Properties

Label 1440.2.q.i.481.1
Level $1440$
Weight $2$
Character 1440.481
Analytic conductor $11.498$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(11.4984578911\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.3010058496.1
Defining polynomial: \(x^{8} - 4 x^{7} + 6 x^{6} + 2 x^{5} - 17 x^{4} + 6 x^{3} + 54 x^{2} - 108 x + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 481.1
Root \(1.14729 + 1.29759i\) of defining polynomial
Character \(\chi\) \(=\) 1440.481
Dual form 1440.2.q.i.961.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.69739 - 0.344784i) q^{3} +(0.500000 - 0.866025i) q^{5} +(1.69739 + 2.93996i) q^{7} +(2.76225 + 1.17046i) q^{9} +O(q^{10})\) \(q+(-1.69739 - 0.344784i) q^{3} +(0.500000 - 0.866025i) q^{5} +(1.69739 + 2.93996i) q^{7} +(2.76225 + 1.17046i) q^{9} +(1.84467 + 3.19507i) q^{11} +(0.867473 - 1.50251i) q^{13} +(-1.14729 + 1.29759i) q^{15} -5.93536 q^{17} +5.10020 q^{19} +(-1.86747 - 5.57549i) q^{21} +(-2.43233 + 4.21293i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-4.28505 - 2.93911i) q^{27} +(-0.600205 - 1.03958i) q^{29} +(-2.28505 + 3.95782i) q^{31} +(-2.02952 - 6.05928i) q^{33} +3.39477 q^{35} -3.14581 q^{37} +(-1.99048 + 2.25125i) q^{39} +(-4.32187 + 7.48570i) q^{41} +(-3.55010 - 6.14896i) q^{43} +(2.39477 - 1.80695i) q^{45} +(1.95292 + 3.38256i) q^{47} +(-2.26225 + 3.91833i) q^{49} +(10.0746 + 2.04641i) q^{51} +8.25944 q^{53} +3.68935 q^{55} +(-8.65702 - 1.75847i) q^{57} +(-1.39477 + 2.41582i) q^{59} +(0.0729031 + 0.126272i) q^{61} +(1.24749 + 10.1076i) q^{63} +(-0.867473 - 1.50251i) q^{65} +(-3.54206 + 6.13503i) q^{67} +(5.58116 - 6.31234i) q^{69} -0.110246 q^{71} +15.3787 q^{73} +(0.550102 + 1.64237i) q^{75} +(-6.26225 + 10.8465i) q^{77} +(2.39477 + 4.14787i) q^{79} +(6.26003 + 6.46622i) q^{81} +(8.38673 + 14.5262i) q^{83} +(-2.96768 + 5.14017i) q^{85} +(0.660348 + 1.97152i) q^{87} -2.37869 q^{89} +5.88975 q^{91} +(5.24321 - 5.93011i) q^{93} +(2.55010 - 4.41691i) q^{95} +(3.76003 + 6.51257i) q^{97} +(1.35574 + 10.9847i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 8 q^{9} + O(q^{10}) \) \( 8 q - 2 q^{3} + 4 q^{5} + 2 q^{7} - 8 q^{9} - 2 q^{11} - 4 q^{15} - 8 q^{17} + 28 q^{19} - 8 q^{21} + 6 q^{23} - 4 q^{25} - 14 q^{27} + 8 q^{29} + 2 q^{31} + 8 q^{33} + 4 q^{35} - 32 q^{37} - 6 q^{39} - 8 q^{41} - 22 q^{43} - 4 q^{45} + 8 q^{47} + 12 q^{49} + 14 q^{51} - 8 q^{53} - 4 q^{55} - 16 q^{57} + 12 q^{59} + 4 q^{61} - 8 q^{63} + 12 q^{69} - 60 q^{71} + 56 q^{73} - 2 q^{75} - 20 q^{77} - 4 q^{79} + 28 q^{81} + 22 q^{83} - 4 q^{85} + 58 q^{87} + 48 q^{89} - 12 q^{91} - 8 q^{93} + 14 q^{95} + 8 q^{97} + 2 q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.69739 0.344784i −0.979987 0.199061i
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 1.69739 + 2.93996i 0.641552 + 1.11120i 0.985086 + 0.172061i \(0.0550425\pi\)
−0.343534 + 0.939140i \(0.611624\pi\)
\(8\) 0 0
\(9\) 2.76225 + 1.17046i 0.920749 + 0.390154i
\(10\) 0 0
\(11\) 1.84467 + 3.19507i 0.556190 + 0.963349i 0.997810 + 0.0661468i \(0.0210706\pi\)
−0.441620 + 0.897202i \(0.645596\pi\)
\(12\) 0 0
\(13\) 0.867473 1.50251i 0.240594 0.416721i −0.720290 0.693673i \(-0.755991\pi\)
0.960884 + 0.276953i \(0.0893245\pi\)
\(14\) 0 0
\(15\) −1.14729 + 1.29759i −0.296228 + 0.335036i
\(16\) 0 0
\(17\) −5.93536 −1.43954 −0.719768 0.694215i \(-0.755752\pi\)
−0.719768 + 0.694215i \(0.755752\pi\)
\(18\) 0 0
\(19\) 5.10020 1.17007 0.585034 0.811009i \(-0.301081\pi\)
0.585034 + 0.811009i \(0.301081\pi\)
\(20\) 0 0
\(21\) −1.86747 5.57549i −0.407516 1.21667i
\(22\) 0 0
\(23\) −2.43233 + 4.21293i −0.507177 + 0.878456i 0.492789 + 0.870149i \(0.335978\pi\)
−0.999965 + 0.00830696i \(0.997356\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −4.28505 2.93911i −0.824658 0.565632i
\(28\) 0 0
\(29\) −0.600205 1.03958i −0.111455 0.193046i 0.804902 0.593408i \(-0.202218\pi\)
−0.916357 + 0.400362i \(0.868884\pi\)
\(30\) 0 0
\(31\) −2.28505 + 3.95782i −0.410407 + 0.710846i −0.994934 0.100528i \(-0.967947\pi\)
0.584527 + 0.811374i \(0.301280\pi\)
\(32\) 0 0
\(33\) −2.02952 6.05928i −0.353294 1.05479i
\(34\) 0 0
\(35\) 3.39477 0.573822
\(36\) 0 0
\(37\) −3.14581 −0.517167 −0.258584 0.965989i \(-0.583256\pi\)
−0.258584 + 0.965989i \(0.583256\pi\)
\(38\) 0 0
\(39\) −1.99048 + 2.25125i −0.318732 + 0.360488i
