Properties

Label 105.3.k.c.62.2
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 62.2
Root \(-0.611750 + 0.253395i\) of \(x^{16} + 433 x^{8} + 16\)
Character \(\chi\) \(=\) 105.62
Dual form 105.3.k.c.83.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.152778 - 2.99611i) q^{3} +3.00000i q^{4} +(-4.24762 + 2.63775i) q^{5} +(2.22660 + 2.01054i) q^{6} +(4.33402 + 5.49694i) q^{7} +(-4.94975 - 4.94975i) q^{8} +(-8.95332 + 0.915476i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.152778 - 2.99611i) q^{3} +3.00000i q^{4} +(-4.24762 + 2.63775i) q^{5} +(2.22660 + 2.01054i) q^{6} +(4.33402 + 5.49694i) q^{7} +(-4.94975 - 4.94975i) q^{8} +(-8.95332 + 0.915476i) q^{9} +(1.13835 - 4.86869i) q^{10} +13.9031i q^{11} +(8.98832 - 0.458333i) q^{12} +(14.6307 + 14.6307i) q^{13} +(-6.95153 - 0.822309i) q^{14} +(8.55193 + 12.3233i) q^{15} -5.00000 q^{16} +(-4.86435 - 4.86435i) q^{17} +(5.68361 - 6.97829i) q^{18} -21.7515 q^{19} +(-7.91326 - 12.7429i) q^{20} +(15.8073 - 13.8250i) q^{21} +(-9.83095 - 9.83095i) q^{22} +(-1.77282 - 1.77282i) q^{23} +(-14.0738 + 15.5862i) q^{24} +(11.0845 - 22.4083i) q^{25} -20.6909 q^{26} +(4.11073 + 26.6852i) q^{27} +(-16.4908 + 13.0020i) q^{28} +28.0452 q^{29} +(-14.7610 - 2.66678i) q^{30} -17.2472i q^{31} +(23.3345 - 23.3345i) q^{32} +(41.6551 - 2.12408i) q^{33} +6.87923 q^{34} +(-32.9088 - 11.9168i) q^{35} +(-2.74643 - 26.8600i) q^{36} +(-6.50714 - 6.50714i) q^{37} +(15.3806 - 15.3806i) q^{38} +(41.5998 - 46.0702i) q^{39} +(34.0808 + 7.96843i) q^{40} -26.7192 q^{41} +(-1.40169 + 20.9532i) q^{42} +(33.1548 - 33.1548i) q^{43} -41.7092 q^{44} +(35.6155 - 27.5052i) q^{45} +2.50714 q^{46} +(18.5656 + 18.5656i) q^{47} +(0.763888 + 14.9805i) q^{48} +(-11.4326 + 47.6476i) q^{49} +(8.00714 + 23.6830i) q^{50} +(-13.8310 + 15.3173i) q^{51} +(-43.8920 + 43.8920i) q^{52} +(48.3021 + 48.3021i) q^{53} +(-21.7760 - 15.9626i) q^{54} +(-36.6728 - 59.0549i) q^{55} +(5.75616 - 48.6607i) q^{56} +(3.32314 + 65.1697i) q^{57} +(-19.8310 + 19.8310i) q^{58} +29.6668i q^{59} +(-36.9700 + 25.6558i) q^{60} -21.0717i q^{61} +(12.1956 + 12.1956i) q^{62} +(-43.8361 - 45.2481i) q^{63} +13.0000i q^{64} +(-100.737 - 23.5534i) q^{65} +(-27.9526 + 30.9565i) q^{66} +(-32.4786 - 32.4786i) q^{67} +(14.5931 - 14.5931i) q^{68} +(-5.04071 + 5.58240i) q^{69} +(31.6965 - 14.8436i) q^{70} +16.0345i q^{71} +(48.8480 + 39.7853i) q^{72} +(57.3597 + 57.3597i) q^{73} +9.20249 q^{74} +(-68.8312 - 29.7869i) q^{75} -65.2544i q^{76} +(-76.4243 + 60.2561i) q^{77} +(3.16110 + 61.9921i) q^{78} +75.8024i q^{79} +(21.2381 - 13.1888i) q^{80} +(79.3238 - 16.3931i) q^{81} +(18.8933 - 18.8933i) q^{82} +(51.9675 - 51.9675i) q^{83} +(41.4750 + 47.4218i) q^{84} +(33.4929 + 7.83095i) q^{85} +46.8879i q^{86} +(-4.28468 - 84.0264i) q^{87} +(68.8167 - 68.8167i) q^{88} +174.294i q^{89} +(-5.73481 + 44.6331i) q^{90} +(-17.0143 + 143.833i) q^{91} +(5.31846 - 5.31846i) q^{92} +(-51.6745 + 2.63499i) q^{93} -26.2557 q^{94} +(92.3919 - 57.3750i) q^{95} +(-73.4777 - 66.3477i) q^{96} +(-16.6658 + 16.6658i) q^{97} +(-25.6079 - 41.7760i) q^{98} +(-12.7279 - 124.479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 32q^{7} + O(q^{10}) \) \( 16q + 32q^{7} + 80q^{15} - 80q^{16} + 8q^{18} - 64q^{21} - 64q^{22} + 224q^{25} - 96q^{28} - 128q^{30} + 96q^{36} - 384q^{37} - 112q^{42} + 64q^{43} + 320q^{46} - 128q^{51} + 408q^{57} - 224q^{58} - 120q^{60} - 72q^{63} + 320q^{67} + 128q^{70} + 56q^{72} - 424q^{78} + 896q^{81} + 256q^{85} + 448q^{88} - 832q^{91} + 32q^{93} + O(q^{100}) \)

Character values

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

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

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
\(7\) 4.33402 + 5.49694i 0.619145 + 0.785277i
\(8\) −4.94975 4.94975i −0.618718 0.618718i
\(9\) −8.95332 + 0.915476i −0.994813 + 0.101720i
\(10\) 1.13835 4.86869i 0.113835 0.486869i
\(11\) 13.9031i 1.26392i 0.775003 + 0.631958i \(0.217748\pi\)
−0.775003 + 0.631958i \(0.782252\pi\)
\(12\) 8.98832 0.458333i 0.749027 0.0381944i
\(13\) 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
\(15\) 8.55193 + 12.3233i 0.570129 + 0.821555i
\(16\) −5.00000 −0.312500
