Properties

Label 70.3.d.a.69.7
Level $70$
Weight $3$
Character 70.69
Analytic conductor $1.907$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 70.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.90736185052\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.211319484596224.6
Defining polynomial: \(x^{8} + 2 x^{6} - 48 x^{5} - 23 x^{4} - 48 x^{3} + 1226 x^{2} - 7512 x + 24408\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 69.7
Root \(-1.28865 + 3.99943i\) of defining polynomial
Character \(\chi\) \(=\) 70.69
Dual form 70.3.d.a.69.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} +2.07875 q^{3} -2.00000 q^{4} +(4.65605 - 1.82242i) q^{5} +2.93980i q^{6} +(3.36740 + 6.13682i) q^{7} -2.82843i q^{8} -4.67878 q^{9} +O(q^{10})\) \(q+1.41421i q^{2} +2.07875 q^{3} -2.00000 q^{4} +(4.65605 - 1.82242i) q^{5} +2.93980i q^{6} +(3.36740 + 6.13682i) q^{7} -2.82843i q^{8} -4.67878 q^{9} +(2.57729 + 6.58465i) q^{10} +1.67878 q^{11} -4.15751 q^{12} -9.81063 q^{13} +(-8.67878 + 4.76222i) q^{14} +(9.67878 - 3.78837i) q^{15} +4.00000 q^{16} +0.498539 q^{17} -6.61679i q^{18} -32.2182i q^{19} +(-9.31210 + 3.64484i) q^{20} +(7.00000 + 12.7570i) q^{21} +2.37415i q^{22} +3.78837i q^{23} -5.87961i q^{24} +(18.3576 - 16.9706i) q^{25} -13.8743i q^{26} -28.4348 q^{27} +(-6.73480 - 12.2736i) q^{28} -39.0363 q^{29} +(5.35756 + 13.6879i) q^{30} -24.9285i q^{31} +5.65685i q^{32} +3.48977 q^{33} +0.705040i q^{34} +(26.8627 + 22.4365i) q^{35} +9.35756 q^{36} -16.0620i q^{37} +45.5634 q^{38} -20.3939 q^{39} +(-5.15459 - 13.1693i) q^{40} +71.1407i q^{41} +(-18.0411 + 9.89949i) q^{42} +37.7295i q^{43} -3.35756 q^{44} +(-21.7846 + 8.52671i) q^{45} -5.35756 q^{46} +71.4209 q^{47} +8.31502 q^{48} +(-26.3212 + 41.3303i) q^{49} +(24.0000 + 25.9615i) q^{50} +1.03634 q^{51} +19.6213 q^{52} +83.0357i q^{53} -40.2129i q^{54} +(7.81648 - 3.05944i) q^{55} +(17.3576 - 9.52445i) q^{56} -66.9737i q^{57} -55.2057i q^{58} -36.4484i q^{59} +(-19.3576 + 7.57673i) q^{60} -50.4424i q^{61} +35.2542 q^{62} +(-15.7553 - 28.7128i) q^{63} -8.00000 q^{64} +(-45.6788 + 17.8791i) q^{65} +4.93528i q^{66} -12.2736i q^{67} -0.997077 q^{68} +7.87508i q^{69} +(-31.7300 + 37.9895i) q^{70} +44.6424 q^{71} +13.2336i q^{72} -102.433 q^{73} +22.7151 q^{74} +(38.1609 - 35.2776i) q^{75} +64.4364i q^{76} +(5.65313 + 10.3024i) q^{77} -28.8413i q^{78} +132.394 q^{79} +(18.6242 - 7.28969i) q^{80} -17.0000 q^{81} -100.608 q^{82} -8.72896 q^{83} +(-14.0000 - 25.5139i) q^{84} +(2.32122 - 0.908548i) q^{85} -53.3576 q^{86} -81.1470 q^{87} -4.74831i q^{88} +54.0872i q^{89} +(-12.0586 - 30.8081i) q^{90} +(-33.0363 - 60.2061i) q^{91} -7.57673i q^{92} -51.8202i q^{93} +101.004i q^{94} +(-58.7151 - 150.009i) q^{95} +11.7592i q^{96} +41.7352 q^{97} +(-58.4499 - 37.2238i) q^{98} -7.85464 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 16q^{4} + 36q^{9} + O(q^{10}) \) \( 8q - 16q^{4} + 36q^{9} - 60q^{11} + 4q^{14} + 4q^{15} + 32q^{16} + 56q^{21} - 92q^{29} - 104q^{30} + 52q^{35} - 72q^{36} + 204q^{39} + 120q^{44} + 104q^{46} - 284q^{49} + 192q^{50} - 212q^{51} - 8q^{56} - 8q^{60} - 64q^{64} - 292q^{65} - 4q^{70} + 504q^{71} - 112q^{74} + 692q^{79} - 136q^{81} - 112q^{84} + 92q^{85} - 280q^{86} - 44q^{91} - 176q^{95} - 944q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(57\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 2.07875 0.692918 0.346459 0.938065i \(-0.387384\pi\)
0.346459 + 0.938065i \(0.387384\pi\)
\(4\) −2.00000 −0.500000
\(5\) 4.65605 1.82242i 0.931210 0.364484i
\(6\) 2.93980i 0.489967i
\(7\) 3.36740 + 6.13682i 0.481057 + 0.876689i
\(8\) 2.82843i 0.353553i
\(9\) −4.67878 −0.519864
\(10\) 2.57729 + 6.58465i 0.257729 + 0.658465i
\(11\) 1.67878 0.152616 0.0763082 0.997084i \(-0.475687\pi\)
0.0763082 + 0.997084i \(0.475687\pi\)
\(12\) −4.15751 −0.346459
\(13\) −9.81063 −0.754664 −0.377332 0.926078i \(-0.623158\pi\)
−0.377332 + 0.926078i \(0.623158\pi\)
\(14\) −8.67878 + 4.76222i −0.619913 + 0.340159i
\(15\) 9.67878 3.78837i 0.645252 0.252558i
\(16\) 4.00000 0.250000
\(17\) 0.498539 0.0293258 0.0146629 0.999892i \(-0.495332\pi\)
0.0146629 + 0.999892i \(0.495332\pi\)
\(18\) 6.61679i 0.367600i
\(19\) 32.2182i 1.69569i −0.530241 0.847847i \(-0.677898\pi\)
0.530241 0.847847i \(-0.322102\pi\)
\(20\) −9.31210 + 3.64484i −0.465605 + 0.182242i
\(21\) 7.00000 + 12.7570i 0.333333 + 0.607474i
\(22\) 2.37415i 0.107916i
\(23\) 3.78837i 0.164712i 0.996603 + 0.0823558i \(0.0262444\pi\)
−0.996603 + 0.0823558i \(0.973756\pi\)
\(24\) 5.87961i 0.244984i
\(25\) 18.3576 16.9706i 0.734302 0.678823i
\(26\) 13.8743i 0.533628i
\(27\) −28.4348 −1.05314
\(28\) −6.73480 12.2736i −0.240529 0.438345i
\(29\) −39.0363 −1.34608 −0.673040 0.739606i \(-0.735012\pi\)
−0.673040 + 0.739606i \(0.735012\pi\)
\(30\) 5.35756 + 13.6879i 0.178585 + 0.456262i
\(31\) 24.9285i 0.804145i −0.915608 0.402073i \(-0.868290\pi\)
0.915608 0.402073i \(-0.131710\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 3.48977 0.105751
