Properties

Label 405.2.r.a.368.13
Level $405$
Weight $2$
Character 405.368
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 368.13
Character \(\chi\) \(=\) 405.368
Dual form 405.2.r.a.197.13

$q$-expansion

\(f(q)\) \(=\) \(q+(1.75676 + 0.153697i) q^{2} +(1.09297 + 0.192720i) q^{4} +(-0.131866 + 2.23218i) q^{5} +(2.75943 + 1.93217i) q^{7} +(-1.51630 - 0.406292i) q^{8} +O(q^{10})\) \(q+(1.75676 + 0.153697i) q^{2} +(1.09297 + 0.192720i) q^{4} +(-0.131866 + 2.23218i) q^{5} +(2.75943 + 1.93217i) q^{7} +(-1.51630 - 0.406292i) q^{8} +(-0.574736 + 3.90113i) q^{10} +(1.11880 - 3.07388i) q^{11} +(0.506571 + 5.79013i) q^{13} +(4.55068 + 3.81848i) q^{14} +(-4.68713 - 1.70598i) q^{16} +(-1.11325 + 0.298295i) q^{17} +(6.40749 - 3.69937i) q^{19} +(-0.574311 + 2.41429i) q^{20} +(2.43791 - 5.22812i) q^{22} +(-1.09807 - 1.56820i) q^{23} +(-4.96522 - 0.588699i) q^{25} +10.2497i q^{26} +(2.64360 + 2.64360i) q^{28} +(-0.381851 + 0.320411i) q^{29} +(0.573116 - 3.25030i) q^{31} +(-5.12653 - 2.39054i) q^{32} +(-2.00157 + 0.352930i) q^{34} +(-4.67682 + 5.90474i) q^{35} +(-1.17991 - 4.40348i) q^{37} +(11.8250 - 5.51409i) q^{38} +(1.10686 - 3.33107i) q^{40} +(1.39279 - 1.65986i) q^{41} +(-1.68889 - 3.62184i) q^{43} +(1.81521 - 3.14404i) q^{44} +(-1.68801 - 2.92372i) q^{46} +(2.84791 - 4.06724i) q^{47} +(1.48701 + 4.08553i) q^{49} +(-8.63222 - 1.79734i) q^{50} +(-0.562207 + 6.42605i) q^{52} +(-1.25033 + 1.25033i) q^{53} +(6.71392 + 2.90271i) q^{55} +(-3.39910 - 4.05089i) q^{56} +(-0.720066 + 0.504196i) q^{58} +(-9.92422 + 3.61212i) q^{59} +(-1.82504 - 10.3503i) q^{61} +(1.50639 - 5.62192i) q^{62} +(0.000691655 + 0.000399327i) q^{64} +(-12.9914 + 0.367231i) q^{65} +(-5.82623 + 0.509729i) q^{67} +(-1.27424 + 0.111481i) q^{68} +(-9.12360 + 9.65440i) q^{70} +(6.62671 + 3.82593i) q^{71} +(-1.84806 + 6.89704i) q^{73} +(-1.39602 - 7.91721i) q^{74} +(7.71612 - 2.80844i) q^{76} +(9.02653 - 6.32044i) q^{77} +(-5.08874 - 6.06452i) q^{79} +(4.42611 - 10.2375i) q^{80} +(2.70191 - 2.70191i) q^{82} +(-0.544416 + 6.22270i) q^{83} +(-0.519047 - 2.52431i) q^{85} +(-2.41031 - 6.62228i) q^{86} +(-2.94533 + 4.20637i) q^{88} +(-0.260380 - 0.450992i) q^{89} +(-9.78968 + 16.9562i) q^{91} +(-0.897929 - 1.92562i) q^{92} +(5.62822 - 6.70745i) q^{94} +(7.41270 + 14.7905i) q^{95} +(4.27963 - 1.99563i) q^{97} +(1.98439 + 7.40585i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.75676 + 0.153697i 1.24222 + 0.108680i 0.689250 0.724523i \(-0.257940\pi\)
0.552967 + 0.833203i \(0.313496\pi\)
\(3\) 0 0
\(4\) 1.09297 + 0.192720i 0.546484 + 0.0963599i
\(5\) −0.131866 + 2.23218i −0.0589725 + 0.998260i
\(6\) 0 0
\(7\) 2.75943 + 1.93217i 1.04297 + 0.730292i 0.963815 0.266570i \(-0.0858904\pi\)
0.0791502 + 0.996863i \(0.474779\pi\)
\(8\) −1.51630 0.406292i −0.536093 0.143646i
\(9\) 0 0
\(10\) −0.574736 + 3.90113i −0.181747 + 1.23365i
\(11\) 1.11880 3.07388i 0.337332 0.926811i −0.648817 0.760945i \(-0.724736\pi\)
0.986148 0.165866i \(-0.0530420\pi\)
\(12\) 0 0
\(13\) 0.506571 + 5.79013i 0.140497 + 1.60589i 0.659893 + 0.751359i \(0.270601\pi\)
−0.519396 + 0.854534i \(0.673843\pi\)
\(14\) 4.55068 + 3.81848i 1.21622 + 1.02053i
\(15\) 0 0
\(16\) −4.68713 1.70598i −1.17178 0.426494i
\(17\) −1.11325 + 0.298295i −0.270003 + 0.0723472i −0.391280 0.920271i \(-0.627968\pi\)
0.121277 + 0.992619i \(0.461301\pi\)
\(18\) 0 0
\(19\) 6.40749 3.69937i 1.46998 0.848693i 0.470546 0.882375i \(-0.344057\pi\)
0.999433 + 0.0336827i \(0.0107236\pi\)
\(20\) −0.574311 + 2.41429i −0.128420 + 0.539851i
\(21\) 0 0
\(22\) 2.43791 5.22812i 0.519765 1.11464i
\(23\) −1.09807 1.56820i −0.228963 0.326993i 0.688189 0.725532i \(-0.258406\pi\)
−0.917151 + 0.398539i \(0.869517\pi\)
\(24\) 0 0
\(25\) −4.96522 0.588699i −0.993044 0.117740i
\(26\) 10.2497i 2.01014i
\(27\) 0 0
\(28\) 2.64360 + 2.64360i 0.499593 + 0.499593i
\(29\) −0.381851 + 0.320411i −0.0709079 + 0.0594988i −0.677553 0.735474i \(-0.736959\pi\)
0.606645 + 0.794973i \(0.292515\pi\)
\(30\) 0 0
\(31\) 0.573116 3.25030i 0.102935 0.583772i −0.889090 0.457732i \(-0.848662\pi\)
0.992025 0.126040i \(-0.0402269\pi\)
\(32\) −5.12653 2.39054i −0.906251 0.422592i
\(33\) 0 0
\(34\) −2.00157 + 0.352930i −0.343266 + 0.0605270i
\(35\) −4.67682 + 5.90474i −0.790528 + 0.998083i
\(36\) 0 0
\(37\) −1.17991 4.40348i −0.193976 0.723928i −0.992530 0.122004i \(-0.961068\pi\)
0.798554 0.601924i \(-0.205599\pi\)
\(38\) 11.8250 5.51409i 1.91827 0.894503i
\(39\) 0 0
\(40\) 1.10686 3.33107i 0.175011 0.526689i
\(41\) 1.39279 1.65986i 0.217517 0.259226i −0.646241 0.763133i \(-0.723660\pi\)
0.863758 + 0.503907i \(0.168105\pi\)
\(42\) 0 0
\(43\) −1.68889 3.62184i −0.257554 0.552325i 0.734431 0.678683i \(-0.237449\pi\)
−0.991985 + 0.126358i \(0.959671\pi\)
\(44\) 1.81521 3.14404i 0.273654 0.473982i
\(45\) 0 0
\(46\) −1.68801 2.92372i −0.248884 0.431080i
\(47\) 2.84791 4.06724i 0.415410 0.593268i −0.555851 0.831282i \(-0.687608\pi\)
0.971262 + 0.238014i \(0.0764965\pi\)
\(48\) 0 0
\(49\) 1.48701 + 4.08553i 0.212430 + 0.583647i
\(50\) −8.63222 1.79734i −1.22078 0.254182i
