Properties

Label 105.3.k.c.62.3
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 62.3
Root \(0.611750 - 0.253395i\) of \(x^{16} + 433 x^{8} + 16\)
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.c.83.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.152778 + 2.99611i) q^{3} +3.00000i q^{4} +(4.24762 - 2.63775i) q^{5} +(-2.22660 - 2.01054i) q^{6} +(5.49694 + 4.33402i) q^{7} +(-4.94975 - 4.94975i) q^{8} +(-8.95332 + 0.915476i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.152778 + 2.99611i) q^{3} +3.00000i q^{4} +(4.24762 - 2.63775i) q^{5} +(-2.22660 - 2.01054i) q^{6} +(5.49694 + 4.33402i) q^{7} +(-4.94975 - 4.94975i) q^{8} +(-8.95332 + 0.915476i) q^{9} +(-1.13835 + 4.86869i) q^{10} +13.9031i q^{11} +(-8.98832 + 0.458333i) q^{12} +(-14.6307 - 14.6307i) q^{13} +(-6.95153 + 0.822309i) q^{14} +(8.55193 + 12.3233i) q^{15} -5.00000 q^{16} +(4.86435 + 4.86435i) q^{17} +(5.68361 - 6.97829i) q^{18} +21.7515 q^{19} +(7.91326 + 12.7429i) q^{20} +(-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} +(-4.11073 - 26.6852i) q^{27} +(-13.0020 + 16.4908i) q^{28} +28.0452 q^{29} +(-14.7610 - 2.66678i) q^{30} +17.2472i q^{31} +(23.3345 - 23.3345i) q^{32} +(-41.6551 + 2.12408i) q^{33} -6.87923 q^{34} +(34.7809 + 3.90969i) q^{35} +(-2.74643 - 26.8600i) q^{36} +(-6.50714 - 6.50714i) q^{37} +(-15.3806 + 15.3806i) q^{38} +(41.5998 - 46.0702i) q^{39} +(-34.0808 - 7.96843i) q^{40} +26.7192 q^{41} +(-3.52576 - 20.7019i) q^{42} +(33.1548 - 33.1548i) q^{43} -41.7092 q^{44} +(-35.6155 + 27.5052i) q^{45} +2.50714 q^{46} +(-18.5656 - 18.5656i) q^{47} +(-0.763888 - 14.9805i) q^{48} +(11.4326 + 47.6476i) q^{49} +(8.00714 + 23.6830i) q^{50} +(-13.8310 + 15.3173i) q^{51} +(43.8920 - 43.8920i) q^{52} +(48.3021 + 48.3021i) q^{53} +(21.7760 + 15.9626i) q^{54} +(36.6728 + 59.0549i) q^{55} +(-5.75616 - 48.6607i) q^{56} +(3.32314 + 65.1697i) q^{57} +(-19.8310 + 19.8310i) q^{58} -29.6668i q^{59} +(-36.9700 + 25.6558i) q^{60} +21.0717i q^{61} +(-12.1956 - 12.1956i) q^{62} +(-53.1835 - 33.7715i) q^{63} +13.0000i q^{64} +(-100.737 - 23.5534i) q^{65} +(27.9526 - 30.9565i) q^{66} +(-32.4786 - 32.4786i) q^{67} +(-14.5931 + 14.5931i) q^{68} +(5.04071 - 5.58240i) q^{69} +(-27.3584 + 21.8293i) q^{70} +16.0345i q^{71} +(48.8480 + 39.7853i) q^{72} +(-57.3597 - 57.3597i) q^{73} +9.20249 q^{74} +(68.8312 + 29.7869i) q^{75} +65.2544i q^{76} +(-60.2561 + 76.4243i) q^{77} +(3.16110 + 61.9921i) q^{78} +75.8024i q^{79} +(-21.2381 + 13.1888i) q^{80} +(79.3238 - 16.3931i) q^{81} +(-18.8933 + 18.8933i) q^{82} +(-51.9675 + 51.9675i) q^{83} +(-51.3947 - 36.4361i) q^{84} +(33.4929 + 7.83095i) q^{85} +46.8879i q^{86} +(4.28468 + 84.0264i) q^{87} +(68.8167 - 68.8167i) q^{88} -174.294i q^{89} +(5.73481 - 44.6331i) q^{90} +(-17.0143 - 143.833i) q^{91} +(5.31846 - 5.31846i) q^{92} +(-51.6745 + 2.63499i) q^{93} +26.2557 q^{94} +(92.3919 - 57.3750i) q^{95} +(73.4777 + 66.3477i) q^{96} +(16.6658 - 16.6658i) q^{97} +(-41.7760 - 25.6079i) q^{98} +(-12.7279 - 124.479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 32q^{7} + O(q^{10}) \) \( 16q + 32q^{7} + 80q^{15} - 80q^{16} + 8q^{18} - 64q^{21} - 64q^{22} + 224q^{25} - 96q^{28} - 128q^{30} + 96q^{36} - 384q^{37} - 112q^{42} + 64q^{43} + 320q^{46} - 128q^{51} + 408q^{57} - 224q^{58} - 120q^{60} - 72q^{63} + 320q^{67} + 128q^{70} + 56q^{72} - 424q^{78} + 896q^{81} + 256q^{85} + 448q^{88} - 832q^{91} + 32q^{93} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.353553 + 0.353553i −0.861430 0.507877i \(-0.830431\pi\)
0.507877 + 0.861430i \(0.330431\pi\)
\(3\) 0.152778 + 2.99611i 0.0509259 + 0.998702i
\(4\) 3.00000i 0.750000i
\(5\) 4.24762 2.63775i 0.849524 0.527550i
\(6\) −2.22660 2.01054i −0.371100 0.335090i
\(7\) 5.49694 + 4.33402i 0.785277 + 0.619145i
\(8\) −4.94975 4.94975i −0.618718 0.618718i
\(9\) −8.95332 + 0.915476i −0.994813 + 0.101720i
\(10\) −1.13835 + 4.86869i −0.113835 + 0.486869i
\(11\) 13.9031i 1.26392i 0.775003 + 0.631958i \(0.217748\pi\)
−0.775003 + 0.631958i \(0.782252\pi\)
\(12\) −8.98832 + 0.458333i −0.749027 + 0.0381944i
\(13\) −14.6307 14.6307i −1.12543 1.12543i −0.990910 0.134524i \(-0.957049\pi\)
−0.134524 0.990910i \(-0.542951\pi\)
\(14\) −6.95153 + 0.822309i −0.496538 + 0.0587364i
\(15\) 8.55193 + 12.3233i 0.570129 + 0.821555i
\(16\) −5.00000 −0.312500
\(17\) 4.86435 + 4.86435i 0.286138 + 0.286138i 0.835551 0.549413i \(-0.185149\pi\)
−0.549413 + 0.835551i \(0.685149\pi\)
\(18\) 5.68361 6.97829i 0.315756 0.387683i
\(19\) 21.7515 1.14481 0.572407 0.819970i \(-0.306010\pi\)
0.572407 + 0.819970i \(0.306010\pi\)
\(20\) 7.91326 + 12.7429i 0.395663 + 0.637143i
\(21\) −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 \(-0.267357\pi\)
−0.744595 + 0.667516i \(0.767357\pi\)
\(24\) 14.0738 15.5862i 0.586407 0.649424i
\(25\) 11.0845 22.4083i 0.443381 0.896333i
\(26\) 20.6909 0.795802
\(27\) −4.11073 26.6852i −0.152249 0.988342i
\(28\) −13.0020 + 16.4908i −0.464359 + 0.588957i
\(29\) 28.0452 0.967076 0.483538 0.875323i \(-0.339352\pi\)
0.483538 + 0.875323i \(0.339352\pi\)
\(30\) −14.7610 2.66678i −0.492035 0.0888928i
\(31\) 17.2472i 0.556362i 0.960529 + 0.278181i \(0.0897315\pi\)
