Properties

Label 1520.2.q.j.961.2
Level $1520$
Weight $2$
Character 1520.961
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 961.2
Root \(0.610938 - 1.05818i\) of defining polynomial
Character \(\chi\) \(=\) 1520.961
Dual form 1520.2.q.j.881.2

$q$-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 \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(401\) \(1141\) \(1217\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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 −0.634001 0.773333i \(-0.718588\pi\)
0.986726 + 0.162394i \(0.0519217\pi\)
\(4\) 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 0.970725 + 0.240192i \(0.0772105\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) −0.610938 1.05818i −0.157744 0.273220i
\(16\) 0 0
\(17\) −3.53865 + 6.12912i −0.858249 + 1.48653i 0.0153485 + 0.999882i \(0.495114\pi\)
−0.873598 + 0.486649i \(0.838219\pi\)
\(18\) 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 0.888101 + 0.459647i \(0.152024\pi\)
−0.0459843 + 0.998942i \(0.514642\pi\)
\(24\) 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 0.855541 0.517735i \(-0.173225\pi\)
−0.876142 + 0.482053i \(0.839891\pi\)
\(30\) 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 −0.432017 0.901865i \(-0.642198\pi\)
0.997047 0.0767950i \(-0.0244687\pi\)
\(42\) 0 0
\(43\) 3.64959 6.32128i 0.556557 0.963985i −0.441223 0.897397i \(-0.645455\pi\)
0.997781 0.0665881i \(-0.0212113\pi\)
\(44\) 0 0
\(45\) 1.50702 0.224653
\(46\) 0 0
\(47\) −1.39608 2.41808i −0.203639 0.352714i 0.746059 0.665880i \(-0.231944\pi\)
−0.949698 + 0.313166i \(0.898610\pi\)
\(48\) 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 0.675476 0.737382i \(-0.263938\pi\)
−0.976329 + 0.216289i \(0.930605\pi\)
\(54\) 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 −0.942478 0.334268i \(-0.891511\pi\)
0.760724 + 0.649076i \(0.224844\pi\)
\(60\) 0 0
\(61\) 6.29216 + 10.8983i 0.805629 + 1.39539i 0.915866 + 0.401484i \(0.131506\pi\)
−0.110237 + 0.993905i \(0.535161\pi\)
\(62\) 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 −0.984143 0.177375i \(-0.943239\pi\)
0.338460 0.940981i \(-0.390094\pi\)
\(68\) 0 0
\(69\) 9.86946 1.18814
\(70\) 0 0
\(71\) −4.92070 + 8.52289i −0.583979 + 1.01148i 0.411023 + 0.911625i \(0.365172\pi\)
−0.995002 + 0.0998563i \(0.968162\pi\)
\(72\) 0 0
\(73\) 7.03865 12.1913i 0.823812 1.42688i −0.0790121 0.996874i \(-0.525177\pi\)
0.902824 0.430010i \(-0.141490\pi\)
\(74\) 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 −0.818016 0.575195i \(-0.804926\pi\)
0.907142 + 0.420826i \(0.138260\pi\)
\(80\) 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 0.770719 0.637175i \(-0.219897\pi\)
−0.937169 + 0.348875i \(0.886564\pi\)
\(90\) 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 −0.658102 0.752929i \(-0.728641\pi\)
0.981106 + 0.193469i \(0.0619738\pi\)
\(98\) 0 0
\(99\) 0.586324 + 1.01554i 0.0589277 + 0.102066i
\(100\) 0 0
\(101\) 3.69726 + 6.40385i 0.367891 + 0.637206i 0.989236 0.146331i \(-0.0467465\pi\)
−0.621344 + 0.783538i \(0.713413\pi\)
\(102\) 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 −0.623978 0.781442i \(-0.714485\pi\)
0.988738 + 0.149660i \(0.0478179\pi\)
\(110\) 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 −0.995635 0.0933378i \(-0.970246\pi\)
