Properties

Label 1134.3.q.c.1079.2
Level $1134$
Weight $3$
Character 1134.1079
Analytic conductor $30.899$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1134.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(30.8992619785\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.12745506816.5
Defining polynomial: \(x^{8} - 8 x^{6} + 55 x^{4} - 72 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1079.2
Root \(1.00781 + 0.581861i\) of defining polynomial
Character \(\chi\) \(=\) 1134.1079
Dual form 1134.3.q.c.701.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(5.25600 - 3.03455i) q^{5} +(1.32288 - 2.29129i) q^{7} -2.82843i q^{8} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(5.25600 - 3.03455i) q^{5} +(1.32288 - 2.29129i) q^{7} -2.82843i q^{8} -8.58301 q^{10} +(-10.5120 - 6.06910i) q^{11} +(9.29150 + 16.0934i) q^{13} +(-3.24037 + 1.87083i) q^{14} +(-2.00000 + 3.46410i) q^{16} +10.9015i q^{17} +20.0000 q^{19} +(10.5120 + 6.06910i) q^{20} +(8.58301 + 14.8662i) q^{22} +(10.5120 - 6.06910i) q^{23} +(5.91699 - 10.2485i) q^{25} -26.2803i q^{26} +5.29150 q^{28} +(36.2316 + 20.9183i) q^{29} +(-12.5830 - 21.7944i) q^{31} +(4.89898 - 2.82843i) q^{32} +(7.70850 - 13.3515i) q^{34} -16.0573i q^{35} +38.0000 q^{37} +(-24.4949 - 14.1421i) q^{38} +(-8.58301 - 14.8662i) q^{40} +(52.5103 - 30.3169i) q^{41} +(-41.7490 + 72.3114i) q^{43} -24.2764i q^{44} -17.1660 q^{46} +(-14.6969 - 8.48528i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(-14.4936 + 8.36789i) q^{50} +(-18.5830 + 32.1867i) q^{52} -94.0424i q^{53} -73.6680 q^{55} +(-6.48074 - 3.74166i) q^{56} +(-29.5830 - 51.2393i) q^{58} +(50.4179 - 29.1088i) q^{59} +(-7.83399 + 13.5689i) q^{61} +35.5901i q^{62} -8.00000 q^{64} +(97.6722 + 56.3911i) q^{65} +(66.3320 + 114.890i) q^{67} +(-18.8819 + 10.9015i) q^{68} +(-11.3542 + 19.6661i) q^{70} +12.1382i q^{71} -76.9150 q^{73} +(-46.5403 - 26.8701i) q^{74} +(20.0000 + 34.6410i) q^{76} +(-27.8121 + 16.0573i) q^{77} +(-16.8340 + 29.1573i) q^{79} +24.2764i q^{80} -85.7490 q^{82} +(-52.4607 - 30.2882i) q^{83} +(33.0810 + 57.2980i) q^{85} +(102.264 - 59.0420i) q^{86} +(-17.1660 + 29.7324i) q^{88} +4.77506i q^{89} +49.1660 q^{91} +(21.0240 + 12.1382i) q^{92} +(12.0000 + 20.7846i) q^{94} +(105.120 - 60.6910i) q^{95} +(94.2065 - 163.170i) q^{97} +9.89949i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} + O(q^{10}) \) \( 8 q + 8 q^{4} + 16 q^{10} + 32 q^{13} - 16 q^{16} + 160 q^{19} - 16 q^{22} + 132 q^{25} - 16 q^{31} + 104 q^{34} + 304 q^{37} + 16 q^{40} - 80 q^{43} + 32 q^{46} - 28 q^{49} - 64 q^{52} - 928 q^{55} - 152 q^{58} - 232 q^{61} - 64 q^{64} + 192 q^{67} - 112 q^{70} - 192 q^{73} + 160 q^{76} - 304 q^{79} - 432 q^{82} - 328 q^{85} + 32 q^{88} + 224 q^{91} + 96 q^{94} + 288 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 0.707107i −0.612372 0.353553i
\(3\) 0 0
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) 5.25600 3.03455i 1.05120 0.606910i 0.128214 0.991746i \(-0.459075\pi\)
0.922985 + 0.384836i \(0.125742\pi\)
\(6\) 0 0
\(7\) 1.32288 2.29129i 0.188982 0.327327i
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) −8.58301 −0.858301
\(11\) −10.5120 6.06910i −0.955636 0.551736i −0.0608086 0.998149i \(-0.519368\pi\)
−0.894827 + 0.446413i \(0.852701\pi\)
\(12\) 0 0
\(13\) 9.29150 + 16.0934i 0.714731 + 1.23795i 0.963063 + 0.269275i \(0.0867842\pi\)
−0.248332 + 0.968675i \(0.579882\pi\)
\(14\) −3.24037 + 1.87083i −0.231455 + 0.133631i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 10.9015i 0.641262i 0.947204 + 0.320631i \(0.103895\pi\)
−0.947204 + 0.320631i \(0.896105\pi\)
\(18\) 0 0
\(19\) 20.0000 1.05263 0.526316 0.850289i \(-0.323573\pi\)
0.526316 + 0.850289i \(0.323573\pi\)
\(20\) 10.5120 + 6.06910i 0.525600 + 0.303455i
\(21\) 0 0
\(22\) 8.58301 + 14.8662i 0.390137 + 0.675736i
\(23\) 10.5120 6.06910i 0.457043 0.263874i −0.253757 0.967268i \(-0.581666\pi\)
0.710800 + 0.703394i \(0.248333\pi\)
\(24\) 0 0
\(25\) 5.91699 10.2485i 0.236680 0.409941i
\(26\) 26.2803i 1.01078i
\(27\) 0 0
\(28\) 5.29150 0.188982
\(29\) 36.2316 + 20.9183i 1.24937 + 0.721322i 0.970983 0.239148i \(-0.0768680\pi\)
0.278384 + 0.960470i \(0.410201\pi\)
\(30\) 0 0
\(31\) −12.5830 21.7944i −0.405903 0.703045i 0.588523 0.808481i \(-0.299710\pi\)
−0.994426 + 0.105435i \(0.966376\pi\)
\(32\) 4.89898 2.82843i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 7.70850 13.3515i 0.226721 0.392691i
\(35\) 16.0573i 0.458781i
\(36\) 0 0
\(37\) 38.0000 1.02703 0.513514 0.858082i \(-0.328344\pi\)
0.513514 + 0.858082i \(0.328344\pi\)
\(38\) −24.4949 14.1421i −0.644603 0.372161i
\(39\) 0 0
\(40\) −8.58301 14.8662i −0.214575 0.371655i