−0.960529 + 0.278181i \(0.910268\pi\)
\(32\) 23.3345 23.3345i 0.729204 0.729204i
\(33\) −41.6551 + 2.12408i −1.26228 + 0.0643660i
\(34\) −6.87923 −0.202330
\(35\) 34.7809 + 3.90969i 0.993741 + 0.111705i
\(36\) −2.74643 26.8600i −0.0762897 0.746110i
\(37\) −6.50714 6.50714i −0.175869 0.175869i 0.613683 0.789552i \(-0.289687\pi\)
−0.789552 + 0.613683i \(0.789687\pi\)
\(38\) −15.3806 + 15.3806i −0.404753 + 0.404753i
\(39\) 41.5998 46.0702i 1.06666 1.18129i
\(40\) −34.0808 7.96843i −0.852021 0.199211i
\(41\) 26.7192 0.651687 0.325844 0.945424i \(-0.394352\pi\)
0.325844 + 0.945424i \(0.394352\pi\)
\(42\) −3.52576 20.7019i −0.0839468 0.492903i
\(43\) 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
\(45\) −35.6155 + 27.5052i −0.791455 + 0.611227i
\(46\) 2.50714 0.0545031
\(47\) −18.5656 18.5656i −0.395012 0.395012i 0.481457 0.876470i \(-0.340108\pi\)
−0.876470 + 0.481457i \(0.840108\pi\)
\(48\) −0.763888 14.9805i −0.0159143 0.312095i
\(49\) 11.4326 + 47.6476i 0.233319 + 0.972400i
\(50\) 8.00714 + 23.6830i 0.160143 + 0.473661i
\(51\) −13.8310 + 15.3173i −0.271195 + 0.300339i
\(52\) 43.8920 43.8920i 0.844076 0.844076i
\(53\) 48.3021 + 48.3021i 0.911361 + 0.911361i 0.996379 0.0850185i \(-0.0270949\pi\)
−0.0850185 + 0.996379i \(0.527095\pi\)
\(54\) 21.7760 + 15.9626i 0.403260 + 0.295603i
\(55\) 36.6728 + 59.0549i 0.666779 + 1.07373i
\(56\) −5.75616 48.6607i −0.102789 0.868942i
\(57\) 3.32314 + 65.1697i 0.0583006 + 1.14333i
\(58\) −19.8310 + 19.8310i −0.341913 + 0.341913i
\(59\) 29.6668i 0.502826i −0.967880 0.251413i \(-0.919105\pi\)
0.967880 0.251413i \(-0.0808953\pi\)
\(60\) −36.9700 + 25.6558i −0.616167 + 0.427597i
\(61\) 21.0717i 0.345438i 0.984971 + 0.172719i \(0.0552552\pi\)
−0.984971 + 0.172719i \(0.944745\pi\)
\(62\) −12.1956 12.1956i −0.196704 0.196704i
\(63\) −53.1835 33.7715i −0.844183 0.536056i
\(64\) 13.0000i 0.203125i
\(65\) −100.737 23.5534i −1.54981 0.362360i
\(66\) 27.9526 30.9565i 0.423525 0.469038i
\(67\) −32.4786 32.4786i −0.484755 0.484755i 0.421892 0.906646i \(-0.361366\pi\)
−0.906646 + 0.421892i \(0.861366\pi\)
\(68\) −14.5931 + 14.5931i −0.214604 + 0.214604i
\(69\) 5.04071 5.58240i 0.0730537 0.0809044i
\(70\) −27.3584 + 21.8293i −0.390834 + 0.311847i
\(71\) 16.0345i 0.225838i 0.993604 + 0.112919i \(0.0360200\pi\)
−0.993604 + 0.112919i \(0.963980\pi\)
\(72\) 48.8480 + 39.7853i 0.678445 + 0.552573i
\(73\) −57.3597 57.3597i −0.785749 0.785749i 0.195045 0.980794i \(-0.437515\pi\)
−0.980794 + 0.195045i \(0.937515\pi\)
\(74\) 9.20249 0.124358
\(75\) 68.8312 + 29.7869i 0.917750 + 0.397159i
\(76\) 65.2544i 0.858610i
\(77\) −60.2561 + 76.4243i −0.782547 + 0.992523i
\(78\) 3.16110 + 61.9921i 0.0405269 + 0.794770i
\(79\) 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
\(87\) 4.28468 + 84.0264i 0.0492492 + 0.965821i
\(88\) 68.8167 68.8167i 0.782008 0.782008i
\(89\) 174.294i 1.95836i −0.202987 0.979181i \(-0.565065\pi\)
0.202987 0.979181i \(-0.434935\pi\)
\(90\) 5.73481 44.6331i 0.0637201 0.495923i
\(91\) −17.0143 143.833i −0.186970 1.58058i
\(92\) 5.31846 5.31846i 0.0578093 0.0578093i
\(93\) −51.6745 + 2.63499i −0.555640 + 0.0283332i
\(94\) 26.2557 0.279316
\(95\) 92.3919 57.3750i 0.972547 0.603947i
\(96\) 73.4777 + 66.3477i 0.765393 + 0.691122i
\(97\) 16.6658 16.6658i 0.171812 0.171812i −0.615963 0.787775i \(-0.711233\pi\)
0.787775 + 0.615963i \(0.211233\pi\)
\(98\) −41.7760 25.6079i −0.426286 0.261305i
\(99\) −12.7279 124.479i −0.128565 1.25736i
\(100\) 67.2250 + 33.2536i 0.672250 + 0.332536i
\(101\) −113.114 −1.11994 −0.559968 0.828514i \(-0.689187\pi\)
−0.559968 + 0.828514i \(0.689187\pi\)
\(102\) −1.05099 20.6109i −0.0103038 0.202068i
\(103\) 16.1826 + 16.1826i 0.157113 + 0.157113i 0.781286 0.624173i \(-0.214564\pi\)
−0.624173 + 0.781286i \(0.714564\pi\)
\(104\) 144.836i 1.39265i
\(105\) −6.40009 + 104.805i −0.0609533 + 0.998141i
\(106\) −68.3095 −0.644429
\(107\) 139.010 139.010i 1.29916 1.29916i 0.370218 0.928945i \(-0.379283\pi\)
0.928945 0.370218i \(-0.120717\pi\)
\(108\) 80.0557 12.3322i 0.741257 0.114187i
\(109\) 3.01429i 0.0276540i 0.999904 + 0.0138270i \(0.00440141\pi\)
−0.999904 + 0.0138270i \(0.995599\pi\)
\(110\) −67.6897 15.8265i −0.615361 0.143877i
\(111\) 18.5020 20.4902i 0.166684 0.184597i
\(112\) −27.4847 21.6701i −0.245399 0.193483i
\(113\) −80.1118 80.1118i −0.708954 0.708954i 0.257361 0.966315i \(-0.417147\pi\)
−0.966315 + 0.257361i \(0.917147\pi\)
\(114\) −48.4318 43.7321i −0.424840 0.383615i
\(115\) −12.2065 2.85400i −0.106144 0.0248174i
\(116\) 84.1356i 0.725307i
\(117\) 144.387 + 117.599i 1.23408 + 1.00512i
\(118\) 20.9776 + 20.9776i 0.177776 + 0.177776i
\(119\) 5.65685 + 47.8212i 0.0475366 + 0.401859i
\(120\) 18.6675 103.327i 0.155562 0.861061i
\(121\) −72.2952 −0.597481
\(122\) −14.8999 14.8999i −0.122131 0.122131i
\(123\) 4.08209 + 80.0535i 0.0331877 + 0.650842i
\(124\) −51.7417 −0.417272
\(125\) −12.0248 124.420i −0.0961984 0.995362i
\(126\) 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 \(0.598093\pi\)
\(132\) −6.37223 124.965i −0.0482745 0.946706i
\(133\) 119.566 + 94.2712i 0.898996 + 0.708806i
\(134\) 45.9316 0.342773
\(135\) −87.8499 102.506i −0.650740 0.759301i
