Properties

Label 1110.2.l.a.697.11
Level $1110$
Weight $2$
Character 1110.697
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.l (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 697.11
Character \(\chi\) \(=\) 1110.697
Dual form 1110.2.l.a.43.11

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-0.0221544 - 2.23596i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.281427 - 0.281427i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-0.0221544 - 2.23596i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.281427 - 0.281427i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(-2.23596 + 0.0221544i) q^{10} -1.64708i q^{11} +(-0.707107 - 0.707107i) q^{12} -3.15714i q^{13} +(-0.281427 + 0.281427i) q^{14} +(1.56540 - 1.59673i) q^{15} +1.00000 q^{16} +3.44561 q^{17} +1.00000 q^{18} +(1.85024 + 1.85024i) q^{19} +(0.0221544 + 2.23596i) q^{20} -0.397998i q^{21} -1.64708 q^{22} -3.91265i 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} -1.00000i q^{32} +(1.16466 - 1.16466i) q^{33} -3.44561i q^{34} +(-0.623024 + 0.635494i) q^{35} -1.00000i q^{36} +(-6.01195 + 0.925435i) q^{37} +(1.85024 - 1.85024i) q^{38} +(2.23244 - 2.23244i) q^{39} +(2.23596 - 0.0221544i) q^{40} -8.72049i q^{41} -0.397998 q^{42} -1.27639i q^{43} +1.64708i q^{44} +(2.23596 - 0.0221544i) q^{45} -3.91265 q^{46} +(-0.752821 - 0.752821i) q^{47} +(0.707107 + 0.707107i) q^{48} -6.84160i q^{49} +(0.0990726 + 4.99902i) q^{50} +(2.43642 + 2.43642i) q^{51} +3.15714i q^{52} +(3.88760 - 3.88760i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-3.68281 + 0.0364901i) q^{55} +(0.281427 - 0.281427i) q^{56} +2.61664i q^{57} +(2.67202 + 2.67202i) q^{58} +(6.53793 + 6.53793i) q^{59} +(-1.56540 + 1.59673i) 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} -3.44561 q^{68} +(2.76666 - 2.76666i) q^{69} +(0.635494 + 0.623024i) q^{70} +11.2201 q^{71} -1.00000 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} +(-0.0221544 - 2.23596i) q^{80} -1.00000 q^{81} -8.72049 q^{82} +(3.45461 - 3.45461i) q^{83} +0.397998i q^{84} +(-0.0763355 - 7.70424i) q^{85} -1.27639 q^{86} -3.77880 q^{87} +1.64708 q^{88} +(-12.5832 + 12.5832i) q^{89} +(-0.0221544 - 2.23596i) q^{90} +(-0.888506 + 0.888506i) q^{91} +3.91265i q^{92} -9.57788i q^{93} +(-0.752821 + 0.752821i) q^{94} +(4.09608 - 4.17806i) q^{95} +(0.707107 - 0.707107i) q^{96} -6.92746 q^{97} -6.84160 q^{98} +1.64708 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 36q^{4} + 4q^{7} + O(q^{10}) \) \( 36q - 36q^{4} + 4q^{7} - 4q^{10} + 4q^{14} + 36q^{16} - 32q^{17} + 36q^{18} + 4q^{19} + 8q^{22} - 4q^{25} + 8q^{26} - 4q^{28} + 36q^{29} - 4q^{31} + 4q^{33} - 12q^{35} - 4q^{37} + 4q^{38} + 4q^{39} + 4q^{40} - 16q^{42} + 4q^{45} + 16q^{47} - 16q^{50} - 8q^{53} + 16q^{55} - 4q^{56} - 36q^{58} - 4q^{59} - 4q^{61} - 4q^{62} - 4q^{63} - 36q^{64} + 52q^{65} - 4q^{66} + 16q^{67} + 32q^{68} - 8q^{69} - 28q^{70} - 8q^{71} - 36q^{72} - 4q^{73} + 28q^{74} + 16q^{75} - 4q^{76} + 8q^{77} - 4q^{78} - 12q^{79} - 36q^{81} - 8q^{82} + 8q^{83} + 8q^{85} + 32q^{86} - 8q^{87} - 8q^{88} - 24q^{89} + 56q^{91} + 16q^{94} - 20q^{95} + 40q^{97} - 12q^{98} - 8q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) −1.00000 −0.500000
\(5\) −0.0221544 2.23596i −0.00990775 0.999951i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) −0.281427 0.281427i −0.106369 0.106369i 0.651919 0.758289i \(-0.273964\pi\)
−0.758289 + 0.651919i \(0.773964\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 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
\(13\) 3.15714i 0.875634i −0.899064 0.437817i \(-0.855752\pi\)
0.899064 0.437817i \(-0.144248\pi\)
\(14\) −0.281427 + 0.281427i −0.0752146 + 0.0752146i
\(15\) 1.56540 1.59673i 0.404183 0.412273i
\(16\) 1.00000 0.250000
\(17\) 3.44561 0.835684 0.417842 0.908520i \(-0.362787\pi\)
0.417842 + 0.908520i \(0.362787\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.85024 + 1.85024i 0.424475 + 0.424475i 0.886741 0.462266i \(-0.152964\pi\)
−0.462266 + 0.886741i \(0.652964\pi\)
\(20\) 0.0221544 + 2.23596i 0.00495387 + 0.499975i
\(21\) 0.397998i 0.0868503i
\(22\) −1.64708 −0.351159
\(23\) 3.91265i 0.815844i −0.913017 0.407922i \(-0.866253\pi\)
0.913017 0.407922i \(-0.133747\pi\)
