Properties

Label 950.2.u.g.149.2
Level $950$
Weight $2$
Character 950.149
Analytic conductor $7.586$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.u (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 149.2
Character \(\chi\) \(=\) 950.149
Dual form 950.2.u.g.899.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.642788 + 0.766044i) q^{2} +(-0.197144 - 0.541649i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.541649 + 0.197144i) q^{6} +(4.21251 - 2.43209i) q^{7} +(0.866025 + 0.500000i) q^{8} +(2.04362 - 1.71480i) q^{9} +O(q^{10})\) \(q+(-0.642788 + 0.766044i) q^{2} +(-0.197144 - 0.541649i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(0.541649 + 0.197144i) q^{6} +(4.21251 - 2.43209i) q^{7} +(0.866025 + 0.500000i) q^{8} +(2.04362 - 1.71480i) q^{9} +(2.68454 - 4.64975i) q^{11} +(-0.499186 + 0.288205i) q^{12} +(-1.31923 + 3.62457i) q^{13} +(-0.844657 + 4.79029i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(0.901248 - 1.07407i) q^{17} +2.66775i q^{18} +(-4.35299 + 0.226908i) q^{19} +(-2.14781 - 1.80223i) q^{21} +(1.83633 + 5.04528i) q^{22} +(-5.25780 + 0.927092i) q^{23} +(0.100093 - 0.567654i) q^{24} +(-1.92859 - 3.34042i) q^{26} +(-2.82926 - 1.63348i) q^{27} +(-3.12664 - 3.72618i) q^{28} +(2.78364 - 2.33575i) q^{29} +(-4.10189 - 7.10468i) q^{31} +(0.342020 - 0.939693i) q^{32} +(-3.04777 - 0.537405i) q^{33} +(0.243471 + 1.38079i) q^{34} +(-2.04362 - 1.71480i) q^{36} +10.4594i q^{37} +(2.62423 - 3.48044i) q^{38} +2.22332 q^{39} +(1.79322 - 0.652678i) q^{41} +(2.76117 - 0.486869i) q^{42} +(1.45618 + 0.256764i) q^{43} +(-5.04528 - 1.83633i) q^{44} +(2.66945 - 4.62363i) q^{46} +(2.00570 + 2.39030i) q^{47} +(0.370510 + 0.441556i) q^{48} +(8.33016 - 14.4283i) q^{49} +(-0.759442 - 0.276414i) q^{51} +(3.79858 + 0.669793i) q^{52} +(1.77266 - 0.312568i) q^{53} +(3.06993 - 1.11736i) q^{54} +4.86419 q^{56} +(0.981070 + 2.31306i) q^{57} +3.63378i q^{58} +(5.61133 + 4.70846i) q^{59} +(1.40916 + 7.99176i) q^{61} +(8.07914 + 1.42457i) q^{62} +(4.43820 - 12.1939i) q^{63} +(0.500000 + 0.866025i) q^{64} +(2.37075 - 1.98929i) q^{66} +(-5.42827 - 6.46916i) q^{67} +(-1.21425 - 0.701047i) q^{68} +(1.53870 + 2.66511i) q^{69} +(1.04647 - 5.93485i) q^{71} +(2.62722 - 0.463250i) q^{72} +(0.436515 + 1.19931i) q^{73} +(-8.01234 - 6.72316i) q^{74} +(0.979350 + 4.24746i) q^{76} -26.1162i q^{77} +(-1.42912 + 1.70316i) q^{78} +(-15.6290 + 5.68848i) q^{79} +(1.06275 - 6.02717i) q^{81} +(-0.652678 + 1.79322i) q^{82} +(12.5236 - 7.23049i) q^{83} +(-1.40188 + 2.42814i) q^{84} +(-1.13271 + 0.950453i) q^{86} +(-1.81393 - 1.04727i) q^{87} +(4.64975 - 2.68454i) q^{88} +(9.02905 + 3.28630i) q^{89} +(3.25800 + 18.4770i) q^{91} +(1.82601 + 5.01693i) q^{92} +(-3.03958 + 3.62243i) q^{93} -3.12031 q^{94} -0.576411 q^{96} +(-3.90758 + 4.65687i) q^{97} +(5.69817 + 15.6556i) q^{98} +(-2.48722 - 14.1057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 36q^{9} + O(q^{10}) \) \( 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.642788 + 0.766044i −0.454519 + 0.541675i
\(3\) −0.197144 0.541649i −0.113821 0.312721i 0.869682 0.493613i \(-0.164324\pi\)
−0.983503 + 0.180892i \(0.942102\pi\)
\(4\) −0.173648 0.984808i −0.0868241 0.492404i
\(5\) 0 0
\(6\) 0.541649 + 0.197144i 0.221127 + 0.0804837i
\(7\) 4.21251 2.43209i 1.59218 0.919245i 0.599247 0.800564i \(-0.295467\pi\)
0.992932 0.118681i \(-0.0378665\pi\)
\(8\) 0.866025 + 0.500000i 0.306186 + 0.176777i
\(9\) 2.04362 1.71480i 0.681205 0.571599i
\(10\) 0 0
\(11\) 2.68454 4.64975i 0.809418 1.40195i −0.103850 0.994593i \(-0.533116\pi\)
0.913268 0.407360i \(-0.133550\pi\)
\(12\) −0.499186 + 0.288205i −0.144103 + 0.0831977i
\(13\) −1.31923 + 3.62457i −0.365890 + 1.00527i 0.611019 + 0.791616i \(0.290760\pi\)
−0.976909 + 0.213658i \(0.931462\pi\)
\(14\) −0.844657 + 4.79029i −0.225744 + 1.28026i
\(15\) 0 0
\(16\) −0.939693 + 0.342020i −0.234923 + 0.0855050i
\(17\) 0.901248 1.07407i 0.218585 0.260499i −0.645598 0.763678i \(-0.723392\pi\)
0.864183 + 0.503178i \(0.167836\pi\)
\(18\) 2.66775i 0.628795i
\(19\) −4.35299 + 0.226908i −0.998644 + 0.0520563i
\(20\) 0 0
\(21\) −2.14781 1.80223i −0.468691 0.393278i
\(22\) 1.83633 + 5.04528i 0.391507 + 1.07566i
\(23\) −5.25780 + 0.927092i −1.09633 + 0.193312i −0.692425 0.721490i \(-0.743457\pi\)
−0.403902 + 0.914802i \(0.632346\pi\)
\(24\) 0.100093 0.567654i 0.0204313 0.115872i
\(25\) 0 0
\(26\) −1.92859 3.34042i −0.378228 0.655110i
\(27\) −2.82926 1.63348i −0.544492 0.314363i
\(28\) −3.12664 3.72618i −0.590879 0.704183i
\(29\) 2.78364 2.33575i 0.516908 0.433738i −0.346644 0.937997i \(-0.612679\pi\)
0.863552 + 0.504259i \(0.168234\pi\)
\(30\) 0 0
\(31\) −4.10189 7.10468i −0.736721 1.27604i −0.953964 0.299920i \(-0.903040\pi\)
0.217244 0.976117i \(-0.430293\pi\)
\(32\) 0.342020 0.939693i 0.0604612 0.166116i
\(33\) −3.04777 0.537405i −0.530549 0.0935501i
\(34\) 0.243471 + 1.38079i 0.0417549 + 0.236804i
\(35\) 0 0
\(36\) −2.04362 1.71480i −0.340603 0.285800i
\(37\) 10.4594i 1.71951i 0.510706 + 0.859755i \(0.329384\pi\)
−0.510706 + 0.859755i \(0.670616\pi\)
\(38\) 2.62423 3.48044i 0.425706 0.564601i
\(39\) 2.22332 0.356016
\(40\) 0 0
\(41\) 1.79322 0.652678i 0.280054 0.101931i −0.198175 0.980167i \(-0.563501\pi\)
0.478228 + 0.878236i \(0.341279\pi\)
\(42\) 2.76117 0.486869i 0.426058 0.0751256i
\(43\) 1.45618 + 0.256764i 0.222065 + 0.0391561i 0.283574 0.958950i \(-0.408480\pi\)
−0.0615084 + 0.998107i \(0.519591\pi\)
