Properties

Label 95.2.e.a.11.1
Level $95$
Weight $2$
Character 95.11
Analytic conductor $0.759$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.758578819202\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 11.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 95.11
Dual form 95.2.e.a.26.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} -4.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} -4.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} +3.00000 q^{11} +4.00000 q^{12} +(-1.00000 - 1.73205i) q^{13} +(-1.00000 - 1.73205i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(-3.50000 - 2.59808i) q^{19} +2.00000 q^{20} +(-4.00000 + 6.92820i) q^{21} +(-0.500000 - 0.866025i) q^{25} +4.00000 q^{27} +(-4.00000 - 6.92820i) q^{28} +(1.50000 + 2.59808i) q^{29} -7.00000 q^{31} +(3.00000 - 5.19615i) q^{33} +(-2.00000 + 3.46410i) q^{35} +(1.00000 - 1.73205i) q^{36} +8.00000 q^{37} -4.00000 q^{39} +(3.00000 - 5.19615i) q^{41} +(2.00000 - 3.46410i) q^{43} +(3.00000 + 5.19615i) q^{44} -1.00000 q^{45} +(-3.00000 - 5.19615i) q^{47} +(4.00000 + 6.92820i) q^{48} +9.00000 q^{49} +(6.00000 + 10.3923i) q^{51} +(2.00000 - 3.46410i) q^{52} +(3.00000 + 5.19615i) q^{53} +(1.50000 - 2.59808i) q^{55} +(-8.00000 + 3.46410i) q^{57} +(7.50000 - 12.9904i) q^{59} +(2.00000 - 3.46410i) q^{60} +(-2.50000 - 4.33013i) q^{61} +(2.00000 + 3.46410i) q^{63} -8.00000 q^{64} -2.00000 q^{65} +(-1.00000 - 1.73205i) q^{67} -12.0000 q^{68} +(1.50000 - 2.59808i) q^{71} +(-4.00000 + 6.92820i) q^{73} -2.00000 q^{75} +(1.00000 - 8.66025i) q^{76} -12.0000 q^{77} +(-2.50000 + 4.33013i) q^{79} +(2.00000 + 3.46410i) q^{80} +(5.50000 - 9.52628i) q^{81} +12.0000 q^{83} -16.0000 q^{84} +(3.00000 + 5.19615i) q^{85} +6.00000 q^{87} +(7.50000 + 12.9904i) q^{89} +(4.00000 + 6.92820i) q^{91} +(-7.00000 + 12.1244i) q^{93} +(-4.00000 + 1.73205i) q^{95} +(-4.00000 + 6.92820i) q^{97} +(-1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} + 2 q^{4} + q^{5} - 8 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} + 2 q^{4} + q^{5} - 8 q^{7} - q^{9} + 6 q^{11} + 8 q^{12} - 2 q^{13} - 2 q^{15} - 4 q^{16} - 6 q^{17} - 7 q^{19} + 4 q^{20} - 8 q^{21} - q^{25} + 8 q^{27} - 8 q^{28} + 3 q^{29} - 14 q^{31} + 6 q^{33} - 4 q^{35} + 2 q^{36} + 16 q^{37} - 8 q^{39} + 6 q^{41} + 4 q^{43} + 6 q^{44} - 2 q^{45} - 6 q^{47} + 8 q^{48} + 18 q^{49} + 12 q^{51} + 4 q^{52} + 6 q^{53} + 3 q^{55} - 16 q^{57} + 15 q^{59} + 4 q^{60} - 5 q^{61} + 4 q^{63} - 16 q^{64} - 4 q^{65} - 2 q^{67} - 24 q^{68} + 3 q^{71} - 8 q^{73} - 4 q^{75} + 2 q^{76} - 24 q^{77} - 5 q^{79} + 4 q^{80} + 11 q^{81} + 24 q^{83} - 32 q^{84} + 6 q^{85} + 12 q^{87} + 15 q^{89} + 8 q^{91} - 14 q^{93} - 8 q^{95} - 8 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(3\) 1.00000 1.73205i 0.577350 1.00000i −0.418432 0.908248i \(-0.637420\pi\)
0.995782 0.0917517i \(-0.0292466\pi\)
\(4\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 4.00000 1.15470
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0 0
\(15\) −1.00000 1.73205i −0.258199 0.447214i
\(16\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(17\) −3.00000 + 5.19615i −0.727607 + 1.26025i 0.230285 + 0.973123i \(0.426034\pi\)
−0.957892 + 0.287129i \(0.907299\pi\)
\(18\) 0 0
\(19\) −3.50000 2.59808i −0.802955 0.596040i
\(20\) 2.00000 0.447214
\(21\) −4.00000 + 6.92820i −0.872872 + 1.51186i
\(22\) 0 0
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 4.00000 0.769800
\(28\) −4.00000 6.92820i −0.755929 1.30931i
\(29\) 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i \(-0.0768152\pi\)
−0.692480 + 0.721437i \(0.743482\pi\)
\(30\) 0 0
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0 0
\(33\) 3.00000 5.19615i 0.522233 0.904534i
\(34\) 0 0
\(35\) −2.00000 + 3.46410i −0.338062 + 0.585540i
\(36\) 1.00000 1.73205i 0.166667 0.288675i
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 0 0
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) 3.00000 5.19615i 0.468521 0.811503i −0.530831 0.847477i \(-0.678120\pi\)
0.999353 + 0.0359748i \(0.0114536\pi\)
\(42\) 0 0
\(43\) 2.00000 3.46410i 0.304997 0.528271i −0.672264 0.740312i \(-0.734678\pi\)
0.977261 + 0.212041i \(0.0680112\pi\)
\(44\) 3.00000 + 5.19615i 0.452267 + 0.783349i
