Properties

Label 1110.2.o.a.253.18
Level $1110$
Weight $2$
Character 1110.253
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 253.18
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.a.487.18

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-1.64803 + 1.51129i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.75974 - 2.75974i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-1.64803 + 1.51129i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.75974 - 2.75974i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(1.64803 - 1.51129i) q^{10} +0.350472i q^{11} +(0.707107 - 0.707107i) q^{12} +3.27075 q^{13} +(-2.75974 + 2.75974i) q^{14} +(-0.0966903 + 2.23398i) q^{15} +1.00000 q^{16} +7.07368i q^{17} +1.00000i q^{18} +(2.01227 + 2.01227i) q^{19} +(-1.64803 + 1.51129i) q^{20} -3.90286i q^{21} -0.350472i q^{22} -1.24836 q^{23} +(-0.707107 + 0.707107i) q^{24} +(0.432008 - 4.98130i) q^{25} -3.27075 q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.75974 - 2.75974i) q^{28} +(6.14644 - 6.14644i) q^{29} +(0.0966903 - 2.23398i) q^{30} +(-2.76854 - 2.76854i) q^{31} -1.00000 q^{32} +(0.247821 + 0.247821i) q^{33} -7.07368i q^{34} +(-0.377368 + 8.71889i) q^{35} -1.00000i q^{36} +(-3.58895 + 4.91116i) q^{37} +(-2.01227 - 2.01227i) q^{38} +(2.31277 - 2.31277i) q^{39} +(1.64803 - 1.51129i) q^{40} -5.57830i q^{41} +3.90286i q^{42} +3.23195 q^{43} +0.350472i q^{44} +(1.51129 + 1.64803i) q^{45} +1.24836 q^{46} +(5.76291 - 5.76291i) q^{47} +(0.707107 - 0.707107i) q^{48} -8.23228i q^{49} +(-0.432008 + 4.98130i) q^{50} +(5.00185 + 5.00185i) q^{51} +3.27075 q^{52} +(-3.45760 - 3.45760i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-0.529665 - 0.577588i) q^{55} +(-2.75974 + 2.75974i) q^{56} +2.84578 q^{57} +(-6.14644 + 6.14644i) q^{58} +(10.6205 + 10.6205i) q^{59} +(-0.0966903 + 2.23398i) q^{60} +(1.30384 + 1.30384i) q^{61} +(2.76854 + 2.76854i) q^{62} +(-2.75974 - 2.75974i) q^{63} +1.00000 q^{64} +(-5.39030 + 4.94305i) q^{65} +(-0.247821 - 0.247821i) q^{66} +(10.6169 + 10.6169i) q^{67} +7.07368i q^{68} +(-0.882722 + 0.882722i) q^{69} +(0.377368 - 8.71889i) q^{70} +15.8980 q^{71} +1.00000i q^{72} +(0.998067 - 0.998067i) q^{73} +(3.58895 - 4.91116i) q^{74} +(-3.21684 - 3.82779i) q^{75} +(2.01227 + 2.01227i) q^{76} +(0.967210 + 0.967210i) q^{77} +(-2.31277 + 2.31277i) q^{78} +(2.47200 + 2.47200i) q^{79} +(-1.64803 + 1.51129i) q^{80} -1.00000 q^{81} +5.57830i q^{82} +(-10.6094 - 10.6094i) q^{83} -3.90286i q^{84} +(-10.6904 - 11.6576i) q^{85} -3.23195 q^{86} -8.69238i q^{87} -0.350472i q^{88} +(3.03601 - 3.03601i) q^{89} +(-1.51129 - 1.64803i) q^{90} +(9.02641 - 9.02641i) q^{91} -1.24836 q^{92} -3.91530 q^{93} +(-5.76291 + 5.76291i) q^{94} +(-6.35741 - 0.275159i) q^{95} +(-0.707107 + 0.707107i) q^{96} -7.94277i q^{97} +8.23228i q^{98} +0.350472 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} + O(q^{10}) \) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} - 4q^{10} - 8q^{13} - 4q^{14} + 36q^{16} - 4q^{19} + 4q^{20} + 4q^{25} + 8q^{26} + 4q^{28} - 36q^{29} - 4q^{31} - 36q^{32} + 4q^{33} + 28q^{35} + 28q^{37} + 4q^{38} - 4q^{39} - 4q^{40} - 32q^{43} + 16q^{47} - 4q^{50} - 8q^{52} - 8q^{53} - 8q^{55} - 4q^{56} - 8q^{57} + 36q^{58} + 4q^{59} - 4q^{61} + 4q^{62} - 4q^{63} + 36q^{64} - 52q^{65} - 4q^{66} - 16q^{67} + 8q^{69} - 28q^{70} - 8q^{71} + 4q^{73} - 28q^{74} + 16q^{75} - 4q^{76} - 8q^{77} + 4q^{78} + 12q^{79} + 4q^{80} - 36q^{81} + 8q^{83} - 8q^{85} + 32q^{86} + 24q^{89} + 56q^{91} - 8q^{93} - 16q^{94} + 20q^{95} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.00000 0.500000
\(5\) −1.64803 + 1.51129i −0.737022 + 0.675869i
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) 2.75974 2.75974i 1.04308 1.04308i 0.0440528 0.999029i \(-0.485973\pi\)
0.999029 0.0440528i \(-0.0140270\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000i 0.333333i
\(10\) 1.64803 1.51129i 0.521153 0.477912i
\(11\) 0.350472i 0.105671i 0.998603 + 0.0528356i \(0.0168259\pi\)
−0.998603 + 0.0528356i \(0.983174\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) 3.27075 0.907143 0.453572 0.891220i \(-0.350150\pi\)
0.453572 + 0.891220i \(0.350150\pi\)
\(14\) −2.75974 + 2.75974i −0.737570 + 0.737570i
\(15\) −0.0966903 + 2.23398i −0.0249653 + 0.576810i
\(16\) 1.00000 0.250000
\(17\) 7.07368i 1.71562i 0.513967 + 0.857810i \(0.328176\pi\)
−0.513967 + 0.857810i \(0.671824\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 2.01227 + 2.01227i 0.461647 + 0.461647i 0.899195 0.437548i \(-0.144153\pi\)
−0.437548 + 0.899195i \(0.644153\pi\)
\(20\) −1.64803 + 1.51129i −0.368511 + 0.337935i
\(21\) 3.90286i 0.851673i
\(22\) 0.350472i 0.0747209i
\(23\) −1.24836 −0.260301 −0.130150 0.991494i \(-0.541546\pi\)
−0.130150 + 0.991494i \(0.541546\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) 0.432008 4.98130i 0.0864015 0.996260i
\(26\) −3.27075 −0.641447
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 2.75974 2.75974i 0.521541 0.521541i
\(29\) 6.14644 6.14644i 1.14137 1.14137i 0.153165 0.988201i \(-0.451053\pi\)
0.988201 0.153165i \(-0.0489467\pi\)
\(30\) 0.0966903 2.23398i 0.0176532 0.407866i
\(31\) −2.76854 2.76854i −0.497244 0.497244i 0.413335 0.910579i \(-0.364364\pi\)
−0.910579 + 0.413335i \(0.864364\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.247821 + 0.247821i 0.0431401 + 0.0431401i
\(34\) 7.07368i 1.21313i
\(35\) −0.377368 + 8.71889i −0.0637869 + 1.47376i
\(36\) 1.00000i 0.166667i
\(37\) −3.58895 + 4.91116i −0.590019 + 0.807389i
\(38\) −2.01227 2.01227i −0.326433 0.326433i
