Properties

Label 1440.2.q.p.481.5
Level $1440$
Weight $2$
Character 1440.481
Analytic conductor $11.498$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.4984578911\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.8528759163648.1
Defining polynomial: \(x^{10} - 2 x^{9} + x^{8} + 9 x^{6} - 36 x^{5} + 27 x^{4} + 27 x^{2} - 162 x + 243\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 481.5
Root \(0.756905 - 1.55791i\) of defining polynomial
Character \(\chi\) \(=\) 1440.481
Dual form 1440.2.q.p.961.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.72765 - 0.123458i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-1.53662 - 2.66151i) q^{7} +(2.96952 - 0.426584i) q^{9} +O(q^{10})\) \(q+(1.72765 - 0.123458i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-1.53662 - 2.66151i) q^{7} +(2.96952 - 0.426584i) q^{9} +(-1.97074 - 3.41342i) q^{11} +(-0.396269 + 0.686358i) q^{13} +(-0.756905 + 1.55791i) q^{15} +4.70838 q^{17} +1.32879 q^{19} +(-2.98333 - 4.40844i) q^{21} +(0.536624 - 0.929459i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(5.07761 - 1.10360i) q^{27} +(-4.39940 - 7.61999i) q^{29} +(-0.855415 + 1.48162i) q^{31} +(-3.82616 - 5.65388i) q^{33} +3.07325 q^{35} +8.11804 q^{37} +(-0.599876 + 1.23471i) q^{39} +(-0.103731 + 0.179667i) q^{41} +(-5.35034 - 9.26705i) q^{43} +(-1.11533 + 2.78497i) q^{45} +(-4.62269 - 8.00673i) q^{47} +(-1.22242 + 2.11730i) q^{49} +(8.13441 - 0.581288i) q^{51} -12.7935 q^{53} +3.94148 q^{55} +(2.29567 - 0.164050i) q^{57} +(5.97265 - 10.3449i) q^{59} +(3.98069 + 6.89477i) q^{61} +(-5.69839 - 7.24790i) q^{63} +(-0.396269 - 0.686358i) q^{65} +(-0.00644531 + 0.0111636i) q^{67} +(0.812346 - 1.67203i) q^{69} +9.44240 q^{71} +7.14123 q^{73} +(-0.970741 - 1.43446i) q^{75} +(-6.05657 + 10.4903i) q^{77} +(3.60423 + 6.24272i) q^{79} +(8.63605 - 2.53349i) q^{81} +(5.70274 + 9.87744i) q^{83} +(-2.35419 + 4.07758i) q^{85} +(-8.54136 - 12.6215i) q^{87} -1.67993 q^{89} +2.43566 q^{91} +(-1.29494 + 2.66533i) q^{93} +(-0.664393 + 1.15076i) q^{95} +(7.12404 + 12.3392i) q^{97} +(-7.30826 - 9.29553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + q^{3} - 5 q^{5} - q^{9} + O(q^{10}) \) \( 10 q + q^{3} - 5 q^{5} - q^{9} - 9 q^{11} - 4 q^{13} - 2 q^{15} + 6 q^{17} + 14 q^{19} + 12 q^{21} - 10 q^{23} - 5 q^{25} - 2 q^{27} - 2 q^{29} - 8 q^{31} - 27 q^{33} + 16 q^{37} + 26 q^{39} - q^{41} - q^{43} - q^{45} - 10 q^{47} - q^{49} - 3 q^{51} - 20 q^{53} + 18 q^{55} - 19 q^{57} - 13 q^{59} - 14 q^{61} - 30 q^{63} - 4 q^{65} - 15 q^{67} + 8 q^{69} + 32 q^{71} - 14 q^{73} + q^{75} + 12 q^{77} - 18 q^{79} + 35 q^{81} + 8 q^{83} - 3 q^{85} - 32 q^{87} + 28 q^{89} - 36 q^{91} + 16 q^{93} - 7 q^{95} + 17 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(641\) \(901\) \(991\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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
\(3\) 1.72765 0.123458i 0.997456 0.0712786i
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −1.53662 2.66151i −0.580789 1.00596i −0.995386 0.0959511i \(-0.969411\pi\)
0.414597 0.910005i \(-0.363923\pi\)
\(8\) 0 0
\(9\) 2.96952 0.426584i 0.989839 0.142195i
\(10\) 0 0
\(11\) −1.97074 3.41342i −0.594201 1.02919i −0.993659 0.112434i \(-0.964135\pi\)
0.399459 0.916751i \(-0.369198\pi\)
\(12\) 0 0
\(13\) −0.396269 + 0.686358i −0.109905 + 0.190361i −0.915732 0.401790i \(-0.868388\pi\)
0.805826 + 0.592152i \(0.201721\pi\)
\(14\) 0 0
\(15\) −0.756905 + 1.55791i −0.195432 + 0.402252i
\(16\) 0 0
\(17\) 4.70838 1.14195 0.570975 0.820967i \(-0.306565\pi\)
0.570975 + 0.820967i \(0.306565\pi\)
\(18\) 0 0
\(19\) 1.32879 0.304845 0.152422 0.988315i \(-0.451293\pi\)
0.152422 + 0.988315i \(0.451293\pi\)
\(20\) 0 0
\(21\) −2.98333 4.40844i −0.651015 0.962000i
\(22\) 0 0
\(23\) 0.536624 0.929459i 0.111894 0.193806i −0.804640 0.593763i \(-0.797642\pi\)
0.916534 + 0.399957i \(0.130975\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 5.07761 1.10360i 0.977186 0.212387i
\(28\) 0 0
\(29\) −4.39940 7.61999i −0.816949 1.41500i −0.907920 0.419143i \(-0.862331\pi\)
0.0909717 0.995853i \(-0.471003\pi\)
\(30\) 0 0
\(31\) −0.855415 + 1.48162i −0.153637 + 0.266107i −0.932562 0.361010i \(-0.882432\pi\)
0.778925 + 0.627117i \(0.215765\pi\)
\(32\) 0 0
\(33\) −3.82616 5.65388i −0.666048 0.984214i
\(34\) 0 0
\(35\) 3.07325 0.519474
\(36\) 0 0