\(34\) 0.705040i 0.0207365i
\(35\) 26.8627 + 22.4365i 0.767505 + 0.641043i
\(36\) 9.35756 0.259932
\(37\) 16.0620i 0.434109i −0.976160 0.217054i \(-0.930355\pi\)
0.976160 0.217054i \(-0.0696449\pi\)
\(38\) 45.5634 1.19904
\(39\) −20.3939 −0.522920
\(40\) −5.15459 13.1693i −0.128865 0.329232i
\(41\) 71.1407i 1.73514i 0.497317 + 0.867569i \(0.334319\pi\)
−0.497317 + 0.867569i \(0.665681\pi\)
\(42\) −18.0411 + 9.89949i −0.429549 + 0.235702i
\(43\) 37.7295i 0.877430i 0.898626 + 0.438715i \(0.144566\pi\)
−0.898626 + 0.438715i \(0.855434\pi\)
\(44\) −3.35756 −0.0763082
\(45\) −21.7846 + 8.52671i −0.484103 + 0.189482i
\(46\) −5.35756 −0.116469
\(47\) 71.4209 1.51959 0.759797 0.650160i \(-0.225298\pi\)
0.759797 + 0.650160i \(0.225298\pi\)
\(48\) 8.31502 0.173230
\(49\) −26.3212 + 41.3303i −0.537168 + 0.843475i
\(50\) 24.0000 + 25.9615i 0.480000 + 0.519230i
\(51\) 1.03634 0.0203204
\(52\) 19.6213 0.377332
\(53\) 83.0357i 1.56671i 0.621574 + 0.783356i \(0.286494\pi\)
−0.621574 + 0.783356i \(0.713506\pi\)
\(54\) 40.2129i 0.744684i
\(55\) 7.81648 3.05944i 0.142118 0.0556263i
\(56\) 17.3576 9.52445i 0.309956 0.170079i
\(57\) 66.9737i 1.17498i
\(58\) 55.2057i 0.951823i
\(59\) 36.4484i 0.617770i −0.951099 0.308885i \(-0.900044\pi\)
0.951099 0.308885i \(-0.0999558\pi\)
\(60\) −19.3576 + 7.57673i −0.322626 + 0.126279i
\(61\) 50.4424i 0.826925i −0.910521 0.413462i \(-0.864319\pi\)
0.910521 0.413462i \(-0.135681\pi\)
\(62\) 35.2542 0.568617
\(63\) −15.7553 28.7128i −0.250085 0.455760i
\(64\) −8.00000 −0.125000
\(65\) −45.6788 + 17.8791i −0.702750 + 0.275063i
\(66\) 4.93528i 0.0747770i
\(67\) 12.2736i 0.183189i −0.995796 0.0915944i \(-0.970804\pi\)
0.995796 0.0915944i \(-0.0291963\pi\)
\(68\) −0.997077 −0.0146629
\(69\) 7.87508i 0.114132i
\(70\) −31.7300 + 37.9895i −0.453286 + 0.542708i
\(71\) 44.6424 0.628767 0.314383 0.949296i \(-0.398202\pi\)
0.314383 + 0.949296i \(0.398202\pi\)
\(72\) 13.2336i 0.183800i
\(73\) −102.433 −1.40319 −0.701596 0.712575i \(-0.747529\pi\)
−0.701596 + 0.712575i \(0.747529\pi\)
\(74\) 22.7151 0.306961
\(75\) 38.1609 35.2776i 0.508811 0.470368i
\(76\) 64.4364i 0.847847i
\(77\) 5.65313 + 10.3024i 0.0734172 + 0.133797i
\(78\) 28.8413i 0.369761i
\(79\) 132.394 1.67587 0.837936 0.545768i \(-0.183762\pi\)
0.837936 + 0.545768i \(0.183762\pi\)
\(80\) 18.6242 7.28969i 0.232802 0.0911211i
\(81\) −17.0000 −0.209877
\(82\) −100.608 −1.22693
\(83\) −8.72896 −0.105168 −0.0525841 0.998617i \(-0.516746\pi\)
−0.0525841 + 0.998617i \(0.516746\pi\)
\(84\) −14.0000 25.5139i −0.166667 0.303737i
\(85\) 2.32122 0.908548i 0.0273085 0.0106888i
\(86\) −53.3576 −0.620437
\(87\) −81.1470 −0.932724
\(88\) 4.74831i 0.0539580i
\(89\) 54.0872i 0.607722i 0.952716 + 0.303861i \(0.0982758\pi\)
−0.952716 + 0.303861i \(0.901724\pi\)
\(90\) −12.0586 30.8081i −0.133984 0.342312i
\(91\) −33.0363 60.2061i −0.363037 0.661606i
\(92\) 7.57673i 0.0823558i
\(93\) 51.8202i 0.557207i
\(94\) 101.004i 1.07452i
\(95\) −58.7151 150.009i −0.618054 1.57905i
\(96\) 11.7592i 0.122492i
\(97\) 41.7352 0.430260 0.215130 0.976585i \(-0.430982\pi\)
0.215130 + 0.976585i \(0.430982\pi\)
\(98\) −58.4499 37.2238i −0.596427 0.379835i
\(99\) −7.85464 −0.0793398
\(100\) −36.7151 + 33.9411i −0.367151 + 0.339411i
\(101\) 103.944i 1.02915i −0.857445 0.514576i \(-0.827950\pi\)
0.857445 0.514576i \(-0.172050\pi\)
\(102\) 1.46561i 0.0143687i
\(103\) 50.8026 0.493229 0.246614 0.969114i \(-0.420682\pi\)
0.246614 + 0.969114i \(0.420682\pi\)
\(104\) 27.7487i 0.266814i
\(105\) 55.8409 + 46.6400i 0.531818 + 0.444191i
\(106\) −117.430 −1.10783
\(107\) 110.463i 1.03236i 0.856479 + 0.516181i \(0.172647\pi\)
−0.856479 + 0.516181i \(0.827353\pi\)
\(108\) 56.8696 0.526571
\(109\) 141.182 1.29524 0.647622 0.761961i \(-0.275763\pi\)
0.647622 + 0.761961i \(0.275763\pi\)
\(110\) 4.32671 + 11.0542i 0.0393337 + 0.100492i
\(111\) 33.3890i 0.300802i
\(112\) 13.4696 + 24.5473i 0.120264 + 0.219172i
\(113\) 82.1272i 0.726789i 0.931635 + 0.363395i \(0.118382\pi\)
−0.931635 + 0.363395i \(0.881618\pi\)
\(114\) 94.7151 0.830834
\(115\) 6.90400 + 17.6388i 0.0600348 + 0.153381i
\(116\) 78.0727 0.673040
\(117\) 45.9018 0.392323
\(118\) 51.5459 0.436829
\(119\) 1.67878 + 3.05944i 0.0141074 + 0.0257096i
\(120\) −10.7151 27.3757i −0.0892927 0.228131i
\(121\) −118.182 −0.976708
\(122\) 71.3363 0.584724
\(123\) 147.884i 1.20231i
\(124\) 49.8570i 0.402073i
\(125\) 54.5462 112.471i 0.436369 0.899768i
\(126\) 40.6061 22.2814i 0.322271 0.176837i
\(127\) 78.3388i 0.616841i 0.951250 + 0.308420i \(0.0998004\pi\)
−0.951250 + 0.308420i \(0.900200\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) 78.4304i 0.607987i
\(130\) −25.2849 64.5996i −0.194499 0.496920i
\(131\) 233.988i 1.78617i 0.449892 + 0.893083i \(0.351463\pi\)
−0.449892 + 0.893083i \(0.648537\pi\)
\(132\) −6.97954 −0.0528753
\(133\) 197.717 108.492i 1.48660 0.815726i
\(134\) 17.3576 0.129534
