Properties

Label 230.2.b.b.139.3
Level $230$
Weight $2$
Character 230.139
Analytic conductor $1.837$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 230.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.83655924649\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.11574317056.3
Defining polynomial: \( x^{8} + 45x^{4} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 139.3
Root \(-0.386289 + 0.386289i\) of defining polynomial
Character \(\chi\) \(=\) 230.139
Dual form 230.2.b.b.139.6

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +1.44270i q^{3} -1.00000 q^{4} +(-0.386289 - 2.20245i) q^{5} +1.44270 q^{6} -3.25886i q^{7} +1.00000i q^{8} +0.918614 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +1.44270i q^{3} -1.00000 q^{4} +(-0.386289 - 2.20245i) q^{5} +1.44270 q^{6} -3.25886i q^{7} +1.00000i q^{8} +0.918614 q^{9} +(-2.20245 + 0.386289i) q^{10} +1.32988 q^{11} -1.44270i q^{12} -1.25886i q^{13} -3.25886 q^{14} +(3.17748 - 0.557299i) q^{15} +1.00000 q^{16} -4.62018i q^{17} -0.918614i q^{18} +3.37169 q^{19} +(0.386289 + 2.20245i) q^{20} +4.70156 q^{21} -1.32988i q^{22} +1.00000i q^{23} -1.44270 q^{24} +(-4.70156 + 1.70156i) q^{25} -1.25886 q^{26} +5.65339i q^{27} +3.25886i q^{28} -4.29207 q^{29} +(-0.557299 - 3.17748i) q^{30} +2.37346 q^{31} -1.00000i q^{32} +1.91861i q^{33} -4.62018 q^{34} +(-7.17748 + 1.25886i) q^{35} -0.918614 q^{36} +5.74514i q^{37} -3.37169i q^{38} +1.81616 q^{39} +(2.20245 - 0.386289i) q^{40} -5.13790 q^{41} -4.70156i q^{42} +10.4678i q^{43} -1.32988 q^{44} +(-0.354850 - 2.02320i) q^{45} +1.00000 q^{46} +6.06288i q^{47} +1.44270i q^{48} -3.62018 q^{49} +(1.70156 + 4.70156i) q^{50} +6.66553 q^{51} +1.25886i q^{52} -11.1275i q^{53} +5.65339 q^{54} +(-0.513716 - 2.92898i) q^{55} +3.25886 q^{56} +4.86433i q^{57} +4.29207i q^{58} +2.72263 q^{59} +(-3.17748 + 0.557299i) q^{60} +12.3653 q^{61} -2.37346i q^{62} -2.99364i q^{63} -1.00000 q^{64} +(-2.77258 + 0.486284i) q^{65} +1.91861 q^{66} +6.60981i q^{67} +4.62018i q^{68} -1.44270 q^{69} +(1.25886 + 7.17748i) q^{70} +0.265226 q^{71} +0.918614i q^{72} +5.26464i q^{73} +5.74514 q^{74} +(-2.45485 - 6.78295i) q^{75} -3.37169 q^{76} -4.33388i q^{77} -1.81616i q^{78} +15.3275 q^{79} +(-0.386289 - 2.20245i) q^{80} -5.40031 q^{81} +5.13790i q^{82} -2.02566i q^{83} -4.70156 q^{84} +(-10.1757 + 1.78472i) q^{85} +10.4678 q^{86} -6.19218i q^{87} +1.32988i q^{88} -16.1500 q^{89} +(-2.02320 + 0.354850i) q^{90} -4.10245 q^{91} -1.00000i q^{92} +3.42419i q^{93} +6.06288 q^{94} +(-1.30244 - 7.42597i) q^{95} +1.44270 q^{96} +8.62018i q^{97} +3.62018i q^{98} +1.22164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4} + 6 q^{6} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{4} + 6 q^{6} - 14 q^{9} + 10 q^{11} - 6 q^{14} - 16 q^{15} + 8 q^{16} + 2 q^{19} + 12 q^{21} - 6 q^{24} - 12 q^{25} + 10 q^{26} - 4 q^{29} - 10 q^{30} + 10 q^{31} + 10 q^{34} - 16 q^{35} + 14 q^{36} + 46 q^{41} - 10 q^{44} - 26 q^{45} + 8 q^{46} + 18 q^{49} - 12 q^{50} + 14 q^{51} - 12 q^{54} - 18 q^{55} + 6 q^{56} - 32 q^{59} + 16 q^{60} + 18 q^{61} - 8 q^{64} - 16 q^{65} - 6 q^{66} - 6 q^{69} - 10 q^{70} + 38 q^{71} + 12 q^{74} - 32 q^{75} - 2 q^{76} + 12 q^{79} + 32 q^{81} - 12 q^{84} - 24 q^{85} - 4 q^{86} - 60 q^{89} - 24 q^{90} - 26 q^{91} - 4 q^{94} + 18 q^{95} + 6 q^{96} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(-1\) \(1\)

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
\(3\) 1.44270i 0.832944i 0.909149 + 0.416472i \(0.136734\pi\)
−0.909149 + 0.416472i \(0.863266\pi\)
\(4\) −1.00000 −0.500000
\(5\) −0.386289 2.20245i −0.172754 0.984965i
\(6\) 1.44270 0.588980
\(7\) 3.25886i 1.23173i −0.787850 0.615867i \(-0.788806\pi\)
0.787850 0.615867i \(-0.211194\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.918614 0.306205
\(10\) −2.20245 + 0.386289i −0.696475 + 0.122155i
\(11\) 1.32988 0.400973 0.200486 0.979696i \(-0.435748\pi\)
0.200486 + 0.979696i \(0.435748\pi\)
\(12\) 1.44270i 0.416472i
\(13\) 1.25886i 0.349145i −0.984644 0.174573i \(-0.944146\pi\)
0.984644 0.174573i \(-0.0558544\pi\)
\(14\) −3.25886 −0.870967
\(15\) 3.17748 0.557299i 0.820421 0.143894i
\(16\) 1.00000 0.250000
\(17\) 4.62018i 1.12056i −0.828304 0.560279i \(-0.810694\pi\)
0.828304 0.560279i \(-0.189306\pi\)
\(18\) 0.918614i 0.216519i
\(19\) 3.37169 0.773518 0.386759 0.922181i \(-0.373595\pi\)
0.386759 + 0.922181i \(0.373595\pi\)
\(20\) 0.386289 + 2.20245i 0.0863768 + 0.492483i
\(21\) 4.70156 1.02596
\(22\) 1.32988i 0.283531i
\(23\) 1.00000i 0.208514i
\(24\) −1.44270 −0.294490
\(25\) −4.70156 + 1.70156i −0.940312 + 0.340312i
\(26\) −1.25886 −0.246883
\(27\) 5.65339i 1.08800i
\(28\) 3.25886i 0.615867i
\(29\) −4.29207 −0.797018 −0.398509 0.917164i \(-0.630472\pi\)
