Properties

Label 441.2.f.h.148.9
Level $441$
Weight $2$
Character 441.148
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 148.9
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.h.295.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.863305 + 1.49529i) q^{2} +(-1.09452 + 1.34239i) q^{3} +(-0.490592 + 0.849731i) q^{4} +(1.75616 - 3.04175i) q^{5} +(-2.95217 - 0.477737i) q^{6} +1.75910 q^{8} +(-0.604030 - 2.93856i) q^{9} +O(q^{10})\) \(q+(0.863305 + 1.49529i) q^{2} +(-1.09452 + 1.34239i) q^{3} +(-0.490592 + 0.849731i) q^{4} +(1.75616 - 3.04175i) q^{5} +(-2.95217 - 0.477737i) q^{6} +1.75910 q^{8} +(-0.604030 - 2.93856i) q^{9} +6.06439 q^{10} +(3.04532 + 5.27465i) q^{11} +(-0.603706 - 1.58862i) q^{12} +(-0.560139 + 0.970190i) q^{13} +(2.16106 + 5.68672i) q^{15} +(2.49982 + 4.32982i) q^{16} -1.20396 q^{17} +(3.87254 - 3.44008i) q^{18} +2.20537 q^{19} +(1.72311 + 2.98452i) q^{20} +(-5.25808 + 9.10727i) q^{22} +(0.636695 - 1.10279i) q^{23} +(-1.92538 + 2.36140i) q^{24} +(-3.66817 - 6.35345i) q^{25} -1.93429 q^{26} +(4.60583 + 2.40548i) q^{27} +(-3.10262 - 5.37390i) q^{29} +(-6.63763 + 8.14079i) q^{30} +(-0.0942019 + 0.163162i) q^{31} +(-2.55712 + 4.42907i) q^{32} +(-10.4138 - 1.68522i) q^{33} +(-1.03938 - 1.80026i) q^{34} +(2.79332 + 0.928373i) q^{36} +3.57670 q^{37} +(1.90391 + 3.29767i) q^{38} +(-0.689288 - 1.81382i) q^{39} +(3.08925 - 5.35074i) q^{40} +(-1.68320 + 2.91538i) q^{41} +(-1.90276 - 3.29567i) q^{43} -5.97604 q^{44} +(-9.99915 - 3.32326i) q^{45} +2.19865 q^{46} +(-2.86035 - 4.95427i) q^{47} +(-8.54843 - 1.38336i) q^{48} +(6.33349 - 10.9699i) q^{50} +(1.31776 - 1.61618i) q^{51} +(-0.549600 - 0.951935i) q^{52} -8.33827 q^{53} +(0.379341 + 8.96371i) q^{54} +21.3922 q^{55} +(-2.41384 + 2.96047i) q^{57} +(5.35702 - 9.27862i) q^{58} +(-5.63427 + 9.75883i) q^{59} +(-5.89238 - 0.953538i) q^{60} +(6.00109 + 10.3942i) q^{61} -0.325300 q^{62} +1.16898 q^{64} +(1.96738 + 3.40761i) q^{65} +(-6.47041 - 17.0265i) q^{66} +(3.95652 - 6.85289i) q^{67} +(0.590651 - 1.02304i) q^{68} +(0.783494 + 2.06172i) q^{69} -12.2052 q^{71} +(-1.06255 - 5.16922i) q^{72} +5.31473 q^{73} +(3.08779 + 5.34820i) q^{74} +(12.5437 + 2.02989i) q^{75} +(-1.08194 + 1.87397i) q^{76} +(2.11712 - 2.59657i) q^{78} +(-4.60855 - 7.98225i) q^{79} +17.5603 q^{80} +(-8.27029 + 3.54996i) q^{81} -5.81246 q^{82} +(-0.624950 - 1.08245i) q^{83} +(-2.11433 + 3.66213i) q^{85} +(3.28532 - 5.69034i) q^{86} +(10.6098 + 1.71693i) q^{87} +(5.35702 + 9.27862i) q^{88} -5.54131 q^{89} +(-3.66308 - 17.8206i) q^{90} +(0.624715 + 1.08204i) q^{92} +(-0.115922 - 0.305041i) q^{93} +(4.93871 - 8.55409i) q^{94} +(3.87298 - 6.70820i) q^{95} +(-3.14671 - 8.28038i) q^{96} +(-8.24277 - 14.2769i) q^{97} +(13.6604 - 12.1349i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} + 8q^{9} + O(q^{10}) \) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} + 8q^{9} + 20q^{11} + 4q^{15} - 12q^{16} + 4q^{18} + 32q^{23} - 12q^{25} + 16q^{29} + 48q^{32} - 4q^{36} + 24q^{37} + 32q^{39} - 112q^{44} - 48q^{46} - 4q^{50} - 56q^{51} - 64q^{53} - 12q^{57} - 88q^{60} + 96q^{64} + 60q^{65} - 12q^{67} - 112q^{71} + 168q^{72} + 68q^{74} - 60q^{78} + 12q^{79} + 80q^{81} + 12q^{85} + 76q^{86} + 16q^{92} - 80q^{93} + 64q^{95} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.863305 + 1.49529i 0.610449 + 1.05733i 0.991165 + 0.132637i \(0.0423443\pi\)
−0.380716 + 0.924692i \(0.624322\pi\)
\(3\) −1.09452 + 1.34239i −0.631924 + 0.775030i
\(4\) −0.490592 + 0.849731i −0.245296 + 0.424865i
\(5\) 1.75616 3.04175i 0.785377 1.36031i −0.143397 0.989665i \(-0.545803\pi\)
0.928774 0.370647i \(-0.120864\pi\)
\(6\) −2.95217 0.477737i −1.20522 0.195035i
\(7\) 0 0
\(8\) 1.75910 0.621935
\(9\) −0.604030 2.93856i −0.201343 0.979521i
\(10\) 6.06439 1.91773
\(11\) 3.04532 + 5.27465i 0.918199 + 1.59037i 0.802150 + 0.597123i \(0.203690\pi\)
0.116049 + 0.993244i \(0.462977\pi\)
\(12\) −0.603706 1.58862i −0.174275 0.458595i
\(13\) −0.560139 + 0.970190i −0.155355 + 0.269082i −0.933188 0.359388i \(-0.882985\pi\)
0.777833 + 0.628471i \(0.216319\pi\)
\(14\) 0 0
\(15\) 2.16106 + 5.68672i 0.557984 + 1.46831i
\(16\) 2.49982 + 4.32982i 0.624956 + 1.08246i
\(17\) −1.20396 −0.292002 −0.146001 0.989284i \(-0.546640\pi\)
−0.146001 + 0.989284i \(0.546640\pi\)
\(18\) 3.87254 3.44008i 0.912766 0.810834i
\(19\) 2.20537 0.505947 0.252974 0.967473i \(-0.418591\pi\)
0.252974 + 0.967473i \(0.418591\pi\)
\(20\) 1.72311 + 2.98452i 0.385300 + 0.667359i
\(21\) 0 0
\(22\) −5.25808 + 9.10727i −1.12103 + 1.94168i
\(23\) 0.636695 1.10279i 0.132760 0.229947i −0.791980 0.610548i \(-0.790949\pi\)
0.924740 + 0.380601i \(0.124283\pi\)
\(24\) −1.92538 + 2.36140i −0.393016 + 0.482018i
\(25\) −3.66817 6.35345i −0.733633 1.27069i
\(26\) −1.93429 −0.379345
\(27\) 4.60583 + 2.40548i 0.886392 + 0.462936i
\(28\) 0 0
\(29\) −3.10262 5.37390i −0.576142 0.997907i −0.995917 0.0902789i \(-0.971224\pi\)
0.419774 0.907628i \(-0.362109\pi\)
\(30\) −6.63763 + 8.14079i −1.21186 + 1.48630i
\(31\) −0.0942019 + 0.163162i −0.0169192 + 0.0293048i −0.874361 0.485276i \(-0.838719\pi\)
0.857442 + 0.514581i \(0.172052\pi\)
\(32\) −2.55712 + 4.42907i −0.452040 + 0.782956i
\(33\) −10.4138 1.68522i −1.81281 0.293360i
\(34\) −1.03938 1.80026i −0.178252 0.308742i
\(35\) 0 0
\(36\) 2.79332 + 0.928373i 0.465553 + 0.154729i
\(37\) 3.57670 0.588006 0.294003 0.955804i \(-0.405012\pi\)
0.294003 + 0.955804i \(0.405012\pi\)
