Properties

Label 1386.2.ba.a.1187.3
Level $1386$
Weight $2$
Character 1386.1187
Analytic conductor $11.067$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.ba (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1187.3
Character \(\chi\) \(=\) 1386.1187
Dual form 1386.2.ba.a.989.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.34835 + 1.35582i) q^{5} +(0.222226 - 2.63640i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.34835 + 1.35582i) q^{5} +(0.222226 - 2.63640i) q^{7} +1.00000 q^{8} +(2.34835 + 1.35582i) q^{10} +(2.77145 + 1.82183i) q^{11} -2.18074i q^{13} +(-2.39430 + 1.12575i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.0281751 - 0.0488007i) q^{17} +(-2.38555 + 1.37730i) q^{19} -2.71165i q^{20} +(0.192032 - 3.31106i) q^{22} +(-6.02718 + 3.47980i) q^{23} +(1.17651 - 2.03778i) q^{25} +(-1.88857 + 1.09037i) q^{26} +(2.17208 + 1.51065i) q^{28} +6.43297 q^{29} +(3.65147 - 6.32453i) q^{31} +(-0.500000 + 0.866025i) q^{32} -0.0563502 q^{34} +(3.05263 + 6.49251i) q^{35} +(-1.62140 - 2.80836i) q^{37} +(2.38555 + 1.37730i) q^{38} +(-2.34835 + 1.35582i) q^{40} +2.71397 q^{41} -10.6345i q^{43} +(-2.96348 + 1.48923i) q^{44} +(6.02718 + 3.47980i) q^{46} +(2.58268 - 1.49111i) q^{47} +(-6.90123 - 1.17175i) q^{49} -2.35302 q^{50} +(1.88857 + 1.09037i) q^{52} +(-10.1931 - 5.88497i) q^{53} +(-8.97843 - 0.520722i) q^{55} +(0.222226 - 2.63640i) q^{56} +(-3.21649 - 5.57112i) q^{58} +(-12.2489 - 7.07189i) q^{59} +(-10.2720 + 5.93056i) q^{61} -7.30294 q^{62} +1.00000 q^{64} +(2.95669 + 5.12114i) q^{65} +(0.749028 - 1.29735i) q^{67} +(0.0281751 + 0.0488007i) q^{68} +(4.09636 - 5.88991i) q^{70} -1.82248i q^{71} +(-6.82420 - 3.93995i) q^{73} +(-1.62140 + 2.80836i) q^{74} -2.75460i q^{76} +(5.41898 - 6.90179i) q^{77} +(7.82062 - 4.51524i) q^{79} +(2.34835 + 1.35582i) q^{80} +(-1.35699 - 2.35037i) q^{82} -17.2299 q^{83} +0.152802i q^{85} +(-9.20975 + 5.31725i) q^{86} +(2.77145 + 1.82183i) q^{88} +(-7.43764 + 4.29412i) q^{89} +(-5.74929 - 0.484616i) q^{91} -6.95959i q^{92} +(-2.58268 - 1.49111i) q^{94} +(3.73475 - 6.46878i) q^{95} +6.25716 q^{97} +(2.43585 + 6.56252i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} + O(q^{10}) \) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} - 2q^{11} - 16q^{16} - 4q^{17} + 4q^{22} + 4q^{25} - 16q^{29} + 4q^{31} - 16q^{32} + 8q^{34} - 16q^{35} + 4q^{37} + 32q^{41} - 2q^{44} + 20q^{49} - 8q^{50} - 12q^{55} + 8q^{58} - 8q^{62} + 32q^{64} - 8q^{67} - 4q^{68} - 4q^{70} + 4q^{74} - 14q^{77} - 16q^{82} - 88q^{83} - 2q^{88} + 24q^{95} - 32q^{97} + 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −2.34835 + 1.35582i −1.05022 + 0.606343i −0.922710 0.385495i \(-0.874031\pi\)
−0.127506 + 0.991838i \(0.540697\pi\)
\(6\) 0 0
