Properties

Label 1134.2.f.b.379.1
Level $1134$
Weight $2$
Character 1134.379
Analytic conductor $9.055$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.f (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 378)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 379.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.379
Dual form 1134.2.f.b.757.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +3.00000 q^{10} +(1.50000 - 2.59808i) q^{11} +(2.00000 + 3.46410i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +6.00000 q^{17} -7.00000 q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +(-1.50000 - 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} -4.00000 q^{26} +1.00000 q^{28} +(-2.50000 - 4.33013i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} +3.00000 q^{35} -7.00000 q^{37} +(3.50000 - 6.06218i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(-4.50000 - 7.79423i) q^{41} +(5.00000 - 8.66025i) q^{43} -3.00000 q^{44} +3.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(2.00000 - 3.46410i) q^{52} -12.0000 q^{53} -9.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-3.00000 - 5.19615i) q^{59} +(-4.00000 + 6.92820i) q^{61} +5.00000 q^{62} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-1.50000 + 2.59808i) q^{70} -9.00000 q^{71} +2.00000 q^{73} +(3.50000 - 6.06218i) q^{74} +(3.50000 + 6.06218i) q^{76} +(1.50000 + 2.59808i) q^{77} +(5.00000 - 8.66025i) q^{79} +3.00000 q^{80} +9.00000 q^{82} +(-9.00000 - 15.5885i) q^{85} +(5.00000 + 8.66025i) q^{86} +(1.50000 - 2.59808i) q^{88} -15.0000 q^{89} -4.00000 q^{91} +(-1.50000 + 2.59808i) q^{92} +(3.00000 + 5.19615i) q^{94} +(10.5000 + 18.1865i) q^{95} +(-4.00000 + 6.92820i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} - 3q^{5} - q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} - 3q^{5} - q^{7} + 2q^{8} + 6q^{10} + 3q^{11} + 4q^{13} - q^{14} - q^{16} + 12q^{17} - 14q^{19} - 3q^{20} + 3q^{22} - 3q^{23} - 4q^{25} - 8q^{26} + 2q^{28} - 5q^{31} - q^{32} - 6q^{34} + 6q^{35} - 14q^{37} + 7q^{38} - 3q^{40} - 9q^{41} + 10q^{43} - 6q^{44} + 6q^{46} + 6q^{47} - q^{49} - 4q^{50} + 4q^{52} - 24q^{53} - 18q^{55} - q^{56} - 6q^{59} - 8q^{61} + 10q^{62} + 2q^{64} + 12q^{65} + 4q^{67} - 6q^{68} - 3q^{70} - 18q^{71} + 4q^{73} + 7q^{74} + 7q^{76} + 3q^{77} + 10q^{79} + 6q^{80} + 18q^{82} - 18q^{85} + 10q^{86} + 3q^{88} - 30q^{89} - 8q^{91} - 3q^{92} + 6q^{94} + 21q^{95} - 8q^{97} + 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 3.00000 0.948683
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0 0
\(13\) 2.00000 + 3.46410i 0.554700 + 0.960769i 0.997927 + 0.0643593i \(0.0205004\pi\)
−0.443227 + 0.896410i \(0.646166\pi\)
\(14\) −0.500000 0.866025i −0.133631 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 0 0
\(19\) −7.00000 −1.60591 −0.802955 0.596040i \(-0.796740\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) −1.50000 + 2.59808i −0.335410 + 0.580948i
\(21\) 0 0
\(22\) 1.50000 + 2.59808i 0.319801 + 0.553912i
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 0 0
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) −4.00000 −0.784465
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(30\) 0 0
\(31\) −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i \(-0.314891\pi\)
−0.998322 + 0.0579057i \(0.981558\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −3.00000 + 5.19615i −0.514496 + 0.891133i
\(35\) 3.00000 0.507093
\(36\) 0 0
\(37\) −7.00000 −1.15079 −0.575396 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) 3.50000 6.06218i 0.567775 0.983415i
\(39\) 0 0
\(40\) −1.50000 2.59808i −0.237171 0.410792i
\(41\) −4.50000 7.79423i −0.702782 1.21725i −0.967486 0.252924i \(-0.918608\pi\)
0.264704 0.964330i \(-0.414726\pi\)
\(42\) 0 0
\(43\) 5.00000 8.66025i 0.762493 1.32068i −0.179069 0.983836i \(-0.557309\pi\)
0.941562 0.336840i \(-0.109358\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) 3.00000 0.442326
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −2.00000 3.46410i −0.282843 0.489898i
\(51\) 0 0
\(52\) 2.00000 3.46410i 0.277350 0.480384i
\(53\) −12.0000 −1.64833 −0.824163 0.566352i \(-0.808354\pi\)
