Properties

Label 276.2.i.a.121.1
Level $276$
Weight $2$
Character 276.121
Analytic conductor $2.204$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 276.i (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.20387109579\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + 15500 x^{12} - 28190 x^{11} + 41920 x^{10} - 33520 x^{9} - 13837 x^{8} + 78980 x^{7} - 92652 x^{6} - 52852 x^{5} + 177374 x^{4} + 151360 x^{3} + 115323 x^{2} + 12834 x + 529\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 121.1
Root \(0.302381 - 2.10310i\) of defining polynomial
Character \(\chi\) \(=\) 276.121
Dual form 276.2.i.a.73.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.959493 - 0.281733i) q^{3} +(-1.52130 + 0.977682i) q^{5} +(0.485296 - 3.37531i) q^{7} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\) \(q+(-0.959493 - 0.281733i) q^{3} +(-1.52130 + 0.977682i) q^{5} +(0.485296 - 3.37531i) q^{7} +(0.841254 + 0.540641i) q^{9} +(-0.800715 - 1.75332i) q^{11} +(-0.753988 - 5.24410i) q^{13} +(1.73512 - 0.509479i) q^{15} +(0.496392 - 0.572867i) q^{17} +(-3.10335 - 3.58146i) q^{19} +(-1.41657 + 3.10186i) q^{21} +(3.36166 - 3.42041i) q^{23} +(-0.718574 + 1.57346i) q^{25} +(-0.654861 - 0.755750i) q^{27} +(-2.79381 + 3.22422i) q^{29} +(3.28356 - 0.964142i) q^{31} +(0.274313 + 1.90789i) q^{33} +(2.56170 + 5.60934i) q^{35} +(-3.09318 - 1.98787i) q^{37} +(-0.753988 + 5.24410i) q^{39} +(-5.92232 + 3.80604i) q^{41} +(3.52444 + 1.03487i) q^{43} -1.80838 q^{45} +10.3519 q^{47} +(-4.44075 - 1.30392i) q^{49} +(-0.637680 + 0.409812i) q^{51} +(-1.11911 + 7.78361i) q^{53} +(2.93232 + 1.88449i) q^{55} +(1.96863 + 4.31070i) q^{57} +(-1.53778 - 10.6955i) q^{59} +(12.3748 - 3.63356i) q^{61} +(2.23309 - 2.57712i) q^{63} +(6.27411 + 7.24071i) q^{65} +(-2.57750 + 5.64394i) q^{67} +(-4.18913 + 2.33477i) q^{69} +(-6.14490 + 13.4555i) q^{71} +(4.97621 + 5.74285i) q^{73} +(1.13276 - 1.30728i) q^{75} +(-6.30658 + 1.85178i) q^{77} +(-0.905219 - 6.29594i) q^{79} +(0.415415 + 0.909632i) q^{81} +(-8.22677 - 5.28702i) q^{83} +(-0.195081 + 1.35682i) q^{85} +(3.58901 - 2.30651i) q^{87} +(-10.6954 - 3.14044i) q^{89} -18.0664 q^{91} -3.42219 q^{93} +(8.22267 + 2.41439i) q^{95} +(6.41054 - 4.11980i) q^{97} +(0.274313 - 1.90789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 2q^{3} - 4q^{5} - 2q^{9} + O(q^{10}) \) \( 20q - 2q^{3} - 4q^{5} - 2q^{9} - 22q^{13} + 7q^{15} + 7q^{17} + 19q^{19} + 20q^{23} + 20q^{25} - 2q^{27} + 32q^{29} - 3q^{31} + 11q^{33} - 26q^{35} - 10q^{37} - 22q^{39} - 40q^{41} + 8q^{43} - 4q^{45} - 18q^{47} - 34q^{49} - 26q^{51} - 34q^{53} - 17q^{55} - 3q^{57} - 32q^{59} + 32q^{61} + 49q^{65} + 35q^{67} - 2q^{69} + 33q^{71} - q^{73} - 2q^{75} - 50q^{77} + 22q^{79} - 2q^{81} - 14q^{83} - 9q^{85} - 12q^{87} + 10q^{89} - 72q^{91} + 30q^{93} - 51q^{95} - 4q^{97} + 11q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(139\) \(185\)
\(\chi(n)\) \(e\left(\frac{9}{11}\right)\) \(1\) \(1\)

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 0
\(3\) −0.959493 0.281733i −0.553964 0.162658i
\(4\) 0 0
\(5\) −1.52130 + 0.977682i −0.680348 + 0.437233i −0.834643 0.550792i \(-0.814326\pi\)
0.154295 + 0.988025i \(0.450689\pi\)
\(6\) 0 0
\(7\) 0.485296 3.37531i 0.183425 1.27575i −0.665165 0.746696i \(-0.731639\pi\)
0.848590 0.529051i \(-0.177452\pi\)
\(8\) 0 0
\(9\) 0.841254 + 0.540641i 0.280418 + 0.180214i
\(10\) 0 0
\(11\) −0.800715 1.75332i −0.241425 0.528646i 0.749669 0.661813i \(-0.230213\pi\)
−0.991094 + 0.133167i \(0.957485\pi\)
\(12\) 0 0
\(13\) −0.753988 5.24410i −0.209119 1.45445i −0.776042 0.630682i \(-0.782775\pi\)
0.566923 0.823771i \(-0.308134\pi\)
\(14\) 0 0
\(15\) 1.73512 0.509479i 0.448007 0.131547i
\(16\) 0 0
\(17\) 0.496392 0.572867i 0.120393 0.138941i −0.692354 0.721558i \(-0.743426\pi\)
0.812746 + 0.582618i \(0.197972\pi\)
\(18\) 0 0
\(19\) −3.10335 3.58146i −0.711958 0.821643i 0.278358 0.960477i \(-0.410210\pi\)
−0.990316 + 0.138834i \(0.955664\pi\)
\(20\) 0 0
\(21\) −1.41657 + 3.10186i −0.309122 + 0.676882i
\(22\) 0 0
\(23\) 3.36166 3.42041i 0.700955 0.713206i
\(24\) 0 0
\(25\) −0.718574 + 1.57346i −0.143715 + 0.314691i
\(26\) 0 0
\(27\) −0.654861 0.755750i −0.126028 0.145444i
\(28\) 0 0
\(29\) −2.79381 + 3.22422i −0.518797 + 0.598723i −0.953329 0.301933i \(-0.902368\pi\)
0.434532 + 0.900656i \(0.356914\pi\)
\(30\) 0 0
\(31\) 3.28356 0.964142i 0.589746 0.173165i 0.0267745 0.999641i \(-0.491476\pi\)
0.562971 + 0.826477i \(0.309658\pi\)
\(32\) 0 0
\(33\) 0.274313 + 1.90789i 0.0477517 + 0.332120i
