Properties

Label 950.2.u.g.99.4
Level $950$
Weight $2$
Character 950.99
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 99.4
Character \(\chi\) \(=\) 950.99
Dual form 950.2.u.g.499.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.342020 - 0.939693i) q^{2} +(-3.13139 + 0.552148i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.552148 + 3.13139i) q^{6} +(-2.89781 - 1.67305i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(6.68164 - 2.43192i) q^{9} +O(q^{10})\) \(q+(0.342020 - 0.939693i) q^{2} +(-3.13139 + 0.552148i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.552148 + 3.13139i) q^{6} +(-2.89781 - 1.67305i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(6.68164 - 2.43192i) q^{9} +(-3.09216 - 5.35578i) q^{11} +(2.75370 + 1.58985i) q^{12} +(-0.727397 - 0.128260i) q^{13} +(-2.56327 + 2.15083i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-0.296919 + 0.815778i) q^{17} -7.11045i q^{18} +(2.59916 - 3.49919i) q^{19} +(9.99794 + 3.63895i) q^{21} +(-6.09037 + 1.07390i) q^{22} +(0.735009 - 0.875950i) q^{23} +(2.43579 - 2.04387i) q^{24} +(-0.369309 + 0.639662i) q^{26} +(-11.3189 + 6.53498i) q^{27} +(1.14444 + 3.14431i) q^{28} +(-7.32010 + 2.66430i) q^{29} +(-3.23887 + 5.60988i) q^{31} +(0.984808 + 0.173648i) q^{32} +(12.6399 + 15.0637i) q^{33} +(0.665029 + 0.558025i) q^{34} +(-6.68164 - 2.43192i) q^{36} -1.68113i q^{37} +(-2.39920 - 3.63921i) q^{38} +2.34858 q^{39} +(1.68282 + 9.54373i) q^{41} +(6.83899 - 8.15040i) q^{42} +(1.19449 + 1.42354i) q^{43} +(-1.07390 + 6.09037i) q^{44} +(-0.571736 - 0.990275i) q^{46} +(0.113446 + 0.311691i) q^{47} +(-1.08752 - 2.98793i) q^{48} +(2.09821 + 3.63420i) q^{49} +(0.479338 - 2.71846i) q^{51} +(0.474775 + 0.565815i) q^{52} +(4.56693 - 5.44265i) q^{53} +(2.26958 + 12.8714i) q^{54} +3.34610 q^{56} +(-6.20691 + 12.3925i) q^{57} +7.78988i q^{58} +(4.56719 + 1.66232i) q^{59} +(5.53664 + 4.64579i) q^{61} +(4.16381 + 4.96223i) q^{62} +(-23.4308 - 4.13149i) q^{63} +(0.500000 - 0.866025i) q^{64} +(18.4784 - 6.72557i) q^{66} +(1.00039 + 2.74854i) q^{67} +(0.751825 - 0.434067i) q^{68} +(-1.81794 + 3.14877i) q^{69} +(-5.27849 + 4.42918i) q^{71} +(-4.57051 + 5.44692i) q^{72} +(-7.69790 + 1.35735i) q^{73} +(-1.57975 - 0.574982i) q^{74} +(-4.24031 + 1.00983i) q^{76} +20.6934i q^{77} +(0.803262 - 2.20694i) q^{78} +(0.399207 + 2.26401i) q^{79} +(15.4949 - 13.0018i) q^{81} +(9.54373 + 1.68282i) q^{82} +(9.91318 + 5.72338i) q^{83} +(-5.31979 - 9.21415i) q^{84} +(1.74623 - 0.635576i) q^{86} +(21.4510 - 12.3847i) q^{87} +(5.35578 + 3.09216i) q^{88} +(-0.404290 + 2.29284i) q^{89} +(1.89328 + 1.58865i) q^{91} +(-1.12610 + 0.198562i) q^{92} +(7.04466 - 19.3550i) q^{93} +0.331695 q^{94} -3.17969 q^{96} +(2.34081 - 6.43131i) q^{97} +(4.13266 - 0.728700i) q^{98} +(-33.6855 - 28.2655i) 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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.342020 0.939693i 0.241845 0.664463i
\(3\) −3.13139 + 0.552148i −1.80791 + 0.318783i −0.972860 0.231396i \(-0.925671\pi\)
−0.835047 + 0.550178i \(0.814560\pi\)
\(4\) −0.766044 0.642788i −0.383022 0.321394i
\(5\) 0 0
\(6\) −0.552148 + 3.13139i −0.225413 + 1.27838i
\(7\) −2.89781 1.67305i −1.09527 0.632354i −0.160295 0.987069i \(-0.551245\pi\)
−0.934975 + 0.354715i \(0.884578\pi\)
\(8\) −0.866025 + 0.500000i −0.306186 + 0.176777i
\(9\) 6.68164 2.43192i 2.22721 0.810639i
\(10\) 0 0
\(11\) −3.09216 5.35578i −0.932322 1.61483i −0.779341 0.626600i \(-0.784446\pi\)
−0.152981 0.988229i \(-0.548887\pi\)
\(12\) 2.75370 + 1.58985i 0.794923 + 0.458949i
\(13\) −0.727397 0.128260i −0.201744 0.0355729i 0.0718630 0.997415i \(-0.477106\pi\)
−0.273607 + 0.961842i \(0.588217\pi\)
\(14\) −2.56327 + 2.15083i −0.685061 + 0.574835i
\(15\) 0 0
\(16\) 0.173648 + 0.984808i 0.0434120 + 0.246202i
\(17\) −0.296919 + 0.815778i −0.0720134 + 0.197855i −0.970477 0.241192i \(-0.922462\pi\)
0.898464 + 0.439047i \(0.144684\pi\)
\(18\) 7.11045i 1.67595i
\(19\) 2.59916 3.49919i 0.596289 0.802770i
\(20\) 0 0
\(21\) 9.99794 + 3.63895i 2.18173 + 0.794085i
\(22\) −6.09037 + 1.07390i −1.29847 + 0.228956i
\(23\) 0.735009 0.875950i 0.153260 0.182648i −0.683951 0.729528i \(-0.739740\pi\)
0.837211 + 0.546879i \(0.184184\pi\)
\(24\) 2.43579 2.04387i 0.497203 0.417203i
\(25\) 0 0
\(26\) −0.369309 + 0.639662i −0.0724275 + 0.125448i
\(27\) −11.3189 + 6.53498i −2.17833 + 1.25766i
\(28\) 1.14444 + 3.14431i 0.216278 + 0.594219i
\(29\) −7.32010 + 2.66430i −1.35931 + 0.494748i −0.915840 0.401543i \(-0.868474\pi\)
−0.443468 + 0.896290i \(0.646252\pi\)
\(30\) 0 0
\(31\) −3.23887 + 5.60988i −0.581718 + 1.00756i 0.413558 + 0.910478i \(0.364286\pi\)
−0.995276 + 0.0970869i \(0.969048\pi\)
\(32\) 0.984808 + 0.173648i 0.174091 + 0.0306970i
\(33\) 12.6399 + 15.0637i 2.20033 + 2.62225i
\(34\) 0.665029 + 0.558025i 0.114051 + 0.0957005i
\(35\) 0 0
\(36\) −6.68164 2.43192i −1.11361 0.405319i
\(37\) 1.68113i 0.276377i −0.990406 0.138188i \(-0.955872\pi\)
0.990406 0.138188i \(-0.0441279\pi\)
\(38\) −2.39920 3.63921i −0.389202 0.590357i
\(39\) 2.34858 0.376074
\(40\) 0 0
\(41\) 1.68282 + 9.54373i 0.262812 + 1.49048i 0.775194 + 0.631723i \(0.217652\pi\)
−0.512383 + 0.858757i \(0.671237\pi\)
\(42\) 6.83899 8.15040i 1.05528 1.25763i
\(43\) 1.19449 + 1.42354i 0.182158 + 0.217088i 0.849395 0.527758i \(-0.176967\pi\)
−0.667236 + 0.744846i \(0.732523\pi\)
\(44\) −1.07390 + 6.09037i −0.161896 + 0.918158i
\(45\) 0 0
