Properties

Label 300.2.e.d.251.8
Level $300$
Weight $2$
Character 300.251
Analytic conductor $2.396$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.4521217600.1
Defining polynomial: \(x^{8} + x^{6} - 2 x^{4} + 4 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.8
Root \(-1.29437 + 0.569745i\) of defining polynomial
Character \(\chi\) \(=\) 300.251
Dual form 300.2.e.d.251.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.29437 + 0.569745i) q^{2} +(0.908080 + 1.47492i) q^{3} +(1.35078 + 1.47492i) q^{4} +(0.335062 + 2.42647i) q^{6} -2.50967i q^{7} +(0.908080 + 2.67869i) q^{8} +(-1.35078 + 2.67869i) q^{9} +O(q^{10})\) \(q+(1.29437 + 0.569745i) q^{2} +(0.908080 + 1.47492i) q^{3} +(1.35078 + 1.47492i) q^{4} +(0.335062 + 2.42647i) q^{6} -2.50967i q^{7} +(0.908080 + 2.67869i) q^{8} +(-1.35078 + 2.67869i) q^{9} -3.36131 q^{11} +(-0.948773 + 3.33164i) q^{12} +3.70156 q^{13} +(1.42987 - 3.24844i) q^{14} +(-0.350781 + 3.98459i) q^{16} -7.63636i q^{17} +(-3.27458 + 2.69761i) q^{18} -0.440172i q^{19} +(3.70156 - 2.27898i) q^{21} +(-4.35078 - 1.91509i) q^{22} -5.17748 q^{23} +(-3.12625 + 3.77181i) q^{24} +(4.79119 + 2.10895i) q^{26} +(-5.17748 + 0.440172i) q^{27} +(3.70156 - 3.39001i) q^{28} +2.27898i q^{29} +3.39001i q^{31} +(-2.72424 + 4.95767i) q^{32} +(-3.05234 - 4.95767i) q^{33} +(4.35078 - 9.88427i) q^{34} +(-5.77547 + 1.62603i) q^{36} +7.40312 q^{37} +(0.250786 - 0.569745i) q^{38} +(3.36131 + 5.45951i) q^{39} -3.07840i q^{41} +(6.08962 - 0.840894i) q^{42} -8.40935i q^{43} +(-4.54040 - 4.95767i) q^{44} +(-6.70156 - 2.94984i) q^{46} +3.63232 q^{47} +(-6.19549 + 3.10095i) q^{48} +0.701562 q^{49} +(11.2630 - 6.93443i) q^{51} +(5.00000 + 5.45951i) q^{52} +2.27898i q^{53} +(-6.95235 - 2.38010i) q^{54} +(6.72263 - 2.27898i) q^{56} +(0.649219 - 0.399712i) q^{57} +(-1.29844 + 2.94984i) q^{58} -5.70156 q^{61} +(-1.93144 + 4.38793i) q^{62} +(6.72263 + 3.39001i) q^{63} +(-6.35078 + 4.86493i) q^{64} +(-1.12625 - 8.15611i) q^{66} +5.45951i q^{67} +(11.2630 - 10.3151i) q^{68} +(-4.70156 - 7.63636i) q^{69} -12.4421 q^{71} +(-8.40201 - 1.18586i) q^{72} -1.29844 q^{73} +(9.58237 + 4.21789i) q^{74} +(0.649219 - 0.594576i) q^{76} +8.43579i q^{77} +(1.24025 + 8.98171i) q^{78} -5.01934i q^{79} +(-5.35078 - 7.23665i) q^{81} +(1.75391 - 3.98459i) q^{82} +1.81616 q^{83} +(8.36131 + 2.38111i) q^{84} +(4.79119 - 10.8848i) q^{86} +(-3.36131 + 2.06950i) q^{87} +(-3.05234 - 9.00393i) q^{88} +5.35738i q^{89} -9.28970i q^{91} +(-6.99364 - 7.63636i) q^{92} +(-5.00000 + 3.07840i) q^{93} +(4.70156 + 2.06950i) q^{94} +(-9.78600 + 0.483926i) q^{96} -11.1047 q^{97} +(0.908080 + 0.399712i) q^{98} +(4.54040 - 9.00393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{4} + 3q^{6} + 2q^{9} + O(q^{10}) \) \( 8q - 2q^{4} + 3q^{6} + 2q^{9} - 11q^{12} + 4q^{13} + 10q^{16} + 7q^{18} + 4q^{21} - 22q^{22} + 13q^{24} + 4q^{28} + 14q^{33} + 22q^{34} - 21q^{36} + 8q^{37} + 36q^{42} - 28q^{46} - 15q^{48} - 20q^{49} + 40q^{52} - 28q^{54} + 18q^{57} - 36q^{58} - 20q^{61} - 38q^{64} + 29q^{66} - 12q^{69} - 51q^{72} - 36q^{73} + 18q^{76} + 22q^{78} - 30q^{81} - 50q^{82} + 40q^{84} + 14q^{88} - 40q^{93} + 12q^{94} - 39q^{96} - 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.29437 + 0.569745i 0.915257 + 0.402871i
\(3\) 0.908080 + 1.47492i 0.524280 + 0.851546i
\(4\) 1.35078 + 1.47492i 0.675391 + 0.737460i
\(5\) 0 0
\(6\) 0.335062 + 2.42647i 0.136788 + 0.990600i
\(7\) 2.50967i 0.948566i −0.880373 0.474283i \(-0.842707\pi\)
0.880373 0.474283i \(-0.157293\pi\)
\(8\) 0.908080 + 2.67869i 0.321055 + 0.947061i
\(9\) −1.35078 + 2.67869i −0.450260 + 0.892897i
\(10\) 0 0
\(11\) −3.36131 −1.01347 −0.506737 0.862101i \(-0.669149\pi\)
−0.506737 + 0.862101i \(0.669149\pi\)
\(12\) −0.948773 + 3.33164i −0.273887 + 0.961762i
\(13\) 3.70156 1.02663 0.513314 0.858201i \(-0.328418\pi\)
0.513314 + 0.858201i \(0.328418\pi\)
\(14\) 1.42987 3.24844i 0.382149 0.868181i
\(15\) 0 0
\(16\) −0.350781 + 3.98459i −0.0876953 + 0.996147i
\(17\) 7.63636i 1.85209i −0.377413 0.926045i \(-0.623186\pi\)
0.377413 0.926045i \(-0.376814\pi\)
\(18\) −3.27458 + 2.69761i −0.771826 + 0.635834i
\(19\) 0.440172i 0.100982i −0.998725 0.0504912i \(-0.983921\pi\)
0.998725 0.0504912i \(-0.0160787\pi\)
\(20\) 0 0
\(21\) 3.70156 2.27898i 0.807747 0.497314i
\(22\) −4.35078 1.91509i −0.927590 0.408299i
\(23\) −5.17748 −1.07958 −0.539789 0.841800i \(-0.681496\pi\)
−0.539789 + 0.841800i \(0.681496\pi\)
\(24\) −3.12625 + 3.77181i −0.638143 + 0.769918i
\(25\) 0 0
\(26\) 4.79119 + 2.10895i 0.939629 + 0.413599i
\(27\) −5.17748 + 0.440172i −0.996406 + 0.0847112i
\(28\) 3.70156 3.39001i 0.699529 0.640652i
\(29\) 2.27898i 0.423196i 0.977357 + 0.211598i \(0.0678668\pi\)
−0.977357 + 0.211598i \(0.932133\pi\)
\(30\) 0 0
\(31\) 3.39001i 0.608864i 0.952534 + 0.304432i \(0.0984667\pi\)
−0.952534 + 0.304432i \(0.901533\pi\)
\(32\) −2.72424 + 4.95767i −0.481582 + 0.876401i
\(33\) −3.05234 4.95767i −0.531345 0.863020i
\(34\) 4.35078 9.88427i 0.746153 1.69514i
\(35\) 0 0
\(36\) −5.77547 + 1.62603i −0.962578 + 0.271005i
