Properties

Label 105.3.k.c.83.3
Level 105
Weight 3
Character 105.83
Analytic conductor 2.861
Analytic rank 0
Dimension 16
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 83.3
Root \(0.611750 + 0.253395i\) of \(x^{16} + 433 x^{8} + 16\)
Character \(\chi\) \(=\) 105.83
Dual form 105.3.k.c.62.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.152778 - 2.99611i) q^{3} -3.00000i q^{4} +(4.24762 + 2.63775i) q^{5} +(-2.22660 + 2.01054i) q^{6} +(5.49694 - 4.33402i) q^{7} +(-4.94975 + 4.94975i) q^{8} +(-8.95332 - 0.915476i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.152778 - 2.99611i) q^{3} -3.00000i q^{4} +(4.24762 + 2.63775i) q^{5} +(-2.22660 + 2.01054i) q^{6} +(5.49694 - 4.33402i) q^{7} +(-4.94975 + 4.94975i) q^{8} +(-8.95332 - 0.915476i) q^{9} +(-1.13835 - 4.86869i) q^{10} -13.9031i q^{11} +(-8.98832 - 0.458333i) q^{12} +(-14.6307 + 14.6307i) q^{13} +(-6.95153 - 0.822309i) q^{14} +(8.55193 - 12.3233i) q^{15} -5.00000 q^{16} +(4.86435 - 4.86435i) q^{17} +(5.68361 + 6.97829i) q^{18} +21.7515 q^{19} +(7.91326 - 12.7429i) q^{20} +(-12.1454 - 17.1316i) q^{21} +(-9.83095 + 9.83095i) q^{22} +(-1.77282 + 1.77282i) q^{23} +(14.0738 + 15.5862i) q^{24} +(11.0845 + 22.4083i) q^{25} +20.6909 q^{26} +(-4.11073 + 26.6852i) q^{27} +(-13.0020 - 16.4908i) q^{28} +28.0452 q^{29} +(-14.7610 + 2.66678i) q^{30} -17.2472i q^{31} +(23.3345 + 23.3345i) q^{32} +(-41.6551 - 2.12408i) q^{33} -6.87923 q^{34} +(34.7809 - 3.90969i) q^{35} +(-2.74643 + 26.8600i) q^{36} +(-6.50714 + 6.50714i) q^{37} +(-15.3806 - 15.3806i) q^{38} +(41.5998 + 46.0702i) q^{39} +(-34.0808 + 7.96843i) q^{40} +26.7192 q^{41} +(-3.52576 + 20.7019i) q^{42} +(33.1548 + 33.1548i) q^{43} -41.7092 q^{44} +(-35.6155 - 27.5052i) q^{45} +2.50714 q^{46} +(-18.5656 + 18.5656i) q^{47} +(-0.763888 + 14.9805i) q^{48} +(11.4326 - 47.6476i) q^{49} +(8.00714 - 23.6830i) q^{50} +(-13.8310 - 15.3173i) q^{51} +(43.8920 + 43.8920i) q^{52} +(48.3021 - 48.3021i) q^{53} +(21.7760 - 15.9626i) q^{54} +(36.6728 - 59.0549i) q^{55} +(-5.75616 + 48.6607i) q^{56} +(3.32314 - 65.1697i) q^{57} +(-19.8310 - 19.8310i) q^{58} +29.6668i q^{59} +(-36.9700 - 25.6558i) q^{60} -21.0717i q^{61} +(-12.1956 + 12.1956i) q^{62} +(-53.1835 + 33.7715i) q^{63} -13.0000i q^{64} +(-100.737 + 23.5534i) q^{65} +(27.9526 + 30.9565i) q^{66} +(-32.4786 + 32.4786i) q^{67} +(-14.5931 - 14.5931i) q^{68} +(5.04071 + 5.58240i) q^{69} +(-27.3584 - 21.8293i) q^{70} -16.0345i q^{71} +(48.8480 - 39.7853i) q^{72} +(-57.3597 + 57.3597i) q^{73} +9.20249 q^{74} +(68.8312 - 29.7869i) q^{75} -65.2544i q^{76} +(-60.2561 - 76.4243i) q^{77} +(3.16110 - 61.9921i) q^{78} -75.8024i q^{79} +(-21.2381 - 13.1888i) q^{80} +(79.3238 + 16.3931i) q^{81} +(-18.8933 - 18.8933i) q^{82} +(-51.9675 - 51.9675i) q^{83} +(-51.3947 + 36.4361i) q^{84} +(33.4929 - 7.83095i) q^{85} -46.8879i q^{86} +(4.28468 - 84.0264i) q^{87} +(68.8167 + 68.8167i) q^{88} +174.294i q^{89} +(5.73481 + 44.6331i) q^{90} +(-17.0143 + 143.833i) q^{91} +(5.31846 + 5.31846i) q^{92} +(-51.6745 - 2.63499i) q^{93} +26.2557 q^{94} +(92.3919 + 57.3750i) q^{95} +(73.4777 - 66.3477i) q^{96} +(16.6658 + 16.6658i) q^{97} +(-41.7760 + 25.6079i) q^{98} +(-12.7279 + 124.479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 32q^{7} + O(q^{10}) \) \( 16q + 32q^{7} + 80q^{15} - 80q^{16} + 8q^{18} - 64q^{21} - 64q^{22} + 224q^{25} - 96q^{28} - 128q^{30} + 96q^{36} - 384q^{37} - 112q^{42} + 64q^{43} + 320q^{46} - 128q^{51} + 408q^{57} - 224q^{58} - 120q^{60} - 72q^{63} + 320q^{67} + 128q^{70} + 56q^{72} - 424q^{78} + 896q^{81} + 256q^{85} + 448q^{88} - 832q^{91} + 32q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\)

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 0.707107i −0.353553 0.353553i 0.507877 0.861430i \(-0.330431\pi\)
−0.861430 + 0.507877i \(0.830431\pi\)
\(3\) 0.152778 2.99611i 0.0509259 0.998702i
\(4\) 3.00000i 0.750000i
\(5\) 4.24762 + 2.63775i 0.849524 + 0.527550i
\(6\) −2.22660 + 2.01054i −0.371100 + 0.335090i
\(7\) 5.49694 4.33402i 0.785277 0.619145i
\(8\) −4.94975 + 4.94975i −0.618718 + 0.618718i
\(9\) −8.95332 0.915476i −0.994813 0.101720i
\(10\) −1.13835 4.86869i −0.113835 0.486869i
\(11\) 13.9031i 1.26392i −0.775003 0.631958i \(-0.782252\pi\)
0.775003 0.631958i \(-0.217748\pi\)
\(12\) −8.98832 0.458333i −0.749027 0.0381944i
\(13\) −14.6307 + 14.6307i −1.12543 + 1.12543i −0.134524 + 0.990910i \(0.542951\pi\)
−0.990910 + 0.134524i \(0.957049\pi\)
\(14\) −6.95153 0.822309i −0.496538 0.0587364i
\(15\) 8.55193 12.3233i 0.570129 0.821555i
\(16\) −5.00000 −0.312500
\(17\) 4.86435 4.86435i 0.286138 0.286138i −0.549413 0.835551i \(-0.685149\pi\)
0.835551 + 0.549413i \(0.185149\pi\)
\(18\) 5.68361 + 6.97829i 0.315756 + 0.387683i
\(19\) 21.7515 1.14481 0.572407 0.819970i \(-0.306010\pi\)
0.572407 + 0.819970i \(0.306010\pi\)
\(20\) 7.91326 12.7429i 0.395663 0.637143i
\(21\) −12.1454 17.1316i −0.578351 0.815788i
\(22\) −9.83095 + 9.83095i −0.446861 + 0.446861i
\(23\) −1.77282 + 1.77282i −0.0770791 + 0.0770791i −0.744595 0.667516i \(-0.767357\pi\)
0.667516 + 0.744595i \(0.267357\pi\)
\(24\) 14.0738 + 15.5862i 0.586407 + 0.649424i
\(25\) 11.0845 + 22.4083i 0.443381 + 0.896333i
\(26\) 20.6909 0.795802
\(27\) −4.11073 + 26.6852i −0.152249 + 0.988342i
\(28\) −13.0020 16.4908i −0.464359 0.588957i
\(29\) 28.0452 0.967076 0.483538 0.875323i \(-0.339352\pi\)
0.483538 + 0.875323i \(0.339352\pi\)
\(30\) −14.7610 + 2.66678i −0.492035 + 0.0888928i
\(31\) 17.2472i 0.556362i −0.960529 0.278181i \(-0.910268\pi\)
0.960529 0.278181i \(-0.0897315\pi\)
\(32\) 23.3345 + 23.3345i 0.729204 + 0.729204i
\(33\) −41.6551 2.12408i −1.26228 0.0643660i
\(34\) −6.87923 −0.202330
\(35\) 34.7809 3.90969i 0.993741 0.111705i
\(36\) −2.74643 + 26.8600i −0.0762897 + 0.746110i
\(37\) −6.50714 + 6.50714i −0.175869 + 0.175869i −0.789552 0.613683i \(-0.789687\pi\)
