Properties

Label 950.2.u.g.199.6
Level $950$
Weight $2$
Character 950.199
Analytic conductor $7.586$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.u (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 199.6
Character \(\chi\) \(=\) 950.199
Dual form 950.2.u.g.549.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.984808 - 0.173648i) q^{2} +(1.49114 + 1.77707i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.77707 + 1.49114i) q^{6} +(4.25802 + 2.45837i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.413538 + 2.34529i) q^{9} +O(q^{10})\) \(q+(0.984808 - 0.173648i) q^{2} +(1.49114 + 1.77707i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.77707 + 1.49114i) q^{6} +(4.25802 + 2.45837i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.413538 + 2.34529i) q^{9} +(-1.42329 - 2.46520i) q^{11} +(2.00901 + 1.15990i) q^{12} +(-4.21784 + 5.02662i) q^{13} +(4.62023 + 1.68163i) q^{14} +(0.766044 - 0.642788i) q^{16} +(2.15794 - 0.380503i) q^{17} +2.38147i q^{18} +(-4.17271 - 1.26036i) q^{19} +(1.98061 + 11.2326i) q^{21} +(-1.82974 - 2.18060i) q^{22} +(-0.908934 - 2.49728i) q^{23} +(2.17990 + 0.793418i) q^{24} +(-3.28089 + 5.68268i) q^{26} +(1.24263 - 0.717435i) q^{27} +(4.84205 + 0.853783i) q^{28} +(1.32004 - 7.48630i) q^{29} +(2.70769 - 4.68986i) q^{31} +(0.642788 - 0.766044i) q^{32} +(2.25852 - 6.20524i) q^{33} +(2.05908 - 0.749444i) q^{34} +(0.413538 + 2.34529i) q^{36} -2.06252i q^{37} +(-4.32817 - 0.516628i) q^{38} -15.2220 q^{39} +(-7.16810 + 6.01475i) q^{41} +(3.90103 + 10.7180i) q^{42} +(-0.593093 + 1.62951i) q^{43} +(-2.18060 - 1.82974i) q^{44} +(-1.32877 - 2.30150i) q^{46} +(-2.95934 - 0.521812i) q^{47} +(2.28456 + 0.402829i) q^{48} +(8.58718 + 14.8734i) q^{49} +(3.89396 + 3.26742i) q^{51} +(-2.24426 + 6.16606i) q^{52} +(-1.44406 - 3.96752i) q^{53} +(1.09917 - 0.922316i) q^{54} +4.91674 q^{56} +(-3.98234 - 9.29456i) q^{57} -7.60179i q^{58} +(0.167500 + 0.949937i) q^{59} +(7.04727 - 2.56500i) q^{61} +(1.85217 - 5.08880i) q^{62} +(-7.52644 + 8.96967i) q^{63} +(0.500000 - 0.866025i) q^{64} +(1.14668 - 6.50315i) q^{66} +(1.89039 + 0.333326i) q^{67} +(1.89766 - 1.09561i) q^{68} +(3.08249 - 5.33902i) q^{69} +(5.79354 + 2.10868i) q^{71} +(0.814510 + 2.23785i) q^{72} +(2.55639 + 3.04659i) q^{73} +(-0.358153 - 2.03119i) q^{74} +(-4.35213 + 0.242800i) q^{76} -13.9959i q^{77} +(-14.9908 + 2.64328i) q^{78} +(-11.7380 + 9.84938i) q^{79} +(9.84141 + 3.58198i) q^{81} +(-6.01475 + 7.16810i) q^{82} +(-1.13628 - 0.656032i) q^{83} +(5.70293 + 9.87776i) q^{84} +(-0.301121 + 1.70774i) q^{86} +(15.2720 - 8.81731i) q^{87} +(-2.46520 - 1.42329i) q^{88} +(8.25512 + 6.92687i) q^{89} +(-30.3170 + 11.0345i) q^{91} +(-1.70824 - 2.03580i) q^{92} +(12.3718 - 2.18147i) q^{93} -3.00499 q^{94} +2.31980 q^{96} +(-2.02308 + 0.356724i) q^{97} +(11.0395 + 13.1563i) q^{98} +(6.37020 - 2.31856i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 36q^{9} + O(q^{10}) \) \( 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.984808 0.173648i 0.696364 0.122788i
\(3\) 1.49114 + 1.77707i 0.860909 + 1.02599i 0.999365 + 0.0356229i \(0.0113415\pi\)
−0.138456 + 0.990369i \(0.544214\pi\)
\(4\) 0.939693 0.342020i 0.469846 0.171010i
\(5\) 0 0
\(6\) 1.77707 + 1.49114i 0.725486 + 0.608755i
\(7\) 4.25802 + 2.45837i 1.60938 + 0.929177i 0.989508 + 0.144475i \(0.0461494\pi\)
0.619873 + 0.784702i \(0.287184\pi\)
\(8\) 0.866025 0.500000i 0.306186 0.176777i
\(9\) −0.413538 + 2.34529i −0.137846 + 0.781763i
\(10\) 0 0
\(11\) −1.42329 2.46520i −0.429137 0.743287i 0.567660 0.823263i \(-0.307849\pi\)
−0.996797 + 0.0799763i \(0.974516\pi\)
\(12\) 2.00901 + 1.15990i 0.579950 + 0.334834i
\(13\) −4.21784 + 5.02662i −1.16982 + 1.39413i −0.267227 + 0.963634i \(0.586107\pi\)
−0.902590 + 0.430500i \(0.858337\pi\)
\(14\) 4.62023 + 1.68163i 1.23481 + 0.449433i
\(15\) 0 0
\(16\) 0.766044 0.642788i 0.191511 0.160697i
\(17\) 2.15794 0.380503i 0.523377 0.0922855i 0.0942832 0.995545i \(-0.469944\pi\)
0.429094 + 0.903260i \(0.358833\pi\)
\(18\) 2.38147i 0.561317i
\(19\) −4.17271 1.26036i −0.957285 0.289146i
\(20\) 0 0
\(21\) 1.98061 + 11.2326i 0.432204 + 2.45115i
\(22\) −1.82974 2.18060i −0.390102 0.464906i
\(23\) −0.908934 2.49728i −0.189526 0.520718i 0.808141 0.588989i \(-0.200474\pi\)
−0.997667 + 0.0682711i \(0.978252\pi\)
\(24\) 2.17990 + 0.793418i 0.444970 + 0.161956i
\(25\) 0 0
\(26\) −3.28089 + 5.68268i −0.643436 + 1.11446i
\(27\) 1.24263 0.717435i 0.239145 0.138070i
\(28\) 4.84205 + 0.853783i 0.915061 + 0.161350i
\(29\) 1.32004 7.48630i 0.245125 1.39017i −0.575079 0.818098i \(-0.695029\pi\)
0.820203 0.572072i \(-0.193860\pi\)
\(30\) 0 0
\(31\) 2.70769 4.68986i 0.486316 0.842324i −0.513560 0.858054i \(-0.671674\pi\)
0.999876 + 0.0157295i \(0.00500705\pi\)
\(32\) 0.642788 0.766044i 0.113630 0.135419i
\(33\) 2.25852 6.20524i 0.393158 1.08019i
\(34\) 2.05908 0.749444i 0.353130 0.128529i
\(35\) 0 0
\(36\) 0.413538 + 2.34529i 0.0689229 + 0.390881i
\(37\) 2.06252i 0.339076i −0.985524 0.169538i \(-0.945772\pi\)
0.985524 0.169538i \(-0.0542276\pi\)
\(38\) −4.32817 0.516628i −0.702123 0.0838081i
\(39\) −15.2220 −2.43748
\(40\) 0 0
\(41\) −7.16810 + 6.01475i −1.11947 + 0.939346i −0.998578 0.0533193i \(-0.983020\pi\)
−0.120892 + 0.992666i \(0.538575\pi\)
\(42\) 3.90103 + 10.7180i 0.601942 + 1.65382i
\(43\) −0.593093 + 1.62951i −0.0904459 + 0.248498i −0.976665 0.214768i \(-0.931100\pi\)
0.886219 + 0.463266i \(0.153323\pi\)
