Properties

Label 1216.2.t.d.1185.2
Level $1216$
Weight $2$
Character 1216.1185
Analytic conductor $9.710$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1216.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.70980888579\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1185.2
Character \(\chi\) \(=\) 1216.1185
Dual form 1216.2.t.d.353.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.17731 + 1.25707i) q^{3} +(-2.95556 + 1.70639i) q^{5} +2.54486 q^{7} +(1.66044 - 2.87597i) q^{9} +O(q^{10})\) \(q+(-2.17731 + 1.25707i) q^{3} +(-2.95556 + 1.70639i) q^{5} +2.54486 q^{7} +(1.66044 - 2.87597i) q^{9} +1.25431i q^{11} +(4.22968 + 2.44201i) q^{13} +(4.29011 - 7.43068i) q^{15} +(3.99152 + 6.91351i) q^{17} +(3.96224 - 1.81677i) q^{19} +(-5.54095 + 3.19907i) q^{21} +(0.355422 - 0.615609i) q^{23} +(3.32356 - 5.75657i) q^{25} +0.806748i q^{27} +(2.45168 + 1.41548i) q^{29} -5.32450 q^{31} +(-1.57676 - 2.73103i) q^{33} +(-7.52150 + 4.34254i) q^{35} +3.20708i q^{37} -12.2791 q^{39} +(5.26481 + 9.11893i) q^{41} +(5.69906 - 3.29035i) q^{43} +11.3335i q^{45} +(-4.00670 + 6.93981i) q^{47} -0.523666 q^{49} +(-17.3815 - 10.0352i) q^{51} +(-0.905488 - 0.522784i) q^{53} +(-2.14035 - 3.70720i) q^{55} +(-6.34320 + 8.93648i) q^{57} +(6.46940 - 3.73511i) q^{59} +(-11.9058 - 6.87382i) q^{61} +(4.22560 - 7.31895i) q^{63} -16.6681 q^{65} +(-2.72163 - 1.57133i) q^{67} +1.78716i q^{69} +(-6.34526 - 10.9903i) q^{71} +(3.03579 + 5.25815i) q^{73} +16.7118i q^{75} +3.19206i q^{77} +(-1.17783 - 2.04006i) q^{79} +(3.96719 + 6.87137i) q^{81} +12.2452i q^{83} +(-23.5943 - 13.6222i) q^{85} -7.11741 q^{87} +(1.39043 - 2.40830i) q^{89} +(10.7640 + 6.21458i) q^{91} +(11.5931 - 6.69327i) q^{93} +(-8.61051 + 12.1307i) q^{95} +(-5.77233 - 9.99797i) q^{97} +(3.60737 + 2.08272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 6 q^{5} + 8 q^{9} + O(q^{10}) \) \( 24 q - 6 q^{5} + 8 q^{9} + 30 q^{13} + 6 q^{17} + 24 q^{21} + 6 q^{25} + 42 q^{29} - 14 q^{33} - 24 q^{41} + 24 q^{49} - 18 q^{53} - 42 q^{57} + 18 q^{61} - 20 q^{65} - 16 q^{73} + 52 q^{81} - 78 q^{85} + 14 q^{89} + 60 q^{93} - 4 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(705\) \(837\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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
\(3\) −2.17731 + 1.25707i −1.25707 + 0.725769i −0.972504 0.232888i \(-0.925182\pi\)
−0.284565 + 0.958657i \(0.591849\pi\)
\(4\) 0 0
\(5\) −2.95556 + 1.70639i −1.32177 + 0.763122i −0.984010 0.178111i \(-0.943001\pi\)
−0.337756 + 0.941234i \(0.609668\pi\)
\(6\) 0 0
\(7\) 2.54486 0.961868 0.480934 0.876757i \(-0.340298\pi\)
0.480934 + 0.876757i \(0.340298\pi\)
\(8\) 0 0
\(9\) 1.66044 2.87597i 0.553481 0.958657i
\(10\) 0 0
\(11\) 1.25431i 0.378190i 0.981959 + 0.189095i \(0.0605554\pi\)
−0.981959 + 0.189095i \(0.939445\pi\)
\(12\) 0 0
\(13\) 4.22968 + 2.44201i 1.17310 + 0.677291i 0.954409 0.298502i \(-0.0964869\pi\)
0.218694 + 0.975793i \(0.429820\pi\)
\(14\) 0 0
\(15\) 4.29011 7.43068i 1.10770 1.91859i
\(16\) 0 0
\(17\) 3.99152 + 6.91351i 0.968085 + 1.67677i 0.701088 + 0.713075i \(0.252698\pi\)
0.266997 + 0.963697i \(0.413968\pi\)
\(18\) 0 0
\(19\) 3.96224 1.81677i 0.909000 0.416796i
\(20\) 0 0
\(21\) −5.54095 + 3.19907i −1.20913 + 0.698094i
\(22\) 0 0
\(23\) 0.355422 0.615609i 0.0741106 0.128363i −0.826589 0.562807i \(-0.809722\pi\)
0.900699 + 0.434443i \(0.143055\pi\)
\(24\) 0 0
\(25\) 3.32356 5.75657i 0.664711 1.15131i
\(26\) 0 0
\(27\) 0.806748i 0.155259i
\(28\) 0 0
\(29\) 2.45168 + 1.41548i 0.455265 + 0.262848i 0.710051 0.704150i \(-0.248672\pi\)
−0.254786 + 0.966997i \(0.582005\pi\)
\(30\) 0 0
\(31\) −5.32450 −0.956309 −0.478155 0.878276i \(-0.658694\pi\)
−0.478155 + 0.878276i \(0.658694\pi\)
\(32\) 0 0
\(33\) −1.57676 2.73103i −0.274479 0.475411i
\(34\) 0 0
\(35\) −7.52150 + 4.34254i −1.27137 + 0.734023i
\(36\) 0 0
\(37\) 3.20708i 0.527240i 0.964627 + 0.263620i \(0.0849165\pi\)
−0.964627 + 0.263620i \(0.915083\pi\)
\(38\) 0 0
\(39\) −12.2791 −1.96623
\(40\) 0 0
\(41\) 5.26481 + 9.11893i 0.822226 + 1.42414i 0.904021 + 0.427488i \(0.140601\pi\)
−0.0817952 + 0.996649i \(0.526065\pi\)
\(42\) 0 0
\(43\) 5.69906 3.29035i 0.869098 0.501774i 0.00204985 0.999998i \(-0.499348\pi\)