\(41\) 52.5103 30.3169i 1.28074 0.739435i 0.303756 0.952750i \(-0.401759\pi\)
0.976984 + 0.213314i \(0.0684258\pi\)
\(42\) 0 0
\(43\) −41.7490 + 72.3114i −0.970907 + 1.68166i −0.278079 + 0.960558i \(0.589698\pi\)
−0.692828 + 0.721103i \(0.743636\pi\)
\(44\) 24.2764i 0.551736i
\(45\) 0 0
\(46\) −17.1660 −0.373174
\(47\) −14.6969 8.48528i −0.312701 0.180538i 0.335434 0.942064i \(-0.391117\pi\)
−0.648134 + 0.761526i \(0.724451\pi\)
\(48\) 0 0
\(49\) −3.50000 6.06218i −0.0714286 0.123718i
\(50\) −14.4936 + 8.36789i −0.289872 + 0.167358i
\(51\) 0 0
\(52\) −18.5830 + 32.1867i −0.357365 + 0.618975i
\(53\) 94.0424i 1.77439i −0.461399 0.887193i \(-0.652652\pi\)
0.461399 0.887193i \(-0.347348\pi\)
\(54\) 0 0
\(55\) −73.6680 −1.33942
\(56\) −6.48074 3.74166i −0.115728 0.0668153i
\(57\) 0 0
\(58\) −29.5830 51.2393i −0.510052 0.883436i
\(59\) 50.4179 29.1088i 0.854540 0.493369i −0.00764008 0.999971i \(-0.502432\pi\)
0.862180 + 0.506602i \(0.169099\pi\)
\(60\) 0 0
\(61\) −7.83399 + 13.5689i −0.128426 + 0.222440i −0.923067 0.384639i \(-0.874326\pi\)
0.794641 + 0.607080i \(0.207659\pi\)
\(62\) 35.5901i 0.574034i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) 97.6722 + 56.3911i 1.50265 + 0.867555i
\(66\) 0 0
\(67\) 66.3320 + 114.890i 0.990030 + 1.71478i 0.617000 + 0.786964i \(0.288348\pi\)
0.373031 + 0.927819i \(0.378319\pi\)
\(68\) −18.8819 + 10.9015i −0.277675 + 0.160316i
\(69\) 0 0
\(70\) −11.3542 + 19.6661i −0.162204 + 0.280945i
\(71\) 12.1382i 0.170961i 0.996340 + 0.0854803i \(0.0272425\pi\)
−0.996340 + 0.0854803i \(0.972758\pi\)
\(72\) 0 0
\(73\) −76.9150 −1.05363 −0.526815 0.849980i \(-0.676614\pi\)
−0.526815 + 0.849980i \(0.676614\pi\)
\(74\) −46.5403 26.8701i −0.628923 0.363109i
\(75\) 0 0
\(76\) 20.0000 + 34.6410i 0.263158 + 0.455803i
\(77\) −27.8121 + 16.0573i −0.361196 + 0.208537i
\(78\) 0 0
\(79\) −16.8340 + 29.1573i −0.213088 + 0.369080i −0.952680 0.303976i \(-0.901686\pi\)
0.739591 + 0.673056i \(0.235019\pi\)
\(80\) 24.2764i 0.303455i
\(81\) 0 0
\(82\) −85.7490 −1.04572
\(83\) −52.4607 30.2882i −0.632057 0.364918i 0.149491 0.988763i \(-0.452236\pi\)
−0.781548 + 0.623845i \(0.785570\pi\)
\(84\) 0 0
\(85\) 33.0810 + 57.2980i 0.389189 + 0.674095i
\(86\) 102.264 59.0420i 1.18911 0.686535i
\(87\) 0 0
\(88\) −17.1660 + 29.7324i −0.195068 + 0.337868i
\(89\) 4.77506i 0.0536523i 0.999640 + 0.0268262i \(0.00854006\pi\)
−0.999640 + 0.0268262i \(0.991460\pi\)
\(90\) 0 0
\(91\) 49.1660 0.540286
\(92\) 21.0240 + 12.1382i 0.228522 + 0.131937i
\(93\) 0 0
\(94\) 12.0000 + 20.7846i 0.127660 + 0.221113i
\(95\) 105.120 60.6910i 1.10653 0.638853i
\(96\) 0 0
\(97\) 94.2065 163.170i 0.971201 1.68217i 0.279261 0.960215i \(-0.409910\pi\)
0.691940 0.721955i \(-0.256756\pi\)
\(98\) 9.89949i 0.101015i
\(99\) 0 0
\(100\) 23.6680 0.236680
\(101\) 92.4162 + 53.3565i 0.915012 + 0.528282i 0.882040 0.471174i \(-0.156170\pi\)
0.0329716 + 0.999456i \(0.489503\pi\)
\(102\) 0 0
\(103\) −65.7490 113.881i −0.638340 1.10564i −0.985797 0.167941i \(-0.946288\pi\)
0.347457 0.937696i \(-0.387045\pi\)
\(104\) 45.5189 26.2803i 0.437682 0.252696i
\(105\) 0 0
\(106\) −66.4980 + 115.178i −0.627340 + 1.08658i
\(107\) 82.3793i 0.769900i −0.922937 0.384950i \(-0.874219\pi\)
0.922937 0.384950i \(-0.125781\pi\)
\(108\) 0 0
\(109\) 33.8301 0.310367 0.155184 0.987886i \(-0.450403\pi\)
0.155184 + 0.987886i \(0.450403\pi\)
\(110\) 90.2245 + 52.0911i 0.820223 + 0.473556i
\(111\) 0 0
\(112\) 5.29150 + 9.16515i 0.0472456 + 0.0818317i
\(113\) 24.6982 14.2595i 0.218568 0.126190i −0.386719 0.922198i \(-0.626392\pi\)
0.605287 + 0.796007i \(0.293058\pi\)
\(114\) 0 0
\(115\) 36.8340 63.7983i 0.320296 0.554768i
\(116\) 83.6734i 0.721322i
\(117\) 0 0
\(118\) −82.3320 −0.697729
\(119\) 24.9784 + 14.4213i 0.209902 + 0.121187i
\(120\) 0 0
\(121\) 13.1680 + 22.8076i 0.108826 + 0.188493i
\(122\) 19.1893 11.0789i 0.157289 0.0908109i
\(123\) 0 0
\(124\) 25.1660 43.5888i 0.202952 0.351523i
\(125\) 79.9059i 0.639247i
\(126\) 0 0
\(127\) 129.668 1.02101 0.510504 0.859875i \(-0.329459\pi\)
0.510504 + 0.859875i \(0.329459\pi\)
\(128\) 9.79796 + 5.65685i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −79.7490 138.129i −0.613454 1.06253i
\(131\) 128.187 74.0087i 0.978525 0.564952i 0.0767004 0.997054i \(-0.475562\pi\)
0.901824 + 0.432103i \(0.142228\pi\)
\(132\) 0 0
\(133\) 26.4575 45.8258i 0.198929 0.344555i
\(134\) 187.615i 1.40011i
\(135\) 0 0
\(136\) 30.8340 0.226721
\(137\) −66.6469 38.4786i −0.486474 0.280866i 0.236637 0.971598i \(-0.423955\pi\)
−0.723111 + 0.690732i \(0.757288\pi\)
\(138\) 0 0
\(139\) −108.664 188.212i −0.781756 1.35404i −0.930918 0.365228i \(-0.880991\pi\)
0.149162 0.988813i \(-0.452342\pi\)