\(44\) −2.18060 1.82974i −0.328738 0.275844i
\(45\) 0 0
\(46\) −1.32877 2.30150i −0.195917 0.339338i
\(47\) −2.95934 0.521812i −0.431664 0.0761140i −0.0464056 0.998923i \(-0.514777\pi\)
−0.385259 + 0.922809i \(0.625888\pi\)
\(48\) 2.28456 + 0.402829i 0.329747 + 0.0581433i
\(49\) 8.58718 + 14.8734i 1.22674 + 2.12478i
\(50\) 0 0
\(51\) 3.89396 + 3.26742i 0.545264 + 0.457531i
\(52\) −2.24426 + 6.16606i −0.311223 + 0.855079i
\(53\) −1.44406 3.96752i −0.198357 0.544981i 0.800139 0.599815i \(-0.204759\pi\)
−0.998495 + 0.0548340i \(0.982537\pi\)
\(54\) 1.09917 0.922316i 0.149579 0.125511i
\(55\) 0 0
\(56\) 4.91674 0.657027
\(57\) −3.98234 9.29456i −0.527474 1.23109i
\(58\) 7.60179i 0.998163i
\(59\) 0.167500 + 0.949937i 0.0218066 + 0.123671i 0.993768 0.111470i \(-0.0355559\pi\)
−0.971961 + 0.235141i \(0.924445\pi\)
\(60\) 0 0
\(61\) 7.04727 2.56500i 0.902311 0.328414i 0.151132 0.988514i \(-0.451708\pi\)
0.751178 + 0.660099i \(0.229486\pi\)
\(62\) 1.85217 5.08880i 0.235226 0.646278i
\(63\) −7.52644 + 8.96967i −0.948243 + 1.13007i
\(64\) 0.500000 0.866025i 0.0625000 0.108253i
\(65\) 0 0
\(66\) 1.14668 6.50315i 0.141147 0.800483i
\(67\) 1.89039 + 0.333326i 0.230948 + 0.0407223i 0.287924 0.957653i \(-0.407035\pi\)
−0.0569765 + 0.998376i \(0.518146\pi\)
\(68\) 1.89766 1.09561i 0.230125 0.132863i
\(69\) 3.08249 5.33902i 0.371088 0.642743i
\(70\) 0 0
\(71\) 5.79354 + 2.10868i 0.687567 + 0.250254i 0.662093 0.749422i \(-0.269668\pi\)
0.0254738 + 0.999675i \(0.491891\pi\)
\(72\) 0.814510 + 2.23785i 0.0959909 + 0.263733i
\(73\) 2.55639 + 3.04659i 0.299203 + 0.356576i 0.894610 0.446848i \(-0.147454\pi\)
−0.595407 + 0.803424i \(0.703009\pi\)
\(74\) −0.358153 2.03119i −0.0416344 0.236121i
\(75\) 0 0
\(76\) −4.35213 + 0.242800i −0.499224 + 0.0278511i
\(77\) 13.9959i 1.59498i
\(78\) −14.9908 + 2.64328i −1.69737 + 0.299292i
\(79\) −11.7380 + 9.84938i −1.32063 + 1.10814i −0.334461 + 0.942409i \(0.608554\pi\)
−0.986171 + 0.165732i \(0.947001\pi\)
\(80\) 0 0
\(81\) 9.84141 + 3.58198i 1.09349 + 0.397998i
\(82\) −6.01475 + 7.16810i −0.664218 + 0.791584i
\(83\) −1.13628 0.656032i −0.124723 0.0720089i 0.436340 0.899782i \(-0.356274\pi\)
−0.561064 + 0.827773i \(0.689608\pi\)
\(84\) 5.70293 + 9.87776i 0.622240 + 1.07775i
\(85\) 0 0
\(86\) −0.301121 + 1.70774i −0.0324708 + 0.184151i
\(87\) 15.2720 8.81731i 1.63733 0.945315i
\(88\) −2.46520 1.42329i −0.262792 0.151723i
\(89\) 8.25512 + 6.92687i 0.875041 + 0.734247i 0.965153 0.261685i \(-0.0842782\pi\)
−0.0901123 + 0.995932i \(0.528723\pi\)
\(90\) 0 0
\(91\) −30.3170 + 11.0345i −3.17808 + 1.15673i
\(92\) −1.70824 2.03580i −0.178096 0.212247i
\(93\) 12.3718 2.18147i 1.28289 0.226208i
\(94\) −3.00499 −0.309941
\(95\) 0 0
\(96\) 2.31980 0.236764
\(97\) −2.02308 + 0.356724i −0.205413 + 0.0362198i −0.275408 0.961328i \(-0.588813\pi\)
0.0699948 + 0.997547i \(0.477702\pi\)
\(98\) 11.0395 + 13.1563i 1.11515 + 1.32899i
\(99\) 6.37020 2.31856i 0.640229 0.233024i
\(100\) 0 0
\(101\) −3.83762 3.22015i −0.381857 0.320416i 0.431574 0.902078i \(-0.357959\pi\)
−0.813431 + 0.581661i \(0.802403\pi\)
\(102\) 4.40219 + 2.54161i 0.435882 + 0.251656i
\(103\) 7.82444 4.51744i 0.770965 0.445117i −0.0622537 0.998060i \(-0.519829\pi\)
0.833219 + 0.552943i \(0.186495\pi\)
\(104\) −1.13944 + 6.46210i −0.111732 + 0.633661i
\(105\) 0 0
\(106\) −2.11108 3.65649i −0.205046 0.355150i
\(107\) −5.16829 2.98391i −0.499637 0.288466i 0.228926 0.973444i \(-0.426478\pi\)
−0.728564 + 0.684978i \(0.759812\pi\)
\(108\) 0.922316 1.09917i 0.0887499 0.105768i
\(109\) −14.8753 5.41417i −1.42480 0.518583i −0.489360 0.872082i \(-0.662770\pi\)
−0.935435 + 0.353499i \(0.884992\pi\)
\(110\) 0 0
\(111\) 3.66524 3.07550i 0.347889 0.291914i
\(112\) 4.84205 0.853783i 0.457530 0.0806750i
\(113\) 18.2051i 1.71259i −0.516485 0.856296i \(-0.672760\pi\)
0.516485 0.856296i \(-0.327240\pi\)
\(114\) −5.53582 8.46183i −0.518477 0.792523i
\(115\) 0 0
\(116\) −1.32004 7.48630i −0.122562 0.695085i
\(117\) −10.0446 11.9707i −0.928628 1.10670i
\(118\) 0.329910 + 0.906420i 0.0303707 + 0.0834427i
\(119\) 10.1240 + 3.68482i 0.928063 + 0.337787i
\(120\) 0 0
\(121\) 1.44851 2.50890i 0.131683 0.228082i
\(122\) 6.49480 3.74977i 0.588012 0.339489i
\(123\) −21.3773 3.76939i −1.92752 0.339874i
\(124\) 0.940372 5.33311i 0.0844479 0.478928i
\(125\) 0 0
\(126\) −5.85453 + 10.1404i −0.521563 + 0.903374i
\(127\) −4.91703 + 5.85989i −0.436316 + 0.519981i −0.938733 0.344644i \(-0.888000\pi\)
0.502418 + 0.864625i \(0.332444\pi\)
\(128\) 0.342020 0.939693i 0.0302306 0.0830579i
\(129\) −3.78014 + 1.37586i −0.332823 + 0.121137i
\(130\) 0 0
\(131\) −2.31209 13.1125i −0.202008 1.14564i −0.902079 0.431571i \(-0.857960\pi\)
0.700071 0.714073i \(-0.253152\pi\)
\(132\) 6.60347i 0.574759i
\(133\) −14.6691 15.6247i −1.27197 1.35483i
\(134\) 1.91955 0.165824
\(135\) 0 0
\(136\) 1.67858 1.40849i 0.143937 0.120777i
\(137\) 2.47153 + 6.79047i 0.211157 + 0.580149i 0.999379 0.0352423i \(-0.0112203\pi\)
−0.788222 + 0.615391i \(0.788998\pi\)
\(138\) 2.10854 5.79318i 0.179491 0.493148i
\(139\) 1.84752 + 1.55026i 0.156705 + 0.131491i 0.717769 0.696281i \(-0.245163\pi\)
−0.561064 + 0.827772i \(0.689608\pi\)
\(140\) 0 0
\(141\) −3.48549 6.03705i −0.293531 0.508411i
\(142\) 6.07169 + 1.07060i 0.509525 + 0.0898430i
\(143\) 18.3948 + 3.24351i 1.53825 + 0.271236i
\(144\) 1.19073 + 2.06241i 0.0992279 + 0.171868i
\(145\) 0 0