\(38\) 1.90391 + 3.29767i 0.308855 + 0.534953i
\(39\) −0.689288 1.81382i −0.110374 0.290444i
\(40\) 3.08925 5.35074i 0.488453 0.846026i
\(41\) −1.68320 + 2.91538i −0.262871 + 0.455307i −0.967004 0.254762i \(-0.918003\pi\)
0.704132 + 0.710069i \(0.251336\pi\)
\(42\) 0 0
\(43\) −1.90276 3.29567i −0.290168 0.502585i 0.683681 0.729781i \(-0.260378\pi\)
−0.973849 + 0.227195i \(0.927044\pi\)
\(44\) −5.97604 −0.900922
\(45\) −9.99915 3.32326i −1.49058 0.495403i
\(46\) 2.19865 0.324173
\(47\) −2.86035 4.95427i −0.417225 0.722654i 0.578434 0.815729i \(-0.303664\pi\)
−0.995659 + 0.0930746i \(0.970331\pi\)
\(48\) −8.54843 1.38336i −1.23386 0.199670i
\(49\) 0 0
\(50\) 6.33349 10.9699i 0.895691 1.55138i
\(51\) 1.31776 1.61618i 0.184523 0.226311i
\(52\) −0.549600 0.951935i −0.0762158 0.132010i
\(53\) −8.33827 −1.14535 −0.572675 0.819783i \(-0.694094\pi\)
−0.572675 + 0.819783i \(0.694094\pi\)
\(54\) 0.379341 + 8.96371i 0.0516218 + 1.21981i
\(55\) 21.3922 2.88453
\(56\) 0 0
\(57\) −2.41384 + 2.96047i −0.319720 + 0.392124i
\(58\) 5.35702 9.27862i 0.703411 1.21834i
\(59\) −5.63427 + 9.75883i −0.733519 + 1.27049i 0.221851 + 0.975081i \(0.428790\pi\)
−0.955370 + 0.295411i \(0.904543\pi\)
\(60\) −5.89238 0.953538i −0.760703 0.123101i
\(61\) 6.00109 + 10.3942i 0.768361 + 1.33084i 0.938451 + 0.345411i \(0.112261\pi\)
−0.170091 + 0.985428i \(0.554406\pi\)
\(62\) −0.325300 −0.0413131
\(63\) 0 0
\(64\) 1.16898 0.146123
\(65\) 1.96738 + 3.40761i 0.244024 + 0.422662i
\(66\) −6.47041 17.0265i −0.796453 2.09582i
\(67\) 3.95652 6.85289i 0.483366 0.837214i −0.516452 0.856316i \(-0.672748\pi\)
0.999818 + 0.0191025i \(0.00608088\pi\)
\(68\) 0.590651 1.02304i 0.0716270 0.124062i
\(69\) 0.783494 + 2.06172i 0.0943217 + 0.248202i
\(70\) 0 0
\(71\) −12.2052 −1.44850 −0.724248 0.689540i \(-0.757813\pi\)
−0.724248 + 0.689540i \(0.757813\pi\)
\(72\) −1.06255 5.16922i −0.125223 0.609198i
\(73\) 5.31473 0.622042 0.311021 0.950403i \(-0.399329\pi\)
0.311021 + 0.950403i \(0.399329\pi\)
\(74\) 3.08779 + 5.34820i 0.358948 + 0.621716i
\(75\) 12.5437 + 2.02989i 1.44842 + 0.234392i
\(76\) −1.08194 + 1.87397i −0.124107 + 0.214959i
\(77\) 0 0
\(78\) 2.11712 2.59657i 0.239717 0.294003i
\(79\) −4.60855 7.98225i −0.518503 0.898073i −0.999769 0.0214988i \(-0.993156\pi\)
0.481266 0.876575i \(-0.340177\pi\)
\(80\) 17.5603 1.96330
\(81\) −8.27029 + 3.54996i −0.918922 + 0.394440i
\(82\) −5.81246 −0.641878
\(83\) −0.624950 1.08245i −0.0685972 0.118814i 0.829687 0.558229i \(-0.188519\pi\)
−0.898284 + 0.439415i \(0.855186\pi\)
\(84\) 0 0
\(85\) −2.11433 + 3.66213i −0.229332 + 0.397214i
\(86\) 3.28532 5.69034i 0.354265 0.613605i
\(87\) 10.6098 + 1.71693i 1.13749 + 0.184074i
\(88\) 5.35702 + 9.27862i 0.571060 + 0.989105i
\(89\) −5.54131 −0.587378 −0.293689 0.955901i \(-0.594883\pi\)
−0.293689 + 0.955901i \(0.594883\pi\)
\(90\) −3.66308 17.8206i −0.386122 1.87846i
\(91\) 0 0
\(92\) 0.624715 + 1.08204i 0.0651310 + 0.112810i
\(93\) −0.115922 0.305041i −0.0120205 0.0316313i
\(94\) 4.93871 8.55409i 0.509389 0.882287i
\(95\) 3.87298 6.70820i 0.397359 0.688246i
\(96\) −3.14671 8.28038i −0.321159 0.845113i
\(97\) −8.24277 14.2769i −0.836926 1.44960i −0.892452 0.451142i \(-0.851017\pi\)
0.0555261 0.998457i \(-0.482316\pi\)
\(98\) 0 0
\(99\) 13.6604 12.1349i 1.37292 1.21960i
\(100\) 7.19829 0.719829
\(101\) −6.48192 11.2270i −0.644975 1.11713i −0.984307 0.176463i \(-0.943534\pi\)
0.339332 0.940667i \(-0.389799\pi\)
\(102\) 3.55429 + 0.575174i 0.351927 + 0.0569507i
\(103\) 1.35091 2.33984i 0.133109 0.230552i −0.791765 0.610826i \(-0.790837\pi\)
0.924873 + 0.380275i \(0.124171\pi\)
\(104\) −0.985340 + 1.70666i −0.0966205 + 0.167352i
\(105\) 0 0
\(106\) −7.19847 12.4681i −0.699177 1.21101i
\(107\) −0.178480 −0.0172544 −0.00862718 0.999963i \(-0.502746\pi\)
−0.00862718 + 0.999963i \(0.502746\pi\)
\(108\) −4.30360 + 2.73360i −0.414114 + 0.263041i
\(109\) 9.35853 0.896385 0.448192 0.893937i \(-0.352068\pi\)
0.448192 + 0.893937i \(0.352068\pi\)
\(110\) 18.4680 + 31.9876i 1.76086 + 3.04989i
\(111\) −3.91479 + 4.80134i −0.371575 + 0.455723i
\(112\) 0 0
\(113\) 4.21019 7.29226i 0.396061 0.685998i −0.597175 0.802111i \(-0.703710\pi\)
0.993236 + 0.116113i \(0.0370434\pi\)
\(114\) −6.51064 1.05359i −0.609777 0.0986776i
\(115\) −2.23627 3.87333i −0.208533 0.361190i
\(116\) 6.08848 0.565302
\(117\) 3.18930 + 1.05998i 0.294851 + 0.0979952i
\(118\) −19.4564 −1.79110
\(119\) 0 0
\(120\) 3.80152 + 10.0035i 0.347030 + 0.913190i
\(121\) −13.0479 + 22.5997i −1.18618 + 2.05452i
\(122\) −10.3615 + 17.9467i −0.938090 + 1.62482i
\(123\) −2.07129 5.45047i −0.186762 0.491453i
\(124\) −0.0924294 0.160092i −0.00830040 0.0143767i
\(125\) −8.20593 −0.733960
\(126\) 0 0
\(127\) −9.92438 −0.880647 −0.440323 0.897839i \(-0.645136\pi\)
−0.440323 + 0.897839i \(0.645136\pi\)
\(128\) 6.12343 + 10.6061i 0.541240 + 0.937455i
\(129\) 6.50670 + 1.05295i 0.572883 + 0.0927071i
\(130\) −3.39691 + 5.88361i −0.297928 + 0.516027i
\(131\) −7.62335 + 13.2040i −0.666055 + 1.15364i 0.312943 + 0.949772i \(0.398685\pi\)
−0.978998 + 0.203870i \(0.934648\pi\)
\(132\) 6.54093 8.02219i 0.569314 0.698242i
\(133\) 0 0
\(134\) 13.6627 1.18028
\(135\) 15.4054 9.78537i 1.32589 0.842191i
\(136\) −2.11788 −0.181606
\(137\) −3.07350 5.32346i −0.262587 0.454814i 0.704342 0.709861i \(-0.251242\pi\)
−0.966929 + 0.255047i \(0.917909\pi\)
\(138\) −2.40647 + 2.95145i −0.204853 + 0.251244i
\(139\) −0.438687 + 0.759829i −0.0372090 + 0.0644478i −0.884030 0.467430i \(-0.845180\pi\)
