Properties

Label 405.2.r.a.152.2
Level $405$
Weight $2$
Character 405.152
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 152.2
Character \(\chi\) \(=\) 405.152
Dual form 405.2.r.a.8.2

$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{17}{18}\right)\)

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 −0.999219 0.0395221i \(-0.987416\pi\)
−0.378892 0.925441i \(-0.623695\pi\)
\(3\) 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 −0.999213 0.0396673i \(-0.987370\pi\)
0.611895 0.790939i \(-0.290408\pi\)
\(8\) 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 0.765630 0.643282i \(-0.222428\pi\)
−0.766459 + 0.642293i \(0.777983\pi\)
\(12\) 0 0
\(13\) 0.792678 + 1.13206i 0.219849 + 0.313977i 0.913893 0.405956i \(-0.133061\pi\)
−0.694043 + 0.719933i \(0.744172\pi\)
\(14\) −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 0.876079 0.482167i \(-0.160150\pi\)
−0.999790 + 0.0204707i \(0.993484\pi\)
\(18\) 0 0
\(19\) −6.69182 + 3.86352i −1.53521 + 0.886353i −0.536099 + 0.844155i \(0.680103\pi\)
−0.999109 + 0.0421981i \(0.986564\pi\)
\(20\) −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 −0.429253 0.903184i \(-0.641223\pi\)
−0.967798 + 0.251729i \(0.919001\pi\)
\(24\) 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 0.521272 + 0.853391i \(0.325458\pi\)
−0.197959 + 0.980210i \(0.563431\pi\)
\(30\) 0 0
\(31\) −5.62932 + 2.04890i −1.01106 + 0.367994i −0.793838 0.608129i \(-0.791920\pi\)
−0.217217 + 0.976123i \(0.569698\pi\)
\(32\) −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 −0.117709 0.993048i \(-0.537555\pi\)
0.394585 + 0.918859i \(0.370888\pi\)
\(38\) 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 0.399330 0.916807i \(-0.369243\pi\)
0.0616809 + 0.998096i \(0.480354\pi\)
\(42\) 0 0
\(43\) −0.628957 + 7.18901i −0.0959151 + 1.09631i 0.783864 + 0.620932i \(0.213246\pi\)
−0.879779 + 0.475382i \(0.842310\pi\)
\(44\) 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 −0.554098 0.832451i \(-0.686937\pi\)
0.281527 + 0.959553i \(0.409159\pi\)
\(48\) 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 0.615782 0.787916i \(-0.288840\pi\)
−0.787916 + 0.615782i \(0.788840\pi\)
\(54\) 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 0.591747 0.806124i \(-0.298439\pi\)
−0.691121 + 0.722739i \(0.742883\pi\)
\(60\) 0 0
\(61\) −6.39745 2.32848i −0.819109 0.298131i −0.101728 0.994812i \(-0.532437\pi\)
−0.717381 + 0.696681i \(0.754659\pi\)
\(62\) 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 −0.932143 0.362090i \(-0.882063\pi\)
0.0214414 + 0.999770i \(0.493174\pi\)
\(68\) 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 −0.0833745 0.996518i \(-0.526570\pi\)
−0.904697 + 0.426055i \(0.859903\pi\)
\(72\) 0 0
\(73\) −2.77741 0.744204i −0.325071 0.0871025i 0.0925931 0.995704i \(-0.470484\pi\)
−0.417664 + 0.908602i \(0.637151\pi\)
\(74\) −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 0.232194 0.972670i \(-0.425410\pi\)
0.550863 + 0.834595i \(0.314299\pi\)
\(80\) −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 −0.999848 0.0174466i \(-0.994446\pi\)
0.358363 + 0.933582i \(0.383335\pi\)
\(84\) 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 0.658891 0.752238i \(-0.271026\pi\)
−0.980903 + 0.194498i \(0.937692\pi\)
\(90\) 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 0.704267 0.709935i \(-0.251276\pi\)
0.570289 + 0.821444i \(0.306831\pi\)
\(98\) −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 −0.827916 0.560852i \(-0.810474\pi\)
0.994729 + 0.102537i \(0.0326961\pi\)
\(102\) 0 0
\(103\) −11.5458 + 1.01013i −1.13764 + 0.0995307i −0.640371 0.768066i \(-0.721219\pi\)
−0.497269 + 0.867596i \(0.665664\pi\)