\(136\) 48.1546i 0.354078i
\(137\) −7.42967 + 7.42967i −0.0542312 + 0.0542312i −0.733702 0.679471i \(-0.762209\pi\)
0.679471 + 0.733702i \(0.262209\pi\)
\(138\) 0.383035 + 7.51167i 0.00277562 + 0.0544324i
\(139\) −179.589 −1.29201 −0.646003 0.763335i \(-0.723561\pi\)
−0.646003 + 0.763335i \(0.723561\pi\)
\(140\) −11.7291 + 104.343i −0.0837790 + 0.745306i
\(141\) 52.7881 58.4609i 0.374384 0.414616i
\(142\) −11.3381 11.3381i −0.0798457 0.0798457i
\(143\) 203.411 203.411i 1.42245 1.42245i
\(144\) 44.7666 4.57738i 0.310879 0.0317874i
\(145\) 119.125 73.9763i 0.821554 0.510181i
\(146\) 81.1188 0.555609
\(147\) −141.011 + 41.5328i −0.959257 + 0.282536i
\(148\) 19.5214 19.5214i 0.131902 0.131902i
\(149\) −24.7386 −0.166031 −0.0830155 0.996548i \(-0.526455\pi\)
−0.0830155 + 0.996548i \(0.526455\pi\)
\(150\) −69.7336 + 27.6085i −0.464890 + 0.184057i
\(151\) −163.324 −1.08161 −0.540807 0.841147i \(-0.681881\pi\)
−0.540807 + 0.841147i \(0.681881\pi\)
\(152\) −107.664 107.664i −0.708317 0.708317i
\(153\) −48.0053 39.0989i −0.313760 0.255548i
\(154\) −11.4326 96.6476i −0.0742378 0.627582i
\(155\) 45.4939 + 73.2596i 0.293509 + 0.472643i
\(156\) 138.211 + 124.799i 0.885966 + 0.799995i
\(157\) −108.368 + 108.368i −0.690244 + 0.690244i −0.962285 0.272042i \(-0.912301\pi\)
0.272042 + 0.962285i \(0.412301\pi\)
\(158\) −53.6004 53.6004i −0.339243 0.339243i
\(159\) −137.339 + 152.098i −0.863766 + 0.956590i
\(160\) 37.5655 160.667i 0.234784 1.00417i
\(161\) −2.06165 17.4285i −0.0128053 0.108252i
\(162\) −44.4987 + 67.6821i −0.274684 + 0.417791i
\(163\) 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
\(165\) −171.332 + 118.898i −1.03838 + 0.720594i
\(166\) 73.4931i 0.442730i
\(167\) 138.252 + 138.252i 0.827855 + 0.827855i 0.987220 0.159365i \(-0.0509447\pi\)
−0.159365 + 0.987220i \(0.550945\pi\)
\(168\) 144.913 24.6804i 0.862579 0.146907i
\(169\) 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
\(175\) 158.049 75.1367i 0.903137 0.429352i
\(176\) 69.5153i 0.394973i
\(177\) 88.8848 4.53242i 0.502174 0.0256069i
\(178\) 123.245 + 123.245i 0.692386 + 0.692386i
\(179\) −187.393 −1.04689 −0.523445 0.852059i \(-0.675354\pi\)
−0.523445 + 0.852059i \(0.675354\pi\)
\(180\) −82.5157 106.846i −0.458420 0.593591i
\(181\) 179.581i 0.992158i 0.868277 + 0.496079i \(0.165227\pi\)
−0.868277 + 0.496079i \(0.834773\pi\)
\(182\) 113.736 + 89.6745i 0.624925 + 0.492717i
\(183\) −63.1331 + 3.21928i −0.344990 + 0.0175917i
\(184\) 17.5500i 0.0953805i
\(185\) −44.8041 10.4756i −0.242184 0.0566250i
\(186\) 34.6762 38.4026i 0.186431 0.206466i
\(187\) −67.6294 + 67.6294i −0.361654 + 0.361654i
\(188\) 55.6968 55.6968i 0.296259 0.296259i
\(189\) 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 \(-0.0904236\pi\)
\(192\) −38.9494 + 1.98611i −0.202861 + 0.0103443i
\(193\) −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
\(195\) 55.1781 305.419i 0.282964 1.56625i
\(196\) −142.943 + 34.2979i −0.729300 + 0.174989i
\(197\) −165.702 + 165.702i −0.841127 + 0.841127i −0.989006 0.147878i \(-0.952756\pi\)
0.147878 + 0.989006i \(0.452756\pi\)
\(198\) 97.0196 + 79.0196i 0.489998 + 0.399089i
\(199\) 220.037 1.10571 0.552857 0.833276i \(-0.313538\pi\)
0.552857 + 0.833276i \(0.313538\pi\)
\(200\) −165.781 + 56.0500i −0.828906 + 0.280250i
\(201\) 92.3473 102.271i 0.459439 0.508812i
\(202\) 79.9833 79.9833i 0.395957 0.395957i
\(203\) 154.163 + 121.548i 0.759422 + 0.598760i
\(204\) −45.9518 41.4929i −0.225254 0.203396i
\(205\) 113.493 70.4786i 0.553624 0.343798i
\(206\) −22.8856 −0.111095
\(207\) 17.4956 + 14.2496i 0.0845197 + 0.0688388i
\(208\) 73.1533 + 73.1533i 0.351698 + 0.351698i
\(209\) 302.412i 1.44695i
\(210\) −69.5826 78.6337i −0.331346 0.374446i
\(211\) 276.590 1.31086 0.655428 0.755258i \(-0.272488\pi\)
0.655428 + 0.755258i \(0.272488\pi\)
\(212\) −144.906 + 144.906i −0.683521 + 0.683521i
\(213\) −48.0411 + 2.44971i −0.225545 + 0.0115010i
\(214\) 196.590i 0.918647i
\(215\) 53.3747 228.283i 0.248255 1.06178i
\(216\) −111.738 + 152.432i −0.517306 + 0.705705i
\(217\) −74.7497 + 94.8069i −0.344469 + 0.436898i
\(218\) −2.13142 2.13142i −0.00977717 0.00977717i
\(219\) 163.092 180.619i 0.744715 0.824744i
\(220\) −177.165 + 110.019i −0.805294 + 0.500084i
\(221\) 142.337i 0.644060i
\(222\) 1.40593 + 27.5717i 0.00633304 + 0.124197i
\(223\) −173.529 173.529i −0.778155 0.778155i 0.201362 0.979517i \(-0.435463\pi\)
−0.979517 + 0.201362i \(0.935463\pi\)
\(224\) 229.401 27.1362i 1.02411 0.121144i
\(225\) −78.7290 + 210.777i −0.349907 + 0.936785i
\(226\) 113.295 0.501306
\(227\) 191.389 + 191.389i 0.843123 + 0.843123i 0.989264 0.146140i \(-0.0466851\pi\)
−0.146140 + 0.989264i \(0.546685\pi\)
\(228\) −195.509 + 9.96941i −0.857496 + 0.0437255i
\(229\) −123.490 −0.539259 −0.269630 0.962964i \(-0.586901\pi\)
−0.269630 + 0.962964i \(0.586901\pi\)
\(230\) 10.6494 6.61323i 0.0463017 0.0287532i
\(231\) −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 \(-0.162049\pi\)
−0.487385 + 0.873187i \(0.662049\pi\)
\(234\) −185.252 + 18.9420i −0.791675 + 0.0809487i
\(235\) −127.831 29.8881i −0.543961 0.127183i
\(236\) 89.0003 0.377120
