.0392443 0.120781i
\(345\) 0 0
\(346\) −0.405655 1.24848i −0.0218081 0.0671185i
\(347\) −13.5974 + 4.41807i −0.729948 + 0.237175i −0.650331 0.759651i \(-0.725370\pi\)
−0.0796174 + 0.996825i \(0.525370\pi\)
\(348\) 10.0587 13.8446i 0.539201 0.742146i
\(349\) −5.62382 −0.301036 −0.150518 0.988607i \(-0.548094\pi\)
−0.150518 + 0.988607i \(0.548094\pi\)
\(350\) 0 0
\(351\) −1.67232 −0.0892620
\(352\) 2.52642 3.47732i 0.134659 0.185342i
\(353\) 1.81649 0.590214i 0.0966821 0.0314139i −0.260276 0.965534i \(-0.583814\pi\)
0.356959 + 0.934120i \(0.383814\pi\)
\(354\) −0.494600 1.52222i −0.0262877 0.0809052i
\(355\) 0 0
\(356\) −4.57355 + 14.0759i −0.242398 + 0.746023i
\(357\) 24.7813i 1.31156i
\(358\) −1.40051 0.455053i −0.0740192 0.0240503i
\(359\) 17.9639 13.0516i 0.948101 0.688835i −0.00225634 0.999997i \(-0.500718\pi\)
0.950357 + 0.311162i \(0.100718\pi\)
\(360\) 0 0
\(361\) 12.9490 + 9.40796i 0.681524 + 0.495156i
\(362\) 2.21976 + 3.05523i 0.116668 + 0.160580i
\(363\) −6.05633 8.33582i −0.317875 0.437517i
\(364\) −1.53751 1.11707i −0.0805875 0.0585503i
\(365\) 0 0
\(366\) −0.199721 + 0.145105i −0.0104396 + 0.00758478i
\(367\) −20.3954 6.62686i −1.06463 0.345919i −0.276236 0.961090i \(-0.589087\pi\)
−0.788394 + 0.615170i \(0.789087\pi\)
\(368\) 3.34077i 0.174149i
\(369\) −0.261424 + 0.804582i −0.0136092 + 0.0418849i
\(370\) 0 0
\(371\) 8.16277 + 25.1224i 0.423790 + 1.30429i
\(372\) 16.7911 5.45574i 0.870576 0.282867i
\(373\) −13.6013 + 18.7206i −0.704248 + 0.969315i 0.295653 + 0.955295i \(0.404463\pi\)
−0.999902 + 0.0140195i \(0.995537\pi\)
\(374\) −1.89142 −0.0978032
\(375\) 0 0
\(376\) 3.06598 0.158116
\(377\) 1.02994 1.41759i 0.0530446 0.0730096i
\(378\) −3.20531 + 1.04147i −0.164863 + 0.0535674i
\(379\) 6.69026 + 20.5905i 0.343656 + 1.05766i 0.962300 + 0.271992i \(0.0876824\pi\)
−0.618644 + 0.785672i \(0.712318\pi\)
\(380\) 0 0
\(381\) 2.66095 8.18955i 0.136324 0.419563i
\(382\) 3.30265i 0.168978i
\(383\) −5.37804 1.74743i −0.274805 0.0892896i 0.168372 0.985723i \(-0.446149\pi\)
−0.443178 + 0.896434i \(0.646149\pi\)
\(384\) −6.69026 + 4.86076i −0.341411 + 0.248050i
\(385\) 0 0
\(386\) 1.00600 + 0.730899i 0.0512039 + 0.0372018i
\(387\) 1.58806 + 2.18577i 0.0807255 + 0.111109i
\(388\) −7.77480 10.7011i −0.394706 0.543266i
\(389\) −6.57411 4.77637i −0.333321 0.242172i 0.408518 0.912750i \(-0.366046\pi\)
−0.741838 + 0.670579i \(0.766046\pi\)
\(390\) 0 0
\(391\) 3.67232 2.66810i 0.185717 0.134932i
\(392\) −2.51047 0.815700i −0.126798 0.0411991i
\(393\) 2.20298i 0.111126i
\(394\) 0.452564 1.39285i 0.0227999 0.0701708i
\(395\) 0 0
\(396\) 1.01282 + 3.11713i 0.0508959 + 0.156641i
\(397\) 19.7524 6.41794i 0.991343 0.322107i 0.231942 0.972730i \(-0.425492\pi\)
