Properties

Label 1170.2.bj.c.199.1
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: \(x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + 190 x^{3} - 1196 x^{2} - 338 x + 2197\)
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 199.1
Root \(-2.39378 - 0.0429626i\) of defining polynomial
Character \(\chi\) \(=\) 1170.199
Dual form 1170.2.bj.c.829.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.10012 - 0.767774i) q^{5} +(0.823063 + 1.42559i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.10012 - 0.767774i) q^{5} +(0.823063 + 1.42559i) q^{7} +1.00000 q^{8} +(1.71497 - 1.43487i) q^{10} +(-2.08305 - 1.20265i) q^{11} +(-3.59643 + 0.256262i) q^{13} -1.64613 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.210702 + 0.121649i) q^{17} +(3.82681 - 2.20941i) q^{19} +(0.385150 + 2.20265i) q^{20} +(2.08305 - 1.20265i) q^{22} +(7.46758 + 4.31141i) q^{23} +(3.82105 + 3.22484i) q^{25} +(1.57629 - 3.24273i) q^{26} +(0.823063 - 1.42559i) q^{28} +(-0.0221633 + 0.0383880i) q^{29} -4.24458i q^{31} +(-0.500000 - 0.866025i) q^{32} -0.243297i q^{34} +(-0.634006 - 3.62584i) q^{35} +(4.47415 - 7.74945i) q^{37} +4.41882i q^{38} +(-2.10012 - 0.767774i) q^{40} +(-0.210702 - 0.121649i) q^{41} +(-5.82728 + 3.36438i) q^{43} +2.40530i q^{44} +(-7.46758 + 4.31141i) q^{46} +7.29560 q^{47} +(2.14514 - 3.71548i) q^{49} +(-4.70332 + 1.69670i) q^{50} +(2.02015 + 2.98647i) q^{52} -2.44613i q^{53} +(3.45130 + 4.12502i) q^{55} +(0.823063 + 1.42559i) q^{56} +(-0.0221633 - 0.0383880i) q^{58} +(8.35669 - 4.82474i) q^{59} +(1.31630 + 2.27990i) q^{61} +(3.67591 + 2.12229i) q^{62} +1.00000 q^{64} +(7.74971 + 2.22307i) q^{65} +(0.937098 - 1.62310i) q^{67} +(0.210702 + 0.121649i) q^{68} +(3.45707 + 1.26385i) q^{70} +(6.53035 - 3.77030i) q^{71} +1.70370 q^{73} +(4.47415 + 7.74945i) q^{74} +(-3.82681 - 2.20941i) q^{76} -3.95942i q^{77} +6.79707 q^{79} +(1.71497 - 1.43487i) q^{80} +(0.210702 - 0.121649i) q^{82} +17.4986 q^{83} +(0.535898 - 0.0937060i) q^{85} -6.72876i q^{86} +(-2.08305 - 1.20265i) q^{88} +(8.69772 + 5.02163i) q^{89} +(-3.32541 - 4.91611i) q^{91} -8.62281i q^{92} +(-3.64780 + 6.31817i) q^{94} +(-9.73310 + 1.70191i) q^{95} +(8.25647 + 14.3006i) q^{97} +(2.14514 + 3.71548i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + O(q^{10}) \) \( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} - 2 q^{20} + 6 q^{22} + 6 q^{23} - 10 q^{25} + 2 q^{26} + 2 q^{28} - 14 q^{29} - 6 q^{32} + 22 q^{35} + 12 q^{37} - 2 q^{40} + 18 q^{41} + 36 q^{43} - 6 q^{46} + 16 q^{47} + 8 q^{49} + 20 q^{50} - 10 q^{52} + 8 q^{55} + 2 q^{56} - 14 q^{58} + 36 q^{59} + 10 q^{61} + 6 q^{62} + 12 q^{64} + 44 q^{65} - 4 q^{67} - 18 q^{68} + 4 q^{70} + 12 q^{71} - 28 q^{73} + 12 q^{74} + 6 q^{76} + 4 q^{79} + 4 q^{80} - 18 q^{82} + 72 q^{83} + 48 q^{85} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 8 q^{94} - 18 q^{95} + 48 q^{97} + 8 q^{98} + O(q^{100}) \)

Character values

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

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

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
\(5\) −2.10012 0.767774i −0.939204 0.343359i
\(6\) 0 0
\(7\) 0.823063 + 1.42559i 0.311088 + 0.538821i 0.978598 0.205780i \(-0.0659731\pi\)
−0.667510 + 0.744601i \(0.732640\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.71497 1.43487i 0.542322 0.453747i
\(11\) −2.08305 1.20265i −0.628063 0.362612i 0.151939 0.988390i \(-0.451448\pi\)
−0.780001 + 0.625778i \(0.784782\pi\)
\(12\) 0 0
\(13\) −3.59643 + 0.256262i −0.997471 + 0.0710744i
\(14\) −1.64613 −0.439946
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.210702 + 0.121649i −0.0511027 + 0.0295041i −0.525334 0.850896i \(-0.676059\pi\)
0.474231 + 0.880400i \(0.342726\pi\)
\(18\) 0 0
\(19\) 3.82681 2.20941i 0.877930 0.506873i 0.00795483 0.999968i \(-0.497468\pi\)
0.869975 + 0.493095i \(0.164135\pi\)
\(20\) 0.385150 + 2.20265i 0.0861222 + 0.492527i
\(21\) 0 0
\(22\) 2.08305 1.20265i 0.444107 0.256405i
\(23\) 7.46758 + 4.31141i 1.55710 + 0.898991i 0.997533 + 0.0702038i \(0.0223650\pi\)
0.559565 + 0.828787i \(0.310968\pi\)
\(24\) 0 0
\(25\) 3.82105 + 3.22484i 0.764209 + 0.644969i
\(26\) 1.57629 3.24273i 0.309135 0.635952i
\(27\) 0 0
\(28\) 0.823063 1.42559i 0.155544 0.269411i
\(29\) −0.0221633 + 0.0383880i −0.00411562 + 0.00712846i −0.868076 0.496432i \(-0.834643\pi\)
0.863960 + 0.503560i \(0.167977\pi\)
\(30\) 0 0
\(31\) 4.24458i 0.762348i −0.924503 0.381174i \(-0.875520\pi\)
0.924503 0.381174i \(-0.124480\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 0.243297i 0.0417251i
\(35\) −0.634006 3.62584i −0.107167 0.612878i
\(36\) 0 0
\(37\) 4.47415 7.74945i 0.735545 1.27400i −0.218939 0.975739i \(-0.570260\pi\)
0.954484 0.298263i \(-0.0964071\pi\)
\(38\) 4.41882i 0.716827i
\(39\) 0 0
\(40\) −2.10012 0.767774i −0.332059 0.121396i