0.613683 + 0.789552i \(0.289687\pi\)
\(38\) −15.3806 15.3806i −0.404753 0.404753i
\(39\) 41.5998 + 46.0702i 1.06666 + 1.18129i
\(40\) −34.0808 + 7.96843i −0.852021 + 0.199211i
\(41\) 26.7192 0.651687 0.325844 0.945424i \(-0.394352\pi\)
0.325844 + 0.945424i \(0.394352\pi\)
\(42\) −3.52576 + 20.7019i −0.0839468 + 0.492903i
\(43\) 33.1548 + 33.1548i 0.771041 + 0.771041i 0.978289 0.207248i \(-0.0664506\pi\)
−0.207248 + 0.978289i \(0.566451\pi\)
\(44\) −41.7092 −0.947936
\(45\) −35.6155 27.5052i −0.791455 0.611227i
\(46\) 2.50714 0.0545031
\(47\) −18.5656 + 18.5656i −0.395012 + 0.395012i −0.876470 0.481457i \(-0.840108\pi\)
0.481457 + 0.876470i \(0.340108\pi\)
\(48\) −0.763888 + 14.9805i −0.0159143 + 0.312095i
\(49\) 11.4326 47.6476i 0.233319 0.972400i
\(50\) 8.00714 23.6830i 0.160143 0.473661i
\(51\) −13.8310 15.3173i −0.271195 0.300339i
\(52\) 43.8920 + 43.8920i 0.844076 + 0.844076i
\(53\) 48.3021 48.3021i 0.911361 0.911361i −0.0850185 0.996379i \(-0.527095\pi\)
0.996379 + 0.0850185i \(0.0270949\pi\)
\(54\) 21.7760 15.9626i 0.403260 0.295603i
\(55\) 36.6728 59.0549i 0.666779 1.07373i
\(56\) −5.75616 + 48.6607i −0.102789 + 0.868942i
\(57\) 3.32314 65.1697i 0.0583006 1.14333i
\(58\) −19.8310 19.8310i −0.341913 0.341913i
\(59\) 29.6668i 0.502826i 0.967880 + 0.251413i \(0.0808953\pi\)
−0.967880 + 0.251413i \(0.919105\pi\)
\(60\) −36.9700 25.6558i −0.616167 0.427597i
\(61\) 21.0717i 0.345438i −0.984971 0.172719i \(-0.944745\pi\)
0.984971 0.172719i \(-0.0552552\pi\)
\(62\) −12.1956 + 12.1956i −0.196704 + 0.196704i
\(63\) −53.1835 + 33.7715i −0.844183 + 0.536056i
\(64\) 13.0000i 0.203125i
\(65\) −100.737 + 23.5534i −1.54981 + 0.362360i
\(66\) 27.9526 + 30.9565i 0.423525 + 0.469038i
\(67\) −32.4786 + 32.4786i −0.484755 + 0.484755i −0.906646 0.421892i \(-0.861366\pi\)
0.421892 + 0.906646i \(0.361366\pi\)
\(68\) −14.5931 14.5931i −0.214604 0.214604i
\(69\) 5.04071 + 5.58240i 0.0730537 + 0.0809044i
\(70\) −27.3584 21.8293i −0.390834 0.311847i
\(71\) 16.0345i 0.225838i −0.993604 0.112919i \(-0.963980\pi\)
0.993604 0.112919i \(-0.0360200\pi\)
\(72\) 48.8480 39.7853i 0.678445 0.552573i
\(73\) −57.3597 + 57.3597i −0.785749 + 0.785749i −0.980794 0.195045i \(-0.937515\pi\)
0.195045 + 0.980794i \(0.437515\pi\)
\(74\) 9.20249 0.124358
\(75\) 68.8312 29.7869i 0.917750 0.397159i
\(76\) 65.2544i 0.858610i
\(77\) −60.2561 76.4243i −0.782547 0.992523i
\(78\) 3.16110 61.9921i 0.0405269 0.794770i
\(79\) 75.8024i 0.959524i −0.877399 0.479762i \(-0.840723\pi\)
0.877399 0.479762i \(-0.159277\pi\)
\(80\) −21.2381 13.1888i −0.265476 0.164860i
\(81\) 79.3238 + 16.3931i 0.979306 + 0.202384i
\(82\) −18.8933 18.8933i −0.230406 0.230406i
\(83\) −51.9675 51.9675i −0.626114 0.626114i 0.320974 0.947088i \(-0.395990\pi\)
−0.947088 + 0.320974i \(0.895990\pi\)
\(84\) −51.3947 + 36.4361i −0.611841 + 0.433763i
\(85\) 33.4929 7.83095i 0.394034 0.0921288i
\(86\) 46.8879i 0.545208i
\(87\) 4.28468 84.0264i 0.0492492 0.965821i
\(88\) 68.8167 + 68.8167i 0.782008 + 0.782008i
\(89\) 174.294i 1.95836i 0.202987 + 0.979181i \(0.434935\pi\)
−0.202987 + 0.979181i \(0.565065\pi\)
\(90\) 5.73481 + 44.6331i 0.0637201 + 0.495923i
\(91\) −17.0143 + 143.833i −0.186970 + 1.58058i
\(92\) 5.31846 + 5.31846i 0.0578093 + 0.0578093i
\(93\) −51.6745 2.63499i −0.555640 0.0283332i
\(94\) 26.2557 0.279316
\(95\) 92.3919 + 57.3750i 0.972547 + 0.603947i
\(96\) 73.4777 66.3477i 0.765393 0.691122i
\(97\) 16.6658 + 16.6658i 0.171812 + 0.171812i 0.787775 0.615963i \(-0.211233\pi\)
−0.615963 + 0.787775i \(0.711233\pi\)
\(98\) −41.7760 + 25.6079i −0.426286 + 0.261305i
\(99\) −12.7279 + 124.479i −0.128565 + 1.25736i
\(100\) 67.2250 33.2536i 0.672250 0.332536i
\(101\) −113.114 −1.11994 −0.559968 0.828514i \(-0.689187\pi\)
−0.559968 + 0.828514i \(0.689187\pi\)
\(102\) −1.05099 + 20.6109i −0.0103038 + 0.202068i
\(103\) 16.1826 16.1826i 0.157113 0.157113i −0.624173 0.781286i \(-0.714564\pi\)
0.781286 + 0.624173i \(0.214564\pi\)
\(104\) 144.836i 1.39265i
\(105\) −6.40009 104.805i −0.0609533 0.998141i
\(106\) −68.3095 −0.644429
\(107\) 139.010 + 139.010i 1.29916 + 1.29916i 0.928945 + 0.370218i \(0.120717\pi\)
0.370218 + 0.928945i \(0.379283\pi\)
\(108\) 80.0557 + 12.3322i 0.741257 + 0.114187i
\(109\) 3.01429i 0.0276540i −0.999904 0.0138270i \(-0.995599\pi\)
0.999904 0.0138270i \(-0.00440141\pi\)
\(110\) −67.6897 + 15.8265i −0.615361 + 0.143877i
\(111\) 18.5020 + 20.4902i 0.166684 + 0.184597i
\(112\) −27.4847 + 21.6701i −0.245399 + 0.193483i
\(113\) −80.1118 + 80.1118i −0.708954 + 0.708954i −0.966315 0.257361i \(-0.917147\pi\)
0.257361 + 0.966315i \(0.417147\pi\)
\(114\) −48.4318 + 43.7321i −0.424840 + 0.383615i
\(115\) −12.2065 + 2.85400i −0.106144 + 0.0248174i
\(116\) 84.1356i 0.725307i
\(117\) 144.387 117.599i 1.23408 1.00512i
\(118\) 20.9776 20.9776i 0.177776 0.177776i
\(119\) 5.65685 47.8212i 0.0475366 0.401859i
\(120\) 18.6675 + 103.327i 0.155562 + 0.861061i
\(121\) −72.2952 −0.597481
\(122\) −14.8999 + 14.8999i −0.122131 + 0.122131i
\(123\) 4.08209 80.0535i 0.0331877 0.650842i
\(124\) −51.7417 −0.417272
\(125\) −12.0248 + 124.420i −0.0961984 + 0.995362i
\(126\) 61.4865 + 13.7264i 0.487988 + 0.108939i
\(127\) −71.6476 + 71.6476i −0.564154 + 0.564154i −0.930485 0.366330i \(-0.880614\pi\)
0.366330 + 0.930485i \(0.380614\pi\)
\(128\) 84.1457 84.1457i 0.657388 0.657388i
\(129\) 104.401 94.2699i 0.809306 0.730775i
\(130\) 87.8869 + 54.5774i 0.676053 + 0.419826i
\(131\) −79.4683 −0.606629 −0.303314 0.952891i \(-0.598093\pi\)
−0.303314 + 0.952891i \(0.598093\pi\)
\(132\) −6.37223 + 124.965i −0.0482745 + 0.946706i
\(133\) 119.566 94.2712i 0.898996 0.708806i
\(134\) 45.9316 0.342773
\(135\) −87.8499 + 102.506i −0.650740 + 0.759301i
\(136\) 48.1546i 0.354078i
\(137\) −7.42967 7.42967i −0.0542312 0.0542312i 0.679471 0.733702i \(-0.262209\pi\)
