Properties

Label 105.3.k.c.62.5
Level 105
Weight 3
Character 105.62
Analytic conductor 2.861
Analytic rank 0
Dimension 16
CM no
Inner twists 8

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 62.5
Root \(-0.817327 - 1.97320i\) of \(x^{16} + 433 x^{8} + 16\)
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.c.83.5

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.353553 0.353553i −0.507877 0.861430i \(-0.669569\pi\)
0.861430 + 0.507877i \(0.169569\pi\)
\(3\) −2.99611 0.152778i −0.998702 0.0509259i
\(4\) 3.00000i 0.750000i
\(5\) 4.24762 2.63775i 0.849524 0.527550i
\(6\) −2.22660 + 2.01054i −0.371100 + 0.335090i
\(7\) 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 \(-0.217748\pi\)
\(12\) 0.458333 8.98832i 0.0381944 0.749027i
\(13\) 14.6307 + 14.6307i 1.12543 + 1.12543i 0.990910 + 0.134524i \(0.0429507\pi\)
0.134524 + 0.990910i \(0.457049\pi\)
\(14\) 6.95153 + 0.822309i 0.496538 + 0.0587364i
\(15\) −13.1293 + 7.25405i −0.875287 + 0.483603i
\(16\) −5.00000 −0.312500
\(17\) 4.86435 + 4.86435i 0.286138 + 0.286138i 0.835551 0.549413i \(-0.185149\pi\)
−0.549413 + 0.835551i \(0.685149\pi\)
\(18\) 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 0.744595 0.667516i \(-0.232643\pi\)
−0.667516 + 0.744595i \(0.732643\pi\)
\(24\) −14.0738 15.5862i −0.586407 0.649424i
\(25\) 11.0845 22.4083i 0.443381 0.896333i
\(26\) 20.6909 0.795802
\(27\) −26.6852 4.11073i −0.988342 0.152249i
\(28\) −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 \(-0.910268\pi\)
0.960529 0.278181i \(-0.0897315\pi\)
\(32\) −23.3345 + 23.3345i −0.729204 + 0.729204i
\(33\) −2.12408 + 41.6551i −0.0643660 + 1.26228i
\(34\) 6.87923 0.202330
\(35\) 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 0.613683 0.789552i \(-0.289687\pi\)
−0.789552 + 0.613683i \(0.789687\pi\)
\(38\) −15.3806 + 15.3806i −0.404753 + 0.404753i
\(39\) −41.5998 46.0702i −1.06666 1.18129i
\(40\) 34.0808 + 7.96843i 0.852021 + 0.199211i
\(41\) 26.7192 0.651687 0.325844 0.945424i \(-0.394352\pi\)
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 −0.207248 0.978289i \(-0.566451\pi\)
0.978289 + 0.207248i \(0.0664506\pi\)
\(44\) 41.7092 0.947936
\(45\) 40.4451 19.7280i 0.898779 0.438401i
\(46\) 2.50714 0.0545031
\(47\) −18.5656 18.5656i −0.395012 0.395012i 0.481457 0.876470i \(-0.340108\pi\)
−0.876470 + 0.481457i \(0.840108\pi\)
\(48\) 14.9805 + 0.763888i 0.312095 + 0.0159143i
\(49\) −11.4326 + 47.6476i −0.233319 + 0.972400i
\(50\) −8.00714 23.6830i −0.160143 0.473661i
\(51\) −13.8310 15.3173i −0.271195 0.300339i
\(52\) −43.8920 + 43.8920i −0.844076 + 0.844076i
\(53\) −48.3021 48.3021i −0.911361 0.911361i 0.0850185 0.996379i \(-0.472905\pi\)
−0.996379 + 0.0850185i \(0.972905\pi\)
\(54\) −21.7760 + 15.9626i −0.403260 + 0.295603i
\(55\) −36.6728 59.0549i −0.666779 1.07373i
\(56\) −5.75616 + 48.6607i −0.102789 + 0.868942i
\(57\) 65.1697 + 3.32314i 1.14333 + 0.0583006i
\(58\) −19.8310 + 19.8310i −0.341913 + 0.341913i
\(59\) 29.6668i 0.502826i −0.967880 0.251413i \(-0.919105\pi\)
0.967880 0.251413i \(-0.0808953\pi\)
