Properties

Label 450.2.p.e.407.2
Level 450
Weight 2
Character 450.407
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: \(\Q(\zeta_{24})\)
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 407.2
Root \(-0.965926 + 0.258819i\) of \(x^{8} - x^{4} + 1\)
Character \(\chi\) \(=\) 450.407
Dual form 450.2.p.e.293.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.258819 + 0.965926i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.866025 + 1.50000i) q^{6} +(4.57081 - 1.22474i) q^{7} +(-0.707107 - 0.707107i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(0.258819 + 0.965926i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.866025 + 1.50000i) q^{6} +(4.57081 - 1.22474i) q^{7} +(-0.707107 - 0.707107i) q^{8} +3.00000i q^{9} +(3.00000 + 1.73205i) q^{11} +(-1.67303 - 0.448288i) q^{12} +(-4.57081 - 1.22474i) q^{13} +(2.36603 + 4.09808i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.89778 + 0.776457i) q^{18} -3.19615i q^{19} +(7.09808 + 4.09808i) q^{21} +(-0.896575 + 3.34607i) q^{22} +(0.568406 - 2.12132i) 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} +(0.965926 + 0.258819i) q^{32} +(1.55291 + 5.79555i) q^{33} +(-1.50000 - 2.59808i) q^{36} +(-5.79555 - 5.79555i) q^{37} +(3.08725 - 0.827225i) q^{38} +(-4.09808 - 7.09808i) q^{39} +(-1.50000 + 0.866025i) q^{41} +(-2.12132 + 7.91688i) q^{42} +(0.120118 + 0.448288i) q^{43} -3.46410 q^{44} +2.19615 q^{46} +(-1.55291 - 5.79555i) q^{47} +(1.67303 - 0.448288i) q^{48} +(13.3301 - 7.69615i) q^{49} +(4.57081 - 1.22474i) 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} +(-10.3664 - 2.77766i) q^{58} +(2.76795 + 4.79423i) q^{59} +(2.00000 - 3.46410i) q^{61} +(0.138701 - 0.138701i) q^{62} +(3.67423 + 13.7124i) q^{63} +1.00000i q^{64} +(-5.19615 + 3.00000i) q^{66} +(1.43280 - 5.34727i) 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} +(15.8338 + 4.24264i) q^{77} +(5.79555 - 5.79555i) q^{78} +(-8.66025 - 5.00000i) q^{79} -9.00000 q^{81} +(-1.22474 - 1.22474i) q^{82} +(16.6102 - 4.45069i) q^{83} -8.19615 q^{84} +(-0.401924 + 0.232051i) q^{86} +(-17.9551 + 4.81105i) q^{87} +(-0.896575 - 3.34607i) q^{88} +8.66025 q^{89} -22.3923 q^{91} +(0.568406 + 2.12132i) q^{92} +(0.0879327 - 0.328169i) q^{93} +(5.19615 - 3.00000i) q^{94} +(0.866025 + 1.50000i) q^{96} +(2.56961 - 0.688524i) 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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.258819 + 0.965926i 0.183013 + 0.683013i
\(3\) 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
\(7\) 4.57081 1.22474i 1.72760 0.462910i 0.747975 0.663727i \(-0.231026\pi\)
0.979629 + 0.200817i \(0.0643596\pi\)
\(8\) −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 \(0.491766\pi\)
\(12\) −1.67303 0.448288i −0.482963 0.129410i
\(13\) −4.57081 1.22474i −1.26771 0.339683i −0.438560 0.898702i \(-0.644511\pi\)
−0.829155 + 0.559019i \(0.811178\pi\)
\(14\) 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 \(0.250000\pi\)
\(18\) −2.89778 + 0.776457i −0.683013 + 0.183013i
\(19\) 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
\(22\) −0.896575 + 3.34607i −0.191151 + 0.713384i
\(23\) 0.568406 2.12132i 0.118521 0.442326i −0.881005 0.473106i \(-0.843133\pi\)
0.999526 + 0.0307805i \(0.00979929\pi\)
\(24\) 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 \(0.639822\pi\)
−0.571173 + 0.820830i \(0.693511\pi\)
\(30\) 0 0
\(31\) −0.0980762 0.169873i −0.0176150 0.0305101i 0.857084 0.515177i \(-0.172274\pi\)
−0.874699 + 0.484667i \(0.838941\pi\)
\(32\) 0.965926 + 0.258819i 0.170753 + 0.0457532i
\(33\) 1.55291 + 5.79555i 0.270328 + 1.00888i
\(34\) 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 \(0.985304\pi\)
\(38\) 3.08725 0.827225i 0.500817 0.134194i
\(39\) −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 \(0.376517\pi\)
\(42\) −2.12132 + 7.91688i −0.327327 + 1.22160i
