Properties

Label 300.2.j.d.7.5
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 7.5
Root \(1.19252 - 0.760198i\) of defining polynomial
Character \(\chi\) \(=\) 300.7
Dual form 300.2.j.d.43.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.19252 - 0.760198i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(0.844199 - 1.81310i) q^{4} +(-1.38078 - 0.305697i) q^{6} +(0.611393 - 0.611393i) q^{7} +(-0.371591 - 2.80391i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(1.19252 - 0.760198i) 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} +(-0.371591 - 2.80391i) q^{8} +1.00000i q^{9} -5.12822i q^{11} +(-1.87899 + 0.685116i) 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} +(0.760198 + 1.19252i) q^{18} +1.22279 q^{19} -0.864641 q^{21} +(-3.89846 - 6.11549i) 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} +(-0.592379 - 1.62465i) q^{28} -0.864641i q^{29} +7.81086i q^{31} +(-5.39747 - 1.69333i) 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} +(1.45820 - 0.929560i) q^{38} +2.49122 q^{39} +5.52311 q^{41} +(-1.03110 + 0.657298i) 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} +(-0.344061 + 3.98518i) q^{48} +6.25240i q^{49} -5.31965i q^{51} +(1.70677 + 4.68098i) 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} +(-0.657298 - 1.03110i) q^{58} +0.528636 q^{59} +4.98168 q^{61} +(5.93780 + 9.31460i) 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} +(9.99558 - 3.64457i) q^{68} +1.52311i q^{69} +8.10243i q^{71} +(2.80391 - 0.371591i) 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} +(2.97082 - 1.89382i) q^{78} -15.9133 q^{79} -1.00000 q^{81} +(6.58641 - 4.19866i) 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} +(-14.3791 + 1.90560i) q^{88} -7.25240i q^{89} +2.15401i q^{91} +(-2.86192 + 1.04351i) 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} +(4.75306 + 7.45610i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.19252 0.760198i 0.843238 0.537541i
\(3\) −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 \(-0.697753\pi\)
0.813145 + 0.582060i \(0.197753\pi\)
\(8\) −0.371591 2.80391i −0.131377 0.991332i
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 5.12822i 1.54622i −0.634274 0.773108i \(-0.718701\pi\)
0.634274 0.773108i \(-0.281299\pi\)
\(12\) −1.87899 + 0.685116i −0.542419 + 0.197776i
\(13\) −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 \(0.526815\pi\)
\(18\) 0.760198 + 1.19252i 0.179180 + 0.281079i
\(19\) 1.22279 0.280527 0.140263 0.990114i \(-0.455205\pi\)
0.140263 + 0.990114i \(0.455205\pi\)
\(20\) 0 0
\(21\) −0.864641 −0.188680
\(22\) −3.89846 6.11549i −0.831154 1.30383i
\(23\) −1.07700 1.07700i −0.224571 0.224571i 0.585849 0.810420i \(-0.300761\pi\)
−0.810420 + 0.585849i \(0.800761\pi\)
\(24\) −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
\(28\) −0.592379 1.62465i −0.111949 0.307031i
\(29\) 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 \(0.247457\pi\)
−0.712732 + 0.701436i \(0.752543\pi\)
\(32\) −5.39747 1.69333i −0.954146 0.299341i
\(33\) −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 \(0.684353\pi\)
\(38\) 1.45820 0.929560i 0.236551 0.150795i
\(39\) 2.49122 0.398914
\(40\) 0 0
\(41\) 5.52311 0.862566 0.431283 0.902217i \(-0.358061\pi\)
0.431283 + 0.902217i \(0.358061\pi\)
\(42\) −1.03110 + 0.657298i −0.159102 + 0.101423i