\(60\) −21.7621 39.3879i −0.362702 0.656465i
\(61\) 21.0717i 0.345438i −0.984971 0.172719i \(-0.944745\pi\)
0.984971 0.172719i \(-0.0552552\pi\)
\(62\) −12.1956 12.1956i −0.196704 0.196704i
\(63\) 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 0.421892 0.906646i \(-0.361366\pi\)
−0.906646 + 0.421892i \(0.861366\pi\)
\(68\) −14.5931 + 14.5931i −0.214604 + 0.214604i
\(69\) −5.04071 5.58240i −0.0730537 0.0809044i
\(70\) 31.6965 14.8436i 0.452807 0.212051i
\(71\) 16.0345i 0.225838i −0.993604 0.112919i \(-0.963980\pi\)
0.993604 0.112919i \(-0.0360200\pi\)
\(72\) 39.7853 + 48.8480i 0.552573 + 0.678445i
\(73\) 57.3597 + 57.3597i 0.785749 + 0.785749i 0.980794 0.195045i \(-0.0624853\pi\)
−0.195045 + 0.980794i \(0.562485\pi\)
\(74\) −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 \(0.159277\pi\)
−0.877399 + 0.479762i \(0.840723\pi\)
\(80\) −21.2381 + 13.1888i −0.265476 + 0.164860i
\(81\) 79.3238 + 16.3931i 0.979306 + 0.202384i
\(82\) 18.8933 18.8933i 0.230406 0.230406i
\(83\) −51.9675 + 51.9675i −0.626114 + 0.626114i −0.947088 0.320974i \(-0.895990\pi\)
0.320974 + 0.947088i \(0.395990\pi\)
\(84\) 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 \(-0.565065\pi\)
0.202987 0.979181i \(-0.434935\pi\)
\(90\) 14.6492 42.5488i 0.162768 0.472765i
\(91\) −17.0143 + 143.833i −0.186970 + 1.58058i
\(92\) −5.31846 + 5.31846i −0.0578093 + 0.0578093i
\(93\) −2.63499 + 51.6745i −0.0283332 + 0.555640i
\(94\) −26.2557 −0.279316
\(95\) −92.3919 + 57.3750i −0.972547 + 0.603947i
\(96\) 73.4777 66.3477i 0.765393 0.691122i
\(97\) −16.6658 + 16.6658i −0.171812 + 0.171812i −0.787775 0.615963i \(-0.788767\pi\)
0.615963 + 0.787775i \(0.288767\pi\)
\(98\) 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 0.624173 0.781286i \(-0.285436\pi\)
−0.781286 + 0.624173i \(0.785436\pi\)
\(104\) 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 −0.370218 + 0.928945i \(0.620717\pi\)
−0.928945 + 0.370218i \(0.879283\pi\)
\(108\) 12.3322 80.0557i 0.114187 0.741257i
\(109\) 3.01429i 0.0276540i 0.999904 + 0.0138270i \(0.00440141\pi\)
−0.999904 + 0.0138270i \(0.995599\pi\)
\(110\) −67.6897 15.8265i −0.615361 0.143877i
\(111\) 18.5020 + 20.4902i 0.166684 + 0.184597i
\(112\) −21.6701 27.4847i −0.193483 0.245399i
\(113\) 80.1118 + 80.1118i 0.708954 + 0.708954i 0.966315 0.257361i \(-0.0828530\pi\)
−0.257361 + 0.966315i \(0.582853\pi\)
\(114\) 48.4318 43.7321i 0.424840 0.383615i
\(115\) 12.2065 + 2.85400i 0.106144 + 0.0248174i
\(116\) 84.1356i 0.725307i
\(117\) 117.599 + 144.387i 1.00512 + 1.23408i
\(118\) −20.9776 20.9776i −0.177776 0.177776i
\(119\) −5.65685 + 47.8212i −0.0475366 + 0.401859i
\(120\) −100.892 29.0811i −0.840771 0.242342i
\(121\) −72.2952 −0.597481
\(122\) −14.8999 14.8999i −0.122131 0.122131i
\(123\) −80.0535 4.08209i −0.650842 0.0331877i
\(124\) 51.7417 0.417272
\(125\) −12.0248 124.420i −0.0961984 0.995362i
\(126\) 61.4865 + 13.7264i 0.487988 + 0.108939i
\(127\) −71.6476 71.6476i −0.564154 0.564154i 0.366330 0.930485i \(-0.380614\pi\)
