Properties

Label 690.2.e.a.551.8
Level $690$
Weight $2$
Character 690.551
Analytic conductor $5.510$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} - 198 x^{7} + 405 x^{6} - 108 x^{5} + 1215 x^{4} - 2916 x^{3} + 2187 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 551.8
Root \(-0.157845 - 1.72484i\) of defining polynomial
Character \(\chi\) \(=\) 690.551
Dual form 690.2.e.a.551.16

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(1.72484 - 0.157845i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.157845 - 1.72484i) q^{6} -4.77029i q^{7} +1.00000i q^{8} +(2.95017 - 0.544517i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(1.72484 - 0.157845i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.157845 - 1.72484i) q^{6} -4.77029i q^{7} +1.00000i q^{8} +(2.95017 - 0.544517i) q^{9} +1.00000i q^{10} -5.68772 q^{11} +(-1.72484 + 0.157845i) q^{12} -5.86303 q^{13} -4.77029 q^{14} +(-1.72484 + 0.157845i) q^{15} +1.00000 q^{16} +1.96521 q^{17} +(-0.544517 - 2.95017i) q^{18} -3.08903i q^{19} +1.00000 q^{20} +(-0.752968 - 8.22800i) q^{21} +5.68772i q^{22} +(1.22009 + 4.63804i) q^{23} +(0.157845 + 1.72484i) q^{24} +1.00000 q^{25} +5.86303i q^{26} +(5.00263 - 1.40488i) q^{27} +4.77029i q^{28} -4.66722i q^{29} +(0.157845 + 1.72484i) q^{30} +7.74501 q^{31} -1.00000i q^{32} +(-9.81042 + 0.897780i) q^{33} -1.96521i q^{34} +4.77029i q^{35} +(-2.95017 + 0.544517i) q^{36} -3.13987i q^{37} -3.08903 q^{38} +(-10.1128 + 0.925453i) q^{39} -1.00000i q^{40} -8.70541i q^{41} +(-8.22800 + 0.752968i) q^{42} +7.75780i q^{43} +5.68772 q^{44} +(-2.95017 + 0.544517i) q^{45} +(4.63804 - 1.22009i) q^{46} -8.55477i q^{47} +(1.72484 - 0.157845i) q^{48} -15.7556 q^{49} -1.00000i q^{50} +(3.38968 - 0.310200i) q^{51} +5.86303 q^{52} +2.37670 q^{53} +(-1.40488 - 5.00263i) q^{54} +5.68772 q^{55} +4.77029 q^{56} +(-0.487590 - 5.32810i) q^{57} -4.66722 q^{58} -2.47606i q^{59} +(1.72484 - 0.157845i) q^{60} +2.31175i q^{61} -7.74501i q^{62} +(-2.59750 - 14.0732i) q^{63} -1.00000 q^{64} +5.86303 q^{65} +(0.897780 + 9.81042i) q^{66} +9.67337i q^{67} -1.96521 q^{68} +(2.83655 + 7.80730i) q^{69} +4.77029 q^{70} -1.59802i q^{71} +(0.544517 + 2.95017i) q^{72} +3.25573 q^{73} -3.13987 q^{74} +(1.72484 - 0.157845i) q^{75} +3.08903i q^{76} +27.1320i q^{77} +(0.925453 + 10.1128i) q^{78} -6.19457i q^{79} -1.00000 q^{80} +(8.40700 - 3.21284i) q^{81} -8.70541 q^{82} +14.7833 q^{83} +(0.752968 + 8.22800i) q^{84} -1.96521 q^{85} +7.75780 q^{86} +(-0.736699 - 8.05022i) q^{87} -5.68772i q^{88} +7.42799 q^{89} +(0.544517 + 2.95017i) q^{90} +27.9683i q^{91} +(-1.22009 - 4.63804i) q^{92} +(13.3589 - 1.22251i) q^{93} -8.55477 q^{94} +3.08903i q^{95} +(-0.157845 - 1.72484i) q^{96} +6.65323i q^{97} +15.7556i q^{98} +(-16.7797 + 3.09706i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{4} - 16q^{5} + 2q^{6} + 2q^{9} + O(q^{10}) \) \( 16q - 16q^{4} - 16q^{5} + 2q^{6} + 2q^{9} - 12q^{11} - 12q^{14} + 16q^{16} + 8q^{18} + 16q^{20} - 4q^{21} + 4q^{23} - 2q^{24} + 16q^{25} + 24q^{27} - 2q^{30} + 4q^{31} - 28q^{33} - 2q^{36} - 16q^{38} - 8q^{39} + 12q^{44} - 2q^{45} - 4q^{46} - 4q^{49} - 2q^{51} - 8q^{53} - 26q^{54} + 12q^{55} + 12q^{56} + 28q^{57} - 8q^{58} - 16q^{64} + 10q^{66} + 30q^{69} + 12q^{70} - 8q^{72} - 16q^{73} - 24q^{74} - 12q^{78} - 16q^{80} + 22q^{81} - 16q^{82} - 40q^{83} + 4q^{84} - 40q^{86} + 20q^{87} + 80q^{89} - 8q^{90} - 4q^{92} - 4q^{93} - 24q^{94} + 2q^{96} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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
\(3\) 1.72484 0.157845i 0.995839 0.0911321i
\(4\) −1.00000 −0.500000
\(5\) −1.00000 −0.447214
\(6\) −0.157845 1.72484i −0.0644401 0.704164i
\(7\) 4.77029i 1.80300i −0.432780 0.901500i \(-0.642467\pi\)
0.432780 0.901500i \(-0.357533\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 2.95017 0.544517i 0.983390 0.181506i
\(10\) 1.00000i 0.316228i
\(11\) −5.68772 −1.71491 −0.857455 0.514558i \(-0.827956\pi\)
−0.857455 + 0.514558i \(0.827956\pi\)
\(12\) −1.72484 + 0.157845i −0.497919 + 0.0455660i
\(13\) −5.86303 −1.62611 −0.813056 0.582185i \(-0.802198\pi\)
−0.813056 + 0.582185i \(0.802198\pi\)
\(14\) −4.77029 −1.27491
\(15\) −1.72484 + 0.157845i −0.445353 + 0.0407555i
\(16\) 1.00000 0.250000
\(17\) 1.96521 0.476634 0.238317 0.971187i \(-0.423404\pi\)
0.238317 + 0.971187i \(0.423404\pi\)
\(18\) −0.544517 2.95017i −0.128344 0.695362i
\(19\) 3.08903i 0.708673i −0.935118 0.354337i \(-0.884707\pi\)
0.935118 0.354337i \(-0.115293\pi\)
\(20\) 1.00000 0.223607
\(21\) −0.752968 8.22800i −0.164311 1.79550i
\(22\) 5.68772i 1.21262i
\(23\) 1.22009 + 4.63804i 0.254405 + 0.967098i
\(24\) 0.157845 + 1.72484i 0.0322201 + 0.352082i
\(25\) 1.00000 0.200000
\(26\) 5.86303i 1.14984i
\(27\) 5.00263 1.40488i 0.962757 0.270369i
\(28\) 4.77029i 0.901500i
\(29\) 4.66722i 0.866681i −0.901230 0.433341i \(-0.857335\pi\)
0.901230 0.433341i \(-0.142665\pi\)
\(30\) 0.157845 + 1.72484i 0.0288185 + 0.314912i
\(31\) 7.74501 1.39105 0.695523 0.718504i \(-0.255173\pi\)
