Properties

Label 1456.2.r.p.625.2
Level $1456$
Weight $2$
Character 1456.625
Analytic conductor $11.626$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.6262185343\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - x^{9} + 8 x^{8} + 7 x^{7} + 41 x^{6} + 18 x^{5} + 58 x^{4} + 28 x^{3} + 64 x^{2} + 16 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 625.2
Root \(-0.862625 + 1.49411i\) of defining polynomial
Character \(\chi\) \(=\) 1456.625
Dual form 1456.2.r.p.417.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.673208 - 1.16603i) q^{3} +(-1.09358 + 1.89414i) q^{5} +(2.19729 - 1.47375i) q^{7} +(0.593582 - 1.02811i) q^{9} +O(q^{10})\) \(q+(-0.673208 - 1.16603i) q^{3} +(-1.09358 + 1.89414i) q^{5} +(2.19729 - 1.47375i) q^{7} +(0.593582 - 1.02811i) q^{9} +(-0.524077 - 0.907729i) q^{11} +1.00000 q^{13} +2.94483 q^{15} +(2.64562 + 4.58236i) q^{17} +(0.378453 - 0.655500i) q^{19} +(-3.19767 - 1.56996i) q^{21} +(0.326792 - 0.566020i) q^{23} +(0.108157 + 0.187333i) q^{25} -5.63766 q^{27} -3.10408 q^{29} +(0.513956 + 0.890198i) q^{31} +(-0.705626 + 1.22218i) q^{33} +(0.388575 + 5.77363i) q^{35} +(5.44661 - 9.43381i) q^{37} +(-0.673208 - 1.16603i) q^{39} +7.32040 q^{41} -0.887771 q^{43} +(1.29826 + 2.24865i) q^{45} +(1.16875 - 2.02434i) q^{47} +(2.65613 - 6.47650i) q^{49} +(3.56211 - 6.16976i) q^{51} +(-2.44407 - 4.23325i) q^{53} +2.29249 q^{55} -1.01911 q^{57} +(-0.524077 - 0.907729i) q^{59} +(6.24989 - 10.8251i) q^{61} +(-0.210913 - 3.13385i) q^{63} +(-1.09358 + 1.89414i) q^{65} +(2.23944 + 3.87883i) q^{67} -0.879996 q^{69} +6.60274 q^{71} +(4.14174 + 7.17370i) q^{73} +(0.145624 - 0.252229i) q^{75} +(-2.48931 - 1.22218i) q^{77} +(1.07007 - 1.85342i) q^{79} +(2.01457 + 3.48935i) q^{81} +6.66558 q^{83} -11.5728 q^{85} +(2.08969 + 3.61946i) q^{87} +(2.88388 - 4.99503i) q^{89} +(2.19729 - 1.47375i) q^{91} +(0.691998 - 1.19858i) q^{93} +(0.827739 + 1.43369i) q^{95} -2.88777 q^{97} -1.24433 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{5} - q^{7} - 3 q^{9} + O(q^{10}) \) \( 10 q - 2 q^{5} - q^{7} - 3 q^{9} + 11 q^{11} + 10 q^{13} + 5 q^{17} + 9 q^{19} + 2 q^{21} + 10 q^{23} - 9 q^{25} - 6 q^{29} - 6 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} + 28 q^{41} - 4 q^{43} + 32 q^{45} + q^{47} - 11 q^{49} - 8 q^{51} - 17 q^{53} - 32 q^{57} + 11 q^{59} + 11 q^{61} - 5 q^{63} - 2 q^{65} + 13 q^{67} + 36 q^{69} - 30 q^{71} - 20 q^{75} - 46 q^{77} + 2 q^{79} + 19 q^{81} - 12 q^{83} - 44 q^{85} - 8 q^{87} + 4 q^{89} - q^{91} - 18 q^{93} - 12 q^{95} - 24 q^{97} - 22 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times\).

\(n\) \(561\) \(911\) \(1093\) \(1249\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −0.673208 1.16603i −0.388677 0.673208i 0.603595 0.797291i \(-0.293734\pi\)
−0.992272 + 0.124083i \(0.960401\pi\)
\(4\) 0 0
\(5\) −1.09358 + 1.89414i −0.489065 + 0.847085i −0.999921 0.0125813i \(-0.995995\pi\)
0.510856 + 0.859666i \(0.329328\pi\)
\(6\) 0 0
\(7\) 2.19729 1.47375i 0.830496 0.557025i
\(8\) 0 0
\(9\) 0.593582 1.02811i 0.197861 0.342705i
\(10\) 0 0
\(11\) −0.524077 0.907729i −0.158015 0.273691i 0.776138 0.630564i \(-0.217176\pi\)
−0.934153 + 0.356873i \(0.883843\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 2.94483 0.760352
\(16\) 0 0
\(17\) 2.64562 + 4.58236i 0.641658 + 1.11138i 0.985063 + 0.172197i \(0.0550865\pi\)
−0.343404 + 0.939188i \(0.611580\pi\)
\(18\) 0 0
\(19\) 0.378453 0.655500i 0.0868231 0.150382i −0.819344 0.573303i \(-0.805662\pi\)
0.906167 + 0.422921i \(0.138995\pi\)
\(20\) 0 0
\(21\) −3.19767 1.56996i −0.697788 0.342594i
\(22\) 0 0
\(23\) 0.326792 0.566020i 0.0681408 0.118023i −0.829942 0.557850i \(-0.811627\pi\)
0.898083 + 0.439826i \(0.144960\pi\)
\(24\) 0 0
\(25\) 0.108157 + 0.187333i 0.0216314 + 0.0374667i
\(26\) 0 0
\(27\) −5.63766 −1.08497
\(28\) 0 0
\(29\) −3.10408 −0.576414 −0.288207 0.957568i \(-0.593059\pi\)
−0.288207 + 0.957568i \(0.593059\pi\)
\(30\) 0 0
\(31\) 0.513956 + 0.890198i 0.0923092 + 0.159884i 0.908482 0.417923i \(-0.137242\pi\)
−0.816173 + 0.577807i \(0.803909\pi\)
\(32\) 0 0
\(33\) −0.705626 + 1.22218i −0.122834 + 0.212754i
\(34\) 0 0
\(35\) 0.388575 + 5.77363i 0.0656811 + 0.975922i
\(36\) 0 0
\(37\) 5.44661 9.43381i 0.895418 1.55091i 0.0621309 0.998068i \(-0.480210\pi\)