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 4.00000 + 6.92820i 0.577350 + 1.00000i
\(49\) 9.00000 1.28571
\(50\) 0 0
\(51\) 6.00000 + 10.3923i 0.840168 + 1.45521i
\(52\) 2.00000 3.46410i 0.277350 0.480384i
\(53\) 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 0 0
\(55\) 1.50000 2.59808i 0.202260 0.350325i
\(56\) 0 0
\(57\) −8.00000 + 3.46410i −1.05963 + 0.458831i
\(58\) 0 0
\(59\) 7.50000 12.9904i 0.976417 1.69120i 0.301239 0.953549i \(-0.402600\pi\)
0.675178 0.737655i \(-0.264067\pi\)
\(60\) 2.00000 3.46410i 0.258199 0.447214i
\(61\) −2.50000 4.33013i −0.320092 0.554416i 0.660415 0.750901i \(-0.270381\pi\)
−0.980507 + 0.196485i \(0.937047\pi\)
\(62\) 0 0
\(63\) 2.00000 + 3.46410i 0.251976 + 0.436436i
\(64\) −8.00000 −1.00000
\(65\) −2.00000 −0.248069
\(66\) 0 0
\(67\) −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) −12.0000 −1.45521
\(69\) 0 0
\(70\) 0 0
\(71\) 1.50000 2.59808i 0.178017 0.308335i −0.763184 0.646181i \(-0.776365\pi\)
0.941201 + 0.337846i \(0.109698\pi\)
\(72\) 0 0
\(73\) −4.00000 + 6.92820i −0.468165 + 0.810885i −0.999338 0.0363782i \(-0.988418\pi\)
0.531174 + 0.847263i \(0.321751\pi\)
\(74\) 0 0
\(75\) −2.00000 −0.230940
\(76\) 1.00000 8.66025i 0.114708 0.993399i
\(77\) −12.0000 −1.36753
\(78\) 0 0
\(79\) −2.50000 + 4.33013i −0.281272 + 0.487177i −0.971698 0.236225i \(-0.924090\pi\)
0.690426 + 0.723403i \(0.257423\pi\)
\(80\) 2.00000 + 3.46410i 0.223607 + 0.387298i
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) −16.0000 −1.74574
\(85\) 3.00000 + 5.19615i 0.325396 + 0.563602i
\(86\) 0 0
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) 7.50000 + 12.9904i 0.794998 + 1.37698i 0.922840 + 0.385183i \(0.125862\pi\)
−0.127842 + 0.991795i \(0.540805\pi\)
\(90\) 0 0
\(91\) 4.00000 + 6.92820i 0.419314 + 0.726273i
\(92\) 0 0
\(93\) −7.00000 + 12.1244i −0.725866 + 1.25724i
\(94\) 0 0
\(95\) −4.00000 + 1.73205i −0.410391 + 0.177705i
\(96\) 0 0
\(97\) −4.00000 + 6.92820i −0.406138 + 0.703452i −0.994453 0.105180i \(-0.966458\pi\)
0.588315 + 0.808632i \(0.299792\pi\)
\(98\) 0 0
\(99\) −1.50000 2.59808i −0.150756 0.261116i
\(100\) 1.00000 1.73205i 0.100000 0.173205i
\(101\) −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i \(-0.898506\pi\)
0.203317 0.979113i \(-0.434828\pi\)
\(102\) 0 0
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) 0 0
\(105\) 4.00000 + 6.92820i 0.390360 + 0.676123i
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 4.00000 + 6.92820i 0.384900 + 0.666667i
\(109\) −5.50000 + 9.52628i −0.526804 + 0.912452i 0.472708 + 0.881219i \(0.343277\pi\)
−0.999512 + 0.0312328i \(0.990057\pi\)
\(110\) 0 0
\(111\) 8.00000 13.8564i 0.759326 1.31519i
\(112\) 8.00000 13.8564i 0.755929 1.30931i
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −3.00000 + 5.19615i −0.278543 + 0.482451i
\(117\) −1.00000 + 1.73205i −0.0924500 + 0.160128i
\(118\) 0 0
\(119\) 12.0000 20.7846i 1.10004 1.90532i
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) −6.00000 10.3923i −0.541002 0.937043i
\(124\) −7.00000 12.1244i −0.628619 1.08880i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −1.00000 1.73205i −0.0887357 0.153695i 0.818241 0.574875i \(-0.194949\pi\)
−0.906977 + 0.421180i \(0.861616\pi\)
\(128\) 0 0
\(129\) −4.00000 6.92820i −0.352180 0.609994i
\(130\) 0 0
\(131\) −6.00000 + 10.3923i −0.524222 + 0.907980i 0.475380 + 0.879781i \(0.342311\pi\)
−0.999602 + 0.0281993i \(0.991023\pi\)
\(132\) 12.0000 1.04447
\(133\) 14.0000 + 10.3923i 1.21395 + 0.901127i
\(134\) 0 0
\(135\) 2.00000 3.46410i 0.172133 0.298142i
\(136\) 0 0
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 0 0
\(139\) 8.00000 + 13.8564i 0.678551 + 1.17529i 0.975417 + 0.220366i \(0.0707252\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(140\) −8.00000 −0.676123
\(141\) −12.0000 −1.01058
\(142\) 0 0
\(143\) −3.00000 5.19615i −0.250873 0.434524i
\(144\) 4.00000 0.333333
\(145\) 3.00000 0.249136
\(146\) 0 0
\(147\) 9.00000 15.5885i 0.742307 1.28571i
\(148\) 8.00000 + 13.8564i 0.657596 + 1.13899i
\(149\) −1.50000 + 2.59808i −0.122885 + 0.212843i −0.920904 0.389789i \(-0.872548\pi\)
0.798019 + 0.602632i \(0.205881\pi\)
\(150\) 0 0
\(151\) 17.0000 1.38344 0.691720 0.722166i \(-0.256853\pi\)
