Properties

Label 1134.2.f.p.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.p.757.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +4.00000 q^{10} +(-2.00000 + 3.46410i) q^{11} +(-1.50000 - 2.59808i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +7.00000 q^{17} +2.00000 q^{19} +(2.00000 - 3.46410i) q^{20} +(2.00000 + 3.46410i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-5.50000 + 9.52628i) q^{25} -3.00000 q^{26} -1.00000 q^{28} +(0.500000 - 0.866025i) q^{29} +(4.50000 + 7.79423i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.50000 - 6.06218i) q^{34} +4.00000 q^{35} +2.00000 q^{37} +(1.00000 - 1.73205i) q^{38} +(-2.00000 - 3.46410i) q^{40} +(3.00000 + 5.19615i) q^{41} +(-5.50000 + 9.52628i) q^{43} +4.00000 q^{44} -1.00000 q^{46} +(-3.00000 + 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(5.50000 + 9.52628i) q^{50} +(-1.50000 + 2.59808i) q^{52} +9.00000 q^{53} -16.0000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-0.500000 - 0.866025i) q^{58} +(-2.50000 - 4.33013i) q^{59} +(3.00000 - 5.19615i) q^{61} +9.00000 q^{62} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +(-3.50000 - 6.06218i) q^{67} +(-3.50000 - 6.06218i) q^{68} +(2.00000 - 3.46410i) q^{70} +7.00000 q^{71} -14.0000 q^{73} +(1.00000 - 1.73205i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(2.00000 + 3.46410i) q^{77} +(3.00000 - 5.19615i) q^{79} -4.00000 q^{80} +6.00000 q^{82} +(-2.00000 + 3.46410i) q^{83} +(14.0000 + 24.2487i) q^{85} +(5.50000 + 9.52628i) q^{86} +(2.00000 - 3.46410i) q^{88} +3.00000 q^{89} -3.00000 q^{91} +(-0.500000 + 0.866025i) q^{92} +(3.00000 + 5.19615i) q^{94} +(4.00000 + 6.92820i) q^{95} +(4.00000 - 6.92820i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} + 4q^{5} + q^{7} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{4} + 4q^{5} + q^{7} - 2q^{8} + 8q^{10} - 4q^{11} - 3q^{13} - q^{14} - q^{16} + 14q^{17} + 4q^{19} + 4q^{20} + 4q^{22} - q^{23} - 11q^{25} - 6q^{26} - 2q^{28} + q^{29} + 9q^{31} + q^{32} + 7q^{34} + 8q^{35} + 4q^{37} + 2q^{38} - 4q^{40} + 6q^{41} - 11q^{43} + 8q^{44} - 2q^{46} - 6q^{47} - q^{49} + 11q^{50} - 3q^{52} + 18q^{53} - 32q^{55} - q^{56} - q^{58} - 5q^{59} + 6q^{61} + 18q^{62} + 2q^{64} + 12q^{65} - 7q^{67} - 7q^{68} + 4q^{70} + 14q^{71} - 28q^{73} + 2q^{74} - 2q^{76} + 4q^{77} + 6q^{79} - 8q^{80} + 12q^{82} - 4q^{83} + 28q^{85} + 11q^{86} + 4q^{88} + 6q^{89} - 6q^{91} - q^{92} + 6q^{94} + 8q^{95} + 8q^{97} - 2q^{98} + O(q^{100}) \)

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
\(5\) 2.00000 + 3.46410i 0.894427 + 1.54919i 0.834512 + 0.550990i \(0.185750\pi\)
0.0599153 + 0.998203i \(0.480917\pi\)
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 4.00000 1.26491
\(11\) −2.00000 + 3.46410i −0.603023 + 1.04447i 0.389338 + 0.921095i \(0.372704\pi\)
−0.992361 + 0.123371i \(0.960630\pi\)
\(12\) 0 0
\(13\) −1.50000 2.59808i −0.416025 0.720577i 0.579510 0.814965i \(-0.303244\pi\)
−0.995535 + 0.0943882i \(0.969911\pi\)
\(14\) −0.500000 0.866025i −0.133631 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 7.00000 1.69775 0.848875 0.528594i \(-0.177281\pi\)
0.848875 + 0.528594i \(0.177281\pi\)
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 2.00000 3.46410i 0.447214 0.774597i
\(21\) 0 0
\(22\) 2.00000 + 3.46410i 0.426401 + 0.738549i
\(23\) −0.500000 0.866025i −0.104257 0.180579i 0.809177 0.587565i \(-0.199913\pi\)
−0.913434 + 0.406986i \(0.866580\pi\)
\(24\) 0 0
\(25\) −5.50000 + 9.52628i −1.10000 + 1.90526i
\(26\) −3.00000 −0.588348
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) 0.500000 0.866025i 0.0928477 0.160817i −0.815861 0.578249i \(-0.803736\pi\)
0.908708 + 0.417432i \(0.137070\pi\)
\(30\) 0 0
\(31\) 4.50000 + 7.79423i 0.808224 + 1.39988i 0.914093 + 0.405505i \(0.132904\pi\)
−0.105869 + 0.994380i \(0.533762\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 3.50000 6.06218i 0.600245 1.03965i
\(35\) 4.00000 0.676123
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 1.00000 1.73205i 0.162221 0.280976i
\(39\) 0 0
\(40\) −2.00000 3.46410i −0.316228 0.547723i
\(41\) 3.00000 + 5.19615i 0.468521 + 0.811503i 0.999353 0.0359748i \(-0.0114536\pi\)
−0.530831 + 0.847477i \(0.678120\pi\)
\(42\) 0 0
\(43\) −5.50000 + 9.52628i −0.838742 + 1.45274i 0.0522047 + 0.998636i \(0.483375\pi\)
−0.890947 + 0.454108i \(0.849958\pi\)
\(44\) 4.00000 0.603023
\(45\) 0 0
\(46\) −1.00000 −0.147442