\(34\) 0 0
\(35\) 2.56170 + 5.60934i 0.433006 + 0.948151i
\(36\) 0 0
\(37\) −3.09318 1.98787i −0.508516 0.326803i 0.261099 0.965312i \(-0.415915\pi\)
−0.769614 + 0.638509i \(0.779552\pi\)
\(38\) 0 0
\(39\) −0.753988 + 5.24410i −0.120735 + 0.839728i
\(40\) 0 0
\(41\) −5.92232 + 3.80604i −0.924911 + 0.594404i −0.914079 0.405537i \(-0.867084\pi\)
−0.0108322 + 0.999941i \(0.503448\pi\)
\(42\) 0 0
\(43\) 3.52444 + 1.03487i 0.537472 + 0.157816i 0.539192 0.842183i \(-0.318730\pi\)
−0.00172068 + 0.999999i \(0.500548\pi\)
\(44\) 0 0
\(45\) −1.80838 −0.269577
\(46\) 0 0
\(47\) 10.3519 1.50998 0.754989 0.655738i \(-0.227642\pi\)
0.754989 + 0.655738i \(0.227642\pi\)
\(48\) 0 0
\(49\) −4.44075 1.30392i −0.634393 0.186275i
\(50\) 0 0
\(51\) −0.637680 + 0.409812i −0.0892930 + 0.0573851i
\(52\) 0 0
\(53\) −1.11911 + 7.78361i −0.153722 + 1.06916i 0.756187 + 0.654355i \(0.227060\pi\)
−0.909910 + 0.414806i \(0.863849\pi\)
\(54\) 0 0
\(55\) 2.93232 + 1.88449i 0.395394 + 0.254104i
\(56\) 0 0
\(57\) 1.96863 + 4.31070i 0.260751 + 0.570966i
\(58\) 0 0
\(59\) −1.53778 10.6955i −0.200202 1.39244i −0.803682 0.595059i \(-0.797129\pi\)
0.603480 0.797378i \(-0.293780\pi\)
\(60\) 0 0
\(61\) 12.3748 3.63356i 1.58443 0.465229i 0.633268 0.773933i \(-0.281713\pi\)
0.951158 + 0.308704i \(0.0998951\pi\)
\(62\) 0 0
\(63\) 2.23309 2.57712i 0.281343 0.324687i
\(64\) 0 0
\(65\) 6.27411 + 7.24071i 0.778208 + 0.898100i
\(66\) 0 0
\(67\) −2.57750 + 5.64394i −0.314892 + 0.689517i −0.999213 0.0396637i \(-0.987371\pi\)
0.684321 + 0.729181i \(0.260099\pi\)
\(68\) 0 0
\(69\) −4.18913 + 2.33477i −0.504312 + 0.281074i
\(70\) 0 0
\(71\) −6.14490 + 13.4555i −0.729266 + 1.59687i 0.0711790 + 0.997464i \(0.477324\pi\)
−0.800445 + 0.599406i \(0.795403\pi\)
\(72\) 0 0
\(73\) 4.97621 + 5.74285i 0.582421 + 0.672150i 0.968124 0.250473i \(-0.0805862\pi\)
−0.385702 + 0.922623i \(0.626041\pi\)
\(74\) 0 0
\(75\) 1.13276 1.30728i 0.130800 0.150951i
\(76\) 0 0
\(77\) −6.30658 + 1.85178i −0.718702 + 0.211030i
\(78\) 0 0
\(79\) −0.905219 6.29594i −0.101845 0.708348i −0.975210 0.221282i \(-0.928976\pi\)
0.873365 0.487067i \(-0.161933\pi\)
\(80\) 0 0
\(81\) 0.415415 + 0.909632i 0.0461572 + 0.101070i
\(82\) 0 0
\(83\) −8.22677 5.28702i −0.903005 0.580326i 0.00467489 0.999989i \(-0.498512\pi\)
−0.907680 + 0.419663i \(0.862148\pi\)
\(84\) 0 0
\(85\) −0.195081 + 1.35682i −0.0211595 + 0.147168i
\(86\) 0 0
\(87\) 3.58901 2.30651i 0.384782 0.247284i
\(88\) 0 0
\(89\) −10.6954 3.14044i −1.13371 0.332886i −0.339543 0.940591i \(-0.610272\pi\)
−0.794163 + 0.607704i \(0.792091\pi\)
\(90\) 0 0
\(91\) −18.0664 −1.89387
\(92\) 0 0
\(93\) −3.42219 −0.354864
\(94\) 0 0
\(95\) 8.22267 + 2.41439i 0.843628 + 0.247712i
\(96\) 0 0
\(97\) 6.41054 4.11980i 0.650892 0.418303i −0.173100 0.984904i \(-0.555378\pi\)
0.823992 + 0.566601i \(0.191742\pi\)
\(98\) 0 0
\(99\) 0.274313 1.90789i 0.0275695 0.191750i
\(100\) 0 0
\(101\) 7.49704 + 4.81805i 0.745983 + 0.479414i 0.857587 0.514339i \(-0.171963\pi\)
−0.111604 + 0.993753i \(0.535599\pi\)
\(102\) 0 0
\(103\) −0.367699 0.805149i −0.0362305 0.0793337i 0.890651 0.454687i \(-0.150249\pi\)
−0.926882 + 0.375353i \(0.877521\pi\)
\(104\) 0 0
\(105\) −0.877598 6.10383i −0.0856448 0.595673i
\(106\) 0 0
\(107\) 7.59185 2.22917i 0.733932 0.215502i 0.106653 0.994296i \(-0.465987\pi\)
0.627279 + 0.778794i \(0.284168\pi\)
\(108\) 0 0
\(109\) 1.15251 1.33007i 0.110391 0.127398i −0.697865 0.716229i \(-0.745866\pi\)
0.808256 + 0.588832i \(0.200412\pi\)
\(110\) 0 0
\(111\) 2.40784 + 2.77879i 0.228542 + 0.263751i
\(112\) 0 0
\(113\) 6.94750 15.2129i 0.653566 1.43111i −0.234832 0.972036i \(-0.575454\pi\)
0.888398 0.459074i \(-0.151819\pi\)
\(114\) 0 0
\(115\) −1.77003 + 8.49012i −0.165056 + 0.791708i
\(116\) 0 0
\(117\) 2.20088 4.81926i 0.203471 0.445540i
\(118\) 0 0
\(119\) −1.69271 1.95349i −0.155170 0.179076i
\(120\) 0 0
\(121\) 4.77048 5.50543i 0.433680 0.500493i
\(122\) 0 0
\(123\) 6.75471 1.98336i 0.609052 0.178834i
\(124\) 0 0
\(125\) −1.73197 12.0461i −0.154912 1.07744i
\(126\) 0 0
\(127\) 0.531324 + 1.16344i 0.0471473 + 0.103238i 0.931740 0.363126i \(-0.118291\pi\)
−0.884593 + 0.466365i \(0.845563\pi\)
\(128\) 0 0
\(129\) −3.09012 1.98590i −0.272070 0.174849i
\(130\) 0 0
\(131\) 1.43523 9.98224i 0.125397 0.872152i −0.825887 0.563835i \(-0.809325\pi\)
0.951284 0.308317i \(-0.0997657\pi\)
\(132\) 0 0
\(133\) −13.5946 + 8.73670i −1.17880 + 0.757568i
\(134\) 0 0
\(135\) 1.73512 + 0.509479i 0.149336 + 0.0438489i
\(136\) 0 0
