Properties

Label 1110.2.l.b.697.4
Level $1110$
Weight $2$
Character 1110.697
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
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.l (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 697.4
Character \(\chi\) \(=\) 1110.697
Dual form 1110.2.l.b.43.4

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.994632 - 2.00267i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.593998 + 0.593998i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.994632 - 2.00267i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.593998 + 0.593998i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(2.00267 - 0.994632i) q^{10} +2.21854i q^{11} +(0.707107 + 0.707107i) q^{12} +0.163340i q^{13} +(-0.593998 + 0.593998i) q^{14} +(-0.712794 + 2.11942i) q^{15} +1.00000 q^{16} +5.23332 q^{17} -1.00000 q^{18} +(-1.67943 - 1.67943i) q^{19} +(0.994632 + 2.00267i) q^{20} -0.840040i q^{21} -2.21854 q^{22} -3.86710i q^{23} +(-0.707107 + 0.707107i) q^{24} +(-3.02141 + 3.98385i) q^{25} -0.163340 q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.593998 - 0.593998i) q^{28} +(4.79365 - 4.79365i) q^{29} +(-2.11942 - 0.712794i) q^{30} +(-5.64797 - 5.64797i) q^{31} +1.00000i q^{32} +(1.56874 - 1.56874i) q^{33} +5.23332i q^{34} +(0.598775 - 1.78039i) q^{35} -1.00000i q^{36} +(-4.51960 + 4.07102i) q^{37} +(1.67943 - 1.67943i) q^{38} +(0.115499 - 0.115499i) q^{39} +(-2.00267 + 0.994632i) q^{40} -5.85724i q^{41} +0.840040 q^{42} -8.94207i q^{43} -2.21854i q^{44} +(2.00267 - 0.994632i) q^{45} +3.86710 q^{46} +(-7.97291 - 7.97291i) q^{47} +(-0.707107 - 0.707107i) q^{48} -6.29433i q^{49} +(-3.98385 - 3.02141i) q^{50} +(-3.70052 - 3.70052i) q^{51} -0.163340i q^{52} +(-7.94704 + 7.94704i) q^{53} +(0.707107 + 0.707107i) q^{54} +(4.44300 - 2.20663i) q^{55} +(0.593998 - 0.593998i) q^{56} +2.37508i q^{57} +(4.79365 + 4.79365i) q^{58} +(1.00057 + 1.00057i) q^{59} +(0.712794 - 2.11942i) q^{60} +(-7.50634 - 7.50634i) q^{61} +(5.64797 - 5.64797i) q^{62} +(-0.593998 + 0.593998i) q^{63} -1.00000 q^{64} +(0.327117 - 0.162463i) q^{65} +(1.56874 + 1.56874i) q^{66} +(5.39694 - 5.39694i) q^{67} -5.23332 q^{68} +(-2.73445 + 2.73445i) q^{69} +(1.78039 + 0.598775i) q^{70} +14.9530 q^{71} +1.00000 q^{72} +(0.258848 + 0.258848i) q^{73} +(-4.07102 - 4.51960i) q^{74} +(4.95347 - 0.680545i) q^{75} +(1.67943 + 1.67943i) q^{76} +(-1.31781 + 1.31781i) q^{77} +(0.115499 + 0.115499i) q^{78} +(-1.08732 - 1.08732i) q^{79} +(-0.994632 - 2.00267i) q^{80} -1.00000 q^{81} +5.85724 q^{82} +(-4.08091 + 4.08091i) q^{83} +0.840040i q^{84} +(-5.20523 - 10.4806i) q^{85} +8.94207 q^{86} -6.77925 q^{87} +2.21854 q^{88} +(12.5864 - 12.5864i) q^{89} +(0.994632 + 2.00267i) q^{90} +(-0.0970237 + 0.0970237i) q^{91} +3.86710i q^{92} +7.98744i q^{93} +(7.97291 - 7.97291i) q^{94} +(-1.69294 + 5.03378i) q^{95} +(0.707107 - 0.707107i) q^{96} -12.7909 q^{97} +6.29433 q^{98} -2.21854 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{4} - 4q^{7} + O(q^{10}) \) \( 40q - 40q^{4} - 4q^{7} + 4q^{14} + 40q^{16} + 24q^{17} - 40q^{18} + 4q^{19} + 8q^{22} + 8q^{25} + 8q^{26} + 4q^{28} + 28q^{31} - 4q^{33} + 20q^{35} + 20q^{37} - 4q^{38} + 4q^{39} + 16q^{42} - 16q^{47} + 16q^{51} + 20q^{53} + 16q^{55} - 4q^{56} - 4q^{59} - 8q^{61} - 28q^{62} + 4q^{63} - 40q^{64} - 4q^{65} - 4q^{66} + 16q^{67} - 24q^{68} - 8q^{69} + 12q^{70} + 40q^{71} + 40q^{72} + 8q^{73} - 8q^{74} + 16q^{75} - 4q^{76} - 24q^{77} + 4q^{78} - 12q^{79} - 40q^{81} - 24q^{82} - 8q^{83} - 8q^{85} + 8q^{87} - 8q^{88} + 12q^{89} - 24q^{91} + 16q^{94} - 28q^{95} + 40q^{97} - 56q^{98} + 8q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) −1.00000 −0.500000
\(5\) −0.994632 2.00267i −0.444813 0.895623i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) 0.593998 + 0.593998i 0.224510 + 0.224510i 0.810395 0.585884i \(-0.199253\pi\)
−0.585884 + 0.810395i \(0.699253\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) 2.00267 0.994632i 0.633301 0.314530i
\(11\) 2.21854i 0.668914i 0.942411 + 0.334457i \(0.108553\pi\)
−0.942411 + 0.334457i \(0.891447\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) 0.163340i 0.0453024i 0.999743 + 0.0226512i \(0.00721072\pi\)
−0.999743 + 0.0226512i \(0.992789\pi\)
\(14\) −0.593998 + 0.593998i −0.158753 + 0.158753i
\(15\) −0.712794 + 2.11942i −0.184043 + 0.547231i
\(16\) 1.00000 0.250000
\(17\) 5.23332 1.26927 0.634634 0.772813i \(-0.281151\pi\)
0.634634 + 0.772813i \(0.281151\pi\)
\(18\) −1.00000 −0.235702
\(19\) −1.67943 1.67943i −0.385289 0.385289i 0.487715 0.873003i \(-0.337831\pi\)
−0.873003 + 0.487715i \(0.837831\pi\)
\(20\) 0.994632 + 2.00267i 0.222407 + 0.447812i
\(21\) 0.840040i 0.183312i
\(22\) −2.21854 −0.472993
\(23\) 3.86710i 0.806346i −0.915124 0.403173i \(-0.867907\pi\)
0.915124 0.403173i \(-0.132093\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) −3.02141 + 3.98385i −0.604283 + 0.796770i
\(26\) −0.163340 −0.0320336
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −0.593998 0.593998i −0.112255 0.112255i
\(29\) 4.79365 4.79365i 0.890159 0.890159i −0.104379 0.994538i \(-0.533285\pi\)
0.994538 + 0.104379i \(0.0332854\pi\)
\(30\) −2.11942 0.712794i −0.386951 0.130138i
\(31\) −5.64797 5.64797i −1.01441 1.01441i −0.999895 0.0145112i \(-0.995381\pi\)
−0.0145112 0.999895i \(-0.504619\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.56874 1.56874i 0.273083 0.273083i
\(34\) 5.23332i 0.897508i
\(35\) 0.598775 1.78039i 0.101212 0.300942i
\(36\) 1.00000i 0.166667i
\(37\) −4.51960 + 4.07102i −0.743018 + 0.669271i
\(38\) 1.67943 1.67943i 0.272440 0.272440i