\(104\) 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 −0.528270 0.849076i \(-0.677159\pi\)
0.849076 + 0.528270i \(0.177159\pi\)
\(108\) 0 0
\(109\) 11.2538i 1.07792i 0.842332 + 0.538960i \(0.181182\pi\)
−0.842332 + 0.538960i \(0.818818\pi\)
\(110\) −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 0.999999 + 0.00150433i \(0.000478843\pi\)
−0.984545 + 0.175129i \(0.943966\pi\)
\(114\) 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 −0.864583 0.502491i \(-0.832417\pi\)
0.999996 0.00287859i \(-0.000916284\pi\)
\(128\) −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 0.923694 + 0.383130i \(0.125154\pi\)
−0.461320 + 0.887234i \(0.652624\pi\)
\(132\) 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 0.702263 0.711917i \(-0.252173\pi\)
−0.428795 + 0.903402i \(0.641062\pi\)
\(138\) 0 0
\(139\) −1.85959 5.10917i −0.157728 0.433354i 0.835506 0.549481i \(-0.185174\pi\)
−0.993234 + 0.116126i \(0.962952\pi\)
\(140\) 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 0.846863 + 0.531811i \(0.178488\pi\)
−0.977681 + 0.210095i \(0.932623\pi\)
\(150\) 0 0
\(151\) 8.68937 7.29124i 0.707131 0.593353i −0.216662 0.976247i \(-0.569517\pi\)
0.923792 + 0.382894i \(0.125072\pi\)
\(152\) 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 0.992520 0.122080i \(-0.0389565\pi\)
−0.998641 + 0.0521239i \(0.983401\pi\)
\(158\) −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 −0.495902 0.868378i \(-0.665163\pi\)
0.868378 + 0.495902i \(0.165163\pi\)
\(164\) 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 −0.362689 0.931910i \(-0.618141\pi\)
−0.195355 + 0.980733i \(0.562586\pi\)
\(168\) 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 −0.00365760 0.999993i \(-0.501164\pi\)
−0.177249 + 0.984166i \(0.556720\pi\)
\(174\) 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 −0.359021 0.933329i \(-0.616889\pi\)
0.987798 0.155743i \(-0.0497772\pi\)
\(180\) 0 0
\(181\) 3.54419 + 6.13871i 0.263437 + 0.456287i 0.967153 0.254195i \(-0.0818105\pi\)
−0.703716 + 0.710482i \(0.748477\pi\)
\(182\) −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 0.112703 0.993629i \(-0.464049\pi\)
0.445747 + 0.895159i \(0.352938\pi\)
\(192\) 0 0
\(193\) −7.85219 + 16.8391i −0.565213 + 1.21210i 0.391259 + 0.920280i \(0.372040\pi\)
−0.956472 + 0.291823i \(0.905738\pi\)
\(194\) −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 0.483045 0.875596i \(-0.339531\pi\)
−0.0194688 + 0.999810i \(0.506198\pi\)
\(198\) 0 0
\(199\) 7.81601 + 4.51257i 0.554062 + 0.319888i 0.750759 0.660576i \(-0.229688\pi\)
−0.196697 + 0.980464i \(0.563021\pi\)
\(200\) −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 0.794820 0.606846i \(-0.207565\pi\)
−0.459607 + 0.888122i \(0.652010\pi\)
\(212\) 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 −0.305214 0.952284i \(-0.598728\pi\)
0.533304 + 0.845924i \(0.320950\pi\)
\(224\) 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 −0.953744 0.300621i \(-0.902806\pi\)
0.991456 0.130438i \(-0.0416383\pi\)
\(228\) 0 0
\(229\) −4.26742 0.752462i −0.281999 0.0497241i 0.0308595 0.999524i \(-0.490176\pi\)
−0.312859 + 0.949800i \(0.601287\pi\)
\(230\) −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 −0.961382 0.275219i \(-0.911250\pi\)
−0.694972 + 0.719037i \(0.744583\pi\)
\(234\) 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 0.281521 0.959555i \(-0.409161\pi\)
0.832448 + 0.554103i \(0.186939\pi\)
\(240\) 0 0
\(241\) −1.09892 6.23226i −0.0707874 0.401455i −0.999528 0.0307248i \(-0.990218\pi\)
0.928740 0.370731i \(-0.120893\pi\)
\(242\) −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 0.462775 0.886476i \(-0.346854\pi\)
0.999098 + 0.0424628i \(0.0135204\pi\)