\(39\) 2.31277 2.31277i 0.370340 0.370340i
\(40\) 1.64803 1.51129i 0.260576 0.238956i
\(41\) 5.57830i 0.871185i −0.900144 0.435592i \(-0.856539\pi\)
0.900144 0.435592i \(-0.143461\pi\)
\(42\) 3.90286i 0.602224i
\(43\) 3.23195 0.492868 0.246434 0.969160i \(-0.420741\pi\)
0.246434 + 0.969160i \(0.420741\pi\)
\(44\) 0.350472i 0.0528356i
\(45\) 1.51129 + 1.64803i 0.225290 + 0.245674i
\(46\) 1.24836 0.184060
\(47\) 5.76291 5.76291i 0.840606 0.840606i −0.148331 0.988938i \(-0.547390\pi\)
0.988938 + 0.148331i \(0.0473902\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 8.23228i 1.17604i
\(50\) −0.432008 + 4.98130i −0.0610951 + 0.704462i
\(51\) 5.00185 + 5.00185i 0.700399 + 0.700399i
\(52\) 3.27075 0.453572
\(53\) −3.45760 3.45760i −0.474938 0.474938i 0.428571 0.903508i \(-0.359017\pi\)
−0.903508 + 0.428571i \(0.859017\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) −0.529665 0.577588i −0.0714200 0.0778820i
\(56\) −2.75974 + 2.75974i −0.368785 + 0.368785i
\(57\) 2.84578 0.376933
\(58\) −6.14644 + 6.14644i −0.807068 + 0.807068i
\(59\) 10.6205 + 10.6205i 1.38267 + 1.38267i 0.839841 + 0.542832i \(0.182648\pi\)
0.542832 + 0.839841i \(0.317352\pi\)
\(60\) −0.0966903 + 2.23398i −0.0124827 + 0.288405i
\(61\) 1.30384 + 1.30384i 0.166940 + 0.166940i 0.785633 0.618693i \(-0.212338\pi\)
−0.618693 + 0.785633i \(0.712338\pi\)
\(62\) 2.76854 + 2.76854i 0.351605 + 0.351605i
\(63\) −2.75974 2.75974i −0.347694 0.347694i
\(64\) 1.00000 0.125000
\(65\) −5.39030 + 4.94305i −0.668584 + 0.613110i
\(66\) −0.247821 0.247821i −0.0305047 0.0305047i
\(67\) 10.6169 + 10.6169i 1.29707 + 1.29707i 0.930322 + 0.366744i \(0.119527\pi\)
0.366744 + 0.930322i \(0.380473\pi\)
\(68\) 7.07368i 0.857810i
\(69\) −0.882722 + 0.882722i −0.106267 + 0.106267i
\(70\) 0.377368 8.71889i 0.0451041 1.04211i
\(71\) 15.8980 1.88675 0.943373 0.331733i \(-0.107633\pi\)
0.943373 + 0.331733i \(0.107633\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 0.998067 0.998067i 0.116815 0.116815i −0.646283 0.763098i \(-0.723677\pi\)
0.763098 + 0.646283i \(0.223677\pi\)
\(74\) 3.58895 4.91116i 0.417207 0.570910i
\(75\) −3.21684 3.82779i −0.371448 0.441995i
\(76\) 2.01227 + 2.01227i 0.230823 + 0.230823i
\(77\) 0.967210 + 0.967210i 0.110224 + 0.110224i
\(78\) −2.31277 + 2.31277i −0.261870 + 0.261870i
\(79\) 2.47200 + 2.47200i 0.278122 + 0.278122i 0.832359 0.554237i \(-0.186990\pi\)
−0.554237 + 0.832359i \(0.686990\pi\)
\(80\) −1.64803 + 1.51129i −0.184255 + 0.168967i
\(81\) −1.00000 −0.111111
\(82\) 5.57830i 0.616020i
\(83\) −10.6094 10.6094i −1.16454 1.16454i −0.983471 0.181065i \(-0.942046\pi\)
−0.181065 0.983471i \(-0.557954\pi\)
\(84\) 3.90286i 0.425836i
\(85\) −10.6904 11.6576i −1.15954 1.26445i
\(86\) −3.23195 −0.348510
\(87\) 8.69238i 0.931921i
\(88\) 0.350472i 0.0373604i
\(89\) 3.03601 3.03601i 0.321816 0.321816i −0.527647 0.849464i \(-0.676926\pi\)
0.849464 + 0.527647i \(0.176926\pi\)
\(90\) −1.51129 1.64803i −0.159304 0.173718i
\(91\) 9.02641 9.02641i 0.946225 0.946225i
\(92\) −1.24836 −0.130150
\(93\) −3.91530 −0.405998
\(94\) −5.76291 + 5.76291i −0.594398 + 0.594398i
\(95\) −6.35741 0.275159i −0.652256 0.0282308i
\(96\) −0.707107 + 0.707107i −0.0721688 + 0.0721688i
\(97\) 7.94277i 0.806466i −0.915097 0.403233i \(-0.867886\pi\)
0.915097 0.403233i \(-0.132114\pi\)
\(98\) 8.23228i 0.831586i
\(99\) 0.350472 0.0352238
\(100\) 0.432008 4.98130i 0.0432008 0.498130i
\(101\) 0.514124i 0.0511573i −0.999673 0.0255786i \(-0.991857\pi\)
0.999673 0.0255786i \(-0.00814282\pi\)
\(102\) −5.00185 5.00185i −0.495257 0.495257i
\(103\) 9.07861i 0.894542i −0.894398 0.447271i \(-0.852396\pi\)
0.894398 0.447271i \(-0.147604\pi\)
\(104\) −3.27075 −0.320724
\(105\) 5.89834 + 6.43202i 0.575620 + 0.627701i
\(106\) 3.45760 + 3.45760i 0.335832 + 0.335832i
\(107\) 1.33354 1.33354i 0.128919 0.128919i −0.639703 0.768622i \(-0.720943\pi\)
0.768622 + 0.639703i \(0.220943\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) −2.30925 2.30925i −0.221186 0.221186i 0.587812 0.808998i \(-0.299990\pi\)
−0.808998 + 0.587812i \(0.799990\pi\)
\(110\) 0.529665 + 0.577588i 0.0505015 + 0.0550709i
\(111\) 0.934944 + 6.01048i 0.0887410 + 0.570490i
\(112\) 2.75974 2.75974i 0.260770 0.260770i
\(113\) 7.85255i 0.738705i −0.929289 0.369353i \(-0.879579\pi\)
0.929289 0.369353i \(-0.120421\pi\)
\(114\) −2.84578 −0.266532
\(115\) 2.05733 1.88663i 0.191847 0.175929i
\(116\) 6.14644 6.14644i 0.570683 0.570683i
\(117\) 3.27075i 0.302381i
\(118\) −10.6205 10.6205i −0.977698 0.977698i
\(119\) 19.5215 + 19.5215i 1.78953 + 1.78953i
\(120\) 0.0966903 2.23398i 0.00882658 0.203933i
\(121\) 10.8772 0.988834
\(122\) −1.30384 1.30384i −0.118044 0.118044i
\(123\) −3.94446 3.94446i −0.355660 0.355660i
\(124\) −2.76854 2.76854i −0.248622 0.248622i
\(125\) 6.81623 + 8.86223i 0.609662 + 0.792662i
\(126\) 2.75974 + 2.75974i 0.245857 + 0.245857i
\(127\) −14.6420 + 14.6420i −1.29927 + 1.29927i −0.370388 + 0.928877i \(0.620775\pi\)
−0.928877 + 0.370388i \(0.879225\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.28533 2.28533i 0.201212 0.201212i
\(130\) 5.39030 4.94305i 0.472760 0.433534i
\(131\) −3.62929 3.62929i −0.317093 0.317093i 0.530557 0.847649i \(-0.321983\pi\)
−0.847649 + 0.530557i \(0.821983\pi\)
\(132\) 0.247821 + 0.247821i 0.0215701 + 0.0215701i
\(133\) 11.1067 0.963070
\(134\) −10.6169 10.6169i −0.917164 0.917164i
\(135\) 2.23398 + 0.0966903i 0.192270 + 0.00832178i
\(136\) 7.07368i 0.606563i
\(137\) −12.5315 + 12.5315i −1.07064 + 1.07064i −0.0733326 + 0.997308i \(0.523363\pi\)
−0.997308 + 0.0733326i \(0.976637\pi\)