\(137\) 6.53140 0.558015 0.279007 0.960289i \(-0.409995\pi\)
0.279007 + 0.960289i \(0.409995\pi\)
\(138\) 0 0
\(139\) −8.55305 −0.725461 −0.362730 0.931894i \(-0.618155\pi\)
−0.362730 + 0.931894i \(0.618155\pi\)
\(140\) 0 0
\(141\) −9.93256 2.91646i −0.836473 0.245610i
\(142\) 0 0
\(143\) −8.59086 + 5.52101i −0.718404 + 0.461690i
\(144\) 0 0
\(145\) 1.09796 7.63648i 0.0911806 0.634175i
\(146\) 0 0
\(147\) 3.89351 + 2.50221i 0.321132 + 0.206379i
\(148\) 0 0
\(149\) 1.34464 + 2.94435i 0.110157 + 0.241211i 0.956680 0.291142i \(-0.0940352\pi\)
−0.846523 + 0.532353i \(0.821308\pi\)
\(150\) 0 0
\(151\) −1.00038 6.95781i −0.0814100 0.566219i −0.989175 0.146740i \(-0.953122\pi\)
0.907765 0.419479i \(-0.137787\pi\)
\(152\) 0 0
\(153\) 0.727307 0.213556i 0.0587993 0.0172650i
\(154\) 0 0
\(155\) −4.05267 + 4.67704i −0.325519 + 0.375668i
\(156\) 0 0
\(157\) 13.1324 + 15.1556i 1.04808 + 1.20955i 0.977257 + 0.212058i \(0.0680167\pi\)
0.0708217 + 0.997489i \(0.477438\pi\)
\(158\) 0 0
\(159\) 3.26668 7.15303i 0.259065 0.567272i
\(160\) 0 0
\(161\) −9.91356 13.0066i −0.781298 1.02506i
\(162\) 0 0
\(163\) −6.16725 + 13.5044i −0.483056 + 1.05775i 0.498556 + 0.866858i \(0.333864\pi\)
−0.981612 + 0.190888i \(0.938863\pi\)
\(164\) 0 0
\(165\) −2.28262 2.63428i −0.177702 0.205079i
\(166\) 0 0
\(167\) 16.1307 18.6159i 1.24823 1.44054i 0.395272 0.918564i \(-0.370650\pi\)
0.852961 0.521974i \(-0.174804\pi\)
\(168\) 0 0
\(169\) −14.4587 + 4.24546i −1.11221 + 0.326574i
\(170\) 0 0
\(171\) −0.674423 4.69071i −0.0515744 0.358708i
\(172\) 0 0
\(173\) −6.48345 14.1968i −0.492928 1.07936i −0.978704 0.205278i \(-0.934190\pi\)
0.485776 0.874083i \(-0.338537\pi\)
\(174\) 0 0
\(175\) 4.96218 + 3.18900i 0.375106 + 0.241066i
\(176\) 0 0
\(177\) −1.53778 + 10.6955i −0.115587 + 0.803924i
\(178\) 0 0
\(179\) −15.2621 + 9.80838i −1.14075 + 0.733113i −0.967775 0.251815i \(-0.918973\pi\)
−0.172970 + 0.984927i \(0.555336\pi\)
\(180\) 0 0
\(181\) 25.5232 + 7.49429i 1.89712 + 0.557046i 0.990967 + 0.134103i \(0.0428154\pi\)
0.906157 + 0.422942i \(0.139003\pi\)
\(182\) 0 0
\(183\) −12.8972 −0.953388
\(184\) 0 0
\(185\) 6.64917 0.488856
\(186\) 0 0
\(187\) −1.40189 0.411631i −0.102516 0.0301015i
\(188\) 0 0
\(189\) −2.86869 + 1.84360i −0.208667 + 0.134102i
\(190\) 0 0
\(191\) 3.52838 24.5404i 0.255305 1.77568i −0.309935 0.950758i \(-0.600307\pi\)
0.565240 0.824927i \(-0.308784\pi\)
\(192\) 0 0
\(193\) −3.96991 2.55131i −0.285761 0.183647i 0.389906 0.920855i \(-0.372508\pi\)
−0.675666 + 0.737208i \(0.736144\pi\)
\(194\) 0 0
\(195\) −3.98002 8.71503i −0.285015 0.624096i
\(196\) 0 0
\(197\) 1.58426 + 11.0188i 0.112874 + 0.785055i 0.965100 + 0.261882i \(0.0843430\pi\)
−0.852226 + 0.523174i \(0.824748\pi\)
\(198\) 0 0
\(199\) 7.56852 2.22232i 0.536518 0.157536i −0.00223844 0.999997i \(-0.500713\pi\)
0.538756 + 0.842462i \(0.318894\pi\)
\(200\) 0 0
\(201\) 4.06318 4.68915i 0.286594 0.330747i
\(202\) 0 0
\(203\) 9.52693 + 10.9947i 0.668660 + 0.771674i
\(204\) 0 0
\(205\) 5.28854 11.5803i 0.369368 0.808803i
\(206\) 0 0
\(207\) 4.67722 1.05999i 0.325090 0.0736741i
\(208\) 0 0
\(209\) −3.79455 + 8.30890i −0.262474 + 0.574738i
\(210\) 0 0
\(211\) 12.2185 + 14.1009i 0.841159 + 0.970749i 0.999863 0.0165774i \(-0.00527698\pi\)
−0.158704 + 0.987326i \(0.550732\pi\)
\(212\) 0 0
\(213\) 9.68683 11.1792i 0.663731 0.765986i
\(214\) 0 0
\(215\) −6.37351 + 1.87143i −0.434670 + 0.127631i
\(216\) 0 0
\(217\) −1.66077 11.5509i −0.112741 0.784129i
\(218\) 0 0
\(219\) −3.15669 6.91219i −0.213309 0.467082i
\(220\) 0 0
\(221\) −3.37845 2.17120i −0.227259 0.146050i
\(222\) 0 0
\(223\) −3.29264 + 22.9008i −0.220491 + 1.53355i 0.515694 + 0.856773i \(0.327534\pi\)
−0.736186 + 0.676779i \(0.763375\pi\)
\(224\) 0 0
\(225\) −1.45518 + 0.935186i −0.0970119 + 0.0623457i
\(226\) 0 0
\(227\) −11.8332 3.47453i −0.785394 0.230613i −0.135641 0.990758i \(-0.543309\pi\)
−0.649753 + 0.760145i \(0.725128\pi\)
\(228\) 0 0
\(229\) −11.4857 −0.758998 −0.379499 0.925192i \(-0.623904\pi\)
−0.379499 + 0.925192i \(0.623904\pi\)
\(230\) 0 0
\(231\) 6.57283 0.432460
\(232\) 0 0
\(233\) 5.13434 + 1.50758i 0.336362 + 0.0987647i 0.445552 0.895256i \(-0.353008\pi\)
−0.109190 + 0.994021i \(0.534826\pi\)
\(234\) 0 0
\(235\) −15.7484 + 10.1209i −1.02731 + 0.660212i
\(236\) 0 0
\(237\) −0.905219 + 6.29594i −0.0588003 + 0.408965i
\(238\) 0 0
\(239\) 9.62507 + 6.18565i 0.622594 + 0.400117i 0.813561 0.581480i \(-0.197526\pi\)
−0.190967 + 0.981596i \(0.561162\pi\)
\(240\) 0 0
