Properties

Label 210.3.o.b.61.7
Level 210
Weight 3
Character 210.61
Analytic conductor 5.722
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 61.7
Root \(0.848921 - 1.47037i\) of \(x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + 4836403 x^{8} - 6808704 x^{7} + 64376800 x^{6} - 91953512 x^{5} + 595763862 x^{4} - 630430976 x^{3} + 1087013404 x^{2} + 294123256 x + 101626561\)
Character \(\chi\) \(=\) 210.61
Dual form 210.3.o.b.31.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} +2.44949i q^{6} +(-6.38854 - 2.86123i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} +2.44949i q^{6} +(-6.38854 - 2.86123i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(2.73861 - 1.58114i) q^{10} +(-9.98749 - 17.2988i) q^{11} +(3.00000 + 1.73205i) q^{12} -3.49788i q^{13} +(-8.02165 + 5.80113i) q^{14} -3.87298 q^{15} +(-2.00000 + 3.46410i) q^{16} +(15.7982 - 9.12112i) q^{17} +(-2.12132 - 3.67423i) q^{18} +(-21.3143 - 12.3058i) q^{19} -4.47214i q^{20} +(12.0607 - 1.24079i) q^{21} -28.2489 q^{22} +(-12.5952 + 21.8155i) q^{23} +(4.24264 - 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-4.28401 - 2.47338i) q^{26} +5.19615i q^{27} +(1.43274 + 13.9265i) q^{28} -53.1223 q^{29} +(-2.73861 + 4.74342i) q^{30} +(26.0944 - 15.0656i) q^{31} +(2.82843 + 4.89898i) q^{32} +(29.9625 + 17.2988i) q^{33} -25.7984i q^{34} +(-9.17240 - 12.6833i) q^{35} -6.00000 q^{36} +(23.3846 - 40.5034i) q^{37} +(-30.1429 + 17.4030i) q^{38} +(3.02925 + 5.24682i) q^{39} +(-5.47723 - 3.16228i) q^{40} +31.5250i q^{41} +(7.00855 - 15.6487i) q^{42} +64.4116 q^{43} +(-19.9750 + 34.5977i) q^{44} +(5.80948 - 3.35410i) q^{45} +(17.8123 + 30.8518i) q^{46} +(-24.3029 - 14.0313i) q^{47} -6.92820i q^{48} +(32.6268 + 36.5581i) q^{49} +7.07107 q^{50} +(-15.7982 + 27.3634i) q^{51} +(-6.05851 + 3.49788i) q^{52} +(32.4374 + 56.1833i) q^{53} +(6.36396 + 3.67423i) q^{54} -44.6654i q^{55} +(18.0695 + 8.09277i) q^{56} +42.6285 q^{57} +(-37.5631 + 65.0613i) q^{58} +(86.7684 - 50.0958i) q^{59} +(3.87298 + 6.70820i) q^{60} +(6.94896 + 4.01198i) q^{61} -42.6119i q^{62} +(-17.0165 + 12.3061i) q^{63} +8.00000 q^{64} +(3.91075 - 6.77362i) q^{65} +(42.3733 - 24.4642i) q^{66} +(-8.13165 - 14.0844i) q^{67} +(-31.5965 - 18.2422i) q^{68} -43.6310i q^{69} +(-22.0197 + 2.26537i) q^{70} -107.725 q^{71} +(-4.24264 + 7.34847i) q^{72} +(44.7395 - 25.8303i) q^{73} +(-33.0709 - 57.2804i) q^{74} +(-7.50000 - 4.33013i) q^{75} +49.2232i q^{76} +(14.3095 + 139.091i) q^{77} +8.56803 q^{78} +(10.9877 - 19.0313i) q^{79} +(-7.74597 + 4.47214i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(38.6101 + 22.2916i) q^{82} -0.417479i q^{83} +(-14.2098 - 19.6489i) q^{84} +40.7909 q^{85} +(45.5459 - 78.8878i) q^{86} +(79.6835 - 46.0053i) q^{87} +(28.2489 + 48.9285i) q^{88} +(-96.3110 - 55.6052i) q^{89} -9.48683i q^{90} +(-10.0082 + 22.3463i) q^{91} +50.3807 q^{92} +(-26.0944 + 45.1968i) q^{93} +(-34.3695 + 19.8432i) q^{94} +(-27.5166 - 47.6601i) q^{95} +(-8.48528 - 4.89898i) q^{96} -74.2244i q^{97} +(67.8449 - 14.1090i) q^{98} -59.9249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 24q^{3} - 16q^{4} + 4q^{7} + 24q^{9} + O(q^{10}) \) \( 16q - 24q^{3} - 16q^{4} + 4q^{7} + 24q^{9} - 4q^{11} + 48q^{12} + 8q^{14} - 32q^{16} + 12q^{17} - 72q^{19} - 24q^{21} - 48q^{22} - 12q^{23} + 40q^{25} + 32q^{28} + 72q^{29} + 120q^{31} + 12q^{33} - 20q^{35} - 96q^{36} + 44q^{37} - 72q^{38} + 36q^{39} - 24q^{42} - 56q^{43} - 8q^{44} + 8q^{46} - 24q^{47} - 40q^{49} - 12q^{51} - 72q^{52} + 32q^{53} + 16q^{56} + 144q^{57} - 88q^{58} + 132q^{59} + 96q^{61} + 60q^{63} + 128q^{64} + 20q^{65} + 72q^{66} - 164q^{67} - 24q^{68} - 136q^{71} - 348q^{73} - 112q^{74} - 120q^{75} + 96q^{77} + 280q^{79} - 72q^{81} + 264q^{82} - 24q^{84} + 120q^{85} - 88q^{86} - 108q^{87} + 48q^{88} - 300q^{89} - 272q^{91} + 48q^{92} - 120q^{93} + 200q^{95} + 384q^{98} - 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 1.22474i 0.353553 0.612372i
\(3\) −1.50000 + 0.866025i −0.500000 + 0.288675i
\(4\) −1.00000 1.73205i −0.250000 0.433013i
\(5\) 1.93649 + 1.11803i 0.387298 + 0.223607i
\(6\) 2.44949i 0.408248i
\(7\) −6.38854 2.86123i −0.912648 0.408747i
\(8\) −2.82843 −0.353553
\(9\) 1.50000 2.59808i 0.166667 0.288675i
\(10\) 2.73861 1.58114i 0.273861 0.158114i
\(11\) −9.98749 17.2988i −0.907953 1.57262i −0.816903 0.576775i \(-0.804311\pi\)
−0.0910503 0.995846i \(-0.529022\pi\)
\(12\) 3.00000 + 1.73205i 0.250000 + 0.144338i
\(13\) 3.49788i 0.269068i −0.990909 0.134534i \(-0.957046\pi\)
0.990909 0.134534i \(-0.0429537\pi\)
\(14\) −8.02165 + 5.80113i −0.572975 + 0.414367i
\(15\) −3.87298 −0.258199
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 15.7982 9.12112i 0.929308 0.536536i 0.0427155 0.999087i \(-0.486399\pi\)
0.886593 + 0.462551i \(0.153066\pi\)
\(18\) −2.12132 3.67423i −0.117851 0.204124i
\(19\) −21.3143 12.3058i −1.12180 0.647673i −0.179942 0.983677i \(-0.557591\pi\)
−0.941861 + 0.336004i \(0.890924\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 12.0607 1.24079i 0.574319 0.0590854i
\(22\) −28.2489 −1.28404
\(23\) −12.5952 + 21.8155i −0.547617 + 0.948500i 0.450820 + 0.892615i \(0.351131\pi\)
−0.998437 + 0.0558853i \(0.982202\pi\)
\(24\) 4.24264 2.44949i 0.176777 0.102062i
\(25\) 2.50000 + 4.33013i 0.100000 + 0.173205i
\(26\) −4.28401 2.47338i −0.164770 0.0951299i
\(27\) 5.19615i 0.192450i
\(28\) 1.43274 + 13.9265i 0.0511694 + 0.497375i
\(29\) −53.1223 −1.83180 −0.915902 0.401402i \(-0.868523\pi\)
−0.915902 + 0.401402i \(0.868523\pi\)
\(30\) −2.73861 + 4.74342i −0.0912871 + 0.158114i
\(31\) 26.0944 15.0656i 0.841754 0.485987i −0.0161061 0.999870i \(-0.505127\pi\)
0.857860 + 0.513883i \(0.171794\pi\)
\(32\) 2.82843 + 4.89898i 0.0883883 + 0.153093i
\(33\) 29.9625 + 17.2988i 0.907953 + 0.524207i
