Properties

Label 1110.2.u.f.401.4
Level $1110$
Weight $2$
Character 1110.401
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 401.4
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.f.191.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.912090 + 1.47244i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.396230 - 1.68612i) q^{6} -2.79858 q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.33618 - 2.68600i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.912090 + 1.47244i) q^{3} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{5} +(-0.396230 - 1.68612i) q^{6} -2.79858 q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.33618 - 2.68600i) q^{9} -1.00000 q^{10} +4.26033 q^{11} +(1.47244 + 0.912090i) q^{12} +(1.77526 - 1.77526i) q^{13} +(1.97890 - 1.97890i) q^{14} +(-1.68612 + 0.396230i) q^{15} -1.00000 q^{16} +(5.48863 + 5.48863i) q^{17} +(2.84412 + 0.954468i) q^{18} +(0.485369 - 0.485369i) q^{19} +(0.707107 - 0.707107i) q^{20} +(2.55256 - 4.12076i) q^{21} +(-3.01251 + 3.01251i) q^{22} +(1.36769 + 1.36769i) q^{23} +(-1.68612 + 0.396230i) q^{24} +1.00000i q^{25} +2.51060i q^{26} +(5.17371 + 0.482424i) q^{27} +2.79858i q^{28} +(-7.02801 + 7.02801i) q^{29} +(0.912090 - 1.47244i) q^{30} +(-3.79775 - 3.79775i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.88581 + 6.27310i) q^{33} -7.76210 q^{34} +(-1.97890 - 1.97890i) q^{35} +(-2.68600 + 1.33618i) q^{36} +(2.97703 + 5.30446i) q^{37} +0.686416i q^{38} +(0.994773 + 4.23317i) q^{39} +1.00000i q^{40} +7.88519 q^{41} +(1.10888 + 4.71875i) q^{42} +(-3.72198 + 3.72198i) q^{43} -4.26033i q^{44} +(0.954468 - 2.84412i) q^{45} -1.93421 q^{46} -2.41387i q^{47} +(0.912090 - 1.47244i) q^{48} +0.832067 q^{49} +(-0.707107 - 0.707107i) q^{50} +(-13.0878 + 3.07558i) q^{51} +(-1.77526 - 1.77526i) q^{52} +2.32891i q^{53} +(-3.99949 + 3.31724i) q^{54} +(3.01251 + 3.01251i) q^{55} +(-1.97890 - 1.97890i) q^{56} +(0.271978 + 1.15738i) q^{57} -9.93910i q^{58} +(-4.84986 - 4.84986i) q^{59} +(0.396230 + 1.68612i) q^{60} +(3.08764 + 3.08764i) q^{61} +5.37083 q^{62} +(3.73942 + 7.51700i) q^{63} +1.00000i q^{64} +2.51060 q^{65} +(-1.68807 - 7.18343i) q^{66} -0.631981i q^{67} +(5.48863 - 5.48863i) q^{68} +(-3.26131 + 0.766391i) q^{69} +2.79858 q^{70} -12.9487i q^{71} +(0.954468 - 2.84412i) q^{72} +8.24407i q^{73} +(-5.85590 - 1.64574i) q^{74} +(-1.47244 - 0.912090i) q^{75} +(-0.485369 - 0.485369i) q^{76} -11.9229 q^{77} +(-3.69671 - 2.28989i) q^{78} +(-4.17614 + 4.17614i) q^{79} +(-0.707107 - 0.707107i) q^{80} +(-5.42923 + 7.17798i) q^{81} +(-5.57567 + 5.57567i) q^{82} +12.6041i q^{83} +(-4.12076 - 2.55256i) q^{84} +7.76210i q^{85} -5.26367i q^{86} +(-3.93817 - 16.7585i) q^{87} +(3.01251 + 3.01251i) q^{88} +(-1.13309 + 1.13309i) q^{89} +(1.33618 + 2.68600i) q^{90} +(-4.96821 + 4.96821i) q^{91} +(1.36769 - 1.36769i) q^{92} +(9.05586 - 2.12808i) q^{93} +(1.70686 + 1.70686i) q^{94} +0.686416 q^{95} +(0.396230 + 1.68612i) q^{96} +(3.82220 - 3.82220i) q^{97} +(-0.588360 + 0.588360i) q^{98} +(-5.69258 - 11.4433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 24q^{7} - 8q^{9} + O(q^{10}) \) \( 40q + 24q^{7} - 8q^{9} - 40q^{10} + 16q^{13} - 40q^{16} + 8q^{18} + 16q^{19} - 16q^{22} - 8q^{31} + 24q^{33} + 24q^{34} + 32q^{37} + 16q^{39} + 12q^{42} + 32q^{43} + 8q^{45} - 56q^{46} - 32q^{49} - 44q^{51} - 16q^{52} - 24q^{54} + 16q^{55} + 8q^{57} - 72q^{61} + 24q^{63} - 28q^{66} + 16q^{69} - 24q^{70} + 8q^{72} - 16q^{76} - 48q^{79} + 120q^{81} - 24q^{82} - 24q^{84} + 20q^{87} + 16q^{88} + 8q^{90} - 92q^{93} - 8q^{94} - 40q^{97} + O(q^{100}) \)

Character values

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

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

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
\(3\) −0.912090 + 1.47244i −0.526596 + 0.850116i
\(4\) 1.00000i 0.500000i
\(5\) 0.707107 + 0.707107i 0.316228 + 0.316228i
\(6\) −0.396230 1.68612i −0.161760 0.688356i
\(7\) −2.79858 −1.05776 −0.528882 0.848695i \(-0.677389\pi\)
−0.528882 + 0.848695i \(0.677389\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −1.33618 2.68600i −0.445394 0.895335i
\(10\) −1.00000 −0.316228
\(11\) 4.26033 1.28454 0.642269 0.766479i \(-0.277993\pi\)
0.642269 + 0.766479i \(0.277993\pi\)
\(12\) 1.47244 + 0.912090i 0.425058 + 0.263298i
\(13\) 1.77526 1.77526i 0.492368 0.492368i −0.416683 0.909052i \(-0.636808\pi\)
0.909052 + 0.416683i \(0.136808\pi\)
\(14\) 1.97890 1.97890i 0.528882 0.528882i
\(15\) −1.68612 + 0.396230i −0.435354 + 0.102306i
\(16\) −1.00000 −0.250000
\(17\) 5.48863 + 5.48863i 1.33119 + 1.33119i 0.904307 + 0.426882i \(0.140388\pi\)
0.426882 + 0.904307i \(0.359612\pi\)
\(18\) 2.84412 + 0.954468i 0.670364 + 0.224970i
\(19\) 0.485369 0.485369i 0.111351 0.111351i −0.649236 0.760587i \(-0.724911\pi\)
0.760587 + 0.649236i \(0.224911\pi\)
\(20\) 0.707107 0.707107i 0.158114 0.158114i
\(21\) 2.55256 4.12076i 0.557014 0.899223i
\(22\) −3.01251 + 3.01251i −0.642269 + 0.642269i
\(23\) 1.36769 + 1.36769i 0.285184 + 0.285184i 0.835172 0.549989i \(-0.185368\pi\)
−0.549989 + 0.835172i \(0.685368\pi\)
\(24\) −1.68612 + 0.396230i −0.344178 + 0.0808801i
\(25\) 1.00000i 0.200000i
\(26\) 2.51060i 0.492368i
\(27\) 5.17371 + 0.482424i 0.995681 + 0.0928426i
\(28\) 2.79858i 0.528882i
\(29\) −7.02801 + 7.02801i −1.30507 + 1.30507i −0.380139 + 0.924929i \(0.624124\pi\)
−0.924929 + 0.380139i \(0.875876\pi\)
\(30\) 0.912090 1.47244i 0.166524 0.268830i
\(31\) −3.79775 3.79775i −0.682096 0.682096i 0.278376 0.960472i \(-0.410204\pi\)
−0.960472 + 0.278376i \(0.910204\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −3.88581 + 6.27310i −0.676432 + 1.09201i
\(34\) −7.76210 −1.33119
\(35\) −1.97890 1.97890i −0.334495 0.334495i