\(37\) 7.40312 1.21707 0.608533 0.793529i \(-0.291758\pi\)
0.608533 + 0.793529i \(0.291758\pi\)
\(38\) 0.250786 0.569745i 0.0406828 0.0924249i
\(39\) 3.36131 + 5.45951i 0.538241 + 0.874221i
\(40\) 0 0
\(41\) 3.07840i 0.480766i −0.970678 0.240383i \(-0.922727\pi\)
0.970678 0.240383i \(-0.0772730\pi\)
\(42\) 6.08962 0.840894i 0.939649 0.129753i
\(43\) 8.40935i 1.28241i −0.767368 0.641207i \(-0.778434\pi\)
0.767368 0.641207i \(-0.221566\pi\)
\(44\) −4.54040 4.95767i −0.684491 0.747397i
\(45\) 0 0
\(46\) −6.70156 2.94984i −0.988091 0.434930i
\(47\) 3.63232 0.529828 0.264914 0.964272i \(-0.414656\pi\)
0.264914 + 0.964272i \(0.414656\pi\)
\(48\) −6.19549 + 3.10095i −0.894242 + 0.447584i
\(49\) 0.701562 0.100223
\(50\) 0 0
\(51\) 11.2630 6.93443i 1.57714 0.971014i
\(52\) 5.00000 + 5.45951i 0.693375 + 0.757098i
\(53\) 2.27898i 0.313042i 0.987675 + 0.156521i \(0.0500279\pi\)
−0.987675 + 0.156521i \(0.949972\pi\)
\(54\) −6.95235 2.38010i −0.946095 0.323890i
\(55\) 0 0
\(56\) 6.72263 2.27898i 0.898349 0.304542i
\(57\) 0.649219 0.399712i 0.0859911 0.0529431i
\(58\) −1.29844 + 2.94984i −0.170493 + 0.387333i
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −5.70156 −0.730010 −0.365005 0.931006i \(-0.618933\pi\)
−0.365005 + 0.931006i \(0.618933\pi\)
\(62\) −1.93144 + 4.38793i −0.245294 + 0.557267i
\(63\) 6.72263 + 3.39001i 0.846972 + 0.427102i
\(64\) −6.35078 + 4.86493i −0.793848 + 0.608117i
\(65\) 0 0
\(66\) −1.12625 8.15611i −0.138632 1.00395i
\(67\) 5.45951i 0.666985i 0.942753 + 0.333493i \(0.108227\pi\)
−0.942753 + 0.333493i \(0.891773\pi\)
\(68\) 11.2630 10.3151i 1.36584 1.25088i
\(69\) −4.70156 7.63636i −0.566002 0.919310i
\(70\) 0 0
\(71\) −12.4421 −1.47661 −0.738304 0.674468i \(-0.764373\pi\)
−0.738304 + 0.674468i \(0.764373\pi\)
\(72\) −8.40201 1.18586i −0.990186 0.139755i
\(73\) −1.29844 −0.151971 −0.0759853 0.997109i \(-0.524210\pi\)
−0.0759853 + 0.997109i \(0.524210\pi\)
\(74\) 9.58237 + 4.21789i 1.11393 + 0.490320i
\(75\) 0 0
\(76\) 0.649219 0.594576i 0.0744705 0.0682026i
\(77\) 8.43579i 0.961347i
\(78\) 1.24025 + 8.98171i 0.140431 + 1.01698i
\(79\) 5.01934i 0.564720i −0.959309 0.282360i \(-0.908883\pi\)
0.959309 0.282360i \(-0.0911172\pi\)
\(80\) 0 0
\(81\) −5.35078 7.23665i −0.594531 0.804073i
\(82\) 1.75391 3.98459i 0.193686 0.440024i
\(83\) 1.81616 0.199349 0.0996747 0.995020i \(-0.468220\pi\)
0.0996747 + 0.995020i \(0.468220\pi\)
\(84\) 8.36131 + 2.38111i 0.912294 + 0.259800i
\(85\) 0 0
\(86\) 4.79119 10.8848i 0.516647 1.17374i
\(87\) −3.36131 + 2.06950i −0.360371 + 0.221873i
\(88\) −3.05234 9.00393i −0.325381 0.959822i
\(89\) 5.35738i 0.567882i 0.958842 + 0.283941i \(0.0916419\pi\)
−0.958842 + 0.283941i \(0.908358\pi\)
\(90\) 0 0
\(91\) 9.28970i 0.973825i
\(92\) −6.99364 7.63636i −0.729137 0.796146i
\(93\) −5.00000 + 3.07840i −0.518476 + 0.319216i
\(94\) 4.70156 + 2.06950i 0.484929 + 0.213452i
\(95\) 0 0
\(96\) −9.78600 + 0.483926i −0.998780 + 0.0493905i
\(97\) −11.1047 −1.12751 −0.563755 0.825942i \(-0.690644\pi\)
−0.563755 + 0.825942i \(0.690644\pi\)
\(98\) 0.908080 + 0.399712i 0.0917299 + 0.0403770i
\(99\) 4.54040 9.00393i 0.456327 0.904929i
\(100\) 0 0
\(101\) 17.5517i 1.74646i 0.487308 + 0.873230i \(0.337979\pi\)
−0.487308 + 0.873230i \(0.662021\pi\)
\(102\) 18.5294 2.55865i 1.83468 0.253344i
\(103\) 10.9190i 1.07588i 0.842982 + 0.537941i \(0.180798\pi\)
−0.842982 + 0.537941i \(0.819202\pi\)
\(104\) 3.36131 + 9.91534i 0.329604 + 0.972280i
\(105\) 0 0
\(106\) −1.29844 + 2.94984i −0.126115 + 0.286514i
\(107\) 6.45162 0.623702 0.311851 0.950131i \(-0.399051\pi\)
0.311851 + 0.950131i \(0.399051\pi\)
\(108\) −7.64285 7.04179i −0.735434 0.677596i
\(109\) 2.29844 0.220150 0.110075 0.993923i \(-0.464891\pi\)
0.110075 + 0.993923i \(0.464891\pi\)
\(110\) 0 0
\(111\) 6.72263 + 10.9190i 0.638084 + 1.03639i
\(112\) 10.0000 + 0.880344i 0.944911 + 0.0831847i
\(113\) 0.799423i 0.0752034i −0.999293 0.0376017i \(-0.988028\pi\)
0.999293 0.0376017i \(-0.0119718\pi\)
\(114\) 1.06806 0.147485i 0.100033 0.0138132i
\(115\) 0 0
\(116\) −3.36131 + 3.07840i −0.312090 + 0.285823i
\(117\) −5.00000 + 9.91534i −0.462250 + 0.916674i
\(118\) 0 0
\(119\) −19.1647 −1.75683
\(120\) 0 0
\(121\) 0.298438 0.0271307
\(122\) −7.37992 3.24844i −0.668147 0.294100i
\(123\) 4.54040 2.79544i 0.409394 0.252056i
\(124\) −5.00000 + 4.57917i −0.449013 + 0.411221i
\(125\) 0 0
\(126\) 6.77012 + 8.21811i 0.603130 + 0.732128i
\(127\) 12.6797i 1.12514i −0.826749 0.562571i \(-0.809812\pi\)
0.826749 0.562571i \(-0.190188\pi\)
\(128\) −10.9920 + 2.67869i −0.971567 + 0.236765i
\(129\) 12.4031 7.63636i 1.09203 0.672344i
\(130\) 0 0
\(131\) 5.71949 0.499714 0.249857 0.968283i \(-0.419616\pi\)
0.249857 + 0.968283i \(0.419616\pi\)
\(132\) 3.18913 11.1987i 0.277578 0.974721i
\(133\) −1.10469 −0.0957885
\(134\) −3.11053 + 7.06662i −0.268709 + 0.610463i
\(135\) 0 0
\(136\) 20.4555 6.93443i 1.75404 0.594623i
\(137\) 9.91534i 0.847125i 0.905867 + 0.423563i \(0.139221\pi\)
−0.905867 + 0.423563i \(0.860779\pi\)
\(138\) −1.73477 12.5630i −0.147674 1.06943i