0.846821 + 0.531878i \(0.178513\pi\)
\(140\) 0 0
\(141\) 9.78129 + 1.58286i 0.823733 + 0.133301i
\(142\) −10.5368 18.2504i −0.884233 1.53154i
\(143\) −6.82321 −0.570586
\(144\) 11.2135 9.96123i 0.934456 0.830102i
\(145\) −21.7947 −1.80995
\(146\) 4.58824 + 7.94706i 0.379725 + 0.657703i
\(147\) 0 0
\(148\) −1.75470 + 3.03923i −0.144236 + 0.249823i
\(149\) −2.88776 + 5.00175i −0.236575 + 0.409760i −0.959729 0.280927i \(-0.909358\pi\)
0.723154 + 0.690686i \(0.242692\pi\)
\(150\) 7.79378 + 20.5089i 0.636359 + 1.67454i
\(151\) 1.01321 + 1.75494i 0.0824541 + 0.142815i 0.904304 0.426890i \(-0.140391\pi\)
−0.821849 + 0.569705i \(0.807058\pi\)
\(152\) 3.87947 0.314666
\(153\) 0.727226 + 3.53790i 0.0587927 + 0.286022i
\(154\) 0 0
\(155\) 0.330866 + 0.573077i 0.0265758 + 0.0460307i
\(156\) 1.87942 + 0.304138i 0.150474 + 0.0243506i
\(157\) −1.52378 + 2.63927i −0.121611 + 0.210636i −0.920403 0.390971i \(-0.872139\pi\)
0.798792 + 0.601607i \(0.205473\pi\)
\(158\) 7.95718 13.7822i 0.633039 1.09646i
\(159\) 9.12644 11.1932i 0.723774 0.887680i
\(160\) 8.98141 + 15.5563i 0.710043 + 1.22983i
\(161\) 0 0
\(162\) −12.4480 9.30178i −0.978008 0.730817i
\(163\) −5.38891 −0.422092 −0.211046 0.977476i \(-0.567687\pi\)
−0.211046 + 0.977476i \(0.567687\pi\)
\(164\) −1.65153 2.86053i −0.128963 0.223370i
\(165\) −23.4143 + 28.7167i −1.82280 + 2.23560i
\(166\) 1.07905 1.86896i 0.0837502 0.145060i
\(167\) 8.30480 14.3843i 0.642645 1.11309i −0.342196 0.939629i \(-0.611171\pi\)
0.984840 0.173464i \(-0.0554961\pi\)
\(168\) 0 0
\(169\) 5.87249 + 10.1714i 0.451730 + 0.782419i
\(170\) −7.30126 −0.559981
\(171\) −1.33211 6.48063i −0.101869 0.495586i
\(172\) 3.73391 0.284708
\(173\) −8.82516 15.2856i −0.670965 1.16214i −0.977631 0.210328i \(-0.932547\pi\)
0.306666 0.951817i \(-0.400786\pi\)
\(174\) 6.59216 + 17.3469i 0.499750 + 1.31507i
\(175\) 0 0
\(176\) −15.2255 + 26.3714i −1.14767 + 1.98782i
\(177\) −6.93333 18.2447i −0.521141 1.37135i
\(178\) −4.78384 8.28586i −0.358564 0.621051i
\(179\) 2.62844 0.196459 0.0982294 0.995164i \(-0.468682\pi\)
0.0982294 + 0.995164i \(0.468682\pi\)
\(180\) 7.72938 6.86621i 0.576114 0.511777i
\(181\) −3.97391 −0.295378 −0.147689 0.989034i \(-0.547184\pi\)
−0.147689 + 0.989034i \(0.547184\pi\)
\(182\) 0 0
\(183\) −20.5214 3.32089i −1.51699 0.245487i
\(184\) 1.12001 1.93991i 0.0825681 0.143012i
\(185\) 6.28125 10.8794i 0.461806 0.799872i
\(186\) 0.356049 0.436680i 0.0261068 0.0320189i
\(187\) −3.66643 6.35045i −0.268116 0.464391i
\(188\) 5.61306 0.409374
\(189\) 0 0
\(190\) 13.3743 0.970270
\(191\) 9.10295 + 15.7668i 0.658666 + 1.14084i 0.980961 + 0.194204i \(0.0622125\pi\)
−0.322295 + 0.946639i \(0.604454\pi\)
\(192\) −1.27948 + 1.56923i −0.0923384 + 0.113249i
\(193\) 0.101193 0.175271i 0.00728401 0.0126163i −0.862360 0.506295i \(-0.831015\pi\)
0.869644 + 0.493679i \(0.164348\pi\)
\(194\) 14.2321 24.6506i 1.02180 1.76981i
\(195\) −6.72770 1.08871i −0.481780 0.0779644i
\(196\) 0 0
\(197\) −1.63136 −0.116229 −0.0581147 0.998310i \(-0.518509\pi\)
−0.0581147 + 0.998310i \(0.518509\pi\)
\(198\) 29.9383 + 9.95014i 2.12762 + 0.707125i
\(199\) −6.29211 −0.446036 −0.223018 0.974814i \(-0.571591\pi\)
−0.223018 + 0.974814i \(0.571591\pi\)
\(200\) −6.45266 11.1763i −0.456272 0.790287i
\(201\) 4.86875 + 12.8119i 0.343415 + 0.903678i
\(202\) 11.1918 19.3847i 0.787449 1.36390i
\(203\) 0 0
\(204\) 0.726835 + 1.91263i 0.0508886 + 0.133911i
\(205\) 5.91192 + 10.2397i 0.412906 + 0.715174i
\(206\) 4.66499 0.325025
\(207\) −3.62519 1.20485i −0.251968 0.0837429i
\(208\) −5.60100 −0.388359
\(209\) 6.71607 + 11.6326i 0.464560 + 0.804642i
\(210\) 0 0
\(211\) 8.14368 14.1053i 0.560634 0.971046i −0.436807 0.899555i \(-0.643891\pi\)
0.997441 0.0714912i \(-0.0227758\pi\)
\(212\) 4.09069 7.08528i 0.280950 0.486619i
\(213\) 13.3589 16.3842i 0.915339 1.12263i
\(214\) −0.154083 0.266880i −0.0105329 0.0182435i
\(215\) −13.3662 −0.911564
\(216\) 8.10210 + 4.23148i 0.551278 + 0.287916i
\(217\) 0 0
\(218\) 8.07927 + 13.9937i 0.547197 + 0.947773i
\(219\) −5.81711 + 7.13445i −0.393084 + 0.482101i
\(220\) −10.4949 + 18.1776i −0.707563 + 1.22554i
\(221\) 0.674383 1.16807i 0.0453639 0.0785726i
\(222\) −10.5590 1.70872i −0.708677 0.114682i
\(223\) 9.98472 + 17.2940i 0.668626 + 1.15809i 0.978288 + 0.207248i \(0.0664507\pi\)
−0.309662 + 0.950847i \(0.600216\pi\)
\(224\) 0 0
\(225\) −16.4543 + 14.6168i −1.09695 + 0.974454i
\(226\) 14.5387 0.967101
\(227\) 1.80642 + 3.12880i 0.119896 + 0.207666i 0.919726 0.392560i \(-0.128411\pi\)
−0.799830 + 0.600226i \(0.795077\pi\)
\(228\) −1.33140 3.50350i −0.0881739 0.232025i
\(229\) 6.85733 11.8772i 0.453145 0.784870i −0.545435 0.838153i \(-0.683635\pi\)
0.998579 + 0.0532835i \(0.0169687\pi\)
\(230\) 3.86117 6.68774i 0.254598 0.440976i
\(231\) 0 0
\(232\) −5.45781 9.45321i −0.358323 0.620634i
\(233\) −25.2542 −1.65445 −0.827227 0.561867i \(-0.810083\pi\)
−0.827227 + 0.561867i \(0.810083\pi\)
\(234\) 1.16837 + 5.68402i 0.0763785 + 0.371576i
\(235\) −20.0929 −1.31071
\(236\) −5.52825 9.57521i −0.359859 0.623293i
\(237\) 15.7595 + 2.55029i 1.02369 + 0.165659i
\(238\) 0 0
\(239\) −4.49495 + 7.78549i −0.290754 + 0.503601i −0.973988 0.226598i \(-0.927240\pi\)
0.683234 + 0.730200i \(0.260573\pi\)
\(240\) −19.2202 + 23.5728i −1.24066 + 1.52162i
\(241\) 4.62862 + 8.01701i 0.298156 + 0.516421i 0.975714 0.219048i \(-0.0702952\pi\)
−0.677558 + 0.735469i \(0.736962\pi\)