−0.930485 + 0.366330i \(0.880614\pi\)
\(128\) −84.1457 84.1457i −0.657388 0.657388i
\(129\) −104.401 + 94.2699i −0.809306 + 0.730775i
\(130\) 87.8869 54.5774i 0.676053 0.419826i
\(131\) −79.4683 −0.606629 −0.303314 0.952891i \(-0.598093\pi\)
−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 −0.679471 0.733702i \(-0.737791\pi\)
0.733702 + 0.679471i \(0.237791\pi\)
\(138\) −7.51167 0.383035i −0.0544324 0.00277562i
\(139\) 179.589 1.29201 0.646003 0.763335i \(-0.276439\pi\)
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 −0.272042 0.962285i \(-0.587699\pi\)
0.962285 + 0.272042i \(0.0876988\pi\)
\(158\) 53.6004 + 53.6004i 0.339243 + 0.339243i
\(159\) 137.339 + 152.098i 0.863766 + 0.956590i
\(160\) −37.5655 + 160.667i −0.234784 + 1.00417i
\(161\) −2.06165 + 17.4285i −0.0128053 + 0.108252i
\(162\) 67.6821 44.4987i 0.417791 0.274684i
\(163\) 38.8452 38.8452i 0.238314 0.238314i −0.577837 0.816152i \(-0.696103\pi\)
0.816152 + 0.577837i \(0.196103\pi\)
\(164\) 80.1575i 0.488765i
\(165\) 100.854 + 182.538i 0.611233 + 1.10629i
\(166\) 73.4931i 0.442730i
\(167\) 138.252 + 138.252i 0.827855 + 0.827855i 0.987220 0.159365i \(-0.0509447\pi\)
−0.159365 + 0.987220i \(0.550945\pi\)
\(168\) 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 −0.780711 0.624893i \(-0.785143\pi\)
0.624893 + 0.780711i \(0.285143\pi\)
\(174\) 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 \(-0.834773\pi\)
0.868277 0.496079i \(-0.165227\pi\)
\(182\) 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 \(0.0904236\pi\)
−0.959922 + 0.280269i \(0.909576\pi\)
\(192\) 1.98611 38.9494i 0.0103443 0.202861i
\(193\) −81.6333 + 81.6333i −0.422971 + 0.422971i −0.886225 0.463255i \(-0.846682\pi\)
0.463255 + 0.886225i \(0.346682\pi\)
\(194\) 23.5689i 0.121489i
\(195\) −298.222 85.9589i −1.52934 0.440815i
\(196\) −142.943 34.2979i −0.729300 0.174989i
\(197\) 165.702 165.702i 0.841127 0.841127i −0.147878 0.989006i \(-0.547244\pi\)
0.989006 + 0.147878i \(0.0472444\pi\)
\(198\) −79.0196 97.0196i −0.399089 0.489998i
\(199\) −220.037 −1.10571 −0.552857 0.833276i \(-0.686462\pi\)
−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 0.979517 0.201362i \(-0.0645368\pi\)
−0.201362 + 0.979517i \(0.564537\pi\)
\(224\) −229.401 27.1362i −1.02411 0.121144i
\(225\) 119.758 190.481i 0.532256 0.846584i
\(226\) 113.295 0.501306
\(227\) 191.389 + 191.389i 0.843123 + 0.843123i 0.989264 0.146140i \(-0.0466851\pi\)
−0.146140 + 0.989264i \(0.546685\pi\)
\(228\) −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 0.487385 0.873187i \(-0.337951\pi\)
−0.873187 + 0.487385i \(0.837951\pi\)
\(234\) 185.252 + 18.9420i 0.791675 + 0.0809487i
\(235\) −127.831 29.8881i −0.543961 0.127183i
\(236\) 89.0003 0.377120
\(237\) 11.5809 227.112i 0.0488646 0.958279i
\(238\) 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 \(0.339021\pi\)
−0.484445 + 0.874822i \(0.660979\pi\)
\(242\) −51.1204 + 51.1204i −0.211242 + 0.211242i
\(243\) −235.158 61.2344i −0.967729 0.251993i
\(244\) 63.2151 0.259078