\(139\) 2.94984i 0.250202i 0.992144 + 0.125101i \(0.0399255\pi\)
−0.992144 + 0.125101i \(0.960074\pi\)
\(140\) 0 0
\(141\) 3.29844 + 5.35738i 0.277779 + 0.451173i
\(142\) −16.1047 7.08883i −1.35148 0.594882i
\(143\) −12.4421 −1.04046
\(144\) −10.1997 6.32194i −0.849972 0.526829i
\(145\) 0 0
\(146\) −1.68066 0.739779i −0.139092 0.0612245i
\(147\) 0.637075 + 1.03475i 0.0525450 + 0.0853446i
\(148\) 10.0000 + 10.9190i 0.821995 + 0.897538i
\(149\) 15.2727i 1.25119i −0.780148 0.625595i \(-0.784856\pi\)
0.780148 0.625595i \(-0.215144\pi\)
\(150\) 0 0
\(151\) 19.3284i 1.57292i 0.617641 + 0.786460i \(0.288089\pi\)
−0.617641 + 0.786460i \(0.711911\pi\)
\(152\) 1.17909 0.399712i 0.0956365 0.0324209i
\(153\) 20.4555 + 10.3151i 1.65373 + 0.833923i
\(154\) −4.80625 + 10.9190i −0.387299 + 0.879880i
\(155\) 0 0
\(156\) −3.51194 + 12.3323i −0.281180 + 0.987372i
\(157\) −11.1047 −0.886250 −0.443125 0.896460i \(-0.646130\pi\)
−0.443125 + 0.896460i \(0.646130\pi\)
\(158\) 2.85974 6.49687i 0.227509 0.516864i
\(159\) −3.36131 + 2.06950i −0.266570 + 0.164122i
\(160\) 0 0
\(161\) 12.9937i 1.02405i
\(162\) −2.80284 12.4155i −0.220212 0.975452i
\(163\) 0.440172i 0.0344769i −0.999851 0.0172385i \(-0.994513\pi\)
0.999851 0.0172385i \(-0.00548745\pi\)
\(164\) 4.54040 4.15825i 0.354546 0.324705i
\(165\) 0 0
\(166\) 2.35078 + 1.03475i 0.182456 + 0.0803120i
\(167\) 15.5324 1.20194 0.600968 0.799273i \(-0.294782\pi\)
0.600968 + 0.799273i \(0.294782\pi\)
\(168\) 9.46600 + 7.84585i 0.730318 + 0.605320i
\(169\) 0.701562 0.0539663
\(170\) 0 0
\(171\) 1.17909 + 0.594576i 0.0901669 + 0.0454684i
\(172\) 12.4031 11.3592i 0.945729 0.866130i
\(173\) 8.43579i 0.641361i 0.947187 + 0.320681i \(0.103912\pi\)
−0.947187 + 0.320681i \(0.896088\pi\)
\(174\) −5.52987 + 0.763599i −0.419218 + 0.0578883i
\(175\) 0 0
\(176\) 1.17909 13.3935i 0.0888769 1.00957i
\(177\) 0 0
\(178\) −3.05234 + 6.93443i −0.228783 + 0.519758i
\(179\) 9.08080 0.678731 0.339365 0.940655i \(-0.389788\pi\)
0.339365 + 0.940655i \(0.389788\pi\)
\(180\) 0 0
\(181\) 10.5078 0.781039 0.390520 0.920595i \(-0.372295\pi\)
0.390520 + 0.920595i \(0.372295\pi\)
\(182\) 5.29276 12.0243i 0.392325 0.891300i
\(183\) −5.17748 8.40935i −0.382730 0.621637i
\(184\) −4.70156 13.8689i −0.346604 1.02243i
\(185\) 0 0
\(186\) −8.22575 + 1.13586i −0.603141 + 0.0832856i
\(187\) 25.6682i 1.87705i
\(188\) 4.90647 + 5.35738i 0.357841 + 0.390727i
\(189\) 1.10469 + 12.9937i 0.0803541 + 0.945156i
\(190\) 0 0
\(191\) −12.4421 −0.900280 −0.450140 0.892958i \(-0.648626\pi\)
−0.450140 + 0.892958i \(0.648626\pi\)
\(192\) −12.9424 4.94915i −0.934038 0.357174i
\(193\) −19.8062 −1.42568 −0.712842 0.701324i \(-0.752593\pi\)
−0.712842 + 0.701324i \(0.752593\pi\)
\(194\) −14.3736 6.32684i −1.03196 0.454241i
\(195\) 0 0
\(196\) 0.947657 + 1.03475i 0.0676898 + 0.0739106i
\(197\) 10.7148i 0.763396i −0.924287 0.381698i \(-0.875340\pi\)
0.924287 0.381698i \(-0.124660\pi\)
\(198\) 11.0069 9.06753i 0.782226 0.644401i
\(199\) 21.0891i 1.49496i 0.664282 + 0.747482i \(0.268737\pi\)
−0.664282 + 0.747482i \(0.731263\pi\)
\(200\) 0 0
\(201\) −8.05234 + 4.95767i −0.567968 + 0.349687i
\(202\) −10.0000 + 22.7184i −0.703598 + 1.59846i
\(203\) 5.71949 0.401429
\(204\) 25.4416 + 7.24518i 1.78127 + 0.507264i
\(205\) 0 0
\(206\) −6.22106 + 14.1332i −0.433442 + 0.984709i
\(207\) 6.99364 13.8689i 0.486091 0.963952i
\(208\) −1.29844 + 14.7492i −0.0900305 + 1.02267i
\(209\) 1.47956i 0.102343i
\(210\) 0 0
\(211\) 18.1392i 1.24876i −0.781123 0.624378i \(-0.785353\pi\)
0.781123 0.624378i \(-0.214647\pi\)
\(212\) −3.36131 + 3.07840i −0.230856 + 0.211426i
\(213\) −11.2984 18.3511i −0.774156 1.25740i
\(214\) 8.35078 + 3.67578i 0.570848 + 0.251271i
\(215\) 0 0
\(216\) −5.88065 13.4691i −0.400127 0.916460i
\(217\) 8.50781 0.577548
\(218\) 2.97503 + 1.30952i 0.201494 + 0.0886921i
\(219\) −1.17909 1.91509i −0.0796752 0.129410i
\(220\) 0 0
\(221\) 28.2665i 1.90141i
\(222\) 2.48050 + 17.9634i 0.166481 + 1.20563i
\(223\) 21.0891i 1.41223i 0.708098 + 0.706114i \(0.249553\pi\)
−0.708098 + 0.706114i \(0.750447\pi\)
\(224\) 12.4421 + 6.83694i 0.831324 + 0.456812i
\(225\) 0 0
\(226\) 0.455467 1.03475i 0.0302972 0.0688304i
\(227\) −22.2551 −1.47712 −0.738560 0.674188i \(-0.764494\pi\)
−0.738560 + 0.674188i \(0.764494\pi\)
\(228\) 1.46650 + 0.417624i 0.0971210 + 0.0276578i
\(229\) 2.29844 0.151885 0.0759425 0.997112i \(-0.475803\pi\)
0.0759425 + 0.997112i \(0.475803\pi\)
\(230\) 0 0
\(231\) −12.4421 + 7.66037i −0.818631 + 0.504015i
\(232\) −6.10469 + 2.06950i −0.400792 + 0.135869i
\(233\) 8.43579i 0.552647i 0.961065 + 0.276323i \(0.0891161\pi\)
−0.961065 + 0.276323i \(0.910884\pi\)
\(234\) −12.1211 + 9.98539i −0.792379 + 0.652765i
\(235\) 0 0
\(236\) 0 0
\(237\) 7.40312 4.55796i 0.480885 0.296071i
\(238\) −24.8062 10.9190i −1.60795 0.707775i
\(239\) 25.8874 1.67452 0.837258 0.546809i \(-0.184158\pi\)
0.837258 + 0.546809i \(0.184158\pi\)
\(240\) 0 0
\(241\) 7.00000 0.450910 0.225455 0.974254i \(-0.427613\pi\)
0.225455 + 0.974254i \(0.427613\pi\)
