Properties

Label 1110.2.l.b.697.17
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 697.17
Character \(\chi\) \(=\) 1110.697
Dual form 1110.2.l.b.43.17

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.07828 + 0.825074i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.45633 + 1.45633i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.07828 + 0.825074i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.45633 + 1.45633i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-0.825074 - 2.07828i) q^{10} +3.60654i q^{11} +(-0.707107 - 0.707107i) q^{12} +0.566998i q^{13} +(-1.45633 + 1.45633i) q^{14} +(-2.05298 - 0.886151i) q^{15} +1.00000 q^{16} -3.56279 q^{17} -1.00000 q^{18} +(-2.60983 - 2.60983i) q^{19} +(2.07828 - 0.825074i) q^{20} +2.05956i q^{21} -3.60654 q^{22} +2.32324i q^{23} +(0.707107 - 0.707107i) q^{24} +(3.63850 - 3.42947i) q^{25} -0.566998 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.45633 - 1.45633i) q^{28} +(0.784491 - 0.784491i) q^{29} +(0.886151 - 2.05298i) q^{30} +(-1.50323 - 1.50323i) q^{31} +1.00000i q^{32} +(-2.55021 + 2.55021i) q^{33} -3.56279i q^{34} +(-4.22824 - 1.82508i) q^{35} -1.00000i q^{36} +(-3.08463 + 5.24262i) q^{37} +(2.60983 - 2.60983i) q^{38} +(-0.400928 + 0.400928i) q^{39} +(0.825074 + 2.07828i) q^{40} +8.53277i q^{41} -2.05956 q^{42} -1.13168i q^{43} -3.60654i q^{44} +(-0.825074 - 2.07828i) q^{45} -2.32324 q^{46} +(-4.15173 - 4.15173i) q^{47} +(0.707107 + 0.707107i) q^{48} -2.75821i q^{49} +(3.42947 + 3.63850i) q^{50} +(-2.51927 - 2.51927i) q^{51} -0.566998i q^{52} +(-4.48711 + 4.48711i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-2.97566 - 7.49540i) q^{55} +(1.45633 - 1.45633i) q^{56} -3.69086i q^{57} +(0.784491 + 0.784491i) q^{58} +(-5.54174 - 5.54174i) q^{59} +(2.05298 + 0.886151i) q^{60} +(-5.08840 - 5.08840i) q^{61} +(1.50323 - 1.50323i) q^{62} +(-1.45633 + 1.45633i) q^{63} -1.00000 q^{64} +(-0.467815 - 1.17838i) q^{65} +(-2.55021 - 2.55021i) q^{66} +(-1.64587 + 1.64587i) q^{67} +3.56279 q^{68} +(-1.64278 + 1.64278i) q^{69} +(1.82508 - 4.22824i) q^{70} -3.57811 q^{71} +1.00000 q^{72} +(-0.352111 - 0.352111i) q^{73} +(-5.24262 - 3.08463i) q^{74} +(4.99781 + 0.147808i) q^{75} +(2.60983 + 2.60983i) q^{76} +(-5.25231 + 5.25231i) q^{77} +(-0.400928 - 0.400928i) q^{78} +(0.260977 + 0.260977i) q^{79} +(-2.07828 + 0.825074i) q^{80} -1.00000 q^{81} -8.53277 q^{82} +(2.52897 - 2.52897i) q^{83} -2.05956i q^{84} +(7.40448 - 2.93957i) q^{85} +1.13168 q^{86} +1.10944 q^{87} +3.60654 q^{88} +(-5.23378 + 5.23378i) q^{89} +(2.07828 - 0.825074i) q^{90} +(-0.825735 + 0.825735i) q^{91} -2.32324i q^{92} -2.12589i q^{93} +(4.15173 - 4.15173i) q^{94} +(7.57726 + 3.27066i) q^{95} +(-0.707107 + 0.707107i) q^{96} +11.4260 q^{97} +2.75821 q^{98} -3.60654 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
\(5\) −2.07828 + 0.825074i −0.929436 + 0.368984i
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) 1.45633 + 1.45633i 0.550441 + 0.550441i 0.926568 0.376127i \(-0.122744\pi\)
−0.376127 + 0.926568i \(0.622744\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) −0.825074 2.07828i −0.260911 0.657210i
\(11\) 3.60654i 1.08741i 0.839276 + 0.543706i \(0.182979\pi\)
−0.839276 + 0.543706i \(0.817021\pi\)
\(12\) −0.707107 0.707107i −0.204124 0.204124i
\(13\) 0.566998i 0.157257i 0.996904 + 0.0786284i \(0.0250541\pi\)
−0.996904 + 0.0786284i \(0.974946\pi\)
\(14\) −1.45633 + 1.45633i −0.389220 + 0.389220i
\(15\) −2.05298 0.886151i −0.530078 0.228803i
\(16\) 1.00000 0.250000
\(17\) −3.56279 −0.864104 −0.432052 0.901849i \(-0.642210\pi\)
−0.432052 + 0.901849i \(0.642210\pi\)
\(18\) −1.00000 −0.235702
\(19\) −2.60983 2.60983i −0.598736 0.598736i 0.341240 0.939976i \(-0.389153\pi\)
−0.939976 + 0.341240i \(0.889153\pi\)
\(20\) 2.07828 0.825074i 0.464718 0.184492i
\(21\) 2.05956i 0.449433i
\(22\) −3.60654 −0.768917
\(23\) 2.32324i 0.484429i 0.970223 + 0.242215i \(0.0778738\pi\)
−0.970223 + 0.242215i \(0.922126\pi\)
\(24\) 0.707107 0.707107i 0.144338 0.144338i
\(25\) 3.63850 3.42947i 0.727701 0.685895i
\(26\) −0.566998 −0.111197
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) −1.45633 1.45633i −0.275220 0.275220i
\(29\) 0.784491 0.784491i 0.145676 0.145676i −0.630507 0.776183i \(-0.717153\pi\)
0.776183 + 0.630507i \(0.217153\pi\)
\(30\) 0.886151 2.05298i 0.161788 0.374822i
\(31\) −1.50323 1.50323i −0.269988 0.269988i 0.559107 0.829095i \(-0.311144\pi\)
−0.829095 + 0.559107i \(0.811144\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −2.55021 + 2.55021i −0.443934 + 0.443934i
\(34\) 3.56279i 0.611014i
\(35\) −4.22824 1.82508i −0.714703 0.308495i
\(36\) 1.00000i 0.166667i
\(37\) −3.08463 + 5.24262i −0.507110 + 0.861882i
\(38\) 2.60983 2.60983i 0.423370 0.423370i
\(39\) −0.400928 + 0.400928i −0.0641998 + 0.0641998i
\(40\) 0.825074 + 2.07828i 0.130456 + 0.328605i
\(41\) 8.53277i 1.33260i 0.745686 + 0.666298i \(0.232122\pi\)
−0.745686 + 0.666298i \(0.767878\pi\)
\(42\) −2.05956 −0.317797
\(43\) 1.13168i 0.172579i −0.996270 0.0862897i \(-0.972499\pi\)
0.996270 0.0862897i \(-0.0275011\pi\)
\(44\) 3.60654i 0.543706i
\(45\) −0.825074 2.07828i −0.122995 0.309812i
\(46\) −2.32324 −0.342543
\(47\) −4.15173 4.15173i −0.605592 0.605592i 0.336199 0.941791i \(-0.390859\pi\)
−0.941791 + 0.336199i \(0.890859\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 2.75821i 0.394030i
\(50\) 3.42947 + 3.63850i 0.485001 + 0.514562i
\(51\) −2.51927 2.51927i −0.352769 0.352769i