\(252\) 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 0.883131 0.469127i \(-0.155431\pi\)
−0.742883 + 0.669421i \(0.766542\pi\)
\(258\) 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 0.682146 + 0.731216i \(0.261047\pi\)
0.121669 + 0.992571i \(0.461176\pi\)
\(264\) 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 0.991135 0.132856i \(-0.0424149\pi\)
−0.738863 + 0.673855i \(0.764637\pi\)
\(278\) −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 0.981580 + 0.191052i \(0.0611900\pi\)
0.0177003 + 0.999843i \(0.494366\pi\)
\(282\) 0 0
\(283\) 4.26583 + 6.09224i 0.253577 + 0.362146i 0.925677 0.378315i \(-0.123496\pi\)
−0.672100 + 0.740461i \(0.734607\pi\)
\(284\) 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 0.189231 0.981933i \(-0.439400\pi\)
−0.630568 + 0.776134i \(0.717178\pi\)
\(294\) 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 −0.578638 0.815584i \(-0.696416\pi\)
−0.0933234 + 0.995636i \(0.529749\pi\)
\(308\) −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 −0.423054 0.906104i \(-0.639042\pi\)
−0.707447 + 0.706767i \(0.750153\pi\)
\(312\) 0 0
\(313\) 0.631317 7.21599i 0.0356842 0.407872i −0.957255 0.289246i \(-0.906596\pi\)
0.992939 0.118626i \(-0.0378489\pi\)
\(314\) −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 −0.293675 0.955905i \(-0.594878\pi\)
0.543496 + 0.839412i \(0.317100\pi\)
\(318\) 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 0.210577 0.977577i \(-0.432466\pi\)
−0.467063 + 0.884224i \(0.654688\pi\)
\(332\) −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 0.0300546 0.999548i \(-0.490432\pi\)
0.949547 + 0.313624i \(0.101543\pi\)
\(338\) −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 −0.645863 0.763454i \(-0.723502\pi\)
0.999992 + 0.00402090i \(0.00127990\pi\)
\(348\) 0 0
\(349\) −23.5190 + 4.14704i −1.25895 + 0.221986i −0.763017 0.646378i \(-0.776283\pi\)
−0.495928 + 0.868364i \(0.665172\pi\)
\(350\) 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 −0.824032 0.566543i \(-0.808280\pi\)
0.814212 + 0.580567i \(0.197169\pi\)
\(354\) 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 0.805508 0.592585i \(-0.201892\pi\)
−0.915947 + 0.401298i \(0.868559\pi\)
\(360\) 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 −0.266337 0.963880i \(-0.585813\pi\)
−0.429667 + 0.902988i \(0.641369\pi\)
\(368\) 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 −0.484452 0.874818i \(-0.660981\pi\)
−0.325182 + 0.945652i \(0.605425\pi\)
\(374\) 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 \(-0.762299\pi\)
0.733894 0.679264i \(-0.237701\pi\)
\(380\) 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 0.917923 + 0.396758i \(0.129865\pi\)
−0.835082 + 0.550126i \(0.814580\pi\)
\(384\) 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 −0.299472 + 0.954105i \(0.596810\pi\)
−0.991613 + 0.129243i \(0.958745\pi\)
\(390\) 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 0.275198 + 0.961388i \(0.411257\pi\)
−0.719022 + 0.694987i \(0.755410\pi\)
\(398\) −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 0.996347 0.0853930i \(-0.0272146\pi\)
−0.818136 + 0.575025i \(0.804992\pi\)
\(402\) 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 0.639078 + 0.769142i \(0.279316\pi\)
0.00483335 + 0.999988i \(0.498461\pi\)
\(410\) 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 0.658497 + 0.752583i \(0.271192\pi\)
−0.876184 + 0.481978i \(0.839919\pi\)
\(420\) 0 0
\(421\) −18.3149 + 15.3680i −0.892611 + 0.748990i −0.968732 0.248109i \(-0.920191\pi\)
0.0761208 + 0.997099i \(0.475747\pi\)
\(422\) −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 \(0.123158\pi\)
−0.926079 + 0.377330i \(0.876842\pi\)
\(432\) 0 0