\(17\) −4.86435 4.86435i −0.286138 0.286138i 0.549413 0.835551i \(-0.314851\pi\)
−0.835551 + 0.549413i \(0.814851\pi\)
\(18\) 5.68361 6.97829i 0.315756 0.387683i
\(19\) −21.7515 −1.14481 −0.572407 0.819970i \(-0.693990\pi\)
−0.572407 + 0.819970i \(0.693990\pi\)
\(20\) −7.91326 12.7429i −0.395663 0.637143i
\(21\) 15.8073 13.8250i 0.752727 0.658333i
\(22\) −9.83095 9.83095i −0.446861 0.446861i
\(23\) −1.77282 1.77282i −0.0770791 0.0770791i 0.667516 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
\(28\) −16.4908 + 13.0020i −0.588957 + 0.464359i
\(29\) 28.0452 0.967076 0.483538 0.875323i \(-0.339352\pi\)
0.483538 + 0.875323i \(0.339352\pi\)
\(30\) −14.7610 2.66678i −0.492035 0.0888928i
\(31\) 17.2472i 0.556362i −0.960529 0.278181i \(-0.910268\pi\)
0.960529 0.278181i \(-0.0897315\pi\)
\(32\) 23.3345 23.3345i 0.729204 0.729204i
\(33\) 41.6551 2.12408i 1.26228 0.0643660i
\(34\) 6.87923 0.202330
\(35\) −32.9088 11.9168i −0.940251 0.340481i
\(36\) −2.74643 26.8600i −0.0762897 0.746110i
\(37\) −6.50714 6.50714i −0.175869 0.175869i 0.613683 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 \(-0.605648\pi\)
−0.325844 + 0.945424i \(0.605648\pi\)
\(42\) −1.40169 + 20.9532i −0.0333735 + 0.498885i
\(43\) 33.1548 33.1548i 0.771041 0.771041i −0.207248 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 0.876470 0.481457i \(-0.159892\pi\)
−0.481457 + 0.876470i \(0.659892\pi\)
\(48\) 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 \(0.0808953\pi\)
−0.967880 + 0.251413i \(0.919105\pi\)
\(60\) −36.9700 + 25.6558i −0.616167 + 0.427597i
\(61\) 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
\(63\) −43.8361 45.2481i −0.695812 0.718224i
\(64\) 13.0000i 0.203125i
\(65\) −100.737 23.5534i −1.54981 0.362360i
\(66\) −27.9526 + 30.9565i −0.423525 + 0.469038i
\(67\) −32.4786 32.4786i −0.484755 0.484755i 0.421892 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 \(0.0360200\pi\)
−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 0.980794 0.195045i \(-0.0624853\pi\)
−0.195045 + 0.980794i \(0.562485\pi\)
\(74\) 9.20249 0.124358
\(75\) −68.8312 29.7869i −0.917750 0.397159i
\(76\) 65.2544i 0.858610i
\(77\) −76.4243 + 60.2561i −0.992523 + 0.782547i
\(78\) 3.16110 + 61.9921i 0.0405269 + 0.794770i
\(79\) 75.8024i 0.959524i 0.877399 + 0.479762i \(0.159277\pi\)
−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 −0.320974 0.947088i \(-0.604010\pi\)
0.947088 + 0.320974i \(0.104010\pi\)
\(84\) 41.4750 + 47.4218i 0.493749 + 0.564545i
\(85\) 33.4929 + 7.83095i 0.394034 + 0.0921288i
\(86\) 46.8879i 0.545208i
\(87\) −4.28468 84.0264i −0.0492492 0.965821i
\(88\) 68.8167 68.8167i 0.782008 0.782008i
\(89\) 174.294i 1.95836i 0.202987 + 0.979181i \(0.434935\pi\)
−0.202987 + 0.979181i \(0.565065\pi\)
\(90\) −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 −0.787775 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 \(-0.310813\pi\)
0.559968 + 0.828514i \(0.310813\pi\)
\(102\) −1.05099 20.6109i −0.0103038 0.202068i
\(103\) −16.1826 16.1826i −0.157113 0.157113i 0.624173 0.781286i \(-0.285436\pi\)
−0.781286 + 0.624173i \(0.785436\pi\)
\(104\) 144.836i 1.39265i
\(105\) −30.6764 + 100.419i −0.292156 + 0.956371i
\(106\) −68.3095 −0.644429
\(107\) 139.010 139.010i 1.29916 1.29916i 0.370218 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
\(112\) −21.6701 27.4847i −0.193483 0.245399i
\(113\) −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
\(126\) 62.9921 + 0.998435i 0.499937 + 0.00792409i
\(127\) −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 \(-0.401907\pi\)
0.303314 + 0.952891i \(0.401907\pi\)
\(132\) 6.37223 + 124.965i 0.0482745 + 0.946706i
\(133\) −94.2712 119.566i −0.708806 0.898996i
\(134\) 45.9316 0.342773
\(135\) −87.8499 102.506i −0.650740 0.759301i
\(136\) 48.1546i 0.354078i
\(137\) −7.42967 + 7.42967i −0.0542312 + 0.0542312i −0.733702 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 \(-0.276439\pi\)
0.646003 + 0.763335i \(0.276439\pi\)
\(140\) 35.7505 98.7264i 0.255361 0.705189i
\(141\) 52.7881 58.4609i 0.374384 0.414616i
\(142\) −11.3381 11.3381i −0.0798457 0.0798457i
\(143\) −203.411 + 203.411i −1.42245 + 1.42245i
