Properties

Label 105.3.k.c.83.5
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 83.5
Root \(-0.817327 + 1.97320i\) of \(x^{16} + 433 x^{8} + 16\)
Character \(\chi\) \(=\) 105.83
Dual form 105.3.k.c.62.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(-2.99611 + 0.152778i) q^{3} -3.00000i q^{4} +(4.24762 + 2.63775i) q^{5} +(-2.22660 - 2.01054i) q^{6} +(4.33402 - 5.49694i) q^{7} +(4.94975 - 4.94975i) q^{8} +(8.95332 - 0.915476i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(-2.99611 + 0.152778i) 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} +(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} +(-12.1454 + 17.1316i) q^{21} +(-9.83095 + 9.83095i) q^{22} +(1.77282 - 1.77282i) q^{23} +(-14.0738 + 15.5862i) q^{24} +(11.0845 + 22.4083i) q^{25} +20.6909 q^{26} +(-26.6852 + 4.11073i) q^{27} +(-16.4908 - 13.0020i) 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} +(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} +(-20.7019 + 3.52576i) 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} +(33.7715 - 53.1835i) 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} +(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} +(76.4243 + 60.2561i) 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} +(51.3947 + 36.4361i) 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} +(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 0.861430 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
\(7\) 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 \(0.217748\pi\)
−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 \(-0.457049\pi\)
0.990910 0.134524i \(-0.0429507\pi\)
\(14\) 6.95153 0.822309i 0.496538 0.0587364i
\(15\) −13.1293 7.25405i −0.875287 0.483603i
\(16\) −5.00000 −0.312500
\(17\) 4.86435 4.86435i 0.286138 0.286138i −0.549413 0.835551i \(-0.685149\pi\)
0.835551 + 0.549413i \(0.185149\pi\)
\(18\) 6.97829 + 5.68361i 0.387683 + 0.315756i
\(19\) −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
\(21\) −12.1454 + 17.1316i −0.578351 + 0.815788i
\(22\) −9.83095 + 9.83095i −0.446861 + 0.446861i
\(23\) 1.77282 1.77282i 0.0770791 0.0770791i −0.667516 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
\(28\) −16.4908 13.0020i −0.588957 0.464359i
\(29\) −28.0452 −0.967076 −0.483538 0.875323i \(-0.660648\pi\)
−0.483538 + 0.875323i \(0.660648\pi\)
\(30\) −4.15444 14.4132i −0.138481 0.480440i
\(31\) 17.2472i 0.556362i 0.960529 + 0.278181i \(0.0897315\pi\)
−0.960529 + 0.278181i \(0.910268\pi\)
\(32\) −23.3345 23.3345i −0.729204 0.729204i
\(33\) −2.12408 41.6551i −0.0643660 1.26228i
\(34\) 6.87923 0.202330
\(35\) 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 \(-0.394352\pi\)
0.325844 + 0.945424i \(0.394352\pi\)
\(42\) −20.7019 + 3.52576i −0.492903 + 0.0839468i
\(43\) 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 −0.876470 0.481457i \(-0.840108\pi\)
0.481457 + 0.876470i \(0.340108\pi\)
\(48\) 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 \(0.0808953\pi\)
−0.967880 + 0.251413i \(0.919105\pi\)
\(60\) −21.7621 + 39.3879i −0.362702 + 0.656465i
