Properties

Label 1170.2.bs.e.361.1
Level $1170$
Weight $2$
Character 1170.361
Analytic conductor $9.342$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bs (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
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: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1170.361
Dual form 1170.2.bs.e.901.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{10} +(-0.401924 + 0.232051i) q^{11} +(1.00000 + 3.46410i) q^{13} -2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-0.464102 - 0.267949i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.232051 - 0.401924i) q^{22} +(0.133975 + 0.232051i) q^{23} -1.00000 q^{25} +(-2.59808 - 2.50000i) q^{26} +(1.73205 - 1.00000i) q^{28} +(1.86603 + 3.23205i) q^{29} +1.73205i q^{31} +(0.866025 + 0.500000i) q^{32} -4.00000i q^{34} +(1.00000 - 1.73205i) q^{35} +(1.03590 - 0.598076i) q^{37} +0.535898 q^{38} +1.00000 q^{40} +(1.73205 - 1.00000i) q^{41} +(0.964102 - 1.66987i) q^{43} +0.464102i q^{44} +(-0.232051 - 0.133975i) q^{46} +10.4641i q^{47} +(-1.50000 - 2.59808i) q^{49} +(0.866025 - 0.500000i) q^{50} +(3.50000 + 0.866025i) q^{52} +12.9282 q^{53} +(0.232051 + 0.401924i) q^{55} +(-1.00000 + 1.73205i) q^{56} +(-3.23205 - 1.86603i) q^{58} +(1.33013 + 0.767949i) q^{59} +(-5.19615 + 9.00000i) q^{61} +(-0.866025 - 1.50000i) q^{62} -1.00000 q^{64} +(3.46410 - 1.00000i) q^{65} +(3.92820 - 2.26795i) q^{67} +(2.00000 + 3.46410i) q^{68} +2.00000i q^{70} +(7.26795 + 4.19615i) q^{71} +2.00000i q^{73} +(-0.598076 + 1.03590i) q^{74} +(-0.464102 + 0.267949i) q^{76} -0.928203 q^{77} -0.0717968 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-1.00000 + 1.73205i) q^{82} +4.92820i q^{83} +(3.46410 + 2.00000i) q^{85} +1.92820i q^{86} +(-0.232051 - 0.401924i) q^{88} +(-6.46410 + 3.73205i) q^{89} +(-1.73205 + 7.00000i) q^{91} +0.267949 q^{92} +(-5.23205 - 9.06218i) q^{94} +(-0.267949 + 0.464102i) q^{95} +(-6.46410 - 3.73205i) q^{97} +(2.59808 + 1.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + O(q^{10}) \) \( 4q + 2q^{4} + 2q^{10} - 12q^{11} + 4q^{13} - 8q^{14} - 2q^{16} - 8q^{17} + 12q^{19} - 6q^{22} + 4q^{23} - 4q^{25} + 4q^{29} + 4q^{35} + 18q^{37} + 16q^{38} + 4q^{40} - 10q^{43} + 6q^{46} - 6q^{49} + 14q^{52} + 24q^{53} - 6q^{55} - 4q^{56} - 6q^{58} - 12q^{59} - 4q^{64} - 12q^{67} + 8q^{68} + 36q^{71} + 8q^{74} + 12q^{76} + 24q^{77} - 28q^{79} - 4q^{82} + 6q^{88} - 12q^{89} + 8q^{92} - 14q^{94} - 8q^{95} - 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 1.73205 + 1.00000i 0.654654 + 0.377964i 0.790237 0.612801i \(-0.209957\pi\)
−0.135583 + 0.990766i \(0.543291\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) −0.401924 + 0.232051i −0.121185 + 0.0699660i −0.559367 0.828920i \(-0.688956\pi\)
0.438182 + 0.898886i \(0.355622\pi\)
\(12\) 0 0
\(13\) 1.00000 + 3.46410i 0.277350 + 0.960769i
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 0 0
\(19\) −0.464102 0.267949i −0.106472 0.0614718i 0.445818 0.895123i \(-0.352913\pi\)
−0.552291 + 0.833652i \(0.686246\pi\)
\(20\) −0.866025 0.500000i −0.193649 0.111803i
\(21\) 0 0
\(22\) 0.232051 0.401924i 0.0494734 0.0856904i
\(23\) 0.133975 + 0.232051i 0.0279356 + 0.0483859i 0.879655 0.475612i \(-0.157773\pi\)
−0.851720 + 0.523998i \(0.824440\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −2.59808 2.50000i −0.509525 0.490290i
\(27\) 0 0
\(28\) 1.73205 1.00000i 0.327327 0.188982i
\(29\) 1.86603 + 3.23205i 0.346512 + 0.600177i 0.985627 0.168934i \(-0.0540326\pi\)
−0.639115 + 0.769111i \(0.720699\pi\)
\(30\) 0 0
\(31\) 1.73205i 0.311086i 0.987829 + 0.155543i \(0.0497126\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 4.00000i 0.685994i
\(35\) 1.00000 1.73205i 0.169031 0.292770i
\(36\) 0 0
\(37\) 1.03590 0.598076i 0.170301 0.0983231i −0.412427 0.910991i \(-0.635319\pi\)
0.582728 + 0.812668i \(0.301985\pi\)
\(38\) 0.535898 0.0869342
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) 1.73205 1.00000i 0.270501 0.156174i −0.358614 0.933486i \(-0.616751\pi\)
0.629115 + 0.777312i \(0.283417\pi\)
\(42\) 0 0
\(43\) 0.964102 1.66987i 0.147024 0.254653i −0.783102 0.621893i \(-0.786364\pi\)
0.930126 + 0.367240i \(0.119697\pi\)
\(44\) 0.464102i 0.0699660i
\(45\) 0 0
\(46\) −0.232051 0.133975i −0.0342140 0.0197535i
\(47\) 10.4641i 1.52635i 0.646194 + 0.763173i \(0.276360\pi\)
−0.646194 + 0.763173i \(0.723640\pi\)
\(48\) 0 0
\(49\) −1.50000 2.59808i −0.214286 0.371154i
\(50\) 0.866025 0.500000i 0.122474 0.0707107i
\(51\) 0 0
\(52\) 3.50000 + 0.866025i 0.485363 + 0.120096i
\(53\) 12.9282 1.77583 0.887913 0.460012i \(-0.152155\pi\)
0.887913 + 0.460012i \(0.152155\pi\)
\(54\) 0 0
\(55\) 0.232051 + 0.401924i 0.0312897 + 0.0541954i
