Properties

Label 1170.2.bj.c.199.5
Level $1170$
Weight $2$
Character 1170.199
Analytic conductor $9.342$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bj (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + 190 x^{3} - 1196 x^{2} - 338 x + 2197 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.5
Root \(2.00607 + 1.30680i\) of defining polynomial
Character \(\chi\) \(=\) 1170.199
Dual form 1170.2.bj.c.829.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.26873 - 1.84128i) q^{5} +(2.17283 + 3.76344i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.26873 - 1.84128i) q^{5} +(2.17283 + 3.76344i) q^{7} +1.00000 q^{8} +(0.960230 + 2.01940i) q^{10} +(2.04055 + 1.17811i) q^{11} +(3.18419 + 1.69144i) q^{13} -4.34565 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.60564 - 1.50437i) q^{17} +(0.585872 - 0.338254i) q^{19} +(-2.22896 - 0.178114i) q^{20} +(-2.04055 + 1.17811i) q^{22} +(-5.58405 - 3.22396i) q^{23} +(-1.78064 - 4.67219i) q^{25} +(-3.05692 + 1.91187i) q^{26} +(2.17283 - 3.76344i) q^{28} +(-4.82620 + 8.35922i) q^{29} -7.11493i q^{31} +(-0.500000 - 0.866025i) q^{32} +3.00874i q^{34} +(9.68629 + 0.774021i) q^{35} +(-3.74165 + 6.48073i) q^{37} +0.676507i q^{38} +(1.26873 - 1.84128i) q^{40} +(2.60564 + 1.50437i) q^{41} +(5.91710 - 3.41624i) q^{43} -2.35623i q^{44} +(5.58405 - 3.22396i) q^{46} +5.61529 q^{47} +(-5.94234 + 10.2924i) q^{49} +(4.93655 + 0.794019i) q^{50} +(-0.127265 - 3.60330i) q^{52} +9.43400i q^{53} +(4.75816 - 2.26252i) q^{55} +(2.17283 + 3.76344i) q^{56} +(-4.82620 - 8.35922i) q^{58} +(4.56364 - 2.63482i) q^{59} +(2.15646 + 3.73509i) q^{61} +(6.16171 + 3.55746i) q^{62} +1.00000 q^{64} +(7.15429 - 3.71700i) q^{65} +(2.91329 - 5.04596i) q^{67} +(-2.60564 - 1.50437i) q^{68} +(-5.51347 + 8.00157i) q^{70} +(-2.52520 + 1.45793i) q^{71} +7.67804 q^{73} +(-3.74165 - 6.48073i) q^{74} +(-0.585872 - 0.338254i) q^{76} +10.2393i q^{77} -3.74519 q^{79} +(0.960230 + 2.01940i) q^{80} +(-2.60564 + 1.50437i) q^{82} +10.3557 q^{83} +(0.535898 - 6.70637i) q^{85} +6.83247i q^{86} +(2.04055 + 1.17811i) q^{88} +(-4.15208 - 2.39720i) q^{89} +(0.553049 + 15.6587i) q^{91} +6.44791i q^{92} +(-2.80764 + 4.86298i) q^{94} +(0.120495 - 1.50791i) q^{95} +(8.17066 + 14.1520i) q^{97} +(-5.94234 - 10.2924i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{23} - 10 q^{25} + 2 q^{26} + 2 q^{28} - 14 q^{29} - 6 q^{32} + 22 q^{35} + 12 q^{37} - 2 q^{40} + 18 q^{41} + 36 q^{43} - 6 q^{46} + 16 q^{47} + 8 q^{49} + 20 q^{50} - 10 q^{52} + 8 q^{55} + 2 q^{56} - 14 q^{58} + 36 q^{59} + 10 q^{61} + 6 q^{62} + 12 q^{64} + 44 q^{65} - 4 q^{67} - 18 q^{68} + 4 q^{70} + 12 q^{71} - 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 4 q^{80} - 18 q^{82} + 72 q^{83} + 48 q^{85} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} - 18 q^{95} + 48 q^{97} + 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.26873 1.84128i 0.567394 0.823446i
\(6\) 0 0
\(7\) 2.17283 + 3.76344i 0.821251 + 1.42245i 0.904751 + 0.425940i \(0.140057\pi\)
−0.0835003 + 0.996508i \(0.526610\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0.960230 + 2.01940i 0.303651 + 0.638589i
\(11\) 2.04055 + 1.17811i 0.615250 + 0.355215i 0.775017 0.631940i \(-0.217741\pi\)
−0.159767 + 0.987155i \(0.551074\pi\)
\(12\) 0 0
\(13\) 3.18419 + 1.69144i 0.883134 + 0.469120i
\(14\) −4.34565 −1.16142
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.60564 1.50437i 0.631962 0.364863i −0.149550 0.988754i \(-0.547782\pi\)
0.781511 + 0.623891i \(0.214449\pi\)
\(18\) 0 0
\(19\) 0.585872 0.338254i 0.134408 0.0776007i −0.431288 0.902214i \(-0.641941\pi\)
0.565696 + 0.824614i \(0.308607\pi\)
\(20\) −2.22896 0.178114i −0.498411 0.0398275i
\(21\) 0 0
\(22\) −2.04055 + 1.17811i −0.435047 + 0.251175i
\(23\) −5.58405 3.22396i −1.16436 0.672241i −0.212012 0.977267i \(-0.568002\pi\)
−0.952344 + 0.305026i \(0.901335\pi\)
\(24\) 0 0
\(25\) −1.78064 4.67219i −0.356127 0.934438i
\(26\) −3.05692 + 1.91187i −0.599511 + 0.374948i
\(27\) 0 0
\(28\) 2.17283 3.76344i 0.410625 0.711224i
\(29\) −4.82620 + 8.35922i −0.896202 + 1.55227i −0.0638921 + 0.997957i \(0.520351\pi\)
−0.832310 + 0.554311i \(0.812982\pi\)
\(30\) 0 0
\(31\) 7.11493i 1.27788i −0.769257 0.638939i \(-0.779374\pi\)
0.769257 0.638939i \(-0.220626\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 3.00874i 0.515995i
\(35\) 9.68629 + 0.774021i 1.63728 + 0.130833i
\(36\) 0 0
\(37\) −3.74165 + 6.48073i −0.615123 + 1.06542i 0.375240 + 0.926928i \(0.377560\pi\)
−0.990363 + 0.138497i \(0.955773\pi\)
\(38\) 0.676507i 0.109744i
\(39\) 0 0
\(40\) 1.26873 1.84128i 0.200604 0.291132i
\(41\) 2.60564 + 1.50437i 0.406933 + 0.234943i 0.689471 0.724313i \(-0.257843\pi\)
−0.282538 + 0.959256i \(0.591176\pi\)
\(42\) 0 0
