Properties

Label 1520.2.q.j.881.2
Level $1520$
Weight $2$
Character 1520.881
Analytic conductor $12.137$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1372611072\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.3518667.1
Defining polynomial: \( x^{6} - x^{5} + 7x^{4} - 8x^{3} + 43x^{2} - 42x + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 881.2
Root \(0.610938 + 1.05818i\) of defining polynomial
Character \(\chi\) \(=\) 1520.881
Dual form 1520.2.q.j.961.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.610938 + 1.05818i) q^{3} +(0.500000 + 0.866025i) q^{5} +0.221876 q^{7} +(0.753509 - 1.30512i) q^{9} +O(q^{10})\) \(q+(0.610938 + 1.05818i) q^{3} +(0.500000 + 0.866025i) q^{5} +0.221876 q^{7} +(0.753509 - 1.30512i) q^{9} +0.778124 q^{11} +(2.50000 - 4.33013i) q^{13} +(-0.610938 + 1.05818i) q^{15} +(-3.53865 - 6.12912i) q^{17} +(-1.33281 - 4.15013i) q^{19} +(0.135553 + 0.234784i) q^{21} +(4.03865 - 6.99515i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.50702 q^{27} +(-0.110938 + 0.192150i) q^{29} -2.50702 q^{31} +(0.475385 + 0.823392i) q^{33} +(0.110938 + 0.192150i) q^{35} -1.90466 q^{37} +6.10938 q^{39} +(3.61796 + 6.26648i) q^{41} +(3.64959 + 6.32128i) q^{43} +1.50702 q^{45} +(-1.39608 + 2.41808i) q^{47} -6.95077 q^{49} +(4.32379 - 7.48903i) q^{51} +(-2.19024 + 3.79361i) q^{53} +(0.389062 + 0.673875i) q^{55} +(3.57730 - 3.94583i) q^{57} +(-1.39608 - 2.41808i) q^{59} +(6.29216 - 10.8983i) q^{61} +(0.167186 - 0.289574i) q^{63} +5.00000 q^{65} +(-5.28514 + 9.15414i) q^{67} +9.86946 q^{69} +(-4.92070 - 8.52289i) q^{71} +(7.03865 + 12.1913i) q^{73} -1.22188 q^{75} +0.172647 q^{77} +(0.792161 + 1.37206i) q^{79} +(1.10392 + 1.91204i) q^{81} +9.52106 q^{83} +(3.53865 - 6.12912i) q^{85} -0.271105 q^{87} +(-1.57028 + 2.71981i) q^{89} +(0.554690 - 0.960752i) q^{91} +(-1.53163 - 2.65287i) q^{93} +(2.92771 - 3.22932i) q^{95} +(3.18122 + 5.51004i) q^{97} +(0.586324 - 1.01554i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{3} + 3 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{3} + 3 q^{5} - 4 q^{7} - 4 q^{9} + 10 q^{11} + 15 q^{13} - q^{15} - q^{17} + 12 q^{21} + 4 q^{23} - 3 q^{25} + 16 q^{27} + 2 q^{29} + 2 q^{31} - 11 q^{33} - 2 q^{35} - 4 q^{37} + 10 q^{39} + 2 q^{41} - q^{43} - 8 q^{45} + 6 q^{47} - 14 q^{49} - 6 q^{51} - 11 q^{53} + 5 q^{55} - 19 q^{57} + 6 q^{59} + 9 q^{61} + 9 q^{63} + 30 q^{65} - 20 q^{67} - 10 q^{69} - 29 q^{71} + 22 q^{73} - 2 q^{75} - 32 q^{77} - 24 q^{79} + 21 q^{81} + 6 q^{83} + q^{85} - 24 q^{87} + 14 q^{89} - 10 q^{91} - 6 q^{93} - 7 q^{97} - 13 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(401\) \(1141\) \(1217\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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
\(3\) 0.610938 + 1.05818i 0.352725 + 0.610938i 0.986726 0.162394i \(-0.0519217\pi\)
−0.634001 + 0.773333i \(0.718588\pi\)
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0.221876 0.0838613 0.0419307 0.999121i \(-0.486649\pi\)
0.0419307 + 0.999121i \(0.486649\pi\)
\(8\) 0 0
\(9\) 0.753509 1.30512i 0.251170 0.435039i
\(10\) 0 0
\(11\) 0.778124 0.234613 0.117307 0.993096i \(-0.462574\pi\)
0.117307 + 0.993096i \(0.462574\pi\)
\(12\) 0 0
\(13\) 2.50000 4.33013i 0.693375 1.20096i −0.277350 0.960769i \(-0.589456\pi\)
0.970725 0.240192i \(-0.0772105\pi\)
\(14\) 0 0
\(15\) −0.610938 + 1.05818i −0.157744 + 0.273220i
\(16\) 0 0
\(17\) −3.53865 6.12912i −0.858249 1.48653i −0.873598 0.486649i \(-0.838219\pi\)
0.0153485 0.999882i \(-0.495114\pi\)
\(18\) 0 0
\(19\) −1.33281 4.15013i −0.305769 0.952106i
\(20\) 0 0
\(21\) 0.135553 + 0.234784i 0.0295800 + 0.0512341i
\(22\) 0 0
\(23\) 4.03865 6.99515i 0.842117 1.45859i −0.0459843 0.998942i \(-0.514642\pi\)
0.888101 0.459647i \(-0.152024\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 5.50702 1.05983
\(28\) 0 0
\(29\) −0.110938 + 0.192150i −0.0206007 + 0.0356814i −0.876142 0.482053i \(-0.839891\pi\)
0.855541 + 0.517735i \(0.173225\pi\)
\(30\) 0 0
\(31\) −2.50702 −0.450274 −0.225137 0.974327i \(-0.572283\pi\)
−0.225137 + 0.974327i \(0.572283\pi\)
\(32\) 0 0
\(33\) 0.475385 + 0.823392i 0.0827540 + 0.143334i
\(34\) 0 0
\(35\) 0.110938 + 0.192150i 0.0187520 + 0.0324793i
\(36\) 0 0
\(37\) −1.90466 −0.313124 −0.156562 0.987668i \(-0.550041\pi\)