\(40\) 0 0
\(41\) −4.32187 + 7.48570i −0.674963 + 1.16907i 0.301517 + 0.953461i \(0.402507\pi\)
−0.976480 + 0.215609i \(0.930826\pi\)
\(42\) 0 0
\(43\) −3.55010 6.14896i −0.541386 0.937707i −0.998825 0.0484664i \(-0.984567\pi\)
0.457439 0.889241i \(-0.348767\pi\)
\(44\) 0 0
\(45\) 2.39477 1.80695i 0.356992 0.269364i
\(46\) 0 0
\(47\) 1.95292 + 3.38256i 0.284863 + 0.493396i 0.972576 0.232586i \(-0.0747187\pi\)
−0.687713 + 0.725982i \(0.741385\pi\)
\(48\) 0 0
\(49\) −2.26225 + 3.91833i −0.323178 + 0.559761i
\(50\) 0 0
\(51\) 10.0746 + 2.04641i 1.41073 + 0.286555i
\(52\) 0 0
\(53\) 8.25944 1.13452 0.567261 0.823538i \(-0.308003\pi\)
0.567261 + 0.823538i \(0.308003\pi\)
\(54\) 0 0
\(55\) 3.68935 0.497471
\(56\) 0 0
\(57\) −8.65702 1.75847i −1.14665 0.232915i
\(58\) 0 0
\(59\) −1.39477 + 2.41582i −0.181584 + 0.314513i −0.942420 0.334431i \(-0.891456\pi\)
0.760836 + 0.648944i \(0.224789\pi\)
\(60\) 0 0
\(61\) 0.0729031 + 0.126272i 0.00933429 + 0.0161675i 0.870655 0.491894i \(-0.163695\pi\)
−0.861321 + 0.508062i \(0.830362\pi\)
\(62\) 0 0
\(63\) 1.24749 + 10.1076i 0.157169 + 1.27344i
\(64\) 0 0
\(65\) −0.867473 1.50251i −0.107597 0.186363i
\(66\) 0 0
\(67\) −3.54206 + 6.13503i −0.432732 + 0.749513i −0.997107 0.0760049i \(-0.975784\pi\)
0.564376 + 0.825518i \(0.309117\pi\)
\(68\) 0 0
\(69\) 5.58116 6.31234i 0.671893 0.759916i
\(70\) 0 0
\(71\) −0.110246 −0.0130837 −0.00654187 0.999979i \(-0.502082\pi\)
−0.00654187 + 0.999979i \(0.502082\pi\)
\(72\) 0 0
\(73\) 15.3787 1.79994 0.899970 0.435952i \(-0.143588\pi\)
0.899970 + 0.435952i \(0.143588\pi\)
\(74\) 0 0
\(75\) 0.550102 + 1.64237i 0.0635203 + 0.189645i
\(76\) 0 0
\(77\) −6.26225 + 10.8465i −0.713649 + 1.23608i
\(78\) 0 0
\(79\) 2.39477 + 4.14787i 0.269433 + 0.466672i 0.968716 0.248174i \(-0.0798303\pi\)
−0.699282 + 0.714846i \(0.746497\pi\)
\(80\) 0 0
\(81\) 6.26003 + 6.46622i 0.695559 + 0.718469i
\(82\) 0 0
\(83\) 8.38673 + 14.5262i 0.920564 + 1.59446i 0.798545 + 0.601935i \(0.205603\pi\)
0.122018 + 0.992528i \(0.461063\pi\)
\(84\) 0 0
\(85\) −2.96768 + 5.14017i −0.321890 + 0.557530i
\(86\) 0 0
\(87\) 0.660348 + 1.97152i 0.0707967 + 0.211369i
\(88\) 0 0
\(89\) −2.37869 −0.252141 −0.126070 0.992021i \(-0.540237\pi\)
−0.126070 + 0.992021i \(0.540237\pi\)
\(90\) 0 0
\(91\) 5.88975 0.617414
\(92\) 0 0
\(93\) 5.24321 5.93011i 0.543695 0.614924i
\(94\) 0 0
\(95\) 2.55010 4.41691i 0.261635 0.453165i
\(96\) 0 0
\(97\) 3.76003 + 6.51257i 0.381773 + 0.661251i 0.991316 0.131502i \(-0.0419801\pi\)
−0.609542 + 0.792753i \(0.708647\pi\)
\(98\) 0 0
\(99\) 1.35574 + 10.9847i 0.136257 + 1.10400i
\(100\) 0 0
\(101\) 1.92931 + 3.34167i 0.191974 + 0.332508i 0.945904 0.324446i \(-0.105178\pi\)
−0.753930 + 0.656954i \(0.771844\pi\)
\(102\) 0 0
\(103\) 2.18484 3.78426i 0.215279 0.372874i −0.738080 0.674713i \(-0.764267\pi\)
0.953359 + 0.301839i \(0.0976005\pi\)
\(104\) 0 0
\(105\) −5.76225 1.17046i −0.562338 0.114225i
\(106\) 0 0
\(107\) −20.0550 −1.93879 −0.969397 0.245499i \(-0.921048\pi\)
−0.969397 + 0.245499i \(0.921048\pi\)
\(108\) 0 0
\(109\) 17.7839 1.70339 0.851696 0.524036i \(-0.175574\pi\)
0.851696 + 0.524036i \(0.175574\pi\)
\(110\) 0 0
\(111\) 5.33965 + 1.08462i 0.506817 + 0.102948i
\(112\) 0 0
\(113\) −8.81907 + 15.2751i −0.829628 + 1.43696i 0.0687022 + 0.997637i \(0.478114\pi\)
−0.898330 + 0.439321i \(0.855219\pi\)
\(114\) 0 0
\(115\) 2.43233 + 4.21293i 0.226816 + 0.392857i
\(116\) 0 0
\(117\) 4.15481 3.13496i 0.384112 0.289827i
\(118\) 0 0
\(119\) −10.0746 17.4497i −0.923537 1.59961i
\(120\) 0 0
\(121\) −1.30563 + 2.26142i −0.118694 + 0.205584i
\(122\) 0 0
\(123\) 9.91684 11.2160i 0.894171 1.01131i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −10.7544 −0.954301 −0.477150 0.878822i \(-0.658330\pi\)
−0.477150 + 0.878822i \(0.658330\pi\)
\(128\) 0 0
\(129\) 3.90584 + 11.6612i 0.343890 + 1.02671i
\(130\) 0 0
\(131\) 0.459419 0.795737i 0.0401396 0.0695238i −0.845258 0.534359i \(-0.820553\pi\)
0.885397 + 0.464835i \(0.153886\pi\)
\(132\) 0 0
\(133\) 8.65702 + 14.9944i 0.750659 + 1.30018i
\(134\) 0 0
\(135\) −4.68787 + 2.24141i −0.403467 + 0.192910i
\(136\) 0 0
\(137\) −5.59518 9.69114i −0.478029 0.827970i 0.521654 0.853157i \(-0.325315\pi\)
−0.999683 + 0.0251870i \(0.991982\pi\)
\(138\) 0 0
\(139\) −5.73495 + 9.93322i −0.486432 + 0.842525i −0.999878 0.0155969i \(-0.995035\pi\)