0.695523 + 0.718504i \(0.255173\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −9.81042 + 0.897780i −1.70777 + 0.156283i
\(34\) 1.96521i 0.337031i
\(35\) 4.77029i 0.806326i
\(36\) −2.95017 + 0.544517i −0.491695 + 0.0907529i
\(37\) 3.13987i 0.516192i −0.966119 0.258096i \(-0.916905\pi\)
0.966119 0.258096i \(-0.0830950\pi\)
\(38\) −3.08903 −0.501108
\(39\) −10.1128 + 0.925453i −1.61935 + 0.148191i
\(40\) 1.00000i 0.158114i
\(41\) 8.70541i 1.35956i −0.733417 0.679779i \(-0.762076\pi\)
0.733417 0.679779i \(-0.237924\pi\)
\(42\) −8.22800 + 0.752968i −1.26961 + 0.116185i
\(43\) 7.75780i 1.18305i 0.806285 + 0.591527i \(0.201475\pi\)
−0.806285 + 0.591527i \(0.798525\pi\)
\(44\) 5.68772 0.857455
\(45\) −2.95017 + 0.544517i −0.439785 + 0.0811718i
\(46\) 4.63804 1.22009i 0.683841 0.179892i
\(47\) 8.55477i 1.24784i −0.781488 0.623921i \(-0.785539\pi\)
0.781488 0.623921i \(-0.214461\pi\)
\(48\) 1.72484 0.157845i 0.248960 0.0227830i
\(49\) −15.7556 −2.25081
\(50\) 1.00000i 0.141421i
\(51\) 3.38968 0.310200i 0.474651 0.0434366i
\(52\) 5.86303 0.813056
\(53\) 2.37670 0.326465 0.163233 0.986588i \(-0.447808\pi\)
0.163233 + 0.986588i \(0.447808\pi\)
\(54\) −1.40488 5.00263i −0.191180 0.680772i
\(55\) 5.68772 0.766931
\(56\) 4.77029 0.637456
\(57\) −0.487590 5.32810i −0.0645829 0.705724i
\(58\) −4.66722 −0.612836
\(59\) 2.47606i 0.322355i −0.986925 0.161178i \(-0.948471\pi\)
0.986925 0.161178i \(-0.0515292\pi\)
\(60\) 1.72484 0.157845i 0.222676 0.0203778i
\(61\) 2.31175i 0.295989i 0.988988 + 0.147994i \(0.0472818\pi\)
−0.988988 + 0.147994i \(0.952718\pi\)
\(62\) 7.74501i 0.983618i
\(63\) −2.59750 14.0732i −0.327255 1.77305i
\(64\) −1.00000 −0.125000
\(65\) 5.86303 0.727220
\(66\) 0.897780 + 9.81042i 0.110509 + 1.20758i
\(67\) 9.67337i 1.18179i 0.806748 + 0.590895i \(0.201225\pi\)
−0.806748 + 0.590895i \(0.798775\pi\)
\(68\) −1.96521 −0.238317
\(69\) 2.83655 + 7.80730i 0.341480 + 0.939889i
\(70\) 4.77029 0.570158
\(71\) 1.59802i 0.189650i −0.995494 0.0948252i \(-0.969771\pi\)
0.995494 0.0948252i \(-0.0302292\pi\)
\(72\) 0.544517 + 2.95017i 0.0641720 + 0.347681i
\(73\) 3.25573 0.381054 0.190527 0.981682i \(-0.438980\pi\)
0.190527 + 0.981682i \(0.438980\pi\)
\(74\) −3.13987 −0.365003
\(75\) 1.72484 0.157845i 0.199168 0.0182264i
\(76\) 3.08903i 0.354337i
\(77\) 27.1320i 3.09198i
\(78\) 0.925453 + 10.1128i 0.104787 + 1.14505i
\(79\) 6.19457i 0.696944i −0.937319 0.348472i \(-0.886701\pi\)
0.937319 0.348472i \(-0.113299\pi\)
\(80\) −1.00000 −0.111803
\(81\) 8.40700 3.21284i 0.934111 0.356982i
\(82\) −8.70541 −0.961352
\(83\) 14.7833 1.62268 0.811339 0.584576i \(-0.198739\pi\)
0.811339 + 0.584576i \(0.198739\pi\)
\(84\) 0.752968 + 8.22800i 0.0821555 + 0.897748i
\(85\) −1.96521 −0.213157
\(86\) 7.75780 0.836546
\(87\) −0.736699 8.05022i −0.0789824 0.863075i
\(88\) 5.68772i 0.606312i
\(89\) 7.42799 0.787366 0.393683 0.919246i \(-0.371201\pi\)
0.393683 + 0.919246i \(0.371201\pi\)
\(90\) 0.544517 + 2.95017i 0.0573971 + 0.310975i
\(91\) 27.9683i 2.93188i
\(92\) −1.22009 4.63804i −0.127203 0.483549i
\(93\) 13.3589 1.22251i 1.38526 0.126769i
\(94\) −8.55477 −0.882357
\(95\) 3.08903i 0.316928i
\(96\) −0.157845 1.72484i −0.0161100 0.176041i
\(97\) 6.65323i 0.675533i 0.941230 + 0.337767i \(0.109671\pi\)
−0.941230 + 0.337767i \(0.890329\pi\)
\(98\) 15.7556i 1.59156i
\(99\) −16.7797 + 3.09706i −1.68643 + 0.311266i
\(100\) −1.00000 −0.100000
\(101\) 7.33256i 0.729617i −0.931083 0.364808i \(-0.881135\pi\)
0.931083 0.364808i \(-0.118865\pi\)
\(102\) −0.310200 3.38968i −0.0307143 0.335629i
\(103\) 9.24100i 0.910543i −0.890353 0.455271i \(-0.849542\pi\)
0.890353 0.455271i \(-0.150458\pi\)
\(104\) 5.86303i 0.574918i
\(105\) 0.752968 + 8.22800i 0.0734821 + 0.802970i
\(106\) 2.37670i 0.230846i
\(107\) 4.05749 0.392252 0.196126 0.980579i \(-0.437164\pi\)
0.196126 + 0.980579i \(0.437164\pi\)
\(108\) −5.00263 + 1.40488i −0.481378 + 0.135184i
\(109\) 12.2955i 1.17769i −0.808245 0.588846i \(-0.799582\pi\)
0.808245 0.588846i \(-0.200418\pi\)
\(110\) 5.68772i 0.542302i
\(111\) −0.495614 5.41579i −0.0470416 0.514044i
\(112\) 4.77029i 0.450750i
\(113\) −16.8426 −1.58442 −0.792208 0.610251i \(-0.791069\pi\)
−0.792208 + 0.610251i \(0.791069\pi\)
\(114\) −5.32810 + 0.487590i −0.499022 + 0.0456670i
\(115\) −1.22009 4.63804i −0.113774 0.432499i
\(116\) 4.66722i 0.433341i
\(117\) −17.2969 + 3.19252i −1.59910 + 0.295149i
\(118\) −2.47606 −0.227940
\(119\) 9.37463i 0.859370i
\(120\) −0.157845 1.72484i −0.0144092 0.157456i
\(121\) 21.3501 1.94092
\(122\) 2.31175 0.209296
\(123\) −1.37411 15.0155i −0.123899 1.35390i
\(124\) −7.74501 −0.695523
\(125\) −1.00000 −0.0894427
\(126\) −14.0732 + 2.59750i −1.25374 + 0.231404i
\(127\) −1.86527 −0.165516 −0.0827580 0.996570i \(-0.526373\pi\)
−0.0827580 + 0.996570i \(0.526373\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 1.22453 + 13.3810i 0.107814 + 1.17813i
\(130\) 5.86303i 0.514222i
\(131\) 16.7197i 1.46081i 0.683016 + 0.730403i \(0.260668\pi\)
−0.683016 + 0.730403i \(0.739332\pi\)
\(132\) 9.81042 0.897780i 0.853887 0.0781417i
\(133\) −14.7356 −1.27774
\(134\) 9.67337 0.835652