−0.156562 + 0.987668i \(0.550041\pi\)
\(38\) 0 0
\(39\) 6.10938 0.978284
\(40\) 0 0
\(41\) 3.61796 + 6.26648i 0.565030 + 0.978661i 0.997047 + 0.0767950i \(0.0244687\pi\)
−0.432017 + 0.901865i \(0.642198\pi\)
\(42\) 0 0
\(43\) 3.64959 + 6.32128i 0.556557 + 0.963985i 0.997781 + 0.0665881i \(0.0212113\pi\)
−0.441223 + 0.897397i \(0.645455\pi\)
\(44\) 0 0
\(45\) 1.50702 0.224653
\(46\) 0 0
\(47\) −1.39608 + 2.41808i −0.203639 + 0.352714i −0.949698 0.313166i \(-0.898610\pi\)
0.746059 + 0.665880i \(0.231944\pi\)
\(48\) 0 0
\(49\) −6.95077 −0.992967
\(50\) 0 0
\(51\) 4.32379 7.48903i 0.605452 1.04867i
\(52\) 0 0
\(53\) −2.19024 + 3.79361i −0.300853 + 0.521093i −0.976329 0.216289i \(-0.930605\pi\)
0.675476 + 0.737382i \(0.263938\pi\)
\(54\) 0 0
\(55\) 0.389062 + 0.673875i 0.0524611 + 0.0908653i
\(56\) 0 0
\(57\) 3.57730 3.94583i 0.473825 0.522637i
\(58\) 0 0
\(59\) −1.39608 2.41808i −0.181754 0.314808i 0.760724 0.649076i \(-0.224844\pi\)
−0.942478 + 0.334268i \(0.891511\pi\)
\(60\) 0 0
\(61\) 6.29216 10.8983i 0.805629 1.39539i −0.110237 0.993905i \(-0.535161\pi\)
0.915866 0.401484i \(-0.131506\pi\)
\(62\) 0 0
\(63\) 0.167186 0.289574i 0.0210634 0.0364829i
\(64\) 0 0
\(65\) 5.00000 0.620174
\(66\) 0 0
\(67\) −5.28514 + 9.15414i −0.645683 + 1.11836i 0.338460 + 0.940981i \(0.390094\pi\)
−0.984143 + 0.177375i \(0.943239\pi\)
\(68\) 0 0
\(69\) 9.86946 1.18814
\(70\) 0 0
\(71\) −4.92070 8.52289i −0.583979 1.01148i −0.995002 0.0998563i \(-0.968162\pi\)
0.411023 0.911625i \(-0.365172\pi\)
\(72\) 0 0
\(73\) 7.03865 + 12.1913i 0.823812 + 1.42688i 0.902824 + 0.430010i \(0.141490\pi\)
−0.0790121 + 0.996874i \(0.525177\pi\)
\(74\) 0 0
\(75\) −1.22188 −0.141090
\(76\) 0 0
\(77\) 0.172647 0.0196750
\(78\) 0 0
\(79\) 0.792161 + 1.37206i 0.0891251 + 0.154369i 0.907142 0.420826i \(-0.138260\pi\)
−0.818016 + 0.575195i \(0.804926\pi\)
\(80\) 0 0
\(81\) 1.10392 + 1.91204i 0.122658 + 0.212449i
\(82\) 0 0
\(83\) 9.52106 1.04507 0.522536 0.852617i \(-0.324986\pi\)
0.522536 + 0.852617i \(0.324986\pi\)
\(84\) 0 0
\(85\) 3.53865 6.12912i 0.383821 0.664797i
\(86\) 0 0
\(87\) −0.271105 −0.0290655
\(88\) 0 0
\(89\) −1.57028 + 2.71981i −0.166450 + 0.288300i −0.937169 0.348875i \(-0.886564\pi\)
0.770719 + 0.637175i \(0.219897\pi\)
\(90\) 0 0
\(91\) 0.554690 0.960752i 0.0581474 0.100714i
\(92\) 0 0
\(93\) −1.53163 2.65287i −0.158823 0.275089i
\(94\) 0 0
\(95\) 2.92771 3.22932i 0.300377 0.331321i
\(96\) 0 0
\(97\) 3.18122 + 5.51004i 0.323004 + 0.559460i 0.981106 0.193469i \(-0.0619738\pi\)
−0.658102 + 0.752929i \(0.728641\pi\)
\(98\) 0 0
\(99\) 0.586324 1.01554i 0.0589277 0.102066i
\(100\) 0 0
\(101\) 3.69726 6.40385i 0.367891 0.637206i −0.621344 0.783538i \(-0.713413\pi\)
0.989236 + 0.146331i \(0.0467465\pi\)
\(102\) 0 0
\(103\) −12.2038 −1.20248 −0.601240 0.799069i \(-0.705326\pi\)
−0.601240 + 0.799069i \(0.705326\pi\)
\(104\) 0 0
\(105\) −0.135553 + 0.234784i −0.0132286 + 0.0229126i
\(106\) 0 0
\(107\) 1.63355 0.157921 0.0789607 0.996878i \(-0.474840\pi\)
0.0789607 + 0.996878i \(0.474840\pi\)
\(108\) 0 0
\(109\) 3.80820 + 6.59600i 0.364759 + 0.631782i 0.988738 0.149660i \(-0.0478179\pi\)
−0.623978 + 0.781442i \(0.714485\pi\)
\(110\) 0 0
\(111\) −1.16363 2.01546i −0.110447 0.191299i
\(112\) 0 0
\(113\) 12.4890 1.17486 0.587432 0.809273i \(-0.300139\pi\)
0.587432 + 0.809273i \(0.300139\pi\)
\(114\) 0 0
\(115\) 8.07730 0.753212
\(116\) 0 0
\(117\) −3.76755 6.52558i −0.348310 0.603290i
\(118\) 0 0
\(119\) −0.785142 1.35991i −0.0719739 0.124662i
\(120\) 0 0
\(121\) −10.3945 −0.944957
\(122\) 0 0
\(123\) −4.42070 + 7.65687i −0.398601 + 0.690397i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −6.52106 + 11.2948i −0.578650 + 1.00225i 0.416984 + 0.908914i \(0.363087\pi\)
−0.995635 + 0.0933378i \(0.970246\pi\)
\(128\) 0 0
\(129\) −4.45935 + 7.72382i −0.392624 + 0.680044i
\(130\) 0 0
\(131\) 3.55469 + 6.15690i 0.310575 + 0.537931i 0.978487 0.206309i \(-0.0661452\pi\)
−0.667912 + 0.744240i \(0.732812\pi\)
\(132\) 0 0
\(133\) −0.295720 0.920816i −0.0256422 0.0798448i
\(134\) 0 0
\(135\) 2.75351 + 4.76922i 0.236984 + 0.410469i
\(136\) 0 0
\(137\) −2.71286 + 4.69880i −0.231775 + 0.401446i −0.958331 0.285662i \(-0.907787\pi\)
0.726556 + 0.687108i \(0.241120\pi\)