\(56\) −1.00000 + 1.73205i −0.133631 + 0.231455i
\(57\) 0 0
\(58\) −3.23205 1.86603i −0.424389 0.245021i
\(59\) 1.33013 + 0.767949i 0.173168 + 0.0999785i 0.584079 0.811697i \(-0.301456\pi\)
−0.410911 + 0.911676i \(0.634789\pi\)
\(60\) 0 0
\(61\) −5.19615 + 9.00000i −0.665299 + 1.15233i 0.313905 + 0.949454i \(0.398363\pi\)
−0.979204 + 0.202878i \(0.934971\pi\)
\(62\) −0.866025 1.50000i −0.109985 0.190500i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 3.46410 1.00000i 0.429669 0.124035i
\(66\) 0 0
\(67\) 3.92820 2.26795i 0.479906 0.277074i −0.240471 0.970656i \(-0.577302\pi\)
0.720377 + 0.693582i \(0.243969\pi\)
\(68\) 2.00000 + 3.46410i 0.242536 + 0.420084i
\(69\) 0 0
\(70\) 2.00000i 0.239046i
\(71\) 7.26795 + 4.19615i 0.862547 + 0.497992i 0.864864 0.502006i \(-0.167404\pi\)
−0.00231747 + 0.999997i \(0.500738\pi\)
\(72\) 0 0
\(73\) 2.00000i 0.234082i 0.993127 + 0.117041i \(0.0373409\pi\)
−0.993127 + 0.117041i \(0.962659\pi\)
\(74\) −0.598076 + 1.03590i −0.0695249 + 0.120421i
\(75\) 0 0
\(76\) −0.464102 + 0.267949i −0.0532361 + 0.0307359i
\(77\) −0.928203 −0.105779
\(78\) 0 0
\(79\) −0.0717968 −0.00807777 −0.00403888 0.999992i \(-0.501286\pi\)
−0.00403888 + 0.999992i \(0.501286\pi\)
\(80\) −0.866025 + 0.500000i −0.0968246 + 0.0559017i
\(81\) 0 0
\(82\) −1.00000 + 1.73205i −0.110432 + 0.191273i
\(83\) 4.92820i 0.540941i 0.962728 + 0.270470i \(0.0871792\pi\)
−0.962728 + 0.270470i \(0.912821\pi\)
\(84\) 0 0
\(85\) 3.46410 + 2.00000i 0.375735 + 0.216930i
\(86\) 1.92820i 0.207924i
\(87\) 0 0
\(88\) −0.232051 0.401924i −0.0247367 0.0428452i
\(89\) −6.46410 + 3.73205i −0.685193 + 0.395597i −0.801809 0.597581i \(-0.796129\pi\)
0.116615 + 0.993177i \(0.462795\pi\)
\(90\) 0 0
\(91\) −1.73205 + 7.00000i −0.181568 + 0.733799i
\(92\) 0.267949 0.0279356
\(93\) 0 0
\(94\) −5.23205 9.06218i −0.539645 0.934692i
\(95\) −0.267949 + 0.464102i −0.0274910 + 0.0476158i
\(96\) 0 0
\(97\) −6.46410 3.73205i −0.656330 0.378932i 0.134547 0.990907i \(-0.457042\pi\)
−0.790877 + 0.611975i \(0.790375\pi\)
\(98\) 2.59808 + 1.50000i 0.262445 + 0.151523i
\(99\) 0 0
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −5.46410 9.46410i −0.543698 0.941713i −0.998688 0.0512163i \(-0.983690\pi\)
0.454989 0.890497i \(-0.349643\pi\)
\(102\) 0 0
\(103\) 15.8564 1.56238 0.781189 0.624295i \(-0.214613\pi\)
0.781189 + 0.624295i \(0.214613\pi\)
\(104\) −3.46410 + 1.00000i −0.339683 + 0.0980581i
\(105\) 0 0
\(106\) −11.1962 + 6.46410i −1.08747 + 0.627849i
\(107\) 9.92820 + 17.1962i 0.959796 + 1.66241i 0.722991 + 0.690858i \(0.242767\pi\)
0.236805 + 0.971557i \(0.423900\pi\)
\(108\) 0 0
\(109\) 11.8564i 1.13564i 0.823154 + 0.567819i \(0.192213\pi\)
−0.823154 + 0.567819i \(0.807787\pi\)
\(110\) −0.401924 0.232051i −0.0383219 0.0221252i
\(111\) 0 0
\(112\) 2.00000i 0.188982i
\(113\) 5.59808 9.69615i 0.526623 0.912137i −0.472896 0.881118i \(-0.656791\pi\)
0.999519 0.0310191i \(-0.00987527\pi\)
\(114\) 0 0
\(115\) 0.232051 0.133975i 0.0216388 0.0124932i
\(116\) 3.73205 0.346512
\(117\) 0 0
\(118\) −1.53590 −0.141391
\(119\) −6.92820 + 4.00000i −0.635107 + 0.366679i
\(120\) 0 0
\(121\) −5.39230 + 9.33975i −0.490210 + 0.849068i
\(122\) 10.3923i 0.940875i
\(123\) 0 0
\(124\) 1.50000 + 0.866025i 0.134704 + 0.0777714i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) −4.46410 7.73205i −0.396125 0.686109i 0.597119 0.802153i \(-0.296312\pi\)
−0.993244 + 0.116044i \(0.962979\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −2.50000 + 2.59808i −0.219265 + 0.227866i
\(131\) 1.33975 0.117054 0.0585271 0.998286i \(-0.481360\pi\)
0.0585271 + 0.998286i \(0.481360\pi\)
\(132\) 0 0
\(133\) −0.535898 0.928203i −0.0464683 0.0804854i
\(134\) −2.26795 + 3.92820i −0.195921 + 0.339345i
\(135\) 0 0
\(136\) −3.46410 2.00000i −0.297044 0.171499i
\(137\) 3.86603 + 2.23205i 0.330297 + 0.190697i 0.655973 0.754784i \(-0.272259\pi\)
−0.325676 + 0.945481i \(0.605592\pi\)
\(138\) 0 0
\(139\) −0.464102 + 0.803848i −0.0393646 + 0.0681815i −0.885036 0.465522i \(-0.845867\pi\)
0.845672 + 0.533703i \(0.179200\pi\)
\(140\) −1.00000 1.73205i −0.0845154 0.146385i
\(141\) 0 0
\(142\) −8.39230 −0.704267
\(143\) −1.20577 1.16025i −0.100832 0.0970253i
\(144\) 0 0
\(145\) 3.23205 1.86603i 0.268407 0.154965i
\(146\) −1.00000 1.73205i −0.0827606 0.143346i
\(147\) 0 0
\(148\) 1.19615i 0.0983231i
\(149\) −17.7224 10.2321i −1.45188 0.838242i −0.453290 0.891363i \(-0.649750\pi\)
−0.998588 + 0.0531208i \(0.983083\pi\)
\(150\) 0 0
\(151\) 10.3923i 0.845714i 0.906196 + 0.422857i \(0.138973\pi\)
−0.906196 + 0.422857i \(0.861027\pi\)
\(152\) 0.267949 0.464102i 0.0217335 0.0376436i
\(153\) 0 0