\(43\) 0.120118 + 0.448288i 0.0183179 + 0.0683632i 0.974480 0.224475i \(-0.0720668\pi\)
−0.956162 + 0.292839i \(0.905400\pi\)
\(44\) −3.46410 −0.522233
\(45\) 0 0
\(46\) 2.19615 0.323805
\(47\) −1.55291 5.79555i −0.226516 0.845369i −0.981792 0.189961i \(-0.939164\pi\)
0.755276 0.655407i \(-0.227503\pi\)
\(48\) 1.67303 0.448288i 0.241481 0.0647048i
\(49\) 13.3301 7.69615i 1.90430 1.09945i
\(50\) 0 0
\(51\) 0 0
\(52\) 4.57081 1.22474i 0.633857 0.169842i
\(53\) −5.79555 5.79555i −0.796081 0.796081i 0.186394 0.982475i \(-0.440320\pi\)
−0.982475 + 0.186394i \(0.940320\pi\)
\(54\) −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
\(58\) −10.3664 2.77766i −1.36117 0.364725i
\(59\) 2.76795 + 4.79423i 0.360356 + 0.624155i 0.988019 0.154330i \(-0.0493218\pi\)
−0.627663 + 0.778485i \(0.715988\pi\)
\(60\) 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
\(63\) 3.67423 + 13.7124i 0.462910 + 1.72760i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −5.19615 + 3.00000i −0.639602 + 0.369274i
\(67\) 1.43280 5.34727i 0.175044 0.653273i −0.821500 0.570208i \(-0.806863\pi\)
0.996544 0.0830646i \(-0.0264708\pi\)
\(68\) 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 \(-0.651650\pi\)
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
\(77\) 15.8338 + 4.24264i 1.80442 + 0.483494i
\(78\) 5.79555 5.79555i 0.656217 0.656217i
\(79\) −8.66025 5.00000i −0.974355 0.562544i −0.0737937 0.997274i \(-0.523511\pi\)
−0.900561 + 0.434730i \(0.856844\pi\)
\(80\) 0 0
\(81\) −9.00000 −1.00000
\(82\) −1.22474 1.22474i −0.135250 0.135250i
\(83\) 16.6102 4.45069i 1.82321 0.488527i 0.826031 0.563625i \(-0.190594\pi\)
0.997176 + 0.0750978i \(0.0239269\pi\)
\(84\) −8.19615 −0.894274
\(85\) 0 0
\(86\) −0.401924 + 0.232051i −0.0433406 + 0.0250227i
\(87\) −17.9551 + 4.81105i −1.92499 + 0.515798i
\(88\) −0.896575 3.34607i −0.0955753 0.356692i
\(89\) 8.66025 0.917985 0.458993 0.888440i \(-0.348210\pi\)
0.458993 + 0.888440i \(0.348210\pi\)
\(90\) 0 0
\(91\) −22.3923 −2.34735
\(92\) 0.568406 + 2.12132i 0.0592604 + 0.221163i
\(93\) 0.0879327 0.328169i 0.00911820 0.0340296i
\(94\) 5.19615 3.00000i 0.535942 0.309426i
\(95\) 0 0
\(96\) 0.866025 + 1.50000i 0.0883883 + 0.153093i
\(97\) 2.56961 0.688524i 0.260904 0.0699091i −0.125996 0.992031i \(-0.540213\pi\)
0.386900 + 0.922122i \(0.373546\pi\)
\(98\) 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
\(103\) 10.0382 + 2.68973i 0.989093 + 0.265027i 0.716869 0.697207i \(-0.245574\pi\)
0.272223 + 0.962234i \(0.412241\pi\)
\(104\) 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 −0.977285 0.211931i \(-0.932025\pi\)
0.211931 + 0.977285i \(0.432025\pi\)
\(108\) 1.34486 5.01910i 0.129410 0.482963i
\(109\) 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
\(112\) 1.22474 4.57081i 0.115728 0.431901i
\(113\) 3.46618 12.9360i 0.326071 1.21691i −0.587160 0.809471i \(-0.699754\pi\)
0.913231 0.407443i \(-0.133579\pi\)
\(114\) 4.79423 + 2.76795i 0.449021 + 0.259242i
\(115\) 0 0
\(116\) 10.7321i 0.996446i
\(117\) 3.67423 13.7124i 0.339683 1.26771i
\(118\) −3.91447 + 3.91447i −0.360356 + 0.360356i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) 3.86370 + 1.03528i 0.349803 + 0.0937295i
\(123\) −2.89778 0.776457i −0.261284 0.0700108i
\(124\) 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 \(0.868468\pi\)
\(128\) −0.965926 + 0.258819i −0.0853766 + 0.0228766i
\(129\) −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
\(133\) −3.91447 14.6090i −0.339428 1.26676i
\(134\) 5.53590 0.478229
\(135\) 0 0
\(136\) 0 0
\(137\) 3.46618 + 12.9360i 0.296136 + 1.10519i 0.940311 + 0.340317i \(0.110534\pi\)
−0.644175 + 0.764878i \(0.722799\pi\)
\(138\) 2.68973 + 2.68973i 0.228965 + 0.228965i
\(139\) 6.92820 4.00000i 0.587643 0.339276i −0.176522 0.984297i \(-0.556485\pi\)
0.764165 + 0.645021i \(0.223151\pi\)
\(140\) 0 0
\(141\) 5.19615 9.00000i 0.437595 0.757937i