\(61\) 21.0717i 0.345438i 0.984971 + 0.172719i \(0.0552552\pi\)
−0.984971 + 0.172719i \(0.944745\pi\)
\(62\) −12.1956 + 12.1956i −0.196704 + 0.196704i
\(63\) 33.7715 53.1835i 0.536056 0.844183i
\(64\) 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 \(0.0360200\pi\)
−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 −0.195045 0.980794i \(-0.562485\pi\)
0.980794 + 0.195045i \(0.0624853\pi\)
\(74\) −9.20249 −0.124358
\(75\) −36.6339 65.4443i −0.488452 0.872591i
\(76\) 65.2544i 0.858610i
\(77\) 76.4243 + 60.2561i 0.992523 + 0.782547i
\(78\) −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 0.320974 0.947088i \(-0.395990\pi\)
−0.947088 + 0.320974i \(0.895990\pi\)
\(84\) 51.3947 + 36.4361i 0.611841 + 0.433763i
\(85\) 33.4929 7.83095i 0.394034 0.0921288i
\(86\) 46.8879i 0.545208i
\(87\) 84.0264 4.28468i 0.965821 0.0492492i
\(88\) 68.8167 + 68.8167i 0.782008 + 0.782008i
\(89\) 174.294i 1.95836i 0.202987 + 0.979181i \(0.434935\pi\)
−0.202987 + 0.979181i \(0.565065\pi\)
\(90\) 14.6492 + 42.5488i 0.162768 + 0.472765i
\(91\) −17.0143 143.833i −0.186970 1.58058i
\(92\) −5.31846 5.31846i −0.0578093 0.0578093i
\(93\) −2.63499 51.6745i −0.0283332 0.555640i
\(94\) −26.2557 −0.279316
\(95\) −92.3919 57.3750i −0.972547 0.603947i
\(96\) 73.4777 + 66.3477i 0.765393 + 0.691122i
\(97\) −16.6658 16.6658i −0.171812 0.171812i 0.615963 0.787775i \(-0.288767\pi\)
−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 \(-0.689187\pi\)
−0.559968 + 0.828514i \(0.689187\pi\)
\(102\) −20.6109 + 1.05099i −0.202068 + 0.0103038i
\(103\) −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
\(105\) −96.7777 + 40.7318i −0.921692 + 0.387922i
\(106\) −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
\(112\) −21.6701 + 27.4847i −0.193483 + 0.245399i
\(113\) 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
\(126\) 61.4865 13.7264i 0.487988 0.108939i
\(127\) −71.6476 + 71.6476i −0.564154 + 0.564154i −0.930485 0.366330i \(-0.880614\pi\)
0.366330 + 0.930485i \(0.380614\pi\)
\(128\) −84.1457 + 84.1457i −0.657388 + 0.657388i
\(129\) −104.401 94.2699i −0.809306 0.730775i
\(130\) 87.8869 + 54.5774i 0.676053 + 0.419826i
\(131\) −79.4683 −0.606629 −0.303314 0.952891i \(-0.598093\pi\)
−0.303314 + 0.952891i \(0.598093\pi\)
\(132\) −124.965 + 6.37223i −0.946706 + 0.0482745i
\(133\) −94.2712 + 119.566i −0.708806 + 0.898996i
\(134\) −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 \(-0.276439\pi\)
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
\(147\) 41.5328 + 141.011i 0.282536 + 0.959257i
\(148\) 19.5214 + 19.5214i 0.131902 + 0.131902i
\(149\) 24.7386 0.166031 0.0830155 0.996548i \(-0.473545\pi\)
0.0830155 + 0.996548i \(0.473545\pi\)
\(150\) 20.3720 72.1802i 0.135813 0.481201i
\(151\) −163.324 −1.08161 −0.540807 0.841147i \(-0.681881\pi\)
−0.540807 + 0.841147i \(0.681881\pi\)
\(152\) −107.664 + 107.664i −0.708317 + 0.708317i
\(153\) 39.0989 48.0053i 0.255548 0.313760i
\(154\) 11.4326 + 96.6476i 0.0742378 + 0.627582i
\(155\) −45.4939 + 73.2596i −0.293509 + 0.472643i
\(156\) 138.211 + 124.799i 0.885966 + 0.799995i