\(146\) 3.04659 + 2.55639i 0.252137 + 0.211568i
\(147\) −13.6264 + 37.4384i −1.12389 + 3.08786i
\(148\) −0.705424 1.93814i −0.0579855 0.159314i
\(149\) 5.34602 4.48584i 0.437963 0.367495i −0.396983 0.917826i \(-0.629943\pi\)
0.834946 + 0.550331i \(0.185499\pi\)
\(150\) 0 0
\(151\) −5.69362 −0.463340 −0.231670 0.972794i \(-0.574419\pi\)
−0.231670 + 0.972794i \(0.574419\pi\)
\(152\) −4.24385 + 0.994851i −0.344222 + 0.0806931i
\(153\) 5.21834i 0.421878i
\(154\) −2.43036 13.7832i −0.195844 1.11068i
\(155\) 0 0
\(156\) −14.3040 + 5.20624i −1.14524 + 0.416833i
\(157\) −1.81744 + 4.99337i −0.145047 + 0.398514i −0.990848 0.134985i \(-0.956901\pi\)
0.845800 + 0.533500i \(0.179123\pi\)
\(158\) −9.84938 + 11.7380i −0.783575 + 0.933828i
\(159\) 4.89727 8.48232i 0.388379 0.672692i
\(160\) 0 0
\(161\) 2.26897 12.8680i 0.178820 1.01414i
\(162\) 10.3139 + 1.81862i 0.810337 + 0.142884i
\(163\) 3.87424 2.23679i 0.303454 0.175199i −0.340540 0.940230i \(-0.610610\pi\)
0.643993 + 0.765031i \(0.277276\pi\)
\(164\) −4.67865 + 8.10365i −0.365341 + 0.632789i
\(165\) 0 0
\(166\) −1.23294 0.448753i −0.0956945 0.0348300i
\(167\) −1.24795 3.42872i −0.0965694 0.265322i 0.881997 0.471256i \(-0.156199\pi\)
−0.978566 + 0.205934i \(0.933977\pi\)
\(168\) 7.33154 + 8.73739i 0.565641 + 0.674104i
\(169\) −5.21936 29.6004i −0.401489 2.27696i
\(170\) 0 0
\(171\) 4.68148 9.26500i 0.358002 0.708512i
\(172\) 1.73409i 0.132223i
\(173\) −1.15844 + 0.204264i −0.0880746 + 0.0155299i −0.217512 0.976058i \(-0.569794\pi\)
0.129437 + 0.991588i \(0.458683\pi\)
\(174\) 13.5089 11.3353i 1.02411 0.859328i
\(175\) 0 0
\(176\) −2.67490 0.973585i −0.201628 0.0733867i
\(177\) −1.43834 + 1.71415i −0.108112 + 0.128843i
\(178\) 9.33254 + 5.38815i 0.699504 + 0.403859i
\(179\) 2.16529 + 3.75038i 0.161841 + 0.280317i 0.935529 0.353250i \(-0.114923\pi\)
−0.773688 + 0.633567i \(0.781590\pi\)
\(180\) 0 0
\(181\) 0.237758 1.34839i 0.0176724 0.100225i −0.974696 0.223536i \(-0.928240\pi\)
0.992368 + 0.123311i \(0.0393511\pi\)
\(182\) −27.9403 + 16.1313i −2.07107 + 1.19573i
\(183\) 15.0666 + 8.69872i 1.11376 + 0.643028i
\(184\) −2.03580 1.70824i −0.150081 0.125933i
\(185\) 0 0
\(186\) 11.8050 4.29667i 0.865584 0.315047i
\(187\) −4.00938 4.77819i −0.293195 0.349416i
\(188\) −2.95934 + 0.521812i −0.215832 + 0.0380570i
\(189\) 7.05488 0.513167
\(190\) 0 0
\(191\) 13.6338 0.986505 0.493252 0.869886i \(-0.335808\pi\)
0.493252 + 0.869886i \(0.335808\pi\)
\(192\) 2.28456 0.402829i 0.164874 0.0290717i
\(193\) 3.35501 + 3.99835i 0.241499 + 0.287807i 0.873156 0.487441i \(-0.162069\pi\)
−0.631657 + 0.775248i \(0.717625\pi\)
\(194\) −1.93040 + 0.702609i −0.138595 + 0.0504444i
\(195\) 0 0
\(196\) 13.1563 + 11.0395i 0.939737 + 0.788533i
\(197\) −2.47286 1.42771i −0.176184 0.101720i 0.409315 0.912393i \(-0.365768\pi\)
−0.585498 + 0.810674i \(0.699101\pi\)
\(198\) 5.87080 3.38951i 0.417220 0.240882i
\(199\) 0.254330 1.44238i 0.0180290 0.102247i −0.974465 0.224538i \(-0.927913\pi\)
0.992494 + 0.122290i \(0.0390239\pi\)
\(200\) 0 0
\(201\) 2.22649 + 3.85639i 0.157044 + 0.272009i
\(202\) −4.33849 2.50483i −0.305255 0.176239i
\(203\) 24.0248 28.6317i 1.68621 2.00955i
\(204\) 4.77666 + 1.73856i 0.334433 + 0.121724i
\(205\) 0 0
\(206\) 6.92112 5.80751i 0.482218 0.404629i
\(207\) 6.23271 1.09900i 0.433203 0.0763855i
\(208\) 6.56179i 0.454978i
\(209\) 2.83192 + 12.0804i 0.195888 + 0.835621i
\(210\) 0 0
\(211\) 0.227567 + 1.29059i 0.0156663 + 0.0888482i 0.991638 0.129047i \(-0.0411919\pi\)
−0.975972 + 0.217896i \(0.930081\pi\)
\(212\) −2.71395 3.23435i −0.186395 0.222136i
\(213\) 4.89171 + 13.4399i 0.335174 + 0.920883i
\(214\) −5.60792 2.04112i −0.383350 0.139528i
\(215\) 0 0
\(216\) 0.717435 1.24263i 0.0488152 0.0845505i
\(217\) 23.0588 13.3130i 1.56534 0.903747i
\(218\) −15.5895 2.74884i −1.05585 0.186175i
\(219\) −1.60206 + 9.08576i −0.108257 + 0.613959i
\(220\) 0 0
\(221\) −7.18919 + 12.4520i −0.483597 + 0.837615i
\(222\) 3.07550 3.66524i 0.206414 0.245995i
\(223\) −9.62115 + 26.4339i −0.644280 + 1.77014i −0.00643379 + 0.999979i \(0.502048\pi\)
−0.637846 + 0.770164i \(0.720174\pi\)
\(224\) 4.62023 1.68163i 0.308702 0.112358i
\(225\) 0 0
\(226\) −3.16128 17.9285i −0.210285 1.19259i
\(227\) 12.6466i 0.839382i 0.907667 + 0.419691i \(0.137862\pi\)
−0.907667 + 0.419691i \(0.862138\pi\)
\(228\) −6.92110 7.37199i −0.458361 0.488222i
\(229\) −13.7440 −0.908227 −0.454113 0.890944i \(-0.650044\pi\)
−0.454113 + 0.890944i \(0.650044\pi\)
\(230\) 0 0
\(231\) 24.8716 20.8698i 1.63643 1.37313i
\(232\) −2.59996 7.14334i −0.170696 0.468983i
\(233\) −8.41990 + 23.1335i −0.551606 + 1.51552i 0.279911 + 0.960026i \(0.409695\pi\)
−0.831517 + 0.555499i \(0.812527\pi\)
\(234\) −11.9707 10.0446i −0.782552 0.656639i
\(235\) 0 0
\(236\) 0.482296 + 0.835361i 0.0313948 + 0.0543774i
\(237\) −35.0061 6.17251i −2.27389 0.400948i
\(238\) 10.6100 + 1.87083i 0.687746 + 0.121268i
\(239\) −8.14698 14.1110i −0.526984 0.912763i −0.999506 0.0314439i \(-0.989989\pi\)
0.472522 0.881319i \(-0.343344\pi\)
\(240\) 0 0
\(241\) −14.7500 12.3767i −0.950133 0.797256i 0.0291873 0.999574i \(-0.490708\pi\)
−0.979320 + 0.202318i \(0.935153\pi\)
\(242\) 0.990842 2.72232i 0.0636938 0.174997i
\(243\) 6.83722 + 18.7851i 0.438608 + 1.20506i
\(244\) 5.74499 4.82062i 0.367785 0.308608i
\(245\) 0 0
\(246\) −21.7070 −1.38399
\(247\) 23.9351 15.6586i 1.52296 0.996335i
\(248\) 5.41539i 0.343877i
\(249\) −0.528538 2.99749i −0.0334947 0.189958i