\(34\) 25.7984i 0.758777i
\(35\) −9.17240 12.6833i −0.262068 0.362381i
\(36\) −6.00000 −0.166667
\(37\) 23.3846 40.5034i 0.632017 1.09469i −0.355122 0.934820i \(-0.615561\pi\)
0.987139 0.159866i \(-0.0511061\pi\)
\(38\) −30.1429 + 17.4030i −0.793234 + 0.457974i
\(39\) 3.02925 + 5.24682i 0.0776732 + 0.134534i
\(40\) −5.47723 3.16228i −0.136931 0.0790569i
\(41\) 31.5250i 0.768903i 0.923145 + 0.384452i \(0.125609\pi\)
−0.923145 + 0.384452i \(0.874391\pi\)
\(42\) 7.00855 15.6487i 0.166870 0.372587i
\(43\) 64.4116 1.49794 0.748972 0.662602i \(-0.230548\pi\)
0.748972 + 0.662602i \(0.230548\pi\)
\(44\) −19.9750 + 34.5977i −0.453977 + 0.786311i
\(45\) 5.80948 3.35410i 0.129099 0.0745356i
\(46\) 17.8123 + 30.8518i 0.387223 + 0.670691i
\(47\) −24.3029 14.0313i −0.517083 0.298538i 0.218657 0.975802i \(-0.429832\pi\)
−0.735740 + 0.677264i \(0.763166\pi\)
\(48\) 6.92820i 0.144338i
\(49\) 32.6268 + 36.5581i 0.665852 + 0.746084i
\(50\) 7.07107 0.141421
\(51\) −15.7982 + 27.3634i −0.309769 + 0.536536i
\(52\) −6.05851 + 3.49788i −0.116510 + 0.0672670i
\(53\) 32.4374 + 56.1833i 0.612027 + 1.06006i 0.990898 + 0.134612i \(0.0429789\pi\)
−0.378872 + 0.925449i \(0.623688\pi\)
\(54\) 6.36396 + 3.67423i 0.117851 + 0.0680414i
\(55\) 44.6654i 0.812098i
\(56\) 18.0695 + 8.09277i 0.322670 + 0.144514i
\(57\) 42.6285 0.747869
\(58\) −37.5631 + 65.0613i −0.647640 + 1.12175i
\(59\) 86.7684 50.0958i 1.47065 0.849081i 0.471194 0.882029i \(-0.343823\pi\)
0.999457 + 0.0329486i \(0.0104897\pi\)
\(60\) 3.87298 + 6.70820i 0.0645497 + 0.111803i
\(61\) 6.94896 + 4.01198i 0.113917 + 0.0657702i 0.555876 0.831265i \(-0.312383\pi\)
−0.441959 + 0.897035i \(0.645716\pi\)
\(62\) 42.6119i 0.687289i
\(63\) −17.0165 + 12.3061i −0.270103 + 0.195334i
\(64\) 8.00000 0.125000
\(65\) 3.91075 6.77362i 0.0601654 0.104210i
\(66\) 42.3733 24.4642i 0.642020 0.370670i
\(67\) −8.13165 14.0844i −0.121368 0.210215i 0.798939 0.601411i \(-0.205395\pi\)
−0.920307 + 0.391196i \(0.872061\pi\)
\(68\) −31.5965 18.2422i −0.464654 0.268268i
\(69\) 43.6310i 0.632333i
\(70\) −22.0197 + 2.26537i −0.314567 + 0.0323624i
\(71\) −107.725 −1.51725 −0.758625 0.651528i \(-0.774128\pi\)
−0.758625 + 0.651528i \(0.774128\pi\)
\(72\) −4.24264 + 7.34847i −0.0589256 + 0.102062i
\(73\) 44.7395 25.8303i 0.612870 0.353840i −0.161218 0.986919i \(-0.551542\pi\)
0.774088 + 0.633078i \(0.218209\pi\)
\(74\) −33.0709 57.2804i −0.446904 0.774060i
\(75\) −7.50000 4.33013i −0.100000 0.0577350i
\(76\) 49.2232i 0.647673i
\(77\) 14.3095 + 139.091i 0.185838 + 1.80637i
\(78\) 8.56803 0.109846
\(79\) 10.9877 19.0313i 0.139085 0.240903i −0.788065 0.615592i \(-0.788917\pi\)
0.927151 + 0.374689i \(0.122250\pi\)
\(80\) −7.74597 + 4.47214i −0.0968246 + 0.0559017i
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 38.6101 + 22.2916i 0.470855 + 0.271848i
\(83\) 0.417479i 0.00502987i −0.999997 0.00251494i \(-0.999199\pi\)
0.999997 0.00251494i \(-0.000800530\pi\)
\(84\) −14.2098 19.6489i −0.169164 0.233916i
\(85\) 40.7909 0.479893
\(86\) 45.5459 78.8878i 0.529603 0.917300i
\(87\) 79.6835 46.0053i 0.915902 0.528796i
\(88\) 28.2489 + 48.9285i 0.321010 + 0.556006i
\(89\) −96.3110 55.6052i −1.08215 0.624778i −0.150672 0.988584i \(-0.548144\pi\)
−0.931475 + 0.363806i \(0.881477\pi\)
\(90\) 9.48683i 0.105409i
\(91\) −10.0082 + 22.3463i −0.109981 + 0.245564i
\(92\) 50.3807 0.547617
\(93\) −26.0944 + 45.1968i −0.280585 + 0.485987i
\(94\) −34.3695 + 19.8432i −0.365633 + 0.211098i
\(95\) −27.5166 47.6601i −0.289648 0.501686i
\(96\) −8.48528 4.89898i −0.0883883 0.0510310i
\(97\) 74.2244i 0.765200i −0.923914 0.382600i \(-0.875029\pi\)
0.923914 0.382600i \(-0.124971\pi\)
\(98\) 67.8449 14.1090i 0.692295 0.143969i
\(99\) −59.9249 −0.605302
\(100\) 5.00000 8.66025i 0.0500000 0.0866025i
\(101\) 75.8587 43.7970i 0.751076 0.433634i −0.0750065 0.997183i \(-0.523898\pi\)
0.826083 + 0.563549i \(0.190564\pi\)
\(102\) 22.3421 + 38.6976i 0.219040 + 0.379388i
\(103\) 120.413 + 69.5206i 1.16906 + 0.674957i 0.953458 0.301525i \(-0.0974956\pi\)
0.215601 + 0.976482i \(0.430829\pi\)
\(104\) 9.89350i 0.0951299i
\(105\) 24.7427 + 11.0815i 0.235645 + 0.105538i
\(106\) 91.7469 0.865537
\(107\) −76.0949 + 131.800i −0.711168 + 1.23178i 0.253252 + 0.967400i \(0.418500\pi\)
−0.964419 + 0.264378i \(0.914833\pi\)
\(108\) 9.00000 5.19615i 0.0833333 0.0481125i
\(109\) −32.3777 56.0798i −0.297043 0.514494i 0.678415 0.734679i \(-0.262667\pi\)
−0.975458 + 0.220185i \(0.929334\pi\)
\(110\) −54.7037 31.5832i −0.497307 0.287120i
\(111\) 81.0068i 0.729791i
\(112\) 22.6887 16.4081i 0.202577 0.146501i
\(113\) 3.25860 0.0288372 0.0144186 0.999896i \(-0.495410\pi\)
0.0144186 + 0.999896i \(0.495410\pi\)
\(114\) 30.1429 52.2090i 0.264411 0.457974i
\(115\) −48.7809 + 28.1637i −0.424182 + 0.244902i
\(116\) 53.1223 + 92.0105i 0.457951 + 0.793194i
\(117\) −9.08776 5.24682i −0.0776732 0.0448446i
\(118\) 141.692i 1.20078i
\(119\) −127.025 + 13.0682i −1.06744 + 0.109817i
\(120\) 10.9545 0.0912871
\(121\) −139.000 + 240.755i −1.14876 + 1.98971i
\(122\) 9.82731 5.67380i 0.0805517 0.0465066i
\(123\) −27.3015 47.2875i −0.221963 0.384452i
\(124\) −52.1887 30.1312i −0.420877 0.242993i
\(125\) 11.1803i 0.0894427i
\(126\) 3.03931 + 29.5426i 0.0241215 + 0.234465i
\(127\) −88.5772 −0.697458 −0.348729 0.937224i \(-0.613387\pi\)
−0.348729 + 0.937224i \(0.613387\pi\)
\(128\) 5.65685 9.79796i 0.0441942 0.0765466i
\(129\) −96.6174 + 55.7821i −0.748972 + 0.432419i
\(130\) −5.53064 9.57934i −0.0425434 0.0736873i
\(131\) −108.361 62.5621i −0.827181 0.477573i 0.0257055 0.999670i \(-0.491817\pi\)
−0.852887 + 0.522096i \(0.825150\pi\)
\(132\) 69.1953i 0.524207i
\(133\) 100.957 + 139.601i 0.759077 + 1.04963i
\(134\) −22.9998 −0.171640
\(135\) −5.80948 + 10.0623i −0.0430331 + 0.0745356i