\(157\) 108.368 + 108.368i 0.690244 + 0.690244i 0.962285 0.272042i \(-0.0876988\pi\)
−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
\(162\) 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 −0.159365 0.987220i \(-0.550945\pi\)
0.987220 + 0.159365i \(0.0509447\pi\)
\(168\) 24.6804 + 144.913i 0.146907 + 0.862579i
\(169\) 259.112i 1.53321i
\(170\) 29.2203 + 18.1457i 0.171884 + 0.106739i
\(171\) −194.748 + 19.9129i −1.13888 + 0.116450i
\(172\) 99.4643 99.4643i 0.578281 0.578281i
\(173\) −26.9566 26.9566i −0.155818 0.155818i 0.624893 0.780711i \(-0.285143\pi\)
−0.780711 + 0.624893i \(0.785143\pi\)
\(174\) 62.4454 + 56.3859i 0.358882 + 0.324057i
\(175\) 171.218 + 36.1871i 0.978387 + 0.206784i
\(176\) 69.5153i 0.394973i
\(177\) −4.53242 88.8848i −0.0256069 0.502174i
\(178\) −123.245 + 123.245i −0.692386 + 0.692386i
\(179\) 187.393 1.04689 0.523445 0.852059i \(-0.324646\pi\)
0.523445 + 0.852059i \(0.324646\pi\)
\(180\) 59.1841 121.335i 0.328801 0.674085i
\(181\) 179.581i 0.992158i 0.868277 + 0.496079i \(0.165227\pi\)
−0.868277 + 0.496079i \(0.834773\pi\)
\(182\) 89.6745 113.736i 0.492717 0.624925i
\(183\) −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
\(189\) −93.0578 + 164.503i −0.492369 + 0.870386i
\(190\) −24.7607 105.901i −0.130320 0.557375i
\(191\) 107.063i 0.560538i −0.959922 0.280269i \(-0.909576\pi\)
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 \(-0.686462\pi\)
−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
\(207\) 14.2496 17.4956i 0.0688388 0.0845197i
\(208\) −73.1533 + 73.1533i −0.351698 + 0.351698i
\(209\) 302.412i 1.44695i
\(210\) −97.2339 39.6304i −0.463019 0.188716i
\(211\) 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
\(217\) 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
\(222\) 27.5717 1.40593i 0.124197 0.00633304i
\(223\) 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
\(225\) 119.758 + 190.481i 0.532256 + 0.846584i
\(226\) 113.295 0.501306
\(227\) 191.389 191.389i 0.843123 0.843123i −0.146140 0.989264i \(-0.546685\pi\)
0.989264 + 0.146140i \(0.0466851\pi\)
\(228\) −9.96941 195.509i −0.0437255 0.857496i
\(229\) 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
\(231\) −238.181 168.858i −1.03109 0.730986i
\(232\) −138.817 + 138.817i −0.598348 + 0.598348i
\(233\) −89.8918 + 89.8918i −0.385802 + 0.385802i −0.873187 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
\(238\) 29.8147 37.8147i 0.125272 0.158885i
\(239\) −49.2786 −0.206187 −0.103093 0.994672i \(-0.532874\pi\)
−0.103093 + 0.994672i \(0.532874\pi\)
\(240\) 65.6465 + 36.2702i 0.273527 + 0.151126i
\(241\) 421.664i 1.74964i −0.484445 0.874822i \(-0.660979\pi\)
0.484445 0.874822i \(-0.339021\pi\)
\(242\) −51.1204 51.1204i −0.211242 0.211242i
\(243\) −235.158 + 61.2344i −0.967729 + 0.251993i
\(244\) 63.2151 0.259078
\(245\) 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 \(-0.258369\pi\)
0.688274 + 0.725450i \(0.258369\pi\)
\(252\) −159.551 101.315i −0.633137 0.402042i
\(253\) 24.6476 + 24.6476i 0.0974214 + 0.0974214i
\(254\) −101.325 −0.398917
\(255\) −99.1518 + 28.5793i −0.388831 + 0.112076i