\(47\) −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 5.50000 + 9.52628i 0.777817 + 1.34722i
\(51\) 0 0
\(52\) −1.50000 + 2.59808i −0.208013 + 0.360288i
\(53\) 9.00000 1.23625 0.618123 0.786082i \(-0.287894\pi\)
0.618123 + 0.786082i \(0.287894\pi\)
\(54\) 0 0
\(55\) −16.0000 −2.15744
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 0 0
\(58\) −0.500000 0.866025i −0.0656532 0.113715i
\(59\) −2.50000 4.33013i −0.325472 0.563735i 0.656136 0.754643i \(-0.272190\pi\)
−0.981608 + 0.190909i \(0.938857\pi\)
\(60\) 0 0
\(61\) 3.00000 5.19615i 0.384111 0.665299i −0.607535 0.794293i \(-0.707841\pi\)
0.991645 + 0.128994i \(0.0411748\pi\)
\(62\) 9.00000 1.14300
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 6.00000 10.3923i 0.744208 1.28901i
\(66\) 0 0
\(67\) −3.50000 6.06218i −0.427593 0.740613i 0.569066 0.822292i \(-0.307305\pi\)
−0.996659 + 0.0816792i \(0.973972\pi\)
\(68\) −3.50000 6.06218i −0.424437 0.735147i
\(69\) 0 0
\(70\) 2.00000 3.46410i 0.239046 0.414039i
\(71\) 7.00000 0.830747 0.415374 0.909651i \(-0.363651\pi\)
0.415374 + 0.909651i \(0.363651\pi\)
\(72\) 0 0
\(73\) −14.0000 −1.63858 −0.819288 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) 0 0
\(76\) −1.00000 1.73205i −0.114708 0.198680i
\(77\) 2.00000 + 3.46410i 0.227921 + 0.394771i
\(78\) 0 0
\(79\) 3.00000 5.19615i 0.337526 0.584613i −0.646440 0.762964i \(-0.723743\pi\)
0.983967 + 0.178352i \(0.0570765\pi\)
\(80\) −4.00000 −0.447214
\(81\) 0 0
\(82\) 6.00000 0.662589
\(83\) −2.00000 + 3.46410i −0.219529 + 0.380235i −0.954664 0.297686i \(-0.903785\pi\)
0.735135 + 0.677920i \(0.237119\pi\)
\(84\) 0 0
\(85\) 14.0000 + 24.2487i 1.51851 + 2.63014i
\(86\) 5.50000 + 9.52628i 0.593080 + 1.02725i
\(87\) 0 0
\(88\) 2.00000 3.46410i 0.213201 0.369274i
\(89\) 3.00000 0.317999 0.159000 0.987279i \(-0.449173\pi\)
0.159000 + 0.987279i \(0.449173\pi\)
\(90\) 0 0
\(91\) −3.00000 −0.314485
\(92\) −0.500000 + 0.866025i −0.0521286 + 0.0902894i
\(93\) 0 0
\(94\) 3.00000 + 5.19615i 0.309426 + 0.535942i
\(95\) 4.00000 + 6.92820i 0.410391 + 0.710819i
\(96\) 0 0
\(97\) 4.00000 6.92820i 0.406138 0.703452i −0.588315 0.808632i \(-0.700208\pi\)
0.994453 + 0.105180i \(0.0335417\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) 11.0000 1.10000
\(101\) 5.00000 8.66025i 0.497519 0.861727i −0.502477 0.864590i \(-0.667578\pi\)
0.999996 + 0.00286291i \(0.000911295\pi\)
\(102\) 0 0
\(103\) −8.50000 14.7224i −0.837530 1.45064i −0.891954 0.452126i \(-0.850666\pi\)
0.0544240 0.998518i \(-0.482668\pi\)
\(104\) 1.50000 + 2.59808i 0.147087 + 0.254762i
\(105\) 0 0
\(106\) 4.50000 7.79423i 0.437079 0.757042i
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) 16.0000 1.53252 0.766261 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) −8.00000 + 13.8564i −0.762770 + 1.32116i
\(111\) 0 0
\(112\) 0.500000 + 0.866025i 0.0472456 + 0.0818317i
\(113\) −4.00000 6.92820i −0.376288 0.651751i 0.614231 0.789127i \(-0.289466\pi\)
−0.990519 + 0.137376i \(0.956133\pi\)
\(114\) 0 0
\(115\) 2.00000 3.46410i 0.186501 0.323029i
\(116\) −1.00000 −0.0928477
\(117\) 0 0
\(118\) −5.00000 −0.460287
\(119\) 3.50000 6.06218i 0.320844 0.555719i
\(120\) 0 0
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) −3.00000 5.19615i −0.271607 0.470438i
\(123\) 0 0
\(124\) 4.50000 7.79423i 0.404112 0.699942i
\(125\) −24.0000 −2.14663
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −6.00000 10.3923i −0.526235 0.911465i
\(131\) 0.500000 + 0.866025i 0.0436852 + 0.0756650i 0.887041 0.461690i \(-0.152757\pi\)
−0.843356 + 0.537355i \(0.819423\pi\)
\(132\) 0 0
\(133\) 1.00000 1.73205i 0.0867110 0.150188i
\(134\) −7.00000 −0.604708
\(135\) 0 0
\(136\) −7.00000 −0.600245
\(137\) 11.0000 19.0526i 0.939793 1.62777i 0.173939 0.984757i \(-0.444351\pi\)
0.765855 0.643013i \(-0.222316\pi\)
\(138\) 0 0
\(139\) −5.00000 8.66025i −0.424094 0.734553i 0.572241 0.820086i \(-0.306074\pi\)
−0.996335 + 0.0855324i \(0.972741\pi\)
\(140\) −2.00000 3.46410i −0.169031 0.292770i
\(141\) 0 0
\(142\) 3.50000 6.06218i 0.293713 0.508727i
\(143\) 12.0000 1.00349
\(144\) 0 0
\(145\) 4.00000 0.332182
\(146\) −7.00000 + 12.1244i −0.579324 + 1.00342i
\(147\) 0 0
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) −1.50000 2.59808i −0.122885 0.212843i 0.798019 0.602632i \(-0.205881\pi\)
−0.920904 + 0.389789i \(0.872548\pi\)
\(150\) 0 0
\(151\) −5.00000 + 8.66025i −0.406894 + 0.704761i −0.994540 0.104357i \(-0.966722\pi\)
