Properties

Label 300.2.j.d.7.2
Level $300$
Weight $2$
Character 300.7
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 7.2
Root \(-0.760198 + 1.19252i\) of defining polynomial
Character \(\chi\) \(=\) 300.7
Dual form 300.2.j.d.43.2

$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

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

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 −0.813145 0.582060i \(-0.802247\pi\)
0.582060 + 0.813145i \(0.302247\pi\)
\(8\) 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 \(0.281299\pi\)
−0.634274 + 0.773108i \(0.718701\pi\)
\(12\) 0.685116 1.87899i 0.197776 0.542419i
\(13\) −1.76156 + 1.76156i −0.488568 + 0.488568i −0.907854 0.419286i \(-0.862280\pi\)
0.419286 + 0.907854i \(0.362280\pi\)
\(14\) −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 0.996454 0.0841421i \(-0.0268150\pi\)
−0.0841421 + 0.996454i \(0.526815\pi\)
\(18\) −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 0.810420 0.585849i \(-0.199239\pi\)
−0.585849 + 0.810420i \(0.699239\pi\)
\(24\) 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 \(-0.974419\pi\)
0.996772 0.0802799i \(-0.0255814\pi\)
\(30\) 0 0
\(31\) 7.81086i 1.40287i −0.712732 0.701436i \(-0.752543\pi\)
0.712732 0.701436i \(-0.247457\pi\)
\(32\) −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 0.836921 0.547323i \(-0.184353\pi\)
−0.547323 + 0.836921i \(0.684353\pi\)
\(38\) 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 0.0523416 0.998629i \(-0.483332\pi\)
−0.998629 + 0.0523416i \(0.983332\pi\)
\(44\) 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 −0.854655 0.519196i \(-0.826231\pi\)
0.519196 + 0.854655i \(0.326231\pi\)
\(48\) −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 −0.503348 0.864084i \(-0.667899\pi\)
0.864084 + 0.503348i \(0.167899\pi\)
\(54\) −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 −0.217886 0.975974i \(-0.569916\pi\)
0.975974 + 0.217886i \(0.0699160\pi\)
\(68\) 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 \(-0.840350\pi\)
0.876835 0.480791i \(-0.159650\pi\)
\(72\) −0.371591 + 2.80391i −0.0437924 + 0.330444i
\(73\) 2.25240 2.25240i 0.263623 0.263623i −0.562901 0.826524i \(-0.690315\pi\)
0.826524 + 0.562901i \(0.190315\pi\)
\(74\) −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 0.992836 0.119481i \(-0.0381231\pi\)
−0.119481 + 0.992836i \(0.538123\pi\)
\(84\) 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 \(-0.874417\pi\)
0.923177 0.384376i \(-0.125583\pi\)
\(90\) 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 0.665657 0.746258i \(-0.268152\pi\)
−0.746258 + 0.665657i \(0.768152\pi\)
\(98\) −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 0.493236 0.869895i \(-0.335814\pi\)
−0.869895 + 0.493236i \(0.835814\pi\)
\(104\) −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 −0.921397 0.388622i \(-0.872951\pi\)
0.388622 + 0.921397i \(0.372951\pi\)
\(108\) 1.87899 + 0.685116i 0.180806 + 0.0659253i
\(109\) 7.31695i 0.700836i −0.936593 0.350418i \(-0.886039\pi\)
0.936593 0.350418i \(-0.113961\pi\)
\(110\) 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 −0.682752 0.730650i \(-0.739217\pi\)
0.730650 + 0.682752i \(0.239217\pi\)
\(114\) 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 −0.291767 0.956489i \(-0.594243\pi\)
0.956489 + 0.291767i \(0.0942433\pi\)
\(128\) −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 \(0.209407\pi\)
−0.791296 + 0.611434i \(0.790593\pi\)
\(132\) 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 0.340869 0.940111i \(-0.389279\pi\)
−0.940111 + 0.340869i \(0.889279\pi\)
\(138\) −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 \(0.136012\pi\)
−0.910090 + 0.414410i \(0.863988\pi\)
\(150\) 0 0
\(151\) 7.93691i 0.645897i −0.946417 0.322948i \(-0.895326\pi\)
0.946417 0.322948i \(-0.104674\pi\)
\(152\) −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 0.249089 0.968481i \(-0.419869\pi\)
−0.968481 + 0.249089i \(0.919869\pi\)
\(158\) −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 0.999682 + 0.0252033i \(0.00802331\pi\)
0.0252033 + 0.999682i \(0.491977\pi\)
\(164\) −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 −0.116216 0.993224i \(-0.537076\pi\)
0.993224 + 0.116216i \(0.0370765\pi\)
\(168\) −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 −0.941839 0.336064i \(-0.890904\pi\)
0.336064 + 0.941839i \(0.390904\pi\)
\(174\) 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 \(0.0820376\pi\)
−0.966971 + 0.254885i \(0.917962\pi\)
\(192\) 3.98810 + 6.93506i 0.287816 + 0.500495i
\(193\) 11.5048 11.5048i 0.828133 0.828133i −0.159125 0.987258i \(-0.550867\pi\)