\(242\) −45.0575 −2.89640
\(243\) 4.28661 14.9875i 0.274986 0.961448i
\(244\) −11.7763 −0.753903
\(245\) 0 0
\(246\) 6.36188 7.80259i 0.405619 0.497475i
\(247\) −1.23532 + 2.13963i −0.0786013 + 0.136141i
\(248\) −0.165710 + 0.287019i −0.0105226 + 0.0182257i
\(249\) 2.13709 + 0.345836i 0.135433 + 0.0219164i
\(250\) −7.08422 12.2702i −0.448045 0.776037i
\(251\) −20.6517 −1.30353 −0.651763 0.758422i \(-0.725970\pi\)
−0.651763 + 0.758422i \(0.725970\pi\)
\(252\) 0 0
\(253\) 7.75576 0.487600
\(254\) −8.56777 14.8398i −0.537590 0.931133i
\(255\) −2.60183 6.84656i −0.162933 0.428748i
\(256\) −9.40380 + 16.2879i −0.587738 + 1.01799i
\(257\) −1.22289 + 2.11811i −0.0762819 + 0.132124i −0.901643 0.432481i \(-0.857638\pi\)
0.825361 + 0.564605i \(0.190972\pi\)
\(258\) 4.04280 + 10.6384i 0.251694 + 0.662318i
\(259\) 0 0
\(260\) −3.86073 −0.239432
\(261\) −13.9174 + 12.3632i −0.861468 + 0.765265i
\(262\) −26.3251 −1.62637
\(263\) 12.2814 + 21.2720i 0.757302 + 1.31169i 0.944222 + 0.329311i \(0.106816\pi\)
−0.186919 + 0.982375i \(0.559850\pi\)
\(264\) −18.3189 2.96447i −1.12745 0.182451i
\(265\) −14.6433 + 25.3629i −0.899531 + 1.55803i
\(266\) 0 0
\(267\) 6.06510 7.43861i 0.371178 0.455236i
\(268\) 3.88207 + 6.72395i 0.237135 + 0.410730i
\(269\) 29.5703 1.80293 0.901466 0.432849i \(-0.142492\pi\)
0.901466 + 0.432849i \(0.142492\pi\)
\(270\) 27.9316 + 14.5878i 1.69986 + 0.887786i
\(271\) 24.7915 1.50598 0.752989 0.658034i \(-0.228612\pi\)
0.752989 + 0.658034i \(0.228612\pi\)
\(272\) −3.00968 5.21291i −0.182488 0.316079i
\(273\) 0 0
\(274\) 5.30674 9.19154i 0.320592 0.555281i
\(275\) 22.3415 38.6966i 1.34724 2.33349i
\(276\) −2.13628 0.345705i −0.128589 0.0208090i
\(277\) −0.939249 1.62683i −0.0564340 0.0977466i 0.836428 0.548076i \(-0.184640\pi\)
−0.892862 + 0.450330i \(0.851306\pi\)
\(278\) −1.51488 −0.0908567
\(279\) 0.536364 + 0.178263i 0.0321113 + 0.0106723i
\(280\) 0 0
\(281\) 6.03965 + 10.4610i 0.360295 + 0.624049i 0.988009 0.154395i \(-0.0493427\pi\)
−0.627714 + 0.778444i \(0.716009\pi\)
\(282\) 6.07740 + 15.9923i 0.361904 + 0.952330i
\(283\) −13.9859 + 24.2244i −0.831378 + 1.43999i 0.0655680 + 0.997848i \(0.479114\pi\)
−0.896946 + 0.442140i \(0.854219\pi\)
\(284\) 5.98779 10.3712i 0.355310 0.615415i
\(285\) 4.76595 + 12.5413i 0.282311 + 0.742885i
\(286\) −5.89052 10.2027i −0.348314 0.603297i
\(287\) 0 0
\(288\) 14.5597 + 4.83897i 0.857937 + 0.285139i
\(289\) −15.5505 −0.914735
\(290\) −18.8155 32.5894i −1.10488 1.91372i
\(291\) 28.1871 + 4.56139i 1.65236 + 0.267394i
\(292\) −2.60736 + 4.51609i −0.152584 + 0.264284i
\(293\) 4.41163 7.64117i 0.257730 0.446402i −0.707903 0.706309i \(-0.750359\pi\)
0.965634 + 0.259908i \(0.0836921\pi\)
\(294\) 0 0
\(295\) 19.7893 + 34.2761i 1.15218 + 1.99563i
\(296\) 6.29177 0.365702
\(297\) 1.33813 + 31.6196i 0.0776463 + 1.83475i
\(298\) −9.97209 −0.577668
\(299\) 0.713276 + 1.23543i 0.0412498 + 0.0714467i
\(300\) −7.87871 + 9.66293i −0.454878 + 0.557889i
\(301\) 0 0
\(302\) −1.74942 + 3.03009i −0.100668 + 0.174362i
\(303\) 22.1657 + 3.58697i 1.27339 + 0.206066i
\(304\) 5.51304 + 9.54887i 0.316195 + 0.547665i
\(305\) 42.1554 2.41381
\(306\) −4.66236 + 4.14170i −0.266530 + 0.236765i
\(307\) −1.05532 −0.0602304 −0.0301152 0.999546i \(-0.509587\pi\)
−0.0301152 + 0.999546i \(0.509587\pi\)
\(308\) 0 0
\(309\) 1.66238 + 4.37446i 0.0945696 + 0.248855i
\(310\) −0.571277 + 0.989481i −0.0324464 + 0.0561988i
\(311\) 1.53608 2.66056i 0.0871029 0.150867i −0.819182 0.573533i \(-0.805572\pi\)
0.906285 + 0.422666i \(0.138906\pi\)
\(312\) −1.21253 3.19069i −0.0686457 0.180637i
\(313\) 14.0810 + 24.3891i 0.795907 + 1.37855i 0.922262 + 0.386566i \(0.126339\pi\)
−0.126355 + 0.991985i \(0.540328\pi\)
\(314\) −5.26196 −0.296949
\(315\) 0 0
\(316\) 9.04368 0.508747
\(317\) −6.42324 11.1254i −0.360765 0.624863i 0.627322 0.778760i \(-0.284151\pi\)
−0.988087 + 0.153897i \(0.950818\pi\)
\(318\) 24.6160 + 3.98350i 1.38040 + 0.223384i
\(319\) 18.8969 32.7305i 1.05803 1.83255i
\(320\) 2.05291 3.55575i 0.114761 0.198772i
\(321\) 0.195351 0.239591i 0.0109034 0.0133726i
\(322\) 0 0
\(323\) −2.65517 −0.147738
\(324\) 1.04083 8.76910i 0.0578240 0.487172i
\(325\) 8.21874 0.455893
\(326\) −4.65227 8.05797i −0.257665 0.446290i
\(327\) −10.2431 + 12.5628i −0.566447 + 0.694725i
\(328\) −2.96091 + 5.12845i −0.163489 + 0.283171i
\(329\) 0 0
\(330\) −63.1535 10.2199i −3.47649 0.562585i
\(331\) 10.7780 + 18.6681i 0.592413 + 1.02609i 0.993906 + 0.110228i \(0.0351581\pi\)
−0.401493 + 0.915862i \(0.631509\pi\)
\(332\) 1.22638 0.0673065
\(333\) −2.16044 10.5104i −0.118391 0.575964i
\(334\) 28.6783 1.56921
\(335\) −13.8965 24.0695i −0.759248 1.31506i
\(336\) 0 0
\(337\) 6.30340 10.9178i 0.343368 0.594731i −0.641688 0.766966i \(-0.721766\pi\)
0.985056 + 0.172235i \(0.0550989\pi\)
\(338\) −10.1395 + 17.5621i −0.551516 + 0.955254i
\(339\) 5.18091 + 13.6333i 0.281389 + 0.740459i
\(340\) −2.07455 3.59323i −0.112508 0.194870i
\(341\) −1.14750 −0.0621406
\(342\) 8.54039 7.58665i 0.461811 0.410239i
\(343\) 0 0
\(344\) −3.34714 5.79741i −0.180466 0.312575i
\(345\) 7.64718 + 1.23751i 0.411711 + 0.0666253i
\(346\) 15.2376 26.3923i 0.819179 1.41886i
\(347\) −11.5683 + 20.0369i −0.621020 + 1.07564i 0.368276 + 0.929716i \(0.379948\pi\)
−0.989296 + 0.145922i \(0.953385\pi\)
\(348\) −6.66400 + 8.17313i −0.357228 + 0.438126i
\(349\) −8.24346 14.2781i −0.441262 0.764289i 0.556521 0.830833i \(-0.312136\pi\)