\(52\) 0.566998i 0.0786284i
\(53\) −4.48711 + 4.48711i −0.616352 + 0.616352i −0.944594 0.328242i \(-0.893544\pi\)
0.328242 + 0.944594i \(0.393544\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) −2.97566 7.49540i −0.401238 1.01068i
\(56\) 1.45633 1.45633i 0.194610 0.194610i
\(57\) 3.69086i 0.488866i
\(58\) 0.784491 + 0.784491i 0.103009 + 0.103009i
\(59\) −5.54174 5.54174i −0.721473 0.721473i 0.247432 0.968905i \(-0.420413\pi\)
−0.968905 + 0.247432i \(0.920413\pi\)
\(60\) 2.05298 + 0.886151i 0.265039 + 0.114402i
\(61\) −5.08840 5.08840i −0.651503 0.651503i 0.301852 0.953355i \(-0.402395\pi\)
−0.953355 + 0.301852i \(0.902395\pi\)
\(62\) 1.50323 1.50323i 0.190910 0.190910i
\(63\) −1.45633 + 1.45633i −0.183480 + 0.183480i
\(64\) −1.00000 −0.125000
\(65\) −0.467815 1.17838i −0.0580253 0.146160i
\(66\) −2.55021 2.55021i −0.313909 0.313909i
\(67\) −1.64587 + 1.64587i −0.201076 + 0.201076i −0.800461 0.599385i \(-0.795412\pi\)
0.599385 + 0.800461i \(0.295412\pi\)
\(68\) 3.56279 0.432052
\(69\) −1.64278 + 1.64278i −0.197767 + 0.197767i
\(70\) 1.82508 4.22824i 0.218139 0.505372i
\(71\) −3.57811 −0.424643 −0.212322 0.977200i \(-0.568102\pi\)
−0.212322 + 0.977200i \(0.568102\pi\)
\(72\) 1.00000 0.117851
\(73\) −0.352111 0.352111i −0.0412114 0.0412114i 0.686201 0.727412i \(-0.259277\pi\)
−0.727412 + 0.686201i \(0.759277\pi\)
\(74\) −5.24262 3.08463i −0.609442 0.358581i
\(75\) 4.99781 + 0.147808i 0.577098 + 0.0170674i
\(76\) 2.60983 + 2.60983i 0.299368 + 0.299368i
\(77\) −5.25231 + 5.25231i −0.598556 + 0.598556i
\(78\) −0.400928 0.400928i −0.0453961 0.0453961i
\(79\) 0.260977 + 0.260977i 0.0293622 + 0.0293622i 0.721635 0.692273i \(-0.243391\pi\)
−0.692273 + 0.721635i \(0.743391\pi\)
\(80\) −2.07828 + 0.825074i −0.232359 + 0.0922461i
\(81\) −1.00000 −0.111111
\(82\) −8.53277 −0.942287
\(83\) 2.52897 2.52897i 0.277590 0.277590i −0.554556 0.832146i \(-0.687112\pi\)
0.832146 + 0.554556i \(0.187112\pi\)
\(84\) 2.05956i 0.224716i
\(85\) 7.40448 2.93957i 0.803129 0.318841i
\(86\) 1.13168 0.122032
\(87\) 1.10944 0.118944
\(88\) 3.60654 0.384458
\(89\) −5.23378 + 5.23378i −0.554780 + 0.554780i −0.927817 0.373037i \(-0.878317\pi\)
0.373037 + 0.927817i \(0.378317\pi\)
\(90\) 2.07828 0.825074i 0.219070 0.0869705i
\(91\) −0.825735 + 0.825735i −0.0865606 + 0.0865606i
\(92\) 2.32324i 0.242215i
\(93\) 2.12589i 0.220444i
\(94\) 4.15173 4.15173i 0.428218 0.428218i
\(95\) 7.57726 + 3.27066i 0.777411 + 0.335562i
\(96\) −0.707107 + 0.707107i −0.0721688 + 0.0721688i
\(97\) 11.4260 1.16014 0.580068 0.814568i \(-0.303026\pi\)
0.580068 + 0.814568i \(0.303026\pi\)
\(98\) 2.75821 0.278621
\(99\) −3.60654 −0.362471
\(100\) −3.63850 + 3.42947i −0.363850 + 0.342947i
\(101\) 2.80173i 0.278783i 0.990237 + 0.139391i \(0.0445146\pi\)
−0.990237 + 0.139391i \(0.955485\pi\)
\(102\) 2.51927 2.51927i 0.249445 0.249445i
\(103\) 10.2094 1.00596 0.502979 0.864298i \(-0.332237\pi\)
0.502979 + 0.864298i \(0.332237\pi\)
\(104\) 0.566998 0.0555987
\(105\) −1.69929 4.28035i −0.165834 0.417719i
\(106\) −4.48711 4.48711i −0.435826 0.435826i
\(107\) 10.7074 + 10.7074i 1.03512 + 1.03512i 0.999360 + 0.0357612i \(0.0113856\pi\)
0.0357612 + 0.999360i \(0.488614\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) 2.12012 + 2.12012i 0.203071 + 0.203071i 0.801314 0.598243i \(-0.204134\pi\)
−0.598243 + 0.801314i \(0.704134\pi\)
\(110\) 7.49540 2.97566i 0.714659 0.283718i
\(111\) −5.88825 + 1.52593i −0.558888 + 0.144835i
\(112\) 1.45633 + 1.45633i 0.137610 + 0.137610i
\(113\) −4.98518 −0.468966 −0.234483 0.972120i \(-0.575340\pi\)
−0.234483 + 0.972120i \(0.575340\pi\)
\(114\) 3.69086 0.345680
\(115\) −1.91685 4.82835i −0.178747 0.450246i
\(116\) −0.784491 + 0.784491i −0.0728381 + 0.0728381i
\(117\) −0.566998 −0.0524189
\(118\) 5.54174 5.54174i 0.510159 0.510159i
\(119\) −5.18860 5.18860i −0.475638 0.475638i
\(120\) −0.886151 + 2.05298i −0.0808942 + 0.187411i
\(121\) −2.00713 −0.182466
\(122\) 5.08840 5.08840i 0.460682 0.460682i
\(123\) −6.03358 + 6.03358i −0.544030 + 0.544030i
\(124\) 1.50323 + 1.50323i 0.134994 + 0.134994i
\(125\) −4.73227 + 10.1294i −0.423267 + 0.906005i
\(126\) −1.45633 1.45633i −0.129740 0.129740i
\(127\) 8.16328 + 8.16328i 0.724374 + 0.724374i 0.969493 0.245119i \(-0.0788271\pi\)
−0.245119 + 0.969493i \(0.578827\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0.800218 0.800218i 0.0704552 0.0704552i
\(130\) 1.17838 0.467815i 0.103351 0.0410301i
\(131\) 5.79100 + 5.79100i 0.505962 + 0.505962i 0.913284 0.407323i \(-0.133538\pi\)
−0.407323 + 0.913284i \(0.633538\pi\)
\(132\) 2.55021 2.55021i 0.221967 0.221967i
\(133\) 7.60154i 0.659137i
\(134\) −1.64587 1.64587i −0.142182 0.142182i
\(135\) 0.886151 2.05298i 0.0762677 0.176693i
\(136\) 3.56279i 0.305507i
\(137\) 11.0100 + 11.0100i 0.940646 + 0.940646i 0.998335 0.0576885i \(-0.0183730\pi\)
−0.0576885 + 0.998335i \(0.518373\pi\)
\(138\) −1.64278 1.64278i −0.139843 0.139843i
\(139\) −10.0881 −0.855664 −0.427832 0.903858i \(-0.640723\pi\)
−0.427832 + 0.903858i \(0.640723\pi\)
\(140\) 4.22824 + 1.82508i 0.357352 + 0.154248i
\(141\) 5.87144i 0.494464i
\(142\) 3.57811i 0.300268i
\(143\) −2.04490 −0.171003
\(144\) 1.00000i 0.0833333i
\(145\) −0.983129 + 2.27766i −0.0816444 + 0.189149i
\(146\) 0.352111 0.352111i 0.0291409 0.0291409i
\(147\) 1.95035 1.95035i 0.160862 0.160862i
\(148\) 3.08463 5.24262i 0.253555 0.430941i
\(149\) 8.10303i 0.663826i 0.943310 + 0.331913i \(0.107694\pi\)
−0.943310 + 0.331913i \(0.892306\pi\)