0.691720 + 0.722166i \(0.256853\pi\)
\(152\) 0 0
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) −3.50000 + 6.06218i −0.281127 + 0.486926i
\(156\) −4.00000 6.92820i −0.320256 0.554700i
\(157\) −1.00000 + 1.73205i −0.0798087 + 0.138233i −0.903167 0.429289i \(-0.858764\pi\)
0.823359 + 0.567521i \(0.192098\pi\)
\(158\) 0 0
\(159\) 12.0000 0.951662
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −10.0000 −0.783260 −0.391630 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(164\) 12.0000 0.937043
\(165\) −3.00000 5.19615i −0.233550 0.404520i
\(166\) 0 0
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) −0.500000 + 4.33013i −0.0382360 + 0.331133i
\(172\) 8.00000 0.609994
\(173\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 0 0
\(175\) 2.00000 + 3.46410i 0.151186 + 0.261861i
\(176\) −6.00000 + 10.3923i −0.452267 + 0.783349i
\(177\) −15.0000 25.9808i −1.12747 1.95283i
\(178\) 0 0
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) −1.00000 1.73205i −0.0745356 0.129099i
\(181\) −1.00000 1.73205i −0.0743294 0.128742i 0.826465 0.562988i \(-0.190348\pi\)
−0.900794 + 0.434246i \(0.857015\pi\)
\(182\) 0 0
\(183\) −10.0000 −0.739221
\(184\) 0 0
\(185\) 4.00000 6.92820i 0.294086 0.509372i
\(186\) 0 0
\(187\) −9.00000 + 15.5885i −0.658145 + 1.13994i
\(188\) 6.00000 10.3923i 0.437595 0.757937i
\(189\) −16.0000 −1.16383
\(190\) 0 0
\(191\) −15.0000 −1.08536 −0.542681 0.839939i \(-0.682591\pi\)
−0.542681 + 0.839939i \(0.682591\pi\)
\(192\) −8.00000 + 13.8564i −0.577350 + 1.00000i
\(193\) 8.00000 13.8564i 0.575853 0.997406i −0.420096 0.907480i \(-0.638004\pi\)
0.995948 0.0899262i \(-0.0286631\pi\)
\(194\) 0 0
\(195\) −2.00000 + 3.46410i −0.143223 + 0.248069i
\(196\) 9.00000 + 15.5885i 0.642857 + 1.11346i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 9.50000 + 16.4545i 0.673437 + 1.16643i 0.976923 + 0.213591i \(0.0685161\pi\)
−0.303486 + 0.952836i \(0.598151\pi\)
\(200\) 0 0
\(201\) −4.00000 −0.282138
\(202\) 0 0
\(203\) −6.00000 10.3923i −0.421117 0.729397i
\(204\) −12.0000 + 20.7846i −0.840168 + 1.45521i
\(205\) −3.00000 5.19615i −0.209529 0.362915i
\(206\) 0 0
\(207\) 0 0
\(208\) 8.00000 0.554700
\(209\) −10.5000 7.79423i −0.726300 0.539138i
\(210\) 0 0
\(211\) 3.50000 6.06218i 0.240950 0.417338i −0.720035 0.693938i \(-0.755874\pi\)
0.960985 + 0.276600i \(0.0892077\pi\)
\(212\) −6.00000 + 10.3923i −0.412082 + 0.713746i
\(213\) −3.00000 5.19615i −0.205557 0.356034i
\(214\) 0 0
\(215\) −2.00000 3.46410i −0.136399 0.236250i
\(216\) 0 0
\(217\) 28.0000 1.90076
\(218\) 0 0
\(219\) 8.00000 + 13.8564i 0.540590 + 0.936329i
\(220\) 6.00000 0.404520
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) 2.00000 3.46410i 0.133930 0.231973i −0.791258 0.611482i \(-0.790574\pi\)
0.925188 + 0.379509i \(0.123907\pi\)
\(224\) 0 0
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) 0 0
\(227\) −24.0000 −1.59294 −0.796468 0.604681i \(-0.793301\pi\)
−0.796468 + 0.604681i \(0.793301\pi\)
\(228\) −14.0000 10.3923i −0.927173 0.688247i
\(229\) −7.00000 −0.462573 −0.231287 0.972886i \(-0.574293\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) 0 0
\(231\) −12.0000 + 20.7846i −0.789542 + 1.36753i
\(232\) 0 0
\(233\) −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) 0 0
\(235\) −6.00000 −0.391397
\(236\) 30.0000 1.95283
\(237\) 5.00000 + 8.66025i 0.324785 + 0.562544i
\(238\) 0 0
\(239\) −3.00000 −0.194054 −0.0970269 0.995282i \(-0.530933\pi\)
−0.0970269 + 0.995282i \(0.530933\pi\)
\(240\) 8.00000 0.516398
\(241\) −2.50000 4.33013i −0.161039 0.278928i 0.774202 0.632938i \(-0.218151\pi\)
−0.935242 + 0.354010i \(0.884818\pi\)
\(242\) 0 0
\(243\) −5.00000 8.66025i −0.320750 0.555556i
\(244\) 5.00000 8.66025i 0.320092 0.554416i
\(245\) 4.50000 7.79423i 0.287494 0.497955i
\(246\) 0 0
\(247\) −1.00000 + 8.66025i −0.0636285 + 0.551039i
\(248\) 0 0
\(249\) 12.0000 20.7846i 0.760469 1.31717i
\(250\) 0 0
\(251\) 7.50000 + 12.9904i 0.473396 + 0.819946i 0.999536 0.0304521i \(-0.00969471\pi\)
−0.526140 + 0.850398i \(0.676361\pi\)
\(252\) −4.00000 + 6.92820i −0.251976 + 0.436436i
\(253\) 0 0
\(254\) 0 0
\(255\) 12.0000 0.751469
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 9.00000 + 15.5885i 0.561405 + 0.972381i 0.997374 + 0.0724199i \(0.0230722\pi\)
