Properties

Label 690.2.j.b.367.12
Level $690$
Weight $2$
Character 690.367
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 367.12
Character \(\chi\) \(=\) 690.367
Dual form 690.2.j.b.643.12

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(2.19853 + 0.408021i) q^{5} +1.00000 q^{6} +(1.64584 - 1.64584i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(2.19853 + 0.408021i) q^{5} +1.00000 q^{6} +(1.64584 - 1.64584i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(1.26608 + 1.84311i) q^{10} -6.11317i q^{11} +(0.707107 + 0.707107i) q^{12} +(-0.241478 + 0.241478i) q^{13} +2.32757 q^{14} +(1.84311 - 1.26608i) q^{15} -1.00000 q^{16} +(0.327163 - 0.327163i) q^{17} +(0.707107 - 0.707107i) q^{18} -0.759529 q^{19} +(-0.408021 + 2.19853i) q^{20} -2.32757i q^{21} +(4.32266 - 4.32266i) q^{22} +(-1.66757 + 4.49658i) q^{23} +1.00000i q^{24} +(4.66704 + 1.79409i) q^{25} -0.341501 q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.64584 + 1.64584i) q^{28} +7.09541i q^{29} +(2.19853 + 0.408021i) q^{30} -8.30560 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.32266 - 4.32266i) q^{33} +0.462678 q^{34} +(4.28997 - 2.94689i) q^{35} +1.00000 q^{36} +(-1.92602 + 1.92602i) q^{37} +(-0.537068 - 0.537068i) q^{38} +0.341501i q^{39} +(-1.84311 + 1.26608i) q^{40} +6.75167 q^{41} +(1.64584 - 1.64584i) q^{42} +(-0.144662 - 0.144662i) q^{43} +6.11317 q^{44} +(0.408021 - 2.19853i) q^{45} +(-4.35871 + 2.00041i) q^{46} +(1.46451 + 1.46451i) q^{47} +(-0.707107 + 0.707107i) q^{48} +1.58240i q^{49} +(2.03148 + 4.56871i) q^{50} -0.462678i q^{51} +(-0.241478 - 0.241478i) q^{52} +(1.45249 + 1.45249i) q^{53} -1.00000i q^{54} +(2.49430 - 13.4400i) q^{55} +2.32757i q^{56} +(-0.537068 + 0.537068i) q^{57} +(-5.01721 + 5.01721i) q^{58} +1.68540i q^{59} +(1.26608 + 1.84311i) q^{60} +8.05915i q^{61} +(-5.87295 - 5.87295i) q^{62} +(-1.64584 - 1.64584i) q^{63} -1.00000i q^{64} +(-0.629423 + 0.432367i) q^{65} -6.11317i q^{66} +(-3.13950 + 3.13950i) q^{67} +(0.327163 + 0.327163i) q^{68} +(2.00041 + 4.35871i) q^{69} +(5.11723 + 0.949699i) q^{70} +6.24090 q^{71} +(0.707107 + 0.707107i) q^{72} +(6.62866 - 6.62866i) q^{73} -2.72380 q^{74} +(4.56871 - 2.03148i) q^{75} -0.759529i q^{76} +(-10.0613 - 10.0613i) q^{77} +(-0.241478 + 0.241478i) q^{78} -3.83429 q^{79} +(-2.19853 - 0.408021i) q^{80} -1.00000 q^{81} +(4.77416 + 4.77416i) q^{82} +(-2.14295 - 2.14295i) q^{83} +2.32757 q^{84} +(0.852765 - 0.585786i) q^{85} -0.204583i q^{86} +(5.01721 + 5.01721i) q^{87} +(4.32266 + 4.32266i) q^{88} +4.64280 q^{89} +(1.84311 - 1.26608i) q^{90} +0.794868i q^{91} +(-4.49658 - 1.66757i) q^{92} +(-5.87295 + 5.87295i) q^{93} +2.07114i q^{94} +(-1.66985 - 0.309904i) q^{95} -1.00000 q^{96} +(-11.2007 + 11.2007i) q^{97} +(-1.11893 + 1.11893i) q^{98} -6.11317 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 24q^{6} + O(q^{10}) \) \( 24q + 24q^{6} + 16q^{13} - 24q^{16} + 16q^{23} - 16q^{25} + 16q^{31} + 24q^{36} + 8q^{46} + 40q^{47} - 8q^{50} + 16q^{52} - 56q^{55} - 16q^{58} - 8q^{62} + 32q^{70} + 64q^{71} - 16q^{73} + 32q^{75} + 16q^{77} + 16q^{78} - 24q^{81} + 24q^{82} - 48q^{85} + 16q^{87} + 16q^{92} - 8q^{93} + 24q^{95} - 24q^{96} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 2.19853 + 0.408021i 0.983211 + 0.182473i
\(6\) 1.00000 0.408248
\(7\) 1.64584 1.64584i 0.622070 0.622070i −0.323990 0.946060i \(-0.605024\pi\)
0.946060 + 0.323990i \(0.105024\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 1.26608 + 1.84311i 0.400369 + 0.582842i
\(11\) 6.11317i 1.84319i −0.388154 0.921595i \(-0.626887\pi\)
0.388154 0.921595i \(-0.373113\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) −0.241478 + 0.241478i −0.0669738 + 0.0669738i −0.739800 0.672826i \(-0.765080\pi\)
0.672826 + 0.739800i \(0.265080\pi\)
\(14\) 2.32757 0.622070
\(15\) 1.84311 1.26608i 0.475888 0.326900i
\(16\) −1.00000 −0.250000
\(17\) 0.327163 0.327163i 0.0793486 0.0793486i −0.666319 0.745667i \(-0.732131\pi\)
0.745667 + 0.666319i \(0.232131\pi\)
\(18\) 0.707107 0.707107i 0.166667 0.166667i
\(19\) −0.759529 −0.174248 −0.0871240 0.996197i \(-0.527768\pi\)
−0.0871240 + 0.996197i \(0.527768\pi\)
\(20\) −0.408021 + 2.19853i −0.0912363 + 0.491605i
\(21\) 2.32757i 0.507918i
\(22\) 4.32266 4.32266i 0.921595 0.921595i
\(23\) −1.66757 + 4.49658i −0.347712 + 0.937601i
\(24\) 1.00000i 0.204124i
\(25\) 4.66704 + 1.79409i 0.933408 + 0.358818i
\(26\) −0.341501 −0.0669738
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 1.64584 + 1.64584i 0.311035 + 0.311035i
\(29\) 7.09541i 1.31758i 0.752325 + 0.658792i \(0.228932\pi\)
−0.752325 + 0.658792i \(0.771068\pi\)
\(30\) 2.19853 + 0.408021i 0.401394 + 0.0744941i
\(31\) −8.30560 −1.49173 −0.745865 0.666097i \(-0.767964\pi\)
−0.745865 + 0.666097i \(0.767964\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −4.32266 4.32266i −0.752479 0.752479i
\(34\) 0.462678 0.0793486
\(35\) 4.28997 2.94689i 0.725137 0.498116i
\(36\) 1.00000 0.166667
\(37\) −1.92602 + 1.92602i −0.316636 + 0.316636i −0.847474 0.530838i \(-0.821877\pi\)
0.530838 + 0.847474i \(0.321877\pi\)
\(38\) −0.537068 0.537068i −0.0871240 0.0871240i
\(39\) 0.341501i 0.0546839i
\(40\) −1.84311 + 1.26608i −0.291421 + 0.200185i
\(41\) 6.75167 1.05443 0.527217 0.849731i \(-0.323235\pi\)
0.527217 + 0.849731i \(0.323235\pi\)
\(42\) 1.64584 1.64584i 0.253959 0.253959i
\(43\) −0.144662 0.144662i −0.0220608 0.0220608i 0.695990 0.718051i \(-0.254966\pi\)
−0.718051 + 0.695990i \(0.754966\pi\)
\(44\) 6.11317 0.921595
\(45\) 0.408021 2.19853i 0.0608242 0.327737i