\(43\) 5.91710 3.41624i 0.902349 0.520971i 0.0243872 0.999703i \(-0.492237\pi\)
0.877961 + 0.478731i \(0.158903\pi\)
\(44\) 2.35623i 0.355215i
\(45\) 0 0
\(46\) 5.58405 3.22396i 0.823324 0.475346i
\(47\) 5.61529 0.819074 0.409537 0.912294i \(-0.365690\pi\)
0.409537 + 0.912294i \(0.365690\pi\)
\(48\) 0 0
\(49\) −5.94234 + 10.2924i −0.848906 + 1.47035i
\(50\) 4.93655 + 0.794019i 0.698134 + 0.112291i
\(51\) 0 0
\(52\) −0.127265 3.60330i −0.0176485 0.499688i
\(53\) 9.43400i 1.29586i 0.761700 + 0.647930i \(0.224365\pi\)
−0.761700 + 0.647930i \(0.775635\pi\)
\(54\) 0 0
\(55\) 4.75816 2.26252i 0.641590 0.305078i
\(56\) 2.17283 + 3.76344i 0.290356 + 0.502911i
\(57\) 0 0
\(58\) −4.82620 8.35922i −0.633711 1.09762i
\(59\) 4.56364 2.63482i 0.594135 0.343024i −0.172596 0.984993i \(-0.555215\pi\)
0.766731 + 0.641969i \(0.221882\pi\)
\(60\) 0 0
\(61\) 2.15646 + 3.73509i 0.276106 + 0.478230i 0.970414 0.241449i \(-0.0776225\pi\)
−0.694307 + 0.719679i \(0.744289\pi\)
\(62\) 6.16171 + 3.55746i 0.782538 + 0.451798i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 7.15429 3.71700i 0.887381 0.461037i
\(66\) 0 0
\(67\) 2.91329 5.04596i 0.355915 0.616463i −0.631359 0.775490i \(-0.717503\pi\)
0.987274 + 0.159028i \(0.0508360\pi\)
\(68\) −2.60564 1.50437i −0.315981 0.182432i
\(69\) 0 0
\(70\) −5.51347 + 8.00157i −0.658986 + 0.956370i
\(71\) −2.52520 + 1.45793i −0.299686 + 0.173024i −0.642302 0.766452i \(-0.722020\pi\)
0.342616 + 0.939476i \(0.388687\pi\)
\(72\) 0 0
\(73\) 7.67804 0.898647 0.449323 0.893369i \(-0.351665\pi\)
0.449323 + 0.893369i \(0.351665\pi\)
\(74\) −3.74165 6.48073i −0.434958 0.753369i
\(75\) 0 0
\(76\) −0.585872 0.338254i −0.0672042 0.0388004i
\(77\) 10.2393i 1.16688i
\(78\) 0 0
\(79\) −3.74519 −0.421367 −0.210683 0.977554i \(-0.567569\pi\)
−0.210683 + 0.977554i \(0.567569\pi\)
\(80\) 0.960230 + 2.01940i 0.107357 + 0.225775i
\(81\) 0 0
\(82\) −2.60564 + 1.50437i −0.287745 + 0.166130i
\(83\) 10.3557 1.13668 0.568341 0.822793i \(-0.307585\pi\)
0.568341 + 0.822793i \(0.307585\pi\)
\(84\) 0 0
\(85\) 0.535898 6.70637i 0.0581263 0.727408i
\(86\) 6.83247i 0.736765i
\(87\) 0 0
\(88\) 2.04055 + 1.17811i 0.217524 + 0.125587i
\(89\) −4.15208 2.39720i −0.440119 0.254103i 0.263529 0.964651i \(-0.415114\pi\)
−0.703648 + 0.710549i \(0.748447\pi\)
\(90\) 0 0
\(91\) 0.553049 + 15.6587i 0.0579753 + 1.64148i
\(92\) 6.44791i 0.672241i
\(93\) 0 0
\(94\) −2.80764 + 4.86298i −0.289586 + 0.501578i
\(95\) 0.120495 1.50791i 0.0123626 0.154708i
\(96\) 0 0
\(97\) 8.17066 + 14.1520i 0.829605 + 1.43692i 0.898349 + 0.439283i \(0.144768\pi\)
−0.0687436 + 0.997634i \(0.521899\pi\)
\(98\) −5.94234 10.2924i −0.600267 1.03969i
\(99\) 0 0
\(100\) −3.15592 + 3.87817i −0.315592 + 0.387817i
\(101\) 6.11911 10.5986i 0.608875 1.05460i −0.382552 0.923934i \(-0.624955\pi\)
0.991426 0.130668i \(-0.0417121\pi\)
\(102\) 0 0
\(103\) 3.75144i 0.369640i −0.982772 0.184820i \(-0.940830\pi\)
0.982772 0.184820i \(-0.0591702\pi\)
\(104\) 3.18419 + 1.69144i 0.312235 + 0.165859i
\(105\) 0 0
\(106\) −8.17008 4.71700i −0.793549 0.458156i
\(107\) 14.3904 + 8.30831i 1.39117 + 0.803194i 0.993445 0.114309i \(-0.0364654\pi\)
0.397728 + 0.917503i \(0.369799\pi\)
\(108\) 0 0
\(109\) 11.1116i 1.06430i −0.846652 0.532148i \(-0.821385\pi\)
0.846652 0.532148i \(-0.178615\pi\)
\(110\) −0.419677 + 5.25194i −0.0400146 + 0.500753i
\(111\) 0 0
\(112\) −4.34565 −0.410625
\(113\) −13.5620 + 7.83002i −1.27581 + 0.736587i −0.976074 0.217437i \(-0.930230\pi\)
−0.299731 + 0.954024i \(0.596897\pi\)
\(114\) 0 0
\(115\) −13.0209 + 6.19148i −1.21420 + 0.577358i
\(116\) 9.65239 0.896202
\(117\) 0 0
\(118\) 5.26964i 0.485109i
\(119\) 11.3232 + 6.53747i 1.03800 + 0.599288i
\(120\) 0 0
\(121\) −2.72410 4.71827i −0.247645 0.428934i
\(122\) −4.31292 −0.390473
\(123\) 0 0
\(124\) −6.16171 + 3.55746i −0.553338 + 0.319470i
\(125\) −10.8620 2.64911i −0.971523 0.236943i
\(126\) 0 0
\(127\) −11.7820 6.80236i −1.04549 0.603611i −0.124103 0.992269i \(-0.539605\pi\)
−0.921382 + 0.388658i \(0.872939\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −0.358130 + 8.05430i −0.0314101 + 0.706409i
\(131\) −10.2122 −0.892246 −0.446123 0.894972i \(-0.647196\pi\)
−0.446123 + 0.894972i \(0.647196\pi\)
\(132\) 0 0
\(133\) 2.54600 + 1.46993i 0.220766 + 0.127459i
\(134\) 2.91329 + 5.04596i 0.251670 + 0.435905i
\(135\) 0 0
\(136\) 2.60564 1.50437i 0.223432 0.128999i
\(137\) −6.20689 10.7506i −0.530290 0.918489i −0.999375 0.0353365i \(-0.988750\pi\)
0.469085 0.883153i \(-0.344584\pi\)
\(138\) 0 0
\(139\) −7.80915 13.5258i −0.662363 1.14725i −0.979993 0.199032i \(-0.936220\pi\)
0.317630 0.948215i \(-0.397113\pi\)
\(140\) −4.17283 8.77559i −0.352668 0.741673i
\(141\) 0 0
\(142\) 2.91585i 0.244693i
\(143\) 4.50479 + 7.20280i 0.376710 + 0.602329i
\(144\) 0 0