−0.997783 + 0.0665448i \(0.978802\pi\)
\(350\) 0 0
\(351\) −4.91368 + 3.12112i −0.262273 + 0.166593i
\(352\) −31.1490 −1.66025
\(353\) −12.2438 21.2068i −0.651669 1.12872i −0.982718 0.185110i \(-0.940736\pi\)
0.331049 0.943614i \(-0.392598\pi\)
\(354\) 21.2955 26.1181i 1.13184 1.38816i
\(355\) −21.4343 + 37.1253i −1.13761 + 1.97041i
\(356\) 2.71852 4.70862i 0.144081 0.249556i
\(357\) 0 0
\(358\) 2.26915 + 3.93028i 0.119928 + 0.207722i
\(359\) 20.4777 1.08077 0.540386 0.841417i \(-0.318278\pi\)
0.540386 + 0.841417i \(0.318278\pi\)
\(360\) −17.5895 5.84595i −0.927047 0.308108i
\(361\) −14.1363 −0.744017
\(362\) −3.43070 5.94214i −0.180313 0.312312i
\(363\) −16.0564 42.2514i −0.842740 2.21762i
\(364\) 0 0
\(365\) 9.33349 16.1661i 0.488537 0.846172i
\(366\) −12.7506 33.5524i −0.666482 1.75381i
\(367\) 11.1269 + 19.2724i 0.580821 + 1.00601i 0.995382 + 0.0959900i \(0.0306017\pi\)
−0.414561 + 0.910021i \(0.636065\pi\)
\(368\) 6.36650 0.331877
\(369\) 9.58374 + 3.18520i 0.498910 + 0.165815i
\(370\) 21.6905 1.12764
\(371\) 0 0
\(372\) 0.316073 + 0.0511487i 0.0163876 + 0.00265194i
\(373\) 16.2684 28.1777i 0.842347 1.45899i −0.0455576 0.998962i \(-0.514506\pi\)
0.887905 0.460027i \(-0.152160\pi\)
\(374\) 6.33050 10.9647i 0.327342 0.566974i
\(375\) 8.98159 11.0156i 0.463807 0.568841i
\(376\) −5.03163 8.71504i −0.259487 0.449444i
\(377\) 6.95160 0.358026
\(378\) 0 0
\(379\) 1.54440 0.0793306 0.0396653 0.999213i \(-0.487371\pi\)
0.0396653 + 0.999213i \(0.487371\pi\)
\(380\) 3.80011 + 6.58198i 0.194941 + 0.337648i
\(381\) 10.8625 13.3224i 0.556502 0.682528i
\(382\) −15.7173 + 27.2231i −0.804165 + 1.39285i
\(383\) 15.8147 27.3919i 0.808093 1.39966i −0.106090 0.994357i \(-0.533833\pi\)
0.914183 0.405302i \(-0.132834\pi\)
\(384\) −20.9398 3.38859i −1.06858 0.172923i
\(385\) 0 0
\(386\) 0.349441 0.0177861
\(387\) −8.53521 + 7.58206i −0.433869 + 0.385418i
\(388\) 16.1753 0.821179
\(389\) 2.62313 + 4.54340i 0.132998 + 0.230359i 0.924831 0.380378i \(-0.124206\pi\)
−0.791833 + 0.610738i \(0.790873\pi\)
\(390\) −4.18012 10.9997i −0.211668 0.556993i
\(391\) −0.766552 + 1.32771i −0.0387662 + 0.0671451i
\(392\) 0 0
\(393\) −9.38103 24.6857i −0.473210 1.24523i
\(394\) −1.40836 2.43935i −0.0709521 0.122893i
\(395\) −32.3734 −1.62888
\(396\) 3.60971 + 17.5610i 0.181395 + 0.882472i
\(397\) −0.0276349 −0.00138696 −0.000693478 1.00000i \(-0.500221\pi\)
−0.000693478 1.00000i \(0.500221\pi\)
\(398\) −5.43201 9.40851i −0.272282 0.471606i
\(399\) 0 0
\(400\) 18.3395 31.7650i 0.916977 1.58825i
\(401\) −6.06885 + 10.5115i −0.303064 + 0.524922i −0.976828 0.214024i \(-0.931343\pi\)
0.673765 + 0.738946i \(0.264676\pi\)
\(402\) −14.9542 + 18.3407i −0.745848 + 0.914753i
\(403\) −0.105532 0.182787i −0.00525694 0.00910529i
\(404\) 12.7199 0.632840
\(405\) −3.72583 + 31.3905i −0.185138 + 1.55980i
\(406\) 0 0
\(407\) 10.8922 + 18.8659i 0.539907 + 0.935146i
\(408\) 2.31807 2.84302i 0.114762 0.140750i
\(409\) 15.6726 27.1458i 0.774963 1.34227i −0.159853 0.987141i \(-0.551102\pi\)
0.934816 0.355134i \(-0.115565\pi\)
\(410\) −10.2076 + 17.6800i −0.504116 + 0.873155i
\(411\) 10.5102 + 1.70082i 0.518429 + 0.0838951i
\(412\) 1.32549 + 2.29582i 0.0653022 + 0.113107i
\(413\) 0 0
\(414\) −1.32805 6.46086i −0.0652701 0.317534i
\(415\) −4.39004 −0.215499
\(416\) −2.86469 4.96179i −0.140453 0.243272i
\(417\) −0.539833 1.42054i −0.0264358 0.0695642i
\(418\) −11.5960 + 20.0849i −0.567181 + 0.982385i
\(419\) −7.44319 + 12.8920i −0.363623 + 0.629814i −0.988554 0.150866i \(-0.951794\pi\)
0.624931 + 0.780680i \(0.285127\pi\)
\(420\) 0 0
\(421\) −4.54213 7.86721i −0.221370 0.383424i 0.733854 0.679307i \(-0.237720\pi\)
−0.955224 + 0.295883i \(0.904386\pi\)
\(422\) 28.1219 1.36895
\(423\) −12.8307 + 11.3978i −0.623849 + 0.554182i
\(424\) −14.6678 −0.712333
\(425\) 4.41631 + 7.64927i 0.214223 + 0.371044i
\(426\) 36.0320 + 5.83089i 1.74575 + 0.282508i
\(427\) 0 0
\(428\) 0.0875611 0.151660i 0.00423243 0.00733078i
\(429\) 7.46818 9.15943i 0.360567 0.442221i
\(430\) −11.5391 19.9863i −0.556463 0.963823i
\(431\) −16.6355 −0.801305 −0.400652 0.916230i \(-0.631216\pi\)
−0.400652 + 0.916230i \(0.631216\pi\)
\(432\) 1.09844 + 25.9557i 0.0528486 + 1.24879i
\(433\) −19.7423 −0.948756 −0.474378 0.880321i \(-0.657327\pi\)
−0.474378 + 0.880321i \(0.657327\pi\)
\(434\) 0 0
\(435\) 23.8549 29.2571i 1.14375 1.40277i
\(436\) −4.59122 + 7.95223i −0.219880 + 0.380843i
\(437\) 1.40415 2.43206i 0.0671696 0.116341i
\(438\) −15.6900 2.53904i −0.749697 0.121320i
\(439\) −3.36757 5.83280i −0.160725 0.278384i 0.774404 0.632692i \(-0.218050\pi\)
−0.935129 + 0.354307i \(0.884717\pi\)
\(440\) 37.6310 1.79399
\(441\) 0 0
\(442\) 2.32879 0.110769
\(443\) −14.3202 24.8033i −0.680372 1.17844i −0.974867 0.222786i \(-0.928485\pi\)
0.294496 0.955653i \(-0.404848\pi\)
\(444\) −2.15928 5.68201i −0.102475 0.269656i
\(445\) −9.73141 + 16.8553i −0.461313 + 0.799017i
\(446\) −17.2397 + 29.8601i −0.816324 + 1.41392i
\(447\) −3.55358 9.35105i −0.168079 0.442290i
\(448\) 0 0
\(449\) −6.66872 −0.314716 −0.157358 0.987542i \(-0.550298\pi\)
−0.157358 + 0.987542i \(0.550298\pi\)
\(450\) −36.0615 11.9852i −1.69995 0.564988i
\(451\) −20.5035 −0.965473
\(452\) 4.13097 + 7.15505i 0.194305 + 0.336545i
\(453\) −3.46480 0.560693i −0.162790 0.0263437i
\(454\) −3.11898 + 5.40223i −0.146381 + 0.253539i
\(455\) 0 0
\(456\) −4.24617 + 5.20776i −0.198845 + 0.243876i
