Properties

Label 403.2.h.b.222.1
Level 403
Weight 2
Character 403.222
Analytic conductor 3.218
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.h (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 222.1
Character \(\chi\) \(=\) 403.222
Dual form 403.2.h.b.118.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.49327 q^{2} +(-1.44053 + 2.49508i) q^{3} +4.21641 q^{4} +(0.778554 + 1.34849i) q^{5} +(3.59165 - 6.22091i) q^{6} +(-0.277831 + 0.481217i) q^{7} -5.52611 q^{8} +(-2.65028 - 4.59042i) q^{9} +O(q^{10})\) \(q-2.49327 q^{2} +(-1.44053 + 2.49508i) q^{3} +4.21641 q^{4} +(0.778554 + 1.34849i) q^{5} +(3.59165 - 6.22091i) q^{6} +(-0.277831 + 0.481217i) q^{7} -5.52611 q^{8} +(-2.65028 - 4.59042i) q^{9} +(-1.94115 - 3.36216i) q^{10} +(-1.79571 - 3.11026i) q^{11} +(-6.07388 + 10.5203i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(0.692707 - 1.19980i) q^{14} -4.48613 q^{15} +5.34528 q^{16} +(-1.01252 + 1.75374i) q^{17} +(6.60787 + 11.4452i) q^{18} +(-0.578215 + 1.00150i) q^{19} +(3.28270 + 5.68580i) q^{20} +(-0.800449 - 1.38642i) q^{21} +(4.47719 + 7.75473i) q^{22} -8.57580 q^{23} +(7.96055 - 13.7881i) q^{24} +(1.28771 - 2.23038i) q^{25} +(1.24664 + 2.15924i) q^{26} +6.62808 q^{27} +(-1.17145 + 2.02901i) q^{28} -4.00739 q^{29} +11.1852 q^{30} +(2.10747 - 5.15350i) q^{31} -2.27502 q^{32} +10.3471 q^{33} +(2.52449 - 4.37255i) q^{34} -0.865224 q^{35} +(-11.1747 - 19.3551i) q^{36} +(4.06515 - 7.04105i) q^{37} +(1.44165 - 2.49701i) q^{38} +2.88107 q^{39} +(-4.30237 - 7.45193i) q^{40} +(-5.94136 - 10.2907i) q^{41} +(1.99574 + 3.45672i) q^{42} +(-1.78415 + 3.09024i) q^{43} +(-7.57145 - 13.1141i) q^{44} +(4.12677 - 7.14778i) q^{45} +21.3818 q^{46} +2.60865 q^{47} +(-7.70006 + 13.3369i) q^{48} +(3.34562 + 5.79478i) q^{49} +(-3.21061 + 5.56094i) q^{50} +(-2.91714 - 5.05264i) q^{51} +(-2.10820 - 3.65152i) q^{52} +(4.10979 + 7.11836i) q^{53} -16.5256 q^{54} +(2.79611 - 4.84301i) q^{55} +(1.53532 - 2.65926i) q^{56} +(-1.66588 - 2.88539i) q^{57} +9.99152 q^{58} +(-2.11371 + 3.66106i) q^{59} -18.9154 q^{60} +0.963652 q^{61} +(-5.25450 + 12.8491i) q^{62} +2.94532 q^{63} -5.01831 q^{64} +(0.778554 - 1.34849i) q^{65} -25.7982 q^{66} +(-2.74115 - 4.74781i) q^{67} +(-4.26920 + 7.39448i) q^{68} +(12.3537 - 21.3973i) q^{69} +2.15724 q^{70} +(-1.95152 - 3.38012i) q^{71} +(14.6457 + 25.3672i) q^{72} +(2.90790 + 5.03663i) q^{73} +(-10.1355 + 17.5553i) q^{74} +(3.70998 + 6.42587i) q^{75} +(-2.43799 + 4.22272i) q^{76} +1.99561 q^{77} -7.18329 q^{78} +(-3.38651 + 5.86560i) q^{79} +(4.16159 + 7.20808i) q^{80} +(-1.59713 + 2.76631i) q^{81} +(14.8134 + 25.6576i) q^{82} +(-0.967334 - 1.67547i) q^{83} +(-3.37502 - 5.84571i) q^{84} -3.15321 q^{85} +(4.44838 - 7.70482i) q^{86} +(5.77279 - 9.99876i) q^{87} +(9.92329 + 17.1876i) q^{88} +7.41559 q^{89} +(-10.2892 + 17.8214i) q^{90} +0.555661 q^{91} -36.1591 q^{92} +(9.82250 + 12.6821i) q^{93} -6.50407 q^{94} -1.80069 q^{95} +(3.27725 - 5.67636i) q^{96} -10.7527 q^{97} +(-8.34154 - 14.4480i) q^{98} +(-9.51827 + 16.4861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} + O(q^{10}) \) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} - 7q^{10} - 5q^{11} - 28q^{12} - 17q^{13} - 7q^{14} + 8q^{15} + 18q^{16} - 8q^{17} + 6q^{18} + 3q^{19} - 8q^{20} + 13q^{21} + 12q^{22} - 14q^{23} - 6q^{24} - 26q^{25} - 3q^{26} + 28q^{27} - 7q^{28} - 18q^{29} - 60q^{30} - 9q^{31} + 58q^{32} - 14q^{33} - 15q^{34} + 50q^{35} - 49q^{36} - 6q^{37} + 2q^{38} + 4q^{39} - 29q^{40} - 5q^{41} + 8q^{42} - q^{43} - 22q^{44} + 13q^{45} + 34q^{46} + 16q^{47} - 49q^{48} + 3q^{49} - 35q^{51} - 17q^{52} + 30q^{53} - 2q^{54} + 21q^{55} - 7q^{56} + 34q^{58} - 9q^{59} - 38q^{60} - 28q^{61} - 62q^{62} + 88q^{63} + 56q^{64} - 5q^{65} + 140q^{66} - 31q^{67} - 39q^{68} + 5q^{69} + 56q^{70} + q^{71} - 32q^{72} - 10q^{73} - 39q^{74} - 2q^{75} - 16q^{76} + 76q^{77} - 23q^{79} - 22q^{80} - 29q^{81} - 10q^{82} + 3q^{83} + 52q^{84} - 32q^{85} + 4q^{86} + 18q^{87} - 10q^{88} + 26q^{89} + 35q^{90} + 4q^{91} - 94q^{92} - 41q^{93} + 70q^{94} + 28q^{95} - 23q^{96} + 32q^{97} - 38q^{98} - 70q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.49327 −1.76301 −0.881505 0.472175i \(-0.843469\pi\)
−0.881505 + 0.472175i \(0.843469\pi\)
\(3\) −1.44053 + 2.49508i −0.831693 + 1.44053i 0.0650016 + 0.997885i \(0.479295\pi\)
−0.896695 + 0.442650i \(0.854039\pi\)
\(4\) 4.21641 2.10820
\(5\) 0.778554 + 1.34849i 0.348180 + 0.603065i 0.985926 0.167181i \(-0.0534665\pi\)
−0.637746 + 0.770246i \(0.720133\pi\)
\(6\) 3.59165 6.22091i 1.46628 2.53968i
\(7\) −0.277831 + 0.481217i −0.105010 + 0.181883i −0.913742 0.406294i \(-0.866821\pi\)
0.808732 + 0.588177i \(0.200154\pi\)
\(8\) −5.52611 −1.95377
\(9\) −2.65028 4.59042i −0.883427 1.53014i
\(10\) −1.94115 3.36216i −0.613844 1.06321i
\(11\) −1.79571 3.11026i −0.541427 0.937779i −0.998822 0.0485156i \(-0.984551\pi\)
0.457395 0.889263i \(-0.348782\pi\)
\(12\) −6.07388 + 10.5203i −1.75338 + 3.03694i
\(13\) −0.500000 0.866025i −0.138675 0.240192i
\(14\) 0.692707 1.19980i 0.185134 0.320661i
\(15\) −4.48613 −1.15831
\(16\) 5.34528 1.33632
\(17\) −1.01252 + 1.75374i −0.245573 + 0.425344i −0.962292 0.272017i \(-0.912309\pi\)
0.716720 + 0.697361i \(0.245643\pi\)
\(18\) 6.60787 + 11.4452i 1.55749 + 2.69765i
\(19\) −0.578215 + 1.00150i −0.132652 + 0.229759i −0.924698 0.380702i \(-0.875682\pi\)
0.792046 + 0.610461i \(0.209016\pi\)
\(20\) 3.28270 + 5.68580i 0.734034 + 1.27138i
\(21\) −0.800449 1.38642i −0.174672 0.302541i
\(22\) 4.47719 + 7.75473i 0.954541 + 1.65331i
\(23\) −8.57580 −1.78818 −0.894089 0.447888i \(-0.852176\pi\)
−0.894089 + 0.447888i \(0.852176\pi\)
\(24\) 7.96055 13.7881i 1.62494 2.81448i