\(24\) −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 −0.910247 0.414066i \(-0.864108\pi\)
0.414066 + 0.910247i \(0.364108\pi\)
\(30\) −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 \(-0.579611\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.16466 1.16466i 0.202742 0.202742i
\(34\) 3.44561i 0.590917i
\(35\) −0.623024 + 0.635494i −0.105310 + 0.107418i
\(36\) 1.00000i 0.166667i
\(37\) −6.01195 + 0.925435i −0.988359 + 0.152141i
\(38\) 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 \(-0.238435\pi\)
\(42\) −0.397998 −0.0614124
\(43\) 1.27639i 0.194647i −0.995253 0.0973237i \(-0.968972\pi\)
0.995253 0.0973237i \(-0.0310282\pi\)
\(44\) 1.64708i 0.248307i
\(45\) 2.23596 0.0221544i 0.333317 0.00330258i
\(46\) −3.91265 −0.576889
\(47\) −0.752821 0.752821i −0.109810 0.109810i 0.650067 0.759877i \(-0.274741\pi\)
−0.759877 + 0.650067i \(0.774741\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 6.84160i 0.977371i
\(50\) 0.0990726 + 4.99902i 0.0140110 + 0.706968i
\(51\) 2.43642 + 2.43642i 0.341166 + 0.341166i
\(52\) 3.15714i 0.437817i
\(53\) 3.88760 3.88760i 0.534003 0.534003i −0.387758 0.921761i \(-0.626750\pi\)
0.921761 + 0.387758i \(0.126750\pi\)
\(54\) 0.707107 + 0.707107i 0.0962250 + 0.0962250i
\(55\) −3.68281 + 0.0364901i −0.496590 + 0.00492033i
\(56\) 0.281427 0.281427i 0.0376073 0.0376073i
\(57\) 2.61664i 0.346582i
\(58\) 2.67202 + 2.67202i 0.350853 + 0.350853i
\(59\) 6.53793 + 6.53793i 0.851166 + 0.851166i 0.990277 0.139111i \(-0.0444244\pi\)
−0.139111 + 0.990277i \(0.544424\pi\)
\(60\) −1.56540 + 1.59673i −0.202092 + 0.206137i
\(61\) −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 \(-0.736451\pi\)
0.736555 + 0.676377i \(0.236451\pi\)
\(68\) −3.44561 −0.417842
\(69\) 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 \(0.268095\pi\)
\(72\) −1.00000 −0.117851
\(73\) −0.804916 0.804916i −0.0942083 0.0942083i 0.658432 0.752640i \(-0.271220\pi\)
−0.752640 + 0.658432i \(0.771220\pi\)
\(74\) 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 0.527446 0.849588i \(-0.323150\pi\)
−0.849588 + 0.527446i \(0.823150\pi\)
\(80\) −0.0221544 2.23596i −0.00247694 0.249988i
\(81\) −1.00000 −0.111111
\(82\) −8.72049 −0.963017
\(83\) 3.45461 3.45461i 0.379192 0.379192i −0.491618 0.870811i \(-0.663594\pi\)
0.870811 + 0.491618i \(0.163594\pi\)
\(84\) 0.397998i 0.0434251i
\(85\) −0.0763355 7.70424i −0.00827974 0.835643i
\(86\) −1.27639 −0.137636
\(87\) −3.77880 −0.405130
\(88\) 1.64708 0.175580
\(89\) −12.5832 + 12.5832i −1.33381 + 1.33381i −0.431885 + 0.901929i \(0.642151\pi\)
−0.901929 + 0.431885i \(0.857849\pi\)
\(90\) −0.0221544 2.23596i −0.00233528 0.235691i
\(91\) −0.888506 + 0.888506i −0.0931407 + 0.0931407i
\(92\) 3.91265i 0.407922i
\(93\) 9.57788i 0.993180i
\(94\) −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
\(97\) −6.92746 −0.703377 −0.351689 0.936117i \(-0.614392\pi\)
−0.351689 + 0.936117i \(0.614392\pi\)
\(98\) −6.84160 −0.691106
\(99\) 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
\(103\) 11.2563 1.10912 0.554560 0.832144i \(-0.312887\pi\)
0.554560 + 0.832144i \(0.312887\pi\)
\(104\) 3.15714 0.309583
\(105\) −0.889907 + 0.00881741i −0.0868460 + 0.000860491i
\(106\) −3.88760 3.88760i −0.377597 0.377597i
\(107\) 8.88960 + 8.88960i 0.859390 + 0.859390i 0.991266 0.131876i \(-0.0421001\pi\)
−0.131876 + 0.991266i \(0.542100\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) −8.94425 8.94425i −0.856704 0.856704i 0.134244 0.990948i \(-0.457139\pi\)
−0.990948 + 0.134244i \(0.957139\pi\)
\(110\) 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
\(113\) −0.196751 −0.0185088 −0.00925440 0.999957i \(-0.502946\pi\)
−0.00925440 + 0.999957i \(0.502946\pi\)
\(114\) 2.61664 0.245071
\(115\) −8.74853 + 0.0866825i −0.815804 + 0.00808318i
\(116\) 2.67202 2.67202i 0.248090 0.248090i
\(117\) 3.15714 0.291878
\(118\) 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
\(125\) 0.332273 + 11.1754i 0.0297194 + 0.999558i
\(126\) −0.281427 0.281427i −0.0250715 0.0250715i
\(127\) 6.37075 + 6.37075i 0.565313 + 0.565313i 0.930812 0.365499i \(-0.119102\pi\)
−0.365499 + 0.930812i \(0.619102\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0.902543 0.902543i 0.0794644 0.0794644i
