Properties

Label 690.2.j.a.643.2
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 643.2
Character \(\chi\) \(=\) 690.643
Dual form 690.2.j.a.367.2

$q$-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} +(4.36621 + 1.98398i) 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} +(1.98398 - 4.36621i) 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 0.277098 0.960842i \(-0.410627\pi\)
−0.960842 + 0.277098i \(0.910627\pi\)
\(8\) 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 \(-0.783777\pi\)
0.778022 0.628236i \(-0.216223\pi\)
\(12\) 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 0.472683 0.881232i \(-0.343285\pi\)
−0.881232 + 0.472683i \(0.843285\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) −5.24101 −1.20237 −0.601185 0.799110i \(-0.705304\pi\)
−0.601185 + 0.799110i \(0.705304\pi\)
\(20\) 2.04715 + 0.899538i 0.457757 + 0.201143i
\(21\) 2.55834i 0.558275i
\(22\) 2.94669 + 2.94669i 0.628236 + 0.628236i
\(23\) 4.36621 + 1.98398i 0.910418 + 0.413689i
\(24\) 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 0.0970994 0.995275i \(-0.469044\pi\)
−0.995275 + 0.0970994i \(0.969044\pi\)
\(38\) 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 −0.999638 0.0268989i \(-0.991437\pi\)
0.0268989 + 0.999638i \(0.491437\pi\)
\(44\) −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 −0.0938519 0.995586i \(-0.529918\pi\)
0.995586 + 0.0938519i \(0.0299180\pi\)
\(54\) 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 \(0.0154781\pi\)
−0.998818 + 0.0486066i \(0.984522\pi\)
\(62\) −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 0.572776 0.819712i \(-0.305867\pi\)
−0.819712 + 0.572776i \(0.805867\pi\)
\(68\) −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 \(-0.374090\pi\)
0.385322 + 0.922782i \(0.374090\pi\)
\(80\) 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 −0.562432 0.826843i \(-0.690134\pi\)
0.826843 + 0.562432i \(0.190134\pi\)
\(84\) −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 \(-0.439101\pi\)
0.190154 + 0.981754i \(0.439101\pi\)
\(90\) 2.08362 0.811485i 0.219633 0.0855381i
\(91\) 11.5377i 1.20948i
\(92\) 1.98398 4.36621i 0.206844 0.455209i
\(93\) 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 0.472086 0.881553i \(-0.343501\pi\)
−0.881553 + 0.472086i \(0.843501\pi\)
\(98\) 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 −0.798706 0.601721i \(-0.794482\pi\)
0.601721 + 0.798706i \(0.294482\pi\)
\(104\) 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 0.335920 0.941891i \(-0.390953\pi\)
−0.941891 + 0.335920i \(0.890953\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) −1.53597 −0.147119 −0.0735595 0.997291i \(-0.523436\pi\)
−0.0735595 + 0.997291i \(0.523436\pi\)
\(110\) −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 \(0.634946\pi\)
−0.911473 + 0.411360i \(0.865054\pi\)
\(114\) 5.24101 0.490865
\(115\) −7.98909 + 7.15363i −0.744986 + 0.667080i
\(116\) −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 \(0.0599819\pi\)
0.187325 + 0.982298i \(0.440018\pi\)
\(138\) −4.36621 1.98398i −0.371677 0.168888i
\(139\) 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 \(-0.544117\pi\)
−0.138154 + 0.990411i \(0.544117\pi\)
\(150\) 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 0.998556 0.0537126i \(-0.0171055\pi\)
−0.0537126 + 0.998556i \(0.517105\pi\)
\(158\) −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 \(0.0841124\pi\)
−0.965289 + 0.261183i \(0.915888\pi\)
\(182\) −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 \(0.298961\pi\)
−0.590422 + 0.807094i \(0.701039\pi\)
\(192\) −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 \(-0.555297\pi\)
−0.172850 + 0.984948i \(0.555297\pi\)
\(200\) 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
\(207\) −1.98398 + 4.36621i −0.137896 + 0.303473i
\(208\) 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 0.699021 0.715101i \(-0.253619\pi\)
−0.715101 + 0.699021i \(0.753619\pi\)
\(228\) −3.70595 + 3.70595i −0.245433 + 0.245433i