−0.824163 + 0.566352i \(0.808354\pi\)
\(54\) 0 0
\(55\) −9.00000 −1.21356
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 0 0
\(58\) 0 0
\(59\) −3.00000 5.19615i −0.390567 0.676481i 0.601958 0.798528i \(-0.294388\pi\)
−0.992524 + 0.122047i \(0.961054\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) 5.00000 0.635001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 6.00000 10.3923i 0.744208 1.28901i
\(66\) 0 0
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) −3.00000 5.19615i −0.363803 0.630126i
\(69\) 0 0
\(70\) −1.50000 + 2.59808i −0.179284 + 0.310530i
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 3.50000 6.06218i 0.406867 0.704714i
\(75\) 0 0
\(76\) 3.50000 + 6.06218i 0.401478 + 0.695379i
\(77\) 1.50000 + 2.59808i 0.170941 + 0.296078i
\(78\) 0 0
\(79\) 5.00000 8.66025i 0.562544 0.974355i −0.434730 0.900561i \(-0.643156\pi\)
0.997274 0.0737937i \(-0.0235106\pi\)
\(80\) 3.00000 0.335410
\(81\) 0 0
\(82\) 9.00000 0.993884
\(83\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(84\) 0 0
\(85\) −9.00000 15.5885i −0.976187 1.69081i
\(86\) 5.00000 + 8.66025i 0.539164 + 0.933859i
\(87\) 0 0
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) −15.0000 −1.59000 −0.794998 0.606612i \(-0.792528\pi\)
−0.794998 + 0.606612i \(0.792528\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) −1.50000 + 2.59808i −0.156386 + 0.270868i
\(93\) 0 0
\(94\) 3.00000 + 5.19615i 0.309426 + 0.535942i
\(95\) 10.5000 + 18.1865i 1.07728 + 1.86590i
\(96\) 0 0
\(97\) −4.00000 + 6.92820i −0.406138 + 0.703452i −0.994453 0.105180i \(-0.966458\pi\)
0.588315 + 0.808632i \(0.299792\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 4.00000 0.400000
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 0 0
\(103\) −2.50000 4.33013i −0.246332 0.426660i 0.716173 0.697923i \(-0.245892\pi\)
−0.962505 + 0.271263i \(0.912559\pi\)
\(104\) 2.00000 + 3.46410i 0.196116 + 0.339683i
\(105\) 0 0
\(106\) 6.00000 10.3923i 0.582772 1.00939i
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) 11.0000 1.05361 0.526804 0.849987i \(-0.323390\pi\)
0.526804 + 0.849987i \(0.323390\pi\)
\(110\) 4.50000 7.79423i 0.429058 0.743151i
\(111\) 0 0
\(112\) −0.500000 0.866025i −0.0472456 0.0818317i
\(113\) −9.00000 15.5885i −0.846649 1.46644i −0.884182 0.467143i \(-0.845283\pi\)
0.0375328 0.999295i \(-0.488050\pi\)
\(114\) 0 0
\(115\) −4.50000 + 7.79423i −0.419627 + 0.726816i
\(116\) 0 0
\(117\) 0 0
\(118\) 6.00000 0.552345
\(119\) −3.00000 + 5.19615i −0.275010 + 0.476331i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −4.00000 6.92820i −0.362143 0.627250i
\(123\) 0 0
\(124\) −2.50000 + 4.33013i −0.224507 + 0.388857i
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 6.00000 + 10.3923i 0.526235 + 0.911465i
\(131\) 3.00000 + 5.19615i 0.262111 + 0.453990i 0.966803 0.255524i \(-0.0822479\pi\)
−0.704692 + 0.709514i \(0.748915\pi\)
\(132\) 0 0
\(133\) 3.50000 6.06218i 0.303488 0.525657i
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) 6.00000 0.514496
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) 0 0
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) −1.50000 2.59808i −0.126773 0.219578i
\(141\) 0 0
\(142\) 4.50000 7.79423i 0.377632 0.654077i
\(143\) 12.0000 1.00349
\(144\) 0 0
\(145\) 0 0
\(146\) −1.00000 + 1.73205i −0.0827606 + 0.143346i
\(147\) 0 0
\(148\) 3.50000 + 6.06218i 0.287698 + 0.498308i
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0 0
\(151\) 5.00000 8.66025i 0.406894 0.704761i −0.587646 0.809118i \(-0.699945\pi\)
0.994540 + 0.104357i \(0.0332784\pi\)
\(152\) −7.00000 −0.567775
\(153\) 0 0
\(154\) −3.00000 −0.241747
\(155\) −7.50000 + 12.9904i −0.602414 + 1.04341i
\(156\) 0 0
\(157\) 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i \(-0.115641\pi\)
−0.775113 + 0.631822i \(0.782307\pi\)
\(158\) 5.00000 + 8.66025i 0.397779 + 0.688973i
\(159\) 0 0
\(160\) −1.50000 + 2.59808i −0.118585 + 0.205396i
\(161\) 3.00000 0.236433
\(162\) 0 0
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) −4.50000 + 7.79423i −0.351391 + 0.608627i
\(165\) 0 0
\(166\) 0 0
\(167\) −9.00000 15.5885i −0.696441 1.20627i −0.969693 0.244328i \(-0.921432\pi\)