\(138\) 0.882722 0.882722i 0.0751423 0.0751423i
\(139\) 3.66631 0.310972 0.155486 0.987838i \(-0.450306\pi\)
0.155486 + 0.987838i \(0.450306\pi\)
\(140\) −0.377368 + 8.71889i −0.0318934 + 0.736880i
\(141\) 8.14998i 0.686352i
\(142\) −15.8980 −1.33413
\(143\) 1.14631i 0.0958590i
\(144\) 1.00000i 0.0833333i
\(145\) −0.840469 + 19.4186i −0.0697972 + 1.61263i
\(146\) −0.998067 + 0.998067i −0.0826007 + 0.0826007i
\(147\) −5.82110 5.82110i −0.480116 0.480116i
\(148\) −3.58895 + 4.91116i −0.295010 + 0.403695i
\(149\) 16.9433i 1.38805i −0.719951 0.694025i \(-0.755836\pi\)
0.719951 0.694025i \(-0.244164\pi\)
\(150\) 3.21684 + 3.82779i 0.262654 + 0.312538i
\(151\) 10.7953i 0.878510i 0.898362 + 0.439255i \(0.144758\pi\)
−0.898362 + 0.439255i \(0.855242\pi\)
\(152\) −2.01227 2.01227i −0.163217 0.163217i
\(153\) 7.07368 0.571873
\(154\) −0.967210 0.967210i −0.0779400 0.0779400i
\(155\) 8.74670 + 0.378572i 0.702552 + 0.0304076i
\(156\) 2.31277 2.31277i 0.185170 0.185170i
\(157\) 6.59408 6.59408i 0.526265 0.526265i −0.393192 0.919457i \(-0.628629\pi\)
0.919457 + 0.393192i \(0.128629\pi\)
\(158\) −2.47200 2.47200i −0.196662 0.196662i
\(159\) −4.88978 −0.387785
\(160\) 1.64803 1.51129i 0.130288 0.119478i
\(161\) −3.44514 + 3.44514i −0.271515 + 0.271515i
\(162\) 1.00000 0.0785674
\(163\) 7.00131i 0.548385i −0.961675 0.274193i \(-0.911589\pi\)
0.961675 0.274193i \(-0.0884106\pi\)
\(164\) 5.57830i 0.435592i
\(165\) −0.782946 0.0338872i −0.0609523 0.00263812i
\(166\) 10.6094 + 10.6094i 0.823451 + 0.823451i
\(167\) 14.7018i 1.13766i 0.822455 + 0.568830i \(0.192604\pi\)
−0.822455 + 0.568830i \(0.807396\pi\)
\(168\) 3.90286i 0.301112i
\(169\) −2.30219 −0.177091
\(170\) 10.6904 + 11.6576i 0.819915 + 0.894101i
\(171\) 2.01227 2.01227i 0.153882 0.153882i
\(172\) 3.23195 0.246434
\(173\) 3.00005 3.00005i 0.228090 0.228090i −0.583805 0.811894i \(-0.698437\pi\)
0.811894 + 0.583805i \(0.198437\pi\)
\(174\) 8.69238i 0.658968i
\(175\) −12.5548 14.9393i −0.949057 1.12931i
\(176\) 0.350472i 0.0264178i
\(177\) 15.0197 1.12895
\(178\) −3.03601 + 3.03601i −0.227559 + 0.227559i
\(179\) −9.62402 + 9.62402i −0.719333 + 0.719333i −0.968469 0.249136i \(-0.919853\pi\)
0.249136 + 0.968469i \(0.419853\pi\)
\(180\) 1.51129 + 1.64803i 0.112645 + 0.122837i
\(181\) 14.0878 1.04713 0.523567 0.851984i \(-0.324601\pi\)
0.523567 + 0.851984i \(0.324601\pi\)
\(182\) −9.02641 + 9.02641i −0.669082 + 0.669082i
\(183\) 1.84391 0.136306
\(184\) 1.24836 0.0920302
\(185\) −1.50749 13.5177i −0.110833 0.993839i
\(186\) 3.91530 0.287084
\(187\) −2.47913 −0.181292
\(188\) 5.76291 5.76291i 0.420303 0.420303i
\(189\) −3.90286 −0.283891
\(190\) 6.35741 + 0.275159i 0.461215 + 0.0199622i
\(191\) 2.11691 2.11691i 0.153174 0.153174i −0.626360 0.779534i \(-0.715456\pi\)
0.779534 + 0.626360i \(0.215456\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) −20.7874 −1.49631 −0.748154 0.663525i \(-0.769060\pi\)
−0.748154 + 0.663525i \(0.769060\pi\)
\(194\) 7.94277i 0.570257i
\(195\) −0.316250 + 7.30678i −0.0226471 + 0.523249i
\(196\) 8.23228i 0.588020i
\(197\) −11.8547 + 11.8547i −0.844614 + 0.844614i −0.989455 0.144841i \(-0.953733\pi\)
0.144841 + 0.989455i \(0.453733\pi\)
\(198\) −0.350472 −0.0249070
\(199\) −6.76638 + 6.76638i −0.479656 + 0.479656i −0.905022 0.425366i \(-0.860146\pi\)
0.425366 + 0.905022i \(0.360146\pi\)
\(200\) −0.432008 + 4.98130i −0.0305476 + 0.352231i
\(201\) 15.0146 1.05905
\(202\) 0.514124i 0.0361737i
\(203\) 33.9251i 2.38108i
\(204\) 5.00185 + 5.00185i 0.350200 + 0.350200i
\(205\) 8.43043 + 9.19321i 0.588807 + 0.642082i
\(206\) 9.07861i 0.632537i
\(207\) 1.24836i 0.0867669i
\(208\) 3.27075 0.226786
\(209\) −0.705244 + 0.705244i −0.0487828 + 0.0487828i
\(210\) −5.89834 6.43202i −0.407024 0.443852i
\(211\) −9.92928 −0.683560 −0.341780 0.939780i \(-0.611030\pi\)
−0.341780 + 0.939780i \(0.611030\pi\)
\(212\) −3.45760 3.45760i −0.237469 0.237469i
\(213\) 11.2416 11.2416i 0.770261 0.770261i
\(214\) −1.33354 + 1.33354i −0.0911592 + 0.0911592i
\(215\) −5.32635 + 4.88441i −0.363254 + 0.333114i
\(216\) 0.707107 + 0.707107i 0.0481125 + 0.0481125i
\(217\) −15.2809 −1.03733
\(218\) 2.30925 + 2.30925i 0.156402 + 0.156402i
\(219\) 1.41148i 0.0953790i
\(220\) −0.529665 0.577588i −0.0357100 0.0389410i
\(221\) 23.1363i 1.55631i
\(222\) −0.934944 6.01048i −0.0627494 0.403397i
\(223\) −6.49659 6.49659i −0.435044 0.435044i 0.455296 0.890340i \(-0.349533\pi\)
−0.890340 + 0.455296i \(0.849533\pi\)
\(224\) −2.75974 + 2.75974i −0.184393 + 0.184393i
\(225\) −4.98130 0.432008i −0.332087 0.0288005i
\(226\) 7.85255i 0.522344i
\(227\) 16.6142i 1.10273i 0.834265 + 0.551363i \(0.185892\pi\)
−0.834265 + 0.551363i \(0.814108\pi\)
\(228\) 2.84578 0.188466
\(229\) 2.86631i 0.189411i −0.995505 0.0947056i \(-0.969809\pi\)
0.995505 0.0947056i \(-0.0301910\pi\)
\(230\) −2.05733 + 1.88663i −0.135656 + 0.124401i
\(231\) 1.36784 0.0899974
\(232\) −6.14644 + 6.14644i −0.403534 + 0.403534i
\(233\) −8.37425 + 8.37425i −0.548615 + 0.548615i −0.926040 0.377425i \(-0.876810\pi\)
0.377425 + 0.926040i \(0.376810\pi\)
\(234\) 3.27075i 0.213816i
\(235\) −0.788024 + 18.2069i −0.0514050 + 1.18769i
\(236\) 10.6205 + 10.6205i 0.691337 + 0.691337i
\(237\) 3.49594 0.227085
\(238\) −19.5215 19.5215i −1.26539 1.26539i
\(239\) −16.9584 16.9584i −1.09695 1.09695i −0.994765 0.102185i \(-0.967417\pi\)
−0.102185 0.994765i \(-0.532583\pi\)
\(240\) −0.0966903 + 2.23398i −0.00624133 + 0.144203i
\(241\) 9.32818 9.32818i 0.600881 0.600881i −0.339665 0.940546i \(-0.610314\pi\)
0.940546 + 0.339665i \(0.110314\pi\)