0.587646 + 0.809118i \(0.300055\pi\)
\(152\) −2.00000 −0.162221
\(153\) 0 0
\(154\) 4.00000 0.322329
\(155\) −18.0000 + 31.1769i −1.44579 + 2.50419i
\(156\) 0 0
\(157\) −8.50000 14.7224i −0.678374 1.17498i −0.975470 0.220131i \(-0.929352\pi\)
0.297097 0.954847i \(-0.403982\pi\)
\(158\) −3.00000 5.19615i −0.238667 0.413384i
\(159\) 0 0
\(160\) −2.00000 + 3.46410i −0.158114 + 0.273861i
\(161\) −1.00000 −0.0788110
\(162\) 0 0
\(163\) −1.00000 −0.0783260 −0.0391630 0.999233i \(-0.512469\pi\)
−0.0391630 + 0.999233i \(0.512469\pi\)
\(164\) 3.00000 5.19615i 0.234261 0.405751i
\(165\) 0 0
\(166\) 2.00000 + 3.46410i 0.155230 + 0.268866i
\(167\) −4.00000 6.92820i −0.309529 0.536120i 0.668730 0.743505i \(-0.266838\pi\)
−0.978259 + 0.207385i \(0.933505\pi\)
\(168\) 0 0
\(169\) 2.00000 3.46410i 0.153846 0.266469i
\(170\) 28.0000 2.14750
\(171\) 0 0
\(172\) 11.0000 0.838742
\(173\) −4.00000 + 6.92820i −0.304114 + 0.526742i −0.977064 0.212947i \(-0.931694\pi\)
0.672949 + 0.739689i \(0.265027\pi\)
\(174\) 0 0
\(175\) 5.50000 + 9.52628i 0.415761 + 0.720119i
\(176\) −2.00000 3.46410i −0.150756 0.261116i
\(177\) 0 0
\(178\) 1.50000 2.59808i 0.112430 0.194734i
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −9.00000 −0.668965 −0.334482 0.942402i \(-0.608561\pi\)
−0.334482 + 0.942402i \(0.608561\pi\)
\(182\) −1.50000 + 2.59808i −0.111187 + 0.192582i
\(183\) 0 0
\(184\) 0.500000 + 0.866025i 0.0368605 + 0.0638442i
\(185\) 4.00000 + 6.92820i 0.294086 + 0.509372i
\(186\) 0 0
\(187\) −14.0000 + 24.2487i −1.02378 + 1.77324i
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i \(-0.690384\pi\)
0.997225 + 0.0744412i \(0.0237173\pi\)
\(192\) 0 0
\(193\) −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i \(-0.224262\pi\)
−0.941865 + 0.335993i \(0.890928\pi\)
\(194\) −4.00000 6.92820i −0.287183 0.497416i
\(195\) 0 0
\(196\) −0.500000 + 0.866025i −0.0357143 + 0.0618590i
\(197\) −26.0000 −1.85242 −0.926212 0.377004i \(-0.876954\pi\)
−0.926212 + 0.377004i \(0.876954\pi\)
\(198\) 0 0
\(199\) −7.00000 −0.496217 −0.248108 0.968732i \(-0.579809\pi\)
−0.248108 + 0.968732i \(0.579809\pi\)
\(200\) 5.50000 9.52628i 0.388909 0.673610i
\(201\) 0 0
\(202\) −5.00000 8.66025i −0.351799 0.609333i
\(203\) −0.500000 0.866025i −0.0350931 0.0607831i
\(204\) 0 0
\(205\) −12.0000 + 20.7846i −0.838116 + 1.45166i
\(206\) −17.0000 −1.18445
\(207\) 0 0
\(208\) 3.00000 0.208013
\(209\) −4.00000 + 6.92820i −0.276686 + 0.479234i
\(210\) 0 0
\(211\) 0.500000 + 0.866025i 0.0344214 + 0.0596196i 0.882723 0.469894i \(-0.155708\pi\)
−0.848301 + 0.529514i \(0.822374\pi\)
\(212\) −4.50000 7.79423i −0.309061 0.535310i
\(213\) 0 0
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) −44.0000 −3.00078
\(216\) 0 0
\(217\) 9.00000 0.610960
\(218\) 8.00000 13.8564i 0.541828 0.938474i
\(219\) 0 0
\(220\) 8.00000 + 13.8564i 0.539360 + 0.934199i
\(221\) −10.5000 18.1865i −0.706306 1.22336i
\(222\) 0 0
\(223\) −4.00000 + 6.92820i −0.267860 + 0.463947i −0.968309 0.249756i \(-0.919650\pi\)
0.700449 + 0.713702i \(0.252983\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −8.00000 −0.532152
\(227\) −4.50000 + 7.79423i −0.298675 + 0.517321i −0.975833 0.218517i \(-0.929878\pi\)
0.677158 + 0.735838i \(0.263211\pi\)
\(228\) 0 0
\(229\) 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i \(-0.0135930\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(230\) −2.00000 3.46410i −0.131876 0.228416i
\(231\) 0 0
\(232\) −0.500000 + 0.866025i −0.0328266 + 0.0568574i
\(233\) 4.00000 0.262049 0.131024 0.991379i \(-0.458173\pi\)
0.131024 + 0.991379i \(0.458173\pi\)
\(234\) 0 0
\(235\) −24.0000 −1.56559
\(236\) −2.50000 + 4.33013i −0.162736 + 0.281867i
\(237\) 0 0
\(238\) −3.50000 6.06218i −0.226871 0.392953i
\(239\) 6.00000 + 10.3923i 0.388108 + 0.672222i 0.992195 0.124696i \(-0.0397955\pi\)
−0.604087 + 0.796918i \(0.706462\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) −5.00000 −0.321412
\(243\) 0 0
\(244\) −6.00000 −0.384111
\(245\) 2.00000 3.46410i 0.127775 0.221313i
\(246\) 0 0
\(247\) −3.00000 5.19615i −0.190885 0.330623i
\(248\) −4.50000 7.79423i −0.285750 0.494934i
\(249\) 0 0
\(250\) −12.0000 + 20.7846i −0.758947 + 1.31453i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 15.0000 + 25.9808i 0.935674 + 1.62064i 0.773427 + 0.633885i \(0.218541\pi\)
0.162247 + 0.986750i \(0.448126\pi\)
\(258\) 0 0