\(39\) 0.115499 0.115499i 0.0184946 0.0184946i
\(40\) −2.00267 + 0.994632i −0.316651 + 0.157265i
\(41\) 5.85724i 0.914748i −0.889275 0.457374i \(-0.848790\pi\)
0.889275 0.457374i \(-0.151210\pi\)
\(42\) 0.840040 0.129621
\(43\) 8.94207i 1.36365i −0.731514 0.681826i \(-0.761186\pi\)
0.731514 0.681826i \(-0.238814\pi\)
\(44\) 2.21854i 0.334457i
\(45\) 2.00267 0.994632i 0.298541 0.148271i
\(46\) 3.86710 0.570173
\(47\) −7.97291 7.97291i −1.16297 1.16297i −0.983823 0.179146i \(-0.942667\pi\)
−0.179146 0.983823i \(-0.557333\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 6.29433i 0.899190i
\(50\) −3.98385 3.02141i −0.563401 0.427292i
\(51\) −3.70052 3.70052i −0.518176 0.518176i
\(52\) 0.163340i 0.0226512i
\(53\) −7.94704 + 7.94704i −1.09161 + 1.09161i −0.0962535 + 0.995357i \(0.530686\pi\)
−0.995357 + 0.0962535i \(0.969314\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) 4.44300 2.20663i 0.599095 0.297541i
\(56\) 0.593998 0.593998i 0.0793763 0.0793763i
\(57\) 2.37508i 0.314587i
\(58\) 4.79365 + 4.79365i 0.629438 + 0.629438i
\(59\) 1.00057 + 1.00057i 0.130263 + 0.130263i 0.769232 0.638969i \(-0.220639\pi\)
−0.638969 + 0.769232i \(0.720639\pi\)
\(60\) 0.712794 2.11942i 0.0920213 0.273615i
\(61\) −7.50634 7.50634i −0.961088 0.961088i 0.0381827 0.999271i \(-0.487843\pi\)
−0.999271 + 0.0381827i \(0.987843\pi\)
\(62\) 5.64797 5.64797i 0.717293 0.717293i
\(63\) −0.593998 + 0.593998i −0.0748367 + 0.0748367i
\(64\) −1.00000 −0.125000
\(65\) 0.327117 0.162463i 0.0405739 0.0201511i
\(66\) 1.56874 + 1.56874i 0.193099 + 0.193099i
\(67\) 5.39694 5.39694i 0.659341 0.659341i −0.295883 0.955224i \(-0.595614\pi\)
0.955224 + 0.295883i \(0.0956138\pi\)
\(68\) −5.23332 −0.634634
\(69\) −2.73445 + 2.73445i −0.329189 + 0.329189i
\(70\) 1.78039 + 0.598775i 0.212798 + 0.0715673i
\(71\) 14.9530 1.77460 0.887299 0.461194i \(-0.152579\pi\)
0.887299 + 0.461194i \(0.152579\pi\)
\(72\) 1.00000 0.117851
\(73\) 0.258848 + 0.258848i 0.0302959 + 0.0302959i 0.722092 0.691797i \(-0.243181\pi\)
−0.691797 + 0.722092i \(0.743181\pi\)
\(74\) −4.07102 4.51960i −0.473246 0.525393i
\(75\) 4.95347 0.680545i 0.571977 0.0785826i
\(76\) 1.67943 + 1.67943i 0.192644 + 0.192644i
\(77\) −1.31781 + 1.31781i −0.150178 + 0.150178i
\(78\) 0.115499 + 0.115499i 0.0130777 + 0.0130777i
\(79\) −1.08732 1.08732i −0.122333 0.122333i 0.643290 0.765623i \(-0.277569\pi\)
−0.765623 + 0.643290i \(0.777569\pi\)
\(80\) −0.994632 2.00267i −0.111203 0.223906i
\(81\) −1.00000 −0.111111
\(82\) 5.85724 0.646824
\(83\) −4.08091 + 4.08091i −0.447938 + 0.447938i −0.894669 0.446731i \(-0.852588\pi\)
0.446731 + 0.894669i \(0.352588\pi\)
\(84\) 0.840040i 0.0916559i
\(85\) −5.20523 10.4806i −0.564587 1.13679i
\(86\) 8.94207 0.964248
\(87\) −6.77925 −0.726812
\(88\) 2.21854 0.236497
\(89\) 12.5864 12.5864i 1.33415 1.33415i 0.432539 0.901615i \(-0.357618\pi\)
0.901615 0.432539i \(-0.142382\pi\)
\(90\) 0.994632 + 2.00267i 0.104843 + 0.211100i
\(91\) −0.0970237 + 0.0970237i −0.0101708 + 0.0101708i
\(92\) 3.86710i 0.403173i
\(93\) 7.98744i 0.828259i
\(94\) 7.97291 7.97291i 0.822343 0.822343i
\(95\) −1.69294 + 5.03378i −0.173692 + 0.516455i
\(96\) 0.707107 0.707107i 0.0721688 0.0721688i
\(97\) −12.7909 −1.29872 −0.649359 0.760482i \(-0.724963\pi\)
−0.649359 + 0.760482i \(0.724963\pi\)
\(98\) 6.29433 0.635824
\(99\) −2.21854 −0.222971
\(100\) 3.02141 3.98385i 0.302141 0.398385i
\(101\) 4.31584i 0.429442i 0.976675 + 0.214721i \(0.0688842\pi\)
−0.976675 + 0.214721i \(0.931116\pi\)
\(102\) 3.70052 3.70052i 0.366406 0.366406i
\(103\) −13.9487 −1.37440 −0.687202 0.726467i \(-0.741161\pi\)
−0.687202 + 0.726467i \(0.741161\pi\)
\(104\) 0.163340 0.0160168
\(105\) −1.68233 + 0.835531i −0.164178 + 0.0815395i
\(106\) −7.94704 7.94704i −0.771885 0.771885i
\(107\) 5.53603 + 5.53603i 0.535189 + 0.535189i 0.922112 0.386923i \(-0.126462\pi\)
−0.386923 + 0.922112i \(0.626462\pi\)
\(108\) −0.707107 + 0.707107i −0.0680414 + 0.0680414i
\(109\) 9.96395 + 9.96395i 0.954373 + 0.954373i 0.999004 0.0446302i \(-0.0142109\pi\)
−0.0446302 + 0.999004i \(0.514211\pi\)
\(110\) 2.20663 + 4.44300i 0.210394 + 0.423624i
\(111\) 6.07449 + 0.317197i 0.576565 + 0.0301070i
\(112\) 0.593998 + 0.593998i 0.0561275 + 0.0561275i
\(113\) 18.7870 1.76733 0.883665 0.468120i \(-0.155068\pi\)
0.883665 + 0.468120i \(0.155068\pi\)
\(114\) −2.37508 −0.222447
\(115\) −7.74455 + 3.84634i −0.722183 + 0.358673i
\(116\) −4.79365 + 4.79365i −0.445080 + 0.445080i
\(117\) −0.163340 −0.0151008
\(118\) −1.00057 + 1.00057i −0.0921100 + 0.0921100i
\(119\) 3.10858 + 3.10858i 0.284963 + 0.284963i
\(120\) 2.11942 + 0.712794i 0.193475 + 0.0650689i
\(121\) 6.07810 0.552555
\(122\) 7.50634 7.50634i 0.679592 0.679592i
\(123\) −4.14170 + 4.14170i −0.373444 + 0.373444i
\(124\) 5.64797 + 5.64797i 0.507203 + 0.507203i
\(125\) 10.9836 + 2.08844i 0.982399 + 0.186796i
\(126\) −0.593998 0.593998i −0.0529175 0.0529175i
\(127\) 4.61246 + 4.61246i 0.409290 + 0.409290i 0.881491 0.472201i \(-0.156540\pi\)
−0.472201 + 0.881491i \(0.656540\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −6.32300 + 6.32300i −0.556709 + 0.556709i
\(130\) 0.162463 + 0.327117i 0.0142490 + 0.0286901i
\(131\) −11.9955 11.9955i −1.04805 1.04805i −0.998786 0.0492667i \(-0.984312\pi\)
−0.0492667 0.998786i \(-0.515688\pi\)
\(132\) −1.56874 + 1.56874i −0.136541 + 0.136541i
\(133\) 1.99516i 0.173002i
\(134\) 5.39694 + 5.39694i 0.466225 + 0.466225i
\(135\) −2.11942 0.712794i −0.182410 0.0613475i
\(136\) 5.23332i 0.448754i
\(137\) −2.69211 2.69211i −0.230002 0.230002i 0.582691 0.812694i \(-0.302000\pi\)