\(154\) 0.803848 0.464102i 0.0647759 0.0373984i
\(155\) 1.73205 0.139122
\(156\) 0 0
\(157\) −5.00000 −0.399043 −0.199522 0.979893i \(-0.563939\pi\)
−0.199522 + 0.979893i \(0.563939\pi\)
\(158\) 0.0621778 0.0358984i 0.00494660 0.00285592i
\(159\) 0 0
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) 0.535898i 0.0422347i
\(162\) 0 0
\(163\) 19.9641 + 11.5263i 1.56371 + 0.902808i 0.996877 + 0.0789748i \(0.0251647\pi\)
0.566833 + 0.823833i \(0.308169\pi\)
\(164\) 2.00000i 0.156174i
\(165\) 0 0
\(166\) −2.46410 4.26795i −0.191251 0.331257i
\(167\) −15.8660 + 9.16025i −1.22775 + 0.708842i −0.966559 0.256445i \(-0.917449\pi\)
−0.261191 + 0.965287i \(0.584115\pi\)
\(168\) 0 0
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) −4.00000 −0.306786
\(171\) 0 0
\(172\) −0.964102 1.66987i −0.0735121 0.127327i
\(173\) −1.46410 + 2.53590i −0.111314 + 0.192801i −0.916300 0.400492i \(-0.868839\pi\)
0.804987 + 0.593293i \(0.202172\pi\)
\(174\) 0 0
\(175\) −1.73205 1.00000i −0.130931 0.0755929i
\(176\) 0.401924 + 0.232051i 0.0302961 + 0.0174915i
\(177\) 0 0
\(178\) 3.73205 6.46410i 0.279729 0.484505i
\(179\) −8.13397 14.0885i −0.607962 1.05302i −0.991576 0.129527i \(-0.958654\pi\)
0.383614 0.923494i \(-0.374679\pi\)
\(180\) 0 0
\(181\) 10.9282 0.812287 0.406143 0.913809i \(-0.366873\pi\)
0.406143 + 0.913809i \(0.366873\pi\)
\(182\) −2.00000 6.92820i −0.148250 0.513553i
\(183\) 0 0
\(184\) −0.232051 + 0.133975i −0.0171070 + 0.00987674i
\(185\) −0.598076 1.03590i −0.0439714 0.0761608i
\(186\) 0 0
\(187\) 1.85641i 0.135754i
\(188\) 9.06218 + 5.23205i 0.660927 + 0.381587i
\(189\) 0 0
\(190\) 0.535898i 0.0388782i
\(191\) 7.26795 12.5885i 0.525890 0.910869i −0.473655 0.880711i \(-0.657066\pi\)
0.999545 0.0301582i \(-0.00960111\pi\)
\(192\) 0 0
\(193\) 20.1962 11.6603i 1.45375 0.839323i 0.455059 0.890461i \(-0.349618\pi\)
0.998692 + 0.0511377i \(0.0162847\pi\)
\(194\) 7.46410 0.535891
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −14.1962 + 8.19615i −1.01143 + 0.583952i −0.911611 0.411054i \(-0.865161\pi\)
−0.0998228 + 0.995005i \(0.531828\pi\)
\(198\) 0 0
\(199\) 9.46410 16.3923i 0.670892 1.16202i −0.306759 0.951787i \(-0.599245\pi\)
0.977651 0.210232i \(-0.0674221\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 0 0
\(202\) 9.46410 + 5.46410i 0.665892 + 0.384453i
\(203\) 7.46410i 0.523877i
\(204\) 0 0
\(205\) −1.00000 1.73205i −0.0698430 0.120972i
\(206\) −13.7321 + 7.92820i −0.956757 + 0.552384i
\(207\) 0 0
\(208\) 2.50000 2.59808i 0.173344 0.180144i
\(209\) 0.248711 0.0172037
\(210\) 0 0
\(211\) −11.6603 20.1962i −0.802725 1.39036i −0.917816 0.397006i \(-0.870049\pi\)
0.115091 0.993355i \(-0.463284\pi\)
\(212\) 6.46410 11.1962i 0.443956 0.768955i
\(213\) 0 0
\(214\) −17.1962 9.92820i −1.17550 0.678678i
\(215\) −1.66987 0.964102i −0.113884 0.0657512i
\(216\) 0 0
\(217\) −1.73205 + 3.00000i −0.117579 + 0.203653i
\(218\) −5.92820 10.2679i −0.401509 0.695433i
\(219\) 0 0
\(220\) 0.464102 0.0312897
\(221\) −14.0000 3.46410i −0.941742 0.233021i
\(222\) 0 0
\(223\) 23.7846 13.7321i 1.59274 0.919566i 0.599900 0.800075i \(-0.295207\pi\)
0.992835 0.119491i \(-0.0381263\pi\)
\(224\) 1.00000 + 1.73205i 0.0668153 + 0.115728i
\(225\) 0 0
\(226\) 11.1962i 0.744757i
\(227\) 3.80385 + 2.19615i 0.252470 + 0.145764i 0.620895 0.783894i \(-0.286769\pi\)
−0.368425 + 0.929658i \(0.620103\pi\)
\(228\) 0 0
\(229\) 19.8564i 1.31215i 0.754696 + 0.656074i \(0.227784\pi\)
−0.754696 + 0.656074i \(0.772216\pi\)
\(230\) −0.133975 + 0.232051i −0.00883402 + 0.0153010i
\(231\) 0 0
\(232\) −3.23205 + 1.86603i −0.212195 + 0.122511i
\(233\) 18.1244 1.18737 0.593683 0.804699i \(-0.297673\pi\)
0.593683 + 0.804699i \(0.297673\pi\)
\(234\) 0 0
\(235\) 10.4641 0.682603
\(236\) 1.33013 0.767949i 0.0865839 0.0499892i
\(237\) 0 0
\(238\) 4.00000 6.92820i 0.259281 0.449089i
\(239\) 4.39230i 0.284115i −0.989858 0.142057i \(-0.954628\pi\)
0.989858 0.142057i \(-0.0453717\pi\)
\(240\) 0 0
\(241\) −12.3564 7.13397i −0.795946 0.459540i 0.0461056 0.998937i \(-0.485319\pi\)
−0.842052 + 0.539397i \(0.818652\pi\)
\(242\) 10.7846i 0.693261i
\(243\) 0 0
\(244\) 5.19615 + 9.00000i 0.332650 + 0.576166i
\(245\) −2.59808 + 1.50000i −0.165985 + 0.0958315i
\(246\) 0 0
\(247\) 0.464102 1.87564i 0.0295301 0.119344i
\(248\) −1.73205 −0.109985
\(249\) 0 0
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) 6.13397 10.6244i 0.387173 0.670603i −0.604895 0.796305i \(-0.706785\pi\)
0.992068 + 0.125702i \(0.0401183\pi\)
\(252\) 0 0
\(253\) −0.107695 0.0621778i −0.00677074 0.00390909i
\(254\) 7.73205 + 4.46410i 0.485152 + 0.280103i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −11.3301 19.6244i −0.706754 1.22413i −0.966055 0.258337i \(-0.916825\pi\)
