Properties

Label 76.2.i.a.17.1
Level $76$
Weight $2$
Character 76.17
Analytic conductor $0.607$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 76.i (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.606863055362\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} - 3969 x^{3} - 2088 x^{2} + 4446 x + 4161\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 17.1
Root \(2.26253 + 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 76.17
Dual form 76.2.i.a.9.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.834130 - 0.699919i) q^{3} +(3.00735 - 1.09458i) q^{5} +(0.278396 + 0.482195i) q^{7} +(-0.315057 - 1.78678i) q^{9} +O(q^{10})\) \(q+(-0.834130 - 0.699919i) q^{3} +(3.00735 - 1.09458i) q^{5} +(0.278396 + 0.482195i) q^{7} +(-0.315057 - 1.78678i) q^{9} +(-1.96291 + 3.39985i) q^{11} +(-3.19334 + 2.67953i) q^{13} +(-3.27464 - 1.19187i) q^{15} +(-0.660076 + 3.74348i) q^{17} +(-1.84488 - 3.94923i) q^{19} +(0.105279 - 0.597068i) q^{21} +(4.67290 + 1.70080i) q^{23} +(4.01579 - 3.36965i) q^{25} +(-2.62112 + 4.53991i) q^{27} +(0.0201569 + 0.114315i) q^{29} +(-3.54372 - 6.13791i) q^{31} +(4.01694 - 1.46205i) q^{33} +(1.36503 + 1.14540i) q^{35} -5.67687 q^{37} +4.53912 q^{39} +(9.20379 + 7.72289i) q^{41} +(6.74642 - 2.45550i) q^{43} +(-2.90326 - 5.02860i) q^{45} +(-0.00419623 - 0.0237980i) q^{47} +(3.34499 - 5.79370i) q^{49} +(3.17072 - 2.66055i) q^{51} +(-8.18260 - 2.97822i) q^{53} +(-2.18171 + 12.3731i) q^{55} +(-1.22527 + 4.58544i) q^{57} +(1.88690 - 10.7011i) q^{59} +(-11.7981 - 4.29417i) q^{61} +(0.773865 - 0.649350i) q^{63} +(-6.67051 + 11.5537i) q^{65} +(2.27074 + 12.8780i) q^{67} +(-2.70739 - 4.68934i) q^{69} +(3.17872 - 1.15696i) q^{71} +(0.338853 + 0.284332i) q^{73} -5.70817 q^{75} -2.18586 q^{77} +(1.31335 + 1.10203i) q^{79} +(0.249157 - 0.0906859i) q^{81} +(-2.90300 - 5.02815i) q^{83} +(2.11247 + 11.9804i) q^{85} +(0.0631980 - 0.109462i) q^{87} +(1.83132 - 1.53666i) q^{89} +(-2.18107 - 0.793845i) q^{91} +(-1.34011 + 7.60013i) q^{93} +(-9.87095 - 9.85733i) q^{95} +(1.86728 - 10.5899i) q^{97} +(6.69320 + 2.43613i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 3q^{3} + 3q^{7} - 3q^{9} + O(q^{10}) \) \( 12q - 3q^{3} + 3q^{7} - 3q^{9} + 3q^{11} - 9q^{13} - 15q^{15} - 3q^{17} - 12q^{19} - 15q^{21} - 12q^{23} - 18q^{25} - 9q^{27} + 27q^{29} + 6q^{31} + 48q^{33} + 33q^{35} - 12q^{37} + 60q^{39} + 3q^{41} + 27q^{43} + 24q^{45} - 15q^{47} + 9q^{49} - 33q^{51} - 21q^{53} - 27q^{55} - 42q^{57} - 48q^{59} - 6q^{61} - 9q^{63} - 33q^{65} + 24q^{67} - 33q^{69} + 30q^{73} + 42q^{75} + 24q^{77} + 3q^{79} + 3q^{81} + 3q^{83} - 42q^{85} - 18q^{87} - 18q^{89} - 24q^{91} - 78q^{93} + 9q^{95} + 12q^{97} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(1\)

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
\(3\) −0.834130 0.699919i −0.481585 0.404098i 0.369414 0.929265i \(-0.379558\pi\)
−0.850999 + 0.525167i \(0.824003\pi\)
\(4\) 0 0
\(5\) 3.00735 1.09458i 1.34493 0.489513i 0.433565 0.901122i \(-0.357255\pi\)
0.911360 + 0.411609i \(0.135033\pi\)
\(6\) 0 0
\(7\) 0.278396 + 0.482195i 0.105224 + 0.182253i 0.913830 0.406098i \(-0.133111\pi\)
−0.808606 + 0.588351i \(0.799777\pi\)
\(8\) 0 0
\(9\) −0.315057 1.78678i −0.105019 0.595592i
\(10\) 0 0
\(11\) −1.96291 + 3.39985i −0.591838 + 1.02509i 0.402147 + 0.915575i \(0.368264\pi\)
−0.993985 + 0.109518i \(0.965069\pi\)
\(12\) 0 0
\(13\) −3.19334 + 2.67953i −0.885674 + 0.743169i −0.967338 0.253491i \(-0.918421\pi\)
0.0816634 + 0.996660i \(0.473977\pi\)
\(14\) 0 0
\(15\) −3.27464 1.19187i −0.845508 0.307740i
\(16\) 0 0
\(17\) −0.660076 + 3.74348i −0.160092 + 0.907926i 0.793890 + 0.608062i \(0.208053\pi\)
−0.953982 + 0.299865i \(0.903058\pi\)
\(18\) 0 0
\(19\) −1.84488 3.94923i −0.423244 0.906016i
\(20\) 0 0
\(21\) 0.105279 0.597068i 0.0229738 0.130291i
\(22\) 0 0
\(23\) 4.67290 + 1.70080i 0.974368 + 0.354641i 0.779648 0.626218i \(-0.215398\pi\)
0.194720 + 0.980859i \(0.437620\pi\)
\(24\) 0 0
\(25\) 4.01579 3.36965i 0.803158 0.673929i
\(26\) 0 0
\(27\) −2.62112 + 4.53991i −0.504435 + 0.873706i
\(28\) 0 0
\(29\) 0.0201569 + 0.114315i 0.00374304 + 0.0212278i 0.986622 0.163024i \(-0.0521249\pi\)
−0.982879 + 0.184252i \(0.941014\pi\)
\(30\) 0 0
\(31\) −3.54372 6.13791i −0.636472 1.10240i −0.986201 0.165550i \(-0.947060\pi\)
0.349730 0.936851i \(-0.386273\pi\)
\(32\) 0 0
\(33\) 4.01694 1.46205i 0.699259 0.254510i
\(34\) 0 0
\(35\) 1.36503 + 1.14540i 0.230733 + 0.193608i
\(36\) 0 0
\(37\) −5.67687 −0.933271 −0.466636 0.884450i \(-0.654534\pi\)
