Properties

Label 1110.2.o.a.253.8
Level $1110$
Weight $2$
Character 1110.253
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 253.8
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.a.487.8

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(2.23596 + 0.0221544i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.281427 + 0.281427i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(2.23596 + 0.0221544i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.281427 + 0.281427i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(-2.23596 - 0.0221544i) q^{10} -1.64708i q^{11} +(-0.707107 + 0.707107i) q^{12} +3.15714 q^{13} +(0.281427 - 0.281427i) q^{14} +(-1.59673 + 1.56540i) q^{15} +1.00000 q^{16} -3.44561i q^{17} +1.00000i q^{18} +(-1.85024 - 1.85024i) q^{19} +(2.23596 + 0.0221544i) q^{20} -0.397998i q^{21} +1.64708i q^{22} +3.91265 q^{23} +(0.707107 - 0.707107i) q^{24} +(4.99902 + 0.0990726i) q^{25} -3.15714 q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.281427 + 0.281427i) q^{28} +(2.67202 - 2.67202i) q^{29} +(1.59673 - 1.56540i) q^{30} +(-6.77259 - 6.77259i) q^{31} -1.00000 q^{32} +(1.16466 + 1.16466i) q^{33} +3.44561i q^{34} +(-0.635494 + 0.623024i) q^{35} -1.00000i q^{36} +(0.925435 + 6.01195i) q^{37} +(1.85024 + 1.85024i) q^{38} +(-2.23244 + 2.23244i) q^{39} +(-2.23596 - 0.0221544i) q^{40} -8.72049i q^{41} +0.397998i q^{42} +1.27639 q^{43} -1.64708i q^{44} +(0.0221544 - 2.23596i) q^{45} -3.91265 q^{46} +(-0.752821 + 0.752821i) q^{47} +(-0.707107 + 0.707107i) q^{48} +6.84160i q^{49} +(-4.99902 - 0.0990726i) q^{50} +(2.43642 + 2.43642i) q^{51} +3.15714 q^{52} +(3.88760 + 3.88760i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(0.0364901 - 3.68281i) q^{55} +(0.281427 - 0.281427i) q^{56} +2.61664 q^{57} +(-2.67202 + 2.67202i) q^{58} +(-6.53793 - 6.53793i) q^{59} +(-1.59673 + 1.56540i) q^{60} +(-0.144746 - 0.144746i) q^{61} +(6.77259 + 6.77259i) q^{62} +(0.281427 + 0.281427i) q^{63} +1.00000 q^{64} +(7.05924 + 0.0699446i) q^{65} +(-1.16466 - 1.16466i) q^{66} +(-0.492575 - 0.492575i) q^{67} -3.44561i q^{68} +(-2.76666 + 2.76666i) q^{69} +(0.635494 - 0.623024i) q^{70} +11.2201 q^{71} +1.00000i q^{72} +(0.804916 - 0.804916i) q^{73} +(-0.925435 - 6.01195i) q^{74} +(-3.60489 + 3.46478i) q^{75} +(-1.85024 - 1.85024i) q^{76} +(0.463534 + 0.463534i) q^{77} +(2.23244 - 2.23244i) q^{78} +(2.86326 + 2.86326i) q^{79} +(2.23596 + 0.0221544i) q^{80} -1.00000 q^{81} +8.72049i q^{82} +(3.45461 + 3.45461i) q^{83} -0.397998i q^{84} +(0.0763355 - 7.70424i) q^{85} -1.27639 q^{86} +3.77880i q^{87} +1.64708i q^{88} +(12.5832 - 12.5832i) q^{89} +(-0.0221544 + 2.23596i) q^{90} +(-0.888506 + 0.888506i) q^{91} +3.91265 q^{92} +9.57788 q^{93} +(0.752821 - 0.752821i) q^{94} +(-4.09608 - 4.17806i) q^{95} +(0.707107 - 0.707107i) q^{96} +6.92746i q^{97} -6.84160i q^{98} -1.64708 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
\(5\) 2.23596 + 0.0221544i 0.999951 + 0.00990775i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) −0.281427 + 0.281427i −0.106369 + 0.106369i −0.758289 0.651919i \(-0.773964\pi\)
0.651919 + 0.758289i \(0.273964\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000i 0.333333i
\(10\) −2.23596 0.0221544i −0.707072 0.00700584i
\(11\) 1.64708i 0.496614i −0.968681 0.248307i \(-0.920126\pi\)
0.968681 0.248307i \(-0.0798742\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) 3.15714 0.875634 0.437817 0.899064i \(-0.355752\pi\)
0.437817 + 0.899064i \(0.355752\pi\)
\(14\) 0.281427 0.281427i 0.0752146 0.0752146i
\(15\) −1.59673 + 1.56540i −0.412273 + 0.404183i
\(16\) 1.00000 0.250000
\(17\) 3.44561i 0.835684i −0.908520 0.417842i \(-0.862787\pi\)
0.908520 0.417842i \(-0.137213\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.85024 1.85024i −0.424475 0.424475i 0.462266 0.886741i \(-0.347036\pi\)
−0.886741 + 0.462266i \(0.847036\pi\)
\(20\) 2.23596 + 0.0221544i 0.499975 + 0.00495387i
\(21\) 0.397998i 0.0868503i
\(22\) 1.64708i 0.351159i
\(23\) 3.91265 0.815844 0.407922 0.913017i \(-0.366253\pi\)
0.407922 + 0.913017i \(0.366253\pi\)
\(24\) 0.707107 0.707107i 0.144338 0.144338i
\(25\) 4.99902 + 0.0990726i 0.999804 + 0.0198145i
\(26\) −3.15714 −0.619167
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) −0.281427 + 0.281427i −0.0531847 + 0.0531847i
\(29\) 2.67202 2.67202i 0.496181 0.496181i −0.414066 0.910247i \(-0.635892\pi\)
0.910247 + 0.414066i \(0.135892\pi\)
\(30\) 1.59673 1.56540i 0.291521 0.285801i
\(31\) −6.77259 6.77259i −1.21639 1.21639i −0.968886 0.247506i \(-0.920389\pi\)
−0.247506 0.968886i \(-0.579611\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.16466 + 1.16466i 0.202742 + 0.202742i
\(34\) 3.44561i 0.590917i
\(35\) −0.635494 + 0.623024i −0.107418 + 0.105310i
\(36\) 1.00000i 0.166667i
\(37\) 0.925435 + 6.01195i 0.152141 + 0.988359i
\(38\) 1.85024 + 1.85024i 0.300149 + 0.300149i
\(39\) −2.23244 + 2.23244i −0.357476 + 0.357476i
\(40\) −2.23596 0.0221544i −0.353536 0.00350292i
\(41\) 8.72049i 1.36191i −0.732325 0.680956i \(-0.761565\pi\)
0.732325 0.680956i \(-0.238435\pi\)
\(42\) 0.397998i 0.0614124i
\(43\) 1.27639 0.194647 0.0973237 0.995253i \(-0.468972\pi\)
0.0973237 + 0.995253i \(0.468972\pi\)
\(44\) 1.64708i 0.248307i
\(45\) 0.0221544 2.23596i 0.00330258 0.333317i
\(46\) −3.91265 −0.576889
\(47\) −0.752821 + 0.752821i −0.109810 + 0.109810i −0.759877 0.650067i \(-0.774741\pi\)
0.650067 + 0.759877i \(0.274741\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 6.84160i 0.977371i