\(51\) 0 0
\(52\) −0.562207 + 6.42605i −0.0779641 + 0.891133i
\(53\) −1.25033 + 1.25033i −0.171746 + 0.171746i −0.787746 0.616000i \(-0.788752\pi\)
0.616000 + 0.787746i \(0.288752\pi\)
\(54\) 0 0
\(55\) 6.71392 + 2.90271i 0.905305 + 0.391401i
\(56\) −3.39910 4.05089i −0.454223 0.541322i
\(57\) 0 0
\(58\) −0.720066 + 0.504196i −0.0945493 + 0.0662041i
\(59\) −9.92422 + 3.61212i −1.29202 + 0.470258i −0.894391 0.447286i \(-0.852391\pi\)
−0.397633 + 0.917545i \(0.630168\pi\)
\(60\) 0 0
\(61\) −1.82504 10.3503i −0.233672 1.32522i −0.845392 0.534146i \(-0.820633\pi\)
0.611720 0.791074i \(-0.290478\pi\)
\(62\) 1.50639 5.62192i 0.191312 0.713985i
\(63\) 0 0
\(64\) 0.000691655 0 0.000399327i 8.64569e−5 0 4.99159e-5i
\(65\) −12.9914 + 0.367231i −1.61138 + 0.0455494i
\(66\) 0 0
\(67\) −5.82623 + 0.509729i −0.711787 + 0.0622733i −0.437298 0.899317i \(-0.644064\pi\)
−0.274490 + 0.961590i \(0.588509\pi\)
\(68\) −1.27424 + 0.111481i −0.154524 + 0.0135191i
\(69\) 0 0
\(70\) −9.12360 + 9.65440i −1.09048 + 1.15392i
\(71\) 6.62671 + 3.82593i 0.786446 + 0.454055i 0.838710 0.544579i \(-0.183310\pi\)
−0.0522640 + 0.998633i \(0.516644\pi\)
\(72\) 0 0
\(73\) −1.84806 + 6.89704i −0.216299 + 0.807238i 0.769407 + 0.638759i \(0.220552\pi\)
−0.985705 + 0.168478i \(0.946115\pi\)
\(74\) −1.39602 7.91721i −0.162284 0.920357i
\(75\) 0 0
\(76\) 7.71612 2.80844i 0.885100 0.322150i
\(77\) 9.02653 6.32044i 1.02867 0.720281i
\(78\) 0 0
\(79\) −5.08874 6.06452i −0.572528 0.682312i 0.399620 0.916681i \(-0.369142\pi\)
−0.972148 + 0.234369i \(0.924698\pi\)
\(80\) 4.42611 10.2375i 0.494854 1.14459i
\(81\) 0 0
\(82\) 2.70191 2.70191i 0.298375 0.298375i
\(83\) −0.544416 + 6.22270i −0.0597574 + 0.683031i 0.905948 + 0.423389i \(0.139160\pi\)
−0.965705 + 0.259641i \(0.916396\pi\)
\(84\) 0 0
\(85\) −0.519047 2.52431i −0.0562985 0.273800i
\(86\) −2.41031 6.62228i −0.259911 0.714099i
\(87\) 0 0
\(88\) −2.94533 + 4.20637i −0.313974 + 0.448401i
\(89\) −0.260380 0.450992i −0.0276002 0.0478050i 0.851895 0.523712i \(-0.175453\pi\)
−0.879496 + 0.475907i \(0.842120\pi\)
\(90\) 0 0
\(91\) −9.78968 + 16.9562i −1.02624 + 1.77750i
\(92\) −0.897929 1.92562i −0.0936156 0.200759i
\(93\) 0 0
\(94\) 5.62822 6.70745i 0.580506 0.691820i
\(95\) 7.41270 + 14.7905i 0.760527 + 1.51747i
\(96\) 0 0
\(97\) 4.27963 1.99563i 0.434531 0.202625i −0.193029 0.981193i \(-0.561831\pi\)
0.627560 + 0.778568i \(0.284054\pi\)
\(98\) 1.98439 + 7.40585i 0.200454 + 0.748103i
\(99\) 0 0
\(100\) −5.31338 1.60033i −0.531338 0.160033i
\(101\) 6.92843 1.22167i 0.689404 0.121561i 0.182038 0.983291i \(-0.441730\pi\)
0.507366 + 0.861731i \(0.330619\pi\)
\(102\) 0 0
\(103\) 6.34471 + 2.95859i 0.625163 + 0.291518i 0.709268 0.704938i \(-0.249025\pi\)
−0.0841052 + 0.996457i \(0.526803\pi\)
\(104\) 1.58437 8.98539i 0.155360 0.881090i
\(105\) 0 0
\(106\) −2.38870 + 2.00436i −0.232011 + 0.194680i
\(107\) 3.17818 + 3.17818i 0.307247 + 0.307247i 0.843841 0.536594i \(-0.180289\pi\)
−0.536594 + 0.843841i \(0.680289\pi\)
\(108\) 0 0
\(109\) 3.14715i 0.301442i 0.988576 + 0.150721i \(0.0481595\pi\)
−0.988576 + 0.150721i \(0.951840\pi\)
\(110\) 11.3486 + 6.13127i 1.08205 + 0.584593i
\(111\) 0 0
\(112\) −9.63755 13.7639i −0.910663 1.30056i
\(113\) −0.190621 + 0.408788i −0.0179321 + 0.0384556i −0.915070 0.403295i \(-0.867865\pi\)
0.897138 + 0.441751i \(0.145643\pi\)
\(114\) 0 0
\(115\) 3.64530 2.24429i 0.339926 0.209281i
\(116\) −0.479100 + 0.276609i −0.0444833 + 0.0256825i
\(117\) 0 0
\(118\) −17.9897 + 4.82031i −1.65608 + 0.443746i
\(119\) −3.64830 1.32787i −0.334439 0.121726i
\(120\) 0 0
\(121\) 0.229444 + 0.192526i 0.0208585 + 0.0175024i
\(122\) −1.61535 18.4635i −0.146247 1.67161i
\(123\) 0 0
\(124\) 1.25280 3.44203i 0.112504 0.309103i
\(125\) 1.96883 11.0056i 0.176097 0.984373i
\(126\) 0 0
\(127\) 0.534026 + 0.143092i 0.0473871 + 0.0126973i 0.282435 0.959287i \(-0.408858\pi\)
−0.235048 + 0.971984i \(0.575525\pi\)
\(128\) 9.26822 + 6.48968i 0.819203 + 0.573612i
\(129\) 0 0
\(130\) −22.8792 1.35160i −2.00664 0.118543i
\(131\) −14.1236 2.49037i −1.23398 0.217585i −0.481648 0.876365i \(-0.659962\pi\)
−0.752336 + 0.658780i \(0.771073\pi\)
\(132\) 0 0
\(133\) 24.8288 + 2.17224i 2.15293 + 0.188357i
\(134\) −10.3136 −0.890962
\(135\) 0 0
\(136\) 1.80922 0.155139
\(137\) −3.37255 0.295060i −0.288136 0.0252087i −0.0578286 0.998327i \(-0.518418\pi\)
−0.230308 + 0.973118i \(0.573973\pi\)
\(138\) 0 0
\(139\) 5.42140 + 0.955940i 0.459837 + 0.0810818i 0.398768 0.917052i \(-0.369438\pi\)
0.0610693 + 0.998134i \(0.480549\pi\)
\(140\) −6.24958 + 5.55238i −0.528186 + 0.469262i
\(141\) 0 0
\(142\) 11.0535 + 7.73975i 0.927590 + 0.649505i
\(143\) 18.3649 + 4.92087i 1.53575 + 0.411504i
\(144\) 0 0
\(145\) −0.664860 0.894609i −0.0552136 0.0742933i
\(146\) −4.30665 + 11.8324i −0.356420 + 0.979257i
\(147\) 0 0
\(148\) −0.440966 5.04026i −0.0362472 0.414307i
\(149\) 10.1897 + 8.55016i 0.834771 + 0.700456i 0.956381 0.292122i \(-0.0943613\pi\)
−0.121610 + 0.992578i \(0.538806\pi\)
\(150\) 0 0