\(250\) 0 0
\(251\) 26.0953 9.49792i 1.64712 0.599504i 0.658860 0.752266i \(-0.271039\pi\)
0.988263 + 0.152762i \(0.0488169\pi\)
\(252\) −4.00474 + 11.0029i −0.252275 + 0.693119i
\(253\) −4.86262 + 5.79505i −0.305710 + 0.364331i
\(254\) −3.82477 + 6.62470i −0.239987 + 0.415671i
\(255\) 0 0
\(256\) 0.173648 0.984808i 0.0108530 0.0615505i
\(257\) 12.8717 + 2.26963i 0.802915 + 0.141576i 0.560022 0.828478i \(-0.310793\pi\)
0.242893 + 0.970053i \(0.421904\pi\)
\(258\) −3.48379 + 2.01137i −0.216891 + 0.125222i
\(259\) 5.07044 8.78226i 0.315062 0.545703i
\(260\) 0 0
\(261\) 17.0116 + 6.19173i 1.05299 + 0.383259i
\(262\) −4.55392 12.5118i −0.281342 0.772981i
\(263\) −9.67780 11.5336i −0.596759 0.711190i 0.380131 0.924933i \(-0.375879\pi\)
−0.976890 + 0.213743i \(0.931434\pi\)
\(264\) −1.14668 6.50315i −0.0705734 0.400241i
\(265\) 0 0
\(266\) −17.1594 12.8401i −1.05211 0.787276i
\(267\) 24.9988i 1.52990i
\(268\) 1.89039 0.333326i 0.115474 0.0203612i
\(269\) −18.7339 + 15.7196i −1.14222 + 0.958439i −0.999509 0.0313248i \(-0.990027\pi\)
−0.142714 + 0.989764i \(0.545583\pi\)
\(270\) 0 0
\(271\) −8.41094 3.06133i −0.510928 0.185963i 0.0736745 0.997282i \(-0.476527\pi\)
−0.584603 + 0.811320i \(0.698750\pi\)
\(272\) 1.40849 1.67858i 0.0854025 0.101779i
\(273\) −64.8158 37.4214i −3.92283 2.26485i
\(274\) 3.61313 + 6.25813i 0.218277 + 0.378067i
\(275\) 0 0
\(276\) 1.07054 6.07131i 0.0644387 0.365450i
\(277\) −6.75622 + 3.90071i −0.405942 + 0.234371i −0.689045 0.724719i \(-0.741970\pi\)
0.283103 + 0.959090i \(0.408636\pi\)
\(278\) 2.08866 + 1.20589i 0.125269 + 0.0723242i
\(279\) 9.87935 + 8.28976i 0.591461 + 0.496295i
\(280\) 0 0
\(281\) −17.1947 + 6.25837i −1.02575 + 0.373343i −0.799462 0.600717i \(-0.794882\pi\)
−0.226290 + 0.974060i \(0.572660\pi\)
\(282\) −4.48086 5.34008i −0.266831 0.317997i
\(283\) 7.11822 1.25513i 0.423134 0.0746100i 0.0419735 0.999119i \(-0.486635\pi\)
0.381161 + 0.924509i \(0.375524\pi\)
\(284\) 6.16536 0.365847
\(285\) 0 0
\(286\) 18.6786 1.10449
\(287\) −45.3084 + 7.98910i −2.67447 + 0.471582i
\(288\) 1.53078 + 1.82431i 0.0902020 + 0.107499i
\(289\) −11.4629 + 4.17214i −0.674286 + 0.245420i
\(290\) 0 0
\(291\) −3.65062 3.06323i −0.214003 0.179570i
\(292\) 3.44421 + 1.98852i 0.201557 + 0.116369i
\(293\) −9.86109 + 5.69330i −0.576091 + 0.332606i −0.759578 0.650416i \(-0.774595\pi\)
0.183488 + 0.983022i \(0.441261\pi\)
\(294\) −6.91833 + 39.2358i −0.403485 + 2.28828i
\(295\) 0 0
\(296\) −1.03126 1.78620i −0.0599408 0.103821i
\(297\) −3.53724 2.04223i −0.205252 0.118502i
\(298\) 4.48584 5.34602i 0.259858 0.309687i
\(299\) 16.3866 + 5.96423i 0.947662 + 0.344921i
\(300\) 0 0
\(301\) −6.53135 + 5.48045i −0.376461 + 0.315888i
\(302\) −5.60712 + 0.988686i −0.322653 + 0.0568925i
\(303\) 11.6214i 0.667632i
\(304\) −4.00662 + 1.71667i −0.229796 + 0.0984580i
\(305\) 0 0
\(306\) 0.906156 + 5.13906i 0.0518015 + 0.293781i
\(307\) 3.17725 + 3.78649i 0.181335 + 0.216107i 0.849053 0.528308i \(-0.177173\pi\)
−0.667718 + 0.744414i \(0.732729\pi\)
\(308\) −4.78687 13.1518i −0.272757 0.749394i
\(309\) 19.6951 + 7.16844i 1.12042 + 0.407798i
\(310\) 0 0
\(311\) −12.0586 + 20.8861i −0.683782 + 1.18434i 0.290036 + 0.957016i \(0.406333\pi\)
−0.973818 + 0.227329i \(0.927001\pi\)
\(312\) −13.1827 + 7.61102i −0.746322 + 0.430889i
\(313\) 30.5050 + 5.37886i 1.72424 + 0.304031i 0.946057 0.324001i \(-0.105028\pi\)
0.778188 + 0.628031i \(0.216139\pi\)
\(314\) −0.922737 + 5.23310i −0.0520731 + 0.295321i
\(315\) 0 0
\(316\) −7.66146 + 13.2700i −0.430991 + 0.746498i
\(317\) 4.44201 5.29378i 0.249488 0.297328i −0.626737 0.779231i \(-0.715610\pi\)
0.876225 + 0.481903i \(0.160054\pi\)
\(318\) 3.34993 9.20386i 0.187855 0.516127i
\(319\) −20.3340 + 7.40098i −1.13849 + 0.414376i
\(320\) 0 0
\(321\) −2.40401 13.6338i −0.134179 0.760966i
\(322\) 13.0665i 0.728166i
\(323\) −9.48402 1.13205i −0.527705 0.0629890i
\(324\) 10.4730 0.581834
\(325\) 0 0
\(326\) 3.42697 2.87557i 0.189802 0.159263i
\(327\) −12.5598 34.5077i −0.694557 1.90828i
\(328\) −3.20038 + 8.79298i −0.176712 + 0.485511i
\(329\) −11.3181 9.49705i −0.623989 0.523589i
\(330\) 0 0
\(331\) −2.08943 3.61900i −0.114845 0.198918i 0.802873 0.596151i \(-0.203304\pi\)
−0.917718 + 0.397233i \(0.869971\pi\)
\(332\) −1.29213 0.227838i −0.0709149 0.0125042i
\(333\) 4.83721 + 0.852930i 0.265077 + 0.0467403i
\(334\) −1.82438 3.15992i −0.0998258 0.172903i
\(335\) 0 0
\(336\) 8.73739 + 7.33154i 0.476664 + 0.399968i
\(337\) 5.88315 16.1638i 0.320476 0.880500i −0.669944 0.742411i \(-0.733682\pi\)
0.990420 0.138088i \(-0.0440958\pi\)
\(338\) −10.2801 28.2444i −0.559165 1.53629i
\(339\) 32.3517 27.1463i 1.75710 1.47439i
\(340\) 0 0
\(341\) −15.4153 −0.834784
\(342\) 3.00151 9.93717i 0.162303 0.537341i
\(343\) 50.0247i 2.70108i
\(344\) 0.301121 + 1.70774i 0.0162354 + 0.0920754i
\(345\) 0 0
\(346\) −1.10537 + 0.402322i −0.0594251 + 0.0216290i
\(347\) 6.31466 17.3494i 0.338989 0.931364i −0.646693 0.762750i \(-0.723849\pi\)
0.985682 0.168614i \(-0.0539291\pi\)
\(348\) 11.3353 13.5089i 0.607637 0.724153i
\(349\) 12.3704 21.4262i 0.662174 1.14692i −0.317870 0.948134i \(-0.602967\pi\)
0.980043 0.198784i \(-0.0636992\pi\)
\(350\) 0 0
\(351\) −1.63495 + 9.27227i −0.0872672 + 0.494917i
\(352\) −2.80333 0.494302i −0.149418 0.0263464i
\(353\) 5.55115 3.20496i 0.295458 0.170583i −0.344943 0.938624i \(-0.612102\pi\)
0.640401 + 0.768041i \(0.278768\pi\)