0.416984 0.908914i \(-0.363087\pi\)
\(128\) 0 0
\(129\) −4.45935 7.72382i −0.392624 0.680044i
\(130\) 0 0
\(131\) 3.55469 6.15690i 0.310575 0.537931i −0.667912 0.744240i \(-0.732812\pi\)
0.978487 + 0.206309i \(0.0661452\pi\)
\(132\) 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 0.726556 0.687108i \(-0.241120\pi\)
−0.958331 + 0.285662i \(0.907787\pi\)
\(138\) 0 0
\(139\) 1.78514 + 3.09196i 0.151414 + 0.262256i 0.931747 0.363107i \(-0.118284\pi\)
−0.780334 + 0.625363i \(0.784951\pi\)
\(140\) 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 −0.846203 0.532861i \(-0.821117\pi\)
0.884573 + 0.466402i \(0.154450\pi\)
\(150\) 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 −0.915096 0.403237i \(-0.867885\pi\)
0.806761 + 0.590878i \(0.201218\pi\)
\(158\) 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 0.993164 0.116724i \(-0.0372393\pi\)
−0.597668 + 0.801744i \(0.703906\pi\)
\(168\) 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 −0.810902 0.585182i \(-0.801023\pi\)
0.912234 + 0.409670i \(0.134356\pi\)
\(174\) 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 0.971273 + 0.237970i \(0.0764820\pi\)
−0.279548 + 0.960132i \(0.590185\pi\)
\(182\) 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 −0.375824 0.926691i \(-0.622640\pi\)
0.990450 0.137872i \(-0.0440262\pi\)
\(194\) 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 0.810975 0.585081i \(-0.198937\pi\)
−0.912183 + 0.409784i \(0.865604\pi\)
\(200\) 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 −0.997954 0.0639367i \(-0.979634\pi\)
0.554348 + 0.832285i \(0.312968\pi\)
\(212\) 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 −0.277389 0.960758i \(-0.589469\pi\)
0.970735 0.240153i \(-0.0771978\pi\)
\(224\) 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 −0.335500 0.942040i \(-0.608905\pi\)
0.983581 0.180468i \(-0.0577614\pi\)
\(234\) 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 0.929855 0.367926i \(-0.119932\pi\)
−0.783561 + 0.621315i \(0.786599\pi\)
\(242\) 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 −0.990295 0.138982i \(-0.955617\pi\)
0.374785 0.927112i \(-0.377716\pi\)
\(252\) 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 0.837203 0.546892i \(-0.184189\pi\)
−0.892224 + 0.451594i \(0.850856\pi\)
\(258\) 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 −0.948378 0.317143i \(-0.897276\pi\)
0.748843 + 0.662748i \(0.230610\pi\)
\(264\) 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 −0.00478280 + 0.999989i \(0.501522\pi\)
−0.863624 + 0.504136i \(0.831811\pi\)
\(270\) 0 0
\(271\) −0.246491 + 0.426934i −0.0149732 + 0.0259344i −0.873415 0.486977i \(-0.838100\pi\)
0.858442 + 0.512911i \(0.171433\pi\)
\(272\) 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 0.928050 0.372455i \(-0.121484\pi\)
−0.786581 + 0.617488i \(0.788151\pi\)
\(282\) 0 0
\(283\) 8.43473 14.6094i 0.501393 0.868438i −0.498606 0.866829i \(-0.666155\pi\)
0.999999 0.00160901i \(-0.000512164\pi\)
\(284\) 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 −0.769653 0.638462i \(-0.779571\pi\)
0.937751 + 0.347308i \(0.112904\pi\)
\(308\) 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 0.937219 0.348740i \(-0.113390\pi\)
−0.770628 + 0.637286i \(0.780057\pi\)
\(314\) 0 0