\(140\) 27.8121 16.0573i 0.198658 0.114695i
\(141\) 0 0
\(142\) 8.58301 14.8662i 0.0604437 0.104692i
\(143\) 225.564i 1.57737i
\(144\) 0 0
\(145\) 253.911 1.75111
\(146\) 94.2013 + 54.3871i 0.645214 + 0.372515i
\(147\) 0 0
\(148\) 38.0000 + 65.8179i 0.256757 + 0.444716i
\(149\) −140.231 + 80.9623i −0.941147 + 0.543371i −0.890320 0.455336i \(-0.849519\pi\)
−0.0508272 + 0.998707i \(0.516186\pi\)
\(150\) 0 0
\(151\) 46.5830 80.6841i 0.308497 0.534332i −0.669537 0.742779i \(-0.733507\pi\)
0.978034 + 0.208447i \(0.0668408\pi\)
\(152\) 56.5685i 0.372161i
\(153\) 0 0
\(154\) 45.4170 0.294916
\(155\) −132.272 76.3675i −0.853371 0.492694i
\(156\) 0 0
\(157\) 92.4980 + 160.211i 0.589159 + 1.02045i 0.994343 + 0.106219i \(0.0338743\pi\)
−0.405183 + 0.914235i \(0.632792\pi\)
\(158\) 41.2347 23.8069i 0.260979 0.150676i
\(159\) 0 0
\(160\) 17.1660 29.7324i 0.107288 0.185828i
\(161\) 32.1147i 0.199470i
\(162\) 0 0
\(163\) 86.9961 0.533718 0.266859 0.963736i \(-0.414014\pi\)
0.266859 + 0.963736i \(0.414014\pi\)
\(164\) 105.021 + 60.6337i 0.640370 + 0.369718i
\(165\) 0 0
\(166\) 42.8340 + 74.1906i 0.258036 + 0.446932i
\(167\) −52.4607 + 30.2882i −0.314136 + 0.181366i −0.648776 0.760980i \(-0.724719\pi\)
0.334640 + 0.942346i \(0.391385\pi\)
\(168\) 0 0
\(169\) −88.1640 + 152.705i −0.521681 + 0.903578i
\(170\) 93.5673i 0.550396i
\(171\) 0 0
\(172\) −166.996 −0.970907
\(173\) 140.791 + 81.2858i 0.813822 + 0.469860i 0.848281 0.529546i \(-0.177638\pi\)
−0.0344594 + 0.999406i \(0.510971\pi\)
\(174\) 0 0
\(175\) −15.6549 27.1151i −0.0894566 0.154943i
\(176\) 42.0480 24.2764i 0.238909 0.137934i
\(177\) 0 0
\(178\) 3.37648 5.84823i 0.0189690 0.0328552i
\(179\) 223.091i 1.24632i −0.782095 0.623159i \(-0.785849\pi\)
0.782095 0.623159i \(-0.214151\pi\)
\(180\) 0 0
\(181\) 188.915 1.04373 0.521865 0.853028i \(-0.325237\pi\)
0.521865 + 0.853028i \(0.325237\pi\)
\(182\) −60.2158 34.7656i −0.330856 0.191020i
\(183\) 0 0
\(184\) −17.1660 29.7324i −0.0932935 0.161589i
\(185\) 199.728 115.313i 1.07961 0.623313i
\(186\) 0 0
\(187\) 66.1621 114.596i 0.353808 0.612813i
\(188\) 33.9411i 0.180538i
\(189\) 0 0
\(190\) −171.660 −0.903474
\(191\) −197.486 114.019i −1.03396 0.596957i −0.115844 0.993267i \(-0.536957\pi\)
−0.918117 + 0.396310i \(0.870291\pi\)
\(192\) 0 0
\(193\) −67.0000 116.047i −0.347150 0.601282i 0.638592 0.769546i \(-0.279517\pi\)
−0.985742 + 0.168264i \(0.946184\pi\)
\(194\) −230.758 + 133.228i −1.18947 + 0.686743i
\(195\) 0 0
\(196\) 7.00000 12.1244i 0.0357143 0.0618590i
\(197\) 188.560i 0.957157i 0.878045 + 0.478579i \(0.158848\pi\)
−0.878045 + 0.478579i \(0.841152\pi\)
\(198\) 0 0
\(199\) 102.494 0.515046 0.257523 0.966272i \(-0.417094\pi\)
0.257523 + 0.966272i \(0.417094\pi\)
\(200\) −28.9872 16.7358i −0.144936 0.0836789i
\(201\) 0 0
\(202\) −75.4575 130.696i −0.373552 0.647011i
\(203\) 95.8599 55.3447i 0.472216 0.272634i
\(204\) 0 0
\(205\) 183.996 318.691i 0.897542 1.55459i
\(206\) 185.966i 0.902749i
\(207\) 0 0
\(208\) −74.3320 −0.357365
\(209\) −210.240 121.382i −1.00593 0.580775i
\(210\) 0 0
\(211\) 42.2510 + 73.1809i 0.200242 + 0.346829i 0.948606 0.316459i \(-0.102494\pi\)
−0.748365 + 0.663288i \(0.769161\pi\)
\(212\) 162.886 94.0424i 0.768331 0.443596i
\(213\) 0 0
\(214\) −58.2510 + 100.894i −0.272201 + 0.471466i
\(215\) 506.758i 2.35701i
\(216\) 0 0
\(217\) −66.5830 −0.306834
\(218\) −41.4332 23.9215i −0.190060 0.109731i
\(219\) 0 0
\(220\) −73.6680 127.597i −0.334854 0.579985i
\(221\) −175.441 + 101.291i −0.793851 + 0.458330i
\(222\) 0 0
\(223\) 79.2470 137.260i 0.355368 0.615515i −0.631813 0.775121i \(-0.717689\pi\)
0.987181 + 0.159606i \(0.0510222\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) 0 0
\(226\) −40.3320 −0.178460
\(227\) 88.1816 + 50.9117i 0.388465 + 0.224281i 0.681495 0.731823i \(-0.261330\pi\)
−0.293030 + 0.956103i \(0.594663\pi\)
\(228\) 0 0
\(229\) 134.458 + 232.887i 0.587151 + 1.01697i 0.994604 + 0.103749i \(0.0330837\pi\)
−0.407453 + 0.913226i \(0.633583\pi\)
\(230\) −90.2245 + 52.0911i −0.392280 + 0.226483i
\(231\) 0 0
\(232\) 59.1660 102.479i 0.255026 0.441718i
\(233\) 26.2748i 0.112767i 0.998409 + 0.0563836i \(0.0179570\pi\)
−0.998409 + 0.0563836i \(0.982043\pi\)
\(234\) 0 0
\(235\) −102.996 −0.438281
\(236\) 100.836 + 58.2175i 0.427270 + 0.246684i
\(237\) 0 0
\(238\) −20.3948 35.3248i −0.0856923 0.148423i
\(239\) −79.9110 + 46.1366i −0.334356 + 0.193040i −0.657773 0.753216i \(-0.728501\pi\)
0.323418 + 0.946256i \(0.395168\pi\)
\(240\) 0 0
\(241\) −171.624 + 297.261i −0.712131 + 1.23345i 0.251925 + 0.967747i \(0.418936\pi\)
−0.964056 + 0.265700i \(0.914397\pi\)
\(242\) 37.2447i 0.153904i
\(243\) 0 0
\(244\) −31.3360 −0.128426