0.759401 + 0.650623i \(0.225492\pi\)
\(398\) 0.560384 0.771303i 0.0280895 0.0386619i
\(399\) −8.30550 −0.415795
\(400\) 0 0
\(401\) 30.1195 1.50410 0.752049 0.659107i \(-0.229066\pi\)
0.752049 + 0.659107i \(0.229066\pi\)
\(402\) −1.09161 + 1.50247i −0.0544445 + 0.0749365i
\(403\) 1.71929 0.558632i 0.0856440 0.0278274i
\(404\) −7.41078 22.8080i −0.368700 1.13474i
\(405\) 0 0
\(406\) 1.09124 3.35848i 0.0541572 0.166679i
\(407\) 16.1760i 0.801815i
\(408\) 5.25121 + 1.70622i 0.259974 + 0.0844706i
\(409\) 8.93579 6.49223i 0.441846 0.321020i −0.344522 0.938778i \(-0.611959\pi\)
0.786368 + 0.617758i \(0.211959\pi\)
\(410\) 0 0
\(411\) −9.34669 6.79077i −0.461038 0.334964i
\(412\) −1.59670 2.19766i −0.0786636 0.108271i
\(413\) 11.3781 + 15.6606i 0.559880 + 0.770608i
\(414\) 0.108577 + 0.0788855i 0.00533625 + 0.00387701i
\(415\) 0 0
\(416\) −0.515302 + 0.374389i −0.0252648 + 0.0183559i
\(417\) 7.54763 + 2.45237i 0.369609 + 0.120093i
\(418\) 0.633915i 0.0310058i
\(419\) 10.1732 31.3099i 0.496993 1.52959i −0.316834 0.948481i \(-0.602620\pi\)
0.813827 0.581107i \(-0.197380\pi\)
\(420\) 0 0
\(421\) −6.26214 19.2729i −0.305198 0.939304i −0.979603 0.200942i \(-0.935600\pi\)
0.674405 0.738362i \(-0.264400\pi\)
\(422\) −2.89218 + 0.939725i −0.140789 + 0.0457451i
\(423\) −2.06710 + 2.84512i −0.100506 + 0.138335i
\(424\) 5.88552 0.285826
\(425\) 0 0
\(426\) −1.60930 −0.0779709
\(427\) 1.75494 2.41547i 0.0849277 0.116893i
\(428\) 29.6026 9.61845i 1.43089 0.464926i
\(429\) −0.269620 0.829805i −0.0130174 0.0400634i
\(430\) 0 0
\(431\) 2.21110 6.80506i 0.106505 0.327788i −0.883576 0.468288i \(-0.844871\pi\)
0.990081 + 0.140500i \(0.0448710\pi\)
\(432\) 21.4405i 1.03156i
\(433\) 5.21430 + 1.69423i 0.250583 + 0.0814195i 0.431615 0.902058i \(-0.357944\pi\)
−0.181032 + 0.983477i \(0.557944\pi\)
\(434\) 2.94744 2.14144i 0.141482 0.102792i
\(435\) 0 0
\(436\) −3.18778 2.31606i −0.152667 0.110919i
\(437\) 0.894219 + 1.23079i 0.0427763 + 0.0588765i
\(438\) −1.39991 1.92681i −0.0668901 0.0920664i
\(439\) −24.8822 18.0780i −1.18756 0.862815i −0.194558 0.980891i \(-0.562327\pi\)
−0.993005 + 0.118076i \(0.962327\pi\)
\(440\) 0 0
\(441\) 2.44951 1.77968i 0.116644 0.0847465i
\(442\) 0.266570 + 0.0866140i 0.0126795 + 0.00411981i
\(443\) 11.3527i 0.539381i −0.962947 0.269691i \(-0.913079\pi\)
0.962947 0.269691i \(-0.0869214\pi\)
\(444\) −7.23434 + 22.2650i −0.343327 + 1.05665i
\(445\) 0 0
\(446\) −0.375171 1.15466i −0.0177649 0.0546747i
\(447\) −26.3503 + 8.56172i −1.24633 + 0.404956i
\(448\) 13.8116 19.0100i 0.652535 0.898137i
\(449\) 15.7661 0.744050 0.372025 0.928223i \(-0.378664\pi\)
0.372025 + 0.928223i \(0.378664\pi\)
\(450\) 0 0
