Properties

Label 105.3.k.c.83.2
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 83.2
Root \(-0.611750 - 0.253395i\) of \(x^{16} + 433 x^{8} + 16\)
Character \(\chi\) \(=\) 105.83
Dual form 105.3.k.c.62.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(-0.152778 + 2.99611i) q^{3} -3.00000i q^{4} +(-4.24762 - 2.63775i) q^{5} +(2.22660 - 2.01054i) q^{6} +(4.33402 - 5.49694i) q^{7} +(-4.94975 + 4.94975i) q^{8} +(-8.95332 - 0.915476i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(-0.152778 + 2.99611i) q^{3} -3.00000i q^{4} +(-4.24762 - 2.63775i) q^{5} +(2.22660 - 2.01054i) q^{6} +(4.33402 - 5.49694i) q^{7} +(-4.94975 + 4.94975i) q^{8} +(-8.95332 - 0.915476i) q^{9} +(1.13835 + 4.86869i) q^{10} -13.9031i q^{11} +(8.98832 + 0.458333i) q^{12} +(14.6307 - 14.6307i) q^{13} +(-6.95153 + 0.822309i) q^{14} +(8.55193 - 12.3233i) q^{15} -5.00000 q^{16} +(-4.86435 + 4.86435i) q^{17} +(5.68361 + 6.97829i) q^{18} -21.7515 q^{19} +(-7.91326 + 12.7429i) q^{20} +(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} +(4.11073 - 26.6852i) q^{27} +(-16.4908 - 13.0020i) q^{28} +28.0452 q^{29} +(-14.7610 + 2.66678i) q^{30} +17.2472i q^{31} +(23.3345 + 23.3345i) q^{32} +(41.6551 + 2.12408i) q^{33} +6.87923 q^{34} +(-32.9088 + 11.9168i) 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} +(-1.40169 - 20.9532i) q^{42} +(33.1548 + 33.1548i) q^{43} -41.7092 q^{44} +(35.6155 + 27.5052i) q^{45} +2.50714 q^{46} +(18.5656 - 18.5656i) q^{47} +(0.763888 - 14.9805i) q^{48} +(-11.4326 - 47.6476i) q^{49} +(8.00714 - 23.6830i) q^{50} +(-13.8310 - 15.3173i) q^{51} +(-43.8920 - 43.8920i) q^{52} +(48.3021 - 48.3021i) q^{53} +(-21.7760 + 15.9626i) q^{54} +(-36.6728 + 59.0549i) q^{55} +(5.75616 + 48.6607i) q^{56} +(3.32314 - 65.1697i) q^{57} +(-19.8310 - 19.8310i) q^{58} -29.6668i q^{59} +(-36.9700 - 25.6558i) q^{60} +21.0717i q^{61} +(12.1956 - 12.1956i) q^{62} +(-43.8361 + 45.2481i) 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} +(31.6965 + 14.8436i) q^{70} -16.0345i q^{71} +(48.8480 - 39.7853i) q^{72} +(57.3597 - 57.3597i) q^{73} +9.20249 q^{74} +(-68.8312 + 29.7869i) q^{75} +65.2544i q^{76} +(-76.4243 - 60.2561i) q^{77} +(3.16110 - 61.9921i) q^{78} -75.8024i q^{79} +(21.2381 + 13.1888i) q^{80} +(79.3238 + 16.3931i) q^{81} +(18.8933 + 18.8933i) q^{82} +(51.9675 + 51.9675i) q^{83} +(41.4750 - 47.4218i) q^{84} +(33.4929 - 7.83095i) q^{85} -46.8879i q^{86} +(-4.28468 + 84.0264i) q^{87} +(68.8167 + 68.8167i) q^{88} -174.294i q^{89} +(-5.73481 - 44.6331i) q^{90} +(-17.0143 - 143.833i) q^{91} +(5.31846 + 5.31846i) q^{92} +(-51.6745 - 2.63499i) q^{93} -26.2557 q^{94} +(92.3919 + 57.3750i) q^{95} +(-73.4777 + 66.3477i) q^{96} +(-16.6658 - 16.6658i) q^{97} +(-25.6079 + 41.7760i) q^{98} +(-12.7279 + 124.479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 32q^{7} + O(q^{10}) \) \( 16q + 32q^{7} + 80q^{15} - 80q^{16} + 8q^{18} - 64q^{21} - 64q^{22} + 224q^{25} - 96q^{28} - 128q^{30} + 96q^{36} - 384q^{37} - 112q^{42} + 64q^{43} + 320q^{46} - 128q^{51} + 408q^{57} - 224q^{58} - 120q^{60} - 72q^{63} + 320q^{67} + 128q^{70} + 56q^{72} - 424q^{78} + 896q^{81} + 256q^{85} + 448q^{88} - 832q^{91} + 32q^{93} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.353553 0.353553i 0.507877 0.861430i \(-0.330431\pi\)
−0.861430 + 0.507877i \(0.830431\pi\)
\(3\) −0.152778 + 2.99611i −0.0509259 + 0.998702i
\(4\) 3.00000i 0.750000i
\(5\) −4.24762 2.63775i −0.849524 0.527550i
\(6\) 2.22660 2.01054i 0.371100 0.335090i
\(7\) 4.33402 5.49694i 0.619145 0.785277i
\(8\) −4.94975 + 4.94975i −0.618718 + 0.618718i
\(9\) −8.95332 0.915476i −0.994813 0.101720i
\(10\) 1.13835 + 4.86869i 0.113835 + 0.486869i
\(11\) 13.9031i 1.26392i −0.775003 0.631958i \(-0.782252\pi\)
0.775003 0.631958i \(-0.217748\pi\)
\(12\) 8.98832 + 0.458333i 0.749027 + 0.0381944i
\(13\) 14.6307 14.6307i 1.12543 1.12543i 0.134524 0.990910i \(-0.457049\pi\)
0.990910 0.134524i \(-0.0429507\pi\)
\(14\) −6.95153 + 0.822309i −0.496538 + 0.0587364i
\(15\) 8.55193 12.3233i 0.570129 0.821555i
\(16\) −5.00000 −0.312500
\(17\) −4.86435 + 4.86435i −0.286138 + 0.286138i −0.835551 0.549413i \(-0.814851\pi\)
0.549413 + 0.835551i \(0.314851\pi\)
\(18\) 5.68361 + 6.97829i 0.315756 + 0.387683i
\(19\) −21.7515 −1.14481 −0.572407 0.819970i \(-0.693990\pi\)
−0.572407 + 0.819970i \(0.693990\pi\)
\(20\) −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 \(-0.767357\pi\)
0.667516 + 0.744595i \(0.267357\pi\)
\(24\) −14.0738 15.5862i −0.586407 0.649424i
\(25\) 11.0845 + 22.4083i 0.443381 + 0.896333i
\(26\) −20.6909 −0.795802
\(27\) 4.11073 26.6852i 0.152249 0.988342i
\(28\) −16.4908 13.0020i −0.588957 0.464359i
\(29\) 28.0452 0.967076 0.483538 0.875323i \(-0.339352\pi\)
0.483538 + 0.875323i \(0.339352\pi\)
\(30\) −14.7610 + 2.66678i −0.492035 + 0.0888928i
\(31\) 17.2472i 0.556362i 0.960529 + 0.278181i \(0.0897315\pi\)
