Properties

Label 546.2.bq.a.503.2
Level $546$
Weight $2$
Character 546.503
Analytic conductor $4.360$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bq (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 503.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 546.503
Dual form 546.2.bq.a.419.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.46410 q^{5} +(-1.50000 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.46410 q^{5} +(-1.50000 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-3.00000 - 1.73205i) q^{10} -1.73205 q^{12} +(-3.50000 - 0.866025i) q^{13} +(1.73205 - 2.00000i) q^{14} +(3.00000 - 5.19615i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.866025 - 1.50000i) q^{17} -3.00000i q^{18} +(-1.73205 - 3.00000i) q^{20} +(3.46410 + 3.00000i) q^{21} +(-2.59808 - 1.50000i) q^{23} +(-1.50000 - 0.866025i) q^{24} +7.00000 q^{25} +(-2.59808 - 2.50000i) q^{26} +5.19615 q^{27} +(2.50000 - 0.866025i) q^{28} +(-5.19615 - 3.00000i) q^{29} +(5.19615 - 3.00000i) q^{30} -1.73205i q^{31} +(-0.866025 + 0.500000i) q^{32} -1.73205i q^{34} +(-1.73205 + 9.00000i) q^{35} +(1.50000 - 2.59808i) q^{36} +(-2.00000 + 3.46410i) q^{37} +(4.33013 - 4.50000i) q^{39} -3.46410i q^{40} +(3.46410 - 6.00000i) q^{41} +(1.50000 + 4.33013i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(5.19615 + 9.00000i) q^{45} +(-1.50000 - 2.59808i) q^{46} -3.46410 q^{47} +(-0.866025 - 1.50000i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(6.06218 + 3.50000i) q^{50} +3.00000 q^{51} +(-1.00000 - 3.46410i) q^{52} +9.00000i q^{53} +(4.50000 + 2.59808i) q^{54} +(2.59808 + 0.500000i) q^{56} +(-3.00000 - 5.19615i) q^{58} +(0.866025 + 1.50000i) q^{59} +6.00000 q^{60} +(-10.5000 + 6.06218i) q^{61} +(0.866025 - 1.50000i) q^{62} +(-7.50000 + 2.59808i) q^{63} -1.00000 q^{64} +(12.1244 + 3.00000i) q^{65} +(3.50000 - 6.06218i) q^{67} +(0.866025 - 1.50000i) q^{68} +(4.50000 - 2.59808i) q^{69} +(-6.00000 + 6.92820i) q^{70} +(-12.9904 + 7.50000i) q^{71} +(2.59808 - 1.50000i) q^{72} +13.8564i q^{73} +(-3.46410 + 2.00000i) q^{74} +(-6.06218 + 10.5000i) q^{75} +(6.00000 - 1.73205i) q^{78} -10.0000 q^{79} +(1.73205 - 3.00000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(6.00000 - 3.46410i) q^{82} -12.1244 q^{83} +(-0.866025 + 4.50000i) q^{84} +(3.00000 + 5.19615i) q^{85} -1.00000i q^{86} +(9.00000 - 5.19615i) q^{87} +(7.79423 - 13.5000i) q^{89} +10.3923i q^{90} +(-4.00000 + 8.66025i) q^{91} -3.00000i q^{92} +(2.59808 + 1.50000i) q^{93} +(-3.00000 - 1.73205i) q^{94} -1.73205i q^{96} +(15.0000 - 8.66025i) q^{97} +(-4.33013 - 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} - 6q^{6} + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 4q + 2q^{4} - 6q^{6} + 2q^{7} - 6q^{9} - 12q^{10} - 14q^{13} + 12q^{15} - 2q^{16} - 6q^{24} + 28q^{25} + 10q^{28} + 6q^{36} - 8q^{37} + 6q^{42} - 2q^{43} - 6q^{46} - 26q^{49} + 12q^{51} - 4q^{52} + 18q^{54} - 12q^{58} + 24q^{60} - 42q^{61} - 30q^{63} - 4q^{64} + 14q^{67} + 18q^{69} - 24q^{70} + 24q^{78} - 40q^{79} - 18q^{81} + 24q^{82} + 12q^{85} + 36q^{87} - 16q^{91} - 12q^{94} + 60q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) −0.866025 + 1.50000i −0.500000 + 0.866025i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −3.46410 −1.54919 −0.774597 0.632456i \(-0.782047\pi\)
−0.774597 + 0.632456i \(0.782047\pi\)
\(6\) −1.50000 + 0.866025i −0.612372 + 0.353553i
\(7\) 0.500000 2.59808i 0.188982 0.981981i
\(8\) 1.00000i 0.353553i
\(9\) −1.50000 2.59808i −0.500000 0.866025i
\(10\) −3.00000 1.73205i −0.948683 0.547723i
\(11\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) −1.73205 −0.500000
\(13\) −3.50000 0.866025i −0.970725 0.240192i
\(14\) 1.73205 2.00000i 0.462910 0.534522i
\(15\) 3.00000 5.19615i 0.774597 1.34164i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.866025 1.50000i −0.210042 0.363803i 0.741685 0.670748i \(-0.234027\pi\)
−0.951727 + 0.306944i \(0.900693\pi\)
\(18\) 3.00000i 0.707107i
\(19\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(20\) −1.73205 3.00000i −0.387298 0.670820i
\(21\) 3.46410 + 3.00000i 0.755929 + 0.654654i
\(22\) 0 0
\(23\) −2.59808 1.50000i −0.541736 0.312772i 0.204046 0.978961i \(-0.434591\pi\)
−0.745782 + 0.666190i \(0.767924\pi\)
\(24\) −1.50000 0.866025i −0.306186 0.176777i
\(25\) 7.00000 1.40000
\(26\) −2.59808 2.50000i −0.509525 0.490290i
\(27\) 5.19615 1.00000
\(28\) 2.50000 0.866025i 0.472456 0.163663i
\(29\) −5.19615 3.00000i −0.964901 0.557086i −0.0672232 0.997738i \(-0.521414\pi\)
−0.897678 + 0.440652i \(0.854747\pi\)
\(30\) 5.19615 3.00000i 0.948683 0.547723i
\(31\) 1.73205i 0.311086i −0.987829 0.155543i \(-0.950287\pi\)
0.987829 0.155543i \(-0.0497126\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 1.73205i 0.297044i
\(35\) −1.73205 + 9.00000i −0.292770 + 1.52128i
\(36\) 1.50000 2.59808i 0.250000 0.433013i
\(37\) −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) 0 0
\(39\) 4.33013 4.50000i 0.693375 0.720577i
\(40\) 3.46410i 0.547723i
\(41\) 3.46410 6.00000i 0.541002 0.937043i −0.457845 0.889032i \(-0.651379\pi\)
0.998847 0.0480106i \(-0.0152881\pi\)
\(42\) 1.50000 + 4.33013i 0.231455 + 0.668153i
\(43\) −0.500000 0.866025i −0.0762493 0.132068i 0.825380 0.564578i \(-0.190961\pi\)
