Properties

Label 690.2.j.a.643.5
Level $690$
Weight $2$
Character 690.643
Analytic conductor $5.510$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 643.5
Character \(\chi\) \(=\) 690.643
Dual form 690.2.j.a.367.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(0.899538 - 2.04715i) q^{5} -1.00000 q^{6} +(1.80902 + 1.80902i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(0.899538 - 2.04715i) q^{5} -1.00000 q^{6} +(1.80902 + 1.80902i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(0.811485 + 2.08362i) q^{10} +4.16725i q^{11} +(0.707107 - 0.707107i) q^{12} +(-3.18894 - 3.18894i) q^{13} -2.55834 q^{14} +(2.08362 - 0.811485i) q^{15} -1.00000 q^{16} +(1.68449 + 1.68449i) q^{17} +(-0.707107 - 0.707107i) q^{18} +5.24101 q^{19} +(-2.04715 - 0.899538i) q^{20} +2.55834i q^{21} +(-2.94669 - 2.94669i) q^{22} +(1.98398 + 4.36621i) q^{23} +1.00000i q^{24} +(-3.38166 - 3.68298i) q^{25} +4.50985 q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.80902 - 1.80902i) q^{28} -3.48107i q^{29} +(-0.899538 + 2.04715i) q^{30} +7.27142 q^{31} +(0.707107 - 0.707107i) q^{32} +(-2.94669 + 2.94669i) q^{33} -2.38223 q^{34} +(5.33061 - 2.07605i) q^{35} +1.00000 q^{36} +(5.46339 + 5.46339i) q^{37} +(-3.70595 + 3.70595i) q^{38} -4.50985i q^{39} +(2.08362 - 0.811485i) q^{40} +4.53754 q^{41} +(-1.80902 - 1.80902i) q^{42} +(6.37868 - 6.37868i) q^{43} +4.16725 q^{44} +(2.04715 + 0.899538i) q^{45} +(-4.49027 - 1.68449i) q^{46} +(-9.09342 + 9.09342i) q^{47} +(-0.707107 - 0.707107i) q^{48} -0.454913i q^{49} +(4.99546 + 0.213067i) q^{50} +2.38223i q^{51} +(-3.18894 + 3.18894i) q^{52} +(-6.56472 + 6.56472i) q^{53} -1.00000i q^{54} +(8.53099 + 3.74860i) q^{55} +2.55834i q^{56} +(3.70595 + 3.70595i) q^{57} +(2.46149 + 2.46149i) q^{58} -6.80402i q^{59} +(-0.811485 - 2.08362i) q^{60} -0.759260i q^{61} +(-5.14167 + 5.14167i) q^{62} +(-1.80902 + 1.80902i) q^{63} +1.00000i q^{64} +(-9.39683 + 3.65967i) q^{65} -4.16725i q^{66} +(2.02126 + 2.02126i) q^{67} +(1.68449 - 1.68449i) q^{68} +(-1.68449 + 4.49027i) q^{69} +(-2.30132 + 5.23730i) q^{70} -9.56406 q^{71} +(-0.707107 + 0.707107i) q^{72} +(-5.78239 - 5.78239i) q^{73} -7.72640 q^{74} +(0.213067 - 4.99546i) q^{75} -5.24101i q^{76} +(-7.53863 + 7.53863i) q^{77} +(3.18894 + 3.18894i) q^{78} -6.84964 q^{79} +(-0.899538 + 2.04715i) q^{80} -1.00000 q^{81} +(-3.20853 + 3.20853i) q^{82} +(-2.40890 + 2.40890i) q^{83} +2.55834 q^{84} +(4.96367 - 1.93314i) q^{85} +9.02081i q^{86} +(2.46149 - 2.46149i) q^{87} +(-2.94669 + 2.94669i) q^{88} -3.58782 q^{89} +(-2.08362 + 0.811485i) q^{90} -11.5377i q^{91} +(4.36621 - 1.98398i) q^{92} +(5.14167 + 5.14167i) q^{93} -12.8600i q^{94} +(4.71449 - 10.7291i) q^{95} +1.00000 q^{96} +(4.03278 + 4.03278i) q^{97} +(0.321672 + 0.321672i) q^{98} -4.16725 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 24q^{6} + O(q^{10}) \) \( 24q - 24q^{6} - 24q^{16} - 8q^{23} - 16q^{25} - 16q^{26} + 16q^{31} - 16q^{35} + 24q^{36} - 8q^{46} - 8q^{47} + 24q^{50} + 24q^{55} + 16q^{58} - 56q^{62} - 32q^{70} - 16q^{71} - 48q^{73} - 24q^{81} + 24q^{82} + 16q^{87} - 8q^{92} + 56q^{93} + 24q^{95} + 24q^{96} - 32q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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 −0.500000 + 0.500000i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 0.899538 2.04715i 0.402286 0.915514i
\(6\) −1.00000 −0.408248
\(7\) 1.80902 + 1.80902i 0.683744 + 0.683744i 0.960842 0.277098i \(-0.0893725\pi\)
−0.277098 + 0.960842i \(0.589373\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 0.811485 + 2.08362i 0.256614 + 0.658900i
\(11\) 4.16725i 1.25647i 0.778022 + 0.628236i \(0.216223\pi\)
−0.778022 + 0.628236i \(0.783777\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) −3.18894 3.18894i −0.884454 0.884454i 0.109530 0.993984i \(-0.465066\pi\)
−0.993984 + 0.109530i \(0.965066\pi\)
\(14\) −2.55834 −0.683744
\(15\) 2.08362 0.811485i 0.537990 0.209525i
\(16\) −1.00000 −0.250000
\(17\) 1.68449 + 1.68449i 0.408549 + 0.408549i 0.881232 0.472683i \(-0.156715\pi\)
−0.472683 + 0.881232i \(0.656715\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) 5.24101 1.20237 0.601185 0.799110i \(-0.294696\pi\)
0.601185 + 0.799110i \(0.294696\pi\)
\(20\) −2.04715 0.899538i −0.457757 0.201143i
\(21\) 2.55834i 0.558275i
\(22\) −2.94669 2.94669i −0.628236 0.628236i
\(23\) 1.98398 + 4.36621i 0.413689 + 0.910418i
\(24\) 1.00000i 0.204124i
\(25\) −3.38166 3.68298i −0.676332 0.736597i
\(26\) 4.50985 0.884454
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 1.80902 1.80902i 0.341872 0.341872i
\(29\) 3.48107i 0.646418i −0.946328 0.323209i \(-0.895238\pi\)
0.946328 0.323209i \(-0.104762\pi\)
\(30\) −0.899538 + 2.04715i −0.164232 + 0.373757i
\(31\) 7.27142 1.30599 0.652993 0.757364i \(-0.273513\pi\)
0.652993 + 0.757364i \(0.273513\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −2.94669 + 2.94669i −0.512953 + 0.512953i
\(34\) −2.38223 −0.408549
\(35\) 5.33061 2.07605i 0.901038 0.350917i
\(36\) 1.00000 0.166667
\(37\) 5.46339 + 5.46339i 0.898175 + 0.898175i 0.995275 0.0970994i \(-0.0309565\pi\)
−0.0970994 + 0.995275i \(0.530956\pi\)
\(38\) −3.70595 + 3.70595i −0.601185 + 0.601185i
\(39\) 4.50985i 0.722154i
\(40\) 2.08362 0.811485i 0.329450 0.128307i
\(41\) 4.53754 0.708645 0.354322 0.935123i \(-0.384712\pi\)
0.354322 + 0.935123i \(0.384712\pi\)
\(42\) −1.80902 1.80902i −0.279137 0.279137i
\(43\) 6.37868 6.37868i 0.972739 0.972739i −0.0268989 0.999638i \(-0.508563\pi\)
0.999638 + 0.0268989i \(0.00856321\pi\)
