Properties

Label 405.2.r.a.8.2
Level $405$
Weight $2$
Character 405.8
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 8.2
Character \(\chi\) \(=\) 405.8
Dual form 405.2.r.a.152.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.94894 + 1.36466i) q^{2} +(1.25203 - 3.43992i) q^{4} +(-0.278496 - 2.21866i) q^{5} +(-1.02475 + 2.19758i) q^{7} +(1.02263 + 3.81650i) q^{8} +O(q^{10})\) \(q+(-1.94894 + 1.36466i) q^{2} +(1.25203 - 3.43992i) q^{4} +(-0.278496 - 2.21866i) q^{5} +(-1.02475 + 2.19758i) q^{7} +(1.02263 + 3.81650i) q^{8} +(3.57049 + 3.94398i) q^{10} +(-0.00275056 + 0.00327799i) q^{11} +(0.792678 - 1.13206i) q^{13} +(-1.00178 - 5.68139i) q^{14} +(-1.59279 - 1.33651i) q^{16} +(-0.510074 + 1.90362i) q^{17} +(-6.69182 - 3.86352i) q^{19} +(-7.98068 - 1.81982i) q^{20} +(0.000887327 - 0.0101422i) q^{22} +(-6.70002 + 3.12427i) q^{23} +(-4.84488 + 1.23578i) q^{25} +3.28806i q^{26} +(6.27648 + 6.27648i) q^{28} +(1.74110 - 9.87424i) q^{29} +(-5.62932 - 2.04890i) q^{31} +(-2.94406 - 0.257571i) q^{32} +(-1.60370 - 4.40613i) q^{34} +(5.16106 + 1.66155i) q^{35} +(1.68417 + 0.451272i) q^{37} +(18.3144 - 1.60230i) q^{38} +(8.18270 - 3.33174i) q^{40} +(2.95191 - 0.520501i) q^{41} +(-0.628957 - 7.18901i) q^{43} +(0.00783223 + 0.0135658i) q^{44} +(8.79437 - 15.2323i) q^{46} +(-1.86865 - 0.871367i) q^{47} +(0.720271 + 0.858385i) q^{49} +(7.75597 - 9.02009i) q^{50} +(-2.90174 - 4.14412i) q^{52} +(-1.25315 + 1.25315i) q^{53} +(0.00803875 + 0.00518964i) q^{55} +(-9.43499 - 1.66364i) q^{56} +(10.0817 + 21.6203i) q^{58} +(-0.763311 + 0.640494i) q^{59} +(-6.39745 + 2.32848i) q^{61} +(13.7673 - 3.68893i) q^{62} +(9.69063 - 5.59489i) q^{64} +(-2.73241 - 1.44340i) q^{65} +(-7.45442 - 5.21964i) q^{67} +(5.90968 + 4.13800i) q^{68} +(-12.3261 + 3.80486i) q^{70} +(-8.32564 + 4.80681i) q^{71} +(-2.77741 + 0.744204i) q^{73} +(-3.89819 + 1.41882i) q^{74} +(-21.6685 + 18.1821i) q^{76} +(-0.00438501 - 0.00940367i) q^{77} +(6.95996 + 1.22723i) q^{79} +(-2.52167 + 3.90606i) q^{80} +(-5.04279 + 5.04279i) q^{82} +(-5.84421 - 8.34640i) q^{83} +(4.36554 + 0.601528i) q^{85} +(11.0364 + 13.1527i) q^{86} +(-0.0153232 - 0.00714534i) q^{88} +(-3.03785 + 5.26171i) q^{89} +(1.67550 + 2.90205i) q^{91} +(2.35862 + 26.9592i) q^{92} +(4.83102 - 0.851839i) q^{94} +(-6.70819 + 15.9228i) q^{95} +(12.5529 - 1.09824i) q^{97} +(-2.57517 - 0.690016i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.94894 + 1.36466i −1.37811 + 0.964963i −0.378892 + 0.925441i \(0.623695\pi\)
−0.999219 + 0.0395221i \(0.987416\pi\)
\(3\) 0 0
\(4\) 1.25203 3.43992i 0.626014 1.71996i
\(5\) −0.278496 2.21866i −0.124547 0.992214i
\(6\) 0 0
\(7\) −1.02475 + 2.19758i −0.387318 + 0.830607i 0.611895 + 0.790939i \(0.290408\pi\)
−0.999213 + 0.0396673i \(0.987370\pi\)
\(8\) 1.02263 + 3.81650i 0.361553 + 1.34934i
\(9\) 0 0
\(10\) 3.57049 + 3.94398i 1.12909 + 1.24720i
\(11\) −0.00275056 + 0.00327799i −0.000829324 + 0.000988350i −0.766459 0.642293i \(-0.777983\pi\)
0.765630 + 0.643282i \(0.222428\pi\)
\(12\) 0 0
\(13\) 0.792678 1.13206i 0.219849 0.313977i −0.694043 0.719933i \(-0.744172\pi\)
0.913893 + 0.405956i \(0.133061\pi\)
\(14\) −1.00178 5.68139i −0.267738 1.51842i
\(15\) 0 0
\(16\) −1.59279 1.33651i −0.398197 0.334127i
\(17\) −0.510074 + 1.90362i −0.123711 + 0.461696i −0.999790 0.0204707i \(-0.993484\pi\)
0.876079 + 0.482167i \(0.160150\pi\)
\(18\) 0 0
\(19\) −6.69182 3.86352i −1.53521 0.886353i −0.999109 0.0421981i \(-0.986564\pi\)
−0.536099 0.844155i \(-0.680103\pi\)
\(20\) −7.98068 1.81982i −1.78453 0.406923i
\(21\) 0 0
\(22\) 0.000887327 0.0101422i 0.000189179 0.00216232i
\(23\) −6.70002 + 3.12427i −1.39705 + 0.651456i −0.967798 0.251729i \(-0.919001\pi\)
−0.429253 + 0.903184i \(0.641223\pi\)
\(24\) 0 0
\(25\) −4.84488 + 1.23578i −0.968976 + 0.247155i
\(26\) 3.28806i 0.644842i
\(27\) 0 0
\(28\) 6.27648 + 6.27648i 1.18614 + 1.18614i
\(29\) 1.74110 9.87424i 0.323313 1.83360i −0.197959 0.980210i \(-0.563431\pi\)
0.521272 0.853391i \(-0.325458\pi\)
\(30\) 0 0
\(31\) −5.62932 2.04890i −1.01106 0.367994i −0.217217 0.976123i \(-0.569698\pi\)
−0.793838 + 0.608129i \(0.791920\pi\)
\(32\) −2.94406 0.257571i −0.520440 0.0455326i
\(33\) 0 0
\(34\) −1.60370 4.40613i −0.275032 0.755645i
\(35\) 5.16106 + 1.66155i 0.872379 + 0.280853i
\(36\) 0 0
\(37\) 1.68417 + 0.451272i 0.276876 + 0.0741887i 0.394585 0.918859i \(-0.370888\pi\)
−0.117709 + 0.993048i \(0.537555\pi\)
\(38\) 18.3144 1.60230i 2.97098 0.259927i
\(39\) 0 0
\(40\) 8.18270 3.33174i 1.29380 0.526795i
\(41\) 2.95191 0.520501i 0.461011 0.0812887i 0.0616809 0.998096i \(-0.480354\pi\)
0.399330 + 0.916807i \(0.369243\pi\)
\(42\) 0 0
\(43\) −0.628957 7.18901i −0.0959151 1.09631i −0.879779 0.475382i \(-0.842310\pi\)
0.783864 0.620932i \(-0.213246\pi\)
\(44\) 0.00783223 + 0.0135658i 0.00118075 + 0.00204512i
\(45\) 0 0
\(46\) 8.79437 15.2323i 1.29666 2.24588i
\(47\) −1.86865 0.871367i −0.272571 0.127102i 0.281527 0.959553i \(-0.409159\pi\)
−0.554098 + 0.832451i \(0.686937\pi\)
\(48\) 0 0
\(49\) 0.720271 + 0.858385i 0.102896 + 0.122626i