\(135\) −5.00263 + 1.40488i −0.430558 + 0.120913i
\(136\) 1.96521i 0.168516i
\(137\) −8.27644 −0.707104 −0.353552 0.935415i \(-0.615026\pi\)
−0.353552 + 0.935415i \(0.615026\pi\)
\(138\) 7.80730 2.83655i 0.664602 0.241463i
\(139\) 1.92339 0.163140 0.0815698 0.996668i \(-0.474007\pi\)
0.0815698 + 0.996668i \(0.474007\pi\)
\(140\) 4.77029i 0.403163i
\(141\) −1.35033 14.7556i −0.113718 1.24265i
\(142\) −1.59802 −0.134103
\(143\) 33.3473 2.78864
\(144\) 2.95017 0.544517i 0.245847 0.0453764i
\(145\) 4.66722i 0.387592i
\(146\) 3.25573i 0.269446i
\(147\) −27.1760 + 2.48695i −2.24144 + 0.205121i
\(148\) 3.13987i 0.258096i
\(149\) 15.1957 1.24488 0.622439 0.782669i \(-0.286142\pi\)
0.622439 + 0.782669i \(0.286142\pi\)
\(150\) −0.157845 1.72484i −0.0128880 0.140833i
\(151\) 8.73197 0.710598 0.355299 0.934753i \(-0.384379\pi\)
0.355299 + 0.934753i \(0.384379\pi\)
\(152\) 3.08903 0.250554
\(153\) 5.79771 1.07009i 0.468717 0.0865118i
\(154\) 27.1320 2.18636
\(155\) −7.74501 −0.622095
\(156\) 10.1128 0.925453i 0.809673 0.0740955i
\(157\) 1.95674i 0.156165i 0.996947 + 0.0780826i \(0.0248798\pi\)
−0.996947 + 0.0780826i \(0.975120\pi\)
\(158\) −6.19457 −0.492813
\(159\) 4.09944 0.375151i 0.325107 0.0297514i
\(160\) 1.00000i 0.0790569i
\(161\) 22.1248 5.82016i 1.74368 0.458693i
\(162\) −3.21284 8.40700i −0.252424 0.660516i
\(163\) −10.7116 −0.839001 −0.419500 0.907755i \(-0.637795\pi\)
−0.419500 + 0.907755i \(0.637795\pi\)
\(164\) 8.70541i 0.679779i
\(165\) 9.81042 0.897780i 0.763740 0.0698921i
\(166\) 14.7833i 1.14741i
\(167\) 0.164537i 0.0127323i 0.999980 + 0.00636614i \(0.00202642\pi\)
−0.999980 + 0.00636614i \(0.997974\pi\)
\(168\) 8.22800 0.752968i 0.634804 0.0580927i
\(169\) 21.3751 1.64424
\(170\) 1.96521i 0.150725i
\(171\) −1.68203 9.11318i −0.128628 0.696902i
\(172\) 7.75780i 0.591527i
\(173\) 4.40561i 0.334953i 0.985876 + 0.167476i \(0.0535618\pi\)
−0.985876 + 0.167476i \(0.946438\pi\)
\(174\) −8.05022 + 0.736699i −0.610286 + 0.0558490i
\(175\) 4.77029i 0.360600i
\(176\) −5.68772 −0.428728
\(177\) −0.390834 4.27081i −0.0293769 0.321014i
\(178\) 7.42799i 0.556752i
\(179\) 21.8808i 1.63545i 0.575612 + 0.817723i \(0.304764\pi\)
−0.575612 + 0.817723i \(0.695236\pi\)
\(180\) 2.95017 0.544517i 0.219893 0.0405859i
\(181\) 13.0668i 0.971248i −0.874168 0.485624i \(-0.838592\pi\)
0.874168 0.485624i \(-0.161408\pi\)
\(182\) 27.9683 2.07315
\(183\) 0.364899 + 3.98740i 0.0269741 + 0.294757i
\(184\) −4.63804 + 1.22009i −0.341921 + 0.0899459i
\(185\) 3.13987i 0.230848i
\(186\) −1.22251 13.3589i −0.0896391 0.979525i
\(187\) −11.1776 −0.817385
\(188\) 8.55477i 0.623921i
\(189\) −6.70167 23.8640i −0.487475 1.73585i
\(190\) 3.08903 0.224102
\(191\) 6.15903 0.445652 0.222826 0.974858i \(-0.428472\pi\)
0.222826 + 0.974858i \(0.428472\pi\)
\(192\) −1.72484 + 0.157845i −0.124480 + 0.0113915i
\(193\) 7.16580 0.515806 0.257903 0.966171i \(-0.416969\pi\)
0.257903 + 0.966171i \(0.416969\pi\)
\(194\) 6.65323 0.477674
\(195\) 10.1128 0.925453i 0.724194 0.0662730i
\(196\) 15.7556 1.12540
\(197\) 5.95934i 0.424585i 0.977206 + 0.212293i \(0.0680930\pi\)
−0.977206 + 0.212293i \(0.931907\pi\)
\(198\) 3.09706 + 16.7797i 0.220098 + 1.19248i
\(199\) 13.4932i 0.956509i 0.878221 + 0.478254i \(0.158730\pi\)
−0.878221 + 0.478254i \(0.841270\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 1.52690 + 16.6851i 0.107699 + 1.17687i
\(202\) −7.33256 −0.515917
\(203\) −22.2640 −1.56263
\(204\) −3.38968 + 0.310200i −0.237325 + 0.0217183i
\(205\) 8.70541i 0.608013i
\(206\) −9.24100 −0.643851
\(207\) 6.12495 + 13.0186i 0.425713 + 0.904858i
\(208\) −5.86303 −0.406528
\(209\) 17.5695i 1.21531i
\(210\) 8.22800 0.752968i 0.567786 0.0519597i
\(211\) −6.51146 −0.448268 −0.224134 0.974558i \(-0.571955\pi\)
−0.224134 + 0.974558i \(0.571955\pi\)
\(212\) −2.37670 −0.163233
\(213\) −0.252241 2.75634i −0.0172832 0.188861i
\(214\) 4.05749i 0.277364i
\(215\) 7.75780i 0.529078i
\(216\) 1.40488 + 5.00263i 0.0955898 + 0.340386i
\(217\) 36.9459i 2.50805i
\(218\) −12.2955 −0.832755
\(219\) 5.61562 0.513902i 0.379468 0.0347263i
\(220\) −5.68772 −0.383466
\(221\) −11.5221 −0.775060
\(222\) −5.41579 + 0.495614i −0.363484 + 0.0332634i
\(223\) −6.93854 −0.464639 −0.232319 0.972640i \(-0.574631\pi\)
−0.232319 + 0.972640i \(0.574631\pi\)
\(224\) −4.77029 −0.318728
\(225\) 2.95017 0.544517i 0.196678 0.0363011i
\(226\) 16.8426i 1.12035i
\(227\) 8.24167 0.547019 0.273509 0.961869i \(-0.411816\pi\)
0.273509 + 0.961869i \(0.411816\pi\)
\(228\) 0.487590 + 5.32810i 0.0322914 + 0.352862i
\(229\) 18.1323i 1.19821i 0.800669 + 0.599107i \(0.204478\pi\)
−0.800669 + 0.599107i \(0.795522\pi\)
\(230\) −4.63804 + 1.22009i −0.305823 + 0.0804501i
\(231\) 4.28267 + 46.7985i 0.281779 + 3.07912i
\(232\) 4.66722 0.306418
\(233\) 9.01790i 0.590782i −0.955376 0.295391i \(-0.904550\pi\)
0.955376 0.295391i \(-0.0954500\pi\)
\(234\) 3.19252 + 17.2969i 0.208702 + 1.13074i
\(235\) 8.55477i 0.558052i
\(236\) 2.47606i 0.161178i
\(237\) −0.977784 10.6847i −0.0635139 0.694043i
\(238\) −9.37463 −0.607667