\(245\) −36.7920 21.2419i −0.150171 0.0867014i
\(246\) 0 0
\(247\) 185.830 + 321.867i 0.752348 + 1.30311i
\(248\) −61.6439 + 35.5901i −0.248564 + 0.143509i
\(249\) 0 0
\(250\) 56.5020 97.8643i 0.226008 0.391457i
\(251\) 356.382i 1.41985i −0.704278 0.709924i \(-0.748729\pi\)
0.704278 0.709924i \(-0.251271\pi\)
\(252\) 0 0
\(253\) −147.336 −0.582356
\(254\) −158.810 91.6891i −0.625237 0.360981i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 220.603 127.365i 0.858377 0.495584i −0.00509129 0.999987i \(-0.501621\pi\)
0.863469 + 0.504403i \(0.168287\pi\)
\(258\) 0 0
\(259\) 50.2693 87.0689i 0.194090 0.336174i
\(260\) 225.564i 0.867555i
\(261\) 0 0
\(262\) −209.328 −0.798962
\(263\) 226.880 + 130.989i 0.862663 + 0.498059i 0.864903 0.501939i \(-0.167380\pi\)
−0.00224015 + 0.999997i \(0.500713\pi\)
\(264\) 0 0
\(265\) −285.376 494.287i −1.07689 1.86523i
\(266\) −64.8074 + 37.4166i −0.243637 + 0.140664i
\(267\) 0 0
\(268\) −132.664 + 229.781i −0.495015 + 0.857391i
\(269\) 93.6246i 0.348047i −0.984742 0.174023i \(-0.944323\pi\)
0.984742 0.174023i \(-0.0556768\pi\)
\(270\) 0 0
\(271\) 1.16601 0.00430262 0.00215131 0.999998i \(-0.499315\pi\)
0.00215131 + 0.999998i \(0.499315\pi\)
\(272\) −37.7638 21.8029i −0.138837 0.0801578i
\(273\) 0 0
\(274\) 54.4170 + 94.2530i 0.198602 + 0.343989i
\(275\) −124.399 + 71.8217i −0.452359 + 0.261170i
\(276\) 0 0
\(277\) −16.0000 + 27.7128i −0.0577617 + 0.100046i −0.893460 0.449142i \(-0.851730\pi\)
0.835699 + 0.549188i \(0.185063\pi\)
\(278\) 307.348i 1.10557i
\(279\) 0 0
\(280\) −45.4170 −0.162204
\(281\) 144.416 + 83.3785i 0.513935 + 0.296721i 0.734450 0.678663i \(-0.237440\pi\)
−0.220514 + 0.975384i \(0.570774\pi\)
\(282\) 0 0
\(283\) −8.16995 14.1508i −0.0288691 0.0500027i 0.851230 0.524793i \(-0.175857\pi\)
−0.880099 + 0.474790i \(0.842524\pi\)
\(284\) −21.0240 + 12.1382i −0.0740281 + 0.0427401i
\(285\) 0 0
\(286\) −159.498 + 276.259i −0.557685 + 0.965939i
\(287\) 160.422i 0.558961i
\(288\) 0 0
\(289\) 170.158 0.588782
\(290\) −310.976 179.542i −1.07233 0.619111i
\(291\) 0 0
\(292\) −76.9150 133.221i −0.263408 0.456235i
\(293\) −319.495 + 184.461i −1.09043 + 0.629558i −0.933690 0.358082i \(-0.883431\pi\)
−0.156737 + 0.987640i \(0.550097\pi\)
\(294\) 0 0
\(295\) 176.664 305.991i 0.598861 1.03726i
\(296\) 107.480i 0.363109i
\(297\) 0 0
\(298\) 228.996 0.768443
\(299\) 195.344 + 112.782i 0.653326 + 0.377198i
\(300\) 0 0
\(301\) 110.458 + 191.318i 0.366968 + 0.635608i
\(302\) −114.105 + 65.8783i −0.377830 + 0.218140i
\(303\) 0 0
\(304\) −40.0000 + 69.2820i −0.131579 + 0.227901i
\(305\) 95.0906i 0.311772i
\(306\) 0 0
\(307\) −192.664 −0.627570 −0.313785 0.949494i \(-0.601597\pi\)
−0.313785 + 0.949494i \(0.601597\pi\)
\(308\) −55.6242 32.1147i −0.180598 0.104268i
\(309\) 0 0
\(310\) 108.000 + 187.061i 0.348387 + 0.603424i
\(311\) −113.688 + 65.6380i −0.365557 + 0.211055i −0.671516 0.740990i \(-0.734356\pi\)
0.305959 + 0.952045i \(0.401023\pi\)
\(312\) 0 0
\(313\) −21.6640 + 37.5232i −0.0692142 + 0.119882i −0.898556 0.438860i \(-0.855383\pi\)
0.829341 + 0.558742i \(0.188716\pi\)
\(314\) 261.624i 0.833197i
\(315\) 0 0
\(316\) −67.3360 −0.213088
\(317\) −218.000 125.862i −0.687696 0.397042i 0.115052 0.993359i \(-0.463297\pi\)
−0.802748 + 0.596318i \(0.796630\pi\)
\(318\) 0 0
\(319\) −253.911 439.787i −0.795960 1.37864i
\(320\) −42.0480 + 24.2764i −0.131400 + 0.0758638i
\(321\) 0 0
\(322\) −22.7085 + 39.3323i −0.0705233 + 0.122150i
\(323\) 218.029i 0.675013i
\(324\) 0 0
\(325\) 219.911 0.676650
\(326\) −106.548 61.5155i −0.326834 0.188698i
\(327\) 0 0
\(328\) −85.7490 148.522i −0.261430 0.452810i
\(329\) −38.8844 + 22.4499i −0.118190 + 0.0682369i
\(330\) 0 0
\(331\) −180.745 + 313.060i −0.546058 + 0.945800i 0.452482 + 0.891774i \(0.350539\pi\)
−0.998540 + 0.0540260i \(0.982795\pi\)
\(332\) 121.153i 0.364918i
\(333\) 0 0
\(334\) 85.6680 0.256491
\(335\) 697.282 + 402.576i 2.08144 + 1.20172i
\(336\) 0 0
\(337\) 149.417 + 258.798i 0.443374 + 0.767946i 0.997937 0.0641954i \(-0.0204481\pi\)
−0.554563 + 0.832141i \(0.687115\pi\)
\(338\) 215.957 124.683i 0.638926 0.368884i
\(339\) 0 0
\(340\) −66.1621 + 114.596i −0.194594 + 0.337047i
\(341\) 305.470i 0.895807i
\(342\) 0 0
\(343\) −18.5203 −0.0539949
\(344\) 204.528 + 118.084i 0.594557 + 0.343268i
\(345\) 0 0
\(346\) −114.956 199.109i −0.332241 0.575459i
\(347\) −178.505 + 103.060i −0.514425 + 0.297003i −0.734651 0.678446i \(-0.762654\pi\)
0.220226 + 0.975449i \(0.429321\pi\)
\(348\) 0 0
\(349\) −217.162 + 376.136i −0.622241 + 1.07775i 0.366827 + 0.930289i \(0.380444\pi\)
−0.989067 + 0.147464i \(0.952889\pi\)
\(350\) 44.2787i 0.126511i
\(351\) 0 0
\(352\) −68.6640 −0.195068