\(50\) 7.75597 9.02009i 1.09686 1.27563i
\(51\) 0 0
\(52\) −2.90174 4.14412i −0.402399 0.574686i
\(53\) −1.25315 + 1.25315i −0.172134 + 0.172134i −0.787916 0.615782i \(-0.788840\pi\)
0.615782 + 0.787916i \(0.288840\pi\)
\(54\) 0 0
\(55\) 0.00803875 + 0.00518964i 0.00108394 + 0.000699770i
\(56\) −9.43499 1.66364i −1.26080 0.222314i
\(57\) 0 0
\(58\) 10.0817 + 21.6203i 1.32380 + 2.83889i
\(59\) −0.763311 + 0.640494i −0.0993747 + 0.0833853i −0.691121 0.722739i \(-0.742883\pi\)
0.591747 + 0.806124i \(0.298439\pi\)
\(60\) 0 0
\(61\) −6.39745 + 2.32848i −0.819109 + 0.298131i −0.717381 0.696681i \(-0.754659\pi\)
−0.101728 + 0.994812i \(0.532437\pi\)
\(62\) 13.7673 3.68893i 1.74845 0.468495i
\(63\) 0 0
\(64\) 9.69063 5.59489i 1.21133 0.699361i
\(65\) −2.73241 1.44340i −0.338914 0.179032i
\(66\) 0 0
\(67\) −7.45442 5.21964i −0.910702 0.637680i 0.0214414 0.999770i \(-0.493174\pi\)
−0.932143 + 0.362090i \(0.882063\pi\)
\(68\) 5.90968 + 4.13800i 0.716654 + 0.501806i
\(69\) 0 0
\(70\) −12.3261 + 3.80486i −1.47325 + 0.454767i
\(71\) −8.32564 + 4.80681i −0.988072 + 0.570464i −0.904697 0.426055i \(-0.859903\pi\)
−0.0833745 + 0.996518i \(0.526570\pi\)
\(72\) 0 0
\(73\) −2.77741 + 0.744204i −0.325071 + 0.0871025i −0.417664 0.908602i \(-0.637151\pi\)
0.0925931 + 0.995704i \(0.470484\pi\)
\(74\) −3.89819 + 1.41882i −0.453155 + 0.164935i
\(75\) 0 0
\(76\) −21.6685 + 18.1821i −2.48555 + 2.08563i
\(77\) −0.00438501 0.00940367i −0.000499718 0.00107165i
\(78\) 0 0
\(79\) 6.95996 + 1.22723i 0.783057 + 0.138074i 0.550863 0.834595i \(-0.314299\pi\)
0.232194 + 0.972670i \(0.425410\pi\)
\(80\) −2.52167 + 3.90606i −0.281931 + 0.436711i
\(81\) 0 0
\(82\) −5.04279 + 5.04279i −0.556883 + 0.556883i
\(83\) −5.84421 8.34640i −0.641485 0.916136i 0.358363 0.933582i \(-0.383335\pi\)
−0.999848 + 0.0174466i \(0.994446\pi\)
\(84\) 0 0
\(85\) 4.36554 + 0.601528i 0.473509 + 0.0652448i
\(86\) 11.0364 + 13.1527i 1.19008 + 1.41829i
\(87\) 0 0
\(88\) −0.0153232 0.00714534i −0.00163346 0.000761696i
\(89\) −3.03785 + 5.26171i −0.322012 + 0.557741i −0.980903 0.194498i \(-0.937692\pi\)
0.658891 + 0.752238i \(0.271026\pi\)
\(90\) 0 0
\(91\) 1.67550 + 2.90205i 0.175640 + 0.304217i
\(92\) 2.35862 + 26.9592i 0.245904 + 2.81069i
\(93\) 0 0
\(94\) 4.83102 0.851839i 0.498281 0.0878604i
\(95\) −6.70819 + 15.9228i −0.688245 + 1.63365i
\(96\) 0 0
\(97\) 12.5529 1.09824i 1.27456 0.111509i 0.570289 0.821444i \(-0.306831\pi\)
0.704267 + 0.709935i \(0.251276\pi\)
\(98\) −2.57517 0.690016i −0.260132 0.0697021i
\(99\) 0 0
\(100\) −1.81496 + 18.2132i −0.181496 + 1.82132i
\(101\) 1.67645 + 4.60600i 0.166813 + 0.458314i 0.994729 0.102537i \(-0.0326961\pi\)
−0.827916 + 0.560852i \(0.810474\pi\)
\(102\) 0 0
\(103\) −11.5458 1.01013i −1.13764 0.0995307i −0.497269 0.867596i \(-0.665664\pi\)
−0.640371 + 0.768066i \(0.721219\pi\)
\(104\) 5.13112 + 1.86758i 0.503148 + 0.183131i
\(105\) 0 0
\(106\) 0.732191 4.15246i 0.0711167 0.403323i
\(107\) 3.31844 + 3.31844i 0.320806 + 0.320806i 0.849076 0.528270i \(-0.177159\pi\)
−0.528270 + 0.849076i \(0.677159\pi\)
\(108\) 0 0
\(109\) 11.2538i 1.07792i −0.842332 0.538960i \(-0.818818\pi\)
0.842332 0.538960i \(-0.181182\pi\)
\(110\) −0.0227492 0.000855890i −0.00216905 8.16059e-5i
\(111\) 0 0
\(112\) 4.56928 2.13069i 0.431757 0.201331i
\(113\) 0.164272 1.87764i 0.0154535 0.176634i −0.984545 0.175129i \(-0.943966\pi\)
0.999999 0.00150433i \(-0.000478843\pi\)
\(114\) 0 0
\(115\) 8.79762 + 13.9950i 0.820382 + 1.30504i
\(116\) −31.7867 18.3520i −2.95132 1.70394i
\(117\) 0 0
\(118\) 0.613590 2.28995i 0.0564856 0.210807i
\(119\) −3.66066 3.07166i −0.335572 0.281579i
\(120\) 0 0
\(121\) 1.91013 + 10.8329i 0.173648 + 0.984806i
\(122\) 9.29066 13.2684i 0.841137 1.20127i
\(123\) 0 0
\(124\) −14.0961 + 16.7991i −1.26587 + 1.50860i
\(125\) 4.09104 + 10.4050i 0.365914 + 0.930649i
\(126\) 0 0
\(127\) 1.52603 + 5.69522i 0.135413 + 0.505369i 0.999996 + 0.00287859i \(0.000916284\pi\)
−0.864583 + 0.502491i \(0.832417\pi\)
\(128\) −8.75341 + 18.7718i −0.773700 + 1.65920i
\(129\) 0 0
\(130\) 7.29508 0.915713i 0.639821 0.0803133i
\(131\) 5.29212 14.5400i 0.462375 1.27036i −0.461320 0.887234i \(-0.652624\pi\)
0.923694 0.383130i \(-0.125154\pi\)
\(132\) 0 0
\(133\) 15.3478 10.7467i 1.33082 0.931854i
\(134\) 21.6513 1.87039
\(135\) 0 0
\(136\) −7.78679 −0.667712
\(137\) 3.20087 2.24127i 0.273468 0.191485i −0.428795 0.903402i \(-0.641062\pi\)
0.702263 + 0.711917i \(0.252173\pi\)
\(138\) 0 0
\(139\) −1.85959 + 5.10917i −0.157728 + 0.433354i −0.993234 0.116126i \(-0.962952\pi\)
0.835506 + 0.549481i \(0.185174\pi\)
\(140\) 12.1774 15.6733i 1.02918 1.32464i
\(141\) 0 0
\(142\) 9.66651 20.7299i 0.811196 1.73961i
\(143\) 0.00153058 + 0.00571218i 0.000127993 + 0.000477677i
\(144\) 0 0
\(145\) −22.3924 1.11295i −1.85959 0.0924257i
\(146\) 4.39742 5.24064i 0.363933 0.433718i
\(147\) 0 0
\(148\) 3.66097 5.22840i 0.300930 0.429772i
\(149\) −1.59684 9.05612i −0.130818 0.741907i −0.977681 0.210095i \(-0.932623\pi\)
0.846863 0.531811i \(-0.178488\pi\)
\(150\) 0 0