\(25\) 1.28771 2.23038i 0.257542 0.446075i
\(26\) 1.24664 + 2.15924i 0.244485 + 0.423461i
\(27\) 6.62808 1.27557
\(28\) −1.17145 + 2.02901i −0.221383 + 0.383446i
\(29\) −4.00739 −0.744154 −0.372077 0.928202i \(-0.621354\pi\)
−0.372077 + 0.928202i \(0.621354\pi\)
\(30\) 11.1852 2.04212
\(31\) 2.10747 5.15350i 0.378513 0.925596i
\(32\) −2.27502 −0.402171
\(33\) 10.3471 1.80120
\(34\) 2.52449 4.37255i 0.432947 0.749886i
\(35\) −0.865224 −0.146250
\(36\) −11.1747 19.3551i −1.86244 3.22585i
\(37\) 4.06515 7.04105i 0.668307 1.15754i −0.310070 0.950714i \(-0.600352\pi\)
0.978377 0.206829i \(-0.0663142\pi\)
\(38\) 1.44165 2.49701i 0.233866 0.405068i
\(39\) 2.88107 0.461340
\(40\) −4.30237 7.45193i −0.680265 1.17825i
\(41\) −5.94136 10.2907i −0.927885 1.60714i −0.786854 0.617139i \(-0.788291\pi\)
−0.141031 0.990005i \(-0.545042\pi\)
\(42\) 1.99574 + 3.45672i 0.307949 + 0.533383i
\(43\) −1.78415 + 3.09024i −0.272081 + 0.471258i −0.969394 0.245508i \(-0.921045\pi\)
0.697314 + 0.716766i \(0.254378\pi\)
\(44\) −7.57145 13.1141i −1.14144 1.97703i
\(45\) 4.12677 7.14778i 0.615183 1.06553i
\(46\) 21.3818 3.15258
\(47\) 2.60865 0.380510 0.190255 0.981735i \(-0.439068\pi\)
0.190255 + 0.981735i \(0.439068\pi\)
\(48\) −7.70006 + 13.3369i −1.11141 + 1.92502i
\(49\) 3.34562 + 5.79478i 0.477946 + 0.827826i
\(50\) −3.21061 + 5.56094i −0.454048 + 0.786435i
\(51\) −2.91714 5.05264i −0.408482 0.707512i
\(52\) −2.10820 3.65152i −0.292355 0.506374i
\(53\) 4.10979 + 7.11836i 0.564522 + 0.977781i 0.997094 + 0.0761819i \(0.0242730\pi\)
−0.432572 + 0.901600i \(0.642394\pi\)
\(54\) −16.5256 −2.24885
\(55\) 2.79611 4.84301i 0.377028 0.653031i
\(56\) 1.53532 2.65926i 0.205166 0.355358i
\(57\) −1.66588 2.88539i −0.220651 0.382179i
\(58\) 9.99152 1.31195
\(59\) −2.11371 + 3.66106i −0.275182 + 0.476629i −0.970181 0.242382i \(-0.922071\pi\)
0.694999 + 0.719011i \(0.255405\pi\)
\(60\) −18.9154 −2.44196
\(61\) 0.963652 0.123383 0.0616915 0.998095i \(-0.480351\pi\)
0.0616915 + 0.998095i \(0.480351\pi\)
\(62\) −5.25450 + 12.8491i −0.667322 + 1.63183i
\(63\) 2.94532 0.371075
\(64\) −5.01831 −0.627289
\(65\) 0.778554 1.34849i 0.0965677 0.167260i
\(66\) −25.7982 −3.17554
\(67\) −2.74115 4.74781i −0.334885 0.580038i 0.648578 0.761148i \(-0.275364\pi\)
−0.983463 + 0.181111i \(0.942031\pi\)
\(68\) −4.26920 + 7.39448i −0.517717 + 0.896712i
\(69\) 12.3537 21.3973i 1.48722 2.57593i
\(70\) 2.15724 0.257839
\(71\) −1.95152 3.38012i −0.231602 0.401147i 0.726677 0.686979i \(-0.241063\pi\)
−0.958280 + 0.285832i \(0.907730\pi\)
\(72\) 14.6457 + 25.3672i 1.72602 + 2.98955i
\(73\) 2.90790 + 5.03663i 0.340344 + 0.589492i 0.984496 0.175404i \(-0.0561233\pi\)
−0.644153 + 0.764897i \(0.722790\pi\)
\(74\) −10.1355 + 17.5553i −1.17823 + 2.04076i
\(75\) 3.70998 + 6.42587i 0.428391 + 0.741995i
\(76\) −2.43799 + 4.22272i −0.279657 + 0.484380i
\(77\) 1.99561 0.227421
\(78\) −7.18329 −0.813348
\(79\) −3.38651 + 5.86560i −0.381012 + 0.659932i −0.991207 0.132319i \(-0.957758\pi\)
0.610195 + 0.792251i \(0.291091\pi\)
\(80\) 4.16159 + 7.20808i 0.465280 + 0.805888i
\(81\) −1.59713 + 2.76631i −0.177459 + 0.307368i
\(82\) 14.8134 + 25.6576i 1.63587 + 2.83341i
\(83\) −0.967334 1.67547i −0.106179 0.183907i 0.808040 0.589127i \(-0.200528\pi\)
−0.914219 + 0.405220i \(0.867195\pi\)
\(84\) −3.37502 5.84571i −0.368245 0.637819i
\(85\) −3.15321 −0.342014
\(86\) 4.44838 7.70482i 0.479681 0.830832i
\(87\) 5.77279 9.99876i 0.618908 1.07198i
\(88\) 9.92329 + 17.1876i 1.05783 + 1.83221i
\(89\) 7.41559 0.786051 0.393025 0.919528i \(-0.371428\pi\)
0.393025 + 0.919528i \(0.371428\pi\)
\(90\) −10.2892 + 17.8214i −1.08457 + 1.87854i
\(91\) 0.555661 0.0582491
\(92\) −36.1591 −3.76985
\(93\) 9.82250 + 12.6821i 1.01855 + 1.31507i
\(94\) −6.50407 −0.670844
\(95\) −1.80069 −0.184746
\(96\) 3.27725 5.67636i 0.334483 0.579341i
\(97\) −10.7527 −1.09177 −0.545886 0.837860i \(-0.683807\pi\)
−0.545886 + 0.837860i \(0.683807\pi\)
\(98\) −8.34154 14.4480i −0.842623 1.45947i
\(99\) −9.51827 + 16.4861i −0.956622 + 1.65692i
\(100\) 5.42950 9.40418i 0.542950 0.940418i
\(101\) 10.0007 0.995106 0.497553 0.867434i \(-0.334232\pi\)
0.497553 + 0.867434i \(0.334232\pi\)
\(102\) 7.27324 + 12.5976i 0.720158 + 1.24735i
\(103\) −7.68910 13.3179i −0.757630 1.31225i −0.944056 0.329785i \(-0.893024\pi\)
0.186426 0.982469i \(-0.440309\pi\)
\(104\) 2.76305 + 4.78575i 0.270940 + 0.469281i
\(105\) 1.24639 2.15880i 0.121635 0.210678i
\(106\) −10.2468 17.7480i −0.995259 1.72384i
\(107\) −9.20859 + 15.9497i −0.890228 + 1.54192i −0.0506256 + 0.998718i \(0.516122\pi\)
−0.839602 + 0.543202i \(0.817212\pi\)
\(108\) 27.9467 2.68917
\(109\) 8.40866 0.805404 0.402702 0.915331i \(-0.368071\pi\)
0.402702 + 0.915331i \(0.368071\pi\)
\(110\) −6.97147 + 12.0749i −0.664704 + 1.15130i
\(111\) 11.7120 + 20.2858i 1.11165 + 1.92544i
\(112\) −1.48508 + 2.57224i −0.140327 + 0.243054i
\(113\) −7.42291 12.8569i −0.698289 1.20947i −0.969059 0.246828i \(-0.920612\pi\)
0.270771 0.962644i \(-0.412721\pi\)
\(114\) 4.15349 + 7.19405i 0.389010 + 0.673785i
\(115\) −6.67672 11.5644i −0.622608 1.07839i
\(116\) −16.8968 −1.56883
\(117\) −2.65028 + 4.59042i −0.245019 + 0.424385i
\(118\) 5.27006 9.12801i 0.485148 0.840302i
\(119\) −0.562619 0.974484i −0.0515752 0.0893308i
\(120\) 24.7909 2.26309
\(121\) −0.949150 + 1.64398i −0.0862864 + 0.149452i
\(122\) −2.40265 −0.217525
\(123\) 34.2350 3.08686
\(124\) 8.88596 21.7293i 0.797983 1.95135i
\(125\) 11.7957 1.05504
\(126\) −7.34347 −0.654209
\(127\) −6.13072 + 10.6187i −0.544013 + 0.942259i 0.454655 + 0.890668i \(0.349763\pi\)
−0.998668 + 0.0515911i \(0.983571\pi\)
\(128\) 17.0621 1.50809