\(256\) −171.000 −0.667969
\(257\) −216.568 + 216.568i −0.842676 + 0.842676i −0.989206 0.146530i \(-0.953190\pi\)
0.146530 + 0.989206i \(0.453190\pi\)
\(258\) −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 \(0.225434\pi\)
−0.759519 + 0.650485i \(0.774566\pi\)
\(270\) −50.3909 125.243i −0.186633 0.463862i
\(271\) 137.978i 0.509143i 0.967054 + 0.254572i \(0.0819344\pi\)
−0.967054 + 0.254572i \(0.918066\pi\)
\(272\) −24.3218 + 24.3218i −0.0894182 + 0.0894182i
\(273\) 72.9511 + 428.340i 0.267220 + 1.56901i
\(274\) 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 \(0.0813658\pi\)
−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 −0.886873 0.462014i \(-0.847127\pi\)
0.462014 + 0.886873i \(0.347127\pi\)
\(284\) 48.1035 0.169378
\(285\) 285.582 + 157.786i 1.00204 + 0.553636i
\(286\) 287.666i 1.00583i
\(287\) 115.801 146.874i 0.403489 0.511755i
\(288\) −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 \(-0.884567\pi\)
−0.354747 0.934962i \(-0.615433\pi\)
\(294\) −70.3415 + 129.078i −0.239257 + 0.439040i
\(295\) −78.2536 + 126.013i −0.265266 + 0.427163i
\(296\) 64.4174i 0.217626i
\(297\) −57.1518 371.007i −0.192430 1.24918i
\(298\) 17.4929 + 17.4929i 0.0587009 + 0.0587009i
\(299\) 51.8750i 0.173495i
\(300\) −196.333 + 109.902i −0.654443 + 0.366339i
\(301\) 325.943 38.5564i 1.08287 0.128094i
\(302\) −115.487 115.487i −0.382409 0.382409i
\(303\) 338.900 17.2812i 1.11848 0.0570337i
\(304\) 108.757 0.357754
\(305\) −55.5820 + 89.5046i −0.182236 + 0.293458i
\(306\) 61.5919 6.29777i 0.201281 0.0205809i
\(307\) −94.6590 94.6590i −0.308335 0.308335i 0.535928 0.844264i \(-0.319962\pi\)
−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 \(-0.615860\pi\)
−0.356000 + 0.934486i \(0.615860\pi\)
\(312\) 22.1277 + 433.944i 0.0709221 + 1.39085i
\(313\) 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
\(315\) 283.733 136.822i 0.900741 0.434357i
\(316\) −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
\(322\) 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
\(327\) 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
\(336\) 60.7268 85.6578i 0.180735 0.254934i
\(337\) 109.576 109.576i 0.325152 0.325152i −0.525588 0.850739i \(-0.676155\pi\)
0.850739 + 0.525588i \(0.176155\pi\)
\(338\) 183.220 183.220i 0.542070 0.542070i
\(339\) −227.784 + 252.263i −0.671930 + 0.744138i
\(340\) −23.4929 100.479i −0.0690966 0.295525i
\(341\) −239.789 −0.703194
\(342\) −151.788 123.627i −0.443825 0.361482i
\(343\) −311.465 143.661i −0.908061 0.418837i
\(344\) 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 \(-0.643537\pi\)
−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 0.279509 0.960143i \(-0.409828\pi\)
−0.960143 + 0.279509i \(0.909828\pi\)
\(354\) 59.6461 66.0559i 0.168492 0.186599i
\(355\) −42.2950 + 68.1084i −0.119141 + 0.191855i
\(356\) 522.883 1.46877
\(357\) 24.2545 + 142.413i 0.0679399 + 0.398916i
\(358\) 132.507 + 132.507i 0.370132 + 0.370132i
\(359\) 161.739 0.450526 0.225263 0.974298i \(-0.427676\pi\)
0.225263 + 0.974298i \(0.427676\pi\)
\(360\) 297.842 102.544i 0.827338 0.284845i
\(361\) 112.126 0.310599