\(142\) −7.02030 + 1.88108i −0.589130 + 0.157857i
\(143\) −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
\(147\) 25.7518 + 6.90018i 2.12397 + 0.569117i
\(148\) 7.91688 + 2.12132i 0.650763 + 0.174371i
\(149\) −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i \(-0.902763\pi\)
0.216394 0.976306i \(-0.430570\pi\)
\(150\) 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
\(157\) −5.13922 + 19.1798i −0.410154 + 1.53072i 0.384194 + 0.923253i \(0.374480\pi\)
−0.794348 + 0.607463i \(0.792187\pi\)
\(158\) 2.58819 9.65926i 0.205905 0.768449i
\(159\) 14.1962i 1.12583i
\(160\) 0 0
\(161\) 10.3923i 0.819028i
\(162\) −2.32937 8.69333i −0.183013 0.683013i
\(163\) −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
\(167\) −15.8338 4.24264i −1.22525 0.328305i −0.412523 0.910947i \(-0.635352\pi\)
−0.812729 + 0.582642i \(0.802019\pi\)
\(168\) −2.12132 7.91688i −0.163663 0.610800i
\(169\) 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
\(173\) −15.8338 + 4.24264i −1.20382 + 0.322562i −0.804334 0.594178i \(-0.797477\pi\)
−0.399484 + 0.916740i \(0.630811\pi\)
\(174\) −9.29423 16.0981i −0.704594 1.22039i
\(175\) 0 0
\(176\) 3.00000 1.73205i 0.226134 0.130558i
\(177\) −2.48168 + 9.26174i −0.186534 + 0.696155i
\(178\) 2.24144 + 8.36516i 0.168003 + 0.626995i
\(179\) −22.8564 −1.70837 −0.854184 0.519971i \(-0.825943\pi\)
−0.854184 + 0.519971i \(0.825943\pi\)
\(180\) 0 0
\(181\) −12.3923 −0.921113 −0.460556 0.887630i \(-0.652350\pi\)
−0.460556 + 0.887630i \(0.652350\pi\)
\(182\) −5.79555 21.6293i −0.429595 1.60327i
\(183\) 6.69213 1.79315i 0.494697 0.132554i
\(184\) −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
\(193\) 10.6945 + 2.86559i 0.769809 + 0.206270i 0.622287 0.782789i \(-0.286204\pi\)
0.147522 + 0.989059i \(0.452870\pi\)
\(194\) 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 −0.252425 0.967617i \(-0.581228\pi\)
0.967617 + 0.252425i \(0.0812280\pi\)
\(198\) −10.0382 2.68973i −0.713384 0.191151i
\(199\) 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
\(202\) −1.88108 + 7.02030i −0.132353 + 0.493947i
\(203\) −13.1440 + 49.0542i −0.922530 + 3.44293i
\(204\) 0 0
\(205\) 0 0
\(206\) 10.3923i 0.724066i
\(207\) 6.36396 + 1.70522i 0.442326 + 0.118521i
\(208\) −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 \(0.846443\pi\)
\(212\) 7.91688 + 2.12132i 0.543733 + 0.145693i
\(213\) −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
\(218\) −1.74238 + 0.466870i −0.118009 + 0.0316204i
\(219\) 9.00000 0.608164
\(220\) 0 0
\(221\) 0 0
\(222\) 13.7124 3.67423i 0.920318 0.246598i
\(223\) 0.656339 + 2.44949i 0.0439517 + 0.164030i 0.984414 0.175869i \(-0.0562736\pi\)
−0.940462 + 0.339899i \(0.889607\pi\)
\(224\) 4.73205 0.316173
\(225\) 0 0
\(226\) 13.3923 0.890843
\(227\) 3.31388 + 12.3676i 0.219950 + 0.820864i 0.984365 + 0.176140i \(0.0563611\pi\)
−0.764415 + 0.644724i \(0.776972\pi\)
\(228\) −1.43280 + 5.34727i −0.0948892 + 0.354131i
\(229\) 5.02628 2.90192i 0.332146 0.191765i −0.324648 0.945835i \(-0.605246\pi\)
0.656793 + 0.754071i \(0.271912\pi\)
\(230\) 0 0
\(231\) 14.1962 + 24.5885i 0.934038 + 1.61780i
\(232\) 10.3664 2.77766i 0.680585 0.182362i
\(233\) −3.25813 3.25813i −0.213447 0.213447i 0.592283 0.805730i \(-0.298227\pi\)
−0.805730 + 0.592283i \(0.798227\pi\)
\(234\) 14.1962 0.928032
\(235\) 0 0
\(236\) −4.79423 2.76795i −0.312078 0.180178i
\(237\) −4.48288 16.7303i −0.291194 1.08675i
\(238\) 0 0
\(239\) 1.90192 + 3.29423i 0.123025 + 0.213086i 0.920959 0.389659i \(-0.127407\pi\)
−0.797934 + 0.602745i \(0.794074\pi\)
\(240\) 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
\(247\) −3.91447 + 14.6090i −0.249072 + 0.929549i
\(248\) −0.0507680 + 0.189469i −0.00322377 + 0.0120313i
\(249\) 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
\(257\) −24.5271 6.57201i −1.52996 0.409951i −0.606952 0.794738i \(-0.707608\pi\)