\(41\) −0.210702 0.121649i −0.0329061 0.0189983i 0.483457 0.875368i \(-0.339381\pi\)
−0.516363 + 0.856370i \(0.672714\pi\)
\(42\) 0 0
\(43\) −5.82728 + 3.36438i −0.888652 + 0.513063i −0.873501 0.486822i \(-0.838156\pi\)
−0.0151507 + 0.999885i \(0.504823\pi\)
\(44\) 2.40530i 0.362612i
\(45\) 0 0
\(46\) −7.46758 + 4.31141i −1.10103 + 0.635682i
\(47\) 7.29560 1.06417 0.532086 0.846690i \(-0.321408\pi\)
0.532086 + 0.846690i \(0.321408\pi\)
\(48\) 0 0
\(49\) 2.14514 3.71548i 0.306448 0.530783i
\(50\) −4.70332 + 1.69670i −0.665150 + 0.239950i
\(51\) 0 0
\(52\) 2.02015 + 2.98647i 0.280144 + 0.414149i
\(53\) 2.44613i 0.336002i −0.985787 0.168001i \(-0.946269\pi\)
0.985787 0.168001i \(-0.0537312\pi\)
\(54\) 0 0
\(55\) 3.45130 + 4.12502i 0.465373 + 0.556218i
\(56\) 0.823063 + 1.42559i 0.109986 + 0.190502i
\(57\) 0 0
\(58\) −0.0221633 0.0383880i −0.00291018 0.00504059i
\(59\) 8.35669 4.82474i 1.08795 0.628127i 0.154919 0.987927i \(-0.450488\pi\)
0.933029 + 0.359800i \(0.117155\pi\)
\(60\) 0 0
\(61\) 1.31630 + 2.27990i 0.168535 + 0.291911i 0.937905 0.346892i \(-0.112763\pi\)
−0.769370 + 0.638804i \(0.779430\pi\)
\(62\) 3.67591 + 2.12229i 0.466841 + 0.269531i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 7.74971 + 2.22307i 0.961233 + 0.275737i
\(66\) 0 0
\(67\) 0.937098 1.62310i 0.114485 0.198293i −0.803089 0.595859i \(-0.796812\pi\)
0.917574 + 0.397566i \(0.130145\pi\)
\(68\) 0.210702 + 0.121649i 0.0255513 + 0.0147521i
\(69\) 0 0
\(70\) 3.45707 + 1.26385i 0.413199 + 0.151059i
\(71\) 6.53035 3.77030i 0.775010 0.447452i −0.0596488 0.998219i \(-0.518998\pi\)
0.834659 + 0.550767i \(0.185665\pi\)
\(72\) 0 0
\(73\) 1.70370 0.199403 0.0997015 0.995017i \(-0.468211\pi\)
0.0997015 + 0.995017i \(0.468211\pi\)
\(74\) 4.47415 + 7.74945i 0.520109 + 0.900855i
\(75\) 0 0
\(76\) −3.82681 2.20941i −0.438965 0.253437i
\(77\) 3.95942i 0.451218i
\(78\) 0 0
\(79\) 6.79707 0.764730 0.382365 0.924011i \(-0.375110\pi\)
0.382365 + 0.924011i \(0.375110\pi\)
\(80\) 1.71497 1.43487i 0.191740 0.160424i
\(81\) 0 0
\(82\) 0.210702 0.121649i 0.0232681 0.0134338i
\(83\) 17.4986 1.92073 0.960363 0.278754i \(-0.0899214\pi\)
0.960363 + 0.278754i \(0.0899214\pi\)
\(84\) 0 0
\(85\) 0.535898 0.0937060i 0.0581263 0.0101638i
\(86\) 6.72876i 0.725581i
\(87\) 0 0
\(88\) −2.08305 1.20265i −0.222054 0.128203i
\(89\) 8.69772 + 5.02163i 0.921956 + 0.532292i 0.884259 0.466997i \(-0.154664\pi\)
0.0376977 + 0.999289i \(0.487998\pi\)
\(90\) 0 0
\(91\) −3.32541 4.91611i −0.348598 0.515348i
\(92\) 8.62281i 0.898991i
\(93\) 0 0
\(94\) −3.64780 + 6.31817i −0.376242 + 0.651670i
\(95\) −9.73310 + 1.70191i −0.998595 + 0.174612i
\(96\) 0 0
\(97\) 8.25647 + 14.3006i 0.838317 + 1.45201i 0.891301 + 0.453413i \(0.149794\pi\)
−0.0529831 + 0.998595i \(0.516873\pi\)
\(98\) 2.14514 + 3.71548i 0.216691 + 0.375321i
\(99\) 0 0
\(100\) 0.882273 4.92154i 0.0882273 0.492154i
\(101\) −5.66777 + 9.81687i −0.563964 + 0.976815i 0.433181 + 0.901307i \(0.357391\pi\)
−0.997145 + 0.0755077i \(0.975942\pi\)
\(102\) 0 0
\(103\) 5.98168i 0.589392i 0.955591 + 0.294696i \(0.0952184\pi\)
−0.955591 + 0.294696i \(0.904782\pi\)
\(104\) −3.59643 + 0.256262i −0.352659 + 0.0251286i
\(105\) 0 0
\(106\) 2.11841 + 1.22307i 0.205758 + 0.118795i
\(107\) −9.24559 5.33795i −0.893805 0.516039i −0.0186200 0.999827i \(-0.505927\pi\)
−0.875185 + 0.483788i \(0.839261\pi\)
\(108\) 0 0
\(109\) 9.50683i 0.910589i 0.890341 + 0.455295i \(0.150466\pi\)
−0.890341 + 0.455295i \(0.849534\pi\)
\(110\) −5.29802 + 0.926401i −0.505147 + 0.0883288i
\(111\) 0 0
\(112\) −1.64613 −0.155544
\(113\) 3.11433 1.79806i 0.292972 0.169147i −0.346310 0.938120i \(-0.612565\pi\)
0.639281 + 0.768973i \(0.279232\pi\)
\(114\) 0 0
\(115\) −12.3727 14.7879i −1.15376 1.37898i
\(116\) 0.0443266 0.00411562
\(117\) 0 0
\(118\) 9.64947i 0.888306i
\(119\) −0.346841 0.200249i −0.0317949 0.0183568i
\(120\) 0 0
\(121\) −2.60727 4.51593i −0.237025 0.410539i
\(122\) −2.63260 −0.238345
\(123\) 0 0
\(124\) −3.67591 + 2.12229i −0.330106 + 0.190587i
\(125\) −5.54872 9.70627i −0.496293 0.868155i
\(126\) 0 0
\(127\) −15.0230 8.67351i −1.33307 0.769650i −0.347303 0.937753i \(-0.612902\pi\)
−0.985769 + 0.168103i \(0.946236\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −5.80009 + 5.59991i −0.508701 + 0.491145i
\(131\) −14.1654 −1.23764 −0.618818 0.785534i \(-0.712388\pi\)
−0.618818 + 0.785534i \(0.712388\pi\)
\(132\) 0 0
\(133\) 6.29941 + 3.63697i 0.546228 + 0.315365i
\(134\) 0.937098 + 1.62310i 0.0809530 + 0.140215i
\(135\) 0 0
\(136\) −0.210702 + 0.121649i −0.0180675 + 0.0104313i
\(137\) −3.66709 6.35158i −0.313300 0.542652i 0.665774 0.746153i \(-0.268101\pi\)
−0.979075 + 0.203501i \(0.934768\pi\)
\(138\) 0 0
\(139\) 7.10185 + 12.3008i 0.602371 + 1.04334i 0.992461 + 0.122561i \(0.0391107\pi\)
−0.390090 + 0.920777i \(0.627556\pi\)
\(140\) −2.82306 + 2.36198i −0.238592 + 0.199624i
