Properties

Label 300.2.j.d.43.2
Level $300$
Weight $2$
Character 300.43
Analytic conductor $2.396$
Analytic rank $0$
Dimension $12$
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.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.426337261060096.1
Defining polynomial: \(x^{12} - 4 x^{9} - 3 x^{8} + 4 x^{7} + 8 x^{6} + 8 x^{5} - 12 x^{4} - 32 x^{3} + 64\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.2
Root \(-0.760198 - 1.19252i\) of defining polynomial
Character \(\chi\) \(=\) 300.43
Dual form 300.2.j.d.7.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.760198 - 1.19252i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.844199 + 1.81310i) q^{4} +(-1.38078 - 0.305697i) q^{6} +(-0.611393 - 0.611393i) q^{7} +(2.80391 - 0.371591i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-0.760198 - 1.19252i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.844199 + 1.81310i) q^{4} +(-1.38078 - 0.305697i) q^{6} +(-0.611393 - 0.611393i) q^{7} +(2.80391 - 0.371591i) q^{8} -1.00000i q^{9} -5.12822i q^{11} +(0.685116 + 1.87899i) q^{12} +(-1.76156 - 1.76156i) q^{13} +(-0.264318 + 1.19388i) q^{14} +(-2.57466 - 3.06123i) q^{16} +(3.76156 - 3.76156i) q^{17} +(-1.19252 + 0.760198i) q^{18} -1.22279 q^{19} -0.864641 q^{21} +(-6.11549 + 3.89846i) q^{22} +(1.07700 - 1.07700i) q^{23} +(1.71991 - 2.24542i) q^{24} +(-0.761557 + 3.43982i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.62465 - 0.592379i) q^{28} +0.864641i q^{29} +7.81086i q^{31} +(-1.69333 + 5.39747i) q^{32} +(-3.62620 - 3.62620i) q^{33} +(-7.34525 - 1.62620i) q^{34} +(1.81310 + 0.844199i) q^{36} +(1.76156 - 1.76156i) q^{37} +(0.929560 + 1.45820i) q^{38} -2.49122 q^{39} +5.52311 q^{41} +(0.657298 + 1.03110i) q^{42} +(-6.20522 + 6.20522i) q^{43} +(9.29797 + 4.32924i) q^{44} +(-2.10308 - 0.465611i) q^{46} +(-2.29979 - 2.29979i) q^{47} +(-3.98518 - 0.344061i) q^{48} -6.25240i q^{49} -5.31965i q^{51} +(4.68098 - 1.70677i) q^{52} +(2.62620 + 2.62620i) q^{53} +(-0.305697 + 1.38078i) q^{54} +(-1.94148 - 1.48710i) q^{56} +(-0.864641 + 0.864641i) q^{57} +(1.03110 - 0.657298i) q^{58} -0.528636 q^{59} +4.98168 q^{61} +(9.31460 - 5.93780i) q^{62} +(-0.611393 + 0.611393i) q^{63} +(7.72384 - 2.08382i) q^{64} +(-1.56768 + 7.08093i) q^{66} +(6.20522 + 6.20522i) q^{67} +(3.64457 + 9.99558i) q^{68} -1.52311i q^{69} +8.10243i q^{71} +(-0.371591 - 2.80391i) q^{72} +(2.25240 + 2.25240i) q^{73} +(-3.43982 - 0.761557i) q^{74} +(1.03228 - 2.21703i) q^{76} +(-3.13536 + 3.13536i) q^{77} +(1.89382 + 2.97082i) q^{78} +15.9133 q^{79} -1.00000 q^{81} +(-4.19866 - 6.58641i) q^{82} +(7.95665 - 7.95665i) q^{83} +(0.729929 - 1.56768i) q^{84} +(12.1170 + 2.68264i) q^{86} +(0.611393 + 0.611393i) q^{87} +(-1.90560 - 14.3791i) q^{88} +7.25240i q^{89} +2.15401i q^{91} +(1.04351 + 2.86192i) q^{92} +(5.52311 + 5.52311i) q^{93} +(-0.994247 + 4.49084i) q^{94} +(2.61922 + 5.01395i) q^{96} +(-0.793833 + 0.793833i) q^{97} +(-7.45610 + 4.75306i) q^{98} -5.12822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{6} + 12q^{8} + O(q^{10}) \) \( 12q - 4q^{6} + 12q^{8} + 8q^{12} + 4q^{13} + 12q^{16} + 20q^{17} - 12q^{22} + 16q^{26} + 4q^{28} - 20q^{32} - 8q^{33} + 4q^{36} - 4q^{37} - 16q^{38} + 16q^{41} - 20q^{42} - 40q^{46} - 16q^{48} + 8q^{52} - 4q^{53} - 64q^{56} + 20q^{58} - 32q^{61} + 56q^{62} - 24q^{66} + 16q^{68} + 12q^{72} - 44q^{73} + 8q^{76} - 48q^{77} + 24q^{78} - 12q^{81} - 16q^{82} + 64q^{86} - 60q^{88} - 56q^{92} + 16q^{93} + 44q^{96} + 20q^{97} - 24q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.760198 1.19252i −0.537541 0.843238i
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) −0.844199 + 1.81310i −0.422099 + 0.906550i
\(5\) 0 0
\(6\) −1.38078 0.305697i −0.563700 0.124800i
\(7\) −0.611393 0.611393i −0.231085 0.231085i 0.582060 0.813145i \(-0.302247\pi\)
−0.813145 + 0.582060i \(0.802247\pi\)
\(8\) 2.80391 0.371591i 0.991332 0.131377i
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 5.12822i 1.54622i −0.634274 0.773108i \(-0.718701\pi\)
0.634274 0.773108i \(-0.281299\pi\)
\(12\) 0.685116 + 1.87899i 0.197776 + 0.542419i
\(13\) −1.76156 1.76156i −0.488568 0.488568i 0.419286 0.907854i \(-0.362280\pi\)
−0.907854 + 0.419286i \(0.862280\pi\)
\(14\) −0.264318 + 1.19388i −0.0706419 + 0.319077i
\(15\) 0 0
\(16\) −2.57466 3.06123i −0.643664 0.765308i
\(17\) 3.76156 3.76156i 0.912312 0.912312i −0.0841421 0.996454i \(-0.526815\pi\)
0.996454 + 0.0841421i \(0.0268150\pi\)
\(18\) −1.19252 + 0.760198i −0.281079 + 0.179180i
\(19\) −1.22279 −0.280527 −0.140263 0.990114i \(-0.544795\pi\)
−0.140263 + 0.990114i \(0.544795\pi\)
\(20\) 0 0
\(21\) −0.864641 −0.188680
\(22\) −6.11549 + 3.89846i −1.30383 + 0.831154i
\(23\) 1.07700 1.07700i 0.224571 0.224571i −0.585849 0.810420i \(-0.699239\pi\)
0.810420 + 0.585849i \(0.199239\pi\)
\(24\) 1.71991 2.24542i 0.351075 0.458344i
\(25\) 0 0
\(26\) −0.761557 + 3.43982i −0.149354 + 0.674604i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 1.62465 0.592379i 0.307031 0.111949i
\(29\) 0.864641i 0.160560i 0.996772 + 0.0802799i \(0.0255814\pi\)
−0.996772 + 0.0802799i \(0.974419\pi\)
\(30\) 0 0
\(31\) 7.81086i 1.40287i 0.712732 + 0.701436i \(0.247457\pi\)
−0.712732 + 0.701436i \(0.752543\pi\)
\(32\) −1.69333 + 5.39747i −0.299341 + 0.954146i