\(259\) 1.00000 1.73205i 0.0621370 0.107624i
\(260\) −12.0000 −0.744208
\(261\) 0 0
\(262\) 1.00000 0.0617802
\(263\) 4.50000 7.79423i 0.277482 0.480613i −0.693276 0.720672i \(-0.743833\pi\)
0.970758 + 0.240059i \(0.0771668\pi\)
\(264\) 0 0
\(265\) 18.0000 + 31.1769i 1.10573 + 1.91518i
\(266\) −1.00000 1.73205i −0.0613139 0.106199i
\(267\) 0 0
\(268\) −3.50000 + 6.06218i −0.213797 + 0.370306i
\(269\) −4.00000 −0.243884 −0.121942 0.992537i \(-0.538912\pi\)
−0.121942 + 0.992537i \(0.538912\pi\)
\(270\) 0 0
\(271\) 3.00000 0.182237 0.0911185 0.995840i \(-0.470956\pi\)
0.0911185 + 0.995840i \(0.470956\pi\)
\(272\) −3.50000 + 6.06218i −0.212219 + 0.367574i
\(273\) 0 0
\(274\) −11.0000 19.0526i −0.664534 1.15101i
\(275\) −22.0000 38.1051i −1.32665 2.29783i
\(276\) 0 0
\(277\) −4.00000 + 6.92820i −0.240337 + 0.416275i −0.960810 0.277207i \(-0.910591\pi\)
0.720473 + 0.693482i \(0.243925\pi\)
\(278\) −10.0000 −0.599760
\(279\) 0 0
\(280\) −4.00000 −0.239046
\(281\) −5.00000 + 8.66025i −0.298275 + 0.516627i −0.975741 0.218926i \(-0.929745\pi\)
0.677466 + 0.735554i \(0.263078\pi\)
\(282\) 0 0
\(283\) −14.0000 24.2487i −0.832214 1.44144i −0.896279 0.443491i \(-0.853740\pi\)
0.0640654 0.997946i \(-0.479593\pi\)
\(284\) −3.50000 6.06218i −0.207687 0.359724i
\(285\) 0 0
\(286\) 6.00000 10.3923i 0.354787 0.614510i
\(287\) 6.00000 0.354169
\(288\) 0 0
\(289\) 32.0000 1.88235
\(290\) 2.00000 3.46410i 0.117444 0.203419i
\(291\) 0 0
\(292\) 7.00000 + 12.1244i 0.409644 + 0.709524i
\(293\) 3.00000 + 5.19615i 0.175262 + 0.303562i 0.940252 0.340480i \(-0.110589\pi\)
−0.764990 + 0.644042i \(0.777256\pi\)
\(294\) 0 0
\(295\) 10.0000 17.3205i 0.582223 1.00844i
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) −3.00000 −0.173785
\(299\) −1.50000 + 2.59808i −0.0867472 + 0.150251i
\(300\) 0 0
\(301\) 5.50000 + 9.52628i 0.317015 + 0.549086i
\(302\) 5.00000 + 8.66025i 0.287718 + 0.498342i
\(303\) 0 0
\(304\) −1.00000 + 1.73205i −0.0573539 + 0.0993399i
\(305\) 24.0000 1.37424
\(306\) 0 0
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) 2.00000 3.46410i 0.113961 0.197386i
\(309\) 0 0
\(310\) 18.0000 + 31.1769i 1.02233 + 1.77073i
\(311\) −4.00000 6.92820i −0.226819 0.392862i 0.730044 0.683400i \(-0.239499\pi\)
−0.956864 + 0.290537i \(0.906166\pi\)
\(312\) 0 0
\(313\) 13.0000 22.5167i 0.734803 1.27272i −0.220006 0.975499i \(-0.570608\pi\)
0.954810 0.297218i \(-0.0960589\pi\)
\(314\) −17.0000 −0.959366
\(315\) 0 0
\(316\) −6.00000 −0.337526
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 0 0
\(319\) 2.00000 + 3.46410i 0.111979 + 0.193952i
\(320\) 2.00000 + 3.46410i 0.111803 + 0.193649i
\(321\) 0 0
\(322\) −0.500000 + 0.866025i −0.0278639 + 0.0482617i
\(323\) 14.0000 0.778981
\(324\) 0 0
\(325\) 33.0000 1.83051
\(326\) −0.500000 + 0.866025i −0.0276924 + 0.0479647i
\(327\) 0 0
\(328\) −3.00000 5.19615i −0.165647 0.286910i
\(329\) 3.00000 + 5.19615i 0.165395 + 0.286473i
\(330\) 0 0
\(331\) 15.5000 26.8468i 0.851957 1.47563i −0.0274825 0.999622i \(-0.508749\pi\)
0.879440 0.476011i \(-0.157918\pi\)
\(332\) 4.00000 0.219529
\(333\) 0 0
\(334\) −8.00000 −0.437741
\(335\) 14.0000 24.2487i 0.764902 1.32485i
\(336\) 0 0
\(337\) −13.5000 23.3827i −0.735392 1.27374i −0.954551 0.298047i \(-0.903665\pi\)
0.219159 0.975689i \(-0.429669\pi\)
\(338\) −2.00000 3.46410i −0.108786 0.188422i
\(339\) 0 0
\(340\) 14.0000 24.2487i 0.759257 1.31507i
\(341\) −36.0000 −1.94951
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 5.50000 9.52628i 0.296540 0.513623i
\(345\) 0 0
\(346\) 4.00000 + 6.92820i 0.215041 + 0.372463i
\(347\) 9.00000 + 15.5885i 0.483145 + 0.836832i 0.999813 0.0193540i \(-0.00616095\pi\)
−0.516667 + 0.856186i \(0.672828\pi\)
\(348\) 0 0
\(349\) −12.5000 + 21.6506i −0.669110 + 1.15893i 0.309044 + 0.951048i \(0.399991\pi\)
−0.978153 + 0.207884i \(0.933342\pi\)
\(350\) 11.0000 0.587975
\(351\) 0 0
\(352\) −4.00000 −0.213201
\(353\) 7.50000 12.9904i 0.399185 0.691408i −0.594441 0.804139i \(-0.702627\pi\)
0.993626 + 0.112731i \(0.0359599\pi\)
\(354\) 0 0
\(355\) 14.0000 + 24.2487i 0.743043 + 1.28699i
\(356\) −1.50000 2.59808i −0.0794998 0.137698i
\(357\) 0 0
\(358\) 6.00000 10.3923i 0.317110 0.549250i
\(359\) 11.0000 0.580558 0.290279 0.956942i \(-0.406252\pi\)
0.290279 + 0.956942i \(0.406252\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) −4.50000 + 7.79423i −0.236515 + 0.409656i
\(363\) 0 0
\(364\) 1.50000 + 2.59808i 0.0786214 + 0.136176i