−0.398509 + 0.917164i \(0.630472\pi\)
\(30\) −0.557299 3.17748i −0.101748 0.580125i
\(31\) 2.37346 0.426286 0.213143 0.977021i \(-0.431630\pi\)
0.213143 + 0.977021i \(0.431630\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.91861i 0.333988i
\(34\) −4.62018 −0.792354
\(35\) −7.17748 + 1.25886i −1.21321 + 0.212786i
\(36\) −0.918614 −0.153102
\(37\) 5.74514i 0.944496i 0.881466 + 0.472248i \(0.156557\pi\)
−0.881466 + 0.472248i \(0.843443\pi\)
\(38\) 3.37169i 0.546960i
\(39\) 1.81616 0.290818
\(40\) 2.20245 0.386289i 0.348238 0.0610776i
\(41\) −5.13790 −0.802405 −0.401202 0.915989i \(-0.631408\pi\)
−0.401202 + 0.915989i \(0.631408\pi\)
\(42\) 4.70156i 0.725467i
\(43\) 10.4678i 1.59632i 0.602445 + 0.798160i \(0.294193\pi\)
−0.602445 + 0.798160i \(0.705807\pi\)
\(44\) −1.32988 −0.200486
\(45\) −0.354850 2.02320i −0.0528979 0.301601i
\(46\) 1.00000 0.147442
\(47\) 6.06288i 0.884362i 0.896926 + 0.442181i \(0.145795\pi\)
−0.896926 + 0.442181i \(0.854205\pi\)
\(48\) 1.44270i 0.208236i
\(49\) −3.62018 −0.517168
\(50\) 1.70156 + 4.70156i 0.240637 + 0.664901i
\(51\) 6.66553 0.933361
\(52\) 1.25886i 0.174573i
\(53\) 11.1275i 1.52848i −0.644930 0.764242i \(-0.723113\pi\)
0.644930 0.764242i \(-0.276887\pi\)
\(54\) 5.65339 0.769329
\(55\) −0.513716 2.92898i −0.0692695 0.394944i
\(56\) 3.25886 0.435484
\(57\) 4.86433i 0.644297i
\(58\) 4.29207i 0.563577i
\(59\) 2.72263 0.354456 0.177228 0.984170i \(-0.443287\pi\)
0.177228 + 0.984170i \(0.443287\pi\)
\(60\) −3.17748 + 0.557299i −0.410210 + 0.0719470i
\(61\) 12.3653 1.58322 0.791609 0.611029i \(-0.209244\pi\)
0.791609 + 0.611029i \(0.209244\pi\)
\(62\) 2.37346i 0.301430i
\(63\) 2.99364i 0.377163i
\(64\) −1.00000 −0.125000
\(65\) −2.77258 + 0.486284i −0.343896 + 0.0603161i
\(66\) 1.91861 0.236165
\(67\) 6.60981i 0.807516i 0.914866 + 0.403758i \(0.132296\pi\)
−0.914866 + 0.403758i \(0.867704\pi\)
\(68\) 4.62018i 0.560279i
\(69\) −1.44270 −0.173681
\(70\) 1.25886 + 7.17748i 0.150463 + 0.857872i
\(71\) 0.265226 0.0314765 0.0157383 0.999876i \(-0.494990\pi\)
0.0157383 + 0.999876i \(0.494990\pi\)
\(72\) 0.918614i 0.108260i
\(73\) 5.26464i 0.616180i 0.951357 + 0.308090i \(0.0996897\pi\)
−0.951357 + 0.308090i \(0.900310\pi\)
\(74\) 5.74514 0.667860
\(75\) −2.45485 6.78295i −0.283461 0.783227i
\(76\) −3.37169 −0.386759
\(77\) 4.33388i 0.493892i
\(78\) 1.81616i 0.205640i
\(79\) 15.3275 1.72448 0.862240 0.506500i \(-0.169061\pi\)
0.862240 + 0.506500i \(0.169061\pi\)
\(80\) −0.386289 2.20245i −0.0431884 0.246241i
\(81\) −5.40031 −0.600034
\(82\) 5.13790i 0.567386i
\(83\) 2.02566i 0.222345i −0.993801 0.111172i \(-0.964539\pi\)
0.993801 0.111172i \(-0.0354606\pi\)
\(84\) −4.70156 −0.512982
\(85\) −10.1757 + 1.78472i −1.10371 + 0.193580i
\(86\) 10.4678 1.12877
\(87\) 6.19218i 0.663871i
\(88\) 1.32988i 0.141765i
\(89\) −16.1500 −1.71190 −0.855951 0.517058i \(-0.827027\pi\)
−0.855951 + 0.517058i \(0.827027\pi\)
\(90\) −2.02320 + 0.354850i −0.213264 + 0.0374045i
\(91\) −4.10245 −0.430054
\(92\) 1.00000i 0.104257i
\(93\) 3.42419i 0.355072i
\(94\) 6.06288 0.625338
\(95\) −1.30244 7.42597i −0.133628 0.761888i
\(96\) 1.44270 0.147245
\(97\) 8.62018i 0.875246i 0.899158 + 0.437623i \(0.144180\pi\)
−0.899158 + 0.437623i \(0.855820\pi\)
\(98\) 3.62018i 0.365693i
\(99\) 1.22164 0.122780
\(100\) 4.70156 1.70156i 0.470156 0.170156i
\(101\) 14.4934 1.44215 0.721075 0.692857i \(-0.243648\pi\)
0.721075 + 0.692857i \(0.243648\pi\)
\(102\) 6.66553i 0.659986i
\(103\) 18.5410i 1.82690i −0.406950 0.913451i \(-0.633408\pi\)
0.406950 0.913451i \(-0.366592\pi\)
\(104\) 1.25886 0.123441
\(105\) −1.81616 10.3550i −0.177239 1.01054i
\(106\) −11.1275 −1.08080
\(107\) 4.48050i 0.433147i 0.976266 + 0.216573i \(0.0694880\pi\)
−0.976266 + 0.216573i \(0.930512\pi\)
\(108\) 5.65339i 0.543998i
\(109\) −17.1298 −1.64073 −0.820367 0.571838i \(-0.806231\pi\)
−0.820367 + 0.571838i \(0.806231\pi\)
\(110\) −2.92898 + 0.513716i −0.279268 + 0.0489809i
\(111\) −8.28853 −0.786712
\(112\) 3.25886i 0.307933i
\(113\) 9.77435i 0.919494i −0.888050 0.459747i \(-0.847940\pi\)
0.888050 0.459747i \(-0.152060\pi\)
\(114\) 4.86433 0.455587
\(115\) 2.20245 0.386289i 0.205379 0.0360216i
\(116\) 4.29207 0.398509
\(117\) 1.15641i 0.106910i
\(118\) 2.72263i 0.250638i
\(119\) −15.0565 −1.38023
\(120\) 0.557299 + 3.17748i 0.0508742 + 0.290062i
\(121\) −9.23143 −0.839221
\(122\) 12.3653i 1.11950i
\(123\) 7.41245i 0.668358i
\(124\) −2.37346 −0.213143
\(125\) 5.56376 + 9.69766i 0.497638 + 0.867385i
\(126\) −2.99364 −0.266694
\(127\) 1.02743i 0.0911699i −0.998960 0.0455849i \(-0.985485\pi\)
0.998960 0.0455849i \(-0.0145152\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −15.1019 −1.32965
\(130\) 0.486284 + 2.77258i 0.0426499 + 0.243171i