\(245\) 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 0.146530 0.989206i \(-0.453190\pi\)
−0.989206 + 0.146530i \(0.953190\pi\)
\(258\) −7.16342 + 140.481i −0.0277652 + 0.544501i
\(259\) 7.56729 63.9714i 0.0292173 0.246994i
\(260\) −70.6602 + 302.212i −0.271770 + 1.16236i
\(261\) −251.098 25.6747i −0.962060 0.0983705i
\(262\) −56.1926 + 56.1926i −0.214476 + 0.214476i
\(263\) 196.555 + 196.555i 0.747359 + 0.747359i 0.973982 0.226623i \(-0.0727686\pi\)
−0.226623 + 0.973982i \(0.572769\pi\)
\(264\) −216.696 + 195.668i −0.820817 + 0.741168i
\(265\) −332.578 77.7599i −1.25501 0.293434i
\(266\) −151.206 17.8864i −0.568444 0.0672422i
\(267\) −26.6283 + 522.204i −0.0997313 + 1.95582i
\(268\) 97.4357 97.4357i 0.363566 0.363566i
\(269\) 349.961i 1.30097i −0.759519 0.650485i \(-0.774566\pi\)
0.759519 0.650485i \(-0.225434\pi\)
\(270\) −50.3909 + 125.243i −0.186633 + 0.463862i
\(271\) 137.978i 0.509143i −0.967054 0.254572i \(-0.918066\pi\)
0.967054 0.254572i \(-0.0819344\pi\)
\(272\) −24.3218 24.3218i −0.0894182 0.0894182i
\(273\) 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 0.904966 0.425484i \(-0.139896\pi\)
−0.425484 + 0.904966i \(0.639896\pi\)
\(278\) 126.989 126.989i 0.456793 0.456793i
\(279\) 15.7894 154.420i 0.0565929 0.553476i
\(280\) 103.905 + 221.876i 0.371089 + 0.792413i
\(281\) 142.098i 0.505687i −0.967507 0.252844i \(-0.918634\pi\)
0.967507 0.252844i \(-0.0813658\pi\)
\(282\) 78.6649 + 4.01128i 0.278954 + 0.0142244i
\(283\) −120.235 120.235i −0.424858 0.424858i 0.462014 0.886873i \(-0.347127\pi\)
−0.886873 + 0.462014i \(0.847127\pi\)
\(284\) 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 −0.354747 + 0.934962i \(0.615433\pi\)
−0.934962 + 0.354747i \(0.884567\pi\)
\(294\) −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 −0.844264 0.535928i \(-0.819962\pi\)
0.535928 + 0.844264i \(0.319962\pi\)
\(308\) 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 0.968989 0.247104i \(-0.0794790\pi\)
−0.247104 + 0.968989i \(0.579479\pi\)
\(314\) 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 −0.842403 0.538848i \(-0.818860\pi\)
0.538848 + 0.842403i \(0.318860\pi\)
\(318\) 204.663 + 10.4362i 0.643593 + 0.0328181i
\(319\) 389.914i 1.22230i
\(320\) 34.2908 + 55.2190i 0.107159 + 0.172559i
\(321\) 437.728 395.253i 1.36364 1.23132i
\(322\) 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 0.850739 0.525588i \(-0.176155\pi\)
−0.525588 + 0.850739i \(0.676155\pi\)
\(338\) 183.220 + 183.220i 0.542070 + 0.542070i
\(339\) −227.784 252.263i −0.671930 0.744138i
\(340\) −23.4929 + 100.479i −0.0690966 + 0.295525i
\(341\) −239.789 −0.703194
\(342\) −151.788 + 123.627i −0.443825 + 0.361482i
\(343\) −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 −0.204752 0.978814i \(-0.565639\pi\)
0.978814 + 0.204752i \(0.0656387\pi\)
\(348\) −12.8540 + 252.079i −0.0369369 + 0.724366i
\(349\) −304.193 −0.871613 −0.435807 0.900040i \(-0.643537\pi\)
−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 \(-0.909828\pi\)
0.279509 + 0.960143i \(0.409828\pi\)
