Properties

Label 475.2.e.g.201.5
Level $475$
Weight $2$
Character 475.201
Analytic conductor $3.793$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \( x^{12} + 6x^{10} + 29x^{8} + 40x^{6} + 43x^{4} + 7x^{2} + 1 \) 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 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.5
Root \(-0.579521 + 1.00376i\) of defining polynomial
Character \(\chi\) \(=\) 475.201
Dual form 475.2.e.g.26.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.431391 - 0.747190i) q^{2} +(1.53957 - 2.66661i) q^{3} +(0.627804 + 1.08739i) q^{4} +(-1.32831 - 2.30070i) q^{6} -0.566520 q^{7} +2.80888 q^{8} +(-3.24054 - 5.61278i) q^{9} +O(q^{10})\) \(q+(0.431391 - 0.747190i) q^{2} +(1.53957 - 2.66661i) q^{3} +(0.627804 + 1.08739i) q^{4} +(-1.32831 - 2.30070i) q^{6} -0.566520 q^{7} +2.80888 q^{8} +(-3.24054 - 5.61278i) q^{9} -1.91223 q^{11} +3.86619 q^{12} +(0.0972656 + 0.168469i) q^{13} +(-0.244391 + 0.423298i) q^{14} +(-0.0438854 + 0.0760118i) q^{16} +(2.64775 - 4.58603i) q^{17} -5.59175 q^{18} +(-2.36834 - 3.65936i) q^{19} +(-0.872196 + 1.51069i) q^{21} +(-0.824918 + 1.42880i) q^{22} +(1.68770 + 2.92318i) q^{23} +(4.32446 - 7.49018i) q^{24} +0.167838 q^{26} -10.7187 q^{27} +(-0.355664 - 0.616027i) q^{28} +(4.36834 + 7.56619i) q^{29} +5.65662 q^{31} +(2.84674 + 4.93070i) q^{32} +(-2.94401 + 5.09917i) q^{33} +(-2.28442 - 3.95674i) q^{34} +(4.06885 - 7.04745i) q^{36} -0.955582 q^{37} +(-3.75592 + 0.190988i) q^{38} +0.598988 q^{39} +(-5.02496 + 8.70349i) q^{41} +(0.752514 + 1.30339i) q^{42} +(-2.46622 + 4.27161i) q^{43} +(-1.20051 - 2.07934i) q^{44} +2.91223 q^{46} +(4.41971 + 7.65516i) q^{47} +(0.135129 + 0.234051i) q^{48} -6.67906 q^{49} +(-8.15277 - 14.1210i) q^{51} +(-0.122128 + 0.211531i) q^{52} +(-4.10305 - 7.10669i) q^{53} +(-4.62395 + 8.00892i) q^{54} -1.59128 q^{56} +(-13.4043 + 0.681609i) q^{57} +7.53785 q^{58} +(-1.85713 + 3.21664i) q^{59} +(1.75561 + 3.04080i) q^{61} +(2.44021 - 4.22657i) q^{62} +(1.83583 + 3.17975i) q^{63} +4.73669 q^{64} +(2.54003 + 4.39947i) q^{66} +(2.02182 + 3.50190i) q^{67} +6.64906 q^{68} +10.3933 q^{69} +(-2.59767 + 4.49929i) q^{71} +(-9.10228 - 15.7656i) q^{72} +(4.30205 - 7.45136i) q^{73} +(-0.412229 + 0.714002i) q^{74} +(2.49230 - 4.87268i) q^{76} +1.08332 q^{77} +(0.258398 - 0.447558i) q^{78} +(-3.31324 + 5.73870i) q^{79} +(-6.78057 + 11.7443i) q^{81} +(4.33544 + 7.50921i) q^{82} +4.51737 q^{83} -2.19027 q^{84} +(2.12780 + 3.68547i) q^{86} +26.9014 q^{87} -5.37122 q^{88} +(-1.68676 - 2.92155i) q^{89} +(-0.0551029 - 0.0954410i) q^{91} +(-2.11909 + 3.67037i) q^{92} +(8.70875 - 15.0840i) q^{93} +7.62648 q^{94} +17.5310 q^{96} +(7.59611 - 13.1568i) q^{97} +(-2.88128 + 4.99053i) q^{98} +(6.19665 + 10.7329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{4} - 12 q^{6} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{4} - 12 q^{6} - 8 q^{9} + 4 q^{11} - 22 q^{14} - 14 q^{16} + 12 q^{19} - 20 q^{21} - 2 q^{24} - 44 q^{26} + 12 q^{29} + 60 q^{31} - 10 q^{34} + 14 q^{36} - 4 q^{39} - 12 q^{41} - 20 q^{44} + 8 q^{46} + 4 q^{49} - 40 q^{51} + 4 q^{54} + 92 q^{56} - 20 q^{59} + 2 q^{61} - 24 q^{64} - 6 q^{66} + 36 q^{69} + 2 q^{71} + 22 q^{74} - 70 q^{76} - 24 q^{79} - 14 q^{81} + 96 q^{84} + 16 q^{86} - 36 q^{89} + 24 q^{91} + 60 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.431391 0.747190i 0.305039 0.528343i −0.672231 0.740342i \(-0.734664\pi\)
0.977270 + 0.211998i \(0.0679971\pi\)
\(3\) 1.53957 2.66661i 0.888870 1.53957i 0.0476573 0.998864i \(-0.484824\pi\)
0.841213 0.540704i \(-0.181842\pi\)
\(4\) 0.627804 + 1.08739i 0.313902 + 0.543695i
\(5\) 0 0
\(6\) −1.32831 2.30070i −0.542280 0.939257i
\(7\) −0.566520 −0.214124 −0.107062 0.994252i \(-0.534144\pi\)
−0.107062 + 0.994252i \(0.534144\pi\)
\(8\) 2.80888 0.993088
\(9\) −3.24054 5.61278i −1.08018 1.87093i
\(10\) 0 0
\(11\) −1.91223 −0.576559 −0.288279 0.957546i \(-0.593083\pi\)
−0.288279 + 0.957546i \(0.593083\pi\)
\(12\) 3.86619 1.11607
\(13\) 0.0972656 + 0.168469i 0.0269766 + 0.0467249i 0.879199 0.476456i \(-0.158079\pi\)
−0.852222 + 0.523180i \(0.824745\pi\)
\(14\) −0.244391 + 0.423298i −0.0653163 + 0.113131i
\(15\) 0 0
\(16\) −0.0438854 + 0.0760118i −0.0109714 + 0.0190029i
\(17\) 2.64775 4.58603i 0.642173 1.11228i −0.342774 0.939418i \(-0.611367\pi\)
0.984947 0.172858i \(-0.0553001\pi\)
\(18\) −5.59175 −1.31799
\(19\) −2.36834 3.65936i −0.543335 0.839516i
\(20\) 0 0
\(21\) −0.872196 + 1.51069i −0.190329 + 0.329659i
\(22\) −0.824918 + 1.42880i −0.175873 + 0.304621i
\(23\) 1.68770 + 2.92318i 0.351910 + 0.609525i 0.986584 0.163254i \(-0.0521991\pi\)
−0.634674 + 0.772780i \(0.718866\pi\)
\(24\) 4.32446 7.49018i 0.882726 1.52893i
\(25\) 0 0
\(26\) 0.167838 0.0329157
\(27\) −10.7187 −2.06282
\(28\) −0.355664 0.616027i −0.0672141 0.116418i
\(29\) 4.36834 + 7.56619i 0.811181 + 1.40501i 0.912038 + 0.410106i \(0.134508\pi\)
−0.100857 + 0.994901i \(0.532158\pi\)
\(30\) 0 0
\(31\) 5.65662 1.01596 0.507980 0.861369i \(-0.330393\pi\)
0.507980 + 0.861369i \(0.330393\pi\)
\(32\) 2.84674 + 4.93070i 0.503238 + 0.871633i
\(33\) −2.94401 + 5.09917i −0.512486 + 0.887651i