\(50\) −4.99902 0.0990726i −0.706968 0.0140110i
\(51\) 2.43642 + 2.43642i 0.341166 + 0.341166i
\(52\) 3.15714 0.437817
\(53\) 3.88760 + 3.88760i 0.534003 + 0.534003i 0.921761 0.387758i \(-0.126750\pi\)
−0.387758 + 0.921761i \(0.626750\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) 0.0364901 3.68281i 0.00492033 0.496590i
\(56\) 0.281427 0.281427i 0.0376073 0.0376073i
\(57\) 2.61664 0.346582
\(58\) −2.67202 + 2.67202i −0.350853 + 0.350853i
\(59\) −6.53793 6.53793i −0.851166 0.851166i 0.139111 0.990277i \(-0.455576\pi\)
−0.990277 + 0.139111i \(0.955576\pi\)
\(60\) −1.59673 + 1.56540i −0.206137 + 0.202092i
\(61\) −0.144746 0.144746i −0.0185328 0.0185328i 0.697780 0.716312i \(-0.254171\pi\)
−0.716312 + 0.697780i \(0.754171\pi\)
\(62\) 6.77259 + 6.77259i 0.860119 + 0.860119i
\(63\) 0.281427 + 0.281427i 0.0354565 + 0.0354565i
\(64\) 1.00000 0.125000
\(65\) 7.05924 + 0.0699446i 0.875591 + 0.00867556i
\(66\) −1.16466 1.16466i −0.143360 0.143360i
\(67\) −0.492575 0.492575i −0.0601777 0.0601777i 0.676377 0.736555i \(-0.263549\pi\)
−0.736555 + 0.676377i \(0.763549\pi\)
\(68\) 3.44561i 0.417842i
\(69\) −2.76666 + 2.76666i −0.333067 + 0.333067i
\(70\) 0.635494 0.623024i 0.0759561 0.0744657i
\(71\) 11.2201 1.33158 0.665790 0.746140i \(-0.268095\pi\)
0.665790 + 0.746140i \(0.268095\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 0.804916 0.804916i 0.0942083 0.0942083i −0.658432 0.752640i \(-0.728780\pi\)
0.752640 + 0.658432i \(0.228780\pi\)
\(74\) −0.925435 6.01195i −0.107580 0.698875i
\(75\) −3.60489 + 3.46478i −0.416257 + 0.400079i
\(76\) −1.85024 1.85024i −0.212237 0.212237i
\(77\) 0.463534 + 0.463534i 0.0528246 + 0.0528246i
\(78\) 2.23244 2.23244i 0.252774 0.252774i
\(79\) 2.86326 + 2.86326i 0.322142 + 0.322142i 0.849588 0.527446i \(-0.176850\pi\)
−0.527446 + 0.849588i \(0.676850\pi\)
\(80\) 2.23596 + 0.0221544i 0.249988 + 0.00247694i
\(81\) −1.00000 −0.111111
\(82\) 8.72049i 0.963017i
\(83\) 3.45461 + 3.45461i 0.379192 + 0.379192i 0.870811 0.491618i \(-0.163594\pi\)
−0.491618 + 0.870811i \(0.663594\pi\)
\(84\) 0.397998i 0.0434251i
\(85\) 0.0763355 7.70424i 0.00827974 0.835643i
\(86\) −1.27639 −0.137636
\(87\) 3.77880i 0.405130i
\(88\) 1.64708i 0.175580i
\(89\) 12.5832 12.5832i 1.33381 1.33381i 0.431885 0.901929i \(-0.357849\pi\)
0.901929 0.431885i \(-0.142151\pi\)
\(90\) −0.0221544 + 2.23596i −0.00233528 + 0.235691i
\(91\) −0.888506 + 0.888506i −0.0931407 + 0.0931407i
\(92\) 3.91265 0.407922
\(93\) 9.57788 0.993180
\(94\) 0.752821 0.752821i 0.0776476 0.0776476i
\(95\) −4.09608 4.17806i −0.420248 0.428660i
\(96\) 0.707107 0.707107i 0.0721688 0.0721688i
\(97\) 6.92746i 0.703377i 0.936117 + 0.351689i \(0.114392\pi\)
−0.936117 + 0.351689i \(0.885608\pi\)
\(98\) 6.84160i 0.691106i
\(99\) −1.64708 −0.165538
\(100\) 4.99902 + 0.0990726i 0.499902 + 0.00990726i
\(101\) 6.04485i 0.601486i −0.953705 0.300743i \(-0.902765\pi\)
0.953705 0.300743i \(-0.0972346\pi\)
\(102\) −2.43642 2.43642i −0.241241 0.241241i
\(103\) 11.2563i 1.10912i 0.832144 + 0.554560i \(0.187113\pi\)
−0.832144 + 0.554560i \(0.812887\pi\)
\(104\) −3.15714 −0.309583
\(105\) 0.00881741 0.889907i 0.000860491 0.0868460i
\(106\) −3.88760 3.88760i −0.377597 0.377597i
\(107\) 8.88960 8.88960i 0.859390 0.859390i −0.131876 0.991266i \(-0.542100\pi\)
0.991266 + 0.131876i \(0.0421001\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) 8.94425 + 8.94425i 0.856704 + 0.856704i 0.990948 0.134244i \(-0.0428607\pi\)
−0.134244 + 0.990948i \(0.542861\pi\)
\(110\) −0.0364901 + 3.68281i −0.00347920 + 0.351142i
\(111\) −4.90547 3.59671i −0.465607 0.341385i
\(112\) −0.281427 + 0.281427i −0.0265924 + 0.0265924i
\(113\) 0.196751i 0.0185088i −0.999957 0.00925440i \(-0.997054\pi\)
0.999957 0.00925440i \(-0.00294581\pi\)
\(114\) −2.61664 −0.245071
\(115\) 8.74853 + 0.0866825i 0.815804 + 0.00808318i
\(116\) 2.67202 2.67202i 0.248090 0.248090i
\(117\) 3.15714i 0.291878i
\(118\) 6.53793 + 6.53793i 0.601865 + 0.601865i
\(119\) 0.969688 + 0.969688i 0.0888912 + 0.0888912i
\(120\) 1.59673 1.56540i 0.145761 0.142900i
\(121\) 8.28712 0.753375
\(122\) 0.144746 + 0.144746i 0.0131047 + 0.0131047i
\(123\) 6.16632 + 6.16632i 0.555998 + 0.555998i
\(124\) −6.77259 6.77259i −0.608196 0.608196i
\(125\) 11.1754 + 0.332273i 0.999558 + 0.0297194i
\(126\) −0.281427 0.281427i −0.0250715 0.0250715i
\(127\) 6.37075 6.37075i 0.565313 0.565313i −0.365499 0.930812i \(-0.619102\pi\)
0.930812 + 0.365499i \(0.119102\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.902543 + 0.902543i −0.0794644 + 0.0794644i
\(130\) −7.05924 0.0699446i −0.619136 0.00613455i
\(131\) −2.48554 2.48554i −0.217162 0.217162i 0.590139 0.807302i \(-0.299073\pi\)
−0.807302 + 0.590139i \(0.799073\pi\)
\(132\) 1.16466 + 1.16466i 0.101371 + 0.101371i
\(133\) 1.04142 0.0903023
\(134\) 0.492575 + 0.492575i 0.0425520 + 0.0425520i
\(135\) 1.56540 + 1.59673i 0.134728 + 0.137424i
\(136\) 3.44561i 0.295459i
\(137\) 15.3866 15.3866i 1.31456 1.31456i 0.396553 0.918012i \(-0.370206\pi\)
0.918012 0.396553i \(-0.129794\pi\)
\(138\) 2.76666 2.76666i 0.235514 0.235514i
\(139\) −2.99885 −0.254359 −0.127180 0.991880i \(-0.540592\pi\)
−0.127180 + 0.991880i \(0.540592\pi\)
\(140\) −0.635494 + 0.623024i −0.0537091 + 0.0526552i
\(141\) 1.06465i 0.0896597i
\(142\) −11.2201 −0.941569
\(143\) 5.20007i 0.434852i
\(144\) 1.00000i 0.0833333i
\(145\) 6.03371 5.91532i 0.501073 0.491240i
\(146\) −0.804916 + 0.804916i −0.0666153 + 0.0666153i
\(147\) −4.83774 4.83774i −0.399010 0.399010i
\(148\) 0.925435 + 6.01195i 0.0760703 + 0.494179i
