Properties

Label 450.2.p.c.443.1
Level 450
Weight 2
Character 450.443
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 443.1
Root \(0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 450.443
Dual form 450.2.p.c.257.1

$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{4}\right)\)

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 0.663727 + 0.747975i \(0.268974\pi\)
−0.200817 + 0.979629i \(0.564360\pi\)
\(8\) −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 0.878668 0.477432i \(-0.158432\pi\)
0.0258656 + 0.999665i \(0.491766\pi\)
\(12\) 0.448288 1.67303i 0.129410 0.482963i
\(13\) −1.22474 + 4.57081i −0.339683 + 1.26771i 0.559019 + 0.829155i \(0.311178\pi\)
−0.898702 + 0.438560i \(0.855489\pi\)
\(14\) −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 \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) 0.776457 + 2.89778i 0.183013 + 0.683013i
\(19\) 3.19615i 0.733248i 0.930369 + 0.366624i \(0.119486\pi\)
−0.930369 + 0.366624i \(0.880514\pi\)
\(20\) 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 \(-0.490201\pi\)
−0.473106 + 0.881005i \(0.656867\pi\)
\(24\) 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 0.425273 0.905065i \(-0.360178\pi\)
0.571173 0.820830i \(-0.306489\pi\)
\(30\) 0 0
\(31\) −0.0980762 0.169873i −0.0176150 0.0305101i 0.857084 0.515177i \(-0.172274\pi\)
−0.874699 + 0.484667i \(0.838941\pi\)
\(32\) −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 \(-0.514696\pi\)
0.998934 + 0.0461511i \(0.0146956\pi\)
\(38\) −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 −0.612536 0.790443i \(-0.709851\pi\)
0.378275 + 0.925693i \(0.376517\pi\)
\(42\) −7.91688 2.12132i −1.22160 0.327327i
\(43\) 0.448288 0.120118i 0.0683632 0.0183179i −0.224475 0.974480i \(-0.572067\pi\)
0.292839 + 0.956162i \(0.405400\pi\)
\(44\) 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 \(-0.439164\pi\)
0.655407 + 0.755276i \(0.272497\pi\)
\(48\) −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 \(-0.940320\pi\)
0.186394 + 0.982475i \(0.440320\pi\)
\(54\) 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 0.627663 0.778485i \(-0.284012\pi\)
−0.988019 + 0.154330i \(0.950678\pi\)
\(60\) 0 0
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) 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 \(-0.306863\pi\)
0.0830646 + 0.996544i \(0.473529\pi\)
\(68\) 0 0
\(69\) −3.29423 + 1.90192i −0.396579 + 0.228965i
\(70\) 0 0
\(71\) 7.26795i 0.862547i 0.902221 + 0.431273i \(0.141936\pi\)
−0.902221 + 0.431273i \(0.858064\pi\)
\(72\) 2.12132 + 2.12132i 0.250000 + 0.250000i
\(73\) −3.67423 3.67423i −0.430037 0.430037i 0.458604 0.888641i \(-0.348350\pi\)
−0.888641 + 0.458604i \(0.848350\pi\)
\(74\) −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 0.900561 0.434730i \(-0.143156\pi\)
0.0737937 + 0.997274i \(0.476489\pi\)
\(80\) 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 −0.563625 0.826031i \(-0.690594\pi\)
0.0750978 0.997176i \(-0.476073\pi\)
\(84\) 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 \(-0.0402126\pi\)
−0.922122 + 0.386900i \(0.873546\pi\)
\(98\) 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 0.779317 0.626629i \(-0.215566\pi\)
−0.153018 + 0.988223i \(0.548899\pi\)
\(102\) 0 0
\(103\) 2.68973 10.0382i 0.265027 0.989093i −0.697207 0.716869i \(-0.745574\pi\)
0.962234 0.272223i \(-0.0877590\pi\)
\(104\) −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 \(-0.432025\pi\)
−0.977285 + 0.211931i \(0.932025\pi\)
\(108\) −5.01910 1.34486i −0.482963 0.129410i
\(109\) 1.80385i 0.172777i −0.996262 0.0863886i \(-0.972467\pi\)
0.996262 0.0863886i \(-0.0275327\pi\)
\(110\) 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 \(-0.633579\pi\)
−0.809471 + 0.587160i \(0.800246\pi\)
\(114\) −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 \(-0.631532\pi\)
0.915833 + 0.401560i \(0.131532\pi\)
\(128\) 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 −0.738661 0.674078i \(-0.764541\pi\)
0.214438 + 0.976738i \(0.431208\pi\)
\(132\) 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 \(-0.777201\pi\)
−0.340317 + 0.940311i \(0.610534\pi\)
\(138\) 2.68973 2.68973i 0.228965 0.228965i
\(139\) −6.92820 + 4.00000i −0.587643 + 0.339276i −0.764165 0.645021i \(-0.776849\pi\)