−0.466636 + 0.884450i \(0.654534\pi\)
\(38\) 0 0
\(39\) 4.53912 0.726841
\(40\) 0 0
\(41\) 9.20379 + 7.72289i 1.43739 + 1.20611i 0.941178 + 0.337912i \(0.109721\pi\)
0.496212 + 0.868201i \(0.334724\pi\)
\(42\) 0 0
\(43\) 6.74642 2.45550i 1.02882 0.374460i 0.228188 0.973617i \(-0.426720\pi\)
0.800631 + 0.599157i \(0.204498\pi\)
\(44\) 0 0
\(45\) −2.90326 5.02860i −0.432793 0.749619i
\(46\) 0 0
\(47\) −0.00419623 0.0237980i −0.000612084 0.00347130i 0.984500 0.175384i \(-0.0561166\pi\)
−0.985112 + 0.171912i \(0.945005\pi\)
\(48\) 0 0
\(49\) 3.34499 5.79370i 0.477856 0.827671i
\(50\) 0 0
\(51\) 3.17072 2.66055i 0.443989 0.372551i
\(52\) 0 0
\(53\) −8.18260 2.97822i −1.12397 0.409090i −0.287868 0.957670i \(-0.592946\pi\)
−0.836098 + 0.548580i \(0.815169\pi\)
\(54\) 0 0
\(55\) −2.18171 + 12.3731i −0.294182 + 1.66839i
\(56\) 0 0
\(57\) −1.22527 + 4.58544i −0.162291 + 0.607356i
\(58\) 0 0
\(59\) 1.88690 10.7011i 0.245653 1.39317i −0.573319 0.819332i \(-0.694344\pi\)
0.818972 0.573834i \(-0.194545\pi\)
\(60\) 0 0
\(61\) −11.7981 4.29417i −1.51060 0.549812i −0.551817 0.833966i \(-0.686065\pi\)
−0.958779 + 0.284154i \(0.908287\pi\)
\(62\) 0 0
\(63\) 0.773865 0.649350i 0.0974978 0.0818104i
\(64\) 0 0
\(65\) −6.67051 + 11.5537i −0.827375 + 1.43306i
\(66\) 0 0
\(67\) 2.27074 + 12.8780i 0.277415 + 1.57330i 0.731184 + 0.682180i \(0.238968\pi\)
−0.453769 + 0.891119i \(0.649921\pi\)
\(68\) 0 0
\(69\) −2.70739 4.68934i −0.325932 0.564530i
\(70\) 0 0
\(71\) 3.17872 1.15696i 0.377244 0.137306i −0.146437 0.989220i \(-0.546781\pi\)
0.523681 + 0.851914i \(0.324558\pi\)
\(72\) 0 0
\(73\) 0.338853 + 0.284332i 0.0396598 + 0.0332785i 0.662402 0.749148i \(-0.269537\pi\)
−0.622742 + 0.782427i \(0.713982\pi\)
\(74\) 0 0
\(75\) −5.70817 −0.659123
\(76\) 0 0
\(77\) −2.18586 −0.249101
\(78\) 0 0
\(79\) 1.31335 + 1.10203i 0.147764 + 0.123988i 0.713673 0.700479i \(-0.247030\pi\)
−0.565909 + 0.824467i \(0.691475\pi\)
\(80\) 0 0
\(81\) 0.249157 0.0906859i 0.0276842 0.0100762i
\(82\) 0 0
\(83\) −2.90300 5.02815i −0.318646 0.551911i 0.661560 0.749892i \(-0.269895\pi\)
−0.980206 + 0.197981i \(0.936561\pi\)
\(84\) 0 0
\(85\) 2.11247 + 11.9804i 0.229130 + 1.29946i
\(86\) 0 0
\(87\) 0.0631980 0.109462i 0.00677553 0.0117356i
\(88\) 0 0
\(89\) 1.83132 1.53666i 0.194120 0.162886i −0.540547 0.841314i \(-0.681783\pi\)
0.734667 + 0.678428i \(0.237338\pi\)
\(90\) 0 0
\(91\) −2.18107 0.793845i −0.228638 0.0832176i
\(92\) 0 0
\(93\) −1.34011 + 7.60013i −0.138963 + 0.788097i
\(94\) 0 0
\(95\) −9.87095 9.85733i −1.01274 1.01134i
\(96\) 0 0
\(97\) 1.86728 10.5899i 0.189594 1.07524i −0.730315 0.683110i \(-0.760627\pi\)
0.919909 0.392131i \(-0.128262\pi\)
\(98\) 0 0
\(99\) 6.69320 + 2.43613i 0.672692 + 0.244840i
\(100\) 0 0
\(101\) 5.12586 4.30110i 0.510042 0.427976i −0.351102 0.936337i \(-0.614193\pi\)
0.861144 + 0.508361i \(0.169749\pi\)
\(102\) 0 0
\(103\) 6.52153 11.2956i 0.642586 1.11299i −0.342268 0.939602i \(-0.611195\pi\)
0.984854 0.173388i \(-0.0554716\pi\)
\(104\) 0 0
\(105\) −0.336930 1.91083i −0.0328810 0.186478i
\(106\) 0 0
\(107\) 4.76100 + 8.24629i 0.460263 + 0.797199i 0.998974 0.0452919i \(-0.0144218\pi\)
−0.538711 + 0.842491i \(0.681088\pi\)
\(108\) 0 0
\(109\) 7.76788 2.82728i 0.744028 0.270804i 0.0579374 0.998320i \(-0.481548\pi\)
0.686090 + 0.727516i \(0.259325\pi\)
\(110\) 0 0
\(111\) 4.73525 + 3.97335i 0.449450 + 0.377133i
\(112\) 0 0
\(113\) 2.08270 0.195924 0.0979618 0.995190i \(-0.468768\pi\)
0.0979618 + 0.995190i \(0.468768\pi\)
\(114\) 0 0
\(115\) 15.9147 1.48405
\(116\) 0 0
\(117\) 5.79381 + 4.86159i 0.535638 + 0.449454i
\(118\) 0 0
\(119\) −1.98885 + 0.723882i −0.182317 + 0.0663581i
\(120\) 0 0
\(121\) −2.20599 3.82089i −0.200545 0.347354i
\(122\) 0 0
\(123\) −2.27176 12.8838i −0.204838 1.16169i
\(124\) 0 0
\(125\) 0.387625 0.671385i 0.0346702 0.0600505i
\(126\) 0 0
\(127\) −12.9449 + 10.8621i −1.14867 + 0.963853i −0.999688 0.0249866i \(-0.992046\pi\)
−0.148987 + 0.988839i \(0.547601\pi\)
\(128\) 0 0
\(129\) −7.34604 2.67374i −0.646783 0.235410i
\(130\) 0 0
\(131\) 0.287814 1.63227i 0.0251464 0.142612i −0.969650 0.244499i \(-0.921377\pi\)
0.994796 + 0.101886i \(0.0324877\pi\)
\(132\) 0 0
\(133\) 1.39069 1.98904i 0.120589 0.172472i
\(134\) 0 0
\(135\) −2.91330 + 16.5221i −0.250737 + 1.42200i
\(136\) 0 0
\(137\) 3.84678 + 1.40012i 0.328653 + 0.119620i 0.501076 0.865403i \(-0.332938\pi\)
−0.172423 + 0.985023i \(0.555160\pi\)
\(138\) 0 0