\(144\) 44.7666 4.57738i 0.310879 0.0317874i
\(145\) −119.125 + 73.9763i −0.821554 + 0.510181i
\(146\) −81.1188 −0.555609
\(147\) 144.504 + 26.9739i 0.983021 + 0.183496i
\(148\) 19.5214 19.5214i 0.131902 0.131902i
\(149\) −24.7386 −0.166031 −0.0830155 0.996548i \(-0.526455\pi\)
−0.0830155 + 0.996548i \(0.526455\pi\)
\(150\) 69.7336 27.6085i 0.464890 0.184057i
\(151\) −163.324 −1.08161 −0.540807 0.841147i \(-0.681881\pi\)
−0.540807 + 0.841147i \(0.681881\pi\)
\(152\) 107.664 + 107.664i 0.708317 + 0.708317i
\(153\) 48.0053 + 39.0989i 0.313760 + 0.255548i
\(154\) 11.4326 96.6476i 0.0742378 0.627582i
\(155\) 45.4939 + 73.2596i 0.293509 + 0.472643i
\(156\) 138.211 + 124.799i 0.885966 + 0.799995i
\(157\) 108.368 108.368i 0.690244 0.690244i −0.272042 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
\(162\) −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 0.159365 0.987220i \(-0.449055\pi\)
−0.987220 + 0.159365i \(0.949055\pi\)
\(168\) −146.672 9.81182i −0.873049 0.0584037i
\(169\) 259.112i 1.53321i
\(170\) −29.2203 + 18.1457i −0.171884 + 0.106739i
\(171\) 194.748 19.9129i 1.13888 0.116450i
\(172\) 99.4643 + 99.4643i 0.578281 + 0.578281i
\(173\) 26.9566 26.9566i 0.155818 0.155818i −0.624893 0.780711i \(-0.714857\pi\)
0.780711 + 0.624893i \(0.214857\pi\)
\(174\) 62.4454 + 56.3859i 0.358882 + 0.324057i
\(175\) 171.218 36.1871i 0.978387 0.206784i
\(176\) 69.5153i 0.394973i
\(177\) 88.8848 4.53242i 0.502174 0.0256069i
\(178\) −123.245 123.245i −0.692386 0.692386i
\(179\) −187.393 −1.04689 −0.523445 0.852059i \(-0.675354\pi\)
−0.523445 + 0.852059i \(0.675354\pi\)
\(180\) 82.5157 + 106.846i 0.458420 + 0.593591i
\(181\) 179.581i 0.992158i −0.868277 0.496079i \(-0.834773\pi\)
0.868277 0.496079i \(-0.165227\pi\)
\(182\) −89.6745 113.736i −0.492717 0.624925i
\(183\) −63.1331 + 3.21928i −0.344990 + 0.0175917i
\(184\) 17.5500i 0.0953805i
\(185\) 44.8041 + 10.4756i 0.242184 + 0.0566250i
\(186\) 34.6762 38.4026i 0.186431 0.206466i
\(187\) 67.6294 67.6294i 0.361654 0.361654i
\(188\) −55.6968 + 55.6968i −0.296259 + 0.296259i
\(189\) −128.871 + 138.251i −0.681858 + 0.731485i
\(190\) −24.7607 + 105.901i −0.130320 + 0.557375i
\(191\) 107.063i 0.560538i −0.959922 0.280269i \(-0.909576\pi\)
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 \(-0.686462\pi\)
−0.552857 + 0.833276i \(0.686462\pi\)
\(200\) −165.781 + 56.0500i −0.828906 + 0.280250i
\(201\) −92.3473 + 102.271i −0.459439 + 0.508812i
\(202\) −79.9833 + 79.9833i −0.395957 + 0.395957i
\(203\) 121.548 + 154.163i 0.598760 + 0.759422i
\(204\) −45.9518 41.4929i −0.225254 0.203396i
\(205\) 113.493 70.4786i 0.553624 0.343798i
\(206\) 22.8856 0.111095
\(207\) 17.4956 + 14.2496i 0.0845197 + 0.0688388i
\(208\) −73.1533 73.1533i −0.351698 0.351698i
\(209\) 302.412i 1.44695i
\(210\) −49.3154 92.6984i −0.234835 0.441421i
\(211\) 276.590 1.31086 0.655428 0.755258i \(-0.272488\pi\)
0.655428 + 0.755258i \(0.272488\pi\)
\(212\) −144.906 + 144.906i −0.683521 + 0.683521i
\(213\) 48.0411 2.44971i 0.225545 0.0115010i
\(214\) 196.590i 0.918647i
\(215\) −53.3747 + 228.283i −0.248255 + 1.06178i
\(216\) 111.738 152.432i 0.517306 0.705705i
\(217\) 94.8069 74.7497i 0.436898 0.344469i
\(218\) −2.13142 2.13142i −0.00977717 0.00977717i
\(219\) 163.092 180.619i 0.744715 0.824744i
\(220\) 177.165 110.019i 0.805294 0.500084i
\(221\) 142.337i 0.644060i
\(222\) −1.40593 27.5717i −0.00633304 0.124197i
\(223\) 173.529 + 173.529i 0.778155 + 0.778155i 0.979517 0.201362i \(-0.0645368\pi\)
−0.201362 + 0.979517i \(0.564537\pi\)
\(224\) 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 0.146140 0.989264i \(-0.453315\pi\)
−0.989264 + 0.146140i \(0.953315\pi\)
\(228\) −195.509 + 9.96941i −0.857496 + 0.0437255i
\(229\) 123.490 0.539259 0.269630 0.962964i \(-0.413099\pi\)
0.269630 + 0.962964i \(0.413099\pi\)
\(230\) −10.6494 + 6.61323i −0.0463017 + 0.0287532i
\(231\) 192.210 + 219.770i 0.832076 + 0.951383i
\(232\) −138.817 138.817i −0.598348 0.598348i
\(233\) 89.8918 + 89.8918i 0.385802 + 0.385802i 0.873187 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
\(238\) 29.8147 + 37.8147i 0.125272 + 0.158885i
\(239\) 49.2786 0.206187 0.103093 0.994672i \(-0.467126\pi\)
