Properties

Label 324.3.o.a.5.4
Level $324$
Weight $3$
Character 324.5
Analytic conductor $8.828$
Analytic rank $0$
Dimension $324$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.o (of order \(54\), degree \(18\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(324\)
Relative dimension: \(18\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 5.4
Character \(\chi\) \(=\) 324.5
Dual form 324.3.o.a.65.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.76434 - 1.16550i) q^{3} +(-0.148228 + 0.110352i) q^{5} +(5.09912 - 3.35374i) q^{7} +(6.28320 + 6.44371i) q^{9} +O(q^{10})\) \(q+(-2.76434 - 1.16550i) q^{3} +(-0.148228 + 0.110352i) q^{5} +(5.09912 - 3.35374i) q^{7} +(6.28320 + 6.44371i) q^{9} +(-1.69174 + 14.4737i) q^{11} +(-2.59671 - 8.67360i) q^{13} +(0.538369 - 0.132290i) q^{15} +(6.34459 + 1.11872i) q^{17} +(-4.95520 - 28.1023i) q^{19} +(-18.0045 + 3.32785i) q^{21} +(24.7802 - 37.6764i) q^{23} +(-7.16029 + 23.9170i) q^{25} +(-9.85875 - 25.1357i) q^{27} +(35.2456 - 33.2525i) q^{29} +(0.345056 - 5.92438i) q^{31} +(21.5457 - 38.0387i) q^{33} +(-0.385742 + 1.05982i) q^{35} +(59.7445 - 21.7452i) q^{37} +(-2.93093 + 27.0033i) q^{39} +(-9.46893 + 39.9526i) q^{41} +(-33.4930 - 77.6454i) q^{43} +(-1.64242 - 0.261777i) q^{45} +(-8.86308 + 0.516216i) q^{47} +(-4.65449 + 10.7903i) q^{49} +(-16.2348 - 10.4872i) q^{51} +(16.9526 + 9.78756i) q^{53} +(-1.34644 - 2.33210i) q^{55} +(-19.0555 + 83.4598i) q^{57} +(-1.86108 - 15.9226i) q^{59} +(-61.9122 - 31.0935i) q^{61} +(53.6493 + 11.7850i) q^{63} +(1.34205 + 0.999121i) q^{65} +(12.7093 - 13.4711i) q^{67} +(-112.413 + 75.2692i) q^{69} +(49.6251 - 59.1408i) q^{71} +(-51.1888 + 42.9525i) q^{73} +(47.6689 - 57.7695i) q^{75} +(39.9148 + 79.4769i) q^{77} +(95.3805 - 22.6056i) q^{79} +(-2.04282 + 80.9742i) q^{81} +(35.6277 + 150.325i) q^{83} +(-1.06390 + 0.534311i) q^{85} +(-136.187 + 50.8425i) q^{87} +(64.2127 + 76.5257i) q^{89} +(-42.3299 - 35.5190i) q^{91} +(-7.85874 + 15.9749i) q^{93} +(3.83564 + 3.61874i) q^{95} +(61.2573 - 82.2829i) q^{97} +(-103.894 + 80.0403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 324 q+O(q^{10}) \) Copy content Toggle raw display \( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{54}\right)\)

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
\(3\) −2.76434 1.16550i −0.921448 0.388501i
\(4\) 0 0
\(5\) −0.148228 + 0.110352i −0.0296456 + 0.0220704i −0.611879 0.790951i \(-0.709586\pi\)
0.582234 + 0.813021i \(0.302179\pi\)
\(6\) 0 0
\(7\) 5.09912 3.35374i 0.728445 0.479106i −0.130322 0.991472i \(-0.541601\pi\)
0.858767 + 0.512366i \(0.171231\pi\)
\(8\) 0 0
\(9\) 6.28320 + 6.44371i 0.698133 + 0.715968i
\(10\) 0 0
\(11\) −1.69174 + 14.4737i −0.153794 + 1.31579i 0.667209 + 0.744871i \(0.267489\pi\)
−0.821003 + 0.570924i \(0.806585\pi\)
\(12\) 0 0
\(13\) −2.59671 8.67360i −0.199747 0.667200i −0.997902 0.0647481i \(-0.979376\pi\)
0.798155 0.602452i \(-0.205810\pi\)
\(14\) 0 0
\(15\) 0.538369 0.132290i 0.0358913 0.00881932i
\(16\) 0 0
\(17\) 6.34459 + 1.11872i 0.373211 + 0.0658072i 0.357108 0.934063i \(-0.383763\pi\)
0.0161033 + 0.999870i \(0.494874\pi\)
\(18\) 0 0
\(19\) −4.95520 28.1023i −0.260800 1.47907i −0.780734 0.624863i \(-0.785155\pi\)
0.519935 0.854206i \(-0.325956\pi\)
\(20\) 0 0
\(21\) −18.0045 + 3.32785i −0.857358 + 0.158469i
\(22\) 0 0
\(23\) 24.7802 37.6764i 1.07740 1.63811i 0.373797 0.927510i \(-0.378056\pi\)
0.703602 0.710595i \(-0.251574\pi\)
\(24\) 0 0
\(25\) −7.16029 + 23.9170i −0.286411 + 0.956681i
\(26\) 0 0
\(27\) −9.85875 25.1357i −0.365139 0.930953i
\(28\) 0 0
\(29\) 35.2456 33.2525i 1.21537 1.14664i 0.230546 0.973061i \(-0.425949\pi\)
0.984820 0.173578i \(-0.0555329\pi\)
\(30\) 0 0
\(31\) 0.345056 5.92438i 0.0111308 0.191109i −0.988159 0.153432i \(-0.950967\pi\)
0.999290 0.0376766i \(-0.0119957\pi\)
\(32\) 0 0
\(33\) 21.5457 38.0387i 0.652901 1.15269i
\(34\) 0 0
\(35\) −0.385742 + 1.05982i −0.0110212 + 0.0302805i
\(36\) 0 0
\(37\) 59.7445 21.7452i 1.61472 0.587709i 0.632352 0.774681i \(-0.282090\pi\)
0.982365 + 0.186972i \(0.0598675\pi\)
\(38\) 0 0
\(39\) −2.93093 + 27.0033i −0.0751521 + 0.692392i
\(40\) 0 0
\(41\) −9.46893 + 39.9526i −0.230950 + 0.974453i 0.726800 + 0.686849i \(0.241007\pi\)
−0.957749 + 0.287604i \(0.907141\pi\)
\(42\) 0 0
\(43\) −33.4930 77.6454i −0.778906 1.80571i −0.556714 0.830704i \(-0.687938\pi\)
−0.222192 0.975003i \(-0.571321\pi\)
\(44\) 0 0
\(45\) −1.64242 0.261777i −0.0364983 0.00581727i
\(46\) 0 0
\(47\) −8.86308 + 0.516216i −0.188576 + 0.0109833i −0.152173 0.988354i \(-0.548627\pi\)