0.833287 0.552841i \(-0.186456\pi\)
\(38\) 0 0
\(39\) −0.673208 1.16603i −0.107800 0.186714i
\(40\) 0 0
\(41\) 7.32040 1.14325 0.571627 0.820514i \(-0.306312\pi\)
0.571627 + 0.820514i \(0.306312\pi\)
\(42\) 0 0
\(43\) −0.887771 −0.135384 −0.0676919 0.997706i \(-0.521563\pi\)
−0.0676919 + 0.997706i \(0.521563\pi\)
\(44\) 0 0
\(45\) 1.29826 + 2.24865i 0.193533 + 0.335210i
\(46\) 0 0
\(47\) 1.16875 2.02434i 0.170480 0.295281i −0.768108 0.640321i \(-0.778801\pi\)
0.938588 + 0.345040i \(0.112135\pi\)
\(48\) 0 0
\(49\) 2.65613 6.47650i 0.379447 0.925214i
\(50\) 0 0
\(51\) 3.56211 6.16976i 0.498795 0.863939i
\(52\) 0 0
\(53\) −2.44407 4.23325i −0.335719 0.581482i 0.647904 0.761722i \(-0.275646\pi\)
−0.983623 + 0.180240i \(0.942313\pi\)
\(54\) 0 0
\(55\) 2.29249 0.309119
\(56\) 0 0
\(57\) −1.01911 −0.134985
\(58\) 0 0
\(59\) −0.524077 0.907729i −0.0682291 0.118176i 0.829893 0.557923i \(-0.188402\pi\)
−0.898122 + 0.439747i \(0.855068\pi\)
\(60\) 0 0
\(61\) 6.24989 10.8251i 0.800217 1.38602i −0.119256 0.992864i \(-0.538051\pi\)
0.919473 0.393153i \(-0.128616\pi\)
\(62\) 0 0
\(63\) −0.210913 3.13385i −0.0265726 0.394828i
\(64\) 0 0
\(65\) −1.09358 + 1.89414i −0.135642 + 0.234939i
\(66\) 0 0
\(67\) 2.23944 + 3.87883i 0.273592 + 0.473875i 0.969779 0.243986i \(-0.0784550\pi\)
−0.696187 + 0.717860i \(0.745122\pi\)
\(68\) 0 0
\(69\) −0.879996 −0.105939
\(70\) 0 0
\(71\) 6.60274 0.783601 0.391801 0.920050i \(-0.371852\pi\)
0.391801 + 0.920050i \(0.371852\pi\)
\(72\) 0 0
\(73\) 4.14174 + 7.17370i 0.484754 + 0.839618i 0.999847 0.0175164i \(-0.00557593\pi\)
−0.515093 + 0.857134i \(0.672243\pi\)
\(74\) 0 0
\(75\) 0.145624 0.252229i 0.0168152 0.0291249i
\(76\) 0 0
\(77\) −2.48931 1.22218i −0.283683 0.139280i
\(78\) 0 0
\(79\) 1.07007 1.85342i 0.120392 0.208526i −0.799530 0.600626i \(-0.794918\pi\)
0.919922 + 0.392100i \(0.128251\pi\)
\(80\) 0 0
\(81\) 2.01457 + 3.48935i 0.223842 + 0.387705i
\(82\) 0 0
\(83\) 6.66558 0.731642 0.365821 0.930685i \(-0.380788\pi\)
0.365821 + 0.930685i \(0.380788\pi\)
\(84\) 0 0
\(85\) −11.5728 −1.25525
\(86\) 0 0
\(87\) 2.08969 + 3.61946i 0.224039 + 0.388047i
\(88\) 0 0
\(89\) 2.88388 4.99503i 0.305691 0.529472i −0.671724 0.740802i \(-0.734446\pi\)
0.977415 + 0.211329i \(0.0677792\pi\)
\(90\) 0 0
\(91\) 2.19729 1.47375i 0.230338 0.154491i
\(92\) 0 0
\(93\) 0.691998 1.19858i 0.0717569 0.124287i
\(94\) 0 0
\(95\) 0.827739 + 1.43369i 0.0849242 + 0.147093i
\(96\) 0 0
\(97\) −2.88777 −0.293209 −0.146604 0.989195i \(-0.546834\pi\)
−0.146604 + 0.989195i \(0.546834\pi\)
\(98\) 0 0
\(99\) −1.24433 −0.125060
\(100\) 0 0
\(101\) 5.62716 + 9.74653i 0.559924 + 0.969816i 0.997502 + 0.0706359i \(0.0225028\pi\)
−0.437579 + 0.899180i \(0.644164\pi\)
\(102\) 0 0
\(103\) 10.1167 17.5226i 0.996828 1.72656i 0.429487 0.903073i \(-0.358694\pi\)
0.567341 0.823483i \(-0.307972\pi\)
\(104\) 0 0
\(105\) 6.47064 4.33994i 0.631470 0.423535i
\(106\) 0 0
\(107\) 4.52758 7.84201i 0.437698 0.758115i −0.559813 0.828619i \(-0.689127\pi\)
0.997512 + 0.0705034i \(0.0224606\pi\)
\(108\) 0 0
\(109\) −7.55070 13.0782i −0.723226 1.25266i −0.959700 0.281026i \(-0.909325\pi\)
0.236474 0.971638i \(-0.424008\pi\)
\(110\) 0 0
\(111\) −14.6668 −1.39211
\(112\) 0 0
\(113\) 3.10408 0.292008 0.146004 0.989284i \(-0.453359\pi\)
0.146004 + 0.989284i \(0.453359\pi\)
\(114\) 0 0
\(115\) 0.714748 + 1.23798i 0.0666506 + 0.115442i
\(116\) 0 0
\(117\) 0.593582 1.02811i 0.0548767 0.0950492i
\(118\) 0 0
\(119\) 12.5664 + 6.16976i 1.15196 + 0.565581i
\(120\) 0 0
\(121\) 4.95069 8.57484i 0.450062 0.779531i
\(122\) 0 0
\(123\) −4.92815 8.53581i −0.444356 0.769648i
\(124\) 0 0
\(125\) −11.4089 −1.02045
\(126\) 0 0
\(127\) −8.78914 −0.779910 −0.389955 0.920834i \(-0.627509\pi\)
−0.389955 + 0.920834i \(0.627509\pi\)
\(128\) 0 0
\(129\) 0.597654 + 1.03517i 0.0526205 + 0.0911414i
\(130\) 0 0
\(131\) −5.25723 + 9.10580i −0.459327 + 0.795577i −0.998925 0.0463451i \(-0.985243\pi\)
0.539599 + 0.841922i \(0.318576\pi\)
\(132\) 0 0
\(133\) −0.134473 1.99807i −0.0116603 0.173254i
\(134\) 0 0
\(135\) 6.16525 10.6785i 0.530620 0.919061i
\(136\) 0 0
\(137\) −4.36583 7.56183i −0.372998 0.646051i 0.617028 0.786942i \(-0.288337\pi\)
−0.990025 + 0.140891i \(0.955003\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −3.14726 −0.265047