\(43\) 6.20522 + 6.20522i 0.946288 + 0.946288i 0.998629 0.0523416i \(-0.0166685\pi\)
−0.0523416 + 0.998629i \(0.516668\pi\)
\(44\) −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 \(-0.673769\pi\)
0.854655 + 0.519196i \(0.173769\pi\)
\(48\) −0.344061 + 3.98518i −0.0496610 + 0.575210i
\(49\) 6.25240i 0.893199i
\(50\) 0 0
\(51\) 5.31965i 0.744899i
\(52\) 1.70677 + 4.68098i 0.236687 + 0.649135i
\(53\) 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
\(58\) −0.657298 1.03110i −0.0863075 0.135390i
\(59\) 0.528636 0.0688225 0.0344113 0.999408i \(-0.489044\pi\)
0.0344113 + 0.999408i \(0.489044\pi\)
\(60\) 0 0
\(61\) 4.98168 0.637838 0.318919 0.947782i \(-0.396680\pi\)
0.318919 + 0.947782i \(0.396680\pi\)
\(62\) 5.93780 + 9.31460i 0.754101 + 1.18295i
\(63\) 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 \(-0.930084\pi\)
0.217886 + 0.975974i \(0.430084\pi\)
\(68\) 9.99558 3.64457i 1.21214 0.441969i
\(69\) 1.52311i 0.183361i
\(70\) 0 0
\(71\) 8.10243i 0.961581i 0.876835 + 0.480791i \(0.159650\pi\)
−0.876835 + 0.480791i \(0.840350\pi\)
\(72\) 2.80391 0.371591i 0.330444 0.0437924i
\(73\) 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
\(78\) 2.97082 1.89382i 0.336379 0.214433i
\(79\) −15.9133 −1.79039 −0.895193 0.445680i \(-0.852962\pi\)
−0.895193 + 0.445680i \(0.852962\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 6.58641 4.19866i 0.727348 0.463664i
\(83\) −7.95665 7.95665i −0.873355 0.873355i 0.119481 0.992836i \(-0.461877\pi\)
−0.992836 + 0.119481i \(0.961877\pi\)
\(84\) −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
\(88\) −14.3791 + 1.90560i −1.53281 + 0.203138i
\(89\) 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
\(92\) −2.86192 + 1.04351i −0.298376 + 0.108793i
\(93\) 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 \(0.768152\pi\)
\(98\) 4.75306 + 7.45610i 0.480131 + 0.753179i
\(99\) 5.12822 0.515405
\(100\) 0 0
\(101\) −10.1170 −1.00668 −0.503341 0.864088i \(-0.667896\pi\)
−0.503341 + 0.864088i \(0.667896\pi\)
\(102\) −4.04398 6.34377i −0.400414 0.628127i
\(103\) 3.82267 + 3.82267i 0.376659 + 0.376659i 0.869895 0.493236i \(-0.164186\pi\)
−0.493236 + 0.869895i \(0.664186\pi\)
\(104\) 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 \(-0.627049\pi\)
0.921397 + 0.388622i \(0.127049\pi\)
\(108\) −0.685116 1.87899i −0.0659253 0.180806i
\(109\) 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
\(112\) −3.44575 0.297490i −0.325592 0.0281101i
\(113\) 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
\(118\) 0.630408 0.401868i 0.0580337 0.0369949i
\(119\) 4.59958 0.421643
\(120\) 0 0
\(121\) −15.2986 −1.39078
\(122\) 5.94074 3.78706i 0.537849 0.342864i
\(123\) −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 \(-0.905757\pi\)
0.291767 + 0.956489i \(0.405757\pi\)
\(128\) −7.62671 + 8.35664i −0.674112 + 0.738629i
\(129\) 8.77551i 0.772641i
\(130\) 0 0
\(131\) 13.9964i 1.22287i −0.791296 0.611434i \(-0.790593\pi\)
0.791296 0.611434i \(-0.209407\pi\)
\(132\) 3.51342 + 9.63589i 0.305804 + 0.838696i
\(133\) 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 \(0.889279\pi\)
\(138\) 1.15787 + 1.81634i 0.0985643 + 0.154617i
\(139\) 2.28006 0.193392 0.0966960 0.995314i \(-0.469173\pi\)
0.0966960 + 0.995314i \(0.469173\pi\)
\(140\) 0 0
