Properties

Label 450.2.p.c.257.2
Level 450
Weight 2
Character 450.257
Analytic conductor 3.593
Analytic rank 0
Dimension 8
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.p (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 257.2
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 450.257
Dual form 450.2.p.c.443.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.965926 + 0.258819i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.866025 - 1.50000i) q^{6} +(-1.22474 + 4.57081i) q^{7} +(0.707107 + 0.707107i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(0.965926 + 0.258819i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.866025 - 1.50000i) q^{6} +(-1.22474 + 4.57081i) q^{7} +(0.707107 + 0.707107i) q^{8} +3.00000i q^{9} +(3.00000 - 1.73205i) q^{11} +(-0.448288 - 1.67303i) q^{12} +(1.22474 + 4.57081i) q^{13} +(-2.36603 + 4.09808i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.776457 + 2.89778i) q^{18} -3.19615i q^{19} +(7.09808 - 4.09808i) q^{21} +(3.34607 - 0.896575i) q^{22} +(2.12132 - 0.568406i) q^{23} -1.73205i q^{24} +4.73205i q^{26} +(3.67423 - 3.67423i) q^{27} +(-3.34607 + 3.34607i) q^{28} +(5.36603 + 9.29423i) q^{29} +(-0.0980762 + 0.169873i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-5.79555 - 1.55291i) q^{33} +(-1.50000 + 2.59808i) q^{36} +(-5.79555 - 5.79555i) q^{37} +(0.827225 - 3.08725i) q^{38} +(4.09808 - 7.09808i) q^{39} +(-1.50000 - 0.866025i) q^{41} +(7.91688 - 2.12132i) q^{42} +(-0.448288 - 0.120118i) q^{43} +3.46410 q^{44} +2.19615 q^{46} +(-5.79555 - 1.55291i) q^{47} +(0.448288 - 1.67303i) q^{48} +(-13.3301 - 7.69615i) q^{49} +(-1.22474 + 4.57081i) q^{52} +(5.79555 + 5.79555i) q^{53} +(4.50000 - 2.59808i) q^{54} +(-4.09808 + 2.36603i) q^{56} +(-3.91447 + 3.91447i) q^{57} +(2.77766 + 10.3664i) q^{58} +(-2.76795 + 4.79423i) q^{59} +(2.00000 + 3.46410i) q^{61} +(-0.138701 + 0.138701i) q^{62} +(-13.7124 - 3.67423i) q^{63} +1.00000i q^{64} +(-5.19615 - 3.00000i) q^{66} +(-5.34727 + 1.43280i) q^{67} +(-3.29423 - 1.90192i) q^{69} -7.26795i q^{71} +(-2.12132 + 2.12132i) q^{72} +(3.67423 - 3.67423i) q^{73} +(-4.09808 - 7.09808i) q^{74} +(1.59808 - 2.76795i) q^{76} +(4.24264 + 15.8338i) q^{77} +(5.79555 - 5.79555i) q^{78} +(8.66025 - 5.00000i) q^{79} -9.00000 q^{81} +(-1.22474 - 1.22474i) q^{82} +(4.45069 - 16.6102i) q^{83} +8.19615 q^{84} +(-0.401924 - 0.232051i) q^{86} +(4.81105 - 17.9551i) q^{87} +(3.34607 + 0.896575i) q^{88} -8.66025 q^{89} -22.3923 q^{91} +(2.12132 + 0.568406i) q^{92} +(0.328169 - 0.0879327i) q^{93} +(-5.19615 - 3.00000i) q^{94} +(0.866025 - 1.50000i) q^{96} +(-0.688524 + 2.56961i) q^{97} +(-10.8840 - 10.8840i) q^{98} +(5.19615 + 9.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 24q^{11} - 12q^{14} + 4q^{16} + 36q^{21} + 36q^{29} + 20q^{31} - 12q^{36} + 12q^{39} - 12q^{41} - 24q^{46} - 72q^{49} + 36q^{54} - 12q^{56} - 36q^{59} + 16q^{61} + 36q^{69} - 12q^{74} - 8q^{76} - 72q^{81} + 24q^{84} - 24q^{86} - 96q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 + 0.258819i 0.683013 + 0.183013i
\(3\) −1.22474 1.22474i −0.707107 0.707107i
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) 0 0
\(6\) −0.866025 1.50000i −0.353553 0.612372i
\(7\) −1.22474 + 4.57081i −0.462910 + 1.72760i 0.200817 + 0.979629i \(0.435640\pi\)
−0.663727 + 0.747975i \(0.731026\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 3.00000i 1.00000i
\(10\) 0 0
\(11\) 3.00000 1.73205i 0.904534 0.522233i 0.0258656 0.999665i \(-0.491766\pi\)
0.878668 + 0.477432i \(0.158432\pi\)
\(12\) −0.448288 1.67303i −0.129410 0.482963i
\(13\) 1.22474 + 4.57081i 0.339683 + 1.26771i 0.898702 + 0.438560i \(0.144511\pi\)
−0.559019 + 0.829155i \(0.688822\pi\)
\(14\) −2.36603 + 4.09808i −0.632347 + 1.09526i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(18\) −0.776457 + 2.89778i −0.183013 + 0.683013i
\(19\) 3.19615i 0.733248i −0.930369 0.366624i \(-0.880514\pi\)
0.930369 0.366624i \(-0.119486\pi\)
\(20\) 0 0
\(21\) 7.09808 4.09808i 1.54893 0.894274i
\(22\) 3.34607 0.896575i 0.713384 0.191151i
\(23\) 2.12132 0.568406i 0.442326 0.118521i −0.0307805 0.999526i \(-0.509799\pi\)
0.473106 + 0.881005i \(0.343133\pi\)
\(24\) 1.73205i 0.353553i
\(25\) 0 0
\(26\) 4.73205i 0.928032i
\(27\) 3.67423 3.67423i 0.707107 0.707107i
\(28\) −3.34607 + 3.34607i −0.632347 + 0.632347i
\(29\) 5.36603 + 9.29423i 0.996446 + 1.72589i 0.571173 + 0.820830i \(0.306489\pi\)
0.425273 + 0.905065i \(0.360178\pi\)
\(30\) 0 0
\(31\) −0.0980762 + 0.169873i −0.0176150 + 0.0305101i −0.874699 0.484667i \(-0.838941\pi\)
0.857084 + 0.515177i \(0.172274\pi\)
\(32\) 0.258819 + 0.965926i 0.0457532 + 0.170753i
\(33\) −5.79555 1.55291i −1.00888 0.270328i
\(34\) 0 0
\(35\) 0 0
\(36\) −1.50000 + 2.59808i −0.250000 + 0.433013i
\(37\) −5.79555 5.79555i −0.952783 0.952783i 0.0461511 0.998934i \(-0.485304\pi\)
−0.998934 + 0.0461511i \(0.985304\pi\)
\(38\) 0.827225 3.08725i 0.134194 0.500817i
\(39\) 4.09808 7.09808i 0.656217 1.13660i
\(40\) 0 0
\(41\) −1.50000 0.866025i −0.234261 0.135250i 0.378275 0.925693i \(-0.376517\pi\)
−0.612536 + 0.790443i \(0.709851\pi\)
\(42\) 7.91688 2.12132i 1.22160 0.327327i
