Properties

Label 105.3.k.c.83.8
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 83.8
Root \(0.817327 - 1.97320i\) of \(x^{16} + 433 x^{8} + 16\)
Character \(\chi\) \(=\) 105.83
Dual form 105.3.k.c.62.8

$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

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 0.861430 0.507877i \(-0.169569\pi\)
−0.507877 + 0.861430i \(0.669569\pi\)
\(3\) 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 \(0.217748\pi\)
−0.775003 + 0.631958i \(0.782252\pi\)
\(12\) −0.458333 8.98832i −0.0381944 0.749027i
\(13\) −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
\(15\) −13.1293 7.25405i −0.875287 0.483603i
\(16\) −5.00000 −0.312500
\(17\) −4.86435 + 4.86435i −0.286138 + 0.286138i −0.835551 0.549413i \(-0.814851\pi\)
0.549413 + 0.835551i \(0.314851\pi\)
\(18\) 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 −0.667516 0.744595i \(-0.732643\pi\)
0.744595 + 0.667516i \(0.232643\pi\)
\(24\) 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 \(-0.910268\pi\)
0.960529 0.278181i \(-0.0897315\pi\)
\(32\) −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 −0.789552 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 \(-0.605648\pi\)
−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 0.978289 0.207248i \(-0.0664506\pi\)
−0.207248 + 0.978289i \(0.566451\pi\)
\(44\) 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 −0.481457 0.876470i \(-0.659892\pi\)
0.876470 + 0.481457i \(0.159892\pi\)
\(48\) −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 −0.996379 0.0850185i \(-0.972905\pi\)
0.0850185 + 0.996379i \(0.472905\pi\)
\(54\) 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 \(-0.919105\pi\)
0.967880 0.251413i \(-0.0808953\pi\)
\(60\) −21.7621 + 39.3879i −0.362702 + 0.656465i
\(61\) 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
\(63\) 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 −0.906646 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 \(0.0360200\pi\)
−0.993604 + 0.112919i \(0.963980\pi\)
\(72\) 39.7853 48.8480i 0.552573 0.678445i
\(73\) −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
\(75\) 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 \(-0.840723\pi\)
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 0.947088 0.320974i \(-0.104010\pi\)
−0.320974 + 0.947088i \(0.604010\pi\)
\(84\) −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 \(-0.565065\pi\)
0.202987 0.979181i \(-0.434935\pi\)
\(90\) −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 0.787775 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 \(-0.310813\pi\)
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 −0.624173 0.781286i \(-0.714564\pi\)
0.781286 + 0.624173i \(0.214564\pi\)
\(104\) 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 −0.928945 0.370218i \(-0.879283\pi\)
−0.370218 0.928945i \(-0.620717\pi\)
\(108\) −12.3322 80.0557i −0.114187 0.741257i
\(109\) 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 −0.257361 0.966315i \(-0.582853\pi\)
0.966315 + 0.257361i \(0.0828530\pi\)
\(114\) 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 −0.930485 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 \(-0.401907\pi\)
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 0.733702 0.679471i \(-0.237791\pi\)
−0.679471 + 0.733702i \(0.737791\pi\)
\(138\) 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 0.272042 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
\(162\) 67.6821 + 44.4987i 0.417791 + 0.274684i
\(163\) 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
\(165\) 100.854 182.538i 0.611233 1.10629i
\(166\) 73.4931i 0.442730i
\(167\) −138.252 + 138.252i −0.827855 + 0.827855i −0.987220 0.159365i \(-0.949055\pi\)
0.159365 + 0.987220i \(0.449055\pi\)
\(168\) 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 0.780711 0.624893i \(-0.214857\pi\)
−0.624893 + 0.780711i \(0.714857\pi\)
\(174\) −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 \(-0.834773\pi\)
0.868277 0.496079i \(-0.165227\pi\)
\(182\) −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 \(-0.909576\pi\)
0.959922 0.280269i \(-0.0904236\pi\)
\(192\) −1.98611 38.9494i −0.0103443 0.202861i
\(193\) −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
\(195\) 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 0.989006 0.147878i \(-0.0472444\pi\)
−0.147878 + 0.989006i \(0.547244\pi\)
\(198\) −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 −0.979517 0.201362i \(-0.935463\pi\)
0.201362 + 0.979517i \(0.435463\pi\)
\(224\) −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 −0.989264 0.146140i \(-0.953315\pi\)
0.146140 + 0.989264i \(0.453315\pi\)
\(228\) −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 −0.873187 0.487385i \(-0.837951\pi\)
0.487385 + 0.873187i \(0.337951\pi\)
\(234\) −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 \(0.339021\pi\)
−0.484445 + 0.874822i \(0.660979\pi\)
\(242\) −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 −0.146530 0.989206i \(-0.546810\pi\)
0.989206 + 0.146530i \(0.0468104\pi\)
\(258\) 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 −0.226623 0.973982i \(-0.572769\pi\)
0.973982 + 0.226623i \(0.0727686\pi\)
\(264\) 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 \(-0.774566\pi\)
0.759519 0.650485i \(-0.225434\pi\)
\(270\) −50.3909 125.243i −0.186633 0.463862i
\(271\) 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
\(273\) −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 −0.425484 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 \(0.0813658\pi\)
−0.967507 + 0.252844i \(0.918634\pi\)
\(282\) 78.6649 4.01128i 0.278954 0.0142244i
\(283\) 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
\(285\) −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 0.934962 + 0.354747i \(0.115433\pi\)
0.354747 + 0.934962i \(0.384567\pi\)
\(294\) 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 0.844264 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 \(-0.384140\pi\)
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 −0.968989 0.247104i \(-0.920521\pi\)
0.247104 + 0.968989i \(0.420521\pi\)
\(314\) 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 0.538848 0.842403i \(-0.318860\pi\)
−0.842403 + 0.538848i \(0.818860\pi\)