\(150\) −0.147808 + 4.99781i −0.0120685 + 0.408070i
\(151\) 7.24237i 0.589375i 0.955594 + 0.294688i \(0.0952156\pi\)
−0.955594 + 0.294688i \(0.904784\pi\)
\(152\) −2.60983 + 2.60983i −0.211685 + 0.211685i
\(153\) 3.56279i 0.288035i
\(154\) −5.25231 5.25231i −0.423243 0.423243i
\(155\) 4.36441 + 1.88386i 0.350558 + 0.151315i
\(156\) 0.400928 0.400928i 0.0320999 0.0320999i
\(157\) 11.2460 + 11.2460i 0.897532 + 0.897532i 0.995217 0.0976855i \(-0.0311439\pi\)
−0.0976855 + 0.995217i \(0.531144\pi\)
\(158\) −0.260977 + 0.260977i −0.0207622 + 0.0207622i
\(159\) −6.34573 −0.503249
\(160\) −0.825074 2.07828i −0.0652279 0.164303i
\(161\) −3.38341 + 3.38341i −0.266650 + 0.266650i
\(162\) 1.00000i 0.0785674i
\(163\) −3.48853 −0.273243 −0.136621 0.990623i \(-0.543624\pi\)
−0.136621 + 0.990623i \(0.543624\pi\)
\(164\) 8.53277i 0.666298i
\(165\) 3.19594 7.40416i 0.248804 0.576413i
\(166\) 2.52897 + 2.52897i 0.196286 + 0.196286i
\(167\) 13.0005 1.00601 0.503005 0.864284i \(-0.332228\pi\)
0.503005 + 0.864284i \(0.332228\pi\)
\(168\) 2.05956 0.158899
\(169\) 12.6785 0.975270
\(170\) 2.93957 + 7.40448i 0.225455 + 0.567898i
\(171\) 2.60983 2.60983i 0.199579 0.199579i
\(172\) 1.13168i 0.0862897i
\(173\) −12.4447 12.4447i −0.946152 0.946152i 0.0524705 0.998622i \(-0.483290\pi\)
−0.998622 + 0.0524705i \(0.983290\pi\)
\(174\) 1.10944i 0.0841062i
\(175\) 10.2933 + 0.304419i 0.778101 + 0.0230119i
\(176\) 3.60654i 0.271853i
\(177\) 7.83720i 0.589080i
\(178\) −5.23378 5.23378i −0.392289 0.392289i
\(179\) −6.17102 + 6.17102i −0.461243 + 0.461243i −0.899063 0.437819i \(-0.855751\pi\)
0.437819 + 0.899063i \(0.355751\pi\)
\(180\) 0.825074 + 2.07828i 0.0614974 + 0.154906i
\(181\) 8.27365 0.614975 0.307488 0.951552i \(-0.400512\pi\)
0.307488 + 0.951552i \(0.400512\pi\)
\(182\) −0.825735 0.825735i −0.0612076 0.0612076i
\(183\) 7.19609i 0.531950i
\(184\) 2.32324 0.171272
\(185\) 2.08517 13.4407i 0.153305 0.988179i
\(186\) 2.12589 0.155878
\(187\) 12.8493i 0.939637i
\(188\) 4.15173 + 4.15173i 0.302796 + 0.302796i
\(189\) −2.05956 −0.149811
\(190\) −3.27066 + 7.57726i −0.237278 + 0.549713i
\(191\) −10.7528 + 10.7528i −0.778044 + 0.778044i −0.979498 0.201454i \(-0.935433\pi\)
0.201454 + 0.979498i \(0.435433\pi\)
\(192\) −0.707107 0.707107i −0.0510310 0.0510310i
\(193\) 6.97010i 0.501719i −0.968024 0.250859i \(-0.919287\pi\)
0.968024 0.250859i \(-0.0807131\pi\)
\(194\) 11.4260i 0.820340i
\(195\) 0.502446 1.16404i 0.0359809 0.0833584i
\(196\) 2.75821i 0.197015i
\(197\) 10.8848 + 10.8848i 0.775511 + 0.775511i 0.979064 0.203553i \(-0.0652488\pi\)
−0.203553 + 0.979064i \(0.565249\pi\)
\(198\) 3.60654i 0.256306i
\(199\) −0.906486 + 0.906486i −0.0642591 + 0.0642591i −0.738506 0.674247i \(-0.764468\pi\)
0.674247 + 0.738506i \(0.264468\pi\)
\(200\) −3.42947 3.63850i −0.242500 0.257281i
\(201\) −2.32762 −0.164178
\(202\) −2.80173 −0.197129
\(203\) 2.28495 0.160372
\(204\) 2.51927 + 2.51927i 0.176384 + 0.176384i
\(205\) −7.04017 17.7335i −0.491707 1.23856i
\(206\) 10.2094i 0.711320i
\(207\) −2.32324 −0.161476
\(208\) 0.566998i 0.0393142i
\(209\) 9.41246 9.41246i 0.651073 0.651073i
\(210\) 4.28035 1.69929i 0.295372 0.117262i
\(211\) −14.3134 −0.985375 −0.492687 0.870206i \(-0.663985\pi\)
−0.492687 + 0.870206i \(0.663985\pi\)
\(212\) 4.48711 4.48711i 0.308176 0.308176i
\(213\) −2.53010 2.53010i −0.173360 0.173360i
\(214\) −10.7074 + 10.7074i −0.731941 + 0.731941i
\(215\) 0.933719 + 2.35195i 0.0636791 + 0.160401i
\(216\) 0.707107 + 0.707107i 0.0481125 + 0.0481125i
\(217\) 4.37839i 0.297225i
\(218\) −2.12012 + 2.12012i −0.143593 + 0.143593i
\(219\) 0.497960i 0.0336490i
\(220\) 2.97566 + 7.49540i 0.200619 + 0.505340i
\(221\) 2.02009i 0.135886i
\(222\) −1.52593 5.88825i −0.102414 0.395194i
\(223\) −9.69983 + 9.69983i −0.649549 + 0.649549i −0.952884 0.303335i \(-0.901900\pi\)
0.303335 + 0.952884i \(0.401900\pi\)
\(224\) −1.45633 + 1.45633i −0.0973051 + 0.0973051i
\(225\) 3.42947 + 3.63850i 0.228632 + 0.242567i
\(226\) 4.98518i 0.331609i
\(227\) −14.0497 −0.932514 −0.466257 0.884649i \(-0.654398\pi\)
−0.466257 + 0.884649i \(0.654398\pi\)
\(228\) 3.69086i 0.244433i
\(229\) 17.6048i 1.16336i 0.813418 + 0.581680i \(0.197604\pi\)
−0.813418 + 0.581680i \(0.802396\pi\)
\(230\) 4.82835 1.91685i 0.318372 0.126393i
\(231\) −7.42789 −0.488719
\(232\) −0.784491 0.784491i −0.0515043 0.0515043i
\(233\) −2.75919 2.75919i −0.180760 0.180760i 0.610927 0.791687i \(-0.290797\pi\)
−0.791687 + 0.610927i \(0.790797\pi\)
\(234\) 0.566998i 0.0370658i
\(235\) 12.0540 + 5.20298i 0.786313 + 0.339405i
\(236\) 5.54174 + 5.54174i 0.360737 + 0.360737i
\(237\) 0.369077i 0.0239741i
\(238\) 5.18860 5.18860i 0.336327 0.336327i
\(239\) −1.97901 1.97901i −0.128011 0.128011i 0.640198 0.768210i \(-0.278852\pi\)
−0.768210 + 0.640198i \(0.778852\pi\)
\(240\) −2.05298 0.886151i −0.132519 0.0572008i
\(241\) −5.52310 + 5.52310i −0.355774 + 0.355774i −0.862253 0.506478i \(-0.830947\pi\)
0.506478 + 0.862253i \(0.330947\pi\)
\(242\) 2.00713i 0.129023i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 5.08840 + 5.08840i 0.325752 + 0.325752i
\(245\) 2.27573 + 5.73234i 0.145391 + 0.366225i
\(246\) −6.03358 6.03358i −0.384687 0.384687i
\(247\) 1.47977 1.47977i 0.0941553 0.0941553i
\(248\) −1.50323 + 1.50323i −0.0954552 + 0.0954552i
\(249\) 3.57650 0.226651
\(250\) −10.1294 4.73227i −0.640642 0.299295i
\(251\) 12.9548 + 12.9548i 0.817701 + 0.817701i 0.985774 0.168073i \(-0.0537546\pi\)