\(149\) 8.60756i 0.705159i 0.935782 + 0.352579i \(0.114695\pi\)
−0.935782 + 0.352579i \(0.885305\pi\)
\(150\) 3.60489 3.46478i 0.294338 0.282898i
\(151\) 2.73615i 0.222665i 0.993783 + 0.111332i \(0.0355118\pi\)
−0.993783 + 0.111332i \(0.964488\pi\)
\(152\) 1.85024 + 1.85024i 0.150075 + 0.150075i
\(153\) −3.44561 −0.278561
\(154\) −0.463534 0.463534i −0.0373526 0.0373526i
\(155\) −14.9932 15.2933i −1.20428 1.22838i
\(156\) −2.23244 + 2.23244i −0.178738 + 0.178738i
\(157\) −4.40198 + 4.40198i −0.351317 + 0.351317i −0.860599 0.509283i \(-0.829911\pi\)
0.509283 + 0.860599i \(0.329911\pi\)
\(158\) −2.86326 2.86326i −0.227789 0.227789i
\(159\) −5.49790 −0.436011
\(160\) −2.23596 0.0221544i −0.176768 0.00175146i
\(161\) −1.10113 + 1.10113i −0.0867809 + 0.0867809i
\(162\) 1.00000 0.0785674
\(163\) 10.2487i 0.802740i 0.915916 + 0.401370i \(0.131466\pi\)
−0.915916 + 0.401370i \(0.868534\pi\)
\(164\) 8.72049i 0.680956i
\(165\) 2.57834 + 2.62994i 0.200723 + 0.204741i
\(166\) −3.45461 3.45461i −0.268130 0.268130i
\(167\) 2.97278i 0.230040i 0.993363 + 0.115020i \(0.0366933\pi\)
−0.993363 + 0.115020i \(0.963307\pi\)
\(168\) 0.397998i 0.0307062i
\(169\) −3.03245 −0.233265
\(170\) −0.0763355 + 7.70424i −0.00585466 + 0.590888i
\(171\) −1.85024 + 1.85024i −0.141492 + 0.141492i
\(172\) 1.27639 0.0973237
\(173\) −5.83257 + 5.83257i −0.443442 + 0.443442i −0.893167 0.449725i \(-0.851522\pi\)
0.449725 + 0.893167i \(0.351522\pi\)
\(174\) 3.77880i 0.286470i
\(175\) −1.43474 + 1.37898i −0.108456 + 0.104241i
\(176\) 1.64708i 0.124153i
\(177\) 9.24603 0.694974
\(178\) −12.5832 + 12.5832i −0.943149 + 0.943149i
\(179\) −4.52269 + 4.52269i −0.338042 + 0.338042i −0.855630 0.517588i \(-0.826830\pi\)
0.517588 + 0.855630i \(0.326830\pi\)
\(180\) 0.0221544 2.23596i 0.00165129 0.166658i
\(181\) −16.8840 −1.25497 −0.627487 0.778627i \(-0.715917\pi\)
−0.627487 + 0.778627i \(0.715917\pi\)
\(182\) 0.888506 0.888506i 0.0658604 0.0658604i
\(183\) 0.204701 0.0151320
\(184\) −3.91265 −0.288445
\(185\) 1.93604 + 13.4630i 0.142341 + 0.989818i
\(186\) −9.57788 −0.702284
\(187\) −5.67521 −0.415012
\(188\) −0.752821 + 0.752821i −0.0549051 + 0.0549051i
\(189\) −0.397998 −0.0289501
\(190\) 4.09608 + 4.17806i 0.297161 + 0.303108i
\(191\) −18.5005 + 18.5005i −1.33865 + 1.33865i −0.441274 + 0.897372i \(0.645473\pi\)
−0.897372 + 0.441274i \(0.854527\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) −17.1049 −1.23124 −0.615620 0.788043i \(-0.711094\pi\)
−0.615620 + 0.788043i \(0.711094\pi\)
\(194\) 6.92746i 0.497363i
\(195\) −5.04109 + 4.94218i −0.361000 + 0.353917i
\(196\) 6.84160i 0.488686i
\(197\) −0.556751 + 0.556751i −0.0396669 + 0.0396669i −0.726662 0.686995i \(-0.758929\pi\)
0.686995 + 0.726662i \(0.258929\pi\)
\(198\) 1.64708 0.117053
\(199\) −7.91159 + 7.91159i −0.560838 + 0.560838i −0.929546 0.368707i \(-0.879800\pi\)
0.368707 + 0.929546i \(0.379800\pi\)
\(200\) −4.99902 0.0990726i −0.353484 0.00700549i
\(201\) 0.696607 0.0491349
\(202\) 6.04485i 0.425314i
\(203\) 1.50396i 0.105557i
\(204\) 2.43642 + 2.43642i 0.170583 + 0.170583i
\(205\) 0.193197 19.4986i 0.0134935 1.36184i
\(206\) 11.2563i 0.784266i
\(207\) 3.91265i 0.271948i
\(208\) 3.15714 0.218908
\(209\) −3.04750 + 3.04750i −0.210800 + 0.210800i
\(210\) −0.00881741 + 0.889907i −0.000608459 + 0.0614094i
\(211\) −1.32938 −0.0915183 −0.0457592 0.998953i \(-0.514571\pi\)
−0.0457592 + 0.998953i \(0.514571\pi\)
\(212\) 3.88760 + 3.88760i 0.267001 + 0.267001i
\(213\) −7.93380 + 7.93380i −0.543615 + 0.543615i
\(214\) −8.88960 + 8.88960i −0.607681 + 0.607681i
\(215\) 2.85395 + 0.0282776i 0.194638 + 0.00192852i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) 3.81198 0.258774
\(218\) −8.94425 8.94425i −0.605781 0.605781i
\(219\) 1.13832i 0.0769207i
\(220\) 0.0364901 3.68281i 0.00246016 0.248295i
\(221\) 10.8783i 0.731753i
\(222\) 4.90547 + 3.59671i 0.329234 + 0.241395i
\(223\) −3.07126 3.07126i −0.205667 0.205667i 0.596756 0.802423i \(-0.296456\pi\)
−0.802423 + 0.596756i \(0.796456\pi\)
\(224\) 0.281427 0.281427i 0.0188036 0.0188036i
\(225\) 0.0990726 4.99902i 0.00660484 0.333268i
\(226\) 0.196751i 0.0130877i
\(227\) 24.6591i 1.63668i −0.574732 0.818342i \(-0.694894\pi\)
0.574732 0.818342i \(-0.305106\pi\)
\(228\) 2.61664 0.173291
\(229\) 14.8812i 0.983377i −0.870771 0.491689i \(-0.836380\pi\)
0.870771 0.491689i \(-0.163620\pi\)
\(230\) −8.74853 0.0866825i −0.576861 0.00571567i
\(231\) −0.655535 −0.0431311
\(232\) −2.67202 + 2.67202i −0.175426 + 0.175426i
\(233\) −14.6836 + 14.6836i −0.961952 + 0.961952i −0.999302 0.0373500i \(-0.988108\pi\)
0.0373500 + 0.999302i \(0.488108\pi\)
\(234\) 3.15714i 0.206389i
\(235\) −1.69995 + 1.66660i −0.110893 + 0.108717i
\(236\) −6.53793 6.53793i −0.425583 0.425583i
\(237\) −4.04926 −0.263028
\(238\) −0.969688 0.969688i −0.0628556 0.0628556i
\(239\) −11.8998 11.8998i −0.769736 0.769736i 0.208324 0.978060i \(-0.433199\pi\)
−0.978060 + 0.208324i \(0.933199\pi\)
\(240\) −1.59673 + 1.56540i −0.103068 + 0.101046i
\(241\) 15.6655 15.6655i 1.00910 1.00910i 0.00914615 0.999958i \(-0.497089\pi\)
0.999958 0.00914615i \(-0.00291135\pi\)
\(242\) −8.28712 −0.532716
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) −0.144746 0.144746i −0.00926640 0.00926640i
\(245\) −0.151571 + 15.2975i −0.00968355 + 0.977323i
\(246\) −6.16632 6.16632i −0.393150 0.393150i
\(247\) −5.84148 5.84148i −0.371685 0.371685i
\(248\) 6.77259 + 6.77259i 0.430060 + 0.430060i
\(249\) −4.88555 −0.309609
\(250\) −11.1754 0.332273i −0.706794 0.0210148i