−0.733702 + 0.679471i \(0.762209\pi\)
\(138\) 0.383035 7.51167i 0.00277562 0.0544324i
\(139\) −179.589 −1.29201 −0.646003 0.763335i \(-0.723561\pi\)
−0.646003 + 0.763335i \(0.723561\pi\)
\(140\) −11.7291 104.343i −0.0837790 0.745306i
\(141\) 52.7881 + 58.4609i 0.374384 + 0.414616i
\(142\) −11.3381 + 11.3381i −0.0798457 + 0.0798457i
\(143\) 203.411 + 203.411i 1.42245 + 1.42245i
\(144\) 44.7666 + 4.57738i 0.310879 + 0.0317874i
\(145\) 119.125 + 73.9763i 0.821554 + 0.510181i
\(146\) 81.1188 0.555609
\(147\) −141.011 41.5328i −0.959257 0.282536i
\(148\) 19.5214 + 19.5214i 0.131902 + 0.131902i
\(149\) −24.7386 −0.166031 −0.0830155 0.996548i \(-0.526455\pi\)
−0.0830155 + 0.996548i \(0.526455\pi\)
\(150\) −69.7336 27.6085i −0.464890 0.184057i
\(151\) −163.324 −1.08161 −0.540807 0.841147i \(-0.681881\pi\)
−0.540807 + 0.841147i \(0.681881\pi\)
\(152\) −107.664 + 107.664i −0.708317 + 0.708317i
\(153\) −48.0053 + 39.0989i −0.313760 + 0.255548i
\(154\) −11.4326 + 96.6476i −0.0742378 + 0.627582i
\(155\) 45.4939 73.2596i 0.293509 0.472643i
\(156\) 138.211 124.799i 0.885966 0.799995i
\(157\) −108.368 108.368i −0.690244 0.690244i 0.272042 0.962285i \(-0.412301\pi\)
−0.962285 + 0.272042i \(0.912301\pi\)
\(158\) −53.6004 + 53.6004i −0.339243 + 0.339243i
\(159\) −137.339 152.098i −0.863766 0.956590i
\(160\) 37.5655 + 160.667i 0.234784 + 1.00417i
\(161\) −2.06165 + 17.4285i −0.0128053 + 0.108252i
\(162\) −44.4987 67.6821i −0.274684 0.417791i
\(163\) 38.8452 + 38.8452i 0.238314 + 0.238314i 0.816152 0.577837i \(-0.196103\pi\)
−0.577837 + 0.816152i \(0.696103\pi\)
\(164\) 80.1575i 0.488765i
\(165\) −171.332 118.898i −1.03838 0.720594i
\(166\) 73.4931i 0.442730i
\(167\) 138.252 138.252i 0.827855 0.827855i −0.159365 0.987220i \(-0.550945\pi\)
0.987220 + 0.159365i \(0.0509447\pi\)
\(168\) 144.913 + 24.6804i 0.862579 + 0.146907i
\(169\) 259.112i 1.53321i
\(170\) −29.2203 18.1457i −0.171884 0.106739i
\(171\) −194.748 19.9129i −1.13888 0.116450i
\(172\) 99.4643 99.4643i 0.578281 0.578281i
\(173\) −26.9566 26.9566i −0.155818 0.155818i 0.624893 0.780711i \(-0.285143\pi\)
−0.780711 + 0.624893i \(0.785143\pi\)
\(174\) −62.4454 + 56.3859i −0.358882 + 0.324057i
\(175\) 158.049 + 75.1367i 0.903137 + 0.429352i
\(176\) 69.5153i 0.394973i
\(177\) 88.8848 + 4.53242i 0.502174 + 0.0256069i
\(178\) 123.245 123.245i 0.692386 0.692386i
\(179\) −187.393 −1.04689 −0.523445 0.852059i \(-0.675354\pi\)
−0.523445 + 0.852059i \(0.675354\pi\)
\(180\) −82.5157 + 106.846i −0.458420 + 0.593591i
\(181\) 179.581i 0.992158i −0.868277 0.496079i \(-0.834773\pi\)
0.868277 0.496079i \(-0.165227\pi\)
\(182\) 113.736 89.6745i 0.624925 0.492717i
\(183\) −63.1331 3.21928i −0.344990 0.0175917i
\(184\) 17.5500i 0.0953805i
\(185\) −44.8041 + 10.4756i −0.242184 + 0.0566250i
\(186\) 34.6762 + 38.4026i 0.186431 + 0.206466i
\(187\) −67.6294 67.6294i −0.361654 0.361654i
\(188\) 55.6968 + 55.6968i 0.296259 + 0.296259i
\(189\) 93.0578 + 164.503i 0.492369 + 0.870386i
\(190\) −24.7607 105.901i −0.130320 0.557375i
\(191\) 107.063i 0.560538i 0.959922 + 0.280269i \(0.0904236\pi\)
−0.959922 + 0.280269i \(0.909576\pi\)
\(192\) −38.9494 1.98611i −0.202861 0.0103443i
\(193\) −81.6333 81.6333i −0.422971 0.422971i 0.463255 0.886225i \(-0.346682\pi\)
−0.886225 + 0.463255i \(0.846682\pi\)
\(194\) 23.5689i 0.121489i
\(195\) 55.1781 + 305.419i 0.282964 + 1.56625i
\(196\) −142.943 34.2979i −0.729300 0.174989i
\(197\) −165.702 165.702i −0.841127 0.841127i 0.147878 0.989006i \(-0.452756\pi\)
−0.989006 + 0.147878i \(0.952756\pi\)
\(198\) 97.0196 79.0196i 0.489998 0.399089i
\(199\) 220.037 1.10571 0.552857 0.833276i \(-0.313538\pi\)
0.552857 + 0.833276i \(0.313538\pi\)
\(200\) −165.781 56.0500i −0.828906 0.280250i
\(201\) 92.3473 + 102.271i 0.459439 + 0.508812i
\(202\) 79.9833 + 79.9833i 0.395957 + 0.395957i
\(203\) 154.163 121.548i 0.759422 0.598760i
\(204\) −45.9518 + 41.4929i −0.225254 + 0.203396i
\(205\) 113.493 + 70.4786i 0.553624 + 0.343798i
\(206\) −22.8856 −0.111095
\(207\) 17.4956 14.2496i 0.0845197 0.0688388i
\(208\) 73.1533 73.1533i 0.351698 0.351698i
\(209\) 302.412i 1.44695i
\(210\) −69.5826 + 78.6337i −0.331346 + 0.374446i
\(211\) 276.590 1.31086 0.655428 0.755258i \(-0.272488\pi\)
0.655428 + 0.755258i \(0.272488\pi\)
\(212\) −144.906 144.906i −0.683521 0.683521i
\(213\) −48.0411 2.44971i −0.225545 0.0115010i
\(214\) 196.590i 0.918647i
\(215\) 53.3747 + 228.283i 0.248255 + 1.06178i
\(216\) −111.738 152.432i −0.517306 0.705705i
\(217\) −74.7497 94.8069i −0.344469 0.436898i
\(218\) −2.13142 + 2.13142i −0.00977717 + 0.00977717i
\(219\) 163.092 + 180.619i 0.744715 + 0.824744i
\(220\) −177.165 110.019i −0.805294 0.500084i
\(221\) 142.337i 0.644060i
\(222\) 1.40593 27.5717i 0.00633304 0.124197i
\(223\) −173.529 + 173.529i −0.778155 + 0.778155i −0.979517 0.201362i \(-0.935463\pi\)
0.201362 + 0.979517i \(0.435463\pi\)
\(224\) 229.401 + 27.1362i 1.02411 + 0.121144i
\(225\) −78.7290 210.777i −0.349907 0.936785i
\(226\) 113.295 0.501306
\(227\) 191.389 191.389i 0.843123 0.843123i −0.146140 0.989264i \(-0.546685\pi\)
0.989264 + 0.146140i \(0.0466851\pi\)
\(228\) −195.509 9.96941i −0.857496 0.0437255i
\(229\) −123.490 −0.539259 −0.269630 0.962964i \(-0.586901\pi\)
−0.269630 + 0.962964i \(0.586901\pi\)
\(230\) 10.6494 + 6.61323i 0.0463017 + 0.0287532i
\(231\) −238.181 + 168.858i −1.03109 + 0.730986i
\(232\) −138.817 + 138.817i −0.598348 + 0.598348i
\(233\) 89.8918 89.8918i 0.385802 0.385802i −0.487385 0.873187i \(-0.662049\pi\)
0.873187 + 0.487385i \(0.162049\pi\)
\(234\) −185.252 18.9420i −0.791675 0.0809487i
\(235\) −127.831 + 29.8881i −0.543961 + 0.127183i
\(236\) 89.0003 0.377120
\(237\) −227.112 11.5809i −0.958279 0.0488646i
\(238\) −37.8147 + 29.8147i −0.158885 + 0.125272i
\(239\) 49.2786 0.206187 0.103093 0.994672i \(-0.467126\pi\)