−0.0364032 + 0.999337i \(0.511590\pi\)
\(48\) 0 0
\(49\) −4.65449 + 10.7903i −0.0949897 + 0.220211i
\(50\) 0 0
\(51\) −16.2348 10.4872i −0.318329 0.205631i
\(52\) 0 0
\(53\) 16.9526 + 9.78756i 0.319860 + 0.184671i 0.651330 0.758795i \(-0.274211\pi\)
−0.331470 + 0.943466i \(0.607545\pi\)
\(54\) 0 0
\(55\) −1.34644 2.33210i −0.0244807 0.0424019i
\(56\) 0 0
\(57\) −19.0555 + 83.4598i −0.334307 + 1.46421i
\(58\) 0 0
\(59\) −1.86108 15.9226i −0.0315437 0.269874i −0.999802 0.0199203i \(-0.993659\pi\)
0.968258 0.249953i \(-0.0804153\pi\)
\(60\) 0 0
\(61\) −61.9122 31.0935i −1.01495 0.509729i −0.138065 0.990423i \(-0.544088\pi\)
−0.876888 + 0.480694i \(0.840385\pi\)
\(62\) 0 0
\(63\) 53.6493 + 11.7850i 0.851577 + 0.187064i
\(64\) 0 0
\(65\) 1.34205 + 0.999121i 0.0206470 + 0.0153711i
\(66\) 0 0
\(67\) 12.7093 13.4711i 0.189691 0.201061i −0.625548 0.780186i \(-0.715124\pi\)
0.815238 + 0.579125i \(0.196606\pi\)
\(68\) 0 0
\(69\) −112.413 + 75.2692i −1.62917 + 1.09086i
\(70\) 0 0
\(71\) 49.6251 59.1408i 0.698945 0.832970i −0.293462 0.955971i \(-0.594807\pi\)
0.992407 + 0.123001i \(0.0392519\pi\)
\(72\) 0 0
\(73\) −51.1888 + 42.9525i −0.701217 + 0.588391i −0.922120 0.386905i \(-0.873544\pi\)
0.220903 + 0.975296i \(0.429100\pi\)
\(74\) 0 0
\(75\) 47.6689 57.7695i 0.635585 0.770261i
\(76\) 0 0
\(77\) 39.9148 + 79.4769i 0.518374 + 1.03217i
\(78\) 0 0
\(79\) 95.3805 22.6056i 1.20735 0.286147i 0.422805 0.906221i \(-0.361046\pi\)
0.784543 + 0.620074i \(0.212898\pi\)
\(80\) 0 0
\(81\) −2.04282 + 80.9742i −0.0252200 + 0.999682i
\(82\) 0 0
\(83\) 35.6277 + 150.325i 0.429249 + 1.81114i 0.570653 + 0.821191i \(0.306690\pi\)
−0.141404 + 0.989952i \(0.545162\pi\)
\(84\) 0 0
\(85\) −1.06390 + 0.534311i −0.0125165 + 0.00628601i
\(86\) 0 0
\(87\) −136.187 + 50.8425i −1.56537 + 0.584397i
\(88\) 0 0
\(89\) 64.2127 + 76.5257i 0.721491 + 0.859840i 0.994775 0.102094i \(-0.0325541\pi\)
−0.273283 + 0.961934i \(0.588110\pi\)
\(90\) 0 0
\(91\) −42.3299 35.5190i −0.465164 0.390319i
\(92\) 0 0
\(93\) −7.85874 + 15.9749i −0.0845026 + 0.171773i
\(94\) 0 0
\(95\) 3.83564 + 3.61874i 0.0403752 + 0.0380920i
\(96\) 0 0
\(97\) 61.2573 82.2829i 0.631519 0.848277i −0.365055 0.930986i \(-0.618950\pi\)
0.996574 + 0.0827091i \(0.0263572\pi\)
\(98\) 0 0
\(99\) −103.894 + 80.0403i −1.04944 + 0.808488i
\(100\) 0 0
\(101\) −4.61707 + 9.19334i −0.0457135 + 0.0910231i −0.915330 0.402705i \(-0.868070\pi\)
0.869616 + 0.493728i \(0.164366\pi\)
\(102\) 0 0
\(103\) −125.490 + 14.6676i −1.21835 + 0.142404i −0.700867 0.713292i \(-0.747204\pi\)
−0.517479 + 0.855696i \(0.673129\pi\)
\(104\) 0 0
\(105\) 2.30154 2.48011i 0.0219195 0.0236201i
\(106\) 0 0
\(107\) 47.4116 27.3731i 0.443099 0.255823i −0.261812 0.965119i \(-0.584320\pi\)
0.704911 + 0.709295i \(0.250987\pi\)
\(108\) 0 0
\(109\) −12.8028 + 22.1750i −0.117456 + 0.203441i −0.918759 0.394819i \(-0.870807\pi\)
0.801303 + 0.598259i \(0.204141\pi\)
\(110\) 0 0
\(111\) −190.499 9.52121i −1.71620 0.0857766i
\(112\) 0 0
\(113\) −6.63526 2.86217i −0.0587191 0.0253289i 0.366518 0.930411i \(-0.380550\pi\)
−0.425237 + 0.905082i \(0.639809\pi\)
\(114\) 0 0
\(115\) 0.484541 + 8.31924i 0.00421340 + 0.0723413i
\(116\) 0 0
\(117\) 39.5746 71.2304i 0.338244 0.608807i
\(118\) 0 0
\(119\) 36.1037 15.5736i 0.303393 0.130871i
\(120\) 0 0
\(121\) −88.8886 21.0670i −0.734617 0.174107i
\(122\) 0 0
\(123\) 72.7403 99.4066i 0.591384 0.808184i
\(124\) 0 0
\(125\) −3.15802 8.67659i −0.0252642 0.0694127i
\(126\) 0 0
\(127\) 164.469 + 59.8617i 1.29503 + 0.471352i 0.895375 0.445313i \(-0.146908\pi\)
0.399655 + 0.916666i \(0.369130\pi\)
\(128\) 0 0
\(129\) 2.09001 + 253.675i 0.0162016 + 1.96647i
\(130\) 0 0
\(131\) −175.399 10.2158i −1.33892 0.0779834i −0.626329 0.779559i \(-0.715443\pi\)
−0.712595 + 0.701576i \(0.752480\pi\)
\(132\) 0 0
\(133\) −119.515 126.679i −0.898609 0.952470i
\(134\) 0 0
\(135\) 4.23512 + 2.63789i 0.0313712 + 0.0195399i
\(136\) 0 0
\(137\) 194.266 + 58.1596i 1.41800 + 0.424522i 0.901878 0.431991i \(-0.142189\pi\)
0.516125 + 0.856513i \(0.327374\pi\)
\(138\) 0 0
\(139\) 13.6911 + 9.00481i 0.0984975 + 0.0647828i 0.597802 0.801644i \(-0.296041\pi\)
−0.499305 + 0.866426i \(0.666411\pi\)
\(140\) 0 0
\(141\) 25.1023 + 8.90296i 0.178030 + 0.0631416i
\(142\) 0 0
\(143\) 129.932 22.9106i 0.908618 0.160214i
\(144\) 0 0
\(145\) −1.55492 + 8.81838i −0.0107236 + 0.0608164i
\(146\) 0 0
\(147\) 25.4428 24.4034i 0.173080 0.166009i
\(148\) 0 0