\(141\) −3.25240 −0.273901
\(142\) 6.15945 + 9.66229i 0.516889 + 0.810842i
\(143\) 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
\(148\) 4.68098 1.70677i 0.384774 0.140296i
\(149\) 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 \(0.104674\pi\)
−0.946417 + 0.322948i \(0.895326\pi\)
\(152\) −0.454377 3.42859i −0.0368548 0.278095i
\(153\) −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 \(0.919869\pi\)
\(158\) −18.9769 + 12.0972i −1.50972 + 0.962405i
\(159\) −3.71400 −0.294540
\(160\) 0 0
\(161\) −1.31695 −0.103790
\(162\) −1.19252 + 0.760198i −0.0936931 + 0.0597268i
\(163\) −13.0849 13.0849i −1.02489 1.02489i −0.999682 0.0252033i \(-0.991977\pi\)
−0.0252033 0.999682i \(-0.508023\pi\)
\(164\) 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 \(-0.962924\pi\)
0.116216 + 0.993224i \(0.462924\pi\)
\(168\) 0.321293 + 2.42438i 0.0247883 + 0.187045i
\(169\) 6.79383i 0.522603i
\(170\) 0 0
\(171\) 1.22279i 0.0935088i
\(172\) 16.4891 6.01224i 1.25728 0.458429i
\(173\) −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
\(178\) −5.51325 8.64861i −0.413236 0.648241i
\(179\) 12.6475 0.945320 0.472660 0.881245i \(-0.343294\pi\)
0.472660 + 0.881245i \(0.343294\pi\)
\(180\) 0 0
\(181\) 7.72928 0.574513 0.287256 0.957854i \(-0.407257\pi\)
0.287256 + 0.957854i \(0.407257\pi\)
\(182\) 1.63747 + 2.56869i 0.121378 + 0.190404i
\(183\) −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
\(188\) −2.22827 6.11123i −0.162513 0.445707i
\(189\) 0.864641i 0.0628934i
\(190\) 0 0
\(191\) 7.04516i 0.509770i −0.966971 0.254885i \(-0.917962\pi\)
0.966971 0.254885i \(-0.0820376\pi\)
\(192\) 6.93506 + 3.98810i 0.500495 + 0.287816i
\(193\) 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 \(0.879920\pi\)
\(198\) 6.11549 3.89846i 0.434609 0.277051i
\(199\) 11.4792 0.813741 0.406870 0.913486i \(-0.366620\pi\)
0.406870 + 0.913486i \(0.366620\pi\)
\(200\) 0 0
\(201\) 8.77551 0.618977
\(202\) −12.0648 + 7.69095i −0.848873 + 0.541133i
\(203\) −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
\(208\) 9.92794 + 0.857132i 0.688379 + 0.0594314i
\(209\) 6.27072i 0.433755i
\(210\) 0 0
\(211\) 5.49134i 0.378039i −0.981973 0.189020i \(-0.939469\pi\)
0.981973 0.189020i \(-0.0605310\pi\)
\(212\) −2.54452 6.97859i −0.174759 0.479292i
\(213\) 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
\(218\) −5.56233 8.72559i −0.376728 0.590972i
\(219\) −3.18537 −0.215247
\(220\) 0 0
\(221\) −13.2524 −0.891453
\(222\) −1.89382 2.97082i −0.127105 0.199389i
\(223\) 10.8678 + 10.8678i 0.727764 + 0.727764i 0.970174 0.242410i \(-0.0779380\pi\)
−0.242410 + 0.970174i \(0.577938\pi\)
\(224\) −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 \(-0.825128\pi\)
0.522155 + 0.852851i \(0.325128\pi\)
\(228\) −2.29761 + 0.837751i −0.152163 + 0.0554814i
\(229\) 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
\(232\) −2.42438 + 0.321293i −0.159168 + 0.0210939i
\(233\) 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
\(238\) 5.48509 3.49659i 0.355545 0.226650i
\(239\) −26.9354 −1.74231 −0.871154 0.491009i \(-0.836628\pi\)
−0.871154 + 0.491009i \(0.836628\pi\)
\(240\) 0 0
\(241\) 14.0925 0.907775 0.453887 0.891059i \(-0.350037\pi\)
0.453887 + 0.891059i \(0.350037\pi\)
\(242\) −18.2439 + 11.6300i −1.17276 + 0.747603i
\(243\) 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