−0.435970 + 0.899961i \(0.643595\pi\)
\(258\) 0 0
\(259\) −32.0000 −1.98838
\(260\) −2.00000 3.46410i −0.124035 0.214834i
\(261\) 1.50000 2.59808i 0.0928477 0.160817i
\(262\) 0 0
\(263\) 9.00000 15.5885i 0.554964 0.961225i −0.442943 0.896550i \(-0.646065\pi\)
0.997906 0.0646755i \(-0.0206012\pi\)
\(264\) 0 0
\(265\) 6.00000 0.368577
\(266\) 0 0
\(267\) 30.0000 1.83597
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) 10.5000 18.1865i 0.640196 1.10885i −0.345192 0.938532i \(-0.612186\pi\)
0.985389 0.170321i \(-0.0544803\pi\)
\(270\) 0 0
\(271\) −5.50000 + 9.52628i −0.334101 + 0.578680i −0.983312 0.181928i \(-0.941766\pi\)
0.649211 + 0.760609i \(0.275099\pi\)
\(272\) −12.0000 20.7846i −0.727607 1.26025i
\(273\) 16.0000 0.968364
\(274\) 0 0
\(275\) −1.50000 2.59808i −0.0904534 0.156670i
\(276\) 0 0
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 0 0
\(279\) 3.50000 + 6.06218i 0.209540 + 0.362933i
\(280\) 0 0
\(281\) −3.00000 5.19615i −0.178965 0.309976i 0.762561 0.646916i \(-0.223942\pi\)
−0.941526 + 0.336939i \(0.890608\pi\)
\(282\) 0 0
\(283\) −7.00000 + 12.1244i −0.416107 + 0.720718i −0.995544 0.0942988i \(-0.969939\pi\)
0.579437 + 0.815017i \(0.303272\pi\)
\(284\) 6.00000 0.356034
\(285\) −1.00000 + 8.66025i −0.0592349 + 0.512989i
\(286\) 0 0
\(287\) −12.0000 + 20.7846i −0.708338 + 1.22688i
\(288\) 0 0
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) 0 0
\(291\) 8.00000 + 13.8564i 0.468968 + 0.812277i
\(292\) −16.0000 −0.936329
\(293\) 24.0000 1.40209 0.701047 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) 0 0
\(295\) −7.50000 12.9904i −0.436667 0.756329i
\(296\) 0 0
\(297\) 12.0000 0.696311
\(298\) 0 0
\(299\) 0 0
\(300\) −2.00000 3.46410i −0.115470 0.200000i
\(301\) −8.00000 + 13.8564i −0.461112 + 0.798670i
\(302\) 0 0
\(303\) −30.0000 −1.72345
\(304\) 16.0000 6.92820i 0.917663 0.397360i
\(305\) −5.00000 −0.286299
\(306\) 0 0
\(307\) 17.0000 29.4449i 0.970241 1.68051i 0.275421 0.961324i \(-0.411183\pi\)
0.694820 0.719183i \(-0.255484\pi\)
\(308\) −12.0000 20.7846i −0.683763 1.18431i
\(309\) −16.0000 + 27.7128i −0.910208 + 1.57653i
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 5.00000 + 8.66025i 0.282617 + 0.489506i 0.972028 0.234863i \(-0.0754642\pi\)
−0.689412 + 0.724370i \(0.742131\pi\)
\(314\) 0 0
\(315\) 4.00000 0.225374
\(316\) −10.0000 −0.562544
\(317\) −12.0000 20.7846i −0.673987 1.16738i −0.976764 0.214318i \(-0.931247\pi\)
0.302777 0.953062i \(-0.402086\pi\)
\(318\) 0 0
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) −4.00000 + 6.92820i −0.223607 + 0.387298i
\(321\) 0 0
\(322\) 0 0
\(323\) 24.0000 10.3923i 1.33540 0.578243i
\(324\) 22.0000 1.22222
\(325\) −1.00000 + 1.73205i −0.0554700 + 0.0960769i
\(326\) 0 0
\(327\) 11.0000 + 19.0526i 0.608301 + 1.05361i
\(328\) 0 0
\(329\) 12.0000 + 20.7846i 0.661581 + 1.14589i
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 12.0000 + 20.7846i 0.658586 + 1.14070i
\(333\) −4.00000 6.92820i −0.219199 0.379663i
\(334\) 0 0
\(335\) −2.00000 −0.109272
\(336\) −16.0000 27.7128i −0.872872 1.51186i
\(337\) 8.00000 13.8564i 0.435788 0.754807i −0.561572 0.827428i \(-0.689803\pi\)
0.997360 + 0.0726214i \(0.0231365\pi\)
\(338\) 0 0
\(339\) 6.00000 10.3923i 0.325875 0.564433i
\(340\) −6.00000 + 10.3923i −0.325396 + 0.563602i
\(341\) −21.0000 −1.13721
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 6.00000 + 10.3923i 0.321634 + 0.557086i
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) −4.00000 6.92820i −0.213504 0.369800i
\(352\) 0 0
\(353\) 12.0000 0.638696 0.319348 0.947638i \(-0.396536\pi\)
0.319348 + 0.947638i \(0.396536\pi\)
\(354\) 0 0
\(355\) −1.50000 2.59808i −0.0796117 0.137892i
\(356\) −15.0000 + 25.9808i −0.794998 + 1.37698i
\(357\) −24.0000 41.5692i −1.27021 2.20008i
\(358\) 0 0
\(359\) −12.0000 + 20.7846i −0.633336 + 1.09697i 0.353529 + 0.935423i \(0.384981\pi\)
−0.986865 + 0.161546i \(0.948352\pi\)
\(360\) 0 0
\(361\) 5.50000 + 18.1865i 0.289474 + 0.957186i
\(362\) 0 0
\(363\) −2.00000 + 3.46410i −0.104973 + 0.181818i
\(364\) −8.00000 + 13.8564i −0.419314 + 0.726273i
\(365\) 4.00000 + 6.92820i 0.209370 + 0.362639i
\(366\) 0 0
