Properties

Label 950.2.u.g.149.5
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 149.5
Character \(\chi\) \(=\) 950.149
Dual form 950.2.u.g.899.5

$q$-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 0.983503 0.180892i \(-0.0578983\pi\)
−0.869682 + 0.493613i \(0.835676\pi\)
\(4\) −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 \(0.704533\pi\)
−0.992932 + 0.118681i \(0.962134\pi\)
\(8\) −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 \(-0.709240\pi\)
0.976909 0.213658i \(-0.0685377\pi\)
\(14\) −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 −0.864183 0.503178i \(-0.832164\pi\)
0.645598 + 0.763678i \(0.276608\pi\)
\(18\) 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 0.403902 0.914802i \(-0.367654\pi\)
0.692425 + 0.721490i \(0.256543\pi\)
\(24\) 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 \(-0.670616\pi\)
0.510706 0.859755i \(-0.329384\pi\)
\(38\) −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 0.0615084 0.998107i \(-0.480409\pi\)
−0.283574 + 0.958950i \(0.591520\pi\)
\(44\) −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 0.599664 0.800252i \(-0.295301\pi\)
−0.892225 + 0.451591i \(0.850857\pi\)
\(48\) −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 −0.294063 0.955786i \(-0.595008\pi\)
0.0505691 + 0.998721i \(0.483896\pi\)
\(54\) 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 0.987837 0.155494i \(-0.0496970\pi\)
−0.324668 + 0.945828i \(0.605253\pi\)
\(68\) 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 0.911523 0.411249i \(-0.134907\pi\)
−0.962613 + 0.270880i \(0.912685\pi\)
\(74\) −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 −0.991508 0.130044i \(-0.958488\pi\)
−0.383133 + 0.923693i \(0.625155\pi\)
\(84\) −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 −0.530273 0.847827i \(-0.677911\pi\)
0.927028 + 0.374993i \(0.122355\pi\)
\(98\) −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 0.780227 0.625496i \(-0.215103\pi\)
−0.151582 + 0.988445i \(0.548437\pi\)
\(104\) −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 −0.818772 0.574119i \(-0.805345\pi\)
0.0878153 + 0.996137i \(0.472011\pi\)
\(108\) 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 \(0.0676134\pi\)
−0.977525 + 0.210820i \(0.932387\pi\)
\(114\) −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 −0.941787 0.336211i \(-0.890855\pi\)
0.937563 + 0.347816i \(0.113077\pi\)
\(128\) 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 0.468004 0.883726i \(-0.344973\pi\)
0.742032 + 0.670364i \(0.233862\pi\)
\(138\) 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 −0.277936 0.960600i \(-0.589650\pi\)
−0.589719 + 0.807609i \(0.700761\pi\)
\(158\) −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 0.285257 0.958451i \(-0.407921\pi\)
−0.687414 + 0.726266i \(0.741254\pi\)
\(164\) −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 −0.442118 0.896957i \(-0.645773\pi\)
−0.108677 + 0.994077i \(0.534661\pi\)
\(168\) 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 −0.877221 0.480087i \(-0.840605\pi\)
0.625121 + 0.780528i \(0.285049\pi\)
\(174\) 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 \(0.0333050\pi\)
−0.694722 + 0.719278i \(0.744473\pi\)
\(194\) −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 −0.261063 0.965322i \(-0.584073\pi\)
0.705462 + 0.708748i \(0.250740\pi\)
\(198\) −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 0.176927 0.984224i \(-0.443384\pi\)
−0.170367 + 0.985381i \(0.554495\pi\)
\(224\) −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 \(-0.848265\pi\)
0.888519 0.458840i \(-0.151735\pi\)
\(228\) −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 0.642113 0.766610i \(-0.278058\pi\)
0.341193 + 0.939993i \(0.389169\pi\)
\(234\) −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 0.530213 0.847865i \(-0.322112\pi\)
−0.927054 + 0.374927i \(0.877668\pi\)
\(258\) −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 \(-0.868278\pi\)
0.442915 0.896564i \(-0.353944\pi\)
\(264\) −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 0.559302 0.828964i \(-0.311069\pi\)
−0.438253 + 0.898852i \(0.644402\pi\)
\(278\) 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 −0.579607 0.814896i \(-0.696794\pi\)
0.903164 + 0.429296i \(0.141238\pi\)
\(284\) −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 0.432984 0.901402i \(-0.357461\pi\)
−0.564145 + 0.825676i \(0.690794\pi\)
\(294\) 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 0.973398 0.229121i \(-0.0735852\pi\)
−0.892942 + 0.450171i \(0.851363\pi\)
\(308\) 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 0.659372 0.751817i \(-0.270822\pi\)
−0.854894 + 0.518803i \(0.826378\pi\)
\(314\) −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 \(-0.704795\pi\)