0.259301 0.965797i \(-0.416508\pi\)
\(258\) 0 0
\(259\) 2.39230 0.148651
\(260\) 0.866025 3.50000i 0.0537086 0.217061i
\(261\) 0 0
\(262\) −1.16025 + 0.669873i −0.0716807 + 0.0413849i
\(263\) −9.06218 15.6962i −0.558798 0.967866i −0.997597 0.0692812i \(-0.977929\pi\)
0.438799 0.898585i \(-0.355404\pi\)
\(264\) 0 0
\(265\) 12.9282i 0.794173i
\(266\) 0.928203 + 0.535898i 0.0569118 + 0.0328580i
\(267\) 0 0
\(268\) 4.53590i 0.277074i
\(269\) 6.00000 10.3923i 0.365826 0.633630i −0.623082 0.782157i \(-0.714120\pi\)
0.988908 + 0.148527i \(0.0474530\pi\)
\(270\) 0 0
\(271\) 7.96410 4.59808i 0.483785 0.279313i −0.238208 0.971214i \(-0.576560\pi\)
0.721992 + 0.691901i \(0.243227\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) −4.46410 −0.269686
\(275\) 0.401924 0.232051i 0.0242369 0.0139932i
\(276\) 0 0
\(277\) −4.96410 + 8.59808i −0.298264 + 0.516608i −0.975739 0.218938i \(-0.929741\pi\)
0.677475 + 0.735546i \(0.263074\pi\)
\(278\) 0.928203i 0.0556699i
\(279\) 0 0
\(280\) 1.73205 + 1.00000i 0.103510 + 0.0597614i
\(281\) 4.92820i 0.293992i −0.989137 0.146996i \(-0.953040\pi\)
0.989137 0.146996i \(-0.0469604\pi\)
\(282\) 0 0
\(283\) −1.96410 3.40192i −0.116754 0.202223i 0.801726 0.597692i \(-0.203915\pi\)
−0.918479 + 0.395469i \(0.870582\pi\)
\(284\) 7.26795 4.19615i 0.431273 0.248996i
\(285\) 0 0
\(286\) 1.62436 + 0.401924i 0.0960502 + 0.0237663i
\(287\) 4.00000 0.236113
\(288\) 0 0
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) −1.86603 + 3.23205i −0.109577 + 0.189793i
\(291\) 0 0
\(292\) 1.73205 + 1.00000i 0.101361 + 0.0585206i
\(293\) −3.58846 2.07180i −0.209640 0.121036i 0.391504 0.920176i \(-0.371955\pi\)
−0.601144 + 0.799141i \(0.705288\pi\)
\(294\) 0 0
\(295\) 0.767949 1.33013i 0.0447117 0.0774430i
\(296\) 0.598076 + 1.03590i 0.0347625 + 0.0602104i
\(297\) 0 0
\(298\) 20.4641 1.18545
\(299\) −0.669873 + 0.696152i −0.0387398 + 0.0402595i
\(300\) 0 0
\(301\) 3.33975 1.92820i 0.192500 0.111140i
\(302\) −5.19615 9.00000i −0.299005 0.517892i
\(303\) 0 0
\(304\) 0.535898i 0.0307359i
\(305\) 9.00000 + 5.19615i 0.515339 + 0.297531i
\(306\) 0 0
\(307\) 12.5359i 0.715462i 0.933825 + 0.357731i \(0.116449\pi\)
−0.933825 + 0.357731i \(0.883551\pi\)
\(308\) −0.464102 + 0.803848i −0.0264446 + 0.0458035i
\(309\) 0 0
\(310\) −1.50000 + 0.866025i −0.0851943 + 0.0491869i
\(311\) 7.60770 0.431393 0.215696 0.976460i \(-0.430798\pi\)
0.215696 + 0.976460i \(0.430798\pi\)
\(312\) 0 0
\(313\) −28.0000 −1.58265 −0.791327 0.611393i \(-0.790609\pi\)
−0.791327 + 0.611393i \(0.790609\pi\)
\(314\) 4.33013 2.50000i 0.244363 0.141083i
\(315\) 0 0
\(316\) −0.0358984 + 0.0621778i −0.00201944 + 0.00349778i
\(317\) 21.4641i 1.20554i −0.797913 0.602772i \(-0.794063\pi\)
0.797913 0.602772i \(-0.205937\pi\)
\(318\) 0 0
\(319\) −1.50000 0.866025i −0.0839839 0.0484881i
\(320\) 1.00000i 0.0559017i
\(321\) 0 0
\(322\) −0.267949 0.464102i −0.0149322 0.0258634i
\(323\) 1.85641 1.07180i 0.103293 0.0596364i
\(324\) 0 0
\(325\) −1.00000 3.46410i −0.0554700 0.192154i
\(326\) −23.0526 −1.27676
\(327\) 0 0
\(328\) 1.00000 + 1.73205i 0.0552158 + 0.0956365i
\(329\) −10.4641 + 18.1244i −0.576905 + 0.999228i
\(330\) 0 0
\(331\) −21.4641 12.3923i −1.17977 0.681143i −0.223812 0.974632i \(-0.571850\pi\)
−0.955962 + 0.293490i \(0.905183\pi\)
\(332\) 4.26795 + 2.46410i 0.234234 + 0.135235i
\(333\) 0 0
\(334\) 9.16025 15.8660i 0.501227 0.868150i
\(335\) −2.26795 3.92820i −0.123911 0.214621i
\(336\) 0 0
\(337\) −25.3205 −1.37930 −0.689648 0.724145i \(-0.742235\pi\)
−0.689648 + 0.724145i \(0.742235\pi\)
\(338\) 6.06218 11.5000i 0.329739 0.625518i
\(339\) 0 0
\(340\) 3.46410 2.00000i 0.187867 0.108465i
\(341\) −0.401924 0.696152i −0.0217654 0.0376988i
\(342\) 0 0
\(343\) 20.0000i 1.07990i
\(344\) 1.66987 + 0.964102i 0.0900335 + 0.0519809i
\(345\) 0 0
\(346\) 2.92820i 0.157421i
\(347\) 11.1962 19.3923i 0.601041 1.04103i −0.391623 0.920126i \(-0.628086\pi\)
0.992664 0.120908i \(-0.0385805\pi\)
\(348\) 0 0
\(349\) −12.5885 + 7.26795i −0.673845 + 0.389044i −0.797532 0.603277i \(-0.793861\pi\)
0.123687 + 0.992321i \(0.460528\pi\)
\(350\) 2.00000 0.106904
\(351\) 0 0
\(352\) −0.464102 −0.0247367
\(353\) 1.73205 1.00000i 0.0921878 0.0532246i −0.453197 0.891410i \(-0.649717\pi\)
0.545385 + 0.838186i \(0.316383\pi\)
\(354\) 0 0
\(355\) 4.19615 7.26795i 0.222709 0.385743i
\(356\) 7.46410i 0.395597i
\(357\) 0 0
\(358\) 14.0885 + 8.13397i 0.744598 + 0.429894i
\(359\) 18.9282i 0.998992i −0.866316 0.499496i \(-0.833518\pi\)
0.866316 0.499496i \(-0.166482\pi\)
\(360\) 0 0
\(361\) −9.35641 16.2058i −0.492442 0.852935i
\(362\) −9.46410 + 5.46410i −0.497422 + 0.287187i
\(363\) 0 0