\(37\) 8.11804 1.33460 0.667299 0.744790i \(-0.267450\pi\)
0.667299 + 0.744790i \(0.267450\pi\)
\(38\) 0 0
\(39\) −0.599876 + 1.23471i −0.0960570 + 0.197711i
\(40\) 0 0
\(41\) −0.103731 + 0.179667i −0.0162001 + 0.0280593i −0.874012 0.485905i \(-0.838490\pi\)
0.857812 + 0.513964i \(0.171824\pi\)
\(42\) 0 0
\(43\) −5.35034 9.26705i −0.815918 1.41321i −0.908667 0.417523i \(-0.862898\pi\)
0.0927481 0.995690i \(-0.470435\pi\)
\(44\) 0 0
\(45\) −1.11533 + 2.78497i −0.166263 + 0.415159i
\(46\) 0 0
\(47\) −4.62269 8.00673i −0.674289 1.16790i −0.976676 0.214717i \(-0.931117\pi\)
0.302388 0.953185i \(-0.402216\pi\)
\(48\) 0 0
\(49\) −1.22242 + 2.11730i −0.174632 + 0.302472i
\(50\) 0 0
\(51\) 8.13441 0.581288i 1.13905 0.0813966i
\(52\) 0 0
\(53\) −12.7935 −1.75733 −0.878664 0.477440i \(-0.841565\pi\)
−0.878664 + 0.477440i \(0.841565\pi\)
\(54\) 0 0
\(55\) 3.94148 0.531469
\(56\) 0 0
\(57\) 2.29567 0.164050i 0.304069 0.0217289i
\(58\) 0 0
\(59\) 5.97265 10.3449i 0.777573 1.34680i −0.155764 0.987794i \(-0.549784\pi\)
0.933337 0.359001i \(-0.116883\pi\)
\(60\) 0 0
\(61\) 3.98069 + 6.89477i 0.509676 + 0.882784i 0.999937 + 0.0112088i \(0.00356795\pi\)
−0.490261 + 0.871575i \(0.663099\pi\)
\(62\) 0 0
\(63\) −5.69839 7.24790i −0.717929 0.913149i
\(64\) 0 0
\(65\) −0.396269 0.686358i −0.0491511 0.0851322i
\(66\) 0 0
\(67\) −0.00644531 + 0.0111636i −0.000787420 + 0.00136385i −0.866419 0.499318i \(-0.833584\pi\)
0.865631 + 0.500682i \(0.166917\pi\)
\(68\) 0 0
\(69\) 0.812346 1.67203i 0.0977950 0.201288i
\(70\) 0 0
\(71\) 9.44240 1.12061 0.560303 0.828287i \(-0.310685\pi\)
0.560303 + 0.828287i \(0.310685\pi\)
\(72\) 0 0
\(73\) 7.14123 0.835818 0.417909 0.908489i \(-0.362763\pi\)
0.417909 + 0.908489i \(0.362763\pi\)
\(74\) 0 0
\(75\) −0.970741 1.43446i −0.112091 0.165637i
\(76\) 0 0
\(77\) −6.05657 + 10.4903i −0.690211 + 1.19548i
\(78\) 0 0
\(79\) 3.60423 + 6.24272i 0.405508 + 0.702360i 0.994380 0.105866i \(-0.0337613\pi\)
−0.588872 + 0.808226i \(0.700428\pi\)
\(80\) 0 0
\(81\) 8.63605 2.53349i 0.959561 0.281499i
\(82\) 0 0
\(83\) 5.70274 + 9.87744i 0.625957 + 1.08419i 0.988355 + 0.152166i \(0.0486250\pi\)
−0.362397 + 0.932024i \(0.618042\pi\)
\(84\) 0 0
\(85\) −2.35419 + 4.07758i −0.255348 + 0.442275i
\(86\) 0 0
\(87\) −8.54136 12.6215i −0.915730 1.35317i
\(88\) 0 0
\(89\) −1.67993 −0.178072 −0.0890361 0.996028i \(-0.528379\pi\)
−0.0890361 + 0.996028i \(0.528379\pi\)
\(90\) 0 0
\(91\) 2.43566 0.255327
\(92\) 0 0
\(93\) −1.29494 + 2.66533i −0.134279 + 0.276381i
\(94\) 0 0
\(95\) −0.664393 + 1.15076i −0.0681653 + 0.118066i
\(96\) 0 0
\(97\) 7.12404 + 12.3392i 0.723337 + 1.25286i 0.959655 + 0.281180i \(0.0907259\pi\)
−0.236318 + 0.971676i \(0.575941\pi\)
\(98\) 0 0
\(99\) −7.30826 9.29553i −0.734507 0.934236i
\(100\) 0 0
\(101\) 1.07570 + 1.86316i 0.107036 + 0.185391i 0.914568 0.404432i \(-0.132531\pi\)
−0.807532 + 0.589823i \(0.799197\pi\)
\(102\) 0 0
\(103\) 7.51572 13.0176i 0.740546 1.28266i −0.211701 0.977334i \(-0.567900\pi\)
0.952247 0.305328i \(-0.0987663\pi\)
\(104\) 0 0
\(105\) 5.30948 0.379417i 0.518152 0.0370273i
\(106\) 0 0
\(107\) −1.91659 −0.185284 −0.0926420 0.995699i \(-0.529531\pi\)
−0.0926420 + 0.995699i \(0.529531\pi\)
\(108\) 0 0
\(109\) −4.82726 −0.462367 −0.231184 0.972910i \(-0.574260\pi\)
−0.231184 + 0.972910i \(0.574260\pi\)
\(110\) 0 0
\(111\) 14.0251 1.00224i 1.33120 0.0951283i
\(112\) 0 0
\(113\) −6.48291 + 11.2287i −0.609861 + 1.05631i 0.381402 + 0.924409i \(0.375441\pi\)
−0.991263 + 0.131901i \(0.957892\pi\)
\(114\) 0 0
\(115\) 0.536624 + 0.929459i 0.0500404 + 0.0866725i
\(116\) 0 0
\(117\) −0.883938 + 2.20719i −0.0817201 + 0.204055i
\(118\) 0 0
\(119\) −7.23501 12.5314i −0.663232 1.14875i
\(120\) 0 0
\(121\) −2.26764 + 3.92766i −0.206149 + 0.357060i
\(122\) 0 0
\(123\) −0.157029 + 0.323208i −0.0141588 + 0.0291427i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 0.0801256 0.00711000 0.00355500 0.999994i \(-0.498868\pi\)
0.00355500 + 0.999994i \(0.498868\pi\)
\(128\) 0 0
\(129\) −10.3876 15.3496i −0.914575 1.35146i
\(130\) 0 0
\(131\) −10.3126 + 17.8620i −0.901017 + 1.56061i −0.0748415 + 0.997195i \(0.523845\pi\)
−0.826176 + 0.563412i \(0.809488\pi\)
\(132\) 0 0
\(133\) −2.04184 3.53658i −0.177050 0.306660i
\(134\) 0 0
\(135\) −1.58306 + 4.94913i −0.136248 + 0.425954i
\(136\) 0 0
\(137\) −0.907864 1.57247i −0.0775640 0.134345i 0.824634 0.565666i \(-0.191381\pi\)