\(44\) 4.16725 0.628236
\(45\) 2.04715 + 0.899538i 0.305171 + 0.134095i
\(46\) −4.49027 1.68449i −0.662054 0.248365i
\(47\) −9.09342 + 9.09342i −1.32641 + 1.32641i −0.417935 + 0.908477i \(0.637246\pi\)
−0.908477 + 0.417935i \(0.862754\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 0.454913i 0.0649875i
\(50\) 4.99546 + 0.213067i 0.706464 + 0.0301322i
\(51\) 2.38223i 0.333579i
\(52\) −3.18894 + 3.18894i −0.442227 + 0.442227i
\(53\) −6.56472 + 6.56472i −0.901734 + 0.901734i −0.995586 0.0938519i \(-0.970082\pi\)
0.0938519 + 0.995586i \(0.470082\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 8.53099 + 3.74860i 1.15032 + 0.505461i
\(56\) 2.55834i 0.341872i
\(57\) 3.70595 + 3.70595i 0.490865 + 0.490865i
\(58\) 2.46149 + 2.46149i 0.323209 + 0.323209i
\(59\) 6.80402i 0.885808i −0.896569 0.442904i \(-0.853948\pi\)
0.896569 0.442904i \(-0.146052\pi\)
\(60\) −0.811485 2.08362i −0.104762 0.268995i
\(61\) 0.759260i 0.0972133i −0.998818 0.0486066i \(-0.984522\pi\)
0.998818 0.0486066i \(-0.0154781\pi\)
\(62\) −5.14167 + 5.14167i −0.652993 + 0.652993i
\(63\) −1.80902 + 1.80902i −0.227915 + 0.227915i
\(64\) 1.00000i 0.125000i
\(65\) −9.39683 + 3.65967i −1.16553 + 0.453927i
\(66\) 4.16725i 0.512953i
\(67\) 2.02126 + 2.02126i 0.246937 + 0.246937i 0.819712 0.572776i \(-0.194133\pi\)
−0.572776 + 0.819712i \(0.694133\pi\)
\(68\) 1.68449 1.68449i 0.204275 0.204275i
\(69\) −1.68449 + 4.49027i −0.202789 + 0.540565i
\(70\) −2.30132 + 5.23730i −0.275061 + 0.625978i
\(71\) −9.56406 −1.13504 −0.567522 0.823358i \(-0.692098\pi\)
−0.567522 + 0.823358i \(0.692098\pi\)
\(72\) −0.707107 + 0.707107i −0.0833333 + 0.0833333i
\(73\) −5.78239 5.78239i −0.676778 0.676778i 0.282492 0.959270i \(-0.408839\pi\)
−0.959270 + 0.282492i \(0.908839\pi\)
\(74\) −7.72640 −0.898175
\(75\) 0.213067 4.99546i 0.0246029 0.576826i
\(76\) 5.24101i 0.601185i
\(77\) −7.53863 + 7.53863i −0.859106 + 0.859106i
\(78\) 3.18894 + 3.18894i 0.361077 + 0.361077i
\(79\) −6.84964 −0.770645 −0.385322 0.922782i \(-0.625910\pi\)
−0.385322 + 0.922782i \(0.625910\pi\)
\(80\) −0.899538 + 2.04715i −0.100571 + 0.228879i
\(81\) −1.00000 −0.111111
\(82\) −3.20853 + 3.20853i −0.354322 + 0.354322i
\(83\) −2.40890 + 2.40890i −0.264411 + 0.264411i −0.826843 0.562432i \(-0.809866\pi\)
0.562432 + 0.826843i \(0.309866\pi\)
\(84\) 2.55834 0.279137
\(85\) 4.96367 1.93314i 0.538386 0.209679i
\(86\) 9.02081i 0.972739i
\(87\) 2.46149 2.46149i 0.263899 0.263899i
\(88\) −2.94669 + 2.94669i −0.314118 + 0.314118i
\(89\) −3.58782 −0.380308 −0.190154 0.981754i \(-0.560899\pi\)
−0.190154 + 0.981754i \(0.560899\pi\)
\(90\) −2.08362 + 0.811485i −0.219633 + 0.0855381i
\(91\) 11.5377i 1.20948i
\(92\) 4.36621 1.98398i 0.455209 0.206844i
\(93\) 5.14167 + 5.14167i 0.533166 + 0.533166i
\(94\) 12.8600i 1.32641i
\(95\) 4.71449 10.7291i 0.483696 1.10079i
\(96\) 1.00000 0.102062
\(97\) 4.03278 + 4.03278i 0.409467 + 0.409467i 0.881553 0.472086i \(-0.156499\pi\)
−0.472086 + 0.881553i \(0.656499\pi\)
\(98\) 0.321672 + 0.321672i 0.0324938 + 0.0324938i
\(99\) −4.16725 −0.418824
\(100\) −3.68298 + 3.38166i −0.368298 + 0.338166i
\(101\) 6.36488 0.633329 0.316665 0.948538i \(-0.397437\pi\)
0.316665 + 0.948538i \(0.397437\pi\)
\(102\) −1.68449 1.68449i −0.166789 0.166789i
\(103\) 1.99918 1.99918i 0.196985 0.196985i −0.601721 0.798706i \(-0.705518\pi\)
0.798706 + 0.601721i \(0.205518\pi\)
\(104\) 4.50985i 0.442227i
\(105\) 5.23730 + 2.30132i 0.511109 + 0.224586i
\(106\) 9.28392i 0.901734i
\(107\) 6.26821 + 6.26821i 0.605971 + 0.605971i 0.941891 0.335920i \(-0.109047\pi\)
−0.335920 + 0.941891i \(0.609047\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) 1.53597 0.147119 0.0735595 0.997291i \(-0.476564\pi\)
0.0735595 + 0.997291i \(0.476564\pi\)
\(110\) −8.68298 + 3.38166i −0.827890 + 0.322429i
\(111\) 7.72640i 0.733357i
\(112\) −1.80902 1.80902i −0.170936 0.170936i
\(113\) 14.0619 14.0619i 1.32283 1.32283i 0.411360 0.911473i \(-0.365054\pi\)
0.911473 0.411360i \(-0.134946\pi\)
\(114\) −5.24101 −0.490865
\(115\) 10.7230 0.133937i 0.999922 0.0124897i
\(116\) −3.48107 −0.323209
\(117\) 3.18894 3.18894i 0.294818 0.294818i
\(118\) 4.81117 + 4.81117i 0.442904 + 0.442904i
\(119\) 6.09455i 0.558686i
\(120\) 2.04715 + 0.899538i 0.186879 + 0.0821162i
\(121\) −6.36597 −0.578724
\(122\) 0.536878 + 0.536878i 0.0486066 + 0.0486066i
\(123\) 3.20853 + 3.20853i 0.289303 + 0.289303i
\(124\) 7.27142i 0.652993i
\(125\) −10.5816 + 3.60979i −0.946444 + 0.322869i
\(126\) 2.55834i 0.227915i
\(127\) −7.12493 + 7.12493i −0.632235 + 0.632235i −0.948628 0.316393i \(-0.897528\pi\)
0.316393 + 0.948628i \(0.397528\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 9.02081 0.794238
\(130\) 4.05678 9.23234i 0.355803 0.809730i
\(131\) 1.98524 0.173451 0.0867257 0.996232i \(-0.472360\pi\)
0.0867257 + 0.996232i \(0.472360\pi\)
\(132\) 2.94669 + 2.94669i 0.256476 + 0.256476i
\(133\) 9.48107 + 9.48107i 0.822113 + 0.822113i
\(134\) −2.85850 −0.246937
\(135\) 0.811485 + 2.08362i 0.0698415 + 0.179330i
\(136\) 2.38223i 0.204275i
\(137\) −13.6901 13.6901i −1.16962 1.16962i −0.982298 0.187325i \(-0.940018\pi\)
−0.187325 0.982298i \(-0.559982\pi\)
\(138\) −1.98398 4.36621i −0.168888 0.371677i
\(139\) 19.4321i 1.64821i −0.566438 0.824104i \(-0.691679\pi\)
0.566438 0.824104i \(-0.308321\pi\)
\(140\) −2.07605 5.33061i −0.175458 0.450519i
\(141\) −12.8600 −1.08301
\(142\) 6.76281 6.76281i 0.567522 0.567522i
\(143\) 13.2891 13.2891i 1.11129 1.11129i
\(144\) 1.00000i 0.0833333i