\(139\) −5.46307 + 4.58406i −0.463372 + 0.388815i −0.844370 0.535761i \(-0.820025\pi\)
0.380998 + 0.924576i \(0.375580\pi\)
\(140\) 0 0
\(141\) −0.0131565 + 0.0227877i −0.00110797 + 0.00191907i
\(142\) 0 0
\(143\) −2.84179 16.1166i −0.237642 1.34774i
\(144\) 0 0
\(145\) 0.185746 + 0.321722i 0.0154254 + 0.0267176i
\(146\) 0 0
\(147\) −6.84527 + 2.49148i −0.564589 + 0.205493i
\(148\) 0 0
\(149\) 4.50092 + 3.77672i 0.368729 + 0.309401i 0.808259 0.588828i \(-0.200410\pi\)
−0.439529 + 0.898228i \(0.644855\pi\)
\(150\) 0 0
\(151\) 6.47180 0.526667 0.263334 0.964705i \(-0.415178\pi\)
0.263334 + 0.964705i \(0.415178\pi\)
\(152\) 0 0
\(153\) 6.89672 0.557567
\(154\) 0 0
\(155\) −17.3757 14.5799i −1.39565 1.17109i
\(156\) 0 0
\(157\) 0.579693 0.210991i 0.0462646 0.0168389i −0.318784 0.947827i \(-0.603275\pi\)
0.365049 + 0.930988i \(0.381052\pi\)
\(158\) 0 0
\(159\) 4.74084 + 8.21138i 0.375973 + 0.651204i
\(160\) 0 0
\(161\) 0.480799 + 2.72675i 0.0378923 + 0.214898i
\(162\) 0 0
\(163\) −11.7455 + 20.3438i −0.919979 + 1.59345i −0.120537 + 0.992709i \(0.538462\pi\)
−0.799443 + 0.600742i \(0.794872\pi\)
\(164\) 0 0
\(165\) 10.4800 8.79375i 0.815866 0.684593i
\(166\) 0 0
\(167\) −14.2110 5.17239i −1.09968 0.400252i −0.272483 0.962160i \(-0.587845\pi\)
−0.827199 + 0.561909i \(0.810067\pi\)
\(168\) 0 0
\(169\) 0.760119 4.31085i 0.0584707 0.331604i
\(170\) 0 0
\(171\) −6.47515 + 4.54062i −0.495167 + 0.347230i
\(172\) 0 0
\(173\) 0.583180 3.30738i 0.0443384 0.251455i −0.954580 0.297955i \(-0.903695\pi\)
0.998918 + 0.0464995i \(0.0148066\pi\)
\(174\) 0 0
\(175\) 2.74280 + 0.998299i 0.207337 + 0.0754643i
\(176\) 0 0
\(177\) −9.06383 + 7.60545i −0.681279 + 0.571661i
\(178\) 0 0
\(179\) 0.0510390 0.0884022i 0.00381484 0.00660749i −0.864112 0.503300i \(-0.832119\pi\)
0.867927 + 0.496693i \(0.165452\pi\)
\(180\) 0 0
\(181\) 1.33951 + 7.59673i 0.0995649 + 0.564660i 0.993253 + 0.115971i \(0.0369980\pi\)
−0.893688 + 0.448689i \(0.851891\pi\)
\(182\) 0 0
\(183\) 6.83561 + 11.8396i 0.505303 + 0.875210i
\(184\) 0 0
\(185\) −17.0723 + 6.21381i −1.25518 + 0.456848i
\(186\) 0 0
\(187\) −11.4316 9.59225i −0.835961 0.701455i
\(188\) 0 0
\(189\) −2.91883 −0.212314
\(190\) 0 0
\(191\) −15.0096 −1.08606 −0.543028 0.839715i \(-0.682722\pi\)
−0.543028 + 0.839715i \(0.682722\pi\)
\(192\) 0 0
\(193\) −1.98477 1.66542i −0.142867 0.119880i 0.568553 0.822646i \(-0.307503\pi\)
−0.711420 + 0.702767i \(0.751948\pi\)
\(194\) 0 0
\(195\) 13.6507 4.96845i 0.977547 0.355798i
\(196\) 0 0
\(197\) 3.21799 + 5.57372i 0.229272 + 0.397111i 0.957593 0.288126i \(-0.0930321\pi\)
−0.728320 + 0.685237i \(0.759699\pi\)
\(198\) 0 0
\(199\) −0.957517 5.43035i −0.0678765 0.384947i −0.999754 0.0221741i \(-0.992941\pi\)
0.931878 0.362773i \(-0.118170\pi\)
\(200\) 0 0
\(201\) 7.11946 12.3313i 0.502168 0.869781i
\(202\) 0 0
\(203\) −0.0495107 + 0.0415444i −0.00347497 + 0.00291585i
\(204\) 0 0
\(205\) 36.1323 + 13.1511i 2.52359 + 0.918512i
\(206\) 0 0
\(207\) 1.56672 8.88528i 0.108894 0.617570i
\(208\) 0 0
\(209\) 17.0481 + 1.47966i 1.17924 + 0.102350i
\(210\) 0 0
\(211\) −1.30065 + 7.37636i −0.0895405 + 0.507809i 0.906744 + 0.421682i \(0.138560\pi\)
−0.996284 + 0.0861271i \(0.972551\pi\)
\(212\) 0 0
\(213\) −3.46124 1.25979i −0.237160 0.0863193i
\(214\) 0 0
\(215\) 17.6011 14.7690i 1.20038 1.00724i
\(216\) 0 0
\(217\) 1.97311 3.41753i 0.133944 0.231997i
\(218\) 0 0
\(219\) −0.0836389 0.474340i −0.00565179 0.0320529i
\(220\) 0 0
\(221\) −7.92292 13.7229i −0.532953 0.923102i
\(222\) 0 0
\(223\) 13.2194 4.81148i 0.885238 0.322200i 0.140916 0.990022i \(-0.454995\pi\)
0.744322 + 0.667821i \(0.232773\pi\)
\(224\) 0 0
\(225\) −7.28601 6.11369i −0.485734 0.407579i
\(226\) 0 0
\(227\) 25.3417 1.68199 0.840994 0.541044i \(-0.181971\pi\)
0.840994 + 0.541044i \(0.181971\pi\)
\(228\) 0 0
\(229\) −19.8311 −1.31047 −0.655237 0.755423i \(-0.727431\pi\)
−0.655237 + 0.755423i \(0.727431\pi\)
\(230\) 0 0
\(231\) 1.82329 + 1.52992i 0.119964 + 0.100661i
\(232\) 0 0
\(233\) −20.8061 + 7.57279i −1.36305 + 0.496110i −0.916996 0.398895i \(-0.869394\pi\)
−0.446055 + 0.895006i \(0.647171\pi\)
\(234\) 0 0
\(235\) −0.0386685 0.0669757i −0.00252245 0.00436901i
\(236\) 0 0
\(237\) −0.324173 1.83848i −0.0210573 0.119422i
\(238\) 0 0
\(239\) −1.02364 + 1.77299i −0.0662135 + 0.114685i −0.897232 0.441560i \(-0.854425\pi\)
0.831018 + 0.556245i \(0.187758\pi\)
\(240\) 0 0
\(241\) 0.941858 0.790313i 0.0606704 0.0509085i −0.611948 0.790898i \(-0.709614\pi\)
0.672619 + 0.739989i \(0.265169\pi\)