\(36\) −2.68600 + 1.33618i −0.447667 + 0.222697i
\(37\) 2.97703 + 5.30446i 0.489421 + 0.872048i
\(38\) 0.686416i 0.111351i
\(39\) 0.994773 + 4.23317i 0.159291 + 0.677849i
\(40\) 1.00000i 0.158114i
\(41\) 7.88519 1.23146 0.615730 0.787957i \(-0.288861\pi\)
0.615730 + 0.787957i \(0.288861\pi\)
\(42\) 1.10888 + 4.71875i 0.171104 + 0.728119i
\(43\) −3.72198 + 3.72198i −0.567596 + 0.567596i −0.931454 0.363858i \(-0.881459\pi\)
0.363858 + 0.931454i \(0.381459\pi\)
\(44\) 4.26033i 0.642269i
\(45\) 0.954468 2.84412i 0.142284 0.423976i
\(46\) −1.93421 −0.285184
\(47\) 2.41387i 0.352099i −0.984381 0.176050i \(-0.943668\pi\)
0.984381 0.176050i \(-0.0563319\pi\)
\(48\) 0.912090 1.47244i 0.131649 0.212529i
\(49\) 0.832067 0.118867
\(50\) −0.707107 0.707107i −0.100000 0.100000i
\(51\) −13.0878 + 3.07558i −1.83266 + 0.430667i
\(52\) −1.77526 1.77526i −0.246184 0.246184i
\(53\) 2.32891i 0.319900i 0.987125 + 0.159950i \(0.0511334\pi\)
−0.987125 + 0.159950i \(0.948867\pi\)
\(54\) −3.99949 + 3.31724i −0.544262 + 0.451419i
\(55\) 3.01251 + 3.01251i 0.406207 + 0.406207i
\(56\) −1.97890 1.97890i −0.264441 0.264441i
\(57\) 0.271978 + 1.15738i 0.0360244 + 0.153299i
\(58\) 9.93910i 1.30507i
\(59\) −4.84986 4.84986i −0.631398 0.631398i 0.317020 0.948419i \(-0.397318\pi\)
−0.948419 + 0.317020i \(0.897318\pi\)
\(60\) 0.396230 + 1.68612i 0.0511531 + 0.217677i
\(61\) 3.08764 + 3.08764i 0.395332 + 0.395332i 0.876583 0.481251i \(-0.159817\pi\)
−0.481251 + 0.876583i \(0.659817\pi\)
\(62\) 5.37083 0.682096
\(63\) 3.73942 + 7.51700i 0.471122 + 0.947054i
\(64\) 1.00000i 0.125000i
\(65\) 2.51060 0.311401
\(66\) −1.68807 7.18343i −0.207787 0.884219i
\(67\) 0.631981i 0.0772088i −0.999255 0.0386044i \(-0.987709\pi\)
0.999255 0.0386044i \(-0.0122912\pi\)
\(68\) 5.48863 5.48863i 0.665595 0.665595i
\(69\) −3.26131 + 0.766391i −0.392615 + 0.0922627i
\(70\) 2.79858 0.334495
\(71\) 12.9487i 1.53672i −0.640015 0.768362i \(-0.721072\pi\)
0.640015 0.768362i \(-0.278928\pi\)
\(72\) 0.954468 2.84412i 0.112485 0.335182i
\(73\) 8.24407i 0.964895i 0.875925 + 0.482448i \(0.160252\pi\)
−0.875925 + 0.482448i \(0.839748\pi\)
\(74\) −5.85590 1.64574i −0.680734 0.191313i
\(75\) −1.47244 0.912090i −0.170023 0.105319i
\(76\) −0.485369 0.485369i −0.0556757 0.0556757i
\(77\) −11.9229 −1.35874
\(78\) −3.69671 2.28989i −0.418570 0.259279i
\(79\) −4.17614 + 4.17614i −0.469852 + 0.469852i −0.901867 0.432014i \(-0.857803\pi\)
0.432014 + 0.901867i \(0.357803\pi\)
\(80\) −0.707107 0.707107i −0.0790569 0.0790569i
\(81\) −5.42923 + 7.17798i −0.603248 + 0.797554i
\(82\) −5.57567 + 5.57567i −0.615730 + 0.615730i
\(83\) 12.6041i 1.38348i 0.722147 + 0.691740i \(0.243156\pi\)
−0.722147 + 0.691740i \(0.756844\pi\)
\(84\) −4.12076 2.55256i −0.449611 0.278507i
\(85\) 7.76210i 0.841918i
\(86\) 5.26367i 0.567596i
\(87\) −3.93817 16.7585i −0.422216 1.79670i
\(88\) 3.01251 + 3.01251i 0.321135 + 0.321135i
\(89\) −1.13309 + 1.13309i −0.120107 + 0.120107i −0.764606 0.644498i \(-0.777066\pi\)
0.644498 + 0.764606i \(0.277066\pi\)
\(90\) 1.33618 + 2.68600i 0.140846 + 0.283130i
\(91\) −4.96821 + 4.96821i −0.520810 + 0.520810i
\(92\) 1.36769 1.36769i 0.142592 0.142592i
\(93\) 9.05586 2.12808i 0.939049 0.220672i
\(94\) 1.70686 + 1.70686i 0.176050 + 0.176050i
\(95\) 0.686416 0.0704248
\(96\) 0.396230 + 1.68612i 0.0404400 + 0.172089i
\(97\) 3.82220 3.82220i 0.388086 0.388086i −0.485918 0.874004i \(-0.661515\pi\)
0.874004 + 0.485918i \(0.161515\pi\)
\(98\) −0.588360 + 0.588360i −0.0594333 + 0.0594333i
\(99\) −5.69258 11.4433i −0.572126 1.15009i
\(100\) 1.00000 0.100000
\(101\) 12.5328 1.24706 0.623529 0.781800i \(-0.285698\pi\)
0.623529 + 0.781800i \(0.285698\pi\)
\(102\) 7.07974 11.4293i 0.700998 1.13167i
\(103\) −3.72362 3.72362i −0.366899 0.366899i 0.499446 0.866345i \(-0.333537\pi\)
−0.866345 + 0.499446i \(0.833537\pi\)
\(104\) 2.51060 0.246184
\(105\) 4.71875 1.10888i 0.460503 0.108216i
\(106\) −1.64679 1.64679i −0.159950 0.159950i
\(107\) 14.1218i 1.36521i 0.730789 + 0.682603i \(0.239152\pi\)
−0.730789 + 0.682603i \(0.760848\pi\)
\(108\) 0.482424 5.17371i 0.0464213 0.497840i
\(109\) 2.78175 2.78175i 0.266443 0.266443i −0.561222 0.827665i \(-0.689669\pi\)
0.827665 + 0.561222i \(0.189669\pi\)
\(110\) −4.26033 −0.406207
\(111\) −10.5258 0.454634i −0.999069 0.0431519i
\(112\) 2.79858 0.264441
\(113\) −12.0063 + 12.0063i −1.12946 + 1.12946i −0.139196 + 0.990265i \(0.544452\pi\)
−0.990265 + 0.139196i \(0.955548\pi\)
\(114\) −1.01071 0.626073i −0.0946615 0.0586371i
\(115\) 1.93421i 0.180366i
\(116\) 7.02801 + 7.02801i 0.652534 + 0.652534i
\(117\) −7.14042 2.39628i −0.660133 0.221536i
\(118\) 6.85874 0.631398
\(119\) −15.3604 15.3604i −1.40809 1.40809i
\(120\) −1.47244 0.912090i −0.134415 0.0832621i
\(121\) 7.15042 0.650038
\(122\) −4.36658 −0.395332
\(123\) −7.19201 + 11.6105i −0.648481 + 1.04688i
\(124\) −3.79775 + 3.79775i −0.341048 + 0.341048i
\(125\) −0.707107 + 0.707107i −0.0632456 + 0.0632456i
\(126\) −7.95949 2.67116i −0.709088 0.237966i
\(127\) −13.9419 −1.23715 −0.618573 0.785728i \(-0.712289\pi\)
−0.618573 + 0.785728i \(0.712289\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −2.08562 8.87518i −0.183629 0.781416i
\(130\) −1.77526 + 1.77526i −0.155701 + 0.155701i
\(131\) −1.96386 + 1.96386i −0.171583 + 0.171583i −0.787675 0.616091i \(-0.788715\pi\)
0.616091 + 0.787675i \(0.288715\pi\)
\(132\) 6.27310 + 3.88581i 0.546003 + 0.338216i
\(133\) −1.35835 + 1.35835i −0.117784 + 0.117784i
\(134\) 0.446878 + 0.446878i 0.0386044 + 0.0386044i
\(135\) 3.31724 + 3.99949i 0.285503 + 0.344221i
\(136\) 7.76210i 0.665595i
\(137\) 6.74701i 0.576436i 0.957565 + 0.288218i \(0.0930627\pi\)
−0.957565 + 0.288218i \(0.906937\pi\)
