Properties

Label 460.2.m.a.81.2
Level $460$
Weight $2$
Character 460.81
Analytic conductor $3.673$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.m (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(3\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 81.2
Character \(\chi\) \(=\) 460.81
Dual form 460.2.m.a.301.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0800965 + 0.557084i) q^{3} +(-0.959493 + 0.281733i) q^{5} +(-2.98213 - 3.44157i) q^{7} +(2.57455 + 0.755957i) q^{9} +O(q^{10})\) \(q+(-0.0800965 + 0.557084i) q^{3} +(-0.959493 + 0.281733i) q^{5} +(-2.98213 - 3.44157i) q^{7} +(2.57455 + 0.755957i) q^{9} +(-1.53046 - 0.983566i) q^{11} +(2.30962 - 2.66544i) q^{13} +(-0.0800965 - 0.557084i) q^{15} +(-2.29511 - 5.02558i) q^{17} +(0.276101 - 0.604578i) q^{19} +(2.15610 - 1.38564i) q^{21} +(0.619255 - 4.75568i) q^{23} +(0.841254 - 0.540641i) q^{25} +(-1.32875 + 2.90955i) q^{27} +(0.245375 + 0.537295i) q^{29} +(-0.421554 - 2.93197i) q^{31} +(0.670513 - 0.773813i) q^{33} +(3.83094 + 2.46199i) q^{35} +(9.01316 + 2.64650i) q^{37} +(1.29988 + 1.50014i) q^{39} +(-8.05868 + 2.36624i) q^{41} +(0.932321 - 6.48444i) q^{43} -2.68324 q^{45} +0.201790 q^{47} +(-1.95505 + 13.5977i) q^{49} +(2.98350 - 0.876034i) q^{51} +(-1.38955 - 1.60363i) q^{53} +(1.74557 + 0.512545i) q^{55} +(0.314685 + 0.202236i) q^{57} +(-3.67179 + 4.23747i) q^{59} +(-1.79974 - 12.5175i) q^{61} +(-5.07598 - 11.1149i) q^{63} +(-1.46512 + 3.20816i) q^{65} +(-3.69170 + 2.37251i) q^{67} +(2.59971 + 0.725891i) q^{69} +(-1.79449 + 1.15325i) q^{71} +(-3.90317 + 8.54674i) q^{73} +(0.233801 + 0.511952i) q^{75} +(1.17903 + 8.20030i) q^{77} +(1.05887 - 1.22201i) q^{79} +(5.25743 + 3.37874i) q^{81} +(-1.80477 - 0.529927i) q^{83} +(3.61801 + 4.17540i) q^{85} +(-0.318972 + 0.0936587i) q^{87} +(-1.01143 + 7.03466i) q^{89} -16.0609 q^{91} +1.66712 q^{93} +(-0.0945881 + 0.657875i) q^{95} +(10.2886 - 3.02100i) q^{97} +(-3.19671 - 3.68920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 3q^{5} + q^{7} + 21q^{9} + O(q^{10}) \) \( 30q - 3q^{5} + q^{7} + 21q^{9} + 2q^{13} + 10q^{17} + 3q^{19} + 39q^{21} + 10q^{23} - 3q^{25} + 21q^{27} + 14q^{29} - 2q^{31} - 50q^{33} - 10q^{35} + 9q^{37} + 38q^{39} - 3q^{41} - 50q^{43} + 10q^{45} - 6q^{47} - 36q^{49} - 36q^{51} - 5q^{53} - 11q^{55} + 23q^{57} + 14q^{59} - 16q^{61} - 52q^{63} + 2q^{65} + 27q^{67} + 42q^{69} + 19q^{71} + 24q^{73} - 10q^{77} - 22q^{79} + 35q^{81} + 36q^{83} + 10q^{85} - 3q^{87} - 28q^{89} - 98q^{91} - 60q^{93} - 19q^{95} - 2q^{97} - 14q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{10}{11}\right)\)

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
\(3\) −0.0800965 + 0.557084i −0.0462437 + 0.321632i 0.953548 + 0.301240i \(0.0974006\pi\)
−0.999792 + 0.0203922i \(0.993509\pi\)
\(4\) 0 0
\(5\) −0.959493 + 0.281733i −0.429098 + 0.125995i
\(6\) 0 0
\(7\) −2.98213 3.44157i −1.12714 1.30079i −0.948465 0.316882i \(-0.897364\pi\)
−0.178676 0.983908i \(-0.557181\pi\)
\(8\) 0 0
\(9\) 2.57455 + 0.755957i 0.858184 + 0.251986i
\(10\) 0 0
\(11\) −1.53046 0.983566i −0.461451 0.296556i 0.289184 0.957273i \(-0.406616\pi\)
−0.750635 + 0.660717i \(0.770252\pi\)
\(12\) 0 0
\(13\) 2.30962 2.66544i 0.640572 0.739260i −0.338904 0.940821i \(-0.610056\pi\)
0.979476 + 0.201561i \(0.0646016\pi\)
\(14\) 0 0
\(15\) −0.0800965 0.557084i −0.0206808 0.143838i
\(16\) 0 0
\(17\) −2.29511 5.02558i −0.556645 1.21888i −0.953609 0.301048i \(-0.902664\pi\)
0.396964 0.917834i \(-0.370064\pi\)
\(18\) 0 0
\(19\) 0.276101 0.604578i 0.0633420 0.138700i −0.875314 0.483556i \(-0.839345\pi\)
0.938656 + 0.344856i \(0.112072\pi\)
\(20\) 0 0
\(21\) 2.15610 1.38564i 0.470499 0.302371i
\(22\) 0 0
\(23\) 0.619255 4.75568i 0.129124 0.991629i
\(24\) 0 0
\(25\) 0.841254 0.540641i 0.168251 0.108128i
\(26\) 0 0
\(27\) −1.32875 + 2.90955i −0.255717 + 0.559943i
\(28\) 0 0
\(29\) 0.245375 + 0.537295i 0.0455649 + 0.0997733i 0.931045 0.364903i \(-0.118898\pi\)
−0.885481 + 0.464676i \(0.846171\pi\)
\(30\) 0 0
\(31\) −0.421554 2.93197i −0.0757133 0.526597i −0.992016 0.126111i \(-0.959750\pi\)
0.916303 0.400486i \(-0.131159\pi\)
\(32\) 0 0
\(33\) 0.670513 0.773813i 0.116721 0.134704i
\(34\) 0 0
\(35\) 3.83094 + 2.46199i 0.647547 + 0.416153i
\(36\) 0 0
\(37\) 9.01316 + 2.64650i 1.48175 + 0.435082i 0.919900 0.392154i \(-0.128270\pi\)
0.561854 + 0.827236i \(0.310088\pi\)
\(38\) 0 0
\(39\) 1.29988 + 1.50014i 0.208147 + 0.240215i
\(40\) 0 0
\(41\) −8.05868 + 2.36624i −1.25855 + 0.369545i −0.841956 0.539546i \(-0.818596\pi\)