0.176522 + 0.984297i \(0.443515\pi\)
\(140\) 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 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0 0
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) −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 \(-0.707813\pi\)
−0.923253 + 0.384194i \(0.874480\pi\)
\(158\) −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 \(-0.0604804\pi\)
−0.188864 + 0.982003i \(0.560480\pi\)
\(164\) −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 −0.582642 0.812729i \(-0.697981\pi\)
0.910947 0.412523i \(-0.135352\pi\)
\(168\) −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 0.916740 + 0.399484i \(0.130811\pi\)
−0.594178 + 0.804334i \(0.702523\pi\)
\(174\) 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 0.604594 0.796534i \(-0.293335\pi\)
−0.387522 + 0.921861i \(0.626669\pi\)
\(192\) −1.22474 1.22474i −0.0883883 0.0883883i
\(193\) 2.86559 10.6945i 0.206270 0.769809i −0.782789 0.622287i \(-0.786204\pi\)
0.989059 0.147522i \(-0.0471298\pi\)
\(194\) −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 \(-0.0812280\pi\)
−0.252425 + 0.967617i \(0.581228\pi\)
\(198\) −2.68973 + 10.0382i −0.191151 + 0.713384i
\(199\) 20.3923i 1.44557i −0.691072 0.722786i \(-0.742861\pi\)
0.691072 0.722786i \(-0.257139\pi\)
\(200\) 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 0.844704 0.535233i \(-0.179776\pi\)
−0.885878 + 0.463919i \(0.846443\pi\)
\(212\) −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 \(-0.556274\pi\)
0.339899 + 0.940462i \(0.389607\pi\)
\(224\) −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 \(-0.723028\pi\)
−0.176140 + 0.984365i \(0.556361\pi\)
\(228\) 5.34727 + 1.43280i 0.354131 + 0.0948892i
\(229\) −5.02628 + 2.90192i −0.332146 + 0.191765i −0.656793 0.754071i \(-0.728088\pi\)
0.324648 + 0.945835i \(0.394754\pi\)
\(230\) 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 \(-0.798227\pi\)
0.592283 + 0.805730i \(0.298227\pi\)
\(234\) −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 0.797934 0.602745i \(-0.205926\pi\)
−0.920959 + 0.389659i \(0.872593\pi\)
\(240\) 0 0
\(241\) −4.69615 + 8.13397i −0.302506 + 0.523955i −0.976703 0.214596i \(-0.931156\pi\)
0.674197 + 0.738551i \(0.264490\pi\)
\(242\) −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 \(0.0916740\pi\)
−0.958813 + 0.284037i \(0.908326\pi\)
\(252\) 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 −0.384787 0.923005i \(-0.625725\pi\)
0.794738 0.606952i \(-0.207608\pi\)
\(258\) −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 0.990659 + 0.136364i \(0.0435416\pi\)
−0.789754 + 0.613424i \(0.789792\pi\)
\(264\) −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 0.934227 + 0.356679i \(0.116091\pi\)
−0.630725 + 0.776007i \(0.717242\pi\)
\(278\) 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 0.743820 0.668380i \(-0.233012\pi\)
−0.206925 + 0.978357i \(0.566345\pi\)
\(282\) −2.68973 + 10.0382i −0.160171 + 0.597766i
\(283\) −1.01669 + 3.79435i −0.0604362 + 0.225551i −0.989538 0.144274i \(-0.953915\pi\)
0.929102 + 0.369824i \(0.120582\pi\)
\(284\) 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 \(-0.452108\pi\)
−0.364542 + 0.931187i \(0.618774\pi\)
\(294\) 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 \(-0.718483\pi\)
0.773543 + 0.633743i \(0.218483\pi\)
\(308\) 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 −0.746582 0.665294i \(-0.768306\pi\)
0.202870 + 0.979206i \(0.434973\pi\)
\(312\) −7.91688 2.12132i −0.448205 0.120096i
\(313\) 19.9563 5.34727i 1.12800 0.302245i 0.353880 0.935291i \(-0.384862\pi\)
0.774115 + 0.633045i \(0.218195\pi\)
\(314\) 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 \(-0.524098\pi\)
0.433068 + 0.901361i \(0.357431\pi\)
\(318\) −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 −0.616648 0.787239i \(-0.711510\pi\)
0.990093 + 0.140414i \(0.0448433\pi\)
\(332\) −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 \(-0.605609\pi\)
−0.754819 + 0.655933i \(0.772275\pi\)
\(338\) 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 \(-0.840898\pi\)
0.999718 + 0.0237644i \(0.00756516\pi\)
\(348\) −13.1440 13.1440i −0.704594 0.704594i