−0.960529 + 0.278181i \(0.910268\pi\)
\(32\) 23.3345 + 23.3345i 0.729204 + 0.729204i
\(33\) 41.6551 + 2.12408i 1.26228 + 0.0643660i
\(34\) 6.87923 0.202330
\(35\) −32.9088 + 11.9168i −0.940251 + 0.340481i
\(36\) −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 \(0.605648\pi\)
\(42\) −1.40169 20.9532i −0.0333735 0.498885i
\(43\) 33.1548 + 33.1548i 0.771041 + 0.771041i 0.978289 0.207248i \(-0.0664506\pi\)
−0.207248 + 0.978289i \(0.566451\pi\)
\(44\) −41.7092 −0.947936
\(45\) 35.6155 + 27.5052i 0.791455 + 0.611227i
\(46\) 2.50714 0.0545031
\(47\) 18.5656 18.5656i 0.395012 0.395012i −0.481457 0.876470i \(-0.659892\pi\)
0.876470 + 0.481457i \(0.159892\pi\)
\(48\) 0.763888 14.9805i 0.0159143 0.312095i
\(49\) −11.4326 47.6476i −0.233319 0.972400i
\(50\) 8.00714 23.6830i 0.160143 0.473661i
\(51\) −13.8310 15.3173i −0.271195 0.300339i
\(52\) −43.8920 43.8920i −0.844076 0.844076i
\(53\) 48.3021 48.3021i 0.911361 0.911361i −0.0850185 0.996379i \(-0.527095\pi\)
0.996379 + 0.0850185i \(0.0270949\pi\)
\(54\) −21.7760 + 15.9626i −0.403260 + 0.295603i
\(55\) −36.6728 + 59.0549i −0.666779 + 1.07373i
\(56\) 5.75616 + 48.6607i 0.102789 + 0.868942i
\(57\) 3.32314 65.1697i 0.0583006 1.14333i
\(58\) −19.8310 19.8310i −0.341913 0.341913i
\(59\) 29.6668i 0.502826i −0.967880 0.251413i \(-0.919105\pi\)
0.967880 0.251413i \(-0.0808953\pi\)
\(60\) −36.9700 25.6558i −0.616167 0.427597i
\(61\) 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
\(63\) −43.8361 + 45.2481i −0.695812 + 0.718224i
\(64\) 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
\(70\) 31.6965 + 14.8436i 0.452807 + 0.212051i
\(71\) 16.0345i 0.225838i −0.993604 0.112919i \(-0.963980\pi\)
0.993604 0.112919i \(-0.0360200\pi\)
\(72\) 48.8480 39.7853i 0.678445 0.552573i
\(73\) 57.3597 57.3597i 0.785749 0.785749i −0.195045 0.980794i \(-0.562485\pi\)
0.980794 + 0.195045i \(0.0624853\pi\)
\(74\) 9.20249 0.124358
\(75\) −68.8312 + 29.7869i −0.917750 + 0.397159i
\(76\) 65.2544i 0.858610i
\(77\) −76.4243 60.2561i −0.992523 0.782547i
\(78\) 3.16110 61.9921i 0.0405269 0.794770i
\(79\) 75.8024i 0.959524i −0.877399 0.479762i \(-0.840723\pi\)
0.877399 0.479762i \(-0.159277\pi\)
\(80\) 21.2381 + 13.1888i 0.265476 + 0.164860i
\(81\) 79.3238 + 16.3931i 0.979306 + 0.202384i
\(82\) 18.8933 + 18.8933i 0.230406 + 0.230406i
\(83\) 51.9675 + 51.9675i 0.626114 + 0.626114i 0.947088 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
\(87\) −4.28468 + 84.0264i −0.0492492 + 0.965821i
\(88\) 68.8167 + 68.8167i 0.782008 + 0.782008i
\(89\) 174.294i 1.95836i −0.202987 0.979181i \(-0.565065\pi\)
0.202987 0.979181i \(-0.434935\pi\)
\(90\) −5.73481 44.6331i −0.0637201 0.495923i
\(91\) −17.0143 143.833i −0.186970 1.58058i
\(92\) 5.31846 + 5.31846i 0.0578093 + 0.0578093i
\(93\) −51.6745 2.63499i −0.555640 0.0283332i
\(94\) −26.2557 −0.279316
\(95\) 92.3919 + 57.3750i 0.972547 + 0.603947i
\(96\) −73.4777 + 66.3477i −0.765393 + 0.691122i
\(97\) −16.6658 16.6658i −0.171812 0.171812i 0.615963 0.787775i \(-0.288767\pi\)
−0.787775 + 0.615963i \(0.788767\pi\)
\(98\) −25.6079 + 41.7760i −0.261305 + 0.426286i
\(99\) −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 \(0.310813\pi\)
\(102\) −1.05099 + 20.6109i −0.0103038 + 0.202068i
\(103\) −16.1826 + 16.1826i −0.157113 + 0.157113i −0.781286 0.624173i \(-0.785436\pi\)
0.624173 + 0.781286i \(0.285436\pi\)
\(104\) 144.836i 1.39265i
\(105\) −30.6764 100.419i −0.292156 0.956371i
\(106\) −68.3095 −0.644429
\(107\) 139.010 + 139.010i 1.29916 + 1.29916i 0.928945 + 0.370218i \(0.120717\pi\)
0.370218 + 0.928945i \(0.379283\pi\)
\(108\) −80.0557 12.3322i −0.741257 0.114187i
\(109\) 3.01429i 0.0276540i −0.999904 0.0138270i \(-0.995599\pi\)
0.999904 0.0138270i \(-0.00440141\pi\)
\(110\) 67.6897 15.8265i 0.615361 0.143877i
\(111\) −18.5020 20.4902i −0.166684 0.184597i
\(112\) −21.6701 + 27.4847i −0.193483 + 0.245399i
\(113\) −80.1118 + 80.1118i −0.708954 + 0.708954i −0.966315 0.257361i \(-0.917147\pi\)
0.257361 + 0.966315i \(0.417147\pi\)
\(114\) −48.4318 + 43.7321i −0.424840 + 0.383615i
\(115\) 12.2065 2.85400i 0.106144 0.0248174i
\(116\) 84.1356i 0.725307i
\(117\) −144.387 + 117.599i −1.23408 + 1.00512i
\(118\) −20.9776 + 20.9776i −0.177776 + 0.177776i
\(119\) 5.65685 + 47.8212i 0.0475366 + 0.401859i
\(120\) 18.6675 + 103.327i 0.155562 + 0.861061i
\(121\) −72.2952 −0.597481
\(122\) 14.8999 14.8999i 0.122131 0.122131i
\(123\) 4.08209 80.0535i 0.0331877 0.650842i
\(124\) 51.7417 0.417272
\(125\) 12.0248 124.420i 0.0961984 0.995362i
\(126\) 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 \(0.401907\pi\)
\(132\) 6.37223 124.965i 0.0482745 0.946706i
\(133\) −94.2712 + 119.566i −0.708806 + 0.898996i
\(134\) 45.9316 0.342773
\(135\) −87.8499 + 102.506i −0.650740 + 0.759301i
\(136\) 48.1546i 0.354078i
\(137\) −7.42967 7.42967i −0.0542312 0.0542312i 0.679471 0.733702i \(-0.262209\pi\)