\(365\) −28.0000 48.4974i −1.46559 2.53847i
\(366\) 0 0
\(367\) 12.5000 21.6506i 0.652495 1.13015i −0.330021 0.943974i \(-0.607056\pi\)
0.982516 0.186180i \(-0.0596109\pi\)
\(368\) 1.00000 0.0521286
\(369\) 0 0
\(370\) 8.00000 0.415900
\(371\) 4.50000 7.79423i 0.233628 0.404656i
\(372\) 0 0
\(373\) 19.0000 + 32.9090i 0.983783 + 1.70396i 0.647225 + 0.762299i \(0.275929\pi\)
0.336557 + 0.941663i \(0.390737\pi\)
\(374\) 14.0000 + 24.2487i 0.723923 + 1.25387i
\(375\) 0 0
\(376\) 3.00000 5.19615i 0.154713 0.267971i
\(377\) −3.00000 −0.154508
\(378\) 0 0
\(379\) −8.00000 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(380\) 4.00000 6.92820i 0.205196 0.355409i
\(381\) 0 0
\(382\) −6.00000 10.3923i −0.306987 0.531717i
\(383\) −2.00000 3.46410i −0.102195 0.177007i 0.810394 0.585886i \(-0.199253\pi\)
−0.912589 + 0.408879i \(0.865920\pi\)
\(384\) 0 0
\(385\) −8.00000 + 13.8564i −0.407718 + 0.706188i
\(386\) −5.00000 −0.254493
\(387\) 0 0
\(388\) −8.00000 −0.406138
\(389\) −7.00000 + 12.1244i −0.354914 + 0.614729i −0.987103 0.160085i \(-0.948823\pi\)
0.632189 + 0.774814i \(0.282157\pi\)
\(390\) 0 0
\(391\) −3.50000 6.06218i −0.177003 0.306578i
\(392\) 0.500000 + 0.866025i 0.0252538 + 0.0437409i
\(393\) 0 0
\(394\) −13.0000 + 22.5167i −0.654931 + 1.13437i
\(395\) 24.0000 1.20757
\(396\) 0 0
\(397\) 6.00000 0.301131 0.150566 0.988600i \(-0.451890\pi\)
0.150566 + 0.988600i \(0.451890\pi\)
\(398\) −3.50000 + 6.06218i −0.175439 + 0.303870i
\(399\) 0 0
\(400\) −5.50000 9.52628i −0.275000 0.476314i
\(401\) 15.0000 + 25.9808i 0.749064 + 1.29742i 0.948272 + 0.317460i \(0.102830\pi\)
−0.199207 + 0.979957i \(0.563837\pi\)
\(402\) 0 0
\(403\) 13.5000 23.3827i 0.672483 1.16477i
\(404\) −10.0000 −0.497519
\(405\) 0 0
\(406\) −1.00000 −0.0496292
\(407\) −4.00000 + 6.92820i −0.198273 + 0.343418i
\(408\) 0 0
\(409\) −1.00000 1.73205i −0.0494468 0.0856444i 0.840243 0.542211i \(-0.182412\pi\)
−0.889689 + 0.456566i \(0.849079\pi\)
\(410\) 12.0000 + 20.7846i 0.592638 + 1.02648i
\(411\) 0 0
\(412\) −8.50000 + 14.7224i −0.418765 + 0.725322i
\(413\) −5.00000 −0.246034
\(414\) 0 0
\(415\) −16.0000 −0.785409
\(416\) 1.50000 2.59808i 0.0735436 0.127381i
\(417\) 0 0
\(418\) 4.00000 + 6.92820i 0.195646 + 0.338869i
\(419\) −16.5000 28.5788i −0.806078 1.39617i −0.915561 0.402179i \(-0.868253\pi\)
0.109483 0.993989i \(-0.465080\pi\)
\(420\) 0 0
\(421\) 3.00000 5.19615i 0.146211 0.253245i −0.783613 0.621249i \(-0.786625\pi\)
0.929824 + 0.368004i \(0.119959\pi\)
\(422\) 1.00000 0.0486792
\(423\) 0 0
\(424\) −9.00000 −0.437079
\(425\) −38.5000 + 66.6840i −1.86752 + 3.23465i
\(426\) 0 0
\(427\) −3.00000 5.19615i −0.145180 0.251459i
\(428\) 6.00000 + 10.3923i 0.290021 + 0.502331i
\(429\) 0 0
\(430\) −22.0000 + 38.1051i −1.06093 + 1.83759i
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 0 0
\(433\) 8.00000 0.384455 0.192228 0.981350i \(-0.438429\pi\)
0.192228 + 0.981350i \(0.438429\pi\)
\(434\) 4.50000 7.79423i 0.216007 0.374135i
\(435\) 0 0
\(436\) −8.00000 13.8564i −0.383131 0.663602i
\(437\) −1.00000 1.73205i −0.0478365 0.0828552i
\(438\) 0 0
\(439\) −4.50000 + 7.79423i −0.214773 + 0.371998i −0.953202 0.302333i \(-0.902235\pi\)
0.738429 + 0.674331i \(0.235568\pi\)
\(440\) 16.0000 0.762770
\(441\) 0 0
\(442\) −21.0000 −0.998868
\(443\) 13.0000 22.5167i 0.617649 1.06980i −0.372265 0.928126i \(-0.621419\pi\)
0.989914 0.141672i \(-0.0452479\pi\)
\(444\) 0 0
\(445\) 6.00000 + 10.3923i 0.284427 + 0.492642i
\(446\) 4.00000 + 6.92820i 0.189405 + 0.328060i
\(447\) 0 0
\(448\) 0.500000 0.866025i 0.0236228 0.0409159i
\(449\) −4.00000 −0.188772 −0.0943858 0.995536i \(-0.530089\pi\)
−0.0943858 + 0.995536i \(0.530089\pi\)
\(450\) 0 0
\(451\) −24.0000 −1.13012
\(452\) −4.00000 + 6.92820i −0.188144 + 0.325875i
\(453\) 0 0
\(454\) 4.50000 + 7.79423i 0.211195 + 0.365801i
\(455\) −6.00000 10.3923i −0.281284 0.487199i
\(456\) 0 0
\(457\) 14.5000 25.1147i 0.678281 1.17482i −0.297217 0.954810i \(-0.596058\pi\)
0.975498 0.220008i \(-0.0706083\pi\)
\(458\) 14.0000 0.654177
\(459\) 0 0
\(460\) −4.00000 −0.186501
\(461\) −7.00000 + 12.1244i −0.326023 + 0.564688i −0.981719 0.190337i \(-0.939042\pi\)
0.655696 + 0.755025i \(0.272375\pi\)
\(462\) 0 0
\(463\) −11.0000 19.0526i −0.511213 0.885448i −0.999916 0.0129968i \(-0.995863\pi\)
0.488702 0.872451i \(-0.337470\pi\)
\(464\) 0.500000 + 0.866025i 0.0232119 + 0.0402042i
