Properties

Label 525.2.i.e.226.1
Level $525$
Weight $2$
Character 525.226
Analytic conductor $4.192$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 525.226
Dual form 525.2.i.e.151.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.00000 q^{6} +(2.50000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.00000 q^{6} +(2.50000 - 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{11} +(1.00000 - 1.73205i) q^{12} -1.00000 q^{13} +(1.00000 - 5.19615i) q^{14} +(2.00000 - 3.46410i) q^{16} +(1.00000 + 1.73205i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(2.00000 + 1.73205i) q^{21} +4.00000 q^{22} +(-1.00000 + 1.73205i) q^{26} -1.00000 q^{27} +(-4.00000 - 3.46410i) q^{28} +4.00000 q^{29} +(-4.50000 - 7.79423i) q^{31} +(-4.00000 - 6.92820i) q^{32} +(-1.00000 + 1.73205i) q^{33} +2.00000 q^{36} +(1.50000 - 2.59808i) q^{37} +(1.00000 + 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{39} -10.0000 q^{41} +(5.00000 - 1.73205i) q^{42} -5.00000 q^{43} +(2.00000 - 3.46410i) q^{44} +(-3.00000 + 5.19615i) q^{47} +4.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +(1.00000 + 1.73205i) q^{52} +(6.00000 + 10.3923i) q^{53} +(-1.00000 + 1.73205i) q^{54} -1.00000 q^{57} +(4.00000 - 6.92820i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-5.00000 + 8.66025i) q^{61} -18.0000 q^{62} +(-0.500000 + 2.59808i) q^{63} -8.00000 q^{64} +(2.00000 + 3.46410i) q^{66} +(-2.50000 - 4.33013i) q^{67} -6.00000 q^{71} +(-1.50000 - 2.59808i) q^{73} +(-3.00000 - 5.19615i) q^{74} +2.00000 q^{76} +(4.00000 + 3.46410i) q^{77} -2.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-10.0000 + 17.3205i) q^{82} -6.00000 q^{83} +(1.00000 - 5.19615i) q^{84} +(-5.00000 + 8.66025i) q^{86} +(2.00000 + 3.46410i) q^{87} +(-8.00000 + 13.8564i) q^{89} +(-2.50000 + 0.866025i) q^{91} +(4.50000 - 7.79423i) q^{93} +(6.00000 + 10.3923i) q^{94} +(4.00000 - 6.92820i) q^{96} +6.00000 q^{97} +(-2.00000 - 13.8564i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + q^{3} - 2q^{4} + 4q^{6} + 5q^{7} - q^{9} + O(q^{10}) \) \( 2q + 2q^{2} + q^{3} - 2q^{4} + 4q^{6} + 5q^{7} - q^{9} + 2q^{11} + 2q^{12} - 2q^{13} + 2q^{14} + 4q^{16} + 2q^{18} - q^{19} + 4q^{21} + 8q^{22} - 2q^{26} - 2q^{27} - 8q^{28} + 8q^{29} - 9q^{31} - 8q^{32} - 2q^{33} + 4q^{36} + 3q^{37} + 2q^{38} - q^{39} - 20q^{41} + 10q^{42} - 10q^{43} + 4q^{44} - 6q^{47} + 8q^{48} + 11q^{49} + 2q^{52} + 12q^{53} - 2q^{54} - 2q^{57} + 8q^{58} + 12q^{59} - 10q^{61} - 36q^{62} - q^{63} - 16q^{64} + 4q^{66} - 5q^{67} - 12q^{71} - 3q^{73} - 6q^{74} + 4q^{76} + 8q^{77} - 4q^{78} + q^{79} - q^{81} - 20q^{82} - 12q^{83} + 2q^{84} - 10q^{86} + 4q^{87} - 16q^{89} - 5q^{91} + 9q^{93} + 12q^{94} + 8q^{96} + 12q^{97} - 4q^{98} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −1.00000 1.73205i −0.500000 0.866025i
\(5\) 0 0
\(6\) 2.00000 0.816497
\(7\) 2.50000 0.866025i 0.944911 0.327327i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 1.00000 1.73205i 0.288675 0.500000i
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 1.00000 5.19615i 0.267261 1.38873i
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 1.00000 + 1.73205i 0.235702 + 0.408248i
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) 2.00000 + 1.73205i 0.436436 + 0.377964i
\(22\) 4.00000 0.852803
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −1.00000 + 1.73205i −0.196116 + 0.339683i
\(27\) −1.00000 −0.192450
\(28\) −4.00000 3.46410i −0.755929 0.654654i
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) −4.50000 7.79423i −0.808224 1.39988i −0.914093 0.405505i \(-0.867096\pi\)
0.105869 0.994380i \(-0.466238\pi\)
\(32\) −4.00000 6.92820i −0.707107 1.22474i
\(33\) −1.00000 + 1.73205i −0.174078 + 0.301511i
\(34\) 0 0
\(35\) 0 0
\(36\) 2.00000 0.333333
\(37\) 1.50000 2.59808i 0.246598 0.427121i −0.715981 0.698119i \(-0.754020\pi\)
0.962580 + 0.270998i \(0.0873538\pi\)
\(38\) 1.00000 + 1.73205i 0.162221 + 0.280976i
\(39\) −0.500000 0.866025i −0.0800641 0.138675i
\(40\) 0 0
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 5.00000 1.73205i 0.771517 0.267261i
\(43\) −5.00000 −0.762493 −0.381246 0.924473i \(-0.624505\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) 2.00000 3.46410i 0.301511 0.522233i
\(45\) 0 0
\(46\) 0 0
\(47\) −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 4.00000 0.577350
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) 0 0
\(51\) 0 0
\(52\) 1.00000 + 1.73205i 0.138675 + 0.240192i