\(362\) −126.983 + 126.983i −0.350781 + 0.350781i
\(363\) 216.604 11.0451i 0.596706 0.0304272i
\(364\) −431.500 + 51.0429i −1.18544 + 0.140228i
\(365\) 394.943 92.3414i 1.08203 0.252990i
\(366\) 42.3655 46.9182i 0.115753 0.128192i
\(367\) 101.051 + 101.051i 0.275343 + 0.275343i 0.831247 0.555904i \(-0.187628\pi\)
−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
\(372\) −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
\(378\) −182.123 + 50.5194i −0.481807 + 0.133649i
\(379\) 261.209i 0.689207i 0.938748 + 0.344604i \(0.111987\pi\)
−0.938748 + 0.344604i \(0.888013\pi\)
\(380\) −172.125 + 277.176i −0.452960 + 0.729410i
\(381\) 203.718 225.610i 0.534692 0.592152i
\(382\) 75.7048 75.7048i 0.198180 0.198180i
\(383\) −163.813 163.813i −0.427710 0.427710i 0.460138 0.887847i \(-0.347800\pi\)
−0.887847 + 0.460138i \(0.847800\pi\)
\(384\) 239.254 264.965i 0.623057 0.690013i
\(385\) 165.680 + 457.533i 0.430339 + 1.18840i
\(386\) 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
\(392\) −292.432 179.255i −0.746001 0.457283i
\(393\) 238.096 12.1410i 0.605841 0.0308931i
\(394\) 234.338i 0.594767i
\(395\) 199.948 321.980i 0.506197 0.815138i
\(396\) 373.436 38.1838i 0.943019 0.0964237i
\(397\) −304.082 304.082i −0.765950 0.765950i 0.211440 0.977391i \(-0.432185\pi\)
−0.977391 + 0.211440i \(0.932185\pi\)
\(398\) −155.590 155.590i −0.390929 0.390929i
\(399\) 264.180 372.636i 0.662104 0.933926i
\(400\) −55.4226 112.042i −0.138557 0.280104i
\(401\) 582.912i 1.45365i −0.686825 0.726823i \(-0.740996\pi\)
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 \(-0.638515\pi\)
−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
\(417\) −538.068 + 27.4372i −1.29033 + 0.0657965i
\(418\) 213.838 213.838i 0.511573 0.511573i
\(419\) 343.927i 0.820828i −0.911899 0.410414i \(-0.865384\pi\)
0.911899 0.410414i \(-0.134616\pi\)
\(420\) 122.195 + 290.333i 0.290942 + 0.691269i
\(421\) 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
\(427\) 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 \(-0.828164\pi\)
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 \(-0.457016\pi\)
0.990896 0.134629i \(-0.0429843\pi\)
\(434\) 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 \(-0.555041\pi\)
−0.172056 + 0.985087i \(0.555041\pi\)
\(440\) 110.786 + 473.828i 0.251785 + 1.07688i
\(441\) −145.980 416.138i −0.331021 0.943624i
\(442\) 100.648 100.648i 0.227710 0.227710i
\(443\) 188.010 188.010i 0.424401 0.424401i −0.462315 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
\(448\) −71.4602 56.3422i −0.159509 0.125764i
\(449\) −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
\(455\) 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 \(-0.566614\pi\)
−0.207750 + 0.978182i \(0.566614\pi\)
\(462\) −49.0189 287.820i −0.106102 0.622987i
\(463\) 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 −0.382536 0.923941i \(-0.624949\pi\)
0.923941 + 0.382536i \(0.124949\pi\)
\(468\) −433.161 352.797i −0.925557 0.753839i
\(469\) 37.7700 + 319.295i 0.0805331 + 0.680800i
\(470\) −111.524 69.2561i −0.237286 0.147353i
