Properties

Label 690.2.j.a.643.7
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 643.7
Character \(\chi\) \(=\) 690.643
Dual form 690.2.j.a.367.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-2.22154 + 0.254460i) q^{5} -1.00000 q^{6} +(2.54671 + 2.54671i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-2.22154 + 0.254460i) q^{5} -1.00000 q^{6} +(2.54671 + 2.54671i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-1.39094 + 1.75080i) q^{10} +3.50160i q^{11} +(-0.707107 + 0.707107i) q^{12} +(2.40571 + 2.40571i) q^{13} +3.60159 q^{14} +(1.75080 + 1.39094i) q^{15} -1.00000 q^{16} +(1.37206 + 1.37206i) q^{17} +(0.707107 + 0.707107i) q^{18} +2.31155 q^{19} +(0.254460 + 2.22154i) q^{20} -3.60159i q^{21} +(2.47600 + 2.47600i) q^{22} +(-2.27923 - 4.21961i) q^{23} +1.00000i q^{24} +(4.87050 - 1.13059i) q^{25} +3.40219 q^{26} +(0.707107 - 0.707107i) q^{27} +(2.54671 - 2.54671i) q^{28} +0.113162i q^{29} +(2.22154 - 0.254460i) q^{30} +1.27272 q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.47600 - 2.47600i) q^{33} +1.94038 q^{34} +(-6.30566 - 5.00959i) q^{35} +1.00000 q^{36} +(3.74806 + 3.74806i) q^{37} +(1.63451 - 1.63451i) q^{38} -3.40219i q^{39} +(1.75080 + 1.39094i) q^{40} +5.08960 q^{41} +(-2.54671 - 2.54671i) q^{42} +(-2.71117 + 2.71117i) q^{43} +3.50160 q^{44} +(-0.254460 - 2.22154i) q^{45} +(-4.59537 - 1.37206i) q^{46} +(-0.775445 + 0.775445i) q^{47} +(0.707107 + 0.707107i) q^{48} +5.97146i q^{49} +(2.64452 - 4.24341i) q^{50} -1.94038i q^{51} +(2.40571 - 2.40571i) q^{52} +(-2.61742 + 2.61742i) q^{53} -1.00000i q^{54} +(-0.891017 - 7.77894i) q^{55} -3.60159i q^{56} +(-1.63451 - 1.63451i) q^{57} +(0.0800174 + 0.0800174i) q^{58} +13.2983i q^{59} +(1.39094 - 1.75080i) q^{60} -0.841493i q^{61} +(0.899946 - 0.899946i) q^{62} +(-2.54671 + 2.54671i) q^{63} +1.00000i q^{64} +(-5.95656 - 4.73224i) q^{65} -3.50160i q^{66} +(5.33351 + 5.33351i) q^{67} +(1.37206 - 1.37206i) q^{68} +(-1.37206 + 4.59537i) q^{69} +(-8.00109 + 0.916462i) q^{70} +14.2568 q^{71} +(0.707107 - 0.707107i) q^{72} +(-7.88793 - 7.88793i) q^{73} +5.30056 q^{74} +(-4.24341 - 2.64452i) q^{75} -2.31155i q^{76} +(-8.91755 + 8.91755i) q^{77} +(-2.40571 - 2.40571i) q^{78} +2.37992 q^{79} +(2.22154 - 0.254460i) q^{80} -1.00000 q^{81} +(3.59889 - 3.59889i) q^{82} +(1.02759 - 1.02759i) q^{83} -3.60159 q^{84} +(-3.39722 - 2.69895i) q^{85} +3.83417i q^{86} +(0.0800174 - 0.0800174i) q^{87} +(2.47600 - 2.47600i) q^{88} -14.7757 q^{89} +(-1.75080 - 1.39094i) q^{90} +12.2533i q^{91} +(-4.21961 + 2.27923i) q^{92} +(-0.899946 - 0.899946i) q^{93} +1.09665i q^{94} +(-5.13520 + 0.588197i) q^{95} +1.00000 q^{96} +(-4.66285 - 4.66285i) q^{97} +(4.22246 + 4.22246i) q^{98} -3.50160 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
\(5\) −2.22154 + 0.254460i −0.993504 + 0.113798i
\(6\) −1.00000 −0.408248
\(7\) 2.54671 + 2.54671i 0.962566 + 0.962566i 0.999324 0.0367582i \(-0.0117032\pi\)
−0.0367582 + 0.999324i \(0.511703\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) −1.39094 + 1.75080i −0.439853 + 0.553651i
\(11\) 3.50160i 1.05577i 0.849316 + 0.527886i \(0.177015\pi\)
−0.849316 + 0.527886i \(0.822985\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) 2.40571 + 2.40571i 0.667225 + 0.667225i 0.957073 0.289848i \(-0.0936046\pi\)
−0.289848 + 0.957073i \(0.593605\pi\)
\(14\) 3.60159 0.962566
\(15\) 1.75080 + 1.39094i 0.452054 + 0.359138i
\(16\) −1.00000 −0.250000
\(17\) 1.37206 + 1.37206i 0.332773 + 0.332773i 0.853639 0.520866i \(-0.174391\pi\)
−0.520866 + 0.853639i \(0.674391\pi\)
\(18\) 0.707107 + 0.707107i 0.166667 + 0.166667i
\(19\) 2.31155 0.530305 0.265153 0.964206i \(-0.414578\pi\)
0.265153 + 0.964206i \(0.414578\pi\)
\(20\) 0.254460 + 2.22154i 0.0568991 + 0.496752i
\(21\) 3.60159i 0.785932i
\(22\) 2.47600 + 2.47600i 0.527886 + 0.527886i
\(23\) −2.27923 4.21961i −0.475252 0.879850i
\(24\) 1.00000i 0.204124i
\(25\) 4.87050 1.13059i 0.974100 0.226118i
\(26\) 3.40219 0.667225
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 2.54671 2.54671i 0.481283 0.481283i
\(29\) 0.113162i 0.0210136i 0.999945 + 0.0105068i \(0.00334448\pi\)
−0.999945 + 0.0105068i \(0.996656\pi\)
\(30\) 2.22154 0.254460i 0.405596 0.0464579i
\(31\) 1.27272 0.228586 0.114293 0.993447i \(-0.463540\pi\)
0.114293 + 0.993447i \(0.463540\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 2.47600 2.47600i 0.431017 0.431017i
\(34\) 1.94038 0.332773
\(35\) −6.30566 5.00959i −1.06585 0.846775i
\(36\) 1.00000 0.166667
\(37\) 3.74806 + 3.74806i 0.616178 + 0.616178i 0.944549 0.328371i \(-0.106500\pi\)
−0.328371 + 0.944549i \(0.606500\pi\)
\(38\) 1.63451 1.63451i 0.265153 0.265153i
\(39\) 3.40219i 0.544787i
\(40\) 1.75080 + 1.39094i 0.276826 + 0.219926i
\(41\) 5.08960 0.794863 0.397431 0.917632i \(-0.369902\pi\)
0.397431 + 0.917632i \(0.369902\pi\)
\(42\) −2.54671 2.54671i −0.392966 0.392966i
\(43\) −2.71117 + 2.71117i −0.413449 + 0.413449i −0.882938 0.469489i \(-0.844438\pi\)
0.469489 + 0.882938i \(0.344438\pi\)
\(44\) 3.50160 0.527886
\(45\) −0.254460 2.22154i −0.0379327 0.331168i
\(46\) −4.59537 1.37206i −0.677551 0.202299i
\(47\) −0.775445 + 0.775445i −0.113110 + 0.113110i −0.761397 0.648286i \(-0.775486\pi\)
0.648286 + 0.761397i \(0.275486\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 5.97146i 0.853066i
\(50\) 2.64452 4.24341i 0.373991 0.600109i
\(51\) 1.94038i 0.271708i
\(52\) 2.40571 2.40571i 0.333613 0.333613i
\(53\) −2.61742 + 2.61742i −0.359530 + 0.359530i −0.863640 0.504110i \(-0.831821\pi\)