\(141\) 0 0
\(142\) 7.54060i 0.632793i
\(143\) 7.79974 + 3.79144i 0.652247 + 0.317056i
\(144\) 0 0
\(145\) 0.0760190 0.0636031i 0.00631303 0.00528195i
\(146\) −0.851850 + 1.47545i −0.0704996 + 0.122109i
\(147\) 0 0
\(148\) −8.94829 −0.735545
\(149\) 9.61623 5.55193i 0.787792 0.454832i −0.0513926 0.998679i \(-0.516366\pi\)
0.839185 + 0.543847i \(0.183033\pi\)
\(150\) 0 0
\(151\) 0.874663i 0.0711791i 0.999366 + 0.0355895i \(0.0113309\pi\)
−0.999366 + 0.0355895i \(0.988669\pi\)
\(152\) 3.82681 2.20941i 0.310395 0.179207i
\(153\) 0 0
\(154\) 3.42896 + 1.97971i 0.276313 + 0.159530i
\(155\) −3.25888 + 8.91414i −0.261759 + 0.716001i
\(156\) 0 0
\(157\) 15.5085i 1.23771i −0.785504 0.618856i \(-0.787596\pi\)
0.785504 0.618856i \(-0.212404\pi\)
\(158\) −3.39854 + 5.88644i −0.270373 + 0.468300i
\(159\) 0 0
\(160\) 0.385150 + 2.20265i 0.0304488 + 0.174135i
\(161\) 14.1942i 1.11866i
\(162\) 0 0
\(163\) −10.9464 18.9597i −0.857388 1.48504i −0.874411 0.485185i \(-0.838752\pi\)
0.0170229 0.999855i \(-0.494581\pi\)
\(164\) 0.243297i 0.0189983i
\(165\) 0 0
\(166\) −8.74932 + 15.1543i −0.679079 + 1.17620i
\(167\) −2.64815 + 4.58673i −0.204920 + 0.354932i −0.950107 0.311923i \(-0.899027\pi\)
0.745187 + 0.666855i \(0.232360\pi\)
\(168\) 0 0
\(169\) 12.8687 1.84326i 0.989897 0.141789i
\(170\) −0.186797 + 0.510955i −0.0143267 + 0.0391884i
\(171\) 0 0
\(172\) 5.82728 + 3.36438i 0.444326 + 0.256532i
\(173\) −14.9469 + 8.62958i −1.13639 + 0.656095i −0.945534 0.325523i \(-0.894460\pi\)
−0.190856 + 0.981618i \(0.561126\pi\)
\(174\) 0 0
\(175\) −1.45233 + 8.10148i −0.109786 + 0.612414i
\(176\) 2.08305 1.20265i 0.157016 0.0906530i
\(177\) 0 0
\(178\) −8.69772 + 5.02163i −0.651922 + 0.376387i
\(179\) 4.17781 7.23617i 0.312264 0.540857i −0.666588 0.745426i \(-0.732246\pi\)
0.978852 + 0.204569i \(0.0655794\pi\)
\(180\) 0 0
\(181\) 12.7335 0.946476 0.473238 0.880935i \(-0.343085\pi\)
0.473238 + 0.880935i \(0.343085\pi\)
\(182\) 5.92018 0.421840i 0.438833 0.0312689i
\(183\) 0 0
\(184\) 7.46758 + 4.31141i 0.550517 + 0.317841i
\(185\) −15.3461 + 12.8397i −1.12827 + 0.943991i
\(186\) 0 0
\(187\) 0.585202 0.0427942
\(188\) −3.64780 6.31817i −0.266043 0.460800i
\(189\) 0 0
\(190\) 3.39265 9.28007i 0.246129 0.673247i
\(191\) 0.207632 + 0.359629i 0.0150237 + 0.0260219i 0.873440 0.486933i \(-0.161884\pi\)
−0.858416 + 0.512955i \(0.828551\pi\)
\(192\) 0 0
\(193\) 12.9918 22.5025i 0.935173 1.61977i 0.160849 0.986979i \(-0.448577\pi\)
0.774324 0.632789i \(-0.218090\pi\)
\(194\) −16.5129 −1.18556
\(195\) 0 0
\(196\) −4.29027 −0.306448
\(197\) −7.72121 + 13.3735i −0.550113 + 0.952824i 0.448152 + 0.893957i \(0.352082\pi\)
−0.998266 + 0.0588672i \(0.981251\pi\)
\(198\) 0 0
\(199\) 6.85286 + 11.8695i 0.485787 + 0.841407i 0.999867 0.0163352i \(-0.00519988\pi\)
−0.514080 + 0.857742i \(0.671867\pi\)
\(200\) 3.82105 + 3.22484i 0.270189 + 0.228031i
\(201\) 0 0
\(202\) −5.66777 9.81687i −0.398783 0.690712i
\(203\) −0.0729671 −0.00512129
\(204\) 0 0
\(205\) 0.349101 + 0.417249i 0.0243823 + 0.0291419i
\(206\) −5.18029 2.99084i −0.360928 0.208382i
\(207\) 0 0
\(208\) 1.57629 3.24273i 0.109296 0.224843i
\(209\) −10.6286 −0.735193
\(210\) 0 0
\(211\) 8.05616 13.9537i 0.554609 0.960611i −0.443325 0.896361i \(-0.646201\pi\)
0.997934 0.0642497i \(-0.0204654\pi\)
\(212\) −2.11841 + 1.22307i −0.145493 + 0.0840005i
\(213\) 0 0
\(214\) 9.24559 5.33795i 0.632016 0.364894i
\(215\) 14.8211 2.59159i 1.01079 0.176745i
\(216\) 0 0
\(217\) 6.05101 3.49355i 0.410769 0.237158i
\(218\) −8.23316 4.75342i −0.557620 0.321942i
\(219\) 0 0
\(220\) 1.84672 5.05142i 0.124506 0.340567i
\(221\) 0.726600 0.491496i 0.0488764 0.0330616i
\(222\) 0 0
\(223\) −5.55886 + 9.62823i −0.372249 + 0.644754i −0.989911 0.141690i \(-0.954747\pi\)
0.617662 + 0.786443i \(0.288080\pi\)
\(224\) 0.823063 1.42559i 0.0549932 0.0952510i
\(225\) 0 0
\(226\) 3.59612i 0.239210i
\(227\) −11.0399 19.1217i −0.732747 1.26915i −0.955705 0.294327i \(-0.904905\pi\)
0.222958 0.974828i \(-0.428429\pi\)
\(228\) 0 0
\(229\) 10.3397i 0.683266i 0.939834 + 0.341633i \(0.110980\pi\)
−0.939834 + 0.341633i \(0.889020\pi\)
\(230\) 18.9930 3.32108i 1.25236 0.218985i
\(231\) 0 0
\(232\) −0.0221633 + 0.0383880i −0.00145509 + 0.00252029i
\(233\) 21.8928i 1.43425i −0.696947 0.717123i \(-0.745459\pi\)
0.696947 0.717123i \(-0.254541\pi\)
\(234\) 0 0
\(235\) −15.3217 5.60137i −0.999475 0.365393i
\(236\) −8.35669 4.82474i −0.543974 0.314064i
\(237\) 0 0
\(238\) 0.346841 0.200249i 0.0224824 0.0129802i
\(239\) 26.2510i 1.69804i 0.528362 + 0.849019i \(0.322806\pi\)
−0.528362 + 0.849019i \(0.677194\pi\)
\(240\) 0 0
\(241\) 22.5952 13.0454i 1.45549 0.840326i 0.456703 0.889619i \(-0.349030\pi\)
0.998784 + 0.0492931i \(0.0156968\pi\)
\(242\) 5.21455 0.335204
\(243\) 0 0
\(244\) 1.31630 2.27990i 0.0842676 0.145956i