0.867049 + 0.498224i \(0.166014\pi\)
\(44\) 0 0
\(45\) 11.3335i 1.68949i
\(46\) 0 0
\(47\) −4.00670 + 6.93981i −0.584437 + 1.01227i 0.410508 + 0.911857i \(0.365351\pi\)
−0.994945 + 0.100418i \(0.967982\pi\)
\(48\) 0 0
\(49\) −0.523666 −0.0748094
\(50\) 0 0
\(51\) −17.3815 10.0352i −2.43390 1.40521i
\(52\) 0 0
\(53\) −0.905488 0.522784i −0.124378 0.0718099i 0.436520 0.899695i \(-0.356211\pi\)
−0.560898 + 0.827885i \(0.689544\pi\)
\(54\) 0 0
\(55\) −2.14035 3.70720i −0.288605 0.499879i
\(56\) 0 0
\(57\) −6.34320 + 8.93648i −0.840177 + 1.18367i
\(58\) 0 0
\(59\) 6.46940 3.73511i 0.842244 0.486270i −0.0157823 0.999875i \(-0.505024\pi\)
0.858026 + 0.513606i \(0.171691\pi\)
\(60\) 0 0
\(61\) −11.9058 6.87382i −1.52438 0.880102i −0.999583 0.0288763i \(-0.990807\pi\)
−0.524799 0.851226i \(-0.675860\pi\)
\(62\) 0 0
\(63\) 4.22560 7.31895i 0.532376 0.922102i
\(64\) 0 0
\(65\) −16.6681 −2.06742
\(66\) 0 0
\(67\) −2.72163 1.57133i −0.332500 0.191969i 0.324450 0.945903i \(-0.394821\pi\)
−0.656951 + 0.753934i \(0.728154\pi\)
\(68\) 0 0
\(69\) 1.78716i 0.215149i
\(70\) 0 0
\(71\) −6.34526 10.9903i −0.753043 1.30431i −0.946341 0.323169i \(-0.895252\pi\)
0.193298 0.981140i \(-0.438082\pi\)
\(72\) 0 0
\(73\) 3.03579 + 5.25815i 0.355313 + 0.615419i 0.987171 0.159664i \(-0.0510411\pi\)
−0.631859 + 0.775083i \(0.717708\pi\)
\(74\) 0 0
\(75\) 16.7118i 1.92971i
\(76\) 0 0
\(77\) 3.19206i 0.363769i
\(78\) 0 0
\(79\) −1.17783 2.04006i −0.132516 0.229525i 0.792130 0.610353i \(-0.208972\pi\)
−0.924646 + 0.380828i \(0.875639\pi\)
\(80\) 0 0
\(81\) 3.96719 + 6.87137i 0.440799 + 0.763486i
\(82\) 0 0
\(83\) 12.2452i 1.34409i 0.740510 + 0.672045i \(0.234584\pi\)
−0.740510 + 0.672045i \(0.765416\pi\)
\(84\) 0 0
\(85\) −23.5943 13.6222i −2.55916 1.47753i
\(86\) 0 0
\(87\) −7.11741 −0.763066
\(88\) 0 0
\(89\) 1.39043 2.40830i 0.147385 0.255279i −0.782875 0.622179i \(-0.786248\pi\)
0.930260 + 0.366900i \(0.119581\pi\)
\(90\) 0 0
\(91\) 10.7640 + 6.21458i 1.12837 + 0.651465i
\(92\) 0 0
\(93\) 11.5931 6.69327i 1.20215 0.694059i
\(94\) 0 0
\(95\) −8.61051 + 12.1307i −0.883419 + 1.24459i
\(96\) 0 0
\(97\) −5.77233 9.99797i −0.586092 1.01514i −0.994738 0.102448i \(-0.967333\pi\)
0.408647 0.912693i \(-0.366001\pi\)
\(98\) 0 0
\(99\) 3.60737 + 2.08272i 0.362555 + 0.209321i
\(100\) 0 0
\(101\) 5.36280 + 3.09621i 0.533618 + 0.308085i 0.742489 0.669859i \(-0.233645\pi\)
−0.208870 + 0.977943i \(0.566979\pi\)
\(102\) 0 0
\(103\) −4.42028 −0.435543 −0.217772 0.976000i \(-0.569879\pi\)
−0.217772 + 0.976000i \(0.569879\pi\)
\(104\) 0 0
\(105\) 10.9177 18.9101i 1.06546 1.84543i
\(106\) 0 0
\(107\) 11.8222i 1.14290i 0.820637 + 0.571450i \(0.193619\pi\)
−0.820637 + 0.571450i \(0.806381\pi\)
\(108\) 0 0
\(109\) −14.6832 + 8.47736i −1.40640 + 0.811984i −0.995039 0.0994901i \(-0.968279\pi\)
−0.411358 + 0.911474i \(0.634946\pi\)
\(110\) 0 0
\(111\) −4.03151 6.98279i −0.382654 0.662777i
\(112\) 0 0
\(113\) 0.817599 0.0769132 0.0384566 0.999260i \(-0.487756\pi\)
0.0384566 + 0.999260i \(0.487756\pi\)
\(114\) 0 0
\(115\) 2.42596i 0.226222i
\(116\) 0 0
\(117\) 14.0463 8.10963i 1.29858 0.749736i
\(118\) 0 0
\(119\) 10.1579 + 17.5939i 0.931170 + 1.61283i
\(120\) 0 0
\(121\) 9.42669 0.856972
\(122\) 0 0
\(123\) −22.9262 13.2365i −2.06719 1.19349i
\(124\) 0 0
\(125\) 5.62125i 0.502779i
\(126\) 0 0
\(127\) −0.759932 + 1.31624i −0.0674330 + 0.116797i −0.897771 0.440463i \(-0.854814\pi\)
0.830338 + 0.557261i \(0.188148\pi\)
\(128\) 0 0
\(129\) −8.27240 + 14.3282i −0.728344 + 1.26153i
\(130\) 0 0
\(131\) −4.05996 + 2.34402i −0.354720 + 0.204798i −0.666762 0.745270i \(-0.732320\pi\)
0.312042 + 0.950068i \(0.398987\pi\)
\(132\) 0 0
\(133\) 10.0834 4.62344i 0.874338 0.400903i
\(134\) 0 0
\(135\) −1.37663 2.38439i −0.118481 0.205216i
\(136\) 0 0
\(137\) 2.65292 4.59500i 0.226655 0.392577i −0.730160 0.683276i \(-0.760554\pi\)
0.956815 + 0.290699i \(0.0938878\pi\)
\(138\) 0 0
\(139\) 13.0038 + 7.50775i 1.10297 + 0.636799i 0.936999 0.349332i \(-0.113592\pi\)
0.165969 + 0.986131i \(0.446925\pi\)
\(140\) 0 0
\(141\) 20.1468i 1.69666i
\(142\) 0 0
\(143\) −3.06305 + 5.30536i −0.256145 + 0.443656i
\(144\) 0 0
\(145\) −9.66145 −0.802339