\(131\) 12.2885 1.07365 0.536827 0.843692i \(-0.319623\pi\)
0.536827 + 0.843692i \(0.319623\pi\)
\(132\) 1.91861i 0.166994i
\(133\) 10.9879i 0.952768i
\(134\) 6.60981 0.571000
\(135\) 12.4513 2.18384i 1.07164 0.187955i
\(136\) 4.62018 0.396177
\(137\) 8.82830i 0.754253i 0.926162 + 0.377126i \(0.123088\pi\)
−0.926162 + 0.377126i \(0.876912\pi\)
\(138\) 1.44270i 0.122811i
\(139\) 11.5532 0.979927 0.489963 0.871743i \(-0.337010\pi\)
0.489963 + 0.871743i \(0.337010\pi\)
\(140\) 7.17748 1.25886i 0.606607 0.106393i
\(141\) −8.74692 −0.736623
\(142\) 0.265226i 0.0222573i
\(143\) 1.67413i 0.139998i
\(144\) 0.918614 0.0765512
\(145\) 1.65798 + 9.45307i 0.137688 + 0.785035i
\(146\) 5.26464 0.435705
\(147\) 5.22283i 0.430772i
\(148\) 5.74514i 0.472248i
\(149\) 11.1333 0.912076 0.456038 0.889960i \(-0.349268\pi\)
0.456038 + 0.889960i \(0.349268\pi\)
\(150\) −6.78295 + 2.45485i −0.553825 + 0.200437i
\(151\) −3.23779 −0.263488 −0.131744 0.991284i \(-0.542058\pi\)
−0.131744 + 0.991284i \(0.542058\pi\)
\(152\) 3.37169i 0.273480i
\(153\) 4.24416i 0.343120i
\(154\) −4.33388 −0.349234
\(155\) −0.916840 5.22742i −0.0736424 0.419877i
\(156\) −1.81616 −0.145409
\(157\) 17.6452i 1.40824i 0.710079 + 0.704122i \(0.248659\pi\)
−0.710079 + 0.704122i \(0.751341\pi\)
\(158\) 15.3275i 1.21939i
\(159\) 16.0537 1.27314
\(160\) −2.20245 + 0.386289i −0.174119 + 0.0305388i
\(161\) 3.25886 0.256834
\(162\) 5.40031i 0.424288i
\(163\) 12.2107i 0.956415i 0.878247 + 0.478207i \(0.158713\pi\)
−0.878247 + 0.478207i \(0.841287\pi\)
\(164\) 5.13790 0.401202
\(165\) 4.22565 0.741139i 0.328966 0.0576976i
\(166\) −2.02566 −0.157222
\(167\) 2.06288i 0.159630i −0.996810 0.0798151i \(-0.974567\pi\)
0.996810 0.0798151i \(-0.0254330\pi\)
\(168\) 4.70156i 0.362733i
\(169\) 11.4153 0.878098
\(170\) 1.78472 + 10.1757i 0.136882 + 0.780441i
\(171\) 3.09728 0.236855
\(172\) 10.4678i 0.798160i
\(173\) 2.10245i 0.159847i −0.996801 0.0799233i \(-0.974532\pi\)
0.996801 0.0799233i \(-0.0254675\pi\)
\(174\) −6.19218 −0.469428
\(175\) 5.54515 + 15.3217i 0.419174 + 1.15821i
\(176\) 1.32988 0.100243
\(177\) 3.92794i 0.295242i
\(178\) 16.1500i 1.21050i
\(179\) −20.4421 −1.52792 −0.763958 0.645266i \(-0.776746\pi\)
−0.763958 + 0.645266i \(0.776746\pi\)
\(180\) 0.354850 + 2.02320i 0.0264490 + 0.150800i
\(181\) −7.12175 −0.529355 −0.264678 0.964337i \(-0.585266\pi\)
−0.264678 + 0.964337i \(0.585266\pi\)
\(182\) 4.10245i 0.304094i
\(183\) 17.8395i 1.31873i
\(184\) −1.00000 −0.0737210
\(185\) 12.6534 2.21928i 0.930296 0.163165i
\(186\) 3.42419 0.251074
\(187\) 6.14426i 0.449313i
\(188\) 6.06288i 0.442181i
\(189\) 18.4236 1.34012
\(190\) −7.42597 + 1.30244i −0.538736 + 0.0944892i
\(191\) −16.7191 −1.20975 −0.604875 0.796320i \(-0.706777\pi\)
−0.604875 + 0.796320i \(0.706777\pi\)
\(192\) 1.44270i 0.104118i
\(193\) 6.51772i 0.469156i −0.972097 0.234578i \(-0.924629\pi\)
0.972097 0.234578i \(-0.0753708\pi\)
\(194\) 8.62018 0.618893
\(195\) −0.701562 4.00000i −0.0502399 0.286446i
\(196\) 3.62018 0.258584
\(197\) 17.8184i 1.26951i −0.772714 0.634754i \(-0.781101\pi\)
0.772714 0.634754i \(-0.218899\pi\)
\(198\) 1.22164i 0.0868184i
\(199\) 3.77435 0.267557 0.133778 0.991011i \(-0.457289\pi\)
0.133778 + 0.991011i \(0.457289\pi\)
\(200\) −1.70156 4.70156i −0.120319 0.332451i
\(201\) −9.53597 −0.672616
\(202\) 14.4934i 1.01975i
\(203\) 13.9873i 0.981714i
\(204\) −6.66553 −0.466681
\(205\) 1.98471 + 11.3160i 0.138618 + 0.790341i
\(206\) −18.5410 −1.29181
\(207\) 0.918614i 0.0638481i
\(208\) 1.25886i 0.0872863i
\(209\) 4.48393 0.310160
\(210\) −10.3550 + 1.81616i −0.714559 + 0.125327i
\(211\) −23.9630 −1.64968 −0.824840 0.565366i \(-0.808735\pi\)
−0.824840 + 0.565366i \(0.808735\pi\)
\(212\) 11.1275i 0.764242i
\(213\) 0.382642i 0.0262182i
\(214\) 4.48050 0.306281
\(215\) 23.0547 4.04358i 1.57232 0.275770i
\(216\) −5.65339 −0.384664
\(217\) 7.73477i 0.525071i
\(218\) 17.1298i 1.16017i
\(219\) −7.59530 −0.513243
\(220\) 0.513716 + 2.92898i 0.0346347 + 0.197472i
\(221\) −5.81616 −0.391237
\(222\) 8.28853i 0.556289i
\(223\) 20.2094i 1.35332i 0.736296 + 0.676660i \(0.236573\pi\)
−0.736296 + 0.676660i \(0.763427\pi\)
\(224\) −3.25886 −0.217742
\(225\) −4.31892 + 1.56308i −0.287928 + 0.104205i
\(226\) −9.77435 −0.650180
\(227\) 1.60666i 0.106638i 0.998578 + 0.0533189i \(0.0169800\pi\)
−0.998578 + 0.0533189i \(0.983020\pi\)
\(228\) 4.86433i 0.322148i
\(229\) 18.9019 1.24907 0.624536 0.780996i \(-0.285288\pi\)
0.624536 + 0.780996i \(0.285288\pi\)
\(230\) −0.386289 2.20245i −0.0254711 0.145225i
\(231\) 6.25250 0.411384
\(232\) 4.29207i 0.281788i
\(233\) 19.0112i 1.24546i −0.782436 0.622731i \(-0.786023\pi\)
0.782436 0.622731i \(-0.213977\pi\)
\(234\) −1.15641 −0.0755967