\(245\) −7.35770 + 6.15600i −0.470066 + 0.393292i
\(246\) 0 0
\(247\) −13.1967 + 8.92666i −0.839684 + 0.567990i
\(248\) 4.24458i 0.269531i
\(249\) 0 0
\(250\) 11.1802 + 0.0478026i 0.707100 + 0.00302330i
\(251\) 0.312397 + 0.541088i 0.0197183 + 0.0341532i 0.875716 0.482826i \(-0.160390\pi\)
−0.855998 + 0.516979i \(0.827056\pi\)
\(252\) 0 0
\(253\) −10.3702 17.9617i −0.651970 1.12924i
\(254\) 15.0230 8.67351i 0.942624 0.544224i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −12.0758 6.97195i −0.753266 0.434898i 0.0736066 0.997287i \(-0.476549\pi\)
−0.826873 + 0.562389i \(0.809882\pi\)
\(258\) 0 0
\(259\) 14.7300 0.915278
\(260\) −1.94962 7.82298i −0.120910 0.485160i
\(261\) 0 0
\(262\) 7.08270 12.2676i 0.437571 0.757894i
\(263\) −16.8325 9.71828i −1.03794 0.599255i −0.118690 0.992931i \(-0.537870\pi\)
−0.919249 + 0.393677i \(0.871203\pi\)
\(264\) 0 0
\(265\) −1.87808 + 5.13718i −0.115369 + 0.315574i
\(266\) −6.29941 + 3.63697i −0.386242 + 0.222997i
\(267\) 0 0
\(268\) −1.87420 −0.114485
\(269\) 1.50069 + 2.59928i 0.0914989 + 0.158481i 0.908142 0.418662i \(-0.137501\pi\)
−0.816643 + 0.577143i \(0.804168\pi\)
\(270\) 0 0
\(271\) −24.6538 14.2339i −1.49761 0.864645i −0.497613 0.867399i \(-0.665790\pi\)
−0.999996 + 0.00275396i \(0.999123\pi\)
\(272\) 0.243297i 0.0147521i
\(273\) 0 0
\(274\) 7.33417 0.443074
\(275\) −4.08107 11.3129i −0.246098 0.682192i
\(276\) 0 0
\(277\) 0.738423 0.426329i 0.0443676 0.0256156i −0.477652 0.878549i \(-0.658512\pi\)
0.522020 + 0.852933i \(0.325179\pi\)
\(278\) −14.2037 −0.851882
\(279\) 0 0
\(280\) −0.634006 3.62584i −0.0378891 0.216685i
\(281\) 15.6851i 0.935697i −0.883809 0.467848i \(-0.845029\pi\)
0.883809 0.467848i \(-0.154971\pi\)
\(282\) 0 0
\(283\) 7.00390 + 4.04370i 0.416339 + 0.240373i 0.693510 0.720447i \(-0.256063\pi\)
−0.277171 + 0.960821i \(0.589397\pi\)
\(284\) −6.53035 3.77030i −0.387505 0.223726i
\(285\) 0 0
\(286\) −7.18335 + 4.85905i −0.424760 + 0.287322i
\(287\) 0.400498i 0.0236406i
\(288\) 0 0
\(289\) −8.47040 + 14.6712i −0.498259 + 0.863010i
\(290\) 0.0170724 + 0.0976359i 0.00100253 + 0.00573338i
\(291\) 0 0
\(292\) −0.851850 1.47545i −0.0498508 0.0863440i
\(293\) 0.967192 + 1.67523i 0.0565040 + 0.0978677i 0.892894 0.450267i \(-0.148671\pi\)
−0.836390 + 0.548135i \(0.815338\pi\)
\(294\) 0 0
\(295\) −21.2544 + 3.71650i −1.23748 + 0.216383i
\(296\) 4.47415 7.74945i 0.260054 0.450427i
\(297\) 0 0
\(298\) 11.1039i 0.643229i
\(299\) −27.9615 13.5920i −1.61705 0.786047i
\(300\) 0 0
\(301\) −9.59244 5.53820i −0.552899 0.319216i
\(302\) −0.757480 0.437332i −0.0435881 0.0251656i
\(303\) 0 0
\(304\) 4.41882i 0.253437i
\(305\) −1.01395 5.79870i −0.0580585 0.332033i
\(306\) 0 0
\(307\) −12.4384 −0.709894 −0.354947 0.934886i \(-0.615501\pi\)
−0.354947 + 0.934886i \(0.615501\pi\)
\(308\) −3.42896 + 1.97971i −0.195383 + 0.112804i
\(309\) 0 0
\(310\) −6.09043 7.27934i −0.345913 0.413439i
\(311\) 18.3700 1.04167 0.520835 0.853657i \(-0.325621\pi\)
0.520835 + 0.853657i \(0.325621\pi\)
\(312\) 0 0
\(313\) 31.9445i 1.80561i 0.430051 + 0.902804i \(0.358496\pi\)
−0.430051 + 0.902804i \(0.641504\pi\)
\(314\) 13.4307 + 7.75425i 0.757941 + 0.437597i
\(315\) 0 0
\(316\) −3.39854 5.88644i −0.191183 0.331138i
\(317\) 23.3625 1.31217 0.656083 0.754689i \(-0.272212\pi\)
0.656083 + 0.754689i \(0.272212\pi\)
\(318\) 0 0
\(319\) 0.0923344 0.0533093i 0.00516973 0.00298475i
\(320\) −2.10012 0.767774i −0.117401 0.0429199i
\(321\) 0 0
\(322\) −12.2926 7.09712i −0.685038 0.395507i
\(323\) −0.537543 + 0.931052i −0.0299097 + 0.0518051i
\(324\) 0 0
\(325\) −14.5685 10.6187i −0.808117 0.589022i
\(326\) 21.8928 1.21253
\(327\) 0 0
\(328\) −0.210702 0.121649i −0.0116341 0.00671692i
\(329\) 6.00474 + 10.4005i 0.331052 + 0.573399i
\(330\) 0 0
\(331\) −18.5879 + 10.7317i −1.02168 + 0.589868i −0.914590 0.404382i \(-0.867487\pi\)
−0.107090 + 0.994249i \(0.534153\pi\)
\(332\) −8.74932 15.1543i −0.480181 0.831698i
\(333\) 0 0
\(334\) −2.64815 4.58673i −0.144900 0.250975i
\(335\) −3.21420 + 2.68924i −0.175610 + 0.146929i
\(336\) 0 0
\(337\) 14.3561i 0.782026i 0.920385 + 0.391013i \(0.127875\pi\)
−0.920385 + 0.391013i \(0.872125\pi\)
\(338\) −4.83802 + 12.0662i −0.263154 + 0.656316i
\(339\) 0 0
\(340\) −0.349101 0.417249i −0.0189327 0.0226285i
\(341\) −5.10473 + 8.84165i −0.276437 + 0.478802i
\(342\) 0 0
\(343\) 18.5852 1.00351
\(344\) −5.82728 + 3.36438i −0.314186 + 0.181395i
\(345\) 0 0
\(346\) 17.2592i 0.927858i
\(347\) 0.576005 0.332557i 0.0309216 0.0178526i −0.484460 0.874814i \(-0.660984\pi\)
0.515381 + 0.856961i \(0.327650\pi\)
\(348\) 0 0
\(349\) 3.25007 + 1.87643i 0.173972 + 0.100443i 0.584458 0.811424i \(-0.301307\pi\)
−0.410485 + 0.911867i \(0.634641\pi\)
\(350\) −6.28992 5.30850i −0.336210 0.283751i
\(351\) 0 0
\(352\) 2.40530i 0.128203i
\(353\) 2.28180 3.95219i 0.121448 0.210354i −0.798891 0.601476i \(-0.794580\pi\)