0.513447 + 0.858122i \(0.328368\pi\)
\(140\) 0 0
\(141\) −2.14861 6.41484i −0.180946 0.540227i
\(142\) 0 0
\(143\) 6.40082 0.535263
\(144\) 0 0
\(145\) −1.20041 −0.0996886
\(146\) 0 0
\(147\) 5.19089 5.87094i 0.428137 0.484227i
\(148\) 0 0
\(149\) 0.467678 0.810042i 0.0383137 0.0663612i −0.846233 0.532814i \(-0.821135\pi\)
0.884546 + 0.466452i \(0.154468\pi\)
\(150\) 0 0
\(151\) 7.73443 + 13.3964i 0.629419 + 1.09019i 0.987669 + 0.156559i \(0.0500403\pi\)
−0.358250 + 0.933626i \(0.616626\pi\)
\(152\) 0 0
\(153\) −16.3949 6.94711i −1.32545 0.561641i
\(154\) 0 0
\(155\) 2.28505 + 3.95782i 0.183540 + 0.317900i
\(156\) 0 0
\(157\) 10.9839 19.0247i 0.876612 1.51834i 0.0215762 0.999767i \(-0.493132\pi\)
0.855036 0.518569i \(-0.173535\pi\)
\(158\) 0 0
\(159\) −14.0195 2.84772i −1.11182 0.225839i
\(160\) 0 0
\(161\) −16.5145 −1.30152
\(162\) 0 0
\(163\) −24.1492 −1.89151 −0.945756 0.324879i \(-0.894676\pi\)
−0.945756 + 0.324879i \(0.894676\pi\)
\(164\) 0 0
\(165\) −6.26225 1.27203i −0.487515 0.0990271i
\(166\) 0 0
\(167\) 9.52302 16.4944i 0.736913 1.27637i −0.216966 0.976179i \(-0.569616\pi\)
0.953879 0.300192i \(-0.0970507\pi\)
\(168\) 0 0
\(169\) 4.99498 + 8.65156i 0.384229 + 0.665504i
\(170\) 0 0
\(171\) 14.0880 + 5.96960i 1.07734 + 0.456507i
\(172\) 0 0
\(173\) −10.2138 17.6909i −0.776544 1.34501i −0.933923 0.357475i \(-0.883638\pi\)
0.157379 0.987538i \(-0.449696\pi\)
\(174\) 0 0
\(175\) 1.69739 2.93996i 0.128310 0.222240i
\(176\) 0 0
\(177\) 3.20041 3.61969i 0.240557 0.272072i
\(178\) 0 0
\(179\) −2.21945 −0.165890 −0.0829448 0.996554i \(-0.526433\pi\)
−0.0829448 + 0.996554i \(0.526433\pi\)
\(180\) 0 0
\(181\) 20.7795 1.54453 0.772264 0.635301i \(-0.219124\pi\)
0.772264 + 0.635301i \(0.219124\pi\)
\(182\) 0 0
\(183\) −0.0802084 0.239468i −0.00592917 0.0177020i
\(184\) 0 0
\(185\) −1.57290 + 2.72435i −0.115642 + 0.200298i
\(186\) 0 0
\(187\) −10.9488 18.9639i −0.800655 1.38677i
\(188\) 0 0
\(189\) 1.36747 17.5867i 0.0994691 1.27924i
\(190\) 0 0
\(191\) 7.02000 + 12.1590i 0.507949 + 0.879794i 0.999958 + 0.00920328i \(0.00292954\pi\)
−0.492009 + 0.870590i \(0.663737\pi\)
\(192\) 0 0
\(193\) −10.9576 + 18.9792i −0.788748 + 1.36615i 0.137986 + 0.990434i \(0.455937\pi\)
−0.926734 + 0.375717i \(0.877396\pi\)
\(194\) 0 0
\(195\) 0.954398 + 2.84943i 0.0683459 + 0.204052i
\(196\) 0 0
\(197\) −16.4599 −1.17272 −0.586358 0.810052i \(-0.699439\pi\)
−0.586358 + 0.810052i \(0.699439\pi\)
\(198\) 0 0
\(199\) 4.69939 0.333131 0.166565 0.986030i \(-0.446732\pi\)
0.166565 + 0.986030i \(0.446732\pi\)
\(200\) 0 0
\(201\) 8.12751 9.19228i 0.573270 0.648373i
\(202\) 0 0
\(203\) 2.03756 3.52916i 0.143009 0.247698i
\(204\) 0 0
\(205\) 4.32187 + 7.48570i 0.301853 + 0.522824i
\(206\) 0 0
\(207\) −11.6498 + 8.79019i −0.809716 + 0.610961i
\(208\) 0 0
\(209\) 9.40821 + 16.2955i 0.650779 + 1.12718i
\(210\) 0 0
\(211\) 1.45594 2.52176i 0.100231 0.173605i −0.811549 0.584285i \(-0.801375\pi\)
0.911780 + 0.410679i \(0.134708\pi\)
\(212\) 0 0
\(213\) 0.187129 + 0.0380109i 0.0128219 + 0.00260446i
\(214\) 0 0
\(215\) −7.10020 −0.484230
\(216\) 0 0
\(217\) −15.5145 −1.05319
\(218\) 0 0
\(219\) −26.1036 5.30232i −1.76392 0.358298i
\(220\) 0 0
\(221\) −5.14876 + 8.91792i −0.346343 + 0.599884i
\(222\) 0 0
\(223\) 3.29309 + 5.70380i 0.220522 + 0.381955i 0.954967 0.296714i \(-0.0958907\pi\)
−0.734445 + 0.678668i \(0.762557\pi\)
\(224\) 0 0
\(225\) −0.367473 2.97741i −0.0244982 0.198494i
\(226\) 0 0
\(227\) 2.61475 + 4.52887i 0.173547 + 0.300592i 0.939657 0.342117i \(-0.111144\pi\)
−0.766111 + 0.642709i \(0.777811\pi\)
\(228\) 0 0
\(229\) 4.82409 8.35556i 0.318785 0.552151i −0.661450 0.749989i \(-0.730059\pi\)
0.980235 + 0.197838i \(0.0633920\pi\)
\(230\) 0 0
\(231\) 14.3692 16.2516i 0.945422 1.06928i
\(232\) 0 0
\(233\) 14.4333 0.945556 0.472778 0.881181i \(-0.343251\pi\)
0.472778 + 0.881181i \(0.343251\pi\)
\(234\) 0 0
\(235\) 3.90584 0.254789
\(236\) 0 0
\(237\) −2.63474 7.86623i −0.171145 0.510966i
\(238\) 0 0
\(239\) 14.1136 24.4455i 0.912935 1.58125i 0.103039 0.994677i \(-0.467143\pi\)
0.809896 0.586573i \(-0.199523\pi\)
\(240\) 0 0
\(241\) −6.97270 12.0771i −0.449151 0.777952i 0.549180 0.835704i \(-0.314940\pi\)
−0.998331 + 0.0577518i \(0.981607\pi\)
\(242\) 0 0
\(243\) −8.39625 13.1340i −0.538620 0.842549i
