Properties

Label 475.2.e.g.201.2
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 201.2
Root \(0.579521 - 1.00376i\) of defining polynomial
Character \(\chi\) \(=\) 475.201
Dual form 475.2.e.g.26.2

$q$-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 −0.977270 0.211998i \(-0.932003\pi\)
0.672231 + 0.740342i \(0.265336\pi\)
\(3\) −1.53957 + 2.66661i −0.888870 + 1.53957i −0.0476573 + 0.998864i \(0.515176\pi\)
−0.841213 + 0.540704i \(0.818158\pi\)
\(4\) 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 \(-0.465856\pi\)
0.107062 + 0.994252i \(0.465856\pi\)
\(8\) −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 0.852222 0.523180i \(-0.175255\pi\)
−0.879199 + 0.476456i \(0.841921\pi\)
\(14\) −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 \(0.388633\pi\)
−0.984947 + 0.172858i \(0.944700\pi\)
\(18\) 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 0.634674 0.772780i \(-0.281134\pi\)
−0.986584 + 0.163254i \(0.947801\pi\)
\(24\) 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 \(-0.474971\pi\)
0.0785484 + 0.996910i \(0.474971\pi\)
\(38\) 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 −0.614396 0.788998i \(-0.710600\pi\)
0.990490 + 0.137583i \(0.0439335\pi\)
\(44\) −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 \(-0.943657\pi\)
0.339694 0.940536i \(-0.389676\pi\)
\(48\) −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 \(0.0239163\pi\)
−0.433581 + 0.901114i \(0.642750\pi\)
\(54\) −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 0.715688 0.698420i \(-0.246113\pi\)
−0.962693 + 0.270594i \(0.912780\pi\)
\(68\) −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 \(0.334627\pi\)
−0.999992 + 0.00406505i \(0.998706\pi\)
\(74\) −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 \(-0.579748\pi\)
−0.247923 + 0.968780i \(0.579748\pi\)
\(84\) −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 \(0.447044\pi\)
−0.936868 + 0.349683i \(0.886289\pi\)
\(98\) 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 \(-0.218712\pi\)
0.773086 + 0.634301i \(0.218712\pi\)
\(104\) 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 \(-0.483725\pi\)
0.0511071 + 0.998693i \(0.483725\pi\)
\(108\) 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 \(-0.621200\pi\)
−0.371627 + 0.928382i \(0.621200\pi\)
\(114\) −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 0.990488 0.137601i \(-0.0439393\pi\)
−0.614410 + 0.788987i \(0.710606\pi\)
\(128\) 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 \(-0.987986\pi\)
0.466965 0.884276i \(-0.345347\pi\)
\(138\) −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 \(0.383321\pi\)
−0.987695 + 0.156395i \(0.950013\pi\)
\(158\) −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 \(-0.382839\pi\)
0.359817 + 0.933023i \(0.382839\pi\)
\(164\) −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 0.919288 0.393585i \(-0.128765\pi\)
−0.800498 + 0.599335i \(0.795432\pi\)
\(168\) 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 −0.993211 0.116328i \(-0.962888\pi\)
0.597348 + 0.801982i \(0.296221\pi\)
\(174\) 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 −0.928674 0.370898i \(-0.879050\pi\)
0.785544 + 0.618806i \(0.212383\pi\)
\(194\) −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 \(-0.273229\pi\)
0.653669 + 0.756781i \(0.273229\pi\)
\(198\) −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 \(0.362344\pi\)
−0.995850 + 0.0910127i \(0.970990\pi\)
\(224\) −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 \(-0.487479\pi\)
0.0393271 + 0.999226i \(0.487479\pi\)
\(228\) 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 −0.817335 0.576163i \(-0.804549\pi\)
0.907639 + 0.419751i \(0.137883\pi\)
\(234\) −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 \(0.0774749\pi\)
−0.276552 + 0.960999i \(0.589192\pi\)
\(258\) −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 −0.969305 0.245863i \(-0.920929\pi\)
0.697576 + 0.716511i \(0.254262\pi\)
\(264\) −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 \(-0.0560242\pi\)
0.984551 + 0.175098i \(0.0560242\pi\)
\(278\) −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 −0.826951 0.562273i \(-0.809927\pi\)
0.900419 + 0.435024i \(0.143260\pi\)
\(284\) −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 \(-0.334286\pi\)
0.497406 + 0.867518i \(0.334286\pi\)
\(294\) 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 \(-0.629027\pi\)
0.993017 0.117972i \(-0.0376395\pi\)
\(308\) −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 0.985790 0.167985i \(-0.0537259\pi\)
