Properties

Label 1050.2.o.f.949.1
Level $1050$
Weight $2$
Character 1050.949
Analytic conductor $8.384$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
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 949.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1050.949
Dual form 1050.2.o.f.499.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(0.866025 - 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(0.866025 - 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +(0.866025 - 0.500000i) q^{12} +4.00000i q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.33013 + 2.50000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-2.00000 - 3.46410i) q^{19} +(2.00000 - 1.73205i) q^{21} +2.00000i q^{22} +(-4.33013 + 2.50000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{26} +1.00000i q^{27} +(-1.73205 - 2.00000i) q^{28} +6.00000 q^{29} +(5.50000 - 9.52628i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.73205 - 1.00000i) q^{33} -5.00000 q^{34} +1.00000 q^{36} +(6.92820 - 4.00000i) q^{37} +(3.46410 + 2.00000i) q^{38} +(-2.00000 + 3.46410i) q^{39} +5.00000 q^{41} +(-0.866025 + 2.50000i) q^{42} +(-1.00000 - 1.73205i) q^{44} +(2.50000 - 4.33013i) q^{46} +(-0.866025 + 0.500000i) q^{47} -1.00000i q^{48} +(-5.50000 - 4.33013i) q^{49} +(2.50000 + 4.33013i) q^{51} +(3.46410 + 2.00000i) q^{52} +(10.3923 + 6.00000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(2.50000 + 0.866025i) q^{56} -4.00000i q^{57} +(-5.19615 + 3.00000i) q^{58} +(-1.00000 + 1.73205i) q^{59} +(-5.00000 - 8.66025i) q^{61} +11.0000i q^{62} +(2.59808 - 0.500000i) q^{63} -1.00000 q^{64} +(-1.00000 + 1.73205i) q^{66} +(4.33013 - 2.50000i) q^{68} -5.00000 q^{69} -1.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(1.73205 + 1.00000i) q^{73} +(-4.00000 + 6.92820i) q^{74} -4.00000 q^{76} +(-3.46410 - 4.00000i) q^{77} -4.00000i q^{78} +(4.50000 + 7.79423i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.33013 + 2.50000i) q^{82} -6.00000i q^{83} +(-0.500000 - 2.59808i) q^{84} +(5.19615 + 3.00000i) q^{87} +(1.73205 + 1.00000i) q^{88} +(5.50000 + 9.52628i) q^{89} +(10.0000 + 3.46410i) q^{91} +5.00000i q^{92} +(9.52628 - 5.50000i) q^{93} +(0.500000 - 0.866025i) q^{94} +(0.500000 + 0.866025i) q^{96} -1.00000i q^{97} +(6.92820 + 1.00000i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} - 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} - 4q^{6} + 2q^{9} + 4q^{11} + 2q^{14} - 2q^{16} - 8q^{19} + 8q^{21} - 2q^{24} - 8q^{26} + 24q^{29} + 22q^{31} - 20q^{34} + 4q^{36} - 8q^{39} + 20q^{41} - 4q^{44} + 10q^{46} - 22q^{49} + 10q^{51} - 2q^{54} + 10q^{56} - 4q^{59} - 20q^{61} - 4q^{64} - 4q^{66} - 20q^{69} - 4q^{71} - 16q^{74} - 16q^{76} + 18q^{79} - 2q^{81} - 2q^{84} + 22q^{89} + 40q^{91} + 2q^{94} + 2q^{96} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) 0.866025 2.50000i 0.327327 0.944911i
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) 0.866025 0.500000i 0.250000 0.144338i
\(13\) 4.00000i 1.10940i 0.832050 + 0.554700i \(0.187167\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0.500000 + 2.59808i 0.133631 + 0.694365i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 4.33013 + 2.50000i 1.05021 + 0.606339i 0.922708 0.385499i \(-0.125971\pi\)
0.127502 + 0.991838i \(0.459304\pi\)
\(18\) −0.866025 0.500000i −0.204124 0.117851i
\(19\) −2.00000 3.46410i −0.458831 0.794719i 0.540068 0.841621i \(-0.318398\pi\)
−0.998899 + 0.0469020i \(0.985065\pi\)
\(20\) 0 0
\(21\) 2.00000 1.73205i 0.436436 0.377964i
\(22\) 2.00000i 0.426401i
\(23\) −4.33013 + 2.50000i −0.902894 + 0.521286i −0.878138 0.478407i \(-0.841214\pi\)
−0.0247559 + 0.999694i \(0.507881\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) −2.00000 3.46410i −0.392232 0.679366i
\(27\) 1.00000i 0.192450i
\(28\) −1.73205 2.00000i −0.327327 0.377964i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 5.50000 9.52628i 0.987829 1.71097i 0.359211 0.933257i \(-0.383046\pi\)
0.628619 0.777714i \(-0.283621\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 1.73205 1.00000i 0.301511 0.174078i
\(34\) −5.00000 −0.857493
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 6.92820 4.00000i 1.13899 0.657596i 0.192809 0.981236i \(-0.438240\pi\)
0.946180 + 0.323640i \(0.104907\pi\)
\(38\) 3.46410 + 2.00000i 0.561951 + 0.324443i
\(39\) −2.00000 + 3.46410i −0.320256 + 0.554700i
\(40\) 0 0
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) −0.866025 + 2.50000i −0.133631 + 0.385758i
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −1.00000 1.73205i −0.150756 0.261116i
\(45\) 0 0
\(46\) 2.50000 4.33013i 0.368605 0.638442i
\(47\) −0.866025 + 0.500000i −0.126323 + 0.0729325i −0.561830 0.827253i \(-0.689902\pi\)
0.435507 + 0.900185i \(0.356569\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −5.50000 4.33013i −0.785714 0.618590i