\(34\) −2.28442 3.95674i −0.391776 0.678575i
\(35\) 0 0
\(36\) 4.06885 7.04745i 0.678142 1.17458i
\(37\) −0.955582 −0.157097 −0.0785484 0.996910i \(-0.525029\pi\)
−0.0785484 + 0.996910i \(0.525029\pi\)
\(38\) −3.75592 + 0.190988i −0.609291 + 0.0309824i
\(39\) 0.598988 0.0959149
\(40\) 0 0
\(41\) −5.02496 + 8.70349i −0.784768 + 1.35926i 0.144370 + 0.989524i \(0.453884\pi\)
−0.929138 + 0.369734i \(0.879449\pi\)
\(42\) 0.752514 + 1.30339i 0.116115 + 0.201118i
\(43\) −2.46622 + 4.27161i −0.376094 + 0.651415i −0.990490 0.137583i \(-0.956066\pi\)
0.614396 + 0.788998i \(0.289400\pi\)
\(44\) −1.20051 2.07934i −0.180983 0.313472i
\(45\) 0 0
\(46\) 2.91223 0.429385
\(47\) 4.41971 + 7.65516i 0.644681 + 1.11662i 0.984375 + 0.176084i \(0.0563430\pi\)
−0.339694 + 0.940536i \(0.610324\pi\)
\(48\) 0.135129 + 0.234051i 0.0195042 + 0.0337823i
\(49\) −6.67906 −0.954151
\(50\) 0 0
\(51\) −8.15277 14.1210i −1.14162 1.97734i
\(52\) −0.122128 + 0.211531i −0.0169361 + 0.0293341i
\(53\) −4.10305 7.10669i −0.563597 0.976179i −0.997179 0.0750646i \(-0.976084\pi\)
0.433581 0.901114i \(-0.357250\pi\)
\(54\) −4.62395 + 8.00892i −0.629240 + 1.08988i
\(55\) 0 0
\(56\) −1.59128 −0.212644
\(57\) −13.4043 + 0.681609i −1.77545 + 0.0902813i
\(58\) 7.53785 0.989768
\(59\) −1.85713 + 3.21664i −0.241777 + 0.418770i −0.961221 0.275781i \(-0.911064\pi\)
0.719443 + 0.694551i \(0.244397\pi\)
\(60\) 0 0
\(61\) 1.75561 + 3.04080i 0.224783 + 0.389335i 0.956254 0.292537i \(-0.0944995\pi\)
−0.731472 + 0.681872i \(0.761166\pi\)
\(62\) 2.44021 4.22657i 0.309907 0.536775i
\(63\) 1.83583 + 3.17975i 0.231293 + 0.400611i
\(64\) 4.73669 0.592086
\(65\) 0 0
\(66\) 2.54003 + 4.39947i 0.312657 + 0.541537i
\(67\) 2.02182 + 3.50190i 0.247005 + 0.427825i 0.962693 0.270594i \(-0.0872202\pi\)
−0.715688 + 0.698420i \(0.753887\pi\)
\(68\) 6.64906 0.806318
\(69\) 10.3933 1.25121
\(70\) 0 0
\(71\) −2.59767 + 4.49929i −0.308286 + 0.533967i −0.977988 0.208663i \(-0.933089\pi\)
0.669701 + 0.742631i \(0.266422\pi\)
\(72\) −9.10228 15.7656i −1.07271 1.85799i
\(73\) 4.30205 7.45136i 0.503516 0.872116i −0.496475 0.868051i \(-0.665373\pi\)
0.999992 0.00406505i \(-0.00129395\pi\)
\(74\) −0.412229 + 0.714002i −0.0479207 + 0.0830010i
\(75\) 0 0
\(76\) 2.49230 4.87268i 0.285886 0.558934i
\(77\) 1.08332 0.123455
\(78\) 0.258398 0.447558i 0.0292578 0.0506760i
\(79\) −3.31324 + 5.73870i −0.372769 + 0.645654i −0.989990 0.141135i \(-0.954925\pi\)
0.617222 + 0.786789i \(0.288258\pi\)
\(80\) 0 0
\(81\) −6.78057 + 11.7443i −0.753397 + 1.30492i
\(82\) 4.33544 + 7.50921i 0.478770 + 0.829253i
\(83\) 4.51737 0.495845 0.247923 0.968780i \(-0.420252\pi\)
0.247923 + 0.968780i \(0.420252\pi\)
\(84\) −2.19027 −0.238978
\(85\) 0 0
\(86\) 2.12780 + 3.68547i 0.229447 + 0.397414i
\(87\) 26.9014 2.88414
\(88\) −5.37122 −0.572574
\(89\) −1.68676 2.92155i −0.178796 0.309684i 0.762672 0.646785i \(-0.223887\pi\)
−0.941468 + 0.337101i \(0.890554\pi\)
\(90\) 0 0
\(91\) −0.0551029 0.0954410i −0.00577635 0.0100049i
\(92\) −2.11909 + 3.67037i −0.220930 + 0.382663i
\(93\) 8.70875 15.0840i 0.903056 1.56414i
\(94\) 7.62648 0.786612
\(95\) 0 0
\(96\) 17.5310 1.78925
\(97\) 7.59611 13.1568i 0.771268 1.33588i −0.165600 0.986193i \(-0.552956\pi\)
0.936868 0.349683i \(-0.113711\pi\)
\(98\) −2.88128 + 4.99053i −0.291053 + 0.504119i
\(99\) 6.19665 + 10.7329i 0.622787 + 1.07870i
\(100\) 0 0
\(101\) −1.77068 3.06690i −0.176189 0.305168i 0.764383 0.644762i \(-0.223044\pi\)
−0.940572 + 0.339594i \(0.889710\pi\)
\(102\) −14.0681 −1.39295
\(103\) −15.6919 −1.54617 −0.773086 0.634301i \(-0.781288\pi\)
−0.773086 + 0.634301i \(0.781288\pi\)
\(104\) 0.273207 + 0.473209i 0.0267902 + 0.0464020i
\(105\) 0 0
\(106\) −7.08007 −0.687677
\(107\) −1.05731 −0.102214 −0.0511071 0.998693i \(-0.516275\pi\)
−0.0511071 + 0.998693i \(0.516275\pi\)
\(108\) −6.72926 11.6554i −0.647523 1.12154i
\(109\) 3.37220 5.84081i 0.322998 0.559449i −0.658107 0.752924i \(-0.728643\pi\)
0.981105 + 0.193476i \(0.0619760\pi\)
\(110\) 0 0
\(111\) −1.47118 + 2.54817i −0.139639 + 0.241861i
\(112\) 0.0248620 0.0430622i 0.00234923 0.00406899i
\(113\) 7.90091 0.743255 0.371627 0.928382i \(-0.378800\pi\)
0.371627 + 0.928382i \(0.378800\pi\)
\(114\) −5.27321 + 10.3096i −0.493881 + 0.965585i
\(115\) 0 0
\(116\) −5.48493 + 9.50018i −0.509263 + 0.882069i
\(117\) 0.630386 1.09186i 0.0582792 0.100943i
\(118\) 1.60229 + 2.77525i 0.147503 + 0.255483i
\(119\) −1.50000 + 2.59808i −0.137505 + 0.238165i
\(120\) 0 0
\(121\) −7.34338 −0.667580
\(122\) 3.02941 0.274270
\(123\) 15.4725 + 26.7992i 1.39511 + 2.41641i
\(124\) 3.55125 + 6.15095i 0.318912 + 0.552371i
\(125\) 0 0
\(126\) 3.16784 0.282213
\(127\) −4.23818 7.34074i −0.376078 0.651385i 0.614410 0.788987i \(-0.289394\pi\)
−0.990488 + 0.137601i \(0.956061\pi\)
\(128\) −3.65012 + 6.32219i −0.322628 + 0.558808i
\(129\) 7.59381 + 13.1529i 0.668598 + 1.15805i
\(130\) 0 0
\(131\) −0.937193 + 1.62327i −0.0818830 + 0.141825i −0.904059 0.427408i \(-0.859427\pi\)
0.822176 + 0.569234i \(0.192760\pi\)
\(132\) −7.39304 −0.643482
\(133\) 1.34171 + 2.07310i 0.116341 + 0.179761i
\(134\) 3.48878 0.301385
\(135\) 0 0