\(145\) −7.12628 3.13136i −0.591805 0.260045i
\(146\) 8.17754 0.676778
\(147\) 0.321672 0.321672i 0.0265310 0.0265310i
\(148\) 5.46339 5.46339i 0.449088 0.449088i
\(149\) 3.37276 0.276307 0.138154 0.990411i \(-0.455883\pi\)
0.138154 + 0.990411i \(0.455883\pi\)
\(150\) 3.38166 + 3.68298i 0.276111 + 0.300714i
\(151\) −18.7035 −1.52207 −0.761035 0.648710i \(-0.775309\pi\)
−0.761035 + 0.648710i \(0.775309\pi\)
\(152\) 3.70595 + 3.70595i 0.300592 + 0.300592i
\(153\) −1.68449 + 1.68449i −0.136183 + 0.136183i
\(154\) 10.6612i 0.859106i
\(155\) 6.54092 14.8857i 0.525379 1.19565i
\(156\) −4.50985 −0.361077
\(157\) −11.8389 11.8389i −0.944844 0.944844i 0.0537126 0.998556i \(-0.482895\pi\)
−0.998556 + 0.0537126i \(0.982895\pi\)
\(158\) 4.84343 4.84343i 0.385322 0.385322i
\(159\) −9.28392 −0.736263
\(160\) −0.811485 2.08362i −0.0641535 0.164725i
\(161\) −4.30950 + 11.4876i −0.339636 + 0.905351i
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) −8.37789 8.37789i −0.656207 0.656207i 0.298274 0.954480i \(-0.403589\pi\)
−0.954480 + 0.298274i \(0.903589\pi\)
\(164\) 4.53754i 0.354322i
\(165\) 3.38166 + 8.68298i 0.263262 + 0.675969i
\(166\) 3.40670i 0.264411i
\(167\) −13.2847 + 13.2847i −1.02800 + 1.02800i −0.0284037 + 0.999597i \(0.509042\pi\)
−0.999597 + 0.0284037i \(0.990958\pi\)
\(168\) −1.80902 + 1.80902i −0.139569 + 0.139569i
\(169\) 7.33872i 0.564517i
\(170\) −2.14291 + 4.87679i −0.164354 + 0.374033i
\(171\) 5.24101i 0.400790i
\(172\) −6.37868 6.37868i −0.486370 0.486370i
\(173\) 13.3807 + 13.3807i 1.01732 + 1.01732i 0.999847 + 0.0174703i \(0.00556124\pi\)
0.0174703 + 0.999847i \(0.494439\pi\)
\(174\) 3.48107i 0.263899i
\(175\) 0.545097 12.7801i 0.0412055 0.966082i
\(176\) 4.16725i 0.314118i
\(177\) 4.81117 4.81117i 0.361630 0.361630i
\(178\) 2.53697 2.53697i 0.190154 0.190154i
\(179\) 17.1255i 1.28002i −0.768367 0.640010i \(-0.778930\pi\)
0.768367 0.640010i \(-0.221070\pi\)
\(180\) 0.899538 2.04715i 0.0670476 0.152586i
\(181\) 7.02770i 0.522365i −0.965289 0.261183i \(-0.915888\pi\)
0.965289 0.261183i \(-0.0841124\pi\)
\(182\) 8.15839 + 8.15839i 0.604740 + 0.604740i
\(183\) 0.536878 0.536878i 0.0396872 0.0396872i
\(184\) −1.68449 + 4.49027i −0.124182 + 0.331027i
\(185\) 16.0989 6.26986i 1.18362 0.460969i
\(186\) −7.27142 −0.533166
\(187\) −7.01970 + 7.01970i −0.513331 + 0.513331i
\(188\) 9.09342 + 9.09342i 0.663206 + 0.663206i
\(189\) −2.55834 −0.186092
\(190\) 4.25300 + 10.9203i 0.308545 + 0.792241i
\(191\) 22.3085i 1.61419i −0.590422 0.807094i \(-0.701039\pi\)
0.590422 0.807094i \(-0.298961\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) −12.5386 12.5386i −0.902550 0.902550i 0.0931061 0.995656i \(-0.470320\pi\)
−0.995656 + 0.0931061i \(0.970320\pi\)
\(194\) −5.70322 −0.409467
\(195\) −9.23234 4.05678i −0.661142 0.290512i
\(196\) −0.454913 −0.0324938
\(197\) −2.02769 + 2.02769i −0.144467 + 0.144467i −0.775641 0.631174i \(-0.782573\pi\)
0.631174 + 0.775641i \(0.282573\pi\)
\(198\) 2.94669 2.94669i 0.209412 0.209412i
\(199\) 4.87669 0.345699 0.172850 0.984948i \(-0.444703\pi\)
0.172850 + 0.984948i \(0.444703\pi\)
\(200\) 0.213067 4.99546i 0.0150661 0.353232i
\(201\) 2.85850i 0.201623i
\(202\) −4.50065 + 4.50065i −0.316665 + 0.316665i
\(203\) 6.29731 6.29731i 0.441985 0.441985i
\(204\) 2.38223 0.166789
\(205\) 4.08169 9.28903i 0.285078 0.648774i
\(206\) 2.82727i 0.196985i
\(207\) −4.36621 + 1.98398i −0.303473 + 0.137896i
\(208\) 3.18894 + 3.18894i 0.221113 + 0.221113i
\(209\) 21.8406i 1.51074i
\(210\) −5.33061 + 2.07605i −0.367847 + 0.143261i
\(211\) −10.4399 −0.718710 −0.359355 0.933201i \(-0.617003\pi\)
−0.359355 + 0.933201i \(0.617003\pi\)
\(212\) 6.56472 + 6.56472i 0.450867 + 0.450867i
\(213\) −6.76281 6.76281i −0.463380 0.463380i
\(214\) −8.86459 −0.605971
\(215\) −7.32026 18.7960i −0.499237 1.28188i
\(216\) −1.00000 −0.0680414
\(217\) 13.1541 + 13.1541i 0.892960 + 0.892960i
\(218\) −1.08609 + 1.08609i −0.0735595 + 0.0735595i
\(219\) 8.17754i 0.552587i
\(220\) 3.74860 8.53099i 0.252731 0.575159i
\(221\) 10.7435i 0.722686i
\(222\) −5.46339 5.46339i −0.366679 0.366679i
\(223\) 11.9073 + 11.9073i 0.797373 + 0.797373i 0.982681 0.185308i \(-0.0593282\pi\)
−0.185308 + 0.982681i \(0.559328\pi\)
\(224\) 2.55834 0.170936
\(225\) 3.68298 3.38166i 0.245532 0.225444i
\(226\) 19.8865i 1.32283i
\(227\) 0.242263 + 0.242263i 0.0160796 + 0.0160796i 0.715101 0.699021i \(-0.246381\pi\)
−0.699021 + 0.715101i \(0.746381\pi\)
\(228\) 3.70595 3.70595i 0.245433 0.245433i
\(229\) −5.80623 −0.383687 −0.191843 0.981426i \(-0.561447\pi\)
−0.191843 + 0.981426i \(0.561447\pi\)
\(230\) −7.48758 + 7.67699i −0.493716 + 0.506206i
\(231\) −10.6612 −0.701457
\(232\) 2.46149 2.46149i 0.161605 0.161605i
\(233\) −11.2922 11.2922i −0.739779 0.739779i 0.232756 0.972535i \(-0.425226\pi\)
−0.972535 + 0.232756i \(0.925226\pi\)
\(234\) 4.50985i 0.294818i
\(235\) 10.4357 + 26.7955i 0.680752 + 1.74795i
\(236\) −6.80402 −0.442904
\(237\) −4.84343 4.84343i −0.314614 0.314614i
\(238\) −4.30950 4.30950i −0.279343 0.279343i
\(239\) 0.457589i 0.0295990i −0.999890 0.0147995i \(-0.995289\pi\)
0.999890 0.0147995i \(-0.00471099\pi\)
\(240\) −2.08362 + 0.811485i −0.134497 + 0.0523811i
\(241\) 22.2609i 1.43395i 0.697098 + 0.716976i \(0.254474\pi\)
−0.697098 + 0.716976i \(0.745526\pi\)
\(242\) 4.50142 4.50142i 0.289362 0.289362i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) −0.759260 −0.0486066
\(245\) −0.931275 0.409211i −0.0594970 0.0261436i
\(246\) −4.53754 −0.289303
\(247\) −16.7133 16.7133i −1.06344 1.06344i