\(129\) −5.14027 8.90320i −0.452575 0.783883i
\(130\) −1.94115 + 3.36216i −0.170250 + 0.294881i
\(131\) 2.05976 3.56761i 0.179962 0.311703i −0.761905 0.647689i \(-0.775736\pi\)
0.941867 + 0.335985i \(0.109069\pi\)
\(132\) 43.6277 3.79731
\(133\) −0.321292 0.556493i −0.0278595 0.0482541i
\(134\) 6.83444 + 11.8376i 0.590405 + 1.02261i
\(135\) 5.16031 + 8.93792i 0.444129 + 0.769254i
\(136\) 5.59530 9.69135i 0.479793 0.831027i
\(137\) −8.99664 15.5826i −0.768635 1.33131i −0.938303 0.345813i \(-0.887603\pi\)
0.169668 0.985501i \(-0.445730\pi\)
\(138\) −30.8013 + 53.3493i −2.62198 + 4.54140i
\(139\) −17.2664 −1.46452 −0.732260 0.681025i \(-0.761534\pi\)
−0.732260 + 0.681025i \(0.761534\pi\)
\(140\) −3.64814 −0.308324
\(141\) −3.75785 + 6.50878i −0.316468 + 0.548139i
\(142\) 4.86566 + 8.42757i 0.408317 + 0.707226i
\(143\) −1.79571 + 3.11026i −0.150165 + 0.260093i
\(144\) −14.1665 24.5371i −1.18054 2.04476i
\(145\) −3.11997 5.40395i −0.259099 0.448773i
\(146\) −7.25018 12.5577i −0.600029 1.03928i
\(147\) −19.2779 −1.59002
\(148\) 17.1404 29.6880i 1.40893 2.44034i
\(149\) −8.48198 + 14.6912i −0.694871 + 1.20355i 0.275353 + 0.961343i \(0.411205\pi\)
−0.970224 + 0.242209i \(0.922128\pi\)
\(150\) −9.24998 16.0214i −0.755258 1.30815i
\(151\) −22.6970 −1.84705 −0.923527 0.383533i \(-0.874707\pi\)
−0.923527 + 0.383533i \(0.874707\pi\)
\(152\) 3.19528 5.53439i 0.259171 0.448898i
\(153\) 10.7339 0.867782
\(154\) −4.97561 −0.400946
\(155\) 8.59025 1.17036i 0.689985 0.0940057i
\(156\) 12.1478 0.972600
\(157\) −6.37607 −0.508866 −0.254433 0.967090i \(-0.581889\pi\)
−0.254433 + 0.967090i \(0.581889\pi\)
\(158\) 8.44348 14.6245i 0.671727 1.16347i
\(159\) −23.6812 −1.87804
\(160\) −1.77123 3.06785i −0.140028 0.242535i
\(161\) 2.38262 4.12682i 0.187777 0.325239i
\(162\) 3.98209 6.89717i 0.312862 0.541893i
\(163\) 15.6119 1.22282 0.611410 0.791314i \(-0.290603\pi\)
0.611410 + 0.791314i \(0.290603\pi\)
\(164\) −25.0512 43.3900i −1.95617 3.38819i
\(165\) 8.05580 + 13.9531i 0.627143 + 1.08624i
\(166\) 2.41183 + 4.17741i 0.187194 + 0.324230i
\(167\) −3.10851 + 5.38410i −0.240544 + 0.416634i −0.960869 0.277002i \(-0.910659\pi\)
0.720325 + 0.693636i \(0.243992\pi\)
\(168\) 4.42337 + 7.66150i 0.341270 + 0.591098i
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) 7.86181 0.602973
\(171\) 6.12973 0.468752
\(172\) −7.52271 + 13.0297i −0.573602 + 0.993507i
\(173\) −11.8858 20.5868i −0.903660 1.56518i −0.822706 0.568467i \(-0.807537\pi\)
−0.0809538 0.996718i \(-0.525797\pi\)
\(174\) −14.3931 + 24.9296i −1.09114 + 1.88991i
\(175\) 0.715529 + 1.23933i 0.0540889 + 0.0936848i
\(176\) −9.59857 16.6252i −0.723520 1.25317i
\(177\) −6.08975 10.5478i −0.457734 0.792818i
\(178\) −18.4891 −1.38582
\(179\) 2.39926 4.15563i 0.179329 0.310607i −0.762322 0.647198i \(-0.775941\pi\)
0.941651 + 0.336591i \(0.109274\pi\)
\(180\) 17.4002 30.1379i 1.29693 2.24635i
\(181\) −8.59696 14.8904i −0.639007 1.10679i −0.985651 0.168796i \(-0.946012\pi\)
0.346644 0.937997i \(-0.387321\pi\)
\(182\) −1.38541 −0.102694
\(183\) −1.38817 + 2.40439i −0.102617 + 0.177737i
\(184\) 47.3908 3.49370
\(185\) 12.6598 0.930764
\(186\) −24.4902 31.6199i −1.79571 2.31849i
\(187\) 7.27278 0.531838
\(188\) 10.9991 0.802194
\(189\) −1.84148 + 3.18954i −0.133948 + 0.232005i
\(190\) 4.48960 0.325710
\(191\) 11.5012 + 19.9207i 0.832201 + 1.44141i 0.896289 + 0.443470i \(0.146253\pi\)
−0.0640883 + 0.997944i \(0.520414\pi\)
\(192\) 7.22905 12.5211i 0.521712 0.903631i
\(193\) −10.8589 + 18.8082i −0.781641 + 1.35384i 0.149345 + 0.988785i \(0.452284\pi\)
−0.930985 + 0.365056i \(0.881050\pi\)
\(194\) 26.8094 1.92480
\(195\) 2.24307 + 3.88511i 0.160629 + 0.278218i
\(196\) 14.1065 + 24.4332i 1.00761 + 1.74523i
\(197\) −6.99005 12.1071i −0.498021 0.862597i 0.501977 0.864881i \(-0.332606\pi\)
−0.999997 + 0.00228395i \(0.999273\pi\)
\(198\) 23.7316 41.1044i 1.68653 2.92116i
\(199\) −6.81031 11.7958i −0.482770 0.836182i 0.517034 0.855965i \(-0.327036\pi\)
−0.999804 + 0.0197825i \(0.993703\pi\)
\(200\) −7.11602 + 12.3253i −0.503178 + 0.871530i
\(201\) 15.7949 1.11409
\(202\) −24.9344 −1.75438
\(203\) 1.11338 1.92842i 0.0781437 0.135349i
\(204\) −12.2999 21.3040i −0.861163 1.49158i
\(205\) 9.25134 16.0238i 0.646142 1.11915i
\(206\) 19.1710 + 33.2052i 1.33571 + 2.31352i
\(207\) 22.7283 + 39.3666i 1.57973 + 2.73616i
\(208\) −2.67264 4.62915i −0.185314 0.320974i
\(209\) 4.15323 0.287285
\(210\) −3.10758 + 5.38248i −0.214443 + 0.371427i
\(211\) 0.224037 0.388043i 0.0154233 0.0267140i −0.858211 0.513298i \(-0.828424\pi\)
0.873634 + 0.486584i \(0.161757\pi\)
\(212\) 17.3285 + 30.0139i 1.19013 + 2.06136i
\(213\) 11.2449 0.770488
\(214\) 22.9595 39.7670i 1.56948 2.71842i
\(215\) −5.55623 −0.378932
\(216\) −36.6275 −2.49218
\(217\) 1.89443 + 2.44595i 0.128602 + 0.166042i
\(218\) −20.9651 −1.41994
\(219\) −16.7557 −1.13225
\(220\) 11.7896 20.4201i 0.794852 1.37672i
\(221\) 2.02504 0.136219
\(222\) −29.2012 50.5779i −1.95986 3.39457i
\(223\) −5.20601 + 9.01707i −0.348620 + 0.603828i −0.986005 0.166718i \(-0.946683\pi\)
0.637384 + 0.770546i \(0.280016\pi\)
\(224\) 0.632071 1.09478i 0.0422320 0.0731480i
\(225\) −13.6512 −0.910077
\(226\) 18.5073 + 32.0556i 1.23109 + 2.13231i
\(227\) −7.86656 13.6253i −0.522122 0.904342i −0.999669 0.0257356i \(-0.991807\pi\)
0.477547 0.878606i \(-0.341526\pi\)
\(228\) −7.02402 12.1660i −0.465177 0.805710i
\(229\) −4.87163 + 8.43790i −0.321926 + 0.557592i −0.980885 0.194586i \(-0.937664\pi\)
0.658959 + 0.752179i \(0.270997\pi\)
\(230\) 16.6469 + 28.8333i 1.09766 + 1.90121i
\(231\) −2.87475 + 4.97921i −0.189145 + 0.327608i
\(232\) 22.1453 1.45391