0.504110 + 0.863640i \(0.331821\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −0.891017 7.77894i −0.120145 1.04891i
\(56\) 3.60159i 0.481283i
\(57\) −1.63451 1.63451i −0.216496 0.216496i
\(58\) 0.0800174 + 0.0800174i 0.0105068 + 0.0105068i
\(59\) 13.2983i 1.73128i 0.500663 + 0.865642i \(0.333090\pi\)
−0.500663 + 0.865642i \(0.666910\pi\)
\(60\) 1.39094 1.75080i 0.179569 0.226027i
\(61\) 0.841493i 0.107742i −0.998548 0.0538710i \(-0.982844\pi\)
0.998548 0.0538710i \(-0.0171560\pi\)
\(62\) 0.899946 0.899946i 0.114293 0.114293i
\(63\) −2.54671 + 2.54671i −0.320855 + 0.320855i
\(64\) 1.00000i 0.125000i
\(65\) −5.95656 4.73224i −0.738820 0.586962i
\(66\) 3.50160i 0.431017i
\(67\) 5.33351 + 5.33351i 0.651592 + 0.651592i 0.953376 0.301784i \(-0.0975822\pi\)
−0.301784 + 0.953376i \(0.597582\pi\)
\(68\) 1.37206 1.37206i 0.166386 0.166386i
\(69\) −1.37206 + 4.59537i −0.165176 + 0.553218i
\(70\) −8.00109 + 0.916462i −0.956313 + 0.109538i
\(71\) 14.2568 1.69198 0.845988 0.533203i \(-0.179012\pi\)
0.845988 + 0.533203i \(0.179012\pi\)
\(72\) 0.707107 0.707107i 0.0833333 0.0833333i
\(73\) −7.88793 7.88793i −0.923212 0.923212i 0.0740430 0.997255i \(-0.476410\pi\)
−0.997255 + 0.0740430i \(0.976410\pi\)
\(74\) 5.30056 0.616178
\(75\) −4.24341 2.64452i −0.489987 0.305362i
\(76\) 2.31155i 0.265153i
\(77\) −8.91755 + 8.91755i −1.01625 + 1.01625i
\(78\) −2.40571 2.40571i −0.272394 0.272394i
\(79\) 2.37992 0.267761 0.133881 0.990997i \(-0.457256\pi\)
0.133881 + 0.990997i \(0.457256\pi\)
\(80\) 2.22154 0.254460i 0.248376 0.0284495i
\(81\) −1.00000 −0.111111
\(82\) 3.59889 3.59889i 0.397431 0.397431i
\(83\) 1.02759 1.02759i 0.112793 0.112793i −0.648458 0.761251i \(-0.724586\pi\)
0.761251 + 0.648458i \(0.224586\pi\)
\(84\) −3.60159 −0.392966
\(85\) −3.39722 2.69895i −0.368480 0.292742i
\(86\) 3.83417i 0.413449i
\(87\) 0.0800174 0.0800174i 0.00857877 0.00857877i
\(88\) 2.47600 2.47600i 0.263943 0.263943i
\(89\) −14.7757 −1.56622 −0.783109 0.621885i \(-0.786367\pi\)
−0.783109 + 0.621885i \(0.786367\pi\)
\(90\) −1.75080 1.39094i −0.184550 0.146618i
\(91\) 12.2533i 1.28450i
\(92\) −4.21961 + 2.27923i −0.439925 + 0.237626i
\(93\) −0.899946 0.899946i −0.0933200 0.0933200i
\(94\) 1.09665i 0.113110i
\(95\) −5.13520 + 0.588197i −0.526860 + 0.0603477i
\(96\) 1.00000 0.102062
\(97\) −4.66285 4.66285i −0.473441 0.473441i 0.429585 0.903026i \(-0.358660\pi\)
−0.903026 + 0.429585i \(0.858660\pi\)
\(98\) 4.22246 + 4.22246i 0.426533 + 0.426533i
\(99\) −3.50160 −0.351924
\(100\) −1.13059 4.87050i −0.113059 0.487050i
\(101\) 0.433231 0.0431081 0.0215541 0.999768i \(-0.493139\pi\)
0.0215541 + 0.999768i \(0.493139\pi\)
\(102\) −1.37206 1.37206i −0.135854 0.135854i
\(103\) −8.99956 + 8.99956i −0.886753 + 0.886753i −0.994210 0.107457i \(-0.965729\pi\)
0.107457 + 0.994210i \(0.465729\pi\)
\(104\) 3.40219i 0.333613i
\(105\) 0.916462 + 8.00109i 0.0894376 + 0.780826i
\(106\) 3.70159i 0.359530i
\(107\) −13.7709 13.7709i −1.33128 1.33128i −0.904225 0.427056i \(-0.859551\pi\)
−0.427056 0.904225i \(-0.640449\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) 3.09267 0.296224 0.148112 0.988971i \(-0.452680\pi\)
0.148112 + 0.988971i \(0.452680\pi\)
\(110\) −6.13059 4.87050i −0.584529 0.464384i
\(111\) 5.30056i 0.503107i
\(112\) −2.54671 2.54671i −0.240641 0.240641i
\(113\) 2.36212 2.36212i 0.222209 0.222209i −0.587219 0.809428i \(-0.699777\pi\)
0.809428 + 0.587219i \(0.199777\pi\)
\(114\) −2.31155 −0.216496
\(115\) 6.13713 + 8.79407i 0.572290 + 0.820051i
\(116\) 0.113162 0.0105068
\(117\) −2.40571 + 2.40571i −0.222408 + 0.222408i
\(118\) 9.40328 + 9.40328i 0.865642 + 0.865642i
\(119\) 6.98846i 0.640631i
\(120\) −0.254460 2.22154i −0.0232289 0.202798i
\(121\) −1.26118 −0.114653
\(122\) −0.595025 0.595025i −0.0538710 0.0538710i
\(123\) −3.59889 3.59889i −0.324501 0.324501i
\(124\) 1.27272i 0.114293i
\(125\) −10.5323 + 3.75100i −0.942040 + 0.335500i
\(126\) 3.60159i 0.320855i
\(127\) 8.49034 8.49034i 0.753396 0.753396i −0.221715 0.975111i \(-0.571166\pi\)
0.975111 + 0.221715i \(0.0711656\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 3.83417 0.337580
\(130\) −7.55812 + 0.865724i −0.662891 + 0.0759290i
\(131\) 18.8562 1.64747 0.823736 0.566973i \(-0.191886\pi\)
0.823736 + 0.566973i \(0.191886\pi\)
\(132\) −2.47600 2.47600i −0.215508 0.215508i
\(133\) 5.88684 + 5.88684i 0.510454 + 0.510454i
\(134\) 7.54272 0.651592
\(135\) −1.39094 + 1.75080i −0.119713 + 0.150685i
\(136\) 1.94038i 0.166386i
\(137\) −3.49960 3.49960i −0.298991 0.298991i 0.541628 0.840618i \(-0.317808\pi\)
−0.840618 + 0.541628i \(0.817808\pi\)
\(138\) 2.27923 + 4.21961i 0.194021 + 0.359197i
\(139\) 14.4705i 1.22737i 0.789552 + 0.613684i \(0.210313\pi\)
−0.789552 + 0.613684i \(0.789687\pi\)
\(140\) −5.00959 + 6.30566i −0.423387 + 0.532926i
\(141\) 1.09665 0.0923542
\(142\) 10.0811 10.0811i 0.845988 0.845988i
\(143\) −8.42384 + 8.42384i −0.704437 + 0.704437i
\(144\) 1.00000i 0.0833333i
\(145\) −0.0287952 0.251394i −0.00239131 0.0208771i
\(146\) −11.1552 −0.923212
\(147\) 4.22246 4.22246i 0.348263 0.348263i
\(148\) 3.74806 3.74806i 0.308089 0.308089i
\(149\) −2.64129 −0.216383 −0.108192 0.994130i \(-0.534506\pi\)
−0.108192 + 0.994130i \(0.534506\pi\)
\(150\) −4.87050 + 1.13059i −0.397675 + 0.0923122i
\(151\) 21.1977 1.72505 0.862524 0.506016i \(-0.168882\pi\)
0.862524 + 0.506016i \(0.168882\pi\)
\(152\) −1.63451 1.63451i −0.132576 0.132576i