\(136\) 7.43719 12.8816i 0.637734 1.10459i
\(137\) 6.23068 + 10.7918i 0.532323 + 0.922010i 0.999288 + 0.0377341i \(0.0120140\pi\)
−0.466965 + 0.884276i \(0.654653\pi\)
\(138\) 4.48357 7.76578i 0.381667 0.661067i
\(139\) 0.156620 + 0.271275i 0.0132844 + 0.0230092i 0.872591 0.488451i \(-0.162438\pi\)
−0.859307 + 0.511460i \(0.829105\pi\)
\(140\) 0 0
\(141\) 27.2178 2.29215
\(142\) 2.24122 + 3.88190i 0.188079 + 0.325762i
\(143\) −0.185994 0.322151i −0.0155536 0.0269397i
\(144\) 0.568850 0.0474041
\(145\) 0 0
\(146\) −3.71172 6.42889i −0.307184 0.532059i
\(147\) −10.2829 + 17.8104i −0.848116 + 1.46898i
\(148\) −0.599919 1.03909i −0.0493130 0.0854127i
\(149\) −2.18291 + 3.78091i −0.178831 + 0.309744i −0.941480 0.337068i \(-0.890565\pi\)
0.762650 + 0.646812i \(0.223898\pi\)
\(150\) 0 0
\(151\) 0.197977 0.0161111 0.00805555 0.999968i \(-0.497436\pi\)
0.00805555 + 0.999968i \(0.497436\pi\)
\(152\) −6.65239 10.2787i −0.539580 0.833713i
\(153\) −34.3205 −2.77465
\(154\) 0.467332 0.809443i 0.0376587 0.0652268i
\(155\) 0 0
\(156\) 0.376047 + 0.651333i 0.0301079 + 0.0521484i
\(157\) 7.88498 13.6572i 0.629290 1.08996i −0.358405 0.933566i \(-0.616679\pi\)
0.987695 0.156395i \(-0.0499874\pi\)
\(158\) 2.85860 + 4.95124i 0.227418 + 0.393900i
\(159\) −25.2677 −2.00386
\(160\) 0 0
\(161\) −0.956115 1.65604i −0.0753524 0.130514i
\(162\) 5.85015 + 10.1328i 0.459631 + 0.796105i
\(163\) −9.18768 −0.719635 −0.359817 0.933023i \(-0.617161\pi\)
−0.359817 + 0.933023i \(0.617161\pi\)
\(164\) −12.6188 −0.985361
\(165\) 0 0
\(166\) 1.94875 3.37533i 0.151252 0.261977i
\(167\) −1.53510 2.65888i −0.118790 0.205750i 0.800498 0.599335i \(-0.204568\pi\)
−0.919288 + 0.393585i \(0.871235\pi\)
\(168\) −2.44989 + 4.24334i −0.189013 + 0.327380i
\(169\) 6.48108 11.2256i 0.498545 0.863504i
\(170\) 0 0
\(171\) −12.8645 + 25.1513i −0.983772 + 1.92337i
\(172\) −6.19320 −0.472227
\(173\) 5.20676 9.01838i 0.395863 0.685655i −0.597348 0.801982i \(-0.703779\pi\)
0.993211 + 0.116328i \(0.0371122\pi\)
\(174\) 11.6050 20.1005i 0.879775 1.52382i
\(175\) 0 0
\(176\) 0.0839190 0.145352i 0.00632563 0.0109563i
\(177\) 5.71834 + 9.90446i 0.429817 + 0.744465i
\(178\) −2.91061 −0.218159
\(179\) −13.4432 −1.00479 −0.502397 0.864637i \(-0.667549\pi\)
−0.502397 + 0.864637i \(0.667549\pi\)
\(180\) 0 0
\(181\) −3.98108 6.89543i −0.295911 0.512533i 0.679285 0.733874i \(-0.262290\pi\)
−0.975196 + 0.221341i \(0.928957\pi\)
\(182\) −0.0950835 −0.00704806
\(183\) 10.8115 0.799210
\(184\) 4.74054 + 8.21086i 0.349477 + 0.605312i
\(185\) 0 0
\(186\) −7.51375 13.0142i −0.550935 0.954247i
\(187\) −5.06310 + 8.76954i −0.370250 + 0.641292i
\(188\) −5.54942 + 9.61189i −0.404733 + 0.701019i
\(189\) 6.07236 0.441699
\(190\) 0 0
\(191\) −14.0999 −1.02023 −0.510115 0.860106i \(-0.670397\pi\)
−0.510115 + 0.860106i \(0.670397\pi\)
\(192\) 7.29245 12.6309i 0.526287 0.911557i
\(193\) 1.98842 3.44405i 0.143130 0.247908i −0.785544 0.618806i \(-0.787617\pi\)
0.928674 + 0.370898i \(0.120950\pi\)
\(194\) −6.55378 11.3515i −0.470534 0.814989i
\(195\) 0 0
\(196\) −4.19314 7.26273i −0.299510 0.518767i
\(197\) −18.3494 −1.30734 −0.653669 0.756781i \(-0.726771\pi\)
−0.653669 + 0.756781i \(0.726771\pi\)
\(198\) 10.6927 0.759898
\(199\) 0.803346 + 1.39144i 0.0569477 + 0.0986363i 0.893094 0.449870i \(-0.148530\pi\)
−0.836146 + 0.548507i \(0.815197\pi\)
\(200\) 0 0
\(201\) 12.4509 0.878222
\(202\) −3.05542 −0.214978
\(203\) −2.47475 4.28640i −0.173694 0.300846i
\(204\) 10.2367 17.7305i 0.716711 1.24138i
\(205\) 0 0
\(206\) −6.76936 + 11.7249i −0.471643 + 0.816910i
\(207\) 10.9381 18.9454i 0.760251 1.31679i
\(208\) −0.0170742 −0.00118388
\(209\) 4.52882 + 6.99754i 0.313265 + 0.484030i
\(210\) 0 0
\(211\) 3.04993 5.28263i 0.209966 0.363671i −0.741738 0.670690i \(-0.765998\pi\)
0.951703 + 0.307019i \(0.0993314\pi\)
\(212\) 5.15182 8.92322i 0.353829 0.612849i
\(213\) 7.99857 + 13.8539i 0.548053 + 0.949255i
\(214\) −0.456115 + 0.790014i −0.0311794 + 0.0540042i
\(215\) 0 0
\(216\) −30.1076 −2.04856
\(217\) −3.20459 −0.217542
\(218\) −2.90947 5.03934i −0.197054 0.341307i
\(219\) −13.2466 22.9438i −0.895121 1.55040i
\(220\) 0 0
\(221\) 1.03014 0.0692946
\(222\) 1.26931 + 2.19851i 0.0851905 + 0.147554i
\(223\) 8.61263 14.9175i 0.576744 0.998950i −0.419106 0.907938i \(-0.637656\pi\)
0.995850 0.0910127i \(-0.0290104\pi\)
\(224\) −1.61274 2.79334i −0.107755 0.186638i
\(225\) 0 0
\(226\) 3.40838 5.90348i 0.226722 0.392694i
\(227\) −1.18505 −0.0786542 −0.0393271 0.999226i \(-0.512521\pi\)
−0.0393271 + 0.999226i \(0.512521\pi\)
\(228\) −9.15647 14.1478i −0.606402 0.936961i
\(229\) 6.24791 0.412873 0.206437 0.978460i \(-0.433813\pi\)
0.206437 + 0.978460i \(0.433813\pi\)
\(230\) 0 0
\(231\) 1.66784 2.88878i 0.109736 0.190068i
\(232\) 12.2701 + 21.2525i 0.805574 + 1.39530i
\(233\) −1.37844 + 2.38752i −0.0903043 + 0.156412i −0.907639 0.419751i \(-0.862117\pi\)
0.817335 + 0.576163i \(0.195451\pi\)
\(234\) −0.543885 0.942037i −0.0355549 0.0615829i
\(235\) 0 0
\(236\) −4.66365 −0.303578
\(237\) 10.2019 + 17.6702i 0.662686 + 1.14781i
\(238\) 1.29417 + 2.24157i 0.0838887 + 0.145299i
\(239\) 17.3055 1.11940 0.559701 0.828695i \(-0.310916\pi\)