\(44\) −5.04528 1.83633i −0.760604 0.276837i
\(45\) 0 0
\(46\) 2.66945 4.62363i 0.393590 0.681717i
\(47\) 2.00570 + 2.39030i 0.292561 + 0.348661i 0.892225 0.451591i \(-0.149143\pi\)
−0.599664 + 0.800252i \(0.704699\pi\)
\(48\) 0.370510 + 0.441556i 0.0534785 + 0.0637331i
\(49\) 8.33016 14.4283i 1.19002 2.06118i
\(50\) 0 0
\(51\) −0.759442 0.276414i −0.106343 0.0387058i
\(52\) 3.79858 + 0.669793i 0.526769 + 0.0928835i
\(53\) 1.77266 0.312568i 0.243494 0.0429346i −0.0505691 0.998721i \(-0.516104\pi\)
0.294063 + 0.955786i \(0.404992\pi\)
\(54\) 3.06993 1.11736i 0.417765 0.152054i
\(55\) 0 0
\(56\) 4.86419 0.650004
\(57\) 0.981070 + 2.31306i 0.129946 + 0.306372i
\(58\) 3.63378i 0.477139i
\(59\) 5.61133 + 4.70846i 0.730532 + 0.612990i 0.930277 0.366859i \(-0.119567\pi\)
−0.199744 + 0.979848i \(0.564011\pi\)
\(60\) 0 0
\(61\) 1.40916 + 7.99176i 0.180425 + 1.02324i 0.931694 + 0.363244i \(0.118331\pi\)
−0.751269 + 0.659996i \(0.770558\pi\)
\(62\) 8.07914 + 1.42457i 1.02605 + 0.180921i
\(63\) 4.43820 12.1939i 0.559161 1.53628i
\(64\) 0.500000 + 0.866025i 0.0625000 + 0.108253i
\(65\) 0 0
\(66\) 2.37075 1.98929i 0.291819 0.244865i
\(67\) −5.42827 6.46916i −0.663169 0.790334i 0.324668 0.945828i \(-0.394747\pi\)
−0.987837 + 0.155494i \(0.950303\pi\)
\(68\) −1.21425 0.701047i −0.147249 0.0850144i
\(69\) 1.53870 + 2.66511i 0.185238 + 0.320842i
\(70\) 0 0
\(71\) 1.04647 5.93485i 0.124194 0.704337i −0.857590 0.514334i \(-0.828039\pi\)
0.981783 0.190003i \(-0.0608498\pi\)
\(72\) 2.62722 0.463250i 0.309621 0.0545945i
\(73\) 0.436515 + 1.19931i 0.0510902 + 0.140369i 0.962613 0.270880i \(-0.0873148\pi\)
−0.911523 + 0.411249i \(0.865093\pi\)
\(74\) −8.01234 6.72316i −0.931416 0.781551i
\(75\) 0 0
\(76\) 0.979350 + 4.24746i 0.112339 + 0.487217i
\(77\) 26.1162i 2.97621i
\(78\) −1.42912 + 1.70316i −0.161816 + 0.192845i
\(79\) −15.6290 + 5.68848i −1.75840 + 0.640004i −0.999931 0.0117101i \(-0.996272\pi\)
−0.758465 + 0.651714i \(0.774050\pi\)
\(80\) 0 0
\(81\) 1.06275 6.02717i 0.118084 0.669685i
\(82\) −0.652678 + 1.79322i −0.0720762 + 0.198028i
\(83\) 12.5236 7.23049i 1.37464 0.793649i 0.383133 0.923693i \(-0.374845\pi\)
0.991508 + 0.130044i \(0.0415119\pi\)
\(84\) −1.40188 + 2.42814i −0.152958 + 0.264931i
\(85\) 0 0
\(86\) −1.13271 + 0.950453i −0.122143 + 0.102490i
\(87\) −1.81393 1.04727i −0.194474 0.112280i
\(88\) 4.64975 2.68454i 0.495665 0.286172i
\(89\) 9.02905 + 3.28630i 0.957077 + 0.348348i 0.772887 0.634543i \(-0.218812\pi\)
0.184190 + 0.982891i \(0.441034\pi\)
\(90\) 0 0
\(91\) 3.25800 + 18.4770i 0.341531 + 1.93692i
\(92\) 1.82601 + 5.01693i 0.190375 + 0.523051i
\(93\) −3.03958 + 3.62243i −0.315189 + 0.375628i
\(94\) −3.12031 −0.321836
\(95\) 0 0
\(96\) −0.576411 −0.0588297
\(97\) −3.90758 + 4.65687i −0.396755 + 0.472834i −0.927028 0.374993i \(-0.877645\pi\)
0.530273 + 0.847827i \(0.322089\pi\)
\(98\) 5.69817 + 15.6556i 0.575602 + 1.58145i
\(99\) −2.48722 14.1057i −0.249975 1.41768i
\(100\) 0 0
\(101\) −1.17995 0.429466i −0.117409 0.0427335i 0.282647 0.959224i \(-0.408787\pi\)
−0.400057 + 0.916490i \(0.631010\pi\)
\(102\) 0.699906 0.404091i 0.0693010 0.0400109i
\(103\) −6.38005 3.68352i −0.628645 0.362948i 0.151582 0.988445i \(-0.451563\pi\)
−0.780227 + 0.625496i \(0.784897\pi\)
\(104\) −2.95477 + 2.47935i −0.289739 + 0.243120i
\(105\) 0 0
\(106\) −0.900005 + 1.55885i −0.0874162 + 0.151409i
\(107\) 7.56108 4.36539i 0.730957 0.422018i −0.0878153 0.996137i \(-0.527989\pi\)
0.818772 + 0.574119i \(0.194655\pi\)
\(108\) −1.11736 + 3.06993i −0.107518 + 0.295404i
\(109\) −1.41173 + 8.00630i −0.135219 + 0.766865i 0.839488 + 0.543378i \(0.182855\pi\)
−0.974707 + 0.223487i \(0.928256\pi\)
\(110\) 0 0
\(111\) 5.66531 2.06200i 0.537727 0.195717i
\(112\) −3.12664 + 3.72618i −0.295440 + 0.352091i
\(113\) 4.48210i 0.421640i −0.977525 0.210820i \(-0.932387\pi\)
0.977525 0.210820i \(-0.0676134\pi\)
\(114\) −2.40253 0.735261i −0.225017 0.0688635i
\(115\) 0 0
\(116\) −2.78364 2.33575i −0.258454 0.216869i
\(117\) 3.51939 + 9.66944i 0.325368 + 0.893940i
\(118\) −7.21378 + 1.27198i −0.664082 + 0.117096i
\(119\) 1.18429 6.71643i 0.108564 0.615694i
\(120\) 0 0
\(121\) −8.91346 15.4386i −0.810314 1.40351i
\(122\) −7.02784 4.05753i −0.636271 0.367351i
\(123\) −0.707045 0.842623i −0.0637521 0.0759768i
\(124\) −6.28445 + 5.27328i −0.564361 + 0.473555i
\(125\) 0 0
\(126\) 6.48822 + 11.2379i 0.578017 + 1.00115i
\(127\) 0.0476033 0.130789i 0.00422411 0.0116057i −0.937563 0.347816i \(-0.886923\pi\)
0.941787 + 0.336211i \(0.109145\pi\)
\(128\) −0.984808 0.173648i −0.0870455 0.0153485i
\(129\) −0.148001 0.839357i −0.0130308 0.0739013i
\(130\) 0 0
\(131\) 9.52200 + 7.98991i 0.831941 + 0.698082i 0.955736 0.294226i \(-0.0950620\pi\)
−0.123795 + 0.992308i \(0.539506\pi\)
\(132\) 3.09479i 0.269367i
\(133\) −17.7851 + 11.5427i −1.54217 + 1.00088i
\(134\) 8.44489 0.729528
\(135\) 0 0
\(136\) 1.31754 0.479544i 0.112978 0.0411206i
\(137\) −14.1631 + 2.49734i −1.21004 + 0.213362i −0.742032 0.670364i \(-0.766138\pi\)
−0.468004 + 0.883726i \(0.655027\pi\)
\(138\) −3.03065 0.534386i −0.257986 0.0454899i
\(139\) 16.7746 + 6.10544i 1.42280 + 0.517857i 0.934859 0.355020i \(-0.115526\pi\)
0.487941 + 0.872877i \(0.337748\pi\)
\(140\) 0 0
\(141\) 0.899291 1.55762i 0.0757340 0.131175i
\(142\) 3.87370 + 4.61650i 0.325074 + 0.387408i
\(143\) 13.3118 + 15.8644i 1.11319 + 1.32665i
\(144\) −1.33388 + 2.31034i −0.111156 + 0.192528i
\(145\) 0 0
\(146\) −1.19931 0.436515i −0.0992559 0.0361262i