\(130\) 0.0699446 + 7.05924i 0.00613455 + 0.619136i
\(131\) −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
\(133\) 1.04142i 0.0903023i
\(134\) −0.492575 0.492575i −0.0425520 0.0425520i
\(135\) 1.59673 + 1.56540i 0.137424 + 0.134728i
\(136\) 3.44561i 0.295459i
\(137\) 15.3866 + 15.3866i 1.31456 + 1.31456i 0.918012 + 0.396553i \(0.129794\pi\)
0.396553 + 0.918012i \(0.370206\pi\)
\(138\) −2.76666 2.76666i −0.235514 0.235514i
\(139\) 2.99885 0.254359 0.127180 0.991880i \(-0.459408\pi\)
0.127180 + 0.991880i \(0.459408\pi\)
\(140\) 0.623024 0.635494i 0.0526552 0.0537091i
\(141\) 1.06465i 0.0896597i
\(142\) 11.2201i 0.941569i
\(143\) −5.20007 −0.434852
\(144\) 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
\(148\) 6.01195 0.925435i 0.494179 0.0760703i
\(149\) 8.60756i 0.705159i −0.935782 0.352579i \(-0.885305\pi\)
0.935782 0.352579i \(-0.114695\pi\)
\(150\) −3.46478 + 3.60489i −0.282898 + 0.294338i
\(151\) 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
\(153\) 3.44561i 0.278561i
\(154\) 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 0.509283 0.860599i \(-0.329911\pi\)
−0.860599 + 0.509283i \(0.829911\pi\)
\(158\) −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
\(162\) 1.00000i 0.0785674i
\(163\) 10.2487 0.802740 0.401370 0.915916i \(-0.368534\pi\)
0.401370 + 0.915916i \(0.368534\pi\)
\(164\) 8.72049i 0.680956i
\(165\) −2.62994 2.57834i −0.204741 0.200723i
\(166\) −3.45461 3.45461i −0.268130 0.268130i
\(167\) −2.97278 −0.230040 −0.115020 0.993363i \(-0.536693\pi\)
−0.115020 + 0.993363i \(0.536693\pi\)
\(168\) 0.397998 0.0307062
\(169\) 3.03245 0.233265
\(170\) −7.70424 + 0.0763355i −0.590888 + 0.00585466i
\(171\) −1.85024 + 1.85024i −0.141492 + 0.141492i
\(172\) 1.27639i 0.0973237i
\(173\) 5.83257 + 5.83257i 0.443442 + 0.443442i 0.893167 0.449725i \(-0.148478\pi\)
−0.449725 + 0.893167i \(0.648478\pi\)
\(174\) 3.77880i 0.286470i
\(175\) 1.43474 + 1.37898i 0.108456 + 0.104241i
\(176\) 1.64708i 0.124153i
\(177\) 9.24603i 0.694974i
\(178\) 12.5832 + 12.5832i 0.943149 + 0.943149i
\(179\) 4.52269 4.52269i 0.338042 0.338042i −0.517588 0.855630i \(-0.673170\pi\)
0.855630 + 0.517588i \(0.173170\pi\)
\(180\) −2.23596 + 0.0221544i −0.166658 + 0.00165129i
\(181\) −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
\(183\) 0.204701i 0.0151320i
\(184\) 3.91265 0.288445
\(185\) 2.20243 + 13.4220i 0.161926 + 0.986803i
\(186\) −9.57788 −0.702284
\(187\) 5.67521i 0.415012i
\(188\) 0.752821 + 0.752821i 0.0549051 + 0.0549051i
\(189\) 0.397998 0.0289501
\(190\) −4.17806 4.09608i −0.303108 0.297161i
\(191\) −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
\(193\) 17.1049i 1.23124i 0.788043 + 0.615620i \(0.211094\pi\)
−0.788043 + 0.615620i \(0.788906\pi\)
\(194\) 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 0.686995 0.726662i \(-0.258929\pi\)
−0.726662 + 0.686995i \(0.758929\pi\)
\(198\) 1.64708i 0.117053i
\(199\) 7.91159 7.91159i 0.560838 0.560838i −0.368707 0.929546i \(-0.620200\pi\)
0.929546 + 0.368707i \(0.120200\pi\)
\(200\) −0.0990726 4.99902i −0.00700549 0.353484i
\(201\) 0.696607 0.0491349
\(202\) −6.04485 −0.425314
\(203\) 1.50396 0.105557
\(204\) −2.43642 2.43642i −0.170583 0.170583i
\(205\) −19.4986 + 0.193197i −1.36184 + 0.0134935i
\(206\) 11.2563i 0.784266i
\(207\) 3.91265 0.271948
\(208\) 3.15714i 0.218908i
\(209\) 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
\(217\) 3.81198i 0.258774i
\(218\) −8.94425 + 8.94425i −0.605781 + 0.605781i
\(219\) 1.13832i 0.0769207i
\(220\) 3.68281 0.0364901i 0.248295 0.00246016i
\(221\) 10.8783i 0.731753i
\(222\) −3.59671 + 4.90547i −0.241395 + 0.329234i
\(223\) −3.07126 + 3.07126i −0.205667 + 0.205667i −0.802423 0.596756i \(-0.796456\pi\)
0.596756 + 0.802423i \(0.296456\pi\)
\(224\) −0.281427 + 0.281427i −0.0188036 + 0.0188036i
\(225\) −0.0990726 4.99902i −0.00660484 0.333268i
\(226\) 0.196751i 0.0130877i
\(227\) 24.6591 1.63668 0.818342 0.574732i \(-0.194894\pi\)
0.818342 + 0.574732i \(0.194894\pi\)
\(228\) 2.61664i 0.173291i
\(229\) 14.8812i 0.983377i 0.870771 + 0.491689i \(0.163620\pi\)
−0.870771 + 0.491689i \(0.836380\pi\)
\(230\) 0.0866825 + 8.74853i 0.00571567 + 0.576861i
\(231\) −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 \(-0.0118916\pi\)