\(50\) 0 0
\(51\) 2.50000 + 4.33013i 0.350070 + 0.606339i
\(52\) 3.46410 + 2.00000i 0.480384 + 0.277350i
\(53\) 10.3923 + 6.00000i 1.42749 + 0.824163i 0.996922 0.0783936i \(-0.0249791\pi\)
0.430570 + 0.902557i \(0.358312\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 0 0
\(56\) 2.50000 + 0.866025i 0.334077 + 0.115728i
\(57\) 4.00000i 0.529813i
\(58\) −5.19615 + 3.00000i −0.682288 + 0.393919i
\(59\) −1.00000 + 1.73205i −0.130189 + 0.225494i −0.923749 0.382998i \(-0.874892\pi\)
0.793560 + 0.608492i \(0.208225\pi\)
\(60\) 0 0
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) 11.0000i 1.39700i
\(63\) 2.59808 0.500000i 0.327327 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −1.00000 + 1.73205i −0.123091 + 0.213201i
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) 4.33013 2.50000i 0.525105 0.303170i
\(69\) −5.00000 −0.601929
\(70\) 0 0
\(71\) −1.00000 −0.118678 −0.0593391 0.998238i \(-0.518899\pi\)
−0.0593391 + 0.998238i \(0.518899\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 1.73205 + 1.00000i 0.202721 + 0.117041i 0.597924 0.801553i \(-0.295992\pi\)
−0.395203 + 0.918594i \(0.629326\pi\)
\(74\) −4.00000 + 6.92820i −0.464991 + 0.805387i
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) −3.46410 4.00000i −0.394771 0.455842i
\(78\) 4.00000i 0.452911i
\(79\) 4.50000 + 7.79423i 0.506290 + 0.876919i 0.999974 + 0.00727784i \(0.00231663\pi\)
−0.493684 + 0.869641i \(0.664350\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −4.33013 + 2.50000i −0.478183 + 0.276079i
\(83\) 6.00000i 0.658586i −0.944228 0.329293i \(-0.893190\pi\)
0.944228 0.329293i \(-0.106810\pi\)
\(84\) −0.500000 2.59808i −0.0545545 0.283473i
\(85\) 0 0
\(86\) 0 0
\(87\) 5.19615 + 3.00000i 0.557086 + 0.321634i
\(88\) 1.73205 + 1.00000i 0.184637 + 0.106600i
\(89\) 5.50000 + 9.52628i 0.582999 + 1.00978i 0.995122 + 0.0986553i \(0.0314541\pi\)
−0.412123 + 0.911128i \(0.635213\pi\)
\(90\) 0 0
\(91\) 10.0000 + 3.46410i 1.04828 + 0.363137i
\(92\) 5.00000i 0.521286i
\(93\) 9.52628 5.50000i 0.987829 0.570323i
\(94\) 0.500000 0.866025i 0.0515711 0.0893237i
\(95\) 0 0
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 1.00000i 0.101535i −0.998711 0.0507673i \(-0.983833\pi\)
0.998711 0.0507673i \(-0.0161667\pi\)
\(98\) 6.92820 + 1.00000i 0.699854 + 0.101015i
\(99\) 2.00000 0.201008
\(100\) 0 0
\(101\) −6.00000 + 10.3923i −0.597022 + 1.03407i 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) −4.33013 2.50000i −0.428746 0.247537i
\(103\) −11.2583 + 6.50000i −1.10932 + 0.640464i −0.938652 0.344865i \(-0.887925\pi\)
−0.170664 + 0.985329i \(0.554591\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) −12.0000 −1.16554
\(107\) 1.73205 1.00000i 0.167444 0.0966736i −0.413936 0.910306i \(-0.635846\pi\)
0.581380 + 0.813632i \(0.302513\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) 2.00000 3.46410i 0.191565 0.331801i −0.754204 0.656640i \(-0.771977\pi\)
0.945769 + 0.324840i \(0.105310\pi\)
\(110\) 0 0
\(111\) 8.00000 0.759326
\(112\) −2.59808 + 0.500000i −0.245495 + 0.0472456i
\(113\) 5.00000i 0.470360i −0.971952 0.235180i \(-0.924432\pi\)
0.971952 0.235180i \(-0.0755680\pi\)
\(114\) 2.00000 + 3.46410i 0.187317 + 0.324443i
\(115\) 0 0
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) −3.46410 + 2.00000i −0.320256 + 0.184900i
\(118\) 2.00000i 0.184115i
\(119\) 10.0000 8.66025i 0.916698 0.793884i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 8.66025 + 5.00000i 0.784063 + 0.452679i
\(123\) 4.33013 + 2.50000i 0.390434 + 0.225417i
\(124\) −5.50000 9.52628i −0.493915 0.855485i
\(125\) 0 0
\(126\) −2.00000 + 1.73205i −0.178174 + 0.154303i
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i \(-0.251085\pi\)
−0.966803 + 0.255524i \(0.917752\pi\)
\(132\) 2.00000i 0.174078i
\(133\) −10.3923 + 2.00000i −0.901127 + 0.173422i
\(134\) 0 0
\(135\) 0 0
\(136\) −2.50000 + 4.33013i −0.214373 + 0.371305i
\(137\) −19.9186 11.5000i −1.70176 0.982511i −0.943981 0.329999i \(-0.892952\pi\)
−0.757778 0.652512i \(-0.773715\pi\)
\(138\) 4.33013 2.50000i 0.368605 0.212814i
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) −1.00000 −0.0842152
\(142\) 0.866025 0.500000i 0.0726752 0.0419591i
\(143\) 6.92820 + 4.00000i 0.579365 + 0.334497i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) −2.59808 6.50000i −0.214286 0.536111i
\(148\) 8.00000i 0.657596i
\(149\) 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0 0
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) 3.46410 2.00000i 0.280976 0.162221i
\(153\) 5.00000i 0.404226i
\(154\) 5.00000 + 1.73205i 0.402911 + 0.139573i
\(155\) 0 0
\(156\) 2.00000 + 3.46410i 0.160128 + 0.277350i
\(157\) 12.1244 + 7.00000i 0.967629 + 0.558661i 0.898513 0.438948i \(-0.144649\pi\)