\(244\) 0 0
\(245\) 2.26225 + 3.91833i 0.144530 + 0.250333i
\(246\) 0 0
\(247\) 4.42429 7.66310i 0.281511 0.487591i
\(248\) 0 0
\(249\) −9.22712 27.5483i −0.584745 1.74580i
\(250\) 0 0
\(251\) 15.5279 0.980112 0.490056 0.871691i \(-0.336976\pi\)
0.490056 + 0.871691i \(0.336976\pi\)
\(252\) 0 0
\(253\) −17.9474 −1.12835
\(254\) 0 0
\(255\) 6.80955 7.70165i 0.426430 0.482296i
\(256\) 0 0
\(257\) −0.119247 + 0.206541i −0.00743841 + 0.0128837i −0.869721 0.493544i \(-0.835701\pi\)
0.862282 + 0.506428i \(0.169034\pi\)
\(258\) 0 0
\(259\) −5.33965 9.24855i −0.331790 0.574677i
\(260\) 0 0
\(261\) −0.441119 3.57411i −0.0273046 0.221232i
\(262\) 0 0
\(263\) −4.92879 8.53692i −0.303922 0.526409i 0.673098 0.739553i \(-0.264963\pi\)
−0.977021 + 0.213144i \(0.931630\pi\)
\(264\) 0 0
\(265\) 4.12972 7.15289i 0.253687 0.439398i
\(266\) 0 0
\(267\) 4.03756 + 0.820134i 0.247095 + 0.0501914i
\(268\) 0 0
\(269\) −26.9534 −1.64338 −0.821688 0.569938i \(-0.806967\pi\)
−0.821688 + 0.569938i \(0.806967\pi\)
\(270\) 0 0
\(271\) 28.4677 1.72929 0.864644 0.502385i \(-0.167544\pi\)
0.864644 + 0.502385i \(0.167544\pi\)
\(272\) 0 0
\(273\) −9.99720 2.03069i −0.605058 0.122903i
\(274\) 0 0
\(275\) 1.84467 3.19507i 0.111238 0.192670i
\(276\) 0 0
\(277\) 16.2817 + 28.2008i 0.978274 + 1.69442i 0.668678 + 0.743552i \(0.266861\pi\)
0.309596 + 0.950868i \(0.399806\pi\)
\(278\) 0 0
\(279\) −10.9444 + 8.25792i −0.655222 + 0.494389i
\(280\) 0 0
\(281\) −6.79781 11.7742i −0.405523 0.702387i 0.588859 0.808236i \(-0.299577\pi\)
−0.994382 + 0.105849i \(0.966244\pi\)
\(282\) 0 0
\(283\) 8.26749 14.3197i 0.491451 0.851218i −0.508501 0.861062i \(-0.669800\pi\)
0.999952 + 0.00984353i \(0.00313334\pi\)
\(284\) 0 0
\(285\) −5.85139 + 6.61797i −0.346606 + 0.392015i
\(286\) 0 0
\(287\) −29.3436 −1.73210
\(288\) 0 0
\(289\) 18.2285 1.07226
\(290\) 0 0
\(291\) −4.13681 12.3507i −0.242504 0.724014i
\(292\) 0 0
\(293\) 12.6570 21.9226i 0.739431 1.28073i −0.213321 0.976982i \(-0.568428\pi\)
0.952752 0.303750i \(-0.0982388\pi\)
\(294\) 0 0
\(295\) 1.39477 + 2.41582i 0.0812069 + 0.140655i
\(296\) 0 0
\(297\) 1.48613 19.1127i 0.0862341 1.10903i
\(298\) 0 0
\(299\) 4.21997 + 7.30920i 0.244047 + 0.422702i
\(300\) 0 0
\(301\) 12.0518 20.8743i 0.694654 1.20318i
\(302\) 0 0
\(303\) −2.12264 6.33730i −0.121942 0.364068i
\(304\) 0 0
\(305\) 0.145806 0.00834884
\(306\) 0 0
\(307\) −6.62323 −0.378008 −0.189004 0.981976i \(-0.560526\pi\)
−0.189004 + 0.981976i \(0.560526\pi\)
\(308\) 0 0
\(309\) −5.01328 + 5.67006i −0.285196 + 0.322558i
\(310\) 0 0
\(311\) 4.01556 6.95516i 0.227702 0.394391i −0.729425 0.684061i \(-0.760212\pi\)
0.957127 + 0.289670i \(0.0935455\pi\)
\(312\) 0 0
\(313\) 10.5407 + 18.2571i 0.595798 + 1.03195i 0.993434 + 0.114408i \(0.0364973\pi\)
−0.397636 + 0.917543i \(0.630169\pi\)
\(314\) 0 0
\(315\) 9.37721 + 3.97346i 0.528346 + 0.223879i
\(316\) 0 0
\(317\) 10.8058 + 18.7162i 0.606913 + 1.05120i 0.991746 + 0.128219i \(0.0409259\pi\)
−0.384832 + 0.922986i \(0.625741\pi\)
\(318\) 0 0
\(319\) 2.21436 3.83539i 0.123980 0.214740i
\(320\) 0 0
\(321\) 34.0412 + 6.91465i 1.89999 + 0.385938i
\(322\) 0 0
\(323\) −30.2715 −1.68435
\(324\) 0 0
\(325\) −1.73495 −0.0962375
\(326\) 0 0
\(327\) −30.1862 6.13161i −1.66930 0.339079i
\(328\) 0 0
\(329\) −6.62972 + 11.4830i −0.365508 + 0.633079i
\(330\) 0 0
\(331\) −11.8146 20.4635i −0.649391 1.12478i −0.983269 0.182162i \(-0.941691\pi\)
0.333877 0.942616i \(-0.391643\pi\)
\(332\) 0 0
\(333\) −8.68950 3.68205i −0.476182 0.201775i
\(334\) 0 0
\(335\) 3.54206 + 6.13503i 0.193523 + 0.335192i
\(336\) 0 0
\(337\) 7.87367 13.6376i 0.428906 0.742887i −0.567870 0.823118i \(-0.692232\pi\)
0.996776 + 0.0802309i \(0.0255658\pi\)
\(338\) 0 0
\(339\) 20.2360 22.8870i 1.09907 1.24305i
\(340\) 0 0
\(341\) −16.8607 −0.913057
\(342\) 0 0
\(343\) 8.40378 0.453761
\(344\) 0 0
\(345\) −2.67607 7.98960i −0.144075 0.430146i
\(346\) 0 0
\(347\) −8.29405 + 14.3657i −0.445248 + 0.771192i −0.998069 0.0621076i \(-0.980218\pi\)
0.552822 + 0.833300i \(0.313551\pi\)
\(348\) 0 0
\(349\) −12.2088 21.1463i −0.653523 1.13194i −0.982262 0.187514i \(-0.939957\pi\)
0.328739 0.944421i \(-0.393376\pi\)
\(350\) 0 0
\(351\) −8.13320 + 3.88872i −0.434118 + 0.207565i
\(352\) 0 0
\(353\) 6.40082 + 11.0865i 0.340681 + 0.590077i 0.984559 0.175051i \(-0.0560090\pi\)