\(248\) 5.14167 + 5.14167i 0.326496 + 0.326496i
\(249\) −3.40670 −0.215891
\(250\) 4.92979 10.0348i 0.311787 0.634656i
\(251\) 26.7068i 1.68572i −0.538135 0.842858i \(-0.680871\pi\)
0.538135 0.842858i \(-0.319129\pi\)
\(252\) 1.80902 + 1.80902i 0.113957 + 0.113957i
\(253\) −18.1951 + 8.26775i −1.14392 + 0.519789i
\(254\) 10.0762i 0.632235i
\(255\) 4.87679 + 2.14291i 0.305396 + 0.134194i
\(256\) 1.00000 0.0625000
\(257\) −5.33827 + 5.33827i −0.332992 + 0.332992i −0.853722 0.520729i \(-0.825660\pi\)
0.520729 + 0.853722i \(0.325660\pi\)
\(258\) −6.37868 + 6.37868i −0.397119 + 0.397119i
\(259\) 19.7667i 1.22824i
\(260\) 3.65967 + 9.39683i 0.226963 + 0.582767i
\(261\) 3.48107 0.215473
\(262\) −1.40378 + 1.40378i −0.0867257 + 0.0867257i
\(263\) −19.5204 + 19.5204i −1.20368 + 1.20368i −0.230639 + 0.973039i \(0.574082\pi\)
−0.973039 + 0.230639i \(0.925918\pi\)
\(264\) −4.16725 −0.256476
\(265\) 7.53377 + 19.3442i 0.462796 + 1.18831i
\(266\) −13.4083 −0.822113
\(267\) −2.53697 2.53697i −0.155260 0.155260i
\(268\) 2.02126 2.02126i 0.123468 0.123468i
\(269\) 4.38872i 0.267585i −0.991009 0.133793i \(-0.957284\pi\)
0.991009 0.133793i \(-0.0427156\pi\)
\(270\) −2.04715 0.899538i −0.124586 0.0547442i
\(271\) 18.9023 1.14823 0.574117 0.818773i \(-0.305345\pi\)
0.574117 + 0.818773i \(0.305345\pi\)
\(272\) −1.68449 1.68449i −0.102137 0.102137i
\(273\) 8.15839 8.15839i 0.493768 0.493768i
\(274\) 19.3607 1.16962
\(275\) 15.3479 14.0922i 0.925514 0.849793i
\(276\) 4.49027 + 1.68449i 0.270282 + 0.101394i
\(277\) 2.44423 2.44423i 0.146860 0.146860i −0.629854 0.776714i \(-0.716885\pi\)
0.776714 + 0.629854i \(0.216885\pi\)
\(278\) 13.7406 + 13.7406i 0.824104 + 0.824104i
\(279\) 7.27142i 0.435328i
\(280\) 5.23730 + 2.30132i 0.312989 + 0.137530i
\(281\) 2.33823i 0.139487i −0.997565 0.0697436i \(-0.977782\pi\)
0.997565 0.0697436i \(-0.0222181\pi\)
\(282\) 9.09342 9.09342i 0.541505 0.541505i
\(283\) −21.6132 + 21.6132i −1.28477 + 1.28477i −0.346850 + 0.937921i \(0.612749\pi\)
−0.937921 + 0.346850i \(0.887251\pi\)
\(284\) 9.56406i 0.567522i
\(285\) 10.9203 4.25300i 0.646862 0.251926i
\(286\) 18.7937i 1.11129i
\(287\) 8.20849 + 8.20849i 0.484532 + 0.484532i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) 11.3250i 0.666175i
\(290\) 7.25324 2.82484i 0.425925 0.165880i
\(291\) 5.70322i 0.334328i
\(292\) −5.78239 + 5.78239i −0.338389 + 0.338389i
\(293\) −21.4487 + 21.4487i −1.25305 + 1.25305i −0.298699 + 0.954347i \(0.596553\pi\)
−0.954347 + 0.298699i \(0.903447\pi\)
\(294\) 0.454913i 0.0265310i
\(295\) −13.9289 6.12048i −0.810970 0.356348i
\(296\) 7.72640i 0.449088i
\(297\) −2.94669 2.94669i −0.170984 0.170984i
\(298\) −2.38490 + 2.38490i −0.138154 + 0.138154i
\(299\) 7.59680 20.2504i 0.439334 1.17111i
\(300\) −4.99546 0.213067i −0.288413 0.0123014i
\(301\) 23.0783 1.33021
\(302\) 13.2254 13.2254i 0.761035 0.761035i
\(303\) 4.50065 + 4.50065i 0.258556 + 0.258556i
\(304\) −5.24101 −0.300592
\(305\) −1.55432 0.682984i −0.0890001 0.0391075i
\(306\) 2.38223i 0.136183i
\(307\) 12.0002 12.0002i 0.684889 0.684889i −0.276209 0.961098i \(-0.589078\pi\)
0.961098 + 0.276209i \(0.0890781\pi\)
\(308\) 7.53863 + 7.53863i 0.429553 + 0.429553i
\(309\) 2.82727 0.160838
\(310\) 5.90065 + 15.1509i 0.335134 + 0.860514i
\(311\) 1.56616 0.0888087 0.0444043 0.999014i \(-0.485861\pi\)
0.0444043 + 0.999014i \(0.485861\pi\)
\(312\) 3.18894 3.18894i 0.180538 0.180538i
\(313\) 8.94733 8.94733i 0.505733 0.505733i −0.407481 0.913214i \(-0.633593\pi\)
0.913214 + 0.407481i \(0.133593\pi\)
\(314\) 16.7427 0.944844
\(315\) 2.07605 + 5.33061i 0.116972 + 0.300346i
\(316\) 6.84964i 0.385322i
\(317\) 8.43391 8.43391i 0.473695 0.473695i −0.429413 0.903108i \(-0.641279\pi\)
0.903108 + 0.429413i \(0.141279\pi\)
\(318\) 6.56472 6.56472i 0.368131 0.368131i
\(319\) 14.5065 0.812207
\(320\) 2.04715 + 0.899538i 0.114439 + 0.0502857i
\(321\) 8.86459i 0.494773i
\(322\) −5.07570 11.1702i −0.282857 0.622493i
\(323\) 8.82843 + 8.82843i 0.491227 + 0.491227i
\(324\) 1.00000i 0.0555556i
\(325\) −0.960900 + 22.5288i −0.0533011 + 1.24967i
\(326\) 11.8481 0.656207
\(327\) 1.08609 + 1.08609i 0.0600611 + 0.0600611i
\(328\) 3.20853 + 3.20853i 0.177161 + 0.177161i
\(329\) −32.9003 −1.81385
\(330\) −8.53099 3.74860i −0.469616 0.206354i
\(331\) 12.9490 0.711741 0.355870 0.934535i \(-0.384184\pi\)
0.355870 + 0.934535i \(0.384184\pi\)
\(332\) 2.40890 + 2.40890i 0.132206 + 0.132206i
\(333\) −5.46339 + 5.46339i −0.299392 + 0.299392i
\(334\) 18.7874i 1.02800i
\(335\) 5.95604 2.31963i 0.325413 0.126735i
\(336\) 2.55834i 0.139569i
\(337\) 4.75471 + 4.75471i 0.259006 + 0.259006i 0.824650 0.565644i \(-0.191372\pi\)
−0.565644 + 0.824650i \(0.691372\pi\)
\(338\) −5.18926 5.18926i −0.282259 0.282259i
\(339\) 19.8865 1.08009
\(340\) −1.93314 4.96367i −0.104839 0.269193i
\(341\) 30.3018i 1.64094i
\(342\) −3.70595 3.70595i −0.200395 0.200395i
\(343\) 13.4861 13.4861i 0.728179 0.728179i
\(344\) 9.02081 0.486370
\(345\) 7.67699 + 7.48758i 0.413315 + 0.403118i
\(346\) −18.9232 −1.01732
\(347\) −3.12333 + 3.12333i −0.167669 + 0.167669i −0.785954 0.618285i \(-0.787828\pi\)
0.618285 + 0.785954i \(0.287828\pi\)
\(348\) −2.46149 2.46149i −0.131950 0.131950i
\(349\) 16.1446i 0.864201i −0.901825 0.432101i \(-0.857773\pi\)
0.901825 0.432101i \(-0.142227\pi\)
\(350\) 8.65143 + 9.42231i 0.462438 + 0.503644i
\(351\) 4.50985 0.240718
\(352\) 2.94669 + 2.94669i 0.157059 + 0.157059i
\(353\) −10.2236 10.2236i −0.544146 0.544146i 0.380596 0.924742i \(-0.375719\pi\)