0.273252 0.961943i \(-0.411901\pi\)
\(168\) 0 0
\(169\) −1.50000 + 2.59808i −0.115385 + 0.199852i
\(170\) 18.0000 1.38054
\(171\) 0 0
\(172\) −10.0000 −0.762493
\(173\) −10.5000 + 18.1865i −0.798300 + 1.38270i 0.122422 + 0.992478i \(0.460934\pi\)
−0.920722 + 0.390218i \(0.872399\pi\)
\(174\) 0 0
\(175\) −2.00000 3.46410i −0.151186 0.261861i
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) 0 0
\(178\) 7.50000 12.9904i 0.562149 0.973670i
\(179\) 24.0000 1.79384 0.896922 0.442189i \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 2.00000 3.46410i 0.148250 0.256776i
\(183\) 0 0
\(184\) −1.50000 2.59808i −0.110581 0.191533i
\(185\) 10.5000 + 18.1865i 0.771975 + 1.33710i
\(186\) 0 0
\(187\) 9.00000 15.5885i 0.658145 1.13994i
\(188\) −6.00000 −0.437595
\(189\) 0 0
\(190\) −21.0000 −1.52350
\(191\) 7.50000 12.9904i 0.542681 0.939951i −0.456068 0.889945i \(-0.650743\pi\)
0.998749 0.0500060i \(-0.0159241\pi\)
\(192\) 0 0
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) −4.00000 6.92820i −0.287183 0.497416i
\(195\) 0 0
\(196\) −0.500000 + 0.866025i −0.0357143 + 0.0618590i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −7.00000 −0.496217 −0.248108 0.968732i \(-0.579809\pi\)
−0.248108 + 0.968732i \(0.579809\pi\)
\(200\) −2.00000 + 3.46410i −0.141421 + 0.244949i
\(201\) 0 0
\(202\) −3.00000 5.19615i −0.211079 0.365600i
\(203\) 0 0
\(204\) 0 0
\(205\) −13.5000 + 23.3827i −0.942881 + 1.63312i
\(206\) 5.00000 0.348367
\(207\) 0 0
\(208\) −4.00000 −0.277350
\(209\) −10.5000 + 18.1865i −0.726300 + 1.25799i
\(210\) 0 0
\(211\) −7.00000 12.1244i −0.481900 0.834675i 0.517884 0.855451i \(-0.326720\pi\)
−0.999784 + 0.0207756i \(0.993386\pi\)
\(212\) 6.00000 + 10.3923i 0.412082 + 0.713746i
\(213\) 0 0
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) −30.0000 −2.04598
\(216\) 0 0
\(217\) 5.00000 0.339422
\(218\) −5.50000 + 9.52628i −0.372507 + 0.645201i
\(219\) 0 0
\(220\) 4.50000 + 7.79423i 0.303390 + 0.525487i
\(221\) 12.0000 + 20.7846i 0.807207 + 1.39812i
\(222\) 0 0
\(223\) 0.500000 0.866025i 0.0334825 0.0579934i −0.848799 0.528716i \(-0.822674\pi\)
0.882281 + 0.470723i \(0.156007\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 18.0000 1.19734
\(227\) −3.00000 + 5.19615i −0.199117 + 0.344881i −0.948242 0.317547i \(-0.897141\pi\)
0.749125 + 0.662428i \(0.230474\pi\)
\(228\) 0 0
\(229\) 2.00000 + 3.46410i 0.132164 + 0.228914i 0.924510 0.381157i \(-0.124474\pi\)
−0.792347 + 0.610071i \(0.791141\pi\)
\(230\) −4.50000 7.79423i −0.296721 0.513936i
\(231\) 0 0
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) −18.0000 −1.17419
\(236\) −3.00000 + 5.19615i −0.195283 + 0.338241i
\(237\) 0 0
\(238\) −3.00000 5.19615i −0.194461 0.336817i
\(239\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(240\) 0 0
\(241\) −13.0000 + 22.5167i −0.837404 + 1.45043i 0.0546547 + 0.998505i \(0.482594\pi\)
−0.892058 + 0.451920i \(0.850739\pi\)
\(242\) −2.00000 −0.128565
\(243\) 0 0
\(244\) 8.00000 0.512148
\(245\) −1.50000 + 2.59808i −0.0958315 + 0.165985i
\(246\) 0 0
\(247\) −14.0000 24.2487i −0.890799 1.54291i
\(248\) −2.50000 4.33013i −0.158750 0.274963i
\(249\) 0 0
\(250\) 1.50000 2.59808i 0.0948683 0.164317i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −9.00000 −0.565825
\(254\) −10.0000 + 17.3205i −0.627456 + 1.08679i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.5000 18.1865i −0.654972 1.13444i −0.981901 0.189396i \(-0.939347\pi\)
0.326929 0.945049i \(-0.393986\pi\)
\(258\) 0 0
\(259\) 3.50000 6.06218i 0.217479 0.376685i
\(260\) −12.0000 −0.744208
\(261\) 0 0
\(262\) −6.00000 −0.370681
\(263\) −7.50000 + 12.9904i −0.462470 + 0.801021i −0.999083 0.0428069i \(-0.986370\pi\)
0.536614 + 0.843828i \(0.319703\pi\)
\(264\) 0 0
\(265\) 18.0000 + 31.1769i 1.10573 + 1.91518i
\(266\) 3.50000 + 6.06218i 0.214599 + 0.371696i
\(267\) 0 0
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) 15.0000 0.914566 0.457283 0.889321i \(-0.348823\pi\)
0.457283 + 0.889321i \(0.348823\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) −3.00000 + 5.19615i −0.181902 + 0.315063i
\(273\) 0 0
\(274\) 6.00000 + 10.3923i 0.362473 + 0.627822i