0.0691164 + 0.997609i \(0.477982\pi\)
\(158\) −7.79423 4.50000i −0.620076 0.358001i
\(159\) 6.00000 + 10.3923i 0.475831 + 0.824163i
\(160\) 0 0
\(161\) 2.50000 + 12.9904i 0.197028 + 1.02379i
\(162\) 1.00000i 0.0785674i
\(163\) −20.7846 + 12.0000i −1.62798 + 0.939913i −0.643280 + 0.765631i \(0.722427\pi\)
−0.984696 + 0.174282i \(0.944240\pi\)
\(164\) 2.50000 4.33013i 0.195217 0.338126i
\(165\) 0 0
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) 16.0000i 1.23812i 0.785345 + 0.619059i \(0.212486\pi\)
−0.785345 + 0.619059i \(0.787514\pi\)
\(168\) 1.73205 + 2.00000i 0.133631 + 0.154303i
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) 2.00000 3.46410i 0.152944 0.264906i
\(172\) 0 0
\(173\) 1.73205 1.00000i 0.131685 0.0760286i −0.432710 0.901533i \(-0.642443\pi\)
0.564396 + 0.825505i \(0.309109\pi\)
\(174\) −6.00000 −0.454859
\(175\) 0 0
\(176\) −2.00000 −0.150756
\(177\) −1.73205 + 1.00000i −0.130189 + 0.0751646i
\(178\) −9.52628 5.50000i −0.714025 0.412242i
\(179\) 11.0000 19.0526i 0.822179 1.42406i −0.0818780 0.996642i \(-0.526092\pi\)
0.904057 0.427413i \(-0.140575\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) −10.3923 + 2.00000i −0.770329 + 0.148250i
\(183\) 10.0000i 0.739221i
\(184\) −2.50000 4.33013i −0.184302 0.319221i
\(185\) 0 0
\(186\) −5.50000 + 9.52628i −0.403280 + 0.698501i
\(187\) 8.66025 5.00000i 0.633300 0.365636i
\(188\) 1.00000i 0.0729325i
\(189\) 2.50000 + 0.866025i 0.181848 + 0.0629941i
\(190\) 0 0
\(191\) 12.5000 + 21.6506i 0.904468 + 1.56658i 0.821629 + 0.570022i \(0.193065\pi\)
0.0828388 + 0.996563i \(0.473601\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) 9.52628 + 5.50000i 0.685717 + 0.395899i 0.802005 0.597317i \(-0.203766\pi\)
−0.116289 + 0.993215i \(0.537100\pi\)
\(194\) 0.500000 + 0.866025i 0.0358979 + 0.0621770i
\(195\) 0 0
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) 24.0000i 1.70993i −0.518686 0.854965i \(-0.673579\pi\)
0.518686 0.854965i \(-0.326421\pi\)
\(198\) −1.73205 + 1.00000i −0.123091 + 0.0710669i
\(199\) 2.50000 4.33013i 0.177220 0.306955i −0.763707 0.645563i \(-0.776623\pi\)
0.940927 + 0.338608i \(0.109956\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 12.0000i 0.844317i
\(203\) 5.19615 15.0000i 0.364698 1.05279i
\(204\) 5.00000 0.350070
\(205\) 0 0
\(206\) 6.50000 11.2583i 0.452876 0.784405i
\(207\) −4.33013 2.50000i −0.300965 0.173762i
\(208\) 3.46410 2.00000i 0.240192 0.138675i
\(209\) −8.00000 −0.553372
\(210\) 0 0
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 10.3923 6.00000i 0.713746 0.412082i
\(213\) −0.866025 0.500000i −0.0593391 0.0342594i
\(214\) −1.00000 + 1.73205i −0.0683586 + 0.118401i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −19.0526 22.0000i −1.29337 1.49346i
\(218\) 4.00000i 0.270914i
\(219\) 1.00000 + 1.73205i 0.0675737 + 0.117041i
\(220\) 0 0
\(221\) −10.0000 + 17.3205i −0.672673 + 1.16510i
\(222\) −6.92820 + 4.00000i −0.464991 + 0.268462i
\(223\) 21.0000i 1.40626i −0.711059 0.703132i \(-0.751784\pi\)
0.711059 0.703132i \(-0.248216\pi\)
\(224\) 2.00000 1.73205i 0.133631 0.115728i
\(225\) 0 0
\(226\) 2.50000 + 4.33013i 0.166298 + 0.288036i
\(227\) −15.5885 9.00000i −1.03464 0.597351i −0.116331 0.993210i \(-0.537113\pi\)
−0.918311 + 0.395860i \(0.870447\pi\)
\(228\) −3.46410 2.00000i −0.229416 0.132453i
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) 0 0
\(231\) −1.00000 5.19615i −0.0657952 0.341882i
\(232\) 6.00000i 0.393919i
\(233\) −22.5167 + 13.0000i −1.47512 + 0.851658i −0.999606 0.0280525i \(-0.991069\pi\)
−0.475509 + 0.879711i \(0.657736\pi\)
\(234\) 2.00000 3.46410i 0.130744 0.226455i
\(235\) 0 0
\(236\) 1.00000 + 1.73205i 0.0650945 + 0.112747i
\(237\) 9.00000i 0.584613i
\(238\) −4.33013 + 12.5000i −0.280680 + 0.810255i
\(239\) −11.0000 −0.711531 −0.355765 0.934575i \(-0.615780\pi\)
−0.355765 + 0.934575i \(0.615780\pi\)
\(240\) 0 0
\(241\) 3.00000 5.19615i 0.193247 0.334714i −0.753077 0.657932i \(-0.771431\pi\)
0.946324 + 0.323218i \(0.104765\pi\)
\(242\) −6.06218 3.50000i −0.389692 0.224989i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) −10.0000 −0.640184
\(245\) 0 0
\(246\) −5.00000 −0.318788
\(247\) 13.8564 8.00000i 0.881662 0.509028i
\(248\) 9.52628 + 5.50000i 0.604919 + 0.349250i
\(249\) 3.00000 5.19615i 0.190117 0.329293i
\(250\) 0 0
\(251\) −8.00000 −0.504956 −0.252478 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) 0.866025 2.50000i 0.0545545 0.157485i
\(253\) 10.0000i 0.628695i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −12.1244 + 7.00000i −0.756297 + 0.436648i −0.827964 0.560781i \(-0.810501\pi\)
0.0716680 + 0.997429i \(0.477168\pi\)
\(258\) 0 0
\(259\) −4.00000 20.7846i −0.248548 1.29149i
\(260\) 0 0
\(261\) 3.00000 + 5.19615i 0.185695 + 0.321634i
\(262\) 5.19615 + 3.00000i 0.321019 + 0.185341i
