Properties

Label 3330.2.d.k.1999.3
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 1999.3
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 3330.1999
Dual form 3330.2.d.k.1999.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +(-0.707107 - 2.12132i) q^{5} -2.41421i q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +(-0.707107 - 2.12132i) q^{5} -2.41421i q^{7} -1.00000i q^{8} +(2.12132 - 0.707107i) q^{10} +6.41421 q^{11} -5.24264i q^{13} +2.41421 q^{14} +1.00000 q^{16} -3.58579i q^{17} +2.17157 q^{19} +(0.707107 + 2.12132i) q^{20} +6.41421i q^{22} +3.00000i q^{23} +(-4.00000 + 3.00000i) q^{25} +5.24264 q^{26} +2.41421i q^{28} +7.07107 q^{29} -3.65685 q^{31} +1.00000i q^{32} +3.58579 q^{34} +(-5.12132 + 1.70711i) q^{35} -1.00000i q^{37} +2.17157i q^{38} +(-2.12132 + 0.707107i) q^{40} +6.58579 q^{41} -10.4853i q^{43} -6.41421 q^{44} -3.00000 q^{46} +11.8995i q^{47} +1.17157 q^{49} +(-3.00000 - 4.00000i) q^{50} +5.24264i q^{52} -3.82843i q^{53} +(-4.53553 - 13.6066i) q^{55} -2.41421 q^{56} +7.07107i q^{58} -13.0711 q^{59} -6.48528 q^{61} -3.65685i q^{62} -1.00000 q^{64} +(-11.1213 + 3.70711i) q^{65} -0.828427i q^{67} +3.58579i q^{68} +(-1.70711 - 5.12132i) q^{70} +9.41421 q^{71} -2.17157i q^{73} +1.00000 q^{74} -2.17157 q^{76} -15.4853i q^{77} -12.2426 q^{79} +(-0.707107 - 2.12132i) q^{80} +6.58579i q^{82} +6.89949i q^{83} +(-7.60660 + 2.53553i) q^{85} +10.4853 q^{86} -6.41421i q^{88} +2.89949 q^{89} -12.6569 q^{91} -3.00000i q^{92} -11.8995 q^{94} +(-1.53553 - 4.60660i) q^{95} -6.72792i q^{97} +1.17157i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4}+O(q^{10}) \) 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
\(7\) 2.41421i 0.912487i −0.889855 0.456243i \(-0.849195\pi\)
0.889855 0.456243i \(-0.150805\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.12132 0.707107i 0.670820 0.223607i
\(11\) 6.41421 1.93396 0.966979 0.254856i \(-0.0820280\pi\)
0.966979 + 0.254856i \(0.0820280\pi\)
\(12\) 0 0
\(13\) 5.24264i 1.45405i −0.686613 0.727023i \(-0.740903\pi\)
0.686613 0.727023i \(-0.259097\pi\)
\(14\) 2.41421 0.645226
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.58579i 0.869681i −0.900508 0.434840i \(-0.856805\pi\)
0.900508 0.434840i \(-0.143195\pi\)
\(18\) 0 0
\(19\) 2.17157 0.498193 0.249096 0.968479i \(-0.419866\pi\)
0.249096 + 0.968479i \(0.419866\pi\)
\(20\) 0.707107 + 2.12132i 0.158114 + 0.474342i
\(21\) 0 0
\(22\) 6.41421i 1.36751i
\(23\) 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
\(26\) 5.24264 1.02817
\(27\) 0 0
\(28\) 2.41421i 0.456243i
\(29\) 7.07107 1.31306 0.656532 0.754298i \(-0.272023\pi\)
0.656532 + 0.754298i \(0.272023\pi\)
\(30\) 0 0
\(31\) −3.65685 −0.656790 −0.328395 0.944540i \(-0.606508\pi\)
−0.328395 + 0.944540i \(0.606508\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 3.58579 0.614957
\(35\) −5.12132 + 1.70711i −0.865661 + 0.288554i
\(36\) 0 0
\(37\) 1.00000i 0.164399i
\(38\) 2.17157i 0.352276i
\(39\) 0 0
\(40\) −2.12132 + 0.707107i −0.335410 + 0.111803i
\(41\) 6.58579 1.02853 0.514264 0.857632i \(-0.328065\pi\)
0.514264 + 0.857632i \(0.328065\pi\)
\(42\) 0 0
\(43\) 10.4853i 1.59899i −0.600672 0.799495i \(-0.705100\pi\)
0.600672 0.799495i \(-0.294900\pi\)
\(44\) −6.41421 −0.966979
\(45\) 0 0
\(46\) −3.00000 −0.442326
\(47\) 11.8995i 1.73572i 0.496809 + 0.867860i \(0.334505\pi\)
−0.496809 + 0.867860i \(0.665495\pi\)
\(48\) 0 0
\(49\) 1.17157 0.167368
\(50\) −3.00000 4.00000i −0.424264 0.565685i
\(51\) 0 0
\(52\) 5.24264i 0.727023i
\(53\) 3.82843i 0.525875i −0.964813 0.262937i \(-0.915309\pi\)
0.964813 0.262937i \(-0.0846913\pi\)
\(54\) 0 0
\(55\) −4.53553 13.6066i −0.611571 1.83471i
\(56\) −2.41421 −0.322613
\(57\) 0 0
\(58\) 7.07107i 0.928477i
\(59\) −13.0711 −1.70171 −0.850854 0.525402i \(-0.823915\pi\)
−0.850854 + 0.525402i \(0.823915\pi\)