−0.812694 + 0.582691i \(0.802000\pi\)
\(138\) −2.73445 2.73445i −0.232772 0.232772i
\(139\) −1.30467 −0.110661 −0.0553305 0.998468i \(-0.517621\pi\)
−0.0553305 + 0.998468i \(0.517621\pi\)
\(140\) −0.598775 + 1.78039i −0.0506058 + 0.150471i
\(141\) 11.2754i 0.949560i
\(142\) 14.9530i 1.25483i
\(143\) −0.362376 −0.0303034
\(144\) 1.00000i 0.0833333i
\(145\) −14.3681 4.83221i −1.19320 0.401293i
\(146\) −0.258848 + 0.258848i −0.0214224 + 0.0214224i
\(147\) −4.45077 + 4.45077i −0.367093 + 0.367093i
\(148\) 4.51960 4.07102i 0.371509 0.334636i
\(149\) 9.07290i 0.743281i 0.928377 + 0.371640i \(0.121205\pi\)
−0.928377 + 0.371640i \(0.878795\pi\)
\(150\) 0.680545 + 4.95347i 0.0555663 + 0.404449i
\(151\) 0.0622104i 0.00506261i 0.999997 + 0.00253130i \(0.000805740\pi\)
−0.999997 + 0.00253130i \(0.999194\pi\)
\(152\) −1.67943 + 1.67943i −0.136220 + 0.136220i
\(153\) 5.23332i 0.423089i
\(154\) −1.31781 1.31781i −0.106192 0.106192i
\(155\) −5.69340 + 16.9287i −0.457305 + 1.35975i
\(156\) −0.115499 + 0.115499i −0.00924731 + 0.00924731i
\(157\) −5.08868 5.08868i −0.406121 0.406121i 0.474263 0.880383i \(-0.342715\pi\)
−0.880383 + 0.474263i \(0.842715\pi\)
\(158\) 1.08732 1.08732i 0.0865023 0.0865023i
\(159\) 11.2388 0.891296
\(160\) 2.00267 0.994632i 0.158325 0.0786326i
\(161\) 2.29705 2.29705i 0.181033 0.181033i
\(162\) 1.00000i 0.0785674i
\(163\) −19.1109 −1.49688 −0.748441 0.663201i \(-0.769197\pi\)
−0.748441 + 0.663201i \(0.769197\pi\)
\(164\) 5.85724i 0.457374i
\(165\) −4.70200 1.58136i −0.366050 0.123109i
\(166\) −4.08091 4.08091i −0.316740 0.316740i
\(167\) −7.28469 −0.563706 −0.281853 0.959458i \(-0.590949\pi\)
−0.281853 + 0.959458i \(0.590949\pi\)
\(168\) −0.840040 −0.0648105
\(169\) 12.9733 0.997948
\(170\) 10.4806 5.20523i 0.803829 0.399223i
\(171\) 1.67943 1.67943i 0.128430 0.128430i
\(172\) 8.94207i 0.681826i
\(173\) 8.94815 + 8.94815i 0.680315 + 0.680315i 0.960071 0.279756i \(-0.0902536\pi\)
−0.279756 + 0.960071i \(0.590254\pi\)
\(174\) 6.77925i 0.513934i
\(175\) −4.16111 + 0.571685i −0.314551 + 0.0432154i
\(176\) 2.21854i 0.167228i
\(177\) 1.41502i 0.106359i
\(178\) 12.5864 + 12.5864i 0.943390 + 0.943390i
\(179\) 17.4301 17.4301i 1.30279 1.30279i 0.376287 0.926503i \(-0.377201\pi\)
0.926503 0.376287i \(-0.122799\pi\)
\(180\) −2.00267 + 0.994632i −0.149271 + 0.0741355i
\(181\) 3.39361 0.252245 0.126122 0.992015i \(-0.459747\pi\)
0.126122 + 0.992015i \(0.459747\pi\)
\(182\) −0.0970237 0.0970237i −0.00719188 0.00719188i
\(183\) 10.6156i 0.784725i
\(184\) −3.86710 −0.285086
\(185\) 12.6483 + 5.00213i 0.929919 + 0.367764i
\(186\) −7.98744 −0.585668
\(187\) 11.6103i 0.849030i
\(188\) 7.97291 + 7.97291i 0.581484 + 0.581484i
\(189\) 0.840040 0.0611039
\(190\) −5.03378 1.69294i −0.365189 0.122819i
\(191\) 1.08400 1.08400i 0.0784355 0.0784355i −0.666801 0.745236i \(-0.732337\pi\)
0.745236 + 0.666801i \(0.232337\pi\)
\(192\) 0.707107 + 0.707107i 0.0510310 + 0.0510310i
\(193\) 4.04039i 0.290834i −0.989370 0.145417i \(-0.953548\pi\)
0.989370 0.145417i \(-0.0464523\pi\)
\(194\) 12.7909i 0.918332i
\(195\) −0.346186 0.116428i −0.0247909 0.00833757i
\(196\) 6.29433i 0.449595i
\(197\) −12.3544 12.3544i −0.880214 0.880214i 0.113342 0.993556i \(-0.463844\pi\)
−0.993556 + 0.113342i \(0.963844\pi\)
\(198\) 2.21854i 0.157664i
\(199\) −5.19861 + 5.19861i −0.368519 + 0.368519i −0.866937 0.498418i \(-0.833915\pi\)
0.498418 + 0.866937i \(0.333915\pi\)
\(200\) 3.98385 + 3.02141i 0.281701 + 0.213646i
\(201\) −7.63243 −0.538350
\(202\) −4.31584 −0.303661
\(203\) 5.69484 0.399699
\(204\) 3.70052 + 3.70052i 0.259088 + 0.259088i
\(205\) −11.7302 + 5.82580i −0.819269 + 0.406892i
\(206\) 13.9487i 0.971850i
\(207\) 3.86710 0.268782
\(208\) 0.163340i 0.0113256i
\(209\) 3.72588 3.72588i 0.257725 0.257725i
\(210\) −0.835531 1.68233i −0.0576571 0.116092i
\(211\) −15.2308 −1.04853 −0.524264 0.851556i \(-0.675660\pi\)
−0.524264 + 0.851556i \(0.675660\pi\)
\(212\) 7.94704 7.94704i 0.545805 0.545805i
\(213\) −10.5734 10.5734i −0.724477 0.724477i
\(214\) −5.53603 + 5.53603i −0.378435 + 0.378435i
\(215\) −17.9081 + 8.89407i −1.22132 + 0.606571i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) 6.70977i 0.455489i
\(218\) −9.96395 + 9.96395i −0.674844 + 0.674844i
\(219\) 0.366066i 0.0247365i
\(220\) −4.44300 + 2.20663i −0.299547 + 0.148771i
\(221\) 0.854812i 0.0575009i
\(222\) −0.317197 + 6.07449i −0.0212888 + 0.407693i
\(223\) 9.25821 9.25821i 0.619976 0.619976i −0.325549 0.945525i \(-0.605549\pi\)
0.945525 + 0.325549i \(0.105549\pi\)
\(224\) −0.593998 + 0.593998i −0.0396882 + 0.0396882i
\(225\) −3.98385 3.02141i −0.265590 0.201428i
\(226\) 18.7870i 1.24969i
\(227\) −12.5313 −0.831734 −0.415867 0.909425i \(-0.636522\pi\)
−0.415867 + 0.909425i \(0.636522\pi\)
\(228\) 2.37508i 0.157293i
\(229\) 7.37486i 0.487345i 0.969858 + 0.243672i \(0.0783521\pi\)
−0.969858 + 0.243672i \(0.921648\pi\)
\(230\) −3.84634 7.74455i −0.253620 0.510660i
\(231\) 1.86366 0.122620
\(232\) −4.79365 4.79365i −0.314719 0.314719i
\(233\) 18.4468 + 18.4468i 1.20849 + 1.20849i 0.971517 + 0.236971i \(0.0761545\pi\)
0.236971 + 0.971517i \(0.423846\pi\)
\(234\) 0.163340i 0.0106779i
\(235\) −8.03703 + 23.8973i −0.524278 + 1.55889i
\(236\) −1.00057 1.00057i −0.0651316 0.0651316i
\(237\) 1.53770i 0.0998843i
\(238\) −3.10858 + 3.10858i −0.201500 + 0.201500i
\(239\) −10.9427 10.9427i −0.707825 0.707825i 0.258252 0.966077i \(-0.416853\pi\)
−0.966077 + 0.258252i \(0.916853\pi\)
\(240\) −0.712794 + 2.11942i −0.0460106 + 0.136808i
\(241\) 11.4584 11.4584i 0.738102 0.738102i −0.234108 0.972211i \(-0.575217\pi\)