\(151\) 8.68937 + 7.29124i 0.707131 + 0.593353i 0.923792 0.382894i \(-0.125072\pi\)
−0.216662 + 0.976247i \(0.569517\pi\)
\(152\) 7.90189 29.4903i 0.640928 2.39198i
\(153\) 0 0
\(154\) 0.0213790 + 0.0123432i 0.00172277 + 0.000994640i
\(155\) −2.97807 + 13.0601i −0.239204 + 1.04902i
\(156\) 0 0
\(157\) −0.0766881 + 0.876549i −0.00612037 + 0.0699562i −0.998641 0.0521239i \(-0.983401\pi\)
0.992520 + 0.122080i \(0.0389565\pi\)
\(158\) −15.2393 + 7.10621i −1.21238 + 0.565340i
\(159\) 0 0
\(160\) 0.248446 + 6.60358i 0.0196414 + 0.522059i
\(161\) 17.9254i 1.41272i
\(162\) 0 0
\(163\) 4.75545 + 4.75545i 0.372476 + 0.372476i 0.868378 0.495902i \(-0.165163\pi\)
−0.495902 + 0.868378i \(0.665163\pi\)
\(164\) 1.90539 10.8060i 0.148786 0.843808i
\(165\) 0 0
\(166\) 22.7800 + 8.29126i 1.76807 + 0.643527i
\(167\) −7.21152 0.630926i −0.558044 0.0488226i −0.195355 0.980733i \(-0.562586\pi\)
−0.362689 + 0.931910i \(0.618141\pi\)
\(168\) 0 0
\(169\) 3.79304 + 10.4213i 0.291772 + 0.801637i
\(170\) −9.32907 + 4.78515i −0.715507 + 0.367004i
\(171\) 0 0
\(172\) −25.5171 6.83728i −1.94566 0.521338i
\(173\) −2.37946 + 0.208175i −0.180907 + 0.0158273i −0.177249 0.984166i \(-0.556720\pi\)
−0.00365760 + 0.999993i \(0.501164\pi\)
\(174\) 0 0
\(175\) 2.24906 11.9134i 0.170013 0.900565i
\(176\) 0.00876211 0.00154500i 0.000660469 0.000116458i
\(177\) 0 0
\(178\) −1.25987 14.4004i −0.0944315 1.07936i
\(179\) 8.41245 + 14.5708i 0.628776 + 1.08907i 0.987798 + 0.155743i \(0.0497772\pi\)
−0.359021 + 0.933329i \(0.616889\pi\)
\(180\) 0 0
\(181\) 3.54419 6.13871i 0.263437 0.456287i −0.703716 0.710482i \(-0.748477\pi\)
0.967153 + 0.254195i \(0.0818105\pi\)
\(182\) −7.22577 3.36943i −0.535610 0.249759i
\(183\) 0 0
\(184\) −18.7754 22.3757i −1.38414 1.64955i
\(185\) 0.532183 3.86228i 0.0391269 0.283960i
\(186\) 0 0
\(187\) −0.00483706 0.00690804i −0.000353721 0.000505166i
\(188\) −5.33703 + 5.33703i −0.389243 + 0.389243i
\(189\) 0 0
\(190\) −8.65544 40.1871i −0.627932 2.91548i
\(191\) 7.71793 + 1.36088i 0.558450 + 0.0984697i 0.445747 0.895159i \(-0.352938\pi\)
0.112703 + 0.993629i \(0.464049\pi\)
\(192\) 0 0
\(193\) −7.85219 16.8391i −0.565213 1.21210i −0.956472 0.291823i \(-0.905738\pi\)
0.391259 0.920280i \(-0.372040\pi\)
\(194\) −22.9662 + 19.2709i −1.64888 + 1.38357i
\(195\) 0 0
\(196\) 3.85457 1.40295i 0.275327 0.100211i
\(197\) 6.50660 1.74344i 0.463576 0.124215i −0.0194688 0.999810i \(-0.506198\pi\)
0.483045 + 0.875596i \(0.339531\pi\)
\(198\) 0 0
\(199\) 7.81601 4.51257i 0.554062 0.319888i −0.196697 0.980464i \(-0.563021\pi\)
0.750759 + 0.660576i \(0.229688\pi\)
\(200\) −9.67084 17.2267i −0.683832 1.21811i
\(201\) 0 0
\(202\) −9.55295 6.68904i −0.672143 0.470640i
\(203\) 19.9152 + 13.9448i 1.39778 + 0.978733i
\(204\) 0 0
\(205\) −1.97691 6.40432i −0.138073 0.447297i
\(206\) 23.8806 13.7874i 1.66384 0.960617i
\(207\) 0 0
\(208\) −2.77557 + 0.743713i −0.192451 + 0.0515672i
\(209\) 0.0310708 0.0113089i 0.00214921 0.000782250i
\(210\) 0 0
\(211\) 4.86924 4.08578i 0.335213 0.281277i −0.459607 0.888122i \(-0.652010\pi\)
0.794820 + 0.606846i \(0.207565\pi\)
\(212\) 2.74176 + 5.87973i 0.188305 + 0.403822i
\(213\) 0 0
\(214\) −10.9960 1.93889i −0.751672 0.132540i
\(215\) −15.7748 + 3.39755i −1.07583 + 0.231711i
\(216\) 0 0
\(217\) 10.2713 10.2713i 0.697258 0.697258i
\(218\) 15.3577 + 21.9330i 1.04015 + 1.48549i
\(219\) 0 0
\(220\) 0.0279167 0.0211551i 0.00188214 0.00142627i
\(221\) 1.75069 + 2.08639i 0.117764 + 0.140346i
\(222\) 0 0
\(223\) 3.40610 + 1.58829i 0.228089 + 0.106360i 0.533304 0.845924i \(-0.320950\pi\)
−0.305214 + 0.952284i \(0.598728\pi\)
\(224\) 3.58295 6.20585i 0.239396 0.414646i
\(225\) 0 0
\(226\) 2.24219 + 3.88359i 0.149149 + 0.258333i
\(227\) 0.568200 + 6.49455i 0.0377127 + 0.431059i 0.991456 + 0.130438i \(0.0416383\pi\)
−0.953744 + 0.300621i \(0.902806\pi\)
\(228\) 0 0
\(229\) −4.26742 + 0.752462i −0.281999 + 0.0497241i −0.312859 0.949800i \(-0.601287\pi\)
0.0308595 + 0.999524i \(0.490176\pi\)
\(230\) −36.2445 15.2696i −2.38989 1.00684i
\(231\) 0 0
\(232\) 39.4655 3.45279i 2.59104 0.226687i
\(233\) −25.2831 6.77460i −1.65635 0.443818i −0.694972 0.719037i \(-0.744583\pi\)
−0.961382 + 0.275219i \(0.911250\pi\)
\(234\) 0 0
\(235\) −1.41285 + 4.38857i −0.0921642 + 0.286279i
\(236\) 1.24756 + 3.42764i 0.0812093 + 0.223121i
\(237\) 0 0
\(238\) 11.3262 + 0.990915i 0.734169 + 0.0642314i
\(239\) 17.2215 + 6.26813i 1.11397 + 0.405452i 0.832448 0.554103i \(-0.186939\pi\)
0.281521 + 0.959555i \(0.409161\pi\)
\(240\) 0 0
\(241\) −1.09892 + 6.23226i −0.0707874 + 0.401455i 0.928740 + 0.370731i \(0.120893\pi\)
−0.999528 + 0.0307248i \(0.990218\pi\)
\(242\) −18.5060 18.5060i −1.18961 1.18961i
\(243\) 0 0
\(244\) 24.9220i 1.59547i
\(245\) 1.70387 1.83709i 0.108856 0.117367i
\(246\) 0 0
\(247\) −9.67820 + 4.51302i −0.615809 + 0.287156i
\(248\) 2.06294 23.5795i 0.130997 1.49730i
\(249\) 0 0
\(250\) −22.1725 14.6958i −1.40231 0.929443i
\(251\) 23.1604 + 13.3717i 1.46187 + 0.844013i 0.999098 0.0424628i \(-0.0135204\pi\)
0.462775 + 0.886476i \(0.346854\pi\)