\(33\) −3.62620 3.62620i −0.631240 0.631240i
\(34\) −7.34525 1.62620i −1.25970 0.278891i
\(35\) 0 0
\(36\) 1.81310 + 0.844199i 0.302183 + 0.140700i
\(37\) 1.76156 1.76156i 0.289598 0.289598i −0.547323 0.836921i \(-0.684353\pi\)
0.836921 + 0.547323i \(0.184353\pi\)
\(38\) 0.929560 + 1.45820i 0.150795 + 0.236551i
\(39\) −2.49122 −0.398914
\(40\) 0 0
\(41\) 5.52311 0.862566 0.431283 0.902217i \(-0.358061\pi\)
0.431283 + 0.902217i \(0.358061\pi\)
\(42\) 0.657298 + 1.03110i 0.101423 + 0.159102i
\(43\) −6.20522 + 6.20522i −0.946288 + 0.946288i −0.998629 0.0523416i \(-0.983332\pi\)
0.0523416 + 0.998629i \(0.483332\pi\)
\(44\) 9.29797 + 4.32924i 1.40172 + 0.652657i
\(45\) 0 0
\(46\) −2.10308 0.465611i −0.310083 0.0686506i
\(47\) −2.29979 2.29979i −0.335459 0.335459i 0.519196 0.854655i \(-0.326231\pi\)
−0.854655 + 0.519196i \(0.826231\pi\)
\(48\) −3.98518 0.344061i −0.575210 0.0496610i
\(49\) 6.25240i 0.893199i
\(50\) 0 0
\(51\) 5.31965i 0.744899i
\(52\) 4.68098 1.70677i 0.649135 0.236687i
\(53\) 2.62620 + 2.62620i 0.360736 + 0.360736i 0.864084 0.503348i \(-0.167899\pi\)
−0.503348 + 0.864084i \(0.667899\pi\)
\(54\) −0.305697 + 1.38078i −0.0416001 + 0.187900i
\(55\) 0 0
\(56\) −1.94148 1.48710i −0.259441 0.198723i
\(57\) −0.864641 + 0.864641i −0.114524 + 0.114524i
\(58\) 1.03110 0.657298i 0.135390 0.0863075i
\(59\) −0.528636 −0.0688225 −0.0344113 0.999408i \(-0.510956\pi\)
−0.0344113 + 0.999408i \(0.510956\pi\)
\(60\) 0 0
\(61\) 4.98168 0.637838 0.318919 0.947782i \(-0.396680\pi\)
0.318919 + 0.947782i \(0.396680\pi\)
\(62\) 9.31460 5.93780i 1.18295 0.754101i
\(63\) −0.611393 + 0.611393i −0.0770283 + 0.0770283i
\(64\) 7.72384 2.08382i 0.965480 0.260477i
\(65\) 0 0
\(66\) −1.56768 + 7.08093i −0.192968 + 0.871603i
\(67\) 6.20522 + 6.20522i 0.758089 + 0.758089i 0.975974 0.217886i \(-0.0699160\pi\)
−0.217886 + 0.975974i \(0.569916\pi\)
\(68\) 3.64457 + 9.99558i 0.441969 + 1.21214i
\(69\) 1.52311i 0.183361i
\(70\) 0 0
\(71\) 8.10243i 0.961581i 0.876835 + 0.480791i \(0.159650\pi\)
−0.876835 + 0.480791i \(0.840350\pi\)
\(72\) −0.371591 2.80391i −0.0437924 0.330444i
\(73\) 2.25240 + 2.25240i 0.263623 + 0.263623i 0.826524 0.562901i \(-0.190315\pi\)
−0.562901 + 0.826524i \(0.690315\pi\)
\(74\) −3.43982 0.761557i −0.399871 0.0885292i
\(75\) 0 0
\(76\) 1.03228 2.21703i 0.118410 0.254311i
\(77\) −3.13536 + 3.13536i −0.357307 + 0.357307i
\(78\) 1.89382 + 2.97082i 0.214433 + 0.336379i
\(79\) 15.9133 1.79039 0.895193 0.445680i \(-0.147038\pi\)
0.895193 + 0.445680i \(0.147038\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) −4.19866 6.58641i −0.463664 0.727348i
\(83\) 7.95665 7.95665i 0.873355 0.873355i −0.119481 0.992836i \(-0.538123\pi\)
0.992836 + 0.119481i \(0.0381231\pi\)
\(84\) 0.729929 1.56768i 0.0796418 0.171048i
\(85\) 0 0
\(86\) 12.1170 + 2.68264i 1.30661 + 0.289277i
\(87\) 0.611393 + 0.611393i 0.0655483 + 0.0655483i
\(88\) −1.90560 14.3791i −0.203138 1.53281i
\(89\) 7.25240i 0.768752i 0.923177 + 0.384376i \(0.125583\pi\)
−0.923177 + 0.384376i \(0.874417\pi\)
\(90\) 0 0
\(91\) 2.15401i 0.225801i
\(92\) 1.04351 + 2.86192i 0.108793 + 0.298376i
\(93\) 5.52311 + 5.52311i 0.572720 + 0.572720i
\(94\) −0.994247 + 4.49084i −0.102549 + 0.463195i
\(95\) 0 0
\(96\) 2.61922 + 5.01395i 0.267323 + 0.511734i
\(97\) −0.793833 + 0.793833i −0.0806015 + 0.0806015i −0.746258 0.665657i \(-0.768152\pi\)
0.665657 + 0.746258i \(0.268152\pi\)
\(98\) −7.45610 + 4.75306i −0.753179 + 0.480131i
\(99\) −5.12822 −0.515405
\(100\) 0 0
\(101\) −10.1170 −1.00668 −0.503341 0.864088i \(-0.667896\pi\)
−0.503341 + 0.864088i \(0.667896\pi\)
\(102\) −6.34377 + 4.04398i −0.628127 + 0.400414i
\(103\) −3.82267 + 3.82267i −0.376659 + 0.376659i −0.869895 0.493236i \(-0.835814\pi\)
0.493236 + 0.869895i \(0.335814\pi\)
\(104\) −5.59383 4.28467i −0.548520 0.420147i
\(105\) 0 0
\(106\) 1.13536 5.12822i 0.110276 0.498097i
\(107\) −5.51107 5.51107i −0.532775 0.532775i 0.388622 0.921397i \(-0.372951\pi\)
−0.921397 + 0.388622i \(0.872951\pi\)
\(108\) 1.87899 0.685116i 0.180806 0.0659253i
\(109\) 7.31695i 0.700836i 0.936593 + 0.350418i \(0.113961\pi\)
−0.936593 + 0.350418i \(0.886039\pi\)
\(110\) 0 0
\(111\) 2.49122i 0.236456i
\(112\) −0.297490 + 3.44575i −0.0281101 + 0.325592i
\(113\) 0.509161 + 0.509161i 0.0478978 + 0.0478978i 0.730650 0.682752i \(-0.239217\pi\)
−0.682752 + 0.730650i \(0.739217\pi\)
\(114\) 1.68840 + 0.373802i 0.158133 + 0.0350098i
\(115\) 0 0
\(116\) −1.56768 0.729929i −0.145555 0.0677722i
\(117\) −1.76156 + 1.76156i −0.162856 + 0.162856i
\(118\) 0.401868 + 0.630408i 0.0369949 + 0.0580337i
\(119\) −4.59958 −0.421643
\(120\) 0 0
\(121\) −15.2986 −1.39078
\(122\) −3.78706 5.94074i −0.342864 0.537849i
\(123\) 3.90543 3.90543i 0.352141 0.352141i
\(124\) −14.1619 6.59392i −1.27177 0.592152i
\(125\) 0 0
\(126\) 1.19388 + 0.264318i 0.106359 + 0.0235473i
\(127\) 7.49103 + 7.49103i 0.664722 + 0.664722i 0.956489 0.291767i \(-0.0942433\pi\)
−0.291767 + 0.956489i \(0.594243\pi\)
\(128\) −8.35664 7.62671i −0.738629 0.674112i
\(129\) 8.77551i 0.772641i
\(130\) 0 0
\(131\) 13.9964i 1.22287i −0.791296 0.611434i \(-0.790593\pi\)
0.791296 0.611434i \(-0.209407\pi\)
\(132\) 9.63589 3.51342i 0.838696 0.305804i
\(133\) 0.747604 + 0.747604i 0.0648255 + 0.0648255i
\(134\) 2.68264 12.1170i 0.231745 1.04675i