0.972211 + 0.234108i \(0.0752170\pi\)
\(242\) 6.07810i 0.390715i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 7.50634 + 7.50634i 0.480544 + 0.480544i
\(245\) −12.6055 + 6.26055i −0.805336 + 0.399972i
\(246\) −4.14170 4.14170i −0.264065 0.264065i
\(247\) 0.274319 0.274319i 0.0174545 0.0174545i
\(248\) −5.64797 + 5.64797i −0.358647 + 0.358647i
\(249\) 5.77128 0.365740
\(250\) −2.08844 + 10.9836i −0.132085 + 0.694661i
\(251\) −4.90961 4.90961i −0.309892 0.309892i 0.534976 0.844867i \(-0.320321\pi\)
−0.844867 + 0.534976i \(0.820321\pi\)
\(252\) 0.593998 0.593998i 0.0374184 0.0374184i
\(253\) 8.57930 0.539376
\(254\) −4.61246 + 4.61246i −0.289412 + 0.289412i
\(255\) −3.73028 + 11.0916i −0.233599 + 0.694582i
\(256\) 1.00000 0.0625000
\(257\) 20.1402 1.25631 0.628155 0.778088i \(-0.283810\pi\)
0.628155 + 0.778088i \(0.283810\pi\)
\(258\) −6.32300 6.32300i −0.393653 0.393653i
\(259\) −5.10281 0.266458i −0.317073 0.0165569i
\(260\) −0.327117 + 0.162463i −0.0202869 + 0.0100756i
\(261\) 4.79365 + 4.79365i 0.296720 + 0.296720i
\(262\) 11.9955 11.9955i 0.741085 0.741085i
\(263\) −5.00770 5.00770i −0.308788 0.308788i 0.535651 0.844439i \(-0.320066\pi\)
−0.844439 + 0.535651i \(0.820066\pi\)
\(264\) −1.56874 1.56874i −0.0965493 0.0965493i
\(265\) 23.8197 + 8.01096i 1.46323 + 0.492109i
\(266\) 1.99516 0.122331
\(267\) −17.7998 −1.08933
\(268\) −5.39694 + 5.39694i −0.329671 + 0.329671i
\(269\) 12.0216i 0.732969i −0.930424 0.366485i \(-0.880561\pi\)
0.930424 0.366485i \(-0.119439\pi\)
\(270\) 0.712794 2.11942i 0.0433792 0.128984i
\(271\) −11.5944 −0.704308 −0.352154 0.935942i \(-0.614551\pi\)
−0.352154 + 0.935942i \(0.614551\pi\)
\(272\) 5.23332 0.317317
\(273\) 0.137212 0.00830446
\(274\) 2.69211 2.69211i 0.162636 0.162636i
\(275\) −8.83831 6.70311i −0.532970 0.404213i
\(276\) 2.73445 2.73445i 0.164595 0.164595i
\(277\) 1.48164i 0.0890229i 0.999009 + 0.0445115i \(0.0141731\pi\)
−0.999009 + 0.0445115i \(0.985827\pi\)
\(278\) 1.30467i 0.0782491i
\(279\) 5.64797 5.64797i 0.338135 0.338135i
\(280\) −1.78039 0.598775i −0.106399 0.0357837i
\(281\) 2.20394 2.20394i 0.131476 0.131476i −0.638306 0.769782i \(-0.720365\pi\)
0.769782 + 0.638306i \(0.220365\pi\)
\(282\) −11.2754 −0.671440
\(283\) 12.9583 0.770291 0.385145 0.922856i \(-0.374151\pi\)
0.385145 + 0.922856i \(0.374151\pi\)
\(284\) −14.9530 −0.887299
\(285\) 4.75651 2.36233i 0.281751 0.139932i
\(286\) 0.362376i 0.0214277i
\(287\) 3.47919 3.47919i 0.205370 0.205370i
\(288\) −1.00000 −0.0589256
\(289\) 10.3877 0.611040
\(290\) 4.83221 14.3681i 0.283757 0.843721i
\(291\) 9.04452 + 9.04452i 0.530199 + 0.530199i
\(292\) −0.258848 0.258848i −0.0151479 0.0151479i
\(293\) −15.2639 + 15.2639i −0.891729 + 0.891729i −0.994686 0.102956i \(-0.967170\pi\)
0.102956 + 0.994686i \(0.467170\pi\)
\(294\) −4.45077 4.45077i −0.259574 0.259574i
\(295\) 1.00862 2.99902i 0.0587240 0.174610i
\(296\) 4.07102 + 4.51960i 0.236623 + 0.262697i
\(297\) 1.56874 + 1.56874i 0.0910276 + 0.0910276i
\(298\) −9.07290 −0.525579
\(299\) 0.631653 0.0365294
\(300\) −4.95347 + 0.680545i −0.285989 + 0.0392913i
\(301\) 5.31157 5.31157i 0.306154 0.306154i
\(302\) −0.0622104 −0.00357980
\(303\) 3.05176 3.05176i 0.175319 0.175319i
\(304\) −1.67943 1.67943i −0.0963222 0.0963222i
\(305\) −7.56671 + 22.4988i −0.433268 + 1.28828i
\(306\) −5.23332 −0.299169
\(307\) −20.5532 + 20.5532i −1.17303 + 1.17303i −0.191547 + 0.981483i \(0.561350\pi\)
−0.981483 + 0.191547i \(0.938650\pi\)
\(308\) 1.31781 1.31781i 0.0750889 0.0750889i
\(309\) 9.86320 + 9.86320i 0.561098 + 0.561098i
\(310\) −16.9287 5.69340i −0.961486 0.323363i
\(311\) 0.612480 + 0.612480i 0.0347305 + 0.0347305i 0.724259 0.689528i \(-0.242182\pi\)
−0.689528 + 0.724259i \(0.742182\pi\)
\(312\) −0.115499 0.115499i −0.00653884 0.00653884i
\(313\) 3.56579i 0.201550i −0.994909 0.100775i \(-0.967868\pi\)
0.994909 0.100775i \(-0.0321322\pi\)
\(314\) 5.08868 5.08868i 0.287171 0.287171i
\(315\) 1.78039 + 0.598775i 0.100314 + 0.0337372i
\(316\) 1.08732 + 1.08732i 0.0611664 + 0.0611664i
\(317\) 4.20992 4.20992i 0.236453 0.236453i −0.578927 0.815380i \(-0.696528\pi\)
0.815380 + 0.578927i \(0.196528\pi\)
\(318\) 11.2388i 0.630242i
\(319\) 10.6349 + 10.6349i 0.595439 + 0.595439i
\(320\) 0.994632 + 2.00267i 0.0556016 + 0.111953i
\(321\) 7.82913i 0.436980i
\(322\) 2.29705 + 2.29705i 0.128010 + 0.128010i
\(323\) −8.78902 8.78902i −0.489034 0.489034i
\(324\) 1.00000 0.0555556
\(325\) −0.650723 0.493518i −0.0360956 0.0273755i
\(326\) 19.1109i 1.05846i
\(327\) 14.0912i 0.779243i
\(328\) −5.85724 −0.323412
\(329\) 9.47178i 0.522196i
\(330\) 1.58136 4.70200i 0.0870509 0.258837i
\(331\) 14.0919 14.0919i 0.774561 0.774561i −0.204339 0.978900i \(-0.565505\pi\)
0.978900 + 0.204339i \(0.0655045\pi\)
\(332\) 4.08091 4.08091i 0.223969 0.223969i
\(333\) −4.07102 4.51960i −0.223090 0.247673i
\(334\) 7.28469i 0.398601i
\(335\) −16.1763 5.44035i −0.883805 0.297238i
\(336\) 0.840040i 0.0458279i
\(337\) −17.5011 + 17.5011i −0.953348 + 0.953348i −0.998959 0.0456112i \(-0.985476\pi\)
0.0456112 + 0.998959i \(0.485476\pi\)
\(338\) 12.9733i 0.705656i
\(339\) −13.2844 13.2844i −0.721510 0.721510i
\(340\) 5.20523 + 10.4806i 0.282293 + 0.568393i
\(341\) 12.5302 12.5302i 0.678550 0.678550i
\(342\) 1.67943 + 1.67943i 0.0908134 + 0.0908134i
\(343\) 7.89681 7.89681i 0.426388 0.426388i
\(344\) −8.94207 −0.482124
\(345\) 8.19600 + 2.75645i 0.441258 + 0.148402i
\(346\) −8.94815 + 8.94815i −0.481055 + 0.481055i
\(347\) 19.3835i 1.04056i 0.853996 + 0.520280i \(0.174173\pi\)
−0.853996 + 0.520280i \(0.825827\pi\)