\(457\) 14.3287 + 24.8180i 0.670266 + 1.16093i 0.977829 + 0.209407i \(0.0671533\pi\)
−0.307563 + 0.951528i \(0.599513\pi\)
\(458\) 23.6799 1.10649
\(459\) −5.54521 2.89610i −0.258828 0.135178i
\(460\) 4.38839 0.204610
\(461\) 10.0087 + 17.3355i 0.466150 + 0.807395i 0.999253 0.0386554i \(-0.0123075\pi\)
−0.533103 + 0.846050i \(0.678974\pi\)
\(462\) 0 0
\(463\) −4.95789 + 8.58731i −0.230413 + 0.399086i −0.957930 0.287003i \(-0.907341\pi\)
0.727517 + 0.686090i \(0.240674\pi\)
\(464\) 15.5120 26.8676i 0.720127 1.24730i
\(465\) −1.13144 0.183095i −0.0524691 0.00849084i
\(466\) −21.8020 37.7623i −1.00996 1.74930i
\(467\) 16.0807 0.744126 0.372063 0.928207i \(-0.378651\pi\)
0.372063 + 0.928207i \(0.378651\pi\)
\(468\) −2.46535 + 2.19003i −0.113961 + 0.101234i
\(469\) 0 0
\(470\) −17.3463 30.0446i −0.800124 1.38586i
\(471\) −1.87511 4.93426i −0.0864007 0.227359i
\(472\) −9.91123 + 17.1667i −0.456201 + 0.790164i
\(473\) 11.5890 20.0728i 0.532863 0.922946i
\(474\) 9.79183 + 25.7667i 0.449754 + 1.18350i
\(475\) −8.08967 14.0117i −0.371180 0.642902i
\(476\) 0 0
\(477\) 5.03657 + 24.5025i 0.230609 + 1.12189i
\(478\) −15.5221 −0.709963
\(479\) 4.10128 + 7.10362i 0.187392 + 0.324573i 0.944380 0.328856i \(-0.106663\pi\)
−0.756988 + 0.653429i \(0.773330\pi\)
\(480\) −30.7130 4.97015i −1.40185 0.226855i
\(481\) −2.00345 + 3.47008i −0.0913496 + 0.158222i
\(482\) −7.99183 + 13.8423i −0.364018 + 0.630497i
\(483\) 0 0
\(484\) −12.8024 22.1745i −0.581929 1.00793i
\(485\) −57.9023 −2.62921
\(486\) 26.1113 6.52907i 1.18443 0.296165i
\(487\) 2.73680 0.124016 0.0620081 0.998076i \(-0.480250\pi\)
0.0620081 + 0.998076i \(0.480250\pi\)
\(488\) 10.5565 + 18.2844i 0.477871 + 0.827696i
\(489\) 5.89829 7.23402i 0.266730 0.327134i
\(490\) 0 0
\(491\) 9.85482 17.0690i 0.444742 0.770315i −0.553293 0.832987i \(-0.686629\pi\)
0.998034 + 0.0626719i \(0.0199622\pi\)
\(492\) 5.64759 + 0.913924i 0.254613 + 0.0412029i
\(493\) 3.73542 + 6.46993i 0.168235 + 0.291391i
\(494\) −4.26582 −0.191928
\(495\) −12.9216 62.8624i −0.580781 2.82545i
\(496\) −0.941952 −0.0422949
\(497\) 0 0
\(498\) 1.32784 + 3.49413i 0.0595018 + 0.156576i
\(499\) 16.5480 28.6619i 0.740789 1.28309i −0.211347 0.977411i \(-0.567785\pi\)
0.952136 0.305674i \(-0.0988817\pi\)
\(500\) 4.02576 6.97283i 0.180038 0.311834i
\(501\) 10.2196 + 26.8923i 0.456578 + 1.20146i
\(502\) −17.8288 30.8803i −0.795737 1.37826i
\(503\) 12.1860 0.543346 0.271673 0.962390i \(-0.412423\pi\)
0.271673 + 0.962390i \(0.412423\pi\)
\(504\) 0 0
\(505\) −45.5331 −2.02619
\(506\) 6.69559 + 11.5971i 0.297655 + 0.515554i
\(507\) −20.0816 3.24972i −0.891857 0.144325i
\(508\) 4.86882 8.43305i 0.216019 0.374156i
\(509\) −6.81965 + 11.8120i −0.302276 + 0.523557i −0.976651 0.214832i \(-0.931080\pi\)
0.674375 + 0.738389i \(0.264413\pi\)
\(510\) 7.99142 9.80116i 0.353866 0.434002i
\(511\) 0 0
\(512\) −7.97968 −0.352656
\(513\) 10.1576 + 5.30499i 0.448468 + 0.234221i
\(514\) −4.22292 −0.186265
\(515\) −4.74481 8.21826i −0.209081 0.362140i
\(516\) −4.08686 + 5.01237i −0.179914 + 0.220657i
\(517\) 17.4214 30.1747i 0.766190 1.32708i
\(518\) 0 0
\(519\) 30.1787 + 4.88368i 1.32470 + 0.214370i
\(520\) 3.46082 + 5.99432i 0.151767 + 0.262868i
\(521\) −35.5490 −1.55743 −0.778714 0.627379i \(-0.784128\pi\)
−0.778714 + 0.627379i \(0.784128\pi\)
\(522\) −30.5016 10.1374i −1.33502 0.443700i
\(523\) 26.7187 1.16833 0.584163 0.811636i \(-0.301423\pi\)
0.584163 + 0.811636i \(0.301423\pi\)
\(524\) −7.47991 12.9556i −0.326761 0.565967i
\(525\) 0 0
\(526\) −21.2052 + 36.7284i −0.924589 + 1.60143i
\(527\) 0.113415 0.196440i 0.00494043 0.00855708i
\(528\) −18.7360 49.3027i −0.815380 2.14563i
\(529\) 10.6892 + 18.5143i 0.464750 + 0.804970i
\(530\) −50.5665 −2.19647
\(531\) 32.0802 + 10.6620i 1.39216 + 0.462692i
\(532\) 0 0
\(533\) −1.88565 3.26604i −0.0816766 0.141468i
\(534\) 16.3589 + 2.64729i 0.707919 + 0.114559i
\(535\) −0.313440 + 0.542893i −0.0135512 + 0.0234713i
\(536\) 6.95990 12.0549i 0.300622 0.520693i
\(537\) −2.87689 + 3.52840i −0.124147 + 0.152262i
\(538\) 25.5282 + 44.2161i 1.10060 + 1.90629i
\(539\) 0 0
\(540\) 0.757146 + 17.8911i 0.0325824 + 0.769910i
\(541\) 37.5855 1.61593 0.807963 0.589233i \(-0.200570\pi\)
0.807963 + 0.589233i \(0.200570\pi\)
\(542\) 21.4026 + 37.0705i 0.919322 + 1.59231i
\(543\) 4.34954 5.33454i 0.186657 0.228927i
\(544\) 3.07866 5.33240i 0.131997 0.228625i
\(545\) 16.4350 28.4663i 0.704000 1.21936i
\(546\) 0 0
\(547\) −9.13381 15.8202i −0.390533 0.676424i 0.601986 0.798506i \(-0.294376\pi\)
−0.992520 + 0.122082i \(0.961043\pi\)
\(548\) 6.03134 0.257646
\(549\) 26.9191 23.9130i 1.14888 1.02058i
\(550\) 77.1501 3.28969
\(551\) −6.84243 11.8514i −0.291498 0.504889i
\(552\) 1.37824 + 3.62677i 0.0586619 + 0.154366i
\(553\) 0 0
\(554\) 1.62172 2.80890i 0.0689002 0.119339i
\(555\) 7.72949 + 20.3397i 0.328098 + 0.863373i
\(556\) −0.430433 0.745532i −0.0182544 0.0316176i
\(557\) −3.89272 −0.164940 −0.0824698 0.996594i \(-0.526281\pi\)
−0.0824698 + 0.996594i \(0.526281\pi\)
\(558\) 0.196491 + 0.955914i 0.00831813 + 0.0404671i
\(559\) 4.26324 0.180316
\(560\) 0 0
\(561\) 12.5378 + 2.02893i 0.529346 + 0.0856617i
\(562\) −10.4281 + 18.0620i −0.439884 + 0.761901i
\(563\) 1.66428 2.88261i 0.0701409 0.121488i −0.828822 0.559512i \(-0.810988\pi\)
0.898963 + 0.438025i \(0.144322\pi\)
\(564\) −6.14363 + 7.53492i −0.258694 + 0.317277i
\(565\) −14.7875 25.6127i −0.622115 1.07753i
\(566\) −48.2965 −2.03006
\(567\) 0 0
\(568\) −21.4702 −0.900870