\(242\) −10.8772 −0.699211
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) 1.30384 + 1.30384i 0.0834698 + 0.0834698i
\(245\) 12.4414 + 13.5670i 0.794849 + 0.866767i
\(246\) 3.94446 + 3.94446i 0.251489 + 0.251489i
\(247\) 6.58164 + 6.58164i 0.418780 + 0.418780i
\(248\) 2.76854 + 2.76854i 0.175802 + 0.175802i
\(249\) −15.0040 −0.950840
\(250\) −6.81623 8.86223i −0.431096 0.560496i
\(251\) −21.5270 21.5270i −1.35877 1.35877i −0.875437 0.483333i \(-0.839426\pi\)
−0.483333 0.875437i \(-0.660574\pi\)
\(252\) −2.75974 2.75974i −0.173847 0.173847i
\(253\) 0.437515i 0.0275063i
\(254\) 14.6420 14.6420i 0.918719 0.918719i
\(255\) −15.8024 0.683957i −0.989587 0.0428310i
\(256\) 1.00000 0.0625000
\(257\) 0.409575i 0.0255486i 0.999918 + 0.0127743i \(0.00406630\pi\)
−0.999918 + 0.0127743i \(0.995934\pi\)
\(258\) −2.28533 + 2.28533i −0.142279 + 0.142279i
\(259\) 3.64895 + 23.4580i 0.226735 + 1.45761i
\(260\) −5.39030 + 4.94305i −0.334292 + 0.306555i
\(261\) −6.14644 6.14644i −0.380455 0.380455i
\(262\) 3.62929 + 3.62929i 0.224218 + 0.224218i
\(263\) −10.0366 + 10.0366i −0.618882 + 0.618882i −0.945245 0.326362i \(-0.894177\pi\)
0.326362 + 0.945245i \(0.394177\pi\)
\(264\) −0.247821 0.247821i −0.0152523 0.0152523i
\(265\) 10.9237 + 0.472795i 0.671035 + 0.0290435i
\(266\) −11.1067 −0.680994
\(267\) 4.29357i 0.262762i
\(268\) 10.6169 + 10.6169i 0.648533 + 0.648533i
\(269\) 19.9758i 1.21794i 0.793192 + 0.608972i \(0.208418\pi\)
−0.793192 + 0.608972i \(0.791582\pi\)
\(270\) −2.23398 0.0966903i −0.135955 0.00588438i
\(271\) 11.0572 0.671678 0.335839 0.941919i \(-0.390980\pi\)
0.335839 + 0.941919i \(0.390980\pi\)
\(272\) 7.07368i 0.428905i
\(273\) 12.7653i 0.772589i
\(274\) 12.5315 12.5315i 0.757057 0.757057i
\(275\) 1.74581 + 0.151407i 0.105276 + 0.00913016i
\(276\) −0.882722 + 0.882722i −0.0531336 + 0.0531336i
\(277\) 24.4538 1.46929 0.734644 0.678453i \(-0.237349\pi\)
0.734644 + 0.678453i \(0.237349\pi\)
\(278\) −3.66631 −0.219890
\(279\) −2.76854 + 2.76854i −0.165748 + 0.165748i
\(280\) 0.377368 8.71889i 0.0225521 0.521053i
\(281\) −7.23968 + 7.23968i −0.431883 + 0.431883i −0.889269 0.457385i \(-0.848786\pi\)
0.457385 + 0.889269i \(0.348786\pi\)
\(282\) 8.14998i 0.485324i
\(283\) 30.2054i 1.79552i 0.440483 + 0.897761i \(0.354807\pi\)
−0.440483 + 0.897761i \(0.645193\pi\)
\(284\) 15.8980 0.943373
\(285\) −4.68993 + 4.30080i −0.277808 + 0.254757i
\(286\) 1.14631i 0.0677825i
\(287\) −15.3946 15.3946i −0.908717 0.908717i
\(288\) 1.00000i 0.0589256i
\(289\) −33.0370 −1.94335
\(290\) 0.840469 19.4186i 0.0493540 1.14030i
\(291\) −5.61638 5.61638i −0.329238 0.329238i
\(292\) 0.998067 0.998067i 0.0584075 0.0584075i
\(293\) −0.618270 0.618270i −0.0361197 0.0361197i 0.688816 0.724936i \(-0.258131\pi\)
−0.724936 + 0.688816i \(0.758131\pi\)
\(294\) 5.82110 + 5.82110i 0.339494 + 0.339494i
\(295\) −33.5536 1.45226i −1.95357 0.0845537i
\(296\) 3.58895 4.91116i 0.208603 0.285455i
\(297\) 0.247821 0.247821i 0.0143800 0.0143800i
\(298\) 16.9433i 0.981499i
\(299\) −4.08307 −0.236130
\(300\) −3.21684 3.82779i −0.185724 0.220997i
\(301\) 8.91933 8.91933i 0.514101 0.514101i
\(302\) 10.7953i 0.621201i
\(303\) −0.363541 0.363541i −0.0208849 0.0208849i
\(304\) 2.01227 + 2.01227i 0.115412 + 0.115412i
\(305\) −4.11925 0.178288i −0.235867 0.0102087i
\(306\) −7.07368 −0.404376
\(307\) −8.55841 8.55841i −0.488454 0.488454i 0.419364 0.907818i \(-0.362253\pi\)
−0.907818 + 0.419364i \(0.862253\pi\)
\(308\) 0.967210 + 0.967210i 0.0551119 + 0.0551119i
\(309\) −6.41955 6.41955i −0.365195 0.365195i
\(310\) −8.74670 0.378572i −0.496779 0.0215014i
\(311\) 7.07966 + 7.07966i 0.401451 + 0.401451i 0.878744 0.477293i \(-0.158382\pi\)
−0.477293 + 0.878744i \(0.658382\pi\)
\(312\) −2.31277 + 2.31277i −0.130935 + 0.130935i
\(313\) −21.8518 −1.23514 −0.617568 0.786518i \(-0.711882\pi\)
−0.617568 + 0.786518i \(0.711882\pi\)
\(314\) −6.59408 + 6.59408i −0.372126 + 0.372126i
\(315\) 8.71889 + 0.377368i 0.491254 + 0.0212623i
\(316\) 2.47200 + 2.47200i 0.139061 + 0.139061i
\(317\) −19.1074 19.1074i −1.07318 1.07318i −0.997102 0.0760779i \(-0.975760\pi\)
−0.0760779 0.997102i \(-0.524240\pi\)
\(318\) 4.88978 0.274205
\(319\) 2.15416 + 2.15416i 0.120610 + 0.120610i
\(320\) −1.64803 + 1.51129i −0.0921277 + 0.0844837i
\(321\) 1.88592i 0.105262i
\(322\) 3.44514 3.44514i 0.191990 0.191990i
\(323\) −14.2342 + 14.2342i −0.792010 + 0.792010i
\(324\) −1.00000 −0.0555556
\(325\) 1.41299 16.2926i 0.0783786 0.903751i
\(326\) 7.00131i 0.387767i
\(327\) −3.26578 −0.180598
\(328\) 5.57830i 0.308010i
\(329\) 31.8082i 1.75364i
\(330\) 0.782946 + 0.0338872i 0.0430998 + 0.00186543i
\(331\) 2.84439 2.84439i 0.156342 0.156342i −0.624602 0.780943i \(-0.714739\pi\)
0.780943 + 0.624602i \(0.214739\pi\)
\(332\) −10.6094 10.6094i −0.582268 0.582268i
\(333\) 4.91116 + 3.58895i 0.269130 + 0.196673i
\(334\) 14.7018i 0.804447i
\(335\) −33.5423 1.45177i −1.83261 0.0793186i
\(336\) 3.90286i 0.212918i
\(337\) 12.4436 + 12.4436i 0.677844 + 0.677844i 0.959512 0.281668i \(-0.0908876\pi\)
−0.281668 + 0.959512i \(0.590888\pi\)
\(338\) 2.30219 0.125222
\(339\) −5.55259 5.55259i −0.301575 0.301575i
\(340\) −10.6904 11.6576i −0.579768 0.632225i
\(341\) 0.970295 0.970295i 0.0525444 0.0525444i
\(342\) −2.01227 + 2.01227i −0.108811 + 0.108811i
\(343\) −3.40077 3.40077i −0.183624 0.183624i
\(344\) −3.23195 −0.174255
\(345\) 0.120704 2.78880i 0.00649849 0.150144i
\(346\) −3.00005 + 3.00005i −0.161284 + 0.161284i
\(347\) −13.9100 −0.746727 −0.373363 0.927685i \(-0.621796\pi\)
−0.373363 + 0.927685i \(0.621796\pi\)