−0.733702 + 0.679471i \(0.762209\pi\)
\(138\) −0.383035 + 7.51167i −0.00277562 + 0.0544324i
\(139\) 179.589 1.29201 0.646003 0.763335i \(-0.276439\pi\)
0.646003 + 0.763335i \(0.276439\pi\)
\(140\) 35.7505 + 98.7264i 0.255361 + 0.705189i
\(141\) 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
\(147\) 144.504 26.9739i 0.983021 0.183496i
\(148\) 19.5214 + 19.5214i 0.131902 + 0.131902i
\(149\) −24.7386 −0.166031 −0.0830155 0.996548i \(-0.526455\pi\)
−0.0830155 + 0.996548i \(0.526455\pi\)
\(150\) 69.7336 + 27.6085i 0.464890 + 0.184057i
\(151\) −163.324 −1.08161 −0.540807 0.841147i \(-0.681881\pi\)
−0.540807 + 0.841147i \(0.681881\pi\)
\(152\) 107.664 107.664i 0.708317 0.708317i
\(153\) 48.0053 39.0989i 0.313760 0.255548i
\(154\) 11.4326 + 96.6476i 0.0742378 + 0.627582i
\(155\) 45.4939 73.2596i 0.293509 0.472643i
\(156\) 138.211 124.799i 0.885966 0.799995i
\(157\) 108.368 + 108.368i 0.690244 + 0.690244i 0.962285 0.272042i \(-0.0876988\pi\)
−0.272042 + 0.962285i \(0.587699\pi\)
\(158\) −53.6004 + 53.6004i −0.339243 + 0.339243i
\(159\) 137.339 + 152.098i 0.863766 + 0.956590i
\(160\) −37.5655 160.667i −0.234784 1.00417i
\(161\) 2.06165 + 17.4285i 0.0128053 + 0.108252i
\(162\) −44.4987 67.6821i −0.274684 0.417791i
\(163\) 38.8452 + 38.8452i 0.238314 + 0.238314i 0.816152 0.577837i \(-0.196103\pi\)
−0.577837 + 0.816152i \(0.696103\pi\)
\(164\) 80.1575i 0.488765i
\(165\) −171.332 118.898i −1.03838 0.720594i
\(166\) 73.4931i 0.442730i
\(167\) −138.252 + 138.252i −0.827855 + 0.827855i −0.987220 0.159365i \(-0.949055\pi\)
0.159365 + 0.987220i \(0.449055\pi\)
\(168\) −146.672 + 9.81182i −0.873049 + 0.0584037i
\(169\) 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
\(175\) 171.218 + 36.1871i 0.978387 + 0.206784i
\(176\) 69.5153i 0.394973i
\(177\) 88.8848 + 4.53242i 0.502174 + 0.0256069i
\(178\) −123.245 + 123.245i −0.692386 + 0.692386i
\(179\) −187.393 −1.04689 −0.523445 0.852059i \(-0.675354\pi\)
−0.523445 + 0.852059i \(0.675354\pi\)
\(180\) 82.5157 106.846i 0.458420 0.593591i
\(181\) 179.581i 0.992158i 0.868277 + 0.496079i \(0.165227\pi\)
−0.868277 + 0.496079i \(0.834773\pi\)
\(182\) −89.6745 + 113.736i −0.492717 + 0.624925i
\(183\) −63.1331 3.21928i −0.344990 0.0175917i
\(184\) 17.5500i 0.0953805i
\(185\) 44.8041 10.4756i 0.242184 0.0566250i
\(186\) 34.6762 + 38.4026i 0.186431 + 0.206466i
\(187\) 67.6294 + 67.6294i 0.361654 + 0.361654i
\(188\) −55.6968 55.6968i −0.296259 0.296259i
\(189\) −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 \(0.909576\pi\)
\(192\) 38.9494 + 1.98611i 0.202861 + 0.0103443i
\(193\) −81.6333 81.6333i −0.422971 0.422971i 0.463255 0.886225i \(-0.346682\pi\)
−0.886225 + 0.463255i \(0.846682\pi\)
\(194\) 23.5689i 0.121489i
\(195\) −55.1781 305.419i −0.282964 1.56625i
\(196\) −142.943 + 34.2979i −0.729300 + 0.174989i
\(197\) −165.702 165.702i −0.841127 0.841127i 0.147878 0.989006i \(-0.452756\pi\)
−0.989006 + 0.147878i \(0.952756\pi\)
\(198\) 97.0196 79.0196i 0.489998 0.399089i
\(199\) −220.037 −1.10571 −0.552857 0.833276i \(-0.686462\pi\)
−0.552857 + 0.833276i \(0.686462\pi\)
\(200\) −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
\(203\) 121.548 154.163i 0.598760 0.759422i
\(204\) −45.9518 + 41.4929i −0.225254 + 0.203396i
\(205\) 113.493 + 70.4786i 0.553624 + 0.343798i
\(206\) 22.8856 0.111095
\(207\) 17.4956 14.2496i 0.0845197 0.0688388i
\(208\) −73.1533 + 73.1533i −0.351698 + 0.351698i
\(209\) 302.412i 1.44695i
\(210\) −49.3154 + 92.6984i −0.234835 + 0.441421i
\(211\) 276.590 1.31086 0.655428 0.755258i \(-0.272488\pi\)
0.655428 + 0.755258i \(0.272488\pi\)
\(212\) −144.906 144.906i −0.683521 0.683521i
\(213\) 48.0411 + 2.44971i 0.225545 + 0.0115010i
\(214\) 196.590i 0.918647i
\(215\) −53.3747 228.283i −0.248255 1.06178i
\(216\) 111.738 + 152.432i 0.517306 + 0.705705i
\(217\) 94.8069 + 74.7497i 0.436898 + 0.344469i
\(218\) −2.13142 + 2.13142i −0.00977717 + 0.00977717i
\(219\) 163.092 + 180.619i 0.744715 + 0.824744i
\(220\) 177.165 + 110.019i 0.805294 + 0.500084i
\(221\) 142.337i 0.644060i
\(222\) −1.40593 + 27.5717i −0.00633304 + 0.124197i
\(223\) 173.529 173.529i 0.778155 0.778155i −0.201362 0.979517i \(-0.564537\pi\)
0.979517 + 0.201362i \(0.0645368\pi\)
\(224\) 229.401 27.1362i 1.02411 0.121144i
\(225\) −78.7290 210.777i −0.349907 0.936785i
\(226\) 113.295 0.501306
\(227\) −191.389 + 191.389i −0.843123 + 0.843123i −0.989264 0.146140i \(-0.953315\pi\)
0.146140 + 0.989264i \(0.453315\pi\)
\(228\) −195.509 9.96941i −0.857496 0.0437255i
\(229\) 123.490 0.539259 0.269630 0.962964i \(-0.413099\pi\)
0.269630 + 0.962964i \(0.413099\pi\)
\(230\) −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 \(-0.662049\pi\)
0.873187 + 0.487385i \(0.162049\pi\)
\(234\) 185.252 + 18.9420i 0.791675 + 0.0809487i
\(235\) −127.831 + 29.8881i −0.543961 + 0.127183i
\(236\) −89.0003 −0.377120
\(237\) 227.112 + 11.5809i 0.958279 + 0.0488646i