\(142\) 0 0
\(143\) −0.524077 0.907729i −0.0438256 0.0759081i
\(144\) 0 0
\(145\) 3.39457 5.87957i 0.281904 0.488272i
\(146\) 0 0
\(147\) −9.33992 + 1.26290i −0.770343 + 0.104163i
\(148\) 0 0
\(149\) −7.69632 + 13.3304i −0.630507 + 1.09207i 0.356941 + 0.934127i \(0.383820\pi\)
−0.987448 + 0.157944i \(0.949514\pi\)
\(150\) 0 0
\(151\) −6.83786 11.8435i −0.556457 0.963812i −0.997789 0.0664680i \(-0.978827\pi\)
0.441331 0.897344i \(-0.354506\pi\)
\(152\) 0 0
\(153\) 6.28158 0.507836
\(154\) 0 0
\(155\) −2.24821 −0.180581
\(156\) 0 0
\(157\) −1.69378 2.93371i −0.135178 0.234136i 0.790487 0.612478i \(-0.209827\pi\)
−0.925666 + 0.378343i \(0.876494\pi\)
\(158\) 0 0
\(159\) −3.29074 + 5.69972i −0.260972 + 0.452017i
\(160\) 0 0
\(161\) −0.116117 1.72532i −0.00915128 0.135974i
\(162\) 0 0
\(163\) −6.90502 + 11.9598i −0.540843 + 0.936767i 0.458013 + 0.888946i \(0.348561\pi\)
−0.998856 + 0.0478219i \(0.984772\pi\)
\(164\) 0 0
\(165\) −1.54332 2.67311i −0.120147 0.208101i
\(166\) 0 0
\(167\) −16.3783 −1.26739 −0.633695 0.773583i \(-0.718462\pi\)
−0.633695 + 0.773583i \(0.718462\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −0.449286 0.778186i −0.0343578 0.0595094i
\(172\) 0 0
\(173\) −2.06273 + 3.57275i −0.156826 + 0.271631i −0.933723 0.357997i \(-0.883460\pi\)
0.776896 + 0.629629i \(0.216793\pi\)
\(174\) 0 0
\(175\) 0.513734 + 0.252229i 0.0388346 + 0.0190667i
\(176\) 0 0
\(177\) −0.705626 + 1.22218i −0.0530381 + 0.0918647i
\(178\) 0 0
\(179\) 7.20679 + 12.4825i 0.538661 + 0.932988i 0.998976 + 0.0452324i \(0.0144028\pi\)
−0.460316 + 0.887755i \(0.652264\pi\)
\(180\) 0 0
\(181\) 18.1014 1.34547 0.672733 0.739885i \(-0.265120\pi\)
0.672733 + 0.739885i \(0.265120\pi\)
\(182\) 0 0
\(183\) −16.8299 −1.24410
\(184\) 0 0
\(185\) 11.9126 + 20.6333i 0.875834 + 1.51699i
\(186\) 0 0
\(187\) 2.77302 4.80302i 0.202784 0.351232i
\(188\) 0 0
\(189\) −12.3876 + 8.30850i −0.901062 + 0.604355i
\(190\) 0 0
\(191\) 2.77068 4.79895i 0.200479 0.347240i −0.748204 0.663469i \(-0.769083\pi\)
0.948683 + 0.316229i \(0.102417\pi\)
\(192\) 0 0
\(193\) 4.37044 + 7.56983i 0.314591 + 0.544888i 0.979351 0.202170i \(-0.0647992\pi\)
−0.664759 + 0.747058i \(0.731466\pi\)
\(194\) 0 0
\(195\) 2.94483 0.210884
\(196\) 0 0
\(197\) −5.46874 −0.389632 −0.194816 0.980840i \(-0.562411\pi\)
−0.194816 + 0.980840i \(0.562411\pi\)
\(198\) 0 0
\(199\) 9.76839 + 16.9193i 0.692463 + 1.19938i 0.971029 + 0.238963i \(0.0768075\pi\)
−0.278566 + 0.960417i \(0.589859\pi\)
\(200\) 0 0
\(201\) 3.01522 5.22252i 0.212677 0.368368i
\(202\) 0 0
\(203\) −6.82056 + 4.57464i −0.478709 + 0.321077i
\(204\) 0 0
\(205\) −8.00546 + 13.8659i −0.559125 + 0.968433i
\(206\) 0 0
\(207\) −0.387956 0.671959i −0.0269648 0.0467044i
\(208\) 0 0
\(209\) −0.793355 −0.0548775
\(210\) 0 0
\(211\) −16.6905 −1.14902 −0.574511 0.818497i \(-0.694808\pi\)
−0.574511 + 0.818497i \(0.694808\pi\)
\(212\) 0 0
\(213\) −4.44502 7.69900i −0.304568 0.527527i
\(214\) 0 0
\(215\) 0.970850 1.68156i 0.0662114 0.114682i
\(216\) 0 0
\(217\) 2.44124 + 1.19858i 0.165722 + 0.0813647i
\(218\) 0 0
\(219\) 5.57650 9.65878i 0.376825 0.652680i
\(220\) 0 0
\(221\) 2.64562 + 4.58236i 0.177964 + 0.308243i
\(222\) 0 0
\(223\) 5.34217 0.357738 0.178869 0.983873i \(-0.442756\pi\)
0.178869 + 0.983873i \(0.442756\pi\)
\(224\) 0 0
\(225\) 0.256800 0.0171200
\(226\) 0 0
\(227\) 10.0608 + 17.4258i 0.667757 + 1.15659i 0.978530 + 0.206104i \(0.0660786\pi\)
−0.310774 + 0.950484i \(0.600588\pi\)
\(228\) 0 0
\(229\) −12.6249 + 21.8669i −0.834275 + 1.44501i 0.0603445 + 0.998178i \(0.480780\pi\)
−0.894619 + 0.446829i \(0.852553\pi\)
\(230\) 0 0
\(231\) 0.250725 + 3.72540i 0.0164965 + 0.245113i
\(232\) 0 0
\(233\) 0.396678 0.687066i 0.0259872 0.0450112i −0.852739 0.522337i \(-0.825060\pi\)
0.878727 + 0.477326i \(0.158394\pi\)
\(234\) 0 0
\(235\) 2.55626 + 4.42757i 0.166752 + 0.288823i
\(236\) 0 0
\(237\) −2.88152 −0.187175
\(238\) 0 0
\(239\) −20.0488 −1.29685 −0.648425 0.761279i \(-0.724572\pi\)
−0.648425 + 0.761279i \(0.724572\pi\)
\(240\) 0 0
\(241\) −6.90602 11.9616i −0.444856 0.770513i 0.553186 0.833058i \(-0.313412\pi\)
−0.998042 + 0.0625446i \(0.980078\pi\)
\(242\) 0 0
\(243\) −5.74404 + 9.94897i −0.368480 + 0.638227i