0.559701 + 0.828695i \(0.310916\pi\)
\(240\) 0 0
\(241\) 2.39331 + 4.14533i 0.154167 + 0.267024i 0.932755 0.360510i \(-0.117397\pi\)
−0.778589 + 0.627535i \(0.784064\pi\)
\(242\) −3.16786 + 5.48690i −0.203638 + 0.352711i
\(243\) 4.80023 + 8.31425i 0.307935 + 0.533359i
\(244\) −2.20436 + 3.81806i −0.141120 + 0.244426i
\(245\) 0 0
\(246\) 26.6988 1.70226
\(247\) 0.386131 0.754923i 0.0245689 0.0480346i
\(248\) 15.8888 1.00894
\(249\) 6.95479 12.0461i 0.440742 0.763388i
\(250\) 0 0
\(251\) 13.1240 + 22.7314i 0.828377 + 1.43479i 0.899311 + 0.437309i \(0.144068\pi\)
−0.0709346 + 0.997481i \(0.522598\pi\)
\(252\) −2.30508 + 3.99252i −0.145207 + 0.251505i
\(253\) −3.22727 5.58979i −0.202897 0.351427i
\(254\) −7.31324 −0.458874
\(255\) 0 0
\(256\) 7.88594 + 13.6589i 0.492871 + 0.853678i
\(257\) −11.1252 19.2695i −0.693974 1.20200i −0.970525 0.240999i \(-0.922525\pi\)
0.276552 0.960999i \(-0.410808\pi\)
\(258\) 13.1036 0.815794
\(259\) 0.541356 0.0336382
\(260\) 0 0
\(261\) 28.3116 49.0371i 1.75244 3.03532i
\(262\) 0.808593 + 1.40052i 0.0499550 + 0.0865246i
\(263\) 4.40671 7.63264i 0.271729 0.470649i −0.697576 0.716511i \(-0.745738\pi\)
0.969305 + 0.245863i \(0.0790712\pi\)
\(264\) −8.26936 + 14.3229i −0.508944 + 0.881516i
\(265\) 0 0
\(266\) 2.12780 0.108199i 0.130464 0.00663409i
\(267\) −10.3875 −0.635706
\(268\) −2.53862 + 4.39702i −0.155071 + 0.268591i
\(269\) 2.38209 4.12590i 0.145239 0.251561i −0.784223 0.620479i \(-0.786938\pi\)
0.929462 + 0.368918i \(0.120272\pi\)
\(270\) 0 0
\(271\) −1.75946 + 3.04748i −0.106880 + 0.185121i −0.914505 0.404576i \(-0.867419\pi\)
0.807625 + 0.589696i \(0.200753\pi\)
\(272\) 0.232395 + 0.402520i 0.0140910 + 0.0244063i
\(273\) −0.339339 −0.0205377
\(274\) 10.7514 0.649517
\(275\) 0 0
\(276\) 6.52496 + 11.3016i 0.392757 + 0.680275i
\(277\) −32.7724 −1.96910 −0.984551 0.175098i \(-0.943976\pi\)
−0.984551 + 0.175098i \(0.943976\pi\)
\(278\) 0.270258 0.0162090
\(279\) −18.3305 31.7494i −1.09742 1.90078i
\(280\) 0 0
\(281\) −4.95997 8.59091i −0.295887 0.512491i 0.679304 0.733857i \(-0.262282\pi\)
−0.975191 + 0.221366i \(0.928948\pi\)
\(282\) 11.7415 20.3369i 0.699195 1.21104i
\(283\) −1.23591 + 2.14066i −0.0734673 + 0.127249i −0.900419 0.435024i \(-0.856740\pi\)
0.826951 + 0.562273i \(0.190073\pi\)
\(284\) −6.52330 −0.387087
\(285\) 0 0
\(286\) −0.320945 −0.0189779
\(287\) 2.84674 4.93070i 0.168038 0.291050i
\(288\) 18.4500 31.9563i 1.08717 1.88304i
\(289\) −5.52111 9.56285i −0.324771 0.562520i
\(290\) 0 0
\(291\) −23.3895 40.5117i −1.37111 2.37484i
\(292\) 10.8034 0.632219
\(293\) −17.0284 −0.994812 −0.497406 0.867518i \(-0.665714\pi\)
−0.497406 + 0.867518i \(0.665714\pi\)
\(294\) 8.87186 + 15.3665i 0.517417 + 0.896193i
\(295\) 0 0
\(296\) −2.68411 −0.156011
\(297\) 20.4966 1.18934
\(298\) 1.88337 + 3.26209i 0.109101 + 0.188968i
\(299\) −0.328310 + 0.568650i −0.0189867 + 0.0328859i
\(300\) 0 0
\(301\) 1.39716 2.41995i 0.0805310 0.139484i
\(302\) 0.0854052 0.147926i 0.00491452 0.00851220i
\(303\) −10.9043 −0.626437
\(304\) 0.382090 0.0194293i 0.0219144 0.00111435i
\(305\) 0 0
\(306\) −14.8055 + 25.6439i −0.846376 + 1.46597i
\(307\) −10.4896 + 18.1686i −0.598676 + 1.03694i 0.394341 + 0.918964i \(0.370973\pi\)
−0.993017 + 0.117972i \(0.962361\pi\)
\(308\) 0.680110 + 1.17799i 0.0387529 + 0.0671220i
\(309\) −24.1588 + 41.8443i −1.37435 + 2.38044i
\(310\) 0 0
\(311\) −3.14805 −0.178509 −0.0892547 0.996009i \(-0.528449\pi\)
−0.0892547 + 0.996009i \(0.528449\pi\)
\(312\) 1.68248 0.0952520
\(313\) −6.14641 10.6459i −0.347416 0.601742i 0.638374 0.769726i \(-0.279607\pi\)
−0.985790 + 0.167985i \(0.946274\pi\)
\(314\) −6.80301 11.7832i −0.383916 0.664962i
\(315\) 0 0
\(316\) −8.32027 −0.468052
\(317\) 5.73095 + 9.92630i 0.321882 + 0.557517i 0.980876 0.194631i \(-0.0623511\pi\)
−0.658994 + 0.752148i \(0.729018\pi\)
\(318\) −10.9002 + 18.8798i −0.611255 + 1.05873i
\(319\) −8.35327 14.4683i −0.467694 0.810069i
\(320\) 0 0
\(321\) −1.62780 + 2.81944i −0.0908552 + 0.157366i
\(322\) −1.64984 −0.0919417
\(323\) −23.0527 + 1.17223i −1.28269 + 0.0652246i
\(324\) −17.0275 −0.945972
\(325\) 0 0
\(326\) −3.96348 + 6.86495i −0.219517 + 0.380214i
\(327\) −10.3834 17.9847i −0.574206 0.994554i
\(328\) −14.1145 + 24.4470i −0.779343 + 1.34986i
\(329\) −2.50385 4.33680i −0.138042 0.239095i
\(330\) 0 0
\(331\) 5.85724 0.321943 0.160972 0.986959i \(-0.448537\pi\)
0.160972 + 0.986959i \(0.448537\pi\)
\(332\) 2.83602 + 4.91213i 0.155647 + 0.269588i
\(333\) 3.09660 + 5.36347i 0.169693 + 0.293916i
\(334\) −2.64892 −0.144942
\(335\) 0 0
\(336\) −0.0765533 0.132594i −0.00417633 0.00723361i
\(337\) 4.30498 7.45644i 0.234507 0.406178i −0.724622 0.689146i \(-0.757986\pi\)
0.959129 + 0.282968i \(0.0913191\pi\)
\(338\) −5.59175 9.68520i −0.304151 0.526805i
\(339\) 12.1640 21.0686i 0.660657 1.14429i
\(340\) 0 0
\(341\) −10.8168 −0.585760
\(342\) 13.2432 + 20.4623i 0.716110 + 1.10647i
\(343\) 7.74945 0.418431
\(344\) −6.92730 + 11.9984i −0.373495 + 0.646912i
\(345\) 0 0
\(346\) −4.49230 7.78089i −0.241507 0.418303i
\(347\) −6.04507 + 10.4704i −0.324517 + 0.562079i −0.981414 0.191900i \(-0.938535\pi\)