\(263\) −18.1865 10.5000i −1.12143 0.647458i −0.179664 0.983728i \(-0.557501\pi\)
−0.941766 + 0.336270i \(0.890834\pi\)
\(264\) 1.00000 + 1.73205i 0.0615457 + 0.106600i
\(265\) 0 0
\(266\) 8.00000 6.92820i 0.490511 0.424795i
\(267\) 11.0000i 0.673189i
\(268\) 0 0
\(269\) −12.0000 + 20.7846i −0.731653 + 1.26726i 0.224523 + 0.974469i \(0.427917\pi\)
−0.956176 + 0.292791i \(0.905416\pi\)
\(270\) 0 0
\(271\) 4.50000 + 7.79423i 0.273356 + 0.473466i 0.969719 0.244224i \(-0.0785331\pi\)
−0.696363 + 0.717689i \(0.745200\pi\)
\(272\) 5.00000i 0.303170i
\(273\) 6.92820 + 8.00000i 0.419314 + 0.484182i
\(274\) 23.0000 1.38948
\(275\) 0 0
\(276\) −2.50000 + 4.33013i −0.150482 + 0.260643i
\(277\) 1.73205 + 1.00000i 0.104069 + 0.0600842i 0.551131 0.834419i \(-0.314196\pi\)
−0.447062 + 0.894503i \(0.647530\pi\)
\(278\) 1.73205 1.00000i 0.103882 0.0599760i
\(279\) 11.0000 0.658553
\(280\) 0 0
\(281\) −29.0000 −1.72999 −0.864997 0.501776i \(-0.832680\pi\)
−0.864997 + 0.501776i \(0.832680\pi\)
\(282\) 0.866025 0.500000i 0.0515711 0.0297746i
\(283\) −22.5167 13.0000i −1.33848 0.772770i −0.351895 0.936039i \(-0.614463\pi\)
−0.986581 + 0.163270i \(0.947796\pi\)
\(284\) −0.500000 + 0.866025i −0.0296695 + 0.0513892i
\(285\) 0 0
\(286\) −8.00000 −0.473050
\(287\) 4.33013 12.5000i 0.255599 0.737852i
\(288\) 1.00000i 0.0589256i
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) 0.500000 0.866025i 0.0293105 0.0507673i
\(292\) 1.73205 1.00000i 0.101361 0.0585206i
\(293\) 18.0000i 1.05157i −0.850617 0.525786i \(-0.823771\pi\)
0.850617 0.525786i \(-0.176229\pi\)
\(294\) 5.50000 + 4.33013i 0.320767 + 0.252538i
\(295\) 0 0
\(296\) 4.00000 + 6.92820i 0.232495 + 0.402694i
\(297\) 1.73205 + 1.00000i 0.100504 + 0.0580259i
\(298\) −15.5885 9.00000i −0.903015 0.521356i
\(299\) −10.0000 17.3205i −0.578315 1.00167i
\(300\) 0 0
\(301\) 0 0
\(302\) 16.0000i 0.920697i
\(303\) −10.3923 + 6.00000i −0.597022 + 0.344691i
\(304\) −2.00000 + 3.46410i −0.114708 + 0.198680i
\(305\) 0 0
\(306\) −2.50000 4.33013i −0.142915 0.247537i
\(307\) 28.0000i 1.59804i 0.601302 + 0.799022i \(0.294649\pi\)
−0.601302 + 0.799022i \(0.705351\pi\)
\(308\) −5.19615 + 1.00000i −0.296078 + 0.0569803i
\(309\) −13.0000 −0.739544
\(310\) 0 0
\(311\) −14.5000 + 25.1147i −0.822220 + 1.42413i 0.0818063 + 0.996648i \(0.473931\pi\)
−0.904026 + 0.427478i \(0.859402\pi\)
\(312\) −3.46410 2.00000i −0.196116 0.113228i
\(313\) 0.866025 0.500000i 0.0489506 0.0282617i −0.475325 0.879810i \(-0.657669\pi\)
0.524276 + 0.851549i \(0.324336\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) 9.00000 0.506290
\(317\) 3.46410 2.00000i 0.194563 0.112331i −0.399554 0.916710i \(-0.630835\pi\)
0.594117 + 0.804379i \(0.297502\pi\)
\(318\) −10.3923 6.00000i −0.582772 0.336463i
\(319\) 6.00000 10.3923i 0.335936 0.581857i
\(320\) 0 0
\(321\) 2.00000 0.111629
\(322\) −8.66025 10.0000i −0.482617 0.557278i
\(323\) 20.0000i 1.11283i
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) 12.0000 20.7846i 0.664619 1.15115i
\(327\) 3.46410 2.00000i 0.191565 0.110600i
\(328\) 5.00000i 0.276079i
\(329\) 0.500000 + 2.59808i 0.0275659 + 0.143237i
\(330\) 0 0
\(331\) −5.00000 8.66025i −0.274825 0.476011i 0.695266 0.718752i \(-0.255287\pi\)
−0.970091 + 0.242742i \(0.921953\pi\)
\(332\) −5.19615 3.00000i −0.285176 0.164646i
\(333\) 6.92820 + 4.00000i 0.379663 + 0.219199i
\(334\) −8.00000 13.8564i −0.437741 0.758189i
\(335\) 0 0
\(336\) −2.50000 0.866025i −0.136386 0.0472456i
\(337\) 13.0000i 0.708155i 0.935216 + 0.354078i \(0.115205\pi\)
−0.935216 + 0.354078i \(0.884795\pi\)
\(338\) 2.59808 1.50000i 0.141317 0.0815892i
\(339\) 2.50000 4.33013i 0.135781 0.235180i
\(340\) 0 0
\(341\) −11.0000 19.0526i −0.595683 1.03175i
\(342\) 4.00000i 0.216295i
\(343\) −15.5885 + 10.0000i −0.841698 + 0.539949i
\(344\) 0 0
\(345\) 0 0
\(346\) −1.00000 + 1.73205i −0.0537603 + 0.0931156i
\(347\) 15.5885 + 9.00000i 0.836832 + 0.483145i 0.856186 0.516667i \(-0.172828\pi\)
−0.0193540 + 0.999813i \(0.506161\pi\)
\(348\) 5.19615 3.00000i 0.278543 0.160817i
\(349\) 4.00000 0.214115 0.107058 0.994253i \(-0.465857\pi\)
0.107058 + 0.994253i \(0.465857\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) 1.73205 1.00000i 0.0923186 0.0533002i
\(353\) 7.79423 + 4.50000i 0.414845 + 0.239511i 0.692869 0.721063i \(-0.256346\pi\)
−0.278024 + 0.960574i \(0.589680\pi\)
\(354\) 1.00000 1.73205i 0.0531494 0.0920575i
\(355\) 0 0
\(356\) 11.0000 0.582999
\(357\) 12.9904 2.50000i 0.687524 0.132314i
\(358\) 22.0000i 1.16274i
\(359\) −10.0000 17.3205i −0.527780 0.914141i −0.999476 0.0323801i \(-0.989691\pi\)
0.471696 0.881761i \(-0.343642\pi\)
\(360\) 0 0
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) 19.0526 11.0000i 1.00138 0.578147i
\(363\) 7.00000i 0.367405i