\(239\) 26.2916i 1.70066i −0.526247 0.850331i \(-0.676401\pi\)
0.526247 0.850331i \(-0.323599\pi\)
\(240\) −1.72484 + 0.157845i −0.111338 + 0.0101889i
\(241\) 6.09867i 0.392850i −0.980519 0.196425i \(-0.937067\pi\)
0.980519 0.196425i \(-0.0629332\pi\)
\(242\) 21.3501i 1.37244i
\(243\) 13.9936 6.86865i 0.897692 0.440624i
\(244\) 2.31175i 0.147994i
\(245\) 15.7556 1.00659
\(246\) −15.0155 + 1.37411i −0.957352 + 0.0876100i
\(247\) 18.1111i 1.15238i
\(248\) 7.74501i 0.491809i
\(249\) 25.4989 2.33347i 1.61593 0.147878i
\(250\) 1.00000i 0.0632456i
\(251\) 13.8819 0.876215 0.438107 0.898923i \(-0.355649\pi\)
0.438107 + 0.898923i \(0.355649\pi\)
\(252\) 2.59750 + 14.0732i 0.163627 + 0.886526i
\(253\) −6.93950 26.3798i −0.436283 1.65849i
\(254\) 1.86527i 0.117038i
\(255\) −3.38968 + 0.310200i −0.212270 + 0.0194255i
\(256\) 1.00000 0.0625000
\(257\) 14.6251i 0.912286i −0.889907 0.456143i \(-0.849231\pi\)
0.889907 0.456143i \(-0.150769\pi\)
\(258\) 13.3810 1.22453i 0.833065 0.0762361i
\(259\) −14.9781 −0.930693
\(260\) −5.86303 −0.363610
\(261\) −2.54138 13.7691i −0.157308 0.852285i
\(262\) 16.7197 1.03295
\(263\) −13.7157 −0.845744 −0.422872 0.906189i \(-0.638978\pi\)
−0.422872 + 0.906189i \(0.638978\pi\)
\(264\) −0.897780 9.81042i −0.0552545 0.603790i
\(265\) −2.37670 −0.146000
\(266\) 14.7356i 0.903496i
\(267\) 12.8121 1.17247i 0.784089 0.0717543i
\(268\) 9.67337i 0.590895i
\(269\) 31.3415i 1.91092i −0.295116 0.955462i \(-0.595358\pi\)
0.295116 0.955462i \(-0.404642\pi\)
\(270\) 1.40488 + 5.00263i 0.0854981 + 0.304450i
\(271\) −4.59208 −0.278949 −0.139475 0.990226i \(-0.544541\pi\)
−0.139475 + 0.990226i \(0.544541\pi\)
\(272\) 1.96521 0.119158
\(273\) 4.41467 + 48.2410i 0.267188 + 2.91968i
\(274\) 8.27644i 0.499998i
\(275\) −5.68772 −0.342982
\(276\) −2.83655 7.80730i −0.170740 0.469944i
\(277\) −14.1389 −0.849524 −0.424762 0.905305i \(-0.639642\pi\)
−0.424762 + 0.905305i \(0.639642\pi\)
\(278\) 1.92339i 0.115357i
\(279\) 22.8491 4.21729i 1.36794 0.252483i
\(280\) −4.77029 −0.285079
\(281\) 6.36108 0.379470 0.189735 0.981835i \(-0.439237\pi\)
0.189735 + 0.981835i \(0.439237\pi\)
\(282\) −14.7556 + 1.35033i −0.878685 + 0.0804110i
\(283\) 26.0151i 1.54644i 0.634141 + 0.773218i \(0.281354\pi\)
−0.634141 + 0.773218i \(0.718646\pi\)
\(284\) 1.59802i 0.0948252i
\(285\) 0.487590 + 5.32810i 0.0288823 + 0.315609i
\(286\) 33.3473i 1.97186i
\(287\) −41.5273 −2.45128
\(288\) −0.544517 2.95017i −0.0320860 0.173840i
\(289\) −13.1379 −0.772820
\(290\) 4.66722 0.274069
\(291\) 1.05018 + 11.4758i 0.0615627 + 0.672722i
\(292\) −3.25573 −0.190527
\(293\) 8.44627 0.493437 0.246718 0.969087i \(-0.420648\pi\)
0.246718 + 0.969087i \(0.420648\pi\)
\(294\) 2.48695 + 27.1760i 0.145042 + 1.58494i
\(295\) 2.47606i 0.144162i
\(296\) 3.13987 0.182501
\(297\) −28.4535 + 7.99054i −1.65104 + 0.463658i
\(298\) 15.1957i 0.880261i
\(299\) −7.15340 27.1930i −0.413692 1.57261i
\(300\) −1.72484 + 0.157845i −0.0995839 + 0.00911321i
\(301\) 37.0070 2.13305
\(302\) 8.73197i 0.502469i
\(303\) −1.15741 12.6475i −0.0664915 0.726581i
\(304\) 3.08903i 0.177168i
\(305\) 2.31175i 0.132370i
\(306\) −1.07009 5.79771i −0.0611731 0.331433i
\(307\) −8.46953 −0.483381 −0.241691 0.970353i \(-0.577702\pi\)
−0.241691 + 0.970353i \(0.577702\pi\)
\(308\) 27.1320i 1.54599i
\(309\) −1.45865 15.9393i −0.0829796 0.906754i
\(310\) 7.74501i 0.439887i
\(311\) 16.1616i 0.916443i 0.888838 + 0.458221i \(0.151513\pi\)
−0.888838 + 0.458221i \(0.848487\pi\)
\(312\) −0.925453 10.1128i −0.0523934 0.572525i
\(313\) 6.86741i 0.388169i 0.980985 + 0.194084i \(0.0621735\pi\)
−0.980985 + 0.194084i \(0.937826\pi\)
\(314\) 1.95674 0.110425
\(315\) 2.59750 + 14.0732i 0.146353 + 0.792933i
\(316\) 6.19457i 0.348472i
\(317\) 18.7231i 1.05159i 0.850610 + 0.525797i \(0.176233\pi\)
−0.850610 + 0.525797i \(0.823767\pi\)
\(318\) −0.375151 4.09944i −0.0210374 0.229885i
\(319\) 26.5458i 1.48628i
\(320\) 1.00000 0.0559017
\(321\) 6.99854 0.640456i 0.390620 0.0357468i
\(322\) −5.82016 22.1248i −0.324345 1.23297i
\(323\) 6.07061i 0.337778i
\(324\) −8.40700 + 3.21284i −0.467056 + 0.178491i
\(325\) −5.86303 −0.325223
\(326\) 10.7116i 0.593263i
\(327\) −1.94078 21.2078i −0.107326 1.17279i
\(328\) 8.70541 0.480676
\(329\) −40.8087 −2.24986
\(330\) −0.897780 9.81042i −0.0494211 0.540046i
\(331\) 13.5890 0.746918 0.373459 0.927647i \(-0.378172\pi\)
0.373459 + 0.927647i \(0.378172\pi\)
\(332\) −14.7833 −0.811339
\(333\) −1.70971 9.26315i −0.0936917 0.507618i
\(334\) 0.164537 0.00900308
\(335\) 9.67337i 0.528513i
\(336\) −0.752968 8.22800i −0.0410778 0.448874i
\(337\) 4.53301i 0.246929i −0.992349 0.123464i \(-0.960599\pi\)
0.992349 0.123464i \(-0.0394005\pi\)
\(338\) 21.3751i 1.16265i
\(339\) −29.0508 + 2.65852i −1.57782 + 0.144391i
\(340\) 1.96521 0.106579
\(341\) −44.0514 −2.38552
\(342\) −9.11318 + 1.68203i −0.492784 + 0.0909539i
\(343\) 41.7669i 2.25520i
\(344\) −7.75780 −0.418273
\(345\) −2.83655 7.80730i −0.152715 0.420331i
\(346\) 4.40561 0.236847
\(347\) 7.21414i 0.387275i 0.981073 + 0.193638i \(0.0620286\pi\)