0.656898 + 0.753980i \(0.271868\pi\)
\(348\) 16.8888 + 29.2523i 0.905337 + 1.56809i
\(349\) 18.9819 1.01608 0.508040 0.861333i \(-0.330370\pi\)
0.508040 + 0.861333i \(0.330370\pi\)
\(350\) 0 0
\(351\) −1.04256 1.80577i −0.0556479 0.0963850i
\(352\) −5.44362 9.42863i −0.290146 0.502548i
\(353\) 7.71759 0.410766 0.205383 0.978682i \(-0.434156\pi\)
0.205383 + 0.978682i \(0.434156\pi\)
\(354\) 9.86736 0.524444
\(355\) 0 0
\(356\) 2.11791 3.66833i 0.112249 0.194421i
\(357\) 4.61870 + 7.99983i 0.244448 + 0.423396i
\(358\) −5.79929 + 10.0447i −0.306502 + 0.530877i
\(359\) 3.51507 6.08828i 0.185518 0.321327i −0.758233 0.651984i \(-0.773937\pi\)
0.943751 + 0.330657i \(0.107270\pi\)
\(360\) 0 0
\(361\) −7.78190 + 17.3333i −0.409573 + 0.912277i
\(362\) −6.86960 −0.361058
\(363\) −11.3056 + 19.5819i −0.593392 + 1.02778i
\(364\) 0.0691877 0.119837i 0.00362642 0.00628114i
\(365\) 0 0
\(366\) 4.66399 8.07826i 0.243790 0.422257i
\(367\) −16.8554 29.1945i −0.879847 1.52394i −0.851508 0.524342i \(-0.824311\pi\)
−0.0283394 0.999598i \(-0.509022\pi\)
\(368\) −0.296261 −0.0154437
\(369\) 65.1344 3.39076
\(370\) 0 0
\(371\) 2.32446 + 4.02608i 0.120680 + 0.209024i
\(372\) 21.8696 1.13388
\(373\) −10.0097 −0.518281 −0.259141 0.965840i \(-0.583439\pi\)
−0.259141 + 0.965840i \(0.583439\pi\)
\(374\) 4.36834 + 7.56619i 0.225882 + 0.391239i
\(375\) 0 0
\(376\) 12.4144 + 21.5024i 0.640225 + 1.10890i
\(377\) −0.849780 + 1.47186i −0.0437659 + 0.0758047i
\(378\) 2.61956 4.53721i 0.134736 0.233369i
\(379\) −35.8064 −1.83925 −0.919626 0.392796i \(-0.871508\pi\)
−0.919626 + 0.392796i \(0.871508\pi\)
\(380\) 0 0
\(381\) −26.0999 −1.33714
\(382\) −6.08255 + 10.5353i −0.311210 + 0.539032i
\(383\) −8.12477 + 14.0725i −0.415156 + 0.719072i −0.995445 0.0953393i \(-0.969606\pi\)
0.580289 + 0.814411i \(0.302940\pi\)
\(384\) 11.2392 + 19.4669i 0.573549 + 0.993416i
\(385\) 0 0
\(386\) −1.71558 2.97146i −0.0873205 0.151244i
\(387\) 31.9675 1.62500
\(388\) 19.0755 0.968411
\(389\) 9.69280 + 16.7884i 0.491445 + 0.851207i 0.999951 0.00985094i \(-0.00313570\pi\)
−0.508507 + 0.861058i \(0.669802\pi\)
\(390\) 0 0
\(391\) 17.8744 0.903947
\(392\) −18.7607 −0.947556
\(393\) 2.88575 + 4.99826i 0.145567 + 0.252129i
\(394\) −7.91574 + 13.7105i −0.398789 + 0.690723i
\(395\) 0 0
\(396\) −7.78057 + 13.4763i −0.390989 + 0.677212i
\(397\) 2.67707 4.63682i 0.134358 0.232716i −0.790994 0.611824i \(-0.790436\pi\)
0.925352 + 0.379109i \(0.123769\pi\)
\(398\) 1.38622 0.0694851
\(399\) 7.59381 0.386145i 0.380166 0.0193314i
\(400\) 0 0
\(401\) −4.16916 + 7.22120i −0.208198 + 0.360609i −0.951147 0.308739i \(-0.900093\pi\)
0.742949 + 0.669348i \(0.233426\pi\)
\(402\) 5.37122 9.30322i 0.267892 0.464003i
\(403\) 0.550195 + 0.952965i 0.0274072 + 0.0474706i
\(404\) 2.22328 3.85083i 0.110612 0.191586i
\(405\) 0 0
\(406\) −4.27034 −0.211933
\(407\) 1.82729 0.0905755
\(408\) −22.9001 39.6642i −1.13373 1.96367i
\(409\) 17.6613 + 30.5903i 0.873297 + 1.51259i 0.858566 + 0.512703i \(0.171356\pi\)
0.0147313 + 0.999891i \(0.495311\pi\)
\(410\) 0 0
\(411\) 38.3702 1.89266
\(412\) −9.85147 17.0632i −0.485347 0.840646i
\(413\) 1.05210 1.82229i 0.0517704 0.0896689i
\(414\) −9.43719 16.3457i −0.463813 0.803347i
\(415\) 0 0
\(416\) −0.553780 + 0.959176i −0.0271513 + 0.0470274i
\(417\) 0.964511 0.0472323
\(418\) 7.18219 0.365214i 0.351292 0.0178632i
\(419\) 21.2453 1.03790 0.518949 0.854805i \(-0.326323\pi\)
0.518949 + 0.854805i \(0.326323\pi\)
\(420\) 0 0
\(421\) 7.43719 12.8816i 0.362467 0.627811i −0.625900 0.779904i \(-0.715268\pi\)
0.988366 + 0.152093i \(0.0486013\pi\)
\(422\) −2.63142 4.55775i −0.128096 0.221868i
\(423\) 28.6445 49.6137i 1.39274 2.41230i
\(424\) −11.5250 19.9618i −0.559702 0.969432i
\(425\) 0 0
\(426\) 13.8020 0.668710
\(427\) −0.994587 1.72268i −0.0481314 0.0833661i
\(428\) −0.663785 1.14971i −0.0320853 0.0555733i
\(429\) −1.14540 −0.0553006
\(430\) 0 0
\(431\) 8.47590 + 14.6807i 0.408270 + 0.707144i 0.994696 0.102858i \(-0.0327989\pi\)
−0.586426 + 0.810003i \(0.699466\pi\)
\(432\) 0.470395 0.814748i 0.0226319 0.0391996i
\(433\) 11.5730 + 20.0450i 0.556161 + 0.963299i 0.997812 + 0.0661122i \(0.0210595\pi\)
−0.441651 + 0.897187i \(0.645607\pi\)
\(434\) −1.38243 + 2.39444i −0.0663587 + 0.114937i
\(435\) 0 0
\(436\) 8.46832 0.405559
\(437\) 6.69993 13.0990i 0.320501 0.626610i
\(438\) −22.8578 −1.09219
\(439\) −16.7729 + 29.0515i −0.800525 + 1.38655i 0.118745 + 0.992925i \(0.462113\pi\)
−0.919271 + 0.393626i \(0.871221\pi\)
\(440\) 0 0
\(441\) 21.6437 + 37.4881i 1.03065 + 1.78515i
\(442\) 0.444392 0.769710i 0.0211376 0.0366114i
\(443\) −15.6789 27.1567i −0.744929 1.29025i −0.950228 0.311555i \(-0.899150\pi\)
0.205299 0.978699i \(-0.434183\pi\)
\(444\) −3.69446 −0.175331
\(445\) 0 0
\(446\) −7.43081 12.8705i −0.351859 0.609438i
\(447\) 6.72147 + 11.6419i 0.317915 + 0.550644i
\(448\) −2.68343 −0.126780
\(449\) −16.0301 −0.756509 −0.378255 0.925702i \(-0.623476\pi\)
−0.378255 + 0.925702i \(0.623476\pi\)
\(450\) 0 0
\(451\) 9.60888 16.6431i 0.452465 0.783692i
\(452\) 4.96022 + 8.59136i 0.233309 + 0.404104i
\(453\) 0.304798 0.527926i 0.0143207 0.0248041i