\(465\) 0 0
\(466\) 2.00000 3.46410i 0.0926482 0.160471i
\(467\) 8.00000 0.370196 0.185098 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) 0 0
\(469\) −7.00000 −0.323230
\(470\) −12.0000 + 20.7846i −0.553519 + 0.958723i
\(471\) 0 0
\(472\) 2.50000 + 4.33013i 0.115072 + 0.199310i
\(473\) −22.0000 38.1051i −1.01156 1.75208i
\(474\) 0 0
\(475\) −11.0000 + 19.0526i −0.504715 + 0.874191i
\(476\) −7.00000 −0.320844
\(477\) 0 0
\(478\) 12.0000 0.548867
\(479\) 4.00000 6.92820i 0.182765 0.316558i −0.760056 0.649857i \(-0.774829\pi\)
0.942821 + 0.333300i \(0.108162\pi\)
\(480\) 0 0
\(481\) −3.00000 5.19615i −0.136788 0.236924i
\(482\) −5.00000 8.66025i −0.227744 0.394464i
\(483\) 0 0
\(484\) −2.50000 + 4.33013i −0.113636 + 0.196824i
\(485\) 32.0000 1.45305
\(486\) 0 0
\(487\) 26.0000 1.17817 0.589086 0.808070i \(-0.299488\pi\)
0.589086 + 0.808070i \(0.299488\pi\)
\(488\) −3.00000 + 5.19615i −0.135804 + 0.235219i
\(489\) 0 0
\(490\) −2.00000 3.46410i −0.0903508 0.156492i
\(491\) 12.0000 + 20.7846i 0.541552 + 0.937996i 0.998815 + 0.0486647i \(0.0154966\pi\)
−0.457263 + 0.889332i \(0.651170\pi\)
\(492\) 0 0
\(493\) 3.50000 6.06218i 0.157632 0.273027i
\(494\) −6.00000 −0.269953
\(495\) 0 0
\(496\) −9.00000 −0.404112
\(497\) 3.50000 6.06218i 0.156996 0.271926i
\(498\) 0 0
\(499\) −14.0000 24.2487i −0.626726 1.08552i −0.988204 0.153141i \(-0.951061\pi\)
0.361478 0.932381i \(-0.382272\pi\)
\(500\) 12.0000 + 20.7846i 0.536656 + 0.929516i
\(501\) 0 0
\(502\) 0 0
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 40.0000 1.77998
\(506\) 2.00000 3.46410i 0.0889108 0.153998i
\(507\) 0 0
\(508\) 0 0
\(509\) −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i \(-0.209119\pi\)
−0.924821 + 0.380402i \(0.875786\pi\)
\(510\) 0 0
\(511\) −7.00000 + 12.1244i −0.309662 + 0.536350i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 30.0000 1.32324
\(515\) 34.0000 58.8897i 1.49822 2.59499i
\(516\) 0 0
\(517\) −12.0000 20.7846i −0.527759 0.914106i
\(518\) −1.00000 1.73205i −0.0439375 0.0761019i
\(519\) 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
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) 0.500000 0.866025i 0.0218426 0.0378325i
\(525\) 0 0
\(526\) −4.50000 7.79423i −0.196209 0.339845i
\(527\) 31.5000 + 54.5596i 1.37216 + 2.37665i
\(528\) 0 0
\(529\) 11.0000 19.0526i 0.478261 0.828372i
\(530\) 36.0000 1.56374
\(531\) 0 0
\(532\) −2.00000 −0.0867110
\(533\) 9.00000 15.5885i 0.389833 0.675211i
\(534\) 0 0
\(535\) −24.0000 41.5692i −1.03761 1.79719i
\(536\) 3.50000 + 6.06218i 0.151177 + 0.261846i
\(537\) 0 0
\(538\) −2.00000 + 3.46410i −0.0862261 + 0.149348i
\(539\) 4.00000 0.172292
\(540\) 0 0
\(541\) −36.0000 −1.54776 −0.773880 0.633332i \(-0.781687\pi\)
−0.773880 + 0.633332i \(0.781687\pi\)
\(542\) 1.50000 2.59808i 0.0644305 0.111597i
\(543\) 0 0
\(544\) 3.50000 + 6.06218i 0.150061 + 0.259914i
\(545\) 32.0000 + 55.4256i 1.37073 + 2.37417i
\(546\) 0 0
\(547\) −18.0000 + 31.1769i −0.769624 + 1.33303i 0.168142 + 0.985763i \(0.446223\pi\)
−0.937767 + 0.347266i \(0.887110\pi\)
\(548\) −22.0000 −0.939793
\(549\) 0 0
\(550\) −44.0000 −1.87617
\(551\) 1.00000 1.73205i 0.0426014 0.0737878i
\(552\) 0 0
\(553\) −3.00000 5.19615i −0.127573 0.220963i
\(554\) 4.00000 + 6.92820i 0.169944 + 0.294351i
\(555\) 0 0
\(556\) −5.00000 + 8.66025i −0.212047 + 0.367277i
\(557\) −1.00000 −0.0423714 −0.0211857 0.999776i \(-0.506744\pi\)
−0.0211857 + 0.999776i \(0.506744\pi\)
\(558\) 0 0
\(559\) 33.0000 1.39575
\(560\) −2.00000 + 3.46410i −0.0845154 + 0.146385i
\(561\) 0 0
\(562\) 5.00000 + 8.66025i 0.210912 + 0.365311i
\(563\) 5.50000 + 9.52628i 0.231797 + 0.401485i 0.958337 0.285640i \(-0.0922060\pi\)
−0.726540 + 0.687124i \(0.758873\pi\)
\(564\) 0 0
\(565\) 16.0000 27.7128i 0.673125 1.16589i
\(566\) −28.0000 −1.17693
\(567\) 0 0
\(568\) −7.00000 −0.293713
\(569\) 6.00000 10.3923i 0.251533 0.435668i −0.712415 0.701758i \(-0.752399\pi\)
0.963948 + 0.266090i \(0.0857319\pi\)
\(570\) 0 0
\(571\) 19.5000 + 33.7750i 0.816050 + 1.41344i 0.908572 + 0.417729i \(0.137174\pi\)
−0.0925222 + 0.995711i \(0.529493\pi\)
\(572\) −6.00000 10.3923i −0.250873 0.434524i
\(573\) 0 0
\(574\) 3.00000 5.19615i 0.125218 0.216883i
\(575\) 11.0000 0.458732
\(576\) 0 0
\(577\) 10.0000 0.416305 0.208153 0.978096i \(-0.433255\pi\)
0.208153 + 0.978096i \(0.433255\pi\)
\(578\) 16.0000 27.7128i 0.665512 1.15270i
\(579\) 0 0
