Properties

Label 3330.2.d.k.1999.4
Level $3330$
Weight $2$
Character 3330.1999
Analytic conductor $26.590$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3330,2,Mod(1999,3330)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3330, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3330.1999");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3330.d (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(26.5901838731\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1110)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1999.4
Root \(-0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 3330.1999
Dual form 3330.2.d.k.1999.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +(0.707107 + 2.12132i) q^{5} +0.414214i q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +(0.707107 + 2.12132i) q^{5} +0.414214i q^{7} -1.00000i q^{8} +(-2.12132 + 0.707107i) q^{10} +3.58579 q^{11} +3.24264i q^{13} -0.414214 q^{14} +1.00000 q^{16} -6.41421i q^{17} +7.82843 q^{19} +(-0.707107 - 2.12132i) q^{20} +3.58579i q^{22} +3.00000i q^{23} +(-4.00000 + 3.00000i) q^{25} -3.24264 q^{26} -0.414214i q^{28} -7.07107 q^{29} +7.65685 q^{31} +1.00000i q^{32} +6.41421 q^{34} +(-0.878680 + 0.292893i) q^{35} -1.00000i q^{37} +7.82843i q^{38} +(2.12132 - 0.707107i) q^{40} +9.41421 q^{41} +6.48528i q^{43} -3.58579 q^{44} -3.00000 q^{46} -7.89949i q^{47} +6.82843 q^{49} +(-3.00000 - 4.00000i) q^{50} -3.24264i q^{52} +1.82843i q^{53} +(2.53553 + 7.60660i) q^{55} +0.414214 q^{56} -7.07107i q^{58} +1.07107 q^{59} +10.4853 q^{61} +7.65685i q^{62} -1.00000 q^{64} +(-6.87868 + 2.29289i) q^{65} +4.82843i q^{67} +6.41421i q^{68} +(-0.292893 - 0.878680i) q^{70} +6.58579 q^{71} -7.82843i q^{73} +1.00000 q^{74} -7.82843 q^{76} +1.48528i q^{77} -3.75736 q^{79} +(0.707107 + 2.12132i) q^{80} +9.41421i q^{82} -12.8995i q^{83} +(13.6066 - 4.53553i) q^{85} -6.48528 q^{86} -3.58579i q^{88} -16.8995 q^{89} -1.34315 q^{91} -3.00000i q^{92} +7.89949 q^{94} +(5.53553 + 16.6066i) q^{95} +18.7279i q^{97} +6.82843i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{4} + 20 q^{11} + 4 q^{14} + 4 q^{16} + 20 q^{19} - 16 q^{25} + 4 q^{26} + 8 q^{31} + 20 q^{34} - 12 q^{35} + 32 q^{41} - 20 q^{44} - 12 q^{46} + 16 q^{49} - 12 q^{50} - 4 q^{55} - 4 q^{56} - 24 q^{59} + 8 q^{61} - 4 q^{64} - 36 q^{65} - 4 q^{70} + 32 q^{71} + 4 q^{74} - 20 q^{76} - 32 q^{79} + 12 q^{85} + 8 q^{86} - 28 q^{89} - 28 q^{91} - 8 q^{94} + 8 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 0.707107 + 2.12132i 0.316228 + 0.948683i
\(6\) 0 0
\(7\) 0.414214i 0.156558i 0.996931 + 0.0782790i \(0.0249425\pi\)
−0.996931 + 0.0782790i \(0.975058\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −2.12132 + 0.707107i −0.670820 + 0.223607i
\(11\) 3.58579 1.08116 0.540578 0.841294i \(-0.318206\pi\)
0.540578 + 0.841294i \(0.318206\pi\)
\(12\) 0 0
\(13\) 3.24264i 0.899347i 0.893193 + 0.449673i \(0.148460\pi\)
−0.893193 + 0.449673i \(0.851540\pi\)
\(14\) −0.414214 −0.110703
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 6.41421i 1.55568i −0.628465 0.777838i \(-0.716317\pi\)
0.628465 0.777838i \(-0.283683\pi\)
\(18\) 0 0
\(19\) 7.82843 1.79596 0.897982 0.440032i \(-0.145033\pi\)
0.897982 + 0.440032i \(0.145033\pi\)
\(20\) −0.707107 2.12132i −0.158114 0.474342i
\(21\) 0 0
\(22\) 3.58579i 0.764492i
\(23\) 3.00000i 0.625543i 0.949828 + 0.312772i \(0.101257\pi\)
−0.949828 + 0.312772i \(0.898743\pi\)
\(24\) 0 0
\(25\) −4.00000 + 3.00000i −0.800000 + 0.600000i
\(26\) −3.24264 −0.635934
\(27\) 0 0
\(28\) 0.414214i 0.0782790i
\(29\) −7.07107 −1.31306 −0.656532 0.754298i \(-0.727977\pi\)
−0.656532 + 0.754298i \(0.727977\pi\)
\(30\) 0 0
\(31\) 7.65685 1.37521 0.687606 0.726084i \(-0.258662\pi\)
0.687606 + 0.726084i \(0.258662\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 6.41421 1.10003
\(35\) −0.878680 + 0.292893i −0.148524 + 0.0495080i
\(36\) 0 0
\(37\) 1.00000i 0.164399i
\(38\) 7.82843i 1.26994i
\(39\) 0 0
\(40\) 2.12132 0.707107i 0.335410 0.111803i