\(251\) 8.27735 + 8.27735i 0.522462 + 0.522462i 0.918314 0.395852i \(-0.129551\pi\)
−0.395852 + 0.918314i \(0.629551\pi\)
\(252\) 0.281427 + 0.281427i 0.0177282 + 0.0177282i
\(253\) 6.44446i 0.405160i
\(254\) −6.37075 + 6.37075i −0.399737 + 0.399737i
\(255\) 5.39375 + 5.50170i 0.337769 + 0.344530i
\(256\) 1.00000 0.0625000
\(257\) 4.24215i 0.264618i −0.991209 0.132309i \(-0.957761\pi\)
0.991209 0.132309i \(-0.0422391\pi\)
\(258\) 0.902543 0.902543i 0.0561898 0.0561898i
\(259\) −1.95237 1.43148i −0.121314 0.0889481i
\(260\) 7.05924 + 0.0699446i 0.437795 + 0.00433778i
\(261\) −2.67202 2.67202i −0.165394 0.165394i
\(262\) 2.48554 + 2.48554i 0.153557 + 0.153557i
\(263\) −22.4018 + 22.4018i −1.38135 + 1.38135i −0.539129 + 0.842223i \(0.681246\pi\)
−0.842223 + 0.539129i \(0.818754\pi\)
\(264\) −1.16466 1.16466i −0.0716801 0.0716801i
\(265\) 8.60638 + 8.77864i 0.528686 + 0.539267i
\(266\) −1.04142 −0.0638534
\(267\) 17.7953i 1.08905i
\(268\) −0.492575 0.492575i −0.0300888 0.0300888i
\(269\) 15.2647i 0.930706i 0.885125 + 0.465353i \(0.154073\pi\)
−0.885125 + 0.465353i \(0.845927\pi\)
\(270\) −1.56540 1.59673i −0.0952669 0.0971737i
\(271\) 14.7969 0.898849 0.449424 0.893318i \(-0.351629\pi\)
0.449424 + 0.893318i \(0.351629\pi\)
\(272\) 3.44561i 0.208921i
\(273\) 1.25654i 0.0760491i
\(274\) −15.3866 + 15.3866i −0.929538 + 0.929538i
\(275\) 0.163181 8.23379i 0.00984017 0.496516i
\(276\) −2.76666 + 2.76666i −0.166534 + 0.166534i
\(277\) 3.00385 0.180484 0.0902420 0.995920i \(-0.471236\pi\)
0.0902420 + 0.995920i \(0.471236\pi\)
\(278\) 2.99885 0.179859
\(279\) −6.77259 + 6.77259i −0.405464 + 0.405464i
\(280\) 0.635494 0.623024i 0.0379780 0.0372328i
\(281\) −8.35723 + 8.35723i −0.498551 + 0.498551i −0.910987 0.412436i \(-0.864678\pi\)
0.412436 + 0.910987i \(0.364678\pi\)
\(282\) 1.06465i 0.0633990i
\(283\) 3.86949i 0.230018i 0.993364 + 0.115009i \(0.0366896\pi\)
−0.993364 + 0.115009i \(0.963310\pi\)
\(284\) 11.2201 0.665790
\(285\) 5.85070 + 0.0579701i 0.346565 + 0.00343385i
\(286\) 5.20007i 0.307487i
\(287\) 2.45418 + 2.45418i 0.144866 + 0.144866i
\(288\) 1.00000i 0.0589256i
\(289\) 5.12776 0.301633
\(290\) −6.03371 + 5.91532i −0.354312 + 0.347359i
\(291\) −4.89845 4.89845i −0.287152 0.287152i
\(292\) 0.804916 0.804916i 0.0471041 0.0471041i
\(293\) 10.7523 + 10.7523i 0.628156 + 0.628156i 0.947604 0.319448i \(-0.103498\pi\)
−0.319448 + 0.947604i \(0.603498\pi\)
\(294\) 4.83774 + 4.83774i 0.282143 + 0.282143i
\(295\) −14.4737 14.7634i −0.842691 0.859557i
\(296\) −0.925435 6.01195i −0.0537898 0.349438i
\(297\) 1.16466 1.16466i 0.0675806 0.0675806i
\(298\) 8.60756i 0.498622i
\(299\) 12.3528 0.714381
\(300\) −3.60489 + 3.46478i −0.208129 + 0.200039i
\(301\) −0.359210 + 0.359210i −0.0207045 + 0.0207045i
\(302\) 2.73615i 0.157448i
\(303\) 4.27436 + 4.27436i 0.245555 + 0.245555i
\(304\) −1.85024 1.85024i −0.106119 0.106119i
\(305\) −0.320439 0.326852i −0.0183483 0.0187155i
\(306\) 3.44561 0.196972
\(307\) −19.3837 19.3837i −1.10629 1.10629i −0.993634 0.112652i \(-0.964065\pi\)
−0.112652 0.993634i \(-0.535935\pi\)
\(308\) 0.463534 + 0.463534i 0.0264123 + 0.0264123i
\(309\) −7.95943 7.95943i −0.452796 0.452796i
\(310\) 14.9932 + 15.2933i 0.851555 + 0.868599i
\(311\) −9.43851 9.43851i −0.535209 0.535209i 0.386909 0.922118i \(-0.373543\pi\)
−0.922118 + 0.386909i \(0.873543\pi\)
\(312\) 2.23244 2.23244i 0.126387 0.126387i
\(313\) −20.7779 −1.17444 −0.587218 0.809429i \(-0.699777\pi\)
−0.587218 + 0.809429i \(0.699777\pi\)
\(314\) 4.40198 4.40198i 0.248418 0.248418i
\(315\) 0.623024 + 0.635494i 0.0351034 + 0.0358060i
\(316\) 2.86326 + 2.86326i 0.161071 + 0.161071i
\(317\) −3.25873 3.25873i −0.183029 0.183029i 0.609646 0.792674i \(-0.291312\pi\)
−0.792674 + 0.609646i \(0.791312\pi\)
\(318\) 5.49790 0.308307
\(319\) −4.40103 4.40103i −0.246410 0.246410i
\(320\) 2.23596 + 0.0221544i 0.124994 + 0.00123847i
\(321\) 12.5718i 0.701689i
\(322\) 1.10113 1.10113i 0.0613634 0.0613634i
\(323\) −6.37522 + 6.37522i −0.354727 + 0.354727i
\(324\) −1.00000 −0.0555556
\(325\) 15.7826 + 0.312786i 0.875462 + 0.0173503i
\(326\) 10.2487i 0.567623i
\(327\) −12.6491 −0.699496
\(328\) 8.72049i 0.481508i
\(329\) 0.423728i 0.0233609i
\(330\) −2.57834 2.62994i −0.141933 0.144773i
\(331\) 2.00568 2.00568i 0.110242 0.110242i −0.649834 0.760076i \(-0.725162\pi\)
0.760076 + 0.649834i \(0.225162\pi\)
\(332\) 3.45461 + 3.45461i 0.189596 + 0.189596i
\(333\) 6.01195 0.925435i 0.329453 0.0507135i
\(334\) 2.97278i 0.162663i
\(335\) −1.09047 1.11229i −0.0595785 0.0607709i
\(336\) 0.397998i 0.0217126i
\(337\) 8.49643 + 8.49643i 0.462830 + 0.462830i 0.899582 0.436752i \(-0.143871\pi\)
−0.436752 + 0.899582i \(0.643871\pi\)
\(338\) 3.03245 0.164944
\(339\) 0.139124 + 0.139124i 0.00755619 + 0.00755619i
\(340\) 0.0763355 7.70424i 0.00413987 0.417821i
\(341\) −11.1550 + 11.1550i −0.604077 + 0.604077i
\(342\) 1.85024 1.85024i 0.100050 0.100050i
\(343\) −3.89540 3.89540i −0.210332 0.210332i
\(344\) −1.27639 −0.0688182
\(345\) −6.24744 + 6.12485i −0.336351 + 0.329751i
\(346\) 5.83257 5.83257i 0.313561 0.313561i
\(347\) −0.455842 −0.0244709 −0.0122354 0.999925i \(-0.503895\pi\)
−0.0122354 + 0.999925i \(0.503895\pi\)
\(348\) 3.77880i 0.202565i
\(349\) 18.0258i 0.964899i 0.875924 + 0.482450i \(0.160253\pi\)
−0.875924 + 0.482450i \(0.839747\pi\)
\(350\) 1.43474 1.37898i 0.0766901 0.0737095i
\(351\) 2.23244 + 2.23244i 0.119159 + 0.119159i
\(352\) 1.64708i 0.0877898i
\(353\) 16.2235i 0.863489i 0.901996 + 0.431745i \(0.142102\pi\)