\(233\) 13.2879 0.870519 0.435259 0.900305i \(-0.356657\pi\)
0.435259 + 0.900305i \(0.356657\pi\)
\(234\) 6.60787 11.4452i 0.431970 0.748194i
\(235\) 2.03097 + 3.51775i 0.132486 + 0.229473i
\(236\) −8.91227 + 15.4365i −0.580140 + 1.00483i
\(237\) −9.75676 16.8992i −0.633770 1.09772i
\(238\) 1.40276 + 2.42966i 0.0909276 + 0.157491i
\(239\) 0.425385 + 0.736788i 0.0275159 + 0.0476589i 0.879455 0.475981i \(-0.157907\pi\)
−0.851940 + 0.523640i \(0.824574\pi\)
\(240\) −23.9796 −1.54788
\(241\) −0.908878 + 1.57422i −0.0585460 + 0.101405i −0.893813 0.448440i \(-0.851980\pi\)
0.835267 + 0.549845i \(0.185313\pi\)
\(242\) 2.36649 4.09888i 0.152124 0.263486i
\(243\) 5.34067 + 9.25030i 0.342604 + 0.593407i
\(244\) 4.06315 0.260117
\(245\) −5.20949 + 9.02310i −0.332822 + 0.576465i
\(246\) −85.3571 −5.44217
\(247\) 1.15643 0.0735819
\(248\) −11.6461 + 28.4788i −0.739529 + 1.80841i
\(249\) 5.57391 0.353232
\(250\) −29.4100 −1.86005
\(251\) 4.97987 8.62539i 0.314327 0.544430i −0.664967 0.746872i \(-0.731555\pi\)
0.979294 + 0.202442i \(0.0648879\pi\)
\(252\) 12.4187 0.782302
\(253\) 15.3997 + 26.6730i 0.968168 + 1.67692i
\(254\) 15.2856 26.4754i 0.959101 1.66121i
\(255\) 4.54231 7.86751i 0.284450 0.492682i
\(256\) −32.5037 −2.03148
\(257\) −7.29132 12.6289i −0.454820 0.787772i 0.543858 0.839177i \(-0.316963\pi\)
−0.998678 + 0.0514059i \(0.983630\pi\)
\(258\) 12.8161 + 22.1981i 0.797895 + 1.38199i
\(259\) 2.25885 + 3.91244i 0.140358 + 0.243107i
\(260\) 3.28270 5.68580i 0.203584 0.352619i
\(261\) 10.6207 + 18.3956i 0.657406 + 1.13866i
\(262\) −5.13554 + 8.89502i −0.317275 + 0.549536i
\(263\) −12.5034 −0.770995 −0.385498 0.922709i \(-0.625970\pi\)
−0.385498 + 0.922709i \(0.625970\pi\)
\(264\) −57.1794 −3.51915
\(265\) −6.39938 + 11.0840i −0.393111 + 0.680888i
\(266\) 0.801068 + 1.38749i 0.0491166 + 0.0850725i
\(267\) −10.6824 + 18.5025i −0.653753 + 1.13233i
\(268\) −11.5578 20.0187i −0.706006 1.22284i
\(269\) 14.5585 + 25.2161i 0.887649 + 1.53745i 0.842648 + 0.538465i \(0.180996\pi\)
0.0450010 + 0.998987i \(0.485671\pi\)
\(270\) −12.8661 22.2847i −0.783004 1.35620i
\(271\) −5.37556 −0.326542 −0.163271 0.986581i \(-0.552204\pi\)
−0.163271 + 0.986581i \(0.552204\pi\)
\(272\) −5.41221 + 9.37422i −0.328164 + 0.568396i
\(273\) −0.800449 + 1.38642i −0.0484454 + 0.0839099i
\(274\) 22.4311 + 38.8518i 1.35511 + 2.34712i
\(275\) −9.24940 −0.557760
\(276\) 52.0884 90.2198i 3.13535 5.43059i
\(277\) 2.04699 0.122992 0.0614958 0.998107i \(-0.480413\pi\)
0.0614958 + 0.998107i \(0.480413\pi\)
\(278\) 43.0499 2.58196
\(279\) −29.2421 + 3.98404i −1.75068 + 0.238518i
\(280\) 4.78132 0.285739
\(281\) −21.5339 −1.28461 −0.642304 0.766450i \(-0.722021\pi\)
−0.642304 + 0.766450i \(0.722021\pi\)
\(282\) 9.36934 16.2282i 0.557936 0.966374i
\(283\) 22.7491 1.35229 0.676146 0.736768i \(-0.263649\pi\)
0.676146 + 0.736768i \(0.263649\pi\)
\(284\) −8.22839 14.2520i −0.488265 0.845700i
\(285\) 2.59395 4.49285i 0.153652 0.266134i
\(286\) 4.47719 7.75473i 0.264742 0.458547i
\(287\) 6.60277 0.389749
\(288\) 6.02945 + 10.4433i 0.355289 + 0.615378i
\(289\) 6.44960 + 11.1710i 0.379388 + 0.657120i
\(290\) 7.77894 + 13.4735i 0.456795 + 0.791192i
\(291\) 15.4896 26.8288i 0.908019 1.57273i
\(292\) 12.2609 + 21.2365i 0.717514 + 1.24277i
\(293\) 12.0567 20.8827i 0.704357 1.21998i −0.262566 0.964914i \(-0.584569\pi\)
0.966923 0.255068i \(-0.0820980\pi\)
\(294\) 48.0651 2.80322
\(295\) −6.58255 −0.383251
\(296\) −22.4645 + 38.9096i −1.30572 + 2.26158i
\(297\) −11.9021 20.6150i −0.690630 1.19621i
\(298\) 21.1479 36.6292i 1.22506 2.12187i
\(299\) 4.28790 + 7.42686i 0.247976 + 0.429507i
\(300\) 15.6428 + 27.0941i 0.903136 + 1.56428i
\(301\) −0.991384 1.71713i −0.0571424 0.0989736i
\(302\) 56.5898 3.25637
\(303\) −14.4063 + 24.9525i −0.827623 + 1.43348i
\(304\) −3.09072 + 5.35329i −0.177265 + 0.307032i
\(305\) 0.750255 + 1.29948i 0.0429595 + 0.0744080i
\(306\) −26.7624 −1.52991
\(307\) 4.21580 7.30198i 0.240608 0.416746i −0.720279 0.693684i \(-0.755986\pi\)
0.960888 + 0.276938i \(0.0893197\pi\)
\(308\) 8.41432 0.479450
\(309\) 44.3057 2.52046
\(310\) −21.4178 + 2.91803i −1.21645 + 0.165733i
\(311\) 22.4824 1.27486 0.637431 0.770508i \(-0.279997\pi\)
0.637431 + 0.770508i \(0.279997\pi\)
\(312\) −15.9211 −0.901355
\(313\) −1.77852 + 3.08049i −0.100528 + 0.174119i −0.911902 0.410407i \(-0.865386\pi\)
0.811374 + 0.584527i \(0.198720\pi\)
\(314\) 15.8973 0.897136
\(315\) 2.29309 + 3.97174i 0.129201 + 0.223782i
\(316\) −14.2789 + 24.7318i −0.803250 + 1.39127i
\(317\) 4.70488 8.14908i 0.264252 0.457698i −0.703115 0.711076i \(-0.748208\pi\)
0.967367 + 0.253378i \(0.0815416\pi\)
\(318\) 59.0436 3.31100
\(319\) 7.19612 + 12.4640i 0.402905 + 0.697852i
\(320\) −3.90702 6.76716i −0.218409 0.378296i
\(321\) −26.5306 45.9523i −1.48079 2.56481i
\(322\) −5.94052 + 10.2893i −0.331052 + 0.573400i
\(323\) −1.17091 2.02808i −0.0651512 0.112845i
\(324\) −6.73416 + 11.6639i −0.374120 + 0.647995i
\(325\) −2.57542 −0.142858
\(326\) −38.9248 −2.15584
\(327\) −12.1130 + 20.9803i −0.669849 + 1.16021i
\(328\) 32.8326 + 56.8678i 1.81288 + 3.14000i
\(329\) −0.724762 + 1.25532i −0.0399574 + 0.0692083i
\(330\) −20.0853 34.7888i −1.10566 1.91506i
\(331\) −14.7420 25.5339i −0.810294 1.40347i −0.912659 0.408723i \(-0.865974\pi\)
0.102365 0.994747i \(-0.467359\pi\)
\(332\) −4.07867 7.06447i −0.223846 0.387713i
\(333\) −43.0952 −2.36160
\(334\) 7.75037 13.4240i 0.424081 0.734530i
\(335\) 4.26827 7.39286i 0.233200 0.403915i
\(336\) −4.27862 7.41079i −0.233418 0.404292i
\(337\) −31.5402 −1.71811 −0.859053 0.511887i \(-0.828947\pi\)
−0.859053 + 0.511887i \(0.828947\pi\)
\(338\) 1.24664 2.15924i 0.0678081 0.117447i