\(138\) 0 0
\(139\) 1.78514 3.09196i 0.151414 0.262256i −0.780334 0.625363i \(-0.784951\pi\)
0.931747 + 0.363107i \(0.118284\pi\)
\(140\) 0 0
\(141\) −3.41168 −0.287315
\(142\) 0 0
\(143\) 1.94531 3.36938i 0.162675 0.281761i
\(144\) 0 0
\(145\) −0.221876 −0.0184258
\(146\) 0 0
\(147\) −4.24649 7.35514i −0.350245 0.606642i
\(148\) 0 0
\(149\) 0.468367 + 0.811235i 0.0383701 + 0.0664590i 0.884573 0.466402i \(-0.154450\pi\)
−0.846203 + 0.532861i \(0.821117\pi\)
\(150\) 0 0
\(151\) 0.971925 0.0790942 0.0395471 0.999218i \(-0.487408\pi\)
0.0395471 + 0.999218i \(0.487408\pi\)
\(152\) 0 0
\(153\) −10.6656 −0.862265
\(154\) 0 0
\(155\) −1.25351 2.17114i −0.100684 0.174390i
\(156\) 0 0
\(157\) −1.35743 2.35114i −0.108335 0.187641i 0.806761 0.590878i \(-0.201218\pi\)
−0.915096 + 0.403237i \(0.867885\pi\)
\(158\) 0 0
\(159\) −5.35241 −0.424474
\(160\) 0 0
\(161\) 0.896081 1.55206i 0.0706210 0.122319i
\(162\) 0 0
\(163\) 3.20384 0.250944 0.125472 0.992097i \(-0.459956\pi\)
0.125472 + 0.992097i \(0.459956\pi\)
\(164\) 0 0
\(165\) −0.475385 + 0.823392i −0.0370087 + 0.0641010i
\(166\) 0 0
\(167\) 5.11094 8.85240i 0.395496 0.685020i −0.597668 0.801744i \(-0.703906\pi\)
0.993164 + 0.116724i \(0.0372393\pi\)
\(168\) 0 0
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) 0 0
\(171\) −6.42070 1.38769i −0.491003 0.106119i
\(172\) 0 0
\(173\) 1.33281 + 2.30850i 0.101332 + 0.175512i 0.912234 0.409670i \(-0.134356\pi\)
−0.810902 + 0.585182i \(0.801023\pi\)
\(174\) 0 0
\(175\) −0.110938 + 0.192150i −0.00838613 + 0.0145252i
\(176\) 0 0
\(177\) 1.70584 2.95460i 0.128219 0.222081i
\(178\) 0 0
\(179\) 12.9367 0.966937 0.483468 0.875362i \(-0.339377\pi\)
0.483468 + 0.875362i \(0.339377\pi\)
\(180\) 0 0
\(181\) 9.30620 16.1188i 0.691724 1.19810i −0.279548 0.960132i \(-0.590185\pi\)
0.971273 0.237970i \(-0.0764820\pi\)
\(182\) 0 0
\(183\) 15.3765 1.13666
\(184\) 0 0
\(185\) −0.952328 1.64948i −0.0700166 0.121272i
\(186\) 0 0
\(187\) −2.75351 4.76922i −0.201357 0.348760i
\(188\) 0 0
\(189\) 1.22188 0.0888784
\(190\) 0 0
\(191\) 23.0421 1.66727 0.833634 0.552317i \(-0.186256\pi\)
0.833634 + 0.552317i \(0.186256\pi\)
\(192\) 0 0
\(193\) 8.53865 + 14.7894i 0.614626 + 1.06456i 0.990450 + 0.137872i \(0.0440262\pi\)
−0.375824 + 0.926691i \(0.622640\pi\)
\(194\) 0 0
\(195\) 3.05469 + 5.29088i 0.218751 + 0.378888i
\(196\) 0 0
\(197\) −8.82024 −0.628416 −0.314208 0.949354i \(-0.601739\pi\)
−0.314208 + 0.949354i \(0.601739\pi\)
\(198\) 0 0
\(199\) −1.42771 + 2.47287i −0.101208 + 0.175297i −0.912183 0.409784i \(-0.865604\pi\)
0.810975 + 0.585081i \(0.198937\pi\)
\(200\) 0 0
\(201\) −12.9156 −0.910995
\(202\) 0 0
\(203\) −0.0246145 + 0.0426336i −0.00172760 + 0.00299229i
\(204\) 0 0
\(205\) −3.61796 + 6.26648i −0.252689 + 0.437670i
\(206\) 0 0
\(207\) −6.08632 10.5418i −0.423029 0.732707i
\(208\) 0 0
\(209\) −1.03709 3.22932i −0.0717373 0.223377i
\(210\) 0 0
\(211\) −6.44375 11.1609i −0.443606 0.768348i 0.554348 0.832285i \(-0.312968\pi\)
−0.997954 + 0.0639367i \(0.979634\pi\)
\(212\) 0 0
\(213\) 6.01248 10.4139i 0.411968 0.713550i
\(214\) 0 0
\(215\) −3.64959 + 6.32128i −0.248900 + 0.431107i
\(216\) 0 0
\(217\) −0.556248 −0.0377606
\(218\) 0 0
\(219\) −8.60036 + 14.8963i −0.581159 + 1.00660i
\(220\) 0 0
\(221\) −35.3865 −2.38035
\(222\) 0 0
\(223\) 10.3539 + 17.9334i 0.693346 + 1.20091i 0.970735 + 0.240153i \(0.0771978\pi\)
−0.277389 + 0.960758i \(0.589469\pi\)
\(224\) 0 0
\(225\) 0.753509 + 1.30512i 0.0502340 + 0.0870078i
\(226\) 0 0
\(227\) −4.00000 −0.265489 −0.132745 0.991150i \(-0.542379\pi\)
−0.132745 + 0.991150i \(0.542379\pi\)
\(228\) 0 0
\(229\) 3.53910 0.233870 0.116935 0.993140i \(-0.462693\pi\)
0.116935 + 0.993140i \(0.462693\pi\)
\(230\) 0 0
\(231\) 0.105477 + 0.182691i 0.00693986 + 0.0120202i
\(232\) 0 0
\(233\) 9.89252 + 17.1344i 0.648081 + 1.12251i 0.983581 + 0.180468i \(0.0577614\pi\)
−0.335500 + 0.942040i \(0.608905\pi\)
\(234\) 0 0
\(235\) −2.79216 −0.182141
\(236\) 0 0
\(237\) −0.967923 + 1.67649i −0.0628733 + 0.108900i
\(238\) 0 0
\(239\) −23.7741 −1.53782 −0.768910 0.639357i \(-0.779201\pi\)
−0.768910 + 0.639357i \(0.779201\pi\)
\(240\) 0 0
\(241\) 2.27111 3.93367i 0.146295 0.253390i −0.783561 0.621315i \(-0.786599\pi\)
0.929855 + 0.367926i \(0.119932\pi\)