0.973830 0.227278i \(-0.0729825\pi\)
\(318\) −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 −0.546436 0.837501i \(-0.684016\pi\)
−0.799924 + 0.600101i \(0.795127\pi\)
\(338\) −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 0.738958 0.673751i \(-0.235318\pi\)
0.463957 + 0.885857i \(0.346429\pi\)
\(348\) 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 0.188822 0.982011i \(-0.439533\pi\)
−0.756036 + 0.654530i \(0.772866\pi\)
\(354\) 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 −0.913420 0.407019i \(-0.866568\pi\)
0.961347 + 0.275340i \(0.0887904\pi\)
\(368\) −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 −0.0228917 0.999738i \(-0.507287\pi\)
0.854353 + 0.519694i \(0.173954\pi\)
\(374\) 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 \(0.155457\pi\)
−0.374895 + 0.927067i \(0.622321\pi\)
\(384\) 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 −0.857639 0.514252i \(-0.828070\pi\)
0.655367 + 0.755311i \(0.272514\pi\)
\(398\) 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 0.682478 0.730906i \(-0.260902\pi\)
0.891304 + 0.453406i \(0.149791\pi\)
\(434\) 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 \(0.385858\pi\)
−0.870746 + 0.491732i \(0.836364\pi\)
\(444\) −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 \(-0.664017\pi\)
0.492774 0.870157i \(-0.335983\pi\)
\(458\) −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 −0.0343994 0.999408i \(-0.510952\pi\)
0.848313 + 0.529495i \(0.177619\pi\)
\(464\) −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 \(-0.974957\pi\)
−0.566518 0.824049i \(-0.691710\pi\)
\(468\) −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 −0.935641 0.352952i \(-0.885178\pi\)
−0.162155 + 0.986765i \(0.551845\pi\)
\(488\) 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 0.717163 0.696905i \(-0.245440\pi\)
−0.810852 + 0.585252i \(0.800996\pi\)
\(504\) 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 0.699300 0.714828i \(-0.253495\pi\)
−0.825400 + 0.564548i \(0.809051\pi\)
\(524\) 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 0.470600 0.882347i \(-0.344038\pi\)
0.744000 + 0.668180i \(0.232926\pi\)
\(548\) −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 \(0.313507\pi\)
−0.959160 + 0.282865i \(0.908715\pi\)
\(558\) −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 −0.375242 0.926927i \(-0.622440\pi\)
0.615121 + 0.788432i \(0.289107\pi\)
\(564\) −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 −0.225539 0.974234i \(-0.572414\pi\)
0.730942 + 0.682439i \(0.239081\pi\)
\(578\) 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 −0.655568 0.755136i \(-0.727571\pi\)
0.857502 + 0.514481i \(0.172015\pi\)
\(588\) 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 −0.360896 0.932606i \(-0.617529\pi\)
−0.0201608 + 0.999797i \(0.506418\pi\)
\(594\) 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 \(0.0134205\pi\)
−0.999111 + 0.0421492i \(0.986580\pi\)
\(608\) 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 0.492230 0.870465i \(-0.336182\pi\)
0.164828 + 0.986322i \(0.447293\pi\)
\(614\) 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 0.976012 0.217717i \(-0.0698610\pi\)
−0.383892 + 0.923378i \(0.625417\pi\)
\(618\) 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 \(-0.988820\pi\)
0.743000 0.669291i \(-0.233402\pi\)
\(644\) 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 \(0.0914641\pi\)
−0.959000 + 0.283405i \(0.908536\pi\)
\(648\) −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 −0.666776 0.745258i \(-0.732326\pi\)
0.312024 + 0.950074i \(0.398993\pi\)
\(654\) −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 0.985811 0.167861i \(-0.0536860\pi\)
0.347533 + 0.937668i \(0.387019\pi\)
\(674\) −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 −0.237325 0.971430i \(-0.576271\pi\)
0.722621 + 0.691245i \(0.242937\pi\)
\(678\) −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 \(0.170064\pi\)
−0.860640 + 0.509214i \(0.829936\pi\)
\(684\) 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 0.922992 0.384818i \(-0.125736\pi\)
0.735714 + 0.677293i \(0.236847\pi\)
\(728\) 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 0.000859816 1.00000i \(-0.499726\pi\)
−0.865595 + 0.500744i \(0.833060\pi\)
\(734\) −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 \(-0.370444\pi\)
0.835615 0.549315i \(-0.185111\pi\)
\(744\) −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 0.927659 0.373429i \(-0.121818\pi\)
−0.950663 + 0.310224i \(0.899596\pi\)
\(758\) −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 \(-0.673417\pi\)
0.946734 0.322018i \(-0.104361\pi\)
\(774\) −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
\(783\)