−0.168073 + 0.985774i \(0.553755\pi\)
\(252\) 1.45633 1.45633i 0.0917401 0.0917401i
\(253\) −8.37886 −0.526775
\(254\) −8.16328 + 8.16328i −0.512210 + 0.512210i
\(255\) 7.31435 + 3.15717i 0.458042 + 0.197710i
\(256\) 1.00000 0.0625000
\(257\) 15.9569 0.995367 0.497683 0.867359i \(-0.334184\pi\)
0.497683 + 0.867359i \(0.334184\pi\)
\(258\) 0.800218 + 0.800218i 0.0498194 + 0.0498194i
\(259\) −12.1272 + 3.14275i −0.753549 + 0.195281i
\(260\) 0.467815 + 1.17838i 0.0290127 + 0.0730800i
\(261\) 0.784491 + 0.784491i 0.0485588 + 0.0485588i
\(262\) −5.79100 + 5.79100i −0.357769 + 0.357769i
\(263\) 18.7568 + 18.7568i 1.15659 + 1.15659i 0.985204 + 0.171388i \(0.0548252\pi\)
0.171388 + 0.985204i \(0.445175\pi\)
\(264\) 2.55021 + 2.55021i 0.156954 + 0.156954i
\(265\) 5.62327 13.0277i 0.345435 0.800283i
\(266\) 7.60154 0.466081
\(267\) −7.40169 −0.452976
\(268\) 1.64587 1.64587i 0.100538 0.100538i
\(269\) 23.7613i 1.44875i −0.689404 0.724377i \(-0.742127\pi\)
0.689404 0.724377i \(-0.257873\pi\)
\(270\) 2.05298 + 0.886151i 0.124941 + 0.0539294i
\(271\) −21.4180 −1.30105 −0.650525 0.759485i \(-0.725451\pi\)
−0.650525 + 0.759485i \(0.725451\pi\)
\(272\) −3.56279 −0.216026
\(273\) −1.16777 −0.0706764
\(274\) −11.0100 + 11.0100i −0.665137 + 0.665137i
\(275\) 12.3685 + 13.1224i 0.745850 + 0.791311i
\(276\) 1.64278 1.64278i 0.0988837 0.0988837i
\(277\) 13.2073i 0.793550i 0.917916 + 0.396775i \(0.129871\pi\)
−0.917916 + 0.396775i \(0.870129\pi\)
\(278\) 10.0881i 0.605046i
\(279\) 1.50323 1.50323i 0.0899960 0.0899960i
\(280\) −1.82508 + 4.22824i −0.109069 + 0.252686i
\(281\) 3.11380 3.11380i 0.185754 0.185754i −0.608104 0.793857i \(-0.708070\pi\)
0.793857 + 0.608104i \(0.208070\pi\)
\(282\) 5.87144 0.349639
\(283\) 2.74240 0.163019 0.0815094 0.996673i \(-0.474026\pi\)
0.0815094 + 0.996673i \(0.474026\pi\)
\(284\) 3.57811 0.212322
\(285\) 3.04523 + 7.67064i 0.180384 + 0.454369i
\(286\) 2.04490i 0.120917i
\(287\) −12.4265 + 12.4265i −0.733515 + 0.733515i
\(288\) −1.00000 −0.0589256
\(289\) −4.30652 −0.253325
\(290\) −2.27766 0.983129i −0.133749 0.0577313i
\(291\) 8.07942 + 8.07942i 0.473624 + 0.473624i
\(292\) 0.352111 + 0.352111i 0.0206057 + 0.0206057i
\(293\) −14.1737 + 14.1737i −0.828037 + 0.828037i −0.987245 0.159208i \(-0.949106\pi\)
0.159208 + 0.987245i \(0.449106\pi\)
\(294\) 1.95035 + 1.95035i 0.113747 + 0.113747i
\(295\) 16.0896 + 6.94495i 0.936775 + 0.404350i
\(296\) 5.24262 + 3.08463i 0.304721 + 0.179290i
\(297\) −2.55021 2.55021i −0.147978 0.147978i
\(298\) −8.10303 −0.469396
\(299\) −1.31727 −0.0761798
\(300\) −4.99781 0.147808i −0.288549 0.00853370i
\(301\) 1.64810 1.64810i 0.0949947 0.0949947i
\(302\) −7.24237 −0.416751
\(303\) −1.98112 + 1.98112i −0.113813 + 0.113813i
\(304\) −2.60983 2.60983i −0.149684 0.149684i
\(305\) 14.7734 + 6.37682i 0.845925 + 0.365136i
\(306\) 3.56279 0.203671
\(307\) 10.5206 10.5206i 0.600445 0.600445i −0.339986 0.940431i \(-0.610422\pi\)
0.940431 + 0.339986i \(0.110422\pi\)
\(308\) 5.25231 5.25231i 0.299278 0.299278i
\(309\) 7.21911 + 7.21911i 0.410681 + 0.410681i
\(310\) −1.88386 + 4.36441i −0.106996 + 0.247882i
\(311\) 23.6104 + 23.6104i 1.33882 + 1.33882i 0.897201 + 0.441622i \(0.145597\pi\)
0.441622 + 0.897201i \(0.354403\pi\)
\(312\) 0.400928 + 0.400928i 0.0226981 + 0.0226981i
\(313\) 31.5356i 1.78250i −0.453512 0.891250i \(-0.649829\pi\)
0.453512 0.891250i \(-0.350171\pi\)
\(314\) −11.2460 + 11.2460i −0.634651 + 0.634651i
\(315\) 1.82508 4.22824i 0.102832 0.238234i
\(316\) −0.260977 0.260977i −0.0146811 0.0146811i
\(317\) 16.4324 16.4324i 0.922933 0.922933i −0.0743023 0.997236i \(-0.523673\pi\)
0.997236 + 0.0743023i \(0.0236730\pi\)
\(318\) 6.34573i 0.355851i
\(319\) 2.82930 + 2.82930i 0.158410 + 0.158410i
\(320\) 2.07828 0.825074i 0.116179 0.0461231i
\(321\) 15.1425i 0.845173i
\(322\) −3.38341 3.38341i −0.188550 0.188550i
\(323\) 9.29828 + 9.29828i 0.517370 + 0.517370i
\(324\) 1.00000 0.0555556
\(325\) 1.94450 + 2.06302i 0.107862 + 0.114436i
\(326\) 3.48853i 0.193212i
\(327\) 2.99831i 0.165807i
\(328\) 8.53277 0.471144
\(329\) 12.0926i 0.666685i
\(330\) 7.40416 + 3.19594i 0.407586 + 0.175931i
\(331\) −13.7264 + 13.7264i −0.754470 + 0.754470i −0.975310 0.220840i \(-0.929120\pi\)
0.220840 + 0.975310i \(0.429120\pi\)
\(332\) −2.52897 + 2.52897i −0.138795 + 0.138795i
\(333\) −5.24262 3.08463i −0.287294 0.169037i
\(334\) 13.0005i 0.711356i
\(335\) 2.06262 4.77856i 0.112693 0.261081i
\(336\) 2.05956i 0.112358i
\(337\) 17.9668 17.9668i 0.978715 0.978715i −0.0210635 0.999778i \(-0.506705\pi\)
0.999778 + 0.0210635i \(0.00670521\pi\)
\(338\) 12.6785i 0.689620i
\(339\) −3.52506 3.52506i −0.191455 0.191455i
\(340\) −7.40448 + 2.93957i −0.401564 + 0.159420i
\(341\) 5.42146 5.42146i 0.293588 0.293588i
\(342\) 2.60983 + 2.60983i 0.141123 + 0.141123i
\(343\) 14.2112 14.2112i 0.767331 0.767331i
\(344\) −1.13168 −0.0610160
\(345\) 2.05874 4.76957i 0.110839 0.256785i
\(346\) 12.4447 12.4447i 0.669030 0.669030i
\(347\) 1.20902i 0.0649038i −0.999473 0.0324519i \(-0.989668\pi\)
0.999473 0.0324519i \(-0.0103316\pi\)
\(348\) −1.10944 −0.0594721
\(349\) 26.9158i 1.44077i 0.693575 + 0.720384i \(0.256034\pi\)
−0.693575 + 0.720384i \(0.743966\pi\)
\(350\) −0.304419 + 10.2933i −0.0162719 + 0.550200i
\(351\) −0.400928 0.400928i −0.0213999 0.0213999i
\(352\) −3.60654 −0.192229
\(353\) 13.0238 0.693186 0.346593 0.938016i \(-0.387338\pi\)
0.346593 + 0.938016i \(0.387338\pi\)
\(354\) 7.83720 0.416543