\(138\) 1.76417 2.84801i 0.150176 0.242439i
\(139\) 17.7822i 1.50827i 0.656720 + 0.754135i \(0.271943\pi\)
−0.656720 + 0.754135i \(0.728057\pi\)
\(140\) −1.97890 + 1.97890i −0.167247 + 0.167247i
\(141\) 3.55429 + 2.20167i 0.299325 + 0.185414i
\(142\) 9.15610 + 9.15610i 0.768362 + 0.768362i
\(143\) 7.56319 7.56319i 0.632466 0.632466i
\(144\) 1.33618 + 2.68600i 0.111349 + 0.223834i
\(145\) −9.93910 −0.825398
\(146\) −5.82944 5.82944i −0.482448 0.482448i
\(147\) −0.758920 + 1.22517i −0.0625947 + 0.101050i
\(148\) 5.30446 2.97703i 0.436024 0.244710i
\(149\) 2.23999i 0.183507i 0.995782 + 0.0917534i \(0.0292471\pi\)
−0.995782 + 0.0917534i \(0.970753\pi\)
\(150\) 1.68612 0.396230i 0.137671 0.0323520i
\(151\) 3.40280i 0.276916i −0.990368 0.138458i \(-0.955785\pi\)
0.990368 0.138458i \(-0.0442146\pi\)
\(152\) 0.686416 0.0556757
\(153\) 7.40867 22.0763i 0.598956 1.78476i
\(154\) 8.43076 8.43076i 0.679370 0.679370i
\(155\) 5.37083i 0.431395i
\(156\) 4.23317 0.994773i 0.338925 0.0796456i
\(157\) −14.8138 −1.18227 −0.591134 0.806574i \(-0.701319\pi\)
−0.591134 + 0.806574i \(0.701319\pi\)
\(158\) 5.90595i 0.469852i
\(159\) −3.42919 2.12418i −0.271952 0.168458i
\(160\) 1.00000 0.0790569
\(161\) −3.82760 3.82760i −0.301657 0.301657i
\(162\) −1.23655 8.91465i −0.0971528 0.700401i
\(163\) 7.65234 + 7.65234i 0.599378 + 0.599378i 0.940147 0.340769i \(-0.110687\pi\)
−0.340769 + 0.940147i \(0.610687\pi\)
\(164\) 7.88519i 0.615730i
\(165\) −7.18343 + 1.68807i −0.559229 + 0.131416i
\(166\) −8.91245 8.91245i −0.691740 0.691740i
\(167\) 11.7216 + 11.7216i 0.907044 + 0.907044i 0.996033 0.0889886i \(-0.0283635\pi\)
−0.0889886 + 0.996033i \(0.528363\pi\)
\(168\) 4.71875 1.10888i 0.364059 0.0855521i
\(169\) 6.69691i 0.515147i
\(170\) −5.48863 5.48863i −0.420959 0.420959i
\(171\) −1.95224 0.655162i −0.149292 0.0501015i
\(172\) 3.72198 + 3.72198i 0.283798 + 0.283798i
\(173\) −4.86504 −0.369882 −0.184941 0.982750i \(-0.559209\pi\)
−0.184941 + 0.982750i \(0.559209\pi\)
\(174\) 14.6348 + 9.06536i 1.10946 + 0.687243i
\(175\) 2.79858i 0.211553i
\(176\) −4.26033 −0.321135
\(177\) 11.5647 2.71764i 0.869254 0.204270i
\(178\) 1.60243i 0.120107i
\(179\) 9.23529 9.23529i 0.690278 0.690278i −0.272015 0.962293i \(-0.587690\pi\)
0.962293 + 0.272015i \(0.0876900\pi\)
\(180\) −2.84412 0.954468i −0.211988 0.0711418i
\(181\) 19.4997 1.44940 0.724699 0.689065i \(-0.241979\pi\)
0.724699 + 0.689065i \(0.241979\pi\)
\(182\) 7.02611i 0.520810i
\(183\) −7.36258 + 1.73017i −0.544258 + 0.127898i
\(184\) 1.93421i 0.142592i
\(185\) −1.64574 + 5.85590i −0.120997 + 0.430534i
\(186\) −4.89868 + 7.90824i −0.359189 + 0.579861i
\(187\) 23.3834 + 23.3834i 1.70996 + 1.70996i
\(188\) −2.41387 −0.176050
\(189\) −14.4791 1.35010i −1.05320 0.0982056i
\(190\) −0.485369 + 0.485369i −0.0352124 + 0.0352124i
\(191\) 2.29567 + 2.29567i 0.166109 + 0.166109i 0.785267 0.619158i \(-0.212526\pi\)
−0.619158 + 0.785267i \(0.712526\pi\)
\(192\) −1.47244 0.912090i −0.106264 0.0658244i
\(193\) 19.1715 19.1715i 1.37999 1.37999i 0.535385 0.844608i \(-0.320166\pi\)
0.844608 0.535385i \(-0.179834\pi\)
\(194\) 5.40541i 0.388086i
\(195\) −2.28989 + 3.69671i −0.163982 + 0.264727i
\(196\) 0.832067i 0.0594333i
\(197\) 16.7875i 1.19606i −0.801473 0.598031i \(-0.795950\pi\)
0.801473 0.598031i \(-0.204050\pi\)
\(198\) 12.1169 + 4.06635i 0.861109 + 0.288983i
\(199\) −5.65815 5.65815i −0.401096 0.401096i 0.477523 0.878619i \(-0.341535\pi\)
−0.878619 + 0.477523i \(0.841535\pi\)
\(200\) −0.707107 + 0.707107i −0.0500000 + 0.0500000i
\(201\) 0.930557 + 0.576424i 0.0656364 + 0.0406578i
\(202\) −8.86201 + 8.86201i −0.623529 + 0.623529i
\(203\) 19.6685 19.6685i 1.38046 1.38046i
\(204\) 3.07558 + 13.0878i 0.215333 + 0.916332i
\(205\) 5.57567 + 5.57567i 0.389422 + 0.389422i
\(206\) 5.26599 0.366899
\(207\) 1.84614 5.50111i 0.128316 0.382354i
\(208\) −1.77526 + 1.77526i −0.123092 + 0.123092i
\(209\) 2.06783 2.06783i 0.143035 0.143035i
\(210\) −2.55256 + 4.12076i −0.176143 + 0.284359i
\(211\) 13.9231 0.958504 0.479252 0.877677i \(-0.340908\pi\)
0.479252 + 0.877677i \(0.340908\pi\)
\(212\) 2.32891 0.159950
\(213\) 19.0662 + 11.8104i 1.30639 + 0.809233i
\(214\) −9.98563 9.98563i −0.682603 0.682603i
\(215\) −5.26367 −0.358979
\(216\) 3.31724 + 3.99949i 0.225710 + 0.272131i
\(217\) 10.6283 + 10.6283i 0.721497 + 0.721497i
\(218\) 3.93399i 0.266443i
\(219\) −12.1389 7.51934i −0.820273 0.508110i
\(220\) 3.01251 3.01251i 0.203103 0.203103i
\(221\) 19.4875 1.31087
\(222\) 7.76437 7.12142i 0.521110 0.477958i
\(223\) −7.53292 −0.504442 −0.252221 0.967670i \(-0.581161\pi\)
−0.252221 + 0.967670i \(0.581161\pi\)
\(224\) −1.97890 + 1.97890i −0.132221 + 0.132221i
\(225\) 2.68600 1.33618i 0.179067 0.0890788i
\(226\) 16.9795i 1.12946i
\(227\) −0.877238 0.877238i −0.0582243 0.0582243i 0.677395 0.735619i \(-0.263109\pi\)
−0.735619 + 0.677395i \(0.763109\pi\)
\(228\) 1.15738 0.271978i 0.0766493 0.0180122i
\(229\) 22.3271 1.47542 0.737708 0.675120i \(-0.235908\pi\)
0.737708 + 0.675120i \(0.235908\pi\)
\(230\) −1.36769 1.36769i −0.0901830 0.0901830i
\(231\) 10.8748 17.5558i 0.715506 1.15509i
\(232\) −9.93910 −0.652534
\(233\) 9.79418 0.641638 0.320819 0.947140i \(-0.396042\pi\)
0.320819 + 0.947140i \(0.396042\pi\)
\(234\) 6.74347 3.35461i 0.440834 0.219298i
\(235\) 1.70686 1.70686i 0.111344 0.111344i
\(236\) −4.84986 + 4.84986i −0.315699 + 0.315699i
\(237\) −2.34011 9.95815i −0.152007 0.646851i
\(238\) 21.7229 1.40809
\(239\) −2.87846 2.87846i −0.186192 0.186192i 0.607856 0.794048i \(-0.292030\pi\)
−0.794048 + 0.607856i \(0.792030\pi\)
\(240\) 1.68612 0.396230i 0.108839 0.0255765i
\(241\) 7.88502 7.88502i 0.507919 0.507919i −0.405968 0.913887i \(-0.633066\pi\)
