Properties

Label 690.2.j.b.643.12
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 643.12
Character \(\chi\) \(=\) 690.643
Dual form 690.2.j.b.367.12

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 24 q^{6} + O(q^{10}) \) \( 24 q + 24 q^{6} + 16 q^{13} - 24 q^{16} + 16 q^{23} - 16 q^{25} + 16 q^{31} + 24 q^{36} + 8 q^{46} + 40 q^{47} - 8 q^{50} + 16 q^{52} - 56 q^{55} - 16 q^{58} - 8 q^{62} + 32 q^{70} + 64 q^{71} - 16 q^{73} + 32 q^{75} + 16 q^{77} + 16 q^{78} - 24 q^{81} + 24 q^{82} - 48 q^{85} + 16 q^{87} + 16 q^{92} - 8 q^{93} + 24 q^{95} - 24 q^{96} + O(q^{100}) \)

Character values

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

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

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
\(5\) 2.19853 0.408021i 0.983211 0.182473i
\(6\) 1.00000 0.408248
\(7\) 1.64584 + 1.64584i 0.622070 + 0.622070i 0.946060 0.323990i \(-0.105024\pi\)
−0.323990 + 0.946060i \(0.605024\pi\)
\(8\) −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 \(0.373113\pi\)
−0.388154 + 0.921595i \(0.626887\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) −0.241478 0.241478i −0.0669738 0.0669738i 0.672826 0.739800i \(-0.265080\pi\)
−0.739800 + 0.672826i \(0.765080\pi\)
\(14\) 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 0.745667 0.666319i \(-0.232131\pi\)
−0.666319 + 0.745667i \(0.732131\pi\)
\(18\) 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 \(-0.771068\pi\)
0.752325 0.658792i \(-0.228932\pi\)
\(30\) 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 0.530838 0.847474i \(-0.321877\pi\)
−0.847474 + 0.530838i \(0.821877\pi\)
\(38\) −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 −0.718051 0.695990i \(-0.754966\pi\)
0.695990 + 0.718051i \(0.254966\pi\)
\(44\) 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 −0.592183 0.805804i \(-0.701734\pi\)
0.805804 + 0.592183i \(0.201734\pi\)
\(48\) −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 −0.600277 0.799792i \(-0.704943\pi\)
0.799792 + 0.600277i \(0.204943\pi\)
\(54\) 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 \(-0.965008\pi\)
0.993964 0.109710i \(-0.0349922\pi\)
\(60\) 1.26608 1.84311i 0.163450 0.237944i
\(61\) 8.05915i 1.03187i −0.856628 0.515934i \(-0.827445\pi\)
0.856628 0.515934i \(-0.172555\pi\)
\(62\) −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 0.488829 0.872380i \(-0.337424\pi\)
−0.872380 + 0.488829i \(0.837424\pi\)
\(68\) 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 0.979118 0.203292i \(-0.0651641\pi\)
−0.203292 + 0.979118i \(0.565164\pi\)
\(74\) −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 −0.814867 0.579648i \(-0.803190\pi\)
0.579648 + 0.814867i \(0.303190\pi\)
\(84\) 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 −0.988940 0.148317i \(-0.952614\pi\)
−0.148317 0.988940i \(-0.547386\pi\)
\(98\) −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 −0.781656 0.623710i \(-0.785625\pi\)
0.623710 + 0.781656i \(0.285625\pi\)
\(104\) 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 0.999310 0.0371390i \(-0.0118244\pi\)
−0.0371390 + 0.999310i \(0.511824\pi\)
\(108\) 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 −0.747512 0.664248i \(-0.768752\pi\)
0.664248 + 0.747512i \(0.268752\pi\)
\(114\) −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 −0.932731 0.360573i \(-0.882581\pi\)
0.360573 + 0.932731i \(0.382581\pi\)
\(128\) 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 0.917388 + 0.397994i \(0.130294\pi\)
0.397994 + 0.917388i \(0.369706\pi\)
\(138\) −1.66757 4.49658i −0.141953 0.382774i