\(433\) 10.5845 10.5845i 0.508657 0.508657i −0.405457 0.914114i \(-0.632888\pi\)
0.914114 + 0.405457i \(0.132888\pi\)
\(434\) −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 −0.646907 0.762569i \(-0.723938\pi\)
0.985729 0.168338i \(-0.0538401\pi\)
\(440\) −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 0.263696 0.964606i \(-0.415059\pi\)
0.0921874 + 0.995742i \(0.470614\pi\)
\(444\) 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 −0.796287 0.604918i \(-0.793206\pi\)
0.922018 + 0.387146i \(0.126539\pi\)
\(450\) 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 −0.999592 0.0285551i \(-0.990909\pi\)
0.368714 + 0.929543i \(0.379798\pi\)
\(458\) 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 −0.530529 0.847667i \(-0.678007\pi\)
−0.208615 + 0.977998i \(0.566896\pi\)
\(462\) 0 0
\(463\) −6.30838 + 13.5284i −0.293175 + 0.628716i −0.996630 0.0820233i \(-0.973862\pi\)
0.703455 + 0.710740i \(0.251640\pi\)
\(464\) −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 0.396552 0.918012i \(-0.370207\pi\)
−0.115583 + 0.993298i \(0.536873\pi\)
\(468\) 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 0.191073 0.981576i \(-0.438803\pi\)
−0.484574 + 0.874750i \(0.661025\pi\)
\(480\) 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 0.389165 0.921168i \(-0.372763\pi\)
−0.921168 + 0.389165i \(0.872763\pi\)
\(488\) −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 −0.951336 0.308157i \(-0.900288\pi\)
0.468673 + 0.883372i \(0.344732\pi\)
\(492\) 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 −0.478363 0.878162i \(-0.658770\pi\)
−0.749863 + 0.661593i \(0.769881\pi\)
\(500\) 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 0.0775431 0.996989i \(-0.475292\pi\)
0.565649 + 0.824646i \(0.308626\pi\)
\(504\) 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 −0.466384 0.884582i \(-0.654443\pi\)
0.211328 + 0.977415i \(0.432221\pi\)
\(510\) 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 −0.859949 0.510381i \(-0.829505\pi\)
0.0120282 + 0.999928i \(0.496171\pi\)
\(522\) 0 0
\(523\) −0.878392 3.27820i −0.0384094 0.143346i 0.944058 0.329778i \(-0.106974\pi\)
−0.982468 + 0.186433i \(0.940307\pi\)
\(524\) −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 0.975389 + 0.220491i \(0.0707658\pi\)
−0.458063 + 0.888920i \(0.651456\pi\)
\(548\) −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 −0.975679 0.219203i \(-0.929654\pi\)
0.735361 0.677675i \(-0.237012\pi\)
\(558\) 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 0.618143 0.786065i \(-0.287885\pi\)
−0.204826 + 0.978798i \(0.565663\pi\)
\(564\) 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 −0.994401 0.105670i \(-0.966301\pi\)
0.898290 0.439402i \(-0.144810\pi\)
\(570\) 0 0
\(571\) −7.42564 + 2.70271i −0.310753 + 0.113105i −0.492689 0.870206i \(-0.663986\pi\)
0.181936 + 0.983310i \(0.441764\pi\)
\(572\) 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 0.307178 0.951652i \(-0.400615\pi\)
0.741850 + 0.670566i \(0.233949\pi\)
\(578\) −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 −0.685875 0.727719i \(-0.740580\pi\)
0.116593 + 0.993180i \(0.462803\pi\)
\(588\) 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 −0.959947 0.280181i \(-0.909605\pi\)
−0.280181 0.959947i \(-0.590395\pi\)
\(594\) 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 0.318292 0.947993i \(-0.396891\pi\)
−0.878320 + 0.478073i \(0.841335\pi\)
\(600\) 0 0
\(601\) −34.7520 12.6487i −1.41757 0.515952i −0.484225 0.874944i \(-0.660898\pi\)
−0.933341 + 0.358992i \(0.883121\pi\)
\(602\) −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 0.447663 0.894203i \(-0.352257\pi\)
0.993385 0.114830i \(-0.0366323\pi\)