\(153\) −1.37206 + 1.37206i −0.110924 + 0.110924i
\(154\) 12.6113i 1.01625i
\(155\) −2.82739 + 0.323856i −0.227102 + 0.0260127i
\(156\) −3.40219 −0.272394
\(157\) −17.0584 17.0584i −1.36141 1.36141i −0.872128 0.489278i \(-0.837260\pi\)
−0.489278 0.872128i \(-0.662740\pi\)
\(158\) 1.68285 1.68285i 0.133881 0.133881i
\(159\) 3.70159 0.293555
\(160\) 1.39094 1.75080i 0.109963 0.138413i
\(161\) 4.94159 16.5507i 0.389452 1.30437i
\(162\) −0.707107 + 0.707107i −0.0555556 + 0.0555556i
\(163\) 2.81143 + 2.81143i 0.220208 + 0.220208i 0.808586 0.588378i \(-0.200233\pi\)
−0.588378 + 0.808586i \(0.700233\pi\)
\(164\) 5.08960i 0.397431i
\(165\) −4.87050 + 6.13059i −0.379168 + 0.477266i
\(166\) 1.45324i 0.112793i
\(167\) −8.40826 + 8.40826i −0.650651 + 0.650651i −0.953150 0.302499i \(-0.902179\pi\)
0.302499 + 0.953150i \(0.402179\pi\)
\(168\) −2.54671 + 2.54671i −0.196483 + 0.196483i
\(169\) 1.42507i 0.109621i
\(170\) −4.31064 + 0.493750i −0.330611 + 0.0378689i
\(171\) 2.31155i 0.176768i
\(172\) 2.71117 + 2.71117i 0.206724 + 0.206724i
\(173\) −8.59500 8.59500i −0.653466 0.653466i 0.300360 0.953826i \(-0.402893\pi\)
−0.953826 + 0.300360i \(0.902893\pi\)
\(174\) 0.113162i 0.00857877i
\(175\) 15.2830 + 9.52447i 1.15529 + 0.719982i
\(176\) 3.50160i 0.263943i
\(177\) 9.40328 9.40328i 0.706794 0.706794i
\(178\) −10.4480 + 10.4480i −0.783109 + 0.783109i
\(179\) 22.1597i 1.65629i −0.560511 0.828147i \(-0.689395\pi\)
0.560511 0.828147i \(-0.310605\pi\)
\(180\) −2.22154 + 0.254460i −0.165584 + 0.0189664i
\(181\) 7.71976i 0.573805i 0.957960 + 0.286903i \(0.0926256\pi\)
−0.957960 + 0.286903i \(0.907374\pi\)
\(182\) 8.66440 + 8.66440i 0.642248 + 0.642248i
\(183\) −0.595025 + 0.595025i −0.0439855 + 0.0439855i
\(184\) −1.37206 + 4.59537i −0.101149 + 0.338775i
\(185\) −9.28022 7.37275i −0.682295 0.542055i
\(186\) −1.27272 −0.0933200
\(187\) −4.80439 + 4.80439i −0.351332 + 0.351332i
\(188\) 0.775445 + 0.775445i 0.0565552 + 0.0565552i
\(189\) 3.60159 0.261977
\(190\) −3.21522 + 4.04705i −0.233256 + 0.293604i
\(191\) 22.6783i 1.64094i −0.571689 0.820471i \(-0.693711\pi\)
0.571689 0.820471i \(-0.306289\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) −13.9176 13.9176i −1.00181 1.00181i −0.999998 0.00180888i \(-0.999424\pi\)
−0.00180888 0.999998i \(-0.500576\pi\)
\(194\) −6.59427 −0.473441
\(195\) 0.865724 + 7.55812i 0.0619958 + 0.541248i
\(196\) 5.97146 0.426533
\(197\) −3.68741 + 3.68741i −0.262717 + 0.262717i −0.826157 0.563440i \(-0.809478\pi\)
0.563440 + 0.826157i \(0.309478\pi\)
\(198\) −2.47600 + 2.47600i −0.175962 + 0.175962i
\(199\) 11.8404 0.839343 0.419672 0.907676i \(-0.362145\pi\)
0.419672 + 0.907676i \(0.362145\pi\)
\(200\) −4.24341 2.64452i −0.300054 0.186996i
\(201\) 7.54272i 0.532023i
\(202\) 0.306341 0.306341i 0.0215541 0.0215541i
\(203\) −0.288190 + 0.288190i −0.0202270 + 0.0202270i
\(204\) −1.94038 −0.135854
\(205\) −11.3068 + 1.29510i −0.789699 + 0.0904539i
\(206\) 12.7273i 0.886753i
\(207\) 4.21961 2.27923i 0.293283 0.158417i
\(208\) −2.40571 2.40571i −0.166806 0.166806i
\(209\) 8.09410i 0.559881i
\(210\) 6.30566 + 5.00959i 0.435132 + 0.345694i
\(211\) −24.3012 −1.67296 −0.836482 0.547994i \(-0.815392\pi\)
−0.836482 + 0.547994i \(0.815392\pi\)
\(212\) 2.61742 + 2.61742i 0.179765 + 0.179765i
\(213\) −10.0811 10.0811i −0.690746 0.690746i
\(214\) −19.4750 −1.33128
\(215\) 5.33309 6.71285i 0.363713 0.457813i
\(216\) −1.00000 −0.0680414
\(217\) 3.24124 + 3.24124i 0.220030 + 0.220030i
\(218\) 2.18685 2.18685i 0.148112 0.148112i
\(219\) 11.1552i 0.753799i
\(220\) −7.77894 + 0.891017i −0.524456 + 0.0600724i
\(221\) 6.60156i 0.444069i
\(222\) −3.74806 3.74806i −0.251554 0.251554i
\(223\) −1.60241 1.60241i −0.107306 0.107306i 0.651416 0.758721i \(-0.274175\pi\)
−0.758721 + 0.651416i \(0.774175\pi\)
\(224\) −3.60159 −0.240641
\(225\) 1.13059 + 4.87050i 0.0753726 + 0.324700i
\(226\) 3.34054i 0.222209i
\(227\) 15.4161 + 15.4161i 1.02320 + 1.02320i 0.999724 + 0.0234786i \(0.00747416\pi\)
0.0234786 + 0.999724i \(0.492526\pi\)
\(228\) −1.63451 + 1.63451i −0.108248 + 0.108248i
\(229\) 12.8440 0.848754 0.424377 0.905486i \(-0.360493\pi\)
0.424377 + 0.905486i \(0.360493\pi\)
\(230\) 10.5580 + 1.87874i 0.696171 + 0.123881i
\(231\) 12.6113 0.829764
\(232\) 0.0800174 0.0800174i 0.00525340 0.00525340i
\(233\) −12.2901 12.2901i −0.805153 0.805153i 0.178743 0.983896i \(-0.442797\pi\)
−0.983896 + 0.178743i \(0.942797\pi\)
\(234\) 3.40219i 0.222408i
\(235\) 1.52536 1.92000i 0.0995038 0.125247i
\(236\) 13.2983 0.865642
\(237\) −1.68285 1.68285i −0.109313 0.109313i
\(238\) 4.94159 + 4.94159i 0.320316 + 0.320316i
\(239\) 18.1727i 1.17549i 0.809045 + 0.587747i \(0.199985\pi\)
−0.809045 + 0.587747i \(0.800015\pi\)
\(240\) −1.75080 1.39094i −0.113014 0.0897846i
\(241\) 11.7886i 0.759373i 0.925115 + 0.379687i \(0.123968\pi\)
−0.925115 + 0.379687i \(0.876032\pi\)
\(242\) −0.891787 + 0.891787i −0.0573263 + 0.0573263i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) −0.841493 −0.0538710
\(245\) −1.51950 13.2659i −0.0970774 0.847525i
\(246\) −5.08960 −0.324501
\(247\) 5.56092 + 5.56092i 0.353833 + 0.353833i
\(248\) −0.899946 0.899946i −0.0571466 0.0571466i
\(249\) −1.45324 −0.0920950
\(250\) −4.79513 + 10.0998i −0.303270 + 0.638770i
\(251\) 12.8428i 0.810631i −0.914177 0.405315i \(-0.867162\pi\)
0.914177 0.405315i \(-0.132838\pi\)
\(252\) 2.54671 + 2.54671i 0.160428 + 0.160428i
\(253\) 14.7754 7.98094i 0.928920 0.501757i
\(254\) 12.0072i 0.753396i