−0.902198 + 0.431321i \(0.858048\pi\)
\(138\) 0 0
\(139\) 1.46129 2.53103i 0.123945 0.214679i −0.797375 0.603484i \(-0.793779\pi\)
0.921320 + 0.388805i \(0.127112\pi\)
\(140\) 0 0
\(141\) −8.97486 13.2621i −0.755820 1.11687i
\(142\) 0 0
\(143\) 3.12377 0.261223
\(144\) 0 0
\(145\) 8.79881 0.730701
\(146\) 0 0
\(147\) −1.85052 + 3.80886i −0.152628 + 0.314150i
\(148\) 0 0
\(149\) −6.05639 + 10.4900i −0.496159 + 0.859372i −0.999990 0.00442972i \(-0.998590\pi\)
0.503831 + 0.863802i \(0.331923\pi\)
\(150\) 0 0
\(151\) 6.71875 + 11.6372i 0.546764 + 0.947023i 0.998494 + 0.0548684i \(0.0174739\pi\)
−0.451729 + 0.892155i \(0.649193\pi\)
\(152\) 0 0
\(153\) 13.9816 2.00852i 1.13035 0.162379i
\(154\) 0 0
\(155\) −0.855415 1.48162i −0.0687086 0.119007i
\(156\) 0 0
\(157\) −10.9538 + 18.9725i −0.874205 + 1.51417i −0.0165983 + 0.999862i \(0.505284\pi\)
−0.857607 + 0.514306i \(0.828050\pi\)
\(158\) 0 0
\(159\) −22.1027 + 1.57947i −1.75286 + 0.125260i
\(160\) 0 0
\(161\) −3.29835 −0.259947
\(162\) 0 0
\(163\) −7.91256 −0.619760 −0.309880 0.950776i \(-0.600289\pi\)
−0.309880 + 0.950776i \(0.600289\pi\)
\(164\) 0 0
\(165\) 6.80948 0.486608i 0.530117 0.0378824i
\(166\) 0 0
\(167\) −0.972828 + 1.68499i −0.0752797 + 0.130388i −0.901208 0.433387i \(-0.857318\pi\)
0.825928 + 0.563775i \(0.190652\pi\)
\(168\) 0 0
\(169\) 6.18594 + 10.7144i 0.475842 + 0.824182i
\(170\) 0 0
\(171\) 3.94585 0.566839i 0.301747 0.0433472i
\(172\) 0 0
\(173\) −2.00429 3.47153i −0.152383 0.263935i 0.779720 0.626128i \(-0.215361\pi\)
−0.932103 + 0.362193i \(0.882028\pi\)
\(174\) 0 0
\(175\) −1.53662 + 2.66151i −0.116158 + 0.201191i
\(176\) 0 0
\(177\) 9.04145 18.6097i 0.679597 1.39879i
\(178\) 0 0
\(179\) −5.68505 −0.424920 −0.212460 0.977170i \(-0.568148\pi\)
−0.212460 + 0.977170i \(0.568148\pi\)
\(180\) 0 0
\(181\) 5.08812 0.378197 0.189098 0.981958i \(-0.439443\pi\)
0.189098 + 0.981958i \(0.439443\pi\)
\(182\) 0 0
\(183\) 7.72844 + 11.4203i 0.571303 + 0.844210i
\(184\) 0 0
\(185\) −4.05902 + 7.03043i −0.298425 + 0.516888i
\(186\) 0 0
\(187\) −9.27900 16.0717i −0.678547 1.17528i
\(188\) 0 0
\(189\) −10.7396 11.8183i −0.781191 0.859654i
\(190\) 0 0
\(191\) 5.14642 + 8.91387i 0.372382 + 0.644985i 0.989931 0.141547i \(-0.0452078\pi\)
−0.617549 + 0.786532i \(0.711874\pi\)
\(192\) 0 0
\(193\) 12.2648 21.2432i 0.882838 1.52912i 0.0346653 0.999399i \(-0.488963\pi\)
0.848172 0.529721i \(-0.177703\pi\)
\(194\) 0 0
\(195\) −0.769349 1.13686i −0.0550942 0.0814123i
\(196\) 0 0
\(197\) −17.9124 −1.27621 −0.638103 0.769951i \(-0.720281\pi\)
−0.638103 + 0.769951i \(0.720281\pi\)
\(198\) 0 0
\(199\) 10.1152 0.717050 0.358525 0.933520i \(-0.383280\pi\)
0.358525 + 0.933520i \(0.383280\pi\)
\(200\) 0 0
\(201\) −0.00975697 + 0.0200825i −0.000688204 + 0.00141651i
\(202\) 0 0
\(203\) −13.5205 + 23.4181i −0.948950 + 1.64363i
\(204\) 0 0
\(205\) −0.103731 0.179667i −0.00724489 0.0125485i
\(206\) 0 0
\(207\) 1.19702 2.98896i 0.0831987 0.207747i
\(208\) 0 0
\(209\) −2.61869 4.53571i −0.181139 0.313742i
\(210\) 0 0
\(211\) −2.90302 + 5.02819i −0.199852 + 0.346155i −0.948480 0.316836i \(-0.897380\pi\)
0.748628 + 0.662990i \(0.230713\pi\)
\(212\) 0 0
\(213\) 16.3131 1.16574i 1.11776 0.0798753i
\(214\) 0 0
\(215\) 10.7007 0.729780
\(216\) 0 0
\(217\) 5.25780 0.356923
\(218\) 0 0
\(219\) 12.3375 0.881643i 0.833692 0.0595759i
\(220\) 0 0
\(221\) −1.86579 + 3.23163i −0.125506 + 0.217383i
\(222\) 0 0
\(223\) 4.06325 + 7.03776i 0.272095 + 0.471283i 0.969398 0.245494i \(-0.0789500\pi\)
−0.697303 + 0.716777i \(0.745617\pi\)
\(224\) 0 0
\(225\) −1.85419 2.35838i −0.123613 0.157226i
\(226\) 0 0
\(227\) −6.68438 11.5777i −0.443658 0.768438i 0.554300 0.832317i \(-0.312986\pi\)
−0.997958 + 0.0638789i \(0.979653\pi\)
\(228\) 0 0
\(229\) 12.3128 21.3264i 0.813653 1.40929i −0.0966389 0.995320i \(-0.530809\pi\)
0.910291 0.413968i \(-0.135857\pi\)
\(230\) 0 0
\(231\) −9.16850 + 18.8712i −0.603243 + 1.24164i
\(232\) 0 0
\(233\) −21.3231 −1.39692 −0.698461 0.715648i \(-0.746131\pi\)
−0.698461 + 0.715648i \(0.746131\pi\)
\(234\) 0 0
\(235\) 9.24538 0.603102
\(236\) 0 0
\(237\) 6.99755 + 10.3402i 0.454540 + 0.671670i
\(238\) 0 0
\(239\) −0.676476 + 1.17169i −0.0437576 + 0.0757903i −0.887075 0.461626i \(-0.847266\pi\)
0.843317 + 0.537416i \(0.180600\pi\)
\(240\) 0 0