0.103093 + 0.994672i \(0.467126\pi\)
\(240\) −42.7597 + 61.6167i −0.178165 + 0.256736i
\(241\) 421.664i 1.74964i 0.484445 + 0.874822i \(0.339021\pi\)
−0.484445 + 0.874822i \(0.660979\pi\)
\(242\) 51.1204 + 51.1204i 0.211242 + 0.211242i
\(243\) 61.2344 235.158i 0.251993 0.967729i
\(244\) −63.2151 −0.259078
\(245\) 174.244 172.232i 0.711200 0.702990i
\(246\) −59.4929 + 53.7199i −0.241841 + 0.218374i
\(247\) −318.238 + 318.238i −1.28841 + 1.28841i
\(248\) 85.3694 + 85.3694i 0.344231 + 0.344231i
\(249\) −163.640 + 147.761i −0.657187 + 0.593417i
\(250\) 96.4812 79.4756i 0.385925 0.317902i
\(251\) 345.514 1.37655 0.688274 0.725450i \(-0.258369\pi\)
0.688274 + 0.725450i \(0.258369\pi\)
\(252\) 101.315 + 159.551i 0.402042 + 0.633137i
\(253\) 24.6476 + 24.6476i 0.0974214 + 0.0974214i
\(254\) 101.325 0.398917
\(255\) −18.3454 101.545i −0.0719428 0.398214i
\(256\) −171.000 −0.667969
\(257\) −216.568 + 216.568i −0.842676 + 0.842676i −0.989206 0.146530i \(-0.953190\pi\)
0.146530 + 0.989206i \(0.453190\pi\)
\(258\) −140.481 7.16342i −0.544501 0.0277652i
\(259\) −7.56729 + 63.9714i −0.0292173 + 0.246994i
\(260\) 70.6602 + 302.212i 0.271770 + 1.16236i
\(261\) −251.098 25.6747i −0.962060 0.0983705i
\(262\) 56.1926 + 56.1926i 0.214476 + 0.214476i
\(263\) −196.555 + 196.555i −0.747359 + 0.747359i −0.973982 0.226623i \(-0.927231\pi\)
0.226623 + 0.973982i \(0.427231\pi\)
\(264\) 216.696 195.668i 0.820817 0.741168i
\(265\) 332.578 77.7599i 1.25501 0.293434i
\(266\) −151.206 17.8864i −0.568444 0.0672422i
\(267\) 522.204 + 26.6283i 1.95582 + 0.0997313i
\(268\) 97.4357 + 97.4357i 0.363566 + 0.363566i
\(269\) 349.961i 1.30097i 0.759519 + 0.650485i \(0.225434\pi\)
−0.759519 + 0.650485i \(0.774566\pi\)
\(270\) 134.602 10.3632i 0.498525 0.0383822i
\(271\) 137.978i 0.509143i −0.967054 0.254572i \(-0.918066\pi\)
0.967054 0.254572i \(-0.0819344\pi\)
\(272\) −24.3218 + 24.3218i −0.0894182 + 0.0894182i
\(273\) 428.340 + 72.9511i 1.56901 + 0.267220i
\(274\) 10.5071i 0.0383472i
\(275\) 311.545 154.109i 1.13289 0.560396i
\(276\) 16.7472 15.1221i 0.0606783 0.0547903i
\(277\) 132.817 132.817i 0.479483 0.479483i −0.425484 0.904966i \(-0.639896\pi\)
0.904966 + 0.425484i \(0.139896\pi\)
\(278\) 126.989 + 126.989i 0.456793 + 0.456793i
\(279\) −15.7894 + 154.420i −0.0565929 + 0.553476i
\(280\) −152.805 + 191.509i −0.545732 + 0.683960i
\(281\) 142.098i 0.505687i −0.967507 0.252844i \(-0.918634\pi\)
0.967507 0.252844i \(-0.0813658\pi\)
\(282\) 4.01128 78.6649i 0.0142244 0.278954i
\(283\) 120.235 120.235i 0.424858 0.424858i −0.462014 0.886873i \(-0.652873\pi\)
0.886873 + 0.462014i \(0.152873\pi\)
\(284\) −48.1035 −0.169378
\(285\) 186.017 268.050i 0.652691 0.940528i
\(286\) 287.666i 1.00583i
\(287\) 146.874 115.801i 0.511755 0.403489i
\(288\) −187.559 230.284i −0.651247 0.799596i
\(289\) 241.676i 0.836250i
\(290\) −31.9252 136.543i −0.110087 0.470840i
\(291\) 52.4786 47.3863i 0.180339 0.162839i
\(292\) 172.079 + 172.079i 0.589312 + 0.589312i
\(293\) −377.885 377.885i −1.28971 1.28971i −0.934962 0.354747i \(-0.884567\pi\)
−0.354747 0.934962i \(-0.615433\pi\)
\(294\) 70.3415 + 129.078i 0.239257 + 0.439040i
\(295\) −78.2536 + 126.013i −0.265266 + 0.427163i
\(296\) 64.4174i 0.217626i
\(297\) 371.007 + 57.1518i 1.24918 + 0.192430i
\(298\) 17.4929 + 17.4929i 0.0587009 + 0.0587009i
\(299\) 51.8750i 0.173495i
\(300\) −89.3608 206.494i −0.297869 0.688312i
\(301\) 325.943 + 38.5564i 1.08287 + 0.128094i
\(302\) 115.487 + 115.487i 0.382409 + 0.382409i
\(303\) −17.2812 + 338.900i −0.0570337 + 1.11848i
\(304\) −108.757 −0.357754
\(305\) 55.5820 89.5046i 0.182236 0.293458i
\(306\) 61.5919 + 6.29777i 0.201281 + 0.0205809i
\(307\) 94.6590 + 94.6590i 0.308335 + 0.308335i 0.844264 0.535928i \(-0.180038\pi\)
−0.535928 + 0.844264i \(0.680038\pi\)
\(308\) −229.273 + 180.768i −0.744392 + 0.586910i
\(309\) −46.0125 50.9571i −0.148908 0.164910i
\(310\) −83.9714 + 19.6333i −0.270876 + 0.0633333i
\(311\) −221.432 −0.712001 −0.356000 0.934486i \(-0.615860\pi\)
−0.356000 + 0.934486i \(0.615860\pi\)
\(312\) −433.944 22.1277i −1.39085 0.0709221i
\(313\) −225.950 + 225.950i −0.721885 + 0.721885i −0.968989 0.247104i \(-0.920521\pi\)
0.247104 + 0.968989i \(0.420521\pi\)
\(314\) 153.256i 0.488076i
\(315\) −314.984 + 3.16355i −0.999950 + 0.0100430i
\(316\) −227.407 −0.719643
\(317\) 96.2271 + 96.2271i 0.303556 + 0.303556i 0.842403 0.538848i \(-0.181140\pi\)
−0.538848 + 0.842403i \(0.681140\pi\)
\(318\) −10.4362 + 204.663i −0.0328181 + 0.643593i
\(319\) 389.914i 1.22230i
\(320\) 34.2908 55.2190i 0.107159 0.172559i
\(321\) 437.728 395.253i 1.36364 1.23132i
\(322\) 13.7816 10.8660i 0.0428000 0.0337453i
\(323\) 105.807 105.807i 0.327575 0.327575i
\(324\) 49.1793 237.971i 0.151788 0.734480i
\(325\) −490.022 165.675i −1.50776 0.509768i
\(326\) 54.9355i 0.168514i
\(327\) −9.03113 0.460516i −0.0276181 0.00140830i
\(328\) −132.253 + 132.253i −0.403211 + 0.403211i
\(329\) −21.5903 + 182.517i −0.0656240 + 0.554764i
\(330\) 37.0765 + 205.224i 0.112353 + 0.621890i
\(331\) 175.014 0.528744 0.264372 0.964421i \(-0.414835\pi\)
0.264372 + 0.964421i \(0.414835\pi\)
\(332\) −155.902 + 155.902i −0.469586 + 0.469586i
\(333\) 64.2177 52.3034i 0.192846 0.157067i
\(334\) −195.517 −0.585382
\(335\) −223.627 + 52.2861i −0.667543 + 0.156078i
\(336\) 60.7268 + 85.6578i 0.180735 + 0.254934i
\(337\) 109.576 109.576i 0.325152 0.325152i −0.525588 0.850739i \(-0.676155\pi\)
0.850739 + 0.525588i \(0.176155\pi\)
\(338\) −183.220 + 183.220i −0.542070 + 0.542070i
\(339\) 227.784 + 252.263i 0.671930 + 0.744138i
\(340\) −23.4929 100.479i −0.0690966 0.295525i
\(341\) −239.789 −0.703194
\(342\) 123.627 + 151.788i 0.361482 + 0.443825i
\(343\) −143.661 311.465i −0.418837 0.908061i
\(344\) −328.215 −0.954114
\(345\) 6.68601 + 37.0081i 0.0193797 + 0.107270i