\(43\) −0.448288 0.120118i −0.0683632 0.0183179i 0.224475 0.974480i \(-0.427933\pi\)
−0.292839 + 0.956162i \(0.594600\pi\)
\(44\) 3.46410 0.522233
\(45\) 0 0
\(46\) 2.19615 0.323805
\(47\) −5.79555 1.55291i −0.845369 0.226516i −0.189961 0.981792i \(-0.560836\pi\)
−0.655407 + 0.755276i \(0.727503\pi\)
\(48\) 0.448288 1.67303i 0.0647048 0.241481i
\(49\) −13.3301 7.69615i −1.90430 1.09945i
\(50\) 0 0
\(51\) 0 0
\(52\) −1.22474 + 4.57081i −0.169842 + 0.633857i
\(53\) 5.79555 + 5.79555i 0.796081 + 0.796081i 0.982475 0.186394i \(-0.0596802\pi\)
−0.186394 + 0.982475i \(0.559680\pi\)
\(54\) 4.50000 2.59808i 0.612372 0.353553i
\(55\) 0 0
\(56\) −4.09808 + 2.36603i −0.547628 + 0.316173i
\(57\) −3.91447 + 3.91447i −0.518484 + 0.518484i
\(58\) 2.77766 + 10.3664i 0.364725 + 1.36117i
\(59\) −2.76795 + 4.79423i −0.360356 + 0.624155i −0.988019 0.154330i \(-0.950678\pi\)
0.627663 + 0.778485i \(0.284012\pi\)
\(60\) 0 0
\(61\) 2.00000 + 3.46410i 0.256074 + 0.443533i 0.965187 0.261562i \(-0.0842377\pi\)
−0.709113 + 0.705095i \(0.750904\pi\)
\(62\) −0.138701 + 0.138701i −0.0176150 + 0.0176150i
\(63\) −13.7124 3.67423i −1.72760 0.462910i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −5.19615 3.00000i −0.639602 0.369274i
\(67\) −5.34727 + 1.43280i −0.653273 + 0.175044i −0.570208 0.821500i \(-0.693137\pi\)
−0.0830646 + 0.996544i \(0.526471\pi\)
\(68\) 0 0
\(69\) −3.29423 1.90192i −0.396579 0.228965i
\(70\) 0 0
\(71\) 7.26795i 0.862547i −0.902221 0.431273i \(-0.858064\pi\)
0.902221 0.431273i \(-0.141936\pi\)
\(72\) −2.12132 + 2.12132i −0.250000 + 0.250000i
\(73\) 3.67423 3.67423i 0.430037 0.430037i −0.458604 0.888641i \(-0.651650\pi\)
0.888641 + 0.458604i \(0.151650\pi\)
\(74\) −4.09808 7.09808i −0.476392 0.825135i
\(75\) 0 0
\(76\) 1.59808 2.76795i 0.183312 0.317506i
\(77\) 4.24264 + 15.8338i 0.483494 + 1.80442i
\(78\) 5.79555 5.79555i 0.656217 0.656217i
\(79\) 8.66025 5.00000i 0.974355 0.562544i 0.0737937 0.997274i \(-0.476489\pi\)
0.900561 + 0.434730i \(0.143156\pi\)
\(80\) 0 0
\(81\) −9.00000 −1.00000
\(82\) −1.22474 1.22474i −0.135250 0.135250i
\(83\) 4.45069 16.6102i 0.488527 1.82321i −0.0750978 0.997176i \(-0.523927\pi\)
0.563625 0.826031i \(-0.309406\pi\)
\(84\) 8.19615 0.894274
\(85\) 0 0
\(86\) −0.401924 0.232051i −0.0433406 0.0250227i
\(87\) 4.81105 17.9551i 0.515798 1.92499i
\(88\) 3.34607 + 0.896575i 0.356692 + 0.0955753i
\(89\) −8.66025 −0.917985 −0.458993 0.888440i \(-0.651790\pi\)
−0.458993 + 0.888440i \(0.651790\pi\)
\(90\) 0 0
\(91\) −22.3923 −2.34735
\(92\) 2.12132 + 0.568406i 0.221163 + 0.0592604i
\(93\) 0.328169 0.0879327i 0.0340296 0.00911820i
\(94\) −5.19615 3.00000i −0.535942 0.309426i
\(95\) 0 0
\(96\) 0.866025 1.50000i 0.0883883 0.153093i
\(97\) −0.688524 + 2.56961i −0.0699091 + 0.260904i −0.992031 0.125996i \(-0.959787\pi\)
0.922122 + 0.386900i \(0.126454\pi\)
\(98\) −10.8840 10.8840i −1.09945 1.09945i
\(99\) 5.19615 + 9.00000i 0.522233 + 0.904534i
\(100\) 0 0
\(101\) 6.29423 3.63397i 0.626299 0.361594i −0.153018 0.988223i \(-0.548899\pi\)
0.779317 + 0.626629i \(0.215566\pi\)
\(102\) 0 0
\(103\) −2.68973 10.0382i −0.265027 0.989093i −0.962234 0.272223i \(-0.912241\pi\)
0.697207 0.716869i \(-0.254426\pi\)
\(104\) −2.36603 + 4.09808i −0.232008 + 0.401849i
\(105\) 0 0
\(106\) 4.09808 + 7.09808i 0.398040 + 0.689426i
\(107\) 7.91688 7.91688i 0.765353 0.765353i −0.211931 0.977285i \(-0.567975\pi\)
0.977285 + 0.211931i \(0.0679753\pi\)
\(108\) 5.01910 1.34486i 0.482963 0.129410i
\(109\) 1.80385i 0.172777i 0.996262 + 0.0863886i \(0.0275327\pi\)
−0.996262 + 0.0863886i \(0.972467\pi\)
\(110\) 0 0
\(111\) 14.1962i 1.34744i
\(112\) −4.57081 + 1.22474i −0.431901 + 0.115728i
\(113\) 12.9360 3.46618i 1.21691 0.326071i 0.407443 0.913231i \(-0.366421\pi\)
0.809471 + 0.587160i \(0.199754\pi\)
\(114\) −4.79423 + 2.76795i −0.449021 + 0.259242i
\(115\) 0 0
\(116\) 10.7321i 0.996446i
\(117\) −13.7124 + 3.67423i −1.26771 + 0.339683i
\(118\) −3.91447 + 3.91447i −0.360356 + 0.360356i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) 1.03528 + 3.86370i 0.0937295 + 0.349803i
\(123\) 0.776457 + 2.89778i 0.0700108 + 0.261284i
\(124\) −0.169873 + 0.0980762i −0.0152550 + 0.00880750i
\(125\) 0 0
\(126\) −12.2942 7.09808i −1.09526 0.632347i
\(127\) −5.79555 5.79555i −0.514272 0.514272i 0.401560 0.915833i \(-0.368468\pi\)
−0.915833 + 0.401560i \(0.868468\pi\)
\(128\) −0.258819 + 0.965926i −0.0228766 + 0.0853766i
\(129\) 0.401924 + 0.696152i 0.0353874 + 0.0612928i
\(130\) 0 0
\(131\) −6.00000 3.46410i −0.524222 0.302660i 0.214438 0.976738i \(-0.431208\pi\)
−0.738661 + 0.674078i \(0.764541\pi\)
\(132\) −4.24264 4.24264i −0.369274 0.369274i
\(133\) 14.6090 + 3.91447i 1.26676 + 0.339428i
\(134\) −5.53590 −0.478229
\(135\) 0 0
\(136\) 0 0
\(137\) 12.9360 + 3.46618i 1.10519 + 0.296136i 0.764878 0.644175i \(-0.222799\pi\)
0.340317 + 0.940311i \(0.389466\pi\)
\(138\) −2.68973 2.68973i −0.228965 0.228965i
\(139\) −6.92820 4.00000i −0.587643 0.339276i 0.176522 0.984297i \(-0.443515\pi\)
−0.764165 + 0.645021i \(0.776849\pi\)
\(140\) 0 0
\(141\) 5.19615 + 9.00000i 0.437595 + 0.757937i
\(142\) 1.88108 7.02030i 0.157857 0.589130i
\(143\) 11.5911 + 11.5911i 0.969297 + 0.969297i
