Properties

Label 105.3.k.c.62.8
Level 105
Weight 3
Character 105.62
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 62.8
Root \(0.817327 + 1.97320i\) of \(x^{16} + 433 x^{8} + 16\)
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.c.83.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(2.99611 + 0.152778i) q^{3} +3.00000i q^{4} +(-4.24762 + 2.63775i) q^{5} +(2.22660 - 2.01054i) q^{6} +(5.49694 + 4.33402i) q^{7} +(4.94975 + 4.94975i) q^{8} +(8.95332 + 0.915476i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(2.99611 + 0.152778i) 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} +(-0.458333 + 8.98832i) q^{12} +(-14.6307 - 14.6307i) q^{13} +(6.95153 - 0.822309i) q^{14} +(-13.1293 + 7.25405i) q^{15} -5.00000 q^{16} +(-4.86435 - 4.86435i) q^{17} +(6.97829 - 5.68361i) q^{18} +21.7515 q^{19} +(-7.91326 - 12.7429i) q^{20} +(15.8073 + 13.8250i) 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} +(26.6852 + 4.11073i) q^{27} +(-13.0020 + 16.4908i) q^{28} -28.0452 q^{29} +(-4.15444 + 14.4132i) q^{30} +17.2472i q^{31} +(-23.3345 + 23.3345i) q^{32} +(2.12408 - 41.6551i) 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} +(20.9532 - 1.40169i) q^{42} +(33.1548 - 33.1548i) q^{43} +41.7092 q^{44} +(-40.4451 + 19.7280i) q^{45} +2.50714 q^{46} +(18.5656 + 18.5656i) q^{47} +(-14.9805 - 0.763888i) 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} +(65.1697 + 3.32314i) q^{57} +(-19.8310 + 19.8310i) q^{58} +29.6668i q^{59} +(-21.7621 - 39.3879i) q^{60} +21.0717i q^{61} +(12.1956 + 12.1956i) q^{62} +(45.2481 + 43.8361i) 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} +(39.7853 + 48.8480i) q^{72} +(-57.3597 - 57.3597i) q^{73} -9.20249 q^{74} +(36.6339 - 65.4443i) q^{75} +65.2544i q^{76} +(60.2561 - 76.4243i) q^{77} +(-61.9921 - 3.16110i) 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} +(-41.4750 + 47.4218i) q^{84} +(33.4929 + 7.83095i) q^{85} -46.8879i q^{86} +(-84.0264 - 4.28468i) q^{87} +(68.8167 - 68.8167i) q^{88} +174.294i q^{89} +(-14.6492 + 42.5488i) q^{90} +(-17.0143 - 143.833i) q^{91} +(-5.31846 + 5.31846i) q^{92} +(-2.63499 + 51.6745i) 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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

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 \(-0.669569\pi\)
0.861430 + 0.507877i \(0.169569\pi\)
\(3\) 2.99611 + 0.152778i 0.998702 + 0.0509259i
\(4\) 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 \(-0.217748\pi\)
\(12\) −0.458333 + 8.98832i −0.0381944 + 0.749027i
\(13\) −14.6307 14.6307i −1.12543 1.12543i −0.990910 0.134524i \(-0.957049\pi\)
−0.134524 0.990910i \(-0.542951\pi\)
\(14\) 6.95153 0.822309i 0.496538 0.0587364i
\(15\) −13.1293 + 7.25405i −0.875287 + 0.483603i
\(16\) −5.00000 −0.312500
\(17\) −4.86435 4.86435i −0.286138 0.286138i 0.549413 0.835551i \(-0.314851\pi\)
−0.835551 + 0.549413i \(0.814851\pi\)
\(18\) 6.97829 5.68361i 0.387683 0.315756i
\(19\) 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
\(21\) 15.8073 + 13.8250i 0.752727 + 0.658333i
\(22\) −9.83095 9.83095i −0.446861 0.446861i
\(23\) 1.77282 + 1.77282i 0.0770791 + 0.0770791i 0.744595 0.667516i \(-0.232643\pi\)
−0.667516 + 0.744595i \(0.732643\pi\)
\(24\) 14.0738 + 15.5862i 0.586407 + 0.649424i
\(25\) 11.0845 22.4083i 0.443381 0.896333i
\(26\) −20.6909 −0.795802
\(27\) 26.6852 + 4.11073i 0.988342 + 0.152249i
\(28\) −13.0020 + 16.4908i −0.464359 + 0.588957i
\(29\) −28.0452 −0.967076 −0.483538 0.875323i \(-0.660648\pi\)
−0.483538 + 0.875323i \(0.660648\pi\)
\(30\) −4.15444 + 14.4132i −0.138481 + 0.480440i
\(31\) 17.2472i 0.556362i 0.960529 + 0.278181i \(0.0897315\pi\)
−0.960529 + 0.278181i \(0.910268\pi\)
\(32\) −23.3345 + 23.3345i −0.729204 + 0.729204i
\(33\) 2.12408 41.6551i 0.0643660 1.26228i
\(34\) −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 0.613683 0.789552i \(-0.289687\pi\)
−0.789552 + 0.613683i \(0.789687\pi\)
\(38\) 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 \(-0.605648\pi\)
−0.325844 + 0.945424i \(0.605648\pi\)
\(42\) 20.9532 1.40169i 0.498885 0.0333735i
\(43\) 33.1548 33.1548i 0.771041 0.771041i −0.207248 0.978289i \(-0.566451\pi\)