0.913887 + 0.405968i \(0.133066\pi\)
\(242\) −5.05611 + 5.05611i −0.325019 + 0.325019i
\(243\) −5.61723 14.5412i −0.360345 0.932819i
\(244\) 3.08764 3.08764i 0.197666 0.197666i
\(245\) 0.588360 + 0.588360i 0.0375889 + 0.0375889i
\(246\) −3.12435 13.2954i −0.199201 0.847683i
\(247\) 1.72331i 0.109652i
\(248\) 5.37083i 0.341048i
\(249\) −18.5588 11.4961i −1.17612 0.728534i
\(250\) 1.00000i 0.0632456i
\(251\) −19.0180 + 19.0180i −1.20040 + 1.20040i −0.226361 + 0.974043i \(0.572683\pi\)
−0.974043 + 0.226361i \(0.927317\pi\)
\(252\) 7.51700 3.73942i 0.473527 0.235561i
\(253\) 5.82682 + 5.82682i 0.366329 + 0.366329i
\(254\) 9.85843 9.85843i 0.618573 0.618573i
\(255\) −11.4293 7.07974i −0.715728 0.443350i
\(256\) 1.00000 0.0625000
\(257\) −1.79625 1.79625i −0.112047 0.112047i 0.648860 0.760907i \(-0.275246\pi\)
−0.760907 + 0.648860i \(0.775246\pi\)
\(258\) 7.75046 + 4.80094i 0.482523 + 0.298894i
\(259\) −8.33147 14.8450i −0.517692 0.922421i
\(260\) 2.51060i 0.155701i
\(261\) 28.2680 + 9.48655i 1.74974 + 0.587203i
\(262\) 2.77732i 0.171583i
\(263\) 25.6368 1.58083 0.790417 0.612569i \(-0.209864\pi\)
0.790417 + 0.612569i \(0.209864\pi\)
\(264\) −7.18343 + 1.68807i −0.442110 + 0.103894i
\(265\) −1.64679 + 1.64679i −0.101161 + 0.101161i
\(266\) 1.92099i 0.117784i
\(267\) −0.634931 2.70189i −0.0388572 0.165353i
\(268\) −0.631981 −0.0386044
\(269\) 20.7163i 1.26310i 0.775337 + 0.631548i \(0.217580\pi\)
−0.775337 + 0.631548i \(0.782420\pi\)
\(270\) −5.17371 0.482424i −0.314862 0.0293594i
\(271\) 7.12296 0.432689 0.216345 0.976317i \(-0.430587\pi\)
0.216345 + 0.976317i \(0.430587\pi\)
\(272\) −5.48863 5.48863i −0.332797 0.332797i
\(273\) −2.78396 11.8469i −0.168493 0.717005i
\(274\) −4.77085 4.77085i −0.288218 0.288218i
\(275\) 4.26033i 0.256908i
\(276\) 0.766391 + 3.26131i 0.0461313 + 0.196308i
\(277\) −9.36210 9.36210i −0.562514 0.562514i 0.367507 0.930021i \(-0.380211\pi\)
−0.930021 + 0.367507i \(0.880211\pi\)
\(278\) −12.5739 12.5739i −0.754135 0.754135i
\(279\) −5.12628 + 15.2753i −0.306903 + 0.914506i
\(280\) 2.79858i 0.167247i
\(281\) 19.0275 + 19.0275i 1.13509 + 1.13509i 0.989319 + 0.145769i \(0.0465655\pi\)
0.145769 + 0.989319i \(0.453434\pi\)
\(282\) −4.07008 + 0.956448i −0.242370 + 0.0569556i
\(283\) −18.3350 18.3350i −1.08990 1.08990i −0.995538 0.0943643i \(-0.969918\pi\)
−0.0943643 0.995538i \(-0.530082\pi\)
\(284\) −12.9487 −0.768362
\(285\) −0.626073 + 1.01071i −0.0370854 + 0.0598692i
\(286\) 10.6960i 0.632466i
\(287\) −22.0674 −1.30260
\(288\) −2.84412 0.954468i −0.167591 0.0562426i
\(289\) 43.2502i 2.54413i
\(290\) 7.02801 7.02801i 0.412699 0.412699i
\(291\) 2.14179 + 9.11417i 0.125554 + 0.534282i
\(292\) 8.24407 0.482448
\(293\) 0.782467i 0.0457122i 0.999739 + 0.0228561i \(0.00727596\pi\)
−0.999739 + 0.0228561i \(0.992724\pi\)
\(294\) −0.329690 1.40296i −0.0192279 0.0818226i
\(295\) 6.85874i 0.399331i
\(296\) −1.64574 + 5.85590i −0.0956567 + 0.340367i
\(297\) 22.0417 + 2.05529i 1.27899 + 0.119260i
\(298\) −1.58391 1.58391i −0.0917534 0.0917534i
\(299\) 4.85602 0.280831
\(300\) −0.912090 + 1.47244i −0.0526596 + 0.0850116i
\(301\) 10.4163 10.4163i 0.600383 0.600383i
\(302\) 2.40614 + 2.40614i 0.138458 + 0.138458i
\(303\) −11.4310 + 18.4538i −0.656695 + 1.06014i
\(304\) −0.485369 + 0.485369i −0.0278378 + 0.0278378i
\(305\) 4.36658i 0.250030i
\(306\) 10.3716 + 20.8490i 0.592904 + 1.19186i
\(307\) 8.87492i 0.506519i −0.967398 0.253259i \(-0.918497\pi\)
0.967398 0.253259i \(-0.0815026\pi\)
\(308\) 11.9229i 0.679370i
\(309\) 8.87909 2.08654i 0.505114 0.118699i
\(310\) 3.79775 + 3.79775i 0.215698 + 0.215698i
\(311\) 2.73004 2.73004i 0.154806 0.154806i −0.625454 0.780261i \(-0.715086\pi\)
0.780261 + 0.625454i \(0.215086\pi\)
\(312\) −2.28989 + 3.69671i −0.129640 + 0.209285i
\(313\) −4.51817 + 4.51817i −0.255382 + 0.255382i −0.823173 0.567791i \(-0.807798\pi\)
0.567791 + 0.823173i \(0.307798\pi\)
\(314\) 10.4749 10.4749i 0.591134 0.591134i
\(315\) −2.67116 + 7.95949i −0.150503 + 0.448467i
\(316\) 4.17614 + 4.17614i 0.234926 + 0.234926i
\(317\) 2.30629 0.129534 0.0647670 0.997900i \(-0.479370\pi\)
0.0647670 + 0.997900i \(0.479370\pi\)
\(318\) 3.92682 0.922783i 0.220205 0.0517471i
\(319\) −29.9416 + 29.9416i −1.67641 + 1.67641i
\(320\) −0.707107 + 0.707107i −0.0395285 + 0.0395285i
\(321\) −20.7936 12.8804i −1.16058 0.718912i
\(322\) 5.41304 0.301657
\(323\) 5.32803 0.296459
\(324\) 7.17798 + 5.42923i 0.398777 + 0.301624i
\(325\) 1.77526 + 1.77526i 0.0984737 + 0.0984737i
\(326\) −10.8220 −0.599378
\(327\) 1.55876 + 6.63317i 0.0861998 + 0.366815i
\(328\) 5.57567 + 5.57567i 0.307865 + 0.307865i
\(329\) 6.75542i 0.372438i
\(330\) 3.88581 6.27310i 0.213907 0.345323i
\(331\) 9.28631 9.28631i 0.510422 0.510422i −0.404234 0.914656i \(-0.632462\pi\)
0.914656 + 0.404234i \(0.132462\pi\)
\(332\) 12.6041 0.691740
\(333\) 10.2699 15.0840i 0.562789 0.826600i
\(334\) −16.5768 −0.907044
\(335\) 0.446878 0.446878i 0.0244156 0.0244156i
\(336\) −2.55256 + 4.12076i −0.139254 + 0.224806i
\(337\) 32.6463i 1.77836i −0.457560 0.889179i \(-0.651277\pi\)
0.457560 0.889179i \(-0.348723\pi\)
\(338\) −4.73543 4.73543i −0.257573 0.257573i
\(339\) −6.72779 28.6295i −0.365403 1.55494i
\(340\) 7.76210 0.420959
\(341\) −16.1797 16.1797i −0.876178 0.876178i
\(342\) 1.84371 0.917176i 0.0996967 0.0495952i
\(343\) 17.2615 0.932032
\(344\) −5.26367 −0.283798
\(345\) −2.84801 1.76417i −0.153332 0.0949799i
\(346\) 3.44010 3.44010i 0.184941 0.184941i
\(347\) −1.60797 + 1.60797i −0.0863203 + 0.0863203i −0.748948 0.662628i \(-0.769441\pi\)
0.662628 + 0.748948i \(0.269441\pi\)
\(348\) −16.7585 + 3.93817i −0.898351 + 0.211108i
\(349\) −26.5611 −1.42178 −0.710892 0.703301i \(-0.751709\pi\)