\(238\) 29.8147 37.8147i 0.125272 0.158885i
\(239\) 49.2786 0.206187 0.103093 0.994672i \(-0.467126\pi\)
0.103093 + 0.994672i \(0.467126\pi\)
\(240\) −42.7597 + 61.6167i −0.178165 + 0.256736i
\(241\) 421.664i 1.74964i −0.484445 0.874822i \(-0.660979\pi\)
0.484445 0.874822i \(-0.339021\pi\)
\(242\) 51.1204 + 51.1204i 0.211242 + 0.211242i
\(243\) −61.2344 + 235.158i −0.251993 + 0.967729i
\(244\) 63.2151 0.259078
\(245\) −77.1212 + 232.545i −0.314780 + 0.949165i
\(246\) −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 \(0.741631\pi\)
\(252\) 135.744 + 131.508i 0.538668 + 0.521859i
\(253\) 24.6476 + 24.6476i 0.0974214 + 0.0974214i
\(254\) 101.325 0.398917
\(255\) 18.3454 + 101.545i 0.0719428 + 0.398214i
\(256\) −171.000 −0.667969
\(257\) 216.568 216.568i 0.842676 0.842676i −0.146530 0.989206i \(-0.546810\pi\)
0.989206 + 0.146530i \(0.0468104\pi\)
\(258\) 140.481 + 7.16342i 0.544501 + 0.0277652i
\(259\) 7.56729 + 63.9714i 0.0292173 + 0.246994i
\(260\) 70.6602 + 302.212i 0.271770 + 1.16236i
\(261\) −251.098 25.6747i −0.962060 0.0983705i
\(262\) −56.1926 56.1926i −0.214476 0.214476i
\(263\) −196.555 + 196.555i −0.747359 + 0.747359i −0.973982 0.226623i \(-0.927231\pi\)
0.226623 + 0.973982i \(0.427231\pi\)
\(264\) −216.696 + 195.668i −0.820817 + 0.741168i
\(265\) −332.578 + 77.7599i −1.25501 + 0.293434i
\(266\) 151.206 17.8864i 0.568444 0.0672422i
\(267\) 522.204 + 26.6283i 1.95582 + 0.0997313i
\(268\) 97.4357 + 97.4357i 0.363566 + 0.363566i
\(269\) 349.961i 1.30097i −0.759519 0.650485i \(-0.774566\pi\)
0.759519 0.650485i \(-0.225434\pi\)
\(270\) 134.602 10.3632i 0.498525 0.0383822i
\(271\) 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
\(273\) 433.539 29.0021i 1.58806 0.106235i
\(274\) 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
\(280\) 103.905 221.876i 0.371089 0.792413i
\(281\) 142.098i 0.505687i −0.967507 0.252844i \(-0.918634\pi\)
0.967507 0.252844i \(-0.0813658\pi\)
\(282\) 4.01128 78.6649i 0.0142244 0.278954i
\(283\) −120.235 + 120.235i −0.424858 + 0.424858i −0.886873 0.462014i \(-0.847127\pi\)
0.462014 + 0.886873i \(0.347127\pi\)
\(284\) −48.1035 −0.169378
\(285\) −186.017 + 268.050i −0.652691 + 0.940528i
\(286\) 287.666i 1.00583i
\(287\) −115.801 + 146.874i −0.403489 + 0.511755i
\(288\) −187.559 230.284i −0.651247 0.799596i
\(289\) 241.676i 0.836250i
\(290\) 31.9252 + 136.543i 0.110087 + 0.470840i
\(291\) 52.4786 47.3863i 0.180339 0.162839i
\(292\) −172.079 172.079i −0.589312 0.589312i
\(293\) 377.885 + 377.885i 1.28971 + 1.28971i 0.934962 + 0.354747i \(0.115433\pi\)
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
\(297\) −371.007 57.1518i −1.24918 0.192430i
\(298\) 17.4929 + 17.4929i 0.0587009 + 0.0587009i
\(299\) 51.8750i 0.173495i
\(300\) 89.3608 + 206.494i 0.297869 + 0.688312i
\(301\) 325.943 38.5564i 1.08287 0.128094i
\(302\) 115.487 + 115.487i 0.382409 + 0.382409i
\(303\) −17.2812 + 338.900i −0.0570337 + 1.11848i
\(304\) 108.757 0.357754
\(305\) 55.5820 89.5046i 0.182236 0.293458i
\(306\) −61.5919 6.29777i −0.201281 0.0205809i
\(307\) −94.6590 94.6590i −0.308335 0.308335i 0.535928 0.844264i \(-0.319962\pi\)
−0.844264 + 0.535928i \(0.819962\pi\)
\(308\) −180.768 + 229.273i −0.586910 + 0.744392i
\(309\) −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 \(0.384140\pi\)
\(312\) −433.944 22.1277i −1.39085 0.0709221i
\(313\) 225.950 225.950i 0.721885 0.721885i −0.247104 0.968989i \(-0.579479\pi\)
0.968989 + 0.247104i \(0.0794790\pi\)
\(314\) 153.256i 0.488076i
\(315\) 305.553 76.5679i 0.970008 0.243073i
\(316\) −227.407 −0.719643
\(317\) 96.2271 + 96.2271i 0.303556 + 0.303556i 0.842403 0.538848i \(-0.181140\pi\)
−0.538848 + 0.842403i \(0.681140\pi\)
\(318\) 10.4362 204.663i 0.0328181 0.643593i
\(319\) 389.914i 1.22230i
\(320\) −34.2908 + 55.2190i −0.107159 + 0.172559i
\(321\) −437.728 + 395.253i −1.36364 + 1.23132i
\(322\) 10.8660 13.7816i 0.0337453 0.0428000i
\(323\) 105.807 105.807i 0.327575 0.327575i
\(324\) 49.1793 237.971i 0.151788 0.734480i
\(325\) 490.022 + 165.675i 1.50776 + 0.509768i
\(326\) 54.9355i 0.168514i
\(327\) 9.03113 + 0.460516i 0.0276181 + 0.00140830i
\(328\) 132.253 132.253i 0.403211 0.403211i
\(329\) −21.5903 182.517i −0.0656240 0.554764i
\(330\) 37.0765 + 205.224i 0.112353 + 0.621890i
\(331\) 175.014 0.528744 0.264372 0.964421i \(-0.414835\pi\)
0.264372 + 0.964421i \(0.414835\pi\)
\(332\) 155.902 155.902i 0.469586 0.469586i
\(333\) 64.2177 52.3034i 0.192846 0.157067i
\(334\) 195.517 0.585382
\(335\) 223.627 52.2861i 0.667543 0.156078i
\(336\) −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
\(342\) −123.627 151.788i −0.361482 0.443825i
\(343\) −311.465 143.661i −0.908061 0.418837i
\(344\) −328.215 −0.954114
\(345\) 6.68601 + 37.0081i 0.0193797 + 0.107270i
\(346\) 38.1223i 0.110180i
\(347\) −268.600 268.600i −0.774062 0.774062i 0.204752 0.978814i \(-0.434361\pi\)