\(46\) −0.571736 0.990275i −0.0842978 0.146008i
\(47\) 0.113446 + 0.311691i 0.0165479 + 0.0454649i 0.947692 0.319188i \(-0.103410\pi\)
−0.931144 + 0.364652i \(0.881188\pi\)
\(48\) −1.08752 2.98793i −0.156970 0.431271i
\(49\) 2.09821 + 3.63420i 0.299744 + 0.519172i
\(50\) 0 0
\(51\) 0.479338 2.71846i 0.0671207 0.380661i
\(52\) 0.474775 + 0.565815i 0.0658394 + 0.0784644i
\(53\) 4.56693 5.44265i 0.627316 0.747606i −0.354994 0.934868i \(-0.615517\pi\)
0.982310 + 0.187263i \(0.0599616\pi\)
\(54\) 2.26958 + 12.8714i 0.308850 + 1.75158i
\(55\) 0 0
\(56\) 3.34610 0.447142
\(57\) −6.20691 + 12.3925i −0.822125 + 1.64142i
\(58\) 7.78988i 1.02286i
\(59\) 4.56719 + 1.66232i 0.594597 + 0.216416i 0.621750 0.783216i \(-0.286422\pi\)
−0.0271531 + 0.999631i \(0.508644\pi\)
\(60\) 0 0
\(61\) 5.53664 + 4.64579i 0.708894 + 0.594833i 0.924289 0.381694i \(-0.124659\pi\)
−0.215394 + 0.976527i \(0.569104\pi\)
\(62\) 4.16381 + 4.96223i 0.528804 + 0.630204i
\(63\) −23.4308 4.13149i −2.95201 0.520519i
\(64\) 0.500000 0.866025i 0.0625000 0.108253i
\(65\) 0 0
\(66\) 18.4784 6.72557i 2.27453 0.827861i
\(67\) 1.00039 + 2.74854i 0.122217 + 0.335787i 0.985681 0.168623i \(-0.0539321\pi\)
−0.863464 + 0.504410i \(0.831710\pi\)
\(68\) 0.751825 0.434067i 0.0911722 0.0526383i
\(69\) −1.81794 + 3.14877i −0.218855 + 0.379068i
\(70\) 0 0
\(71\) −5.27849 + 4.42918i −0.626442 + 0.525647i −0.899821 0.436259i \(-0.856303\pi\)
0.273379 + 0.961906i \(0.411859\pi\)
\(72\) −4.57051 + 5.44692i −0.538640 + 0.641926i
\(73\) −7.69790 + 1.35735i −0.900972 + 0.158866i −0.604901 0.796301i \(-0.706787\pi\)
−0.296070 + 0.955166i \(0.595676\pi\)
\(74\) −1.57975 0.574982i −0.183642 0.0668403i
\(75\) 0 0
\(76\) −4.24031 + 1.00983i −0.486397 + 0.115835i
\(77\) 20.6934i 2.35823i
\(78\) 0.803262 2.20694i 0.0909515 0.249887i
\(79\) 0.399207 + 2.26401i 0.0449143 + 0.254721i 0.998995 0.0448292i \(-0.0142744\pi\)
−0.954080 + 0.299551i \(0.903163\pi\)
\(80\) 0 0
\(81\) 15.4949 13.0018i 1.72165 1.44464i
\(82\) 9.54373 + 1.68282i 1.05393 + 0.185836i
\(83\) 9.91318 + 5.72338i 1.08811 + 0.628223i 0.933074 0.359686i \(-0.117116\pi\)
0.155040 + 0.987908i \(0.450449\pi\)
\(84\) −5.31979 9.21415i −0.580437 1.00535i
\(85\) 0 0
\(86\) 1.74623 0.635576i 0.188301 0.0685359i
\(87\) 21.4510 12.3847i 2.29978 1.32778i
\(88\) 5.35578 + 3.09216i 0.570928 + 0.329626i
\(89\) −0.404290 + 2.29284i −0.0428546 + 0.243041i −0.998709 0.0508007i \(-0.983823\pi\)
0.955854 + 0.293841i \(0.0949338\pi\)
\(90\) 0 0
\(91\) 1.89328 + 1.58865i 0.198469 + 0.166535i
\(92\) −1.12610 + 0.198562i −0.117404 + 0.0207015i
\(93\) 7.04466 19.3550i 0.730497 2.00702i
\(94\) 0.331695 0.0342117
\(95\) 0 0
\(96\) −3.17969 −0.324526
\(97\) 2.34081 6.43131i 0.237673 0.653000i −0.762311 0.647211i \(-0.775935\pi\)
0.999983 0.00578901i \(-0.00184271\pi\)
\(98\) 4.13266 0.728700i 0.417462 0.0736098i
\(99\) −33.6855 28.2655i −3.38552 2.84079i
\(100\) 0 0
\(101\) 1.76892 10.0321i 0.176015 0.998228i −0.760952 0.648809i \(-0.775268\pi\)
0.936966 0.349420i \(-0.113621\pi\)
\(102\) −2.39057 1.38020i −0.236702 0.136660i
\(103\) 1.79310 1.03525i 0.176680 0.102006i −0.409052 0.912511i \(-0.634141\pi\)
0.585732 + 0.810505i \(0.300807\pi\)
\(104\) 0.694074 0.252622i 0.0680596 0.0247717i
\(105\) 0 0
\(106\) −3.55244 6.15300i −0.345043 0.597632i
\(107\) −12.6761 7.31857i −1.22545 0.707513i −0.259374 0.965777i \(-0.583516\pi\)
−0.966075 + 0.258264i \(0.916850\pi\)
\(108\) 12.8714 + 2.26958i 1.23855 + 0.218390i
\(109\) 6.66091 5.58917i 0.637999 0.535345i −0.265404 0.964137i \(-0.585505\pi\)
0.903403 + 0.428792i \(0.141061\pi\)
\(110\) 0 0
\(111\) 0.928235 + 5.26428i 0.0881041 + 0.499663i
\(112\) 1.14444 3.14431i 0.108139 0.297109i
\(113\) 10.8308i 1.01888i 0.860507 + 0.509439i \(0.170147\pi\)
−0.860507 + 0.509439i \(0.829853\pi\)
\(114\) 9.52221 + 10.0711i 0.891836 + 0.943240i
\(115\) 0 0
\(116\) 7.32010 + 2.66430i 0.679654 + 0.247374i
\(117\) −5.17212 + 0.911985i −0.478163 + 0.0843130i
\(118\) 3.12414 3.72320i 0.287600 0.342749i
\(119\) 2.22526 1.86721i 0.203989 0.171167i
\(120\) 0 0
\(121\) −13.6229 + 23.5956i −1.23845 + 2.14506i
\(122\) 6.25926 3.61379i 0.566687 0.327177i
\(123\) −10.5391 28.9559i −0.950279 2.61087i
\(124\) 6.08708 2.21552i 0.546636 0.198959i
\(125\) 0 0
\(126\) −11.8962 + 20.6047i −1.05979 + 1.83562i
\(127\) 11.0540 + 1.94911i 0.980880 + 0.172956i 0.641023 0.767522i \(-0.278510\pi\)
0.339857 + 0.940477i \(0.389621\pi\)
\(128\) −0.642788 0.766044i −0.0568149 0.0677094i
\(129\) −4.52642 3.79812i −0.398529 0.334406i
\(130\) 0 0
\(131\) −14.2703 5.19396i −1.24680 0.453798i −0.367481 0.930031i \(-0.619780\pi\)
−0.879319 + 0.476233i \(0.842002\pi\)
\(132\) 19.6643i 1.71155i
\(133\) −13.3862 + 5.79147i −1.16073 + 0.502184i
\(134\) 2.92493 0.252676
\(135\) 0 0
\(136\) −0.150750 0.854944i −0.0129267 0.0733109i
\(137\) −5.49600 + 6.54988i −0.469555 + 0.559594i −0.947896 0.318580i \(-0.896794\pi\)
0.478341 + 0.878174i \(0.341238\pi\)
\(138\) 2.33710 + 2.78525i 0.198948 + 0.237096i
\(139\) −1.52883 + 8.67044i −0.129674 + 0.735417i 0.848748 + 0.528798i \(0.177357\pi\)
−0.978421 + 0.206619i \(0.933754\pi\)
\(140\) 0 0
\(141\) −0.527344 0.913387i −0.0444104 0.0769210i
\(142\) 2.35672 + 6.47503i 0.197771 + 0.543372i
\(143\) 1.56230 + 4.29238i 0.130646 + 0.358947i
\(144\) 3.55522 + 6.15783i 0.296269 + 0.513152i
\(145\) 0 0
\(146\) −1.35735 + 7.69790i −0.112335 + 0.637083i