\(580\) −2.00000 3.46410i −0.0830455 0.143839i
\(581\) 2.00000 + 3.46410i 0.0829740 + 0.143715i
\(582\) 0 0
\(583\) −18.0000 + 31.1769i −0.745484 + 1.29122i
\(584\) 14.0000 0.579324
\(585\) 0 0
\(586\) 6.00000 0.247858
\(587\) −12.5000 + 21.6506i −0.515930 + 0.893617i 0.483899 + 0.875124i \(0.339220\pi\)
−0.999829 + 0.0184934i \(0.994113\pi\)
\(588\) 0 0
\(589\) 9.00000 + 15.5885i 0.370839 + 0.642311i
\(590\) −10.0000 17.3205i −0.411693 0.713074i
\(591\) 0 0
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) 18.0000 0.739171 0.369586 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) 0 0
\(595\) 28.0000 1.14789
\(596\) −1.50000 + 2.59808i −0.0614424 + 0.106421i
\(597\) 0 0
\(598\) 1.50000 + 2.59808i 0.0613396 + 0.106243i
\(599\) 10.5000 + 18.1865i 0.429018 + 0.743082i 0.996786 0.0801071i \(-0.0255262\pi\)
−0.567768 + 0.823189i \(0.692193\pi\)
\(600\) 0 0
\(601\) 14.0000 24.2487i 0.571072 0.989126i −0.425384 0.905013i \(-0.639861\pi\)
0.996456 0.0841128i \(-0.0268056\pi\)
\(602\) 11.0000 0.448327
\(603\) 0 0
\(604\) 10.0000 0.406894
\(605\) 10.0000 17.3205i 0.406558 0.704179i
\(606\) 0 0
\(607\) −19.5000 33.7750i −0.791481 1.37088i −0.925050 0.379845i \(-0.875977\pi\)
0.133570 0.991039i \(-0.457356\pi\)
\(608\) 1.00000 + 1.73205i 0.0405554 + 0.0702439i
\(609\) 0 0
\(610\) 12.0000 20.7846i 0.485866 0.841544i
\(611\) 18.0000 0.728202
\(612\) 0 0
\(613\) −6.00000 −0.242338 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) −1.00000 + 1.73205i −0.0403567 + 0.0698999i
\(615\) 0 0
\(616\) −2.00000 3.46410i −0.0805823 0.139573i
\(617\) 7.00000 + 12.1244i 0.281809 + 0.488108i 0.971830 0.235681i \(-0.0757321\pi\)
−0.690021 + 0.723789i \(0.742399\pi\)
\(618\) 0 0
\(619\) 7.00000 12.1244i 0.281354 0.487319i −0.690365 0.723462i \(-0.742550\pi\)
0.971718 + 0.236143i \(0.0758832\pi\)
\(620\) 36.0000 1.44579
\(621\) 0 0
\(622\) −8.00000 −0.320771
\(623\) 1.50000 2.59808i 0.0600962 0.104090i
\(624\) 0 0
\(625\) −20.5000 35.5070i −0.820000 1.42028i
\(626\) −13.0000 22.5167i −0.519584 0.899947i
\(627\) 0 0
\(628\) −8.50000 + 14.7224i −0.339187 + 0.587489i
\(629\) 14.0000 0.558217
\(630\) 0 0
\(631\) −4.00000 −0.159237 −0.0796187 0.996825i \(-0.525370\pi\)
−0.0796187 + 0.996825i \(0.525370\pi\)
\(632\) −3.00000 + 5.19615i −0.119334 + 0.206692i
\(633\) 0 0
\(634\) 9.00000 + 15.5885i 0.357436 + 0.619097i
\(635\) 0 0
\(636\) 0 0
\(637\) −1.50000 + 2.59808i −0.0594322 + 0.102940i
\(638\) 4.00000 0.158362
\(639\) 0 0
\(640\) 4.00000 0.158114
\(641\) −14.0000 + 24.2487i −0.552967 + 0.957767i 0.445092 + 0.895485i \(0.353171\pi\)
−0.998059 + 0.0622816i \(0.980162\pi\)
\(642\) 0 0
\(643\) 2.00000 + 3.46410i 0.0788723 + 0.136611i 0.902764 0.430137i \(-0.141535\pi\)
−0.823891 + 0.566748i \(0.808201\pi\)
\(644\) 0.500000 + 0.866025i 0.0197028 + 0.0341262i
\(645\) 0 0
\(646\) 7.00000 12.1244i 0.275411 0.477026i
\(647\) −42.0000 −1.65119 −0.825595 0.564263i \(-0.809160\pi\)
−0.825595 + 0.564263i \(0.809160\pi\)
\(648\) 0 0
\(649\) 20.0000 0.785069
\(650\) 16.5000 28.5788i 0.647183 1.12095i
\(651\) 0 0
\(652\) 0.500000 + 0.866025i 0.0195815 + 0.0339162i
\(653\) 1.50000 + 2.59808i 0.0586995 + 0.101671i 0.893882 0.448303i \(-0.147971\pi\)
−0.835182 + 0.549973i \(0.814638\pi\)
\(654\) 0 0
\(655\) −2.00000 + 3.46410i −0.0781465 + 0.135354i
\(656\) −6.00000 −0.234261
\(657\) 0 0
\(658\) 6.00000 0.233904
\(659\) −14.0000 + 24.2487i −0.545363 + 0.944596i 0.453221 + 0.891398i \(0.350275\pi\)
−0.998584 + 0.0531977i \(0.983059\pi\)
\(660\) 0 0
\(661\) 7.00000 + 12.1244i 0.272268 + 0.471583i 0.969442 0.245319i \(-0.0788928\pi\)
−0.697174 + 0.716902i \(0.745559\pi\)
\(662\) −15.5000 26.8468i −0.602425 1.04343i
\(663\) 0 0
\(664\) 2.00000 3.46410i 0.0776151 0.134433i
\(665\) 8.00000 0.310227
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) −4.00000 + 6.92820i −0.154765 + 0.268060i
\(669\) 0 0
\(670\) −14.0000 24.2487i −0.540867 0.936809i
\(671\) 12.0000 + 20.7846i 0.463255 + 0.802381i
\(672\) 0 0
\(673\) −11.5000 + 19.9186i −0.443292 + 0.767805i −0.997932 0.0642860i \(-0.979523\pi\)
0.554639 + 0.832091i \(0.312856\pi\)
\(674\) −27.0000 −1.04000
\(675\) 0 0
\(676\) −4.00000 −0.153846
\(677\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(678\) 0 0
\(679\) −4.00000 6.92820i −0.153506 0.265880i
\(680\) −14.0000 24.2487i −0.536875 0.929896i
\(681\) 0 0
\(682\) −18.0000 + 31.1769i −0.689256 + 1.19383i