\(252\) 0 0
\(253\) 0.00818747 0.0305561i 0.000514742 0.00192104i
\(254\) −10.7462 9.01714i −0.674277 0.565786i
\(255\) 0 0
\(256\) −4.67107 26.4910i −0.291942 1.65569i
\(257\) 2.24834 3.21096i 0.140248 0.200294i −0.742883 0.669421i \(-0.766542\pi\)
0.883131 + 0.469127i \(0.155431\pi\)
\(258\) 0 0
\(259\) −2.71756 + 3.23866i −0.168861 + 0.201240i
\(260\) −8.38625 + 7.59209i −0.520093 + 0.470841i
\(261\) 0 0
\(262\) 9.52815 + 35.5596i 0.588651 + 2.19688i
\(263\) 13.0357 27.9551i 0.803815 1.72379i 0.121669 0.992571i \(-0.461176\pi\)
0.682146 0.731216i \(-0.261047\pi\)
\(264\) 0 0
\(265\) 3.12932 + 2.43132i 0.192233 + 0.149355i
\(266\) −15.2464 + 41.8892i −0.934819 + 2.56839i
\(267\) 0 0
\(268\) −27.2883 + 19.1074i −1.66690 + 1.16717i
\(269\) −11.5179 −0.702257 −0.351128 0.936327i \(-0.614202\pi\)
−0.351128 + 0.936327i \(0.614202\pi\)
\(270\) 0 0
\(271\) −6.78072 −0.411899 −0.205950 0.978563i \(-0.566028\pi\)
−0.205950 + 0.978563i \(0.566028\pi\)
\(272\) 3.35665 2.35035i 0.203527 0.142511i
\(273\) 0 0
\(274\) −3.17972 + 8.73621i −0.192094 + 0.527774i
\(275\) 0.00927526 0.0192805i 0.000559319 0.00116266i
\(276\) 0 0
\(277\) 4.19864 9.00402i 0.252272 0.540999i −0.738863 0.673855i \(-0.764637\pi\)
0.991135 + 0.132856i \(0.0424149\pi\)
\(278\) −3.34808 12.4952i −0.200804 0.749412i
\(279\) 0 0
\(280\) −1.06344 + 21.3963i −0.0635529 + 1.27867i
\(281\) 16.7510 19.9630i 0.999280 1.19090i 0.0177003 0.999843i \(-0.494366\pi\)
0.981580 0.191052i \(-0.0611900\pi\)
\(282\) 0 0
\(283\) 4.26583 6.09224i 0.253577 0.362146i −0.672100 0.740461i \(-0.734607\pi\)
0.925677 + 0.378315i \(0.123496\pi\)
\(284\) 6.11110 + 34.6578i 0.362627 + 2.05656i
\(285\) 0 0
\(286\) −0.0107782 0.00904400i −0.000637329 0.000534783i
\(287\) −1.88112 + 7.02044i −0.111039 + 0.414403i
\(288\) 0 0
\(289\) 11.3588 + 6.55802i 0.668166 + 0.385766i
\(290\) 45.1604 28.3891i 2.65191 1.66706i
\(291\) 0 0
\(292\) −0.917390 + 10.4858i −0.0536862 + 0.613636i
\(293\) −7.55448 + 3.52271i −0.441337 + 0.205799i −0.630568 0.776134i \(-0.717178\pi\)
0.189231 + 0.981933i \(0.439400\pi\)
\(294\) 0 0
\(295\) 1.63362 + 1.51515i 0.0951128 + 0.0882155i
\(296\) 6.88912i 0.400422i
\(297\) 0 0
\(298\) 15.4707 + 15.4707i 0.896194 + 0.896194i
\(299\) −1.77409 + 10.0614i −0.102598 + 0.581864i
\(300\) 0 0
\(301\) 16.4429 + 5.98474i 0.947755 + 0.344955i
\(302\) −26.8852 2.35215i −1.54707 0.135351i
\(303\) 0 0
\(304\) 5.49502 + 15.0974i 0.315161 + 0.865897i
\(305\) 6.94777 + 13.5453i 0.397828 + 0.775600i
\(306\) 0 0
\(307\) −11.7737 3.15476i −0.671962 0.180052i −0.0933234 0.995636i \(-0.529749\pi\)
−0.578638 + 0.815584i \(0.696416\pi\)
\(308\) −0.0378380 + 0.00331040i −0.00215602 + 0.000188627i
\(309\) 0 0
\(310\) −12.0186 29.5175i −0.682611 1.67648i
\(311\) −19.9366 + 3.51536i −1.13050 + 0.199338i −0.707447 0.706767i \(-0.750153\pi\)
−0.423054 + 0.906104i \(0.639042\pi\)
\(312\) 0 0
\(313\) 0.631317 + 7.21599i 0.0356842 + 0.407872i 0.992939 + 0.118626i \(0.0378489\pi\)
−0.957255 + 0.289246i \(0.906596\pi\)
\(314\) −1.04673 1.81300i −0.0590706 0.102313i
\(315\) 0 0
\(316\) 12.9356 22.4052i 0.727686 1.26039i
\(317\) 4.44794 + 2.07411i 0.249821 + 0.116493i 0.543496 0.839412i \(-0.317100\pi\)
−0.293675 + 0.955905i \(0.594878\pi\)
\(318\) 0 0
\(319\) 0.0275787 + 0.0328670i 0.00154411 + 0.00184020i
\(320\) −15.1120 19.9420i −0.844784 1.11479i
\(321\) 0 0
\(322\) 24.4622 + 34.9356i 1.36322 + 1.94688i
\(323\) 10.7680 10.7680i 0.599148 0.599148i
\(324\) 0 0
\(325\) −2.44145 + 6.46427i −0.135427 + 0.358573i
\(326\) −15.7577 2.77851i −0.872739 0.153887i
\(327\) 0 0
\(328\) 5.00520 + 10.7337i 0.276366 + 0.592668i
\(329\) 3.82979 3.21358i 0.211143 0.177170i
\(330\) 0 0
\(331\) −4.66635 + 1.69841i −0.256486 + 0.0933531i −0.467063 0.884224i \(-0.654688\pi\)
0.210577 + 0.977577i \(0.432466\pi\)
\(332\) −36.0280 + 9.65368i −1.97729 + 0.529814i
\(333\) 0 0
\(334\) 14.9158 8.61167i 0.816159 0.471209i
\(335\) −9.50456 + 17.9924i −0.519290 + 0.983032i
\(336\) 0 0
\(337\) 17.9831 + 12.5919i 0.979602 + 0.685925i 0.949547 0.313624i \(-0.101543\pi\)
0.0300546 + 0.999548i \(0.490432\pi\)
\(338\) −21.6140 15.1343i −1.17564 0.823195i
\(339\) 0 0
\(340\) 7.53498 14.2640i 0.408642 0.773572i
\(341\) 0.0222000 0.0128172i 0.00120220 0.000694090i
\(342\) 0 0
\(343\) −19.0194 + 5.09624i −1.02695 + 0.275171i
\(344\) 26.7937 9.75210i 1.44462 0.525798i
\(345\) 0 0
\(346\) 4.35333 3.65288i 0.234037 0.196380i
\(347\) 6.59670 + 14.1467i 0.354129 + 0.759433i 0.999992 0.00402090i \(-0.00127990\pi\)
−0.645863 + 0.763454i \(0.723502\pi\)
\(348\) 0 0
\(349\) −23.5190 4.14704i −1.25895 0.221986i −0.495928 0.868364i \(-0.665172\pi\)
−0.763017 + 0.646378i \(0.776283\pi\)
\(350\) 11.8744 + 26.2877i 0.634715 + 1.40513i
\(351\) 0 0
\(352\) 0.00894211 0.00894211i 0.000476616 0.000476616i
\(353\) −0.184497 0.263489i −0.00981980 0.0140241i 0.814212 0.580567i \(-0.197169\pi\)
−0.824032 + 0.566543i \(0.808280\pi\)
\(354\) 0 0
\(355\) 12.9833 + 17.1331i 0.689084 + 0.909329i
\(356\) 14.2964 + 17.0378i 0.757707 + 0.903000i
\(357\) 0 0