\(60\) 0 0
\(61\) −6.48528 −0.830355 −0.415178 0.909740i \(-0.636281\pi\)
−0.415178 + 0.909740i \(0.636281\pi\)
\(62\) 3.65685i 0.464421i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −11.1213 + 3.70711i −1.37943 + 0.459810i
\(66\) 0 0
\(67\) 0.828427i 0.101208i −0.998719 0.0506042i \(-0.983885\pi\)
0.998719 0.0506042i \(-0.0161147\pi\)
\(68\) 3.58579i 0.434840i
\(69\) 0 0
\(70\) −1.70711 5.12132i −0.204038 0.612115i
\(71\) 9.41421 1.11726 0.558631 0.829416i \(-0.311327\pi\)
0.558631 + 0.829416i \(0.311327\pi\)
\(72\) 0 0
\(73\) 2.17157i 0.254163i −0.991892 0.127082i \(-0.959439\pi\)
0.991892 0.127082i \(-0.0405610\pi\)
\(74\) 1.00000 0.116248
\(75\) 0 0
\(76\) −2.17157 −0.249096
\(77\) 15.4853i 1.76471i
\(78\) 0 0
\(79\) −12.2426 −1.37740 −0.688702 0.725044i \(-0.741819\pi\)
−0.688702 + 0.725044i \(0.741819\pi\)
\(80\) −0.707107 2.12132i −0.0790569 0.237171i
\(81\) 0 0
\(82\) 6.58579i 0.727278i
\(83\) 6.89949i 0.757318i 0.925536 + 0.378659i \(0.123615\pi\)
−0.925536 + 0.378659i \(0.876385\pi\)
\(84\) 0 0
\(85\) −7.60660 + 2.53553i −0.825052 + 0.275017i
\(86\) 10.4853 1.13066
\(87\) 0 0
\(88\) 6.41421i 0.683757i
\(89\) 2.89949 0.307346 0.153673 0.988122i \(-0.450890\pi\)
0.153673 + 0.988122i \(0.450890\pi\)
\(90\) 0 0
\(91\) −12.6569 −1.32680
\(92\) 3.00000i 0.312772i
\(93\) 0 0
\(94\) −11.8995 −1.22734
\(95\) −1.53553 4.60660i −0.157542 0.472627i
\(96\) 0 0
\(97\) 6.72792i 0.683117i −0.939861 0.341558i \(-0.889045\pi\)
0.939861 0.341558i \(-0.110955\pi\)
\(98\) 1.17157i 0.118347i
\(99\) 0 0
\(100\) 4.00000 3.00000i 0.400000 0.300000i
\(101\) 5.31371 0.528734 0.264367 0.964422i \(-0.414837\pi\)
0.264367 + 0.964422i \(0.414837\pi\)
\(102\) 0 0
\(103\) 15.0711i 1.48500i 0.669848 + 0.742498i \(0.266359\pi\)
−0.669848 + 0.742498i \(0.733641\pi\)
\(104\) −5.24264 −0.514083
\(105\) 0 0
\(106\) 3.82843 0.371850
\(107\) 16.0711i 1.55365i −0.629717 0.776824i \(-0.716829\pi\)
0.629717 0.776824i \(-0.283171\pi\)
\(108\) 0 0
\(109\) −4.75736 −0.455672 −0.227836 0.973699i \(-0.573165\pi\)
−0.227836 + 0.973699i \(0.573165\pi\)
\(110\) 13.6066 4.53553i 1.29734 0.432446i
\(111\) 0 0
\(112\) 2.41421i 0.228122i
\(113\) 2.82843i 0.266076i −0.991111 0.133038i \(-0.957527\pi\)
0.991111 0.133038i \(-0.0424732\pi\)
\(114\) 0 0
\(115\) 6.36396 2.12132i 0.593442 0.197814i
\(116\) −7.07107 −0.656532
\(117\) 0 0
\(118\) 13.0711i 1.20329i
\(119\) −8.65685 −0.793573
\(120\) 0 0
\(121\) 30.1421 2.74019
\(122\) 6.48528i 0.587150i
\(123\) 0 0
\(124\) 3.65685 0.328395
\(125\) 9.19239 + 6.36396i 0.822192 + 0.569210i
\(126\) 0 0
\(127\) 9.58579i 0.850601i 0.905052 + 0.425300i \(0.139832\pi\)
−0.905052 + 0.425300i \(0.860168\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −3.70711 11.1213i −0.325135 0.975404i
\(131\) −1.89949 −0.165960 −0.0829798 0.996551i \(-0.526444\pi\)
−0.0829798 + 0.996551i \(0.526444\pi\)
\(132\) 0 0
\(133\) 5.24264i 0.454595i
\(134\) 0.828427 0.0715652
\(135\) 0 0
\(136\) −3.58579 −0.307479
\(137\) 17.5563i 1.49994i −0.661472 0.749970i \(-0.730068\pi\)
0.661472 0.749970i \(-0.269932\pi\)
\(138\) 0 0
\(139\) 2.48528 0.210799 0.105399 0.994430i \(-0.466388\pi\)
0.105399 + 0.994430i \(0.466388\pi\)
\(140\) 5.12132 1.70711i 0.432831 0.144277i
\(141\) 0 0
\(142\) 9.41421i 0.790023i
\(143\) 33.6274i 2.81207i
\(144\) 0 0
\(145\) −5.00000 15.0000i −0.415227 1.24568i
\(146\) 2.17157 0.179721
\(147\) 0 0
\(148\) 1.00000i 0.0821995i
\(149\) 3.51472 0.287937 0.143968 0.989582i \(-0.454014\pi\)
0.143968 + 0.989582i \(0.454014\pi\)
\(150\) 0 0
\(151\) 2.41421 0.196466 0.0982330 0.995163i \(-0.468681\pi\)
0.0982330 + 0.995163i \(0.468681\pi\)
\(152\) 2.17157i 0.176138i
\(153\) 0 0
\(154\) 15.4853 1.24784
\(155\) 2.58579 + 7.75736i 0.207695 + 0.623086i
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 12.2426i 0.973972i