\(147\) −8.57692 10.2216i −0.707413 0.843061i
\(148\) −1.08061 + 1.28782i −0.0888258 + 0.105858i
\(149\) −0.132240 0.749969i −0.0108335 0.0614398i 0.978912 0.204284i \(-0.0654865\pi\)
−0.989745 + 0.142844i \(0.954375\pi\)
\(150\) 0 0
\(151\) −6.08784 −0.495421 −0.247711 0.968834i \(-0.579678\pi\)
−0.247711 + 0.968834i \(0.579678\pi\)
\(152\) −0.501343 + 4.32997i −0.0406643 + 0.351207i
\(153\) 6.17282i 0.499043i
\(154\) 19.4454 + 7.07756i 1.56696 + 0.570326i
\(155\) 0 0
\(156\) −1.79912 1.50964i −0.144045 0.120868i
\(157\) −15.6683 18.6728i −1.25047 1.49025i −0.803034 0.595933i \(-0.796782\pi\)
−0.447434 0.894317i \(-0.647662\pi\)
\(158\) 2.26401 + 0.399207i 0.180115 + 0.0317592i
\(159\) −11.2957 + 19.5647i −0.895804 + 1.55158i
\(160\) 0 0
\(161\) −3.59543 + 1.30863i −0.283360 + 0.103134i
\(162\) −6.91809 19.0073i −0.543536 1.49335i
\(163\) −3.73250 + 2.15496i −0.292352 + 0.168789i −0.639002 0.769205i \(-0.720652\pi\)
0.346650 + 0.937994i \(0.387319\pi\)
\(164\) 4.84548 8.39261i 0.378368 0.655353i
\(165\) 0 0
\(166\) 8.76873 7.35783i 0.680585 0.571079i
\(167\) 3.34993 3.99229i 0.259225 0.308933i −0.620697 0.784051i \(-0.713150\pi\)
0.879922 + 0.475118i \(0.157595\pi\)
\(168\) −10.4779 + 1.84754i −0.808391 + 0.142541i
\(169\) −11.7033 4.25967i −0.900258 0.327667i
\(170\) 0 0
\(171\) 8.85690 29.7013i 0.677304 2.27131i
\(172\) 1.85830i 0.141694i
\(173\) 2.40637 6.61144i 0.182953 0.502658i −0.813983 0.580889i \(-0.802705\pi\)
0.996935 + 0.0782309i \(0.0249271\pi\)
\(174\) −4.30117 24.3931i −0.326071 1.84924i
\(175\) 0 0
\(176\) 4.73747 3.97521i 0.357100 0.299642i
\(177\) −15.2195 2.68360i −1.14397 0.201712i
\(178\) 2.01629 + 1.16411i 0.151127 + 0.0872534i
\(179\) 1.59972 + 2.77080i 0.119569 + 0.207099i 0.919597 0.392863i \(-0.128515\pi\)
−0.800028 + 0.599963i \(0.795182\pi\)
\(180\) 0 0
\(181\) 4.44963 1.61953i 0.330738 0.120379i −0.171313 0.985217i \(-0.554801\pi\)
0.502052 + 0.864838i \(0.332579\pi\)
\(182\) 2.14038 1.23575i 0.158655 0.0915997i
\(183\) −19.9025 11.4907i −1.47124 0.849419i
\(184\) −0.198562 + 1.12610i −0.0146382 + 0.0830172i
\(185\) 0 0
\(186\) −15.7784 13.2396i −1.15693 0.970777i
\(187\) 5.28725 0.932285i 0.386642 0.0681754i
\(188\) 0.113446 0.311691i 0.00827393 0.0227324i
\(189\) 43.7335 3.18114
\(190\) 0 0
\(191\) −18.4307 −1.33360 −0.666800 0.745237i \(-0.732336\pi\)
−0.666800 + 0.745237i \(0.732336\pi\)
\(192\) −1.08752 + 2.98793i −0.0784849 + 0.215636i
\(193\) 13.3437 2.35285i 0.960501 0.169362i 0.328649 0.944452i \(-0.393407\pi\)
0.631851 + 0.775090i \(0.282295\pi\)
\(194\) −5.24285 4.39927i −0.376415 0.315849i
\(195\) 0 0
\(196\) 0.728700 4.13266i 0.0520500 0.295190i
\(197\) 7.09361 + 4.09550i 0.505399 + 0.291792i 0.730940 0.682441i \(-0.239082\pi\)
−0.225541 + 0.974234i \(0.572415\pi\)
\(198\) −38.0820 + 21.9867i −2.70637 + 1.56252i
\(199\) 5.58408 2.03244i 0.395845 0.144076i −0.136425 0.990650i \(-0.543561\pi\)
0.532270 + 0.846575i \(0.321339\pi\)
\(200\) 0 0
\(201\) −4.65019 8.05437i −0.327999 0.568112i
\(202\) −8.82205 5.09342i −0.620718 0.358371i
\(203\) 25.6698 + 4.52627i 1.80166 + 0.317682i
\(204\) −2.11459 + 1.77435i −0.148051 + 0.124229i
\(205\) 0 0
\(206\) −0.359538 2.03904i −0.0250502 0.142067i
\(207\) 2.78083 7.64026i 0.193281 0.531035i
\(208\) 0.738619i 0.0512140i
\(209\) −26.7779 3.10047i −1.85227 0.214464i
\(210\) 0 0
\(211\) 1.63846 + 0.596352i 0.112796 + 0.0410545i 0.397802 0.917471i \(-0.369773\pi\)
−0.285005 + 0.958526i \(0.591995\pi\)
\(212\) −6.99694 + 1.23375i −0.480552 + 0.0847342i
\(213\) 14.0834 16.7840i 0.964981 1.15002i
\(214\) −11.2127 + 9.40858i −0.766485 + 0.643157i
\(215\) 0 0
\(216\) 6.53498 11.3189i 0.444649 0.770155i
\(217\) 18.7713 10.8376i 1.27428 0.735703i
\(218\) −2.97393 8.17082i −0.201420 0.553397i
\(219\) 23.3557 8.50076i 1.57823 0.574428i
\(220\) 0 0
\(221\) 0.320610 0.555312i 0.0215665 0.0373543i
\(222\) 5.26428 + 0.928235i 0.353315 + 0.0622990i
\(223\) 16.9959 + 20.2549i 1.13813 + 1.35637i 0.925281 + 0.379283i \(0.123829\pi\)
0.212848 + 0.977085i \(0.431726\pi\)
\(224\) −2.56327 2.15083i −0.171265 0.143709i
\(225\) 0 0
\(226\) 10.1777 + 3.70436i 0.677007 + 0.246411i
\(227\) 27.4472i 1.82174i 0.412697 + 0.910869i \(0.364587\pi\)
−0.412697 + 0.910869i \(0.635413\pi\)
\(228\) 12.7205 5.50345i 0.842434 0.364475i
\(229\) 11.5722 0.764711 0.382355 0.924015i \(-0.375113\pi\)
0.382355 + 0.924015i \(0.375113\pi\)
\(230\) 0 0
\(231\) −11.4258 64.7990i −0.751764 4.26346i
\(232\) 5.00724 5.96740i 0.328741 0.391779i
\(233\) 8.26488 + 9.84970i 0.541450 + 0.645275i 0.965512 0.260358i \(-0.0838406\pi\)
−0.424062 + 0.905633i \(0.639396\pi\)
\(234\) −0.911985 + 5.17212i −0.0596183 + 0.338112i
\(235\) 0 0
\(236\) −2.43015 4.20914i −0.158189 0.273992i
\(237\) −2.50014 6.86908i −0.162402 0.446195i
\(238\) −0.993522 2.72968i −0.0644005 0.176939i
\(239\) −5.65708 9.79836i −0.365926 0.633803i 0.622998 0.782223i \(-0.285914\pi\)
−0.988924 + 0.148420i \(0.952581\pi\)
\(240\) 0 0
\(241\) −4.13196 + 23.4335i −0.266163 + 1.50948i 0.499541 + 0.866290i \(0.333502\pi\)
−0.765704 + 0.643193i \(0.777609\pi\)
\(242\) 17.5133 + 20.8715i 1.12580 + 1.34167i
\(243\) −16.1379 + 19.2325i −1.03525 + 1.23376i
\(244\) −1.25506 7.11777i −0.0803467 0.455669i
\(245\) 0 0
\(246\) −30.8143 −1.96465
\(247\) −2.33943 + 2.21194i −0.148854 + 0.140742i
\(248\) 6.47773i 0.411337i
\(249\) −34.2022 12.4486i −2.16747 0.788896i
\(250\) 0 0