\(147\) −9.45729 1.66758i −0.780024 0.137539i
\(148\) 10.3005 1.81625i 0.846694 0.149295i
\(149\) −2.71250 + 0.987271i −0.222217 + 0.0808804i −0.450729 0.892661i \(-0.648836\pi\)
0.228512 + 0.973541i \(0.426614\pi\)
\(150\) 0 0
\(151\) 2.01805 0.164226 0.0821132 0.996623i \(-0.473833\pi\)
0.0821132 + 0.996623i \(0.473833\pi\)
\(152\) −3.88325 1.97999i −0.314973 0.160598i
\(153\) 3.74044i 0.302396i
\(154\) 20.0061 + 16.7871i 1.61214 + 1.35275i
\(155\) 0 0
\(156\) −0.386076 2.18954i −0.0309108 0.175304i
\(157\) 10.8717 + 1.91697i 0.867655 + 0.152991i 0.589719 0.807609i \(-0.299239\pi\)
0.277936 + 0.960600i \(0.410350\pi\)
\(158\) 5.68848 15.6290i 0.452551 1.24337i
\(159\) −0.518772 0.898540i −0.0411413 0.0712589i
\(160\) 0 0
\(161\) −19.8938 + 16.6928i −1.56785 + 1.31558i
\(162\) 3.93395 + 4.68830i 0.309081 + 0.368348i
\(163\) 5.13439 + 2.96434i 0.402157 + 0.232185i 0.687414 0.726266i \(-0.258746\pi\)
−0.285257 + 0.958451i \(0.592079\pi\)
\(164\) −0.954151 1.65264i −0.0745067 0.129049i
\(165\) 0 0
\(166\) −2.51112 + 14.2413i −0.194901 + 1.10534i
\(167\) 7.11784 1.25507i 0.550795 0.0971200i 0.108677 0.994077i \(-0.465339\pi\)
0.442118 + 0.896957i \(0.354227\pi\)
\(168\) −0.958946 2.63468i −0.0739843 0.203270i
\(169\) −1.43852 1.20707i −0.110656 0.0928512i
\(170\) 0 0
\(171\) −8.50673 + 7.92821i −0.650526 + 0.606285i
\(172\) 1.47864i 0.112745i
\(173\) 3.31585 3.95167i 0.252099 0.300440i −0.625121 0.780528i \(-0.714951\pi\)
0.877221 + 0.480087i \(0.159395\pi\)
\(174\) 1.96823 0.716378i 0.149211 0.0543085i
\(175\) 0 0
\(176\) −0.932329 + 5.28750i −0.0702770 + 0.398560i
\(177\) 1.44409 3.96761i 0.108545 0.298224i
\(178\) −8.32122 + 4.80426i −0.623701 + 0.360094i
\(179\) 4.09186 7.08730i 0.305840 0.529730i −0.671608 0.740906i \(-0.734396\pi\)
0.977448 + 0.211177i \(0.0677295\pi\)
\(180\) 0 0
\(181\) −2.62934 + 2.20628i −0.195437 + 0.163991i −0.735255 0.677791i \(-0.762938\pi\)
0.539818 + 0.841782i \(0.318493\pi\)
\(182\) −16.2484 9.38103i −1.20441 0.695368i
\(183\) 4.05092 2.33880i 0.299453 0.172889i
\(184\) −5.01693 1.82601i −0.369853 0.134616i
\(185\) 0 0
\(186\) −0.821137 4.65690i −0.0602087 0.341461i
\(187\) −2.57471 7.07395i −0.188281 0.517298i
\(188\) 2.00570 2.39030i 0.146281 0.174330i
\(189\) −15.8911 −1.15591
\(190\) 0 0
\(191\) 3.77584 0.273210 0.136605 0.990626i \(-0.456381\pi\)
0.136605 + 0.990626i \(0.456381\pi\)
\(192\) 0.370510 0.441556i 0.0267392 0.0318666i
\(193\) −4.16508 11.4435i −0.299809 0.823718i −0.994531 0.104440i \(-0.966695\pi\)
0.694722 0.719278i \(-0.255527\pi\)
\(194\) −1.05563 5.98676i −0.0757896 0.429824i
\(195\) 0 0
\(196\) −15.6556 5.69817i −1.11826 0.407012i
\(197\) −6.23743 + 3.60118i −0.444399 + 0.256574i −0.705462 0.708748i \(-0.749260\pi\)
0.261063 + 0.965322i \(0.415927\pi\)
\(198\) 12.4044 + 7.16167i 0.881541 + 0.508958i
\(199\) −4.47147 + 3.75201i −0.316974 + 0.265973i −0.787367 0.616484i \(-0.788557\pi\)
0.470393 + 0.882457i \(0.344112\pi\)
\(200\) 0 0
\(201\) −2.43386 + 4.21557i −0.171671 + 0.297344i
\(202\) 1.08745 0.627838i 0.0765125 0.0441745i
\(203\) 6.04534 16.6094i 0.424299 1.16575i
\(204\) −0.140339 + 0.795903i −0.00982571 + 0.0557244i
\(205\) 0 0
\(206\) 6.92276 2.51968i 0.482332 0.175554i
\(207\) −9.15514 + 10.9107i −0.636327 + 0.758344i
\(208\) 3.85718i 0.267448i
\(209\) −10.6307 + 20.8495i −0.735340 + 1.44219i
\(210\) 0 0
\(211\) 8.17443 + 6.85916i 0.562751 + 0.472204i 0.879231 0.476395i \(-0.158057\pi\)
−0.316481 + 0.948599i \(0.602501\pi\)
\(212\) −0.615640 1.69146i −0.0422823 0.116170i
\(213\) −3.42091 + 0.603199i −0.234397 + 0.0413305i
\(214\) −1.51608 + 8.59814i −0.103637 + 0.587757i
\(215\) 0 0
\(216\) −1.63348 2.82926i −0.111144 0.192507i
\(217\) −34.5585 19.9523i −2.34598 1.35445i
\(218\) −5.22574 6.22780i −0.353932 0.421800i
\(219\) 0.563551 0.472875i 0.0380812 0.0319539i
\(220\) 0 0
\(221\) 2.70407 + 4.68358i 0.181895 + 0.315052i
\(222\) −2.06200 + 5.66531i −0.138393 + 0.380231i
\(223\) −0.0979573 0.0172725i −0.00655971 0.00115665i 0.170367 0.985381i \(-0.445505\pi\)
−0.176927 + 0.984224i \(0.556616\pi\)
\(224\) −0.844657 4.79029i −0.0564360 0.320065i
\(225\) 0 0
\(226\) 3.43349 + 2.88104i 0.228392 + 0.191644i
\(227\) 13.8262i 0.917680i 0.888519 + 0.458840i \(0.151735\pi\)
−0.888519 + 0.458840i \(0.848265\pi\)
\(228\) 2.10756 1.36782i 0.139576 0.0905864i
\(229\) −15.5752 −1.02924 −0.514619 0.857419i \(-0.672066\pi\)
−0.514619 + 0.857419i \(0.672066\pi\)
\(230\) 0 0
\(231\) −14.1458 + 5.14865i −0.930725 + 0.338756i
\(232\) 3.57857 0.630999i 0.234945 0.0414271i
\(233\) −15.0095 2.64658i −0.983307 0.173384i −0.341193 0.939993i \(-0.610831\pi\)
−0.642113 + 0.766610i \(0.721942\pi\)
\(234\) −9.66944 3.51939i −0.632111 0.230070i
\(235\) 0 0
\(236\) 3.66253 6.34369i 0.238411 0.412939i
\(237\) 6.16232 + 7.34396i 0.400285 + 0.477042i
\(238\) 4.38384 + 5.22446i 0.284162 + 0.338651i
\(239\) 8.41167 14.5694i 0.544106 0.942419i −0.454557 0.890718i \(-0.650202\pi\)
0.998663 0.0517011i \(-0.0164643\pi\)
\(240\) 0 0
\(241\) 8.55776 + 3.11477i 0.551254 + 0.200640i 0.602604 0.798041i \(-0.294130\pi\)
−0.0513496 + 0.998681i \(0.516352\pi\)
\(242\) 17.5561 + 3.09561i 1.12855 + 0.198993i
\(243\) −13.1261 + 2.31448i −0.842039 + 0.148474i
\(244\) 7.62565 2.77551i 0.488182 0.177684i
\(245\) 0 0
\(246\) 1.09997 0.0701313
\(247\) 4.92017 16.0770i 0.313063 1.02296i
\(248\) 8.20377i 0.520940i
\(249\) −6.38533 5.35793i −0.404654 0.339545i
\(250\) 0 0