−0.978814 + 0.204752i \(0.934361\pi\)
\(348\) 252.079 + 12.8540i 0.724366 + 0.0369369i
\(349\) −304.193 −0.871613 −0.435807 0.900040i \(-0.643537\pi\)
−0.435807 + 0.900040i \(0.643537\pi\)
\(350\) −95.4810 146.657i −0.272803 0.419021i
\(351\) −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
\(357\) −144.142 + 9.64254i −0.403758 + 0.0270099i
\(358\) 132.507 + 132.507i 0.370132 + 0.370132i
\(359\) −161.739 −0.450526 −0.225263 0.974298i \(-0.572324\pi\)
−0.225263 + 0.974298i \(0.572324\pi\)
\(360\) −312.432 + 40.1437i −0.867865 + 0.111510i
\(361\) 112.126 0.310599
\(362\) 126.983 126.983i 0.350781 0.350781i
\(363\) 11.0451 216.604i 0.0304272 0.596706i
\(364\) −431.500 + 51.0429i −1.18544 + 0.140228i
\(365\) −394.943 + 92.3414i −1.08203 + 0.252990i
\(366\) 42.3655 + 46.9182i 0.115753 + 0.128192i
\(367\) 101.051 + 101.051i 0.275343 + 0.275343i 0.831247 0.555904i \(-0.187628\pi\)
−0.555904 + 0.831247i \(0.687628\pi\)
\(368\) 8.86409 8.86409i 0.0240872 0.0240872i
\(369\) 239.225 + 24.4608i 0.648307 + 0.0662893i
\(370\) −39.0887 24.2739i −0.105645 0.0656051i
\(371\) −56.1715 474.856i −0.151406 1.27993i
\(372\) −7.90497 + 155.024i −0.0212499 + 0.416730i
\(373\) −369.464 369.464i −0.990521 0.990521i 0.00943464 0.999955i \(-0.496997\pi\)
−0.999955 + 0.00943464i \(0.996997\pi\)
\(374\) 95.6424i 0.255728i
\(375\) 370.939 + 55.0362i 0.989172 + 0.146763i
\(376\) 183.790i 0.488803i
\(377\) 410.320 410.320i 1.08838 1.08838i
\(378\) −6.63236 + 188.884i −0.0175459 + 0.499692i
\(379\) 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
\(385\) 165.680 + 457.533i 0.430339 + 1.18840i
\(386\) 115.447i 0.299085i
\(387\) −266.493 327.197i −0.688612 0.845472i
\(388\) −49.9973 + 49.9973i −0.128859 + 0.128859i
\(389\) 401.000 1.03085 0.515425 0.856935i \(-0.327634\pi\)
0.515425 + 0.856935i \(0.327634\pi\)
\(390\) −176.947 + 254.980i −0.453710 + 0.653796i
\(391\) 17.2472i 0.0441105i
\(392\) 292.432 + 179.255i 0.746001 + 0.457283i
\(393\) −12.1410 + 238.096i −0.0308931 + 0.605841i
\(394\) 234.338i 0.594767i
\(395\) −199.948 + 321.980i −0.506197 + 0.815138i
\(396\) 373.436 + 38.1838i 0.943019 + 0.0964237i
\(397\) −304.082 304.082i −0.765950 0.765950i 0.211440 0.977391i \(-0.432185\pi\)
−0.977391 + 0.211440i \(0.932185\pi\)
\(398\) 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 \(0.740996\pi\)
\(402\) −7.01732 + 137.616i −0.0174560 + 0.342329i
\(403\) 252.338 + 252.338i 0.626149 + 0.626149i
\(404\) 339.341i 0.839952i
\(405\) −293.696 278.868i −0.725176 0.688563i
\(406\) −194.957 + 23.0618i −0.480190 + 0.0568025i
\(407\) 90.4693 + 90.4693i 0.222283 + 0.222283i
\(408\) 144.276 + 7.35694i 0.353619 + 0.0180317i
\(409\) −344.830 −0.843104 −0.421552 0.906804i \(-0.638515\pi\)
−0.421552 + 0.906804i \(0.638515\pi\)
\(410\) −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
\(413\) −163.076 128.576i −0.394858 0.311323i
\(414\) −22.4473 2.29523i −0.0542204 0.00554403i
\(415\) −83.6607 357.815i −0.201592 0.862206i
\(416\) 682.799 1.64134
\(417\) −27.4372 + 538.068i −0.0657965 + 1.29033i
\(418\) 213.838 213.838i 0.511573 0.511573i
\(419\) 343.927i 0.820828i 0.911899 + 0.410414i \(0.134616\pi\)
−0.911899 + 0.410414i \(0.865384\pi\)
\(420\) −301.257 + 92.0291i −0.717278 + 0.219117i
\(421\) 14.6762 0.0348603 0.0174302 0.999848i \(-0.494452\pi\)
0.0174302 + 0.999848i \(0.494452\pi\)
\(422\) −195.579 195.579i −0.463457 0.463457i
\(423\) −183.220 + 149.227i −0.433144 + 0.352783i
\(424\) 478.167i 1.12775i
\(425\) −162.921 55.0830i −0.383343 0.129607i
\(426\) −32.2379 35.7024i −0.0756759 0.0838084i
\(427\) 115.830 + 91.3251i 0.271264 + 0.213876i
\(428\) 417.031 417.031i 0.974372 0.974372i
\(429\) 640.518 578.364i 1.49305 1.34817i
\(430\) −123.679 + 199.162i −0.287625 + 0.463167i
\(431\) 443.066i 1.02800i 0.857791 + 0.513998i \(0.171836\pi\)
−0.857791 + 0.513998i \(0.828164\pi\)
\(432\) −20.5537 + 133.426i −0.0475779 + 0.308857i
\(433\) 487.352 487.352i 1.12553 1.12553i 0.134629 0.990896i \(-0.457016\pi\)
0.990896 0.134629i \(-0.0429843\pi\)
\(434\) −14.1825 119.895i −0.0326787 0.276255i
\(435\) 239.841 345.610i 0.551358 0.794506i
\(436\) −9.04287 −0.0207405
\(437\) 38.5614 38.5614i 0.0882412 0.0882412i
\(438\) 12.3931 243.041i 0.0282948 0.554888i
\(439\) −151.065 −0.344111 −0.172056 0.985087i \(-0.555041\pi\)
−0.172056 + 0.985087i \(0.555041\pi\)
\(440\) −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 \(-0.847019\pi\)
0.462315 + 0.886716i \(0.347019\pi\)
\(444\) −61.4707 + 55.5059i −0.138448 + 0.125013i
\(445\) −459.745 + 740.336i −1.03314 + 1.66368i
\(446\) −245.406 −0.550239
\(447\) 3.77951 74.1196i 0.00845528 0.165816i
\(448\) −71.4602 56.3422i −0.159509 0.125764i
\(449\) 397.613 0.885552 0.442776 0.896632i \(-0.353994\pi\)
0.442776 + 0.896632i \(0.353994\pi\)
\(450\) −93.3717 + 204.711i −0.207493 + 0.454914i
\(451\) 371.478i 0.823677i