\(348\) 8.69238i 0.465961i
\(349\) 0.414422i 0.0221835i −0.999938 0.0110918i \(-0.996469\pi\)
0.999938 0.0110918i \(-0.00353069\pi\)
\(350\) 12.5548 + 14.9393i 0.671085 + 0.798539i
\(351\) −2.31277 2.31277i −0.123447 0.123447i
\(352\) 0.350472i 0.0186802i
\(353\) 29.7855i 1.58532i 0.609661 + 0.792662i \(0.291305\pi\)
−0.609661 + 0.792662i \(0.708695\pi\)
\(354\) −15.0197 −0.798287
\(355\) −26.2004 + 24.0265i −1.39057 + 1.27519i
\(356\) 3.03601 3.03601i 0.160908 0.160908i
\(357\) 27.6076 1.46115
\(358\) 9.62402 9.62402i 0.508645 0.508645i
\(359\) 8.57788i 0.452723i −0.974043 0.226362i \(-0.927317\pi\)
0.974043 0.226362i \(-0.0726831\pi\)
\(360\) −1.51129 1.64803i −0.0796520 0.0868588i
\(361\) 10.9015i 0.573765i
\(362\) −14.0878 −0.740436
\(363\) 7.69132 7.69132i 0.403690 0.403690i
\(364\) 9.02641 9.02641i 0.473112 0.473112i
\(365\) −0.136476 + 3.15321i −0.00714350 + 0.165047i
\(366\) −1.84391 −0.0963826
\(367\) −9.30759 + 9.30759i −0.485852 + 0.485852i −0.906995 0.421142i \(-0.861629\pi\)
0.421142 + 0.906995i \(0.361629\pi\)
\(368\) −1.24836 −0.0650752
\(369\) −5.57830 −0.290395
\(370\) 1.50749 + 13.5177i 0.0783706 + 0.702750i
\(371\) −19.0841 −0.990798
\(372\) −3.91530 −0.202999
\(373\) −18.3349 + 18.3349i −0.949345 + 0.949345i −0.998777 0.0494321i \(-0.984259\pi\)
0.0494321 + 0.998777i \(0.484259\pi\)
\(374\) 2.47913 0.128193
\(375\) 11.0863 + 1.44674i 0.572496 + 0.0747093i
\(376\) −5.76291 + 5.76291i −0.297199 + 0.297199i
\(377\) 20.1035 20.1035i 1.03538 1.03538i
\(378\) 3.90286 0.200741
\(379\) 0.736373i 0.0378249i 0.999821 + 0.0189125i \(0.00602038\pi\)
−0.999821 + 0.0189125i \(0.993980\pi\)
\(380\) −6.35741 0.275159i −0.326128 0.0141154i
\(381\) 20.7069i 1.06085i
\(382\) −2.11691 + 2.11691i −0.108311 + 0.108311i
\(383\) 2.85854 0.146065 0.0730323 0.997330i \(-0.476732\pi\)
0.0730323 + 0.997330i \(0.476732\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) −3.05573 0.132257i −0.155734 0.00674044i
\(386\) 20.7874 1.05805
\(387\) 3.23195i 0.164289i
\(388\) 7.94277i 0.403233i
\(389\) 14.3095 + 14.3095i 0.725519 + 0.725519i 0.969724 0.244205i \(-0.0785269\pi\)
−0.244205 + 0.969724i \(0.578527\pi\)
\(390\) 0.316250 7.30678i 0.0160139 0.369993i
\(391\) 8.83049i 0.446577i
\(392\) 8.23228i 0.415793i
\(393\) −5.13259 −0.258905
\(394\) 11.8547 11.8547i 0.597233 0.597233i
\(395\) −7.80984 0.338023i −0.392956 0.0170078i
\(396\) 0.350472 0.0176119
\(397\) −0.498839 0.498839i −0.0250360 0.0250360i 0.694478 0.719514i \(-0.255635\pi\)
−0.719514 + 0.694478i \(0.755635\pi\)
\(398\) 6.76638 6.76638i 0.339168 0.339168i
\(399\) 7.85360 7.85360i 0.393172 0.393172i
\(400\) 0.432008 4.98130i 0.0216004 0.249065i
\(401\) 10.8582 + 10.8582i 0.542234 + 0.542234i 0.924183 0.381949i \(-0.124747\pi\)
−0.381949 + 0.924183i \(0.624747\pi\)
\(402\) −15.0146 −0.748861
\(403\) −9.05520 9.05520i −0.451072 0.451072i
\(404\) 0.514124i 0.0255786i
\(405\) 1.64803 1.51129i 0.0818913 0.0750966i
\(406\) 33.9251i 1.68368i
\(407\) −1.72122 1.25783i −0.0853179 0.0623481i
\(408\) −5.00185 5.00185i −0.247628 0.247628i
\(409\) 7.92408 7.92408i 0.391820 0.391820i −0.483515 0.875336i \(-0.660640\pi\)
0.875336 + 0.483515i \(0.160640\pi\)
\(410\) −8.43043 9.19321i −0.416349 0.454020i
\(411\) 17.7222i 0.874174i
\(412\) 9.07861i 0.447271i
\(413\) 58.6196 2.88448
\(414\) 1.24836i 0.0613535i
\(415\) 33.5186 + 1.45074i 1.64536 + 0.0712141i
\(416\) −3.27075 −0.160362
\(417\) 2.59247 2.59247i 0.126954 0.126954i
\(418\) 0.705244 0.705244i 0.0344946 0.0344946i
\(419\) 13.1368i 0.641775i 0.947117 + 0.320887i \(0.103981\pi\)
−0.947117 + 0.320887i \(0.896019\pi\)
\(420\) 5.89834 + 6.43202i 0.287810 + 0.313851i
\(421\) 10.6585 + 10.6585i 0.519461 + 0.519461i 0.917408 0.397947i \(-0.130277\pi\)
−0.397947 + 0.917408i \(0.630277\pi\)
\(422\) 9.92928 0.483350
\(423\) −5.76291 5.76291i −0.280202 0.280202i
\(424\) 3.45760 + 3.45760i 0.167916 + 0.167916i
\(425\) 35.2362 + 3.05589i 1.70920 + 0.148232i
\(426\) −11.2416 + 11.2416i −0.544657 + 0.544657i
\(427\) 7.19651 0.348263
\(428\) 1.33354 1.33354i 0.0644593 0.0644593i
\(429\) 0.810561 + 0.810561i 0.0391343 + 0.0391343i
\(430\) 5.32635 4.88441i 0.256859 0.235547i
\(431\) −13.6585 13.6585i −0.657907 0.657907i 0.296978 0.954884i \(-0.404021\pi\)
−0.954884 + 0.296978i \(0.904021\pi\)
\(432\) −0.707107 0.707107i −0.0340207 0.0340207i
\(433\) −16.2196 16.2196i −0.779466 0.779466i 0.200274 0.979740i \(-0.435817\pi\)
−0.979740 + 0.200274i \(0.935817\pi\)
\(434\) 15.2809 0.733505
\(435\) 13.1367 + 14.3253i 0.629857 + 0.686846i
\(436\) −2.30925 2.30925i −0.110593 0.110593i
\(437\) −2.51203 2.51203i −0.120167 0.120167i
\(438\) 1.41148i 0.0674431i
\(439\) −4.52525 + 4.52525i −0.215979 + 0.215979i −0.806801 0.590823i \(-0.798803\pi\)
0.590823 + 0.806801i \(0.298803\pi\)
\(440\) 0.529665 + 0.577588i 0.0252508 + 0.0275354i
\(441\) −8.23228 −0.392013
\(442\) 23.1363i 1.10048i
\(443\) 17.5292 17.5292i 0.832839 0.832839i −0.155066 0.987904i \(-0.549559\pi\)
0.987904 + 0.155066i \(0.0495589\pi\)
\(444\) 0.934944 + 6.01048i 0.0443705 + 0.285245i
\(445\) −0.415146 + 9.59172i −0.0196798 + 0.454691i
\(446\) 6.49659 + 6.49659i 0.307623 + 0.307623i
\(447\) −11.9807 11.9807i −0.566669 0.566669i
\(448\) 2.75974 2.75974i 0.130385 0.130385i
\(449\) −24.1689 24.1689i −1.14060 1.14060i −0.988340 0.152263i \(-0.951344\pi\)
−0.152263 0.988340i \(-0.548656\pi\)
\(450\) 4.98130 + 0.432008i 0.234821 + 0.0203650i
\(451\) 1.95504 0.0920592
\(452\) 7.85255i 0.369353i
\(453\) 7.63344 + 7.63344i 0.358650 + 0.358650i
\(454\) 16.6142i 0.779745i