\(251\) 2.91829 + 16.5504i 0.184201 + 1.04465i 0.926978 + 0.375116i \(0.122397\pi\)
−0.742777 + 0.669539i \(0.766492\pi\)
\(252\) −12.7793 2.25334i −0.805020 0.141947i
\(253\) −9.80400 + 26.9363i −0.616372 + 1.69347i
\(254\) 0.0695914 + 0.120536i 0.00436655 + 0.00756309i
\(255\) 0 0
\(256\) 0.766044 0.642788i 0.0478778 0.0401742i
\(257\) 6.36185 + 7.58176i 0.396841 + 0.472937i 0.927054 0.374927i \(-0.122332\pi\)
−0.530213 + 0.847865i \(0.677888\pi\)
\(258\) 0.738118 + 0.426153i 0.0459532 + 0.0265311i
\(259\) 25.4382 + 44.0602i 1.58065 + 2.73777i
\(260\) 0 0
\(261\) 1.68335 9.54674i 0.104197 0.590929i
\(262\) −12.2412 + 2.15846i −0.756267 + 0.133350i
\(263\) 7.66554 + 21.0609i 0.472677 + 1.29867i 0.915593 + 0.402107i \(0.131722\pi\)
−0.442915 + 0.896564i \(0.646056\pi\)
\(264\) −2.37075 1.98929i −0.145909 0.122432i
\(265\) 0 0
\(266\) 2.58983 21.0437i 0.158793 1.29027i
\(267\) 5.53845i 0.338948i
\(268\) −5.42827 + 6.46916i −0.331584 + 0.395167i
\(269\) 7.02217 2.55586i 0.428149 0.155834i −0.118952 0.992900i \(-0.537953\pi\)
0.547101 + 0.837066i \(0.315731\pi\)
\(270\) 0 0
\(271\) −1.84950 + 10.4890i −0.112349 + 0.637163i 0.875680 + 0.482893i \(0.160414\pi\)
−0.988029 + 0.154271i \(0.950697\pi\)
\(272\) −0.479544 + 1.31754i −0.0290766 + 0.0798874i
\(273\) 9.36576 5.40733i 0.566842 0.327266i
\(274\) 7.19080 12.4548i 0.434412 0.752424i
\(275\) 0 0
\(276\) 2.35743 1.97812i 0.141900 0.119069i
\(277\) −2.01467 1.16317i −0.121050 0.0698880i 0.438253 0.898852i \(-0.355598\pi\)
−0.559302 + 0.828964i \(0.688931\pi\)
\(278\) −15.4595 + 8.92555i −0.927200 + 0.535319i
\(279\) −20.5658 7.48532i −1.23124 0.448135i
\(280\) 0 0
\(281\) −2.96472 16.8137i −0.176860 1.00302i −0.935975 0.352067i \(-0.885479\pi\)
0.759115 0.650957i \(-0.225632\pi\)
\(282\) 0.615151 + 1.69011i 0.0366317 + 0.100645i
\(283\) −5.44307 + 6.48680i −0.323557 + 0.385600i −0.903164 0.429296i \(-0.858762\pi\)
0.579607 + 0.814896i \(0.303206\pi\)
\(284\) −6.02641 −0.357601
\(285\) 0 0
\(286\) −20.7095 −1.22458
\(287\) 5.96658 7.11069i 0.352196 0.419731i
\(288\) −0.912424 2.50687i −0.0537651 0.147718i
\(289\) 2.61065 + 14.8057i 0.153568 + 0.870925i
\(290\) 0 0
\(291\) 3.29275 + 1.19846i 0.193024 + 0.0702551i
\(292\) 1.10529 0.638142i 0.0646824 0.0373444i
\(293\) 2.24512 + 1.29622i 0.131161 + 0.0757260i 0.564145 0.825676i \(-0.309206\pi\)
−0.432984 + 0.901402i \(0.642539\pi\)
\(294\) 7.35647 6.17281i 0.429038 0.360006i
\(295\) 0 0
\(296\) −5.22969 + 9.05808i −0.303969 + 0.526490i
\(297\) −15.1905 + 8.77025i −0.881443 + 0.508901i
\(298\) 0.987271 2.71250i 0.0571911 0.157131i
\(299\) 3.57596 20.2803i 0.206803 1.17284i
\(300\) 0 0
\(301\) 6.75864 2.45994i 0.389562 0.141789i
\(302\) −1.29718 + 1.54591i −0.0746441 + 0.0889573i
\(303\) 0.723785i 0.0415804i
\(304\) 4.01286 1.70203i 0.230154 0.0976183i
\(305\) 0 0
\(306\) 2.86534 + 2.40431i 0.163801 + 0.137445i
\(307\) −1.40970 3.87311i −0.0804557 0.221050i 0.892942 0.450171i \(-0.148637\pi\)
−0.973398 + 0.229121i \(0.926415\pi\)
\(308\) −25.7194 + 4.53502i −1.46550 + 0.258407i
\(309\) −0.737387 + 4.18193i −0.0419485 + 0.237902i
\(310\) 0 0
\(311\) −1.24153 2.15040i −0.0704008 0.121938i 0.828676 0.559728i \(-0.189094\pi\)
−0.899077 + 0.437791i \(0.855761\pi\)
\(312\) 1.92545 + 1.11166i 0.109007 + 0.0629354i
\(313\) 3.45913 + 4.12243i 0.195522 + 0.233014i 0.854894 0.518803i \(-0.173622\pi\)
−0.659372 + 0.751817i \(0.729178\pi\)
\(314\) −8.45667 + 7.09599i −0.477238 + 0.400450i
\(315\) 0 0
\(316\) 8.31600 + 14.4037i 0.467812 + 0.810273i
\(317\) −6.65753 + 18.2914i −0.373924 + 1.02735i 0.599906 + 0.800071i \(0.295205\pi\)
−0.973830 + 0.227278i \(0.927017\pi\)
\(318\) 1.02178 + 0.180168i 0.0572987 + 0.0101033i
\(319\) −3.38788 19.2136i −0.189685 1.07576i
\(320\) 0 0
\(321\) −3.85513 3.23484i −0.215172 0.180551i
\(322\) 25.9695i 1.44722i
\(323\) −3.67941 + 4.87990i −0.204728 + 0.271525i
\(324\) −6.12015 −0.340008
\(325\) 0 0
\(326\) −5.57114 + 2.02773i −0.308557 + 0.112306i
\(327\) 4.61492 0.813735i 0.255206 0.0449996i
\(328\) 1.87931 + 0.331373i 0.103768 + 0.0182970i
\(329\) 14.2625 + 5.19111i 0.786315 + 0.286195i
\(330\) 0 0
\(331\) 9.35511 16.2035i 0.514203 0.890626i −0.485661 0.874147i \(-0.661421\pi\)
0.999864 0.0164787i \(-0.00524557\pi\)
\(332\) −9.29534 11.0778i −0.510148 0.607971i
\(333\) 17.9357 + 21.3749i 0.982870 + 1.17134i
\(334\) −3.61382 + 6.25932i −0.197739 + 0.342495i
\(335\) 0 0
\(336\) 2.63468 + 0.958946i 0.143734 + 0.0523148i
\(337\) 24.7159 + 4.35808i 1.34636 + 0.237400i 0.799924 0.600101i \(-0.204873\pi\)
0.546436 + 0.837501i \(0.315984\pi\)
\(338\) 1.84933 0.326087i 0.100590 0.0177368i
\(339\) −2.42772 + 0.883619i −0.131856 + 0.0479916i
\(340\) 0 0
\(341\) −44.0466 −2.38526
\(342\) −0.605335 11.6127i −0.0327328 0.627942i
\(343\) 46.9896i 2.53720i
\(344\) 1.13271 + 0.950453i 0.0610714 + 0.0512450i
\(345\) 0 0
\(346\) 0.895772 + 5.08018i 0.0481570 + 0.273112i
\(347\) −22.4078 3.95111i −1.20292 0.212107i −0.463957 0.885857i \(-0.653571\pi\)
−0.738958 + 0.673751i \(0.764682\pi\)
\(348\) −0.716378 + 1.96823i −0.0384019 + 0.105508i
\(349\) 6.58190 + 11.4002i 0.352321 + 0.610238i 0.986656 0.162820i \(-0.0520591\pi\)
−0.634335 + 0.773059i \(0.718726\pi\)
\(350\) 0 0
\(351\) 9.65310 8.09992i 0.515245 0.432341i
\(352\) −3.45117 4.11295i −0.183948 0.219221i
\(353\) 10.6570 + 6.15281i 0.567213 + 0.327481i 0.756036 0.654530i \(-0.227134\pi\)
−0.188822 + 0.982011i \(0.560467\pi\)