\(248\) 21.9010 2.90245i 1.39071 0.184306i
\(249\) 11.2524i 0.713092i
\(250\) 0 0
\(251\) 17.2471i 1.08863i 0.838882 + 0.544314i \(0.183210\pi\)
−0.838882 + 0.544314i \(0.816790\pi\)
\(252\) 1.62465 0.592379i 0.102344 0.0373164i
\(253\) −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 \(0.519607\pi\)
\(258\) −6.67112 10.4650i −0.415326 0.651520i
\(259\) 2.15401 0.133844
\(260\) 0 0
\(261\) 0.864641 0.0535199
\(262\) −10.6400 16.6909i −0.657341 1.03117i
\(263\) 6.73386 + 6.73386i 0.415228 + 0.415228i 0.883555 0.468327i \(-0.155143\pi\)
−0.468327 + 0.883555i \(0.655143\pi\)
\(264\) 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
\(268\) 6.01224 + 16.4891i 0.367256 + 1.00723i
\(269\) 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 \(-0.990996\pi\)
0.999600 0.0282839i \(-0.00900423\pi\)
\(272\) 1.83029 21.1997i 0.110977 1.28542i
\(273\) 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 \(0.363365\pi\)
\(278\) 2.71901 1.73330i 0.163075 0.103956i
\(279\) −7.81086 −0.467624
\(280\) 0 0
\(281\) 8.56934 0.511204 0.255602 0.966782i \(-0.417726\pi\)
0.255602 + 0.966782i \(0.417726\pi\)
\(282\) −3.87854 + 2.47246i −0.230964 + 0.147233i
\(283\) −11.5705 11.5705i −0.687796 0.687796i 0.273949 0.961744i \(-0.411670\pi\)
−0.961744 + 0.273949i \(0.911670\pi\)
\(284\) 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
\(288\) 1.69333 5.39747i 0.0997803 0.318049i
\(289\) 11.2986i 0.664625i
\(290\) 0 0
\(291\) 1.12265i 0.0658108i
\(292\) −2.18235 5.98529i −0.127712 0.350262i
\(293\) −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
\(298\) 7.69095 + 12.0648i 0.445525 + 0.698892i
\(299\) 3.79441 0.219436
\(300\) 0 0
\(301\) 7.58767 0.437346
\(302\) 6.03362 + 9.46491i 0.347196 + 0.544644i
\(303\) 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 \(-0.770640\pi\)
0.659801 + 0.751440i \(0.270640\pi\)
\(308\) −8.33158 + 3.03785i −0.474736 + 0.173098i
\(309\) 5.40608i 0.307541i
\(310\) 0 0
\(311\) 19.4161i 1.10099i 0.834839 + 0.550494i \(0.185561\pi\)
−0.834839 + 0.550494i \(0.814439\pi\)
\(312\) −0.925715 6.98516i −0.0524083 0.395457i
\(313\) −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 \(0.649885\pi\)
\(318\) −4.42902 + 2.82338i −0.248367 + 0.158327i
\(319\) −4.43407 −0.248260
\(320\) 0 0
\(321\) −7.79383 −0.435009
\(322\) −1.57048 + 1.00114i −0.0875196 + 0.0557914i
\(323\) 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
\(328\) −2.05234 15.4863i −0.113322 0.855089i
\(329\) 2.81215i 0.155039i
\(330\) 0 0
\(331\) 31.7005i 1.74242i −0.490912 0.871209i \(-0.663336\pi\)
0.490912 0.871209i \(-0.336664\pi\)
\(332\) −21.1432 + 7.70919i −1.16038 + 0.423097i
\(333\) −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 \(-0.510686\pi\)
\(338\) 5.16466 + 8.10177i 0.280920 + 0.440678i
\(339\) −0.720062 −0.0391084
\(340\) 0 0
\(341\) 40.0558 2.16914
\(342\) 0.929560 + 1.45820i 0.0502648 + 0.0788502i
\(343\) 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 \(-0.655336\pi\)
0.883271 + 0.468863i \(0.155336\pi\)
\(348\) 0.592379 + 1.62465i 0.0317549 + 0.0870906i
\(349\) 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
\(352\) −8.68375 + 27.6794i −0.462846 + 1.47532i
\(353\) 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
\(358\) 15.0824 9.61461i 0.797129 0.508148i