\(136\) −44.6842 + 25.7984i −0.328560 + 0.189694i
\(137\) 19.4769 + 33.7349i 0.142167 + 0.246240i 0.928312 0.371801i \(-0.121260\pi\)
−0.786145 + 0.618042i \(0.787926\pi\)
\(138\) −53.4368 30.8518i −0.387223 0.223564i
\(139\) 98.9454i 0.711837i −0.934517 0.355919i \(-0.884168\pi\)
0.934517 0.355919i \(-0.115832\pi\)
\(140\) −12.7958 + 28.5704i −0.0913985 + 0.204074i
\(141\) 48.6058 0.344722
\(142\) −76.1729 + 131.935i −0.536429 + 0.929122i
\(143\) −60.5093 + 34.9351i −0.423142 + 0.244301i
\(144\) 6.00000 + 10.3923i 0.0416667 + 0.0721688i
\(145\) −102.871 59.3925i −0.709455 0.409604i
\(146\) 73.0593i 0.500406i
\(147\) −80.6004 26.5815i −0.548302 0.180827i
\(148\) −93.5385 −0.632017
\(149\) 93.2324 161.483i 0.625721 1.08378i −0.362680 0.931914i \(-0.618138\pi\)
0.988401 0.151867i \(-0.0485284\pi\)
\(150\) −10.6066 + 6.12372i −0.0707107 + 0.0408248i
\(151\) −77.4202 134.096i −0.512716 0.888051i −0.999891 0.0147462i \(-0.995306\pi\)
0.487175 0.873304i \(-0.338027\pi\)
\(152\) 60.2858 + 34.8060i 0.396617 + 0.228987i
\(153\) 54.7267i 0.357691i
\(154\) 180.469 + 80.8265i 1.17188 + 0.524847i
\(155\) 67.3754 0.434680
\(156\) 6.05851 10.4936i 0.0388366 0.0672670i
\(157\) −43.4777 + 25.1019i −0.276928 + 0.159885i −0.632032 0.774942i \(-0.717779\pi\)
0.355104 + 0.934827i \(0.384446\pi\)
\(158\) −15.5390 26.9143i −0.0983481 0.170344i
\(159\) −97.3123 56.1833i −0.612027 0.353354i
\(160\) 12.6491i 0.0790569i
\(161\) 142.884 103.331i 0.887477 0.641810i
\(162\) −12.7279 −0.0785674
\(163\) 57.9054 100.295i 0.355248 0.615308i −0.631912 0.775040i \(-0.717730\pi\)
0.987160 + 0.159732i \(0.0510631\pi\)
\(164\) 54.6029 31.5250i 0.332945 0.192226i
\(165\) 38.6814 + 66.9981i 0.234433 + 0.406049i
\(166\) −0.511306 0.295202i −0.00308015 0.00177833i
\(167\) 61.3210i 0.367191i 0.983002 + 0.183596i \(0.0587737\pi\)
−0.983002 + 0.183596i \(0.941226\pi\)
\(168\) −34.1128 + 3.50949i −0.203052 + 0.0208898i
\(169\) 156.765 0.927602
\(170\) 28.8435 49.9584i 0.169668 0.293873i
\(171\) −63.9428 + 36.9174i −0.373934 + 0.215891i
\(172\) −64.4116 111.564i −0.374486 0.648629i
\(173\) 27.4544 + 15.8508i 0.158696 + 0.0916232i 0.577245 0.816571i \(-0.304128\pi\)
−0.418549 + 0.908194i \(0.637461\pi\)
\(174\) 130.123i 0.747831i
\(175\) −3.58186 34.8162i −0.0204678 0.198950i
\(176\) 79.8999 0.453977
\(177\) −86.7684 + 150.287i −0.490217 + 0.849081i
\(178\) −136.204 + 78.6376i −0.765193 + 0.441784i
\(179\) −65.9472 114.224i −0.368420 0.638122i 0.620899 0.783891i \(-0.286768\pi\)
−0.989319 + 0.145768i \(0.953435\pi\)
\(180\) −11.6190 6.70820i −0.0645497 0.0372678i
\(181\) 55.1431i 0.304658i −0.988330 0.152329i \(-0.951323\pi\)
0.988330 0.152329i \(-0.0486773\pi\)
\(182\) 20.2917 + 28.0588i 0.111493 + 0.154169i
\(183\) −13.8979 −0.0759449
\(184\) 35.6246 61.7035i 0.193612 0.335345i
\(185\) 90.5683 52.2896i 0.489558 0.282647i
\(186\) 36.9030 + 63.9179i 0.198403 + 0.343645i
\(187\) −315.569 182.194i −1.68754 0.974300i
\(188\) 56.1252i 0.298538i
\(189\) 14.8674 33.1958i 0.0786633 0.175639i
\(190\) −77.8287 −0.409625
\(191\) −97.5822 + 169.017i −0.510901 + 0.884907i 0.489019 + 0.872273i \(0.337355\pi\)
−0.999920 + 0.0126340i \(0.995978\pi\)
\(192\) −12.0000 + 6.92820i −0.0625000 + 0.0360844i
\(193\) −174.380 302.035i −0.903523 1.56495i −0.822888 0.568204i \(-0.807639\pi\)
−0.0806348 0.996744i \(-0.525695\pi\)
\(194\) −90.9060 52.4846i −0.468588 0.270539i
\(195\) 13.5472i 0.0694730i
\(196\) 30.6937 93.0693i 0.156601 0.474843i
\(197\) −56.3808 −0.286197 −0.143098 0.989708i \(-0.545707\pi\)
−0.143098 + 0.989708i \(0.545707\pi\)
\(198\) −42.3733 + 73.3927i −0.214007 + 0.370670i
\(199\) 148.357 85.6540i 0.745513 0.430422i −0.0785571 0.996910i \(-0.525031\pi\)
0.824070 + 0.566487i \(0.191698\pi\)
\(200\) −7.07107 12.2474i −0.0353553 0.0612372i
\(201\) 24.3950 + 14.0844i 0.121368 + 0.0700718i
\(202\) 123.877i 0.613251i
\(203\) 339.374 + 151.995i 1.67179 + 0.748744i
\(204\) 63.1930 0.309769
\(205\) −35.2460 + 61.0479i −0.171932 + 0.297795i
\(206\) 170.290 98.3169i 0.826650 0.477267i
\(207\) 37.7856 + 65.4465i 0.182539 + 0.316167i
\(208\) 12.1170 + 6.99576i 0.0582549 + 0.0336335i
\(209\) 491.616i 2.35223i
\(210\) 31.0677 22.4677i 0.147942 0.106989i
\(211\) 162.038 0.767954 0.383977 0.923343i \(-0.374554\pi\)
0.383977 + 0.923343i \(0.374554\pi\)
\(212\) 64.8748 112.367i 0.306013 0.530031i
\(213\) 161.587 93.2923i 0.758625 0.437992i
\(214\) 107.614 + 186.394i 0.502871 + 0.870999i
\(215\) 124.733 + 72.0144i 0.580151 + 0.334951i
\(216\) 14.6969i 0.0680414i
\(217\) −209.811 + 21.5851i −0.966870 + 0.0994707i
\(218\) −91.5779 −0.420082
\(219\) −44.7395 + 77.4910i −0.204290 + 0.353840i
\(220\) −77.3627 + 44.6654i −0.351649 + 0.203025i
\(221\) −31.9046 55.2604i −0.144365 0.250047i
\(222\) 99.2126 + 57.2804i 0.446904 + 0.258020i
\(223\) 365.329i 1.63825i 0.573618 + 0.819123i \(0.305539\pi\)
−0.573618 + 0.819123i \(0.694461\pi\)
\(224\) −4.05241 39.3901i −0.0180911 0.175849i
\(225\) 15.0000 0.0666667
\(226\) 2.30418 3.99096i 0.0101955 0.0176591i
\(227\) 223.325 128.937i 0.983811 0.568004i 0.0803928 0.996763i \(-0.474383\pi\)
0.903419 + 0.428759i \(0.141049\pi\)
\(228\) −42.6285 73.8347i −0.186967 0.323837i
\(229\) −13.3634 7.71538i −0.0583556 0.0336916i 0.470538 0.882380i \(-0.344060\pi\)
−0.528894 + 0.848688i \(0.677393\pi\)
\(230\) 79.6589i 0.346343i
\(231\) −141.920 196.244i −0.614374 0.849539i
\(232\) 150.253 0.647640
\(233\) 62.6734 108.553i 0.268984 0.465895i −0.699615 0.714520i \(-0.746645\pi\)
0.968600 + 0.248625i \(0.0799786\pi\)
\(234\) −12.8520 + 7.42013i −0.0549232 + 0.0317100i
\(235\) −31.3749 54.3430i −0.133510 0.231247i
\(236\) −173.537 100.192i −0.735326 0.424540i
\(237\) 38.0626i 0.160602i
\(238\) −73.8151 + 164.814i −0.310148 + 0.692496i