\(275\) 6.00000 + 10.3923i 0.361814 + 0.626680i
\(276\) 0 0
\(277\) −8.50000 + 14.7224i −0.510716 + 0.884585i 0.489207 + 0.872167i \(0.337286\pi\)
−0.999923 + 0.0124177i \(0.996047\pi\)
\(278\) −4.00000 −0.239904
\(279\) 0 0
\(280\) 3.00000 0.179284
\(281\) 9.00000 15.5885i 0.536895 0.929929i −0.462174 0.886789i \(-0.652930\pi\)
0.999069 0.0431402i \(-0.0137362\pi\)
\(282\) 0 0
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) 4.50000 + 7.79423i 0.267026 + 0.462502i
\(285\) 0 0
\(286\) −6.00000 + 10.3923i −0.354787 + 0.614510i
\(287\) 9.00000 0.531253
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) 0 0
\(292\) −1.00000 1.73205i −0.0585206 0.101361i
\(293\) 9.00000 + 15.5885i 0.525786 + 0.910687i 0.999549 + 0.0300351i \(0.00956192\pi\)
−0.473763 + 0.880652i \(0.657105\pi\)
\(294\) 0 0
\(295\) −9.00000 + 15.5885i −0.524000 + 0.907595i
\(296\) −7.00000 −0.406867
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) 6.00000 10.3923i 0.346989 0.601003i
\(300\) 0 0
\(301\) 5.00000 + 8.66025i 0.288195 + 0.499169i
\(302\) 5.00000 + 8.66025i 0.287718 + 0.498342i
\(303\) 0 0
\(304\) 3.50000 6.06218i 0.200739 0.347690i
\(305\) 24.0000 1.37424
\(306\) 0 0
\(307\) 29.0000 1.65512 0.827559 0.561379i \(-0.189729\pi\)
0.827559 + 0.561379i \(0.189729\pi\)
\(308\) 1.50000 2.59808i 0.0854704 0.148039i
\(309\) 0 0
\(310\) −7.50000 12.9904i −0.425971 0.737804i
\(311\) 6.00000 + 10.3923i 0.340229 + 0.589294i 0.984475 0.175525i \(-0.0561621\pi\)
−0.644246 + 0.764818i \(0.722829\pi\)
\(312\) 0 0
\(313\) 14.0000 24.2487i 0.791327 1.37062i −0.133819 0.991006i \(-0.542724\pi\)
0.925146 0.379612i \(-0.123943\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) −15.0000 + 25.9808i −0.842484 + 1.45922i 0.0453045 + 0.998973i \(0.485574\pi\)
−0.887788 + 0.460252i \(0.847759\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.50000 2.59808i −0.0838525 0.145237i
\(321\) 0 0
\(322\) −1.50000 + 2.59808i −0.0835917 + 0.144785i
\(323\) −42.0000 −2.33694
\(324\) 0 0
\(325\) −16.0000 −0.887520
\(326\) 8.00000 13.8564i 0.443079 0.767435i
\(327\) 0 0
\(328\) −4.50000 7.79423i −0.248471 0.430364i
\(329\) 3.00000 + 5.19615i 0.165395 + 0.286473i
\(330\) 0 0
\(331\) 14.0000 24.2487i 0.769510 1.33283i −0.168320 0.985732i \(-0.553834\pi\)
0.937829 0.347097i \(-0.112833\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 18.0000 0.984916
\(335\) 6.00000 10.3923i 0.327815 0.567792i
\(336\) 0 0
\(337\) 6.50000 + 11.2583i 0.354078 + 0.613280i 0.986960 0.160968i \(-0.0514616\pi\)
−0.632882 + 0.774248i \(0.718128\pi\)
\(338\) −1.50000 2.59808i −0.0815892 0.141317i
\(339\) 0 0
\(340\) −9.00000 + 15.5885i −0.488094 + 0.845403i
\(341\) −15.0000 −0.812296
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 5.00000 8.66025i 0.269582 0.466930i
\(345\) 0 0
\(346\) −10.5000 18.1865i −0.564483 0.977714i
\(347\) 1.50000 + 2.59808i 0.0805242 + 0.139472i 0.903475 0.428640i \(-0.141007\pi\)
−0.822951 + 0.568112i \(0.807674\pi\)
\(348\) 0 0
\(349\) 5.00000 8.66025i 0.267644 0.463573i −0.700609 0.713545i \(-0.747088\pi\)
0.968253 + 0.249973i \(0.0804216\pi\)
\(350\) 4.00000 0.213809
\(351\) 0 0
\(352\) −3.00000 −0.159901
\(353\) 10.5000 18.1865i 0.558859 0.967972i −0.438733 0.898617i \(-0.644573\pi\)
0.997592 0.0693543i \(-0.0220939\pi\)
\(354\) 0 0
\(355\) 13.5000 + 23.3827i 0.716506 + 1.24102i
\(356\) 7.50000 + 12.9904i 0.397499 + 0.688489i
\(357\) 0 0
\(358\) −12.0000 + 20.7846i −0.634220 + 1.09850i
\(359\) 12.0000 0.633336 0.316668 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) 0 0
\(361\) 30.0000 1.57895
\(362\) −1.00000 + 1.73205i −0.0525588 + 0.0910346i
\(363\) 0 0
\(364\) 2.00000 + 3.46410i 0.104828 + 0.181568i
\(365\) −3.00000 5.19615i −0.157027 0.271979i
\(366\) 0 0
\(367\) −8.50000 + 14.7224i −0.443696 + 0.768505i −0.997960 0.0638362i \(-0.979666\pi\)
0.554264 + 0.832341i \(0.313000\pi\)
\(368\) 3.00000 0.156386
\(369\) 0 0
\(370\) −21.0000 −1.09174
\(371\) 6.00000 10.3923i 0.311504 0.539542i
\(372\) 0 0
\(373\) 6.50000 + 11.2583i 0.336557 + 0.582934i 0.983783 0.179364i \(-0.0574041\pi\)
−0.647225 + 0.762299i \(0.724071\pi\)
\(374\) 9.00000 + 15.5885i 0.465379 + 0.806060i