\(454\) −0.511217 + 0.885455i −0.0239926 + 0.0415564i
\(455\) 0 0
\(456\) −37.6511 + 1.91456i −1.76317 + 0.0896573i
\(457\) 15.3980 0.720286 0.360143 0.932897i \(-0.382728\pi\)
0.360143 + 0.932897i \(0.382728\pi\)
\(458\) 2.69529 4.66837i 0.125943 0.218139i
\(459\) −28.3804 + 49.1563i −1.32469 + 2.29442i
\(460\) 0 0
\(461\) 2.90705 5.03517i 0.135395 0.234511i −0.790353 0.612651i \(-0.790103\pi\)
0.925748 + 0.378140i \(0.123436\pi\)
\(462\) −1.43898 2.49238i −0.0669474 0.115956i
\(463\) 32.6788 1.51871 0.759356 0.650675i \(-0.225514\pi\)
0.759356 + 0.650675i \(0.225514\pi\)
\(464\) −0.766826 −0.0355990
\(465\) 0 0
\(466\) 1.18929 + 2.05991i 0.0550927 + 0.0954234i
\(467\) −6.59041 −0.304968 −0.152484 0.988306i \(-0.548727\pi\)
−0.152484 + 0.988306i \(0.548727\pi\)
\(468\) 1.58304 0.0731759
\(469\) −1.14540 1.98390i −0.0528898 0.0916078i
\(470\) 0 0
\(471\) −24.2789 42.0523i −1.11871 1.93767i
\(472\) −5.21644 + 9.03514i −0.240106 + 0.415876i
\(473\) 4.71597 8.16830i 0.216841 0.375579i
\(474\) 17.6040 0.808581
\(475\) 0 0
\(476\) −3.76683 −0.172652
\(477\) −26.5922 + 46.0590i −1.21757 + 2.10890i
\(478\) 7.46545 12.9305i 0.341462 0.591429i
\(479\) 18.4032 + 31.8753i 0.840864 + 1.45642i 0.889165 + 0.457586i \(0.151286\pi\)
−0.0483016 + 0.998833i \(0.515381\pi\)
\(480\) 0 0
\(481\) −0.0929453 0.160986i −0.00423794 0.00734033i
\(482\) 4.12980 0.188107
\(483\) −5.88801 −0.267914
\(484\) −4.61021 7.98511i −0.209555 0.362960i
\(485\) 0 0
\(486\) 8.28310 0.375729
\(487\) 2.45475 0.111235 0.0556176 0.998452i \(-0.482287\pi\)
0.0556176 + 0.998452i \(0.482287\pi\)
\(488\) 4.93129 + 8.54125i 0.223229 + 0.386644i
\(489\) −14.1451 + 24.5000i −0.639662 + 1.10793i
\(490\) 0 0
\(491\) −8.89716 + 15.4103i −0.401523 + 0.695459i −0.993910 0.110195i \(-0.964852\pi\)
0.592387 + 0.805654i \(0.298186\pi\)
\(492\) −19.4275 + 33.6494i −0.875858 + 1.51703i
\(493\) 46.2651 2.08367
\(494\) −0.397498 0.614180i −0.0178843 0.0276333i
\(495\) 0 0
\(496\) −0.248243 + 0.429970i −0.0111464 + 0.0193062i
\(497\) 1.47163 2.54894i 0.0660116 0.114335i
\(498\) −6.00046 10.3931i −0.268887 0.465726i
\(499\) 14.6399 25.3570i 0.655371 1.13514i −0.326429 0.945222i \(-0.605845\pi\)
0.981801 0.189915i \(-0.0608213\pi\)
\(500\) 0 0
\(501\) −9.45359 −0.422355
\(502\) 22.6462 1.01075
\(503\) 14.7189 + 25.4939i 0.656283 + 1.13672i 0.981571 + 0.191100i \(0.0612056\pi\)
−0.325287 + 0.945615i \(0.605461\pi\)
\(504\) 5.15662 + 8.93153i 0.229694 + 0.397842i
\(505\) 0 0
\(506\) −5.56885 −0.247566
\(507\) −19.9561 34.5650i −0.886283 1.53509i
\(508\) 5.32149 9.21710i 0.236103 0.408943i
\(509\) −3.34723 5.79757i −0.148363 0.256973i 0.782259 0.622953i \(-0.214067\pi\)
−0.930623 + 0.365980i \(0.880734\pi\)
\(510\) 0 0
\(511\) −2.43719 + 4.22134i −0.107815 + 0.186741i
\(512\) −0.992797 −0.0438758
\(513\) 25.3856 + 39.2237i 1.12080 + 1.73177i
\(514\) −19.1973 −0.846757
\(515\) 0 0
\(516\) −9.53486 + 16.5149i −0.419749 + 0.727026i
\(517\) −8.45150 14.6384i −0.371696 0.643797i
\(518\) 0.233536 0.404496i 0.0102610 0.0177725i
\(519\) −16.0323 27.7688i −0.703741 1.21892i
\(520\) 0 0
\(521\) 20.0801 0.879724 0.439862 0.898065i \(-0.355027\pi\)
0.439862 + 0.898065i \(0.355027\pi\)
\(522\) −24.4267 42.3083i −1.06913 1.85178i
\(523\) −18.2220 31.5615i −0.796793 1.38009i −0.921694 0.387918i \(-0.873195\pi\)
0.124901 0.992169i \(-0.460139\pi\)
\(524\) −2.35350 −0.102813
\(525\) 0 0
\(526\) −3.80202 6.58530i −0.165776 0.287133i
\(527\) 14.9773 25.9414i 0.652421 1.13003i
\(528\) −0.258398 0.447558i −0.0112453 0.0194775i
\(529\) 5.80335 10.0517i 0.252319 0.437030i
\(530\) 0 0
\(531\) 24.0724 1.04465
\(532\) −1.41193 + 2.76047i −0.0612151 + 0.119681i
\(533\) −1.95503 −0.0846816
\(534\) −4.48108 + 7.76146i −0.193915 + 0.335871i
\(535\) 0 0
\(536\) 5.67906 + 9.83641i 0.245298 + 0.424868i
\(537\) −20.6968 + 35.8479i −0.893132 + 1.54695i
\(538\) −2.05522 3.55975i −0.0886069 0.153472i
\(539\) 12.7719 0.550124
\(540\) 0 0
\(541\) 7.31456 + 12.6692i 0.314478 + 0.544691i 0.979326 0.202287i \(-0.0648373\pi\)
−0.664849 + 0.746978i \(0.731504\pi\)
\(542\) 1.51803 + 2.62930i 0.0652049 + 0.112938i
\(543\) −24.5166 −1.05211
\(544\) 30.1498 1.29266
\(545\) 0 0
\(546\) −0.146388 + 0.253551i −0.00626481 + 0.0108510i
\(547\) 10.2093 + 17.6831i 0.436519 + 0.756073i 0.997418 0.0718112i \(-0.0228779\pi\)
−0.560899 + 0.827884i \(0.689545\pi\)
\(548\) −7.82329 + 13.5503i −0.334194 + 0.578842i
\(549\) 11.3782 19.7077i 0.485611 0.841104i
\(550\) 0 0
\(551\) 17.3417 33.9047i 0.738782 1.44439i
\(552\) 29.1935 1.24256
\(553\) 1.87702 3.25109i 0.0798188 0.138250i
\(554\) −14.1377 + 24.4872i −0.600653 + 1.04036i
\(555\) 0 0
\(556\) −0.196654 + 0.340615i −0.00833999 + 0.0144453i
\(557\) 17.9399 + 31.0728i 0.760138 + 1.31660i 0.942779 + 0.333418i \(0.108202\pi\)
−0.182641 + 0.983180i \(0.558465\pi\)
\(558\) −31.6304 −1.33902
\(559\) −0.959512 −0.0405830
\(560\) 0 0
\(561\) 15.5900 + 27.0026i 0.658209 + 1.14005i
\(562\) −8.55873 −0.361028
\(563\) −37.7708 −1.59185 −0.795925 0.605395i \(-0.793015\pi\)
−0.795925 + 0.605395i \(0.793015\pi\)
\(564\) 17.0874 + 29.5963i 0.719511 + 1.24623i
