Properties

Label 1170.2.bj.c.829.5
Level $1170$
Weight $2$
Character 1170.829
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: \(x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + 190 x^{3} - 1196 x^{2} - 338 x + 2197\)
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 829.5
Root \(2.00607 - 1.30680i\) of defining polynomial
Character \(\chi\) \(=\) 1170.829
Dual form 1170.2.bj.c.199.5

$q$-expansion

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

Character values

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

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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 −0.0835003 0.996508i \(-0.526610\pi\)
0.904751 0.425940i \(-0.140057\pi\)
\(8\) 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 −0.159767 0.987155i \(-0.551074\pi\)
0.775017 + 0.631940i \(0.217741\pi\)
\(12\) 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 0.781511 0.623891i \(-0.214449\pi\)
−0.149550 + 0.988754i \(0.547782\pi\)
\(18\) 0 0
\(19\) 0.585872 + 0.338254i 0.134408 + 0.0776007i 0.565696 0.824614i \(-0.308607\pi\)
−0.431288 + 0.902214i \(0.641941\pi\)
\(20\) −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 −0.952344 0.305026i \(-0.901335\pi\)
−0.212012 + 0.977267i \(0.568002\pi\)
\(24\) 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 −0.832310 0.554311i \(-0.812982\pi\)
−0.0638921 0.997957i \(-0.520351\pi\)
\(30\) 0 0
\(31\) 7.11493i 1.27788i 0.769257 + 0.638939i \(0.220626\pi\)
−0.769257 + 0.638939i \(0.779374\pi\)
\(32\) −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 −0.990363 0.138497i \(-0.955773\pi\)
0.375240 0.926928i \(-0.377560\pi\)
\(38\) 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 −0.282538 0.959256i \(-0.591176\pi\)
0.689471 + 0.724313i \(0.257843\pi\)
\(42\) 0 0
\(43\) 5.91710 + 3.41624i 0.902349 + 0.520971i 0.877961 0.478731i \(-0.158903\pi\)
0.0243872 + 0.999703i \(0.492237\pi\)
\(44\) 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 \(-0.775635\pi\)
0.761700 0.647930i \(-0.224365\pi\)
\(54\) 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 0.766731 0.641969i \(-0.221882\pi\)
−0.172596 + 0.984993i \(0.555215\pi\)
\(60\) 0 0
\(61\) 2.15646 3.73509i 0.276106 0.478230i −0.694307 0.719679i \(-0.744289\pi\)
0.970414 + 0.241449i \(0.0776225\pi\)
\(62\) 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 0.987274 0.159028i \(-0.0508360\pi\)
−0.631359 + 0.775490i \(0.717503\pi\)
\(68\) −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 0.342616 0.939476i \(-0.388687\pi\)
−0.642302 + 0.766452i \(0.722020\pi\)
\(72\) 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 −0.703648 0.710549i \(-0.748447\pi\)
0.263529 + 0.964651i \(0.415114\pi\)
\(90\) 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 −0.0687436 0.997634i \(-0.521899\pi\)
0.898349 0.439283i \(-0.144768\pi\)
\(98\) −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 0.991426 + 0.130668i \(0.0417121\pi\)
−0.382552 + 0.923934i \(0.624955\pi\)
\(102\) 0 0
\(103\) 3.75144i 0.369640i 0.982772 + 0.184820i \(0.0591702\pi\)
−0.982772 + 0.184820i \(0.940830\pi\)
\(104\) 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 0.397728 0.917503i \(-0.369799\pi\)
0.993445 + 0.114309i \(0.0364654\pi\)
\(108\) 0 0
\(109\) 11.1116i 1.06430i 0.846652 + 0.532148i \(0.178615\pi\)
−0.846652 + 0.532148i \(0.821385\pi\)
\(110\) −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 −0.299731 0.954024i \(-0.596897\pi\)
−0.976074 + 0.217437i \(0.930230\pi\)
\(114\) 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 −0.921382 0.388658i \(-0.872939\pi\)
−0.124103 + 0.992269i \(0.539605\pi\)
\(128\) −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 0.469085 + 0.883153i \(0.344584\pi\)
−0.999375 + 0.0353365i \(0.988750\pi\)
\(138\) 0 0
\(139\) −7.80915 + 13.5258i −0.662363 + 1.14725i 0.317630 + 0.948215i \(0.397113\pi\)
−0.979993 + 0.199032i \(0.936220\pi\)
\(140\) −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 −0.392569 0.919722i \(-0.628414\pi\)
−0.992788 + 0.119886i \(0.961747\pi\)