−0.981073 + 0.193638i \(0.937971\pi\)
\(348\) 0.736699 + 8.05022i 0.0394912 + 0.431537i
\(349\) −0.988122 −0.0528930 −0.0264465 0.999650i \(-0.508419\pi\)
−0.0264465 + 0.999650i \(0.508419\pi\)
\(350\) −4.77029 −0.254983
\(351\) −29.3306 + 8.23684i −1.56555 + 0.439650i
\(352\) 5.68772i 0.303156i
\(353\) 12.2940i 0.654342i 0.944965 + 0.327171i \(0.106095\pi\)
−0.944965 + 0.327171i \(0.893905\pi\)
\(354\) −4.27081 + 0.390834i −0.226991 + 0.0207726i
\(355\) 1.59802i 0.0848143i
\(356\) −7.42799 −0.393683
\(357\) −1.47974 16.1698i −0.0783162 0.855794i
\(358\) 21.8808 1.15644
\(359\) 0.189672 0.0100105 0.00500526 0.999987i \(-0.498407\pi\)
0.00500526 + 0.999987i \(0.498407\pi\)
\(360\) −0.544517 2.95017i −0.0286986 0.155488i
\(361\) 9.45787 0.497782
\(362\) −13.0668 −0.686776
\(363\) 36.8256 3.37002i 1.93284 0.176880i
\(364\) 27.9683i 1.46594i
\(365\) −3.25573 −0.170413
\(366\) 3.98740 0.364899i 0.208425 0.0190736i
\(367\) 20.2545i 1.05728i 0.848847 + 0.528638i \(0.177297\pi\)
−0.848847 + 0.528638i \(0.822703\pi\)
\(368\) 1.22009 + 4.63804i 0.0636014 + 0.241774i
\(369\) −4.74025 25.6824i −0.246767 1.33697i
\(370\) 3.13987 0.163234
\(371\) 11.3375i 0.588616i
\(372\) −13.3589 + 1.22251i −0.692629 + 0.0633844i
\(373\) 31.1346i 1.61209i −0.591854 0.806045i \(-0.701604\pi\)
0.591854 0.806045i \(-0.298396\pi\)
\(374\) 11.1776i 0.577978i
\(375\) −1.72484 + 0.157845i −0.0890705 + 0.00815110i
\(376\) 8.55477 0.441179
\(377\) 27.3641i 1.40932i
\(378\) −23.8640 + 6.70167i −1.22743 + 0.344697i
\(379\) 21.8934i 1.12459i 0.826937 + 0.562295i \(0.190081\pi\)
−0.826937 + 0.562295i \(0.809919\pi\)
\(380\) 3.08903i 0.158464i
\(381\) −3.21730 + 0.294424i −0.164827 + 0.0150838i
\(382\) 6.15903i 0.315123i
\(383\) −20.5229 −1.04867 −0.524334 0.851512i \(-0.675686\pi\)
−0.524334 + 0.851512i \(0.675686\pi\)
\(384\) 0.157845 + 1.72484i 0.00805501 + 0.0880205i
\(385\) 27.1320i 1.38278i
\(386\) 7.16580i 0.364730i
\(387\) 4.22426 + 22.8868i 0.214731 + 1.16340i
\(388\) 6.65323i 0.337767i
\(389\) 6.78101 0.343811 0.171905 0.985113i \(-0.445008\pi\)
0.171905 + 0.985113i \(0.445008\pi\)
\(390\) −0.925453 10.1128i −0.0468621 0.512082i
\(391\) 2.39773 + 9.11473i 0.121258 + 0.460952i
\(392\) 15.7556i 0.795780i
\(393\) 2.63913 + 28.8388i 0.133126 + 1.45473i
\(394\) 5.95934 0.300227
\(395\) 6.19457i 0.311683i
\(396\) 16.7797 3.09706i 0.843213 0.155633i
\(397\) −10.4669 −0.525320 −0.262660 0.964888i \(-0.584600\pi\)
−0.262660 + 0.964888i \(0.584600\pi\)
\(398\) 13.4932 0.676354
\(399\) −25.4166 + 2.32594i −1.27242 + 0.116443i
\(400\) 1.00000 0.0500000
\(401\) −6.92220 −0.345678 −0.172839 0.984950i \(-0.555294\pi\)
−0.172839 + 0.984950i \(0.555294\pi\)
\(402\) 16.6851 1.52690i 0.832175 0.0761547i
\(403\) −45.4093 −2.26200
\(404\) 7.33256i 0.364808i
\(405\) −8.40700 + 3.21284i −0.417747 + 0.159647i
\(406\) 22.2640i 1.10494i
\(407\) 17.8587i 0.885223i
\(408\) 0.310200 + 3.38968i 0.0153572 + 0.167814i
\(409\) −0.551195 −0.0272549 −0.0136274 0.999907i \(-0.504338\pi\)
−0.0136274 + 0.999907i \(0.504338\pi\)
\(410\) 8.70541 0.429930
\(411\) −14.2756 + 1.30640i −0.704162 + 0.0644399i
\(412\) 9.24100i 0.455271i
\(413\) −11.8115 −0.581206
\(414\) 13.0186 6.12495i 0.639831 0.301025i
\(415\) −14.7833 −0.725683
\(416\) 5.86303i 0.287459i
\(417\) 3.31754 0.303598i 0.162461 0.0148673i
\(418\) 17.5695 0.859355
\(419\) −29.7594 −1.45384 −0.726921 0.686721i \(-0.759049\pi\)
−0.726921 + 0.686721i \(0.759049\pi\)
\(420\) −0.752968 8.22800i −0.0367411 0.401485i
\(421\) 25.4818i 1.24191i −0.783847 0.620953i \(-0.786746\pi\)
0.783847 0.620953i \(-0.213254\pi\)
\(422\) 6.51146i 0.316973i
\(423\) −4.65822 25.2380i −0.226490 1.22711i
\(424\) 2.37670i 0.115423i
\(425\) 1.96521 0.0953268
\(426\) −2.75634 + 0.252241i −0.133545 + 0.0122211i
\(427\) 11.0277 0.533668
\(428\) −4.05749 −0.196126
\(429\) 57.5188 5.26371i 2.77703 0.254134i
\(430\) −7.75780 −0.374115
\(431\) −25.7344 −1.23958 −0.619791 0.784767i \(-0.712783\pi\)
−0.619791 + 0.784767i \(0.712783\pi\)
\(432\) 5.00263 1.40488i 0.240689 0.0675922i
\(433\) 39.5558i 1.90093i −0.310827 0.950466i \(-0.600606\pi\)
0.310827 0.950466i \(-0.399394\pi\)
\(434\) −36.9459 −1.77346
\(435\) 0.736699 + 8.05022i 0.0353220 + 0.385979i
\(436\) 12.2955i 0.588846i
\(437\) 14.3271 3.76889i 0.685356 0.180290i
\(438\) −0.513902 5.61562i −0.0245552 0.268325i
\(439\) 12.4645 0.594900 0.297450 0.954737i \(-0.403864\pi\)
0.297450 + 0.954737i \(0.403864\pi\)
\(440\) 5.68772i 0.271151i
\(441\) −46.4818 + 8.57922i −2.21342 + 0.408534i
\(442\) 11.5221i 0.548050i
\(443\) 12.1118i 0.575450i 0.957713 + 0.287725i \(0.0928989\pi\)
−0.957713 + 0.287725i \(0.907101\pi\)
\(444\) 0.495614 + 5.41579i 0.0235208 + 0.257022i
\(445\) −7.42799 −0.352121
\(446\) 6.93854i 0.328549i
\(447\) 26.2101 2.39857i 1.23970 0.113448i
\(448\) 4.77029i 0.225375i
\(449\) 15.0035i 0.708060i 0.935234 + 0.354030i \(0.115189\pi\)
−0.935234 + 0.354030i \(0.884811\pi\)
\(450\) −0.544517 2.95017i −0.0256688 0.139072i
\(451\) 49.5139i 2.33152i
\(452\) 16.8426 0.792208
\(453\) 15.0613 1.37830i 0.707641 0.0647583i