\(565\) 0 0
\(566\) 1.06632 + 1.84692i 0.0448208 + 0.0776319i
\(567\) 3.84133 6.65338i 0.161321 0.279416i
\(568\) −7.29653 + 12.6380i −0.306155 + 0.530277i
\(569\) 28.0844 1.17736 0.588681 0.808366i \(-0.299648\pi\)
0.588681 + 0.808366i \(0.299648\pi\)
\(570\) 0 0
\(571\) 20.6040 0.862253 0.431126 0.902292i \(-0.358116\pi\)
0.431126 + 0.902292i \(0.358116\pi\)
\(572\) 0.233536 0.404496i 0.00976463 0.0169128i
\(573\) −21.7077 + 37.5988i −0.906852 + 1.57071i
\(574\) −2.45611 4.25412i −0.102516 0.177563i
\(575\) 0 0
\(576\) −15.3494 26.5860i −0.639559 1.10775i
\(577\) 43.8371 1.82496 0.912481 0.409119i \(-0.134164\pi\)
0.912481 + 0.409119i \(0.134164\pi\)
\(578\) −9.52702 −0.396272
\(579\) −6.12263 10.6047i −0.254448 0.440717i
\(580\) 0 0
\(581\) −2.55918 −0.106173
\(582\) −40.3600 −1.67297
\(583\) 7.84597 + 13.5896i 0.324947 + 0.562825i
\(584\) 12.0839 20.9300i 0.500036 0.866088i
\(585\) 0 0
\(586\) −7.34591 + 12.7235i −0.303457 + 0.525602i
\(587\) −18.9905 + 32.8925i −0.783821 + 1.35762i 0.145880 + 0.989302i \(0.453399\pi\)
−0.929701 + 0.368315i \(0.879935\pi\)
\(588\) −25.8225 −1.06490
\(589\) −13.3968 20.6996i −0.552006 0.852914i
\(590\) 0 0
\(591\) −28.2501 + 48.9306i −1.16205 + 2.01274i
\(592\) 0.0419361 0.0726355i 0.00172356 0.00298530i
\(593\) 2.69007 + 4.65934i 0.110468 + 0.191336i 0.915959 0.401272i \(-0.131432\pi\)
−0.805491 + 0.592608i \(0.798098\pi\)
\(594\) 8.84206 15.3149i 0.362794 0.628378i
\(595\) 0 0
\(596\) −5.48175 −0.224541
\(597\) 4.94722 0.202476
\(598\) 0.283260 + 0.490620i 0.0115834 + 0.0200630i
\(599\) −11.2143 19.4237i −0.458202 0.793629i 0.540664 0.841239i \(-0.318173\pi\)
−0.998866 + 0.0476095i \(0.984840\pi\)
\(600\) 0 0
\(601\) −29.5732 −1.20632 −0.603159 0.797621i \(-0.706091\pi\)
−0.603159 + 0.797621i \(0.706091\pi\)
\(602\) −1.20544 2.08789i −0.0491302 0.0850960i
\(603\) 13.1036 22.6961i 0.533620 0.924257i
\(604\) 0.124291 + 0.215278i 0.00505731 + 0.00875952i
\(605\) 0 0
\(606\) −4.70402 + 8.14760i −0.191088 + 0.330974i
\(607\) 24.5915 0.998139 0.499069 0.866562i \(-0.333675\pi\)
0.499069 + 0.866562i \(0.333675\pi\)
\(608\) 11.3012 22.0949i 0.458323 0.896065i
\(609\) −15.2402 −0.617564
\(610\) 0 0
\(611\) −0.859772 + 1.48917i −0.0347826 + 0.0602453i
\(612\) −21.5466 37.3197i −0.870968 1.50856i
\(613\) −14.9450 + 25.8856i −0.603624 + 1.04551i 0.388643 + 0.921388i \(0.372944\pi\)
−0.992267 + 0.124119i \(0.960389\pi\)
\(614\) 9.05027 + 15.6755i 0.365239 + 0.632613i
\(615\) 0 0
\(616\) 3.04290 0.122602
\(617\) −20.3570 35.2594i −0.819544 1.41949i −0.906019 0.423238i \(-0.860894\pi\)
0.0864749 0.996254i \(-0.472440\pi\)
\(618\) 20.8438 + 36.1025i 0.838459 + 1.45225i
\(619\) −28.4784 −1.14464 −0.572322 0.820029i \(-0.693957\pi\)
−0.572322 + 0.820029i \(0.693957\pi\)
\(620\) 0 0
\(621\) −18.0900 31.3327i −0.725925 1.25734i
\(622\) −1.35804 + 2.35219i −0.0544524 + 0.0943143i
\(623\) 0.955582 + 1.65512i 0.0382846 + 0.0663109i
\(624\) −0.0262868 + 0.0455302i −0.00105232 + 0.00182266i
\(625\) 0 0
\(626\) −10.6060 −0.423902
\(627\) 25.6321 1.30339i 1.02365 0.0520525i
\(628\) 19.8009 0.790141
\(629\) −2.53014 + 4.38233i −0.100883 + 0.174735i
\(630\) 0 0
\(631\) −21.2101 36.7369i −0.844359 1.46247i −0.886176 0.463348i \(-0.846648\pi\)
0.0418172 0.999125i \(-0.486685\pi\)
\(632\) −9.30649 + 16.1193i −0.370192 + 0.641192i
\(633\) −9.39114 16.2659i −0.373264 0.646513i
\(634\) 9.88912 0.392747
\(635\) 0 0
\(636\) −15.8632 27.4758i −0.629016 1.08949i
\(637\) −0.649643 1.12521i −0.0257398 0.0445826i
\(638\) −14.4141 −0.570659
\(639\) 33.6714 1.33202
\(640\) 0 0
\(641\) 14.7630 25.5702i 0.583102 1.00996i −0.412007 0.911181i \(-0.635172\pi\)
0.995109 0.0987822i \(-0.0314947\pi\)
\(642\) 1.40444 + 2.43256i 0.0554288 + 0.0960055i
\(643\) 10.7985 18.7036i 0.425852 0.737597i −0.570648 0.821195i \(-0.693308\pi\)
0.996500 + 0.0835979i \(0.0266411\pi\)
\(644\) 1.20051 2.07934i 0.0473066 0.0819374i
\(645\) 0 0
\(646\) −9.06885 + 17.7305i −0.356809 + 0.697596i
\(647\) 12.6128 0.495861 0.247930 0.968778i \(-0.420250\pi\)
0.247930 + 0.968778i \(0.420250\pi\)
\(648\) −19.0458 + 32.9883i −0.748190 + 1.29590i
\(649\) 3.55125 6.15095i 0.139399 0.241446i
\(650\) 0 0
\(651\) −4.93368 + 8.54538i −0.193366 + 0.334920i
\(652\) −5.76807 9.99059i −0.225895 0.391262i
\(653\) 26.6312 1.04216 0.521080 0.853508i \(-0.325529\pi\)
0.521080 + 0.853508i \(0.325529\pi\)
\(654\) −17.9173 −0.700621
\(655\) 0 0
\(656\) −0.441045 0.763913i −0.0172199 0.0298258i
\(657\) −55.7638 −2.17555
\(658\) −4.32055 −0.168433
\(659\) −19.9772 34.6016i −0.778202 1.34789i −0.932977 0.359936i \(-0.882798\pi\)
0.154775 0.987950i \(-0.450535\pi\)
\(660\) 0 0
\(661\) 6.76165 + 11.7115i 0.262998 + 0.455526i 0.967037 0.254635i \(-0.0819555\pi\)
−0.704039 + 0.710161i \(0.748622\pi\)
\(662\) 2.52676 4.37648i 0.0982053 0.170097i
\(663\) 1.58597 2.74698i 0.0615939 0.106684i
\(664\) 12.6887 0.492418
\(665\) 0 0
\(666\) 5.34338 0.207052
\(667\) −14.7449 + 25.5389i −0.570925 + 0.988871i
\(668\) 1.92749 3.33851i 0.0745768 0.129171i
\(669\) −26.5195 45.9330i −1.02530 1.77587i
\(670\) 0 0
\(671\) −3.35713 5.81471i −0.129600 0.224475i