\(455\) −1.23428 + 28.5173i −0.0578638 + 1.33691i
\(456\) −2.84578 −0.133266
\(457\) 15.3091i 0.716131i 0.933697 + 0.358065i \(0.116564\pi\)
−0.933697 + 0.358065i \(0.883436\pi\)
\(458\) 2.86631i 0.133934i
\(459\) 5.00185 5.00185i 0.233466 0.233466i
\(460\) 2.05733 1.88663i 0.0959236 0.0879646i
\(461\) 19.6061 19.6061i 0.913145 0.913145i −0.0833730 0.996518i \(-0.526569\pi\)
0.996518 + 0.0833730i \(0.0265693\pi\)
\(462\) −1.36784 −0.0636377
\(463\) −25.4617 −1.18331 −0.591653 0.806192i \(-0.701525\pi\)
−0.591653 + 0.806192i \(0.701525\pi\)
\(464\) 6.14644 6.14644i 0.285341 0.285341i
\(465\) 6.45254 5.91716i 0.299229 0.274402i
\(466\) 8.37425 8.37425i 0.387930 0.387930i
\(467\) 18.9252i 0.875752i −0.899035 0.437876i \(-0.855731\pi\)
0.899035 0.437876i \(-0.144269\pi\)
\(468\) 3.27075i 0.151191i
\(469\) 58.5999 2.70589
\(470\) 0.788024 18.2069i 0.0363488 0.839820i
\(471\) 9.32544i 0.429694i
\(472\) −10.6205 10.6205i −0.488849 0.488849i
\(473\) 1.13271i 0.0520820i
\(474\) −3.49594 −0.160574
\(475\) 10.8930 9.15441i 0.499807 0.420033i
\(476\) 19.5215 + 19.5215i 0.894766 + 0.894766i
\(477\) −3.45760 + 3.45760i −0.158313 + 0.158313i
\(478\) 16.9584 + 16.9584i 0.775661 + 0.775661i
\(479\) −3.00653 3.00653i −0.137372 0.137372i 0.635077 0.772449i \(-0.280968\pi\)
−0.772449 + 0.635077i \(0.780968\pi\)
\(480\) 0.0966903 2.23398i 0.00441329 0.101967i
\(481\) −11.7386 + 16.0632i −0.535232 + 0.732418i
\(482\) −9.32818 + 9.32818i −0.424887 + 0.424887i
\(483\) 4.87216i 0.221691i
\(484\) 10.8772 0.494417
\(485\) 12.0038 + 13.0899i 0.545065 + 0.594383i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) 42.0200i 1.90411i 0.305929 + 0.952054i \(0.401033\pi\)
−0.305929 + 0.952054i \(0.598967\pi\)
\(488\) −1.30384 1.30384i −0.0590221 0.0590221i
\(489\) −4.95068 4.95068i −0.223877 0.223877i
\(490\) −12.4414 13.5670i −0.562043 0.612897i
\(491\) 14.2813 0.644507 0.322254 0.946653i \(-0.395560\pi\)
0.322254 + 0.946653i \(0.395560\pi\)
\(492\) −3.94446 3.94446i −0.177830 0.177830i
\(493\) 43.4780 + 43.4780i 1.95815 + 1.95815i
\(494\) −6.58164 6.58164i −0.296122 0.296122i
\(495\) −0.577588 + 0.529665i −0.0259607 + 0.0238067i
\(496\) −2.76854 2.76854i −0.124311 0.124311i
\(497\) 43.8743 43.8743i 1.96803 1.96803i
\(498\) 15.0040 0.672345
\(499\) 4.58214 4.58214i 0.205125 0.205125i −0.597067 0.802192i \(-0.703667\pi\)
0.802192 + 0.597067i \(0.203667\pi\)
\(500\) 6.81623 + 8.86223i 0.304831 + 0.396331i
\(501\) 10.3957 + 10.3957i 0.464447 + 0.464447i
\(502\) 21.5270 + 21.5270i 0.960795 + 0.960795i
\(503\) 4.41445 0.196831 0.0984153 0.995145i \(-0.468623\pi\)
0.0984153 + 0.995145i \(0.468623\pi\)
\(504\) 2.75974 + 2.75974i 0.122928 + 0.122928i
\(505\) 0.776991 + 0.847293i 0.0345756 + 0.0377040i
\(506\) 0.437515i 0.0194499i
\(507\) −1.62789 + 1.62789i −0.0722972 + 0.0722972i
\(508\) −14.6420 + 14.6420i −0.649633 + 0.649633i
\(509\) 23.7000 1.05048 0.525242 0.850953i \(-0.323975\pi\)
0.525242 + 0.850953i \(0.323975\pi\)
\(510\) 15.8024 + 0.683957i 0.699744 + 0.0302861i
\(511\) 5.50880i 0.243695i
\(512\) −1.00000 −0.0441942
\(513\) 2.84578i 0.125644i
\(514\) 0.409575i 0.0180656i
\(515\) 13.7204 + 14.9618i 0.604594 + 0.659297i
\(516\) 2.28533 2.28533i 0.100606 0.100606i
\(517\) 2.01974 + 2.01974i 0.0888279 + 0.0888279i
\(518\) −3.64895 23.4580i −0.160326 1.03069i
\(519\) 4.24271i 0.186234i
\(520\) 5.39030 4.94305i 0.236380 0.216767i
\(521\) 22.6223i 0.991100i 0.868579 + 0.495550i \(0.165034\pi\)
−0.868579 + 0.495550i \(0.834966\pi\)
\(522\) 6.14644 + 6.14644i 0.269023 + 0.269023i
\(523\) −38.2884 −1.67424 −0.837118 0.547023i \(-0.815761\pi\)
−0.837118 + 0.547023i \(0.815761\pi\)
\(524\) −3.62929 3.62929i −0.158546 0.158546i
\(525\) −19.4413 1.68606i −0.848488 0.0735858i
\(526\) 10.0366 10.0366i 0.437616 0.437616i
\(527\) 19.5838 19.5838i 0.853082 0.853082i
\(528\) 0.247821 + 0.247821i 0.0107850 + 0.0107850i
\(529\) −21.4416 −0.932244
\(530\) −10.9237 0.472795i −0.474494 0.0205369i
\(531\) 10.6205 10.6205i 0.460891 0.460891i
\(532\) 11.1067 0.481535
\(533\) 18.2452i 0.790289i
\(534\) 4.29357i 0.185801i
\(535\) −0.182350 + 4.21309i −0.00788367 + 0.182148i
\(536\) −10.6169 10.6169i −0.458582 0.458582i
\(537\) 13.6104i 0.587333i
\(538\) 19.9758i 0.861217i
\(539\) 2.88518 0.124274
\(540\) 2.23398 + 0.0966903i 0.0961350 + 0.00416089i
\(541\) 8.89780 8.89780i 0.382546 0.382546i −0.489472 0.872019i \(-0.662811\pi\)
0.872019 + 0.489472i \(0.162811\pi\)
\(542\) −11.0572 −0.474948
\(543\) 9.96155 9.96155i 0.427491 0.427491i
\(544\) 7.07368i 0.303282i
\(545\) 7.29567 + 0.315769i 0.312512 + 0.0135260i
\(546\) 12.7653i 0.546303i
\(547\) 7.12339 0.304574 0.152287 0.988336i \(-0.451336\pi\)
0.152287 + 0.988336i \(0.451336\pi\)
\(548\) −12.5315 + 12.5315i −0.535320 + 0.535320i
\(549\) 1.30384 1.30384i 0.0556465 0.0556465i
\(550\) −1.74581 0.151407i −0.0744414 0.00645600i
\(551\) 24.7366 1.05382
\(552\) 0.882722 0.882722i 0.0375712 0.0375712i
\(553\) 13.6441 0.580208
\(554\) −24.4538 −1.03894
\(555\) −10.6244 8.49248i −0.450980 0.360486i
\(556\) 3.66631 0.155486
\(557\) 45.3868 1.92310 0.961551 0.274626i \(-0.0885539\pi\)
0.961551 + 0.274626i \(0.0885539\pi\)
\(558\) 2.76854 2.76854i 0.117202 0.117202i
\(559\) 10.5709 0.447102
\(560\) −0.377368 + 8.71889i −0.0159467 + 0.368440i
\(561\) −1.75301 + 1.75301i −0.0740121 + 0.0740121i
\(562\) 7.23968 7.23968i 0.305388 0.305388i
\(563\) 5.35148 0.225538 0.112769 0.993621i \(-0.464028\pi\)
0.112769 + 0.993621i \(0.464028\pi\)
\(564\) 8.14998i 0.343176i
\(565\) 11.8675 + 12.9412i 0.499268 + 0.544442i
\(566\) 30.2054i 1.26963i