\(146\) 0 0
\(147\) 1.14018 0.658284i 0.0940405 0.0542943i
\(148\) 0 0
\(149\) −17.0410 + 9.83861i −1.39605 + 0.806011i −0.993976 0.109596i \(-0.965044\pi\)
−0.402075 + 0.915607i \(0.631711\pi\)
\(150\) 0 0
\(151\) 22.4999 1.83102 0.915510 0.402296i \(-0.131788\pi\)
0.915510 + 0.402296i \(0.131788\pi\)
\(152\) 0 0
\(153\) 26.5107 2.14327
\(154\) 0 0
\(155\) 15.7369 9.08570i 1.26402 0.729781i
\(156\) 0 0
\(157\) 5.35902 3.09403i 0.427696 0.246931i −0.270668 0.962673i \(-0.587245\pi\)
0.698365 + 0.715742i \(0.253911\pi\)
\(158\) 0 0
\(159\) 2.62870 0.208469
\(160\) 0 0
\(161\) 0.904501 1.56664i 0.0712847 0.123469i
\(162\) 0 0
\(163\) 7.52027i 0.589033i −0.955646 0.294516i \(-0.904841\pi\)
0.955646 0.294516i \(-0.0951586\pi\)
\(164\) 0 0
\(165\) 9.32042 + 5.38114i 0.725593 + 0.418922i
\(166\) 0 0
\(167\) 7.11147 12.3174i 0.550302 0.953151i −0.447951 0.894058i \(-0.647846\pi\)
0.998253 0.0590926i \(-0.0188207\pi\)
\(168\) 0 0
\(169\) 5.42682 + 9.39952i 0.417447 + 0.723040i
\(170\) 0 0
\(171\) 1.35408 14.4119i 0.103549 1.10211i
\(172\) 0 0
\(173\) 11.2682 6.50571i 0.856706 0.494620i −0.00620155 0.999981i \(-0.501974\pi\)
0.862908 + 0.505361i \(0.168641\pi\)
\(174\) 0 0
\(175\) 8.45800 14.6497i 0.639365 1.10741i
\(176\) 0 0
\(177\) −9.39058 + 16.2650i −0.705839 + 1.22255i
\(178\) 0 0
\(179\) 0.503659i 0.0376452i −0.999823 0.0188226i \(-0.994008\pi\)
0.999823 0.0188226i \(-0.00599178\pi\)
\(180\) 0 0
\(181\) 16.2259 + 9.36803i 1.20606 + 0.696320i 0.961897 0.273413i \(-0.0881527\pi\)
0.244165 + 0.969734i \(0.421486\pi\)
\(182\) 0 0
\(183\) 34.5634 2.55500
\(184\) 0 0
\(185\) −5.47253 9.47871i −0.402349 0.696888i
\(186\) 0 0
\(187\) −8.67172 + 5.00662i −0.634139 + 0.366120i
\(188\) 0 0
\(189\) 2.05306i 0.149338i
\(190\) 0 0
\(191\) −15.3309 −1.10930 −0.554651 0.832083i \(-0.687148\pi\)
−0.554651 + 0.832083i \(0.687148\pi\)
\(192\) 0 0
\(193\) −8.31994 14.4106i −0.598882 1.03729i −0.992986 0.118229i \(-0.962278\pi\)
0.394104 0.919066i \(-0.371055\pi\)
\(194\) 0 0
\(195\) 36.2916 20.9530i 2.59889 1.50047i
\(196\) 0 0
\(197\) 0.155717i 0.0110943i 0.999985 + 0.00554717i \(0.00176573\pi\)
−0.999985 + 0.00554717i \(0.998234\pi\)
\(198\) 0 0
\(199\) −4.88153 + 8.45506i −0.346043 + 0.599363i −0.985543 0.169428i \(-0.945808\pi\)
0.639500 + 0.768791i \(0.279141\pi\)
\(200\) 0 0
\(201\) 7.90110 0.557300
\(202\) 0 0
\(203\) 6.23919 + 3.60220i 0.437905 + 0.252825i
\(204\) 0 0
\(205\) −31.1210 17.9677i −2.17358 1.25492i
\(206\) 0 0
\(207\) −1.18032 2.04437i −0.0820376 0.142093i
\(208\) 0 0
\(209\) 2.27881 + 4.96990i 0.157628 + 0.343775i
\(210\) 0 0
\(211\) −19.8853 + 11.4808i −1.36896 + 0.790368i −0.990795 0.135372i \(-0.956777\pi\)
−0.378162 + 0.925739i \(0.623444\pi\)
\(212\) 0 0
\(213\) 27.6311 + 15.9528i 1.89325 + 1.09307i
\(214\) 0 0
\(215\) −11.2293 + 19.4497i −0.765830 + 1.32646i
\(216\) 0 0
\(217\) −13.5501 −0.919844
\(218\) 0 0
\(219\) −13.2197 7.63240i −0.893304 0.515750i
\(220\) 0 0
\(221\) 38.9893i 2.62270i
\(222\) 0 0
\(223\) 5.46950 + 9.47346i 0.366265 + 0.634390i 0.988978 0.148061i \(-0.0473030\pi\)
−0.622713 + 0.782450i \(0.713970\pi\)
\(224\) 0 0
\(225\) −11.0371 19.1169i −0.735810 1.27446i
\(226\) 0 0
\(227\) 16.6384i 1.10433i −0.833736 0.552164i \(-0.813802\pi\)
0.833736 0.552164i \(-0.186198\pi\)
\(228\) 0 0
\(229\) 7.56617i 0.499986i −0.968248 0.249993i \(-0.919572\pi\)
0.968248 0.249993i \(-0.0804284\pi\)
\(230\) 0 0
\(231\) −4.01264 6.95010i −0.264012 0.457283i
\(232\) 0 0
\(233\) 2.50589 + 4.34033i 0.164166 + 0.284345i 0.936359 0.351044i \(-0.114173\pi\)
−0.772193 + 0.635389i \(0.780840\pi\)
\(234\) 0 0
\(235\) 27.3480i 1.78399i
\(236\) 0 0
\(237\) 5.12899 + 2.96122i 0.333164 + 0.192352i
\(238\) 0 0
\(239\) −15.8860 −1.02758 −0.513791 0.857915i \(-0.671759\pi\)
−0.513791 + 0.857915i \(0.671759\pi\)
\(240\) 0 0
\(241\) −1.00532 + 1.74127i −0.0647585 + 0.112165i −0.896587 0.442868i \(-0.853961\pi\)
0.831828 + 0.555033i \(0.187294\pi\)
\(242\) 0 0
\(243\) −19.3716 11.1842i −1.24269 0.717465i
\(244\) 0 0
\(245\) 1.54773 0.893580i 0.0988806 0.0570887i
\(246\) 0 0
\(247\) 21.1956 + 1.99145i 1.34864 + 0.126713i
\(248\) 0 0
\(249\) −15.3931 26.6616i −0.975499 1.68961i