\(159\) 0 0
\(160\) 2.12132 0.707107i 0.167705 0.0559017i
\(161\) 7.24264 0.570800
\(162\) 0 0
\(163\) 15.1421i 1.18602i −0.805194 0.593012i \(-0.797939\pi\)
0.805194 0.593012i \(-0.202061\pi\)
\(164\) −6.58579 −0.514264
\(165\) 0 0
\(166\) −6.89949 −0.535505
\(167\) 18.6569i 1.44371i 0.692044 + 0.721855i \(0.256710\pi\)
−0.692044 + 0.721855i \(0.743290\pi\)
\(168\) 0 0
\(169\) −14.4853 −1.11425
\(170\) −2.53553 7.60660i −0.194467 0.583400i
\(171\) 0 0
\(172\) 10.4853i 0.799495i
\(173\) 0.656854i 0.0499397i 0.999688 + 0.0249699i \(0.00794898\pi\)
−0.999688 + 0.0249699i \(0.992051\pi\)
\(174\) 0 0
\(175\) 7.24264 + 9.65685i 0.547492 + 0.729990i
\(176\) 6.41421 0.483490
\(177\) 0 0
\(178\) 2.89949i 0.217326i
\(179\) −18.8284 −1.40730 −0.703651 0.710545i \(-0.748448\pi\)
−0.703651 + 0.710545i \(0.748448\pi\)
\(180\) 0 0
\(181\) 20.5858 1.53013 0.765065 0.643953i \(-0.222707\pi\)
0.765065 + 0.643953i \(0.222707\pi\)
\(182\) 12.6569i 0.938188i
\(183\) 0 0
\(184\) 3.00000 0.221163
\(185\) −2.12132 + 0.707107i −0.155963 + 0.0519875i
\(186\) 0 0
\(187\) 23.0000i 1.68193i
\(188\) 11.8995i 0.867860i
\(189\) 0 0
\(190\) 4.60660 1.53553i 0.334198 0.111399i
\(191\) −8.65685 −0.626388 −0.313194 0.949689i \(-0.601399\pi\)
−0.313194 + 0.949689i \(0.601399\pi\)
\(192\) 0 0
\(193\) 9.31371i 0.670415i 0.942144 + 0.335208i \(0.108806\pi\)
−0.942144 + 0.335208i \(0.891194\pi\)
\(194\) 6.72792 0.483037
\(195\) 0 0
\(196\) −1.17157 −0.0836838
\(197\) 15.1421i 1.07883i −0.842039 0.539416i \(-0.818645\pi\)
0.842039 0.539416i \(-0.181355\pi\)
\(198\) 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
\(202\) 5.31371i 0.373871i
\(203\) 17.0711i 1.19815i
\(204\) 0 0
\(205\) −4.65685 13.9706i −0.325249 0.975746i
\(206\) −15.0711 −1.05005
\(207\) 0 0
\(208\) 5.24264i 0.363512i
\(209\) 13.9289 0.963484
\(210\) 0 0
\(211\) 10.3848 0.714917 0.357459 0.933929i \(-0.383643\pi\)
0.357459 + 0.933929i \(0.383643\pi\)
\(212\) 3.82843i 0.262937i
\(213\) 0 0
\(214\) 16.0711 1.09860
\(215\) −22.2426 + 7.41421i −1.51694 + 0.505645i
\(216\) 0 0
\(217\) 8.82843i 0.599313i
\(218\) 4.75736i 0.322209i
\(219\) 0 0
\(220\) 4.53553 + 13.6066i 0.305786 + 0.917357i
\(221\) −18.7990 −1.26456
\(222\) 0 0
\(223\) 9.65685i 0.646671i −0.946284 0.323335i \(-0.895196\pi\)
0.946284 0.323335i \(-0.104804\pi\)
\(224\) 2.41421 0.161306
\(225\) 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
\(229\) −18.7279 −1.23758 −0.618788 0.785558i \(-0.712376\pi\)
−0.618788 + 0.785558i \(0.712376\pi\)
\(230\) 2.12132 + 6.36396i 0.139876 + 0.419627i
\(231\) 0 0
\(232\) 7.07107i 0.464238i
\(233\) 2.48528i 0.162816i −0.996681 0.0814081i \(-0.974058\pi\)
0.996681 0.0814081i \(-0.0259417\pi\)
\(234\) 0 0
\(235\) 25.2426 8.41421i 1.64665 0.548883i
\(236\) 13.0711 0.850854
\(237\) 0 0
\(238\) 8.65685i 0.561141i
\(239\) 20.6274 1.33428 0.667138 0.744934i \(-0.267519\pi\)
0.667138 + 0.744934i \(0.267519\pi\)
\(240\) 0 0
\(241\) 2.58579 0.166565 0.0832826 0.996526i \(-0.473460\pi\)
0.0832826 + 0.996526i \(0.473460\pi\)
\(242\) 30.1421i 1.93761i
\(243\) 0 0
\(244\) 6.48528 0.415178
\(245\) −0.828427 2.48528i −0.0529263 0.158779i
\(246\) 0 0
\(247\) 11.3848i 0.724396i
\(248\) 3.65685i 0.232210i
\(249\) 0 0
\(250\) −6.36396 + 9.19239i −0.402492 + 0.581378i
\(251\) −4.82843 −0.304768 −0.152384 0.988321i \(-0.548695\pi\)
−0.152384 + 0.988321i \(0.548695\pi\)
\(252\) 0 0
\(253\) 19.2426i 1.20977i
\(254\) −9.58579 −0.601466
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 9.58579i 0.597945i 0.954262 + 0.298972i \(0.0966439\pi\)
−0.954262 + 0.298972i \(0.903356\pi\)
\(258\) 0 0
\(259\) −2.41421 −0.150012
\(260\) 11.1213 3.70711i 0.689715 0.229905i
\(261\) 0 0
\(262\) 1.89949i 0.117351i
\(263\) 31.4142i 1.93708i 0.248851 + 0.968542i \(0.419947\pi\)