\(239\) −3.62565 −0.0151701 −0.00758503 0.999971i \(-0.502414\pi\)
−0.00758503 + 0.999971i \(0.502414\pi\)
\(240\) 7.74597 13.4164i 0.0322749 0.0559017i
\(241\) 83.6915 48.3193i 0.347268 0.200495i −0.316213 0.948688i \(-0.602412\pi\)
0.663481 + 0.748193i \(0.269078\pi\)
\(242\) 196.575 + 340.479i 0.812295 + 1.40694i
\(243\) 13.5000 + 7.79423i 0.0555556 + 0.0320750i
\(244\) 16.0479i 0.0657702i
\(245\) 22.3083 + 107.272i 0.0910541 + 0.437846i
\(246\) −77.2202 −0.313903
\(247\) −43.0442 + 74.5548i −0.174268 + 0.301841i
\(248\) −73.8060 + 42.6119i −0.297605 + 0.171822i
\(249\) 0.361548 + 0.626219i 0.00145200 + 0.00251494i
\(250\) 13.6931 + 7.90569i 0.0547723 + 0.0316228i
\(251\) 29.7311i 0.118450i 0.998245 + 0.0592252i \(0.0188630\pi\)
−0.998245 + 0.0592252i \(0.981137\pi\)
\(252\) 38.3312 + 17.1674i 0.152108 + 0.0681245i
\(253\) 503.177 1.98884
\(254\) −62.6336 + 108.484i −0.246589 + 0.427104i
\(255\) −61.1863 + 35.3259i −0.239946 + 0.138533i
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 382.457 + 220.811i 1.48816 + 0.859189i 0.999909 0.0135154i \(-0.00430222\pi\)
0.488250 + 0.872704i \(0.337636\pi\)
\(258\) 157.776i 0.611533i
\(259\) −265.283 + 191.848i −1.02426 + 0.740728i
\(260\) −15.6430 −0.0601654
\(261\) −79.6835 + 138.016i −0.305301 + 0.528796i
\(262\) −153.245 + 88.4762i −0.584905 + 0.337695i
\(263\) −171.523 297.087i −0.652180 1.12961i −0.982593 0.185772i \(-0.940521\pi\)
0.330413 0.943836i \(-0.392812\pi\)
\(264\) −84.7466 48.9285i −0.321010 0.185335i
\(265\) 145.065i 0.547413i
\(266\) 242.363 24.9341i 0.911139 0.0937371i
\(267\) 192.622 0.721431
\(268\) −16.2633 + 28.1689i −0.0606840 + 0.105108i
\(269\) 401.274 231.676i 1.49172 0.861247i 0.491769 0.870726i \(-0.336350\pi\)
0.999955 + 0.00947852i \(0.00301715\pi\)
\(270\) 8.21584 + 14.2302i 0.0304290 + 0.0527046i
\(271\) 211.814 + 122.291i 0.781600 + 0.451257i 0.836997 0.547207i \(-0.184309\pi\)
−0.0553967 + 0.998464i \(0.517642\pi\)
\(272\) 72.9689i 0.268268i
\(273\) −4.34015 42.1869i −0.0158980 0.154531i
\(274\) 55.0889 0.201054
\(275\) 49.9374 86.4942i 0.181591 0.314524i
\(276\) −75.5711 + 43.6310i −0.273808 + 0.158083i
\(277\) −70.5092 122.126i −0.254546 0.440887i 0.710226 0.703974i \(-0.248593\pi\)
−0.964772 + 0.263087i \(0.915259\pi\)
\(278\) −121.183 69.9650i −0.435910 0.251673i
\(279\) 90.3935i 0.323991i
\(280\) 25.9435 + 35.8739i 0.0926552 + 0.128121i
\(281\) 84.9953 0.302475 0.151237 0.988497i \(-0.451674\pi\)
0.151237 + 0.988497i \(0.451674\pi\)
\(282\) 34.3695 59.5297i 0.121878 0.211098i
\(283\) −101.047 + 58.3392i −0.357055 + 0.206146i −0.667788 0.744351i \(-0.732759\pi\)
0.310733 + 0.950497i \(0.399425\pi\)
\(284\) 107.725 + 186.585i 0.379312 + 0.656988i
\(285\) 82.5498 + 47.6601i 0.289648 + 0.167229i
\(286\) 98.8112i 0.345494i
\(287\) 90.2003 201.399i 0.314287 0.701738i
\(288\) 16.9706 0.0589256
\(289\) 21.8896 37.9138i 0.0757424 0.131190i
\(290\) −145.481 + 83.9937i −0.501660 + 0.289634i
\(291\) 64.2802 + 111.337i 0.220894 + 0.382600i
\(292\) −89.4789 51.6607i −0.306435 0.176920i
\(293\) 131.882i 0.450110i −0.974346 0.225055i \(-0.927744\pi\)
0.974346 0.225055i \(-0.0722562\pi\)
\(294\) −89.5487 + 79.9189i −0.304587 + 0.271833i
\(295\) 224.035 0.759441
\(296\) −66.1417 + 114.561i −0.223452 + 0.387030i
\(297\) 89.8874 51.8965i 0.302651 0.174736i
\(298\) −131.851 228.372i −0.442451 0.766348i
\(299\) 76.3080 + 44.0565i 0.255211 + 0.147346i
\(300\) 17.3205i 0.0577350i
\(301\) −411.496 184.296i −1.36710 0.612280i
\(302\) −218.977 −0.725090
\(303\) −75.8587 + 131.391i −0.250359 + 0.433634i
\(304\) 85.2570 49.2232i 0.280451 0.161918i
\(305\) 8.97107 + 15.5383i 0.0294133 + 0.0509454i
\(306\) −67.0263 38.6976i −0.219040 0.126463i
\(307\) 429.871i 1.40023i −0.714030 0.700115i \(-0.753132\pi\)
0.714030 0.700115i \(-0.246868\pi\)
\(308\) 226.603 163.875i 0.735723 0.532063i
\(309\) −240.826 −0.779373
\(310\) 47.6416 82.5176i 0.153683 0.266186i
\(311\) −217.786 + 125.739i −0.700277 + 0.404305i −0.807451 0.589935i \(-0.799153\pi\)
0.107174 + 0.994240i \(0.465820\pi\)
\(312\) −8.56803 14.8403i −0.0274616 0.0475649i
\(313\) 11.8674 + 6.85166i 0.0379151 + 0.0218903i 0.518838 0.854873i \(-0.326365\pi\)
−0.480923 + 0.876763i \(0.659698\pi\)
\(314\) 70.9988i 0.226111i
\(315\) −46.7109 + 4.80557i −0.148289 + 0.0152558i
\(316\) −43.9509 −0.139085
\(317\) 16.4651 28.5183i 0.0519403 0.0899632i −0.838886 0.544307i \(-0.816793\pi\)
0.890827 + 0.454343i \(0.150126\pi\)
\(318\) −137.620 + 79.4551i −0.432768 + 0.249859i
\(319\) 530.558 + 918.954i 1.66319 + 2.88073i
\(320\) 15.4919 + 8.94427i 0.0484123 + 0.0279508i
\(321\) 263.601i 0.821186i
\(322\) −25.5204 248.063i −0.0792560 0.770381i
\(323\) −448.970 −1.39000
\(324\) −9.00000 + 15.5885i −0.0277778 + 0.0481125i
\(325\) 15.1463 8.74471i 0.0466039 0.0269068i
\(326\) −81.8906 141.839i −0.251198 0.435088i
\(327\) 97.1331 + 56.0798i 0.297043 + 0.171498i
\(328\) 89.1662i 0.271848i
\(329\) 115.113 + 159.176i 0.349888 + 0.483816i
\(330\) 109.407 0.331538
\(331\) 208.940 361.895i 0.631240 1.09334i −0.356059 0.934464i \(-0.615880\pi\)
0.987299 0.158876i \(-0.0507869\pi\)
\(332\) −0.723095 + 0.417479i −0.00217800 + 0.00125747i
\(333\) −70.1539 121.510i −0.210672 0.364895i
\(334\) 75.1025 + 43.3605i 0.224858 + 0.129822i
\(335\) 36.3658i 0.108555i
\(336\) −19.8232 + 44.2611i −0.0589975 + 0.131729i
\(337\) −286.688 −0.850705 −0.425353 0.905028i \(-0.639850\pi\)
−0.425353 + 0.905028i \(0.639850\pi\)
\(338\) 110.849 191.997i 0.327957 0.568038i
\(339\) −4.88790 + 2.82203i −0.0144186 + 0.00832458i
\(340\) −40.7909 70.6519i −0.119973 0.207800i
\(341\) −521.234 300.935i −1.52855 0.882507i
\(342\) 104.418i 0.305316i
\(343\) −103.836 326.905i −0.302729 0.953077i
\(344\) −182.184 −0.529603