\(367\) 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i \(-0.133375\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) 0 0
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) −12.0000 20.7846i −0.623009 1.07908i
\(372\) −28.0000 −1.45173
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 0 0
\(375\) −1.00000 + 1.73205i −0.0516398 + 0.0894427i
\(376\) 0 0
\(377\) 3.00000 5.19615i 0.154508 0.267615i
\(378\) 0 0
\(379\) −37.0000 −1.90056 −0.950281 0.311393i \(-0.899204\pi\)
−0.950281 + 0.311393i \(0.899204\pi\)
\(380\) −7.00000 5.19615i −0.359092 0.266557i
\(381\) −4.00000 −0.204926
\(382\) 0 0
\(383\) −15.0000 + 25.9808i −0.766464 + 1.32755i 0.173005 + 0.984921i \(0.444652\pi\)
−0.939469 + 0.342634i \(0.888681\pi\)
\(384\) 0 0
\(385\) −6.00000 + 10.3923i −0.305788 + 0.529641i
\(386\) 0 0
\(387\) −4.00000 −0.203331
\(388\) −16.0000 −0.812277
\(389\) −7.50000 12.9904i −0.380265 0.658638i 0.610835 0.791758i \(-0.290834\pi\)
−0.991100 + 0.133120i \(0.957501\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 12.0000 + 20.7846i 0.605320 + 1.04844i
\(394\) 0 0
\(395\) 2.50000 + 4.33013i 0.125789 + 0.217872i
\(396\) 3.00000 5.19615i 0.150756 0.261116i
\(397\) −4.00000 + 6.92820i −0.200754 + 0.347717i −0.948772 0.315963i \(-0.897673\pi\)
0.748017 + 0.663679i \(0.231006\pi\)
\(398\) 0 0
\(399\) 32.0000 13.8564i 1.60200 0.693688i
\(400\) 4.00000 0.200000
\(401\) 16.5000 28.5788i 0.823971 1.42716i −0.0787327 0.996896i \(-0.525087\pi\)
0.902703 0.430263i \(-0.141579\pi\)
\(402\) 0 0
\(403\) 7.00000 + 12.1244i 0.348695 + 0.603957i
\(404\) 15.0000 25.9808i 0.746278 1.29259i
\(405\) −5.50000 9.52628i −0.273297 0.473365i
\(406\) 0 0
\(407\) 24.0000 1.18964
\(408\) 0 0
\(409\) −11.5000 19.9186i −0.568638 0.984911i −0.996701 0.0811615i \(-0.974137\pi\)
0.428063 0.903749i \(-0.359196\pi\)
\(410\) 0 0
\(411\) 24.0000 1.18383
\(412\) −16.0000 27.7128i −0.788263 1.36531i
\(413\) −30.0000 + 51.9615i −1.47620 + 2.55686i
\(414\) 0 0
\(415\) 6.00000 10.3923i 0.294528 0.510138i
\(416\) 0 0
\(417\) 32.0000 1.56705
\(418\) 0 0
\(419\) −3.00000 −0.146560 −0.0732798 0.997311i \(-0.523347\pi\)
−0.0732798 + 0.997311i \(0.523347\pi\)
\(420\) −8.00000 + 13.8564i −0.390360 + 0.676123i
\(421\) 9.50000 16.4545i 0.463002 0.801942i −0.536107 0.844150i \(-0.680106\pi\)
0.999109 + 0.0422075i \(0.0134391\pi\)
\(422\) 0 0
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 0 0
\(425\) 6.00000 0.291043
\(426\) 0 0
\(427\) 10.0000 + 17.3205i 0.483934 + 0.838198i
\(428\) 0 0
\(429\) −12.0000 −0.579365
\(430\) 0 0
\(431\) 7.50000 + 12.9904i 0.361262 + 0.625725i 0.988169 0.153370i \(-0.0490126\pi\)
−0.626907 + 0.779094i \(0.715679\pi\)
\(432\) −8.00000 + 13.8564i −0.384900 + 0.666667i
\(433\) −4.00000 6.92820i −0.192228 0.332948i 0.753760 0.657149i \(-0.228238\pi\)
−0.945988 + 0.324201i \(0.894905\pi\)
\(434\) 0 0
\(435\) 3.00000 5.19615i 0.143839 0.249136i
\(436\) −22.0000 −1.05361
\(437\) 0 0
\(438\) 0 0
\(439\) 6.50000 11.2583i 0.310228 0.537331i −0.668184 0.743996i \(-0.732928\pi\)
0.978412 + 0.206666i \(0.0662612\pi\)
\(440\) 0 0
\(441\) −4.50000 7.79423i −0.214286 0.371154i
\(442\) 0 0
\(443\) 6.00000 + 10.3923i 0.285069 + 0.493753i 0.972626 0.232377i \(-0.0746503\pi\)
−0.687557 + 0.726130i \(0.741317\pi\)
\(444\) 32.0000 1.51865
\(445\) 15.0000 0.711068
\(446\) 0 0
\(447\) 3.00000 + 5.19615i 0.141895 + 0.245770i
\(448\) 32.0000 1.51186
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 0 0
\(451\) 9.00000 15.5885i 0.423793 0.734032i
\(452\) 6.00000 + 10.3923i 0.282216 + 0.488813i
\(453\) 17.0000 29.4449i 0.798730 1.38344i
\(454\) 0 0
\(455\) 8.00000 0.375046
\(456\) 0 0
\(457\) −22.0000 −1.02912 −0.514558 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 0 0
\(459\) −12.0000 + 20.7846i −0.560112 + 0.970143i
\(460\) 0 0
\(461\) 4.50000 7.79423i 0.209586 0.363013i −0.741998 0.670402i \(-0.766122\pi\)
0.951584 + 0.307388i \(0.0994551\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) −12.0000 −0.557086
\(465\) 7.00000 + 12.1244i 0.324617 + 0.562254i
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) −4.00000 −0.184900
\(469\) 4.00000 + 6.92820i 0.184703 + 0.319915i
\(470\) 0 0
\(471\) 2.00000 + 3.46410i 0.0921551 + 0.159617i
\(472\) 0 0
\(473\) 6.00000 10.3923i 0.275880 0.477839i
\(474\) 0 0