\(244\) 0 0
\(245\) 9.36269 + 12.1137i 0.598161 + 0.773913i
\(246\) 0 0
\(247\) 0.378453 0.655500i 0.0240804 0.0417085i
\(248\) 0 0
\(249\) −4.48732 7.77227i −0.284372 0.492547i
\(250\) 0 0
\(251\) 26.1095 1.64802 0.824010 0.566576i \(-0.191732\pi\)
0.824010 + 0.566576i \(0.191732\pi\)
\(252\) 0 0
\(253\) −0.685057 −0.0430692
\(254\) 0 0
\(255\) 7.79092 + 13.4943i 0.487886 + 0.845044i
\(256\) 0 0
\(257\) −5.30990 + 9.19701i −0.331222 + 0.573694i −0.982752 0.184930i \(-0.940794\pi\)
0.651530 + 0.758623i \(0.274128\pi\)
\(258\) 0 0
\(259\) −1.93531 28.7557i −0.120254 1.78679i
\(260\) 0 0
\(261\) −1.84253 + 3.19135i −0.114050 + 0.197540i
\(262\) 0 0
\(263\) 5.17888 + 8.97008i 0.319343 + 0.553119i 0.980351 0.197260i \(-0.0632044\pi\)
−0.661008 + 0.750379i \(0.729871\pi\)
\(264\) 0 0
\(265\) 10.6912 0.656753
\(266\) 0 0
\(267\) −7.76581 −0.475260
\(268\) 0 0
\(269\) −5.98503 10.3664i −0.364914 0.632049i 0.623849 0.781545i \(-0.285568\pi\)
−0.988762 + 0.149496i \(0.952235\pi\)
\(270\) 0 0
\(271\) −1.37845 + 2.38755i −0.0837351 + 0.145033i −0.904852 0.425727i \(-0.860018\pi\)
0.821116 + 0.570761i \(0.193352\pi\)
\(272\) 0 0
\(273\) −3.19767 1.56996i −0.193532 0.0950184i
\(274\) 0 0
\(275\) 0.113365 0.196354i 0.00683618 0.0118406i
\(276\) 0 0
\(277\) 11.9637 + 20.7218i 0.718831 + 1.24505i 0.961463 + 0.274933i \(0.0886558\pi\)
−0.242632 + 0.970118i \(0.578011\pi\)
\(278\) 0 0
\(279\) 1.22030 0.0730574
\(280\) 0 0
\(281\) −3.87870 −0.231384 −0.115692 0.993285i \(-0.536909\pi\)
−0.115692 + 0.993285i \(0.536909\pi\)
\(282\) 0 0
\(283\) −3.10499 5.37801i −0.184573 0.319689i 0.758860 0.651254i \(-0.225757\pi\)
−0.943432 + 0.331565i \(0.892423\pi\)
\(284\) 0 0
\(285\) 1.11448 1.93034i 0.0660162 0.114343i
\(286\) 0 0
\(287\) 16.0850 10.7884i 0.949468 0.636821i
\(288\) 0 0
\(289\) −5.49866 + 9.52395i −0.323450 + 0.560232i
\(290\) 0 0
\(291\) 1.94407 + 3.36723i 0.113963 + 0.197390i
\(292\) 0 0
\(293\) 16.5754 0.968347 0.484174 0.874972i \(-0.339120\pi\)
0.484174 + 0.874972i \(0.339120\pi\)
\(294\) 0 0
\(295\) 2.29249 0.133474
\(296\) 0 0
\(297\) 2.95457 + 5.11747i 0.171442 + 0.296946i
\(298\) 0 0
\(299\) 0.326792 0.566020i 0.0188989 0.0327338i
\(300\) 0 0
\(301\) −1.95069 + 1.30835i −0.112436 + 0.0754121i
\(302\) 0 0
\(303\) 7.57650 13.1229i 0.435259 0.753890i
\(304\) 0 0
\(305\) 13.6695 + 23.6763i 0.782716 + 1.35570i
\(306\) 0 0
\(307\) 7.05788 0.402815 0.201407 0.979508i \(-0.435449\pi\)
0.201407 + 0.979508i \(0.435449\pi\)
\(308\) 0 0
\(309\) −27.2426 −1.54978
\(310\) 0 0
\(311\) 10.5551 + 18.2820i 0.598525 + 1.03668i 0.993039 + 0.117785i \(0.0375795\pi\)
−0.394514 + 0.918890i \(0.629087\pi\)
\(312\) 0 0
\(313\) −0.990260 + 1.71518i −0.0559728 + 0.0969477i −0.892654 0.450742i \(-0.851159\pi\)
0.836681 + 0.547690i \(0.184493\pi\)
\(314\) 0 0
\(315\) 6.16660 + 3.02762i 0.347449 + 0.170587i
\(316\) 0 0
\(317\) 9.02297 15.6282i 0.506781 0.877770i −0.493189 0.869922i \(-0.664169\pi\)
0.999969 0.00784727i \(-0.00249789\pi\)
\(318\) 0 0
\(319\) 1.62678 + 2.81767i 0.0910822 + 0.157759i
\(320\) 0 0
\(321\) −12.1920 −0.680492
\(322\) 0 0
\(323\) 4.00498 0.222843
\(324\) 0 0
\(325\) 0.108157 + 0.187333i 0.00599947 + 0.0103914i
\(326\) 0 0
\(327\) −10.1664 + 17.6087i −0.562202 + 0.973763i
\(328\) 0 0
\(329\) −0.415285 6.17051i −0.0228954 0.340191i
\(330\) 0 0
\(331\) −7.33689 + 12.7079i −0.403272 + 0.698488i −0.994119 0.108296i \(-0.965460\pi\)
0.590847 + 0.806784i \(0.298794\pi\)
\(332\) 0 0
\(333\) −6.46602 11.1995i −0.354336 0.613728i
\(334\) 0 0
\(335\) −9.79606 −0.535216
\(336\) 0 0
\(337\) 12.8080 0.697698 0.348849 0.937179i \(-0.386573\pi\)
0.348849 + 0.937179i \(0.386573\pi\)
\(338\) 0 0
\(339\) −2.08969 3.61946i −0.113497 0.196582i
\(340\) 0 0
\(341\) 0.538705 0.933065i 0.0291725 0.0505283i
\(342\) 0 0
\(343\) −3.70846 18.1452i −0.200238 0.979747i
\(344\) 0 0
\(345\) 0.962348 1.66684i 0.0518111 0.0897394i
\(346\) 0 0
\(347\) 10.1027 + 17.4984i 0.542342 + 0.939363i 0.998769 + 0.0496025i \(0.0157954\pi\)
−0.456428 + 0.889761i \(0.650871\pi\)
\(348\) 0 0
\(349\) −18.4434 −0.987252 −0.493626 0.869674i \(-0.664329\pi\)
−0.493626 + 0.869674i \(0.664329\pi\)
\(350\) 0 0
\(351\) −5.63766 −0.300916
\(352\) 0 0
\(353\) 4.07218 + 7.05322i 0.216740 + 0.375405i 0.953810 0.300412i \(-0.0971242\pi\)