\(339\) 42.7718 2.32305
\(340\) −13.2952 −0.721034
\(341\) −19.8131 + 2.69940i −1.07294 + 0.146181i
\(342\) −15.2831 −0.826415
\(343\) −7.60769 −0.410777
\(344\) 9.85942 17.0770i 0.531584 0.920731i
\(345\) 38.4722 2.07127
\(346\) 29.6345 + 51.3285i 1.59316 + 2.75944i
\(347\) −0.927776 + 1.60696i −0.0498056 + 0.0862659i −0.889853 0.456247i \(-0.849194\pi\)
0.840048 + 0.542512i \(0.182527\pi\)
\(348\) 24.3404 42.1589i 1.30478 2.25995i
\(349\) −16.1865 −0.866446 −0.433223 0.901287i \(-0.642624\pi\)
−0.433223 + 0.901287i \(0.642624\pi\)
\(350\) −1.78401 3.09000i −0.0953593 0.165167i
\(351\) −3.31404 5.74008i −0.176890 0.306383i
\(352\) 4.08528 + 7.07591i 0.217746 + 0.377147i
\(353\) −16.0898 + 27.8684i −0.856376 + 1.48329i 0.0189873 + 0.999820i \(0.493956\pi\)
−0.875363 + 0.483466i \(0.839378\pi\)
\(354\) 15.1834 + 26.2984i 0.806989 + 1.39775i
\(355\) 3.03872 5.26322i 0.161278 0.279343i
\(356\) 31.2671 1.65716
\(357\) 3.24189 0.171579
\(358\) −5.98200 + 10.3611i −0.316158 + 0.547603i
\(359\) −1.92910 3.34130i −0.101814 0.176347i 0.810618 0.585575i \(-0.199131\pi\)
−0.912432 + 0.409228i \(0.865798\pi\)
\(360\) −22.8050 + 39.4994i −1.20193 + 2.08180i
\(361\) 8.83133 + 15.2963i 0.464807 + 0.805069i
\(362\) 21.4346 + 37.1258i 1.12658 + 1.95129i
\(363\) −2.73457 4.73641i −0.143528 0.248597i
\(364\) 2.34289 0.122801
\(365\) −4.52791 + 7.84257i −0.237002 + 0.410499i
\(366\) 3.46110 5.99480i 0.180914 0.313353i
\(367\) 0.245949 + 0.425997i 0.0128385 + 0.0222369i 0.872373 0.488840i \(-0.162580\pi\)
−0.859535 + 0.511077i \(0.829247\pi\)
\(368\) −45.8401 −2.38958
\(369\) −31.4926 + 54.5467i −1.63944 + 2.83959i
\(370\) −31.5642 −1.64095
\(371\) −4.56730 −0.237122
\(372\) 41.4157 + 53.4729i 2.14730 + 2.77244i
\(373\) 0.335471 0.0173700 0.00868501 0.999962i \(-0.497235\pi\)
0.00868501 + 0.999962i \(0.497235\pi\)
\(374\) −18.1330 −0.937636
\(375\) −16.9922 + 29.4313i −0.877472 + 1.51983i
\(376\) −14.4157 −0.743432
\(377\) 2.00370 + 3.47050i 0.103196 + 0.178740i
\(378\) 4.59132 7.95239i 0.236152 0.409027i
\(379\) 6.77322 11.7316i 0.347917 0.602610i −0.637962 0.770068i \(-0.720222\pi\)
0.985879 + 0.167458i \(0.0535558\pi\)
\(380\) −7.59243 −0.389483
\(381\) −17.6630 30.5933i −0.904904 1.56734i
\(382\) −28.6757 49.6678i −1.46718 2.54123i
\(383\) −3.45793 5.98931i −0.176692 0.306039i 0.764054 0.645153i \(-0.223206\pi\)
−0.940745 + 0.339113i \(0.889873\pi\)
\(384\) −24.5785 + 42.5712i −1.25427 + 2.17245i
\(385\) 1.55369 + 2.69107i 0.0791835 + 0.137150i
\(386\) 27.0742 46.8939i 1.37804 2.38684i
\(387\) 18.9140 0.961454
\(388\) −45.3378 −2.30168
\(389\) 4.97047 8.60911i 0.252013 0.436499i −0.712067 0.702112i \(-0.752241\pi\)
0.964080 + 0.265612i \(0.0855741\pi\)
\(390\) −5.59258 9.68663i −0.283191 0.490502i
\(391\) 8.68319 15.0397i 0.439128 0.760591i
\(392\) −18.4883 32.0226i −0.933798 1.61739i
\(393\) 5.93431 + 10.2785i 0.299346 + 0.518483i
\(394\) 17.4281 + 30.1864i 0.878015 + 1.52077i
\(395\) −10.5463 −0.530642
\(396\) −40.1329 + 69.5122i −2.01675 + 3.49312i
\(397\) −6.05106 + 10.4807i −0.303694 + 0.526013i −0.976970 0.213378i \(-0.931553\pi\)
0.673276 + 0.739391i \(0.264887\pi\)
\(398\) 16.9800 + 29.4101i 0.851128 + 1.47420i
\(399\) 1.85133 0.0926823
\(400\) 6.88316 11.9220i 0.344158 0.596099i
\(401\) 12.2445 0.611463 0.305732 0.952118i \(-0.401099\pi\)
0.305732 + 0.952118i \(0.401099\pi\)
\(402\) −39.3810 −1.96414
\(403\) −5.51680 + 0.751626i −0.274811 + 0.0374411i
\(404\) 42.1670 2.09789
\(405\) −4.97381 −0.247151
\(406\) −2.77595 + 4.80809i −0.137768 + 0.238621i
\(407\) −29.1994 −1.44736
\(408\) 16.1205 + 27.9215i 0.798082 + 1.38232i
\(409\) −10.8913 + 18.8643i −0.538539 + 0.932778i 0.460444 + 0.887689i \(0.347690\pi\)
−0.998983 + 0.0450887i \(0.985643\pi\)
\(410\) −23.0661 + 39.9517i −1.13915 + 1.97307i
\(411\) 51.8399 2.55707
\(412\) −32.4204 56.1538i −1.59724 2.76650i
\(413\) −1.17451 2.03431i −0.0577938 0.100102i
\(414\) −56.6678 98.1515i −2.78507 4.82389i
\(415\) 1.50624 2.60889i 0.0739386 0.128065i
\(416\) 1.13751 + 1.97023i 0.0557711 + 0.0965983i
\(417\) 24.8729 43.0811i 1.21803 2.10969i
\(418\) −10.3551 −0.506486
\(419\) −13.9437 −0.681193 −0.340596 0.940210i \(-0.610629\pi\)
−0.340596 + 0.940210i \(0.610629\pi\)
\(420\) 5.25527 9.10239i 0.256431 0.444151i
\(421\) 5.71663 + 9.90150i 0.278612 + 0.482570i 0.971040 0.238917i \(-0.0767924\pi\)
−0.692428 + 0.721487i \(0.743459\pi\)
\(422\) −0.558585 + 0.967498i −0.0271915 + 0.0470970i
\(423\) −6.91365 11.9748i −0.336153 0.582234i
\(424\) −22.7111 39.3368i −1.10295 1.91036i
\(425\) 2.60766 + 4.51661i 0.126490 + 0.219088i
\(426\) −28.0366 −1.35838
\(427\) −0.267732 + 0.463725i −0.0129565 + 0.0224412i
\(428\) −38.8272 + 67.2506i −1.87678 + 3.25068i
\(429\) −5.17357 8.96088i −0.249782 0.432635i
\(430\) 13.8532 0.668061
\(431\) −3.49987 + 6.06195i −0.168583 + 0.291994i −0.937922 0.346847i \(-0.887252\pi\)
0.769339 + 0.638841i \(0.220586\pi\)
\(432\) 35.4289 1.70457
\(433\) −20.9730 −1.00790 −0.503949 0.863733i \(-0.668120\pi\)
−0.503949 + 0.863733i \(0.668120\pi\)
\(434\) −4.72333 6.09842i −0.226727 0.292734i
\(435\) 17.9777 0.861965
\(436\) 35.4544 1.69796
\(437\) 4.95866 8.58865i 0.237205 0.410851i
\(438\) 41.7765 1.99616
\(439\) −9.22512 15.9784i −0.440291 0.762606i 0.557420 0.830231i \(-0.311791\pi\)
−0.997711 + 0.0676243i \(0.978458\pi\)
\(440\) −15.4516 + 26.7630i −0.736627 + 1.27588i
\(441\) 17.7337 30.7156i 0.844460 1.46265i
\(442\) −5.04898 −0.240156
\(443\) −4.97714 8.62067i −0.236471 0.409580i 0.723228 0.690609i \(-0.242658\pi\)
−0.959699 + 0.281029i \(0.909324\pi\)
\(444\) 49.3825 + 85.5331i 2.34359 + 4.05922i
\(445\) 5.77343 + 9.99988i 0.273687 + 0.474040i
