Properties

Label 1110.2.o.a.253.16
Level $1110$
Weight $2$
Character 1110.253
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

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 253.16
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.a.487.16

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(0.914315 - 2.04060i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.867388 - 0.867388i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(0.914315 - 2.04060i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.867388 - 0.867388i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(-0.914315 + 2.04060i) q^{10} +1.09838i q^{11} +(0.707107 - 0.707107i) q^{12} -4.92901 q^{13} +(-0.867388 + 0.867388i) q^{14} +(-0.796400 - 2.08944i) q^{15} +1.00000 q^{16} -2.47393i q^{17} +1.00000i q^{18} +(-5.01453 - 5.01453i) q^{19} +(0.914315 - 2.04060i) q^{20} -1.22667i q^{21} -1.09838i q^{22} -0.254201 q^{23} +(-0.707107 + 0.707107i) q^{24} +(-3.32806 - 3.73149i) q^{25} +4.92901 q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.867388 - 0.867388i) q^{28} +(4.52766 - 4.52766i) q^{29} +(0.796400 + 2.08944i) q^{30} +(3.38961 + 3.38961i) q^{31} -1.00000 q^{32} +(0.776669 + 0.776669i) q^{33} +2.47393i q^{34} +(-0.976922 - 2.56305i) q^{35} -1.00000i q^{36} +(0.134999 + 6.08126i) q^{37} +(5.01453 + 5.01453i) q^{38} +(-3.48534 + 3.48534i) q^{39} +(-0.914315 + 2.04060i) q^{40} -5.96538i q^{41} +1.22667i q^{42} -11.5248 q^{43} +1.09838i q^{44} +(-2.04060 - 0.914315i) q^{45} +0.254201 q^{46} +(2.51562 - 2.51562i) q^{47} +(0.707107 - 0.707107i) q^{48} +5.49528i q^{49} +(3.32806 + 3.73149i) q^{50} +(-1.74934 - 1.74934i) q^{51} -4.92901 q^{52} +(-1.28565 - 1.28565i) q^{53} +(0.707107 + 0.707107i) q^{54} +(2.24134 + 1.00426i) q^{55} +(-0.867388 + 0.867388i) q^{56} -7.09162 q^{57} +(-4.52766 + 4.52766i) q^{58} +(3.61042 + 3.61042i) q^{59} +(-0.796400 - 2.08944i) q^{60} +(0.890776 + 0.890776i) q^{61} +(-3.38961 - 3.38961i) q^{62} +(-0.867388 - 0.867388i) q^{63} +1.00000 q^{64} +(-4.50667 + 10.0581i) q^{65} +(-0.776669 - 0.776669i) q^{66} +(-8.08465 - 8.08465i) q^{67} -2.47393i q^{68} +(-0.179747 + 0.179747i) q^{69} +(0.976922 + 2.56305i) q^{70} +12.9448 q^{71} +1.00000i q^{72} +(9.56625 - 9.56625i) q^{73} +(-0.134999 - 6.08126i) q^{74} +(-4.99186 - 0.285272i) q^{75} +(-5.01453 - 5.01453i) q^{76} +(0.952718 + 0.952718i) q^{77} +(3.48534 - 3.48534i) q^{78} +(-1.43534 - 1.43534i) q^{79} +(0.914315 - 2.04060i) q^{80} -1.00000 q^{81} +5.96538i q^{82} +(7.34416 + 7.34416i) q^{83} -1.22667i q^{84} +(-5.04830 - 2.26195i) q^{85} +11.5248 q^{86} -6.40308i q^{87} -1.09838i q^{88} +(-9.93692 + 9.93692i) q^{89} +(2.04060 + 0.914315i) q^{90} +(-4.27537 + 4.27537i) q^{91} -0.254201 q^{92} +4.79363 q^{93} +(-2.51562 + 2.51562i) q^{94} +(-14.8175 + 5.64777i) q^{95} +(-0.707107 + 0.707107i) q^{96} +5.50451i q^{97} -5.49528i q^{98} +1.09838 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
\(5\) 0.914315 2.04060i 0.408894 0.912582i
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) 0.867388 0.867388i 0.327842 0.327842i −0.523924 0.851765i \(-0.675532\pi\)
0.851765 + 0.523924i \(0.175532\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000i 0.333333i
\(10\) −0.914315 + 2.04060i −0.289132 + 0.645293i
\(11\) 1.09838i 0.331173i 0.986195 + 0.165586i \(0.0529517\pi\)
−0.986195 + 0.165586i \(0.947048\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) −4.92901 −1.36706 −0.683531 0.729921i \(-0.739557\pi\)
−0.683531 + 0.729921i \(0.739557\pi\)
\(14\) −0.867388 + 0.867388i −0.231819 + 0.231819i
\(15\) −0.796400 2.08944i −0.205630 0.539490i
\(16\) 1.00000 0.250000
\(17\) 2.47393i 0.600017i −0.953937 0.300009i \(-0.903010\pi\)
0.953937 0.300009i \(-0.0969895\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −5.01453 5.01453i −1.15041 1.15041i −0.986470 0.163943i \(-0.947579\pi\)
−0.163943 0.986470i \(-0.552421\pi\)
\(20\) 0.914315 2.04060i 0.204447 0.456291i
\(21\) 1.22667i 0.267682i
\(22\) 1.09838i 0.234175i
\(23\) −0.254201 −0.0530046 −0.0265023 0.999649i \(-0.508437\pi\)
−0.0265023 + 0.999649i \(0.508437\pi\)
\(24\) −0.707107 + 0.707107i −0.144338 + 0.144338i
\(25\) −3.32806 3.73149i −0.665611 0.746299i
\(26\) 4.92901 0.966659
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 0.867388 0.867388i 0.163921 0.163921i
\(29\) 4.52766 4.52766i 0.840765 0.840765i −0.148193 0.988958i \(-0.547346\pi\)
0.988958 + 0.148193i \(0.0473458\pi\)
\(30\) 0.796400 + 2.08944i 0.145402 + 0.381477i
\(31\) 3.38961 + 3.38961i 0.608792 + 0.608792i 0.942630 0.333838i \(-0.108344\pi\)
−0.333838 + 0.942630i \(0.608344\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.776669 + 0.776669i 0.135201 + 0.135201i
\(34\) 2.47393i 0.424276i
\(35\) −0.976922 2.56305i −0.165130 0.433235i
\(36\) 1.00000i 0.166667i
\(37\) 0.134999 + 6.08126i 0.0221937 + 0.999754i
\(38\) 5.01453 + 5.01453i 0.813465 + 0.813465i
\(39\) −3.48534 + 3.48534i −0.558101 + 0.558101i
\(40\) −0.914315 + 2.04060i −0.144566 + 0.322646i
\(41\) 5.96538i 0.931635i −0.884881 0.465818i \(-0.845760\pi\)
0.884881 0.465818i \(-0.154240\pi\)
\(42\) 1.22667i 0.189280i
\(43\) −11.5248 −1.75752 −0.878760 0.477264i \(-0.841629\pi\)
−0.878760 + 0.477264i \(0.841629\pi\)
\(44\) 1.09838i 0.165586i
\(45\) −2.04060 0.914315i −0.304194 0.136298i
\(46\) 0.254201 0.0374799
\(47\) 2.51562 2.51562i 0.366941 0.366941i −0.499419 0.866360i \(-0.666453\pi\)
0.866360 + 0.499419i \(0.166453\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 5.49528i 0.785040i