\(475\) −0.500000 + 4.33013i −0.0229416 + 0.198680i
\(476\) 48.0000 2.20008
\(477\) 3.00000 5.19615i 0.137361 0.237915i
\(478\) 0 0
\(479\) −7.50000 12.9904i −0.342684 0.593546i 0.642246 0.766498i \(-0.278003\pi\)
−0.984930 + 0.172953i \(0.944669\pi\)
\(480\) 0 0
\(481\) −8.00000 13.8564i −0.364769 0.631798i
\(482\) 0 0
\(483\) 0 0
\(484\) −2.00000 3.46410i −0.0909091 0.157459i
\(485\) 4.00000 + 6.92820i 0.181631 + 0.314594i
\(486\) 0 0
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) 0 0
\(489\) −10.0000 + 17.3205i −0.452216 + 0.783260i
\(490\) 0 0
\(491\) 7.50000 12.9904i 0.338470 0.586248i −0.645675 0.763612i \(-0.723424\pi\)
0.984145 + 0.177365i \(0.0567572\pi\)
\(492\) 12.0000 20.7846i 0.541002 0.937043i
\(493\) −18.0000 −0.810679
\(494\) 0 0
\(495\) −3.00000 −0.134840
\(496\) 14.0000 24.2487i 0.628619 1.08880i
\(497\) −6.00000 + 10.3923i −0.269137 + 0.466159i
\(498\) 0 0
\(499\) −10.0000 + 17.3205i −0.447661 + 0.775372i −0.998233 0.0594153i \(-0.981076\pi\)
0.550572 + 0.834788i \(0.314410\pi\)
\(500\) −1.00000 1.73205i −0.0447214 0.0774597i
\(501\) 0 0
\(502\) 0 0
\(503\) 21.0000 + 36.3731i 0.936344 + 1.62179i 0.772220 + 0.635355i \(0.219146\pi\)
0.164124 + 0.986440i \(0.447520\pi\)
\(504\) 0 0
\(505\) −15.0000 −0.667491
\(506\) 0 0
\(507\) −9.00000 15.5885i −0.399704 0.692308i
\(508\) 2.00000 3.46410i 0.0887357 0.153695i
\(509\) 9.00000 + 15.5885i 0.398918 + 0.690946i 0.993593 0.113020i \(-0.0360525\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(510\) 0 0
\(511\) 16.0000 27.7128i 0.707798 1.22594i
\(512\) 0 0
\(513\) −14.0000 10.3923i −0.618115 0.458831i
\(514\) 0 0
\(515\) −8.00000 + 13.8564i −0.352522 + 0.610586i
\(516\) 8.00000 13.8564i 0.352180 0.609994i
\(517\) −9.00000 15.5885i −0.395820 0.685580i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −45.0000 −1.97149 −0.985743 0.168259i \(-0.946186\pi\)
−0.985743 + 0.168259i \(0.946186\pi\)
\(522\) 0 0
\(523\) −13.0000 22.5167i −0.568450 0.984585i −0.996719 0.0809336i \(-0.974210\pi\)
0.428269 0.903651i \(-0.359124\pi\)
\(524\) −24.0000 −1.04844
\(525\) 8.00000 0.349149
\(526\) 0 0
\(527\) 21.0000 36.3731i 0.914774 1.58444i
\(528\) 12.0000 + 20.7846i 0.522233 + 0.904534i
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) 0 0
\(531\) −15.0000 −0.650945
\(532\) −4.00000 + 34.6410i −0.173422 + 1.50188i
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −9.00000 + 15.5885i −0.388379 + 0.672692i
\(538\) 0 0
\(539\) 27.0000 1.16297
\(540\) 8.00000 0.344265
\(541\) 18.5000 + 32.0429i 0.795377 + 1.37763i 0.922599 + 0.385759i \(0.126061\pi\)
−0.127222 + 0.991874i \(0.540606\pi\)
\(542\) 0 0
\(543\) −4.00000 −0.171656
\(544\) 0 0
\(545\) 5.50000 + 9.52628i 0.235594 + 0.408061i
\(546\) 0 0
\(547\) 2.00000 + 3.46410i 0.0855138 + 0.148114i 0.905610 0.424111i \(-0.139413\pi\)
−0.820096 + 0.572226i \(0.806080\pi\)
\(548\) −12.0000 + 20.7846i −0.512615 + 0.887875i
\(549\) −2.50000 + 4.33013i −0.106697 + 0.184805i
\(550\) 0 0
\(551\) 1.50000 12.9904i 0.0639021 0.553409i
\(552\) 0 0
\(553\) 10.0000 17.3205i 0.425243 0.736543i
\(554\) 0 0
\(555\) −8.00000 13.8564i −0.339581 0.588172i
\(556\) −16.0000 + 27.7128i −0.678551 + 1.17529i
\(557\) −6.00000 10.3923i −0.254228 0.440336i 0.710457 0.703740i \(-0.248488\pi\)
−0.964686 + 0.263404i \(0.915155\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) −8.00000 13.8564i −0.338062 0.585540i
\(561\) 18.0000 + 31.1769i 0.759961 + 1.31629i
\(562\) 0 0
\(563\) 6.00000 0.252870 0.126435 0.991975i \(-0.459647\pi\)
0.126435 + 0.991975i \(0.459647\pi\)
\(564\) −12.0000 20.7846i −0.505291 0.875190i
\(565\) 3.00000 5.19615i 0.126211 0.218604i
\(566\) 0 0
\(567\) −22.0000 + 38.1051i −0.923913 + 1.60026i
\(568\) 0 0
\(569\) 39.0000 1.63497 0.817483 0.575953i \(-0.195369\pi\)
0.817483 + 0.575953i \(0.195369\pi\)
\(570\) 0 0
\(571\) −7.00000 −0.292941 −0.146470 0.989215i \(-0.546791\pi\)
−0.146470 + 0.989215i \(0.546791\pi\)
\(572\) 6.00000 10.3923i 0.250873 0.434524i
\(573\) −15.0000 + 25.9808i −0.626634 + 1.08536i
\(574\) 0 0
\(575\) 0 0
\(576\) 4.00000 + 6.92820i 0.166667 + 0.288675i
\(577\) −16.0000 −0.666089 −0.333044 0.942911i \(-0.608076\pi\)
−0.333044 + 0.942911i \(0.608076\pi\)
\(578\) 0 0
\(579\) −16.0000 27.7128i −0.664937 1.15171i