−0.924742 + 0.380596i \(0.875719\pi\)
\(354\) 6.80402i 0.361630i
\(355\) −8.60324 + 19.5791i −0.456612 + 1.03915i
\(356\) 3.58782i 0.190154i
\(357\) −4.30950 + 4.30950i −0.228083 + 0.228083i
\(358\) 12.1096 + 12.1096i 0.640010 + 0.640010i
\(359\) 18.2877 0.965188 0.482594 0.875844i \(-0.339695\pi\)
0.482594 + 0.875844i \(0.339695\pi\)
\(360\) 0.811485 + 2.08362i 0.0427690 + 0.109817i
\(361\) 8.46813 0.445691
\(362\) 4.96934 + 4.96934i 0.261183 + 0.261183i
\(363\) −4.50142 4.50142i −0.236263 0.236263i
\(364\) −11.5377 −0.604740
\(365\) −17.0389 + 6.63595i −0.891858 + 0.347341i
\(366\) 0.759260i 0.0396872i
\(367\) −7.66636 7.66636i −0.400181 0.400181i 0.478116 0.878297i \(-0.341320\pi\)
−0.878297 + 0.478116i \(0.841320\pi\)
\(368\) −1.98398 4.36621i −0.103422 0.227605i
\(369\) 4.53754i 0.236215i
\(370\) −6.95019 + 15.8171i −0.361323 + 0.822292i
\(371\) −23.7514 −1.23311
\(372\) 5.14167 5.14167i 0.266583 0.266583i
\(373\) −18.9572 + 18.9572i −0.981564 + 0.981564i −0.999833 0.0182689i \(-0.994185\pi\)
0.0182689 + 0.999833i \(0.494185\pi\)
\(374\) 9.92735i 0.513331i
\(375\) −10.0348 4.92979i −0.518195 0.254573i
\(376\) −12.8600 −0.663206
\(377\) −11.1009 + 11.1009i −0.571727 + 0.571727i
\(378\) 1.80902 1.80902i 0.0930458 0.0930458i
\(379\) −21.8702 −1.12340 −0.561699 0.827341i \(-0.689852\pi\)
−0.561699 + 0.827341i \(0.689852\pi\)
\(380\) −10.7291 4.71449i −0.550393 0.241848i
\(381\) −10.0762 −0.516218
\(382\) 15.7745 + 15.7745i 0.807094 + 0.807094i
\(383\) 20.5841 20.5841i 1.05180 1.05180i 0.0532143 0.998583i \(-0.483053\pi\)
0.998583 0.0532143i \(-0.0169466\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 8.65143 + 22.2140i 0.440918 + 1.13213i
\(386\) 17.7323 0.902550
\(387\) 6.37868 + 6.37868i 0.324246 + 0.324246i
\(388\) 4.03278 4.03278i 0.204734 0.204734i
\(389\) 2.71068 0.137437 0.0687184 0.997636i \(-0.478109\pi\)
0.0687184 + 0.997636i \(0.478109\pi\)
\(390\) 9.39683 3.65967i 0.475827 0.185315i
\(391\) −4.01285 + 10.6968i −0.202938 + 0.540963i
\(392\) 0.321672 0.321672i 0.0162469 0.0162469i
\(393\) 1.40378 + 1.40378i 0.0708113 + 0.0708113i
\(394\) 2.86759i 0.144467i
\(395\) −6.16152 + 14.0223i −0.310020 + 0.705536i
\(396\) 4.16725i 0.209412i
\(397\) 26.9536 26.9536i 1.35276 1.35276i 0.470203 0.882558i \(-0.344181\pi\)
0.882558 0.470203i \(-0.155819\pi\)
\(398\) −3.44834 + 3.44834i −0.172850 + 0.172850i
\(399\) 13.4083i 0.671252i
\(400\) 3.38166 + 3.68298i 0.169083 + 0.184149i
\(401\) 9.86390i 0.492580i 0.969196 + 0.246290i \(0.0792115\pi\)
−0.969196 + 0.246290i \(0.920788\pi\)
\(402\) −2.02126 2.02126i −0.100812 0.100812i
\(403\) −23.1881 23.1881i −1.15508 1.15508i
\(404\) 6.36488i 0.316665i
\(405\) −0.899538 + 2.04715i −0.0446984 + 0.101724i
\(406\) 8.90575i 0.441985i
\(407\) −22.7673 + 22.7673i −1.12853 + 1.12853i
\(408\) −1.68449 + 1.68449i −0.0833947 + 0.0833947i
\(409\) 30.0925i 1.48798i 0.668191 + 0.743990i \(0.267069\pi\)
−0.668191 + 0.743990i \(0.732931\pi\)
\(410\) 3.68215 + 9.45453i 0.181848 + 0.466926i
\(411\) 19.3607i 0.954993i
\(412\) −1.99918 1.99918i −0.0984926 0.0984926i
\(413\) 12.3086 12.3086i 0.605666 0.605666i
\(414\) 1.68449 4.49027i 0.0827882 0.220685i
\(415\) 2.76449 + 7.09828i 0.135703 + 0.348441i
\(416\) −4.50985 −0.221113
\(417\) 13.7406 13.7406i 0.672878 0.672878i
\(418\) −15.4436 15.4436i −0.755372 0.755372i
\(419\) −7.59626 −0.371102 −0.185551 0.982635i \(-0.559407\pi\)
−0.185551 + 0.982635i \(0.559407\pi\)
\(420\) 2.30132 5.23730i 0.112293 0.255554i
\(421\) 23.4653i 1.14363i 0.820382 + 0.571816i \(0.193761\pi\)
−0.820382 + 0.571816i \(0.806239\pi\)
\(422\) 7.38210 7.38210i 0.359355 0.359355i
\(423\) −9.09342 9.09342i −0.442137 0.442137i
\(424\) −9.28392 −0.450867
\(425\) 0.507575 11.9003i 0.0246210 0.577251i
\(426\) 9.56406 0.463380
\(427\) 1.37351 1.37351i 0.0664690 0.0664690i
\(428\) 6.26821 6.26821i 0.302985 0.302985i
\(429\) 18.7937 0.907366
\(430\) 18.4670 + 8.11457i 0.890557 + 0.391319i
\(431\) 21.7988i 1.05001i −0.851099 0.525005i \(-0.824063\pi\)
0.851099 0.525005i \(-0.175937\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) −17.0890 + 17.0890i −0.821245 + 0.821245i −0.986287 0.165041i \(-0.947224\pi\)
0.165041 + 0.986287i \(0.447224\pi\)
\(434\) −18.6027 −0.892960
\(435\) −2.82484 7.25324i −0.135441 0.347766i
\(436\) 1.53597i 0.0735595i
\(437\) 10.3981 + 22.8833i 0.497407 + 1.09466i
\(438\) 5.78239 + 5.78239i 0.276293 + 0.276293i
\(439\) 18.6384i 0.889563i 0.895639 + 0.444781i \(0.146719\pi\)
−0.895639 + 0.444781i \(0.853281\pi\)
\(440\) 3.38166 + 8.68298i 0.161214 + 0.413945i
\(441\) 0.454913 0.0216625
\(442\) 7.59680 + 7.59680i 0.361343 + 0.361343i
\(443\) 7.32527 + 7.32527i 0.348034 + 0.348034i 0.859377 0.511343i \(-0.170852\pi\)
−0.511343 + 0.859377i \(0.670852\pi\)
\(444\) 7.72640 0.366679
\(445\) −3.22738 + 7.34481i −0.152993 + 0.348177i
\(446\) −16.8395 −0.797373
\(447\) 2.38490 + 2.38490i 0.112802 + 0.112802i
\(448\) −1.80902 + 1.80902i −0.0854680 + 0.0854680i
\(449\) 12.9705i 0.612116i −0.952013 0.306058i \(-0.900990\pi\)
0.952013 0.306058i \(-0.0990102\pi\)
\(450\) −0.213067 + 4.99546i −0.0100441 + 0.235488i
\(451\) 18.9091i 0.890393i
\(452\) −14.0619 14.0619i −0.661417 0.661417i
\(453\) −13.2254 13.2254i −0.621383 0.621383i
\(454\) −0.342612 −0.0160796
\(455\) −23.6194 10.3786i −1.10730 0.486557i
\(456\) 5.24101i 0.245433i
\(457\) 27.4401 + 27.4401i 1.28360 + 1.28360i 0.938607 + 0.344988i \(0.112117\pi\)
0.344988 + 0.938607i \(0.387883\pi\)