\(353\) −160.595 92.7197i −0.454944 0.262662i 0.254972 0.966948i \(-0.417934\pi\)
−0.709916 + 0.704286i \(0.751267\pi\)
\(354\) 0 0
\(355\) 36.8340 + 63.7983i 0.103758 + 0.179714i
\(356\) −8.27064 + 4.77506i −0.0232321 + 0.0134131i
\(357\) 0 0
\(358\) −157.749 + 273.229i −0.440640 + 0.763210i
\(359\) 516.767i 1.43946i 0.694254 + 0.719731i \(0.255735\pi\)
−0.694254 + 0.719731i \(0.744265\pi\)
\(360\) 0 0
\(361\) 39.0000 0.108033
\(362\) −231.373 133.583i −0.639151 0.369014i
\(363\) 0 0
\(364\) 49.1660 + 85.1580i 0.135071 + 0.233951i
\(365\) −404.265 + 233.403i −1.10758 + 0.639459i
\(366\) 0 0
\(367\) 58.7451 101.749i 0.160068 0.277246i −0.774825 0.632176i \(-0.782162\pi\)
0.934893 + 0.354930i \(0.115495\pi\)
\(368\) 48.5528i 0.131937i
\(369\) 0 0
\(370\) −326.154 −0.881498
\(371\) −215.478 124.406i −0.580804 0.335327i
\(372\) 0 0
\(373\) 201.332 + 348.717i 0.539764 + 0.934899i 0.998916 + 0.0465413i \(0.0148199\pi\)
−0.459152 + 0.888358i \(0.651847\pi\)
\(374\) −162.063 + 93.5673i −0.433324 + 0.250180i
\(375\) 0 0
\(376\) −24.0000 + 41.5692i −0.0638298 + 0.110556i
\(377\) 777.451i 2.06221i
\(378\) 0 0
\(379\) 398.834 1.05233 0.526166 0.850382i \(-0.323629\pi\)
0.526166 + 0.850382i \(0.323629\pi\)
\(380\) 210.240 + 121.382i 0.553263 + 0.319426i
\(381\) 0 0
\(382\) 161.247 + 279.288i 0.422113 + 0.731121i
\(383\) −645.019 + 372.402i −1.68412 + 0.972329i −0.725255 + 0.688481i \(0.758278\pi\)
−0.958869 + 0.283849i \(0.908389\pi\)
\(384\) 0 0
\(385\) −97.4536 + 168.795i −0.253126 + 0.438427i
\(386\) 189.505i 0.490945i
\(387\) 0 0
\(388\) 376.826 0.971201
\(389\) −463.464 267.581i −1.19142 0.687869i −0.232795 0.972526i \(-0.574787\pi\)
−0.958630 + 0.284656i \(0.908121\pi\)
\(390\) 0 0
\(391\) 66.1621 + 114.596i 0.169212 + 0.293085i
\(392\) −17.1464 + 9.89949i −0.0437409 + 0.0252538i
\(393\) 0 0
\(394\) 133.332 230.938i 0.338406 0.586137i
\(395\) 204.334i 0.517302i
\(396\) 0 0
\(397\) −94.3241 −0.237592 −0.118796 0.992919i \(-0.537904\pi\)
−0.118796 + 0.992919i \(0.537904\pi\)
\(398\) −125.529 72.4743i −0.315400 0.182096i
\(399\) 0 0
\(400\) 23.6680 + 40.9941i 0.0591699 + 0.102485i
\(401\) 89.7138 51.7963i 0.223725 0.129168i −0.383949 0.923354i \(-0.625436\pi\)
0.607674 + 0.794187i \(0.292103\pi\)
\(402\) 0 0
\(403\) 233.830 405.006i 0.580223 1.00498i
\(404\) 213.426i 0.528282i
\(405\) 0 0
\(406\) −156.539 −0.385563
\(407\) −399.456 230.626i −0.981464 0.566648i
\(408\) 0 0
\(409\) 4.87844 + 8.44971i 0.0119277 + 0.0206594i 0.871928 0.489635i \(-0.162870\pi\)
−0.860000 + 0.510294i \(0.829537\pi\)
\(410\) −450.696 + 260.210i −1.09926 + 0.634658i
\(411\) 0 0
\(412\) 131.498 227.761i 0.319170 0.552819i
\(413\) 154.029i 0.372952i
\(414\) 0 0
\(415\) −367.644 −0.885890
\(416\) 91.0378 + 52.5607i 0.218841 + 0.126348i
\(417\) 0 0
\(418\) 171.660 + 297.324i 0.410670 + 0.711301i
\(419\) −293.939 + 169.706i −0.701525 + 0.405025i −0.807915 0.589299i \(-0.799404\pi\)
0.106390 + 0.994324i \(0.466071\pi\)
\(420\) 0 0
\(421\) 299.660 519.027i 0.711782 1.23284i −0.252406 0.967621i \(-0.581222\pi\)
0.964188 0.265221i \(-0.0854448\pi\)
\(422\) 119.504i 0.283184i
\(423\) 0 0
\(424\) −265.992 −0.627340
\(425\) 111.724 + 64.5039i 0.262880 + 0.151774i
\(426\) 0 0
\(427\) 20.7268 + 35.8998i 0.0485405 + 0.0840746i
\(428\) 142.685 82.3793i 0.333377 0.192475i
\(429\) 0 0
\(430\) 358.332 620.649i 0.833330 1.44337i
\(431\) 710.978i 1.64960i −0.565424 0.824800i \(-0.691288\pi\)
0.565424 0.824800i \(-0.308712\pi\)
\(432\) 0 0
\(433\) 377.984 0.872943 0.436471 0.899718i \(-0.356228\pi\)
0.436471 + 0.899718i \(0.356228\pi\)
\(434\) 81.5472 + 47.0813i 0.187897 + 0.108482i
\(435\) 0 0
\(436\) 33.8301 + 58.5954i 0.0775919 + 0.134393i
\(437\) 210.240 121.382i 0.481098 0.277762i
\(438\) 0 0
\(439\) −264.073 + 457.388i −0.601533 + 1.04189i 0.391056 + 0.920367i \(0.372110\pi\)
−0.992589 + 0.121519i \(0.961223\pi\)
\(440\) 208.365i 0.473556i
\(441\) 0 0
\(442\) 286.494 0.648177
\(443\) 31.7345 + 18.3219i 0.0716354 + 0.0413587i 0.535390 0.844605i \(-0.320165\pi\)
−0.463754 + 0.885964i \(0.653498\pi\)
\(444\) 0 0
\(445\) 14.4902 + 25.0977i 0.0325622 + 0.0563993i
\(446\) −194.115 + 112.072i −0.435235 + 0.251283i
\(447\) 0 0
\(448\) −10.5830 + 18.3303i −0.0236228 + 0.0409159i
\(449\) 397.612i 0.885550i 0.896633 + 0.442775i \(0.146006\pi\)
−0.896633 + 0.442775i \(0.853994\pi\)
\(450\) 0 0
\(451\) −735.984 −1.63189
\(452\) 49.3964 + 28.5190i 0.109284 + 0.0630952i
\(453\) 0 0
\(454\) −72.0000 124.708i −0.158590 0.274686i
\(455\) 258.416 149.197i 0.567948 0.327905i
\(456\) 0 0
\(457\) −172.162 + 298.193i −0.376722 + 0.652502i −0.990583 0.136912i \(-0.956282\pi\)
0.613861 + 0.789414i \(0.289616\pi\)