\(7\) 0.222226 2.63640i 0.0839935 0.996466i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 2.34835 + 1.35582i 0.742615 + 0.428749i
\(11\) 2.77145 + 1.82183i 0.835623 + 0.549304i
\(12\) 0 0
\(13\) 2.18074i 0.604827i −0.953177 0.302414i \(-0.902208\pi\)
0.953177 0.302414i \(-0.0977924\pi\)
\(14\) −2.39430 + 1.12575i −0.639905 + 0.300869i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.0281751 0.0488007i 0.00683347 0.0118359i −0.862588 0.505906i \(-0.831158\pi\)
0.869422 + 0.494070i \(0.164491\pi\)
\(18\) 0 0
\(19\) −2.38555 + 1.37730i −0.547284 + 0.315974i −0.748026 0.663670i \(-0.768998\pi\)
0.200742 + 0.979644i \(0.435665\pi\)
\(20\) 2.71165i 0.606343i
\(21\) 0 0
\(22\) 0.192032 3.31106i 0.0409413 0.705921i
\(23\) −6.02718 + 3.47980i −1.25675 + 0.725587i −0.972442 0.233144i \(-0.925099\pi\)
−0.284312 + 0.958732i \(0.591765\pi\)
\(24\) 0 0
\(25\) 1.17651 2.03778i 0.235302 0.407556i
\(26\) −1.88857 + 1.09037i −0.370379 + 0.213839i
\(27\) 0 0
\(28\) 2.17208 + 1.51065i 0.410484 + 0.285487i
\(29\) 6.43297 1.19457 0.597286 0.802028i \(-0.296246\pi\)
0.597286 + 0.802028i \(0.296246\pi\)
\(30\) 0 0
\(31\) 3.65147 6.32453i 0.655823 1.13592i −0.325864 0.945417i \(-0.605655\pi\)
0.981687 0.190502i \(-0.0610116\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −0.0563502 −0.00966399
\(35\) 3.05263 + 6.49251i 0.515989 + 1.09743i
\(36\) 0 0
\(37\) −1.62140 2.80836i −0.266557 0.461691i 0.701413 0.712755i \(-0.252553\pi\)
−0.967970 + 0.251064i \(0.919219\pi\)
\(38\) 2.38555 + 1.37730i 0.386988 + 0.223428i
\(39\) 0 0
\(40\) −2.34835 + 1.35582i −0.371307 + 0.214374i
\(41\) 2.71397 0.423852 0.211926 0.977286i \(-0.432026\pi\)
0.211926 + 0.977286i \(0.432026\pi\)
\(42\) 0 0
\(43\) 10.6345i 1.62175i −0.585221 0.810874i \(-0.698992\pi\)
0.585221 0.810874i \(-0.301008\pi\)
\(44\) −2.96348 + 1.48923i −0.446761 + 0.224509i
\(45\) 0 0
\(46\) 6.02718 + 3.47980i 0.888660 + 0.513068i
\(47\) 2.58268 1.49111i 0.376723 0.217501i −0.299669 0.954043i \(-0.596876\pi\)
0.676391 + 0.736542i \(0.263543\pi\)
\(48\) 0 0
\(49\) −6.90123 1.17175i −0.985890 0.167393i
\(50\) −2.35302 −0.332768
\(51\) 0 0
\(52\) 1.88857 + 1.09037i 0.261898 + 0.151207i
\(53\) −10.1931 5.88497i −1.40012 0.808362i −0.405719 0.913998i \(-0.632979\pi\)
−0.994405 + 0.105636i \(0.966312\pi\)
\(54\) 0 0
\(55\) −8.97843 0.520722i −1.21065 0.0702142i
\(56\) 0.222226 2.63640i 0.0296962 0.352304i
\(57\) 0 0
\(58\) −3.21649 5.57112i −0.422345 0.731524i
\(59\) −12.2489 7.07189i −1.59467 0.920681i −0.992491 0.122317i \(-0.960967\pi\)
−0.602175 0.798364i \(-0.705699\pi\)
\(60\) 0 0
\(61\) −10.2720 + 5.93056i −1.31520 + 0.759331i −0.982952 0.183861i \(-0.941140\pi\)
−0.332247 + 0.943192i \(0.607807\pi\)
\(62\) −7.30294 −0.927474
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 2.95669 + 5.12114i 0.366732 + 0.635199i
