Properties

Label 450.2.p.e.407.1
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 407.1
Root \(0.965926 - 0.258819i\) of \(x^{8} - x^{4} + 1\)
Character \(\chi\) \(=\) 450.407
Dual form 450.2.p.e.293.1

$q$-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 −0.979629 0.200817i \(-0.935640\pi\)
−0.747975 + 0.663727i \(0.768974\pi\)
\(8\) 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 0.829155 0.559019i \(-0.188822\pi\)
0.438560 + 0.898702i \(0.355489\pi\)
\(14\) 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 −0.999526 0.0307805i \(-0.990201\pi\)
0.881005 + 0.473106i \(0.156867\pi\)
\(24\) 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 0.998934 0.0461511i \(-0.0146956\pi\)
−0.0461511 + 0.998934i \(0.514696\pi\)
\(38\) −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 0.956162 0.292839i \(-0.0945999\pi\)
−0.974480 + 0.224475i \(0.927933\pi\)
\(44\) −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 \(0.0608363\pi\)
−0.755276 + 0.655407i \(0.772497\pi\)
\(48\) −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 0.982475 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
\(58\) 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 \(0.193137\pi\)
−0.996544 + 0.0830646i \(0.973529\pi\)
\(68\) 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 −0.888641 0.458604i \(-0.848350\pi\)
0.458604 + 0.888641i \(0.348350\pi\)
\(74\) 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 −0.997176 0.0750978i \(-0.976073\pi\)
−0.826031 + 0.563625i \(0.809406\pi\)
\(84\) −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 −0.386900 0.922122i \(-0.626454\pi\)
0.125996 + 0.992031i \(0.459787\pi\)
\(98\) −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 −0.272223 0.962234i \(-0.587759\pi\)
−0.716869 + 0.697207i \(0.754426\pi\)
\(104\) 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 \(0.0679753\pi\)
\(108\) −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 \(0.300246\pi\)
−0.913231 + 0.407443i \(0.866421\pi\)
\(114\) 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 0.915833 0.401560i \(-0.131532\pi\)
−0.401560 + 0.915833i \(0.631532\pi\)
\(128\) 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 \(-0.889466\pi\)
0.644175 0.764878i \(-0.277201\pi\)
\(138\) −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 \(-0.625520\pi\)
0.794348 0.607463i \(-0.207813\pi\)
\(158\) −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 −0.188864 0.982003i \(-0.560480\pi\)
0.982003 + 0.188864i \(0.0604804\pi\)
\(164\) 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 0.812729 0.582642i \(-0.197981\pi\)
0.412523 + 0.910947i \(0.364648\pi\)
\(168\) 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 0.399484 0.916740i \(-0.369189\pi\)
0.804334 + 0.594178i \(0.202523\pi\)
\(174\) −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 −0.147522 0.989059i \(-0.547130\pi\)
−0.622287 + 0.782789i \(0.713796\pi\)
\(194\) 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 \(0.418772\pi\)
\(198\) 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 0.940462 0.339899i \(-0.110393\pi\)
−0.984414 + 0.175869i \(0.943726\pi\)
\(224\) 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 \(-0.943639\pi\)
0.764415 0.644724i \(-0.223028\pi\)
\(228\) 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 0.805730 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
\(237\) 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 0.923005 0.384787i \(-0.125725\pi\)
0.606952 + 0.794738i \(0.292392\pi\)
\(258\) 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 0.136364 0.990659i \(-0.456458\pi\)
0.613424 + 0.789754i \(0.289792\pi\)
\(264\) 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 −0.776007 0.630725i \(-0.782758\pi\)
−0.356679 + 0.934227i \(0.616091\pi\)
\(278\) −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 0.369824 0.929102i \(-0.379418\pi\)
−0.144274 + 0.989538i \(0.546085\pi\)
\(284\) −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 −0.988703 0.149891i \(-0.952108\pi\)
0.931187 + 0.364542i \(0.118774\pi\)
\(294\) 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 0.773543 0.633743i \(-0.218483\pi\)
−0.633743 + 0.773543i \(0.718483\pi\)
\(308\) 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 \(-0.884862\pi\)
0.633045 0.774115i \(-0.281805\pi\)
\(314\) −19.8564 −1.12056
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) 1.70522 + 6.36396i 0.0957746 + 0.357436i 0.997136 0.0756325i \(-0.0240976\pi\)
−0.901361 + 0.433068i \(0.857431\pi\)
\(318\) −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 \(-0.727725\pi\)