\(255\) 0.493750 + 4.31064i 0.0309198 + 0.269943i
\(256\) 1.00000 0.0625000
\(257\) 1.42623 1.42623i 0.0889659 0.0889659i −0.661223 0.750189i \(-0.729962\pi\)
0.750189 + 0.661223i \(0.229962\pi\)
\(258\) 2.71117 2.71117i 0.168790 0.168790i
\(259\) 19.0905i 1.18622i
\(260\) −4.73224 + 5.95656i −0.293481 + 0.369410i
\(261\) −0.113162 −0.00700453
\(262\) 13.3333 13.3333i 0.823736 0.823736i
\(263\) 18.6079 18.6079i 1.14741 1.14741i 0.160349 0.987060i \(-0.448738\pi\)
0.987060 0.160349i \(-0.0512621\pi\)
\(264\) −3.50160 −0.215508
\(265\) 5.14867 6.48073i 0.316281 0.398108i
\(266\) 8.32525 0.510454
\(267\) 10.4480 + 10.4480i 0.639406 + 0.639406i
\(268\) 5.33351 5.33351i 0.325796 0.325796i
\(269\) 13.7120i 0.836034i 0.908439 + 0.418017i \(0.137275\pi\)
−0.908439 + 0.418017i \(0.862725\pi\)
\(270\) 0.254460 + 2.22154i 0.0154860 + 0.135199i
\(271\) −11.6831 −0.709696 −0.354848 0.934924i \(-0.615467\pi\)
−0.354848 + 0.934924i \(0.615467\pi\)
\(272\) −1.37206 1.37206i −0.0831932 0.0831932i
\(273\) 8.66440 8.66440i 0.524394 0.524394i
\(274\) −4.94918 −0.298991
\(275\) 3.95887 + 17.0545i 0.238729 + 1.02843i
\(276\) 4.59537 + 1.37206i 0.276609 + 0.0825881i
\(277\) 10.3117 10.3117i 0.619572 0.619572i −0.325850 0.945422i \(-0.605650\pi\)
0.945422 + 0.325850i \(0.105650\pi\)
\(278\) 10.2322 + 10.2322i 0.613684 + 0.613684i
\(279\) 1.27272i 0.0761955i
\(280\) 0.916462 + 8.00109i 0.0547691 + 0.478157i
\(281\) 29.4216i 1.75514i −0.479445 0.877572i \(-0.659162\pi\)
0.479445 0.877572i \(-0.340838\pi\)
\(282\) 0.775445 0.775445i 0.0461771 0.0461771i
\(283\) −18.0041 + 18.0041i −1.07023 + 1.07023i −0.0728932 + 0.997340i \(0.523223\pi\)
−0.997340 + 0.0728932i \(0.976777\pi\)
\(284\) 14.2568i 0.845988i
\(285\) 4.04705 + 3.21522i 0.239727 + 0.190453i
\(286\) 11.9131i 0.704437i
\(287\) 12.9617 + 12.9617i 0.765108 + 0.765108i
\(288\) −0.707107 0.707107i −0.0416667 0.0416667i
\(289\) 13.2349i 0.778525i
\(290\) −0.198123 0.157401i −0.0116342 0.00924289i
\(291\) 6.59427i 0.386563i
\(292\) −7.88793 + 7.88793i −0.461606 + 0.461606i
\(293\) −11.1818 + 11.1818i −0.653249 + 0.653249i −0.953774 0.300525i \(-0.902838\pi\)
0.300525 + 0.953774i \(0.402838\pi\)
\(294\) 5.97146i 0.348263i
\(295\) −3.38388 29.5426i −0.197017 1.72004i
\(296\) 5.30056i 0.308089i
\(297\) 2.47600 + 2.47600i 0.143672 + 0.143672i
\(298\) −1.86768 + 1.86768i −0.108192 + 0.108192i
\(299\) 4.66800 15.6344i 0.269958 0.904158i
\(300\) −2.64452 + 4.24341i −0.152681 + 0.244993i
\(301\) −13.8091 −0.795944
\(302\) 14.9891 14.9891i 0.862524 0.862524i
\(303\) −0.306341 0.306341i −0.0175988 0.0175988i
\(304\) −2.31155 −0.132576
\(305\) 0.214126 + 1.86941i 0.0122608 + 0.107042i
\(306\) 1.94038i 0.110924i
\(307\) 9.99514 9.99514i 0.570453 0.570453i −0.361802 0.932255i \(-0.617838\pi\)
0.932255 + 0.361802i \(0.117838\pi\)
\(308\) 8.91755 + 8.91755i 0.508125 + 0.508125i
\(309\) 12.7273 0.724031
\(310\) −1.77027 + 2.22827i −0.100544 + 0.126557i
\(311\) 3.18731 0.180736 0.0903678 0.995908i \(-0.471196\pi\)
0.0903678 + 0.995908i \(0.471196\pi\)
\(312\) −2.40571 + 2.40571i −0.136197 + 0.136197i
\(313\) 19.6532 19.6532i 1.11086 1.11086i 0.117830 0.993034i \(-0.462406\pi\)
0.993034 0.117830i \(-0.0375936\pi\)
\(314\) −24.1242 −1.36141
\(315\) 5.00959 6.30566i 0.282258 0.355284i
\(316\) 2.37992i 0.133881i
\(317\) 3.39018 3.39018i 0.190411 0.190411i −0.605463 0.795874i \(-0.707012\pi\)
0.795874 + 0.605463i \(0.207012\pi\)
\(318\) 2.61742 2.61742i 0.146777 0.146777i
\(319\) −0.396247 −0.0221856
\(320\) −0.254460 2.22154i −0.0142248 0.124188i
\(321\) 19.4750i 1.08699i
\(322\) −8.20885 15.1973i −0.457462 0.846913i
\(323\) 3.17157 + 3.17157i 0.176471 + 0.176471i
\(324\) 1.00000i 0.0555556i
\(325\) 14.4369 + 8.99716i 0.800816 + 0.499073i
\(326\) 3.97596 0.220208
\(327\) −2.18685 2.18685i −0.120933 0.120933i
\(328\) −3.59889 3.59889i −0.198716 0.198716i
\(329\) −3.94967 −0.217752
\(330\) 0.891017 + 7.77894i 0.0490489 + 0.428217i
\(331\) −2.32929 −0.128029 −0.0640146 0.997949i \(-0.520390\pi\)
−0.0640146 + 0.997949i \(0.520390\pi\)
\(332\) −1.02759 1.02759i −0.0563965 0.0563965i
\(333\) −3.74806 + 3.74806i −0.205393 + 0.205393i
\(334\) 11.8911i 0.650651i
\(335\) −13.2058 10.4915i −0.721509 0.573209i
\(336\) 3.60159i 0.196483i
\(337\) −19.2106 19.2106i −1.04647 1.04647i −0.998866 0.0476036i \(-0.984842\pi\)
−0.0476036 0.998866i \(-0.515158\pi\)
\(338\) −1.00768 1.00768i −0.0548104 0.0548104i
\(339\) −3.34054 −0.181433
\(340\) −2.69895 + 3.39722i −0.146371 + 0.184240i
\(341\) 4.45654i 0.241335i
\(342\) 1.63451 + 1.63451i 0.0883842 + 0.0883842i
\(343\) 2.61938 2.61938i 0.141433 0.141433i
\(344\) 3.83417 0.206724
\(345\) 1.87874 10.5580i 0.101148 0.568421i
\(346\) −12.1552 −0.653466
\(347\) −6.50382 + 6.50382i −0.349143 + 0.349143i −0.859790 0.510647i \(-0.829406\pi\)
0.510647 + 0.859790i \(0.329406\pi\)
\(348\) −0.0800174 0.0800174i −0.00428938 0.00428938i
\(349\) 4.27903i 0.229051i −0.993420 0.114526i \(-0.963465\pi\)
0.993420 0.114526i \(-0.0365348\pi\)
\(350\) 17.5416 4.07192i 0.937635 0.217653i
\(351\) 3.40219 0.181596
\(352\) −2.47600 2.47600i −0.131971 0.131971i
\(353\) 16.8716 + 16.8716i 0.897983 + 0.897983i 0.995258 0.0972747i \(-0.0310125\pi\)
−0.0972747 + 0.995258i \(0.531013\pi\)
\(354\) 13.2983i 0.706794i
\(355\) −31.6722 + 3.62780i −1.68098 + 0.192544i
\(356\) 14.7757i 0.783109i
\(357\) 4.94159 4.94159i 0.261537 0.261537i
\(358\) −15.6693 15.6693i −0.828147 0.828147i
\(359\) 24.2841 1.28166 0.640832 0.767681i \(-0.278590\pi\)