\(150\) 0 0
\(151\) 11.5027i 0.936079i −0.883707 0.468040i \(-0.844960\pi\)
0.883707 0.468040i \(-0.155040\pi\)
\(152\) 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 \(0.0571600\pi\)
−0.983920 + 0.178610i \(0.942840\pi\)
\(158\) 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 −0.976977 0.213343i \(-0.931565\pi\)
0.673249 + 0.739416i \(0.264898\pi\)
\(164\) 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 0.878844 0.477108i \(-0.158315\pi\)
−0.852610 + 0.522547i \(0.824982\pi\)
\(168\) 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 0.523579 0.851977i \(-0.324596\pi\)
−0.476044 + 0.879421i \(0.657930\pi\)
\(174\) 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 0.722007 0.691886i \(-0.243220\pi\)
−0.960194 + 0.279333i \(0.909887\pi\)
\(180\) 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 −0.855214 0.518275i \(-0.826574\pi\)
0.876446 + 0.481499i \(0.159908\pi\)
\(192\) 0 0
\(193\) −11.3135 19.5955i −0.814363 1.41052i −0.909784 0.415081i \(-0.863753\pi\)
0.0954215 0.995437i \(-0.469580\pi\)
\(194\) −16.3413 −1.17324
\(195\) 0 0
\(196\) 11.8847 0.848906
\(197\) −0.823770 1.42681i −0.0586912 0.101656i 0.835187 0.549966i \(-0.185359\pi\)
−0.893878 + 0.448310i \(0.852026\pi\)
\(198\) 0 0
\(199\) −5.13665 + 8.89694i −0.364127 + 0.630687i −0.988636 0.150331i \(-0.951966\pi\)
0.624508 + 0.781018i \(0.285299\pi\)
\(200\) −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 0.890543 + 0.454900i \(0.150325\pi\)
−0.0513166 + 0.998682i \(0.516342\pi\)
\(212\) 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 0.777919 0.628364i \(-0.216275\pi\)
−0.933139 + 0.359516i \(0.882942\pi\)
\(224\) 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 0.404015 + 0.914753i \(0.367615\pi\)
−0.994206 + 0.107489i \(0.965719\pi\)
\(228\) 0 0
\(229\) 15.3361i 1.01344i 0.862111 + 0.506720i \(0.169142\pi\)
−0.862111 + 0.506720i \(0.830858\pi\)
\(230\) 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 \(0.0817593\pi\)
−0.967194 + 0.254039i \(0.918241\pi\)
\(234\) 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 \(0.205984\pi\)
−0.797824 + 0.602890i \(0.794016\pi\)
\(240\) 0 0
\(241\) −2.65884 1.53508i −0.171271 0.0988833i 0.411914 0.911223i \(-0.364860\pi\)
−0.583185 + 0.812339i \(0.698194\pi\)
\(242\) 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 −0.731347 0.682005i \(-0.761108\pi\)
0.956307 + 0.292363i \(0.0944415\pi\)
\(252\) 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 −0.0632261 0.997999i \(-0.520139\pi\)
0.832680 + 0.553755i \(0.186806\pi\)
\(258\) 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 −0.0287845 0.999586i \(-0.509164\pi\)
0.851274 + 0.524721i \(0.175830\pi\)
\(264\) 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 0.0999185 + 0.994996i \(0.468142\pi\)
−0.911651 + 0.410966i \(0.865192\pi\)
\(270\) 0 0
\(271\) −6.66899 + 3.85034i −0.405112 + 0.233892i −0.688687 0.725058i \(-0.741813\pi\)
0.283575 + 0.958950i \(0.408479\pi\)
\(272\) 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 0.0793871 0.996844i \(-0.474704\pi\)
−0.823599 + 0.567173i \(0.808037\pi\)
\(278\) 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 \(0.0763769\pi\)
−0.971351 + 0.237649i \(0.923623\pi\)
\(282\) 0 0
\(283\) 12.7095 7.33785i 0.755503 0.436190i −0.0721756 0.997392i \(-0.522994\pi\)
0.827679 + 0.561202i \(0.189661\pi\)
\(284\) 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 −0.948689 0.316210i \(-0.897589\pi\)
0.748191 + 0.663484i \(0.230923\pi\)
\(294\) 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 \(-0.868814\pi\)
0.916268 0.400565i \(-0.131186\pi\)
\(314\) 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 −0.259873 0.965643i \(-0.583681\pi\)
−0.966208 + 0.257765i \(0.917014\pi\)
\(332\) −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 \(-0.993306\pi\)
0.999779 0.0210289i \(-0.00669420\pi\)
\(338\) −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 0.953565 0.301188i \(-0.0973830\pi\)
0.215946 + 0.976405i \(0.430716\pi\)
\(348\) 0 0