\(359\) 14.2334 0.751211 0.375606 0.926780i \(-0.377435\pi\)
0.375606 + 0.926780i \(0.377435\pi\)
\(360\) 0 0
\(361\) −17.5048 −0.921305
\(362\) 9.21731 5.87578i 0.484451 0.308824i
\(363\) 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 \(-0.784037\pi\)
0.627602 + 0.778534i \(0.284037\pi\)
\(368\) −0.524045 + 6.06988i −0.0273177 + 0.316414i
\(369\) 5.52311i 0.287522i
\(370\) 0 0
\(371\) 3.21128i 0.166721i
\(372\) −5.35135 14.6766i −0.277454 0.760944i
\(373\) 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
\(378\) −0.657298 1.03110i −0.0338078 0.0530341i
\(379\) 15.4562 0.793932 0.396966 0.917833i \(-0.370063\pi\)
0.396966 + 0.917833i \(0.370063\pi\)
\(380\) 0 0
\(381\) 10.5939 0.542743
\(382\) −5.35571 8.40148i −0.274022 0.429857i
\(383\) −12.5562 12.5562i −0.641593 0.641593i 0.309354 0.950947i \(-0.399887\pi\)
−0.950947 + 0.309354i \(0.899887\pi\)
\(384\) 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
\(388\) −2.10945 + 0.769144i −0.107091 + 0.0390474i
\(389\) 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
\(392\) 17.5312 2.32333i 0.885458 0.117346i
\(393\) −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 \(0.710782\pi\)
\(398\) 13.6892 8.72648i 0.686177 0.437419i
\(399\) −1.05727 −0.0529298
\(400\) 0 0
\(401\) 3.49521 0.174542 0.0872712 0.996185i \(-0.472185\pi\)
0.0872712 + 0.996185i \(0.472185\pi\)
\(402\) 10.4650 6.67112i 0.521945 0.332725i
\(403\) −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
\(408\) −14.9158 + 1.97673i −0.738443 + 0.0978629i
\(409\) 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
\(412\) 10.1580 3.70379i 0.500448 0.182473i
\(413\) 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
\(418\) −4.76699 7.47795i −0.233161 0.365758i
\(419\) −19.0701 −0.931634 −0.465817 0.884881i \(-0.654240\pi\)
−0.465817 + 0.884881i \(0.654240\pi\)
\(420\) 0 0
\(421\) −20.8034 −1.01390 −0.506948 0.861976i \(-0.669226\pi\)
−0.506948 + 0.861976i \(0.669226\pi\)
\(422\) −4.17450 6.54852i −0.203212 0.318777i
\(423\) 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
\(428\) −5.33968 14.6446i −0.258103 0.707872i
\(429\) 12.7755i 0.616807i
\(430\) 0 0
\(431\) 15.3302i 0.738428i 0.929344 + 0.369214i \(0.120373\pi\)
−0.929344 + 0.369214i \(0.879627\pi\)
\(432\) −3.98518 0.344061i −0.191737 0.0165537i
\(433\) −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
\(438\) −3.79861 + 2.42151i −0.181505 + 0.115704i
\(439\) 24.6554 1.17674 0.588368 0.808593i \(-0.299770\pi\)
0.588368 + 0.808593i \(0.299770\pi\)
\(440\) 0 0
\(441\) −6.25240 −0.297733
\(442\) −15.8037 + 10.0744i −0.751706 + 0.479192i
\(443\) −1.77116 1.77116i −0.0841501 0.0841501i 0.663779 0.747929i \(-0.268952\pi\)
−0.747929 + 0.663779i \(0.768952\pi\)
\(444\) −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
\(448\) −3.44827 + 5.99634i −0.162916 + 0.283300i
\(449\) 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
\(452\) −0.493326 1.35299i −0.0232041 0.0636394i
\(453\) 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 \(0.670149\pi\)
\(458\) −19.5806 30.7159i −0.914939 1.43526i
\(459\) 5.31965 0.248300
\(460\) 0 0
\(461\) −27.0216 −1.25852 −0.629262 0.777193i \(-0.716643\pi\)
−0.629262 + 0.777193i \(0.716643\pi\)
\(462\) 3.37077 + 5.28771i 0.156822 + 0.246006i