\(569\) 18.3122 + 31.7177i 0.767688 + 1.32967i 0.938814 + 0.344425i \(0.111926\pi\)
−0.171126 + 0.985249i \(0.554741\pi\)
\(570\) −14.6385 + 17.9535i −0.613137 + 0.751989i
\(571\) 11.2912 19.5569i 0.472522 0.818432i −0.526984 0.849875i \(-0.676677\pi\)
0.999506 + 0.0314435i \(0.0100104\pi\)
\(572\) 3.34742 5.79789i 0.139962 0.242422i
\(573\) −31.1286 5.03740i −1.30042 0.210441i
\(574\) 0 0
\(575\) −9.34201 −0.389589
\(576\) −0.706100 3.43512i −0.0294208 0.143130i
\(577\) −22.5449 −0.938557 −0.469279 0.883050i \(-0.655486\pi\)
−0.469279 + 0.883050i \(0.655486\pi\)
\(578\) −13.4248 23.2525i −0.558399 0.967175i
\(579\) 0.124524 + 0.327678i 0.00517505 + 0.0136179i
\(580\) 10.6923 18.5197i 0.443975 0.768987i
\(581\) 0 0
\(582\) 17.5135 + 46.0857i 0.725957 + 1.91031i
\(583\) −25.3927 43.9814i −1.05166 1.82152i
\(584\) 9.34913 0.386870
\(585\) 8.82511 7.83958i 0.364873 0.324127i
\(586\) 15.2343 0.629325
\(587\) 12.1198 + 20.9921i 0.500237 + 0.866436i 1.00000 0.000273884i \(8.71801e-5\pi\)
−0.499763 + 0.866162i \(0.666579\pi\)
\(588\) 0 0
\(589\) −0.207750 + 0.359834i −0.00856020 + 0.0148267i
\(590\) −34.1684 + 59.1814i −1.40669 + 2.43646i
\(591\) 1.78556 2.18992i 0.0734482 0.0900813i
\(592\) 8.94112 + 15.4865i 0.367478 + 0.636490i
\(593\) 45.7326 1.87801 0.939007 0.343898i \(-0.111747\pi\)
0.939007 + 0.343898i \(0.111747\pi\)
\(594\) −46.1252 + 29.2983i −1.89254 + 1.20212i
\(595\) 0 0
\(596\) −2.83343 4.90764i −0.116062 0.201025i
\(597\) 6.88687 8.44647i 0.281861 0.345691i
\(598\) −1.23155 + 2.13311i −0.0503618 + 0.0872292i
\(599\) 15.0834 26.1252i 0.616290 1.06745i −0.373866 0.927483i \(-0.621968\pi\)
0.990157 0.139963i \(-0.0446985\pi\)
\(600\) 22.0656 + 3.57078i 0.900825 + 0.145777i
\(601\) −7.36933 12.7641i −0.300601 0.520657i 0.675671 0.737203i \(-0.263854\pi\)
−0.976272 + 0.216547i \(0.930521\pi\)
\(602\) 0 0
\(603\) −22.5275 7.48712i −0.917391 0.304899i
\(604\) −1.98830 −0.0809027
\(605\) 45.8285 + 79.3772i 1.86319 + 3.22714i
\(606\) 13.7722 + 36.2407i 0.559457 + 1.47218i
\(607\) −3.03918 + 5.26401i −0.123356 + 0.213660i −0.921089 0.389351i \(-0.872699\pi\)
0.797733 + 0.603011i \(0.206033\pi\)
\(608\) −5.63941 + 9.76774i −0.228708 + 0.396134i
\(609\) 0 0
\(610\) 36.3930 + 63.0345i 1.47351 + 2.55219i
\(611\) 6.40877 0.259271
\(612\) −3.36303 1.11772i −0.135943 0.0451811i
\(613\) 11.7734 0.475522 0.237761 0.971324i \(-0.423587\pi\)
0.237761 + 0.971324i \(0.423587\pi\)
\(614\) −0.911065 1.57801i −0.0367676 0.0636833i
\(615\) −20.2165 3.27154i −0.815207 0.131921i
\(616\) 0 0
\(617\) −16.0319 + 27.7680i −0.645418 + 1.11790i 0.338786 + 0.940863i \(0.389984\pi\)
−0.984205 + 0.177034i \(0.943350\pi\)
\(618\) −5.10594 + 6.26224i −0.205391 + 0.251904i
\(619\) −6.27588 10.8701i −0.252249 0.436908i 0.711896 0.702285i \(-0.247837\pi\)
−0.964145 + 0.265377i \(0.914504\pi\)
\(620\) −0.649282 −0.0260758
\(621\) 5.58524 3.54769i 0.224128 0.142364i
\(622\) 5.30441 0.212688
\(623\) 0 0
\(624\) 6.13043 7.51873i 0.245414 0.300990i
\(625\) 3.92995 6.80687i 0.157198 0.272275i
\(626\) −24.3125 + 42.1104i −0.971721 + 1.68307i
\(627\) −22.9664 3.71655i −0.917188 0.148425i
\(628\) −1.49511 2.58961i −0.0596614 0.103337i
\(629\) −4.30619 −0.171699
\(630\) 0 0
\(631\) 33.4642 1.33219 0.666095 0.745867i \(-0.267964\pi\)
0.666095 + 0.745867i \(0.267964\pi\)
\(632\) −8.10690 14.0416i −0.322475 0.558543i
\(633\) 10.0213 + 26.3706i 0.398312 + 1.04814i
\(634\) 11.0904 19.2092i 0.440457 0.762894i
\(635\) −17.4288 + 30.1875i −0.691639 + 1.19795i
\(636\) 5.03386 + 13.2463i 0.199606 + 0.525251i
\(637\) 0 0
\(638\) 65.2553 2.58348
\(639\) 7.37233 + 35.8659i 0.291645 + 1.41883i
\(640\) 43.0148 1.70031
\(641\) 9.49183 + 16.4403i 0.374905 + 0.649354i 0.990313 0.138855i \(-0.0443421\pi\)
−0.615408 + 0.788209i \(0.711009\pi\)
\(642\) 0.526905 + 0.0852667i 0.0207953 + 0.00336521i
\(643\) −4.81347 + 8.33718i −0.189825 + 0.328786i −0.945192 0.326516i \(-0.894125\pi\)
0.755367 + 0.655302i \(0.227459\pi\)
\(644\) 0 0
\(645\) 14.6296 17.9426i 0.576039 0.706490i
\(646\) −2.29222 3.97025i −0.0901864 0.156207i
\(647\) 7.81214 0.307127 0.153564 0.988139i \(-0.450925\pi\)
0.153564 + 0.988139i \(0.450925\pi\)
\(648\) −14.5483 + 6.24473i −0.571510 + 0.245316i
\(649\) −68.6326 −2.69406
\(650\) 7.09528 + 12.2894i 0.278300 + 0.482029i
\(651\) 0 0
\(652\) 2.64376 4.57912i 0.103537 0.179332i
\(653\) −15.8714 + 27.4901i −0.621097 + 1.07577i 0.368185 + 0.929753i \(0.379979\pi\)
−0.989282 + 0.146019i \(0.953354\pi\)
\(654\) −27.6280 4.47092i −1.08034 0.174827i
\(655\) 26.7756 + 46.3767i 1.04621 + 1.81209i
\(656\) −16.8308 −0.657132
\(657\) −3.21026 15.6177i −0.125244 0.609303i
\(658\) 0 0
\(659\) 3.10685 + 5.38122i 0.121026 + 0.209623i 0.920172 0.391513i \(-0.128048\pi\)
−0.799147 + 0.601136i \(0.794715\pi\)
\(660\) −12.9146 33.9841i −0.502700 1.32283i
\(661\) 13.7631 23.8384i 0.535324 0.927208i −0.463824 0.885927i \(-0.653523\pi\)
0.999148 0.0412802i \(-0.0131436\pi\)
\(662\) −18.6094 + 32.2325i −0.723276 + 1.25275i
\(663\) 0.829873 + 2.18376i 0.0322296 + 0.0848103i
\(664\) −1.09935 1.90413i −0.0426630 0.0738945i
\(665\) 0 0
\(666\) 13.8509 12.3041i 0.536712 0.476775i
\(667\) −7.90169 −0.305955
\(668\) 8.14854 + 14.1137i 0.315276 + 0.546075i
\(669\) −34.1439 5.52536i −1.32008 0.213623i
\(670\) 23.9939 41.5586i 0.926965 1.60555i
\(671\) −36.5505 + 63.3073i −1.41102 + 2.44395i
\(672\) 0 0