\(46\) −4.35871 + 2.00041i −0.642657 + 0.294945i
\(47\) 1.46451 + 1.46451i 0.213621 + 0.213621i 0.805804 0.592183i \(-0.201734\pi\)
−0.592183 + 0.805804i \(0.701734\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 1.58240i 0.226057i
\(50\) 2.03148 + 4.56871i 0.287295 + 0.646113i
\(51\) 0.462678i 0.0647879i
\(52\) −0.241478 0.241478i −0.0334869 0.0334869i
\(53\) 1.45249 + 1.45249i 0.199515 + 0.199515i 0.799792 0.600277i \(-0.204943\pi\)
−0.600277 + 0.799792i \(0.704943\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 2.49430 13.4400i 0.336332 1.81224i
\(56\) 2.32757i 0.311035i
\(57\) −0.537068 + 0.537068i −0.0711365 + 0.0711365i
\(58\) −5.01721 + 5.01721i −0.658792 + 0.658792i
\(59\) 1.68540i 0.219420i 0.993964 + 0.109710i \(0.0349922\pi\)
−0.993964 + 0.109710i \(0.965008\pi\)
\(60\) 1.26608 + 1.84311i 0.163450 + 0.237944i
\(61\) 8.05915i 1.03187i 0.856628 + 0.515934i \(0.172555\pi\)
−0.856628 + 0.515934i \(0.827445\pi\)
\(62\) −5.87295 5.87295i −0.745865 0.745865i
\(63\) −1.64584 1.64584i −0.207357 0.207357i
\(64\) 1.00000i 0.125000i
\(65\) −0.629423 + 0.432367i −0.0780703 + 0.0536285i
\(66\) 6.11317i 0.752479i
\(67\) −3.13950 + 3.13950i −0.383551 + 0.383551i −0.872380 0.488829i \(-0.837424\pi\)
0.488829 + 0.872380i \(0.337424\pi\)
\(68\) 0.327163 + 0.327163i 0.0396743 + 0.0396743i
\(69\) 2.00041 + 4.35871i 0.240821 + 0.524727i
\(70\) 5.11723 + 0.949699i 0.611626 + 0.113511i
\(71\) 6.24090 0.740658 0.370329 0.928901i \(-0.379245\pi\)
0.370329 + 0.928901i \(0.379245\pi\)
\(72\) 0.707107 + 0.707107i 0.0833333 + 0.0833333i
\(73\) 6.62866 6.62866i 0.775826 0.775826i −0.203292 0.979118i \(-0.565164\pi\)
0.979118 + 0.203292i \(0.0651641\pi\)
\(74\) −2.72380 −0.316636
\(75\) 4.56871 2.03148i 0.527549 0.234575i
\(76\) 0.759529i 0.0871240i
\(77\) −10.0613 10.0613i −1.14659 1.14659i
\(78\) −0.241478 + 0.241478i −0.0273419 + 0.0273419i
\(79\) −3.83429 −0.431391 −0.215695 0.976461i \(-0.569202\pi\)
−0.215695 + 0.976461i \(0.569202\pi\)
\(80\) −2.19853 0.408021i −0.245803 0.0456181i
\(81\) −1.00000 −0.111111
\(82\) 4.77416 + 4.77416i 0.527217 + 0.527217i
\(83\) −2.14295 2.14295i −0.235219 0.235219i 0.579648 0.814867i \(-0.303190\pi\)
−0.814867 + 0.579648i \(0.803190\pi\)
\(84\) 2.32757 0.253959
\(85\) 0.852765 0.585786i 0.0924953 0.0635375i
\(86\) 0.204583i 0.0220608i
\(87\) 5.01721 + 5.01721i 0.537901 + 0.537901i
\(88\) 4.32266 + 4.32266i 0.460797 + 0.460797i
\(89\) 4.64280 0.492136 0.246068 0.969253i \(-0.420861\pi\)
0.246068 + 0.969253i \(0.420861\pi\)
\(90\) 1.84311 1.26608i 0.194281 0.133456i
\(91\) 0.794868i 0.0833248i
\(92\) −4.49658 1.66757i −0.468801 0.173856i
\(93\) −5.87295 + 5.87295i −0.608996 + 0.608996i
\(94\) 2.07114i 0.213621i
\(95\) −1.66985 0.309904i −0.171323 0.0317955i
\(96\) −1.00000 −0.102062
\(97\) −11.2007 + 11.2007i −1.13726 + 1.13726i −0.148317 + 0.988940i \(0.547386\pi\)
−0.988940 + 0.148317i \(0.952614\pi\)
\(98\) −1.11893 + 1.11893i −0.113029 + 0.113029i
\(99\) −6.11317 −0.614396
\(100\) −1.79409 + 4.66704i −0.179409 + 0.466704i
\(101\) −16.0613 −1.59816 −0.799080 0.601224i \(-0.794680\pi\)
−0.799080 + 0.601224i \(0.794680\pi\)
\(102\) 0.327163 0.327163i 0.0323939 0.0323939i
\(103\) −1.60298 1.60298i −0.157946 0.157946i 0.623710 0.781656i \(-0.285625\pi\)
−0.781656 + 0.623710i \(0.785625\pi\)
\(104\) 0.341501i 0.0334869i
\(105\) 0.949699 5.11723i 0.0926812 0.499391i
\(106\) 2.05413i 0.199515i
\(107\) 9.95278 9.95278i 0.962171 0.962171i −0.0371390 0.999310i \(-0.511824\pi\)
0.999310 + 0.0371390i \(0.0118244\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) −14.4446 −1.38354 −0.691771 0.722117i \(-0.743169\pi\)
−0.691771 + 0.722117i \(0.743169\pi\)
\(110\) 11.2672 7.73975i 1.07429 0.737956i
\(111\) 2.72380i 0.258532i
\(112\) −1.64584 + 1.64584i −0.155518 + 0.155518i
\(113\) −0.885110 0.885110i −0.0832642 0.0832642i 0.664248 0.747512i \(-0.268752\pi\)
−0.747512 + 0.664248i \(0.768752\pi\)
\(114\) −0.759529 −0.0711365
\(115\) −5.50089 + 9.20544i −0.512961 + 0.858412i
\(116\) −7.09541 −0.658792
\(117\) 0.241478 + 0.241478i 0.0223246 + 0.0223246i
\(118\) −1.19176 + 1.19176i −0.109710 + 0.109710i
\(119\) 1.07692i 0.0987208i
\(120\) −0.408021 + 2.19853i −0.0372471 + 0.200697i
\(121\) −26.3708 −2.39735
\(122\) −5.69868 + 5.69868i −0.515934 + 0.515934i
\(123\) 4.77416 4.77416i 0.430471 0.430471i
\(124\) 8.30560i 0.745865i
\(125\) 9.52858 + 5.84861i 0.852262 + 0.523115i
\(126\) 2.32757i 0.207357i
\(127\) −6.44789 6.44789i −0.572158 0.572158i 0.360573 0.932731i \(-0.382581\pi\)
−0.932731 + 0.360573i \(0.882581\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) −0.204583 −0.0180125
\(130\) −0.750799 0.139340i −0.0658494 0.0122209i
\(131\) 10.5482 0.921604 0.460802 0.887503i \(-0.347562\pi\)
0.460802 + 0.887503i \(0.347562\pi\)
\(132\) 4.32266 4.32266i 0.376239 0.376239i
\(133\) −1.25007 + 1.25007i −0.108395 + 0.108395i
\(134\) −4.43992 −0.383551
\(135\) −1.26608 1.84311i −0.108967 0.158629i
\(136\) 0.462678i 0.0396743i
\(137\) 15.3962 15.3962i 1.31538 1.31538i 0.397994 0.917388i \(-0.369706\pi\)
0.917388 0.397994i \(-0.130294\pi\)
\(138\) −1.66757 + 4.49658i −0.141953 + 0.382774i
\(139\) 5.75151i 0.487837i 0.969796 + 0.243918i \(0.0784329\pi\)
−0.969796 + 0.243918i \(0.921567\pi\)
\(140\) 2.94689 + 4.28997i 0.249058 + 0.362569i
\(141\) 2.07114 0.174421
\(142\) 4.41298 + 4.41298i 0.370329 + 0.370329i
\(143\) 1.47619 + 1.47619i 0.123445 + 0.123445i
\(144\) 1.00000i 0.0833333i
\(145\) −2.89508 + 15.5994i −0.240423 + 1.29546i
\(146\) 9.37434 0.775826