\(241\) 6.94106 + 12.0223i 0.447113 + 0.774423i 0.998197 0.0600272i \(-0.0191187\pi\)
−0.551083 + 0.834450i \(0.685785\pi\)
\(242\) 0 0
\(243\) 14.6073 5.44317i 0.937056 0.349180i
\(244\) 0 0
\(245\) −1.22242 2.11730i −0.0780978 0.135269i
\(246\) 0 0
\(247\) −0.526557 + 0.912023i −0.0335040 + 0.0580306i
\(248\) 0 0
\(249\) 11.0718 + 16.3607i 0.701645 + 1.03682i
\(250\) 0 0
\(251\) 8.48547 0.535598 0.267799 0.963475i \(-0.413704\pi\)
0.267799 + 0.963475i \(0.413704\pi\)
\(252\) 0 0
\(253\) −4.23018 −0.265949
\(254\) 0 0
\(255\) −3.56380 + 7.33525i −0.223174 + 0.459351i
\(256\) 0 0
\(257\) 10.2765 17.7995i 0.641033 1.11030i −0.344169 0.938908i \(-0.611839\pi\)
0.985202 0.171395i \(-0.0548274\pi\)
\(258\) 0 0
\(259\) −12.4744 21.6063i −0.775120 1.34255i
\(260\) 0 0
\(261\) −16.3147 20.7510i −1.00985 1.28445i
\(262\) 0 0
\(263\) −8.90021 15.4156i −0.548811 0.950568i −0.998356 0.0573104i \(-0.981748\pi\)
0.449546 0.893257i \(-0.351586\pi\)
\(264\) 0 0
\(265\) 6.39677 11.0795i 0.392951 0.680610i
\(266\) 0 0
\(267\) −2.90232 + 0.207401i −0.177619 + 0.0126927i
\(268\) 0 0
\(269\) −3.05081 −0.186011 −0.0930055 0.995666i \(-0.529647\pi\)
−0.0930055 + 0.995666i \(0.529647\pi\)
\(270\) 0 0
\(271\) 6.75047 0.410062 0.205031 0.978755i \(-0.434270\pi\)
0.205031 + 0.978755i \(0.434270\pi\)
\(272\) 0 0
\(273\) 4.20796 0.300703i 0.254678 0.0181994i
\(274\) 0 0
\(275\) −1.97074 + 3.41342i −0.118840 + 0.205837i
\(276\) 0 0
\(277\) −1.55047 2.68550i −0.0931590 0.161356i 0.815680 0.578504i \(-0.196363\pi\)
−0.908839 + 0.417148i \(0.863030\pi\)
\(278\) 0 0
\(279\) −1.90813 + 4.76461i −0.114237 + 0.285250i
\(280\) 0 0
\(281\) −4.28629 7.42408i −0.255699 0.442883i 0.709386 0.704820i \(-0.248972\pi\)
−0.965085 + 0.261937i \(0.915639\pi\)
\(282\) 0 0
\(283\) −10.1865 + 17.6435i −0.605524 + 1.04880i 0.386445 + 0.922313i \(0.373703\pi\)
−0.991968 + 0.126485i \(0.959630\pi\)
\(284\) 0 0
\(285\) −1.00576 + 2.07013i −0.0595764 + 0.122624i
\(286\) 0 0
\(287\) 0.637582 0.0376353
\(288\) 0 0
\(289\) 5.16885 0.304050
\(290\) 0 0
\(291\) 13.8312 + 20.4382i 0.810799 + 1.19811i
\(292\) 0 0
\(293\) 8.57795 14.8574i 0.501129 0.867981i −0.498870 0.866677i \(-0.666251\pi\)
0.999999 0.00130436i \(-0.000415189\pi\)
\(294\) 0 0
\(295\) 5.97265 + 10.3449i 0.347741 + 0.602305i
\(296\) 0 0
\(297\) −13.7737 15.1571i −0.799230 0.879505i
\(298\) 0 0
\(299\) 0.425295 + 0.736632i 0.0245954 + 0.0426005i
\(300\) 0 0
\(301\) −16.4429 + 28.4799i −0.947753 + 1.64156i
\(302\) 0 0
\(303\) 2.08844 + 3.08608i 0.119978 + 0.177290i
\(304\) 0 0
\(305\) −7.96139 −0.455868
\(306\) 0 0
\(307\) −34.9119 −1.99253 −0.996263 0.0863739i \(-0.972472\pi\)
−0.996263 + 0.0863739i \(0.972472\pi\)
\(308\) 0 0
\(309\) 11.3774 23.4177i 0.647236 1.33219i
\(310\) 0 0
\(311\) 5.25737 9.10603i 0.298118 0.516355i −0.677587 0.735442i \(-0.736974\pi\)
0.975705 + 0.219087i \(0.0703078\pi\)
\(312\) 0 0
\(313\) 13.7184 + 23.7610i 0.775412 + 1.34305i 0.934562 + 0.355799i \(0.115791\pi\)
−0.159150 + 0.987254i \(0.550875\pi\)
\(314\) 0 0
\(315\) 9.12606 1.31100i 0.514195 0.0738663i
\(316\) 0 0
\(317\) 13.0212 + 22.5535i 0.731346 + 1.26673i 0.956308 + 0.292361i \(0.0944408\pi\)
−0.224962 + 0.974367i \(0.572226\pi\)
\(318\) 0 0
\(319\) −17.3402 + 30.0340i −0.970863 + 1.68158i
\(320\) 0 0
\(321\) −3.31119 + 0.236619i −0.184813 + 0.0132068i
\(322\) 0 0
\(323\) 6.25643 0.348117
\(324\) 0 0
\(325\) 0.792538 0.0439621
\(326\) 0 0
\(327\) −8.33979 + 0.595964i −0.461191 + 0.0329569i
\(328\) 0 0
\(329\) −14.2067 + 24.6067i −0.783239 + 1.35661i
\(330\) 0 0
\(331\) 14.1007 + 24.4232i 0.775046 + 1.34242i 0.934769 + 0.355257i \(0.115607\pi\)
−0.159723 + 0.987162i \(0.551060\pi\)
\(332\) 0 0
\(333\) 24.1067 3.46303i 1.32104 0.189773i
\(334\) 0 0
\(335\) −0.00644531 0.0111636i −0.000352145 0.000609933i
\(336\) 0 0
\(337\) −0.0283554 + 0.0491129i −0.00154461 + 0.00267535i −0.866797 0.498662i \(-0.833825\pi\)
0.865252 + 0.501337i \(0.167158\pi\)
\(338\) 0 0
\(339\) −9.81389 + 20.1996i −0.533017 + 1.09709i
\(340\) 0 0
\(341\) 6.74320 0.365165
\(342\) 0 0
\(343\) −13.9991 −0.755881
\(344\) 0 0
\(345\) 1.04184 + 1.53953i 0.0560910 + 0.0828853i
\(346\) 0 0
\(347\) −11.4717 + 19.8695i −0.615831 + 1.06665i 0.374407 + 0.927264i \(0.377846\pi\)
−0.990238 + 0.139386i \(0.955487\pi\)
\(348\) 0 0
\(349\) 13.8610 + 24.0079i 0.741960 + 1.28511i 0.951602 + 0.307334i \(0.0994370\pi\)