\(144\) −2.59808 + 1.50000i −0.216506 + 0.125000i
\(145\) 0 0
\(146\) 4.50000 2.59808i 0.372423 0.215018i
\(147\) 6.90018 + 25.7518i 0.569117 + 2.12397i
\(148\) −2.12132 7.91688i −0.174371 0.650763i
\(149\) 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i \(-0.569430\pi\)
0.953703 0.300750i \(-0.0972370\pi\)
\(150\) 0 0
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 2.26002 2.26002i 0.183312 0.183312i
\(153\) 0 0
\(154\) 16.3923i 1.32093i
\(155\) 0 0
\(156\) 7.09808 4.09808i 0.568301 0.328109i
\(157\) 19.1798 5.13922i 1.53072 0.410154i 0.607463 0.794348i \(-0.292187\pi\)
0.923253 + 0.384194i \(0.125520\pi\)
\(158\) 9.65926 2.58819i 0.768449 0.205905i
\(159\) 14.1962i 1.12583i
\(160\) 0 0
\(161\) 10.3923i 0.819028i
\(162\) −8.69333 2.32937i −0.683013 0.183013i
\(163\) −10.1261 + 10.1261i −0.793140 + 0.793140i −0.982003 0.188864i \(-0.939520\pi\)
0.188864 + 0.982003i \(0.439520\pi\)
\(164\) −0.866025 1.50000i −0.0676252 0.117130i
\(165\) 0 0
\(166\) 8.59808 14.8923i 0.667340 1.15587i
\(167\) −4.24264 15.8338i −0.328305 1.22525i −0.910947 0.412523i \(-0.864648\pi\)
0.582642 0.812729i \(-0.302019\pi\)
\(168\) 7.91688 + 2.12132i 0.610800 + 0.163663i
\(169\) −8.13397 + 4.69615i −0.625690 + 0.361242i
\(170\) 0 0
\(171\) 9.58846 0.733248
\(172\) −0.328169 0.328169i −0.0250227 0.0250227i
\(173\) −4.24264 + 15.8338i −0.322562 + 1.20382i 0.594178 + 0.804334i \(0.297477\pi\)
−0.916740 + 0.399484i \(0.869189\pi\)
\(174\) 9.29423 16.0981i 0.704594 1.22039i
\(175\) 0 0
\(176\) 3.00000 + 1.73205i 0.226134 + 0.130558i
\(177\) 9.26174 2.48168i 0.696155 0.186534i
\(178\) −8.36516 2.24144i −0.626995 0.168003i
\(179\) 22.8564 1.70837 0.854184 0.519971i \(-0.174057\pi\)
0.854184 + 0.519971i \(0.174057\pi\)
\(180\) 0 0
\(181\) −12.3923 −0.921113 −0.460556 0.887630i \(-0.652350\pi\)
−0.460556 + 0.887630i \(0.652350\pi\)
\(182\) −21.6293 5.79555i −1.60327 0.429595i
\(183\) 1.79315 6.69213i 0.132554 0.494697i
\(184\) 1.90192 + 1.09808i 0.140212 + 0.0809513i
\(185\) 0 0
\(186\) 0.339746 0.0249114
\(187\) 0 0
\(188\) −4.24264 4.24264i −0.309426 0.309426i
\(189\) 12.2942 + 21.2942i 0.894274 + 1.54893i
\(190\) 0 0
\(191\) 3.00000 1.73205i 0.217072 0.125327i −0.387522 0.921861i \(-0.626669\pi\)
0.604594 + 0.796534i \(0.293335\pi\)
\(192\) 1.22474 1.22474i 0.0883883 0.0883883i
\(193\) −2.86559 10.6945i −0.206270 0.769809i −0.989059 0.147522i \(-0.952870\pi\)
0.782789 0.622287i \(-0.213796\pi\)
\(194\) −1.33013 + 2.30385i −0.0954976 + 0.165407i
\(195\) 0 0
\(196\) −7.69615 13.3301i −0.549725 0.952152i
\(197\) −10.0382 + 10.0382i −0.715192 + 0.715192i −0.967617 0.252425i \(-0.918772\pi\)
0.252425 + 0.967617i \(0.418772\pi\)
\(198\) 2.68973 + 10.0382i 0.191151 + 0.713384i
\(199\) 20.3923i 1.44557i 0.691072 + 0.722786i \(0.257139\pi\)
−0.691072 + 0.722786i \(0.742861\pi\)
\(200\) 0 0
\(201\) 8.30385 + 4.79423i 0.585708 + 0.338159i
\(202\) 7.02030 1.88108i 0.493947 0.132353i
\(203\) −49.0542 + 13.1440i −3.44293 + 0.922530i
\(204\) 0 0
\(205\) 0 0
\(206\) 10.3923i 0.724066i
\(207\) 1.70522 + 6.36396i 0.118521 + 0.442326i
\(208\) −3.34607 + 3.34607i −0.232008 + 0.232008i
\(209\) −5.53590 9.58846i −0.382926 0.663247i
\(210\) 0 0
\(211\) −0.598076 + 1.03590i −0.0411733 + 0.0713142i −0.885878 0.463919i \(-0.846443\pi\)
0.844704 + 0.535233i \(0.179776\pi\)
\(212\) 2.12132 + 7.91688i 0.145693 + 0.543733i
\(213\) −8.90138 + 8.90138i −0.609913 + 0.609913i
\(214\) 9.69615 5.59808i 0.662815 0.382677i
\(215\) 0 0
\(216\) 5.19615 0.353553
\(217\) −0.656339 0.656339i −0.0445552 0.0445552i
\(218\) −0.466870 + 1.74238i −0.0316204 + 0.118009i
\(219\) −9.00000 −0.608164
\(220\) 0 0
\(221\) 0 0
\(222\) −3.67423 + 13.7124i −0.246598 + 0.920318i
\(223\) −2.44949 0.656339i −0.164030 0.0439517i 0.175869 0.984414i \(-0.443726\pi\)
−0.339899 + 0.940462i \(0.610393\pi\)
\(224\) −4.73205 −0.316173
\(225\) 0 0
\(226\) 13.3923 0.890843
\(227\) 12.3676 + 3.31388i 0.820864 + 0.219950i 0.644724 0.764415i \(-0.276972\pi\)
0.176140 + 0.984365i \(0.443639\pi\)
\(228\) −5.34727 + 1.43280i −0.354131 + 0.0948892i
\(229\) −5.02628 2.90192i −0.332146 0.191765i 0.324648 0.945835i \(-0.394754\pi\)
−0.656793 + 0.754071i \(0.728088\pi\)
\(230\) 0 0
\(231\) 14.1962 24.5885i 0.934038 1.61780i
\(232\) −2.77766 + 10.3664i −0.182362 + 0.680585i
\(233\) 3.25813 + 3.25813i 0.213447 + 0.213447i 0.805730 0.592283i \(-0.201773\pi\)
−0.592283 + 0.805730i \(0.701773\pi\)
\(234\) −14.1962 −0.928032
\(235\) 0 0
\(236\) −4.79423 + 2.76795i −0.312078 + 0.180178i
\(237\) −16.7303 4.48288i −1.08675 0.291194i
\(238\) 0 0
\(239\) −1.90192 + 3.29423i −0.123025 + 0.213086i −0.920959 0.389659i \(-0.872593\pi\)
0.797934 + 0.602745i \(0.205926\pi\)
\(240\) 0 0
\(241\) −4.69615 8.13397i −0.302506 0.523955i 0.674197 0.738551i \(-0.264490\pi\)
−0.976703 + 0.214596i \(0.931156\pi\)
\(242\) 0.707107 0.707107i 0.0454545 0.0454545i
\(243\) 11.0227 + 11.0227i 0.707107 + 0.707107i
\(244\) 4.00000i 0.256074i
\(245\) 0 0
\(246\) 3.00000i 0.191273i
\(247\) 14.6090 3.91447i 0.929549 0.249072i
\(248\) −0.189469 + 0.0507680i −0.0120313 + 0.00322377i
\(249\) −25.7942 + 14.8923i −1.63464 + 0.943761i
\(250\) 0 0