\(145\) 9.26852 + 19.4920i 0.769709 + 1.61872i
\(146\) −3.83902 + 6.64938i −0.317720 + 0.550307i
\(147\) 0 0
\(148\) 7.48330 0.615123
\(149\) −16.9104 + 9.76324i −1.38536 + 0.799836i −0.992788 0.119886i \(-0.961747\pi\)
−0.392569 + 0.919722i \(0.628414\pi\)
\(150\) 0 0
\(151\) 11.5027i 0.936079i 0.883707 + 0.468040i \(0.155040\pi\)
−0.883707 + 0.468040i \(0.844960\pi\)
\(152\) 0.585872 0.338254i 0.0475205 0.0274360i
\(153\) 0 0
\(154\) −8.86753 5.11967i −0.714566 0.412555i
\(155\) −13.1006 9.02694i −1.05226 0.725061i
\(156\) 0 0
\(157\) 4.47595i 0.357220i −0.983920 0.178610i \(-0.942840\pi\)
0.983920 0.178610i \(-0.0571600\pi\)
\(158\) 1.87260 3.24343i 0.148976 0.258033i
\(159\) 0 0
\(160\) −2.22896 0.178114i −0.176215 0.0140811i
\(161\) 28.0204i 2.20831i
\(162\) 0 0
\(163\) −3.87774 6.71645i −0.303728 0.526073i 0.673249 0.739416i \(-0.264898\pi\)
−0.976977 + 0.213343i \(0.931565\pi\)
\(164\) 3.00874i 0.234943i
\(165\) 0 0
\(166\) −5.17783 + 8.96827i −0.401878 + 0.696073i
\(167\) 0.339021 0.587202i 0.0262342 0.0454390i −0.852610 0.522547i \(-0.824982\pi\)
0.878844 + 0.477108i \(0.158315\pi\)
\(168\) 0 0
\(169\) 7.27808 + 10.7717i 0.559852 + 0.828593i
\(170\) 5.53994 + 3.81729i 0.424894 + 0.292772i
\(171\) 0 0
\(172\) −5.91710 3.41624i −0.451174 0.260486i
\(173\) 0.625226 0.360974i 0.0475350 0.0274444i −0.476044 0.879421i \(-0.657930\pi\)
0.523579 + 0.851977i \(0.324596\pi\)
\(174\) 0 0
\(175\) 13.7145 16.8532i 1.03672 1.27398i
\(176\) −2.04055 + 1.17811i −0.153812 + 0.0888037i
\(177\) 0 0
\(178\) 4.15208 2.39720i 0.311211 0.179678i
\(179\) −3.18673 + 5.51958i −0.238187 + 0.412553i −0.960194 0.279333i \(-0.909887\pi\)
0.722007 + 0.691886i \(0.243220\pi\)
\(180\) 0 0
\(181\) 22.0214 1.63683 0.818417 0.574624i \(-0.194852\pi\)
0.818417 + 0.574624i \(0.194852\pi\)
\(182\) −13.8374 7.35040i −1.02569 0.544848i
\(183\) 0 0
\(184\) −5.58405 3.22396i −0.411662 0.237673i
\(185\) 7.18569 + 15.1117i 0.528302 + 1.11104i
\(186\) 0 0
\(187\) 7.08928 0.518419
\(188\) −2.80764 4.86298i −0.204768 0.354669i
\(189\) 0 0
\(190\) 1.24564 + 0.858307i 0.0903682 + 0.0622681i
\(191\) 0.293441 + 0.508255i 0.0212326 + 0.0367760i 0.876446 0.481499i \(-0.159908\pi\)
−0.855214 + 0.518275i \(0.826574\pi\)
\(192\) 0 0
\(193\) −11.3135 + 19.5955i −0.814363 + 1.41052i 0.0954215 + 0.995437i \(0.469580\pi\)
−0.909784 + 0.415081i \(0.863753\pi\)
\(194\) −16.3413 −1.17324
\(195\) 0 0
\(196\) 11.8847 0.848906
\(197\) −0.823770 + 1.42681i −0.0586912 + 0.101656i −0.893878 0.448310i \(-0.852026\pi\)
0.835187 + 0.549966i \(0.185359\pi\)
\(198\) 0 0
\(199\) −5.13665 8.89694i −0.364127 0.630687i 0.624508 0.781018i \(-0.285299\pi\)
−0.988636 + 0.150331i \(0.951966\pi\)
\(200\) −1.78064 4.67219i −0.125910 0.330374i
\(201\) 0 0
\(202\) 6.11911 + 10.5986i 0.430539 + 0.745716i
\(203\) −41.9459 −2.94403
\(204\) 0 0
\(205\) 6.07583 2.88908i 0.424355 0.201782i
\(206\) 3.24884 + 1.87572i 0.226357 + 0.130688i
\(207\) 0 0
\(208\) −3.05692 + 1.91187i −0.211959 + 0.132564i
\(209\) 1.59401 0.110260
\(210\) 0 0
\(211\) 12.1905 21.1145i 0.839226 1.45358i −0.0513166 0.998682i \(-0.516342\pi\)
0.890543 0.454900i \(-0.150325\pi\)
\(212\) 8.17008 4.71700i 0.561124 0.323965i
\(213\) 0 0
\(214\) −14.3904 + 8.30831i −0.983708 + 0.567944i
\(215\) 1.21696 15.2293i 0.0829959 1.03863i
\(216\) 0 0
\(217\) 26.7766 15.4595i 1.81772 1.04946i
\(218\) 9.62290 + 5.55578i 0.651745 + 0.376285i
\(219\) 0 0
\(220\) −4.33848 2.98942i −0.292500 0.201547i
\(221\) 10.8414 0.382907i 0.729272 0.0257571i
\(222\) 0 0
\(223\) −2.31792 + 4.01476i −0.155220 + 0.268848i −0.933139 0.359516i \(-0.882942\pi\)
0.777919 + 0.628364i \(0.216275\pi\)
\(224\) 2.17283 3.76344i 0.145178 0.251456i
\(225\) 0 0
\(226\) 15.6600i 1.04169i
\(227\) −8.89213 15.4016i −0.590192 1.02224i −0.994206 0.107489i \(-0.965719\pi\)
0.404015 0.914753i \(-0.367615\pi\)
\(228\) 0 0
\(229\) 15.3361i 1.01344i −0.862111 0.506720i \(-0.830858\pi\)
0.862111 0.506720i \(-0.169142\pi\)
\(230\) 1.14846 14.3722i 0.0757274 0.947672i
\(231\) 0 0
\(232\) −4.82620 + 8.35922i −0.316855 + 0.548809i
\(233\) 7.75548i 0.508079i −0.967194 0.254039i \(-0.918241\pi\)
0.967194 0.254039i \(-0.0817593\pi\)
\(234\) 0 0
\(235\) 7.12430 10.3393i 0.464738 0.674463i
\(236\) −4.56364 2.63482i −0.297068 0.171512i
\(237\) 0 0
\(238\) −11.3232 + 6.53747i −0.733975 + 0.423761i
\(239\) 18.6409i 1.20578i −0.797824 0.602890i \(-0.794016\pi\)
0.797824 0.602890i \(-0.205984\pi\)
\(240\) 0 0
\(241\) −2.65884 + 1.53508i −0.171271 + 0.0988833i −0.583185 0.812339i \(-0.698194\pi\)
0.411914 + 0.911223i \(0.364860\pi\)
\(242\) 5.44819 0.350223
\(243\) 0 0
\(244\) 2.15646 3.73509i 0.138053 0.239115i
\(245\) 11.4120 + 23.9999i 0.729088 + 1.53330i
\(246\) 0 0
\(247\) 2.43766 0.0860957i 0.155105 0.00547814i