−0.416598 + 0.909091i \(0.636778\pi\)
\(42\) 0 0
\(43\) 0.932321 6.48444i 0.142178 0.988867i −0.786397 0.617722i \(-0.788056\pi\)
0.928575 0.371146i \(-0.121035\pi\)
\(44\) 0 0
\(45\) −2.68324 −0.399994
\(46\) 0 0
\(47\) 0.201790 0.0294341 0.0147171 0.999892i \(-0.495315\pi\)
0.0147171 + 0.999892i \(0.495315\pi\)
\(48\) 0 0
\(49\) −1.95505 + 13.5977i −0.279293 + 1.94252i
\(50\) 0 0
\(51\) 2.98350 0.876034i 0.417773 0.122669i
\(52\) 0 0
\(53\) −1.38955 1.60363i −0.190870 0.220276i 0.652246 0.758007i \(-0.273827\pi\)
−0.843116 + 0.537732i \(0.819281\pi\)
\(54\) 0 0
\(55\) 1.74557 + 0.512545i 0.235372 + 0.0691115i
\(56\) 0 0
\(57\) 0.314685 + 0.202236i 0.0416811 + 0.0267868i
\(58\) 0 0
\(59\) −3.67179 + 4.23747i −0.478026 + 0.551672i −0.942627 0.333849i \(-0.891653\pi\)
0.464600 + 0.885521i \(0.346198\pi\)
\(60\) 0 0
\(61\) −1.79974 12.5175i −0.230433 1.60270i −0.696239 0.717810i \(-0.745145\pi\)
0.465806 0.884887i \(-0.345764\pi\)
\(62\) 0 0
\(63\) −5.07598 11.1149i −0.639514 1.40034i
\(64\) 0 0
\(65\) −1.46512 + 3.20816i −0.181726 + 0.397924i
\(66\) 0 0
\(67\) −3.69170 + 2.37251i −0.451013 + 0.289848i −0.746361 0.665541i \(-0.768201\pi\)
0.295348 + 0.955390i \(0.404564\pi\)
\(68\) 0 0
\(69\) 2.59971 + 0.725891i 0.312969 + 0.0873870i
\(70\) 0 0
\(71\) −1.79449 + 1.15325i −0.212966 + 0.136865i −0.642776 0.766055i \(-0.722217\pi\)
0.429809 + 0.902920i \(0.358581\pi\)
\(72\) 0 0
\(73\) −3.90317 + 8.54674i −0.456831 + 1.00032i 0.531367 + 0.847141i \(0.321678\pi\)
−0.988198 + 0.153179i \(0.951049\pi\)
\(74\) 0 0
\(75\) 0.233801 + 0.511952i 0.0269970 + 0.0591151i
\(76\) 0 0
\(77\) 1.17903 + 8.20030i 0.134362 + 0.934511i
\(78\) 0 0
\(79\) 1.05887 1.22201i 0.119133 0.137486i −0.693050 0.720889i \(-0.743734\pi\)
0.812183 + 0.583403i \(0.198279\pi\)
\(80\) 0 0
\(81\) 5.25743 + 3.37874i 0.584159 + 0.375416i
\(82\) 0 0
\(83\) −1.80477 0.529927i −0.198099 0.0581671i 0.181178 0.983450i \(-0.442009\pi\)
−0.379277 + 0.925283i \(0.623827\pi\)
\(84\) 0 0
\(85\) 3.61801 + 4.17540i 0.392428 + 0.452886i
\(86\) 0 0
\(87\) −0.318972 + 0.0936587i −0.0341974 + 0.0100413i
\(88\) 0 0
\(89\) −1.01143 + 7.03466i −0.107212 + 0.745673i 0.863313 + 0.504669i \(0.168386\pi\)
−0.970524 + 0.241003i \(0.922524\pi\)
\(90\) 0 0
\(91\) −16.0609 −1.68364
\(92\) 0 0
\(93\) 1.66712 0.172872
\(94\) 0 0
\(95\) −0.0945881 + 0.657875i −0.00970453 + 0.0674965i
\(96\) 0 0
\(97\) 10.2886 3.02100i 1.04465 0.306736i 0.285994 0.958231i \(-0.407676\pi\)
0.758652 + 0.651496i \(0.225858\pi\)
\(98\) 0 0
\(99\) −3.19671 3.68920i −0.321282 0.370779i
\(100\) 0 0
\(101\) 18.5598 + 5.44964i 1.84676 + 0.542259i 0.999946 + 0.0103769i \(0.00330312\pi\)
0.846818 + 0.531882i \(0.178515\pi\)
\(102\) 0 0
\(103\) 2.75222 + 1.76875i 0.271185 + 0.174280i 0.669164 0.743114i \(-0.266652\pi\)
−0.397980 + 0.917394i \(0.630289\pi\)
\(104\) 0 0
\(105\) −1.67838 + 1.93696i −0.163793 + 0.189027i
\(106\) 0 0
\(107\) 1.98679 + 13.8184i 0.192070 + 1.33588i 0.826518 + 0.562911i \(0.190318\pi\)
−0.634448 + 0.772966i \(0.718772\pi\)
\(108\) 0 0
\(109\) 1.68546 + 3.69065i 0.161438 + 0.353500i 0.973014 0.230747i \(-0.0741171\pi\)
−0.811576 + 0.584247i \(0.801390\pi\)
\(110\) 0 0
\(111\) −2.19625 + 4.80911i −0.208458 + 0.456460i
\(112\) 0 0
\(113\) −2.13239 + 1.37040i −0.200599 + 0.128917i −0.637084 0.770795i \(-0.719859\pi\)
0.436485 + 0.899711i \(0.356223\pi\)
\(114\) 0 0
\(115\) 0.745660 + 4.73751i 0.0695331 + 0.441775i
\(116\) 0 0
\(117\) 7.96118 5.11634i 0.736012 0.473006i
\(118\) 0 0
\(119\) −10.4516 + 22.8857i −0.958092 + 2.09793i
\(120\) 0 0
\(121\) −3.19466 6.99534i −0.290424 0.635940i
\(122\) 0 0
\(123\) −0.672722 4.67888i −0.0606573 0.421881i
\(124\) 0 0
\(125\) −0.654861 + 0.755750i −0.0585725 + 0.0675963i
\(126\) 0 0
\(127\) −17.5453 11.2757i −1.55690 1.00056i −0.983422 0.181334i \(-0.941958\pi\)
−0.573475 0.819223i \(-0.694405\pi\)
\(128\) 0 0
\(129\) 3.53770 + 1.03876i 0.311477 + 0.0914579i
\(130\) 0 0
\(131\) 7.35032 + 8.48272i 0.642200 + 0.741139i 0.979762 0.200165i \(-0.0641477\pi\)
−0.337562 + 0.941303i \(0.609602\pi\)
\(132\) 0 0
\(133\) −2.90406 + 0.852710i −0.251814 + 0.0739394i
\(134\) 0 0
\(135\) 0.455208 3.16604i 0.0391781 0.272489i
\(136\) 0 0
\(137\) −2.68463 −0.229364 −0.114682 0.993402i \(-0.536585\pi\)
−0.114682 + 0.993402i \(0.536585\pi\)
\(138\) 0 0
\(139\) −0.337259 −0.0286059 −0.0143030 0.999898i \(-0.504553\pi\)
−0.0143030 + 0.999898i \(0.504553\pi\)
\(140\) 0 0
\(141\) −0.0161627 + 0.112414i −0.00136114 + 0.00946697i