\(358\) −36.2796 16.9175i −1.91744 0.894116i
\(359\) −2.09252 + 3.62435i −0.110439 + 0.191286i −0.915947 0.401298i \(-0.868559\pi\)
0.805508 + 0.592585i \(0.201892\pi\)
\(360\) 0 0
\(361\) 20.3536 + 35.2535i 1.07124 + 1.85545i
\(362\) 1.46986 + 16.8006i 0.0772543 + 0.883021i
\(363\) 0 0
\(364\) 12.0806 2.13013i 0.633194 0.111649i
\(365\) 2.42463 + 5.95486i 0.126911 + 0.311691i
\(366\) 0 0
\(367\) −13.3335 + 1.16653i −0.696004 + 0.0608924i −0.429667 0.902988i \(-0.641369\pi\)
−0.266337 + 0.963880i \(0.585813\pi\)
\(368\) 14.8473 + 3.97833i 0.773970 + 0.207385i
\(369\) 0 0
\(370\) 4.23351 + 8.25360i 0.220090 + 0.429084i
\(371\) −1.46974 4.03807i −0.0763050 0.209646i
\(372\) 0 0
\(373\) −15.6366 1.36803i −0.809634 0.0708338i −0.325182 0.945652i \(-0.605425\pi\)
−0.484452 + 0.874818i \(0.660981\pi\)
\(374\) 0.0188543 + 0.00686241i 0.000974933 + 0.000354847i
\(375\) 0 0
\(376\) 1.41463 8.02279i 0.0729542 0.413744i
\(377\) −9.79812 9.79812i −0.504629 0.504629i
\(378\) 0 0
\(379\) 26.4477i 1.35853i 0.733894 + 0.679264i \(0.237701\pi\)
−0.733894 + 0.679264i \(0.762299\pi\)
\(380\) 46.3744 + 43.0114i 2.37896 + 2.20644i
\(381\) 0 0
\(382\) −16.8989 + 7.88010i −0.864625 + 0.403181i
\(383\) 1.62124 18.5309i 0.0828415 0.946883i −0.835082 0.550126i \(-0.814580\pi\)
0.917923 0.396758i \(-0.129865\pi\)
\(384\) 0 0
\(385\) −0.0196423 + 0.0123477i −0.00100107 + 0.000629298i
\(386\) 38.2831 + 22.1028i 1.94856 + 1.12500i
\(387\) 0 0
\(388\) 11.9388 44.5560i 0.606098 2.26199i
\(389\) −25.4642 21.3670i −1.29108 1.08335i −0.991613 0.129243i \(-0.958745\pi\)
−0.299472 0.954105i \(-0.596810\pi\)
\(390\) 0 0
\(391\) −2.52993 14.3479i −0.127944 0.725606i
\(392\) −2.53946 + 3.62672i −0.128262 + 0.183177i
\(393\) 0 0
\(394\) −10.3018 + 12.2772i −0.518996 + 0.618515i
\(395\) 0.784477 15.7836i 0.0394713 0.794157i
\(396\) 0 0
\(397\) −8.84314 33.0030i −0.443824 1.65637i −0.719022 0.694987i \(-0.755410\pi\)
0.275198 0.961388i \(-0.411257\pi\)
\(398\) −9.07480 + 19.4610i −0.454879 + 0.975490i
\(399\) 0 0
\(400\) 9.36849 + 4.50689i 0.468424 + 0.225344i
\(401\) 3.56868 9.80487i 0.178211 0.489632i −0.818136 0.575025i \(-0.804992\pi\)
0.996347 + 0.0853930i \(0.0272146\pi\)
\(402\) 0 0
\(403\) −6.78172 + 4.74861i −0.337821 + 0.236545i
\(404\) 17.9432 0.892709
\(405\) 0 0
\(406\) −57.8436 −2.87073
\(407\) −0.00611167 + 0.00427944i −0.000302944 + 0.000212124i
\(408\) 0 0
\(409\) 13.0223 35.7785i 0.643911 1.76913i 0.00483335 0.999988i \(-0.498461\pi\)
0.639078 0.769142i \(-0.279316\pi\)
\(410\) 12.5926 + 9.78383i 0.621906 + 0.483189i
\(411\) 0 0
\(412\) −17.9304 + 38.4519i −0.883367 + 1.89439i
\(413\) −0.625335 2.33378i −0.0307707 0.114838i
\(414\) 0 0
\(415\) −16.8902 + 15.2907i −0.829107 + 0.750593i
\(416\) −2.62527 + 3.12868i −0.128715 + 0.153396i
\(417\) 0 0
\(418\) −0.0451224 + 0.0644415i −0.00220701 + 0.00315194i
\(419\) −4.45593 25.2708i −0.217686 1.23456i −0.876184 0.481978i \(-0.839919\pi\)
0.658497 0.752583i \(-0.271192\pi\)
\(420\) 0 0
\(421\) −18.3149 15.3680i −0.892611 0.748990i 0.0761208 0.997099i \(-0.475747\pi\)
−0.968732 + 0.248109i \(0.920191\pi\)
\(422\) −3.91416 + 14.6078i −0.190538 + 0.711098i
\(423\) 0 0
\(424\) −6.06417 3.50115i −0.294502 0.170031i
\(425\) 0.118797 9.85316i 0.00576248 0.477948i
\(426\) 0 0
\(427\) 1.43875 16.4450i 0.0696260 0.795829i
\(428\) 15.5699 7.26039i 0.752602 0.350944i
\(429\) 0 0
\(430\) 26.1076 28.1489i 1.25902 1.35746i
\(431\) 15.6671i 0.754660i −0.926079 0.377330i \(-0.876842\pi\)
0.926079 0.377330i \(-0.123158\pi\)
\(432\) 0 0
\(433\) 10.5845 + 10.5845i 0.508657 + 0.508657i 0.914114 0.405457i \(-0.132888\pi\)
−0.405457 + 0.914114i \(0.632888\pi\)
\(434\) −6.00127 + 34.0349i −0.288070 + 1.63373i
\(435\) 0 0
\(436\) −38.7122 14.0901i −1.85398 0.674792i
\(437\) 56.9060 + 4.97863i 2.72218 + 0.238160i
\(438\) 0 0
\(439\) 7.09912 + 19.5047i 0.338823 + 0.930907i 0.985729 + 0.168338i \(0.0538401\pi\)
−0.646907 + 0.762569i \(0.723938\pi\)
\(440\) −0.0115856 + 0.0359869i −0.000552321 + 0.00171561i
\(441\) 0 0
\(442\) −6.25923 1.67715i −0.297721 0.0797741i
\(443\) 7.49047 0.655331i 0.355883 0.0311357i 0.0921874 0.995742i \(-0.470614\pi\)
0.263696 + 0.964606i \(0.415059\pi\)
\(444\) 0 0
\(445\) 12.5200 + 5.27458i 0.593504 + 0.250039i
\(446\) −8.80576 + 1.55269i −0.416965 + 0.0735222i
\(447\) 0 0
\(448\) 2.36476 + 27.0293i 0.111724 + 1.27701i
\(449\) 2.66419 + 4.61452i 0.125731 + 0.217773i 0.922018 0.387146i \(-0.126539\pi\)
−0.796287 + 0.604918i \(0.793206\pi\)
\(450\) 0 0
\(451\) −0.00641320 + 0.0111080i −0.000301986 + 0.000523055i
\(452\) −6.25326 2.91594i −0.294129 0.137154i
\(453\) 0 0
\(454\) −9.97027 11.8821i −0.467928 0.557655i
\(455\) 5.97203 4.52557i 0.279973 0.212162i
\(456\) 0 0
\(457\) −13.4866 19.2609i −0.630879 0.900988i 0.368714 0.929543i \(-0.379798\pi\)
−0.999592 + 0.0285551i \(0.990909\pi\)
\(458\) 7.29010 7.29010i 0.340644 0.340644i
\(459\) 0 0
\(460\) 59.1563 12.7410i 2.75818 0.594053i
\(461\) −15.8701 2.79833i −0.739145 0.130331i −0.208615 0.977998i \(-0.566896\pi\)