\(237\) −227.112 + 11.5809i −0.958279 + 0.0488646i
\(238\) −37.8147 29.8147i −0.158885 0.125272i
\(239\) 49.2786 0.206187 0.103093 0.994672i \(-0.467126\pi\)
0.103093 + 0.994672i \(0.467126\pi\)
\(240\) −42.7597 61.6167i −0.178165 0.256736i
\(241\) 421.664i 1.74964i −0.484445 0.874822i \(-0.660979\pi\)
0.484445 0.874822i \(-0.339021\pi\)
\(242\) 51.1204 51.1204i 0.211242 0.211242i
\(243\) 61.2344 + 235.158i 0.251993 + 0.967729i
\(244\) −63.2151 −0.259078
\(245\) 174.244 + 172.232i 0.711200 + 0.702990i
\(246\) −59.4929 53.7199i −0.241841 0.218374i
\(247\) −318.238 318.238i −1.28841 1.28841i
\(248\) 85.3694 85.3694i 0.344231 0.344231i
\(249\) −163.640 147.761i −0.657187 0.593417i
\(250\) 96.4812 + 79.4756i 0.385925 + 0.317902i
\(251\) 345.514 1.37655 0.688274 0.725450i \(-0.258369\pi\)
0.688274 + 0.725450i \(0.258369\pi\)
\(252\) 101.315 159.551i 0.402042 0.633137i
\(253\) 24.6476 24.6476i 0.0974214 0.0974214i
\(254\) 101.325 0.398917
\(255\) −18.3454 + 101.545i −0.0719428 + 0.398214i
\(256\) −171.000 −0.667969
\(257\) −216.568 216.568i −0.842676 0.842676i 0.146530 0.989206i \(-0.453190\pi\)
−0.989206 + 0.146530i \(0.953190\pi\)
\(258\) −140.481 + 7.16342i −0.544501 + 0.0277652i
\(259\) −7.56729 63.9714i −0.0292173 0.246994i
\(260\) 70.6602 302.212i 0.271770 1.16236i
\(261\) −251.098 + 25.6747i −0.962060 + 0.0983705i
\(262\) 56.1926 56.1926i 0.214476 0.214476i
\(263\) −196.555 196.555i −0.747359 0.747359i 0.226623 0.973982i \(-0.427231\pi\)
−0.973982 + 0.226623i \(0.927231\pi\)
\(264\) 216.696 + 195.668i 0.820817 + 0.741168i
\(265\) 332.578 + 77.7599i 1.25501 + 0.293434i
\(266\) −151.206 + 17.8864i −0.568444 + 0.0672422i
\(267\) 522.204 26.6283i 1.95582 0.0997313i
\(268\) 97.4357 97.4357i 0.363566 0.363566i
\(269\) 349.961i 1.30097i −0.759519 0.650485i \(-0.774566\pi\)
0.759519 0.650485i \(-0.225434\pi\)
\(270\) 134.602 + 10.3632i 0.498525 + 0.0383822i
\(271\) 137.978i 0.509143i 0.967054 + 0.254572i \(0.0819344\pi\)
−0.967054 + 0.254572i \(0.918066\pi\)
\(272\) −24.3218 24.3218i −0.0894182 0.0894182i
\(273\) 428.340 72.9511i 1.56901 0.267220i
\(274\) 10.5071i 0.0383472i
\(275\) 311.545 + 154.109i 1.13289 + 0.560396i
\(276\) 16.7472 + 15.1221i 0.0606783 + 0.0547903i
\(277\) 132.817 + 132.817i 0.479483 + 0.479483i 0.904966 0.425484i \(-0.139896\pi\)
−0.425484 + 0.904966i \(0.639896\pi\)
\(278\) 126.989 126.989i 0.456793 0.456793i
\(279\) −15.7894 154.420i −0.0565929 0.553476i
\(280\) −152.805 191.509i −0.545732 0.683960i
\(281\) 142.098i 0.505687i 0.967507 + 0.252844i \(0.0813658\pi\)
−0.967507 + 0.252844i \(0.918634\pi\)
\(282\) 4.01128 + 78.6649i 0.0142244 + 0.278954i
\(283\) 120.235 + 120.235i 0.424858 + 0.424858i 0.886873 0.462014i \(-0.152873\pi\)
−0.462014 + 0.886873i \(0.652873\pi\)
\(284\) −48.1035 −0.169378
\(285\) 186.017 + 268.050i 0.652691 + 0.940528i
\(286\) 287.666i 1.00583i
\(287\) 146.874 + 115.801i 0.511755 + 0.403489i
\(288\) −187.559 + 230.284i −0.651247 + 0.799596i
\(289\) 241.676i 0.836250i
\(290\) −31.9252 + 136.543i −0.110087 + 0.470840i
\(291\) 52.4786 + 47.3863i 0.180339 + 0.162839i
\(292\) 172.079 172.079i 0.589312 0.589312i
\(293\) −377.885 + 377.885i −1.28971 + 1.28971i −0.354747 + 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
\(297\) 371.007 57.1518i 1.24918 0.192430i
\(298\) 17.4929 17.4929i 0.0587009 0.0587009i
\(299\) 51.8750i 0.173495i
\(300\) −89.3608 + 206.494i −0.297869 + 0.688312i
\(301\) 325.943 38.5564i 1.08287 0.128094i
\(302\) 115.487 115.487i 0.382409 0.382409i
\(303\) −17.2812 338.900i −0.0570337 1.11848i
\(304\) −108.757 −0.357754
\(305\) 55.5820 + 89.5046i 0.182236 + 0.293458i
\(306\) 61.5919 6.29777i 0.201281 0.0205809i
\(307\) 94.6590 94.6590i 0.308335 0.308335i −0.535928 0.844264i \(-0.680038\pi\)
0.844264 + 0.535928i \(0.180038\pi\)
\(308\) −229.273 180.768i −0.744392 0.586910i
\(309\) −46.0125 + 50.9571i −0.148908 + 0.164910i
\(310\) −83.9714 19.6333i −0.270876 0.0633333i
\(311\) −221.432 −0.712001 −0.356000 0.934486i \(-0.615860\pi\)
−0.356000 + 0.934486i \(0.615860\pi\)
\(312\) −433.944 + 22.1277i −1.39085 + 0.0709221i
\(313\) −225.950 225.950i −0.721885 0.721885i 0.247104 0.968989i \(-0.420521\pi\)
−0.968989 + 0.247104i \(0.920521\pi\)
\(314\) 153.256i 0.488076i
\(315\) −314.984 3.16355i −0.999950 0.0100430i
\(316\) −227.407 −0.719643
\(317\) 96.2271 96.2271i 0.303556 0.303556i −0.538848 0.842403i \(-0.681140\pi\)
0.842403 + 0.538848i \(0.181140\pi\)
\(318\) −10.4362 204.663i −0.0328181 0.643593i
\(319\) 389.914i 1.22230i
\(320\) 34.2908 + 55.2190i 0.107159 + 0.172559i
\(321\) 437.728 + 395.253i 1.36364 + 1.23132i
\(322\) 13.7816 + 10.8660i 0.0428000 + 0.0337453i
\(323\) 105.807 + 105.807i 0.327575 + 0.327575i
\(324\) 49.1793 + 237.971i 0.151788 + 0.734480i
\(325\) −490.022 + 165.675i −1.50776 + 0.509768i
\(326\) 54.9355i 0.168514i
\(327\) −9.03113 + 0.460516i −0.0276181 + 0.00140830i
\(328\) −132.253 132.253i −0.403211 0.403211i
\(329\) −21.5903 182.517i −0.0656240 0.554764i
\(330\) 37.0765 205.224i 0.112353 0.621890i
\(331\) 175.014 0.528744 0.264372 0.964421i \(-0.414835\pi\)
0.264372 + 0.964421i \(0.414835\pi\)
\(332\) −155.902 155.902i −0.469586 0.469586i