0.978289 + 0.207248i \(0.0664506\pi\)
\(44\) 41.7092 0.947936
\(45\) −40.4451 + 19.7280i −0.898779 + 0.438401i
\(46\) 2.50714 0.0545031
\(47\) 18.5656 + 18.5656i 0.395012 + 0.395012i 0.876470 0.481457i \(-0.159892\pi\)
−0.481457 + 0.876470i \(0.659892\pi\)
\(48\) −14.9805 0.763888i −0.312095 0.0159143i
\(49\) 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 \(-0.472905\pi\)
−0.996379 + 0.0850185i \(0.972905\pi\)
\(54\) 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
\(57\) 65.1697 + 3.32314i 1.14333 + 0.0583006i
\(58\) −19.8310 + 19.8310i −0.341913 + 0.341913i
\(59\) 29.6668i 0.502826i 0.967880 + 0.251413i \(0.0808953\pi\)
−0.967880 + 0.251413i \(0.919105\pi\)
\(60\) −21.7621 39.3879i −0.362702 0.656465i
\(61\) 21.0717i 0.345438i 0.984971 + 0.172719i \(0.0552552\pi\)
−0.984971 + 0.172719i \(0.944745\pi\)
\(62\) 12.1956 + 12.1956i 0.196704 + 0.196704i
\(63\) 45.2481 + 43.8361i 0.718224 + 0.695812i
\(64\) 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 0.421892 0.906646i \(-0.361366\pi\)
−0.906646 + 0.421892i \(0.861366\pi\)
\(68\) 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 \(-0.0360200\pi\)
\(72\) 39.7853 + 48.8480i 0.552573 + 0.678445i
\(73\) −57.3597 57.3597i −0.785749 0.785749i 0.195045 0.980794i \(-0.437515\pi\)
−0.980794 + 0.195045i \(0.937515\pi\)
\(74\) −9.20249 −0.124358
\(75\) 36.6339 65.4443i 0.488452 0.872591i
\(76\) 65.2544i 0.858610i
\(77\) 60.2561 76.4243i 0.782547 0.992523i
\(78\) −61.9921 3.16110i −0.794770 0.0405269i
\(79\) 75.8024i 0.959524i 0.877399 + 0.479762i \(0.159277\pi\)
−0.877399 + 0.479762i \(0.840723\pi\)
\(80\) 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 \(-0.604010\pi\)
0.947088 + 0.320974i \(0.104010\pi\)
\(84\) −41.4750 + 47.4218i −0.493749 + 0.564545i
\(85\) 33.4929 + 7.83095i 0.394034 + 0.0921288i
\(86\) 46.8879i 0.545208i
\(87\) −84.0264 4.28468i −0.965821 0.0492492i
\(88\) 68.8167 68.8167i 0.782008 0.782008i
\(89\) 174.294i 1.95836i 0.202987 + 0.979181i \(0.434935\pi\)
−0.202987 + 0.979181i \(0.565065\pi\)
\(90\) −14.6492 + 42.5488i −0.162768 + 0.472765i
\(91\) −17.0143 143.833i −0.186970 1.58058i
\(92\) −5.31846 + 5.31846i −0.0578093 + 0.0578093i
\(93\) −2.63499 + 51.6745i −0.0283332 + 0.555640i
\(94\) 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 −0.615963 0.787775i \(-0.711233\pi\)
0.787775 + 0.615963i \(0.211233\pi\)
\(98\) 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 \(-0.310813\pi\)
0.559968 + 0.828514i \(0.310813\pi\)
\(102\) −20.6109 1.05099i −0.202068 0.0103038i
\(103\) 16.1826 + 16.1826i 0.157113 + 0.157113i 0.781286 0.624173i \(-0.214564\pi\)
−0.624173 + 0.781286i \(0.714564\pi\)
\(104\) 144.836i 1.39265i
\(105\) −103.610 17.0276i −0.986763 0.162168i
\(106\) −68.3095 −0.644429
\(107\) −139.010 + 139.010i −1.29916 + 1.29916i −0.370218 + 0.928945i \(0.620717\pi\)
−0.928945 + 0.370218i \(0.879283\pi\)
\(108\) −12.3322 + 80.0557i −0.114187 + 0.741257i
\(109\) 3.01429i 0.0276540i 0.999904 + 0.0138270i \(0.00440141\pi\)
−0.999904 + 0.0138270i \(0.995599\pi\)
\(110\) 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 \(-0.0828530\pi\)
−0.257361 + 0.966315i \(0.582853\pi\)
\(114\) 48.4318 43.7321i 0.424840 0.383615i
\(115\) −12.2065 2.85400i −0.106144 0.0248174i
\(116\) 84.1356i 0.725307i
\(117\) −117.599 144.387i −1.00512 1.23408i
\(118\) 20.9776 + 20.9776i 0.177776 + 0.177776i
\(119\) −5.65685 47.8212i −0.0475366 0.401859i
\(120\) −100.892 29.0811i −0.840771 0.242342i
\(121\) −72.2952 −0.597481
\(122\) 14.8999 + 14.8999i 0.122131 + 0.122131i
\(123\) −80.0535 4.08209i −0.650842 0.0331877i
\(124\) −51.7417 −0.417272
\(125\) 12.0248 + 124.420i 0.0961984 + 0.995362i
\(126\) 62.9921 0.998435i 0.499937 0.00792409i
\(127\) −71.6476 71.6476i −0.564154 0.564154i 0.366330 0.930485i \(-0.380614\pi\)
−0.930485 + 0.366330i \(0.880614\pi\)
\(128\) −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 \(-0.401907\pi\)
0.303314 + 0.952891i \(0.401907\pi\)
\(132\) 124.965 + 6.37223i 0.946706 + 0.0482745i
\(133\) 119.566 + 94.2712i 0.898996 + 0.708806i
\(134\) −45.9316 −0.342773
\(135\) −124.192 + 52.9282i −0.919939 + 0.392061i
\(136\) 48.1546i 0.354078i