0.987258 + 0.159125i \(0.0508674\pi\)
\(194\) 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 0.368358 0.929684i \(-0.379920\pi\)
−0.929684 + 0.368358i \(0.879920\pi\)
\(198\) 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 \(0.0605310\pi\)
−0.981973 + 0.189020i \(0.939469\pi\)
\(212\) −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 0.242410 0.970174i \(-0.422062\pi\)
−0.970174 + 0.242410i \(0.922062\pi\)
\(224\) 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 −0.522155 0.852851i \(-0.674872\pi\)
0.852851 + 0.522155i \(0.174872\pi\)
\(228\) −0.837751 + 2.29761i −0.0554814 + 0.152163i
\(229\) 25.7572i 1.70208i −0.525098 0.851041i \(-0.675972\pi\)
0.525098 0.851041i \(-0.324028\pi\)
\(230\) 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 −0.683287 0.730150i \(-0.739450\pi\)
0.730150 + 0.683287i \(0.239450\pi\)
\(234\) 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 \(-0.816790\pi\)
0.838882 0.544314i \(-0.183210\pi\)
\(252\) −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 0.998103 0.0615588i \(-0.0196072\pi\)
−0.0615588 + 0.998103i \(0.519607\pi\)
\(258\) 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 0.468327 0.883555i \(-0.344857\pi\)
−0.883555 + 0.468327i \(0.844857\pi\)
\(264\) −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 \(0.286630\pi\)
−0.621238 + 0.783622i \(0.713370\pi\)
\(270\) 0 0
\(271\) 0.931222i 0.0565677i 0.999600 + 0.0282839i \(0.00900423\pi\)
−0.999600 + 0.0282839i \(0.990996\pi\)
\(272\) −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 0.909277 + 0.416190i \(0.136635\pi\)
0.416190 + 0.909277i \(0.363365\pi\)
\(278\) 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 0.961744 0.273949i \(-0.0883299\pi\)
−0.273949 + 0.961744i \(0.588330\pi\)
\(284\) −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 −0.975121 0.221675i \(-0.928848\pi\)
0.221675 + 0.975121i \(0.428848\pi\)
\(294\) −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 −0.659801 0.751440i \(-0.729360\pi\)
0.751440 + 0.659801i \(0.229360\pi\)
\(308\) −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 \(-0.814439\pi\)
0.834839 0.550494i \(-0.185561\pi\)
\(312\) −6.98516 0.925715i −0.395457 0.0524083i
\(313\) −17.7110 + 17.7110i −1.00108 + 1.00108i −0.00108322 + 0.999999i \(0.500345\pi\)
−0.999999 + 0.00108322i \(0.999655\pi\)
\(314\) 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 0.891170 0.453670i \(-0.149885\pi\)
−0.453670 + 0.891170i \(0.649885\pi\)
\(318\) −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 \(0.336664\pi\)
−0.490912 + 0.871209i \(0.663336\pi\)
\(332\) 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 −0.999437 0.0335632i \(-0.989314\pi\)
−0.0335632 0.999437i \(-0.510686\pi\)
\(338\) −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 −0.883271 0.468863i \(-0.844664\pi\)
0.468863 + 0.883271i \(0.344664\pi\)
\(348\) −1.62465 0.592379i −0.0870906 0.0317549i
\(349\) 27.0741i 1.44925i 0.689146 + 0.724623i \(0.257986\pi\)
−0.689146 + 0.724623i \(0.742014\pi\)
\(350\) 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 −0.390201 0.920730i \(-0.627595\pi\)
0.920730 + 0.390201i \(0.127595\pi\)
\(354\) 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 −0.627602 0.778534i \(-0.715963\pi\)
0.778534 + 0.627602i \(0.215963\pi\)
\(368\) −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 −0.351783 0.936081i \(-0.614425\pi\)
0.936081 + 0.351783i \(0.114425\pi\)
\(374\) −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 0.950947 0.309354i \(-0.100113\pi\)
−0.309354 + 0.950947i \(0.600113\pi\)
\(384\) −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 \(-0.958215\pi\)
0.991396 0.130894i \(-0.0417848\pi\)
\(390\) 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 0.788646 0.614847i \(-0.210782\pi\)
−0.614847 + 0.788646i \(0.710782\pi\)
\(398\) 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 \(-0.880730\pi\)
0.930618 0.365991i \(-0.119270\pi\)
\(410\) 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 \(-0.879627\pi\)
0.929344 0.369214i \(-0.120373\pi\)
\(432\) −0.344061 3.98518i −0.0165537 0.191737i
\(433\) −16.2803 + 16.2803i −0.782381 + 0.782381i −0.980232 0.197851i \(-0.936604\pi\)
0.197851 + 0.980232i \(0.436604\pi\)
\(434\) −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 0.747929 0.663779i \(-0.231048\pi\)
−0.663779 + 0.747929i \(0.731048\pi\)
\(444\) 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 \(-0.714071\pi\)
0.622963 0.782251i \(-0.285929\pi\)
\(450\) 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 0.860504 0.509444i \(-0.170149\pi\)