\(333\) 64.2177 + 52.3034i 0.192846 + 0.157067i
\(334\) −195.517 −0.585382
\(335\) −223.627 52.2861i −0.667543 0.156078i
\(336\) 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
\(342\) 123.627 151.788i 0.361482 0.443825i
\(343\) −143.661 + 311.465i −0.418837 + 0.908061i
\(344\) −328.215 −0.954114
\(345\) 6.68601 37.0081i 0.0193797 0.107270i
\(346\) 38.1223i 0.110180i
\(347\) −268.600 + 268.600i −0.774062 + 0.774062i −0.978814 0.204752i \(-0.934361\pi\)
0.204752 + 0.978814i \(0.434361\pi\)
\(348\) −252.079 + 12.8540i −0.724366 + 0.0369369i
\(349\) 304.193 0.871613 0.435807 0.900040i \(-0.356463\pi\)
0.435807 + 0.900040i \(0.356463\pi\)
\(350\) −58.6279 + 164.887i −0.167508 + 0.471106i
\(351\) −330.280 + 450.565i −0.940968 + 1.28366i
\(352\) 324.421 + 324.421i 0.921652 + 0.921652i
\(353\) −240.264 + 240.264i −0.680635 + 0.680635i −0.960143 0.279509i \(-0.909828\pi\)
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
\(357\) −142.413 + 24.2545i −0.398916 + 0.0679399i
\(358\) 132.507 132.507i 0.370132 0.370132i
\(359\) −161.739 −0.450526 −0.225263 0.974298i \(-0.572324\pi\)
−0.225263 + 0.974298i \(0.572324\pi\)
\(360\) 312.432 + 40.1437i 0.867865 + 0.111510i
\(361\) 112.126 0.310599
\(362\) −126.983 126.983i −0.350781 0.350781i
\(363\) −11.0451 216.604i −0.0304272 0.596706i
\(364\) 431.500 51.0429i 1.18544 0.140228i
\(365\) −394.943 92.3414i −1.08203 0.252990i
\(366\) 42.3655 46.9182i 0.115753 0.128192i
\(367\) −101.051 + 101.051i −0.275343 + 0.275343i −0.831247 0.555904i \(-0.812372\pi\)
0.555904 + 0.831247i \(0.312372\pi\)
\(368\) 8.86409 + 8.86409i 0.0240872 + 0.0240872i
\(369\) −239.225 + 24.4608i −0.648307 + 0.0662893i
\(370\) 39.0887 24.2739i 0.105645 0.0656051i
\(371\) 56.1715 + 474.856i 0.151406 + 1.27993i
\(372\) −7.90497 155.024i −0.0212499 0.416730i
\(373\) −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
\(375\) 370.939 55.0362i 0.989172 0.146763i
\(376\) 183.790i 0.488803i
\(377\) −410.320 410.320i −1.08838 1.08838i
\(378\) 50.5194 + 182.123i 0.133649 + 0.481807i
\(379\) 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
\(385\) −54.3566 + 483.562i −0.141186 + 1.25600i
\(386\) 115.447i 0.299085i
\(387\) −266.493 + 327.197i −0.688612 + 0.845472i
\(388\) 49.9973 + 49.9973i 0.128859 + 0.128859i
\(389\) 401.000 1.03085 0.515425 0.856935i \(-0.327634\pi\)
0.515425 + 0.856935i \(0.327634\pi\)
\(390\) 176.947 + 254.980i 0.453710 + 0.653796i
\(391\) 17.2472i 0.0441105i
\(392\) 179.255 292.432i 0.457283 0.746001i
\(393\) −12.1410 238.096i −0.0308931 0.605841i
\(394\) 234.338i 0.594767i
\(395\) 199.948 + 321.980i 0.506197 + 0.815138i
\(396\) 373.436 38.1838i 0.943019 0.0964237i
\(397\) 304.082 304.082i 0.765950 0.765950i −0.211440 0.977391i \(-0.567815\pi\)
0.977391 + 0.211440i \(0.0678154\pi\)
\(398\) −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 \(-0.259004\pi\)
\(402\) 7.01732 + 137.616i 0.0174560 + 0.342329i
\(403\) 252.338 252.338i 0.626149 0.626149i
\(404\) 339.341i 0.839952i
\(405\) 293.696 278.868i 0.725176 0.688563i
\(406\) −194.957 + 23.0618i −0.480190 + 0.0568025i
\(407\) 90.4693 90.4693i 0.222283 0.222283i
\(408\) 144.276 7.35694i 0.353619 0.0180317i
\(409\) 344.830 0.843104 0.421552 0.906804i \(-0.361485\pi\)
0.421552 + 0.906804i \(0.361485\pi\)
\(410\) −30.4157 + 130.087i −0.0741846 + 0.317286i
\(411\) −23.3952 21.1250i −0.0569226 0.0513991i
\(412\) −48.5478 + 48.5478i −0.117834 + 0.117834i
\(413\) 128.576 163.076i 0.311323 0.394858i
\(414\) −22.4473 + 2.29523i −0.0542204 + 0.00554403i
\(415\) −83.6607 + 357.815i −0.201592 + 0.862206i
\(416\) −682.799 −1.64134
\(417\) −27.4372 538.068i −0.0657965 1.29033i
\(418\) −213.838 213.838i −0.511573 0.511573i
\(419\) 343.927i 0.820828i 0.911899 + 0.410414i \(0.134616\pi\)
−0.911899 + 0.410414i \(0.865384\pi\)
\(420\) −314.414 19.2003i −0.748605 0.0457149i
\(421\) 14.6762 0.0348603 0.0174302 0.999848i \(-0.494452\pi\)
0.0174302 + 0.999848i \(0.494452\pi\)
\(422\) −195.579 + 195.579i −0.463457 + 0.463457i
\(423\) 183.220 + 149.227i 0.433144 + 0.352783i
\(424\) 478.167i 1.12775i
\(425\) 162.921 55.0830i 0.383343 0.129607i
\(426\) 32.2379 35.7024i 0.0756759 0.0838084i
\(427\) −91.3251 + 115.830i −0.213876 + 0.271264i
\(428\) 417.031 + 417.031i 0.974372 + 0.974372i
\(429\) 640.518 + 578.364i 1.49305 + 1.34817i
\(430\) 123.679 + 199.162i 0.287625 + 0.463167i
\(431\) 443.066i 1.02800i −0.857791 0.513998i \(-0.828164\pi\)
0.857791 0.513998i \(-0.171836\pi\)
\(432\) 20.5537 + 133.426i 0.0475779 + 0.308857i
\(433\) −487.352 487.352i −1.12553 1.12553i −0.990896 0.134629i \(-0.957016\pi\)
−0.134629 0.990896i \(-0.542984\pi\)
\(434\) −14.1825 119.895i −0.0326787 0.276255i
\(435\) 239.841 + 345.610i 0.551358 + 0.794506i
\(436\) −9.04287 −0.0207405
\(437\) −38.5614 38.5614i −0.0882412 0.0882412i
\(438\) 12.3931 + 243.041i 0.0282948 + 0.554888i
\(439\) 151.065 0.344111 0.172056 0.985087i \(-0.444959\pi\)
0.172056 + 0.985087i \(0.444959\pi\)
\(440\) 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 \(-0.347019\pi\)
−0.886716 + 0.462315i \(0.847019\pi\)
\(444\) 61.4707 + 55.5059i 0.138448 + 0.125013i