−0.710892 + 0.703301i \(0.751709\pi\)
\(350\) 1.97890 + 1.97890i 0.105776 + 0.105776i
\(351\) 10.0411 8.32825i 0.535955 0.444529i
\(352\) 3.01251 3.01251i 0.160567 0.160567i
\(353\) −13.7402 + 13.7402i −0.731319 + 0.731319i −0.970881 0.239562i \(-0.922996\pi\)
0.239562 + 0.970881i \(0.422996\pi\)
\(354\) −6.25579 + 10.0991i −0.332492 + 0.536762i
\(355\) 9.15610 9.15610i 0.485955 0.485955i
\(356\) 1.13309 + 1.13309i 0.0600537 + 0.0600537i
\(357\) 36.6274 8.60725i 1.93853 0.455544i
\(358\) 13.0607i 0.690278i
\(359\) 27.5625i 1.45469i −0.686270 0.727347i \(-0.740753\pi\)
0.686270 0.727347i \(-0.259247\pi\)
\(360\) 2.68600 1.33618i 0.141565 0.0704230i
\(361\) 18.5288i 0.975202i
\(362\) −13.7883 + 13.7883i −0.724699 + 0.724699i
\(363\) −6.52183 + 10.5286i −0.342307 + 0.552608i
\(364\) 4.96821 + 4.96821i 0.260405 + 0.260405i
\(365\) −5.82944 + 5.82944i −0.305127 + 0.305127i
\(366\) 3.98272 6.42955i 0.208180 0.336078i
\(367\) 10.1661 0.530669 0.265334 0.964156i \(-0.414518\pi\)
0.265334 + 0.964156i \(0.414518\pi\)
\(368\) −1.36769 1.36769i −0.0712959 0.0712959i
\(369\) −10.5361 21.1797i −0.548485 1.10257i
\(370\) −2.97703 5.30446i −0.154768 0.275766i
\(371\) 6.51765i 0.338379i
\(372\) −2.12808 9.05586i −0.110336 0.469525i
\(373\) 29.8152i 1.54377i −0.635759 0.771887i \(-0.719313\pi\)
0.635759 0.771887i \(-0.280687\pi\)
\(374\) −33.0691 −1.70996
\(375\) −0.396230 1.68612i −0.0204612 0.0870709i
\(376\) 1.70686 1.70686i 0.0880248 0.0880248i
\(377\) 24.9531i 1.28515i
\(378\) 11.1929 9.28357i 0.575701 0.477495i
\(379\) 11.8696 0.609703 0.304851 0.952400i \(-0.401393\pi\)
0.304851 + 0.952400i \(0.401393\pi\)
\(380\) 0.686416i 0.0352124i
\(381\) 12.7163 20.5287i 0.651475 1.05172i
\(382\) −3.24657 −0.166109
\(383\) −2.09268 2.09268i −0.106931 0.106931i 0.651617 0.758548i \(-0.274091\pi\)
−0.758548 + 0.651617i \(0.774091\pi\)
\(384\) 1.68612 0.396230i 0.0860445 0.0202200i
\(385\) −8.43076 8.43076i −0.429671 0.429671i
\(386\) 27.1126i 1.37999i
\(387\) 14.9705 + 5.02400i 0.760993 + 0.255385i
\(388\) −3.82220 3.82220i −0.194043 0.194043i
\(389\) 6.62618 + 6.62618i 0.335961 + 0.335961i 0.854845 0.518884i \(-0.173652\pi\)
−0.518884 + 0.854845i \(0.673652\pi\)
\(390\) −0.994773 4.23317i −0.0503723 0.214355i
\(391\) 15.0135i 0.759266i
\(392\) 0.588360 + 0.588360i 0.0297167 + 0.0297167i
\(393\) −1.10046 4.68289i −0.0555106 0.236220i
\(394\) 11.8706 + 11.8706i 0.598031 + 0.598031i
\(395\) −5.90595 −0.297161
\(396\) −11.4433 + 5.69258i −0.575046 + 0.286063i
\(397\) 0.443718i 0.0222695i −0.999938 0.0111348i \(-0.996456\pi\)
0.999938 0.0111348i \(-0.00354438\pi\)
\(398\) 8.00183 0.401096
\(399\) −0.761154 3.23902i −0.0381054 0.162154i
\(400\) 1.00000i 0.0500000i
\(401\) 17.4046 17.4046i 0.869144 0.869144i −0.123233 0.992378i \(-0.539326\pi\)
0.992378 + 0.123233i \(0.0393263\pi\)
\(402\) −1.06560 + 0.250410i −0.0531471 + 0.0124893i
\(403\) −13.4840 −0.671685
\(404\) 12.5328i 0.623529i
\(405\) −8.91465 + 1.23655i −0.442972 + 0.0614448i
\(406\) 27.8154i 1.38046i
\(407\) 12.6831 + 22.5988i 0.628680 + 1.12018i
\(408\) −11.4293 7.07974i −0.565833 0.350499i
\(409\) −25.8916 25.8916i −1.28026 1.28026i −0.940520 0.339738i \(-0.889662\pi\)
−0.339738 0.940520i \(-0.610338\pi\)
\(410\) −7.88519 −0.389422
\(411\) −9.93459 6.15388i −0.490037 0.303549i
\(412\) −3.72362 + 3.72362i −0.183449 + 0.183449i
\(413\) 13.5727 + 13.5727i 0.667871 + 0.667871i
\(414\) 2.58446 + 5.19529i 0.127019 + 0.255335i
\(415\) −8.91245 + 8.91245i −0.437495 + 0.437495i
\(416\) 2.51060i 0.123092i
\(417\) −26.1833 16.2190i −1.28220 0.794248i
\(418\) 2.92436i 0.143035i
\(419\) 39.7747i 1.94312i −0.236791 0.971561i \(-0.576096\pi\)
0.236791 0.971561i \(-0.423904\pi\)
\(420\) −1.10888 4.71875i −0.0541079 0.230251i
\(421\) −9.15823 9.15823i −0.446345 0.446345i 0.447793 0.894137i \(-0.352210\pi\)
−0.894137 + 0.447793i \(0.852210\pi\)
\(422\) −9.84510 + 9.84510i −0.479252 + 0.479252i
\(423\) −6.48367 + 3.22537i −0.315247 + 0.156823i
\(424\) −1.64679 + 1.64679i −0.0799751 + 0.0799751i
\(425\) −5.48863 + 5.48863i −0.266238 + 0.266238i
\(426\) −21.8330 + 5.13065i −1.05781 + 0.248581i
\(427\) −8.64102 8.64102i −0.418168 0.418168i
\(428\) 14.1218 0.682603
\(429\) 4.23806 + 18.0347i 0.204616 + 0.870723i
\(430\) 3.72198 3.72198i 0.179490 0.179490i
\(431\) −22.4447 + 22.4447i −1.08112 + 1.08112i −0.0847166 + 0.996405i \(0.526998\pi\)
−0.996405 + 0.0847166i \(0.973002\pi\)
\(432\) −5.17371 0.482424i −0.248920 0.0232106i
\(433\) −25.9555 −1.24734 −0.623671 0.781687i \(-0.714359\pi\)
−0.623671 + 0.781687i \(0.714359\pi\)
\(434\) −15.0307 −0.721497
\(435\) 9.06536 14.6348i 0.434651 0.701684i
\(436\) −2.78175 2.78175i −0.133222 0.133222i
\(437\) 1.32767 0.0635111
\(438\) 13.9005 3.26655i 0.664191 0.156082i
\(439\) 14.5503 + 14.5503i 0.694446 + 0.694446i 0.963207 0.268761i \(-0.0866141\pi\)
−0.268761 + 0.963207i \(0.586614\pi\)
\(440\) 4.26033i 0.203103i
\(441\) −1.11179 2.23493i −0.0529425 0.106425i
\(442\) −13.7797 + 13.7797i −0.655436 + 0.655436i
\(443\) 15.0026 0.712797 0.356399 0.934334i \(-0.384005\pi\)
0.356399 + 0.934334i \(0.384005\pi\)
\(444\) −0.454634 + 10.5258i −0.0215760 + 0.499534i
\(445\) −1.60243 −0.0759626
\(446\) 5.32658 5.32658i 0.252221 0.252221i
\(447\) −3.29825 2.04307i −0.156002 0.0966339i
\(448\) 2.79858i 0.132221i
\(449\) −19.8528 19.8528i −0.936912 0.936912i 0.0612124 0.998125i \(-0.480503\pi\)
−0.998125 + 0.0612124i \(0.980503\pi\)
\(450\) −0.954468 + 2.84412i −0.0449940 + 0.134073i
\(451\) 33.5935 1.58186
\(452\) 12.0063 + 12.0063i 0.564730 + 0.564730i
\(453\) 5.01043 + 3.10366i 0.235411 + 0.145823i
\(454\) 1.24060 0.0582243
\(455\) −7.02611 −0.329389
\(456\) −0.626073 + 1.01071i −0.0293186 + 0.0473308i