\(567\) −2.75974 + 2.75974i −0.115898 + 0.115898i
\(568\) −15.8980 −0.667066
\(569\) −13.2588 + 13.2588i −0.555837 + 0.555837i −0.928119 0.372283i \(-0.878575\pi\)
0.372283 + 0.928119i \(0.378575\pi\)
\(570\) 4.68993 4.30080i 0.196440 0.180141i
\(571\) −39.9897 −1.67352 −0.836758 0.547574i \(-0.815552\pi\)
−0.836758 + 0.547574i \(0.815552\pi\)
\(572\) 1.14631i 0.0479295i
\(573\) 2.99376i 0.125066i
\(574\) 15.3946 + 15.3946i 0.642560 + 0.642560i
\(575\) −0.539300 + 6.21845i −0.0224904 + 0.259327i
\(576\) 1.00000i 0.0416667i
\(577\) 2.19671i 0.0914503i −0.998954 0.0457251i \(-0.985440\pi\)
0.998954 0.0457251i \(-0.0145598\pi\)
\(578\) 33.0370 1.37416
\(579\) −14.6989 + 14.6989i −0.610865 + 0.610865i
\(580\) −0.840469 + 19.4186i −0.0348986 + 0.806313i
\(581\) −58.5584 −2.42941
\(582\) 5.61638 + 5.61638i 0.232807 + 0.232807i
\(583\) 1.21179 1.21179i 0.0501873 0.0501873i
\(584\) −0.998067 + 0.998067i −0.0413003 + 0.0413003i
\(585\) 4.94305 + 5.39030i 0.204370 + 0.222861i
\(586\) 0.618270 + 0.618270i 0.0255405 + 0.0255405i
\(587\) 40.3393 1.66498 0.832490 0.554041i \(-0.186915\pi\)
0.832490 + 0.554041i \(0.186915\pi\)
\(588\) −5.82110 5.82110i −0.240058 0.240058i
\(589\) 11.1421i 0.459102i
\(590\) 33.5536 + 1.45226i 1.38138 + 0.0597885i
\(591\) 16.7651i 0.689625i
\(592\) −3.58895 + 4.91116i −0.147505 + 0.201847i
\(593\) −14.1348 14.1348i −0.580448 0.580448i 0.354579 0.935026i \(-0.384624\pi\)
−0.935026 + 0.354579i \(0.884624\pi\)
\(594\) −0.247821 + 0.247821i −0.0101682 + 0.0101682i
\(595\) −61.6747 2.66938i −2.52841 0.109434i
\(596\) 16.9433i 0.694025i
\(597\) 9.56911i 0.391638i
\(598\) 4.08307 0.166969
\(599\) 23.9120i 0.977016i −0.872559 0.488508i \(-0.837541\pi\)
0.872559 0.488508i \(-0.162459\pi\)
\(600\) 3.21684 + 3.82779i 0.131327 + 0.156269i
\(601\) −24.5648 −1.00202 −0.501009 0.865442i \(-0.667038\pi\)
−0.501009 + 0.865442i \(0.667038\pi\)
\(602\) −8.91933 + 8.91933i −0.363525 + 0.363525i
\(603\) 10.6169 10.6169i 0.432355 0.432355i
\(604\) 10.7953i 0.439255i
\(605\) −17.9259 + 16.4386i −0.728792 + 0.668322i
\(606\) 0.363541 + 0.363541i 0.0147678 + 0.0147678i
\(607\) −28.5020 −1.15686 −0.578430 0.815732i \(-0.696334\pi\)
−0.578430 + 0.815732i \(0.696334\pi\)
\(608\) −2.01227 2.01227i −0.0816084 0.0816084i
\(609\) −23.9887 23.9887i −0.972070 0.972070i
\(610\) 4.11925 + 0.178288i 0.166783 + 0.00721867i
\(611\) 18.8490 18.8490i 0.762550 0.762550i
\(612\) 7.07368 0.285937
\(613\) 20.5098 20.5098i 0.828384 0.828384i −0.158909 0.987293i \(-0.550798\pi\)
0.987293 + 0.158909i \(0.0507978\pi\)
\(614\) 8.55841 + 8.55841i 0.345389 + 0.345389i
\(615\) 12.4618 + 0.539368i 0.502508 + 0.0217494i
\(616\) −0.967210 0.967210i −0.0389700 0.0389700i
\(617\) 14.5571 + 14.5571i 0.586047 + 0.586047i 0.936559 0.350511i \(-0.113992\pi\)
−0.350511 + 0.936559i \(0.613992\pi\)
\(618\) 6.41955 + 6.41955i 0.258232 + 0.258232i
\(619\) 22.6423 0.910070 0.455035 0.890474i \(-0.349627\pi\)
0.455035 + 0.890474i \(0.349627\pi\)
\(620\) 8.74670 + 0.378572i 0.351276 + 0.0152038i
\(621\) 0.882722 + 0.882722i 0.0354224 + 0.0354224i
\(622\) −7.07966 7.07966i −0.283869 0.283869i
\(623\) 16.7572i 0.671362i
\(624\) 2.31277 2.31277i 0.0925849 0.0925849i
\(625\) −24.6267 4.30392i −0.985070 0.172157i
\(626\) 21.8518 0.873372
\(627\) 0.997366i 0.0398310i
\(628\) 6.59408 6.59408i 0.263132 0.263132i
\(629\) −34.7400 25.3871i −1.38517 1.01225i
\(630\) −8.71889 0.377368i −0.347369 0.0150347i
\(631\) 23.0961 + 23.0961i 0.919443 + 0.919443i 0.996989 0.0775462i \(-0.0247085\pi\)
−0.0775462 + 0.996989i \(0.524709\pi\)
\(632\) −2.47200 2.47200i −0.0983309 0.0983309i
\(633\) −7.02106 + 7.02106i −0.279062 + 0.279062i
\(634\) 19.1074 + 19.1074i 0.758853 + 0.758853i
\(635\) 2.00215 46.2587i 0.0794531 1.83572i
\(636\) −4.88978 −0.193893
\(637\) 26.9257i 1.06684i
\(638\) −2.15416 2.15416i −0.0852839 0.0852839i
\(639\) 15.8980i 0.628916i
\(640\) 1.64803 1.51129i 0.0651441 0.0597390i
\(641\) −42.5772 −1.68170 −0.840849 0.541269i \(-0.817944\pi\)
−0.840849 + 0.541269i \(0.817944\pi\)
\(642\) 1.88592i 0.0744312i
\(643\) 19.1904i 0.756794i 0.925643 + 0.378397i \(0.123525\pi\)
−0.925643 + 0.378397i \(0.876475\pi\)
\(644\) −3.44514 + 3.44514i −0.135757 + 0.135757i
\(645\) −0.312498 + 7.22010i −0.0123046 + 0.284291i
\(646\) 14.2342 14.2342i 0.560036 0.560036i
\(647\) −28.2302 −1.10984 −0.554921 0.831903i \(-0.687251\pi\)
−0.554921 + 0.831903i \(0.687251\pi\)
\(648\) 1.00000 0.0392837
\(649\) −3.72219 + 3.72219i −0.146109 + 0.146109i
\(650\) −1.41299 + 16.2926i −0.0554220 + 0.639048i
\(651\) −10.8052 + 10.8052i −0.423489 + 0.423489i
\(652\) 7.00131i 0.274193i
\(653\) 5.24225i 0.205145i 0.994726 + 0.102573i \(0.0327074\pi\)
−0.994726 + 0.102573i \(0.967293\pi\)
\(654\) 3.26578 0.127702
\(655\) 11.4661 + 0.496272i 0.448017 + 0.0193910i
\(656\) 5.57830i 0.217796i
\(657\) −0.998067 0.998067i −0.0389383 0.0389383i
\(658\) 31.8082i 1.24001i
\(659\) 30.0925 1.17224 0.586119 0.810225i \(-0.300655\pi\)
0.586119 + 0.810225i \(0.300655\pi\)
\(660\) −0.782946 0.0338872i −0.0304761 0.00131906i
\(661\) −32.5054 32.5054i −1.26432 1.26432i −0.948981 0.315335i \(-0.897883\pi\)
−0.315335 0.948981i \(-0.602117\pi\)
\(662\) −2.84439 + 2.84439i −0.110550 + 0.110550i
\(663\) 16.3598 + 16.3598i 0.635362 + 0.635362i
\(664\) 10.6094 + 10.6094i 0.411726 + 0.411726i
\(665\) −18.3041 + 16.7854i −0.709804 + 0.650910i
\(666\) −4.91116 3.58895i −0.190303 0.139069i
\(667\) −7.67296 + 7.67296i −0.297098 + 0.297098i
\(668\) 14.7018i 0.568830i
\(669\) −9.18757 −0.355212