\(454\) 8.24167i 0.386801i
\(455\) 27.9683i 1.31118i
\(456\) 5.32810 0.487590i 0.249511 0.0228335i
\(457\) 1.63920i 0.0766785i −0.999265 0.0383392i \(-0.987793\pi\)
0.999265 0.0383392i \(-0.0122068\pi\)
\(458\) 18.1323 0.847266
\(459\) 9.83123 2.76088i 0.458883 0.128867i
\(460\) 1.22009 + 4.63804i 0.0568868 + 0.216250i
\(461\) 11.3693i 0.529520i 0.964314 + 0.264760i \(0.0852928\pi\)
−0.964314 + 0.264760i \(0.914707\pi\)
\(462\) 46.7985 4.28267i 2.17726 0.199248i
\(463\) 33.7826 1.57001 0.785006 0.619488i \(-0.212660\pi\)
0.785006 + 0.619488i \(0.212660\pi\)
\(464\) 4.66722i 0.216670i
\(465\) −13.3589 + 1.22251i −0.619506 + 0.0566928i
\(466\) −9.01790 −0.417746
\(467\) −16.9801 −0.785747 −0.392873 0.919593i \(-0.628519\pi\)
−0.392873 + 0.919593i \(0.628519\pi\)
\(468\) 17.2969 3.19252i 0.799551 0.147574i
\(469\) 46.1448 2.13077
\(470\) 8.55477 0.394602
\(471\) 0.308863 + 3.37508i 0.0142317 + 0.155515i
\(472\) 2.47606 0.113970
\(473\) 44.1242i 2.02883i
\(474\) −10.6847 + 0.977784i −0.490763 + 0.0449111i
\(475\) 3.08903i 0.141735i
\(476\) 9.37463i 0.429685i
\(477\) 7.01167 1.29415i 0.321042 0.0592553i
\(478\) −26.2916 −1.20255
\(479\) 21.1756 0.967540 0.483770 0.875195i \(-0.339267\pi\)
0.483770 + 0.875195i \(0.339267\pi\)
\(480\) 0.157845 + 1.72484i 0.00720462 + 0.0787280i
\(481\) 18.4092i 0.839386i
\(482\) −6.09867 −0.277787
\(483\) 37.2431 13.5312i 1.69462 0.615689i
\(484\) −21.3501 −0.970459
\(485\) 6.65323i 0.302108i
\(486\) −6.86865 13.9936i −0.311568 0.634764i
\(487\) 14.8247 0.671772 0.335886 0.941903i \(-0.390964\pi\)
0.335886 + 0.941903i \(0.390964\pi\)
\(488\) −2.31175 −0.104648
\(489\) −18.4759 + 1.69078i −0.835509 + 0.0764599i
\(490\) 15.7556i 0.711767i
\(491\) 39.8929i 1.80034i −0.435536 0.900171i \(-0.643441\pi\)
0.435536 0.900171i \(-0.356559\pi\)
\(492\) 1.37411 + 15.0155i 0.0619496 + 0.676950i
\(493\) 9.17208i 0.413090i
\(494\) 18.1111 0.814857
\(495\) 16.7797 3.09706i 0.754193 0.139202i
\(496\) 7.74501 0.347761
\(497\) −7.62303 −0.341940
\(498\) −2.33347 25.4989i −0.104566 1.14263i
\(499\) −19.4748 −0.871811 −0.435906 0.899992i \(-0.643572\pi\)
−0.435906 + 0.899992i \(0.643572\pi\)
\(500\) 1.00000 0.0447214
\(501\) 0.0259715 + 0.283801i 0.00116032 + 0.0126793i
\(502\) 13.8819i 0.619577i
\(503\) 30.4466 1.35755 0.678774 0.734348i \(-0.262512\pi\)
0.678774 + 0.734348i \(0.262512\pi\)
\(504\) 14.0732 2.59750i 0.626868 0.115702i
\(505\) 7.33256i 0.326294i
\(506\) −26.3798 + 6.93950i −1.17273 + 0.308498i
\(507\) 36.8688 3.37397i 1.63740 0.149843i
\(508\) 1.86527 0.0827580
\(509\) 3.89849i 0.172798i −0.996261 0.0863988i \(-0.972464\pi\)
0.996261 0.0863988i \(-0.0275359\pi\)
\(510\) 0.310200 + 3.38968i 0.0137359 + 0.150098i
\(511\) 15.5308i 0.687040i
\(512\) 1.00000i 0.0441942i
\(513\) −4.33972 15.4533i −0.191603 0.682280i
\(514\) −14.6251 −0.645083
\(515\) 9.24100i 0.407207i
\(516\) −1.22453 13.3810i −0.0539071 0.589066i
\(517\) 48.6571i 2.13994i
\(518\) 14.9781i 0.658099i
\(519\) 0.695406 + 7.59899i 0.0305249 + 0.333559i
\(520\) 5.86303i 0.257111i
\(521\) 13.7197 0.601072 0.300536 0.953770i \(-0.402834\pi\)
0.300536 + 0.953770i \(0.402834\pi\)
\(522\) −13.7691 + 2.54138i −0.602657 + 0.111233i
\(523\) 23.2611i 1.01714i −0.861022 0.508568i \(-0.830175\pi\)
0.861022 0.508568i \(-0.169825\pi\)
\(524\) 16.7197i 0.730403i
\(525\) −0.752968 8.22800i −0.0328622 0.359099i
\(526\) 13.7157i 0.598031i
\(527\) 15.2206 0.663020
\(528\) −9.81042 + 0.897780i −0.426944 + 0.0390708i
\(529\) −20.0228 + 11.3176i −0.870556 + 0.492070i
\(530\) 2.37670i 0.103237i
\(531\) −1.34826 7.30479i −0.0585093 0.317001i
\(532\) 14.7356 0.638868
\(533\) 51.0401i 2.21079i
\(534\) −1.17247 12.8121i −0.0507379 0.554435i
\(535\) −4.05749 −0.175421
\(536\) −9.67337 −0.417826
\(537\) 3.45378 + 37.7409i 0.149042 + 1.62864i
\(538\) −31.3415 −1.35123
\(539\) 89.6136 3.85993
\(540\) 5.00263 1.40488i 0.215279 0.0604563i
\(541\) −20.3714 −0.875837 −0.437918 0.899015i \(-0.644284\pi\)
−0.437918 + 0.899015i \(0.644284\pi\)
\(542\) 4.59208i 0.197247i
\(543\) −2.06254 22.5382i −0.0885119 0.967207i
\(544\) 1.96521i 0.0842578i
\(545\) 12.2955i 0.526680i
\(546\) 48.2410 4.41467i 2.06453 0.188931i
\(547\) 22.9836 0.982706 0.491353 0.870960i \(-0.336502\pi\)
0.491353 + 0.870960i \(0.336502\pi\)
\(548\) 8.27644 0.353552
\(549\) 1.25879 + 6.82005i 0.0537237 + 0.291072i
\(550\) 5.68772i 0.242525i
\(551\) −14.4172 −0.614194
\(552\) −7.80730 + 2.83655i −0.332301 + 0.120732i
\(553\) −29.5499 −1.25659
\(554\) 14.1389i 0.600704i
\(555\) 0.495614 + 5.41579i 0.0210377 + 0.229887i
\(556\) −1.92339 −0.0815698
\(557\) 28.2412 1.19662 0.598310 0.801265i \(-0.295839\pi\)
0.598310 + 0.801265i \(0.295839\pi\)
\(558\) −4.21729 22.8491i −0.178532 0.967280i
\(559\) 45.4843i 1.92378i
\(560\) 4.77029i 0.201581i
\(561\) −19.2796 + 1.76433i −0.813983 + 0.0744900i
\(562\) 6.36108i 0.268326i
\(563\) −26.5126 −1.11737 −0.558687 0.829379i \(-0.688695\pi\)
−0.558687 + 0.829379i \(0.688695\pi\)
\(564\) 1.35033 + 14.7556i 0.0568592 + 0.621324i
\(565\) 16.8426 0.708573
\(566\) 26.0151 1.09349