\(346\) 38.1223i 0.110180i
\(347\) −268.600 268.600i −0.774062 0.774062i 0.204752 0.978814i \(-0.434361\pi\)
−0.978814 + 0.204752i \(0.934361\pi\)
\(348\) −252.079 12.8540i −0.724366 0.0369369i
\(349\) 304.193 0.871613 0.435807 0.900040i \(-0.356463\pi\)
0.435807 + 0.900040i \(0.356463\pi\)
\(350\) −58.6279 164.887i −0.167508 0.471106i
\(351\) −330.280 450.565i −0.940968 1.28366i
\(352\) 324.421 324.421i 0.921652 0.921652i
\(353\) −240.264 240.264i −0.680635 0.680635i 0.279509 0.960143i \(-0.409828\pi\)
−0.960143 + 0.279509i \(0.909828\pi\)
\(354\) −59.6461 66.0559i −0.168492 0.186599i
\(355\) 42.2950 68.1084i 0.119141 0.191855i
\(356\) 522.883 1.46877
\(357\) −142.413 24.2545i −0.398916 0.0679399i
\(358\) 132.507 + 132.507i 0.370132 + 0.370132i
\(359\) −161.739 −0.450526 −0.225263 0.974298i \(-0.572324\pi\)
−0.225263 + 0.974298i \(0.572324\pi\)
\(360\) 312.432 40.1437i 0.867865 0.111510i
\(361\) 112.126 0.310599
\(362\) −126.983 + 126.983i −0.350781 + 0.350781i
\(363\) −11.0451 + 216.604i −0.0304272 + 0.596706i
\(364\) 431.500 + 51.0429i 1.18544 + 0.140228i
\(365\) −394.943 + 92.3414i −1.08203 + 0.252990i
\(366\) 42.3655 + 46.9182i 0.115753 + 0.128192i
\(367\) −101.051 101.051i −0.275343 0.275343i 0.555904 0.831247i \(-0.312372\pi\)
−0.831247 + 0.555904i \(0.812372\pi\)
\(368\) 8.86409 8.86409i 0.0240872 0.0240872i
\(369\) −239.225 24.4608i −0.648307 0.0662893i
\(370\) 39.0887 + 24.2739i 0.105645 + 0.0656051i
\(371\) 56.1715 474.856i 0.151406 1.27993i
\(372\) −7.90497 + 155.024i −0.0212499 + 0.416730i
\(373\) −369.464 369.464i −0.990521 0.990521i 0.00943464 0.999955i \(-0.496997\pi\)
−0.999955 + 0.00943464i \(0.996997\pi\)
\(374\) 95.6424i 0.255728i
\(375\) 370.939 + 55.0362i 0.989172 + 0.146763i
\(376\) 183.790i 0.488803i
\(377\) −410.320 + 410.320i −1.08838 + 1.08838i
\(378\) 50.5194 182.123i 0.133649 0.481807i
\(379\) 261.209i 0.689207i 0.938748 + 0.344604i \(0.111987\pi\)
−0.938748 + 0.344604i \(0.888013\pi\)
\(380\) 172.125 277.176i 0.452960 0.729410i
\(381\) 203.718 + 225.610i 0.534692 + 0.592152i
\(382\) 75.7048 75.7048i 0.198180 0.198180i
\(383\) −163.813 163.813i −0.427710 0.427710i 0.460138 0.887847i \(-0.347800\pi\)
−0.887847 + 0.460138i \(0.847800\pi\)
\(384\) −239.254 264.965i −0.623057 0.690013i
\(385\) −54.3566 483.562i −0.141186 1.25600i
\(386\) 115.447i 0.299085i
\(387\) −266.493 327.197i −0.688612 0.845472i
\(388\) 49.9973 49.9973i 0.128859 0.128859i
\(389\) 401.000 1.03085 0.515425 0.856935i \(-0.327634\pi\)
0.515425 + 0.856935i \(0.327634\pi\)
\(390\) 176.947 254.980i 0.453710 0.653796i
\(391\) 17.2472i 0.0441105i
\(392\) 179.255 + 292.432i 0.457283 + 0.746001i
\(393\) −12.1410 + 238.096i −0.0308931 + 0.605841i
\(394\) 234.338i 0.594767i
\(395\) 199.948 321.980i 0.506197 0.815138i
\(396\) 373.436 + 38.1838i 0.943019 + 0.0964237i
\(397\) 304.082 + 304.082i 0.765950 + 0.765950i 0.977391 0.211440i \(-0.0678154\pi\)
−0.211440 + 0.977391i \(0.567815\pi\)
\(398\) −155.590 155.590i −0.390929 0.390929i
\(399\) −264.180 372.636i −0.662104 0.933926i
\(400\) −55.4226 112.042i −0.138557 0.280104i
\(401\) 582.912i 1.45365i 0.686825 + 0.726823i \(0.259004\pi\)
−0.686825 + 0.726823i \(0.740996\pi\)
\(402\) 7.01732 137.616i 0.0174560 0.342329i
\(403\) 252.338 + 252.338i 0.626149 + 0.626149i
\(404\) 339.341i 0.839952i
\(405\) 293.696 + 278.868i 0.725176 + 0.688563i
\(406\) −194.957 23.0618i −0.480190 0.0568025i
\(407\) 90.4693 + 90.4693i 0.222283 + 0.222283i
\(408\) 144.276 + 7.35694i 0.353619 + 0.0180317i
\(409\) 344.830 0.843104 0.421552 0.906804i \(-0.361485\pi\)
0.421552 + 0.906804i \(0.361485\pi\)
\(410\) −30.4157 130.087i −0.0741846 0.317286i
\(411\) −23.3952 + 21.1250i −0.0569226 + 0.0513991i
\(412\) −48.5478 48.5478i −0.117834 0.117834i
\(413\) 128.576 + 163.076i 0.311323 + 0.394858i
\(414\) −22.4473 2.29523i −0.0542204 0.00554403i
\(415\) −83.6607 357.815i −0.201592 0.862206i
\(416\) −682.799 −1.64134
\(417\) −27.4372 + 538.068i −0.0657965 + 1.29033i
\(418\) −213.838 + 213.838i −0.511573 + 0.511573i
\(419\) 343.927i 0.820828i −0.911899 0.410414i \(-0.865384\pi\)
0.911899 0.410414i \(-0.134616\pi\)
\(420\) −314.414 + 19.2003i −0.748605 + 0.0457149i
\(421\) 14.6762 0.0348603 0.0174302 0.999848i \(-0.494452\pi\)
0.0174302 + 0.999848i \(0.494452\pi\)
\(422\) −195.579 195.579i −0.463457 0.463457i
\(423\) 183.220 149.227i 0.433144 0.352783i
\(424\) 478.167i 1.12775i
\(425\) 162.921 + 55.0830i 0.383343 + 0.129607i
\(426\) 32.2379 + 35.7024i 0.0756759 + 0.0838084i
\(427\) −91.3251 115.830i −0.213876 0.271264i
\(428\) 417.031 417.031i 0.974372 0.974372i
\(429\) 640.518 578.364i 1.49305 1.34817i
\(430\) 123.679 199.162i 0.287625 0.463167i
\(431\) 443.066i 1.02800i 0.857791 + 0.513998i \(0.171836\pi\)
−0.857791 + 0.513998i \(0.828164\pi\)
\(432\) 20.5537 133.426i 0.0475779 0.308857i
\(433\) −487.352 + 487.352i −1.12553 + 1.12553i −0.134629 + 0.990896i \(0.542984\pi\)
−0.990896 + 0.134629i \(0.957016\pi\)
\(434\) −14.1825 + 119.895i −0.0326787 + 0.276255i
\(435\) 239.841 345.610i 0.551358 0.794506i
\(436\) −9.04287 −0.0207405
\(437\) −38.5614 + 38.5614i −0.0882412 + 0.0882412i
\(438\) 12.3931 243.041i 0.0282948 0.554888i
\(439\) 151.065 0.344111 0.172056 0.985087i \(-0.444959\pi\)
0.172056 + 0.985087i \(0.444959\pi\)
\(440\) 110.786 + 473.828i 0.251785 + 1.07688i
\(441\) −145.980 + 416.138i −0.331021 + 0.943624i
\(442\) 100.648 100.648i 0.227710 0.227710i
\(443\) −188.010 + 188.010i −0.424401 + 0.424401i −0.886716 0.462315i \(-0.847019\pi\)
0.462315 + 0.886716i \(0.347019\pi\)
\(444\) 61.4707 55.5059i 0.138448 0.125013i
\(445\) −459.745 + 740.336i −1.03314 + 1.66368i
\(446\) 245.406 0.550239
\(447\) −3.77951 + 74.1196i −0.00845528 + 0.165816i
\(448\) −56.3422 71.4602i −0.125764 0.159509i
\(449\) 397.613 0.885552 0.442776 0.896632i \(-0.353994\pi\)