\(53\) 6.00000 + 10.3923i 0.824163 + 1.42749i 0.902557 + 0.430570i \(0.141688\pi\)
−0.0783936 + 0.996922i \(0.524979\pi\)
\(54\) −1.00000 + 1.73205i −0.136083 + 0.235702i
\(55\) 0 0
\(56\) 0 0
\(57\) −1.00000 −0.132453
\(58\) 4.00000 6.92820i 0.525226 0.909718i
\(59\) 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) 0 0
\(61\) −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i \(0.387809\pi\)
−0.985391 + 0.170305i \(0.945525\pi\)
\(62\) −18.0000 −2.28600
\(63\) −0.500000 + 2.59808i −0.0629941 + 0.327327i
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 2.00000 + 3.46410i 0.246183 + 0.426401i
\(67\) −2.50000 4.33013i −0.305424 0.529009i 0.671932 0.740613i \(-0.265465\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) −1.50000 2.59808i −0.175562 0.304082i 0.764794 0.644275i \(-0.222841\pi\)
−0.940356 + 0.340193i \(0.889507\pi\)
\(74\) −3.00000 5.19615i −0.348743 0.604040i
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) 4.00000 + 3.46410i 0.455842 + 0.394771i
\(78\) −2.00000 −0.226455
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −10.0000 + 17.3205i −1.10432 + 1.91273i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 1.00000 5.19615i 0.109109 0.566947i
\(85\) 0 0
\(86\) −5.00000 + 8.66025i −0.539164 + 0.933859i
\(87\) 2.00000 + 3.46410i 0.214423 + 0.371391i
\(88\) 0 0
\(89\) −8.00000 + 13.8564i −0.847998 + 1.46878i 0.0349934 + 0.999388i \(0.488859\pi\)
−0.882992 + 0.469389i \(0.844474\pi\)
\(90\) 0 0
\(91\) −2.50000 + 0.866025i −0.262071 + 0.0907841i
\(92\) 0 0
\(93\) 4.50000 7.79423i 0.466628 0.808224i
\(94\) 6.00000 + 10.3923i 0.618853 + 1.07188i
\(95\) 0 0
\(96\) 4.00000 6.92820i 0.408248 0.707107i
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) −2.00000 13.8564i −0.202031 1.39971i
\(99\) −2.00000 −0.201008
\(100\) 0 0
\(101\) −1.00000 1.73205i −0.0995037 0.172345i 0.811976 0.583691i \(-0.198392\pi\)
−0.911479 + 0.411346i \(0.865059\pi\)
\(102\) 0 0
\(103\) −3.50000 + 6.06218i −0.344865 + 0.597324i −0.985329 0.170664i \(-0.945409\pi\)
0.640464 + 0.767988i \(0.278742\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 24.0000 2.33109
\(107\) −4.00000 + 6.92820i −0.386695 + 0.669775i −0.992003 0.126217i \(-0.959717\pi\)
0.605308 + 0.795991i \(0.293050\pi\)
\(108\) 1.00000 + 1.73205i 0.0962250 + 0.166667i
\(109\) −4.50000 7.79423i −0.431022 0.746552i 0.565940 0.824447i \(-0.308513\pi\)
−0.996962 + 0.0778949i \(0.975180\pi\)
\(110\) 0 0
\(111\) 3.00000 0.284747
\(112\) 2.00000 10.3923i 0.188982 0.981981i
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) −1.00000 + 1.73205i −0.0936586 + 0.162221i
\(115\) 0 0
\(116\) −4.00000 6.92820i −0.371391 0.643268i
\(117\) 0.500000 0.866025i 0.0462250 0.0800641i
\(118\) 24.0000 2.20938
\(119\) 0 0
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 10.0000 + 17.3205i 0.905357 + 1.56813i
\(123\) −5.00000 8.66025i −0.450835 0.780869i
\(124\) −9.00000 + 15.5885i −0.808224 + 1.39988i
\(125\) 0 0
\(126\) 4.00000 + 3.46410i 0.356348 + 0.308607i
\(127\) 15.0000 1.33103 0.665517 0.746382i \(-0.268211\pi\)
0.665517 + 0.746382i \(0.268211\pi\)
\(128\) 0 0
\(129\) −2.50000 4.33013i −0.220113 0.381246i
\(130\) 0 0
\(131\) 7.00000 12.1244i 0.611593 1.05931i −0.379379 0.925241i \(-0.623862\pi\)
0.990972 0.134069i \(-0.0428042\pi\)
\(132\) 4.00000 0.348155
\(133\) −0.500000 + 2.59808i −0.0433555 + 0.225282i
\(134\) −10.0000 −0.863868
\(135\) 0 0
\(136\) 0 0
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) 0 0
\(139\) −3.00000 −0.254457 −0.127228 0.991873i \(-0.540608\pi\)
−0.127228 + 0.991873i \(0.540608\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) −6.00000 + 10.3923i −0.503509 + 0.872103i
\(143\) −1.00000 1.73205i −0.0836242 0.144841i
\(144\) 2.00000 + 3.46410i 0.166667 + 0.288675i
\(145\) 0 0
\(146\) −6.00000 −0.496564
\(147\) 6.50000 + 2.59808i 0.536111 + 0.214286i
\(148\) −6.00000 −0.493197
\(149\) 6.00000 10.3923i 0.491539 0.851371i −0.508413 0.861113i \(-0.669768\pi\)
0.999953 + 0.00974235i \(0.00310113\pi\)
\(150\) 0 0
\(151\) 8.00000 + 13.8564i 0.651031 + 1.12762i 0.982873 + 0.184284i \(0.0589965\pi\)
−0.331842 + 0.943335i \(0.607670\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 10.0000 3.46410i 0.805823 0.279145i
\(155\) 0 0
\(156\) −1.00000 + 1.73205i −0.0800641 + 0.138675i
\(157\) −7.00000 12.1244i −0.558661 0.967629i −0.997609 0.0691164i \(-0.977982\pi\)
0.438948 0.898513i \(-0.355351\pi\)