−0.901629 + 0.432511i \(0.857628\pi\)
\(44\) 0 0
\(45\) 5.19615 + 9.00000i 0.774597 + 1.34164i
\(46\) −1.50000 2.59808i −0.221163 0.383065i
\(47\) −3.46410 −0.505291 −0.252646 0.967559i \(-0.581301\pi\)
−0.252646 + 0.967559i \(0.581301\pi\)
\(48\) −0.866025 1.50000i −0.125000 0.216506i
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 6.06218 + 3.50000i 0.857321 + 0.494975i
\(51\) 3.00000 0.420084
\(52\) −1.00000 3.46410i −0.138675 0.480384i
\(53\) 9.00000i 1.23625i 0.786082 + 0.618123i \(0.212106\pi\)
−0.786082 + 0.618123i \(0.787894\pi\)
\(54\) 4.50000 + 2.59808i 0.612372 + 0.353553i
\(55\) 0 0
\(56\) 2.59808 + 0.500000i 0.347183 + 0.0668153i
\(57\) 0 0
\(58\) −3.00000 5.19615i −0.393919 0.682288i
\(59\) 0.866025 + 1.50000i 0.112747 + 0.195283i 0.916877 0.399170i \(-0.130702\pi\)
−0.804130 + 0.594454i \(0.797368\pi\)
\(60\) 6.00000 0.774597
\(61\) −10.5000 + 6.06218i −1.34439 + 0.776182i −0.987448 0.157945i \(-0.949513\pi\)
−0.356939 + 0.934128i \(0.616180\pi\)
\(62\) 0.866025 1.50000i 0.109985 0.190500i
\(63\) −7.50000 + 2.59808i −0.944911 + 0.327327i
\(64\) −1.00000 −0.125000
\(65\) 12.1244 + 3.00000i 1.50384 + 0.372104i
\(66\) 0 0
\(67\) 3.50000 6.06218i 0.427593 0.740613i −0.569066 0.822292i \(-0.692695\pi\)
0.996659 + 0.0816792i \(0.0260283\pi\)
\(68\) 0.866025 1.50000i 0.105021 0.181902i
\(69\) 4.50000 2.59808i 0.541736 0.312772i
\(70\) −6.00000 + 6.92820i −0.717137 + 0.828079i
\(71\) −12.9904 + 7.50000i −1.54167 + 0.890086i −0.542941 + 0.839771i \(0.682689\pi\)
−0.998733 + 0.0503155i \(0.983977\pi\)
\(72\) 2.59808 1.50000i 0.306186 0.176777i
\(73\) 13.8564i 1.62177i 0.585206 + 0.810885i \(0.301014\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) −3.46410 + 2.00000i −0.402694 + 0.232495i
\(75\) −6.06218 + 10.5000i −0.700000 + 1.21244i
\(76\) 0 0
\(77\) 0 0
\(78\) 6.00000 1.73205i 0.679366 0.196116i
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 1.73205 3.00000i 0.193649 0.335410i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 6.00000 3.46410i 0.662589 0.382546i
\(83\) −12.1244 −1.33082 −0.665410 0.746478i \(-0.731743\pi\)
−0.665410 + 0.746478i \(0.731743\pi\)
\(84\) −0.866025 + 4.50000i −0.0944911 + 0.490990i
\(85\) 3.00000 + 5.19615i 0.325396 + 0.563602i
\(86\) 1.00000i 0.107833i
\(87\) 9.00000 5.19615i 0.964901 0.557086i
\(88\) 0 0
\(89\) 7.79423 13.5000i 0.826187 1.43100i −0.0748225 0.997197i \(-0.523839\pi\)
0.901009 0.433800i \(-0.142828\pi\)
\(90\) 10.3923i 1.09545i
\(91\) −4.00000 + 8.66025i −0.419314 + 0.907841i
\(92\) 3.00000i 0.312772i
\(93\) 2.59808 + 1.50000i 0.269408 + 0.155543i
\(94\) −3.00000 1.73205i −0.309426 0.178647i
\(95\) 0 0
\(96\) 1.73205i 0.176777i
\(97\) 15.0000 8.66025i 1.52302 0.879316i 0.523390 0.852093i \(-0.324667\pi\)
0.999629 0.0272222i \(-0.00866617\pi\)
\(98\) −4.33013 5.50000i −0.437409 0.555584i
\(99\) 0 0
\(100\) 3.50000 + 6.06218i 0.350000 + 0.606218i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 2.59808 + 1.50000i 0.257248 + 0.148522i
\(103\) 8.66025i 0.853320i −0.904412 0.426660i \(-0.859690\pi\)
0.904412 0.426660i \(-0.140310\pi\)
\(104\) 0.866025 3.50000i 0.0849208 0.343203i
\(105\) −12.0000 10.3923i −1.17108 1.01419i
\(106\) −4.50000 + 7.79423i −0.437079 + 0.757042i
\(107\) −15.5885 9.00000i −1.50699 0.870063i −0.999967 0.00813215i \(-0.997411\pi\)
−0.507026 0.861931i \(-0.669255\pi\)
\(108\) 2.59808 + 4.50000i 0.250000 + 0.433013i
\(109\) 16.0000 1.53252 0.766261 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) 0 0
\(111\) −3.46410 6.00000i −0.328798 0.569495i
\(112\) 2.00000 + 1.73205i 0.188982 + 0.163663i
\(113\) −5.19615 + 3.00000i −0.488813 + 0.282216i −0.724082 0.689714i \(-0.757736\pi\)
0.235269 + 0.971930i \(0.424403\pi\)
\(114\) 0 0
\(115\) 9.00000 + 5.19615i 0.839254 + 0.484544i
\(116\) 6.00000i 0.557086i
\(117\) 3.00000 + 10.3923i 0.277350 + 0.960769i
\(118\) 1.73205i 0.159448i
\(119\) −4.33013 + 1.50000i −0.396942 + 0.137505i
\(120\) 5.19615 + 3.00000i 0.474342 + 0.273861i
\(121\) −5.50000 9.52628i −0.500000 0.866025i
\(122\) −12.1244 −1.09769
\(123\) 6.00000 + 10.3923i 0.541002 + 0.937043i
\(124\) 1.50000 0.866025i 0.134704 0.0777714i
\(125\) −6.92820 −0.619677
\(126\) −7.79423 1.50000i −0.694365 0.133631i
\(127\) −10.0000 + 17.3205i −0.887357 + 1.53695i −0.0443678 + 0.999015i \(0.514127\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 1.73205 0.152499
\(130\) 9.00000 + 8.66025i 0.789352 + 0.759555i
\(131\) 15.5885 1.36197 0.680985 0.732297i \(-0.261552\pi\)
0.680985 + 0.732297i \(0.261552\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 6.06218 3.50000i 0.523692 0.302354i
\(135\) −18.0000 −1.54919
\(136\) 1.50000 0.866025i 0.128624 0.0742611i
\(137\) 10.3923 6.00000i 0.887875 0.512615i 0.0146279 0.999893i \(-0.495344\pi\)
0.873247 + 0.487278i \(0.162010\pi\)
\(138\) 5.19615 0.442326
\(139\) −6.00000 + 3.46410i −0.508913 + 0.293821i −0.732387 0.680889i \(-0.761594\pi\)
0.223474 + 0.974710i \(0.428260\pi\)
\(140\) −8.66025 + 3.00000i −0.731925 + 0.253546i
\(141\) 3.00000 5.19615i 0.252646 0.437595i
\(142\) −15.0000 −1.25877
\(143\) 0 0
\(144\) 3.00000 0.250000
\(145\) 18.0000 + 10.3923i 1.49482 + 0.863034i