\(248\) 7.11493i 0.451798i
\(249\) 0 0
\(250\) 7.72518 8.08218i 0.488583 0.511162i
\(251\) 3.56404 + 6.17309i 0.224960 + 0.389642i 0.956307 0.292363i \(-0.0944415\pi\)
−0.731347 + 0.682005i \(0.761108\pi\)
\(252\) 0 0
\(253\) −7.59637 13.1573i −0.477580 0.827193i
\(254\) 11.7820 6.80236i 0.739270 0.426818i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 12.3353 + 7.12178i 0.769454 + 0.444244i 0.832680 0.553755i \(-0.186806\pi\)
−0.0632261 + 0.997999i \(0.520139\pi\)
\(258\) 0 0
\(259\) −32.5198 −2.02068
\(260\) −6.79616 4.33730i −0.421480 0.268988i
\(261\) 0 0
\(262\) 5.10611 8.84404i 0.315457 0.546387i
\(263\) 13.3385 + 7.70101i 0.822490 + 0.474865i 0.851274 0.524721i \(-0.175830\pi\)
−0.0287845 + 0.999586i \(0.509164\pi\)
\(264\) 0 0
\(265\) 17.3707 + 11.9692i 1.06707 + 0.735264i
\(266\) −2.54600 + 1.46993i −0.156105 + 0.0901273i
\(267\) 0 0
\(268\) −5.82658 −0.355915
\(269\) −13.3134 23.0595i −0.811732 1.40596i −0.911651 0.410966i \(-0.865192\pi\)
0.0999185 0.994996i \(-0.468142\pi\)
\(270\) 0 0
\(271\) −6.66899 3.85034i −0.405112 0.233892i 0.283575 0.958950i \(-0.408479\pi\)
−0.688687 + 0.725058i \(0.741813\pi\)
\(272\) 3.00874i 0.182432i
\(273\) 0 0
\(274\) 12.4138 0.749943
\(275\) 1.87089 11.6316i 0.112819 0.701414i
\(276\) 0 0
\(277\) −12.3861 + 7.15114i −0.744211 + 0.429671i −0.823599 0.567173i \(-0.808037\pi\)
0.0793871 + 0.996844i \(0.474704\pi\)
\(278\) 15.6183 0.936723
\(279\) 0 0
\(280\) 9.68629 + 0.774021i 0.578867 + 0.0462566i
\(281\) 7.96746i 0.475299i −0.971351 0.237649i \(-0.923623\pi\)
0.971351 0.237649i \(-0.0763769\pi\)
\(282\) 0 0
\(283\) 12.7095 + 7.33785i 0.755503 + 0.436190i 0.827679 0.561202i \(-0.189661\pi\)
−0.0721756 + 0.997392i \(0.522994\pi\)
\(284\) 2.52520 + 1.45793i 0.149843 + 0.0865120i
\(285\) 0 0
\(286\) −8.49021 + 0.299865i −0.502036 + 0.0177314i
\(287\) 13.0749i 0.771789i
\(288\) 0 0
\(289\) −3.97374 + 6.88273i −0.233750 + 0.404866i
\(290\) −21.5148 1.71923i −1.26339 0.100956i
\(291\) 0 0
\(292\) −3.83902 6.64938i −0.224662 0.389125i
\(293\) −3.43198 5.94436i −0.200498 0.347273i 0.748191 0.663484i \(-0.230923\pi\)
−0.948689 + 0.316210i \(0.897589\pi\)
\(294\) 0 0
\(295\) 0.938596 11.7458i 0.0546472 0.683868i
\(296\) −3.74165 + 6.48073i −0.217479 + 0.376685i
\(297\) 0 0
\(298\) 19.5265i 1.13114i
\(299\) −12.3275 19.7108i −0.712921 1.13990i
\(300\) 0 0
\(301\) 25.7136 + 14.8458i 1.48211 + 0.855696i
\(302\) −9.96166 5.75137i −0.573229 0.330954i
\(303\) 0 0
\(304\) 0.676507i 0.0388004i
\(305\) 9.61333 + 0.768190i 0.550458 + 0.0439865i
\(306\) 0 0
\(307\) −10.9917 −0.627328 −0.313664 0.949534i \(-0.601557\pi\)
−0.313664 + 0.949534i \(0.601557\pi\)
\(308\) 8.86753 5.11967i 0.505275 0.291720i
\(309\) 0 0
\(310\) 14.3678 6.83197i 0.816039 0.388030i
\(311\) 13.9044 0.788446 0.394223 0.919015i \(-0.371014\pi\)
0.394223 + 0.919015i \(0.371014\pi\)
\(312\) 0 0
\(313\) 14.1734i 0.801130i 0.916268 + 0.400565i \(0.131186\pi\)
−0.916268 + 0.400565i \(0.868814\pi\)
\(314\) 3.87629 + 2.23798i 0.218752 + 0.126296i
\(315\) 0 0
\(316\) 1.87260 + 3.24343i 0.105342 + 0.182457i
\(317\) −3.20808 −0.180184 −0.0900920 0.995933i \(-0.528716\pi\)
−0.0900920 + 0.995933i \(0.528716\pi\)
\(318\) 0 0
\(319\) −19.6962 + 11.3716i −1.10278 + 0.636688i
\(320\) 1.26873 1.84128i 0.0709243 0.102931i
\(321\) 0 0
\(322\) 24.2664 + 14.0102i 1.35231 + 0.780757i
\(323\) 1.01772 1.76274i 0.0566273 0.0980813i
\(324\) 0 0
\(325\) 2.23284 17.8889i 0.123856 0.992300i
\(326\) 7.75548 0.429537
\(327\) 0 0
\(328\) 2.60564 + 1.50437i 0.143873 + 0.0830649i
\(329\) 12.2010 + 21.1328i 0.672665 + 1.16509i
\(330\) 0 0
\(331\) −22.3066 + 12.8787i −1.22608 + 0.707878i −0.966208 0.257765i \(-0.917014\pi\)
−0.259873 + 0.965643i \(0.583681\pi\)
\(332\) −5.17783 8.96827i −0.284170 0.492198i
\(333\) 0 0
\(334\) 0.339021 + 0.587202i 0.0185504 + 0.0321302i
\(335\) −5.59485 11.7662i −0.305680 0.642854i
\(336\) 0 0
\(337\) 0.772078i 0.0420578i 0.999779 + 0.0210289i \(0.00669420\pi\)
−0.999779 + 0.0210289i \(0.993306\pi\)
\(338\) −12.9676 + 0.917149i −0.705345 + 0.0498863i
\(339\) 0 0
\(340\) −6.07583 + 2.88908i −0.329508 + 0.156682i
\(341\) 8.38219 14.5184i 0.453921 0.786215i
\(342\) 0 0
\(343\) −21.2271 −1.14616
\(344\) 5.91710 3.41624i 0.319028 0.184191i
\(345\) 0 0
\(346\) 0.721948i 0.0388122i
\(347\) 21.7856 12.5779i 1.16951 0.675218i 0.215946 0.976405i \(-0.430716\pi\)
0.953565 + 0.301188i \(0.0973830\pi\)
\(348\) 0 0
\(349\) −23.6602 13.6602i −1.26650 0.731214i −0.292176 0.956365i \(-0.594379\pi\)
−0.974324 + 0.225151i \(0.927713\pi\)
\(350\) 7.73802 + 20.3037i 0.413614 + 1.08528i
\(351\) 0 0
\(352\) 2.35623i 0.125587i
\(353\) 3.75948 6.51161i 0.200097 0.346578i −0.748462 0.663177i \(-0.769208\pi\)
0.948559 + 0.316599i \(0.102541\pi\)