\(345\) 48.7809 84.4911i 0.141394 0.244902i
\(346\) 38.8264 22.4164i 0.112215 0.0647874i
\(347\) −153.398 265.693i −0.442069 0.765685i 0.555774 0.831333i \(-0.312422\pi\)
−0.997843 + 0.0656479i \(0.979089\pi\)
\(348\) −159.367 92.0105i −0.457951 0.264398i
\(349\) 340.162i 0.974676i 0.873214 + 0.487338i \(0.162032\pi\)
−0.873214 + 0.487338i \(0.837968\pi\)
\(350\) −45.1738 20.2319i −0.129068 0.0578055i
\(351\) 18.1755 0.0517821
\(352\) 56.4978 97.8570i 0.160505 0.278003i
\(353\) −324.761 + 187.501i −0.920004 + 0.531165i −0.883636 0.468174i \(-0.844912\pi\)
−0.0363676 + 0.999338i \(0.511579\pi\)
\(354\) 122.709 + 212.538i 0.346636 + 0.600391i
\(355\) −208.608 120.440i −0.587628 0.339267i
\(356\) 222.421i 0.624778i
\(357\) 179.220 129.609i 0.502018 0.363051i
\(358\) −186.527 −0.521025
\(359\) 164.750 285.356i 0.458915 0.794863i −0.539989 0.841672i \(-0.681572\pi\)
0.998904 + 0.0468084i \(0.0149050\pi\)
\(360\) −16.4317 + 9.48683i −0.0456435 + 0.0263523i
\(361\) 122.365 + 211.942i 0.338961 + 0.587098i
\(362\) −67.5362 38.9920i −0.186564 0.107713i
\(363\) 481.509i 1.32647i
\(364\) 48.7132 5.01157i 0.133828 0.0137681i
\(365\) 115.517 0.316484
\(366\) −9.82731 + 17.0214i −0.0268506 + 0.0465066i
\(367\) 23.5163 13.5772i 0.0640772 0.0369950i −0.467619 0.883930i \(-0.654888\pi\)
0.531696 + 0.846935i \(0.321555\pi\)
\(368\) −50.3807 87.2620i −0.136904 0.237125i
\(369\) 81.9044 + 47.2875i 0.221963 + 0.128151i
\(370\) 147.897i 0.399723i
\(371\) −46.4745 451.740i −0.125268 1.21763i
\(372\) 104.377 0.280585
\(373\) −63.7488 + 110.416i −0.170908 + 0.296022i −0.938738 0.344633i \(-0.888004\pi\)
0.767829 + 0.640654i \(0.221337\pi\)
\(374\) −446.283 + 257.661i −1.19327 + 0.688934i
\(375\) −9.68246 16.7705i −0.0258199 0.0447214i
\(376\) 68.7390 + 39.6865i 0.182817 + 0.105549i
\(377\) 185.816i 0.492880i
\(378\) −30.1436 41.6817i −0.0797449 0.110269i
\(379\) 319.795 0.843785 0.421893 0.906646i \(-0.361366\pi\)
0.421893 + 0.906646i \(0.361366\pi\)
\(380\) −55.0332 + 95.3202i −0.144824 + 0.250843i
\(381\) 132.866 76.7101i 0.348729 0.201339i
\(382\) 138.002 + 239.027i 0.361262 + 0.625724i
\(383\) 354.155 + 204.471i 0.924686 + 0.533867i 0.885127 0.465350i \(-0.154071\pi\)
0.0395587 + 0.999217i \(0.487405\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −127.798 + 285.346i −0.331942 + 0.741160i
\(386\) −493.221 −1.27777
\(387\) 96.6174 167.346i 0.249657 0.432419i
\(388\) −128.560 + 74.2244i −0.331341 + 0.191300i
\(389\) −193.576 335.284i −0.497626 0.861913i 0.502370 0.864652i \(-0.332461\pi\)
−0.999996 + 0.00273932i \(0.999128\pi\)
\(390\) 16.5919 + 9.57934i 0.0425434 + 0.0245624i
\(391\) 459.529i 1.17526i
\(392\) −92.2824 103.402i −0.235414 0.263780i
\(393\) 216.721 0.551454
\(394\) −39.8672 + 69.0521i −0.101186 + 0.175259i
\(395\) 42.5553 24.5693i 0.107735 0.0622008i
\(396\) 59.9249 + 103.793i 0.151326 + 0.262104i
\(397\) 26.0771 + 15.0556i 0.0656853 + 0.0379234i 0.532483 0.846441i \(-0.321259\pi\)
−0.466798 + 0.884364i \(0.654592\pi\)
\(398\) 242.266i 0.608709i
\(399\) −272.334 121.970i −0.682541 0.305689i
\(400\) −20.0000 −0.0500000
\(401\) −68.3852 + 118.447i −0.170537 + 0.295378i −0.938608 0.344987i \(-0.887883\pi\)
0.768071 + 0.640365i \(0.221217\pi\)
\(402\) 34.4997 19.9184i 0.0858201 0.0495482i
\(403\) −52.6977 91.2750i −0.130763 0.226489i
\(404\) −151.717 87.5941i −0.375538 0.216817i
\(405\) 20.1246i 0.0496904i
\(406\) 426.129 308.170i 1.04958 0.759038i
\(407\) −934.215 −2.29537
\(408\) 44.6842 77.3952i 0.109520 0.189694i
\(409\) −426.838 + 246.435i −1.04361 + 0.602531i −0.920855 0.389906i \(-0.872507\pi\)
−0.122759 + 0.992437i \(0.539174\pi\)
\(410\) 49.8454 + 86.3348i 0.121574 + 0.210573i
\(411\) −58.4306 33.7349i −0.142167 0.0820801i
\(412\) 278.082i 0.674957i
\(413\) −697.659 + 71.7744i −1.68925 + 0.173788i
\(414\) 106.874 0.258149
\(415\) 0.466756 0.808445i 0.00112471 0.00194806i
\(416\) 17.1361 9.89350i 0.0411924 0.0237825i
\(417\) 85.6892 + 148.418i 0.205490 + 0.355919i
\(418\) 602.104 + 347.625i 1.44044 + 0.831638i
\(419\) 311.640i 0.743771i 0.928279 + 0.371885i \(0.121289\pi\)
−0.928279 + 0.371885i \(0.878711\pi\)
\(420\) −5.54900 53.9371i −0.0132119 0.128422i
\(421\) −539.935 −1.28250 −0.641252 0.767330i \(-0.721585\pi\)
−0.641252 + 0.767330i \(0.721585\pi\)
\(422\) 114.578 198.456i 0.271513 0.470274i
\(423\) −72.9087 + 42.0939i −0.172361 + 0.0995127i
\(424\) −91.7469 158.910i −0.216384 0.374788i
\(425\) 78.9912 + 45.6056i 0.185862 + 0.107307i
\(426\) 263.871i 0.619414i
\(427\) −32.9145 45.5132i −0.0770831 0.106588i
\(428\) 304.380 0.711168
\(429\) 60.5093 104.805i 0.141047 0.244301i
\(430\) 176.398 101.844i 0.410229 0.236846i
\(431\) 314.021 + 543.900i 0.728586 + 1.26195i 0.957481 + 0.288497i \(0.0931555\pi\)
−0.228895 + 0.973451i \(0.573511\pi\)
\(432\) −18.0000 10.3923i −0.0416667 0.0240563i
\(433\) 706.789i 1.63231i −0.577836 0.816153i \(-0.696103\pi\)
0.577836 0.816153i \(-0.303897\pi\)
\(434\) −121.922 + 272.228i −0.280927 + 0.627253i
\(435\) 205.742 0.472970
\(436\) −64.7554 + 112.160i −0.148522 + 0.257247i
\(437\) 536.914 309.987i 1.22864 0.709353i
\(438\) 63.2712 + 109.589i 0.144455 + 0.250203i
\(439\) 564.452 + 325.886i 1.28577 + 0.742338i 0.977896 0.209090i \(-0.0670501\pi\)
0.307871 + 0.951428i \(0.400383\pi\)
\(440\) 126.333i 0.287120i
\(441\) 143.921 29.9297i 0.326351 0.0678677i
\(442\) −90.2398 −0.204162
\(443\) 11.8129 20.4605i 0.0266657 0.0461863i −0.852385 0.522915i \(-0.824844\pi\)
0.879050 + 0.476729i \(0.158178\pi\)
\(444\) 140.308 81.0068i 0.316009 0.182448i
\(445\) −124.337 215.358i −0.279409 0.483951i
\(446\) 447.435 + 258.326i 1.00322 + 0.579207i
\(447\) 322.967i 0.722520i
\(448\) −51.1083 22.8898i −0.114081 0.0510933i
\(449\) −55.1499 −0.122828 −0.0614141 0.998112i \(-0.519561\pi\)