−0.643878 + 0.765128i \(0.722676\pi\)
\(354\) 0 0
\(355\) −0.0551228 + 0.0954754i −0.00292561 + 0.00506731i
\(356\) 0 0
\(357\) 11.0841 + 33.0925i 0.586634 + 1.75144i
\(358\) 0 0
\(359\) −21.4568 −1.13244 −0.566222 0.824252i \(-0.691596\pi\)
−0.566222 + 0.824252i \(0.691596\pi\)
\(360\) 0 0
\(361\) 7.01209 0.369057
\(362\) 0 0
\(363\) 2.99587 3.38835i 0.157242 0.177842i
\(364\) 0 0
\(365\) 7.68935 13.3183i 0.402479 0.697114i
\(366\) 0 0
\(367\) −10.9098 18.8962i −0.569484 0.986376i −0.996617 0.0821868i \(-0.973810\pi\)
0.427133 0.904189i \(-0.359524\pi\)
\(368\) 0 0
\(369\) −20.6998 + 15.6188i −1.07759 + 0.813081i
\(370\) 0 0
\(371\) 14.0195 + 24.2824i 0.727855 + 1.26068i
\(372\) 0 0
\(373\) −11.1197 + 19.2599i −0.575755 + 0.997237i 0.420204 + 0.907430i \(0.361959\pi\)
−0.995959 + 0.0898076i \(0.971375\pi\)
\(374\) 0 0
\(375\) 1.69739 + 0.344784i 0.0876527 + 0.0178046i
\(376\) 0 0
\(377\) −2.08265 −0.107262
\(378\) 0 0
\(379\) 0.880753 0.0452413 0.0226206 0.999744i \(-0.492799\pi\)
0.0226206 + 0.999744i \(0.492799\pi\)
\(380\) 0 0
\(381\) 18.2544 + 3.70795i 0.935202 + 0.189964i
\(382\) 0 0
\(383\) 3.87419 6.71029i 0.197962 0.342880i −0.749906 0.661545i \(-0.769901\pi\)
0.947867 + 0.318665i \(0.103234\pi\)
\(384\) 0 0
\(385\) 6.26225 + 10.8465i 0.319154 + 0.552790i
\(386\) 0 0
\(387\) −2.60914 21.1402i −0.132630 1.07462i
\(388\) 0 0
\(389\) 7.02730 + 12.1716i 0.356298 + 0.617127i 0.987339 0.158623i \(-0.0507054\pi\)
−0.631041 + 0.775750i \(0.717372\pi\)
\(390\) 0 0
\(391\) 14.4368 25.0052i 0.730099 1.26457i
\(392\) 0 0
\(393\) −1.05417 + 1.19227i −0.0531758 + 0.0601422i
\(394\) 0 0
\(395\) 4.78955 0.240988
\(396\) 0 0
\(397\) 4.16232 0.208901 0.104451 0.994530i \(-0.466692\pi\)
0.104451 + 0.994530i \(0.466692\pi\)
\(398\) 0 0
\(399\) −9.52450 28.4361i −0.476821 1.42359i
\(400\) 0 0
\(401\) −6.49941 + 11.2573i −0.324565 + 0.562163i −0.981424 0.191850i \(-0.938551\pi\)
0.656859 + 0.754013i \(0.271885\pi\)
\(402\) 0 0
\(403\) 3.96444 + 6.86661i 0.197483 + 0.342050i
\(404\) 0 0
\(405\) 8.72993 2.18824i 0.433794 0.108734i
\(406\) 0 0
\(407\) −5.80298 10.0511i −0.287643 0.498213i
\(408\) 0 0
\(409\) −8.05460 + 13.9510i −0.398274 + 0.689832i −0.993513 0.113717i \(-0.963724\pi\)
0.595239 + 0.803549i \(0.297058\pi\)
\(410\) 0 0
\(411\) 6.15585 + 18.3788i 0.303646 + 0.906557i
\(412\) 0 0
\(413\) −9.46989 −0.465983
\(414\) 0 0
\(415\) 16.7735 0.823377
\(416\) 0 0
\(417\) 13.1592 14.8832i 0.644411 0.728834i
\(418\) 0 0
\(419\) −5.73443 + 9.93232i −0.280145 + 0.485226i −0.971420 0.237366i \(-0.923716\pi\)
0.691275 + 0.722592i \(0.257049\pi\)
\(420\) 0 0
\(421\) −3.32409 5.75749i −0.162006 0.280603i 0.773582 0.633696i \(-0.218463\pi\)
−0.935588 + 0.353093i \(0.885130\pi\)
\(422\) 0 0
\(423\) 1.43529 + 11.6293i 0.0697863 + 0.565435i
\(424\) 0 0
\(425\) 2.96768 + 5.14017i 0.143954 + 0.249335i
\(426\) 0 0
\(427\) −0.247490 + 0.428665i −0.0119769 + 0.0207445i
\(428\) 0 0
\(429\) −10.8647 2.20690i −0.524551 0.106550i
\(430\) 0 0
\(431\) 10.4599 0.503833 0.251917 0.967749i \(-0.418939\pi\)
0.251917 + 0.967749i \(0.418939\pi\)
\(432\) 0 0
\(433\) 24.3831 1.17178 0.585889 0.810391i \(-0.300745\pi\)
0.585889 + 0.810391i \(0.300745\pi\)
\(434\) 0 0
\(435\) 2.03756 + 0.413882i 0.0976935 + 0.0198441i
\(436\) 0 0
\(437\) −12.4054 + 21.4868i −0.593431 + 1.02785i
\(438\) 0 0
\(439\) −13.2594 22.9660i −0.632839 1.09611i −0.986969 0.160913i \(-0.948556\pi\)
0.354130 0.935196i \(-0.384777\pi\)
\(440\) 0 0
\(441\) −10.8352 + 8.17552i −0.515960 + 0.389310i
\(442\) 0 0
\(443\) −6.77199 11.7294i −0.321747 0.557282i 0.659102 0.752054i \(-0.270937\pi\)
−0.980849 + 0.194772i \(0.937603\pi\)
\(444\) 0 0
\(445\) −1.18935 + 2.06001i −0.0563804 + 0.0976537i
\(446\) 0 0
\(447\) −1.07312 + 1.21371i −0.0507568 + 0.0574064i
\(448\) 0 0
\(449\) −18.5511 −0.875478 −0.437739 0.899102i \(-0.644221\pi\)
−0.437739 + 0.899102i \(0.644221\pi\)
\(450\) 0 0
\(451\) −31.8898 −1.50163
\(452\) 0 0
\(453\) −8.50945 25.4056i −0.399809 1.19366i
\(454\) 0 0
\(455\) 2.94488 5.10068i 0.138058 0.239123i
\(456\) 0 0
\(457\) −15.9606 27.6446i −0.746605 1.29316i −0.949441 0.313945i \(-0.898349\pi\)
0.202836 0.979213i \(-0.434984\pi\)
\(458\) 0 0
\(459\) 25.4333 + 17.4446i 1.18712 + 0.814247i
\(460\) 0 0
\(461\) 3.03454 + 5.25597i 0.141333 + 0.244795i 0.927999 0.372584i \(-0.121528\pi\)