\(251\) 19.9736 + 16.7599i 1.26072 + 1.05787i 0.995604 + 0.0936578i \(0.0298560\pi\)
0.265120 + 0.964215i \(0.414588\pi\)
\(252\) 15.2934 + 18.2260i 0.963394 + 1.14813i
\(253\) −6.96417 1.22797i −0.437833 0.0772018i
\(254\) 5.61224 9.72069i 0.352143 0.609930i
\(255\) 0 0
\(256\) −0.939693 + 0.342020i −0.0587308 + 0.0213763i
\(257\) −3.47247 9.54054i −0.216607 0.595122i 0.783032 0.621981i \(-0.213672\pi\)
−0.999639 + 0.0268585i \(0.991450\pi\)
\(258\) −5.11719 + 2.95441i −0.318582 + 0.183934i
\(259\) −2.81263 + 4.87161i −0.174768 + 0.302707i
\(260\) 0 0
\(261\) −42.4309 + 35.6037i −2.62641 + 2.20382i
\(262\) −9.76144 + 11.6332i −0.603064 + 0.718704i
\(263\) −16.8663 + 2.97399i −1.04002 + 0.183384i −0.667477 0.744630i \(-0.732626\pi\)
−0.372545 + 0.928014i \(0.621515\pi\)
\(264\) −18.4784 6.72557i −1.13726 0.413930i
\(265\) 0 0
\(266\) 0.863848 + 14.5597i 0.0529659 + 0.892714i
\(267\) 7.40300i 0.453056i
\(268\) 1.00039 2.74854i 0.0611083 0.167894i
\(269\) −3.96080 22.4628i −0.241495 1.36958i −0.828495 0.559997i \(-0.810802\pi\)
0.587000 0.809587i \(-0.300309\pi\)
\(270\) 0 0
\(271\) 13.6282 11.4354i 0.827852 0.694650i −0.126945 0.991910i \(-0.540517\pi\)
0.954797 + 0.297260i \(0.0960727\pi\)
\(272\) −0.854944 0.150750i −0.0518386 0.00914054i
\(273\) −6.80574 3.92930i −0.411902 0.237812i
\(274\) 4.27513 + 7.40475i 0.258270 + 0.447337i
\(275\) 0 0
\(276\) 3.41662 1.24355i 0.205656 0.0748527i
\(277\) 18.0765 10.4365i 1.08611 0.627066i 0.153572 0.988137i \(-0.450922\pi\)
0.932538 + 0.361071i \(0.117589\pi\)
\(278\) 7.62466 + 4.40210i 0.457296 + 0.264020i
\(279\) −7.99817 + 45.3598i −0.478838 + 2.71562i
\(280\) 0 0
\(281\) −20.8354 17.4830i −1.24294 1.04295i −0.997289 0.0735907i \(-0.976554\pi\)
−0.245650 0.969359i \(-0.579001\pi\)
\(282\) −1.03867 + 0.183145i −0.0618516 + 0.0109061i
\(283\) −6.73563 + 18.5060i −0.400392 + 1.10007i 0.561700 + 0.827341i \(0.310148\pi\)
−0.962092 + 0.272726i \(0.912075\pi\)
\(284\) 6.89058 0.408881
\(285\) 0 0
\(286\) 4.56786 0.270103
\(287\) 11.0907 30.4714i 0.654662 1.79867i
\(288\) 7.00242 1.23472i 0.412622 0.0727564i
\(289\) 12.4454 + 10.4429i 0.732084 + 0.614291i
\(290\) 0 0
\(291\) −3.77893 + 21.4314i −0.221525 + 1.25633i
\(292\) 6.76942 + 3.90833i 0.396151 + 0.228718i
\(293\) −12.7973 + 7.38854i −0.747628 + 0.431643i −0.824836 0.565372i \(-0.808733\pi\)
0.0772085 + 0.997015i \(0.475399\pi\)
\(294\) −12.5386 + 4.56368i −0.731267 + 0.266159i
\(295\) 0 0
\(296\) 0.840567 + 1.45590i 0.0488570 + 0.0846227i
\(297\) 69.9999 + 40.4145i 4.06181 + 2.34508i
\(298\) −0.749969 0.132240i −0.0434445 0.00766044i
\(299\) −0.646993 + 0.542892i −0.0374166 + 0.0313962i
\(300\) 0 0
\(301\) −1.07976 6.12360i −0.0622361 0.352958i
\(302\) −2.08216 + 5.72070i −0.119815 + 0.329189i
\(303\) 32.3910i 1.86081i
\(304\) 3.89737 + 1.95205i 0.223530 + 0.111958i
\(305\) 0 0
\(306\) 5.80055 + 2.11123i 0.331595 + 0.120691i
\(307\) −4.17455 + 0.736086i −0.238254 + 0.0420106i −0.291500 0.956571i \(-0.594154\pi\)
0.0532459 + 0.998581i \(0.483043\pi\)
\(308\) 13.3015 15.8521i 0.757921 0.903255i
\(309\) −5.04328 + 4.23182i −0.286902 + 0.240740i
\(310\) 0 0
\(311\) 3.49343 6.05079i 0.198094 0.343109i −0.749816 0.661646i \(-0.769858\pi\)
0.947910 + 0.318537i \(0.103192\pi\)
\(312\) −2.03393 + 1.17429i −0.115149 + 0.0664811i
\(313\) 2.60608 + 7.16016i 0.147305 + 0.404716i 0.991298 0.131638i \(-0.0420235\pi\)
−0.843993 + 0.536354i \(0.819801\pi\)
\(314\) −22.9056 + 8.33694i −1.29264 + 0.470481i
\(315\) 0 0
\(316\) 1.14947 1.99094i 0.0646627 0.111999i
\(317\) −13.5297 2.38566i −0.759905 0.133992i −0.219749 0.975557i \(-0.570524\pi\)
−0.540156 + 0.841565i \(0.681635\pi\)
\(318\) 14.5214 + 17.3060i 0.814321 + 0.970470i
\(319\) 36.9043 + 30.9664i 2.06625 + 1.73379i
\(320\) 0 0
\(321\) 43.7348 + 15.9182i 2.44104 + 0.888466i
\(322\) 3.82618i 0.213224i
\(323\) 2.08283 + 3.15932i 0.115892 + 0.175789i
\(324\) −20.2271 −1.12373
\(325\) 0 0
\(326\) 0.748409 + 4.24444i 0.0414506 + 0.235078i
\(327\) −17.7718 + 21.1796i −0.982785 + 1.17124i
\(328\) −6.22923 7.42370i −0.343952 0.409905i
\(329\) 0.192730 1.09302i 0.0106255 0.0602604i
\(330\) 0 0
\(331\) 3.32212 + 5.75409i 0.182600 + 0.316273i 0.942765 0.333457i \(-0.108215\pi\)
−0.760165 + 0.649730i \(0.774882\pi\)
\(332\) −3.91502 10.7564i −0.214865 0.590336i
\(333\) −4.08838 11.2327i −0.224042 0.615550i
\(334\) −2.60578 4.51335i −0.142582 0.246959i
\(335\) 0 0
\(336\) −1.84754 + 10.4779i −0.100792 + 0.571619i
\(337\) 11.8323 + 14.1012i 0.644545 + 0.768139i 0.985081 0.172093i \(-0.0550528\pi\)
−0.340536 + 0.940232i \(0.610608\pi\)
\(338\) −8.00556 + 9.54066i −0.435445 + 0.518943i
\(339\) −5.98022 33.9155i −0.324801 1.84204i
\(340\) 0 0
\(341\) 40.0604 2.16939
\(342\) −24.8808 18.4812i −1.34540 0.999349i
\(343\) 9.38108i 0.506531i
\(344\) −1.74623 0.635576i −0.0941504 0.0342680i
\(345\) 0 0
\(346\) −5.38969 4.52249i −0.289752 0.243131i
\(347\) −4.76787 5.68212i −0.255952 0.305032i 0.622732 0.782435i \(-0.286023\pi\)
−0.878684 + 0.477403i \(0.841578\pi\)
\(348\) −24.3931 4.30117i −1.30761 0.230567i
\(349\) 9.57581 16.5858i 0.512581 0.887817i −0.487312 0.873228i \(-0.662023\pi\)
0.999894 0.0145891i \(-0.00464403\pi\)
\(350\) 0 0
\(351\) 9.07153 3.30177i 0.484202 0.176235i
\(352\) −2.11516 5.81136i −0.112739 0.309747i
\(353\) −1.38857 + 0.801691i −0.0739061 + 0.0426697i −0.536498 0.843902i \(-0.680253\pi\)
0.462592 + 0.886572i \(0.346920\pi\)
\(354\) −7.72713 + 13.3838i −0.410692 + 0.711340i