\(354\) 0 0
\(355\) −0.519354 + 6.49932i −0.0275644 + 0.344948i
\(356\) 4.79440i 0.254103i
\(357\) 0 0
\(358\) −3.18673 5.51958i −0.168424 0.291719i
\(359\) 10.8402i 0.572124i 0.958211 + 0.286062i \(0.0923463\pi\)
−0.958211 + 0.286062i \(0.907654\pi\)
\(360\) 0 0
\(361\) −9.27117 + 16.0581i −0.487956 + 0.845165i
\(362\) −11.0107 + 19.0711i −0.578708 + 1.00235i
\(363\) 0 0
\(364\) 13.2843 8.30831i 0.696287 0.435474i
\(365\) 9.74138 14.1374i 0.509887 0.739987i
\(366\) 0 0
\(367\) −6.50838 3.75761i −0.339735 0.196146i 0.320420 0.947276i \(-0.396176\pi\)
−0.660155 + 0.751130i \(0.729509\pi\)
\(368\) 5.58405 3.22396i 0.291089 0.168060i
\(369\) 0 0
\(370\) −16.6800 1.33288i −0.867151 0.0692931i
\(371\) −35.5043 + 20.4984i −1.84329 + 1.06423i
\(372\) 0 0
\(373\) −19.8135 + 11.4393i −1.02590 + 0.592305i −0.915808 0.401616i \(-0.868449\pi\)
−0.110095 + 0.993921i \(0.535115\pi\)
\(374\) −3.54464 + 6.13949i −0.183289 + 0.317466i
\(375\) 0 0
\(376\) 5.61529 0.289586
\(377\) −29.5066 + 18.4541i −1.51967 + 0.950434i
\(378\) 0 0
\(379\) −22.6152 13.0569i −1.16166 0.670687i −0.209962 0.977710i \(-0.567334\pi\)
−0.951702 + 0.307022i \(0.900667\pi\)
\(380\) −1.36614 + 0.649603i −0.0700813 + 0.0333239i
\(381\) 0 0
\(382\) −0.586882 −0.0300275
\(383\) 6.84652 + 11.8585i 0.349841 + 0.605942i 0.986221 0.165434i \(-0.0529024\pi\)
−0.636380 + 0.771376i \(0.719569\pi\)
\(384\) 0 0
\(385\) 18.8535 + 12.9910i 0.960864 + 0.662082i
\(386\) −11.3135 19.5955i −0.575842 0.997387i
\(387\) 0 0
\(388\) 8.17066 14.1520i 0.414802 0.718459i
\(389\) −24.9403 −1.26452 −0.632261 0.774755i \(-0.717873\pi\)
−0.632261 + 0.774755i \(0.717873\pi\)
\(390\) 0 0
\(391\) −19.4001 −0.981104
\(392\) −5.94234 + 10.2924i −0.300134 + 0.519847i
\(393\) 0 0
\(394\) −0.823770 1.42681i −0.0415009 0.0718817i
\(395\) −4.75165 + 6.89595i −0.239081 + 0.346973i
\(396\) 0 0
\(397\) −14.5517 25.2043i −0.730328 1.26497i −0.956743 0.290934i \(-0.906034\pi\)
0.226415 0.974031i \(-0.427300\pi\)
\(398\) 10.2733 0.514954
\(399\) 0 0
\(400\) 4.93655 + 0.794019i 0.246828 + 0.0397009i
\(401\) 14.4596 + 8.34823i 0.722076 + 0.416891i 0.815516 0.578734i \(-0.196453\pi\)
−0.0934404 + 0.995625i \(0.529786\pi\)
\(402\) 0 0
\(403\) 12.0345 22.6552i 0.599479 1.12854i
\(404\) −12.2382 −0.608875
\(405\) 0 0
\(406\) 20.9730 36.3262i 1.04087 1.80284i
\(407\) −15.2701 + 8.81618i −0.756909 + 0.437002i
\(408\) 0 0
\(409\) 21.3140 12.3056i 1.05391 0.608475i 0.130168 0.991492i \(-0.458448\pi\)
0.923741 + 0.383017i \(0.125115\pi\)
\(410\) −0.535898 + 6.70637i −0.0264661 + 0.331204i
\(411\) 0 0
\(412\) −3.24884 + 1.87572i −0.160059 + 0.0924100i
\(413\) 19.8320 + 11.4500i 0.975868 + 0.563418i
\(414\) 0 0
\(415\) 13.1386 19.0677i 0.644947 0.935996i
\(416\) −0.127265 3.60330i −0.00623968 0.176667i
\(417\) 0 0
\(418\) −0.797003 + 1.38045i −0.0389827 + 0.0675200i
\(419\) 13.5527 23.4739i 0.662091 1.14678i −0.317974 0.948099i \(-0.603002\pi\)
0.980065 0.198676i \(-0.0636643\pi\)
\(420\) 0 0
\(421\) 32.9996i 1.60830i −0.594425 0.804151i \(-0.702620\pi\)
0.594425 0.804151i \(-0.297380\pi\)
\(422\) 12.1905 + 21.1145i 0.593422 + 1.02784i
\(423\) 0 0
\(424\) 9.43400i 0.458156i
\(425\) −11.6684 9.49533i −0.566000 0.460591i
\(426\) 0 0
\(427\) −9.37121 + 16.2314i −0.453505 + 0.785493i
\(428\) 16.6166i 0.803194i
\(429\) 0 0
\(430\) 12.5805 + 8.66858i 0.606686 + 0.418036i
\(431\) −7.45678 4.30517i −0.359180 0.207373i 0.309541 0.950886i \(-0.399825\pi\)
−0.668721 + 0.743513i \(0.733158\pi\)
\(432\) 0 0
\(433\) 2.99201 1.72744i 0.143787 0.0830155i −0.426381 0.904544i \(-0.640212\pi\)
0.570168 + 0.821528i \(0.306878\pi\)
\(434\) 30.9190i 1.48416i
\(435\) 0 0
\(436\) −9.62290 + 5.55578i −0.460853 + 0.266074i
\(437\) −4.36206 −0.208666
\(438\) 0 0
\(439\) −12.1229 + 20.9974i −0.578593 + 1.00215i 0.417049 + 0.908884i \(0.363064\pi\)
−0.995641 + 0.0932675i \(0.970269\pi\)
\(440\) 4.75816 2.26252i 0.226836 0.107861i
\(441\) 0 0
\(442\) −5.08909 + 9.58038i −0.242064 + 0.455692i
\(443\) 13.1629i 0.625390i −0.949854 0.312695i \(-0.898768\pi\)
0.949854 0.312695i \(-0.101232\pi\)
\(444\) 0 0
\(445\) −9.68180 + 4.60373i −0.458961 + 0.218238i
\(446\) −2.31792 4.01476i −0.109757 0.190104i
\(447\) 0 0
\(448\) 2.17283 + 3.76344i 0.102656 + 0.177806i
\(449\) −2.17774 + 1.25732i −0.102774 + 0.0593365i −0.550506 0.834831i \(-0.685565\pi\)
0.447732 + 0.894168i \(0.352232\pi\)
\(450\) 0 0
\(451\) 3.54464 + 6.13949i 0.166910 + 0.289097i
\(452\) 13.5620 + 7.83002i 0.637903 + 0.368293i
\(453\) 0 0
\(454\) 17.7843 0.834657
\(455\) 29.5338 + 18.8484i 1.38456 + 0.883626i
\(456\) 0 0
\(457\) −5.38493 + 9.32698i −0.251897 + 0.436298i −0.964048 0.265728i \(-0.914388\pi\)
0.712151 + 0.702026i \(0.247721\pi\)
\(458\) 13.2815 + 7.66806i 0.620602 + 0.358305i