−0.786666 + 0.617379i \(0.788195\pi\)
\(462\) 0 0
\(463\) −12.4989 + 21.6487i −0.580873 + 1.00610i 0.414503 + 0.910048i \(0.363955\pi\)
−0.995376 + 0.0960534i \(0.969378\pi\)
\(464\) 0 0
\(465\) −2.51402 7.50580i −0.116585 0.348073i
\(466\) 0 0
\(467\) 4.46089 0.206425 0.103213 0.994659i \(-0.467088\pi\)
0.103213 + 0.994659i \(0.467088\pi\)
\(468\) 0 0
\(469\) −24.0490 −1.11048
\(470\) 0 0
\(471\) −25.2034 + 28.5052i −1.16131 + 1.31345i
\(472\) 0 0
\(473\) 13.0976 22.6856i 0.602226 1.04309i
\(474\) 0 0
\(475\) −2.55010 4.41691i −0.117007 0.202662i
\(476\) 0 0
\(477\) 22.8146 + 9.66737i 1.04461 + 0.442639i
\(478\) 0 0
\(479\) 14.5496 + 25.2006i 0.664787 + 1.15145i 0.979343 + 0.202206i \(0.0648112\pi\)
−0.314556 + 0.949239i \(0.601855\pi\)
\(480\) 0 0
\(481\) −2.72890 + 4.72660i −0.124427 + 0.215514i
\(482\) 0 0
\(483\) 28.0314 + 5.69392i 1.27547 + 0.259082i
\(484\) 0 0
\(485\) 7.52007 0.341469
\(486\) 0 0
\(487\) −14.1873 −0.642887 −0.321444 0.946929i \(-0.604168\pi\)
−0.321444 + 0.946929i \(0.604168\pi\)
\(488\) 0 0
\(489\) 40.9905 + 8.32625i 1.85366 + 0.376526i
\(490\) 0 0
\(491\) 19.0902 33.0651i 0.861527 1.49221i −0.00892773 0.999960i \(-0.502842\pi\)
0.870455 0.492248i \(-0.163825\pi\)
\(492\) 0 0
\(493\) 3.56243 + 6.17031i 0.160444 + 0.277897i
\(494\) 0 0
\(495\) 10.1909 + 4.31824i 0.458046 + 0.194091i
\(496\) 0 0
\(497\) −0.187129 0.324118i −0.00839390 0.0145387i
\(498\) 0 0
\(499\) −2.70839 + 4.69106i −0.121244 + 0.210001i −0.920259 0.391311i \(-0.872022\pi\)
0.799014 + 0.601312i \(0.205355\pi\)
\(500\) 0 0
\(501\) −21.8512 + 24.7139i −0.976241 + 1.10414i
\(502\) 0 0
\(503\) −11.1544 −0.497349 −0.248674 0.968587i \(-0.579995\pi\)
−0.248674 + 0.968587i \(0.579995\pi\)
\(504\) 0 0
\(505\) 3.85863 0.171707
\(506\) 0 0
\(507\) −5.49550 16.4072i −0.244064 0.728671i
\(508\) 0 0
\(509\) 9.90821 17.1615i 0.439174 0.760671i −0.558452 0.829537i \(-0.688605\pi\)
0.997626 + 0.0688656i \(0.0219380\pi\)
\(510\) 0 0
\(511\) 26.1036 + 45.2128i 1.15476 + 2.00009i
\(512\) 0 0
\(513\) −21.8546 14.9900i −0.964905 0.661827i
\(514\) 0 0
\(515\) −2.18484 3.78426i −0.0962758 0.166755i
\(516\) 0 0
\(517\) −7.20499 + 12.4794i −0.316875 + 0.548844i
\(518\) 0 0
\(519\) 11.2373 + 33.5499i 0.493263 + 1.47268i
\(520\) 0 0
\(521\) −13.7807 −0.603743 −0.301871 0.953349i \(-0.597611\pi\)
−0.301871 + 0.953349i \(0.597611\pi\)
\(522\) 0 0
\(523\) −1.66117 −0.0726381 −0.0363190 0.999340i \(-0.511563\pi\)
−0.0363190 + 0.999340i \(0.511563\pi\)
\(524\) 0 0
\(525\) −3.89477 + 4.40502i −0.169982 + 0.192251i
\(526\) 0 0
\(527\) 13.5626 23.4911i 0.590795 1.02329i
\(528\) 0 0
\(529\) −0.332502 0.575910i −0.0144566 0.0250395i
\(530\) 0 0
\(531\) −6.68034 + 5.04057i −0.289902 + 0.218742i
\(532\) 0 0
\(533\) 7.49822 + 12.9873i 0.324784 + 0.562542i
\(534\) 0 0
\(535\) −10.0275 + 17.3682i −0.433527 + 0.750892i
\(536\) 0 0
\(537\) 3.76727 + 0.765231i 0.162570 + 0.0330221i
\(538\) 0 0
\(539\) −16.6924 −0.718994
\(540\) 0 0
\(541\) −38.9678 −1.67536 −0.837679 0.546163i \(-0.816088\pi\)
−0.837679 + 0.546163i \(0.816088\pi\)
\(542\) 0 0
\(543\) −35.2709 7.16444i −1.51362 0.307455i
\(544\) 0 0
\(545\) 8.89197 15.4013i 0.380890 0.659721i
\(546\) 0 0
\(547\) 11.3706 + 19.6945i 0.486174 + 0.842078i 0.999874 0.0158922i \(-0.00505885\pi\)
−0.513700 + 0.857970i \(0.671726\pi\)
\(548\) 0 0
\(549\) 0.0535799 + 0.434125i 0.00228674 + 0.0185280i
\(550\) 0 0
\(551\) −3.06117 5.30210i −0.130410 0.225877i
\(552\) 0 0
\(553\) −8.12972 + 14.0811i −0.345711 + 0.598789i
\(554\) 0 0
\(555\) 3.60914 4.08196i 0.153199 0.173270i
\(556\) 0 0
\(557\) 32.7193 1.38636 0.693181 0.720764i \(-0.256209\pi\)
0.693181 + 0.720764i \(0.256209\pi\)
\(558\) 0 0
\(559\) −12.3185 −0.521016
\(560\) 0 0
\(561\) 12.0459 + 35.9640i 0.508579 + 1.51840i
\(562\) 0 0
\(563\) 9.75251 16.8918i 0.411019 0.711906i −0.583982 0.811766i \(-0.698506\pi\)
0.995001 + 0.0998602i \(0.0318395\pi\)
\(564\) 0 0
\(565\) 8.81907 + 15.2751i 0.371021 + 0.642627i
\(566\) 0 0
\(567\) −8.38473 + 29.3799i −0.352126 + 1.23384i
\(568\) 0 0
\(569\) −6.46989 11.2062i −0.271232 0.469788i 0.697946 0.716151i \(-0.254098\pi\)
−0.969178 + 0.246363i \(0.920764\pi\)
\(570\) 0 0
\(571\) −0.123678 + 0.214217i −0.00517578 + 0.00896472i −0.868602 0.495511i \(-0.834981\pi\)