−0.0373500 + 0.999302i \(0.511892\pi\)
\(234\) 3.15714i 0.206389i
\(235\) −1.66660 + 1.69995i −0.108717 + 0.110893i
\(236\) −6.53793 6.53793i −0.425583 0.425583i
\(237\) 4.04926i 0.263028i
\(238\) −0.969688 + 0.969688i −0.0628556 + 0.0628556i
\(239\) 11.8998 + 11.8998i 0.769736 + 0.769736i 0.978060 0.208324i \(-0.0668009\pi\)
−0.208324 + 0.978060i \(0.566801\pi\)
\(240\) 1.56540 1.59673i 0.101046 0.103068i
\(241\) 15.6655 15.6655i 1.00910 1.00910i 0.00914615 0.999958i \(-0.497089\pi\)
0.999958 0.00914615i \(-0.00291135\pi\)
\(242\) 8.28712i 0.532716i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 0.144746 + 0.144746i 0.00926640 + 0.00926640i
\(245\) −15.2975 + 0.151571i −0.977323 + 0.00968355i
\(246\) −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
\(253\) −6.44446 −0.405160
\(254\) 6.37075 6.37075i 0.399737 0.399737i
\(255\) 5.39375 5.50170i 0.337769 0.344530i
\(256\) 1.00000 0.0625000
\(257\) 4.24215 0.264618 0.132309 0.991209i \(-0.457761\pi\)
0.132309 + 0.991209i \(0.457761\pi\)
\(258\) −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 0.842223 + 0.539129i \(0.181246\pi\)
0.539129 + 0.842223i \(0.318754\pi\)
\(264\) 1.16466 + 1.16466i 0.0716801 + 0.0716801i
\(265\) −8.77864 8.60638i −0.539267 0.528686i
\(266\) −1.04142 −0.0638534
\(267\) −17.7953 −1.08905
\(268\) −0.492575 + 0.492575i −0.0300888 + 0.0300888i
\(269\) 15.2647i 0.930706i −0.885125 0.465353i \(-0.845927\pi\)
0.885125 0.465353i \(-0.154073\pi\)
\(270\) 1.56540 1.59673i 0.0952669 0.0971737i
\(271\) 14.7969 0.898849 0.449424 0.893318i \(-0.351629\pi\)
0.449424 + 0.893318i \(0.351629\pi\)
\(272\) 3.44561 0.208921
\(273\) −1.25654 −0.0760491
\(274\) 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
\(277\) 3.00385i 0.180484i 0.995920 + 0.0902420i \(0.0287640\pi\)
−0.995920 + 0.0902420i \(0.971236\pi\)
\(278\) 2.99885i 0.179859i
\(279\) 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 \(0.364678\pi\)
\(282\) −1.06465 −0.0633990
\(283\) 3.86949 0.230018 0.115009 0.993364i \(-0.463310\pi\)
0.115009 + 0.993364i \(0.463310\pi\)
\(284\) −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
\(288\) 1.00000 0.0589256
\(289\) −5.12776 −0.301633
\(290\) 5.91532 6.03371i 0.347359 0.354312i
\(291\) −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 −0.319448 0.947604i \(-0.603498\pi\)
0.947604 + 0.319448i \(0.103498\pi\)
\(294\) −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
\(298\) −8.60756 −0.498622
\(299\) −12.3528 −0.714381
\(300\) 3.60489 + 3.46478i 0.208129 + 0.200039i
\(301\) −0.359210 + 0.359210i −0.0207045 + 0.0207045i
\(302\) 2.73615 0.157448
\(303\) 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 0.112652 0.993634i \(-0.464065\pi\)
0.993634 0.112652i \(-0.0359347\pi\)
\(308\) 0.463534 0.463534i 0.0264123 0.0264123i
\(309\) 7.95943 + 7.95943i 0.452796 + 0.452796i
\(310\) 15.2933 + 14.9932i 0.868599 + 0.851555i
\(311\) −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
\(313\) 20.7779i 1.17444i 0.809429 + 0.587218i \(0.199777\pi\)
−0.809429 + 0.587218i \(0.800223\pi\)
\(314\) −4.40198 + 4.40198i −0.248418 + 0.248418i
\(315\) −0.635494 0.623024i −0.0358060 0.0351034i
\(316\) 2.86326 + 2.86326i 0.161071 + 0.161071i
\(317\) 3.25873 3.25873i 0.183029 0.183029i −0.609646 0.792674i \(-0.708688\pi\)
0.792674 + 0.609646i \(0.208688\pi\)
\(318\) 5.49790i 0.308307i
\(319\) 4.40103 + 4.40103i 0.246410 + 0.246410i
\(320\) 0.0221544 + 2.23596i 0.00123847 + 0.124994i
\(321\) 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
\(325\) 0.312786 + 15.7826i 0.0173503 + 0.875462i
\(326\) 10.2487i 0.567623i
\(327\) 12.6491i 0.699496i
\(328\) 8.72049 0.481508
\(329\) 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
\(333\) −0.925435 6.01195i −0.0507135 0.329453i
\(334\) 2.97278i 0.162663i
\(335\) −1.11229 1.09047i −0.0607709 0.0595785i
\(336\) 0.397998i 0.0217126i
\(337\) −8.49643 + 8.49643i −0.462830 + 0.462830i −0.899582 0.436752i \(-0.856129\pi\)
0.436752 + 0.899582i \(0.356129\pi\)
\(338\) 3.03245i 0.164944i
\(339\) −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
\(347\) 0.455842i 0.0244709i −0.999925 0.0122354i \(-0.996105\pi\)
0.999925 0.0122354i \(-0.00389476\pi\)