\(375\) 0 0
\(376\) 3.00000 5.19615i 0.154713 0.267971i
\(377\) 0 0
\(378\) 0 0
\(379\) 2.00000 0.102733 0.0513665 0.998680i \(-0.483642\pi\)
0.0513665 + 0.998680i \(0.483642\pi\)
\(380\) 10.5000 18.1865i 0.538639 0.932949i
\(381\) 0 0
\(382\) 7.50000 + 12.9904i 0.383733 + 0.664646i
\(383\) −15.0000 25.9808i −0.766464 1.32755i −0.939469 0.342634i \(-0.888681\pi\)
0.173005 0.984921i \(-0.444652\pi\)
\(384\) 0 0
\(385\) 4.50000 7.79423i 0.229341 0.397231i
\(386\) 14.0000 0.712581
\(387\) 0 0
\(388\) 8.00000 0.406138
\(389\) 6.00000 10.3923i 0.304212 0.526911i −0.672874 0.739758i \(-0.734940\pi\)
0.977086 + 0.212847i \(0.0682735\pi\)
\(390\) 0 0
\(391\) −9.00000 15.5885i −0.455150 0.788342i
\(392\) −0.500000 0.866025i −0.0252538 0.0437409i
\(393\) 0 0
\(394\) −9.00000 + 15.5885i −0.453413 + 0.785335i
\(395\) −30.0000 −1.50946
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) 3.50000 6.06218i 0.175439 0.303870i
\(399\) 0 0
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) 12.0000 + 20.7846i 0.599251 + 1.03793i 0.992932 + 0.118686i \(0.0378683\pi\)
−0.393680 + 0.919247i \(0.628798\pi\)
\(402\) 0 0
\(403\) 10.0000 17.3205i 0.498135 0.862796i
\(404\) 6.00000 0.298511
\(405\) 0 0
\(406\) 0 0
\(407\) −10.5000 + 18.1865i −0.520466 + 0.901473i
\(408\) 0 0
\(409\) 11.0000 + 19.0526i 0.543915 + 0.942088i 0.998674 + 0.0514740i \(0.0163919\pi\)
−0.454759 + 0.890614i \(0.650275\pi\)
\(410\) −13.5000 23.3827i −0.666717 1.15479i
\(411\) 0 0
\(412\) −2.50000 + 4.33013i −0.123166 + 0.213330i
\(413\) 6.00000 0.295241
\(414\) 0 0
\(415\) 0 0
\(416\) 2.00000 3.46410i 0.0980581 0.169842i
\(417\) 0 0
\(418\) −10.5000 18.1865i −0.513572 0.889532i
\(419\) 9.00000 + 15.5885i 0.439679 + 0.761546i 0.997665 0.0683046i \(-0.0217590\pi\)
−0.557986 + 0.829851i \(0.688426\pi\)
\(420\) 0 0
\(421\) −8.50000 + 14.7224i −0.414265 + 0.717527i −0.995351 0.0963145i \(-0.969295\pi\)
0.581086 + 0.813842i \(0.302628\pi\)
\(422\) 14.0000 0.681509
\(423\) 0 0
\(424\) −12.0000 −0.582772
\(425\) −12.0000 + 20.7846i −0.582086 + 1.00820i
\(426\) 0 0
\(427\) −4.00000 6.92820i −0.193574 0.335279i
\(428\) −6.00000 10.3923i −0.290021 0.502331i
\(429\) 0 0
\(430\) 15.0000 25.9808i 0.723364 1.25290i
\(431\) −3.00000 −0.144505 −0.0722525 0.997386i \(-0.523019\pi\)
−0.0722525 + 0.997386i \(0.523019\pi\)
\(432\) 0 0
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) −2.50000 + 4.33013i −0.120004 + 0.207853i
\(435\) 0 0
\(436\) −5.50000 9.52628i −0.263402 0.456226i
\(437\) 10.5000 + 18.1865i 0.502283 + 0.869980i
\(438\) 0 0
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) −9.00000 −0.429058
\(441\) 0 0
\(442\) −24.0000 −1.14156
\(443\) −1.50000 + 2.59808i −0.0712672 + 0.123438i −0.899457 0.437009i \(-0.856038\pi\)
0.828190 + 0.560448i \(0.189371\pi\)
\(444\) 0 0
\(445\) 22.5000 + 38.9711i 1.06660 + 1.84741i
\(446\) 0.500000 + 0.866025i 0.0236757 + 0.0410075i
\(447\) 0 0
\(448\) −0.500000 + 0.866025i −0.0236228 + 0.0409159i
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) −27.0000 −1.27138
\(452\) −9.00000 + 15.5885i −0.423324 + 0.733219i
\(453\) 0 0
\(454\) −3.00000 5.19615i −0.140797 0.243868i
\(455\) 6.00000 + 10.3923i 0.281284 + 0.487199i
\(456\) 0 0
\(457\) 9.50000 16.4545i 0.444391 0.769708i −0.553618 0.832771i \(-0.686753\pi\)
0.998010 + 0.0630623i \(0.0200867\pi\)
\(458\) −4.00000 −0.186908
\(459\) 0 0
\(460\) 9.00000 0.419627
\(461\) 13.5000 23.3827i 0.628758 1.08904i −0.359044 0.933321i \(-0.616897\pi\)
0.987801 0.155719i \(-0.0497696\pi\)
\(462\) 0 0
\(463\) −7.00000 12.1244i −0.325318 0.563467i 0.656259 0.754536i \(-0.272138\pi\)
−0.981577 + 0.191069i \(0.938805\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 3.00000 5.19615i 0.138972 0.240707i
\(467\) −6.00000 −0.277647 −0.138823 0.990317i \(-0.544332\pi\)
−0.138823 + 0.990317i \(0.544332\pi\)
\(468\) 0 0
\(469\) −4.00000 −0.184703
\(470\) 9.00000 15.5885i 0.415139 0.719042i
\(471\) 0 0
\(472\) −3.00000 5.19615i −0.138086 0.239172i
\(473\) −15.0000 25.9808i −0.689701 1.19460i
\(474\) 0 0
\(475\) 14.0000 24.2487i 0.642364 1.11261i
\(476\) 6.00000 0.275010
\(477\) 0 0
\(478\) 0 0