\(50\) 3.32806 + 3.73149i 0.470658 + 0.527713i
\(51\) −1.74934 1.74934i −0.244956 0.244956i
\(52\) −4.92901 −0.683531
\(53\) −1.28565 1.28565i −0.176598 0.176598i 0.613273 0.789871i \(-0.289853\pi\)
−0.789871 + 0.613273i \(0.789853\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) 2.24134 + 1.00426i 0.302222 + 0.135415i
\(56\) −0.867388 + 0.867388i −0.115910 + 0.115910i
\(57\) −7.09162 −0.939308
\(58\) −4.52766 + 4.52766i −0.594511 + 0.594511i
\(59\) 3.61042 + 3.61042i 0.470037 + 0.470037i 0.901926 0.431890i \(-0.142153\pi\)
−0.431890 + 0.901926i \(0.642153\pi\)
\(60\) −0.796400 2.08944i −0.102815 0.269745i
\(61\) 0.890776 + 0.890776i 0.114052 + 0.114052i 0.761830 0.647777i \(-0.224301\pi\)
−0.647777 + 0.761830i \(0.724301\pi\)
\(62\) −3.38961 3.38961i −0.430481 0.430481i
\(63\) −0.867388 0.867388i −0.109281 0.109281i
\(64\) 1.00000 0.125000
\(65\) −4.50667 + 10.0581i −0.558984 + 1.24756i
\(66\) −0.776669 0.776669i −0.0956014 0.0956014i
\(67\) −8.08465 8.08465i −0.987697 0.987697i 0.0122281 0.999925i \(-0.496108\pi\)
−0.999925 + 0.0122281i \(0.996108\pi\)
\(68\) 2.47393i 0.300009i
\(69\) −0.179747 + 0.179747i −0.0216390 + 0.0216390i
\(70\) 0.976922 + 2.56305i 0.116764 + 0.306343i
\(71\) 12.9448 1.53626 0.768130 0.640294i \(-0.221187\pi\)
0.768130 + 0.640294i \(0.221187\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 9.56625 9.56625i 1.11964 1.11964i 0.127851 0.991793i \(-0.459192\pi\)
0.991793 0.127851i \(-0.0408081\pi\)
\(74\) −0.134999 6.08126i −0.0156933 0.706933i
\(75\) −4.99186 0.285272i −0.576410 0.0329404i
\(76\) −5.01453 5.01453i −0.575206 0.575206i
\(77\) 0.952718 + 0.952718i 0.108572 + 0.108572i
\(78\) 3.48534 3.48534i 0.394637 0.394637i
\(79\) −1.43534 1.43534i −0.161488 0.161488i 0.621737 0.783226i \(-0.286427\pi\)
−0.783226 + 0.621737i \(0.786427\pi\)
\(80\) 0.914315 2.04060i 0.102223 0.228145i
\(81\) −1.00000 −0.111111
\(82\) 5.96538i 0.658766i
\(83\) 7.34416 + 7.34416i 0.806127 + 0.806127i 0.984045 0.177919i \(-0.0569364\pi\)
−0.177919 + 0.984045i \(0.556936\pi\)
\(84\) 1.22667i 0.133841i
\(85\) −5.04830 2.26195i −0.547565 0.245343i
\(86\) 11.5248 1.24275
\(87\) 6.40308i 0.686482i
\(88\) 1.09838i 0.117087i
\(89\) −9.93692 + 9.93692i −1.05331 + 1.05331i −0.0548149 + 0.998497i \(0.517457\pi\)
−0.998497 + 0.0548149i \(0.982543\pi\)
\(90\) 2.04060 + 0.914315i 0.215098 + 0.0963772i
\(91\) −4.27537 + 4.27537i −0.448180 + 0.448180i
\(92\) −0.254201 −0.0265023
\(93\) 4.79363 0.497077
\(94\) −2.51562 + 2.51562i −0.259467 + 0.259467i
\(95\) −14.8175 + 5.64777i −1.52024 + 0.579449i
\(96\) −0.707107 + 0.707107i −0.0721688 + 0.0721688i
\(97\) 5.50451i 0.558899i 0.960160 + 0.279449i \(0.0901519\pi\)
−0.960160 + 0.279449i \(0.909848\pi\)
\(98\) 5.49528i 0.555107i
\(99\) 1.09838 0.110391
\(100\) −3.32806 3.73149i −0.332806 0.373149i
\(101\) 18.0390i 1.79495i −0.441068 0.897473i \(-0.645400\pi\)
0.441068 0.897473i \(-0.354600\pi\)
\(102\) 1.74934 + 1.74934i 0.173210 + 0.173210i
\(103\) 16.4190i 1.61781i −0.587941 0.808904i \(-0.700061\pi\)
0.587941 0.808904i \(-0.299939\pi\)
\(104\) 4.92901 0.483330
\(105\) −2.50314 1.12156i −0.244281 0.109453i
\(106\) 1.28565 + 1.28565i 0.124874 + 0.124874i
\(107\) −3.46603 + 3.46603i −0.335073 + 0.335073i −0.854509 0.519436i \(-0.826142\pi\)
0.519436 + 0.854509i \(0.326142\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) −9.52466 9.52466i −0.912297 0.912297i 0.0841554 0.996453i \(-0.473181\pi\)
−0.996453 + 0.0841554i \(0.973181\pi\)
\(110\) −2.24134 1.00426i −0.213703 0.0957526i
\(111\) 4.39556 + 4.20464i 0.417208 + 0.399087i
\(112\) 0.867388 0.867388i 0.0819604 0.0819604i
\(113\) 12.6239i 1.18755i −0.804629 0.593777i \(-0.797636\pi\)
0.804629 0.593777i \(-0.202364\pi\)
\(114\) 7.09162 0.664191
\(115\) −0.232420 + 0.518722i −0.0216733 + 0.0483711i
\(116\) 4.52766 4.52766i 0.420383 0.420383i
\(117\) 4.92901i 0.455687i
\(118\) −3.61042 3.61042i −0.332366 0.332366i
\(119\) −2.14586 2.14586i −0.196711 0.196711i
\(120\) 0.796400 + 2.08944i 0.0727011 + 0.190739i
\(121\) 9.79357 0.890325
\(122\) −0.890776 0.890776i −0.0806471 0.0806471i
\(123\) −4.21816 4.21816i −0.380339 0.380339i
\(124\) 3.38961 + 3.38961i 0.304396 + 0.304396i
\(125\) −10.6574 + 3.37946i −0.953223 + 0.302268i
\(126\) 0.867388 + 0.867388i 0.0772730 + 0.0772730i
\(127\) −9.16645 + 9.16645i −0.813391 + 0.813391i −0.985141 0.171750i \(-0.945058\pi\)
0.171750 + 0.985141i \(0.445058\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −8.14929 + 8.14929i −0.717505 + 0.717505i
\(130\) 4.50667 10.0581i 0.395261 0.882156i
\(131\) 12.3216 + 12.3216i 1.07655 + 1.07655i 0.996816 + 0.0797308i \(0.0254061\pi\)
0.0797308 + 0.996816i \(0.474594\pi\)
\(132\) 0.776669 + 0.776669i 0.0676004 + 0.0676004i
\(133\) −8.69909 −0.754307
\(134\) 8.08465 + 8.08465i 0.698407 + 0.698407i
\(135\) −2.08944 + 0.796400i −0.179830 + 0.0685432i
\(136\) 2.47393i 0.212138i
\(137\) 6.64965 6.64965i 0.568118 0.568118i −0.363483 0.931601i \(-0.618412\pi\)
0.931601 + 0.363483i \(0.118412\pi\)
\(138\) 0.179747 0.179747i 0.0153011 0.0153011i
\(139\) 11.9768 1.01586 0.507928 0.861399i \(-0.330411\pi\)
0.507928 + 0.861399i \(0.330411\pi\)
\(140\) −0.976922 2.56305i −0.0825650 0.216617i
\(141\) 3.55763i 0.299606i
\(142\) −12.9448 −1.08630
\(143\) 5.41391i 0.452734i
\(144\) 1.00000i 0.0833333i
\(145\) −5.09941 13.3788i −0.423483 1.11105i
\(146\) −9.56625 + 9.56625i −0.791708 + 0.791708i
\(147\) 3.88575 + 3.88575i 0.320491 + 0.320491i