\(457\) 19.3136 19.3136i 0.903451 0.903451i −0.0922815 0.995733i \(-0.529416\pi\)
0.995733 + 0.0922815i \(0.0294160\pi\)
\(458\) −15.7876 + 15.7876i −0.737708 + 0.737708i
\(459\) 25.7487 + 31.0444i 1.20185 + 1.44903i
\(460\) 1.93421 0.0901830
\(461\) 9.75740 + 9.75740i 0.454447 + 0.454447i 0.896828 0.442380i \(-0.145866\pi\)
−0.442380 + 0.896828i \(0.645866\pi\)
\(462\) 4.72421 + 20.1034i 0.219790 + 0.935296i
\(463\) −13.2936 + 13.2936i −0.617806 + 0.617806i −0.944968 0.327163i \(-0.893908\pi\)
0.327163 + 0.944968i \(0.393908\pi\)
\(464\) 7.02801 7.02801i 0.326267 0.326267i
\(465\) 7.90824 + 4.89868i 0.366736 + 0.227171i
\(466\) −6.92553 + 6.92553i −0.320819 + 0.320819i
\(467\) −16.8533 16.8533i −0.779876 0.779876i 0.199934 0.979809i \(-0.435927\pi\)
−0.979809 + 0.199934i \(0.935927\pi\)
\(468\) −2.39628 + 7.14042i −0.110768 + 0.330066i
\(469\) 1.76865i 0.0816687i
\(470\) 2.41387i 0.111344i
\(471\) 13.5115 21.8124i 0.622577 1.00506i
\(472\) 6.85874i 0.315699i
\(473\) −15.8569 + 15.8569i −0.729099 + 0.729099i
\(474\) 8.69618 + 5.38676i 0.399429 + 0.247422i
\(475\) 0.485369 + 0.485369i 0.0222703 + 0.0222703i
\(476\) −15.3604 + 15.3604i −0.704043 + 0.704043i
\(477\) 6.25546 3.11185i 0.286418 0.142482i
\(478\) 4.07076 0.186192
\(479\) −1.79186 1.79186i −0.0818722 0.0818722i 0.664985 0.746857i \(-0.268438\pi\)
−0.746857 + 0.664985i \(0.768438\pi\)
\(480\) −0.912090 + 1.47244i −0.0416310 + 0.0672076i
\(481\) 14.7018 + 4.13179i 0.670344 + 0.188393i
\(482\) 11.1511i 0.507919i
\(483\) 9.12704 2.14481i 0.415295 0.0975922i
\(484\) 7.15042i 0.325019i
\(485\) 5.40541 0.245447
\(486\) 14.2542 + 6.31021i 0.646582 + 0.286237i
\(487\) −8.70006 + 8.70006i −0.394237 + 0.394237i −0.876195 0.481957i \(-0.839926\pi\)
0.481957 + 0.876195i \(0.339926\pi\)
\(488\) 4.36658i 0.197666i
\(489\) −18.2473 + 4.28802i −0.825170 + 0.193911i
\(490\) −0.832067 −0.0375889
\(491\) 1.24916i 0.0563736i 0.999603 + 0.0281868i \(0.00897333\pi\)
−0.999603 + 0.0281868i \(0.991027\pi\)
\(492\) 11.6105 + 7.19201i 0.523442 + 0.324241i
\(493\) −77.1483 −3.47459
\(494\) 1.21857 + 1.21857i 0.0548259 + 0.0548259i
\(495\) 4.06635 12.1169i 0.182769 0.544613i
\(496\) 3.79775 + 3.79775i 0.170524 + 0.170524i
\(497\) 36.2379i 1.62549i
\(498\) 21.2520 4.99412i 0.952326 0.223792i
\(499\) 26.1302 + 26.1302i 1.16975 + 1.16975i 0.982269 + 0.187479i \(0.0600316\pi\)
0.187479 + 0.982269i \(0.439968\pi\)
\(500\) 0.707107 + 0.707107i 0.0316228 + 0.0316228i
\(501\) −27.9505 + 6.56824i −1.24874 + 0.293447i
\(502\) 26.8955i 1.20040i
\(503\) −25.6242 25.6242i −1.14253 1.14253i −0.987987 0.154538i \(-0.950611\pi\)
−0.154538 0.987987i \(-0.549389\pi\)
\(504\) −2.67116 + 7.95949i −0.118983 + 0.354544i
\(505\) 8.86201 + 8.86201i 0.394354 + 0.394354i
\(506\) −8.24037 −0.366329
\(507\) −9.86082 6.10818i −0.437934 0.271274i
\(508\) 13.9419i 0.618573i
\(509\) 35.7638 1.58520 0.792601 0.609741i \(-0.208726\pi\)
0.792601 + 0.609741i \(0.208726\pi\)
\(510\) 13.0878 3.07558i 0.579539 0.136189i
\(511\) 23.0717i 1.02063i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 2.74531 2.27700i 0.121209 0.100532i
\(514\) 2.54028 0.112047
\(515\) 5.26599i 0.232047i
\(516\) −8.87518 + 2.08562i −0.390708 + 0.0918145i
\(517\) 10.2839i 0.452285i
\(518\) 16.3882 + 4.60574i 0.720057 + 0.202365i
\(519\) 4.43736 7.16350i 0.194778 0.314443i
\(520\) 1.77526 + 1.77526i 0.0778503 + 0.0778503i
\(521\) 9.65846 0.423145 0.211572 0.977362i \(-0.432142\pi\)
0.211572 + 0.977362i \(0.432142\pi\)
\(522\) −26.6965 + 13.2805i −1.16847 + 0.581270i
\(523\) 7.75116 7.75116i 0.338934 0.338934i −0.517032 0.855966i \(-0.672963\pi\)
0.855966 + 0.517032i \(0.172963\pi\)
\(524\) 1.96386 + 1.96386i 0.0857916 + 0.0857916i
\(525\) 4.12076 + 2.55256i 0.179845 + 0.111403i
\(526\) −18.1280 + 18.1280i −0.790417 + 0.790417i
\(527\) 41.6889i 1.81600i
\(528\) 3.88581 6.27310i 0.169108 0.273002i
\(529\) 19.2588i 0.837341i
\(530\) 2.32891i 0.101161i
\(531\) −6.54645 + 19.5071i −0.284092 + 0.846534i
\(532\) 1.35835 + 1.35835i 0.0588918 + 0.0588918i
\(533\) 13.9983 13.9983i 0.606332 0.606332i
\(534\) 2.35949 + 1.46156i 0.102105 + 0.0632480i
\(535\) −9.98563 + 9.98563i −0.431716 + 0.431716i
\(536\) 0.446878 0.446878i 0.0193022 0.0193022i
\(537\) 5.17503 + 22.0219i 0.223319 + 0.950314i
\(538\) −14.6486 14.6486i −0.631548 0.631548i
\(539\) 3.54488 0.152689
\(540\) 3.99949 3.31724i 0.172111 0.142751i
\(541\) −12.0747 + 12.0747i −0.519132 + 0.519132i −0.917309 0.398177i \(-0.869643\pi\)
0.398177 + 0.917309i \(0.369643\pi\)
\(542\) −5.03670 + 5.03670i −0.216345 + 0.216345i
\(543\) −17.7855 + 28.7122i −0.763247 + 1.23216i
\(544\) 7.76210 0.332797
\(545\) 3.93399 0.168513
\(546\) 10.3456 + 6.40845i 0.442749 + 0.274256i
\(547\) −21.3535 21.3535i −0.913010 0.913010i 0.0834976 0.996508i \(-0.473391\pi\)
−0.996508 + 0.0834976i \(0.973391\pi\)
\(548\) 6.74701 0.288218
\(549\) 4.16776 12.4191i 0.177876 0.530033i
\(550\) −3.01251 3.01251i −0.128454 0.128454i
\(551\) 6.82236i 0.290642i
\(552\) −2.84801 1.76417i −0.121220 0.0750882i
\(553\) 11.6873 11.6873i 0.496993 0.496993i
\(554\) 13.2400 0.562514
\(555\) −7.12142 7.76437i −0.302287 0.329579i
\(556\) 17.7822 0.754135
\(557\) 10.3385 10.3385i 0.438055 0.438055i −0.453302 0.891357i \(-0.649754\pi\)
0.891357 + 0.453302i \(0.149754\pi\)
\(558\) −7.17641 14.4261i −0.303802 0.610704i
\(559\) 13.2150i 0.558933i
\(560\) 1.97890 + 1.97890i 0.0836237 + 0.0836237i
\(561\) −55.7585 + 13.1030i −2.35413 + 0.553208i
\(562\) −26.9090 −1.13509
\(563\) 27.7261 + 27.7261i 1.16852 + 1.16852i 0.982558 + 0.185959i \(0.0595391\pi\)
0.185959 + 0.982558i \(0.440461\pi\)
\(564\) 2.20167 3.55429i 0.0927069 0.149663i
\(565\) −16.9795 −0.714334