\(445\) −459.745 740.336i −1.03314 1.66368i
\(446\) 245.406 0.550239
\(447\) −3.77951 74.1196i −0.00845528 0.165816i
\(448\) −56.3422 + 71.4602i −0.125764 + 0.159509i
\(449\) 397.613 0.885552 0.442776 0.896632i \(-0.353994\pi\)
0.442776 + 0.896632i \(0.353994\pi\)
\(450\) −93.3717 204.711i −0.207493 0.454914i
\(451\) 371.478i 0.823677i
\(452\) 240.335 240.335i 0.531716 0.531716i
\(453\) −24.9522 489.336i −0.0550821 1.08021i
\(454\) −270.665 −0.596178
\(455\) −451.667 566.069i −0.992674 1.24411i
\(456\) 306.125 339.022i 0.671327 0.743470i
\(457\) −66.2262 66.2262i −0.144915 0.144915i 0.630927 0.775842i \(-0.282675\pi\)
−0.775842 + 0.630927i \(0.782675\pi\)
\(458\) 87.3209 87.3209i 0.190657 0.190657i
\(459\) 109.810 149.802i 0.239238 0.326367i
\(460\) 8.56200 36.6195i 0.0186130 0.0796077i
\(461\) −191.545 −0.415499 −0.207750 0.978182i \(-0.566614\pi\)
−0.207750 + 0.978182i \(0.566614\pi\)
\(462\) 287.820 49.0189i 0.622987 0.106102i
\(463\) 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
\(465\) −212.543 + 147.497i −0.457082 + 0.317198i
\(466\) −127.126 −0.272803
\(467\) 252.836 + 252.836i 0.541405 + 0.541405i 0.923941 0.382536i \(-0.124949\pi\)
−0.382536 + 0.923941i \(0.624949\pi\)
\(468\) −352.797 + 433.161i −0.753839 + 0.925557i
\(469\) −37.7700 319.295i −0.0805331 0.680800i
\(470\) 111.524 69.2561i 0.237286 0.147353i
\(471\) −341.239 308.127i −0.724500 0.654197i
\(472\) −146.843 + 146.843i −0.311108 + 0.311108i
\(473\) 460.953 + 460.953i 0.974530 + 0.974530i
\(474\) 152.404 168.781i 0.321526 0.356079i
\(475\) 241.105 487.414i 0.507589 1.02613i
\(476\) −143.464 + 16.9706i −0.301394 + 0.0356524i
\(477\) −476.684 388.245i −0.999337 0.813930i
\(478\) −34.8452 + 34.8452i −0.0728980 + 0.0728980i
\(479\) 91.5191i 0.191063i 0.995426 + 0.0955314i \(0.0304550\pi\)
−0.995426 + 0.0955314i \(0.969545\pi\)
\(480\) 487.114 + 88.0038i 1.01482 + 0.183341i
\(481\) 190.408i 0.395858i
\(482\) 298.161 + 298.161i 0.618592 + 0.618592i
\(483\) 51.9027 8.83960i 0.107459 0.0183015i
\(484\) 216.886i 0.448111i
\(485\) 26.8296 114.750i 0.0553189 0.236598i
\(486\) −209.581 122.983i −0.431237 0.253051i
\(487\) 252.690 + 252.690i 0.518872 + 0.518872i 0.917230 0.398358i \(-0.130420\pi\)
−0.398358 + 0.917230i \(0.630420\pi\)
\(488\) 104.300 104.300i 0.213729 0.213729i
\(489\) 122.319 + 110.450i 0.250141 + 0.225869i
\(490\) −244.996 + 1.42238i −0.499992 + 0.00290281i
\(491\) 518.117i 1.05523i 0.849484 + 0.527614i \(0.176913\pi\)
−0.849484 + 0.527614i \(0.823087\pi\)
\(492\) −240.161 + 12.2463i −0.488131 + 0.0248908i
\(493\) 136.422 + 136.422i 0.276717 + 0.276717i
\(494\) 450.057 0.911046
\(495\) −382.407 495.164i −0.772539 1.00033i
\(496\) 86.2361i 0.173863i
\(497\) −69.4937 + 88.1406i −0.139826 + 0.177345i
\(498\) 220.193 11.2281i 0.442155 0.0225464i
\(499\) 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
\(507\) −776.327 + 39.5865i −1.53122 + 0.0780798i
\(508\) 214.943 214.943i 0.423116 0.423116i
\(509\) 611.593i 1.20156i 0.799415 + 0.600779i \(0.205143\pi\)
−0.799415 + 0.600779i \(0.794857\pi\)
\(510\) −58.8307 84.7750i −0.115354 0.166226i
\(511\) −66.7048 563.900i −0.130538 1.10352i
\(512\) −215.668 + 215.668i −0.421226 + 0.421226i
\(513\) −89.4144 580.443i −0.174297 1.13147i
\(514\) 306.273 0.595862
\(515\) 111.423 + 26.0518i 0.216356 + 0.0505860i
\(516\) −282.810 + 313.202i −0.548081 + 0.606980i
\(517\) 258.119 258.119i 0.499262 0.499262i
\(518\) 50.5855 + 39.8837i 0.0976554 + 0.0769956i
\(519\) −84.8831 76.6464i −0.163551 0.147681i
\(520\) 382.042 + 615.208i 0.734695 + 1.18309i
\(521\) 692.510 1.32919 0.664597 0.747202i \(-0.268603\pi\)
0.664597 + 0.747202i \(0.268603\pi\)
\(522\) 159.398 195.708i 0.305360 0.374919i
\(523\) 583.903 + 583.903i 1.11645 + 1.11645i 0.992258 + 0.124191i \(0.0396337\pi\)
0.124191 + 0.992258i \(0.460366\pi\)
\(524\) 238.405i 0.454971i
\(525\) 249.264 + 462.053i 0.474788 + 0.880100i
\(526\) 277.971 0.528463
\(527\) −83.8965 + 83.8965i −0.159196 + 0.159196i
\(528\) 208.275 10.6204i 0.394461 0.0201144i
\(529\) 522.714i 0.988118i
\(530\) −290.153 + 180.184i −0.547458 + 0.339969i
\(531\) 27.1592 + 265.616i 0.0511473 + 0.500218i
\(532\) −282.814 + 358.699i −0.531604 + 0.674247i
\(533\) −390.919 390.919i −0.733431 0.733431i
\(534\) −350.425 + 388.083i −0.656227 + 0.726748i
\(535\) 223.788 957.138i 0.418296 1.78904i
\(536\) 321.521i 0.599853i
\(537\) −28.6295 561.451i −0.0533138 1.04553i
\(538\) 247.460 + 247.460i 0.459963 + 0.459963i
\(539\) −662.448 + 158.948i −1.22903 + 0.294895i
\(540\) 307.517 263.550i 0.569476 0.488055i
\(541\) 314.562 0.581445 0.290723 0.956807i \(-0.406104\pi\)
0.290723 + 0.956807i \(0.406104\pi\)
\(542\) −97.5650 97.5650i −0.180009 0.180009i
\(543\) −538.043 + 27.4359i −0.990871 + 0.0505265i
\(544\) 227.015 0.417306
\(545\) 7.95095 + 12.8035i 0.0145889 + 0.0234927i
\(546\) −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
\(552\) −52.5817 + 2.68125i −0.0952567 + 0.00485733i
\(553\) −328.529 + 416.681i −0.594084 + 0.753492i
\(554\) −187.831 −0.339045
\(555\) 24.5411 135.838i 0.0442181 0.244754i
\(556\) 538.767i 0.969005i
\(557\) 245.854 245.854i 0.441390 0.441390i −0.451089 0.892479i \(-0.648964\pi\)