\(148\) 0.134999 + 6.08126i 0.0110968 + 0.499877i
\(149\) 15.0455i 1.23258i −0.787520 0.616289i \(-0.788635\pi\)
0.787520 0.616289i \(-0.211365\pi\)
\(150\) 4.99186 + 0.285272i 0.407583 + 0.0232924i
\(151\) 14.4920i 1.17934i 0.807644 + 0.589671i \(0.200743\pi\)
−0.807644 + 0.589671i \(0.799257\pi\)
\(152\) 5.01453 + 5.01453i 0.406732 + 0.406732i
\(153\) −2.47393 −0.200006
\(154\) −0.952718 0.952718i −0.0767722 0.0767722i
\(155\) 10.0160 3.81765i 0.804504 0.306641i
\(156\) −3.48534 + 3.48534i −0.279050 + 0.279050i
\(157\) −9.44787 + 9.44787i −0.754022 + 0.754022i −0.975227 0.221205i \(-0.929001\pi\)
0.221205 + 0.975227i \(0.429001\pi\)
\(158\) 1.43534 + 1.43534i 0.114190 + 0.114190i
\(159\) −1.81819 −0.144192
\(160\) −0.914315 + 2.04060i −0.0722829 + 0.161323i
\(161\) −0.220491 + 0.220491i −0.0173771 + 0.0173771i
\(162\) 1.00000 0.0785674
\(163\) 9.52839i 0.746321i −0.927767 0.373161i \(-0.878274\pi\)
0.927767 0.373161i \(-0.121726\pi\)
\(164\) 5.96538i 0.465818i
\(165\) 2.29499 0.874747i 0.178665 0.0680990i
\(166\) −7.34416 7.34416i −0.570018 0.570018i
\(167\) 5.43514i 0.420584i −0.977639 0.210292i \(-0.932559\pi\)
0.977639 0.210292i \(-0.0674415\pi\)
\(168\) 1.22667i 0.0946398i
\(169\) 11.2952 0.868860
\(170\) 5.04830 + 2.26195i 0.387187 + 0.173484i
\(171\) −5.01453 + 5.01453i −0.383471 + 0.383471i
\(172\) −11.5248 −0.878760
\(173\) −5.41742 + 5.41742i −0.411879 + 0.411879i −0.882393 0.470514i \(-0.844069\pi\)
0.470514 + 0.882393i \(0.344069\pi\)
\(174\) 6.40308i 0.485416i
\(175\) −6.12337 0.349935i −0.462883 0.0264526i
\(176\) 1.09838i 0.0827932i
\(177\) 5.10591 0.383783
\(178\) 9.93692 9.93692i 0.744804 0.744804i
\(179\) 1.11655 1.11655i 0.0834548 0.0834548i −0.664147 0.747602i \(-0.731205\pi\)
0.747602 + 0.664147i \(0.231205\pi\)
\(180\) −2.04060 0.914315i −0.152097 0.0681490i
\(181\) −3.70989 −0.275754 −0.137877 0.990449i \(-0.544028\pi\)
−0.137877 + 0.990449i \(0.544028\pi\)
\(182\) 4.27537 4.27537i 0.316911 0.316911i
\(183\) 1.25975 0.0931232
\(184\) 0.254201 0.0187400
\(185\) 12.5328 + 5.28471i 0.921432 + 0.388540i
\(186\) −4.79363 −0.351486
\(187\) 2.71731 0.198709
\(188\) 2.51562 2.51562i 0.183471 0.183471i
\(189\) −1.22667 −0.0892272
\(190\) 14.8175 5.64777i 1.07497 0.409732i
\(191\) −4.79894 + 4.79894i −0.347239 + 0.347239i −0.859080 0.511841i \(-0.828964\pi\)
0.511841 + 0.859080i \(0.328964\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) −2.16290 −0.155689 −0.0778444 0.996966i \(-0.524804\pi\)
−0.0778444 + 0.996966i \(0.524804\pi\)
\(194\) 5.50451i 0.395201i
\(195\) 3.92547 + 10.2989i 0.281109 + 0.737517i
\(196\) 5.49528i 0.392520i
\(197\) 3.85768 3.85768i 0.274848 0.274848i −0.556200 0.831048i \(-0.687741\pi\)
0.831048 + 0.556200i \(0.187741\pi\)
\(198\) −1.09838 −0.0780582
\(199\) 11.9163 11.9163i 0.844724 0.844724i −0.144745 0.989469i \(-0.546236\pi\)
0.989469 + 0.144745i \(0.0462362\pi\)
\(200\) 3.32806 + 3.73149i 0.235329 + 0.263856i
\(201\) −11.4334 −0.806451
\(202\) 18.0390i 1.26922i
\(203\) 7.85447i 0.551276i
\(204\) −1.74934 1.74934i −0.122478 0.122478i
\(205\) −12.1729 5.45423i −0.850194 0.380940i
\(206\) 16.4190i 1.14396i
\(207\) 0.254201i 0.0176682i
\(208\) −4.92901 −0.341766
\(209\) 5.50784 5.50784i 0.380986 0.380986i
\(210\) 2.50314 + 1.12156i 0.172733 + 0.0773953i
\(211\) 25.4750 1.75377 0.876885 0.480700i \(-0.159617\pi\)
0.876885 + 0.480700i \(0.159617\pi\)
\(212\) −1.28565 1.28565i −0.0882989 0.0882989i
\(213\) 9.15333 9.15333i 0.627176 0.627176i
\(214\) 3.46603 3.46603i 0.236933 0.236933i
\(215\) −10.5373 + 23.5175i −0.718639 + 1.60388i
\(216\) 0.707107 + 0.707107i 0.0481125 + 0.0481125i
\(217\) 5.88021 0.399175
\(218\) 9.52466 + 9.52466i 0.645092 + 0.645092i
\(219\) 13.5287i 0.914186i
\(220\) 2.24134 + 1.00426i 0.151111 + 0.0677073i
\(221\) 12.1941i 0.820261i
\(222\) −4.39556 4.20464i −0.295011 0.282197i
\(223\) −3.60544 3.60544i −0.241438 0.241438i 0.576007 0.817445i \(-0.304610\pi\)
−0.817445 + 0.576007i \(0.804610\pi\)
\(224\) −0.867388 + 0.867388i −0.0579548 + 0.0579548i
\(225\) −3.73149 + 3.32806i −0.248766 + 0.221870i
\(226\) 12.6239i 0.839728i
\(227\) 11.2463i 0.746442i −0.927742 0.373221i \(-0.878253\pi\)
0.927742 0.373221i \(-0.121747\pi\)
\(228\) −7.09162 −0.469654
\(229\) 18.6659i 1.23348i 0.787168 + 0.616739i \(0.211546\pi\)
−0.787168 + 0.616739i \(0.788454\pi\)
\(230\) 0.232420 0.518722i 0.0153253 0.0342035i
\(231\) 1.34735 0.0886489
\(232\) −4.52766 + 4.52766i −0.297255 + 0.297255i
\(233\) −1.86289 + 1.86289i −0.122042 + 0.122042i −0.765490 0.643448i \(-0.777503\pi\)
0.643448 + 0.765490i \(0.277503\pi\)
\(234\) 4.92901i 0.322220i
\(235\) −2.83330 7.43344i −0.184824 0.484904i
\(236\) 3.61042 + 3.61042i 0.235018 + 0.235018i
\(237\) −2.02988 −0.131855
\(238\) 2.14586 + 2.14586i 0.139095 + 0.139095i
\(239\) 12.7842 + 12.7842i 0.826943 + 0.826943i 0.987093 0.160149i \(-0.0511976\pi\)
−0.160149 + 0.987093i \(0.551198\pi\)
\(240\) −0.796400 2.08944i −0.0514074 0.134873i
\(241\) −1.85063 + 1.85063i −0.119210 + 0.119210i −0.764195 0.644985i \(-0.776863\pi\)
0.644985 + 0.764195i \(0.276863\pi\)
\(242\) −9.79357 −0.629555
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) 0.890776 + 0.890776i 0.0570261 + 0.0570261i
\(245\) 11.2136 + 5.02441i 0.716413 + 0.320998i
\(246\) 4.21816 + 4.21816i 0.268940 + 0.268940i
\(247\) 24.7167 + 24.7167i 1.57269 + 1.57269i
\(248\) −3.38961 3.38961i −0.215241 0.215241i
\(249\) 10.3862 0.658200
\(250\) 10.6574 3.37946i 0.674030 0.213736i