\(135\) 0 0
\(136\) 9.14931 11.9448i 0.784547 1.02426i
\(137\) −7.01395 + 7.01395i −0.599242 + 0.599242i −0.940111 0.340869i \(-0.889279\pi\)
0.340869 + 0.940111i \(0.389279\pi\)
\(138\) −1.81634 + 1.15787i −0.154617 + 0.0985643i
\(139\) −2.28006 −0.193392 −0.0966960 0.995314i \(-0.530827\pi\)
−0.0966960 + 0.995314i \(0.530827\pi\)
\(140\) 0 0
\(141\) −3.25240 −0.273901
\(142\) 9.66229 6.15945i 0.810842 0.516889i
\(143\) −9.03365 + 9.03365i −0.755432 + 0.755432i
\(144\) −3.06123 + 2.57466i −0.255103 + 0.214555i
\(145\) 0 0
\(146\) 0.973757 4.39829i 0.0805887 0.364005i
\(147\) −4.42111 4.42111i −0.364647 0.364647i
\(148\) 1.70677 + 4.68098i 0.140296 + 0.384774i
\(149\) 10.1170i 0.828820i −0.910090 0.414410i \(-0.863988\pi\)
0.910090 0.414410i \(-0.136012\pi\)
\(150\) 0 0
\(151\) 7.93691i 0.645897i 0.946417 + 0.322948i \(0.104674\pi\)
−0.946417 + 0.322948i \(0.895326\pi\)
\(152\) −3.42859 + 0.454377i −0.278095 + 0.0368548i
\(153\) −3.76156 3.76156i −0.304104 0.304104i
\(154\) 6.12247 + 1.35548i 0.493362 + 0.109228i
\(155\) 0 0
\(156\) 2.10308 4.51683i 0.168381 0.361635i
\(157\) −9.01395 + 9.01395i −0.719392 + 0.719392i −0.968481 0.249089i \(-0.919869\pi\)
0.249089 + 0.968481i \(0.419869\pi\)
\(158\) −12.0972 18.9769i −0.962405 1.50972i
\(159\) 3.71400 0.294540
\(160\) 0 0
\(161\) −1.31695 −0.103790
\(162\) 0.760198 + 1.19252i 0.0597268 + 0.0936931i
\(163\) 13.0849 13.0849i 1.02489 1.02489i 0.0252033 0.999682i \(-0.491977\pi\)
0.999682 0.0252033i \(-0.00802331\pi\)
\(164\) −4.66261 + 10.0140i −0.364088 + 0.781958i
\(165\) 0 0
\(166\) −15.5371 3.43982i −1.20591 0.266982i
\(167\) 11.3334 + 11.3334i 0.877008 + 0.877008i 0.993224 0.116216i \(-0.0370765\pi\)
−0.116216 + 0.993224i \(0.537076\pi\)
\(168\) −2.42438 + 0.321293i −0.187045 + 0.0247883i
\(169\) 6.79383i 0.522603i
\(170\) 0 0
\(171\) 1.22279i 0.0935088i
\(172\) −6.01224 16.4891i −0.458429 1.25728i
\(173\) −7.96772 7.96772i −0.605775 0.605775i 0.336064 0.941839i \(-0.390904\pi\)
−0.941839 + 0.336064i \(0.890904\pi\)
\(174\) 0.264318 1.19388i 0.0200379 0.0905076i
\(175\) 0 0
\(176\) −15.6987 + 13.2034i −1.18333 + 0.995244i
\(177\) −0.373802 + 0.373802i −0.0280967 + 0.0280967i
\(178\) 8.64861 5.51325i 0.648241 0.413236i
\(179\) −12.6475 −0.945320 −0.472660 0.881245i \(-0.656706\pi\)
−0.472660 + 0.881245i \(0.656706\pi\)
\(180\) 0 0
\(181\) 7.72928 0.574513 0.287256 0.957854i \(-0.407257\pi\)
0.287256 + 0.957854i \(0.407257\pi\)
\(182\) 2.56869 1.63747i 0.190404 0.121378i
\(183\) 3.52258 3.52258i 0.260396 0.260396i
\(184\) 2.61962 3.42003i 0.193121 0.252128i
\(185\) 0 0
\(186\) 2.38776 10.7851i 0.175079 0.790800i
\(187\) −19.2901 19.2901i −1.41063 1.41063i
\(188\) 6.11123 2.22827i 0.445707 0.162513i
\(189\) 0.864641i 0.0628934i
\(190\) 0 0
\(191\) 7.04516i 0.509770i −0.966971 0.254885i \(-0.917962\pi\)
0.966971 0.254885i \(-0.0820376\pi\)
\(192\) 3.98810 6.93506i 0.287816 0.500495i
\(193\) 11.5048 + 11.5048i 0.828133 + 0.828133i 0.987258 0.159125i \(-0.0508674\pi\)
−0.159125 + 0.987258i \(0.550867\pi\)
\(194\) 1.55013 + 0.343190i 0.111293 + 0.0246396i
\(195\) 0 0
\(196\) 11.3362 + 5.27827i 0.809730 + 0.377019i
\(197\) −7.87859 + 7.87859i −0.561327 + 0.561327i −0.929684 0.368358i \(-0.879920\pi\)
0.368358 + 0.929684i \(0.379920\pi\)
\(198\) 3.89846 + 6.11549i 0.277051 + 0.434609i
\(199\) −11.4792 −0.813741 −0.406870 0.913486i \(-0.633380\pi\)
−0.406870 + 0.913486i \(0.633380\pi\)
\(200\) 0 0
\(201\) 8.77551 0.618977
\(202\) 7.69095 + 12.0648i 0.541133 + 0.848873i
\(203\) 0.528636 0.528636i 0.0371030 0.0371030i
\(204\) 9.64504 + 4.49084i 0.675288 + 0.314422i
\(205\) 0 0
\(206\) 7.46460 + 1.65262i 0.520083 + 0.115143i
\(207\) −1.07700 1.07700i −0.0748570 0.0748570i
\(208\) −0.857132 + 9.92794i −0.0594314 + 0.688379i
\(209\) 6.27072i 0.433755i
\(210\) 0 0
\(211\) 5.49134i 0.378039i −0.981973 0.189020i \(-0.939469\pi\)
0.981973 0.189020i \(-0.0605310\pi\)
\(212\) −6.97859 + 2.54452i −0.479292 + 0.174759i
\(213\) 5.72928 + 5.72928i 0.392564 + 0.392564i
\(214\) −2.38255 + 10.7616i −0.162868 + 0.735645i
\(215\) 0 0
\(216\) −2.24542 1.71991i −0.152781 0.117025i
\(217\) 4.77551 4.77551i 0.324183 0.324183i
\(218\) 8.72559 5.56233i 0.590972 0.376728i
\(219\) 3.18537 0.215247
\(220\) 0 0
\(221\) −13.2524 −0.891453
\(222\) −2.97082 + 1.89382i −0.199389 + 0.127105i
\(223\) −10.8678 + 10.8678i −0.727764 + 0.727764i −0.970174 0.242410i \(-0.922062\pi\)
0.242410 + 0.970174i \(0.422062\pi\)
\(224\) 4.33526 2.26469i 0.289662 0.151316i
\(225\) 0 0
\(226\) 0.220121 0.994247i 0.0146422 0.0661363i
\(227\) 4.98244 + 4.98244i 0.330696 + 0.330696i 0.852851 0.522155i \(-0.174872\pi\)
−0.522155 + 0.852851i \(0.674872\pi\)
\(228\) −0.837751 2.29761i −0.0554814 0.152163i
\(229\) 25.7572i 1.70208i 0.525098 + 0.851041i \(0.324028\pi\)
−0.525098 + 0.851041i \(0.675972\pi\)
\(230\) 0 0
\(231\) 4.43407i 0.291740i
\(232\) 0.321293 + 2.42438i 0.0210939 + 0.159168i
\(233\) 0.715328 + 0.715328i 0.0468627 + 0.0468627i 0.730150 0.683287i \(-0.239450\pi\)
−0.683287 + 0.730150i \(0.739450\pi\)
\(234\) 3.43982 + 0.761557i 0.224868 + 0.0497846i
\(235\) 0 0
\(236\) 0.446274 0.958469i 0.0290499 0.0623910i
\(237\) 11.2524 11.2524i 0.730922 0.730922i
\(238\) 3.49659 + 5.48509i 0.226650 + 0.355545i