\(137\) 7.42967 7.42967i 0.0542312 0.0542312i −0.679471 0.733702i \(-0.737791\pi\)
0.733702 + 0.679471i \(0.237791\pi\)
\(138\) 7.51167 + 0.383035i 0.0544324 + 0.00277562i
\(139\) −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
\(147\) 26.9739 + 144.504i 0.183496 + 0.983021i
\(148\) 19.5214 19.5214i 0.131902 0.131902i
\(149\) 24.7386 0.166031 0.0830155 0.996548i \(-0.473545\pi\)
0.0830155 + 0.996548i \(0.473545\pi\)
\(150\) −20.3720 72.1802i −0.135813 0.481201i
\(151\) −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
\(153\) −39.0989 48.0053i −0.255548 0.313760i
\(154\) −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 −0.962285 0.272042i \(-0.912301\pi\)
0.272042 + 0.962285i \(0.412301\pi\)
\(158\) 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
\(162\) 67.6821 44.4987i 0.417791 0.274684i
\(163\) 38.8452 38.8452i 0.238314 0.238314i −0.577837 0.816152i \(-0.696103\pi\)
0.816152 + 0.577837i \(0.196103\pi\)
\(164\) 80.1575i 0.488765i
\(165\) 100.854 + 182.538i 0.611233 + 1.10629i
\(166\) 73.4931i 0.442730i
\(167\) −138.252 138.252i −0.827855 0.827855i 0.159365 0.987220i \(-0.449055\pi\)
−0.987220 + 0.159365i \(0.949055\pi\)
\(168\) 9.81182 + 146.672i 0.0584037 + 0.873049i
\(169\) 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 \(-0.714857\pi\)
0.780711 + 0.624893i \(0.214857\pi\)
\(174\) −62.4454 + 56.3859i −0.358882 + 0.324057i
\(175\) 158.049 75.1367i 0.903137 0.429352i
\(176\) 69.5153i 0.394973i
\(177\) −4.53242 + 88.8848i −0.0256069 + 0.502174i
\(178\) 123.245 + 123.245i 0.692386 + 0.692386i
\(179\) 187.393 1.04689 0.523445 0.852059i \(-0.324646\pi\)
0.523445 + 0.852059i \(0.324646\pi\)
\(180\) −59.1841 121.335i −0.328801 0.674085i
\(181\) 179.581i 0.992158i 0.868277 + 0.496079i \(0.165227\pi\)
−0.868277 + 0.496079i \(0.834773\pi\)
\(182\) −113.736 89.6745i −0.624925 0.492717i
\(183\) −3.21928 + 63.1331i −0.0175917 + 0.344990i
\(184\) 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
\(189\) 128.871 + 138.251i 0.681858 + 0.731485i
\(190\) −24.7607 + 105.901i −0.130320 + 0.557375i
\(191\) 107.063i 0.560538i 0.959922 + 0.280269i \(0.0904236\pi\)
−0.959922 + 0.280269i \(0.909576\pi\)
\(192\) −1.98611 + 38.9494i −0.0103443 + 0.202861i
\(193\) −81.6333 + 81.6333i −0.422971 + 0.422971i −0.886225 0.463255i \(-0.846682\pi\)
0.463255 + 0.886225i \(0.346682\pi\)
\(194\) 23.5689i 0.121489i
\(195\) 298.222 + 85.9589i 1.52934 + 0.440815i
\(196\) −142.943 + 34.2979i −0.729300 + 0.174989i
\(197\) 165.702 165.702i 0.841127 0.841127i −0.147878 0.989006i \(-0.547244\pi\)
0.989006 + 0.147878i \(0.0472444\pi\)
\(198\) −79.0196 97.0196i −0.399089 0.489998i
\(199\) 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
\(207\) 14.2496 + 17.4956i 0.0688388 + 0.0845197i
\(208\) 73.1533 + 73.1533i 0.351698 + 0.351698i
\(209\) 302.412i 1.44695i
\(210\) −85.3038 + 61.2231i −0.406208 + 0.291539i
\(211\) 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
\(213\) 2.44971 48.0411i 0.0115010 0.225545i
\(214\) 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
\(222\) −27.5717 1.40593i −0.124197 0.00633304i
\(223\) −173.529 173.529i −0.778155 0.778155i 0.201362 0.979517i \(-0.435463\pi\)
−0.979517 + 0.201362i \(0.935463\pi\)
\(224\) −229.401 + 27.1362i −1.02411 + 0.121144i
\(225\) 119.758 190.481i 0.532256 0.846584i
\(226\) 113.295 0.501306
\(227\) −191.389 191.389i −0.843123 0.843123i 0.146140 0.989264i \(-0.453315\pi\)
−0.989264 + 0.146140i \(0.953315\pi\)
\(228\) −9.96941 + 195.509i −0.0437255 + 0.857496i
\(229\) −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
\(231\) 192.210 219.770i 0.832076 0.951383i
\(232\) −138.817 138.817i −0.598348 0.598348i
\(233\) −89.8918 89.8918i −0.385802 0.385802i 0.487385 0.873187i \(-0.337951\pi\)
−0.873187 + 0.487385i \(0.837951\pi\)
\(234\) −185.252 18.9420i −0.791675 0.0809487i
\(235\) −127.831 29.8881i −0.543961 0.127183i
\(236\) −89.0003 −0.377120
\(237\) −11.5809 + 227.112i −0.0488646 + 0.958279i
\(238\) −37.8147 29.8147i −0.158885 0.125272i
\(239\) −49.2786 −0.206187 −0.103093 0.994672i \(-0.532874\pi\)
−0.103093 + 0.994672i \(0.532874\pi\)
\(240\) 65.6465 36.2702i 0.273527 0.151126i