\(242\) 0 0
\(243\) 6.91168 11.9714i 0.443384 0.767964i
\(244\) 0 0
\(245\) −3.47539 6.01954i −0.222034 0.384575i
\(246\) 0 0
\(247\) −21.3026 4.60408i −1.35545 0.292950i
\(248\) 0 0
\(249\) 5.81678 + 10.0750i 0.368623 + 0.638474i
\(250\) 0 0
\(251\) −9.75151 + 16.8901i −0.615510 + 1.06609i 0.374785 + 0.927112i \(0.377716\pi\)
−0.990295 + 0.138982i \(0.955617\pi\)
\(252\) 0 0
\(253\) 3.14257 5.44309i 0.197572 0.342204i
\(254\) 0 0
\(255\) 8.64759 0.541533
\(256\) 0 0
\(257\) −0.882043 + 1.52774i −0.0550203 + 0.0952980i −0.892224 0.451594i \(-0.850856\pi\)
0.837203 + 0.546892i \(0.184189\pi\)
\(258\) 0 0
\(259\) −0.422598 −0.0262590
\(260\) 0 0
\(261\) 0.167186 + 0.289574i 0.0103485 + 0.0179242i
\(262\) 0 0
\(263\) −3.23591 5.60477i −0.199535 0.345605i 0.748843 0.662748i \(-0.230610\pi\)
−0.948378 + 0.317143i \(0.897276\pi\)
\(264\) 0 0
\(265\) −4.38049 −0.269091
\(266\) 0 0
\(267\) −3.83739 −0.234844
\(268\) 0 0
\(269\) −14.2429 24.6695i −0.868407 1.50412i −0.863624 0.504136i \(-0.831811\pi\)
−0.00478280 0.999989i \(-0.501522\pi\)
\(270\) 0 0
\(271\) −0.246491 0.426934i −0.0149732 0.0259344i 0.858442 0.512911i \(-0.171433\pi\)
−0.873415 + 0.486977i \(0.838100\pi\)
\(272\) 0 0
\(273\) 1.35553 0.0820402
\(274\) 0 0
\(275\) −0.389062 + 0.673875i −0.0234613 + 0.0406362i
\(276\) 0 0
\(277\) −8.78905 −0.528083 −0.264041 0.964511i \(-0.585056\pi\)
−0.264041 + 0.964511i \(0.585056\pi\)
\(278\) 0 0
\(279\) −1.88906 + 3.27195i −0.113095 + 0.195887i
\(280\) 0 0
\(281\) 2.37147 4.10750i 0.141470 0.245033i −0.786581 0.617488i \(-0.788151\pi\)
0.928050 + 0.372455i \(0.121484\pi\)
\(282\) 0 0
\(283\) 8.43473 + 14.6094i 0.501393 + 0.868438i 0.999999 + 0.00160901i \(0.000512164\pi\)
−0.498606 + 0.866829i \(0.666155\pi\)
\(284\) 0 0
\(285\) 5.20584 + 1.12512i 0.308367 + 0.0666465i
\(286\) 0 0
\(287\) 0.802738 + 1.39038i 0.0473841 + 0.0820717i
\(288\) 0 0
\(289\) −16.5441 + 28.6552i −0.973183 + 1.68560i
\(290\) 0 0
\(291\) −3.88706 + 6.73259i −0.227864 + 0.394671i
\(292\) 0 0
\(293\) 11.6336 0.679639 0.339820 0.940491i \(-0.389634\pi\)
0.339820 + 0.940491i \(0.389634\pi\)
\(294\) 0 0
\(295\) 1.39608 2.41808i 0.0812830 0.140786i
\(296\) 0 0
\(297\) 4.28514 0.248649
\(298\) 0 0
\(299\) −20.1933 34.9758i −1.16781 2.02270i
\(300\) 0 0
\(301\) 0.809757 + 1.40254i 0.0466736 + 0.0808411i
\(302\) 0 0
\(303\) 9.03519 0.519058
\(304\) 0 0
\(305\) 12.5843 0.720576
\(306\) 0 0
\(307\) 2.94531 + 5.10143i 0.168098 + 0.291154i 0.937751 0.347308i \(-0.112904\pi\)
−0.769653 + 0.638462i \(0.779571\pi\)
\(308\) 0 0
\(309\) −7.45579 12.9138i −0.424145 0.734641i
\(310\) 0 0
\(311\) −14.8202 −0.840378 −0.420189 0.907437i \(-0.638036\pi\)
−0.420189 + 0.907437i \(0.638036\pi\)
\(312\) 0 0
\(313\) 2.94731 5.10489i 0.166592 0.288546i −0.770628 0.637286i \(-0.780057\pi\)
0.937219 + 0.348740i \(0.113390\pi\)
\(314\) 0 0
\(315\) 0.334372 0.0188397
\(316\) 0 0
\(317\) 2.07930 3.60146i 0.116785 0.202278i −0.801707 0.597718i \(-0.796074\pi\)
0.918492 + 0.395439i \(0.129408\pi\)
\(318\) 0 0
\(319\) −0.0863236 + 0.149517i −0.00483319 + 0.00837133i
\(320\) 0 0
\(321\) 0.997999 + 1.72858i 0.0557029 + 0.0964802i
\(322\) 0 0
\(323\) −20.7203 + 22.8549i −1.15291 + 1.27168i
\(324\) 0 0
\(325\) 2.50000 + 4.33013i 0.138675 + 0.240192i
\(326\) 0 0
\(327\) −4.65315 + 8.05949i −0.257320 + 0.445691i
\(328\) 0 0
\(329\) −0.309757 + 0.536515i −0.0170775 + 0.0295790i
\(330\) 0 0
\(331\) −10.6797 −0.587008 −0.293504 0.955958i \(-0.594821\pi\)
−0.293504 + 0.955958i \(0.594821\pi\)
\(332\) 0 0
\(333\) −1.43518 + 2.48580i −0.0786472 + 0.136221i
\(334\) 0 0
\(335\) −10.5703 −0.577516
\(336\) 0 0
\(337\) 13.1726 + 22.8157i 0.717560 + 1.24285i 0.961964 + 0.273177i \(0.0880743\pi\)
−0.244404 + 0.969673i \(0.578592\pi\)
\(338\) 0 0
\(339\) 7.62999 + 13.2155i 0.414404 + 0.717769i
\(340\) 0 0
\(341\) −1.95077 −0.105640
\(342\) 0 0
\(343\) −3.09534 −0.167133
\(344\) 0 0
\(345\) 4.93473 + 8.54721i 0.265677 + 0.460166i
\(346\) 0 0
\(347\) −8.44175 14.6215i −0.453177 0.784925i 0.545404 0.838173i \(-0.316376\pi\)
−0.998581 + 0.0532476i \(0.983043\pi\)
\(348\) 0 0
\(349\) 4.61640 0.247110 0.123555 0.992338i \(-0.460570\pi\)
0.123555 + 0.992338i \(0.460570\pi\)
\(350\) 0 0
\(351\) 13.7675 23.8461i 0.734857 1.27281i