\(250\) 0 0
\(251\) −22.2501 12.8461i −1.40441 0.810839i −0.409572 0.912278i \(-0.634322\pi\)
−0.994842 + 0.101439i \(0.967655\pi\)
\(252\) 0 0
\(253\) 0.772168 + 0.445811i 0.0485458 + 0.0280279i
\(254\) 0 0
\(255\) 68.4961 4.28939
\(256\) 0 0
\(257\) 7.11189 12.3182i 0.443628 0.768385i −0.554328 0.832298i \(-0.687025\pi\)
0.997955 + 0.0639129i \(0.0203580\pi\)
\(258\) 0 0
\(259\) 8.16157i 0.507136i
\(260\) 0 0
\(261\) 8.14174 4.70064i 0.503961 0.290962i
\(262\) 0 0
\(263\) −7.24739 12.5529i −0.446893 0.774042i 0.551289 0.834315i \(-0.314136\pi\)
−0.998182 + 0.0602727i \(0.980803\pi\)
\(264\) 0 0
\(265\) 3.56830 0.219199
\(266\) 0 0
\(267\) 6.99146i 0.427871i
\(268\) 0 0
\(269\) 11.1770 6.45302i 0.681471 0.393448i −0.118938 0.992902i \(-0.537949\pi\)
0.800409 + 0.599454i \(0.204616\pi\)
\(270\) 0 0
\(271\) 9.89868 + 17.1450i 0.601302 + 1.04149i 0.992624 + 0.121232i \(0.0386845\pi\)
−0.391322 + 0.920254i \(0.627982\pi\)
\(272\) 0 0
\(273\) −31.2486 −1.89125
\(274\) 0 0
\(275\) 7.22055 + 4.16879i 0.435416 + 0.251387i
\(276\) 0 0
\(277\) 2.10309i 0.126362i −0.998002 0.0631812i \(-0.979875\pi\)
0.998002 0.0631812i \(-0.0201246\pi\)
\(278\) 0 0
\(279\) −8.84103 + 15.3131i −0.529299 + 0.916772i
\(280\) 0 0
\(281\) 2.20156 3.81321i 0.131334 0.227477i −0.792857 0.609408i \(-0.791407\pi\)
0.924191 + 0.381931i \(0.124741\pi\)
\(282\) 0 0
\(283\) 0.911785 0.526419i 0.0542000 0.0312924i −0.472655 0.881247i \(-0.656704\pi\)
0.526855 + 0.849955i \(0.323371\pi\)
\(284\) 0 0
\(285\) 3.49857 37.2363i 0.207237 2.20569i
\(286\) 0 0
\(287\) 13.3982 + 23.2064i 0.790873 + 1.36983i
\(288\) 0 0
\(289\) −23.3644 + 40.4683i −1.37438 + 2.38049i
\(290\) 0 0
\(291\) 25.1363 + 14.5124i 1.47351 + 0.850734i
\(292\) 0 0
\(293\) 8.56042i 0.500105i 0.968232 + 0.250052i \(0.0804479\pi\)
−0.968232 + 0.250052i \(0.919552\pi\)
\(294\) 0 0
\(295\) −12.7471 + 22.0787i −0.742167 + 1.28547i
\(296\) 0 0
\(297\) −1.01192 −0.0587173
\(298\) 0 0
\(299\) 3.00665 1.73589i 0.173879 0.100389i
\(300\) 0 0
\(301\) 14.5033 8.37350i 0.835958 0.482641i
\(302\) 0 0
\(303\) −15.5686 −0.894393
\(304\) 0 0
\(305\) 46.9178 2.68650
\(306\) 0 0
\(307\) 16.9636 9.79391i 0.968161 0.558968i 0.0694860 0.997583i \(-0.477864\pi\)
0.898675 + 0.438615i \(0.144531\pi\)
\(308\) 0 0
\(309\) 9.62431 5.55660i 0.547508 0.316104i
\(310\) 0 0
\(311\) −25.7890 −1.46236 −0.731179 0.682186i \(-0.761029\pi\)
−0.731179 + 0.682186i \(0.761029\pi\)
\(312\) 0 0
\(313\) 5.50828 9.54062i 0.311346 0.539268i −0.667308 0.744782i \(-0.732553\pi\)
0.978654 + 0.205514i \(0.0658868\pi\)
\(314\) 0 0
\(315\) 28.8421i 1.62507i
\(316\) 0 0
\(317\) −15.6002 9.00676i −0.876193 0.505870i −0.00679167 0.999977i \(-0.502162\pi\)
−0.869401 + 0.494107i \(0.835495\pi\)
\(318\) 0 0
\(319\) −1.77545 + 3.07518i −0.0994064 + 0.172177i
\(320\) 0 0
\(321\) −14.8614 25.7406i −0.829481 1.43670i
\(322\) 0 0
\(323\) 28.3756 + 20.1413i 1.57886 + 1.12069i
\(324\) 0 0
\(325\) 28.1152 16.2323i 1.55955 0.900407i
\(326\) 0 0
\(327\) 21.3132 36.9156i 1.17862 2.04144i
\(328\) 0 0
\(329\) −10.1965 + 17.6609i −0.562151 + 0.973675i
\(330\) 0 0
\(331\) 31.3668i 1.72407i −0.506846 0.862037i \(-0.669189\pi\)
0.506846 0.862037i \(-0.330811\pi\)
\(332\) 0 0
\(333\) 9.22346 + 5.32517i 0.505442 + 0.291817i
\(334\) 0 0
\(335\) 10.7253 0.585983
\(336\) 0 0
\(337\) 9.22394 + 15.9763i 0.502460 + 0.870286i 0.999996 + 0.00284285i \(0.000904908\pi\)
−0.497536 + 0.867443i \(0.665762\pi\)
\(338\) 0 0
\(339\) −1.78016 + 1.02778i −0.0966852 + 0.0558212i
\(340\) 0 0
\(341\) 6.67861i 0.361667i
\(342\) 0 0
\(343\) −19.1467 −1.03383
\(344\) 0 0
\(345\) −3.04960 5.28206i −0.164185 0.284376i
\(346\) 0 0
\(347\) −4.77429 + 2.75644i −0.256297 + 0.147973i −0.622644 0.782505i \(-0.713942\pi\)
0.366347 + 0.930478i \(0.380608\pi\)
\(348\) 0 0
\(349\) 30.1208i 1.61233i 0.591690 + 0.806166i \(0.298461\pi\)
−0.591690 + 0.806166i \(0.701539\pi\)
\(350\) 0 0
\(351\) −1.97008 + 3.41229i −0.105155 + 0.182134i
\(352\) 0 0
\(353\) −19.5925 −1.04280 −0.521402 0.853311i \(-0.674591\pi\)
−0.521402 + 0.853311i \(0.674591\pi\)
\(354\) 0 0
\(355\) 37.5076 + 21.6550i 1.99069 + 1.14933i
\(356\) 0 0
\(357\) −44.2336 25.5383i −2.34109 1.35163i
\(358\) 0 0