\(608\) 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 0.263101 0.964768i \(-0.415255\pi\)
−0.254532 + 0.967064i \(0.581921\pi\)
\(614\) 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 −0.522932 0.852374i \(-0.675162\pi\)
0.989091 0.147307i \(-0.0470604\pi\)
\(618\) 0 0
\(619\) −40.1687 + 7.08283i −1.61452 + 0.284683i −0.906720 0.421733i \(-0.861422\pi\)
−0.707797 + 0.706416i \(0.750311\pi\)
\(620\) 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 0.0525304 + 0.998619i \(0.483271\pi\)
−0.891095 + 0.453817i \(0.850062\pi\)
\(632\) 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 −0.626432 0.779476i \(-0.715486\pi\)
0.980912 0.194450i \(-0.0622922\pi\)
\(642\) 0 0
\(643\) −29.4868 + 2.57976i −1.16284 + 0.101736i −0.652194 0.758052i \(-0.726151\pi\)
−0.510651 + 0.859788i \(0.670596\pi\)
\(644\) −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 −0.771012 0.636821i \(-0.780249\pi\)
0.636821 + 0.771012i \(0.280249\pi\)
\(648\) 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 −0.550005 0.835161i \(-0.685374\pi\)
0.396625 0.917981i \(-0.370181\pi\)
\(654\) 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 0.208535 0.978015i \(-0.433130\pi\)
0.999368 0.0355365i \(-0.0113140\pi\)
\(660\) 0 0
\(661\) −2.96480 + 16.8142i −0.115318 + 0.653998i 0.871275 + 0.490795i \(0.163294\pi\)
−0.986593 + 0.163203i \(0.947817\pi\)
\(662\) 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 0.946011 0.324135i \(-0.105073\pi\)
0.0189672 + 0.999820i \(0.493962\pi\)
\(674\) −52.2317 −2.01189
\(675\) 0 0
\(676\) 40.5973 1.56144
\(677\) −17.6437 12.3542i −0.678102 0.474812i 0.183087 0.983097i \(-0.441391\pi\)
−0.861189 + 0.508284i \(0.830280\pi\)
\(678\) 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 −0.904907 0.425609i \(-0.860060\pi\)
0.996477 + 0.0838658i \(0.0267267\pi\)
\(684\) 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 −0.288099 0.957601i \(-0.593023\pi\)
0.893024 + 0.450008i \(0.148579\pi\)
\(692\) −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 \(0.0358262\pi\)
−0.993673 + 0.112314i \(0.964174\pi\)
\(702\) 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 −0.937846 0.347051i \(-0.887183\pi\)
0.941512 + 0.336980i \(0.109405\pi\)
\(710\) −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 −0.999996 0.00265626i \(-0.999154\pi\)
0.502299 + 0.864694i \(0.332488\pi\)
\(720\) 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 −0.247067 + 0.968998i \(0.579467\pi\)
−0.826059 + 0.563584i \(0.809422\pi\)
\(728\) −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 −0.295580 0.955318i \(-0.595513\pi\)
0.921811 0.387639i \(-0.126709\pi\)
\(734\) 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 0.802932 0.596070i \(-0.203272\pi\)
−0.114746 + 0.993395i \(0.536605\pi\)
\(740\) −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 −0.908156 0.418631i \(-0.862510\pi\)
0.0827765 + 0.996568i \(0.473621\pi\)
\(744\) 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 0.979184 + 0.202976i \(0.0650615\pi\)
0.369926 + 0.929061i \(0.379383\pi\)
\(752\) 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 0.998052 0.0623799i \(-0.0198691\pi\)
−0.0623799 + 0.998052i \(0.519869\pi\)
\(758\) −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 −0.896918 0.442197i \(-0.854199\pi\)
0.591227 + 0.806505i \(0.298644\pi\)
\(762\) 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 0.106214 0.994343i \(-0.466127\pi\)
−0.240277 + 0.970704i \(0.577238\pi\)
\(770\) 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 0.178119 0.984009i \(-0.442999\pi\)
0.646260 + 0.763117i \(0.276332\pi\)
\(774\) 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
\(787\) −2.14886