\(235\) 13.3532 2.34202i 0.871065 0.152777i
\(236\) −2.72263 −0.177228
\(237\) 22.1130i 1.43640i
\(238\) 15.0565i 0.975969i
\(239\) −28.3387 −1.83308 −0.916538 0.399947i \(-0.869028\pi\)
−0.916538 + 0.399947i \(0.869028\pi\)
\(240\) 3.17748 0.557299i 0.205105 0.0359735i
\(241\) 6.35140 0.409130 0.204565 0.978853i \(-0.434422\pi\)
0.204565 + 0.978853i \(0.434422\pi\)
\(242\) 9.23143i 0.593419i
\(243\) 9.16914i 0.588200i
\(244\) −12.3653 −0.791609
\(245\) 1.39843 + 7.97325i 0.0893426 + 0.509392i
\(246\) −7.41245 −0.472601
\(247\) 4.24448i 0.270070i
\(248\) 2.37346i 0.150715i
\(249\) 2.92242 0.185201
\(250\) 9.69766 5.56376i 0.613334 0.351883i
\(251\) 19.7231 1.24491 0.622455 0.782655i \(-0.286135\pi\)
0.622455 + 0.782655i \(0.286135\pi\)
\(252\) 2.99364i 0.188581i
\(253\) 1.32988i 0.0836086i
\(254\) −1.02743 −0.0644668
\(255\) −2.57482 14.6805i −0.161241 0.919328i
\(256\) 1.00000 0.0625000
\(257\) 1.18102i 0.0736701i −0.999321 0.0368351i \(-0.988272\pi\)
0.999321 0.0368351i \(-0.0117276\pi\)
\(258\) 15.1019i 0.940201i
\(259\) 18.7226 1.16337
\(260\) 2.77258 0.486284i 0.171948 0.0301580i
\(261\) −3.94276 −0.244051
\(262\) 12.2885i 0.759188i
\(263\) 24.3189i 1.49957i 0.661682 + 0.749784i \(0.269843\pi\)
−0.661682 + 0.749784i \(0.730157\pi\)
\(264\) −1.91861 −0.118083
\(265\) −24.5078 + 4.29844i −1.50550 + 0.264051i
\(266\) −10.9879 −0.673709
\(267\) 23.2997i 1.42592i
\(268\) 6.60981i 0.403758i
\(269\) −7.91283 −0.482454 −0.241227 0.970469i \(-0.577550\pi\)
−0.241227 + 0.970469i \(0.577550\pi\)
\(270\) −2.18384 12.4513i −0.132904 0.757762i
\(271\) −18.2979 −1.11152 −0.555758 0.831344i \(-0.687572\pi\)
−0.555758 + 0.831344i \(0.687572\pi\)
\(272\) 4.62018i 0.280139i
\(273\) 5.91861i 0.358211i
\(274\) 8.82830 0.533337
\(275\) −6.25250 + 2.26287i −0.377040 + 0.136456i
\(276\) 1.44270 0.0868404
\(277\) 28.6550i 1.72171i −0.508847 0.860857i \(-0.669928\pi\)
0.508847 0.860857i \(-0.330072\pi\)
\(278\) 11.5532i 0.692913i
\(279\) 2.18029 0.130531
\(280\) −1.25886 7.17748i −0.0752313 0.428936i
\(281\) 2.74692 0.163867 0.0819337 0.996638i \(-0.473890\pi\)
0.0819337 + 0.996638i \(0.473890\pi\)
\(282\) 8.74692i 0.520871i
\(283\) 5.45307i 0.324151i −0.986778 0.162076i \(-0.948181\pi\)
0.986778 0.162076i \(-0.0518189\pi\)
\(284\) −0.265226 −0.0157383
\(285\) 10.7134 1.87904i 0.634610 0.111305i
\(286\) −1.67413 −0.0989934
\(287\) 16.7437i 0.988349i
\(288\) 0.918614i 0.0541298i
\(289\) −4.34603 −0.255649
\(290\) 9.45307 1.65798i 0.555103 0.0973599i
\(291\) −12.4363 −0.729031
\(292\) 5.26464i 0.308090i
\(293\) 18.3806i 1.07381i 0.843644 + 0.536903i \(0.180406\pi\)
−0.843644 + 0.536903i \(0.819594\pi\)
\(294\) −5.22283 −0.304602
\(295\) −1.05172 5.99645i −0.0612336 0.349127i
\(296\) −5.74514 −0.333930
\(297\) 7.51831i 0.436256i
\(298\) 11.1333i 0.644935i
\(299\) 1.25886 0.0728018
\(300\) 2.45485 + 6.78295i 0.141731 + 0.391614i
\(301\) 34.1130 1.96624
\(302\) 3.23779i 0.186314i
\(303\) 20.9097i 1.20123i
\(304\) 3.37169 0.193379
\(305\) −4.77658 27.2340i −0.273506 1.55941i
\(306\) −4.24416 −0.242622
\(307\) 15.9234i 0.908797i 0.890799 + 0.454398i \(0.150146\pi\)
−0.890799 + 0.454398i \(0.849854\pi\)
\(308\) 4.33388i 0.246946i
\(309\) 26.7492 1.52171
\(310\) −5.22742 + 0.916840i −0.296898 + 0.0520730i
\(311\) −11.3518 −0.643702 −0.321851 0.946790i \(-0.604305\pi\)
−0.321851 + 0.946790i \(0.604305\pi\)
\(312\) 1.81616i 0.102820i
\(313\) 28.7913i 1.62738i −0.581299 0.813690i \(-0.697455\pi\)
0.581299 0.813690i \(-0.302545\pi\)
\(314\) 17.6452 0.995779
\(315\) −6.59333 + 1.15641i −0.371492 + 0.0651562i
\(316\) −15.3275 −0.862240
\(317\) 31.2299i 1.75404i 0.480451 + 0.877022i \(0.340473\pi\)
−0.480451 + 0.877022i \(0.659527\pi\)
\(318\) 16.0537i 0.900246i
\(319\) −5.70793 −0.319583
\(320\) 0.386289 + 2.20245i 0.0215942 + 0.123121i
\(321\) −6.46403 −0.360787
\(322\) 3.25886i 0.181609i
\(323\) 15.5778i 0.866771i
\(324\) 5.40031 0.300017
\(325\) 2.14203 + 5.91861i 0.118818 + 0.328306i
\(326\) 12.2107 0.676287
\(327\) 24.7131i 1.36664i
\(328\) 5.13790i 0.283693i
\(329\) 19.7581 1.08930
\(330\) −0.741139 4.22565i −0.0407984 0.232614i
\(331\) 17.6917 0.972421 0.486211 0.873842i \(-0.338379\pi\)
0.486211 + 0.873842i \(0.338379\pi\)
\(332\) 2.02566i 0.111172i
\(333\) 5.27757i 0.289209i
\(334\) −2.06288 −0.112876
\(335\) 14.5578 2.55329i 0.795375 0.139501i
\(336\) 4.70156 0.256491
\(337\) 1.33801i 0.0728863i 0.999336 + 0.0364431i \(0.0116028\pi\)
−0.999336 + 0.0364431i \(0.988397\pi\)
\(338\) 11.4153i 0.620909i
\(339\) 14.1015 0.765886
\(340\) 10.1757 1.78472i 0.551855 0.0967901i
\(341\) 3.15641 0.170929
\(342\) 3.09728i 0.167482i
\(343\) 11.0144i 0.594720i
\(344\) −10.4678 −0.564385
\(345\) 0.557299 + 3.17748i 0.0300040 + 0.171070i