0.920339 + 0.391122i \(0.127913\pi\)
\(354\) 0 0
\(355\) −16.6093 + 2.90426i −0.881530 + 0.154142i
\(356\) 10.0433i 0.532292i
\(357\) 0 0
\(358\) 4.17781 + 7.23617i 0.220804 + 0.382444i
\(359\) 4.75785i 0.251110i 0.992087 + 0.125555i \(0.0400711\pi\)
−0.992087 + 0.125555i \(0.959929\pi\)
\(360\) 0 0
\(361\) 0.262979 0.455494i 0.0138410 0.0239733i
\(362\) −6.36677 + 11.0276i −0.334630 + 0.579596i
\(363\) 0 0
\(364\) −2.59477 + 5.33795i −0.136003 + 0.279784i
\(365\) −3.57798 1.30806i −0.187280 0.0684668i
\(366\) 0 0
\(367\) 1.29432 + 0.747277i 0.0675630 + 0.0390075i 0.533401 0.845863i \(-0.320914\pi\)
−0.465838 + 0.884870i \(0.654247\pi\)
\(368\) −7.46758 + 4.31141i −0.389274 + 0.224748i
\(369\) 0 0
\(370\) −3.44644 19.7099i −0.179172 1.02467i
\(371\) 3.48717 2.01332i 0.181045 0.104526i
\(372\) 0 0
\(373\) 17.8323 10.2955i 0.923323 0.533081i 0.0386291 0.999254i \(-0.487701\pi\)
0.884694 + 0.466173i \(0.154368\pi\)
\(374\) −0.292601 + 0.506800i −0.0151300 + 0.0262060i
\(375\) 0 0
\(376\) 7.29560 0.376242
\(377\) 0.0698714 0.143739i 0.00359856 0.00740295i
\(378\) 0 0
\(379\) −18.4173 10.6332i −0.946032 0.546192i −0.0541858 0.998531i \(-0.517256\pi\)
−0.891846 + 0.452339i \(0.850590\pi\)
\(380\) 6.34045 + 7.57816i 0.325258 + 0.388751i
\(381\) 0 0
\(382\) −0.415264 −0.0212468
\(383\) −5.31095 9.19884i −0.271377 0.470039i 0.697838 0.716256i \(-0.254146\pi\)
−0.969215 + 0.246217i \(0.920812\pi\)
\(384\) 0 0
\(385\) −3.03994 + 8.31527i −0.154930 + 0.423786i
\(386\) 12.9918 + 22.5025i 0.661267 + 1.14535i
\(387\) 0 0
\(388\) 8.25647 14.3006i 0.419159 0.726004i
\(389\) 37.0443 1.87822 0.939111 0.343613i \(-0.111651\pi\)
0.939111 + 0.343613i \(0.111651\pi\)
\(390\) 0 0
\(391\) −2.09791 −0.106096
\(392\) 2.14514 3.71548i 0.108346 0.187660i
\(393\) 0 0
\(394\) −7.72121 13.3735i −0.388989 0.673749i
\(395\) −14.2747 5.21862i −0.718238 0.262577i
\(396\) 0 0
\(397\) −0.843593 1.46115i −0.0423387 0.0733328i 0.844079 0.536218i \(-0.180148\pi\)
−0.886418 + 0.462885i \(0.846814\pi\)
\(398\) −13.7057 −0.687006
\(399\) 0 0
\(400\) −4.70332 + 1.69670i −0.235166 + 0.0848351i
\(401\) −17.2949 9.98524i −0.863668 0.498639i 0.00157101 0.999999i \(-0.499500\pi\)
−0.865239 + 0.501360i \(0.832833\pi\)
\(402\) 0 0
\(403\) 1.08772 + 15.2653i 0.0541834 + 0.760420i
\(404\) 11.3355 0.563964
\(405\) 0 0
\(406\) 0.0364836 0.0631914i 0.00181065 0.00313614i
\(407\) −18.6397 + 10.7616i −0.923936 + 0.533435i
\(408\) 0 0
\(409\) 10.6603 6.15471i 0.527117 0.304331i −0.212725 0.977112i \(-0.568234\pi\)
0.739842 + 0.672781i \(0.234900\pi\)
\(410\) −0.535898 + 0.0937060i −0.0264661 + 0.00462781i
\(411\) 0 0
\(412\) 5.18029 2.99084i 0.255214 0.147348i
\(413\) 13.7562 + 7.94212i 0.676896 + 0.390806i
\(414\) 0 0
\(415\) −36.7493 13.4350i −1.80395 0.659498i
\(416\) 2.02015 + 2.98647i 0.0990458 + 0.146424i
\(417\) 0 0
\(418\) 5.31428 9.20461i 0.259930 0.450212i
\(419\) −11.0411 + 19.1238i −0.539393 + 0.934256i 0.459544 + 0.888155i \(0.348013\pi\)
−0.998937 + 0.0461011i \(0.985320\pi\)
\(420\) 0 0
\(421\) 8.98036i 0.437676i 0.975761 + 0.218838i \(0.0702266\pi\)
−0.975761 + 0.218838i \(0.929773\pi\)
\(422\) 8.05616 + 13.9537i 0.392168 + 0.679254i
\(423\) 0 0
\(424\) 2.44613i 0.118795i
\(425\) −1.19740 0.214655i −0.0580824 0.0104123i
\(426\) 0 0
\(427\) −2.16680 + 3.75300i −0.104859 + 0.181621i
\(428\) 10.6759i 0.516039i
\(429\) 0 0
\(430\) −5.16617 + 14.1312i −0.249135 + 0.681469i
\(431\) −7.16090 4.13435i −0.344928 0.199145i 0.317521 0.948251i \(-0.397150\pi\)
−0.662449 + 0.749107i \(0.730483\pi\)
\(432\) 0 0
\(433\) 17.1825 9.92035i 0.825740 0.476741i −0.0266515 0.999645i \(-0.508484\pi\)
0.852392 + 0.522903i \(0.175151\pi\)
\(434\) 6.98710i 0.335392i
\(435\) 0 0
\(436\) 8.23316 4.75342i 0.394297 0.227647i
\(437\) 38.1027 1.82270
\(438\) 0 0
\(439\) −14.4415 + 25.0134i −0.689255 + 1.19382i 0.282824 + 0.959172i \(0.408729\pi\)
−0.972079 + 0.234653i \(0.924605\pi\)
\(440\) 3.45130 + 4.12502i 0.164534 + 0.196653i
\(441\) 0 0
\(442\) 0.0623479 + 0.875002i 0.00296559 + 0.0416196i
\(443\) 5.76986i 0.274134i −0.990562 0.137067i \(-0.956232\pi\)
0.990562 0.137067i \(-0.0437676\pi\)
\(444\) 0 0
\(445\) −14.4108 17.2239i −0.683138 0.816493i
\(446\) −5.55886 9.62823i −0.263220 0.455910i
\(447\) 0 0
\(448\) 0.823063 + 1.42559i 0.0388861 + 0.0673526i
\(449\) 33.9034 19.5741i 1.60000 0.923760i 0.608514 0.793543i \(-0.291766\pi\)
0.991486 0.130217i \(-0.0415674\pi\)
\(450\) 0 0
\(451\) 0.292601 + 0.506800i 0.0137780 + 0.0238643i
\(452\) −3.11433 1.79806i −0.146486 0.0845736i
\(453\) 0 0
\(454\) 22.0799 1.03626
\(455\) 3.20932 + 12.8776i 0.150455 + 0.603711i
\(456\) 0 0
\(457\) −12.2403 + 21.2008i −0.572575 + 0.991730i 0.423725 + 0.905791i \(0.360722\pi\)
−0.996300 + 0.0859387i \(0.972611\pi\)
\(458\) −8.95443 5.16984i −0.418413 0.241571i
\(459\) 0 0