\(354\) 2.11112 + 3.65657i 0.112205 + 0.194345i
\(355\) 0 0
\(356\) 1.66850 9.46254i 0.0884304 0.501513i
\(357\) −3.87142 + 0.682636i −0.204897 + 0.0361290i
\(358\) 2.79899 + 7.69017i 0.147931 + 0.406438i
\(359\) −9.62244 8.07418i −0.507853 0.426139i 0.352520 0.935804i \(-0.385325\pi\)
−0.860373 + 0.509665i \(0.829769\pi\)
\(360\) 0 0
\(361\) 18.8970 1.97546i 0.994580 0.103972i
\(362\) 3.43236i 0.180401i
\(363\) −6.60504 + 7.87158i −0.346675 + 0.413151i
\(364\) 17.6306 6.41700i 0.924093 0.336342i
\(365\) 0 0
\(366\) −0.812257 + 4.60654i −0.0424574 + 0.240788i
\(367\) −0.918156 + 2.52261i −0.0479274 + 0.131679i −0.961347 0.275340i \(-0.911210\pi\)
0.913420 + 0.407019i \(0.133432\pi\)
\(368\) 4.62363 2.66945i 0.241023 0.139155i
\(369\) 2.54544 4.40883i 0.132510 0.229514i
\(370\) 0 0
\(371\) 6.70717 5.62798i 0.348219 0.292190i
\(372\) 4.09521 + 2.36437i 0.212327 + 0.122587i
\(373\) −16.0582 + 9.27119i −0.831461 + 0.480044i −0.854353 0.519694i \(-0.826046\pi\)
0.0228917 + 0.999738i \(0.492713\pi\)
\(374\) 7.07395 + 2.57471i 0.365785 + 0.133135i
\(375\) 0 0
\(376\) 0.541837 + 3.07291i 0.0279431 + 0.158473i
\(377\) 4.79381 + 13.1709i 0.246894 + 0.678334i
\(378\) 10.2146 12.1733i 0.525381 0.626125i
\(379\) −11.5855 −0.595108 −0.297554 0.954705i \(-0.596171\pi\)
−0.297554 + 0.954705i \(0.596171\pi\)
\(380\) 0 0
\(381\) −0.0802265 −0.00411013
\(382\) −2.42706 + 2.89246i −0.124179 + 0.147991i
\(383\) −9.94564 27.3254i −0.508199 1.39626i −0.883094 0.469197i \(-0.844543\pi\)
0.374895 0.927067i \(-0.377679\pi\)
\(384\) 0.100093 + 0.567654i 0.00510783 + 0.0289680i
\(385\) 0 0
\(386\) 11.4435 + 4.16508i 0.582457 + 0.211997i
\(387\) 3.41617 1.97233i 0.173654 0.100259i
\(388\) 5.26467 + 3.03956i 0.267273 + 0.154310i
\(389\) −22.8144 + 19.1436i −1.15674 + 0.970618i −0.999856 0.0169993i \(-0.994589\pi\)
−0.156882 + 0.987617i \(0.550144\pi\)
\(390\) 0 0
\(391\) −3.74282 + 6.48276i −0.189283 + 0.327847i
\(392\) 14.4283 8.33016i 0.728737 0.420737i
\(393\) 2.45052 6.73274i 0.123612 0.339622i
\(394\) 1.25068 7.09294i 0.0630082 0.357337i
\(395\) 0 0
\(396\) −13.4595 + 4.89887i −0.676367 + 0.246178i
\(397\) 4.03025 4.80307i 0.202273 0.241059i −0.655367 0.755311i \(-0.727486\pi\)
0.857639 + 0.514252i \(0.171930\pi\)
\(398\) 5.83709i 0.292587i
\(399\) 9.75834 + 7.35772i 0.488528 + 0.368347i
\(400\) 0 0
\(401\) 7.58485 + 6.36445i 0.378769 + 0.317825i 0.812219 0.583353i \(-0.198259\pi\)
−0.433450 + 0.901178i \(0.642704\pi\)
\(402\) −1.66486 4.57417i −0.0830357 0.228139i
\(403\) 31.1627 5.49483i 1.55233 0.273717i
\(404\) −0.218046 + 1.23660i −0.0108482 + 0.0615231i
\(405\) 0 0
\(406\) 8.83769 + 15.3073i 0.438607 + 0.759690i
\(407\) 48.6335 + 28.0786i 2.41067 + 1.39180i
\(408\) −0.519489 0.619103i −0.0257185 0.0306502i
\(409\) 23.4859 19.7070i 1.16130 0.974449i 0.161380 0.986892i \(-0.448405\pi\)
0.999923 + 0.0124433i \(0.00396092\pi\)
\(410\) 0 0
\(411\) 4.14486 + 7.17910i 0.204451 + 0.354119i
\(412\) −2.51968 + 6.92276i −0.124136 + 0.341060i
\(413\) 35.0892 + 6.18717i 1.72663 + 0.304451i
\(414\) −2.47325 14.0265i −0.121554 0.689365i
\(415\) 0 0
\(416\) 2.95477 + 2.47935i 0.144870 + 0.121560i
\(417\) 10.2896i 0.503882i
\(418\) −9.13834 21.5454i −0.446971 1.05382i
\(419\) −17.9296 −0.875916 −0.437958 0.898995i \(-0.644298\pi\)
−0.437958 + 0.898995i \(0.644298\pi\)
\(420\) 0 0
\(421\) 30.2850 11.0228i 1.47600 0.537220i 0.526278 0.850313i \(-0.323587\pi\)
0.949723 + 0.313093i \(0.101365\pi\)
\(422\) −10.5088 + 1.85299i −0.511562 + 0.0902022i
\(423\) 8.19775 + 1.44549i 0.398588 + 0.0702819i
\(424\) 1.69146 + 0.615640i 0.0821444 + 0.0298981i
\(425\) 0 0
\(426\) 1.73684 3.00830i 0.0841503 0.145753i
\(427\) 25.3728 + 30.2382i 1.22788 + 1.46333i
\(428\) −5.61204 6.68816i −0.271268 0.323285i
\(429\) 5.96858 10.3379i 0.288166 0.499118i
\(430\) 0 0
\(431\) 1.30703 + 0.475720i 0.0629575 + 0.0229146i 0.373307 0.927708i \(-0.378224\pi\)
−0.310349 + 0.950623i \(0.600446\pi\)
\(432\) 3.21732 + 0.567300i 0.154793 + 0.0272942i
\(433\) −32.7483 + 5.77441i −1.57378 + 0.277500i −0.891304 0.453406i \(-0.850209\pi\)
−0.682478 + 0.730906i \(0.739098\pi\)
\(434\) 37.4981 13.6482i 1.79997 0.655135i
\(435\) 0 0
\(436\) 8.12981 0.389347
\(437\) 22.6768 5.22866i 1.08478 0.250121i
\(438\) 0.735663i 0.0351513i
\(439\) 27.6648 + 23.2135i 1.32037 + 1.10792i 0.986227 + 0.165397i \(0.0528906\pi\)
0.334141 + 0.942523i \(0.391554\pi\)
\(440\) 0 0
\(441\) −7.71789 43.7704i −0.367519 2.08430i
\(442\) −5.32597 0.939112i −0.253330 0.0446690i
\(443\) 10.9404 30.0586i 0.519795 1.42813i −0.350951 0.936394i \(-0.614142\pi\)
0.870746 0.491732i \(-0.163636\pi\)
\(444\) −3.01445 5.22118i −0.143059 0.247786i
\(445\) 0 0
\(446\) 0.0761973 0.0639371i 0.00360805 0.00302751i
\(447\) 1.06951 + 1.27459i 0.0505860 + 0.0602860i
\(448\) 4.21251 + 2.43209i 0.199022 + 0.114906i
\(449\) −1.09116 1.88995i −0.0514951 0.0891922i 0.839129 0.543933i \(-0.183065\pi\)
−0.890624 + 0.454741i \(0.849732\pi\)
\(450\) 0 0
\(451\) 1.77917 10.0902i 0.0837777 0.475127i
\(452\) −4.41400 + 0.778308i −0.207617 + 0.0366085i
\(453\) −0.397846 1.09307i −0.0186924 0.0513570i
\(454\) −10.5915 8.88734i −0.497084 0.417103i
\(455\) 0 0
\(456\) −0.306897 + 2.49370i −0.0143718 + 0.116778i
\(457\) 37.2037i 1.74031i 0.492774 + 0.870157i \(0.335983\pi\)
−0.492774 + 0.870157i \(0.664017\pi\)
\(458\) 10.0115 11.9313i 0.467808 0.557512i
\(459\) −4.30433 + 1.56665i −0.200909 + 0.0731248i
\(460\) 0 0