\(146\) −6.92820 + 12.0000i −0.573382 + 0.993127i
\(147\) 9.52628 7.50000i 0.785714 0.618590i
\(148\) −4.00000 −0.328798
\(149\) 18.1865 10.5000i 1.48990 0.860194i 0.489966 0.871742i \(-0.337009\pi\)
0.999933 + 0.0115483i \(0.00367601\pi\)
\(150\) −10.5000 + 6.06218i −0.857321 + 0.494975i
\(151\) 16.0000 1.30206 0.651031 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 0 0
\(153\) −2.59808 + 4.50000i −0.210042 + 0.363803i
\(154\) 0 0
\(155\) 6.00000i 0.481932i
\(156\) 6.06218 + 1.50000i 0.485363 + 0.120096i
\(157\) 13.8564i 1.10586i 0.833227 + 0.552931i \(0.186491\pi\)
−0.833227 + 0.552931i \(0.813509\pi\)
\(158\) −8.66025 5.00000i −0.688973 0.397779i
\(159\) −13.5000 7.79423i −1.07062 0.618123i
\(160\) 3.00000 1.73205i 0.237171 0.136931i
\(161\) −5.19615 + 6.00000i −0.409514 + 0.472866i
\(162\) −7.79423 + 4.50000i −0.612372 + 0.353553i
\(163\) 3.50000 + 6.06218i 0.274141 + 0.474826i 0.969918 0.243432i \(-0.0782731\pi\)
−0.695777 + 0.718258i \(0.744940\pi\)
\(164\) 6.92820 0.541002
\(165\) 0 0
\(166\) −10.5000 6.06218i −0.814958 0.470516i
\(167\) −3.46410 + 6.00000i −0.268060 + 0.464294i −0.968361 0.249554i \(-0.919716\pi\)
0.700301 + 0.713848i \(0.253049\pi\)
\(168\) −3.00000 + 3.46410i −0.231455 + 0.267261i
\(169\) 11.5000 + 6.06218i 0.884615 + 0.466321i
\(170\) 6.00000i 0.460179i
\(171\) 0 0
\(172\) 0.500000 0.866025i 0.0381246 0.0660338i
\(173\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(174\) 10.3923 0.787839
\(175\) 3.50000 18.1865i 0.264575 1.37477i
\(176\) 0 0
\(177\) −3.00000 −0.225494
\(178\) 13.5000 7.79423i 1.01187 0.584202i
\(179\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(180\) −5.19615 + 9.00000i −0.387298 + 0.670820i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) −7.79423 + 5.50000i −0.577747 + 0.407687i
\(183\) 21.0000i 1.55236i
\(184\) 1.50000 2.59808i 0.110581 0.191533i
\(185\) 6.92820 12.0000i 0.509372 0.882258i
\(186\) 1.50000 + 2.59808i 0.109985 + 0.190500i
\(187\) 0 0
\(188\) −1.73205 3.00000i −0.126323 0.218797i
\(189\) 2.59808 13.5000i 0.188982 0.981981i
\(190\) 0 0
\(191\) 12.9904 7.50000i 0.939951 0.542681i 0.0500060 0.998749i \(-0.484076\pi\)
0.889945 + 0.456068i \(0.150743\pi\)
\(192\) 0.866025 1.50000i 0.0625000 0.108253i
\(193\) 7.00000 12.1244i 0.503871 0.872730i −0.496119 0.868255i \(-0.665242\pi\)
0.999990 0.00447566i \(-0.00142465\pi\)
\(194\) 17.3205 1.24354
\(195\) −15.0000 + 15.5885i −1.07417 + 1.11631i
\(196\) −1.00000 6.92820i −0.0714286 0.494872i
\(197\) −12.9904 7.50000i −0.925526 0.534353i −0.0401324 0.999194i \(-0.512778\pi\)
−0.885394 + 0.464841i \(0.846111\pi\)
\(198\) 0 0
\(199\) 1.50000 0.866025i 0.106332 0.0613909i −0.445891 0.895087i \(-0.647113\pi\)
0.552223 + 0.833696i \(0.313780\pi\)
\(200\) 7.00000i 0.494975i
\(201\) 6.06218 + 10.5000i 0.427593 + 0.740613i
\(202\) 0 0
\(203\) −10.3923 + 12.0000i −0.729397 + 0.842235i
\(204\) 1.50000 + 2.59808i 0.105021 + 0.181902i
\(205\) −12.0000 + 20.7846i −0.838116 + 1.45166i
\(206\) 4.33013 7.50000i 0.301694 0.522550i
\(207\) 9.00000i 0.625543i
\(208\) 2.50000 2.59808i 0.173344 0.180144i
\(209\) 0 0
\(210\) −5.19615 15.0000i −0.358569 1.03510i
\(211\) 10.0000 17.3205i 0.688428 1.19239i −0.283918 0.958849i \(-0.591634\pi\)
0.972346 0.233544i \(-0.0750324\pi\)
\(212\) −7.79423 + 4.50000i −0.535310 + 0.309061i
\(213\) 25.9808i 1.78017i
\(214\) −9.00000 15.5885i −0.615227 1.06561i
\(215\) 1.73205 + 3.00000i 0.118125 + 0.204598i
\(216\) 5.19615i 0.353553i
\(217\) −4.50000 0.866025i −0.305480 0.0587896i
\(218\) 13.8564 + 8.00000i 0.938474 + 0.541828i
\(219\) −20.7846 12.0000i −1.40449 0.810885i
\(220\) 0 0
\(221\) 1.73205 + 6.00000i 0.116510 + 0.403604i
\(222\) 6.92820i 0.464991i
\(223\) −4.50000 2.59808i −0.301342 0.173980i 0.341703 0.939808i \(-0.388996\pi\)
−0.643046 + 0.765828i \(0.722329\pi\)
\(224\) 0.866025 + 2.50000i 0.0578638 + 0.167038i
\(225\) −10.5000 18.1865i −0.700000 1.21244i
\(226\) −6.00000 −0.399114
\(227\) −5.19615 9.00000i −0.344881 0.597351i 0.640451 0.767999i \(-0.278747\pi\)
−0.985332 + 0.170648i \(0.945414\pi\)
\(228\) 0 0
\(229\) 15.5885i 1.03011i 0.857156 + 0.515057i \(0.172229\pi\)
−0.857156 + 0.515057i \(0.827771\pi\)
\(230\) 5.19615 + 9.00000i 0.342624 + 0.593442i
\(231\) 0 0
\(232\) 3.00000 5.19615i 0.196960 0.341144i
\(233\) 18.0000i 1.17922i 0.807688 + 0.589610i \(0.200718\pi\)
−0.807688 + 0.589610i \(0.799282\pi\)
\(234\) −2.59808 + 10.5000i −0.169842 + 0.686406i
\(235\) 12.0000 0.782794
\(236\) −0.866025 + 1.50000i −0.0563735 + 0.0976417i
\(237\) 8.66025 15.0000i 0.562544 0.974355i
\(238\) −4.50000 0.866025i −0.291692 0.0561361i
\(239\) 21.0000i 1.35838i −0.733964 0.679189i \(-0.762332\pi\)
0.733964 0.679189i \(-0.237668\pi\)
\(240\) 3.00000 + 5.19615i 0.193649 + 0.335410i
\(241\) −9.00000 + 5.19615i −0.579741 + 0.334714i −0.761030 0.648716i \(-0.775306\pi\)
0.181289 + 0.983430i \(0.441973\pi\)
\(242\) 11.0000i 0.707107i
\(243\) −7.79423 13.5000i −0.500000 0.866025i
\(244\) −10.5000 6.06218i −0.672194 0.388091i
\(245\) 22.5167 + 9.00000i 1.43854 + 0.574989i
\(246\) 12.0000i 0.765092i
\(247\) 0 0
\(248\) 1.73205 0.109985
\(249\) 10.5000 18.1865i 0.665410 1.15252i