\(66\) 0 0
\(67\) 0.749028 1.29735i 0.0915083 0.158497i −0.816638 0.577151i \(-0.804165\pi\)
0.908146 + 0.418654i \(0.137498\pi\)
\(68\) 0.0281751 + 0.0488007i 0.00341674 + 0.00591796i
\(69\) 0 0
\(70\) 4.09636 5.88991i 0.489609 0.703979i
\(71\) 1.82248i 0.216288i −0.994135 0.108144i \(-0.965509\pi\)
0.994135 0.108144i \(-0.0344908\pi\)
\(72\) 0 0
\(73\) −6.82420 3.93995i −0.798712 0.461137i 0.0443085 0.999018i \(-0.485892\pi\)
−0.843021 + 0.537881i \(0.819225\pi\)
\(74\) −1.62140 + 2.80836i −0.188484 + 0.326465i
\(75\) 0 0
\(76\) 2.75460i 0.315974i
\(77\) 5.41898 6.90179i 0.617550 0.786532i
\(78\) 0 0
\(79\) 7.82062 4.51524i 0.879889 0.508004i 0.00926708 0.999957i \(-0.497050\pi\)
0.870622 + 0.491953i \(0.163717\pi\)
\(80\) 2.34835 + 1.35582i 0.262554 + 0.151586i
\(81\) 0 0
\(82\) −1.35699 2.35037i −0.149854 0.259555i
\(83\) −17.2299 −1.89123 −0.945615 0.325288i \(-0.894539\pi\)
−0.945615 + 0.325288i \(0.894539\pi\)
\(84\) 0 0
\(85\) 0.152802i 0.0165737i
\(86\) −9.20975 + 5.31725i −0.993113 + 0.573374i
\(87\) 0 0
\(88\) 2.77145 + 1.82183i 0.295437 + 0.194208i
\(89\) −7.43764 + 4.29412i −0.788388 + 0.455176i −0.839395 0.543522i \(-0.817090\pi\)
0.0510066 + 0.998698i \(0.483757\pi\)
\(90\) 0 0
\(91\) −5.74929 0.484616i −0.602690 0.0508015i
\(92\) 6.95959i 0.725587i
\(93\) 0 0
\(94\) −2.58268 1.49111i −0.266383 0.153796i
\(95\) 3.73475 6.46878i 0.383177 0.663683i
\(96\) 0 0
\(97\) 6.25716 0.635319 0.317659 0.948205i \(-0.397103\pi\)
0.317659 + 0.948205i \(0.397103\pi\)
\(98\) 2.43585 + 6.56252i 0.246058 + 0.662914i
\(99\) 0 0
\(100\) 1.17651 + 2.03778i 0.117651 + 0.203778i
\(101\) 7.86795 13.6277i 0.782891 1.35601i −0.147360 0.989083i \(-0.547078\pi\)
0.930251 0.366924i \(-0.119589\pi\)
\(102\) 0 0
\(103\) −4.13406 7.16040i −0.407341 0.705535i 0.587250 0.809406i \(-0.300211\pi\)
−0.994591 + 0.103870i \(0.966877\pi\)
\(104\) 2.18074i 0.213839i
\(105\) 0 0
\(106\) 11.7699i 1.14320i
\(107\) −5.86711 10.1621i −0.567195 0.982410i −0.996842 0.0794132i \(-0.974695\pi\)
0.429647 0.902997i \(-0.358638\pi\)
\(108\) 0 0
\(109\) 5.76234 + 3.32689i 0.551932 + 0.318658i 0.749901 0.661550i \(-0.230101\pi\)
−0.197969 + 0.980208i \(0.563434\pi\)
\(110\) 4.03825 + 8.03591i 0.385032 + 0.766194i
\(111\) 0 0
\(112\) −2.39430 + 1.12575i −0.226240 + 0.106373i
\(113\) 12.8006i 1.20418i 0.798428 + 0.602090i \(0.205665\pi\)
−0.798428 + 0.602090i \(0.794335\pi\)
\(114\) 0 0
\(115\) 9.43597 16.3436i 0.879909 1.52405i
\(116\) −3.21649 + 5.57112i −0.298643 + 0.517265i
\(117\) 0 0
\(118\) 14.1438i 1.30204i
\(119\) −0.122397 0.0851257i −0.0112201 0.00780346i
\(120\) 0 0
\(121\) 4.36184 + 10.0982i 0.396531 + 0.918022i
\(122\) 10.2720 + 5.93056i 0.929987 + 0.536928i
\(123\) 0 0
\(124\) 3.65147 + 6.32453i 0.327911 + 0.567959i