\(355\) 7.43631 2.95220i 0.394678 0.156687i
\(356\) 5.23378 5.23378i 0.277390 0.277390i
\(357\) 7.33778i 0.388357i
\(358\) −6.17102 6.17102i −0.326148 0.326148i
\(359\) 6.68890i 0.353027i −0.984298 0.176513i \(-0.943518\pi\)
0.984298 0.176513i \(-0.0564819\pi\)
\(360\) −2.07828 + 0.825074i −0.109535 + 0.0434852i
\(361\) 5.37757i 0.283030i
\(362\) 8.27365i 0.434853i
\(363\) −1.41925 1.41925i −0.0744915 0.0744915i
\(364\) 0.825735 0.825735i 0.0432803 0.0432803i
\(365\) 1.02230 + 0.441268i 0.0535098 + 0.0230970i
\(366\) 7.19609 0.376145
\(367\) −0.221534 0.221534i −0.0115640 0.0115640i 0.701301 0.712865i \(-0.252603\pi\)
−0.712865 + 0.701301i \(0.752603\pi\)
\(368\) 2.32324i 0.121107i
\(369\) −8.53277 −0.444199
\(370\) 13.4407 + 2.08517i 0.698748 + 0.108403i
\(371\) −13.0694 −0.678530
\(372\) 2.12589i 0.110222i
\(373\) 2.85523 + 2.85523i 0.147838 + 0.147838i 0.777152 0.629314i \(-0.216664\pi\)
−0.629314 + 0.777152i \(0.716664\pi\)
\(374\) 12.8493 0.664424
\(375\) −10.5088 + 3.81638i −0.542673 + 0.197077i
\(376\) −4.15173 + 4.15173i −0.214109 + 0.214109i
\(377\) 0.444804 + 0.444804i 0.0229086 + 0.0229086i
\(378\) 2.05956i 0.105932i
\(379\) 15.3156i 0.786711i 0.919386 + 0.393355i \(0.128686\pi\)
−0.919386 + 0.393355i \(0.871314\pi\)
\(380\) −7.57726 3.27066i −0.388705 0.167781i
\(381\) 11.5446i 0.591449i
\(382\) −10.7528 10.7528i −0.550160 0.550160i
\(383\) 26.5555i 1.35692i 0.734636 + 0.678461i \(0.237353\pi\)
−0.734636 + 0.678461i \(0.762647\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) 6.58223 15.2493i 0.335462 0.777177i
\(386\) 6.97010 0.354769
\(387\) 1.13168 0.0575265
\(388\) −11.4260 −0.580068
\(389\) −5.00317 5.00317i −0.253671 0.253671i 0.568803 0.822474i \(-0.307407\pi\)
−0.822474 + 0.568803i \(0.807407\pi\)
\(390\) 1.16404 + 0.502446i 0.0589433 + 0.0254423i
\(391\) 8.27723i 0.418597i
\(392\) −2.75821 −0.139311
\(393\) 8.18971i 0.413116i
\(394\) −10.8848 + 10.8848i −0.548369 + 0.548369i
\(395\) −0.757709 0.327058i −0.0381245 0.0164561i
\(396\) 3.60654 0.181235
\(397\) −12.2545 + 12.2545i −0.615035 + 0.615035i −0.944254 0.329219i \(-0.893215\pi\)
0.329219 + 0.944254i \(0.393215\pi\)
\(398\) −0.906486 0.906486i −0.0454381 0.0454381i
\(399\) 5.37510 5.37510i 0.269092 0.269092i
\(400\) 3.63850 3.42947i 0.181925 0.171474i
\(401\) −11.3153 11.3153i −0.565059 0.565059i 0.365681 0.930740i \(-0.380836\pi\)
−0.930740 + 0.365681i \(0.880836\pi\)
\(402\) 2.32762i 0.116091i
\(403\) 0.852327 0.852327i 0.0424575 0.0424575i
\(404\) 2.80173i 0.139391i
\(405\) 2.07828 0.825074i 0.103271 0.0409983i
\(406\) 2.28495i 0.113400i
\(407\) −18.9077 11.1248i −0.937221 0.551437i
\(408\) −2.51927 + 2.51927i −0.124723 + 0.124723i
\(409\) 20.6313 20.6313i 1.02015 1.02015i 0.0203618 0.999793i \(-0.493518\pi\)
0.999793 0.0203618i \(-0.00648181\pi\)
\(410\) 17.7335 7.04017i 0.875795 0.347689i
\(411\) 15.5705i 0.768034i
\(412\) −10.2094 −0.502979
\(413\) 16.1412i 0.794256i
\(414\) 2.32324i 0.114181i
\(415\) −3.16932 + 7.34249i −0.155576 + 0.360429i
\(416\) −0.566998 −0.0277993
\(417\) −7.13339 7.13339i −0.349324 0.349324i
\(418\) 9.41246 + 9.41246i 0.460378 + 0.460378i
\(419\) 33.3394i 1.62873i −0.580350 0.814367i \(-0.697084\pi\)
0.580350 0.814367i \(-0.302916\pi\)
\(420\) 1.69929 + 4.28035i 0.0829169 + 0.208859i
\(421\) 18.2239 + 18.2239i 0.888180 + 0.888180i 0.994348 0.106169i \(-0.0338583\pi\)
−0.106169 + 0.994348i \(0.533858\pi\)
\(422\) 14.3134i 0.696765i
\(423\) 4.15173 4.15173i 0.201864 0.201864i
\(424\) 4.48711 + 4.48711i 0.217913 + 0.217913i
\(425\) −12.9632 + 12.2185i −0.628809 + 0.592684i
\(426\) 2.53010 2.53010i 0.122584 0.122584i
\(427\) 14.8208i 0.717228i
\(428\) −10.7074 10.7074i −0.517561 0.517561i
\(429\) −1.44596 1.44596i −0.0698117 0.0698117i
\(430\) −2.35195 + 0.933719i −0.113421 + 0.0450279i
\(431\) −7.25652 7.25652i −0.349534 0.349534i 0.510402 0.859936i \(-0.329497\pi\)
−0.859936 + 0.510402i \(0.829497\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) 28.6180 28.6180i 1.37529 1.37529i 0.522901 0.852393i \(-0.324850\pi\)
0.852393 0.522901i \(-0.175150\pi\)
\(434\) 4.37839 0.210170
\(435\) −2.30572 + 0.915368i −0.110551 + 0.0438886i
\(436\) −2.12012 2.12012i −0.101535 0.101535i
\(437\) 6.06327 6.06327i 0.290045 0.290045i
\(438\) 0.497960 0.0237934
\(439\) −16.0555 + 16.0555i −0.766287 + 0.766287i −0.977451 0.211164i \(-0.932275\pi\)
0.211164 + 0.977451i \(0.432275\pi\)
\(440\) −7.49540 + 2.97566i −0.357329 + 0.141859i
\(441\) 2.75821 0.131343
\(442\) 2.02009 0.0960861
\(443\) −0.486475 0.486475i −0.0231131 0.0231131i 0.695456 0.718569i \(-0.255203\pi\)
−0.718569 + 0.695456i \(0.755203\pi\)
\(444\) 5.88825 1.52593i 0.279444 0.0724175i
\(445\) 6.55901 15.1955i 0.310927 0.720337i
\(446\) −9.69983 9.69983i −0.459300 0.459300i
\(447\) −5.72971 + 5.72971i −0.271006 + 0.271006i
\(448\) −1.45633 1.45633i −0.0688051 0.0688051i
\(449\) −23.6298 23.6298i −1.11516 1.11516i −0.992442 0.122716i \(-0.960840\pi\)
−0.122716 0.992442i \(-0.539160\pi\)
\(450\) −3.63850 + 3.42947i −0.171521 + 0.161667i
\(451\) −30.7738 −1.44908
\(452\) 4.98518 0.234483
\(453\) −5.12113 + 5.12113i −0.240612 + 0.240612i
\(454\) 14.0497i 0.659387i
\(455\) 1.03482 2.39740i 0.0485130 0.112392i
\(456\) −3.69086 −0.172840
\(457\) 25.3719 1.18685 0.593423 0.804890i \(-0.297776\pi\)
0.593423 + 0.804890i \(0.297776\pi\)
\(458\) −17.6048 −0.822620
\(459\) 2.51927 2.51927i 0.117590 0.117590i
\(460\) 1.91685 + 4.82835i 0.0893735 + 0.225123i