\(251\) 14.6527 + 14.6527i 0.924870 + 0.924870i 0.997369 0.0724987i \(-0.0230973\pi\)
−0.0724987 + 0.997369i \(0.523097\pi\)
\(252\) −0.867388 0.867388i −0.0546403 0.0546403i
\(253\) 0.279209i 0.0175537i
\(254\) 9.16645 9.16645i 0.575154 0.575154i
\(255\) −5.16913 + 1.97024i −0.323703 + 0.123381i
\(256\) 1.00000 0.0625000
\(257\) 7.08582i 0.442001i 0.975274 + 0.221001i \(0.0709323\pi\)
−0.975274 + 0.221001i \(0.929068\pi\)
\(258\) 8.14929 8.14929i 0.507352 0.507352i
\(259\) 5.39191 + 5.15772i 0.335037 + 0.320485i
\(260\) −4.50667 + 10.0581i −0.279492 + 0.623778i
\(261\) −4.52766 4.52766i −0.280255 0.280255i
\(262\) −12.3216 12.3216i −0.761234 0.761234i
\(263\) 17.6568 17.6568i 1.08876 1.08876i 0.0931078 0.995656i \(-0.470320\pi\)
0.995656 0.0931078i \(-0.0296801\pi\)
\(264\) −0.776669 0.776669i −0.0478007 0.0478007i
\(265\) −3.79899 + 1.44800i −0.233370 + 0.0889502i
\(266\) 8.69909 0.533375
\(267\) 14.0529i 0.860025i
\(268\) −8.08465 8.08465i −0.493849 0.493849i
\(269\) 22.9016i 1.39633i 0.715935 + 0.698167i \(0.246001\pi\)
−0.715935 + 0.698167i \(0.753999\pi\)
\(270\) 2.08944 0.796400i 0.127159 0.0484674i
\(271\) 10.0289 0.609213 0.304607 0.952478i \(-0.401475\pi\)
0.304607 + 0.952478i \(0.401475\pi\)
\(272\) 2.47393i 0.150004i
\(273\) 6.04628i 0.365938i
\(274\) −6.64965 + 6.64965i −0.401720 + 0.401720i
\(275\) 4.09858 3.65546i 0.247154 0.220432i
\(276\) −0.179747 + 0.179747i −0.0108195 + 0.0108195i
\(277\) −2.84725 −0.171074 −0.0855372 0.996335i \(-0.527261\pi\)
−0.0855372 + 0.996335i \(0.527261\pi\)
\(278\) −11.9768 −0.718319
\(279\) 3.38961 3.38961i 0.202931 0.202931i
\(280\) 0.976922 + 2.56305i 0.0583822 + 0.153172i
\(281\) 13.1664 13.1664i 0.785440 0.785440i −0.195303 0.980743i \(-0.562569\pi\)
0.980743 + 0.195303i \(0.0625691\pi\)
\(282\) 3.55763i 0.211854i
\(283\) 17.3118i 1.02908i 0.857467 + 0.514539i \(0.172037\pi\)
−0.857467 + 0.514539i \(0.827963\pi\)
\(284\) 12.9448 0.768130
\(285\) −6.48397 + 14.4711i −0.384077 + 0.857196i
\(286\) 5.41391i 0.320131i
\(287\) −5.17429 5.17429i −0.305429 0.305429i
\(288\) 1.00000i 0.0589256i
\(289\) 10.8797 0.639979
\(290\) 5.09941 + 13.3788i 0.299448 + 0.785631i
\(291\) 3.89228 + 3.89228i 0.228169 + 0.228169i
\(292\) 9.56625 9.56625i 0.559822 0.559822i
\(293\) −6.15715 6.15715i −0.359705 0.359705i 0.503999 0.863704i \(-0.331861\pi\)
−0.863704 + 0.503999i \(0.831861\pi\)
\(294\) −3.88575 3.88575i −0.226621 0.226621i
\(295\) 10.6685 4.06635i 0.621142 0.236752i
\(296\) −0.134999 6.08126i −0.00784665 0.353466i
\(297\) 0.776669 0.776669i 0.0450669 0.0450669i
\(298\) 15.0455i 0.871564i
\(299\) 1.25296 0.0724606
\(300\) −4.99186 0.285272i −0.288205 0.0164702i
\(301\) −9.99650 + 9.99650i −0.576188 + 0.576188i
\(302\) 14.4920i 0.833921i
\(303\) −12.7555 12.7555i −0.732784 0.732784i
\(304\) −5.01453 5.01453i −0.287603 0.287603i
\(305\) 2.63216 1.00326i 0.150717 0.0574467i
\(306\) 2.47393 0.141425
\(307\) 10.3124 + 10.3124i 0.588562 + 0.588562i 0.937242 0.348680i \(-0.113370\pi\)
−0.348680 + 0.937242i \(0.613370\pi\)
\(308\) 0.952718 + 0.952718i 0.0542861 + 0.0542861i
\(309\) −11.6100 11.6100i −0.660467 0.660467i
\(310\) −10.0160 + 3.81765i −0.568870 + 0.216828i
\(311\) 10.4943 + 10.4943i 0.595076 + 0.595076i 0.938998 0.343922i \(-0.111756\pi\)
−0.343922 + 0.938998i \(0.611756\pi\)
\(312\) 3.48534 3.48534i 0.197318 0.197318i
\(313\) 1.40586 0.0794637 0.0397319 0.999210i \(-0.487350\pi\)
0.0397319 + 0.999210i \(0.487350\pi\)
\(314\) 9.44787 9.44787i 0.533174 0.533174i
\(315\) −2.56305 + 0.976922i −0.144412 + 0.0550433i
\(316\) −1.43534 1.43534i −0.0807442 0.0807442i
\(317\) −8.94726 8.94726i −0.502528 0.502528i 0.409694 0.912223i \(-0.365635\pi\)
−0.912223 + 0.409694i \(0.865635\pi\)
\(318\) 1.81819 0.101959
\(319\) 4.97307 + 4.97307i 0.278439 + 0.278439i
\(320\) 0.914315 2.04060i 0.0511117 0.114073i
\(321\) 4.90170i 0.273586i
\(322\) 0.220491 0.220491i 0.0122875 0.0122875i
\(323\) −12.4056 + 12.4056i −0.690267 + 0.690267i
\(324\) −1.00000 −0.0555556
\(325\) 16.4040 + 18.3926i 0.909932 + 1.02024i
\(326\) 9.52839i 0.527729i
\(327\) −13.4699 −0.744888
\(328\) 5.96538i 0.329383i
\(329\) 4.36404i 0.240597i
\(330\) −2.29499 + 0.874747i −0.126335 + 0.0481533i
\(331\) 10.3088 10.3088i 0.566624 0.566624i −0.364557 0.931181i \(-0.618780\pi\)
0.931181 + 0.364557i \(0.118780\pi\)
\(332\) 7.34416 + 7.34416i 0.403063 + 0.403063i
\(333\) 6.08126 0.134999i 0.333251 0.00739790i
\(334\) 5.43514i 0.297398i
\(335\) −23.8894 + 9.10558i −1.30522 + 0.497491i
\(336\) 1.22667i 0.0669204i
\(337\) −2.99336 2.99336i −0.163059 0.163059i 0.620861 0.783920i \(-0.286783\pi\)
−0.783920 + 0.620861i \(0.786783\pi\)
\(338\) −11.2952 −0.614376
\(339\) −8.92643 8.92643i −0.484817 0.484817i
\(340\) −5.04830 2.26195i −0.273782 0.122672i
\(341\) −3.72307 + 3.72307i −0.201615 + 0.201615i
\(342\) 5.01453 5.01453i 0.271155 0.271155i
\(343\) 10.8383 + 10.8383i 0.585211 + 0.585211i
\(344\) 11.5248 0.621377
\(345\) 0.202446 + 0.531137i 0.0108993 + 0.0285955i
\(346\) 5.41742 5.41742i 0.291242 0.291242i
\(347\) 20.2118 1.08503 0.542513 0.840048i \(-0.317473\pi\)
0.542513 + 0.840048i \(0.317473\pi\)
\(348\) 6.40308i 0.343241i
\(349\) 15.7463i 0.842880i −0.906856 0.421440i \(-0.861525\pi\)
0.906856 0.421440i \(-0.138475\pi\)
\(350\) 6.12337 + 0.349935i 0.327308 + 0.0187048i
\(351\) 3.48534 + 3.48534i 0.186034 + 0.186034i
\(352\) 1.09838i 0.0585436i
\(353\) 3.15443i 0.167893i 0.996470 + 0.0839467i \(0.0267526\pi\)