\(239\) 26.9354 1.74231 0.871154 0.491009i \(-0.163372\pi\)
0.871154 + 0.491009i \(0.163372\pi\)
\(240\) 0 0
\(241\) 14.0925 0.907775 0.453887 0.891059i \(-0.350037\pi\)
0.453887 + 0.891059i \(0.350037\pi\)
\(242\) 11.6300 + 18.2439i 0.747603 + 1.17276i
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) −4.20553 + 9.03228i −0.269231 + 0.578232i
\(245\) 0 0
\(246\) −7.62620 1.68840i −0.486229 0.107648i
\(247\) 2.15401 + 2.15401i 0.137056 + 0.137056i
\(248\) 2.90245 + 21.9010i 0.184306 + 1.39071i
\(249\) 11.2524i 0.713092i
\(250\) 0 0
\(251\) 17.2471i 1.08863i 0.838882 + 0.544314i \(0.183210\pi\)
−0.838882 + 0.544314i \(0.816790\pi\)
\(252\) −0.592379 1.62465i −0.0373164 0.102344i
\(253\) −5.52311 5.52311i −0.347235 0.347235i
\(254\) 3.23853 14.6279i 0.203203 0.917834i
\(255\) 0 0
\(256\) −2.74229 + 15.7632i −0.171393 + 0.985203i
\(257\) 15.0140 15.0140i 0.936545 0.936545i −0.0615588 0.998103i \(-0.519607\pi\)
0.998103 + 0.0615588i \(0.0196072\pi\)
\(258\) 10.4650 6.67112i 0.651520 0.415326i
\(259\) −2.15401 −0.133844
\(260\) 0 0
\(261\) 0.864641 0.0535199
\(262\) −16.6909 + 10.6400i −1.03117 + 0.657341i
\(263\) −6.73386 + 6.73386i −0.415228 + 0.415228i −0.883555 0.468327i \(-0.844857\pi\)
0.468327 + 0.883555i \(0.344857\pi\)
\(264\) −11.5150 8.82008i −0.708699 0.542838i
\(265\) 0 0
\(266\) 0.323204 1.45986i 0.0198169 0.0895096i
\(267\) 5.12822 + 5.12822i 0.313842 + 0.313842i
\(268\) −16.4891 + 6.01224i −1.00723 + 0.367256i
\(269\) 25.7047i 1.56724i −0.621238 0.783622i \(-0.713370\pi\)
0.621238 0.783622i \(-0.286630\pi\)
\(270\) 0 0
\(271\) 0.931222i 0.0565677i −0.999600 0.0282839i \(-0.990996\pi\)
0.999600 0.0282839i \(-0.00900423\pi\)
\(272\) −21.1997 1.83029i −1.28542 0.110977i
\(273\) 1.52311 + 1.52311i 0.0921831 + 0.0921831i
\(274\) 13.6963 + 3.03228i 0.827421 + 0.183186i
\(275\) 0 0
\(276\) 2.76156 + 1.28581i 0.166226 + 0.0773968i
\(277\) 22.0602 22.0602i 1.32547 1.32547i 0.416190 0.909277i \(-0.363365\pi\)
0.909277 0.416190i \(-0.136635\pi\)
\(278\) 1.73330 + 2.71901i 0.103956 + 0.163075i
\(279\) 7.81086 0.467624
\(280\) 0 0
\(281\) 8.56934 0.511204 0.255602 0.966782i \(-0.417726\pi\)
0.255602 + 0.966782i \(0.417726\pi\)
\(282\) 2.47246 + 3.87854i 0.147233 + 0.230964i
\(283\) 11.5705 11.5705i 0.687796 0.687796i −0.273949 0.961744i \(-0.588330\pi\)
0.961744 + 0.273949i \(0.0883299\pi\)
\(284\) −14.6905 6.84006i −0.871721 0.405883i
\(285\) 0 0
\(286\) 17.6402 + 3.90543i 1.04308 + 0.230933i
\(287\) −3.37680 3.37680i −0.199326 0.199326i
\(288\) 5.39747 + 1.69333i 0.318049 + 0.0997803i
\(289\) 11.2986i 0.664625i
\(290\) 0 0
\(291\) 1.12265i 0.0658108i
\(292\) −5.98529 + 2.18235i −0.350262 + 0.127712i
\(293\) −12.8969 12.8969i −0.753446 0.753446i 0.221675 0.975121i \(-0.428848\pi\)
−0.975121 + 0.221675i \(0.928848\pi\)
\(294\) −1.91134 + 8.63317i −0.111471 + 0.503497i
\(295\) 0 0
\(296\) 4.28467 5.59383i 0.249041 0.325135i
\(297\) −3.62620 + 3.62620i −0.210413 + 0.210413i
\(298\) −12.0648 + 7.69095i −0.698892 + 0.445525i
\(299\) −3.79441 −0.219436
\(300\) 0 0
\(301\) 7.58767 0.437346
\(302\) 9.46491 6.03362i 0.544644 0.347196i
\(303\) −7.15383 + 7.15383i −0.410977 + 0.410977i
\(304\) 3.14826 + 3.74324i 0.180565 + 0.214689i
\(305\) 0 0
\(306\) −1.62620 + 7.34525i −0.0929636 + 0.419900i
\(307\) 1.60564 + 1.60564i 0.0916387 + 0.0916387i 0.751440 0.659801i \(-0.229360\pi\)
−0.659801 + 0.751440i \(0.729360\pi\)
\(308\) −3.03785 8.33158i −0.173098 0.474736i
\(309\) 5.40608i 0.307541i
\(310\) 0 0
\(311\) 19.4161i 1.10099i 0.834839 + 0.550494i \(0.185561\pi\)
−0.834839 + 0.550494i \(0.814439\pi\)
\(312\) −6.98516 + 0.925715i −0.395457 + 0.0524083i
\(313\) −17.7110 17.7110i −1.00108 1.00108i −0.999999 0.00108322i \(-0.999655\pi\)
−0.00108322 0.999999i \(-0.500345\pi\)
\(314\) 17.6017 + 3.89692i 0.993321 + 0.219916i
\(315\) 0 0
\(316\) −13.4340 + 28.8524i −0.755721 + 1.62307i
\(317\) 7.78946 7.78946i 0.437500 0.437500i −0.453670 0.891170i \(-0.649885\pi\)
0.891170 + 0.453670i \(0.149885\pi\)
\(318\) −2.82338 4.42902i −0.158327 0.248367i
\(319\) 4.43407 0.248260
\(320\) 0 0
\(321\) −7.79383 −0.435009
\(322\) 1.00114 + 1.57048i 0.0557914 + 0.0875196i
\(323\) −4.59958 + 4.59958i −0.255928 + 0.255928i
\(324\) 0.844199 1.81310i 0.0468999 0.100728i
\(325\) 0 0
\(326\) −25.5510 5.65685i −1.41514 0.313304i
\(327\) 5.17386 + 5.17386i 0.286115 + 0.286115i
\(328\) 15.4863 2.05234i 0.855089 0.113322i
\(329\) 2.81215i 0.155039i
\(330\) 0 0
\(331\) 31.7005i 1.74242i −0.490912 0.871209i \(-0.663336\pi\)
0.490912 0.871209i \(-0.336664\pi\)
\(332\) 7.70919 + 21.1432i 0.423097 + 1.16038i
\(333\) −1.76156 1.76156i −0.0965327 0.0965327i
\(334\) 4.89968 22.1310i 0.268098 1.21095i
\(335\) 0 0
\(336\) 2.22615 + 2.64687i 0.121447 + 0.144398i
\(337\) −18.9634 + 18.9634i −1.03300 + 1.03300i −0.0335632 + 0.999437i \(0.510686\pi\)
−0.999437 + 0.0335632i \(0.989314\pi\)
\(338\) −8.10177 + 5.16466i −0.440678 + 0.280920i
\(339\) 0.720062 0.0391084
\(340\) 0 0
\(341\) 40.0558 2.16914
\(342\) 1.45820 0.929560i 0.0788502 0.0502648i
\(343\) −8.10243 + 8.10243i −0.437490 + 0.437490i
\(344\) −15.0931 + 19.7047i −0.813765 + 1.06241i
\(345\) 0 0
\(346\) −3.44461 + 15.5587i −0.185183 + 0.836441i
\(347\) −7.71957 7.71957i −0.414408 0.414408i 0.468863 0.883271i \(-0.344664\pi\)