−0.901996 + 0.431745i \(0.857898\pi\)
\(354\) −9.24603 −0.491421
\(355\) 25.0876 + 0.248574i 1.33151 + 0.0131930i
\(356\) 12.5832 12.5832i 0.666907 0.666907i
\(357\) −1.37135 −0.0725794
\(358\) 4.52269 4.52269i 0.239031 0.239031i
\(359\) 19.2940i 1.01830i 0.860678 + 0.509149i \(0.170040\pi\)
−0.860678 + 0.509149i \(0.829960\pi\)
\(360\) −0.0221544 + 2.23596i −0.00116764 + 0.117845i
\(361\) 12.1532i 0.639642i
\(362\) 16.8840 0.887401
\(363\) −5.85988 + 5.85988i −0.307564 + 0.307564i
\(364\) −0.888506 + 0.888506i −0.0465703 + 0.0465703i
\(365\) 1.81759 1.78193i 0.0951370 0.0932703i
\(366\) −0.204701 −0.0106999
\(367\) −3.21053 + 3.21053i −0.167588 + 0.167588i −0.785919 0.618330i \(-0.787810\pi\)
0.618330 + 0.785919i \(0.287810\pi\)
\(368\) 3.91265 0.203961
\(369\) −8.72049 −0.453970
\(370\) −1.93604 13.4630i −0.100650 0.699907i
\(371\) −2.18815 −0.113603
\(372\) 9.57788 0.496590
\(373\) −2.94440 + 2.94440i −0.152455 + 0.152455i −0.779214 0.626759i \(-0.784381\pi\)
0.626759 + 0.779214i \(0.284381\pi\)
\(374\) 5.67521 0.293458
\(375\) −8.13715 + 7.66725i −0.420201 + 0.395935i
\(376\) 0.752821 0.752821i 0.0388238 0.0388238i
\(377\) 8.43593 8.43593i 0.434473 0.434473i
\(378\) 0.397998 0.0204708
\(379\) 25.1637i 1.29257i 0.763094 + 0.646287i \(0.223679\pi\)
−0.763094 + 0.646287i \(0.776321\pi\)
\(380\) −4.09608 4.17806i −0.210124 0.214330i
\(381\) 9.00960i 0.461576i
\(382\) 18.5005 18.5005i 0.946566 0.946566i
\(383\) −0.995617 −0.0508736 −0.0254368 0.999676i \(-0.508098\pi\)
−0.0254368 + 0.999676i \(0.508098\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) 1.02617 + 1.04671i 0.0522986 + 0.0533453i
\(386\) 17.1049 0.870618
\(387\) 1.27639i 0.0648824i
\(388\) 6.92746i 0.351689i
\(389\) −19.4231 19.4231i −0.984788 0.984788i 0.0150980 0.999886i \(-0.495194\pi\)
−0.999886 + 0.0150980i \(0.995194\pi\)
\(390\) 5.04109 4.94218i 0.255266 0.250257i
\(391\) 13.4815i 0.681788i
\(392\) 6.84160i 0.345553i
\(393\) 3.51508 0.177312
\(394\) 0.556751 0.556751i 0.0280487 0.0280487i
\(395\) 6.33870 + 6.46557i 0.318935 + 0.325318i
\(396\) −1.64708 −0.0827690
\(397\) 6.49757 + 6.49757i 0.326104 + 0.326104i 0.851103 0.524999i \(-0.175934\pi\)
−0.524999 + 0.851103i \(0.675934\pi\)
\(398\) 7.91159 7.91159i 0.396572 0.396572i
\(399\) −0.736393 + 0.736393i −0.0368658 + 0.0368658i
\(400\) 4.99902 + 0.0990726i 0.249951 + 0.00495363i
\(401\) −24.2700 24.2700i −1.21199 1.21199i −0.970372 0.241616i \(-0.922322\pi\)
−0.241616 0.970372i \(-0.577678\pi\)
\(402\) −0.696607 −0.0347436
\(403\) −21.3820 21.3820i −1.06511 1.06511i
\(404\) 6.04485i 0.300743i
\(405\) −2.23596 0.0221544i −0.111106 0.00110086i
\(406\) 1.50396i 0.0746401i
\(407\) 9.90218 1.52427i 0.490833 0.0755551i
\(408\) −2.43642 2.43642i −0.120621 0.120621i
\(409\) 24.0003 24.0003i 1.18674 1.18674i 0.208776 0.977963i \(-0.433052\pi\)
0.977963 0.208776i \(-0.0669481\pi\)
\(410\) −0.193197 + 19.4986i −0.00954133 + 0.962969i
\(411\) 21.7599i 1.07334i
\(412\) 11.2563i 0.554560i
\(413\) 3.67990 0.181076
\(414\) 3.91265i 0.192296i
\(415\) 7.64782 + 7.80089i 0.375417 + 0.382931i
\(416\) −3.15714 −0.154792
\(417\) 2.12051 2.12051i 0.103842 0.103842i
\(418\) 3.04750 3.04750i 0.149058 0.149058i
\(419\) 32.2473i 1.57538i 0.616070 + 0.787692i \(0.288724\pi\)
−0.616070 + 0.787692i \(0.711276\pi\)
\(420\) 0.00881741 0.889907i 0.000430245 0.0434230i
\(421\) −3.85720 3.85720i −0.187988 0.187988i 0.606838 0.794826i \(-0.292438\pi\)
−0.794826 + 0.606838i \(0.792438\pi\)
\(422\) 1.32938 0.0647132
\(423\) 0.752821 + 0.752821i 0.0366034 + 0.0366034i
\(424\) −3.88760 3.88760i −0.188798 0.188798i
\(425\) 0.341366 17.2247i 0.0165587 0.835519i
\(426\) 7.93380 7.93380i 0.384394 0.384394i
\(427\) 0.0814708 0.00394265
\(428\) 8.88960 8.88960i 0.429695 0.429695i
\(429\) 3.67701 + 3.67701i 0.177528 + 0.177528i
\(430\) −2.85395 0.0282776i −0.137630 0.00136367i
\(431\) −15.1362 15.1362i −0.729087 0.729087i 0.241351 0.970438i \(-0.422410\pi\)
−0.970438 + 0.241351i \(0.922410\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) −27.7575 27.7575i −1.33394 1.33394i −0.901811 0.432130i \(-0.857762\pi\)
−0.432130 0.901811i \(-0.642238\pi\)
\(434\) −3.81198 −0.182981
\(435\) −0.0837171 + 8.44924i −0.00401393 + 0.405110i
\(436\) 8.94425 + 8.94425i 0.428352 + 0.428352i
\(437\) −7.23936 7.23936i −0.346306 0.346306i
\(438\) 1.13832i 0.0543912i
\(439\) 17.1813 17.1813i 0.820020 0.820020i −0.166091 0.986110i \(-0.553115\pi\)
0.986110 + 0.166091i \(0.0531145\pi\)
\(440\) −0.0364901 + 3.68281i −0.00173960 + 0.175571i
\(441\) 6.84160 0.325790
\(442\) 10.8783i 0.517427i
\(443\) −7.22878 + 7.22878i −0.343450 + 0.343450i −0.857663 0.514213i \(-0.828084\pi\)
0.514213 + 0.857663i \(0.328084\pi\)
\(444\) −4.90547 3.59671i −0.232803 0.170692i
\(445\) 28.4142 27.8567i 1.34696 1.32053i
\(446\) 3.07126 + 3.07126i 0.145429 + 0.145429i
\(447\) −6.08646 6.08646i −0.287880 0.287880i
\(448\) −0.281427 + 0.281427i −0.0132962 + 0.0132962i
\(449\) 9.76421 + 9.76421i 0.460802 + 0.460802i 0.898918 0.438116i \(-0.144354\pi\)
−0.438116 + 0.898918i \(0.644354\pi\)
\(450\) −0.0990726 + 4.99902i −0.00467033 + 0.235656i
\(451\) −14.3634 −0.676344
\(452\) 0.196751i 0.00925440i
\(453\) −1.93475 1.93475i −0.0909024 0.0909024i
\(454\) 24.6591i 1.15731i
\(455\) −2.00635 + 1.96698i −0.0940589 + 0.0922133i
\(456\) −2.61664 −0.122535
\(457\) 20.5176i 0.959771i 0.877331 + 0.479886i \(0.159322\pi\)
−0.877331 + 0.479886i \(0.840678\pi\)
\(458\) 14.8812i 0.695353i
\(459\) 2.43642 2.43642i 0.113722 0.113722i