\(446\) 12.9800 22.4820i 0.614621 1.06455i
\(447\) −24.4372 42.3264i −1.15584 2.00197i
\(448\) 1.39424 2.41489i 0.0658716 0.114093i
\(449\) 19.8008 0.934456 0.467228 0.884137i \(-0.345253\pi\)
0.467228 + 0.884137i \(0.345253\pi\)
\(450\) 34.0360 1.60447
\(451\) −21.3379 + 36.9584i −1.00476 + 1.74030i
\(452\) −31.2980 54.2098i −1.47213 2.54981i
\(453\) 32.6958 56.6308i 1.53618 2.66075i
\(454\) 19.6135 + 33.9715i 0.920506 + 1.59436i
\(455\) 0.432612 + 0.749306i 0.0202812 + 0.0351280i
\(456\) 9.20582 + 15.9450i 0.431102 + 0.746691i
\(457\) 4.83375 0.226113 0.113057 0.993589i \(-0.463936\pi\)
0.113057 + 0.993589i \(0.463936\pi\)
\(458\) 12.1463 21.0380i 0.567559 0.983041i
\(459\) −6.71107 + 11.6239i −0.313246 + 0.542558i
\(460\) −28.1518 48.7603i −1.31258 2.27346i
\(461\) 14.1690 0.659915 0.329957 0.943996i \(-0.392966\pi\)
0.329957 + 0.943996i \(0.392966\pi\)
\(462\) 7.16753 12.4145i 0.333464 0.577576i
\(463\) −24.4650 −1.13699 −0.568493 0.822688i \(-0.692473\pi\)
−0.568493 + 0.822688i \(0.692473\pi\)
\(464\) −21.4206 −0.994428
\(465\) −9.45440 + 23.1193i −0.438437 + 1.07213i
\(466\) −33.1303 −1.53473
\(467\) 16.9234 0.783122 0.391561 0.920152i \(-0.371935\pi\)
0.391561 + 0.920152i \(0.371935\pi\)
\(468\) −11.1747 + 19.3551i −0.516549 + 0.894689i
\(469\) 3.04630 0.140665
\(470\) −5.06377 8.77070i −0.233574 0.404562i
\(471\) 9.18495 15.9088i 0.423220 0.733039i
\(472\) 11.6806 20.2314i 0.537643 0.931226i
\(473\) 12.8153 0.589247
\(474\) 24.3263 + 42.1343i 1.11734 + 1.93529i
\(475\) 1.48914 + 2.57927i 0.0683266 + 0.118345i
\(476\) −2.37223 4.10882i −0.108731 0.188328i
\(477\) 21.7842 37.7313i 0.997428 1.72760i
\(478\) −1.06060 1.83701i −0.0485108 0.0840231i
\(479\) 16.3875 28.3840i 0.748766 1.29690i −0.199649 0.979867i \(-0.563980\pi\)
0.948415 0.317033i \(-0.102686\pi\)
\(480\) 10.2061 0.465841
\(481\) −8.13031 −0.370710
\(482\) 2.26608 3.92497i 0.103217 0.178777i
\(483\) 6.86450 + 11.8897i 0.312345 + 0.540998i
\(484\) −4.00200 + 6.93167i −0.181909 + 0.315076i
\(485\) −8.37156 14.5000i −0.380133 0.658409i
\(486\) −13.3157 23.0635i −0.604014 1.04618i
\(487\) −13.8452 23.9805i −0.627384 1.08666i −0.988075 0.153976i \(-0.950792\pi\)
0.360691 0.932686i \(-0.382541\pi\)
\(488\) −5.32525 −0.241063
\(489\) −22.4895 + 38.9530i −1.01701 + 1.76151i
\(490\) 12.9887 22.4971i 0.586769 1.01631i
\(491\) 5.29201 + 9.16604i 0.238825 + 0.413657i 0.960377 0.278703i \(-0.0899044\pi\)
−0.721552 + 0.692360i \(0.756571\pi\)
\(492\) 144.349 6.50774
\(493\) 4.05757 7.02792i 0.182744 0.316522i
\(494\) −2.88330 −0.129726
\(495\) −29.6419 −1.33231
\(496\) 11.2650 27.5469i 0.505815 1.23689i
\(497\) 2.16876 0.0972823
\(498\) −13.8973 −0.622752
\(499\) −6.54541 + 11.3370i −0.293013 + 0.507513i −0.974521 0.224298i \(-0.927991\pi\)
0.681508 + 0.731811i \(0.261325\pi\)
\(500\) 49.7356 2.22425
\(501\) −8.95584 15.5120i −0.400117 0.693024i
\(502\) −12.4162 + 21.5055i −0.554161 + 0.959835i
\(503\) −10.7082 + 18.5471i −0.477453 + 0.826973i −0.999666 0.0258423i \(-0.991773\pi\)
0.522213 + 0.852815i \(0.325107\pi\)
\(504\) −16.2761 −0.724997
\(505\) 7.78607 + 13.4859i 0.346476 + 0.600114i
\(506\) −38.3955 66.5030i −1.70689 2.95642i
\(507\) −1.44053 2.49508i −0.0639764 0.110810i
\(508\) −25.8496 + 44.7728i −1.14689 + 1.98647i
\(509\) 4.86313 + 8.42319i 0.215555 + 0.373352i 0.953444 0.301570i \(-0.0975107\pi\)
−0.737889 + 0.674922i \(0.764177\pi\)
\(510\) −11.3252 + 19.6158i −0.501489 + 0.868604i
\(511\) −3.23161 −0.142958
\(512\) 46.9166 2.07344
\(513\) −3.83245 + 6.63800i −0.169207 + 0.293075i
\(514\) 18.1793 + 31.4874i 0.801852 + 1.38885i
\(515\) 11.9728 20.7374i 0.527583 0.913800i
\(516\) −21.6735 37.5395i −0.954121 1.65259i
\(517\) −4.68438 8.11358i −0.206019 0.356835i
\(518\) −5.63192 9.75478i −0.247453 0.428600i
\(519\) 68.4876 3.00627
\(520\) −4.30237 + 7.45193i −0.188672 + 0.326789i
\(521\) −12.2327 + 21.1877i −0.535926 + 0.928250i 0.463192 + 0.886258i \(0.346704\pi\)
−0.999118 + 0.0419926i \(0.986629\pi\)
\(522\) −26.4803 45.8653i −1.15901 2.00747i
\(523\) 18.4931 0.808646 0.404323 0.914616i \(-0.367507\pi\)
0.404323 + 0.914616i \(0.367507\pi\)
\(524\) 8.68479 15.0425i 0.379397 0.657135i
\(525\) −4.12298 −0.179942
\(526\) 31.1745 1.35927
\(527\) 6.90403 + 8.91398i 0.300744 + 0.388299i
\(528\) 55.3083 2.40699
\(529\) 50.5444 2.19758
\(530\) 15.9554 27.6355i 0.693058 1.20041i
\(531\) 22.4077 0.972412
\(532\) −1.35470 2.34640i −0.0587335 0.101729i
\(533\) −5.94136 + 10.2907i −0.257349 + 0.445742i
\(534\) 26.6342 46.1317i 1.15257 1.99632i
\(535\) −28.6775 −1.23984
\(536\) 15.1479 + 26.2369i 0.654290 + 1.13326i
\(537\) 6.91242 + 11.9727i 0.298293 + 0.516659i
\(538\) −36.2984 62.8706i −1.56493 2.71054i
\(539\) 12.0155 20.8115i 0.517545 0.896415i
\(540\) 21.7580 + 37.6859i 0.936315 + 1.62174i
\(541\) 18.8671 32.6788i 0.811159 1.40497i −0.100894 0.994897i \(-0.532170\pi\)
0.912053 0.410072i \(-0.134497\pi\)
\(542\) 13.4027 0.575696
\(543\) 49.5369 2.12583
\(544\) 2.30351 3.98979i 0.0987621 0.171061i
\(545\) 6.54660 + 11.3390i 0.280425 + 0.485711i
\(546\) 1.99574 3.45672i 0.0854097 0.147934i
\(547\) 12.3683 + 21.4225i 0.528830 + 0.915960i 0.999435 + 0.0336164i \(0.0107024\pi\)
−0.470605 + 0.882344i \(0.655964\pi\)
\(548\) −37.9335 65.7028i −1.62044 2.80668i
\(549\) −2.55395 4.42357i −0.109000 0.188793i
\(550\) 23.0613 0.983336
\(551\) 2.31714 4.01340i 0.0987133 0.170976i
\(552\) −68.2681 + 118.244i −2.90569 + 5.03279i
\(553\) −1.88175 3.25929i −0.0800201 0.138599i
\(554\) −5.10370 −0.216836
\(555\) −18.2368 + 31.5871i −0.774110 + 1.34080i
\(556\) −72.8023 −3.08751
\(557\) −40.6086 −1.72064 −0.860321 0.509753i \(-0.829737\pi\)