−0.209641 + 0.977778i \(0.567230\pi\)
\(350\) 0 0
\(351\) −1.25464 + 3.92238i −0.0669675 + 0.209361i
\(352\) 0 0
\(353\) 4.04406 + 7.00452i 0.215244 + 0.372813i 0.953348 0.301874i \(-0.0976121\pi\)
−0.738104 + 0.674687i \(0.764279\pi\)
\(354\) 0 0
\(355\) −4.72120 + 8.17736i −0.250575 + 0.434009i
\(356\) 0 0
\(357\) −14.0466 20.7566i −0.743427 1.09856i
\(358\) 0 0
\(359\) 9.65559 0.509603 0.254801 0.966993i \(-0.417990\pi\)
0.254801 + 0.966993i \(0.417990\pi\)
\(360\) 0 0
\(361\) −17.2343 −0.907070
\(362\) 0 0
\(363\) −3.43277 + 7.06556i −0.180174 + 0.370846i
\(364\) 0 0
\(365\) −3.57062 + 6.18449i −0.186895 + 0.323711i
\(366\) 0 0
\(367\) 9.51291 + 16.4768i 0.496570 + 0.860084i 0.999992 0.00395655i \(-0.00125941\pi\)
−0.503423 + 0.864040i \(0.667926\pi\)
\(368\) 0 0
\(369\) −0.231388 + 0.577775i −0.0120456 + 0.0300778i
\(370\) 0 0
\(371\) 19.6589 + 34.0501i 1.02064 + 1.76780i
\(372\) 0 0
\(373\) 7.88569 13.6584i 0.408306 0.707206i −0.586394 0.810026i \(-0.699453\pi\)
0.994700 + 0.102820i \(0.0327864\pi\)
\(374\) 0 0
\(375\) 1.72765 0.123458i 0.0892152 0.00637535i
\(376\) 0 0
\(377\) 6.97339 0.359148
\(378\) 0 0
\(379\) −0.168851 −0.00867331 −0.00433665 0.999991i \(-0.501380\pi\)
−0.00433665 + 0.999991i \(0.501380\pi\)
\(380\) 0 0
\(381\) 0.138429 0.00989216i 0.00709191 0.000506791i
\(382\) 0 0
\(383\) 5.83924 10.1139i 0.298371 0.516794i −0.677392 0.735622i \(-0.736890\pi\)
0.975764 + 0.218828i \(0.0702233\pi\)
\(384\) 0 0
\(385\) −6.05657 10.4903i −0.308672 0.534635i
\(386\) 0 0
\(387\) −19.8411 25.2363i −1.00858 1.28283i
\(388\) 0 0
\(389\) −1.32640 2.29740i −0.0672513 0.116483i 0.830439 0.557109i \(-0.188090\pi\)
−0.897690 + 0.440627i \(0.854756\pi\)
\(390\) 0 0
\(391\) 2.52663 4.37625i 0.127777 0.221316i
\(392\) 0 0
\(393\) −15.6113 + 32.1323i −0.787488 + 1.62086i
\(394\) 0 0
\(395\) −7.20847 −0.362697
\(396\) 0 0
\(397\) 24.2138 1.21525 0.607627 0.794223i \(-0.292122\pi\)
0.607627 + 0.794223i \(0.292122\pi\)
\(398\) 0 0
\(399\) −3.96420 5.85787i −0.198458 0.293260i
\(400\) 0 0
\(401\) 15.1748 26.2836i 0.757796 1.31254i −0.186177 0.982516i \(-0.559610\pi\)
0.943972 0.330025i \(-0.107057\pi\)
\(402\) 0 0
\(403\) −0.677949 1.17424i −0.0337710 0.0584931i
\(404\) 0 0
\(405\) −2.12396 + 8.74579i −0.105540 + 0.434582i
\(406\) 0 0
\(407\) −15.9986 27.7103i −0.793019 1.37355i
\(408\) 0 0
\(409\) −10.9849 + 19.0265i −0.543170 + 0.940798i 0.455550 + 0.890210i \(0.349443\pi\)
−0.998720 + 0.0505874i \(0.983891\pi\)
\(410\) 0 0
\(411\) −1.76260 2.60458i −0.0869426 0.128474i
\(412\) 0 0
\(413\) −36.7109 −1.80642
\(414\) 0 0
\(415\) −11.4055 −0.559873
\(416\) 0 0
\(417\) 2.21211 4.55312i 0.108328 0.222967i
\(418\) 0 0
\(419\) −11.4500 + 19.8319i −0.559367 + 0.968852i 0.438182 + 0.898886i \(0.355622\pi\)
−0.997549 + 0.0699660i \(0.977711\pi\)
\(420\) 0 0
\(421\) 5.53297 + 9.58338i 0.269660 + 0.467065i 0.968774 0.247945i \(-0.0797552\pi\)
−0.699114 + 0.715010i \(0.746422\pi\)
\(422\) 0 0
\(423\) −17.1427 21.8042i −0.833506 1.06015i
\(424\) 0 0
\(425\) −2.35419 4.07758i −0.114195 0.197792i
\(426\) 0 0
\(427\) 12.2337 21.1893i 0.592028 1.02542i
\(428\) 0 0
\(429\) 5.39677 0.385655i 0.260559 0.0186196i
\(430\) 0 0
\(431\) 23.0586 1.11069 0.555346 0.831619i \(-0.312586\pi\)
0.555346 + 0.831619i \(0.312586\pi\)
\(432\) 0 0
\(433\) −12.3970 −0.595763 −0.297881 0.954603i \(-0.596280\pi\)
−0.297881 + 0.954603i \(0.596280\pi\)
\(434\) 0 0
\(435\) 15.2012 1.08628i 0.728842 0.0520833i
\(436\) 0 0
\(437\) 0.713058 1.23505i 0.0341102 0.0590806i
\(438\) 0 0
\(439\) 0.116062 + 0.201026i 0.00553934 + 0.00959443i 0.868782 0.495195i \(-0.164903\pi\)
−0.863242 + 0.504790i \(0.831570\pi\)
\(440\) 0 0
\(441\) −2.72680 + 6.80883i −0.129848 + 0.324230i
\(442\) 0 0
\(443\) −18.7924 32.5493i −0.892852 1.54646i −0.836441 0.548057i \(-0.815368\pi\)
−0.0564112 0.998408i \(-0.517966\pi\)
\(444\) 0 0
\(445\) 0.839965 1.45486i 0.0398182 0.0689671i
\(446\) 0 0
\(447\) −9.16822 + 18.8707i −0.433642 + 0.892552i
\(448\) 0 0
\(449\) 15.5247 0.732658 0.366329 0.930485i \(-0.380614\pi\)
0.366329 + 0.930485i \(0.380614\pi\)
\(450\) 0 0
\(451\) 0.817708 0.0385044
\(452\) 0 0
\(453\) 13.0443 + 19.2755i 0.612876 + 0.905642i
\(454\) 0 0
\(455\) −1.21783 + 2.10935i −0.0570929 + 0.0988877i
\(456\) 0 0
\(457\) −16.9907 29.4287i −0.794791 1.37662i −0.922972 0.384868i \(-0.874247\pi\)