\(479\) −12.0000 + 20.7846i −0.548294 + 0.949673i 0.450098 + 0.892979i \(0.351389\pi\)
−0.998392 + 0.0566937i \(0.981944\pi\)
\(480\) 0 0
\(481\) −14.0000 24.2487i −0.638345 1.10565i
\(482\) −13.0000 22.5167i −0.592134 1.02561i
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 24.0000 1.08978
\(486\) 0 0
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) −4.00000 + 6.92820i −0.181071 + 0.313625i
\(489\) 0 0
\(490\) −1.50000 2.59808i −0.0677631 0.117369i
\(491\) −4.50000 7.79423i −0.203082 0.351749i 0.746438 0.665455i \(-0.231763\pi\)
−0.949520 + 0.313707i \(0.898429\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 28.0000 1.25978
\(495\) 0 0
\(496\) 5.00000 0.224507
\(497\) 4.50000 7.79423i 0.201853 0.349619i
\(498\) 0 0
\(499\) 11.0000 + 19.0526i 0.492428 + 0.852910i 0.999962 0.00872186i \(-0.00277629\pi\)
−0.507534 + 0.861632i \(0.669443\pi\)
\(500\) 1.50000 + 2.59808i 0.0670820 + 0.116190i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 4.50000 7.79423i 0.200049 0.346496i
\(507\) 0 0
\(508\) −10.0000 17.3205i −0.443678 0.768473i
\(509\) −15.0000 25.9808i −0.664863 1.15158i −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) 0 0
\(511\) −1.00000 + 1.73205i −0.0442374 + 0.0766214i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 21.0000 0.926270
\(515\) −7.50000 + 12.9904i −0.330489 + 0.572425i
\(516\) 0 0
\(517\) −9.00000 15.5885i −0.395820 0.685580i
\(518\) 3.50000 + 6.06218i 0.153781 + 0.266357i
\(519\) 0 0
\(520\) 6.00000 10.3923i 0.263117 0.455733i
\(521\) 15.0000 0.657162 0.328581 0.944476i \(-0.393430\pi\)
0.328581 + 0.944476i \(0.393430\pi\)
\(522\) 0 0
\(523\) 29.0000 1.26808 0.634041 0.773300i \(-0.281395\pi\)
0.634041 + 0.773300i \(0.281395\pi\)
\(524\) 3.00000 5.19615i 0.131056 0.226995i
\(525\) 0 0
\(526\) −7.50000 12.9904i −0.327016 0.566408i
\(527\) −15.0000 25.9808i −0.653410 1.13174i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) −36.0000 −1.56374
\(531\) 0 0
\(532\) −7.00000 −0.303488
\(533\) 18.0000 31.1769i 0.779667 1.35042i
\(534\) 0 0
\(535\) −18.0000 31.1769i −0.778208 1.34790i
\(536\) 2.00000 + 3.46410i 0.0863868 + 0.149626i
\(537\) 0 0
\(538\) −7.50000 + 12.9904i −0.323348 + 0.560055i
\(539\) −3.00000 −0.129219
\(540\) 0 0
\(541\) −7.00000 −0.300954 −0.150477 0.988614i \(-0.548081\pi\)
−0.150477 + 0.988614i \(0.548081\pi\)
\(542\) 8.00000 13.8564i 0.343629 0.595184i
\(543\) 0 0
\(544\) −3.00000 5.19615i −0.128624 0.222783i
\(545\) −16.5000 28.5788i −0.706782 1.22418i
\(546\) 0 0
\(547\) 14.0000 24.2487i 0.598597 1.03680i −0.394432 0.918925i \(-0.629059\pi\)
0.993028 0.117875i \(-0.0376081\pi\)
\(548\) −12.0000 −0.512615
\(549\) 0 0
\(550\) −12.0000 −0.511682
\(551\) 0 0
\(552\) 0 0
\(553\) 5.00000 + 8.66025i 0.212622 + 0.368271i
\(554\) −8.50000 14.7224i −0.361130 0.625496i
\(555\) 0 0
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) 42.0000 1.77960 0.889799 0.456354i \(-0.150845\pi\)
0.889799 + 0.456354i \(0.150845\pi\)
\(558\) 0 0
\(559\) 40.0000 1.69182
\(560\) −1.50000 + 2.59808i −0.0633866 + 0.109789i
\(561\) 0 0
\(562\) 9.00000 + 15.5885i 0.379642 + 0.657559i
\(563\) −12.0000 20.7846i −0.505740 0.875967i −0.999978 0.00664037i \(-0.997886\pi\)
0.494238 0.869326i \(-0.335447\pi\)
\(564\) 0 0
\(565\) −27.0000 + 46.7654i −1.13590 + 1.96743i
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) −9.00000 −0.377632
\(569\) 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) 0 0
\(571\) −7.00000 12.1244i −0.292941 0.507388i 0.681563 0.731760i \(-0.261301\pi\)
−0.974504 + 0.224371i \(0.927967\pi\)
\(572\) −6.00000 10.3923i −0.250873 0.434524i
\(573\) 0 0
\(574\) −4.50000 + 7.79423i −0.187826 + 0.325325i
\(575\) 12.0000 0.500435
\(576\) 0 0
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) −9.50000 + 16.4545i −0.395148 + 0.684416i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −18.0000 + 31.1769i −0.745484 + 1.29122i
\(584\) 2.00000 0.0827606
\(585\) 0 0
\(586\) −18.0000 −0.743573
\(587\) 9.00000 15.5885i 0.371470 0.643404i −0.618322 0.785925i \(-0.712187\pi\)
0.989792 + 0.142520i \(0.0455206\pi\)
\(588\) 0 0
\(589\) 17.5000 + 30.3109i 0.721075 + 1.24894i