−0.638374 + 0.769726i \(0.720393\pi\)
\(314\) −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 0.658994 0.752148i \(-0.270982\pi\)
−0.980876 + 0.194631i \(0.937649\pi\)
\(318\) 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 −0.959129 0.282968i \(-0.908681\pi\)
0.724622 + 0.689146i \(0.242014\pi\)
\(338\) 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 −0.656898 0.753980i \(-0.728132\pi\)
0.981414 + 0.191900i \(0.0614651\pi\)
\(348\) −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 \(-0.565844\pi\)
−0.205383 + 0.978682i \(0.565844\pi\)
\(354\) 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 \(0.175689\pi\)
0.0283394 + 0.999598i \(0.490978\pi\)
\(368\) 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 \(-0.416561\pi\)
0.259141 + 0.965840i \(0.416561\pi\)
\(374\) 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 −0.580289 0.814411i \(-0.697060\pi\)
0.995445 + 0.0953393i \(0.0303936\pi\)
\(384\) 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 −0.925352 0.379109i \(-0.876231\pi\)
0.790994 + 0.611824i \(0.209564\pi\)
\(398\) −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 \(-0.978940\pi\)
0.441651 0.897187i \(-0.354393\pi\)
\(434\) −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 \(0.100850\pi\)
−0.205299 + 0.978699i \(0.565817\pi\)
\(444\) −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 \(-0.617272\pi\)
−0.360143 + 0.932897i \(0.617272\pi\)
\(458\) −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 \(-0.774486\pi\)
−0.759356 + 0.650675i \(0.774486\pi\)
\(464\) −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 \(-0.451273\pi\)
0.152484 + 0.988306i \(0.451273\pi\)
\(468\) −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 \(-0.517713\pi\)
−0.0556176 + 0.998452i \(0.517713\pi\)
\(488\) −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 \(-0.938794\pi\)
0.325287 0.945615i \(-0.394539\pi\)
\(504\) 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 \(0.126805\pi\)
−0.124901 + 0.992169i \(0.539861\pi\)
\(524\) −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 0.560899 0.827884i \(-0.310455\pi\)
−0.997418 + 0.0718112i \(0.977122\pi\)
\(548\) 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 \(-0.891798\pi\)
0.182641 0.983180i \(-0.441535\pi\)
\(558\) 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 \(-0.206985\pi\)
0.795925 + 0.605395i \(0.206985\pi\)
\(564\) 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 \(-0.865836\pi\)
−0.912481 + 0.409119i \(0.865836\pi\)
\(578\) 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 \(-0.546601\pi\)
0.929701 0.368315i \(-0.120065\pi\)
\(588\) 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 0.805491 0.592608i \(-0.201902\pi\)
−0.915959 + 0.401272i \(0.868568\pi\)
\(594\) 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 \(-0.666325\pi\)
−0.499069 + 0.866562i \(0.666325\pi\)
\(608\) −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 \(-0.627056\pi\)
0.992267 0.124119i \(-0.0396106\pi\)
\(614\) 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 \(0.139106\pi\)
−0.0864749 + 0.996254i \(0.527560\pi\)
\(618\) −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 −0.996500 0.0835979i \(-0.973359\pi\)
0.570648 + 0.821195i \(0.306692\pi\)
\(644\) 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 \(-0.579750\pi\)
−0.247930 + 0.968778i \(0.579750\pi\)
\(648\) 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 \(-0.674471\pi\)
−0.521080 + 0.853508i \(0.674471\pi\)
\(654\) −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 \(-0.269188\pi\)
0.663224 + 0.748421i \(0.269188\pi\)
\(674\) −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 \(-0.693080\pi\)
−0.570059 + 0.821604i \(0.693080\pi\)
\(678\) 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 \(-0.679214\pi\)
−0.533740 + 0.845648i \(0.679214\pi\)
\(684\) −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 −0.856063 0.516871i \(-0.827097\pi\)
0.875655 + 0.482937i \(0.160430\pi\)
\(728\) 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 \(-0.376392\pi\)
0.378639 + 0.925545i \(0.376392\pi\)
\(734\) −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 −0.961619 0.274388i \(-0.911525\pi\)
0.718437 + 0.695592i \(0.244858\pi\)
\(744\) 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 \(0.509635\pi\)
−0.850497 + 0.525980i \(0.823699\pi\)
\(758\) 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 0.830972 0.556314i \(-0.187785\pi\)
−0.897268 + 0.441486i \(0.854452\pi\)
\(774\) 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