\(459\) 0 0
\(460\) 11.8724 + 8.18068i 0.553554 + 0.381426i
\(461\) −10.2984 + 5.94576i −0.479642 + 0.276922i −0.720267 0.693697i \(-0.755981\pi\)
0.240625 + 0.970618i \(0.422648\pi\)
\(462\) 0 0
\(463\) −29.9462 −1.39172 −0.695860 0.718178i \(-0.744976\pi\)
−0.695860 + 0.718178i \(0.744976\pi\)
\(464\) −4.82620 8.35922i −0.224051 0.388067i
\(465\) 0 0
\(466\) 6.71645 + 3.87774i 0.311133 + 0.179633i
\(467\) 21.8940i 1.01313i −0.862201 0.506566i \(-0.830915\pi\)
0.862201 0.506566i \(-0.169085\pi\)
\(468\) 0 0
\(469\) 25.3203 1.16918
\(470\) 5.39197 + 11.3395i 0.248713 + 0.523051i
\(471\) 0 0
\(472\) 4.56364 2.63482i 0.210059 0.121277i
\(473\) 16.0989 0.740227
\(474\) 0 0
\(475\) −2.62361 2.13500i −0.120379 0.0979605i
\(476\) 13.0749i 0.599288i
\(477\) 0 0
\(478\) 16.1435 + 9.32045i 0.738386 + 0.426307i
\(479\) 7.90106 + 4.56168i 0.361009 + 0.208429i 0.669523 0.742791i \(-0.266498\pi\)
−0.308514 + 0.951220i \(0.599832\pi\)
\(480\) 0 0
\(481\) −22.8758 + 14.3071i −1.04305 + 0.652346i
\(482\) 3.07016i 0.139842i
\(483\) 0 0
\(484\) −2.72410 + 4.71827i −0.123823 + 0.214467i
\(485\) 36.4242 + 2.91062i 1.65394 + 0.132164i
\(486\) 0 0
\(487\) 10.8587 + 18.8079i 0.492056 + 0.852265i 0.999958 0.00914916i \(-0.00291231\pi\)
−0.507902 + 0.861415i \(0.669579\pi\)
\(488\) 2.15646 + 3.73509i 0.0976183 + 0.169080i
\(489\) 0 0
\(490\) −26.4905 2.11683i −1.19672 0.0956285i
\(491\) −16.5438 + 28.6548i −0.746613 + 1.29317i 0.202824 + 0.979215i \(0.434988\pi\)
−0.949437 + 0.313957i \(0.898345\pi\)
\(492\) 0 0
\(493\) 29.0415i 1.30796i
\(494\) −1.14427 + 2.15412i −0.0514831 + 0.0969187i
\(495\) 0 0
\(496\) 6.16171 + 3.55746i 0.276669 + 0.159735i
\(497\) −10.9736 6.33564i −0.492235 0.284192i
\(498\) 0 0
\(499\) 10.4889i 0.469546i 0.972050 + 0.234773i \(0.0754347\pi\)
−0.972050 + 0.234773i \(0.924565\pi\)
\(500\) 3.13679 + 10.7313i 0.140281 + 0.479918i
\(501\) 0 0
\(502\) −7.12807 −0.318142
\(503\) 7.14818 4.12700i 0.318722 0.184014i −0.332101 0.943244i \(-0.607757\pi\)
0.650823 + 0.759230i \(0.274424\pi\)
\(504\) 0 0
\(505\) −11.7515 24.7138i −0.522936 1.09975i
\(506\) 15.1927 0.675400
\(507\) 0 0
\(508\) 13.6047i 0.603611i
\(509\) −5.84526 3.37476i −0.259087 0.149584i 0.364831 0.931074i \(-0.381127\pi\)
−0.623918 + 0.781490i \(0.714460\pi\)
\(510\) 0 0
\(511\) 16.6830 + 28.8959i 0.738014 + 1.27828i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −12.3353 + 7.12178i −0.544086 + 0.314128i
\(515\) −6.90745 4.75957i −0.304379 0.209732i
\(516\) 0 0
\(517\) 11.4583 + 6.61545i 0.503935 + 0.290947i
\(518\) 16.2599 28.1630i 0.714419 1.23741i
\(519\) 0 0
\(520\) 7.15429 3.71700i 0.313737 0.163001i
\(521\) 30.4048 1.33206 0.666029 0.745926i \(-0.267993\pi\)
0.666029 + 0.745926i \(0.267993\pi\)
\(522\) 0 0
\(523\) −2.72235 1.57175i −0.119040 0.0687279i 0.439298 0.898342i \(-0.355227\pi\)
−0.558338 + 0.829614i \(0.688561\pi\)
\(524\) 5.10611 + 8.84404i 0.223062 + 0.386354i
\(525\) 0 0
\(526\) −13.3385 + 7.70101i −0.581588 + 0.335780i
\(527\) −10.7035 18.5390i −0.466251 0.807570i
\(528\) 0 0
\(529\) 9.28778 + 16.0869i 0.403816 + 0.699431i
\(530\) −19.0510 + 9.05881i −0.827522 + 0.393490i
\(531\) 0 0
\(532\) 2.93986i 0.127459i
\(533\) 5.75231 + 9.19748i 0.249160 + 0.398387i
\(534\) 0 0
\(535\) 33.5555 15.9558i 1.45073 0.689828i
\(536\) 2.91329 5.04596i 0.125835 0.217952i
\(537\) 0 0
\(538\) 26.6268 1.14796
\(539\) −24.2513 + 14.0015i −1.04458 + 0.603088i
\(540\) 0 0
\(541\) 17.6144i 0.757301i −0.925540 0.378650i \(-0.876388\pi\)
0.925540 0.378650i \(-0.123612\pi\)
\(542\) 6.66899 3.85034i 0.286458 0.165386i
\(543\) 0 0
\(544\) −2.60564 1.50437i −0.111716 0.0644993i
\(545\) −20.4595 14.0976i −0.876390 0.603875i
\(546\) 0 0
\(547\) 40.8067i 1.74477i −0.488820 0.872385i \(-0.662572\pi\)
0.488820 0.872385i \(-0.337428\pi\)
\(548\) −6.20689 + 10.7506i −0.265145 + 0.459245i
\(549\) 0 0
\(550\) 9.13785 + 7.43606i 0.389639 + 0.317075i
\(551\) 6.52991i 0.278184i
\(552\) 0 0
\(553\) −8.13765 14.0948i −0.346048 0.599373i
\(554\) 14.3023i 0.607646i
\(555\) 0 0
\(556\) −7.80915 + 13.5258i −0.331182 + 0.573623i
\(557\) 12.6109 21.8427i 0.534340 0.925504i −0.464855 0.885387i \(-0.653894\pi\)
0.999195 0.0401170i \(-0.0127731\pi\)
\(558\) 0 0
\(559\) 24.6195 0.869535i 1.04129 0.0367774i
\(560\) −5.51347 + 8.00157i −0.232987 + 0.338128i
\(561\) 0 0
\(562\) 6.90002 + 3.98373i 0.291060 + 0.168043i
\(563\) −31.5356 + 18.2071i −1.32907 + 0.767337i −0.985155 0.171664i \(-0.945086\pi\)
−0.343912 + 0.939002i \(0.611752\pi\)
\(564\) 0 0
\(565\) −2.78927 + 34.9057i −0.117346 + 1.46849i
\(566\) −12.7095 + 7.33785i −0.534222 + 0.308433i
\(567\) 0 0
\(568\) −2.52520 + 1.45793i −0.105955 + 0.0611732i
\(569\) 13.6768 23.6888i 0.573360 0.993088i −0.422858 0.906196i \(-0.638973\pi\)