\(149\) −107.890 + 32.3001i −0.724092 + 0.216779i −0.627579 0.778553i \(-0.715954\pi\)
−0.0965129 + 0.995332i \(0.530769\pi\)
\(150\) 0 0
\(151\) −55.2751 6.46073i −0.366060 0.0427863i −0.0689252 0.997622i \(-0.521957\pi\)
−0.297135 + 0.954836i \(0.596031\pi\)
\(152\) 0 0
\(153\) 32.6556 + 47.9119i 0.213435 + 0.313149i
\(154\) 0 0
\(155\) 0.602619 + 0.916237i 0.00388786 + 0.00591121i
\(156\) 0 0
\(157\) −76.4112 102.638i −0.486695 0.653746i 0.489152 0.872199i \(-0.337306\pi\)
−0.975847 + 0.218453i \(0.929899\pi\)
\(158\) 0 0
\(159\) −35.4553 46.8145i −0.222989 0.294431i
\(160\) 0 0
\(161\) 275.223i 1.70946i
\(162\) 0 0
\(163\) 153.676 0.942799 0.471400 0.881920i \(-0.343749\pi\)
0.471400 + 0.881920i \(0.343749\pi\)
\(164\) 0 0
\(165\) 1.00395 + 8.01601i 0.00608453 + 0.0485819i
\(166\) 0 0
\(167\) −122.997 + 91.5682i −0.736512 + 0.548313i −0.898762 0.438437i \(-0.855532\pi\)
0.162250 + 0.986750i \(0.448125\pi\)
\(168\) 0 0
\(169\) 72.7089 47.8214i 0.430230 0.282967i
\(170\) 0 0
\(171\) 149.949 208.502i 0.876893 1.21931i
\(172\) 0 0
\(173\) −31.3999 + 268.643i −0.181502 + 1.55285i 0.528672 + 0.848826i \(0.322690\pi\)
−0.710175 + 0.704025i \(0.751384\pi\)
\(174\) 0 0
\(175\) 43.7004 + 145.969i 0.249717 + 0.834111i
\(176\) 0 0
\(177\) −13.4131 + 46.1845i −0.0757805 + 0.260930i
\(178\) 0 0
\(179\) −188.199 33.1845i −1.05139 0.185388i −0.378856 0.925455i \(-0.623683\pi\)
−0.672533 + 0.740067i \(0.734794\pi\)
\(180\) 0 0
\(181\) −3.61813 20.5195i −0.0199897 0.113367i 0.973180 0.230044i \(-0.0738870\pi\)
−0.993170 + 0.116677i \(0.962776\pi\)
\(182\) 0 0
\(183\) 134.907 + 158.112i 0.737197 + 0.864000i
\(184\) 0 0
\(185\) −6.45620 + 9.81617i −0.0348984 + 0.0530604i
\(186\) 0 0
\(187\) −26.9255 + 89.9374i −0.143987 + 0.480948i
\(188\) 0 0
\(189\) −134.570 95.1063i −0.712009 0.503208i
\(190\) 0 0
\(191\) −59.7436 + 56.3652i −0.312794 + 0.295106i −0.826588 0.562808i \(-0.809721\pi\)
0.513794 + 0.857914i \(0.328240\pi\)
\(192\) 0 0
\(193\) 1.57864 27.1043i 0.00817950 0.140437i −0.991746 0.128219i \(-0.959074\pi\)
0.999925 0.0122175i \(-0.00388904\pi\)
\(194\) 0 0
\(195\) −2.54542 4.32608i −0.0130534 0.0221850i
\(196\) 0 0
\(197\) 57.0836 156.836i 0.289764 0.796121i −0.706335 0.707878i \(-0.749653\pi\)
0.996099 0.0882429i \(-0.0281252\pi\)
\(198\) 0 0
\(199\) 83.2970 30.3176i 0.418578 0.152350i −0.124141 0.992265i \(-0.539617\pi\)
0.542718 + 0.839915i \(0.317395\pi\)
\(200\) 0 0
\(201\) −50.8334 + 22.4259i −0.252903 + 0.111572i
\(202\) 0 0
\(203\) 68.2012 287.763i 0.335966 1.41755i
\(204\) 0 0
\(205\) −3.00528 6.96701i −0.0146599 0.0339854i
\(206\) 0 0
\(207\) 398.475 77.0522i 1.92500 0.372233i
\(208\) 0 0
\(209\) 415.128 24.1785i 1.98626 0.115686i
\(210\) 0 0
\(211\) −52.4140 + 121.509i −0.248407 + 0.575873i −0.996106 0.0881652i \(-0.971900\pi\)
0.747698 + 0.664038i \(0.231159\pi\)
\(212\) 0 0
\(213\) −206.110 + 105.647i −0.967651 + 0.495997i
\(214\) 0 0
\(215\) 13.5329 + 7.81323i 0.0629438 + 0.0363406i
\(216\) 0 0
\(217\) −18.1094 31.3663i −0.0834532 0.144545i
\(218\) 0 0
\(219\) 191.565 59.0748i 0.874725 0.269748i
\(220\) 0 0
\(221\) −6.77168 57.9355i −0.0306411 0.262151i
\(222\) 0 0
\(223\) −196.257 98.5641i −0.880078 0.441992i −0.0494220 0.998778i \(-0.515738\pi\)
−0.830656 + 0.556786i \(0.812034\pi\)
\(224\) 0 0
\(225\) −199.104 + 104.137i −0.884906 + 0.462829i
\(226\) 0 0
\(227\) −98.1389 73.0617i −0.432330 0.321858i 0.358901 0.933376i \(-0.383152\pi\)
−0.791230 + 0.611518i \(0.790559\pi\)
\(228\) 0 0
\(229\) −160.177 + 169.778i −0.699465 + 0.741390i −0.975558 0.219741i \(-0.929479\pi\)
0.276093 + 0.961131i \(0.410960\pi\)
\(230\) 0 0
\(231\) −17.7076 266.222i −0.0766562 1.15248i
\(232\) 0 0
\(233\) −35.5242 + 42.3360i −0.152464 + 0.181700i −0.836870 0.547401i \(-0.815617\pi\)
0.684406 + 0.729101i \(0.260062\pi\)
\(234\) 0 0
\(235\) 1.25679 1.05457i 0.00534806 0.00448755i
\(236\) 0 0
\(237\) −290.011 48.6767i −1.22368 0.205387i
\(238\) 0 0
\(239\) −36.5797 72.8363i −0.153053 0.304754i 0.804019 0.594604i \(-0.202691\pi\)
−0.957072 + 0.289850i \(0.906395\pi\)
\(240\) 0 0
\(241\) 327.819 77.6946i 1.36025 0.322384i 0.515196 0.857072i \(-0.327719\pi\)
0.845049 + 0.534688i \(0.179571\pi\)
\(242\) 0 0
\(243\) 100.023 221.460i 0.411617 0.911357i
\(244\) 0 0
\(245\) −0.500805 2.11306i −0.00204410 0.00862475i
\(246\) 0 0
\(247\) −230.881 + 115.953i −0.934741 + 0.469445i
\(248\) 0 0
\(249\) 76.7172 457.074i 0.308101 1.83564i
\(250\) 0 0
\(251\) −73.1008 87.1181i −0.291238 0.347084i 0.600509 0.799618i \(-0.294965\pi\)