−0.996470 + 0.0839467i \(0.973247\pi\)
\(354\) −5.10591 −0.271376
\(355\) 11.8356 26.4150i 0.628167 1.40196i
\(356\) −9.93692 + 9.93692i −0.526656 + 0.526656i
\(357\) −3.03470 −0.160614
\(358\) −1.11655 + 1.11655i −0.0590114 + 0.0590114i
\(359\) 6.13746i 0.323922i −0.986797 0.161961i \(-0.948218\pi\)
0.986797 0.161961i \(-0.0517820\pi\)
\(360\) 2.04060 + 0.914315i 0.107549 + 0.0481886i
\(361\) 31.2911i 1.64690i
\(362\) 3.70989 0.194988
\(363\) 6.92510 6.92510i 0.363473 0.363473i
\(364\) −4.27537 + 4.27537i −0.224090 + 0.224090i
\(365\) −10.7743 28.2674i −0.563951 1.47958i
\(366\) −1.25975 −0.0658480
\(367\) 10.0667 10.0667i 0.525478 0.525478i −0.393743 0.919221i \(-0.628820\pi\)
0.919221 + 0.393743i \(0.128820\pi\)
\(368\) −0.254201 −0.0132512
\(369\) −5.96538 −0.310545
\(370\) −12.5328 5.28471i −0.651551 0.274739i
\(371\) −2.23032 −0.115792
\(372\) 4.79363 0.248538
\(373\) 15.0617 15.0617i 0.779867 0.779867i −0.199941 0.979808i \(-0.564075\pi\)
0.979808 + 0.199941i \(0.0640751\pi\)
\(374\) −2.71731 −0.140509
\(375\) −5.14625 + 9.92553i −0.265751 + 0.512552i
\(376\) −2.51562 + 2.51562i −0.129733 + 0.129733i
\(377\) −22.3169 + 22.3169i −1.14938 + 1.14938i
\(378\) 1.22667 0.0630932
\(379\) 28.1933i 1.44819i 0.689699 + 0.724097i \(0.257743\pi\)
−0.689699 + 0.724097i \(0.742257\pi\)
\(380\) −14.8175 + 5.64777i −0.760121 + 0.289725i
\(381\) 12.9633i 0.664131i
\(382\) 4.79894 4.79894i 0.245535 0.245535i
\(383\) 28.9731 1.48045 0.740227 0.672357i \(-0.234718\pi\)
0.740227 + 0.672357i \(0.234718\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) 2.81520 1.07303i 0.143476 0.0546865i
\(386\) 2.16290 0.110089
\(387\) 11.5248i 0.585840i
\(388\) 5.50451i 0.279449i
\(389\) −15.5001 15.5001i −0.785886 0.785886i 0.194931 0.980817i \(-0.437552\pi\)
−0.980817 + 0.194931i \(0.937552\pi\)
\(390\) −3.92547 10.2989i −0.198774 0.521503i
\(391\) 0.628877i 0.0318037i
\(392\) 5.49528i 0.277553i
\(393\) 17.4254 0.878997
\(394\) −3.85768 + 3.85768i −0.194347 + 0.194347i
\(395\) −4.24130 + 1.61660i −0.213403 + 0.0813397i
\(396\) 1.09838 0.0551955
\(397\) 11.9173 + 11.9173i 0.598111 + 0.598111i 0.939810 0.341699i \(-0.111002\pi\)
−0.341699 + 0.939810i \(0.611002\pi\)
\(398\) −11.9163 + 11.9163i −0.597310 + 0.597310i
\(399\) −6.15119 + 6.15119i −0.307944 + 0.307944i
\(400\) −3.32806 3.73149i −0.166403 0.186575i
\(401\) −24.2655 24.2655i −1.21176 1.21176i −0.970448 0.241312i \(-0.922422\pi\)
−0.241312 0.970448i \(-0.577578\pi\)
\(402\) 11.4334 0.570247
\(403\) −16.7074 16.7074i −0.832257 0.832257i
\(404\) 18.0390i 0.897473i
\(405\) −0.914315 + 2.04060i −0.0454327 + 0.101398i
\(406\) 7.85447i 0.389811i
\(407\) −6.67952 + 0.148280i −0.331091 + 0.00734995i
\(408\) 1.74934 + 1.74934i 0.0866050 + 0.0866050i
\(409\) 24.8350 24.8350i 1.22801 1.22801i 0.263299 0.964714i \(-0.415189\pi\)
0.964714 0.263299i \(-0.0848106\pi\)
\(410\) 12.1729 + 5.45423i 0.601178 + 0.269365i
\(411\) 9.40403i 0.463866i
\(412\) 16.4190i 0.808904i
\(413\) 6.26327 0.308195
\(414\) 0.254201i 0.0124933i
\(415\) 21.7013 8.27159i 1.06528 0.406036i
\(416\) 4.92901 0.241665
\(417\) 8.46886 8.46886i 0.414722 0.414722i
\(418\) −5.50784 + 5.50784i −0.269397 + 0.269397i
\(419\) 14.9938i 0.732494i 0.930518 + 0.366247i \(0.119358\pi\)
−0.930518 + 0.366247i \(0.880642\pi\)
\(420\) −2.50314 1.12156i −0.122141 0.0547267i
\(421\) −14.6084 14.6084i −0.711970 0.711970i 0.254977 0.966947i \(-0.417932\pi\)
−0.966947 + 0.254977i \(0.917932\pi\)
\(422\) −25.4750 −1.24010
\(423\) −2.51562 2.51562i −0.122314 0.122314i
\(424\) 1.28565 + 1.28565i 0.0624368 + 0.0624368i
\(425\) −9.23147 + 8.23339i −0.447792 + 0.399378i
\(426\) −9.15333 + 9.15333i −0.443480 + 0.443480i
\(427\) 1.54530 0.0747821
\(428\) −3.46603 + 3.46603i −0.167537 + 0.167537i
\(429\) −3.82821 3.82821i −0.184828 0.184828i
\(430\) 10.5373 23.5175i 0.508155 1.13412i
\(431\) −28.1159 28.1159i −1.35430 1.35430i −0.880790 0.473507i \(-0.842988\pi\)
−0.473507 0.880790i \(-0.657012\pi\)
\(432\) −0.707107 0.707107i −0.0340207 0.0340207i
\(433\) 3.11871 + 3.11871i 0.149876 + 0.149876i 0.778062 0.628187i \(-0.216203\pi\)
−0.628187 + 0.778062i \(0.716203\pi\)
\(434\) −5.88021 −0.282259
\(435\) −13.0661 5.85443i −0.626471 0.280698i
\(436\) −9.52466 9.52466i −0.456149 0.456149i
\(437\) 1.27470 + 1.27470i 0.0609772 + 0.0609772i
\(438\) 13.5287i 0.646427i
\(439\) −0.948240 + 0.948240i −0.0452570 + 0.0452570i −0.729373 0.684116i \(-0.760188\pi\)
0.684116 + 0.729373i \(0.260188\pi\)
\(440\) −2.24134 1.00426i −0.106852 0.0478763i
\(441\) 5.49528 0.261680
\(442\) 12.1941i 0.580012i
\(443\) 8.59429 8.59429i 0.408327 0.408327i −0.472828 0.881155i \(-0.656767\pi\)
0.881155 + 0.472828i \(0.156767\pi\)
\(444\) 4.39556 + 4.20464i 0.208604 + 0.199544i
\(445\) 11.1918 + 29.3627i 0.530540 + 1.39193i
\(446\) 3.60544 + 3.60544i 0.170723 + 0.170723i
\(447\) −10.6388 10.6388i −0.503198 0.503198i
\(448\) 0.867388 0.867388i 0.0409802 0.0409802i
\(449\) 19.1095 + 19.1095i 0.901831 + 0.901831i 0.995595 0.0937631i \(-0.0298896\pi\)
−0.0937631 + 0.995595i \(0.529890\pi\)
\(450\) 3.73149 3.32806i 0.175904 0.156886i
\(451\) 6.55223 0.308532
\(452\) 12.6239i 0.593777i
\(453\) 10.2474 + 10.2474i 0.481464 + 0.481464i
\(454\) 11.2463i 0.527814i
\(455\) 4.81526 + 12.6333i 0.225743 + 0.592259i
\(456\) 7.09162 0.332096
\(457\) 15.6387i 0.731546i 0.930704 + 0.365773i \(0.119195\pi\)
−0.930704 + 0.365773i \(0.880805\pi\)
\(458\) 18.6659i 0.872200i
\(459\) −1.74934 + 1.74934i −0.0816520 + 0.0816520i