\(41\) 9.41421 1.47025 0.735127 0.677930i \(-0.237123\pi\)
0.735127 + 0.677930i \(0.237123\pi\)
\(42\) 0 0
\(43\) 6.48528i 0.988996i 0.869179 + 0.494498i \(0.164648\pi\)
−0.869179 + 0.494498i \(0.835352\pi\)
\(44\) −3.58579 −0.540578
\(45\) 0 0
\(46\) −3.00000 −0.442326
\(47\) 7.89949i 1.15226i −0.817358 0.576130i \(-0.804562\pi\)
0.817358 0.576130i \(-0.195438\pi\)
\(48\) 0 0
\(49\) 6.82843 0.975490
\(50\) −3.00000 4.00000i −0.424264 0.565685i
\(51\) 0 0
\(52\) 3.24264i 0.449673i
\(53\) 1.82843i 0.251154i 0.992084 + 0.125577i \(0.0400782\pi\)
−0.992084 + 0.125577i \(0.959922\pi\)
\(54\) 0 0
\(55\) 2.53553 + 7.60660i 0.341891 + 1.02567i
\(56\) 0.414214 0.0553516
\(57\) 0 0
\(58\) 7.07107i 0.928477i
\(59\) 1.07107 0.139441 0.0697206 0.997567i \(-0.477789\pi\)
0.0697206 + 0.997567i \(0.477789\pi\)
\(60\) 0 0
\(61\) 10.4853 1.34250 0.671251 0.741230i \(-0.265757\pi\)
0.671251 + 0.741230i \(0.265757\pi\)
\(62\) 7.65685i 0.972421i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −6.87868 + 2.29289i −0.853195 + 0.284398i
\(66\) 0 0
\(67\) 4.82843i 0.589886i 0.955515 + 0.294943i \(0.0953007\pi\)
−0.955515 + 0.294943i \(0.904699\pi\)
\(68\) 6.41421i 0.777838i
\(69\) 0 0
\(70\) −0.292893 0.878680i −0.0350074 0.105022i
\(71\) 6.58579 0.781589 0.390795 0.920478i \(-0.372200\pi\)
0.390795 + 0.920478i \(0.372200\pi\)
\(72\) 0 0
\(73\) 7.82843i 0.916248i −0.888888 0.458124i \(-0.848522\pi\)
0.888888 0.458124i \(-0.151478\pi\)
\(74\) 1.00000 0.116248
\(75\) 0 0
\(76\) −7.82843 −0.897982
\(77\) 1.48528i 0.169264i
\(78\) 0 0
\(79\) −3.75736 −0.422736 −0.211368 0.977407i \(-0.567792\pi\)
−0.211368 + 0.977407i \(0.567792\pi\)
\(80\) 0.707107 + 2.12132i 0.0790569 + 0.237171i
\(81\) 0 0
\(82\) 9.41421i 1.03963i
\(83\) 12.8995i 1.41590i −0.706261 0.707952i \(-0.749619\pi\)
0.706261 0.707952i \(-0.250381\pi\)
\(84\) 0 0
\(85\) 13.6066 4.53553i 1.47584 0.491948i
\(86\) −6.48528 −0.699326
\(87\) 0 0
\(88\) 3.58579i 0.382246i
\(89\) −16.8995 −1.79134 −0.895671 0.444716i \(-0.853304\pi\)
−0.895671 + 0.444716i \(0.853304\pi\)
\(90\) 0 0
\(91\) −1.34315 −0.140800
\(92\) 3.00000i 0.312772i
\(93\) 0 0
\(94\) 7.89949 0.814771
\(95\) 5.53553 + 16.6066i 0.567934 + 1.70380i
\(96\) 0 0
\(97\) 18.7279i 1.90153i 0.309909 + 0.950766i \(0.399701\pi\)
−0.309909 + 0.950766i \(0.600299\pi\)
\(98\) 6.82843i 0.689775i
\(99\) 0 0
\(100\) 4.00000 3.00000i 0.400000 0.300000i
\(101\) −17.3137 −1.72278 −0.861389 0.507946i \(-0.830405\pi\)
−0.861389 + 0.507946i \(0.830405\pi\)
\(102\) 0 0
\(103\) 0.928932i 0.0915304i 0.998952 + 0.0457652i \(0.0145726\pi\)
−0.998952 + 0.0457652i \(0.985427\pi\)
\(104\) 3.24264 0.317967
\(105\) 0 0
\(106\) −1.82843 −0.177593
\(107\) 1.92893i 0.186477i −0.995644 0.0932385i \(-0.970278\pi\)
0.995644 0.0932385i \(-0.0297219\pi\)
\(108\) 0 0
\(109\) −13.2426 −1.26841 −0.634207 0.773163i \(-0.718673\pi\)
−0.634207 + 0.773163i \(0.718673\pi\)
\(110\) −7.60660 + 2.53553i −0.725261 + 0.241754i
\(111\) 0 0
\(112\) 0.414214i 0.0391395i
\(113\) 2.82843i 0.266076i 0.991111 + 0.133038i \(0.0424732\pi\)
−0.991111 + 0.133038i \(0.957527\pi\)
\(114\) 0 0
\(115\) −6.36396 + 2.12132i −0.593442 + 0.197814i
\(116\) 7.07107 0.656532
\(117\) 0 0
\(118\) 1.07107i 0.0985998i
\(119\) 2.65685 0.243553
\(120\) 0 0
\(121\) 1.85786 0.168897
\(122\) 10.4853i 0.949293i
\(123\) 0 0
\(124\) −7.65685 −0.687606
\(125\) −9.19239 6.36396i −0.822192 0.569210i
\(126\) 0 0
\(127\) 12.4142i 1.10158i 0.834643 + 0.550792i \(0.185674\pi\)
−0.834643 + 0.550792i \(0.814326\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −2.29289 6.87868i −0.201100 0.603300i
\(131\) 17.8995 1.56389 0.781943 0.623350i \(-0.214229\pi\)
0.781943 + 0.623350i \(0.214229\pi\)
\(132\) 0 0
\(133\) 3.24264i 0.281173i
\(134\) −4.82843 −0.417113
\(135\) 0 0
\(136\) −6.41421 −0.550014
\(137\) 13.5563i 1.15820i 0.815258 + 0.579099i \(0.196595\pi\)
−0.815258 + 0.579099i \(0.803405\pi\)
\(138\) 0 0
\(139\) −14.4853 −1.22863 −0.614313 0.789063i \(-0.710567\pi\)