\(251\) 9.00000i 0.568075i −0.958813 0.284037i \(-0.908326\pi\)
0.958813 0.284037i \(-0.0916740\pi\)
\(252\) −10.0382 10.0382i −0.632347 0.632347i
\(253\) 5.37945 5.37945i 0.338203 0.338203i
\(254\) −4.09808 7.09808i −0.257136 0.445373i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −6.57201 24.5271i −0.409951 1.52996i −0.794738 0.606952i \(-0.792392\pi\)
0.384787 0.923005i \(-0.374275\pi\)
\(258\) 0.208051 + 0.776457i 0.0129527 + 0.0483401i
\(259\) 33.5885 19.3923i 2.08709 1.20498i
\(260\) 0 0
\(261\) −27.8827 + 16.0981i −1.72589 + 0.996446i
\(262\) −4.89898 4.89898i −0.302660 0.302660i
\(263\) −3.25813 + 12.1595i −0.200905 + 0.749788i 0.789754 + 0.613424i \(0.210208\pi\)
−0.990659 + 0.136364i \(0.956458\pi\)
\(264\) −3.00000 5.19615i −0.184637 0.319801i
\(265\) 0 0
\(266\) 13.0981 + 7.56218i 0.803095 + 0.463667i
\(267\) 10.6066 + 10.6066i 0.649113 + 0.649113i
\(268\) −5.34727 1.43280i −0.326636 0.0875219i
\(269\) −10.0526 −0.612915 −0.306458 0.951884i \(-0.599144\pi\)
−0.306458 + 0.951884i \(0.599144\pi\)
\(270\) 0 0
\(271\) 26.5885 1.61513 0.807567 0.589776i \(-0.200784\pi\)
0.807567 + 0.589776i \(0.200784\pi\)
\(272\) 0 0
\(273\) 27.4249 + 27.4249i 1.65983 + 1.65983i
\(274\) 11.5981 + 6.69615i 0.700665 + 0.404529i
\(275\) 0 0
\(276\) −1.90192 3.29423i −0.114482 0.198289i
\(277\) −5.05128 + 18.8516i −0.303502 + 1.13269i 0.630725 + 0.776007i \(0.282758\pi\)
−0.934227 + 0.356679i \(0.883909\pi\)
\(278\) −5.65685 5.65685i −0.339276 0.339276i
\(279\) −0.509619 0.294229i −0.0305101 0.0176150i
\(280\) 0 0
\(281\) 9.00000 5.19615i 0.536895 0.309976i −0.206925 0.978357i \(-0.566345\pi\)
0.743820 + 0.668380i \(0.233012\pi\)
\(282\) 2.68973 + 10.0382i 0.160171 + 0.597766i
\(283\) 1.01669 + 3.79435i 0.0604362 + 0.225551i 0.989538 0.144274i \(-0.0460845\pi\)
−0.929102 + 0.369824i \(0.879418\pi\)
\(284\) 3.63397 6.29423i 0.215637 0.373494i
\(285\) 0 0
\(286\) 8.19615 + 14.1962i 0.484649 + 0.839436i
\(287\) 5.79555 5.79555i 0.342101 0.342101i
\(288\) −2.89778 + 0.776457i −0.170753 + 0.0457532i
\(289\) 17.0000i 1.00000i
\(290\) 0 0
\(291\) 3.99038 2.30385i 0.233920 0.135054i
\(292\) 5.01910 1.34486i 0.293720 0.0787022i
\(293\) 3.67423 0.984508i 0.214651 0.0575156i −0.149891 0.988703i \(-0.547892\pi\)
0.364542 + 0.931187i \(0.381226\pi\)
\(294\) 26.6603i 1.55486i
\(295\) 0 0
\(296\) 8.19615i 0.476392i
\(297\) 4.65874 17.3867i 0.270328 1.00888i
\(298\) 12.7279 12.7279i 0.737309 0.737309i
\(299\) 5.19615 + 9.00000i 0.300501 + 0.520483i
\(300\) 0 0
\(301\) 1.09808 1.90192i 0.0632921 0.109625i
\(302\) 2.07055 + 7.72741i 0.119147 + 0.444662i
\(303\) −12.1595 3.25813i −0.698546 0.187175i
\(304\) 2.76795 1.59808i 0.158753 0.0916560i
\(305\) 0 0
\(306\) 0 0
\(307\) −2.44949 2.44949i −0.139800 0.139800i 0.633743 0.773543i \(-0.281517\pi\)
−0.773543 + 0.633743i \(0.781517\pi\)
\(308\) −4.24264 + 15.8338i −0.241747 + 0.902212i
\(309\) −9.00000 + 15.5885i −0.511992 + 0.886796i
\(310\) 0 0
\(311\) −9.58846 5.53590i −0.543712 0.313912i 0.202870 0.979206i \(-0.434973\pi\)
−0.746582 + 0.665294i \(0.768306\pi\)
\(312\) 7.91688 2.12132i 0.448205 0.120096i
\(313\) −19.9563 5.34727i −1.12800 0.302245i −0.353880 0.935291i \(-0.615138\pi\)
−0.774115 + 0.633045i \(0.781805\pi\)
\(314\) 19.8564 1.12056
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) −6.36396 1.70522i −0.357436 0.0957746i 0.0756325 0.997136i \(-0.475902\pi\)
−0.433068 + 0.901361i \(0.642569\pi\)
\(318\) 3.67423 13.7124i 0.206041 0.768955i
\(319\) 32.1962 + 18.5885i 1.80264 + 1.04075i
\(320\) 0 0
\(321\) −19.3923 −1.08237
\(322\) −2.68973 + 10.0382i −0.149893 + 0.559407i
\(323\) 0 0
\(324\) −7.79423 4.50000i −0.433013 0.250000i
\(325\) 0 0
\(326\) −12.4019 + 7.16025i −0.686879 + 0.396570i
\(327\) 2.20925 2.20925i 0.122172 0.122172i
\(328\) −0.448288 1.67303i −0.0247525 0.0923778i
\(329\) 14.1962 24.5885i 0.782659 1.35561i
\(330\) 0 0
\(331\) 6.79423 + 11.7679i 0.373445 + 0.646825i 0.990093 0.140414i \(-0.0448433\pi\)
−0.616648 + 0.787239i \(0.711510\pi\)
\(332\) 12.1595 12.1595i 0.667340 0.667340i
\(333\) 17.3867 17.3867i 0.952783 0.952783i
\(334\) 16.3923i 0.896947i
\(335\) 0 0
\(336\) 7.09808 + 4.09808i 0.387232 + 0.223568i
\(337\) 19.8362 5.31508i 1.08054 0.289531i 0.325725 0.945464i \(-0.394391\pi\)
0.754819 + 0.655933i \(0.227725\pi\)
\(338\) −9.07227 + 2.43091i −0.493466 + 0.132224i
\(339\) −20.0885 11.5981i −1.09106 0.629921i
\(340\) 0 0
\(341\) 0.679492i 0.0367966i
\(342\) 9.26174 + 2.48168i 0.500817 + 0.134194i
\(343\) 28.0812 28.0812i 1.51624 1.51624i
\(344\) −0.232051 0.401924i −0.0125113 0.0216703i
\(345\) 0 0
\(346\) −8.19615 + 14.1962i −0.440628 + 0.763190i
\(347\) −2.27362 8.48528i −0.122055 0.455514i 0.877663 0.479278i \(-0.159102\pi\)
−0.999718 + 0.0237644i \(0.992435\pi\)
\(348\) 13.1440 13.1440i 0.704594 0.704594i
\(349\) 1.73205 1.00000i 0.0927146 0.0535288i −0.452926 0.891548i \(-0.649620\pi\)
0.545640 + 0.838019i \(0.316286\pi\)
\(350\) 0 0
\(351\) 21.2942 + 12.2942i 1.13660 + 0.656217i
\(352\) 2.44949 + 2.44949i 0.130558 + 0.130558i
\(353\) 3.88229 14.4889i 0.206633 0.771166i −0.782312 0.622886i \(-0.785960\pi\)
0.988946 0.148279i \(-0.0473735\pi\)
\(354\) 9.58846 0.509621