\(461\) −0.847556 + 4.80673i −0.0394746 + 0.223872i −0.998163 0.0605870i \(-0.980703\pi\)
0.958688 + 0.284459i \(0.0918138\pi\)
\(462\) 5.14865 14.1458i 0.239537 0.658122i
\(463\) −17.5133 + 10.1113i −0.813914 + 0.469913i −0.848313 0.529495i \(-0.822381\pi\)
0.0343994 + 0.999408i \(0.489048\pi\)
\(464\) −1.81689 + 3.14694i −0.0843470 + 0.146093i
\(465\) 0 0
\(466\) 11.6753 9.79677i 0.540850 0.453827i
\(467\) 33.7859 + 19.5063i 1.56342 + 0.902644i 0.996907 + 0.0785944i \(0.0250432\pi\)
0.566518 + 0.824049i \(0.308290\pi\)
\(468\) 8.91140 5.14500i 0.411930 0.237828i
\(469\) −38.6003 14.0493i −1.78239 0.648739i
\(470\) 0 0
\(471\) −1.10496 6.26656i −0.0509140 0.288748i
\(472\) 2.50532 + 6.88331i 0.115317 + 0.316830i
\(473\) 5.10305 6.08158i 0.234639 0.279631i
\(474\) −9.58686 −0.440339
\(475\) 0 0
\(476\) −6.82004 −0.312596
\(477\) 3.08665 3.67853i 0.141328 0.168428i
\(478\) 5.75392 + 15.8088i 0.263178 + 0.723076i
\(479\) 5.39865 + 30.6172i 0.246670 + 1.39894i 0.816581 + 0.577231i \(0.195867\pi\)
−0.569911 + 0.821707i \(0.693022\pi\)
\(480\) 0 0
\(481\) −37.9107 13.7984i −1.72858 0.629151i
\(482\) −7.88688 + 4.55349i −0.359237 + 0.207406i
\(483\) 12.9636 + 7.48453i 0.589864 + 0.340558i
\(484\) −13.6562 + 11.4589i −0.620737 + 0.520860i
\(485\) 0 0
\(486\) 6.66429 11.5429i 0.302298 0.523596i
\(487\) 24.2263 13.9870i 1.09780 0.633813i 0.162155 0.986765i \(-0.448155\pi\)
0.935641 + 0.352952i \(0.114822\pi\)
\(488\) −2.77551 + 7.62565i −0.125641 + 0.345197i
\(489\) 0.593418 3.36544i 0.0268353 0.152191i
\(490\) 0 0
\(491\) −2.79400 + 1.01693i −0.126091 + 0.0458935i −0.404295 0.914629i \(-0.632483\pi\)
0.278204 + 0.960522i \(0.410261\pi\)
\(492\) −0.707045 + 0.842623i −0.0318760 + 0.0379884i
\(493\) 5.09490i 0.229463i
\(494\) 9.15311 + 14.1032i 0.411818 + 0.634533i
\(495\) 0 0
\(496\) 6.28445 + 5.27328i 0.282180 + 0.236777i
\(497\) −10.0258 27.5458i −0.449720 1.23560i
\(498\) 8.20883 1.44744i 0.367846 0.0648612i
\(499\) −3.20155 + 18.1569i −0.143321 + 0.812815i 0.825379 + 0.564580i \(0.190962\pi\)
−0.968700 + 0.248235i \(0.920149\pi\)
\(500\) 0 0
\(501\) −2.08304 3.60794i −0.0930636 0.161191i
\(502\) −14.5542 8.40288i −0.649586 0.375039i
\(503\) 2.10120 + 2.50412i 0.0936881 + 0.111653i 0.810852 0.585252i \(-0.199004\pi\)
−0.717163 + 0.696905i \(0.754560\pi\)
\(504\) 9.94053 8.34110i 0.442786 0.371542i
\(505\) 0 0
\(506\) −14.3325 24.8246i −0.637157 1.10359i
\(507\) −0.370209 + 1.01714i −0.0164416 + 0.0451728i
\(508\) −0.137068 0.0241688i −0.00608142 0.00107232i
\(509\) −6.53272 37.0489i −0.289558 1.64216i −0.688536 0.725202i \(-0.741746\pi\)
0.398978 0.916960i \(-0.369365\pi\)
\(510\) 0 0
\(511\) 4.75567 + 3.99048i 0.210378 + 0.176528i
\(512\) 1.00000i 0.0441942i
\(513\) 12.6864 + 6.46852i 0.560118 + 0.285592i
\(514\) −9.89728 −0.436550
\(515\) 0 0
\(516\) −0.800905 + 0.291506i −0.0352579 + 0.0128328i
\(517\) 16.4987 2.90916i 0.725610 0.127945i
\(518\) −50.1034 8.83459i −2.20142 0.388169i
\(519\) −2.79412 1.01698i −0.122648 0.0446403i
\(520\) 0 0
\(521\) −15.7203 + 27.2284i −0.688719 + 1.19290i 0.283533 + 0.958962i \(0.408493\pi\)
−0.972252 + 0.233934i \(0.924840\pi\)
\(522\) 6.23119 + 7.42605i 0.272732 + 0.325029i
\(523\) 2.88381 + 3.43679i 0.126100 + 0.150280i 0.825400 0.564548i \(-0.190949\pi\)
−0.699300 + 0.714828i \(0.746505\pi\)
\(524\) 6.21505 10.7648i 0.271506 0.470261i
\(525\) 0 0
\(526\) −21.0609 7.66554i −0.918299 0.334233i
\(527\) −11.3277 1.99738i −0.493443 0.0870073i
\(528\) 3.04777 0.537405i 0.132637 0.0233875i
\(529\) 5.17201 1.88246i 0.224870 0.0818460i
\(530\) 0 0
\(531\) 19.5415 0.848027
\(532\) 14.4557 + 15.5106i 0.626735 + 0.672469i
\(533\) 7.36067i 0.318826i
\(534\) 4.24270 + 3.56005i 0.183599 + 0.154058i
\(535\) 0 0
\(536\) −1.46644 8.31660i −0.0633406 0.359222i
\(537\) −4.64551 0.819129i −0.200469 0.0353480i
\(538\) −2.55586 + 7.02217i −0.110191 + 0.302747i
\(539\) −44.7252 77.4664i −1.92645 3.33671i
\(540\) 0 0
\(541\) 17.0269 14.2873i 0.732045 0.614259i −0.198643 0.980072i \(-0.563653\pi\)
0.930688 + 0.365813i \(0.119209\pi\)
\(542\) −6.84623 8.15902i −0.294071 0.350460i
\(543\) 1.71339 + 0.989225i 0.0735285 + 0.0424517i
\(544\) −0.701047 1.21425i −0.0300571 0.0520605i
\(545\) 0 0
\(546\) −1.87794 + 10.6504i −0.0803686 + 0.455793i
\(547\) −28.4071 + 5.00894i −1.21460 + 0.214167i −0.744000 0.668180i \(-0.767074\pi\)
−0.470600 + 0.882347i \(0.655962\pi\)
\(548\) 4.91880 + 13.5143i 0.210121 + 0.577302i
\(549\) 16.5840 + 13.9157i 0.707790 + 0.593906i
\(550\) 0 0
\(551\) −11.5871 + 10.7991i −0.493629 + 0.460058i
\(552\) 3.07740i 0.130983i
\(553\) −52.0023 + 61.9739i −2.21136 + 2.63540i
\(554\) 2.18604 0.795654i 0.0928760 0.0338041i
\(555\) 0 0
\(556\) 3.09981 17.5799i 0.131461 0.745554i
\(557\) 9.58721 26.3406i 0.406223 1.11609i −0.552937 0.833223i \(-0.686493\pi\)
0.959160 0.282865i \(-0.0912850\pi\)
\(558\) 18.9535 10.9428i 0.802366 0.463246i
\(559\) −2.85170 + 4.93929i −0.120614 + 0.208910i
\(560\) 0 0
\(561\) −3.32401 + 2.78917i −0.140340 + 0.117759i
\(562\) 14.7858 + 8.53656i 0.623699 + 0.360093i
\(563\) −5.69177 + 3.28614i −0.239879 + 0.138494i −0.615121 0.788432i \(-0.710893\pi\)
0.375242 + 0.926927i \(0.377560\pi\)
\(564\) −1.69011 0.615151i −0.0711666 0.0259025i
\(565\) 0 0
\(566\) −1.47044 8.33927i −0.0618071 0.350526i
\(567\) −10.1818 27.9742i −0.427595 1.17481i
\(568\) 3.87370 4.61650i 0.162537 0.193704i
\(569\) −3.90032 −0.163510 −0.0817549 0.996652i \(-0.526052\pi\)