\(158\) −1.00000 1.73205i −0.0795557 0.137795i
\(159\) −6.00000 + 10.3923i −0.475831 + 0.824163i
\(160\) 0 0
\(161\) 0 0
\(162\) −2.00000 −0.157135
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) 10.0000 + 17.3205i 0.780869 + 1.35250i
\(165\) 0 0
\(166\) −6.00000 + 10.3923i −0.465690 + 0.806599i
\(167\) 14.0000 1.08335 0.541676 0.840587i \(-0.317790\pi\)
0.541676 + 0.840587i \(0.317790\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −0.500000 0.866025i −0.0382360 0.0662266i
\(172\) 5.00000 + 8.66025i 0.381246 + 0.660338i
\(173\) 4.00000 6.92820i 0.304114 0.526742i −0.672949 0.739689i \(-0.734973\pi\)
0.977064 + 0.212947i \(0.0683062\pi\)
\(174\) 8.00000 0.606478
\(175\) 0 0
\(176\) 8.00000 0.603023
\(177\) −6.00000 + 10.3923i −0.450988 + 0.781133i
\(178\) 16.0000 + 27.7128i 1.19925 + 2.07716i
\(179\) −1.00000 1.73205i −0.0747435 0.129460i 0.826231 0.563331i \(-0.190480\pi\)
−0.900975 + 0.433872i \(0.857147\pi\)
\(180\) 0 0
\(181\) 13.0000 0.966282 0.483141 0.875542i \(-0.339496\pi\)
0.483141 + 0.875542i \(0.339496\pi\)
\(182\) −1.00000 + 5.19615i −0.0741249 + 0.385164i
\(183\) −10.0000 −0.739221
\(184\) 0 0
\(185\) 0 0
\(186\) −9.00000 15.5885i −0.659912 1.14300i
\(187\) 0 0
\(188\) 12.0000 0.875190
\(189\) −2.50000 + 0.866025i −0.181848 + 0.0629941i
\(190\) 0 0
\(191\) −5.00000 + 8.66025i −0.361787 + 0.626634i −0.988255 0.152813i \(-0.951167\pi\)
0.626468 + 0.779447i \(0.284500\pi\)
\(192\) −4.00000 6.92820i −0.288675 0.500000i
\(193\) 5.50000 + 9.52628i 0.395899 + 0.685717i 0.993215 0.116289i \(-0.0370998\pi\)
−0.597317 + 0.802005i \(0.703766\pi\)
\(194\) 6.00000 10.3923i 0.430775 0.746124i
\(195\) 0 0
\(196\) −13.0000 5.19615i −0.928571 0.371154i
\(197\) −16.0000 −1.13995 −0.569976 0.821661i \(-0.693048\pi\)
−0.569976 + 0.821661i \(0.693048\pi\)
\(198\) −2.00000 + 3.46410i −0.142134 + 0.246183i
\(199\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(200\) 0 0
\(201\) 2.50000 4.33013i 0.176336 0.305424i
\(202\) −4.00000 −0.281439
\(203\) 10.0000 3.46410i 0.701862 0.243132i
\(204\) 0 0
\(205\) 0 0
\(206\) 7.00000 + 12.1244i 0.487713 + 0.844744i
\(207\) 0 0
\(208\) −2.00000 + 3.46410i −0.138675 + 0.240192i
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 12.0000 20.7846i 0.824163 1.42749i
\(213\) −3.00000 5.19615i −0.205557 0.356034i
\(214\) 8.00000 + 13.8564i 0.546869 + 0.947204i
\(215\) 0 0
\(216\) 0 0
\(217\) −18.0000 15.5885i −1.22192 1.05821i
\(218\) −18.0000 −1.21911
\(219\) 1.50000 2.59808i 0.101361 0.175562i
\(220\) 0 0
\(221\) 0 0
\(222\) 3.00000 5.19615i 0.201347 0.348743i
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) −16.0000 13.8564i −1.06904 0.925820i
\(225\) 0 0
\(226\) −10.0000 + 17.3205i −0.665190 + 1.15214i
\(227\) 9.00000 + 15.5885i 0.597351 + 1.03464i 0.993210 + 0.116331i \(0.0371134\pi\)
−0.395860 + 0.918311i \(0.629553\pi\)
\(228\) 1.00000 + 1.73205i 0.0662266 + 0.114708i
\(229\) 9.50000 16.4545i 0.627778 1.08734i −0.360219 0.932868i \(-0.617298\pi\)
0.987997 0.154475i \(-0.0493686\pi\)
\(230\) 0 0
\(231\) −1.00000 + 5.19615i −0.0657952 + 0.341882i
\(232\) 0 0
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) −1.00000 1.73205i −0.0653720 0.113228i
\(235\) 0 0
\(236\) 12.0000 20.7846i 0.781133 1.35296i
\(237\) 1.00000 0.0649570
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) −7.00000 12.1244i −0.450910 0.780998i 0.547533 0.836784i \(-0.315567\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) −7.00000 12.1244i −0.449977 0.779383i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 20.0000 1.28037
\(245\) 0 0
\(246\) −20.0000 −1.27515
\(247\) 0.500000 0.866025i 0.0318142 0.0551039i
\(248\) 0 0
\(249\) −3.00000 5.19615i −0.190117 0.329293i
\(250\) 0 0
\(251\) −8.00000 −0.504956 −0.252478 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) 5.00000 1.73205i 0.314970 0.109109i
\(253\) 0 0
\(254\) 15.0000 25.9808i 0.941184 1.63018i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 13.0000 22.5167i 0.810918 1.40455i −0.101305 0.994855i \(-0.532302\pi\)
0.912222 0.409695i \(-0.134365\pi\)
\(258\) −10.0000 −0.622573
\(259\) 1.50000 7.79423i 0.0932055 0.484310i
\(260\) 0 0
\(261\) −2.00000 + 3.46410i −0.123797 + 0.214423i
\(262\) −14.0000 24.2487i −0.864923 1.49809i
\(263\) 2.00000 + 3.46410i 0.123325 + 0.213606i 0.921077 0.389380i \(-0.127311\pi\)
−0.797752 + 0.602986i \(0.793977\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 4.00000 + 3.46410i 0.245256 + 0.212398i