\(241\) 1.45687 + 3.19010i 0.0938452 + 0.205492i 0.950733 0.310010i \(-0.100333\pi\)
−0.856888 + 0.515503i \(0.827605\pi\)
\(242\) 0 0
\(243\) −0.142315 0.989821i −0.00912950 0.0634971i
\(244\) 0 0
\(245\) 8.03055 2.35798i 0.513053 0.150646i
\(246\) 0 0
\(247\) −16.4416 + 18.9747i −1.04616 + 1.20733i
\(248\) 0 0
\(249\) 6.40400 + 7.39061i 0.405837 + 0.468361i
\(250\) 0 0
\(251\) −4.91943 + 10.7720i −0.310512 + 0.679925i −0.998971 0.0453492i \(-0.985560\pi\)
0.688460 + 0.725275i \(0.258287\pi\)
\(252\) 0 0
\(253\) −8.68881 3.15529i −0.546261 0.198371i
\(254\) 0 0
\(255\) 0.569439 1.24690i 0.0356596 0.0780837i
\(256\) 0 0
\(257\) 16.7144 + 19.2895i 1.04262 + 1.20324i 0.978702 + 0.205287i \(0.0658129\pi\)
0.0639142 + 0.997955i \(0.479642\pi\)
\(258\) 0 0
\(259\) −8.21077 + 9.47573i −0.510192 + 0.588794i
\(260\) 0 0
\(261\) −4.09345 + 1.20194i −0.253378 + 0.0743985i
\(262\) 0 0
\(263\) 0.511613 + 3.55835i 0.0315474 + 0.219417i 0.999496 0.0317294i \(-0.0101015\pi\)
−0.967949 + 0.251147i \(0.919192\pi\)
\(264\) 0 0
\(265\) −5.90739 12.9354i −0.362888 0.794614i
\(266\) 0 0
\(267\) 9.37736 + 6.02646i 0.573885 + 0.368814i
\(268\) 0 0
\(269\) −2.30719 + 16.0468i −0.140672 + 0.978393i 0.790148 + 0.612915i \(0.210003\pi\)
−0.930820 + 0.365478i \(0.880906\pi\)
\(270\) 0 0
\(271\) −3.65183 + 2.34689i −0.221833 + 0.142563i −0.646838 0.762628i \(-0.723909\pi\)
0.425005 + 0.905191i \(0.360272\pi\)
\(272\) 0 0
\(273\) 17.3346 + 5.08989i 1.04914 + 0.308054i
\(274\) 0 0
\(275\) 3.33415 0.201057
\(276\) 0 0
\(277\) 28.6009 1.71846 0.859230 0.511589i \(-0.170943\pi\)
0.859230 + 0.511589i \(0.170943\pi\)
\(278\) 0 0
\(279\) 3.28356 + 0.964142i 0.196582 + 0.0577216i
\(280\) 0 0
\(281\) −9.53062 + 6.12496i −0.568549 + 0.365384i −0.793113 0.609075i \(-0.791541\pi\)
0.224563 + 0.974459i \(0.427904\pi\)
\(282\) 0 0
\(283\) 0.759137 5.27992i 0.0451260 0.313858i −0.954739 0.297444i \(-0.903866\pi\)
0.999865 0.0164143i \(-0.00522508\pi\)
\(284\) 0 0
\(285\) −7.20938 4.63319i −0.427047 0.274446i
\(286\) 0 0
\(287\) 9.97249 + 21.8367i 0.588658 + 1.28898i
\(288\) 0 0
\(289\) 2.33758 + 16.2582i 0.137505 + 0.956367i
\(290\) 0 0
\(291\) −7.31155 + 2.14687i −0.428611 + 0.125851i
\(292\) 0 0
\(293\) 15.4905 17.8770i 0.904963 1.04438i −0.0938455 0.995587i \(-0.529916\pi\)
0.998809 0.0487965i \(-0.0155386\pi\)
\(294\) 0 0
\(295\) 12.7963 + 14.7677i 0.745027 + 0.859806i
\(296\) 0 0
\(297\) −0.800715 + 1.75332i −0.0464622 + 0.101738i
\(298\) 0 0
\(299\) −20.4717 15.0499i −1.18391 0.870361i
\(300\) 0 0
\(301\) 5.20340 11.3939i 0.299919 0.656731i
\(302\) 0 0
\(303\) −5.83595 6.73505i −0.335267 0.386918i
\(304\) 0 0
\(305\) −15.2733 + 17.6263i −0.874547 + 1.00928i
\(306\) 0 0
\(307\) 18.7890 5.51696i 1.07235 0.314870i 0.302534 0.953139i \(-0.402167\pi\)
0.769813 + 0.638269i \(0.220349\pi\)
\(308\) 0 0
\(309\) 0.125968 + 0.876128i 0.00716608 + 0.0498412i
\(310\) 0 0
\(311\) −0.797463 1.74620i −0.0452200 0.0990179i 0.885674 0.464308i \(-0.153697\pi\)
−0.930894 + 0.365290i \(0.880970\pi\)
\(312\) 0 0
\(313\) −10.6720 6.85849i −0.603219 0.387665i 0.203090 0.979160i \(-0.434902\pi\)
−0.806309 + 0.591495i \(0.798538\pi\)
\(314\) 0 0
\(315\) −0.877598 + 6.10383i −0.0494471 + 0.343912i
\(316\) 0 0
\(317\) 2.62869 1.68936i 0.147642 0.0948838i −0.464734 0.885450i \(-0.653850\pi\)
0.612376 + 0.790566i \(0.290214\pi\)
\(318\) 0 0
\(319\) 7.89014 + 2.31675i 0.441763 + 0.129713i
\(320\) 0 0
\(321\) −7.91236 −0.441625
\(322\) 0 0
\(323\) −3.59218 −0.199874
\(324\) 0 0
\(325\) 8.79317 + 2.58191i 0.487757 + 0.143218i
\(326\) 0 0
\(327\) −1.48055 + 0.951493i −0.0818747 + 0.0526177i
\(328\) 0 0
\(329\) 5.02373 34.9408i 0.276967 1.92635i
\(330\) 0 0
\(331\) −10.8260 6.95744i −0.595050 0.382415i 0.208175 0.978092i \(-0.433248\pi\)
−0.803225 + 0.595676i \(0.796884\pi\)
\(332\) 0 0
\(333\) −1.52743 3.34460i −0.0837025 0.183283i
\(334\) 0 0
\(335\) −1.59682 11.1061i −0.0872436 0.606792i
\(336\) 0 0
\(337\) 14.8281 4.35393i 0.807739 0.237174i 0.148311 0.988941i \(-0.452616\pi\)
0.659429 + 0.751767i \(0.270798\pi\)
\(338\) 0 0
\(339\) −10.9520 + 12.6393i −0.594834 + 0.686475i
\(340\) 0 0
\(341\) −4.31965 4.98514i −0.233922 0.269960i
\(342\) 0 0
\(343\) 3.35979 7.35691i 0.181412 0.397236i
\(344\) 0 0
\(345\) 4.09027 7.64754i 0.220213 0.411730i
\(346\) 0 0
\(347\) −7.54167 + 16.5140i −0.404858 + 0.886516i 0.591896 + 0.806014i \(0.298380\pi\)
−0.996754 + 0.0805017i \(0.974348\pi\)
\(348\) 0 0
\(349\) −14.3287 16.5361i −0.766995 0.885160i 0.229104 0.973402i \(-0.426420\pi\)