\(242\) 0.386289 + 0.170034i 0.0248316 + 0.0109302i
\(243\) 5.81455 14.4634i 0.373004 0.927830i
\(244\) −7.70156 8.40935i −0.493042 0.538354i
\(245\) 0 0
\(246\) 7.46964 1.03146i 0.476247 0.0657632i
\(247\) 1.62932i 0.103671i
\(248\) −9.08080 + 3.07840i −0.576631 + 0.195479i
\(249\) 1.64922 + 2.67869i 0.104515 + 0.169755i
\(250\) 0 0
\(251\) 22.5261 1.42183 0.710916 0.703277i \(-0.248281\pi\)
0.710916 + 0.703277i \(0.248281\pi\)
\(252\) 4.08080 + 14.4945i 0.257066 + 0.913068i
\(253\) 17.4031 1.09413
\(254\) 7.22420 16.4122i 0.453287 1.02979i
\(255\) 0 0
\(256\) −15.7539 2.79544i −0.984619 0.174715i
\(257\) 4.55796i 0.284318i −0.989844 0.142159i \(-0.954596\pi\)
0.989844 0.142159i \(-0.0454044\pi\)
\(258\) 20.4050 2.81765i 1.27036 0.175419i
\(259\) 18.5794i 1.15447i
\(260\) 0 0
\(261\) −6.10469 3.07840i −0.377871 0.190548i
\(262\) 7.40312 + 3.25865i 0.457367 + 0.201320i
\(263\) 18.6227 1.14833 0.574164 0.818741i \(-0.305327\pi\)
0.574164 + 0.818741i \(0.305327\pi\)
\(264\) 10.5083 12.6783i 0.646741 0.780292i
\(265\) 0 0
\(266\) −1.42987 0.629390i −0.0876710 0.0385904i
\(267\) −7.90172 + 4.86493i −0.483577 + 0.297729i
\(268\) −8.05234 + 7.37460i −0.491875 + 0.450476i
\(269\) 8.43579i 0.514339i 0.966366 + 0.257170i \(0.0827899\pi\)
−0.966366 + 0.257170i \(0.917210\pi\)
\(270\) 0 0
\(271\) 9.15833i 0.556329i −0.960533 0.278165i \(-0.910274\pi\)
0.960533 0.278165i \(-0.0897260\pi\)
\(272\) 30.4278 + 2.67869i 1.84495 + 0.162420i
\(273\) 13.7016 8.43579i 0.829256 0.510557i
\(274\) −5.64922 + 12.8341i −0.341282 + 0.775337i
\(275\) 0 0
\(276\) 4.91225 17.2495i 0.295683 1.03830i
\(277\) 8.89531 0.534468 0.267234 0.963632i \(-0.413890\pi\)
0.267234 + 0.963632i \(0.413890\pi\)
\(278\) −1.68066 + 3.81818i −0.100799 + 0.228999i
\(279\) −9.08080 4.57917i −0.543653 0.274147i
\(280\) 0 0
\(281\) 17.5517i 1.04705i −0.852011 0.523524i \(-0.824617\pi\)
0.852011 0.523524i \(-0.175383\pi\)
\(282\) 1.21705 + 8.81370i 0.0724744 + 0.524848i
\(283\) 16.3785i 0.973603i −0.873513 0.486801i \(-0.838164\pi\)
0.873513 0.486801i \(-0.161836\pi\)
\(284\) −16.8066 18.3511i −0.997287 1.08894i
\(285\) 0 0
\(286\) −16.1047 7.08883i −0.952290 0.419172i
\(287\) −7.72577 −0.456038
\(288\) −9.60022 13.9941i −0.565699 0.824612i
\(289\) −41.3141 −2.43024
\(290\) 0 0
\(291\) −10.0839 16.3785i −0.591131 0.960126i
\(292\) −1.75391 1.91509i −0.102640 0.112072i
\(293\) 21.4295i 1.25193i −0.779852 0.625963i \(-0.784706\pi\)
0.779852 0.625963i \(-0.215294\pi\)
\(294\) 0.235067 + 1.70232i 0.0137094 + 0.0992811i
\(295\) 0 0
\(296\) 6.72263 + 19.8307i 0.390745 + 1.15264i
\(297\) 17.4031 1.47956i 1.00983 0.0858526i
\(298\) 8.70156 19.7685i 0.504068 1.14516i
\(299\) −19.1647 −1.10833
\(300\) 0 0
\(301\) −21.1047 −1.21645
\(302\) −11.0122 + 25.0180i −0.633683 + 1.43963i
\(303\) −25.8874 + 15.9384i −1.48719 + 0.915635i
\(304\) 1.75391 + 0.154404i 0.100593 + 0.00885568i
\(305\) 0 0
\(306\) 20.6000 + 25.0059i 1.17762 + 1.42949i
\(307\) 26.4172i 1.50771i −0.657041 0.753855i \(-0.728192\pi\)
0.657041 0.753855i \(-0.271808\pi\)
\(308\) −12.4421 + 11.3949i −0.708955 + 0.649285i
\(309\) −16.1047 + 9.91534i −0.916164 + 0.564064i
\(310\) 0 0
\(311\) 13.4453 0.762411 0.381205 0.924490i \(-0.375509\pi\)
0.381205 + 0.924490i \(0.375509\pi\)
\(312\) −11.5720 + 13.9616i −0.655136 + 0.790420i
\(313\) −16.2984 −0.921242 −0.460621 0.887597i \(-0.652373\pi\)
−0.460621 + 0.887597i \(0.652373\pi\)
\(314\) −14.3736 6.32684i −0.811147 0.357044i
\(315\) 0 0
\(316\) 7.40312 6.78003i 0.416458 0.381406i
\(317\) 16.8716i 0.947602i −0.880632 0.473801i \(-0.842882\pi\)
0.880632 0.473801i \(-0.157118\pi\)
\(318\) −5.52987 + 0.763599i −0.310100 + 0.0428205i
\(319\) 7.66037i 0.428898i
\(320\) 0 0
\(321\) 5.85859 + 9.51563i 0.326995 + 0.531111i
\(322\) −7.40312 + 16.8187i −0.412560 + 0.937270i
\(323\) −3.36131 −0.187029
\(324\) 3.44575 17.6671i 0.191431 0.981506i
\(325\) 0 0
\(326\) 0.250786 0.569745i 0.0138897 0.0315553i
\(327\) 2.08717 + 3.39001i 0.115421 + 0.187468i
\(328\) 8.24609 2.79544i 0.455314 0.154352i
\(329\) 9.11592i 0.502577i
\(330\) 0 0
\(331\) 17.1275i 0.941413i −0.882290 0.470707i \(-0.843999\pi\)
0.882290 0.470707i \(-0.156001\pi\)
\(332\) 2.45323 + 2.67869i 0.134639 + 0.147012i
\(333\) −10.0000 + 19.8307i −0.547997 + 1.08672i
\(334\) 20.1047 + 8.84952i 1.10008 + 0.484224i
\(335\) 0 0
\(336\) 7.78236 + 15.5486i 0.424563 + 0.848247i
\(337\) 12.4031 0.675641 0.337821 0.941211i \(-0.390310\pi\)
0.337821 + 0.941211i \(0.390310\pi\)
\(338\) 0.908080 + 0.399712i 0.0493930 + 0.0217414i
\(339\) 1.17909 0.725940i 0.0640391 0.0394277i
\(340\) 0 0
\(341\) 11.3949i 0.617069i
\(342\) 1.18741 + 1.44138i 0.0642080 + 0.0779409i
\(343\) 19.3284i 1.04363i
\(344\) 22.5261 7.63636i 1.21452 0.411725i
\(345\) 0 0
\(346\) −4.80625 + 10.9190i −0.258386 + 0.587010i
\(347\) −19.4358 −1.04337 −0.521683 0.853139i \(-0.674696\pi\)
−0.521683 + 0.853139i \(0.674696\pi\)
\(348\) −7.59274 2.16224i −0.407014 0.115908i
\(349\) 26.2094 1.40296 0.701478 0.712691i \(-0.252524\pi\)
0.701478 + 0.712691i \(0.252524\pi\)