−0.737069 + 0.675817i \(0.763791\pi\)
\(354\) 0 0
\(355\) −7.22064 + 12.5065i −0.383232 + 0.663777i
\(356\) 0 0
\(357\) −1.26570 18.8064i −0.0669879 0.995339i
\(358\) 0 0
\(359\) −16.3050 + 28.2411i −0.860545 + 1.49051i 0.0108595 + 0.999941i \(0.496543\pi\)
−0.871404 + 0.490566i \(0.836790\pi\)
\(360\) 0 0
\(361\) 9.21355 + 15.9583i 0.484923 + 0.839912i
\(362\) 0 0
\(363\) −13.3314 −0.699715
\(364\) 0 0
\(365\) −18.1173 −0.948304
\(366\) 0 0
\(367\) −1.58006 2.73675i −0.0824786 0.142857i 0.821835 0.569725i \(-0.192950\pi\)
−0.904314 + 0.426868i \(0.859617\pi\)
\(368\) 0 0
\(369\) 4.34526 7.52621i 0.226205 0.391799i
\(370\) 0 0
\(371\) −11.6091 5.69972i −0.602713 0.295915i
\(372\) 0 0
\(373\) 0.738849 1.27972i 0.0382561 0.0662616i −0.846263 0.532765i \(-0.821153\pi\)
0.884520 + 0.466503i \(0.154486\pi\)
\(374\) 0 0
\(375\) 7.68059 + 13.3032i 0.396624 + 0.686972i
\(376\) 0 0
\(377\) −3.10408 −0.159868
\(378\) 0 0
\(379\) −10.7254 −0.550927 −0.275463 0.961312i \(-0.588831\pi\)
−0.275463 + 0.961312i \(0.588831\pi\)
\(380\) 0 0
\(381\) 5.91692 + 10.2484i 0.303133 + 0.525042i
\(382\) 0 0
\(383\) −10.7054 + 18.5424i −0.547023 + 0.947471i 0.451454 + 0.892294i \(0.350906\pi\)
−0.998477 + 0.0551766i \(0.982428\pi\)
\(384\) 0 0
\(385\) 5.03725 3.37855i 0.256722 0.172187i
\(386\) 0 0
\(387\) −0.526965 + 0.912730i −0.0267871 + 0.0463967i
\(388\) 0 0
\(389\) −17.3909 30.1220i −0.881755 1.52725i −0.849388 0.527769i \(-0.823029\pi\)
−0.0323675 0.999476i \(-0.510305\pi\)
\(390\) 0 0
\(391\) 3.45828 0.174893
\(392\) 0 0
\(393\) 14.1568 0.714119
\(394\) 0 0
\(395\) 2.34042 + 4.05373i 0.117759 + 0.203965i
\(396\) 0 0
\(397\) −2.22605 + 3.85564i −0.111722 + 0.193509i −0.916465 0.400115i \(-0.868970\pi\)
0.804742 + 0.593624i \(0.202303\pi\)
\(398\) 0 0
\(399\) −2.23928 + 1.50191i −0.112104 + 0.0751897i
\(400\) 0 0
\(401\) 6.87687 11.9111i 0.343415 0.594811i −0.641650 0.766998i \(-0.721750\pi\)
0.985064 + 0.172186i \(0.0550831\pi\)
\(402\) 0 0
\(403\) 0.513956 + 0.890198i 0.0256020 + 0.0443439i
\(404\) 0 0
\(405\) −8.81241 −0.437892
\(406\) 0 0
\(407\) −11.4178 −0.565959
\(408\) 0 0
\(409\) 1.74603 + 3.02422i 0.0863358 + 0.149538i 0.905960 0.423364i \(-0.139151\pi\)
−0.819624 + 0.572902i \(0.805818\pi\)
\(410\) 0 0
\(411\) −5.87822 + 10.1814i −0.289951 + 0.502210i
\(412\) 0 0
\(413\) −2.48931 1.22218i −0.122491 0.0601396i
\(414\) 0 0
\(415\) −7.28935 + 12.6255i −0.357820 + 0.619763i
\(416\) 0 0
\(417\) −2.69283 4.66412i −0.131869 0.228403i
\(418\) 0 0
\(419\) 3.56737 0.174278 0.0871388 0.996196i \(-0.472228\pi\)
0.0871388 + 0.996196i \(0.472228\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 0 0
\(423\) −1.38750 2.40323i −0.0674627 0.116849i
\(424\) 0 0
\(425\) −0.572285 + 0.991227i −0.0277599 + 0.0480816i
\(426\) 0 0
\(427\) −2.22073 32.9967i −0.107469 1.59682i
\(428\) 0 0
\(429\) −0.705626 + 1.22218i −0.0340680 + 0.0590074i
\(430\) 0 0
\(431\) −5.68211 9.84171i −0.273698 0.474059i 0.696108 0.717937i \(-0.254913\pi\)
−0.969806 + 0.243879i \(0.921580\pi\)
\(432\) 0 0
\(433\) −21.2136 −1.01946 −0.509731 0.860334i \(-0.670255\pi\)
−0.509731 + 0.860334i \(0.670255\pi\)
\(434\) 0 0
\(435\) −9.14101 −0.438278
\(436\) 0 0
\(437\) −0.247351 0.428424i −0.0118324 0.0204943i
\(438\) 0 0
\(439\) −12.2503 + 21.2182i −0.584676 + 1.01269i 0.410239 + 0.911978i \(0.365445\pi\)
−0.994916 + 0.100711i \(0.967888\pi\)
\(440\) 0 0
\(441\) −5.08195 6.57513i −0.241997 0.313102i
\(442\) 0 0
\(443\) 20.2344 35.0470i 0.961366 1.66513i 0.242288 0.970204i \(-0.422102\pi\)
0.719077 0.694930i \(-0.244565\pi\)
\(444\) 0 0
\(445\) 6.30753 + 10.9250i 0.299005 + 0.517893i
\(446\) 0 0
\(447\) 20.7249 0.980254
\(448\) 0 0
\(449\) −27.7638 −1.31025 −0.655127 0.755519i \(-0.727385\pi\)
−0.655127 + 0.755519i \(0.727385\pi\)
\(450\) 0 0
\(451\) −3.83646 6.64494i −0.180652 0.312898i
\(452\) 0 0
\(453\) −9.20661 + 15.9463i −0.432564 + 0.749223i
\(454\) 0 0
\(455\) 0.388575 + 5.77363i 0.0182167 + 0.270672i
\(456\) 0 0
\(457\) 5.59696 9.69422i 0.261815 0.453476i −0.704910 0.709297i \(-0.749012\pi\)
0.966724 + 0.255821i \(0.0823457\pi\)
\(458\) 0 0
\(459\) −14.9151 25.8338i −0.696179 1.20582i
\(460\) 0 0
\(461\) −9.29773 −0.433038 −0.216519 0.976278i \(-0.569470\pi\)