−0.996099 + 0.0882423i \(0.971875\pi\)
\(350\) 0 0
\(351\) −3.46947 + 4.00398i −0.185187 + 0.213717i
\(352\) 0 0
\(353\) −11.6096 + 3.40888i −0.617916 + 0.181436i −0.575685 0.817672i \(-0.695265\pi\)
−0.0422305 + 0.999108i \(0.513446\pi\)
\(354\) 0 0
\(355\) −3.80691 26.4776i −0.202050 1.40529i
\(356\) 0 0
\(357\) 1.07378 + 2.35125i 0.0568304 + 0.124441i
\(358\) 0 0
\(359\) −2.98260 1.91680i −0.157415 0.101165i 0.459562 0.888146i \(-0.348007\pi\)
−0.616977 + 0.786981i \(0.711643\pi\)
\(360\) 0 0
\(361\) −0.492073 + 3.42244i −0.0258986 + 0.180129i
\(362\) 0 0
\(363\) −6.12830 + 3.93842i −0.321652 + 0.206713i
\(364\) 0 0
\(365\) −13.1850 3.87147i −0.690135 0.202642i
\(366\) 0 0
\(367\) −26.1379 −1.36439 −0.682194 0.731171i \(-0.738974\pi\)
−0.682194 + 0.731171i \(0.738974\pi\)
\(368\) 0 0
\(369\) −7.03987 −0.366481
\(370\) 0 0
\(371\) 25.7290 + 7.55472i 1.33578 + 0.392221i
\(372\) 0 0
\(373\) 12.1660 7.81858i 0.629929 0.404831i −0.186354 0.982483i \(-0.559667\pi\)
0.816283 + 0.577652i \(0.196031\pi\)
\(374\) 0 0
\(375\) −1.73197 + 12.0461i −0.0894384 + 0.622058i
\(376\) 0 0
\(377\) 19.0147 + 12.2200i 0.979305 + 0.629361i
\(378\) 0 0
\(379\) −11.6229 25.4505i −0.597026 1.30730i −0.931102 0.364758i \(-0.881152\pi\)
0.334076 0.942546i \(-0.391576\pi\)
\(380\) 0 0
\(381\) −0.182023 1.26600i −0.00932534 0.0648592i
\(382\) 0 0
\(383\) 17.7316 5.20645i 0.906040 0.266037i 0.204667 0.978832i \(-0.434389\pi\)
0.701373 + 0.712794i \(0.252571\pi\)
\(384\) 0 0
\(385\) 7.78377 8.98295i 0.396698 0.457814i
\(386\) 0 0
\(387\) 2.40545 + 2.77604i 0.122276 + 0.141114i
\(388\) 0 0
\(389\) 10.6824 23.3913i 0.541621 1.18598i −0.418965 0.908002i \(-0.637607\pi\)
0.960586 0.277982i \(-0.0896656\pi\)
\(390\) 0 0
\(391\) −0.290741 3.62365i −0.0147034 0.183256i
\(392\) 0 0
\(393\) −4.18941 + 9.17354i −0.211328 + 0.462744i
\(394\) 0 0
\(395\) 7.53254 + 8.69302i 0.379003 + 0.437393i
\(396\) 0 0
\(397\) 18.2955 21.1141i 0.918225 1.05969i −0.0797958 0.996811i \(-0.525427\pi\)
0.998021 0.0628775i \(-0.0200277\pi\)
\(398\) 0 0
\(399\) 15.5053 4.55277i 0.776237 0.227924i
\(400\) 0 0
\(401\) −3.47619 24.1775i −0.173593 1.20737i −0.871216 0.490900i \(-0.836668\pi\)
0.697623 0.716465i \(-0.254241\pi\)
\(402\) 0 0
\(403\) −7.53183 16.4924i −0.375187 0.821545i
\(404\) 0 0
\(405\) −1.52130 0.977682i −0.0755942 0.0485814i
\(406\) 0 0
\(407\) −1.00861 + 7.01505i −0.0499950 + 0.347723i
\(408\) 0 0
\(409\) −30.4357 + 19.5599i −1.50495 + 0.967173i −0.510738 + 0.859736i \(0.670628\pi\)
−0.994212 + 0.107437i \(0.965736\pi\)
\(410\) 0 0
\(411\) −6.26683 1.84011i −0.309120 0.0907658i
\(412\) 0 0
\(413\) −36.8470 −1.81312
\(414\) 0 0
\(415\) 17.6844 0.868095
\(416\) 0 0
\(417\) 8.20660 + 2.40967i 0.401879 + 0.118002i
\(418\) 0 0
\(419\) 6.96574 4.47661i 0.340299 0.218697i −0.359318 0.933215i \(-0.616991\pi\)
0.699617 + 0.714519i \(0.253354\pi\)
\(420\) 0 0
\(421\) −5.08820 + 35.3892i −0.247984 + 1.72476i 0.361852 + 0.932236i \(0.382145\pi\)
−0.609836 + 0.792528i \(0.708765\pi\)
\(422\) 0 0
\(423\) 8.70856 + 5.59665i 0.423425 + 0.272119i
\(424\) 0 0
\(425\) 0.544687 + 1.19270i 0.0264212 + 0.0578544i
\(426\) 0 0
\(427\) −6.25896 43.5320i −0.302892 2.10666i
\(428\) 0 0
\(429\) 9.79832 2.87705i 0.473067 0.138905i
\(430\) 0 0
\(431\) −14.2907 + 16.4924i −0.688361 + 0.794411i −0.987131 0.159914i \(-0.948878\pi\)
0.298770 + 0.954325i \(0.403424\pi\)
\(432\) 0 0
\(433\) −19.9066 22.9735i −0.956651 1.10403i −0.994499 0.104751i \(-0.966596\pi\)
0.0378476 0.999284i \(-0.487950\pi\)
\(434\) 0 0
\(435\) −3.20493 + 7.01782i −0.153665 + 0.336479i
\(436\) 0 0
\(437\) −22.6825 1.42490i −1.08505 0.0681621i
\(438\) 0 0
\(439\) 8.60356 18.8392i 0.410626 0.899145i −0.585456 0.810704i \(-0.699084\pi\)
0.996081 0.0884405i \(-0.0281883\pi\)
\(440\) 0 0
\(441\) −3.03084 3.49778i −0.144326 0.166561i
\(442\) 0 0
\(443\) −16.1133 + 18.5958i −0.765567 + 0.883512i −0.995980 0.0895812i \(-0.971447\pi\)
0.230412 + 0.973093i \(0.425993\pi\)
\(444\) 0 0
\(445\) 19.3412 5.67910i 0.916863 0.269215i
\(446\) 0 0
\(447\) −0.460654 3.20392i −0.0217882 0.151540i
\(448\) 0 0
\(449\) 16.3387 + 35.7767i 0.771070 + 1.68841i 0.724283 + 0.689502i \(0.242171\pi\)
0.0467864 + 0.998905i \(0.485102\pi\)
\(450\) 0 0
\(451\) 11.4153 + 7.33617i 0.537525 + 0.345447i
\(452\) 0 0
\(453\) −1.00038 + 6.95781i −0.0470021 + 0.326907i
\(454\) 0 0
\(455\) 27.4844 17.6632i 1.28849 0.828063i
\(456\) 0 0
\(457\) −16.4781 4.83841i −0.770814 0.226331i −0.127401 0.991851i \(-0.540664\pi\)
−0.643412 + 0.765520i \(0.722482\pi\)