\(359\) 9.14429 + 15.8384i 0.482617 + 0.835917i 0.999801 0.0199571i \(-0.00635297\pi\)
−0.517184 + 0.855874i \(0.673020\pi\)
\(360\) 0 0
\(361\) 12.3987 14.3970i 0.652562 0.757736i
\(362\) 0 0
\(363\) −20.5248 + 11.8500i −1.07727 + 0.621964i
\(364\) 0 0
\(365\) −17.9449 10.3605i −0.939281 0.542294i
\(366\) 0 0
\(367\) −1.03238 + 1.78813i −0.0538896 + 0.0933395i −0.891712 0.452604i \(-0.850495\pi\)
0.837822 + 0.545943i \(0.183829\pi\)
\(368\) 0 0
\(369\) 34.9677 1.82034
\(370\) 0 0
\(371\) −2.30434 1.33041i −0.119636 0.0690716i
\(372\) 0 0
\(373\) 22.5069i 1.16536i −0.812701 0.582680i \(-0.802004\pi\)
0.812701 0.582680i \(-0.197996\pi\)
\(374\) 0 0
\(375\) −7.06629 12.2392i −0.364902 0.632028i
\(376\) 0 0
\(377\) 6.91322 + 11.9740i 0.356049 + 0.616695i
\(378\) 0 0
\(379\) 27.4490i 1.40996i 0.709228 + 0.704980i \(0.249044\pi\)
−0.709228 + 0.704980i \(0.750956\pi\)
\(380\) 0 0
\(381\) 3.82115i 0.195763i
\(382\) 0 0
\(383\) −10.0380 17.3863i −0.512918 0.888399i −0.999888 0.0149807i \(-0.995231\pi\)
0.486970 0.873419i \(-0.338102\pi\)
\(384\) 0 0
\(385\) −5.44691 9.43433i −0.277600 0.480818i
\(386\) 0 0
\(387\) 21.8538i 1.11089i
\(388\) 0 0
\(389\) −14.7087 8.49210i −0.745763 0.430567i 0.0783979 0.996922i \(-0.475020\pi\)
−0.824161 + 0.566356i \(0.808353\pi\)
\(390\) 0 0
\(391\) 5.67469 0.286982
\(392\) 0 0
\(393\) 5.89318 10.2073i 0.297272 0.514890i
\(394\) 0 0
\(395\) 6.96229 + 4.01968i 0.350311 + 0.202252i
\(396\) 0 0
\(397\) −2.01293 + 1.16217i −0.101026 + 0.0583274i −0.549662 0.835387i \(-0.685243\pi\)
0.448636 + 0.893715i \(0.351910\pi\)
\(398\) 0 0
\(399\) −16.1426 + 22.7421i −0.808140 + 1.13853i
\(400\) 0 0
\(401\) −6.79543 11.7700i −0.339348 0.587767i 0.644963 0.764214i \(-0.276873\pi\)
−0.984310 + 0.176447i \(0.943540\pi\)
\(402\) 0 0
\(403\) −22.5210 13.0025i −1.12185 0.647700i
\(404\) 0 0
\(405\) −23.4505 13.5392i −1.16527 0.672767i
\(406\) 0 0
\(407\) −4.02268 −0.199397
\(408\) 0 0
\(409\) 1.93142 3.34532i 0.0955025 0.165415i −0.814316 0.580422i \(-0.802888\pi\)
0.909818 + 0.415007i \(0.136221\pi\)
\(410\) 0 0
\(411\) 13.3396i 0.657995i
\(412\) 0 0
\(413\) 16.4637 9.50535i 0.810128 0.467728i
\(414\) 0 0
\(415\) −20.8952 36.1915i −1.02571 1.77657i
\(416\) 0 0
\(417\) −37.7510 −1.84867
\(418\) 0 0
\(419\) 14.0401i 0.685904i 0.939353 + 0.342952i \(0.111427\pi\)
−0.939353 + 0.342952i \(0.888573\pi\)
\(420\) 0 0
\(421\) 26.7712 15.4564i 1.30475 0.753298i 0.323535 0.946216i \(-0.395129\pi\)
0.981215 + 0.192919i \(0.0617953\pi\)
\(422\) 0 0
\(423\) 13.3058 + 23.0463i 0.646949 + 1.12055i
\(424\) 0 0
\(425\) 53.0641 2.57399
\(426\) 0 0
\(427\) −30.2987 17.4929i −1.46625 0.846543i
\(428\) 0 0
\(429\) 15.4018i 0.743608i
\(430\) 0 0
\(431\) −2.67813 + 4.63865i −0.129001 + 0.223436i −0.923290 0.384104i \(-0.874510\pi\)
0.794289 + 0.607540i \(0.207844\pi\)
\(432\) 0 0
\(433\) −12.1157 + 20.9850i −0.582242 + 1.00847i 0.412971 + 0.910744i \(0.364491\pi\)
−0.995213 + 0.0977288i \(0.968842\pi\)
\(434\) 0 0
\(435\) 21.0359 12.1451i 1.00860 0.582313i
\(436\) 0 0
\(437\) 0.289845 3.08491i 0.0138652 0.147571i
\(438\) 0 0
\(439\) 5.93350 + 10.2771i 0.283190 + 0.490500i 0.972169 0.234282i \(-0.0752738\pi\)
−0.688978 + 0.724782i \(0.741941\pi\)
\(440\) 0 0
\(441\) −0.869517 + 1.50605i −0.0414056 + 0.0717165i
\(442\) 0 0
\(443\) 6.68234 + 3.85805i 0.317488 + 0.183302i 0.650272 0.759701i \(-0.274655\pi\)
−0.332784 + 0.943003i \(0.607988\pi\)
\(444\) 0 0
\(445\) 9.49048i 0.449892i
\(446\) 0 0
\(447\) 24.7356 42.8433i 1.16995 2.02642i
\(448\) 0 0
\(449\) 9.64706 0.455273 0.227636 0.973746i \(-0.426900\pi\)
0.227636 + 0.973746i \(0.426900\pi\)
\(450\) 0 0
\(451\) −11.4380 + 6.60374i −0.538595 + 0.310958i
\(452\) 0 0
\(453\) −48.9893 + 28.2840i −2.30172 + 1.32890i
\(454\) 0 0
\(455\) −42.4181 −1.98859
\(456\) 0 0
\(457\) −33.8154 −1.58182 −0.790908 0.611935i \(-0.790391\pi\)
−0.790908 + 0.611935i \(0.790391\pi\)
\(458\) 0 0
\(459\) −5.57746 + 3.22015i −0.260333 + 0.150304i
\(460\) 0 0
\(461\) 22.0916 12.7546i 1.02891 0.594042i 0.112238 0.993681i \(-0.464198\pi\)
0.916672 + 0.399640i \(0.130865\pi\)
\(462\) 0 0
\(463\) 18.6279 0.865713 0.432856 0.901463i \(-0.357506\pi\)
0.432856 + 0.901463i \(0.357506\pi\)