−0.883271 + 0.468863i \(0.844664\pi\)
\(348\) −1.62465 + 0.592379i −0.0870906 + 0.0317549i
\(349\) 27.0741i 1.44925i −0.689146 0.724623i \(-0.742014\pi\)
0.689146 0.724623i \(-0.257986\pi\)
\(350\) 0 0
\(351\) 2.49122i 0.132971i
\(352\) 27.6794 + 8.68375i 1.47532 + 0.462846i
\(353\) 9.96772 + 9.96772i 0.530528 + 0.530528i 0.920730 0.390201i \(-0.127595\pi\)
−0.390201 + 0.920730i \(0.627595\pi\)
\(354\) 0.729929 + 0.161602i 0.0387953 + 0.00858906i
\(355\) 0 0
\(356\) −13.1493 6.12247i −0.696912 0.324490i
\(357\) −3.25240 + 3.25240i −0.172135 + 0.172135i
\(358\) 9.61461 + 15.0824i 0.508148 + 0.797129i
\(359\) −14.2334 −0.751211 −0.375606 0.926780i \(-0.622565\pi\)
−0.375606 + 0.926780i \(0.622565\pi\)
\(360\) 0 0
\(361\) −17.5048 −0.921305
\(362\) −5.87578 9.21731i −0.308824 0.484451i
\(363\) −10.8178 + 10.8178i −0.567785 + 0.567785i
\(364\) −3.90543 1.81841i −0.204700 0.0953107i
\(365\) 0 0
\(366\) −6.87859 1.52288i −0.359550 0.0796023i
\(367\) 2.89145 + 2.89145i 0.150933 + 0.150933i 0.778534 0.627602i \(-0.215963\pi\)
−0.627602 + 0.778534i \(0.715963\pi\)
\(368\) −6.06988 0.524045i −0.316414 0.0273177i
\(369\) 5.52311i 0.287522i
\(370\) 0 0
\(371\) 3.21128i 0.166721i
\(372\) −14.6766 + 5.35135i −0.760944 + 0.277454i
\(373\) 11.2847 + 11.2847i 0.584298 + 0.584298i 0.936081 0.351783i \(-0.114425\pi\)
−0.351783 + 0.936081i \(0.614425\pi\)
\(374\) −8.33950 + 37.6681i −0.431225 + 1.94777i
\(375\) 0 0
\(376\) −7.30299 5.59383i −0.376623 0.288480i
\(377\) 1.52311 1.52311i 0.0784444 0.0784444i
\(378\) 1.03110 0.657298i 0.0530341 0.0338078i
\(379\) −15.4562 −0.793932 −0.396966 0.917833i \(-0.629937\pi\)
−0.396966 + 0.917833i \(0.629937\pi\)
\(380\) 0 0
\(381\) 10.5939 0.542743
\(382\) −8.40148 + 5.35571i −0.429857 + 0.274022i
\(383\) 12.5562 12.5562i 0.641593 0.641593i −0.309354 0.950947i \(-0.600113\pi\)
0.950947 + 0.309354i \(0.100113\pi\)
\(384\) −11.3019 + 0.516138i −0.576749 + 0.0263390i
\(385\) 0 0
\(386\) 4.97376 22.4656i 0.253158 1.14347i
\(387\) 6.20522 + 6.20522i 0.315429 + 0.315429i
\(388\) −0.769144 2.10945i −0.0390474 0.107091i
\(389\) 5.16327i 0.261788i 0.991396 + 0.130894i \(0.0417848\pi\)
−0.991396 + 0.130894i \(0.958215\pi\)
\(390\) 0 0
\(391\) 8.10243i 0.409757i
\(392\) −2.32333 17.5312i −0.117346 0.885458i
\(393\) −9.89692 9.89692i −0.499233 0.499233i
\(394\) 15.3847 + 3.40608i 0.775068 + 0.171596i
\(395\) 0 0
\(396\) 4.32924 9.29797i 0.217552 0.467240i
\(397\) 3.46293 3.46293i 0.173800 0.173800i −0.614847 0.788646i \(-0.710782\pi\)
0.788646 + 0.614847i \(0.210782\pi\)
\(398\) 8.72648 + 13.6892i 0.437419 + 0.686177i
\(399\) 1.05727 0.0529298
\(400\) 0 0
\(401\) 3.49521 0.174542 0.0872712 0.996185i \(-0.472185\pi\)
0.0872712 + 0.996185i \(0.472185\pi\)
\(402\) −6.67112 10.4650i −0.332725 0.521945i
\(403\) 13.7593 13.7593i 0.685399 0.685399i
\(404\) 8.54079 18.3432i 0.424920 0.912608i
\(405\) 0 0
\(406\) −1.03228 0.228540i −0.0512310 0.0113423i
\(407\) −9.03365 9.03365i −0.447781 0.447781i
\(408\) −1.97673 14.9158i −0.0978629 0.738443i
\(409\) 14.8034i 0.731982i 0.930618 + 0.365991i \(0.119270\pi\)
−0.930618 + 0.365991i \(0.880730\pi\)
\(410\) 0 0
\(411\) 9.91923i 0.489279i
\(412\) −3.70379 10.1580i −0.182473 0.500448i
\(413\) 0.323204 + 0.323204i 0.0159039 + 0.0159039i
\(414\) −0.465611 + 2.10308i −0.0228835 + 0.103361i
\(415\) 0 0
\(416\) 12.4908 6.52505i 0.612414 0.319917i
\(417\) −1.61224 + 1.61224i −0.0789520 + 0.0789520i
\(418\) 7.47795 4.76699i 0.365758 0.233161i
\(419\) 19.0701 0.931634 0.465817 0.884881i \(-0.345760\pi\)
0.465817 + 0.884881i \(0.345760\pi\)
\(420\) 0 0
\(421\) −20.8034 −1.01390 −0.506948 0.861976i \(-0.669226\pi\)
−0.506948 + 0.861976i \(0.669226\pi\)
\(422\) −6.54852 + 4.17450i −0.318777 + 0.203212i
\(423\) −2.29979 + 2.29979i −0.111820 + 0.111820i
\(424\) 8.33950 + 6.38776i 0.405002 + 0.310217i
\(425\) 0 0
\(426\) 2.47689 11.1877i 0.120006 0.542044i
\(427\) −3.04577 3.04577i −0.147395 0.147395i
\(428\) 14.6446 5.33968i 0.707872 0.258103i
\(429\) 12.7755i 0.616807i
\(430\) 0 0
\(431\) 15.3302i 0.738428i 0.929344 + 0.369214i \(0.120373\pi\)
−0.929344 + 0.369214i \(0.879627\pi\)
\(432\) −0.344061 + 3.98518i −0.0165537 + 0.191737i
\(433\) −16.2803 16.2803i −0.782381 0.782381i 0.197851 0.980232i \(-0.436604\pi\)
−0.980232 + 0.197851i \(0.936604\pi\)
\(434\) −9.32521 2.06455i −0.447625 0.0991016i
\(435\) 0 0
\(436\) −13.2663 6.17696i −0.635343 0.295823i
\(437\) −1.31695 + 1.31695i −0.0629981 + 0.0629981i
\(438\) −2.42151 3.79861i −0.115704 0.181505i
\(439\) −24.6554 −1.17674 −0.588368 0.808593i \(-0.700230\pi\)
−0.588368 + 0.808593i \(0.700230\pi\)
\(440\) 0 0
\(441\) −6.25240 −0.297733
\(442\) 10.0744 + 15.8037i 0.479192 + 0.751706i
\(443\) 1.77116 1.77116i 0.0841501 0.0841501i −0.663779 0.747929i \(-0.731048\pi\)
0.747929 + 0.663779i \(0.231048\pi\)
\(444\) 4.51683 + 2.10308i 0.214359 + 0.0998079i
\(445\) 0 0
\(446\) 21.2218 + 4.69839i 1.00488 + 0.222475i
\(447\) −7.15383 7.15383i −0.338364 0.338364i
\(448\) −5.99634 3.44827i −0.283300 0.162916i
\(449\) 33.1512i 1.56450i 0.622963 + 0.782251i \(0.285929\pi\)
−0.622963 + 0.782251i \(0.714071\pi\)
\(450\) 0 0
\(451\) 28.3237i 1.33371i
\(452\) −1.35299 + 0.493326i −0.0636394 + 0.0232041i
\(453\) 5.61224 + 5.61224i 0.263686 + 0.263686i