−0.0614141 + 0.998112i \(0.519561\pi\)
\(450\) 10.6066 18.3712i 0.0235702 0.0408248i
\(451\) 545.346 314.856i 1.20919 0.698128i
\(452\) −3.25860 5.64407i −0.00720930 0.0124869i
\(453\) 232.260 + 134.096i 0.512716 + 0.296017i
\(454\) 364.689i 0.803279i
\(455\) −44.3648 + 32.0840i −0.0975051 + 0.0705142i
\(456\) −120.572 −0.264411
\(457\) −175.386 + 303.778i −0.383778 + 0.664723i −0.991599 0.129351i \(-0.958710\pi\)
0.607821 + 0.794074i \(0.292044\pi\)
\(458\) −18.8987 + 10.9112i −0.0412636 + 0.0238236i
\(459\) 47.3947 + 82.0901i 0.103256 + 0.178845i
\(460\) 97.5619 + 56.3274i 0.212091 + 0.122451i
\(461\) 471.598i 1.02299i 0.859287 + 0.511494i \(0.170908\pi\)
−0.859287 + 0.511494i \(0.829092\pi\)
\(462\) −340.701 + 35.0510i −0.737448 + 0.0758680i
\(463\) 387.112 0.836094 0.418047 0.908425i \(-0.362715\pi\)
0.418047 + 0.908425i \(0.362715\pi\)
\(464\) 106.245 184.021i 0.228975 0.396597i
\(465\) −101.063 + 58.3488i −0.217340 + 0.125481i
\(466\) −88.6336 153.518i −0.190201 0.329437i
\(467\) −254.045 146.673i −0.543994 0.314075i 0.202702 0.979240i \(-0.435028\pi\)
−0.746696 + 0.665166i \(0.768361\pi\)
\(468\) 20.9873i 0.0448446i
\(469\) 11.6506 + 113.245i 0.0248413 + 0.241461i
\(470\) −88.7417 −0.188812
\(471\) 43.4777 75.3056i 0.0923094 0.159885i
\(472\) −245.418 + 141.692i −0.519954 + 0.300195i
\(473\) −643.310 1114.25i −1.36006 2.35570i
\(474\) 46.6170 + 26.9143i 0.0983481 + 0.0567813i
\(475\) 123.058i 0.259069i
\(476\) 149.660 + 206.946i 0.314412 + 0.434760i
\(477\) 194.625 0.408018
\(478\) −2.56372 + 4.44049i −0.00536343 + 0.00928973i
\(479\) −660.805 + 381.516i −1.37955 + 0.796484i −0.992105 0.125409i \(-0.959976\pi\)
−0.387445 + 0.921893i \(0.626642\pi\)
\(480\) −10.9545 18.9737i −0.0228218 0.0395285i
\(481\) −141.676 81.7967i −0.294545 0.170056i
\(482\) 136.668i 0.283543i
\(483\) −124.838 + 278.738i −0.258464 + 0.577098i
\(484\) 555.999 1.14876
\(485\) 82.9854 143.735i 0.171104 0.296361i
\(486\) 19.0919 11.0227i 0.0392837 0.0226805i
\(487\) 111.944 + 193.893i 0.229865 + 0.398138i 0.957768 0.287542i \(-0.0928382\pi\)
−0.727903 + 0.685680i \(0.759505\pi\)
\(488\) −19.6546 11.3476i −0.0402759 0.0232533i
\(489\) 200.590i 0.410205i
\(490\) 147.155 + 48.5310i 0.300317 + 0.0990429i
\(491\) −837.694 −1.70610 −0.853049 0.521830i \(-0.825249\pi\)
−0.853049 + 0.521830i \(0.825249\pi\)
\(492\) −54.6029 + 94.5751i −0.110982 + 0.192226i
\(493\) −839.239 + 484.535i −1.70231 + 0.982829i
\(494\) 60.8737 + 105.436i 0.123226 + 0.213434i
\(495\) −116.044 66.9981i −0.234433 0.135350i
\(496\) 120.525i 0.242993i
\(497\) 688.203 + 308.225i 1.38471 + 0.620171i
\(498\) 1.02261 0.00205344
\(499\) −87.3234 + 151.249i −0.174997 + 0.303103i −0.940160 0.340733i \(-0.889325\pi\)
0.765163 + 0.643836i \(0.222658\pi\)
\(500\) 19.3649 11.1803i 0.0387298 0.0223607i
\(501\) −53.1055 91.9814i −0.105999 0.183596i
\(502\) 36.4130 + 21.0230i 0.0725358 + 0.0418786i
\(503\) 747.962i 1.48700i 0.668734 + 0.743501i \(0.266836\pi\)
−0.668734 + 0.743501i \(0.733164\pi\)
\(504\) 48.1299 34.8068i 0.0954958 0.0690611i
\(505\) 195.866 0.387854
\(506\) 355.800 616.263i 0.703162 1.21791i
\(507\) −235.147 + 135.762i −0.463801 + 0.267776i
\(508\) 88.5772 + 153.420i 0.174365 + 0.302008i
\(509\) −203.021 117.214i −0.398863 0.230284i 0.287130 0.957892i \(-0.407299\pi\)
−0.685993 + 0.727608i \(0.740632\pi\)
\(510\) 99.9168i 0.195915i
\(511\) −359.726 + 37.0083i −0.703965 + 0.0724233i
\(512\) −22.6274 −0.0441942
\(513\) 63.9428 110.752i 0.124645 0.215891i
\(514\) 540.875 312.275i 1.05229 0.607538i
\(515\) 155.453 + 269.252i 0.301850 + 0.522819i
\(516\) 193.235 + 111.564i 0.374486 + 0.216210i
\(517\) 560.549i 1.08423i
\(518\) 47.3821 + 460.561i 0.0914712 + 0.889114i
\(519\) −54.9088 −0.105797
\(520\) −11.0613 + 19.1587i −0.0212717 + 0.0368436i
\(521\) 186.068 107.427i 0.357137 0.206193i −0.310687 0.950512i \(-0.600559\pi\)
0.667824 + 0.744319i \(0.267226\pi\)
\(522\) 112.689 + 195.184i 0.215880 + 0.373915i
\(523\) 801.108 + 462.520i 1.53176 + 0.884360i 0.999281 + 0.0379137i \(0.0120712\pi\)
0.532475 + 0.846446i \(0.321262\pi\)
\(524\) 250.248i 0.477573i
\(525\) 35.5245 + 49.1224i 0.0676658 + 0.0935664i
\(526\) −485.141 −0.922321
\(527\) 274.830 476.020i 0.521499 0.903263i
\(528\) −119.850 + 69.1953i −0.226988 + 0.131052i
\(529\) −52.7773 91.4130i −0.0997681 0.172803i
\(530\) 177.667 + 102.576i 0.335221 + 0.193540i
\(531\) 300.575i 0.566054i
\(532\) 140.839 314.464i 0.264734 0.591098i
\(533\) 110.271 0.206887
\(534\) 136.204 235.913i 0.255064 0.441784i
\(535\) −294.714 + 170.153i −0.550868 + 0.318044i
\(536\) 22.9998 + 39.8368i 0.0429100 + 0.0743224i
\(537\) 197.842 + 114.224i 0.368420 + 0.212707i
\(538\) 655.277i 1.21799i
\(539\) 306.553 929.528i 0.568744 1.72454i
\(540\) 23.2379 0.0430331
\(541\) 57.1560 98.9971i 0.105649 0.182989i −0.808354 0.588696i \(-0.799641\pi\)
0.914003 + 0.405707i \(0.132975\pi\)
\(542\) 299.550 172.945i 0.552675 0.319087i
\(543\) 47.7553 + 82.7146i 0.0879472 + 0.152329i
\(544\) 89.3683 + 51.5968i 0.164280 + 0.0948471i
\(545\) 144.797i 0.265683i
\(546\) −54.7371 24.5151i −0.100251 0.0448994i
\(547\) −57.7698 −0.105612 −0.0528060 0.998605i \(-0.516817\pi\)
−0.0528060 + 0.998605i \(0.516817\pi\)
\(548\) 38.9538 67.4699i 0.0710835 0.123120i
\(549\) 20.8469 12.0359i 0.0379725 0.0219234i
\(550\) −70.6222 122.321i −0.128404 0.222402i
\(551\) 1132.26 + 653.712i 2.05492 + 1.18641i
\(552\) 123.407i 0.223564i
\(553\) −124.648 + 90.1438i −0.225404 + 0.163009i
\(554\) −199.430 −0.359982
\(555\) −90.5683 + 156.869i −0.163186 + 0.282647i
\(556\) −171.378 + 98.9454i −0.308235 + 0.177959i
\(557\) 203.076 + 351.738i 0.364589 + 0.631487i 0.988710 0.149841i \(-0.0478762\pi\)
−0.624121 + 0.781328i \(0.714543\pi\)