−0.614313 + 0.789063i \(0.710567\pi\)
\(140\) 0.878680 0.292893i 0.0742620 0.0247540i
\(141\) 0 0
\(142\) 6.58579i 0.552667i
\(143\) 11.6274i 0.972333i
\(144\) 0 0
\(145\) −5.00000 15.0000i −0.415227 1.24568i
\(146\) 7.82843 0.647885
\(147\) 0 0
\(148\) 1.00000i 0.0821995i
\(149\) 20.4853 1.67822 0.839110 0.543962i \(-0.183076\pi\)
0.839110 + 0.543962i \(0.183076\pi\)
\(150\) 0 0
\(151\) −0.414214 −0.0337082 −0.0168541 0.999858i \(-0.505365\pi\)
−0.0168541 + 0.999858i \(0.505365\pi\)
\(152\) 7.82843i 0.634969i
\(153\) 0 0
\(154\) −1.48528 −0.119687
\(155\) 5.41421 + 16.2426i 0.434880 + 1.30464i
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 3.75736i 0.298919i
\(159\) 0 0
\(160\) −2.12132 + 0.707107i −0.167705 + 0.0559017i
\(161\) −1.24264 −0.0979338
\(162\) 0 0
\(163\) 13.1421i 1.02937i 0.857379 + 0.514686i \(0.172091\pi\)
−0.857379 + 0.514686i \(0.827909\pi\)
\(164\) −9.41421 −0.735127
\(165\) 0 0
\(166\) 12.8995 1.00119
\(167\) 7.34315i 0.568230i 0.958790 + 0.284115i \(0.0916997\pi\)
−0.958790 + 0.284115i \(0.908300\pi\)
\(168\) 0 0
\(169\) 2.48528 0.191175
\(170\) 4.53553 + 13.6066i 0.347860 + 1.04358i
\(171\) 0 0
\(172\) 6.48528i 0.494498i
\(173\) 10.6569i 0.810226i −0.914267 0.405113i \(-0.867232\pi\)
0.914267 0.405113i \(-0.132768\pi\)
\(174\) 0 0
\(175\) −1.24264 1.65685i −0.0939348 0.125246i
\(176\) 3.58579 0.270289
\(177\) 0 0
\(178\) 16.8995i 1.26667i
\(179\) −13.1716 −0.984490 −0.492245 0.870457i \(-0.663824\pi\)
−0.492245 + 0.870457i \(0.663824\pi\)
\(180\) 0 0
\(181\) 23.4142 1.74036 0.870182 0.492730i \(-0.164001\pi\)
0.870182 + 0.492730i \(0.164001\pi\)
\(182\) 1.34315i 0.0995606i
\(183\) 0 0
\(184\) 3.00000 0.221163
\(185\) 2.12132 0.707107i 0.155963 0.0519875i
\(186\) 0 0
\(187\) 23.0000i 1.68193i
\(188\) 7.89949i 0.576130i
\(189\) 0 0
\(190\) −16.6066 + 5.53553i −1.20477 + 0.401590i
\(191\) 2.65685 0.192243 0.0961216 0.995370i \(-0.469356\pi\)
0.0961216 + 0.995370i \(0.469356\pi\)
\(192\) 0 0
\(193\) 13.3137i 0.958342i −0.877722 0.479171i \(-0.840937\pi\)
0.877722 0.479171i \(-0.159063\pi\)
\(194\) −18.7279 −1.34459
\(195\) 0 0
\(196\) −6.82843 −0.487745
\(197\) 13.1421i 0.936338i 0.883639 + 0.468169i \(0.155086\pi\)
−0.883639 + 0.468169i \(0.844914\pi\)
\(198\) 0 0
\(199\) −20.0000 −1.41776 −0.708881 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) 3.00000 + 4.00000i 0.212132 + 0.282843i
\(201\) 0 0
\(202\) 17.3137i 1.21819i
\(203\) 2.92893i 0.205571i
\(204\) 0 0
\(205\) 6.65685 + 19.9706i 0.464935 + 1.39480i
\(206\) −0.928932 −0.0647218
\(207\) 0 0
\(208\) 3.24264i 0.224837i
\(209\) 28.0711 1.94172
\(210\) 0 0
\(211\) −26.3848 −1.81640 −0.908201 0.418533i \(-0.862544\pi\)
−0.908201 + 0.418533i \(0.862544\pi\)
\(212\) 1.82843i 0.125577i
\(213\) 0 0
\(214\) 1.92893 0.131859
\(215\) −13.7574 + 4.58579i −0.938244 + 0.312748i
\(216\) 0 0
\(217\) 3.17157i 0.215300i
\(218\) 13.2426i 0.896905i
\(219\) 0 0
\(220\) −2.53553 7.60660i −0.170946 0.512837i
\(221\) 20.7990 1.39909
\(222\) 0 0
\(223\) 1.65685i 0.110951i 0.998460 + 0.0554756i \(0.0176675\pi\)
−0.998460 + 0.0554756i \(0.982333\pi\)
\(224\) −0.414214 −0.0276758
\(225\) 0 0
\(226\) −2.82843 −0.188144
\(227\) 12.0000i 0.796468i −0.917284 0.398234i \(-0.869623\pi\)
0.917284 0.398234i \(-0.130377\pi\)
\(228\) 0 0
\(229\) 6.72792 0.444594 0.222297 0.974979i \(-0.428645\pi\)
0.222297 + 0.974979i \(0.428645\pi\)
\(230\) −2.12132 6.36396i −0.139876 0.419627i
\(231\) 0 0
\(232\) 7.07107i 0.464238i
\(233\) 14.4853i 0.948962i 0.880266 + 0.474481i \(0.157364\pi\)
−0.880266 + 0.474481i \(0.842636\pi\)
\(234\) 0 0
\(235\) 16.7574 5.58579i 1.09313 0.364377i
\(236\) −1.07107 −0.0697206
\(237\) 0 0
\(238\) 2.65685i 0.172218i
\(239\) −24.6274 −1.59302 −0.796508 0.604629i \(-0.793322\pi\)
−0.796508 + 0.604629i \(0.793322\pi\)
\(240\) 0 0
\(241\) 5.41421 0.348760 0.174380 0.984678i \(-0.444208\pi\)
0.174380 + 0.984678i \(0.444208\pi\)
\(242\) 1.85786i 0.119428i
\(243\) 0 0