\(354\) −1.11883 + 1.93787i −0.0594651 + 0.102997i
\(355\) 0 0
\(356\) 10.1264 + 3.68571i 0.536698 + 0.195342i
\(357\) 8.54805 + 23.4856i 0.452411 + 1.24299i
\(358\) 2.78364 + 3.31741i 0.147120 + 0.175331i
\(359\) 6.39293 + 36.2561i 0.337406 + 1.91353i 0.402051 + 0.915617i \(0.368297\pi\)
−0.0646449 + 0.997908i \(0.520591\pi\)
\(360\) 0 0
\(361\) 15.8230 + 10.5182i 0.832789 + 0.553591i
\(362\) 1.36920i 0.0719633i
\(363\) 6.61843 1.16701i 0.347377 0.0612520i
\(364\) −24.7146 + 20.7380i −1.29540 + 1.08697i
\(365\) 0 0
\(366\) 16.3483 + 5.95028i 0.854537 + 0.311026i
\(367\) −9.39999 + 11.2025i −0.490676 + 0.584764i −0.953389 0.301743i \(-0.902431\pi\)
0.462714 + 0.886508i \(0.346876\pi\)
\(368\) −2.30150 1.32877i −0.119974 0.0692671i
\(369\) −11.1420 19.2986i −0.580032 1.00464i
\(370\) 0 0
\(371\) 3.60480 20.4438i 0.187152 1.06139i
\(372\) 10.8795 6.28130i 0.564078 0.325670i
\(373\) −11.7411 6.77871i −0.607930 0.350989i 0.164225 0.986423i \(-0.447488\pi\)
−0.772155 + 0.635434i \(0.780821\pi\)
\(374\) −4.77819 4.00938i −0.247075 0.207320i
\(375\) 0 0
\(376\) −2.82377 + 1.02777i −0.145625 + 0.0530031i
\(377\) 32.0631 + 38.2113i 1.65133 + 1.96798i
\(378\) 6.94770 1.22507i 0.357351 0.0630107i
\(379\) −30.2899 −1.55589 −0.777944 0.628333i \(-0.783738\pi\)
−0.777944 + 0.628333i \(0.783738\pi\)
\(380\) 0 0
\(381\) −17.7454 −0.909124
\(382\) 13.4266 2.36748i 0.686967 0.121131i
\(383\) 18.4242 + 21.9571i 0.941433 + 1.12196i 0.992375 + 0.123254i \(0.0393330\pi\)
−0.0509425 + 0.998702i \(0.516223\pi\)
\(384\) 2.17990 0.793418i 0.111242 0.0404889i
\(385\) 0 0
\(386\) 3.99835 + 3.35501i 0.203511 + 0.170766i
\(387\) −3.57641 2.06484i −0.181799 0.104962i
\(388\) −1.77907 + 1.02715i −0.0903186 + 0.0521454i
\(389\) −2.97395 + 16.8661i −0.150785 + 0.855145i 0.811754 + 0.584000i \(0.198513\pi\)
−0.962539 + 0.271145i \(0.912598\pi\)
\(390\) 0 0
\(391\) −2.91165 5.04312i −0.147248 0.255041i
\(392\) 14.8734 + 8.58718i 0.751222 + 0.433718i
\(393\) 19.8542 23.6613i 1.00151 1.19355i
\(394\) −2.68321 0.976608i −0.135178 0.0492008i
\(395\) 0 0
\(396\) 5.19303 4.35747i 0.260960 0.218971i
\(397\) −25.7084 + 4.53308i −1.29027 + 0.227509i −0.776334 0.630322i \(-0.782923\pi\)
−0.513932 + 0.857831i \(0.671812\pi\)
\(398\) 1.46463i 0.0734151i
\(399\) 5.89259 49.3665i 0.294998 2.47142i
\(400\) 0 0
\(401\) −1.61683 9.16948i −0.0807405 0.457902i −0.998195 0.0600607i \(-0.980871\pi\)
0.917454 0.397841i \(-0.130241\pi\)
\(402\) 2.86232 + 3.41117i 0.142759 + 0.170134i
\(403\) 12.1536 + 33.3916i 0.605412 + 1.66336i
\(404\) −4.70754 1.71340i −0.234209 0.0852450i
\(405\) 0 0
\(406\) 18.6880 32.3686i 0.927471 1.60643i
\(407\) −5.08453 + 2.93556i −0.252031 + 0.145510i
\(408\) 5.00598 + 0.882690i 0.247833 + 0.0436997i
\(409\) −2.53175 + 14.3583i −0.125187 + 0.709972i 0.856009 + 0.516960i \(0.172937\pi\)
−0.981196 + 0.193012i \(0.938175\pi\)
\(410\) 0 0
\(411\) −8.38174 + 14.5176i −0.413441 + 0.716101i
\(412\) 5.80751 6.92112i 0.286116 0.340979i
\(413\) −1.62208 + 4.45663i −0.0798174 + 0.219297i
\(414\) 5.94718 2.16460i 0.292288 0.106384i
\(415\) 0 0
\(416\) 1.13944 + 6.46210i 0.0558658 + 0.316831i
\(417\) 5.59483i 0.273980i
\(418\) 4.88664 + 11.4051i 0.239013 + 0.557844i
\(419\) −14.5969 −0.713103 −0.356552 0.934276i \(-0.616048\pi\)
−0.356552 + 0.934276i \(0.616048\pi\)
\(420\) 0 0
\(421\) −30.0605 + 25.2237i −1.46506 + 1.22933i −0.544478 + 0.838775i \(0.683272\pi\)
−0.920580 + 0.390554i \(0.872283\pi\)
\(422\) 0.448219 + 1.23147i 0.0218190 + 0.0599471i
\(423\) 2.44760 6.72472i 0.119006 0.326967i
\(424\) −3.23435 2.71395i −0.157074 0.131801i
\(425\) 0 0
\(426\) 7.15120 + 12.3862i 0.346477 + 0.600115i
\(427\) 36.3132 + 6.40299i 1.75732 + 0.309862i
\(428\) −5.87716 1.03630i −0.284083 0.0500916i
\(429\) 21.6653 + 37.5254i 1.04601 + 1.81174i
\(430\) 0 0
\(431\) 16.7585 + 14.0620i 0.807228 + 0.677345i 0.949944 0.312419i \(-0.101139\pi\)
−0.142716 + 0.989764i \(0.545584\pi\)
\(432\) 0.490754 1.34834i 0.0236114 0.0648718i
\(433\) −0.376798 1.03524i −0.0181078 0.0497507i 0.930309 0.366776i \(-0.119538\pi\)
−0.948417 + 0.317025i \(0.897316\pi\)
\(434\) 20.3967 17.1149i 0.979075 0.821542i
\(435\) 0 0
\(436\) −15.8300 −0.758118
\(437\) 0.645253 + 11.5660i 0.0308666 + 0.553276i
\(438\) 9.22592i 0.440832i
\(439\) 0.732304 + 4.15310i 0.0349510 + 0.198217i 0.997284 0.0736582i \(-0.0234674\pi\)
−0.962333 + 0.271875i \(0.912356\pi\)
\(440\) 0 0
\(441\) −38.4336 + 13.9887i −1.83017 + 0.666128i
\(442\) −4.91770 + 13.5113i −0.233911 + 0.642665i
\(443\) 4.87432 5.80899i 0.231586 0.275993i −0.637719 0.770269i \(-0.720122\pi\)
0.869305 + 0.494275i \(0.164567\pi\)
\(444\) 2.39232 4.14362i 0.113534 0.196647i
\(445\) 0 0
\(446\) −4.88478 + 27.7030i −0.231301 + 1.31177i
\(447\) 15.9433 + 2.81124i 0.754093 + 0.132967i
\(448\) 4.25802 2.45837i 0.201173 0.116147i
\(449\) 14.8487 25.7188i 0.700756 1.21374i −0.267446 0.963573i \(-0.586180\pi\)
0.968202 0.250171i \(-0.0804870\pi\)
\(450\) 0 0
\(451\) 25.0298 + 9.11012i 1.17861 + 0.428979i
\(452\) −6.22651 17.1072i −0.292871 0.804655i
\(453\) −8.48997 10.1180i −0.398894 0.475383i
\(454\) 2.19605 + 12.4544i 0.103066 + 0.584515i
\(455\) 0 0
\(456\) −8.09609 6.05816i −0.379134 0.283699i
\(457\) 9.12576i 0.426885i 0.976956 + 0.213442i \(0.0684676\pi\)
−0.976956 + 0.213442i \(0.931532\pi\)
\(458\) −13.5352 + 2.38661i −0.632456 + 0.111519i
\(459\) 2.40854 2.02101i 0.112421 0.0943324i