\(241\) 421.664i 1.74964i −0.484445 0.874822i \(-0.660979\pi\)
0.484445 0.874822i \(-0.339021\pi\)
\(242\) −51.1204 + 51.1204i −0.211242 + 0.211242i
\(243\) 235.158 + 61.2344i 0.967729 + 0.251993i
\(244\) −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 \(-0.741631\pi\)
−0.688274 + 0.725450i \(0.741631\pi\)
\(252\) −131.508 + 135.744i −0.521859 + 0.538668i
\(253\) 24.6476 24.6476i 0.0974214 0.0974214i
\(254\) −101.325 −0.398917
\(255\) 99.1518 + 28.5793i 0.388831 + 0.112076i
\(256\) −171.000 −0.667969
\(257\) 216.568 + 216.568i 0.842676 + 0.842676i 0.989206 0.146530i \(-0.0468104\pi\)
−0.146530 + 0.989206i \(0.546810\pi\)
\(258\) 7.16342 140.481i 0.0277652 0.544501i
\(259\) −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 \(-0.0727686\pi\)
−0.226623 + 0.973982i \(0.572769\pi\)
\(264\) 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
\(267\) −26.6283 + 522.204i −0.0997313 + 1.95582i
\(268\) 97.4357 97.4357i 0.363566 0.363566i
\(269\) 349.961i 1.30097i 0.759519 + 0.650485i \(0.225434\pi\)
−0.759519 + 0.650485i \(0.774566\pi\)
\(270\) −50.3909 + 125.243i −0.186633 + 0.463862i
\(271\) 137.978i 0.509143i 0.967054 + 0.254572i \(0.0819344\pi\)
−0.967054 + 0.254572i \(0.918066\pi\)
\(272\) 24.3218 + 24.3218i 0.0894182 + 0.0894182i
\(273\) −29.0021 433.539i −0.106235 1.58806i
\(274\) 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 0.904966 0.425484i \(-0.139896\pi\)
−0.425484 + 0.904966i \(0.639896\pi\)
\(278\) −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 \(-0.0813658\pi\)
\(282\) 78.6649 + 4.01128i 0.278954 + 0.0142244i
\(283\) 120.235 + 120.235i 0.424858 + 0.424858i 0.886873 0.462014i \(-0.152873\pi\)
−0.462014 + 0.886873i \(0.652873\pi\)
\(284\) 48.1035 0.169378
\(285\) −285.582 + 157.786i −1.00204 + 0.553636i
\(286\) 287.666i 1.00583i
\(287\) −146.874 115.801i −0.511755 0.403489i
\(288\) −230.284 + 187.559i −0.799596 + 0.651247i
\(289\) 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 0.354747 0.934962i \(-0.384567\pi\)
0.934962 0.354747i \(-0.115433\pi\)
\(294\) 121.253 + 83.1064i 0.412426 + 0.282675i
\(295\) −78.2536 126.013i −0.265266 0.427163i
\(296\) 64.4174i 0.217626i
\(297\) 57.1518 371.007i 0.192430 1.24918i
\(298\) 17.4929 17.4929i 0.0587009 0.0587009i
\(299\) 51.8750i 0.173495i
\(300\) 196.333 + 109.902i 0.654443 + 0.366339i
\(301\) 325.943 38.5564i 1.08287 0.128094i
\(302\) −115.487 + 115.487i −0.382409 + 0.382409i
\(303\) 338.900 + 17.2812i 1.11848 + 0.0570337i
\(304\) −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 −0.535928 0.844264i \(-0.680038\pi\)
0.844264 + 0.535928i \(0.180038\pi\)
\(308\) 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 \(-0.384140\pi\)
0.356000 + 0.934486i \(0.384140\pi\)
\(312\) 22.1277 433.944i 0.0709221 1.39085i
\(313\) −225.950 225.950i −0.721885 0.721885i 0.247104 0.968989i \(-0.420521\pi\)
−0.968989 + 0.247104i \(0.920521\pi\)
\(314\) 153.256i 0.488076i
\(315\) −307.826 66.8458i −0.977224 0.212209i
\(316\) −227.407 −0.719643
\(317\) −96.2271 + 96.2271i −0.303556 + 0.303556i −0.842403 0.538848i \(-0.818860\pi\)
0.538848 + 0.842403i \(0.318860\pi\)
\(318\) −204.663 10.4362i −0.643593 0.0328181i
\(319\) 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
\(327\) −0.460516 + 9.03113i −0.00140830 + 0.0276181i
\(328\) −132.253 132.253i −0.403211 0.403211i
\(329\) 21.5903 + 182.517i 0.0656240 + 0.554764i
\(330\) 200.388 + 57.7594i 0.607236 + 0.175029i
\(331\) 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
\(333\) −52.3034 64.2177i −0.157067 0.192846i
\(334\) −195.517 −0.585382
\(335\) 223.627 + 52.2861i 0.667543 + 0.156078i
\(336\) −79.0364 69.1249i −0.235227 0.205729i
\(337\) 109.576 + 109.576i 0.325152 + 0.325152i 0.850739 0.525588i \(-0.176155\pi\)
−0.525588 + 0.850739i \(0.676155\pi\)
\(338\) 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
\(342\) 151.788 123.627i 0.443825 0.361482i
\(343\) −143.661 + 311.465i −0.418837 + 0.908061i
\(344\) 328.215 0.954114
\(345\) −36.1360 10.4158i −0.104742 0.0301906i
\(346\) 38.1223i 0.110180i
\(347\) 268.600 268.600i 0.774062 0.774062i −0.204752 0.978814i \(-0.565639\pi\)
0.978814 + 0.204752i \(0.0656387\pi\)