−0.0817549 + 0.996652i \(0.526052\pi\)
\(570\) 0 0
\(571\) 18.1559 0.759802 0.379901 0.925027i \(-0.375958\pi\)
0.379901 + 0.925027i \(0.375958\pi\)
\(572\) 13.3118 15.8644i 0.556594 0.663323i
\(573\) −0.744385 2.04518i −0.0310971 0.0854386i
\(574\) 1.61186 + 9.14132i 0.0672778 + 0.381551i
\(575\) 0 0
\(576\) 2.50687 + 0.912424i 0.104453 + 0.0380177i
\(577\) −12.1402 + 7.00915i −0.505403 + 0.291795i −0.730942 0.682439i \(-0.760919\pi\)
0.225539 + 0.974234i \(0.427586\pi\)
\(578\) −13.0199 7.51707i −0.541558 0.312669i
\(579\) −5.37721 + 4.51202i −0.223469 + 0.187513i
\(580\) 0 0
\(581\) 35.1705 60.9170i 1.45912 2.52726i
\(582\) −3.03461 + 1.75203i −0.125789 + 0.0726241i
\(583\) 3.30541 9.08155i 0.136896 0.376119i
\(584\) −0.221624 + 1.25689i −0.00917088 + 0.0520106i
\(585\) 0 0
\(586\) −2.43610 + 0.886667i −0.100634 + 0.0366279i
\(587\) −4.89246 + 5.83061i −0.201933 + 0.240655i −0.857502 0.514481i \(-0.827985\pi\)
0.655568 + 0.755136i \(0.272429\pi\)
\(588\) 9.60319i 0.396029i
\(589\) 19.4676 + 29.9958i 0.802148 + 1.23596i
\(590\) 0 0
\(591\) 3.18025 + 2.66855i 0.130818 + 0.109769i
\(592\) −3.57732 9.82860i −0.147027 0.403953i
\(593\) 9.27933 1.63620i 0.381056 0.0671905i 0.0201608 0.999797i \(-0.493582\pi\)
0.360896 + 0.932606i \(0.382471\pi\)
\(594\) 3.04587 17.2740i 0.124974 0.708761i
\(595\) 0 0
\(596\) 1.44329 + 2.49986i 0.0591196 + 0.102398i
\(597\) 2.91380 + 1.68228i 0.119254 + 0.0688512i
\(598\) 13.2370 + 15.7753i 0.541302 + 0.645099i
\(599\) −10.7502 + 9.02053i −0.439243 + 0.368569i −0.835426 0.549603i \(-0.814779\pi\)
0.396183 + 0.918172i \(0.370335\pi\)
\(600\) 0 0
\(601\) 6.78599 + 11.7537i 0.276806 + 0.479443i 0.970589 0.240742i \(-0.0773906\pi\)
−0.693783 + 0.720184i \(0.744057\pi\)
\(602\) −2.45994 + 6.75864i −0.100260 + 0.275462i
\(603\) −22.1866 3.91210i −0.903508 0.159313i
\(604\) −0.350430 1.98739i −0.0142588 0.0808657i
\(605\) 0 0
\(606\) −0.554451 0.465240i −0.0225231 0.0188991i
\(607\) 2.07689i 0.0842984i −0.999111 0.0421492i \(-0.986580\pi\)
0.999111 0.0421492i \(-0.0134205\pi\)
\(608\) −1.27559 + 4.16808i −0.0517318 + 0.169038i
\(609\) −10.1883 −0.412850
\(610\) 0 0
\(611\) −11.3098 + 4.11642i −0.457545 + 0.166533i
\(612\) −3.68361 + 0.649520i −0.148901 + 0.0262553i
\(613\) −16.2680 2.86849i −0.657059 0.115857i −0.164828 0.986322i \(-0.552707\pi\)
−0.492230 + 0.870465i \(0.663818\pi\)
\(614\) 3.87311 + 1.40970i 0.156306 + 0.0568908i
\(615\) 0 0
\(616\) 13.0581 22.6173i 0.526125 0.911275i
\(617\) −14.7080 17.5283i −0.592120 0.705661i 0.383892 0.923378i \(-0.374583\pi\)
−0.976012 + 0.217717i \(0.930139\pi\)
\(618\) −2.72956 3.25297i −0.109799 0.130853i
\(619\) −6.66514 + 11.5444i −0.267895 + 0.464007i −0.968318 0.249721i \(-0.919661\pi\)
0.700423 + 0.713728i \(0.252995\pi\)
\(620\) 0 0
\(621\) 16.3901 + 5.96550i 0.657711 + 0.239387i
\(622\) 2.44534 + 0.431179i 0.0980492 + 0.0172887i
\(623\) 46.0276 8.11590i 1.84406 0.325157i
\(624\) −2.08924 + 0.760421i −0.0836365 + 0.0304412i
\(625\) 0 0
\(626\) −5.38145 −0.215086
\(627\) 13.3889 + 1.64775i 0.534700 + 0.0658048i
\(628\) 11.0394i 0.440520i
\(629\) 11.2341 + 9.42649i 0.447931 + 0.375859i
\(630\) 0 0
\(631\) 1.51546 + 8.59462i 0.0603297 + 0.342147i 1.00000 6.52024e-5i \(2.07546e-5\pi\)
−0.939670 + 0.342081i \(0.888868\pi\)
\(632\) −16.3793 2.88812i −0.651534 0.114883i
\(633\) 2.10372 5.77991i 0.0836152 0.229731i
\(634\) −9.73266 16.8575i −0.386533 0.669495i
\(635\) 0 0
\(636\) −0.794805 + 0.666921i −0.0315161 + 0.0264451i
\(637\) 41.3068 + 49.2275i 1.63663 + 1.95046i
\(638\) 16.8962 + 9.75501i 0.668926 + 0.386204i
\(639\) −8.03848 13.9230i −0.317997 0.550787i
\(640\) 0 0
\(641\) −0.151753 + 0.860632i −0.00599387 + 0.0339929i −0.987658 0.156626i \(-0.949938\pi\)
0.981664 + 0.190619i \(0.0610494\pi\)
\(642\) 4.95606 0.873887i 0.195600 0.0344896i
\(643\) 6.50122 + 17.8620i 0.256383 + 0.704407i 0.999383 + 0.0351158i \(0.0111800\pi\)
−0.743000 + 0.669291i \(0.766598\pi\)
\(644\) 19.8938 + 16.6928i 0.783924 + 0.657790i
\(645\) 0 0
\(646\) −1.37314 5.95533i −0.0540255 0.234309i
\(647\) 14.4175i 0.566810i −0.959000 0.283405i \(-0.908536\pi\)
0.959000 0.283405i \(-0.0914641\pi\)
\(648\) 3.93395 4.68830i 0.154540 0.184174i
\(649\) 36.9570 13.4512i 1.45069 0.528007i
\(650\) 0 0
\(651\) −3.99417 + 22.6520i −0.156544 + 0.887804i
\(652\) 2.02773 5.57114i 0.0794121 0.218183i
\(653\) 9.06528 5.23384i 0.354752 0.204816i −0.312024 0.950074i \(-0.601007\pi\)
0.666776 + 0.745258i \(0.267674\pi\)
\(654\) −2.34306 + 4.05829i −0.0916207 + 0.158692i
\(655\) 0 0
\(656\) −1.46184 + 1.22663i −0.0570755 + 0.0478920i
\(657\) 2.94865 + 1.70240i 0.115038 + 0.0664171i
\(658\) −13.1444 + 7.58889i −0.512420 + 0.295846i
\(659\) 5.20991 + 1.89625i 0.202949 + 0.0738675i 0.441495 0.897264i \(-0.354448\pi\)
−0.238545 + 0.971131i \(0.576671\pi\)
\(660\) 0 0
\(661\) 5.00125 + 28.3635i 0.194526 + 1.10321i 0.913092 + 0.407753i \(0.133688\pi\)
−0.718566 + 0.695459i \(0.755201\pi\)
\(662\) 6.39927 + 17.5818i 0.248715 + 0.683338i
\(663\) 2.00376 2.38799i 0.0778198 0.0927420i
\(664\) 14.4610 0.561195
\(665\) 0 0
\(666\) −27.9030 −1.08122
\(667\) −12.4703 + 14.8616i −0.482854 + 0.575443i
\(668\) −2.47200 6.79176i −0.0956445 0.262781i
\(669\) 0.00995606 + 0.0564636i 0.000384924 + 0.00218301i
\(670\) 0 0
\(671\) 40.9427 + 14.9019i 1.58057 + 0.575282i
\(672\) −2.42814 + 1.40188i −0.0936674 + 0.0540789i
\(673\) −34.5899 19.9705i −1.33334 0.769807i −0.347533 0.937668i \(-0.612981\pi\)