−0.923005 + 0.384787i \(0.874275\pi\)
\(258\) −0.776457 0.208051i −0.0483401 0.0129527i
\(259\) −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
\(263\) −12.1595 + 3.25813i −0.749788 + 0.200905i −0.613424 0.789754i \(-0.710208\pi\)
−0.136364 + 0.990659i \(0.543542\pi\)
\(264\) 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
\(268\) 1.43280 + 5.34727i 0.0875219 + 0.326636i
\(269\) 10.0526 0.612915 0.306458 0.951884i \(-0.400856\pi\)
0.306458 + 0.951884i \(0.400856\pi\)
\(270\) 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
\(277\) 18.8516 5.05128i 1.13269 0.303502i 0.356679 0.934227i \(-0.383909\pi\)
0.776007 + 0.630725i \(0.217242\pi\)
\(278\) 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 \(0.566345\pi\)
\(282\) 10.0382 + 2.68973i 0.597766 + 0.160171i
\(283\) −3.79435 1.01669i −0.225551 0.0604362i 0.144274 0.989538i \(-0.453915\pi\)
−0.369824 + 0.929102i \(0.620582\pi\)
\(284\) −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
\(288\) −0.776457 + 2.89778i −0.0457532 + 0.170753i
\(289\) 17.0000i 1.00000i
\(290\) 0 0
\(291\) 3.99038 + 2.30385i 0.233920 + 0.135054i
\(292\) −1.34486 + 5.01910i −0.0787022 + 0.293720i
\(293\) 0.984508 3.67423i 0.0575156 0.214651i −0.931187 0.364542i \(-0.881226\pi\)
0.988703 + 0.149891i \(0.0478922\pi\)
\(294\) 26.6603i 1.55486i
\(295\) 0 0
\(296\) 8.19615i 0.476392i
\(297\) −17.3867 + 4.65874i −1.00888 + 0.270328i
\(298\) 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
\(302\) 7.72741 + 2.07055i 0.444662 + 0.119147i
\(303\) 3.25813 + 12.1595i 0.187175 + 0.698546i
\(304\) −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 \(0.781517\pi\)
\(308\) −15.8338 + 4.24264i −0.902212 + 0.241747i
\(309\) 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 \(0.434973\pi\)
\(312\) −2.12132 + 7.91688i −0.120096 + 0.448205i
\(313\) 5.34727 + 19.9563i 0.302245 + 1.12800i 0.935291 + 0.353880i \(0.115138\pi\)
−0.633045 + 0.774115i \(0.718195\pi\)
\(314\) −19.8564 −1.12056
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) −1.70522 6.36396i −0.0957746 0.357436i 0.901361 0.433068i \(-0.142569\pi\)
−0.997136 + 0.0756325i \(0.975902\pi\)
\(318\) 13.7124 3.67423i 0.768955 0.206041i
\(319\) −32.1962 + 18.5885i −1.80264 + 1.04075i
\(320\) 0 0
\(321\) −19.3923 −1.08237
\(322\) 10.0382 2.68973i 0.559407 0.149893i
\(323\) 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
\(328\) 1.67303 + 0.448288i 0.0923778 + 0.0247525i
\(329\) −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
\(337\) −5.31508 + 19.8362i −0.289531 + 1.08054i 0.655933 + 0.754819i \(0.272275\pi\)
−0.945464 + 0.325725i \(0.894391\pi\)
\(338\) −2.43091 + 9.07227i −0.132224 + 0.493466i
\(339\) 20.0885 11.5981i 1.09106 0.629921i
\(340\) 0 0
\(341\) 0.679492i 0.0367966i
\(342\) 2.48168 + 9.26174i 0.134194 + 0.500817i
\(343\) 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
\(347\) −8.48528 2.27362i −0.455514 0.122055i 0.0237644 0.999718i \(-0.492435\pi\)
−0.479278 + 0.877663i \(0.659102\pi\)
\(348\) 13.1440 13.1440i 0.704594 0.704594i
\(349\) −1.73205 1.00000i −0.0927146 0.0535288i 0.452926 0.891548i \(-0.350380\pi\)
−0.545640 + 0.838019i \(0.683714\pi\)
\(350\) 0 0
\(351\) 21.2942 12.2942i 1.13660 0.656217i
\(352\) 2.44949 + 2.44949i 0.130558 + 0.130558i
\(353\) 14.4889 3.88229i 0.771166 0.206633i 0.148279 0.988946i \(-0.452627\pi\)
0.622886 + 0.782312i \(0.285960\pi\)
\(354\) −9.58846 −0.509621
\(355\) 0 0
\(356\) −7.50000 + 4.33013i −0.397499 + 0.229496i
\(357\) 0 0
\(358\) −5.91567 22.0776i −0.312653 1.16684i
\(359\) 35.3205 1.86415 0.932073 0.362272i \(-0.117999\pi\)
0.932073 + 0.362272i \(0.117999\pi\)
\(360\) 0 0
\(361\) 8.78461 0.462348
\(362\) −3.20736 11.9700i −0.168575 0.629132i
\(363\) −0.448288 + 1.67303i −0.0235290 + 0.0878114i
\(364\) 19.3923 11.1962i 1.01643 0.586838i
\(365\) 0 0