\(142\) 0 0
\(143\) −6.15641 + 1.80768i −0.514825 + 0.151166i
\(144\) 0 0
\(145\) −0.386809 0.446401i −0.0321227 0.0370716i
\(146\) 0 0
\(147\) −7.41845 2.17825i −0.611863 0.179659i
\(148\) 0 0
\(149\) 12.3544 + 7.93972i 1.01212 + 0.650447i 0.937940 0.346798i \(-0.112731\pi\)
0.0741758 + 0.997245i \(0.476367\pi\)
\(150\) 0 0
\(151\) 11.4935 13.2642i 0.935324 1.07942i −0.0613649 0.998115i \(-0.519545\pi\)
0.996689 0.0813064i \(-0.0259092\pi\)
\(152\) 0 0
\(153\) −2.10975 14.6736i −0.170563 1.18629i
\(154\) 0 0
\(155\) 1.23051 + 2.69444i 0.0988369 + 0.216423i
\(156\) 0 0
\(157\) 4.30629 9.42946i 0.343679 0.752553i −0.656319 0.754484i \(-0.727887\pi\)
0.999998 + 0.00193093i \(0.000614634\pi\)
\(158\) 0 0
\(159\) 1.00465 0.645652i 0.0796743 0.0512035i
\(160\) 0 0
\(161\) −18.2137 + 12.0509i −1.43544 + 0.949742i
\(162\) 0 0
\(163\) 5.95110 3.82454i 0.466126 0.299561i −0.286416 0.958105i \(-0.592464\pi\)
0.752542 + 0.658544i \(0.228828\pi\)
\(164\) 0 0
\(165\) −0.425344 + 0.931374i −0.0331130 + 0.0725073i
\(166\) 0 0
\(167\) −5.31458 11.6373i −0.411254 0.900521i −0.996004 0.0893075i \(-0.971535\pi\)
0.584750 0.811214i \(-0.301193\pi\)
\(168\) 0 0
\(169\) 0.0798549 + 0.555403i 0.00614268 + 0.0427233i
\(170\) 0 0
\(171\) 1.16787 1.34780i 0.0893094 0.103069i
\(172\) 0 0
\(173\) −10.6803 6.86378i −0.812004 0.521844i 0.0675084 0.997719i \(-0.478495\pi\)
−0.879513 + 0.475875i \(0.842131\pi\)
\(174\) 0 0
\(175\) −4.36938 1.28297i −0.330294 0.0969831i
\(176\) 0 0
\(177\) −2.06653 2.38490i −0.155330 0.179260i
\(178\) 0 0
\(179\) 15.2097 4.46596i 1.13682 0.333801i 0.341437 0.939905i \(-0.389086\pi\)
0.795386 + 0.606103i \(0.207268\pi\)
\(180\) 0 0
\(181\) 2.07418 14.4262i 0.154172 1.07229i −0.754956 0.655776i \(-0.772342\pi\)
0.909128 0.416517i \(-0.136749\pi\)
\(182\) 0 0
\(183\) 7.11742 0.526135
\(184\) 0 0
\(185\) −9.39367 −0.690636
\(186\) 0 0
\(187\) −1.43043 + 9.94883i −0.104603 + 0.727530i
\(188\) 0 0
\(189\) 13.9759 4.10369i 1.01660 0.298500i
\(190\) 0 0
\(191\) 12.6491 + 14.5979i 0.915260 + 1.05627i 0.998216 + 0.0597133i \(0.0190187\pi\)
−0.0829553 + 0.996553i \(0.526436\pi\)
\(192\) 0 0
\(193\) 23.1904 + 6.80932i 1.66928 + 0.490146i 0.973611 0.228214i \(-0.0732887\pi\)
0.695672 + 0.718360i \(0.255107\pi\)
\(194\) 0 0
\(195\) −1.66986 1.07316i −0.119581 0.0768503i
\(196\) 0 0
\(197\) −11.2417 + 12.9736i −0.800938 + 0.924331i −0.998432 0.0559727i \(-0.982174\pi\)
0.197495 + 0.980304i \(0.436719\pi\)
\(198\) 0 0
\(199\) 3.18766 + 22.1707i 0.225967 + 1.57164i 0.714844 + 0.699284i \(0.246498\pi\)
−0.488876 + 0.872353i \(0.662593\pi\)
\(200\) 0 0
\(201\) −1.02599 2.24661i −0.0723680 0.158464i
\(202\) 0 0
\(203\) 1.11740 2.44676i 0.0784259 0.171729i
\(204\) 0 0
\(205\) 7.06560 4.54078i 0.493483 0.317142i
\(206\) 0 0
\(207\) 5.18940 11.7756i 0.360688 0.818463i
\(208\) 0 0
\(209\) −1.01720 + 0.653717i −0.0703615 + 0.0452186i
\(210\) 0 0
\(211\) 7.14518 15.6458i 0.491894 1.07710i −0.487125 0.873332i \(-0.661954\pi\)
0.979020 0.203766i \(-0.0653182\pi\)
\(212\) 0 0
\(213\) −0.498723 1.09205i −0.0341719 0.0748261i
\(214\) 0 0
\(215\) 0.932321 + 6.48444i 0.0635838 + 0.442235i
\(216\) 0 0
\(217\) −8.83344 + 10.1943i −0.599653 + 0.692036i
\(218\) 0 0
\(219\) −4.44862 2.85895i −0.300610 0.193190i
\(220\) 0 0
\(221\) −18.6962 5.48969i −1.25764 0.369277i
\(222\) 0 0
\(223\) −7.61939 8.79325i −0.510232 0.588840i 0.440926 0.897544i \(-0.354650\pi\)
−0.951158 + 0.308704i \(0.900105\pi\)
\(224\) 0 0
\(225\) 2.57455 0.755957i 0.171637 0.0503971i
\(226\) 0 0
\(227\) 4.02109 27.9673i 0.266889 1.85626i −0.210539 0.977586i \(-0.567522\pi\)
0.477428 0.878671i \(-0.341569\pi\)
\(228\) 0 0
\(229\) −2.55126 −0.168592 −0.0842959 0.996441i \(-0.526864\pi\)
−0.0842959 + 0.996441i \(0.526864\pi\)
\(230\) 0 0
\(231\) −4.66269 −0.306782
\(232\) 0 0
\(233\) 3.03889 21.1360i 0.199084 1.38466i −0.607864 0.794041i \(-0.707974\pi\)
0.806949 0.590622i \(-0.201117\pi\)
\(234\) 0 0
\(235\) −0.193616 + 0.0568509i −0.0126301 + 0.00370854i
\(236\) 0 0
\(237\) 0.595947 + 0.687759i 0.0387109 + 0.0446748i
\(238\) 0 0
\(239\) 5.00997 + 1.47106i 0.324068 + 0.0951550i 0.439720 0.898135i \(-0.355078\pi\)
−0.115652 + 0.993290i \(0.536896\pi\)
\(240\) 0 0
\(241\) −22.4875 14.4518i −1.44854 0.930923i −0.999296 0.0375167i \(-0.988055\pi\)
−0.449249 0.893407i \(-0.648308\pi\)
\(242\) 0 0
\(243\) −8.58725 + 9.91022i −0.550873 + 0.635741i
\(244\) 0 0
\(245\) −1.95505 13.5977i −0.124904 0.868723i
\(246\) 0 0