\(354\) 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 −0.555904 0.831247i \(-0.687628\pi\)
0.831247 + 0.555904i \(0.187628\pi\)
\(368\) −8.86409 8.86409i −0.0240872 0.0240872i
\(369\) 239.225 + 24.4608i 0.648307 + 0.0662893i
\(370\) −39.0887 + 24.2739i −0.105645 + 0.0656051i
\(371\) 56.1715 474.856i 0.151406 1.27993i
\(372\) −155.024 7.90497i −0.416730 0.0212499i
\(373\) −369.464 + 369.464i −0.990521 + 0.990521i −0.999955 0.00943464i \(-0.996997\pi\)
0.00943464 + 0.999955i \(0.496997\pi\)
\(374\) 95.6424i 0.255728i
\(375\) 17.0190 + 374.614i 0.0453839 + 0.998970i
\(376\) 183.790i 0.488803i
\(377\) −410.320 410.320i −1.08838 1.08838i
\(378\) −182.123 50.5194i −0.481807 0.133649i
\(379\) 261.209i 0.689207i −0.938748 0.344604i \(-0.888013\pi\)
0.938748 0.344604i \(-0.111987\pi\)
\(380\) −172.125 277.176i −0.452960 0.729410i
\(381\) 203.718 + 225.610i 0.534692 + 0.592152i
\(382\) 75.7048 + 75.7048i 0.198180 + 0.198180i
\(383\) −163.813 + 163.813i −0.427710 + 0.427710i −0.887847 0.460138i \(-0.847800\pi\)
0.460138 + 0.887847i \(0.347800\pi\)
\(384\) 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 −0.977391 0.211440i \(-0.932185\pi\)
0.211440 + 0.977391i \(0.432185\pi\)
\(398\) −155.590 + 155.590i −0.390929 + 0.390929i
\(399\) 264.180 + 372.636i 0.662104 + 0.933926i
\(400\) −55.4226 + 112.042i −0.138557 + 0.280104i
\(401\) 582.912i 1.45365i 0.686825 + 0.726823i \(0.259004\pi\)
−0.686825 + 0.726823i \(0.740996\pi\)
\(402\) 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 \(0.134616\pi\)
−0.911899 + 0.410414i \(0.865384\pi\)
\(420\) 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 \(0.171836\pi\)
−0.857791 + 0.513998i \(0.828164\pi\)
\(432\) 133.426 + 20.5537i 0.308857 + 0.0475779i
\(433\) 487.352 + 487.352i 1.12553 + 1.12553i 0.990896 + 0.134629i \(0.0429843\pi\)
0.134629 + 0.990896i \(0.457016\pi\)
\(434\) 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 0.886716 0.462315i \(-0.152981\pi\)
−0.462315 + 0.886716i \(0.652981\pi\)
\(444\) −61.4707 + 55.5059i −0.138448 + 0.125013i
\(445\) −459.745 740.336i −1.03314 1.66368i
\(446\) 245.406 0.550239
\(447\) −74.1196 3.77951i −0.165816 0.00845528i
\(448\) −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 0.630927 0.775842i \(-0.282675\pi\)
−0.775842 + 0.630927i \(0.782675\pi\)
\(458\) 87.3209 87.3209i 0.190657 0.190657i
\(459\) −109.810 149.802i −0.239238 0.326367i
\(460\) −8.56200 + 36.6195i −0.0186130 + 0.0796077i
\(461\) −191.545 −0.415499 −0.207750 0.978182i \(-0.566614\pi\)
−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 −0.659161 0.752002i \(-0.729088\pi\)
0.752002 + 0.659161i \(0.229088\pi\)
\(464\) 140.226 0.302211
\(465\) 125.112 + 226.444i 0.269058 + 0.486977i
\(466\) −127.126 −0.272803
\(467\) 252.836 + 252.836i 0.541405 + 0.541405i 0.923941 0.382536i \(-0.124949\pi\)
−0.382536 + 0.923941i \(0.624949\pi\)
\(468\) −433.161 + 352.797i −0.925557 + 0.753839i
\(469\) 37.7700 319.295i 0.0805331 0.680800i
\(470\) −111.524 + 69.2561i −0.237286 + 0.147353i
\(471\) −341.239 + 308.127i −0.724500 + 0.654197i