−0.891747 + 0.452534i \(0.850520\pi\)
\(252\) 0 0
\(253\) 503.397 + 422.400i 1.98971 + 1.66957i
\(254\) 0 0
\(255\) 3.56373 0.237039i 0.0139754 0.000929563i
\(256\) 0 0
\(257\) 6.47174 + 6.10577i 0.0251819 + 0.0237579i 0.698730 0.715386i \(-0.253749\pi\)
−0.673548 + 0.739144i \(0.735230\pi\)
\(258\) 0 0
\(259\) 231.716 311.249i 0.894658 1.20173i
\(260\) 0 0
\(261\) 435.725 + 18.1803i 1.66944 + 0.0696565i
\(262\) 0 0
\(263\) −94.9764 + 189.114i −0.361127 + 0.719063i −0.998681 0.0513428i \(-0.983650\pi\)
0.637554 + 0.770405i \(0.279946\pi\)
\(264\) 0 0
\(265\) −3.59292 + 0.419952i −0.0135582 + 0.00158473i
\(266\) 0 0
\(267\) −88.3150 286.384i −0.330768 1.07260i
\(268\) 0 0
\(269\) 229.643 132.585i 0.853692 0.492880i −0.00820252 0.999966i \(-0.502611\pi\)
0.861895 + 0.507087i \(0.169278\pi\)
\(270\) 0 0
\(271\) 176.250 305.273i 0.650368 1.12647i −0.332666 0.943045i \(-0.607948\pi\)
0.983034 0.183425i \(-0.0587186\pi\)
\(272\) 0 0
\(273\) 75.6169 + 147.523i 0.276985 + 0.540376i
\(274\) 0 0
\(275\) −334.055 144.097i −1.21475 0.523991i
\(276\) 0 0
\(277\) −7.98803 137.149i −0.0288377 0.495123i −0.981545 0.191233i \(-0.938751\pi\)
0.952707 0.303890i \(-0.0982857\pi\)
\(278\) 0 0
\(279\) 40.3430 35.0006i 0.144599 0.125450i
\(280\) 0 0
\(281\) −212.139 + 91.5077i −0.754942 + 0.325650i −0.738535 0.674215i \(-0.764482\pi\)
−0.0164068 + 0.999865i \(0.505223\pi\)
\(282\) 0 0
\(283\) 304.073 + 72.0665i 1.07446 + 0.254652i 0.729511 0.683969i \(-0.239748\pi\)
0.344950 + 0.938621i \(0.387896\pi\)
\(284\) 0 0
\(285\) −6.38537 14.4739i −0.0224048 0.0507856i
\(286\) 0 0
\(287\) 85.7074 + 235.479i 0.298632 + 0.820485i
\(288\) 0 0
\(289\) −232.569 84.6481i −0.804737 0.292900i
\(290\) 0 0
\(291\) −265.237 + 156.062i −0.911469 + 0.536297i
\(292\) 0 0
\(293\) −91.7426 5.34340i −0.313115 0.0182369i −0.0991320 0.995074i \(-0.531607\pi\)
−0.213983 + 0.976837i \(0.568644\pi\)
\(294\) 0 0
\(295\) 2.03295 + 2.15480i 0.00689135 + 0.00730440i
\(296\) 0 0
\(297\) 380.486 100.170i 1.28110 0.337272i
\(298\) 0 0
\(299\) −391.137 117.099i −1.30815 0.391635i
\(300\) 0 0
\(301\) −431.187 283.596i −1.43252 0.942180i
\(302\) 0 0
\(303\) 23.4780 20.0323i 0.0774853 0.0661133i
\(304\) 0 0
\(305\) 12.6084 2.22319i 0.0413389 0.00728916i
\(306\) 0 0
\(307\) −82.4546 + 467.623i −0.268582 + 1.52320i 0.490057 + 0.871691i \(0.336976\pi\)
−0.758638 + 0.651512i \(0.774135\pi\)
\(308\) 0 0
\(309\) 363.992 + 105.712i 1.17797 + 0.342111i
\(310\) 0 0
\(311\) −209.104 + 62.6017i −0.672360 + 0.201291i −0.604744 0.796420i \(-0.706725\pi\)
−0.0676164 + 0.997711i \(0.521539\pi\)
\(312\) 0 0
\(313\) −459.937 53.7590i −1.46945 0.171754i −0.656604 0.754235i \(-0.728008\pi\)
−0.812844 + 0.582481i \(0.802082\pi\)
\(314\) 0 0
\(315\) −9.25284 + 4.17343i −0.0293741 + 0.0132490i
\(316\) 0 0
\(317\) −256.694 390.284i −0.809760 1.23118i −0.969759 0.244063i \(-0.921520\pi\)
0.160000 0.987117i \(-0.448851\pi\)
\(318\) 0 0
\(319\) 421.662 + 566.390i 1.32182 + 1.77552i
\(320\) 0 0
\(321\) −162.965 + 20.4102i −0.507681 + 0.0635833i
\(322\) 0 0
\(323\) 183.841i 0.569168i
\(324\) 0 0
\(325\) 226.040 0.695507
\(326\) 0 0
\(327\) 61.2363 46.3777i 0.187267 0.141828i
\(328\) 0 0
\(329\) −43.4626 + 32.3567i −0.132105 + 0.0983487i
\(330\) 0 0
\(331\) −433.787 + 285.306i −1.31054 + 0.861953i −0.996178 0.0873513i \(-0.972160\pi\)
−0.314358 + 0.949304i \(0.601789\pi\)
\(332\) 0 0
\(333\) 515.507 + 248.347i 1.54807 + 0.745786i
\(334\) 0 0
\(335\) −0.397319 + 3.39928i −0.00118603 + 0.0101471i
\(336\) 0 0
\(337\) 84.3456 + 281.734i 0.250284 + 0.836006i 0.987126 + 0.159942i \(0.0511306\pi\)
−0.736843 + 0.676064i \(0.763684\pi\)
\(338\) 0 0
\(339\) 15.0063 + 15.6454i 0.0442663 + 0.0461518i
\(340\) 0 0
\(341\) 85.1641 + 15.0167i 0.249748 + 0.0440373i
\(342\) 0 0
\(343\) 64.3845 + 365.143i 0.187710 + 1.06456i
\(344\) 0 0
\(345\) 8.35668 23.5620i 0.0242223 0.0682956i
\(346\) 0 0
\(347\) −361.424 + 549.519i −1.04157 + 1.58363i −0.254193 + 0.967153i \(0.581810\pi\)
−0.787375 + 0.616474i \(0.788560\pi\)
\(348\) 0 0
\(349\) 31.6683 105.779i 0.0907400 0.303093i −0.900557 0.434738i \(-0.856841\pi\)
0.991297 + 0.131645i \(0.0420260\pi\)
\(350\) 0 0
\(351\) −192.417 + 150.781i −0.548197 + 0.429576i
\(352\) 0 0
\(353\) 50.7656 47.8949i 0.143812 0.135680i −0.610974 0.791650i \(-0.709222\pi\)
0.754786 + 0.655971i \(0.227741\pi\)
\(354\) 0 0
\(355\) −0.829534 + 14.2426i −0.00233672 + 0.0401199i
\(356\) 0 0
\(357\) −117.954 + 0.971817i −0.330404 + 0.00272218i
\(358\) 0 0