\(558\) −110.709 63.9179i −0.198403 0.114548i
\(559\) 225.304i 0.403049i
\(560\) 62.2812 6.40743i 0.111216 0.0114418i
\(561\) 631.139 1.12502
\(562\) 60.1008 104.098i 0.106941 0.185227i
\(563\) −370.911 + 214.146i −0.658813 + 0.380366i −0.791824 0.610749i \(-0.790869\pi\)
0.133012 + 0.991114i \(0.457535\pi\)
\(564\) −48.6058 84.1878i −0.0861805 0.149269i
\(565\) 6.31026 + 3.64323i 0.0111686 + 0.00644819i
\(566\) 165.008i 0.291534i
\(567\) 6.44735 + 62.6692i 0.0113710 + 0.110528i
\(568\) 304.691 0.536429
\(569\) 457.897 793.100i 0.804739 1.39385i −0.111728 0.993739i \(-0.535638\pi\)
0.916467 0.400110i \(-0.131028\pi\)
\(570\) 116.743 67.4016i 0.204812 0.118248i
\(571\) 356.947 + 618.250i 0.625125 + 1.08275i 0.988517 + 0.151112i \(0.0482855\pi\)
−0.363391 + 0.931637i \(0.618381\pi\)
\(572\) 121.019 + 69.8701i 0.211571 + 0.122151i
\(573\) 338.035i 0.589938i
\(574\) −182.881 252.883i −0.318608 0.440562i
\(575\) −125.952 −0.219047
\(576\) 12.0000 20.7846i 0.0208333 0.0360844i
\(577\) −75.8591 + 43.7973i −0.131472 + 0.0759052i −0.564293 0.825574i \(-0.690851\pi\)
0.432822 + 0.901480i \(0.357518\pi\)
\(578\) −30.9565 53.6183i −0.0535580 0.0927652i
\(579\) 523.140 + 302.035i 0.903523 + 0.521649i
\(580\) 237.570i 0.409604i
\(581\) −1.19450 + 2.66708i −0.00205594 + 0.00459050i
\(582\) 181.812 0.312392
\(583\) 647.937 1122.26i 1.11138 1.92497i
\(584\) −126.542 + 73.0593i −0.216682 + 0.125101i
\(585\) −11.7323 20.3209i −0.0200551 0.0347365i
\(586\) −161.522 93.2548i −0.275635 0.159138i
\(587\) 169.908i 0.289452i 0.989472 + 0.144726i \(0.0462300\pi\)
−0.989472 + 0.144726i \(0.953770\pi\)
\(588\) 34.5598 + 166.186i 0.0587752 + 0.282628i
\(589\) −741.576 −1.25904
\(590\) 158.417 274.386i 0.268503 0.465061i
\(591\) 84.5712 48.8272i 0.143098 0.0826179i
\(592\) 93.5385 + 162.014i 0.158004 + 0.273671i
\(593\) 173.424 + 100.126i 0.292452 + 0.168847i 0.639047 0.769168i \(-0.279329\pi\)
−0.346595 + 0.938015i \(0.612662\pi\)
\(594\) 146.785i 0.247114i
\(595\) −260.594 116.712i −0.437973 0.196155i
\(596\) −372.930 −0.625721
\(597\) −148.357 + 256.962i −0.248504 + 0.430422i
\(598\) 107.916 62.3053i 0.180461 0.104189i
\(599\) 350.201 + 606.566i 0.584643 + 1.01263i 0.994920 + 0.100671i \(0.0320988\pi\)
−0.410277 + 0.911961i \(0.634568\pi\)
\(600\) 21.2132 + 12.2474i 0.0353553 + 0.0204124i
\(601\) 1039.21i 1.72914i −0.502515 0.864569i \(-0.667592\pi\)
0.502515 0.864569i \(-0.332408\pi\)
\(602\) −516.687 + 373.660i −0.858285 + 0.620698i
\(603\) −48.7899 −0.0809119
\(604\) −154.840 + 268.191i −0.256358 + 0.444025i
\(605\) −538.344 + 310.813i −0.889825 + 0.513740i
\(606\) 107.280 + 185.815i 0.177030 + 0.306626i
\(607\) 52.9655 + 30.5796i 0.0872578 + 0.0503783i 0.542994 0.839737i \(-0.317291\pi\)
−0.455736 + 0.890115i \(0.650624\pi\)
\(608\) 139.224i 0.228987i
\(609\) −640.692 + 65.9138i −1.05204 + 0.108233i
\(610\) 25.3740 0.0415967
\(611\) −49.0798 + 85.0087i −0.0803270 + 0.139130i
\(612\) −94.7894 + 54.7267i −0.154885 + 0.0894227i
\(613\) 261.359 + 452.688i 0.426361 + 0.738479i 0.996546 0.0830371i \(-0.0264620\pi\)
−0.570185 + 0.821516i \(0.693129\pi\)
\(614\) −526.482 303.965i −0.857462 0.495056i
\(615\) 122.096i 0.198530i
\(616\) −40.4734 393.408i −0.0657036 0.638649i
\(617\) −608.200 −0.985738 −0.492869 0.870104i \(-0.664052\pi\)
−0.492869 + 0.870104i \(0.664052\pi\)
\(618\) −170.290 + 294.951i −0.275550 + 0.477267i
\(619\) 902.671 521.157i 1.45827 0.841934i 0.459346 0.888257i \(-0.348084\pi\)
0.998927 + 0.0463229i \(0.0147503\pi\)
\(620\) −67.3754 116.698i −0.108670 0.188222i
\(621\) −113.357 65.4465i −0.182539 0.105389i
\(622\) 355.643i 0.571774i
\(623\) 456.187 + 630.804i 0.732243 + 1.01253i
\(624\) −24.2340 −0.0388366
\(625\) −12.5000 + 21.6506i −0.0200000 + 0.0346410i
\(626\) 16.7831 9.68972i 0.0268100 0.0154788i
\(627\) −425.752 737.424i −0.679030 1.17611i
\(628\) 86.9554 + 50.2037i 0.138464 + 0.0799423i
\(629\) 853.176i 1.35640i
\(630\) −27.1440 + 60.6070i −0.0430857 + 0.0962015i
\(631\) −235.274 −0.372859 −0.186430 0.982468i \(-0.559692\pi\)
−0.186430 + 0.982468i \(0.559692\pi\)
\(632\) −31.0780 + 53.8287i −0.0491741 + 0.0851720i
\(633\) −243.057 + 140.329i −0.383977 + 0.221689i
\(634\) −23.2851 40.3310i −0.0367273 0.0636136i
\(635\) −171.529 99.0323i −0.270124 0.155956i
\(636\) 224.733i 0.353354i
\(637\) 127.876 114.125i 0.200747 0.179159i
\(638\) 1500.65 2.35211
\(639\) −161.587 + 279.877i −0.252875 + 0.437992i
\(640\) 21.9089 12.6491i 0.0342327 0.0197642i
\(641\) 58.4900 + 101.308i 0.0912481 + 0.158046i 0.908037 0.418891i \(-0.137581\pi\)
−0.816788 + 0.576937i \(0.804248\pi\)
\(642\) −322.843 186.394i −0.502871 0.290333i
\(643\) 874.209i 1.35958i 0.733408 + 0.679789i \(0.237929\pi\)
−0.733408 + 0.679789i \(0.762071\pi\)
\(644\) −321.859 144.151i −0.499781 0.223837i
\(645\) −249.465 −0.386768
\(646\) −317.470 + 549.874i −0.491439 + 0.851198i
\(647\) −10.1185 + 5.84189i −0.0156390 + 0.00902920i −0.507799 0.861476i \(-0.669541\pi\)
0.492160 + 0.870505i \(0.336207\pi\)
\(648\) 12.7279 + 22.0454i 0.0196419 + 0.0340207i
\(649\) −1733.20 1000.66i −2.67057 1.54185i
\(650\) 24.7338i 0.0380519i
\(651\) 296.023 214.079i 0.454720 0.328847i
\(652\) −231.622 −0.355248
\(653\) −319.067 + 552.641i −0.488618 + 0.846311i −0.999914 0.0130935i \(-0.995832\pi\)
0.511296 + 0.859404i \(0.329165\pi\)
\(654\) 137.367 79.3088i 0.210041 0.121267i
\(655\) −139.893 242.302i −0.213577 0.369927i
\(656\) −109.206 63.0500i −0.166472 0.0961129i
\(657\) 154.982i 0.235894i
\(658\) 276.347 28.4303i 0.419980 0.0432071i
\(659\) 870.363 1.32073 0.660367 0.750943i \(-0.270401\pi\)
0.660367 + 0.750943i \(0.270401\pi\)
\(660\) 77.3627 133.996i 0.117216 0.203025i
\(661\) 417.571 241.085i 0.631727 0.364728i −0.149694 0.988732i \(-0.547829\pi\)