\(364\) 5.19615 + 5.00000i 0.272352 + 0.262071i
\(365\) 2.00000 0.104685
\(366\) 0 0
\(367\) −18.1962 31.5167i −0.949831 1.64516i −0.745776 0.666197i \(-0.767921\pi\)
−0.204056 0.978959i \(-0.565412\pi\)
\(368\) 0.133975 0.232051i 0.00698391 0.0120965i
\(369\) 0 0
\(370\) 1.03590 + 0.598076i 0.0538538 + 0.0310925i
\(371\) 22.3923 + 12.9282i 1.16255 + 0.671199i
\(372\) 0 0
\(373\) −12.8923 + 22.3301i −0.667538 + 1.15621i 0.311052 + 0.950393i \(0.399319\pi\)
−0.978590 + 0.205817i \(0.934015\pi\)
\(374\) 0.928203 + 1.60770i 0.0479962 + 0.0831319i
\(375\) 0 0
\(376\) −10.4641 −0.539645
\(377\) −9.33013 + 9.69615i −0.480526 + 0.499377i
\(378\) 0 0
\(379\) −0.124356 + 0.0717968i −0.00638772 + 0.00368795i −0.503190 0.864176i \(-0.667841\pi\)
0.496803 + 0.867863i \(0.334507\pi\)
\(380\) 0.267949 + 0.464102i 0.0137455 + 0.0238079i
\(381\) 0 0
\(382\) 14.5359i 0.743721i
\(383\) 3.99038 + 2.30385i 0.203899 + 0.117721i 0.598473 0.801143i \(-0.295774\pi\)
−0.394574 + 0.918864i \(0.629108\pi\)
\(384\) 0 0
\(385\) 0.928203i 0.0473056i
\(386\) −11.6603 + 20.1962i −0.593491 + 1.02796i
\(387\) 0 0
\(388\) −6.46410 + 3.73205i −0.328165 + 0.189466i
\(389\) 20.2679 1.02763 0.513813 0.857902i \(-0.328233\pi\)
0.513813 + 0.857902i \(0.328233\pi\)
\(390\) 0 0
\(391\) −1.07180 −0.0542031
\(392\) 2.59808 1.50000i 0.131223 0.0757614i
\(393\) 0 0
\(394\) 8.19615 14.1962i 0.412916 0.715192i
\(395\) 0.0717968i 0.00361249i
\(396\) 0 0
\(397\) 10.5000 + 6.06218i 0.526980 + 0.304252i 0.739786 0.672843i \(-0.234927\pi\)
−0.212806 + 0.977095i \(0.568260\pi\)
\(398\) 18.9282i 0.948785i
\(399\) 0 0
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) −27.7128 + 16.0000i −1.38391 + 0.799002i −0.992620 0.121265i \(-0.961305\pi\)
−0.391292 + 0.920267i \(0.627972\pi\)
\(402\) 0 0
\(403\) −6.00000 + 1.73205i −0.298881 + 0.0862796i
\(404\) −10.9282 −0.543698
\(405\) 0 0
\(406\) −3.73205 6.46410i −0.185219 0.320808i
\(407\) −0.277568 + 0.480762i −0.0137585 + 0.0238305i
\(408\) 0 0
\(409\) −3.46410 2.00000i −0.171289 0.0988936i 0.411905 0.911227i \(-0.364864\pi\)
−0.583193 + 0.812333i \(0.698197\pi\)
\(410\) 1.73205 + 1.00000i 0.0855399 + 0.0493865i
\(411\) 0 0
\(412\) 7.92820 13.7321i 0.390595 0.676530i
\(413\) 1.53590 + 2.66025i 0.0755766 + 0.130903i
\(414\) 0 0
\(415\) 4.92820 0.241916
\(416\) −0.866025 + 3.50000i −0.0424604 + 0.171602i
\(417\) 0 0
\(418\) −0.215390 + 0.124356i −0.0105351 + 0.00608243i
\(419\) 0.803848 + 1.39230i 0.0392705 + 0.0680185i 0.884993 0.465605i \(-0.154163\pi\)
−0.845722 + 0.533624i \(0.820830\pi\)
\(420\) 0 0
\(421\) 16.3923i 0.798912i −0.916752 0.399456i \(-0.869199\pi\)
0.916752 0.399456i \(-0.130801\pi\)
\(422\) 20.1962 + 11.6603i 0.983133 + 0.567612i
\(423\) 0 0
\(424\) 12.9282i 0.627849i
\(425\) 2.00000 3.46410i 0.0970143 0.168034i
\(426\) 0 0
\(427\) −18.0000 + 10.3923i −0.871081 + 0.502919i
\(428\) 19.8564 0.959796
\(429\) 0 0
\(430\) 1.92820 0.0929862
\(431\) 6.58846 3.80385i 0.317355 0.183225i −0.332858 0.942977i \(-0.608013\pi\)
0.650213 + 0.759752i \(0.274680\pi\)
\(432\) 0 0
\(433\) 7.66025 13.2679i 0.368128 0.637617i −0.621145 0.783696i \(-0.713332\pi\)
0.989273 + 0.146079i \(0.0466654\pi\)
\(434\) 3.46410i 0.166282i
\(435\) 0 0
\(436\) 10.2679 + 5.92820i 0.491746 + 0.283909i
\(437\) 0.143594i 0.00686901i
\(438\) 0 0
\(439\) −4.92820 8.53590i −0.235210 0.407396i 0.724123 0.689670i \(-0.242245\pi\)
−0.959334 + 0.282274i \(0.908911\pi\)
\(440\) −0.401924 + 0.232051i −0.0191610 + 0.0110626i
\(441\) 0 0
\(442\) 13.8564 4.00000i 0.659082 0.190261i
\(443\) 4.39230 0.208685 0.104342 0.994541i \(-0.466726\pi\)
0.104342 + 0.994541i \(0.466726\pi\)
\(444\) 0 0
\(445\) 3.73205 + 6.46410i 0.176916 + 0.306428i
\(446\) −13.7321 + 23.7846i −0.650231 + 1.12623i
\(447\) 0 0
\(448\) −1.73205 1.00000i −0.0818317 0.0472456i
\(449\) 34.3923 + 19.8564i 1.62307 + 0.937082i 0.986092 + 0.166203i \(0.0531506\pi\)
0.636982 + 0.770879i \(0.280183\pi\)
\(450\) 0 0
\(451\) −0.464102 + 0.803848i −0.0218537 + 0.0378517i
\(452\) −5.59808 9.69615i −0.263311 0.456069i
\(453\) 0 0
\(454\) −4.39230 −0.206141
\(455\) 7.00000 + 1.73205i 0.328165 + 0.0811998i
\(456\) 0 0
\(457\) −27.2487 + 15.7321i −1.27464 + 0.735914i −0.975858 0.218407i \(-0.929914\pi\)
−0.298783 + 0.954321i \(0.596581\pi\)
\(458\) −9.92820 17.1962i −0.463914 0.803523i
\(459\) 0 0
\(460\) 0.267949i 0.0124932i
\(461\) −5.59808 3.23205i −0.260728 0.150532i 0.363938 0.931423i \(-0.381432\pi\)
−0.624667 + 0.780891i \(0.714765\pi\)
\(462\) 0 0
\(463\) 20.9282i 0.972616i 0.873787 + 0.486308i \(0.161657\pi\)
−0.873787 + 0.486308i \(0.838343\pi\)
\(464\) 1.86603 3.23205i 0.0866281 0.150044i
\(465\) 0 0