\(355\) 0 0
\(356\) −7.50000 4.33013i −0.397499 0.229496i
\(357\) 0 0
\(358\) 22.0776 + 5.91567i 1.16684 + 0.312653i
\(359\) −35.3205 −1.86415 −0.932073 0.362272i \(-0.882001\pi\)
−0.932073 + 0.362272i \(0.882001\pi\)
\(360\) 0 0
\(361\) 8.78461 0.462348
\(362\) −11.9700 3.20736i −0.629132 0.168575i
\(363\) −1.67303 + 0.448288i −0.0878114 + 0.0235290i
\(364\) −19.3923 11.1962i −1.01643 0.586838i
\(365\) 0 0
\(366\) 3.46410 6.00000i 0.181071 0.313625i
\(367\) −1.07244 + 4.00240i −0.0559810 + 0.208924i −0.988251 0.152839i \(-0.951158\pi\)
0.932270 + 0.361763i \(0.117825\pi\)
\(368\) 1.55291 + 1.55291i 0.0809513 + 0.0809513i
\(369\) 2.59808 4.50000i 0.135250 0.234261i
\(370\) 0 0
\(371\) −33.5885 + 19.3923i −1.74383 + 1.00680i
\(372\) 0.328169 + 0.0879327i 0.0170148 + 0.00455910i
\(373\) −6.03579 22.5259i −0.312521 1.16635i −0.926275 0.376848i \(-0.877008\pi\)
0.613754 0.789498i \(-0.289659\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 5.19615i −0.154713 0.267971i
\(377\) −35.9101 + 35.9101i −1.84947 + 1.84947i
\(378\) 6.36396 + 23.7506i 0.327327 + 1.22160i
\(379\) 0.392305i 0.0201513i 0.999949 + 0.0100757i \(0.00320724\pi\)
−0.999949 + 0.0100757i \(0.996793\pi\)
\(380\) 0 0
\(381\) 14.1962i 0.727291i
\(382\) 3.34607 0.896575i 0.171200 0.0458728i
\(383\) 5.22715 1.40061i 0.267095 0.0715678i −0.122786 0.992433i \(-0.539183\pi\)
0.389881 + 0.920865i \(0.372516\pi\)
\(384\) 1.50000 0.866025i 0.0765466 0.0441942i
\(385\) 0 0
\(386\) 11.0718i 0.563540i
\(387\) 0.360355 1.34486i 0.0183179 0.0683632i
\(388\) −1.88108 + 1.88108i −0.0954976 + 0.0954976i
\(389\) 5.19615 + 9.00000i 0.263455 + 0.456318i 0.967158 0.254177i \(-0.0818045\pi\)
−0.703702 + 0.710495i \(0.748471\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −3.98382 14.8678i −0.201213 0.750939i
\(393\) 3.10583 + 11.5911i 0.156668 + 0.584694i
\(394\) −12.2942 + 7.09808i −0.619374 + 0.357596i
\(395\) 0 0
\(396\) 10.3923i 0.522233i
\(397\) 10.9348 + 10.9348i 0.548800 + 0.548800i 0.926094 0.377293i \(-0.123145\pi\)
−0.377293 + 0.926094i \(0.623145\pi\)
\(398\) −5.27792 + 19.6975i −0.264558 + 0.987344i
\(399\) −13.0981 22.6865i −0.655724 1.13575i
\(400\) 0 0
\(401\) 9.00000 + 5.19615i 0.449439 + 0.259483i 0.707593 0.706620i \(-0.249781\pi\)
−0.258154 + 0.966104i \(0.583114\pi\)
\(402\) 6.78006 + 6.78006i 0.338159 + 0.338159i
\(403\) −0.896575 0.240237i −0.0446616 0.0119670i
\(404\) 7.26795 0.361594
\(405\) 0 0
\(406\) −50.7846 −2.52040
\(407\) −27.4249 7.34847i −1.35940 0.364250i
\(408\) 0 0
\(409\) −18.5263 10.6962i −0.916066 0.528891i −0.0336878 0.999432i \(-0.510725\pi\)
−0.882378 + 0.470542i \(0.844059\pi\)
\(410\) 0 0
\(411\) −11.5981 20.0885i −0.572091 0.990891i
\(412\) 2.68973 10.0382i 0.132513 0.494546i
\(413\) −18.5235 18.5235i −0.911481 0.911481i
\(414\) 6.58846i 0.323805i
\(415\) 0 0
\(416\) −4.09808 + 2.36603i −0.200925 + 0.116004i
\(417\) 3.58630 + 13.3843i 0.175622 + 0.655430i
\(418\) −2.86559 10.6945i −0.140161 0.523087i
\(419\) −4.50000 + 7.79423i −0.219839 + 0.380773i −0.954759 0.297382i \(-0.903887\pi\)
0.734919 + 0.678155i \(0.237220\pi\)
\(420\) 0 0
\(421\) −11.2942 19.5622i −0.550447 0.953402i −0.998242 0.0592661i \(-0.981124\pi\)
0.447795 0.894136i \(-0.352209\pi\)
\(422\) −0.845807 + 0.845807i −0.0411733 + 0.0411733i
\(423\) 4.65874 17.3867i 0.226516 0.845369i
\(424\) 8.19615i 0.398040i
\(425\) 0 0
\(426\) −10.9019 + 6.29423i −0.528200 + 0.304956i
\(427\) −18.2832 + 4.89898i −0.884788 + 0.237078i
\(428\) 10.8147 2.89778i 0.522746 0.140069i
\(429\) 28.3923i 1.37079i
\(430\) 0 0
\(431\) 21.1244i 1.01752i 0.860907 + 0.508762i \(0.169897\pi\)
−0.860907 + 0.508762i \(0.830103\pi\)
\(432\) 5.01910 + 1.34486i 0.241481 + 0.0647048i
\(433\) −12.0716 + 12.0716i −0.580123 + 0.580123i −0.934937 0.354814i \(-0.884544\pi\)
0.354814 + 0.934937i \(0.384544\pi\)
\(434\) −0.464102 0.803848i −0.0222776 0.0385859i
\(435\) 0 0
\(436\) −0.901924 + 1.56218i −0.0431943 + 0.0748147i
\(437\) −1.81671 6.78006i −0.0869051 0.324334i
\(438\) −8.69333 2.32937i −0.415383 0.111302i
\(439\) −1.22243 + 0.705771i −0.0583435 + 0.0336846i −0.528888 0.848692i \(-0.677391\pi\)
0.470545 + 0.882376i \(0.344058\pi\)
\(440\) 0 0
\(441\) 23.0885 39.9904i 1.09945 1.90430i
\(442\) 0 0
\(443\) 2.68973 10.0382i 0.127793 0.476929i −0.872131 0.489272i \(-0.837262\pi\)
0.999924 + 0.0123433i \(0.00392908\pi\)
\(444\) −7.09808 + 12.2942i −0.336860 + 0.583458i
\(445\) 0 0
\(446\) −2.19615 1.26795i −0.103991 0.0600391i
\(447\) −30.1146 + 8.06918i −1.42437 + 0.381659i
\(448\) −4.57081 1.22474i −0.215950 0.0578638i
\(449\) 30.1244 1.42166 0.710828 0.703366i \(-0.248320\pi\)
0.710828 + 0.703366i \(0.248320\pi\)
\(450\) 0 0
\(451\) −6.00000 −0.282529
\(452\) 12.9360 + 3.46618i 0.608457 + 0.163036i
\(453\) 3.58630 13.3843i 0.168499 0.628847i
\(454\) 11.0885 + 6.40192i 0.520407 + 0.300457i
\(455\) 0 0
\(456\) −5.53590 −0.259242
\(457\) 7.14042 26.6484i 0.334015 1.24656i −0.570919 0.821007i \(-0.693413\pi\)
0.904933 0.425553i \(-0.139920\pi\)
\(458\) −4.10394 4.10394i −0.191765 0.191765i
\(459\) 0 0
\(460\) 0 0
\(461\) −8.70577 + 5.02628i −0.405468 + 0.234097i −0.688841 0.724913i \(-0.741880\pi\)