\(458\) 380.303i 0.830357i
\(459\) 0 0
\(460\) 147.336 0.320296
\(461\) −321.240 185.468i −0.696833 0.402317i 0.109334 0.994005i \(-0.465128\pi\)
−0.806167 + 0.591688i \(0.798462\pi\)
\(462\) 0 0
\(463\) −39.1660 67.8375i −0.0845918 0.146517i 0.820625 0.571467i \(-0.193625\pi\)
−0.905217 + 0.424949i \(0.860292\pi\)
\(464\) −144.927 + 83.6734i −0.312342 + 0.180331i
\(465\) 0 0
\(466\) 18.5791 32.1799i 0.0398692 0.0690556i
\(467\) 399.758i 0.856014i 0.903775 + 0.428007i \(0.140784\pi\)
−0.903775 + 0.428007i \(0.859216\pi\)
\(468\) 0 0
\(469\) 350.996 0.748392
\(470\) 126.144 + 72.8292i 0.268391 + 0.154956i
\(471\) 0 0
\(472\) −82.3320 142.603i −0.174432 0.302126i
\(473\) 877.731 506.758i 1.85567 1.07137i
\(474\) 0 0
\(475\) 118.340 204.971i 0.249137 0.431517i
\(476\) 57.6851i 0.121187i
\(477\) 0 0
\(478\) 130.494 0.273000
\(479\) −609.100 351.664i −1.27161 0.734163i −0.296317 0.955090i \(-0.595759\pi\)
−0.975290 + 0.220927i \(0.929092\pi\)
\(480\) 0 0
\(481\) 353.077 + 611.547i 0.734048 + 1.27141i
\(482\) 420.390 242.712i 0.872179 0.503553i
\(483\) 0 0
\(484\) −26.3360 + 45.6152i −0.0544131 + 0.0942463i
\(485\) 1143.50i 2.35773i
\(486\) 0 0
\(487\) −82.5098 −0.169425 −0.0847124 0.996405i \(-0.526997\pi\)
−0.0847124 + 0.996405i \(0.526997\pi\)
\(488\) 38.3786 + 22.1579i 0.0786446 + 0.0454055i
\(489\) 0 0
\(490\) 30.0405 + 52.0317i 0.0613072 + 0.106187i
\(491\) 159.524 92.1014i 0.324897 0.187579i −0.328676 0.944443i \(-0.606603\pi\)
0.653573 + 0.756863i \(0.273269\pi\)
\(492\) 0 0
\(493\) −228.041 + 394.978i −0.462557 + 0.801172i
\(494\) 525.607i 1.06398i
\(495\) 0 0
\(496\) 100.664 0.202952
\(497\) 27.8121 + 16.0573i 0.0559600 + 0.0323085i
\(498\) 0 0
\(499\) −376.405 651.953i −0.754319 1.30652i −0.945712 0.325005i \(-0.894634\pi\)
0.191393 0.981513i \(-0.438699\pi\)
\(500\) −138.401 + 79.9059i −0.276802 + 0.159812i
\(501\) 0 0
\(502\) −252.000 + 436.477i −0.501992 + 0.869476i
\(503\) 662.540i 1.31718i 0.752504 + 0.658588i \(0.228846\pi\)
−0.752504 + 0.658588i \(0.771154\pi\)
\(504\) 0 0
\(505\) 647.652 1.28248
\(506\) 180.449 + 104.182i 0.356618 + 0.205894i
\(507\) 0 0
\(508\) 129.668 + 224.592i 0.255252 + 0.442109i
\(509\) −821.958 + 474.557i −1.61485 + 0.932333i −0.626623 + 0.779322i \(0.715563\pi\)
−0.988225 + 0.153010i \(0.951103\pi\)
\(510\) 0 0
\(511\) −101.749 + 176.234i −0.199117 + 0.344882i
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) −360.243 −0.700862
\(515\) −691.153 399.037i −1.34204 0.774830i
\(516\) 0 0
\(517\) 102.996 + 178.394i 0.199219 + 0.345057i
\(518\) −123.134 + 71.0915i −0.237711 + 0.137242i
\(519\) 0 0
\(520\) 159.498 276.259i 0.306727 0.531267i
\(521\) 714.344i 1.37110i −0.728025 0.685551i \(-0.759561\pi\)
0.728025 0.685551i \(-0.240439\pi\)
\(522\) 0 0
\(523\) −232.000 −0.443595 −0.221797 0.975093i \(-0.571192\pi\)
−0.221797 + 0.975093i \(0.571192\pi\)
\(524\) 256.373 + 148.017i 0.489262 + 0.282476i
\(525\) 0 0
\(526\) −185.247 320.857i −0.352181 0.609995i
\(527\) 237.591 137.173i 0.450837 0.260291i
\(528\) 0 0
\(529\) −190.832 + 330.531i −0.360741 + 0.624822i
\(530\) 807.167i 1.52296i
\(531\) 0 0
\(532\) 105.830 0.198929
\(533\) 975.800 + 563.378i 1.83077 + 1.05699i
\(534\) 0 0
\(535\) −249.984 432.985i −0.467260 0.809319i
\(536\) 324.959 187.615i 0.606267 0.350029i
\(537\) 0 0
\(538\) −66.2026 + 114.666i −0.123053 + 0.213134i
\(539\) 84.9674i 0.157639i
\(540\) 0 0
\(541\) 165.668 0.306225 0.153113 0.988209i \(-0.451070\pi\)
0.153113 + 0.988209i \(0.451070\pi\)
\(542\) −1.42807 0.824494i −0.00263481 0.00152121i
\(543\) 0 0
\(544\) 30.8340 + 53.4060i 0.0566801 + 0.0981729i
\(545\) 177.811 102.659i 0.326258 0.188365i
\(546\) 0 0
\(547\) −147.838 + 256.063i −0.270270 + 0.468122i −0.968931 0.247331i \(-0.920446\pi\)
0.698661 + 0.715453i \(0.253780\pi\)
\(548\) 153.915i 0.280866i
\(549\) 0 0
\(550\) 203.142 0.369350
\(551\) 724.633 + 418.367i 1.31512 + 0.759287i
\(552\) 0 0
\(553\) 44.5385 + 77.1430i 0.0805399 + 0.139499i
\(554\) 39.1918 22.6274i 0.0707434 0.0408437i
\(555\) 0 0
\(556\) 217.328 376.423i 0.390878 0.677020i
\(557\) 76.8426i 0.137958i −0.997618 0.0689790i \(-0.978026\pi\)
0.997618 0.0689790i \(-0.0219742\pi\)
\(558\) 0 0
\(559\) −1551.64 −2.77575
\(560\) 55.6242 + 32.1147i 0.0993290 + 0.0573476i
\(561\) 0 0
\(562\) −117.915 204.235i −0.209813 0.363407i
\(563\) −880.170 + 508.167i −1.56336 + 0.902605i −0.566444 + 0.824100i \(0.691681\pi\)
−0.996914 + 0.0785049i \(0.974985\pi\)
\(564\) 0 0
\(565\) 86.5425 149.896i 0.153173 0.265303i
\(566\) 23.1081i 0.0408270i
\(567\) 0 0
\(568\) 34.3320 0.0604437
\(569\) −507.952 293.266i −0.892710 0.515406i −0.0178822 0.999840i \(-0.505692\pi\)