\(349\) 1.73205 + 1.00000i 0.0927146 + 0.0535288i 0.545640 0.838019i \(-0.316286\pi\)
−0.452926 + 0.891548i \(0.649620\pi\)
\(350\) 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 −0.988946 0.148279i \(-0.952627\pi\)
0.782312 0.622886i \(-0.214040\pi\)
\(354\) 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 \(-0.0488416\pi\)
−0.932270 + 0.361763i \(0.882175\pi\)
\(368\) −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 −0.613754 0.789498i \(-0.710341\pi\)
0.926275 0.376848i \(-0.122992\pi\)
\(374\) 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 \(-0.996793\pi\)
0.999949 0.0100757i \(-0.00320724\pi\)
\(380\) 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 \(-0.460817\pi\)
−0.389881 + 0.920865i \(0.627484\pi\)
\(384\) 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 −0.703702 0.710495i \(-0.748471\pi\)
0.967158 + 0.254177i \(0.0818045\pi\)
\(390\) 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 \(-0.876855\pi\)
0.377293 + 0.926094i \(0.376855\pi\)
\(398\) 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 −0.258154 0.966104i \(-0.583114\pi\)
0.707593 + 0.706620i \(0.249781\pi\)
\(402\) −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 −0.882378 0.470542i \(-0.844059\pi\)
−0.0336878 + 0.999432i \(0.510725\pi\)
\(410\) 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 0.734919 0.678155i \(-0.237220\pi\)
−0.954759 + 0.297382i \(0.903887\pi\)
\(420\) 0 0
\(421\) −11.2942 + 19.5622i −0.550447 + 0.953402i 0.447795 + 0.894136i \(0.352209\pi\)
−0.998242 + 0.0592661i \(0.981124\pi\)
\(422\) 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 \(-0.830103\pi\)
0.860907 0.508762i \(-0.169897\pi\)
\(432\) −5.01910 + 1.34486i −0.241481 + 0.0647048i
\(433\) 12.0716 + 12.0716i 0.580123 + 0.580123i 0.934937 0.354814i \(-0.115456\pi\)
−0.354814 + 0.934937i \(0.615456\pi\)
\(434\) −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 0.470545 0.882376i \(-0.344058\pi\)
−0.528888 + 0.848692i \(0.677391\pi\)
\(440\) 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 \(-0.162738\pi\)
−0.999924 + 0.0123433i \(0.996071\pi\)
\(444\) −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 −0.904933 0.425553i \(-0.860080\pi\)
0.570919 0.821007i \(-0.306587\pi\)
\(458\) 4.10394 4.10394i 0.191765 0.191765i
\(459\) 0 0
\(460\) 0 0
\(461\) −8.70577 5.02628i −0.405468 0.234097i 0.283373 0.959010i \(-0.408547\pi\)
−0.688841 + 0.724913i \(0.741880\pi\)
\(462\) −20.0764 20.0764i −0.934038 0.934038i
\(463\) 0.568406 2.12132i 0.0264161 0.0985861i −0.951459 0.307775i \(-0.900416\pi\)
0.977875 + 0.209189i \(0.0670823\pi\)
\(464\) −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 \(-0.321210\pi\)
−0.846358 + 0.532614i \(0.821210\pi\)
\(468\) 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 −0.899505 0.436910i \(-0.856073\pi\)
0.828128 + 0.560540i \(0.189406\pi\)
\(480\) 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 \(-0.631511\pi\)
0.915858 + 0.401501i \(0.131511\pi\)
\(488\) 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 −0.818918 0.573910i \(-0.805426\pi\)
0.0875619 + 0.996159i \(0.472092\pi\)
\(492\) 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 −0.258253 0.966077i \(-0.583147\pi\)
0.707521 + 0.706692i \(0.249813\pi\)
\(500\) 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 \(-0.788496\pi\)
0.616633 + 0.787250i \(0.288496\pi\)
\(504\) −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 0.998992 0.0448779i \(-0.0142899\pi\)
−0.538362 + 0.842714i \(0.680957\pi\)
\(510\) 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 \(0.0194283\pi\)
−0.998138 + 0.0609980i \(0.980572\pi\)
\(522\) 31.0991 + 8.33298i 1.36117 + 0.364725i
\(523\) 23.9909 + 23.9909i 1.04905 + 1.04905i 0.998733 + 0.0503137i \(0.0160221\pi\)
0.0503137 + 0.998733i \(0.483978\pi\)
\(524\) −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 0.716964 + 0.697110i \(0.245531\pi\)
−0.272354 + 0.962197i \(0.587802\pi\)
\(548\) −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 \(-0.279663\pi\)
−0.769838 + 0.638240i \(0.779663\pi\)
\(558\) 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 \(-0.400484\pi\)
−0.209399 + 0.977830i \(0.567151\pi\)