0.283373 + 0.959010i \(0.408547\pi\)
\(462\) 20.0764 20.0764i 0.934038 0.934038i
\(463\) −0.568406 2.12132i −0.0264161 0.0985861i 0.951459 0.307775i \(-0.0995844\pi\)
−0.977875 + 0.209189i \(0.932918\pi\)
\(464\) −5.36603 + 9.29423i −0.249111 + 0.431474i
\(465\) 0 0
\(466\) 2.30385 + 3.99038i 0.106724 + 0.184851i
\(467\) 6.78006 6.78006i 0.313744 0.313744i −0.532614 0.846358i \(-0.678790\pi\)
0.846358 + 0.532614i \(0.178790\pi\)
\(468\) −13.7124 3.67423i −0.633857 0.169842i
\(469\) 26.1962i 1.20963i
\(470\) 0 0
\(471\) −29.7846 17.1962i −1.37240 0.792357i
\(472\) −5.34727 + 1.43280i −0.246128 + 0.0659498i
\(473\) −1.55291 + 0.416102i −0.0714031 + 0.0191324i
\(474\) −15.0000 8.66025i −0.688973 0.397779i
\(475\) 0 0
\(476\) 0 0
\(477\) −17.3867 + 17.3867i −0.796081 + 0.796081i
\(478\) −2.68973 + 2.68973i −0.123025 + 0.123025i
\(479\) −1.56218 2.70577i −0.0713777 0.123630i 0.828128 0.560540i \(-0.189406\pi\)
−0.899505 + 0.436910i \(0.856073\pi\)
\(480\) 0 0
\(481\) 19.3923 33.5885i 0.884213 1.53150i
\(482\) −2.43091 9.07227i −0.110725 0.413231i
\(483\) 12.7279 12.7279i 0.579141 0.579141i
\(484\) 0.866025 0.500000i 0.0393648 0.0227273i
\(485\) 0 0
\(486\) 7.79423 + 13.5000i 0.353553 + 0.612372i
\(487\) −11.3509 11.3509i −0.514357 0.514357i 0.401501 0.915858i \(-0.368489\pi\)
−0.915858 + 0.401501i \(0.868489\pi\)
\(488\) −1.03528 + 3.86370i −0.0468648 + 0.174902i
\(489\) 24.8038 1.12167
\(490\) 0 0
\(491\) −16.2058 9.35641i −0.731356 0.422249i 0.0875619 0.996159i \(-0.472092\pi\)
−0.818918 + 0.573910i \(0.805426\pi\)
\(492\) −0.776457 + 2.89778i −0.0350054 + 0.130642i
\(493\) 0 0
\(494\) 15.1244 0.680477
\(495\) 0 0
\(496\) −0.196152 −0.00880750
\(497\) 33.2204 + 8.90138i 1.49014 + 0.399282i
\(498\) −28.7697 + 7.70882i −1.28920 + 0.345441i
\(499\) 10.0359 + 5.79423i 0.449269 + 0.259385i 0.707521 0.706692i \(-0.249813\pi\)
−0.258253 + 0.966077i \(0.583147\pi\)
\(500\) 0 0
\(501\) −14.1962 + 24.5885i −0.634237 + 1.09853i
\(502\) 2.32937 8.69333i 0.103965 0.388002i
\(503\) 3.82654 + 3.82654i 0.170617 + 0.170617i 0.787250 0.616633i \(-0.211504\pi\)
−0.616633 + 0.787250i \(0.711504\pi\)
\(504\) −7.09808 12.2942i −0.316173 0.547628i
\(505\) 0 0
\(506\) 6.58846 3.80385i 0.292893 0.169102i
\(507\) 15.7136 + 4.21046i 0.697867 + 0.186993i
\(508\) −2.12132 7.91688i −0.0941184 0.351255i
\(509\) 10.3923 18.0000i 0.460631 0.797836i −0.538362 0.842714i \(-0.680957\pi\)
0.998992 + 0.0448779i \(0.0142899\pi\)
\(510\) 0 0
\(511\) 12.2942 + 21.2942i 0.543865 + 0.942001i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −11.7434 11.7434i −0.518484 0.518484i
\(514\) 25.3923i 1.12001i
\(515\) 0 0
\(516\) 0.803848i 0.0353874i
\(517\) −20.0764 + 5.37945i −0.882959 + 0.236588i
\(518\) 37.4631 10.0382i 1.64603 0.441053i
\(519\) 24.5885 14.1962i 1.07931 0.623142i
\(520\) 0 0
\(521\) 2.78461i 0.121996i −0.998138 0.0609980i \(-0.980572\pi\)
0.998138 0.0609980i \(-0.0194283\pi\)
\(522\) −31.0991 + 8.33298i −1.36117 + 0.364725i
\(523\) −23.9909 + 23.9909i −1.04905 + 1.04905i −0.0503137 + 0.998733i \(0.516022\pi\)
−0.998733 + 0.0503137i \(0.983978\pi\)
\(524\) −3.46410 6.00000i −0.151330 0.262111i
\(525\) 0 0
\(526\) −6.29423 + 10.9019i −0.274441 + 0.475346i
\(527\) 0 0
\(528\) −1.55291 5.79555i −0.0675819 0.252219i
\(529\) −15.7417 + 9.08846i −0.684420 + 0.395150i
\(530\) 0 0
\(531\) −14.3827 8.30385i −0.624155 0.360356i
\(532\) 10.6945 + 10.6945i 0.463667 + 0.463667i
\(533\) 2.12132 7.91688i 0.0918846 0.342918i
\(534\) 7.50000 + 12.9904i 0.324557 + 0.562149i
\(535\) 0 0
\(536\) −4.79423 2.76795i −0.207079 0.119557i
\(537\) −27.9933 27.9933i −1.20800 1.20800i
\(538\) −9.71003 2.60179i −0.418629 0.112171i
\(539\) −53.3205 −2.29668
\(540\) 0 0
\(541\) −8.39230 −0.360813 −0.180407 0.983592i \(-0.557741\pi\)
−0.180407 + 0.983592i \(0.557741\pi\)
\(542\) 25.6825 + 6.88160i 1.10316 + 0.295590i
\(543\) 15.1774 + 15.1774i 0.651325 + 0.651325i
\(544\) 0 0
\(545\) 0 0
\(546\) 19.3923 + 33.5885i 0.829914 + 1.43745i
\(547\) −10.3986 + 38.8079i −0.444610 + 1.65931i 0.272354 + 0.962197i \(0.412198\pi\)
−0.716964 + 0.697110i \(0.754469\pi\)
\(548\) 9.46979 + 9.46979i 0.404529 + 0.404529i
\(549\) −10.3923 + 6.00000i −0.443533 + 0.256074i
\(550\) 0 0
\(551\) 29.7058 17.1506i 1.26551 0.730642i
\(552\) −0.984508 3.67423i −0.0419035 0.156386i
\(553\) 12.2474 + 45.7081i 0.520814 + 1.94371i
\(554\) −9.75833 + 16.9019i −0.414592 + 0.718094i
\(555\) 0 0
\(556\) −4.00000 6.92820i −0.169638 0.293821i
\(557\) 3.10583 3.10583i 0.131598 0.131598i −0.638240 0.769838i \(-0.720337\pi\)
0.769838 + 0.638240i \(0.220337\pi\)
\(558\) −0.416102 0.416102i −0.0176150 0.0176150i
\(559\) 2.19615i 0.0928874i
\(560\) 0 0
\(561\) 0 0
\(562\) 10.0382 2.68973i 0.423436 0.113459i
\(563\) −2.32937 + 0.624153i −0.0981713 + 0.0263049i −0.307570 0.951525i \(-0.599516\pi\)
0.209399 + 0.977830i \(0.432849\pi\)
\(564\) 10.3923i 0.437595i
\(565\) 0 0
\(566\) 3.92820i 0.165115i
\(567\) 11.0227 41.1373i 0.462910 1.72760i
\(568\) 5.13922 5.13922i 0.215637 0.215637i
\(569\) −12.4641 21.5885i −0.522522 0.905035i −0.999657 0.0262048i \(-0.991658\pi\)
0.477134 0.878830i \(-0.341676\pi\)
\(570\) 0 0