\(463\) −27.7123 27.7123i −1.28790 1.28790i −0.936059 0.351843i \(-0.885555\pi\)
−0.351843 0.936059i \(-0.614445\pi\)
\(464\) −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 \(-0.729068\pi\)
0.752043 + 0.659114i \(0.229068\pi\)
\(468\) −4.68098 + 1.70677i −0.216378 + 0.0788956i
\(469\) 7.58767i 0.350366i
\(470\) 0 0
\(471\) 12.7477i 0.587381i
\(472\) −0.196436 1.48225i −0.00904172 0.0682260i
\(473\) 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
\(478\) −32.1210 + 20.4763i −1.46918 + 0.936562i
\(479\) −13.7593 −0.628678 −0.314339 0.949311i \(-0.601783\pi\)
−0.314339 + 0.949311i \(0.601783\pi\)
\(480\) 0 0
\(481\) −6.20617 −0.282977
\(482\) 16.8055 10.7131i 0.765470 0.487966i
\(483\) 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 \(-0.465340\pi\)
0.994078 0.108671i \(-0.0346596\pi\)
\(488\) −1.85115 13.9682i −0.0837975 0.632310i
\(489\) 18.5048i 0.836816i
\(490\) 0 0
\(491\) 28.8918i 1.30387i −0.758275 0.651935i \(-0.773957\pi\)
0.758275 0.651935i \(-0.226043\pi\)
\(492\) −10.3779 + 3.78397i −0.467872 + 0.170595i
\(493\) 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
\(498\) 8.55405 + 13.4187i 0.383316 + 0.601306i
\(499\) −12.5365 −0.561211 −0.280605 0.959823i \(-0.590535\pi\)
−0.280605 + 0.959823i \(0.590535\pi\)
\(500\) 0 0
\(501\) 16.0279 0.716074
\(502\) 13.1112 + 20.5675i 0.585182 + 0.917972i
\(503\) 9.01392 + 9.01392i 0.401911 + 0.401911i 0.878906 0.476995i \(-0.158274\pi\)
−0.476995 + 0.878906i \(0.658274\pi\)
\(504\) 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
\(508\) 7.25806 + 19.9059i 0.322025 + 0.883182i
\(509\) 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
\(512\) 8.71295 + 20.8826i 0.385062 + 0.922891i
\(513\) 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
\(518\) 2.56869 1.63747i 0.112862 0.0719464i
\(519\) 11.2681 0.494613
\(520\) 0 0
\(521\) −18.9046 −0.828226 −0.414113 0.910225i \(-0.635908\pi\)
−0.414113 + 0.910225i \(0.635908\pi\)
\(522\) 1.03110 0.657298i 0.0451300 0.0287692i
\(523\) 21.8269 + 21.8269i 0.954426 + 0.954426i 0.999006 0.0445800i \(-0.0141949\pi\)
−0.0445800 + 0.999006i \(0.514195\pi\)
\(524\) −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
\(528\) 20.4368 + 1.76442i 0.889400 + 0.0767866i
\(529\) 20.6801i 0.899136i
\(530\) 0 0
\(531\) 0.528636i 0.0229408i
\(532\) −0.724353 1.98661i −0.0314047 0.0861303i
\(533\) −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
\(538\) 19.5407 + 30.6533i 0.842457 + 1.32156i
\(539\) 32.0637 1.38108
\(540\) 0 0
\(541\) 7.85838 0.337858 0.168929 0.985628i \(-0.445969\pi\)
0.168929 + 0.985628i \(0.445969\pi\)
\(542\) −0.707913 1.11050i −0.0304075 0.0477000i
\(543\) −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 \(-0.931000\pi\)
0.215076 + 0.976597i \(0.431000\pi\)
\(548\) −18.6382 + 6.79582i −0.796183 + 0.290303i
\(549\) 4.98168i 0.212613i
\(550\) 0 0
\(551\) 1.05727i 0.0450413i
\(552\) 4.27068 0.565976i 0.181772 0.0240895i
\(553\) −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 \(0.996463\pi\)
\(558\) −9.31460 + 5.93780i −0.394318 + 0.251367i
\(559\) −21.8617 −0.924652
\(560\) 0 0
\(561\) −27.2803 −1.15178
\(562\) 10.2191 6.51439i 0.431067 0.274793i
\(563\) 5.27400 + 5.27400i 0.222273 + 0.222273i 0.809455 0.587182i \(-0.199763\pi\)
−0.587182 + 0.809455i \(0.699763\pi\)
\(564\) −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