\(454\) 2.15401 9.72928i 0.101093 0.456618i
\(455\) 0 0
\(456\) −2.10308 + 2.74567i −0.0984859 + 0.128578i
\(457\) 7.50479 7.50479i 0.351059 0.351059i −0.509444 0.860504i \(-0.670149\pi\)
0.860504 + 0.509444i \(0.170149\pi\)
\(458\) 30.7159 19.5806i 1.43526 0.914939i
\(459\) −5.31965 −0.248300
\(460\) 0 0
\(461\) −27.0216 −1.25852 −0.629262 0.777193i \(-0.716643\pi\)
−0.629262 + 0.777193i \(0.716643\pi\)
\(462\) 5.28771 3.37077i 0.246006 0.156822i
\(463\) 27.7123 27.7123i 1.28790 1.28790i 0.351843 0.936059i \(-0.385555\pi\)
0.936059 0.351843i \(-0.114445\pi\)
\(464\) 2.64687 2.22615i 0.122878 0.103347i
\(465\) 0 0
\(466\) 0.309251 1.39683i 0.0143258 0.0647070i
\(467\) −2.00823 2.00823i −0.0929296 0.0929296i 0.659114 0.752043i \(-0.270932\pi\)
−0.752043 + 0.659114i \(0.770932\pi\)
\(468\) −1.70677 4.68098i −0.0788956 0.216378i
\(469\) 7.58767i 0.350366i
\(470\) 0 0
\(471\) 12.7477i 0.587381i
\(472\) −1.48225 + 0.196436i −0.0682260 + 0.00904172i
\(473\) 31.8217 + 31.8217i 1.46317 + 1.46317i
\(474\) −21.9727 4.86464i −1.00924 0.223440i
\(475\) 0 0
\(476\) 3.88296 8.33950i 0.177975 0.382240i
\(477\) 2.62620 2.62620i 0.120245 0.120245i
\(478\) −20.4763 32.1210i −0.936562 1.46918i
\(479\) 13.7593 0.628678 0.314339 0.949311i \(-0.398217\pi\)
0.314339 + 0.949311i \(0.398217\pi\)
\(480\) 0 0
\(481\) −6.20617 −0.282977
\(482\) −10.7131 16.8055i −0.487966 0.765470i
\(483\) −0.931222 + 0.931222i −0.0423721 + 0.0423721i
\(484\) 12.9151 27.7379i 0.587049 1.26081i
\(485\) 0 0
\(486\) 1.38078 + 0.305697i 0.0626334 + 0.0138667i
\(487\) −24.3355 24.3355i −1.10275 1.10275i −0.994078 0.108671i \(-0.965340\pi\)
−0.108671 0.994078i \(-0.534660\pi\)
\(488\) 13.9682 1.85115i 0.632310 0.0837975i
\(489\) 18.5048i 0.836816i
\(490\) 0 0
\(491\) 28.8918i 1.30387i −0.758275 0.651935i \(-0.773957\pi\)
0.758275 0.651935i \(-0.226043\pi\)
\(492\) 3.78397 + 10.3779i 0.170595 + 0.467872i
\(493\) 3.25240 + 3.25240i 0.146481 + 0.146481i
\(494\) 0.931222 4.20617i 0.0418977 0.189244i
\(495\) 0 0
\(496\) 23.9109 20.1103i 1.07363 0.902979i
\(497\) 4.95377 4.95377i 0.222207 0.222207i
\(498\) −13.4187 + 8.55405i −0.601306 + 0.383316i
\(499\) 12.5365 0.561211 0.280605 0.959823i \(-0.409465\pi\)
0.280605 + 0.959823i \(0.409465\pi\)
\(500\) 0 0
\(501\) 16.0279 0.716074
\(502\) 20.5675 13.1112i 0.917972 0.585182i
\(503\) −9.01392 + 9.01392i −0.401911 + 0.401911i −0.878906 0.476995i \(-0.841726\pi\)
0.476995 + 0.878906i \(0.341726\pi\)
\(504\) −1.48710 + 1.94148i −0.0662409 + 0.0864805i
\(505\) 0 0
\(506\) −2.38776 + 10.7851i −0.106149 + 0.479455i
\(507\) −4.80397 4.80397i −0.213352 0.213352i
\(508\) −19.9059 + 7.25806i −0.883182 + 0.322025i
\(509\) 22.5448i 0.999279i 0.866233 + 0.499640i \(0.166534\pi\)
−0.866233 + 0.499640i \(0.833466\pi\)
\(510\) 0 0
\(511\) 2.75420i 0.121839i
\(512\) 20.8826 8.71295i 0.922891 0.385062i
\(513\) 0.864641 + 0.864641i 0.0381748 + 0.0381748i
\(514\) −29.3180 6.49084i −1.29316 0.286299i
\(515\) 0 0
\(516\) −15.9109 7.40828i −0.700437 0.326131i
\(517\) −11.7938 + 11.7938i −0.518692 + 0.518692i
\(518\) 1.63747 + 2.56869i 0.0719464 + 0.112862i
\(519\) −11.2681 −0.494613
\(520\) 0 0
\(521\) −18.9046 −0.828226 −0.414113 0.910225i \(-0.635908\pi\)
−0.414113 + 0.910225i \(0.635908\pi\)
\(522\) −0.657298 1.03110i −0.0287692 0.0451300i
\(523\) −21.8269 + 21.8269i −0.954426 + 0.954426i −0.999006 0.0445800i \(-0.985805\pi\)
0.0445800 + 0.999006i \(0.485805\pi\)
\(524\) 25.3768 + 11.8157i 1.10859 + 0.516172i
\(525\) 0 0
\(526\) 13.1493 + 2.91118i 0.573337 + 0.126934i
\(527\) 29.3810 + 29.3810i 1.27986 + 1.27986i
\(528\) −1.76442 + 20.4368i −0.0767866 + 0.889400i
\(529\) 20.6801i 0.899136i
\(530\) 0 0
\(531\) 0.528636i 0.0229408i
\(532\) −1.98661 + 0.724353i −0.0861303 + 0.0314047i
\(533\) −9.72928 9.72928i −0.421422 0.421422i
\(534\) 2.21703 10.0140i 0.0959404 0.433346i
\(535\) 0 0
\(536\) 19.7047 + 15.0931i 0.851114 + 0.651922i
\(537\) −8.94315 + 8.94315i −0.385925 + 0.385925i
\(538\) −30.6533 + 19.5407i −1.32156 + 0.842457i
\(539\) −32.0637 −1.38108
\(540\) 0 0
\(541\) 7.85838 0.337858 0.168929 0.985628i \(-0.445969\pi\)
0.168929 + 0.985628i \(0.445969\pi\)
\(542\) −1.11050 + 0.707913i −0.0477000 + 0.0304075i
\(543\) 5.46543 5.46543i 0.234544 0.234544i
\(544\) 13.9333 + 26.6724i 0.597387 + 1.14357i
\(545\) 0 0
\(546\) 0.658473 2.97421i 0.0281801 0.127284i
\(547\) 17.8105 + 17.8105i 0.761522 + 0.761522i 0.976597 0.215076i \(-0.0689998\pi\)
−0.215076 + 0.976597i \(0.569000\pi\)
\(548\) −6.79582 18.6382i −0.290303 0.796183i
\(549\) 4.98168i 0.212613i
\(550\) 0 0
\(551\) 1.05727i 0.0450413i
\(552\) −0.565976 4.27068i −0.0240895 0.181772i
\(553\) −9.72928 9.72928i −0.413731 0.413731i
\(554\) −43.0773 9.53707i −1.83018 0.405191i
\(555\) 0 0
\(556\) 1.92482 4.13397i 0.0816307 0.175319i
\(557\) −23.3372 + 23.3372i −0.988827 + 0.988827i −0.999938 0.0111112i \(-0.996463\pi\)
0.0111112 + 0.999938i \(0.496463\pi\)
\(558\) −5.93780 9.31460i −0.251367 0.394318i
\(559\) 21.8617 0.924652
\(560\) 0 0
\(561\) −27.2803 −1.15178
\(562\) −6.51439 10.2191i −0.274793 0.431067i
\(563\) −5.27400 + 5.27400i −0.222273 + 0.222273i −0.809455 0.587182i \(-0.800237\pi\)
0.587182 + 0.809455i \(0.300237\pi\)
\(564\) 2.74567 5.89692i 0.115614 0.248305i
\(565\) 0 0