\(147\) 1.11893 + 1.11893i 0.0922874 + 0.0922874i
\(148\) −1.92602 1.92602i −0.158318 0.158318i
\(149\) −17.6985 −1.44992 −0.724960 0.688791i \(-0.758142\pi\)
−0.724960 + 0.688791i \(0.758142\pi\)
\(150\) 4.66704 + 1.79409i 0.381062 + 0.146487i
\(151\) −11.9117 −0.969359 −0.484680 0.874692i \(-0.661064\pi\)
−0.484680 + 0.874692i \(0.661064\pi\)
\(152\) 0.537068 0.537068i 0.0435620 0.0435620i
\(153\) −0.327163 0.327163i −0.0264495 0.0264495i
\(154\) 14.2288i 1.14659i
\(155\) −18.2601 3.38886i −1.46669 0.272200i
\(156\) −0.341501 −0.0273419
\(157\) −5.35896 + 5.35896i −0.427692 + 0.427692i −0.887841 0.460150i \(-0.847796\pi\)
0.460150 + 0.887841i \(0.347796\pi\)
\(158\) −2.71125 2.71125i −0.215695 0.215695i
\(159\) 2.05413 0.162903
\(160\) −1.26608 1.84311i −0.100092 0.145710i
\(161\) 4.65610 + 10.1452i 0.366952 + 0.799555i
\(162\) −0.707107 0.707107i −0.0555556 0.0555556i
\(163\) 1.79995 1.79995i 0.140983 0.140983i −0.633093 0.774076i \(-0.718215\pi\)
0.774076 + 0.633093i \(0.218215\pi\)
\(164\) 6.75167i 0.527217i
\(165\) −7.73975 11.2672i −0.602539 0.877152i
\(166\) 3.03059i 0.235219i
\(167\) 9.84687 + 9.84687i 0.761974 + 0.761974i 0.976679 0.214705i \(-0.0688791\pi\)
−0.214705 + 0.976679i \(0.568879\pi\)
\(168\) 1.64584 + 1.64584i 0.126980 + 0.126980i
\(169\) 12.8834i 0.991029i
\(170\) 1.01721 + 0.188782i 0.0780164 + 0.0144789i
\(171\) 0.759529i 0.0580827i
\(172\) 0.144662 0.144662i 0.0110304 0.0110304i
\(173\) 12.1316 12.1316i 0.922351 0.922351i −0.0748442 0.997195i \(-0.523846\pi\)
0.997195 + 0.0748442i \(0.0238459\pi\)
\(174\) 7.09541i 0.537901i
\(175\) 10.6340 4.72842i 0.803855 0.357435i
\(176\) 6.11317i 0.460797i
\(177\) 1.19176 + 1.19176i 0.0895778 + 0.0895778i
\(178\) 3.28296 + 3.28296i 0.246068 + 0.246068i
\(179\) 1.62037i 0.121112i 0.998165 + 0.0605561i \(0.0192874\pi\)
−0.998165 + 0.0605561i \(0.980713\pi\)
\(180\) 2.19853 + 0.408021i 0.163868 + 0.0304121i
\(181\) 20.5841i 1.53000i −0.644030 0.765000i \(-0.722739\pi\)
0.644030 0.765000i \(-0.277261\pi\)
\(182\) −0.562057 + 0.562057i −0.0416624 + 0.0416624i
\(183\) 5.69868 + 5.69868i 0.421258 + 0.421258i
\(184\) −2.00041 4.35871i −0.147472 0.321328i
\(185\) −5.02026 + 3.44855i −0.369097 + 0.253542i
\(186\) −8.30560 −0.608996
\(187\) −2.00000 2.00000i −0.146254 0.146254i
\(188\) −1.46451 + 1.46451i −0.106811 + 0.106811i
\(189\) −2.32757 −0.169306
\(190\) −0.961624 1.39989i −0.0697635 0.101559i
\(191\) 20.8203i 1.50650i −0.657734 0.753251i \(-0.728485\pi\)
0.657734 0.753251i \(-0.271515\pi\)
\(192\) −0.707107 0.707107i −0.0510310 0.0510310i
\(193\) 5.74993 5.74993i 0.413889 0.413889i −0.469202 0.883091i \(-0.655458\pi\)
0.883091 + 0.469202i \(0.155458\pi\)
\(194\) −15.8402 −1.13726
\(195\) −0.139340 + 0.750799i −0.00997831 + 0.0537658i
\(196\) −1.58240 −0.113029
\(197\) 1.24668 + 1.24668i 0.0888223 + 0.0888223i 0.750122 0.661300i \(-0.229995\pi\)
−0.661300 + 0.750122i \(0.729995\pi\)
\(198\) −4.32266 4.32266i −0.307198 0.307198i
\(199\) −4.17076 −0.295658 −0.147829 0.989013i \(-0.547228\pi\)
−0.147829 + 0.989013i \(0.547228\pi\)
\(200\) −4.56871 + 2.03148i −0.323056 + 0.143647i
\(201\) 4.43992i 0.313168i
\(202\) −11.3571 11.3571i −0.799080 0.799080i
\(203\) 11.6779 + 11.6779i 0.819630 + 0.819630i
\(204\) 0.462678 0.0323939
\(205\) 14.8437 + 2.75483i 1.03673 + 0.192405i
\(206\) 2.26695i 0.157946i
\(207\) 4.49658 + 1.66757i 0.312534 + 0.115904i
\(208\) 0.241478 0.241478i 0.0167435 0.0167435i
\(209\) 4.64313i 0.321172i
\(210\) 4.28997 2.94689i 0.296036 0.203355i
\(211\) 6.87441 0.473254 0.236627 0.971601i \(-0.423958\pi\)
0.236627 + 0.971601i \(0.423958\pi\)
\(212\) −1.45249 + 1.45249i −0.0997574 + 0.0997574i
\(213\) 4.41298 4.41298i 0.302373 0.302373i
\(214\) 14.0754 0.962171
\(215\) −0.259018 0.377069i −0.0176649 0.0257159i
\(216\) 1.00000 0.0680414
\(217\) −13.6697 + 13.6697i −0.927961 + 0.927961i
\(218\) −10.2139 10.2139i −0.691771 0.691771i
\(219\) 9.37434i 0.633459i
\(220\) 13.4400 + 2.49430i 0.906122 + 0.168166i
\(221\) 0.158005i 0.0106286i
\(222\) −1.92602 + 1.92602i −0.129266 + 0.129266i
\(223\) 11.2802 11.2802i 0.755379 0.755379i −0.220098 0.975478i \(-0.570638\pi\)
0.975478 + 0.220098i \(0.0706379\pi\)
\(224\) −2.32757 −0.155518
\(225\) 1.79409 4.66704i 0.119606 0.311136i
\(226\) 1.25173i 0.0832642i
\(227\) −2.22998 + 2.22998i −0.148009 + 0.148009i −0.777228 0.629219i \(-0.783375\pi\)
0.629219 + 0.777228i \(0.283375\pi\)
\(228\) −0.537068 0.537068i −0.0355682 0.0355682i
\(229\) −5.86090 −0.387299 −0.193650 0.981071i \(-0.562032\pi\)
−0.193650 + 0.981071i \(0.562032\pi\)
\(230\) −10.3989 + 2.61951i −0.685686 + 0.172725i
\(231\) −14.2288 −0.936190
\(232\) −5.01721 5.01721i −0.329396 0.329396i
\(233\) 13.1762 13.1762i 0.863199 0.863199i −0.128510 0.991708i \(-0.541019\pi\)
0.991708 + 0.128510i \(0.0410193\pi\)
\(234\) 0.341501i 0.0223246i
\(235\) 2.62222 + 3.81733i 0.171055 + 0.249015i
\(236\) −1.68540 −0.109710
\(237\) −2.71125 + 2.71125i −0.176115 + 0.176115i
\(238\) 0.761495 0.761495i 0.0493604 0.0493604i
\(239\) 22.8269i 1.47655i 0.674499 + 0.738276i \(0.264360\pi\)
−0.674499 + 0.738276i \(0.735640\pi\)
\(240\) −1.84311 + 1.26608i −0.118972 + 0.0817250i
\(241\) 18.6517i 1.20146i −0.799451 0.600731i \(-0.794876\pi\)
0.799451 0.600731i \(-0.205124\pi\)
\(242\) −18.6470 18.6470i −1.19867 1.19867i
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) −8.05915 −0.515934
\(245\) −0.645653 + 3.47895i −0.0412492 + 0.222262i
\(246\) 6.75167 0.430471
\(247\) 0.183409 0.183409i 0.0116701 0.0116701i
\(248\) 5.87295 5.87295i 0.372933 0.372933i