\(350\) 0 0
\(351\) −19.1647 + 1.62932i −1.02294 + 0.0869669i
\(352\) 9.15703 16.6643i 0.488071 0.888210i
\(353\) 26.6676i 1.41937i −0.704517 0.709687i \(-0.748836\pi\)
0.704517 0.709687i \(-0.251164\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −7.90172 + 7.23665i −0.418790 + 0.383542i
\(357\) −17.4031 28.2665i −0.921071 1.49602i
\(358\) 11.7539 + 5.17374i 0.621213 + 0.273441i
\(359\) 7.72577 0.407751 0.203875 0.978997i \(-0.434646\pi\)
0.203875 + 0.978997i \(0.434646\pi\)
\(360\) 0 0
\(361\) 18.8062 0.989803
\(362\) 13.6010 + 5.98677i 0.714852 + 0.314658i
\(363\) 0.271006 + 0.440172i 0.0142241 + 0.0231030i
\(364\) 13.7016 12.5483i 0.718157 0.657712i
\(365\) 0 0
\(366\) −1.91038 13.8346i −0.0998569 0.723148i
\(367\) 2.50967i 0.131004i −0.997852 0.0655018i \(-0.979135\pi\)
0.997852 0.0655018i \(-0.0208648\pi\)
\(368\) 1.81616 20.6301i 0.0946739 1.07542i
\(369\) 8.24609 + 4.15825i 0.429275 + 0.216470i
\(370\) 0 0
\(371\) 5.71949 0.296941
\(372\) −11.2943 3.21635i −0.585582 0.166760i
\(373\) 23.7016 1.22722 0.613610 0.789609i \(-0.289717\pi\)
0.613610 + 0.789609i \(0.289717\pi\)
\(374\) −14.6243 + 33.2241i −0.756207 + 1.71798i
\(375\) 0 0
\(376\) 3.29844 + 9.72987i 0.170104 + 0.501780i
\(377\) 8.43579i 0.434465i
\(378\) −5.97325 + 17.4481i −0.307231 + 0.897433i
\(379\) 13.1199i 0.673923i 0.941518 + 0.336961i \(0.109399\pi\)
−0.941518 + 0.336961i \(0.890601\pi\)
\(380\) 0 0
\(381\) 18.7016 11.5142i 0.958110 0.589890i
\(382\) −16.1047 7.08883i −0.823987 0.362696i
\(383\) −7.26464 −0.371206 −0.185603 0.982625i \(-0.559424\pi\)
−0.185603 + 0.982625i \(0.559424\pi\)
\(384\) −13.9325 13.7799i −0.710990 0.703202i
\(385\) 0 0
\(386\) −25.6366 11.2845i −1.30487 0.574367i
\(387\) 22.5261 + 11.3592i 1.14506 + 0.577420i
\(388\) −15.0000 16.3785i −0.761510 0.831494i
\(389\) 37.3824i 1.89536i 0.319218 + 0.947681i \(0.396580\pi\)
−0.319218 + 0.947681i \(0.603420\pi\)
\(390\) 0 0
\(391\) 39.5371i 1.99948i
\(392\) 0.637075 + 1.87927i 0.0321771 + 0.0949174i
\(393\) 5.19375 + 8.43579i 0.261990 + 0.425529i
\(394\) 6.10469 13.8689i 0.307550 0.698703i
\(395\) 0 0
\(396\) 19.4132 5.46560i 0.975548 0.274657i
\(397\) 15.9109 0.798547 0.399273 0.916832i \(-0.369262\pi\)
0.399273 + 0.916832i \(0.369262\pi\)
\(398\) −12.0154 + 27.2970i −0.602277 + 1.36828i
\(399\) −1.00314 1.62932i −0.0502200 0.0815683i
\(400\) 0 0
\(401\) 9.23521i 0.461184i 0.973050 + 0.230592i \(0.0740663\pi\)
−0.973050 + 0.230592i \(0.925934\pi\)
\(402\) −13.2473 + 1.82927i −0.660716 + 0.0912359i
\(403\) 12.5483i 0.625078i
\(404\) −25.8874 + 23.7085i −1.28795 + 1.17954i
\(405\) 0 0
\(406\) 7.40312 + 3.25865i 0.367411 + 0.161724i
\(407\) −24.8842 −1.23347
\(408\) 28.8029 + 23.8732i 1.42596 + 1.18190i
\(409\) 11.2094 0.554268 0.277134 0.960831i \(-0.410615\pi\)
0.277134 + 0.960831i \(0.410615\pi\)
\(410\) 0 0
\(411\) −14.6243 + 9.00393i −0.721366 + 0.444131i
\(412\) −16.1047 + 14.7492i −0.793421 + 0.726641i
\(413\) 0 0
\(414\) 16.9541 13.9668i 0.833247 0.686432i
\(415\) 0 0
\(416\) −10.0839 + 18.3511i −0.494406 + 0.899738i
\(417\) −4.35078 + 2.67869i −0.213059 + 0.131176i
\(418\) −0.842970 + 1.91509i −0.0412310 + 0.0936702i
\(419\) 34.9682 1.70831 0.854154 0.520021i \(-0.174076\pi\)
0.854154 + 0.520021i \(0.174076\pi\)
\(420\) 0 0
\(421\) −14.2094 −0.692522 −0.346261 0.938138i \(-0.612549\pi\)
−0.346261 + 0.938138i \(0.612549\pi\)
\(422\) 10.3347 23.4788i 0.503087 1.14293i
\(423\) −4.90647 + 9.72987i −0.238561 + 0.473082i
\(424\) −6.10469 + 2.06950i −0.296470 + 0.100504i
\(425\) 0 0
\(426\) −4.16888 30.1904i −0.201983 1.46273i
\(427\) 14.3090i 0.692463i
\(428\) 8.71473 + 9.51563i 0.421242 + 0.459955i
\(429\) −11.2984 18.3511i −0.545494 0.886001i
\(430\) 0 0
\(431\) 5.71949 0.275498 0.137749 0.990467i \(-0.456013\pi\)
0.137749 + 0.990467i \(0.456013\pi\)
\(432\) 0.0622549 20.7845i 0.00299524 0.999996i
\(433\) 7.20937 0.346460 0.173230 0.984881i \(-0.444580\pi\)
0.173230 + 0.984881i \(0.444580\pi\)
\(434\) 11.0122 + 4.84728i 0.528605 + 0.232677i
\(435\) 0 0
\(436\) 3.10469 + 3.39001i 0.148688 + 0.162352i
\(437\) 2.27898i 0.109018i
\(438\) −0.435057 3.15061i −0.0207878 0.150542i
\(439\) 23.4674i 1.12004i 0.828480 + 0.560018i \(0.189206\pi\)
−0.828480 + 0.560018i \(0.810794\pi\)
\(440\) 0 0
\(441\) −0.947657 + 1.87927i −0.0451265 + 0.0894890i
\(442\) 16.1047 36.5872i 0.766022 1.74028i
\(443\) 29.7907 1.41540 0.707699 0.706514i \(-0.249733\pi\)
0.707699 + 0.706514i \(0.249733\pi\)
\(444\) −7.02389 + 24.6645i −0.333339 + 1.17053i
\(445\) 0 0
\(446\) −12.0154 + 27.2970i −0.568945 + 1.29255i
\(447\) 22.5261 13.8689i 1.06545 0.655975i
\(448\) 12.2094 + 15.9384i 0.576839 + 0.753017i
\(449\) 29.7460i 1.40380i −0.712274 0.701901i \(-0.752335\pi\)
0.712274 0.701901i \(-0.247665\pi\)
\(450\) 0 0
\(451\) 10.3475i 0.487244i
\(452\) 1.17909 1.07985i 0.0554595 0.0507917i
\(453\) −28.5078 + 17.5517i −1.33941 + 0.824651i
\(454\) −28.8062 12.6797i −1.35194 0.595088i
\(455\) 0 0
\(456\) 1.66025 + 1.37609i 0.0777482 + 0.0644412i
\(457\) −36.1047 −1.68891 −0.844453 0.535630i \(-0.820074\pi\)