\(244\) −10.4853 −0.671251
\(245\) 4.82843 + 14.4853i 0.308477 + 0.925431i
\(246\) 0 0
\(247\) 25.3848i 1.61519i
\(248\) 7.65685i 0.486211i
\(249\) 0 0
\(250\) 6.36396 9.19239i 0.402492 0.581378i
\(251\) 0.828427 0.0522899 0.0261449 0.999658i \(-0.491677\pi\)
0.0261449 + 0.999658i \(0.491677\pi\)
\(252\) 0 0
\(253\) 10.7574i 0.676309i
\(254\) −12.4142 −0.778937
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 12.4142i 0.774377i 0.922001 + 0.387189i \(0.126554\pi\)
−0.922001 + 0.387189i \(0.873446\pi\)
\(258\) 0 0
\(259\) 0.414214 0.0257380
\(260\) 6.87868 2.29289i 0.426598 0.142199i
\(261\) 0 0
\(262\) 17.8995i 1.10583i
\(263\) 28.5858i 1.76268i 0.472487 + 0.881338i \(0.343356\pi\)
−0.472487 + 0.881338i \(0.656644\pi\)
\(264\) 0 0
\(265\) −3.87868 + 1.29289i −0.238265 + 0.0794218i
\(266\) −3.24264 −0.198819
\(267\) 0 0
\(268\) 4.82843i 0.294943i
\(269\) 19.6274 1.19670 0.598352 0.801233i \(-0.295822\pi\)
0.598352 + 0.801233i \(0.295822\pi\)
\(270\) 0 0
\(271\) −1.17157 −0.0711680 −0.0355840 0.999367i \(-0.511329\pi\)
−0.0355840 + 0.999367i \(0.511329\pi\)
\(272\) 6.41421i 0.388919i
\(273\) 0 0
\(274\) −13.5563 −0.818969
\(275\) −14.3431 + 10.7574i −0.864924 + 0.648693i
\(276\) 0 0
\(277\) 16.8995i 1.01539i 0.861536 + 0.507696i \(0.169503\pi\)
−0.861536 + 0.507696i \(0.830497\pi\)
\(278\) 14.4853i 0.868769i
\(279\) 0 0
\(280\) 0.292893 + 0.878680i 0.0175037 + 0.0525112i
\(281\) −23.3848 −1.39502 −0.697509 0.716576i \(-0.745708\pi\)
−0.697509 + 0.716576i \(0.745708\pi\)
\(282\) 0 0
\(283\) 20.7990i 1.23637i −0.786032 0.618186i \(-0.787868\pi\)
0.786032 0.618186i \(-0.212132\pi\)
\(284\) −6.58579 −0.390795
\(285\) 0 0
\(286\) −11.6274 −0.687544
\(287\) 3.89949i 0.230180i
\(288\) 0 0
\(289\) −24.1421 −1.42013
\(290\) 15.0000 5.00000i 0.880830 0.293610i
\(291\) 0 0
\(292\) 7.82843i 0.458124i
\(293\) 2.65685i 0.155215i 0.996984 + 0.0776075i \(0.0247281\pi\)
−0.996984 + 0.0776075i \(0.975272\pi\)
\(294\) 0 0
\(295\) 0.757359 + 2.27208i 0.0440952 + 0.132285i
\(296\) −1.00000 −0.0581238
\(297\) 0 0
\(298\) 20.4853i 1.18668i
\(299\) −9.72792 −0.562580
\(300\) 0 0
\(301\) −2.68629 −0.154835
\(302\) 0.414214i 0.0238353i
\(303\) 0 0
\(304\) 7.82843 0.448991
\(305\) 7.41421 + 22.2426i 0.424537 + 1.27361i
\(306\) 0 0
\(307\) 5.89949i 0.336702i 0.985727 + 0.168351i \(0.0538442\pi\)
−0.985727 + 0.168351i \(0.946156\pi\)
\(308\) 1.48528i 0.0846318i
\(309\) 0 0
\(310\) −16.2426 + 5.41421i −0.922520 + 0.307507i
\(311\) 7.17157 0.406663 0.203331 0.979110i \(-0.434823\pi\)
0.203331 + 0.979110i \(0.434823\pi\)
\(312\) 0 0
\(313\) 22.7279i 1.28466i −0.766429 0.642329i \(-0.777968\pi\)
0.766429 0.642329i \(-0.222032\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 3.75736 0.211368
\(317\) 26.8284i 1.50683i −0.657543 0.753417i \(-0.728404\pi\)
0.657543 0.753417i \(-0.271596\pi\)
\(318\) 0 0
\(319\) −25.3553 −1.41963
\(320\) −0.707107 2.12132i −0.0395285 0.118585i
\(321\) 0 0
\(322\) 1.24264i 0.0692497i
\(323\) 50.2132i 2.79394i
\(324\) 0 0
\(325\) −9.72792 12.9706i −0.539608 0.719477i
\(326\) −13.1421 −0.727876
\(327\) 0 0
\(328\) 9.41421i 0.519813i
\(329\) 3.27208 0.180395
\(330\) 0 0
\(331\) −27.4558 −1.50911 −0.754555 0.656237i \(-0.772147\pi\)
−0.754555 + 0.656237i \(0.772147\pi\)
\(332\) 12.8995i 0.707952i
\(333\) 0 0
\(334\) −7.34315 −0.401799
\(335\) −10.2426 + 3.41421i −0.559615 + 0.186538i
\(336\) 0 0
\(337\) 5.97056i 0.325237i −0.986689 0.162619i \(-0.948006\pi\)
0.986689 0.162619i \(-0.0519940\pi\)
\(338\) 2.48528i 0.135181i
\(339\) 0 0
\(340\) −13.6066 + 4.53553i −0.737922 + 0.245974i
\(341\) 27.4558 1.48682
\(342\) 0 0
\(343\) 5.72792i 0.309279i
\(344\) 6.48528 0.349663
\(345\) 0 0
\(346\) 10.6569 0.572916
\(347\) 7.55635i 0.405646i −0.979215 0.202823i \(-0.934988\pi\)
0.979215 0.202823i \(-0.0650116\pi\)
\(348\) 0 0
\(349\) 20.0416 1.07280 0.536402 0.843963i \(-0.319783\pi\)
0.536402 + 0.843963i \(0.319783\pi\)
\(350\) 1.65685 1.24264i 0.0885626 0.0664219i
\(351\) 0 0