\(567\) −15.3262 40.1038i −0.643638 1.68420i
\(568\) 1.59802 0.0670516
\(569\) −27.8748 −1.16857 −0.584285 0.811548i \(-0.698625\pi\)
−0.584285 + 0.811548i \(0.698625\pi\)
\(570\) 5.32810 0.487590i 0.223170 0.0204229i
\(571\) 40.1603i 1.68066i −0.542077 0.840329i \(-0.682362\pi\)
0.542077 0.840329i \(-0.317638\pi\)
\(572\) −33.3473 −1.39432
\(573\) 10.6234 0.972175i 0.443797 0.0406132i
\(574\) 41.5273i 1.73332i
\(575\) 1.22009 + 4.63804i 0.0508811 + 0.193420i
\(576\) −2.95017 + 0.544517i −0.122924 + 0.0226882i
\(577\) 12.9838 0.540523 0.270261 0.962787i \(-0.412890\pi\)
0.270261 + 0.962787i \(0.412890\pi\)
\(578\) 13.1379i 0.546466i
\(579\) 12.3599 1.13109i 0.513660 0.0470065i
\(580\) 4.66722i 0.193796i
\(581\) 70.5206i 2.92569i
\(582\) 11.4758 1.05018i 0.475686 0.0435314i
\(583\) −13.5180 −0.559858
\(584\) 3.25573i 0.134723i
\(585\) 17.2969 3.19252i 0.715140 0.131995i
\(586\) 8.44627i 0.348912i
\(587\) 26.6529i 1.10008i 0.835137 + 0.550041i \(0.185388\pi\)
−0.835137 + 0.550041i \(0.814612\pi\)
\(588\) 27.1760 2.48695i 1.12072 0.102560i
\(589\) 23.9246i 0.985797i
\(590\) 2.47606 0.101938
\(591\) 0.940654 + 10.2789i 0.0386933 + 0.422818i
\(592\) 3.13987i 0.129048i
\(593\) 13.5281i 0.555534i −0.960648 0.277767i \(-0.910406\pi\)
0.960648 0.277767i \(-0.0895943\pi\)
\(594\) 7.99054 + 28.4535i 0.327856 + 1.16746i
\(595\) 9.37463i 0.384322i
\(596\) −15.1957 −0.622439
\(597\) 2.12984 + 23.2737i 0.0871686 + 0.952529i
\(598\) −27.1930 + 7.15340i −1.11200 + 0.292524i
\(599\) 8.13093i 0.332221i 0.986107 + 0.166110i \(0.0531208\pi\)
−0.986107 + 0.166110i \(0.946879\pi\)
\(600\) 0.157845 + 1.72484i 0.00644401 + 0.0704164i
\(601\) −1.00715 −0.0410827 −0.0205413 0.999789i \(-0.506539\pi\)
−0.0205413 + 0.999789i \(0.506539\pi\)
\(602\) 37.0070i 1.50829i
\(603\) 5.26732 + 28.5381i 0.214502 + 1.16216i
\(604\) −8.73197 −0.355299
\(605\) −21.3501 −0.868005
\(606\) −12.6475 + 1.15741i −0.513770 + 0.0470166i
\(607\) −32.1949 −1.30675 −0.653375 0.757034i \(-0.726648\pi\)
−0.653375 + 0.757034i \(0.726648\pi\)
\(608\) −3.08903 −0.125277
\(609\) −38.4019 + 3.51427i −1.55612 + 0.142405i
\(610\) −2.31175 −0.0935999
\(611\) 50.1569i 2.02913i
\(612\) −5.79771 + 1.07009i −0.234358 + 0.0432559i
\(613\) 24.0591i 0.971739i 0.874031 + 0.485869i \(0.161497\pi\)
−0.874031 + 0.485869i \(0.838503\pi\)
\(614\) 8.46953i 0.341802i
\(615\) 1.37411 + 15.0155i 0.0554094 + 0.605482i
\(616\) −27.1320 −1.09318
\(617\) 10.6333 0.428081 0.214041 0.976825i \(-0.431338\pi\)
0.214041 + 0.976825i \(0.431338\pi\)
\(618\) −15.9393 + 1.45865i −0.641172 + 0.0586755i
\(619\) 12.3292i 0.495553i −0.968817 0.247776i \(-0.920300\pi\)
0.968817 0.247776i \(-0.0796999\pi\)
\(620\) 7.74501 0.311047
\(621\) 12.6195 + 21.4883i 0.506404 + 0.862297i
\(622\) 16.1616 0.648023
\(623\) 35.4337i 1.41962i
\(624\) −10.1128 + 0.925453i −0.404837 + 0.0370478i
\(625\) 1.00000 0.0400000
\(626\) 6.86741 0.274477
\(627\) 2.77327 + 30.3047i 0.110754 + 1.21025i
\(628\) 1.95674i 0.0780826i
\(629\) 6.17051i 0.246034i
\(630\) 14.0732 2.59750i 0.560688 0.103487i
\(631\) 9.73351i 0.387485i −0.981052 0.193742i \(-0.937937\pi\)
0.981052 0.193742i \(-0.0620626\pi\)
\(632\) 6.19457 0.246407
\(633\) −11.2313 + 1.02780i −0.446402 + 0.0408516i
\(634\) 18.7231 0.743589
\(635\) 1.86527 0.0740210
\(636\) −4.09944 + 0.375151i −0.162553 + 0.0148757i
\(637\) 92.3758 3.66006
\(638\) 26.5458 1.05096
\(639\) −0.870151 4.71444i −0.0344226 0.186500i
\(640\) 1.00000i 0.0395285i
\(641\) 37.1576 1.46764 0.733819 0.679345i \(-0.237736\pi\)
0.733819 + 0.679345i \(0.237736\pi\)
\(642\) −0.640456 6.99854i −0.0252768 0.276210i
\(643\) 20.5307i 0.809652i 0.914394 + 0.404826i \(0.132668\pi\)
−0.914394 + 0.404826i \(0.867332\pi\)
\(644\) −22.1248 + 5.82016i −0.871838 + 0.229346i
\(645\) −1.22453 13.3810i −0.0482160 0.526876i
\(646\) −6.07061 −0.238845
\(647\) 10.6897i 0.420254i 0.977674 + 0.210127i \(0.0673878\pi\)
−0.977674 + 0.210127i \(0.932612\pi\)
\(648\) 3.21284 + 8.40700i 0.126212 + 0.330258i
\(649\) 14.0831i 0.552810i
\(650\) 5.86303i 0.229967i
\(651\) −5.83175 63.7260i −0.228564 2.49762i
\(652\) 10.7116 0.419500
\(653\) 5.99567i 0.234629i 0.993095 + 0.117314i \(0.0374285\pi\)
−0.993095 + 0.117314i \(0.962572\pi\)
\(654\) −21.2078 + 1.94078i −0.829289 + 0.0758907i
\(655\) 16.7197i 0.653292i
\(656\) 8.70541i 0.339889i
\(657\) 9.60495 1.77280i 0.374725 0.0691635i
\(658\) 40.8087i 1.59089i
\(659\) 5.16327 0.201132 0.100566 0.994930i \(-0.467935\pi\)
0.100566 + 0.994930i \(0.467935\pi\)
\(660\) −9.81042 + 0.897780i −0.381870 + 0.0349460i
\(661\) 0.430476i 0.0167436i −0.999965 0.00837179i \(-0.997335\pi\)
0.999965 0.00837179i \(-0.00266485\pi\)
\(662\) 13.5890i 0.528151i
\(663\) −19.8738 + 1.81871i −0.771835 + 0.0706329i
\(664\) 14.7833i 0.573703i
\(665\) 14.7356 0.571421
\(666\) −9.26315 + 1.70971i −0.358940 + 0.0662501i
\(667\) 21.6467 5.69441i 0.838165 0.220488i
\(668\) 0.164537i 0.00636614i
\(669\) −11.9679 + 1.09522i −0.462705 + 0.0423435i
\(670\) −9.67337 −0.373715
\(671\) 13.1486i 0.507594i
\(672\) −8.22800 + 0.752968i −0.317402 + 0.0290464i