\(250\) −6.00000 3.46410i −0.379473 0.219089i
\(251\) 9.52628 + 16.5000i 0.601293 + 1.04147i 0.992626 + 0.121221i \(0.0386810\pi\)
−0.391332 + 0.920250i \(0.627986\pi\)
\(252\) −6.00000 5.19615i −0.377964 0.327327i
\(253\) 0 0
\(254\) −17.3205 + 10.0000i −1.08679 + 0.627456i
\(255\) −10.3923 −0.650791
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 7.79423 13.5000i 0.486191 0.842107i −0.513683 0.857980i \(-0.671719\pi\)
0.999874 + 0.0158730i \(0.00505273\pi\)
\(258\) 1.50000 + 0.866025i 0.0933859 + 0.0539164i
\(259\) 8.00000 + 6.92820i 0.497096 + 0.430498i
\(260\) 3.46410 + 12.0000i 0.214834 + 0.744208i
\(261\) 18.0000i 1.11417i
\(262\) 13.5000 + 7.79423i 0.834033 + 0.481529i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 31.1769i 1.91518i
\(266\) 0 0
\(267\) 13.5000 + 23.3827i 0.826187 + 1.43100i
\(268\) 7.00000 0.427593
\(269\) −6.92820 12.0000i −0.422420 0.731653i 0.573756 0.819027i \(-0.305486\pi\)
−0.996176 + 0.0873736i \(0.972153\pi\)
\(270\) −15.5885 9.00000i −0.948683 0.547723i
\(271\) −7.50000 4.33013i −0.455593 0.263036i 0.254597 0.967047i \(-0.418057\pi\)
−0.710189 + 0.704011i \(0.751391\pi\)
\(272\) 1.73205 0.105021
\(273\) −9.52628 13.5000i −0.576557 0.817057i
\(274\) 12.0000 0.724947
\(275\) 0 0
\(276\) 4.50000 + 2.59808i 0.270868 + 0.156386i
\(277\) −1.00000 1.73205i −0.0600842 0.104069i 0.834419 0.551131i \(-0.185804\pi\)
−0.894503 + 0.447062i \(0.852470\pi\)
\(278\) −6.92820 −0.415526
\(279\) −4.50000 + 2.59808i −0.269408 + 0.155543i
\(280\) −9.00000 1.73205i −0.537853 0.103510i
\(281\) 12.0000i 0.715860i 0.933748 + 0.357930i \(0.116517\pi\)
−0.933748 + 0.357930i \(0.883483\pi\)
\(282\) 5.19615 3.00000i 0.309426 0.178647i
\(283\) −21.0000 12.1244i −1.24832 0.720718i −0.277546 0.960712i \(-0.589521\pi\)
−0.970774 + 0.239994i \(0.922854\pi\)
\(284\) −12.9904 7.50000i −0.770837 0.445043i
\(285\) 0 0
\(286\) 0 0
\(287\) −13.8564 12.0000i −0.817918 0.708338i
\(288\) 2.59808 + 1.50000i 0.153093 + 0.0883883i
\(289\) 7.00000 12.1244i 0.411765 0.713197i
\(290\) 10.3923 + 18.0000i 0.610257 + 1.05700i
\(291\) 30.0000i 1.75863i
\(292\) −12.0000 + 6.92820i −0.702247 + 0.405442i
\(293\) 8.66025 + 15.0000i 0.505937 + 0.876309i 0.999976 + 0.00686959i \(0.00218668\pi\)
−0.494039 + 0.869440i \(0.664480\pi\)
\(294\) 12.0000 1.73205i 0.699854 0.101015i
\(295\) −3.00000 5.19615i −0.174667 0.302532i
\(296\) −3.46410 2.00000i −0.201347 0.116248i
\(297\) 0 0
\(298\) 21.0000 1.21650
\(299\) 7.79423 + 7.50000i 0.450752 + 0.433736i
\(300\) −12.1244 −0.700000
\(301\) −2.50000 + 0.866025i −0.144098 + 0.0499169i
\(302\) 13.8564 + 8.00000i 0.797347 + 0.460348i
\(303\) 0 0
\(304\) 0 0
\(305\) 36.3731 21.0000i 2.08272 1.20246i
\(306\) −4.50000 + 2.59808i −0.257248 + 0.148522i
\(307\) 24.2487i 1.38395i 0.721923 + 0.691974i \(0.243259\pi\)
−0.721923 + 0.691974i \(0.756741\pi\)
\(308\) 0 0
\(309\) 12.9904 + 7.50000i 0.738997 + 0.426660i
\(310\) −3.00000 + 5.19615i −0.170389 + 0.295122i
\(311\) −13.8564 −0.785725 −0.392862 0.919597i \(-0.628515\pi\)
−0.392862 + 0.919597i \(0.628515\pi\)
\(312\) 4.50000 + 4.33013i 0.254762 + 0.245145i
\(313\) 3.46410i 0.195803i −0.995196 0.0979013i \(-0.968787\pi\)
0.995196 0.0979013i \(-0.0312129\pi\)
\(314\) −6.92820 + 12.0000i −0.390981 + 0.677199i
\(315\) 25.9808 9.00000i 1.46385 0.507093i
\(316\) −5.00000 8.66025i −0.281272 0.487177i
\(317\) 3.00000i 0.168497i 0.996445 + 0.0842484i \(0.0268489\pi\)
−0.996445 + 0.0842484i \(0.973151\pi\)
\(318\) −7.79423 13.5000i −0.437079 0.757042i
\(319\) 0 0
\(320\) 3.46410 0.193649
\(321\) 27.0000 15.5885i 1.50699 0.870063i
\(322\) −7.50000 + 2.59808i −0.417959 + 0.144785i
\(323\) 0 0
\(324\) −9.00000 −0.500000
\(325\) −24.5000 6.06218i −1.35902 0.336269i
\(326\) 7.00000i 0.387694i
\(327\) −13.8564 + 24.0000i −0.766261 + 1.32720i
\(328\) 6.00000 + 3.46410i 0.331295 + 0.191273i
\(329\) −1.73205 + 9.00000i −0.0954911 + 0.496186i
\(330\) 0 0
\(331\) −14.0000 24.2487i −0.769510 1.33283i −0.937829 0.347097i \(-0.887167\pi\)
0.168320 0.985732i \(-0.446166\pi\)
\(332\) −6.06218 10.5000i −0.332705 0.576262i
\(333\) 12.0000 0.657596
\(334\) −6.00000 + 3.46410i −0.328305 + 0.189547i
\(335\) −12.1244 + 21.0000i −0.662424 + 1.14735i
\(336\) −4.33013 + 1.50000i −0.236228 + 0.0818317i
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) 6.92820 + 11.0000i 0.376845 + 0.598321i
\(339\) 10.3923i 0.564433i
\(340\) −3.00000 + 5.19615i −0.162698 + 0.281801i
\(341\) 0 0
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 0.866025 0.500000i 0.0466930 0.0269582i
\(345\) −15.5885 + 9.00000i −0.839254 + 0.484544i
\(346\) 0 0
\(347\) −10.3923 + 6.00000i −0.557888 + 0.322097i −0.752297 0.658824i \(-0.771054\pi\)
0.194409 + 0.980921i \(0.437721\pi\)
\(348\) 9.00000 + 5.19615i 0.482451 + 0.278543i
\(349\) −25.5000 14.7224i −1.36498 0.788074i −0.374701 0.927146i \(-0.622255\pi\)
−0.990282 + 0.139072i \(0.955588\pi\)
\(350\) 12.1244 14.0000i 0.648074 0.748331i
\(351\) −18.1865 4.50000i −0.970725 0.240192i
\(352\) 0 0
\(353\) −6.06218 + 10.5000i −0.322657 + 0.558859i −0.981035 0.193829i \(-0.937909\pi\)
0.658378 + 0.752687i \(0.271243\pi\)
\(354\) −2.59808 1.50000i −0.138086 0.0797241i