0.781420 + 0.624005i \(0.214495\pi\)
\(662\) −295.486 511.797i −0.446354 0.773108i
\(663\) 95.7138 + 55.2604i 0.144365 + 0.0833490i
\(664\) 1.18081i 0.00177833i
\(665\) 39.4242 + 383.210i 0.0592846 + 0.576255i
\(666\) −198.425 −0.297936
\(667\) 669.085 1158.89i 1.00313 1.73747i
\(668\) 106.211 61.3210i 0.158999 0.0917978i
\(669\) −316.384 547.993i −0.472921 0.819123i
\(670\) −44.5389 25.7145i −0.0664759 0.0383799i
\(671\) 160.279i 0.238865i
\(672\) 40.1914 + 55.5756i 0.0598087 + 0.0827018i
\(673\) −399.323 −0.593347 −0.296674 0.954979i \(-0.595877\pi\)
−0.296674 + 0.954979i \(0.595877\pi\)
\(674\) −202.719 + 351.119i −0.300770 + 0.520948i
\(675\) −22.5000 + 12.9904i −0.0333333 + 0.0192450i
\(676\) −156.765 271.525i −0.231901 0.401664i
\(677\) 122.405 + 70.6707i 0.180805 + 0.104388i 0.587671 0.809100i \(-0.300045\pi\)
−0.406866 + 0.913488i \(0.633378\pi\)
\(678\) 7.98191i 0.0117727i
\(679\) −212.373 + 474.185i −0.312773 + 0.698358i
\(680\) −115.374 −0.169668
\(681\) −223.325 + 386.811i −0.327937 + 0.568004i
\(682\) −737.137 + 425.586i −1.08085 + 0.624026i
\(683\) −494.088 855.785i −0.723408 1.25298i −0.959626 0.281279i \(-0.909241\pi\)
0.236218 0.971700i \(-0.424092\pi\)
\(684\) 127.886 + 73.8347i 0.186967 + 0.107946i
\(685\) 87.1032i 0.127158i
\(686\) −473.799 103.984i −0.690669 0.151580i
\(687\) 26.7268 0.0389037
\(688\) −128.823 + 223.128i −0.187243 + 0.324314i
\(689\) 196.522 113.462i 0.285228 0.164677i
\(690\) −68.9867 119.488i −0.0999807 0.173172i
\(691\) 303.829 + 175.415i 0.439694 + 0.253857i 0.703468 0.710727i \(-0.251634\pi\)
−0.263774 + 0.964585i \(0.584967\pi\)
\(692\) 63.4033i 0.0916232i
\(693\) 382.832 + 171.459i 0.552428 + 0.247415i
\(694\) −433.875 −0.625180
\(695\) 110.624 191.607i 0.159172 0.275693i
\(696\) −225.379 + 130.123i −0.323820 + 0.186958i
\(697\) 287.543 + 498.040i 0.412544 + 0.714548i
\(698\) 416.611 + 240.531i 0.596864 + 0.344600i
\(699\) 217.107i 0.310597i
\(700\) −56.7216 + 41.0202i −0.0810309 + 0.0586003i
\(701\) 307.500 0.438659 0.219330 0.975651i \(-0.429613\pi\)
0.219330 + 0.975651i \(0.429613\pi\)
\(702\) 12.8520 22.2604i 0.0183077 0.0317100i
\(703\) −996.852 + 575.533i −1.41800 + 0.818681i
\(704\) −79.8999 138.391i −0.113494 0.196578i
\(705\) 94.1248 + 54.3430i 0.133510 + 0.0770822i
\(706\) 530.333i 0.751180i
\(707\) −609.939 + 62.7500i −0.862715 + 0.0887552i
\(708\) 347.074 0.490217
\(709\) 49.0712 84.9938i 0.0692118 0.119878i −0.829343 0.558740i \(-0.811285\pi\)
0.898555 + 0.438862i \(0.144618\pi\)
\(710\) −295.016 + 170.328i −0.415516 + 0.239898i
\(711\) −32.9632 57.0939i −0.0463617 0.0803009i
\(712\) 272.409 + 157.275i 0.382597 + 0.220892i
\(713\) 759.016i 1.06454i
\(714\) −32.0105 311.147i −0.0448326 0.435780i
\(715\) −156.234 −0.218510
\(716\) −131.894 + 228.448i −0.184210 + 0.319061i
\(717\) 5.43847 3.13990i 0.00758503 0.00437922i
\(718\) −232.992 403.554i −0.324502 0.562053i
\(719\) 612.340 + 353.535i 0.851655 + 0.491703i 0.861209 0.508251i \(-0.169708\pi\)
−0.00955403 + 0.999954i \(0.503041\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) −570.349 788.664i −0.791053 1.09385i
\(722\) 346.100 0.479363
\(723\) −83.6915 + 144.958i −0.115756 + 0.200495i
\(724\) −95.5106 + 55.1431i −0.131921 + 0.0761645i
\(725\) −132.806 230.026i −0.183180 0.317278i
\(726\) −589.726 340.479i −0.812295 0.468979i
\(727\) 1353.85i 1.86225i 0.364705 + 0.931123i \(0.381170\pi\)
−0.364705 + 0.931123i \(0.618830\pi\)
\(728\) 28.3076 63.2050i 0.0388840 0.0868201i
\(729\) −27.0000 −0.0370370
\(730\) 81.6827 141.479i 0.111894 0.193806i
\(731\) 1017.59 587.506i 1.39205 0.803701i
\(732\) 13.8979 + 24.0719i 0.0189862 + 0.0328851i
\(733\) −478.941 276.517i −0.653398 0.377240i 0.136359 0.990660i \(-0.456460\pi\)
−0.789757 + 0.613420i \(0.789793\pi\)
\(734\) 38.4020i 0.0523188i
\(735\) −126.363 141.589i −0.171922 0.192638i
\(736\) −142.498 −0.193612
\(737\) −162.429 + 281.336i −0.220393 + 0.381732i
\(738\) 115.830 66.8747i 0.156952 0.0906161i
\(739\) −466.739 808.416i −0.631582 1.09393i −0.987228 0.159312i \(-0.949072\pi\)
0.355646 0.934621i \(-0.384261\pi\)
\(740\) −181.137 104.579i −0.244779 0.141323i
\(741\) 149.110i 0.201227i
\(742\) −586.128 262.509i −0.789930 0.353785i
\(743\) 554.921 0.746865 0.373432 0.927657i \(-0.378181\pi\)
0.373432 + 0.927657i \(0.378181\pi\)
\(744\) 73.8060 127.836i 0.0992016 0.171822i
\(745\) 361.088 208.474i 0.484681 0.279831i
\(746\) 90.1544 + 156.152i 0.120850 + 0.209319i
\(747\) −1.08464 0.626219i −0.00145200 0.000838312i
\(748\) 728.776i 0.974300i
\(749\) 863.246 624.286i 1.15253 0.833492i
\(750\) −27.3861 −0.0365148
\(751\) −363.974 + 630.421i −0.484652 + 0.839442i −0.999845 0.0176322i \(-0.994387\pi\)
0.515192 + 0.857075i \(0.327721\pi\)
\(752\) 97.2117 56.1252i 0.129271 0.0746345i
\(753\) −25.7479 44.5966i −0.0341937 0.0592252i
\(754\) 227.577 + 131.391i 0.301826 + 0.174259i
\(755\) 346.233i 0.458587i
\(756\) −72.3642 + 7.44476i −0.0957198 + 0.00984756i
\(757\) 667.167 0.881330 0.440665 0.897672i \(-0.354743\pi\)
0.440665 + 0.897672i \(0.354743\pi\)
\(758\) 226.129 391.667i 0.298323 0.516711i
\(759\) −754.765 + 435.764i −0.994421 + 0.574129i
\(760\) 77.8287 + 134.803i 0.102406 + 0.177373i
\(761\) −630.061 363.766i −0.827938 0.478010i 0.0252080 0.999682i \(-0.491975\pi\)
−0.853146 + 0.521672i \(0.825309\pi\)
\(762\) 216.969i 0.284736i
\(763\) 46.3890 + 450.908i 0.0607981 + 0.590967i
\(764\) 390.329 0.510901
\(765\) 61.1863 105.978i 0.0799821 0.138533i
\(766\) 500.850 289.166i 0.653851 0.377501i
\(767\) −175.229 303.506i −0.228460 0.395705i
\(768\) 24.0000 + 13.8564i 0.0312500 + 0.0180422i
\(769\) 1374.28i 1.78709i −0.448969 0.893547i \(-0.648209\pi\)
0.448969 0.893547i \(-0.351791\pi\)
\(770\) 259.110 + 358.290i 0.336506