\(460\) −6.62037 + 18.1090i −0.308677 + 0.844336i
\(461\) −3.02923 + 1.74893i −0.141085 + 0.0814557i −0.568881 0.822420i \(-0.692624\pi\)
0.427796 + 0.903875i \(0.359290\pi\)
\(462\) 0 0
\(463\) 18.3063 0.850767 0.425384 0.905013i \(-0.360139\pi\)
0.425384 + 0.905013i \(0.360139\pi\)
\(464\) −0.0221633 0.0383880i −0.00102891 0.00178212i
\(465\) 0 0
\(466\) 18.9597 + 10.9464i 0.878292 + 0.507082i
\(467\) 6.46019i 0.298942i −0.988766 0.149471i \(-0.952243\pi\)
0.988766 0.149471i \(-0.0477571\pi\)
\(468\) 0 0
\(469\) 3.08516 0.142460
\(470\) 12.5118 10.4683i 0.577125 0.482865i
\(471\) 0 0
\(472\) 8.35669 4.82474i 0.384648 0.222077i
\(473\) 16.1847 0.744172
\(474\) 0 0
\(475\) 21.7474 + 3.89860i 0.997840 + 0.178880i
\(476\) 0.400498i 0.0183568i
\(477\) 0 0
\(478\) −22.7341 13.1255i −1.03983 0.600347i
\(479\) −26.5980 15.3564i −1.21529 0.701651i −0.251387 0.967887i \(-0.580887\pi\)
−0.963908 + 0.266236i \(0.914220\pi\)
\(480\) 0 0
\(481\) −14.1051 + 29.0169i −0.643136 + 1.32306i
\(482\) 26.0907i 1.18840i
\(483\) 0 0
\(484\) −2.60727 + 4.51593i −0.118512 + 0.205270i
\(485\) −6.35996 36.3722i −0.288791 1.65158i
\(486\) 0 0
\(487\) 6.23335 + 10.7965i 0.282460 + 0.489235i 0.971990 0.235022i \(-0.0755162\pi\)
−0.689530 + 0.724257i \(0.742183\pi\)
\(488\) 1.31630 + 2.27990i 0.0595862 + 0.103206i
\(489\) 0 0
\(490\) −1.65240 9.44996i −0.0746478 0.426906i
\(491\) −1.29120 + 2.23642i −0.0582710 + 0.100928i −0.893689 0.448686i \(-0.851892\pi\)
0.835418 + 0.549615i \(0.185225\pi\)
\(492\) 0 0
\(493\) 0.0107845i 0.000485711i
\(494\) −1.13238 15.8920i −0.0509480 0.715014i
\(495\) 0 0
\(496\) 3.67591 + 2.12229i 0.165053 + 0.0952935i
\(497\) 10.7498 + 6.20639i 0.482194 + 0.278395i
\(498\) 0 0
\(499\) 20.2443i 0.906261i −0.891444 0.453130i \(-0.850307\pi\)
0.891444 0.453130i \(-0.149693\pi\)
\(500\) −5.63152 + 9.65847i −0.251849 + 0.431940i
\(501\) 0 0
\(502\) −0.624794 −0.0278859
\(503\) 7.33148 4.23283i 0.326894 0.188733i −0.327567 0.944828i \(-0.606229\pi\)
0.654461 + 0.756095i \(0.272895\pi\)
\(504\) 0 0
\(505\) 19.4402 16.2651i 0.865076 0.723786i
\(506\) 20.7404 0.922024
\(507\) 0 0
\(508\) 17.3470i 0.769650i
\(509\) 33.4172 + 19.2935i 1.48119 + 0.855167i 0.999773 0.0213225i \(-0.00678766\pi\)
0.481421 + 0.876490i \(0.340121\pi\)
\(510\) 0 0
\(511\) 1.40225 + 2.42877i 0.0620320 + 0.107443i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 12.0758 6.97195i 0.532640 0.307520i
\(515\) 4.59258 12.5623i 0.202373 0.553560i
\(516\) 0 0
\(517\) −15.1971 8.77404i −0.668367 0.385882i
\(518\) −7.36500 + 12.7566i −0.323600 + 0.560491i
\(519\) 0 0
\(520\) 7.74971 + 2.22307i 0.339847 + 0.0974879i
\(521\) −12.5345 −0.549148 −0.274574 0.961566i \(-0.588537\pi\)
−0.274574 + 0.961566i \(0.588537\pi\)
\(522\) 0 0
\(523\) 11.0846 + 6.39970i 0.484696 + 0.279839i 0.722371 0.691505i \(-0.243052\pi\)
−0.237676 + 0.971345i \(0.576386\pi\)
\(524\) 7.08270 + 12.2676i 0.309409 + 0.535912i
\(525\) 0 0
\(526\) 16.8325 9.71828i 0.733934 0.423737i
\(527\) 0.516347 + 0.894339i 0.0224924 + 0.0389580i
\(528\) 0 0
\(529\) 25.6765 + 44.4729i 1.11637 + 1.93361i
\(530\) −3.50989 4.19505i −0.152460 0.182221i
\(531\) 0 0
\(532\) 7.27393i 0.315365i
\(533\) 0.788948 + 0.383506i 0.0341731 + 0.0166115i
\(534\) 0 0
\(535\) 15.3186 + 18.3089i 0.662279 + 0.791562i
\(536\) 0.937098 1.62310i 0.0404765 0.0701073i
\(537\) 0 0
\(538\) −3.00139 −0.129399
\(539\) −8.93684 + 5.15969i −0.384937 + 0.222243i
\(540\) 0 0
\(541\) 24.9605i 1.07314i 0.843857 + 0.536568i \(0.180280\pi\)
−0.843857 + 0.536568i \(0.819720\pi\)
\(542\) 24.6538 14.2339i 1.05897 0.611396i
\(543\) 0 0
\(544\) 0.210702 + 0.121649i 0.00903376 + 0.00521564i
\(545\) 7.29910 19.9655i 0.312659 0.855229i
\(546\) 0 0
\(547\) 10.4152i 0.445321i −0.974896 0.222660i \(-0.928526\pi\)
0.974896 0.222660i \(-0.0714741\pi\)
\(548\) −3.66709 + 6.35158i −0.156650 + 0.271326i
\(549\) 0 0
\(550\) 11.8378 + 2.12213i 0.504764 + 0.0904878i
\(551\) 0.195871i 0.00834439i
\(552\) 0 0
\(553\) 5.59442 + 9.68981i 0.237899 + 0.412053i
\(554\) 0.852658i 0.0362260i
\(555\) 0 0
\(556\) 7.10185 12.3008i 0.301186 0.521669i
\(557\) −0.697392 + 1.20792i −0.0295495 + 0.0511812i −0.880422 0.474191i \(-0.842741\pi\)
0.850872 + 0.525372i \(0.176074\pi\)
\(558\) 0 0
\(559\) 20.0953 13.5931i 0.849939 0.574926i
\(560\) 3.45707 + 1.26385i 0.146088 + 0.0534075i
\(561\) 0 0
\(562\) 13.5837 + 7.84257i 0.572995 + 0.330819i
\(563\) 14.0404 8.10624i 0.591733 0.341637i −0.174049 0.984737i \(-0.555685\pi\)
0.765782 + 0.643100i \(0.222352\pi\)
\(564\) 0 0
\(565\) −7.92099 + 1.38505i −0.333238 + 0.0582693i
\(566\) −7.00390 + 4.04370i −0.294396 + 0.169970i
\(567\) 0 0
\(568\) 6.53035 3.77030i 0.274007 0.158198i
\(569\) −19.6198 + 33.9825i −0.822505 + 1.42462i 0.0813055 + 0.996689i \(0.474091\pi\)
−0.903811 + 0.427932i \(0.859242\pi\)
\(570\) 0 0