\(451\) −2.03029 −0.0956027
\(452\) −12.0526 + 16.5890i −0.566907 + 0.780280i
\(453\) −5.44279 + 1.76847i −0.255725 + 0.0830900i
\(454\) 0.758027 + 2.33297i 0.0355760 + 0.109492i
\(455\) 0 0
\(456\) −0.571844 + 1.75996i −0.0267791 + 0.0824175i
\(457\) 4.16714i 0.194931i −0.995239 0.0974653i \(-0.968926\pi\)
0.995239 0.0974653i \(-0.0310735\pi\)
\(458\) −1.75718 0.570941i −0.0821075 0.0266783i
\(459\) −23.5684 + 17.1234i −1.10008 + 0.799254i
\(460\) 0 0
\(461\) 19.3933 + 14.0900i 0.903235 + 0.656239i 0.939295 0.343111i \(-0.111481\pi\)
−0.0360595 + 0.999350i \(0.511481\pi\)
\(462\) −1.03355 1.42256i −0.0480852 0.0661836i
\(463\) 24.2900 + 33.4324i 1.12885 + 1.55373i 0.790229 + 0.612812i \(0.209962\pi\)
0.338624 + 0.940922i \(0.390038\pi\)
\(464\) 18.1747 + 13.2047i 0.843737 + 0.613011i
\(465\) 0 0
\(466\) 3.26098 2.36924i 0.151062 0.109753i
\(467\) −9.88775 3.21272i −0.457550 0.148667i 0.0711682 0.997464i \(-0.477327\pi\)
−0.528719 + 0.848797i \(0.677327\pi\)
\(468\) 0.485697i 0.0224513i
\(469\) 6.94082 21.3616i 0.320497 0.986389i
\(470\) 0 0
\(471\) −1.94851 5.99689i −0.0897825 0.276322i
\(472\) 4.10192 1.33279i 0.188806 0.0613468i
\(473\) −3.81119 + 5.24565i −0.175239 + 0.241195i
\(474\) 2.09243 0.0961086
\(475\) 0 0
\(476\) −33.1065 −1.51743
\(477\) −3.96806 + 5.46156i −0.181685 + 0.250068i
\(478\) 1.31706 0.427937i 0.0602407 0.0195734i
\(479\) −11.1271 34.2458i −0.508411 1.56473i −0.794959 0.606663i \(-0.792508\pi\)
0.286548 0.958066i \(-0.407492\pi\)
\(480\) 0 0
\(481\) −0.740748 + 2.27979i −0.0337752 + 0.103949i
\(482\) 3.73571i 0.170157i
\(483\) 4.01342 + 1.30404i 0.182617 + 0.0593358i
\(484\) 11.1362 8.09094i 0.506192 0.367770i
\(485\) 0 0
\(486\) −1.24217 0.902487i −0.0563458 0.0409377i
\(487\) −6.25275 8.60617i −0.283339 0.389983i 0.643497 0.765448i \(-0.277483\pi\)
−0.926836 + 0.375466i \(0.877483\pi\)
\(488\) −0.391014 0.538185i −0.0177004 0.0243625i
\(489\) −18.7274 13.6063i −0.846883 0.615296i
\(490\) 0 0
\(491\) 14.2947 10.3857i 0.645112 0.468701i −0.216491 0.976285i \(-0.569461\pi\)
0.861603 + 0.507583i \(0.169461\pi\)
\(492\) 2.79454 + 0.908000i 0.125987 + 0.0409358i
\(493\) 30.5243i 1.37475i
\(494\) −0.0290289 + 0.0893417i −0.00130607 + 0.00401967i
\(495\) 0 0
\(496\) 7.16211 + 22.0427i 0.321588 + 0.989747i
\(497\) 18.5107 6.01450i 0.830319 0.269787i
\(498\) 2.30038 3.16620i 0.103082 0.141881i
\(499\) 9.41734 0.421578 0.210789 0.977532i \(-0.432397\pi\)
0.210789 + 0.977532i \(0.432397\pi\)
\(500\) 0 0
\(501\) −30.9595 −1.38317
\(502\) 1.13821 1.56661i 0.0508007 0.0699211i
\(503\) −17.1316 + 5.56641i −0.763862 + 0.248194i −0.664935 0.746901i \(-0.731541\pi\)
−0.0989268 + 0.995095i \(0.531541\pi\)