\(135\) −132.394 + 51.8202i −0.980696 + 0.383854i
\(136\) 1.41008i 0.0103682i
\(137\) 151.827i 1.10822i −0.832443 0.554111i \(-0.813058\pi\)
0.832443 0.554111i \(-0.186942\pi\)
\(138\) −11.1371 −0.0807033
\(139\) 80.1865i 0.576882i −0.957498 0.288441i \(-0.906863\pi\)
0.957498 0.288441i \(-0.0931368\pi\)
\(140\) −53.7253 44.8730i −0.383752 0.320522i
\(141\) 148.467 1.05295
\(142\) 63.1339i 0.444605i
\(143\) −16.4699 −0.115174
\(144\) −18.7151 −0.129966
\(145\) −181.755 + 71.1407i −1.25348 + 0.490625i
\(146\) 144.862i 0.992207i
\(147\) −54.7154 + 85.9155i −0.372213 + 0.584459i
\(148\) 32.1240i 0.217054i
\(149\) 91.3576 0.613138 0.306569 0.951848i \(-0.400819\pi\)
0.306569 + 0.951848i \(0.400819\pi\)
\(150\) 49.8901 + 53.9676i 0.332601 + 0.359784i
\(151\) −174.467 −1.15541 −0.577704 0.816246i \(-0.696051\pi\)
−0.577704 + 0.816246i \(0.696051\pi\)
\(152\) −91.1268 −0.599518
\(153\) −2.33255 −0.0152454
\(154\) −14.5698 + 7.99473i −0.0946088 + 0.0519138i
\(155\) −45.4302 116.068i −0.293098 0.748828i
\(156\) 40.7878 0.261460
\(157\) 38.5839 0.245757 0.122879 0.992422i \(-0.460787\pi\)
0.122879 + 0.992422i \(0.460787\pi\)
\(158\) 187.233i 1.18502i
\(159\) 172.611i 1.08560i
\(160\) 10.3092 + 26.3386i 0.0644323 + 0.164616i
\(161\) −23.2485 + 12.7570i −0.144401 + 0.0792357i
\(162\) 24.0416i 0.148405i
\(163\) 291.379i 1.78760i −0.448462 0.893802i \(-0.648028\pi\)
0.448462 0.893802i \(-0.351972\pi\)
\(164\) 142.281i 0.867569i
\(165\) 16.2485 6.35983i 0.0984760 0.0385444i
\(166\) 12.3446i 0.0743651i
\(167\) −205.458 −1.23029 −0.615145 0.788414i \(-0.710902\pi\)
−0.615145 + 0.788414i \(0.710902\pi\)
\(168\) 36.0821 19.7990i 0.214774 0.117851i
\(169\) −72.7515 −0.430482
\(170\) 1.28488 + 3.28270i 0.00755812 + 0.0193100i
\(171\) 150.742i 0.881531i
\(172\) 75.4590i 0.438715i
\(173\) −173.102 −1.00059 −0.500294 0.865856i \(-0.666775\pi\)
−0.500294 + 0.865856i \(0.666775\pi\)
\(174\) 114.759i 0.659535i
\(175\) 165.963 + 55.5104i 0.948358 + 0.317202i
\(176\) 6.71512 0.0381541
\(177\) 75.7673i 0.428064i
\(178\) −76.4909 −0.429724
\(179\) −14.0727 −0.0786183 −0.0393092 0.999227i \(-0.512516\pi\)
−0.0393092 + 0.999227i \(0.512516\pi\)
\(180\) 43.5692 17.0534i 0.242051 0.0947412i
\(181\) 170.269i 0.940714i −0.882476 0.470357i \(-0.844125\pi\)
0.882476 0.470357i \(-0.155875\pi\)
\(182\) 85.1443 46.7204i 0.467826 0.256706i
\(183\) 104.857i 0.572991i
\(184\) 10.7151 0.0582343
\(185\) −29.2718 74.7855i −0.158226 0.404246i
\(186\) 73.2849 0.394005
\(187\) 0.836937 0.00447560
\(188\) −142.842 −0.759797
\(189\) −95.7515 174.500i −0.506621 0.923278i
\(190\) 212.145 83.0357i 1.11655 0.437030i
\(191\) 151.254 0.791908 0.395954 0.918270i \(-0.370414\pi\)
0.395954 + 0.918270i \(0.370414\pi\)
\(192\) −16.6300 −0.0866148
\(193\) 336.686i 1.74449i 0.489074 + 0.872243i \(0.337335\pi\)
−0.489074 + 0.872243i \(0.662665\pi\)
\(194\) 59.0225i 0.304240i
\(195\) −94.9550 + 37.1663i −0.486949 + 0.190596i
\(196\) 52.6424 82.6606i 0.268584 0.421738i
\(197\) 2.72564i 0.0138358i 0.999976 + 0.00691788i \(0.00220205\pi\)
−0.999976 + 0.00691788i \(0.997798\pi\)
\(198\) 11.1081i 0.0561017i
\(199\) 87.4762i 0.439579i 0.975547 + 0.219790i \(0.0705371\pi\)
−0.975547 + 0.219790i \(0.929463\pi\)
\(200\) −48.0000 51.9230i −0.240000 0.259615i
\(201\) 25.5139i 0.126935i
\(202\) 146.999 0.727720
\(203\) −131.451 239.559i −0.647542 1.18009i
\(204\) −2.07268 −0.0101602
\(205\) 129.648 + 331.234i 0.632431 + 1.61578i
\(206\) 71.8457i 0.348766i
\(207\) 17.7249i 0.0856277i
\(208\) −39.2425 −0.188666
\(209\) 54.0872i 0.258791i
\(210\) −65.9589 + 78.9709i −0.314090 + 0.376052i
\(211\) −14.6119 −0.0692509 −0.0346254 0.999400i \(-0.511024\pi\)
−0.0346254 + 0.999400i \(0.511024\pi\)
\(212\) 166.071i 0.783356i
\(213\) 92.8007 0.435684
\(214\) −156.218 −0.729991
\(215\) 68.7590 + 175.670i 0.319809 + 0.817071i
\(216\) 80.4258i 0.372342i
\(217\) 152.982 83.9443i 0.704985 0.386840i
\(218\) 199.661i 0.915876i
\(219\) −212.933 −0.972298
\(220\) −15.6330 + 6.11889i −0.0710589 + 0.0278131i
\(221\) −4.89098 −0.0221311
\(222\) 47.2192 0.212699
\(223\) 129.964 0.582800 0.291400 0.956601i \(-0.405879\pi\)
0.291400 + 0.956601i \(0.405879\pi\)
\(224\) −34.7151 + 19.0489i −0.154978 + 0.0850397i
\(225\) −85.8910 + 79.4015i −0.381738 + 0.352896i
\(226\) −116.145 −0.513918
\(227\) 133.276 0.587119 0.293559 0.955941i \(-0.405160\pi\)
0.293559 + 0.955941i \(0.405160\pi\)
\(228\) 133.947i 0.587489i
\(229\) 220.579i 0.963228i −0.876383 0.481614i \(-0.840051\pi\)
0.876383 0.481614i \(-0.159949\pi\)
\(230\) −24.9451 + 9.76373i −0.108457 + 0.0424510i
\(231\) 11.7515 + 21.4161i 0.0508721 + 0.0927104i
\(232\) 110.411i 0.475911i
\(233\) 216.983i 0.931258i −0.884980 0.465629i \(-0.845828\pi\)
0.884980 0.465629i \(-0.154172\pi\)
\(234\) 64.9149i 0.277414i
\(235\) 332.539 130.159i 1.41506 0.553868i
\(236\) 72.8969i 0.308885i
\(237\) 275.214 1.16124
\(238\) −4.32671 + 2.37415i −0.0181794 + 0.00997543i