0.128181 0.991751i \(-0.459086\pi\)
\(458\) 0 0
\(459\) 23.9073 5.19615i 1.11590 0.242536i
\(460\) 0 0
\(461\) 10.5502 + 18.2735i 0.491371 + 0.851080i 0.999951 0.00993538i \(-0.00316258\pi\)
−0.508580 + 0.861015i \(0.669829\pi\)
\(462\) 0 0
\(463\) −4.62933 + 8.01824i −0.215143 + 0.372639i −0.953317 0.301972i \(-0.902355\pi\)
0.738174 + 0.674611i \(0.235689\pi\)
\(464\) 0 0
\(465\) −1.66077 2.45411i −0.0770164 0.113807i
\(466\) 0 0
\(467\) 32.8904 1.52199 0.760993 0.648761i \(-0.224712\pi\)
0.760993 + 0.648761i \(0.224712\pi\)
\(468\) 0 0
\(469\) 0.0396161 0.00182930
\(470\) 0 0
\(471\) −16.5819 + 34.1300i −0.764054 + 1.57263i
\(472\) 0 0
\(473\) −21.0882 + 36.5259i −0.969639 + 1.67946i
\(474\) 0 0
\(475\) −0.664393 1.15076i −0.0304845 0.0528006i
\(476\) 0 0
\(477\) −37.9906 + 5.45752i −1.73947 + 0.249883i
\(478\) 0 0
\(479\) −8.33678 14.4397i −0.380917 0.659768i 0.610276 0.792189i \(-0.291058\pi\)
−0.991194 + 0.132421i \(0.957725\pi\)
\(480\) 0 0
\(481\) −3.21693 + 5.57188i −0.146679 + 0.254056i
\(482\) 0 0
\(483\) −5.69839 + 0.407209i −0.259286 + 0.0185286i
\(484\) 0 0
\(485\) −14.2481 −0.646972
\(486\) 0 0
\(487\) 17.0258 0.771513 0.385757 0.922601i \(-0.373940\pi\)
0.385757 + 0.922601i \(0.373940\pi\)
\(488\) 0 0
\(489\) −13.6701 + 0.976870i −0.618183 + 0.0441756i
\(490\) 0 0
\(491\) −19.1292 + 33.1328i −0.863290 + 1.49526i 0.00544576 + 0.999985i \(0.498267\pi\)
−0.868735 + 0.495276i \(0.835067\pi\)
\(492\) 0 0
\(493\) −20.7141 35.8778i −0.932914 1.61586i
\(494\) 0 0
\(495\) 11.7043 1.68137i 0.526069 0.0755720i
\(496\) 0 0
\(497\) −14.5094 25.1310i −0.650836 1.12728i
\(498\) 0 0
\(499\) 4.77992 8.27906i 0.213978 0.370622i −0.738978 0.673730i \(-0.764691\pi\)
0.952956 + 0.303108i \(0.0980244\pi\)
\(500\) 0 0
\(501\) −1.47268 + 3.03116i −0.0657943 + 0.135422i
\(502\) 0 0
\(503\) −11.7155 −0.522370 −0.261185 0.965289i \(-0.584113\pi\)
−0.261185 + 0.965289i \(0.584113\pi\)
\(504\) 0 0
\(505\) −2.15139 −0.0957357
\(506\) 0 0
\(507\) 12.0099 + 17.7469i 0.533378 + 0.788168i
\(508\) 0 0
\(509\) 17.0776 29.5793i 0.756953 1.31108i −0.187445 0.982275i \(-0.560021\pi\)
0.944398 0.328806i \(-0.106646\pi\)
\(510\) 0 0
\(511\) −10.9734 19.0065i −0.485434 0.840796i
\(512\) 0 0
\(513\) 6.74705 1.46644i 0.297890 0.0647451i
\(514\) 0 0
\(515\) 7.51572 + 13.0176i 0.331182 + 0.573624i
\(516\) 0 0
\(517\) −18.2202 + 31.5584i −0.801325 + 1.38794i
\(518\) 0 0
\(519\) −3.89128 5.75012i −0.170808 0.252402i
\(520\) 0 0
\(521\) 14.5007 0.635288 0.317644 0.948210i \(-0.397108\pi\)
0.317644 + 0.948210i \(0.397108\pi\)
\(522\) 0 0
\(523\) 11.4900 0.502424 0.251212 0.967932i \(-0.419171\pi\)
0.251212 + 0.967932i \(0.419171\pi\)
\(524\) 0 0
\(525\) −2.32616 + 4.78785i −0.101522 + 0.208959i
\(526\) 0 0
\(527\) −4.02762 + 6.97604i −0.175446 + 0.303881i
\(528\) 0 0
\(529\) 10.9241 + 18.9210i 0.474960 + 0.822654i
\(530\) 0 0
\(531\) 13.3229 33.2673i 0.578165 1.44368i
\(532\) 0 0
\(533\) −0.0822108 0.142393i −0.00356094 0.00616774i
\(534\) 0 0
\(535\) 0.958297 1.65982i 0.0414308 0.0717602i
\(536\) 0 0
\(537\) −9.82175 + 0.701866i −0.423840 + 0.0302877i
\(538\) 0 0
\(539\) 9.63632 0.415066
\(540\) 0 0
\(541\) 38.1707 1.64109 0.820543 0.571585i \(-0.193671\pi\)
0.820543 + 0.571585i \(0.193671\pi\)
\(542\) 0 0
\(543\) 8.79046 0.628170i 0.377235 0.0269573i
\(544\) 0 0
\(545\) 2.41363 4.18053i 0.103388 0.179074i
\(546\) 0 0
\(547\) −13.5359 23.4449i −0.578754 1.00243i −0.995623 0.0934646i \(-0.970206\pi\)
0.416869 0.908967i \(-0.363128\pi\)
\(548\) 0 0
\(549\) 14.7619 + 18.7760i 0.630024 + 0.801341i
\(550\) 0 0
\(551\) −5.84587 10.1253i −0.249042 0.431354i
\(552\) 0 0
\(553\) 11.0767 19.1854i 0.471029 0.815847i
\(554\) 0 0
\(555\) −6.14459 + 12.6472i −0.260823 + 0.536844i
\(556\) 0 0
\(557\) 20.3337 0.861568 0.430784 0.902455i \(-0.358237\pi\)
0.430784 + 0.902455i \(0.358237\pi\)
\(558\) 0 0
\(559\) 8.48069 0.358695
\(560\) 0 0
\(561\) −18.0150 26.6206i −0.760594 1.12392i
\(562\) 0 0
\(563\) 0.0968695 0.167783i 0.00408256 0.00707121i −0.863977 0.503531i \(-0.832034\pi\)
0.868059 + 0.496460i \(0.165367\pi\)
\(564\) 0 0
\(565\) −6.48291 11.2287i −0.272738 0.472396i
\(566\) 0 0
\(567\) −20.0133 19.0919i −0.840479 0.801785i
\(568\) 0 0
\(569\) 8.59136 + 14.8807i 0.360168 + 0.623830i 0.987988 0.154529i \(-0.0493859\pi\)
−0.627820 + 0.778359i \(0.716053\pi\)
\(570\) 0 0