\(460\) −0.232420 + 0.518722i −0.0108366 + 0.0241855i
\(461\) −0.984005 + 0.984005i −0.0458297 + 0.0458297i −0.729650 0.683821i \(-0.760317\pi\)
0.683821 + 0.729650i \(0.260317\pi\)
\(462\) −1.34735 −0.0626842
\(463\) 7.27134 0.337928 0.168964 0.985622i \(-0.445958\pi\)
0.168964 + 0.985622i \(0.445958\pi\)
\(464\) 4.52766 4.52766i 0.210191 0.210191i
\(465\) 4.38289 9.78187i 0.203252 0.453623i
\(466\) 1.86289 1.86289i 0.0862969 0.0862969i
\(467\) 21.2081i 0.981395i 0.871330 + 0.490697i \(0.163258\pi\)
−0.871330 + 0.490697i \(0.836742\pi\)
\(468\) 4.92901i 0.227844i
\(469\) −14.0251 −0.647617
\(470\) 2.83330 + 7.43344i 0.130690 + 0.342879i
\(471\) 13.3613i 0.615657i
\(472\) −3.61042 3.61042i −0.166183 0.166183i
\(473\) 12.6586i 0.582043i
\(474\) 2.02988 0.0932353
\(475\) −2.02304 + 35.4003i −0.0928235 + 1.62428i
\(476\) −2.14586 2.14586i −0.0983553 0.0983553i
\(477\) −1.28565 + 1.28565i −0.0588660 + 0.0588660i
\(478\) −12.7842 12.7842i −0.584737 0.584737i
\(479\) −29.4758 29.4758i −1.34678 1.34678i −0.889133 0.457649i \(-0.848691\pi\)
−0.457649 0.889133i \(-0.651309\pi\)
\(480\) 0.796400 + 2.08944i 0.0363505 + 0.0953693i
\(481\) −0.665412 29.9746i −0.0303402 1.36673i
\(482\) 1.85063 1.85063i 0.0842940 0.0842940i
\(483\) 0.311821i 0.0141884i
\(484\) 9.79357 0.445162
\(485\) 11.2325 + 5.03286i 0.510041 + 0.228530i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) 0.739280i 0.0335000i 0.999860 + 0.0167500i \(0.00533194\pi\)
−0.999860 + 0.0167500i \(0.994668\pi\)
\(488\) −0.890776 0.890776i −0.0403235 0.0403235i
\(489\) −6.73759 6.73759i −0.304684 0.304684i
\(490\) −11.2136 5.02441i −0.506580 0.226980i
\(491\) −21.9916 −0.992467 −0.496233 0.868189i \(-0.665284\pi\)
−0.496233 + 0.868189i \(0.665284\pi\)
\(492\) −4.21816 4.21816i −0.190169 0.190169i
\(493\) −11.2011 11.2011i −0.504473 0.504473i
\(494\) −24.7167 24.7167i −1.11206 1.11206i
\(495\) 1.00426 2.24134i 0.0451382 0.100741i
\(496\) 3.38961 + 3.38961i 0.152198 + 0.152198i
\(497\) 11.2281 11.2281i 0.503650 0.503650i
\(498\) −10.3862 −0.465417
\(499\) −23.3699 + 23.3699i −1.04618 + 1.04618i −0.0473000 + 0.998881i \(0.515062\pi\)
−0.998881 + 0.0473000i \(0.984938\pi\)
\(500\) −10.6574 + 3.37946i −0.476612 + 0.151134i
\(501\) −3.84323 3.84323i −0.171703 0.171703i
\(502\) −14.6527 14.6527i −0.653982 0.653982i
\(503\) −2.74856 −0.122552 −0.0612762 0.998121i \(-0.519517\pi\)
−0.0612762 + 0.998121i \(0.519517\pi\)
\(504\) 0.867388 + 0.867388i 0.0386365 + 0.0386365i
\(505\) −36.8103 16.4933i −1.63804 0.733943i
\(506\) 0.279209i 0.0124123i
\(507\) 7.98689 7.98689i 0.354710 0.354710i
\(508\) −9.16645 + 9.16645i −0.406695 + 0.406695i
\(509\) −15.4259 −0.683740 −0.341870 0.939747i \(-0.611060\pi\)
−0.341870 + 0.939747i \(0.611060\pi\)
\(510\) 5.16913 1.97024i 0.228893 0.0872438i
\(511\) 16.5953i 0.734133i
\(512\) −1.00000 −0.0441942
\(513\) 7.09162i 0.313103i
\(514\) 7.08582i 0.312542i
\(515\) −33.5045 15.0121i −1.47638 0.661512i
\(516\) −8.14929 + 8.14929i −0.358752 + 0.358752i
\(517\) 2.76310 + 2.76310i 0.121521 + 0.121521i
\(518\) −5.39191 5.15772i −0.236907 0.226617i
\(519\) 7.66138i 0.336297i
\(520\) 4.50667 10.0581i 0.197631 0.441078i
\(521\) 2.41859i 0.105960i −0.998596 0.0529802i \(-0.983128\pi\)
0.998596 0.0529802i \(-0.0168720\pi\)
\(522\) 4.52766 + 4.52766i 0.198170 + 0.198170i
\(523\) −25.0092 −1.09358 −0.546789 0.837270i \(-0.684150\pi\)
−0.546789 + 0.837270i \(0.684150\pi\)
\(524\) 12.3216 + 12.3216i 0.538274 + 0.538274i
\(525\) −4.57732 + 4.08243i −0.199770 + 0.178172i
\(526\) −17.6568 + 17.6568i −0.769872 + 0.769872i
\(527\) 8.38567 8.38567i 0.365286 0.365286i
\(528\) 0.776669 + 0.776669i 0.0338002 + 0.0338002i
\(529\) −22.9354 −0.997191
\(530\) 3.79899 1.44800i 0.165017 0.0628973i
\(531\) 3.61042 3.61042i 0.156679 0.156679i
\(532\) −8.69909 −0.377153
\(533\) 29.4034i 1.27360i
\(534\) 14.0529i 0.608130i
\(535\) 3.90372 + 10.2418i 0.168772 + 0.442791i
\(536\) 8.08465 + 8.08465i 0.349204 + 0.349204i
\(537\) 1.57904i 0.0681405i
\(538\) 22.9016i 0.987357i
\(539\) −6.03588 −0.259984
\(540\) −2.08944 + 0.796400i −0.0899150 + 0.0342716i
\(541\) 17.7792 17.7792i 0.764388 0.764388i −0.212724 0.977112i \(-0.568234\pi\)
0.977112 + 0.212724i \(0.0682337\pi\)
\(542\) −10.0289 −0.430779
\(543\) −2.62329 + 2.62329i −0.112576 + 0.112576i
\(544\) 2.47393i 0.106069i
\(545\) −28.1445 + 10.7274i −1.20558 + 0.459513i
\(546\) 6.04628i 0.258757i
\(547\) 24.0509 1.02834 0.514172 0.857687i \(-0.328099\pi\)
0.514172 + 0.857687i \(0.328099\pi\)
\(548\) 6.64965 6.64965i 0.284059 0.284059i
\(549\) 0.890776 0.890776i 0.0380174 0.0380174i
\(550\) −4.09858 + 3.65546i −0.174764 + 0.155869i
\(551\) −45.4082 −1.93445
\(552\) 0.179747 0.179747i 0.00765056 0.00765056i
\(553\) −2.48999 −0.105885
\(554\) 2.84725 0.120968
\(555\) 12.5989 5.12519i 0.534794 0.217552i
\(556\) 11.9768 0.507928
\(557\) −32.7565 −1.38794 −0.693968 0.720006i \(-0.744139\pi\)
−0.693968 + 0.720006i \(0.744139\pi\)
\(558\) −3.38961 + 3.38961i −0.143494 + 0.143494i
\(559\) 56.8060 2.40264
\(560\) −0.976922 2.56305i −0.0412825 0.108309i
\(561\) 1.92143 1.92143i 0.0811228 0.0811228i
\(562\) −13.1664 + 13.1664i −0.555390 + 0.555390i
\(563\) 30.9683 1.30516 0.652580 0.757720i \(-0.273687\pi\)
0.652580 + 0.757720i \(0.273687\pi\)
\(564\) 3.55763i 0.149803i
\(565\) −25.7602 11.5422i −1.08374 0.485584i
\(566\) 17.3118i 0.727667i
\(567\) −0.867388 + 0.867388i −0.0364269 + 0.0364269i
\(568\) −12.9448 −0.543150