\(472\) 146.843 146.843i 0.311108 0.311108i
\(473\) −460.953 460.953i −0.974530 0.974530i
\(474\) −152.404 168.781i −0.321526 0.356079i
\(475\) −241.105 + 487.414i −0.507589 + 1.02613i
\(476\) −143.464 16.9706i −0.301394 0.0356524i
\(477\) −388.245 476.684i −0.813930 0.999337i
\(478\) −34.8452 + 34.8452i −0.0728980 + 0.0728980i
\(479\) 91.5191i 0.191063i 0.995426 + 0.0955314i \(0.0304550\pi\)
−0.995426 + 0.0955314i \(0.969545\pi\)
\(480\) 137.096 475.636i 0.285618 0.990908i
\(481\) 190.408i 0.395858i
\(482\) 298.161 + 298.161i 0.618592 + 0.618592i
\(483\) 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 0.917230 0.398358i \(-0.130420\pi\)
−0.398358 + 0.917230i \(0.630420\pi\)
\(488\) 104.300 104.300i 0.213729 0.213729i
\(489\) −122.319 + 110.450i −0.250141 + 0.225869i
\(490\) 218.967 + 109.901i 0.446872 + 0.224289i
\(491\) 518.117i 1.05523i −0.849484 0.527614i \(-0.823087\pi\)
0.849484 0.527614i \(-0.176913\pi\)
\(492\) 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 \(0.0698561\pi\)
−0.976015 + 0.217702i \(0.930144\pi\)
\(500\) 373.261 36.0744i 0.746522 0.0721488i
\(501\) −393.095 435.339i −0.784621 0.868940i
\(502\) 244.315 244.315i 0.486684 0.486684i
\(503\) −12.7399 + 12.7399i −0.0253279 + 0.0253279i −0.719657 0.694329i \(-0.755701\pi\)
0.694329 + 0.719657i \(0.255701\pi\)
\(504\) −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 \(0.205143\pi\)
−0.799415 + 0.600779i \(0.794857\pi\)
\(510\) −90.3195 + 49.9023i −0.177097 + 0.0978476i
\(511\) −66.7048 + 563.900i −0.130538 + 1.10352i
\(512\) 215.668 215.668i 0.421226 0.421226i
\(513\) 580.443 + 89.4144i 1.13147 + 0.174297i
\(514\) −306.273 −0.595862
\(515\) −111.423 26.0518i −0.216356 0.0505860i
\(516\) −282.810 313.202i −0.548081 0.606980i
\(517\) −258.119 + 258.119i −0.499262 + 0.499262i
\(518\) −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 −0.992258 0.124191i \(-0.960366\pi\)
−0.124191 0.992258i \(-0.539634\pi\)
\(524\) 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 0.881495 0.472193i \(-0.156538\pi\)
−0.472193 + 0.881495i \(0.656538\pi\)
\(548\) 22.2890 + 22.2890i 0.0406734 + 0.0406734i
\(549\) 19.2906 188.662i 0.0351378 0.343646i
\(550\) −329.267 + 111.324i −0.598667 + 0.202407i
\(551\) 610.024 1.10712
\(552\) 2.68125 52.5817i 0.00485733 0.0952567i
\(553\) −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 −0.892479 0.451089i \(-0.851036\pi\)
0.451089 + 0.892479i \(0.351036\pi\)
\(558\) −98.0265 120.356i −0.175675 0.215692i
\(559\) 970.151 1.73551
\(560\) −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 \(-0.579473\pi\)
0.968993 + 0.247086i \(0.0794732\pi\)
\(564\) −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 −0.451366 0.892339i \(-0.649063\pi\)
0.892339 + 0.451366i \(0.149063\pi\)
\(578\) −170.891 170.891i −0.295659 0.295659i
\(579\) 257.054 232.110i 0.443962 0.400882i
\(580\) −221.929 357.376i −0.382636 0.616165i
\(581\) −510.890 60.4341i −0.879329 0.104017i
\(582\) 3.60081 70.6151i 0.00618695 0.121332i