\(249\) −3.03059 −0.192056
\(250\) 2.60213 + 10.8733i 0.164573 + 0.687689i
\(251\) 24.1095i 1.52178i −0.648880 0.760890i \(-0.724762\pi\)
0.648880 0.760890i \(-0.275238\pi\)
\(252\) 1.64584 1.64584i 0.103678 0.103678i
\(253\) 27.4883 + 10.1941i 1.72818 + 0.640900i
\(254\) 9.11869i 0.572158i
\(255\) 0.188782 1.01721i 0.0118220 0.0637001i
\(256\) 1.00000 0.0625000
\(257\) −16.3759 16.3759i −1.02150 1.02150i −0.999764 0.0217381i \(-0.993080\pi\)
−0.0217381 0.999764i \(-0.506920\pi\)
\(258\) −0.144662 0.144662i −0.00900627 0.00900627i
\(259\) 6.33986i 0.393939i
\(260\) −0.432367 0.629423i −0.0268143 0.0390351i
\(261\) 7.09541 0.439195
\(262\) 7.45873 + 7.45873i 0.460802 + 0.460802i
\(263\) −16.2523 16.2523i −1.00216 1.00216i −0.999998 0.00216013i \(-0.999312\pi\)
−0.00216013 0.999998i \(-0.500688\pi\)
\(264\) 6.11317 0.376239
\(265\) 2.60069 + 3.78598i 0.159759 + 0.232571i
\(266\) −1.76786 −0.108395
\(267\) 3.28296 3.28296i 0.200914 0.200914i
\(268\) −3.13950 3.13950i −0.191775 0.191775i
\(269\) 27.3620i 1.66829i 0.551546 + 0.834144i \(0.314038\pi\)
−0.551546 + 0.834144i \(0.685962\pi\)
\(270\) 0.408021 2.19853i 0.0248314 0.133798i
\(271\) −30.7037 −1.86512 −0.932559 0.361017i \(-0.882430\pi\)
−0.932559 + 0.361017i \(0.882430\pi\)
\(272\) −0.327163 + 0.327163i −0.0198371 + 0.0198371i
\(273\) 0.562057 + 0.562057i 0.0340172 + 0.0340172i
\(274\) 21.7734 1.31538
\(275\) 10.9676 28.5304i 0.661370 1.72045i
\(276\) −4.35871 + 2.00041i −0.262364 + 0.120411i
\(277\) 2.21937 + 2.21937i 0.133349 + 0.133349i 0.770631 0.637282i \(-0.219941\pi\)
−0.637282 + 0.770631i \(0.719941\pi\)
\(278\) −4.06693 + 4.06693i −0.243918 + 0.243918i
\(279\) 8.30560i 0.497243i
\(280\) −0.949699 + 5.11723i −0.0567554 + 0.305813i
\(281\) 26.0473i 1.55385i 0.629592 + 0.776926i \(0.283222\pi\)
−0.629592 + 0.776926i \(0.716778\pi\)
\(282\) 1.46451 + 1.46451i 0.0872106 + 0.0872106i
\(283\) −5.48295 5.48295i −0.325928 0.325928i 0.525108 0.851036i \(-0.324025\pi\)
−0.851036 + 0.525108i \(0.824025\pi\)
\(284\) 6.24090i 0.370329i
\(285\) −1.39989 + 0.961624i −0.0829226 + 0.0569617i
\(286\) 2.08765i 0.123445i
\(287\) 11.1122 11.1122i 0.655932 0.655932i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) 16.7859i 0.987408i
\(290\) −13.0776 + 8.98334i −0.767943 + 0.527520i
\(291\) 15.8402i 0.928566i
\(292\) 6.62866 + 6.62866i 0.387913 + 0.387913i
\(293\) 18.5543 + 18.5543i 1.08395 + 1.08395i 0.996137 + 0.0878182i \(0.0279894\pi\)
0.0878182 + 0.996137i \(0.472011\pi\)
\(294\) 1.58240i 0.0922874i
\(295\) −0.687677 + 3.70539i −0.0400381 + 0.215736i
\(296\) 2.72380i 0.158318i
\(297\) −4.32266 + 4.32266i −0.250826 + 0.250826i
\(298\) −12.5148 12.5148i −0.724960 0.724960i
\(299\) −0.683142 1.48850i −0.0395071 0.0860824i
\(300\) 2.03148 + 4.56871i 0.117288 + 0.263774i
\(301\) −0.476182 −0.0274467
\(302\) −8.42283 8.42283i −0.484680 0.484680i
\(303\) −11.3571 + 11.3571i −0.652446 + 0.652446i
\(304\) 0.759529 0.0435620
\(305\) −3.28830 + 17.7183i −0.188288 + 1.01454i
\(306\) 0.462678i 0.0264495i
\(307\) 20.3743 + 20.3743i 1.16282 + 1.16282i 0.983855 + 0.178966i \(0.0572752\pi\)
0.178966 + 0.983855i \(0.442725\pi\)
\(308\) 10.0613 10.0613i 0.573297 0.573297i
\(309\) −2.26695 −0.128962
\(310\) −10.5155 15.3081i −0.597243 0.869443i
\(311\) 16.5017 0.935724 0.467862 0.883801i \(-0.345024\pi\)
0.467862 + 0.883801i \(0.345024\pi\)
\(312\) −0.241478 0.241478i −0.0136710 0.0136710i
\(313\) −4.53498 4.53498i −0.256332 0.256332i 0.567228 0.823561i \(-0.308016\pi\)
−0.823561 + 0.567228i \(0.808016\pi\)
\(314\) −7.57872 −0.427692
\(315\) −2.94689 4.28997i −0.166039 0.241712i
\(316\) 3.83429i 0.215695i
\(317\) −12.5140 12.5140i −0.702856 0.702856i 0.262167 0.965023i \(-0.415563\pi\)
−0.965023 + 0.262167i \(0.915563\pi\)
\(318\) 1.45249 + 1.45249i 0.0814516 + 0.0814516i
\(319\) 43.3754 2.42856
\(320\) 0.408021 2.19853i 0.0228091 0.122901i
\(321\) 14.0754i 0.785609i
\(322\) −3.88139 + 10.4661i −0.216301 + 0.583254i
\(323\) −0.248490 + 0.248490i −0.0138263 + 0.0138263i
\(324\) 1.00000i 0.0555556i
\(325\) −1.56022 + 0.693752i −0.0865453 + 0.0384824i
\(326\) 2.54552 0.140983
\(327\) −10.2139 + 10.2139i −0.564828 + 0.564828i
\(328\) −4.77416 + 4.77416i −0.263609 + 0.263609i
\(329\) 4.82072 0.265775
\(330\) 2.49430 13.4400i 0.137307 0.739846i
\(331\) 24.3710 1.33955 0.669775 0.742564i \(-0.266390\pi\)
0.669775 + 0.742564i \(0.266390\pi\)
\(332\) 2.14295 2.14295i 0.117610 0.117610i
\(333\) 1.92602 + 1.92602i 0.105545 + 0.105545i
\(334\) 13.9256i 0.761974i
\(335\) −8.18325 + 5.62129i −0.447099 + 0.307124i
\(336\) 2.32757i 0.126980i
\(337\) 15.7870 15.7870i 0.859971 0.859971i −0.131363 0.991334i \(-0.541935\pi\)
0.991334 + 0.131363i \(0.0419354\pi\)
\(338\) −9.10992 + 9.10992i −0.495515 + 0.495515i
\(339\) −1.25173 −0.0679849
\(340\) 0.585786 + 0.852765i 0.0317687 + 0.0462477i
\(341\) 50.7735i 2.74954i
\(342\) −0.537068 + 0.537068i −0.0290413 + 0.0290413i
\(343\) 14.1253 + 14.1253i 0.762694 + 0.762694i
\(344\) 0.204583 0.0110304
\(345\) 2.61951 + 10.3989i 0.141030 + 0.559861i
\(346\) 17.1567 0.922351
\(347\) −11.4749 11.4749i −0.616007 0.616007i 0.328498 0.944505i \(-0.393458\pi\)
−0.944505 + 0.328498i \(0.893458\pi\)
\(348\) −5.01721 + 5.01721i −0.268951 + 0.268951i
\(349\) 5.86005i 0.313682i −0.987624 0.156841i \(-0.949869\pi\)
0.987624 0.156841i \(-0.0501309\pi\)
\(350\) 10.8629 + 4.17588i 0.580645 + 0.223210i
\(351\) 0.341501 0.0182280
\(352\) −4.32266 + 4.32266i −0.230399 + 0.230399i
\(353\) 3.94327 3.94327i 0.209879 0.209879i −0.594337 0.804216i \(-0.702586\pi\)