\(452\) 240.335 + 240.335i 0.531716 + 0.531716i
\(453\) 24.9522 489.336i 0.0550821 1.08021i
\(454\) 270.665 0.596178
\(455\) −307.126 + 655.828i −0.675003 + 1.44138i
\(456\) 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 \(0.433386\pi\)
\(462\) −291.313 + 19.4878i −0.630548 + 0.0421813i
\(463\) 42.9857 + 42.9857i 0.0928417 + 0.0928417i 0.752002 0.659161i \(-0.229088\pi\)
−0.659161 + 0.752002i \(0.729088\pi\)
\(464\) −140.226 −0.302211
\(465\) 212.543 + 147.497i 0.457082 + 0.317198i
\(466\) −127.126 −0.272803
\(467\) −252.836 + 252.836i −0.541405 + 0.541405i −0.923941 0.382536i \(-0.875051\pi\)
0.382536 + 0.923941i \(0.375051\pi\)
\(468\) 352.797 + 433.161i 0.753839 + 0.925557i
\(469\) 37.7700 + 319.295i 0.0805331 + 0.680800i
\(470\) 111.524 + 69.2561i 0.237286 + 0.147353i
\(471\) −341.239 + 308.127i −0.724500 + 0.654197i
\(472\) 146.843 + 146.843i 0.311108 + 0.311108i
\(473\) 460.953 460.953i 0.974530 0.974530i
\(474\) −152.404 168.781i −0.321526 0.356079i
\(475\) −241.105 487.414i −0.507589 1.02613i
\(476\) 143.464 16.9706i 0.301394 0.0356524i
\(477\) −476.684 + 388.245i −0.999337 + 0.813930i
\(478\) −34.8452 34.8452i −0.0728980 0.0728980i
\(479\) 91.5191i 0.191063i 0.995426 + 0.0955314i \(0.0304550\pi\)
−0.995426 + 0.0955314i \(0.969545\pi\)
\(480\) 487.114 88.0038i 1.01482 0.183341i
\(481\) 190.408i 0.395858i
\(482\) −298.161 + 298.161i −0.618592 + 0.618592i
\(483\) −52.5326 + 3.51424i −0.108763 + 0.00727585i
\(484\) 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
\(490\) 218.967 109.901i 0.446872 0.224289i
\(491\) 518.117i 1.05523i −0.849484 0.527614i \(-0.823087\pi\)
0.849484 0.527614i \(-0.176913\pi\)
\(492\) −240.161 12.2463i −0.488131 0.0248908i
\(493\) −136.422 + 136.422i −0.276717 + 0.276717i
\(494\) 450.057 0.911046
\(495\) 382.407 495.164i 0.772539 1.00033i
\(496\) 86.2361i 0.173863i
\(497\) −88.1406 69.4937i −0.177345 0.139826i
\(498\) 220.193 + 11.2281i 0.442155 + 0.0225464i
\(499\) 217.267i 0.435404i −0.976015 0.217702i \(-0.930144\pi\)
0.976015 0.217702i \(-0.0698561\pi\)
\(500\) −373.261 36.0744i −0.746522 0.0721488i
\(501\) −393.095 435.339i −0.784621 0.868940i
\(502\) 244.315 + 244.315i 0.486684 + 0.486684i
\(503\) 12.7399 + 12.7399i 0.0253279 + 0.0253279i 0.719657 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
\(507\) 776.327 + 39.5865i 1.53122 + 0.0780798i
\(508\) 214.943 + 214.943i 0.423116 + 0.423116i
\(509\) 611.593i 1.20156i 0.799415 + 0.600779i \(0.205143\pi\)
−0.799415 + 0.600779i \(0.794857\pi\)
\(510\) 58.8307 84.7750i 0.115354 0.166226i
\(511\) −66.7048 563.900i −0.130538 1.10352i
\(512\) −215.668 215.668i −0.421226 0.421226i
\(513\) −89.4144 + 580.443i −0.174297 + 1.13147i
\(514\) −306.273 −0.595862
\(515\) 111.423 26.0518i 0.216356 0.0505860i
\(516\) 282.810 + 313.202i 0.548081 + 0.606980i
\(517\) −258.119 258.119i −0.499262 0.499262i
\(518\) 39.8837 50.5855i 0.0769956 0.0976554i
\(519\) −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 \(0.731397\pi\)
\(522\) 159.398 + 195.708i 0.305360 + 0.374919i
\(523\) −583.903 + 583.903i −1.11645 + 1.11645i −0.124191 + 0.992258i \(0.539634\pi\)
−0.992258 + 0.124191i \(0.960366\pi\)
\(524\) 238.405i 0.454971i
\(525\) −134.579 + 507.458i −0.256340 + 0.966587i
\(526\) 277.971 0.528463
\(527\) −83.8965 83.8965i −0.159196 0.159196i
\(528\) −208.275 10.6204i −0.394461 0.0201144i
\(529\) 522.714i 0.988118i
\(530\) 290.153 + 180.184i 0.547458 + 0.339969i
\(531\) −27.1592 + 265.616i −0.0511473 + 0.500218i
\(532\) 358.699 + 282.814i 0.674247 + 0.531604i
\(533\) −390.919 + 390.919i −0.733431 + 0.733431i
\(534\) −350.425 388.083i −0.656227 0.726748i
\(535\) −223.788 957.138i −0.418296 1.78904i
\(536\) 321.521i 0.599853i
\(537\) 28.6295 561.451i 0.0533138 1.04553i
\(538\) −247.460 + 247.460i −0.459963 + 0.459963i
\(539\) −662.448 + 158.948i −1.22903 + 0.294895i
\(540\) 307.517 + 263.550i 0.569476 + 0.488055i
\(541\) 314.562 0.581445 0.290723 0.956807i \(-0.406104\pi\)
0.290723 + 0.956807i \(0.406104\pi\)
\(542\) 97.5650 97.5650i 0.180009 0.180009i
\(543\) −538.043 27.4359i −0.990871 0.0505265i
\(544\) −227.015 −0.417306
\(545\) −7.95095 + 12.8035i −0.0145889 + 0.0234927i
\(546\) −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
\(552\) 52.5817 + 2.68125i 0.0952567 + 0.00485733i
\(553\) −416.681 328.529i −0.753492 0.594084i
\(554\) −187.831 −0.339045
\(555\) 24.5411 + 135.838i 0.0442181 + 0.244754i
\(556\) 538.767i 0.969005i
\(557\) 245.854 + 245.854i 0.441390 + 0.441390i 0.892479 0.451089i \(-0.148964\pi\)
−0.451089 + 0.892479i \(0.648964\pi\)
\(558\) −120.356 + 98.0265i −0.215692 + 0.175675i
\(559\) 970.151 1.73551
\(560\) 164.544 59.5841i 0.293829 0.106400i
\(561\) −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
\(567\) 433.902 364.990i 0.765260 0.643721i
\(568\) 79.3667 + 79.3667i 0.139730 + 0.139730i
\(569\) −690.156 −1.21293 −0.606464 0.795111i \(-0.707413\pi\)