\(471\) −341.239 308.127i −0.724500 0.654197i
\(472\) 146.843 + 146.843i 0.311108 + 0.311108i
\(473\) −460.953 + 460.953i −0.974530 + 0.974530i
\(474\) −152.404 + 168.781i −0.321526 + 0.356079i
\(475\) −241.105 487.414i −0.507589 1.02613i
\(476\) −143.464 + 16.9706i −0.301394 + 0.0356524i
\(477\) −388.245 + 476.684i −0.813930 + 0.999337i
\(478\) −34.8452 34.8452i −0.0728980 0.0728980i
\(479\) 91.5191i 0.191063i −0.995426 0.0955314i \(-0.969545\pi\)
0.995426 0.0955314i \(-0.0304550\pi\)
\(480\) 137.096 + 475.636i 0.285618 + 0.990908i
\(481\) 190.408i 0.395858i
\(482\) 298.161 298.161i 0.618592 0.618592i
\(483\) 8.83960 + 51.9027i 0.0183015 + 0.107459i
\(484\) 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 \(0.176913\pi\)
−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
\(497\) 88.1406 + 69.4937i 0.177345 + 0.139826i
\(498\) 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 0.694329 0.719657i \(-0.255701\pi\)
−0.719657 + 0.694329i \(0.755701\pi\)
\(504\) −96.0845 430.405i −0.190644 0.853979i
\(505\) −480.463 298.365i −0.951412 0.590823i
\(506\) 34.8570i 0.0688873i
\(507\) 39.5865 + 776.327i 0.0780798 + 1.53122i
\(508\) 214.943 + 214.943i 0.423116 + 0.423116i
\(509\) 611.593i 1.20156i −0.799415 0.600779i \(-0.794857\pi\)
0.799415 0.600779i \(-0.205143\pi\)
\(510\) −90.3195 49.9023i −0.177097 0.0978476i
\(511\) −66.7048 563.900i −0.130538 1.10352i
\(512\) 215.668 + 215.668i 0.421226 + 0.421226i
\(513\) 580.443 89.4144i 1.13147 0.174297i
\(514\) −306.273 −0.595862
\(515\) −111.423 + 26.0518i −0.216356 + 0.0505860i
\(516\) −282.810 + 313.202i −0.548081 + 0.606980i
\(517\) −258.119 258.119i −0.499262 0.499262i
\(518\) −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 \(-0.268603\pi\)
0.664597 + 0.747202i \(0.268603\pi\)
\(522\) −195.708 159.398i −0.374919 0.305360i
\(523\) −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
\(525\) −518.515 82.2623i −0.987648 0.156690i
\(526\) 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
\(532\) 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
\(537\) −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
\(546\) −251.298 + 354.467i −0.460253 + 0.649206i
\(547\) 223.888 223.888i 0.409302 0.409302i −0.472193 0.881495i \(-0.656538\pi\)
0.881495 + 0.472193i \(0.156538\pi\)
\(548\) 22.2890 22.2890i 0.0406734 0.0406734i
\(549\) 19.2906 + 188.662i 0.0351378 + 0.343646i
\(550\) −329.267 111.324i −0.598667 0.202407i
\(551\) 610.024 1.10712
\(552\) 2.68125 + 52.5817i 0.00485733 + 0.0952567i
\(553\) −416.681 328.529i −0.753492 0.594084i
\(554\) 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
\(560\) −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 0.968993 0.247086i \(-0.0794732\pi\)
−0.247086 + 0.968993i \(0.579473\pi\)
\(564\) −175.383 158.364i −0.310962 0.280788i
\(565\) 551.600 128.969i 0.976283 0.228264i
\(566\) −170.038 −0.300420
\(567\) 253.679 507.086i 0.447405 0.894331i
\(568\) 79.3667 + 79.3667i 0.139730 + 0.139730i
\(569\) 690.156 1.21293 0.606464 0.795111i \(-0.292587\pi\)
0.606464 + 0.795111i \(0.292587\pi\)
\(570\) 90.3651 + 313.508i 0.158535 + 0.550015i