\(348\) 3.77880 0.202565
\(349\) 18.0258i 0.964899i −0.875924 0.482450i \(-0.839747\pi\)
0.875924 0.482450i \(-0.160253\pi\)
\(350\) 1.37898 1.43474i 0.0737095 0.0766901i
\(351\) 2.23244 + 2.23244i 0.119159 + 0.119159i
\(352\) −1.64708 −0.0877898
\(353\) 16.2235 0.863489 0.431745 0.901996i \(-0.357898\pi\)
0.431745 + 0.901996i \(0.357898\pi\)
\(354\) 9.24603 0.491421
\(355\) −0.248574 25.0876i −0.0131930 1.33151i
\(356\) 12.5832 12.5832i 0.666907 0.666907i
\(357\) 1.37135i 0.0725794i
\(358\) −4.52269 4.52269i −0.239031 0.239031i
\(359\) 19.2940i 1.01830i −0.860678 0.509149i \(-0.829960\pi\)
0.860678 0.509149i \(-0.170040\pi\)
\(360\) 0.0221544 + 2.23596i 0.00116764 + 0.117845i
\(361\) 12.1532i 0.639642i
\(362\) 16.8840i 0.887401i
\(363\) 5.85988 + 5.85988i 0.307564 + 0.307564i
\(364\) 0.888506 0.888506i 0.0465703 0.0465703i
\(365\) −1.78193 + 1.81759i −0.0932703 + 0.0951370i
\(366\) −0.204701 −0.0106999
\(367\) −3.21053 3.21053i −0.167588 0.167588i 0.618330 0.785919i \(-0.287810\pi\)
−0.785919 + 0.618330i \(0.787810\pi\)
\(368\) 3.91265i 0.203961i
\(369\) 8.72049 0.453970
\(370\) 13.4220 2.20243i 0.697775 0.114499i
\(371\) −2.18815 −0.113603
\(372\) 9.57788i 0.496590i
\(373\) 2.94440 + 2.94440i 0.152455 + 0.152455i 0.779214 0.626759i \(-0.215619\pi\)
−0.626759 + 0.779214i \(0.715619\pi\)
\(374\) −5.67521 −0.293458
\(375\) −7.66725 + 8.13715i −0.395935 + 0.420201i
\(376\) 0.752821 0.752821i 0.0388238 0.0388238i
\(377\) 8.43593 + 8.43593i 0.434473 + 0.434473i
\(378\) 0.397998i 0.0204708i
\(379\) 25.1637i 1.29257i −0.763094 0.646287i \(-0.776321\pi\)
0.763094 0.646287i \(-0.223679\pi\)
\(380\) −4.09608 + 4.17806i −0.210124 + 0.214330i
\(381\) 9.00960i 0.461576i
\(382\) 18.5005 + 18.5005i 0.946566 + 0.946566i
\(383\) 0.995617i 0.0508736i 0.999676 + 0.0254368i \(0.00809766\pi\)
−0.999676 + 0.0254368i \(0.991902\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) 1.04671 + 1.02617i 0.0533453 + 0.0522986i
\(386\) 17.1049 0.870618
\(387\) 1.27639 0.0648824
\(388\) 6.92746 0.351689
\(389\) 19.4231 + 19.4231i 0.984788 + 0.984788i 0.999886 0.0150980i \(-0.00480602\pi\)
−0.0150980 + 0.999886i \(0.504806\pi\)
\(390\) −4.94218 + 5.04109i −0.250257 + 0.255266i
\(391\) 13.4815i 0.681788i
\(392\) 6.84160 0.345553
\(393\) 3.51508i 0.177312i
\(394\) −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 \(-0.824066\pi\)
0.524999 + 0.851103i \(0.324066\pi\)
\(398\) −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 \(-0.577678\pi\)
\(402\) 0.696607i 0.0347436i
\(403\) −21.3820 + 21.3820i −1.06511 + 1.06511i
\(404\) 6.04485i 0.300743i
\(405\) 0.0221544 + 2.23596i 0.00110086 + 0.111106i
\(406\) 1.50396i 0.0746401i
\(407\) 1.52427 + 9.90218i 0.0755551 + 0.490833i
\(408\) −2.43642 + 2.43642i −0.120621 + 0.120621i
\(409\) −24.0003 + 24.0003i −1.18674 + 1.18674i −0.208776 + 0.977963i \(0.566948\pi\)
−0.977963 + 0.208776i \(0.933052\pi\)
\(410\) 0.193197 + 19.4986i 0.00954133 + 0.962969i
\(411\) 21.7599i 1.07334i
\(412\) −11.2563 −0.554560
\(413\) 3.67990i 0.181076i
\(414\) 3.91265i 0.192296i
\(415\) −7.80089 7.64782i −0.382931 0.375417i
\(416\) −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 \(-0.711276\pi\)
0.616070 0.787692i \(-0.288724\pi\)
\(420\) 0.889907 0.00881741i 0.0434230 0.000430245i
\(421\) −3.85720 3.85720i −0.187988 0.187988i 0.606838 0.794826i \(-0.292438\pi\)
−0.794826 + 0.606838i \(0.792438\pi\)
\(422\) 1.32938i 0.0647132i
\(423\) 0.752821 0.752821i 0.0366034 0.0366034i
\(424\) 3.88760 + 3.88760i 0.188798 + 0.188798i
\(425\) −17.2247 + 0.341366i −0.835519 + 0.0165587i
\(426\) 7.93380 7.93380i 0.384394 0.384394i
\(427\) 0.0814708i 0.00394265i
\(428\) −8.88960 8.88960i −0.429695 0.429695i
\(429\) −3.67701 3.67701i −0.177528 0.177528i
\(430\) 0.0282776 + 2.85395i 0.00136367 + 0.137630i
\(431\) −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 −0.432130 + 0.901811i \(0.642238\pi\)
−0.901811 + 0.432130i \(0.857762\pi\)
\(434\) 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
\(438\) −1.13832 −0.0543912
\(439\) −17.1813 + 17.1813i −0.820020 + 0.820020i −0.986110 0.166091i \(-0.946885\pi\)
0.166091 + 0.986110i \(0.446885\pi\)
\(440\) −0.0364901 3.68281i −0.00173960 0.175571i
\(441\) 6.84160 0.325790