\(464\) 0 0
\(465\) −22.8427 + 39.5647i −1.05930 + 1.83477i
\(466\) 0 0
\(467\) 30.6406i 1.41788i 0.705270 + 0.708939i \(0.250826\pi\)
−0.705270 + 0.708939i \(0.749174\pi\)
\(468\) 0 0
\(469\) −6.92618 3.99883i −0.319821 0.184649i
\(470\) 0 0
\(471\) −7.77882 + 13.4733i −0.358429 + 0.620817i
\(472\) 0 0
\(473\) 4.12714 + 7.14841i 0.189766 + 0.328684i
\(474\) 0 0
\(475\) 2.71035 28.8470i 0.124359 1.32359i
\(476\) 0 0
\(477\) −3.00702 + 1.73610i −0.137682 + 0.0794907i
\(478\) 0 0
\(479\) −19.2670 + 33.3715i −0.880333 + 1.52478i −0.0293614 + 0.999569i \(0.509347\pi\)
−0.850971 + 0.525212i \(0.823986\pi\)
\(480\) 0 0
\(481\) −7.83171 + 13.5649i −0.357095 + 0.618507i
\(482\) 0 0
\(483\) 4.54808i 0.206945i
\(484\) 0 0
\(485\) 34.1210 + 19.6997i 1.54935 + 0.894519i
\(486\) 0 0
\(487\) 12.2713 0.556064 0.278032 0.960572i \(-0.410318\pi\)
0.278032 + 0.960572i \(0.410318\pi\)
\(488\) 0 0
\(489\) 9.45349 + 16.3739i 0.427502 + 0.740455i
\(490\) 0 0
\(491\) 1.79067 1.03384i 0.0808117 0.0466567i −0.459050 0.888411i \(-0.651810\pi\)
0.539861 + 0.841754i \(0.318477\pi\)
\(492\) 0 0
\(493\) 22.5996i 1.01784i
\(494\) 0 0
\(495\) −14.2157 −0.638950
\(496\) 0 0
\(497\) −16.1478 27.9688i −0.724328 1.25457i
\(498\) 0 0
\(499\) −22.5746 + 13.0335i −1.01058 + 0.583458i −0.911361 0.411607i \(-0.864968\pi\)
−0.0992183 + 0.995066i \(0.531634\pi\)
\(500\) 0 0
\(501\) 35.7584i 1.59757i
\(502\) 0 0
\(503\) 18.4953 32.0348i 0.824664 1.42836i −0.0775123 0.996991i \(-0.524698\pi\)
0.902176 0.431368i \(-0.141969\pi\)
\(504\) 0 0
\(505\) −21.1334 −0.940425
\(506\) 0 0
\(507\) −23.6317 13.6438i −1.04952 0.605941i
\(508\) 0 0
\(509\) 3.49285 + 2.01660i 0.154818 + 0.0893840i 0.575407 0.817867i \(-0.304843\pi\)
−0.420590 + 0.907251i \(0.638177\pi\)
\(510\) 0 0
\(511\) 7.72568 + 13.3813i 0.341764 + 0.591952i
\(512\) 0 0
\(513\) 1.46568 + 3.19653i 0.0647112 + 0.141130i
\(514\) 0 0
\(515\) 13.0644 7.54274i 0.575687 0.332373i
\(516\) 0 0
\(517\) −8.70470 5.02566i −0.382832 0.221028i
\(518\) 0 0
\(519\) −16.3562 + 28.3298i −0.717959 + 1.24354i
\(520\) 0 0
\(521\) −15.8053 −0.692443 −0.346222 0.938153i \(-0.612536\pi\)
−0.346222 + 0.938153i \(0.612536\pi\)
\(522\) 0 0
\(523\) 6.25047 + 3.60871i 0.273314 + 0.157798i 0.630393 0.776276i \(-0.282894\pi\)
−0.357079 + 0.934074i \(0.616227\pi\)
\(524\) 0 0
\(525\) 42.5291i 1.85612i
\(526\) 0 0
\(527\) −21.2528 36.8110i −0.925789 1.60351i
\(528\) 0 0
\(529\) 11.2474 + 19.4810i 0.489015 + 0.846999i
\(530\) 0 0
\(531\) 24.8077i 1.07656i
\(532\) 0 0
\(533\) 51.4269i 2.22755i
\(534\) 0 0
\(535\) −20.1734 34.9413i −0.872172 1.51065i
\(536\) 0 0
\(537\) 0.633134 + 1.09662i 0.0273217 + 0.0473226i
\(538\) 0 0
\(539\) 0.656842i 0.0282922i
\(540\) 0 0
\(541\) 3.82654 + 2.20926i 0.164516 + 0.0949833i 0.579997 0.814618i \(-0.303054\pi\)
−0.415481 + 0.909602i \(0.636387\pi\)
\(542\) 0 0
\(543\) −47.1050 −2.02147
\(544\) 0 0
\(545\) 28.9314 50.1107i 1.23929 2.14651i
\(546\) 0 0
\(547\) −4.90706 2.83309i −0.209811 0.121134i 0.391413 0.920215i \(-0.371987\pi\)
−0.601223 + 0.799081i \(0.705320\pi\)
\(548\) 0 0
\(549\) −39.5378 + 22.8272i −1.68743 + 0.974240i
\(550\) 0 0
\(551\) 12.2857 + 1.15432i 0.523390 + 0.0491755i
\(552\) 0 0
\(553\) −2.99742 5.19168i −0.127463 0.220773i
\(554\) 0 0
\(555\) 23.8308 + 13.7587i 1.01156 + 0.584024i
\(556\) 0 0
\(557\) 22.0524 + 12.7319i 0.934389 + 0.539470i 0.888197 0.459463i \(-0.151958\pi\)
0.0461920 + 0.998933i \(0.485291\pi\)
\(558\) 0 0
\(559\) 32.1403 1.35939
\(560\) 0 0
\(561\) 12.5873 21.8019i 0.531437 0.920476i
\(562\) 0 0
\(563\) 29.5332i 1.24468i −0.782748 0.622339i \(-0.786183\pi\)
0.782748 0.622339i \(-0.213817\pi\)
\(564\) 0 0
\(565\) −2.41646 + 1.39515i −0.101661 + 0.0586942i
\(566\) 0 0
\(567\) 10.0960 + 17.4867i 0.423990 + 0.734373i
\(568\) 0 0
\(569\) 29.8114 1.24976 0.624879 0.780722i \(-0.285148\pi\)
0.624879 + 0.780722i \(0.285148\pi\)
\(570\) 0 0
\(571\) 2.87084i 0.120141i −0.998194 0.0600705i \(-0.980867\pi\)
0.998194 0.0600705i \(-0.0191326\pi\)
\(572\) 0 0
\(573\) 33.3800 19.2719i 1.39447 0.805097i
\(574\) 0 0
\(575\) −2.36253 4.09202i −0.0985244 0.170649i
\(576\) 0 0
\(577\) 38.3067 1.59473 0.797364 0.603499i \(-0.206227\pi\)