\(247\) −0.973776 2.13227i −0.0619599 0.135673i
\(248\) 0 0
\(249\) 0.439769 0.962960i 0.0278692 0.0610251i
\(250\) 0 0
\(251\) 21.1883 13.6169i 1.33739 0.859491i 0.340655 0.940188i \(-0.389351\pi\)
0.996739 + 0.0806977i \(0.0257148\pi\)
\(252\) 0 0
\(253\) −5.62527 + 6.66930i −0.353658 + 0.419295i
\(254\) 0 0
\(255\) −2.61584 + 1.68110i −0.163810 + 0.105274i
\(256\) 0 0
\(257\) 0.687842 1.50616i 0.0429064 0.0939519i −0.886965 0.461837i \(-0.847191\pi\)
0.929871 + 0.367885i \(0.119918\pi\)
\(258\) 0 0
\(259\) −17.7703 38.9116i −1.10419 2.41785i
\(260\) 0 0
\(261\) 0.225558 + 1.56879i 0.0139617 + 0.0971055i
\(262\) 0 0
\(263\) −19.1207 + 22.0665i −1.17903 + 1.36068i −0.260432 + 0.965492i \(0.583865\pi\)
−0.918601 + 0.395185i \(0.870680\pi\)
\(264\) 0 0
\(265\) 1.78506 + 1.14719i 0.109655 + 0.0704713i
\(266\) 0 0
\(267\) −3.83788 1.12690i −0.234875 0.0689654i
\(268\) 0 0
\(269\) −12.5900 14.5296i −0.767626 0.885888i 0.228525 0.973538i \(-0.426610\pi\)
−0.996151 + 0.0876501i \(0.972064\pi\)
\(270\) 0 0
\(271\) 25.0272 7.34864i 1.52029 0.446398i 0.588229 0.808694i \(-0.299825\pi\)
0.932063 + 0.362296i \(0.118007\pi\)
\(272\) 0 0
\(273\) 1.28642 8.94724i 0.0778576 0.541512i
\(274\) 0 0
\(275\) −1.81926 −0.109706
\(276\) 0 0
\(277\) 32.1051 1.92901 0.964504 0.264067i \(-0.0850641\pi\)
0.964504 + 0.264067i \(0.0850641\pi\)
\(278\) 0 0
\(279\) 1.13113 7.86719i 0.0677190 0.470996i
\(280\) 0 0
\(281\) −1.43237 + 0.420582i −0.0854481 + 0.0250898i −0.324177 0.945996i \(-0.605087\pi\)
0.238729 + 0.971086i \(0.423269\pi\)
\(282\) 0 0
\(283\) 2.75024 + 3.17395i 0.163485 + 0.188672i 0.831581 0.555403i \(-0.187436\pi\)
−0.668096 + 0.744075i \(0.732891\pi\)
\(284\) 0 0
\(285\) −0.358915 0.105387i −0.0212603 0.00624258i
\(286\) 0 0
\(287\) 32.1756 + 20.6780i 1.89927 + 1.22059i
\(288\) 0 0
\(289\) −8.85630 + 10.2207i −0.520959 + 0.601219i
\(290\) 0 0
\(291\) 0.858869 + 5.97357i 0.0503478 + 0.350177i
\(292\) 0 0
\(293\) −2.14175 4.68979i −0.125123 0.273980i 0.836696 0.547667i \(-0.184484\pi\)
−0.961819 + 0.273687i \(0.911757\pi\)
\(294\) 0 0
\(295\) 2.32922 5.10029i 0.135613 0.296950i
\(296\) 0 0
\(297\) 4.89532 3.14603i 0.284055 0.182551i
\(298\) 0 0
\(299\) −11.2457 12.6344i −0.650358 0.730665i
\(300\) 0 0
\(301\) −25.0969 + 16.1288i −1.44656 + 0.929649i
\(302\) 0 0
\(303\) −4.52247 + 9.90284i −0.259809 + 0.568903i
\(304\) 0 0
\(305\) 5.25341 + 11.5034i 0.300810 + 0.658681i
\(306\) 0 0
\(307\) 3.95665 + 27.5191i 0.225818 + 1.57060i 0.715446 + 0.698668i \(0.246224\pi\)
−0.489628 + 0.871932i \(0.662867\pi\)
\(308\) 0 0
\(309\) −1.20578 + 1.39155i −0.0685946 + 0.0791624i
\(310\) 0 0
\(311\) −1.48547 0.954651i −0.0842330 0.0541333i 0.497846 0.867265i \(-0.334124\pi\)
−0.582079 + 0.813132i \(0.697761\pi\)
\(312\) 0 0
\(313\) −2.66727 0.783180i −0.150763 0.0442680i 0.205480 0.978661i \(-0.434124\pi\)
−0.356243 + 0.934393i \(0.615943\pi\)
\(314\) 0 0
\(315\) 8.00179 + 9.23456i 0.450850 + 0.520308i
\(316\) 0 0
\(317\) −1.61247 + 0.473465i −0.0905655 + 0.0265924i −0.326701 0.945128i \(-0.605937\pi\)
0.236136 + 0.971720i \(0.424119\pi\)
\(318\) 0 0
\(319\) 0.152930 1.06365i 0.00856243 0.0595530i
\(320\) 0 0
\(321\) −7.85714 −0.438543
\(322\) 0 0
\(323\) −3.67203 −0.204317
\(324\) 0 0
\(325\) 0.501927 3.49098i 0.0278419 0.193645i
\(326\) 0 0
\(327\) −2.19100 + 0.643335i −0.121163 + 0.0355765i
\(328\) 0 0
\(329\) −0.601765 0.694474i −0.0331764 0.0382876i
\(330\) 0 0
\(331\) 20.9443 + 6.14981i 1.15120 + 0.338024i 0.801009 0.598653i \(-0.204297\pi\)
0.350195 + 0.936677i \(0.386115\pi\)
\(332\) 0 0
\(333\) 21.2042 + 13.6271i 1.16198 + 0.746761i
\(334\) 0 0
\(335\) 2.87374 3.31648i 0.157009 0.181199i
\(336\) 0 0
\(337\) 1.51817 + 10.5591i 0.0827001 + 0.575192i 0.988469 + 0.151421i \(0.0483848\pi\)
−0.905769 + 0.423771i \(0.860706\pi\)
\(338\) 0 0
\(339\) −0.592633 1.29768i −0.0321874 0.0704806i
\(340\) 0 0
\(341\) −2.23862 + 4.90189i −0.121228 + 0.265452i
\(342\) 0 0
\(343\) 25.8109 16.5877i 1.39366 0.895651i
\(344\) 0 0
\(345\) −2.69891 + 0.0359368i −0.145305 + 0.00193477i
\(346\) 0 0
\(347\) 3.33689 2.14449i 0.179134 0.115122i −0.448001 0.894033i \(-0.647864\pi\)
0.627135 + 0.778911i \(0.284228\pi\)
\(348\) 0 0
\(349\) 8.61657 18.8677i 0.461235 1.00996i −0.525970 0.850503i \(-0.676298\pi\)
0.987204 0.159460i \(-0.0509752\pi\)
\(350\) 0 0
\(351\) 4.68633 + 10.2616i 0.250138 + 0.547725i
\(352\) 0 0
\(353\) 0.934309 + 6.49826i 0.0497283 + 0.345868i 0.999462 + 0.0328079i \(0.0104449\pi\)