−0.248851 + 0.968542i \(0.580053\pi\)
\(264\) 0 0
\(265\) −8.12132 + 2.70711i −0.498889 + 0.166296i
\(266\) 5.24264 0.321447
\(267\) 0 0
\(268\) 0.828427i 0.0506042i
\(269\) −25.6274 −1.56253 −0.781266 0.624199i \(-0.785426\pi\)
−0.781266 + 0.624199i \(0.785426\pi\)
\(270\) 0 0
\(271\) −6.82843 −0.414797 −0.207399 0.978256i \(-0.566500\pi\)
−0.207399 + 0.978256i \(0.566500\pi\)
\(272\) 3.58579i 0.217420i
\(273\) 0 0
\(274\) 17.5563 1.06062
\(275\) −25.6569 + 19.2426i −1.54717 + 1.16037i
\(276\) 0 0
\(277\) 2.89949i 0.174214i −0.996199 0.0871069i \(-0.972238\pi\)
0.996199 0.0871069i \(-0.0277622\pi\)
\(278\) 2.48528i 0.149057i
\(279\) 0 0
\(280\) 1.70711 + 5.12132i 0.102019 + 0.306057i
\(281\) 13.3848 0.798469 0.399234 0.916849i \(-0.369276\pi\)
0.399234 + 0.916849i \(0.369276\pi\)
\(282\) 0 0
\(283\) 18.7990i 1.11748i 0.829342 + 0.558742i \(0.188716\pi\)
−0.829342 + 0.558742i \(0.811284\pi\)
\(284\) −9.41421 −0.558631
\(285\) 0 0
\(286\) 33.6274 1.98843
\(287\) 15.8995i 0.938518i
\(288\) 0 0
\(289\) 4.14214 0.243655
\(290\) 15.0000 5.00000i 0.880830 0.293610i
\(291\) 0 0
\(292\) 2.17157i 0.127082i
\(293\) 8.65685i 0.505739i −0.967500 0.252869i \(-0.918626\pi\)
0.967500 0.252869i \(-0.0813743\pi\)
\(294\) 0 0
\(295\) 9.24264 + 27.7279i 0.538127 + 1.61438i
\(296\) −1.00000 −0.0581238
\(297\) 0 0
\(298\) 3.51472i 0.203602i
\(299\) 15.7279 0.909569
\(300\) 0 0
\(301\) −25.3137 −1.45906
\(302\) 2.41421i 0.138922i
\(303\) 0 0
\(304\) 2.17157 0.124548
\(305\) 4.58579 + 13.7574i 0.262581 + 0.787744i
\(306\) 0 0
\(307\) 13.8995i 0.793286i −0.917973 0.396643i \(-0.870175\pi\)
0.917973 0.396643i \(-0.129825\pi\)
\(308\) 15.4853i 0.882356i
\(309\) 0 0
\(310\) −7.75736 + 2.58579i −0.440588 + 0.146863i
\(311\) 12.8284 0.727433 0.363717 0.931510i \(-0.381508\pi\)
0.363717 + 0.931510i \(0.381508\pi\)
\(312\) 0 0
\(313\) 2.72792i 0.154191i 0.997024 + 0.0770956i \(0.0245647\pi\)
−0.997024 + 0.0770956i \(0.975435\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 12.2426 0.688702
\(317\) 21.1716i 1.18911i −0.804053 0.594557i \(-0.797327\pi\)
0.804053 0.594557i \(-0.202673\pi\)
\(318\) 0 0
\(319\) 45.3553 2.53941
\(320\) 0.707107 + 2.12132i 0.0395285 + 0.118585i
\(321\) 0 0
\(322\) 7.24264i 0.403617i
\(323\) 7.78680i 0.433269i
\(324\) 0 0
\(325\) 15.7279 + 20.9706i 0.872428 + 1.16324i
\(326\) 15.1421 0.838645
\(327\) 0 0
\(328\) 6.58579i 0.363639i
\(329\) 28.7279 1.58382
\(330\) 0 0
\(331\) 23.4558 1.28925 0.644625 0.764499i \(-0.277014\pi\)
0.644625 + 0.764499i \(0.277014\pi\)
\(332\) 6.89949i 0.378659i
\(333\) 0 0
\(334\) −18.6569 −1.02086
\(335\) −1.75736 + 0.585786i −0.0960148 + 0.0320049i
\(336\) 0 0
\(337\) 27.9706i 1.52365i 0.647781 + 0.761827i \(0.275697\pi\)
−0.647781 + 0.761827i \(0.724303\pi\)
\(338\) 14.4853i 0.787895i
\(339\) 0 0
\(340\) 7.60660 2.53553i 0.412526 0.137509i
\(341\) −23.4558 −1.27021
\(342\) 0 0
\(343\) 19.7279i 1.06521i
\(344\) −10.4853 −0.565328
\(345\) 0 0
\(346\) −0.656854 −0.0353127
\(347\) 23.5563i 1.26457i 0.774735 + 0.632286i \(0.217883\pi\)
−0.774735 + 0.632286i \(0.782117\pi\)
\(348\) 0 0
\(349\) −28.0416 −1.50103 −0.750517 0.660851i \(-0.770195\pi\)
−0.750517 + 0.660851i \(0.770195\pi\)
\(350\) −9.65685 + 7.24264i −0.516181 + 0.387135i
\(351\) 0 0
\(352\) 6.41421i 0.341879i
\(353\) 16.1421i 0.859159i 0.903029 + 0.429580i \(0.141338\pi\)
−0.903029 + 0.429580i \(0.858662\pi\)
\(354\) 0 0
\(355\) −6.65685 19.9706i −0.353309 1.05993i
\(356\) −2.89949 −0.153673
\(357\) 0 0
\(358\) 18.8284i 0.995113i
\(359\) 29.0711 1.53431 0.767156 0.641460i \(-0.221671\pi\)
0.767156 + 0.641460i \(0.221671\pi\)
\(360\) 0 0
\(361\) −14.2843 −0.751804
\(362\) 20.5858i 1.08196i
\(363\) 0 0
\(364\) 12.6569 0.663399
\(365\) −4.60660 + 1.53553i −0.241121 + 0.0803735i
\(366\) 0 0
\(367\) 15.2426i 0.795659i 0.917459 + 0.397830i \(0.130237\pi\)