\(267\) −16.0000 −0.979184
\(268\) −5.00000 + 8.66025i −0.305424 + 0.529009i
\(269\) −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i \(-0.225219\pi\)
−0.942871 + 0.333157i \(0.891886\pi\)
\(270\) 0 0
\(271\) −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i \(-0.994865\pi\)
0.513905 + 0.857847i \(0.328199\pi\)
\(272\) 0 0
\(273\) −2.00000 1.73205i −0.121046 0.104828i
\(274\) −24.0000 −1.44989
\(275\) 0 0
\(276\) 0 0
\(277\) 6.50000 + 11.2583i 0.390547 + 0.676448i 0.992522 0.122068i \(-0.0389525\pi\)
−0.601975 + 0.798515i \(0.705619\pi\)
\(278\) −3.00000 + 5.19615i −0.179928 + 0.311645i
\(279\) 9.00000 0.538816
\(280\) 0 0
\(281\) −4.00000 −0.238620 −0.119310 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) −6.00000 + 10.3923i −0.357295 + 0.618853i
\(283\) −5.50000 9.52628i −0.326941 0.566279i 0.654962 0.755662i \(-0.272685\pi\)
−0.981903 + 0.189383i \(0.939351\pi\)
\(284\) 6.00000 + 10.3923i 0.356034 + 0.616670i
\(285\) 0 0
\(286\) −4.00000 −0.236525
\(287\) −25.0000 + 8.66025i −1.47570 + 0.511199i
\(288\) 8.00000 0.471405
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 0 0
\(291\) 3.00000 + 5.19615i 0.175863 + 0.304604i
\(292\) −3.00000 + 5.19615i −0.175562 + 0.304082i
\(293\) −8.00000 −0.467365 −0.233682 0.972313i \(-0.575078\pi\)
−0.233682 + 0.972313i \(0.575078\pi\)
\(294\) 11.0000 8.66025i 0.641533 0.505076i
\(295\) 0 0
\(296\) 0 0
\(297\) −1.00000 1.73205i −0.0580259 0.100504i
\(298\) −12.0000 20.7846i −0.695141 1.20402i
\(299\) 0 0
\(300\) 0 0
\(301\) −12.5000 + 4.33013i −0.720488 + 0.249584i
\(302\) 32.0000 1.84139
\(303\) 1.00000 1.73205i 0.0574485 0.0995037i
\(304\) 2.00000 + 3.46410i 0.114708 + 0.198680i
\(305\) 0 0
\(306\) 0 0
\(307\) 17.0000 0.970241 0.485121 0.874447i \(-0.338776\pi\)
0.485121 + 0.874447i \(0.338776\pi\)
\(308\) 2.00000 10.3923i 0.113961 0.592157i
\(309\) −7.00000 −0.398216
\(310\) 0 0
\(311\) 3.00000 + 5.19615i 0.170114 + 0.294647i 0.938460 0.345389i \(-0.112253\pi\)
−0.768345 + 0.640036i \(0.778920\pi\)
\(312\) 0 0
\(313\) −0.500000 + 0.866025i −0.0282617 + 0.0489506i −0.879810 0.475325i \(-0.842331\pi\)
0.851549 + 0.524276i \(0.175664\pi\)
\(314\) −28.0000 −1.58013
\(315\) 0 0
\(316\) −2.00000 −0.112509
\(317\) 12.0000 20.7846i 0.673987 1.16738i −0.302777 0.953062i \(-0.597914\pi\)
0.976764 0.214318i \(-0.0687530\pi\)
\(318\) 12.0000 + 20.7846i 0.672927 + 1.16554i
\(319\) 4.00000 + 6.92820i 0.223957 + 0.387905i
\(320\) 0 0
\(321\) −8.00000 −0.446516
\(322\) 0 0
\(323\) 0 0
\(324\) −1.00000 + 1.73205i −0.0555556 + 0.0962250i
\(325\) 0 0
\(326\) −4.00000 6.92820i −0.221540 0.383718i
\(327\) 4.50000 7.79423i 0.248851 0.431022i
\(328\) 0 0
\(329\) −3.00000 + 15.5885i −0.165395 + 0.859419i
\(330\) 0 0
\(331\) 12.5000 21.6506i 0.687062 1.19003i −0.285722 0.958313i \(-0.592233\pi\)
0.972784 0.231714i \(-0.0744333\pi\)
\(332\) 6.00000 + 10.3923i 0.329293 + 0.570352i
\(333\) 1.50000 + 2.59808i 0.0821995 + 0.142374i
\(334\) 14.0000 24.2487i 0.766046 1.32683i
\(335\) 0 0
\(336\) 10.0000 3.46410i 0.545545 0.188982i
\(337\) −13.0000 −0.708155 −0.354078 0.935216i \(-0.615205\pi\)
−0.354078 + 0.935216i \(0.615205\pi\)
\(338\) −12.0000 + 20.7846i −0.652714 + 1.13053i
\(339\) −5.00000 8.66025i −0.271563 0.470360i
\(340\) 0 0
\(341\) 9.00000 15.5885i 0.487377 0.844162i
\(342\) −2.00000 −0.108148
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) −8.00000 13.8564i −0.430083 0.744925i
\(347\) 16.0000 + 27.7128i 0.858925 + 1.48770i 0.872955 + 0.487800i \(0.162201\pi\)
−0.0140303 + 0.999902i \(0.504466\pi\)
\(348\) 4.00000 6.92820i 0.214423 0.371391i
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 8.00000 13.8564i 0.426401 0.738549i
\(353\) 17.0000 + 29.4449i 0.904819 + 1.56719i 0.821160 + 0.570697i \(0.193327\pi\)
0.0836583 + 0.996495i \(0.473340\pi\)
\(354\) 12.0000 + 20.7846i 0.637793 + 1.10469i
\(355\) 0 0
\(356\) 32.0000 1.69600
\(357\) 0 0
\(358\) −4.00000 −0.211407
\(359\) −10.0000 + 17.3205i −0.527780 + 0.914141i 0.471696 + 0.881761i \(0.343642\pi\)
−0.999476 + 0.0323801i \(0.989691\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 13.0000 22.5167i 0.683265 1.18345i
\(363\) 7.00000 0.367405
\(364\) 4.00000 + 3.46410i 0.209657 + 0.181568i
\(365\) 0 0
\(366\) −10.0000 + 17.3205i −0.522708 + 0.905357i
\(367\) −4.50000 7.79423i −0.234898 0.406855i 0.724345 0.689438i \(-0.242142\pi\)