\(442\) −10.8783 −0.517427
\(443\) 7.22878 + 7.22878i 0.343450 + 0.343450i 0.857663 0.514213i \(-0.171916\pi\)
−0.514213 + 0.857663i \(0.671916\pi\)
\(444\) 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 0.438116 0.898918i \(-0.355646\pi\)
−0.898918 + 0.438116i \(0.855646\pi\)
\(450\) −4.99902 + 0.0990726i −0.235656 + 0.00467033i
\(451\) −14.3634 −0.676344
\(452\) 0.196751 0.00925440
\(453\) −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
\(457\) −20.5176 −0.959771 −0.479886 0.877331i \(-0.659322\pi\)
−0.479886 + 0.877331i \(0.659322\pi\)
\(458\) 14.8812 0.695353
\(459\) −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 \(-0.00221127\pi\)
\(462\) 0.655535i 0.0304983i
\(463\) 1.38040i 0.0641527i −0.999485 0.0320764i \(-0.989788\pi\)
0.999485 0.0320764i \(-0.0102120\pi\)
\(464\) −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
\(467\) 0.453871 0.0210026 0.0105013 0.999945i \(-0.496657\pi\)
0.0105013 + 0.999945i \(0.496657\pi\)
\(468\) −3.15714 −0.145939
\(469\) −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
\(473\) −2.10232 −0.0966646
\(474\) −4.04926 −0.185989
\(475\) −9.43271 9.06609i −0.432802 0.415981i
\(476\) 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 0.417521 0.908667i \(-0.362899\pi\)
−0.908667 + 0.417521i \(0.862899\pi\)
\(480\) −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
\(483\) −1.55723 −0.0708563
\(484\) −8.28712 −0.376687
\(485\) 0.153474 + 15.4895i 0.00696888 + 0.703343i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) 13.2268 0.599365 0.299682 0.954039i \(-0.403119\pi\)
0.299682 + 0.954039i \(0.403119\pi\)
\(488\) 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
\(495\) −0.0364901 3.68281i −0.00164011 0.165530i
\(496\) −6.77259 6.77259i −0.304098 0.304098i
\(497\) −3.15764 3.15764i −0.141639 0.141639i
\(498\) 4.88555i 0.218927i
\(499\) 6.74452 6.74452i 0.301926 0.301926i −0.539841 0.841767i \(-0.681516\pi\)
0.841767 + 0.539841i \(0.181516\pi\)
\(500\) −0.332273 11.1754i −0.0148597 0.499779i
\(501\) −2.10207 2.10207i −0.0939136 0.0939136i
\(502\) 8.27735 8.27735i 0.369436 0.369436i
\(503\) 31.0691i 1.38530i −0.721272 0.692652i \(-0.756442\pi\)
0.721272 0.692652i \(-0.243558\pi\)
\(504\) 0.281427 + 0.281427i 0.0125358 + 0.0125358i
\(505\) −13.5160 + 0.133920i −0.601456 + 0.00595937i
\(506\) 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 \(-0.420986\pi\)
0.245688 + 0.969349i \(0.420986\pi\)
\(510\) −5.50170 5.39375i −0.243619 0.238839i
\(511\) 0.453050i 0.0200418i
\(512\) 1.00000i 0.0441942i
\(513\) −2.61664 −0.115527
\(514\) 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
\(518\) 1.43148 1.95237i 0.0628958 0.0857822i
\(519\) 8.24851i 0.362069i
\(520\) −0.0699446 7.05924i −0.00306727 0.309568i
\(521\) 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
\(523\) 9.72492i 0.425241i 0.977135 + 0.212620i \(0.0681998\pi\)
−0.977135 + 0.212620i \(0.931800\pi\)
\(524\) 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
\(532\) 1.04142i 0.0451512i
\(533\) −27.5318 −1.19254
\(534\) 17.7953i 0.770078i
\(535\) 19.6798 20.0737i 0.850833 0.867863i
\(536\) 0.492575 + 0.492575i 0.0212760 + 0.0212760i
\(537\) 6.39605 0.276010
\(538\) −15.2647 −0.658108
\(539\) −11.2687 −0.485376
\(540\) −1.59673 1.56540i −0.0687122 0.0673639i
\(541\) −22.2929 + 22.2929i −0.958445 + 0.958445i −0.999170 0.0407258i \(-0.987033\pi\)
0.0407258 + 0.999170i \(0.487033\pi\)
\(542\) 14.7969i 0.635582i
\(543\) −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
\(547\) 33.1369i 1.41683i 0.705795 + 0.708416i \(0.250590\pi\)
−0.705795 + 0.708416i \(0.749410\pi\)
\(548\) −15.3866 15.3866i −0.657282 0.657282i
\(549\) 0.144746 0.144746i 0.00617760 0.00617760i
\(550\) 8.23379 0.163181i 0.351090 0.00695805i
\(551\) −9.88776 −0.421233
\(552\) 2.76666 + 2.76666i 0.117757 + 0.117757i
\(553\) 1.61160i 0.0685322i
\(554\) 3.00385 0.127621
\(555\) −7.93342 + 11.0481i −0.336755 + 0.468966i
\(556\) −2.99885 −0.127180
\(557\) 3.42489i 0.145117i 0.997364 + 0.0725586i \(0.0231164\pi\)
−0.997364 + 0.0725586i \(0.976884\pi\)
\(558\) −6.77259 6.77259i −0.286706 0.286706i
\(559\) −4.02974 −0.170440
\(560\) −0.623024 + 0.635494i −0.0263276 + 0.0268545i