−0.917459 + 0.397830i \(0.869763\pi\)
\(368\) 3.00000i 0.156386i
\(369\) 0 0
\(370\) −0.707107 2.12132i −0.0367607 0.110282i
\(371\) −9.24264 −0.479854
\(372\) 0 0
\(373\) 1.75736i 0.0909926i −0.998965 0.0454963i \(-0.985513\pi\)
0.998965 0.0454963i \(-0.0144869\pi\)
\(374\) 23.0000 1.18930
\(375\) 0 0
\(376\) 11.8995 0.613670
\(377\) 37.0711i 1.90926i
\(378\) 0 0
\(379\) 28.7279 1.47565 0.737827 0.674990i \(-0.235852\pi\)
0.737827 + 0.674990i \(0.235852\pi\)
\(380\) 1.53553 + 4.60660i 0.0787712 + 0.236314i
\(381\) 0 0
\(382\) 8.65685i 0.442923i
\(383\) 14.6569i 0.748930i −0.927241 0.374465i \(-0.877826\pi\)
0.927241 0.374465i \(-0.122174\pi\)
\(384\) 0 0
\(385\) −32.8492 + 10.9497i −1.67415 + 0.558051i
\(386\) −9.31371 −0.474055
\(387\) 0 0
\(388\) 6.72792i 0.341558i
\(389\) −22.9706 −1.16465 −0.582327 0.812955i \(-0.697858\pi\)
−0.582327 + 0.812955i \(0.697858\pi\)
\(390\) 0 0
\(391\) 10.7574 0.544023
\(392\) 1.17157i 0.0591734i
\(393\) 0 0
\(394\) 15.1421 0.762850
\(395\) 8.65685 + 25.9706i 0.435574 + 1.30672i
\(396\) 0 0
\(397\) 8.48528i 0.425864i −0.977067 0.212932i \(-0.931699\pi\)
0.977067 0.212932i \(-0.0683013\pi\)
\(398\) 20.0000i 1.00251i
\(399\) 0 0
\(400\) −4.00000 + 3.00000i −0.200000 + 0.150000i
\(401\) 15.0416 0.751143 0.375572 0.926793i \(-0.377446\pi\)
0.375572 + 0.926793i \(0.377446\pi\)
\(402\) 0 0
\(403\) 19.1716i 0.955004i
\(404\) −5.31371 −0.264367
\(405\) 0 0
\(406\) 17.0711 0.847223
\(407\) 6.41421i 0.317941i
\(408\) 0 0
\(409\) −32.3848 −1.60132 −0.800662 0.599116i \(-0.795519\pi\)
−0.800662 + 0.599116i \(0.795519\pi\)
\(410\) 13.9706 4.65685i 0.689957 0.229986i
\(411\) 0 0
\(412\) 15.0711i 0.742498i
\(413\) 31.5563i 1.55279i
\(414\) 0 0
\(415\) 14.6360 4.87868i 0.718455 0.239485i
\(416\) 5.24264 0.257042
\(417\) 0 0
\(418\) 13.9289i 0.681286i
\(419\) −27.7279 −1.35460 −0.677299 0.735708i \(-0.736850\pi\)
−0.677299 + 0.735708i \(0.736850\pi\)
\(420\) 0 0
\(421\) −13.4558 −0.655798 −0.327899 0.944713i \(-0.606341\pi\)
−0.327899 + 0.944713i \(0.606341\pi\)
\(422\) 10.3848i 0.505523i
\(423\) 0 0
\(424\) −3.82843 −0.185925
\(425\) 10.7574 + 14.3431i 0.521809 + 0.695745i
\(426\) 0 0
\(427\) 15.6569i 0.757688i
\(428\) 16.0711i 0.776824i
\(429\) 0 0
\(430\) −7.41421 22.2426i −0.357545 1.07264i
\(431\) −29.8284 −1.43678 −0.718392 0.695638i \(-0.755122\pi\)
−0.718392 + 0.695638i \(0.755122\pi\)
\(432\) 0 0
\(433\) 23.4853i 1.12863i −0.825559 0.564315i \(-0.809140\pi\)
0.825559 0.564315i \(-0.190860\pi\)
\(434\) −8.82843 −0.423778
\(435\) 0 0
\(436\) 4.75736 0.227836
\(437\) 6.51472i 0.311641i
\(438\) 0 0
\(439\) −24.7279 −1.18020 −0.590100 0.807330i \(-0.700912\pi\)
−0.590100 + 0.807330i \(0.700912\pi\)
\(440\) −13.6066 + 4.53553i −0.648669 + 0.216223i
\(441\) 0 0
\(442\) 18.7990i 0.894177i
\(443\) 23.6569i 1.12397i 0.827147 + 0.561986i \(0.189962\pi\)
−0.827147 + 0.561986i \(0.810038\pi\)
\(444\) 0 0
\(445\) −2.05025 6.15076i −0.0971913 0.291574i
\(446\) 9.65685 0.457265
\(447\) 0 0
\(448\) 2.41421i 0.114061i
\(449\) −13.7990 −0.651215 −0.325607 0.945505i \(-0.605569\pi\)
−0.325607 + 0.945505i \(0.605569\pi\)
\(450\) 0 0
\(451\) 42.2426 1.98913
\(452\) 2.82843i 0.133038i
\(453\) 0 0
\(454\) 12.0000 0.563188
\(455\) 8.94975 + 26.8492i 0.419571 + 1.25871i
\(456\) 0 0
\(457\) 0.970563i 0.0454010i 0.999742 + 0.0227005i \(0.00722642\pi\)
−0.999742 + 0.0227005i \(0.992774\pi\)
\(458\) 18.7279i 0.875098i
\(459\) 0 0
\(460\) −6.36396 + 2.12132i −0.296721 + 0.0989071i
\(461\) −20.8284 −0.970077 −0.485038 0.874493i \(-0.661194\pi\)
−0.485038 + 0.874493i \(0.661194\pi\)
\(462\) 0 0
\(463\) 29.8995i 1.38955i −0.719228 0.694774i \(-0.755505\pi\)
0.719228 0.694774i \(-0.244495\pi\)
\(464\) 7.07107 0.328266
\(465\) 0 0
\(466\) 2.48528 0.115128
\(467\) 40.2426i 1.86221i −0.364755 0.931104i \(-0.618847\pi\)