\(366\) 3.46410 + 6.00000i 0.181071 + 0.313625i
\(367\) 4.00240 1.07244i 0.208924 0.0559810i −0.152839 0.988251i \(-0.548842\pi\)
0.361763 + 0.932270i \(0.382175\pi\)
\(368\) −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
\(372\) 0.0879327 + 0.328169i 0.00455910 + 0.0170148i
\(373\) 22.5259 + 6.03579i 1.16635 + 0.312521i 0.789498 0.613754i \(-0.210341\pi\)
0.376848 + 0.926275i \(0.377008\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) 35.9101 35.9101i 1.84947 1.84947i
\(378\) −23.7506 6.36396i −1.22160 0.327327i
\(379\) 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
\(382\) −0.896575 + 3.34607i −0.0458728 + 0.171200i
\(383\) 1.40061 5.22715i 0.0715678 0.267095i −0.920865 0.389881i \(-0.872516\pi\)
0.992433 + 0.122786i \(0.0391829\pi\)
\(384\) −1.50000 0.866025i −0.0765466 0.0441942i
\(385\) 0 0
\(386\) 11.0718i 0.563540i
\(387\) −1.34486 + 0.360355i −0.0683632 + 0.0183179i
\(388\) −1.88108 + 1.88108i −0.0954976 + 0.0954976i
\(389\) −5.19615 + 9.00000i −0.263455 + 0.456318i −0.967158 0.254177i \(-0.918196\pi\)
0.703702 + 0.710495i \(0.251529\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −14.8678 3.98382i −0.750939 0.201213i
\(393\) −11.5911 3.10583i −0.584694 0.156668i
\(394\) 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 \(0.623145\pi\)
\(398\) −19.6975 + 5.27792i −0.987344 + 0.264558i
\(399\) 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
\(403\) 0.240237 + 0.896575i 0.0119670 + 0.0446616i
\(404\) −7.26795 −0.361594
\(405\) 0 0
\(406\) −50.7846 −2.52040
\(407\) −7.34847 27.4249i −0.364250 1.35940i
\(408\) 0 0
\(409\) 18.5263 10.6962i 0.916066 0.528891i 0.0336878 0.999432i \(-0.489275\pi\)
0.882378 + 0.470542i \(0.155941\pi\)
\(410\) 0 0
\(411\) −11.5981 + 20.0885i −0.572091 + 0.990891i
\(412\) −10.0382 + 2.68973i −0.494546 + 0.132513i
\(413\) 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
\(417\) 13.3843 + 3.58630i 0.655430 + 0.175622i
\(418\) 10.6945 + 2.86559i 0.523087 + 0.140161i
\(419\) 4.50000 + 7.79423i 0.219839 + 0.380773i 0.954759 0.297382i \(-0.0961133\pi\)
−0.734919 + 0.678155i \(0.762780\pi\)
\(420\) 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
\(423\) 17.3867 4.65874i 0.845369 0.226516i
\(424\) 8.19615i 0.398040i
\(425\) 0 0
\(426\) −10.9019 6.29423i −0.528200 0.304956i
\(427\) 4.89898 18.2832i 0.237078 0.884788i
\(428\) 2.89778 10.8147i 0.140069 0.522746i
\(429\) 28.3923i 1.37079i
\(430\) 0 0
\(431\) 21.1244i 1.01752i −0.860907 0.508762i \(-0.830103\pi\)
0.860907 0.508762i \(-0.169897\pi\)
\(432\) 1.34486 + 5.01910i 0.0647048 + 0.241481i
\(433\) −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
\(437\) −6.78006 1.81671i −0.324334 0.0869051i
\(438\) 2.32937 + 8.69333i 0.111302 + 0.415383i
\(439\) 1.22243 + 0.705771i 0.0583435 + 0.0336846i 0.528888 0.848692i \(-0.322609\pi\)
−0.470545 + 0.882376i \(0.655942\pi\)
\(440\) 0 0
\(441\) 23.0885 + 39.9904i 1.09945 + 1.90430i
\(442\) 0 0
\(443\) 10.0382 2.68973i 0.476929 0.127793i −0.0123433 0.999924i \(-0.503929\pi\)
0.489272 + 0.872131i \(0.337262\pi\)
\(444\) 7.09808 + 12.2942i 0.336860 + 0.583458i
\(445\) 0 0
\(446\) −2.19615 + 1.26795i −0.103991 + 0.0600391i
\(447\) 8.06918 30.1146i 0.381659 1.42437i
\(448\) 1.22474 + 4.57081i 0.0578638 + 0.215950i
\(449\) −30.1244 −1.42166 −0.710828 0.703366i \(-0.751680\pi\)
−0.710828 + 0.703366i \(0.751680\pi\)
\(450\) 0 0
\(451\) −6.00000 −0.282529
\(452\) 3.46618 + 12.9360i 0.163036 + 0.608457i
\(453\) 13.3843 3.58630i 0.628847 0.168499i
\(454\) −11.0885 + 6.40192i −0.520407 + 0.300457i
\(455\) 0 0
\(456\) −5.53590 −0.259242
\(457\) −26.6484 + 7.14042i −1.24656 + 0.334015i −0.821007 0.570919i \(-0.806587\pi\)
−0.425553 + 0.904933i \(0.639920\pi\)
\(458\) 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
\(463\) 2.12132 + 0.568406i 0.0985861 + 0.0264161i 0.307775 0.951459i \(-0.400416\pi\)