−0.874828 + 0.484434i \(0.839026\pi\)
\(570\) 0 0
\(571\) −475.822 824.148i −0.833314 1.44334i −0.895396 0.445271i \(-0.853107\pi\)
0.0620822 0.998071i \(-0.480226\pi\)
\(572\) 390.689 225.564i 0.683022 0.394343i
\(573\) 0 0
\(574\) −113.435 + 196.476i −0.197622 + 0.342292i
\(575\) 143.643i 0.249815i
\(576\) 0 0
\(577\) −148.672 −0.257664 −0.128832 0.991666i \(-0.541123\pi\)
−0.128832 + 0.991666i \(0.541123\pi\)
\(578\) −208.400 120.320i −0.360554 0.208166i
\(579\) 0 0
\(580\) 253.911 + 439.787i 0.437778 + 0.758253i
\(581\) −138.798 + 80.1351i −0.238895 + 0.137926i
\(582\) 0 0
\(583\) −570.753 + 988.573i −0.978993 + 1.69567i
\(584\) 217.549i 0.372515i
\(585\) 0 0
\(586\) 521.733 0.890330
\(587\) 288.009 + 166.282i 0.490645 + 0.283274i 0.724842 0.688915i \(-0.241913\pi\)
−0.234197 + 0.972189i \(0.575246\pi\)
\(588\) 0 0
\(589\) −251.660 435.888i −0.427267 0.740048i
\(590\) −432.737 + 249.841i −0.733452 + 0.423459i
\(591\) 0 0
\(592\) −76.0000 + 131.636i −0.128378 + 0.222358i
\(593\) 217.251i 0.366359i −0.983079 0.183180i \(-0.941361\pi\)
0.983079 0.183180i \(-0.0586390\pi\)
\(594\) 0 0
\(595\) 175.048 0.294199
\(596\) −280.462 161.925i −0.470573 0.271686i
\(597\) 0 0
\(598\) −159.498 276.259i −0.266719 0.461971i
\(599\) 149.111 86.0896i 0.248934 0.143722i −0.370342 0.928895i \(-0.620760\pi\)
0.619276 + 0.785173i \(0.287426\pi\)
\(600\) 0 0
\(601\) 209.000 361.999i 0.347754 0.602327i −0.638096 0.769957i \(-0.720278\pi\)
0.985850 + 0.167629i \(0.0536112\pi\)
\(602\) 312.421i 0.518972i
\(603\) 0 0
\(604\) 186.332 0.308497
\(605\) 138.422 + 79.9178i 0.228796 + 0.132096i
\(606\) 0 0
\(607\) −313.579 543.135i −0.516605 0.894786i −0.999814 0.0192808i \(-0.993862\pi\)
0.483209 0.875505i \(-0.339471\pi\)
\(608\) 97.9796 56.5685i 0.161151 0.0930404i
\(609\) 0 0
\(610\) 67.2392 116.462i 0.110228 0.190921i
\(611\) 315.364i 0.516144i
\(612\) 0 0
\(613\) −279.328 −0.455674 −0.227837 0.973699i \(-0.573165\pi\)
−0.227837 + 0.973699i \(0.573165\pi\)
\(614\) 235.964 + 136.234i 0.384307 + 0.221880i
\(615\) 0 0
\(616\) 45.4170 + 78.6645i 0.0737289 + 0.127702i
\(617\) −310.366 + 179.190i −0.503025 + 0.290422i −0.729962 0.683488i \(-0.760462\pi\)
0.226937 + 0.973909i \(0.427129\pi\)
\(618\) 0 0
\(619\) 491.822 851.861i 0.794543 1.37619i −0.128586 0.991698i \(-0.541044\pi\)
0.923129 0.384491i \(-0.125623\pi\)
\(620\) 305.470i 0.492694i
\(621\) 0 0
\(622\) 185.652 0.298476
\(623\) 10.9410 + 6.31681i 0.0175619 + 0.0101393i
\(624\) 0 0
\(625\) 390.403 + 676.198i 0.624645 + 1.08192i
\(626\) 53.0658 30.6376i 0.0847697 0.0489418i
\(627\) 0 0
\(628\) −184.996 + 320.423i −0.294580 + 0.510227i
\(629\) 414.256i 0.658594i
\(630\) 0 0
\(631\) −298.996 −0.473845 −0.236922 0.971529i \(-0.576139\pi\)
−0.236922 + 0.971529i \(0.576139\pi\)
\(632\) 82.4694 + 47.6137i 0.130490 + 0.0753382i
\(633\) 0 0
\(634\) 177.996 + 308.298i 0.280751 + 0.486275i
\(635\) 681.534 393.484i 1.07328 0.619660i
\(636\) 0 0
\(637\) 65.0405 112.653i 0.102104 0.176850i
\(638\) 718.169i 1.12566i
\(639\) 0 0
\(640\) 68.6640 0.107288
\(641\) −270.163 155.979i −0.421471 0.243336i 0.274236 0.961663i \(-0.411575\pi\)
−0.695706 + 0.718326i \(0.744909\pi\)
\(642\) 0 0
\(643\) 302.000 + 523.079i 0.469673 + 0.813498i 0.999399 0.0346710i \(-0.0110383\pi\)
−0.529725 + 0.848169i \(0.677705\pi\)
\(644\) 55.6242 32.1147i 0.0863730 0.0498675i
\(645\) 0 0
\(646\) 154.170 267.030i 0.238653 0.413359i
\(647\) 179.600i 0.277588i −0.990321 0.138794i \(-0.955677\pi\)
0.990321 0.138794i \(-0.0443226\pi\)
\(648\) 0 0
\(649\) −706.656 −1.08884
\(650\) −269.335 155.501i −0.414362 0.239232i
\(651\) 0 0
\(652\) 86.9961 + 150.682i 0.133430 + 0.231107i
\(653\) −417.331 + 240.946i −0.639097 + 0.368983i −0.784267 0.620424i \(-0.786961\pi\)
0.145169 + 0.989407i \(0.453627\pi\)
\(654\) 0 0
\(655\) 449.166 777.978i 0.685750 1.18775i
\(656\) 242.535i 0.369718i
\(657\) 0 0
\(658\) 63.4980 0.0965016
\(659\) 759.857 + 438.704i 1.15305 + 0.665711i 0.949628 0.313380i \(-0.101462\pi\)
0.203418 + 0.979092i \(0.434795\pi\)
\(660\) 0 0
\(661\) 260.822 + 451.757i 0.394587 + 0.683445i 0.993048 0.117707i \(-0.0375543\pi\)
−0.598461 + 0.801152i \(0.704221\pi\)
\(662\) 442.733 255.612i 0.668781 0.386121i
\(663\) 0 0
\(664\) −85.6680 + 148.381i −0.129018 + 0.223466i
\(665\) 321.147i 0.482927i
\(666\) 0 0
\(667\) 507.822 0.761353
\(668\) −104.921 60.5764i −0.157068 0.0906832i
\(669\) 0 0
\(670\) −569.328 986.105i −0.849743 1.47180i
\(671\) 164.702 95.0906i 0.245457 0.141715i
\(672\) 0 0
\(673\) 329.996 571.570i 0.490336 0.849287i −0.509602 0.860410i \(-0.670207\pi\)
0.999938 + 0.0111234i \(0.00354077\pi\)
\(674\) 422.615i 0.627025i
\(675\) 0 0