\(466\) −15.6962 + 9.06218i −0.727110 + 0.419797i
\(467\) −11.8564 −0.548649 −0.274325 0.961637i \(-0.588454\pi\)
−0.274325 + 0.961637i \(0.588454\pi\)
\(468\) 0 0
\(469\) 9.07180 0.418897
\(470\) −9.06218 + 5.23205i −0.418007 + 0.241337i
\(471\) 0 0
\(472\) −0.767949 + 1.33013i −0.0353477 + 0.0612241i
\(473\) 0.894882i 0.0411467i
\(474\) 0 0
\(475\) 0.464102 + 0.267949i 0.0212944 + 0.0122944i
\(476\) 8.00000i 0.366679i
\(477\) 0 0
\(478\) 2.19615 + 3.80385i 0.100450 + 0.173984i
\(479\) −1.26795 + 0.732051i −0.0579341 + 0.0334483i −0.528687 0.848817i \(-0.677316\pi\)
0.470753 + 0.882265i \(0.343982\pi\)
\(480\) 0 0
\(481\) 3.10770 + 2.99038i 0.141699 + 0.136350i
\(482\) 14.2679 0.649887
\(483\) 0 0
\(484\) 5.39230 + 9.33975i 0.245105 + 0.424534i
\(485\) −3.73205 + 6.46410i −0.169464 + 0.293520i
\(486\) 0 0
\(487\) 33.9282 + 19.5885i 1.53743 + 0.887638i 0.998988 + 0.0449775i \(0.0143216\pi\)
0.538446 + 0.842660i \(0.319012\pi\)
\(488\) −9.00000 5.19615i −0.407411 0.235219i
\(489\) 0 0
\(490\) 1.50000 2.59808i 0.0677631 0.117369i
\(491\) 8.66025 + 15.0000i 0.390832 + 0.676941i 0.992559 0.121761i \(-0.0388541\pi\)
−0.601728 + 0.798701i \(0.705521\pi\)
\(492\) 0 0
\(493\) −14.9282 −0.672332
\(494\) 0.535898 + 1.85641i 0.0241112 + 0.0835237i
\(495\) 0 0
\(496\) 1.50000 0.866025i 0.0673520 0.0388857i
\(497\) 8.39230 + 14.5359i 0.376446 + 0.652024i
\(498\) 0 0
\(499\) 13.4641i 0.602736i 0.953508 + 0.301368i \(0.0974433\pi\)
−0.953508 + 0.301368i \(0.902557\pi\)
\(500\) 0.866025 + 0.500000i 0.0387298 + 0.0223607i
\(501\) 0 0
\(502\) 12.2679i 0.547545i
\(503\) 15.5885 27.0000i 0.695055 1.20387i −0.275107 0.961414i \(-0.588713\pi\)
0.970162 0.242457i \(-0.0779533\pi\)
\(504\) 0 0
\(505\) −9.46410 + 5.46410i −0.421147 + 0.243149i
\(506\) 0.124356 0.00552828
\(507\) 0 0
\(508\) −8.92820 −0.396125
\(509\) −16.7942 + 9.69615i −0.744391 + 0.429774i −0.823664 0.567079i \(-0.808074\pi\)
0.0792726 + 0.996853i \(0.474740\pi\)
\(510\) 0 0
\(511\) −2.00000 + 3.46410i −0.0884748 + 0.153243i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 19.6244 + 11.3301i 0.865593 + 0.499750i
\(515\) 15.8564i 0.698717i
\(516\) 0 0
\(517\) −2.42820 4.20577i −0.106792 0.184970i
\(518\) −2.07180 + 1.19615i −0.0910295 + 0.0525559i
\(519\) 0 0
\(520\) 1.00000 + 3.46410i 0.0438529 + 0.151911i
\(521\) −17.3205 −0.758825 −0.379413 0.925228i \(-0.623874\pi\)
−0.379413 + 0.925228i \(0.623874\pi\)
\(522\) 0 0
\(523\) 14.8923 + 25.7942i 0.651195 + 1.12790i 0.982833 + 0.184496i \(0.0590653\pi\)
−0.331638 + 0.943407i \(0.607601\pi\)
\(524\) 0.669873 1.16025i 0.0292635 0.0506859i
\(525\) 0 0
\(526\) 15.6962 + 9.06218i 0.684385 + 0.395130i
\(527\) −6.00000 3.46410i −0.261364 0.150899i
\(528\) 0 0
\(529\) 11.4641 19.8564i 0.498439 0.863322i
\(530\) 6.46410 + 11.1962i 0.280783 + 0.486330i
\(531\) 0 0
\(532\) −1.07180 −0.0464683
\(533\) 5.19615 + 5.00000i 0.225070 + 0.216574i
\(534\) 0 0
\(535\) 17.1962 9.92820i 0.743455 0.429234i
\(536\) 2.26795 + 3.92820i 0.0979605 + 0.169673i
\(537\) 0 0
\(538\) 12.0000i 0.517357i
\(539\) 1.20577 + 0.696152i 0.0519362 + 0.0299854i
\(540\) 0 0
\(541\) 13.0718i 0.562000i 0.959708 + 0.281000i \(0.0906662\pi\)
−0.959708 + 0.281000i \(0.909334\pi\)
\(542\) −4.59808 + 7.96410i −0.197504 + 0.342087i
\(543\) 0 0
\(544\) −3.46410 + 2.00000i −0.148522 + 0.0857493i
\(545\) 11.8564 0.507873
\(546\) 0 0
\(547\) 9.07180 0.387882 0.193941 0.981013i \(-0.437873\pi\)
0.193941 + 0.981013i \(0.437873\pi\)
\(548\) 3.86603 2.23205i 0.165148 0.0953485i
\(549\) 0 0
\(550\) −0.232051 + 0.401924i −0.00989468 + 0.0171381i
\(551\) 2.00000i 0.0852029i
\(552\) 0 0
\(553\) −0.124356 0.0717968i −0.00528814 0.00305311i
\(554\) 9.92820i 0.421809i
\(555\) 0 0
\(556\) 0.464102 + 0.803848i 0.0196823 + 0.0340907i
\(557\) −32.6603 + 18.8564i −1.38386 + 0.798972i −0.992614 0.121315i \(-0.961289\pi\)
−0.391245 + 0.920286i \(0.627956\pi\)
\(558\) 0 0
\(559\) 6.74871 + 1.66987i 0.285440 + 0.0706281i
\(560\) −2.00000 −0.0845154
\(561\) 0 0
\(562\) 2.46410 + 4.26795i 0.103942 + 0.180033i
\(563\) −19.6603 + 34.0526i −0.828581 + 1.43514i 0.0705706 + 0.997507i \(0.477518\pi\)
−0.899152 + 0.437637i \(0.855815\pi\)
\(564\) 0 0
\(565\) −9.69615 5.59808i −0.407920 0.235513i
\(566\) 3.40192 + 1.96410i 0.142994 + 0.0825573i
\(567\) 0 0
\(568\) −4.19615 + 7.26795i −0.176067 + 0.304956i
\(569\) −2.66025 4.60770i −0.111524 0.193165i 0.804861 0.593463i \(-0.202240\pi\)
−0.916385 + 0.400299i \(0.868906\pi\)
\(570\) 0 0
\(571\) 45.1769 1.89060 0.945298 0.326209i \(-0.105771\pi\)
0.945298 + 0.326209i \(0.105771\pi\)
\(572\) −1.60770 + 0.464102i −0.0672211 + 0.0194051i
\(573\) 0 0
\(574\) −3.46410 + 2.00000i −0.144589 + 0.0834784i