\(355\) 0 0
\(356\) 1.78351 1.49655i 0.0945261 0.0793168i
\(357\) −5.93716 + 7.07563i −0.314228 + 0.374482i
\(358\) 3.15084 0.555577i 0.166527 0.0293632i
\(359\) −20.2961 7.38717i −1.07119 0.389880i −0.254566 0.967055i \(-0.581933\pi\)
−0.816620 + 0.577175i \(0.804155\pi\)
\(360\) 0 0
\(361\) −5.48872 18.1899i −0.288880 0.957365i
\(362\) 4.73520i 0.248876i
\(363\) 29.6304 81.4089i 1.55519 4.27286i
\(364\) −0.429171 2.43395i −0.0224947 0.127574i
\(365\) 0 0
\(366\) −17.6048 + 14.7722i −0.920219 + 0.772155i
\(367\) −19.4420 3.42815i −1.01486 0.178948i −0.358610 0.933488i \(-0.616749\pi\)
−0.656255 + 0.754540i \(0.727860\pi\)
\(368\) 0.990275 + 0.571736i 0.0516217 + 0.0298038i
\(369\) 34.4535 + 59.6753i 1.79358 + 3.10657i
\(370\) 0 0
\(371\) −22.3399 + 8.13107i −1.15983 + 0.422144i
\(372\) −17.8377 + 10.2986i −0.924842 + 0.533958i
\(373\) 20.0572 + 11.5800i 1.03852 + 0.599592i 0.919415 0.393289i \(-0.128663\pi\)
0.119109 + 0.992881i \(0.461996\pi\)
\(374\) 0.932285 5.28725i 0.0482073 0.273397i
\(375\) 0 0
\(376\) −0.254093 0.213209i −0.0131039 0.0109954i
\(377\) 5.66634 0.999129i 0.291831 0.0514578i
\(378\) 14.9577 41.0960i 0.769343 2.11375i
\(379\) 3.52957 0.181302 0.0906508 0.995883i \(-0.471105\pi\)
0.0906508 + 0.995883i \(0.471105\pi\)
\(380\) 0 0
\(381\) −35.6904 −1.82847
\(382\) −6.30368 + 17.3192i −0.322524 + 0.886128i
\(383\) −36.1246 + 6.36973i −1.84588 + 0.325478i −0.983517 0.180815i \(-0.942127\pi\)
−0.862362 + 0.506293i \(0.831015\pi\)
\(384\) 2.43579 + 2.04387i 0.124301 + 0.104301i
\(385\) 0 0
\(386\) 2.35285 13.3437i 0.119757 0.679176i
\(387\) 11.4431 + 6.60667i 0.581685 + 0.335836i
\(388\) −5.92713 + 3.42203i −0.300904 + 0.173727i
\(389\) −23.1021 + 8.40847i −1.17132 + 0.426327i −0.853129 0.521699i \(-0.825298\pi\)
−0.318193 + 0.948026i \(0.603076\pi\)
\(390\) 0 0
\(391\) 0.496343 + 0.859691i 0.0251011 + 0.0434764i
\(392\) −3.63420 2.09821i −0.183555 0.105976i
\(393\) 47.5536 + 8.38498i 2.39876 + 0.422966i
\(394\) 6.27467 5.26507i 0.316113 0.265251i
\(395\) 0 0
\(396\) 7.63589 + 43.3053i 0.383718 + 2.17617i
\(397\) −6.96208 + 19.1282i −0.349417 + 0.960015i 0.633137 + 0.774039i \(0.281767\pi\)
−0.982554 + 0.185976i \(0.940455\pi\)
\(398\) 5.94246i 0.297868i
\(399\) 38.7197 25.5265i 1.93841 1.27792i
\(400\) 0 0
\(401\) −18.9313 6.89045i −0.945386 0.344092i −0.177096 0.984194i \(-0.556670\pi\)
−0.768291 + 0.640101i \(0.778892\pi\)
\(402\) −9.15910 + 1.61500i −0.456814 + 0.0805487i
\(403\) 3.07547 3.66520i 0.153200 0.182576i
\(404\) −7.80356 + 6.54797i −0.388242 + 0.325774i
\(405\) 0 0
\(406\) 13.0329 22.5736i 0.646811 1.12031i
\(407\) −9.00379 + 5.19834i −0.446301 + 0.257672i
\(408\) 0.944111 + 2.59392i 0.0467405 + 0.128418i
\(409\) 12.1073 4.40670i 0.598668 0.217897i −0.0248698 0.999691i \(-0.507917\pi\)
0.623537 + 0.781794i \(0.285695\pi\)
\(410\) 0 0
\(411\) 13.5936 23.5448i 0.670523 1.16138i
\(412\) −2.03904 0.359538i −0.100456 0.0177132i
\(413\) −10.4537 12.4582i −0.514393 0.613030i
\(414\) −6.22840 5.22625i −0.306109 0.256856i
\(415\) 0 0
\(416\) −0.694074 0.252622i −0.0340298 0.0123858i
\(417\) 27.9946i 1.37090i
\(418\) −12.0721 + 24.1026i −0.590465 + 1.17890i
\(419\) −20.0166 −0.977876 −0.488938 0.872319i \(-0.662616\pi\)
−0.488938 + 0.872319i \(0.662616\pi\)
\(420\) 0 0
\(421\) 1.16311 + 6.59634i 0.0566867 + 0.321486i 0.999944 0.0105764i \(-0.00336662\pi\)
−0.943257 + 0.332062i \(0.892256\pi\)
\(422\) 1.12077 1.33569i 0.0545585 0.0650202i
\(423\) 1.51601 + 1.80672i 0.0737112 + 0.0878455i
\(424\) −1.23375 + 6.99694i −0.0599161 + 0.339801i
\(425\) 0 0
\(426\) −10.9550 18.9746i −0.530770 0.919321i
\(427\) −8.27149 22.7257i −0.400285 1.09978i
\(428\) 5.00620 + 13.7544i 0.241984 + 0.664845i
\(429\) −7.26219 12.5785i −0.350622 0.607295i
\(430\) 0 0
\(431\) −4.86528 + 27.5924i −0.234352 + 1.32908i 0.609621 + 0.792693i \(0.291321\pi\)
−0.843974 + 0.536385i \(0.819790\pi\)
\(432\) −8.40121 10.0122i −0.404203 0.481711i
\(433\) 14.5384 17.3262i 0.698673 0.832646i −0.293702 0.955897i \(-0.594887\pi\)
0.992376 + 0.123251i \(0.0393319\pi\)
\(434\) −3.76386 21.3459i −0.180671 1.02464i
\(435\) 0 0
\(436\) −8.69520 −0.416425
\(437\) −1.15471 4.84868i −0.0552373 0.231944i
\(438\) 24.8546i 1.18760i
\(439\) −3.88563 1.41425i −0.185451 0.0674986i 0.247626 0.968856i \(-0.420350\pi\)
−0.433076 + 0.901357i \(0.642572\pi\)
\(440\) 0 0
\(441\) 22.8575 + 19.1798i 1.08845 + 0.913322i
\(442\) −0.412168 0.491202i −0.0196048 0.0233641i
\(443\) −28.5001 5.02534i −1.35408 0.238761i −0.550937 0.834547i \(-0.685730\pi\)
−0.803144 + 0.595786i \(0.796841\pi\)
\(444\) 2.67274 4.62933i 0.126843 0.219698i
\(445\) 0 0
\(446\) 24.8463 9.04332i 1.17651 0.428214i
\(447\) 0.828187 + 2.27543i 0.0391719 + 0.107624i
\(448\) −2.89781 + 1.67305i −0.136909 + 0.0790443i
\(449\) −2.78070 + 4.81632i −0.131229 + 0.227296i −0.924151 0.382028i \(-0.875226\pi\)
0.792921 + 0.609324i \(0.208559\pi\)
\(450\) 0 0
\(451\) 45.9106 38.5236i 2.16185 1.81400i
\(452\) 6.96192 8.29690i 0.327461 0.390253i
\(453\) 19.0634 3.36139i 0.895676 0.157932i
\(454\) 25.7920 + 9.38751i 1.21048 + 0.440578i
\(455\) 0 0
\(456\) −0.820886 13.8356i −0.0384415 0.647913i
\(457\) 3.44090i 0.160959i 0.996756 + 0.0804793i \(0.0256451\pi\)
−0.996756 + 0.0804793i \(0.974355\pi\)
\(458\) 3.95792 10.8743i 0.184941 0.508122i
\(459\) −1.97029 11.1741i −0.0919654 0.521562i
\(460\) 0 0