\(348\) 6.77925 0.363406
\(349\) 14.5408i 0.778350i 0.921164 + 0.389175i \(0.127240\pi\)
−0.921164 + 0.389175i \(0.872760\pi\)
\(350\) −0.571685 4.16111i −0.0305579 0.222421i
\(351\) 0.115499 + 0.115499i 0.00616488 + 0.00616488i
\(352\) −2.21854 −0.118248
\(353\) 26.3150 1.40060 0.700302 0.713847i \(-0.253049\pi\)
0.700302 + 0.713847i \(0.253049\pi\)
\(354\) 1.41502 0.0752075
\(355\) −14.8728 29.9461i −0.789365 1.58937i
\(356\) −12.5864 + 12.5864i −0.667077 + 0.667077i
\(357\) 4.39620i 0.232672i
\(358\) 17.4301 + 17.4301i 0.921212 + 0.921212i
\(359\) 6.12864i 0.323457i −0.986835 0.161729i \(-0.948293\pi\)
0.986835 0.161729i \(-0.0517069\pi\)
\(360\) −0.994632 2.00267i −0.0524217 0.105550i
\(361\) 13.3590i 0.703105i
\(362\) 3.39361i 0.178364i
\(363\) −4.29787 4.29787i −0.225580 0.225580i
\(364\) 0.0970237 0.0970237i 0.00508542 0.00508542i
\(365\) 0.260930 0.775847i 0.0136577 0.0406097i
\(366\) −10.6156 −0.554884
\(367\) 21.0105 + 21.0105i 1.09674 + 1.09674i 0.994789 + 0.101950i \(0.0325083\pi\)
0.101950 + 0.994789i \(0.467492\pi\)
\(368\) 3.86710i 0.201587i
\(369\) 5.85724 0.304916
\(370\) −5.00213 + 12.6483i −0.260048 + 0.657552i
\(371\) −9.44106 −0.490155
\(372\) 7.98744i 0.414129i
\(373\) 2.15543 + 2.15543i 0.111604 + 0.111604i 0.760703 0.649100i \(-0.224854\pi\)
−0.649100 + 0.760703i \(0.724854\pi\)
\(374\) −11.6103 −0.600355
\(375\) −6.28979 9.24330i −0.324803 0.477322i
\(376\) −7.97291 + 7.97291i −0.411171 + 0.411171i
\(377\) 0.782996 + 0.782996i 0.0403263 + 0.0403263i
\(378\) 0.840040i 0.0432070i
\(379\) 37.8733i 1.94542i 0.232022 + 0.972711i \(0.425466\pi\)
−0.232022 + 0.972711i \(0.574534\pi\)
\(380\) 1.69294 5.03378i 0.0868461 0.258228i
\(381\) 6.52301i 0.334184i
\(382\) 1.08400 + 1.08400i 0.0554622 + 0.0554622i
\(383\) 33.6750i 1.72071i 0.509695 + 0.860355i \(0.329758\pi\)
−0.509695 + 0.860355i \(0.670242\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) 3.94987 + 1.32840i 0.201304 + 0.0677017i
\(386\) 4.04039 0.205650
\(387\) 8.94207 0.454551
\(388\) 12.7909 0.649359
\(389\) 6.96706 + 6.96706i 0.353244 + 0.353244i 0.861315 0.508071i \(-0.169641\pi\)
−0.508071 + 0.861315i \(0.669641\pi\)
\(390\) 0.116428 0.346186i 0.00589555 0.0175298i
\(391\) 20.2378i 1.02347i
\(392\) −6.29433 −0.317912
\(393\) 16.9642i 0.855731i
\(394\) 12.3544 12.3544i 0.622405 0.622405i
\(395\) −1.09606 + 3.25902i −0.0551489 + 0.163979i
\(396\) 2.21854 0.111486
\(397\) −2.14584 + 2.14584i −0.107697 + 0.107697i −0.758902 0.651205i \(-0.774264\pi\)
0.651205 + 0.758902i \(0.274264\pi\)
\(398\) −5.19861 5.19861i −0.260583 0.260583i
\(399\) −1.41079 + 1.41079i −0.0706279 + 0.0706279i
\(400\) −3.02141 + 3.98385i −0.151071 + 0.199192i
\(401\) 3.17371 + 3.17371i 0.158488 + 0.158488i 0.781896 0.623409i \(-0.214253\pi\)
−0.623409 + 0.781896i \(0.714253\pi\)
\(402\) 7.63243i 0.380671i
\(403\) 0.922541 0.922541i 0.0459550 0.0459550i
\(404\) 4.31584i 0.214721i
\(405\) 0.994632 + 2.00267i 0.0494237 + 0.0995137i
\(406\) 5.69484i 0.282630i
\(407\) −9.03170 10.0269i −0.447685 0.497015i
\(408\) −3.70052 + 3.70052i −0.183203 + 0.183203i
\(409\) −7.23143 + 7.23143i −0.357571 + 0.357571i −0.862917 0.505346i \(-0.831365\pi\)
0.505346 + 0.862917i \(0.331365\pi\)
\(410\) −5.82580 11.7302i −0.287716 0.579311i
\(411\) 3.80721i 0.187796i
\(412\) 13.9487 0.687202
\(413\) 1.18867i 0.0584908i
\(414\) 3.86710i 0.190058i
\(415\) 12.2317 + 4.11373i 0.600432 + 0.201935i
\(416\) −0.163340 −0.00800841
\(417\) 0.922543 + 0.922543i 0.0451771 + 0.0451771i
\(418\) 3.72588 + 3.72588i 0.182239 + 0.182239i
\(419\) 1.66410i 0.0812966i 0.999174 + 0.0406483i \(0.0129423\pi\)
−0.999174 + 0.0406483i \(0.987058\pi\)
\(420\) 1.68233 0.835531i 0.0820892 0.0407697i
\(421\) −1.49656 1.49656i −0.0729381 0.0729381i 0.669697 0.742635i \(-0.266424\pi\)
−0.742635 + 0.669697i \(0.766424\pi\)
\(422\) 15.2308i 0.741422i
\(423\) 7.97291 7.97291i 0.387656 0.387656i
\(424\) 7.94704 + 7.94704i 0.385943 + 0.385943i
\(425\) −15.8120 + 20.8488i −0.766996 + 1.01131i
\(426\) 10.5734 10.5734i 0.512283 0.512283i
\(427\) 8.91750i 0.431548i
\(428\) −5.53603 5.53603i −0.267594 0.267594i
\(429\) 0.256238 + 0.256238i 0.0123713 + 0.0123713i
\(430\) −8.89407 17.9081i −0.428910 0.863603i
\(431\) 1.82566 + 1.82566i 0.0879392 + 0.0879392i 0.749708 0.661769i \(-0.230194\pi\)
−0.661769 + 0.749708i \(0.730194\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) 8.92738 8.92738i 0.429023 0.429023i −0.459273 0.888295i \(-0.651890\pi\)
0.888295 + 0.459273i \(0.151890\pi\)
\(434\) 6.70977 0.322079
\(435\) 6.74286 + 13.5766i 0.323295 + 0.650950i
\(436\) −9.96395 9.96395i −0.477187 0.477187i
\(437\) −6.49454 + 6.49454i −0.310676 + 0.310676i
\(438\) 0.366066 0.0174913
\(439\) −12.1430 + 12.1430i −0.579555 + 0.579555i −0.934781 0.355225i \(-0.884404\pi\)
0.355225 + 0.934781i \(0.384404\pi\)
\(440\) −2.20663 4.44300i −0.105197 0.211812i
\(441\) 6.29433 0.299730
\(442\) −0.854812 −0.0406593
\(443\) −20.3377 20.3377i −0.966271 0.966271i 0.0331781 0.999449i \(-0.489437\pi\)
−0.999449 + 0.0331781i \(0.989437\pi\)
\(444\) −6.07449 0.317197i −0.288282 0.0150535i
\(445\) −37.7253 12.6876i −1.78835 0.601451i
\(446\) 9.25821 + 9.25821i 0.438389 + 0.438389i
\(447\) 6.41551 6.41551i 0.303443 0.303443i
\(448\) −0.593998 0.593998i −0.0280638 0.0280638i
\(449\) −5.53101 5.53101i −0.261024 0.261024i 0.564446 0.825470i \(-0.309090\pi\)
−0.825470 + 0.564446i \(0.809090\pi\)
\(450\) 3.02141 3.98385i 0.142431 0.187800i
\(451\) 12.9945 0.611887
\(452\) −18.7870 −0.883665
\(453\) 0.0439894 0.0439894i 0.00206680 0.00206680i
\(454\) 12.5313i 0.588125i