\(561\) 4.01298 4.01298i 0.169428 0.169428i
\(562\) 8.35723 + 8.35723i 0.352529 + 0.352529i
\(563\) 17.6124i 0.742273i −0.928578 0.371136i \(-0.878968\pi\)
0.928578 0.371136i \(-0.121032\pi\)
\(564\) 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
\(568\) 11.2201i 0.470784i
\(569\) 13.6557 13.6557i 0.572477 0.572477i −0.360343 0.932820i \(-0.617340\pi\)
0.932820 + 0.360343i \(0.117340\pi\)
\(570\) −0.0579701 5.85070i −0.00242810 0.245059i
\(571\) 36.6093 1.53205 0.766025 0.642811i \(-0.222232\pi\)
0.766025 + 0.642811i \(0.222232\pi\)
\(572\) 5.20007 0.217426
\(573\) −26.1636 −1.09300
\(574\) 2.45418 + 2.45418i 0.102436 + 0.102436i
\(575\) 0.387637 + 19.5594i 0.0161656 + 0.815684i
\(576\) 1.00000i 0.0416667i
\(577\) −28.6229 −1.19159 −0.595794 0.803137i \(-0.703163\pi\)
−0.595794 + 0.803137i \(0.703163\pi\)
\(578\) 5.12776i 0.213287i
\(579\) −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
\(587\) 17.5944i 0.726197i −0.931751 0.363099i \(-0.881719\pi\)
0.931751 0.363099i \(-0.118281\pi\)
\(588\) −4.83774 + 4.83774i −0.199505 + 0.199505i
\(589\) 25.0619i 1.03266i
\(590\) −14.7634 14.4737i −0.607799 0.595873i
\(591\) 0.787365i 0.0323879i
\(592\) −6.01195 + 0.925435i −0.247090 + 0.0380351i
\(593\) −5.00469 + 5.00469i −0.205518 + 0.205518i −0.802359 0.596841i \(-0.796422\pi\)
0.596841 + 0.802359i \(0.296422\pi\)
\(594\) 1.16466 1.16466i 0.0477867 0.0477867i
\(595\) −2.14670 + 2.18967i −0.0880061 + 0.0897675i
\(596\) 8.60756i 0.352579i
\(597\) 11.1887 0.457922
\(598\) 12.3528i 0.505144i
\(599\) 35.1064i 1.43441i 0.696863 + 0.717204i \(0.254579\pi\)
−0.696863 + 0.717204i \(0.745421\pi\)
\(600\) 3.46478 3.60489i 0.141449 0.147169i
\(601\) −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
\(605\) −0.183596 18.5297i −0.00746425 0.753338i
\(606\) −4.27436 4.27436i −0.173634 0.173634i
\(607\) 2.58147i 0.104779i −0.998627 0.0523894i \(-0.983316\pi\)
0.998627 0.0523894i \(-0.0166837\pi\)
\(608\) 1.85024 1.85024i 0.0750373 0.0750373i
\(609\) 1.06346 + 1.06346i 0.0430935 + 0.0430935i
\(610\) 0.326852 + 0.320439i 0.0132339 + 0.0129742i
\(611\) −2.37676 + 2.37676i −0.0961535 + 0.0961535i
\(612\) 3.44561i 0.139281i
\(613\) −7.76986 7.76986i −0.313822 0.313822i 0.532566 0.846388i \(-0.321228\pi\)
−0.846388 + 0.532566i \(0.821228\pi\)
\(614\) −19.3837 19.3837i −0.782263 0.782263i
\(615\) −13.9242 13.6510i −0.561479 0.550462i
\(616\) −0.463534 0.463534i −0.0186763 0.0186763i
\(617\) 19.3110 19.3110i 0.777430 0.777430i −0.201963 0.979393i \(-0.564732\pi\)
0.979393 + 0.201963i \(0.0647322\pi\)
\(618\) 7.95943 7.95943i 0.320175 0.320175i
\(619\) −22.9273 −0.921528 −0.460764 0.887523i \(-0.652425\pi\)
−0.460764 + 0.887523i \(0.652425\pi\)
\(620\) 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
\(623\) 7.08249 0.283754
\(624\) 2.23244 2.23244i 0.0893690 0.0893690i
\(625\) 24.9804 0.990532i 0.999215 0.0396213i
\(626\) 20.7779 0.830451
\(627\) 4.30982 0.172118
\(628\) 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
\(635\) 14.1036 14.3859i 0.559684 0.570886i
\(636\) −5.49790 −0.218006
\(637\) −21.5999 −0.855819
\(638\) 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 \(0.457214\pi\)
\(642\) 12.5718 0.496169
\(643\) 36.8670 1.45389 0.726945 0.686695i \(-0.240939\pi\)
0.726945 + 0.686695i \(0.240939\pi\)
\(644\) 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
\(647\) 19.1501i 0.752868i −0.926443 0.376434i \(-0.877150\pi\)
0.926443 0.376434i \(-0.122850\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 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
\(652\) −10.2487 −0.401370
\(653\) −19.8305 −0.776029 −0.388015 0.921653i \(-0.626839\pi\)
−0.388015 + 0.921653i \(0.626839\pi\)
\(654\) −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
\(658\) 0.423728 0.0165187
\(659\) −21.4129 −0.834127 −0.417064 0.908877i \(-0.636941\pi\)
−0.417064 + 0.908877i \(0.636941\pi\)
\(660\) 2.62994 + 2.57834i 0.102370 + 0.100362i
\(661\) 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
\(668\) 2.97278 0.115020
\(669\) −4.34342 −0.167926
\(670\) −1.09047 + 1.11229i −0.0421284 + 0.0429715i
\(671\) −0.238408 + 0.238408i −0.00920365 + 0.00920365i
\(672\) −0.397998 −0.0153531