\(575\) −0.133975 0.232051i −0.00558713 0.00967719i
\(576\) 0 0
\(577\) 10.0000i 0.416305i −0.978096 0.208153i \(-0.933255\pi\)
0.978096 0.208153i \(-0.0667451\pi\)
\(578\) −0.866025 0.500000i −0.0360219 0.0207973i
\(579\) 0 0
\(580\) 3.73205i 0.154965i
\(581\) −4.92820 + 8.53590i −0.204456 + 0.354129i
\(582\) 0 0
\(583\) −5.19615 + 3.00000i −0.215203 + 0.124247i
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) 4.14359 0.171170
\(587\) 15.9282 9.19615i 0.657427 0.379566i −0.133869 0.990999i \(-0.542740\pi\)
0.791296 + 0.611433i \(0.209407\pi\)
\(588\) 0 0
\(589\) 0.464102 0.803848i 0.0191230 0.0331220i
\(590\) 1.53590i 0.0632319i
\(591\) 0 0
\(592\) −1.03590 0.598076i −0.0425752 0.0245808i
\(593\) 31.1051i 1.27733i 0.769483 + 0.638667i \(0.220514\pi\)
−0.769483 + 0.638667i \(0.779486\pi\)
\(594\) 0 0
\(595\) 4.00000 + 6.92820i 0.163984 + 0.284029i
\(596\) −17.7224 + 10.2321i −0.725939 + 0.419121i
\(597\) 0 0
\(598\) 0.232051 0.937822i 0.00948926 0.0383504i
\(599\) −10.3923 −0.424618 −0.212309 0.977203i \(-0.568098\pi\)
−0.212309 + 0.977203i \(0.568098\pi\)
\(600\) 0 0
\(601\) −10.8923 18.8660i −0.444306 0.769561i 0.553697 0.832718i \(-0.313216\pi\)
−0.998004 + 0.0631568i \(0.979883\pi\)
\(602\) −1.92820 + 3.33975i −0.0785877 + 0.136118i
\(603\) 0 0
\(604\) 9.00000 + 5.19615i 0.366205 + 0.211428i
\(605\) 9.33975 + 5.39230i 0.379715 + 0.219228i
\(606\) 0 0
\(607\) −21.5885 + 37.3923i −0.876248 + 1.51771i −0.0208216 + 0.999783i \(0.506628\pi\)
−0.855427 + 0.517924i \(0.826705\pi\)
\(608\) −0.267949 0.464102i −0.0108668 0.0188218i
\(609\) 0 0
\(610\) −10.3923 −0.420772
\(611\) −36.2487 + 10.4641i −1.46647 + 0.423332i
\(612\) 0 0
\(613\) 0.820508 0.473721i 0.0331400 0.0191334i −0.483338 0.875434i \(-0.660576\pi\)
0.516478 + 0.856300i \(0.327243\pi\)
\(614\) −6.26795 10.8564i −0.252954 0.438129i
\(615\) 0 0
\(616\) 0.928203i 0.0373984i
\(617\) −13.4545 7.76795i −0.541657 0.312726i 0.204093 0.978951i \(-0.434575\pi\)
−0.745750 + 0.666226i \(0.767909\pi\)
\(618\) 0 0
\(619\) 24.2487i 0.974638i 0.873224 + 0.487319i \(0.162025\pi\)
−0.873224 + 0.487319i \(0.837975\pi\)
\(620\) 0.866025 1.50000i 0.0347804 0.0602414i
\(621\) 0 0
\(622\) −6.58846 + 3.80385i −0.264173 + 0.152520i
\(623\) −14.9282 −0.598086
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 24.2487 14.0000i 0.969173 0.559553i
\(627\) 0 0
\(628\) −2.50000 + 4.33013i −0.0997609 + 0.172791i
\(629\) 4.78461i 0.190775i
\(630\) 0 0
\(631\) −21.2487 12.2679i −0.845898 0.488379i 0.0133668 0.999911i \(-0.495745\pi\)
−0.859265 + 0.511531i \(0.829078\pi\)
\(632\) 0.0717968i 0.00285592i
\(633\) 0 0
\(634\) 10.7321 + 18.5885i 0.426224 + 0.738242i
\(635\) −7.73205 + 4.46410i −0.306837 + 0.177152i
\(636\) 0 0
\(637\) 7.50000 7.79423i 0.297161 0.308819i
\(638\) 1.73205 0.0685725
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 13.9282 24.1244i 0.550131 0.952855i −0.448134 0.893967i \(-0.647911\pi\)
0.998265 0.0588882i \(-0.0187555\pi\)
\(642\) 0 0
\(643\) 23.7846 + 13.7321i 0.937973 + 0.541539i 0.889324 0.457277i \(-0.151175\pi\)
0.0486490 + 0.998816i \(0.484508\pi\)
\(644\) 0.464102 + 0.267949i 0.0182882 + 0.0105587i
\(645\) 0 0
\(646\) −1.07180 + 1.85641i −0.0421693 + 0.0730393i
\(647\) 10.6603 + 18.4641i 0.419098 + 0.725899i 0.995849 0.0910212i \(-0.0290131\pi\)
−0.576751 + 0.816920i \(0.695680\pi\)
\(648\) 0 0
\(649\) −0.712813 −0.0279804
\(650\) 2.59808 + 2.50000i 0.101905 + 0.0980581i
\(651\) 0 0
\(652\) 19.9641 11.5263i 0.781855 0.451404i
\(653\) −22.1244 38.3205i −0.865793 1.49960i −0.866258 0.499597i \(-0.833481\pi\)
0.000464739 1.00000i \(-0.499852\pi\)
\(654\) 0 0
\(655\) 1.33975i 0.0523482i
\(656\) −1.73205 1.00000i −0.0676252 0.0390434i
\(657\) 0 0
\(658\) 20.9282i 0.815866i
\(659\) −1.86603 + 3.23205i −0.0726900 + 0.125903i −0.900079 0.435726i \(-0.856492\pi\)
0.827389 + 0.561629i \(0.189825\pi\)
\(660\) 0 0
\(661\) 37.5167 21.6603i 1.45923 0.842486i 0.460256 0.887786i \(-0.347758\pi\)
0.998973 + 0.0453002i \(0.0144244\pi\)
\(662\) 24.7846 0.963281
\(663\) 0 0
\(664\) −4.92820 −0.191251
\(665\) −0.928203 + 0.535898i −0.0359942 + 0.0207812i
\(666\) 0 0
\(667\) −0.500000 + 0.866025i −0.0193601 + 0.0335326i
\(668\) 18.3205i 0.708842i
\(669\) 0 0
\(670\) 3.92820 + 2.26795i 0.151760 + 0.0876185i
\(671\) 4.82309i 0.186193i
\(672\) 0 0
\(673\) −16.0000 27.7128i −0.616755 1.06825i −0.990074 0.140548i \(-0.955114\pi\)
0.373319 0.927703i \(-0.378220\pi\)
\(674\) 21.9282 12.6603i 0.844643 0.487655i
\(675\) 0 0
\(676\) 0.500000 + 12.9904i 0.0192308 + 0.499630i
\(677\) −11.6077 −0.446120 −0.223060 0.974805i \(-0.571605\pi\)
−0.223060 + 0.974805i \(0.571605\pi\)
\(678\) 0 0