\(151\) 13.7660 + 5.01040i 1.12026 + 0.407741i 0.834747 0.550634i \(-0.185614\pi\)
0.285512 + 0.958375i \(0.407836\pi\)
\(152\) −11.2187 + 3.00604i −0.909957 + 0.243822i
\(153\) 0 0
\(154\) 16.8289 9.71616i 1.35611 0.782950i
\(155\) 7.17968 + 1.70790i 0.576686 + 0.137182i
\(156\) 0 0
\(157\) −2.34570 + 5.03036i −0.187207 + 0.401467i −0.977402 0.211389i \(-0.932201\pi\)
0.790195 + 0.612855i \(0.209979\pi\)
\(158\) −8.00759 11.4360i −0.637050 0.909802i
\(159\) 0 0
\(160\) 6.01213 11.1281i 0.475300 0.879753i
\(161\) 6.44900i 0.508252i
\(162\) 0 0
\(163\) 5.06235 + 5.06235i 0.396514 + 0.396514i 0.877002 0.480488i \(-0.159540\pi\)
−0.480488 + 0.877002i \(0.659540\pi\)
\(164\) 1.84216 1.54575i 0.143848 0.120703i
\(165\) 0 0
\(166\) −1.91282 + 10.8481i −0.148463 + 0.841978i
\(167\) 12.7047 + 5.92432i 0.983123 + 0.458438i 0.846618 0.532202i \(-0.178635\pi\)
0.136505 + 0.990639i \(0.456413\pi\)
\(168\) 0 0
\(169\) −20.4665 + 3.60879i −1.57434 + 0.277599i
\(170\) −0.523863 4.51439i −0.0401784 0.346238i
\(171\) 0 0
\(172\) −1.14791 4.28404i −0.0875269 0.326655i
\(173\) −8.87248 + 4.13731i −0.674563 + 0.314554i −0.729544 0.683934i \(-0.760268\pi\)
0.0549816 + 0.998487i \(0.482490\pi\)
\(174\) 0 0
\(175\) −12.5637 11.2181i −0.949727 0.848011i
\(176\) −10.4879 + 12.4990i −0.790558 + 0.942151i
\(177\) 0 0
\(178\) −0.388110 0.832304i −0.0290900 0.0623838i
\(179\) −5.82103 + 10.0823i −0.435084 + 0.753588i −0.997303 0.0734009i \(-0.976615\pi\)
0.562218 + 0.826989i \(0.309948\pi\)
\(180\) 0 0
\(181\) −10.5182 18.2180i −0.781810 1.35413i −0.930886 0.365309i \(-0.880963\pi\)
0.149076 0.988826i \(-0.452370\pi\)
\(182\) −19.8042 + 28.2834i −1.46799 + 2.09650i
\(183\) 0 0
\(184\) 1.02785 + 2.82400i 0.0757743 + 0.208188i
\(185\) 9.98494 2.05309i 0.734108 0.150947i
\(186\) 0 0
\(187\) −0.328585 + 3.75574i −0.0240285 + 0.274647i
\(188\) 3.89651 3.89651i 0.284182 0.284182i
\(189\) 0 0
\(190\) 10.7491 + 27.1226i 0.779822 + 1.96768i
\(191\) −16.1454 19.2414i −1.16824 1.39226i −0.903854 0.427841i \(-0.859274\pi\)
−0.264388 0.964416i \(-0.585170\pi\)
\(192\) 0 0
\(193\) −3.27354 + 2.29216i −0.235635 + 0.164993i −0.685430 0.728138i \(-0.740386\pi\)
0.449795 + 0.893132i \(0.351497\pi\)
\(194\) 7.82501 2.84807i 0.561803 0.204480i
\(195\) 0 0
\(196\) 0.837894 + 4.75193i 0.0598496 + 0.339424i
\(197\) −2.68314 + 10.0136i −0.191166 + 0.713441i 0.802060 + 0.597243i \(0.203737\pi\)
−0.993226 + 0.116198i \(0.962929\pi\)
\(198\) 0 0
\(199\) −10.6933 6.17378i −0.758027 0.437647i 0.0705597 0.997508i \(-0.477521\pi\)
−0.828587 + 0.559860i \(0.810855\pi\)
\(200\) 7.28959 + 2.90997i 0.515452 + 0.205766i
\(201\) 0 0
\(202\) 12.3593 1.08130i 0.869601 0.0760802i
\(203\) −1.67278 + 0.146349i −0.117406 + 0.0102717i
\(204\) 0 0
\(205\) 3.52143 + 3.32782i 0.245948 + 0.232425i
\(206\) 10.6914 + 6.17269i 0.744906 + 0.430072i
\(207\) 0 0
\(208\) 7.50345 28.0033i 0.520271 1.94168i
\(209\) −4.20271 23.8347i −0.290707 1.64868i
\(210\) 0 0
\(211\) 8.83540 3.21582i 0.608254 0.221386i −0.0194850 0.999810i \(-0.506203\pi\)
0.627739 + 0.778424i \(0.283980\pi\)
\(212\) −1.60753 + 1.12561i −0.110406 + 0.0773070i
\(213\) 0 0
\(214\) 5.09483 + 6.07178i 0.348275 + 0.415058i
\(215\) 8.30729 3.29230i 0.566553 0.224533i
\(216\) 0 0
\(217\) 7.86162 7.86162i 0.533682 0.533682i
\(218\) −0.483706 + 5.52878i −0.0327607 + 0.374456i
\(219\) 0 0
\(220\) 6.77869 + 4.46647i 0.457019 + 0.301129i
\(221\) −2.29111 6.29477i −0.154117 0.423432i
\(222\) 0 0
\(223\) 8.07893 11.5379i 0.541005 0.772635i −0.451833 0.892102i \(-0.649230\pi\)
0.992838 + 0.119467i \(0.0381186\pi\)
\(224\) −9.52736 16.5019i −0.636573 1.10258i
\(225\) 0 0
\(226\) −0.397705 + 0.688845i −0.0264549 + 0.0458213i
\(227\) 11.1767 + 23.9686i 0.741825 + 1.59085i 0.805301 + 0.592866i \(0.202004\pi\)
−0.0634761 + 0.997983i \(0.520219\pi\)
\(228\) 0 0
\(229\) −6.42008 + 7.65115i −0.424251 + 0.505602i −0.935254 0.353976i \(-0.884829\pi\)
0.511004 + 0.859579i \(0.329274\pi\)
\(230\) 6.74886 3.38240i 0.445007 0.223029i
\(231\) 0 0
\(232\) 0.709181 0.330696i 0.0465600 0.0217113i
\(233\) −7.01401 26.1766i −0.459503 1.71489i −0.674500 0.738274i \(-0.735641\pi\)
0.214997 0.976615i \(-0.431026\pi\)
\(234\) 0 0
\(235\) 8.70325 + 6.89337i 0.567737 + 0.449674i
\(236\) −11.5430 + 2.03534i −0.751385 + 0.132489i
\(237\) 0 0
\(238\) −6.20510 2.89348i −0.402217 0.187557i
\(239\) −4.31982 + 24.4989i −0.279426 + 1.58470i 0.445117 + 0.895472i \(0.353162\pi\)
−0.724543 + 0.689230i \(0.757949\pi\)
\(240\) 0 0
\(241\) −21.8499 + 18.3342i −1.40747 + 1.18101i −0.449808 + 0.893125i \(0.648508\pi\)
−0.957665 + 0.287885i \(0.907048\pi\)
\(242\) 0.373487 + 0.373487i 0.0240087 + 0.0240087i
\(243\) 0 0
\(244\) 11.6643i 0.746728i
\(245\) −9.31571 + 2.78053i −0.595159 + 0.177641i
\(246\) 0 0
\(247\) 24.6656 + 35.2262i 1.56944 + 2.24139i
\(248\) −2.18959 + 4.69559i −0.139039 + 0.298170i
\(249\) 0 0
\(250\) 5.15028 19.0316i 0.325732 1.20367i
\(251\) −9.61601 + 5.55181i −0.606957 + 0.350427i −0.771774 0.635897i \(-0.780630\pi\)
0.164816 + 0.986324i \(0.447297\pi\)
\(252\) 0 0