\(458\) 4.10563 4.10563i 0.191843 0.191843i
\(459\) −2.38223 −0.111193
\(460\) −0.133937 10.7230i −0.00624484 0.499961i
\(461\) 10.2068 0.475376 0.237688 0.971342i \(-0.423610\pi\)
0.237688 + 0.971342i \(0.423610\pi\)
\(462\) 7.53863 7.53863i 0.350729 0.350729i
\(463\) −8.13895 8.13895i −0.378249 0.378249i 0.492221 0.870470i \(-0.336185\pi\)
−0.870470 + 0.492221i \(0.836185\pi\)
\(464\) 3.48107i 0.161605i
\(465\) 15.1509 5.90065i 0.702607 0.273636i
\(466\) 15.9696 0.739779
\(467\) 20.9496 + 20.9496i 0.969434 + 0.969434i 0.999547 0.0301128i \(-0.00958666\pi\)
−0.0301128 + 0.999547i \(0.509587\pi\)
\(468\) −3.18894 3.18894i −0.147409 0.147409i
\(469\) 7.31300i 0.337683i
\(470\) −26.3265 11.5681i −1.21435 0.533597i
\(471\) 16.7427i 0.771462i
\(472\) 4.81117 4.81117i 0.221452 0.221452i
\(473\) 26.5815 + 26.5815i 1.22222 + 1.22222i
\(474\) 6.84964 0.314614
\(475\) −17.7233 19.3025i −0.813201 0.885661i
\(476\) 6.09455 0.279343
\(477\) −6.56472 6.56472i −0.300578 0.300578i
\(478\) 0.323564 + 0.323564i 0.0147995 + 0.0147995i
\(479\) −23.4064 −1.06947 −0.534733 0.845021i \(-0.679588\pi\)
−0.534733 + 0.845021i \(0.679588\pi\)
\(480\) 0.899538 2.04715i 0.0410581 0.0934393i
\(481\) 34.8449i 1.58879i
\(482\) −15.7409 15.7409i −0.716976 0.716976i
\(483\) −11.1702 + 5.07570i −0.508264 + 0.230952i
\(484\) 6.36597i 0.289362i
\(485\) 11.8834 4.62808i 0.539596 0.210150i
\(486\) 1.00000 0.0453609
\(487\) 22.9383 22.9383i 1.03943 1.03943i 0.0402440 0.999190i \(-0.487186\pi\)
0.999190 0.0402440i \(-0.0128135\pi\)
\(488\) 0.536878 0.536878i 0.0243033 0.0243033i
\(489\) 11.8481i 0.535791i
\(490\) 0.947867 0.369155i 0.0428203 0.0166767i
\(491\) 30.8377 1.39169 0.695844 0.718193i \(-0.255031\pi\)
0.695844 + 0.718193i \(0.255031\pi\)
\(492\) 3.20853 3.20853i 0.144651 0.144651i
\(493\) 5.86383 5.86383i 0.264094 0.264094i
\(494\) 23.6361 1.06344
\(495\) −3.74860 + 8.53099i −0.168487 + 0.383440i
\(496\) −7.27142 −0.326496
\(497\) −17.3015 17.3015i −0.776080 0.776080i
\(498\) 2.40890 2.40890i 0.107945 0.107945i
\(499\) 25.4897i 1.14107i 0.821272 + 0.570537i \(0.193265\pi\)
−0.821272 + 0.570537i \(0.806735\pi\)
\(500\) 3.60979 + 10.5816i 0.161435 + 0.473222i
\(501\) −18.7874 −0.839359
\(502\) 18.8845 + 18.8845i 0.842858 + 0.842858i
\(503\) −3.49872 + 3.49872i −0.156000 + 0.156000i −0.780792 0.624792i \(-0.785184\pi\)
0.624792 + 0.780792i \(0.285184\pi\)
\(504\) −2.55834 −0.113957
\(505\) 5.72545 13.0299i 0.254779 0.579822i
\(506\) 7.01970 18.7121i 0.312064 0.831852i
\(507\) −5.18926 + 5.18926i −0.230463 + 0.230463i
\(508\) 7.12493 + 7.12493i 0.316117 + 0.316117i
\(509\) 26.2453i 1.16330i 0.813439 + 0.581651i \(0.197593\pi\)
−0.813439 + 0.581651i \(0.802407\pi\)
\(510\) −4.96367 + 1.93314i −0.219795 + 0.0856011i
\(511\) 20.9209i 0.925486i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −3.70595 + 3.70595i −0.163622 + 0.163622i
\(514\) 7.54946i 0.332992i
\(515\) −2.29429 5.89097i −0.101098 0.259587i
\(516\) 9.02081i 0.397119i
\(517\) −37.8946 37.8946i −1.66660 1.66660i
\(518\) −13.9772 13.9772i −0.614122 0.614122i
\(519\) 18.9232i 0.830636i
\(520\) −9.23234 4.05678i −0.404865 0.177902i
\(521\) 16.1892i 0.709263i 0.935006 + 0.354631i \(0.115394\pi\)
−0.935006 + 0.354631i \(0.884606\pi\)
\(522\) −2.46149 + 2.46149i −0.107736 + 0.107736i
\(523\) −1.41722 + 1.41722i −0.0619705 + 0.0619705i −0.737413 0.675442i \(-0.763953\pi\)
0.675442 + 0.737413i \(0.263953\pi\)
\(524\) 1.98524i 0.0867257i
\(525\) 9.42231 8.65143i 0.411223 0.377579i
\(526\) 27.6060i 1.20368i
\(527\) 12.2486 + 12.2486i 0.533559 + 0.533559i
\(528\) 2.94669 2.94669i 0.128238 0.128238i
\(529\) −15.1276 + 17.3250i −0.657723 + 0.753260i
\(530\) −19.0056 8.35125i −0.825551 0.362755i
\(531\) 6.80402 0.295269
\(532\) 9.48107 9.48107i 0.411056 0.411056i
\(533\) −14.4700 14.4700i −0.626764 0.626764i
\(534\) 3.58782 0.155260
\(535\) 18.4705 7.19348i 0.798548 0.311001i
\(536\) 2.85850i 0.123468i
\(537\) 12.1096 12.1096i 0.522566 0.522566i
\(538\) 3.10329 + 3.10329i 0.133793 + 0.133793i
\(539\) 1.89573 0.0816551
\(540\) 2.08362 0.811485i 0.0896649 0.0349208i
\(541\) −3.67997 −0.158214 −0.0791072 0.996866i \(-0.525207\pi\)
−0.0791072 + 0.996866i \(0.525207\pi\)
\(542\) −13.3660 + 13.3660i −0.574117 + 0.574117i
\(543\) 4.96934 4.96934i 0.213255 0.213255i
\(544\) 2.38223 0.102137
\(545\) 1.38166 3.14436i 0.0591839 0.134689i
\(546\) 11.5377i 0.493768i
\(547\) −4.37686 + 4.37686i −0.187141 + 0.187141i −0.794459 0.607318i \(-0.792245\pi\)
0.607318 + 0.794459i \(0.292245\pi\)
\(548\) −13.6901 + 13.6901i −0.584812 + 0.584812i
\(549\) 0.759260 0.0324044
\(550\) −0.887903 + 20.8173i −0.0378603 + 0.887653i
\(551\) 18.2443i 0.777233i
\(552\) −4.36621 + 1.98398i −0.185838 + 0.0844439i
\(553\) −12.3911 12.3911i −0.526924 0.526924i
\(554\) 3.45666i 0.146860i
\(555\) 15.8171 + 6.95019i 0.671399 + 0.295019i
\(556\) −19.4321 −0.824104
\(557\) −3.04302 3.04302i −0.128937 0.128937i 0.639693 0.768630i \(-0.279061\pi\)
−0.768630 + 0.639693i \(0.779061\pi\)
\(558\) −5.14167 5.14167i −0.217664 0.217664i
\(559\) −40.6825 −1.72069
\(560\) −5.33061 + 2.07605i −0.225260 + 0.0877292i
\(561\) −9.92735 −0.419133
\(562\) 1.65338 + 1.65338i 0.0697436 + 0.0697436i
\(563\) 27.0816 27.0816i 1.14135 1.14135i 0.153151 0.988203i \(-0.451058\pi\)
0.988203 0.153151i \(-0.0489420\pi\)
\(564\) 12.8600i 0.541505i
\(565\) −16.1376 41.4361i −0.678915 1.74323i
\(566\) 30.5657i 1.28477i
\(567\) −1.80902 1.80902i −0.0759716 0.0759716i
\(568\) −6.76281 6.76281i −0.283761 0.283761i