\(352\) 0 0
\(353\) −24.9508 −1.32800 −0.663998 0.747735i \(-0.731142\pi\)
−0.663998 + 0.747735i \(0.731142\pi\)
\(354\) 0 0
\(355\) 4.92070 8.52289i 0.261163 0.452348i
\(356\) 0 0
\(357\) 0.959347 1.66164i 0.0507740 0.0879432i
\(358\) 0 0
\(359\) 5.90110 + 10.2210i 0.311448 + 0.539444i 0.978676 0.205410i \(-0.0658527\pi\)
−0.667228 + 0.744854i \(0.732519\pi\)
\(360\) 0 0
\(361\) −15.4472 + 11.0627i −0.813011 + 0.582248i
\(362\) 0 0
\(363\) −6.35041 10.9992i −0.333310 0.577310i
\(364\) 0 0
\(365\) −7.03865 + 12.1913i −0.368420 + 0.638122i
\(366\) 0 0
\(367\) 13.1164 22.7183i 0.684670 1.18588i −0.288870 0.957368i \(-0.593279\pi\)
0.973540 0.228516i \(-0.0733872\pi\)
\(368\) 0 0
\(369\) 10.9047 0.567674
\(370\) 0 0
\(371\) −0.485963 + 0.841712i −0.0252299 + 0.0436995i
\(372\) 0 0
\(373\) 11.9960 0.621129 0.310565 0.950552i \(-0.399482\pi\)
0.310565 + 0.950552i \(0.399482\pi\)
\(374\) 0 0
\(375\) −0.610938 1.05818i −0.0315487 0.0546440i
\(376\) 0 0
\(377\) 0.554690 + 0.960752i 0.0285680 + 0.0494812i
\(378\) 0 0
\(379\) −0.313217 −0.0160889 −0.00804444 0.999968i \(-0.502561\pi\)
−0.00804444 + 0.999968i \(0.502561\pi\)
\(380\) 0 0
\(381\) −15.9358 −0.816418
\(382\) 0 0
\(383\) 15.0441 + 26.0572i 0.768718 + 1.33146i 0.938258 + 0.345936i \(0.112439\pi\)
−0.169540 + 0.985523i \(0.554228\pi\)
\(384\) 0 0
\(385\) 0.0863236 + 0.149517i 0.00439946 + 0.00762008i
\(386\) 0 0
\(387\) 11.0000 0.559161
\(388\) 0 0
\(389\) 17.8609 30.9360i 0.905583 1.56852i 0.0854503 0.996342i \(-0.472767\pi\)
0.820133 0.572173i \(-0.193900\pi\)
\(390\) 0 0
\(391\) −57.1655 −2.89099
\(392\) 0 0
\(393\) −4.34339 + 7.52297i −0.219095 + 0.379484i
\(394\) 0 0
\(395\) −0.792161 + 1.37206i −0.0398580 + 0.0690360i
\(396\) 0 0
\(397\) −4.77657 8.27326i −0.239729 0.415223i 0.720907 0.693031i \(-0.243725\pi\)
−0.960636 + 0.277809i \(0.910392\pi\)
\(398\) 0 0
\(399\) 0.793718 0.875485i 0.0397356 0.0438291i
\(400\) 0 0
\(401\) −15.4418 26.7459i −0.771124 1.33563i −0.936947 0.349471i \(-0.886361\pi\)
0.165823 0.986156i \(-0.446972\pi\)
\(402\) 0 0
\(403\) −6.26755 + 10.8557i −0.312209 + 0.540761i
\(404\) 0 0
\(405\) −1.10392 + 1.91204i −0.0548542 + 0.0950103i
\(406\) 0 0
\(407\) −1.48206 −0.0734629
\(408\) 0 0
\(409\) −15.7816 + 27.3345i −0.780349 + 1.35160i 0.151389 + 0.988474i \(0.451625\pi\)
−0.931738 + 0.363130i \(0.881708\pi\)
\(410\) 0 0
\(411\) −6.62955 −0.327012
\(412\) 0 0
\(413\) −0.309757 0.536515i −0.0152421 0.0264002i
\(414\) 0 0
\(415\) 4.76053 + 8.24548i 0.233685 + 0.404755i
\(416\) 0 0
\(417\) 4.36245 0.213630
\(418\) 0 0
\(419\) 26.5070 1.29495 0.647476 0.762086i \(-0.275824\pi\)
0.647476 + 0.762086i \(0.275824\pi\)
\(420\) 0 0
\(421\) 10.1180 + 17.5248i 0.493119 + 0.854107i 0.999969 0.00792731i \(-0.00252337\pi\)
−0.506850 + 0.862035i \(0.669190\pi\)
\(422\) 0 0
\(423\) 2.10392 + 3.64410i 0.102296 + 0.177182i
\(424\) 0 0
\(425\) 7.07730 0.343300
\(426\) 0 0
\(427\) 1.39608 2.41808i 0.0675611 0.117019i
\(428\) 0 0
\(429\) 4.75385 0.229518
\(430\) 0 0
\(431\) −5.73045 + 9.92543i −0.276026 + 0.478091i −0.970394 0.241529i \(-0.922351\pi\)
0.694367 + 0.719621i \(0.255684\pi\)
\(432\) 0 0
\(433\) −12.9734 + 22.4706i −0.623461 + 1.07987i 0.365375 + 0.930860i \(0.380941\pi\)
−0.988836 + 0.149006i \(0.952393\pi\)
\(434\) 0 0
\(435\) −0.135553 0.234784i −0.00649925 0.0112570i
\(436\) 0 0
\(437\) −34.4136 7.43771i −1.64622 0.355794i
\(438\) 0 0
\(439\) 12.6562 + 21.9211i 0.604046 + 1.04624i 0.992202 + 0.124644i \(0.0397789\pi\)
−0.388156 + 0.921594i \(0.626888\pi\)
\(440\) 0 0
\(441\) −5.23747 + 9.07157i −0.249403 + 0.431979i
\(442\) 0 0
\(443\) 10.0125 17.3421i 0.475707 0.823949i −0.523905 0.851776i \(-0.675525\pi\)
0.999613 + 0.0278272i \(0.00885883\pi\)
\(444\) 0 0
\(445\) −3.14057 −0.148877
\(446\) 0 0
\(447\) −0.572286 + 0.991229i −0.0270682 + 0.0468835i
\(448\) 0 0
\(449\) 19.7601 0.932536 0.466268 0.884644i \(-0.345598\pi\)
0.466268 + 0.884644i \(0.345598\pi\)
\(450\) 0 0
\(451\) 2.81522 + 4.87610i 0.132563 + 0.229607i
\(452\) 0 0
\(453\) 0.593786 + 1.02847i 0.0278985 + 0.0483216i
\(454\) 0 0
\(455\) 1.10938 0.0520086
\(456\) 0 0
\(457\) −34.4647 −1.61219 −0.806096 0.591785i \(-0.798423\pi\)
−0.806096 + 0.591785i \(0.798423\pi\)
\(458\) 0 0