\(349\) −23.6602 + 13.6602i −1.26650 + 0.731214i −0.974324 0.225151i \(-0.927713\pi\)
−0.292176 + 0.956365i \(0.594379\pi\)
\(350\) 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 0.948559 0.316599i \(-0.102541\pi\)
−0.748462 + 0.663177i \(0.769208\pi\)
\(354\) 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 \(-0.907654\pi\)
0.958211 0.286062i \(-0.0923463\pi\)
\(360\) 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 −0.660155 0.751130i \(-0.729509\pi\)
0.320420 + 0.947276i \(0.396176\pi\)
\(368\) 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 −0.110095 0.993921i \(-0.535115\pi\)
−0.915808 + 0.401616i \(0.868449\pi\)
\(374\) −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 −0.951702 0.307022i \(-0.900667\pi\)
−0.209962 + 0.977710i \(0.567334\pi\)
\(380\) −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 −0.636380 0.771376i \(-0.719569\pi\)
0.986221 + 0.165434i \(0.0529024\pi\)
\(384\) 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 0.226415 + 0.974031i \(0.427300\pi\)
−0.956743 + 0.290934i \(0.906034\pi\)
\(398\) 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 −0.0934404 0.995625i \(-0.529786\pi\)
0.815516 + 0.578734i \(0.196453\pi\)
\(402\) 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 0.923741 0.383017i \(-0.125115\pi\)
0.130168 + 0.991492i \(0.458448\pi\)
\(410\) −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 0.980065 + 0.198676i \(0.0636643\pi\)
−0.317974 + 0.948099i \(0.603002\pi\)
\(420\) 0 0
\(421\) 32.9996i 1.60830i 0.594425 + 0.804151i \(0.297380\pi\)
−0.594425 + 0.804151i \(0.702620\pi\)
\(422\) 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 −0.668721 0.743513i \(-0.733158\pi\)
0.309541 + 0.950886i \(0.399825\pi\)
\(432\) 0 0
\(433\) 2.99201 + 1.72744i 0.143787 + 0.0830155i 0.570168 0.821528i \(-0.306878\pi\)
−0.426381 + 0.904544i \(0.640212\pi\)
\(434\) 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 −0.995641 0.0932675i \(-0.970269\pi\)
0.417049 0.908884i \(-0.363064\pi\)
\(440\) 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 \(0.101232\pi\)
−0.949854 + 0.312695i \(0.898768\pi\)
\(444\) 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 0.447732 0.894168i \(-0.352232\pi\)
−0.550506 + 0.834831i \(0.685565\pi\)
\(450\) 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 0.712151 0.702026i \(-0.247721\pi\)
−0.964048 + 0.265728i \(0.914388\pi\)
\(458\) 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 0.240625 0.970618i \(-0.422648\pi\)
−0.720267 + 0.693697i \(0.755981\pi\)
\(462\) 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 \(0.169085\pi\)
−0.862201 + 0.506566i \(0.830915\pi\)
\(468\) 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 −0.308514 0.951220i \(-0.599832\pi\)
0.669523 + 0.742791i \(0.266498\pi\)
\(480\) 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 −0.507902 0.861415i \(-0.669579\pi\)
0.999958 + 0.00914916i \(0.00291231\pi\)
\(488\) 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 −0.949437 0.313957i \(-0.898345\pi\)
0.202824 0.979215i \(-0.434988\pi\)
\(492\) 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 \(-0.924565\pi\)
0.972050 0.234773i \(-0.0754347\pi\)
\(500\) 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 0.650823 0.759230i \(-0.274424\pi\)
−0.332101 + 0.943244i \(0.607757\pi\)
\(504\) 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 −0.623918 0.781490i \(-0.714460\pi\)
0.364831 + 0.931074i \(0.381127\pi\)
\(510\) 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 −0.558338 0.829614i \(-0.688561\pi\)
0.439298 + 0.898342i \(0.355227\pi\)
\(524\) 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 \(0.123612\pi\)
−0.925540 + 0.378650i \(0.876388\pi\)
\(542\) 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 \(0.337428\pi\)
−0.488820 + 0.872385i \(0.662572\pi\)
\(548\) −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 0.999195 + 0.0401170i \(0.0127731\pi\)
−0.464855 + 0.885387i \(0.653894\pi\)
\(558\) 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 −0.343912 0.939002i \(-0.611752\pi\)