\(461\) −3.88985 + 3.26397i −0.181169 + 0.152018i −0.728862 0.684661i \(-0.759950\pi\)
0.547693 + 0.836679i \(0.315506\pi\)
\(462\) −64.7990 11.4258i −3.01472 0.531577i
\(463\) 4.44107 + 2.56405i 0.206394 + 0.119162i 0.599634 0.800274i \(-0.295313\pi\)
−0.393240 + 0.919436i \(0.628646\pi\)
\(464\) −3.89494 6.74624i −0.180818 0.313186i
\(465\) 0 0
\(466\) 12.0824 4.39765i 0.559708 0.203717i
\(467\) −25.6535 + 14.8110i −1.18710 + 0.685373i −0.957646 0.287947i \(-0.907027\pi\)
−0.229454 + 0.973320i \(0.573694\pi\)
\(468\) 4.54829 + 2.62595i 0.210245 + 0.121385i
\(469\) 1.69952 9.63844i 0.0784764 0.445062i
\(470\) 0 0
\(471\) 59.3737 + 49.8205i 2.73580 + 2.29561i
\(472\) −4.78646 + 0.843982i −0.220315 + 0.0388474i
\(473\) 3.93061 10.7993i 0.180729 0.496550i
\(474\) −7.30992 −0.335756
\(475\) 0 0
\(476\) −2.90486 −0.133144
\(477\) 17.2785 47.4722i 0.791127 2.17360i
\(478\) −11.1423 + 1.96468i −0.509636 + 0.0898626i
\(479\) 28.8677 + 24.2229i 1.31900 + 1.10677i 0.986516 + 0.163664i \(0.0523314\pi\)
0.332485 + 0.943109i \(0.392113\pi\)
\(480\) 0 0
\(481\) −0.215622 + 1.22285i −0.00983151 + 0.0557573i
\(482\) 20.6071 + 11.8975i 0.938626 + 0.541916i
\(483\) 10.5361 6.08303i 0.479410 0.276788i
\(484\) 25.6027 9.31863i 1.16376 0.423574i
\(485\) 0 0
\(486\) 12.5531 + 21.7426i 0.569420 + 0.986264i
\(487\) −15.3757 8.87714i −0.696738 0.402262i 0.109393 0.993999i \(-0.465109\pi\)
−0.806131 + 0.591737i \(0.798442\pi\)
\(488\) −7.11777 1.25506i −0.322206 0.0568137i
\(489\) 10.4980 8.80890i 0.474738 0.398352i
\(490\) 0 0
\(491\) −3.87201 21.9592i −0.174741 0.991006i −0.938442 0.345436i \(-0.887731\pi\)
0.763701 0.645570i \(-0.223380\pi\)
\(492\) −10.5391 + 28.9559i −0.475139 + 1.30543i
\(493\) 6.76266i 0.304575i
\(494\) 1.27841 + 2.95487i 0.0575183 + 0.132946i
\(495\) 0 0
\(496\) −6.08708 2.21552i −0.273318 0.0994796i
\(497\) 22.7063 4.00374i 1.01852 0.179592i
\(498\) −23.3957 + 27.8819i −1.04838 + 1.24942i
\(499\) 14.4603 12.1337i 0.647334 0.543177i −0.258927 0.965897i \(-0.583369\pi\)
0.906261 + 0.422719i \(0.138924\pi\)
\(500\) 0 0
\(501\) −8.28559 + 14.3511i −0.370173 + 0.641158i
\(502\) 22.5805 13.0369i 1.00782 0.581864i
\(503\) −13.9751 38.3963i −0.623119 1.71201i −0.699221 0.714905i \(-0.746470\pi\)
0.0761023 0.997100i \(-0.475752\pi\)
\(504\) 22.3575 8.13745i 0.995880 0.362471i
\(505\) 0 0
\(506\) −3.53580 + 6.12418i −0.157185 + 0.272253i
\(507\) 38.9997 + 6.87669i 1.73204 + 0.305405i
\(508\) −7.21496 8.59845i −0.320112 0.381495i
\(509\) 10.1977 + 8.55692i 0.452007 + 0.379279i 0.840180 0.542308i \(-0.182449\pi\)
−0.388173 + 0.921586i \(0.626894\pi\)
\(510\) 0 0
\(511\) 24.5780 + 8.94566i 1.08727 + 0.395733i
\(512\) 1.00000i 0.0441942i
\(513\) −6.55254 + 56.5926i −0.289302 + 2.49862i
\(514\) −10.1528 −0.447822
\(515\) 0 0
\(516\) 1.02606 + 5.81905i 0.0451696 + 0.256170i
\(517\) 1.31856 1.57139i 0.0579900 0.0691098i
\(518\) 3.61584 + 4.30919i 0.158871 + 0.189335i
\(519\) −3.88477 + 22.0316i −0.170523 + 0.967082i
\(520\) 0 0
\(521\) 13.8343 + 23.9617i 0.606091 + 1.04978i 0.991878 + 0.127193i \(0.0405968\pi\)
−0.385787 + 0.922588i \(0.626070\pi\)
\(522\) 18.9443 + 52.0492i 0.829172 + 2.27813i
\(523\) 0.367514 + 1.00974i 0.0160703 + 0.0441527i 0.947468 0.319849i \(-0.103632\pi\)
−0.931398 + 0.364002i \(0.881410\pi\)
\(524\) 7.59305 + 13.1516i 0.331704 + 0.574528i
\(525\) 0 0
\(526\) −2.97399 + 16.8663i −0.129672 + 0.735407i
\(527\) −3.61474 4.30788i −0.157460 0.187654i
\(528\) −12.6399 + 15.0637i −0.550083 + 0.655563i
\(529\) 3.76686 + 21.3629i 0.163776 + 0.928822i
\(530\) 0 0
\(531\) 34.5589 1.49973
\(532\) 13.9771 + 4.16797i 0.605985 + 0.180704i
\(533\) 7.15792i 0.310044i
\(534\) −6.95655 2.53198i −0.301039 0.109569i
\(535\) 0 0
\(536\) −2.24063 1.88011i −0.0967804 0.0812084i
\(537\) −6.53924 7.79316i −0.282189 0.336300i
\(538\) −22.4628 3.96080i −0.968442 0.170762i
\(539\) 12.9760 22.4751i 0.558916 0.968071i
\(540\) 0 0
\(541\) −14.5180 + 5.28411i −0.624177 + 0.227182i −0.634695 0.772763i \(-0.718874\pi\)
0.0105181 + 0.999945i \(0.496652\pi\)
\(542\) −6.08464 16.7174i −0.261358 0.718074i
\(543\) −13.0393 + 7.52824i −0.559569 + 0.323068i
\(544\) −0.434067 + 0.751825i −0.0186104 + 0.0322342i
\(545\) 0 0
\(546\) −6.02003 + 5.05141i −0.257634 + 0.216180i
\(547\) −21.5990 + 25.7407i −0.923508 + 1.10059i 0.0711601 + 0.997465i \(0.477330\pi\)
−0.994668 + 0.103129i \(0.967115\pi\)
\(548\) 8.42037 1.48474i 0.359700 0.0634248i
\(549\) 48.2920 + 17.5769i 2.06105 + 0.750162i
\(550\) 0 0
\(551\) −9.70322 + 32.5394i −0.413371 + 1.38622i
\(552\) 3.63589i 0.154754i
\(553\) 2.63099 7.22858i 0.111881 0.307391i
\(554\) −3.62454 20.5558i −0.153992 0.873333i
\(555\) 0 0
\(556\) 6.74440 5.65923i 0.286026 0.240005i
\(557\) 14.0324 + 2.47429i 0.594571 + 0.104839i 0.462833 0.886446i \(-0.346833\pi\)
0.131739 + 0.991285i \(0.457944\pi\)
\(558\) 39.8888 + 23.0298i 1.68863 + 0.974929i
\(559\) −0.686287 1.18868i −0.0290269 0.0502760i
\(560\) 0 0
\(561\) −16.0417 + 5.83869i −0.677280 + 0.246510i
\(562\) −23.5548 + 13.5994i −0.993599 + 0.573655i
\(563\) −12.7930 7.38607i −0.539163 0.311286i 0.205577 0.978641i \(-0.434093\pi\)
−0.744740 + 0.667355i \(0.767426\pi\)
\(564\) −0.183145 + 1.03867i −0.00771178 + 0.0437357i
\(565\) 0 0
\(566\) 15.0862 + 12.6588i 0.634122 + 0.532091i
\(567\) −66.6539 + 11.7529i −2.79920 + 0.493574i
\(568\) 2.35672 6.47503i 0.0988857 0.271686i
\(569\) −19.4550 −0.815598 −0.407799 0.913072i \(-0.633704\pi\)