\(346\) −2.10245 −0.113029
\(347\) 5.36355i 0.287930i 0.989583 + 0.143965i \(0.0459853\pi\)
−0.989583 + 0.143965i \(0.954015\pi\)
\(348\) 6.19218i 0.331936i
\(349\) 18.4306 0.986565 0.493283 0.869869i \(-0.335797\pi\)
0.493283 + 0.869869i \(0.335797\pi\)
\(350\) 15.3217 5.54515i 0.818981 0.296401i
\(351\) 7.11683 0.379868
\(352\) 1.32988i 0.0708826i
\(353\) 6.76477i 0.360052i 0.983662 + 0.180026i \(0.0576182\pi\)
−0.983662 + 0.180026i \(0.942382\pi\)
\(354\) 3.92794 0.208768
\(355\) −0.102454 0.584146i −0.00543768 0.0310033i
\(356\) 16.1500 0.855951
\(357\) 21.7220i 1.14965i
\(358\) 20.4421i 1.08040i
\(359\) −27.5324 −1.45311 −0.726553 0.687111i \(-0.758879\pi\)
−0.726553 + 0.687111i \(0.758879\pi\)
\(360\) 2.02320 0.354850i 0.106632 0.0187022i
\(361\) −7.63174 −0.401670
\(362\) 7.12175i 0.374311i
\(363\) 13.3182i 0.699024i
\(364\) 4.10245 0.215027
\(365\) 11.5951 2.03367i 0.606915 0.106447i
\(366\) 17.8395 0.932484
\(367\) 24.0744i 1.25668i −0.777941 0.628338i \(-0.783736\pi\)
0.777941 0.628338i \(-0.216264\pi\)
\(368\) 1.00000i 0.0521286i
\(369\) −4.71975 −0.245700
\(370\) −2.21928 12.6534i −0.115375 0.657818i
\(371\) −36.2631 −1.88268
\(372\) 3.42419i 0.177536i
\(373\) 1.31459i 0.0680668i −0.999421 0.0340334i \(-0.989165\pi\)
0.999421 0.0340334i \(-0.0108353\pi\)
\(374\) −6.14426 −0.317712
\(375\) −13.9908 + 8.02685i −0.722483 + 0.414505i
\(376\) −6.06288 −0.312669
\(377\) 5.40312i 0.278275i
\(378\) 18.4236i 0.947608i
\(379\) −8.38961 −0.430945 −0.215473 0.976510i \(-0.569129\pi\)
−0.215473 + 0.976510i \(0.569129\pi\)
\(380\) 1.30244 + 7.42597i 0.0668140 + 0.380944i
\(381\) 1.48228 0.0759394
\(382\) 16.7191i 0.855423i
\(383\) 24.1258i 1.23277i −0.787446 0.616384i \(-0.788597\pi\)
0.787446 0.616384i \(-0.211403\pi\)
\(384\) −1.44270 −0.0736225
\(385\) −9.54515 + 1.67413i −0.486466 + 0.0853216i
\(386\) −6.51772 −0.331743
\(387\) 9.61584i 0.488801i
\(388\) 8.62018i 0.437623i
\(389\) −12.5702 −0.637336 −0.318668 0.947866i \(-0.603235\pi\)
−0.318668 + 0.947866i \(0.603235\pi\)
\(390\) −4.00000 + 0.701562i −0.202548 + 0.0355250i
\(391\) 4.62018 0.233652
\(392\) 3.62018i 0.182847i
\(393\) 17.7287i 0.894293i
\(394\) −17.8184 −0.897678
\(395\) −5.92085 33.7581i −0.297910 1.69855i
\(396\) −1.22164 −0.0613899
\(397\) 28.5318i 1.43197i −0.698115 0.715986i \(-0.745977\pi\)
0.698115 0.715986i \(-0.254023\pi\)
\(398\) 3.77435i 0.189191i
\(399\) 15.8522 0.793602
\(400\) −4.70156 + 1.70156i −0.235078 + 0.0850781i
\(401\) −19.7130 −0.984422 −0.492211 0.870476i \(-0.663811\pi\)
−0.492211 + 0.870476i \(0.663811\pi\)
\(402\) 9.53597i 0.475611i
\(403\) 2.98786i 0.148836i
\(404\) −14.4934 −0.721075
\(405\) 2.08608 + 11.8939i 0.103658 + 0.591013i
\(406\) 13.9873 0.694177
\(407\) 7.64033i 0.378717i
\(408\) 6.66553i 0.329993i
\(409\) −20.3400 −1.00575 −0.502874 0.864360i \(-0.667724\pi\)
−0.502874 + 0.864360i \(0.667724\pi\)
\(410\) 11.3160 1.98471i 0.558855 0.0980179i
\(411\) −12.7366 −0.628250
\(412\) 18.5410i 0.913451i
\(413\) 8.87267i 0.436596i
\(414\) 0.918614 0.0451474
\(415\) −4.46141 + 0.782489i −0.219002 + 0.0384109i
\(416\) −1.25886 −0.0617207
\(417\) 16.6678i 0.816224i
\(418\) 4.48393i 0.219316i
\(419\) −9.91146 −0.484207 −0.242103 0.970250i \(-0.577837\pi\)
−0.242103 + 0.970250i \(0.577837\pi\)
\(420\) 1.81616 + 10.3550i 0.0886195 + 0.505270i
\(421\) −28.7927 −1.40327 −0.701634 0.712537i \(-0.747546\pi\)
−0.701634 + 0.712537i \(0.747546\pi\)
\(422\) 23.9630i 1.16650i
\(423\) 5.56944i 0.270796i
\(424\) 11.1275 0.540401
\(425\) 7.86152 + 21.7220i 0.381340 + 1.05367i
\(426\) 0.382642 0.0185390
\(427\) 40.2969i 1.95010i
\(428\) 4.48050i 0.216573i
\(429\) 2.41527 0.116610
\(430\) −4.04358 23.0547i −0.194999 1.11180i
\(431\) 36.6821 1.76691 0.883456 0.468513i \(-0.155210\pi\)
0.883456 + 0.468513i \(0.155210\pi\)
\(432\) 5.65339i 0.271999i
\(433\) 29.6894i 1.42678i −0.700766 0.713391i \(-0.747158\pi\)
0.700766 0.713391i \(-0.252842\pi\)
\(434\) −7.73477 −0.371281
\(435\) −13.6380 + 2.39197i −0.653890 + 0.114686i
\(436\) 17.1298 0.820367
\(437\) 3.37169i 0.161290i
\(438\) 7.59530i 0.362918i
\(439\) −34.5378 −1.64840 −0.824200 0.566299i \(-0.808375\pi\)
−0.824200 + 0.566299i \(0.808375\pi\)
\(440\) 2.92898 0.513716i 0.139634 0.0244905i
\(441\) −3.32554 −0.158359
\(442\) 5.81616i 0.276647i
\(443\) 36.6735i 1.74241i 0.490917 + 0.871206i \(0.336662\pi\)
−0.490917 + 0.871206i \(0.663338\pi\)
\(444\) 8.28853 0.393356
\(445\) 6.23858 + 35.5696i 0.295737 + 1.68616i
\(446\) 20.2094 0.956942
\(447\) 16.0620i 0.759708i
\(448\) 3.25886i 0.153967i
\(449\) 13.2138 0.623599 0.311800 0.950148i \(-0.399068\pi\)
0.311800 + 0.950148i \(0.399068\pi\)
\(450\) 1.56308 + 4.31892i 0.0736842 + 0.203596i
\(451\) −6.83277 −0.321743