0.804216 + 0.594337i \(0.202586\pi\)
\(354\) 1.68540i 0.0895778i
\(355\) 13.7208 + 2.54642i 0.728224 + 0.135150i
\(356\) 4.64280i 0.246068i
\(357\) −0.761495 0.761495i −0.0403026 0.0403026i
\(358\) −1.14577 + 1.14577i −0.0605561 + 0.0605561i
\(359\) 32.6374 1.72254 0.861269 0.508150i \(-0.169670\pi\)
0.861269 + 0.508150i \(0.169670\pi\)
\(360\) 1.26608 + 1.84311i 0.0667282 + 0.0971403i
\(361\) −18.4231 −0.969638
\(362\) 14.5551 14.5551i 0.765000 0.765000i
\(363\) −18.6470 + 18.6470i −0.978713 + 0.978713i
\(364\) −0.794868 −0.0416624
\(365\) 17.2779 11.8687i 0.904368 0.621234i
\(366\) 8.05915i 0.421258i
\(367\) 22.9985 22.9985i 1.20051 1.20051i 0.226499 0.974011i \(-0.427272\pi\)
0.974011 0.226499i \(-0.0727281\pi\)
\(368\) 1.66757 4.49658i 0.0869281 0.234400i
\(369\) 6.75167i 0.351478i
\(370\) −5.98836 1.11137i −0.311320 0.0577774i
\(371\) 4.78114 0.248224
\(372\) −5.87295 5.87295i −0.304498 0.304498i
\(373\) 15.4627 + 15.4627i 0.800629 + 0.800629i 0.983194 0.182564i \(-0.0584398\pi\)
−0.182564 + 0.983194i \(0.558440\pi\)
\(374\) 2.82843i 0.146254i
\(375\) 10.8733 2.60213i 0.561495 0.134374i
\(376\) −2.07114 −0.106811
\(377\) −1.71338 1.71338i −0.0882436 0.0882436i
\(378\) −1.64584 1.64584i −0.0846530 0.0846530i
\(379\) −11.0986 −0.570095 −0.285048 0.958513i \(-0.592009\pi\)
−0.285048 + 0.958513i \(0.592009\pi\)
\(380\) 0.309904 1.66985i 0.0158977 0.0856613i
\(381\) −9.11869 −0.467165
\(382\) 14.7221 14.7221i 0.753251 0.753251i
\(383\) 18.4090 + 18.4090i 0.940653 + 0.940653i 0.998335 0.0576815i \(-0.0183708\pi\)
−0.0576815 + 0.998335i \(0.518371\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −18.0148 26.2253i −0.918121 1.33656i
\(386\) 8.13163 0.413889
\(387\) −0.144662 + 0.144662i −0.00735359 + 0.00735359i
\(388\) −11.2007 11.2007i −0.568628 0.568628i
\(389\) −21.2944 −1.07967 −0.539833 0.841772i \(-0.681513\pi\)
−0.539833 + 0.841772i \(0.681513\pi\)
\(390\) −0.629423 + 0.432367i −0.0318721 + 0.0218937i
\(391\) 0.925546 + 2.01668i 0.0468069 + 0.101988i
\(392\) −1.11893 1.11893i −0.0565143 0.0565143i
\(393\) 7.45873 7.45873i 0.376243 0.376243i
\(394\) 1.76307i 0.0888223i
\(395\) −8.42978 1.56447i −0.424148 0.0787170i
\(396\) 6.11317i 0.307198i
\(397\) −17.4767 17.4767i −0.877130 0.877130i 0.116107 0.993237i \(-0.462959\pi\)
−0.993237 + 0.116107i \(0.962959\pi\)
\(398\) −2.94918 2.94918i −0.147829 0.147829i
\(399\) 1.76786i 0.0885037i
\(400\) −4.66704 1.79409i −0.233352 0.0897045i
\(401\) 9.34370i 0.466602i 0.972405 + 0.233301i \(0.0749528\pi\)
−0.972405 + 0.233301i \(0.925047\pi\)
\(402\) −3.13950 + 3.13950i −0.156584 + 0.156584i
\(403\) 2.00562 2.00562i 0.0999069 0.0999069i
\(404\) 16.0613i 0.799080i
\(405\) −2.19853 0.408021i −0.109246 0.0202747i
\(406\) 16.5151i 0.819630i
\(407\) 11.7741 + 11.7741i 0.583620 + 0.583620i
\(408\) 0.327163 + 0.327163i 0.0161970 + 0.0161970i
\(409\) 15.8867i 0.785545i −0.919636 0.392773i \(-0.871516\pi\)
0.919636 0.392773i \(-0.128484\pi\)
\(410\) 8.54815 + 12.4441i 0.422163 + 0.614568i
\(411\) 21.7734i 1.07401i
\(412\) 1.60298 1.60298i 0.0789730 0.0789730i
\(413\) 2.77390 + 2.77390i 0.136495 + 0.136495i
\(414\) 2.00041 + 4.35871i 0.0983148 + 0.214219i
\(415\) −3.83697 5.58570i −0.188349 0.274191i
\(416\) 0.341501 0.0167435
\(417\) 4.06693 + 4.06693i 0.199159 + 0.199159i
\(418\) −3.28319 + 3.28319i −0.160586 + 0.160586i
\(419\) −5.11030 −0.249654 −0.124827 0.992178i \(-0.539838\pi\)
−0.124827 + 0.992178i \(0.539838\pi\)
\(420\) 5.11723 + 0.949699i 0.249695 + 0.0463406i
\(421\) 5.71253i 0.278412i 0.990263 + 0.139206i \(0.0444550\pi\)
−0.990263 + 0.139206i \(0.955545\pi\)
\(422\) 4.86094 + 4.86094i 0.236627 + 0.236627i
\(423\) 1.46451 1.46451i 0.0712071 0.0712071i
\(424\) −2.05413 −0.0997574
\(425\) 2.11384 0.939921i 0.102536 0.0455929i
\(426\) 6.24090 0.302373
\(427\) 13.2641 + 13.2641i 0.641895 + 0.641895i
\(428\) 9.95278 + 9.95278i 0.481086 + 0.481086i
\(429\) 2.08765 0.100793
\(430\) 0.0834743 0.449782i 0.00402549 0.0216904i
\(431\) 3.28744i 0.158351i −0.996861 0.0791753i \(-0.974771\pi\)
0.996861 0.0791753i \(-0.0252287\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) −11.6374 11.6374i −0.559256 0.559256i 0.369840 0.929096i \(-0.379413\pi\)
−0.929096 + 0.369840i \(0.879413\pi\)
\(434\) −19.3319 −0.927961
\(435\) 8.98334 + 13.0776i 0.430718 + 0.627023i
\(436\) 14.4446i 0.691771i
\(437\) 1.26657 3.41528i 0.0605882 0.163375i
\(438\) 6.62866 6.62866i 0.316730 0.316730i
\(439\) 12.3751i 0.590631i 0.955400 + 0.295316i \(0.0954248\pi\)
−0.955400 + 0.295316i \(0.904575\pi\)
\(440\) 7.73975 + 11.2672i 0.368978 + 0.537144i
\(441\) 1.58240 0.0753524
\(442\) −0.111726 + 0.111726i −0.00531428 + 0.00531428i
\(443\) 24.4511 24.4511i 1.16171 1.16171i 0.177606 0.984102i \(-0.443165\pi\)
0.984102 0.177606i \(-0.0568354\pi\)
\(444\) −2.72380 −0.129266
\(445\) 10.2073 + 1.89436i 0.483873 + 0.0898013i
\(446\) 15.9526 0.755379
\(447\) −12.5148 + 12.5148i −0.591927 + 0.591927i
\(448\) −1.64584 1.64584i −0.0777588 0.0777588i
\(449\) 41.0277i 1.93622i 0.250534 + 0.968108i \(0.419394\pi\)
−0.250534 + 0.968108i \(0.580606\pi\)
\(450\) 4.56871 2.03148i 0.215371 0.0957649i
\(451\) 41.2741i 1.94352i
\(452\) 0.885110 0.885110i 0.0416321 0.0416321i
\(453\) −8.42283 + 8.42283i −0.395739 + 0.395739i
\(454\) −3.15367 −0.148009
\(455\) −0.324323 + 1.74754i −0.0152045 + 0.0819259i
\(456\) 0.759529i 0.0355682i
\(457\) 18.5456 18.5456i 0.867526 0.867526i −0.124672 0.992198i \(-0.539788\pi\)
0.992198 + 0.124672i \(0.0397878\pi\)
\(458\) −4.14428 4.14428i −0.193650 0.193650i