\(571\) 612.476 1.07264 0.536319 0.844015i \(-0.319814\pi\)
0.536319 + 0.844015i \(0.319814\pi\)
\(572\) 610.233 610.233i 1.06684 1.06684i
\(573\) 16.3568 + 320.771i 0.0285459 + 0.559810i
\(574\) 185.739 21.9714i 0.323587 0.0382777i
\(575\) 59.3768 + 20.0751i 0.103264 + 0.0349131i
\(576\) −11.9012 116.393i −0.0206618 0.202071i
\(577\) 254.442 + 254.442i 0.440973 + 0.440973i 0.892339 0.451366i \(-0.149063\pi\)
−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
\(582\) 3.60081 + 70.6151i 0.00618695 + 0.121332i
\(583\) −671.548 671.548i −1.15188 1.15188i
\(584\) 567.832i 0.972315i
\(585\) 880.372 303.104i 1.50491 0.518126i
\(586\) 534.410i 0.911962i
\(587\) −195.495 + 195.495i −0.333040 + 0.333040i −0.853740 0.520700i \(-0.825671\pi\)
0.520700 + 0.853740i \(0.325671\pi\)
\(588\) 423.032 124.599i 0.719442 0.211902i
\(589\) 375.152i 0.636931i
\(590\) −144.438 + 33.7711i −0.244811 + 0.0572391i
\(591\) −521.777 471.146i −0.882871 0.797201i
\(592\) 32.5357 32.5357i 0.0549590 0.0549590i
\(593\) −181.904 181.904i −0.306751 0.306751i 0.536897 0.843648i \(-0.319597\pi\)
−0.843648 + 0.536897i \(0.819597\pi\)
\(594\) 221.929 302.754i 0.373618 0.509686i
\(595\) 102.112 218.048i 0.171617 0.366466i
\(596\) 74.2159i 0.124523i
\(597\) 659.255 33.6167i 1.10428 0.0563094i
\(598\) 36.6812 36.6812i 0.0613397 0.0613397i
\(599\) 376.201 0.628048 0.314024 0.949415i \(-0.398323\pi\)
0.314024 + 0.949415i \(0.398323\pi\)
\(600\) −505.261 142.604i −0.842102 0.237674i
\(601\) 1122.87i 1.86834i 0.356832 + 0.934169i \(0.383857\pi\)
−0.356832 + 0.934169i \(0.616143\pi\)
\(602\) 257.740 + 203.213i 0.428139 + 0.337563i
\(603\) −261.058 + 320.524i −0.432931 + 0.531549i
\(604\) 489.971i 0.811211i
\(605\) −307.083 190.697i −0.507574 0.315202i
\(606\) 251.858 + 227.419i 0.415608 + 0.375279i
\(607\) 127.880 + 127.880i 0.210675 + 0.210675i 0.804554 0.593879i \(-0.202404\pi\)
−0.593879 + 0.804554i \(0.702404\pi\)
\(608\) 507.560 + 507.560i 0.834803 + 0.834803i
\(609\) 340.619 480.458i 0.559309 0.788929i
\(610\) −102.592 + 23.9869i −0.168183 + 0.0393228i
\(611\) 543.253i 0.889122i
\(612\) −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 \(-0.127454\pi\)
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
\(627\) 46.2018 + 906.059i 0.0736870 + 1.44507i
\(628\) 325.105 325.105i 0.517683 0.517683i
\(629\) 63.3061i 0.100646i
\(630\) 297.378 + 103.882i 0.472028 + 0.164892i
\(631\) −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
\(637\) −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 \(0.0466304\pi\)
−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 \(0.570136\pi\)
−0.975824 + 0.218559i \(0.929864\pi\)
\(644\) −52.2855 + 6.18494i −0.0811886 + 0.00960395i
\(645\) −194.793 675.805i −0.302004 1.04776i
\(646\) −149.633 −0.231631
\(647\) 573.588 573.588i 0.886535 0.886535i −0.107654 0.994188i \(-0.534334\pi\)
0.994188 + 0.107654i \(0.0343337\pi\)
\(648\) 311.491 473.774i 0.480696 0.731133i
\(649\) −412.459 −0.635530
\(650\) 229.348 + 463.648i 0.352844 + 0.713304i
\(651\) −295.472 209.474i −0.453874 0.321772i