−0.844453 + 0.535630i \(0.820074\pi\)
\(458\) 2.97503 + 1.30952i 0.139014 + 0.0611900i
\(459\) 3.36131 + 39.5371i 0.156893 + 1.84543i
\(460\) 0 0
\(461\) 17.5517i 0.817465i 0.912654 + 0.408732i \(0.134029\pi\)
−0.912654 + 0.408732i \(0.865971\pi\)
\(462\) −20.4691 + 2.82651i −0.952311 + 0.131501i
\(463\) 5.01934i 0.233268i −0.993175 0.116634i \(-0.962789\pi\)
0.993175 0.116634i \(-0.0372105\pi\)
\(464\) −9.08080 0.799423i −0.421566 0.0371123i
\(465\) 0 0
\(466\) −4.80625 + 10.9190i −0.222645 + 0.505814i
\(467\) 29.5197 1.36601 0.683004 0.730414i \(-0.260673\pi\)
0.683004 + 0.730414i \(0.260673\pi\)
\(468\) −21.3783 + 6.01886i −0.988210 + 0.278222i
\(469\) 13.7016 0.632679
\(470\) 0 0
\(471\) −10.0839 16.3785i −0.464644 0.754683i
\(472\) 0 0
\(473\) 28.2665i 1.29969i
\(474\) 12.1792 1.68179i 0.559411 0.0772471i
\(475\) 0 0
\(476\) −25.8874 28.2665i −1.18655 1.29559i
\(477\) −6.10469 3.07840i −0.279514 0.140950i
\(478\) 33.5078 + 14.7492i 1.53261 + 0.674613i
\(479\) −33.6131 −1.53582 −0.767912 0.640555i \(-0.778704\pi\)
−0.767912 + 0.640555i \(0.778704\pi\)
\(480\) 0 0
\(481\) 27.4031 1.24947
\(482\) 9.06058 + 3.98822i 0.412698 + 0.181658i
\(483\) −19.1647 + 11.7994i −0.872026 + 0.536890i
\(484\) 0.403124 + 0.440172i 0.0183238 + 0.0200078i
\(485\) 0 0
\(486\) 15.7666 15.4082i 0.715189 0.698931i
\(487\) 0.131364i 0.00595267i −0.999996 0.00297634i \(-0.999053\pi\)
0.999996 0.00297634i \(-0.000947399\pi\)
\(488\) −5.17748 15.2727i −0.234373 0.691364i
\(489\) 0.649219 0.399712i 0.0293587 0.0180756i
\(490\) 0 0
\(491\) 13.4453 0.606776 0.303388 0.952867i \(-0.401882\pi\)
0.303388 + 0.952867i \(0.401882\pi\)
\(492\) 10.2561 + 2.92071i 0.462382 + 0.131676i
\(493\) 17.4031 0.783797
\(494\) 0.928300 2.10895i 0.0417662 0.0948860i
\(495\) 0 0
\(496\) −13.5078 1.18915i −0.606519 0.0533945i
\(497\) 31.2256i 1.40066i
\(498\) 0.608526 + 4.40685i 0.0272687 + 0.197476i
\(499\) 40.2861i 1.80345i −0.432308 0.901726i \(-0.642301\pi\)
0.432308 0.901726i \(-0.357699\pi\)
\(500\) 0 0
\(501\) 14.1047 + 22.9091i 0.630151 + 1.02350i
\(502\) 29.1570 + 12.8341i 1.30134 + 0.572814i
\(503\) 12.9841 0.578934 0.289467 0.957188i \(-0.406522\pi\)
0.289467 + 0.957188i \(0.406522\pi\)
\(504\) −2.97611 + 21.0863i −0.132567 + 0.939257i
\(505\) 0 0
\(506\) 22.5261 + 9.91534i 1.00141 + 0.440791i
\(507\) 0.637075 + 1.03475i 0.0282935 + 0.0459548i
\(508\) 18.7016 17.1275i 0.829748 0.759910i
\(509\) 2.95911i 0.131160i −0.997847 0.0655802i \(-0.979110\pi\)
0.997847 0.0655802i \(-0.0208898\pi\)
\(510\) 0 0
\(511\) 3.25865i 0.144154i
\(512\) −18.7987 12.5940i −0.830792 0.556583i
\(513\) 0.193752 + 2.27898i 0.00855434 + 0.100619i
\(514\) 2.59688 5.89968i 0.114543 0.260224i
\(515\) 0 0
\(516\) 28.0169 + 7.97857i 1.23338 + 0.351237i
\(517\) −12.2094 −0.536968
\(518\) 10.5855 24.0486i 0.465101 1.05663i
\(519\) −12.4421 + 7.66037i −0.546148 + 0.336253i
\(520\) 0 0
\(521\) 3.07840i 0.134867i 0.997724 + 0.0674337i \(0.0214811\pi\)
−0.997724 + 0.0674337i \(0.978519\pi\)
\(522\) −6.14781 7.46270i −0.269082 0.326634i
\(523\) 14.0002i 0.612187i −0.952001 0.306094i \(-0.900978\pi\)
0.952001 0.306094i \(-0.0990220\pi\)
\(524\) 7.72577 + 8.43579i 0.337502 + 0.368519i
\(525\) 0 0
\(526\) 24.1047 + 10.6102i 1.05101 + 0.462627i
\(527\) 25.8874 1.12767
\(528\) 20.8250 10.4233i 0.906291 0.453615i
\(529\) 3.80625 0.165489
\(530\) 0 0
\(531\) 0 0
\(532\) −1.49219 1.62932i −0.0646946 0.0706402i
\(533\) 11.3949i 0.493568i
\(534\) −12.9995 + 1.79505i −0.562544 + 0.0776796i
\(535\) 0 0
\(536\) −14.6243 + 4.95767i −0.631676 + 0.214139i
\(537\) 8.24609 + 13.3935i 0.355845 + 0.577970i
\(538\) −4.80625 + 10.9190i −0.207212 + 0.470752i
\(539\) −2.35817 −0.101574
\(540\) 0 0
\(541\) −25.7016 −1.10500 −0.552498 0.833514i \(-0.686325\pi\)
−0.552498 + 0.833514i \(0.686325\pi\)
\(542\) 5.21791 11.8543i 0.224129 0.509184i
\(543\) 9.54193 + 15.4982i 0.409484 + 0.665091i
\(544\) 37.8586 + 20.8033i 1.62317 + 0.891934i
\(545\) 0 0
\(546\) 22.5411 3.11262i 0.964671 0.133208i
\(547\) 4.71053i 0.201408i −0.994916 0.100704i \(-0.967891\pi\)
0.994916 0.100704i \(-0.0321095\pi\)
\(548\) −14.6243 + 13.3935i −0.624721 + 0.572140i
\(549\) 7.70156 15.2727i 0.328695 0.651824i
\(550\) 0 0
\(551\) 1.00314 0.0427354
\(552\) 16.1861 19.5285i 0.688925 0.831187i
\(553\) −12.5969 −0.535674
\(554\) 11.5138 + 5.06806i 0.489175 + 0.215321i
\(555\) 0 0
\(556\) −4.35078 + 3.98459i −0.184514 + 0.168984i
\(557\) 36.7023i 1.55512i 0.628806 + 0.777562i \(0.283544\pi\)
−0.628806 + 0.777562i \(0.716456\pi\)
\(558\) −9.14495 11.1009i −0.387137 0.469937i
\(559\) 31.1277i 1.31656i
\(560\) 0 0
\(561\) −37.8586 + 23.3088i −1.59839 + 0.984098i
\(562\) 10.0000 22.7184i 0.421825 0.958317i
\(563\) −23.3391 −0.983625 −0.491812 0.870701i \(-0.663665\pi\)
−0.491812 + 0.870701i \(0.663665\pi\)
\(564\) −3.44625 + 12.1016i −0.145113 + 0.509569i
\(565\) 0 0
\(566\) 9.33159 21.1999i 0.392236 0.891096i
\(567\) −18.1616 + 13.4287i −0.762716 + 0.563952i
\(568\) −11.2984 33.3286i −0.474072 1.39844i