0.797364 + 0.603499i \(0.206227\pi\)
\(578\) 0 0
\(579\) 36.2301 + 20.9175i 1.50567 + 0.869300i
\(580\) 0 0
\(581\) 31.1625i 1.29284i
\(582\) 0 0
\(583\) 0.655735 1.13577i 0.0271578 0.0470387i
\(584\) 0 0
\(585\) −27.6764 + 47.9370i −1.14428 + 1.98195i
\(586\) 0 0
\(587\) −18.9662 + 10.9501i −0.782819 + 0.451961i −0.837428 0.546547i \(-0.815942\pi\)
0.0546095 + 0.998508i \(0.482609\pi\)
\(588\) 0 0
\(589\) −21.0970 + 9.67341i −0.869285 + 0.398586i
\(590\) 0 0
\(591\) −0.195746 0.339043i −0.00805193 0.0139464i
\(592\) 0 0
\(593\) 10.0441 17.3968i 0.412461 0.714403i −0.582697 0.812689i \(-0.698003\pi\)
0.995158 + 0.0982863i \(0.0313361\pi\)
\(594\) 0 0
\(595\) −60.0444 34.6666i −2.46158 1.42119i
\(596\) 0 0
\(597\) 24.5457i 1.00459i
\(598\) 0 0
\(599\) −1.88758 + 3.26938i −0.0771244 + 0.133583i −0.902008 0.431719i \(-0.857907\pi\)
0.824884 + 0.565302i \(0.191241\pi\)
\(600\) 0 0
\(601\) 9.29129 0.379000 0.189500 0.981881i \(-0.439313\pi\)
0.189500 + 0.981881i \(0.439313\pi\)
\(602\) 0 0
\(603\) −9.03822 + 5.21822i −0.368065 + 0.212502i
\(604\) 0 0
\(605\) −27.8612 + 16.0856i −1.13272 + 0.653975i
\(606\) 0 0
\(607\) 1.55590 0.0631519 0.0315759 0.999501i \(-0.489947\pi\)
0.0315759 + 0.999501i \(0.489947\pi\)
\(608\) 0 0
\(609\) −18.1128 −0.733969
\(610\) 0 0
\(611\) −33.8941 + 19.5688i −1.37121 + 0.791668i
\(612\) 0 0
\(613\) −19.9323 + 11.5079i −0.805059 + 0.464801i −0.845237 0.534391i \(-0.820541\pi\)
0.0401778 + 0.999193i \(0.487208\pi\)
\(614\) 0 0
\(615\) 90.3465 3.64312
\(616\) 0 0
\(617\) 5.63489 9.75992i 0.226852 0.392920i −0.730021 0.683424i \(-0.760490\pi\)
0.956874 + 0.290505i \(0.0938232\pi\)
\(618\) 0 0
\(619\) 4.18227i 0.168100i 0.996462 + 0.0840498i \(0.0267855\pi\)
−0.996462 + 0.0840498i \(0.973215\pi\)
\(620\) 0 0
\(621\) 0.496641 + 0.286736i 0.0199295 + 0.0115063i
\(622\) 0 0
\(623\) 3.53846 6.12879i 0.141765 0.245545i
\(624\) 0 0
\(625\) 7.02573 + 12.1689i 0.281029 + 0.486757i
\(626\) 0 0
\(627\) −11.2092 7.95637i −0.447651 0.317747i
\(628\) 0 0
\(629\) −22.1722 + 12.8011i −0.884062 + 0.510413i
\(630\) 0 0
\(631\) 19.6870 34.0989i 0.783728 1.35746i −0.146029 0.989280i \(-0.546649\pi\)
0.929756 0.368176i \(-0.120018\pi\)
\(632\) 0 0
\(633\) 28.8642 49.9942i 1.14725 1.98709i
\(634\) 0 0
\(635\) 5.18697i 0.205839i
\(636\) 0 0
\(637\) −2.21494 1.27880i −0.0877592 0.0506678i
\(638\) 0 0
\(639\) −42.1437 −1.66718
\(640\) 0 0
\(641\) −1.89633 3.28455i −0.0749007 0.129732i 0.826142 0.563461i \(-0.190531\pi\)
−0.901043 + 0.433730i \(0.857197\pi\)
\(642\) 0 0
\(643\) −12.4215 + 7.17154i −0.489855 + 0.282818i −0.724514 0.689260i \(-0.757936\pi\)
0.234659 + 0.972078i \(0.424603\pi\)
\(644\) 0 0
\(645\) 56.4639i 2.22326i
\(646\) 0 0
\(647\) 4.09464 0.160977 0.0804884 0.996756i \(-0.474352\pi\)
0.0804884 + 0.996756i \(0.474352\pi\)
\(648\) 0 0
\(649\) 4.68500 + 8.11466i 0.183902 + 0.318528i
\(650\) 0 0
\(651\) 29.5028 17.0335i 1.15631 0.667594i
\(652\) 0 0
\(653\) 41.4592i 1.62242i 0.584753 + 0.811211i \(0.301191\pi\)
−0.584753 + 0.811211i \(0.698809\pi\)
\(654\) 0 0
\(655\) 7.99963 13.8558i 0.312572 0.541390i
\(656\) 0 0
\(657\) 20.1630 0.786635
\(658\) 0 0
\(659\) 1.94461 + 1.12272i 0.0757514 + 0.0437351i 0.537397 0.843329i \(-0.319408\pi\)
−0.461646 + 0.887064i \(0.652741\pi\)
\(660\) 0 0
\(661\) −12.6664 7.31294i −0.492665 0.284440i 0.233014 0.972473i \(-0.425141\pi\)
−0.725679 + 0.688033i \(0.758474\pi\)
\(662\) 0 0
\(663\) −49.0122 84.8916i −1.90348 3.29692i
\(664\) 0 0
\(665\) −21.9126 + 30.8710i −0.849733 + 1.19713i
\(666\) 0 0
\(667\) 1.74276 1.00618i 0.0674800 0.0389596i
\(668\) 0 0
\(669\) −23.8176 13.7511i −0.920840 0.531647i
\(670\) 0 0
\(671\) 8.62193 14.9336i 0.332846 0.576506i
\(672\) 0 0
\(673\) 21.2119 0.817659 0.408829 0.912611i \(-0.365937\pi\)
0.408829 + 0.912611i \(0.365937\pi\)
\(674\) 0 0
\(675\) 4.64410 + 2.68127i 0.178751 + 0.103202i
\(676\) 0 0
\(677\) 10.0144i 0.384885i 0.981308 + 0.192443i \(0.0616409\pi\)
−0.981308 + 0.192443i \(0.938359\pi\)
\(678\) 0 0
\(679\) −14.6898 25.4435i −0.563743 0.976431i
\(680\) 0 0
\(681\) 20.9156 + 36.2268i 0.801486 + 1.38822i
\(682\) 0 0
\(683\) 3.77839i 0.144576i 0.997384 + 0.0722881i \(0.0230301\pi\)