\(459\) −19.4874 33.7532i −0.909595 1.57546i
\(460\) 0 0
\(461\) 3.96637 + 6.86995i 0.184732 + 0.319965i 0.943486 0.331412i \(-0.107525\pi\)
−0.758754 + 0.651377i \(0.774192\pi\)
\(462\) 0 0
\(463\) −9.25395 −0.430068 −0.215034 0.976607i \(-0.568986\pi\)
−0.215034 + 0.976607i \(0.568986\pi\)
\(464\) 0 0
\(465\) 1.53163 2.65287i 0.0710278 0.123024i
\(466\) 0 0
\(467\) −9.47183 −0.438304 −0.219152 0.975691i \(-0.570329\pi\)
−0.219152 + 0.975691i \(0.570329\pi\)
\(468\) 0 0
\(469\) −1.17265 + 2.03108i −0.0541478 + 0.0937868i
\(470\) 0 0
\(471\) 1.65861 2.87280i 0.0764247 0.132371i
\(472\) 0 0
\(473\) 2.83983 + 4.91873i 0.130576 + 0.226164i
\(474\) 0 0
\(475\) 4.26053 + 0.920816i 0.195486 + 0.0422499i
\(476\) 0 0
\(477\) 3.30074 + 5.71704i 0.151130 + 0.261765i
\(478\) 0 0
\(479\) −17.3574 + 30.0639i −0.793081 + 1.37366i 0.130969 + 0.991386i \(0.458191\pi\)
−0.924050 + 0.382270i \(0.875142\pi\)
\(480\) 0 0
\(481\) −4.76164 + 8.24740i −0.217112 + 0.376049i
\(482\) 0 0
\(483\) 2.18980 0.0996393
\(484\) 0 0
\(485\) −3.18122 + 5.51004i −0.144452 + 0.250198i
\(486\) 0 0
\(487\) 28.5070 1.29178 0.645888 0.763432i \(-0.276487\pi\)
0.645888 + 0.763432i \(0.276487\pi\)
\(488\) 0 0
\(489\) 1.95735 + 3.39022i 0.0885142 + 0.153311i
\(490\) 0 0
\(491\) −15.5949 27.0112i −0.703788 1.21900i −0.967127 0.254293i \(-0.918157\pi\)
0.263339 0.964703i \(-0.415176\pi\)
\(492\) 0 0
\(493\) 1.57028 0.0707221
\(494\) 0 0
\(495\) 1.17265 0.0527066
\(496\) 0 0
\(497\) −1.09178 1.89103i −0.0489732 0.0848242i
\(498\) 0 0
\(499\) 8.09334 + 14.0181i 0.362308 + 0.627535i 0.988340 0.152262i \(-0.0486556\pi\)
−0.626032 + 0.779797i \(0.715322\pi\)
\(500\) 0 0
\(501\) 12.4899 0.558006
\(502\) 0 0
\(503\) 8.61094 14.9146i 0.383943 0.665008i −0.607679 0.794183i \(-0.707899\pi\)
0.991622 + 0.129174i \(0.0412327\pi\)
\(504\) 0 0
\(505\) 7.39452 0.329052
\(506\) 0 0
\(507\) 7.33126 12.6981i 0.325593 0.563943i
\(508\) 0 0
\(509\) 18.2956 31.6889i 0.810939 1.40459i −0.101268 0.994859i \(-0.532290\pi\)
0.912207 0.409729i \(-0.134377\pi\)
\(510\) 0 0
\(511\) 1.56171 + 2.70496i 0.0690859 + 0.119660i
\(512\) 0 0
\(513\) −7.33983 22.8549i −0.324062 1.00907i
\(514\) 0 0
\(515\) −6.10192 10.5688i −0.268883 0.465718i
\(516\) 0 0
\(517\) −1.08632 + 1.88157i −0.0477765 + 0.0827512i
\(518\) 0 0
\(519\) −1.62853 + 2.82070i −0.0714847 + 0.123815i
\(520\) 0 0
\(521\) −3.63667 −0.159325 −0.0796626 0.996822i \(-0.525384\pi\)
−0.0796626 + 0.996822i \(0.525384\pi\)
\(522\) 0 0
\(523\) −17.8117 + 30.8507i −0.778850 + 1.34901i 0.153756 + 0.988109i \(0.450863\pi\)
−0.932605 + 0.360898i \(0.882470\pi\)
\(524\) 0 0
\(525\) −0.271105 −0.0118320
\(526\) 0 0
\(527\) 8.87147 + 15.3658i 0.386447 + 0.669346i
\(528\) 0 0
\(529\) −21.1214 36.5834i −0.918322 1.59058i
\(530\) 0 0
\(531\) −4.20784 −0.182605
\(532\) 0 0
\(533\) 36.1796 1.56711
\(534\) 0 0
\(535\) 0.816776 + 1.41470i 0.0353123 + 0.0611627i
\(536\) 0 0
\(537\) 7.90354 + 13.6893i 0.341063 + 0.590739i
\(538\) 0 0
\(539\) −5.40856 −0.232963
\(540\) 0 0
\(541\) −1.58632 + 2.74759i −0.0682014 + 0.118128i −0.898110 0.439772i \(-0.855059\pi\)
0.829908 + 0.557900i \(0.188393\pi\)
\(542\) 0 0
\(543\) 22.7420 0.975955
\(544\) 0 0
\(545\) −3.80820 + 6.59600i −0.163125 + 0.282541i
\(546\) 0 0
\(547\) −14.1902 + 24.5782i −0.606731 + 1.05089i 0.385044 + 0.922898i \(0.374186\pi\)
−0.991775 + 0.127991i \(0.959147\pi\)
\(548\) 0 0
\(549\) −9.48240 16.4240i −0.404699 0.700959i
\(550\) 0 0
\(551\) 0.945310 + 0.204307i 0.0402715 + 0.00870377i
\(552\) 0 0
\(553\) 0.175762 + 0.304428i 0.00747415 + 0.0129456i
\(554\) 0 0
\(555\) 1.16363 2.01546i 0.0493932 0.0855516i
\(556\) 0 0
\(557\) −1.06527 + 1.84510i −0.0451368 + 0.0781793i −0.887711 0.460401i \(-0.847706\pi\)
0.842574 + 0.538580i \(0.181039\pi\)
\(558\) 0 0
\(559\) 36.4959 1.54361
\(560\) 0 0
\(561\) 3.36445 5.82739i 0.142047 0.246033i
\(562\) 0 0
\(563\) 20.2609 0.853894 0.426947 0.904277i \(-0.359589\pi\)
0.426947 + 0.904277i \(0.359589\pi\)
\(564\) 0 0
\(565\) 6.24449 + 10.8158i 0.262708 + 0.455023i
\(566\) 0 0
\(567\) 0.244933 + 0.424237i 0.0102862 + 0.0178163i
\(568\) 0 0
\(569\) −34.7530 −1.45692 −0.728460 0.685088i \(-0.759764\pi\)
−0.728460 + 0.685088i \(0.759764\pi\)
\(570\) 0 0
\(571\) −32.0702 −1.34210 −0.671048 0.741414i \(-0.734155\pi\)