0.442776 + 0.896632i \(0.353994\pi\)
\(450\) −93.3717 + 204.711i −0.207493 + 0.454914i
\(451\) 371.478i 0.823677i
\(452\) 240.335 + 240.335i 0.531716 + 0.531716i
\(453\) −24.9522 + 489.336i −0.0550821 + 1.08021i
\(454\) −270.665 −0.596178
\(455\) −451.667 + 566.069i −0.992674 + 1.24411i
\(456\) 306.125 + 339.022i 0.671327 + 0.743470i
\(457\) −66.2262 + 66.2262i −0.144915 + 0.144915i −0.775842 0.630927i \(-0.782675\pi\)
0.630927 + 0.775842i \(0.282675\pi\)
\(458\) 87.3209 + 87.3209i 0.190657 + 0.190657i
\(459\) 109.810 + 149.802i 0.239238 + 0.326367i
\(460\) 8.56200 + 36.6195i 0.0186130 + 0.0796077i
\(461\) −191.545 −0.415499 −0.207750 0.978182i \(-0.566614\pi\)
−0.207750 + 0.978182i \(0.566614\pi\)
\(462\) 287.820 + 49.0189i 0.622987 + 0.106102i
\(463\) 42.9857 + 42.9857i 0.0928417 + 0.0928417i 0.752002 0.659161i \(-0.229088\pi\)
−0.659161 + 0.752002i \(0.729088\pi\)
\(464\) −140.226 −0.302211
\(465\) −212.543 147.497i −0.457082 0.317198i
\(466\) −127.126 −0.272803
\(467\) 252.836 252.836i 0.541405 0.541405i −0.382536 0.923941i \(-0.624949\pi\)
0.923941 + 0.382536i \(0.124949\pi\)
\(468\) −352.797 433.161i −0.753839 0.925557i
\(469\) −37.7700 + 319.295i −0.0805331 + 0.680800i
\(470\) 111.524 + 69.2561i 0.237286 + 0.147353i
\(471\) −341.239 + 308.127i −0.724500 + 0.654197i
\(472\) −146.843 146.843i −0.311108 0.311108i
\(473\) 460.953 460.953i 0.974530 0.974530i
\(474\) 152.404 + 168.781i 0.321526 + 0.356079i
\(475\) 241.105 + 487.414i 0.507589 + 1.02613i
\(476\) −143.464 16.9706i −0.301394 0.0356524i
\(477\) −476.684 + 388.245i −0.999337 + 0.813930i
\(478\) −34.8452 34.8452i −0.0728980 0.0728980i
\(479\) 91.5191i 0.191063i −0.995426 0.0955314i \(-0.969545\pi\)
0.995426 0.0955314i \(-0.0304550\pi\)
\(480\) 487.114 88.0038i 1.01482 0.183341i
\(481\) 190.408i 0.395858i
\(482\) 298.161 298.161i 0.618592 0.618592i
\(483\) 51.9027 + 8.83960i 0.107459 + 0.0183015i
\(484\) 216.886i 0.448111i
\(485\) 26.8296 + 114.750i 0.0553189 + 0.236598i
\(486\) −209.581 + 122.983i −0.431237 + 0.253051i
\(487\) 252.690 252.690i 0.518872 0.518872i −0.398358 0.917230i \(-0.630420\pi\)
0.917230 + 0.398358i \(0.130420\pi\)
\(488\) 104.300 + 104.300i 0.213729 + 0.213729i
\(489\) 122.319 110.450i 0.250141 0.225869i
\(490\) −244.996 1.42238i −0.499992 0.00290281i
\(491\) 518.117i 1.05523i −0.849484 0.527614i \(-0.823087\pi\)
0.849484 0.527614i \(-0.176913\pi\)
\(492\) −240.161 12.2463i −0.488131 0.0248908i
\(493\) 136.422 136.422i 0.276717 0.276717i
\(494\) 450.057 0.911046
\(495\) −382.407 + 495.164i −0.772539 + 1.00033i
\(496\) 86.2361i 0.173863i
\(497\) −69.4937 88.1406i −0.139826 0.177345i
\(498\) 220.193 + 11.2281i 0.442155 + 0.0225464i
\(499\) 217.267i 0.435404i −0.976015 0.217702i \(-0.930144\pi\)
0.976015 0.217702i \(-0.0698561\pi\)
\(500\) 373.261 + 36.0744i 0.746522 + 0.0721488i
\(501\) −393.095 435.339i −0.784621 0.868940i
\(502\) −244.315 244.315i −0.486684 0.486684i
\(503\) −12.7399 12.7399i −0.0253279 0.0253279i 0.694329 0.719657i \(-0.255701\pi\)
−0.719657 + 0.694329i \(0.755701\pi\)
\(504\) 96.0845 430.405i 0.190644 0.853979i
\(505\) −480.463 298.365i −0.951412 0.590823i
\(506\) 34.8570i 0.0688873i
\(507\) −776.327 39.5865i −1.53122 0.0780798i
\(508\) 214.943 + 214.943i 0.423116 + 0.423116i
\(509\) 611.593i 1.20156i −0.799415 0.600779i \(-0.794857\pi\)
0.799415 0.600779i \(-0.205143\pi\)
\(510\) −58.8307 + 84.7750i −0.115354 + 0.166226i
\(511\) −66.7048 + 563.900i −0.130538 + 1.10352i
\(512\) −215.668 215.668i −0.421226 0.421226i
\(513\) −89.4144 + 580.443i −0.174297 + 1.13147i
\(514\) 306.273 0.595862
\(515\) 111.423 26.0518i 0.216356 0.0505860i
\(516\) −282.810 313.202i −0.548081 0.606980i
\(517\) 258.119 + 258.119i 0.499262 + 0.499262i
\(518\) 50.5855 39.8837i 0.0976554 0.0769956i
\(519\) −84.8831 + 76.6464i −0.163551 + 0.147681i
\(520\) 382.042 615.208i 0.734695 1.18309i
\(521\) 692.510 1.32919 0.664597 0.747202i \(-0.268603\pi\)
0.664597 + 0.747202i \(0.268603\pi\)
\(522\) 159.398 + 195.708i 0.305360 + 0.374919i
\(523\) 583.903 583.903i 1.11645 1.11645i 0.124191 0.992258i \(-0.460366\pi\)
0.992258 0.124191i \(-0.0396337\pi\)
\(524\) 238.405i 0.454971i
\(525\) 249.264 462.053i 0.474788 0.880100i
\(526\) 277.971 0.528463
\(527\) −83.8965 83.8965i −0.159196 0.159196i
\(528\) 208.275 + 10.6204i 0.394461 + 0.0201144i
\(529\) 522.714i 0.988118i
\(530\) −290.153 180.184i −0.547458 0.339969i
\(531\) 27.1592 265.616i 0.0511473 0.500218i
\(532\) −282.814 358.699i −0.531604 0.674247i
\(533\) −390.919 + 390.919i −0.733431 + 0.733431i
\(534\) −350.425 388.083i −0.656227 0.726748i
\(535\) 223.788 + 957.138i 0.418296 + 1.78904i
\(536\) 321.521i 0.599853i
\(537\) −28.6295 + 561.451i −0.0533138 + 1.04553i
\(538\) 247.460 247.460i 0.459963 0.459963i
\(539\) −662.448 158.948i −1.22903 0.294895i
\(540\) 307.517 + 263.550i 0.569476 + 0.488055i
\(541\) 314.562 0.581445 0.290723 0.956807i \(-0.406104\pi\)
0.290723 + 0.956807i \(0.406104\pi\)
\(542\) −97.5650 + 97.5650i −0.180009 + 0.180009i
\(543\) −538.043 27.4359i −0.990871 0.0505265i
\(544\) 227.015 0.417306
\(545\) 7.95095 12.8035i 0.0145889 0.0234927i
\(546\) −251.298 354.467i −0.460253 0.649206i
\(547\) 223.888 223.888i 0.409302 0.409302i −0.472193 0.881495i \(-0.656538\pi\)
0.881495 + 0.472193i \(0.156538\pi\)
\(548\) −22.2890 + 22.2890i −0.0406734 + 0.0406734i
\(549\) −19.2906 + 188.662i −0.0351378 + 0.343646i
\(550\) −329.267 111.324i −0.598667 0.202407i
\(551\) 610.024 1.10712
\(552\) −52.5817 2.68125i −0.0952567 0.00485733i
\(553\) −328.529 416.681i −0.594084 0.753492i
\(554\) −187.831 −0.339045
\(555\) 24.5411 + 135.838i 0.0442181 + 0.244754i
\(556\) 538.767i 0.969005i
\(557\) 245.854 + 245.854i 0.441390 + 0.441390i 0.892479 0.451089i \(-0.148964\pi\)
−0.451089 + 0.892479i \(0.648964\pi\)
\(558\) 120.356 98.0265i 0.215692 0.175675i