\(460\) 8.74853 + 0.0866825i 0.407902 + 0.00404159i
\(461\) 21.6195 21.6195i 1.00692 1.00692i 0.00694687 0.999976i \(-0.497789\pi\)
0.999976 0.00694687i \(-0.00221127\pi\)
\(462\) 0.655535 0.0304983
\(463\) 1.38040 0.0641527 0.0320764 0.999485i \(-0.489788\pi\)
0.0320764 + 0.999485i \(0.489788\pi\)
\(464\) 2.67202 2.67202i 0.124045 0.124045i
\(465\) 21.4157 + 0.212192i 0.993131 + 0.00984018i
\(466\) 14.6836 14.6836i 0.680203 0.680203i
\(467\) 0.453871i 0.0210026i −0.999945 0.0105013i \(-0.996657\pi\)
0.999945 0.0105013i \(-0.00334274\pi\)
\(468\) 3.15714i 0.145939i
\(469\) 0.277248 0.0128021
\(470\) 1.69995 1.66660i 0.0784131 0.0768744i
\(471\) 6.22534i 0.286849i
\(472\) 6.53793 + 6.53793i 0.300933 + 0.300933i
\(473\) 2.10232i 0.0966646i
\(474\) 4.04926 0.185989
\(475\) −9.06609 9.43271i −0.415981 0.432802i
\(476\) 0.969688 + 0.969688i 0.0444456 + 0.0444456i
\(477\) 3.88760 3.88760i 0.178001 0.178001i
\(478\) 11.8998 + 11.8998i 0.544285 + 0.544285i
\(479\) 10.7493 + 10.7493i 0.491147 + 0.491147i 0.908667 0.417521i \(-0.137101\pi\)
−0.417521 + 0.908667i \(0.637101\pi\)
\(480\) 1.59673 1.56540i 0.0728803 0.0714502i
\(481\) 2.92173 + 18.9806i 0.133219 + 0.865440i
\(482\) −15.6655 + 15.6655i −0.713545 + 0.713545i
\(483\) 1.55723i 0.0708563i
\(484\) 8.28712 0.376687
\(485\) −0.153474 + 15.4895i −0.00696888 + 0.703343i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) 13.2268i 0.599365i −0.954039 0.299682i \(-0.903119\pi\)
0.954039 0.299682i \(-0.0968807\pi\)
\(488\) 0.144746 + 0.144746i 0.00655233 + 0.00655233i
\(489\) −7.24692 7.24692i −0.327717 0.327717i
\(490\) 0.151571 15.2975i 0.00684730 0.691072i
\(491\) −30.4522 −1.37429 −0.687145 0.726520i \(-0.741136\pi\)
−0.687145 + 0.726520i \(0.741136\pi\)
\(492\) 6.16632 + 6.16632i 0.277999 + 0.277999i
\(493\) −9.20673 9.20673i −0.414650 0.414650i
\(494\) 5.84148 + 5.84148i 0.262821 + 0.262821i
\(495\) −3.68281 0.0364901i −0.165530 0.00164011i
\(496\) −6.77259 6.77259i −0.304098 0.304098i
\(497\) −3.15764 + 3.15764i −0.141639 + 0.141639i
\(498\) 4.88555 0.218927
\(499\) −6.74452 + 6.74452i −0.301926 + 0.301926i −0.841767 0.539841i \(-0.818484\pi\)
0.539841 + 0.841767i \(0.318484\pi\)
\(500\) 11.1754 + 0.332273i 0.499779 + 0.0148597i
\(501\) −2.10207 2.10207i −0.0939136 0.0939136i
\(502\) −8.27735 8.27735i −0.369436 0.369436i
\(503\) 31.0691 1.38530 0.692652 0.721272i \(-0.256442\pi\)
0.692652 + 0.721272i \(0.256442\pi\)
\(504\) −0.281427 0.281427i −0.0125358 0.0125358i
\(505\) 0.133920 13.5160i 0.00595937 0.601456i
\(506\) 6.44446i 0.286491i
\(507\) 2.14427 2.14427i 0.0952302 0.0952302i
\(508\) 6.37075 6.37075i 0.282656 0.282656i
\(509\) −11.0860 −0.491377 −0.245688 0.969349i \(-0.579014\pi\)
−0.245688 + 0.969349i \(0.579014\pi\)
\(510\) −5.39375 5.50170i −0.238839 0.243619i
\(511\) 0.453050i 0.0200418i
\(512\) −1.00000 −0.0441942
\(513\) 2.61664i 0.115527i
\(514\) 4.24215i 0.187113i
\(515\) −0.249377 + 25.1687i −0.0109889 + 1.10907i
\(516\) −0.902543 + 0.902543i −0.0397322 + 0.0397322i
\(517\) 1.23996 + 1.23996i 0.0545333 + 0.0545333i
\(518\) 1.95237 + 1.43148i 0.0857822 + 0.0628958i
\(519\) 8.24851i 0.362069i
\(520\) −7.05924 0.0699446i −0.309568 0.00306727i
\(521\) 32.8476i 1.43908i 0.694451 + 0.719540i \(0.255647\pi\)
−0.694451 + 0.719540i \(0.744353\pi\)
\(522\) 2.67202 + 2.67202i 0.116951 + 0.116951i
\(523\) −9.72492 −0.425241 −0.212620 0.977135i \(-0.568200\pi\)
−0.212620 + 0.977135i \(0.568200\pi\)
\(524\) −2.48554 2.48554i −0.108581 0.108581i
\(525\) 0.0394307 1.98960i 0.00172090 0.0868332i
\(526\) 22.4018 22.4018i 0.976763 0.976763i
\(527\) −23.3357 + 23.3357i −1.01652 + 1.01652i
\(528\) 1.16466 + 1.16466i 0.0506854 + 0.0506854i
\(529\) −7.69115 −0.334398
\(530\) −8.60638 8.77864i −0.373837 0.381320i
\(531\) −6.53793 + 6.53793i −0.283722 + 0.283722i
\(532\) 1.04142 0.0451512
\(533\) 27.5318i 1.19254i
\(534\) 17.7953i 0.770078i
\(535\) 20.0737 19.6798i 0.867863 0.850833i
\(536\) 0.492575 + 0.492575i 0.0212760 + 0.0212760i
\(537\) 6.39605i 0.276010i
\(538\) 15.2647i 0.658108i
\(539\) 11.2687 0.485376
\(540\) 1.56540 + 1.59673i 0.0673639 + 0.0687122i
\(541\) −22.2929 + 22.2929i −0.958445 + 0.958445i −0.999170 0.0407258i \(-0.987033\pi\)
0.0407258 + 0.999170i \(0.487033\pi\)
\(542\) −14.7969 −0.635582
\(543\) 11.9388 11.9388i 0.512341 0.512341i
\(544\) 3.44561i 0.147729i
\(545\) 19.8008 + 20.1971i 0.848174 + 0.865150i
\(546\) 1.25654i 0.0537748i
\(547\) 33.1369 1.41683 0.708416 0.705795i \(-0.249410\pi\)
0.708416 + 0.705795i \(0.249410\pi\)
\(548\) 15.3866 15.3866i 0.657282 0.657282i
\(549\) −0.144746 + 0.144746i −0.00617760 + 0.00617760i
\(550\) −0.163181 + 8.23379i −0.00695805 + 0.351090i
\(551\) −9.88776 −0.421233
\(552\) 2.76666 2.76666i 0.117757 0.117757i
\(553\) −1.61160 −0.0685322
\(554\) −3.00385 −0.127621
\(555\) −10.8888 8.15077i −0.462202 0.345981i
\(556\) −2.99885 −0.127180
\(557\) 3.42489 0.145117 0.0725586 0.997364i \(-0.476884\pi\)
0.0725586 + 0.997364i \(0.476884\pi\)
\(558\) 6.77259 6.77259i 0.286706 0.286706i
\(559\) 4.02974 0.170440
\(560\) −0.635494 + 0.623024i −0.0268545 + 0.0263276i
\(561\) 4.01298 4.01298i 0.169428 0.169428i
\(562\) 8.35723 8.35723i 0.352529 0.352529i
\(563\) 17.6124 0.742273 0.371136 0.928578i \(-0.378968\pi\)
0.371136 + 0.928578i \(0.378968\pi\)
\(564\) 1.06465i 0.0448298i
\(565\) 0.00435891 0.439928i 0.000183381 0.0185079i
\(566\) 3.86949i 0.162647i
\(567\) 0.281427 0.281427i 0.0118188 0.0118188i
\(568\) −11.2201 −0.470784