\(564\) 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 0.477134 + 0.878830i \(0.341676\pi\)
−0.999657 + 0.0262048i \(0.991658\pi\)
\(570\) 0 0
\(571\) −9.59808 16.6244i −0.401667 0.695708i 0.592260 0.805747i \(-0.298236\pi\)
−0.993927 + 0.110039i \(0.964902\pi\)
\(572\) −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 \(-0.905274\pi\)
0.293217 + 0.956046i \(0.405274\pi\)
\(578\) 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 \(-0.612226\pi\)
0.170197 + 0.985410i \(0.445559\pi\)
\(588\) 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 \(-0.608096\pi\)
0.942890 + 0.333105i \(0.108096\pi\)
\(594\) 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 0.782186 0.623045i \(-0.214105\pi\)
−0.930666 + 0.365870i \(0.880771\pi\)
\(600\) 0 0
\(601\) 14.3923 24.9282i 0.587074 1.01684i −0.407539 0.913188i \(-0.633613\pi\)
0.994613 0.103655i \(-0.0330537\pi\)
\(602\) −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 0.995519 + 0.0945643i \(0.0301458\pi\)
0.909427 + 0.415864i \(0.136521\pi\)
\(608\) −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 \(-0.157445\pi\)
−0.474706 + 0.880145i \(0.657445\pi\)
\(614\) −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 \(-0.992901\pi\)
0.876960 + 0.480564i \(0.159568\pi\)
\(618\) 12.7279 + 12.7279i 0.511992 + 0.511992i
\(619\) −41.2128 23.7942i −1.65648 0.956371i −0.974319 0.225171i \(-0.927706\pi\)
−0.682164 0.731200i \(-0.738961\pi\)
\(620\) 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 −0.292919 0.956137i \(-0.594627\pi\)
−0.974499 + 0.224393i \(0.927960\pi\)
\(642\) 18.7315 5.01910i 0.739274 0.198088i
\(643\) −9.67784 + 36.1182i −0.381657 + 1.42436i 0.461713 + 0.887029i \(0.347235\pi\)
−0.843370 + 0.537333i \(0.819432\pi\)
\(644\) −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 \(-0.340021\pi\)
−0.876338 + 0.481696i \(0.840021\pi\)
\(648\) 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 \(-0.365398\pi\)
−0.100564 + 0.994931i \(0.532065\pi\)
\(654\) 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 −0.147925 0.988999i \(-0.547260\pi\)
0.930461 0.366392i \(-0.119407\pi\)
\(660\) 0 0
\(661\) 19.5885 + 33.9282i 0.761903 + 1.31965i 0.941869 + 0.335981i \(0.109068\pi\)
−0.179966 + 0.983673i \(0.557599\pi\)
\(662\) −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 \(-0.441290\pi\)
0.650348 + 0.759636i \(0.274623\pi\)
\(674\) 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 \(-0.739984\pi\)
−0.228301 + 0.973591i \(0.573317\pi\)
\(678\) 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 \(-0.801449\pi\)
0.584096 + 0.811685i \(0.301449\pi\)
\(684\) 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 0.0696602 + 0.997571i \(0.477808\pi\)
−0.898752 + 0.438458i \(0.855525\pi\)
\(692\) 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 \(0.0885145\pi\)
−0.961585 + 0.274507i \(0.911485\pi\)
\(702\) −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 −0.221876 0.975075i \(-0.571218\pi\)
−0.955378 + 0.295387i \(0.904551\pi\)
\(710\) 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 \(-0.124342\pi\)
−0.991173 + 0.132575i \(0.957675\pi\)
\(728\) 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 \(-0.997527\pi\)
0.869884 + 0.493256i \(0.164193\pi\)
\(734\) −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 \(0.117321\pi\)
−0.932842 + 0.360287i \(0.882679\pi\)
\(740\) 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 \(-0.626370\pi\)
−0.795965 + 0.605342i \(0.793036\pi\)
\(744\) 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 0.753116 0.657887i \(-0.228550\pi\)
−0.946305 + 0.323274i \(0.895216\pi\)
\(752\) 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 0.00552030 0.999985i \(-0.498243\pi\)
0.999985 0.00552030i \(-0.00175717\pi\)
\(758\) 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 −0.999927 0.0120501i \(-0.996164\pi\)
−0.489528 + 0.871988i \(0.662831\pi\)
\(762\) 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 −0.290043 0.957014i \(-0.593669\pi\)
0.683777 + 0.729691i \(0.260336\pi\)
\(770\) 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 −0.357800 + 0.933798i \(0.616473\pi\)
−0.933798 + 0.357800i \(0.883527\pi\)
\(774\) 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