\(348\) 12.8540 252.079i 0.0369369 0.724366i
\(349\) 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 \(-0.590172\pi\)
0.960143 + 0.279509i \(0.0901715\pi\)
\(354\) 59.6461 + 66.0559i 0.168492 + 0.186599i
\(355\) 42.2950 + 68.1084i 0.119141 + 0.191855i
\(356\) −522.883 −1.46877
\(357\) −9.64254 144.142i −0.0270099 0.403758i
\(358\) 132.507 132.507i 0.370132 0.370132i
\(359\) 161.739 0.450526 0.225263 0.974298i \(-0.427676\pi\)
0.225263 + 0.974298i \(0.427676\pi\)
\(360\) −297.842 102.544i −0.827338 0.284845i
\(361\) 112.126 0.310599
\(362\) 126.983 + 126.983i 0.350781 + 0.350781i
\(363\) −216.604 11.0451i −0.596706 0.0304272i
\(364\) 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 −0.831247 0.555904i \(-0.812372\pi\)
0.555904 + 0.831247i \(0.312372\pi\)
\(368\) −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
\(372\) −155.024 7.90497i −0.416730 0.0212499i
\(373\) −369.464 + 369.464i −0.990521 + 0.990521i −0.999955 0.00943464i \(-0.996997\pi\)
0.00943464 + 0.999955i \(0.496997\pi\)
\(374\) 95.6424i 0.255728i
\(375\) 17.0190 + 374.614i 0.0453839 + 0.998970i
\(376\) 183.790i 0.488803i
\(377\) 410.320 + 410.320i 1.08838 + 1.08838i
\(378\) 188.884 + 6.63236i 0.499692 + 0.0175459i
\(379\) 261.209i 0.689207i −0.938748 0.344604i \(-0.888013\pi\)
0.938748 0.344604i \(-0.111987\pi\)
\(380\) −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 \(-0.652200\pi\)
0.887847 + 0.460138i \(0.152200\pi\)
\(384\) −239.254 264.965i −0.623057 0.690013i
\(385\) −54.3566 + 483.562i −0.141186 + 1.25600i
\(386\) 115.447i 0.299085i
\(387\) 327.197 266.493i 0.845472 0.688612i
\(388\) 49.9973 + 49.9973i 0.128859 + 0.128859i
\(389\) −401.000 −1.03085 −0.515425 0.856935i \(-0.672366\pi\)
−0.515425 + 0.856935i \(0.672366\pi\)
\(390\) 271.657 150.093i 0.696556 0.384853i
\(391\) 17.2472i 0.0441105i
\(392\) −179.255 + 292.432i −0.457283 + 0.746001i
\(393\) 238.096 + 12.1410i 0.605841 + 0.0308931i
\(394\) 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 −0.211440 0.977391i \(-0.567815\pi\)
0.977391 + 0.211440i \(0.0678154\pi\)
\(398\) 155.590 155.590i 0.390929 0.390929i
\(399\) 343.831 + 300.714i 0.861733 + 0.753668i
\(400\) −55.4226 + 112.042i −0.138557 + 0.280104i
\(401\) 582.912i 1.45365i 0.686825 + 0.726823i \(0.259004\pi\)
−0.686825 + 0.726823i \(0.740996\pi\)
\(402\) −137.616 7.01732i −0.342329 0.0174560i
\(403\) 252.338 252.338i 0.626149 0.626149i
\(404\) 339.341i 0.839952i
\(405\) −380.178 + 139.605i −0.938712 + 0.344704i
\(406\) −194.957 + 23.0618i −0.480190 + 0.0568025i
\(407\) −90.4693 + 90.4693i −0.222283 + 0.222283i
\(408\) 7.35694 144.276i 0.0180317 0.353619i
\(409\) 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
\(417\) −538.068 27.4372i −1.29033 0.0657965i
\(418\) −213.838 213.838i −0.511573 0.511573i
\(419\) 343.927i 0.820828i −0.911899 0.410414i \(-0.865384\pi\)
0.911899 0.410414i \(-0.134616\pi\)
\(420\) 51.0828 310.830i 0.121626 0.740072i
\(421\) 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
\(423\) 149.227 + 183.220i 0.352783 + 0.433144i
\(424\) 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 \(0.828164\pi\)
\(432\) −133.426 20.5537i −0.308857 0.0475779i
\(433\) −487.352 487.352i −1.12553 1.12553i −0.990896 0.134629i \(-0.957016\pi\)
−0.134629 0.990896i \(-0.542984\pi\)
\(434\) 14.1825 + 119.895i 0.0326787 + 0.276255i
\(435\) 368.214 203.441i 0.846469 0.467681i
\(436\) −9.04287 −0.0207405
\(437\) 38.5614 + 38.5614i 0.0882412 + 0.0882412i
\(438\) −243.041 12.3931i −0.554888 0.0282948i
\(439\) 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
\(441\) 58.7396 + 437.071i 0.133196 + 0.991090i
\(442\) 100.648 + 100.648i 0.227710 + 0.227710i
\(443\) 188.010 + 188.010i 0.424401 + 0.424401i 0.886716 0.462315i \(-0.152981\pi\)
−0.462315 + 0.886716i \(0.652981\pi\)
\(444\) 61.4707 55.5059i 0.138448 0.125013i
\(445\) −459.745 740.336i −1.03314 1.66368i
\(446\) −245.406 −0.550239
\(447\) 74.1196 + 3.77951i 0.165816 + 0.00845528i
\(448\) −56.3422 + 71.4602i −0.125764 + 0.159509i
\(449\) −397.613 −0.885552 −0.442776 0.896632i \(-0.646006\pi\)
−0.442776 + 0.896632i \(0.646006\pi\)
\(450\) −50.0092 219.372i −0.111132 0.487493i