\(461\) 15.0045 15.0045i 0.698830 0.698830i −0.265328 0.964158i \(-0.585480\pi\)
0.964158 + 0.265328i \(0.0854803\pi\)
\(462\) 7.42789i 0.345577i
\(463\) 30.1885i 1.40298i 0.712681 + 0.701488i \(0.247481\pi\)
−0.712681 + 0.701488i \(0.752519\pi\)
\(464\) 0.784491 0.784491i 0.0364191 0.0364191i
\(465\) 1.75401 + 4.41819i 0.0813405 + 0.204889i
\(466\) 2.75919 2.75919i 0.127817 0.127817i
\(467\) −4.43185 −0.205082 −0.102541 0.994729i \(-0.532697\pi\)
−0.102541 + 0.994729i \(0.532697\pi\)
\(468\) 0.566998 0.0262095
\(469\) −4.79387 −0.221360
\(470\) −5.20298 + 12.0540i −0.239996 + 0.556007i
\(471\) 15.9043i 0.732832i
\(472\) −5.54174 + 5.54174i −0.255079 + 0.255079i
\(473\) 4.08144 0.187665
\(474\) −0.369077 −0.0169523
\(475\) −18.4462 0.545538i −0.846371 0.0250310i
\(476\) 5.18860 + 5.18860i 0.237819 + 0.237819i
\(477\) −4.48711 4.48711i −0.205451 0.205451i
\(478\) 1.97901 1.97901i 0.0905177 0.0905177i
\(479\) −8.37886 8.37886i −0.382840 0.382840i 0.489284 0.872124i \(-0.337258\pi\)
−0.872124 + 0.489284i \(0.837258\pi\)
\(480\) 0.886151 2.05298i 0.0404471 0.0937054i
\(481\) −2.97255 1.74898i −0.135537 0.0797465i
\(482\) −5.52310 5.52310i −0.251570 0.251570i
\(483\) −4.78486 −0.217719
\(484\) 2.00713 0.0912331
\(485\) −23.7465 + 9.42732i −1.07827 + 0.428072i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) −9.23525 −0.418489 −0.209245 0.977863i \(-0.567100\pi\)
−0.209245 + 0.977863i \(0.567100\pi\)
\(488\) −5.08840 + 5.08840i −0.230341 + 0.230341i
\(489\) −2.46676 2.46676i −0.111551 0.111551i
\(490\) −5.73234 + 2.27573i −0.258961 + 0.102807i
\(491\) −29.1580 −1.31588 −0.657941 0.753069i \(-0.728572\pi\)
−0.657941 + 0.753069i \(0.728572\pi\)
\(492\) 6.03358 6.03358i 0.272015 0.272015i
\(493\) −2.79498 + 2.79498i −0.125879 + 0.125879i
\(494\) 1.47977 + 1.47977i 0.0665779 + 0.0665779i
\(495\) 7.49540 2.97566i 0.336893 0.133746i
\(496\) −1.50323 1.50323i −0.0674970 0.0674970i
\(497\) −5.21090 5.21090i −0.233741 0.233741i
\(498\) 3.57650i 0.160267i
\(499\) −3.77024 + 3.77024i −0.168779 + 0.168779i −0.786442 0.617664i \(-0.788079\pi\)
0.617664 + 0.786442i \(0.288079\pi\)
\(500\) 4.73227 10.1294i 0.211633 0.453003i
\(501\) 9.19275 + 9.19275i 0.410702 + 0.410702i
\(502\) −12.9548 + 12.9548i −0.578202 + 0.578202i
\(503\) 36.6383i 1.63362i −0.576906 0.816810i \(-0.695740\pi\)
0.576906 0.816810i \(-0.304260\pi\)
\(504\) 1.45633 + 1.45633i 0.0648701 + 0.0648701i
\(505\) −2.31164 5.82279i −0.102867 0.259111i
\(506\) 8.37886i 0.372486i
\(507\) 8.96506 + 8.96506i 0.398152 + 0.398152i
\(508\) −8.16328 8.16328i −0.362187 0.362187i
\(509\) −29.0584 −1.28799 −0.643996 0.765029i \(-0.722725\pi\)
−0.643996 + 0.765029i \(0.722725\pi\)
\(510\) −3.15717 + 7.31435i −0.139802 + 0.323885i
\(511\) 1.02558i 0.0453689i
\(512\) 1.00000i 0.0441942i
\(513\) 3.69086 0.162955
\(514\) 15.9569i 0.703831i
\(515\) −21.2179 + 8.42348i −0.934974 + 0.371183i
\(516\) −0.800218 + 0.800218i −0.0352276 + 0.0352276i
\(517\) 14.9734 14.9734i 0.658529 0.658529i
\(518\) −3.14275 12.1272i −0.138084 0.532839i
\(519\) 17.5994i 0.772530i
\(520\) −1.17838 + 0.467815i −0.0516754 + 0.0205151i
\(521\) 20.4068i 0.894036i −0.894525 0.447018i \(-0.852486\pi\)
0.894525 0.447018i \(-0.147514\pi\)
\(522\) −0.784491 + 0.784491i −0.0343362 + 0.0343362i
\(523\) 7.81649i 0.341791i −0.985289 0.170896i \(-0.945334\pi\)
0.985289 0.170896i \(-0.0546661\pi\)
\(524\) −5.79100 5.79100i −0.252981 0.252981i
\(525\) 7.06321 + 7.49372i 0.308264 + 0.327053i
\(526\) −18.7568 + 18.7568i −0.817834 + 0.817834i
\(527\) 5.35569 + 5.35569i 0.233298 + 0.233298i
\(528\) −2.55021 + 2.55021i −0.110984 + 0.110984i
\(529\) 17.6025 0.765328
\(530\) 13.0277 + 5.62327i 0.565886 + 0.244259i
\(531\) 5.54174 5.54174i 0.240491 0.240491i
\(532\) 7.60154i 0.329569i
\(533\) −4.83806 −0.209560
\(534\) 7.40169i 0.320302i
\(535\) −31.0873 13.4186i −1.34402 0.580135i
\(536\) 1.64587 + 1.64587i 0.0710910 + 0.0710910i
\(537\) −8.72713 −0.376604
\(538\) 23.7613 1.02442
\(539\) 9.94759 0.428473
\(540\) −0.886151 + 2.05298i −0.0381339 + 0.0883463i
\(541\) −12.4935 + 12.4935i −0.537139 + 0.537139i −0.922688 0.385548i \(-0.874012\pi\)
0.385548 + 0.922688i \(0.374012\pi\)
\(542\) 21.4180i 0.919982i
\(543\) 5.85035 + 5.85035i 0.251063 + 0.251063i
\(544\) 3.56279i 0.152753i
\(545\) −6.15547 2.65695i −0.263671 0.113811i
\(546\) 1.16777i 0.0499758i
\(547\) 35.8153i 1.53135i 0.643227 + 0.765675i \(0.277595\pi\)
−0.643227 + 0.765675i \(0.722405\pi\)
\(548\) −11.0100 11.0100i −0.470323 0.470323i
\(549\) 5.08840 5.08840i 0.217168 0.217168i
\(550\) −13.1224 + 12.3685i −0.559542 + 0.527396i
\(551\) −4.09478 −0.174443
\(552\) 1.64278 + 1.64278i 0.0699214 + 0.0699214i
\(553\) 0.760137i 0.0323243i
\(554\) −13.2073 −0.561124
\(555\) 10.9784 8.02956i 0.466009 0.340836i
\(556\) 10.0881 0.427832
\(557\) 27.7893i 1.17747i −0.808327 0.588734i \(-0.799626\pi\)
0.808327 0.588734i \(-0.200374\pi\)
\(558\) 1.50323 + 1.50323i 0.0636368 + 0.0636368i
\(559\) 0.641659 0.0271393
\(560\) −4.22824 1.82508i −0.178676 0.0771238i
\(561\) 9.08586 9.08586i 0.383605 0.383605i
\(562\) 3.11380 + 3.11380i 0.131348 + 0.131348i
\(563\) 4.47346i 0.188534i 0.995547 + 0.0942669i \(0.0300507\pi\)
−0.995547 + 0.0942669i \(0.969949\pi\)
\(564\) 5.87144i 0.247232i
\(565\) 10.3606 4.11315i 0.435874 0.173041i
\(566\) 2.74240i 0.115272i
\(567\) −1.45633 1.45633i −0.0611601 0.0611601i
\(568\) 3.57811i 0.150134i
\(569\) 21.9727 21.9727i 0.921144 0.921144i −0.0759661 0.997110i \(-0.524204\pi\)