\(242\) 0 0
\(243\) 14.5070 + 5.28011i 0.930623 + 0.338719i
\(244\) 0 0
\(245\) 3.71786 21.0850i 0.237525 1.34707i
\(246\) 0 0
\(247\) 16.4734 + 7.66784i 1.04818 + 0.487893i
\(248\) 0 0
\(249\) −1.09781 + 6.22600i −0.0695710 + 0.394557i
\(250\) 0 0
\(251\) −6.52471 2.37480i −0.411836 0.149896i 0.127789 0.991801i \(-0.459212\pi\)
−0.539625 + 0.841905i \(0.681434\pi\)
\(252\) 0 0
\(253\) −14.9549 + 12.5487i −0.940208 + 0.788928i
\(254\) 0 0
\(255\) 6.62325 11.4718i 0.414764 0.718392i
\(256\) 0 0
\(257\) 1.71799 + 9.74318i 0.107165 + 0.607763i 0.990333 + 0.138707i \(0.0442946\pi\)
−0.883168 + 0.469056i \(0.844594\pi\)
\(258\) 0 0
\(259\) −1.58041 2.73736i −0.0982022 0.170091i
\(260\) 0 0
\(261\) 0.197905 0.0720317i 0.0122500 0.00445865i
\(262\) 0 0
\(263\) 1.64566 + 1.38087i 0.101476 + 0.0851483i 0.692114 0.721788i \(-0.256680\pi\)
−0.590638 + 0.806936i \(0.701124\pi\)
\(264\) 0 0
\(265\) −27.8678 −1.71191
\(266\) 0 0
\(267\) −2.60310 −0.159307
\(268\) 0 0
\(269\) 7.58263 + 6.36258i 0.462321 + 0.387933i 0.843984 0.536368i \(-0.180204\pi\)
−0.381663 + 0.924301i \(0.624649\pi\)
\(270\) 0 0
\(271\) −17.4238 + 6.34176i −1.05842 + 0.385234i −0.811836 0.583886i \(-0.801531\pi\)
−0.246587 + 0.969121i \(0.579309\pi\)
\(272\) 0 0
\(273\) 1.26367 + 2.18874i 0.0764809 + 0.132469i
\(274\) 0 0
\(275\) 3.57369 + 20.2674i 0.215501 + 1.22217i
\(276\) 0 0
\(277\) 13.1235 22.7305i 0.788514 1.36575i −0.138364 0.990381i \(-0.544184\pi\)
0.926877 0.375364i \(-0.122482\pi\)
\(278\) 0 0
\(279\) −9.85060 + 8.26563i −0.589740 + 0.494850i
\(280\) 0 0
\(281\) 20.0065 + 7.28179i 1.19349 + 0.434395i 0.860948 0.508693i \(-0.169871\pi\)
0.332543 + 0.943088i \(0.392093\pi\)
\(282\) 0 0
\(283\) 2.89350 16.4099i 0.172001 0.975465i −0.769548 0.638589i \(-0.779518\pi\)
0.941549 0.336876i \(-0.109370\pi\)
\(284\) 0 0
\(285\) 1.33433 + 15.1312i 0.0790391 + 0.896292i
\(286\) 0 0
\(287\) −1.16165 + 6.58804i −0.0685700 + 0.388880i
\(288\) 0 0
\(289\) 2.39686 + 0.872386i 0.140992 + 0.0513168i
\(290\) 0 0
\(291\) −8.96963 + 7.52641i −0.525809 + 0.441206i
\(292\) 0 0
\(293\) −10.8152 + 18.7324i −0.631828 + 1.09436i 0.355349 + 0.934734i \(0.384362\pi\)
−0.987178 + 0.159625i \(0.948971\pi\)
\(294\) 0 0
\(295\) −6.03873 34.2473i −0.351588 1.99396i
\(296\) 0 0
\(297\) −10.2900 17.8228i −0.597087 1.03419i
\(298\) 0 0
\(299\) −19.4795 + 7.08997i −1.12653 + 0.410024i
\(300\) 0 0
\(301\) 3.06220 + 2.56949i 0.176502 + 0.148103i
\(302\) 0 0
\(303\) −7.28606 −0.418573
\(304\) 0 0
\(305\) −40.1814 −2.30078
\(306\) 0 0
\(307\) −7.14077 5.99182i −0.407545 0.341971i 0.415856 0.909430i \(-0.363482\pi\)
−0.823401 + 0.567459i \(0.807926\pi\)
\(308\) 0 0
\(309\) −13.3458 + 4.85748i −0.759217 + 0.276333i
\(310\) 0 0
\(311\) 16.5503 + 28.6659i 0.938481 + 1.62550i 0.768306 + 0.640083i \(0.221100\pi\)
0.170175 + 0.985414i \(0.445567\pi\)
\(312\) 0 0
\(313\) −1.53367 8.69786i −0.0866880 0.491632i −0.996980 0.0776645i \(-0.975254\pi\)
0.910292 0.413968i \(-0.135857\pi\)
\(314\) 0 0
\(315\) 1.61651 2.79988i 0.0910800 0.157755i
\(316\) 0 0
\(317\) 22.3790 18.7782i 1.25693 1.05469i 0.260928 0.965358i \(-0.415971\pi\)
0.996002 0.0893315i \(-0.0284730\pi\)
\(318\) 0 0
\(319\) −0.428221 0.155860i −0.0239758 0.00872647i
\(320\) 0 0
\(321\) 1.80044 10.2108i 0.100491 0.569911i
\(322\) 0 0
\(323\) 16.0016 4.29946i 0.890354 0.239229i
\(324\) 0 0
\(325\) −3.79471 + 21.5209i −0.210493 + 1.19376i
\(326\) 0 0
\(327\) −8.45829 3.07856i −0.467744 0.170245i
\(328\) 0 0
\(329\) 0.0103071 0.00864867i 0.000568248 0.000476816i
\(330\) 0 0
\(331\) 5.83418 10.1051i 0.320676 0.555426i −0.659952 0.751308i \(-0.729423\pi\)
0.980628 + 0.195881i \(0.0627567\pi\)
\(332\) 0 0
\(333\) 1.78854 + 10.1433i 0.0980112 + 0.555849i
\(334\) 0 0
\(335\) 20.9250 + 36.2431i 1.14325 + 1.98017i
\(336\) 0 0
\(337\) −2.01893 + 0.734831i −0.109978 + 0.0400288i −0.396423 0.918068i \(-0.629749\pi\)
0.286445 + 0.958097i \(0.407526\pi\)
\(338\) 0 0
\(339\) −1.73724 1.45772i −0.0943539 0.0791723i
\(340\) 0 0
\(341\) 27.8240 1.50675
\(342\) 0 0
\(343\) 7.62246 0.411574
\(344\) 0 0
\(345\) −13.2749 11.1390i −0.714699 0.599703i
\(346\) 0 0
\(347\) 5.81918 2.11801i 0.312390 0.113701i −0.181067 0.983471i \(-0.557955\pi\)
0.493457 + 0.869770i \(0.335733\pi\)
\(348\) 0 0
\(349\) −5.71083 9.89145i −0.305694 0.529477i 0.671722 0.740803i \(-0.265555\pi\)
−0.977416 + 0.211326i \(0.932222\pi\)
\(350\) 0 0
\(351\) −3.79471 21.5209i −0.202547 1.14870i
\(352\) 0 0