\(569\) 10.5955i 0.444186i 0.975026 + 0.222093i \(0.0712888\pi\)
−0.975026 + 0.222093i \(0.928711\pi\)
\(570\) 0 0
\(571\) 16.9501i 0.709338i 0.934992 + 0.354669i \(0.115406\pi\)
−0.934992 + 0.354669i \(0.884594\pi\)
\(572\) −16.8066 18.3511i −0.702718 0.767299i
\(573\) −11.2984 18.3511i −0.471999 0.766630i
\(574\) −10.0000 4.40172i −0.417392 0.183724i
\(575\) 0 0
\(576\) −4.45314 23.5832i −0.185548 0.982635i
\(577\) 12.4031 0.516349 0.258174 0.966098i \(-0.416879\pi\)
0.258174 + 0.966098i \(0.416879\pi\)
\(578\) −53.4756 23.5385i −2.22429 0.979072i
\(579\) −17.9857 29.2126i −0.747459 1.21404i
\(580\) 0 0
\(581\) 4.55796i 0.189096i
\(582\) −3.72076 26.9451i −0.154230 1.11691i
\(583\) 7.66037i 0.317260i
\(584\) −1.17909 3.47812i −0.0487909 0.143925i
\(585\) 0 0
\(586\) 12.2094 27.7377i 0.504365 1.14583i
\(587\) −31.3359 −1.29337 −0.646685 0.762758i \(-0.723845\pi\)
−0.646685 + 0.762758i \(0.723845\pi\)
\(588\) −0.665623 + 2.33735i −0.0274498 + 0.0963908i
\(589\) 1.49219 0.0614846
\(590\) 0 0
\(591\) 15.8034 9.72987i 0.650066 0.400233i
\(592\) −2.59688 + 29.4984i −0.106731 + 1.21238i
\(593\) 10.5955i 0.435104i 0.976049 + 0.217552i \(0.0698072\pi\)
−0.976049 + 0.217552i \(0.930193\pi\)
\(594\) 23.3690 + 8.00025i 0.958843 + 0.328254i
\(595\) 0 0
\(596\) 22.5261 20.6301i 0.922703 0.845042i
\(597\) −31.1047 + 19.1506i −1.27303 + 0.783780i
\(598\) −24.8062 10.9190i −1.01440 0.446512i
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −40.0156 −1.63227 −0.816136 0.577860i \(-0.803888\pi\)
−0.816136 + 0.577860i \(0.803888\pi\)
\(602\) −27.3172 12.0243i −1.11337 0.490074i
\(603\) −14.6243 7.37460i −0.595549 0.300317i
\(604\) −28.5078 + 26.1084i −1.15997 + 1.06234i
\(605\) 0 0
\(606\) −42.5886 + 5.88091i −1.73004 + 0.238896i
\(607\) 3.25865i 0.132264i 0.997811 + 0.0661322i \(0.0210659\pi\)
−0.997811 + 0.0661322i \(0.978934\pi\)
\(608\) 2.18223 + 1.19913i 0.0885011 + 0.0486313i
\(609\) 5.19375 + 8.43579i 0.210461 + 0.341835i
\(610\) 0 0
\(611\) 13.4453 0.543937
\(612\) 12.4170 + 44.1036i 0.501926 + 1.78278i
\(613\) −4.80625 −0.194123 −0.0970613 0.995278i \(-0.530944\pi\)
−0.0970613 + 0.995278i \(0.530944\pi\)
\(614\) 15.0511 34.1936i 0.607412 1.37994i
\(615\) 0 0
\(616\) −22.5969 + 7.66037i −0.910454 + 0.308645i
\(617\) 22.1097i 0.890102i −0.895505 0.445051i \(-0.853186\pi\)
0.895505 0.445051i \(-0.146814\pi\)
\(618\) −26.4946 + 3.65855i −1.06577 + 0.147168i
\(619\) 5.15070i 0.207024i 0.994628 + 0.103512i \(0.0330080\pi\)
−0.994628 + 0.103512i \(0.966992\pi\)
\(620\) 0 0
\(621\) 26.8062 2.27898i 1.07570 0.0914523i
\(622\) 17.4031 + 7.66037i 0.697802 + 0.307153i
\(623\) 13.4453 0.538673
\(624\) −22.9330 + 11.4784i −0.918054 + 0.459502i
\(625\) 0 0
\(626\) −21.0962 9.28595i −0.843173 0.371141i
\(627\) −2.18223 + 1.34356i −0.0871498 + 0.0536565i
\(628\) −15.0000 16.3785i −0.598565 0.653574i
\(629\) 56.5330i 2.25412i
\(630\) 0 0
\(631\) 42.0468i 1.67385i −0.547314 0.836927i \(-0.684350\pi\)
0.547314 0.836927i \(-0.315650\pi\)
\(632\) 13.4453 4.55796i 0.534824 0.181306i
\(633\) 26.7539 16.4719i 1.06337 0.654698i
\(634\) 9.61250 21.8380i 0.381761 0.867299i
\(635\) 0 0
\(636\) −7.59274 2.16224i −0.301072 0.0857382i
\(637\) 2.59688 0.102892
\(638\) 4.36446 9.91534i 0.172791 0.392552i
\(639\) 16.8066 33.3286i 0.664858 1.31846i
\(640\) 0 0
\(641\) 12.3136i 0.486359i −0.969981 0.243179i \(-0.921810\pi\)
0.969981 0.243179i \(-0.0781903\pi\)
\(642\) 2.16169 + 15.6546i 0.0853152 + 0.617839i
\(643\) 24.4791i 0.965360i 0.875797 + 0.482680i \(0.160337\pi\)
−0.875797 + 0.482680i \(0.839663\pi\)
\(644\) −19.1647 + 17.5517i −0.755197 + 0.691634i
\(645\) 0 0
\(646\) −4.35078 1.91509i −0.171179 0.0753483i
\(647\) −10.3550 −0.407095 −0.203548 0.979065i \(-0.565247\pi\)
−0.203548 + 0.979065i \(0.565247\pi\)
\(648\) 14.5258 20.9046i 0.570628 0.821208i
\(649\) 0 0
\(650\) 0 0
\(651\) 7.72577 + 12.5483i 0.302797 + 0.491808i
\(652\) 0.649219 0.594576i 0.0254254 0.0232854i
\(653\) 25.9875i 1.01697i 0.861071 + 0.508485i \(0.169794\pi\)
−0.861071 + 0.508485i \(0.830206\pi\)
\(654\) 0.770119 + 5.57708i 0.0301140 + 0.218081i
\(655\) 0 0
\(656\) 12.2662 + 1.07985i 0.478914 + 0.0421609i
\(657\) 1.75391 3.47812i 0.0684264 0.135694i
\(658\) 5.19375 11.7994i 0.202474 0.459987i
\(659\) −16.8066 −0.654691 −0.327346 0.944905i \(-0.606154\pi\)
−0.327346 + 0.944905i \(0.606154\pi\)
\(660\) 0 0
\(661\) −18.0000 −0.700119 −0.350059 0.936727i \(-0.613839\pi\)
−0.350059 + 0.936727i \(0.613839\pi\)
\(662\) 9.75831 22.1693i 0.379268 0.861635i
\(663\) 41.6908 25.6682i 1.61914 0.996871i
\(664\) 1.64922 + 4.86493i 0.0640021 + 0.188796i
\(665\) 0 0
\(666\) −24.2421 + 19.9708i −0.939363 + 0.773852i
\(667\) 11.7994i 0.456873i
\(668\) 20.9809 + 22.9091i 0.811776 + 0.886379i
\(669\) −31.1047 + 19.1506i −1.20258 + 0.740403i
\(670\) 0 0
\(671\) 19.1647 0.739847
\(672\) 1.21449 + 24.5596i 0.0468501 + 0.947408i
\(673\) −24.8062 −0.956211 −0.478105 0.878303i \(-0.658676\pi\)
−0.478105 + 0.878303i \(0.658676\pi\)
\(674\) 16.0542 + 7.06662i 0.618385 + 0.272196i
\(675\) 0 0