\(239\) −315.897 −1.32174 −0.660872 0.750499i \(-0.729813\pi\)
−0.660872 + 0.750499i \(0.729813\pi\)
\(240\) 38.7151 15.1535i 0.161313 0.0631394i
\(241\) 228.001i 0.946064i 0.881045 + 0.473032i \(0.156840\pi\)
−0.881045 + 0.473032i \(0.843160\pi\)
\(242\) 167.134i 0.690637i
\(243\) 220.575 0.907714
\(244\) 100.885i 0.413462i
\(245\) −47.2316 + 240.404i −0.192782 + 0.981242i
\(246\) −209.140 −0.850161
\(247\) 316.081i 1.27968i
\(248\) −70.5085 −0.284308
\(249\) −18.1454 −0.0728729
\(250\) 159.058 + 77.1399i 0.636232 + 0.308560i
\(251\) 83.9638i 0.334517i −0.985913 0.167259i \(-0.946509\pi\)
0.985913 0.167259i \(-0.0534915\pi\)
\(252\) 31.5107 + 57.4257i 0.125042 + 0.227880i
\(253\) 6.35983i 0.0251377i
\(254\) −110.788 −0.436172
\(255\) 4.82525 1.88865i 0.0189225 0.00740646i
\(256\) 16.0000 0.0625000
\(257\) −174.597 −0.679367 −0.339683 0.940540i \(-0.610320\pi\)
−0.339683 + 0.940540i \(0.610320\pi\)
\(258\) −110.917 −0.429912
\(259\) 98.5698 54.0872i 0.380578 0.208831i
\(260\) 91.3576 35.7582i 0.351375 0.137532i
\(261\) 182.642 0.699779
\(262\) −330.909 −1.26301
\(263\) 151.672i 0.576701i 0.957525 + 0.288350i \(0.0931068\pi\)
−0.957525 + 0.288350i \(0.906893\pi\)
\(264\) 9.87056i 0.0373885i
\(265\) 151.326 + 386.618i 0.571042 + 1.45894i
\(266\) 153.430 + 279.615i 0.576805 + 1.05118i
\(267\) 112.434i 0.421102i
\(268\) 24.5473i 0.0915944i
\(269\) 440.120i 1.63613i −0.575123 0.818067i \(-0.695046\pi\)
0.575123 0.818067i \(-0.304954\pi\)
\(270\) −73.2849 187.233i −0.271425 0.693456i
\(271\) 376.269i 1.38845i −0.719760 0.694223i \(-0.755748\pi\)
0.719760 0.694223i \(-0.244252\pi\)
\(272\) 1.99415 0.00733145
\(273\) −68.6744 125.154i −0.251555 0.458439i
\(274\) 214.715 0.783632
\(275\) 30.8183 28.4898i 0.112067 0.103599i
\(276\) 15.7502i 0.0570658i
\(277\) 333.960i 1.20563i −0.797880 0.602816i \(-0.794045\pi\)
0.797880 0.602816i \(-0.205955\pi\)
\(278\) 113.401 0.407917
\(279\) 116.635i 0.418047i
\(280\) 63.4601 75.9791i 0.226643 0.271354i
\(281\) 378.612 1.34737 0.673687 0.739017i \(-0.264710\pi\)
0.673687 + 0.739017i \(0.264710\pi\)
\(282\) 209.963i 0.744551i
\(283\) 279.447 0.987447 0.493723 0.869619i \(-0.335636\pi\)
0.493723 + 0.869619i \(0.335636\pi\)
\(284\) −89.2849 −0.314383
\(285\) −122.054 311.833i −0.428261 1.09415i
\(286\) 23.2919i 0.0814404i
\(287\) −436.578 + 239.559i −1.52118 + 0.834701i
\(288\) 26.4672i 0.0918999i
\(289\) −288.751 −0.999140
\(290\) −100.608 257.040i −0.346924 0.886346i
\(291\) 86.7573 0.298135
\(292\) 204.866 0.701596
\(293\) 235.954 0.805303 0.402651 0.915353i \(-0.368089\pi\)
0.402651 + 0.915353i \(0.368089\pi\)
\(294\) −121.503 77.3792i −0.413275 0.263195i
\(295\) −66.4244 169.706i −0.225167 0.575273i
\(296\) −45.4302 −0.153481
\(297\) −47.7358 −0.160727
\(298\) 129.199i 0.433554i
\(299\) 37.1663i 0.124302i
\(300\) −76.3217 + 70.5553i −0.254406 + 0.235184i
\(301\) −231.539 + 127.050i −0.769233 + 0.422094i
\(302\) 246.733i 0.816997i
\(303\) 216.075i 0.713117i
\(304\) 128.873i 0.423924i
\(305\) −91.9273 234.862i −0.301401 0.770040i
\(306\) 3.29873i 0.0107802i
\(307\) −425.450 −1.38583 −0.692915 0.721019i \(-0.743674\pi\)
−0.692915 + 0.721019i \(0.743674\pi\)
\(308\) −11.3063 20.6048i −0.0367086 0.0668986i
\(309\) 105.606 0.341767
\(310\) 164.145 64.2481i 0.529501 0.207252i
\(311\) 199.881i 0.642704i −0.946960 0.321352i \(-0.895863\pi\)
0.946960 0.321352i \(-0.104137\pi\)
\(312\) 57.6827i 0.184880i
\(313\) −412.243 −1.31707 −0.658535 0.752550i \(-0.728824\pi\)
−0.658535 + 0.752550i \(0.728824\pi\)
\(314\) 54.5658i 0.173776i
\(315\) −125.684 104.976i −0.398998 0.333256i
\(316\) −264.788 −0.837936
\(317\) 107.891i 0.340351i 0.985414 + 0.170176i \(0.0544335\pi\)
−0.985414 + 0.170176i \(0.945566\pi\)
\(318\) −244.109 −0.767637
\(319\) −65.5334 −0.205434
\(320\) −37.2484 + 14.5794i −0.116401 + 0.0455605i
\(321\) 229.625i 0.715343i
\(322\) −18.0411 32.8784i −0.0560281 0.102107i
\(323\) 16.0620i 0.0497276i
\(324\) 34.0000 0.104938
\(325\) −180.099 + 166.492i −0.554152 + 0.512283i
\(326\) 412.073 1.26403
\(327\) 293.482 0.897499
\(328\) 201.216 0.613464
\(329\) 240.503 + 438.298i 0.731012 + 1.33221i
\(330\) 8.99416 + 22.9789i 0.0272550 + 0.0696331i
\(331\) −38.0727 −0.115023 −0.0575116 0.998345i \(-0.518317\pi\)
−0.0575116 + 0.998345i \(0.518317\pi\)
\(332\) 17.4579 0.0525841
\(333\) 75.1506i 0.225678i
\(334\) 290.562i 0.869946i
\(335\) −22.3678 57.1467i −0.0667694 0.170587i
\(336\) 28.0000 + 51.0278i 0.0833333 + 0.151868i
\(337\) 260.626i 0.773372i −0.922211 0.386686i \(-0.873620\pi\)
0.922211 0.386686i \(-0.126380\pi\)
\(338\) 102.886i 0.304397i
\(339\) 170.722i 0.503605i
\(340\) −4.64244 + 1.81710i −0.0136542 + 0.00534440i
\(341\) 41.8495i 0.122726i
\(342\) −213.181 −0.623337
\(343\) −342.271 22.3530i −0.997874 0.0651691i
\(344\) 106.715 0.310218
\(345\) 14.3517 + 36.6668i 0.0415992 + 0.106280i
\(346\) 244.803i 0.707522i
\(347\) 390.785i 1.12618i 0.826395 + 0.563091i \(0.190388\pi\)