−0.949733 + 0.313060i \(0.898646\pi\)
\(354\) 0 0
\(355\) 1.39689 1.61210i 0.0741393 0.0855613i
\(356\) 0 0
\(357\) −11.9121 7.65545i −0.630456 0.405170i
\(358\) 0 0
\(359\) −25.5840 7.51214i −1.35027 0.396475i −0.474948 0.880014i \(-0.657533\pi\)
−0.875323 + 0.483539i \(0.839351\pi\)
\(360\) 0 0
\(361\) 12.1531 + 14.0254i 0.639635 + 0.738179i
\(362\) 0 0
\(363\) 4.15287 1.21939i 0.217969 0.0640015i
\(364\) 0 0
\(365\) 1.33717 9.30019i 0.0699904 0.486794i
\(366\) 0 0
\(367\) −23.3278 −1.21770 −0.608851 0.793285i \(-0.708369\pi\)
−0.608851 + 0.793285i \(0.708369\pi\)
\(368\) 0 0
\(369\) −22.5363 −1.17319
\(370\) 0 0
\(371\) −1.37516 + 9.56448i −0.0713950 + 0.496563i
\(372\) 0 0
\(373\) −2.39654 + 0.703687i −0.124088 + 0.0364355i −0.343187 0.939267i \(-0.611506\pi\)
0.219099 + 0.975703i \(0.429688\pi\)
\(374\) 0 0
\(375\) −0.368564 0.425345i −0.0190325 0.0219647i
\(376\) 0 0
\(377\) 1.99885 + 0.586915i 0.102946 + 0.0302277i
\(378\) 0 0
\(379\) 22.8199 + 14.6655i 1.17218 + 0.753316i 0.973933 0.226836i \(-0.0728382\pi\)
0.198249 + 0.980152i \(0.436475\pi\)
\(380\) 0 0
\(381\) 7.68683 8.87107i 0.393808 0.454479i
\(382\) 0 0
\(383\) 3.20873 + 22.3172i 0.163958 + 1.14035i 0.891080 + 0.453846i \(0.149948\pi\)
−0.727122 + 0.686509i \(0.759142\pi\)
\(384\) 0 0
\(385\) −3.44156 7.53596i −0.175398 0.384068i
\(386\) 0 0
\(387\) 7.30226 15.9897i 0.371195 0.812804i
\(388\) 0 0
\(389\) 30.5671 19.6443i 1.54981 0.996004i 0.564463 0.825458i \(-0.309083\pi\)
0.985350 0.170546i \(-0.0545531\pi\)
\(390\) 0 0
\(391\) −25.3213 + 7.80268i −1.28055 + 0.394598i
\(392\) 0 0
\(393\) −5.31432 + 3.41531i −0.268072 + 0.172279i
\(394\) 0 0
\(395\) −0.671703 + 1.47082i −0.0337970 + 0.0740052i
\(396\) 0 0
\(397\) −4.95528 10.8505i −0.248698 0.544573i 0.743574 0.668654i \(-0.233129\pi\)
−0.992272 + 0.124080i \(0.960402\pi\)
\(398\) 0 0
\(399\) −0.242425 1.68611i −0.0121364 0.0844109i
\(400\) 0 0
\(401\) −20.3756 + 23.5147i −1.01751 + 1.17427i −0.0329066 + 0.999458i \(0.510476\pi\)
−0.984602 + 0.174809i \(0.944069\pi\)
\(402\) 0 0
\(403\) −8.78861 5.64810i −0.437792 0.281352i
\(404\) 0 0
\(405\) −5.99637 1.76069i −0.297962 0.0874895i
\(406\) 0 0
\(407\) −11.1913 12.9154i −0.554730 0.640193i
\(408\) 0 0
\(409\) −8.90235 + 2.61397i −0.440193 + 0.129252i −0.494317 0.869282i \(-0.664582\pi\)
0.0541236 + 0.998534i \(0.482763\pi\)
\(410\) 0 0
\(411\) 0.215030 1.49556i 0.0106066 0.0737707i
\(412\) 0 0
\(413\) 25.5333 1.25641
\(414\) 0 0
\(415\) 1.88096 0.0923326
\(416\) 0 0
\(417\) 0.0270133 0.187881i 0.00132284 0.00920059i
\(418\) 0 0
\(419\) −26.8145 + 7.87345i −1.30997 + 0.384643i −0.860865 0.508834i \(-0.830077\pi\)
−0.449109 + 0.893477i \(0.648259\pi\)
\(420\) 0 0
\(421\) −7.13210 8.23088i −0.347597 0.401149i 0.554849 0.831951i \(-0.312776\pi\)
−0.902446 + 0.430802i \(0.858231\pi\)
\(422\) 0 0
\(423\) 0.519519 + 0.152545i 0.0252599 + 0.00741698i
\(424\) 0 0
\(425\) −4.64780 2.98696i −0.225451 0.144889i
\(426\) 0 0
\(427\) −37.7126 + 43.5227i −1.82504 + 2.10621i
\(428\) 0 0
\(429\) −0.513924 3.57442i −0.0248125 0.172575i
\(430\) 0 0
\(431\) 10.2348 + 22.4110i 0.492992 + 1.07950i 0.978684 + 0.205372i \(0.0658404\pi\)
−0.485692 + 0.874130i \(0.661432\pi\)
\(432\) 0 0
\(433\) −12.6015 + 27.5935i −0.605591 + 1.32606i 0.319959 + 0.947431i \(0.396331\pi\)
−0.925549 + 0.378627i \(0.876396\pi\)
\(434\) 0 0
\(435\) 0.279665 0.179730i 0.0134089 0.00861738i
\(436\) 0 0
\(437\) −2.70420 1.68744i −0.129360 0.0807211i
\(438\) 0 0
\(439\) 30.0948 19.3408i 1.43635 0.923084i 0.436621 0.899646i \(-0.356175\pi\)
0.999725 0.0234381i \(-0.00746126\pi\)
\(440\) 0 0
\(441\) −15.3126 + 33.5300i −0.729173 + 1.59667i
\(442\) 0 0
\(443\) 9.75929 + 21.3699i 0.463678 + 1.01531i 0.986634 + 0.162953i \(0.0521020\pi\)
−0.522956 + 0.852360i \(0.675171\pi\)
\(444\) 0 0
\(445\) −1.01143 7.03466i −0.0479465 0.333475i
\(446\) 0 0
\(447\) −5.41264 + 6.24651i −0.256009 + 0.295450i
\(448\) 0 0
\(449\) −6.64071 4.26773i −0.313395 0.201407i 0.374482 0.927234i \(-0.377821\pi\)
−0.687877 + 0.725828i \(0.741457\pi\)
\(450\) 0 0
\(451\) 14.6608 + 4.30481i 0.690352 + 0.202705i
\(452\) 0 0
\(453\) 6.46866 + 7.46523i 0.303924 + 0.350747i
\(454\) 0 0
\(455\) 15.4103 4.52487i 0.722445 0.212129i
\(456\) 0 0
\(457\) −1.52428 + 10.6016i −0.0713029 + 0.495923i 0.922608 + 0.385738i \(0.126053\pi\)
−0.993911 + 0.110184i \(0.964856\pi\)
\(458\) 0 0
\(459\) 17.6718 0.824848
\(460\) 0 0
\(461\) −22.3297 −1.04000 −0.519999 0.854167i \(-0.674068\pi\)