\(318\) −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 −0.525588 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
\(342\) 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 0.978814 0.204752i \(-0.0656387\pi\)
−0.204752 + 0.978814i \(0.565639\pi\)
\(348\) 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 0.960143 0.279509i \(-0.0901715\pi\)
−0.279509 + 0.960143i \(0.590172\pi\)
\(354\) 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 0.555904 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
\(372\) −155.024 + 7.90497i −0.416730 + 0.0212499i
\(373\) −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
\(375\) 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 \(0.111987\pi\)
−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 0.887847 0.460138i \(-0.152200\pi\)
−0.460138 + 0.887847i \(0.652200\pi\)
\(384\) −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 0.977391 0.211440i \(-0.0678154\pi\)
−0.211440 + 0.977391i \(0.567815\pi\)
\(398\) 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 \(-0.740996\pi\)
0.686825 0.726823i \(-0.259004\pi\)
\(402\) −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 \(0.134616\pi\)
−0.911899 + 0.410414i \(0.865384\pi\)
\(420\) 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 \(-0.828164\pi\)
0.857791 0.513998i \(-0.171836\pi\)
\(432\) −133.426 + 20.5537i −0.308857 + 0.0475779i
\(433\) −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
\(435\) 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 −0.462315 0.886716i \(-0.652981\pi\)
0.886716 + 0.462315i \(0.152981\pi\)
\(444\) 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 −0.775842 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 \(-0.433386\pi\)
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 0.752002 0.659161i \(-0.229088\pi\)
−0.659161 + 0.752002i \(0.729088\pi\)
\(464\) 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 −0.923941 0.382536i \(-0.875051\pi\)
0.382536 + 0.923941i \(0.375051\pi\)
\(468\) 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 \(0.0304550\pi\)
−0.995426 + 0.0955314i \(0.969545\pi\)
\(480\) 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 −0.398358 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 \(0.176913\pi\)
−0.849484 + 0.527614i \(0.823087\pi\)
\(492\) 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 \(-0.930144\pi\)
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 0.719657 0.694329i \(-0.244299\pi\)
−0.694329 + 0.719657i \(0.744299\pi\)
\(504\) 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 \(0.205143\pi\)
−0.799415 + 0.600779i \(0.794857\pi\)
\(510\) 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 0.124191 0.992258i \(-0.460366\pi\)
0.992258 0.124191i \(-0.0396337\pi\)
\(524\) 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 −0.472193 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
\(552\) −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 0.451089 0.892479i \(-0.351036\pi\)
−0.892479 + 0.451089i \(0.851036\pi\)
\(558\) 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 0.247086 0.968993i \(-0.420527\pi\)
−0.968993 + 0.247086i \(0.920527\pi\)
\(564\) −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 0.451366 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
\(582\) 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 −0.520700 0.853740i \(-0.674329\pi\)
0.853740 + 0.520700i \(0.174329\pi\)
\(588\) −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 0.843648 0.536897i \(-0.180403\pi\)
−0.536897 + 0.843648i \(0.680403\pi\)
\(594\) −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 \(-0.616143\pi\)
0.356832 0.934169i \(-0.383857\pi\)
\(602\) 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 0.593879 0.804554i \(-0.297596\pi\)
−0.804554 + 0.593879i \(0.797596\pi\)
\(608\) −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 0.995416 + 0.0956388i \(0.0304894\pi\)
0.0956388 + 0.995416i \(0.469511\pi\)
\(614\) 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 0.283691 0.958916i \(-0.408441\pi\)
−0.958916 + 0.283691i \(0.908441\pi\)
\(618\) 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 \(0.0466304\pi\)
−0.989289 + 0.145970i \(0.953370\pi\)
\(642\) −30.0346 589.006i −0.0467829 0.917455i
\(643\) 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
\(645\) −194.793 675.805i −0.302004 1.04776i
\(646\) −149.633 −0.231631
\(647\) −573.588 + 573.588i −0.886535 + 0.886535i −0.994188 0.107654i \(-0.965666\pi\)
0.107654 + 0.994188i \(0.465666\pi\)
\(648\) 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 −0.807683 0.589616i \(-0.799279\pi\)
0.589616 + 0.807683i \(0.299279\pi\)
\(654\) 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 \(-0.977146\pi\)
0.997424 0.0717364i \(-0.0228540\pi\)
\(662\) 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 0.296880 0.954915i \(-0.404054\pi\)
−0.954915 + 0.296880i \(0.904054\pi\)
\(674\) 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 −0.955586 0.294714i \(-0.904776\pi\)
0.294714 + 0.955586i \(0.404776\pi\)
\(678\) 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 −0.837990 0.545686i \(-0.816269\pi\)
0.545686 + 0.837990i \(0.316269\pi\)
\(684\) −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 \(0.0479031\pi\)
−0.988697 + 0.149925i \(0.952097\pi\)
\(692\) 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 \(-0.998155\pi\)
0.999983 0.00579527i \(-0.00184470\pi\)
\(702\) −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 \(0.205778\pi\)
−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
\(714\) −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 \(0.329336\pi\)
−0.510837 + 0.859678i \(0.670664\pi\)
\(720\) 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 0.119351 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
\(732\) −189.399 + 9.65785i −0.258742 + 0.0131938i
\(733\) −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
\(735\) −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 \(-0.563181\pi\)
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 −0.727592 0.686010i \(-0.759361\pi\)
0.686010 + 0.727592i \(0.259361\pi\)
\(744\) −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 −0.555401 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 \(-0.345305\pi\)
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