\(673\) 43.9112 1.69265 0.846327 0.532664i \(-0.178809\pi\)
0.846327 + 0.532664i \(0.178809\pi\)
\(674\) −4.53301 −0.174605
\(675\) 5.00263 1.40488i 0.192551 0.0540738i
\(676\) −21.3751 −0.822121
\(677\) −27.5574 −1.05912 −0.529558 0.848274i \(-0.677642\pi\)
−0.529558 + 0.848274i \(0.677642\pi\)
\(678\) 2.65852 + 29.0508i 0.102100 + 1.11569i
\(679\) 31.7378 1.21799
\(680\) 1.96521i 0.0753624i
\(681\) 14.2156 1.30091i 0.544742 0.0498509i
\(682\) 44.0514i 1.68682i
\(683\) 26.2484i 1.00437i −0.864761 0.502184i \(-0.832530\pi\)
0.864761 0.502184i \(-0.167470\pi\)
\(684\) 1.68203 + 9.11318i 0.0643141 + 0.348451i
\(685\) 8.27644 0.316227
\(686\) 41.7669 1.59467
\(687\) 2.86210 + 31.2753i 0.109196 + 1.19323i
\(688\) 7.75780i 0.295764i
\(689\) −13.9347 −0.530869
\(690\) −7.80730 + 2.83655i −0.297219 + 0.107986i
\(691\) −38.6282 −1.46948 −0.734742 0.678347i \(-0.762697\pi\)
−0.734742 + 0.678347i \(0.762697\pi\)
\(692\) 4.40561i 0.167476i
\(693\) 14.7739 + 80.0441i 0.561212 + 3.04062i
\(694\) 7.21414 0.273845
\(695\) −1.92339 −0.0729583
\(696\) 8.05022 0.736699i 0.305143 0.0279245i
\(697\) 17.1080i 0.648011i
\(698\) 0.988122i 0.0374010i
\(699\) −1.42343 15.5545i −0.0538392 0.588324i
\(700\) 4.77029i 0.180300i
\(701\) 33.5349 1.26659 0.633297 0.773909i \(-0.281701\pi\)
0.633297 + 0.773909i \(0.281701\pi\)
\(702\) 8.23684 + 29.3306i 0.310880 + 1.10701i
\(703\) −9.69917 −0.365811
\(704\) 5.68772 0.214364
\(705\) 1.35033 + 14.7556i 0.0508564 + 0.555729i
\(706\) 12.2940 0.462690
\(707\) −34.9784 −1.31550
\(708\) 0.390834 + 4.27081i 0.0146884 + 0.160507i
\(709\) 38.3106i 1.43879i −0.694604 0.719393i \(-0.744420\pi\)
0.694604 0.719393i \(-0.255580\pi\)
\(710\) 1.59802 0.0599727
\(711\) −3.37305 18.2750i −0.126499 0.685367i
\(712\) 7.42799i 0.278376i
\(713\) 9.44958 + 35.9217i 0.353890 + 1.34528i
\(714\) −16.1698 + 1.47974i −0.605138 + 0.0553779i
\(715\) −33.3473 −1.24712
\(716\) 21.8808i 0.817723i
\(717\) −4.15001 45.3489i −0.154985 1.69359i
\(718\) 0.189672i 0.00707851i
\(719\) 17.1239i 0.638612i −0.947652 0.319306i \(-0.896550\pi\)
0.947652 0.319306i \(-0.103450\pi\)
\(720\) −2.95017 + 0.544517i −0.109946 + 0.0202930i
\(721\) −44.0822 −1.64171
\(722\) 9.45787i 0.351985i
\(723\) −0.962646 10.5192i −0.0358012 0.391215i
\(724\) 13.0668i 0.485624i
\(725\) 4.66722i 0.173336i
\(726\) −3.37002 36.8256i −0.125073 1.36673i
\(727\) 29.1589i 1.08144i 0.841201 + 0.540722i \(0.181849\pi\)
−0.841201 + 0.540722i \(0.818151\pi\)
\(728\) −27.9683 −1.03658
\(729\) 23.0526 14.0562i 0.853801 0.520599i
\(730\) 3.25573i 0.120500i
\(731\) 15.2457i 0.563884i
\(732\) −0.364899 3.98740i −0.0134870 0.147379i
\(733\) 19.6633i 0.726282i 0.931734 + 0.363141i \(0.118296\pi\)
−0.931734 + 0.363141i \(0.881704\pi\)
\(734\) 20.2545 0.747607
\(735\) 27.1760 2.48695i 1.00240 0.0917327i
\(736\) 4.63804 1.22009i 0.170960 0.0449729i
\(737\) 55.0194i 2.02667i
\(738\) −25.6824 + 4.74025i −0.945384 + 0.174491i
\(739\) 2.45920 0.0904632 0.0452316 0.998977i \(-0.485597\pi\)
0.0452316 + 0.998977i \(0.485597\pi\)
\(740\) 3.13987i 0.115424i
\(741\) 2.85876 + 31.2388i 0.105019 + 1.14759i
\(742\) −11.3375 −0.416214
\(743\) 30.2633 1.11025 0.555127 0.831765i \(-0.312670\pi\)
0.555127 + 0.831765i \(0.312670\pi\)
\(744\) 1.22251 + 13.3589i 0.0448196 + 0.489762i
\(745\) −15.1957 −0.556726
\(746\) −31.1346 −1.13992
\(747\) 43.6132 8.04976i 1.59572 0.294525i
\(748\) 11.1776 0.408692
\(749\) 19.3554i 0.707231i
\(750\) 0.157845 + 1.72484i 0.00576370 + 0.0629824i
\(751\) 20.4106i 0.744794i −0.928074 0.372397i \(-0.878536\pi\)
0.928074 0.372397i \(-0.121464\pi\)
\(752\) 8.55477i 0.311960i
\(753\) 23.9440 2.19119i 0.872569 0.0798513i
\(754\) 27.3641 0.996540
\(755\) −8.73197 −0.317789
\(756\) 6.70167 + 23.8640i 0.243737 + 0.867925i
\(757\) 14.2385i 0.517507i −0.965943 0.258754i \(-0.916688\pi\)
0.965943 0.258754i \(-0.0833118\pi\)
\(758\) 21.8934 0.795205
\(759\) −16.1335 44.4057i −0.585608 1.61183i
\(760\) −3.08903 −0.112051
\(761\) 26.2699i 0.952284i −0.879368 0.476142i \(-0.842035\pi\)
0.879368 0.476142i \(-0.157965\pi\)
\(762\) 0.294424 + 3.21730i 0.0106659 + 0.116551i
\(763\) −58.6529 −2.12338
\(764\) −6.15903 −0.222826
\(765\) −5.79771 + 1.07009i −0.209617 + 0.0386892i
\(766\) 20.5229i 0.741521i
\(767\) 14.5172i 0.524186i
\(768\) 1.72484 0.157845i 0.0622399 0.00569576i
\(769\) 16.3030i 0.587902i 0.955820 + 0.293951i \(0.0949703\pi\)
−0.955820 + 0.293951i \(0.905030\pi\)
\(770\) −27.1320 −0.977771
\(771\) −2.30850 25.2259i −0.0831385 0.908489i
\(772\) −7.16580 −0.257903
\(773\) −17.7749 −0.639320 −0.319660 0.947532i \(-0.603569\pi\)
−0.319660 + 0.947532i \(0.603569\pi\)
\(774\) 22.8868 4.22426i 0.822650 0.151838i
\(775\) 7.74501 0.278209
\(776\) −6.65323 −0.238837
\(777\) −25.8349 + 2.36422i −0.926820 + 0.0848160i
\(778\) 6.78101i 0.243111i
\(779\) −26.8913 −0.963482
\(780\) −10.1128 + 0.925453i −0.362097 + 0.0331365i
\(781\) 9.08910i 0.325234i
\(782\) 9.11473 2.39773i 0.325942 0.0857425i
\(783\) −6.55687 23.3484i −0.234324 0.834403i
\(784\) −15.7556 −0.562701