\(566\) 25.9296 1.08990
\(567\) 15.1942 20.0882i 0.638095 0.843624i
\(568\) 9.15610 9.15610i 0.384181 0.384181i
\(569\) 24.9520 24.9520i 1.04604 1.04604i 0.0471533 0.998888i \(-0.484985\pi\)
0.998888 0.0471533i \(-0.0150149\pi\)
\(570\) −0.271978 1.15738i −0.0113919 0.0484773i
\(571\) −33.1993 −1.38935 −0.694675 0.719324i \(-0.744452\pi\)
−0.694675 + 0.719324i \(0.744452\pi\)
\(572\) −7.56319 7.56319i −0.316233 0.316233i
\(573\) −5.47412 + 1.28639i −0.228684 + 0.0537397i
\(574\) 15.6040 15.6040i 0.651298 0.651298i
\(575\) −1.36769 + 1.36769i −0.0570367 + 0.0570367i
\(576\) 2.68600 1.33618i 0.111917 0.0556743i
\(577\) −20.4920 + 20.4920i −0.853092 + 0.853092i −0.990513 0.137421i \(-0.956119\pi\)
0.137421 + 0.990513i \(0.456119\pi\)
\(578\) −30.5825 30.5825i −1.27206 1.27206i
\(579\) 10.7428 + 45.7150i 0.446456 + 1.89985i
\(580\) 9.93910i 0.412699i
\(581\) 35.2736i 1.46340i
\(582\) −7.95917 4.93022i −0.329918 0.204364i
\(583\) 9.92193i 0.410924i
\(584\) −5.82944 + 5.82944i −0.241224 + 0.241224i
\(585\) −3.35461 6.74347i −0.138696 0.278808i
\(586\) −0.553288 0.553288i −0.0228561 0.0228561i
\(587\) 3.35864 3.35864i 0.138626 0.138626i −0.634388 0.773014i \(-0.718748\pi\)
0.773014 + 0.634388i \(0.218748\pi\)
\(588\) 1.22517 + 0.758920i 0.0505252 + 0.0312973i
\(589\) −3.68662 −0.151905
\(590\) 4.84986 + 4.84986i 0.199666 + 0.199666i
\(591\) 24.7187 + 15.3118i 1.01679 + 0.629841i
\(592\) −2.97703 5.30446i −0.122355 0.218012i
\(593\) 29.3236i 1.20417i 0.798430 + 0.602087i \(0.205664\pi\)
−0.798430 + 0.602087i \(0.794336\pi\)
\(594\) −17.0392 + 14.1325i −0.699125 + 0.579865i
\(595\) 21.7229i 0.890551i
\(596\) 2.23999 0.0917534
\(597\) 13.4921 3.17056i 0.552193 0.129763i
\(598\) −3.43372 + 3.43372i −0.140415 + 0.140415i
\(599\) 39.8668i 1.62891i −0.580225 0.814456i \(-0.697035\pi\)
0.580225 0.814456i \(-0.302965\pi\)
\(600\) −0.396230 1.68612i −0.0161760 0.0688356i
\(601\) 0.173361 0.00707156 0.00353578 0.999994i \(-0.498875\pi\)
0.00353578 + 0.999994i \(0.498875\pi\)
\(602\) 14.7308i 0.600383i
\(603\) −1.69750 + 0.844442i −0.0691277 + 0.0343883i
\(604\) −3.40280 −0.138458
\(605\) 5.05611 + 5.05611i 0.205560 + 0.205560i
\(606\) −4.96586 21.1318i −0.201724 0.858419i
\(607\) −8.00701 8.00701i −0.324995 0.324995i 0.525685 0.850679i \(-0.323809\pi\)
−0.850679 + 0.525685i \(0.823809\pi\)
\(608\) 0.686416i 0.0278378i
\(609\) 11.0213 + 46.9001i 0.446605 + 1.90049i
\(610\) −3.08764 3.08764i −0.125015 0.125015i
\(611\) −4.28525 4.28525i −0.173363 0.173363i
\(612\) −22.0763 7.40867i −0.892382 0.299478i
\(613\) 23.8974i 0.965205i 0.875839 + 0.482603i \(0.160308\pi\)
−0.875839 + 0.482603i \(0.839692\pi\)
\(614\) 6.27552 + 6.27552i 0.253259 + 0.253259i
\(615\) −13.2954 + 3.12435i −0.536122 + 0.125986i
\(616\) −8.43076 8.43076i −0.339685 0.339685i
\(617\) 2.77943 0.111896 0.0559478 0.998434i \(-0.482182\pi\)
0.0559478 + 0.998434i \(0.482182\pi\)
\(618\) −4.80306 + 7.75387i −0.193207 + 0.311907i
\(619\) 0.897258i 0.0360638i −0.999837 0.0180319i \(-0.994260\pi\)
0.999837 0.0180319i \(-0.00574005\pi\)
\(620\) −5.37083 −0.215698
\(621\) 6.41623 + 7.73585i 0.257475 + 0.310429i
\(622\) 3.86086i 0.154806i
\(623\) 3.17105 3.17105i 0.127045 0.127045i
\(624\) −0.994773 4.23317i −0.0398228 0.169462i
\(625\) −1.00000 −0.0400000
\(626\) 6.38966i 0.255382i
\(627\) 1.15872 + 4.93082i 0.0462747 + 0.196918i
\(628\) 14.8138i 0.591134i
\(629\) −12.7744 + 45.4541i −0.509349 + 1.81237i
\(630\) −3.73942 7.51700i −0.148982 0.299485i
\(631\) 4.89754 + 4.89754i 0.194968 + 0.194968i 0.797839 0.602871i \(-0.205977\pi\)
−0.602871 + 0.797839i \(0.705977\pi\)
\(632\) −5.90595 −0.234926
\(633\) −12.6991 + 20.5009i −0.504744 + 0.814839i
\(634\) −1.63079 + 1.63079i −0.0647670 + 0.0647670i
\(635\) −9.85843 9.85843i −0.391220 0.391220i
\(636\) −2.12418 + 3.42919i −0.0842290 + 0.135976i
\(637\) 1.47713 1.47713i 0.0585262 0.0585262i
\(638\) 42.3439i 1.67641i
\(639\) −34.7802 + 17.3018i −1.37588 + 0.684448i
\(640\) 1.00000i 0.0395285i
\(641\) 38.4671i 1.51936i 0.650298 + 0.759679i \(0.274644\pi\)
−0.650298 + 0.759679i \(0.725356\pi\)
\(642\) 23.8111 5.59548i 0.939748 0.220836i
\(643\) −16.9600 16.9600i −0.668837 0.668837i 0.288610 0.957447i \(-0.406807\pi\)
−0.957447 + 0.288610i \(0.906807\pi\)
\(644\) −3.82760 + 3.82760i −0.150829 + 0.150829i
\(645\) 4.80094 7.75046i 0.189037 0.305174i
\(646\) −3.76748 + 3.76748i −0.148230 + 0.148230i
\(647\) −22.8453 + 22.8453i −0.898142 + 0.898142i −0.995272 0.0971299i \(-0.969034\pi\)
0.0971299 + 0.995272i \(0.469034\pi\)
\(648\) −8.91465 + 1.23655i −0.350200 + 0.0485764i
\(649\) −20.6620 20.6620i −0.811055 0.811055i
\(650\) −2.51060 −0.0984737
\(651\) −25.3436 + 5.95562i −0.993293 + 0.233419i
\(652\) 7.65234 7.65234i 0.299689 0.299689i
\(653\) 33.5975 33.5975i 1.31477 1.31477i 0.396917 0.917854i \(-0.370080\pi\)
0.917854 0.396917i \(-0.129920\pi\)
\(654\) −5.79257 3.58815i −0.226508 0.140308i
\(655\) −2.77732 −0.108519
\(656\) −7.88519 −0.307865
\(657\) 22.1436 11.0156i 0.863904 0.429759i
\(658\) −4.77680 4.77680i −0.186219 0.186219i
\(659\) 18.7953 0.732162 0.366081 0.930583i \(-0.380699\pi\)
0.366081 + 0.930583i \(0.380699\pi\)
\(660\) 1.68807 + 7.18343i 0.0657081 + 0.279615i
\(661\) 12.8955 + 12.8955i 0.501575 + 0.501575i 0.911927 0.410352i \(-0.134594\pi\)
−0.410352 + 0.911927i \(0.634594\pi\)
\(662\) 13.1328i 0.510422i
\(663\) −17.7744 + 28.6943i −0.690299 + 1.11439i
\(664\) −8.91245 + 8.91245i −0.345870 + 0.345870i
\(665\) −1.92099 −0.0744928
\(666\) 3.40409 + 17.9280i 0.131906 + 0.694695i
\(667\) −19.2243 −0.744368
\(668\) 11.7216 11.7216i 0.453522 0.453522i
\(669\) 6.87070 11.0918i 0.265637 0.428834i
\(670\) 0.631981i 0.0244156i