−0.209189 + 0.977875i \(0.567082\pi\)
\(464\) 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 −0.846358 0.532614i \(-0.821210\pi\)
0.532614 + 0.846358i \(0.321210\pi\)
\(468\) 3.67423 + 13.7124i 0.169842 + 0.633857i
\(469\) 26.1962i 1.20963i
\(470\) 0 0
\(471\) −29.7846 + 17.1962i −1.37240 + 0.792357i
\(472\) 1.43280 5.34727i 0.0659498 0.246128i
\(473\) −0.416102 + 1.55291i −0.0191324 + 0.0714031i
\(474\) 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 \(-0.810594\pi\)
0.899505 + 0.436910i \(0.143927\pi\)
\(480\) 0 0
\(481\) 19.3923 + 33.5885i 0.884213 + 1.53150i
\(482\) −9.07227 2.43091i −0.413231 0.110725i
\(483\) 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 \(0.868489\pi\)
\(488\) −3.86370 + 1.03528i −0.174902 + 0.0468648i
\(489\) −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 \(0.472092\pi\)
\(492\) 2.89778 0.776457i 0.130642 0.0350054i
\(493\) 0 0
\(494\) −15.1244 −0.680477
\(495\) 0 0
\(496\) −0.196152 −0.00880750
\(497\) 8.90138 + 33.2204i 0.399282 + 1.49014i
\(498\) −7.70882 + 28.7697i −0.345441 + 1.28920i
\(499\) −10.0359 + 5.79423i −0.449269 + 0.259385i −0.707521 0.706692i \(-0.750187\pi\)
0.258253 + 0.966077i \(0.416853\pi\)
\(500\) 0 0
\(501\) −14.1962 24.5885i −0.634237 1.09853i
\(502\) −8.69333 + 2.32937i −0.388002 + 0.103965i
\(503\) −3.82654 3.82654i −0.170617 0.170617i 0.616633 0.787250i \(-0.288496\pi\)
−0.787250 + 0.616633i \(0.788496\pi\)
\(504\) 7.09808 12.2942i 0.316173 0.547628i
\(505\) 0 0
\(506\) 6.58846 + 3.80385i 0.292893 + 0.169102i
\(507\) 4.21046 + 15.7136i 0.186993 + 0.697867i
\(508\) 7.91688 + 2.12132i 0.351255 + 0.0941184i
\(509\) −10.3923 18.0000i −0.460631 0.797836i 0.538362 0.842714i \(-0.319043\pi\)
−0.998992 + 0.0448779i \(0.985710\pi\)
\(510\) 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
\(517\) 5.37945 20.0764i 0.236588 0.882959i
\(518\) 10.0382 37.4631i 0.441053 1.64603i
\(519\) −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 \(0.980572\pi\)
\(522\) 8.33298 31.0991i 0.364725 1.36117i
\(523\) −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
\(528\) 5.79555 + 1.55291i 0.252219 + 0.0675819i
\(529\) 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
\(533\) 7.91688 2.12132i 0.342918 0.0918846i
\(534\) −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
\(538\) 2.60179 + 9.71003i 0.112171 + 0.418629i
\(539\) 53.3205 2.29668
\(540\) 0 0
\(541\) −8.39230 −0.360813 −0.180407 0.983592i \(-0.557741\pi\)
−0.180407 + 0.983592i \(0.557741\pi\)
\(542\) 6.88160 + 25.6825i 0.295590 + 1.10316i
\(543\) −15.1774 15.1774i −0.651325 0.651325i
\(544\) 0 0
\(545\) 0 0
\(546\) 19.3923 33.5885i 0.829914 1.43745i
\(547\) 38.8079 10.3986i 1.65931 0.444610i 0.697110 0.716964i \(-0.254469\pi\)
0.962197 + 0.272354i \(0.0878023\pi\)
\(548\) −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
\(552\) −3.67423 0.984508i −0.156386 0.0419035i
\(553\) −45.7081 12.2474i −1.94371 0.520814i
\(554\) 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 −0.769838 0.638240i \(-0.779663\pi\)
0.638240 + 0.769838i \(0.279663\pi\)
\(558\) 0.416102 + 0.416102i 0.0176150 + 0.0176150i
\(559\) 2.19615i 0.0928874i
\(560\) 0 0
\(561\) 0 0
\(562\) −2.68973 + 10.0382i −0.113459 + 0.423436i
\(563\) −0.624153 + 2.32937i −0.0263049 + 0.0981713i −0.977830 0.209399i \(-0.932849\pi\)
0.951525 + 0.307570i \(0.0995159\pi\)
\(564\) 10.3923i 0.437595i
\(565\) 0 0
\(566\) 3.92820i 0.165115i
\(567\) −41.1373 + 11.0227i −1.72760 + 0.462910i
\(568\) 5.13922 5.13922i 0.215637 0.215637i
\(569\) 12.4641 21.5885i 0.522522 0.905035i −0.477134 0.878830i \(-0.658324\pi\)
0.999657 0.0262048i \(-0.00834220\pi\)
\(570\) 0 0
\(571\) −9.59808 16.6244i −0.401667 0.695708i 0.592260 0.805747i \(-0.298236\pi\)
−0.993927 + 0.110039i \(0.964902\pi\)
\(572\) 15.8338 + 4.24264i 0.662042 + 0.177394i
\(573\) 1.55291 + 5.79555i 0.0648739 + 0.242113i