\(352\) 3.58579i 0.191123i
\(353\) 12.1421i 0.646261i −0.946354 0.323130i \(-0.895265\pi\)
0.946354 0.323130i \(-0.104735\pi\)
\(354\) 0 0
\(355\) 4.65685 + 13.9706i 0.247160 + 0.741480i
\(356\) 16.8995 0.895671
\(357\) 0 0
\(358\) 13.1716i 0.696139i
\(359\) 14.9289 0.787919 0.393959 0.919128i \(-0.371105\pi\)
0.393959 + 0.919128i \(0.371105\pi\)
\(360\) 0 0
\(361\) 42.2843 2.22549
\(362\) 23.4142i 1.23062i
\(363\) 0 0
\(364\) 1.34315 0.0704000
\(365\) 16.6066 5.53553i 0.869229 0.289743i
\(366\) 0 0
\(367\) 6.75736i 0.352731i 0.984325 + 0.176366i \(0.0564341\pi\)
−0.984325 + 0.176366i \(0.943566\pi\)
\(368\) 3.00000i 0.156386i
\(369\) 0 0
\(370\) 0.707107 + 2.12132i 0.0367607 + 0.110282i
\(371\) −0.757359 −0.0393201
\(372\) 0 0
\(373\) 10.2426i 0.530344i −0.964201 0.265172i \(-0.914571\pi\)
0.964201 0.265172i \(-0.0854287\pi\)
\(374\) 23.0000 1.18930
\(375\) 0 0
\(376\) −7.89949 −0.407385
\(377\) 22.9289i 1.18090i
\(378\) 0 0
\(379\) 3.27208 0.168075 0.0840377 0.996463i \(-0.473218\pi\)
0.0840377 + 0.996463i \(0.473218\pi\)
\(380\) −5.53553 16.6066i −0.283967 0.851901i
\(381\) 0 0
\(382\) 2.65685i 0.135936i
\(383\) 3.34315i 0.170827i −0.996346 0.0854134i \(-0.972779\pi\)
0.996346 0.0854134i \(-0.0272211\pi\)
\(384\) 0 0
\(385\) −3.15076 + 1.05025i −0.160577 + 0.0535258i
\(386\) 13.3137 0.677650
\(387\) 0 0
\(388\) 18.7279i 0.950766i
\(389\) 10.9706 0.556230 0.278115 0.960548i \(-0.410290\pi\)
0.278115 + 0.960548i \(0.410290\pi\)
\(390\) 0 0
\(391\) 19.2426 0.973142
\(392\) 6.82843i 0.344888i
\(393\) 0 0
\(394\) −13.1421 −0.662091
\(395\) −2.65685 7.97056i −0.133681 0.401043i
\(396\) 0 0
\(397\) 8.48528i 0.425864i 0.977067 + 0.212932i \(0.0683013\pi\)
−0.977067 + 0.212932i \(0.931699\pi\)
\(398\) 20.0000i 1.00251i
\(399\) 0 0
\(400\) −4.00000 + 3.00000i −0.200000 + 0.150000i
\(401\) −33.0416 −1.65002 −0.825010 0.565118i \(-0.808831\pi\)
−0.825010 + 0.565118i \(0.808831\pi\)
\(402\) 0 0
\(403\) 24.8284i 1.23679i
\(404\) 17.3137 0.861389
\(405\) 0 0
\(406\) 2.92893 0.145360
\(407\) 3.58579i 0.177741i
\(408\) 0 0
\(409\) 4.38478 0.216813 0.108407 0.994107i \(-0.465425\pi\)
0.108407 + 0.994107i \(0.465425\pi\)
\(410\) −19.9706 + 6.65685i −0.986276 + 0.328759i
\(411\) 0 0
\(412\) 0.928932i 0.0457652i
\(413\) 0.443651i 0.0218306i
\(414\) 0 0
\(415\) 27.3640 9.12132i 1.34324 0.447748i
\(416\) −3.24264 −0.158984
\(417\) 0 0
\(418\) 28.0711i 1.37300i
\(419\) −2.27208 −0.110998 −0.0554991 0.998459i \(-0.517675\pi\)
−0.0554991 + 0.998459i \(0.517675\pi\)
\(420\) 0 0
\(421\) 37.4558 1.82549 0.912743 0.408534i \(-0.133960\pi\)
0.912743 + 0.408534i \(0.133960\pi\)
\(422\) 26.3848i 1.28439i
\(423\) 0 0
\(424\) 1.82843 0.0887963
\(425\) 19.2426 + 25.6569i 0.933405 + 1.24454i
\(426\) 0 0
\(427\) 4.34315i 0.210180i
\(428\) 1.92893i 0.0932385i
\(429\) 0 0
\(430\) −4.58579 13.7574i −0.221146 0.663439i
\(431\) −24.1716 −1.16430 −0.582152 0.813080i \(-0.697789\pi\)
−0.582152 + 0.813080i \(0.697789\pi\)
\(432\) 0 0
\(433\) 6.51472i 0.313077i −0.987672 0.156539i \(-0.949966\pi\)
0.987672 0.156539i \(-0.0500336\pi\)
\(434\) −3.17157 −0.152240
\(435\) 0 0
\(436\) 13.2426 0.634207
\(437\) 23.4853i 1.12345i
\(438\) 0 0
\(439\) 0.727922 0.0347418 0.0173709 0.999849i \(-0.494470\pi\)
0.0173709 + 0.999849i \(0.494470\pi\)
\(440\) 7.60660 2.53553i 0.362631 0.120877i
\(441\) 0 0
\(442\) 20.7990i 0.989307i
\(443\) 12.3431i 0.586441i 0.956045 + 0.293220i \(0.0947269\pi\)
−0.956045 + 0.293220i \(0.905273\pi\)
\(444\) 0 0
\(445\) −11.9497 35.8492i −0.566472 1.69942i
\(446\) −1.65685 −0.0784543
\(447\) 0 0
\(448\) 0.414214i 0.0195698i
\(449\) 25.7990 1.21753 0.608765 0.793351i \(-0.291665\pi\)
0.608765 + 0.793351i \(0.291665\pi\)
\(450\) 0 0
\(451\) 33.7574 1.58957
\(452\) 2.82843i 0.133038i
\(453\) 0 0
\(454\) 12.0000 0.563188
\(455\) −0.949747 2.84924i −0.0445248 0.133575i
\(456\) 0 0
\(457\) 32.9706i 1.54230i −0.636655 0.771149i \(-0.719682\pi\)
0.636655 0.771149i \(-0.280318\pi\)
\(458\) 6.72792i 0.314375i