\(672\) −9.93166 −0.383122
\(673\) −34.4110 −1.32645 −0.663224 0.748421i \(-0.730812\pi\)
−0.663224 + 0.748421i \(0.730812\pi\)
\(674\) −3.71425 6.43327i −0.143068 0.247800i
\(675\) 0 0
\(676\) 16.2754 0.625977
\(677\) 29.6650 1.14012 0.570059 0.821604i \(-0.306920\pi\)
0.570059 + 0.821604i \(0.306920\pi\)
\(678\) −10.4949 18.1776i −0.403053 0.698108i
\(679\) −4.30335 + 7.45361i −0.165147 + 0.286043i
\(680\) 0 0
\(681\) −1.82446 + 3.16005i −0.0699134 + 0.121094i
\(682\) −4.66625 + 8.08217i −0.178680 + 0.309482i
\(683\) 27.8978 1.06748 0.533740 0.845648i \(-0.320786\pi\)
0.533740 + 0.845648i \(0.320786\pi\)
\(684\) −35.4256 + 1.80139i −1.35453 + 0.0688779i
\(685\) 0 0
\(686\) 3.34304 5.79032i 0.127638 0.221075i
\(687\) 9.61907 16.6607i 0.366991 0.635646i
\(688\) −0.216462 0.374923i −0.00825253 0.0142938i
\(689\) 0.798172 1.38247i 0.0304079 0.0526680i
\(690\) 0 0
\(691\) −49.6386 −1.88834 −0.944170 0.329459i \(-0.893134\pi\)
−0.944170 + 0.329459i \(0.893134\pi\)
\(692\) 13.0753 0.497049
\(693\) −3.51053 6.08041i −0.133354 0.230976i
\(694\) 5.21558 + 9.03364i 0.197981 + 0.342912i
\(695\) 0 0
\(696\) 75.5629 2.86420
\(697\) 26.6097 + 46.0893i 1.00791 + 1.74576i
\(698\) 8.18863 14.1831i 0.309944 0.536839i
\(699\) 4.24439 + 7.35150i 0.160538 + 0.278059i
\(700\) 0 0
\(701\) 24.9906 43.2851i 0.943883 1.63485i 0.185911 0.982567i \(-0.440476\pi\)
0.757972 0.652287i \(-0.226190\pi\)
\(702\) −1.79901 −0.0678991
\(703\) 2.26315 + 3.49682i 0.0853562 + 0.131885i
\(704\) −9.05763 −0.341372
\(705\) 0 0
\(706\) 3.32929 5.76651i 0.125300 0.217025i
\(707\) 1.00312 + 1.73746i 0.0377264 + 0.0653440i
\(708\) −7.18000 + 12.4361i −0.269841 + 0.467378i
\(709\) −12.5938 21.8131i −0.472971 0.819209i 0.526551 0.850144i \(-0.323485\pi\)
−0.999521 + 0.0309345i \(0.990152\pi\)
\(710\) 0 0
\(711\) 42.9468 1.61063
\(712\) −4.73790 8.20628i −0.177560 0.307543i
\(713\) 9.54667 + 16.5353i 0.357526 + 0.619253i
\(714\) 7.96986 0.298265
\(715\) 0 0
\(716\) −8.43972 14.6180i −0.315407 0.546301i
\(717\) 26.6431 46.1471i 0.995003 1.72340i
\(718\) −3.03274 5.25285i −0.113181 0.196035i
\(719\) −8.58777 + 14.8745i −0.320270 + 0.554724i −0.980544 0.196301i \(-0.937107\pi\)
0.660274 + 0.751025i \(0.270440\pi\)
\(720\) 0 0
\(721\) 8.88979 0.331073
\(722\) 9.59421 + 13.2920i 0.357060 + 0.494676i
\(723\) 14.7386 0.548136
\(724\) 4.99868 8.65796i 0.185774 0.321771i
\(725\) 0 0
\(726\) 9.75429 + 16.8949i 0.362016 + 0.627029i
\(727\) −0.528264 + 0.914981i −0.0195922 + 0.0339348i −0.875655 0.482937i \(-0.839570\pi\)
0.856063 + 0.516871i \(0.172903\pi\)
\(728\) −0.154777 0.268082i −0.00573643 0.00993579i
\(729\) −11.1223 −0.411937
\(730\) 0 0
\(731\) 13.0598 + 22.6203i 0.483035 + 0.836641i
\(732\) 6.78752 + 11.7563i 0.250874 + 0.434526i
\(733\) −20.5025 −0.757277 −0.378639 0.925545i \(-0.623608\pi\)
−0.378639 + 0.925545i \(0.623608\pi\)
\(734\) −29.0851 −1.07355
\(735\) 0 0
\(736\) −9.60888 + 16.6431i −0.354188 + 0.613472i
\(737\) −3.86619 6.69644i −0.142413 0.246666i
\(738\) 28.0984 48.6678i 1.03431 1.79149i
\(739\) −12.4548 + 21.5723i −0.458157 + 0.793551i −0.998864 0.0476601i \(-0.984824\pi\)
0.540707 + 0.841211i \(0.318157\pi\)
\(740\) 0 0
\(741\) −1.41861 2.19192i −0.0521139 0.0805221i
\(742\) 4.01100 0.147248
\(743\) 6.62867 11.4812i 0.243182 0.421204i −0.718437 0.695592i \(-0.755142\pi\)
0.961619 + 0.274388i \(0.0884754\pi\)
\(744\) 24.4618 42.3691i 0.896814 1.55333i
\(745\) 0 0
\(746\) −4.31808 + 7.47913i −0.158096 + 0.273830i
\(747\) −14.6387 25.3550i −0.535602 0.927690i
\(748\) −12.7145 −0.464889
\(749\) 0.598988 0.0218866
\(750\) 0 0
\(751\) −12.4183 21.5091i −0.453149 0.784877i 0.545430 0.838156i \(-0.316366\pi\)
−0.998580 + 0.0532786i \(0.983033\pi\)
\(752\) −0.775843 −0.0282921
\(753\) 80.8209 2.94528
\(754\) 0.733174 + 1.26989i 0.0267006 + 0.0462468i
\(755\) 0 0
\(756\) 3.81226 + 6.60302i 0.138650 + 0.240150i
\(757\) 24.2329 41.9726i 0.880760 1.52552i 0.0302631 0.999542i \(-0.490365\pi\)
0.850497 0.525980i \(-0.176301\pi\)
\(758\) −15.4465 + 26.7542i −0.561044 + 0.971756i
\(759\) −19.8744 −0.721395
\(760\) 0 0
\(761\) 40.3726 1.46351 0.731753 0.681570i \(-0.238702\pi\)
0.731753 + 0.681570i \(0.238702\pi\)
\(762\) −11.2592 + 19.5016i −0.407879 + 0.706467i
\(763\) −1.91042 + 3.30894i −0.0691617 + 0.119792i
\(764\) −8.85195 15.3320i −0.320252 0.554693i
\(765\) 0 0
\(766\) 7.00989 + 12.1415i 0.253278 + 0.438690i
\(767\) −0.722538 −0.0260893
\(768\) 48.5638 1.75239
\(769\) 22.4772 + 38.9317i 0.810550 + 1.40391i 0.912480 + 0.409121i \(0.134165\pi\)
−0.101930 + 0.994792i \(0.532502\pi\)
\(770\) 0 0
\(771\) −68.5123 −2.46741
\(772\) 4.99337 0.179715
\(773\) 1.84323 + 3.19256i 0.0662962 + 0.114828i 0.897268 0.441486i \(-0.145548\pi\)
−0.830972 + 0.556314i \(0.812215\pi\)
\(774\) 13.7905 23.8858i 0.495688 0.858557i
\(775\) 0 0
\(776\) 21.3365 36.9560i 0.765937 1.32664i
\(777\) 0.833455 1.44359i 0.0299000 0.0517884i
\(778\) 16.7255 0.599639
\(779\) 43.7501 2.22469i 1.56751 0.0797078i
\(780\) 0 0
\(781\) 4.96733 8.60367i 0.177745 0.307864i
\(782\) 7.71084 13.3556i 0.275739 0.477594i
\(783\) −46.8230 81.0999i −1.67332 2.89827i