\(590\) −9.00000 15.5885i −0.370524 0.641767i
\(591\) 0 0
\(592\) 3.50000 6.06218i 0.143849 0.249154i
\(593\) −33.0000 −1.35515 −0.677574 0.735455i \(-0.736969\pi\)
−0.677574 + 0.735455i \(0.736969\pi\)
\(594\) 0 0
\(595\) 18.0000 0.737928
\(596\) 3.00000 5.19615i 0.122885 0.212843i
\(597\) 0 0
\(598\) 6.00000 + 10.3923i 0.245358 + 0.424973i
\(599\) −16.5000 28.5788i −0.674172 1.16770i −0.976710 0.214563i \(-0.931167\pi\)
0.302539 0.953137i \(-0.402166\pi\)
\(600\) 0 0
\(601\) 14.0000 24.2487i 0.571072 0.989126i −0.425384 0.905013i \(-0.639861\pi\)
0.996456 0.0841128i \(-0.0268056\pi\)
\(602\) −10.0000 −0.407570
\(603\) 0 0
\(604\) −10.0000 −0.406894
\(605\) 3.00000 5.19615i 0.121967 0.211254i
\(606\) 0 0
\(607\) 2.00000 + 3.46410i 0.0811775 + 0.140604i 0.903756 0.428048i \(-0.140799\pi\)
−0.822578 + 0.568652i \(0.807465\pi\)
\(608\) 3.50000 + 6.06218i 0.141944 + 0.245854i
\(609\) 0 0
\(610\) −12.0000 + 20.7846i −0.485866 + 0.841544i
\(611\) 24.0000 0.970936
\(612\) 0 0
\(613\) 29.0000 1.17130 0.585649 0.810564i \(-0.300840\pi\)
0.585649 + 0.810564i \(0.300840\pi\)
\(614\) −14.5000 + 25.1147i −0.585172 + 1.01355i
\(615\) 0 0
\(616\) 1.50000 + 2.59808i 0.0604367 + 0.104679i
\(617\) 9.00000 + 15.5885i 0.362326 + 0.627568i 0.988343 0.152242i \(-0.0486493\pi\)
−0.626017 + 0.779809i \(0.715316\pi\)
\(618\) 0 0
\(619\) −17.5000 + 30.3109i −0.703384 + 1.21830i 0.263887 + 0.964554i \(0.414995\pi\)
−0.967271 + 0.253744i \(0.918338\pi\)
\(620\) 15.0000 0.602414
\(621\) 0 0
\(622\) −12.0000 −0.481156
\(623\) 7.50000 12.9904i 0.300481 0.520449i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 14.0000 + 24.2487i 0.559553 + 0.969173i
\(627\) 0 0
\(628\) 2.00000 3.46410i 0.0798087 0.138233i
\(629\) −42.0000 −1.67465
\(630\) 0 0
\(631\) 38.0000 1.51276 0.756378 0.654135i \(-0.226967\pi\)
0.756378 + 0.654135i \(0.226967\pi\)
\(632\) 5.00000 8.66025i 0.198889 0.344486i
\(633\) 0 0
\(634\) −15.0000 25.9808i −0.595726 1.03183i
\(635\) −30.0000 51.9615i −1.19051 2.06203i
\(636\) 0 0
\(637\) 2.00000 3.46410i 0.0792429 0.137253i
\(638\) 0 0
\(639\) 0 0
\(640\) 3.00000 0.118585
\(641\) −3.00000 + 5.19615i −0.118493 + 0.205236i −0.919171 0.393860i \(-0.871140\pi\)
0.800678 + 0.599095i \(0.204473\pi\)
\(642\) 0 0
\(643\) −2.50000 4.33013i −0.0985904 0.170764i 0.812511 0.582946i \(-0.198100\pi\)
−0.911101 + 0.412182i \(0.864767\pi\)
\(644\) −1.50000 2.59808i −0.0591083 0.102379i
\(645\) 0 0
\(646\) 21.0000 36.3731i 0.826234 1.43108i
\(647\) 6.00000 0.235884 0.117942 0.993020i \(-0.462370\pi\)
0.117942 + 0.993020i \(0.462370\pi\)
\(648\) 0 0
\(649\) −18.0000 −0.706562
\(650\) 8.00000 13.8564i 0.313786 0.543493i
\(651\) 0 0
\(652\) 8.00000 + 13.8564i 0.313304 + 0.542659i
\(653\) 3.00000 + 5.19615i 0.117399 + 0.203341i 0.918736 0.394872i \(-0.129211\pi\)
−0.801337 + 0.598213i \(0.795878\pi\)
\(654\) 0 0
\(655\) 9.00000 15.5885i 0.351659 0.609091i
\(656\) 9.00000 0.351391
\(657\) 0 0
\(658\) −6.00000 −0.233904
\(659\) −4.50000 + 7.79423i −0.175295 + 0.303620i −0.940263 0.340448i \(-0.889421\pi\)
0.764968 + 0.644068i \(0.222755\pi\)
\(660\) 0 0
\(661\) 20.0000 + 34.6410i 0.777910 + 1.34738i 0.933144 + 0.359502i \(0.117053\pi\)
−0.155235 + 0.987878i \(0.549613\pi\)
\(662\) 14.0000 + 24.2487i 0.544125 + 0.942453i
\(663\) 0 0
\(664\) 0 0
\(665\) −21.0000 −0.814345
\(666\) 0 0
\(667\) 0 0
\(668\) −9.00000 + 15.5885i −0.348220 + 0.603136i
\(669\) 0 0
\(670\) 6.00000 + 10.3923i 0.231800 + 0.401490i
\(671\) 12.0000 + 20.7846i 0.463255 + 0.802381i
\(672\) 0 0
\(673\) 23.0000 39.8372i 0.886585 1.53561i 0.0426985 0.999088i \(-0.486405\pi\)
0.843886 0.536522i \(-0.180262\pi\)
\(674\) −13.0000 −0.500741
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) 7.50000 12.9904i 0.288248 0.499261i −0.685143 0.728408i \(-0.740260\pi\)
0.973392 + 0.229147i \(0.0735938\pi\)
\(678\) 0 0
\(679\) −4.00000 6.92820i −0.153506 0.265880i
\(680\) −9.00000 15.5885i −0.345134 0.597790i
\(681\) 0 0
\(682\) 7.50000 12.9904i 0.287190 0.497427i
\(683\) 15.0000 0.573959 0.286980 0.957937i \(-0.407349\pi\)
0.286980 + 0.957937i \(0.407349\pi\)
\(684\) 0 0
\(685\) −36.0000 −1.37549