\(676\) −352.656 −0.521681
\(677\) 880.121 + 508.138i 1.30003 + 0.750573i 0.980409 0.196972i \(-0.0631108\pi\)
0.319622 + 0.947545i \(0.396444\pi\)
\(678\) 0 0
\(679\) −249.247 431.709i −0.367080 0.635801i
\(680\) 162.063 93.5673i 0.238328 0.137599i
\(681\) 0 0
\(682\) 216.000 374.123i 0.316716 0.548567i
\(683\) 235.114i 0.344238i 0.985076 + 0.172119i \(0.0550613\pi\)
−0.985076 + 0.172119i \(0.944939\pi\)
\(684\) 0 0
\(685\) −467.061 −0.681841
\(686\) 22.6826 + 13.0958i 0.0330650 + 0.0190901i
\(687\) 0 0
\(688\) −166.996 289.246i −0.242727 0.420415i
\(689\) 1513.46 873.795i 2.19660 1.26821i
\(690\) 0 0
\(691\) 25.4902 44.1502i 0.0368888 0.0638933i −0.846992 0.531606i \(-0.821589\pi\)
0.883880 + 0.467713i \(0.154922\pi\)
\(692\) 325.143i 0.469860i
\(693\) 0 0
\(694\) 291.498 0.420026
\(695\) −1142.28 659.493i −1.64356 0.948911i
\(696\) 0 0
\(697\) 330.498 + 572.439i 0.474172 + 0.821290i
\(698\) 531.936 307.114i 0.762086 0.439991i
\(699\) 0 0
\(700\) 31.3098 54.2302i 0.0447283 0.0774716i
\(701\) 141.530i 0.201898i −0.994892 0.100949i \(-0.967812\pi\)
0.994892 0.100949i \(-0.0321879\pi\)
\(702\) 0 0
\(703\) 760.000 1.08108
\(704\) 84.0959 + 48.5528i 0.119454 + 0.0689671i
\(705\) 0 0
\(706\) 131.125 + 227.116i 0.185730 + 0.321694i
\(707\) 244.510 141.168i 0.345842 0.199672i
\(708\) 0 0
\(709\) 27.7490 48.0627i 0.0391382 0.0677894i −0.845793 0.533512i \(-0.820872\pi\)
0.884931 + 0.465722i \(0.154205\pi\)
\(710\) 104.182i 0.146736i
\(711\) 0 0
\(712\) 13.5059 0.0189690
\(713\) −264.545 152.735i −0.371031 0.214215i
\(714\) 0 0
\(715\) −684.486 1185.56i −0.957323 1.65813i
\(716\) 386.405 223.091i 0.539671 0.311579i
\(717\) 0 0
\(718\) 365.409 632.907i 0.508926 0.881486i
\(719\) 1009.03i 1.40338i 0.712484 + 0.701688i \(0.247570\pi\)
−0.712484 + 0.701688i \(0.752430\pi\)
\(720\) 0 0
\(721\) −347.911 −0.482540
\(722\) −47.7650 27.5772i −0.0661566 0.0381955i
\(723\) 0 0
\(724\) 188.915 + 327.210i 0.260932 + 0.451948i
\(725\) 428.765 247.547i 0.591400 0.341445i
\(726\) 0 0
\(727\) 182.591 316.257i 0.251157 0.435016i −0.712688 0.701481i \(-0.752522\pi\)
0.963845 + 0.266465i \(0.0858557\pi\)
\(728\) 139.062i 0.191020i
\(729\) 0 0
\(730\) 660.162 0.904332
\(731\) −788.300 455.125i −1.07839 0.622606i
\(732\) 0 0
\(733\) 176.539 + 305.774i 0.240844 + 0.417154i 0.960955 0.276705i \(-0.0892425\pi\)
−0.720111 + 0.693859i \(0.755909\pi\)
\(734\) −143.895 + 83.0781i −0.196043 + 0.113185i
\(735\) 0 0
\(736\) 34.3320 59.4648i 0.0466468 0.0807946i
\(737\) 1610.30i 2.18494i
\(738\) 0 0
\(739\) 329.684 0.446121 0.223061 0.974805i \(-0.428395\pi\)
0.223061 + 0.974805i \(0.428395\pi\)
\(740\) 399.456 + 230.626i 0.539805 + 0.311657i
\(741\) 0 0
\(742\) 175.937 + 304.732i 0.237112 + 0.410690i
\(743\) 97.0478 56.0306i 0.130616 0.0754112i −0.433268 0.901265i \(-0.642640\pi\)
0.563884 + 0.825854i \(0.309306\pi\)
\(744\) 0 0
\(745\) −491.369 + 851.075i −0.659555 + 1.14238i
\(746\) 569.453i 0.763342i
\(747\) 0 0
\(748\) 264.648 0.353808
\(749\) −188.755 108.978i −0.252009 0.145497i
\(750\) 0 0
\(751\) 72.4131 + 125.423i 0.0964222 + 0.167008i 0.910201 0.414166i \(-0.135927\pi\)
−0.813779 + 0.581174i \(0.802593\pi\)
\(752\) 58.7878 33.9411i 0.0781752 0.0451345i
\(753\) 0 0
\(754\) 549.741 952.180i 0.729100 1.26284i
\(755\) 565.434i 0.748919i
\(756\) 0 0
\(757\) 78.1699 0.103263 0.0516314 0.998666i \(-0.483558\pi\)
0.0516314 + 0.998666i \(0.483558\pi\)
\(758\) −488.470 282.018i −0.644419 0.372056i
\(759\) 0 0
\(760\) −171.660 297.324i −0.225869 0.391216i
\(761\) −1269.16 + 732.752i −1.66776 + 0.962880i −0.698915 + 0.715205i \(0.746333\pi\)
−0.968843 + 0.247676i \(0.920333\pi\)
\(762\) 0 0
\(763\) 44.7530 77.5144i 0.0586539 0.101592i
\(764\) 456.076i 0.596957i
\(765\) 0 0
\(766\) 1053.31 1.37508
\(767\) 936.915 + 540.928i 1.22153 + 0.705252i
\(768\) 0 0
\(769\) −364.660 631.610i −0.474200 0.821339i 0.525363 0.850878i \(-0.323929\pi\)
−0.999564 + 0.0295389i \(0.990596\pi\)
\(770\) 238.712 137.820i 0.310015 0.178987i
\(771\) 0 0
\(772\) 134.000 232.095i 0.173575 0.300641i
\(773\) 434.559i 0.562172i 0.959683 + 0.281086i \(0.0906947\pi\)
−0.959683 + 0.281086i \(0.909305\pi\)
\(774\) 0 0
\(775\) −297.814 −0.384277
\(776\) −461.516 266.456i −0.594737 0.343372i
\(777\) 0 0
\(778\) 378.417 + 655.437i 0.486397 + 0.842465i
\(779\) 1050.21 606.337i 1.34815 0.778353i
\(780\) 0 0
\(781\) 73.6680 127.597i 0.0943252 0.163376i
\(782\) 187.135i 0.239303i
\(783\) 0 0
\(784\) 28.0000 0.0357143
\(785\) 972.339 + 561.380i 1.23865 + 0.715134i
\(786\) 0 0
\(787\) 7.67585 + 13.2950i 0.00975331 + 0.0168932i 0.870861 0.491530i \(-0.163562\pi\)
−0.861108 + 0.508423i \(0.830229\pi\)
\(788\) −326.595 + 188.560i