−0.671048 + 0.741414i \(0.734155\pi\)
\(572\) 0 0
\(573\) 14.0773 + 24.3826i 0.588088 + 1.01860i
\(574\) 0 0
\(575\) 4.03865 + 6.99515i 0.168423 + 0.291718i
\(576\) 0 0
\(577\) 30.2740 1.26032 0.630162 0.776464i \(-0.282988\pi\)
0.630162 + 0.776464i \(0.282988\pi\)
\(578\) 0 0
\(579\) −10.4332 + 18.0708i −0.433588 + 0.750996i
\(580\) 0 0
\(581\) 2.11250 0.0876411
\(582\) 0 0
\(583\) −1.70428 + 2.95190i −0.0705841 + 0.122255i
\(584\) 0 0
\(585\) 3.76755 6.52558i 0.155769 0.269800i
\(586\) 0 0
\(587\) 1.24805 + 2.16168i 0.0515125 + 0.0892222i 0.890632 0.454725i \(-0.150262\pi\)
−0.839119 + 0.543947i \(0.816929\pi\)
\(588\) 0 0
\(589\) 3.34139 + 10.4045i 0.137680 + 0.428708i
\(590\) 0 0
\(591\) −5.38862 9.33336i −0.221658 0.383923i
\(592\) 0 0
\(593\) 4.98196 8.62901i 0.204585 0.354351i −0.745416 0.666600i \(-0.767749\pi\)
0.950000 + 0.312249i \(0.101082\pi\)
\(594\) 0 0
\(595\) 0.785142 1.35991i 0.0321877 0.0557507i
\(596\) 0 0
\(597\) −3.48898 −0.142794
\(598\) 0 0
\(599\) 16.0351 27.7736i 0.655176 1.13480i −0.326673 0.945137i \(-0.605928\pi\)
0.981850 0.189661i \(-0.0607389\pi\)
\(600\) 0 0
\(601\) 3.68278 0.150224 0.0751119 0.997175i \(-0.476069\pi\)
0.0751119 + 0.997175i \(0.476069\pi\)
\(602\) 0 0
\(603\) 7.96481 + 13.7955i 0.324352 + 0.561794i
\(604\) 0 0
\(605\) −5.19726 9.00192i −0.211299 0.365980i
\(606\) 0 0
\(607\) 20.4850 0.831460 0.415730 0.909488i \(-0.363526\pi\)
0.415730 + 0.909488i \(0.363526\pi\)
\(608\) 0 0
\(609\) −0.0601518 −0.00243747
\(610\) 0 0
\(611\) 6.98040 + 12.0904i 0.282397 + 0.489126i
\(612\) 0 0
\(613\) −5.35587 9.27664i −0.216322 0.374680i 0.737359 0.675501i \(-0.236073\pi\)
−0.953681 + 0.300821i \(0.902739\pi\)
\(614\) 0 0
\(615\) −8.84139 −0.356519
\(616\) 0 0
\(617\) 8.86600 15.3564i 0.356932 0.618224i −0.630515 0.776177i \(-0.717156\pi\)
0.987447 + 0.157953i \(0.0504895\pi\)
\(618\) 0 0
\(619\) 13.2780 0.533689 0.266844 0.963740i \(-0.414019\pi\)
0.266844 + 0.963740i \(0.414019\pi\)
\(620\) 0 0
\(621\) 22.2409 38.5224i 0.892498 1.54585i
\(622\) 0 0
\(623\) −0.348409 + 0.603462i −0.0139587 + 0.0241772i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 2.78359 3.07034i 0.111166 0.122618i
\(628\) 0 0
\(629\) 6.73992 + 11.6739i 0.268738 + 0.465468i
\(630\) 0 0
\(631\) 2.03208 3.51966i 0.0808957 0.140115i −0.822739 0.568419i \(-0.807555\pi\)
0.903635 + 0.428304i \(0.140889\pi\)
\(632\) 0 0
\(633\) 7.87347 13.6372i 0.312942 0.542032i
\(634\) 0 0
\(635\) −13.0421 −0.517560
\(636\) 0 0
\(637\) −17.3769 + 30.0977i −0.688499 + 1.19252i
\(638\) 0 0
\(639\) −14.8312 −0.586712
\(640\) 0 0
\(641\) −2.49254 4.31720i −0.0984493 0.170519i 0.812594 0.582831i \(-0.198055\pi\)
−0.911043 + 0.412311i \(0.864722\pi\)
\(642\) 0 0
\(643\) −2.93829 5.08927i −0.115875 0.200701i 0.802254 0.596983i \(-0.203634\pi\)
−0.918129 + 0.396281i \(0.870300\pi\)
\(644\) 0 0
\(645\) −8.91869 −0.351173
\(646\) 0 0
\(647\) −16.9757 −0.667385 −0.333692 0.942682i \(-0.608295\pi\)
−0.333692 + 0.942682i \(0.608295\pi\)
\(648\) 0 0
\(649\) −1.08632 1.88157i −0.0426419 0.0738580i
\(650\) 0 0
\(651\) −0.339833 0.588608i −0.0133191 0.0230694i
\(652\) 0 0
\(653\) 24.6797 0.965790 0.482895 0.875678i \(-0.339585\pi\)
0.482895 + 0.875678i \(0.339585\pi\)
\(654\) 0 0
\(655\) −3.55469 + 6.15690i −0.138893 + 0.240570i
\(656\) 0 0
\(657\) 21.2148 0.827667
\(658\) 0 0
\(659\) 0.943308 1.63386i 0.0367461 0.0636461i −0.847067 0.531485i \(-0.821634\pi\)
0.883814 + 0.467839i \(0.154967\pi\)
\(660\) 0 0
\(661\) −22.3749 + 38.7545i −0.870284 + 1.50738i −0.00858048 + 0.999963i \(0.502731\pi\)
−0.861703 + 0.507413i \(0.830602\pi\)
\(662\) 0 0
\(663\) −21.6190 37.4452i −0.839611 1.45425i
\(664\) 0 0
\(665\) 0.649590 0.716509i 0.0251900 0.0277850i
\(666\) 0 0
\(667\) 0.896081 + 1.55206i 0.0346964 + 0.0600959i
\(668\) 0 0
\(669\) −12.6511 + 21.9124i −0.489122 + 0.847183i
\(670\) 0 0
\(671\) 4.89608 8.48026i 0.189011 0.327377i
\(672\) 0 0
\(673\) 25.4046 0.979274 0.489637 0.871926i \(-0.337129\pi\)
0.489637 + 0.871926i \(0.337129\pi\)
\(674\) 0 0
\(675\) −2.75351 + 4.76922i −0.105983 + 0.183567i
\(676\) 0 0
\(677\) −3.86946 −0.148716 −0.0743578 0.997232i \(-0.523691\pi\)
−0.0743578 + 0.997232i \(0.523691\pi\)
\(678\) 0 0