0.103093 + 0.994672i \(0.467126\pi\)
\(240\) −42.7597 61.6167i −0.178165 0.256736i
\(241\) 421.664i 1.74964i 0.484445 + 0.874822i \(0.339021\pi\)
−0.484445 + 0.874822i \(0.660979\pi\)
\(242\) 51.1204 51.1204i 0.211242 0.211242i
\(243\) −61.2344 235.158i −0.251993 0.967729i
\(244\) 63.2151 0.259078
\(245\) −77.1212 232.545i −0.314780 0.949165i
\(246\) −59.4929 53.7199i −0.241841 0.218374i
\(247\) −318.238 318.238i −1.28841 1.28841i
\(248\) −85.3694 + 85.3694i −0.344231 + 0.344231i
\(249\) −163.640 147.761i −0.657187 0.593417i
\(250\) −96.4812 79.4756i −0.385925 0.317902i
\(251\) −345.514 −1.37655 −0.688274 0.725450i \(-0.741631\pi\)
−0.688274 + 0.725450i \(0.741631\pi\)
\(252\) 135.744 131.508i 0.538668 0.521859i
\(253\) 24.6476 24.6476i 0.0974214 0.0974214i
\(254\) 101.325 0.398917
\(255\) 18.3454 101.545i 0.0719428 0.398214i
\(256\) −171.000 −0.667969
\(257\) 216.568 + 216.568i 0.842676 + 0.842676i 0.989206 0.146530i \(-0.0468104\pi\)
−0.146530 + 0.989206i \(0.546810\pi\)
\(258\) 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 \(0.225434\pi\)
−0.759519 + 0.650485i \(0.774566\pi\)
\(270\) 134.602 + 10.3632i 0.498525 + 0.0383822i
\(271\) 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
\(273\) 433.539 + 29.0021i 1.58806 + 0.106235i
\(274\) 10.5071i 0.0383472i
\(275\) 311.545 + 154.109i 1.13289 + 0.560396i
\(276\) −16.7472 15.1221i −0.0606783 0.0547903i
\(277\) 132.817 + 132.817i 0.479483 + 0.479483i 0.904966 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 \(0.0813658\pi\)
−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 0.462014 0.886873i \(-0.347127\pi\)
−0.886873 + 0.462014i \(0.847127\pi\)
\(284\) −48.1035 −0.169378
\(285\) −186.017 268.050i −0.652691 0.940528i
\(286\) 287.666i 1.00583i
\(287\) −115.801 146.874i −0.403489 0.511755i
\(288\) −187.559 + 230.284i −0.651247 + 0.799596i
\(289\) 241.676i 0.836250i
\(290\) 31.9252 136.543i 0.110087 0.470840i
\(291\) 52.4786 + 47.3863i 0.180339 + 0.162839i
\(292\) −172.079 + 172.079i −0.589312 + 0.589312i
\(293\) 377.885 377.885i 1.28971 1.28971i 0.354747 0.934962i \(-0.384567\pi\)
0.934962 0.354747i \(-0.115433\pi\)
\(294\) −121.253 + 83.1064i −0.412426 + 0.282675i
\(295\) −78.2536 126.013i −0.265266 0.427163i
\(296\) 64.4174i 0.217626i
\(297\) −371.007 + 57.1518i −1.24918 + 0.192430i
\(298\) 17.4929 17.4929i 0.0587009 0.0587009i
\(299\) 51.8750i 0.173495i
\(300\) 89.3608 206.494i 0.297869 0.688312i
\(301\) 325.943 + 38.5564i 1.08287 + 0.128094i
\(302\) 115.487 115.487i 0.382409 0.382409i
\(303\) −17.2812 338.900i −0.0570337 1.11848i
\(304\) 108.757 0.357754
\(305\) 55.5820 + 89.5046i 0.182236 + 0.293458i
\(306\) −61.5919 + 6.29777i −0.201281 + 0.0205809i
\(307\) −94.6590 + 94.6590i −0.308335 + 0.308335i −0.844264 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 \(-0.384140\pi\)
0.356000 + 0.934486i \(0.384140\pi\)
\(312\) −433.944 + 22.1277i −1.39085 + 0.0709221i
\(313\) 225.950 + 225.950i 0.721885 + 0.721885i 0.968989 0.247104i \(-0.0794790\pi\)
−0.247104 + 0.968989i \(0.579479\pi\)
\(314\) 153.256i 0.488076i
\(315\) 305.553 + 76.5679i 0.970008 + 0.243073i
\(316\) −227.407 −0.719643
\(317\) 96.2271 96.2271i 0.303556 0.303556i −0.538848 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
\(322\) 10.8660 + 13.7816i 0.0337453 + 0.0428000i
\(323\) 105.807 + 105.807i 0.327575 + 0.327575i
\(324\) 49.1793 + 237.971i 0.151788 + 0.734480i
\(325\) 490.022 165.675i 1.50776 0.509768i
\(326\) 54.9355i 0.168514i
\(327\) 9.03113 0.460516i 0.0276181 0.00140830i
\(328\) 132.253 + 132.253i 0.403211 + 0.403211i
\(329\) −21.5903 + 182.517i −0.0656240 + 0.554764i
\(330\) 37.0765 205.224i 0.112353 0.621890i
\(331\) 175.014 0.528744 0.264372 0.964421i \(-0.414835\pi\)
0.264372 + 0.964421i \(0.414835\pi\)
\(332\) 155.902 + 155.902i 0.469586 + 0.469586i
\(333\) 64.2177 + 52.3034i 0.192846 + 0.157067i
\(334\) 195.517 0.585382
\(335\) 223.627 + 52.2861i 0.667543 + 0.156078i
\(336\) −79.0364 + 69.1249i −0.235227 + 0.205729i
\(337\) 109.576 + 109.576i 0.325152 + 0.325152i 0.850739 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
\(343\) −311.465 + 143.661i −0.908061 + 0.418837i
\(344\) −328.215 −0.954114