−0.407799 + 0.913072i \(0.633704\pi\)
\(570\) 0 0
\(571\) −39.3956 −1.64866 −0.824328 0.566112i \(-0.808447\pi\)
−0.824328 + 0.566112i \(0.808447\pi\)
\(572\) 1.56230 4.29238i 0.0653230 0.179473i
\(573\) 57.7137 10.1765i 2.41102 0.425129i
\(574\) −24.8405 20.8436i −1.03682 0.869997i
\(575\) 0 0
\(576\) 1.23472 7.00242i 0.0514465 0.291768i
\(577\) −13.7657 7.94763i −0.573073 0.330864i 0.185303 0.982682i \(-0.440673\pi\)
−0.758376 + 0.651818i \(0.774007\pi\)
\(578\) 14.0697 8.12317i 0.585224 0.337879i
\(579\) −40.4852 + 14.7354i −1.68251 + 0.612382i
\(580\) 0 0
\(581\) −19.1510 33.1706i −0.794519 1.37615i
\(582\) 18.8464 + 10.8810i 0.781210 + 0.451032i
\(583\) −43.2713 7.62990i −1.79212 0.315998i
\(584\) 5.98791 5.02445i 0.247781 0.207913i
\(585\) 0 0
\(586\) 2.56601 + 14.5526i 0.106001 + 0.601161i
\(587\) 4.40009 12.0891i 0.181611 0.498973i −0.815163 0.579232i \(-0.803353\pi\)
0.996774 + 0.0802592i \(0.0255748\pi\)
\(588\) 13.3433i 0.550269i
\(589\) 11.2117 + 25.9144i 0.461971 + 1.06778i
\(590\) 0 0
\(591\) −24.4742 8.90787i −1.00673 0.366421i
\(592\) 1.65559 0.291926i 0.0680445 0.0119981i
\(593\) −1.39986 + 1.66829i −0.0574855 + 0.0685086i −0.794021 0.607890i \(-0.792016\pi\)
0.736535 + 0.676399i \(0.236460\pi\)
\(594\) 61.9185 51.9558i 2.54055 2.13177i
\(595\) 0 0
\(596\) −0.380769 + 0.659512i −0.0155969 + 0.0270146i
\(597\) −16.3637 + 9.44759i −0.669722 + 0.386664i
\(598\) 0.288867 + 0.793654i 0.0118126 + 0.0324549i
\(599\) 3.32108 1.20877i 0.135696 0.0493891i −0.273280 0.961935i \(-0.588108\pi\)
0.408975 + 0.912545i \(0.365886\pi\)
\(600\) 0 0
\(601\) −11.2019 + 19.4022i −0.456935 + 0.791434i −0.998797 0.0490333i \(-0.984386\pi\)
0.541863 + 0.840467i \(0.317719\pi\)
\(602\) −6.12360 1.07976i −0.249579 0.0440076i
\(603\) 13.3684 + 15.9319i 0.544405 + 0.648796i
\(604\) 4.66356 + 3.91319i 0.189757 + 0.159225i
\(605\) 0 0
\(606\) 30.4376 + 11.0784i 1.23644 + 0.450028i
\(607\) 12.5717i 0.510269i 0.966906 + 0.255134i \(0.0821197\pi\)
−0.966906 + 0.255134i \(0.917880\pi\)
\(608\) 3.16730 2.99469i 0.128451 0.121451i
\(609\) −82.8812 −3.35851
\(610\) 0 0
\(611\) −0.0425431 0.241274i −0.00172111 0.00976090i
\(612\) 3.96781 4.72865i 0.160389 0.191144i
\(613\) −30.1404 35.9199i −1.21736 1.45079i −0.854901 0.518791i \(-0.826382\pi\)
−0.362458 0.932000i \(-0.618062\pi\)
\(614\) −0.736086 + 4.17455i −0.0297060 + 0.168471i
\(615\) 0 0
\(616\) −10.3467 17.9210i −0.416880 0.722058i
\(617\) 0.180720 + 0.496525i 0.00727553 + 0.0199893i 0.943277 0.332006i \(-0.107725\pi\)
−0.936002 + 0.351995i \(0.885503\pi\)
\(618\) 2.25170 + 6.18650i 0.0905768 + 0.248858i
\(619\) 10.9317 + 18.9343i 0.439383 + 0.761034i 0.997642 0.0686330i \(-0.0218637\pi\)
−0.558259 + 0.829667i \(0.688530\pi\)
\(620\) 0 0
\(621\) −2.59520 + 14.7181i −0.104142 + 0.590616i
\(622\) −4.49106 5.35224i −0.180075 0.214605i
\(623\) 5.00760 5.96783i 0.200625 0.239096i
\(624\) 0.407827 + 2.31290i 0.0163261 + 0.0925901i
\(625\) 0 0
\(626\) 7.61968 0.304544
\(627\) 85.5640 5.07663i 3.41710 0.202741i
\(628\) 24.3756i 0.972692i
\(629\) 1.37143 + 0.499161i 0.0546826 + 0.0199028i
\(630\) 0 0
\(631\) 23.0776 + 19.3644i 0.918705 + 0.770885i 0.973755 0.227598i \(-0.0730873\pi\)
−0.0550497 + 0.998484i \(0.517532\pi\)
\(632\) −1.47773 1.76109i −0.0587810 0.0700524i
\(633\) −5.45993 0.962734i −0.217013 0.0382652i
\(634\) −6.86922 + 11.8978i −0.272812 + 0.472524i
\(635\) 0 0
\(636\) 21.2289 7.72669i 0.841781 0.306383i
\(637\) −1.06011 2.91263i −0.0420031 0.115402i
\(638\) 41.7209 24.0876i 1.65175 0.953637i
\(639\) −24.4976 + 42.4310i −0.969109 + 1.67855i
\(640\) 0 0
\(641\) 24.6653 20.6967i 0.974223 0.817470i −0.00898505 0.999960i \(-0.502860\pi\)
0.983208 + 0.182490i \(0.0584156\pi\)
\(642\) 29.9164 35.6530i 1.18071 1.40711i
\(643\) 25.2027 4.44391i 0.993896 0.175251i 0.347030 0.937854i \(-0.387190\pi\)
0.646866 + 0.762604i \(0.276079\pi\)
\(644\) 3.59543 + 1.30863i 0.141680 + 0.0515672i
\(645\) 0 0
\(646\) 3.68115 0.876666i 0.144833 0.0344920i
\(647\) 18.8860i 0.742483i 0.928536 + 0.371242i \(0.121068\pi\)
−0.928536 + 0.371242i \(0.878932\pi\)
\(648\) −6.91809 + 19.0073i −0.271768 + 0.746677i
\(649\) −5.21946 29.6010i −0.204882 1.16194i
\(650\) 0 0
\(651\) −52.7961 + 44.3012i −2.06924 + 1.73630i
\(652\) 4.24444 + 0.748409i 0.166225 + 0.0293100i
\(653\) −21.5038 12.4152i −0.841510 0.485846i 0.0162674 0.999868i \(-0.494822\pi\)
−0.857777 + 0.514022i \(0.828155\pi\)
\(654\) 13.8240 + 23.9439i 0.540562 + 0.936282i
\(655\) 0 0
\(656\) −9.10652 + 3.31450i −0.355550 + 0.129410i
\(657\) −48.1336 + 27.7900i −1.87787 + 1.08419i
\(658\) −0.961190 0.554943i −0.0374711 0.0216339i
\(659\) −5.44946 + 30.9054i −0.212281 + 1.20391i 0.673282 + 0.739386i \(0.264884\pi\)
−0.885563 + 0.464519i \(0.846227\pi\)
\(660\) 0 0
\(661\) −14.2738 11.9771i −0.555186 0.465857i 0.321506 0.946907i \(-0.395811\pi\)
−0.876693 + 0.481051i \(0.840255\pi\)
\(662\) 6.54331 1.15376i 0.254313 0.0448422i
\(663\) −0.697338 + 1.91592i −0.0270824 + 0.0744082i
\(664\) −11.4468 −0.444220
\(665\) 0 0
\(666\) −11.9536 −0.463193
\(667\) −3.04655 + 8.37032i −0.117963 + 0.324100i
\(668\) −5.13239 + 0.904979i −0.198578 + 0.0350147i
\(669\) −64.4044 54.0417i −2.49002 2.08937i
\(670\) 0 0
\(671\) 7.76167 44.0186i 0.299636 1.69932i
\(672\) 9.21415 + 5.31979i 0.355444 + 0.205215i
\(673\) −12.6234 + 7.28810i −0.486594 + 0.280935i −0.723161 0.690680i \(-0.757311\pi\)
0.236566 + 0.971615i \(0.423978\pi\)