\(452\) 9.77435i 0.459747i
\(453\) 4.67117i 0.219471i
\(454\) 1.60666 0.0754044
\(455\) 1.58473 + 9.03544i 0.0742934 + 0.423588i
\(456\) −4.86433 −0.227793
\(457\) 12.2292i 0.572058i 0.958221 + 0.286029i \(0.0923353\pi\)
−0.958221 + 0.286029i \(0.907665\pi\)
\(458\) 18.9019i 0.883227i
\(459\) 26.1196 1.21916
\(460\) −2.20245 + 0.386289i −0.102690 + 0.0180108i
\(461\) 24.0872 1.12185 0.560926 0.827866i \(-0.310445\pi\)
0.560926 + 0.827866i \(0.310445\pi\)
\(462\) 6.25250i 0.290892i
\(463\) 15.9173i 0.739740i 0.929084 + 0.369870i \(0.120598\pi\)
−0.929084 + 0.369870i \(0.879402\pi\)
\(464\) −4.29207 −0.199254
\(465\) 7.54161 1.32273i 0.349734 0.0613400i
\(466\) −19.0112 −0.880675
\(467\) 9.70011i 0.448868i −0.974489 0.224434i \(-0.927947\pi\)
0.974489 0.224434i \(-0.0720533\pi\)
\(468\) 1.15641i 0.0534550i
\(469\) 21.5404 0.994645
\(470\) −2.34202 13.3532i −0.108029 0.615936i
\(471\) −25.4568 −1.17299
\(472\) 2.72263i 0.125319i
\(473\) 13.9208i 0.640081i
\(474\) 22.1130 1.01568
\(475\) −15.8522 + 5.73713i −0.727348 + 0.263238i
\(476\) 15.0565 0.690114
\(477\) 10.2219i 0.468029i
\(478\) 28.3387i 1.29618i
\(479\) −14.1385 −0.646004 −0.323002 0.946398i \(-0.604692\pi\)
−0.323002 + 0.946398i \(0.604692\pi\)
\(480\) −0.557299 3.17748i −0.0254371 0.145031i
\(481\) 7.23234 0.329766
\(482\) 6.35140i 0.289298i
\(483\) 4.70156i 0.213928i
\(484\) 9.23143 0.419610
\(485\) 18.9855 3.32988i 0.862087 0.151202i
\(486\) 9.16914 0.415920
\(487\) 3.75006i 0.169932i −0.996384 0.0849658i \(-0.972922\pi\)
0.996384 0.0849658i \(-0.0270781\pi\)
\(488\) 12.3653i 0.559752i
\(489\) −17.6164 −0.796640
\(490\) 7.97325 1.39843i 0.360195 0.0631748i
\(491\) −3.19020 −0.143972 −0.0719860 0.997406i \(-0.522934\pi\)
−0.0719860 + 0.997406i \(0.522934\pi\)
\(492\) 7.41245i 0.334179i
\(493\) 19.8301i 0.893104i
\(494\) −4.24448 −0.190968
\(495\) −0.471907 2.69061i −0.0212106 0.120934i
\(496\) 2.37346 0.106571
\(497\) 0.864334i 0.0387707i
\(498\) 2.92242i 0.130957i
\(499\) −12.9355 −0.579075 −0.289537 0.957167i \(-0.593501\pi\)
−0.289537 + 0.957167i \(0.593501\pi\)
\(500\) −5.56376 9.69766i −0.248819 0.433692i
\(501\) 2.97611 0.132963
\(502\) 19.7231i 0.880285i
\(503\) 15.8845i 0.708254i 0.935197 + 0.354127i \(0.115222\pi\)
−0.935197 + 0.354127i \(0.884778\pi\)
\(504\) 2.99364 0.133347
\(505\) −5.59865 31.9210i −0.249137 1.42047i
\(506\) 1.32988 0.0591202
\(507\) 16.4688i 0.731406i
\(508\) 1.02743i 0.0455849i
\(509\) −22.6470 −1.00381 −0.501906 0.864922i \(-0.667368\pi\)
−0.501906 + 0.864922i \(0.667368\pi\)
\(510\) −14.6805 + 2.57482i −0.650063 + 0.114015i
\(511\) 17.1567 0.758969
\(512\) 1.00000i 0.0441942i
\(513\) 19.0614i 0.841583i
\(514\) −1.18102 −0.0520927
\(515\) −40.8357 + 7.16219i −1.79943 + 0.315604i
\(516\) 15.1019 0.664823
\(517\) 8.06288i 0.354605i
\(518\) 18.7226i 0.822625i
\(519\) 3.03321 0.133143
\(520\) −0.486284 2.77258i −0.0213250 0.121586i
\(521\) 22.7728 0.997693 0.498847 0.866690i \(-0.333757\pi\)
0.498847 + 0.866690i \(0.333757\pi\)
\(522\) 3.94276i 0.172570i
\(523\) 16.1920i 0.708026i 0.935241 + 0.354013i \(0.115183\pi\)
−0.935241 + 0.354013i \(0.884817\pi\)
\(524\) −12.2885 −0.536827
\(525\) −22.1047 + 8.00000i −0.964728 + 0.349149i
\(526\) 24.3189 1.06036
\(527\) 10.9658i 0.477678i
\(528\) 1.91861i 0.0834970i
\(529\) −1.00000 −0.0434783
\(530\) 4.29844 + 24.5078i 0.186712 + 1.06455i
\(531\) 2.50105 0.108536
\(532\) 10.9879i 0.476384i
\(533\) 6.46790i 0.280156i
\(534\) −23.2997 −1.00828
\(535\) 9.86808 1.73077i 0.426634 0.0748276i
\(536\) −6.60981 −0.285500
\(537\) 29.4919i 1.27267i
\(538\) 7.91283i 0.341147i
\(539\) −4.81439 −0.207370
\(540\) −12.4513 + 2.18384i −0.535819 + 0.0939775i
\(541\) 14.4350 0.620610 0.310305 0.950637i \(-0.399569\pi\)
0.310305 + 0.950637i \(0.399569\pi\)
\(542\) 18.2979i 0.785960i
\(543\) 10.2746i 0.440923i
\(544\) −4.62018 −0.198088
\(545\) 6.61703 + 37.7274i 0.283443 + 1.61607i
\(546\) −5.91861 −0.253293
\(547\) 0.846151i 0.0361788i 0.999836 + 0.0180894i \(0.00575835\pi\)
−0.999836 + 0.0180894i \(0.994242\pi\)
\(548\) 8.82830i 0.377126i
\(549\) 11.3590 0.484788
\(550\) 2.26287 + 6.25250i 0.0964890 + 0.266607i
\(551\) −14.4715 −0.616508
\(552\) 1.44270i 0.0614054i
\(553\) 49.9503i 2.12410i
\(554\) −28.6550 −1.21744
\(555\) 3.20176 + 18.2551i 0.135907 + 0.774884i
\(556\) −11.5532 −0.489963
\(557\) 19.3532i 0.820020i −0.912081 0.410010i \(-0.865525\pi\)
0.912081 0.410010i \(-0.134475\pi\)
\(558\) 2.18029i 0.0922992i
\(559\) 13.1775 0.557348
\(560\) −7.17748 + 1.25886i −0.303304 + 0.0531966i
\(561\) 8.86433 0.374252
\(562\) 2.74692i 0.115872i
\(563\) 29.3647i 1.23758i −0.785558 0.618788i \(-0.787624\pi\)
0.785558 0.618788i \(-0.212376\pi\)
\(564\) 8.74692 0.368312