−0.530529 + 0.847667i \(0.678007\pi\)
\(462\) 0 0
\(463\) −6.30838 13.5284i −0.293175 0.628716i 0.703455 0.710740i \(-0.251640\pi\)
−0.996630 + 0.0820233i \(0.973862\pi\)
\(464\) −15.9702 + 13.4006i −0.741398 + 0.622106i
\(465\) 0 0
\(466\) 58.5204 21.2997i 2.71091 0.986689i
\(467\) 6.07179 1.62693i 0.280969 0.0752854i −0.115583 0.993298i \(-0.536873\pi\)
0.396552 + 0.918012i \(0.370207\pi\)
\(468\) 0 0
\(469\) 19.1095 11.0329i 0.882393 0.509450i
\(470\) −3.23536 10.4811i −0.149236 0.483459i
\(471\) 0 0
\(472\) −3.22503 2.25819i −0.148444 0.103942i
\(473\) 0.0252955 + 0.0177121i 0.00116309 + 0.000814402i
\(474\) 0 0
\(475\) 37.1955 + 10.4487i 1.70665 + 0.479420i
\(476\) −15.1495 + 8.74657i −0.694377 + 0.400899i
\(477\) 0 0
\(478\) −42.1177 + 11.2854i −1.92642 + 0.516182i
\(479\) −6.42357 + 2.33799i −0.293501 + 0.106825i −0.484574 0.874750i \(-0.661025\pi\)
0.191073 + 0.981576i \(0.438803\pi\)
\(480\) 0 0
\(481\) 1.84587 1.54887i 0.0841645 0.0706224i
\(482\) −6.36322 13.6460i −0.289837 0.621557i
\(483\) 0 0
\(484\) 39.6557 + 6.99237i 1.80253 + 0.317835i
\(485\) −5.93256 27.5448i −0.269384 1.25074i
\(486\) 0 0
\(487\) −11.7403 + 11.7403i −0.532002 + 0.532002i −0.921168 0.389165i \(-0.872763\pi\)
0.389165 + 0.921168i \(0.372763\pi\)
\(488\) −15.4289 22.0347i −0.698431 0.997463i
\(489\) 0 0
\(490\) −0.813732 + 5.90559i −0.0367606 + 0.266788i
\(491\) −10.6951 12.7459i −0.482663 0.575215i 0.468673 0.883372i \(-0.344732\pi\)
−0.951336 + 0.308157i \(0.900288\pi\)
\(492\) 0 0
\(493\) 17.9087 + 8.35099i 0.806569 + 0.376109i
\(494\) 12.7035 22.0031i 0.571557 0.989966i
\(495\) 0 0
\(496\) 6.22793 + 10.7871i 0.279642 + 0.484355i
\(497\) −2.03166 23.2220i −0.0911326 1.04165i
\(498\) 0 0
\(499\) −27.4365 + 4.83779i −1.22823 + 0.216569i −0.749863 0.661593i \(-0.769881\pi\)
−0.478363 + 0.878162i \(0.658770\pi\)
\(500\) 40.9143 1.04555i 1.82974 0.0467584i
\(501\) 0 0
\(502\) −63.3862 + 5.54557i −2.82906 + 0.247511i
\(503\) 14.4253 + 3.86525i 0.643192 + 0.172343i 0.565649 0.824646i \(-0.308626\pi\)
0.0775431 + 0.996989i \(0.475292\pi\)
\(504\) 0 0
\(505\) 9.75226 5.00222i 0.433970 0.222596i
\(506\) 0.0257419 + 0.0707252i 0.00114436 + 0.00314412i
\(507\) 0 0
\(508\) 21.5017 + 1.88116i 0.953985 + 0.0834629i
\(509\) −5.75433 2.09440i −0.255056 0.0928328i 0.211328 0.977415i \(-0.432221\pi\)
−0.466384 + 0.884582i \(0.654443\pi\)
\(510\) 0 0
\(511\) 1.21069 6.86619i 0.0535580 0.303742i
\(512\) 15.9632 + 15.9632i 0.705482 + 0.705482i
\(513\) 0 0
\(514\) 9.32621i 0.411361i
\(515\) 0.974338 + 25.8975i 0.0429345 + 1.14118i
\(516\) 0 0
\(517\) 0.00799616 0.00372867i 0.000351671 0.000163987i
\(518\) 0.876681 10.0205i 0.0385191 0.440276i
\(519\) 0 0
\(520\) 2.71451 11.9043i 0.119039 0.522039i
\(521\) −19.3541 11.1741i −0.847920 0.489547i 0.0120282 0.999928i \(-0.496171\pi\)
−0.859949 + 0.510381i \(0.829505\pi\)
\(522\) 0 0
\(523\) −0.878392 + 3.27820i −0.0384094 + 0.143346i −0.982468 0.186433i \(-0.940307\pi\)
0.944058 + 0.329778i \(0.106974\pi\)
\(524\) −43.3905 36.4089i −1.89552 1.59053i
\(525\) 0 0
\(526\) 12.7435 + 72.2722i 0.555645 + 3.15122i
\(527\) 6.77171 9.67101i 0.294980 0.421276i
\(528\) 0 0
\(529\) 20.3451 24.2463i 0.884569 1.05419i
\(530\) −9.41680 0.468035i −0.409040 0.0203302i
\(531\) 0 0
\(532\) −17.7517 66.2503i −0.769635 2.87232i
\(533\) 1.75067 3.75433i 0.0758301 0.162618i
\(534\) 0 0
\(535\) 6.43831 8.28666i 0.278353 0.358264i
\(536\) 12.2976 33.7875i 0.531178 1.45940i
\(537\) 0 0
\(538\) 22.4477 15.7180i 0.967787 0.677652i
\(539\) −0.00479492 −0.000206532
\(540\) 0 0
\(541\) −32.7244 −1.40693 −0.703466 0.710729i \(-0.748365\pi\)
−0.703466 + 0.710729i \(0.748365\pi\)
\(542\) 13.2152 9.25340i 0.567642 0.397467i
\(543\) 0 0
\(544\) 1.99201 5.47299i 0.0854065 0.234653i
\(545\) −24.9683 + 3.13414i −1.06953 + 0.134252i
\(546\) 0 0
\(547\) 12.0993 25.9469i 0.517327 1.10941i −0.458063 0.888920i \(-0.651456\pi\)
0.975389 0.220491i \(-0.0707658\pi\)
\(548\) −3.70221 13.8168i −0.158151 0.590226i
\(549\) 0 0
\(550\) 0.00823449 + 0.0502342i 0.000351120 + 0.00214200i
\(551\) −49.8005 + 59.3499i −2.12157 + 2.52839i
\(552\) 0 0
\(553\) −9.82914 + 14.0375i −0.417977 + 0.596934i
\(554\) 4.10455 + 23.2780i 0.174385 + 0.988989i
\(555\) 0 0
\(556\) 15.2469 + 12.7937i 0.646612 + 0.542572i
\(557\) −5.67171 + 21.1671i −0.240318 + 0.896879i 0.735361 + 0.677675i \(0.237012\pi\)
−0.975679 + 0.219203i \(0.929654\pi\)
\(558\) 0 0
\(559\) −8.63696 4.98655i −0.365304 0.210909i
\(560\) −5.99980 9.54429i −0.253538 0.403320i
\(561\) 0 0
\(562\) −5.40385 + 61.7663i −0.227948 + 2.60545i
\(563\) 9.80704 4.57310i 0.413317 0.192733i −0.204826 0.978798i \(-0.565663\pi\)
0.618143 + 0.786065i \(0.287885\pi\)
\(564\) 0 0
\(565\) −4.21160 + 0.158452i −0.177183 + 0.00666614i
\(566\) 17.6948i 0.743770i
\(567\) 0 0
\(568\) −26.8592 26.8592i −1.12699 1.12699i
\(569\) −2.29260 + 13.0020i −0.0961109 + 0.545072i 0.898290 + 0.439402i \(0.144810\pi\)
−0.994401 + 0.105670i \(0.966301\pi\)
\(570\) 0 0
\(571\) −7.42564 2.70271i −0.310753 0.113105i 0.181936 0.983310i \(-0.441764\pi\)