\(674\) 17.2976 6.29582i 0.666280 0.242506i
\(675\) 0 0
\(676\) 6.22722 + 10.7859i 0.239509 + 0.414841i
\(677\) 2.11001 + 1.21821i 0.0810941 + 0.0468197i 0.539999 0.841666i \(-0.318425\pi\)
−0.458905 + 0.888486i \(0.651758\pi\)
\(678\) −33.9155 5.98022i −1.30252 0.229669i
\(679\) −17.5431 + 14.7204i −0.673244 + 0.564918i
\(680\) 0 0
\(681\) −15.1549 85.9479i −0.580738 3.29353i
\(682\) 13.7015 37.6445i 0.524656 1.44148i
\(683\) 15.0962i 0.577639i 0.957384 + 0.288820i \(0.0932628\pi\)
−0.957384 + 0.288820i \(0.906737\pi\)
\(684\) −25.8764 + 17.0594i −0.989409 + 0.652282i
\(685\) 0 0
\(686\) 8.81533 + 3.20852i 0.336571 + 0.122502i
\(687\) −36.2370 + 6.38955i −1.38253 + 0.243777i
\(688\) −1.19449 + 1.42354i −0.0455396 + 0.0542720i
\(689\) −4.02004 + 3.37322i −0.153151 + 0.128509i
\(690\) 0 0
\(691\) 6.12019 10.6005i 0.232823 0.403261i −0.725815 0.687890i \(-0.758537\pi\)
0.958638 + 0.284629i \(0.0918704\pi\)
\(692\) −6.09314 + 3.51787i −0.231626 + 0.133729i
\(693\) 50.3246 + 138.266i 1.91167 + 5.25228i
\(694\) −6.97015 + 2.53693i −0.264583 + 0.0963005i
\(695\) 0 0
\(696\) −12.3847 + 21.4510i −0.469442 + 0.813097i
\(697\) −8.28523 1.46091i −0.313825 0.0553359i
\(698\) −12.3104 14.6710i −0.465956 0.555305i
\(699\) −31.3190 26.2798i −1.18459 0.993992i
\(700\) 0 0
\(701\) −41.9967 15.2856i −1.58620 0.577328i −0.609656 0.792666i \(-0.708692\pi\)
−0.976539 + 0.215339i \(0.930914\pi\)
\(702\) 9.65372i 0.364356i
\(703\) −5.88261 4.36954i −0.221867 0.164800i
\(704\) −6.18432 −0.233080
\(705\) 0 0
\(706\) 0.278424 + 1.57902i 0.0104786 + 0.0594273i
\(707\) −21.9102 + 26.1115i −0.824017 + 0.982026i
\(708\) 9.93381 + 11.8386i 0.373335 + 0.444924i
\(709\) 2.78707 15.8063i 0.104671 0.593617i −0.886681 0.462382i \(-0.846995\pi\)
0.991351 0.131235i \(-0.0418941\pi\)
\(710\) 0 0
\(711\) 8.17325 + 14.1565i 0.306521 + 0.530910i
\(712\) −0.796295 2.18780i −0.0298424 0.0819914i
\(713\) 2.53338 + 6.96040i 0.0948758 + 0.260669i
\(714\) 4.61829 + 7.99911i 0.172835 + 0.299359i
\(715\) 0 0
\(716\) 0.555577 3.15084i 0.0207629 0.117752i
\(717\) 23.1247 + 27.5589i 0.863606 + 1.02921i
\(718\) −13.8833 + 16.5455i −0.518122 + 0.617474i
\(719\) 0.265213 + 1.50410i 0.00989079 + 0.0560934i 0.989354 0.145531i \(-0.0464891\pi\)
−0.979463 + 0.201624i \(0.935378\pi\)
\(720\) 0 0
\(721\) −6.92809 −0.258016
\(722\) −18.9702 1.06362i −0.705998 0.0395838i
\(723\) 75.6608i 2.81385i
\(724\) −4.44963 1.61953i −0.165369 0.0601894i
\(725\) 0 0
\(726\) −66.3651 55.6869i −2.46304 2.06674i
\(727\) 24.4052 + 29.0850i 0.905139 + 1.07870i 0.996559 + 0.0828900i \(0.0264150\pi\)
−0.0914199 + 0.995812i \(0.529141\pi\)
\(728\) −2.43395 0.429171i −0.0902081 0.0159061i
\(729\) 9.57428 16.5831i 0.354603 0.614190i
\(730\) 0 0
\(731\) −1.51596 + 0.551764i −0.0560698 + 0.0204077i
\(732\) 7.86012 + 21.5955i 0.290519 + 0.798193i
\(733\) −27.7319 + 16.0110i −1.02430 + 0.591381i −0.915347 0.402666i \(-0.868084\pi\)
−0.108955 + 0.994047i \(0.534750\pi\)
\(734\) −9.87097 + 17.0970i −0.364344 + 0.631062i
\(735\) 0 0
\(736\) 0.875950 0.735009i 0.0322879 0.0270928i
\(737\) 11.6272 13.8568i 0.428294 0.510421i
\(738\) 67.8602 11.9656i 2.49797 0.440459i
\(739\) −36.3892 13.2446i −1.33860 0.487210i −0.429228 0.903196i \(-0.641214\pi\)
−0.909371 + 0.415986i \(0.863436\pi\)
\(740\) 0 0
\(741\) 6.10434 8.21814i 0.224249 0.301901i
\(742\) 23.7737i 0.872758i
\(743\) −10.6802 + 29.3436i −0.391819 + 1.07651i 0.574351 + 0.818609i \(0.305254\pi\)
−0.966170 + 0.257905i \(0.916968\pi\)
\(744\) 3.57667 + 20.2843i 0.131127 + 0.743658i
\(745\) 0 0
\(746\) 17.7417 14.8870i 0.649568 0.545052i
\(747\) 80.1551 + 14.1335i 2.93272 + 0.517118i
\(748\) −4.64953 2.68441i −0.170004 0.0981517i
\(749\) 24.4887 + 42.4157i 0.894798 + 1.54984i
\(750\) 0 0
\(751\) 32.3847 11.7871i 1.18173 0.430116i 0.324920 0.945741i \(-0.394663\pi\)
0.856814 + 0.515625i \(0.172440\pi\)
\(752\) −0.287256 + 0.165847i −0.0104752 + 0.00604784i
\(753\) −71.7991 41.4532i −2.61650 1.51064i
\(754\) 0.999129 5.66634i 0.0363861 0.206356i
\(755\) 0 0
\(756\) −33.5018 28.1113i −1.21845 1.02240i
\(757\) −2.66191 + 0.469366i −0.0967487 + 0.0170594i −0.221813 0.975089i \(-0.571197\pi\)
0.125064 + 0.992149i \(0.460086\pi\)
\(758\) 1.20718 3.31671i 0.0438468 0.120468i
\(759\) 22.4855 0.816173
\(760\) 0 0
\(761\) 9.19327 0.333256 0.166628 0.986020i \(-0.446712\pi\)
0.166628 + 0.986020i \(0.446712\pi\)
\(762\) −12.2068 + 33.5380i −0.442207 + 1.21495i
\(763\) −28.6530 + 5.05230i −1.03731 + 0.182906i
\(764\) 14.1187 + 11.8470i 0.510798 + 0.428611i
\(765\) 0 0
\(766\) −6.36973 + 36.1246i −0.230148 + 1.30523i
\(767\) −3.10895 1.79495i −0.112258 0.0648120i
\(768\) 2.75370 1.58985i 0.0993654 0.0573686i
\(769\) 0.0570740 0.0207732i 0.00205814 0.000749102i −0.340991 0.940067i \(-0.610763\pi\)
0.343049 + 0.939318i \(0.388540\pi\)
\(770\) 0 0
\(771\) 16.1414 + 27.9578i 0.581320 + 1.00688i
\(772\) −11.7343 6.77477i −0.422325 0.243829i
\(773\) 9.75016 + 1.71922i 0.350689 + 0.0618359i 0.346218 0.938154i \(-0.387466\pi\)
0.00447097 + 0.999990i \(0.498577\pi\)
\(774\) 10.1220 8.49337i 0.363828 0.305288i
\(775\) 0 0
\(776\) 1.18846 + 6.74008i 0.0426632 + 0.241955i
\(777\) 6.11757 16.8079i 0.219466 0.602979i
\(778\) 24.5847i 0.881405i
\(779\) 37.7693 + 18.9172i 1.35322 + 0.677779i
\(780\) 0 0
\(781\) 40.0437 + 14.5747i 1.43288 + 0.521524i
\(782\) 0.977604 0.172378i 0.0349591 0.00616423i
\(783\) 65.4445