\(460\) 0 0
\(461\) 24.7943 + 9.02439i 1.15479 + 0.420308i 0.847232 0.531223i \(-0.178267\pi\)
0.307554 + 0.951531i \(0.400490\pi\)
\(462\) 20.8698 24.8716i 0.970949 1.15713i
\(463\) −13.6156 7.86094i −0.632768 0.365329i 0.149055 0.988829i \(-0.452377\pi\)
−0.781823 + 0.623500i \(0.785710\pi\)
\(464\) −3.80089 6.58334i −0.176452 0.305624i
\(465\) 0 0
\(466\) −4.27489 + 24.2441i −0.198031 + 1.12309i
\(467\) −5.97499 + 3.44966i −0.276490 + 0.159631i −0.631833 0.775104i \(-0.717697\pi\)
0.355344 + 0.934736i \(0.384364\pi\)
\(468\) −13.5331 7.81335i −0.625568 0.361172i
\(469\) 7.22988 + 6.06659i 0.333845 + 0.280129i
\(470\) 0 0
\(471\) −11.5836 + 4.21609i −0.533745 + 0.194267i
\(472\) 0.620028 + 0.738920i 0.0285391 + 0.0340116i
\(473\) 4.86122 0.857164i 0.223519 0.0394124i
\(474\) −35.5461 −1.63269
\(475\) 0 0
\(476\) 10.7737 0.493812
\(477\) 9.90216 1.74602i 0.453389 0.0799447i
\(478\) −10.4735 12.4819i −0.479049 0.570908i
\(479\) −3.42858 + 1.24790i −0.156656 + 0.0570180i −0.419158 0.907913i \(-0.637675\pi\)
0.262502 + 0.964931i \(0.415452\pi\)
\(480\) 0 0
\(481\) 10.3675 + 8.69938i 0.472718 + 0.396657i
\(482\) −16.6751 9.62739i −0.759532 0.438516i
\(483\) 26.2506 15.1558i 1.19444 0.689612i
\(484\) 0.503064 2.85302i 0.0228665 0.129683i
\(485\) 0 0
\(486\) 9.99534 + 17.3124i 0.453398 + 0.785308i
\(487\) 19.4986 + 11.2575i 0.883568 + 0.510128i 0.871833 0.489803i \(-0.162931\pi\)
0.0117346 + 0.999931i \(0.496265\pi\)
\(488\) 4.82062 5.74499i 0.218219 0.260063i
\(489\) 9.75196 + 3.54942i 0.440999 + 0.160510i
\(490\) 0 0
\(491\) 19.2746 16.1733i 0.869849 0.729890i −0.0942175 0.995552i \(-0.530035\pi\)
0.964066 + 0.265662i \(0.0855905\pi\)
\(492\) −21.3773 + 3.76939i −0.963761 + 0.169937i
\(493\) 16.6573i 0.750205i
\(494\) 20.8524 19.5770i 0.938195 0.880813i
\(495\) 0 0
\(496\) −0.940372 5.33311i −0.0422239 0.239464i
\(497\) 19.4851 + 23.2215i 0.874027 + 1.04163i
\(498\) −1.04102 2.86017i −0.0466490 0.128167i
\(499\) 29.8561 + 10.8667i 1.33654 + 0.486461i 0.908721 0.417403i \(-0.137060\pi\)
0.427819 + 0.903864i \(0.359282\pi\)
\(500\) 0 0
\(501\) 4.23220 7.33039i 0.189081 0.327498i
\(502\) 24.0496 13.8850i 1.07339 0.619719i
\(503\) 25.1737 + 4.43880i 1.12244 + 0.197917i 0.703912 0.710287i \(-0.251435\pi\)
0.418528 + 0.908204i \(0.362546\pi\)
\(504\) −2.03326 + 11.5312i −0.0905685 + 0.513640i
\(505\) 0 0
\(506\) −3.78245 + 6.55139i −0.168150 + 0.291245i
\(507\) 44.8192 53.4135i 1.99049 2.37218i
\(508\) −2.61630 + 7.18822i −0.116079 + 0.318926i
\(509\) 9.28595 3.37981i 0.411592 0.149807i −0.127921 0.991784i \(-0.540830\pi\)
0.539513 + 0.841977i \(0.318608\pi\)
\(510\) 0 0
\(511\) 3.39553 + 19.2570i 0.150209 + 0.851879i
\(512\) 1.00000i 0.0441942i
\(513\) −6.08937 + 1.42748i −0.268852 + 0.0630248i
\(514\) 13.0703 0.576505
\(515\) 0 0
\(516\) −3.08160 + 2.58577i −0.135660 + 0.113832i
\(517\) 2.92562 + 8.03806i 0.128668 + 0.353514i
\(518\) 3.46839 9.52932i 0.152392 0.418694i
\(519\) −2.09039 1.75404i −0.0917578 0.0769940i
\(520\) 0 0
\(521\) 2.14888 + 3.72196i 0.0941440 + 0.163062i 0.909251 0.416248i \(-0.136655\pi\)
−0.815107 + 0.579310i \(0.803322\pi\)
\(522\) 17.8284 + 3.14362i 0.780327 + 0.137593i
\(523\) −24.5247 4.32437i −1.07239 0.189092i −0.390543 0.920585i \(-0.627713\pi\)
−0.681849 + 0.731493i \(0.738824\pi\)
\(524\) −6.65739 11.5309i −0.290829 0.503731i
\(525\) 0 0
\(526\) −11.5336 9.67780i −0.502887 0.421972i
\(527\) 4.05853 11.1507i 0.176792 0.485733i
\(528\) −2.25852 6.20524i −0.0982895 0.270048i
\(529\) 12.2088 10.2444i 0.530817 0.445408i
\(530\) 0 0
\(531\) −2.29714 −0.0996876
\(532\) −19.1284 9.66531i −0.829320 0.419044i
\(533\) 61.4006i 2.65955i
\(534\) 4.34100 + 24.6191i 0.187854 + 1.06537i
\(535\) 0 0
\(536\) 1.80379 0.656525i 0.0779118 0.0283576i
\(537\) −3.43595 + 9.44020i −0.148272 + 0.407375i
\(538\) −15.7196 + 18.7339i −0.677719 + 0.807674i
\(539\) 24.4440 42.3383i 1.05288 1.82364i
\(540\) 0 0
\(541\) −3.80139 + 21.5587i −0.163434 + 0.926882i 0.787230 + 0.616660i \(0.211515\pi\)
−0.950664 + 0.310222i \(0.899596\pi\)
\(542\) −8.81475 1.55428i −0.378626 0.0667620i
\(543\) 2.75072 1.58813i 0.118045 0.0681531i
\(544\) 1.09561 1.89766i 0.0469741 0.0813615i
\(545\) 0 0
\(546\) −70.3292 25.5978i −3.00981 1.09548i
\(547\) −1.01317 2.78367i −0.0433202 0.119021i 0.916146 0.400844i \(-0.131283\pi\)
−0.959466 + 0.281823i \(0.909061\pi\)
\(548\) 4.64495 + 5.53564i 0.198423 + 0.236471i
\(549\) 3.10135 + 17.5886i 0.132362 + 0.750663i
\(550\) 0 0
\(551\) −14.9435 + 29.5744i −0.636617 + 1.25991i
\(552\) 6.16497i 0.262399i
\(553\) −74.1943 + 13.0825i −3.15506 + 0.556322i
\(554\) −5.97623 + 5.01465i −0.253906 + 0.213052i
\(555\) 0 0
\(556\) 2.26632 + 0.824874i 0.0961135 + 0.0349825i
\(557\) 19.7784 23.5710i 0.838038 0.998734i −0.161891 0.986809i \(-0.551759\pi\)
0.999929 0.0119259i \(-0.00379621\pi\)
\(558\) 11.1688 + 6.44829i 0.472811 + 0.272978i
\(559\) −5.68936 9.85426i −0.240634 0.416791i
\(560\) 0 0
\(561\) 2.51264 14.2499i 0.106084 0.601631i
\(562\) −15.8467 + 9.14912i −0.668455 + 0.385933i
\(563\) −30.7518 17.7546i −1.29603 0.748266i −0.316318 0.948653i \(-0.602447\pi\)
−0.979717 + 0.200387i \(0.935780\pi\)
\(564\) −5.34008 4.48086i −0.224858 0.188678i
\(565\) 0 0
\(566\) 6.79213 2.47213i 0.285494 0.103911i
\(567\) 33.0991 + 39.4460i 1.39003 + 1.65658i
\(568\) 6.07169 1.07060i 0.254763 0.0449215i
\(569\) −33.0813 −1.38684 −0.693421 0.720533i \(-0.743897\pi\)