\(253\) −6.04899 + 1.62082i −0.380297 + 0.101900i
\(254\) 0.916163 + 0.333456i 0.0574852 + 0.0209229i
\(255\) 0 0
\(256\) 15.2834 + 12.8243i 0.955211 + 0.801518i
\(257\) −2.45897 28.1062i −0.153386 1.75321i −0.549941 0.835203i \(-0.685350\pi\)
0.396555 0.918011i \(-0.370206\pi\)
\(258\) 0 0
\(259\) 5.25241 14.4309i 0.326369 0.896691i
\(260\) −14.2700 2.10233i −0.884985 0.130381i
\(261\) 0 0
\(262\) −24.4290 6.54573i −1.50923 0.404397i
\(263\) −2.02429 1.41742i −0.124823 0.0874019i 0.509498 0.860472i \(-0.329831\pi\)
−0.634321 + 0.773070i \(0.718720\pi\)
\(264\) 0 0
\(265\) −2.62608 2.95583i −0.161319 0.181575i
\(266\) 43.2844 + 7.63221i 2.65394 + 0.467961i
\(267\) 0 0
\(268\) −6.46612 0.565712i −0.394981 0.0345564i
\(269\) −2.07465 −0.126494 −0.0632468 0.997998i \(-0.520146\pi\)
−0.0632468 + 0.997998i \(0.520146\pi\)
\(270\) 0 0
\(271\) −18.0921 −1.09901 −0.549507 0.835489i \(-0.685184\pi\)
−0.549507 + 0.835489i \(0.685184\pi\)
\(272\) 5.72684 + 0.501034i 0.347241 + 0.0303796i
\(273\) 0 0
\(274\) −5.87941 1.03670i −0.355188 0.0626293i
\(275\) −7.36469 + 14.6039i −0.444108 + 0.880647i
\(276\) 0 0
\(277\) 21.0713 + 14.7543i 1.26605 + 0.886497i 0.997058 0.0766456i \(-0.0244210\pi\)
0.268991 + 0.963143i \(0.413310\pi\)
\(278\) 9.37718 + 2.51261i 0.562406 + 0.150696i
\(279\) 0 0
\(280\) 9.49052 7.05321i 0.567167 0.421510i
\(281\) −0.952631 + 2.61733i −0.0568292 + 0.156137i −0.964859 0.262769i \(-0.915364\pi\)
0.908029 + 0.418906i \(0.137586\pi\)
\(282\) 0 0
\(283\) 1.78620 + 20.4164i 0.106179 + 1.21363i 0.843140 + 0.537694i \(0.180704\pi\)
−0.736962 + 0.675935i \(0.763740\pi\)
\(284\) 6.50545 + 5.45872i 0.386028 + 0.323916i
\(285\) 0 0
\(286\) 31.5065 + 11.4674i 1.86302 + 0.678083i
\(287\) 7.05042 1.88915i 0.416173 0.111513i
\(288\) 0 0
\(289\) −13.5721 + 7.83584i −0.798358 + 0.460932i
\(290\) −1.03050 1.67380i −0.0605131 0.0982890i
\(291\) 0 0
\(292\) −3.34907 + 7.18209i −0.195989 + 0.420300i
\(293\) 17.9864 + 25.6873i 1.05078 + 1.50067i 0.854036 + 0.520213i \(0.174148\pi\)
0.196743 + 0.980455i \(0.436964\pi\)
\(294\) 0 0
\(295\) −6.75422 22.6289i −0.393246 1.31751i
\(296\) 7.15639i 0.415957i
\(297\) 0 0
\(298\) 16.5867 + 16.5867i 0.960842 + 0.960842i
\(299\) 8.52385 7.15236i 0.492947 0.413631i
\(300\) 0 0
\(301\) 2.33764 13.2574i 0.134740 0.764146i
\(302\) 23.4134 + 10.9179i 1.34729 + 0.628252i
\(303\) 0 0
\(304\) −36.3437 + 6.40838i −2.08446 + 0.367546i
\(305\) 23.3444 2.70895i 1.33669 0.155114i
\(306\) 0 0
\(307\) 2.49145 + 9.29823i 0.142195 + 0.530678i 0.999864 + 0.0164767i \(0.00524495\pi\)
−0.857669 + 0.514201i \(0.828088\pi\)
\(308\) 11.0838 5.16845i 0.631557 0.294500i
\(309\) 0 0
\(310\) 12.3505 + 4.10387i 0.701460 + 0.233084i
\(311\) 0.00272616 0.00324891i 0.000154586 0.000184229i −0.765967 0.642880i \(-0.777740\pi\)
0.766122 + 0.642695i \(0.222184\pi\)
\(312\) 0 0
\(313\) −10.0379 21.5265i −0.567378 1.21675i −0.955460 0.295122i \(-0.904640\pi\)
0.388081 0.921625i \(-0.373138\pi\)
\(314\) −4.89398 + 8.47662i −0.276183 + 0.478363i
\(315\) 0 0
\(316\) −4.39308 7.60903i −0.247130 0.428041i
\(317\) −0.455273 + 0.650197i −0.0255707 + 0.0365187i −0.831734 0.555175i \(-0.812651\pi\)
0.806163 + 0.591693i \(0.201540\pi\)
\(318\) 0 0
\(319\) 0.557690 + 1.53224i 0.0312246 + 0.0857890i
\(320\) −0.000982575 0.00149124i −5.49276e−5 8.33628e-5i
\(321\) 0 0
\(322\) 0.991189 11.3293i 0.0552368 0.631359i
\(323\) −6.02965 + 6.02965i −0.335499 + 0.335499i
\(324\) 0 0
\(325\) 0.893405 29.0475i 0.0495572 1.61127i
\(326\) 8.11527 + 9.67140i 0.449463 + 0.535649i
\(327\) 0 0
\(328\) −2.78627 + 1.95097i −0.153846 + 0.107724i
\(329\) 15.7172 5.72060i 0.866518 0.315387i
\(330\) 0 0
\(331\) −0.994980 5.64281i −0.0546891 0.310157i 0.945176 0.326560i \(-0.105890\pi\)
−0.999865 + 0.0164031i \(0.994778\pi\)
\(332\) −1.79427 + 6.69630i −0.0984733 + 0.367507i
\(333\) 0 0
\(334\) 21.4086 + 12.3603i 1.17143 + 0.676325i
\(335\) −0.369521 13.0724i −0.0201891 0.714221i
\(336\) 0 0
\(337\) −25.4396 + 2.22568i −1.38578 + 0.121240i −0.755512 0.655135i \(-0.772612\pi\)
−0.630271 + 0.776375i \(0.717056\pi\)
\(338\) −36.5094 + 3.19415i −1.98585 + 0.173739i
\(339\) 0 0
\(340\) −0.0808168 2.85902i −0.00438291 0.155052i
\(341\) −9.34986 5.39814i −0.506323 0.292326i
\(342\) 0 0
\(343\) 2.31243 8.63010i 0.124859 0.465982i
\(344\) 1.08934 + 6.17798i 0.0587335 + 0.333094i
\(345\) 0 0
\(346\) −16.2227 + 5.90459i −0.872139 + 0.317433i
\(347\) −9.96940 + 6.98065i −0.535185 + 0.374741i −0.809702 0.586842i \(-0.800371\pi\)
0.274516 + 0.961582i \(0.411482\pi\)
\(348\) 0 0
\(349\) −0.0762364 0.0908550i −0.00408084 0.00486336i 0.764000 0.645216i \(-0.223233\pi\)
−0.768081 + 0.640353i \(0.778788\pi\)
\(350\) −20.3472 21.6386i −1.08761 1.15663i
\(351\) 0 0
\(352\) −13.0838 + 13.0838i −0.697370 + 0.697370i
\(353\) 1.88537 21.5499i 0.100348 1.14699i −0.764387 0.644758i \(-0.776958\pi\)
0.864735 0.502228i \(-0.167486\pi\)
\(354\) 0 0
\(355\) −9.41400 + 14.2875i −0.499643 + 0.758300i
\(356\) −0.197672 0.543100i −0.0104766 0.0287842i
\(357\) 0 0