\(571\) −9.59808 + 16.6244i −0.401667 + 0.695708i −0.993927 0.110039i \(-0.964902\pi\)
0.592260 + 0.805747i \(0.298236\pi\)
\(572\) 4.24264 + 15.8338i 0.177394 + 0.662042i
\(573\) −5.79555 1.55291i −0.242113 0.0648739i
\(574\) 7.09808 4.09808i 0.296268 0.171050i
\(575\) 0 0
\(576\) −3.00000 −0.125000
\(577\) 15.9217 + 15.9217i 0.662828 + 0.662828i 0.956046 0.293217i \(-0.0947260\pi\)
−0.293217 + 0.956046i \(0.594726\pi\)
\(578\) −4.39992 + 16.4207i −0.183013 + 0.683013i
\(579\) −9.58846 + 16.6077i −0.398483 + 0.690192i
\(580\) 0 0
\(581\) 70.4711 + 40.6865i 2.92364 + 1.68796i
\(582\) 4.45069 1.19256i 0.184487 0.0494332i
\(583\) 27.4249 + 7.34847i 1.13582 + 0.304342i
\(584\) 5.19615 0.215018
\(585\) 0 0
\(586\) 3.80385 0.157135
\(587\) 4.24264 + 1.13681i 0.175113 + 0.0469213i 0.345310 0.938489i \(-0.387774\pi\)
−0.170197 + 0.985410i \(0.554441\pi\)
\(588\) −6.90018 + 25.7518i −0.284559 + 1.06199i
\(589\) 0.542940 + 0.313467i 0.0223715 + 0.0129162i
\(590\) 0 0
\(591\) 24.5885 1.01143
\(592\) 2.12132 7.91688i 0.0871857 0.325382i
\(593\) −14.8492 14.8492i −0.609785 0.609785i 0.333105 0.942890i \(-0.391904\pi\)
−0.942890 + 0.333105i \(0.891904\pi\)
\(594\) 9.00000 15.5885i 0.369274 0.639602i
\(595\) 0 0
\(596\) 15.5885 9.00000i 0.638528 0.368654i
\(597\) 24.9754 24.9754i 1.02217 1.02217i
\(598\) 2.68973 + 10.0382i 0.109991 + 0.410492i
\(599\) −3.63397 + 6.29423i −0.148480 + 0.257175i −0.930666 0.365870i \(-0.880771\pi\)
0.782186 + 0.623045i \(0.214105\pi\)
\(600\) 0 0
\(601\) 14.3923 + 24.9282i 0.587074 + 1.01684i 0.994613 + 0.103655i \(0.0330537\pi\)
−0.407539 + 0.913188i \(0.633613\pi\)
\(602\) 1.55291 1.55291i 0.0632921 0.0632921i
\(603\) −4.29839 16.0418i −0.175044 0.653273i
\(604\) 8.00000i 0.325515i
\(605\) 0 0
\(606\) −10.9019 6.29423i −0.442860 0.255686i
\(607\) −46.9328 + 12.5756i −1.90495 + 0.510429i −0.909427 + 0.415864i \(0.863479\pi\)
−0.995519 + 0.0945643i \(0.969854\pi\)
\(608\) 3.08725 0.827225i 0.125204 0.0335484i
\(609\) 76.1769 + 43.9808i 3.08684 + 1.78219i
\(610\) 0 0
\(611\) 28.3923i 1.14863i
\(612\) 0 0
\(613\) −10.0382 + 10.0382i −0.405439 + 0.405439i −0.880145 0.474706i \(-0.842555\pi\)
0.474706 + 0.880145i \(0.342555\pi\)
\(614\) −1.73205 3.00000i −0.0698999 0.121070i
\(615\) 0 0
\(616\) −8.19615 + 14.1962i −0.330232 + 0.571979i
\(617\) 3.05008 + 11.3831i 0.122792 + 0.458265i 0.999751 0.0222993i \(-0.00709866\pi\)
−0.876960 + 0.480564i \(0.840432\pi\)
\(618\) −12.7279 + 12.7279i −0.511992 + 0.511992i
\(619\) −41.2128 + 23.7942i −1.65648 + 0.956371i −0.682164 + 0.731200i \(0.738961\pi\)
−0.974319 + 0.225171i \(0.927706\pi\)
\(620\) 0 0
\(621\) 5.70577 9.88269i 0.228965 0.396579i
\(622\) −7.82894 7.82894i −0.313912 0.313912i
\(623\) 10.6066 39.5844i 0.424945 1.58591i
\(624\) 8.19615 0.328109
\(625\) 0 0
\(626\) −17.8923 10.3301i −0.715120 0.412875i
\(627\) −4.96335 + 18.5235i −0.198217 + 0.739756i
\(628\) 19.1798 + 5.13922i 0.765358 + 0.205077i
\(629\) 0 0
\(630\) 0 0
\(631\) −0.784610 −0.0312348 −0.0156174 0.999878i \(-0.504971\pi\)
−0.0156174 + 0.999878i \(0.504971\pi\)
\(632\) 9.65926 + 2.58819i 0.384225 + 0.102953i
\(633\) 2.00120 0.536220i 0.0795406 0.0213128i
\(634\) −5.70577 3.29423i −0.226605 0.130831i
\(635\) 0 0
\(636\) 7.09808 12.2942i 0.281457 0.487498i
\(637\) 18.8516 70.3553i 0.746929 2.78758i
\(638\) 26.2880 + 26.2880i 1.04075 + 1.04075i
\(639\) 21.8038 0.862547
\(640\) 0 0
\(641\) −32.0885 + 18.5263i −1.26742 + 0.731744i −0.974499 0.224393i \(-0.927960\pi\)
−0.292919 + 0.956137i \(0.594627\pi\)
\(642\) −18.7315 5.01910i −0.739274 0.198088i
\(643\) 9.67784 + 36.1182i 0.381657 + 1.42436i 0.843370 + 0.537333i \(0.180568\pi\)
−0.461713 + 0.887029i \(0.652765\pi\)
\(644\) −5.19615 + 9.00000i −0.204757 + 0.354650i
\(645\) 0 0
\(646\) 0 0
\(647\) 10.0382 10.0382i 0.394642 0.394642i −0.481696 0.876338i \(-0.659979\pi\)
0.876338 + 0.481696i \(0.159979\pi\)
\(648\) −6.36396 6.36396i −0.250000 0.250000i
\(649\) 19.1769i 0.752760i
\(650\) 0 0
\(651\) 1.60770i 0.0630105i
\(652\) −13.8325 + 3.70642i −0.541724 + 0.145155i
\(653\) −7.91688 + 2.12132i −0.309811 + 0.0830137i −0.410375 0.911917i \(-0.634602\pi\)
0.100564 + 0.994931i \(0.467935\pi\)
\(654\) 2.70577 1.56218i 0.105804 0.0610860i
\(655\) 0 0
\(656\) 1.73205i 0.0676252i
\(657\) 11.0227 + 11.0227i 0.430037 + 0.430037i
\(658\) 20.0764 20.0764i 0.782659 0.782659i
\(659\) 20.0885 + 34.7942i 0.782535 + 1.35539i 0.930461 + 0.366392i \(0.119407\pi\)
−0.147925 + 0.988999i \(0.547260\pi\)
\(660\) 0 0
\(661\) 19.5885 33.9282i 0.761903 1.31965i −0.179966 0.983673i \(-0.557599\pi\)
0.941869 0.335981i \(-0.109068\pi\)
\(662\) 3.51695 + 13.1254i 0.136690 + 0.510135i
\(663\) 0 0
\(664\) 14.8923 8.59808i 0.577934 0.333670i
\(665\) 0 0
\(666\) 21.2942 12.2942i 0.825135 0.476392i
\(667\) 16.6660 + 16.6660i 0.645308 + 0.645308i
\(668\) 4.24264 15.8338i 0.164153 0.612626i
\(669\) 2.19615 + 3.80385i 0.0849082 + 0.147065i
\(670\) 0 0
\(671\) 12.0000 + 6.92820i 0.463255 + 0.267460i
\(672\) 5.79555 + 5.79555i 0.223568 + 0.223568i
\(673\) −21.6293 5.79555i −0.833748 0.223402i −0.183400 0.983038i \(-0.558710\pi\)
−0.650348 + 0.759636i \(0.725377\pi\)
\(674\) 20.5359 0.791013
\(675\) 0 0