0.640832 + 0.767681i \(0.278590\pi\)
\(360\) −1.39094 + 1.75080i −0.0733088 + 0.0922752i
\(361\) −13.6568 −0.718777
\(362\) 5.45870 + 5.45870i 0.286903 + 0.286903i
\(363\) 0.891787 + 0.891787i 0.0468067 + 0.0468067i
\(364\) 12.2533 0.642248
\(365\) 19.5305 + 15.5162i 1.02227 + 0.812155i
\(366\) 0.841493i 0.0439855i
\(367\) 16.5877 + 16.5877i 0.865871 + 0.865871i 0.992012 0.126141i \(-0.0402593\pi\)
−0.126141 + 0.992012i \(0.540259\pi\)
\(368\) 2.27923 + 4.21961i 0.118813 + 0.219962i
\(369\) 5.08960i 0.264954i
\(370\) −11.7754 + 1.34878i −0.612175 + 0.0701199i
\(371\) −13.3316 −0.692143
\(372\) −0.899946 + 0.899946i −0.0466600 + 0.0466600i
\(373\) 0.545949 0.545949i 0.0282682 0.0282682i −0.692831 0.721100i \(-0.743637\pi\)
0.721100 + 0.692831i \(0.243637\pi\)
\(374\) 6.79443i 0.351332i
\(375\) 10.0998 + 4.79513i 0.521554 + 0.247619i
\(376\) 1.09665 0.0565552
\(377\) −0.272235 + 0.272235i −0.0140208 + 0.0140208i
\(378\) 2.54671 2.54671i 0.130989 0.130989i
\(379\) 11.6412 0.597971 0.298985 0.954258i \(-0.403352\pi\)
0.298985 + 0.954258i \(0.403352\pi\)
\(380\) 0.588197 + 5.13520i 0.0301739 + 0.263430i
\(381\) −12.0072 −0.615145
\(382\) −16.0360 16.0360i −0.820471 0.820471i
\(383\) 15.6586 15.6586i 0.800116 0.800116i −0.182997 0.983113i \(-0.558580\pi\)
0.983113 + 0.182997i \(0.0585800\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 17.5416 22.0799i 0.894000 1.12529i
\(386\) −19.6824 −1.00181
\(387\) −2.71117 2.71117i −0.137816 0.137816i
\(388\) −4.66285 + 4.66285i −0.236720 + 0.236720i
\(389\) 34.3765 1.74296 0.871478 0.490435i \(-0.163162\pi\)
0.871478 + 0.490435i \(0.163162\pi\)
\(390\) 5.95656 + 4.73224i 0.301622 + 0.239626i
\(391\) 2.66231 8.91678i 0.134639 0.450941i
\(392\) 4.22246 4.22246i 0.213267 0.213267i
\(393\) −13.3333 13.3333i −0.672578 0.672578i
\(394\) 5.21479i 0.262717i
\(395\) −5.28708 + 0.605594i −0.266022 + 0.0304707i
\(396\) 3.50160i 0.175962i
\(397\) 3.67637 3.67637i 0.184512 0.184512i −0.608807 0.793318i \(-0.708352\pi\)
0.793318 + 0.608807i \(0.208352\pi\)
\(398\) 8.37242 8.37242i 0.419672 0.419672i
\(399\) 8.32525i 0.416784i
\(400\) −4.87050 + 1.13059i −0.243525 + 0.0565294i
\(401\) 8.61364i 0.430145i 0.976598 + 0.215072i \(0.0689988\pi\)
−0.976598 + 0.215072i \(0.931001\pi\)
\(402\) −5.33351 5.33351i −0.266011 0.266011i
\(403\) 3.06179 + 3.06179i 0.152519 + 0.152519i
\(404\) 0.433231i 0.0215541i
\(405\) 2.22154 0.254460i 0.110389 0.0126442i
\(406\) 0.407562i 0.0202270i
\(407\) −13.1242 + 13.1242i −0.650543 + 0.650543i
\(408\) −1.37206 + 1.37206i −0.0679269 + 0.0679269i
\(409\) 10.5576i 0.522038i 0.965334 + 0.261019i \(0.0840585\pi\)
−0.965334 + 0.261019i \(0.915941\pi\)
\(410\) −7.07932 + 8.91087i −0.349623 + 0.440077i
\(411\) 4.94918i 0.244125i
\(412\) 8.99956 + 8.99956i 0.443377 + 0.443377i
\(413\) −33.8668 + 33.8668i −1.66648 + 1.66648i
\(414\) 1.37206 4.59537i 0.0674329 0.225850i
\(415\) −2.02136 + 2.54432i −0.0992246 + 0.124896i
\(416\) −3.40219 −0.166806
\(417\) 10.2322 10.2322i 0.501071 0.501071i
\(418\) 5.72339 + 5.72339i 0.279940 + 0.279940i
\(419\) −31.5043 −1.53909 −0.769543 0.638594i \(-0.779516\pi\)
−0.769543 + 0.638594i \(0.779516\pi\)
\(420\) 8.00109 0.916462i 0.390413 0.0447188i
\(421\) 29.1199i 1.41922i −0.704595 0.709609i \(-0.748871\pi\)
0.704595 0.709609i \(-0.251129\pi\)
\(422\) −17.1835 + 17.1835i −0.836482 + 0.836482i
\(423\) −0.775445 0.775445i −0.0377034 0.0377034i
\(424\) 3.70159 0.179765
\(425\) 8.23383 + 5.13137i 0.399400 + 0.248908i
\(426\) −14.2568 −0.690746
\(427\) 2.14304 2.14304i 0.103709 0.103709i
\(428\) −13.7709 + 13.7709i −0.665641 + 0.665641i
\(429\) 11.9131 0.575170
\(430\) −0.975644 8.51777i −0.0470497 0.410763i
\(431\) 29.7497i 1.43299i 0.697592 + 0.716495i \(0.254255\pi\)
−0.697592 + 0.716495i \(0.745745\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) 15.2332 15.2332i 0.732060 0.732060i −0.238967 0.971028i \(-0.576809\pi\)
0.971028 + 0.238967i \(0.0768089\pi\)
\(434\) 4.58380 0.220030
\(435\) −0.157401 + 0.198123i −0.00754679 + 0.00949929i
\(436\) 3.09267i 0.148112i
\(437\) −5.26854 9.75383i −0.252029 0.466589i
\(438\) 7.88793 + 7.88793i 0.376900 + 0.376900i
\(439\) 32.1103i 1.53254i −0.642518 0.766271i \(-0.722110\pi\)
0.642518 0.766271i \(-0.277890\pi\)
\(440\) −4.87050 + 6.13059i −0.232192 + 0.292264i
\(441\) −5.97146 −0.284355
\(442\) 4.66800 + 4.66800i 0.222034 + 0.222034i
\(443\) 5.81843 + 5.81843i 0.276442 + 0.276442i 0.831687 0.555245i \(-0.187375\pi\)
−0.555245 + 0.831687i \(0.687375\pi\)
\(444\) −5.30056 −0.251554
\(445\) 32.8248 3.75982i 1.55604 0.178233i
\(446\) −2.26616 −0.107306
\(447\) 1.86768 + 1.86768i 0.0883380 + 0.0883380i
\(448\) −2.54671 + 2.54671i −0.120321 + 0.120321i
\(449\) 9.11228i 0.430035i 0.976610 + 0.215018i \(0.0689809\pi\)
−0.976610 + 0.215018i \(0.931019\pi\)
\(450\) 4.24341 + 2.64452i 0.200036 + 0.124664i
\(451\) 17.8217i 0.839193i
\(452\) −2.36212 2.36212i −0.111105 0.111105i
\(453\) −14.9891 14.9891i −0.704248 0.704248i
\(454\) 21.8017 1.02320
\(455\) −3.11798 27.2213i −0.146173 1.27615i
\(456\) 2.31155i 0.108248i
\(457\) −1.84839 1.84839i −0.0864641 0.0864641i 0.662552 0.749016i \(-0.269473\pi\)
−0.749016 + 0.662552i \(0.769473\pi\)
\(458\) 9.08206 9.08206i 0.424377 0.424377i
\(459\) 1.94038 0.0905692
\(460\) 8.79407 6.13713i 0.410026 0.286145i
\(461\) 24.8093 1.15549 0.577743 0.816219i \(-0.303934\pi\)
0.577743 + 0.816219i \(0.303934\pi\)
\(462\) 8.91755 8.91755i 0.414882 0.414882i