\(504\) −0.610113 1.87774i −0.0271766 0.0836410i
\(505\) 0 0
\(506\) −0.0995303 + 0.306323i −0.00442466 + 0.0136177i
\(507\) 19.0060i 0.844088i
\(508\) 10.9408 + 3.55489i 0.485420 + 0.157723i
\(509\) −12.9835 + 9.43307i −0.575484 + 0.418114i −0.837093 0.547060i \(-0.815747\pi\)
0.261609 + 0.965174i \(0.415747\pi\)
\(510\) 0 0
\(511\) 23.3033 + 16.9308i 1.03088 + 0.748976i
\(512\) −8.04540 11.0735i −0.355560 0.489386i
\(513\) −5.73896 7.89900i −0.253381 0.348749i
\(514\) 3.00380 + 2.18239i 0.132492 + 0.0962611i
\(515\) 0 0
\(516\) 7.59180 5.51577i 0.334210 0.242818i
\(517\) −8.02684 2.60808i −0.353020 0.114703i
\(518\) 4.83095i 0.212260i
\(519\) 3.25979 10.0326i 0.143089 0.440383i
\(520\) 0 0
\(521\) −0.680052 2.09298i −0.0297936 0.0916953i 0.935054 0.354505i \(-0.115351\pi\)
−0.964848 + 0.262810i \(0.915351\pi\)
\(522\) 0.858316 0.278884i 0.0375675 0.0122064i
\(523\) 4.37070 6.01575i 0.191117 0.263050i −0.702695 0.711491i \(-0.748020\pi\)
0.893813 + 0.448440i \(0.148020\pi\)
\(524\) −2.94307 −0.128569
\(525\) 0 0
\(526\) 5.14547 0.224353
\(527\) 18.5103 25.4773i 0.806323 1.10981i
\(528\) 10.6388 3.45675i 0.462993 0.150436i
\(529\) 6.86853 + 21.1392i 0.298632 + 0.919094i
\(530\) 0 0
\(531\) −1.52875 + 4.70502i −0.0663423 + 0.204181i
\(532\) 11.0957i 0.481061i
\(533\) 0.286142 + 0.0929731i 0.0123942 + 0.00402711i
\(534\) 1.64172 1.19278i 0.0710441 0.0516165i
\(535\) 0 0
\(536\) −4.04870 2.94155i −0.174877 0.127056i
\(537\) −6.95555 9.57350i −0.300154 0.413127i
\(538\) 2.18809 + 3.01165i 0.0943353 + 0.129841i
\(539\) 5.87861 + 4.27106i 0.253210 + 0.183968i
\(540\) 0 0
\(541\) −16.7041 + 12.1362i −0.718165 + 0.521777i −0.885797 0.464072i \(-0.846388\pi\)
0.167632 + 0.985850i \(0.446388\pi\)
\(542\) 5.47824 + 1.77999i 0.235310 + 0.0764570i
\(543\) 30.3473i 1.30233i
\(544\) −3.42878 + 10.5527i −0.147008 + 0.452443i
\(545\) 0 0
\(546\) 0.0805217 + 0.247820i 0.00344601 + 0.0106057i
\(547\) −29.8405 + 9.69577i −1.27589 + 0.414561i −0.867130 0.498082i \(-0.834038\pi\)
−0.408758 + 0.912643i \(0.634038\pi\)
\(548\) 9.07211 12.4867i 0.387541 0.533405i
\(549\) 0.763042 0.0325658
\(550\) 0 0
\(551\) 10.2303 0.435825
\(552\) 0.552658 0.760668i 0.0235227 0.0323762i
\(553\) −24.0678 + 7.82012i −1.02347 + 0.332545i
\(554\) 0.788511 + 2.42679i 0.0335006 + 0.103104i
\(555\) 0 0
\(556\) −3.27624 + 10.0832i −0.138944 + 0.427625i
\(557\) 22.3515i 0.947064i −0.880776 0.473532i \(-0.842979\pi\)
0.880776 0.473532i \(-0.157021\pi\)
\(558\) 0.885518 + 0.287722i 0.0374870 + 0.0121803i
\(559\) 0.777350 0.564778i 0.0328784 0.0238875i
\(560\) 0 0
\(561\) −12.2965 8.93390i −0.519157 0.377189i
\(562\) −2.78614 3.83480i −0.117526 0.161761i