\(652\) 116.536 116.536i 0.178736 0.178736i
\(653\) −142.398 + 142.398i −0.218067 + 0.218067i −0.807683 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
\(658\) −113.793 + 144.326i −0.172937 + 0.219340i
\(659\) −960.106 −1.45691 −0.728457 0.685092i \(-0.759762\pi\)
−0.728457 + 0.685092i \(0.759762\pi\)
\(660\) −547.613 302.561i −0.829717 0.458425i
\(661\) 94.8355i 0.143473i 0.997424 + 0.0717364i \(0.0228540\pi\)
−0.997424 + 0.0717364i \(0.977146\pi\)
\(662\) 123.754 + 123.754i 0.186939 + 0.186939i
\(663\) 21.7459 + 426.458i 0.0327993 + 0.643224i
\(664\) −514.452 −0.774777
\(665\) −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
\(672\) 683.163 116.350i 1.01661 0.173140i
\(673\) −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 −0.294714 0.955586i \(-0.595224\pi\)
0.955586 + 0.294714i \(0.0952243\pi\)
\(678\) −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 \(-0.952097\pi\)
0.988697 0.149925i \(-0.0479031\pi\)
\(692\) −80.8697 + 80.8697i −0.116864 + 0.116864i
\(693\) 739.414 + 469.527i 1.06698 + 0.677529i
\(694\) 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 \(-0.998155\pi\)
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
\(707\) −490.236 + 621.778i −0.693403 + 0.879459i
\(708\) −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
\(714\) −83.5508 + 117.852i −0.117018 + 0.165059i
\(715\) 327.464 + 1400.56i 0.457992 + 1.95882i
\(716\) 562.180i 0.785168i
\(717\) 147.644 7.52867i 0.205919 0.0105002i
\(718\) 114.367 + 114.367i 0.159285 + 0.159285i
\(719\) 1236.22i 1.71936i −0.510837 0.859678i \(-0.670664\pi\)
0.510837 0.859678i \(-0.329336\pi\)
\(720\) −202.225 98.6402i −0.280869 0.137000i
\(721\) 18.8191 + 159.090i 0.0261014 + 0.220652i
\(722\) 79.2852 + 79.2852i 0.109813 + 0.109813i
\(723\) 64.4208 + 1263.35i 0.0891021 + 1.74737i
\(724\) 538.742 0.744118
\(725\) −310.868 628.446i −0.428783 0.866822i
\(726\) 160.972 + 145.352i 0.221725 + 0.200210i
\(727\) 635.035 + 635.035i 0.873501 + 0.873501i 0.992852 0.119351i \(-0.0380815\pi\)
−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
\(732\) −189.399 + 9.65785i −0.258742 + 0.0131938i
\(733\) 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
\(735\) −195.536 + 708.513i −0.266035 + 0.963963i
\(736\) −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
\(742\) −296.055 + 375.493i −0.398995 + 0.506055i
\(743\) −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
\(756\) 493.509 + 279.173i 0.652790 + 0.369277i
\(757\) 209.069 209.069i 0.276181 0.276181i −0.555401 0.831582i \(-0.687435\pi\)
0.831582 + 0.555401i \(0.187435\pi\)
\(758\) −184.703 + 184.703i −0.243672 + 0.243672i
\(759\) −77.6125 70.0813i −0.102256 0.0923337i
\(760\) −741.308 + 173.325i −0.975406 + 0.228059i
\(761\) −710.902 −0.934168 −0.467084 0.884213i \(-0.654695\pi\)
−0.467084 + 0.884213i \(0.654695\pi\)
\(762\) 303.581 15.4802i 0.398400 0.0203152i
\(763\) −16.5694 13.0640i −0.0217161 0.0171219i
\(764\) −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 \(-0.448394\pi\)
0.161417 + 0.986886i \(0.448394\pi\)
\(770\) −206.371 + 440.679i −0.268014 + 0.572310i