\(459\) 0 0
\(460\) 6.36396 2.12132i 0.296721 0.0989071i
\(461\) −15.1716 −0.706611 −0.353305 0.935508i \(-0.614942\pi\)
−0.353305 + 0.935508i \(0.614942\pi\)
\(462\) 0 0
\(463\) 10.1005i 0.469410i −0.972067 0.234705i \(-0.924588\pi\)
0.972067 0.234705i \(-0.0754125\pi\)
\(464\) −7.07107 −0.328266
\(465\) 0 0
\(466\) −14.4853 −0.671018
\(467\) 31.7574i 1.46956i −0.678308 0.734778i \(-0.737286\pi\)
0.678308 0.734778i \(-0.262714\pi\)
\(468\) 0 0
\(469\) −2.00000 −0.0923514
\(470\) 5.58579 + 16.7574i 0.257653 + 0.772959i
\(471\) 0 0
\(472\) 1.07107i 0.0492999i
\(473\) 23.2548i 1.06926i
\(474\) 0 0
\(475\) −31.3137 + 23.4853i −1.43677 + 1.07758i
\(476\) −2.65685 −0.121777
\(477\) 0 0
\(478\) 24.6274i 1.12643i
\(479\) 11.8284 0.540455 0.270227 0.962797i \(-0.412901\pi\)
0.270227 + 0.962797i \(0.412901\pi\)
\(480\) 0 0
\(481\) 3.24264 0.147852
\(482\) 5.41421i 0.246611i
\(483\) 0 0
\(484\) −1.85786 −0.0844484
\(485\) −39.7279 + 13.2426i −1.80395 + 0.601317i
\(486\) 0 0
\(487\) 30.0000i 1.35943i 0.733476 + 0.679715i \(0.237896\pi\)
−0.733476 + 0.679715i \(0.762104\pi\)
\(488\) 10.4853i 0.474646i
\(489\) 0 0
\(490\) −14.4853 + 4.82843i −0.654378 + 0.218126i
\(491\) 13.5858 0.613118 0.306559 0.951852i \(-0.400822\pi\)
0.306559 + 0.951852i \(0.400822\pi\)
\(492\) 0 0
\(493\) 45.3553i 2.04270i
\(494\) −25.3848 −1.14212
\(495\) 0 0
\(496\) 7.65685 0.343803
\(497\) 2.72792i 0.122364i
\(498\) 0 0
\(499\) 9.48528 0.424620 0.212310 0.977202i \(-0.431901\pi\)
0.212310 + 0.977202i \(0.431901\pi\)
\(500\) 9.19239 + 6.36396i 0.411096 + 0.284605i
\(501\) 0 0
\(502\) 0.828427i 0.0369745i
\(503\) 12.3431i 0.550354i 0.961394 + 0.275177i \(0.0887364\pi\)
−0.961394 + 0.275177i \(0.911264\pi\)
\(504\) 0 0
\(505\) −12.2426 36.7279i −0.544790 1.63437i
\(506\) −10.7574 −0.478223
\(507\) 0 0
\(508\) 12.4142i 0.550792i
\(509\) −7.68629 −0.340689 −0.170344 0.985385i \(-0.554488\pi\)
−0.170344 + 0.985385i \(0.554488\pi\)
\(510\) 0 0
\(511\) 3.24264 0.143446
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −12.4142 −0.547567
\(515\) −1.97056 + 0.656854i −0.0868334 + 0.0289445i
\(516\) 0 0
\(517\) 28.3259i 1.24577i
\(518\) 0.414214i 0.0181995i
\(519\) 0 0
\(520\) 2.29289 + 6.87868i 0.100550 + 0.301650i
\(521\) −32.0416 −1.40377 −0.701885 0.712291i \(-0.747658\pi\)
−0.701885 + 0.712291i \(0.747658\pi\)
\(522\) 0 0
\(523\) 34.0000i 1.48672i −0.668894 0.743358i \(-0.733232\pi\)
0.668894 0.743358i \(-0.266768\pi\)
\(524\) −17.8995 −0.781943
\(525\) 0 0
\(526\) −28.5858 −1.24640
\(527\) 49.1127i 2.13938i
\(528\) 0 0
\(529\) 14.0000 0.608696
\(530\) −1.29289 3.87868i −0.0561597 0.168479i
\(531\) 0 0
\(532\) 3.24264i 0.140586i
\(533\) 30.5269i 1.32227i
\(534\) 0 0
\(535\) 4.09188 1.36396i 0.176908 0.0589692i
\(536\) 4.82843 0.208556
\(537\) 0 0
\(538\) 19.6274i 0.846198i
\(539\) 24.4853 1.05466
\(540\) 0 0
\(541\) −6.21320 −0.267126 −0.133563 0.991040i \(-0.542642\pi\)
−0.133563 + 0.991040i \(0.542642\pi\)
\(542\) 1.17157i 0.0503234i
\(543\) 0 0
\(544\) 6.41421 0.275007
\(545\) −9.36396 28.0919i −0.401108 1.20332i
\(546\) 0 0
\(547\) 45.6274i 1.95089i −0.220249 0.975444i \(-0.570687\pi\)
0.220249 0.975444i \(-0.429313\pi\)
\(548\) 13.5563i 0.579099i
\(549\) 0 0
\(550\) −10.7574 14.3431i −0.458695 0.611594i
\(551\) −55.3553 −2.35822
\(552\) 0 0
\(553\) 1.55635i 0.0661827i
\(554\) −16.8995 −0.717991
\(555\) 0 0
\(556\) 14.4853 0.614313
\(557\) 6.44365i 0.273026i 0.990638 + 0.136513i \(0.0435896\pi\)
−0.990638 + 0.136513i \(0.956410\pi\)
\(558\) 0 0
\(559\) −21.0294 −0.889450
\(560\) −0.878680 + 0.292893i −0.0371310 + 0.0123770i
\(561\) 0 0
\(562\) 23.3848i 0.986427i
\(563\) 19.4142i 0.818212i 0.912487 + 0.409106i \(0.134159\pi\)
−0.912487 + 0.409106i \(0.865841\pi\)
\(564\) 0 0
\(565\) −6.00000 + 2.00000i −0.252422 + 0.0841406i
\(566\) 20.7990 0.874247
\(567\) 0 0
\(568\) 6.58579i 0.276333i
\(569\) −11.0416 −0.462889 −0.231445 0.972848i \(-0.574345\pi\)
−0.231445 + 0.972848i \(0.574345\pi\)
\(570\) 0 0