\(229\) 5.80623 0.383687 0.191843 0.981426i \(-0.438553\pi\)
0.191843 + 0.981426i \(0.438553\pi\)
\(230\) 0.590758 10.7075i 0.0389534 0.706033i
\(231\) −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 \(-0.745526\pi\)
0.697098 0.716976i \(-0.254474\pi\)
\(242\) 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 \(0.319129\pi\)
−0.538135 + 0.842858i \(0.680871\pi\)
\(252\) −1.80902 1.80902i −0.113957 0.113957i
\(253\) 8.26775 18.1951i 0.519789 1.14392i
\(254\) 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 \(-0.425918\pi\)
0.973039 0.230639i \(-0.0740817\pi\)
\(264\) 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 \(0.0222181\pi\)
−0.997565 + 0.0697436i \(0.977782\pi\)
\(282\) 9.09342 9.09342i 0.541505 0.541505i
\(283\) 21.6132 21.6132i 1.28477 1.28477i 0.346850 0.937921i \(-0.387251\pi\)
0.937921 0.346850i \(-0.112749\pi\)
\(284\) 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 \(-0.403447\pi\)
0.954347 0.298699i \(-0.0965528\pi\)
\(294\) 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 −0.913214 0.407481i \(-0.866407\pi\)
0.407481 + 0.913214i \(0.366407\pi\)
\(314\) −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
\(322\) 11.1702 + 5.07570i 0.622493 + 0.282857i
\(323\) 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 0.565644 0.824650i \(-0.308628\pi\)
−0.824650 + 0.565644i \(0.808628\pi\)
\(338\) −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
\(345\) −10.7075 0.590758i −0.576474 0.0318053i
\(346\) −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 \(-0.660305\pi\)
−0.482594 + 0.875844i \(0.660305\pi\)
\(360\) −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 0.878297 0.478116i \(-0.158680\pi\)
−0.478116 + 0.878297i \(0.658680\pi\)
\(368\) −4.36621 1.98398i −0.227605 0.103422i
\(369\) 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 −0.0182689 0.999833i \(-0.505815\pi\)
0.999833 + 0.0182689i \(0.00581550\pi\)
\(374\) 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 \(-0.310148\pi\)
0.561699 + 0.827341i \(0.310148\pi\)
\(380\) −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 \(0.516947\pi\)
−0.998583 + 0.0532143i \(0.983053\pi\)
\(384\) 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 \(-0.521891\pi\)
−0.0687184 + 0.997636i \(0.521891\pi\)
\(390\) −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 \(-0.920788\pi\)
0.969196 0.246290i \(-0.0792115\pi\)
\(402\) 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 \(-0.440593\pi\)
0.185551 + 0.982635i \(0.440593\pi\)
\(420\) 2.30132 5.23730i 0.112293 0.255554i
\(421\) 23.4653i 1.14363i −0.820382 0.571816i \(-0.806239\pi\)
0.820382 0.571816i \(-0.193761\pi\)
\(422\) 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 \(0.175937\pi\)
−0.851099 + 0.525005i \(0.824063\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) 17.0890 17.0890i 0.821245 0.821245i −0.165041 0.986287i \(-0.552776\pi\)
0.986287 + 0.165041i \(0.0527757\pi\)
\(434\) 18.6027 0.892960
\(435\) 2.82484 + 7.25324i 0.135441 + 0.347766i
\(436\) 1.53597i 0.0735595i
\(437\) −22.8833 10.3981i −1.09466 0.497407i
\(438\) 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 \(-0.887883\pi\)
−0.344988 0.938607i \(-0.612117\pi\)
\(458\) −4.10563 + 4.10563i −0.191843 + 0.191843i
\(459\) 2.38223 0.111193
\(460\) 7.15363 + 7.98909i 0.333540 + 0.372493i
\(461\) 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 0.0301128 0.999547i \(-0.490413\pi\)
−0.999547 + 0.0301128i \(0.990413\pi\)
\(468\) −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 \(-0.320412\pi\)
0.534733 + 0.845021i \(0.320412\pi\)
\(480\) −0.899538 + 2.04715i −0.0410581 + 0.0934393i
\(481\) 34.8449i 1.58879i
\(482\) 15.7409 + 15.7409i 0.716976 + 0.716976i
\(483\) 5.07570 11.1702i 0.230952 0.508264i
\(484\) 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 −0.624792 0.780792i \(-0.714816\pi\)
0.780792 + 0.624792i \(0.214816\pi\)
\(504\) 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 \(-0.884606\pi\)