\(359\) 104.050 285.875i 0.289833 0.796309i −0.706256 0.707956i \(-0.749617\pi\)
0.996089 0.0883529i \(-0.0281603\pi\)
\(360\) 0 0
\(361\) −425.957 + 155.036i −1.17994 + 0.429462i
\(362\) 0 0
\(363\) 221.165 + 161.836i 0.609270 + 0.445830i
\(364\) 0 0
\(365\) 2.84774 12.0156i 0.00780202 0.0329193i
\(366\) 0 0
\(367\) 144.368 + 334.683i 0.393373 + 0.911942i 0.993688 + 0.112178i \(0.0357828\pi\)
−0.600315 + 0.799764i \(0.704958\pi\)
\(368\) 0 0
\(369\) −316.938 + 190.015i −0.858911 + 0.514946i
\(370\) 0 0
\(371\) 119.268 6.94657i 0.321477 0.0187239i
\(372\) 0 0
\(373\) −287.463 + 666.414i −0.770678 + 1.78663i −0.172956 + 0.984929i \(0.555332\pi\)
−0.597722 + 0.801704i \(0.703927\pi\)
\(374\) 0 0
\(375\) −1.38275 + 27.6658i −0.00368733 + 0.0737753i
\(376\) 0 0
\(377\) −379.942 219.360i −1.00780 0.581856i
\(378\) 0 0
\(379\) 268.913 + 465.771i 0.709532 + 1.22895i 0.965031 + 0.262136i \(0.0844271\pi\)
−0.255499 + 0.966809i \(0.582240\pi\)
\(380\) 0 0
\(381\) −384.879 357.168i −1.01018 0.937448i
\(382\) 0 0
\(383\) 12.1868 + 104.265i 0.0318194 + 0.272232i 0.999777 + 0.0211185i \(0.00672273\pi\)
−0.967958 + 0.251114i \(0.919203\pi\)
\(384\) 0 0
\(385\) −14.6869 7.37605i −0.0381479 0.0191586i
\(386\) 0 0
\(387\) 289.882 703.680i 0.749048 1.81830i
\(388\) 0 0
\(389\) 385.857 + 287.260i 0.991919 + 0.738456i 0.965288 0.261189i \(-0.0841145\pi\)
0.0266314 + 0.999645i \(0.491522\pi\)
\(390\) 0 0
\(391\) 199.370 211.319i 0.509897 0.540459i
\(392\) 0 0
\(393\) 472.957 + 232.668i 1.20345 + 0.592031i
\(394\) 0 0
\(395\) −11.6435 + 13.8762i −0.0294772 + 0.0351296i
\(396\) 0 0
\(397\) 423.731 355.553i 1.06733 0.895599i 0.0725251 0.997367i \(-0.476894\pi\)
0.994808 + 0.101768i \(0.0324498\pi\)
\(398\) 0 0
\(399\) 182.736 + 489.478i 0.457986 + 1.22676i
\(400\) 0 0
\(401\) 75.0448 + 149.426i 0.187144 + 0.372635i 0.967566 0.252619i \(-0.0812919\pi\)
−0.780422 + 0.625254i \(0.784996\pi\)
\(402\) 0 0
\(403\) −52.2817 + 12.3910i −0.129731 + 0.0307469i
\(404\) 0 0
\(405\) −8.63285 12.2281i −0.0213157 0.0301928i
\(406\) 0 0
\(407\) 213.663 + 901.514i 0.524970 + 2.21502i
\(408\) 0 0
\(409\) −183.275 + 92.0444i −0.448106 + 0.225047i −0.658517 0.752566i \(-0.728816\pi\)
0.210411 + 0.977613i \(0.432520\pi\)
\(410\) 0 0
\(411\) −469.234 387.191i −1.14169 0.942072i
\(412\) 0 0
\(413\) −62.8900 74.9494i −0.152276 0.181476i
\(414\) 0 0
\(415\) −21.8696 18.3508i −0.0526979 0.0442188i
\(416\) 0 0
\(417\) −27.3519 40.8495i −0.0655921 0.0979604i
\(418\) 0 0
\(419\) −237.074 223.667i −0.565808 0.533813i 0.349305 0.937009i \(-0.386418\pi\)
−0.915113 + 0.403196i \(0.867899\pi\)
\(420\) 0 0
\(421\) 163.489 219.603i 0.388334 0.521623i −0.564370 0.825522i \(-0.690881\pi\)
0.952704 + 0.303899i \(0.0982884\pi\)
\(422\) 0 0
\(423\) −59.0149 53.8676i −0.139515 0.127347i
\(424\) 0 0
\(425\) −72.1856 + 143.733i −0.169849 + 0.338196i
\(426\) 0 0
\(427\) −419.977 + 49.0883i −0.983553 + 0.114961i
\(428\) 0 0
\(429\) −385.880 88.1040i −0.899488 0.205371i
\(430\) 0 0
\(431\) −516.658 + 298.293i −1.19874 + 0.692095i −0.960275 0.279056i \(-0.909979\pi\)
−0.238468 + 0.971150i \(0.576645\pi\)
\(432\) 0 0
\(433\) 144.682 250.597i 0.334139 0.578745i −0.649180 0.760635i \(-0.724888\pi\)
0.983319 + 0.181889i \(0.0582213\pi\)
\(434\) 0 0
\(435\) 14.5762 22.5648i 0.0335085 0.0518731i
\(436\) 0 0
\(437\) −1181.59 509.686i −2.70386 1.16633i
\(438\) 0 0
\(439\) 12.2298 + 209.978i 0.0278583 + 0.478309i 0.983168 + 0.182703i \(0.0584846\pi\)
−0.955310 + 0.295606i \(0.904478\pi\)
\(440\) 0 0
\(441\) −98.7749 + 37.8056i −0.223979 + 0.0857269i
\(442\) 0 0
\(443\) −258.564 + 111.534i −0.583667 + 0.251769i −0.667376 0.744721i \(-0.732583\pi\)
0.0837093 + 0.996490i \(0.473323\pi\)
\(444\) 0 0
\(445\) −17.9629 4.25728i −0.0403660 0.00956693i
\(446\) 0 0
\(447\) 335.890 + 36.4574i 0.751432 + 0.0815603i
\(448\) 0 0
\(449\) −112.247 308.396i −0.249993 0.686851i −0.999686 0.0250648i \(-0.992021\pi\)
0.749692 0.661786i \(-0.230201\pi\)
\(450\) 0 0
\(451\) −562.244 204.640i −1.24666 0.453747i
\(452\) 0 0
\(453\) 145.269 + 82.2830i 0.320683 + 0.181640i
\(454\) 0 0
\(455\) 10.1941 + 0.593738i 0.0224046 + 0.00130492i
\(456\) 0 0
\(457\) 105.495 + 111.819i 0.230843 + 0.244680i 0.832433 0.554125i \(-0.186947\pi\)
−0.601590 + 0.798805i \(0.705466\pi\)
\(458\) 0 0
\(459\) −34.4298 170.505i −0.0750106 0.371471i
\(460\) 0 0
\(461\) 557.250 + 166.830i 1.20878 + 0.361886i 0.826914 0.562329i \(-0.190095\pi\)
0.381871 + 0.924215i \(0.375280\pi\)
\(462\) 0 0