\(673\) −19.4561 + 19.4561i −0.749979 + 0.749979i −0.974475 0.224496i \(-0.927926\pi\)
0.224496 + 0.974475i \(0.427926\pi\)
\(674\) 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 \(-0.790938\pi\)
0.610577 + 0.791957i \(0.290938\pi\)
\(678\) −0.139124 + 0.139124i −0.00534303 + 0.00534303i
\(679\) 1.94958 + 1.94958i 0.0748178 + 0.0748178i
\(680\) 7.70424 0.0763355i 0.295444 0.00292733i
\(681\) 17.4366 + 17.4366i 0.668173 + 0.668173i
\(682\) 11.1550 + 11.1550i 0.427147 + 0.427147i
\(683\) 23.5379i 0.900653i −0.892864 0.450327i \(-0.851308\pi\)
0.892864 0.450327i \(-0.148692\pi\)
\(684\) 1.85024 1.85024i 0.0707458 0.0707458i
\(685\) 34.0629 34.7446i 1.30148 1.32752i
\(686\) 3.89540 + 3.89540i 0.148727 + 0.148727i
\(687\) −10.5226 + 10.5226i −0.401462 + 0.401462i
\(688\) 1.27639i 0.0486618i
\(689\) −12.2737 12.2737i −0.467591 0.467591i
\(690\) −6.12485 + 6.24744i −0.233169 + 0.237836i
\(691\) 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
\(695\) −0.0664378 6.70531i −0.00252013 0.254347i
\(696\) 3.77880i 0.143235i
\(697\) 30.0474i 1.13813i
\(698\) −18.0258 −0.682287
\(699\) 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
\(703\) −12.8359 9.41129i −0.484113 0.354954i
\(704\) 1.64708i 0.0620767i
\(705\) −2.38051 + 0.0235867i −0.0896553 + 0.000888326i
\(706\) 16.2235i 0.610579i
\(707\) −1.70119 + 1.70119i −0.0639797 + 0.0639797i
\(708\) 9.24603i 0.347487i
\(709\) −17.6567 17.6567i −0.663111 0.663111i 0.293001 0.956112i \(-0.405346\pi\)
−0.956112 + 0.293001i \(0.905346\pi\)
\(710\) −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
\(717\) 16.8289i 0.628486i
\(718\) −19.2940 −0.720046
\(719\) 7.51201i 0.280151i −0.990141 0.140075i \(-0.955266\pi\)
0.990141 0.140075i \(-0.0447345\pi\)
\(720\) 2.23596 0.0221544i 0.0833292 0.000825646i
\(721\) −3.16784 3.16784i −0.117976 0.117976i
\(722\) −12.1532 −0.452295
\(723\) 22.1544 0.823930
\(724\) 16.8840 0.627487
\(725\) 13.0927 13.6222i 0.486252 0.505915i
\(726\) 5.85988 5.85988i 0.217481 0.217481i
\(727\) 44.5433i 1.65202i −0.563655 0.826010i \(-0.690605\pi\)
0.563655 0.826010i \(-0.309395\pi\)
\(728\) −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
\(732\) 0.204701i 0.00756598i
\(733\) 21.8867 + 21.8867i 0.808404 + 0.808404i 0.984392 0.175988i \(-0.0563121\pi\)
−0.175988 + 0.984392i \(0.556312\pi\)
\(734\) −3.21053 + 3.21053i −0.118503 + 0.118503i
\(735\) −10.9242 10.7098i −0.402944 0.395037i
\(736\) −3.91265 −0.144222
\(737\) −0.811312 0.811312i −0.0298851 0.0298851i
\(738\) 8.72049i 0.321006i
\(739\) 4.64271 0.170785 0.0853925 0.996347i \(-0.472786\pi\)
0.0853925 + 0.996347i \(0.472786\pi\)
\(740\) −2.20243 13.4220i −0.0809628 0.493401i
\(741\) 8.26110 0.303479
\(742\) 2.18815i 0.0803296i
\(743\) 38.1619 + 38.1619i 1.40003 + 1.40003i 0.799921 + 0.600105i \(0.204874\pi\)
0.600105 + 0.799921i \(0.295126\pi\)
\(744\) 9.57788 0.351142
\(745\) −19.2461 + 0.190695i −0.705124 + 0.00698653i
\(746\) 2.94440 2.94440i 0.107802 0.107802i
\(747\) 3.45461 + 3.45461i 0.126397 + 0.126397i
\(748\) 5.67521i 0.207506i
\(749\) 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
\(753\) 11.7059i 0.426588i
\(754\) 8.43593 8.43593i 0.307219 0.307219i
\(755\) 6.11791 0.0606177i 0.222654 0.00220610i
\(756\) −0.397998 −0.0144750
\(757\) 17.1425 0.623054 0.311527 0.950237i \(-0.399160\pi\)
0.311527 + 0.950237i \(0.399160\pi\)
\(758\) −25.1637 −0.913989
\(759\) −4.55692 4.55692i −0.165406 0.165406i
\(760\) 4.17806 + 4.09608i 0.151554 + 0.148580i
\(761\) 35.6476i 1.29222i 0.763243 + 0.646112i \(0.223606\pi\)
−0.763243 + 0.646112i \(0.776394\pi\)
\(762\) 9.00960 0.326384
\(763\) 5.03431i 0.182254i
\(764\) 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 −0.898830 0.438297i \(-0.855582\pi\)
0.438297 + 0.898830i \(0.355582\pi\)
\(770\) 1.02617 1.04671i 0.0369807 0.0377208i
\(771\) 2.99965 + 2.99965i 0.108030 + 0.108030i
\(772\) 17.1049i 0.615620i
\(773\) 11.0549 11.0549i 0.397617 0.397617i −0.479775 0.877392i \(-0.659282\pi\)
0.877392 + 0.479775i \(0.159282\pi\)
\(774\) 1.27639i 0.0458788i
\(775\) 34.5273 + 33.1853i 1.24026 + 1.19205i
\(776\) 6.92746i 0.248681i
\(777\) 0.368321 + 2.39275i 0.0132135 + 0.0858393i
\(778\) 19.4231 19.4231i 0.696350 0.696350i
\(779\) 16.1350 16.1350i 0.578097 0.578097i