−0.860321 + 0.509753i \(0.829737\pi\)
\(558\) 72.9086 9.93329i 3.08647 0.420510i
\(559\) 3.56830 0.150923
\(560\) −4.62486 −0.195436
\(561\) −10.4767 + 18.1462i −0.442326 + 0.766132i
\(562\) 53.6900 2.26478
\(563\) 17.2955 + 29.9567i 0.728920 + 1.26253i 0.957340 + 0.288964i \(0.0933107\pi\)
−0.228420 + 0.973563i \(0.573356\pi\)
\(564\) −15.8446 + 27.4437i −0.667179 + 1.15559i
\(565\) 11.5583 20.0195i 0.486260 0.842227i
\(566\) −56.7196 −2.38410
\(567\) −0.887464 1.53713i −0.0372700 0.0645535i
\(568\) 10.7843 + 18.6789i 0.452499 + 0.783751i
\(569\) −14.6619 25.3951i −0.614659 1.06462i −0.990444 0.137913i \(-0.955960\pi\)
0.375786 0.926707i \(-0.377373\pi\)
\(570\) −6.46743 + 11.2019i −0.270891 + 0.469196i
\(571\) 10.1038 + 17.5003i 0.422830 + 0.732364i 0.996215 0.0869226i \(-0.0277033\pi\)
−0.573385 + 0.819286i \(0.694370\pi\)
\(572\) −7.57145 + 13.1141i −0.316578 + 0.548329i
\(573\) −66.2718 −2.76854
\(574\) −16.4625 −0.687132
\(575\) −11.0431 + 19.1273i −0.460531 + 0.797662i
\(576\) 13.2999 + 23.0362i 0.554164 + 0.959840i
\(577\) −2.17047 + 3.75936i −0.0903578 + 0.156504i −0.907662 0.419702i \(-0.862134\pi\)
0.817304 + 0.576207i \(0.195468\pi\)
\(578\) −16.0806 27.8524i −0.668865 1.15851i
\(579\) −31.2852 54.1876i −1.30017 2.25196i
\(580\) −13.1551 22.7853i −0.546235 0.946106i
\(581\) 1.07502 0.0445993
\(582\) −38.6199 + 66.8916i −1.60085 + 2.77275i
\(583\) 14.7600 25.5650i 0.611295 1.05879i
\(584\) −16.0694 27.8329i −0.664955 1.15174i
\(585\) −8.25354 −0.341242
\(586\) −30.0605 + 52.0664i −1.24179 + 2.15084i
\(587\) 34.4381 1.42141 0.710707 0.703488i \(-0.248375\pi\)
0.710707 + 0.703488i \(0.248375\pi\)
\(588\) −81.2836 −3.35208
\(589\) 3.94265 + 5.09046i 0.162454 + 0.209749i
\(590\) 16.4121 0.675676
\(591\) 40.2777 1.65680
\(592\) 21.7294 37.6364i 0.893072 1.54685i
\(593\) −45.0974 −1.85193 −0.925964 0.377611i \(-0.876746\pi\)
−0.925964 + 0.377611i \(0.876746\pi\)
\(594\) 29.6752 + 51.3989i 1.21759 + 2.10892i
\(595\) 0.876058 1.51738i 0.0359149 0.0622064i
\(596\) −35.7635 + 61.9442i −1.46493 + 2.53733i
\(597\) 39.2419 1.60607
\(598\) −10.6909 18.5172i −0.437184 0.757225i
\(599\) 18.0305 + 31.2297i 0.736706 + 1.27601i 0.953971 + 0.299900i \(0.0969532\pi\)
−0.217265 + 0.976113i \(0.569713\pi\)
\(600\) −20.5017 35.5101i −0.836980 1.44969i
\(601\) 7.31944 12.6776i 0.298566 0.517132i −0.677242 0.735760i \(-0.736825\pi\)
0.975808 + 0.218629i \(0.0701583\pi\)
\(602\) 2.47179 + 4.28127i 0.100743 + 0.174491i
\(603\) −14.5296 + 25.1661i −0.591693 + 1.02484i
\(604\) −95.6997 −3.89397
\(605\) −2.95586 −0.120173
\(606\) 35.9189 62.2134i 1.45911 2.52725i
\(607\) −17.6227 30.5234i −0.715282 1.23890i −0.962851 0.270034i \(-0.912965\pi\)
0.247569 0.968870i \(-0.420368\pi\)
\(608\) 1.31545 2.27843i 0.0533486 0.0924025i
\(609\) 3.20771 + 5.55592i 0.129983 + 0.225137i
\(610\) −1.87059 3.23996i −0.0757380 0.131182i
\(611\) −1.30432 2.25916i −0.0527673 0.0913957i
\(612\) 45.2584 1.82946
\(613\) −3.88894 + 6.73584i −0.157073 + 0.272058i −0.933812 0.357765i \(-0.883539\pi\)
0.776739 + 0.629823i \(0.216872\pi\)
\(614\) −10.5111 + 18.2058i −0.424195 + 0.734727i
\(615\) 26.6538 + 46.1657i 1.07478 + 1.86158i
\(616\) −11.0280 −0.444330
\(617\) −6.38270 + 11.0552i −0.256958 + 0.445064i −0.965425 0.260679i \(-0.916054\pi\)
0.708468 + 0.705743i \(0.249387\pi\)
\(618\) −110.466 −4.44360
\(619\) 23.3653 0.939131 0.469565 0.882898i \(-0.344411\pi\)
0.469565 + 0.882898i \(0.344411\pi\)
\(620\) 36.2200 4.93472i 1.45463 0.198183i
\(621\) −56.8411 −2.28095
\(622\) −56.0548 −2.24759
\(623\) −2.06028 + 3.56850i −0.0825433 + 0.142969i
\(624\) 15.4001 0.616498
\(625\) 2.74507 + 4.75461i 0.109803 + 0.190184i
\(626\) 4.43433 7.68049i 0.177232 0.306974i
\(627\) −5.98287 + 10.3626i −0.238933 + 0.413844i
\(628\) −26.8841 −1.07279
\(629\) 8.23211 + 14.2584i 0.328236 + 0.568521i
\(630\) −5.71729 9.90263i −0.227782 0.394530i
\(631\) −0.321643 0.557102i −0.0128044 0.0221779i 0.859552 0.511048i \(-0.170743\pi\)
−0.872357 + 0.488870i \(0.837409\pi\)
\(632\) 18.7142 32.4139i 0.744411 1.28936i
\(633\) 0.645466 + 1.11798i 0.0256550 + 0.0444357i
\(634\) −11.7305 + 20.3179i −0.465879 + 0.806926i
\(635\) −19.0924 −0.757658
\(636\) −99.8494 −3.95929
\(637\) 3.34562 5.79478i 0.132558 0.229598i
\(638\) −17.9419 31.0762i −0.710326 1.23032i
\(639\) −10.3441 + 17.9166i −0.409207 + 0.708768i
\(640\) 13.2837 + 23.0081i 0.525086 + 0.909475i
\(641\) 3.54201 + 6.13494i 0.139901 + 0.242315i 0.927459 0.373925i \(-0.121988\pi\)
−0.787558 + 0.616240i \(0.788655\pi\)
\(642\) 66.1480 + 114.572i 2.61065 + 4.52178i
\(643\) 6.02780 0.237713 0.118857 0.992911i \(-0.462077\pi\)
0.118857 + 0.992911i \(0.462077\pi\)
\(644\) 10.0461 17.4004i 0.395872 0.685670i
\(645\) 8.00395 13.8632i 0.315155 0.545865i
\(646\) 2.91940 + 5.05655i 0.114862 + 0.198947i
\(647\) 5.72271 0.224983 0.112491 0.993653i \(-0.464117\pi\)
0.112491 + 0.993653i \(0.464117\pi\)
\(648\) 8.82593 15.2870i 0.346715 0.600528i
\(649\) 15.1825 0.595964
\(650\) 6.42122 0.251861
\(651\) −8.83183 + 1.20328i −0.346147 + 0.0471601i
\(652\) 65.8262 2.57795
\(653\) −4.52278 −0.176990 −0.0884950 0.996077i \(-0.528206\pi\)
−0.0884950 + 0.996077i \(0.528206\pi\)
\(654\) 30.2009 52.3096i 1.18095 2.04547i
\(655\) 6.41454 0.250637
\(656\) −31.7583 55.0069i −1.23995 2.14766i
\(657\) 15.4135 26.6969i 0.601337 1.04155i
\(658\) 1.80703 3.12987i 0.0704453 0.122015i
\(659\) 1.75700 0.0684431 0.0342215 0.999414i \(-0.489105\pi\)
0.0342215 + 0.999414i \(0.489105\pi\)
\(660\) 33.9665 + 58.8318i 1.32215 + 2.29002i
\(661\) −0.604777 1.04750i −0.0235231 0.0407432i 0.854024 0.520233i \(-0.174155\pi\)