0.996218 0.0868922i \(-0.0276936\pi\)
\(570\) 0 0
\(571\) 45.7020 1.91257 0.956285 0.292438i \(-0.0944664\pi\)
0.956285 + 0.292438i \(0.0944664\pi\)
\(572\) 3.98541 7.50267i 0.166638 0.313702i
\(573\) 0 0
\(574\) −11.3232 6.53747i −0.472622 0.272869i
\(575\) −5.11976 + 31.8304i −0.213509 + 1.32742i
\(576\) 0 0
\(577\) −31.1697 −1.29761 −0.648806 0.760954i \(-0.724731\pi\)
−0.648806 + 0.760954i \(0.724731\pi\)
\(578\) −3.97374 6.88273i −0.165286 0.286284i
\(579\) 0 0
\(580\) 12.2463 17.7728i 0.508500 0.737974i
\(581\) 22.5011 + 38.9730i 0.933501 + 1.61687i
\(582\) 0 0
\(583\) −11.1143 + 19.2506i −0.460308 + 0.797278i
\(584\) 7.67804 0.317720
\(585\) 0 0
\(586\) 6.86396 0.283547
\(587\) 7.61411 13.1880i 0.314268 0.544328i −0.665014 0.746831i \(-0.731574\pi\)
0.979282 + 0.202503i \(0.0649076\pi\)
\(588\) 0 0
\(589\) −2.40665 4.16844i −0.0991643 0.171758i
\(590\) 9.70288 + 6.68576i 0.399461 + 0.275248i
\(591\) 0 0
\(592\) −3.74165 6.48073i −0.153781 0.266356i
\(593\) −15.1921 −0.623865 −0.311933 0.950104i \(-0.600976\pi\)
−0.311933 + 0.950104i \(0.600976\pi\)
\(594\) 0 0
\(595\) 26.4035 12.5549i 1.08244 0.514703i
\(596\) 16.9104 + 9.76324i 0.692678 + 0.399918i
\(597\) 0 0
\(598\) 23.2338 0.820594i 0.950100 0.0335566i
\(599\) −4.34655 −0.177595 −0.0887975 0.996050i \(-0.528302\pi\)
−0.0887975 + 0.996050i \(0.528302\pi\)
\(600\) 0 0
\(601\) −5.14622 + 8.91351i −0.209918 + 0.363590i −0.951689 0.307065i \(-0.900653\pi\)
0.741770 + 0.670654i \(0.233987\pi\)
\(602\) −25.7136 + 14.8458i −1.04801 + 0.605069i
\(603\) 0 0
\(604\) 9.96166 5.75137i 0.405334 0.234020i
\(605\) −12.1438 0.970399i −0.493716 0.0394523i
\(606\) 0 0
\(607\) 37.6094 21.7138i 1.52652 0.881335i 0.527012 0.849858i \(-0.323312\pi\)
0.999504 0.0314772i \(-0.0100212\pi\)
\(608\) −0.585872 0.338254i −0.0237603 0.0137180i
\(609\) 0 0
\(610\) −5.47194 + 7.94129i −0.221552 + 0.321534i
\(611\) 17.8801 + 9.49791i 0.723352 + 0.384244i
\(612\) 0 0
\(613\) −16.3258 + 28.2771i −0.659392 + 1.14210i 0.321382 + 0.946950i \(0.395853\pi\)
−0.980773 + 0.195150i \(0.937481\pi\)
\(614\) 5.49584 9.51907i 0.221794 0.384159i
\(615\) 0 0
\(616\) 10.2393i 0.412555i
\(617\) −4.83488 8.37426i −0.194645 0.337135i 0.752139 0.659004i \(-0.229022\pi\)
−0.946784 + 0.321869i \(0.895689\pi\)
\(618\) 0 0
\(619\) 5.20064i 0.209031i 0.994523 + 0.104516i \(0.0333292\pi\)
−0.994523 + 0.104516i \(0.966671\pi\)
\(620\) −1.26727 + 15.8589i −0.0508947 + 0.636909i
\(621\) 0 0
\(622\) −6.95220 + 12.0416i −0.278758 + 0.482823i
\(623\) 20.8348i 0.834729i
\(624\) 0 0
\(625\) −18.6587 + 16.6389i −0.746347 + 0.665557i
\(626\) −12.2746 7.08672i −0.490590 0.283242i
\(627\) 0 0
\(628\) −3.87629 + 2.23798i −0.154681 + 0.0893050i
\(629\) 22.5153i 0.897743i
\(630\) 0 0
\(631\) −6.86811 + 3.96531i −0.273415 + 0.157856i −0.630439 0.776239i \(-0.717125\pi\)
0.357023 + 0.934095i \(0.383792\pi\)
\(632\) −3.74519 −0.148976
\(633\) 0 0
\(634\) 1.60404 2.77828i 0.0637046 0.110340i
\(635\) −27.4733 + 13.0637i −1.09024 + 0.518415i
\(636\) 0 0
\(637\) −36.3305 + 22.7219i −1.43947 + 0.900276i
\(638\) 22.7432i 0.900413i
\(639\) 0 0
\(640\) 0.960230 + 2.01940i 0.0379564 + 0.0798236i
\(641\) 1.69937 + 2.94340i 0.0671212 + 0.116257i 0.897633 0.440744i \(-0.145285\pi\)
−0.830512 + 0.557001i \(0.811952\pi\)
\(642\) 0 0
\(643\) −4.69916 8.13918i −0.185317 0.320978i 0.758367 0.651828i \(-0.225998\pi\)
−0.943683 + 0.330851i \(0.892664\pi\)
\(644\) −24.2664 + 14.0102i −0.956228 + 0.552079i
\(645\) 0 0
\(646\) 1.01772 + 1.76274i 0.0400415 + 0.0693540i
\(647\) −34.6972 20.0324i −1.36409 0.787555i −0.373921 0.927461i \(-0.621987\pi\)
−0.990165 + 0.139905i \(0.955320\pi\)
\(648\) 0 0
\(649\) 12.4165 0.487389
\(650\) 14.3759 + 10.8782i 0.563868 + 0.426677i
\(651\) 0 0
\(652\) −3.87774 + 6.71645i −0.151864 + 0.263036i
\(653\) 27.1900 + 15.6981i 1.06403 + 0.614316i 0.926543 0.376189i \(-0.122766\pi\)
0.137483 + 0.990504i \(0.456099\pi\)
\(654\) 0 0
\(655\) −12.9566 + 18.8036i −0.506255 + 0.734717i
\(656\) −2.60564 + 1.50437i −0.101733 + 0.0587358i
\(657\) 0 0
\(658\) −24.4021 −0.951292
\(659\) −9.48950 16.4363i −0.369659 0.640268i 0.619853 0.784718i \(-0.287192\pi\)
−0.989512 + 0.144450i \(0.953859\pi\)
\(660\) 0 0
\(661\) 11.4484 + 6.60972i 0.445290 + 0.257088i 0.705839 0.708372i \(-0.250570\pi\)
−0.260549 + 0.965461i \(0.583904\pi\)
\(662\) 25.7574i 1.00109i
\(663\) 0 0
\(664\) 10.3557 0.401878
\(665\) 5.93675 2.82295i 0.230217 0.109469i
\(666\) 0 0
\(667\) 53.8995 31.1189i 2.08700 1.20493i
\(668\) −0.678042 −0.0262342
\(669\) 0 0
\(670\) 12.9872 + 1.03779i 0.501740 + 0.0400935i
\(671\) 10.1622i 0.392308i
\(672\) 0 0
\(673\) −7.44817 4.30020i −0.287106 0.165761i 0.349530 0.936925i \(-0.386341\pi\)
−0.636636 + 0.771164i \(0.719675\pi\)