\(455\) 0.290810 + 0.0978040i 0.0136334 + 0.00458512i
\(456\) 2.37508 0.111223
\(457\) −23.3394 −1.09177 −0.545884 0.837861i \(-0.683806\pi\)
−0.545884 + 0.837861i \(0.683806\pi\)
\(458\) −7.37486 −0.344605
\(459\) 3.70052 3.70052i 0.172725 0.172725i
\(460\) 7.74455 3.84634i 0.361091 0.179337i
\(461\) 22.7009 22.7009i 1.05728 1.05728i 0.0590285 0.998256i \(-0.481200\pi\)
0.998256 0.0590285i \(-0.0188003\pi\)
\(462\) 1.86366i 0.0867052i
\(463\) 0.607463i 0.0282312i −0.999900 0.0141156i \(-0.995507\pi\)
0.999900 0.0141156i \(-0.00449329\pi\)
\(464\) 4.79365 4.79365i 0.222540 0.222540i
\(465\) 15.9962 7.94457i 0.741808 0.368420i
\(466\) −18.4468 + 18.4468i −0.854530 + 0.854530i
\(467\) −8.76294 −0.405500 −0.202750 0.979230i \(-0.564988\pi\)
−0.202750 + 0.979230i \(0.564988\pi\)
\(468\) 0.163340 0.00755040
\(469\) 6.41155 0.296058
\(470\) −23.8973 8.03703i −1.10230 0.370721i
\(471\) 7.19648i 0.331596i
\(472\) 1.00057 1.00057i 0.0460550 0.0460550i
\(473\) 19.8383 0.912166
\(474\) −1.53770 −0.0706288
\(475\) 11.7649 1.61635i 0.539810 0.0741632i
\(476\) −3.10858 3.10858i −0.142482 0.142482i
\(477\) −7.94704 7.94704i −0.363870 0.363870i
\(478\) 10.9427 10.9427i 0.500508 0.500508i
\(479\) −6.88917 6.88917i −0.314774 0.314774i 0.531982 0.846756i \(-0.321448\pi\)
−0.846756 + 0.531982i \(0.821448\pi\)
\(480\) −2.11942 0.712794i −0.0967377 0.0325344i
\(481\) −0.664961 0.738233i −0.0303196 0.0336605i
\(482\) 11.4584 + 11.4584i 0.521917 + 0.521917i
\(483\) −3.24852 −0.147813
\(484\) −6.07810 −0.276277
\(485\) 12.7222 + 25.6160i 0.577686 + 1.16316i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) 18.0453 0.817709 0.408855 0.912599i \(-0.365928\pi\)
0.408855 + 0.912599i \(0.365928\pi\)
\(488\) −7.50634 + 7.50634i −0.339796 + 0.339796i
\(489\) 13.5135 + 13.5135i 0.611100 + 0.611100i
\(490\) −6.26055 12.6055i −0.282823 0.569459i
\(491\) 41.7594 1.88457 0.942287 0.334807i \(-0.108671\pi\)
0.942287 + 0.334807i \(0.108671\pi\)
\(492\) 4.14170 4.14170i 0.186722 0.186722i
\(493\) 25.0867 25.0867i 1.12985 1.12985i
\(494\) 0.274319 + 0.274319i 0.0123422 + 0.0123422i
\(495\) 2.20663 + 4.44300i 0.0991805 + 0.199698i
\(496\) −5.64797 5.64797i −0.253601 0.253601i
\(497\) 8.88207 + 8.88207i 0.398415 + 0.398415i
\(498\) 5.77128i 0.258617i
\(499\) −6.17352 + 6.17352i −0.276365 + 0.276365i −0.831656 0.555291i \(-0.812607\pi\)
0.555291 + 0.831656i \(0.312607\pi\)
\(500\) −10.9836 2.08844i −0.491199 0.0933980i
\(501\) 5.15105 + 5.15105i 0.230132 + 0.230132i
\(502\) 4.90961 4.90961i 0.219127 0.219127i
\(503\) 0.796966i 0.0355350i 0.999842 + 0.0177675i \(0.00565586\pi\)
−0.999842 + 0.0177675i \(0.994344\pi\)
\(504\) 0.593998 + 0.593998i 0.0264588 + 0.0264588i
\(505\) 8.64322 4.29267i 0.384618 0.191021i
\(506\) 8.57930i 0.381396i
\(507\) −9.17352 9.17352i −0.407410 0.407410i
\(508\) −4.61246 4.61246i −0.204645 0.204645i
\(509\) 4.90293 0.217319 0.108659 0.994079i \(-0.465344\pi\)
0.108659 + 0.994079i \(0.465344\pi\)
\(510\) −11.0916 3.73028i −0.491144 0.165180i
\(511\) 0.307510i 0.0136035i
\(512\) 1.00000i 0.0441942i
\(513\) −2.37508 −0.104862
\(514\) 20.1402i 0.888346i
\(515\) 13.8738 + 27.9347i 0.611353 + 1.23095i
\(516\) 6.32300 6.32300i 0.278354 0.278354i
\(517\) 17.6882 17.6882i 0.777925 0.777925i
\(518\) 0.266458 5.10281i 0.0117075 0.224205i
\(519\) 12.6546i 0.555475i
\(520\) −0.162463 0.327117i −0.00712449 0.0143450i
\(521\) 27.5443i 1.20674i −0.797462 0.603369i \(-0.793825\pi\)
0.797462 0.603369i \(-0.206175\pi\)
\(522\) −4.79365 + 4.79365i −0.209813 + 0.209813i
\(523\) 43.9195i 1.92046i −0.279204 0.960232i \(-0.590070\pi\)
0.279204 0.960232i \(-0.409930\pi\)
\(524\) 11.9955 + 11.9955i 0.524026 + 0.524026i
\(525\) 3.34659 + 2.53811i 0.146057 + 0.110772i
\(526\) 5.00770 5.00770i 0.218346 0.218346i
\(527\) −29.5577 29.5577i −1.28755 1.28755i
\(528\) 1.56874 1.56874i 0.0682707 0.0682707i
\(529\) 8.04553 0.349806
\(530\) −8.01096 + 23.8197i −0.347974 + 1.03466i
\(531\) −1.00057 + 1.00057i −0.0434211 + 0.0434211i
\(532\) 1.99516i 0.0865012i
\(533\) 0.956723 0.0414403
\(534\) 17.7998i 0.770274i
\(535\) 5.58056 16.5932i 0.241269 0.717386i
\(536\) −5.39694 5.39694i −0.233112 0.233112i
\(537\) −24.6499 −1.06372
\(538\) 12.0216 0.518288
\(539\) 13.9642 0.601481
\(540\) 2.11942 + 0.712794i 0.0912052 + 0.0306738i
\(541\) 6.90527 6.90527i 0.296881 0.296881i −0.542910 0.839791i \(-0.682678\pi\)
0.839791 + 0.542910i \(0.182678\pi\)
\(542\) 11.5944i 0.498021i
\(543\) −2.39964 2.39964i −0.102979 0.102979i
\(544\) 5.23332i 0.224377i
\(545\) 10.0441 29.8650i 0.430241 1.27928i
\(546\) 0.137212i 0.00587214i
\(547\) 19.7636i 0.845030i 0.906356 + 0.422515i \(0.138853\pi\)
−0.906356 + 0.422515i \(0.861147\pi\)
\(548\) 2.69211 + 2.69211i 0.115001 + 0.115001i
\(549\) 7.50634 7.50634i 0.320363 0.320363i
\(550\) 6.70311 8.83831i 0.285822 0.376867i
\(551\) −16.1013 −0.685936
\(552\) 2.73445 + 2.73445i 0.116386 + 0.116386i
\(553\) 1.29173i 0.0549299i
\(554\) −1.48164 −0.0629487
\(555\) −5.40664 12.4807i −0.229499 0.529777i
\(556\) 1.30467 0.0553305
\(557\) 32.5498i 1.37918i 0.724201 + 0.689589i \(0.242209\pi\)
−0.724201 + 0.689589i \(0.757791\pi\)
\(558\) 5.64797 + 5.64797i 0.239098 + 0.239098i
\(559\) 1.46060 0.0617767
\(560\) 0.598775 1.78039i 0.0253029 0.0752354i
\(561\) 8.20973 8.20973i 0.346615 0.346615i
\(562\) 2.20394 + 2.20394i 0.0929675 + 0.0929675i
\(563\) 9.04112i 0.381038i 0.981684 + 0.190519i \(0.0610170\pi\)
−0.981684 + 0.190519i \(0.938983\pi\)
\(564\) 11.2754i 0.474780i
\(565\) −18.6861 37.6242i −0.786132 1.58286i
\(566\) 12.9583i 0.544678i