−0.519999 + 0.854167i \(0.674068\pi\)
\(462\) 0 0
\(463\) −5.03246 + 35.0015i −0.233878 + 1.62666i 0.447189 + 0.894439i \(0.352425\pi\)
−0.681068 + 0.732221i \(0.738484\pi\)
\(464\) 0 0
\(465\) −1.59959 + 0.469681i −0.0741791 + 0.0217809i
\(466\) 0 0
\(467\) 4.67281 + 5.39271i 0.216232 + 0.249545i 0.853495 0.521102i \(-0.174479\pi\)
−0.637263 + 0.770647i \(0.719933\pi\)
\(468\) 0 0
\(469\) 19.1743 + 5.63008i 0.885386 + 0.259973i
\(470\) 0 0
\(471\) 4.90808 + 3.15423i 0.226152 + 0.145339i
\(472\) 0 0
\(473\) −7.80475 + 9.00716i −0.358863 + 0.414150i
\(474\) 0 0
\(475\) −0.0945881 0.657875i −0.00434000 0.0301854i
\(476\) 0 0
\(477\) −2.36520 5.17907i −0.108295 0.237133i
\(478\) 0 0
\(479\) −8.20741 + 17.9717i −0.375006 + 0.821149i 0.624198 + 0.781266i \(0.285426\pi\)
−0.999204 + 0.0398831i \(0.987301\pi\)
\(480\) 0 0
\(481\) 27.8710 17.9116i 1.27081 0.816699i
\(482\) 0 0
\(483\) −5.25449 11.1118i −0.239088 0.505604i
\(484\) 0 0
\(485\) −9.02070 + 5.79725i −0.409609 + 0.263240i
\(486\) 0 0
\(487\) 7.20195 15.7701i 0.326352 0.714610i −0.673343 0.739330i \(-0.735142\pi\)
0.999694 + 0.0247202i \(0.00786948\pi\)
\(488\) 0 0
\(489\) 1.65393 + 3.62159i 0.0747931 + 0.163774i
\(490\) 0 0
\(491\) 2.14963 + 14.9510i 0.0970113 + 0.674729i 0.979060 + 0.203571i \(0.0652547\pi\)
−0.882049 + 0.471158i \(0.843836\pi\)
\(492\) 0 0
\(493\) 2.13706 2.46630i 0.0962483 0.111077i
\(494\) 0 0
\(495\) 4.10659 + 2.63915i 0.184578 + 0.118621i
\(496\) 0 0
\(497\) 9.32038 + 2.73671i 0.418076 + 0.122758i
\(498\) 0 0
\(499\) −0.706792 0.815681i −0.0316404 0.0365149i 0.739709 0.672927i \(-0.234963\pi\)
−0.771349 + 0.636412i \(0.780418\pi\)
\(500\) 0 0
\(501\) 6.90863 2.02856i 0.308655 0.0906292i
\(502\) 0 0
\(503\) 0.717503 4.99034i 0.0319919 0.222508i −0.967553 0.252667i \(-0.918692\pi\)
0.999545 + 0.0301588i \(0.00960131\pi\)
\(504\) 0 0
\(505\) −19.3433 −0.860765
\(506\) 0 0
\(507\) −0.315802 −0.0140253
\(508\) 0 0
\(509\) −3.88031 + 26.9882i −0.171992 + 1.19623i 0.702677 + 0.711509i \(0.251988\pi\)
−0.874669 + 0.484721i \(0.838921\pi\)
\(510\) 0 0
\(511\) 41.0539 12.0545i 1.81612 0.533261i
\(512\) 0 0
\(513\) 1.39218 + 1.60666i 0.0614662 + 0.0709357i
\(514\) 0 0
\(515\) −3.13905 0.921709i −0.138323 0.0406153i
\(516\) 0 0
\(517\) −0.308832 0.198474i −0.0135824 0.00872888i
\(518\) 0 0
\(519\) 4.67915 5.40003i 0.205392 0.237035i
\(520\) 0 0
\(521\) −5.63797 39.2129i −0.247004 1.71795i −0.615344 0.788259i \(-0.710983\pi\)
0.368340 0.929691i \(-0.379926\pi\)
\(522\) 0 0
\(523\) 0.925255 + 2.02603i 0.0404586 + 0.0885919i 0.928782 0.370626i \(-0.120857\pi\)
−0.888324 + 0.459218i \(0.848130\pi\)
\(524\) 0 0
\(525\) 1.06469 2.33135i 0.0464670 0.101748i
\(526\) 0 0
\(527\) −13.7673 + 8.84773i −0.599715 + 0.385413i
\(528\) 0 0
\(529\) −22.2330 5.88996i −0.966654 0.256085i
\(530\) 0 0
\(531\) −12.6566 + 8.13388i −0.549248 + 0.352980i
\(532\) 0 0
\(533\) −12.3054 + 26.9450i −0.533005 + 1.16712i
\(534\) 0 0
\(535\) −5.79941 12.6989i −0.250730 0.549023i
\(536\) 0 0
\(537\) 1.26967 + 8.83075i 0.0547903 + 0.381075i
\(538\) 0 0
\(539\) 16.3663 18.8878i 0.704948 0.813553i
\(540\) 0 0
\(541\) −21.3697 13.7335i −0.918757 0.590449i −0.00646031 0.999979i \(-0.502056\pi\)
−0.912297 + 0.409530i \(0.865693\pi\)
\(542\) 0 0
\(543\) 7.87047 + 2.31098i 0.337754 + 0.0991736i
\(544\) 0 0
\(545\) −2.65697 3.06630i −0.113812 0.131346i
\(546\) 0 0
\(547\) 3.96789 1.16508i 0.169655 0.0498151i −0.195802 0.980643i \(-0.562731\pi\)
0.365457 + 0.930828i \(0.380913\pi\)
\(548\) 0 0
\(549\) 4.82914 33.5874i 0.206103 1.43347i
\(550\) 0 0
\(551\) 0.392585 0.0167247
\(552\) 0 0
\(553\) −7.36331 −0.313120
\(554\) 0 0
\(555\) 0.752400 5.23306i 0.0319376 0.222131i
\(556\) 0 0
\(557\) 18.0076 5.28750i 0.763005 0.224038i 0.122997 0.992407i \(-0.460749\pi\)
0.640008 + 0.768369i \(0.278931\pi\)
\(558\) 0 0
\(559\) −15.1306 17.4616i −0.639955 0.738547i
\(560\) 0 0
\(561\) −5.42776 1.59373i −0.229160 0.0672875i
\(562\) 0 0
\(563\) 31.3641 + 20.1565i 1.32184 + 0.849493i 0.995407 0.0957284i \(-0.0305180\pi\)
0.326430 + 0.945222i \(0.394154\pi\)
\(564\) 0 0
\(565\) 1.65993 1.91566i 0.0698337 0.0805923i
\(566\) 0 0
\(567\) −4.05019 28.1697i −0.170092 1.18301i
\(568\) 0 0
\(569\) −14.0687 30.8062i −0.589791 1.29146i −0.935568 0.353145i \(-0.885112\pi\)
0.345778 0.938316i \(-0.387615\pi\)
\(570\) 0 0
\(571\) −9.51477 + 20.8344i −0.398181 + 0.871894i 0.599271 + 0.800546i \(0.295457\pi\)
−0.997452 + 0.0713477i \(0.977270\pi\)
\(572\) 0 0
\(573\) −9.14540 + 5.87739i −0.382055 + 0.245532i