\(674\) −0.668639 0.386039i −0.0257550 0.0148697i
\(675\) 0 0
\(676\) 5.68953 11.6889i 0.218828 0.449571i
\(677\) 25.8539i 0.993646i 0.867852 + 0.496823i \(0.165500\pi\)
−0.867852 + 0.496823i \(0.834500\pi\)
\(678\) 0 0
\(679\) −35.5068 + 61.4997i −1.36263 + 2.36014i
\(680\) 0.535898 6.70637i 0.0205508 0.257177i
\(681\) 0 0
\(682\) 8.38219 + 14.5184i 0.320971 + 0.555938i
\(683\) 10.4524 + 18.1041i 0.399950 + 0.692734i 0.993719 0.111901i \(-0.0356941\pi\)
−0.593769 + 0.804636i \(0.702361\pi\)
\(684\) 0 0
\(685\) −27.6698 2.21107i −1.05721 0.0844805i
\(686\) 10.6136 18.3832i 0.405228 0.701875i
\(687\) 0 0
\(688\) 6.83247i 0.260486i
\(689\) −15.9570 + 30.0396i −0.607914 + 1.14442i
\(690\) 0 0
\(691\) −42.3440 24.4473i −1.61084 0.930019i −0.989176 0.146736i \(-0.953123\pi\)
−0.621665 0.783283i \(-0.713543\pi\)
\(692\) −0.625226 0.360974i −0.0237675 0.0137222i
\(693\) 0 0
\(694\) 25.1558i 0.954902i
\(695\) −34.8126 2.78184i −1.32052 0.105521i
\(696\) 0 0
\(697\) 9.05251 0.342888
\(698\) 23.6602 13.6602i 0.895551 0.517046i
\(699\) 0 0
\(700\) −21.4525 3.45053i −0.810829 0.130418i
\(701\) −31.9805 −1.20789 −0.603944 0.797027i \(-0.706405\pi\)
−0.603944 + 0.797027i \(0.706405\pi\)
\(702\) 0 0
\(703\) 5.06250i 0.190936i
\(704\) 2.04055 + 1.17811i 0.0769062 + 0.0444018i
\(705\) 0 0
\(706\) 3.75948 + 6.51161i 0.141490 + 0.245068i
\(707\) 53.1831 2.00016
\(708\) 0 0
\(709\) −5.42026 + 3.12939i −0.203562 + 0.117527i −0.598316 0.801260i \(-0.704163\pi\)
0.394754 + 0.918787i \(0.370830\pi\)
\(710\) −5.36890 3.69944i −0.201491 0.138837i
\(711\) 0 0
\(712\) −4.15208 2.39720i −0.155606 0.0898389i
\(713\) −22.9382 + 39.7301i −0.859043 + 1.48791i
\(714\) 0 0
\(715\) 18.9778 + 0.843835i 0.709728 + 0.0315577i
\(716\) 6.37346 0.238187
\(717\) 0 0
\(718\) −9.38789 5.42010i −0.350353 0.202276i
\(719\) 9.52308 + 16.4945i 0.355151 + 0.615140i 0.987144 0.159835i \(-0.0510961\pi\)
−0.631993 + 0.774974i \(0.717763\pi\)
\(720\) 0 0
\(721\) 14.1183 8.15122i 0.525794 0.303567i
\(722\) −9.27117 16.0581i −0.345037 0.597622i
\(723\) 0 0
\(724\) −11.0107 19.0711i −0.409209 0.708770i
\(725\) 47.6495 + 7.66418i 1.76966 + 0.284640i
\(726\) 0 0
\(727\) 28.2602i 1.04811i 0.851684 + 0.524056i \(0.175582\pi\)
−0.851684 + 0.524056i \(0.824418\pi\)
\(728\) 0.553049 + 15.6587i 0.0204974 + 0.580350i
\(729\) 0 0
\(730\) 7.37269 + 15.5050i 0.272875 + 0.573866i
\(731\) 10.2786 17.8030i 0.380166 0.658468i
\(732\) 0 0
\(733\) 5.28165 0.195082 0.0975410 0.995232i \(-0.468902\pi\)
0.0975410 + 0.995232i \(0.468902\pi\)
\(734\) 6.50838 3.75761i 0.240229 0.138696i
\(735\) 0 0
\(736\) 6.44791i 0.237673i
\(737\) 11.8894 6.86437i 0.437953 0.252852i
\(738\) 0 0
\(739\) 34.5736 + 19.9611i 1.27181 + 0.734280i 0.975329 0.220758i \(-0.0708533\pi\)
0.296482 + 0.955038i \(0.404187\pi\)
\(740\) 9.49430 13.7789i 0.349018 0.506521i
\(741\) 0 0
\(742\) 40.9969i 1.50504i
\(743\) −9.28543 + 16.0828i −0.340650 + 0.590022i −0.984553 0.175084i \(-0.943980\pi\)
0.643904 + 0.765106i \(0.277314\pi\)
\(744\) 0 0
\(745\) −3.47794 + 43.5238i −0.127422 + 1.59459i
\(746\) 22.8786i 0.837646i
\(747\) 0 0
\(748\) −3.54464 6.13949i −0.129605 0.224482i
\(749\) 72.2100i 2.63850i
\(750\) 0 0
\(751\) 15.1001 26.1541i 0.551010 0.954377i −0.447192 0.894438i \(-0.647576\pi\)
0.998202 0.0599394i \(-0.0190907\pi\)
\(752\) −2.80764 + 4.86298i −0.102384 + 0.177335i
\(753\) 0 0
\(754\) −1.22841 34.7805i −0.0447361 1.26663i
\(755\) 21.1798 + 14.5939i 0.770811 + 0.531126i
\(756\) 0 0
\(757\) 4.85341 + 2.80211i 0.176400 + 0.101845i 0.585600 0.810600i \(-0.300859\pi\)
−0.409200 + 0.912445i \(0.634192\pi\)
\(758\) 22.6152 13.0569i 0.821421 0.474247i
\(759\) 0 0
\(760\) 0.120495 1.50791i 0.00437083 0.0546976i
\(761\) 5.77640 3.33501i 0.209394 0.120894i −0.391635 0.920120i \(-0.628091\pi\)
0.601030 + 0.799227i \(0.294757\pi\)
\(762\) 0 0
\(763\) 41.8178 24.1435i 1.51391 0.874053i
\(764\) 0.293441 0.508255i 0.0106163 0.0183880i
\(765\) 0 0
\(766\) −13.6930 −0.494750
\(767\) 18.9881 0.670640i 0.685621 0.0242154i
\(768\) 0 0
\(769\) 6.03234 + 3.48277i 0.217532 + 0.125592i 0.604807 0.796372i \(-0.293250\pi\)
−0.387275 + 0.921964i \(0.626584\pi\)
\(770\) −20.6773 + 9.83213i −0.745158 + 0.354325i
\(771\) 0 0
\(772\) 22.6270 0.814363
\(773\) −10.6748 18.4893i −0.383945 0.665013i 0.607677 0.794184i \(-0.292102\pi\)
−0.991622 + 0.129172i \(0.958768\pi\)
\(774\) 0 0
\(775\) −33.2423 + 12.6691i −1.19410 + 0.455087i
\(776\) 8.17066 + 14.1520i 0.293310 + 0.508027i
\(777\) 0 0
\(778\) 12.4701 21.5989i 0.447076 0.774359i
\(779\) 2.03543 0.0729270
\(780\) 0 0
\(781\) −6.87041 −0.245843
\(782\) 9.70004 16.8010i 0.346873 0.600801i
\(783\) 0 0
\(784\) −5.94234 10.2924i −0.212226 0.367587i
\(785\) −8.24149 5.67879i −0.294151 0.202685i
\(786\) 0 0