\(139\) 5.75151i 0.487837i −0.969796 0.243918i \(-0.921567\pi\)
0.969796 0.243918i \(-0.0784329\pi\)
\(140\) 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 0.460150 0.887841i \(-0.347796\pi\)
−0.887841 + 0.460150i \(0.847796\pi\)
\(158\) −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 0.774076 0.633093i \(-0.218215\pi\)
−0.633093 + 0.774076i \(0.718215\pi\)
\(164\) 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 −0.214705 0.976679i \(-0.568879\pi\)
0.976679 + 0.214705i \(0.0688791\pi\)
\(168\) 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 0.997195 0.0748442i \(-0.0238459\pi\)
−0.0748442 + 0.997195i \(0.523846\pi\)
\(174\) 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 \(-0.980713\pi\)
0.998165 0.0605561i \(-0.0192874\pi\)
\(180\) 2.19853 0.408021i 0.163868 0.0304121i
\(181\) 20.5841i 1.53000i 0.644030 + 0.765000i \(0.277261\pi\)
−0.644030 + 0.765000i \(0.722739\pi\)
\(182\) −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 \(0.271515\pi\)
−0.657734 + 0.753251i \(0.728485\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) 5.74993 + 5.74993i 0.413889 + 0.413889i 0.883091 0.469202i \(-0.155458\pi\)
−0.469202 + 0.883091i \(0.655458\pi\)
\(194\) −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 −0.661300 0.750122i \(-0.729995\pi\)
0.750122 + 0.661300i \(0.229995\pi\)
\(198\) −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 0.975478 0.220098i \(-0.0706379\pi\)
−0.220098 + 0.975478i \(0.570638\pi\)
\(224\) −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 0.629219 0.777228i \(-0.283375\pi\)
−0.777228 + 0.629219i \(0.783375\pi\)
\(228\) −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 0.991708 0.128510i \(-0.0410193\pi\)
−0.128510 + 0.991708i \(0.541019\pi\)
\(234\) 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 \(-0.735640\pi\)
0.674499 0.738276i \(-0.264360\pi\)
\(240\) −1.84311 1.26608i −0.118972 0.0817250i
\(241\) 18.6517i 1.20146i 0.799451 + 0.600731i \(0.205124\pi\)
−0.799451 + 0.600731i \(0.794876\pi\)
\(242\) −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 \(0.275238\pi\)
−0.648880 + 0.760890i \(0.724762\pi\)
\(252\) 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 −0.0217381 + 0.999764i \(0.506920\pi\)
−0.999764 + 0.0217381i \(0.993080\pi\)
\(258\) −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 −0.00216013 + 0.999998i \(0.500688\pi\)
−0.999998 + 0.00216013i \(0.999312\pi\)
\(264\) 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 \(-0.685962\pi\)
0.551546 0.834144i \(-0.314038\pi\)
\(270\) 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 −0.637282 0.770631i \(-0.719941\pi\)
0.770631 + 0.637282i \(0.219941\pi\)
\(278\) −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 \(-0.716778\pi\)
0.629592 0.776926i \(-0.283222\pi\)
\(282\) 1.46451 1.46451i 0.0872106 0.0872106i
\(283\) −5.48295 + 5.48295i −0.325928 + 0.325928i −0.851036 0.525108i \(-0.824025\pi\)
0.525108 + 0.851036i \(0.324025\pi\)
\(284\) 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 0.0878182 0.996137i \(-0.472011\pi\)
0.996137 0.0878182i \(-0.0279894\pi\)
\(294\) 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 0.178966 0.983855i \(-0.442725\pi\)
0.983855 0.178966i \(-0.0572752\pi\)
\(308\) 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 −0.823561 0.567228i \(-0.808016\pi\)
0.567228 + 0.823561i \(0.308016\pi\)
\(314\) −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 −0.965023 0.262167i \(-0.915563\pi\)
0.262167 + 0.965023i \(0.415563\pi\)
\(318\) 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 0.991334 0.131363i \(-0.0419354\pi\)