\(686\) −0.500000 + 0.866025i −0.0190901 + 0.0330650i
\(687\) 0 0
\(688\) 5.00000 + 8.66025i 0.190623 + 0.330169i
\(689\) −24.0000 41.5692i −0.914327 1.58366i
\(690\) 0 0
\(691\) 14.0000 24.2487i 0.532585 0.922464i −0.466691 0.884420i \(-0.654554\pi\)
0.999276 0.0380440i \(-0.0121127\pi\)
\(692\) 21.0000 0.798300
\(693\) 0 0
\(694\) −3.00000 −0.113878
\(695\) 6.00000 10.3923i 0.227593 0.394203i
\(696\) 0 0
\(697\) −27.0000 46.7654i −1.02270 1.77136i
\(698\) 5.00000 + 8.66025i 0.189253 + 0.327795i
\(699\) 0 0
\(700\) −2.00000 + 3.46410i −0.0755929 + 0.130931i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 49.0000 1.84807
\(704\) 1.50000 2.59808i 0.0565334 0.0979187i
\(705\) 0 0
\(706\) 10.5000 + 18.1865i 0.395173 + 0.684459i
\(707\) −3.00000 5.19615i −0.112827 0.195421i
\(708\) 0 0
\(709\) −17.5000 + 30.3109i −0.657226 + 1.13835i 0.324104 + 0.946021i \(0.394937\pi\)
−0.981331 + 0.192328i \(0.938396\pi\)
\(710\) −27.0000 −1.01329
\(711\) 0 0
\(712\) −15.0000 −0.562149
\(713\) −7.50000 + 12.9904i −0.280877 + 0.486494i
\(714\) 0 0
\(715\) −18.0000 31.1769i −0.673162 1.16595i
\(716\) −12.0000 20.7846i −0.448461 0.776757i
\(717\) 0 0
\(718\) −6.00000 + 10.3923i −0.223918 + 0.387837i
\(719\) 30.0000 1.11881 0.559406 0.828894i \(-0.311029\pi\)
0.559406 + 0.828894i \(0.311029\pi\)
\(720\) 0 0
\(721\) 5.00000 0.186210
\(722\) −15.0000 + 25.9808i −0.558242 + 0.966904i
\(723\) 0 0
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) 0 0
\(726\) 0 0
\(727\) −4.00000 + 6.92820i −0.148352 + 0.256953i −0.930618 0.365991i \(-0.880730\pi\)
0.782267 + 0.622944i \(0.214063\pi\)
\(728\) −4.00000 −0.148250
\(729\) 0 0
\(730\) 6.00000 0.222070
\(731\) 30.0000 51.9615i 1.10959 1.92187i
\(732\) 0 0
\(733\) 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i \(-0.0334875\pi\)
−0.588177 + 0.808732i \(0.700154\pi\)
\(734\) −8.50000 14.7224i −0.313741 0.543415i
\(735\) 0 0
\(736\) −1.50000 + 2.59808i −0.0552907 + 0.0957664i
\(737\) 12.0000 0.442026
\(738\) 0 0
\(739\) −34.0000 −1.25071 −0.625355 0.780340i \(-0.715046\pi\)
−0.625355 + 0.780340i \(0.715046\pi\)
\(740\) 10.5000 18.1865i 0.385988 0.668550i
\(741\) 0 0
\(742\) 6.00000 + 10.3923i 0.220267 + 0.381514i
\(743\) 4.50000 + 7.79423i 0.165089 + 0.285943i 0.936687 0.350168i \(-0.113876\pi\)
−0.771598 + 0.636111i \(0.780542\pi\)
\(744\) 0 0
\(745\) 9.00000 15.5885i 0.329734 0.571117i
\(746\) −13.0000 −0.475964
\(747\) 0 0
\(748\) −18.0000 −0.658145
\(749\) −6.00000 + 10.3923i −0.219235 + 0.379727i
\(750\) 0 0
\(751\) 11.0000 + 19.0526i 0.401396 + 0.695238i 0.993895 0.110333i \(-0.0351919\pi\)
−0.592499 + 0.805571i \(0.701859\pi\)
\(752\) 3.00000 + 5.19615i 0.109399 + 0.189484i
\(753\) 0 0
\(754\) 0 0
\(755\) −30.0000 −1.09181
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −1.00000 + 1.73205i −0.0363216 + 0.0629109i
\(759\) 0 0
\(760\) 10.5000 + 18.1865i 0.380875 + 0.659695i
\(761\) 21.0000 + 36.3731i 0.761249 + 1.31852i 0.942207 + 0.335032i \(0.108747\pi\)
−0.180957 + 0.983491i \(0.557920\pi\)
\(762\) 0 0
\(763\) −5.50000 + 9.52628i −0.199113 + 0.344874i
\(764\) −15.0000 −0.542681
\(765\) 0 0
\(766\) 30.0000 1.08394
\(767\) 12.0000 20.7846i 0.433295 0.750489i
\(768\) 0 0
\(769\) 2.00000 + 3.46410i 0.0721218 + 0.124919i 0.899831 0.436239i \(-0.143690\pi\)
−0.827709 + 0.561157i \(0.810356\pi\)
\(770\) 4.50000 + 7.79423i 0.162169 + 0.280885i
\(771\) 0 0
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) −39.0000 −1.40273 −0.701366 0.712801i \(-0.747426\pi\)
−0.701366 + 0.712801i \(0.747426\pi\)
\(774\) 0 0
\(775\) 20.0000 0.718421
\(776\) −4.00000 + 6.92820i −0.143592 + 0.248708i
\(777\) 0 0
\(778\) 6.00000 + 10.3923i 0.215110 + 0.372582i
\(779\) 31.5000 + 54.5596i 1.12860 + 1.95480i
\(780\) 0 0
\(781\) −13.5000 + 23.3827i −0.483068 + 0.836698i
\(782\) 18.0000 0.643679
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 6.00000 10.3923i 0.214149 0.370917i
\(786\) 0 0
\(787\) −16.0000 27.7128i −0.570338 0.987855i −0.996531 0.0832226i \(-0.973479\pi\)
0.426193 0.904632i \(-0.359855\pi\)
\(788\) −9.00000 15.5885i −0.320612 0.555316i
\(789\) 0 0
\(790\) 15.0000 25.9808i 0.533676 0.924354i
\(791\) 18.0000 0.640006
\