\(567\) −0.593998 0.593998i −0.0249456 0.0249456i
\(568\) 14.9530i 0.627415i
\(569\) −20.6513 + 20.6513i −0.865749 + 0.865749i −0.991999 0.126249i \(-0.959706\pi\)
0.126249 + 0.991999i \(0.459706\pi\)
\(570\) 2.36233 + 4.75651i 0.0989471 + 0.199228i
\(571\) 18.5622 0.776802 0.388401 0.921490i \(-0.373027\pi\)
0.388401 + 0.921490i \(0.373027\pi\)
\(572\) 0.362376 0.0151517
\(573\) −1.53301 −0.0640423
\(574\) 3.47919 + 3.47919i 0.145219 + 0.145219i
\(575\) 15.4060 + 11.6841i 0.642473 + 0.487261i
\(576\) 1.00000i 0.0416667i
\(577\) 43.8508 1.82553 0.912766 0.408483i \(-0.133942\pi\)
0.912766 + 0.408483i \(0.133942\pi\)
\(578\) 10.3877i 0.432070i
\(579\) −2.85699 + 2.85699i −0.118732 + 0.118732i
\(580\) 14.3681 + 4.83221i 0.596601 + 0.200646i
\(581\) −4.84810 −0.201133
\(582\) −9.04452 + 9.04452i −0.374907 + 0.374907i
\(583\) −17.6308 17.6308i −0.730193 0.730193i
\(584\) 0.258848 0.258848i 0.0107112 0.0107112i
\(585\) 0.162463 + 0.327117i 0.00671703 + 0.0135246i
\(586\) −15.2639 15.2639i −0.630548 0.630548i
\(587\) 29.8581i 1.23238i 0.787599 + 0.616188i \(0.211324\pi\)
−0.787599 + 0.616188i \(0.788676\pi\)
\(588\) 4.45077 4.45077i 0.183546 0.183546i
\(589\) 18.9708i 0.781678i
\(590\) 2.99902 + 1.00862i 0.123468 + 0.0415241i
\(591\) 17.4717i 0.718692i
\(592\) −4.51960 + 4.07102i −0.185755 + 0.167318i
\(593\) 28.1350 28.1350i 1.15537 1.15537i 0.169905 0.985460i \(-0.445654\pi\)
0.985460 0.169905i \(-0.0543461\pi\)
\(594\) −1.56874 + 1.56874i −0.0643662 + 0.0643662i
\(595\) 3.13359 9.31738i 0.128464 0.381975i
\(596\) 9.07290i 0.371640i
\(597\) 7.35194 0.300895
\(598\) 0.631653i 0.0258302i
\(599\) 18.0057i 0.735692i −0.929887 0.367846i \(-0.880095\pi\)
0.929887 0.367846i \(-0.119905\pi\)
\(600\) −0.680545 4.95347i −0.0277831 0.202225i
\(601\) −3.53685 −0.144271 −0.0721356 0.997395i \(-0.522981\pi\)
−0.0721356 + 0.997395i \(0.522981\pi\)
\(602\) 5.31157 + 5.31157i 0.216483 + 0.216483i
\(603\) 5.39694 + 5.39694i 0.219780 + 0.219780i
\(604\) 0.0622104i 0.00253130i
\(605\) −6.04548 12.1725i −0.245784 0.494881i
\(606\) 3.05176 + 3.05176i 0.123969 + 0.123969i
\(607\) 4.86568i 0.197492i 0.995113 + 0.0987459i \(0.0314831\pi\)
−0.995113 + 0.0987459i \(0.968517\pi\)
\(608\) 1.67943 1.67943i 0.0681101 0.0681101i
\(609\) −4.02686 4.02686i −0.163177 0.163177i
\(610\) −22.4988 7.56671i −0.910950 0.306367i
\(611\) 1.30230 1.30230i 0.0526853 0.0526853i
\(612\) 5.23332i 0.211545i
\(613\) 23.1044 + 23.1044i 0.933179 + 0.933179i 0.997903 0.0647244i \(-0.0206168\pi\)
−0.0647244 + 0.997903i \(0.520617\pi\)
\(614\) −20.5532 20.5532i −0.829458 0.829458i
\(615\) 12.4139 + 4.17501i 0.500578 + 0.168353i
\(616\) 1.31781 + 1.31781i 0.0530959 + 0.0530959i
\(617\) −25.4761 + 25.4761i −1.02563 + 1.02563i −0.0259665 + 0.999663i \(0.508266\pi\)
−0.999663 + 0.0259665i \(0.991734\pi\)
\(618\) −9.86320 + 9.86320i −0.396756 + 0.396756i
\(619\) 31.1893 1.25360 0.626801 0.779179i \(-0.284364\pi\)
0.626801 + 0.779179i \(0.284364\pi\)
\(620\) 5.69340 16.9287i 0.228652 0.679873i
\(621\) −2.73445 2.73445i −0.109730 0.109730i
\(622\) −0.612480 + 0.612480i −0.0245582 + 0.0245582i
\(623\) 14.9526 0.599062
\(624\) 0.115499 0.115499i 0.00462366 0.00462366i
\(625\) −6.74212 24.0737i −0.269685 0.962949i
\(626\) 3.56579 0.142517
\(627\) −5.26920 −0.210431
\(628\) 5.08868 + 5.08868i 0.203060 + 0.203060i
\(629\) −23.6525 + 21.3050i −0.943089 + 0.849484i
\(630\) −0.598775 + 1.78039i −0.0238558 + 0.0709326i
\(631\) 19.9604 + 19.9604i 0.794612 + 0.794612i 0.982240 0.187628i \(-0.0600800\pi\)
−0.187628 + 0.982240i \(0.560080\pi\)
\(632\) −1.08732 + 1.08732i −0.0432512 + 0.0432512i
\(633\) 10.7698 + 10.7698i 0.428060 + 0.428060i
\(634\) 4.20992 + 4.20992i 0.167197 + 0.167197i
\(635\) 4.64956 13.8250i 0.184512 0.548627i
\(636\) −11.2388 −0.445648
\(637\) 1.02812 0.0407355
\(638\) −10.6349 + 10.6349i −0.421039 + 0.421039i
\(639\) 14.9530i 0.591533i
\(640\) −2.00267 + 0.994632i −0.0791627 + 0.0393163i
\(641\) −0.397393 −0.0156961 −0.00784804 0.999969i \(-0.502498\pi\)
−0.00784804 + 0.999969i \(0.502498\pi\)
\(642\) 7.82913 0.308991
\(643\) 21.4396 0.845495 0.422748 0.906247i \(-0.361066\pi\)
0.422748 + 0.906247i \(0.361066\pi\)
\(644\) −2.29705 + 2.29705i −0.0905165 + 0.0905165i
\(645\) 18.9520 + 6.37385i 0.746233 + 0.250970i
\(646\) 8.78902 8.78902i 0.345800 0.345800i
\(647\) 5.00707i 0.196848i −0.995145 0.0984241i \(-0.968620\pi\)
0.995145 0.0984241i \(-0.0313802\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −2.21980 + 2.21980i −0.0871348 + 0.0871348i
\(650\) 0.493518 0.650723i 0.0193574 0.0255234i
\(651\) −4.74452 + 4.74452i −0.185953 + 0.185953i
\(652\) 19.1109 0.748441
\(653\) −28.3624 −1.10991 −0.554954 0.831881i \(-0.687264\pi\)
−0.554954 + 0.831881i \(0.687264\pi\)
\(654\) 14.0912 0.551008
\(655\) −12.0920 + 35.9542i −0.472473 + 1.40485i
\(656\) 5.85724i 0.228687i
\(657\) −0.258848 + 0.258848i −0.0100986 + 0.0100986i
\(658\) 9.47178 0.369249
\(659\) 13.0798 0.509518 0.254759 0.967005i \(-0.418004\pi\)
0.254759 + 0.967005i \(0.418004\pi\)
\(660\) 4.70200 + 1.58136i 0.183025 + 0.0615543i
\(661\) −21.4953 21.4953i −0.836072 0.836072i 0.152267 0.988339i \(-0.451343\pi\)
−0.988339 + 0.152267i \(0.951343\pi\)
\(662\) 14.0919 + 14.0919i 0.547697 + 0.547697i
\(663\) 0.604443 0.604443i 0.0234746 0.0234746i
\(664\) 4.08091 + 4.08091i 0.158370 + 0.158370i
\(665\) −3.99566 + 1.98445i −0.154945 + 0.0769537i
\(666\) 4.51960 4.07102i 0.175131 0.157749i
\(667\) −18.5375 18.5375i −0.717776 0.717776i
\(668\) 7.28469 0.281853
\(669\) −13.0931 −0.506208
\(670\) 5.44035 16.1763i 0.210179 0.624945i