\(364\) 8.00000 6.92820i 0.419314 0.363137i
\(365\) 0 0
\(366\) 5.00000 + 8.66025i 0.261354 + 0.452679i
\(367\) 3.46410 + 2.00000i 0.180825 + 0.104399i 0.587680 0.809093i \(-0.300041\pi\)
−0.406855 + 0.913493i \(0.633375\pi\)
\(368\) 4.33013 + 2.50000i 0.225723 + 0.130322i
\(369\) 2.50000 + 4.33013i 0.130145 + 0.225417i
\(370\) 0 0
\(371\) 24.0000 20.7846i 1.24602 1.07908i
\(372\) 11.0000i 0.570323i
\(373\) 27.7128 16.0000i 1.43492 0.828449i 0.437425 0.899255i \(-0.355891\pi\)
0.997490 + 0.0708063i \(0.0225572\pi\)
\(374\) −5.00000 + 8.66025i −0.258544 + 0.447811i
\(375\) 0 0
\(376\) −0.500000 0.866025i −0.0257855 0.0446619i
\(377\) 24.0000i 1.23606i
\(378\) −2.59808 + 0.500000i −0.133631 + 0.0257172i
\(379\) 2.00000 0.102733 0.0513665 0.998680i \(-0.483642\pi\)
0.0513665 + 0.998680i \(0.483642\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −21.6506 12.5000i −1.10774 0.639556i
\(383\) −2.59808 + 1.50000i −0.132755 + 0.0766464i −0.564907 0.825155i \(-0.691088\pi\)
0.432151 + 0.901801i \(0.357755\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −11.0000 −0.559885
\(387\) 0 0
\(388\) −0.866025 0.500000i −0.0439658 0.0253837i
\(389\) 12.0000 20.7846i 0.608424 1.05382i −0.383076 0.923717i \(-0.625135\pi\)
0.991500 0.130105i \(-0.0415314\pi\)
\(390\) 0 0
\(391\) −25.0000 −1.26430
\(392\) 4.33013 5.50000i 0.218704 0.277792i
\(393\) 6.00000i 0.302660i
\(394\) 12.0000 + 20.7846i 0.604551 + 1.04711i
\(395\) 0 0
\(396\) 1.00000 1.73205i 0.0502519 0.0870388i
\(397\) −29.4449 + 17.0000i −1.47780 + 0.853206i −0.999685 0.0250943i \(-0.992011\pi\)
−0.478110 + 0.878300i \(0.658678\pi\)
\(398\) 5.00000i 0.250627i
\(399\) −10.0000 3.46410i −0.500626 0.173422i
\(400\) 0 0
\(401\) 3.00000 + 5.19615i 0.149813 + 0.259483i 0.931158 0.364615i \(-0.118800\pi\)
−0.781345 + 0.624099i \(0.785466\pi\)
\(402\) 0 0
\(403\) 38.1051 + 22.0000i 1.89815 + 1.09590i
\(404\) 6.00000 + 10.3923i 0.298511 + 0.517036i
\(405\) 0 0
\(406\) 3.00000 + 15.5885i 0.148888 + 0.773642i
\(407\) 16.0000i 0.793091i
\(408\) −4.33013 + 2.50000i −0.214373 + 0.123768i
\(409\) −17.5000 + 30.3109i −0.865319 + 1.49878i 0.00141047 + 0.999999i \(0.499551\pi\)
−0.866730 + 0.498778i \(0.833782\pi\)
\(410\) 0 0
\(411\) −11.5000 19.9186i −0.567253 0.982511i
\(412\) 13.0000i 0.640464i
\(413\) 3.46410 + 4.00000i 0.170457 + 0.196827i
\(414\) 5.00000 0.245737
\(415\) 0 0
\(416\) −2.00000 + 3.46410i −0.0980581 + 0.169842i
\(417\) −1.73205 1.00000i −0.0848189 0.0489702i
\(418\) 6.92820 4.00000i 0.338869 0.195646i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 28.0000 1.36464 0.682318 0.731055i \(-0.260972\pi\)
0.682318 + 0.731055i \(0.260972\pi\)
\(422\) 13.8564 8.00000i 0.674519 0.389434i
\(423\) −0.866025 0.500000i −0.0421076 0.0243108i
\(424\) −6.00000 + 10.3923i −0.291386 + 0.504695i
\(425\) 0 0
\(426\) 1.00000 0.0484502
\(427\) −25.9808 + 5.00000i −1.25730 + 0.241967i
\(428\) 2.00000i 0.0966736i
\(429\) 4.00000 + 6.92820i 0.193122 + 0.334497i
\(430\) 0 0
\(431\) 1.50000 2.59808i 0.0722525 0.125145i −0.827636 0.561266i \(-0.810315\pi\)
0.899888 + 0.436121i \(0.143648\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 9.00000i 0.432512i 0.976337 + 0.216256i \(0.0693846\pi\)
−0.976337 + 0.216256i \(0.930615\pi\)
\(434\) 27.5000 + 9.52628i 1.32004 + 0.457276i
\(435\) 0 0
\(436\) −2.00000 3.46410i −0.0957826 0.165900i
\(437\) 17.3205 + 10.0000i 0.828552 + 0.478365i
\(438\) −1.73205 1.00000i −0.0827606 0.0477818i
\(439\) 17.5000 + 30.3109i 0.835229 + 1.44666i 0.893843 + 0.448379i \(0.147999\pi\)
−0.0586141 + 0.998281i \(0.518668\pi\)
\(440\) 0 0
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 20.0000i 0.951303i
\(443\) 6.92820 4.00000i 0.329169 0.190046i −0.326303 0.945265i \(-0.605803\pi\)
0.655472 + 0.755219i \(0.272470\pi\)
\(444\) 4.00000 6.92820i 0.189832 0.328798i
\(445\) 0 0
\(446\) 10.5000 + 18.1865i 0.497189 + 0.861157i
\(447\) 18.0000i 0.851371i
\(448\) −0.866025 + 2.50000i −0.0409159 + 0.118114i
\(449\) −37.0000 −1.74614 −0.873069 0.487597i \(-0.837874\pi\)
−0.873069 + 0.487597i \(0.837874\pi\)
\(450\) 0 0
\(451\) 5.00000 8.66025i 0.235441 0.407795i
\(452\) −4.33013 2.50000i −0.203672 0.117590i
\(453\) 13.8564 8.00000i 0.651031 0.375873i
\(454\) 18.0000 0.844782
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) 12.1244 7.00000i 0.567153 0.327446i −0.188858 0.982004i \(-0.560479\pi\)
0.756012 + 0.654558i \(0.227145\pi\)
\(458\) 12.1244 + 7.00000i 0.566534 + 0.327089i
\(459\) −2.50000 + 4.33013i −0.116690 + 0.202113i
\(460\) 0 0
\(461\) 20.0000 0.931493 0.465746 0.884918i \(-0.345786\pi\)
0.465746 + 0.884918i \(0.345786\pi\)
\(462\) 3.46410 + 4.00000i 0.161165 + 0.186097i
\(463\) 13.0000i 0.604161i −0.953282 0.302081i \(-0.902319\pi\)