0.863426 + 0.504476i \(0.168314\pi\)
\(572\) 0 0
\(573\) −7.72343 23.0589i −0.322651 0.963299i
\(574\) 0 0
\(575\) 4.86467 0.202871
\(576\) 0 0
\(577\) 19.0431 0.792774 0.396387 0.918084i \(-0.370264\pi\)
0.396387 + 0.918084i \(0.370264\pi\)
\(578\) 0 0
\(579\) 25.1431 28.4370i 1.04491 1.18180i
\(580\) 0 0
\(581\) −28.4711 + 49.3133i −1.18118 + 2.04586i
\(582\) 0 0
\(583\) 15.2360 + 26.3895i 0.631009 + 1.09294i
\(584\) 0 0
\(585\) −0.637547 5.16565i −0.0263593 0.213573i
\(586\) 0 0
\(587\) −0.408861 0.708167i −0.0168755 0.0292292i 0.857464 0.514543i \(-0.172039\pi\)
−0.874340 + 0.485314i \(0.838705\pi\)
\(588\) 0 0
\(589\) −11.6542 + 20.1857i −0.480204 + 0.831737i
\(590\) 0 0
\(591\) 27.9387 + 5.67509i 1.14925 + 0.233442i
\(592\) 0 0
\(593\) 45.3441 1.86206 0.931030 0.364942i \(-0.118911\pi\)
0.931030 + 0.364942i \(0.118911\pi\)
\(594\) 0 0
\(595\) −20.1492 −0.826037
\(596\) 0 0
\(597\) −7.97668 1.62027i −0.326464 0.0663133i
\(598\) 0 0
\(599\) 1.43594 2.48713i 0.0586711 0.101621i −0.835198 0.549949i \(-0.814647\pi\)
0.893869 + 0.448328i \(0.147980\pi\)
\(600\) 0 0
\(601\) −23.3821 40.4990i −0.953775 1.65199i −0.737147 0.675733i \(-0.763827\pi\)
−0.216628 0.976254i \(-0.569506\pi\)
\(602\) 0 0
\(603\) −16.9649 + 12.8006i −0.690863 + 0.521282i
\(604\) 0 0
\(605\) 1.30563 + 2.26142i 0.0530816 + 0.0919400i
\(606\) 0 0
\(607\) −7.89123 + 13.6680i −0.320295 + 0.554768i −0.980549 0.196275i \(-0.937115\pi\)
0.660254 + 0.751043i \(0.270449\pi\)
\(608\) 0 0
\(609\) −4.67532 + 5.28783i −0.189454 + 0.214274i
\(610\) 0 0
\(611\) 6.77642 0.274145
\(612\) 0 0
\(613\) 10.6216 0.429003 0.214502 0.976724i \(-0.431187\pi\)
0.214502 + 0.976724i \(0.431187\pi\)
\(614\) 0 0
\(615\) −4.75494 14.1962i −0.191738 0.572448i
\(616\) 0 0
\(617\) 15.2789 26.4639i 0.615106 1.06540i −0.375260 0.926920i \(-0.622446\pi\)
0.990366 0.138475i \(-0.0442202\pi\)
\(618\) 0 0
\(619\) −9.57358 16.5819i −0.384795 0.666484i 0.606946 0.794743i \(-0.292394\pi\)
−0.991741 + 0.128259i \(0.959061\pi\)
\(620\) 0 0
\(621\) 22.8049 10.9037i 0.915130 0.437551i
\(622\) 0 0
\(623\) −4.03756 6.99326i −0.161761 0.280179i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −10.3510 30.9036i −0.413377 1.23417i
\(628\) 0 0
\(629\) 18.6715 0.744481
\(630\) 0 0
\(631\) 32.5750 1.29679 0.648395 0.761304i \(-0.275441\pi\)
0.648395 + 0.761304i \(0.275441\pi\)
\(632\) 0 0
\(633\) −3.34076 + 3.77843i −0.132783 + 0.150179i
\(634\) 0 0
\(635\) −5.37721 + 9.31360i −0.213388 + 0.369599i
\(636\) 0 0
\(637\) 3.92488 + 6.79809i 0.155509 + 0.269350i
\(638\) 0 0
\(639\) −0.304526 0.129038i −0.0120468 0.00510468i
\(640\) 0 0
\(641\) 4.51624 + 7.82235i 0.178381 + 0.308964i 0.941326 0.337499i \(-0.109581\pi\)
−0.762945 + 0.646463i \(0.776247\pi\)
\(642\) 0 0
\(643\) 7.02656 12.1704i 0.277101 0.479952i −0.693562 0.720397i \(-0.743960\pi\)
0.970663 + 0.240444i \(0.0772931\pi\)
\(644\) 0 0
\(645\) 12.0518 + 2.44803i 0.474539 + 0.0963913i
\(646\) 0 0
\(647\) 17.4970 0.687879 0.343940 0.938992i \(-0.388238\pi\)
0.343940 + 0.938992i \(0.388238\pi\)
\(648\) 0 0
\(649\) −10.2916 −0.403981
\(650\) 0 0
\(651\) 26.3340 + 5.34913i 1.03211 + 0.209649i
\(652\) 0 0
\(653\) 16.8102 29.1162i 0.657835 1.13940i −0.323340 0.946283i \(-0.604806\pi\)
0.981175 0.193120i \(-0.0618608\pi\)
\(654\) 0 0
\(655\) −0.459419 0.795737i −0.0179510 0.0310920i
\(656\) 0 0
\(657\) 42.4798 + 18.0002i 1.65729 + 0.702254i
\(658\) 0 0
\(659\) 12.9944 + 22.5069i 0.506190 + 0.876746i 0.999974 + 0.00716194i \(0.00227973\pi\)
−0.493785 + 0.869584i \(0.664387\pi\)
\(660\) 0 0
\(661\) 19.0902 33.0651i 0.742521 1.28608i −0.208823 0.977954i \(-0.566963\pi\)
0.951344 0.308131i \(-0.0997035\pi\)
\(662\) 0 0
\(663\) 11.8142 13.3620i 0.458826 0.518935i
\(664\) 0 0
\(665\) 17.3140 0.671410
\(666\) 0 0
\(667\) 5.83959 0.226110
\(668\) 0 0
\(669\) −3.62307 10.8170i −0.140076 0.418208i
\(670\) 0 0
\(671\) −0.268965 + 0.465861i −0.0103833 + 0.0179844i
\(672\) 0 0
\(673\) −14.4436 25.0171i −0.556760 0.964337i −0.997764 0.0668322i \(-0.978711\pi\)
0.441004 0.897505i \(-0.354623\pi\)
\(674\) 0 0
\(675\) −0.402817 + 5.18052i −0.0155044 + 0.199398i
\(676\) 0 0
\(677\) −0.372494 0.645178i −0.0143161 0.0247962i 0.858779 0.512347i \(-0.171224\pi\)
−0.873095 + 0.487551i \(0.837890\pi\)
\(678\) 0 0
\(679\) −12.7645 + 22.1087i −0.489855 + 0.848454i