−0.693421 + 0.720533i \(0.743897\pi\)
\(570\) 0 0
\(571\) 2.29342 0.0959766 0.0479883 0.998848i \(-0.484719\pi\)
0.0479883 + 0.998848i \(0.484719\pi\)
\(572\) 18.3948 3.24351i 0.769127 0.135618i
\(573\) 20.3298 + 24.2282i 0.849291 + 1.01215i
\(574\) −43.2328 + 15.7355i −1.80450 + 0.656785i
\(575\) 0 0
\(576\) 1.82431 + 1.53078i 0.0760129 + 0.0637824i
\(577\) 13.5997 + 7.85178i 0.566162 + 0.326874i 0.755615 0.655016i \(-0.227338\pi\)
−0.189453 + 0.981890i \(0.560671\pi\)
\(578\) −10.5642 + 6.09926i −0.439414 + 0.253696i
\(579\) −2.10255 + 11.9242i −0.0873792 + 0.495552i
\(580\) 0 0
\(581\) −3.22554 5.58680i −0.133818 0.231780i
\(582\) −4.12708 2.38277i −0.171073 0.0987691i
\(583\) −7.72544 + 9.20682i −0.319955 + 0.381308i
\(584\) 3.73719 + 1.36023i 0.154646 + 0.0562865i
\(585\) 0 0
\(586\) −8.72264 + 7.31917i −0.360329 + 0.302352i
\(587\) 26.1082 4.60359i 1.07760 0.190010i 0.393448 0.919347i \(-0.371282\pi\)
0.684155 + 0.729337i \(0.260171\pi\)
\(588\) 39.8411i 1.64302i
\(589\) −17.2093 + 16.1568i −0.709098 + 0.665728i
\(590\) 0 0
\(591\) −1.15024 6.52335i −0.0473146 0.268335i
\(592\) −1.32576 1.57998i −0.0544885 0.0649369i
\(593\) −1.00184 2.75254i −0.0411408 0.113033i 0.917421 0.397918i \(-0.130267\pi\)
−0.958562 + 0.284884i \(0.908045\pi\)
\(594\) −3.83813 1.39697i −0.157481 0.0573182i
\(595\) 0 0
\(596\) 3.48937 6.04376i 0.142930 0.247562i
\(597\) 2.94244 1.69882i 0.120426 0.0695281i
\(598\) 17.1733 + 3.02812i 0.702270 + 0.123829i
\(599\) −6.43428 + 36.4906i −0.262897 + 1.49097i 0.512059 + 0.858950i \(0.328883\pi\)
−0.774956 + 0.632015i \(0.782228\pi\)
\(600\) 0 0
\(601\) 4.84799 8.39697i 0.197754 0.342520i −0.750046 0.661386i \(-0.769969\pi\)
0.947800 + 0.318866i \(0.103302\pi\)
\(602\) −5.48045 + 6.53135i −0.223367 + 0.266198i
\(603\) −1.56349 + 4.29566i −0.0636704 + 0.174933i
\(604\) −5.35025 + 1.94733i −0.217699 + 0.0792358i
\(605\) 0 0
\(606\) −2.01803 11.4448i −0.0819771 0.464915i
\(607\) 38.0294i 1.54357i −0.635886 0.771783i \(-0.719365\pi\)
0.635886 0.771783i \(-0.280635\pi\)
\(608\) −3.64766 + 2.38634i −0.147932 + 0.0967787i
\(609\) 86.7049 3.51346
\(610\) 0 0
\(611\) 15.1050 12.6746i 0.611081 0.512758i
\(612\) 1.78478 + 4.90364i 0.0721454 + 0.198218i
\(613\) 7.81429 21.4696i 0.315616 0.867149i −0.675880 0.737012i \(-0.736236\pi\)
0.991496 0.130137i \(-0.0415416\pi\)
\(614\) 3.78649 + 3.17725i 0.152810 + 0.128223i
\(615\) 0 0
\(616\) −6.99793 12.1208i −0.281955 0.488360i
\(617\) −25.0606 4.41886i −1.00890 0.177896i −0.355313 0.934747i \(-0.615626\pi\)
−0.653588 + 0.756851i \(0.726737\pi\)
\(618\) 20.6407 + 3.63951i 0.830291 + 0.146403i
\(619\) 7.95778 + 13.7833i 0.319850 + 0.553997i 0.980457 0.196736i \(-0.0630341\pi\)
−0.660606 + 0.750733i \(0.729701\pi\)
\(620\) 0 0
\(621\) −2.92110 2.45110i −0.117220 0.0983591i
\(622\) −8.24858 + 22.6628i −0.330738 + 0.908695i
\(623\) 18.1217 + 49.7889i 0.726030 + 1.99475i
\(624\) −11.6608 + 9.78453i −0.466804 + 0.391695i
\(625\) 0 0
\(626\) 30.9756 1.23803
\(627\) −17.2450 + 23.0461i −0.688698 + 0.920372i
\(628\) 5.31383i 0.212045i
\(629\) −0.784795 4.45079i −0.0312918 0.177465i
\(630\) 0 0
\(631\) 18.7345 6.81880i 0.745808 0.271452i 0.0589675 0.998260i \(-0.481219\pi\)
0.686841 + 0.726808i \(0.258997\pi\)
\(632\) −5.24075 + 14.3988i −0.208466 + 0.572755i
\(633\) −1.95414 + 2.32886i −0.0776702 + 0.0925637i
\(634\) 3.45527 5.98470i 0.137226 0.237683i
\(635\) 0 0
\(636\) 1.70080 9.64574i 0.0674413 0.382478i
\(637\) −110.982 19.5692i −4.39728 0.775360i
\(638\) −18.7399 + 10.8195i −0.741922 + 0.428349i
\(639\) −7.34130 + 12.7155i −0.290417 + 0.503018i
\(640\) 0 0
\(641\) −2.28156 0.830421i −0.0901163 0.0327996i 0.296569 0.955012i \(-0.404158\pi\)
−0.386685 + 0.922212i \(0.626380\pi\)
\(642\) −4.73498 13.0093i −0.186875 0.513434i
\(643\) 4.30313 + 5.12827i 0.169699 + 0.202239i 0.844191 0.536043i \(-0.180082\pi\)
−0.674492 + 0.738282i \(0.735637\pi\)
\(644\) −2.26897 12.8680i −0.0894099 0.507069i
\(645\) 0 0
\(646\) −9.53651 + 0.532031i −0.375209 + 0.0209325i
\(647\) 28.2280i 1.10976i 0.831932 + 0.554878i \(0.187235\pi\)
−0.831932 + 0.554878i \(0.812765\pi\)
\(648\) 10.3139 1.81862i 0.405168 0.0714421i
\(649\) 2.10339 1.76495i 0.0825652 0.0692805i
\(650\) 0 0
\(651\) 58.0421 + 21.1256i 2.27485 + 0.827977i
\(652\) 2.87557 3.42697i 0.112616 0.134210i
\(653\) 14.7075 + 8.49136i 0.575548 + 0.332293i 0.759362 0.650668i \(-0.225511\pi\)
−0.183814 + 0.982961i \(0.558844\pi\)
\(654\) −18.3612 31.8025i −0.717978 1.24358i
\(655\) 0 0
\(656\) −1.62488 + 9.21513i −0.0634408 + 0.359791i
\(657\) −8.20228 + 4.73559i −0.320002 + 0.184753i
\(658\) −12.7953 7.38739i −0.498814 0.287990i
\(659\) 14.0188 + 11.7632i 0.546095 + 0.458228i 0.873616 0.486616i \(-0.161769\pi\)
−0.327521 + 0.944844i \(0.606213\pi\)
\(660\) 0 0
\(661\) −5.11150 + 1.86043i −0.198814 + 0.0723625i −0.439508 0.898239i \(-0.644847\pi\)
0.240694 + 0.970601i \(0.422625\pi\)
\(662\) −2.68612 3.20119i −0.104399 0.124418i
\(663\) −32.8482 + 5.79203i −1.27572 + 0.224944i
\(664\) −1.31206 −0.0509180
\(665\) 0 0
\(666\) 4.91183 0.190329
\(667\) −19.8952 + 3.50806i −0.770344 + 0.135833i
\(668\) −2.34538 2.79512i −0.0907456 0.108146i
\(669\) −61.3213 + 22.3191i −2.37082 + 0.862907i
\(670\) 0 0
\(671\) −16.3535 13.7222i −0.631321 0.529741i
\(672\) 9.87776 + 5.70293i 0.381043 + 0.219995i
\(673\) 25.9066 14.9572i 0.998626 0.576557i 0.0907847 0.995871i \(-0.471062\pi\)