\(569\) −13.6557 + 13.6557i −0.572477 + 0.572477i −0.932820 0.360343i \(-0.882660\pi\)
0.360343 + 0.932820i \(0.382660\pi\)
\(570\) −5.85070 0.0579701i −0.245059 0.00242810i
\(571\) 36.6093 1.53205 0.766025 0.642811i \(-0.222232\pi\)
0.766025 + 0.642811i \(0.222232\pi\)
\(572\) 5.20007i 0.217426i
\(573\) 26.1636i 1.09300i
\(574\) −2.45418 2.45418i −0.102436 0.102436i
\(575\) 19.5594 + 0.387637i 0.815684 + 0.0161656i
\(576\) 1.00000i 0.0416667i
\(577\) 28.6229i 1.19159i 0.803137 + 0.595794i \(0.203163\pi\)
−0.803137 + 0.595794i \(0.796837\pi\)
\(578\) −5.12776 −0.213287
\(579\) 12.0950 12.0950i 0.502652 0.502652i
\(580\) 6.03371 5.91532i 0.250536 0.245620i
\(581\) −1.94444 −0.0806690
\(582\) 4.89845 + 4.89845i 0.203047 + 0.203047i
\(583\) 6.40320 6.40320i 0.265193 0.265193i
\(584\) −0.804916 + 0.804916i −0.0333077 + 0.0333077i
\(585\) 0.0699446 7.05924i 0.00289185 0.291864i
\(586\) −10.7523 10.7523i −0.444173 0.444173i
\(587\) −17.5944 −0.726197 −0.363099 0.931751i \(-0.618281\pi\)
−0.363099 + 0.931751i \(0.618281\pi\)
\(588\) −4.83774 4.83774i −0.199505 0.199505i
\(589\) 25.0619i 1.03266i
\(590\) 14.4737 + 14.7634i 0.595873 + 0.607799i
\(591\) 0.787365i 0.0323879i
\(592\) 0.925435 + 6.01195i 0.0380351 + 0.247090i
\(593\) −5.00469 5.00469i −0.205518 0.205518i 0.596841 0.802359i \(-0.296422\pi\)
−0.802359 + 0.596841i \(0.796422\pi\)
\(594\) −1.16466 + 1.16466i −0.0477867 + 0.0477867i
\(595\) 2.14670 + 2.18967i 0.0880061 + 0.0897675i
\(596\) 8.60756i 0.352579i
\(597\) 11.1887i 0.457922i
\(598\) −12.3528 −0.505144
\(599\) 35.1064i 1.43441i −0.696863 0.717204i \(-0.745421\pi\)
0.696863 0.717204i \(-0.254579\pi\)
\(600\) 3.60489 3.46478i 0.147169 0.141449i
\(601\) −28.3290 −1.15556 −0.577782 0.816191i \(-0.696082\pi\)
−0.577782 + 0.816191i \(0.696082\pi\)
\(602\) 0.359210 0.359210i 0.0146403 0.0146403i
\(603\) −0.492575 + 0.492575i −0.0200592 + 0.0200592i
\(604\) 2.73615i 0.111332i
\(605\) 18.5297 + 0.183596i 0.753338 + 0.00746425i
\(606\) −4.27436 4.27436i −0.173634 0.173634i
\(607\) −2.58147 −0.104779 −0.0523894 0.998627i \(-0.516684\pi\)
−0.0523894 + 0.998627i \(0.516684\pi\)
\(608\) 1.85024 + 1.85024i 0.0750373 + 0.0750373i
\(609\) −1.06346 1.06346i −0.0430935 0.0430935i
\(610\) 0.320439 + 0.326852i 0.0129742 + 0.0132339i
\(611\) −2.37676 + 2.37676i −0.0961535 + 0.0961535i
\(612\) −3.44561 −0.139281
\(613\) 7.76986 7.76986i 0.313822 0.313822i −0.532566 0.846388i \(-0.678772\pi\)
0.846388 + 0.532566i \(0.178772\pi\)
\(614\) 19.3837 + 19.3837i 0.782263 + 0.782263i
\(615\) 13.6510 + 13.9242i 0.550462 + 0.561479i
\(616\) −0.463534 0.463534i −0.0186763 0.0186763i
\(617\) −19.3110 19.3110i −0.777430 0.777430i 0.201963 0.979393i \(-0.435268\pi\)
−0.979393 + 0.201963i \(0.935268\pi\)
\(618\) 7.95943 + 7.95943i 0.320175 + 0.320175i
\(619\) 22.9273 0.921528 0.460764 0.887523i \(-0.347575\pi\)
0.460764 + 0.887523i \(0.347575\pi\)
\(620\) −14.9932 15.2933i −0.602140 0.614192i
\(621\) 2.76666 + 2.76666i 0.111022 + 0.111022i
\(622\) 9.43851 + 9.43851i 0.378450 + 0.378450i
\(623\) 7.08249i 0.283754i
\(624\) −2.23244 + 2.23244i −0.0893690 + 0.0893690i
\(625\) 24.9804 + 0.990532i 0.999215 + 0.0396213i
\(626\) 20.7779 0.830451
\(627\) 4.30982i 0.172118i
\(628\) −4.40198 + 4.40198i −0.175658 + 0.175658i
\(629\) 20.7149 3.18869i 0.825955 0.127141i
\(630\) −0.623024 0.635494i −0.0248219 0.0253187i
\(631\) −18.8706 18.8706i −0.751225 0.751225i 0.223483 0.974708i \(-0.428257\pi\)
−0.974708 + 0.223483i \(0.928257\pi\)
\(632\) −2.86326 2.86326i −0.113894 0.113894i
\(633\) 0.940014 0.940014i 0.0373622 0.0373622i
\(634\) 3.25873 + 3.25873i 0.129421 + 0.129421i
\(635\) 14.3859 14.1036i 0.570886 0.559684i
\(636\) −5.49790 −0.218006
\(637\) 21.5999i 0.855819i
\(638\) 4.40103 + 4.40103i 0.174238 + 0.174238i
\(639\) 11.2201i 0.443860i
\(640\) −2.23596 0.0221544i −0.0883840 0.000875730i
\(641\) 6.78574 0.268021 0.134010 0.990980i \(-0.457214\pi\)
0.134010 + 0.990980i \(0.457214\pi\)
\(642\) 12.5718i 0.496169i
\(643\) 36.8670i 1.45389i 0.686695 + 0.726945i \(0.259061\pi\)
−0.686695 + 0.726945i \(0.740939\pi\)
\(644\) −1.10113 + 1.10113i −0.0433905 + 0.0433905i
\(645\) −2.03804 + 1.99805i −0.0802479 + 0.0786732i
\(646\) 6.37522 6.37522i 0.250830 0.250830i
\(647\) −19.1501 −0.752868 −0.376434 0.926443i \(-0.622850\pi\)
−0.376434 + 0.926443i \(0.622850\pi\)
\(648\) 1.00000 0.0392837
\(649\) −10.7685 + 10.7685i −0.422701 + 0.422701i
\(650\) −15.7826 0.312786i −0.619045 0.0122685i
\(651\) −2.69548 + 2.69548i −0.105644 + 0.105644i
\(652\) 10.2487i 0.401370i
\(653\) 19.8305i 0.776029i −0.921653 0.388015i \(-0.873161\pi\)
0.921653 0.388015i \(-0.126839\pi\)
\(654\) 12.6491 0.494618
\(655\) −5.50249 5.61263i −0.215000 0.219303i
\(656\) 8.72049i 0.340478i
\(657\) −0.804916 0.804916i −0.0314028 0.0314028i
\(658\) 0.423728i 0.0165187i
\(659\) 21.4129 0.834127 0.417064 0.908877i \(-0.363059\pi\)
0.417064 + 0.908877i \(0.363059\pi\)
\(660\) 2.57834 + 2.62994i 0.100362 + 0.102370i
\(661\) 34.3523 + 34.3523i 1.33615 + 1.33615i 0.899754 + 0.436397i \(0.143746\pi\)
0.436397 + 0.899754i \(0.356254\pi\)
\(662\) −2.00568 + 2.00568i −0.0779530 + 0.0779530i
\(663\) 7.69211 + 7.69211i 0.298737 + 0.298737i
\(664\) −3.45461 3.45461i −0.134065 0.134065i
\(665\) 2.32857 + 0.0230720i 0.0902979 + 0.000894693i
\(666\) −6.01195 + 0.925435i −0.232958 + 0.0358599i
\(667\) 10.4547 10.4547i 0.404806 0.404806i
\(668\) 2.97278i 0.115020i
\(669\) 4.34342 0.167926
\(670\) 1.09047 + 1.11229i 0.0421284 + 0.0429715i
\(671\) −0.238408 + 0.238408i −0.00920365 + 0.00920365i