0.935006 0.354631i \(-0.115394\pi\)
\(522\) −2.46149 + 2.46149i −0.107736 + 0.107736i
\(523\) 1.41722 1.41722i 0.0619705 0.0619705i −0.675442 0.737413i \(-0.736047\pi\)
0.737413 + 0.675442i \(0.236047\pi\)
\(524\) 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
\(552\) −1.98398 + 4.36621i −0.0844439 + 0.185838i
\(553\) −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 0.768630 0.639693i \(-0.220939\pi\)
−0.639693 + 0.768630i \(0.720939\pi\)
\(558\) −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 \(0.548942\pi\)
−0.988203 + 0.153151i \(0.951058\pi\)
\(564\) 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 \(-0.241079\pi\)
0.726644 + 0.687014i \(0.241079\pi\)
\(570\) −4.71449 + 10.7291i −0.197468 + 0.449394i
\(571\) 9.50431i 0.397743i 0.980026 + 0.198871i \(0.0637276\pi\)
−0.980026 + 0.198871i \(0.936272\pi\)
\(572\) 13.2891 + 13.2891i 0.555646 + 0.555646i
\(573\) −15.7745 + 15.7745i −0.658990 + 0.658990i
\(574\) 11.6086 0.484532
\(575\) −7.45808 22.7898i −0.311023 0.950402i
\(576\) −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
\(598\) 19.6910 + 8.94746i 0.805223 + 0.365889i
\(599\) 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 \(-0.467238\pi\)
0.994708 0.102742i \(-0.0327615\pi\)
\(614\) 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 0.987790 0.155789i \(-0.0497919\pi\)
−0.155789 + 0.987790i \(0.549792\pi\)
\(618\) 1.99918 1.99918i 0.0804189 0.0804189i
\(619\) −44.8826 −1.80398 −0.901991 0.431754i \(-0.857895\pi\)
−0.901991 + 0.431754i \(0.857895\pi\)
\(620\) 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 \(-0.710218\pi\)
0.613448 0.789735i \(-0.289782\pi\)
\(632\) 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 \(0.135601\pi\)
−0.910625 + 0.413233i \(0.864399\pi\)
\(642\) 6.26821 + 6.26821i 0.247387 + 0.247387i
\(643\) −19.5758 + 19.5758i −0.771994 + 0.771994i −0.978455 0.206461i \(-0.933805\pi\)
0.206461 + 0.978455i \(0.433805\pi\)
\(644\) −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 \(-0.601950\pi\)
−0.314837 + 0.949146i \(0.601950\pi\)
\(660\) 8.68298 3.38166i 0.337985 0.131631i
\(661\) 20.0621i 0.780326i 0.920746 + 0.390163i \(0.127581\pi\)
−0.920746 + 0.390163i \(0.872419\pi\)
\(662\) −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
\(667\) 6.90638 15.1991i 0.267416 0.588511i
\(668\) 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 0.922893 0.385057i \(-0.125818\pi\)
−0.385057 + 0.922893i \(0.625818\pi\)
\(678\) 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
\(690\) 7.98909 7.15363i 0.304139 0.272334i
\(691\) 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 \(-0.899421\pi\)
0.950493 0.310746i \(-0.100579\pi\)
\(702\) −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 \(-0.830884\pi\)
−0.862153 + 0.506648i \(0.830884\pi\)
\(710\) 7.76109 + 19.9279i 0.291269 + 0.747881i
\(711\) 6.84964i 0.256882i
\(712\) 2.53697 + 2.53697i 0.0950770 + 0.0950770i
\(713\) 31.7486 + 14.4264i 1.18899 + 0.540272i
\(714\) 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 0.920104 0.391674i \(-0.128104\pi\)
−0.391674 + 0.920104i \(0.628104\pi\)
\(728\) −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 −0.614882 0.788619i \(-0.710797\pi\)
0.788619 + 0.614882i \(0.210797\pi\)
\(734\) −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 −0.278503 0.960435i \(-0.589838\pi\)
0.960435 + 0.278503i \(0.0898383\pi\)
\(744\) 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 \(-0.860146\pi\)
0.905022 0.425364i \(-0.139854\pi\)
\(752\) 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 0.640196 0.768212i \(-0.278853\pi\)
−0.768212 + 0.640196i \(0.778853\pi\)
\(758\) −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 \(-0.582944\pi\)
−0.257638 + 0.966241i \(0.582944\pi\)
\(770\) 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 −0.698071 0.716029i \(-0.745958\pi\)
0.716029 + 0.698071i \(0.245958\pi\)
\(774\) 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