−0.997384 + 0.0722881i \(0.976970\pi\)
\(684\) 0 0
\(685\) 18.1077i 0.691861i
\(686\) 0 0
\(687\) 9.51119 + 16.4739i 0.362874 + 0.628517i
\(688\) 0 0
\(689\) −2.55328 4.42242i −0.0972724 0.168481i
\(690\) 0 0
\(691\) 27.7719i 1.05649i 0.849091 + 0.528246i \(0.177150\pi\)
−0.849091 + 0.528246i \(0.822850\pi\)
\(692\) 0 0
\(693\) 9.18027 + 5.30023i 0.348730 + 0.201339i
\(694\) 0 0
\(695\) −51.2447 −1.94382
\(696\) 0 0
\(697\) −42.0292 + 72.7967i −1.59197 + 2.75737i
\(698\) 0 0
\(699\) −10.9122 6.30015i −0.412737 0.238294i
\(700\) 0 0
\(701\) 25.2750 14.5925i 0.954622 0.551151i 0.0601085 0.998192i \(-0.480855\pi\)
0.894514 + 0.447040i \(0.147522\pi\)
\(702\) 0 0
\(703\) 5.82653 + 12.7072i 0.219752 + 0.479261i
\(704\) 0 0
\(705\) 34.3783 + 59.5450i 1.29476 + 2.24259i
\(706\) 0 0
\(707\) 13.6476 + 7.87944i 0.513271 + 0.296337i
\(708\) 0 0
\(709\) 3.35449 + 1.93671i 0.125980 + 0.0727348i 0.561666 0.827364i \(-0.310161\pi\)
−0.435685 + 0.900099i \(0.643494\pi\)
\(710\) 0 0
\(711\) −7.82287 −0.293381
\(712\) 0 0
\(713\) −1.89245 + 3.27781i −0.0708727 + 0.122755i
\(714\) 0 0
\(715\) 20.9071i 0.781880i
\(716\) 0 0
\(717\) 34.5887 19.9698i 1.29174 0.745787i
\(718\) 0 0
\(719\) 9.24280 + 16.0090i 0.344698 + 0.597035i 0.985299 0.170839i \(-0.0546479\pi\)
−0.640601 + 0.767874i \(0.721315\pi\)
\(720\) 0 0
\(721\) −11.2490 −0.418935
\(722\) 0 0
\(723\) 5.05504i 0.187999i
\(724\) 0 0
\(725\) 16.2966 9.40884i 0.605240 0.349436i
\(726\) 0 0
\(727\) 24.8764 + 43.0871i 0.922613 + 1.59801i 0.795355 + 0.606144i \(0.207284\pi\)
0.127258 + 0.991870i \(0.459382\pi\)
\(728\) 0 0
\(729\) 32.4340 1.20126
\(730\) 0 0
\(731\) 45.4958 + 26.2670i 1.68272 + 0.971520i
\(732\) 0 0
\(733\) 15.3497i 0.566954i −0.958979 0.283477i \(-0.908512\pi\)
0.958979 0.283477i \(-0.0914879\pi\)
\(734\) 0 0
\(735\) −2.24658 + 3.89119i −0.0828664 + 0.143529i
\(736\) 0 0
\(737\) 1.97095 3.41378i 0.0726008 0.125748i
\(738\) 0 0
\(739\) 12.0680 6.96744i 0.443927 0.256302i −0.261335 0.965248i \(-0.584163\pi\)
0.705262 + 0.708947i \(0.250829\pi\)
\(740\) 0 0
\(741\) −48.6527 + 22.3083i −1.78730 + 0.819516i
\(742\) 0 0
\(743\) −24.7117 42.8020i −0.906585 1.57025i −0.818775 0.574114i \(-0.805347\pi\)
−0.0878096 0.996137i \(-0.527987\pi\)
\(744\) 0 0
\(745\) 33.5771 58.1572i 1.23017 2.13072i
\(746\) 0 0
\(747\) 35.2170 + 20.3325i 1.28852 + 0.743928i
\(748\) 0 0
\(749\) 30.0860i 1.09932i
\(750\) 0 0
\(751\) 14.9614 25.9140i 0.545951 0.945615i −0.452596 0.891716i \(-0.649502\pi\)
0.998546 0.0538987i \(-0.0171648\pi\)
\(752\) 0 0
\(753\) 64.5937 2.35393
\(754\) 0 0
\(755\) −66.4999 + 38.3938i −2.42018 + 1.39729i
\(756\) 0 0
\(757\) 41.5430 23.9849i 1.50991 0.871744i 0.509972 0.860191i \(-0.329656\pi\)
0.999933 0.0115535i \(-0.00367768\pi\)
\(758\) 0 0
\(759\) −2.24166 −0.0813671
\(760\) 0 0
\(761\) −42.6841 −1.54730 −0.773648 0.633616i \(-0.781570\pi\)
−0.773648 + 0.633616i \(0.781570\pi\)
\(762\) 0 0
\(763\) −37.3668 + 21.5737i −1.35277 + 0.781021i
\(764\) 0 0
\(765\) −78.3541 + 45.2377i −2.83290 + 1.63557i
\(766\) 0 0
\(767\) 36.4847 1.31739
\(768\) 0 0
\(769\) 15.0008 25.9821i 0.540942 0.936940i −0.457908 0.889000i \(-0.651401\pi\)
0.998850 0.0479400i \(-0.0152656\pi\)
\(770\) 0 0
\(771\) 35.7605i 1.28788i
\(772\) 0 0
\(773\) 16.0137 + 9.24549i 0.575971 + 0.332537i 0.759531 0.650471i \(-0.225429\pi\)
−0.183559 + 0.983009i \(0.558762\pi\)
\(774\) 0 0
\(775\) −17.6963 + 30.6509i −0.635670 + 1.10101i
\(776\) 0 0
\(777\) −10.2597 17.7702i −0.368063 0.637504i
\(778\) 0 0
\(779\) 37.4275 + 26.5664i 1.34098 + 0.951840i
\(780\) 0 0
\(781\) 13.7853 7.95895i 0.493277 0.284794i
\(782\) 0 0
\(783\) −1.14193 + 1.97789i −0.0408094 + 0.0706839i
\(784\) 0 0
\(785\) −10.5593 + 18.2892i −0.376876 + 0.652769i
\(786\) 0 0
\(787\) 38.4519i 1.37066i −0.728232 0.685331i \(-0.759658\pi\)
0.728232 0.685331i \(-0.240342\pi\)
\(788\) 0 0
\(789\) 31.5596 + 18.2209i 1.12355 + 0.648682i
\(790\) 0 0
\(791\) 2.08068 0.0739804
\(792\) 0 0
\(793\) −33.5719 58.1482i −1.19217 2.06490i
\(794\) 0 0
\(795\) −7.76928 + 4.48559i −0.275548 + 0.159088i
\(796\) 0 0
\(797\) 17.9520i 0.635894i −0.948108 0.317947i \(-0.897007\pi\)
0.948108 0.317947i \(-0.102993\pi\)
\(798\)