\(583\) −671.548 + 671.548i −1.15188 + 1.15188i
\(584\) 567.832i 0.972315i
\(585\) 880.372 + 303.104i 1.50491 + 0.518126i
\(586\) 534.410i 0.911962i
\(587\) −195.495 195.495i −0.333040 0.333040i 0.520700 0.853740i \(-0.325671\pi\)
−0.853740 + 0.520700i \(0.825671\pi\)
\(588\) 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 −0.843648 0.536897i \(-0.819597\pi\)
0.536897 + 0.843648i \(0.319597\pi\)
\(594\) 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 \(-0.616143\pi\)
0.356832 0.934169i \(-0.383857\pi\)
\(602\) 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 −0.593879 0.804554i \(-0.702404\pi\)
0.804554 + 0.593879i \(0.202404\pi\)
\(608\) 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 0.0956388 0.995416i \(-0.469511\pi\)
0.995416 0.0956388i \(-0.0304894\pi\)
\(614\) 133.868i 0.218026i
\(615\) −350.804 + 193.822i −0.570414 + 0.315158i
\(616\) 676.533 + 80.0283i 1.09827 + 0.129916i
\(617\) −416.614 + 416.614i −0.675225 + 0.675225i −0.958916 0.283691i \(-0.908441\pi\)
0.283691 + 0.958916i \(0.408441\pi\)
\(618\) 68.5679 + 3.49641i 0.110951 + 0.00565763i
\(619\) 1140.08 1.84180 0.920902 0.389794i \(-0.127454\pi\)
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 \(-0.953370\pi\)
0.989289 0.145970i \(-0.0466304\pi\)
\(642\) 30.0346 589.006i 0.0467829 0.917455i
\(643\) −767.988 767.988i −1.19438 1.19438i −0.975824 0.218559i \(-0.929864\pi\)
−0.218559 0.975824i \(-0.570136\pi\)
\(644\) −52.2855 6.18494i −0.0811886 0.00960395i
\(645\) −194.793 + 675.805i −0.302004 + 1.04776i
\(646\) −149.633 −0.231631
\(647\) 573.588 + 573.588i 0.886535 + 0.886535i 0.994188 0.107654i \(-0.0343337\pi\)
−0.107654 + 0.994188i \(0.534334\pi\)
\(648\) 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 0.589616 0.807683i \(-0.299279\pi\)
−0.807683 + 0.589616i \(0.799279\pi\)
\(654\) −6.06034 6.71161i −0.00926658 0.0102624i
\(655\) −337.551 + 209.618i −0.515345 + 0.320027i
\(656\) −133.596 −0.203652
\(657\) 461.048 + 566.071i 0.701747 + 0.861600i
\(658\) −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 \(-0.977146\pi\)
0.997424 0.0717364i \(-0.0228540\pi\)
\(662\) 123.754 123.754i 0.186939 0.186939i
\(663\) 21.7459 426.458i 0.0327993 0.643224i
\(664\) −514.452 −0.774777
\(665\) −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 −0.954915 0.296880i \(-0.904054\pi\)
0.296880 + 0.954915i \(0.404054\pi\)
\(674\) 154.964 0.229917
\(675\) −387.908 + 552.406i −0.574678 + 0.818379i
\(676\) −777.336 −1.14990
\(677\) 447.410 + 447.410i 0.660872 + 0.660872i 0.955586 0.294714i \(-0.0952243\pi\)
−0.294714 + 0.955586i \(0.595224\pi\)
\(678\) −339.445 17.3090i −0.500656 0.0255295i
\(679\) −163.840 19.3810i −0.241296 0.0285434i
\(680\) 127.020 + 204.542i 0.186794 + 0.300798i
\(681\) −544.182 602.662i −0.799093 0.884966i
\(682\) −169.557 + 169.557i −0.248617 + 0.248617i
\(683\) −199.643 199.643i −0.292303 0.292303i 0.545686 0.837990i \(-0.316269\pi\)
−0.837990 + 0.545686i \(0.816269\pi\)
\(684\) 59.7388 584.243i 0.0873375 0.854157i
\(685\) 11.9608 51.1561i 0.0174610 0.0746804i