\(683\) 48.0000 1.83667 0.918334 0.395805i \(-0.129534\pi\)
0.918334 + 0.395805i \(0.129534\pi\)
\(684\) 0 0
\(685\) 88.0000 3.36231
\(686\) −0.500000 + 0.866025i −0.0190901 + 0.0330650i
\(687\) 0 0
\(688\) −5.50000 9.52628i −0.209686 0.363186i
\(689\) −13.5000 23.3827i −0.514309 0.890809i
\(690\) 0 0
\(691\) 20.0000 34.6410i 0.760836 1.31781i −0.181584 0.983375i \(-0.558123\pi\)
0.942420 0.334431i \(-0.108544\pi\)
\(692\) 8.00000 0.304114
\(693\) 0 0
\(694\) 18.0000 0.683271
\(695\) 20.0000 34.6410i 0.758643 1.31401i
\(696\) 0 0
\(697\) 21.0000 + 36.3731i 0.795432 + 1.37773i
\(698\) 12.5000 + 21.6506i 0.473132 + 0.819489i
\(699\) 0 0
\(700\) 5.50000 9.52628i 0.207880 0.360060i
\(701\) 2.00000 0.0755390 0.0377695 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) 0 0
\(703\) 4.00000 0.150863
\(704\) −2.00000 + 3.46410i −0.0753778 + 0.130558i
\(705\) 0 0
\(706\) −7.50000 12.9904i −0.282266 0.488899i
\(707\) −5.00000 8.66025i −0.188044 0.325702i
\(708\) 0 0
\(709\) 20.0000 34.6410i 0.751116 1.30097i −0.196167 0.980571i \(-0.562849\pi\)
0.947282 0.320400i \(-0.103817\pi\)
\(710\) 28.0000 1.05082
\(711\) 0 0
\(712\) −3.00000 −0.112430
\(713\) 4.50000 7.79423i 0.168526 0.291896i
\(714\) 0 0
\(715\) 24.0000 + 41.5692i 0.897549 + 1.55460i
\(716\) −6.00000 10.3923i −0.224231 0.388379i
\(717\) 0 0
\(718\) 5.50000 9.52628i 0.205258 0.355518i
\(719\) −48.0000 −1.79010 −0.895049 0.445968i \(-0.852860\pi\)
−0.895049 + 0.445968i \(0.852860\pi\)
\(720\) 0 0
\(721\) −17.0000 −0.633113
\(722\) −7.50000 + 12.9904i −0.279121 + 0.483452i
\(723\) 0 0
\(724\) 4.50000 + 7.79423i 0.167241 + 0.289670i
\(725\) 5.50000 + 9.52628i 0.204265 + 0.353797i
\(726\) 0 0
\(727\) 14.5000 25.1147i 0.537775 0.931454i −0.461248 0.887271i \(-0.652598\pi\)
0.999023 0.0441829i \(-0.0140684\pi\)
\(728\) 3.00000 0.111187
\(729\) 0 0
\(730\) −56.0000 −2.07265
\(731\) −38.5000 + 66.6840i −1.42397 + 2.46640i
\(732\) 0 0
\(733\) 7.50000 + 12.9904i 0.277019 + 0.479811i 0.970642 0.240527i \(-0.0773202\pi\)
−0.693624 + 0.720338i \(0.743987\pi\)
\(734\) −12.5000 21.6506i −0.461383 0.799140i
\(735\) 0 0
\(736\) 0.500000 0.866025i 0.0184302 0.0319221i
\(737\) 28.0000 1.03139
\(738\) 0 0
\(739\) 12.0000 0.441427 0.220714 0.975339i \(-0.429161\pi\)
0.220714 + 0.975339i \(0.429161\pi\)
\(740\) 4.00000 6.92820i 0.147043 0.254686i
\(741\) 0 0
\(742\) −4.50000 7.79423i −0.165200 0.286135i
\(743\) 25.5000 + 44.1673i 0.935504 + 1.62034i 0.773732 + 0.633513i \(0.218388\pi\)
0.161772 + 0.986828i \(0.448279\pi\)
\(744\) 0 0
\(745\) 6.00000 10.3923i 0.219823 0.380745i
\(746\) 38.0000 1.39128
\(747\) 0 0
\(748\) 28.0000 1.02378
\(749\) −6.00000 + 10.3923i −0.219235 + 0.379727i
\(750\) 0 0
\(751\) −3.00000 5.19615i −0.109472 0.189610i 0.806085 0.591800i \(-0.201583\pi\)
−0.915556 + 0.402190i \(0.868249\pi\)
\(752\) −3.00000 5.19615i −0.109399 0.189484i
\(753\) 0 0
\(754\) −1.50000 + 2.59808i −0.0546268 + 0.0946164i
\(755\) −40.0000 −1.45575
\(756\) 0 0
\(757\) −12.0000 −0.436147 −0.218074 0.975932i \(-0.569977\pi\)
−0.218074 + 0.975932i \(0.569977\pi\)
\(758\) −4.00000 + 6.92820i −0.145287 + 0.251644i
\(759\) 0 0
\(760\) −4.00000 6.92820i −0.145095 0.251312i
\(761\) −6.50000 11.2583i −0.235625 0.408114i 0.723829 0.689979i \(-0.242380\pi\)
−0.959454 + 0.281865i \(0.909047\pi\)
\(762\) 0 0
\(763\) 8.00000 13.8564i 0.289619 0.501636i
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) −4.00000 −0.144526
\(767\) −7.50000 + 12.9904i −0.270809 + 0.469055i
\(768\) 0 0
\(769\) −2.00000 3.46410i −0.0721218 0.124919i 0.827709 0.561157i \(-0.189644\pi\)
−0.899831 + 0.436239i \(0.856310\pi\)
\(770\) 8.00000 + 13.8564i 0.288300 + 0.499350i
\(771\) 0 0
\(772\) −2.50000 + 4.33013i −0.0899770 + 0.155845i
\(773\) −4.00000 −0.143870 −0.0719350 0.997409i \(-0.522917\pi\)
−0.0719350 + 0.997409i \(0.522917\pi\)
\(774\) 0 0
\(775\) −99.0000 −3.55618
\(776\) −4.00000 + 6.92820i −0.143592 + 0.248708i
\(777\) 0 0
\(778\) 7.00000 + 12.1244i 0.250962 + 0.434679i
\(779\) 6.00000 + 10.3923i 0.214972 + 0.372343i
\(780\) 0 0
\(781\) −14.0000 + 24.2487i −0.500959 + 0.867687i
\(782\) −7.00000 −0.250319
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 34.0000 58.8897i 1.21351 2.10186i
\(786\) 0 0
\(787\) −9.00000 15.5885i −0.320815 0.555668i 0.659841 0.751405i \(-0.270624\pi\)
−0.980656 + 0.195737i \(0.937290\pi\)
\(788\) 13.0000 + 22.5167i 0.463106 + 0.802123i
\(789\) 0 0
\(790\)