−0.877547 + 0.479490i \(0.840822\pi\)
\(662\) 36.7558 + 63.6630i 1.42856 + 2.47433i
\(663\) −2.91714 + 5.05264i −0.113293 + 0.196228i
\(664\) 5.34559 + 9.25884i 0.207449 + 0.359313i
\(665\) 0.500286 0.866520i 0.0194002 0.0336022i
\(666\) 107.448 4.16353
\(667\) 34.3666 1.33068
\(668\) −13.1068 + 22.7016i −0.507116 + 0.878350i
\(669\) −14.9989 25.9788i −0.579890 1.00440i
\(670\) −10.6420 + 18.4324i −0.411134 + 0.712106i
\(671\) −1.73044 2.99721i −0.0668029 0.115706i
\(672\) 1.82104 + 3.15413i 0.0702481 + 0.121673i
\(673\) −2.24304 3.88507i −0.0864630 0.149758i 0.819551 0.573007i \(-0.194223\pi\)
−0.906014 + 0.423248i \(0.860890\pi\)
\(674\) 78.6384 3.02904
\(675\) 8.53503 14.7831i 0.328513 0.569002i
\(676\) −2.10820 + 3.65152i −0.0810848 + 0.140443i
\(677\) 1.28839 + 2.23156i 0.0495170 + 0.0857659i 0.889722 0.456504i \(-0.150898\pi\)
−0.840205 + 0.542270i \(0.817565\pi\)
\(678\) −106.642 −4.09556
\(679\) 2.98743 5.17438i 0.114647 0.198574i
\(680\) 17.4250 0.668217
\(681\) 45.3282 1.73698
\(682\) 49.3996 6.73035i 1.89161 0.257718i
\(683\) 11.5867 0.443353 0.221676 0.975120i \(-0.428847\pi\)
0.221676 + 0.975120i \(0.428847\pi\)
\(684\) 25.8454 0.988225
\(685\) 14.0087 24.2638i 0.535246 0.927074i
\(686\) 18.9680 0.724203
\(687\) −14.0355 24.3102i −0.535487 0.927491i
\(688\) −9.53679 + 16.5182i −0.363587 + 0.629751i
\(689\) 4.10979 7.11836i 0.156570 0.271188i
\(690\) −95.9217 −3.65168
\(691\) 2.76942 + 4.79677i 0.105354 + 0.182478i 0.913883 0.405978i \(-0.133069\pi\)
−0.808529 + 0.588456i \(0.799736\pi\)
\(692\) −50.1153 86.8023i −1.90510 3.29973i
\(693\) −5.28893 9.16070i −0.200910 0.347986i
\(694\) 2.31320 4.00658i 0.0878078 0.152088i
\(695\) −13.4428 23.2837i −0.509916 0.883201i
\(696\) −31.9011 + 55.2543i −1.20921 + 2.09441i
\(697\) 24.0630 0.911453
\(698\) 40.3575 1.52755
\(699\) −19.1417 + 33.1543i −0.724004 + 1.25401i
\(700\) 3.01696 + 5.22553i 0.114031 + 0.197507i
\(701\) −18.8164 + 32.5910i −0.710686 + 1.23094i 0.253914 + 0.967227i \(0.418282\pi\)
−0.964600 + 0.263718i \(0.915051\pi\)
\(702\) 8.26280 + 14.3116i 0.311859 + 0.540156i
\(703\) 4.70107 + 8.14249i 0.177304 + 0.307100i
\(704\) 9.01143 + 15.6083i 0.339631 + 0.588258i
\(705\) −11.7027 −0.440751
\(706\) 40.1163 69.4836i 1.50980 2.61505i
\(707\) −2.77850 + 4.81250i −0.104496 + 0.180993i
\(708\) −25.6769 44.4737i −0.964996 1.67142i
\(709\) −35.3759 −1.32857 −0.664285 0.747479i \(-0.731264\pi\)
−0.664285 + 0.747479i \(0.731264\pi\)
\(710\) −7.57636 + 13.1226i −0.284336 + 0.492484i
\(711\) 35.9008 1.34638
\(712\) −40.9793 −1.53577
\(713\) −18.0733 + 44.1954i −0.676849 + 1.65513i
\(714\) −8.08291 −0.302495
\(715\) −5.59223 −0.209137
\(716\) 10.1162 17.5218i 0.378062 0.654822i
\(717\) −2.45113 −0.0915390
\(718\) 4.80977 + 8.33076i 0.179499 + 0.310901i
\(719\) −4.18401 + 7.24691i −0.156037 + 0.270264i −0.933436 0.358744i \(-0.883205\pi\)
0.777399 + 0.629008i \(0.216539\pi\)
\(720\) 22.0587 38.2069i 0.822081 1.42389i
\(721\) 8.54507 0.318235
\(722\) −22.0189 38.1379i −0.819460 1.41935i
\(723\) −2.61854 4.53545i −0.0973846 0.168675i
\(724\) −36.2483 62.7839i −1.34716 2.33335i
\(725\) −5.16035 + 8.93799i −0.191651 + 0.331949i
\(726\) 6.81802 + 11.8092i 0.253040 + 0.438279i
\(727\) −11.8589 + 20.5402i −0.439822 + 0.761794i −0.997675 0.0681454i \(-0.978292\pi\)
0.557853 + 0.829940i \(0.311625\pi\)
\(728\) −3.07064 −0.113806
\(729\) −40.3564 −1.49468
\(730\) 11.2893 19.5537i 0.417836 0.723713i
\(731\) −3.61299 6.25787i −0.133631 0.231456i
\(732\) −5.85311 + 10.1379i −0.216337 + 0.374707i
\(733\) −4.24009 7.34406i −0.156611 0.271259i 0.777033 0.629460i \(-0.216724\pi\)
−0.933645 + 0.358201i \(0.883390\pi\)
\(734\) −0.613219 1.06213i −0.0226343 0.0392038i
\(735\) −15.0089 25.9962i −0.553612 0.958884i
\(736\) 19.5101 0.719153
\(737\) −9.84463 + 17.0514i −0.362631 + 0.628096i
\(738\) 78.5196 136.000i 2.89034 5.00622i
\(739\) 22.3917 + 38.7835i 0.823691 + 1.42667i 0.902916 + 0.429817i \(0.141422\pi\)
−0.0792252 + 0.996857i \(0.525245\pi\)
\(740\) 53.3787 1.96224
\(741\) −1.66588 + 2.88539i −0.0611976 + 0.105997i
\(742\) 11.3875 0.418049
\(743\) 12.0562 0.442298 0.221149 0.975240i \(-0.429019\pi\)
0.221149 + 0.975240i \(0.429019\pi\)
\(744\) −54.2802 70.0827i −1.99001 2.56936i
\(745\) −26.4147 −0.967760
\(746\) −0.836420 −0.0306235
\(747\) −5.12741 + 8.88094i −0.187602 + 0.324937i
\(748\) 30.6650 1.12122
\(749\) −5.11685 8.86265i −0.186966 0.323834i
\(750\) 42.3661 73.3803i 1.54699 2.67947i
\(751\) −1.25096 + 2.16672i −0.0456481 + 0.0790649i −0.887947 0.459946i \(-0.847869\pi\)
0.842299 + 0.539011i \(0.181202\pi\)
\(752\) 13.9440 0.508484
\(753\) 14.3474 + 24.8504i 0.522847 + 0.905597i
\(754\) −4.99576 8.65291i −0.181935 0.315121i
\(755\) −17.6708 30.6068i −0.643107 1.11389i
\(756\) −7.76444 + 13.4484i −0.282390 + 0.489114i
\(757\) 20.0902 + 34.7972i 0.730190 + 1.26473i 0.956802 + 0.290741i \(0.0939017\pi\)
−0.226612 + 0.973985i \(0.572765\pi\)
\(758\) −16.8875 + 29.2500i −0.613381 + 1.06241i
\(759\) −88.7350 −3.22088
\(760\) 9.95079 0.360953
\(761\) −11.8050 + 20.4468i −0.427930 + 0.741196i −0.996689 0.0813081i \(-0.974090\pi\)
0.568759 + 0.822504i \(0.307424\pi\)
\(762\) 44.0387 + 76.2773i 1.59536 + 2.76324i
\(763\) −2.33618 + 4.04639i −0.0845755 + 0.146489i
\(764\) 48.4939 + 83.9940i 1.75445 + 3.03880i
\(765\) 8.35689 + 14.4746i 0.302144 + 0.523329i
\(766\) 8.62156 + 14.9330i 0.311509 + 0.539550i
\(767\) 4.22743 0.152643
\(768\) 46.8228 81.0994i 1.68957 2.92642i
\(769\) 11.6952 20.2567i 0.421740 0.730476i −0.574370 0.818596i \(-0.694753\pi\)
0.996110 + 0.0881205i \(0.0280861\pi\)
\(770\) −3.87378 6.70958i −0.139601 0.241796i
\(771\) 42.0136 1.51308
\(772\)