\(571\) 20.0416 0.838716 0.419358 0.907821i \(-0.362255\pi\)
0.419358 + 0.907821i \(0.362255\pi\)
\(572\) 11.6274i 0.486167i
\(573\) 0 0
\(574\) −3.89949 −0.162762
\(575\) −9.00000 12.0000i −0.375326 0.500435i
\(576\) 0 0
\(577\) 26.4853i 1.10260i 0.834308 + 0.551298i \(0.185867\pi\)
−0.834308 + 0.551298i \(0.814133\pi\)
\(578\) 24.1421i 1.00418i
\(579\) 0 0
\(580\) 5.00000 + 15.0000i 0.207614 + 0.622841i
\(581\) 5.34315 0.221671
\(582\) 0 0
\(583\) 6.55635i 0.271536i
\(584\) −7.82843 −0.323943
\(585\) 0 0
\(586\) −2.65685 −0.109754
\(587\) 2.82843i 0.116742i −0.998295 0.0583708i \(-0.981409\pi\)
0.998295 0.0583708i \(-0.0185906\pi\)
\(588\) 0 0
\(589\) 59.9411 2.46983
\(590\) −2.27208 + 0.757359i −0.0935400 + 0.0311800i
\(591\) 0 0
\(592\) 1.00000i 0.0410997i
\(593\) 28.9706i 1.18968i −0.803845 0.594839i \(-0.797216\pi\)
0.803845 0.594839i \(-0.202784\pi\)
\(594\) 0 0
\(595\) 1.87868 + 5.63604i 0.0770184 + 0.231055i
\(596\) −20.4853 −0.839110
\(597\) 0 0
\(598\) 9.72792i 0.397804i
\(599\) −20.8701 −0.852727 −0.426364 0.904552i \(-0.640206\pi\)
−0.426364 + 0.904552i \(0.640206\pi\)
\(600\) 0 0
\(601\) −23.9706 −0.977780 −0.488890 0.872346i \(-0.662598\pi\)
−0.488890 + 0.872346i \(0.662598\pi\)
\(602\) 2.68629i 0.109485i
\(603\) 0 0
\(604\) 0.414214 0.0168541
\(605\) 1.31371 + 3.94113i 0.0534098 + 0.160230i
\(606\) 0 0
\(607\) 40.1421i 1.62932i −0.579940 0.814660i \(-0.696924\pi\)
0.579940 0.814660i \(-0.303076\pi\)
\(608\) 7.82843i 0.317485i
\(609\) 0 0
\(610\) −22.2426 + 7.41421i −0.900578 + 0.300193i
\(611\) 25.6152 1.03628
\(612\) 0 0
\(613\) 21.3137i 0.860853i 0.902626 + 0.430426i \(0.141637\pi\)
−0.902626 + 0.430426i \(0.858363\pi\)
\(614\) −5.89949 −0.238084
\(615\) 0 0
\(616\) 1.48528 0.0598437
\(617\) 23.6985i 0.954065i −0.878886 0.477033i \(-0.841712\pi\)
0.878886 0.477033i \(-0.158288\pi\)
\(618\) 0 0
\(619\) −35.2132 −1.41534 −0.707669 0.706544i \(-0.750253\pi\)
−0.707669 + 0.706544i \(0.750253\pi\)
\(620\) −5.41421 16.2426i −0.217440 0.652320i
\(621\) 0 0
\(622\) 7.17157i 0.287554i
\(623\) 7.00000i 0.280449i
\(624\) 0 0
\(625\) 7.00000 24.0000i 0.280000 0.960000i
\(626\) 22.7279 0.908390
\(627\) 0 0
\(628\) 0 0
\(629\) −6.41421 −0.255751
\(630\) 0 0
\(631\) 24.4853 0.974744 0.487372 0.873195i \(-0.337956\pi\)
0.487372 + 0.873195i \(0.337956\pi\)
\(632\) 3.75736i 0.149460i
\(633\) 0 0
\(634\) 26.8284 1.06549
\(635\) −26.3345 + 8.77817i −1.04505 + 0.348351i
\(636\) 0 0
\(637\) 22.1421i 0.877303i
\(638\) 25.3553i 1.00383i
\(639\) 0 0
\(640\) 2.12132 0.707107i 0.0838525 0.0279508i
\(641\) 21.1716 0.836227 0.418113 0.908395i \(-0.362691\pi\)
0.418113 + 0.908395i \(0.362691\pi\)
\(642\) 0 0
\(643\) 32.4558i 1.27993i −0.768403 0.639967i \(-0.778948\pi\)
0.768403 0.639967i \(-0.221052\pi\)
\(644\) 1.24264 0.0489669
\(645\) 0 0
\(646\) 50.2132 1.97561
\(647\) 21.0000i 0.825595i 0.910823 + 0.412798i \(0.135448\pi\)
−0.910823 + 0.412798i \(0.864552\pi\)
\(648\) 0 0
\(649\) 3.84062 0.150758
\(650\) 12.9706 9.72792i 0.508747 0.381560i
\(651\) 0 0
\(652\) 13.1421i 0.514686i
\(653\) 3.51472i 0.137542i 0.997632 + 0.0687708i \(0.0219077\pi\)
−0.997632 + 0.0687708i \(0.978092\pi\)
\(654\) 0 0
\(655\) 12.6569 + 37.9706i 0.494544 + 1.48363i
\(656\) 9.41421 0.367563
\(657\) 0 0
\(658\) 3.27208i 0.127559i
\(659\) −11.1127 −0.432889 −0.216445 0.976295i \(-0.569446\pi\)
−0.216445 + 0.976295i \(0.569446\pi\)
\(660\) 0 0
\(661\) 16.7574 0.651786 0.325893 0.945407i \(-0.394335\pi\)
0.325893 + 0.945407i \(0.394335\pi\)
\(662\) 27.4558i 1.06710i
\(663\) 0 0
\(664\) −12.8995 −0.500597
\(665\) −6.87868 + 2.29289i −0.266744 + 0.0889146i
\(666\) 0 0
\(667\) 21.2132i 0.821379i
\(668\) 7.34315i 0.284115i
\(669\) 0 0
\(670\) −3.41421 10.2426i −0.131903 0.395708i
\(671\) 37.5980 1.45145
\(672\) 0 0
\(673\) 33.9706i 1.30947i −0.755859 0.654734i \(-0.772780\pi\)
0.755859 0.654734i \(-0.227220\pi\)
\(674\) 5.97056 0.229977
\(675\) 0 0
\(676\) −2.48528 −0.0955877