−0.985811 + 0.167861i \(0.946314\pi\)
\(674\) −19.2255 + 16.1322i −0.740540 + 0.621387i
\(675\) 0 0
\(676\) −0.938930 + 1.62627i −0.0361127 + 0.0625490i
\(677\) −12.6270 + 7.29022i −0.485296 + 0.280186i −0.722621 0.691245i \(-0.757063\pi\)
0.237325 + 0.971430i \(0.423729\pi\)
\(678\) 0.883619 2.42772i 0.0339352 0.0932361i
\(679\) −5.13477 + 29.1207i −0.197054 + 1.11755i
\(680\) 0 0
\(681\) 7.48897 2.72576i 0.286978 0.104451i
\(682\) 28.3126 33.7417i 1.08415 1.29204i
\(683\) 26.6159i 1.01843i −0.860640 0.509214i \(-0.829936\pi\)
0.860640 0.509214i \(-0.170064\pi\)
\(684\) 9.28494 + 7.00078i 0.355018 + 0.267681i
\(685\) 0 0
\(686\) 35.9961 + 30.2043i 1.37434 + 1.15321i
\(687\) 3.07056 + 8.43628i 0.117149 + 0.321864i
\(688\) −1.45618 + 0.256764i −0.0555163 + 0.00978902i
\(689\) −1.20563 + 6.83749i −0.0459310 + 0.260488i
\(690\) 0 0
\(691\) −18.6248 32.2591i −0.708521 1.22719i −0.965406 0.260752i \(-0.916029\pi\)
0.256885 0.966442i \(-0.417304\pi\)
\(692\) −4.46743 2.57927i −0.169826 0.0980492i
\(693\) −44.7839 53.3714i −1.70120 2.02741i
\(694\) 17.4302 14.6257i 0.661642 0.555183i
\(695\) 0 0
\(696\) −1.04727 1.81393i −0.0396968 0.0687569i
\(697\) 0.915115 2.51426i 0.0346625 0.0952344i
\(698\) −12.9638 2.28587i −0.490688 0.0865215i
\(699\) 1.52552 + 8.65165i 0.0577004 + 0.327235i
\(700\) 0 0
\(701\) −30.3425 25.4604i −1.14602 0.961626i −0.146402 0.989225i \(-0.546769\pi\)
−0.999619 + 0.0275989i \(0.991214\pi\)
\(702\) 12.6012i 0.475603i
\(703\) −2.37332 45.5295i −0.0895114 1.71718i
\(704\) 5.36907 0.202354
\(705\) 0 0
\(706\) −11.5635 + 4.20877i −0.435198 + 0.158399i
\(707\) −6.01505 + 1.06062i −0.226219 + 0.0398886i
\(708\) −4.15810 0.733185i −0.156271 0.0275548i
\(709\) −34.4453 12.5371i −1.29362 0.470839i −0.398707 0.917079i \(-0.630541\pi\)
−0.894914 + 0.446239i \(0.852763\pi\)
\(710\) 0 0
\(711\) −22.1850 + 38.4256i −0.832003 + 1.44107i
\(712\) 6.17623 + 7.36055i 0.231464 + 0.275848i
\(713\) 28.1536 + 33.5521i 1.05436 + 1.25654i
\(714\) 1.96557 3.40447i 0.0735597 0.127409i
\(715\) 0 0
\(716\) −7.69017 2.79899i −0.287395 0.104603i
\(717\) −9.54983 1.68389i −0.356645 0.0628861i
\(718\) 12.3704 2.18123i 0.461658 0.0814028i
\(719\) 10.3333 3.76101i 0.385367 0.140262i −0.142069 0.989857i \(-0.545376\pi\)
0.527436 + 0.849595i \(0.323153\pi\)
\(720\) 0 0
\(721\) −35.8347 −1.33455
\(722\) −10.6335 + 15.7458i −0.395737 + 0.585997i
\(723\) 5.24936i 0.195226i
\(724\) 2.62934 + 2.20628i 0.0977187 + 0.0819957i
\(725\) 0 0
\(726\) −1.78434 10.1195i −0.0662232 0.375570i
\(727\) −44.7236 7.88597i −1.65871 0.292475i −0.735714 0.677293i \(-0.763153\pi\)
−0.922992 + 0.384818i \(0.874264\pi\)
\(728\) −6.41700 + 17.6306i −0.237830 + 0.653432i
\(729\) −5.33885 9.24717i −0.197735 0.342488i
\(730\) 0 0
\(731\) 1.58816 1.33262i 0.0587402 0.0492889i
\(732\) −3.00670 3.58325i −0.111131 0.132441i
\(733\) 23.4118 + 13.5168i 0.864735 + 0.499255i 0.865595 0.500744i \(-0.166940\pi\)
−0.000859816 1.00000i \(0.500274\pi\)
\(734\) −1.34225 2.32485i −0.0495435 0.0858119i
\(735\) 0 0
\(736\) −0.927092 + 5.25780i −0.0341731 + 0.193805i
\(737\) −44.6524 + 7.87342i −1.64479 + 0.290021i
\(738\) 1.74118 + 4.78386i 0.0640938 + 0.176096i
\(739\) 0.964167 + 0.809032i 0.0354675 + 0.0297607i 0.660349 0.750959i \(-0.270408\pi\)
−0.624882 + 0.780720i \(0.714853\pi\)
\(740\) 0 0
\(741\) −9.67809 + 0.504490i −0.355534 + 0.0185329i
\(742\) 8.75559i 0.321428i
\(743\) −33.5678 + 40.0045i −1.23148 + 1.46762i −0.395867 + 0.918308i \(0.629556\pi\)
−0.835615 + 0.549315i \(0.814889\pi\)
\(744\) −4.44356 + 1.61733i −0.162909 + 0.0592940i
\(745\) 0 0
\(746\) 3.21985 18.2607i 0.117887 0.668571i
\(747\) 13.1945 36.2517i 0.482763 1.32638i
\(748\) −6.51938 + 3.76397i −0.238372 + 0.137624i
\(749\) 21.2341 36.7785i 0.775876 1.34386i
\(750\) 0 0
\(751\) 0.810409 0.680014i 0.0295723 0.0248141i −0.627882 0.778309i \(-0.716078\pi\)
0.657454 + 0.753495i \(0.271633\pi\)
\(752\) −2.70227 1.56016i −0.0985417 0.0568931i
\(753\) 8.38920 4.84351i 0.305720 0.176507i
\(754\) −13.1709 4.79381i −0.479655 0.174580i
\(755\) 0 0
\(756\) 2.75945 + 15.6496i 0.100360 + 0.569172i
\(757\) 0.632944 + 1.73900i 0.0230047 + 0.0632050i 0.950663 0.310224i \(-0.100404\pi\)
−0.927659 + 0.373429i \(0.878182\pi\)
\(758\) 7.44703 8.87503i 0.270488 0.322355i
\(759\) 16.5228 0.599739
\(760\) 0 0
\(761\) −31.8442 −1.15435 −0.577176 0.816620i \(-0.695845\pi\)
−0.577176 + 0.816620i \(0.695845\pi\)
\(762\) 0.0515686 0.0614570i 0.00186813 0.00222635i
\(763\) 13.5252 + 37.1601i 0.489644 + 1.34529i
\(764\) −0.655668 3.71848i −0.0237212 0.134530i
\(765\) 0 0
\(766\) 27.3254 + 9.94564i 0.987308 + 0.359351i
\(767\) −24.4688 + 14.1271i −0.883517 + 0.510099i
\(768\) −0.499186 0.288205i −0.0180128 0.0103997i
\(769\) −0.0929228 + 0.0779715i −0.00335088 + 0.00281172i −0.644462 0.764637i \(-0.722918\pi\)
0.641111 + 0.767448i \(0.278474\pi\)
\(770\) 0 0
\(771\) 2.85245 4.94059i 0.102728 0.177931i
\(772\) −10.5463 + 6.08894i −0.379571 + 0.219146i
\(773\) −11.9131 + 32.7308i −0.428483 + 1.17725i 0.518251 + 0.855229i \(0.326583\pi\)
−0.946734 + 0.322018i \(0.895639\pi\)
\(774\) −0.684981 + 3.88472i −0.0246211 + 0.139633i
\(775\) 0 0
\(776\) −5.71250 + 2.07918i −0.205067 + 0.0746382i
\(777\) 18.8502 22.4648i 0.676246 0.805919i
\(778\) 29.7821i 1.06774i
\(779\) −7.65776 + 3.24800i −0.274368 + 0.116372i
\(780\) 0 0
\(781\) −24.7863 20.7982i −0.886923 0.744217i
\(782\) −2.56024 7.03421i −0.0915541 0.251543i
\(783\)