\(571\) −16.0498 −0.671662 −0.335831 0.941922i \(-0.609017\pi\)
−0.335831 + 0.941922i \(0.609017\pi\)
\(572\) −0.616387 8.65049i −0.0257724 0.361695i
\(573\) 0 0
\(574\) 0.346841 + 0.200249i 0.0144769 + 0.00835823i
\(575\) 14.6303 + 40.5558i 0.610127 + 1.69130i
\(576\) 0 0
\(577\) 28.5363 1.18798 0.593992 0.804471i \(-0.297551\pi\)
0.593992 + 0.804471i \(0.297551\pi\)
\(578\) −8.47040 14.6712i −0.352322 0.610240i
\(579\) 0 0
\(580\) −0.0930914 0.0340328i −0.00386541 0.00141314i
\(581\) 14.4025 + 24.9458i 0.597515 + 1.03493i
\(582\) 0 0
\(583\) −2.94183 + 5.09541i −0.121838 + 0.211030i
\(584\) 1.70370 0.0704996
\(585\) 0 0
\(586\) −1.93438 −0.0799087
\(587\) −22.5265 + 39.0171i −0.929770 + 1.61041i −0.146066 + 0.989275i \(0.546661\pi\)
−0.783704 + 0.621134i \(0.786672\pi\)
\(588\) 0 0
\(589\) −9.37800 16.2432i −0.386414 0.669289i
\(590\) 7.40862 20.2651i 0.305008 0.834301i
\(591\) 0 0
\(592\) 4.47415 + 7.74945i 0.183886 + 0.318500i
\(593\) −37.0634 −1.52201 −0.761005 0.648746i \(-0.775294\pi\)
−0.761005 + 0.648746i \(0.775294\pi\)
\(594\) 0 0
\(595\) 0.574664 + 0.686844i 0.0235589 + 0.0281578i
\(596\) −9.61623 5.55193i −0.393896 0.227416i
\(597\) 0 0
\(598\) 25.7518 17.4193i 1.05307 0.712330i
\(599\) −18.6309 −0.761238 −0.380619 0.924732i \(-0.624289\pi\)
−0.380619 + 0.924732i \(0.624289\pi\)
\(600\) 0 0
\(601\) 9.69008 16.7837i 0.395266 0.684622i −0.597869 0.801594i \(-0.703986\pi\)
0.993135 + 0.116972i \(0.0373189\pi\)
\(602\) 9.59244 5.53820i 0.390958 0.225720i
\(603\) 0 0
\(604\) 0.757480 0.437332i 0.0308214 0.0177948i
\(605\) 2.00839 + 11.4858i 0.0816525 + 0.466965i
\(606\) 0 0
\(607\) 30.2066 17.4398i 1.22605 0.707858i 0.259846 0.965650i \(-0.416328\pi\)
0.966200 + 0.257792i \(0.0829949\pi\)
\(608\) −3.82681 2.20941i −0.155198 0.0896034i
\(609\) 0 0
\(610\) 5.52879 + 2.02124i 0.223854 + 0.0818378i
\(611\) −26.2381 + 1.86959i −1.06148 + 0.0756354i
\(612\) 0 0
\(613\) −4.07179 + 7.05254i −0.164458 + 0.284849i −0.936463 0.350767i \(-0.885921\pi\)
0.772005 + 0.635617i \(0.219254\pi\)
\(614\) 6.21918 10.7719i 0.250986 0.434720i
\(615\) 0 0
\(616\) 3.95942i 0.159530i
\(617\) 16.7288 + 28.9752i 0.673477 + 1.16650i 0.976912 + 0.213644i \(0.0685332\pi\)
−0.303435 + 0.952852i \(0.598133\pi\)
\(618\) 0 0
\(619\) 41.1780i 1.65508i −0.561404 0.827542i \(-0.689739\pi\)
0.561404 0.827542i \(-0.310261\pi\)
\(620\) 9.34931 1.63480i 0.375477 0.0656551i
\(621\) 0 0
\(622\) −9.18502 + 15.9089i −0.368286 + 0.637890i
\(623\) 16.5325i 0.662359i
\(624\) 0 0
\(625\) 4.20078 + 24.6445i 0.168031 + 0.985782i
\(626\) −27.6647 15.9722i −1.10571 0.638379i
\(627\) 0 0
\(628\) −13.4307 + 7.75425i −0.535945 + 0.309428i
\(629\) 2.17709i 0.0868065i
\(630\) 0 0
\(631\) 12.6839 7.32307i 0.504939 0.291527i −0.225812 0.974171i \(-0.572503\pi\)
0.730751 + 0.682644i \(0.239170\pi\)
\(632\) 6.79707 0.270373
\(633\) 0 0
\(634\) −11.6812 + 20.2325i −0.463921 + 0.803535i
\(635\) 24.8908 + 29.7497i 0.987761 + 1.18058i
\(636\) 0 0
\(637\) −6.76270 + 13.9122i −0.267948 + 0.551222i
\(638\) 0.106619i 0.00422107i
\(639\) 0 0
\(640\) 1.71497 1.43487i 0.0677903 0.0567184i
\(641\) −23.9793 41.5334i −0.947125 1.64047i −0.751439 0.659803i \(-0.770640\pi\)
−0.195686 0.980667i \(-0.562693\pi\)
\(642\) 0 0
\(643\) −1.99884 3.46209i −0.0788265 0.136531i 0.823917 0.566710i \(-0.191784\pi\)
−0.902744 + 0.430178i \(0.858451\pi\)
\(644\) 12.2926 7.09712i 0.484395 0.279666i
\(645\) 0 0
\(646\) −0.537543 0.931052i −0.0211494 0.0366318i
\(647\) 20.4521 + 11.8080i 0.804053 + 0.464220i 0.844886 0.534946i \(-0.179668\pi\)
−0.0408333 + 0.999166i \(0.513001\pi\)
\(648\) 0 0
\(649\) −23.2098 −0.911066
\(650\) 16.4804 7.30736i 0.646413 0.286618i
\(651\) 0 0
\(652\) −10.9464 + 18.9597i −0.428694 + 0.742520i
\(653\) 30.5411 + 17.6329i 1.19516 + 0.690029i 0.959473 0.281799i \(-0.0909312\pi\)
0.235692 + 0.971828i \(0.424265\pi\)
\(654\) 0 0
\(655\) 29.7491 + 10.8758i 1.16239 + 0.424954i
\(656\) 0.210702 0.121649i 0.00822652 0.00474958i
\(657\) 0 0
\(658\) −12.0095 −0.468178
\(659\) −12.6686 21.9427i −0.493499 0.854765i 0.506473 0.862256i \(-0.330949\pi\)
−0.999972 + 0.00749088i \(0.997616\pi\)
\(660\) 0 0
\(661\) 4.21373 + 2.43280i 0.163895 + 0.0946248i 0.579704 0.814827i \(-0.303168\pi\)
−0.415809 + 0.909452i \(0.636502\pi\)
\(662\) 21.4634i 0.834199i
\(663\) 0 0
\(664\) 17.4986 0.679079
\(665\) −10.4372 12.4746i −0.404736 0.483744i
\(666\) 0 0
\(667\) −0.331012 + 0.191110i −0.0128168 + 0.00739981i
\(668\) 5.29630 0.204920
\(669\) 0 0
\(670\) −0.721847 4.12820i −0.0278874 0.159486i
\(671\) 6.33219i 0.244452i
\(672\) 0 0
\(673\) 6.48493 + 3.74408i 0.249976 + 0.144324i 0.619753 0.784797i \(-0.287233\pi\)
−0.369777 + 0.929120i \(0.620566\pi\)
\(674\) −12.4327 7.17805i −0.478891 0.276488i
\(675\) 0 0
\(676\) −8.03064 10.2230i −0.308871 0.393191i
\(677\) 37.4181i 1.43810i 0.694961 + 0.719048i \(0.255422\pi\)