\(459\) −0.462678 −0.0215960
\(460\) −9.20544 5.50089i −0.429206 0.256481i
\(461\) 21.4962 1.00118 0.500588 0.865686i \(-0.333117\pi\)
0.500588 + 0.865686i \(0.333117\pi\)
\(462\) −10.0613 10.0613i −0.468095 0.468095i
\(463\) −14.7714 + 14.7714i −0.686485 + 0.686485i −0.961453 0.274968i \(-0.911333\pi\)
0.274968 + 0.961453i \(0.411333\pi\)
\(464\) 7.09541i 0.329396i
\(465\) −15.3081 + 10.5155i −0.709897 + 0.487647i
\(466\) 18.6339 0.863199
\(467\) −23.9052 + 23.9052i −1.10620 + 1.10620i −0.112554 + 0.993646i \(0.535903\pi\)
−0.993646 + 0.112554i \(0.964097\pi\)
\(468\) −0.241478 + 0.241478i −0.0111623 + 0.0111623i
\(469\) 10.3342i 0.477191i
\(470\) −0.845067 + 4.55345i −0.0389800 + 0.210035i
\(471\) 7.57872i 0.349209i
\(472\) −1.19176 1.19176i −0.0548550 0.0548550i
\(473\) −0.884344 + 0.884344i −0.0406622 + 0.0406622i
\(474\) −3.83429 −0.176115
\(475\) −3.54475 1.36266i −0.162644 0.0625233i
\(476\) 1.07692 0.0493604
\(477\) 1.45249 1.45249i 0.0665049 0.0665049i
\(478\) −16.1411 + 16.1411i −0.738276 + 0.738276i
\(479\) −11.0131 −0.503199 −0.251600 0.967831i \(-0.580957\pi\)
−0.251600 + 0.967831i \(0.580957\pi\)
\(480\) −2.19853 0.408021i −0.100349 0.0186235i
\(481\) 0.930181i 0.0424126i
\(482\) 13.1887 13.1887i 0.600731 0.600731i
\(483\) 10.4661 + 3.88139i 0.476225 + 0.176609i
\(484\) 26.3708i 1.19867i
\(485\) −29.1951 + 20.0549i −1.32568 + 0.910645i
\(486\) −1.00000 −0.0453609
\(487\) 25.8202 + 25.8202i 1.17002 + 1.17002i 0.982203 + 0.187820i \(0.0601422\pi\)
0.187820 + 0.982203i \(0.439858\pi\)
\(488\) −5.69868 5.69868i −0.257967 0.257967i
\(489\) 2.54552i 0.115112i
\(490\) −2.91653 + 2.00344i −0.131756 + 0.0905063i
\(491\) −21.1318 −0.953665 −0.476832 0.878994i \(-0.658215\pi\)
−0.476832 + 0.878994i \(0.658215\pi\)
\(492\) 4.77416 + 4.77416i 0.215236 + 0.215236i
\(493\) 2.32135 + 2.32135i 0.104548 + 0.104548i
\(494\) 0.259380 0.0116701
\(495\) −13.4400 2.49430i −0.604081 0.112111i
\(496\) 8.30560 0.372933
\(497\) 10.2715 10.2715i 0.460742 0.460742i
\(498\) −2.14295 2.14295i −0.0960279 0.0960279i
\(499\) 25.7570i 1.15304i −0.817083 0.576520i \(-0.804410\pi\)
0.817083 0.576520i \(-0.195590\pi\)
\(500\) −5.84861 + 9.52858i −0.261558 + 0.426131i
\(501\) 13.9256 0.622149
\(502\) 17.0480 17.0480i 0.760890 0.760890i
\(503\) 2.42325 + 2.42325i 0.108048 + 0.108048i 0.759064 0.651016i \(-0.225657\pi\)
−0.651016 + 0.759064i \(0.725657\pi\)
\(504\) 2.32757 0.103678
\(505\) −35.3112 6.55336i −1.57133 0.291621i
\(506\) 12.2288 + 26.6455i 0.543639 + 1.18454i
\(507\) 9.10992 + 9.10992i 0.404586 + 0.404586i
\(508\) 6.44789 6.44789i 0.286079 0.286079i
\(509\) 37.8408i 1.67726i −0.544698 0.838632i \(-0.683356\pi\)
0.544698 0.838632i \(-0.316644\pi\)
\(510\) 0.852765 0.585786i 0.0377611 0.0259391i
\(511\) 21.8195i 0.965237i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0.537068 + 0.537068i 0.0237122 + 0.0237122i
\(514\) 23.1590i 1.02150i
\(515\) −2.87014 4.17824i −0.126473 0.184115i
\(516\) 0.204583i 0.00900627i
\(517\) 8.95282 8.95282i 0.393745 0.393745i
\(518\) −4.48296 + 4.48296i −0.196970 + 0.196970i
\(519\) 17.1567i 0.753096i
\(520\) 0.139340 0.750799i 0.00611044 0.0329247i
\(521\) 8.64661i 0.378815i 0.981899 + 0.189407i \(0.0606567\pi\)
−0.981899 + 0.189407i \(0.939343\pi\)
\(522\) 5.01721 + 5.01721i 0.219597 + 0.219597i
\(523\) −22.1099 22.1099i −0.966800 0.966800i 0.0326665 0.999466i \(-0.489600\pi\)
−0.999466 + 0.0326665i \(0.989600\pi\)
\(524\) 10.5482i 0.460802i
\(525\) 4.17588 10.8629i 0.182250 0.474095i
\(526\) 22.9842i 1.00216i
\(527\) −2.71728 + 2.71728i −0.118367 + 0.118367i
\(528\) 4.32266 + 4.32266i 0.188120 + 0.188120i
\(529\) −17.4384 14.9967i −0.758192 0.652031i
\(530\) −0.838129 + 4.51606i −0.0364060 + 0.196165i
\(531\) 1.68540 0.0731400
\(532\) −1.25007 1.25007i −0.0541973 0.0541973i
\(533\) −1.63038 + 1.63038i −0.0706195 + 0.0706195i
\(534\) 4.64280 0.200914
\(535\) 25.9424 17.8205i 1.12159 0.770447i
\(536\) 4.43992i 0.191775i
\(537\) 1.14577 + 1.14577i 0.0494438 + 0.0494438i
\(538\) −19.3478 + 19.3478i −0.834144 + 0.834144i
\(539\) 9.67348 0.416666
\(540\) 1.84311 1.26608i 0.0793147 0.0544833i
\(541\) 31.2535 1.34369 0.671846 0.740691i \(-0.265502\pi\)
0.671846 + 0.740691i \(0.265502\pi\)
\(542\) −21.7108 21.7108i −0.932559 0.932559i
\(543\) −14.5551 14.5551i −0.624620 0.624620i
\(544\) −0.462678 −0.0198371
\(545\) −31.7568 5.89370i −1.36031 0.252458i
\(546\) 0.794868i 0.0340172i
\(547\) 12.6714 + 12.6714i 0.541792 + 0.541792i 0.924054 0.382262i \(-0.124855\pi\)
−0.382262 + 0.924054i \(0.624855\pi\)
\(548\) 15.3962 + 15.3962i 0.657691 + 0.657691i
\(549\) 8.05915 0.343956
\(550\) 27.9293 12.4188i 1.19091 0.529539i
\(551\) 5.38917i 0.229586i
\(552\) −4.49658 1.66757i −0.191387 0.0709765i
\(553\) −6.31063 + 6.31063i −0.268355 + 0.268355i
\(554\) 3.13866i 0.133349i
\(555\) −1.11137 + 5.98836i −0.0471750 + 0.254192i
\(556\) −5.75151 −0.243918
\(557\) −2.52234 + 2.52234i −0.106875 + 0.106875i −0.758522 0.651647i \(-0.774078\pi\)
0.651647 + 0.758522i \(0.274078\pi\)
\(558\) −5.87295 + 5.87295i −0.248622 + 0.248622i
\(559\) 0.0698653 0.00295499
\(560\) −4.28997 + 2.94689i −0.181284 + 0.124529i
\(561\) −2.82843 −0.119416
\(562\) −18.4182 + 18.4182i −0.776926 + 0.776926i
\(563\) −26.8499 26.8499i −1.13159 1.13159i −0.989913 0.141675i \(-0.954751\pi\)
−0.141675 0.989913i \(-0.545249\pi\)
\(564\) 2.07114i 0.0872106i
\(565\) −1.58479 2.30708i −0.0666728 0.0970597i
\(566\) 7.75406i 0.325928i
\(567\) −1.64584 + 1.64584i −0.0691189 + 0.0691189i