\(315\) 0.334372 0.0188397
\(316\) 0 0
\(317\) 2.07930 + 3.60146i 0.116785 + 0.202278i 0.918492 0.395439i \(-0.129408\pi\)
−0.801707 + 0.597718i \(0.796074\pi\)
\(318\) 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 −0.244404 0.969673i \(-0.578592\pi\)
0.961964 0.273177i \(-0.0880743\pi\)
\(338\) 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 −0.998581 0.0532476i \(-0.983043\pi\)
0.545404 + 0.838173i \(0.316376\pi\)
\(348\) 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 −0.667228 0.744854i \(-0.732519\pi\)
0.978676 + 0.205410i \(0.0658527\pi\)
\(360\) 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 0.973540 + 0.228516i \(0.0733872\pi\)
−0.288870 + 0.957368i \(0.593279\pi\)
\(368\) 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 −0.169540 0.985523i \(-0.554228\pi\)
0.938258 0.345936i \(-0.112439\pi\)
\(384\) 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 0.820133 + 0.572173i \(0.193900\pi\)
0.0854503 + 0.996342i \(0.472767\pi\)
\(390\) 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 −0.960636 0.277809i \(-0.910392\pi\)
0.720907 + 0.693031i \(0.243725\pi\)
\(398\) 0 0
\(399\) 0.793718 + 0.875485i 0.0397356 + 0.0438291i
\(400\) 0 0
\(401\) −15.4418 + 26.7459i −0.771124 + 1.33563i 0.165823 + 0.986156i \(0.446972\pi\)
−0.936947 + 0.349471i \(0.886361\pi\)
\(402\) 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 −0.931738 0.363130i \(-0.881708\pi\)
0.151389 0.988474i \(-0.451625\pi\)
\(410\) 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 −0.506850 0.862035i \(-0.669190\pi\)
0.999969 + 0.00792731i \(0.00252337\pi\)
\(422\) 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 0.694367 0.719621i \(-0.255684\pi\)
−0.970394 + 0.241529i \(0.922351\pi\)
\(432\) 0 0
\(433\) −12.9734 22.4706i −0.623461 1.07987i −0.988836 0.149006i \(-0.952393\pi\)
0.365375 0.930860i \(-0.380941\pi\)
\(434\) 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 −0.388156 0.921594i \(-0.626888\pi\)
0.992202 0.124644i \(-0.0397789\pi\)
\(440\) 0 0
\(441\) −5.23747 9.07157i −0.249403 0.431979i
\(442\) 0 0
\(443\) 10.0125 + 17.3421i 0.475707 + 0.823949i 0.999613 0.0278272i \(-0.00885883\pi\)
−0.523905 + 0.851776i \(0.675525\pi\)
\(444\) 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 −0.758754 0.651377i \(-0.774192\pi\)
0.943486 + 0.331412i \(0.107525\pi\)
\(462\) 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 −0.924050 0.382270i \(-0.875142\pi\)
0.130969 0.991386i \(-0.458191\pi\)
\(480\) 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 0.263339 + 0.964703i \(0.415176\pi\)
−0.967127 + 0.254293i \(0.918157\pi\)
\(492\) 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 −0.626032 0.779797i \(-0.715322\pi\)
0.988340 + 0.152262i \(0.0486556\pi\)
\(500\) 0 0
\(501\) 12.4899 0.558006
\(502\) 0 0
\(503\) 8.61094 + 14.9146i 0.383943 + 0.665008i 0.991622 0.129174i \(-0.0412327\pi\)
−0.607679 + 0.794183i \(0.707899\pi\)
\(504\) 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 0.912207 + 0.409729i \(0.134377\pi\)
−0.101268 + 0.994859i \(0.532290\pi\)
\(510\) 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 −0.932605 0.360898i \(-0.882470\pi\)
0.153756 0.988109i \(-0.450863\pi\)
\(524\) 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 0.829908 0.557900i \(-0.188393\pi\)