\(686\) −118.655 + 321.823i −0.172967 + 0.469129i
\(687\) −369.991 18.8666i −0.538560 0.0274622i
\(688\) −165.774 + 165.774i −0.240950 + 0.240950i
\(689\) 1413.38i 2.05135i
\(690\) −32.9171 + 18.1869i −0.0477059 + 0.0263579i
\(691\) 207.196i 0.299849i 0.988697 + 0.149925i \(0.0479031\pi\)
−0.988697 + 0.149925i \(0.952097\pi\)
\(692\) −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 \(0.00184470\pi\)
−0.999983 + 0.00579527i \(0.998155\pi\)
\(702\) −552.141 85.0546i −0.786525 0.121160i
\(703\) 141.540 + 141.540i 0.201337 + 0.201337i
\(704\) 180.740 0.256733
\(705\) 378.429 + 109.078i 0.536779 + 0.154720i
\(706\) 339.785i 0.481281i
\(707\) −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 \(-0.794222\pi\)
0.798214 0.602374i \(-0.205778\pi\)
\(710\) −78.0670 18.2528i −0.109954 0.0257082i
\(711\) −69.3953 + 678.683i −0.0976023 + 0.954547i
\(712\) 862.713 862.713i 1.21168 1.21168i
\(713\) 30.5762 30.5762i 0.0428839 0.0428839i
\(714\) −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 \(0.329336\pi\)
−0.510837 + 0.859678i \(0.670664\pi\)
\(720\) −202.225 + 98.6402i −0.280869 + 0.137000i
\(721\) 18.8191 159.090i 0.0261014 0.220652i
\(722\) 79.2852 79.2852i 0.109813 0.109813i
\(723\) 64.4208 1263.35i 0.0891021 1.74737i
\(724\) 538.742 0.744118
\(725\) −310.868 + 628.446i −0.428783 + 0.866822i
\(726\) 160.972 145.352i 0.221725 0.200210i
\(727\) 635.035 635.035i 0.873501 0.873501i −0.119351 0.992852i \(-0.538081\pi\)
0.992852 + 0.119351i \(0.0380815\pi\)
\(728\) −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 0.816246 0.577704i \(-0.196051\pi\)
−0.577704 + 0.816246i \(0.696051\pi\)
\(734\) 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 \(0.436819\pi\)
−0.197187 + 0.980366i \(0.563181\pi\)
\(740\) 31.4269 134.412i 0.0424688 0.181638i
\(741\) 904.856 + 1002.10i 1.22113 + 1.35236i
\(742\) −296.055 375.493i −0.398995 0.506055i
\(743\) −30.8955 30.8955i −0.0415822 0.0415822i 0.686010 0.727592i \(-0.259361\pi\)
−0.727592 + 0.686010i \(0.759361\pi\)
\(744\) −268.818 + 242.733i −0.361315 + 0.326254i
\(745\) 105.080 65.2544i 0.141047 0.0875898i
\(746\) 522.501i 0.700404i
\(747\) −512.856 + 417.706i −0.686555 + 0.559179i
\(748\) 202.888 + 202.888i 0.271241 + 0.271241i
\(749\) −1366.61 161.658i −1.82457 0.215832i
\(750\) 276.926 + 252.858i 0.369235 + 0.337143i
\(751\) 1095.21 1.45833 0.729167 0.684335i \(-0.239908\pi\)
0.729167 + 0.684335i \(0.239908\pi\)
\(752\) 92.8279 + 92.8279i 0.123441 + 0.123441i
\(753\) −1035.20 52.7867i −1.37476 0.0701019i
\(754\) −580.279 −0.769601
\(755\) −693.737 + 430.808i −0.918857 + 0.570606i
\(756\) 493.509 279.173i 0.652790 0.369277i
\(757\) 209.069 + 209.069i 0.276181 + 0.276181i 0.831582 0.555401i \(-0.187435\pi\)
−0.555401 + 0.831582i \(0.687435\pi\)
\(758\) −184.703 184.703i −0.243672 0.243672i
\(759\) −77.6125 + 70.0813i −0.102256 + 0.0923337i
\(760\) −741.308 173.325i −0.975406 0.228059i
\(761\) −710.902 −0.934168 −0.467084 0.884213i \(-0.654695\pi\)
−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