\(355\) 45.0000 25.9808i 2.38835 1.37892i
\(356\) 15.5885 0.826187
\(357\) 1.50000 7.79423i 0.0793884 0.412514i
\(358\) 0 0
\(359\) 24.0000i 1.26667i −0.773877 0.633336i \(-0.781685\pi\)
0.773877 0.633336i \(-0.218315\pi\)
\(360\) −9.00000 + 5.19615i −0.474342 + 0.273861i
\(361\) −9.50000 + 16.4545i −0.500000 + 0.866025i
\(362\) 0 0
\(363\) 19.0526 1.00000
\(364\) −9.50000 + 0.866025i −0.497935 + 0.0453921i
\(365\) 48.0000i 2.51243i
\(366\) 10.5000 18.1865i 0.548844 0.950625i
\(367\) −10.5000 6.06218i −0.548096 0.316443i 0.200258 0.979743i \(-0.435822\pi\)
−0.748354 + 0.663300i \(0.769155\pi\)
\(368\) 2.59808 1.50000i 0.135434 0.0781929i
\(369\) −20.7846 −1.08200
\(370\) 12.0000 6.92820i 0.623850 0.360180i
\(371\) 23.3827 + 4.50000i 1.21397 + 0.233628i
\(372\) 3.00000i 0.155543i
\(373\) −7.00000 12.1244i −0.362446 0.627775i 0.625917 0.779890i \(-0.284725\pi\)
−0.988363 + 0.152115i \(0.951392\pi\)
\(374\) 0 0
\(375\) 6.00000 10.3923i 0.309839 0.536656i
\(376\) 3.46410i 0.178647i
\(377\) 15.5885 + 15.0000i 0.802846 + 0.772539i
\(378\) 9.00000 10.3923i 0.462910 0.534522i
\(379\) 10.0000 17.3205i 0.513665 0.889695i −0.486209 0.873843i \(-0.661621\pi\)
0.999874 0.0158521i \(-0.00504609\pi\)
\(380\) 0 0
\(381\) −17.3205 30.0000i −0.887357 1.53695i
\(382\) 15.0000 0.767467
\(383\) −12.1244 21.0000i −0.619526 1.07305i −0.989572 0.144037i \(-0.953992\pi\)
0.370047 0.929013i \(-0.379342\pi\)
\(384\) 1.50000 0.866025i 0.0765466 0.0441942i
\(385\) 0 0
\(386\) 12.1244 7.00000i 0.617113 0.356291i
\(387\) −1.50000 + 2.59808i −0.0762493 + 0.132068i
\(388\) 15.0000 + 8.66025i 0.761510 + 0.439658i
\(389\) 9.00000i 0.456318i −0.973624 0.228159i \(-0.926729\pi\)
0.973624 0.228159i \(-0.0732706\pi\)
\(390\) −20.7846 + 6.00000i −1.05247 + 0.303822i
\(391\) 5.19615i 0.262781i
\(392\) 2.59808 6.50000i 0.131223 0.328300i
\(393\) −13.5000 + 23.3827i −0.680985 + 1.17950i
\(394\) −7.50000 12.9904i −0.377845 0.654446i
\(395\) 34.6410 1.74298
\(396\) 0 0
\(397\) −10.5000 + 6.06218i −0.526980 + 0.304252i −0.739786 0.672843i \(-0.765073\pi\)
0.212806 + 0.977095i \(0.431740\pi\)
\(398\) 1.73205 0.0868199
\(399\) 0 0
\(400\) −3.50000 + 6.06218i −0.175000 + 0.303109i
\(401\) −15.5885 9.00000i −0.778450 0.449439i 0.0574304 0.998350i \(-0.481709\pi\)
−0.835881 + 0.548911i \(0.815043\pi\)
\(402\) 12.1244i 0.604708i
\(403\) −1.50000 + 6.06218i −0.0747203 + 0.301979i
\(404\) 0 0
\(405\) 15.5885 27.0000i 0.774597 1.34164i
\(406\) −15.0000 + 5.19615i −0.744438 + 0.257881i
\(407\) 0 0
\(408\) 3.00000i 0.148522i
\(409\) −12.0000 + 6.92820i −0.593362 + 0.342578i −0.766426 0.642333i \(-0.777967\pi\)
0.173064 + 0.984911i \(0.444633\pi\)
\(410\) −20.7846 + 12.0000i −1.02648 + 0.592638i
\(411\) 20.7846i 1.02523i
\(412\) 7.50000 4.33013i 0.369498 0.213330i
\(413\) 4.33013 1.50000i 0.213072 0.0738102i
\(414\) −4.50000 + 7.79423i −0.221163 + 0.383065i
\(415\) 42.0000 2.06170
\(416\) 3.46410 1.00000i 0.169842 0.0490290i
\(417\) 12.0000i 0.587643i
\(418\) 0 0
\(419\) 9.52628 16.5000i 0.465389 0.806078i −0.533830 0.845592i \(-0.679248\pi\)
0.999219 + 0.0395142i \(0.0125810\pi\)
\(420\) 3.00000 15.5885i 0.146385 0.760639i
\(421\) 14.0000 0.682318 0.341159 0.940006i \(-0.389181\pi\)
0.341159 + 0.940006i \(0.389181\pi\)
\(422\) 17.3205 10.0000i 0.843149 0.486792i
\(423\) 5.19615 + 9.00000i 0.252646 + 0.437595i
\(424\) −9.00000 −0.437079
\(425\) −6.06218 10.5000i −0.294059 0.509325i
\(426\) 12.9904 22.5000i 0.629386 1.09013i
\(427\) 10.5000 + 30.3109i 0.508131 + 1.46685i
\(428\) 18.0000i 0.870063i
\(429\) 0 0
\(430\) 3.46410i 0.167054i
\(431\) 2.59808 + 1.50000i 0.125145 + 0.0722525i 0.561266 0.827636i \(-0.310315\pi\)
−0.436121 + 0.899888i \(0.643648\pi\)
\(432\) −2.59808 + 4.50000i −0.125000 + 0.216506i
\(433\) 6.00000 3.46410i 0.288342 0.166474i −0.348852 0.937178i \(-0.613428\pi\)
0.637194 + 0.770704i \(0.280095\pi\)
\(434\) −3.46410 3.00000i −0.166282 0.144005i
\(435\) −31.1769 + 18.0000i −1.49482 + 0.863034i
\(436\) 8.00000 + 13.8564i 0.383131 + 0.663602i
\(437\) 0 0
\(438\) −12.0000 20.7846i −0.573382 0.993127i
\(439\) −3.00000 1.73205i −0.143182 0.0826663i 0.426698 0.904394i \(-0.359677\pi\)
−0.569880 + 0.821728i \(0.693010\pi\)
\(440\) 0 0
\(441\) 3.00000 + 20.7846i 0.142857 + 0.989743i
\(442\) −1.50000 + 6.06218i −0.0713477 + 0.288348i
\(443\) 18.0000i 0.855206i 0.903967 + 0.427603i \(0.140642\pi\)
−0.903967 + 0.427603i \(0.859358\pi\)
\(444\) 3.46410 6.00000i 0.164399 0.284747i
\(445\) −27.0000 + 46.7654i −1.27992 + 2.21689i
\(446\) −2.59808 4.50000i −0.123022 0.213081i
\(447\) 36.3731i 1.72039i
\(448\) −0.500000 + 2.59808i −0.0236228 + 0.122748i
\(449\) 5.19615 3.00000i 0.245222 0.141579i −0.372353 0.928091i \(-0.621449\pi\)
0.617574 + 0.786513i \(0.288115\pi\)
\(450\) 21.0000i 0.989949i
\(451\) 0 0
\(452\) −5.19615 3.00000i −0.244406 0.141108i
\(453\) −13.8564 + 24.0000i −0.651031 + 1.12762i
\(454\) 10.3923i 0.487735i
\(455\) 13.8564 30.0000i 0.649598 1.40642i
\(456\) 0 0
\(457\) −15.5000 + 26.8468i −0.725059 + 1.25584i 0.233890 + 0.972263i \(0.424854\pi\)
−0.958950 + 0.283577i \(0.908479\pi\)
\(458\) −7.79423 + 13.5000i −0.364200 + 0.630814i
\(459\) −4.50000 7.79423i −0.210042 0.363803i