−0.131363 + 0.991334i \(0.541935\pi\)
\(338\) −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 −0.944505 0.328498i \(-0.893458\pi\)
0.328498 + 0.944505i \(0.393458\pi\)
\(348\) −5.01721 5.01721i −0.268951 0.268951i
\(349\) 5.86005i 0.313682i 0.987624 + 0.156841i \(0.0501309\pi\)
−0.987624 + 0.156841i \(0.949869\pi\)
\(350\) 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 0.804216 0.594337i \(-0.202586\pi\)
−0.594337 + 0.804216i \(0.702586\pi\)
\(354\) 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 0.974011 + 0.226499i \(0.0727281\pi\)
0.226499 + 0.974011i \(0.427272\pi\)
\(368\) 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 −0.182564 0.983194i \(-0.558440\pi\)
0.983194 + 0.182564i \(0.0584398\pi\)
\(374\) 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 −0.0576815 0.998335i \(-0.518371\pi\)
0.998335 + 0.0576815i \(0.0183708\pi\)
\(384\) 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 −0.993237 0.116107i \(-0.962959\pi\)
0.116107 + 0.993237i \(0.462959\pi\)
\(398\) −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 \(-0.925047\pi\)
0.972405 0.233301i \(-0.0749528\pi\)
\(402\) −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 \(0.128484\pi\)
−0.919636 + 0.392773i \(0.871516\pi\)
\(410\) 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 \(-0.955545\pi\)
0.990263 0.139206i \(-0.0444550\pi\)
\(422\) 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 \(0.0252287\pi\)
−0.996861 + 0.0791753i \(0.974771\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) −11.6374 + 11.6374i −0.559256 + 0.559256i −0.929096 0.369840i \(-0.879413\pi\)
0.369840 + 0.929096i \(0.379413\pi\)
\(434\) −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 \(-0.904575\pi\)
0.955400 0.295316i \(-0.0954248\pi\)
\(440\) 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 0.984102 + 0.177606i \(0.0568354\pi\)
0.177606 + 0.984102i \(0.443165\pi\)
\(444\) −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 \(-0.580606\pi\)
0.250534 0.968108i \(-0.419394\pi\)
\(450\) 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 0.992198 0.124672i \(-0.0397878\pi\)
−0.124672 + 0.992198i \(0.539788\pi\)
\(458\) −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 0.274968 0.961453i \(-0.411333\pi\)
−0.961453 + 0.274968i \(0.911333\pi\)
\(464\) 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 −0.993646 0.112554i \(-0.964097\pi\)
−0.112554 0.993646i \(-0.535903\pi\)
\(468\) −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 0.187820 0.982203i \(-0.439858\pi\)
0.982203 0.187820i \(-0.0601422\pi\)
\(488\) −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 \(0.195590\pi\)
−0.817083 + 0.576520i \(0.804410\pi\)
\(500\) −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 −0.651016 0.759064i \(-0.725657\pi\)
0.759064 + 0.651016i \(0.225657\pi\)
\(504\) 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 \(0.316644\pi\)
−0.544698 + 0.838632i \(0.683356\pi\)
\(510\) 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 \(-0.939343\pi\)
0.981899 0.189407i \(-0.0606567\pi\)
\(522\) 5.01721 5.01721i 0.219597 0.219597i
\(523\) −22.1099 + 22.1099i −0.966800 + 0.966800i −0.999466 0.0326665i \(-0.989600\pi\)
0.0326665 + 0.999466i \(0.489600\pi\)
\(524\) 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 −0.382262 0.924054i \(-0.624855\pi\)
0.924054 + 0.382262i \(0.124855\pi\)
\(548\) 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 0.651647 0.758522i \(-0.274078\pi\)
−0.758522 + 0.651647i \(0.774078\pi\)
\(558\) −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 −0.141675 + 0.989913i \(0.545249\pi\)