\(353\) −1.61637 + 2.79963i −0.0860305 + 0.149009i −0.905830 0.423642i \(-0.860752\pi\)
0.819799 + 0.572651i \(0.194085\pi\)
\(354\) 0 0
\(355\) 8.29311 6.95874i 0.440152 0.369332i
\(356\) 0 0
\(357\) 2.16562 + 0.788220i 0.114617 + 0.0417170i
\(358\) 0 0
\(359\) 0.981506 5.56640i 0.0518019 0.293783i −0.947890 0.318597i \(-0.896788\pi\)
0.999692 + 0.0248140i \(0.00789935\pi\)
\(360\) 0 0
\(361\) −12.1929 + 14.5717i −0.641729 + 0.766931i
\(362\) 0 0
\(363\) −0.834227 + 4.73114i −0.0437856 + 0.248320i
\(364\) 0 0
\(365\) 1.33027 + 0.484180i 0.0696298 + 0.0253432i
\(366\) 0 0
\(367\) −0.742863 + 0.623336i −0.0387771 + 0.0325379i −0.661970 0.749530i \(-0.730279\pi\)
0.623193 + 0.782068i \(0.285835\pi\)
\(368\) 0 0
\(369\) 10.8994 18.8783i 0.567398 0.982763i
\(370\) 0 0
\(371\) −0.841914 4.77473i −0.0437100 0.247892i
\(372\) 0 0
\(373\) 8.27654 + 14.3354i 0.428543 + 0.742258i 0.996744 0.0806318i \(-0.0256938\pi\)
−0.568201 + 0.822890i \(0.692360\pi\)
\(374\) 0 0
\(375\) −0.793245 + 0.288717i −0.0409630 + 0.0149093i
\(376\) 0 0
\(377\) −0.370680 0.311037i −0.0190910 0.0160192i
\(378\) 0 0
\(379\) 22.9306 1.17787 0.588934 0.808181i \(-0.299548\pi\)
0.588934 + 0.808181i \(0.299548\pi\)
\(380\) 0 0
\(381\) 18.4003 0.942676
\(382\) 0 0
\(383\) −12.8570 10.7883i −0.656963 0.551257i 0.252212 0.967672i \(-0.418842\pi\)
−0.909175 + 0.416415i \(0.863286\pi\)
\(384\) 0 0
\(385\) −6.57362 + 2.39260i −0.335023 + 0.121938i
\(386\) 0 0
\(387\) −6.51293 11.2807i −0.331071 0.573431i
\(388\) 0 0
\(389\) 2.18972 + 12.4185i 0.111023 + 0.629643i 0.988643 + 0.150285i \(0.0480192\pi\)
−0.877620 + 0.479358i \(0.840870\pi\)
\(390\) 0 0
\(391\) −9.45137 + 16.3703i −0.477976 + 0.827879i
\(392\) 0 0
\(393\) −1.38253 + 1.16008i −0.0697396 + 0.0585185i
\(394\) 0 0
\(395\) 5.15597 + 1.87662i 0.259425 + 0.0944229i
\(396\) 0 0
\(397\) 3.86953 21.9452i 0.194206 1.10140i −0.719339 0.694659i \(-0.755555\pi\)
0.913545 0.406738i \(-0.133334\pi\)
\(398\) 0 0
\(399\) −2.55219 + 0.685746i −0.127769 + 0.0343302i
\(400\) 0 0
\(401\) 5.54626 31.4544i 0.276967 1.57076i −0.455677 0.890145i \(-0.650603\pi\)
0.732644 0.680612i \(-0.238286\pi\)
\(402\) 0 0
\(403\) 27.7631 + 10.1049i 1.38298 + 0.503362i
\(404\) 0 0
\(405\) 0.650039 0.545448i 0.0323007 0.0271035i
\(406\) 0 0
\(407\) 11.1432 19.3005i 0.552346 0.956691i
\(408\) 0 0
\(409\) 1.86728 + 10.5899i 0.0923313 + 0.523637i 0.995533 + 0.0944194i \(0.0300995\pi\)
−0.903201 + 0.429217i \(0.858789\pi\)
\(410\) 0 0
\(411\) −2.22875 3.86031i −0.109936 0.190415i
\(412\) 0 0
\(413\) 5.68533 2.06929i 0.279757 0.101823i
\(414\) 0 0
\(415\) −14.2341 11.9438i −0.698723 0.586298i
\(416\) 0 0
\(417\) 7.76538 0.380272
\(418\) 0 0
\(419\) 5.43928 0.265726 0.132863 0.991134i \(-0.457583\pi\)
0.132863 + 0.991134i \(0.457583\pi\)
\(420\) 0 0
\(421\) −1.90505 1.59852i −0.0928463 0.0779073i 0.595183 0.803590i \(-0.297080\pi\)
−0.688029 + 0.725683i \(0.741524\pi\)
\(422\) 0 0
\(423\) −0.0411997 + 0.0149955i −0.00200320 + 0.000729104i
\(424\) 0 0
\(425\) 9.96347 + 17.2572i 0.483299 + 0.837099i
\(426\) 0 0
\(427\) −1.21392 6.88448i −0.0587457 0.333163i
\(428\) 0 0
\(429\) −8.90986 + 15.4323i −0.430172 + 0.745080i
\(430\) 0 0
\(431\) −20.2174 + 16.9644i −0.973840 + 0.817149i −0.983149 0.182808i \(-0.941481\pi\)
0.00930869 + 0.999957i \(0.497037\pi\)
\(432\) 0 0
\(433\) 4.03750 + 1.46953i 0.194030 + 0.0706211i 0.437207 0.899361i \(-0.355968\pi\)
−0.243178 + 0.969982i \(0.578190\pi\)
\(434\) 0 0
\(435\) 0.0702426 0.398366i 0.00336788 0.0191002i
\(436\) 0 0
\(437\) −1.90409 21.5921i −0.0910851 1.03289i
\(438\) 0 0
\(439\) −5.68530 + 32.2429i −0.271345 + 1.53887i 0.478994 + 0.877818i \(0.341002\pi\)
−0.750339 + 0.661054i \(0.770110\pi\)
\(440\) 0 0
\(441\) −11.4059 4.15141i −0.543138 0.197686i
\(442\) 0 0
\(443\) −29.9985 + 25.1718i −1.42527 + 1.19595i −0.476833 + 0.878994i \(0.658215\pi\)
−0.948441 + 0.316953i \(0.897340\pi\)
\(444\) 0 0
\(445\) 3.82541 6.62580i 0.181342 0.314093i
\(446\) 0 0
\(447\) −1.11096 6.30055i −0.0525465 0.298006i
\(448\) 0 0
\(449\) 13.6553 + 23.6517i 0.644435 + 1.11619i 0.984432 + 0.175768i \(0.0562408\pi\)
−0.339997 + 0.940427i \(0.610426\pi\)
\(450\) 0 0
\(451\) −44.3229 + 16.1322i −2.08708 + 0.759636i
\(452\) 0 0
\(453\) −5.39832 4.52973i −0.253635 0.212825i
\(454\) 0 0
\(455\) −7.42816 −0.348238
\(456\) 0 0
\(457\) 15.2138 0.711670 0.355835 0.934549i \(-0.384196\pi\)
0.355835 + 0.934549i \(0.384196\pi\)
\(458\) 0 0
\(459\) −15.2649 12.8088i −0.712505 0.597863i
\(460\) 0 0