\(460\) 10.3923i 0.484544i
\(461\) 3.46410 + 6.00000i 0.161339 + 0.279448i 0.935349 0.353726i \(-0.115085\pi\)
−0.774010 + 0.633173i \(0.781752\pi\)
\(462\) 0 0
\(463\) 14.0000 0.650635 0.325318 0.945605i \(-0.394529\pi\)
0.325318 + 0.945605i \(0.394529\pi\)
\(464\) 5.19615 3.00000i 0.241225 0.139272i
\(465\) −9.00000 5.19615i −0.417365 0.240966i
\(466\) −9.00000 + 15.5885i −0.416917 + 0.722121i
\(467\) −15.5885 −0.721348 −0.360674 0.932692i \(-0.617453\pi\)
−0.360674 + 0.932692i \(0.617453\pi\)
\(468\) −7.50000 + 7.79423i −0.346688 + 0.360288i
\(469\) −14.0000 12.1244i −0.646460 0.559851i
\(470\) 10.3923 + 6.00000i 0.479361 + 0.276759i
\(471\) −20.7846 12.0000i −0.957704 0.552931i
\(472\) −1.50000 + 0.866025i −0.0690431 + 0.0398621i
\(473\) 0 0
\(474\) 15.0000 8.66025i 0.688973 0.397779i
\(475\) 0 0
\(476\) −3.46410 3.00000i −0.158777 0.137505i
\(477\) 23.3827 13.5000i 1.07062 0.618123i
\(478\) 10.5000 18.1865i 0.480259 0.831833i
\(479\) −12.1244 + 21.0000i −0.553976 + 0.959514i 0.444006 + 0.896024i \(0.353557\pi\)
−0.997982 + 0.0634909i \(0.979777\pi\)
\(480\) 6.00000i 0.273861i
\(481\) 10.0000 10.3923i 0.455961 0.473848i
\(482\) −10.3923 −0.473357
\(483\) −4.50000 12.9904i −0.204757 0.591083i
\(484\) 5.50000 9.52628i 0.250000 0.433013i
\(485\) −51.9615 + 30.0000i −2.35945 + 1.36223i
\(486\) 15.5885i 0.707107i
\(487\) 1.00000 + 1.73205i 0.0453143 + 0.0784867i 0.887793 0.460243i \(-0.152238\pi\)
−0.842479 + 0.538730i \(0.818904\pi\)
\(488\) −6.06218 10.5000i −0.274422 0.475313i
\(489\) −12.1244 −0.548282
\(490\) 15.0000 + 19.0526i 0.677631 + 0.860707i
\(491\) 31.1769 + 18.0000i 1.40699 + 0.812329i 0.995097 0.0989017i \(-0.0315329\pi\)
0.411897 + 0.911230i \(0.364866\pi\)
\(492\) −6.00000 + 10.3923i −0.270501 + 0.468521i
\(493\) 10.3923i 0.468046i
\(494\) 0 0
\(495\) 0 0
\(496\) 1.50000 + 0.866025i 0.0673520 + 0.0388857i
\(497\) 12.9904 + 37.5000i 0.582698 + 1.68210i
\(498\) 18.1865 10.5000i 0.814958 0.470516i
\(499\) −17.0000 −0.761025 −0.380512 0.924776i \(-0.624252\pi\)
−0.380512 + 0.924776i \(0.624252\pi\)
\(500\) −3.46410 6.00000i −0.154919 0.268328i
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) 19.0526i 0.850357i
\(503\) 3.46410 + 6.00000i 0.154457 + 0.267527i 0.932861 0.360236i \(-0.117304\pi\)
−0.778404 + 0.627763i \(0.783971\pi\)
\(504\) −2.59808 7.50000i −0.115728 0.334077i
\(505\) 0 0
\(506\) 0 0
\(507\) −19.0526 + 12.0000i −0.846154 + 0.532939i
\(508\) −20.0000 −0.887357
\(509\) −1.73205 + 3.00000i −0.0767718 + 0.132973i −0.901855 0.432038i \(-0.857795\pi\)
0.825084 + 0.565011i \(0.191128\pi\)
\(510\) −9.00000 5.19615i −0.398527 0.230089i
\(511\) 36.0000 + 6.92820i 1.59255 + 0.306486i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 13.5000 7.79423i 0.595459 0.343789i
\(515\) 30.0000i 1.32196i
\(516\) 0.866025 + 1.50000i 0.0381246 + 0.0660338i
\(517\) 0 0
\(518\) 3.46410 + 10.0000i 0.152204 + 0.439375i
\(519\) 0 0
\(520\) −3.00000 + 12.1244i −0.131559 + 0.531688i
\(521\) 13.8564 0.607060 0.303530 0.952822i \(-0.401835\pi\)
0.303530 + 0.952822i \(0.401835\pi\)
\(522\) −9.00000 + 15.5885i −0.393919 + 0.682288i
\(523\) −18.0000 10.3923i −0.787085 0.454424i 0.0518503 0.998655i \(-0.483488\pi\)
−0.838935 + 0.544231i \(0.816821\pi\)
\(524\) 7.79423 + 13.5000i 0.340492 + 0.589750i
\(525\) 24.2487 + 21.0000i 1.05830 + 0.916515i
\(526\) 0 0
\(527\) −2.59808 + 1.50000i −0.113174 + 0.0653410i
\(528\) 0 0
\(529\) −7.00000 12.1244i −0.304348 0.527146i
\(530\) 15.5885 27.0000i 0.677119 1.17281i
\(531\) 2.59808 4.50000i 0.112747 0.195283i
\(532\) 0 0
\(533\) −17.3205 + 18.0000i −0.750234 + 0.779667i
\(534\) 27.0000i 1.16840i
\(535\) 54.0000 + 31.1769i 2.33462 + 1.34790i
\(536\) 6.06218 + 3.50000i 0.261846 + 0.151177i
\(537\) 0 0
\(538\) 13.8564i 0.597392i
\(539\) 0 0
\(540\) −9.00000 15.5885i −0.387298 0.670820i
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) −4.33013 7.50000i −0.185995 0.322153i
\(543\) 0 0
\(544\) 1.50000 + 0.866025i 0.0643120 + 0.0371305i
\(545\) −55.4256 −2.37417
\(546\) −1.50000 16.4545i −0.0641941 0.704187i
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 10.3923 + 6.00000i 0.443937 + 0.256307i
\(549\) 31.5000 + 18.1865i 1.34439 + 0.776182i
\(550\) 0 0
\(551\) 0 0
\(552\) 2.59808 + 4.50000i 0.110581 + 0.191533i
\(553\) −5.00000 + 25.9808i −0.212622 + 1.10481i
\(554\) 2.00000i 0.0849719i
\(555\) 12.0000 + 20.7846i 0.509372 + 0.882258i
\(556\) −6.00000 3.46410i −0.254457 0.146911i
\(557\) 18.1865 + 10.5000i 0.770588 + 0.444899i 0.833084 0.553146i \(-0.186573\pi\)
−0.0624962 + 0.998045i \(0.519906\pi\)
\(558\) −5.19615 −0.219971
\(559\) 1.00000 + 3.46410i 0.0422955 + 0.146516i
\(560\) −6.92820 6.00000i −0.292770 0.253546i
\(561\) 0 0
\(562\) −6.00000 + 10.3923i −0.253095 + 0.438373i
\(563\) 5.19615 + 9.00000i 0.218992 + 0.379305i 0.954500 0.298211i \(-0.0963899\pi\)
−0.735508 + 0.677516i \(0.763057\pi\)
\(564\) 6.00000 0.252646
\(565\) 18.0000 10.3923i 0.757266 0.437208i
\(566\) −12.1244 21.0000i −0.509625 0.882696i
\(567\) 18.0000 + 15.5885i 0.755929 + 0.654654i
\(568\) −7.50000 12.9904i −0.314693 0.545064i
\(569\) 15.5885 + 9.00000i 0.653502 + 0.377300i 0.789797 0.613369i \(-0.210186\pi\)