\(563\) −20.2000 27.8029i −0.851329 1.17175i −0.983568 0.180536i \(-0.942217\pi\)
0.132240 0.991218i \(-0.457783\pi\)
\(564\) 9.88191 + 7.17963i 0.416104 + 0.302317i
\(565\) 0 0
\(566\) −3.51678 + 2.55509i −0.147821 + 0.107398i
\(567\) −18.0041 5.84987i −0.756099 0.245672i
\(568\) 4.33657i 0.181958i
\(569\) −9.93991 + 30.5919i −0.416703 + 1.28248i 0.494017 + 0.869452i \(0.335528\pi\)
−0.910719 + 0.413026i \(0.864472\pi\)
\(570\) 0 0
\(571\) −8.39501 25.8372i −0.351320 1.08125i −0.958112 0.286392i \(-0.907544\pi\)
0.606792 0.794861i \(-0.292456\pi\)
\(572\) 1.10858 0.360198i 0.0463519 0.0150607i
\(573\) −15.5996 + 21.4710i −0.651684 + 0.896966i
\(574\) 0.606344 0.0253083
\(575\) 0 0
\(576\) 6.00521 0.250217
\(577\) 8.14100 11.2051i 0.338914 0.466476i −0.605210 0.796066i \(-0.706911\pi\)
0.944124 + 0.329591i \(0.106911\pi\)
\(578\) 1.68219 0.546575i 0.0699697 0.0227345i
\(579\) 3.08784 + 9.50340i 0.128326 + 0.394948i
\(580\) 0 0
\(581\) −14.6266 + 45.0159i −0.606812 + 1.86757i
\(582\) 1.81360i 0.0751759i
\(583\) −15.4085 5.00652i −0.638154 0.207349i
\(584\) 5.19215 3.77232i 0.214853 0.156100i
\(585\) 0 0
\(586\) 1.82315 + 1.32460i 0.0753138 + 0.0547187i
\(587\) −25.9507 35.7180i −1.07110 1.47424i −0.868959 0.494884i \(-0.835211\pi\)
−0.202139 0.979357i \(-0.564789\pi\)
\(588\) −6.18131 8.50785i −0.254913 0.350858i
\(589\) 8.53877 + 6.20378i 0.351834 + 0.255622i
\(590\) 0 0
\(591\) 9.52115 6.91752i 0.391648 0.284549i
\(592\) −29.2287 9.49699i −1.20129 0.390324i
\(593\) 16.2531i 0.667437i 0.942673 + 0.333718i \(0.108303\pi\)
−0.942673 + 0.333718i \(0.891697\pi\)
\(594\) 0.638770 1.96593i 0.0262091 0.0806632i
\(595\) 0 0
\(596\) −11.4380 35.2026i −0.468520 1.44196i
\(597\) 7.28630 2.36746i 0.298208 0.0968938i
\(598\) 0.0280549 0.0386142i 0.00114725 0.00157905i
\(599\) −30.4822 −1.24547 −0.622734 0.782433i \(-0.713978\pi\)
−0.622734 + 0.782433i \(0.713978\pi\)
\(600\) 0 0
\(601\) −28.9162 −1.17952 −0.589758 0.807580i \(-0.700777\pi\)
−0.589758 + 0.807580i \(0.700777\pi\)
\(602\) 1.13821 1.56661i 0.0463899 0.0638502i
\(603\) 5.45932 1.77384i 0.222321 0.0722364i
\(604\) −2.36259 7.27129i −0.0961322 0.295865i
\(605\) 0 0
\(606\) −1.01609 + 3.12721i −0.0412760 + 0.127034i
\(607\) 8.23276i 0.334157i 0.985944 + 0.167079i \(0.0534334\pi\)
−0.985944 + 0.167079i \(0.946567\pi\)
\(608\) −3.53676 1.14916i −0.143435 0.0466047i
\(609\) 22.9577 16.6797i 0.930293 0.675897i
\(610\) 0 0
\(611\) 1.01184 + 0.735146i 0.0409347 + 0.0297408i
\(612\) −4.97320 6.84503i −0.201030 0.276694i
\(613\) 2.82026 + 3.88175i 0.113909 + 0.156783i 0.862165 0.506628i \(-0.169108\pi\)
−0.748256 + 0.663411i \(0.769108\pi\)
\(614\) 0.634619 + 0.461078i 0.0256111 + 0.0186076i
\(615\) 0 0