\(566\) −22.5939 5.00217i −0.949693 0.210257i
\(567\) 0.611393 + 0.611393i 0.0256761 + 0.0256761i
\(568\) 3.01079 + 22.7185i 0.126330 + 0.953247i
\(569\) 28.5606i 1.19732i −0.801002 0.598661i \(-0.795699\pi\)
0.801002 0.598661i \(-0.204301\pi\)
\(570\) 0 0
\(571\) 32.2837i 1.35103i 0.737347 + 0.675515i \(0.236078\pi\)
−0.737347 + 0.675515i \(0.763922\pi\)
\(572\) −8.75270 24.0051i −0.365969 1.00370i
\(573\) −4.98168 4.98168i −0.208113 0.208113i
\(574\) −1.45986 + 6.59392i −0.0609333 + 0.275225i
\(575\) 0 0
\(576\) −2.08382 7.72384i −0.0868257 0.321827i
\(577\) −27.0279 + 27.0279i −1.12519 + 1.12519i −0.134237 + 0.990949i \(0.542858\pi\)
−0.990949 + 0.134237i \(0.957142\pi\)
\(578\) −13.4738 + 8.58919i −0.560437 + 0.357263i
\(579\) 16.2702 0.676168
\(580\) 0 0
\(581\) −9.72928 −0.403639
\(582\) 1.33878 0.853435i 0.0554942 0.0353760i
\(583\) 13.4677 13.4677i 0.557776 0.557776i
\(584\) 7.15249 + 5.47855i 0.295972 + 0.226704i
\(585\) 0 0
\(586\) −5.57560 + 25.1840i −0.230326 + 1.04034i
\(587\) 17.1558 + 17.1558i 0.708096 + 0.708096i 0.966135 0.258039i \(-0.0830761\pi\)
−0.258039 + 0.966135i \(0.583076\pi\)
\(588\) 11.7482 4.28362i 0.484488 0.176653i
\(589\) 9.55102i 0.393543i
\(590\) 0 0
\(591\) 11.1420i 0.458321i
\(592\) −9.92794 0.857132i −0.408036 0.0352279i
\(593\) 21.5833 + 21.5833i 0.886320 + 0.886320i 0.994167 0.107848i \(-0.0343959\pi\)
−0.107848 + 0.994167i \(0.534396\pi\)
\(594\) 7.08093 + 1.56768i 0.290534 + 0.0643227i
\(595\) 0 0
\(596\) 18.3432 + 8.54079i 0.751366 + 0.349844i
\(597\) −8.11704 + 8.11704i −0.332208 + 0.332208i
\(598\) 2.88450 + 4.52490i 0.117956 + 0.185037i
\(599\) 23.7636 0.970955 0.485478 0.874249i \(-0.338646\pi\)
0.485478 + 0.874249i \(0.338646\pi\)
\(600\) 0 0
\(601\) 22.1695 0.904314 0.452157 0.891938i \(-0.350655\pi\)
0.452157 + 0.891938i \(0.350655\pi\)
\(602\) −5.76813 9.04843i −0.235091 0.368786i
\(603\) 6.20522 6.20522i 0.252696 0.252696i
\(604\) −14.3904 6.70033i −0.585537 0.272633i
\(605\) 0 0
\(606\) 13.9694 + 3.09275i 0.567468 + 0.125634i
\(607\) 9.35348 + 9.35348i 0.379646 + 0.379646i 0.870974 0.491328i \(-0.163489\pi\)
−0.491328 + 0.870974i \(0.663489\pi\)
\(608\) 2.07058 6.59995i 0.0839731 0.267663i
\(609\) 0.747604i 0.0302944i
\(610\) 0 0
\(611\) 8.10243i 0.327789i
\(612\) 9.99558 3.64457i 0.404047 0.147323i
\(613\) 24.1247 + 24.1247i 0.974389 + 0.974389i 0.999680 0.0252913i \(-0.00805134\pi\)
−0.0252913 + 0.999680i \(0.508051\pi\)
\(614\) 0.694151 3.13536i 0.0280137 0.126533i
\(615\) 0 0
\(616\) −7.62620 + 9.95634i −0.307268 + 0.401152i
\(617\) −3.82611 + 3.82611i −0.154033 + 0.154033i −0.779917 0.625883i \(-0.784739\pi\)
0.625883 + 0.779917i \(0.284739\pi\)
\(618\) 6.44685 4.10969i 0.259330 0.165316i
\(619\) −30.1297 −1.21101 −0.605507 0.795840i \(-0.707029\pi\)
−0.605507 + 0.795840i \(0.707029\pi\)
\(620\) 0 0
\(621\) −1.52311 −0.0611205
\(622\) 23.1541 14.7601i 0.928395 0.591826i
\(623\) 4.43407 4.43407i 0.177647 0.177647i
\(624\) 6.41403 + 7.62620i 0.256767 + 0.305292i
\(625\) 0 0
\(626\) −7.65681 + 34.5845i −0.306028 + 1.38227i
\(627\) 4.43407 + 4.43407i 0.177080 + 0.177080i
\(628\) −8.73362 23.9528i −0.348509 0.955819i
\(629\) 13.2524i 0.528408i
\(630\) 0 0
\(631\) 21.5701i 0.858694i 0.903140 + 0.429347i \(0.141256\pi\)
−0.903140 + 0.429347i \(0.858744\pi\)
\(632\) 44.6195 5.91324i 1.77487 0.235216i
\(633\) −3.88296 3.88296i −0.154334 0.154334i
\(634\) −15.2106 3.36754i −0.604090 0.133742i
\(635\) 0 0
\(636\) −3.13536 + 6.73386i −0.124325 + 0.267015i
\(637\) −11.0140 + 11.0140i −0.436389 + 0.436389i
\(638\) −3.37077 5.28771i −0.133450 0.209342i
\(639\) 8.10243 0.320527
\(640\) 0 0
\(641\) 48.3911 1.91133 0.955666 0.294452i \(-0.0951370\pi\)
0.955666 + 0.294452i \(0.0951370\pi\)
\(642\) 5.92485 + 9.29429i 0.233835 + 0.366816i
\(643\) −23.3413 + 23.3413i −0.920491 + 0.920491i −0.997064 0.0765729i \(-0.975602\pi\)
0.0765729 + 0.997064i \(0.475602\pi\)
\(644\) 1.11177 2.38776i 0.0438097 0.0940907i
\(645\) 0 0
\(646\) 8.98168 + 1.98849i 0.353379 + 0.0782362i
\(647\) −32.4465 32.4465i −1.27560 1.27560i −0.943103 0.332501i \(-0.892108\pi\)
−0.332501 0.943103i \(-0.607892\pi\)
\(648\) −2.80391 + 0.371591i −0.110148 + 0.0145975i
\(649\) 2.71096i 0.106414i
\(650\) 0 0
\(651\) 6.75359i 0.264694i
\(652\) 12.6779 + 34.7704i 0.496506 + 1.36171i
\(653\) −18.4725 18.4725i −0.722885 0.722885i 0.246307 0.969192i \(-0.420783\pi\)
−0.969192 + 0.246307i \(0.920783\pi\)
\(654\) 2.23677 10.1031i 0.0874645 0.395062i
\(655\) 0 0
\(656\) −14.2201 16.9075i −0.555202 0.660128i
\(657\) 2.25240 2.25240i 0.0878743 0.0878743i
\(658\) 3.35355 2.13779i 0.130735 0.0833399i
\(659\) 47.5028 1.85045 0.925223 0.379423i \(-0.123878\pi\)
0.925223 + 0.379423i \(0.123878\pi\)
\(660\) 0 0
\(661\) −46.1204 −1.79387 −0.896937 0.442158i \(-0.854213\pi\)
−0.896937 + 0.442158i \(0.854213\pi\)
\(662\) −37.8035 + 24.0987i −1.46927 + 0.936621i
\(663\) −9.37086 + 9.37086i −0.363934 + 0.363934i
\(664\) 19.3531 25.2663i 0.751046 0.980525i
\(665\) 0 0
\(666\) −0.761557 + 3.43982i −0.0295097 + 0.133290i
\(667\) 0.931222 + 0.931222i 0.0360571 + 0.0360571i
\(668\) −30.1163 + 10.9810i −1.16524 + 0.424867i
\(669\) 15.3694i 0.594217i
\(670\) 0 0
\(671\) 25.5471i 0.986236i
\(672\) 1.46412 4.66687i 0.0564797 0.180028i