0.907842 + 0.419313i \(0.137729\pi\)
\(674\) 2.98695 16.9399i 0.115053 0.652499i
\(675\) 0 0
\(676\) −15.0285 26.0302i −0.578021 1.00116i
\(677\) 27.2420 + 15.7282i 1.04700 + 0.604483i 0.921807 0.387650i \(-0.126713\pi\)
0.125189 + 0.992133i \(0.460046\pi\)
\(678\) 27.1463 32.3517i 1.04255 1.24246i
\(679\) −9.49130 3.45455i −0.364243 0.132573i
\(680\) 0 0
\(681\) −22.4738 + 18.8578i −0.861199 + 0.722631i
\(682\) −15.1811 + 2.67684i −0.581314 + 0.102501i
\(683\) 49.8920i 1.90906i 0.298109 + 0.954532i \(0.403644\pi\)
−0.298109 + 0.954532i \(0.596356\pi\)
\(684\) 1.23033 10.3074i 0.0470430 0.394114i
\(685\) 0 0
\(686\) 8.68670 + 49.2647i 0.331660 + 1.88094i
\(687\) −20.4941 24.4240i −0.781900 0.931833i
\(688\) 0.593093 + 1.62951i 0.0226115 + 0.0621245i
\(689\) 26.0341 + 9.47562i 0.991818 + 0.360992i
\(690\) 0 0
\(691\) −9.36370 + 16.2184i −0.356212 + 0.616977i −0.987325 0.158714i \(-0.949265\pi\)
0.631113 + 0.775691i \(0.282599\pi\)
\(692\) −1.01872 + 0.588156i −0.0387258 + 0.0223583i
\(693\) 32.8243 + 5.78782i 1.24689 + 0.219861i
\(694\) 3.20604 18.1823i 0.121699 0.690192i
\(695\) 0 0
\(696\) 8.81731 15.2720i 0.334219 0.578885i
\(697\) −13.1797 + 15.7069i −0.499217 + 0.594943i
\(698\) 8.46187 23.2488i 0.320286 0.879980i
\(699\) −53.6650 + 19.5325i −2.02980 + 0.738786i
\(700\) 0 0
\(701\) −3.10915 17.6329i −0.117431 0.665984i −0.985518 0.169572i \(-0.945761\pi\)
0.868087 0.496412i \(-0.165350\pi\)
\(702\) 9.41531i 0.355358i
\(703\) −2.59952 + 8.60630i −0.0980426 + 0.324593i
\(704\) −2.84657 −0.107284
\(705\) 0 0
\(706\) 4.91028 4.12021i 0.184801 0.155066i
\(707\) −8.42437 23.1458i −0.316831 0.870486i
\(708\) −0.765324 + 2.10271i −0.0287627 + 0.0790247i
\(709\) −20.6673 17.3419i −0.776177 0.651290i 0.166106 0.986108i \(-0.446881\pi\)
−0.942283 + 0.334818i \(0.891325\pi\)
\(710\) 0 0
\(711\) −18.2455 31.6022i −0.684260 1.18517i
\(712\) 10.6126 + 1.87128i 0.397723 + 0.0701293i
\(713\) −14.1730 2.49908i −0.530783 0.0935913i
\(714\) 12.4964 + 21.6444i 0.467667 + 0.810023i
\(715\) 0 0
\(716\) 3.31741 + 2.78364i 0.123977 + 0.104029i
\(717\) 12.9279 35.5192i 0.482802 1.32649i
\(718\) 12.5916 + 34.5952i 0.469915 + 1.29108i
\(719\) −32.4936 + 27.2653i −1.21180 + 1.01683i −0.212593 + 0.977141i \(0.568191\pi\)
−0.999212 + 0.0396842i \(0.987365\pi\)
\(720\) 0 0
\(721\) 44.4222 1.65437
\(722\) 17.4091 + 7.61079i 0.647899 + 0.283244i
\(723\) 44.6672i 1.66119i
\(724\) −0.237758 1.34839i −0.00883622 0.0501127i
\(725\) 0 0
\(726\) 6.31523 2.29856i 0.234380 0.0853074i
\(727\) −14.7217 + 40.4476i −0.545999 + 1.50012i 0.293068 + 0.956092i \(0.405324\pi\)
−0.839067 + 0.544028i \(0.816898\pi\)
\(728\) −20.7380 + 24.7146i −0.768602 + 0.915984i
\(729\) −7.47766 + 12.9517i −0.276950 + 0.479692i
\(730\) 0 0
\(731\) −0.659826 + 3.74206i −0.0244045 + 0.138405i
\(732\) 17.1331 + 3.02104i 0.633259 + 0.111661i
\(733\) 26.3235 15.1979i 0.972282 0.561347i 0.0723507 0.997379i \(-0.476950\pi\)
0.899931 + 0.436032i \(0.143617\pi\)
\(734\) −7.31190 + 12.6646i −0.269887 + 0.467458i
\(735\) 0 0
\(736\) −2.49728 0.908934i −0.0920508 0.0335038i
\(737\) −1.86885 5.13461i −0.0688398 0.189136i
\(738\) −14.3239 17.0706i −0.527272 0.628378i
\(739\) 6.40630 + 36.3319i 0.235659 + 1.33649i 0.841221 + 0.540692i \(0.181838\pi\)
−0.605561 + 0.795799i \(0.707051\pi\)
\(740\) 0 0
\(741\) 63.5171 + 19.1852i 2.33336 + 0.704787i
\(742\) 20.7592i 0.762095i
\(743\) 24.1976 4.26670i 0.887725 0.156530i 0.288852 0.957374i \(-0.406726\pi\)
0.598873 + 0.800844i \(0.295615\pi\)
\(744\) 9.62352 8.07509i 0.352815 0.296047i
\(745\) 0 0
\(746\) −12.7398 4.63691i −0.466438 0.169769i
\(747\) 2.00848 2.39361i 0.0734865 0.0875778i
\(748\) −5.40182 3.11874i −0.197510 0.114033i
\(749\) −14.6711 25.4112i −0.536072 0.928503i
\(750\) 0 0
\(751\) 1.64514 9.33008i 0.0600322 0.340459i −0.939967 0.341264i \(-0.889145\pi\)
1.00000 0.000804564i \(0.000256101\pi\)
\(752\) −2.60240 + 1.50250i −0.0948998 + 0.0547904i
\(753\) 55.7902 + 32.2105i 2.03311 + 1.17382i
\(754\) 38.2113 + 32.0631i 1.39157 + 1.16767i
\(755\) 0 0
\(756\) 6.62942 2.41291i 0.241110 0.0877568i
\(757\) −4.54780 5.41985i −0.165292 0.196988i 0.677040 0.735946i \(-0.263262\pi\)
−0.842332 + 0.538958i \(0.818818\pi\)
\(758\) −29.8298 + 5.25979i −1.08347 + 0.191044i
\(759\) −17.5490 −0.636990
\(760\) 0 0
\(761\) −45.9880 −1.66706 −0.833531 0.552472i \(-0.813684\pi\)
−0.833531 + 0.552472i \(0.813684\pi\)
\(762\) −17.4758 + 3.08146i −0.633082 + 0.111629i
\(763\) −50.0293 59.6227i −1.81118 2.15849i
\(764\) 12.8116 4.66302i 0.463506 0.168702i
\(765\) 0 0
\(766\) 21.9571 + 18.4242i 0.793342 + 0.665693i
\(767\) −5.48146 3.16472i −0.197924 0.114272i
\(768\) 2.00901 1.15990i 0.0724937 0.0418543i
\(769\) 7.83899 44.4571i 0.282681 1.60317i −0.430771 0.902461i \(-0.641758\pi\)
0.713452 0.700704i \(-0.247131\pi\)
\(770\) 0 0
\(771\) 15.1602 + 26.2582i 0.545981 + 0.945667i
\(772\) 4.52019 + 2.60974i 0.162685 + 0.0939264i
\(773\) −0.495905 + 0.590996i −0.0178364 + 0.0212567i −0.774889 0.632097i \(-0.782194\pi\)
0.757052 + 0.653354i \(0.226639\pi\)
\(774\) −3.88063 1.41243i −0.139486 0.0507689i
\(775\) 0 0
\(776\) −1.57368 + 1.32047i −0.0564918 + 0.0474022i
\(777\) 23.1674 4.08504i 0.831127 0.146550i
\(778\) 17.1263i 0.614007i
\(779\) 37.4911 16.0634i 1.34326 0.575532i
\(780\) 0 0
\(781\) −3.04755 17.2835i −0.109050 0.618452i
\(782\) −3.74314 4.46090i −0.133854 0.159521i
\(783\) −3.73061 10.2498i