0.997110 + 0.0759661i \(0.0242041\pi\)
\(570\) −7.67064 + 3.04523i −0.321288 + 0.127551i
\(571\) 11.4199 0.477906 0.238953 0.971031i \(-0.423196\pi\)
0.238953 + 0.971031i \(0.423196\pi\)
\(572\) 2.04490 0.0855015
\(573\) −15.2067 −0.635270
\(574\) −12.4265 12.4265i −0.518673 0.518673i
\(575\) 7.96749 + 8.45313i 0.332267 + 0.352520i
\(576\) 1.00000i 0.0416667i
\(577\) −10.5104 −0.437555 −0.218778 0.975775i \(-0.570207\pi\)
−0.218778 + 0.975775i \(0.570207\pi\)
\(578\) 4.30652i 0.179128i
\(579\) 4.92860 4.92860i 0.204826 0.204826i
\(580\) 0.983129 2.27766i 0.0408222 0.0945745i
\(581\) 7.36601 0.305594
\(582\) −8.07942 + 8.07942i −0.334903 + 0.334903i
\(583\) −16.1829 16.1829i −0.670229 0.670229i
\(584\) −0.352111 + 0.352111i −0.0145704 + 0.0145704i
\(585\) 1.17838 0.467815i 0.0487200 0.0193418i
\(586\) −14.1737 14.1737i −0.585511 0.585511i
\(587\) 28.8278i 1.18985i −0.803781 0.594925i \(-0.797182\pi\)
0.803781 0.594925i \(-0.202818\pi\)
\(588\) −1.95035 + 1.95035i −0.0804310 + 0.0804310i
\(589\) 7.84635i 0.323303i
\(590\) −6.94495 + 16.0896i −0.285919 + 0.662400i
\(591\) 15.3935i 0.633202i
\(592\) −3.08463 + 5.24262i −0.126777 + 0.215470i
\(593\) −28.5378 + 28.5378i −1.17191 + 1.17191i −0.190150 + 0.981755i \(0.560897\pi\)
−0.981755 + 0.190150i \(0.939103\pi\)
\(594\) 2.55021 2.55021i 0.104636 0.104636i
\(595\) 15.0643 + 6.50239i 0.617578 + 0.266572i
\(596\) 8.10303i 0.331913i
\(597\) −1.28197 −0.0524673
\(598\) 1.31727i 0.0538673i
\(599\) 18.9390i 0.773826i 0.922116 + 0.386913i \(0.126459\pi\)
−0.922116 + 0.386913i \(0.873541\pi\)
\(600\) 0.147808 4.99781i 0.00603423 0.204035i
\(601\) −0.127289 −0.00519224 −0.00259612 0.999997i \(-0.500826\pi\)
−0.00259612 + 0.999997i \(0.500826\pi\)
\(602\) 1.64810 + 1.64810i 0.0671714 + 0.0671714i
\(603\) −1.64587 1.64587i −0.0670252 0.0670252i
\(604\) 7.24237i 0.294688i
\(605\) 4.17138 1.65603i 0.169591 0.0673272i
\(606\) −1.98112 1.98112i −0.0804777 0.0804777i
\(607\) 26.8510i 1.08985i −0.838485 0.544925i \(-0.816558\pi\)
0.838485 0.544925i \(-0.183442\pi\)
\(608\) 2.60983 2.60983i 0.105843 0.105843i
\(609\) 1.61571 + 1.61571i 0.0654717 + 0.0654717i
\(610\) −6.37682 + 14.7734i −0.258190 + 0.598159i
\(611\) 2.35402 2.35402i 0.0952335 0.0952335i
\(612\) 3.56279i 0.144017i
\(613\) −2.19500 2.19500i −0.0886554 0.0886554i 0.661388 0.750044i \(-0.269968\pi\)
−0.750044 + 0.661388i \(0.769968\pi\)
\(614\) 10.5206 + 10.5206i 0.424579 + 0.424579i
\(615\) 7.56133 17.5176i 0.304902 0.706379i
\(616\) 5.25231 + 5.25231i 0.211622 + 0.211622i
\(617\) 20.4982 20.4982i 0.825228 0.825228i −0.161625 0.986852i \(-0.551673\pi\)
0.986852 + 0.161625i \(0.0516734\pi\)
\(618\) −7.21911 + 7.21911i −0.290395 + 0.290395i
\(619\) −38.1723 −1.53428 −0.767138 0.641482i \(-0.778320\pi\)
−0.767138 + 0.641482i \(0.778320\pi\)
\(620\) −4.36441 1.88386i −0.175279 0.0756575i
\(621\) −1.64278 1.64278i −0.0659225 0.0659225i
\(622\) −23.6104 + 23.6104i −0.946691 + 0.946691i
\(623\) −15.2442 −0.610747
\(624\) −0.400928 + 0.400928i −0.0160500 + 0.0160500i
\(625\) 1.47743 24.9563i 0.0590973 0.998252i
\(626\) 31.5356 1.26042
\(627\) 13.3112 0.531599
\(628\) −11.2460 11.2460i −0.448766 0.448766i
\(629\) 10.9899 18.6784i 0.438195 0.744755i
\(630\) 4.22824 + 1.82508i 0.168457 + 0.0727130i
\(631\) −21.7435 21.7435i −0.865594 0.865594i 0.126387 0.991981i \(-0.459662\pi\)
−0.991981 + 0.126387i \(0.959662\pi\)
\(632\) 0.260977 0.260977i 0.0103811 0.0103811i
\(633\) −10.1211 10.1211i −0.402278 0.402278i
\(634\) 16.4324 + 16.4324i 0.652613 + 0.652613i
\(635\) −23.7009 10.2303i −0.940541 0.405976i
\(636\) 6.34573 0.251625
\(637\) 1.56390 0.0619639
\(638\) −2.82930 + 2.82930i −0.112013 + 0.112013i
\(639\) 3.57811i 0.141548i
\(640\) 0.825074 + 2.07828i 0.0326139 + 0.0821513i
\(641\) −8.82193 −0.348445 −0.174223 0.984706i \(-0.555741\pi\)
−0.174223 + 0.984706i \(0.555741\pi\)
\(642\) −15.1425 −0.597628
\(643\) 44.2809 1.74627 0.873134 0.487480i \(-0.162084\pi\)
0.873134 + 0.487480i \(0.162084\pi\)
\(644\) 3.38341 3.38341i 0.133325 0.133325i
\(645\) −1.00284 + 2.32332i −0.0394867 + 0.0914805i
\(646\) −9.29828 + 9.29828i −0.365836 + 0.365836i
\(647\) 31.8355i 1.25158i 0.779991 + 0.625791i \(0.215224\pi\)
−0.779991 + 0.625791i \(0.784776\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 19.9865 19.9865i 0.784539 0.784539i
\(650\) −2.06302 + 1.94450i −0.0809184 + 0.0762697i
\(651\) 3.09599 3.09599i 0.121341 0.121341i
\(652\) 3.48853 0.136621
\(653\) −29.8088 −1.16651 −0.583254 0.812290i \(-0.698221\pi\)
−0.583254 + 0.812290i \(0.698221\pi\)
\(654\) −2.99831 −0.117243
\(655\) −16.8133 7.25732i −0.656951 0.283567i
\(656\) 8.53277i 0.333149i
\(657\) 0.352111 0.352111i 0.0137371 0.0137371i
\(658\) 12.0926 0.471418
\(659\) 40.0379 1.55965 0.779827 0.625995i \(-0.215307\pi\)
0.779827 + 0.625995i \(0.215307\pi\)
\(660\) −3.19594 + 7.40416i −0.124402 + 0.288207i
\(661\) 20.8346 + 20.8346i 0.810373 + 0.810373i 0.984690 0.174316i \(-0.0557716\pi\)
−0.174316 + 0.984690i \(0.555772\pi\)
\(662\) −13.7264 13.7264i −0.533491 0.533491i
\(663\) 1.42842 1.42842i 0.0554753 0.0554753i
\(664\) −2.52897 2.52897i −0.0981429 0.0981429i
\(665\) 6.27184 + 15.7981i 0.243211 + 0.612626i
\(666\) 3.08463 5.24262i 0.119527 0.203147i
\(667\) 1.82256 + 1.82256i 0.0705699 + 0.0705699i
\(668\) −13.0005 −0.503005
\(669\) −13.7176 −0.530354
\(670\) 4.77856 + 2.06262i 0.184612 + 0.0796860i
\(671\) 18.3515 18.3515i 0.708453 0.708453i
\(672\) −2.05956 −0.0794493