−0.959243 + 0.282582i \(0.908809\pi\)
\(368\) 0 0
\(369\) 5.00000 8.66025i 0.260290 0.450835i
\(370\) 0 0
\(371\) 24.0000 + 20.7846i 1.24602 + 1.07908i
\(372\) −18.0000 −0.933257
\(373\) 11.5000 19.9186i 0.595447 1.03135i −0.398036 0.917370i \(-0.630308\pi\)
0.993484 0.113975i \(-0.0363585\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.00000 −0.206010
\(378\) −1.00000 + 5.19615i −0.0514344 + 0.267261i
\(379\) 3.00000 0.154100 0.0770498 0.997027i \(-0.475450\pi\)
0.0770498 + 0.997027i \(0.475450\pi\)
\(380\) 0 0
\(381\) 7.50000 + 12.9904i 0.384237 + 0.665517i
\(382\) 10.0000 + 17.3205i 0.511645 + 0.886194i
\(383\) −6.00000 + 10.3923i −0.306586 + 0.531022i −0.977613 0.210411i \(-0.932520\pi\)
0.671027 + 0.741433i \(0.265853\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 22.0000 1.11977
\(387\) 2.50000 4.33013i 0.127082 0.220113i
\(388\) −6.00000 10.3923i −0.304604 0.527589i
\(389\) 3.00000 + 5.19615i 0.152106 + 0.263455i 0.932002 0.362454i \(-0.118061\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 14.0000 0.706207
\(394\) −16.0000 + 27.7128i −0.806068 + 1.39615i
\(395\) 0 0
\(396\) 2.00000 + 3.46410i 0.100504 + 0.174078i
\(397\) −4.50000 + 7.79423i −0.225849 + 0.391181i −0.956574 0.291491i \(-0.905849\pi\)
0.730725 + 0.682672i \(0.239182\pi\)
\(398\) 0 0
\(399\) −2.50000 + 0.866025i −0.125157 + 0.0433555i
\(400\) 0 0
\(401\) 18.0000 31.1769i 0.898877 1.55690i 0.0699455 0.997551i \(-0.477717\pi\)
0.828932 0.559350i \(-0.188949\pi\)
\(402\) −5.00000 8.66025i −0.249377 0.431934i
\(403\) 4.50000 + 7.79423i 0.224161 + 0.388258i
\(404\) −2.00000 + 3.46410i −0.0995037 + 0.172345i
\(405\) 0 0
\(406\) 4.00000 20.7846i 0.198517 1.03152i
\(407\) 6.00000 0.297409
\(408\) 0 0
\(409\) −2.50000 4.33013i −0.123617 0.214111i 0.797574 0.603220i \(-0.206116\pi\)
−0.921192 + 0.389109i \(0.872783\pi\)
\(410\) 0 0
\(411\) 6.00000 10.3923i 0.295958 0.512615i
\(412\) 14.0000 0.689730
\(413\) 24.0000 + 20.7846i 1.18096 + 1.02274i
\(414\) 0 0
\(415\) 0 0
\(416\) 4.00000 + 6.92820i 0.196116 + 0.339683i
\(417\) −1.50000 2.59808i −0.0734553 0.127228i
\(418\) −2.00000 + 3.46410i −0.0978232 + 0.169435i
\(419\) 30.0000 1.46560 0.732798 0.680446i \(-0.238214\pi\)
0.732798 + 0.680446i \(0.238214\pi\)
\(420\) 0 0
\(421\) −7.00000 −0.341159 −0.170580 0.985344i \(-0.554564\pi\)
−0.170580 + 0.985344i \(0.554564\pi\)
\(422\) 4.00000 6.92820i 0.194717 0.337260i
\(423\) −3.00000 5.19615i −0.145865 0.252646i
\(424\) 0 0
\(425\) 0 0
\(426\) −12.0000 −0.581402
\(427\) −5.00000 + 25.9808i −0.241967 + 1.25730i
\(428\) 16.0000 0.773389
\(429\) 1.00000 1.73205i 0.0482805 0.0836242i
\(430\) 0 0
\(431\) 9.00000 + 15.5885i 0.433515 + 0.750870i 0.997173 0.0751385i \(-0.0239399\pi\)
−0.563658 + 0.826008i \(0.690607\pi\)
\(432\) −2.00000 + 3.46410i −0.0962250 + 0.166667i
\(433\) −31.0000 −1.48976 −0.744882 0.667196i \(-0.767494\pi\)
−0.744882 + 0.667196i \(0.767494\pi\)
\(434\) −45.0000 + 15.5885i −2.16007 + 0.748270i
\(435\) 0 0
\(436\) −9.00000 + 15.5885i −0.431022 + 0.746552i
\(437\) 0 0
\(438\) −3.00000 5.19615i −0.143346 0.248282i
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 0 0
\(441\) 1.00000 + 6.92820i 0.0476190 + 0.329914i
\(442\) 0 0
\(443\) 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i \(-0.741317\pi\)
0.972626 + 0.232377i \(0.0746503\pi\)
\(444\) −3.00000 5.19615i −0.142374 0.246598i
\(445\) 0 0
\(446\) −16.0000 + 27.7128i −0.757622 + 1.31224i
\(447\) 12.0000 0.567581
\(448\) −20.0000 + 6.92820i −0.944911 + 0.327327i
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) −10.0000 17.3205i −0.470882 0.815591i
\(452\) 10.0000 + 17.3205i 0.470360 + 0.814688i
\(453\) −8.00000 + 13.8564i −0.375873 + 0.651031i
\(454\) 36.0000 1.68956
\(455\) 0 0
\(456\) 0 0
\(457\) −5.50000 + 9.52628i −0.257279 + 0.445621i −0.965512 0.260358i \(-0.916159\pi\)
0.708233 + 0.705979i \(0.249493\pi\)
\(458\) −19.0000 32.9090i −0.887812 1.53773i
\(459\) 0 0
\(460\) 0 0
\(461\) 20.0000 0.931493 0.465746 0.884918i \(-0.345786\pi\)
0.465746 + 0.884918i \(0.345786\pi\)
\(462\) 8.00000 + 6.92820i 0.372194 + 0.322329i
\(463\) 17.0000 0.790057 0.395029 0.918669i \(-0.370735\pi\)
0.395029 + 0.918669i \(0.370735\pi\)
\(464\) 8.00000 13.8564i 0.371391 0.643268i
\(465\) 0 0
\(466\) −6.00000 10.3923i −0.277945 0.481414i
\(467\) 3.00000 5.19615i 0.138823 0.240449i −0.788228 0.615383i \(-0.789001\pi\)
0.927052 + 0.374934i \(0.122335\pi\)