\(568\) 22.7185 3.01079i 0.953247 0.126330i
\(569\) 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 \(0.236078\pi\)
−0.737347 + 0.675515i \(0.763922\pi\)
\(572\) 24.0051 8.75270i 1.00370 0.365969i
\(573\) −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 \(-0.542858\pi\)
\(578\) 8.58919 + 13.4738i 0.357263 + 0.560437i
\(579\) −16.2702 −0.676168
\(580\) 0 0
\(581\) −9.72928 −0.403639
\(582\) 0.853435 + 1.33878i 0.0353760 + 0.0554942i
\(583\) −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 \(-0.916924\pi\)
0.258039 + 0.966135i \(0.416924\pi\)
\(588\) −4.28362 11.7482i −0.176653 0.484488i
\(589\) 9.55102i 0.393543i
\(590\) 0 0
\(591\) 11.1420i 0.458321i
\(592\) 0.857132 9.92794i 0.0352279 0.408036i
\(593\) 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
\(598\) 4.52490 2.88450i 0.185037 0.117956i
\(599\) −23.7636 −0.970955 −0.485478 0.874249i \(-0.661354\pi\)
−0.485478 + 0.874249i \(0.661354\pi\)
\(600\) 0 0
\(601\) 22.1695 0.904314 0.452157 0.891938i \(-0.350655\pi\)
0.452157 + 0.891938i \(0.350655\pi\)
\(602\) 9.04843 5.76813i 0.368786 0.235091i
\(603\) −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 \(-0.836511\pi\)
0.491328 + 0.870974i \(0.336511\pi\)
\(608\) −6.59995 2.07058i −0.267663 0.0839731i
\(609\) 0.747604i 0.0302944i
\(610\) 0 0
\(611\) 8.10243i 0.327789i
\(612\) 3.64457 + 9.99558i 0.147323 + 0.404047i
\(613\) 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 \(0.784739\pi\)
\(618\) −4.10969 6.44685i −0.165316 0.259330i
\(619\) 30.1297 1.21101 0.605507 0.795840i \(-0.292971\pi\)
0.605507 + 0.795840i \(0.292971\pi\)
\(620\) 0 0
\(621\) −1.52311 −0.0611205
\(622\) 14.7601 + 23.1541i 0.591826 + 0.928395i
\(623\) −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
\(628\) −23.9528 + 8.73362i −0.955819 + 0.348509i
\(629\) 13.2524i 0.528408i
\(630\) 0 0
\(631\) 21.5701i 0.858694i 0.903140 + 0.429347i \(0.141256\pi\)
−0.903140 + 0.429347i \(0.858744\pi\)
\(632\) 5.91324 + 44.6195i 0.235216 + 1.77487i
\(633\) −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
\(638\) −5.28771 + 3.37077i −0.209342 + 0.133450i
\(639\) −8.10243 −0.320527
\(640\) 0 0
\(641\) 48.3911 1.91133 0.955666 0.294452i \(-0.0951370\pi\)
0.955666 + 0.294452i \(0.0951370\pi\)
\(642\) −9.29429 + 5.92485i −0.366816 + 0.233835i
\(643\) 23.3413 + 23.3413i 0.920491 + 0.920491i 0.997064 0.0765729i \(-0.0243978\pi\)
−0.0765729 + 0.997064i \(0.524398\pi\)
\(644\) −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 \(-0.392108\pi\)
0.943103 0.332501i \(-0.107892\pi\)
\(648\) 0.371591 + 2.80391i 0.0145975 + 0.110148i
\(649\) 2.71096i 0.106414i
\(650\) 0 0
\(651\) 6.75359i 0.264694i
\(652\) −34.7704 + 12.6779i −1.36171 + 0.496506i
\(653\) −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
\(658\) −2.13779 3.35355i −0.0833399 0.130735i
\(659\) −47.5028 −1.85045 −0.925223 0.379423i \(-0.876122\pi\)
−0.925223 + 0.379423i \(0.876122\pi\)
\(660\) 0 0
\(661\) −46.1204 −1.79387 −0.896937 0.442158i \(-0.854213\pi\)
−0.896937 + 0.442158i \(0.854213\pi\)
\(662\) −24.0987 37.8035i −0.936621 1.46927i
\(663\) 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
\(668\) 10.9810 + 30.1163i 0.424867 + 1.16524i
\(669\) 15.3694i 0.594217i
\(670\) 0 0
\(671\) 25.5471i 0.986236i
\(672\) 4.66687 + 1.46412i 0.180028 + 0.0564797i