\(358\) −11.7758 + 16.8175i −0.622369 + 0.888835i
\(359\) −15.2804 26.4664i −0.806468 1.39684i −0.915296 0.402782i \(-0.868043\pi\)
0.108828 0.994061i \(-0.465290\pi\)
\(360\) 0 0
\(361\) 17.8706 30.9528i 0.940558 1.62910i
\(362\) −15.6779 33.6213i −0.824011 1.76710i
\(363\) 0 0
\(364\) −13.9676 + 16.6460i −0.732102 + 0.872485i
\(365\) −15.1517 5.03468i −0.793077 0.263527i
\(366\) 0 0
\(367\) −13.9364 + 6.49863i −0.727472 + 0.339226i −0.750825 0.660502i \(-0.770344\pi\)
0.0233530 + 0.999727i \(0.492566\pi\)
\(368\) 2.47147 + 9.22364i 0.128834 + 0.480816i
\(369\) 0 0
\(370\) 17.8567 2.07214i 0.928326 0.107726i
\(371\) −5.86604 + 1.03434i −0.304550 + 0.0537003i
\(372\) 0 0
\(373\) −25.2501 11.7743i −1.30740 0.609651i −0.360976 0.932575i \(-0.617556\pi\)
−0.946425 + 0.322924i \(0.895334\pi\)
\(374\) −1.15449 + 6.54744i −0.0596973 + 0.338560i
\(375\) 0 0
\(376\) −5.97077 + 5.01007i −0.307919 + 0.258375i
\(377\) −2.04865 2.04865i −0.105511 0.105511i
\(378\) 0 0
\(379\) 16.6622i 0.855880i 0.903807 + 0.427940i \(0.140760\pi\)
−0.903807 + 0.427940i \(0.859240\pi\)
\(380\) 5.25143 + 17.5941i 0.269393 + 0.902558i
\(381\) 0 0
\(382\) −25.4063 36.2840i −1.29990 1.85645i
\(383\) 13.4360 28.8135i 0.686546 1.47230i −0.185381 0.982667i \(-0.559352\pi\)
0.871927 0.489636i \(-0.162870\pi\)
\(384\) 0 0
\(385\) 12.9180 + 20.9823i 0.658365 + 1.06935i
\(386\) −6.10313 + 3.52364i −0.310641 + 0.179349i
\(387\) 0 0
\(388\) 5.06210 1.35639i 0.256989 0.0688601i
\(389\) 10.3645 + 3.77237i 0.525501 + 0.191267i 0.591128 0.806577i \(-0.298683\pi\)
−0.0656273 + 0.997844i \(0.520905\pi\)
\(390\) 0 0
\(391\) 1.69021 + 1.41826i 0.0854778 + 0.0717244i
\(392\) −0.594840 6.79905i −0.0300440 0.343404i
\(393\) 0 0
\(394\) −6.25270 + 17.1791i −0.315006 + 0.865473i
\(395\) 14.2081 10.5593i 0.714888 0.531294i
\(396\) 0 0
\(397\) −15.3279 4.10710i −0.769286 0.206129i −0.147230 0.989102i \(-0.547036\pi\)
−0.622056 + 0.782973i \(0.713702\pi\)
\(398\) −17.8367 12.4894i −0.894071 0.626035i
\(399\) 0 0
\(400\) 22.2683 + 11.2299i 1.11342 + 0.561493i
\(401\) 18.2547 + 3.21880i 0.911598 + 0.160739i 0.609729 0.792610i \(-0.291278\pi\)
0.301869 + 0.953349i \(0.402389\pi\)
\(402\) 0 0
\(403\) 19.1100 + 1.67191i 0.951937 + 0.0832837i
\(404\) 7.80799 0.388462
\(405\) 0 0
\(406\) −2.96116 −0.146960
\(407\) −14.8559 1.29972i −0.736379 0.0644248i
\(408\) 0 0
\(409\) 15.3828 + 2.71240i 0.760628 + 0.134119i 0.540491 0.841350i \(-0.318238\pi\)
0.220137 + 0.975469i \(0.429350\pi\)
\(410\) 5.67484 + 6.38742i 0.280260 + 0.315452i
\(411\) 0 0
\(412\) 6.36439 + 4.45640i 0.313551 + 0.219551i
\(413\) −34.3644 9.20792i −1.69096 0.453092i
\(414\) 0 0
\(415\) −13.8184 2.03580i −0.678318 0.0999334i
\(416\) 11.2446 30.8943i 0.551311 1.51472i
\(417\) 0 0
\(418\) −3.71983 42.5179i −0.181943 2.07962i
\(419\) −8.40402 7.05181i −0.410563 0.344503i 0.413996 0.910279i \(-0.364133\pi\)
−0.824560 + 0.565775i \(0.808577\pi\)
\(420\) 0 0
\(421\) −4.13716 1.50580i −0.201633 0.0733884i 0.239230 0.970963i \(-0.423105\pi\)
−0.440863 + 0.897575i \(0.645327\pi\)
\(422\) 16.0159 4.29146i 0.779644 0.208905i
\(423\) 0 0
\(424\) 2.40387 1.38788i 0.116742 0.0674012i
\(425\) 5.70315 0.825732i 0.276644 0.0400539i
\(426\) 0 0
\(427\) 14.9625 32.0872i 0.724086 1.55281i
\(428\) 2.86115 + 4.08615i 0.138299 + 0.197512i
\(429\) 0 0
\(430\) 15.0999 4.50699i 0.728184 0.217346i
\(431\) 22.9617i 1.10603i −0.833173 0.553013i \(-0.813478\pi\)
0.833173 0.553013i \(-0.186522\pi\)
\(432\) 0 0
\(433\) −11.8168 11.8168i −0.567878 0.567878i 0.363655 0.931534i \(-0.381529\pi\)
−0.931534 + 0.363655i \(0.881529\pi\)
\(434\) 15.0193 12.6027i 0.720949 0.604948i
\(435\) 0 0
\(436\) −0.606518 + 3.43973i −0.0290469 + 0.164733i
\(437\) −12.8372 5.98609i −0.614087 0.286353i
\(438\) 0 0
\(439\) 15.4676 2.72735i 0.738226 0.130169i 0.208124 0.978103i \(-0.433264\pi\)
0.530103 + 0.847933i \(0.322153\pi\)
\(440\) −9.00098 7.12918i −0.429105 0.339871i
\(441\) 0 0
\(442\) −3.05744 11.4105i −0.145428 0.542744i
\(443\) −21.0959 + 9.83716i −1.00229 + 0.467378i −0.853278 0.521457i \(-0.825389\pi\)
−0.149017 + 0.988835i \(0.547611\pi\)
\(444\) 0 0
\(445\) 1.04103 0.521744i 0.0493495 0.0247330i
\(446\) 15.9661 19.0276i 0.756016 0.900984i
\(447\) 0 0
\(448\) 0.00113700 + 0.00243831i 5.37184e−5 + 0.000115199i
\(449\) −15.4027 + 26.6783i −0.726900 + 1.25903i 0.231288 + 0.972885i \(0.425706\pi\)
−0.958187 + 0.286142i \(0.907627\pi\)
\(450\) 0 0
\(451\) −3.54396 6.13831i −0.166878 0.289042i
\(452\) −0.287125 + 0.410056i −0.0135052 + 0.0192874i
\(453\) 0 0
\(454\) 15.9509 + 43.8248i 0.748615 + 2.05680i
\(455\) −36.5584 24.0883i −1.71388 1.12927i
\(456\) 0 0
\(457\) 2.28713 26.1420i 0.106988 1.22287i −0.732985 0.680245i \(-0.761874\pi\)
0.839973 0.542629i \(-0.182571\pi\)
\(458\) −12.4545 + 12.4545i −0.581961 + 0.581961i
\(459\) 0 0
\(460\) 4.41672 1.75041i 0.205931 0.0816134i
\(461\) 12.6198 + 15.0397i 0.587761 + 0.700467i 0.975174 0.221440i \(-0.0710756\pi\)
−0.387413 + 0.921906i \(0.626631\pi\)
\(462\) 0 0
\(463\) −6.86273 + 4.80533i −0.318938 + 0.223323i −0.722072 0.691818i \(-0.756810\pi\)