−0.216519 + 0.976278i \(0.569470\pi\)
\(462\) 0 0
\(463\) −28.2439 −1.31260 −0.656302 0.754499i \(-0.727880\pi\)
−0.656302 + 0.754499i \(0.727880\pi\)
\(464\) 0 0
\(465\) 1.51351 + 2.62148i 0.0701875 + 0.121568i
\(466\) 0 0
\(467\) 11.1303 19.2783i 0.515050 0.892093i −0.484797 0.874626i \(-0.661107\pi\)
0.999847 0.0174663i \(-0.00555997\pi\)
\(468\) 0 0
\(469\) 10.6371 + 5.22252i 0.491177 + 0.241154i
\(470\) 0 0
\(471\) −2.28053 + 3.95000i −0.105081 + 0.182006i
\(472\) 0 0
\(473\) 0.465261 + 0.805855i 0.0213927 + 0.0370533i
\(474\) 0 0
\(475\) 0.163729 0.00751242
\(476\) 0 0
\(477\) −5.80302 −0.265702
\(478\) 0 0
\(479\) −16.4382 28.4718i −0.751081 1.30091i −0.947299 0.320350i \(-0.896200\pi\)
0.196219 0.980560i \(-0.437134\pi\)
\(480\) 0 0
\(481\) 5.44661 9.43381i 0.248344 0.430145i
\(482\) 0 0
\(483\) −1.93360 + 1.29689i −0.0879820 + 0.0590107i
\(484\) 0 0
\(485\) 3.15801 5.46984i 0.143398 0.248373i
\(486\) 0 0
\(487\) −13.9462 24.1555i −0.631962 1.09459i −0.987150 0.159796i \(-0.948916\pi\)
0.355188 0.934795i \(-0.384417\pi\)
\(488\) 0 0
\(489\) 18.5941 0.840852
\(490\) 0 0
\(491\) −10.6571 −0.480948 −0.240474 0.970656i \(-0.577303\pi\)
−0.240474 + 0.970656i \(0.577303\pi\)
\(492\) 0 0
\(493\) −8.21224 14.2240i −0.369861 0.640618i
\(494\) 0 0
\(495\) 1.36078 2.35694i 0.0611625 0.105936i
\(496\) 0 0
\(497\) 14.5081 9.73078i 0.650777 0.436485i
\(498\) 0 0
\(499\) −12.2557 + 21.2275i −0.548641 + 0.950274i 0.449727 + 0.893166i \(0.351521\pi\)
−0.998368 + 0.0571077i \(0.981812\pi\)
\(500\) 0 0
\(501\) 11.0260 + 19.0976i 0.492605 + 0.853217i
\(502\) 0 0
\(503\) 38.0054 1.69458 0.847288 0.531134i \(-0.178234\pi\)
0.847288 + 0.531134i \(0.178234\pi\)
\(504\) 0 0
\(505\) −24.6151 −1.09536
\(506\) 0 0
\(507\) −0.673208 1.16603i −0.0298982 0.0517852i
\(508\) 0 0
\(509\) −19.9250 + 34.5112i −0.883161 + 1.52968i −0.0353545 + 0.999375i \(0.511256\pi\)
−0.847807 + 0.530305i \(0.822077\pi\)
\(510\) 0 0
\(511\) 19.6728 + 9.65878i 0.870274 + 0.427279i
\(512\) 0 0
\(513\) −2.13359 + 3.69549i −0.0942004 + 0.163160i
\(514\) 0 0
\(515\) 22.1269 + 38.3249i 0.975027 + 1.68880i
\(516\) 0 0
\(517\) −2.45007 −0.107754
\(518\) 0 0
\(519\) 5.55459 0.243819
\(520\) 0 0
\(521\) 9.81670 + 17.0030i 0.430077 + 0.744916i 0.996880 0.0789382i \(-0.0251530\pi\)
−0.566802 + 0.823854i \(0.691820\pi\)
\(522\) 0 0
\(523\) 11.4162 19.7734i 0.499195 0.864632i −0.500804 0.865561i \(-0.666962\pi\)
1.00000 0.000928862i \(0.000295666\pi\)
\(524\) 0 0
\(525\) −0.0517436 0.768832i −0.00225828 0.0335546i
\(526\) 0 0
\(527\) −2.71947 + 4.71026i −0.118462 + 0.205182i
\(528\) 0 0
\(529\) 11.2864 + 19.5486i 0.490714 + 0.849941i
\(530\) 0 0
\(531\) −1.24433 −0.0539994
\(532\) 0 0
\(533\) 7.32040 0.317082
\(534\) 0 0
\(535\) 9.90257 + 17.1518i 0.428125 + 0.741535i
\(536\) 0 0
\(537\) 9.70333 16.8067i 0.418730 0.725261i
\(538\) 0 0
\(539\) −7.27092 + 0.983142i −0.313181 + 0.0423469i
\(540\) 0 0
\(541\) 4.82334 8.35427i 0.207372 0.359178i −0.743514 0.668720i \(-0.766842\pi\)
0.950886 + 0.309542i \(0.100176\pi\)
\(542\) 0 0
\(543\) −12.1860 21.1068i −0.522952 0.905779i
\(544\) 0 0
\(545\) 33.0292 1.41482
\(546\) 0 0
\(547\) 43.8570 1.87519 0.937596 0.347728i \(-0.113047\pi\)
0.937596 + 0.347728i \(0.113047\pi\)
\(548\) 0 0
\(549\) −7.41965 12.8512i −0.316663 0.548476i
\(550\) 0 0
\(551\) −1.17475 + 2.03473i −0.0500461 + 0.0866823i
\(552\) 0 0
\(553\) −0.380221 5.64950i −0.0161686 0.240241i
\(554\) 0 0
\(555\) 16.0394 27.7810i 0.680833 1.17924i
\(556\) 0 0
\(557\) −7.45977 12.9207i −0.316080 0.547467i 0.663586 0.748100i \(-0.269034\pi\)
−0.979667 + 0.200633i \(0.935700\pi\)
\(558\) 0 0
\(559\) −0.887771 −0.0375487
\(560\) 0 0
\(561\) −7.46729 −0.315269
\(562\) 0 0
\(563\) −8.63486 14.9560i −0.363916 0.630321i 0.624686 0.780876i \(-0.285227\pi\)
−0.988602 + 0.150555i \(0.951894\pi\)
\(564\) 0 0
\(565\) −3.39457 + 5.87957i −0.142811 + 0.247355i
\(566\) 0 0
\(567\) 9.56902 + 4.69811i 0.401861 + 0.197302i
\(568\) 0 0
\(569\) −13.2662 + 22.9777i −0.556148 + 0.963277i 0.441665 + 0.897180i \(0.354388\pi\)
−0.997813 + 0.0660972i \(0.978945\pi\)
\(570\) 0 0
\(571\) −0.992844 1.71966i −0.0415492 0.0719654i 0.844503 0.535551i \(-0.179896\pi\)
−0.886052 + 0.463586i \(0.846563\pi\)
\(572\) 0 0