0.953282 0.302081i \(-0.0976812\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) 0 0
\(466\) 13.0000 22.5167i 0.602213 1.04306i
\(467\) −29.4449 + 17.0000i −1.36255 + 0.786666i −0.989962 0.141332i \(-0.954861\pi\)
−0.372584 + 0.927999i \(0.621528\pi\)
\(468\) 4.00000i 0.184900i
\(469\) 0 0
\(470\) 0 0
\(471\) 7.00000 + 12.1244i 0.322543 + 0.558661i
\(472\) −1.73205 1.00000i −0.0797241 0.0460287i
\(473\) 0 0
\(474\) −4.50000 7.79423i −0.206692 0.358001i
\(475\) 0 0
\(476\) −2.50000 12.9904i −0.114587 0.595413i
\(477\) 12.0000i 0.549442i
\(478\) 9.52628 5.50000i 0.435722 0.251564i
\(479\) −1.50000 + 2.59808i −0.0685367 + 0.118709i −0.898257 0.439470i \(-0.855166\pi\)
0.829721 + 0.558179i \(0.188500\pi\)
\(480\) 0 0
\(481\) 16.0000 + 27.7128i 0.729537 + 1.26360i
\(482\) 6.00000i 0.273293i
\(483\) −4.33013 + 12.5000i −0.197028 + 0.568770i
\(484\) 7.00000 0.318182
\(485\) 0 0
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) 33.7750 + 19.5000i 1.53049 + 0.883629i 0.999339 + 0.0363527i \(0.0115740\pi\)
0.531152 + 0.847277i \(0.321759\pi\)
\(488\) 8.66025 5.00000i 0.392031 0.226339i
\(489\) −24.0000 −1.08532
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 4.33013 2.50000i 0.195217 0.112709i
\(493\) 25.9808 + 15.0000i 1.17011 + 0.675566i
\(494\) −8.00000 + 13.8564i −0.359937 + 0.623429i
\(495\) 0 0
\(496\) −11.0000 −0.493915
\(497\) −0.866025 + 2.50000i −0.0388465 + 0.112140i
\(498\) 6.00000i 0.268866i
\(499\) 11.0000 + 19.0526i 0.492428 + 0.852910i 0.999962 0.00872186i \(-0.00277629\pi\)
−0.507534 + 0.861632i \(0.669443\pi\)
\(500\) 0 0
\(501\) −8.00000 + 13.8564i −0.357414 + 0.619059i
\(502\) 6.92820 4.00000i 0.309221 0.178529i
\(503\) 8.00000i 0.356702i −0.983967 0.178351i \(-0.942924\pi\)
0.983967 0.178351i \(-0.0570763\pi\)
\(504\) 0.500000 + 2.59808i 0.0222718 + 0.115728i
\(505\) 0 0
\(506\) −5.00000 8.66025i −0.222277 0.384995i
\(507\) −2.59808 1.50000i −0.115385 0.0666173i
\(508\) 0 0
\(509\) 1.00000 + 1.73205i 0.0443242 + 0.0767718i 0.887336 0.461123i \(-0.152553\pi\)
−0.843012 + 0.537895i \(0.819220\pi\)
\(510\) 0 0
\(511\) 4.00000 3.46410i 0.176950 0.153243i
\(512\) 1.00000i 0.0441942i
\(513\) 3.46410 2.00000i 0.152944 0.0883022i
\(514\) 7.00000 12.1244i 0.308757 0.534782i
\(515\) 0 0
\(516\) 0 0
\(517\) 2.00000i 0.0879599i
\(518\) 13.8564 + 16.0000i 0.608816 + 0.703000i
\(519\) 2.00000 0.0877903
\(520\) 0 0
\(521\) 1.50000 2.59808i 0.0657162 0.113824i −0.831295 0.555831i \(-0.812400\pi\)
0.897011 + 0.442007i \(0.145733\pi\)
\(522\) −5.19615 3.00000i −0.227429 0.131306i
\(523\) 12.1244 7.00000i 0.530161 0.306089i −0.210921 0.977503i \(-0.567646\pi\)
0.741082 + 0.671414i \(0.234313\pi\)
\(524\) −6.00000 −0.262111
\(525\) 0 0
\(526\) 21.0000 0.915644
\(527\) 47.6314 27.5000i 2.07486 1.19792i
\(528\) −1.73205 1.00000i −0.0753778 0.0435194i
\(529\) 1.00000 1.73205i 0.0434783 0.0753066i
\(530\) 0 0
\(531\) −2.00000 −0.0867926
\(532\) −3.46410 + 10.0000i −0.150188 + 0.433555i
\(533\) 20.0000i 0.866296i
\(534\) −5.50000 9.52628i −0.238008 0.412242i
\(535\) 0 0
\(536\) 0 0
\(537\) 19.0526 11.0000i 0.822179 0.474685i
\(538\) 24.0000i 1.03471i
\(539\) −13.0000 + 5.19615i −0.559950 + 0.223814i
\(540\) 0 0
\(541\) 2.00000 + 3.46410i 0.0859867 + 0.148933i 0.905811 0.423681i \(-0.139262\pi\)
−0.819825 + 0.572615i \(0.805929\pi\)
\(542\) −7.79423 4.50000i −0.334791 0.193292i
\(543\) −19.0526 11.0000i −0.817624 0.472055i
\(544\) 2.50000 + 4.33013i 0.107187 + 0.185653i
\(545\) 0 0
\(546\) −10.0000 3.46410i −0.427960 0.148250i
\(547\) 8.00000i 0.342055i 0.985266 + 0.171028i \(0.0547087\pi\)
−0.985266 + 0.171028i \(0.945291\pi\)
\(548\) −19.9186 + 11.5000i −0.850880 + 0.491256i
\(549\) 5.00000 8.66025i 0.213395 0.369611i
\(550\) 0 0
\(551\) −12.0000 20.7846i −0.511217 0.885454i
\(552\) 5.00000i 0.212814i
\(553\) 23.3827 4.50000i 0.994333 0.191359i
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) −1.00000 + 1.73205i −0.0424094 + 0.0734553i
\(557\) −32.9090 19.0000i −1.39440 0.805056i −0.400599 0.916253i \(-0.631198\pi\)
−0.993798 + 0.111198i \(0.964531\pi\)
\(558\) −9.52628 + 5.50000i −0.403280 + 0.232834i
\(559\) 0 0
\(560\) 0 0
\(561\) 10.0000 0.422200
\(562\) 25.1147 14.5000i 1.05940 0.611646i
\(563\) −31.1769 18.0000i −1.31395 0.758610i −0.331202 0.943560i \(-0.607454\pi\)
−0.982748 + 0.184950i \(0.940788\pi\)
\(564\) −0.500000 + 0.866025i −0.0210538 + 0.0364662i
\(565\) 0 0
\(566\) 26.0000 1.09286
\(567\) 1.73205 + 2.00000i 0.0727393 + 0.0839921i
\(568\) 1.00000i 0.0419591i
\(569\) 4.50000 + 7.79423i 0.188650 + 0.326751i 0.944800 0.327647i \(-0.106256\pi\)
−0.756151 + 0.654398i \(0.772922\pi\)
\(570\) 0 0
\(571\) 22.0000 38.1051i 0.920671 1.59465i 0.122292 0.992494i \(-0.460975\pi\)
0.798379 0.602155i \(-0.205691\pi\)
\(572\) 6.92820 4.00000i 0.289683 0.167248i