\(571\) 12.8366 22.2336i 0.537195 0.930449i −0.461859 0.886953i \(-0.652817\pi\)
0.999054 0.0434953i \(-0.0138494\pi\)
\(572\) 0 0
\(573\) 9.99168 + 14.7646i 0.417409 + 0.616801i
\(574\) 0 0
\(575\) −1.07325 −0.0447575
\(576\) 0 0
\(577\) −17.3942 −0.724132 −0.362066 0.932153i \(-0.617928\pi\)
−0.362066 + 0.932153i \(0.617928\pi\)
\(578\) 0 0
\(579\) 18.5665 38.2149i 0.771599 1.58816i
\(580\) 0 0
\(581\) 17.5259 30.3558i 0.727099 1.25937i
\(582\) 0 0
\(583\) 25.2128 + 43.6698i 1.04421 + 1.80862i
\(584\) 0 0
\(585\) −1.46952 1.86911i −0.0607570 0.0772781i
\(586\) 0 0
\(587\) −6.75930 11.7074i −0.278986 0.483218i 0.692147 0.721757i \(-0.256665\pi\)
−0.971133 + 0.238539i \(0.923332\pi\)
\(588\) 0 0
\(589\) −1.13666 + 1.96876i −0.0468354 + 0.0811213i
\(590\) 0 0
\(591\) −30.9463 + 2.21143i −1.27296 + 0.0909662i
\(592\) 0 0
\(593\) −37.8636 −1.55487 −0.777437 0.628961i \(-0.783480\pi\)
−0.777437 + 0.628961i \(0.783480\pi\)
\(594\) 0 0
\(595\) 14.4700 0.593213
\(596\) 0 0
\(597\) 17.4755 1.24881i 0.715226 0.0511103i
\(598\) 0 0
\(599\) −22.1071 + 38.2907i −0.903273 + 1.56451i −0.0800542 + 0.996791i \(0.525509\pi\)
−0.823219 + 0.567724i \(0.807824\pi\)
\(600\) 0 0
\(601\) 18.3066 + 31.7080i 0.746742 + 1.29340i 0.949376 + 0.314141i \(0.101717\pi\)
−0.202634 + 0.979255i \(0.564950\pi\)
\(602\) 0 0
\(603\) −0.0143772 + 0.0359000i −0.000585487 + 0.00146196i
\(604\) 0 0
\(605\) −2.26764 3.92766i −0.0921925 0.159682i
\(606\) 0 0
\(607\) 2.31634 4.01202i 0.0940174 0.162843i −0.815181 0.579207i \(-0.803362\pi\)
0.909198 + 0.416364i \(0.136696\pi\)
\(608\) 0 0
\(609\) −20.4674 + 42.1274i −0.829380 + 1.70709i
\(610\) 0 0
\(611\) 7.32731 0.296431
\(612\) 0 0
\(613\) 43.3957 1.75273 0.876367 0.481644i \(-0.159960\pi\)
0.876367 + 0.481644i \(0.159960\pi\)
\(614\) 0 0
\(615\) −0.201392 0.297595i −0.00812091 0.0120002i
\(616\) 0 0
\(617\) 10.5390 18.2540i 0.424283 0.734879i −0.572070 0.820205i \(-0.693860\pi\)
0.996353 + 0.0853252i \(0.0271929\pi\)
\(618\) 0 0
\(619\) −19.2694 33.3755i −0.774502 1.34148i −0.935074 0.354452i \(-0.884667\pi\)
0.160572 0.987024i \(-0.448666\pi\)
\(620\) 0 0
\(621\) 1.69901 5.31164i 0.0681791 0.213149i
\(622\) 0 0
\(623\) 2.58142 + 4.47115i 0.103422 + 0.179133i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −5.08414 7.51280i −0.203041 0.300032i
\(628\) 0 0
\(629\) 38.2228 1.52404
\(630\) 0 0
\(631\) 17.6062 0.700891 0.350446 0.936583i \(-0.386030\pi\)
0.350446 + 0.936583i \(0.386030\pi\)
\(632\) 0 0
\(633\) −4.39463 + 9.04532i −0.174671 + 0.359519i
\(634\) 0 0
\(635\) −0.0400628 + 0.0693908i −0.00158984 + 0.00275369i
\(636\) 0 0
\(637\) −0.968818 1.67804i −0.0383859 0.0664864i
\(638\) 0 0
\(639\) 28.0394 4.02797i 1.10922 0.159344i
\(640\) 0 0
\(641\) 24.6556 + 42.7047i 0.973836 + 1.68673i 0.683722 + 0.729742i \(0.260360\pi\)
0.290114 + 0.956992i \(0.406307\pi\)
\(642\) 0 0
\(643\) 19.7262 34.1668i 0.777926 1.34741i −0.155209 0.987882i \(-0.549605\pi\)
0.933135 0.359526i \(-0.117061\pi\)
\(644\) 0 0
\(645\) 18.4870 1.32108i 0.727923 0.0520177i
\(646\) 0 0
\(647\) −27.4491 −1.07914 −0.539568 0.841942i \(-0.681412\pi\)
−0.539568 + 0.841942i \(0.681412\pi\)
\(648\) 0 0
\(649\) −47.0822 −1.84814
\(650\) 0 0
\(651\) 9.08362 0.649119i 0.356015 0.0254410i
\(652\) 0 0
\(653\) −9.35165 + 16.1975i −0.365958 + 0.633858i −0.988929 0.148387i \(-0.952592\pi\)
0.622971 + 0.782245i \(0.285925\pi\)
\(654\) 0 0
\(655\) −10.3126 17.8620i −0.402947 0.697925i
\(656\) 0 0
\(657\) 21.2060 3.04633i 0.827325 0.118849i
\(658\) 0 0
\(659\) 2.00345 + 3.47008i 0.0780435 + 0.135175i 0.902406 0.430887i \(-0.141799\pi\)
−0.824362 + 0.566063i \(0.808466\pi\)
\(660\) 0 0
\(661\) 8.56654 14.8377i 0.333200 0.577119i −0.649938 0.759988i \(-0.725205\pi\)
0.983137 + 0.182869i \(0.0585383\pi\)
\(662\) 0 0
\(663\) −2.82444 + 5.81346i −0.109692 + 0.225776i
\(664\) 0 0
\(665\) 4.08369 0.158359
\(666\) 0 0
\(667\) −9.44329 −0.365646
\(668\) 0 0
\(669\) 7.88873 + 11.6571i 0.304996 + 0.450690i
\(670\) 0 0
\(671\) 15.6898 27.1756i 0.605699 1.04910i
\(672\) 0 0
\(673\) −24.1171 41.7720i −0.929646 1.61019i −0.783914 0.620870i \(-0.786779\pi\)
−0.145732 0.989324i \(-0.546554\pi\)
\(674\) 0 0
\(675\) −3.49455 3.84554i −0.134505 0.148015i
\(676\) 0 0
\(677\) −13.2099 22.8803i −0.507699 0.879361i −0.999960 0.00891350i \(-0.997163\pi\)
0.492261 0.870448i \(-0.336171\pi\)
\(678\) 0 0