\(680\) 0 0
\(681\) −2.87676 8.58877i −0.110238 0.329123i
\(682\) 0 0
\(683\) −14.3877 −0.550530 −0.275265 0.961368i \(-0.588766\pi\)
−0.275265 + 0.961368i \(0.588766\pi\)
\(684\) 0 0
\(685\) −11.1904 −0.427562
\(686\) 0 0
\(687\) −11.0692 + 12.5194i −0.422317 + 0.477644i
\(688\) 0 0
\(689\) 7.16485 12.4099i 0.272959 0.472779i
\(690\) 0 0
\(691\) −1.49498 2.58938i −0.0568717 0.0985047i 0.836188 0.548443i \(-0.184779\pi\)
−0.893060 + 0.449938i \(0.851446\pi\)
\(692\) 0 0
\(693\) −29.9934 + 22.6311i −1.13935 + 0.859684i
\(694\) 0 0
\(695\) 5.73495 + 9.93322i 0.217539 + 0.376788i
\(696\) 0 0
\(697\) 25.6518 44.4303i 0.971633 1.68292i
\(698\) 0 0
\(699\) −24.4989 4.97636i −0.926633 0.188223i
\(700\) 0 0
\(701\) −22.3731 −0.845020 −0.422510 0.906358i \(-0.638851\pi\)
−0.422510 + 0.906358i \(0.638851\pi\)
\(702\) 0 0
\(703\) −16.0443 −0.605121
\(704\) 0 0
\(705\) −6.62972 1.34667i −0.249690 0.0507185i
\(706\) 0 0
\(707\) −6.54958 + 11.3442i −0.246322 + 0.426643i
\(708\) 0 0
\(709\) −20.7494 35.9390i −0.779260 1.34972i −0.932369 0.361509i \(-0.882262\pi\)
0.153109 0.988209i \(-0.451072\pi\)
\(710\) 0 0
\(711\) 1.76003 + 14.2604i 0.0660064 + 0.534809i
\(712\) 0 0
\(713\) −11.1160 19.2535i −0.416298 0.721049i
\(714\) 0 0
\(715\) 3.20041 5.54327i 0.119689 0.207307i
\(716\) 0 0
\(717\) −32.3847 + 36.6274i −1.20943 + 1.36788i
\(718\) 0 0
\(719\) −20.5511 −0.766425 −0.383213 0.923660i \(-0.625182\pi\)
−0.383213 + 0.923660i \(0.625182\pi\)
\(720\) 0 0
\(721\) 14.8341 0.552451
\(722\) 0 0
\(723\) 7.67139 + 22.9035i 0.285302 + 0.851792i
\(724\) 0 0
\(725\) −0.600205 + 1.03958i −0.0222910 + 0.0386092i
\(726\) 0 0
\(727\) 19.0475 + 32.9913i 0.706433 + 1.22358i 0.966172 + 0.257899i \(0.0830303\pi\)
−0.259739 + 0.965679i \(0.583636\pi\)
\(728\) 0 0
\(729\) 9.72329 + 25.1884i 0.360122 + 0.932905i
\(730\) 0 0
\(731\) 21.0711 + 36.4963i 0.779344 + 1.34986i
\(732\) 0 0
\(733\) −13.3287 + 23.0859i −0.492305 + 0.852698i −0.999961 0.00886253i \(-0.997179\pi\)
0.507656 + 0.861560i \(0.330512\pi\)
\(734\) 0 0
\(735\) −2.48894 7.43091i −0.0918058 0.274093i
\(736\) 0 0
\(737\) −26.1358 −0.962723
\(738\) 0 0
\(739\) −23.4888 −0.864048 −0.432024 0.901862i \(-0.642200\pi\)
−0.432024 + 0.901862i \(0.642200\pi\)
\(740\) 0 0
\(741\) −10.1518 + 11.4818i −0.372938 + 0.421795i
\(742\) 0 0
\(743\) 15.3838 26.6455i 0.564376 0.977528i −0.432731 0.901523i \(-0.642450\pi\)
0.997107 0.0760050i \(-0.0242165\pi\)
\(744\) 0 0
\(745\) −0.467678 0.810042i −0.0171344 0.0296776i
\(746\) 0 0
\(747\) 6.16380 + 49.9415i 0.225522 + 1.82726i
\(748\) 0 0
\(749\) −34.0412 58.9610i −1.24384 2.15439i
\(750\) 0 0
\(751\) 0.981478 1.69997i 0.0358146 0.0620328i −0.847562 0.530696i \(-0.821931\pi\)
0.883377 + 0.468663i \(0.155264\pi\)
\(752\) 0 0
\(753\) −26.3568 5.35376i −0.960497 0.195102i
\(754\) 0 0
\(755\) 15.4689 0.562969
\(756\) 0 0
\(757\) −26.4631 −0.961818 −0.480909 0.876771i \(-0.659693\pi\)
−0.480909 + 0.876771i \(0.659693\pi\)
\(758\) 0 0
\(759\) 30.4638 + 6.18799i 1.10576 + 0.224610i
\(760\) 0 0
\(761\) 5.08618 8.80953i 0.184374 0.319345i −0.758991 0.651101i \(-0.774308\pi\)
0.943365 + 0.331756i \(0.107641\pi\)
\(762\) 0 0
\(763\) 30.1862 + 52.2841i 1.09282 + 1.89281i
\(764\) 0 0
\(765\) −14.2138 + 10.7249i −0.513903 + 0.387758i
\(766\) 0 0
\(767\) 2.41986 + 4.19132i 0.0873761 + 0.151340i
\(768\) 0 0
\(769\) −6.06406 + 10.5033i −0.218675 + 0.378757i −0.954403 0.298520i \(-0.903507\pi\)
0.735728 + 0.677277i \(0.236840\pi\)
\(770\) 0 0
\(771\) 0.273620 0.309467i 0.00985419 0.0111452i
\(772\) 0 0
\(773\) 39.3385 1.41491 0.707454 0.706759i \(-0.249844\pi\)
0.707454 + 0.706759i \(0.249844\pi\)
\(774\) 0 0
\(775\) 4.57010 0.164163
\(776\) 0 0
\(777\) 5.87471 + 17.5394i 0.210754 + 0.629222i
\(778\) 0 0
\(779\) −22.0424 + 38.1786i −0.789752 + 1.36789i
\(780\) 0 0
\(781\) −0.203367 0.352242i −0.00727704 0.0126042i
\(782\) 0 0
\(783\) −0.483545 + 6.21874i −0.0172805 + 0.222240i
\(784\) 0 0
\(785\) −10.9839 19.0247i −0.392033 0.679021i
\(786\) 0 0
\(787\) 2.13924 3.70528i 0.0762558 0.132079i −0.825376 0.564584i \(-0.809037\pi\)
0.901632 + 0.432505i \(0.142370\pi\)
\(788\) 0 0
\(789\) 5.42268 + 16.1898i 0.193053 + 0.576373i
\(790\) 0 0
\(791\) −59.8775 −2.12900
\(792\) 0 0
\(793\) 0.252966 0.00898309
\(794\) 0 0
\(795\) −9.47594 + 10.7174i −0.336077 + 0.380106i