\(568\) −4.41298 + 4.41298i −0.185165 + 0.185165i
\(569\) 17.2543 0.723337 0.361668 0.932307i \(-0.382207\pi\)
0.361668 + 0.932307i \(0.382207\pi\)
\(570\) −1.66985 0.309904i −0.0699421 0.0129805i
\(571\) 43.9751i 1.84030i 0.391565 + 0.920151i \(0.371934\pi\)
−0.391565 + 0.920151i \(0.628066\pi\)
\(572\) −1.47619 + 1.47619i −0.0617227 + 0.0617227i
\(573\) −14.7221 14.7221i −0.615027 0.615027i
\(574\) 15.7150 0.655932
\(575\) −15.8499 + 17.9939i −0.660986 + 0.750399i
\(576\) −1.00000 −0.0416667
\(577\) 3.00797 + 3.00797i 0.125223 + 0.125223i 0.766941 0.641718i \(-0.221778\pi\)
−0.641718 + 0.766941i \(0.721778\pi\)
\(578\) −11.8694 + 11.8694i −0.493704 + 0.493704i
\(579\) 8.13163i 0.337939i
\(580\) −15.5994 2.89508i −0.647731 0.120211i
\(581\) −7.05392 −0.292646
\(582\) −11.2007 + 11.2007i −0.464283 + 0.464283i
\(583\) 8.87931 8.87931i 0.367744 0.367744i
\(584\) 9.37434i 0.387913i
\(585\) 0.432367 + 0.629423i 0.0178762 + 0.0260234i
\(586\) 26.2398i 1.08395i
\(587\) −22.9088 22.9088i −0.945548 0.945548i 0.0530437 0.998592i \(-0.483108\pi\)
−0.998592 + 0.0530437i \(0.983108\pi\)
\(588\) −1.11893 + 1.11893i −0.0461437 + 0.0461437i
\(589\) 6.30835 0.259931
\(590\) −3.10637 + 2.13384i −0.127887 + 0.0878490i
\(591\) 1.76307 0.0725231
\(592\) 1.92602 1.92602i 0.0791590 0.0791590i
\(593\) −11.7866 + 11.7866i −0.484017 + 0.484017i −0.906412 0.422395i \(-0.861190\pi\)
0.422395 + 0.906412i \(0.361190\pi\)
\(594\) −6.11317 −0.250826
\(595\) 0.439405 2.36763i 0.0180138 0.0970634i
\(596\) 17.6985i 0.724960i
\(597\) −2.94918 + 2.94918i −0.120702 + 0.120702i
\(598\) 0.569476 1.53558i 0.0232876 0.0627947i
\(599\) 46.9341i 1.91767i −0.283957 0.958837i \(-0.591647\pi\)
0.283957 0.958837i \(-0.408353\pi\)
\(600\) −1.79409 + 4.66704i −0.0732434 + 0.190531i
\(601\) −2.50913 −0.102350 −0.0511748 0.998690i \(-0.516297\pi\)
−0.0511748 + 0.998690i \(0.516297\pi\)
\(602\) −0.336712 0.336712i −0.0137234 0.0137234i
\(603\) 3.13950 + 3.13950i 0.127850 + 0.127850i
\(604\) 11.9117i 0.484680i
\(605\) −57.9769 10.7599i −2.35710 0.437450i
\(606\) −16.0613 −0.652446
\(607\) −4.62585 4.62585i −0.187758 0.187758i 0.606968 0.794726i \(-0.292385\pi\)
−0.794726 + 0.606968i \(0.792385\pi\)
\(608\) 0.537068 + 0.537068i 0.0217810 + 0.0217810i
\(609\) 16.5151 0.669225
\(610\) −14.8539 + 10.2035i −0.601416 + 0.413128i
\(611\) −0.707295 −0.0286141
\(612\) 0.327163 0.327163i 0.0132248 0.0132248i
\(613\) 4.93150 + 4.93150i 0.199181 + 0.199181i 0.799649 0.600468i \(-0.205019\pi\)
−0.600468 + 0.799649i \(0.705019\pi\)
\(614\) 28.8136i 1.16282i
\(615\) 12.4441 8.54815i 0.501793 0.344695i
\(616\) 14.2288 0.573297
\(617\) −27.5512 + 27.5512i −1.10917 + 1.10917i −0.115911 + 0.993260i \(0.536979\pi\)
−0.993260 + 0.115911i \(0.963021\pi\)
\(618\) −1.60298 1.60298i −0.0644812 0.0644812i
\(619\) −14.2298 −0.571945 −0.285972 0.958238i \(-0.592317\pi\)
−0.285972 + 0.958238i \(0.592317\pi\)
\(620\) 3.38886 18.2601i 0.136100 0.733343i
\(621\) 4.35871 2.00041i 0.174909 0.0802737i
\(622\) 11.6684 + 11.6684i 0.467862 + 0.467862i
\(623\) 7.64132 7.64132i 0.306143 0.306143i
\(624\) 0.341501i 0.0136710i
\(625\) 18.5625 + 16.7462i 0.742499 + 0.669847i
\(626\) 6.41343i 0.256332i
\(627\) 3.28319 + 3.28319i 0.131118 + 0.131118i
\(628\) −5.35896 5.35896i −0.213846 0.213846i
\(629\) 1.26024i 0.0502492i
\(630\) 0.949699 5.11723i 0.0378369 0.203875i
\(631\) 19.7938i 0.787979i 0.919115 + 0.393990i \(0.128905\pi\)
−0.919115 + 0.393990i \(0.871095\pi\)
\(632\) 2.71125 2.71125i 0.107848 0.107848i
\(633\) 4.86094 4.86094i 0.193205 0.193205i
\(634\) 17.6975i 0.702856i
\(635\) −11.5450 16.8067i −0.458149 0.666955i
\(636\) 2.05413i 0.0814516i
\(637\) −0.382114 0.382114i −0.0151399 0.0151399i
\(638\) 30.6710 + 30.6710i 1.21428 + 1.21428i
\(639\) 6.24090i 0.246886i
\(640\) 1.84311 1.26608i 0.0728552 0.0500461i
\(641\) 31.1566i 1.23061i 0.788289 + 0.615306i \(0.210967\pi\)
−0.788289 + 0.615306i \(0.789033\pi\)
\(642\) 9.95278 9.95278i 0.392805 0.392805i
\(643\) −21.5814 21.5814i −0.851087 0.851087i 0.139180 0.990267i \(-0.455553\pi\)
−0.990267 + 0.139180i \(0.955553\pi\)
\(644\) −10.1452 + 4.65610i −0.399778 + 0.183476i
\(645\) −0.449782 0.0834743i −0.0177101 0.00328680i
\(646\) −0.351417 −0.0138263
\(647\) 1.34183 + 1.34183i 0.0527528 + 0.0527528i 0.732991 0.680238i \(-0.238124\pi\)
−0.680238 + 0.732991i \(0.738124\pi\)
\(648\) 0.707107 0.707107i 0.0277778 0.0277778i
\(649\) 10.3031 0.404432
\(650\) −1.59380 0.612683i −0.0625139 0.0240314i
\(651\) 19.3319i 0.757677i
\(652\) 1.79995 + 1.79995i 0.0704916 + 0.0704916i
\(653\) −25.9393 + 25.9393i −1.01508 + 1.01508i −0.0151973 + 0.999885i \(0.504838\pi\)
−0.999885 + 0.0151973i \(0.995162\pi\)
\(654\) −14.4446 −0.564828
\(655\) 23.1906 + 4.30391i 0.906131 + 0.168168i
\(656\) −6.75167 −0.263609
\(657\) −6.62866 6.62866i −0.258609 0.258609i
\(658\) 3.40877 + 3.40877i 0.132888 + 0.132888i
\(659\) 3.80748 0.148318 0.0741592 0.997246i \(-0.476373\pi\)
0.0741592 + 0.997246i \(0.476373\pi\)
\(660\) 11.2672 7.73975i 0.438576 0.301269i
\(661\) 4.54043i 0.176602i −0.996094 0.0883010i \(-0.971856\pi\)
0.996094 0.0883010i \(-0.0281438\pi\)
\(662\) 17.2329 + 17.2329i 0.669775 + 0.669775i
\(663\) 0.111726 + 0.111726i 0.00433909 + 0.00433909i
\(664\) 3.03059 0.117610
\(665\) −3.25836 + 2.23825i −0.126354 + 0.0867956i
\(666\) 2.72380i 0.105545i
\(667\) −31.9050 11.8321i −1.23537 0.458140i
\(668\) −9.84687 + 9.84687i −0.380987 + 0.380987i
\(669\) 15.9526i 0.616765i
\(670\) −9.76128 1.81158i −0.377111 0.0699875i
\(671\) 49.2669 1.90193