−0.826395 + 0.563091i \(0.809612\pi\)
\(348\) 162.294 0.466362
\(349\) 561.118i 1.60779i 0.594773 + 0.803894i \(0.297242\pi\)
−0.594773 + 0.803894i \(0.702758\pi\)
\(350\) −78.5036 + 234.707i −0.224296 + 0.670590i
\(351\) 278.964 0.794768
\(352\) 9.49661i 0.0269790i
\(353\) 254.916 0.722143 0.361071 0.932538i \(-0.382411\pi\)
0.361071 + 0.932538i \(0.382411\pi\)
\(354\) 107.151 0.302687
\(355\) 207.857 81.3573i 0.585514 0.229176i
\(356\) 108.174i 0.303861i
\(357\) 3.48977 + 6.35983i 0.00977527 + 0.0178147i
\(358\) 19.9018i 0.0555915i
\(359\) 36.9332 0.102878 0.0514389 0.998676i \(-0.483619\pi\)
0.0514389 + 0.998676i \(0.483619\pi\)
\(360\) 24.1172 + 61.6162i 0.0669922 + 0.171156i
\(361\) −677.012 −1.87538
\(362\) 240.797 0.665185
\(363\) −245.671 −0.676779
\(364\) 66.0727 + 120.412i 0.181518 + 0.330803i
\(365\) −476.933 + 186.676i −1.30667 + 0.511442i
\(366\) 148.291 0.405166
\(367\) 267.483 0.728835 0.364418 0.931236i \(-0.381268\pi\)
0.364418 + 0.931236i \(0.381268\pi\)
\(368\) 15.1535i 0.0411779i
\(369\) 332.852i 0.902037i
\(370\) 105.763 41.3965i 0.285845 0.111882i
\(371\) −509.576 + 279.615i −1.37352 + 0.753678i
\(372\) 103.640i 0.278603i
\(373\) 126.971i 0.340404i −0.985409 0.170202i \(-0.945558\pi\)
0.985409 0.170202i \(-0.0544421\pi\)
\(374\) 1.18361i 0.00316473i
\(375\) 113.388 233.800i 0.302368 0.623465i
\(376\) 202.009i 0.537258i
\(377\) 382.971 1.01584
\(378\) 246.780 135.413i 0.652856 0.358235i
\(379\) 519.939 1.37187 0.685935 0.727662i \(-0.259393\pi\)
0.685935 + 0.727662i \(0.259393\pi\)
\(380\) 117.430 + 300.019i 0.309027 + 0.789523i
\(381\) 162.847i 0.427420i
\(382\) 213.906i 0.559963i
\(383\) 393.703 1.02795 0.513973 0.857806i \(-0.328173\pi\)
0.513973 + 0.857806i \(0.328173\pi\)
\(384\) 23.5184i 0.0612459i
\(385\) 45.0965 + 37.6660i 0.117134 + 0.0978337i
\(386\) −476.145 −1.23354
\(387\) 176.528i 0.456145i
\(388\) −83.4705 −0.215130
\(389\) 106.031 0.272572 0.136286 0.990670i \(-0.456483\pi\)
0.136286 + 0.990670i \(0.456483\pi\)
\(390\) −52.5611 134.287i −0.134772 0.344325i
\(391\) 1.88865i 0.00483030i
\(392\) 116.900 + 74.4477i 0.298214 + 0.189917i
\(393\) 486.403i 1.23767i
\(394\) −3.85464 −0.00978335
\(395\) 616.432 241.277i 1.56059 0.610829i
\(396\) 15.7093 0.0396699
\(397\) −391.625 −0.986460 −0.493230 0.869899i \(-0.664184\pi\)
−0.493230 + 0.869899i \(0.664184\pi\)
\(398\) −123.710 −0.310829
\(399\) 411.006 225.527i 1.03009 0.565231i
\(400\) 73.4302 67.8823i 0.183576 0.169706i
\(401\) 41.1090 0.102516 0.0512581 0.998685i \(-0.483677\pi\)
0.0512581 + 0.998685i \(0.483677\pi\)
\(402\) 36.0821 0.0897565
\(403\) 244.564i 0.606860i
\(404\) 207.889i 0.514576i
\(405\) −79.1528 + 30.9812i −0.195439 + 0.0764967i
\(406\) 338.788 185.900i 0.834453 0.457881i
\(407\) 26.9646i 0.0662521i
\(408\) 2.93121i 0.00718434i
\(409\) 511.846i 1.25146i 0.780041 + 0.625729i \(0.215198\pi\)
−0.780041 + 0.625729i \(0.784802\pi\)
\(410\) −468.436 + 183.350i −1.14253 + 0.447196i
\(411\) 315.610i 0.767908i
\(412\) −101.605 −0.246614
\(413\) 223.678 122.736i 0.541592 0.297183i
\(414\) 25.0668 0.0605479
\(415\) −40.6424 + 15.9078i −0.0979336 + 0.0383321i
\(416\) 55.4973i 0.133407i
\(417\) 166.688i 0.399732i
\(418\) 76.4909 0.182993
\(419\) 82.5281i 0.196965i −0.995139 0.0984823i \(-0.968601\pi\)
0.995139 0.0984823i \(-0.0313988\pi\)
\(420\) −111.682 93.2800i −0.265909 0.222095i
\(421\) −227.400 −0.540142 −0.270071 0.962840i \(-0.587047\pi\)
−0.270071 + 0.962840i \(0.587047\pi\)
\(422\) 20.6644i 0.0489678i
\(423\) −334.163 −0.789983
\(424\) 234.860 0.553916
\(425\) 9.15195 8.46048i 0.0215340 0.0199070i
\(426\) 131.240i 0.308075i
\(427\) 309.556 169.860i 0.724956 0.397798i
\(428\) 220.926i 0.516181i
\(429\) −34.2369 −0.0798062
\(430\) −248.435 + 97.2400i −0.577757 + 0.226139i
\(431\) 254.964 0.591563 0.295782 0.955256i \(-0.404420\pi\)
0.295782 + 0.955256i \(0.404420\pi\)
\(432\) −113.739 −0.263285
\(433\) −675.154 −1.55925 −0.779624 0.626248i \(-0.784590\pi\)
−0.779624 + 0.626248i \(0.784590\pi\)
\(434\) 118.715 + 216.349i 0.273537 + 0.498500i
\(435\) −377.824 + 147.884i −0.868561 + 0.339963i
\(436\) −282.363 −0.647622
\(437\) 122.054 0.279300
\(438\) 301.133i 0.687518i
\(439\) 3.77730i 0.00860432i −0.999991 0.00430216i \(-0.998631\pi\)
0.999991 0.00430216i \(-0.00136942\pi\)
\(440\) −8.65342 22.1083i −0.0196669 0.0502462i
\(441\) 123.151 193.375i 0.279254 0.438493i
\(442\) 6.91689i 0.0156491i
\(443\) 273.500i 0.617382i 0.951162 + 0.308691i \(0.0998909\pi\)
−0.951162 + 0.308691i \(0.900109\pi\)
\(444\) 66.7780i 0.150401i
\(445\) 98.5698 + 251.833i 0.221505 + 0.565916i
\(446\) 183.797i 0.412102i
\(447\) 189.910 0.424854
\(448\) −26.9392 49.0946i −0.0601322 0.109586i
\(449\) 232.042 0.516798 0.258399 0.966038i \(-0.416805\pi\)
0.258399 + 0.966038i \(0.416805\pi\)
\(450\) −112.291 121.468i −0.249535 0.269929i
\(451\) 119.430i 0.264810i
\(452\) 164.254i 0.363395i
\(453\) −362.673 −0.800603