\(463\) −11.8812 11.8812i −0.552166 0.552166i 0.374899 0.927065i \(-0.377677\pi\)
−0.927065 + 0.374899i \(0.877677\pi\)
\(464\) 0.113162i 0.00525340i
\(465\) 2.22827 + 1.77027i 0.103333 + 0.0820942i
\(466\) −17.3809 −0.805153
\(467\) −19.0071 19.0071i −0.879542 0.879542i 0.113945 0.993487i \(-0.463651\pi\)
−0.993487 + 0.113945i \(0.963651\pi\)
\(468\) 2.40571 + 2.40571i 0.111204 + 0.111204i
\(469\) 27.1658i 1.25440i
\(470\) −0.279053 2.43624i −0.0128717 0.112376i
\(471\) 24.1242i 1.11158i
\(472\) 9.40328 9.40328i 0.432821 0.432821i
\(473\) −9.49341 9.49341i −0.436507 0.436507i
\(474\) −2.37992 −0.109313
\(475\) 11.2584 2.61341i 0.516570 0.119911i
\(476\) 6.98846 0.320316
\(477\) −2.61742 2.61742i −0.119843 0.119843i
\(478\) 12.8500 + 12.8500i 0.587747 + 0.587747i
\(479\) 4.09469 0.187091 0.0935455 0.995615i \(-0.470180\pi\)
0.0935455 + 0.995615i \(0.470180\pi\)
\(480\) −2.22154 + 0.254460i −0.101399 + 0.0116145i
\(481\) 18.0335i 0.822259i
\(482\) 8.33583 + 8.33583i 0.379687 + 0.379687i
\(483\) −15.1973 + 8.20885i −0.691502 + 0.373516i
\(484\) 1.26118i 0.0573263i
\(485\) 11.5452 + 9.17221i 0.524242 + 0.416489i
\(486\) 1.00000 0.0453609
\(487\) 21.9539 21.9539i 0.994826 0.994826i −0.00516029 0.999987i \(-0.501643\pi\)
0.999987 + 0.00516029i \(0.00164258\pi\)
\(488\) −0.595025 + 0.595025i −0.0269355 + 0.0269355i
\(489\) 3.97596i 0.179799i
\(490\) −10.4548 8.30593i −0.472301 0.375224i
\(491\) 27.8777 1.25810 0.629051 0.777364i \(-0.283444\pi\)
0.629051 + 0.777364i \(0.283444\pi\)
\(492\) −3.59889 + 3.59889i −0.162251 + 0.162251i
\(493\) −0.155264 + 0.155264i −0.00699275 + 0.00699275i
\(494\) 7.86433 0.353833
\(495\) 7.77894 0.891017i 0.349638 0.0400483i
\(496\) −1.27272 −0.0571466
\(497\) 36.3080 + 36.3080i 1.62864 + 1.62864i
\(498\) −1.02759 + 1.02759i −0.0460475 + 0.0460475i
\(499\) 3.43975i 0.153984i −0.997032 0.0769921i \(-0.975468\pi\)
0.997032 0.0769921i \(-0.0245316\pi\)
\(500\) 3.75100 + 10.5323i 0.167750 + 0.471020i
\(501\) 11.8911 0.531254
\(502\) −9.08123 9.08123i −0.405315 0.405315i
\(503\) −10.5623 + 10.5623i −0.470951 + 0.470951i −0.902222 0.431271i \(-0.858065\pi\)
0.431271 + 0.902222i \(0.358065\pi\)
\(504\) 3.60159 0.160428
\(505\) −0.962442 + 0.110240i −0.0428281 + 0.00490562i
\(506\) 4.80439 16.0911i 0.213581 0.715339i
\(507\) −1.00768 + 1.00768i −0.0447525 + 0.0447525i
\(508\) −8.49034 8.49034i −0.376698 0.376698i
\(509\) 26.4803i 1.17372i −0.809690 0.586858i \(-0.800364\pi\)
0.809690 0.586858i \(-0.199636\pi\)
\(510\) 3.39722 + 2.69895i 0.150431 + 0.119511i
\(511\) 40.1765i 1.77730i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 1.63451 1.63451i 0.0721654 0.0721654i
\(514\) 2.01700i 0.0889659i
\(515\) 17.7029 22.2829i 0.780082 0.981904i
\(516\) 3.83417i 0.168790i
\(517\) −2.71530 2.71530i −0.119419 0.119419i
\(518\) 13.4990 + 13.4990i 0.593112 + 0.593112i
\(519\) 12.1552i 0.533553i
\(520\) 0.865724 + 7.55812i 0.0379645 + 0.331445i
\(521\) 36.7888i 1.61175i 0.592089 + 0.805873i \(0.298304\pi\)
−0.592089 + 0.805873i \(0.701696\pi\)
\(522\) −0.0800174 + 0.0800174i −0.00350227 + 0.00350227i
\(523\) 0.561001 0.561001i 0.0245309 0.0245309i −0.694735 0.719266i \(-0.744478\pi\)
0.719266 + 0.694735i \(0.244478\pi\)
\(524\) 18.8562i 0.823736i
\(525\) −4.07192 17.5416i −0.177713 0.765576i
\(526\) 26.3155i 1.14741i
\(527\) 1.74624 + 1.74624i 0.0760673 + 0.0760673i
\(528\) −2.47600 + 2.47600i −0.107754 + 0.107754i
\(529\) −12.6102 + 19.2349i −0.548271 + 0.836301i
\(530\) −0.941907 8.22323i −0.0409138 0.357194i
\(531\) −13.2983 −0.577095
\(532\) 5.88684 5.88684i 0.255227 0.255227i
\(533\) 12.2441 + 12.2441i 0.530352 + 0.530352i
\(534\) 14.7757 0.639406
\(535\) 34.0967 + 27.0885i 1.47413 + 1.17114i
\(536\) 7.54272i 0.325796i
\(537\) −15.6693 + 15.6693i −0.676179 + 0.676179i
\(538\) 9.69584 + 9.69584i 0.418017 + 0.418017i
\(539\) −20.9097 −0.900643
\(540\) 1.75080 + 1.39094i 0.0753424 + 0.0598564i
\(541\) −34.6074 −1.48789 −0.743945 0.668241i \(-0.767047\pi\)
−0.743945 + 0.668241i \(0.767047\pi\)
\(542\) −8.26118 + 8.26118i −0.354848 + 0.354848i
\(543\) 5.45870 5.45870i 0.234255 0.234255i
\(544\) −1.94038 −0.0831932
\(545\) −6.87050 + 0.786962i −0.294300 + 0.0337098i
\(546\) 12.2533i 0.524394i
\(547\) −32.8328 + 32.8328i −1.40383 + 1.40383i −0.616378 + 0.787451i \(0.711401\pi\)
−0.787451 + 0.616378i \(0.788599\pi\)
\(548\) −3.49960 + 3.49960i −0.149495 + 0.149495i
\(549\) 0.841493 0.0359140
\(550\) 14.8587 + 9.26003i 0.633578 + 0.394849i
\(551\) 0.261579i 0.0111436i
\(552\) 4.21961 2.27923i 0.179599 0.0970104i
\(553\) 6.06095 + 6.06095i 0.257738 + 0.257738i
\(554\) 14.5830i 0.619572i
\(555\) 1.34878 + 11.7754i 0.0572527 + 0.499839i
\(556\) 14.4705 0.613684
\(557\) 1.66595 + 1.66595i 0.0705886 + 0.0705886i 0.741520 0.670931i \(-0.234105\pi\)
−0.670931 + 0.741520i \(0.734105\pi\)
\(558\) 0.899946 + 0.899946i 0.0380977 + 0.0380977i
\(559\) −13.0446 −0.551727
\(560\) 6.30566 + 5.00959i 0.266463 + 0.211694i
\(561\) 6.79443 0.286861
\(562\) −20.8042 20.8042i −0.877572 0.877572i
\(563\) 4.02393 4.02393i 0.169588 0.169588i −0.617210 0.786798i \(-0.711737\pi\)
0.786798 + 0.617210i \(0.211737\pi\)
\(564\) 1.09665i 0.0461771i
\(565\) −4.64648 + 5.84861i −0.195479 + 0.246053i
\(566\) 25.4617i 1.07023i
\(567\) −2.54671 2.54671i −0.106952 0.106952i
\(568\) −10.0811 10.0811i −0.422994 0.422994i
\(569\) −21.4834 −0.900630 −0.450315 0.892870i \(-0.648688\pi\)
−0.450315 + 0.892870i \(0.648688\pi\)