\(676\) −9.39230 −0.361242
\(677\) 23.7506 + 6.36396i 0.912811 + 0.244587i 0.684510 0.729004i \(-0.260016\pi\)
0.228301 + 0.973591i \(0.426683\pi\)
\(678\) −16.4022 16.4022i −0.629921 0.629921i
\(679\) −10.9019 6.29423i −0.418377 0.241550i
\(680\) 0 0
\(681\) −11.0885 19.2058i −0.424911 0.735967i
\(682\) −0.175865 + 0.656339i −0.00673424 + 0.0251325i
\(683\) 5.94786 + 5.94786i 0.227588 + 0.227588i 0.811685 0.584096i \(-0.198551\pi\)
−0.584096 + 0.811685i \(0.698551\pi\)
\(684\) 8.30385 + 4.79423i 0.317506 + 0.183312i
\(685\) 0 0
\(686\) 34.3923 19.8564i 1.31310 0.758121i
\(687\) 2.60179 + 9.71003i 0.0992646 + 0.370461i
\(688\) −0.120118 0.448288i −0.00457947 0.0170908i
\(689\) −19.3923 + 33.5885i −0.738788 + 1.27962i
\(690\) 0 0
\(691\) −21.7942 37.7487i −0.829092 1.43603i −0.898752 0.438458i \(-0.855525\pi\)
0.0696602 0.997571i \(-0.477808\pi\)
\(692\) −11.5911 + 11.5911i −0.440628 + 0.440628i
\(693\) −47.5013 + 12.7279i −1.80442 + 0.483494i
\(694\) 8.78461i 0.333459i
\(695\) 0 0
\(696\) 16.0981 9.29423i 0.610196 0.352297i
\(697\) 0 0
\(698\) 1.93185 0.517638i 0.0731217 0.0195929i
\(699\) 7.98076i 0.301860i
\(700\) 0 0
\(701\) 14.5359i 0.549013i −0.961585 0.274507i \(-0.911485\pi\)
0.961585 0.274507i \(-0.0885145\pi\)
\(702\) 17.3867 + 17.3867i 0.656217 + 0.656217i
\(703\) −18.5235 + 18.5235i −0.698626 + 0.698626i
\(704\) 1.73205 + 3.00000i 0.0652791 + 0.113067i
\(705\) 0 0
\(706\) 7.50000 12.9904i 0.282266 0.488899i
\(707\) 8.90138 + 33.2204i 0.334771 + 1.24938i
\(708\) 9.26174 + 2.48168i 0.348077 + 0.0932671i
\(709\) −31.3468 + 18.0981i −1.17725 + 0.679688i −0.955378 0.295387i \(-0.904551\pi\)
−0.221876 + 0.975075i \(0.571218\pi\)
\(710\) 0 0
\(711\) 15.0000 + 25.9808i 0.562544 + 0.974355i
\(712\) −6.12372 6.12372i −0.229496 0.229496i
\(713\) −0.111494 + 0.416102i −0.00417549 + 0.0155831i
\(714\) 0 0
\(715\) 0 0
\(716\) 19.7942 + 11.4282i 0.739745 + 0.427092i
\(717\) 6.36396 1.70522i 0.237666 0.0636825i
\(718\) −34.1170 9.14162i −1.27323 0.341162i
\(719\) −14.8756 −0.554768 −0.277384 0.960759i \(-0.589467\pi\)
−0.277384 + 0.960759i \(0.589467\pi\)
\(720\) 0 0
\(721\) 49.1769 1.83144
\(722\) 8.48528 + 2.27362i 0.315789 + 0.0846155i
\(723\) −4.21046 + 15.7136i −0.156589 + 0.584396i
\(724\) −10.7321 6.19615i −0.398854 0.230278i
\(725\) 0 0
\(726\) −1.73205 −0.0642824
\(727\) 1.79315 6.69213i 0.0665043 0.248197i −0.924669 0.380773i \(-0.875658\pi\)
0.991173 + 0.132575i \(0.0423247\pi\)
\(728\) −15.8338 15.8338i −0.586838 0.586838i
\(729\) 27.0000i 1.00000i
\(730\) 0 0
\(731\) 0 0
\(732\) 4.89898 4.89898i 0.181071 0.181071i
\(733\) 3.52193 + 13.1440i 0.130085 + 0.485486i 0.999970 0.00777015i \(-0.00247334\pi\)
−0.869884 + 0.493256i \(0.835807\pi\)
\(734\) −2.07180 + 3.58846i −0.0764714 + 0.132452i
\(735\) 0 0
\(736\) 1.09808 + 1.90192i 0.0404756 + 0.0701058i
\(737\) −13.5601 + 13.5601i −0.499494 + 0.499494i
\(738\) 3.67423 3.67423i 0.135250 0.135250i
\(739\) 19.5885i 0.720573i −0.932842 0.360287i \(-0.882679\pi\)
0.932842 0.360287i \(-0.117321\pi\)
\(740\) 0 0
\(741\) −22.6865 13.0981i −0.833411 0.481170i
\(742\) −37.4631 + 10.0382i −1.37531 + 0.368514i
\(743\) 32.2359 8.63759i 1.18262 0.316882i 0.386655 0.922224i \(-0.373630\pi\)
0.795965 + 0.605342i \(0.206964\pi\)
\(744\) 0.294229 + 0.169873i 0.0107869 + 0.00622785i
\(745\) 0 0
\(746\) 23.3205i 0.853824i
\(747\) 49.8306 + 13.3521i 1.82321 + 0.488527i
\(748\) 0 0
\(749\) 26.4904 + 45.8827i 0.967937 + 1.67652i
\(750\) 0 0
\(751\) −5.29423 + 9.16987i −0.193189 + 0.334613i −0.946305 0.323274i \(-0.895216\pi\)
0.753116 + 0.657887i \(0.228550\pi\)
\(752\) −1.55291 5.79555i −0.0566290 0.211342i
\(753\) −11.0227 + 11.0227i −0.401690 + 0.401690i
\(754\) −43.9808 + 25.3923i −1.60168 + 0.924733i
\(755\) 0 0
\(756\) 24.5885i 0.894274i
\(757\) −27.6651 27.6651i −1.00551 1.00551i −0.999985 0.00552030i \(-0.998243\pi\)
−0.00552030 0.999985i \(-0.501757\pi\)
\(758\) −0.101536 + 0.378937i −0.00368795 + 0.0137636i
\(759\) −13.1769 −0.478292
\(760\) 0 0
\(761\) −41.0885 23.7224i −1.48946 0.859937i −0.489528 0.871988i \(-0.662831\pi\)
−0.999927 + 0.0120501i \(0.996164\pi\)
\(762\) −3.67423 + 13.7124i −0.133103 + 0.496749i
\(763\) −8.24504 2.20925i −0.298491 0.0799803i
\(764\) 3.46410 0.125327
\(765\) 0 0
\(766\) 5.41154 0.195527
\(767\) −25.3035 6.78006i −0.913658 0.244814i
\(768\) 1.67303 0.448288i 0.0603704 0.0161762i
\(769\) 10.9186 + 6.30385i 0.393734 + 0.227323i 0.683777 0.729691i \(-0.260336\pi\)
−0.290043 + 0.957014i \(0.593669\pi\)
\(770\) 0 0
\(771\) −21.9904 + 38.0885i −0.791964 + 1.37172i
\(772\) 2.86559 10.6945i 0.103135 0.384905i
\(773\) 35.9101 + 35.9101i 1.29160 + 1.29160i 0.933798 + 0.357800i \(0.116473\pi\)
0.357800 + 0.933798i \(0.383527\pi\)
\(774\) 0.696152 1.20577i 0.0250227 0.0433406i
\(775\) 0 0
\(776\) −2.30385 + 1.33013i −0.0827033 + 0.0477488i
\(777\) −64.8879 17.3867i −2.32784 0.623743i
\(778\) 2.68973 + 10.0382i 0.0964314 + 0.359887i
\(779\) −2.76795 + 4.79423i −0.0991721 + 0.171771i
\(780\) 0 0
\(781\) −12.5885 21.8038i −0.450450 0.780203i
\(782\) 0 0
\(783\) 53.8652 + 14.4331i 1.92499 + 0.515798i
\(784\) 15.3923i 0.549725i
\(785\) 0 0
\(786\) 12.0000i