−0.898110 + 0.439772i \(0.855059\pi\)
\(542\) 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 −0.991775 0.127991i \(-0.959147\pi\)
0.385044 0.922898i \(-0.374186\pi\)
\(548\) 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 0.842574 0.538580i \(-0.181039\pi\)
−0.887711 + 0.460401i \(0.847706\pi\)
\(558\) 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 −0.839119 0.543947i \(-0.816929\pi\)
0.890632 + 0.454725i \(0.150262\pi\)
\(588\) 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 0.950000 0.312249i \(-0.101082\pi\)
−0.745416 + 0.666600i \(0.767749\pi\)
\(594\) 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 0.981850 + 0.189661i \(0.0607389\pi\)
−0.326673 + 0.945137i \(0.605928\pi\)
\(600\) 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 −0.953681 0.300821i \(-0.902739\pi\)
0.737359 + 0.675501i \(0.236073\pi\)
\(614\) 0 0
\(615\) −8.84139 −0.356519
\(616\) 0 0
\(617\) 8.86600 + 15.3564i 0.356932 + 0.618224i 0.987447 0.157953i \(-0.0504895\pi\)
−0.630515 + 0.776177i \(0.717156\pi\)
\(618\) 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 0.903635 0.428304i \(-0.140889\pi\)
−0.822739 + 0.568419i \(0.807555\pi\)
\(632\) 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 −0.911043 0.412311i \(-0.864722\pi\)
0.812594 + 0.582831i \(0.198055\pi\)
\(642\) 0 0
\(643\) −2.93829 + 5.08927i −0.115875 + 0.200701i −0.918129 0.396281i \(-0.870300\pi\)
0.802254 + 0.596983i \(0.203634\pi\)
\(644\) 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 0.883814 0.467839i \(-0.154967\pi\)
−0.847067 + 0.531485i \(0.821634\pi\)
\(660\) 0 0
\(661\) −22.3749 38.7545i −0.870284 1.50738i −0.861703 0.507413i \(-0.830602\pi\)
−0.00858048 0.999963i \(-0.502731\pi\)
\(662\) 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 0.459728 + 0.888060i \(0.347947\pi\)
−0.998946 + 0.0458939i \(0.985386\pi\)
\(702\) 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 0.623066 0.782169i \(-0.285887\pi\)
−0.988911 + 0.148507i \(0.952553\pi\)
\(710\) 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 −0.825199 0.564843i \(-0.808937\pi\)
0.901767 + 0.432221i \(0.142270\pi\)
\(720\) 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 −0.957856 0.287250i \(-0.907259\pi\)
0.727694 + 0.685902i \(0.240592\pi\)
\(728\) 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 0.0315597 + 0.999502i \(0.489953\pi\)
−0.881374 + 0.472419i \(0.843381\pi\)
\(740\) 0 0
\(741\) −8.14267 + 25.3547i −0.299128 + 0.931430i
\(742\) 0 0
\(743\) −12.4066 + 21.4888i −0.455153 + 0.788347i −0.998697 0.0510331i \(-0.983749\pi\)
0.543544 + 0.839380i \(0.317082\pi\)
\(744\) 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 0.753720 0.657196i \(-0.228258\pi\)
−0.946008 + 0.324142i \(0.894924\pi\)
\(752\) 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 −0.804211 0.594344i \(-0.797412\pi\)
0.916823 + 0.399295i \(0.130745\pi\)
\(758\) 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 0.867424 0.497570i \(-0.165774\pi\)
−0.864620 + 0.502426i \(0.832441\pi\)
\(770\) 0 0
\(771\) −2.15550 −0.0776283
\(772\) 0 0
\(773\) 2.54411 + 4.40653i 0.0915054 + 0.158492i 0.908145 0.418656i \(-0.137499\pi\)
−0.816639 + 0.577148i \(0.804165\pi\)
\(774\) 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