−0.492689 + 0.870206i \(0.663986\pi\)
\(572\) 0.0215658 + 0.00188676i 0.000901710 + 7.88894e-5i
\(573\) 0 0
\(574\) −5.91434 16.2495i −0.246860 0.678242i
\(575\) 28.5999 23.4164i 1.19270 0.976533i
\(576\) 0 0
\(577\) 25.1985 + 6.75192i 1.04903 + 0.281086i 0.741850 0.670566i \(-0.233949\pi\)
0.307178 + 0.951652i \(0.400615\pi\)
\(578\) −31.0872 + 2.71978i −1.29306 + 0.113128i
\(579\) 0 0
\(580\) −31.8644 + 75.6347i −1.32310 + 3.14056i
\(581\) 24.3307 4.29016i 1.00941 0.177986i
\(582\) 0 0
\(583\) −0.000660950 0.00755470i −2.73738e−5 0.000312884i
\(584\) −5.68051 9.83893i −0.235061 0.407138i
\(585\) 0 0
\(586\) 9.91592 17.1749i 0.409623 0.709488i
\(587\) −13.7926 6.43160i −0.569282 0.265460i 0.116593 0.993180i \(-0.462803\pi\)
−0.685875 + 0.727719i \(0.740580\pi\)
\(588\) 0 0
\(589\) 29.7544 + 35.4599i 1.22601 + 1.46110i
\(590\) −5.25150 0.723604i −0.216201 0.0297903i
\(591\) 0 0
\(592\) −2.07940 2.96969i −0.0854627 0.122053i
\(593\) −30.1991 + 30.1991i −1.24013 + 1.24013i −0.280181 + 0.959947i \(0.590395\pi\)
−0.959947 + 0.280181i \(0.909605\pi\)
\(594\) 0 0
\(595\) −5.79548 + 8.97720i −0.237592 + 0.368029i
\(596\) −33.1516 5.84552i −1.35794 0.239442i
\(597\) 0 0
\(598\) −10.2728 22.0301i −0.420086 0.900876i
\(599\) −13.7064 + 11.5010i −0.560028 + 0.469920i −0.878320 0.478073i \(-0.841335\pi\)
0.318292 + 0.947993i \(0.396891\pi\)
\(600\) 0 0
\(601\) −34.7520 + 12.6487i −1.41757 + 0.515952i −0.933341 0.358992i \(-0.883121\pi\)
−0.484225 + 0.874944i \(0.660898\pi\)
\(602\) −40.2135 + 10.7752i −1.63898 + 0.439163i
\(603\) 0 0
\(604\) 35.9606 20.7619i 1.46322 0.844788i
\(605\) 23.5025 7.25483i 0.955511 0.294951i
\(606\) 0 0
\(607\) 35.5036 + 24.8599i 1.44105 + 1.00903i 0.993385 + 0.114830i \(0.0366323\pi\)
0.447663 + 0.894203i \(0.352257\pi\)
\(608\) 18.7059 + 13.0980i 0.758626 + 0.531196i
\(609\) 0 0
\(610\) −32.0255 16.9176i −1.29668 0.684973i
\(611\) −2.46768 + 1.42471i −0.0998316 + 0.0576378i
\(612\) 0 0
\(613\) 0.212147 0.0568446i 0.00856854 0.00229593i −0.254532 0.967064i \(-0.581921\pi\)
0.263101 + 0.964768i \(0.415255\pi\)
\(614\) 27.2515 9.91873i 1.09978 0.400287i
\(615\) 0 0
\(616\) 0.0314049 0.0263518i 0.00126534 0.00106175i
\(617\) 11.5791 + 24.8316i 0.466159 + 0.999681i 0.989091 + 0.147307i \(0.0470604\pi\)
−0.522932 + 0.852374i \(0.675162\pi\)
\(618\) 0 0
\(619\) −40.1687 7.08283i −1.61452 0.284683i −0.707797 0.706416i \(-0.750311\pi\)
−0.906720 + 0.421733i \(0.861422\pi\)
\(620\) 41.1972 + 26.5960i 1.65452 + 1.06812i
\(621\) 0 0
\(622\) 34.0580 34.0580i 1.36560 1.36560i
\(623\) −8.45000 12.0678i −0.338542 0.483488i
\(624\) 0 0
\(625\) 21.9457 11.9744i 0.877829 0.478975i
\(626\) −11.0778 13.2020i −0.442758 0.527658i
\(627\) 0 0
\(628\) 2.91924 + 1.36126i 0.116490 + 0.0543203i
\(629\) −1.71810 + 2.97584i −0.0685053 + 0.118655i
\(630\) 0 0
\(631\) −21.0645 36.4848i −0.838565 1.45244i −0.891095 0.453817i \(-0.850062\pi\)
0.0525304 0.998619i \(-0.483271\pi\)
\(632\) 2.43373 + 27.8177i 0.0968087 + 1.10653i
\(633\) 0 0
\(634\) −11.4992 + 2.02762i −0.456693 + 0.0805272i
\(635\) 12.2108 4.97184i 0.484569 0.197301i
\(636\) 0 0
\(637\) 1.54269 0.134968i 0.0611235 0.00534761i
\(638\) −0.0986016 0.0264202i −0.00390367 0.00104599i
\(639\) 0 0
\(640\) 44.0859 + 14.1930i 1.74265 + 0.561026i
\(641\) 8.97472 + 24.6578i 0.354480 + 0.973926i 0.980912 + 0.194450i \(0.0622922\pi\)
−0.626432 + 0.779476i \(0.715486\pi\)
\(642\) 0 0
\(643\) −29.4868 2.57976i −1.16284 0.101736i −0.510651 0.859788i \(-0.670596\pi\)
−0.652194 + 0.758052i \(0.726151\pi\)
\(644\) −61.6619 22.4431i −2.42982 0.884382i
\(645\) 0 0
\(646\) −6.29152 + 35.6810i −0.247536 + 1.40385i
\(647\) −3.41329 3.41329i −0.134190 0.134190i 0.636821 0.771012i \(-0.280249\pi\)
−0.771012 + 0.636821i \(0.780249\pi\)
\(648\) 0 0
\(649\) 0.00426384i 0.000167370i
\(650\) −4.06331 15.9303i −0.159376 0.624836i
\(651\) 0 0
\(652\) 22.3123 10.4044i 0.873818 0.407468i
\(653\) −3.91945 + 44.7996i −0.153380 + 1.75314i 0.396625 + 0.917981i \(0.370181\pi\)
−0.550005 + 0.835161i \(0.685374\pi\)
\(654\) 0 0
\(655\) −33.7331 7.69207i −1.31806 0.300554i
\(656\) −5.39742 3.11620i −0.210734 0.121667i
\(657\) 0 0
\(658\) −3.07859 + 11.4895i −0.120016 + 0.447906i
\(659\) 31.0081 + 26.0189i 1.20790 + 1.01355i 0.999368 + 0.0355365i \(0.0113140\pi\)
0.208535 + 0.978015i \(0.433130\pi\)
\(660\) 0 0
\(661\) −2.96480 16.8142i −0.115318 0.653998i −0.986593 0.163203i \(-0.947817\pi\)
0.871275 0.490795i \(-0.163294\pi\)
\(662\) 6.77668 9.67810i 0.263383 0.376150i
\(663\) 0 0
\(664\) 25.8776 30.8397i 1.00424 1.19681i
\(665\) −28.1175 31.0586i −1.09035 1.20440i
\(666\) 0 0
\(667\) 19.1844 + 71.5973i 0.742824 + 2.77226i
\(668\) −11.1994 + 24.0171i −0.433316 + 0.929250i
\(669\) 0 0
\(670\) −6.02980 48.0368i −0.232952 1.85582i
\(671\) 0.00996382 0.0273754i 0.000384649 0.00105681i
\(672\) 0 0
\(673\) 25.0337 17.5288i 0.964978 0.675685i 0.0189672 0.999820i \(-0.493962\pi\)
0.946011 + 0.324135i \(0.105073\pi\)
\(674\) −52.2317 −2.01189
\(675\) 0 0
\(676\) 40.5973 1.56144