−0.136295 + 0.990668i \(0.543519\pi\)
\(570\) 0 0
\(571\) −37.0000 −1.54840 −0.774201 0.632940i \(-0.781848\pi\)
−0.774201 + 0.632940i \(0.781848\pi\)
\(572\) 0 0
\(573\) 25.9808i 1.08536i
\(574\) −6.00000 17.3205i −0.250435 0.722944i
\(575\) −18.1865 10.5000i −0.758431 0.437880i
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) 10.3923i 0.432637i −0.976323 0.216319i \(-0.930595\pi\)
0.976323 0.216319i \(-0.0694050\pi\)
\(578\) 12.1244 7.00000i 0.504307 0.291162i
\(579\) 12.1244 + 21.0000i 0.503871 + 0.872730i
\(580\) 20.7846i 0.863034i
\(581\) −6.06218 + 31.5000i −0.251502 + 1.30684i
\(582\) −15.0000 + 25.9808i −0.621770 + 1.07694i
\(583\) 0 0
\(584\) −13.8564 −0.573382
\(585\) −10.3923 36.0000i −0.429669 1.48842i
\(586\) 17.3205i 0.715504i
\(587\) 2.59808 4.50000i 0.107234 0.185735i −0.807415 0.589984i \(-0.799134\pi\)
0.914649 + 0.404249i \(0.132467\pi\)
\(588\) 11.2583 + 4.50000i 0.464286 + 0.185577i
\(589\) 0 0
\(590\) 6.00000i 0.247016i
\(591\) 22.5000 12.9904i 0.925526 0.534353i
\(592\) −2.00000 3.46410i −0.0821995 0.142374i
\(593\) 39.8372 1.63592 0.817958 0.575278i \(-0.195106\pi\)
0.817958 + 0.575278i \(0.195106\pi\)
\(594\) 0 0
\(595\) 15.0000 5.19615i 0.614940 0.213021i
\(596\) 18.1865 + 10.5000i 0.744949 + 0.430097i
\(597\) 3.00000i 0.122782i
\(598\) 3.00000 + 10.3923i 0.122679 + 0.424973i
\(599\) 33.0000i 1.34834i 0.738575 + 0.674172i \(0.235499\pi\)
−0.738575 + 0.674172i \(0.764501\pi\)
\(600\) −10.5000 6.06218i −0.428661 0.247487i
\(601\) 27.0000 + 15.5885i 1.10135 + 0.635866i 0.936576 0.350464i \(-0.113976\pi\)
0.164777 + 0.986331i \(0.447310\pi\)
\(602\) −2.59808 0.500000i −0.105890 0.0203785i
\(603\) −21.0000 −0.855186
\(604\) 8.00000 + 13.8564i 0.325515 + 0.563809i
\(605\) 19.0526 + 33.0000i 0.774597 + 1.34164i
\(606\) 0 0
\(607\) 4.50000 2.59808i 0.182649 0.105453i −0.405887 0.913923i \(-0.633038\pi\)
0.588537 + 0.808470i \(0.299704\pi\)
\(608\) 0 0
\(609\) −9.00000 25.9808i −0.364698 1.05279i
\(610\) 42.0000 1.70053
\(611\) 12.1244 + 3.00000i 0.490499 + 0.121367i
\(612\) −5.19615 −0.210042
\(613\) 5.00000 8.66025i 0.201948 0.349784i −0.747208 0.664590i \(-0.768606\pi\)
0.949156 + 0.314806i \(0.101939\pi\)
\(614\) −12.1244 + 21.0000i −0.489299 + 0.847491i
\(615\) −20.7846 36.0000i −0.838116 1.45166i
\(616\) 0 0
\(617\) −41.5692 + 24.0000i −1.67351 + 0.966204i −0.707867 + 0.706346i \(0.750342\pi\)
−0.965647 + 0.259858i \(0.916324\pi\)
\(618\) 7.50000 + 12.9904i 0.301694 + 0.522550i
\(619\) 38.1051i 1.53157i −0.643094 0.765787i \(-0.722350\pi\)
0.643094 0.765787i \(-0.277650\pi\)
\(620\) −5.19615 + 3.00000i −0.208683 + 0.120483i
\(621\) −13.5000 7.79423i −0.541736 0.312772i
\(622\) −12.0000 6.92820i −0.481156 0.277796i
\(623\) −31.1769 27.0000i −1.24908 1.08173i
\(624\) 1.73205 + 6.00000i 0.0693375 + 0.240192i
\(625\) −11.0000 −0.440000
\(626\) 1.73205 3.00000i 0.0692267 0.119904i
\(627\) 0 0
\(628\) −12.0000 + 6.92820i −0.478852 + 0.276465i
\(629\) 6.92820 0.276246
\(630\) 27.0000 + 5.19615i 1.07571 + 0.207020i
\(631\) −10.0000 17.3205i −0.398094 0.689519i 0.595397 0.803432i \(-0.296995\pi\)
−0.993491 + 0.113913i \(0.963661\pi\)
\(632\) 10.0000i 0.397779i
\(633\) 17.3205 + 30.0000i 0.688428 + 1.19239i
\(634\) −1.50000 + 2.59808i −0.0595726 + 0.103183i
\(635\) 34.6410 60.0000i 1.37469 2.38103i
\(636\) 15.5885i 0.618123i
\(637\) 20.5000 + 14.7224i 0.812240 + 0.583324i
\(638\) 0 0
\(639\) 38.9711 + 22.5000i 1.54167 + 0.890086i
\(640\) 3.00000 + 1.73205i 0.118585 + 0.0684653i
\(641\) −10.3923 + 6.00000i −0.410471 + 0.236986i −0.690992 0.722862i \(-0.742826\pi\)
0.280521 + 0.959848i \(0.409493\pi\)
\(642\) 31.1769 1.23045
\(643\) −6.00000 + 3.46410i −0.236617 + 0.136611i −0.613621 0.789601i \(-0.710288\pi\)
0.377004 + 0.926212i \(0.376954\pi\)
\(644\) −7.79423 1.50000i −0.307136 0.0591083i
\(645\) −6.00000 −0.236250
\(646\) 0 0
\(647\) 10.3923 18.0000i 0.408564 0.707653i −0.586165 0.810191i \(-0.699363\pi\)
0.994729 + 0.102538i \(0.0326965\pi\)
\(648\) −7.79423 4.50000i −0.306186 0.176777i
\(649\) 0 0
\(650\) −18.1865 17.5000i −0.713335 0.686406i
\(651\) 5.19615 6.00000i 0.203653 0.235159i
\(652\) −3.50000 + 6.06218i −0.137071 + 0.237413i
\(653\) −33.7750 19.5000i −1.32172 0.763094i −0.337715 0.941248i \(-0.609654\pi\)
−0.984003 + 0.178154i \(0.942987\pi\)
\(654\) −24.0000 + 13.8564i −0.938474 + 0.541828i
\(655\) −54.0000 −2.10995
\(656\) 3.46410 + 6.00000i 0.135250 + 0.234261i
\(657\) 36.0000 20.7846i 1.40449 0.810885i
\(658\) −6.00000 + 6.92820i −0.233904 + 0.270089i
\(659\) 5.19615 3.00000i 0.202413 0.116863i −0.395367 0.918523i \(-0.629383\pi\)
0.597781 + 0.801660i \(0.296049\pi\)
\(660\) 0 0
\(661\) 10.5000 + 6.06218i 0.408403 + 0.235791i 0.690103 0.723711i \(-0.257565\pi\)
−0.281701 + 0.959502i \(0.590898\pi\)
\(662\) 28.0000i 1.08825i
\(663\) −10.5000 2.59808i −0.407786 0.100901i
\(664\) 12.1244i 0.470516i
\(665\) 0 0
\(666\) 10.3923 + 6.00000i 0.402694 + 0.232495i
\(667\) 9.00000 + 15.5885i 0.348481 + 0.603587i
\(668\) −6.92820 −0.268060
\(669\) 7.79423 4.50000i 0.301342 0.173980i
\(670\) −21.0000 + 12.1244i −0.811301 + 0.468405i
\(671\) 0 0
\(672\) −4.50000 0.866025i −0.173591 0.0334077i