−0.694961 + 0.719048i \(0.744578\pi\)
\(678\) 0 0
\(679\) −13.5912 + 23.5406i −0.521582 + 0.903406i
\(680\) 0.535898 0.0937060i 0.0205508 0.00359346i
\(681\) 0 0
\(682\) −5.10473 8.84165i −0.195470 0.338564i
\(683\) 3.13940 + 5.43761i 0.120126 + 0.208064i 0.919817 0.392347i \(-0.128337\pi\)
−0.799691 + 0.600411i \(0.795003\pi\)
\(684\) 0 0
\(685\) 2.82476 + 16.1546i 0.107928 + 0.617236i
\(686\) −9.29260 + 16.0953i −0.354793 + 0.614520i
\(687\) 0 0
\(688\) 6.72876i 0.256532i
\(689\) 0.626851 + 8.79735i 0.0238811 + 0.335152i
\(690\) 0 0
\(691\) −9.17461 5.29696i −0.349019 0.201506i 0.315234 0.949014i \(-0.397917\pi\)
−0.664253 + 0.747508i \(0.731250\pi\)
\(692\) 14.9469 + 8.62958i 0.568195 + 0.328047i
\(693\) 0 0
\(694\) 0.665114i 0.0252474i
\(695\) −5.47056 31.2858i −0.207510 1.18674i
\(696\) 0 0
\(697\) 0.0591936 0.00224212
\(698\) −3.25007 + 1.87643i −0.123017 + 0.0710239i
\(699\) 0 0
\(700\) 7.74225 2.79298i 0.292630 0.105565i
\(701\) 29.6773 1.12090 0.560449 0.828189i \(-0.310629\pi\)
0.560449 + 0.828189i \(0.310629\pi\)
\(702\) 0 0
\(703\) 39.5409i 1.49131i
\(704\) −2.08305 1.20265i −0.0785078 0.0453265i
\(705\) 0 0
\(706\) 2.28180 + 3.95219i 0.0858766 + 0.148743i
\(707\) −18.6597 −0.701771
\(708\) 0 0
\(709\) 0.563901 0.325568i 0.0211777 0.0122270i −0.489374 0.872074i \(-0.662775\pi\)
0.510551 + 0.859847i \(0.329441\pi\)
\(710\) 5.78948 15.8362i 0.217275 0.594322i
\(711\) 0 0
\(712\) 8.69772 + 5.02163i 0.325961 + 0.188194i
\(713\) 18.3001 31.6967i 0.685344 1.18705i
\(714\) 0 0
\(715\) −13.4694 13.9509i −0.503729 0.521735i
\(716\) −8.35561 −0.312264
\(717\) 0 0
\(718\) −4.12042 2.37892i −0.153773 0.0887807i
\(719\) 3.21203 + 5.56340i 0.119789 + 0.207480i 0.919684 0.392660i \(-0.128445\pi\)
−0.799895 + 0.600140i \(0.795112\pi\)
\(720\) 0 0
\(721\) −8.52740 + 4.92330i −0.317577 + 0.183353i
\(722\) 0.262979 + 0.455494i 0.00978708 + 0.0169517i
\(723\) 0 0
\(724\) −6.36677 11.0276i −0.236619 0.409836i
\(725\) −0.208482 + 0.0752090i −0.00774283 + 0.00279319i
\(726\) 0 0
\(727\) 16.3170i 0.605165i 0.953123 + 0.302583i \(0.0978488\pi\)
−0.953123 + 0.302583i \(0.902151\pi\)
\(728\) −3.32541 4.91611i −0.123248 0.182203i
\(729\) 0 0
\(730\) 2.92180 2.44459i 0.108141 0.0904785i
\(731\) 0.818545 1.41776i 0.0302750 0.0524378i
\(732\) 0 0
\(733\) 24.4136 0.901735 0.450868 0.892591i \(-0.351115\pi\)
0.450868 + 0.892591i \(0.351115\pi\)
\(734\) −1.29432 + 0.747277i −0.0477743 + 0.0275825i
\(735\) 0 0
\(736\) 8.62281i 0.317841i
\(737\) −3.90404 + 2.25400i −0.143807 + 0.0830271i
\(738\) 0 0
\(739\) 4.75775 + 2.74689i 0.175017 + 0.101046i 0.584949 0.811070i \(-0.301114\pi\)
−0.409932 + 0.912116i \(0.634448\pi\)
\(740\) 18.7925 + 6.87027i 0.690827 + 0.252556i
\(741\) 0 0
\(742\) 4.02664i 0.147823i
\(743\) 10.6512 18.4484i 0.390753 0.676804i −0.601796 0.798650i \(-0.705548\pi\)
0.992549 + 0.121845i \(0.0388812\pi\)
\(744\) 0 0
\(745\) −24.4579 + 4.27666i −0.896068 + 0.156685i
\(746\) 20.5910i 0.753890i
\(747\) 0 0
\(748\) −0.292601 0.506800i −0.0106986 0.0185304i
\(749\) 17.5739i 0.642135i
\(750\) 0 0
\(751\) −15.4023 + 26.6776i −0.562040 + 0.973481i 0.435279 + 0.900296i \(0.356650\pi\)
−0.997318 + 0.0731853i \(0.976684\pi\)
\(752\) −3.64780 + 6.31817i −0.133022 + 0.230400i
\(753\) 0 0
\(754\) 0.0895462 + 0.132380i 0.00326108 + 0.00482100i
\(755\) 0.671544 1.83690i 0.0244400 0.0668517i
\(756\) 0 0
\(757\) −30.4180 17.5618i −1.10556 0.638296i −0.167885 0.985807i \(-0.553694\pi\)
−0.937676 + 0.347511i \(0.887027\pi\)
\(758\) 18.4173 10.6332i 0.668946 0.386216i
\(759\) 0 0
\(760\) −9.73310 + 1.70191i −0.353057 + 0.0617347i
\(761\) 25.0686 14.4734i 0.908737 0.524659i 0.0287122 0.999588i \(-0.490859\pi\)
0.880024 + 0.474928i \(0.157526\pi\)
\(762\) 0 0
\(763\) −13.5528 + 7.82472i −0.490645 + 0.283274i
\(764\) 0.207632 0.359629i 0.00751187 0.0130109i
\(765\) 0 0
\(766\) 10.6219 0.383785
\(767\) −28.8179 + 19.4933i −1.04055 + 0.703864i
\(768\) 0 0
\(769\) −34.3740 19.8459i −1.23956 0.715660i −0.270555 0.962704i \(-0.587207\pi\)
−0.969004 + 0.247045i \(0.920541\pi\)
\(770\) −5.68127 6.79030i −0.204739 0.244706i
\(771\) 0 0
\(772\) −25.9837 −0.935173
\(773\) 7.16938 + 12.4177i 0.257865 + 0.446635i 0.965670 0.259773i \(-0.0836478\pi\)
−0.707805 + 0.706408i \(0.750314\pi\)
\(774\) 0 0
\(775\) 13.6881 16.2187i 0.491691 0.582594i
\(776\) 8.25647 + 14.3006i 0.296390 + 0.513363i
\(777\) 0 0
\(778\) −18.5222 + 32.0813i −0.664052 + 1.15017i
\(779\) −1.07509 −0.0385190
\(780\) 0 0
\(781\) −18.1374 −0.649007
\(782\) 1.04895 1.81684i 0.0375105 0.0649701i
\(783\) 0 0
\(784\) 2.14514 + 3.71548i 0.0766120 + 0.132696i
\(785\) −11.9070 + 32.5698i −0.424980 + 1.16246i
\(786\) 0 0
\(787\) 5.52776 + 9.57437i 0.197043 + 0.341289i 0.947568 0.319553i \(-0.103533\pi\)
−0.750525 + 0.660842i \(0.770199\pi\)
\(788\) 15.4424