\(616\) 3.83337 2.78510i 0.154451 0.112215i
\(617\) −1.93239 0.627872i −0.0777951 0.0252772i 0.269861 0.962899i \(-0.413022\pi\)
−0.347656 + 0.937622i \(0.613022\pi\)
\(618\) 0.372454i 0.0149823i
\(619\) −2.51571 + 7.74255i −0.101115 + 0.311200i −0.988799 0.149253i \(-0.952313\pi\)
0.887684 + 0.460453i \(0.152313\pi\)
\(620\) 0 0
\(621\) 1.53299 + 4.71806i 0.0615167 + 0.189329i
\(622\) −4.46783 + 1.45169i −0.179144 + 0.0582073i
\(623\) −14.4258 + 19.8554i −0.577956 + 0.795488i
\(624\) −1.65769 −0.0663605
\(625\) 0 0
\(626\) −4.09413 −0.163634
\(627\) 2.99421 4.12118i 0.119577 0.164584i
\(628\) 8.01153 2.60310i 0.319695 0.103875i
\(629\) 12.9040 + 39.7143i 0.514515 + 1.58351i
\(630\) 0 0
\(631\) 10.2855 31.6557i 0.409461 1.26019i −0.507651 0.861563i \(-0.669486\pi\)
0.917112 0.398629i \(-0.130514\pi\)
\(632\) 5.63846i 0.224286i
\(633\) −23.2412 7.55152i −0.923754 0.300146i
\(634\) 3.24873 2.36034i 0.129024 0.0937412i
\(635\) 0 0
\(636\) 18.9695 + 13.7822i 0.752191 + 0.546499i
\(637\) −0.632925 0.871147i −0.0250774 0.0345161i
\(638\) 1.27308 + 1.75224i 0.0504015 + 0.0693718i
\(639\) 4.02419 + 2.92375i 0.159195 + 0.115662i
\(640\) 0 0
\(641\) 32.3996 23.5397i 1.27971 0.929761i 0.280162 0.959953i \(-0.409612\pi\)
0.999544 + 0.0301916i \(0.00961174\pi\)
\(642\) −4.05881 1.31879i −0.160189 0.0520484i
\(643\) 11.6870i 0.460890i 0.973085 + 0.230445i \(0.0740182\pi\)
−0.973085 + 0.230445i \(0.925982\pi\)
\(644\) −1.74213 + 5.36172i −0.0686495 + 0.211281i
\(645\) 0 0
\(646\) 0.505688 + 1.55635i 0.0198960 + 0.0612337i
\(647\) 7.56029 2.45649i 0.297226 0.0965745i −0.156608 0.987661i \(-0.550056\pi\)
0.453834 + 0.891086i \(0.350056\pi\)
\(648\) −2.47920 + 3.41233i −0.0973923 + 0.134049i
\(649\) −11.8727 −0.466044
\(650\) 0 0
\(651\) 29.2766 1.14744
\(652\) 18.1773 25.0188i 0.711876 0.979814i
\(653\) 3.17402 1.03130i 0.124209 0.0403579i −0.246253 0.969206i \(-0.579199\pi\)
0.370462 + 0.928848i \(0.379199\pi\)
\(654\) 0.166948 + 0.513814i 0.00652820 + 0.0200917i
\(655\) 0 0
\(656\) −1.19199 + 3.66857i −0.0465394 + 0.143234i
\(657\) 7.36146i 0.287198i
\(658\) 2.39721 + 0.778899i 0.0934528 + 0.0303647i
\(659\) −24.3116 + 17.6634i −0.947046 + 0.688069i −0.950106 0.311926i \(-0.899026\pi\)
0.00306074 + 0.999995i \(0.499026\pi\)
\(660\) 0 0
\(661\) 5.32670 + 3.87008i 0.207185 + 0.150529i 0.686539 0.727093i \(-0.259129\pi\)
−0.479354 + 0.877621i \(0.659129\pi\)
\(662\) 0.965008 + 1.32822i 0.0375061 + 0.0516227i
\(663\) 1.32391 + 1.82220i 0.0514163 + 0.0707685i
\(664\) 8.53192 + 6.19880i 0.331103 + 0.240560i
\(665\) 0 0
\(666\) −0.998835 + 0.725696i −0.0387041 + 0.0281202i
\(667\) −4.94352 1.60625i −0.191414 0.0621941i
\(668\) 41.3603i 1.60028i