\(454\) 188.481i 0.415156i
\(455\) −263.540 220.117i −0.579208 0.483773i
\(456\) −189.430 −0.415417
\(457\) 371.243i 0.812349i −0.913796 0.406174i \(-0.866863\pi\)
0.913796 0.406174i \(-0.133137\pi\)
\(458\) 311.946 0.681105
\(459\) −14.1759 −0.0308842
\(460\) −13.8080 35.2776i −0.0300174 0.0766905i
\(461\) 12.2378i 0.0265462i 0.999912 + 0.0132731i \(0.00422508\pi\)
−0.999912 + 0.0132731i \(0.995775\pi\)
\(462\) −30.2870 + 16.6191i −0.0655562 + 0.0359720i
\(463\) 266.232i 0.575015i 0.957778 + 0.287507i \(0.0928266\pi\)
−0.957778 + 0.287507i \(0.907173\pi\)
\(464\) −156.145 −0.336520
\(465\) −94.4383 241.277i −0.203093 0.518876i
\(466\) 306.860 0.658499
\(467\) −287.932 −0.616556 −0.308278 0.951296i \(-0.599753\pi\)
−0.308278 + 0.951296i \(0.599753\pi\)
\(468\) −91.8036 −0.196162
\(469\) 75.3212 41.3303i 0.160600 0.0881243i
\(470\) 184.073 + 470.282i 0.391644 + 1.00060i
\(471\) 80.2064 0.170290
\(472\) −103.092 −0.218415
\(473\) 63.3395i 0.133910i
\(474\) 389.212i 0.821122i
\(475\) −546.761 591.447i −1.15108 1.24515i
\(476\) −3.35756 6.11889i −0.00705370 0.0128548i
\(477\) 388.506i 0.814478i
\(478\) 446.746i 0.934614i
\(479\) 235.159i 0.490937i −0.969405 0.245468i \(-0.921058\pi\)
0.969405 0.245468i \(-0.0789417\pi\)
\(480\) 21.4302 + 54.7514i 0.0446463 + 0.114066i
\(481\) 157.579i 0.327606i
\(482\) −322.443 −0.668968
\(483\) −48.3280 + 26.5186i −0.100058 + 0.0549039i
\(484\) 236.363 0.488354
\(485\) 194.321 76.0592i 0.400662 0.156823i
\(486\) 311.940i 0.641851i
\(487\) 291.379i 0.598315i −0.954204 0.299157i \(-0.903294\pi\)
0.954204 0.299157i \(-0.0967056\pi\)
\(488\) −142.673 −0.292362
\(489\) 605.706i 1.23866i
\(490\) −339.983 66.7956i −0.693843 0.136318i
\(491\) 610.260 1.24289 0.621446 0.783457i \(-0.286545\pi\)
0.621446 + 0.783457i \(0.286545\pi\)
\(492\) 295.768i 0.601154i
\(493\) −19.4611 −0.0394749
\(494\) −447.006 −0.904870
\(495\) −36.5716 + 14.3145i −0.0738820 + 0.0289181i
\(496\) 99.7140i 0.201036i
\(497\) 150.329 + 273.963i 0.302473 + 0.551233i
\(498\) 25.6614i 0.0515289i
\(499\) 49.6788 0.0995567 0.0497783 0.998760i \(-0.484149\pi\)
0.0497783 + 0.998760i \(0.484149\pi\)
\(500\) −109.092 + 224.942i −0.218185 + 0.449884i
\(501\) −427.097 −0.852490
\(502\) 118.743 0.236539
\(503\) 441.083 0.876904 0.438452 0.898755i \(-0.355527\pi\)
0.438452 + 0.898755i \(0.355527\pi\)
\(504\) −81.2122 + 44.5628i −0.161135 + 0.0884183i
\(505\) −189.430 483.969i −0.375109 0.958355i
\(506\) −8.99416 −0.0177750
\(507\) −151.232 −0.298289
\(508\) 156.678i 0.308420i
\(509\) 420.460i 0.826051i 0.910719 + 0.413026i \(0.135528\pi\)
−0.910719 + 0.413026i \(0.864472\pi\)
\(510\) 2.67095 + 6.82393i 0.00523716 + 0.0133803i
\(511\) −344.933 628.614i −0.675016 1.23016i
\(512\) 22.6274i 0.0441942i
\(513\) 916.119i 1.78581i
\(514\) 246.918i 0.480385i
\(515\) 236.539 92.5837i 0.459300 0.179774i
\(516\) 156.861i 0.303994i
\(517\) 119.900 0.231915
\(518\) 76.4909 + 139.399i 0.147666 + 0.269109i
\(519\) −359.836 −0.693325
\(520\) 50.5698 + 129.199i 0.0972495 + 0.248460i
\(521\) 698.451i 1.34060i −0.742092 0.670298i \(-0.766166\pi\)
0.742092 0.670298i \(-0.233834\pi\)
\(522\) 258.295i 0.494819i
\(523\) 434.940 0.831625 0.415813 0.909450i \(-0.363497\pi\)
0.415813 + 0.909450i \(0.363497\pi\)
\(524\) 467.976i 0.893083i
\(525\) 344.996 + 115.393i 0.657134 + 0.219795i
\(526\) −214.497 −0.407789
\(527\) 12.4278i 0.0235822i
\(528\) 13.9591 0.0264377
\(529\) 514.648 0.972870
\(530\) −546.761 + 214.007i −1.03162 + 0.403788i
\(531\) 170.534i 0.321157i
\(532\) −395.435 + 216.983i −0.743298 + 0.407863i
\(533\) 697.935i 1.30945i
\(534\) −159.006 −0.297764
\(535\) 201.310 + 514.320i 0.376280 + 0.961346i
\(536\) −34.7151 −0.0647670
\(537\) −29.2536 −0.0544761
\(538\) 622.424 1.15692
\(539\) −44.1875 + 69.3845i −0.0819806 + 0.128728i
\(540\) 264.788 103.640i 0.490348 0.191927i
\(541\) 769.254 1.42191 0.710956 0.703237i \(-0.248262\pi\)
0.710956 + 0.703237i \(0.248262\pi\)
\(542\) 532.125 0.981780
\(543\) 353.948i 0.651838i
\(544\) 2.82016i 0.00518412i
\(545\) 657.349 257.293i 1.20614 0.472096i
\(546\) 176.994 97.1203i 0.324165 0.177876i
\(547\) 242.885i 0.444031i 0.975043 + 0.222016i \(0.0712636\pi\)
−0.975043 + 0.222016i \(0.928736\pi\)
\(548\) 303.653i 0.554111i
\(549\) 236.009i 0.429889i
\(550\) 40.2907 + 43.5837i 0.0732558 + 0.0792430i
\(551\) 1257.68i 2.28254i
\(552\) 22.2741 0.0403516
\(553\) 445.823 + 812.478i 0.806191 + 1.46922i
\(554\) 472.291 0.852510
\(555\) −60.8488 155.461i −0.109637 0.280109i
\(556\) 160.373i 0.288441i
\(557\) 766.109i 1.37542i 0.725985 + 0.687710i \(0.241384\pi\)
−0.725985 + 0.687710i \(0.758616\pi\)
\(558\) −164.947 −0.295604
\(559\) 370.150i 0.662165i
\(560\) 107.451 + 89.7461i 0.191876 + 0.160261i
\(561\) 1.73979 0.00310122
\(562\) 535.438i 0.952737i
\(563\) −586.605 −1.04193 −0.520963 0.853579i \(-0.674427\pi\)
−0.520963 + 0.853579i \(0.674427\pi\)
\(564\) −296.933 −0.526477
\(565\) 149.670 + 382.388i 0.264903 + 0.676793i