\(580\) 3.00000 + 5.19615i 0.124568 + 0.215758i
\(581\) −48.0000 −1.99138
\(582\) 0 0
\(583\) 9.00000 + 15.5885i 0.372742 + 0.645608i
\(584\) 0 0
\(585\) 1.00000 + 1.73205i 0.0413449 + 0.0716115i
\(586\) 0 0
\(587\) 18.0000 31.1769i 0.742940 1.28681i −0.208212 0.978084i \(-0.566764\pi\)
0.951151 0.308725i \(-0.0999023\pi\)
\(588\) 36.0000 1.48461
\(589\) 24.5000 + 18.1865i 1.00950 + 0.749363i
\(590\) 0 0
\(591\) −18.0000 + 31.1769i −0.740421 + 1.28245i
\(592\) −16.0000 + 27.7128i −0.657596 + 1.13899i
\(593\) −6.00000 10.3923i −0.246390 0.426761i 0.716131 0.697966i \(-0.245911\pi\)
−0.962522 + 0.271205i \(0.912578\pi\)
\(594\) 0 0
\(595\) −12.0000 20.7846i −0.491952 0.852086i
\(596\) −6.00000 −0.245770
\(597\) 38.0000 1.55524
\(598\) 0 0
\(599\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) 0 0
\(601\) −31.0000 −1.26452 −0.632258 0.774758i \(-0.717872\pi\)
−0.632258 + 0.774758i \(0.717872\pi\)
\(602\) 0 0
\(603\) −1.00000 + 1.73205i −0.0407231 + 0.0705346i
\(604\) 17.0000 + 29.4449i 0.691720 + 1.19809i
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) 0 0
\(607\) 2.00000 0.0811775 0.0405887 0.999176i \(-0.487077\pi\)
0.0405887 + 0.999176i \(0.487077\pi\)
\(608\) 0 0
\(609\) −24.0000 −0.972529
\(610\) 0 0
\(611\) −6.00000 + 10.3923i −0.242734 + 0.420428i
\(612\) 6.00000 + 10.3923i 0.242536 + 0.420084i
\(613\) −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i \(-0.846193\pi\)
0.845124 + 0.534570i \(0.179527\pi\)
\(614\) 0 0
\(615\) −12.0000 −0.483887
\(616\) 0 0
\(617\) −18.0000 31.1769i −0.724653 1.25514i −0.959117 0.283011i \(-0.908667\pi\)
0.234464 0.972125i \(-0.424666\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) −14.0000 −0.562254
\(621\) 0 0
\(622\) 0 0
\(623\) −30.0000 51.9615i −1.20192 2.08179i
\(624\) 8.00000 13.8564i 0.320256 0.554700i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −24.0000 + 10.3923i −0.958468 + 0.415029i
\(628\) −4.00000 −0.159617
\(629\) −24.0000 + 41.5692i −0.956943 + 1.65747i
\(630\) 0 0
\(631\) 9.50000 + 16.4545i 0.378189 + 0.655043i 0.990799 0.135343i \(-0.0432136\pi\)
−0.612610 + 0.790386i \(0.709880\pi\)
\(632\) 0 0
\(633\) −7.00000 12.1244i −0.278225 0.481900i
\(634\) 0 0
\(635\) −2.00000 −0.0793676
\(636\) 12.0000 + 20.7846i 0.475831 + 0.824163i
\(637\) −9.00000 15.5885i −0.356593 0.617637i
\(638\) 0 0
\(639\) −3.00000 −0.118678
\(640\) 0 0
\(641\) −4.50000 + 7.79423i −0.177739 + 0.307854i −0.941106 0.338112i \(-0.890212\pi\)
0.763367 + 0.645966i \(0.223545\pi\)
\(642\) 0 0
\(643\) 17.0000 29.4449i 0.670415 1.16119i −0.307372 0.951589i \(-0.599450\pi\)
0.977787 0.209603i \(-0.0672170\pi\)
\(644\) 0 0
\(645\) −8.00000 −0.315000
\(646\) 0 0
\(647\) 18.0000 0.707653 0.353827 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(648\) 0 0
\(649\) 22.5000 38.9711i 0.883202 1.52975i
\(650\) 0 0
\(651\) 28.0000 48.4974i 1.09741 1.90076i
\(652\) −10.0000 17.3205i −0.391630 0.678323i
\(653\) 24.0000 0.939193 0.469596 0.882881i \(-0.344399\pi\)
0.469596 + 0.882881i \(0.344399\pi\)
\(654\) 0 0
\(655\) 6.00000 + 10.3923i 0.234439 + 0.406061i
\(656\) 12.0000 + 20.7846i 0.468521 + 0.811503i
\(657\) 8.00000 0.312110
\(658\) 0 0
\(659\) 6.00000 + 10.3923i 0.233727 + 0.404827i 0.958902 0.283738i \(-0.0915745\pi\)
−0.725175 + 0.688565i \(0.758241\pi\)
\(660\) 6.00000 10.3923i 0.233550 0.404520i
\(661\) −2.50000 4.33013i −0.0972387 0.168422i 0.813302 0.581842i \(-0.197668\pi\)
−0.910541 + 0.413419i \(0.864334\pi\)
\(662\) 0 0
\(663\) 12.0000 20.7846i 0.466041 0.807207i
\(664\) 0 0
\(665\) 16.0000 6.92820i 0.620453 0.268664i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −4.00000 6.92820i −0.154649 0.267860i
\(670\) 0 0
\(671\) −7.50000 12.9904i −0.289534 0.501488i
\(672\) 0 0
\(673\) −4.00000 −0.154189 −0.0770943 0.997024i \(-0.524564\pi\)
−0.0770943 + 0.997024i \(0.524564\pi\)
\(674\) 0 0
\(675\) −2.00000 3.46410i −0.0769800 0.133333i
\(676\) 18.0000 0.692308
\(677\) 48.0000 1.84479 0.922395 0.386248i \(-0.126229\pi\)
0.922395 + 0.386248i \(0.126229\pi\)
\(678\) 0 0
\(679\) 16.0000 27.7128i 0.614024 1.06352i
\(680\) 0 0
\(681\) −24.0000 + 41.5692i −0.919682 + 1.59294i
\(682\) 0 0
\(683\) −18.0000 −0.688751 −0.344375 0.938832i \(-0.611909\pi\)