\(458\) 0 0
\(459\) −0.758011 −0.0353809
\(460\) 0 0
\(461\) 1.59212 0.0741524 0.0370762 0.999312i \(-0.488196\pi\)
0.0370762 + 0.999312i \(0.488196\pi\)
\(462\) 0 0
\(463\) 14.0004 + 4.11088i 0.650653 + 0.191049i 0.590371 0.807132i \(-0.298982\pi\)
0.0602827 + 0.998181i \(0.480800\pi\)
\(464\) 0 0
\(465\) 5.20619 3.34581i 0.241431 0.155158i
\(466\) 0 0
\(467\) 4.20501 29.2465i 0.194585 1.35337i −0.625097 0.780547i \(-0.714940\pi\)
0.819681 0.572820i \(-0.194150\pi\)
\(468\) 0 0
\(469\) 17.7992 + 11.4388i 0.821890 + 0.528197i
\(470\) 0 0
\(471\) −8.33061 18.2415i −0.383854 0.840524i
\(472\) 0 0
\(473\) −1.00761 7.00810i −0.0463301 0.322233i
\(474\) 0 0
\(475\) 7.86526 2.30945i 0.360883 0.105965i
\(476\) 0 0
\(477\) −5.14960 + 5.94295i −0.235784 + 0.272109i
\(478\) 0 0
\(479\) −2.07544 2.39519i −0.0948293 0.109439i 0.706351 0.707861i \(-0.250340\pi\)
−0.801181 + 0.598423i \(0.795794\pi\)
\(480\) 0 0
\(481\) −8.09235 + 17.7198i −0.368979 + 0.807952i
\(482\) 0 0
\(483\) 5.84762 + 15.2727i 0.266076 + 0.694931i
\(484\) 0 0
\(485\) −5.72452 + 12.5349i −0.259937 + 0.569183i
\(486\) 0 0
\(487\) −20.8452 24.0567i −0.944586 1.09011i −0.995812 0.0914238i \(-0.970858\pi\)
0.0512256 0.998687i \(-0.483687\pi\)
\(488\) 0 0
\(489\) 9.72205 11.2198i 0.439647 0.507379i
\(490\) 0 0
\(491\) −10.7015 + 3.14225i −0.482953 + 0.141808i −0.514141 0.857706i \(-0.671889\pi\)
0.0311880 + 0.999514i \(0.490071\pi\)
\(492\) 0 0
\(493\) 0.460228 + 3.20096i 0.0207276 + 0.144164i
\(494\) 0 0
\(495\) 1.44799 + 3.17066i 0.0650825 + 0.142511i
\(496\) 0 0
\(497\) 42.4343 + 27.2708i 1.90344 + 1.22326i
\(498\) 0 0
\(499\) −0.553581 + 3.85024i −0.0247817 + 0.172360i −0.998453 0.0555942i \(-0.982295\pi\)
0.973672 + 0.227955i \(0.0732038\pi\)
\(500\) 0 0
\(501\) −20.7220 + 13.3172i −0.925791 + 0.594970i
\(502\) 0 0
\(503\) −36.0920 10.5976i −1.60926 0.472523i −0.651160 0.758940i \(-0.725717\pi\)
−0.958105 + 0.286418i \(0.907536\pi\)
\(504\) 0 0
\(505\) −16.1158 −0.717143
\(506\) 0 0
\(507\) 15.0691 0.669243
\(508\) 0 0
\(509\) −18.9608 5.56740i −0.840424 0.246771i −0.166935 0.985968i \(-0.553387\pi\)
−0.673489 + 0.739197i \(0.735205\pi\)
\(510\) 0 0
\(511\) 21.7988 14.0093i 0.964324 0.619733i
\(512\) 0 0
\(513\) −0.674423 + 4.69071i −0.0297765 + 0.207100i
\(514\) 0 0
\(515\) 1.34656 + 0.865383i 0.0593366 + 0.0381333i
\(516\) 0 0
\(517\) −8.28891 18.1502i −0.364546 0.798244i
\(518\) 0 0
\(519\) 2.22113 + 15.4483i 0.0974969 + 0.678106i
\(520\) 0 0
\(521\) −26.3779 + 7.74525i −1.15564 + 0.339326i −0.802736 0.596335i \(-0.796623\pi\)
−0.352901 + 0.935660i \(0.614805\pi\)
\(522\) 0 0
\(523\) 5.32266 6.14267i 0.232744 0.268600i −0.627349 0.778738i \(-0.715860\pi\)
0.860093 + 0.510138i \(0.170406\pi\)
\(524\) 0 0
\(525\) −3.86274 4.45783i −0.168584 0.194556i
\(526\) 0 0
\(527\) 1.07761 2.35964i 0.0469414 0.102787i
\(528\) 0 0
\(529\) −0.398477 22.9965i −0.0173251 0.999850i
\(530\) 0 0
\(531\) 4.48877 9.82903i 0.194796 0.426544i
\(532\) 0 0
\(533\) 24.4246 + 28.1875i 1.05795 + 1.22094i
\(534\) 0 0
\(535\) −9.37009 + 10.8137i −0.405104 + 0.467515i
\(536\) 0 0
\(537\) 17.4072 5.11123i 0.751178 0.220566i
\(538\) 0 0
\(539\) 1.26958 + 8.83013i 0.0546847 + 0.380341i
\(540\) 0 0
\(541\) 9.72352 + 21.2915i 0.418047 + 0.915395i 0.995117 + 0.0987006i \(0.0314686\pi\)
−0.577070 + 0.816695i \(0.695804\pi\)
\(542\) 0 0
\(543\) −22.3779 14.3814i −0.960329 0.617166i
\(544\) 0 0
\(545\) −0.452935 + 3.15023i −0.0194016 + 0.134941i
\(546\) 0 0
\(547\) 13.7794 8.85546i 0.589163 0.378632i −0.211829 0.977307i \(-0.567942\pi\)
0.800992 + 0.598675i \(0.204306\pi\)
\(548\) 0 0
\(549\) 12.3748 + 3.63356i 0.528142 + 0.155076i
\(550\) 0 0
\(551\) 20.2176 0.861298
\(552\) 0 0
\(553\) −21.6900 −0.922354
\(554\) 0 0
\(555\) −6.37983 1.87329i −0.270809 0.0795166i
\(556\) 0 0
\(557\) 16.0768 10.3319i 0.681196 0.437778i −0.153750 0.988110i \(-0.549135\pi\)
0.834946 + 0.550332i \(0.185499\pi\)
\(558\) 0 0
\(559\) 2.76957 19.2628i 0.117140 0.814729i
\(560\) 0 0
\(561\) 1.22913 + 0.789915i 0.0518940 + 0.0333502i
\(562\) 0 0
\(563\) 8.42062 + 18.4386i 0.354887 + 0.777094i 0.999916 + 0.0129360i \(0.00411778\pi\)
−0.645030 + 0.764158i \(0.723155\pi\)
\(564\) 0 0
\(565\) 4.30413 + 29.9359i 0.181076 + 1.25941i
\(566\) 0 0
\(567\) 3.27189 0.960713i 0.137406 0.0403462i
\(568\) 0 0
\(569\) 12.1549 14.0276i 0.509562 0.588066i −0.441425 0.897298i \(-0.645527\pi\)
0.950986 + 0.309233i \(0.100072\pi\)
\(570\) 0 0
\(571\) 30.6110 + 35.3269i 1.28103 + 1.47839i 0.797838 + 0.602872i \(0.205977\pi\)