0.364755 0.931104i \(-0.381153\pi\)
\(468\) 0 0
\(469\) −2.00000 −0.0923514
\(470\) 8.41421 + 25.2426i 0.388119 + 1.16436i
\(471\) 0 0
\(472\) 13.0711i 0.601645i
\(473\) 67.2548i 3.09238i
\(474\) 0 0
\(475\) −8.68629 + 6.51472i −0.398554 + 0.298916i
\(476\) 8.65685 0.396786
\(477\) 0 0
\(478\) 20.6274i 0.943476i
\(479\) 6.17157 0.281986 0.140993 0.990011i \(-0.454970\pi\)
0.140993 + 0.990011i \(0.454970\pi\)
\(480\) 0 0
\(481\) −5.24264 −0.239044
\(482\) 2.58579i 0.117779i
\(483\) 0 0
\(484\) −30.1421 −1.37010
\(485\) −14.2721 + 4.75736i −0.648062 + 0.216021i
\(486\) 0 0
\(487\) 30.0000i 1.35943i 0.733476 + 0.679715i \(0.237896\pi\)
−0.733476 + 0.679715i \(0.762104\pi\)
\(488\) 6.48528i 0.293575i
\(489\) 0 0
\(490\) 2.48528 0.828427i 0.112274 0.0374245i
\(491\) 16.4142 0.740763 0.370382 0.928880i \(-0.379227\pi\)
0.370382 + 0.928880i \(0.379227\pi\)
\(492\) 0 0
\(493\) 25.3553i 1.14195i
\(494\) 11.3848 0.512225
\(495\) 0 0
\(496\) −3.65685 −0.164198
\(497\) 22.7279i 1.01949i
\(498\) 0 0
\(499\) −7.48528 −0.335087 −0.167544 0.985865i \(-0.553583\pi\)
−0.167544 + 0.985865i \(0.553583\pi\)
\(500\) −9.19239 6.36396i −0.411096 0.284605i
\(501\) 0 0
\(502\) 4.82843i 0.215503i
\(503\) 23.6569i 1.05481i 0.849615 + 0.527403i \(0.176834\pi\)
−0.849615 + 0.527403i \(0.823166\pi\)
\(504\) 0 0
\(505\) −3.75736 11.2721i −0.167200 0.501601i
\(506\) −19.2426 −0.855440
\(507\) 0 0
\(508\) 9.58579i 0.425300i
\(509\) −30.3137 −1.34363 −0.671816 0.740718i \(-0.734485\pi\)
−0.671816 + 0.740718i \(0.734485\pi\)
\(510\) 0 0
\(511\) −5.24264 −0.231921
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −9.58579 −0.422811
\(515\) 31.9706 10.6569i 1.40879 0.469597i
\(516\) 0 0
\(517\) 76.3259i 3.35681i
\(518\) 2.41421i 0.106074i
\(519\) 0 0
\(520\) 3.70711 + 11.1213i 0.162567 + 0.487702i
\(521\) 16.0416 0.702797 0.351398 0.936226i \(-0.385706\pi\)
0.351398 + 0.936226i \(0.385706\pi\)
\(522\) 0 0
\(523\) 34.0000i 1.48672i −0.668894 0.743358i \(-0.733232\pi\)
0.668894 0.743358i \(-0.266768\pi\)
\(524\) 1.89949 0.0829798
\(525\) 0 0
\(526\) −31.4142 −1.36972
\(527\) 13.1127i 0.571198i
\(528\) 0 0
\(529\) 14.0000 0.608696
\(530\) −2.70711 8.12132i −0.117589 0.352768i
\(531\) 0 0
\(532\) 5.24264i 0.227297i
\(533\) 34.5269i 1.49553i
\(534\) 0 0
\(535\) −34.0919 + 11.3640i −1.47392 + 0.491307i
\(536\) −0.828427 −0.0357826
\(537\) 0 0
\(538\) 25.6274i 1.10488i
\(539\) 7.51472 0.323682
\(540\) 0 0
\(541\) 36.2132 1.55693 0.778464 0.627690i \(-0.215999\pi\)
0.778464 + 0.627690i \(0.215999\pi\)
\(542\) 6.82843i 0.293306i
\(543\) 0 0
\(544\) 3.58579 0.153739
\(545\) 3.36396 + 10.0919i 0.144096 + 0.432289i
\(546\) 0 0
\(547\) 0.372583i 0.0159305i −0.999968 0.00796525i \(-0.997465\pi\)
0.999968 0.00796525i \(-0.00253544\pi\)
\(548\) 17.5563i 0.749970i
\(549\) 0 0
\(550\) −19.2426 25.6569i −0.820509 1.09401i
\(551\) 15.3553 0.654159
\(552\) 0 0
\(553\) 29.5563i 1.25686i
\(554\) 2.89949 0.123188
\(555\) 0 0
\(556\) −2.48528 −0.105399
\(557\) 37.5563i 1.59131i 0.605748 + 0.795657i \(0.292874\pi\)
−0.605748 + 0.795657i \(0.707126\pi\)
\(558\) 0 0
\(559\) −54.9706 −2.32501
\(560\) −5.12132 + 1.70711i −0.216415 + 0.0721384i
\(561\) 0 0
\(562\) 13.3848i 0.564603i
\(563\) 16.5858i 0.699008i 0.936935 + 0.349504i \(0.113650\pi\)
−0.936935 + 0.349504i \(0.886350\pi\)
\(564\) 0 0
\(565\) −6.00000 + 2.00000i −0.252422 + 0.0841406i
\(566\) −18.7990 −0.790180
\(567\) 0 0
\(568\) 9.41421i 0.395012i
\(569\) 37.0416 1.55287 0.776433 0.630200i \(-0.217027\pi\)
0.776433 + 0.630200i \(0.217027\pi\)
\(570\) 0 0
\(571\) −28.0416 −1.17351 −0.586753 0.809766i \(-0.699594\pi\)
−0.586753 + 0.809766i \(0.699594\pi\)
\(572\) 33.6274i 1.40603i
\(573\) 0 0
\(574\) 15.8995 0.663632
\(575\) −9.00000 12.0000i −0.375326 0.500435i
\(576\) 0 0