\(677\) 40.7990i 1.56803i −0.620740 0.784016i \(-0.713168\pi\)
0.620740 0.784016i \(-0.286832\pi\)
\(678\) 0 0
\(679\) −7.75736 −0.297700
\(680\) −4.53553 13.6066i −0.173930 0.521789i
\(681\) 0 0
\(682\) 27.4558i 1.05134i
\(683\) 31.0711i 1.18890i −0.804132 0.594451i \(-0.797370\pi\)
0.804132 0.594451i \(-0.202630\pi\)
\(684\) 0 0
\(685\) −28.7574 + 9.58579i −1.09876 + 0.366254i
\(686\) −5.72792 −0.218693
\(687\) 0 0
\(688\) 6.48528i 0.247249i
\(689\) −5.92893 −0.225874
\(690\) 0 0
\(691\) 33.4142 1.27114 0.635568 0.772045i \(-0.280766\pi\)
0.635568 + 0.772045i \(0.280766\pi\)
\(692\) 10.6569i 0.405113i
\(693\) 0 0
\(694\) 7.55635 0.286835
\(695\) −10.2426 30.7279i −0.388526 1.16558i
\(696\) 0 0
\(697\) 60.3848i 2.28724i
\(698\) 20.0416i 0.758587i
\(699\) 0 0
\(700\) 1.24264 + 1.65685i 0.0469674 + 0.0626232i
\(701\) 30.6274 1.15678 0.578391 0.815760i \(-0.303681\pi\)
0.578391 + 0.815760i \(0.303681\pi\)
\(702\) 0 0
\(703\) 7.82843i 0.295255i
\(704\) −3.58579 −0.135144
\(705\) 0 0
\(706\) 12.1421 0.456975
\(707\) 7.17157i 0.269715i
\(708\) 0 0
\(709\) −29.9289 −1.12400 −0.562002 0.827136i \(-0.689969\pi\)
−0.562002 + 0.827136i \(0.689969\pi\)
\(710\) −13.9706 + 4.65685i −0.524306 + 0.174769i
\(711\) 0 0
\(712\) 16.8995i 0.633335i
\(713\) 22.9706i 0.860254i
\(714\) 0 0
\(715\) −24.6655 + 8.22183i −0.922437 + 0.307479i
\(716\) 13.1716 0.492245
\(717\) 0 0
\(718\) 14.9289i 0.557143i
\(719\) −1.41421 −0.0527413 −0.0263706 0.999652i \(-0.508395\pi\)
−0.0263706 + 0.999652i \(0.508395\pi\)
\(720\) 0 0
\(721\) −0.384776 −0.0143298
\(722\) 42.2843i 1.57366i
\(723\) 0 0
\(724\) −23.4142 −0.870182
\(725\) 28.2843 21.2132i 1.05045 0.787839i
\(726\) 0 0
\(727\) 16.3848i 0.607678i −0.952723 0.303839i \(-0.901732\pi\)
0.952723 0.303839i \(-0.0982684\pi\)
\(728\) 1.34315i 0.0497803i
\(729\) 0 0
\(730\) 5.53553 + 16.6066i 0.204879 + 0.614638i
\(731\) 41.5980 1.53856
\(732\) 0 0
\(733\) 22.9706i 0.848437i −0.905560 0.424219i \(-0.860549\pi\)
0.905560 0.424219i \(-0.139451\pi\)
\(734\) −6.75736 −0.249419
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) 17.3137i 0.637759i
\(738\) 0 0
\(739\) 10.0000 0.367856 0.183928 0.982940i \(-0.441119\pi\)
0.183928 + 0.982940i \(0.441119\pi\)
\(740\) −2.12132 + 0.707107i −0.0779813 + 0.0259938i
\(741\) 0 0
\(742\) 0.757359i 0.0278035i
\(743\) 19.3553i 0.710079i −0.934851 0.355039i \(-0.884467\pi\)
0.934851 0.355039i \(-0.115533\pi\)
\(744\) 0 0
\(745\) 14.4853 + 43.4558i 0.530700 + 1.59210i
\(746\) 10.2426 0.375010
\(747\) 0 0
\(748\) 23.0000i 0.840963i
\(749\) 0.798990 0.0291945
\(750\) 0 0
\(751\) 27.1127 0.989356 0.494678 0.869076i \(-0.335286\pi\)
0.494678 + 0.869076i \(0.335286\pi\)
\(752\) 7.89949i 0.288065i
\(753\) 0 0
\(754\) 22.9289 0.835022
\(755\) −0.292893 0.878680i −0.0106595 0.0319784i
\(756\) 0 0
\(757\) 26.2132i 0.952735i 0.879246 + 0.476368i \(0.158047\pi\)
−0.879246 + 0.476368i \(0.841953\pi\)
\(758\) 3.27208i 0.118847i
\(759\) 0 0
\(760\) 16.6066 5.53553i 0.602385 0.200795i
\(761\) −2.68629 −0.0973780 −0.0486890 0.998814i \(-0.515504\pi\)
−0.0486890 + 0.998814i \(0.515504\pi\)
\(762\) 0 0
\(763\) 5.48528i 0.198581i
\(764\) −2.65685 −0.0961216
\(765\) 0 0
\(766\) 3.34315 0.120793
\(767\) 3.47309i 0.125406i
\(768\) 0 0
\(769\) −11.5563 −0.416733 −0.208366 0.978051i \(-0.566815\pi\)
−0.208366 + 0.978051i \(0.566815\pi\)
\(770\) −1.05025 3.15076i −0.0378485 0.113545i
\(771\) 0 0
\(772\) 13.3137i 0.479171i
\(773\) 3.34315i 0.120245i 0.998191 + 0.0601223i \(0.0191491\pi\)
−0.998191 + 0.0601223i \(0.980851\pi\)
\(774\) 0 0
\(775\) −30.6274 + 22.9706i −1.10017 + 0.825127i
\(776\) 18.7279 0.672293
\(777\) 0 0
\(778\) 10.9706i 0.393314i
\(779\) 73.6985 2.64052
\(780\) 0 0
\(781\) 23.6152 0.845019
\(782\) 19.2426i 0.688115i
\(783\) 0 0
\(784\) 6.82843 0.243872
\(785\) 0 0
\(786\) 0 0
\(787\) 21.5147i 0.766917i −0.923558 0.383458i \(-0.874733\pi\)
0.923558 0.383458i \(-0.125267\pi\)
\(788\) 13.1421i 0.468169i
\(789\) 0 0
\(790\) 7.97056 2.65685i 0.283580 0.0945266<