\(559\) −970.151 −1.73551
\(560\) −173.905 + 19.5484i −0.310544 + 0.0349079i
\(561\) −212.957 + 192.293i −0.379603 + 0.342768i
\(562\) −100.479 + 100.479i −0.178787 + 0.178787i
\(563\) 406.434 + 406.434i 0.721907 + 0.721907i 0.968993 0.247086i \(-0.0794732\pi\)
−0.247086 + 0.968993i \(0.579473\pi\)
\(564\) 175.383 158.364i 0.310962 0.280788i
\(565\) −551.600 + 128.969i −0.976283 + 0.228264i
\(566\) −170.038 −0.300420
\(567\) 507.086 253.679i 0.894331 0.447405i
\(568\) 79.3667 + 79.3667i 0.139730 + 0.139730i
\(569\) −690.156 −1.21293 −0.606464 0.795111i \(-0.707413\pi\)
−0.606464 + 0.795111i \(0.707413\pi\)
\(570\) −321.074 + 58.0064i −0.563288 + 0.101766i
\(571\) 612.476 1.07264 0.536319 0.844015i \(-0.319814\pi\)
0.536319 + 0.844015i \(0.319814\pi\)
\(572\) 610.233 610.233i 1.06684 1.06684i
\(573\) 320.771 + 16.3568i 0.559810 + 0.0285459i
\(574\) −185.739 21.9714i −0.323587 0.0382777i
\(575\) −59.3768 20.0751i −0.103264 0.0349131i
\(576\) −11.9012 + 116.393i −0.0206618 + 0.202071i
\(577\) −254.442 254.442i −0.440973 0.440973i 0.451366 0.892339i \(-0.350937\pi\)
−0.892339 + 0.451366i \(0.850937\pi\)
\(578\) 170.891 170.891i 0.295659 0.295659i
\(579\) −257.054 + 232.110i −0.443962 + 0.400882i
\(580\) 221.929 357.376i 0.382636 0.616165i
\(581\) −510.890 60.4341i −0.879329 0.104017i
\(582\) −70.6151 3.60081i −0.121332 0.00618695i
\(583\) −671.548 671.548i −1.15188 1.15188i
\(584\) 567.832i 0.972315i
\(585\) 923.497 118.658i 1.57863 0.202835i
\(586\) 534.410i 0.911962i
\(587\) −195.495 + 195.495i −0.333040 + 0.333040i −0.853740 0.520700i \(-0.825671\pi\)
0.520700 + 0.853740i \(0.325671\pi\)
\(588\) −124.599 + 423.032i −0.211902 + 0.719442i
\(589\) 375.152i 0.636931i
\(590\) 144.438 33.7711i 0.244811 0.0572391i
\(591\) −521.777 + 471.146i −0.882871 + 0.797201i
\(592\) 32.5357 32.5357i 0.0549590 0.0549590i
\(593\) −181.904 181.904i −0.306751 0.306751i 0.536897 0.843648i \(-0.319597\pi\)
−0.843648 + 0.536897i \(0.819597\pi\)
\(594\) −221.929 302.754i −0.373618 0.509686i
\(595\) 150.169 188.205i 0.252384 0.316311i
\(596\) 74.2159i 0.124523i
\(597\) 33.6167 659.255i 0.0563094 1.10428i
\(598\) −36.6812 + 36.6812i −0.0613397 + 0.0613397i
\(599\) −376.201 −0.628048 −0.314024 0.949415i \(-0.601677\pi\)
−0.314024 + 0.949415i \(0.601677\pi\)
\(600\) −193.259 + 488.135i −0.322099 + 0.813558i
\(601\) 1122.87i 1.86834i −0.356832 0.934169i \(-0.616143\pi\)
0.356832 0.934169i \(-0.383857\pi\)
\(602\) −203.213 257.740i −0.337563 0.428139i
\(603\) 320.524 261.058i 0.531549 0.432931i
\(604\) 489.971i 0.811211i
\(605\) −307.083 190.697i −0.507574 0.315202i
\(606\) 251.858 227.419i 0.415608 0.375279i
\(607\) −127.880 127.880i −0.210675 0.210675i 0.593879 0.804554i \(-0.297596\pi\)
−0.804554 + 0.593879i \(0.797596\pi\)
\(608\) 507.560 + 507.560i 0.834803 + 0.834803i
\(609\) −340.619 480.458i −0.559309 0.788929i
\(610\) −102.592 + 23.9869i −0.168183 + 0.0393228i
\(611\) 543.253i 0.889122i
\(612\) 117.297 + 144.016i 0.191661 + 0.235320i
\(613\) 668.817 + 668.817i 1.09105 + 1.09105i 0.995416 + 0.0956388i \(0.0304894\pi\)
0.0956388 + 0.995416i \(0.469511\pi\)
\(614\) 133.868i 0.218026i
\(615\) 228.501 329.269i 0.371546 0.535397i
\(616\) 676.533 + 80.0283i 1.09827 + 0.129916i
\(617\) 416.614 + 416.614i 0.675225 + 0.675225i 0.958916 0.283691i \(-0.0915589\pi\)
−0.283691 + 0.958916i \(0.591559\pi\)
\(618\) −3.49641 + 68.5679i −0.00565763 + 0.110951i
\(619\) −1140.08 −1.84180 −0.920902 0.389794i \(-0.872546\pi\)
−0.920902 + 0.389794i \(0.872546\pi\)
\(620\) −219.779 136.482i −0.354482 0.220132i
\(621\) −40.0205 54.5957i −0.0644453 0.0879157i
\(622\) 156.576 + 156.576i 0.251730 + 0.251730i
\(623\) 755.394 + 958.085i 1.21251 + 1.53786i
\(624\) −207.999 230.351i −0.333331 0.369153i
\(625\) −379.267 + 496.771i −0.606827 + 0.794834i
\(626\) 319.542 0.510450
\(627\) −906.059 46.2018i −1.44507 0.0736870i
\(628\) −325.105 + 325.105i −0.517683 + 0.517683i
\(629\) 63.3061i 0.100646i
\(630\) 224.964 + 220.490i 0.357086 + 0.349985i
\(631\) −76.8167 −0.121738 −0.0608690 0.998146i \(-0.519387\pi\)
−0.0608690 + 0.998146i \(0.519387\pi\)
\(632\) 375.203 + 375.203i 0.593675 + 0.593675i
\(633\) 42.2568 828.695i 0.0667564 1.30915i
\(634\) 136.086i 0.214646i
\(635\) −493.320 + 115.343i −0.776883 + 0.181643i
\(636\) −456.293 + 412.017i −0.717443 + 0.647825i
\(637\) 529.849 + 864.382i 0.831788 + 1.35696i
\(638\) −275.711 + 275.711i −0.432149 + 0.432149i
\(639\) −14.6792 + 143.562i −0.0229721 + 0.224666i
\(640\) 579.374 135.463i 0.905272 0.211661i
\(641\) 187.134i 0.291941i −0.989289 0.145970i \(-0.953370\pi\)
0.989289 0.145970i \(-0.0466304\pi\)
\(642\) −589.006 30.0346i −0.917455 0.0467829i
\(643\) 767.988 767.988i 1.19438 1.19438i 0.218559 0.975824i \(-0.429864\pi\)
0.975824 0.218559i \(-0.0701356\pi\)
\(644\) 52.2855 + 6.18494i 0.0811886 + 0.00960395i
\(645\) 692.114 125.040i 1.07305 0.193860i
\(646\) −149.633 −0.231631
\(647\) 573.588 573.588i 0.886535 0.886535i −0.107654 0.994188i \(-0.534334\pi\)
0.994188 + 0.107654i \(0.0343337\pi\)
\(648\) −473.774 + 311.491i −0.731133 + 0.480696i
\(649\) 412.459 0.635530
\(650\) 229.348 + 463.648i 0.352844 + 0.713304i
\(651\) −295.472 + 209.474i −0.453874 + 0.321772i
\(652\) 116.536 116.536i 0.178736 0.178736i
\(653\) 142.398 142.398i 0.218067 0.218067i −0.589616 0.807683i \(-0.700721\pi\)
0.807683 + 0.589616i \(0.200721\pi\)
\(654\) 6.06034 + 6.71161i 0.00926658 + 0.0102624i
\(655\) −337.551 209.618i −0.515345 0.320027i
\(656\) −133.596 −0.203652
\(657\) 566.071 461.048i 0.861600 0.701747i
\(658\) 144.326 113.793i 0.219340 0.172937i
\(659\) 960.106 1.45691 0.728457 0.685092i \(-0.240238\pi\)
0.728457 + 0.685092i \(0.240238\pi\)
\(660\) −356.694 + 513.996i −0.540446 + 0.778782i
\(661\) 94.8355i 0.143473i −0.997424 0.0717364i \(-0.977146\pi\)