\(468\) −2.00000 −0.0924500
\(469\) −10.0000 8.66025i −0.461757 0.399893i
\(470\) 0 0
\(471\) 7.00000 12.1244i 0.322543 0.558661i
\(472\) 0 0
\(473\) −5.00000 8.66025i −0.229900 0.398199i
\(474\) 1.00000 1.73205i 0.0459315 0.0795557i
\(475\) 0 0
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) 6.00000 10.3923i 0.274434 0.475333i
\(479\) 14.0000 + 24.2487i 0.639676 + 1.10795i 0.985504 + 0.169654i \(0.0542649\pi\)
−0.345827 + 0.938298i \(0.612402\pi\)
\(480\) 0 0
\(481\) −1.50000 + 2.59808i −0.0683941 + 0.118462i
\(482\) −28.0000 −1.27537
\(483\) 0 0
\(484\) −14.0000 −0.636364
\(485\) 0 0
\(486\) −1.00000 1.73205i −0.0453609 0.0785674i
\(487\) 15.5000 + 26.8468i 0.702372 + 1.21654i 0.967632 + 0.252367i \(0.0812090\pi\)
−0.265260 + 0.964177i \(0.585458\pi\)
\(488\) 0 0
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) −28.0000 −1.26362 −0.631811 0.775122i \(-0.717688\pi\)
−0.631811 + 0.775122i \(0.717688\pi\)
\(492\) −10.0000 + 17.3205i −0.450835 + 0.780869i
\(493\) 0 0
\(494\) −1.00000 1.73205i −0.0449921 0.0779287i
\(495\) 0 0
\(496\) −36.0000 −1.61645
\(497\) −15.0000 + 5.19615i −0.672842 + 0.233079i
\(498\) −12.0000 −0.537733
\(499\) −18.5000 + 32.0429i −0.828174 + 1.43444i 0.0712957 + 0.997455i \(0.477287\pi\)
−0.899469 + 0.436984i \(0.856047\pi\)
\(500\) 0 0
\(501\) 7.00000 + 12.1244i 0.312737 + 0.541676i
\(502\) −8.00000 + 13.8564i −0.357057 + 0.618442i
\(503\) 42.0000 1.87269 0.936344 0.351085i \(-0.114187\pi\)
0.936344 + 0.351085i \(0.114187\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −6.00000 10.3923i −0.266469 0.461538i
\(508\) −15.0000 25.9808i −0.665517 1.15271i
\(509\) −1.00000 + 1.73205i −0.0443242 + 0.0767718i −0.887336 0.461123i \(-0.847447\pi\)
0.843012 + 0.537895i \(0.180780\pi\)
\(510\) 0 0
\(511\) −6.00000 5.19615i −0.265424 0.229864i
\(512\) −32.0000 −1.41421
\(513\) 0.500000 0.866025i 0.0220755 0.0382360i
\(514\) −26.0000 45.0333i −1.14681 1.98633i
\(515\) 0 0
\(516\) −5.00000 + 8.66025i −0.220113 + 0.381246i
\(517\) −12.0000 −0.527759
\(518\) −12.0000 10.3923i −0.527250 0.456612i
\(519\) 8.00000 0.351161
\(520\) 0 0
\(521\) −6.00000 10.3923i −0.262865 0.455295i 0.704137 0.710064i \(-0.251334\pi\)
−0.967002 + 0.254769i \(0.918001\pi\)
\(522\) 4.00000 + 6.92820i 0.175075 + 0.303239i
\(523\) 15.5000 26.8468i 0.677768 1.17393i −0.297884 0.954602i \(-0.596281\pi\)
0.975652 0.219326i \(-0.0703858\pi\)
\(524\) −28.0000 −1.22319
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) 0 0
\(528\) 4.00000 + 6.92820i 0.174078 + 0.301511i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) −12.0000 −0.520756
\(532\) 5.00000 1.73205i 0.216777 0.0750939i
\(533\) 10.0000 0.433148
\(534\) −16.0000 + 27.7128i −0.692388 + 1.19925i
\(535\) 0 0
\(536\) 0 0
\(537\) 1.00000 1.73205i 0.0431532 0.0747435i
\(538\) −12.0000 −0.517357
\(539\) 13.0000 + 5.19615i 0.559950 + 0.223814i
\(540\) 0 0
\(541\) 9.50000 16.4545i 0.408437 0.707433i −0.586278 0.810110i \(-0.699407\pi\)
0.994715 + 0.102677i \(0.0327407\pi\)
\(542\) 16.0000 + 27.7128i 0.687259 + 1.19037i
\(543\) 6.50000 + 11.2583i 0.278942 + 0.483141i
\(544\) 0 0
\(545\) 0 0
\(546\) −5.00000 + 1.73205i −0.213980 + 0.0741249i
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −12.0000 + 20.7846i −0.512615 + 0.887875i
\(549\) −5.00000 8.66025i −0.213395 0.369611i
\(550\) 0 0
\(551\) −2.00000 + 3.46410i −0.0852029 + 0.147576i
\(552\) 0 0
\(553\) 0.500000 2.59808i 0.0212622 0.110481i
\(554\) 26.0000 1.10463
\(555\) 0 0
\(556\) 3.00000 + 5.19615i 0.127228 + 0.220366i
\(557\) −1.00000 1.73205i −0.0423714 0.0733893i 0.844062 0.536246i \(-0.180158\pi\)
−0.886433 + 0.462856i \(0.846825\pi\)
\(558\) 9.00000 15.5885i 0.381000 0.659912i
\(559\) 5.00000 0.211477
\(560\) 0 0
\(561\) 0 0
\(562\) −4.00000 + 6.92820i −0.168730 + 0.292249i
\(563\) −13.0000 22.5167i −0.547885 0.948964i −0.998419 0.0562051i \(-0.982100\pi\)
0.450535 0.892759i \(-0.351233\pi\)
\(564\) 6.00000 + 10.3923i 0.252646 + 0.437595i
\(565\) 0 0
\(566\) −22.0000 −0.924729
\(567\) −2.00000 1.73205i −0.0839921 0.0727393i
\(568\) 0 0
\(569\) 13.0000 22.5167i 0.544988 0.943948i −0.453619 0.891196i \(-0.649867\pi\)
0.998608 0.0527519i \(-0.0167993\pi\)
\(570\) 0 0
\(571\) 9.50000 + 16.4545i 0.397563 + 0.688599i 0.993425 0.114488i \(-0.0365228\pi\)
−0.595862 + 0.803087i \(0.703189\pi\)
\(572\) −2.00000 + 3.46410i −0.0836242 + 0.144841i
\(573\) −10.0000 −0.417756