\(574\) −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 \(0.594726\pi\)
\(578\) −16.4207 + 4.39992i −0.683013 + 0.183013i
\(579\) 9.58846 + 16.6077i 0.398483 + 0.690192i
\(580\) 0 0
\(581\) 70.4711 40.6865i 2.92364 1.68796i
\(582\) −1.19256 + 4.45069i −0.0494332 + 0.184487i
\(583\) −7.34847 27.4249i −0.304342 1.13582i
\(584\) −5.19615 −0.215018
\(585\) 0 0
\(586\) 3.80385 0.157135
\(587\) 1.13681 + 4.24264i 0.0469213 + 0.175113i 0.985410 0.170197i \(-0.0544405\pi\)
−0.938489 + 0.345310i \(0.887774\pi\)
\(588\) −25.7518 + 6.90018i −1.06199 + 0.284559i
\(589\) −0.542940 + 0.313467i −0.0223715 + 0.0129162i
\(590\) 0 0
\(591\) 24.5885 1.01143
\(592\) −7.91688 + 2.12132i −0.325382 + 0.0871857i
\(593\) 14.8492 + 14.8492i 0.609785 + 0.609785i 0.942890 0.333105i \(-0.108096\pi\)
−0.333105 + 0.942890i \(0.608096\pi\)
\(594\) −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
\(598\) −10.0382 2.68973i −0.410492 0.109991i
\(599\) 3.63397 + 6.29423i 0.148480 + 0.257175i 0.930666 0.365870i \(-0.119229\pi\)
−0.782186 + 0.623045i \(0.785895\pi\)
\(600\) 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
\(603\) 16.0418 + 4.29839i 0.653273 + 0.175044i
\(604\) 8.00000i 0.325515i
\(605\) 0 0
\(606\) −10.9019 + 6.29423i −0.442860 + 0.255686i
\(607\) 12.5756 46.9328i 0.510429 1.90495i 0.0945643 0.995519i \(-0.469854\pi\)
0.415864 0.909427i \(-0.363479\pi\)
\(608\) 0.827225 3.08725i 0.0335484 0.125204i
\(609\) −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
\(617\) 11.3831 + 3.05008i 0.458265 + 0.122792i 0.480564 0.876960i \(-0.340432\pi\)
−0.0222993 + 0.999751i \(0.507099\pi\)
\(618\) −12.7279 + 12.7279i −0.511992 + 0.511992i
\(619\) 41.2128 + 23.7942i 1.65648 + 0.956371i 0.974319 + 0.225171i \(0.0722941\pi\)
0.682164 + 0.731200i \(0.261039\pi\)
\(620\) 0 0
\(621\) 5.70577 + 9.88269i 0.228965 + 0.396579i
\(622\) −7.82894 7.82894i −0.313912 0.313912i
\(623\) 39.5844 10.6066i 1.58591 0.424945i
\(624\) −8.19615 −0.328109
\(625\) 0 0
\(626\) −17.8923 + 10.3301i −0.715120 + 0.412875i
\(627\) 18.5235 4.96335i 0.739756 0.198217i
\(628\) −5.13922 19.1798i −0.205077 0.765358i
\(629\) 0 0
\(630\) 0 0
\(631\) −0.784610 −0.0312348 −0.0156174 0.999878i \(-0.504971\pi\)
−0.0156174 + 0.999878i \(0.504971\pi\)
\(632\) 2.58819 + 9.65926i 0.102953 + 0.384225i
\(633\) 0.536220 2.00120i 0.0213128 0.0795406i
\(634\) 5.70577 3.29423i 0.226605 0.130831i
\(635\) 0 0
\(636\) 7.09808 + 12.2942i 0.281457 + 0.487498i
\(637\) −70.3553 + 18.8516i −2.78758 + 0.746929i
\(638\) −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 \(0.927960\pi\)
\(642\) −5.01910 18.7315i −0.198088 0.739274i
\(643\) −36.1182 9.67784i −1.42436 0.381657i −0.537333 0.843370i \(-0.680568\pi\)
−0.887029 + 0.461713i \(0.847235\pi\)
\(644\) 5.19615 + 9.00000i 0.204757 + 0.354650i
\(645\) 0 0
\(646\) 0 0
\(647\) −10.0382 + 10.0382i −0.394642 + 0.394642i −0.876338 0.481696i \(-0.840021\pi\)
0.481696 + 0.876338i \(0.340021\pi\)
\(648\) 6.36396 + 6.36396i 0.250000 + 0.250000i
\(649\) 19.1769i 0.752760i
\(650\) 0 0
\(651\) 1.60770i 0.0630105i
\(652\) 3.70642 13.8325i 0.145155 0.541724i
\(653\) −2.12132 + 7.91688i −0.0830137 + 0.309811i −0.994931 0.100564i \(-0.967935\pi\)
0.911917 + 0.410375i \(0.134602\pi\)
\(654\) −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 \(0.452740\pi\)
−0.930461 + 0.366392i \(0.880593\pi\)
\(660\) 0 0
\(661\) 19.5885 + 33.9282i 0.761903 + 1.31965i 0.941869 + 0.335981i \(0.109068\pi\)
−0.179966 + 0.983673i \(0.557599\pi\)
\(662\) 13.1254 + 3.51695i 0.510135 + 0.136690i
\(663\) 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
\(668\) 15.8338 4.24264i 0.612626 0.164153i
\(669\) −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
\(673\) 5.79555 + 21.6293i 0.223402 + 0.833748i 0.983038 + 0.183400i \(0.0587104\pi\)
−0.759636 + 0.650348i \(0.774623\pi\)