\(565\) −21.5275 + 3.77572i −0.905669 + 0.158846i
\(566\) −5.45307 −0.229210
\(567\) 17.5988i 0.739082i
\(568\) 0.265226i 0.0111286i
\(569\) −6.41900 −0.269098 −0.134549 0.990907i \(-0.542959\pi\)
−0.134549 + 0.990907i \(0.542959\pi\)
\(570\) −1.87904 10.7134i −0.0787042 0.448737i
\(571\) 35.3009 1.47730 0.738648 0.674092i \(-0.235465\pi\)
0.738648 + 0.674092i \(0.235465\pi\)
\(572\) 1.67413i 0.0699989i
\(573\) 24.1206i 1.00765i
\(574\) 16.7437 0.698868
\(575\) −1.70156 4.70156i −0.0709600 0.196069i
\(576\) −0.918614 −0.0382756
\(577\) 6.96339i 0.289890i 0.989440 + 0.144945i \(0.0463004\pi\)
−0.989440 + 0.144945i \(0.953700\pi\)
\(578\) 4.34603i 0.180771i
\(579\) 9.40312 0.390781
\(580\) −1.65798 9.45307i −0.0688438 0.392517i
\(581\) −6.60134 −0.273870
\(582\) 12.4363i 0.515503i
\(583\) 14.7982i 0.612880i
\(584\) −5.26464 −0.217852
\(585\) −2.54693 + 0.446707i −0.105303 + 0.0184691i
\(586\) 18.3806 0.759296
\(587\) 23.7392i 0.979823i −0.871772 0.489912i \(-0.837029\pi\)
0.871772 0.489912i \(-0.162971\pi\)
\(588\) 5.22283i 0.215386i
\(589\) 8.00256 0.329740
\(590\) −5.99645 + 1.05172i −0.246870 + 0.0432987i
\(591\) 25.7066 1.05743
\(592\) 5.74514i 0.236124i
\(593\) 23.1612i 0.951116i 0.879684 + 0.475558i \(0.157754\pi\)
−0.879684 + 0.475558i \(0.842246\pi\)
\(594\) 7.51831 0.308480
\(595\) 5.81616 + 33.1612i 0.238439 + 1.35948i
\(596\) −11.1333 −0.456038
\(597\) 5.44526i 0.222860i
\(598\) 1.25886i 0.0514787i
\(599\) −33.1344 −1.35383 −0.676916 0.736060i \(-0.736684\pi\)
−0.676916 + 0.736060i \(0.736684\pi\)
\(600\) 6.78295 2.45485i 0.276913 0.100219i
\(601\) 40.0432 1.63340 0.816698 0.577065i \(-0.195802\pi\)
0.816698 + 0.577065i \(0.195802\pi\)
\(602\) 34.1130i 1.39034i
\(603\) 6.07186i 0.247265i
\(604\) 3.23779 0.131744
\(605\) 3.56600 + 20.3317i 0.144978 + 0.826603i
\(606\) 20.9097 0.849398
\(607\) 1.81294i 0.0735849i 0.999323 + 0.0367925i \(0.0117140\pi\)
−0.999323 + 0.0367925i \(0.988286\pi\)
\(608\) 3.37169i 0.136740i
\(609\) −20.1794 −0.817713
\(610\) −27.2340 + 4.77658i −1.10267 + 0.193398i
\(611\) 7.63232 0.308771
\(612\) 4.24416i 0.171560i
\(613\) 11.9329i 0.481964i −0.970530 0.240982i \(-0.922531\pi\)
0.970530 0.240982i \(-0.0774694\pi\)
\(614\) 15.9234 0.642616
\(615\) −16.3255 + 2.86335i −0.658309 + 0.115461i
\(616\) 4.33388 0.174617
\(617\) 16.5923i 0.667982i 0.942576 + 0.333991i \(0.108396\pi\)
−0.942576 + 0.333991i \(0.891604\pi\)
\(618\) 26.7492i 1.07601i
\(619\) 1.43811 0.0578025 0.0289013 0.999582i \(-0.490799\pi\)
0.0289013 + 0.999582i \(0.490799\pi\)
\(620\) 0.916840 + 5.22742i 0.0368212 + 0.209938i
\(621\) −5.65339 −0.226863
\(622\) 11.3518i 0.455166i
\(623\) 52.6307i 2.10861i
\(624\) 1.81616 0.0727046
\(625\) 19.2094 16.0000i 0.768375 0.640000i
\(626\) −28.7913 −1.15073
\(627\) 6.46896i 0.258346i
\(628\) 17.6452i 0.704122i
\(629\) 26.5436 1.05836
\(630\) 1.15641 + 6.59333i 0.0460724 + 0.262685i
\(631\) 7.67446 0.305515 0.152758 0.988264i \(-0.451185\pi\)
0.152758 + 0.988264i \(0.451185\pi\)
\(632\) 15.3275i 0.609696i
\(633\) 34.5714i 1.37409i
\(634\) 31.2299 1.24030
\(635\) −2.26287 + 0.396885i −0.0897991 + 0.0157499i
\(636\) −16.0537 −0.636570
\(637\) 4.55730i 0.180567i
\(638\) 5.70793i 0.225979i
\(639\) 0.243640 0.00963826
\(640\) 2.20245 0.386289i 0.0870594 0.0152694i
\(641\) −23.0562 −0.910665 −0.455332 0.890322i \(-0.650480\pi\)
−0.455332 + 0.890322i \(0.650480\pi\)
\(642\) 6.46403i 0.255115i
\(643\) 9.51595i 0.375272i −0.982239 0.187636i \(-0.939917\pi\)
0.982239 0.187636i \(-0.0600826\pi\)
\(644\) −3.25886 −0.128417
\(645\) 5.83368 + 33.2611i 0.229701 + 1.30965i
\(646\) −15.5778 −0.612900
\(647\) 38.9857i 1.53269i −0.642432 0.766343i \(-0.722074\pi\)
0.642432 0.766343i \(-0.277926\pi\)
\(648\) 5.40031i 0.212144i
\(649\) 3.62076 0.142127
\(650\) 5.91861 2.14203i 0.232147 0.0840173i
\(651\) 11.1590 0.437354
\(652\) 12.2107i 0.478207i
\(653\) 7.32529i 0.286661i 0.989675 + 0.143330i \(0.0457811\pi\)
−0.989675 + 0.143330i \(0.954219\pi\)
\(654\) −24.7131 −0.966360
\(655\) −4.74692 27.0649i −0.185477 1.05751i
\(656\) −5.13790 −0.200601
\(657\) 4.83617i 0.188677i
\(658\) 19.7581i 0.770250i
\(659\) 20.7177 0.807048 0.403524 0.914969i \(-0.367785\pi\)
0.403524 + 0.914969i \(0.367785\pi\)
\(660\) −4.22565 + 0.741139i −0.164483 + 0.0288488i
\(661\) 12.9749 0.504666 0.252333 0.967640i \(-0.418802\pi\)
0.252333 + 0.967640i \(0.418802\pi\)
\(662\) 17.6917i 0.687606i
\(663\) 8.39098i 0.325879i
\(664\) 2.02566 0.0786108
\(665\) −24.2002 + 4.24448i −0.938443 + 0.164594i
\(666\) 5.27757 0.204502
\(667\) 4.29207i 0.166190i
\(668\) 2.06288i 0.0798151i
\(669\) −29.1561 −1.12724
\(670\) −2.55329 14.5578i −0.0986423 0.562415i
\(671\) 16.4443 0.634827
\(672\) 4.70156i 0.181367i
\(673\) 15.8660i 0.611589i −0.952098 0.305794i \(-0.901078\pi\)