\(461\) −7.80157 + 2.83954i −0.363356 + 0.132251i −0.517245 0.855838i \(-0.673042\pi\)
0.153889 + 0.988088i \(0.450820\pi\)
\(462\) 0 0
\(463\) −18.3022 31.7003i −0.850574 1.47324i −0.880691 0.473690i \(-0.842922\pi\)
0.0301179 0.999546i \(-0.490412\pi\)
\(464\) 0 0
\(465\) 4.28882 + 24.3231i 0.198889 + 1.12796i
\(466\) 0 0
\(467\) −3.06233 + 5.30410i −0.141708 + 0.245445i −0.928140 0.372232i \(-0.878593\pi\)
0.786432 + 0.617677i \(0.211926\pi\)
\(468\) 0 0
\(469\) −5.57755 + 4.68012i −0.257547 + 0.216108i
\(470\) 0 0
\(471\) −0.631217 0.229744i −0.0290849 0.0105860i
\(472\) 0 0
\(473\) −4.89426 + 27.7567i −0.225038 + 1.27626i
\(474\) 0 0
\(475\) −20.7161 9.64269i −0.950522 0.442437i
\(476\) 0 0
\(477\) −2.74343 + 15.5588i −0.125613 + 0.712388i
\(478\) 0 0
\(479\) −21.2232 7.72462i −0.969713 0.352947i −0.191881 0.981418i \(-0.561459\pi\)
−0.777833 + 0.628471i \(0.783681\pi\)
\(480\) 0 0
\(481\) 18.1282 15.2114i 0.826575 0.693578i
\(482\) 0 0
\(483\) 1.50745 2.61098i 0.0685914 0.118804i
\(484\) 0 0
\(485\) −5.97597 33.8914i −0.271355 1.53893i
\(486\) 0 0
\(487\) 2.27441 + 3.93940i 0.103063 + 0.178511i 0.912945 0.408082i \(-0.133802\pi\)
−0.809882 + 0.586593i \(0.800469\pi\)
\(488\) 0 0
\(489\) 24.0363 8.74850i 1.08696 0.395621i
\(490\) 0 0
\(491\) 31.2170 + 26.1941i 1.40880 + 1.18213i 0.957029 + 0.289993i \(0.0936528\pi\)
0.451773 + 0.892133i \(0.350792\pi\)
\(492\) 0 0
\(493\) −0.441242 −0.0198725
\(494\) 0 0
\(495\) 22.7953 1.02457
\(496\) 0 0
\(497\) 1.44282 + 1.21067i 0.0647193 + 0.0543060i
\(498\) 0 0
\(499\) −7.41383 + 2.69841i −0.331889 + 0.120798i −0.502589 0.864525i \(-0.667619\pi\)
0.170701 + 0.985323i \(0.445397\pi\)
\(500\) 0 0
\(501\) 8.23360 + 14.2610i 0.367850 + 0.637135i
\(502\) 0 0
\(503\) 2.85027 + 16.1647i 0.127087 + 0.720748i 0.980046 + 0.198770i \(0.0636946\pi\)
−0.852959 + 0.521978i \(0.825194\pi\)
\(504\) 0 0
\(505\) 10.7073 18.5456i 0.476469 0.825268i
\(506\) 0 0
\(507\) −3.65128 + 3.06379i −0.162159 + 0.136068i
\(508\) 0 0
\(509\) −35.7499 13.0119i −1.58459 0.576743i −0.608392 0.793637i \(-0.708185\pi\)
−0.976195 + 0.216894i \(0.930407\pi\)
\(510\) 0 0
\(511\) −0.0427682 + 0.242550i −0.00189195 + 0.0107298i
\(512\) 0 0
\(513\) 22.7648 + 1.97582i 1.00509 + 0.0872347i
\(514\) 0 0
\(515\) 7.24848 41.1082i 0.319406 1.81144i
\(516\) 0 0
\(517\) 0.0891465 + 0.0324467i 0.00392066 + 0.00142700i
\(518\) 0 0
\(519\) −2.80134 + 2.35061i −0.122965 + 0.103180i
\(520\) 0 0
\(521\) 4.73838 8.20711i 0.207592 0.359560i −0.743363 0.668888i \(-0.766771\pi\)
0.950955 + 0.309328i \(0.100104\pi\)
\(522\) 0 0
\(523\) 2.07903 + 11.7907i 0.0909095 + 0.515573i 0.995924 + 0.0901932i \(0.0287484\pi\)
−0.905015 + 0.425380i \(0.860140\pi\)
\(524\) 0 0
\(525\) −1.58913 2.75245i −0.0693553 0.120127i
\(526\) 0 0
\(527\) 25.3162 9.21436i 1.10279 0.401384i
\(528\) 0 0
\(529\) 1.32430 + 1.11122i 0.0575783 + 0.0483139i
\(530\) 0 0
\(531\) −19.7150 −0.855557
\(532\) 0 0
\(533\) −50.0846 −2.16941
\(534\) 0 0
\(535\) 23.3442 + 19.5881i 1.00926 + 0.846868i
\(536\) 0 0
\(537\) −0.104448 + 0.0380158i −0.00450724 + 0.00164050i
\(538\) 0 0
\(539\) 13.1318 + 22.7450i 0.565627 + 0.979694i
\(540\) 0 0
\(541\) −5.84939 33.1736i −0.251485 1.42624i −0.804937 0.593361i \(-0.797801\pi\)
0.553452 0.832881i \(-0.313310\pi\)
\(542\) 0 0
\(543\) 4.19977 7.27421i 0.180229 0.312166i
\(544\) 0 0
\(545\) 20.2660 17.0052i 0.868100 0.728422i
\(546\) 0 0
\(547\) −14.2090 5.17166i −0.607534 0.221124i 0.0198899 0.999802i \(-0.493668\pi\)
−0.627424 + 0.778678i \(0.715891\pi\)
\(548\) 0 0
\(549\) −3.95564 + 22.4335i −0.168822 + 0.957439i
\(550\) 0 0
\(551\) 0.414271 0.290502i 0.0176485 0.0123758i
\(552\) 0 0
\(553\) −0.165764 + 0.940092i −0.00704899 + 0.0399768i
\(554\) 0 0
\(555\) 18.5897 + 6.76609i 0.789088 + 0.287205i
\(556\) 0 0
\(557\) 14.7963 12.4155i 0.626937 0.526063i −0.273038 0.962003i \(-0.588029\pi\)
0.899976 + 0.435940i \(0.143584\pi\)
\(558\) 0 0
\(559\) −14.9641 + 25.9185i −0.632912 + 1.09624i
\(560\) 0 0
\(561\) 2.82165 + 16.0024i 0.119130 + 0.675621i
\(562\) 0 0
\(563\) −19.1965 33.2493i −0.809037 1.40129i −0.913532 0.406767i \(-0.866656\pi\)
0.104495 0.994525i \(-0.466677\pi\)
\(564\) 0 0
\(565\) 6.26338 2.27969i 0.263503 0.0959071i
\(566\) 0 0
\(567\) 0.113093 + 0.0948960i 0.00474944 + 0.00398526i
\(568\) 0 0
\(569\) −4.84346 −0.203048 −0.101524 0.994833i \(-0.532372\pi\)
−0.101524 + 0.994833i \(0.532372\pi\)
\(570\) 0 0
\(571\) 37.5129 1.56987 0.784934 0.619580i \(-0.212697\pi\)