\(577\) 9.51472i 0.396103i 0.980192 + 0.198051i \(0.0634613\pi\)
−0.980192 + 0.198051i \(0.936539\pi\)
\(578\) 4.14214i 0.172290i
\(579\) 0 0
\(580\) 5.00000 + 15.0000i 0.207614 + 0.622841i
\(581\) 16.6569 0.691043
\(582\) 0 0
\(583\) 24.5563i 1.01702i
\(584\) −2.17157 −0.0898603
\(585\) 0 0
\(586\) 8.65685 0.357611
\(587\) 2.82843i 0.116742i 0.998295 + 0.0583708i \(0.0185906\pi\)
−0.998295 + 0.0583708i \(0.981409\pi\)
\(588\) 0 0
\(589\) −7.94113 −0.327208
\(590\) −27.7279 + 9.24264i −1.14154 + 0.380513i
\(591\) 0 0
\(592\) 1.00000i 0.0410997i
\(593\) 4.97056i 0.204117i 0.994778 + 0.102058i \(0.0325428\pi\)
−0.994778 + 0.102058i \(0.967457\pi\)
\(594\) 0 0
\(595\) 6.12132 + 18.3640i 0.250950 + 0.752849i
\(596\) −3.51472 −0.143968
\(597\) 0 0
\(598\) 15.7279i 0.643163i
\(599\) 32.8701 1.34303 0.671517 0.740989i \(-0.265643\pi\)
0.671517 + 0.740989i \(0.265643\pi\)
\(600\) 0 0
\(601\) 9.97056 0.406708 0.203354 0.979105i \(-0.434816\pi\)
0.203354 + 0.979105i \(0.434816\pi\)
\(602\) 25.3137i 1.03171i
\(603\) 0 0
\(604\) −2.41421 −0.0982330
\(605\) −21.3137 63.9411i −0.866525 2.59958i
\(606\) 0 0
\(607\) 11.8579i 0.481296i −0.970612 0.240648i \(-0.922640\pi\)
0.970612 0.240648i \(-0.0773599\pi\)
\(608\) 2.17157i 0.0880689i
\(609\) 0 0
\(610\) −13.7574 + 4.58579i −0.557019 + 0.185673i
\(611\) 62.3848 2.52382
\(612\) 0 0
\(613\) 1.31371i 0.0530602i −0.999648 0.0265301i \(-0.991554\pi\)
0.999648 0.0265301i \(-0.00844578\pi\)
\(614\) 13.8995 0.560938
\(615\) 0 0
\(616\) −15.4853 −0.623920
\(617\) 35.6985i 1.43717i 0.695441 + 0.718583i \(0.255209\pi\)
−0.695441 + 0.718583i \(0.744791\pi\)
\(618\) 0 0
\(619\) 7.21320 0.289923 0.144962 0.989437i \(-0.453694\pi\)
0.144962 + 0.989437i \(0.453694\pi\)
\(620\) −2.58579 7.75736i −0.103848 0.311543i
\(621\) 0 0
\(622\) 12.8284i 0.514373i
\(623\) 7.00000i 0.280449i
\(624\) 0 0
\(625\) 7.00000 24.0000i 0.280000 0.960000i
\(626\) −2.72792 −0.109030
\(627\) 0 0
\(628\) 0 0
\(629\) −3.58579 −0.142975
\(630\) 0 0
\(631\) 7.51472 0.299156 0.149578 0.988750i \(-0.452208\pi\)
0.149578 + 0.988750i \(0.452208\pi\)
\(632\) 12.2426i 0.486986i
\(633\) 0 0
\(634\) 21.1716 0.840831
\(635\) 20.3345 6.77817i 0.806951 0.268984i
\(636\) 0 0
\(637\) 6.14214i 0.243360i
\(638\) 45.3553i 1.79564i
\(639\) 0 0
\(640\) −2.12132 + 0.707107i −0.0838525 + 0.0279508i
\(641\) 26.8284 1.05966 0.529830 0.848104i \(-0.322256\pi\)
0.529830 + 0.848104i \(0.322256\pi\)
\(642\) 0 0
\(643\) 18.4558i 0.727827i 0.931433 + 0.363914i \(0.118560\pi\)
−0.931433 + 0.363914i \(0.881440\pi\)
\(644\) −7.24264 −0.285400
\(645\) 0 0
\(646\) 7.78680 0.306367
\(647\) 21.0000i 0.825595i 0.910823 + 0.412798i \(0.135448\pi\)
−0.910823 + 0.412798i \(0.864552\pi\)
\(648\) 0 0
\(649\) −83.8406 −3.29103
\(650\) −20.9706 + 15.7279i −0.822533 + 0.616900i
\(651\) 0 0
\(652\) 15.1421i 0.593012i
\(653\) 20.4853i 0.801651i 0.916154 + 0.400826i \(0.131277\pi\)
−0.916154 + 0.400826i \(0.868723\pi\)
\(654\) 0 0
\(655\) 1.34315 + 4.02944i 0.0524810 + 0.157443i
\(656\) 6.58579 0.257132
\(657\) 0 0
\(658\) 28.7279i 1.11993i
\(659\) 51.1127 1.99107 0.995534 0.0944035i \(-0.0300944\pi\)
0.995534 + 0.0944035i \(0.0300944\pi\)
\(660\) 0 0
\(661\) 25.2426 0.981825 0.490912 0.871209i \(-0.336663\pi\)
0.490912 + 0.871209i \(0.336663\pi\)
\(662\) 23.4558i 0.911637i
\(663\) 0 0
\(664\) 6.89949 0.267752
\(665\) −11.1213 + 3.70711i −0.431266 + 0.143755i
\(666\) 0 0
\(667\) 21.2132i 0.821379i
\(668\) 18.6569i 0.721855i
\(669\) 0 0
\(670\) −0.585786 1.75736i −0.0226309 0.0678927i
\(671\) −41.5980 −1.60587
\(672\) 0 0
\(673\) 0.0294373i 0.00113472i −1.00000 0.000567361i \(-0.999819\pi\)
1.00000 0.000567361i \(-0.000180597\pi\)
\(674\) −27.9706 −1.07739
\(675\) 0 0
\(676\) 14.4853 0.557126
\(677\) 1.20101i 0.0461586i −0.999734 0.0230793i \(-0.992653\pi\)