\(574\) −10.0000 + 51.9615i −0.417392 + 2.16883i
\(575\) 0 0
\(576\) 4.00000 6.92820i 0.166667 0.288675i
\(577\) −8.50000 14.7224i −0.353860 0.612903i 0.633062 0.774101i \(-0.281798\pi\)
−0.986922 + 0.161198i \(0.948464\pi\)
\(578\) −17.0000 29.4449i −0.707107 1.22474i
\(579\) −5.50000 + 9.52628i −0.228572 + 0.395899i
\(580\) 0 0
\(581\) −15.0000 + 5.19615i −0.622305 + 0.215573i
\(582\) 12.0000 0.497416
\(583\) −12.0000 + 20.7846i −0.496989 + 0.860811i
\(584\) 0 0
\(585\) 0 0
\(586\) −8.00000 + 13.8564i −0.330477 + 0.572403i
\(587\) −16.0000 −0.660391 −0.330195 0.943913i \(-0.607115\pi\)
−0.330195 + 0.943913i \(0.607115\pi\)
\(588\) −2.00000 13.8564i −0.0824786 0.571429i
\(589\) 9.00000 0.370839
\(590\) 0 0
\(591\) −8.00000 13.8564i −0.329076 0.569976i
\(592\) −6.00000 10.3923i −0.246598 0.427121i
\(593\) −3.00000 + 5.19615i −0.123195 + 0.213380i −0.921026 0.389501i \(-0.872647\pi\)
0.797831 + 0.602881i \(0.205981\pi\)
\(594\) −4.00000 −0.164122
\(595\) 0 0
\(596\) −24.0000 −0.983078
\(597\) 0 0
\(598\) 0 0
\(599\) −6.00000 10.3923i −0.245153 0.424618i 0.717021 0.697051i \(-0.245505\pi\)
−0.962175 + 0.272433i \(0.912172\pi\)
\(600\) 0 0
\(601\) −9.00000 −0.367118 −0.183559 0.983009i \(-0.558762\pi\)
−0.183559 + 0.983009i \(0.558762\pi\)
\(602\) −5.00000 + 25.9808i −0.203785 + 1.05890i
\(603\) 5.00000 0.203616
\(604\) 16.0000 27.7128i 0.651031 1.12762i
\(605\) 0 0
\(606\) −2.00000 3.46410i −0.0812444 0.140720i
\(607\) 11.5000 19.9186i 0.466771 0.808470i −0.532509 0.846424i \(-0.678751\pi\)
0.999279 + 0.0379540i \(0.0120840\pi\)
\(608\) 8.00000 0.324443
\(609\) 8.00000 + 6.92820i 0.324176 + 0.280745i
\(610\) 0 0
\(611\) 3.00000 5.19615i 0.121367 0.210214i
\(612\) 0 0
\(613\) 17.0000 + 29.4449i 0.686624 + 1.18927i 0.972924 + 0.231127i \(0.0742412\pi\)
−0.286300 + 0.958140i \(0.592425\pi\)
\(614\) 17.0000 29.4449i 0.686064 1.18830i
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) −7.00000 + 12.1244i −0.281581 + 0.487713i
\(619\) 14.5000 + 25.1147i 0.582804 + 1.00945i 0.995145 + 0.0984169i \(0.0313779\pi\)
−0.412341 + 0.911030i \(0.635289\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) −8.00000 + 41.5692i −0.320513 + 1.66544i
\(624\) −4.00000 −0.160128
\(625\) 0 0
\(626\) 1.00000 + 1.73205i 0.0399680 + 0.0692267i
\(627\) −1.00000 1.73205i −0.0399362 0.0691714i
\(628\) −14.0000 + 24.2487i −0.558661 + 0.967629i
\(629\) 0 0
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) 2.00000 + 3.46410i 0.0794929 + 0.137686i
\(634\) −24.0000 41.5692i −0.953162 1.65092i
\(635\) 0 0
\(636\) 24.0000 0.951662
\(637\) −5.50000 + 4.33013i −0.217918 + 0.171566i
\(638\) 16.0000 0.633446
\(639\) 3.00000 5.19615i 0.118678 0.205557i
\(640\) 0 0
\(641\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(642\) −8.00000 + 13.8564i −0.315735 + 0.546869i
\(643\) 19.0000 0.749287 0.374643 0.927169i \(-0.377765\pi\)
0.374643 + 0.927169i \(0.377765\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.00000 + 1.73205i 0.0393141 + 0.0680939i 0.885013 0.465566i \(-0.154149\pi\)
−0.845699 + 0.533660i \(0.820816\pi\)
\(648\) 0 0
\(649\) −12.0000 + 20.7846i −0.471041 + 0.815867i
\(650\) 0 0
\(651\) 4.50000 23.3827i 0.176369 0.916440i
\(652\) −8.00000 −0.313304
\(653\) 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i \(-0.718768\pi\)
0.986634 + 0.162951i \(0.0521013\pi\)
\(654\) −9.00000 15.5885i −0.351928 0.609557i
\(655\) 0 0
\(656\) −20.0000 + 34.6410i −0.780869 + 1.35250i
\(657\) 3.00000 0.117041
\(658\) 24.0000 + 20.7846i 0.935617 + 0.810268i
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) 20.5000 + 35.5070i 0.797358 + 1.38106i 0.921331 + 0.388778i \(0.127103\pi\)
−0.123974 + 0.992286i \(0.539564\pi\)
\(662\) −25.0000 43.3013i −0.971653 1.68295i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) 0 0
\(668\) −14.0000 24.2487i −0.541676 0.938211i
\(669\) −8.00000 13.8564i −0.309298 0.535720i
\(670\) 0 0
\(671\) −20.0000 −0.772091
\(672\) 4.00000 20.7846i 0.154303 0.801784i
\(673\) 41.0000 1.58043 0.790217 0.612827i \(-0.209968\pi\)
0.790217 + 0.612827i \(0.209968\pi\)
\(674\) −13.0000 + 22.5167i −0.500741 + 0.867309i
\(675\) 0 0
\(676\) 12.0000 + 20.7846i 0.461538 + 0.799408i
\(677\) 6.00000 10.3923i 0.230599 0.399409i −0.727386 0.686229i \(-0.759265\pi\)
0.957984 + 0.286820i \(0.0925982\pi\)
\(678\) −20.0000 −0.768095
\(679\) 15.0000 5.19615i 0.575647 0.199410i
\(680\) 0 0
\(681\) −9.00000 + 15.5885i −0.344881 + 0.597351i