\(673\) −3.60599 3.60599i −0.139001 0.139001i 0.634183 0.773183i \(-0.281337\pi\)
−0.773183 + 0.634183i \(0.781337\pi\)
\(674\) 37.0300 + 8.19825i 1.42634 + 0.315785i
\(675\) 0 0
\(676\) 12.3179 + 5.73535i 0.473765 + 0.220590i
\(677\) 8.26635 8.26635i 0.317702 0.317702i −0.530182 0.847884i \(-0.677876\pi\)
0.847884 + 0.530182i \(0.177876\pi\)
\(678\) −0.547390 0.858688i −0.0210224 0.0329777i
\(679\) 0.970688 0.0372516
\(680\) 0 0
\(681\) 7.04623 0.270012
\(682\) −30.4503 47.7673i −1.16600 1.82910i
\(683\) −8.43079 + 8.43079i −0.322595 + 0.322595i −0.849762 0.527167i \(-0.823254\pi\)
0.527167 + 0.849762i \(0.323254\pi\)
\(684\) −2.21703 1.03228i −0.0847704 0.0394700i
\(685\) 0 0
\(686\) 15.8217 + 3.50285i 0.604077 + 0.133739i
\(687\) 18.2131 + 18.2131i 0.694872 + 0.694872i
\(688\) 34.9719 + 3.01932i 1.33329 + 0.115110i
\(689\) 9.25240i 0.352488i
\(690\) 0 0
\(691\) 21.9182i 0.833809i 0.908950 + 0.416905i \(0.136885\pi\)
−0.908950 + 0.416905i \(0.863115\pi\)
\(692\) 21.1726 7.71993i 0.804862 0.293468i
\(693\) 3.13536 + 3.13536i 0.119102 + 0.119102i
\(694\) −3.33733 + 15.0741i −0.126683 + 0.572206i
\(695\) 0 0
\(696\) 1.94148 + 1.48710i 0.0735917 + 0.0563686i
\(697\) 20.7755 20.7755i 0.786929 0.786929i
\(698\) −32.2864 + 20.5817i −1.22206 + 0.779029i
\(699\) 1.01163 0.0382633
\(700\) 0 0
\(701\) −21.8184 −0.824070 −0.412035 0.911168i \(-0.635182\pi\)
−0.412035 + 0.911168i \(0.635182\pi\)
\(702\) 2.97082 1.89382i 0.112126 0.0714776i
\(703\) −2.15401 + 2.15401i −0.0812400 + 0.0812400i
\(704\) −10.6863 39.6095i −0.402754 1.49284i
\(705\) 0 0
\(706\) 4.30925 19.4641i 0.162181 0.732542i
\(707\) 6.18549 + 6.18549i 0.232629 + 0.232629i
\(708\) −0.362177 0.993303i −0.0136114 0.0373306i
\(709\) 31.7938i 1.19404i 0.802225 + 0.597021i \(0.203649\pi\)
−0.802225 + 0.597021i \(0.796351\pi\)
\(710\) 0 0
\(711\) 15.9133i 0.596795i
\(712\) 2.69493 + 20.3351i 0.100997 + 0.762089i
\(713\) 8.41233 + 8.41233i 0.315044 + 0.315044i
\(714\) 6.35101 + 1.40608i 0.237680 + 0.0526211i
\(715\) 0 0
\(716\) 10.6770 22.9312i 0.399019 0.856979i
\(717\) 19.0462 19.0462i 0.711294 0.711294i
\(718\) 10.8202 + 16.9736i 0.403807 + 0.633450i
\(719\) −52.0874 −1.94253 −0.971265 0.237999i \(-0.923508\pi\)
−0.971265 + 0.237999i \(0.923508\pi\)
\(720\) 0 0
\(721\) 4.67432 0.174081
\(722\) 13.3071 + 20.8748i 0.495239 + 0.776879i
\(723\) 9.96487 9.96487i 0.370598 0.370598i
\(724\) −6.52505 + 14.0140i −0.242502 + 0.520824i
\(725\) 0 0
\(726\) 21.1240 + 4.67674i 0.783986 + 0.173570i
\(727\) −8.13069 8.13069i −0.301551 0.301551i 0.540070 0.841620i \(-0.318398\pi\)
−0.841620 + 0.540070i \(0.818398\pi\)
\(728\) 0.800411 + 6.03965i 0.0296652 + 0.223844i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 46.6826i 1.72662i
\(732\) 3.41303 + 9.36054i 0.126149 + 0.345976i
\(733\) 29.9956 + 29.9956i 1.10791 + 1.10791i 0.993424 + 0.114489i \(0.0365232\pi\)
0.114489 + 0.993424i \(0.463477\pi\)
\(734\) 1.25003 5.64618i 0.0461396 0.208404i
\(735\) 0 0
\(736\) 3.98937 + 7.63682i 0.147050 + 0.281497i
\(737\) 31.8217 31.8217i 1.17217 1.17217i
\(738\) −6.58641 + 4.19866i −0.242449 + 0.154555i
\(739\) 39.4719 1.45200 0.725999 0.687696i \(-0.241378\pi\)
0.725999 + 0.687696i \(0.241378\pi\)
\(740\) 0 0
\(741\) 3.04623 0.111906
\(742\) −3.82951 + 2.44121i −0.140586 + 0.0896196i
\(743\) 12.2252 12.2252i 0.448499 0.448499i −0.446356 0.894855i \(-0.647279\pi\)
0.894855 + 0.446356i \(0.147279\pi\)
\(744\) 17.5387 + 13.4340i 0.642999 + 0.492514i
\(745\) 0 0
\(746\) 4.87859 22.0358i 0.178618 0.806786i
\(747\) −7.95665 7.95665i −0.291118 0.291118i
\(748\) 51.2595 18.6902i 1.87423 0.683380i
\(749\) 6.73887i 0.246233i
\(750\) 0 0
\(751\) 28.9069i 1.05483i −0.849609 0.527413i \(-0.823162\pi\)
0.849609 0.527413i \(-0.176838\pi\)
\(752\) −1.11902 + 12.9614i −0.0408066 + 0.472652i
\(753\) 12.1955 + 12.1955i 0.444430 + 0.444430i
\(754\) −2.97421 0.658473i −0.108314 0.0239802i
\(755\) 0 0
\(756\) −1.56768 0.729929i −0.0570160 0.0265473i
\(757\) 16.2018 16.2018i 0.588864 0.588864i −0.348459 0.937324i \(-0.613295\pi\)
0.937324 + 0.348459i \(0.113295\pi\)
\(758\) 11.7498 + 18.4318i 0.426771 + 0.669474i
\(759\) −7.81086 −0.283516
\(760\) 0 0
\(761\) −6.64641 −0.240932 −0.120466 0.992717i \(-0.538439\pi\)
−0.120466 + 0.992717i \(0.538439\pi\)
\(762\) −8.05348 12.6334i −0.291747 0.457661i
\(763\) 4.47353 4.47353i 0.161953 0.161953i
\(764\) 12.7736 + 5.94751i 0.462131 + 0.215173i
\(765\) 0 0
\(766\) −24.5187 5.42831i −0.885898 0.196133i
\(767\) 0.931222 + 0.931222i 0.0336245 + 0.0336245i
\(768\) 9.20720 + 13.0854i 0.332236 + 0.472178i
\(769\) 29.3449i 1.05820i −0.848559 0.529101i \(-0.822529\pi\)
0.848559 0.529101i \(-0.177471\pi\)
\(770\) 0 0
\(771\) 21.2329i 0.764686i
\(772\) −30.5717 + 11.1470i −1.10030 + 0.401189i
\(773\) −37.5833 37.5833i −1.35178 1.35178i −0.883674 0.468104i \(-0.844937\pi\)
−0.468104 0.883674i \(-0.655063\pi\)
\(774\) 2.68264 12.1170i 0.0964257 0.435538i
\(775\) 0 0
\(776\) −1.93086 + 2.52082i −0.0693137 + 0.0904921i
\(777\) −1.52311 + 1.52311i −0.0546414 + 0.0546414i
\(778\) 6.15729 3.92510i 0.220749 0.140722i
\(779\) −6.75359 −0.241973
\(780\) 0 0
\(781\) 41.5510 1.48681
\(782\) −9.66229 + 6.15945i −0.345523 + 0.220261i
\(783\) 0.611393 0.611393i 0.0218494 0.0218494i
\(784\) −19.1400 + 16.0978i −0.683573 + 0.574920i