−0.606464 + 0.795111i \(0.707413\pi\)
\(570\) 321.074 58.0064i 0.563288 0.101766i
\(571\) 612.476 1.07264 0.536319 0.844015i \(-0.319814\pi\)
0.536319 + 0.844015i \(0.319814\pi\)
\(572\) −610.233 + 610.233i −1.06684 + 1.06684i
\(573\) −320.771 16.3568i −0.559810 0.0285459i
\(574\) 185.739 21.9714i 0.323587 0.0382777i
\(575\) −59.3768 20.0751i −0.103264 0.0349131i
\(576\) −11.9012 + 116.393i −0.0206618 + 0.202071i
\(577\) 254.442 + 254.442i 0.440973 + 0.440973i 0.892339 0.451366i \(-0.149063\pi\)
−0.451366 + 0.892339i \(0.649063\pi\)
\(578\) 170.891 170.891i 0.295659 0.295659i
\(579\) 257.054 232.110i 0.443962 0.400882i
\(580\) −221.929 + 357.376i −0.382636 + 0.616165i
\(581\) 510.890 60.4341i 0.879329 0.104017i
\(582\) −70.6151 3.60081i −0.121332 0.00618695i
\(583\) −671.548 671.548i −1.15188 1.15188i
\(584\) 567.832i 0.972315i
\(585\) 923.497 118.658i 1.57863 0.202835i
\(586\) 534.410i 0.911962i
\(587\) 195.495 195.495i 0.333040 0.333040i −0.520700 0.853740i \(-0.674329\pi\)
0.853740 + 0.520700i \(0.174329\pi\)
\(588\) −80.9216 433.512i −0.137622 0.737265i
\(589\) 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
\(595\) 102.112 218.048i 0.171617 0.366466i
\(596\) 74.2159i 0.124523i
\(597\) 33.6167 659.255i 0.0563094 1.10428i
\(598\) 36.6812 36.6812i 0.0613397 0.0613397i
\(599\) −376.201 −0.628048 −0.314024 0.949415i \(-0.601677\pi\)
−0.314024 + 0.949415i \(0.601677\pi\)
\(600\) 193.259 488.135i 0.322099 0.813558i
\(601\) 1122.87i 1.86834i 0.356832 + 0.934169i \(0.383857\pi\)
−0.356832 + 0.934169i \(0.616143\pi\)
\(602\) −257.740 203.213i −0.428139 0.337563i
\(603\) 320.524 261.058i 0.531549 0.432931i
\(604\) 489.971i 0.811211i
\(605\) 307.083 + 190.697i 0.507574 + 0.315202i
\(606\) 251.858 227.419i 0.415608 0.375279i
\(607\) 127.880 + 127.880i 0.210675 + 0.210675i 0.804554 0.593879i \(-0.202404\pi\)
−0.593879 + 0.804554i \(0.702404\pi\)
\(608\) −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
\(612\) −117.297 144.016i −0.191661 0.235320i
\(613\) 668.817 + 668.817i 1.09105 + 1.09105i 0.995416 + 0.0956388i \(0.0304894\pi\)
0.0956388 + 0.995416i \(0.469511\pi\)
\(614\) 133.868i 0.218026i
\(615\) −228.501 + 329.269i −0.371546 + 0.535397i
\(616\) 676.533 80.0283i 1.09827 0.129916i
\(617\) 416.614 + 416.614i 0.675225 + 0.675225i 0.958916 0.283691i \(-0.0915589\pi\)
−0.283691 + 0.958916i \(0.591559\pi\)
\(618\) −3.49641 + 68.5679i −0.00565763 + 0.110951i
\(619\) 1140.08 1.84180 0.920902 0.389794i \(-0.127454\pi\)
0.920902 + 0.389794i \(0.127454\pi\)
\(620\) −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
\(623\) −958.085 755.394i −1.53786 1.21251i
\(624\) −207.999 230.351i −0.333331 0.369153i
\(625\) −379.267 + 496.771i −0.606827 + 0.794834i
\(626\) −319.542 −0.510450
\(627\) −906.059 46.2018i −1.44507 0.0736870i
\(628\) 325.105 325.105i 0.517683 0.517683i
\(629\) 63.3061i 0.100646i
\(630\) −270.200 161.917i −0.428889 0.257010i
\(631\) −76.8167 −0.121738 −0.0608690 0.998146i \(-0.519387\pi\)
−0.0608690 + 0.998146i \(0.519387\pi\)
\(632\) 375.203 + 375.203i 0.593675 + 0.593675i
\(633\) −42.2568 + 828.695i −0.0667564 + 1.30915i
\(634\) 136.086i 0.214646i
\(635\) 493.320 115.343i 0.776883 0.181643i
\(636\) 456.293 412.017i 0.717443 0.647825i
\(637\) −864.382 529.849i −1.35696 0.831788i
\(638\) −275.711 + 275.711i −0.432149 + 0.432149i
\(639\) −14.6792 + 143.562i −0.0229721 + 0.224666i
\(640\) −579.374 + 135.463i −0.905272 + 0.211661i
\(641\) 187.134i 0.291941i −0.989289 0.145970i \(-0.953370\pi\)
0.989289 0.145970i \(-0.0466304\pi\)
\(642\) 589.006 + 30.0346i 0.917455 + 0.0467829i
\(643\) −767.988 + 767.988i −1.19438 + 1.19438i −0.218559 + 0.975824i \(0.570136\pi\)
−0.975824 + 0.218559i \(0.929864\pi\)
\(644\) 52.2855 6.18494i 0.0811886 0.00960395i
\(645\) 692.114 125.040i 1.07305 0.193860i
\(646\) −149.633 −0.231631
\(647\) −573.588 + 573.588i −0.886535 + 0.886535i −0.994188 0.107654i \(-0.965666\pi\)
0.107654 + 0.994188i \(0.465666\pi\)
\(648\) −473.774 + 311.491i −0.731133 + 0.480696i
\(649\) −412.459 −0.635530
\(650\) −229.348 463.648i −0.352844 0.713304i
\(651\) −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 \(-0.700721\pi\)
0.807683 + 0.589616i \(0.200721\pi\)
\(654\) −6.06034 6.71161i −0.00926658 0.0102624i
\(655\) −337.551 209.618i −0.515345 0.320027i
\(656\) 133.596 0.203652
\(657\) −566.071 + 461.048i −0.861600 + 0.701747i
\(658\) −113.793 + 144.326i −0.172937 + 0.219340i
\(659\) 960.106 1.45691 0.728457 0.685092i \(-0.240238\pi\)
0.728457 + 0.685092i \(0.240238\pi\)
\(660\) −356.694 + 513.996i −0.540446 + 0.778782i
\(661\) 94.8355i 0.143473i 0.997424 + 0.0717364i \(0.0228540\pi\)
−0.997424 + 0.0717364i \(0.977146\pi\)
\(662\) −123.754 123.754i −0.186939 0.186939i
\(663\) −426.458 21.7459i −0.643224 0.0327993i
\(664\) −514.452 −0.774777
\(665\) 715.815 259.208i 1.07641 0.389787i