\(574\) 0 0
\(575\) −2.05017 4.33553i −0.0854978 0.180804i
\(576\) 0 0
\(577\) 6.54447 4.20587i 0.272450 0.175093i −0.397281 0.917697i \(-0.630046\pi\)
0.669730 + 0.742604i \(0.266410\pi\)
\(578\) 0 0
\(579\) −5.65083 + 12.3736i −0.234841 + 0.514229i
\(580\) 0 0
\(581\) 3.55828 + 7.79154i 0.147622 + 0.323247i
\(582\) 0 0
\(583\) 0.549378 + 3.82101i 0.0227529 + 0.158250i
\(584\) 0 0
\(585\) −6.19726 + 7.15202i −0.256225 + 0.295700i
\(586\) 0 0
\(587\) 1.95601 + 1.25705i 0.0807334 + 0.0518842i 0.580385 0.814342i \(-0.302902\pi\)
−0.499651 + 0.866227i \(0.666539\pi\)
\(588\) 0 0
\(589\) −1.88899 0.554659i −0.0778347 0.0228543i
\(590\) 0 0
\(591\) −6.32696 7.30170i −0.260256 0.300352i
\(592\) 0 0
\(593\) 2.47864 0.727794i 0.101785 0.0298869i −0.230443 0.973086i \(-0.574018\pi\)
0.332229 + 0.943199i \(0.392199\pi\)
\(594\) 0 0
\(595\) 3.58054 24.9032i 0.146788 1.02093i
\(596\) 0 0
\(597\) −12.6062 −0.515939
\(598\) 0 0
\(599\) 42.1037 1.72031 0.860154 0.510034i \(-0.170367\pi\)
0.860154 + 0.510034i \(0.170367\pi\)
\(600\) 0 0
\(601\) 0.583040 4.05513i 0.0237827 0.165412i −0.974469 0.224523i \(-0.927918\pi\)
0.998251 + 0.0591111i \(0.0188266\pi\)
\(602\) 0 0
\(603\) −11.2980 + 3.31739i −0.460089 + 0.135094i
\(604\) 0 0
\(605\) 5.03607 + 5.81194i 0.204745 + 0.236289i
\(606\) 0 0
\(607\) −0.00235333 0.000691000i −9.55187e−5 2.80468e-5i 0.281685 0.959507i \(-0.409107\pi\)
−0.281780 + 0.959479i \(0.590925\pi\)
\(608\) 0 0
\(609\) 1.27355 + 0.818461i 0.0516068 + 0.0331657i
\(610\) 0 0
\(611\) 0.466058 0.537859i 0.0188547 0.0217595i
\(612\) 0 0
\(613\) −3.28902 22.8756i −0.132842 0.923939i −0.941824 0.336105i \(-0.890890\pi\)
0.808982 0.587833i \(-0.200019\pi\)
\(614\) 0 0
\(615\) 1.96367 + 4.29983i 0.0791827 + 0.173386i
\(616\) 0 0
\(617\) 7.61888 16.6830i 0.306725 0.671633i −0.692012 0.721886i \(-0.743275\pi\)
0.998737 + 0.0502528i \(0.0160027\pi\)
\(618\) 0 0
\(619\) −22.9352 + 14.7396i −0.921846 + 0.592434i −0.913193 0.407528i \(-0.866391\pi\)
−0.00865299 + 0.999963i \(0.502754\pi\)
\(620\) 0 0
\(621\) 13.0141 + 8.12085i 0.522236 + 0.325878i
\(622\) 0 0
\(623\) 27.2265 17.4974i 1.09081 0.701018i
\(624\) 0 0
\(625\) 0.415415 0.909632i 0.0166166 0.0363853i
\(626\) 0 0
\(627\) −0.282701 0.619028i −0.0112900 0.0247216i
\(628\) 0 0
\(629\) −7.38594 51.3703i −0.294497 2.04827i
\(630\) 0 0
\(631\) 1.47107 1.69771i 0.0585626 0.0675848i −0.725712 0.687998i \(-0.758490\pi\)
0.784275 + 0.620413i \(0.213035\pi\)
\(632\) 0 0
\(633\) 8.14369 + 5.23363i 0.323683 + 0.208018i
\(634\) 0 0
\(635\) 20.0114 + 5.87587i 0.794127 + 0.233177i
\(636\) 0 0
\(637\) 31.7283 + 36.6165i 1.25712 + 1.45080i
\(638\) 0 0
\(639\) −5.49181 + 1.61254i −0.217252 + 0.0637911i
\(640\) 0 0
\(641\) 4.62591 32.1739i 0.182712 1.27079i −0.667602 0.744518i \(-0.732679\pi\)
0.850315 0.526275i \(-0.176412\pi\)
\(642\) 0 0
\(643\) −33.5736 −1.32401 −0.662006 0.749498i \(-0.730295\pi\)
−0.662006 + 0.749498i \(0.730295\pi\)
\(644\) 0 0
\(645\) −3.68705 −0.145177
\(646\) 0 0
\(647\) −0.713613 + 4.96329i −0.0280550 + 0.195127i −0.999029 0.0440583i \(-0.985971\pi\)
0.970974 + 0.239185i \(0.0768803\pi\)
\(648\) 0 0
\(649\) 9.78736 2.87383i 0.384187 0.112808i
\(650\) 0 0
\(651\) −4.97157 5.73749i −0.194851 0.224870i
\(652\) 0 0
\(653\) 23.4184 + 6.87626i 0.916433 + 0.269089i 0.705746 0.708465i \(-0.250612\pi\)
0.210687 + 0.977554i \(0.432430\pi\)
\(654\) 0 0
\(655\) −9.44244 6.06829i −0.368947 0.237108i
\(656\) 0 0
\(657\) −16.5099 + 19.0534i −0.644111 + 0.743344i
\(658\) 0 0
\(659\) −2.27247 15.8054i −0.0885230 0.615691i −0.984994 0.172589i \(-0.944787\pi\)
0.896471 0.443102i \(-0.146122\pi\)
\(660\) 0 0
\(661\) 8.07431 + 17.6803i 0.314054 + 0.687683i 0.999169 0.0407518i \(-0.0129753\pi\)
−0.685115 + 0.728435i \(0.740248\pi\)
\(662\) 0 0
\(663\) 4.55572 9.97563i 0.176929 0.387421i
\(664\) 0 0
\(665\) 2.54619 1.63634i 0.0987371 0.0634545i
\(666\) 0 0
\(667\) 2.70716 0.834201i 0.104822 0.0323004i
\(668\) 0 0
\(669\) 5.50886 3.54033i 0.212985 0.136877i
\(670\) 0 0
\(671\) −9.55733 + 20.9276i −0.368956 + 0.807902i
\(672\) 0 0
\(673\) −17.4626 38.2379i −0.673136 1.47396i −0.869756 0.493482i \(-0.835724\pi\)
0.196621 0.980480i \(-0.437003\pi\)
\(674\) 0 0
\(675\) 0.455208 + 3.16604i 0.0175210 + 0.121861i
\(676\) 0 0
\(677\) 4.32917 4.99613i 0.166383 0.192017i −0.666435 0.745563i \(-0.732180\pi\)
0.832818 + 0.553547i \(0.186726\pi\)
\(678\) 0 0
\(679\) −41.0789 26.3998i −1.57646 1.01313i
\(680\) 0 0