\(673\) −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 \(0.677876\pi\)
\(678\) −0.858688 + 0.547390i −0.0329777 + 0.0210224i
\(679\) −0.970688 −0.0372516
\(680\) 0 0
\(681\) 7.04623 0.270012
\(682\) 47.7673 30.4503i 1.82910 1.16600i
\(683\) 8.43079 + 8.43079i 0.322595 + 0.322595i 0.849762 0.527167i \(-0.176746\pi\)
−0.527167 + 0.849762i \(0.676746\pi\)
\(684\) 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
\(688\) 3.01932 34.9719i 0.115110 1.33329i
\(689\) 9.25240i 0.352488i
\(690\) 0 0
\(691\) 21.9182i 0.833809i 0.908950 + 0.416905i \(0.136885\pi\)
−0.908950 + 0.416905i \(0.863115\pi\)
\(692\) 7.71993 + 21.1726i 0.293468 + 0.804862i
\(693\) 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
\(698\) 20.5817 + 32.2864i 0.779029 + 1.22206i
\(699\) −1.01163 −0.0382633
\(700\) 0 0
\(701\) −21.8184 −0.824070 −0.412035 0.911168i \(-0.635182\pi\)
−0.412035 + 0.911168i \(0.635182\pi\)
\(702\) 1.89382 + 2.97082i 0.0714776 + 0.112126i
\(703\) 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
\(708\) −0.993303 + 0.362177i −0.0373306 + 0.0136114i
\(709\) 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
\(712\) −20.3351 + 2.69493i −0.762089 + 0.100997i
\(713\) 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
\(718\) 16.9736 10.8202i 0.633450 0.403807i
\(719\) 52.0874 1.94253 0.971265 0.237999i \(-0.0764916\pi\)
0.971265 + 0.237999i \(0.0764916\pi\)
\(720\) 0 0
\(721\) 4.67432 0.174081
\(722\) −20.8748 + 13.3071i −0.776879 + 0.495239i
\(723\) −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 \(-0.681602\pi\)
0.841620 + 0.540070i \(0.181602\pi\)
\(728\) 6.03965 0.800411i 0.223844 0.0296652i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 46.6826i 1.72662i
\(732\) −9.36054 + 3.41303i −0.345976 + 0.126149i
\(733\) 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
\(738\) 4.19866 + 6.58641i 0.154555 + 0.242449i
\(739\) −39.4719 −1.45200 −0.725999 0.687696i \(-0.758622\pi\)
−0.725999 + 0.687696i \(0.758622\pi\)
\(740\) 0 0
\(741\) 3.04623 0.111906
\(742\) −2.44121 3.82951i −0.0896196 0.140586i
\(743\) −12.2252 12.2252i −0.448499 0.448499i 0.446356 0.894855i \(-0.352721\pi\)
−0.894855 + 0.446356i \(0.852721\pi\)
\(744\) −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
\(748\) −18.6902 51.2595i −0.683380 1.87423i
\(749\) 6.73887i 0.246233i
\(750\) 0 0
\(751\) 28.9069i 1.05483i −0.849609 0.527413i \(-0.823162\pi\)
0.849609 0.527413i \(-0.176838\pi\)
\(752\) −12.9614 1.11902i −0.472652 0.0408066i
\(753\) 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 \(0.613295\pi\)
\(758\) 18.4318 11.7498i 0.669474 0.426771i
\(759\) 7.81086 0.283516
\(760\) 0 0
\(761\) −6.64641 −0.240932 −0.120466 0.992717i \(-0.538439\pi\)
−0.120466 + 0.992717i \(0.538439\pi\)
\(762\) 12.6334 8.05348i 0.457661 0.291747i
\(763\) −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
\(768\) 13.0854 9.20720i 0.472178 0.332236i
\(769\) 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
\(772\) −11.1470 30.5717i −0.401189 1.10030i
\(773\) −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
\(778\) −3.92510 6.15729i −0.140722 0.220749i
\(779\) 6.75359 0.241973
\(780\) 0 0
\(781\) 41.5510 1.48681
\(782\) −6.15945 9.66229i −0.220261 0.345523i
\(783\) −0.611393 0.611393i −0.0218494 0.0218494i