\(672\) 0.397998i 0.0153531i
\(673\) −19.4561 19.4561i −0.749979 0.749979i 0.224496 0.974475i \(-0.427926\pi\)
−0.974475 + 0.224496i \(0.927926\pi\)
\(674\) −8.49643 8.49643i −0.327270 0.327270i
\(675\) 3.46478 + 3.60489i 0.133360 + 0.138752i
\(676\) −3.03245 −0.116633
\(677\) 4.71937 + 4.71937i 0.181380 + 0.181380i 0.791957 0.610577i \(-0.209062\pi\)
−0.610577 + 0.791957i \(0.709062\pi\)
\(678\) −0.139124 0.139124i −0.00534303 0.00534303i
\(679\) −1.94958 1.94958i −0.0748178 0.0748178i
\(680\) −0.0763355 + 7.70424i −0.00292733 + 0.295444i
\(681\) 17.4366 + 17.4366i 0.668173 + 0.668173i
\(682\) 11.1550 11.1550i 0.427147 0.427147i
\(683\) 23.5379 0.900653 0.450327 0.892864i \(-0.351308\pi\)
0.450327 + 0.892864i \(0.351308\pi\)
\(684\) −1.85024 + 1.85024i −0.0707458 + 0.0707458i
\(685\) 34.7446 34.0629i 1.32752 1.30148i
\(686\) 3.89540 + 3.89540i 0.148727 + 0.148727i
\(687\) 10.5226 + 10.5226i 0.401462 + 0.401462i
\(688\) 1.27639 0.0486618
\(689\) 12.2737 + 12.2737i 0.467591 + 0.467591i
\(690\) 6.24744 6.12485i 0.237836 0.233169i
\(691\) 8.31048i 0.316145i 0.987427 + 0.158073i \(0.0505280\pi\)
−0.987427 + 0.158073i \(0.949472\pi\)
\(692\) −5.83257 + 5.83257i −0.221721 + 0.221721i
\(693\) 0.463534 0.463534i 0.0176082 0.0176082i
\(694\) 0.455842 0.0173035
\(695\) −6.70531 0.0664378i −0.254347 0.00252013i
\(696\) 3.77880i 0.143235i
\(697\) −30.0474 −1.13813
\(698\) 18.0258i 0.682287i
\(699\) 20.7657i 0.785431i
\(700\) −1.43474 + 1.37898i −0.0542281 + 0.0521205i
\(701\) 26.9263 26.9263i 1.01699 1.01699i 0.0171385 0.999853i \(-0.494544\pi\)
0.999853 0.0171385i \(-0.00545561\pi\)
\(702\) −2.23244 2.23244i −0.0842579 0.0842579i
\(703\) 9.41129 12.8359i 0.354954 0.484113i
\(704\) 1.64708i 0.0620767i
\(705\) 0.0235867 2.38051i 0.000888326 0.0896553i
\(706\) 16.2235i 0.610579i
\(707\) 1.70119 + 1.70119i 0.0639797 + 0.0639797i
\(708\) 9.24603 0.347487
\(709\) 17.6567 + 17.6567i 0.663111 + 0.663111i 0.956112 0.293001i \(-0.0946539\pi\)
−0.293001 + 0.956112i \(0.594654\pi\)
\(710\) −25.0876 0.248574i −0.941522 0.00932883i
\(711\) 2.86326 2.86326i 0.107381 0.107381i
\(712\) −12.5832 + 12.5832i −0.471574 + 0.471574i
\(713\) −26.4988 26.4988i −0.992387 0.992387i
\(714\) 1.37135 0.0513214
\(715\) 0.115205 11.6271i 0.00430840 0.434831i
\(716\) −4.52269 + 4.52269i −0.169021 + 0.169021i
\(717\) 16.8289 0.628486
\(718\) 19.2940i 0.720046i
\(719\) 7.51201i 0.280151i 0.990141 + 0.140075i \(0.0447345\pi\)
−0.990141 + 0.140075i \(0.955266\pi\)
\(720\) 0.0221544 2.23596i 0.000825646 0.0833292i
\(721\) −3.16784 3.16784i −0.117976 0.117976i
\(722\) 12.1532i 0.452295i
\(723\) 22.1544i 0.823930i
\(724\) −16.8840 −0.627487
\(725\) 13.6222 13.0927i 0.505915 0.486252i
\(726\) 5.85988 5.85988i 0.217481 0.217481i
\(727\) −44.5433 −1.65202 −0.826010 0.563655i \(-0.809395\pi\)
−0.826010 + 0.563655i \(0.809395\pi\)
\(728\) 0.888506 0.888506i 0.0329302 0.0329302i
\(729\) 1.00000i 0.0370370i
\(730\) −1.81759 + 1.78193i −0.0672720 + 0.0659520i
\(731\) 4.39794i 0.162664i
\(732\) 0.204701 0.00756598
\(733\) −21.8867 + 21.8867i −0.808404 + 0.808404i −0.984392 0.175988i \(-0.943688\pi\)
0.175988 + 0.984392i \(0.443688\pi\)
\(734\) 3.21053 3.21053i 0.118503 0.118503i
\(735\) −10.7098 10.9242i −0.395037 0.402944i
\(736\) −3.91265 −0.144222
\(737\) −0.811312 + 0.811312i −0.0298851 + 0.0298851i
\(738\) 8.72049 0.321006
\(739\) −4.64271 −0.170785 −0.0853925 0.996347i \(-0.527214\pi\)
−0.0853925 + 0.996347i \(0.527214\pi\)
\(740\) 1.93604 + 13.4630i 0.0711703 + 0.494909i
\(741\) 8.26110 0.303479
\(742\) 2.18815 0.0803296
\(743\) −38.1619 + 38.1619i −1.40003 + 1.40003i −0.600105 + 0.799921i \(0.704874\pi\)
−0.799921 + 0.600105i \(0.795126\pi\)
\(744\) −9.57788 −0.351142
\(745\) −0.190695 + 19.2461i −0.00698653 + 0.705124i
\(746\) 2.94440 2.94440i 0.107802 0.107802i
\(747\) 3.45461 3.45461i 0.126397 0.126397i
\(748\) −5.67521 −0.207506
\(749\) 5.00355i 0.182826i
\(750\) 8.13715 7.66725i 0.297127 0.279968i
\(751\) 36.4153i 1.32881i 0.747371 + 0.664406i \(0.231316\pi\)
−0.747371 + 0.664406i \(0.768684\pi\)
\(752\) −0.752821 + 0.752821i −0.0274526 + 0.0274526i
\(753\) −11.7059 −0.426588
\(754\) −8.43593 + 8.43593i −0.307219 + 0.307219i
\(755\) −0.0606177 + 6.11791i −0.00220610 + 0.222654i
\(756\) −0.397998 −0.0144750
\(757\) 17.1425i 0.623054i −0.950237 0.311527i \(-0.899160\pi\)
0.950237 0.311527i \(-0.100840\pi\)
\(758\) 25.1637i 0.913989i
\(759\) 4.55692 + 4.55692i 0.165406 + 0.165406i
\(760\) 4.09608 + 4.17806i 0.148580 + 0.151554i
\(761\) 35.6476i 1.29222i 0.763243 + 0.646112i \(0.223606\pi\)
−0.763243 + 0.646112i \(0.776394\pi\)
\(762\) 9.00960i 0.326384i
\(763\) −5.03431 −0.182254
\(764\) −18.5005 + 18.5005i −0.669323 + 0.669323i
\(765\) −7.70424 0.0763355i −0.278548 0.00275991i
\(766\) 0.995617 0.0359731
\(767\) −20.6412 20.6412i −0.745310 0.745310i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 12.7710 12.7710i 0.460533 0.460533i −0.438297 0.898830i \(-0.644418\pi\)
0.898830 + 0.438297i \(0.144418\pi\)
\(770\) −1.02617 1.04671i −0.0369807 0.0377208i
\(771\) 2.99965 + 2.99965i 0.108030 + 0.108030i
\(772\) −17.1049 −0.615620
\(773\) 11.0549 + 11.0549i 0.397617 + 0.397617i 0.877392 0.479775i \(-0.159282\pi\)
−0.479775 + 0.877392i \(0.659282\pi\)
\(774\) 1.27639i 0.0458788i
\(775\) −33.1853 34.5273i −1.19205 1.24026i
\(776\) 6.92746i 0.248681i
\(777\) 2.39275 0.368321i 0.0858393 0.0132135i
\(778\) 19.4231 + 19.4231i 0.696350 + 0.696350i
\(779\) −16.1350 + 16.1350i −0.578097 + 0.578097i