\(681\) 15.2581 + 4.48017i 0.584690 + 0.171681i
\(682\) 0 0
\(683\) 12.6311 + 14.5770i 0.483314 + 0.557774i 0.944067 0.329755i \(-0.106966\pi\)
−0.460753 + 0.887528i \(0.652421\pi\)
\(684\) 0 0
\(685\) 2.57589 0.756348i 0.0984195 0.0288986i
\(686\) 0 0
\(687\) 0.204347 1.42126i 0.00779632 0.0542246i
\(688\) 0 0
\(689\) −7.48371 −0.285107
\(690\) 0 0
\(691\) 10.1722 0.386970 0.193485 0.981103i \(-0.438021\pi\)
0.193485 + 0.981103i \(0.438021\pi\)
\(692\) 0 0
\(693\) −3.16361 + 22.0034i −0.120176 + 0.835840i
\(694\) 0 0
\(695\) 0.323597 0.0950168i 0.0122747 0.00360419i
\(696\) 0 0
\(697\) 30.3872 + 35.0687i 1.15100 + 1.32832i
\(698\) 0 0
\(699\) 11.5311 + 3.38583i 0.436146 + 0.128064i
\(700\) 0 0
\(701\) 2.57505 + 1.65489i 0.0972583 + 0.0625041i 0.588366 0.808595i \(-0.299771\pi\)
−0.491108 + 0.871099i \(0.663408\pi\)
\(702\) 0 0
\(703\) 4.08856 4.71845i 0.154203 0.177960i
\(704\) 0 0
\(705\) −0.0161627 0.112414i −0.000608722 0.00423376i
\(706\) 0 0
\(707\) −36.5924 80.1262i −1.37620 3.01345i
\(708\) 0 0
\(709\) −3.76120 + 8.23589i −0.141255 + 0.309305i −0.967016 0.254714i \(-0.918019\pi\)
0.825761 + 0.564020i \(0.190746\pi\)
\(710\) 0 0
\(711\) 3.64991 2.34565i 0.136882 0.0879689i
\(712\) 0 0
\(713\) −14.2046 + 0.189138i −0.531965 + 0.00708327i
\(714\) 0 0
\(715\) 5.39775 3.46892i 0.201864 0.129730i
\(716\) 0 0
\(717\) −1.22079 + 2.67315i −0.0455911 + 0.0998305i
\(718\) 0 0
\(719\) −9.79675 21.4519i −0.365357 0.800021i −0.999638 0.0269178i \(-0.991431\pi\)
0.634280 0.773103i \(-0.281296\pi\)
\(720\) 0 0
\(721\) −2.12024 14.7466i −0.0789619 0.549192i
\(722\) 0 0
\(723\) 9.85204 11.3699i 0.366401 0.422849i
\(724\) 0 0
\(725\) 0.496906 + 0.319342i 0.0184546 + 0.0118601i
\(726\) 0 0
\(727\) 26.7171 + 7.84485i 0.990882 + 0.290949i 0.736709 0.676210i \(-0.236379\pi\)
0.254173 + 0.967159i \(0.418197\pi\)
\(728\) 0 0
\(729\) 7.44468 + 8.59162i 0.275729 + 0.318208i
\(730\) 0 0
\(731\) −34.7278 + 10.1970i −1.28446 + 0.377150i
\(732\) 0 0
\(733\) −3.84269 + 26.7265i −0.141933 + 0.987166i 0.787009 + 0.616941i \(0.211628\pi\)
−0.928942 + 0.370225i \(0.879281\pi\)
\(734\) 0 0
\(735\) 7.73163 0.285186
\(736\) 0 0
\(737\) 7.98351 0.294076
\(738\) 0 0
\(739\) −3.35011 + 23.3005i −0.123236 + 0.857123i 0.830616 + 0.556845i \(0.187988\pi\)
−0.953852 + 0.300278i \(0.902921\pi\)
\(740\) 0 0
\(741\) 1.26585 0.371687i 0.0465022 0.0136543i
\(742\) 0 0
\(743\) −29.9064 34.5138i −1.09716 1.26619i −0.961313 0.275460i \(-0.911170\pi\)
−0.135847 0.990730i \(-0.543376\pi\)
\(744\) 0 0
\(745\) −14.0909 4.13746i −0.516250 0.151585i
\(746\) 0 0
\(747\) −4.24586 2.72865i −0.155348 0.0998361i
\(748\) 0 0
\(749\) 41.6321 48.0460i 1.52120 1.75556i
\(750\) 0 0
\(751\) −0.164132 1.14156i −0.00598927 0.0416563i 0.986608 0.163111i \(-0.0521530\pi\)
−0.992597 + 0.121455i \(0.961244\pi\)
\(752\) 0 0
\(753\) 5.88864 + 12.8943i 0.214594 + 0.469895i
\(754\) 0 0
\(755\) −7.29095 + 15.9649i −0.265345 + 0.581024i
\(756\) 0 0
\(757\) 0.0292610 0.0188049i 0.00106351 0.000683475i −0.540109 0.841595i \(-0.681617\pi\)
0.541172 + 0.840912i \(0.317981\pi\)
\(758\) 0 0
\(759\) −3.26479 3.66794i −0.118504 0.133138i
\(760\) 0 0
\(761\) 27.9854 17.9851i 1.01447 0.651960i 0.0759230 0.997114i \(-0.475810\pi\)
0.938546 + 0.345154i \(0.112173\pi\)
\(762\) 0 0
\(763\) 7.67533 16.8066i 0.277866 0.608441i
\(764\) 0 0
\(765\) 6.15832 + 13.4848i 0.222655 + 0.487546i
\(766\) 0 0
\(767\) 2.81430 + 19.5739i 0.101618 + 0.706771i
\(768\) 0 0
\(769\) −12.7498 + 14.7141i −0.459771 + 0.530604i −0.937538 0.347883i \(-0.886901\pi\)
0.477767 + 0.878486i \(0.341446\pi\)
\(770\) 0 0
\(771\) 0.783965 + 0.503824i 0.0282338 + 0.0181448i
\(772\) 0 0
\(773\) −43.2250 12.6920i −1.55470 0.456500i −0.612196 0.790706i \(-0.709714\pi\)
−0.942500 + 0.334206i \(0.891532\pi\)
\(774\) 0 0
\(775\) −1.93978 2.23862i −0.0696788 0.0804136i
\(776\) 0 0
\(777\) 23.1004 6.78288i 0.828721 0.243334i
\(778\) 0 0
\(779\) −0.794435 + 5.52542i −0.0284636 + 0.197969i
\(780\) 0 0
\(781\) 3.88068 0.138862
\(782\) 0 0
\(783\) −1.88933 −0.0675190
\(784\) 0 0
\(785\) −1.47527 + 10.2607i −0.0526546 + 0.366221i
\(786\) 0 0
\(787\) −3.91948 + 1.15086i −0.139714 + 0.0410238i −0.350842 0.936435i \(-0.614105\pi\)
0.211128 + 0.977458i \(0.432286\pi\)
\(788\) 0 0
\(789\) −10.7614 12.4193i −0.383115 0.442138i
\(790\) 0 0
\(791\) 11.0754 + 3.25204i 0.393796 + 0.115629i
\(792\) 0 0
\(793\) −37.5212 24.1134i −1.33242 0.856293i
\(794\) 0 0
\(795\) −0.782058 + 0.902543i −0.0277367 + 0.0320099i
\(796\)