0.892479 + 0.451089i \(0.148964\pi\)
\(558\) 120.356 + 98.0265i 0.215692 + 0.175675i
\(559\) −970.151 −1.73551
\(560\) −173.905 19.5484i −0.310544 0.0349079i
\(561\) −212.957 192.293i −0.379603 0.342768i
\(562\) −100.479 100.479i −0.178787 0.178787i
\(563\) 406.434 406.434i 0.721907 0.721907i −0.247086 0.968993i \(-0.579473\pi\)
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
\(567\) 507.086 + 253.679i 0.894331 + 0.447405i
\(568\) 79.3667 79.3667i 0.139730 0.139730i
\(569\) −690.156 −1.21293 −0.606464 0.795111i \(-0.707413\pi\)
−0.606464 + 0.795111i \(0.707413\pi\)
\(570\) −321.074 58.0064i −0.563288 0.101766i
\(571\) 612.476 1.07264 0.536319 0.844015i \(-0.319814\pi\)
0.536319 + 0.844015i \(0.319814\pi\)
\(572\) 610.233 + 610.233i 1.06684 + 1.06684i
\(573\) 320.771 16.3568i 0.559810 0.0285459i
\(574\) −185.739 + 21.9714i −0.323587 + 0.0382777i
\(575\) −59.3768 + 20.0751i −0.103264 + 0.0349131i
\(576\) −11.9012 116.393i −0.0206618 0.202071i
\(577\) −254.442 + 254.442i −0.440973 + 0.440973i −0.892339 0.451366i \(-0.850937\pi\)
0.451366 + 0.892339i \(0.350937\pi\)
\(578\) 170.891 + 170.891i 0.295659 + 0.295659i
\(579\) −257.054 232.110i −0.443962 0.400882i
\(580\) 221.929 + 357.376i 0.382636 + 0.616165i
\(581\) −510.890 + 60.4341i −0.879329 + 0.104017i
\(582\) −70.6151 + 3.60081i −0.121332 + 0.00618695i
\(583\) −671.548 + 671.548i −1.15188 + 1.15188i
\(584\) 567.832i 0.972315i
\(585\) 923.497 + 118.658i 1.57863 + 0.202835i
\(586\) 534.410i 0.911962i
\(587\) −195.495 195.495i −0.333040 0.333040i 0.520700 0.853740i \(-0.325671\pi\)
−0.853740 + 0.520700i \(0.825671\pi\)
\(588\) −124.599 423.032i −0.211902 0.719442i
\(589\) 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
\(595\) 150.169 + 188.205i 0.252384 + 0.316311i
\(596\) 74.2159i 0.124523i
\(597\) 33.6167 + 659.255i 0.0563094 + 1.10428i
\(598\) −36.6812 36.6812i −0.0613397 0.0613397i
\(599\) −376.201 −0.628048 −0.314024 0.949415i \(-0.601677\pi\)
−0.314024 + 0.949415i \(0.601677\pi\)
\(600\) −193.259 488.135i −0.322099 0.813558i
\(601\) 1122.87i 1.86834i 0.356832 + 0.934169i \(0.383857\pi\)
−0.356832 + 0.934169i \(0.616143\pi\)
\(602\) −203.213 + 257.740i −0.337563 + 0.428139i
\(603\) 320.524 + 261.058i 0.531549 + 0.432931i
\(604\) 489.971i 0.811211i
\(605\) −307.083 + 190.697i −0.507574 + 0.315202i
\(606\) 251.858 + 227.419i 0.415608 + 0.375279i
\(607\) −127.880 + 127.880i −0.210675 + 0.210675i −0.804554 0.593879i \(-0.797596\pi\)
0.593879 + 0.804554i \(0.297596\pi\)
\(608\) 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
\(612\) 117.297 144.016i 0.191661 0.235320i
\(613\) 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
\(615\) 228.501 + 329.269i 0.371546 + 0.535397i
\(616\) 676.533 80.0283i 1.09827 0.129916i
\(617\) 416.614 416.614i 0.675225 0.675225i −0.283691 0.958916i \(-0.591559\pi\)
0.958916 + 0.283691i \(0.0915589\pi\)
\(618\) −3.49641 68.5679i −0.00565763 0.110951i
\(619\) −1140.08 −1.84180 −0.920902 0.389794i \(-0.872546\pi\)
−0.920902 + 0.389794i \(0.872546\pi\)
\(620\) −219.779 + 136.482i −0.354482 + 0.220132i
\(621\) −40.0205 + 54.5957i −0.0644453 + 0.0879157i
\(622\) 156.576 156.576i 0.251730 0.251730i
\(623\) 755.394 958.085i 1.21251 1.53786i
\(624\) −207.999 + 230.351i −0.333331 + 0.369153i
\(625\) −379.267 496.771i −0.606827 0.794834i
\(626\) 319.542 0.510450
\(627\) −906.059 + 46.2018i −1.44507 + 0.0736870i
\(628\) −325.105 325.105i −0.517683 0.517683i
\(629\) 63.3061i 0.100646i
\(630\) 224.964 220.490i 0.357086 0.349985i
\(631\) −76.8167 −0.121738 −0.0608690 0.998146i \(-0.519387\pi\)
−0.0608690 + 0.998146i \(0.519387\pi\)
\(632\) 375.203 375.203i 0.593675 0.593675i
\(633\) 42.2568 + 828.695i 0.0667564 + 1.30915i
\(634\) 136.086i 0.214646i
\(635\) −493.320 115.343i −0.776883 0.181643i
\(636\) −456.293 412.017i −0.717443 0.647825i
\(637\) 529.849 864.382i 0.831788 1.35696i
\(638\) −275.711 275.711i −0.432149 0.432149i
\(639\) −14.6792 143.562i −0.0229721 0.224666i
\(640\) 579.374 + 135.463i 0.905272 + 0.211661i
\(641\) 187.134i 0.291941i 0.989289 + 0.145970i \(0.0466304\pi\)
−0.989289 + 0.145970i \(0.953370\pi\)
\(642\) −589.006 + 30.0346i −0.917455 + 0.0467829i
\(643\) 767.988 + 767.988i 1.19438 + 1.19438i 0.975824 + 0.218559i \(0.0701356\pi\)
0.218559 + 0.975824i \(0.429864\pi\)
\(644\) 52.2855 6.18494i 0.0811886 0.00960395i
\(645\) 692.114 + 125.040i 1.07305 + 0.193860i
\(646\) −149.633 −0.231631
\(647\) 573.588 + 573.588i 0.886535 + 0.886535i 0.994188 0.107654i \(-0.0343337\pi\)
−0.107654 + 0.994188i \(0.534334\pi\)
\(648\) −473.774 311.491i −0.731133 0.480696i
\(649\) 412.459 0.635530
\(650\) 229.348 463.648i 0.352844 0.713304i
\(651\) −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 \(-0.200721\pi\)
−0.589616 + 0.807683i \(0.700721\pi\)
\(654\) 6.06034 6.71161i 0.00926658 0.0102624i
\(655\) −337.551 + 209.618i −0.515345 + 0.320027i
\(656\) −133.596 −0.203652
\(657\) 566.071 + 461.048i 0.861600 + 0.701747i
\(658\) 144.326 + 113.793i 0.219340 + 0.172937i
\(659\) 960.106 1.45691 0.728457 0.685092i \(-0.240238\pi\)
0.728457 + 0.685092i \(0.240238\pi\)
\(660\) −356.694 513.996i −0.540446 0.778782i