\(573\) 25.0000i 1.04439i
\(574\) 2.50000 + 12.9904i 0.104348 + 0.542208i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 1.73205 + 1.00000i 0.0721062 + 0.0416305i 0.535620 0.844459i \(-0.320078\pi\)
−0.463513 + 0.886090i \(0.653411\pi\)
\(578\) −6.92820 4.00000i −0.288175 0.166378i
\(579\) 5.50000 + 9.52628i 0.228572 + 0.395899i
\(580\) 0 0
\(581\) −15.0000 5.19615i −0.622305 0.215573i
\(582\) 1.00000i 0.0414513i
\(583\) 20.7846 12.0000i 0.860811 0.496989i
\(584\) −1.00000 + 1.73205i −0.0413803 + 0.0716728i
\(585\) 0 0
\(586\) 9.00000 + 15.5885i 0.371787 + 0.643953i
\(587\) 6.00000i 0.247647i 0.992304 + 0.123823i \(0.0395156\pi\)
−0.992304 + 0.123823i \(0.960484\pi\)
\(588\) −6.92820 1.00000i −0.285714 0.0412393i
\(589\) −44.0000 −1.81299
\(590\) 0 0
\(591\) 12.0000 20.7846i 0.493614 0.854965i
\(592\) −6.92820 4.00000i −0.284747 0.164399i
\(593\) −7.79423 + 4.50000i −0.320071 + 0.184793i −0.651424 0.758714i \(-0.725828\pi\)
0.331353 + 0.943507i \(0.392495\pi\)
\(594\) −2.00000 −0.0820610
\(595\) 0 0
\(596\) 18.0000 0.737309
\(597\) 4.33013 2.50000i 0.177220 0.102318i
\(598\) 17.3205 + 10.0000i 0.708288 + 0.408930i
\(599\) 8.50000 14.7224i 0.347301 0.601542i −0.638468 0.769648i \(-0.720432\pi\)
0.985769 + 0.168106i \(0.0537650\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −8.00000 13.8564i −0.325515 0.563809i
\(605\) 0 0
\(606\) 6.00000 10.3923i 0.243733 0.422159i
\(607\) −23.3827 + 13.5000i −0.949074 + 0.547948i −0.892793 0.450467i \(-0.851258\pi\)
−0.0562808 + 0.998415i \(0.517924\pi\)
\(608\) 4.00000i 0.162221i
\(609\) 12.0000 10.3923i 0.486265 0.421117i
\(610\) 0 0
\(611\) −2.00000 3.46410i −0.0809113 0.140143i
\(612\) 4.33013 + 2.50000i 0.175035 + 0.101057i
\(613\) 29.4449 + 17.0000i 1.18927 + 0.686624i 0.958140 0.286300i \(-0.0924254\pi\)
0.231127 + 0.972924i \(0.425759\pi\)
\(614\) −14.0000 24.2487i −0.564994 0.978598i
\(615\) 0 0
\(616\) 4.00000 3.46410i 0.161165 0.139573i
\(617\) 29.0000i 1.16750i 0.811935 + 0.583748i \(0.198414\pi\)
−0.811935 + 0.583748i \(0.801586\pi\)
\(618\) 11.2583 6.50000i 0.452876 0.261468i
\(619\) −7.00000 + 12.1244i −0.281354 + 0.487319i −0.971718 0.236143i \(-0.924117\pi\)
0.690365 + 0.723462i \(0.257450\pi\)
\(620\) 0 0
\(621\) −2.50000 4.33013i −0.100322 0.173762i
\(622\) 29.0000i 1.16279i
\(623\) 28.5788 5.50000i 1.14499 0.220353i
\(624\) 4.00000 0.160128
\(625\) 0 0
\(626\) −0.500000 + 0.866025i −0.0199840 + 0.0346133i
\(627\) −6.92820 4.00000i −0.276686 0.159745i
\(628\) 12.1244 7.00000i 0.483814 0.279330i
\(629\) 40.0000 1.59490
\(630\) 0 0
\(631\) 33.0000 1.31371 0.656855 0.754017i \(-0.271887\pi\)
0.656855 + 0.754017i \(0.271887\pi\)
\(632\) −7.79423 + 4.50000i −0.310038 + 0.179000i
\(633\) −13.8564 8.00000i −0.550743 0.317971i
\(634\) −2.00000 + 3.46410i −0.0794301 + 0.137577i
\(635\) 0 0
\(636\) 12.0000 0.475831
\(637\) 17.3205 22.0000i 0.686264 0.871672i
\(638\) 12.0000i 0.475085i
\(639\) −0.500000 0.866025i −0.0197797 0.0342594i
\(640\) 0 0
\(641\) 7.50000 12.9904i 0.296232 0.513089i −0.679039 0.734103i \(-0.737603\pi\)
0.975271 + 0.221013i \(0.0709364\pi\)
\(642\) −1.73205 + 1.00000i −0.0683586 + 0.0394669i
\(643\) 26.0000i 1.02534i −0.858586 0.512670i \(-0.828656\pi\)
0.858586 0.512670i \(-0.171344\pi\)
\(644\) 12.5000 + 4.33013i 0.492569 + 0.170631i
\(645\) 0 0
\(646\) 10.0000 + 17.3205i 0.393445 + 0.681466i
\(647\) 24.2487 + 14.0000i 0.953315 + 0.550397i 0.894109 0.447849i \(-0.147810\pi\)
0.0592060 + 0.998246i \(0.481143\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) 2.00000 + 3.46410i 0.0785069 + 0.135978i
\(650\) 0 0
\(651\) −5.50000 28.5788i −0.215562 1.12009i
\(652\) 24.0000i 0.939913i
\(653\) −24.2487 + 14.0000i −0.948925 + 0.547862i −0.892747 0.450558i \(-0.851225\pi\)
−0.0561784 + 0.998421i \(0.517892\pi\)
\(654\) −2.00000 + 3.46410i −0.0782062 + 0.135457i
\(655\) 0 0
\(656\) −2.50000 4.33013i −0.0976086 0.169063i
\(657\) 2.00000i 0.0780274i
\(658\) −1.73205 2.00000i −0.0675224 0.0779681i
\(659\) 14.0000 0.545363 0.272681 0.962104i \(-0.412090\pi\)
0.272681 + 0.962104i \(0.412090\pi\)
\(660\) 0 0
\(661\) −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i \(-0.921107\pi\)
0.697174 + 0.716902i \(0.254441\pi\)
\(662\) 8.66025 + 5.00000i 0.336590 + 0.194331i
\(663\) −17.3205 + 10.0000i −0.672673 + 0.388368i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) −8.00000 −0.309994
\(667\) −25.9808 + 15.0000i −1.00598 + 0.580802i
\(668\) 13.8564 + 8.00000i 0.536120 + 0.309529i
\(669\) 10.5000 18.1865i 0.405953 0.703132i
\(670\) 0 0
\(671\) −20.0000 −0.772091
\(672\) 2.59808 0.500000i 0.100223 0.0192879i
\(673\) 19.0000i 0.732396i −0.930537 0.366198i \(-0.880659\pi\)
0.930537 0.366198i \(-0.119341\pi\)
\(674\) −6.50000 11.2583i −0.250371 0.433655i
\(675\) 0 0