−0.344375 + 0.938832i \(0.611909\pi\)
\(684\) −8.00000 + 3.46410i −0.305888 + 0.132453i
\(685\) 12.0000 0.458496
\(686\) 0 0
\(687\) −7.00000 + 12.1244i −0.267067 + 0.462573i
\(688\) 8.00000 + 13.8564i 0.304997 + 0.528271i
\(689\) 6.00000 10.3923i 0.228582 0.395915i
\(690\) 0 0
\(691\) −37.0000 −1.40755 −0.703773 0.710425i \(-0.748503\pi\)
−0.703773 + 0.710425i \(0.748503\pi\)
\(692\) 0 0
\(693\) 6.00000 + 10.3923i 0.227921 + 0.394771i
\(694\) 0 0
\(695\) 16.0000 0.606915
\(696\) 0 0
\(697\) 18.0000 + 31.1769i 0.681799 + 1.18091i
\(698\) 0 0
\(699\) 6.00000 + 10.3923i 0.226941 + 0.393073i
\(700\) −4.00000 + 6.92820i −0.151186 + 0.261861i
\(701\) −3.00000 + 5.19615i −0.113308 + 0.196256i −0.917102 0.398652i \(-0.869478\pi\)
0.803794 + 0.594908i \(0.202811\pi\)
\(702\) 0 0
\(703\) −28.0000 20.7846i −1.05604 0.783906i
\(704\) −24.0000 −0.904534
\(705\) −6.00000 + 10.3923i −0.225973 + 0.391397i
\(706\) 0 0
\(707\) 30.0000 + 51.9615i 1.12827 + 1.95421i
\(708\) 30.0000 51.9615i 1.12747 1.95283i
\(709\) 15.5000 + 26.8468i 0.582115 + 1.00825i 0.995228 + 0.0975728i \(0.0311079\pi\)
−0.413114 + 0.910679i \(0.635559\pi\)
\(710\) 0 0
\(711\) 5.00000 0.187515
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −6.00000 −0.224387
\(716\) −9.00000 15.5885i −0.336346 0.582568i
\(717\) −3.00000 + 5.19615i −0.112037 + 0.194054i
\(718\) 0 0
\(719\) −7.50000 + 12.9904i −0.279703 + 0.484459i −0.971311 0.237814i \(-0.923569\pi\)
0.691608 + 0.722273i \(0.256903\pi\)
\(720\) 2.00000 3.46410i 0.0745356 0.129099i
\(721\) 64.0000 2.38348
\(722\) 0 0
\(723\) −10.0000 −0.371904
\(724\) 2.00000 3.46410i 0.0743294 0.128742i
\(725\) 1.50000 2.59808i 0.0557086 0.0964901i
\(726\) 0 0
\(727\) −7.00000 + 12.1244i −0.259616 + 0.449667i −0.966139 0.258022i \(-0.916929\pi\)
0.706523 + 0.707690i \(0.250263\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 12.0000 + 20.7846i 0.443836 + 0.768747i
\(732\) −10.0000 17.3205i −0.369611 0.640184i
\(733\) 32.0000 1.18195 0.590973 0.806691i \(-0.298744\pi\)
0.590973 + 0.806691i \(0.298744\pi\)
\(734\) 0 0
\(735\) −9.00000 15.5885i −0.331970 0.574989i
\(736\) 0 0
\(737\) −3.00000 5.19615i −0.110506 0.191403i
\(738\) 0 0
\(739\) −17.5000 + 30.3109i −0.643748 + 1.11500i 0.340841 + 0.940121i \(0.389288\pi\)
−0.984589 + 0.174883i \(0.944045\pi\)
\(740\) 16.0000 0.588172
\(741\) 14.0000 + 10.3923i 0.514303 + 0.381771i
\(742\) 0 0
\(743\) 12.0000 20.7846i 0.440237 0.762513i −0.557470 0.830197i \(-0.688228\pi\)
0.997707 + 0.0676840i \(0.0215610\pi\)
\(744\) 0 0
\(745\) 1.50000 + 2.59808i 0.0549557 + 0.0951861i
\(746\) 0 0
\(747\) −6.00000 10.3923i −0.219529 0.380235i
\(748\) −36.0000 −1.31629
\(749\) 0 0
\(750\) 0 0
\(751\) 3.50000 + 6.06218i 0.127717 + 0.221212i 0.922792 0.385299i \(-0.125902\pi\)
−0.795075 + 0.606511i \(0.792568\pi\)
\(752\) 24.0000 0.875190
\(753\) 30.0000 1.09326
\(754\) 0 0
\(755\) 8.50000 14.7224i 0.309347 0.535804i
\(756\) −16.0000 27.7128i −0.581914 1.00791i
\(757\) 5.00000 8.66025i 0.181728 0.314762i −0.760741 0.649056i \(-0.775164\pi\)
0.942469 + 0.334293i \(0.108498\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 0 0
\(763\) 22.0000 38.1051i 0.796453 1.37950i
\(764\) −15.0000 25.9808i −0.542681 0.939951i
\(765\) 3.00000 5.19615i 0.108465 0.187867i
\(766\) 0 0
\(767\) −30.0000 −1.08324
\(768\) −32.0000 −1.15470
\(769\) −14.5000 25.1147i −0.522883 0.905661i −0.999645 0.0266282i \(-0.991523\pi\)
0.476762 0.879032i \(-0.341810\pi\)
\(770\) 0 0
\(771\) 36.0000 1.29651
\(772\) 32.0000 1.15171
\(773\) −15.0000 25.9808i −0.539513 0.934463i −0.998930 0.0462427i \(-0.985275\pi\)
0.459418 0.888220i \(-0.348058\pi\)
\(774\) 0 0
\(775\) 3.50000 + 6.06218i 0.125724 + 0.217760i
\(776\) 0 0
\(777\) −32.0000 + 55.4256i −1.14799 + 1.98838i
\(778\) 0 0
\(779\) −24.0000 + 10.3923i −0.859889 + 0.372343i
\(780\) −8.00000 −0.286446
\(781\) 4.50000 7.79423i 0.161023 0.278899i
\(782\) 0 0
\(783\) 6.00000 + 10.3923i 0.214423 + 0.371391i
\(784\) −18.0000 + 31.1769i −0.642857 + 1.11346i
\(785\) 1.00000 + 1.73205i 0.0356915 + 0.0618195i
\(786\) 0 0
\(787\) −34.0000 −1.21197 −0.605985 0.795476i \(-0.707221\pi\)
−0.605985 + 0.795476i \(0.707221\pi\)
\(788\) −18.0000 31.1769i −0.641223 1.11063i
\(789\) −18.0000