\(451\) 371.478i 0.823677i
\(452\) −240.335 + 240.335i −0.531716 + 0.531716i
\(453\) −489.336 24.9522i −1.08021 0.0550821i
\(454\) −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 0.630927 0.775842i \(-0.282675\pi\)
−0.775842 + 0.630927i \(0.782675\pi\)
\(458\) −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 \(-0.433386\pi\)
0.207750 + 0.978182i \(0.433386\pi\)
\(462\) −19.4878 291.313i −0.0421813 0.630548i
\(463\) 42.9857 42.9857i 0.0928417 0.0928417i −0.659161 0.752002i \(-0.729088\pi\)
0.752002 + 0.659161i \(0.229088\pi\)
\(464\) 140.226 0.302211
\(465\) −125.112 226.444i −0.269058 0.486977i
\(466\) −127.126 −0.272803
\(467\) −252.836 252.836i −0.541405 0.541405i 0.382536 0.923941i \(-0.375051\pi\)
−0.923941 + 0.382536i \(0.875051\pi\)
\(468\) 433.161 352.797i 0.925557 0.753839i
\(469\) −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
\(477\) −388.245 476.684i −0.813930 0.999337i
\(478\) −34.8452 + 34.8452i −0.0728980 + 0.0728980i
\(479\) 91.5191i 0.191063i −0.995426 0.0955314i \(-0.969545\pi\)
0.995426 0.0955314i \(-0.0304550\pi\)
\(480\) 137.096 475.636i 0.285618 0.990908i
\(481\) 190.408i 0.395858i
\(482\) −298.161 298.161i −0.618592 0.618592i
\(483\) 3.51424 + 52.5326i 0.00727585 + 0.108763i
\(484\) 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 0.917230 0.398358i \(-0.130420\pi\)
−0.398358 + 0.917230i \(0.630420\pi\)
\(488\) −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 \(-0.176913\pi\)
\(492\) 12.2463 240.161i 0.0248908 0.488131i
\(493\) 136.422 + 136.422i 0.276717 + 0.276717i
\(494\) −450.057 −0.911046
\(495\) 274.280 + 562.311i 0.554102 + 1.13598i
\(496\) 86.2361i 0.173863i
\(497\) 69.4937 88.1406i 0.139826 0.177345i
\(498\) 11.2281 220.193i 0.0225464 0.442155i
\(499\) 217.267i 0.435404i 0.976015 + 0.217702i \(0.0698561\pi\)
−0.976015 + 0.217702i \(0.930144\pi\)
\(500\) −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 \(-0.744299\pi\)
0.719657 + 0.694329i \(0.244299\pi\)
\(504\) 6.98904 + 440.945i 0.0138671 + 0.874890i
\(505\) −480.463 + 298.365i −0.951412 + 0.590823i
\(506\) 34.8570i 0.0688873i
\(507\) −39.5865 + 776.327i −0.0780798 + 1.53122i
\(508\) 214.943 214.943i 0.423116 0.423116i
\(509\) 611.593i 1.20156i −0.799415 0.600779i \(-0.794857\pi\)
0.799415 0.600779i \(-0.205143\pi\)
\(510\) 90.3195 49.9023i 0.177097 0.0978476i
\(511\) −66.7048 563.900i −0.130538 1.10352i
\(512\) 215.668 215.668i 0.421226 0.421226i
\(513\) 580.443 + 89.4144i 1.13147 + 0.174297i
\(514\) 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 \(-0.731397\pi\)
−0.664597 + 0.747202i \(0.731397\pi\)
\(522\) −195.708 + 159.398i −0.374919 + 0.305360i
\(523\) 583.903 + 583.903i 1.11645 + 1.11645i 0.992258 + 0.124191i \(0.0396337\pi\)
0.124191 + 0.992258i \(0.460366\pi\)
\(524\) 238.405i 0.454971i
\(525\) 485.011 200.971i 0.923830 0.382802i
\(526\) 277.971 0.528463
\(527\) 83.8965 83.8965i 0.159196 0.159196i
\(528\) −10.6204 + 208.275i −0.0201144 + 0.394461i
\(529\) 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
\(537\) 561.451 + 28.6295i 1.04553 + 0.0533138i
\(538\) 247.460 + 247.460i 0.459963 + 0.459963i
\(539\) 662.448 158.948i 1.22903 0.294895i
\(540\) −158.785 372.575i −0.294046 0.689954i
\(541\) 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
\(543\) −27.4359 + 538.043i −0.0505265 + 0.990871i
\(544\) 227.015 0.417306
\(545\) −7.95095 12.8035i −0.0145889 0.0234927i
\(546\) −327.066 286.051i −0.599022 0.523903i
\(547\) 223.888 + 223.888i 0.409302 + 0.409302i 0.881495 0.472193i \(-0.156538\pi\)
−0.472193 + 0.881495i \(0.656538\pi\)
\(548\) 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
\(552\) −2.68125 + 52.5817i −0.00485733 + 0.0952567i
\(553\) −328.529 + 416.681i −0.594084 + 0.753492i
\(554\) 187.831 0.339045
\(555\) 132.637 + 38.2312i 0.238986 + 0.0688850i
\(556\) 538.767i 0.969005i
\(557\) −245.854 + 245.854i −0.441390 + 0.441390i −0.892479 0.451089i \(-0.851036\pi\)
0.451089 + 0.892479i \(0.351036\pi\)
\(558\) 98.0265 + 120.356i 0.175675 + 0.215692i
\(559\) −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 \(-0.920527\pi\)
0.247086 + 0.968993i \(0.420527\pi\)
\(564\) −175.383 + 158.364i −0.310962 + 0.280788i