\(677\) −17.6437 + 12.3542i −0.678102 + 0.474812i −0.861189 0.508284i \(-0.830280\pi\)
0.183087 + 0.983097i \(0.441391\pi\)
\(678\) 0 0
\(679\) −10.4501 + 28.7114i −0.401038 + 1.10184i
\(680\) 2.16859 + 17.2762i 0.0831617 + 0.662513i
\(681\) 0 0
\(682\) −0.0257754 + 0.0552756i −0.000986992 + 0.00211661i
\(683\) 2.39311 + 8.93120i 0.0915697 + 0.341743i 0.996477 0.0838658i \(-0.0267267\pi\)
−0.904907 + 0.425609i \(0.860060\pi\)
\(684\) 0 0
\(685\) −5.86404 6.47744i −0.224053 0.247490i
\(686\) 30.1131 35.8874i 1.14972 1.37019i
\(687\) 0 0
\(688\) −8.60637 + 12.2912i −0.328115 + 0.468597i
\(689\) 0.425300 + 2.41199i 0.0162026 + 0.0918897i
\(690\) 0 0
\(691\) 15.9016 + 13.3430i 0.604925 + 0.507592i 0.893024 0.450008i \(-0.148579\pi\)
−0.288099 + 0.957601i \(0.593023\pi\)
\(692\) −2.26304 + 8.44577i −0.0860278 + 0.321060i
\(693\) 0 0
\(694\) −32.1620 18.5688i −1.22085 0.704860i
\(695\) 11.8534 + 2.70290i 0.449625 + 0.102527i
\(696\) 0 0
\(697\) −0.514855 + 5.88482i −0.0195015 + 0.222903i
\(698\) 51.4966 24.0132i 1.94917 0.908915i
\(699\) 0 0
\(700\) −38.1651 22.6524i −1.44250 0.856182i
\(701\) 5.94733i 0.224627i −0.993673 0.112314i \(-0.964174\pi\)
0.993673 0.112314i \(-0.0358262\pi\)
\(702\) 0 0
\(703\) −9.52667 9.52667i −0.359305 0.359305i
\(704\) −0.00831467 + 0.0471548i −0.000313371 + 0.00177721i
\(705\) 0 0
\(706\) 0.719149 + 0.261749i 0.0270655 + 0.00985105i
\(707\) −11.8400 1.03586i −0.445289 0.0389577i
\(708\) 0 0
\(709\) 0.0976022 + 0.268160i 0.00366553 + 0.0100710i 0.941512 0.336980i \(-0.109405\pi\)
−0.937846 + 0.347051i \(0.887183\pi\)
\(710\) −48.6846 15.6735i −1.82710 0.588215i
\(711\) 0 0
\(712\) −23.1879 6.21318i −0.869004 0.232849i
\(713\) 44.1179 3.85981i 1.65223 0.144551i
\(714\) 0 0
\(715\) 0.0122471 0.00498664i 0.000458016 0.000186490i
\(716\) 60.6550 10.6951i 2.26678 0.399695i
\(717\) 0 0
\(718\) −0.867822 9.91925i −0.0323868 0.370183i
\(719\) −13.3454 23.1148i −0.497698 0.862038i 0.502299 0.864694i \(-0.332488\pi\)
−0.999996 + 0.00265626i \(0.999154\pi\)
\(720\) 0 0
\(721\) 14.0514 24.3377i 0.523300 0.906382i
\(722\) −87.7772 40.9312i −3.26673 1.52330i
\(723\) 0 0
\(724\) −16.6792 19.8775i −0.619879 0.738743i
\(725\) 3.76695 + 49.9911i 0.139901 + 1.85662i
\(726\) 0 0
\(727\) −28.9346 41.3229i −1.07313 1.53258i −0.826059 0.563584i \(-0.809422\pi\)
−0.247067 0.968998i \(-0.579467\pi\)
\(728\) −9.36225 + 9.36225i −0.346988 + 0.346988i
\(729\) 0 0
\(730\) −12.8518 8.29686i −0.475668 0.307081i
\(731\) 14.0060 + 2.46963i 0.518030 + 0.0913427i
\(732\) 0 0
\(733\) 16.9546 + 36.3592i 0.626231 + 1.34296i 0.921811 + 0.387639i \(0.126709\pi\)
−0.295580 + 0.955318i \(0.595513\pi\)
\(734\) 24.3943 20.4693i 0.900411 0.755535i
\(735\) 0 0
\(736\) 20.5300 7.47229i 0.756744 0.275432i
\(737\) 0.0376137 0.0100786i 0.00138552 0.000371249i
\(738\) 0 0
\(739\) 18.7080 10.8011i 0.688186 0.397324i −0.114746 0.993395i \(-0.536605\pi\)
0.802932 + 0.596070i \(0.203272\pi\)
\(740\) −12.6196 6.66634i −0.463906 0.245060i
\(741\) 0 0
\(742\) 8.37505 + 5.86427i 0.307458 + 0.215284i
\(743\) −22.4982 15.7534i −0.825380 0.577937i 0.0827765 0.996568i \(-0.473621\pi\)
−0.908156 + 0.418631i \(0.862510\pi\)
\(744\) 0 0
\(745\) −19.6477 + 6.06494i −0.719837 + 0.222202i
\(746\) 32.3418 18.6725i 1.18412 0.683650i
\(747\) 0 0
\(748\) −0.0298192 + 0.00799004i −0.00109030 + 0.000292145i
\(749\) −10.6931 + 3.89197i −0.390717 + 0.142210i
\(750\) 0 0
\(751\) 36.9715 31.0228i 1.34911 1.13204i 0.369926 0.929061i \(-0.379383\pi\)
0.979184 0.202976i \(-0.0650615\pi\)
\(752\) 1.81178 + 3.88537i 0.0660687 + 0.141685i
\(753\) 0 0
\(754\) 32.4671 + 5.72483i 1.18238 + 0.208486i
\(755\) 13.7568 21.3093i 0.500662 0.775525i
\(756\) 0 0
\(757\) 25.7438 25.7438i 0.935673 0.935673i −0.0623799 0.998052i \(-0.519869\pi\)
0.998052 + 0.0623799i \(0.0198691\pi\)
\(758\) −36.0923 51.5451i −1.31093 1.87220i
\(759\) 0 0
\(760\) −67.6294 9.31866i −2.45318 0.338023i
\(761\) −8.43284 10.0499i −0.305690 0.364308i 0.591227 0.806505i \(-0.298644\pi\)
−0.896918 + 0.442197i \(0.854199\pi\)
\(762\) 0 0
\(763\) 24.7311 + 11.5323i 0.895327 + 0.417498i
\(764\) 14.3444 24.8452i 0.518961 0.898867i
\(765\) 0 0
\(766\) 22.1287 + 38.3280i 0.799543 + 1.38485i
\(767\) 0.120019 + 1.37182i 0.00433362 + 0.0495336i
\(768\) 0 0
\(769\) −3.71767 + 0.655525i −0.134062 + 0.0236388i −0.240277 0.970704i \(-0.577238\pi\)
0.106214 + 0.994343i \(0.466127\pi\)
\(770\) 0.0214313 0.0508701i 0.000772329 0.00183323i
\(771\) 0 0
\(772\) −67.7562 + 5.92790i −2.43860 + 0.213350i
\(773\) 22.9201 + 6.14142i 0.824379 + 0.220892i 0.646260 0.763117i \(-0.276332\pi\)
0.178119 + 0.984009i \(0.442999\pi\)
\(774\) 0 0
\(775\) 29.8054 + 2.97012i 1.07064 + 0.106690i
\(776\) 17.0284 + 46.7851i 0.611284 + 1.67949i
\(777\) 0 0
\(778\) 78.7869 + 6.89296i 2.82465 + 0.247125i
\(779\) −21.7646 7.92167i −0.779798 0.283823i
\(780\) 0 0
\(781\) 0.00714349 0.0405128i 0.000255614 0.00144966i
\(782\) 24.5108 + 24.5108i 0.876503 + 0.876503i
\(783\) 0 0
\(784\) 2.32987i 0.0832097i
\(785\) 1.96612 0.0739711i 0.0701738 0.00264014i
\(786\) 0 0