\(671\) 13.1544 + 13.1544i 0.507819 + 0.507819i
\(672\) −1.10888 4.71875i −0.0427761 0.182030i
\(673\) 18.9774 0.731524 0.365762 0.930708i \(-0.380808\pi\)
0.365762 + 0.930708i \(0.380808\pi\)
\(674\) 23.0844 + 23.0844i 0.889179 + 0.889179i
\(675\) −0.482424 + 5.17371i −0.0185685 + 0.199136i
\(676\) 6.69691 0.257573
\(677\) −13.4356 −0.516374 −0.258187 0.966095i \(-0.583125\pi\)
−0.258187 + 0.966095i \(0.583125\pi\)
\(678\) 25.0014 + 15.4869i 0.960172 + 0.594769i
\(679\) −10.6968 + 10.6968i −0.410504 + 0.410504i
\(680\) −5.48863 + 5.48863i −0.210479 + 0.210479i
\(681\) 2.09180 0.491563i 0.0801581 0.0188368i
\(682\) 22.8815 0.876178
\(683\) 35.2795 + 35.2795i 1.34993 + 1.34993i 0.885728 + 0.464204i \(0.153660\pi\)
0.464204 + 0.885728i \(0.346340\pi\)
\(684\) −0.655162 + 1.95224i −0.0250507 + 0.0746460i
\(685\) −4.77085 + 4.77085i −0.182285 + 0.182285i
\(686\) −12.2057 + 12.2057i −0.466016 + 0.466016i
\(687\) −20.3643 + 32.8754i −0.776948 + 1.25428i
\(688\) 3.72198 3.72198i 0.141899 0.141899i
\(689\) 4.13442 + 4.13442i 0.157509 + 0.157509i
\(690\) 3.26131 0.766391i 0.124156 0.0291760i
\(691\) 45.3698i 1.72595i −0.505249 0.862974i \(-0.668599\pi\)
0.505249 0.862974i \(-0.331401\pi\)
\(692\) 4.86504i 0.184941i
\(693\) 15.9312 + 32.0249i 0.605175 + 1.21653i
\(694\) 2.27401i 0.0863203i
\(695\) −12.5739 + 12.5739i −0.476957 + 0.476957i
\(696\) 9.06536 14.6348i 0.343622 0.554730i
\(697\) 43.2789 + 43.2789i 1.63931 + 1.63931i
\(698\) 18.7815 18.7815i 0.710892 0.710892i
\(699\) −8.93318 + 14.4214i −0.337884 + 0.545467i
\(700\) −2.79858 −0.105776
\(701\) −9.83366 9.83366i −0.371412 0.371412i 0.496579 0.867991i \(-0.334589\pi\)
−0.867991 + 0.496579i \(0.834589\pi\)
\(702\) −1.21117 + 12.9891i −0.0457128 + 0.490242i
\(703\) 4.01958 + 1.12966i 0.151601 + 0.0426060i
\(704\) 4.26033i 0.160567i
\(705\) 0.956448 + 4.07008i 0.0360219 + 0.153288i
\(706\) 19.4316i 0.731319i
\(707\) −35.0740 −1.31909
\(708\) −2.71764 11.5647i −0.102135 0.434627i
\(709\) 20.5292 20.5292i 0.770992 0.770992i −0.207288 0.978280i \(-0.566464\pi\)
0.978280 + 0.207288i \(0.0664638\pi\)
\(710\) 12.9487i 0.485955i
\(711\) 16.7972 + 5.63704i 0.629945 + 0.211406i
\(712\) −1.60243 −0.0600537
\(713\) 10.3883i 0.389045i
\(714\) −19.8132 + 31.9857i −0.741491 + 1.19704i
\(715\) 10.6960 0.400007
\(716\) −9.23529 9.23529i −0.345139 0.345139i
\(717\) 6.86378 1.61296i 0.256333 0.0602369i
\(718\) 19.4896 + 19.4896i 0.727347 + 0.727347i
\(719\) 40.7293i 1.51894i 0.650539 + 0.759472i \(0.274543\pi\)
−0.650539 + 0.759472i \(0.725457\pi\)
\(720\) −0.954468 + 2.84412i −0.0355709 + 0.105994i
\(721\) 10.4209 + 10.4209i 0.388093 + 0.388093i
\(722\) −13.1019 13.1019i −0.487601 0.487601i
\(723\) 4.41840 + 18.8021i 0.164322 + 0.699258i
\(724\) 19.4997i 0.724699i
\(725\) −7.02801 7.02801i −0.261014 0.261014i
\(726\) −2.83321 12.0565i −0.105150 0.447458i
\(727\) −26.8295 26.8295i −0.995051 0.995051i 0.00493697 0.999988i \(-0.498429\pi\)
−0.999988 + 0.00493697i \(0.998429\pi\)
\(728\) −7.02611 −0.260405
\(729\) 26.5345 + 4.99184i 0.982761 + 0.184883i
\(730\) 8.24407i 0.305127i
\(731\) −40.8571 −1.51116
\(732\) 1.73017 + 7.36258i 0.0639489 + 0.272129i
\(733\) 30.8995i 1.14130i −0.821194 0.570649i \(-0.806692\pi\)
0.821194 0.570649i \(-0.193308\pi\)
\(734\) −7.18855 + 7.18855i −0.265334 + 0.265334i
\(735\) −1.40296 + 0.329690i −0.0517491 + 0.0121608i
\(736\) 1.93421 0.0712959
\(737\) 2.69245i 0.0991776i
\(738\) 22.4264 + 7.52616i 0.825527 + 0.277042i
\(739\) 29.0826i 1.06982i −0.844909 0.534910i \(-0.820345\pi\)
0.844909 0.534910i \(-0.179655\pi\)
\(740\) 5.85590 + 1.64574i 0.215267 + 0.0604986i
\(741\) 2.53748 + 1.57182i 0.0932167 + 0.0577421i
\(742\) 4.60867 + 4.60867i 0.169190 + 0.169190i
\(743\) −47.5193 −1.74331 −0.871657 0.490117i \(-0.836954\pi\)
−0.871657 + 0.490117i \(0.836954\pi\)
\(744\) 7.90824 + 4.89868i 0.289930 + 0.179594i
\(745\) −1.58391 + 1.58391i −0.0580299 + 0.0580299i
\(746\) 21.0826 + 21.0826i 0.771887 + 0.771887i
\(747\) 33.8547 16.8414i 1.23868 0.616194i
\(748\) 23.3834 23.3834i 0.854982 0.854982i
\(749\) 39.5210i 1.44407i
\(750\) 1.47244 + 0.912090i 0.0537661 + 0.0333048i
\(751\) 26.5041i 0.967149i 0.875303 + 0.483574i \(0.160662\pi\)
−0.875303 + 0.483574i \(0.839338\pi\)
\(752\) 2.41387i 0.0880248i
\(753\) −10.6568 45.3490i −0.388355 1.65261i
\(754\) −17.6445 17.6445i −0.642574 0.642574i
\(755\) 2.40614 2.40614i 0.0875685 0.0875685i
\(756\) −1.35010 + 14.4791i −0.0491028 + 0.526598i
\(757\) −5.02571 + 5.02571i −0.182662 + 0.182662i −0.792515 0.609852i \(-0.791229\pi\)
0.609852 + 0.792515i \(0.291229\pi\)
\(758\) −8.39311 + 8.39311i −0.304851 + 0.304851i
\(759\) −13.8943 + 3.26508i −0.504330 + 0.118515i
\(760\) 0.485369 + 0.485369i 0.0176062 + 0.0176062i
\(761\) −38.7905 −1.40616 −0.703078 0.711113i \(-0.748191\pi\)
−0.703078 + 0.711113i \(0.748191\pi\)
\(762\) 5.52420 + 23.5078i 0.200121 + 0.851596i
\(763\) −7.78495 + 7.78495i −0.281834 + 0.281834i
\(764\) 2.29567 2.29567i 0.0830546 0.0830546i
\(765\) 20.8490 10.3716i 0.753798 0.374985i
\(766\) 2.95950 0.106931
\(767\) −17.2195 −0.621761
\(768\) −0.912090 + 1.47244i −0.0329122 + 0.0531322i
\(769\) 3.86885 + 3.86885i 0.139514 + 0.139514i 0.773415 0.633900i \(-0.218547\pi\)
−0.633900 + 0.773415i \(0.718547\pi\)
\(770\) 11.9229 0.429671
\(771\) 4.28322 1.00653i 0.154256 0.0362495i
\(772\) −19.1715 19.1715i −0.689997 0.689997i
\(773\) 20.4737i 0.736387i −0.929749 0.368194i \(-0.879976\pi\)
0.929749 0.368194i \(-0.120024\pi\)
\(774\) −14.1382 + 7.03323i −0.508189 + 0.252804i
\(775\) 3.79775 3.79775i 0.136419 0.136419i
\(776\) 5.40541 0.194043
\(777\) 29.4574 + 1.27233i 1.05678 + 0.0456446i
\(778\) −9.37084 −0.335961
\(779\) 3.82723 3.82723i 0.137125