\(569\) 32.3758 32.3758i 1.35726 1.35726i 0.479987 0.877275i \(-0.340641\pi\)
0.877275 0.479987i \(-0.159359\pi\)
\(570\) 6.48397 14.4711i 0.271584 0.606129i
\(571\) 40.5248 1.69591 0.847955 0.530068i \(-0.177833\pi\)
0.847955 + 0.530068i \(0.177833\pi\)
\(572\) 5.41391i 0.226367i
\(573\) 6.78673i 0.283520i
\(574\) 5.17429 + 5.17429i 0.215971 + 0.215971i
\(575\) 0.845996 + 0.948550i 0.0352805 + 0.0395573i
\(576\) 1.00000i 0.0416667i
\(577\) 16.8563i 0.701738i −0.936425 0.350869i \(-0.885886\pi\)
0.936425 0.350869i \(-0.114114\pi\)
\(578\) −10.8797 −0.452534
\(579\) −1.52940 + 1.52940i −0.0635597 + 0.0635597i
\(580\) −5.09941 13.3788i −0.211742 0.555525i
\(581\) 12.7405 0.528564
\(582\) −3.89228 3.89228i −0.161340 0.161340i
\(583\) 1.41213 1.41213i 0.0584844 0.0584844i
\(584\) −9.56625 + 9.56625i −0.395854 + 0.395854i
\(585\) 10.0581 + 4.50667i 0.415852 + 0.186328i
\(586\) 6.15715 + 6.15715i 0.254350 + 0.254350i
\(587\) 21.5366 0.888910 0.444455 0.895801i \(-0.353397\pi\)
0.444455 + 0.895801i \(0.353397\pi\)
\(588\) 3.88575 + 3.88575i 0.160246 + 0.160246i
\(589\) 33.9946i 1.40072i
\(590\) −10.6685 + 4.06635i −0.439214 + 0.167409i
\(591\) 5.45559i 0.224413i
\(592\) 0.134999 + 6.08126i 0.00554842 + 0.249938i
\(593\) 19.1371 + 19.1371i 0.785866 + 0.785866i 0.980814 0.194948i \(-0.0624538\pi\)
−0.194948 + 0.980814i \(0.562454\pi\)
\(594\) −0.776669 + 0.776669i −0.0318671 + 0.0318671i
\(595\) −6.34082 + 2.41684i −0.259948 + 0.0990808i
\(596\) 15.0455i 0.616289i
\(597\) 16.8522i 0.689714i
\(598\) −1.25296 −0.0512374
\(599\) 28.8022i 1.17683i 0.808560 + 0.588414i \(0.200247\pi\)
−0.808560 + 0.588414i \(0.799753\pi\)
\(600\) 4.99186 + 0.285272i 0.203792 + 0.0116462i
\(601\) 29.7406 1.21314 0.606572 0.795028i \(-0.292544\pi\)
0.606572 + 0.795028i \(0.292544\pi\)
\(602\) 9.99650 9.99650i 0.407427 0.407427i
\(603\) −8.08465 + 8.08465i −0.329232 + 0.329232i
\(604\) 14.4920i 0.589671i
\(605\) 8.95441 19.9847i 0.364048 0.812494i
\(606\) 12.7555 + 12.7555i 0.518157 + 0.518157i
\(607\) −34.8254 −1.41352 −0.706760 0.707454i \(-0.749844\pi\)
−0.706760 + 0.707454i \(0.749844\pi\)
\(608\) 5.01453 + 5.01453i 0.203366 + 0.203366i
\(609\) −5.55395 5.55395i −0.225057 0.225057i
\(610\) −2.63216 + 1.00326i −0.106573 + 0.0406209i
\(611\) −12.3995 + 12.3995i −0.501632 + 0.501632i
\(612\) −2.47393 −0.100003
\(613\) −20.5948 + 20.5948i −0.831815 + 0.831815i −0.987765 0.155950i \(-0.950156\pi\)
0.155950 + 0.987765i \(0.450156\pi\)
\(614\) −10.3124 10.3124i −0.416176 0.416176i
\(615\) −12.4643 + 4.75083i −0.502608 + 0.191572i
\(616\) −0.952718 0.952718i −0.0383861 0.0383861i
\(617\) −27.4236 27.4236i −1.10403 1.10403i −0.993919 0.110115i \(-0.964878\pi\)
−0.110115 0.993919i \(-0.535122\pi\)
\(618\) 11.6100 + 11.6100i 0.467021 + 0.467021i
\(619\) −4.08288 −0.164105 −0.0820525 0.996628i \(-0.526148\pi\)
−0.0820525 + 0.996628i \(0.526148\pi\)
\(620\) 10.0160 3.81765i 0.402252 0.153321i
\(621\) 0.179747 + 0.179747i 0.00721301 + 0.00721301i
\(622\) −10.4943 10.4943i −0.420782 0.420782i
\(623\) 17.2383i 0.690639i
\(624\) −3.48534 + 3.48534i −0.139525 + 0.139525i
\(625\) −2.84807 + 24.8372i −0.113923 + 0.993490i
\(626\) −1.40586 −0.0561893
\(627\) 7.78927i 0.311073i
\(628\) −9.44787 + 9.44787i −0.377011 + 0.377011i
\(629\) 15.0446 0.333978i 0.599869 0.0133166i
\(630\) 2.56305 0.976922i 0.102114 0.0389215i
\(631\) 3.77897 + 3.77897i 0.150439 + 0.150439i 0.778314 0.627875i \(-0.216075\pi\)
−0.627875 + 0.778314i \(0.716075\pi\)
\(632\) 1.43534 + 1.43534i 0.0570948 + 0.0570948i
\(633\) 18.0135 18.0135i 0.715974 0.715974i
\(634\) 8.94726 + 8.94726i 0.355341 + 0.355341i
\(635\) 10.3240 + 27.0860i 0.409695 + 1.07488i
\(636\) −1.81819 −0.0720958
\(637\) 27.0863i 1.07320i
\(638\) −4.97307 4.97307i −0.196886 0.196886i
\(639\) 12.9448i 0.512087i
\(640\) −0.914315 + 2.04060i −0.0361415 + 0.0806616i
\(641\) −24.9603 −0.985873 −0.492937 0.870065i \(-0.664077\pi\)
−0.492937 + 0.870065i \(0.664077\pi\)
\(642\) 4.90170i 0.193455i
\(643\) 2.83684i 0.111874i −0.998434 0.0559370i \(-0.982185\pi\)
0.998434 0.0559370i \(-0.0178146\pi\)
\(644\) −0.220491 + 0.220491i −0.00868856 + 0.00868856i
\(645\) 9.17838 + 24.0804i 0.361398 + 0.948165i
\(646\) 12.4056 12.4056i 0.488093 0.488093i
\(647\) 13.4627 0.529272 0.264636 0.964348i \(-0.414748\pi\)
0.264636 + 0.964348i \(0.414748\pi\)
\(648\) 1.00000 0.0392837
\(649\) −3.96560 + 3.96560i −0.155663 + 0.155663i
\(650\) −16.4040 18.3926i −0.643419 0.721416i
\(651\) 4.15794 4.15794i 0.162963 0.162963i
\(652\) 9.52839i 0.373161i
\(653\) 10.3817i 0.406266i 0.979151 + 0.203133i \(0.0651124\pi\)
−0.979151 + 0.203133i \(0.934888\pi\)
\(654\) 13.4699 0.526715
\(655\) 36.4094 13.8776i 1.42263 0.542244i
\(656\) 5.96538i 0.232909i
\(657\) −9.56625 9.56625i −0.373215 0.373215i
\(658\) 4.36404i 0.170128i
\(659\) 8.07050 0.314382 0.157191 0.987568i \(-0.449756\pi\)
0.157191 + 0.987568i \(0.449756\pi\)
\(660\) 2.29499 0.874747i 0.0893323 0.0340495i
\(661\) −19.6260 19.6260i −0.763361 0.763361i 0.213567 0.976928i \(-0.431492\pi\)
−0.976928 + 0.213567i \(0.931492\pi\)
\(662\) −10.3088 + 10.3088i −0.400663 + 0.400663i
\(663\) 8.62250 + 8.62250i 0.334870 + 0.334870i
\(664\) −7.34416 7.34416i −0.285009 0.285009i
\(665\) −7.95371 + 17.7513i −0.308432 + 0.688367i
\(666\) −6.08126 + 0.134999i −0.235644 + 0.00523110i
\(667\) −1.15094 + 1.15094i −0.0445644 + 0.0445644i
\(668\) 5.43514i 0.210292i
\(669\) −5.09887 −0.197134
\(670\) 23.8894 9.10558i 0.922928 0.351779i
\(671\) −0.978407 + 0.978407i −0.0377710 + 0.0377710i