\(669\) 3.01483 9.27870i 0.116560 0.358735i
\(670\) 0 0
\(671\) 0.565881 + 1.74160i 0.0218456 + 0.0672339i
\(672\) −9.81044 + 3.18760i −0.378446 + 0.122964i
\(673\) −3.95662 + 5.44582i −0.152516 + 0.209921i −0.878438 0.477857i \(-0.841414\pi\)
0.725921 + 0.687778i \(0.241414\pi\)
\(674\) 5.32730 0.205200
\(675\) 0 0
\(676\) 25.3911 0.976580
\(677\) 8.02200 11.0413i 0.308310 0.424353i −0.626543 0.779387i \(-0.715531\pi\)
0.934853 + 0.355034i \(0.115531\pi\)
\(678\) 2.67386 0.868788i 0.102689 0.0333656i
\(679\) −6.77801 20.8606i −0.260116 0.800555i
\(680\) 0 0
\(681\) −6.09142 + 18.7474i −0.233424 + 0.718404i
\(682\) 2.23453i 0.0855645i
\(683\) −1.11483 0.362229i −0.0426577 0.0138603i 0.287610 0.957747i \(-0.407139\pi\)
−0.330268 + 0.943887i \(0.607139\pi\)
\(684\) 2.29413 1.66678i 0.0877181 0.0637309i
\(685\) 0 0
\(686\) 1.62693 + 1.18203i 0.0621164 + 0.0451302i
\(687\) −8.72692 12.0116i −0.332953 0.458270i
\(688\) 7.24091 + 9.96625i 0.276057 + 0.379960i
\(689\) 1.94235 + 1.41120i 0.0739978 + 0.0537625i
\(690\) 0 0
\(691\) −9.92451 + 7.21058i −0.377546 + 0.274303i −0.760333 0.649533i \(-0.774964\pi\)
0.382787 + 0.923837i \(0.374964\pi\)
\(692\) 13.4031 + 4.35492i 0.509508 + 0.165549i
\(693\) 5.43497i 0.206457i
\(694\) −0.809268 + 2.49067i −0.0307194 + 0.0945445i
\(695\) 0 0
\(696\) −1.95381 6.01321i −0.0740590 0.227930i
\(697\) 4.98464 1.61961i 0.188807 0.0613471i
\(698\) −0.605493 + 0.833390i −0.0229183 + 0.0315443i
\(699\) 32.3910 1.22514
\(700\) 0 0
\(701\) −20.0271 −0.756415 −0.378207 0.925721i \(-0.623459\pi\)
−0.378207 + 0.925721i \(0.623459\pi\)
\(702\) −0.180052 + 0.247820i −0.00679562 + 0.00935337i
\(703\) −13.3103 + 4.32479i −0.502009 + 0.163113i
\(704\) 4.45354 + 13.7066i 0.167849 + 0.516586i
\(705\) 0 0
\(706\) 0.108111 0.332731i 0.00406880 0.0125225i
\(707\) 39.7677i 1.49562i
\(708\) 16.3418 + 5.30979i 0.614164 + 0.199554i
\(709\) −3.55571 + 2.58337i −0.133537 + 0.0970206i −0.652549 0.757747i \(-0.726300\pi\)
0.519011 + 0.854767i \(0.326300\pi\)
\(710\) 0 0
\(711\) −5.23230 3.80149i −0.196227 0.142567i
\(712\) 3.21417 + 4.42392i 0.120456 + 0.165793i
\(713\) −3.15209 4.33848i −0.118047 0.162477i
\(714\) 3.67232 + 2.66810i 0.137433 + 0.0998511i
\(715\) 0 0
\(716\) 12.7897 9.29226i 0.477974 0.347268i
\(717\) 10.5837 + 3.43885i 0.395256 + 0.128426i
\(718\) 4.06727i 0.151789i
\(719\) 3.37704 10.3934i 0.125942 0.387610i −0.868129 0.496338i \(-0.834678\pi\)
0.994072 + 0.108728i \(0.0346777\pi\)
\(720\) 0 0
\(721\) −1.39199 4.28409i −0.0518403 0.159548i
\(722\) 2.78832 0.905980i 0.103771 0.0337171i
\(723\) 17.6452 24.2865i 0.656230 0.903224i
\(724\) −40.5425 −1.50675
\(725\) 0 0
\(726\) −1.88734 −0.0700458