0.403134 + 0.915141i \(0.367921\pi\)
\(464\) 2.33640 0.850378i 0.108464 0.0394778i
\(465\) 0 0
\(466\) −8.29867 47.0641i −0.384429 2.18020i
\(467\) 0.507459 1.89386i 0.0234824 0.0876375i −0.953190 0.302371i \(-0.902222\pi\)
0.976673 + 0.214734i \(0.0688884\pi\)
\(468\) 0 0
\(469\) −17.0619 9.85072i −0.787847 0.454864i
\(470\) 14.2300 + 13.4477i 0.656382 + 0.620294i
\(471\) 0 0
\(472\) 16.5157 1.44494i 0.760196 0.0665085i
\(473\) −13.0227 + 1.13933i −0.598782 + 0.0523867i
\(474\) 0 0
\(475\) −33.9924 + 14.5961i −1.55968 + 0.669715i
\(476\) −3.73157 2.15442i −0.171036 0.0987478i
\(477\) 0 0
\(478\) −11.3543 + 42.3747i −0.519333 + 1.93818i
\(479\) 3.17060 + 17.9814i 0.144868 + 0.821589i 0.967473 + 0.252975i \(0.0814091\pi\)
−0.822604 + 0.568614i \(0.807480\pi\)
\(480\) 0 0
\(481\) 24.8990 9.06251i 1.13530 0.413215i
\(482\) −41.2029 + 28.8506i −1.87674 + 1.31411i
\(483\) 0 0
\(484\) 0.213671 + 0.254643i 0.00971233 + 0.0115747i
\(485\) 3.89025 + 9.81605i 0.176647 + 0.445724i
\(486\) 0 0
\(487\) −23.0616 + 23.0616i −1.04502 + 1.04502i −0.0460835 + 0.998938i \(0.514674\pi\)
−0.998938 + 0.0460835i \(0.985326\pi\)
\(488\) −1.43793 + 16.4357i −0.0650922 + 0.744008i
\(489\) 0 0
\(490\) −16.7928 + 3.45293i −0.758623 + 0.155987i
\(491\) −1.13497 3.11830i −0.0512204 0.140727i 0.911444 0.411423i \(-0.134968\pi\)
−0.962665 + 0.270697i \(0.912746\pi\)
\(492\) 0 0
\(493\) 0.329519 0.470602i 0.0148408 0.0211949i
\(494\) 37.9175 + 65.6750i 1.70599 + 2.95486i
\(495\) 0 0
\(496\) −8.23121 + 14.2569i −0.369592 + 0.640153i
\(497\) 10.8936 + 23.3613i 0.488643 + 1.04790i
\(498\) 0 0
\(499\) 4.13042 4.92245i 0.184903 0.220359i −0.665628 0.746284i \(-0.731836\pi\)
0.850531 + 0.525925i \(0.176281\pi\)
\(500\) 4.27287 11.6494i 0.191088 0.520976i
\(501\) 0 0
\(502\) −17.7463 + 8.27524i −0.792057 + 0.369342i
\(503\) −1.67013 6.23303i −0.0744676 0.277917i 0.918644 0.395085i \(-0.129285\pi\)
−0.993112 + 0.117168i \(0.962618\pi\)
\(504\) 0 0
\(505\) 1.81335 + 15.6266i 0.0806931 + 0.695373i
\(506\) −10.8757 + 1.91769i −0.483486 + 0.0852516i
\(507\) 0 0
\(508\) 0.556097 + 0.259312i 0.0246728 + 0.0115051i
\(509\) 2.35893 13.3781i 0.104558 0.592976i −0.886838 0.462080i \(-0.847103\pi\)
0.991396 0.130896i \(-0.0417854\pi\)
\(510\) 0 0
\(511\) −18.4259 + 15.4611i −0.815112 + 0.683960i
\(512\) 8.87720 + 8.87720i 0.392320 + 0.392320i
\(513\) 0 0
\(514\) 49.7537i 2.19454i
\(515\) −7.44075 + 13.7724i −0.327878 + 0.606884i
\(516\) 0 0
\(517\) −9.31597 13.3046i −0.409716 0.585135i
\(518\) 11.4452 24.5443i 0.502874 1.07842i
\(519\) 0 0
\(520\) 19.8481 + 4.72146i 0.870395 + 0.207050i
\(521\) 26.9126 15.5380i 1.17906 0.680731i 0.223263 0.974758i \(-0.428329\pi\)
0.955797 + 0.294027i \(0.0949957\pi\)
\(522\) 0 0
\(523\) 3.82198 1.02410i 0.167124 0.0447807i −0.174287 0.984695i \(-0.555762\pi\)
0.341411 + 0.939914i \(0.389095\pi\)
\(524\) −14.9567 5.44379i −0.653386 0.237813i
\(525\) 0 0
\(526\) −3.33833 2.80120i −0.145558 0.122138i
\(527\) 0.331527 + 3.78937i 0.0144415 + 0.165068i
\(528\) 0 0
\(529\) 6.61296 18.1689i 0.287520 0.789954i
\(530\) −4.15909 5.59630i −0.180659 0.243088i
\(531\) 0 0
\(532\) 26.7185 + 7.15919i 1.15839 + 0.310390i
\(533\) 10.3163 + 7.22357i 0.446850 + 0.312888i
\(534\) 0 0
\(535\) −7.51336 + 6.67517i −0.324831 + 0.288593i
\(536\) 9.04142 + 1.59425i 0.390530 + 0.0688609i
\(537\) 0 0
\(538\) −3.64466 0.318866i −0.157132 0.0137473i
\(539\) 14.2221 0.612590
\(540\) 0 0
\(541\) 43.8935 1.88713 0.943565 0.331186i \(-0.107449\pi\)
0.943565 + 0.331186i \(0.107449\pi\)
\(542\) −31.7834 2.78069i −1.36521 0.119441i
\(543\) 0 0
\(544\) 6.42021 + 1.13206i 0.275264 + 0.0485365i
\(545\) −7.02499 0.415003i −0.300917 0.0177768i
\(546\) 0 0
\(547\) −19.7055 13.7979i −0.842546 0.589957i 0.0706388 0.997502i \(-0.477496\pi\)
−0.913185 + 0.407545i \(0.866385\pi\)
\(548\) −3.62923 0.972448i −0.155033 0.0415409i
\(549\) 0 0
\(550\) −15.1826 + 24.5236i −0.647387 + 1.04569i
\(551\) −1.26139 + 3.46563i −0.0537369 + 0.147641i
\(552\) 0 0
\(553\) −2.32430 26.5669i −0.0988395 1.12974i
\(554\) 34.7495 + 29.1583i 1.47636 + 1.23882i
\(555\) 0 0
\(556\) 5.74120 + 2.08962i 0.243481 + 0.0886198i
\(557\) 25.5871 6.85604i 1.08416 0.290500i 0.327861 0.944726i \(-0.393672\pi\)
0.756299 + 0.654226i \(0.227006\pi\)
\(558\) 0 0
\(559\) 20.1154 11.6136i 0.850790 0.491204i
\(560\) 31.9942 19.6977i 1.35200 0.832381i
\(561\) 0 0
\(562\) −2.07582 + 4.45161i −0.0875632 + 0.187780i
\(563\) 12.3664 + 17.6610i 0.521181 + 0.744323i 0.990320 0.138801i \(-0.0443248\pi\)
−0.469140 + 0.883124i \(0.655436\pi\)
\(564\) 0 0
\(565\) −0.887351 0.479406i −0.0373311 0.0201687i
\(566\) 36.1412i 1.51913i
\(567\) 0 0
\(568\) −8.49364 8.49364i −0.356385 0.356385i
\(569\) −8.77990 + 7.36721i −0.368073 + 0.308850i −0.807999 0.589184i \(-0.799449\pi\)
0.439926 + 0.898034i \(0.355005\pi\)
\(570\) 0 0
\(571\) 1.87072 10.6094i 0.0782872 0.443989i −0.920317 0.391173i \(-0.872069\pi\)
0.998604 0.0528155i \(-0.0168195\pi\)
\(572\) 19.1239 + 8.91764i 0.799612 + 0.372865i