\(670\) 33.5423 + 1.45177i 1.29585 + 0.0560867i
\(671\) −0.456959 + 0.456959i −0.0176407 + 0.0176407i
\(672\) 3.90286i 0.150556i
\(673\) −9.11977 9.11977i −0.351541 0.351541i 0.509141 0.860683i \(-0.329963\pi\)
−0.860683 + 0.509141i \(0.829963\pi\)
\(674\) −12.4436 12.4436i −0.479308 0.479308i
\(675\) −3.82779 + 3.21684i −0.147332 + 0.123816i
\(676\) −2.30219 −0.0885456
\(677\) −19.8062 19.8062i −0.761213 0.761213i 0.215329 0.976542i \(-0.430918\pi\)
−0.976542 + 0.215329i \(0.930918\pi\)
\(678\) 5.55259 + 5.55259i 0.213246 + 0.213246i
\(679\) −21.9199 21.9199i −0.841210 0.841210i
\(680\) 10.6904 + 11.6576i 0.409958 + 0.447050i
\(681\) 11.7480 + 11.7480i 0.450186 + 0.450186i
\(682\) −0.970295 + 0.970295i −0.0371545 + 0.0371545i
\(683\) −9.00362 −0.344514 −0.172257 0.985052i \(-0.555106\pi\)
−0.172257 + 0.985052i \(0.555106\pi\)
\(684\) 2.01227 2.01227i 0.0769411 0.0769411i
\(685\) 1.71357 39.5911i 0.0654721 1.51270i
\(686\) 3.40077 + 3.40077i 0.129842 + 0.129842i
\(687\) −2.02679 2.02679i −0.0773268 0.0773268i
\(688\) 3.23195 0.123217
\(689\) −11.3089 11.3089i −0.430837 0.430837i
\(690\) −0.120704 + 2.78880i −0.00459513 + 0.106168i
\(691\) 8.79710i 0.334657i −0.985901 0.167329i \(-0.946486\pi\)
0.985901 0.167329i \(-0.0535141\pi\)
\(692\) 3.00005 3.00005i 0.114045 0.114045i
\(693\) 0.967210 0.967210i 0.0367413 0.0367413i
\(694\) 13.9100 0.528016
\(695\) −6.04219 + 5.54085i −0.229193 + 0.210176i
\(696\) 8.69238i 0.329484i
\(697\) 39.4592 1.49462
\(698\) 0.414422i 0.0156861i
\(699\) 11.8430i 0.447943i
\(700\) −12.5548 14.9393i −0.474529 0.564653i
\(701\) 6.74494 6.74494i 0.254753 0.254753i −0.568163 0.822916i \(-0.692346\pi\)
0.822916 + 0.568163i \(0.192346\pi\)
\(702\) 2.31277 + 2.31277i 0.0872899 + 0.0872899i
\(703\) −17.1045 + 2.66065i −0.645109 + 0.100348i
\(704\) 0.350472i 0.0132089i
\(705\) 12.3170 + 13.4314i 0.463884 + 0.505856i
\(706\) 29.7855i 1.12099i
\(707\) −1.41885 1.41885i −0.0533612 0.0533612i
\(708\) 15.0197 0.564474
\(709\) 27.6225 + 27.6225i 1.03739 + 1.03739i 0.999273 + 0.0381132i \(0.0121347\pi\)
0.0381132 + 0.999273i \(0.487865\pi\)
\(710\) 26.2004 24.0265i 0.983284 0.901698i
\(711\) 2.47200 2.47200i 0.0927072 0.0927072i
\(712\) −3.03601 + 3.03601i −0.113779 + 0.113779i
\(713\) 3.45613 + 3.45613i 0.129433 + 0.129433i
\(714\) −27.6076 −1.03319
\(715\) −1.73240 1.88915i −0.0647881 0.0706501i
\(716\) −9.62402 + 9.62402i −0.359666 + 0.359666i
\(717\) −23.9829 −0.895656
\(718\) 8.57788i 0.320124i
\(719\) 11.0173i 0.410878i 0.978670 + 0.205439i \(0.0658622\pi\)
−0.978670 + 0.205439i \(0.934138\pi\)
\(720\) 1.51129 + 1.64803i 0.0563224 + 0.0614185i
\(721\) −25.0546 25.0546i −0.933081 0.933081i
\(722\) 10.9015i 0.405713i
\(723\) 13.1920i 0.490617i
\(724\) 14.0878 0.523567
\(725\) −27.9620 33.2726i −1.03848 1.23571i
\(726\) −7.69132 + 7.69132i −0.285452 + 0.285452i
\(727\) 8.80697 0.326632 0.163316 0.986574i \(-0.447781\pi\)
0.163316 + 0.986574i \(0.447781\pi\)
\(728\) −9.02641 + 9.02641i −0.334541 + 0.334541i
\(729\) 1.00000i 0.0370370i
\(730\) 0.136476 3.15321i 0.00505122 0.116706i
\(731\) 22.8618i 0.845574i
\(732\) 1.84391 0.0681528
\(733\) 11.9215 11.9215i 0.440331 0.440331i −0.451792 0.892123i \(-0.649215\pi\)
0.892123 + 0.451792i \(0.149215\pi\)
\(734\) 9.30759 9.30759i 0.343549 0.343549i
\(735\) 18.3907 + 0.795982i 0.678352 + 0.0293602i
\(736\) 1.24836 0.0460151
\(737\) −3.72094 + 3.72094i −0.137063 + 0.137063i
\(738\) 5.57830 0.205340
\(739\) −1.03649 −0.0381277 −0.0190639 0.999818i \(-0.506069\pi\)
−0.0190639 + 0.999818i \(0.506069\pi\)
\(740\) −1.50749 13.5177i −0.0554164 0.496920i
\(741\) 9.30784 0.341932
\(742\) 19.0841 0.700600
\(743\) 16.2854 16.2854i 0.597453 0.597453i −0.342181 0.939634i \(-0.611166\pi\)
0.939634 + 0.342181i \(0.111166\pi\)
\(744\) 3.91530 0.143542
\(745\) 25.6062 + 27.9231i 0.938140 + 1.02302i
\(746\) 18.3349 18.3349i 0.671289 0.671289i
\(747\) −10.6094 + 10.6094i −0.388179 + 0.388179i
\(748\) −2.47913 −0.0906459
\(749\) 7.36046i 0.268945i
\(750\) −11.0863 1.44674i −0.404816 0.0528274i
\(751\) 44.5447i 1.62546i 0.582641 + 0.812729i \(0.302019\pi\)
−0.582641 + 0.812729i \(0.697981\pi\)
\(752\) 5.76291 5.76291i 0.210152 0.210152i
\(753\) −30.4437 −1.10943
\(754\) −20.1035 + 20.1035i −0.732126 + 0.732126i
\(755\) −16.3148 17.7910i −0.593758 0.647481i
\(756\) −3.90286 −0.141945
\(757\) 6.50328i 0.236366i 0.992992 + 0.118183i \(0.0377069\pi\)
−0.992992 + 0.118183i \(0.962293\pi\)
\(758\) 0.736373i 0.0267463i
\(759\) −0.309369 0.309369i −0.0112294 0.0112294i
\(760\) 6.35741 + 0.275159i 0.230607 + 0.00998108i
\(761\) 30.3235i 1.09923i 0.835419 + 0.549613i \(0.185225\pi\)
−0.835419 + 0.549613i \(0.814775\pi\)
\(762\) 20.7069i 0.750131i
\(763\) −12.7459 −0.461431
\(764\) 2.11691 2.11691i 0.0765871 0.0765871i
\(765\) −11.6576 + 10.6904i −0.421483 + 0.386512i
\(766\) −2.85854 −0.103283
\(767\) 34.7371 + 34.7371i 1.25428 + 1.25428i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) −20.4408 + 20.4408i −0.737113 + 0.737113i −0.972018 0.234906i \(-0.924522\pi\)
0.234906 + 0.972018i \(0.424522\pi\)
\(770\) 3.05573 + 0.132257i 0.110121 + 0.00476621i
\(771\) 0.289614 + 0.289614i 0.0104302 + 0.0104302i
\(772\) −20.7874 −0.748154
\(773\) −12.8496 12.8496i −0.462167 0.462167i 0.437198 0.899365i \(-0.355971\pi\)
−0.899365 + 0.437198i \(0.855971\pi\)
\(774\) 3.23195i 0.116170i
\(775\) −14.9870 + 12.5949i −0.538347 + 0.452422i
\(776\) 7.94277i 0.285129i
\(777\) 19.1675 + 14.0071i 0.687632 + 0.502503i
\(778\) −14.3095 14.3095i −0.513019 0.513019i
\(779\) 11.2251 11.2251i 0.402179 0.402179i
\(780\)