\(727\) −19.3400 + 26.6193i −0.717282 + 0.987254i 0.282328 + 0.959318i \(0.408893\pi\)
−0.999610 + 0.0279359i \(0.991107\pi\)
\(728\) −0.667799 + 0.216981i −0.0247503 + 0.00804185i
\(729\) −9.19466 28.2982i −0.340543 1.04808i
\(730\) 0 0
\(731\) 5.17242 15.9191i 0.191309 0.588788i
\(732\) 2.65026i 0.0979564i
\(733\) 13.0768 + 4.24891i 0.483002 + 0.156937i 0.540389 0.841415i \(-0.318277\pi\)
−0.0573871 + 0.998352i \(0.518277\pi\)
\(734\) −3.17792 + 2.30889i −0.117299 + 0.0852227i
\(735\) 0 0
\(736\) 1.52862 + 1.11061i 0.0563456 + 0.0409375i
\(737\) 8.09739 + 11.1451i 0.298271 + 0.410535i
\(738\) 0.0910839 + 0.125366i 0.00335285 + 0.00461480i
\(739\) −34.9409 25.3860i −1.28532 0.933840i −0.285621 0.958343i \(-0.592200\pi\)
−0.999700 + 0.0245030i \(0.992200\pi\)
\(740\) 0 0
\(741\) −0.610715 + 0.443711i −0.0224352 + 0.0163001i
\(742\) 4.60173 + 1.49519i 0.168935 + 0.0548902i
\(743\) 31.8479i 1.16838i 0.811615 + 0.584192i \(0.198589\pi\)
−0.811615 + 0.584192i \(0.801411\pi\)
\(744\) 2.01573 6.20378i 0.0739003 0.227442i
\(745\) 0 0
\(746\) 1.30979 + 4.03113i 0.0479550 + 0.147590i
\(747\) −11.5046 + 3.73806i −0.420930 + 0.136768i
\(748\) 11.9352 16.4274i 0.436395 0.600646i
\(749\) 51.6145 1.88595
\(750\) 0 0
\(751\) −29.5952 −1.07995 −0.539973 0.841682i \(-0.681565\pi\)
−0.539973 + 0.841682i \(0.681565\pi\)
\(752\) −9.42517 + 12.9726i −0.343700 + 0.473063i
\(753\) 14.7993 4.80860i 0.539318 0.175235i
\(754\) −0.0991824 0.305252i −0.00361201 0.0111166i
\(755\) 0 0
\(756\) 11.1807 34.4107i 0.406639 1.25150i
\(757\) 0.0984401i 0.00357786i 0.999998 + 0.00178893i \(0.000569435\pi\)
−0.999998 + 0.00178893i \(0.999431\pi\)
\(758\) 3.77161 + 1.22547i 0.136991 + 0.0445111i
\(759\) −2.09394 + 1.52134i −0.0760052 + 0.0552210i
\(760\) 0 0
\(761\) 2.86717 + 2.08312i 0.103935 + 0.0755131i 0.638539 0.769590i \(-0.279539\pi\)
−0.534604 + 0.845103i \(0.679539\pi\)
\(762\) −0.927111 1.27606i −0.0335857 0.0462267i
\(763\) −3.84059 5.28612i −0.139039 0.191370i
\(764\) −28.6842 20.8403i −1.03776 0.753975i
\(765\) 0 0
\(766\) −0.837983 + 0.608830i −0.0302775 + 0.0219979i
\(767\) 1.67330 + 0.543687i 0.0604192 + 0.0196314i
\(768\) 19.6989i 0.710822i
\(769\) −0.441149 + 1.35772i −0.0159083 + 0.0489606i −0.958696 0.284434i \(-0.908194\pi\)
0.942787 + 0.333395i \(0.108194\pi\)
\(770\) 0 0
\(771\) 9.21997 + 28.3762i 0.332049 + 1.02194i
\(772\) −12.6960 + 4.12520i −0.456941 + 0.148469i
\(773\) 19.8558 27.3292i 0.714163 0.982962i −0.285534 0.958369i \(-0.592171\pi\)
0.999698 0.0245930i \(-0.00782898\pi\)
\(774\) 0.494888 0.0177884
\(775\) 0 0
\(776\) −4.88708 −0.175436
\(777\) −22.8184 + 31.4068i −0.818604 + 1.12671i
\(778\) −1.41562 + 0.459961i −0.0507523 + 0.0164904i