\(570\) 5.13520 0.588197i 0.215090 0.0246369i
\(571\) 5.17146i 0.216419i 0.994128 + 0.108209i \(0.0345117\pi\)
−0.994128 + 0.108209i \(0.965488\pi\)
\(572\) 8.42384 + 8.42384i 0.352219 + 0.352219i
\(573\) −16.0360 + 16.0360i −0.669911 + 0.669911i
\(574\) 18.3307 0.765108
\(575\) −15.8716 17.9747i −0.661893 0.749599i
\(576\) −1.00000 −0.0416667
\(577\) −16.9864 + 16.9864i −0.707152 + 0.707152i −0.965935 0.258784i \(-0.916678\pi\)
0.258784 + 0.965935i \(0.416678\pi\)
\(578\) −9.35850 9.35850i −0.389262 0.389262i
\(579\) 19.6824i 0.817972i
\(580\) −0.251394 + 0.0287952i −0.0104385 + 0.00119565i
\(581\) 5.23396 0.217141
\(582\) 4.66285 + 4.66285i 0.193281 + 0.193281i
\(583\) −9.16514 9.16514i −0.379581 0.379581i
\(584\) 11.1552i 0.461606i
\(585\) 4.73224 5.95656i 0.195654 0.246273i
\(586\) 15.8135i 0.653249i
\(587\) 1.63768 1.63768i 0.0675943 0.0675943i −0.672501 0.740096i \(-0.734780\pi\)
0.740096 + 0.672501i \(0.234780\pi\)
\(588\) −4.22246 4.22246i −0.174131 0.174131i
\(589\) 2.94194 0.121221
\(590\) −23.2826 18.4970i −0.958528 0.761511i
\(591\) 5.21479 0.214508
\(592\) −3.74806 3.74806i −0.154044 0.154044i
\(593\) 32.8241 + 32.8241i 1.34792 + 1.34792i 0.887914 + 0.460010i \(0.152154\pi\)
0.460010 + 0.887914i \(0.347846\pi\)
\(594\) 3.50160 0.143672
\(595\) −1.77829 15.5252i −0.0729026 0.636470i
\(596\) 2.64129i 0.108192i
\(597\) −8.37242 8.37242i −0.342660 0.342660i
\(598\) −7.75438 14.3559i −0.317100 0.587058i
\(599\) 7.24916i 0.296193i 0.988973 + 0.148096i \(0.0473146\pi\)
−0.988973 + 0.148096i \(0.952685\pi\)
\(600\) 1.13059 + 4.87050i 0.0461561 + 0.198837i
\(601\) −36.4196 −1.48559 −0.742793 0.669522i \(-0.766499\pi\)
−0.742793 + 0.669522i \(0.766499\pi\)
\(602\) −9.76452 + 9.76452i −0.397972 + 0.397972i
\(603\) −5.33351 + 5.33351i −0.217197 + 0.217197i
\(604\) 21.1977i 0.862524i
\(605\) 2.80176 0.320920i 0.113908 0.0130472i
\(606\) −0.433231 −0.0175988
\(607\) −27.1733 + 27.1733i −1.10293 + 1.10293i −0.108877 + 0.994055i \(0.534725\pi\)
−0.994055 + 0.108877i \(0.965275\pi\)
\(608\) −1.63451 + 1.63451i −0.0662881 + 0.0662881i
\(609\) 0.407562 0.0165153
\(610\) 1.47328 + 1.17046i 0.0596515 + 0.0473907i
\(611\) −3.73100 −0.150940
\(612\) 1.37206 + 1.37206i 0.0554621 + 0.0554621i
\(613\) 16.1170 16.1170i 0.650961 0.650961i −0.302264 0.953224i \(-0.597742\pi\)
0.953224 + 0.302264i \(0.0977423\pi\)
\(614\) 14.1353i 0.570453i
\(615\) 8.91087 + 7.07932i 0.359321 + 0.285466i
\(616\) 12.6113 0.508125
\(617\) −23.2043 23.2043i −0.934171 0.934171i 0.0637926 0.997963i \(-0.479680\pi\)
−0.997963 + 0.0637926i \(0.979680\pi\)
\(618\) 8.99956 8.99956i 0.362016 0.362016i
\(619\) −46.2965 −1.86081 −0.930407 0.366527i \(-0.880547\pi\)
−0.930407 + 0.366527i \(0.880547\pi\)
\(620\) 0.323856 + 2.82739i 0.0130064 + 0.113551i
\(621\) −4.59537 1.37206i −0.184406 0.0550587i
\(622\) 2.25377 2.25377i 0.0903678 0.0903678i
\(623\) −37.6293 37.6293i −1.50759 1.50759i
\(624\) 3.40219i 0.136197i
\(625\) 22.4435 11.0131i 0.897742 0.440523i
\(626\) 27.7938i 1.11086i
\(627\) 5.72339 5.72339i 0.228570 0.228570i
\(628\) −17.0584 + 17.0584i −0.680703 + 0.680703i
\(629\) 10.2851i 0.410094i
\(630\) −0.916462 8.00109i −0.0365127 0.318771i
\(631\) 5.61950i 0.223709i −0.993725 0.111854i \(-0.964321\pi\)
0.993725 0.111854i \(-0.0356790\pi\)
\(632\) −1.68285 1.68285i −0.0669403 0.0669403i
\(633\) 17.1835 + 17.1835i 0.682985 + 0.682985i
\(634\) 4.79443i 0.190411i
\(635\) −16.7012 + 21.0221i −0.662767 + 0.834237i
\(636\) 3.70159i 0.146777i
\(637\) −14.3656 + 14.3656i −0.569187 + 0.569187i
\(638\) −0.280189 + 0.280189i −0.0110928 + 0.0110928i
\(639\) 14.2568i 0.563992i
\(640\) −1.75080 1.39094i −0.0692064 0.0549816i
\(641\) 34.0178i 1.34362i 0.740723 + 0.671810i \(0.234483\pi\)
−0.740723 + 0.671810i \(0.765517\pi\)
\(642\) 13.7709 + 13.7709i 0.543493 + 0.543493i
\(643\) −20.2441 + 20.2441i −0.798350 + 0.798350i −0.982835 0.184486i \(-0.940938\pi\)
0.184486 + 0.982835i \(0.440938\pi\)
\(644\) −16.5507 4.94159i −0.652187 0.194726i
\(645\) −8.51777 + 0.975644i −0.335387 + 0.0384159i
\(646\) 4.48528 0.176471
\(647\) −14.0759 + 14.0759i −0.553381 + 0.553381i −0.927415 0.374034i \(-0.877974\pi\)
0.374034 + 0.927415i \(0.377974\pi\)
\(648\) 0.707107 + 0.707107i 0.0277778 + 0.0277778i
\(649\) −46.5651 −1.82784
\(650\) 16.5704 3.84648i 0.649944 0.150871i
\(651\) 4.58380i 0.179653i
\(652\) 2.81143 2.81143i 0.110104 0.110104i
\(653\) −1.54803 1.54803i −0.0605792 0.0605792i 0.676168 0.736747i \(-0.263639\pi\)
−0.736747 + 0.676168i \(0.763639\pi\)
\(654\) −3.09267 −0.120933
\(655\) −41.8898 + 4.79815i −1.63677 + 0.187479i
\(656\) −5.08960 −0.198716
\(657\) 7.88793 7.88793i 0.307737 0.307737i
\(658\) −2.79284 + 2.79284i −0.108876 + 0.108876i
\(659\) 27.5842 1.07453 0.537264 0.843414i \(-0.319458\pi\)
0.537264 + 0.843414i \(0.319458\pi\)
\(660\) 6.13059 + 4.87050i 0.238633 + 0.189584i
\(661\) 41.5932i 1.61779i −0.587954 0.808894i \(-0.700066\pi\)
0.587954 0.808894i \(-0.299934\pi\)
\(662\) −1.64705 + 1.64705i −0.0640146 + 0.0640146i
\(663\) 4.66800 4.66800i 0.181290 0.181290i
\(664\) −1.45324 −0.0563965
\(665\) −14.5758 11.5799i −0.565226 0.449049i
\(666\) 5.30056i 0.205393i
\(667\) 0.477498 0.257921i 0.0184888 0.00998676i
\(668\) 8.40826 + 8.40826i 0.325325 + 0.325325i
\(669\) 2.26616i 0.0876147i
\(670\) −16.7565 + 1.91932i −0.647359 + 0.0741499i
\(671\) 2.94657 0.113751
\(672\) 2.54671 + 2.54671i 0.0982415 + 0.0982415i
\(673\) −27.7520 27.7520i −1.06976 1.06976i −0.997377 0.0723860i \(-0.976939\pi\)