−0.509444 + 0.860504i \(0.670149\pi\)
\(458\) 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 0.936059 + 0.351843i \(0.114445\pi\)
0.351843 + 0.936059i \(0.385555\pi\)
\(464\) 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 −0.752043 0.659114i \(-0.770932\pi\)
0.659114 + 0.752043i \(0.270932\pi\)
\(468\) −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 −0.108671 + 0.994078i \(0.534660\pi\)
−0.994078 + 0.108671i \(0.965340\pi\)
\(488\) 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 \(0.226043\pi\)
−0.758275 + 0.651935i \(0.773957\pi\)
\(492\) 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 0.476995 0.878906i \(-0.341726\pi\)
−0.878906 + 0.476995i \(0.841726\pi\)
\(504\) −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 \(-0.833466\pi\)
0.866233 0.499640i \(-0.166534\pi\)
\(510\) 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 0.0445800 0.999006i \(-0.485805\pi\)
−0.999006 + 0.0445800i \(0.985805\pi\)
\(524\) 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 −0.215076 0.976597i \(-0.569000\pi\)
0.976597 + 0.215076i \(0.0689998\pi\)
\(548\) −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 0.0111112 0.999938i \(-0.496463\pi\)
−0.999938 + 0.0111112i \(0.996463\pi\)
\(558\) −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 0.587182 0.809455i \(-0.300237\pi\)
−0.809455 + 0.587182i \(0.800237\pi\)
\(564\) 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 \(0.204301\pi\)
−0.801002 + 0.598661i \(0.795699\pi\)
\(570\) 0 0
\(571\) 32.2837i 1.35103i −0.737347 0.675515i \(-0.763922\pi\)
0.737347 0.675515i \(-0.236078\pi\)
\(572\) −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 −0.990949 0.134237i \(-0.957142\pi\)
−0.134237 0.990949i \(-0.542858\pi\)
\(578\) −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 −0.258039 0.966135i \(-0.583076\pi\)
0.966135 + 0.258039i \(0.0830761\pi\)
\(588\) 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 −0.107848 0.994167i \(-0.534396\pi\)
0.994167 + 0.107848i \(0.0343959\pi\)
\(594\) 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 −0.491328 0.870974i \(-0.663489\pi\)
0.870974 + 0.491328i \(0.163489\pi\)
\(608\) 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 −0.0252913 0.999680i \(-0.508051\pi\)
0.999680 + 0.0252913i \(0.00805134\pi\)
\(614\) 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 0.625883 0.779917i \(-0.284739\pi\)
−0.779917 + 0.625883i \(0.784739\pi\)
\(618\) 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 \(-0.858744\pi\)
0.903140 0.429347i \(-0.141256\pi\)
\(632\) 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 0.0765729 0.997064i \(-0.475602\pi\)
−0.997064 + 0.0765729i \(0.975602\pi\)
\(644\) 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 −0.332501 + 0.943103i \(0.607892\pi\)
−0.943103 + 0.332501i \(0.892108\pi\)
\(648\) −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 −0.969192 0.246307i \(-0.920783\pi\)
0.246307 + 0.969192i \(0.420783\pi\)
\(654\) 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 −0.773183 0.634183i \(-0.781337\pi\)
0.634183 + 0.773183i \(0.281337\pi\)
\(674\) 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 0.847884 0.530182i \(-0.177876\pi\)
−0.530182 + 0.847884i \(0.677876\pi\)
\(678\) −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 0.527167 0.849762i \(-0.323254\pi\)
−0.849762 + 0.527167i \(0.823254\pi\)
\(684\) −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 \(-0.863115\pi\)
0.908950 0.416905i \(-0.136885\pi\)
\(692\) 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 \(-0.796351\pi\)
0.802225 0.597021i \(-0.203649\pi\)
\(710\) 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 −0.841620 0.540070i \(-0.818398\pi\)
0.540070 + 0.841620i \(0.318398\pi\)
\(728\) 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 0.114489 0.993424i \(-0.463477\pi\)
0.993424 0.114489i \(-0.0365232\pi\)
\(734\) 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 0.894855 0.446356i \(-0.147279\pi\)
−0.446356 + 0.894855i \(0.647279\pi\)
\(744\) 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 \(0.176838\pi\)
−0.849609 + 0.527413i \(0.823162\pi\)
\(752\) −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 0.937324 0.348459i \(-0.113295\pi\)
−0.348459 + 0.937324i \(0.613295\pi\)
\(758\) 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 \(0.177471\pi\)
−0.848559 + 0.529101i \(0.822529\pi\)
\(770\) 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 −0.468104 + 0.883674i \(0.655063\pi\)
−0.883674 + 0.468104i \(0.844937\pi\)
\(774\) 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