0.945464 0.325725i \(-0.105609\pi\)
\(338\) 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 0.479278 0.877663i \(-0.340898\pi\)
−0.0237644 + 0.999718i \(0.507565\pi\)
\(348\) −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 −0.622886 0.782312i \(-0.714040\pi\)
−0.148279 + 0.988946i \(0.547373\pi\)
\(354\) −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 −0.361763 0.932270i \(-0.617825\pi\)
0.152839 + 0.988251i \(0.451158\pi\)
\(368\) 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 −0.376848 0.926275i \(-0.622992\pi\)
−0.789498 + 0.613754i \(0.789659\pi\)
\(374\) 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 −0.992433 0.122786i \(-0.960817\pi\)
0.920865 + 0.389881i \(0.127484\pi\)
\(384\) −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 0.377293 0.926094i \(-0.376855\pi\)
−0.926094 + 0.377293i \(0.876855\pi\)
\(398\) 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 −0.354814 0.934937i \(-0.615456\pi\)
0.934937 + 0.354814i \(0.115456\pi\)
\(434\) 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 −0.489272 0.872131i \(-0.662738\pi\)
0.0123433 + 0.999924i \(0.496071\pi\)
\(444\) 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 0.425553 0.904933i \(-0.360080\pi\)
0.821007 + 0.570919i \(0.193413\pi\)
\(458\) −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 0.209189 0.977875i \(-0.432918\pi\)
−0.307775 + 0.951459i \(0.599584\pi\)
\(464\) 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 \(0.178790\pi\)
\(468\) −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 0.915858 0.401501i \(-0.131511\pi\)
−0.401501 + 0.915858i \(0.631511\pi\)
\(488\) 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 0.787250 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
\(507\) −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 \(-0.483978\pi\)
0.998733 0.0503137i \(-0.0160221\pi\)
\(524\) 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 −0.962197 0.272354i \(-0.912198\pi\)
−0.697110 + 0.716964i \(0.745531\pi\)
\(548\) 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 −0.638240 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
\(562\) 2.68973 10.0382i 0.113459 0.423436i
\(563\) 0.624153 2.32937i 0.0263049 0.0981713i −0.951525 0.307570i \(-0.900484\pi\)
0.977830 + 0.209399i \(0.0671507\pi\)
\(564\) 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 0.293217 0.956046i \(-0.405274\pi\)
−0.956046 + 0.293217i \(0.905274\pi\)
\(578\) 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 0.938489 0.345310i \(-0.112226\pi\)
−0.985410 + 0.170197i \(0.945559\pi\)
\(588\) 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 0.333105 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
\(598\) 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 \(0.530146\pi\)
−0.415864 + 0.909427i \(0.636521\pi\)
\(608\) −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 −0.474706 0.880145i \(-0.657445\pi\)
0.880145 + 0.474706i \(0.157445\pi\)
\(614\) 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 0.0222993 0.999751i \(-0.492901\pi\)
−0.480564 + 0.876960i \(0.659568\pi\)
\(618\) 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 0.887029 0.461713i \(-0.152765\pi\)
0.537333 + 0.843370i \(0.319432\pi\)
\(644\) 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
\(652\) −3.70642 + 13.8325i −0.145155 + 0.541724i
\(653\) 2.12132 7.91688i 0.0830137 0.309811i −0.911917 0.410375i \(-0.865398\pi\)
0.994931 + 0.100564i \(0.0320646\pi\)
\(654\) −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 \(-0.941290\pi\)
0.759636 0.650348i \(-0.225377\pi\)
\(674\) −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 \(-0.926683\pi\)
0.729004 0.684510i \(-0.239984\pi\)
\(678\) −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 0.811685 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
\(687\) −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 −0.132575 0.991173i \(-0.542325\pi\)
0.380773 + 0.924669i \(0.375658\pi\)
\(728\) −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 0.493256 0.869884i \(-0.335807\pi\)
−0.00777015 + 0.999970i \(0.502473\pi\)
\(734\) 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 \(0.293036\pi\)
−0.922224 + 0.386655i \(0.873630\pi\)
\(744\) −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 \(0.00175717\pi\)
0.00552030 + 0.999985i \(0.498243\pi\)
\(758\) 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 \(0.116473\pi\)
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
\(777\) 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