0.952098 0.305794i \(-0.0989220\pi\)
\(674\) 1.33801 0.0515384
\(675\) −9.61959 26.5798i −0.370258 1.02306i
\(676\) −11.4153 −0.439049
\(677\) 23.2787i 0.894675i −0.894365 0.447337i \(-0.852372\pi\)
0.894365 0.447337i \(-0.147628\pi\)
\(678\) 14.1015i 0.541564i
\(679\) 28.0920 1.07807
\(680\) −1.78472 10.1757i −0.0684410 0.390220i
\(681\) −2.31793 −0.0888234
\(682\) 3.15641i 0.120865i
\(683\) 27.5797i 1.05531i −0.849460 0.527654i \(-0.823072\pi\)
0.849460 0.527654i \(-0.176928\pi\)
\(684\) −3.09728 −0.118427
\(685\) 19.4439 3.41027i 0.742913 0.130300i
\(686\) −11.0144 −0.420531
\(687\) 27.2698i 1.04041i
\(688\) 10.4678i 0.399080i
\(689\) −14.0080 −0.533663
\(690\) 3.17748 0.557299i 0.120964 0.0212160i
\(691\) 8.61472 0.327719 0.163860 0.986484i \(-0.447606\pi\)
0.163860 + 0.986484i \(0.447606\pi\)
\(692\) 2.10245i 0.0799233i
\(693\) 3.98116i 0.151232i
\(694\) 5.36355 0.203597
\(695\) −4.46286 25.4453i −0.169286 0.965194i
\(696\) 6.19218 0.234714
\(697\) 23.7380i 0.899141i
\(698\) 18.4306i 0.697607i
\(699\) 27.4274 1.03740
\(700\) −5.54515 15.3217i −0.209587 0.579107i
\(701\) 17.4254 0.658148 0.329074 0.944304i \(-0.393264\pi\)
0.329074 + 0.944304i \(0.393264\pi\)
\(702\) 7.11683i 0.268607i
\(703\) 19.3708i 0.730584i
\(704\) −1.32988 −0.0501216
\(705\) 3.37884 + 19.2646i 0.127254 + 0.725548i
\(706\) 6.76477 0.254595
\(707\) 47.2321i 1.77635i
\(708\) 3.92794i 0.147621i
\(709\) 6.42019 0.241115 0.120558 0.992706i \(-0.461532\pi\)
0.120558 + 0.992706i \(0.461532\pi\)
\(710\) −0.584146 + 0.102454i −0.0219226 + 0.00384502i
\(711\) 14.0801 0.528044
\(712\) 16.1500i 0.605248i
\(713\) 2.37346i 0.0888867i
\(714\) −21.7220 −0.812927
\(715\) −3.68719 + 0.646697i −0.137893 + 0.0241851i
\(716\) 20.4421 0.763958
\(717\) 40.8842i 1.52685i
\(718\) 27.5324i 1.02750i
\(719\) −1.50079 −0.0559699 −0.0279849 0.999608i \(-0.508909\pi\)
−0.0279849 + 0.999608i \(0.508909\pi\)
\(720\) −0.354850 2.02320i −0.0132245 0.0754002i
\(721\) −60.4226 −2.25026
\(722\) 7.63174i 0.284024i
\(723\) 9.16318i 0.340782i
\(724\) 7.12175 0.264678
\(725\) 20.1794 7.30323i 0.749446 0.271235i
\(726\) −13.3182 −0.494284
\(727\) 6.97867i 0.258825i −0.991591 0.129412i \(-0.958691\pi\)
0.991591 0.129412i \(-0.0413091\pi\)
\(728\) 4.10245i 0.152047i
\(729\) −29.4292 −1.08997
\(730\) −2.03367 11.5951i −0.0752695 0.429154i
\(731\) 48.3630 1.78877
\(732\) 17.8395i 0.659365i
\(733\) 3.61138i 0.133389i −0.997773 0.0666947i \(-0.978755\pi\)
0.997773 0.0666947i \(-0.0212453\pi\)
\(734\) −24.0744 −0.888604
\(735\) −11.5030 + 2.01752i −0.424295 + 0.0744174i
\(736\) 1.00000 0.0368605
\(737\) 8.79022i 0.323792i
\(738\) 4.71975i 0.173736i
\(739\) −5.24953 −0.193107 −0.0965536 0.995328i \(-0.530782\pi\)
−0.0965536 + 0.995328i \(0.530782\pi\)
\(740\) −12.6534 + 2.21928i −0.465148 + 0.0815825i
\(741\) 6.12352 0.224953
\(742\) 36.2631i 1.33126i
\(743\) 2.72603i 0.100008i 0.998749 + 0.0500042i \(0.0159235\pi\)
−0.998749 + 0.0500042i \(0.984077\pi\)
\(744\) −3.42419 −0.125537
\(745\) −4.30067 24.5205i −0.157564 0.898363i
\(746\) −1.31459 −0.0481305
\(747\) 1.86080i 0.0680831i
\(748\) 6.14426i 0.224657i
\(749\) 14.6013 0.533521
\(750\) 8.02685 + 13.9908i 0.293099 + 0.510872i
\(751\) −20.6729 −0.754364 −0.377182 0.926139i \(-0.623107\pi\)
−0.377182 + 0.926139i \(0.623107\pi\)
\(752\) 6.06288i 0.221090i
\(753\) 28.4545i 1.03694i
\(754\) 5.40312 0.196770
\(755\) 1.25072 + 7.13107i 0.0455185 + 0.259526i
\(756\) −18.4236 −0.670060
\(757\) 8.87759i 0.322661i −0.986900 0.161331i \(-0.948421\pi\)
0.986900 0.161331i \(-0.0515786\pi\)
\(758\) 8.38961i 0.304724i
\(759\) −1.91861 −0.0696413
\(760\) 7.42597 1.30244i 0.269368 0.0472446i
\(761\) 31.8816 1.15571 0.577853 0.816141i \(-0.303891\pi\)
0.577853 + 0.816141i \(0.303891\pi\)
\(762\) 1.48228i 0.0536973i
\(763\) 55.8235i 2.02095i
\(764\) 16.7191 0.604875
\(765\) −9.34754 + 1.63947i −0.337961 + 0.0592752i
\(766\) −24.1258 −0.871699
\(767\) 3.42741i 0.123757i
\(768\) 1.44270i 0.0520590i
\(769\) −37.6697 −1.35841 −0.679203 0.733951i \(-0.737674\pi\)
−0.679203 + 0.733951i \(0.737674\pi\)
\(770\) 1.67413 + 9.54515i 0.0603314 + 0.343983i
\(771\) 1.70386 0.0613631
\(772\) 6.51772i 0.234578i
\(773\) 6.14066i 0.220864i −0.993884 0.110432i \(-0.964777\pi\)
0.993884 0.110432i \(-0.0352235\pi\)
\(774\) 9.61584 0.345634
\(775\) −11.1590 + 4.03859i −0.400842 + 0.145070i
\(776\) −8.62018 −0.309446
\(777\) 27.0112i 0.969020i
\(778\) 12.5702i 0.450665i
\(779\) −17.3234 −0.620674
\(780\) 0.701562 + 4.00000i 0.0251200 + 0.143223i
\(781\) 0.352718 0.0126212
\(782\) 4.62018i 0.165217i
\(783\) 24.2648i 0.867152i
\(784\) −3.62018 −0.129292
\(785\) 38.8628 6.81616i 1.38707 0.243279i
\(786\) 17.7287 0.632361
\(787\)