\(463\) 116.031 + 76.3146i 0.250606 + 0.164826i 0.668597 0.743625i \(-0.266895\pi\)
−0.417991 + 0.908451i \(0.637266\pi\)
\(464\) 0 0
\(465\) −0.597967 3.23515i −0.00128595 0.00695731i
\(466\) 0 0
\(467\) 648.396 114.330i 1.38843 0.244818i 0.571049 0.820916i \(-0.306537\pi\)
0.817380 + 0.576098i \(0.195426\pi\)
\(468\) 0 0
\(469\) 19.6277 111.314i 0.0418501 0.237344i
\(470\) 0 0
\(471\) 91.6018 + 372.784i 0.194484 + 0.791474i
\(472\) 0 0
\(473\) 1180.48 353.413i 2.49573 0.747172i
\(474\) 0 0
\(475\) 707.604 + 82.7071i 1.48969 + 0.174120i
\(476\) 0 0
\(477\) 43.4481 + 170.735i 0.0910861 + 0.357934i
\(478\) 0 0
\(479\) 107.308 + 163.155i 0.224026 + 0.340615i 0.929959 0.367664i \(-0.119842\pi\)
−0.705933 + 0.708279i \(0.749472\pi\)
\(480\) 0 0
\(481\) −343.748 461.734i −0.714654 0.959947i
\(482\) 0 0
\(483\) −320.773 + 760.811i −0.664127 + 1.57518i
\(484\) 0 0
\(485\) 18.9565i 0.0390856i
\(486\) 0 0
\(487\) 284.987 0.585188 0.292594 0.956237i \(-0.405482\pi\)
0.292594 + 0.956237i \(0.405482\pi\)
\(488\) 0 0
\(489\) −424.814 179.110i −0.868741 0.366279i
\(490\) 0 0
\(491\) 433.321 322.595i 0.882527 0.657017i −0.0574153 0.998350i \(-0.518286\pi\)
0.939942 + 0.341333i \(0.110878\pi\)
\(492\) 0 0
\(493\) 260.820 171.544i 0.529046 0.347959i
\(494\) 0 0
\(495\) 6.56744 23.3291i 0.0132676 0.0471296i
\(496\) 0 0
\(497\) 54.7009 467.996i 0.110062 0.941642i
\(498\) 0 0
\(499\) −259.835 867.908i −0.520711 1.73929i −0.662173 0.749351i \(-0.730366\pi\)
0.141462 0.989944i \(-0.454820\pi\)
\(500\) 0 0
\(501\) 446.730 109.772i 0.891677 0.219106i
\(502\) 0 0
\(503\) −23.6992 4.17881i −0.0471157 0.00830777i 0.150041 0.988680i \(-0.452060\pi\)
−0.197156 + 0.980372i \(0.563171\pi\)
\(504\) 0 0
\(505\) −0.330122 1.87221i −0.000653706 0.00370735i
\(506\) 0 0
\(507\) −256.729 + 47.4523i −0.506368 + 0.0935943i
\(508\) 0 0
\(509\) −318.908 + 484.875i −0.626537 + 0.952604i 0.373154 + 0.927769i \(0.378276\pi\)
−0.999692 + 0.0248346i \(0.992094\pi\)
\(510\) 0 0
\(511\) −116.966 + 390.694i −0.228897 + 0.764568i
\(512\) 0 0
\(513\) −657.520 + 401.606i −1.28172 + 0.782858i
\(514\) 0 0
\(515\) 16.9825 16.0222i 0.0329757 0.0311110i
\(516\) 0 0
\(517\) 7.52243 129.155i 0.0145502 0.249817i
\(518\) 0 0
\(519\) 399.905 706.026i 0.770530 1.36036i
\(520\) 0 0
\(521\) 8.04582 22.1057i 0.0154430 0.0424294i −0.931732 0.363148i \(-0.881702\pi\)
0.947175 + 0.320718i \(0.103924\pi\)
\(522\) 0 0
\(523\) 417.356 151.905i 0.798004 0.290450i 0.0893450 0.996001i \(-0.471523\pi\)
0.708659 + 0.705551i \(0.249300\pi\)
\(524\) 0 0
\(525\) 49.3251 454.443i 0.0939526 0.865606i
\(526\) 0 0
\(527\) 8.81697 37.2017i 0.0167305 0.0705915i
\(528\) 0 0
\(529\) −595.930 1381.52i −1.12652 2.61157i
\(530\) 0 0
\(531\) 90.9068 112.037i 0.171199 0.210992i
\(532\) 0 0
\(533\) 371.121 21.6153i 0.696287 0.0405541i
\(534\) 0 0
\(535\) −4.00706 + 9.28942i −0.00748984 + 0.0173634i
\(536\) 0 0
\(537\) 481.569 + 311.080i 0.896777 + 0.579292i
\(538\) 0 0
\(539\) −148.302 85.6223i −0.275143 0.158854i
\(540\) 0 0
\(541\) 94.2767 + 163.292i 0.174264 + 0.301834i 0.939906 0.341433i \(-0.110912\pi\)
−0.765642 + 0.643266i \(0.777579\pi\)
\(542\) 0 0
\(543\) −13.9138 + 60.9398i −0.0256239 + 0.112228i
\(544\) 0 0
\(545\) −0.549324 4.69977i −0.00100793 0.00862343i
\(546\) 0 0
\(547\) −139.195 69.9063i −0.254470 0.127799i 0.316992 0.948428i \(-0.397327\pi\)
−0.571462 + 0.820629i \(0.693623\pi\)
\(548\) 0 0
\(549\) −188.649 594.311i −0.343623 1.08253i
\(550\) 0 0
\(551\) −1109.12 825.711i −2.01293 1.49857i
\(552\) 0 0
\(553\) 410.543 435.150i 0.742392 0.786890i
\(554\) 0 0
\(555\) 29.2879 19.6106i 0.0527711 0.0353343i
\(556\) 0 0
\(557\) −257.459 + 306.827i −0.462224 + 0.550857i −0.945929 0.324374i \(-0.894846\pi\)
0.483705 + 0.875231i \(0.339291\pi\)
\(558\) 0 0
\(559\) −586.494 + 492.127i −1.04918 + 0.880370i
\(560\) 0 0
\(561\) 179.254 217.236i 0.319525 0.387230i
\(562\) 0 0
\(563\) 160.112 + 318.808i 0.284390 + 0.566267i 0.989788 0.142544i \(-0.0455282\pi\)
−0.705399 + 0.708811i \(0.749232\pi\)
\(564\) 0 0
\(565\) 1.29938 0.307958i 0.00229978 0.000545059i
\(566\) 0 0
\(567\) 261.150 + 419.748i 0.460582 + 0.740297i
\(568\) 0 0
\(569\) 70.6356 + 298.035i 0.124140 + 0.523787i 0.999208 + 0.0397879i \(0.0126682\pi\)
−0.875068 + 0.484000i \(0.839184\pi\)
\(570\) 0 0
\(571\) 176.526 88.6548i 0.309153 0.155262i −0.287458 0.957793i \(-0.592810\pi\)
0.596610 + 0.802531i \(0.296514\pi\)
\(572\) 0 0
\(573\) 230.846 86.1814i 0.402872 0.150404i
\(574\) 0 0
\(575\) 723.675 + 862.442i 1.25856 + 1.49990i
\(576\) 0 0