\(673\) 20.5000 35.5070i 0.790217 1.36870i −0.135615 0.990762i \(-0.543301\pi\)
0.925832 0.377934i \(-0.123365\pi\)
\(674\) −12.1244 7.00000i −0.467013 0.269630i
\(675\) 36.3731 1.40000
\(676\) 0.500000 + 12.9904i 0.0192308 + 0.499630i
\(677\) 20.7846 0.798817 0.399409 0.916773i \(-0.369215\pi\)
0.399409 + 0.916773i \(0.369215\pi\)
\(678\) 5.19615 9.00000i 0.199557 0.345643i
\(679\) −15.0000 43.3013i −0.575647 1.66175i
\(680\) −5.19615 + 3.00000i −0.199263 + 0.115045i
\(681\) 18.0000 0.689761
\(682\) 0 0
\(683\) −10.3923 + 6.00000i −0.397650 + 0.229584i −0.685470 0.728101i \(-0.740403\pi\)
0.287819 + 0.957685i \(0.407070\pi\)
\(684\) 0 0
\(685\) −36.0000 + 20.7846i −1.37549 + 0.794139i
\(686\) −16.4545 + 8.50000i −0.628235 + 0.324532i
\(687\) −23.3827 13.5000i −0.892105 0.515057i
\(688\) 1.00000 0.0381246
\(689\) 7.79423 31.5000i 0.296936 1.20005i
\(690\) −18.0000 −0.685248
\(691\) −39.0000 22.5167i −1.48363 0.856574i −0.483803 0.875177i \(-0.660745\pi\)
−0.999827 + 0.0186028i \(0.994078\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 20.7846 12.0000i 0.788405 0.455186i
\(696\) 5.19615 + 9.00000i 0.196960 + 0.341144i
\(697\) −12.0000 −0.454532
\(698\) −14.7224 25.5000i −0.557252 0.965189i
\(699\) −27.0000 15.5885i −1.02123 0.589610i
\(700\) 17.5000 6.06218i 0.661438 0.229129i
\(701\) 33.0000i 1.24639i −0.782065 0.623196i \(-0.785834\pi\)
0.782065 0.623196i \(-0.214166\pi\)
\(702\) −13.5000 12.9904i −0.509525 0.490290i
\(703\) 0 0
\(704\) 0 0
\(705\) −10.3923 + 18.0000i −0.391397 + 0.677919i
\(706\) −10.5000 + 6.06218i −0.395173 + 0.228153i
\(707\) 0 0
\(708\) −1.50000 2.59808i −0.0563735 0.0976417i
\(709\) −14.0000 24.2487i −0.525781 0.910679i −0.999549 0.0300298i \(-0.990440\pi\)
0.473768 0.880650i \(-0.342894\pi\)
\(710\) 51.9615 1.95008
\(711\) 15.0000 + 25.9808i 0.562544 + 0.974355i
\(712\) 13.5000 + 7.79423i 0.505934 + 0.292101i
\(713\) −2.59808 + 4.50000i −0.0972987 + 0.168526i
\(714\) 5.19615 6.00000i 0.194461 0.224544i
\(715\) 0 0
\(716\) 0 0
\(717\) 31.5000 + 18.1865i 1.17639 + 0.679189i
\(718\) 12.0000 20.7846i 0.447836 0.775675i
\(719\) −12.1244 21.0000i −0.452162 0.783168i 0.546358 0.837552i \(-0.316014\pi\)
−0.998520 + 0.0543839i \(0.982681\pi\)
\(720\) −10.3923 −0.387298
\(721\) −22.5000 4.33013i −0.837944 0.161262i
\(722\) −16.4545 + 9.50000i −0.612372 + 0.353553i
\(723\) 18.0000i 0.669427i
\(724\) 0 0
\(725\) −36.3731 21.0000i −1.35086 0.779920i
\(726\) 16.5000 + 9.52628i 0.612372 + 0.353553i
\(727\) 12.1244i 0.449667i 0.974397 + 0.224834i \(0.0721839\pi\)
−0.974397 + 0.224834i \(0.927816\pi\)
\(728\) −8.66025 4.00000i −0.320970 0.148250i
\(729\) 27.0000 1.00000
\(730\) 24.0000 41.5692i 0.888280 1.53855i
\(731\) −0.866025 + 1.50000i −0.0320311 + 0.0554795i
\(732\) 18.1865 10.5000i 0.672194 0.388091i
\(733\) 8.66025i 0.319874i −0.987127 0.159937i \(-0.948871\pi\)
0.987127 0.159937i \(-0.0511291\pi\)
\(734\) −6.06218 10.5000i −0.223759 0.387562i
\(735\) −33.0000 + 25.9808i −1.21722 + 0.958315i
\(736\) 3.00000 0.110581
\(737\) 0 0
\(738\) −18.0000 10.3923i −0.662589 0.382546i
\(739\) 3.50000 6.06218i 0.128750 0.223001i −0.794443 0.607339i \(-0.792237\pi\)
0.923192 + 0.384338i \(0.125570\pi\)
\(740\) 13.8564 0.509372
\(741\) 0 0
\(742\) 18.0000 + 15.5885i 0.660801 + 0.572270i
\(743\) 23.3827 + 13.5000i 0.857828 + 0.495267i 0.863284 0.504718i \(-0.168404\pi\)
−0.00545664 + 0.999985i \(0.501737\pi\)
\(744\) −1.50000 + 2.59808i −0.0549927 + 0.0952501i
\(745\) −63.0000 + 36.3731i −2.30814 + 1.33261i
\(746\) 14.0000i 0.512576i
\(747\) 18.1865 + 31.5000i 0.665410 + 1.15252i
\(748\) 0 0
\(749\) −31.1769 + 36.0000i −1.13918 + 1.31541i
\(750\) 10.3923 6.00000i 0.379473 0.219089i
\(751\) −2.00000 + 3.46410i −0.0729810 + 0.126407i −0.900207 0.435463i \(-0.856585\pi\)
0.827225 + 0.561870i \(0.189918\pi\)
\(752\) 1.73205 3.00000i 0.0631614 0.109399i
\(753\) −33.0000 −1.20259
\(754\) 6.00000 + 20.7846i 0.218507 + 0.756931i
\(755\) −55.4256 −2.01715
\(756\) 12.9904 4.50000i 0.472456 0.163663i
\(757\) −11.0000 + 19.0526i −0.399802 + 0.692477i −0.993701 0.112062i \(-0.964254\pi\)
0.593899 + 0.804539i \(0.297588\pi\)
\(758\) 17.3205 10.0000i 0.629109 0.363216i
\(759\) 0 0
\(760\) 0 0
\(761\) 24.2487 + 42.0000i 0.879015 + 1.52250i 0.852423 + 0.522852i \(0.175132\pi\)
0.0265919 + 0.999646i \(0.491535\pi\)
\(762\) 34.6410i 1.25491i
\(763\) 8.00000 41.5692i 0.289619 1.50491i
\(764\) 12.9904 + 7.50000i 0.469975 + 0.271340i
\(765\) 9.00000 15.5885i 0.325396 0.563602i
\(766\) 24.2487i 0.876142i
\(767\) −1.73205 6.00000i −0.0625407 0.216647i
\(768\) 1.73205 0.0625000
\(769\) 36.0000 + 20.7846i 1.29819 + 0.749512i 0.980092 0.198545i \(-0.0636214\pi\)
0.318101 + 0.948057i \(0.396955\pi\)
\(770\) 0 0
\(771\) 13.5000 + 23.3827i 0.486191 + 0.842107i
\(772\) 14.0000 0.503871
\(773\) 17.3205 + 30.0000i 0.622975 + 1.07903i 0.988929 + 0.148392i \(0.0474097\pi\)
−0.365953 + 0.930633i \(0.619257\pi\)
\(774\) −2.59808 + 1.50000i −0.0933859 + 0.0539164i
\(775\) 12.1244i 0.435520i
\(776\) 8.66025 + 15.0000i 0.310885 + 0.538469i
\(777\) −17.3205 + 6.00000i −0.621370 + 0.215249i
\(778\) 4.50000 7.79423i 0.161333 0.279437i
\(779\) 0 0
\(780\) −21.0000 5.19615i −0.751921 0.186052i
\(781\) 0