−0.0723860 0.997377i \(-0.523061\pi\)
\(674\) −27.1679 −1.04647
\(675\) 2.64452 4.24341i 0.101787 0.163329i
\(676\) −1.42507 −0.0548104
\(677\) −0.758084 0.758084i −0.0291355 0.0291355i 0.692389 0.721524i \(-0.256558\pi\)
−0.721524 + 0.692389i \(0.756558\pi\)
\(678\) −2.36212 + 2.36212i −0.0907165 + 0.0907165i
\(679\) 23.7499i 0.911436i
\(680\) 0.493750 + 4.31064i 0.0189345 + 0.165305i
\(681\) 21.8017i 0.835442i
\(682\) 3.15125 + 3.15125i 0.120667 + 0.120667i
\(683\) 29.8443 + 29.8443i 1.14196 + 1.14196i 0.988091 + 0.153870i \(0.0491737\pi\)
0.153870 + 0.988091i \(0.450826\pi\)
\(684\) 2.31155 0.0883842
\(685\) 8.66501 + 6.88400i 0.331073 + 0.263024i
\(686\) 3.70436i 0.141433i
\(687\) −9.08206 9.08206i −0.346502 0.346502i
\(688\) 2.71117 2.71117i 0.103362 0.103362i
\(689\) −12.5935 −0.479775
\(690\) −6.13713 8.79407i −0.233636 0.334785i
\(691\) 29.2340 1.11211 0.556056 0.831145i \(-0.312314\pi\)
0.556056 + 0.831145i \(0.312314\pi\)
\(692\) −8.59500 + 8.59500i −0.326733 + 0.326733i
\(693\) −8.91755 8.91755i −0.338750 0.338750i
\(694\) 9.19779i 0.349143i
\(695\) −3.68216 32.1467i −0.139672 1.21940i
\(696\) −0.113162 −0.00428938
\(697\) 6.98323 + 6.98323i 0.264509 + 0.264509i
\(698\) −3.02573 3.02573i −0.114526 0.114526i
\(699\) 17.3809i 0.657404i
\(700\) 9.52447 15.2830i 0.359991 0.577644i
\(701\) 14.5948i 0.551239i −0.961267 0.275619i \(-0.911117\pi\)
0.961267 0.275619i \(-0.0888830\pi\)
\(702\) 2.40571 2.40571i 0.0907979 0.0907979i
\(703\) 8.66382 + 8.66382i 0.326762 + 0.326762i
\(704\) −3.50160 −0.131971
\(705\) −2.43624 + 0.279053i −0.0917542 + 0.0105097i
\(706\) 23.8600 0.897983
\(707\) 1.10331 + 1.10331i 0.0414944 + 0.0414944i
\(708\) −9.40328 9.40328i −0.353397 0.353397i
\(709\) −40.4789 −1.52022 −0.760109 0.649796i \(-0.774854\pi\)
−0.760109 + 0.649796i \(0.774854\pi\)
\(710\) −19.8304 + 24.9608i −0.744220 + 0.936764i
\(711\) 2.37992i 0.0892538i
\(712\) 10.4480 + 10.4480i 0.391554 + 0.391554i
\(713\) −2.90081 5.37036i −0.108636 0.201122i
\(714\) 6.98846i 0.261537i
\(715\) 16.5704 20.8575i 0.619697 0.780025i
\(716\) −22.1597 −0.828147
\(717\) 12.8500 12.8500i 0.479893 0.479893i
\(718\) 17.1714 17.1714i 0.640832 0.640832i
\(719\) 34.5861i 1.28984i −0.764249 0.644922i \(-0.776890\pi\)
0.764249 0.644922i \(-0.223110\pi\)
\(720\) 0.254460 + 2.22154i 0.00948318 + 0.0827920i
\(721\) −45.8386 −1.70712
\(722\) −9.65678 + 9.65678i −0.359388 + 0.359388i
\(723\) 8.33583 8.33583i 0.310013 0.310013i
\(724\) 7.71976 0.286903
\(725\) 0.127939 + 0.551154i 0.00475155 + 0.0204693i
\(726\) 1.26118 0.0468067
\(727\) 28.3874 + 28.3874i 1.05283 + 1.05283i 0.998524 + 0.0543047i \(0.0172942\pi\)
0.0543047 + 0.998524i \(0.482706\pi\)
\(728\) 8.66440 8.66440i 0.321124 0.321124i
\(729\) 1.00000i 0.0370370i
\(730\) 24.7818 2.83856i 0.917215 0.105060i
\(731\) −7.43975 −0.275169
\(732\) 0.595025 + 0.595025i 0.0219928 + 0.0219928i
\(733\) −19.5867 + 19.5867i −0.723452 + 0.723452i −0.969307 0.245855i \(-0.920931\pi\)
0.245855 + 0.969307i \(0.420931\pi\)
\(734\) 23.4586 0.865871
\(735\) −8.30593 + 10.4548i −0.306369 + 0.385632i
\(736\) 4.59537 + 1.37206i 0.169388 + 0.0505747i
\(737\) −18.6758 + 18.6758i −0.687932 + 0.687932i
\(738\) 3.59889 + 3.59889i 0.132477 + 0.132477i
\(739\) 7.22496i 0.265775i −0.991131 0.132887i \(-0.957575\pi\)
0.991131 0.132887i \(-0.0424248\pi\)
\(740\) −7.37275 + 9.28022i −0.271028 + 0.341148i
\(741\) 7.86433i 0.288903i
\(742\) −9.42687 + 9.42687i −0.346071 + 0.346071i
\(743\) 38.0467 38.0467i 1.39580 1.39580i 0.584157 0.811641i \(-0.301425\pi\)
0.811641 0.584157i \(-0.198575\pi\)
\(744\) 1.27272i 0.0466600i
\(745\) 5.86774 0.672104i 0.214977 0.0246240i
\(746\) 0.772089i 0.0282682i
\(747\) 1.02759 + 1.02759i 0.0375976 + 0.0375976i
\(748\) 4.80439 + 4.80439i 0.175666 + 0.175666i
\(749\) 70.1409i 2.56289i
\(750\) 10.5323 3.75100i 0.384586 0.136967i
\(751\) 14.7440i 0.538017i −0.963138 0.269009i \(-0.913304\pi\)
0.963138 0.269009i \(-0.0866960\pi\)
\(752\) 0.775445 0.775445i 0.0282776 0.0282776i
\(753\) −9.08123 + 9.08123i −0.330939 + 0.330939i
\(754\) 0.384998i 0.0140208i
\(755\) −47.0917 + 5.39399i −1.71384 + 0.196307i
\(756\) 3.60159i 0.130989i
\(757\) −5.21529 5.21529i −0.189553 0.189553i 0.605950 0.795503i \(-0.292793\pi\)
−0.795503 + 0.605950i \(0.792793\pi\)
\(758\) 8.23160 8.23160i 0.298985 0.298985i
\(759\) −16.0911 4.80439i −0.584072 0.174388i
\(760\) 4.04705 + 3.21522i 0.146802 + 0.116628i
\(761\) 9.25446 0.335474 0.167737 0.985832i \(-0.446354\pi\)
0.167737 + 0.985832i \(0.446354\pi\)
\(762\) −8.49034 + 8.49034i −0.307573 + 0.307573i
\(763\) 7.87614 + 7.87614i 0.285135 + 0.285135i
\(764\) −22.6783 −0.820471
\(765\) 2.69895 3.39722i 0.0975807 0.122827i
\(766\) 22.1446i 0.800116i
\(767\) −31.9918 + 31.9918i −1.15516 + 1.15516i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) −13.1928 −0.475744 −0.237872 0.971296i \(-0.576450\pi\)
−0.237872 + 0.971296i \(0.576450\pi\)
\(770\) −3.20908 28.0166i −0.115647 1.00965i
\(771\) −2.01700 −0.0726404
\(772\) −13.9176 + 13.9176i −0.500904 + 0.500904i
\(773\) −15.6399 + 15.6399i −0.562527 + 0.562527i −0.930025 0.367497i \(-0.880215\pi\)
0.367497 + 0.930025i \(0.380215\pi\)
\(774\) −3.83417 −0.137816
\(775\) 6.19876 1.43892i 0.222666 0.0516875i
\(776\) 6.59427i 0.236720i
\(777\) 13.4990 13.4990i 0.484274 0.484274i
\(778\) 24.3078 24.3078i 0.871478 0.871478i
\(779\) 11.7649 0.421520
\(780\) 7.55812 0.865724i 0.270624 0.0309979i