\(679\) −7.46410 12.9282i −0.286446 0.496139i
\(680\) −2.00000 + 3.46410i −0.0766965 + 0.132842i
\(681\) 0 0
\(682\) 0.696152 + 0.401924i 0.0266571 + 0.0153905i
\(683\) 0.679492 + 0.392305i 0.0260000 + 0.0150111i 0.512944 0.858422i \(-0.328555\pi\)
−0.486944 + 0.873433i \(0.661888\pi\)
\(684\) 0 0
\(685\) 2.23205 3.86603i 0.0852823 0.147713i
\(686\) 10.0000 + 17.3205i 0.381802 + 0.661300i
\(687\) 0 0
\(688\) −1.92820 −0.0735121
\(689\) 12.9282 + 44.7846i 0.492525 + 1.70616i
\(690\) 0 0
\(691\) −30.4641 + 17.5885i −1.15891 + 0.669096i −0.951042 0.309061i \(-0.899985\pi\)
−0.207867 + 0.978157i \(0.566652\pi\)
\(692\) 1.46410 + 2.53590i 0.0556568 + 0.0964004i
\(693\) 0 0
\(694\) 22.3923i 0.850000i
\(695\) 0.803848 + 0.464102i 0.0304917 + 0.0176044i
\(696\) 0 0
\(697\) 8.00000i 0.303022i
\(698\) 7.26795 12.5885i 0.275096 0.476480i
\(699\) 0 0
\(700\) −1.73205 + 1.00000i −0.0654654 + 0.0377964i
\(701\) 3.73205 0.140958 0.0704788 0.997513i \(-0.477547\pi\)
0.0704788 + 0.997513i \(0.477547\pi\)
\(702\) 0 0
\(703\) −0.641016 −0.0241764
\(704\) 0.401924 0.232051i 0.0151481 0.00874574i
\(705\) 0 0
\(706\) −1.00000 + 1.73205i −0.0376355 + 0.0651866i
\(707\) 21.8564i 0.821995i
\(708\) 0 0
\(709\) 7.85641 + 4.53590i 0.295054 + 0.170349i 0.640219 0.768193i \(-0.278844\pi\)
−0.345165 + 0.938542i \(0.612177\pi\)
\(710\) 8.39230i 0.314958i
\(711\) 0 0
\(712\) −3.73205 6.46410i −0.139865 0.242252i
\(713\) −0.401924 + 0.232051i −0.0150522 + 0.00869037i
\(714\) 0 0
\(715\) −1.16025 + 1.20577i −0.0433910 + 0.0450933i
\(716\) −16.2679 −0.607962
\(717\) 0 0
\(718\) 9.46410 + 16.3923i 0.353197 + 0.611755i
\(719\) 17.3205 30.0000i 0.645946 1.11881i −0.338136 0.941097i \(-0.609796\pi\)
0.984082 0.177714i \(-0.0568702\pi\)
\(720\) 0 0
\(721\) 27.4641 + 15.8564i 1.02282 + 0.590523i
\(722\) 16.2058 + 9.35641i 0.603116 + 0.348209i
\(723\) 0 0
\(724\) 5.46410 9.46410i 0.203072 0.351731i
\(725\) −1.86603 3.23205i −0.0693024 0.120035i
\(726\) 0 0
\(727\) 23.7128 0.879460 0.439730 0.898130i \(-0.355074\pi\)
0.439730 + 0.898130i \(0.355074\pi\)
\(728\) −7.00000 1.73205i −0.259437 0.0641941i
\(729\) 0 0
\(730\) −1.73205 + 1.00000i −0.0641061 + 0.0370117i
\(731\) 3.85641 + 6.67949i 0.142634 + 0.247050i
\(732\) 0 0
\(733\) 37.0718i 1.36928i −0.728882 0.684639i \(-0.759960\pi\)
0.728882 0.684639i \(-0.240040\pi\)
\(734\) 31.5167 + 18.1962i 1.16330 + 0.671632i
\(735\) 0 0
\(736\) 0.267949i 0.00987674i
\(737\) −1.05256 + 1.82309i −0.0387715 + 0.0671542i
\(738\) 0 0
\(739\) −13.2679 + 7.66025i −0.488069 + 0.281787i −0.723773 0.690038i \(-0.757594\pi\)
0.235704 + 0.971825i \(0.424260\pi\)
\(740\) −1.19615 −0.0439714
\(741\) 0 0
\(742\) −25.8564 −0.949219
\(743\) −29.0429 + 16.7679i −1.06548 + 0.615156i −0.926944 0.375201i \(-0.877574\pi\)
−0.138539 + 0.990357i \(0.544240\pi\)
\(744\) 0 0
\(745\) −10.2321 + 17.7224i −0.374873 + 0.649300i
\(746\) 25.7846i 0.944042i
\(747\) 0 0
\(748\) −1.60770 0.928203i −0.0587832 0.0339385i
\(749\) 39.7128i 1.45107i
\(750\) 0 0
\(751\) −13.9641 24.1865i −0.509557 0.882579i −0.999939 0.0110712i \(-0.996476\pi\)
0.490381 0.871508i \(-0.336857\pi\)
\(752\) 9.06218 5.23205i 0.330464 0.190793i
\(753\) 0 0
\(754\) 3.23205 13.0622i 0.117704 0.475696i
\(755\) 10.3923 0.378215
\(756\) 0 0
\(757\) 9.00000 + 15.5885i 0.327111 + 0.566572i 0.981937 0.189207i \(-0.0605917\pi\)
−0.654827 + 0.755779i \(0.727258\pi\)
\(758\) 0.0717968 0.124356i 0.00260778 0.00451680i
\(759\) 0 0
\(760\) −0.464102 0.267949i −0.0168347 0.00971954i
\(761\) 16.3923 + 9.46410i 0.594221 + 0.343073i 0.766765 0.641928i \(-0.221865\pi\)
−0.172544 + 0.985002i \(0.555199\pi\)
\(762\) 0 0
\(763\) −11.8564 + 20.5359i −0.429231 + 0.743449i
\(764\) −7.26795 12.5885i −0.262945 0.455434i
\(765\) 0 0
\(766\) −4.60770 −0.166483
\(767\) −1.33013 + 5.37564i −0.0480281 + 0.194103i
\(768\) 0 0
\(769\) −16.9641 + 9.79423i −0.611741 + 0.353189i −0.773647 0.633617i \(-0.781569\pi\)
0.161905 + 0.986806i \(0.448236\pi\)
\(770\) −0.464102 0.803848i −0.0167251 0.0289687i
\(771\) 0 0
\(772\) 23.3205i 0.839323i
\(773\) −24.0000 13.8564i −0.863220 0.498380i 0.00186926 0.999998i \(-0.499405\pi\)
−0.865089 + 0.501618i \(0.832738\pi\)
\(774\) 0 0
\(775\) 1.73205i 0.0622171i
\(776\) 3.73205 6.46410i 0.133973 0.232048i
\(777\) 0 0
\(778\) −17.5526 + 10.1340i −0.629290 + 0.363321i
\(779\) −1.07180 −0.0384011
\(780\) 0 0
\(781\) −3.89488 −0.139370
\(782\) 0.928203 0.535898i 0.0331925 0.0191637i
\(783\) 0 0
\(784\) −1.50000 + 2.59808i −0.0535714 + 0.0927884i
\(785\) 5.00000i 0.178458i
\(786\) 0 0
\(787\) 1.50000 + 0.866025i 0.0534692 + 0.0308705i 0.526496 0.850177i \(-0.323505\pi\)
−0.473027 + 0.881048i \(0.656839\pi\)
\(788\) 16.3923i 0.583952i