\(577\) 109.656 + 92.0120i 0.190044 + 0.159466i 0.732846 0.680395i \(-0.238192\pi\)
−0.542801 + 0.839861i \(0.682636\pi\)
\(578\) 0 0
\(579\) −35.9541 + 73.0856i −0.0620968 + 0.126227i
\(580\) 0 0
\(581\) 685.821 + 647.038i 1.18041 + 1.11366i
\(582\) 0 0
\(583\) −170.342 + 228.809i −0.292182 + 0.392468i
\(584\) 0 0
\(585\) 1.99434 + 14.9255i 0.00340912 + 0.0255136i
\(586\) 0 0
\(587\) 395.206 786.920i 0.673264 1.34058i −0.254376 0.967105i \(-0.581870\pi\)
0.927641 0.373474i \(-0.121834\pi\)
\(588\) 0 0
\(589\) −168.198 + 19.6596i −0.285566 + 0.0333779i
\(590\) 0 0
\(591\) −340.592 + 367.017i −0.576297 + 0.621010i
\(592\) 0 0
\(593\) 796.616 459.926i 1.34337 0.775592i 0.356065 0.934461i \(-0.384118\pi\)
0.987300 + 0.158869i \(0.0507847\pi\)
\(594\) 0 0
\(595\) −3.63301 + 6.29256i −0.00610590 + 0.0105757i
\(596\) 0 0
\(597\) −265.597 13.2746i −0.444886 0.0222356i
\(598\) 0 0
\(599\) −429.366 185.210i −0.716804 0.309199i 0.00625952 0.999980i \(-0.498008\pi\)
−0.723064 + 0.690781i \(0.757267\pi\)
\(600\) 0 0
\(601\) −8.36225 143.574i −0.0139139 0.238892i −0.998094 0.0617190i \(-0.980342\pi\)
0.984180 0.177173i \(-0.0566953\pi\)
\(602\) 0 0
\(603\) 166.659 2.74636i 0.276382 0.00455450i
\(604\) 0 0
\(605\) 15.5006 6.68630i 0.0256208 0.0110517i
\(606\) 0 0
\(607\) 660.131 + 156.454i 1.08753 + 0.257750i 0.735011 0.678055i \(-0.237177\pi\)
0.352520 + 0.935804i \(0.385325\pi\)
\(608\) 0 0
\(609\) −523.921 + 715.988i −0.860297 + 1.17568i
\(610\) 0 0
\(611\) 27.4923 + 75.5344i 0.0449955 + 0.123624i
\(612\) 0 0
\(613\) −374.930 136.463i −0.611631 0.222616i 0.0175855 0.999845i \(-0.494402\pi\)
−0.629217 + 0.777230i \(0.716624\pi\)
\(614\) 0 0
\(615\) 0.187533 + 22.7619i 0.000304932 + 0.0370112i
\(616\) 0 0
\(617\) 117.178 + 6.82482i 0.189915 + 0.0110613i 0.152839 0.988251i \(-0.451158\pi\)
0.0370763 + 0.999312i \(0.488196\pi\)
\(618\) 0 0
\(619\) 641.919 + 680.395i 1.03703 + 1.09918i 0.994981 + 0.100068i \(0.0319060\pi\)
0.0420456 + 0.999116i \(0.486613\pi\)
\(620\) 0 0
\(621\) −1191.33 251.425i −1.91840 0.404872i
\(622\) 0 0
\(623\) 584.076 + 174.861i 0.937522 + 0.280676i
\(624\) 0 0
\(625\) −520.041 342.036i −0.832066 0.547258i
\(626\) 0 0
\(627\) −1175.74 416.996i −1.87518 0.665066i
\(628\) 0 0
\(629\) 403.382 71.1270i 0.641306 0.113080i
\(630\) 0 0
\(631\) −62.4220 + 354.013i −0.0989255 + 0.561034i 0.894548 + 0.446972i \(0.147498\pi\)
−0.993474 + 0.114063i \(0.963614\pi\)
\(632\) 0 0
\(633\) 286.510 274.805i 0.452622 0.434131i
\(634\) 0 0
\(635\) −30.9848 + 9.27623i −0.0487949 + 0.0146082i
\(636\) 0 0
\(637\) 105.677 + 12.3519i 0.165899 + 0.0193908i
\(638\) 0 0
\(639\) 692.891 51.8242i 1.08434 0.0811020i
\(640\) 0 0
\(641\) −217.294 330.379i −0.338992 0.515412i 0.625254 0.780421i \(-0.284995\pi\)
−0.964246 + 0.265009i \(0.914625\pi\)
\(642\) 0 0
\(643\) 249.878 + 335.645i 0.388613 + 0.521998i 0.952779 0.303663i \(-0.0982098\pi\)
−0.564167 + 0.825661i \(0.690802\pi\)
\(644\) 0 0
\(645\) −28.3033 37.3711i −0.0438810 0.0579397i
\(646\) 0 0
\(647\) 928.853i 1.43563i −0.696234 0.717815i \(-0.745142\pi\)
0.696234 0.717815i \(-0.254858\pi\)
\(648\) 0 0
\(649\) 233.607 0.359950
\(650\) 0 0
\(651\) 13.5029 + 107.814i 0.0207418 + 0.165613i
\(652\) 0 0
\(653\) 279.299 207.931i 0.427717 0.318424i −0.361685 0.932301i \(-0.617798\pi\)
0.789402 + 0.613877i \(0.210391\pi\)
\(654\) 0 0
\(655\) 27.1264 17.8413i 0.0414144 0.0272387i
\(656\) 0 0
\(657\) −598.403 59.9667i −0.910812 0.0912736i
\(658\) 0 0
\(659\) −138.049 + 1181.08i −0.209482 + 1.79223i 0.323625 + 0.946185i \(0.395098\pi\)
−0.533107 + 0.846048i \(0.678976\pi\)
\(660\) 0 0
\(661\) 107.407 + 358.764i 0.162491 + 0.542759i 0.999993 0.00367540i \(-0.00116992\pi\)
−0.837502 + 0.546435i \(0.815985\pi\)
\(662\) 0 0
\(663\) −48.8048 + 168.046i −0.0736120 + 0.253463i
\(664\) 0 0
\(665\) 31.6947 + 5.58863i 0.0476612 + 0.00840396i
\(666\) 0 0
\(667\) −379.444 2151.93i −0.568881 3.22629i
\(668\) 0 0
\(669\) 427.646 + 501.204i 0.639232 + 0.749184i
\(670\) 0 0
\(671\) 554.778 843.499i 0.826792 1.25708i
\(672\) 0 0
\(673\) 101.898 340.363i 0.151409 0.505741i −0.848309 0.529502i \(-0.822379\pi\)
0.999718 + 0.0237612i \(0.00756412\pi\)
\(674\) 0 0
\(675\) 671.763 55.8130i 0.995205 0.0826859i
\(676\) 0 0
\(677\) 436.430 411.750i 0.644652 0.608198i −0.292858 0.956156i \(-0.594606\pi\)
0.937510 + 0.347958i \(0.113125\pi\)
\(678\) 0 0
\(679\) 36.4028 625.011i 0.0536123 0.920488i
\(680\) 0 0
\(681\) 186.136 + 316.349i 0.273327 + 0.464536i
\(682\) 0 0