\(566\) 395.198i 0.698230i
\(567\) −57.2458 104.326i −0.100963 0.183996i
\(568\) 126.268i 0.222303i
\(569\) −744.375 −1.30822 −0.654108 0.756401i \(-0.726956\pi\)
−0.654108 + 0.756401i \(0.726956\pi\)
\(570\) 440.998 172.611i 0.773681 0.302826i
\(571\) −323.503 −0.566555 −0.283278 0.959038i \(-0.591422\pi\)
−0.283278 + 0.959038i \(0.591422\pi\)
\(572\) 32.9398 0.0575870
\(573\) 314.421 0.548727
\(574\) −338.788 617.414i −0.590223 1.07563i
\(575\) 64.2907 + 69.5452i 0.111810 + 0.120948i
\(576\) 37.4302 0.0649831
\(577\) −394.936 −0.684465 −0.342232 0.939615i \(-0.611183\pi\)
−0.342232 + 0.939615i \(0.611183\pi\)
\(578\) 408.356i 0.706499i
\(579\) 699.887i 1.20879i
\(580\) 363.510 142.281i 0.626742 0.245313i
\(581\) −29.3939 53.5681i −0.0505919 0.0921998i
\(582\) 122.693i 0.210813i
\(583\) 139.399i 0.239106i
\(584\) 289.724i 0.496103i
\(585\) 213.721 83.6524i 0.365335 0.142996i
\(586\) 333.689i 0.569435i
\(587\) −63.9610 −0.108962 −0.0544812 0.998515i \(-0.517351\pi\)
−0.0544812 + 0.998515i \(0.517351\pi\)
\(588\) 109.431 171.831i 0.186107 0.292230i
\(589\) −803.151 −1.36358
\(590\) 240.000 93.9383i 0.406780 0.159217i
\(591\) 5.66594i 0.00958704i
\(592\) 64.2481i 0.108527i
\(593\) −310.432 −0.523495 −0.261747 0.965136i \(-0.584299\pi\)
−0.261747 + 0.965136i \(0.584299\pi\)
\(594\) 67.5086i 0.113651i
\(595\) 13.3921 + 11.1855i 0.0225077 + 0.0187991i
\(596\) −182.715 −0.306569
\(597\) 181.842i 0.304592i
\(598\) 52.5611 0.0878947
\(599\) −429.885 −0.717671 −0.358836 0.933401i \(-0.616826\pi\)
−0.358836 + 0.933401i \(0.616826\pi\)
\(600\) −99.7802 107.935i −0.166300 0.179892i
\(601\) 67.8163i 0.112839i −0.998407 0.0564196i \(-0.982032\pi\)
0.998407 0.0564196i \(-0.0179684\pi\)
\(602\) −179.676 327.446i −0.298466 0.543930i
\(603\) 57.4257i 0.0952333i
\(604\) 348.933 0.577704
\(605\) −550.260 + 215.377i −0.909520 + 0.355995i
\(606\) 305.576 0.504250
\(607\) 389.350 0.641433 0.320716 0.947175i \(-0.396076\pi\)
0.320716 + 0.947175i \(0.396076\pi\)
\(608\) 182.254 0.299759
\(609\) −273.254 497.985i −0.448694 0.817709i
\(610\) 332.145 130.005i 0.544501 0.213123i
\(611\) −700.685 −1.14678
\(612\) 4.66511 0.00762272
\(613\) 822.472i 1.34172i −0.741586 0.670858i \(-0.765926\pi\)
0.741586 0.670858i \(-0.234074\pi\)
\(614\) 601.677i 0.979930i
\(615\) 269.507 + 688.555i 0.438223 + 1.11960i
\(616\) 29.1395 15.9895i 0.0473044 0.0259569i
\(617\) 507.916i 0.823203i 0.911364 + 0.411602i \(0.135031\pi\)
−0.911364 + 0.411602i \(0.864969\pi\)
\(618\) 149.350i 0.241666i
\(619\) 167.210i 0.270129i −0.990837 0.135064i \(-0.956876\pi\)
0.990837 0.135064i \(-0.0431242\pi\)
\(620\) 90.8605 + 232.137i 0.146549 + 0.374414i
\(621\) 107.722i 0.173465i
\(622\) 282.674 0.454460
\(623\) −331.924 + 182.133i −0.532783 + 0.292349i
\(624\) −81.5756 −0.130730
\(625\) 49.0000 623.076i 0.0784000 0.996922i
\(626\) 583.000i 0.931309i
\(627\) 112.434i 0.179321i
\(628\) −77.1677 −0.122879
\(629\) 8.00754i 0.0127306i
\(630\) 148.458 177.745i 0.235647 0.282134i
\(631\) 538.696 0.853718 0.426859 0.904318i \(-0.359620\pi\)
0.426859 + 0.904318i \(0.359620\pi\)
\(632\) 374.466i 0.592510i
\(633\) −30.3746 −0.0479852
\(634\) −152.581 −0.240665
\(635\) 142.766 + 364.749i 0.224829 + 0.574408i
\(636\) 345.222i 0.542801i
\(637\) 258.228 405.476i 0.405381 0.636541i
\(638\) 92.6783i 0.145264i
\(639\) −208.872 −0.326873
\(640\) −20.6183 52.6772i −0.0322162 0.0823081i
\(641\) 520.788 0.812461 0.406231 0.913771i \(-0.366843\pi\)
0.406231 + 0.913771i \(0.366843\pi\)
\(642\) −324.739 −0.505824
\(643\) −547.317 −0.851192 −0.425596 0.904913i \(-0.639936\pi\)
−0.425596 + 0.904913i \(0.639936\pi\)
\(644\) 46.4971 25.5139i 0.0722004 0.0396179i
\(645\) 142.933 + 365.175i 0.221602 + 0.566163i
\(646\) 22.7151 0.0351627
\(647\) −639.806 −0.988881 −0.494441 0.869211i \(-0.664627\pi\)
−0.494441 + 0.869211i \(0.664627\pi\)
\(648\) 48.0833i 0.0742026i
\(649\) 61.1889i 0.0942818i
\(650\) −235.455 254.699i −0.362239 0.391844i
\(651\) 318.012 174.500i 0.488497 0.268048i
\(652\) 582.759i 0.893802i
\(653\) 386.397i 0.591726i −0.955230 0.295863i \(-0.904393\pi\)
0.955230 0.295863i \(-0.0956071\pi\)
\(654\) 415.046i 0.634627i
\(655\) 426.424 + 1089.46i 0.651030 + 1.66330i
\(656\) 284.563i 0.433785i
\(657\) 479.262 0.729470
\(658\) −619.847 + 340.122i −0.942016 + 0.516903i
\(659\) −684.042 −1.03800 −0.519000 0.854774i \(-0.673696\pi\)
−0.519000 + 0.854774i \(0.673696\pi\)
\(660\) −32.4971 + 12.7197i −0.0492380 + 0.0192722i
\(661\) 36.5809i 0.0553417i 0.999617 + 0.0276709i \(0.00880903\pi\)
−0.999617 + 0.0276709i \(0.991191\pi\)
\(662\) 53.8429i 0.0813337i
\(663\) −10.1671 −0.0153351
\(664\) 24.6892i 0.0371826i
\(665\) 722.864 865.466i 1.08701 1.30145i
\(666\) −106.279 −0.159578
\(667\) 147.884i 0.221715i
\(668\) 410.917 0.615145
\(669\) 270.164 0.403833
\(670\) 80.8176 31.6328i 0.120623 0.0472131i
\(671\) 84.6817i 0.126202i
\(672\) −72.1642 + 39.5980i −0.107387 + 0.0589256i