\(673\) −16.7404 + 16.7404i −0.645295 + 0.645295i −0.951852 0.306557i \(-0.900823\pi\)
0.306557 + 0.951852i \(0.400823\pi\)
\(674\) 17.9668 + 17.9668i 0.692056 + 0.692056i
\(675\) −0.147808 + 4.99781i −0.00568913 + 0.192366i
\(676\) −12.6785 −0.487635
\(677\) 4.30980 4.30980i 0.165639 0.165639i −0.619420 0.785059i \(-0.712632\pi\)
0.785059 + 0.619420i \(0.212632\pi\)
\(678\) 3.52506 3.52506i 0.135379 0.135379i
\(679\) 16.6400 + 16.6400i 0.638586 + 0.638586i
\(680\) −2.93957 7.40448i −0.112727 0.283949i
\(681\) −9.93466 9.93466i −0.380697 0.380697i
\(682\) 5.42146 + 5.42146i 0.207598 + 0.207598i
\(683\) 36.6278i 1.40152i −0.713395 0.700762i \(-0.752843\pi\)
0.713395 0.700762i \(-0.247157\pi\)
\(684\) −2.60983 + 2.60983i −0.0997894 + 0.0997894i
\(685\) −31.9659 13.7978i −1.22135 0.527186i
\(686\) 14.2112 + 14.2112i 0.542585 + 0.542585i
\(687\) −12.4485 + 12.4485i −0.474940 + 0.474940i
\(688\) 1.13168i 0.0431448i
\(689\) −2.54418 2.54418i −0.0969255 0.0969255i
\(690\) 4.76957 + 2.05874i 0.181575 + 0.0783750i
\(691\) 31.0649i 1.18177i 0.806757 + 0.590883i \(0.201220\pi\)
−0.806757 + 0.590883i \(0.798780\pi\)
\(692\) 12.4447 + 12.4447i 0.473076 + 0.473076i
\(693\) −5.25231 5.25231i −0.199519 0.199519i
\(694\) 1.20902 0.0458939
\(695\) 20.9660 8.32346i 0.795285 0.315727i
\(696\) 1.10944i 0.0420531i
\(697\) 30.4005i 1.15150i
\(698\) −26.9158 −1.01878
\(699\) 3.90208i 0.147590i
\(700\) −10.2933 0.304419i −0.389050 0.0115060i
\(701\) −11.6605 + 11.6605i −0.440411 + 0.440411i −0.892150 0.451739i \(-0.850804\pi\)
0.451739 + 0.892150i \(0.350804\pi\)
\(702\) 0.400928 0.400928i 0.0151320 0.0151320i
\(703\) 21.7327 5.63200i 0.819664 0.212415i
\(704\) 3.60654i 0.135927i
\(705\) 4.84437 + 12.2025i 0.182450 + 0.459573i
\(706\) 13.0238i 0.490157i
\(707\) −4.08025 + 4.08025i −0.153453 + 0.153453i
\(708\) 7.83720i 0.294540i
\(709\) −12.6150 12.6150i −0.473768 0.473768i 0.429364 0.903132i \(-0.358738\pi\)
−0.903132 + 0.429364i \(0.858738\pi\)
\(710\) 2.95220 + 7.43631i 0.110794 + 0.279080i
\(711\) −0.260977 + 0.260977i −0.00978740 + 0.00978740i
\(712\) 5.23378 + 5.23378i 0.196144 + 0.196144i
\(713\) 3.49237 3.49237i 0.130790 0.130790i
\(714\) 7.33778 0.274610
\(715\) 4.24988 1.68719i 0.158936 0.0630975i
\(716\) 6.17102 6.17102i 0.230622 0.230622i
\(717\) 2.79874i 0.104521i
\(718\) 6.68890 0.249628
\(719\) 15.6860i 0.584988i −0.956267 0.292494i \(-0.905515\pi\)
0.956267 0.292494i \(-0.0944852\pi\)
\(720\) −0.825074 2.07828i −0.0307487 0.0774530i
\(721\) 14.8682 + 14.8682i 0.553721 + 0.553721i
\(722\) 5.37757 0.200133
\(723\) −7.81085 −0.290488
\(724\) −8.27365 −0.307488
\(725\) 0.163984 5.54476i 0.00609020 0.205927i
\(726\) 1.41925 1.41925i 0.0526735 0.0526735i
\(727\) 44.2369i 1.64065i 0.571894 + 0.820327i \(0.306209\pi\)
−0.571894 + 0.820327i \(0.693791\pi\)
\(728\) 0.825735 + 0.825735i 0.0306038 + 0.0306038i
\(729\) 1.00000i 0.0370370i
\(730\) −0.441268 + 1.02230i −0.0163320 + 0.0378371i
\(731\) 4.03193i 0.149126i
\(732\) 7.19609i 0.265975i
\(733\) 27.8801 + 27.8801i 1.02977 + 1.02977i 0.999543 + 0.0302314i \(0.00962443\pi\)
0.0302314 + 0.999543i \(0.490376\pi\)
\(734\) 0.221534 0.221534i 0.00817696 0.00817696i
\(735\) −2.44419 + 5.66256i −0.0901553 + 0.208867i
\(736\) −2.32324 −0.0856358
\(737\) −5.93591 5.93591i −0.218652 0.218652i
\(738\) 8.53277i 0.314096i
\(739\) −44.3607 −1.63183 −0.815917 0.578169i \(-0.803768\pi\)
−0.815917 + 0.578169i \(0.803768\pi\)
\(740\) −2.08517 + 13.4407i −0.0766524 + 0.494089i
\(741\) 2.09271 0.0768775
\(742\) 13.0694i 0.479793i
\(743\) 7.56548 + 7.56548i 0.277551 + 0.277551i 0.832131 0.554580i \(-0.187121\pi\)
−0.554580 + 0.832131i \(0.687121\pi\)
\(744\) −2.12589 −0.0779388
\(745\) −6.68560 16.8404i −0.244942 0.616984i
\(746\) −2.85523 + 2.85523i −0.104537 + 0.104537i
\(747\) 2.52897 + 2.52897i 0.0925300 + 0.0925300i
\(748\) 12.8493i 0.469819i
\(749\) 31.1869i 1.13955i
\(750\) −3.81638 10.5088i −0.139355 0.383728i
\(751\) 5.20586i 0.189964i −0.995479 0.0949822i \(-0.969721\pi\)
0.995479 0.0949822i \(-0.0302794\pi\)
\(752\) −4.15173 4.15173i −0.151398 0.151398i
\(753\) 18.3209i 0.667650i
\(754\) −0.444804 + 0.444804i −0.0161988 + 0.0161988i
\(755\) −5.97549 15.0517i −0.217470 0.547786i
\(756\) 2.05956 0.0749055
\(757\) −27.0653 −0.983705 −0.491853 0.870678i \(-0.663680\pi\)
−0.491853 + 0.870678i \(0.663680\pi\)
\(758\) −15.3156 −0.556289
\(759\) −5.92475 5.92475i −0.215055 0.215055i
\(760\) 3.27066 7.57726i 0.118639 0.274856i
\(761\) 1.85691i 0.0673130i 0.999433 + 0.0336565i \(0.0107152\pi\)
−0.999433 + 0.0336565i \(0.989285\pi\)
\(762\) −11.5446 −0.418217
\(763\) 6.17519i 0.223557i
\(764\) 10.7528 10.7528i 0.389022 0.389022i
\(765\) 2.93957 + 7.40448i 0.106280 + 0.267710i
\(766\) −26.5555 −0.959489
\(767\) 3.14215 3.14215i 0.113457 0.113457i
\(768\) 0.707107 + 0.707107i 0.0255155 + 0.0255155i
\(769\) 20.3839 20.3839i 0.735061 0.735061i −0.236557 0.971618i \(-0.576019\pi\)
0.971618 + 0.236557i \(0.0760189\pi\)
\(770\) 15.2493 + 6.58223i 0.549547 + 0.237207i
\(771\) 11.2833 + 11.2833i 0.406357 + 0.406357i
\(772\) 6.97010i 0.250859i
\(773\) −29.3204 + 29.3204i −1.05458 + 1.05458i −0.0561599 + 0.998422i \(0.517886\pi\)
−0.998422 + 0.0561599i \(0.982114\pi\)
\(774\) 1.13168i 0.0406774i
\(775\) −10.6248 0.314223i −0.381654 0.0112872i
\(776\) 11.4260i 0.410170i
\(777\) −10.7975 6.35298i −0.387358 0.227912i
\(778\) 5.00317 5.00317i 0.179373 0.179373i
\(779\) 22.2691 22.2691i 0.797873 0.797873i