\(683\) −315.507 + 866.849i −0.461943 + 1.26918i 0.462078 + 0.886839i \(0.347104\pi\)
−0.924022 + 0.382340i \(0.875118\pi\)
\(684\) 0 0
\(685\) −35.2138 + 12.8168i −0.0514070 + 0.0187106i
\(686\) 0 0
\(687\) 640.663 282.638i 0.932552 0.411409i
\(688\) 0 0
\(689\) 40.8726 172.455i 0.0593217 0.250298i
\(690\) 0 0
\(691\) −360.092 834.788i −0.521118 1.20809i −0.952117 0.305734i \(-0.901098\pi\)
0.430999 0.902352i \(-0.358161\pi\)
\(692\) 0 0
\(693\) −261.334 + 756.569i −0.377105 + 1.09173i
\(694\) 0 0
\(695\) −3.02311 + 0.176076i −0.00434980 + 0.000253347i
\(696\) 0 0
\(697\) −104.772 + 242.890i −0.150319 + 0.348479i
\(698\) 0 0
\(699\) 147.544 75.6278i 0.211078 0.108194i
\(700\) 0 0
\(701\) −619.626 357.741i −0.883917 0.510330i −0.0119692 0.999928i \(-0.503810\pi\)
−0.871948 + 0.489599i \(0.837143\pi\)
\(702\) 0 0
\(703\) −907.137 1571.21i −1.29038 2.23500i
\(704\) 0 0
\(705\) −4.70332 + 1.45041i −0.00667138 + 0.00205732i
\(706\) 0 0
\(707\) 7.28911 + 62.3624i 0.0103099 + 0.0882070i
\(708\) 0 0
\(709\) −381.413 191.553i −0.537959 0.270173i 0.159007 0.987277i \(-0.449171\pi\)
−0.696966 + 0.717104i \(0.745467\pi\)
\(710\) 0 0
\(711\) 744.958 + 472.569i 1.04776 + 0.664654i
\(712\) 0 0
\(713\) −214.659 159.808i −0.301064 0.224134i
\(714\) 0 0
\(715\) −16.7314 + 17.7343i −0.0234006 + 0.0248032i
\(716\) 0 0
\(717\) 16.2280 + 243.978i 0.0226332 + 0.340277i
\(718\) 0 0
\(719\) −886.267 + 1056.21i −1.23264 + 1.46900i −0.398759 + 0.917056i \(0.630559\pi\)
−0.833880 + 0.551946i \(0.813885\pi\)
\(720\) 0 0
\(721\) −590.695 + 495.652i −0.819272 + 0.687451i
\(722\) 0 0
\(723\) −996.758 167.300i −1.37864 0.231397i
\(724\) 0 0
\(725\) 542.933 + 1081.07i 0.748873 + 1.49113i
\(726\) 0 0
\(727\) −468.329 + 110.996i −0.644194 + 0.152677i −0.539712 0.841850i \(-0.681467\pi\)
−0.104482 + 0.994527i \(0.533319\pi\)
\(728\) 0 0
\(729\) −534.610 + 495.614i −0.733347 + 0.679854i
\(730\) 0 0
\(731\) −125.635 530.098i −0.171868 0.725168i
\(732\) 0 0
\(733\) 688.942 346.000i 0.939894 0.472033i 0.0882181 0.996101i \(-0.471883\pi\)
0.851676 + 0.524069i \(0.175586\pi\)
\(734\) 0 0
\(735\) −1.07839 + 6.42493i −0.00146719 + 0.00874140i
\(736\) 0 0
\(737\) 173.476 + 206.740i 0.235381 + 0.280516i
\(738\) 0 0
\(739\) 19.5958 + 16.4429i 0.0265167 + 0.0222501i 0.655950 0.754805i \(-0.272268\pi\)
−0.629433 + 0.777055i \(0.716713\pi\)
\(740\) 0 0
\(741\) 773.378 51.4407i 1.04370 0.0694206i
\(742\) 0 0
\(743\) 659.369 + 622.083i 0.887442 + 0.837258i 0.987483 0.157725i \(-0.0504159\pi\)
−0.100041 + 0.994983i \(0.531897\pi\)
\(744\) 0 0
\(745\) 12.4279 16.6936i 0.0166818 0.0224075i
\(746\) 0 0
\(747\) −744.795 + 1174.10i −0.997048 + 1.57175i
\(748\) 0 0
\(749\) 149.955 298.585i 0.200207 0.398645i
\(750\) 0 0
\(751\) 861.679 100.716i 1.14738 0.134109i 0.478918 0.877859i \(-0.341029\pi\)
0.668457 + 0.743751i \(0.266955\pi\)
\(752\) 0 0
\(753\) 100.539 + 326.024i 0.133518 + 0.432966i
\(754\) 0 0
\(755\) 8.90628 5.14204i 0.0117964 0.00681065i
\(756\) 0 0
\(757\) 391.491 678.081i 0.517161 0.895748i −0.482641 0.875818i \(-0.660322\pi\)
0.999801 0.0199300i \(-0.00634432\pi\)
\(758\) 0 0
\(759\) −899.253 1754.37i −1.18479 2.31142i
\(760\) 0 0
\(761\) 468.294 + 202.002i 0.615366 + 0.265443i 0.680864 0.732410i \(-0.261604\pi\)
−0.0654980 + 0.997853i \(0.520864\pi\)
\(762\) 0 0
\(763\) 9.08656 + 156.010i 0.0119090 + 0.204469i
\(764\) 0 0
\(765\) −10.1276 3.49829i −0.0132387 0.00457292i
\(766\) 0 0
\(767\) −133.273 + 57.4885i −0.173759 + 0.0749524i
\(768\) 0 0
\(769\) 706.113 + 167.352i 0.918223 + 0.217623i 0.662443 0.749112i \(-0.269520\pi\)
0.255780 + 0.966735i \(0.417668\pi\)
\(770\) 0 0
\(771\) −10.7738 24.4213i −0.0139738 0.0316748i
\(772\) 0 0
\(773\) 311.464 + 855.741i 0.402929 + 1.10704i 0.960832 + 0.277133i \(0.0893841\pi\)
−0.557902 + 0.829907i \(0.688394\pi\)
\(774\) 0 0
\(775\) 139.223 + 50.6729i 0.179642 + 0.0653844i
\(776\) 0 0
\(777\) −1003.31 + 590.334i −1.29126 + 0.759760i
\(778\) 0 0
\(779\) 1169.68 + 68.1261i 1.50151 + 0.0874533i
\(780\) 0 0
\(781\) 772.036 + 818.311i 0.988523 + 1.04777i
\(782\) 0 0
\(783\) −1183.30 558.096i −1.51125 0.712767i
\(784\) 0 0
\(785\) 22.6526 + 6.78174i 0.0288568 + 0.00863916i
\(786\) 0 0
\(787\) −572.616 376.616i −0.727594 0.478546i 0.130883 0.991398i \(-0.458219\pi\)
−0.858477 + 0.512852i \(0.828589\pi\)
\(788\) 0 0
\(789\) 482.960 412.079i 0.612117 0.522281i
\(790\) 0 0
\(791\) −43.4329 + 7.65840i −0.0549089 + 0.00968192i
\(792\) 0 0
\(793\) −108.925 + 617.742i −0.137358 + 0.778994i
\(794\) 0 0