\(672\) −1.64584 + 1.64584i −0.0634898 + 0.0634898i
\(673\) 22.6605 22.6605i 0.873499 0.873499i −0.119353 0.992852i \(-0.538082\pi\)
0.992852 + 0.119353i \(0.0380821\pi\)
\(674\) 22.3261 0.859971
\(675\) −2.03148 4.56871i −0.0781917 0.175850i
\(676\) −12.8834 −0.495515
\(677\) −33.2731 + 33.2731i −1.27879 + 1.27879i −0.337440 + 0.941347i \(0.609561\pi\)
−0.941347 + 0.337440i \(0.890439\pi\)
\(678\) −0.885110 0.885110i −0.0339925 0.0339925i
\(679\) 36.8691i 1.41491i
\(680\) −0.188782 + 1.01721i −0.00723947 + 0.0390082i
\(681\) 3.15367i 0.120849i
\(682\) −35.9023 + 35.9023i −1.37477 + 1.37477i
\(683\) 16.5376 16.5376i 0.632793 0.632793i −0.315975 0.948768i \(-0.602332\pi\)
0.948768 + 0.315975i \(0.102332\pi\)
\(684\) −0.759529 −0.0290413
\(685\) 40.1308 27.5669i 1.53332 1.05328i
\(686\) 19.9762i 0.762694i
\(687\) −4.14428 + 4.14428i −0.158114 + 0.158114i
\(688\) 0.144662 + 0.144662i 0.00551519 + 0.00551519i
\(689\) −0.701487 −0.0267245
\(690\) −5.50089 + 9.20544i −0.209415 + 0.350445i
\(691\) −38.2075 −1.45348 −0.726741 0.686912i \(-0.758966\pi\)
−0.726741 + 0.686912i \(0.758966\pi\)
\(692\) 12.1316 + 12.1316i 0.461176 + 0.461176i
\(693\) −10.0613 + 10.0613i −0.382198 + 0.382198i
\(694\) 16.2280i 0.616007i
\(695\) −2.34674 + 12.6448i −0.0890168 + 0.479646i
\(696\) −7.09541 −0.268951
\(697\) 2.20890 2.20890i 0.0836679 0.0836679i
\(698\) 4.14368 4.14368i 0.156841 0.156841i
\(699\) 18.6339i 0.704799i
\(700\) 4.72842 + 10.6340i 0.178717 + 0.401928i
\(701\) 5.54946i 0.209600i −0.994493 0.104800i \(-0.966580\pi\)
0.994493 0.104800i \(-0.0334203\pi\)
\(702\) 0.241478 + 0.241478i 0.00911398 + 0.00911398i
\(703\) 1.46287 1.46287i 0.0551732 0.0551732i
\(704\) −6.11317 −0.230399
\(705\) 4.55345 + 0.845067i 0.171493 + 0.0318271i
\(706\) 5.57662 0.209879
\(707\) −26.4344 + 26.4344i −0.994168 + 0.994168i
\(708\) −1.19176 + 1.19176i −0.0447889 + 0.0447889i
\(709\) −41.0934 −1.54329 −0.771647 0.636051i \(-0.780567\pi\)
−0.771647 + 0.636051i \(0.780567\pi\)
\(710\) 7.90147 + 11.5026i 0.296537 + 0.431687i
\(711\) 3.83429i 0.143797i
\(712\) −3.28296 + 3.28296i −0.123034 + 0.123034i
\(713\) 13.8502 37.3468i 0.518693 1.39865i
\(714\) 1.07692i 0.0403026i
\(715\) 2.64313 + 3.84777i 0.0988475 + 0.143898i
\(716\) −1.62037 −0.0605561
\(717\) 16.1411 + 16.1411i 0.602800 + 0.602800i
\(718\) 23.0781 + 23.0781i 0.861269 + 0.861269i
\(719\) 1.72658i 0.0643905i −0.999482 0.0321952i \(-0.989750\pi\)
0.999482 0.0321952i \(-0.0102498\pi\)
\(720\) −0.408021 + 2.19853i −0.0152060 + 0.0819342i
\(721\) −5.27650 −0.196507
\(722\) −13.0271 13.0271i −0.484819 0.484819i
\(723\) −13.1887 13.1887i −0.490495 0.490495i
\(724\) 20.5841 0.765000
\(725\) −12.7298 + 33.1145i −0.472773 + 1.22984i
\(726\) −26.3708 −0.978713
\(727\) −3.72425 + 3.72425i −0.138125 + 0.138125i −0.772788 0.634664i \(-0.781139\pi\)
0.634664 + 0.772788i \(0.281139\pi\)
\(728\) −0.562057 0.562057i −0.0208312 0.0208312i
\(729\) 1.00000i 0.0370370i
\(730\) 20.6097 + 3.82493i 0.762801 + 0.141567i
\(731\) −0.0946561 −0.00350098
\(732\) −5.69868 + 5.69868i −0.210629 + 0.210629i
\(733\) −6.33773 6.33773i −0.234089 0.234089i 0.580308 0.814397i \(-0.302932\pi\)
−0.814397 + 0.580308i \(0.802932\pi\)
\(734\) 32.5248 1.20051
\(735\) 2.00344 + 2.91653i 0.0738981 + 0.107578i
\(736\) 4.35871 2.00041i 0.160664 0.0737361i
\(737\) 19.1923 + 19.1923i 0.706956 + 0.706956i
\(738\) 4.77416 4.77416i 0.175739 0.175739i
\(739\) 27.5093i 1.01195i −0.862549 0.505973i \(-0.831133\pi\)
0.862549 0.505973i \(-0.168867\pi\)
\(740\) −3.44855 5.02026i −0.126771 0.184549i
\(741\) 0.259380i 0.00952856i
\(742\) 3.38078 + 3.38078i 0.124112 + 0.124112i
\(743\) 20.8781 + 20.8781i 0.765942 + 0.765942i 0.977389 0.211448i \(-0.0678178\pi\)
−0.211448 + 0.977389i \(0.567818\pi\)
\(744\) 8.30560i 0.304498i
\(745\) −38.9107 7.22137i −1.42558 0.264571i
\(746\) 21.8676i 0.800629i
\(747\) −2.14295 + 2.14295i −0.0784065 + 0.0784065i
\(748\) 2.00000 2.00000i 0.0731272 0.0731272i
\(749\) 32.7614i 1.19708i
\(750\) 9.52858 + 5.84861i 0.347935 + 0.213561i
\(751\) 12.1937i 0.444954i 0.974938 + 0.222477i \(0.0714142\pi\)
−0.974938 + 0.222477i \(0.928586\pi\)
\(752\) −1.46451 1.46451i −0.0534053 0.0534053i
\(753\) −17.0480 17.0480i −0.621264 0.621264i
\(754\) 2.42309i 0.0882436i
\(755\) −26.1882 4.86022i −0.953085 0.176881i
\(756\) 2.32757i 0.0846530i
\(757\) 13.7127 13.7127i 0.498396 0.498396i −0.412543 0.910938i \(-0.635359\pi\)
0.910938 + 0.412543i \(0.135359\pi\)
\(758\) −7.84787 7.84787i −0.285048 0.285048i
\(759\) 26.6455 12.2288i 0.967171 0.443879i
\(760\) 1.39989 0.961624i 0.0507795 0.0348818i
\(761\) 15.5354 0.563159 0.281580 0.959538i \(-0.409142\pi\)
0.281580 + 0.959538i \(0.409142\pi\)
\(762\) −6.44789 6.44789i −0.233582 0.233582i
\(763\) −23.7735 + 23.7735i −0.860660 + 0.860660i
\(764\) 20.8203 0.753251
\(765\) −0.585786 0.852765i −0.0211792 0.0308318i
\(766\) 26.0342i 0.940653i
\(767\) −0.406985 0.406985i −0.0146954 0.0146954i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) 30.1885 1.08863 0.544313 0.838882i \(-0.316790\pi\)
0.544313 + 0.838882i \(0.316790\pi\)
\(770\) 5.80567 31.2825i 0.209222 1.12734i
\(771\) −23.1590 −0.834053
\(772\) 5.74993 + 5.74993i 0.206945 + 0.206945i
\(773\) 8.94529 + 8.94529i 0.321740 + 0.321740i 0.849434 0.527694i \(-0.176943\pi\)
−0.527694 + 0.849434i \(0.676943\pi\)
\(774\) −0.204583 −0.00735359
\(775\) −38.7626 14.9010i −1.39239 0.535260i
\(776\) 15.8402i 0.568628i
\(777\) 4.48296 + 4.48296i 0.160825 + 0.160825i
\(778\) −15.0574 15.0574i −0.539833 0.539833i
\(779\) −5.12810 −0.183733