0.483191 + 0.875515i \(0.339478\pi\)
\(572\) 0 0
\(573\) −10.2993 + 22.5523i −0.430260 + 0.942137i
\(574\) 0 0
\(575\) 2.96628 + 7.74725i 0.123702 + 0.323083i
\(576\) 0 0
\(577\) −14.8811 + 32.5851i −0.619509 + 1.35653i 0.296368 + 0.955074i \(0.404225\pi\)
−0.915876 + 0.401461i \(0.868503\pi\)
\(578\) 0 0
\(579\) 3.09032 + 3.56642i 0.128429 + 0.148215i
\(580\) 0 0
\(581\) −21.8378 + 25.2021i −0.905983 + 1.04556i
\(582\) 0 0
\(583\) 14.5433 4.27029i 0.602320 0.176857i
\(584\) 0 0
\(585\) 1.36349 + 9.48331i 0.0563736 + 0.392087i
\(586\) 0 0
\(587\) 0.00770622 + 0.0168743i 0.000318070 + 0.000696476i 0.909791 0.415067i \(-0.136242\pi\)
−0.909473 + 0.415763i \(0.863515\pi\)
\(588\) 0 0
\(589\) −13.6431 8.76788i −0.562154 0.361274i
\(590\) 0 0
\(591\) 1.58426 11.0188i 0.0651678 0.453252i
\(592\) 0 0
\(593\) −5.46726 + 3.51359i −0.224513 + 0.144286i −0.648063 0.761587i \(-0.724420\pi\)
0.423549 + 0.905873i \(0.360784\pi\)
\(594\) 0 0
\(595\) 4.48501 + 1.31692i 0.183867 + 0.0539883i
\(596\) 0 0
\(597\) −7.88804 −0.322836
\(598\) 0 0
\(599\) −7.49989 −0.306437 −0.153219 0.988192i \(-0.548964\pi\)
−0.153219 + 0.988192i \(0.548964\pi\)
\(600\) 0 0
\(601\) −24.6872 7.24882i −1.00701 0.295686i −0.263682 0.964610i \(-0.584937\pi\)
−0.743331 + 0.668924i \(0.766755\pi\)
\(602\) 0 0
\(603\) −5.21968 + 3.35448i −0.212562 + 0.136605i
\(604\) 0 0
\(605\) −1.87479 + 13.0394i −0.0762210 + 0.530129i
\(606\) 0 0
\(607\) 24.3740 + 15.6642i 0.989309 + 0.635790i 0.931959 0.362564i \(-0.118098\pi\)
0.0573502 + 0.998354i \(0.481735\pi\)
\(608\) 0 0
\(609\) −6.04347 13.2334i −0.244894 0.536242i
\(610\) 0 0
\(611\) −7.80520 54.2863i −0.315765 2.19619i
\(612\) 0 0
\(613\) −2.25859 + 0.663181i −0.0912235 + 0.0267856i −0.327026 0.945015i \(-0.606046\pi\)
0.235802 + 0.971801i \(0.424228\pi\)
\(614\) 0 0
\(615\) −8.33686 + 9.62125i −0.336175 + 0.387966i
\(616\) 0 0
\(617\) −9.99989 11.5405i −0.402580 0.464603i 0.517871 0.855458i \(-0.326725\pi\)
−0.920452 + 0.390856i \(0.872179\pi\)
\(618\) 0 0
\(619\) −4.77631 + 10.4587i −0.191976 + 0.420369i −0.981004 0.193988i \(-0.937858\pi\)
0.789028 + 0.614358i \(0.210585\pi\)
\(620\) 0 0
\(621\) −4.78640 0.300678i −0.192071 0.0120658i
\(622\) 0 0
\(623\) −15.7904 + 34.5761i −0.632628 + 1.38526i
\(624\) 0 0
\(625\) 8.74830 + 10.0961i 0.349932 + 0.403843i
\(626\) 0 0
\(627\) 5.98173 6.90328i 0.238887 0.275690i
\(628\) 0 0
\(629\) −2.67421 + 0.785219i −0.106628 + 0.0313087i
\(630\) 0 0
\(631\) 2.01067 + 13.9845i 0.0800436 + 0.556715i 0.989897 + 0.141786i \(0.0452845\pi\)
−0.909854 + 0.414929i \(0.863806\pi\)
\(632\) 0 0
\(633\) −7.75090 16.9721i −0.308071 0.674581i
\(634\) 0 0
\(635\) −1.94578 1.25047i −0.0772158 0.0496235i
\(636\) 0 0
\(637\) −3.48963 + 24.2709i −0.138264 + 0.961648i
\(638\) 0 0
\(639\) −12.4440 + 7.99727i −0.492277 + 0.316367i
\(640\) 0 0
\(641\) 23.8830 + 7.01267i 0.943320 + 0.276984i 0.717003 0.697070i \(-0.245513\pi\)
0.226317 + 0.974054i \(0.427331\pi\)
\(642\) 0 0
\(643\) 23.5235 0.927678 0.463839 0.885919i \(-0.346472\pi\)
0.463839 + 0.885919i \(0.346472\pi\)
\(644\) 0 0
\(645\) 6.64258 0.261551
\(646\) 0 0
\(647\) 19.2110 + 5.64087i 0.755264 + 0.221766i 0.636627 0.771172i \(-0.280329\pi\)
0.118637 + 0.992938i \(0.462147\pi\)
\(648\) 0 0
\(649\) −17.5213 + 11.2603i −0.687773 + 0.442005i
\(650\) 0 0
\(651\) −1.66077 + 11.5509i −0.0650909 + 0.452717i
\(652\) 0 0
\(653\) −6.28245 4.03749i −0.245851 0.157999i 0.411912 0.911224i \(-0.364861\pi\)
−0.657764 + 0.753224i \(0.728497\pi\)
\(654\) 0 0
\(655\) 7.57604 + 16.5892i 0.296020 + 0.648194i
\(656\) 0 0
\(657\) 1.08143 + 7.52154i 0.0421907 + 0.293443i
\(658\) 0 0
\(659\) −10.4634 + 3.07234i −0.407597 + 0.119681i −0.479102 0.877759i \(-0.659038\pi\)
0.0715057 + 0.997440i \(0.477220\pi\)
\(660\) 0 0
\(661\) −11.3039 + 13.0454i −0.439672 + 0.507409i −0.931729 0.363154i \(-0.881700\pi\)
0.492057 + 0.870563i \(0.336245\pi\)
\(662\) 0 0
\(663\) 2.62990 + 3.03506i 0.102137 + 0.117872i
\(664\) 0 0
\(665\) 12.1398 26.5824i 0.470759 1.03082i
\(666\) 0 0
\(667\) 1.63636 + 20.3947i 0.0633600 + 0.789687i
\(668\) 0 0
\(669\) 9.61117 21.0455i 0.371589 0.813667i
\(670\) 0 0
\(671\) −16.2794 18.7875i −0.628461 0.725283i
\(672\) 0 0
\(673\) 4.61892 5.33051i 0.178046 0.205476i −0.659711 0.751520i \(-0.729321\pi\)
0.837757 + 0.546043i \(0.183867\pi\)
\(674\) 0 0
\(675\) 1.65971 0.487333i 0.0638821 0.0187575i
\(676\) 0 0
\(677\) −3.71912 25.8671i −0.142937 0.994152i −0.927426 0.374008i \(-0.877983\pi\)