\(661\) 94.8355i 0.143473i 0.997424 + 0.0717364i \(0.0228540\pi\)
−0.997424 + 0.0717364i \(0.977146\pi\)
\(662\) −123.754 + 123.754i −0.186939 + 0.186939i
\(663\) 426.458 21.7459i 0.643224 0.0327993i
\(664\) 514.452 0.774777
\(665\) 756.537 + 85.0414i 1.13765 + 0.127882i
\(666\) −82.3928 + 8.42466i −0.123713 + 0.0126496i
\(667\) −49.7191 49.7191i −0.0745413 0.0745413i
\(668\) −414.755 + 414.755i −0.620891 + 0.620891i
\(669\) 493.399 546.421i 0.737517 0.816773i
\(670\) 195.100 121.156i 0.291194 0.180830i
\(671\) −292.961 −0.436604
\(672\) 116.350 + 683.163i 0.173140 + 1.01661i
\(673\) −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
\(675\) −643.537 203.679i −0.953388 0.301746i
\(676\) −777.336 −1.14990
\(677\) 447.410 + 447.410i 0.660872 + 0.660872i 0.955586 0.294714i \(-0.0952243\pi\)
−0.294714 + 0.955586i \(0.595224\pi\)
\(678\) 17.3090 + 339.445i 0.0255295 + 0.500656i
\(679\) 163.840 19.3810i 0.241296 0.0285434i
\(680\) −127.020 204.542i −0.186794 0.300798i
\(681\) −544.182 + 602.662i −0.799093 + 0.884966i
\(682\) 169.557 169.557i 0.248617 0.248617i
\(683\) 199.643 + 199.643i 0.292303 + 0.292303i 0.837990 0.545686i \(-0.183731\pi\)
−0.545686 + 0.837990i \(0.683731\pi\)
\(684\) −59.7388 584.243i −0.0873375 0.854157i
\(685\) −11.9608 + 51.1561i −0.0174610 + 0.0746804i
\(686\) −118.655 321.823i −0.172967 0.469129i
\(687\) −18.8666 369.991i −0.0274622 0.538560i
\(688\) −165.774 + 165.774i −0.240950 + 0.240950i
\(689\) 1413.38i 2.05135i
\(690\) 21.4409 + 30.8964i 0.0310738 + 0.0447773i
\(691\) 207.196i 0.299849i −0.988697 0.149925i \(-0.952097\pi\)
0.988697 0.149925i \(-0.0479031\pi\)
\(692\) −80.8697 80.8697i −0.116864 0.116864i
\(693\) 469.527 739.414i 0.677529 1.06698i
\(694\) 379.857i 0.547345i
\(695\) −762.825 + 473.711i −1.09759 + 0.681599i
\(696\) 394.702 437.118i 0.567100 0.628043i
\(697\) 129.971 + 129.971i 0.186473 + 0.186473i
\(698\) −215.097 + 215.097i −0.308162 + 0.308162i
\(699\) −255.592 + 283.059i −0.365654 + 0.404948i
\(700\) 225.410 + 474.147i 0.322014 + 0.677353i
\(701\) 8.12497i 0.0115905i −0.999983 0.00579527i \(-0.998155\pi\)
0.999983 0.00579527i \(-0.00184470\pi\)
\(702\) −85.0546 552.141i −0.121160 0.786525i
\(703\) −141.540 141.540i −0.201337 0.201337i
\(704\) −180.740 −0.256733
\(705\) 70.0183 387.561i 0.0993167 0.549733i
\(706\) 339.785i 0.481281i
\(707\) −621.778 490.236i −0.879459 0.693403i
\(708\) 13.5972 + 266.654i 0.0192052 + 0.376631i
\(709\) 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
\(717\) 7.52867 + 147.644i 0.0105002 + 0.205919i
\(718\) 114.367 114.367i 0.159285 0.159285i
\(719\) 1236.22i 1.71936i 0.510837 + 0.859678i \(0.329336\pi\)
−0.510837 + 0.859678i \(0.670664\pi\)
\(720\) 178.077 137.526i 0.247330 0.191009i
\(721\) 18.8191 + 159.090i 0.0261014 + 0.220652i
\(722\) −79.2852 + 79.2852i −0.109813 + 0.109813i
\(723\) 1263.35 64.4208i 1.74737 0.0891021i
\(724\) −538.742 −0.744118
\(725\) 310.868 628.446i 0.428783 0.866822i
\(726\) 160.972 + 145.352i 0.221725 + 0.200210i
\(727\) −635.035 + 635.035i −0.873501 + 0.873501i −0.992852 0.119351i \(-0.961919\pi\)
0.119351 + 0.992852i \(0.461919\pi\)
\(728\) −627.722 + 796.155i −0.862255 + 1.09362i
\(729\) −695.204 + 219.392i −0.953640 + 0.300949i
\(730\) 344.562 213.971i 0.472003 0.293112i
\(731\) 322.553 0.441249
\(732\) −9.65785 189.399i −0.0131938 0.258742i
\(733\) −174.851 174.851i −0.238542 0.238542i 0.577704 0.816246i \(-0.303949\pi\)
−0.816246 + 0.577704i \(0.803949\pi\)
\(734\) 142.908i 0.194697i
\(735\) −489.406 + 548.367i −0.665859 + 0.746078i
\(736\) −82.7358 −0.112413
\(737\) 451.552 451.552i 0.612689 0.612689i
\(738\) 151.861 186.454i 0.205774 0.252648i
\(739\) 1448.98i 1.96073i 0.197187 + 0.980366i \(0.436819\pi\)
−0.197187 + 0.980366i \(0.563181\pi\)
\(740\) 31.4269 134.412i 0.0424688 0.181638i
\(741\) 904.856 1002.10i 1.22113 1.35236i
\(742\) −375.493 296.055i −0.506055 0.398995i
\(743\) 30.8955 + 30.8955i 0.0415822 + 0.0415822i 0.727592 0.686010i \(-0.240639\pi\)
−0.686010 + 0.727592i \(0.740639\pi\)
\(744\) 268.818 + 242.733i 0.361315 + 0.326254i
\(745\) −105.080 + 65.2544i −0.141047 + 0.0875898i
\(746\) 522.501i 0.700404i
\(747\) 417.706 512.856i 0.559179 0.686555i
\(748\) −202.888 202.888i −0.271241 0.271241i
\(749\) 1366.61 161.658i 1.82457 0.215832i
\(750\) −223.377 + 301.210i −0.297836 + 0.401614i
\(751\) 1095.21 1.45833 0.729167 0.684335i \(-0.239908\pi\)
0.729167 + 0.684335i \(0.239908\pi\)
\(752\) 92.8279 + 92.8279i 0.123441 + 0.123441i
\(753\) 52.7867 + 1035.20i 0.0701019 + 1.37476i
\(754\) 580.279 0.769601
\(755\) −693.737 + 430.808i −0.918857 + 0.570606i
\(756\) 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 \(0.654695\pi\)
\(762\) 15.4802 + 303.581i 0.0203152 + 0.398400i
\(763\) −13.0640 + 16.5694i −0.0171219 + 0.0217161i
\(764\) 321.188 0.420403
\(765\) −307.041 39.4511i −0.401361 0.0515701i
\(766\) 231.666i 0.302436i
\(767\) −434.044 + 434.044i −0.565898 + 0.565898i
\(768\) −26.1250 512.334i −0.0340169 0.667102i
\(769\) −248.259 −0.322833 −0.161417 0.986886i \(-0.551606\pi\)
−0.161417 + 0.986886i \(0.551606\pi\)
\(770\) −303.494 380.366i −0.394148