\(679\) 21.8939 37.9214i 0.840212 1.45529i
\(680\) 0 0
\(681\) −12.9776 19.1769i −0.497303 0.734861i
\(682\) 0 0
\(683\) 22.7063 0.868832 0.434416 0.900712i \(-0.356955\pi\)
0.434416 + 0.900712i \(0.356955\pi\)
\(684\) 0 0
\(685\) 1.81573 0.0693754
\(686\) 0 0
\(687\) 18.6392 38.3646i 0.711131 1.46370i
\(688\) 0 0
\(689\) 5.06968 8.78095i 0.193140 0.334528i
\(690\) 0 0
\(691\) 24.4050 + 42.2707i 0.928411 + 1.60805i 0.785982 + 0.618249i \(0.212158\pi\)
0.142429 + 0.989805i \(0.454509\pi\)
\(692\) 0 0
\(693\) −13.5101 + 33.7347i −0.513206 + 1.28148i
\(694\) 0 0
\(695\) 1.46129 + 2.53103i 0.0554299 + 0.0960073i
\(696\) 0 0
\(697\) −0.488405 + 0.845943i −0.0184997 + 0.0320424i
\(698\) 0 0
\(699\) −36.8387 + 2.63251i −1.39337 + 0.0995706i
\(700\) 0 0
\(701\) 52.3028 1.97545 0.987724 0.156208i \(-0.0499271\pi\)
0.987724 + 0.156208i \(0.0499271\pi\)
\(702\) 0 0
\(703\) 10.7871 0.406845
\(704\) 0 0
\(705\) 15.9727 1.14142i 0.601568 0.0429883i
\(706\) 0 0
\(707\) 3.30588 5.72595i 0.124330 0.215347i
\(708\) 0 0
\(709\) −23.0672 39.9535i −0.866307 1.50049i −0.865744 0.500487i \(-0.833154\pi\)
−0.000562604 1.00000i \(-0.500179\pi\)
\(710\) 0 0
\(711\) 13.3659 + 17.0003i 0.501259 + 0.637562i
\(712\) 0 0
\(713\) 0.918072 + 1.59015i 0.0343821 + 0.0595515i
\(714\) 0 0
\(715\) −1.56189 + 2.70527i −0.0584112 + 0.101171i
\(716\) 0 0
\(717\) −1.02406 + 2.10778i −0.0382440 + 0.0787165i
\(718\) 0 0
\(719\) 21.8099 0.813371 0.406685 0.913568i \(-0.366685\pi\)
0.406685 + 0.913568i \(0.366685\pi\)
\(720\) 0 0
\(721\) −46.1953 −1.72040
\(722\) 0 0
\(723\) 13.4759 + 19.9133i 0.501176 + 0.740584i
\(724\) 0 0
\(725\) −4.39940 + 7.61999i −0.163390 + 0.282999i
\(726\) 0 0
\(727\) −0.596047 1.03238i −0.0221061 0.0382890i 0.854761 0.519022i \(-0.173704\pi\)
−0.876867 + 0.480733i \(0.840371\pi\)
\(728\) 0 0
\(729\) 24.5641 11.2073i 0.909783 0.415083i
\(730\) 0 0
\(731\) −25.1914 43.6328i −0.931738 1.61382i
\(732\) 0 0
\(733\) 12.8883 22.3231i 0.476039 0.824523i −0.523585 0.851974i \(-0.675406\pi\)
0.999623 + 0.0274508i \(0.00873895\pi\)
\(734\) 0 0
\(735\) −2.37331 3.50703i −0.0875410 0.129359i
\(736\) 0 0
\(737\) 0.0508081 0.00187154
\(738\) 0 0
\(739\) −45.7839 −1.68419 −0.842094 0.539331i \(-0.818677\pi\)
−0.842094 + 0.539331i \(0.818677\pi\)
\(740\) 0 0
\(741\) −0.797107 + 1.64066i −0.0292824 + 0.0602712i
\(742\) 0 0
\(743\) 11.0670 19.1686i 0.406009 0.703228i −0.588430 0.808549i \(-0.700254\pi\)
0.994438 + 0.105321i \(0.0335869\pi\)
\(744\) 0 0
\(745\) −6.05639 10.4900i −0.221889 0.384323i
\(746\) 0 0
\(747\) 21.1479 + 26.8985i 0.773763 + 0.984166i
\(748\) 0 0
\(749\) 2.94508 + 5.10103i 0.107611 + 0.186388i
\(750\) 0 0
\(751\) −7.62749 + 13.2112i −0.278331 + 0.482084i −0.970970 0.239201i \(-0.923115\pi\)
0.692639 + 0.721284i \(0.256448\pi\)
\(752\) 0 0
\(753\) 14.6599 1.04760i 0.534236 0.0381767i
\(754\) 0 0
\(755\) −13.4375 −0.489041
\(756\) 0 0
\(757\) −28.3178 −1.02923 −0.514614 0.857422i \(-0.672065\pi\)
−0.514614 + 0.857422i \(0.672065\pi\)
\(758\) 0 0
\(759\) −7.30826 + 0.522251i −0.265273 + 0.0189565i
\(760\) 0 0
\(761\) 9.79106 16.9586i 0.354925 0.614749i −0.632180 0.774822i \(-0.717840\pi\)
0.987105 + 0.160073i \(0.0511729\pi\)
\(762\) 0 0
\(763\) 7.41768 + 12.8478i 0.268538 + 0.465121i
\(764\) 0 0
\(765\) −5.25138 + 13.1127i −0.189864 + 0.474090i
\(766\) 0 0
\(767\) 4.73355 + 8.19875i 0.170919 + 0.296040i
\(768\) 0 0
\(769\) 12.0853 20.9324i 0.435809 0.754843i −0.561553 0.827441i \(-0.689796\pi\)
0.997361 + 0.0725983i \(0.0231291\pi\)
\(770\) 0 0
\(771\) 15.5567 32.0200i 0.560262 1.15317i
\(772\) 0 0
\(773\) 33.7841 1.21513 0.607565 0.794270i \(-0.292147\pi\)
0.607565 + 0.794270i \(0.292147\pi\)
\(774\) 0 0
\(775\) 1.71083 0.0614548
\(776\) 0 0
\(777\) −24.2188 35.7879i −0.868843 1.28388i
\(778\) 0 0
\(779\) −0.137836 + 0.238740i −0.00493850 + 0.00855374i
\(780\) 0 0
\(781\) −18.6085 32.2309i −0.665865 1.15331i
\(782\) 0 0
\(783\) −30.7478 33.8361i −1.09884 1.20920i
\(784\) 0 0
\(785\) −10.9538 18.9725i −0.390956 0.677156i
\(786\) 0 0
\(787\) 1.92949 3.34198i 0.0687791 0.119129i −0.829585 0.558380i \(-0.811423\pi\)
0.898364 + 0.439252i \(0.144756\pi\)
\(788\) 0 0
\(789\) −17.2796 25.5339i −0.615170 0.909031i
\(790\) 0 0
\(791\) 39.8472 1.41680
\(792\) 0 0
\(793\) −6.30970 −0.224064
\(794\) 0 0
\(795\) 9.68349 19.9312i 0.343438 0.706888i
\(796\)