0.784488 0.620144i \(-0.212926\pi\)
\(678\) 0 0
\(679\) −10.7946 23.6369i −0.414259 0.907100i
\(680\) 0 0
\(681\) 10.3749 + 6.66757i 0.397569 + 0.255502i
\(682\) 0 0
\(683\) 0.601211 4.18151i 0.0230047 0.160001i −0.975081 0.221850i \(-0.928791\pi\)
0.998086 + 0.0618487i \(0.0196996\pi\)
\(684\) 0 0
\(685\) −9.93623 + 6.38563i −0.379644 + 0.243982i
\(686\) 0 0
\(687\) 11.0205 + 3.23590i 0.420457 + 0.123457i
\(688\) 0 0
\(689\) 41.6619 1.58719
\(690\) 0 0
\(691\) 35.2154 1.33966 0.669829 0.742516i \(-0.266367\pi\)
0.669829 + 0.742516i \(0.266367\pi\)
\(692\) 0 0
\(693\) −6.30658 1.85178i −0.239567 0.0703433i
\(694\) 0 0
\(695\) 13.0118 8.36217i 0.493565 0.317195i
\(696\) 0 0
\(697\) −0.759435 + 5.28199i −0.0287657 + 0.200070i
\(698\) 0 0
\(699\) −4.50163 2.89302i −0.170267 0.109424i
\(700\) 0 0
\(701\) 16.0954 + 35.2441i 0.607917 + 1.33115i 0.923990 + 0.382417i \(0.124908\pi\)
−0.316073 + 0.948735i \(0.602365\pi\)
\(702\) 0 0
\(703\) 2.47976 + 17.2471i 0.0935261 + 0.650488i
\(704\) 0 0
\(705\) 17.9618 5.27406i 0.676481 0.198633i
\(706\) 0 0
\(707\) 19.9007 22.9666i 0.748443 0.863749i
\(708\) 0 0
\(709\) 9.24611 + 10.6706i 0.347245 + 0.400742i 0.902326 0.431054i \(-0.141858\pi\)
−0.555081 + 0.831796i \(0.687313\pi\)
\(710\) 0 0
\(711\) 2.64232 5.78588i 0.0990948 0.216987i
\(712\) 0 0
\(713\) 7.74047 14.4723i 0.289883 0.541991i
\(714\) 0 0
\(715\) 7.67151 16.7983i 0.286898 0.628220i
\(716\) 0 0
\(717\) −7.49248 8.64679i −0.279812 0.322920i
\(718\) 0 0
\(719\) −31.2454 + 36.0591i −1.16526 + 1.34478i −0.237590 + 0.971365i \(0.576358\pi\)
−0.927666 + 0.373412i \(0.878188\pi\)
\(720\) 0 0
\(721\) −2.89607 + 0.850363i −0.107855 + 0.0316692i
\(722\) 0 0
\(723\) −0.499101 3.47132i −0.0185618 0.129100i
\(724\) 0 0
\(725\) −3.06562 6.71278i −0.113854 0.249306i
\(726\) 0 0
\(727\) −30.9527 19.8921i −1.14797 0.737756i −0.178736 0.983897i \(-0.557201\pi\)
−0.969234 + 0.246141i \(0.920837\pi\)
\(728\) 0 0
\(729\) −0.142315 + 0.989821i −0.00527092 + 0.0366601i
\(730\) 0 0
\(731\) 2.34234 1.50533i 0.0866347 0.0556768i
\(732\) 0 0
\(733\) −23.7585 6.97613i −0.877541 0.257669i −0.188221 0.982127i \(-0.560272\pi\)
−0.689320 + 0.724457i \(0.742090\pi\)
\(734\) 0 0
\(735\) −8.36958 −0.308717
\(736\) 0 0
\(737\) 11.9595 0.440533
\(738\) 0 0
\(739\) −18.0128 5.28903i −0.662611 0.194560i −0.0669010 0.997760i \(-0.521311\pi\)
−0.595710 + 0.803199i \(0.703129\pi\)
\(740\) 0 0
\(741\) 21.1214 13.5739i 0.775915 0.498650i
\(742\) 0 0
\(743\) 4.33086 30.1218i 0.158884 1.10506i −0.741811 0.670609i \(-0.766033\pi\)
0.900695 0.434452i \(-0.143058\pi\)
\(744\) 0 0
\(745\) −4.92425 3.16462i −0.180411 0.115943i
\(746\) 0 0
\(747\) −4.06242 8.89545i −0.148636 0.325468i
\(748\) 0 0
\(749\) −3.83984 26.7067i −0.140305 0.975840i
\(750\) 0 0
\(751\) −34.7928 + 10.2161i −1.26961 + 0.372790i −0.846062 0.533085i \(-0.821033\pi\)
−0.423545 + 0.905875i \(0.639215\pi\)
\(752\) 0 0
\(753\) 7.75499 8.94974i 0.282608 0.326147i
\(754\) 0 0
\(755\) 8.32442 + 9.60689i 0.302957 + 0.349631i
\(756\) 0 0
\(757\) −18.1304 + 39.7001i −0.658961 + 1.44292i 0.224526 + 0.974468i \(0.427917\pi\)
−0.883487 + 0.468456i \(0.844811\pi\)
\(758\) 0 0
\(759\) 7.44791 + 5.47540i 0.270342 + 0.198744i
\(760\) 0 0
\(761\) −1.29149 + 2.82797i −0.0468164 + 0.102514i −0.931595 0.363498i \(-0.881582\pi\)
0.884779 + 0.466012i \(0.154310\pi\)
\(762\) 0 0
\(763\) −3.93009 4.53557i −0.142279 0.164198i
\(764\) 0 0
\(765\) −0.897664 + 1.03596i −0.0324551 + 0.0374552i
\(766\) 0 0
\(767\) −54.9289 + 16.1286i −1.98337 + 0.582369i
\(768\) 0 0
\(769\) 6.34944 + 44.1613i 0.228967 + 1.59250i 0.702475 + 0.711709i \(0.252078\pi\)
−0.473508 + 0.880790i \(0.657012\pi\)
\(770\) 0 0
\(771\) −10.6029 23.2171i −0.381854 0.836143i
\(772\) 0 0
\(773\) 14.3965 + 9.25209i 0.517807 + 0.332774i 0.773304 0.634035i \(-0.218603\pi\)
−0.255497 + 0.966810i \(0.582239\pi\)
\(774\) 0 0
\(775\) −0.842448 + 5.85936i −0.0302616 + 0.210474i
\(776\) 0 0
\(777\) 10.5478 6.77866i 0.378400 0.243183i
\(778\) 0 0
\(779\) 32.0102 + 9.39905i 1.14689 + 0.336756i
\(780\) 0 0
\(781\) 28.5121 1.02024
\(782\) 0 0
\(783\) 4.26626 0.152464
\(784\) 0 0
\(785\) −34.7957 10.2169i −1.24191 0.364658i
\(786\) 0 0
\(787\) −36.8248 + 23.6658i −1.31266 + 0.843596i −0.994530 0.104451i \(-0.966692\pi\)
−0.318131 + 0.948047i \(0.603055\pi\)
\(788\) 0 0
\(789\) 0.511613 3.55835i 0.0182139 0.126681i
\(790\) 0 0
\(791\) −47.9767 30.8327i −1.70585 1.09629i
\(792\) 0 0
\(793\) −28.3852 62.1549i −1.00799 2.20718i
\(794\)