\(573\) 0 0
\(574\) 12.6763 2.23517i 0.529097 0.0932940i
\(575\) 4.52895 + 8.43290i 0.188870 + 0.351676i
\(576\) 0 0
\(577\) 6.65499 + 24.8368i 0.277051 + 1.03397i 0.954454 + 0.298357i \(0.0964385\pi\)
−0.677403 + 0.735612i \(0.736895\pi\)
\(578\) −25.0472 + 11.6797i −1.04183 + 0.485812i
\(579\) 0 0
\(580\) −0.554262 1.10591i −0.0230145 0.0459205i
\(581\) −13.5256 + 16.1192i −0.561137 + 0.668737i
\(582\) 0 0
\(583\) 2.44449 + 5.24223i 0.101241 + 0.217111i
\(584\) 5.60442 9.70714i 0.231913 0.401684i
\(585\) 0 0
\(586\) 27.6498 + 47.8909i 1.14220 + 1.97835i
\(587\) 21.1711 30.2354i 0.873824 1.24795i −0.0938095 0.995590i \(-0.529904\pi\)
0.967633 0.252360i \(-0.0812067\pi\)
\(588\) 0 0
\(589\) −8.35183 22.9465i −0.344131 0.945492i
\(590\) −8.38756 40.7917i −0.345310 1.67937i
\(591\) 0 0
\(592\) −1.98184 + 22.6526i −0.0814533 + 0.931016i
\(593\) 21.8217 21.8217i 0.896109 0.896109i −0.0989808 0.995089i \(-0.531558\pi\)
0.995089 + 0.0989808i \(0.0315582\pi\)
\(594\) 0 0
\(595\) 3.44513 7.96854i 0.141237 0.326678i
\(596\) 9.48922 + 11.3088i 0.388693 + 0.463227i
\(597\) 0 0
\(598\) 16.0736 11.2549i 0.657300 0.460247i
\(599\) −16.2128 + 5.90099i −0.662438 + 0.241108i −0.651289 0.758830i \(-0.725771\pi\)
−0.0111496 + 0.999938i \(0.503549\pi\)
\(600\) 0 0
\(601\) 7.91812 + 44.9059i 0.322987 + 1.83175i 0.523460 + 0.852050i \(0.324641\pi\)
−0.200473 + 0.979699i \(0.564248\pi\)
\(602\) 6.14430 22.9308i 0.250423 0.934592i
\(603\) 0 0
\(604\) 14.0802 + 8.12919i 0.572914 + 0.330772i
\(605\) −0.460008 + 0.486771i −0.0187020 + 0.0197901i
\(606\) 0 0
\(607\) 47.7085 4.17395i 1.93643 0.169416i 0.947703 0.319153i \(-0.103398\pi\)
0.988726 + 0.149737i \(0.0478428\pi\)
\(608\) −41.6917 + 3.64755i −1.69082 + 0.147928i
\(609\) 0 0
\(610\) 41.4268 1.17102i 1.67732 0.0474133i
\(611\) 24.9925 + 14.4294i 1.01109 + 0.583752i
\(612\) 0 0
\(613\) −4.15240 + 15.4970i −0.167714 + 0.625916i 0.829965 + 0.557816i \(0.188360\pi\)
−0.997678 + 0.0681004i \(0.978306\pi\)
\(614\) 2.94778 + 16.7177i 0.118963 + 0.674671i
\(615\) 0 0
\(616\) −16.2549 + 5.91629i −0.654927 + 0.238374i
\(617\) −20.9035 + 14.6368i −0.841541 + 0.589254i −0.912894 0.408198i \(-0.866157\pi\)
0.0713522 + 0.997451i \(0.477269\pi\)
\(618\) 0 0
\(619\) 27.5321 + 32.8114i 1.10661 + 1.31880i 0.943193 + 0.332245i \(0.107806\pi\)
0.163414 + 0.986558i \(0.447749\pi\)
\(620\) 7.51802 + 3.25035i 0.301931 + 0.130537i
\(621\) 0 0
\(622\) 0.00528856 0.00528856i 0.000212052 0.000212052i
\(623\) 0.152893 1.74758i 0.00612554 0.0700152i
\(624\) 0 0
\(625\) 24.3069 + 5.84604i 0.972275 + 0.233842i
\(626\) −14.3257 39.3596i −0.572571 1.57313i
\(627\) 0 0
\(628\) −3.53322 + 5.04597i −0.140991 + 0.201356i
\(629\) 2.62708 + 4.55023i 0.104748 + 0.181430i
\(630\) 0 0
\(631\) −6.58555 + 11.4065i −0.262167 + 0.454086i −0.966817 0.255468i \(-0.917770\pi\)
0.704651 + 0.709554i \(0.251104\pi\)
\(632\) 5.25209 + 11.2631i 0.208917 + 0.448024i
\(633\) 0 0
\(634\) −0.899738 + 1.07227i −0.0357332 + 0.0425851i
\(635\) −0.389826 + 1.17317i −0.0154698 + 0.0465559i
\(636\) 0 0
\(637\) −22.9025 + 10.6796i −0.907429 + 0.423141i
\(638\) 0.744227 + 2.77749i 0.0294642 + 0.109962i
\(639\) 0 0
\(640\) −15.7083 + 19.8325i −0.620924 + 0.783950i
\(641\) −2.12742 + 0.375121i −0.0840278 + 0.0148164i −0.215504 0.976503i \(-0.569139\pi\)
0.131476 + 0.991319i \(0.458028\pi\)
\(642\) 0 0
\(643\) 4.05710 + 1.89186i 0.159996 + 0.0746075i 0.500967 0.865466i \(-0.332978\pi\)
−0.340970 + 0.940074i \(0.610756\pi\)
\(644\) 1.24285 7.04855i 0.0489751 0.277752i
\(645\) 0 0
\(646\) −11.5194 + 9.66592i −0.453224 + 0.380300i
\(647\) 35.0743 + 35.0743i 1.37891 + 1.37891i 0.846461 + 0.532451i \(0.178729\pi\)
0.532451 + 0.846461i \(0.321271\pi\)
\(648\) 0 0
\(649\) 34.5472i 1.35609i
\(650\) 6.03400 50.8922i 0.236673 1.99616i
\(651\) 0 0
\(652\) 4.55737 + 6.50860i 0.178481 + 0.254897i
\(653\) −1.35569 + 2.90729i −0.0530523 + 0.113771i −0.931047 0.364899i \(-0.881103\pi\)
0.877995 + 0.478670i \(0.158881\pi\)
\(654\) 0 0
\(655\) 7.42137 31.1979i 0.289977 1.21900i
\(656\) −9.35984 + 5.40391i −0.365440 + 0.210987i
\(657\) 0 0
\(658\) 28.4906 7.63403i 1.11068 0.297606i
\(659\) 16.5503 + 6.02381i 0.644708 + 0.234654i 0.643620 0.765345i \(-0.277432\pi\)
0.00108739 + 0.999999i \(0.499654\pi\)
\(660\) 0 0
\(661\) −31.9596 26.8173i −1.24309 1.04307i −0.997276 0.0737542i \(-0.976502\pi\)
−0.245809 0.969318i \(-0.579054\pi\)
\(662\) −0.880660 10.0660i −0.0342278 0.391226i
\(663\) 0 0
\(664\) 3.35373 9.21430i 0.130150 0.357584i
\(665\) −8.12291 + 55.1358i −0.314993 + 2.13808i
\(666\) 0 0
\(667\) 0.921766 + 0.246987i 0.0356909 + 0.00956336i
\(668\) 12.7441 + 8.92355i 0.493086 + 0.345263i
\(669\) 0 0
\(670\) 1.36002 23.0218i 0.0525423 0.889412i
\(671\) −33.8575 5.96999i −1.30705 0.230469i
\(672\) 0 0
\(673\) −7.51557 0.657527i −0.289704 0.0253458i −0.0586226 0.998280i \(-0.518671\pi\)
−0.231081 + 0.972934i \(0.574226\pi\)
\(674\) −45.0333 −1.73462
\(675\) 0 0
\(676\) −23.0647 −0.887104
\(677\) 20.9561 + 1.83342i 0.805407 + 0.0704639i 0.482420 0.875940i \(-0.339758\pi\)