0.999734 0.0230793i \(-0.00734702\pi\)
\(678\) 0 0
\(679\) −16.2426 −0.623335
\(680\) 2.53553 + 7.60660i 0.0972333 + 0.291700i
\(681\) 0 0
\(682\) 23.4558i 0.898171i
\(683\) 16.9289i 0.647768i −0.946097 0.323884i \(-0.895011\pi\)
0.946097 0.323884i \(-0.104989\pi\)
\(684\) 0 0
\(685\) −37.2426 + 12.4142i −1.42297 + 0.474323i
\(686\) 19.7279 0.753216
\(687\) 0 0
\(688\) 10.4853i 0.399748i
\(689\) −20.0711 −0.764647
\(690\) 0 0
\(691\) 30.5858 1.16354 0.581769 0.813354i \(-0.302361\pi\)
0.581769 + 0.813354i \(0.302361\pi\)
\(692\) 0.656854i 0.0249699i
\(693\) 0 0
\(694\) −23.5563 −0.894187
\(695\) −1.75736 5.27208i −0.0666604 0.199981i
\(696\) 0 0
\(697\) 23.6152i 0.894490i
\(698\) 28.0416i 1.06139i
\(699\) 0 0
\(700\) −7.24264 9.65685i −0.273746 0.364995i
\(701\) −14.6274 −0.552470 −0.276235 0.961090i \(-0.589087\pi\)
−0.276235 + 0.961090i \(0.589087\pi\)
\(702\) 0 0
\(703\) 2.17157i 0.0819024i
\(704\) −6.41421 −0.241745
\(705\) 0 0
\(706\) −16.1421 −0.607517
\(707\) 12.8284i 0.482463i
\(708\) 0 0
\(709\) −44.0711 −1.65512 −0.827562 0.561375i \(-0.810273\pi\)
−0.827562 + 0.561375i \(0.810273\pi\)
\(710\) 19.9706 6.65685i 0.749482 0.249827i
\(711\) 0 0
\(712\) 2.89949i 0.108663i
\(713\) 10.9706i 0.410851i
\(714\) 0 0
\(715\) −71.3345 + 23.7782i −2.66776 + 0.889253i
\(716\) 18.8284 0.703651
\(717\) 0 0
\(718\) 29.0711i 1.08492i
\(719\) 1.41421 0.0527413 0.0263706 0.999652i \(-0.491605\pi\)
0.0263706 + 0.999652i \(0.491605\pi\)
\(720\) 0 0
\(721\) 36.3848 1.35504
\(722\) 14.2843i 0.531606i
\(723\) 0 0
\(724\) −20.5858 −0.765065
\(725\) −28.2843 + 21.2132i −1.05045 + 0.787839i
\(726\) 0 0
\(727\) 20.3848i 0.756030i 0.925800 + 0.378015i \(0.123393\pi\)
−0.925800 + 0.378015i \(0.876607\pi\)
\(728\) 12.6569i 0.469094i
\(729\) 0 0
\(730\) −1.53553 4.60660i −0.0568327 0.170498i
\(731\) −37.5980 −1.39061
\(732\) 0 0
\(733\) 10.9706i 0.405207i 0.979261 + 0.202603i \(0.0649403\pi\)
−0.979261 + 0.202603i \(0.935060\pi\)
\(734\) −15.2426 −0.562616
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) 5.31371i 0.195733i
\(738\) 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
\(742\) 9.24264i 0.339308i
\(743\) 51.3553i 1.88404i 0.335550 + 0.942022i \(0.391078\pi\)
−0.335550 + 0.942022i \(0.608922\pi\)
\(744\) 0 0
\(745\) −2.48528 7.45584i −0.0910537 0.273161i
\(746\) 1.75736 0.0643415
\(747\) 0 0
\(748\) 23.0000i 0.840963i
\(749\) −38.7990 −1.41768
\(750\) 0 0
\(751\) −35.1127 −1.28128 −0.640640 0.767841i \(-0.721331\pi\)
−0.640640 + 0.767841i \(0.721331\pi\)
\(752\) 11.8995i 0.433930i
\(753\) 0 0
\(754\) 37.0711 1.35005
\(755\) −1.70711 5.12132i −0.0621280 0.186384i
\(756\) 0 0
\(757\) 16.2132i 0.589279i −0.955608 0.294639i \(-0.904800\pi\)
0.955608 0.294639i \(-0.0951995\pi\)
\(758\) 28.7279i 1.04345i
\(759\) 0 0
\(760\) −4.60660 + 1.53553i −0.167099 + 0.0556997i
\(761\) −25.3137 −0.917621 −0.458811 0.888534i \(-0.651724\pi\)
−0.458811 + 0.888534i \(0.651724\pi\)
\(762\) 0 0
\(763\) 11.4853i 0.415795i
\(764\) 8.65685 0.313194
\(765\) 0 0
\(766\) 14.6569 0.529574
\(767\) 68.5269i 2.47436i
\(768\) 0 0
\(769\) 19.5563 0.705220 0.352610 0.935770i \(-0.385294\pi\)
0.352610 + 0.935770i \(0.385294\pi\)
\(770\) −10.9497 32.8492i −0.394602 1.18380i
\(771\) 0 0
\(772\) 9.31371i 0.335208i
\(773\) 14.6569i 0.527170i 0.964636 + 0.263585i \(0.0849050\pi\)
−0.964636 + 0.263585i \(0.915095\pi\)
\(774\) 0 0
\(775\) 14.6274 10.9706i 0.525432 0.394074i
\(776\) −6.72792 −0.241518
\(777\) 0 0
\(778\) 22.9706i 0.823535i
\(779\) 14.3015 0.512405
\(780\) 0 0
\(781\) 60.3848 2.16074
\(782\) 10.7574i 0.384682i
\(783\) 0 0
\(784\) 1.17157 0.0418419
\(785\) 0 0
\(786\) 0 0
\(787\) 38.4853i 1.37185i −0.727671 0.685926i \(-0.759397\pi\)
0.727671 0.685926i \(-0.240603\pi\)
\(788\) 15.1421i 0.539416i
\(789\) 0 0
\(790\) −25.9706 + 8.65685i −0.923991 + 0.307997i