\(573\) −7.46097 −0.311686
\(574\) 0 0
\(575\) 0.141379 0.00589593
\(576\) 0 0
\(577\) −5.94915 10.3042i −0.247666 0.428971i 0.715212 0.698908i \(-0.246330\pi\)
−0.962878 + 0.269937i \(0.912997\pi\)
\(578\) 0 0
\(579\) 5.88443 10.1921i 0.244549 0.423571i
\(580\) 0 0
\(581\) 14.6462 9.82339i 0.607626 0.407543i
\(582\) 0 0
\(583\) −2.56176 + 4.43711i −0.106097 + 0.183766i
\(584\) 0 0
\(585\) 1.29826 + 2.24865i 0.0536765 + 0.0929704i
\(586\) 0 0
\(587\) −33.5122 −1.38320 −0.691598 0.722283i \(-0.743093\pi\)
−0.691598 + 0.722283i \(0.743093\pi\)
\(588\) 0 0
\(589\) 0.778033 0.0320583
\(590\) 0 0
\(591\) 3.68160 + 6.37672i 0.151441 + 0.262303i
\(592\) 0 0
\(593\) −17.6408 + 30.5547i −0.724419 + 1.25473i 0.234793 + 0.972045i \(0.424559\pi\)
−0.959213 + 0.282686i \(0.908775\pi\)
\(594\) 0 0
\(595\) −25.4288 + 17.0554i −1.04248 + 0.699205i
\(596\) 0 0
\(597\) 13.1523 22.7805i 0.538288 0.932343i
\(598\) 0 0
\(599\) −12.5034 21.6565i −0.510876 0.884863i −0.999921 0.0126040i \(-0.995988\pi\)
0.489045 0.872259i \(-0.337345\pi\)
\(600\) 0 0
\(601\) −28.4688 −1.16127 −0.580634 0.814165i \(-0.697195\pi\)
−0.580634 + 0.814165i \(0.697195\pi\)
\(602\) 0 0
\(603\) 5.31717 0.216532
\(604\) 0 0
\(605\) 10.8280 + 18.7546i 0.440219 + 0.762482i
\(606\) 0 0
\(607\) 18.0234 31.2175i 0.731549 1.26708i −0.224672 0.974434i \(-0.572131\pi\)
0.956221 0.292646i \(-0.0945356\pi\)
\(608\) 0 0
\(609\) 9.92583 + 4.87330i 0.402215 + 0.197476i
\(610\) 0 0
\(611\) 1.16875 2.02434i 0.0472827 0.0818961i
\(612\) 0 0
\(613\) −9.16264 15.8702i −0.370075 0.640989i 0.619501 0.784996i \(-0.287335\pi\)
−0.989577 + 0.144006i \(0.954001\pi\)
\(614\) 0 0
\(615\) 21.5573 0.869276
\(616\) 0 0
\(617\) 44.3782 1.78660 0.893299 0.449463i \(-0.148385\pi\)
0.893299 + 0.449463i \(0.148385\pi\)
\(618\) 0 0
\(619\) −12.5043 21.6580i −0.502588 0.870509i −0.999996 0.00299144i \(-0.999048\pi\)
0.497407 0.867517i \(-0.334286\pi\)
\(620\) 0 0
\(621\) −1.84234 + 3.19103i −0.0739307 + 0.128052i
\(622\) 0 0
\(623\) −1.02471 15.2256i −0.0410541 0.610002i
\(624\) 0 0
\(625\) 11.9358 20.6734i 0.477433 0.826938i
\(626\) 0 0
\(627\) 0.534093 + 0.925076i 0.0213296 + 0.0369440i
\(628\) 0 0
\(629\) 57.6388 2.29821
\(630\) 0 0
\(631\) 18.4638 0.735032 0.367516 0.930017i \(-0.380208\pi\)
0.367516 + 0.930017i \(0.380208\pi\)
\(632\) 0 0
\(633\) 11.2362 + 19.4616i 0.446598 + 0.773531i
\(634\) 0 0
\(635\) 9.61165 16.6479i 0.381427 0.660650i
\(636\) 0 0
\(637\) 2.65613 6.47650i 0.105240 0.256608i
\(638\) 0 0
\(639\) 3.91927 6.78837i 0.155044 0.268544i
\(640\) 0 0
\(641\) 10.6284 + 18.4088i 0.419795 + 0.727106i 0.995919 0.0902567i \(-0.0287687\pi\)
−0.576124 + 0.817362i \(0.695435\pi\)
\(642\) 0 0
\(643\) 36.0554 1.42188 0.710942 0.703251i \(-0.248269\pi\)
0.710942 + 0.703251i \(0.248269\pi\)
\(644\) 0 0
\(645\) −2.61434 −0.102939
\(646\) 0 0
\(647\) 19.9117 + 34.4881i 0.782809 + 1.35587i 0.930299 + 0.366802i \(0.119547\pi\)
−0.147490 + 0.989064i \(0.547119\pi\)
\(648\) 0 0
\(649\) −0.549314 + 0.951440i −0.0215625 + 0.0373473i
\(650\) 0 0
\(651\) −0.245883 3.65345i −0.00963691 0.143190i
\(652\) 0 0
\(653\) 16.2335 28.1172i 0.635265 1.10031i −0.351195 0.936303i \(-0.614224\pi\)
0.986459 0.164008i \(-0.0524423\pi\)
\(654\) 0 0
\(655\) −11.4984 19.9159i −0.449281 0.778177i
\(656\) 0 0
\(657\) 9.83384 0.383655
\(658\) 0 0
\(659\) −23.5230 −0.916327 −0.458164 0.888868i \(-0.651493\pi\)
−0.458164 + 0.888868i \(0.651493\pi\)
\(660\) 0 0
\(661\) −7.01944 12.1580i −0.273025 0.472893i 0.696610 0.717450i \(-0.254691\pi\)
−0.969635 + 0.244557i \(0.921357\pi\)
\(662\) 0 0
\(663\) 3.56211 6.16976i 0.138341 0.239614i
\(664\) 0 0
\(665\) 3.93167 + 1.93034i 0.152464 + 0.0748553i
\(666\) 0 0
\(667\) −1.01439 + 1.75698i −0.0392773 + 0.0680303i
\(668\) 0 0
\(669\) −3.59639 6.22913i −0.139044 0.240832i
\(670\) 0 0
\(671\) −13.1017 −0.505786
\(672\) 0 0
\(673\) −47.1937 −1.81918 −0.909592 0.415502i \(-0.863606\pi\)
−0.909592 + 0.415502i \(0.863606\pi\)
\(674\) 0 0
\(675\) −0.609753 1.05612i −0.0234694 0.0406502i
\(676\) 0 0
\(677\) 4.79438 8.30411i 0.184263 0.319153i −0.759065 0.651015i \(-0.774344\pi\)
0.943328 + 0.331862i \(0.107677\pi\)
\(678\) 0 0
\(679\) −6.34526 + 4.25585i −0.243509 + 0.163325i
\(680\) 0 0