\(676\) 0.947657 + 1.03475i 0.0364483 + 0.0397980i
\(677\) 12.9937i 0.499390i 0.968324 + 0.249695i \(0.0803304\pi\)
−0.968324 + 0.249695i \(0.919670\pi\)
\(678\) 1.93977 0.267856i 0.0744965 0.0102870i
\(679\) 27.8691i 1.06952i
\(680\) 0 0
\(681\) −20.2094 32.8244i −0.774425 1.25784i
\(682\) 6.49219 14.7492i 0.248599 0.564776i
\(683\) 11.6291 0.444975 0.222488 0.974936i \(-0.428582\pi\)
0.222488 + 0.974936i \(0.428582\pi\)
\(684\) 0.715734 + 2.54220i 0.0273668 + 0.0972034i
\(685\) 0 0
\(686\) 11.0122 25.0180i 0.420449 0.955193i
\(687\) 2.08717 + 3.39001i 0.0796303 + 0.129337i
\(688\) 33.5078 + 2.94984i 1.27747 + 0.112462i
\(689\) 8.43579i 0.321378i
\(690\) 0 0
\(691\) 1.18915i 0.0452375i −0.999744 0.0226187i \(-0.992800\pi\)
0.999744 0.0226187i \(-0.00720038\pi\)
\(692\) −12.4421 + 11.3949i −0.472978 + 0.433169i
\(693\) −22.5969 11.3949i −0.858384 0.432857i
\(694\) −25.1570 11.0734i −0.954948 0.420341i
\(695\) 0 0
\(696\) −8.59589 7.12466i −0.325826 0.270059i
\(697\) −23.5078 −0.890422
\(698\) 33.9246 + 14.9327i 1.28406 + 0.565210i
\(699\) −12.4421 + 7.66037i −0.470604 + 0.289742i
\(700\) 0 0
\(701\) 11.3949i 0.430380i 0.976572 + 0.215190i \(0.0690370\pi\)
−0.976572 + 0.215190i \(0.930963\pi\)
\(702\) −25.7345 8.81007i −0.971288 0.332515i
\(703\) 3.25865i 0.122902i
\(704\) 21.3470 16.3526i 0.804544 0.616311i
\(705\) 0 0
\(706\) 15.1938 34.5177i 0.571824 1.29909i
\(707\) 44.0490 1.65663
\(708\) 0 0
\(709\) −17.7016 −0.664796 −0.332398 0.943139i \(-0.607858\pi\)
−0.332398 + 0.943139i \(0.607858\pi\)
\(710\) 0 0
\(711\) 13.4453 + 6.78003i 0.504237 + 0.254271i
\(712\) −14.3508 + 4.86493i −0.537818 + 0.182321i
\(713\) 17.5517i 0.657317i
\(714\) −6.42137 46.5026i −0.240314 1.74032i
\(715\) 0 0
\(716\) 12.2662 + 13.3935i 0.458408 + 0.500537i
\(717\) 23.5078 + 38.1818i 0.877915 + 1.42593i
\(718\) 10.0000 + 4.40172i 0.373197 + 0.164271i
\(719\) 44.0490 1.64275 0.821375 0.570389i \(-0.193207\pi\)
0.821375 + 0.570389i \(0.193207\pi\)
\(720\) 0 0
\(721\) 27.4031 1.02055
\(722\) 24.3422 + 10.7148i 0.905924 + 0.398762i
\(723\) 6.35656 + 10.3244i 0.236403 + 0.383970i
\(724\) 14.1938 + 15.4982i 0.527507 + 0.575986i
\(725\) 0 0
\(726\) 0.0999951 + 0.724149i 0.00371117 + 0.0268757i
\(727\) 40.5488i 1.50387i 0.659236 + 0.751936i \(0.270880\pi\)
−0.659236 + 0.751936i \(0.729120\pi\)
\(728\) 24.8842 8.43579i 0.922271 0.312651i
\(729\) 26.6125 4.55796i 0.985648 0.168813i
\(730\) 0 0
\(731\) −64.2169 −2.37515
\(732\) 5.40949 18.9956i 0.199940 0.702096i
\(733\) −4.80625 −0.177523 −0.0887614 0.996053i \(-0.528291\pi\)
−0.0887614 + 0.996053i \(0.528291\pi\)
\(734\) 1.42987 3.24844i 0.0527775 0.119902i
\(735\) 0 0
\(736\) 14.1047 25.6682i 0.519906 0.946143i
\(737\) 18.3511i 0.675973i
\(738\) 8.30435 + 10.0805i 0.305687 + 0.371068i
\(739\) 29.2357i 1.07545i 0.843120 + 0.537726i \(0.180717\pi\)
−0.843120 + 0.537726i \(0.819283\pi\)
\(740\) 0 0
\(741\) 2.40312 1.47956i 0.0882810 0.0543529i
\(742\) 7.40312 + 3.25865i 0.271777 + 0.119629i
\(743\) −40.8778 −1.49966 −0.749830 0.661630i \(-0.769865\pi\)
−0.749830 + 0.661630i \(0.769865\pi\)
\(744\) −12.7865 10.5980i −0.468776 0.388542i
\(745\) 0 0
\(746\) 30.6786 + 13.5038i 1.12322 + 0.494411i
\(747\) −2.45323 + 4.86493i −0.0897592 + 0.177999i
\(748\) −37.8586 + 34.6722i −1.38425 + 1.26774i
\(749\) 16.1914i 0.591622i
\(750\) 0 0
\(751\) 36.2784i 1.32382i −0.749584 0.661909i \(-0.769746\pi\)
0.749584 0.661909i \(-0.230254\pi\)
\(752\) −1.27415 + 14.4733i −0.0464634 + 0.527787i
\(753\) 20.4555 + 33.2241i 0.745439 + 1.21076i
\(754\) −4.80625 + 10.9190i −0.175033 + 0.397647i
\(755\) 0 0
\(756\) −17.6726 + 19.1810i −0.642745 + 0.697607i
\(757\) 35.9109 1.30521 0.652603 0.757700i \(-0.273677\pi\)
0.652603 + 0.757700i \(0.273677\pi\)
\(758\) −7.47499 + 16.9820i −0.271504 + 0.616813i
\(759\) 15.8034 + 25.6682i 0.573628 + 0.931698i
\(760\) 0 0
\(761\) 20.6301i 0.747841i 0.927461 + 0.373920i \(0.121987\pi\)
−0.927461 + 0.373920i \(0.878013\pi\)
\(762\) 30.7669 4.24849i 1.11457 0.153906i
\(763\) 5.76832i 0.208827i
\(764\) −16.8066 18.3511i −0.608041 0.663921i
\(765\) 0 0
\(766\) −9.40312 4.13899i −0.339749 0.149548i
\(767\) 0 0
\(768\) −10.1828 25.7742i −0.367439 0.930048i
\(769\) −14.1938 −0.511840 −0.255920 0.966698i \(-0.582378\pi\)
−0.255920 + 0.966698i \(0.582378\pi\)
\(770\) 0 0
\(771\) 6.72263 4.13899i 0.242110 0.149062i
\(772\) −26.7539 29.2126i −0.962894 1.05139i
\(773\) 2.27898i 0.0819692i 0.999160 + 0.0409846i \(0.0130495\pi\)
−0.999160 + 0.0409846i \(0.986951\pi\)
\(774\) 22.6852 + 27.5371i 0.815402 + 0.989800i
\(775\) 0 0
\(776\) −10.0839 29.7460i −0.361993 1.06782i
\(777\) 27.4031 16.8716i 0.983082 0.605264i
\(778\) −21.2984 + 48.3866i −0.763586 + 1.73474i
\(779\) −1.35503 −0.0485489
\(780\) 0 0
\(781\) 41.8219 1.49650
\(782\) −22.5261 + 51.1756i −0.805530 + 1.83003i
\(783\) −1.00314 11.7994i −0.0358494 0.421675i
\(784\) −0.246095 + 2.79544i −0.00878910 + 0.0998370i
\(785\) 0 0
\(786\) 1.91638 + 13.8781i 0.0683551 + 0.495017i
\(787\) 18.4480i 0.657601i −0.944399 0.328801i \(-0.893356\pi\)