\(569\) −34.6663 −1.45329 −0.726644 0.687014i \(-0.758921\pi\)
−0.726644 + 0.687014i \(0.758921\pi\)
\(570\) −4.71449 + 10.7291i −0.197468 + 0.449394i
\(571\) 9.50431i 0.397743i −0.980026 0.198871i \(-0.936272\pi\)
0.980026 0.198871i \(-0.0637276\pi\)
\(572\) −13.2891 13.2891i −0.555646 0.555646i
\(573\) 15.7745 15.7745i 0.658990 0.658990i
\(574\) −11.6086 −0.484532
\(575\) 9.37153 22.0720i 0.390820 0.920467i
\(576\) −1.00000 −0.0416667
\(577\) −5.16579 + 5.16579i −0.215054 + 0.215054i −0.806411 0.591356i \(-0.798593\pi\)
0.591356 + 0.806411i \(0.298593\pi\)
\(578\) 8.00797 + 8.00797i 0.333088 + 0.333088i
\(579\) 17.7323i 0.736929i
\(580\) −3.13136 + 7.12628i −0.130022 + 0.295903i
\(581\) −8.71549 −0.361579
\(582\) −4.03278 4.03278i −0.167164 0.167164i
\(583\) −27.3568 27.3568i −1.13300 1.13300i
\(584\) 8.17754i 0.338389i
\(585\) −3.65967 9.39683i −0.151309 0.388511i
\(586\) 30.3330i 1.25305i
\(587\) −3.80896 + 3.80896i −0.157213 + 0.157213i −0.781330 0.624118i \(-0.785459\pi\)
0.624118 + 0.781330i \(0.285459\pi\)
\(588\) −0.321672 0.321672i −0.0132655 0.0132655i
\(589\) 38.1095 1.57028
\(590\) 14.1770 5.52136i 0.583659 0.227311i
\(591\) −2.86759 −0.117957
\(592\) −5.46339 5.46339i −0.224544 0.224544i
\(593\) −1.75845 1.75845i −0.0722109 0.0722109i 0.670079 0.742290i \(-0.266260\pi\)
−0.742290 + 0.670079i \(0.766260\pi\)
\(594\) 4.16725 0.170984
\(595\) 12.4765 + 5.48228i 0.511485 + 0.224752i
\(596\) 3.37276i 0.138154i
\(597\) 3.44834 + 3.44834i 0.141131 + 0.141131i
\(598\) 8.94746 + 19.6910i 0.365889 + 0.805223i
\(599\) 36.0972i 1.47489i −0.675407 0.737445i \(-0.736032\pi\)
0.675407 0.737445i \(-0.263968\pi\)
\(600\) 3.68298 3.38166i 0.150357 0.138056i
\(601\) 24.9687 1.01849 0.509247 0.860620i \(-0.329924\pi\)
0.509247 + 0.860620i \(0.329924\pi\)
\(602\) −16.3188 + 16.3188i −0.665105 + 0.665105i
\(603\) −2.02126 + 2.02126i −0.0823122 + 0.0823122i
\(604\) 18.7035i 0.761035i
\(605\) −5.72643 + 13.0321i −0.232813 + 0.529830i
\(606\) −6.36488 −0.258556
\(607\) −25.6608 + 25.6608i −1.04154 + 1.04154i −0.0424416 + 0.999099i \(0.513514\pi\)
−0.999099 + 0.0424416i \(0.986486\pi\)
\(608\) 3.70595 3.70595i 0.150296 0.150296i
\(609\) 8.90575 0.360879
\(610\) 1.58201 0.616128i 0.0640538 0.0249463i
\(611\) 57.9968 2.34630
\(612\) 1.68449 + 1.68449i 0.0680915 + 0.0680915i
\(613\) −27.1716 + 27.1716i −1.09745 + 1.09745i −0.102742 + 0.994708i \(0.532762\pi\)
−0.994708 + 0.102742i \(0.967238\pi\)
\(614\) 16.9709i 0.684889i
\(615\) 9.45453 3.68215i 0.381243 0.148478i
\(616\) −10.6612 −0.429553
\(617\) −20.6665 20.6665i −0.832002 0.832002i 0.155789 0.987790i \(-0.450208\pi\)
−0.987790 + 0.155789i \(0.950208\pi\)
\(618\) −1.99918 + 1.99918i −0.0804189 + 0.0804189i
\(619\) 44.8826 1.80398 0.901991 0.431754i \(-0.142105\pi\)
0.901991 + 0.431754i \(0.142105\pi\)
\(620\) −14.8857 6.54092i −0.597824 0.262690i
\(621\) −4.49027 1.68449i −0.180188 0.0675963i
\(622\) −1.10744 + 1.10744i −0.0444043 + 0.0444043i
\(623\) −6.49043 6.49043i −0.260033 0.260033i
\(624\) 4.50985i 0.180538i
\(625\) −2.12873 + 24.9092i −0.0851494 + 0.996368i
\(626\) 12.6534i 0.505733i
\(627\) −15.4436 + 15.4436i −0.616759 + 0.616759i
\(628\) −11.8389 + 11.8389i −0.472422 + 0.472422i
\(629\) 18.4061i 0.733897i
\(630\) −5.23730 2.30132i −0.208659 0.0916869i
\(631\) 39.6759i 1.57947i 0.613448 + 0.789735i \(0.289782\pi\)
−0.613448 + 0.789735i \(0.710218\pi\)
\(632\) −4.84343 4.84343i −0.192661 0.192661i
\(633\) −7.38210 7.38210i −0.293412 0.293412i
\(634\) 11.9273i 0.473695i
\(635\) 8.17666 + 20.9949i 0.324481 + 0.833159i
\(636\) 9.28392i 0.368131i
\(637\) −1.45069 + 1.45069i −0.0574785 + 0.0574785i
\(638\) −10.2576 + 10.2576i −0.406104 + 0.406104i
\(639\) 9.56406i 0.378348i
\(640\) −2.08362 + 0.811485i −0.0823625 + 0.0320768i
\(641\) 20.9245i 0.826466i −0.910625 0.413233i \(-0.864399\pi\)
0.910625 0.413233i \(-0.135601\pi\)
\(642\) −6.26821 6.26821i −0.247387 0.247387i
\(643\) 19.5758 19.5758i 0.771994 0.771994i −0.206461 0.978455i \(-0.566195\pi\)
0.978455 + 0.206461i \(0.0661947\pi\)
\(644\) 11.4876 + 4.30950i 0.452675 + 0.169818i
\(645\) 8.11457 18.4670i 0.319511 0.727136i
\(646\) −12.4853 −0.491227
\(647\) 27.6953 27.6953i 1.08881 1.08881i 0.0931635 0.995651i \(-0.470302\pi\)
0.995651 0.0931635i \(-0.0296979\pi\)
\(648\) −0.707107 0.707107i −0.0277778 0.0277778i
\(649\) 28.3541 1.11299
\(650\) −15.2508 16.6097i −0.598185 0.651486i
\(651\) 18.6027i 0.729099i
\(652\) −8.37789 + 8.37789i −0.328103 + 0.328103i
\(653\) −22.7542 22.7542i −0.890442 0.890442i 0.104122 0.994564i \(-0.466797\pi\)
−0.994564 + 0.104122i \(0.966797\pi\)
\(654\) −1.53597 −0.0600611
\(655\) 1.78580 4.06409i 0.0697771 0.158797i
\(656\) −4.53754 −0.177161
\(657\) 5.78239 5.78239i 0.225593 0.225593i
\(658\) 23.2640 23.2640i 0.906927 0.906927i
\(659\) 16.1643 0.629673 0.314837 0.949146i \(-0.398050\pi\)
0.314837 + 0.949146i \(0.398050\pi\)
\(660\) 8.68298 3.38166i 0.337985 0.131631i
\(661\) 20.0621i 0.780326i −0.920746 0.390163i \(-0.872419\pi\)
0.920746 0.390163i \(-0.127581\pi\)
\(662\) −9.15632 + 9.15632i −0.355870 + 0.355870i
\(663\) 7.59680 7.59680i 0.295035 0.295035i
\(664\) −3.40670 −0.132206
\(665\) 27.9378 10.8806i 1.08338 0.421932i
\(666\) 7.72640i 0.299392i
\(667\) 15.1991 6.90638i 0.588511 0.267416i
\(668\) 13.2847 + 13.2847i 0.514000 + 0.514000i
\(669\) 16.8395i 0.651052i
\(670\) −2.57133 + 5.85178i −0.0993391 + 0.226074i
\(671\) 3.16403 0.122146
\(672\) 1.80902 + 1.80902i 0.0697844 + 0.0697844i