\(345\) 6.68601 37.0081i 0.0193797 0.107270i
\(346\) 38.1223i 0.110180i
\(347\) −268.600 + 268.600i −0.774062 + 0.774062i −0.978814 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 \(-0.643537\pi\)
−0.435807 + 0.900040i \(0.643537\pi\)
\(350\) −95.4810 + 146.657i −0.272803 + 0.419021i
\(351\) −330.280 + 450.565i −0.940968 + 1.28366i
\(352\) 324.421 + 324.421i 0.921652 + 0.921652i
\(353\) 240.264 240.264i 0.680635 0.680635i −0.279509 0.960143i \(-0.590172\pi\)
0.960143 + 0.279509i \(0.0901715\pi\)
\(354\) −59.6461 + 66.0559i −0.168492 + 0.186599i
\(355\) −42.2950 68.1084i −0.119141 0.191855i
\(356\) −522.883 −1.46877
\(357\) −144.142 9.64254i −0.403758 0.0270099i
\(358\) 132.507 132.507i 0.370132 0.370132i
\(359\) −161.739 −0.450526 −0.225263 0.974298i \(-0.572324\pi\)
−0.225263 + 0.974298i \(0.572324\pi\)
\(360\) −312.432 40.1437i −0.867865 0.111510i
\(361\) 112.126 0.310599
\(362\) 126.983 + 126.983i 0.350781 + 0.350781i
\(363\) 11.0451 + 216.604i 0.0304272 + 0.596706i
\(364\) −431.500 51.0429i −1.18544 0.140228i
\(365\) −394.943 92.3414i −1.08203 0.252990i
\(366\) 42.3655 46.9182i 0.115753 0.128192i
\(367\) 101.051 101.051i 0.275343 0.275343i −0.555904 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
\(372\) −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
\(378\) −6.63236 188.884i −0.0175459 0.499692i
\(379\) 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 −0.460138 0.887847i \(-0.652200\pi\)
0.887847 + 0.460138i \(0.152200\pi\)
\(384\) 239.254 264.965i 0.623057 0.690013i
\(385\) 165.680 457.533i 0.430339 1.18840i
\(386\) 115.447i 0.299085i
\(387\) −266.493 + 327.197i −0.688612 + 0.845472i
\(388\) −49.9973 49.9973i −0.128859 0.128859i
\(389\) 401.000 1.03085 0.515425 0.856935i \(-0.327634\pi\)
0.515425 + 0.856935i \(0.327634\pi\)
\(390\) −176.947 254.980i −0.453710 0.653796i
\(391\) 17.2472i 0.0441105i
\(392\) 292.432 179.255i 0.746001 0.457283i
\(393\) −12.1410 238.096i −0.0308931 0.605841i
\(394\) 234.338i 0.594767i
\(395\) −199.948 321.980i −0.506197 0.815138i
\(396\) 373.436 38.1838i 0.943019 0.0964237i
\(397\) −304.082 + 304.082i −0.765950 + 0.765950i −0.977391 0.211440i \(-0.932185\pi\)
0.211440 + 0.977391i \(0.432185\pi\)
\(398\) 155.590 155.590i 0.390929 0.390929i
\(399\) −343.831 + 300.714i −0.861733 + 0.753668i
\(400\) −55.4226 + 112.042i −0.138557 + 0.280104i
\(401\) 582.912i 1.45365i −0.686825 0.726823i \(-0.740996\pi\)
0.686825 0.726823i \(-0.259004\pi\)
\(402\) −7.01732 137.616i −0.0174560 0.342329i
\(403\) 252.338 252.338i 0.626149 0.626149i
\(404\) 339.341i 0.839952i
\(405\) −293.696 + 278.868i −0.725176 + 0.688563i
\(406\) −194.957 23.0618i −0.480190 0.0568025i
\(407\) 90.4693 90.4693i 0.222283 0.222283i
\(408\) 144.276 7.35694i 0.353619 0.0180317i
\(409\) −344.830 −0.843104 −0.421552 0.906804i \(-0.638515\pi\)
−0.421552 + 0.906804i \(0.638515\pi\)
\(410\) −30.4157 + 130.087i −0.0741846 + 0.317286i
\(411\) 23.3952 + 21.1250i 0.0569226 + 0.0513991i
\(412\) 48.5478 48.5478i 0.117834 0.117834i
\(413\) −163.076 + 128.576i −0.394858 + 0.311323i
\(414\) −22.4473 + 2.29523i −0.0542204 + 0.00554403i
\(415\) −83.6607 + 357.815i −0.201592 + 0.862206i
\(416\) 682.799 1.64134
\(417\) −27.4372 538.068i −0.0657965 1.29033i
\(418\) 213.838 + 213.838i 0.511573 + 0.511573i
\(419\) 343.927i 0.820828i −0.911899 0.410414i \(-0.865384\pi\)
0.911899 0.410414i \(-0.134616\pi\)
\(420\) −301.257 92.0291i −0.717278 0.219117i
\(421\) 14.6762 0.0348603 0.0174302 0.999848i \(-0.494452\pi\)
0.0174302 + 0.999848i \(0.494452\pi\)
\(422\) −195.579 + 195.579i −0.463457 + 0.463457i
\(423\) −183.220 149.227i −0.433144 0.352783i
\(424\) 478.167i 1.12775i
\(425\) −162.921 + 55.0830i −0.383343 + 0.129607i
\(426\) −32.2379 + 35.7024i −0.0756759 + 0.0838084i
\(427\) 115.830 91.3251i 0.271264 0.213876i
\(428\) 417.031 + 417.031i 0.974372 + 0.974372i
\(429\) 640.518 + 578.364i 1.49305 + 1.34817i
\(430\) −123.679 199.162i −0.287625 0.463167i
\(431\) 443.066i 1.02800i −0.857791 0.513998i \(-0.828164\pi\)
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 \(0.0429843\pi\)
0.134629 + 0.990896i \(0.457016\pi\)
\(434\) −14.1825 + 119.895i −0.0326787 + 0.276255i