\(671\) 16.6531 16.6531i 0.642885 0.642885i
\(672\) 0.840040 0.0324052
\(673\) 17.5609 17.5609i 0.676922 0.676922i −0.282380 0.959303i \(-0.591124\pi\)
0.959303 + 0.282380i \(0.0911240\pi\)
\(674\) −17.5011 17.5011i −0.674119 0.674119i
\(675\) 0.680545 + 4.95347i 0.0261942 + 0.190659i
\(676\) −12.9733 −0.498974
\(677\) 27.0147 27.0147i 1.03826 1.03826i 0.0390206 0.999238i \(-0.487576\pi\)
0.999238 0.0390206i \(-0.0124238\pi\)
\(678\) 13.2844 13.2844i 0.510184 0.510184i
\(679\) −7.59776 7.59776i −0.291575 0.291575i
\(680\) −10.4806 + 5.20523i −0.401914 + 0.199612i
\(681\) 8.86099 + 8.86099i 0.339554 + 0.339554i
\(682\) 12.5302 + 12.5302i 0.479807 + 0.479807i
\(683\) 24.3629i 0.932219i −0.884727 0.466109i \(-0.845655\pi\)
0.884727 0.466109i \(-0.154345\pi\)
\(684\) −1.67943 + 1.67943i −0.0642148 + 0.0642148i
\(685\) −2.71376 + 8.06907i −0.103687 + 0.308303i
\(686\) 7.89681 + 7.89681i 0.301502 + 0.301502i
\(687\) 5.21481 5.21481i 0.198958 0.198958i
\(688\) 8.94207i 0.340913i
\(689\) −1.29807 1.29807i −0.0494526 0.0494526i
\(690\) −2.75645 + 8.19600i −0.104936 + 0.312016i
\(691\) 37.9850i 1.44502i 0.691361 + 0.722509i \(0.257011\pi\)
−0.691361 + 0.722509i \(0.742989\pi\)
\(692\) −8.94815 8.94815i −0.340158 0.340158i
\(693\) −1.31781 1.31781i −0.0500593 0.0500593i
\(694\) −19.3835 −0.735787
\(695\) 1.29767 + 2.61284i 0.0492234 + 0.0991105i
\(696\) 6.77925i 0.256967i
\(697\) 30.6528i 1.16106i
\(698\) −14.5408 −0.550377
\(699\) 26.0877i 0.986726i
\(700\) 4.16111 0.571685i 0.157275 0.0216077i
\(701\) −2.11618 + 2.11618i −0.0799271 + 0.0799271i −0.745940 0.666013i \(-0.768000\pi\)
0.666013 + 0.745940i \(0.268000\pi\)
\(702\) −0.115499 + 0.115499i −0.00435923 + 0.00435923i
\(703\) 14.4274 + 0.753367i 0.544139 + 0.0284138i
\(704\) 2.21854i 0.0836142i
\(705\) 22.5810 11.2149i 0.850448 0.422377i
\(706\) 26.3150i 0.990376i
\(707\) −2.56360 + 2.56360i −0.0964141 + 0.0964141i
\(708\) 1.41502i 0.0531797i
\(709\) −10.3418 10.3418i −0.388395 0.388395i 0.485720 0.874114i \(-0.338557\pi\)
−0.874114 + 0.485720i \(0.838557\pi\)
\(710\) 29.9461 14.8728i 1.12386 0.558165i
\(711\) 1.08732 1.08732i 0.0407776 0.0407776i
\(712\) −12.5864 12.5864i −0.471695 0.471695i
\(713\) −21.8413 + 21.8413i −0.817962 + 0.817962i
\(714\) 4.39620 0.164524
\(715\) 0.360431 + 0.725721i 0.0134793 + 0.0271404i
\(716\) −17.4301 + 17.4301i −0.651395 + 0.651395i
\(717\) 15.4753i 0.577937i
\(718\) 6.12864 0.228719
\(719\) 8.49669i 0.316873i 0.987369 + 0.158436i \(0.0506453\pi\)
−0.987369 + 0.158436i \(0.949355\pi\)
\(720\) 2.00267 0.994632i 0.0746353 0.0370678i
\(721\) −8.28548 8.28548i −0.308568 0.308568i
\(722\) 13.3590 0.497170
\(723\) −16.2047 −0.602658
\(724\) −3.39361 −0.126122
\(725\) 4.61359 + 33.5808i 0.171344 + 1.24716i
\(726\) 4.29787 4.29787i 0.159509 0.159509i
\(727\) 4.28583i 0.158953i 0.996837 + 0.0794764i \(0.0253248\pi\)
−0.996837 + 0.0794764i \(0.974675\pi\)
\(728\) 0.0970237 + 0.0970237i 0.00359594 + 0.00359594i
\(729\) 1.00000i 0.0370370i
\(730\) 0.775847 + 0.260930i 0.0287154 + 0.00965745i
\(731\) 46.7967i 1.73084i
\(732\) 10.6156i 0.392363i
\(733\) 2.83283 + 2.83283i 0.104633 + 0.104633i 0.757485 0.652852i \(-0.226428\pi\)
−0.652852 + 0.757485i \(0.726428\pi\)
\(734\) −21.0105 + 21.0105i −0.775512 + 0.775512i
\(735\) 13.3403 + 4.48656i 0.492065 + 0.165489i
\(736\) 3.86710 0.142543
\(737\) 11.9733 + 11.9733i 0.441042 + 0.441042i
\(738\) 5.85724i 0.215608i
\(739\) −41.7623 −1.53625 −0.768126 0.640299i \(-0.778810\pi\)
−0.768126 + 0.640299i \(0.778810\pi\)
\(740\) −12.6483 5.00213i −0.464960 0.183882i
\(741\) −0.387946 −0.0142515
\(742\) 9.44106i 0.346592i
\(743\) −36.8937 36.8937i −1.35350 1.35350i −0.881712 0.471788i \(-0.843609\pi\)
−0.471788 0.881712i \(-0.656391\pi\)
\(744\) 7.98744 0.292834
\(745\) 18.1701 9.02420i 0.665700 0.330621i
\(746\) −2.15543 + 2.15543i −0.0789157 + 0.0789157i
\(747\) −4.08091 4.08091i −0.149313 0.149313i
\(748\) 11.6103i 0.424515i
\(749\) 6.57679i 0.240311i
\(750\) 9.24330 6.28979i 0.337517 0.229671i
\(751\) 26.9870i 0.984768i −0.870378 0.492384i \(-0.836125\pi\)
0.870378 0.492384i \(-0.163875\pi\)
\(752\) −7.97291 7.97291i −0.290742 0.290742i
\(753\) 6.94324i 0.253026i
\(754\) −0.782996 + 0.782996i −0.0285150 + 0.0285150i
\(755\) 0.124587 0.0618764i 0.00453419 0.00225191i
\(756\) −0.840040 −0.0305520
\(757\) −36.8457 −1.33918 −0.669590 0.742731i \(-0.733530\pi\)
−0.669590 + 0.742731i \(0.733530\pi\)
\(758\) −37.8733 −1.37562
\(759\) −6.06648 6.06648i −0.220199 0.220199i
\(760\) 5.03378 + 1.69294i 0.182594 + 0.0614094i
\(761\) 38.2000i 1.38475i −0.721538 0.692374i \(-0.756565\pi\)
0.721538 0.692374i \(-0.243435\pi\)
\(762\) 6.52301 0.236304
\(763\) 11.8371i 0.428533i
\(764\) −1.08400 + 1.08400i −0.0392177 + 0.0392177i
\(765\) 10.4806 5.20523i 0.378929 0.188196i
\(766\) −33.6750 −1.21673
\(767\) −0.163433 + 0.163433i −0.00590124 + 0.00590124i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) −23.0452 + 23.0452i −0.831031 + 0.831031i −0.987658 0.156627i \(-0.949938\pi\)
0.156627 + 0.987658i \(0.449938\pi\)
\(770\) −1.32840 + 3.94987i −0.0478724 + 0.142343i
\(771\) −14.2413 14.2413i −0.512887 0.512887i
\(772\) 4.04039i 0.145417i
\(773\) −15.2548 + 15.2548i −0.548676 + 0.548676i −0.926058 0.377382i \(-0.876824\pi\)
0.377382 + 0.926058i \(0.376824\pi\)
\(774\) 8.94207i 0.321416i
\(775\) 39.5655 5.43582i 1.42124 0.195260i
\(776\) 12.7909i 0.459166i
\(777\) 3.41982 + 3.79665i 0.122685 + 0.136204i
\(778\) −6.96706 + 6.96706i −0.249781 + 0.249781i
\(779\) −9.83686 + 9.83686i −0.352442 + 0.352442i
\(780\) 0.346186 +