\(565\) −551.600 128.969i −0.976283 0.228264i
\(566\) 170.038 0.300420
\(567\) 364.990 + 433.902i 0.643721 + 0.765260i
\(568\) 79.3667 79.3667i 0.139730 0.139730i
\(569\) 690.156 1.21293 0.606464 0.795111i \(-0.292587\pi\)
0.606464 + 0.795111i \(0.292587\pi\)
\(570\) −90.3651 + 313.508i −0.158535 + 0.550015i
\(571\) 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
\(573\) −16.3568 + 320.771i −0.0285459 + 0.559810i
\(574\) −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 −0.892339 0.451366i \(-0.850937\pi\)
0.451366 + 0.892339i \(0.350937\pi\)
\(578\) −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
\(582\) 3.60081 70.6151i 0.00618695 0.121332i
\(583\) −671.548 + 671.548i −1.15188 + 1.15188i
\(584\) 567.832i 0.972315i
\(585\) 880.372 + 303.104i 1.50491 + 0.518126i
\(586\) 534.410i 0.911962i
\(587\) 195.495 + 195.495i 0.333040 + 0.333040i 0.853740 0.520700i \(-0.174329\pi\)
−0.520700 + 0.853740i \(0.674329\pi\)
\(588\) −433.512 + 80.9216i −0.737265 + 0.137622i
\(589\) 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 \(-0.680403\pi\)
0.843648 + 0.536897i \(0.180403\pi\)
\(594\) −221.929 302.754i −0.373618 0.509686i
\(595\) 150.169 + 188.205i 0.252384 + 0.316311i
\(596\) 74.2159i 0.124523i
\(597\) 659.255 + 33.6167i 1.10428 + 0.0563094i
\(598\) −36.6812 36.6812i −0.0613397 0.0613397i
\(599\) 376.201 0.628048 0.314024 0.949415i \(-0.398323\pi\)
0.314024 + 0.949415i \(0.398323\pi\)
\(600\) 505.261 142.604i 0.842102 0.237674i
\(601\) 1122.87i 1.86834i 0.356832 + 0.934169i \(0.383857\pi\)
−0.356832 + 0.934169i \(0.616143\pi\)
\(602\) 203.213 257.740i 0.337563 0.428139i
\(603\) −261.058 320.524i −0.432931 0.531549i
\(604\) 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 −0.804554 0.593879i \(-0.797596\pi\)
0.593879 + 0.804554i \(0.297596\pi\)
\(608\) −507.560 + 507.560i −0.834803 + 0.834803i
\(609\) −443.318 387.724i −0.727944 0.636658i
\(610\) −102.592 23.9869i −0.168183 0.0393228i
\(611\) 543.253i 0.889122i
\(612\) 144.016 117.297i 0.235320 0.191661i
\(613\) 668.817 668.817i 1.09105 1.09105i 0.0956388 0.995416i \(-0.469511\pi\)
0.995416 0.0956388i \(-0.0304894\pi\)
\(614\) 133.868i 0.218026i
\(615\) 350.804 193.822i 0.570414 0.315158i
\(616\) 676.533 80.0283i 1.09827 0.129916i
\(617\) −416.614 + 416.614i −0.675225 + 0.675225i −0.958916 0.283691i \(-0.908441\pi\)
0.283691 + 0.958916i \(0.408441\pi\)
\(618\) 68.5679 + 3.49641i 0.110951 + 0.00565763i
\(619\) −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
\(627\) 46.2018 906.059i 0.0736870 1.44507i
\(628\) −325.105 325.105i −0.517683 0.517683i
\(629\) 63.3061i 0.100646i
\(630\) −264.933 + 170.399i −0.420528 + 0.270474i
\(631\) −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
\(633\) 828.695 + 42.2568i 1.30915 + 0.0667564i
\(634\) 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 \(-0.0466304\pi\)
\(642\) −30.0346 + 589.006i −0.0467829 + 0.917455i
\(643\) 767.988 + 767.988i 1.19438 + 1.19438i 0.975824 + 0.218559i \(0.0701356\pi\)
0.218559 + 0.975824i \(0.429864\pi\)
\(644\) −52.2855 + 6.18494i −0.0811886 + 0.00960395i
\(645\) −194.793 + 675.805i −0.302004 + 1.04776i
\(646\) −149.633 −0.231631
\(647\) −573.588 573.588i −0.886535 0.886535i 0.107654 0.994188i \(-0.465666\pi\)
−0.994188 + 0.107654i \(0.965666\pi\)
\(648\) 311.491 + 473.774i 0.480696 + 0.731133i
\(649\) 412.459 0.635530
\(650\) −229.348 + 463.648i −0.352844 + 0.713304i
\(651\) −238.443 + 272.632i −0.366271 + 0.418789i
\(652\) 116.536 + 116.536i 0.178736 + 0.178736i
\(653\) −142.398 142.398i −0.218067 0.218067i 0.589616 0.807683i \(-0.299279\pi\)
−0.807683 + 0.589616i \(0.799279\pi\)
\(654\) 6.06034 + 6.71161i 0.00926658 + 0.0102624i
\(655\) −337.551 + 209.618i −0.515345 + 0.320027i
\(656\) 133.596 0.203652
\(657\) −461.048 566.071i −0.701747 0.861600i
\(658\) 144.326 + 113.793i 0.219340 + 0.172937i
\(659\) −960.106 −1.45691 −0.728457 0.685092i \(-0.759762\pi\)
−0.728457 + 0.685092i \(0.759762\pi\)
\(660\) −547.613 + 302.561i −0.829717 + 0.458425i
\(661\) 94.8355i 0.143473i 0.997424 + 0.0717364i \(0.0228540\pi\)
−0.997424 + 0.0717364i \(0.977146\pi\)
\(662\) 123.754 123.754i 0.186939 0.186939i