\(679\) 0.705838 + 1.22255i 0.0270876 + 0.0469170i
\(680\) 0 0
\(681\) −2.44375 4.23270i −0.0936448 0.162198i
\(682\) 0 0
\(683\) 48.5171 1.85645 0.928227 0.372015i \(-0.121333\pi\)
0.928227 + 0.372015i \(0.121333\pi\)
\(684\) 0 0
\(685\) −5.42571 −0.207306
\(686\) 0 0
\(687\) 2.16217 + 3.74499i 0.0824919 + 0.142880i
\(688\) 0 0
\(689\) 10.9512 + 18.9681i 0.417208 + 0.722626i
\(690\) 0 0
\(691\) 47.6374 1.81221 0.906105 0.423052i \(-0.139041\pi\)
0.906105 + 0.423052i \(0.139041\pi\)
\(692\) 0 0
\(693\) 0.130091 0.225325i 0.00494176 0.00855937i
\(694\) 0 0
\(695\) 3.57028 0.135429
\(696\) 0 0
\(697\) 25.6054 44.3498i 0.969873 1.67987i
\(698\) 0 0
\(699\) −12.0874 + 20.9361i −0.457189 + 0.791874i
\(700\) 0 0
\(701\) −14.2766 24.7277i −0.539218 0.933954i −0.998946 0.0458939i \(-0.985386\pi\)
0.459728 0.888060i \(-0.347947\pi\)
\(702\) 0 0
\(703\) 2.53855 + 7.90458i 0.0957434 + 0.298127i
\(704\) 0 0
\(705\) −1.70584 2.95460i −0.0642456 0.111277i
\(706\) 0 0
\(707\) 0.820334 1.42086i 0.0308518 0.0534370i
\(708\) 0 0
\(709\) −9.74137 + 16.8726i −0.365845 + 0.633662i −0.988911 0.148507i \(-0.952553\pi\)
0.623066 + 0.782169i \(0.285887\pi\)
\(710\) 0 0
\(711\) 2.38760 0.0895421
\(712\) 0 0
\(713\) −10.1250 + 17.5370i −0.379183 + 0.656765i
\(714\) 0 0
\(715\) 3.89062 0.145501
\(716\) 0 0
\(717\) −14.5245 25.1572i −0.542428 0.939513i
\(718\) 0 0
\(719\) 2.05313 + 3.55613i 0.0765689 + 0.132621i 0.901767 0.432221i \(-0.142270\pi\)
−0.825199 + 0.564843i \(0.808937\pi\)
\(720\) 0 0
\(721\) −2.70774 −0.100842
\(722\) 0 0
\(723\) 5.55002 0.206407
\(724\) 0 0
\(725\) −0.110938 0.192150i −0.00412014 0.00713629i
\(726\) 0 0
\(727\) −6.20584 10.7488i −0.230162 0.398652i 0.727694 0.685902i \(-0.240592\pi\)
−0.957856 + 0.287250i \(0.907259\pi\)
\(728\) 0 0
\(729\) 23.5139 0.870887
\(730\) 0 0
\(731\) 25.8293 44.7376i 0.955330 1.65468i
\(732\) 0 0
\(733\) −16.3985 −0.605693 −0.302847 0.953039i \(-0.597937\pi\)
−0.302847 + 0.953039i \(0.597937\pi\)
\(734\) 0 0
\(735\) 4.24649 7.35514i 0.156634 0.271298i
\(736\) 0 0
\(737\) −4.11250 + 7.12305i −0.151486 + 0.262381i
\(738\) 0 0
\(739\) −23.1018 40.0135i −0.849814 1.47192i −0.881374 0.472419i \(-0.843381\pi\)
0.0315597 0.999502i \(-0.489953\pi\)
\(740\) 0 0
\(741\) −8.14267 25.3547i −0.299128 0.931430i
\(742\) 0 0
\(743\) −12.4066 21.4888i −0.455153 0.788347i 0.543544 0.839380i \(-0.317082\pi\)
−0.998697 + 0.0510331i \(0.983749\pi\)
\(744\) 0 0
\(745\) −0.468367 + 0.811235i −0.0171596 + 0.0297214i
\(746\) 0 0
\(747\) 7.17420 12.4261i 0.262490 0.454647i
\(748\) 0 0
\(749\) 0.362446 0.0132435
\(750\) 0 0
\(751\) −5.26955 + 9.12712i −0.192289 + 0.333054i −0.946008 0.324142i \(-0.894924\pi\)
0.753720 + 0.657196i \(0.228258\pi\)
\(752\) 0 0
\(753\) −23.8303 −0.868423
\(754\) 0 0
\(755\) 0.485963 + 0.841712i 0.0176860 + 0.0306330i
\(756\) 0 0
\(757\) 3.09836 + 5.36652i 0.112612 + 0.195049i 0.916823 0.399295i \(-0.130745\pi\)
−0.804211 + 0.594344i \(0.797412\pi\)
\(758\) 0 0
\(759\) 7.67967 0.278754
\(760\) 0 0
\(761\) 35.6084 1.29080 0.645402 0.763843i \(-0.276690\pi\)
0.645402 + 0.763843i \(0.276690\pi\)
\(762\) 0 0
\(763\) 0.844949 + 1.46349i 0.0305892 + 0.0529820i
\(764\) 0 0
\(765\) −5.33281 9.23671i −0.192808 0.333954i
\(766\) 0 0
\(767\) −13.9608 −0.504095
\(768\) 0 0
\(769\) 0.0777477 0.134663i 0.00280365 0.00485607i −0.864620 0.502426i \(-0.832441\pi\)
0.867424 + 0.497570i \(0.165774\pi\)
\(770\) 0 0
\(771\) −2.15550 −0.0776283
\(772\) 0 0
\(773\) 2.54411 4.40653i 0.0915054 0.158492i −0.816639 0.577148i \(-0.804165\pi\)
0.908145 + 0.418656i \(0.137499\pi\)
\(774\) 0 0
\(775\) 1.25351 2.17114i 0.0450274 0.0779897i
\(776\) 0 0
\(777\) −0.258181 0.447183i −0.00926220 0.0160426i
\(778\) 0 0
\(779\) 21.1847 23.3671i 0.759020 0.837212i
\(780\) 0 0
\(781\) −3.82891 6.63187i −0.137009 0.237307i
\(782\) 0 0
\(783\) −0.610938 + 1.05818i −0.0218331 + 0.0378161i
\(784\) 0 0
\(785\) 1.35743 2.35114i 0.0484487 0.0839156i
\(786\) 0 0
\(787\) 22.5070 0.802289 0.401144 0.916015i \(-0.368613\pi\)
0.401144 + 0.916015i \(0.368613\pi\)
\(788\) 0 0
\(789\) 3.95389 6.84833i 0.140762 0.243807i
\(790\) 0 0
\(791\) 2.77101 0.0985257
\(792\) 0 0
\(793\) −31.4608 54.4917i −1.11721 1.93506i
\(794\) 0 0
\(795\) −2.67621 4.63532i −0.0949152 0.164398i