0.322986 + 0.946404i \(0.395313\pi\)
\(678\) 0 0
\(679\) 15.6652 + 2.76220i 0.601177 + 0.106004i
\(680\) −0.238576 + 4.03850i −0.00914896 + 0.154869i
\(681\) 0 0
\(682\) −15.5958 10.9203i −0.597193 0.418159i
\(683\) −4.72063 1.26489i −0.180630 0.0483997i 0.167370 0.985894i \(-0.446472\pi\)
−0.348000 + 0.937494i \(0.613139\pi\)
\(684\) 0 0
\(685\) 1.10335 7.48922i 0.0421569 0.286148i
\(686\) 5.38880 14.8056i 0.205745 0.565281i
\(687\) 0 0
\(688\) 1.73728 + 19.8572i 0.0662333 + 0.757050i
\(689\) −7.87294 6.60618i −0.299935 0.251676i
\(690\) 0 0
\(691\) 39.6616 + 14.4357i 1.50880 + 0.549158i 0.958322 0.285692i \(-0.0922233\pi\)
0.550478 + 0.834850i \(0.314445\pi\)
\(692\) −10.4947 + 2.81204i −0.398948 + 0.106898i
\(693\) 0 0
\(694\) −18.5867 + 10.7311i −0.705543 + 0.407346i
\(695\) −2.84873 + 11.9755i −0.108058 + 0.454256i
\(696\) 0 0
\(697\) −1.05540 + 2.26330i −0.0399759 + 0.0857287i
\(698\) −0.119965 0.171328i −0.00454074 0.00648485i
\(699\) 0 0
\(700\) −11.5698 14.6823i −0.437296 0.554940i
\(701\) 3.71261i 0.140223i −0.997539 0.0701117i \(-0.977664\pi\)
0.997539 0.0701117i \(-0.0223356\pi\)
\(702\) 0 0
\(703\) −23.8504 23.8504i −0.899533 0.899533i
\(704\) 0.00200131 0.00167930i 7.54273e−5 6.32910e-5i
\(705\) 0 0
\(706\) 6.62429 37.5682i 0.249309 1.41390i
\(707\) 21.4790 + 10.0158i 0.807800 + 0.376683i
\(708\) 0 0
\(709\) −18.4462 + 3.25257i −0.692763 + 0.122153i −0.508934 0.860805i \(-0.669960\pi\)
−0.183829 + 0.982958i \(0.558849\pi\)
\(710\) −18.7341 + 23.6528i −0.703077 + 0.887673i
\(711\) 0 0
\(712\) 0.211580 + 0.789629i 0.00792931 + 0.0295926i
\(713\) −5.72646 + 2.67029i −0.214457 + 0.100003i
\(714\) 0 0
\(715\) −13.4060 + 40.3449i −0.501355 + 1.50881i
\(716\) −8.30527 + 9.89783i −0.310382 + 0.369899i
\(717\) 0 0
\(718\) −22.7762 48.8436i −0.849999 1.82283i
\(719\) 7.23920 12.5387i 0.269977 0.467613i −0.698879 0.715240i \(-0.746317\pi\)
0.968856 + 0.247627i \(0.0796506\pi\)
\(720\) 0 0
\(721\) 11.7913 + 20.4231i 0.439130 + 0.760596i
\(722\) 36.1517 51.6300i 1.34543 1.92147i
\(723\) 0 0
\(724\) −7.98507 21.9388i −0.296763 0.815349i
\(725\) 2.08460 1.36612i 0.0774200 0.0507363i
\(726\) 0 0
\(727\) 0.355020 4.05790i 0.0131670 0.150499i −0.986765 0.162156i \(-0.948155\pi\)
0.999932 + 0.0116572i \(0.00371069\pi\)
\(728\) 21.7333 21.7333i 0.805489 0.805489i
\(729\) 0 0
\(730\) −25.8441 11.1735i −0.956534 0.413549i
\(731\) 2.96054 + 3.52824i 0.109500 + 0.130497i
\(732\) 0 0
\(733\) −0.238710 + 0.167146i −0.00881695 + 0.00617370i −0.577977 0.816053i \(-0.696158\pi\)
0.569160 + 0.822227i \(0.307269\pi\)
\(734\) −25.4816 + 9.27456i −0.940545 + 0.342330i
\(735\) 0 0
\(736\) 1.88042 + 10.6644i 0.0693133 + 0.393096i
\(737\) −4.95155 + 18.4794i −0.182393 + 0.680699i
\(738\) 0 0
\(739\) 0.493834 + 0.285115i 0.0181660 + 0.0104881i 0.509055 0.860734i \(-0.329995\pi\)
−0.490890 + 0.871222i \(0.663328\pi\)
\(740\) 11.3089 0.319672i 0.415723 0.0117514i
\(741\) 0 0
\(742\) −10.4642 + 0.915499i −0.384153 + 0.0336090i
\(743\) 45.2865 3.96205i 1.66140 0.145354i 0.782594 0.622533i \(-0.213896\pi\)
0.878806 + 0.477179i \(0.158341\pi\)
\(744\) 0 0
\(745\) −20.4291 + 21.6177i −0.748466 + 0.792011i
\(746\) −42.5487 24.5655i −1.55782 0.899407i
\(747\) 0 0
\(748\) −1.08294 + 4.04158i −0.0395962 + 0.147775i
\(749\) 2.62917 + 14.9108i 0.0960678 + 0.544827i
\(750\) 0 0
\(751\) 21.7741 7.92512i 0.794547 0.289192i 0.0873224 0.996180i \(-0.472169\pi\)
0.707225 + 0.706988i \(0.249947\pi\)
\(752\) −20.2871 + 14.2052i −0.739795 + 0.518010i
\(753\) 0 0
\(754\) −3.28412 3.91386i −0.119601 0.142535i
\(755\) −12.9994 + 30.0674i −0.473096 + 1.09426i
\(756\) 0 0
\(757\) −8.24491 + 8.24491i −0.299666 + 0.299666i −0.840883 0.541217i \(-0.817964\pi\)
0.541217 + 0.840883i \(0.317964\pi\)
\(758\) −2.56092 + 29.2715i −0.0930169 + 1.06319i
\(759\) 0 0
\(760\) −5.23065 25.4385i −0.189735 0.922752i
\(761\) −13.7885 37.8835i −0.499832 1.37328i −0.891437 0.453144i \(-0.850302\pi\)
0.391605 0.920133i \(-0.371920\pi\)
\(762\) 0 0
\(763\) −6.08083 + 8.68433i −0.220141 + 0.314394i
\(764\) −13.9383 24.1418i −0.504268 0.873418i
\(765\) 0 0
\(766\) 28.0323 48.5534i 1.01285 1.75431i
\(767\) −25.9420 55.6327i −0.936710 2.00878i
\(768\) 0 0
\(769\) −13.5646 + 16.1656i −0.489151 + 0.582947i −0.953001 0.302966i \(-0.902023\pi\)
0.463850 + 0.885914i \(0.346468\pi\)
\(770\) 19.4690 + 38.8463i 0.701614 + 1.39992i
\(771\) 0 0
\(772\) −4.01963 + 1.87438i −0.144669 + 0.0674605i
\(773\) −6.07695 22.6795i −0.218573 0.815724i −0.984878 0.173248i \(-0.944574\pi\)
0.766306 0.642476i \(-0.222093\pi\)
\(774\) 0 0
\(775\) −4.75910 + 15.8011i −0.170952 + 0.567592i
\(776\) −7.30002 + 1.28719i −0.262055 + 0.0462074i
\(777\) 0 0
\(778\) 17.6281 + 8.22014i 0.632000 + 0.294706i
\(779\) 2.78384 15.7879i 0.0997414 0.565662i
\(780\) 0 0
\(781\) 19.1745 16.0893i 0.686116 0.575720i
\(782\) 2.75132 + 2.75132i 0.0983870 + 0.0983870i
\(783\) 0 0
\(784\) 21.6862i 0.774507i
\(785\) −10.9193 5.89934i −0.389728 0.210557i
\(786\) 0 0
\(787\) 4.65344 +