0.784934 + 0.619580i \(0.212697\pi\)
\(572\) 0 0
\(573\) 12.5200 + 10.5055i 0.523029 + 0.438873i
\(574\) 0 0
\(575\) 24.4965 8.91599i 1.02157 0.371822i
\(576\) 0 0
\(577\) −1.22241 2.11728i −0.0508896 0.0881433i 0.839458 0.543424i \(-0.182872\pi\)
−0.890348 + 0.455280i \(0.849539\pi\)
\(578\) 0 0
\(579\) 0.489900 + 2.77836i 0.0203596 + 0.115465i
\(580\) 0 0
\(581\) 1.61637 2.79963i 0.0670582 0.116148i
\(582\) 0 0
\(583\) 26.1872 21.9736i 1.08456 0.910055i
\(584\) 0 0
\(585\) 22.7454 + 8.27865i 0.940407 + 0.342280i
\(586\) 0 0
\(587\) 1.79011 10.1522i 0.0738856 0.419026i −0.925320 0.379186i \(-0.876204\pi\)
0.999206 0.0398401i \(-0.0126849\pi\)
\(588\) 0 0
\(589\) −17.7023 + 25.3187i −0.729410 + 1.04324i
\(590\) 0 0
\(591\) 1.21693 6.90154i 0.0500577 0.283891i
\(592\) 0 0
\(593\) −9.02362 3.28433i −0.370556 0.134871i 0.150028 0.988682i \(-0.452064\pi\)
−0.520584 + 0.853810i \(0.674286\pi\)
\(594\) 0 0
\(595\) −5.18880 + 4.35392i −0.212720 + 0.178493i
\(596\) 0 0
\(597\) −3.00211 + 5.19980i −0.122868 + 0.212814i
\(598\) 0 0
\(599\) 3.30188 + 18.7259i 0.134911 + 0.765118i 0.974922 + 0.222548i \(0.0714375\pi\)
−0.840011 + 0.542570i \(0.817451\pi\)
\(600\) 0 0
\(601\) −7.65441 13.2578i −0.312230 0.540798i 0.666615 0.745402i \(-0.267743\pi\)
−0.978845 + 0.204604i \(0.934409\pi\)
\(602\) 0 0
\(603\) 22.2947 8.11461i 0.907911 0.330452i
\(604\) 0 0
\(605\) −10.8165 9.07610i −0.439752 0.368996i
\(606\) 0 0
\(607\) 3.95975 0.160721 0.0803607 0.996766i \(-0.474393\pi\)
0.0803607 + 0.996766i \(0.474393\pi\)
\(608\) 0 0
\(609\) 0.0703761 0.00285178
\(610\) 0 0
\(611\) 0.0771676 + 0.0647513i 0.00312187 + 0.00261956i
\(612\) 0 0
\(613\) 10.0409 3.65457i 0.405547 0.147607i −0.131189 0.991357i \(-0.541879\pi\)
0.536736 + 0.843751i \(0.319657\pi\)
\(614\) 0 0
\(615\) −20.9344 36.2594i −0.844156 1.46212i
\(616\) 0 0
\(617\) 0.954966 + 5.41588i 0.0384455 + 0.218035i 0.997978 0.0635633i \(-0.0202465\pi\)
−0.959532 + 0.281599i \(0.909135\pi\)
\(618\) 0 0
\(619\) 13.8634 24.0122i 0.557219 0.965131i −0.440508 0.897748i \(-0.645202\pi\)
0.997727 0.0673827i \(-0.0214648\pi\)
\(620\) 0 0
\(621\) −19.9697 + 16.7566i −0.801357 + 0.672418i
\(622\) 0 0
\(623\) 1.25080 + 0.455254i 0.0501123 + 0.0182394i
\(624\) 0 0
\(625\) −4.12069 + 23.3696i −0.164828 + 0.934784i
\(626\) 0 0
\(627\) −13.1847 13.1665i −0.526547 0.525820i
\(628\) 0 0
\(629\) 3.74716 21.2512i 0.149409 0.847342i
\(630\) 0 0
\(631\) −0.0204469 0.00744206i −0.000813978 0.000296264i 0.341613 0.939841i \(-0.389027\pi\)
−0.342427 + 0.939544i \(0.611249\pi\)
\(632\) 0 0
\(633\) 6.24776 5.24249i 0.248326 0.208370i
\(634\) 0 0
\(635\) −27.0404 + 46.8353i −1.07306 + 1.85860i
\(636\) 0 0
\(637\) 4.84269 + 27.4643i 0.191875 + 1.08817i
\(638\) 0 0
\(639\) −3.06870 5.31515i −0.121396 0.210264i
\(640\) 0 0
\(641\) −27.9085 + 10.1579i −1.10232 + 0.401211i −0.828170 0.560476i \(-0.810618\pi\)
−0.274148 + 0.961687i \(0.588396\pi\)
\(642\) 0 0
\(643\) 12.1147 + 10.1655i 0.477758 + 0.400887i 0.849615 0.527404i \(-0.176834\pi\)
−0.371857 + 0.928290i \(0.621279\pi\)
\(644\) 0 0
\(645\) −25.0187 −0.985111
\(646\) 0 0
\(647\) −35.3133 −1.38831 −0.694154 0.719826i \(-0.744221\pi\)
−0.694154 + 0.719826i \(0.744221\pi\)
\(648\) 0 0
\(649\) 32.6784 + 27.4204i 1.28274 + 1.07635i
\(650\) 0 0
\(651\) −4.03783 + 1.46965i −0.158255 + 0.0576001i
\(652\) 0 0
\(653\) −24.0337 41.6275i −0.940510 1.62901i −0.764500 0.644623i \(-0.777014\pi\)
−0.176010 0.984388i \(-0.556319\pi\)
\(654\) 0 0
\(655\) −0.921106 5.22385i −0.0359906 0.204113i
\(656\) 0 0
\(657\) 0.401279 0.695036i 0.0156554 0.0271159i
\(658\) 0 0
\(659\) 4.45303 3.73654i 0.173466 0.145555i −0.551922 0.833896i \(-0.686105\pi\)
0.725387 + 0.688341i \(0.241661\pi\)
\(660\) 0 0
\(661\) −26.1778 9.52794i −1.01820 0.370594i −0.221623 0.975133i \(-0.571135\pi\)
−0.796576 + 0.604539i \(0.793357\pi\)
\(662\) 0 0
\(663\) −2.99616 + 16.9921i −0.116361 + 0.659918i
\(664\) 0 0
\(665\) 2.00513 7.50396i 0.0777555 0.290991i
\(666\) 0 0
\(667\) −0.100236 + 0.568468i −0.00388116 + 0.0220112i
\(668\) 0 0
\(669\) −14.3944 5.23912i −0.556518 0.202556i
\(670\) 0 0
\(671\) 37.7581 31.6828i 1.45764 1.22310i
\(672\) 0 0
\(673\) −22.5701 + 39.0926i −0.870015 + 1.50691i −0.00803563 + 0.999968i \(0.502558\pi\)
−0.861980 + 0.506943i \(0.830775\pi\)
\(674\) 0 0
\(675\) 4.77204 + 27.0636i 0.183676 + 1.04168i
\(676\) 0 0
\(677\) −2.71076 4.69517i −0.104183 0.180450i 0.809221 0.587504i \(-0.199889\pi\)
−0.913404 + 0.407054i \(0.866556\pi\)