\(676\) −1.50000 + 2.59808i −0.0576923 + 0.0999260i
\(677\) −15.5885 + 9.00000i −0.599113 + 0.345898i −0.768693 0.639618i \(-0.779092\pi\)
0.169580 + 0.985517i \(0.445759\pi\)
\(678\) 5.00000i 0.192024i
\(679\) −2.50000 0.866025i −0.0959412 0.0332350i
\(680\) 0 0
\(681\) −9.00000 15.5885i −0.344881 0.597351i
\(682\) 19.0526 + 11.0000i 0.729560 + 0.421212i
\(683\) −1.73205 1.00000i −0.0662751 0.0382639i 0.466496 0.884523i \(-0.345516\pi\)
−0.532771 + 0.846259i \(0.678849\pi\)
\(684\) −2.00000 3.46410i −0.0764719 0.132453i
\(685\) 0 0
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 14.0000i 0.534133i
\(688\) 0 0
\(689\) −24.0000 + 41.5692i −0.914327 + 1.58366i
\(690\) 0 0
\(691\) 1.00000 + 1.73205i 0.0380418 + 0.0658903i 0.884419 0.466693i \(-0.154555\pi\)
−0.846378 + 0.532583i \(0.821221\pi\)
\(692\) 2.00000i 0.0760286i
\(693\) 1.73205 5.00000i 0.0657952 0.189934i
\(694\) −18.0000 −0.683271
\(695\) 0 0
\(696\) −3.00000 + 5.19615i −0.113715 + 0.196960i
\(697\) 21.6506 + 12.5000i 0.820076 + 0.473471i
\(698\) −3.46410 + 2.00000i −0.131118 + 0.0757011i
\(699\) −26.0000 −0.983410
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 3.46410 2.00000i 0.130744 0.0754851i
\(703\) −27.7128 16.0000i −1.04521 0.603451i
\(704\) −1.00000 + 1.73205i −0.0376889 + 0.0652791i
\(705\) 0 0
\(706\) −9.00000 −0.338719
\(707\) 20.7846 + 24.0000i 0.781686 + 0.902613i
\(708\) 2.00000i 0.0751646i
\(709\) 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i \(-0.106538\pi\)
−0.756730 + 0.653727i \(0.773204\pi\)
\(710\) 0 0
\(711\) −4.50000 + 7.79423i −0.168763 + 0.292306i
\(712\) −9.52628 + 5.50000i −0.357012 + 0.206121i
\(713\) 55.0000i 2.05977i
\(714\) −10.0000 + 8.66025i −0.374241 + 0.324102i
\(715\) 0 0
\(716\) −11.0000 19.0526i −0.411089 0.712028i
\(717\) −9.52628 5.50000i −0.355765 0.205401i
\(718\) 17.3205 + 10.0000i 0.646396 + 0.373197i
\(719\) −1.50000 2.59808i −0.0559406 0.0968919i 0.836699 0.547663i \(-0.184482\pi\)
−0.892640 + 0.450771i \(0.851149\pi\)
\(720\) 0 0
\(721\) 6.50000 + 33.7750i 0.242073 + 1.25785i
\(722\) 3.00000i 0.111648i
\(723\) 5.19615 3.00000i 0.193247 0.111571i
\(724\) −11.0000 + 19.0526i −0.408812 + 0.708083i
\(725\) 0 0
\(726\) −3.50000 6.06218i −0.129897 0.224989i
\(727\) 33.0000i 1.22390i −0.790896 0.611951i \(-0.790385\pi\)
0.790896 0.611951i \(-0.209615\pi\)
\(728\) −3.46410 + 10.0000i −0.128388 + 0.370625i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) −8.66025 5.00000i −0.320092 0.184805i
\(733\) −25.9808 + 15.0000i −0.959621 + 0.554038i −0.896056 0.443940i \(-0.853580\pi\)
−0.0635649 + 0.997978i \(0.520247\pi\)
\(734\) −4.00000 −0.147643
\(735\) 0 0
\(736\) −5.00000 −0.184302
\(737\) 0 0
\(738\) −4.33013 2.50000i −0.159394 0.0920263i
\(739\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(740\) 0 0
\(741\) 16.0000 0.587775
\(742\) −10.3923 + 30.0000i −0.381514 + 1.10133i
\(743\) 33.0000i 1.21065i 0.795977 + 0.605326i \(0.206957\pi\)
−0.795977 + 0.605326i \(0.793043\pi\)
\(744\) 5.50000 + 9.52628i 0.201640 + 0.349250i
\(745\) 0 0
\(746\) −16.0000 + 27.7128i −0.585802 + 1.01464i
\(747\) 5.19615 3.00000i 0.190117 0.109764i
\(748\) 10.0000i 0.365636i
\(749\) −1.00000 5.19615i −0.0365392 0.189863i
\(750\) 0 0
\(751\) 16.0000 + 27.7128i 0.583848 + 1.01125i 0.995018 + 0.0996961i \(0.0317870\pi\)
−0.411170 + 0.911559i \(0.634880\pi\)
\(752\) 0.866025 + 0.500000i 0.0315807 + 0.0182331i
\(753\) −6.92820 4.00000i −0.252478 0.145768i
\(754\) −12.0000 20.7846i −0.437014 0.756931i
\(755\) 0 0
\(756\) 2.00000 1.73205i 0.0727393 0.0629941i
\(757\) 28.0000i 1.01768i 0.860862 + 0.508839i \(0.169925\pi\)
−0.860862 + 0.508839i \(0.830075\pi\)
\(758\) −1.73205 + 1.00000i −0.0629109 + 0.0363216i
\(759\) −5.00000 + 8.66025i −0.181489 + 0.314347i
\(760\) 0 0
\(761\) −8.50000 14.7224i −0.308125 0.533688i 0.669827 0.742517i \(-0.266368\pi\)
−0.977952 + 0.208829i \(0.933035\pi\)
\(762\) 0 0
\(763\) −6.92820 8.00000i −0.250818 0.289619i
\(764\) 25.0000 0.904468
\(765\) 0 0
\(766\) 1.50000 2.59808i 0.0541972 0.0938723i
\(767\) −6.92820 4.00000i −0.250163 0.144432i
\(768\) −0.866025 + 0.500000i −0.0312500 + 0.0180422i
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) −14.0000 −0.504198
\(772\) 9.52628 5.50000i 0.342858 0.197949i
\(773\) −3.46410 2.00000i −0.124595 0.0719350i 0.436407 0.899749i \(-0.356251\pi\)
−0.561002 + 0.827814i \(0.689584\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 1.00000 0.0358979
\(777\) 6.92820 20.0000i 0.248548 0.717496i
\(778\) 24.0000i 0.860442i
\(779\) −10.0000 17.3205i −0.358287 0.620572i
\(780\) 0 0
\(781\) −1.00000 + 1.73205i −0.0357828 + 0.0619777i
\(782\) 21.6506 12.5000i 0.774225 0.446999i
\(783\) 6.00000i 0.214423i
\(784\) −1.00000 + 6.92820i −0.0357143 + 0.247436i
\(785\) 0 0
\(786\) 3.00000 +