−0.985155 + 0.171664i \(0.945086\pi\)
\(564\) 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 0.996218 + 0.0868922i \(0.0276936\pi\)
−0.422858 + 0.906196i \(0.638973\pi\)
\(570\) 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 0.979282 0.202503i \(-0.0649076\pi\)
−0.665014 + 0.746831i \(0.731574\pi\)
\(588\) 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 0.741770 0.670654i \(-0.233987\pi\)
−0.951689 + 0.307065i \(0.900653\pi\)
\(602\) −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 0.999504 + 0.0314772i \(0.0100212\pi\)
0.527012 + 0.849858i \(0.323312\pi\)
\(608\) −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 −0.980773 0.195150i \(-0.937481\pi\)
0.321382 0.946950i \(-0.395853\pi\)
\(614\) 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 −0.946784 0.321869i \(-0.895689\pi\)
0.752139 + 0.659004i \(0.229022\pi\)
\(618\) 0 0
\(619\) 5.20064i 0.209031i −0.994523 0.104516i \(-0.966671\pi\)
0.994523 0.104516i \(-0.0333292\pi\)
\(620\) −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 0.357023 0.934095i \(-0.383792\pi\)
−0.630439 + 0.776239i \(0.717125\pi\)
\(632\) −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 −0.830512 0.557001i \(-0.811952\pi\)
0.897633 + 0.440744i \(0.145285\pi\)
\(642\) 0 0
\(643\) −4.69916 + 8.13918i −0.185317 + 0.320978i −0.943683 0.330851i \(-0.892664\pi\)
0.758367 + 0.651828i \(0.225998\pi\)
\(644\) −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 −0.990165 0.139905i \(-0.955320\pi\)
−0.373921 + 0.927461i \(0.621987\pi\)
\(648\) 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 0.137483 0.990504i \(-0.456099\pi\)
0.926543 + 0.376189i \(0.122766\pi\)
\(654\) 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 −0.989512 0.144450i \(-0.953859\pi\)
0.619853 + 0.784718i \(0.287192\pi\)
\(660\) 0 0
\(661\) 11.4484 6.60972i 0.445290 0.257088i −0.260549 0.965461i \(-0.583904\pi\)
0.705839 + 0.708372i \(0.250570\pi\)
\(662\) 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 −0.636636 0.771164i \(-0.719675\pi\)
0.349530 + 0.936925i \(0.386341\pi\)
\(674\) −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 \(-0.834500\pi\)
0.867852 0.496823i \(-0.165500\pi\)
\(678\) 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 −0.593769 0.804636i \(-0.702361\pi\)
0.993719 + 0.111901i \(0.0356941\pi\)
\(684\) 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 −0.621665 + 0.783283i \(0.713543\pi\)
−0.989176 + 0.146736i \(0.953123\pi\)
\(692\) −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 0.394754 0.918787i \(-0.370830\pi\)
−0.598316 + 0.801260i \(0.704163\pi\)
\(710\) −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 −0.631993 0.774974i \(-0.717763\pi\)
0.987144 + 0.159835i \(0.0510961\pi\)
\(720\) 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 \(-0.824418\pi\)
0.851684 0.524056i \(-0.175582\pi\)
\(728\) 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 0.296482 0.955038i \(-0.404187\pi\)
0.975329 + 0.220758i \(0.0708533\pi\)
\(740\) 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 0.643904 0.765106i \(-0.277314\pi\)
−0.984553 + 0.175084i \(0.943980\pi\)
\(744\) 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 0.998202 + 0.0599394i \(0.0190907\pi\)
−0.447192 + 0.894438i \(0.647576\pi\)
\(752\) −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 −0.409200 0.912445i \(-0.634192\pi\)
0.585600 + 0.810600i \(0.300859\pi\)
\(758\) 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 0.601030 0.799227i \(-0.294757\pi\)
−0.391635 + 0.920120i \(0.628091\pi\)
\(762\) 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 −0.387275 0.921964i \(-0.626584\pi\)
0.604807 + 0.796372i \(0.293250\pi\)
\(770\) −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 −0.991622 0.129172i \(-0.958768\pi\)
0.607677 + 0.794184i \(0.292102\pi\)
\(774\) 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
\(787\) −9.61648 + 16.6562i −0.342791 + 0.593731i −0.984950 0.172841i \(-0.944705\pi\)
0.642159 + 0.766571i \(0.278039\pi\)
\(788\) 1.64754