\(672\) 1.22667i 0.0473199i
\(673\) −16.3159 16.3159i −0.628931 0.628931i 0.318868 0.947799i \(-0.396697\pi\)
−0.947799 + 0.318868i \(0.896697\pi\)
\(674\) 2.99336 + 2.99336i 0.115300 + 0.115300i
\(675\) −0.285272 + 4.99186i −0.0109801 + 0.192137i
\(676\) 11.2952 0.434430
\(677\) −0.868664 0.868664i −0.0333855 0.0333855i 0.690217 0.723602i \(-0.257515\pi\)
−0.723602 + 0.690217i \(0.757515\pi\)
\(678\) 8.92643 + 8.92643i 0.342817 + 0.342817i
\(679\) 4.77455 + 4.77455i 0.183230 + 0.183230i
\(680\) 5.04830 + 2.26195i 0.193593 + 0.0867420i
\(681\) −7.95232 7.95232i −0.304734 0.304734i
\(682\) 3.72307 3.72307i 0.142564 0.142564i
\(683\) −0.517143 −0.0197879 −0.00989397 0.999951i \(-0.503149\pi\)
−0.00989397 + 0.999951i \(0.503149\pi\)
\(684\) −5.01453 + 5.01453i −0.191735 + 0.191735i
\(685\) −7.48937 19.6491i −0.286154 0.750754i
\(686\) −10.8383 10.8383i −0.413806 0.413806i
\(687\) 13.1988 + 13.1988i 0.503565 + 0.503565i
\(688\) −11.5248 −0.439380
\(689\) 6.33700 + 6.33700i 0.241420 + 0.241420i
\(690\) −0.202446 0.531137i −0.00770699 0.0202201i
\(691\) 19.4361i 0.739384i −0.929154 0.369692i \(-0.879463\pi\)
0.929154 0.369692i \(-0.120537\pi\)
\(692\) −5.41742 + 5.41742i −0.205939 + 0.205939i
\(693\) 0.952718 0.952718i 0.0361908 0.0361908i
\(694\) −20.2118 −0.767229
\(695\) 10.9505 24.4397i 0.415378 0.927052i
\(696\) 6.40308i 0.242708i
\(697\) −14.7579 −0.558997
\(698\) 15.7463i 0.596006i
\(699\) 2.63453i 0.0996471i
\(700\) −6.12337 0.349935i −0.231442 0.0132263i
\(701\) 0.871318 0.871318i 0.0329092 0.0329092i −0.690461 0.723370i \(-0.742592\pi\)
0.723370 + 0.690461i \(0.242592\pi\)
\(702\) −3.48534 3.48534i −0.131546 0.131546i
\(703\) 29.8177 31.1717i 1.12460 1.17566i
\(704\) 1.09838i 0.0413966i
\(705\) −7.25968 3.25279i −0.273415 0.122507i
\(706\) 3.15443i 0.118719i
\(707\) −15.6468 15.6468i −0.588459 0.588459i
\(708\) 5.10591 0.191892
\(709\) −19.1416 19.1416i −0.718880 0.718880i 0.249496 0.968376i \(-0.419735\pi\)
−0.968376 + 0.249496i \(0.919735\pi\)
\(710\) −11.8356 + 26.4150i −0.444181 + 0.991338i
\(711\) −1.43534 + 1.43534i −0.0538295 + 0.0538295i
\(712\) 9.93692 9.93692i 0.372402 0.372402i
\(713\) −0.861643 0.861643i −0.0322688 0.0322688i
\(714\) 3.03470 0.113571
\(715\) −11.0476 4.95002i −0.413157 0.185120i
\(716\) 1.11655 1.11655i 0.0417274 0.0417274i
\(717\) 18.0796 0.675196
\(718\) 6.13746i 0.229048i
\(719\) 12.8203i 0.478117i −0.971005 0.239058i \(-0.923161\pi\)
0.971005 0.239058i \(-0.0768388\pi\)
\(720\) −2.04060 0.914315i −0.0760485 0.0340745i
\(721\) −14.2416 14.2416i −0.530385 0.530385i
\(722\) 31.2911i 1.16453i
\(723\) 2.61719i 0.0973343i
\(724\) −3.70989 −0.137877
\(725\) −31.9632 1.82662i −1.18708 0.0678389i
\(726\) −6.92510 + 6.92510i −0.257015 + 0.257015i
\(727\) 37.5040 1.39095 0.695474 0.718551i \(-0.255195\pi\)
0.695474 + 0.718551i \(0.255195\pi\)
\(728\) 4.27537 4.27537i 0.158456 0.158456i
\(729\) 1.00000i 0.0370370i
\(730\) 10.7743 + 28.2674i 0.398774 + 1.04622i
\(731\) 28.5117i 1.05454i
\(732\) 1.25975 0.0465616
\(733\) −18.9861 + 18.9861i −0.701269 + 0.701269i −0.964683 0.263414i \(-0.915152\pi\)
0.263414 + 0.964683i \(0.415152\pi\)
\(734\) −10.0667 + 10.0667i −0.371569 + 0.371569i
\(735\) 11.4820 4.37644i 0.423521 0.161427i
\(736\) 0.254201 0.00936998
\(737\) 8.87999 8.87999i 0.327098 0.327098i
\(738\) 5.96538 0.219589
\(739\) −5.07356 −0.186634 −0.0933169 0.995636i \(-0.529747\pi\)
−0.0933169 + 0.995636i \(0.529747\pi\)
\(740\) 12.5328 + 5.28471i 0.460716 + 0.194270i
\(741\) 34.9547 1.28409
\(742\) 2.23032 0.0818775
\(743\) −1.23779 + 1.23779i −0.0454102 + 0.0454102i −0.729447 0.684037i \(-0.760223\pi\)
0.684037 + 0.729447i \(0.260223\pi\)
\(744\) −4.79363 −0.175743
\(745\) −30.7018 13.7564i −1.12483 0.503994i
\(746\) −15.0617 + 15.0617i −0.551449 + 0.551449i
\(747\) 7.34416 7.34416i 0.268709 0.268709i
\(748\) 2.71731 0.0993547
\(749\) 6.01278i 0.219702i
\(750\) 5.14625 9.92553i 0.187915 0.362429i
\(751\) 9.88564i 0.360732i 0.983600 + 0.180366i \(0.0577282\pi\)
−0.983600 + 0.180366i \(0.942272\pi\)
\(752\) 2.51562 2.51562i 0.0917353 0.0917353i
\(753\) 20.7220 0.755153
\(754\) 22.3169 22.3169i 0.812733 0.812733i
\(755\) 29.5723 + 13.2502i 1.07625 + 0.482226i
\(756\) −1.22667 −0.0446136
\(757\) 36.7008i 1.33391i 0.745097 + 0.666956i \(0.232403\pi\)
−0.745097 + 0.666956i \(0.767597\pi\)
\(758\) 28.1933i 1.02403i
\(759\) −0.197430 0.197430i −0.00716626 0.00716626i
\(760\) 14.8175 5.64777i 0.537487 0.204866i
\(761\) 37.6951i 1.36645i −0.730209 0.683224i \(-0.760577\pi\)
0.730209 0.683224i \(-0.239423\pi\)
\(762\) 12.9633i 0.469611i
\(763\) −16.5232 −0.598178
\(764\) −4.79894 + 4.79894i −0.173620 + 0.173620i
\(765\) −2.26195 + 5.04830i −0.0817811 + 0.182522i
\(766\) −28.9731 −1.04684
\(767\) −17.7958 17.7958i −0.642570 0.642570i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) −34.1561 + 34.1561i −1.23170 + 1.23170i −0.268392 + 0.963310i \(0.586492\pi\)
−0.963310 + 0.268392i \(0.913508\pi\)
\(770\) −2.81520 + 1.07303i −0.101453 + 0.0386692i
\(771\) 5.01043 + 5.01043i 0.180446 + 0.180446i
\(772\) −2.16290 −0.0778444
\(773\) 28.6997 + 28.6997i 1.03226 + 1.03226i 0.999462 + 0.0327935i \(0.0104404\pi\)
0.0327935 + 0.999462i \(0.489560\pi\)
\(774\) 11.5248i 0.414251i
\(775\) 1.36749 23.9291i 0.0491217 0.859560i
\(776\) 5.50451i 0.197601i
\(777\) 7.45971 0.165599i 0.267616 0.00594084i
\(778\) 15.5001 + 15.5001i 0.555706 + 0.555706i
\(779\) −29.9136 + 29.9136i −1.07177 + 1.07177i