\(673\) −8.10894 14.0451i −0.312577 0.541399i 0.666343 0.745646i \(-0.267859\pi\)
−0.978919 + 0.204247i \(0.934526\pi\)
\(674\) 21.7670 0.838434
\(675\) −1.61181 38.0866i −0.0620387 1.46595i
\(676\) −11.5240 −0.443230
\(677\) −10.2545 17.7613i −0.394112 0.682623i 0.598875 0.800842i \(-0.295615\pi\)
−0.992987 + 0.118220i \(0.962281\pi\)
\(678\) −15.9130 + 19.5167i −0.611135 + 0.749532i
\(679\) 0 0
\(680\) −3.71932 + 6.44205i −0.142629 + 0.247041i
\(681\) −6.17725 0.999637i −0.236713 0.0383062i
\(682\) −0.990642 1.71584i −0.0379337 0.0657030i
\(683\) −0.112308 −0.00429736 −0.00214868 0.999998i \(-0.500684\pi\)
−0.00214868 + 0.999998i \(0.500684\pi\)
\(684\) 6.16031 + 2.04741i 0.235545 + 0.0782846i
\(685\) −21.5902 −0.824918
\(686\) 0 0
\(687\) 8.43839 + 22.2052i 0.321945 + 0.847179i
\(688\) 9.51311 16.4772i 0.362684 0.628187i
\(689\) 4.67059 8.08970i 0.177935 0.308193i
\(690\) 4.75142 + 12.5031i 0.180883 + 0.475985i
\(691\) 9.43351 + 16.3393i 0.358868 + 0.621577i 0.987772 0.155906i \(-0.0498296\pi\)
−0.628904 + 0.777483i \(0.716496\pi\)
\(692\) 17.3182 0.658340
\(693\) 0 0
\(694\) −39.9480 −1.51640
\(695\) 1.54081 + 2.66876i 0.0584461 + 0.101232i
\(696\) 18.6636 + 3.02025i 0.707443 + 0.114482i
\(697\) 2.02650 3.51000i 0.0767590 0.132951i
\(698\) 14.2332 24.6527i 0.538736 0.933118i
\(699\) 27.6413 33.9010i 1.04549 1.28225i
\(700\) 0 0
\(701\) −3.16006 −0.119354 −0.0596770 0.998218i \(-0.519007\pi\)
−0.0596770 + 0.998218i \(0.519007\pi\)
\(702\) −8.90898 4.65289i −0.336248 0.175612i
\(703\) 7.88796 0.297500
\(704\) 3.55992 + 6.16596i 0.134170 + 0.232388i
\(705\) 21.9921 26.9725i 0.828272 1.01584i
\(706\) 21.1402 36.6159i 0.795622 1.37806i
\(707\) 0 0
\(708\) 18.9045 + 3.05923i 0.710475 + 0.114973i
\(709\) 10.7606 + 18.6378i 0.404121 + 0.699959i 0.994219 0.107373i \(-0.0342440\pi\)
−0.590097 + 0.807332i \(0.700911\pi\)
\(710\) −74.0174 −2.77782
\(711\) −20.6726 + 18.3640i −0.775284 + 0.688705i
\(712\) −9.74771 −0.365311
\(713\) 0.119956 + 0.207769i 0.00449237 + 0.00778102i
\(714\) 0 0
\(715\) −11.9826 + 20.7545i −0.448125 + 0.776175i
\(716\) −1.28949 + 2.23347i −0.0481906 + 0.0834685i
\(717\) −5.53133 14.5554i −0.206571 0.543581i
\(718\) 17.6785 + 30.6201i 0.659757 + 1.14273i
\(719\) 18.8302 0.702246 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(720\) −10.6070 51.6021i −0.395298 1.92310i
\(721\) 0 0
\(722\) −12.2040 21.1379i −0.454185 0.786671i
\(723\) −15.8281 2.56139i −0.588654 0.0952592i
\(724\) 1.94957 3.37675i 0.0724551 0.125496i
\(725\) −22.7618 + 39.4247i −0.845354 + 1.46420i
\(726\) 49.3165 60.4847i 1.83031 2.24480i
\(727\) 19.5426 + 33.8489i 0.724797 + 1.25538i 0.959058 + 0.283211i \(0.0913996\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(728\) 0 0
\(729\) 15.4273 + 22.1585i 0.571381 + 0.820685i
\(730\) 32.2306 1.19291
\(731\) 2.29084 + 3.96784i 0.0847296 + 0.146756i
\(732\) 12.8895 15.8085i 0.476410 0.584298i
\(733\) 9.29924 16.1068i 0.343475 0.594917i −0.641600 0.767039i \(-0.721729\pi\)
0.985076 + 0.172123i \(0.0550625\pi\)
\(734\) −19.2119 + 33.2759i −0.709123 + 1.22824i
\(735\) 0 0
\(736\) 3.25621 + 5.63993i 0.120026 + 0.207890i
\(737\) 48.1954 1.77530
\(738\) 3.51090 + 17.0803i 0.129238 + 0.628733i
\(739\) 5.50136 0.202371 0.101185 0.994868i \(-0.467736\pi\)
0.101185 + 0.994868i \(0.467736\pi\)
\(740\) 6.16306 + 10.6747i 0.226559 + 0.392411i
\(741\) −1.52014 4.00016i −0.0558436 0.146949i
\(742\) 0 0
\(743\) 10.2326 17.7234i 0.375399 0.650210i −0.614988 0.788537i \(-0.710839\pi\)
0.990387 + 0.138327i \(0.0441725\pi\)
\(744\) −0.203917 0.536597i −0.00747597 0.0196726i
\(745\) 10.1427 + 17.5677i 0.371601 + 0.643631i
\(746\) 56.1785 2.05684
\(747\) −2.80334 + 2.49028i −0.102569 + 0.0911147i
\(748\) 7.19489 0.263071
\(749\) 0 0
\(750\) 24.2253 + 3.92027i 0.884583 + 0.143148i
\(751\) −19.0230 + 32.9488i −0.694159 + 1.20232i 0.276305 + 0.961070i \(0.410890\pi\)
−0.970463 + 0.241248i \(0.922443\pi\)
\(752\) 14.3007 24.7696i 0.521494 0.903254i
\(753\) 22.6039 27.7227i 0.823730 1.01027i
\(754\) 6.00135 + 10.3946i 0.218556 + 0.378551i
\(755\) 7.11744 0.259030
\(756\) 0 0
\(757\) −51.0780 −1.85646 −0.928230 0.372006i \(-0.878670\pi\)
−0.928230 + 0.372006i \(0.878670\pi\)
\(758\) 1.33329 + 2.30933i 0.0484273 + 0.0838786i
\(759\) −8.48887 + 10.4113i −0.308126 + 0.377905i
\(760\) 6.81295 11.8004i 0.247132 0.428045i
\(761\) −20.0375 + 34.7059i −0.726357 + 1.25809i 0.232055 + 0.972703i \(0.425455\pi\)
−0.958413 + 0.285385i \(0.907878\pi\)
\(762\) 29.2985 + 4.74124i 1.06137 + 0.171757i
\(763\) 0 0
\(764\) −17.8633 −0.646273
\(765\) 12.0385 + 4.00106i 0.435254 + 0.144659i
\(766\) 54.6116 1.97320
\(767\) −6.31195 10.9326i −0.227911 0.394754i
\(768\) −11.5720 30.4511i −0.417568 1.09881i
\(769\) −22.4828 + 38.9414i −0.810751 + 1.40426i 0.101587 + 0.994827i \(0.467608\pi\)
−0.912339 + 0.409436i \(0.865726\pi\)
\(770\) 0 0
\(771\) −1.50485 3.95993i −0.0541958 0.142613i
\(772\) 0.0992886 + 0.171973i 0.00357348 + 0.00618944i
\(773\) 24.3561 0.876029 0.438014 0.898968i \(-0.355682\pi\)
0.438014 + 0.898968i \(0.355682\pi\)
\(774\) −18.7059 6.21698i −0.672368 0.223465i
\(775\) 1.38219 0.0496498
\(776\) −14.4998 25.1145i −0.520514 0.901556i
\(777\) 0 0
\(778\) −4.52913 + 7.84468i −0.162377 + 0.281245i
\(779\) −3.71208 + 6.42951i −0.132999 + 0.230361i
\(780\) 4.22567 5.18261i 0.151303 0.185567i
\(781\) −37.1689 64.3784i −1.33001 2.30364i
\(782\) −2.64707 −0.0946592
\(783\) −1.36331 32.2145i −0.0487207 1.15125i
\(784\)