\(673\) 85.1447i 0.126515i −0.997997 0.0632575i \(-0.979851\pi\)
0.997997 0.0632575i \(-0.0201490\pi\)
\(674\) 368.581 0.546857
\(675\) −521.994 + 482.555i −0.773324 + 0.714896i
\(676\) 145.503 0.215241
\(677\) −623.768 −0.921371 −0.460686 0.887563i \(-0.652396\pi\)
−0.460686 + 0.887563i \(0.652396\pi\)
\(678\) −241.438 −0.356103
\(679\) 140.539 + 256.122i 0.206980 + 0.377204i
\(680\) −2.56976 6.56540i −0.00377906 0.00965500i
\(681\) 277.048 0.406825
\(682\) 59.1841 0.0867802
\(683\) 898.085i 1.31491i −0.753493 0.657456i \(-0.771632\pi\)
0.753493 0.657456i \(-0.228368\pi\)
\(684\) 301.484i 0.440766i
\(685\) −276.692 706.912i −0.403930 1.03199i
\(686\) 31.6119 484.044i 0.0460815 0.705604i
\(687\) 458.530i 0.667438i
\(688\) 150.918i 0.219358i
\(689\) 814.633i 1.18234i
\(690\) −51.8546 + 20.2964i −0.0751517 + 0.0294151i
\(691\) 487.503i 0.705504i 0.935717 + 0.352752i \(0.114754\pi\)
−0.935717 + 0.352752i \(0.885246\pi\)
\(692\) 346.203 0.500294
\(693\) −26.4497 48.2026i −0.0381670 0.0695564i
\(694\) −552.654 −0.796332
\(695\) −146.134 373.352i −0.210264 0.537198i
\(696\) 229.518i 0.329768i
\(697\) 35.4664i 0.0508843i
\(698\) −793.540 −1.13688
\(699\) 451.055i 0.645286i
\(700\) −331.925 111.021i −0.474179 0.158601i
\(701\) 399.170 0.569429 0.284715 0.958612i \(-0.408101\pi\)
0.284715 + 0.958612i \(0.408101\pi\)
\(702\) 394.514i 0.561986i
\(703\) −517.489 −0.736115
\(704\) −13.4302 −0.0190770
\(705\) 691.267 270.569i 0.980521 0.383785i
\(706\) 360.506i 0.510632i
\(707\) 637.888 350.022i 0.902246 0.495081i
\(708\) 151.535i 0.214032i
\(709\) −241.751 −0.340975 −0.170488 0.985360i \(-0.554534\pi\)
−0.170488 + 0.985360i \(0.554534\pi\)
\(710\) 115.057 + 293.955i 0.162052 + 0.414021i
\(711\) −619.442 −0.871226
\(712\) 152.982 0.214862
\(713\) 94.4383 0.132452
\(714\) −8.99416 + 4.93528i −0.0125969 + 0.00691216i
\(715\) −76.6846 + 30.0151i −0.107251 + 0.0419791i
\(716\) 28.1454 0.0393092
\(717\) −656.672 −0.915860
\(718\) 52.2314i 0.0727456i
\(719\) 544.197i 0.756880i −0.925626 0.378440i \(-0.876461\pi\)
0.925626 0.378440i \(-0.123539\pi\)
\(720\) −87.1385 + 34.1068i −0.121026 + 0.0473706i
\(721\) 171.073 + 311.767i 0.237271 + 0.432409i
\(722\) 957.439i 1.32609i
\(723\) 473.959i 0.655545i
\(724\) 340.539i 0.470357i
\(725\) −716.612 + 662.469i −0.988430 + 0.913750i
\(726\) 347.431i 0.478555i
\(727\) −211.414 −0.290803 −0.145401 0.989373i \(-0.546447\pi\)
−0.145401 + 0.989373i \(0.546447\pi\)
\(728\) −170.289 + 93.4409i −0.233913 + 0.128353i
\(729\) 611.520 0.838848
\(730\) −264.000 674.485i −0.361644 0.923953i
\(731\) 18.8096i 0.0257313i
\(732\) 209.715i 0.286496i
\(733\) 1085.37 1.48072 0.740359 0.672211i \(-0.234655\pi\)
0.740359 + 0.672211i \(0.234655\pi\)
\(734\) 378.277i 0.515364i
\(735\) −98.1830 + 499.741i −0.133582 + 0.679920i
\(736\) −21.4302 −0.0291172
\(737\) 20.6048i 0.0279576i
\(738\) 470.723 0.637836
\(739\) −671.193 −0.908245 −0.454123 0.890939i \(-0.650047\pi\)
−0.454123 + 0.890939i \(0.650047\pi\)
\(740\) 58.5435 + 149.571i 0.0791129 + 0.202123i
\(741\) 657.054i 0.886713i
\(742\) −395.435 720.649i −0.532931 0.971225i
\(743\) 194.699i 0.262044i −0.991379 0.131022i \(-0.958174\pi\)
0.991379 0.131022i \(-0.0418259\pi\)
\(744\) −146.570 −0.197002
\(745\) 425.365 166.492i 0.570960 0.223479i
\(746\) 179.564 0.240702
\(747\) 40.8409 0.0546732
\(748\) −1.67387 −0.00223780
\(749\) −677.891 + 371.973i −0.905061 + 0.496626i
\(750\) 330.642 + 160.355i 0.440857 + 0.213807i
\(751\) 218.115 0.290433 0.145216 0.989400i \(-0.453612\pi\)
0.145216 + 0.989400i \(0.453612\pi\)
\(752\) 285.684 0.379899
\(753\) 174.540i 0.231793i
\(754\) 541.603i 0.718307i
\(755\) −812.325 + 317.952i −1.07593 + 0.421128i
\(756\) 191.503 + 348.999i 0.253311 + 0.461639i
\(757\) 1248.55i 1.64934i 0.565611 + 0.824672i \(0.308640\pi\)
−0.565611 + 0.824672i \(0.691360\pi\)
\(758\) 735.305i 0.970059i
\(759\) 13.2205i 0.0174184i
\(760\) −424.291 + 166.071i −0.558277 + 0.218515i
\(761\) 947.736i 1.24538i −0.782468 0.622691i \(-0.786039\pi\)
0.782468 0.622691i \(-0.213961\pi\)
\(762\) −230.301 −0.302232
\(763\) 475.415 + 866.407i 0.623087 + 1.13553i
\(764\) −302.509 −0.395954
\(765\) −10.8605 + 4.25089i −0.0141967 + 0.00555673i
\(766\) 556.781i 0.726868i
\(767\) 357.582i 0.466209i
\(768\) 33.2601 0.0433074
\(769\) 127.967i 0.166407i 0.996533 + 0.0832034i \(0.0265151\pi\)
−0.996533 + 0.0832034i \(0.973485\pi\)
\(770\) −53.2677 + 63.7761i −0.0691789 + 0.0828261i
\(771\) −362.945 −0.470746
\(772\) 673.371i 0.872243i
\(773\) 698.585 0.903733 0.451866 0.892086i \(-0.350758\pi\)
0.451866 + 0.892086i \(0.350758\pi\)
\(774\) 249.648 0.322543
\(775\) −423.051 457.626i −0.545872 0.590486i
\(776\) 118.045i 0.152120i
\(777\) 204.902 112.434i 0.263710 0.144703i
\(778\) 149.950i 0.192738i
\(779\) 2292.02 2.94226
\(780\) 189.910 74.3326i 0.243474 0.0952982i
\(781\) 74.9448 0.0959601
\(782\) −2.67095 −0.00341554
\(783\) 1109.99 1.41761
\(784\) −105.285