\(435\) 239.841 + 345.610i 0.551358 + 0.794506i
\(436\) −9.04287 −0.0207405
\(437\) 38.5614 + 38.5614i 0.0882412 + 0.0882412i
\(438\) 12.3931 + 243.041i 0.0282948 + 0.554888i
\(439\) −151.065 −0.344111 −0.172056 0.985087i \(-0.555041\pi\)
−0.172056 + 0.985087i \(0.555041\pi\)
\(440\) −110.786 + 473.828i −0.251785 + 1.07688i
\(441\) 58.7396 437.071i 0.133196 0.991090i
\(442\) 100.648 + 100.648i 0.227710 + 0.227710i
\(443\) −188.010 188.010i −0.424401 0.424401i 0.462315 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
\(448\) −71.4602 + 56.3422i −0.159509 + 0.125764i
\(449\) 397.613 0.885552 0.442776 0.896632i \(-0.353994\pi\)
0.442776 + 0.896632i \(0.353994\pi\)
\(450\) −93.3717 204.711i −0.207493 0.454914i
\(451\) 371.478i 0.823677i
\(452\) 240.335 240.335i 0.531716 0.531716i
\(453\) 24.9522 + 489.336i 0.0550821 + 1.08021i
\(454\) 270.665 0.596178
\(455\) −307.126 655.828i −0.675003 1.44138i
\(456\) 306.125 339.022i 0.671327 0.743470i
\(457\) −66.2262 66.2262i −0.144915 0.144915i 0.630927 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 \(-0.433386\pi\)
0.207750 + 0.978182i \(0.433386\pi\)
\(462\) −291.313 19.4878i −0.630548 0.0421813i
\(463\) 42.9857 42.9857i 0.0928417 0.0928417i −0.659161 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 0.382536 0.923941i \(-0.375051\pi\)
−0.923941 + 0.382536i \(0.875051\pi\)
\(468\) 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 \(-0.969545\pi\)
0.995426 0.0955314i \(-0.0304550\pi\)
\(480\) 487.114 + 88.0038i 1.01482 + 0.183341i
\(481\) 190.408i 0.395858i
\(482\) −298.161 298.161i −0.618592 0.618592i
\(483\) −52.5326 3.51424i −0.108763 0.00727585i
\(484\) 216.886i 0.448111i
\(485\) 26.8296 114.750i 0.0553189 0.236598i
\(486\) 209.581 + 122.983i 0.431237 + 0.253051i
\(487\) 252.690 + 252.690i 0.518872 + 0.518872i 0.917230 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 \(0.176913\pi\)
−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
\(497\) −88.1406 + 69.4937i −0.177345 + 0.139826i
\(498\) 220.193 11.2281i 0.442155 0.0225464i
\(499\) 217.267i 0.435404i 0.976015 + 0.217702i \(0.0698561\pi\)
−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 −0.694329 0.719657i \(-0.744299\pi\)
0.719657 + 0.694329i \(0.244299\pi\)
\(504\) −6.98904 + 440.945i −0.0138671 + 0.874890i
\(505\) −480.463 + 298.365i −0.951412 + 0.590823i
\(506\) 34.8570i 0.0688873i
\(507\) 776.327 39.5865i 1.53122 0.0780798i
\(508\) 214.943 214.943i 0.423116 0.423116i
\(509\) 611.593i 1.20156i −0.799415 0.600779i \(-0.794857\pi\)
0.799415 0.600779i \(-0.205143\pi\)
\(510\) 58.8307 + 84.7750i 0.115354 + 0.166226i
\(511\) −66.7048 + 563.900i −0.130538 + 1.10352i
\(512\) −215.668 + 215.668i −0.421226 + 0.421226i
\(513\) −89.4144 580.443i −0.174297 1.13147i
\(514\) −306.273 −0.595862
\(515\) 111.423 + 26.0518i 0.216356 + 0.0505860i
\(516\) 282.810 313.202i 0.548081 0.606980i
\(517\) −258.119 + 258.119i −0.499262 + 0.499262i
\(518\) 39.8837 + 50.5855i 0.0769956 + 0.0976554i
\(519\) −84.8831 76.6464i −0.163551 0.147681i
\(520\) 382.042 + 615.208i 0.734695 + 1.18309i
\(521\) −692.510 −1.32919 −0.664597 0.747202i \(-0.731397\pi\)
−0.664597 + 0.747202i \(0.731397\pi\)
\(522\) 159.398 195.708i 0.305360 0.374919i
\(523\) −583.903 583.903i −1.11645 1.11645i −0.992258 0.124191i \(-0.960366\pi\)
−0.124191 0.992258i \(-0.539634\pi\)
\(524\) 238.405i 0.454971i
\(525\) −134.579 507.458i −0.256340 0.966587i
\(526\) 277.971 0.528463
\(527\) −83.8965 + 83.8965i −0.159196 + 0.159196i
\(528\) −208.275 + 10.6204i −0.394461 + 0.0201144i
\(529\) 522.714i 0.988118i
\(530\) 290.153 180.184i 0.547458 0.339969i
\(531\) −27.1592 265.616i −0.0511473 0.500218i
\(532\) 358.699 282.814i 0.674247 0.531604i
\(533\) −390.919 390.919i −0.733431 0.733431i
\(534\) −350.425 + 388.083i −0.656227 + 0.726748i
\(535\) −223.788 + 957.138i −0.418296 + 1.78904i
\(536\) 321.521i 0.599853i
\(537\) 28.6295 + 561.451i 0.0533138 + 1.04553i
\(538\) −247.460 247.460i −0.459963 0.459963i
\(539\) −662.448 158.948i −1.22903 0.294895i
\(540\) 307.517 263.550i 0.569476 0.488055i
\(541\) 314.562 0.581445 0.290723 0.956807i \(-0.406104\pi\)
0.290723 + 0.956807i \(0.406104\pi\)