\(666\) −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
\(672\) 46.2557 + 691.455i 0.0688329 + 1.02895i
\(673\) −442.857 442.857i −0.658034 0.658034i 0.296880 0.954915i \(-0.404054\pi\)
−0.954915 + 0.296880i \(0.904054\pi\)
\(674\) −154.964 −0.229917
\(675\) 643.537 203.679i 0.953388 0.301746i
\(676\) −777.336 −1.14990
\(677\) −447.410 + 447.410i −0.660872 + 0.660872i −0.955586 0.294714i \(-0.904776\pi\)
0.294714 + 0.955586i \(0.404776\pi\)
\(678\) −17.3090 + 339.445i −0.0255295 + 0.500656i
\(679\) −163.840 + 19.3810i −0.241296 + 0.0285434i
\(680\) −127.020 + 204.542i −0.186794 + 0.300798i
\(681\) −544.182 602.662i −0.799093 0.884966i
\(682\) −169.557 169.557i −0.248617 0.248617i
\(683\) 199.643 199.643i 0.292303 0.292303i −0.545686 0.837990i \(-0.683731\pi\)
0.837990 + 0.545686i \(0.183731\pi\)
\(684\) 59.7388 584.243i 0.0873375 0.854157i
\(685\) 11.9608 + 51.1561i 0.0174610 + 0.0746804i
\(686\) 118.655 + 321.823i 0.172967 + 0.469129i
\(687\) −18.8666 + 369.991i −0.0274622 + 0.538560i
\(688\) −165.774 165.774i −0.240950 0.240950i
\(689\) 1413.38i 2.05135i
\(690\) 21.4409 30.8964i 0.0310738 0.0447773i
\(691\) 207.196i 0.299849i −0.988697 0.149925i \(-0.952097\pi\)
0.988697 0.149925i \(-0.0479031\pi\)
\(692\) 80.8697 80.8697i 0.116864 0.116864i
\(693\) 629.088 + 609.457i 0.907775 + 0.879447i
\(694\) 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
\(700\) 108.561 513.653i 0.155088 0.733790i
\(701\) 8.12497i 0.0115905i 0.999983 + 0.00579527i \(0.00184470\pi\)
−0.999983 + 0.00579527i \(0.998155\pi\)
\(702\) −85.0546 + 552.141i −0.121160 + 0.786525i
\(703\) 141.540 141.540i 0.201337 0.201337i
\(704\) −180.740 −0.256733
\(705\) −70.0183 387.561i −0.0993167 0.549733i
\(706\) 339.785i 0.481281i
\(707\) 490.236 621.778i 0.693403 0.879459i
\(708\) 13.5972 266.654i 0.0192052 0.376631i
\(709\) 854.167i 1.20475i 0.798214 + 0.602374i \(0.205778\pi\)
−0.798214 + 0.602374i \(0.794222\pi\)
\(710\) 78.0670 18.2528i 0.109954 0.0257082i
\(711\) −69.3953 + 678.683i −0.0976023 + 0.954547i
\(712\) 862.713 + 862.713i 1.21168 + 1.21168i
\(713\) −30.5762 30.5762i −0.0428839 0.0428839i
\(714\) 108.742 + 95.1052i 0.152300 + 0.133201i
\(715\) 327.464 + 1400.56i 0.457992 + 1.95882i
\(716\) 562.180i 0.785168i
\(717\) −7.52867 + 147.644i −0.0105002 + 0.205919i
\(718\) 114.367 + 114.367i 0.159285 + 0.159285i
\(719\) 1236.22i 1.71936i 0.510837 + 0.859678i \(0.329336\pi\)
−0.510837 + 0.859678i \(0.670664\pi\)
\(720\) −178.077 137.526i −0.247330 0.191009i
\(721\) 18.8191 + 159.090i 0.0261014 + 0.220652i
\(722\) −79.2852 79.2852i −0.109813 0.109813i
\(723\) 1263.35 + 64.4208i 1.74737 + 0.0891021i
\(724\) 538.742 0.744118
\(725\) 310.868 + 628.446i 0.428783 + 0.866822i
\(726\) −160.972 + 145.352i −0.221725 + 0.200210i
\(727\) 635.035 + 635.035i 0.873501 + 0.873501i 0.992852 0.119351i \(-0.0380815\pi\)
−0.119351 + 0.992852i \(0.538081\pi\)
\(728\) 796.155 + 627.722i 1.09362 + 0.862255i
\(729\) −695.204 219.392i −0.953640 0.300949i
\(730\) 344.562 + 213.971i 0.472003 + 0.293112i
\(731\) −322.553 −0.441249
\(732\) −9.65785 + 189.399i −0.0131938 + 0.258742i
\(733\) 174.851 174.851i 0.238542 0.238542i −0.577704 0.816246i \(-0.696051\pi\)
0.816246 + 0.577704i \(0.196051\pi\)
\(734\) 142.908i 0.194697i
\(735\) −684.948 266.591i −0.931902 0.362709i
\(736\) −82.7358 −0.112413
\(737\) 451.552 + 451.552i 0.612689 + 0.612689i
\(738\) −151.861 186.454i −0.205774 0.252648i
\(739\) 1448.98i 1.96073i −0.197187 0.980366i \(-0.563181\pi\)
0.197187 0.980366i \(-0.436819\pi\)
\(740\) −31.4269 134.412i −0.0424688 0.181638i
\(741\) −904.856 1002.10i −1.22113 1.35236i
\(742\) −296.055 + 375.493i −0.398995 + 0.506055i
\(743\) 30.8955 30.8955i 0.0415822 0.0415822i −0.686010 0.727592i \(-0.740639\pi\)
0.727592 + 0.686010i \(0.240639\pi\)
\(744\) 268.818 242.733i 0.361315 0.326254i
\(745\) 105.080 + 65.2544i 0.141047 + 0.0875898i
\(746\) 522.501i 0.700404i
\(747\) −417.706 512.856i −0.559179 0.686555i
\(748\) 202.888 202.888i 0.271241 0.271241i
\(749\) 1366.61 161.658i 1.82457 0.215832i
\(750\) −223.377 301.210i −0.297836 0.401614i
\(751\) 1095.21 1.45833 0.729167 0.684335i \(-0.239908\pi\)
0.729167 + 0.684335i \(0.239908\pi\)
\(752\) −92.8279 + 92.8279i −0.123441 + 0.123441i
\(753\) 52.7867 1035.20i 0.0701019 1.37476i
\(754\) −580.279 −0.769601
\(755\) 693.737 + 430.808i 0.918857 + 0.570606i
\(756\) −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 \(0.345305\pi\)
\(762\) −15.4802 + 303.581i −0.0203152 + 0.398400i
\(763\) −16.5694 13.0640i −0.0217161 0.0171219i
\(764\) 321.188 0.420403
\(765\) −307.041 + 39.4511i −0.401361 + 0.0515701i
\(766\) 231.666i 0.302436i
\(767\) −434.044 434.044i −0.565898 0.565898i
\(768\) 26.1250 512.334i 0.0340169 0.667102i
\(769\) 248.259 0.322833 0.161417 0.986886i \(-0.448394\pi\)
0.161417 + 0.986886i \(0.448394\pi\)
\(770\) 206.371 440.679i 0.268014 &mi