\(674\) −20.5359 −0.791013
\(675\) 0 0
\(676\) −9.39230 −0.361242
\(677\) 6.36396 + 23.7506i 0.244587 + 0.912811i 0.973591 + 0.228301i \(0.0733170\pi\)
−0.729004 + 0.684510i \(0.760016\pi\)
\(678\) 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
\(682\) 0.656339 0.175865i 0.0251325 0.00673424i
\(683\) −5.94786 5.94786i −0.227588 0.227588i 0.584096 0.811685i \(-0.301449\pi\)
−0.811685 + 0.584096i \(0.801449\pi\)
\(684\) −8.30385 + 4.79423i −0.317506 + 0.183312i
\(685\) 0 0
\(686\) 34.3923 + 19.8564i 1.31310 + 0.758121i
\(687\) 9.71003 + 2.60179i 0.370461 + 0.0992646i
\(688\) 0.448288 + 0.120118i 0.0170908 + 0.00457947i
\(689\) 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
\(693\) −12.7279 + 47.5013i −0.483494 + 1.80442i
\(694\) 8.78461i 0.333459i
\(695\) 0 0
\(696\) 16.0981 + 9.29423i 0.610196 + 0.352297i
\(697\) 0 0
\(698\) 0.517638 1.93185i 0.0195929 0.0731217i
\(699\) 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
\(707\) 33.2204 + 8.90138i 1.24938 + 0.334771i
\(708\) −2.48168 9.26174i −0.0932671 0.348077i
\(709\) 31.3468 + 18.0981i 1.17725 + 0.679688i 0.955378 0.295387i \(-0.0954487\pi\)
0.221876 + 0.975075i \(0.428782\pi\)
\(710\) 0 0
\(711\) 15.0000 25.9808i 0.562544 0.974355i
\(712\) −6.12372 6.12372i −0.229496 0.229496i
\(713\) −0.416102 + 0.111494i −0.0155831 + 0.00417549i
\(714\) 0 0
\(715\) 0 0
\(716\) 19.7942 11.4282i 0.739745 0.427092i
\(717\) −1.70522 + 6.36396i −0.0636825 + 0.237666i
\(718\) 9.14162 + 34.1170i 0.341162 + 1.27323i
\(719\) 14.8756 0.554768 0.277384 0.960759i \(-0.410533\pi\)
0.277384 + 0.960759i \(0.410533\pi\)
\(720\) 0 0
\(721\) 49.1769 1.83144
\(722\) 2.27362 + 8.48528i 0.0846155 + 0.315789i
\(723\) −15.7136 + 4.21046i −0.584396 + 0.156589i
\(724\) 10.7321 6.19615i 0.398854 0.230278i
\(725\) 0 0
\(726\) −1.73205 −0.0642824
\(727\) −6.69213 + 1.79315i −0.248197 + 0.0665043i −0.380773 0.924669i \(-0.624342\pi\)
0.132575 + 0.991173i \(0.457675\pi\)
\(728\) 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
\(733\) −13.1440 3.52193i −0.485486 0.130085i 0.00777015 0.999970i \(-0.497527\pi\)
−0.493256 + 0.869884i \(0.664193\pi\)
\(734\) 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
\(742\) 10.0382 37.4631i 0.368514 1.37531i
\(743\) 8.63759 32.2359i 0.316882 1.18262i −0.605342 0.795965i \(-0.706964\pi\)
0.922224 0.386655i \(-0.126370\pi\)
\(744\) −0.294229 + 0.169873i −0.0107869 + 0.00622785i
\(745\) 0 0
\(746\) 23.3205i 0.853824i
\(747\) 13.3521 + 49.8306i 0.488527 + 1.82321i
\(748\) 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 \(0.895216\pi\)
\(752\) −5.79555 1.55291i −0.211342 0.0566290i
\(753\) −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 \(-0.501757\pi\)
\(758\) −0.378937 + 0.101536i −0.0137636 + 0.00368795i
\(759\) 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 \(0.662831\pi\)
\(762\) 13.7124 3.67423i 0.496749 0.133103i
\(763\) 2.20925 + 8.24504i 0.0799803 + 0.298491i
\(764\) −3.46410 −0.125327
\(765\) 0 0
\(766\) 5.41154 0.195527
\(767\) −6.78006 25.3035i −0.244814 0.913658i
\(768\) 0.448288 1.67303i 0.0161762 0.0603704i
\(769\) −10.9186 + 6.30385i −0.393734 + 0.227323i −0.683777 0.729691i \(-0.739664\pi\)
0.290043 + 0.957014i \(0.406331\pi\)
\(770\) 0 0
\(771\) −21.9904 38.0885i −0.791964 1.37172i
\(772\) −10.6945 + 2.86559i −0.384905 + 0.103135i
\(773\) −35.9101 35.9101i −1.29160 1.29160i −0.933798 0.357800i \(-0.883527\pi\)
−0.357800 0.933798i \(-0.616473\pi\)
\(774\) −0.696152 1.20577i −0.0250227 0.0433406i
\(775\) 0 0
\(776\) −2.30385 1.33013i −0.0827033 0.0477488i
\(777\) −17.3867 64.8879i −0.623743 2.32784i
\(778\) −10.0382 2.68973i −0.359887 0.0964314i
\(779\) 2.76795 + 4.79423i 0.0991721 + 0.171771i
\(780\) 0 0
\(781\) −12.5885 + 21.8038i −0.450450 + 0.780203i
\(782\) 0 0
\(783\) −14.4331 53.8652i −0.515798 1.92499i
\(784\) 15.3923i 0.549725i
\(785\) 0 0