\(542\) 97.5650 + 97.5650i 0.180009 + 0.180009i
\(543\) −538.043 + 27.4359i −0.990871 + 0.0505265i
\(544\) −227.015 −0.417306
\(545\) −7.95095 12.8035i −0.0145889 0.0234927i
\(546\) −327.066 + 286.051i −0.599022 + 0.523903i
\(547\) 223.888 + 223.888i 0.409302 + 0.409302i 0.881495 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
\(553\) −416.681 + 328.529i −0.753492 + 0.594084i
\(554\) −187.831 −0.339045
\(555\) 24.5411 135.838i 0.0442181 0.244754i
\(556\) 538.767i 0.969005i
\(557\) 245.854 245.854i 0.441390 0.441390i −0.451089 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
\(560\) 164.544 + 59.5841i 0.293829 + 0.106400i
\(561\) −212.957 192.293i −0.379603 0.342768i
\(562\) −100.479 100.479i −0.178787 0.178787i
\(563\) −406.434 + 406.434i −0.721907 + 0.721907i −0.968993 0.247086i \(-0.920527\pi\)
0.247086 + 0.968993i \(0.420527\pi\)
\(564\) 175.383 + 158.364i 0.310962 + 0.280788i
\(565\) 551.600 + 128.969i 0.976283 + 0.228264i
\(566\) 170.038 0.300420
\(567\) 433.902 + 364.990i 0.765260 + 0.643721i
\(568\) 79.3667 79.3667i 0.139730 0.139730i
\(569\) −690.156 −1.21293 −0.606464 0.795111i \(-0.707413\pi\)
−0.606464 + 0.795111i \(0.707413\pi\)
\(570\) 321.074 + 58.0064i 0.563288 + 0.101766i
\(571\) 612.476 1.07264 0.536319 0.844015i \(-0.319814\pi\)
0.536319 + 0.844015i \(0.319814\pi\)
\(572\) −610.233 610.233i −1.06684 1.06684i
\(573\) −320.771 + 16.3568i −0.559810 + 0.0285459i
\(574\) 185.739 + 21.9714i 0.323587 + 0.0382777i
\(575\) −59.3768 + 20.0751i −0.103264 + 0.0349131i
\(576\) −11.9012 116.393i −0.0206618 0.202071i
\(577\) 254.442 254.442i 0.440973 0.440973i −0.451366 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
\(582\) −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 0.853740 0.520700i \(-0.174329\pi\)
−0.520700 + 0.853740i \(0.674329\pi\)
\(588\) −80.9216 + 433.512i −0.137622 + 0.737265i
\(589\) 375.152i 0.636931i
\(590\) 144.438 + 33.7711i 0.244811 + 0.0572391i
\(591\) 521.777 + 471.146i 0.882871 + 0.797201i
\(592\) 32.5357 + 32.5357i 0.0549590 + 0.0549590i
\(593\) 181.904 181.904i 0.306751 0.306751i −0.536897 0.843648i \(-0.680403\pi\)
0.843648 + 0.536897i \(0.180403\pi\)
\(594\) 221.929 302.754i 0.373618 0.509686i
\(595\) 102.112 + 218.048i 0.171617 + 0.366466i
\(596\) 74.2159i 0.124523i
\(597\) 33.6167 + 659.255i 0.0563094 + 1.10428i
\(598\) 36.6812 + 36.6812i 0.0613397 + 0.0613397i
\(599\) −376.201 −0.628048 −0.314024 0.949415i \(-0.601677\pi\)
−0.314024 + 0.949415i \(0.601677\pi\)
\(600\) 193.259 + 488.135i 0.322099 + 0.813558i
\(601\) 1122.87i 1.86834i −0.356832 0.934169i \(-0.616143\pi\)
0.356832 0.934169i \(-0.383857\pi\)
\(602\) −257.740 + 203.213i −0.428139 + 0.337563i
\(603\) 320.524 + 261.058i 0.531549 + 0.432931i
\(604\) 489.971i 0.811211i
\(605\) 307.083 190.697i 0.507574 0.315202i
\(606\) 251.858 + 227.419i 0.415608 + 0.375279i
\(607\) 127.880 127.880i 0.210675 0.210675i −0.593879 0.804554i \(-0.702404\pi\)
0.804554 + 0.593879i \(0.202404\pi\)
\(608\) −507.560 + 507.560i −0.834803 + 0.834803i
\(609\) 443.318 387.724i 0.727944 0.636658i
\(610\) −102.592 23.9869i −0.168183 0.0393228i
\(611\) 543.253i 0.889122i
\(612\) −117.297 + 144.016i −0.191661 + 0.235320i
\(613\) 668.817 668.817i 1.09105 1.09105i 0.0956388 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 \(-0.127454\pi\)
0.920902 + 0.389794i \(0.127454\pi\)
\(620\) −219.779 + 136.482i −0.354482 + 0.220132i
\(621\) 40.0205 54.5957i 0.0644453 0.0879157i
\(622\) −156.576 + 156.576i −0.251730 + 0.251730i
\(623\) −958.085 + 755.394i −1.53786 + 1.21251i
\(624\) −207.999 + 230.351i −0.333331 + 0.369153i
\(625\) −379.267 496.771i −0.606827 0.794834i
\(626\) −319.542 −0.510450
\(627\) −906.059 + 46.2018i −1.44507 + 0.0736870i
\(628\) 325.105 + 325.105i 0.517683 + 0.517683i
\(629\) 63.3061i 0.100646i
\(630\) −270.200 + 161.917i −0.428889 + 0.257010i
\(631\) −76.8167 −0.121738 −0.0608690 0.998146i \(-0.519387\pi\)
−0.0608690 + 0.998146i \(0.519387\pi\)
\(632\) 375.203 375.203i 0.593675 0.593675i
\(633\) −42.2568 828.695i −0.0667564 1.30915i
\(634\) 136.086i 0.214646i
\(635\) 493.320 + 115.343i 0.776883 + 0.181643i
\(636\) 456.293 + 412.017i 0.717443 + 0.647825i