\(663\) −21.7459 + 426.458i −0.0327993 + 0.643224i
\(664\) 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
\(672\) −691.455 + 46.2557i −1.02895 + 0.0688329i
\(673\) −442.857 + 442.857i −0.658034 + 0.658034i −0.954915 0.296880i \(-0.904054\pi\)
0.296880 + 0.954915i \(0.404054\pi\)
\(674\) 154.964 0.229917
\(675\) 387.908 552.406i 0.574678 0.818379i
\(676\) −777.336 −1.14990
\(677\) −447.410 447.410i −0.660872 0.660872i 0.294714 0.955586i \(-0.404776\pi\)
−0.955586 + 0.294714i \(0.904776\pi\)
\(678\) 339.445 + 17.3090i 0.500656 + 0.0255295i
\(679\) 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 \(-0.316269\pi\)
−0.837990 + 0.545686i \(0.816269\pi\)
\(684\) −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
\(687\) −369.991 18.8666i −0.538560 0.0274622i
\(688\) −165.774 + 165.774i −0.240950 + 0.240950i
\(689\) 1413.38i 2.05135i
\(690\) −32.9171 + 18.1869i −0.0477059 + 0.0263579i
\(691\) 207.196i 0.299849i −0.988697 0.149925i \(-0.952097\pi\)
0.988697 0.149925i \(-0.0479031\pi\)
\(692\) 80.8697 + 80.8697i 0.116864 + 0.116864i
\(693\) 609.457 629.088i 0.879447 0.907775i
\(694\) 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 \(0.998155\pi\)
\(702\) −552.141 85.0546i −0.786525 0.121160i
\(703\) −141.540 141.540i −0.201337 0.201337i
\(704\) 180.740 0.256733
\(705\) −378.429 109.078i −0.536779 0.154720i
\(706\) 339.785i 0.481281i
\(707\) 621.778 + 490.236i 0.879459 + 0.693403i
\(708\) −266.654 13.5972i −0.376631 0.0192052i
\(709\) 854.167i 1.20475i −0.798214 0.602374i \(-0.794222\pi\)
0.798214 0.602374i \(-0.205778\pi\)
\(710\) 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
\(714\) −108.742 95.1052i −0.152300 0.133201i
\(715\) 327.464 1400.56i 0.457992 1.95882i
\(716\) 562.180i 0.785168i
\(717\) −147.644 7.52867i −0.205919 0.0105002i
\(718\) 114.367 114.367i 0.159285 0.159285i
\(719\) 1236.22i 1.71936i −0.510837 0.859678i \(-0.670664\pi\)
0.510837 0.859678i \(-0.329336\pi\)
\(720\) 202.225 98.6402i 0.280869 0.137000i
\(721\) 18.8191 + 159.090i 0.0261014 + 0.220652i
\(722\) 79.2852 79.2852i 0.109813 0.109813i
\(723\) 64.4208 1263.35i 0.0891021 1.74737i
\(724\) −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 −0.992852 0.119351i \(-0.961919\pi\)
0.119351 + 0.992852i \(0.461919\pi\)
\(728\) 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
\(732\) −189.399 9.65785i −0.258742 0.0131938i
\(733\) −174.851 174.851i −0.238542 0.238542i 0.577704 0.816246i \(-0.303949\pi\)
−0.816246 + 0.577704i \(0.803949\pi\)
\(734\) 142.908i 0.194697i
\(735\) −495.741 542.648i −0.674477 0.738296i
\(736\) −82.7358 −0.112413
\(737\) −451.552 + 451.552i −0.612689 + 0.612689i
\(738\) −186.454 + 151.861i −0.252648 + 0.205774i
\(739\) 1448.98i 1.96073i 0.197187 + 0.980366i \(0.436819\pi\)
−0.197187 + 0.980366i \(0.563181\pi\)
\(740\) −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 \(-0.259361\pi\)
−0.727592 + 0.686010i \(0.759361\pi\)
\(744\) −268.818 + 242.733i −0.361315 + 0.326254i
\(745\) −105.080 + 65.2544i −0.141047 + 0.0875898i
\(746\) 522.501i 0.700404i
\(747\) 512.856 417.706i 0.686555 0.559179i
\(748\) −202.888 202.888i −0.271241 0.271241i
\(749\) −1366.61 + 161.658i −1.82457 + 0.215832i
\(750\) 276.926 + 252.858i 0.369235 + 0.337143i
\(751\) 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
\(753\) −1035.20 52.7867i −1.37476 0.0701019i
\(754\) 580.279 0.769601
\(755\) 693.737 430.808i 0.918857 0.570606i
\(756\) −414.752 + 386.613i −0.548614 + 0.511393i
\(757\) 209.069 + 209.069i 0.276181 + 0.276181i 0.831582 0.555401i \(-0.187435\pi\)
−0.555401 + 0.831582i \(0.687435\pi\)
\(758\) −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 \(-0.345305\pi\)
0.467084 + 0.884213i \(0.345305\pi\)
\(762\) −303.581 15.4802i −0.398400 0.0203152i
\(763\) −13.0640 + 16.5694i −0.0171219 + 0.0217161i
\(764\) −321.188 −0.420403
\(765\) 292.703 + 100.775i 0.382618 + 0.131732i
\(766\) 231.666i 0.302436i
\(767\) 434.044 434.044i 0.565898 0.565898i
\(768\) −512.334 26.1250i −0.667102 0.0340169i
\(769\) −248.259 −0.322833 −0.161417 0.986886i \(-0.551606\pi\)
−0.161417 + 0.986886i \(0.551606\pi\)
\(770\) 303.494 + 380.366i 0.394148 +