\(682\) −18.0000 31.1769i −0.689256 1.19383i
\(683\) −6.00000 10.3923i −0.229584 0.397650i 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) −1.00000 + 1.73205i −0.0382360 + 0.0662266i
\(685\) 0 0
\(686\) −17.0000 32.9090i −0.649063 1.25647i
\(687\) 19.0000 0.724895
\(688\) −10.0000 + 17.3205i −0.381246 + 0.660338i
\(689\) −6.00000 10.3923i −0.228582 0.395915i
\(690\) 0 0
\(691\) 18.5000 32.0429i 0.703773 1.21897i −0.263359 0.964698i \(-0.584830\pi\)
0.967132 0.254273i \(-0.0818362\pi\)
\(692\) −16.0000 −0.608229
\(693\) −5.00000 + 1.73205i −0.189934 + 0.0657952i
\(694\) 64.0000 2.42941
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −14.0000 + 24.2487i −0.529908 + 0.917827i
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 1.00000 1.73205i 0.0377426 0.0653720i
\(703\) 1.50000 + 2.59808i 0.0565736 + 0.0979883i
\(704\) −8.00000 13.8564i −0.301511 0.522233i
\(705\) 0 0
\(706\) 68.0000 2.55921
\(707\) −4.00000 3.46410i −0.150435 0.130281i
\(708\) 24.0000 0.901975
\(709\) −15.0000 + 25.9808i −0.563337 + 0.975728i 0.433865 + 0.900978i \(0.357149\pi\)
−0.997202 + 0.0747503i \(0.976184\pi\)
\(710\) 0 0
\(711\) 0.500000 + 0.866025i 0.0187515 + 0.0324785i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −2.00000 + 3.46410i −0.0747435 + 0.129460i
\(717\) 3.00000 + 5.19615i 0.112037 + 0.194054i
\(718\) 20.0000 + 34.6410i 0.746393 + 1.29279i
\(719\) 9.00000 15.5885i 0.335643 0.581351i −0.647965 0.761670i \(-0.724380\pi\)
0.983608 + 0.180319i \(0.0577130\pi\)
\(720\) 0 0
\(721\) −3.50000 + 18.1865i −0.130347 + 0.677302i
\(722\) 36.0000 1.33978
\(723\) 7.00000 12.1244i 0.260333 0.450910i
\(724\) −13.0000 22.5167i −0.483141 0.836825i
\(725\) 0 0
\(726\) 7.00000 12.1244i 0.259794 0.449977i
\(727\) 13.0000 0.482143 0.241072 0.970507i \(-0.422501\pi\)
0.241072 + 0.970507i \(0.422501\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 10.0000 + 17.3205i 0.369611 + 0.640184i
\(733\) −7.50000 + 12.9904i −0.277019 + 0.479811i −0.970642 0.240527i \(-0.922680\pi\)
0.693624 + 0.720338i \(0.256013\pi\)
\(734\) −18.0000 −0.664392
\(735\) 0 0
\(736\) 0 0
\(737\) 5.00000 8.66025i 0.184177 0.319005i
\(738\) −10.0000 17.3205i −0.368105 0.637577i
\(739\) 7.50000 + 12.9904i 0.275892 + 0.477859i 0.970360 0.241665i \(-0.0776935\pi\)
−0.694468 + 0.719524i \(0.744360\pi\)
\(740\) 0 0
\(741\) 1.00000 0.0367359
\(742\) 60.0000 20.7846i 2.20267 0.763027i
\(743\) −42.0000 −1.54083 −0.770415 0.637542i \(-0.779951\pi\)
−0.770415 + 0.637542i \(0.779951\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −23.0000 39.8372i −0.842090 1.45854i
\(747\) 3.00000 5.19615i 0.109764 0.190117i
\(748\) 0 0
\(749\) −4.00000 + 20.7846i −0.146157 + 0.759453i
\(750\) 0 0
\(751\) −6.50000 + 11.2583i −0.237188 + 0.410822i −0.959906 0.280321i \(-0.909559\pi\)
0.722718 + 0.691143i \(0.242893\pi\)
\(752\) 12.0000 + 20.7846i 0.437595 + 0.757937i
\(753\) −4.00000 6.92820i −0.145768 0.252478i
\(754\) −4.00000 + 6.92820i −0.145671 + 0.252310i
\(755\) 0 0
\(756\) 4.00000 + 3.46410i 0.145479 + 0.125988i
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) 3.00000 5.19615i 0.108965 0.188733i
\(759\) 0 0
\(760\) 0 0
\(761\) 24.0000 41.5692i 0.869999 1.50688i 0.00800331 0.999968i \(-0.497452\pi\)
0.861996 0.506915i \(-0.169214\pi\)
\(762\) 30.0000 1.08679
\(763\) −18.0000 15.5885i −0.651644 0.564340i
\(764\) 20.0000 0.723575
\(765\) 0 0
\(766\) 12.0000 + 20.7846i 0.433578 + 0.750978i
\(767\) −6.00000 10.3923i −0.216647 0.375244i
\(768\) 8.00000 13.8564i 0.288675 0.500000i
\(769\) −49.0000 −1.76699 −0.883493 0.468445i \(-0.844814\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 0 0
\(771\) 26.0000 0.936367
\(772\) 11.0000 19.0526i 0.395899 0.685717i
\(773\) −17.0000 29.4449i −0.611448 1.05906i −0.990997 0.133887i \(-0.957254\pi\)
0.379549 0.925172i \(-0.376079\pi\)
\(774\) −5.00000 8.66025i −0.179721 0.311286i
\(775\) 0 0
\(776\) 0 0
\(777\) 7.50000 2.59808i 0.269061 0.0932055i
\(778\) 12.0000 0.430221
\(779\) 5.00000 8.66025i 0.179144 0.310286i
\(780\) 0 0
\(781\) −6.00000 10.3923i −0.214697 0.371866i
\(782\) 0 0
\(783\) −4.00000 −0.142948
\(784\) −4.00000 27.7128i −0.142857 0.989743i
\(785\) 0 0
\(786\) 14.0000 24.2487i 0.499363 0.864923i
\(787\) 20.0000 + 34.6410i 0.712923 + 1.23482i 0.963755 + 0.266788i \(0.0859624\pi\)
−0.250832 + 0.968031i \(0.580704\pi\)
\(788\) 16.0000 + 27.7128i 0.569976 + 0.987228i
\(789\) −2.00000 + 3.46410i