\(637\) −864.382 + 529.849i −1.35696 + 0.831788i
\(638\) −275.711 275.711i −0.432149 0.432149i
\(639\) −14.6792 143.562i −0.0229721 0.224666i
\(640\) −579.374 135.463i −0.905272 0.211661i
\(641\) 187.134i 0.291941i 0.989289 + 0.145970i \(0.0466304\pi\)
−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 \(-0.929864\pi\)
−0.218559 0.975824i \(-0.570136\pi\)
\(644\) 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 0.107654 0.994188i \(-0.465666\pi\)
−0.994188 + 0.107654i \(0.965666\pi\)
\(648\) −473.774 311.491i −0.731133 0.480696i
\(649\) −412.459 −0.635530
\(650\) −229.348 + 463.648i −0.352844 + 0.713304i
\(651\) −238.443 272.632i −0.366271 0.418789i
\(652\) 116.536 + 116.536i 0.178736 + 0.178736i
\(653\) 142.398 + 142.398i 0.218067 + 0.218067i 0.807683 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
\(658\) −113.793 144.326i −0.172937 0.219340i
\(659\) 960.106 1.45691 0.728457 0.685092i \(-0.240238\pi\)
0.728457 + 0.685092i \(0.240238\pi\)
\(660\) −356.694 513.996i −0.540446 0.778782i
\(661\) 94.8355i 0.143473i −0.997424 0.0717364i \(-0.977146\pi\)
0.997424 0.0717364i \(-0.0228540\pi\)
\(662\) −123.754 + 123.754i −0.186939 + 0.186939i
\(663\) −426.458 + 21.7459i −0.643224 + 0.0327993i
\(664\) −514.452 −0.774777
\(665\) 715.815 + 259.208i 1.07641 + 0.389787i
\(666\) −82.3928 + 8.42466i −0.123713 + 0.0126496i
\(667\) −49.7191 49.7191i −0.0745413 0.0745413i
\(668\) 414.755 414.755i 0.620891 0.620891i
\(669\) 493.399 546.421i 0.737517 0.816773i
\(670\) −195.100 + 121.156i −0.291194 + 0.180830i
\(671\) 292.961 0.436604
\(672\) 46.2557 691.455i 0.0688329 1.02895i
\(673\) −442.857 + 442.857i −0.658034 + 0.658034i −0.954915 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 0.294714 0.955586i \(-0.404776\pi\)
−0.955586 + 0.294714i \(0.904776\pi\)
\(678\) −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 \(0.0479031\pi\)
−0.988697 + 0.149925i \(0.952097\pi\)
\(692\) 80.8697 + 80.8697i 0.116864 + 0.116864i
\(693\) 629.088 609.457i 0.907775 0.879447i
\(694\) 379.857i 0.547345i
\(695\) −762.825 + 473.711i −1.09759 + 0.681599i
\(696\) −394.702 + 437.118i −0.567100 + 0.628043i
\(697\) 129.971 + 129.971i 0.186473 + 0.186473i
\(698\) 215.097 215.097i 0.308162 0.308162i
\(699\) 255.592 283.059i 0.365654 0.404948i
\(700\) 108.561 + 513.653i 0.155088 + 0.733790i
\(701\) 8.12497i 0.0115905i −0.999983 0.00579527i \(-0.998155\pi\)
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
\(707\) 490.236 + 621.778i 0.693403 + 0.879459i
\(708\) 13.5972 + 266.654i 0.0192052 + 0.376631i
\(709\) 854.167i 1.20475i −0.798214 0.602374i \(-0.794222\pi\)
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
\(714\) 108.742 95.1052i 0.152300 0.133201i
\(715\) 327.464 1400.56i 0.457992 1.95882i
\(716\) 562.180i 0.785168i
\(717\) −7.52867 147.644i −0.0105002 0.205919i
\(718\) 114.367 114.367i 0.159285 0.159285i
\(719\) 1236.22i 1.71936i −0.510837 0.859678i \(-0.670664\pi\)
0.510837 0.859678i \(-0.329336\pi\)
\(720\) −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 −0.119351 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
\(732\) −9.65785 189.399i −0.0131938 0.258742i
\(733\) 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
\(735\) −684.948 + 266.591i −0.931902 + 0.362709i
\(736\) −82.7358 −0.112413
\(737\) 451.552 451.552i 0.612689 0.612689i
\(738\) −151.861 + 186.454i −0.205774 + 0.252648i
\(739\) 1448.98i 1.96073i 0.197187 + 0.980366i \(0.436819\pi\)
−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 0.727592 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
\(756\) −414.752 386.613i −0.548614 0.511393i
\(757\) 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 \(-0.345305\pi\)
0.467084 + 0.884213i \(0.345305\pi\)
\(762\) −15.4802 303.581i −0.0203152 0.398400i
\(763\) −16.5694 + 13.0640i −0.0217161 + 0.0171219i
\(764\) 321.188 0.420403
\(765\) −307.041 39.4511i −0.401361 0.0515701i
\(766\) 231.666i 0.302436i
\(767\) −434.044 + 434.044i −0.565898 + 0.565898i
\(768\) 26.1250 + 512.334i 0.0340169 + 0.667102i
\(769\) 248.259 0.322833 0.161417 0.986886i \(-0.448394\pi\)
0.161417 + 0.986886i \(0.448394\pi\)
\(770\) 206.371 + 440.679i 0.268014 + 0.572310i