−0.989913 + 0.141675i \(0.954751\pi\)
\(564\) 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 \(-0.628066\pi\)
0.391565 0.920151i \(-0.371934\pi\)
\(572\) −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 −0.641718 0.766941i \(-0.721778\pi\)
0.766941 + 0.641718i \(0.221778\pi\)
\(578\) −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 −0.998592 0.0530437i \(-0.983108\pi\)
0.0530437 + 0.998592i \(0.483108\pi\)
\(588\) −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 0.422395 0.906412i \(-0.361190\pi\)
−0.906412 + 0.422395i \(0.861190\pi\)
\(594\) −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 \(0.408353\pi\)
−0.283957 + 0.958837i \(0.591647\pi\)
\(600\) −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 −0.794726 0.606968i \(-0.792385\pi\)
0.606968 + 0.794726i \(0.292385\pi\)
\(608\) 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 −0.600468 0.799649i \(-0.705019\pi\)
0.799649 + 0.600468i \(0.205019\pi\)
\(614\) 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 −0.993260 0.115911i \(-0.963021\pi\)
−0.115911 0.993260i \(-0.536979\pi\)
\(618\) −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 \(-0.871095\pi\)
0.919115 0.393990i \(-0.128905\pi\)
\(632\) 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 \(-0.789033\pi\)
0.788289 0.615306i \(-0.210967\pi\)
\(642\) 9.95278 + 9.95278i 0.392805 + 0.392805i
\(643\) −21.5814 + 21.5814i −0.851087 + 0.851087i −0.990267 0.139180i \(-0.955553\pi\)
0.139180 + 0.990267i \(0.455553\pi\)
\(644\) −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 −0.680238 0.732991i \(-0.738124\pi\)
0.732991 + 0.680238i \(0.238124\pi\)
\(648\) 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 −0.999885 0.0151973i \(-0.995162\pi\)
−0.0151973 0.999885i \(-0.504838\pi\)
\(654\) −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 \(0.0281438\pi\)
−0.996094 + 0.0883010i \(0.971856\pi\)
\(662\) 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 0.992852 0.119353i \(-0.0380821\pi\)
−0.119353 + 0.992852i \(0.538082\pi\)
\(674\) 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 −0.941347 0.337440i \(-0.890439\pi\)
−0.337440 0.941347i \(-0.609561\pi\)
\(678\) −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 0.948768 0.315975i \(-0.102332\pi\)
−0.315975 + 0.948768i \(0.602332\pi\)
\(684\) −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 \(0.0334203\pi\)
−0.994493 + 0.104800i \(0.966580\pi\)
\(702\) 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 \(0.0102498\pi\)
−0.999482 + 0.0321952i \(0.989750\pi\)
\(720\) −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 0.634664 0.772788i \(-0.281139\pi\)
−0.772788 + 0.634664i \(0.781139\pi\)
\(728\) −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 −0.814397 0.580308i \(-0.802932\pi\)
0.580308 + 0.814397i \(0.302932\pi\)
\(734\) 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 \(0.168867\pi\)
−0.862549 + 0.505973i \(0.831133\pi\)
\(740\) −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 −0.211448 0.977389i \(-0.567818\pi\)
0.977389 + 0.211448i \(0.0678178\pi\)
\(744\) 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 \(-0.928586\pi\)
0.974938 0.222477i \(-0.0714142\pi\)
\(752\) −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 0.910938 0.412543i \(-0.135359\pi\)
−0.412543 + 0.910938i \(0.635359\pi\)
\(758\) −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 −0.527694 0.849434i \(-0.676943\pi\)
0.849434 + 0.527694i \(0.176943\pi\)
\(774\) −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