\(678\) 0 0
\(679\) 5.62624 2.04778i 0.215915 0.0785868i
\(680\) 0 0
\(681\) −21.1383 17.7371i −0.810021 0.679689i
\(682\) 0 0
\(683\) −33.9254 −1.29812 −0.649060 0.760738i \(-0.724837\pi\)
−0.649060 + 0.760738i \(0.724837\pi\)
\(684\) 0 0
\(685\) 13.1012 0.500569
\(686\) 0 0
\(687\) 16.5417 + 13.8801i 0.631105 + 0.529560i
\(688\) 0 0
\(689\) 34.1101 12.4151i 1.29949 0.472976i
\(690\) 0 0
\(691\) 14.2022 + 24.5990i 0.540278 + 0.935788i 0.998888 + 0.0471508i \(0.0150141\pi\)
−0.458610 + 0.888638i \(0.651653\pi\)
\(692\) 0 0
\(693\) 0.688669 + 3.90564i 0.0261604 + 0.148363i
\(694\) 0 0
\(695\) −11.4117 + 19.7656i −0.432870 + 0.749753i
\(696\) 0 0
\(697\) −34.9857 + 29.3565i −1.32518 + 1.11196i
\(698\) 0 0
\(699\) 22.6553 + 8.24586i 0.856903 + 0.311887i
\(700\) 0 0
\(701\) −3.72496 + 21.1253i −0.140690 + 0.797891i 0.830038 + 0.557707i \(0.188319\pi\)
−0.970727 + 0.240184i \(0.922792\pi\)
\(702\) 0 0
\(703\) 10.4731 + 22.4193i 0.395002 + 0.845559i
\(704\) 0 0
\(705\) −0.0146230 + 0.0829313i −0.000550735 + 0.00312337i
\(706\) 0 0
\(707\) 3.50099 + 1.27426i 0.131668 + 0.0479233i
\(708\) 0 0
\(709\) 4.40631 3.69734i 0.165483 0.138856i −0.556286 0.830991i \(-0.687774\pi\)
0.721768 + 0.692135i \(0.243330\pi\)
\(710\) 0 0
\(711\) 1.55531 2.69387i 0.0583285 0.101028i
\(712\) 0 0
\(713\) −6.12014 34.7090i −0.229201 1.29986i
\(714\) 0 0
\(715\) −26.1872 45.3575i −0.979345 1.69627i
\(716\) 0 0
\(717\) 2.09479 0.762442i 0.0782315 0.0284739i
\(718\) 0 0
\(719\) −9.67624 8.11933i −0.360863 0.302800i 0.444272 0.895892i \(-0.353463\pi\)
−0.805135 + 0.593092i \(0.797907\pi\)
\(720\) 0 0
\(721\) 7.26226 0.270461
\(722\) 0 0
\(723\) −1.33879 −0.0497900
\(724\) 0 0
\(725\) 0.466148 + 0.391145i 0.0173123 + 0.0145267i
\(726\) 0 0
\(727\) 19.6845 7.16458i 0.730058 0.265719i 0.0498687 0.998756i \(-0.484120\pi\)
0.680189 + 0.733036i \(0.261897\pi\)
\(728\) 0 0
\(729\) −8.80279 15.2469i −0.326029 0.564699i
\(730\) 0 0
\(731\) 4.73894 + 26.8759i 0.175276 + 0.994040i
\(732\) 0 0
\(733\) −13.8459 + 23.9818i −0.511410 + 0.885788i 0.488503 + 0.872562i \(0.337543\pi\)
−0.999913 + 0.0132253i \(0.995790\pi\)
\(734\) 0 0
\(735\) −17.8590 + 14.9855i −0.658738 + 0.552747i
\(736\) 0 0
\(737\) −48.2406 17.5581i −1.77696 0.646762i
\(738\) 0 0
\(739\) 1.13266 6.42366i 0.0416658 0.236298i −0.956862 0.290543i \(-0.906164\pi\)
0.998528 + 0.0542449i \(0.0172752\pi\)
\(740\) 0 0
\(741\) −8.37412 17.9260i −0.307631 0.658530i
\(742\) 0 0
\(743\) 8.37272 47.4840i 0.307165 1.74202i −0.305969 0.952042i \(-0.598980\pi\)
0.613134 0.789979i \(-0.289909\pi\)
\(744\) 0 0
\(745\) 17.6697 + 6.43126i 0.647369 + 0.235623i
\(746\) 0 0
\(747\) −8.06957 + 6.77117i −0.295250 + 0.247744i
\(748\) 0 0
\(749\) −2.65088 + 4.59146i −0.0968611 + 0.167768i
\(750\) 0 0
\(751\) −1.08778 6.16908i −0.0396935 0.225113i 0.958508 0.285067i \(-0.0920158\pi\)
−0.998201 + 0.0599538i \(0.980905\pi\)
\(752\) 0 0
\(753\) 3.78029 + 6.54766i 0.137762 + 0.238610i
\(754\) 0 0
\(755\) 19.4629 7.08392i 0.708328 0.257810i
\(756\) 0 0
\(757\) 24.5477 + 20.5979i 0.892200 + 0.748645i 0.968650 0.248429i \(-0.0799142\pi\)
−0.0764503 + 0.997073i \(0.524359\pi\)
\(758\) 0 0
\(759\) 21.2574 0.771595
\(760\) 0 0
\(761\) 43.1308 1.56349 0.781745 0.623598i \(-0.214330\pi\)
0.781745 + 0.623598i \(0.214330\pi\)
\(762\) 0 0
\(763\) 3.52584 + 2.95853i 0.127644 + 0.107106i
\(764\) 0 0
\(765\) 20.7408 7.54904i 0.749885 0.272936i
\(766\) 0 0
\(767\) 22.6485 + 39.2283i 0.817790 + 1.41645i
\(768\) 0 0
\(769\) −5.88829 33.3942i −0.212337 1.20422i −0.885468 0.464701i \(-0.846162\pi\)
0.673131 0.739524i \(-0.264949\pi\)
\(770\) 0 0
\(771\) 5.38641 9.32954i 0.193987 0.335995i
\(772\) 0 0
\(773\) 14.2612 11.9666i 0.512939 0.430407i −0.349223 0.937040i \(-0.613554\pi\)
0.862162 + 0.506633i \(0.169110\pi\)
\(774\) 0 0
\(775\) −34.9134 12.7074i −1.25413 0.456465i
\(776\) 0 0
\(777\) −0.597656 + 3.38948i −0.0214408 + 0.121597i
\(778\) 0 0
\(779\) 13.5196 50.5957i 0.484391 1.81278i
\(780\) 0 0
\(781\) −2.30603 + 13.0782i −0.0825163 + 0.467973i
\(782\) 0 0
\(783\) −0.571815 0.208124i −0.0204350 0.00743774i
\(784\) 0 0
\(785\) 1.51239 1.26905i 0.0539795 0.0452942i
\(786\) 0 0
\(787\) 7.59309 13.1516i 0.270664 0.468804i −0.698368 0.715739i \(-0.746090\pi\)
0.969032 + 0.246935i \(0.0794233\pi\)
\(788\) 0 0
\(789\) −0.406197 2.30366i −0.0144610 0.0820123i
\(790\) 0 0
\(791\) 0.579813 + 1.00427i 0.0206158 + 0.0357076i
\(792\) 0 0
\(793\) 49.1818 17.9007i 1.74650 0.635673i
\(794\) 0 0