0.997424 0.0717364i \(-0.0228540\pi\)
\(662\) −123.754 123.754i −0.186939 0.186939i
\(663\) 426.458 + 21.7459i 0.643224 + 0.0327993i
\(664\) 514.452 0.774777
\(665\) 756.537 85.0414i 1.13765 0.127882i
\(666\) −82.3928 8.42466i −0.123713 0.0126496i
\(667\) −49.7191 + 49.7191i −0.0745413 + 0.0745413i
\(668\) −414.755 414.755i −0.620891 0.620891i
\(669\) 493.399 + 546.421i 0.737517 + 0.816773i
\(670\) 195.100 + 121.156i 0.291194 + 0.180830i
\(671\) −292.961 −0.436604
\(672\) 116.350 683.163i 0.173140 1.01661i
\(673\) −442.857 442.857i −0.658034 0.658034i 0.296880 0.954915i \(-0.404054\pi\)
−0.954915 + 0.296880i \(0.904054\pi\)
\(674\) −154.964 −0.229917
\(675\) −643.537 + 203.679i −0.953388 + 0.301746i
\(676\) −777.336 −1.14990
\(677\) 447.410 447.410i 0.660872 0.660872i −0.294714 0.955586i \(-0.595224\pi\)
0.955586 + 0.294714i \(0.0952243\pi\)
\(678\) 17.3090 339.445i 0.0255295 0.500656i
\(679\) 163.840 + 19.3810i 0.241296 + 0.0285434i
\(680\) −127.020 + 204.542i −0.186794 + 0.300798i
\(681\) −544.182 602.662i −0.799093 0.884966i
\(682\) 169.557 + 169.557i 0.248617 + 0.248617i
\(683\) 199.643 199.643i 0.292303 0.292303i −0.545686 0.837990i \(-0.683731\pi\)
0.837990 + 0.545686i \(0.183731\pi\)
\(684\) −59.7388 + 584.243i −0.0873375 + 0.854157i
\(685\) −11.9608 51.1561i −0.0174610 0.0746804i
\(686\) −118.655 + 321.823i −0.172967 + 0.469129i
\(687\) −18.8666 + 369.991i −0.0274622 + 0.538560i
\(688\) −165.774 165.774i −0.240950 0.240950i
\(689\) 1413.38i 2.05135i
\(690\) 21.4409 30.8964i 0.0310738 0.0447773i
\(691\) 207.196i 0.299849i 0.988697 + 0.149925i \(0.0479031\pi\)
−0.988697 + 0.149925i \(0.952097\pi\)
\(692\) −80.8697 + 80.8697i −0.116864 + 0.116864i
\(693\) 469.527 + 739.414i 0.677529 + 1.06698i
\(694\) 379.857i 0.547345i
\(695\) −762.825 473.711i −1.09759 0.681599i
\(696\) 394.702 + 437.118i 0.567100 + 0.628043i
\(697\) 129.971 129.971i 0.186473 0.186473i
\(698\) −215.097 215.097i −0.308162 0.308162i
\(699\) −255.592 283.059i −0.365654 0.404948i
\(700\) 225.410 474.147i 0.322014 0.677353i
\(701\) 8.12497i 0.0115905i 0.999983 + 0.00579527i \(0.00184470\pi\)
−0.999983 + 0.00579527i \(0.998155\pi\)
\(702\) −85.0546 + 552.141i −0.121160 + 0.786525i
\(703\) −141.540 + 141.540i −0.201337 + 0.201337i
\(704\) −180.740 −0.256733
\(705\) 70.0183 + 387.561i 0.0993167 + 0.549733i
\(706\) 339.785i 0.481281i
\(707\) −621.778 + 490.236i −0.879459 + 0.693403i
\(708\) 13.5972 266.654i 0.0192052 0.376631i
\(709\) 854.167i 1.20475i 0.798214 + 0.602374i \(0.205778\pi\)
−0.798214 + 0.602374i \(0.794222\pi\)
\(710\) −78.0670 + 18.2528i −0.109954 + 0.0257082i
\(711\) −69.3953 + 678.683i −0.0976023 + 0.954547i
\(712\) −862.713 862.713i −1.21168 1.21168i
\(713\) 30.5762 + 30.5762i 0.0428839 + 0.0428839i
\(714\) 83.5508 + 117.852i 0.117018 + 0.165059i
\(715\) 327.464 + 1400.56i 0.457992 + 1.95882i
\(716\) 562.180i 0.785168i
\(717\) 7.52867 147.644i 0.0105002 0.205919i
\(718\) 114.367 + 114.367i 0.159285 + 0.159285i
\(719\) 1236.22i 1.71936i −0.510837 0.859678i \(-0.670664\pi\)
0.510837 0.859678i \(-0.329336\pi\)
\(720\) 178.077 + 137.526i 0.247330 + 0.191009i
\(721\) 18.8191 159.090i 0.0261014 0.220652i
\(722\) −79.2852 79.2852i −0.109813 0.109813i
\(723\) 1263.35 + 64.4208i 1.74737 + 0.0891021i
\(724\) −538.742 −0.744118
\(725\) 310.868 + 628.446i 0.428783 + 0.866822i
\(726\) 160.972 145.352i 0.221725 0.200210i
\(727\) −635.035 635.035i −0.873501 0.873501i 0.119351 0.992852i \(-0.461919\pi\)
−0.992852 + 0.119351i \(0.961919\pi\)
\(728\) −627.722 796.155i −0.862255 1.09362i
\(729\) −695.204 219.392i −0.953640 0.300949i
\(730\) 344.562 + 213.971i 0.472003 + 0.293112i
\(731\) 322.553 0.441249
\(732\) −9.65785 + 189.399i −0.0131938 + 0.258742i
\(733\) −174.851 + 174.851i −0.238542 + 0.238542i −0.816246 0.577704i \(-0.803949\pi\)
0.577704 + 0.816246i \(0.303949\pi\)
\(734\) 142.908i 0.194697i
\(735\) −489.406 548.367i −0.665859 0.746078i
\(736\) −82.7358 −0.112413
\(737\) 451.552 + 451.552i 0.612689 + 0.612689i
\(738\) 151.861 + 186.454i 0.205774 + 0.252648i
\(739\) 1448.98i 1.96073i −0.197187 0.980366i \(-0.563181\pi\)
0.197187 0.980366i \(-0.436819\pi\)
\(740\) 31.4269 + 134.412i 0.0424688 + 0.181638i
\(741\) 904.856 + 1002.10i 1.22113 + 1.35236i
\(742\) −375.493 + 296.055i −0.506055 + 0.398995i
\(743\) 30.8955 30.8955i 0.0415822 0.0415822i −0.686010 0.727592i \(-0.740639\pi\)
0.727592 + 0.686010i \(0.240639\pi\)
\(744\) 268.818 242.733i 0.361315 0.326254i
\(745\) −105.080 65.2544i −0.141047 0.0875898i
\(746\) 522.501i 0.700404i
\(747\) 417.706 + 512.856i 0.559179 + 0.686555i
\(748\) −202.888 + 202.888i −0.271241 + 0.271241i
\(749\) 1366.61 + 161.658i 1.82457 + 0.215832i
\(750\) −223.377 301.210i −0.297836 0.401614i
\(751\) 1095.21 1.45833 0.729167 0.684335i \(-0.239908\pi\)
0.729167 + 0.684335i \(0.239908\pi\)
\(752\) 92.8279 92.8279i 0.123441 0.123441i
\(753\) 52.7867 1035.20i 0.0701019 1.37476i
\(754\) 580.279 0.769601
\(755\) −693.737 430.808i −0.918857 0.570606i
\(756\) 493.509 279.173i 0.652790 0.369277i
\(757\) 209.069 209.069i 0.276181 0.276181i −0.555401 0.831582i \(-0.687435\pi\)
0.831582 + 0.555401i \(0.187435\pi\)
\(758\) 184.703 184.703i 0.243672 0.243672i
\(759\) 77.6125 70.0813i 0.102256 0.0923337i
\(760\) −741.308 + 173.325i −0.975406 + 0.228059i
\(761\) −710.902 −0.934168 −0.467084 0.884213i \(-0.654695\pi\)
−0.467084 + 0.884213i \(0.654695\pi\)
\(762\) 15.4802 303.581i 0.0203152 0.398400i
\(763\) −13.0640 16.5694i −0.0171219 0.0217161i
\(764\) 321.188 0.420403
\(765\) −307.041 + 39.4511i −0.401361 + 0.0515701i
\(766\) 231.666i 0.302436i
\(767\) −434.044 434.044i −0.565898 0.565898i
\(768\) −26.1250 + 512.334i −0.0340169 + 0.667102i
\(769\) −248.259 −0.322833 −0.161417 0.986886i \(-0.551606\pi\)
−0.161417 + 0.986886i \(0.551606\pi\)
\(770\) −303.494 + 380.366i