\(673\) −24.4850 24.4850i −0.943829 0.943829i 0.0546752 0.998504i \(-0.482588\pi\)
−0.998504 + 0.0546752i \(0.982588\pi\)
\(674\) −6.72418 −0.259006
\(675\) 4.99546 + 0.213067i 0.192275 + 0.00820095i
\(676\) 7.33872 0.282259
\(677\) −13.9941 13.9941i −0.537836 0.537836i 0.385057 0.922893i \(-0.374182\pi\)
−0.922893 + 0.385057i \(0.874182\pi\)
\(678\) −14.0619 + 14.0619i −0.540044 + 0.540044i
\(679\) 14.5907i 0.559942i
\(680\) 4.87679 + 2.14291i 0.187016 + 0.0821768i
\(681\) 0.342612i 0.0131289i
\(682\) −21.4266 21.4266i −0.820468 0.820468i
\(683\) 2.28231 + 2.28231i 0.0873303 + 0.0873303i 0.749422 0.662092i \(-0.230331\pi\)
−0.662092 + 0.749422i \(0.730331\pi\)
\(684\) 5.24101 0.200395
\(685\) −40.3405 + 15.7109i −1.54133 + 0.600284i
\(686\) 19.0722i 0.728179i
\(687\) −4.10563 4.10563i −0.156639 0.156639i
\(688\) −6.37868 + 6.37868i −0.243185 + 0.243185i
\(689\) 41.8691 1.59508
\(690\) −10.7230 + 0.133937i −0.408216 + 0.00509889i
\(691\) 15.2845 0.581450 0.290725 0.956807i \(-0.406103\pi\)
0.290725 + 0.956807i \(0.406103\pi\)
\(692\) 13.3807 13.3807i 0.508659 0.508659i
\(693\) −7.53863 7.53863i −0.286369 0.286369i
\(694\) 4.41705i 0.167669i
\(695\) −39.7805 17.4799i −1.50896 0.663051i
\(696\) 3.48107 0.131950
\(697\) 7.64345 + 7.64345i 0.289516 + 0.289516i
\(698\) 11.4160 + 11.4160i 0.432101 + 0.432101i
\(699\) 15.9696i 0.604027i
\(700\) −12.7801 0.545097i −0.483041 0.0206027i
\(701\) 16.4549i 0.621493i 0.950493 + 0.310746i \(0.100579\pi\)
−0.950493 + 0.310746i \(0.899421\pi\)
\(702\) −3.18894 + 3.18894i −0.120359 + 0.120359i
\(703\) 28.6336 + 28.6336i 1.07994 + 1.07994i
\(704\) −4.16725 −0.157059
\(705\) −11.5681 + 26.3265i −0.435680 + 0.991512i
\(706\) 14.4583 0.544146
\(707\) 11.5142 + 11.5142i 0.433035 + 0.433035i
\(708\) −4.81117 4.81117i −0.180815 0.180815i
\(709\) 45.9132 1.72431 0.862153 0.506648i \(-0.169116\pi\)
0.862153 + 0.506648i \(0.169116\pi\)
\(710\) −7.76109 19.9279i −0.291269 0.747881i
\(711\) 6.84964i 0.256882i
\(712\) −2.53697 2.53697i −0.0950770 0.0950770i
\(713\) 14.4264 + 31.7486i 0.540272 + 1.18899i
\(714\) 6.09455i 0.228083i
\(715\) −15.2508 39.1589i −0.570347 1.46446i
\(716\) −17.1255 −0.640010
\(717\) 0.323564 0.323564i 0.0120837 0.0120837i
\(718\) −12.9314 + 12.9314i −0.482594 + 0.482594i
\(719\) 30.7995i 1.14863i 0.818635 + 0.574314i \(0.194731\pi\)
−0.818635 + 0.574314i \(0.805269\pi\)
\(720\) −2.04715 0.899538i −0.0762928 0.0335238i
\(721\) 7.23311 0.269375
\(722\) −5.98787 + 5.98787i −0.222846 + 0.222846i
\(723\) −15.7409 + 15.7409i −0.585409 + 0.585409i
\(724\) −7.02770 −0.261183
\(725\) −12.8207 + 11.7718i −0.476150 + 0.437194i
\(726\) 6.36597 0.236263
\(727\) −14.2480 14.2480i −0.528429 0.528429i 0.391674 0.920104i \(-0.371896\pi\)
−0.920104 + 0.391674i \(0.871896\pi\)
\(728\) 8.15839 8.15839i 0.302370 0.302370i
\(729\) 1.00000i 0.0370370i
\(730\) 7.35601 16.7407i 0.272258 0.619600i
\(731\) 21.4897 0.794824
\(732\) −0.536878 0.536878i −0.0198436 0.0198436i
\(733\) −4.70374 + 4.70374i −0.173737 + 0.173737i −0.788619 0.614882i \(-0.789203\pi\)
0.614882 + 0.788619i \(0.289203\pi\)
\(734\) 10.8419 0.400181
\(735\) −0.369155 0.947867i −0.0136165 0.0349626i
\(736\) 4.49027 + 1.68449i 0.165513 + 0.0620912i
\(737\) −8.42311 + 8.42311i −0.310269 + 0.310269i
\(738\) −3.20853 3.20853i −0.118107 0.118107i
\(739\) 35.3216i 1.29932i 0.760223 + 0.649662i \(0.225090\pi\)
−0.760223 + 0.649662i \(0.774910\pi\)
\(740\) −6.26986 16.0989i −0.230484 0.591808i
\(741\) 23.6361i 0.868295i
\(742\) 16.7948 16.7948i 0.616556 0.616556i
\(743\) −18.5881 + 18.5881i −0.681932 + 0.681932i −0.960435 0.278503i \(-0.910162\pi\)
0.278503 + 0.960435i \(0.410162\pi\)
\(744\) 7.27142i 0.266583i
\(745\) 3.03393 6.90455i 0.111155 0.252963i
\(746\) 26.8095i 0.981564i
\(747\) −2.40890 2.40890i −0.0881371 0.0881371i
\(748\) 7.01970 + 7.01970i 0.256665 + 0.256665i
\(749\) 22.6786i 0.828658i
\(750\) 10.5816 3.60979i 0.386384 0.131811i
\(751\) 23.3137i 0.850727i 0.905022 + 0.425364i \(0.139854\pi\)
−0.905022 + 0.425364i \(0.860146\pi\)
\(752\) 9.09342 9.09342i 0.331603 0.331603i
\(753\) 18.8845 18.8845i 0.688191 0.688191i
\(754\) 15.6991i 0.571727i
\(755\) −16.8245 + 38.2889i −0.612307 + 1.39348i
\(756\) 2.55834i 0.0930458i
\(757\) 3.52220 + 3.52220i 0.128016 + 0.128016i 0.768212 0.640196i \(-0.221147\pi\)
−0.640196 + 0.768212i \(0.721147\pi\)
\(758\) 15.4646 15.4646i 0.561699 0.561699i
\(759\) −18.7121 7.01970i −0.679205 0.254799i
\(760\) 10.9203 4.25300i 0.396120 0.154272i
\(761\) −14.8262 −0.537449 −0.268724 0.963217i \(-0.586602\pi\)
−0.268724 + 0.963217i \(0.586602\pi\)
\(762\) 7.12493 7.12493i 0.258109 0.258109i
\(763\) 2.77859 + 2.77859i 0.100592 + 0.100592i
\(764\) −22.3085 −0.807094
\(765\) 1.93314 + 4.96367i 0.0698930 + 0.179462i
\(766\) 29.1103i 1.05180i
\(767\) −21.6976 + 21.6976i −0.783456 + 0.783456i
\(768\) 0.707107 + 0.707107i 0.0255155 + 0.0255155i
\(769\) 14.2891 0.515277 0.257638 0.966241i \(-0.417056\pi\)
0.257638 + 0.966241i \(0.417056\pi\)
\(770\) −21.8252 9.59018i −0.786524 0.345606i
\(771\) −7.54946 −0.271887
\(772\) −12.5386 + 12.5386i −0.451275 + 0.451275i
\(773\) −0.499292 + 0.499292i −0.0179583 + 0.0179583i −0.716029 0.698071i \(-0.754042\pi\)
0.698071 + 0.716029i \(0.254042\pi\)
\(774\) −9.02081 −0.324246
\(775\) −24.5895 26.7805i −0.883280 0.961985i
\(776\) 5.70322i 0.204734i
\(777\) −13.9772 + 13.9772i −0.501429 + 0.501429i
\(778\) −1.91674 + 1.91674i −0.0687184 + 0.0687184i
\(779\) 23.7813 0.852052
\(780\) −4.05678 + 9.23234i −0.145256 + 0.330571i