\(681\) 13.5460 23.4623i 0.519083 0.899078i
\(682\) 0 0
\(683\) 23.6581 + 40.9769i 0.905250 + 1.56794i 0.820581 + 0.571530i \(0.193650\pi\)
0.0846691 + 0.996409i \(0.473017\pi\)
\(684\) 0 0
\(685\) 19.0976 0.729680
\(686\) 0 0
\(687\) 33.9967 1.29705
\(688\) 0 0
\(689\) −2.44407 4.23325i −0.0931117 0.161274i
\(690\) 0 0
\(691\) −13.5559 + 23.4796i −0.515692 + 0.893205i 0.484142 + 0.874990i \(0.339132\pi\)
−0.999834 + 0.0182158i \(0.994201\pi\)
\(692\) 0 0
\(693\) −2.73415 + 1.83383i −0.103862 + 0.0696615i
\(694\) 0 0
\(695\) −4.37433 + 7.57656i −0.165928 + 0.287395i
\(696\) 0 0
\(697\) 19.3670 + 33.5447i 0.733578 + 1.27059i
\(698\) 0 0
\(699\) −1.06819 −0.0404025
\(700\) 0 0
\(701\) −1.79821 −0.0679176 −0.0339588 0.999423i \(-0.510811\pi\)
−0.0339588 + 0.999423i \(0.510811\pi\)
\(702\) 0 0
\(703\) −4.12258 7.14051i −0.155486 0.269310i
\(704\) 0 0
\(705\) 3.44179 5.96135i 0.129625 0.224517i
\(706\) 0 0
\(707\) 26.7284 + 13.1229i 1.00523 + 0.493537i
\(708\) 0 0
\(709\) 14.1615 24.5284i 0.531846 0.921185i −0.467462 0.884013i \(-0.654832\pi\)
0.999309 0.0371721i \(-0.0118350\pi\)
\(710\) 0 0
\(711\) −1.27035 2.20031i −0.0476418 0.0825180i
\(712\) 0 0
\(713\) 0.671827 0.0251601
\(714\) 0 0
\(715\) 2.29249 0.0857341
\(716\) 0 0
\(717\) 13.4970 + 23.3775i 0.504055 + 0.873050i
\(718\) 0 0
\(719\) −20.9485 + 36.2839i −0.781249 + 1.35316i 0.149966 + 0.988691i \(0.452084\pi\)
−0.931215 + 0.364471i \(0.881250\pi\)
\(720\) 0 0
\(721\) −3.59469 53.4117i −0.133873 1.98916i
\(722\) 0 0
\(723\) −9.29838 + 16.1053i −0.345810 + 0.598961i
\(724\) 0 0
\(725\) −0.335728 0.581499i −0.0124686 0.0215963i
\(726\) 0 0
\(727\) −19.5123 −0.723670 −0.361835 0.932242i \(-0.617850\pi\)
−0.361835 + 0.932242i \(0.617850\pi\)
\(728\) 0 0
\(729\) 27.5552 1.02056
\(730\) 0 0
\(731\) −2.34871 4.06808i −0.0868701 0.150463i
\(732\) 0 0
\(733\) −8.87698 + 15.3754i −0.327879 + 0.567902i −0.982091 0.188409i \(-0.939667\pi\)
0.654212 + 0.756311i \(0.273000\pi\)
\(734\) 0 0
\(735\) 7.82185 19.0722i 0.288513 0.703488i
\(736\) 0 0
\(737\) 2.34728 4.06562i 0.0864633 0.149759i
\(738\) 0 0
\(739\) 22.1571 + 38.3772i 0.815061 + 1.41173i 0.909284 + 0.416176i \(0.136630\pi\)
−0.0942227 + 0.995551i \(0.530037\pi\)
\(740\) 0 0
\(741\) −1.01911 −0.0374380
\(742\) 0 0
\(743\) 7.16727 0.262941 0.131471 0.991320i \(-0.458030\pi\)
0.131471 + 0.991320i \(0.458030\pi\)
\(744\) 0 0
\(745\) −16.8331 29.1558i −0.616718 1.06819i
\(746\) 0 0
\(747\) 3.95657 6.85297i 0.144763 0.250737i
\(748\) 0 0
\(749\) −1.60875 23.9036i −0.0587826 0.873420i
\(750\) 0 0
\(751\) −16.9532 + 29.3639i −0.618632 + 1.07150i 0.371103 + 0.928592i \(0.378980\pi\)
−0.989736 + 0.142911i \(0.954354\pi\)
\(752\) 0 0
\(753\) −17.5772 30.4445i −0.640547 1.10946i
\(754\) 0 0
\(755\) 29.9110 1.08857
\(756\) 0 0
\(757\) −0.906670 −0.0329535 −0.0164767 0.999864i \(-0.505245\pi\)
−0.0164767 + 0.999864i \(0.505245\pi\)
\(758\) 0 0
\(759\) 0.461186 + 0.798798i 0.0167400 + 0.0289945i
\(760\) 0 0
\(761\) −10.1247 + 17.5365i −0.367020 + 0.635697i −0.989098 0.147258i \(-0.952955\pi\)
0.622079 + 0.782955i \(0.286288\pi\)
\(762\) 0 0
\(763\) −35.8650 17.6087i −1.29840 0.637477i
\(764\) 0 0
\(765\) −6.86942 + 11.8982i −0.248364 + 0.430180i
\(766\) 0 0
\(767\) −0.524077 0.907729i −0.0189233 0.0327762i
\(768\) 0 0
\(769\) −36.9094 −1.33099 −0.665494 0.746403i \(-0.731779\pi\)
−0.665494 + 0.746403i \(0.731779\pi\)
\(770\) 0 0
\(771\) 14.2987 0.514954
\(772\) 0 0
\(773\) 4.94018 + 8.55665i 0.177686 + 0.307761i 0.941088 0.338163i \(-0.109806\pi\)
−0.763402 + 0.645924i \(0.776472\pi\)
\(774\) 0 0
\(775\) −0.111176 + 0.192562i −0.00399355 + 0.00691704i
\(776\) 0 0
\(777\) −32.2272 + 21.6152i −1.15614 + 0.775441i
\(778\) 0 0
\(779\) 2.77043 4.79852i 0.0992609 0.171925i
\(780\) 0 0
\(781\) −3.46035 5.99350i −0.123821 0.214464i
\(782\) 0 0
\(783\) 17.4998 0.625391
\(784\) 0 0
\(785\) 7.40915 0.264444
\(786\) 0 0
\(787\) 18.8411 + 32.6337i 0.671611 + 1.16326i 0.977447 + 0.211180i \(0.0677307\pi\)
−0.305836 + 0.952084i \(0.598936\pi\)
\(788\) 0 0
\(789\) 6.97292 12.0775i 0.248243 0.429969i
\(790\) 0 0
\(791\) 6.82056 4.57464i 0.242511 0.162656i
\(792\) 0 0
\(793\) 6.24989 10.8251i 0.221940 0.384412i
\(794\) 0 0
\(795\) −7.19738 12.4662i −0.255265 0.442131i
\(796\) 0 0
\(797\)