\(125\) 7.17766i 0.641989i
\(126\) 0 0
\(127\) 5.80675i 0.515265i −0.966243 0.257633i \(-0.917058\pi\)
0.966243 0.257633i \(-0.0829424\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 2.95669 5.12114i 0.259319 0.449154i
\(131\) 0.981044 + 1.69922i 0.0857142 + 0.148461i 0.905695 0.423929i \(-0.139349\pi\)
−0.819981 + 0.572391i \(0.806016\pi\)
\(132\) 0 0
\(133\) 3.10098 + 6.59535i 0.268889 + 0.571889i
\(134\) −1.49806 −0.129412
\(135\) 0 0
\(136\) 0.0281751 0.0488007i 0.00241600 0.00418463i
\(137\) −5.51740 3.18547i −0.471383 0.272153i 0.245435 0.969413i \(-0.421069\pi\)
−0.716819 + 0.697260i \(0.754402\pi\)
\(138\) 0 0
\(139\) 11.2048i 0.950382i −0.879883 0.475191i \(-0.842379\pi\)
0.879883 0.475191i \(-0.157621\pi\)
\(140\) −7.14899 0.602598i −0.604200 0.0509288i
\(141\) 0 0
\(142\) −1.57831 + 0.911240i −0.132449 + 0.0764695i
\(143\) 3.97294 6.04379i 0.332234 0.505407i
\(144\) 0 0
\(145\) −15.1069 + 8.72197i −1.25456 + 0.724320i
\(146\) 7.87991i 0.652146i
\(147\) 0 0
\(148\) 3.24281 0.266557
\(149\) −8.08008 13.9951i −0.661946 1.14652i −0.980104 0.198487i \(-0.936397\pi\)
0.318157 0.948038i \(-0.396936\pi\)
\(150\) 0 0
\(151\) 11.4616 + 6.61738i 0.932734 + 0.538514i 0.887675 0.460470i \(-0.152319\pi\)
0.0450590 + 0.998984i \(0.485652\pi\)
\(152\) −2.38555 + 1.37730i −0.193494 + 0.111714i
\(153\) 0 0
\(154\) −8.68661 1.24208i −0.699987 0.100089i
\(155\) 19.8030i 1.59061i
\(156\) 0 0
\(157\) −0.671466 + 1.16301i −0.0535888 + 0.0928185i −0.891575 0.452872i \(-0.850399\pi\)
0.837987 + 0.545691i \(0.183733\pi\)
\(158\) −7.82062 4.51524i −0.622175 0.359213i
\(159\) 0 0
\(160\) 2.71165i 0.214374i
\(161\) 7.83474 + 16.6634i 0.617464 + 1.31326i
\(162\) 0 0
\(163\) 9.16486 + 15.8740i 0.717847 + 1.24335i 0.961851 + 0.273574i \(0.0882057\pi\)
−0.244004 + 0.969774i \(0.578461\pi\)
\(164\) −1.35699 + 2.35037i −0.105963 + 0.183533i
\(165\) 0 0
\(166\) 8.61496 + 14.9216i 0.668651 + 1.15814i
\(167\) −5.04452 −0.390357 −0.195178 0.980768i \(-0.562529\pi\)
−0.195178 + 0.980768i \(0.562529\pi\)
\(168\) 0 0
\(169\) 8.24439 0.634184
\(170\) 0.132330 0.0764010i 0.0101493 0.00585969i
\(171\) 0 0
\(172\) 9.20975 + 5.31725i 0.702237 + 0.405437i
\(173\) 0.459832 + 0.796453i 0.0349604 + 0.0605532i 0.882976 0.469418i \(-0.155536\pi\)
−0.848016 + 0.529971i \(0.822203\pi\)
\(174\) 0 0
\(175\) −5.11095 3.55461i −0.386352 0.268703i
\(176\) 0.192032 3.31106i 0.0144749 0.249581i
\(177\) 0 0
\(178\) 7.43764 + 4.29412i 0.557475 + 0.321858i
\(179\) 14.9660 + 8.64063i 1.11861 + 0.645831i 0.941046 0.338278i \(-0.109844\pi\)
0.177566 + 0.984109i \(0.443178\pi\)
\(180\) 0 0
\(181\) −9.68621 −0.719970 −0.359985 0.932958i \(-0.617218\pi\)
−0.359985 + 0.932958i \(0.617218\pi\)
\(182\) 2.45496 + 5.22134i 0.181974 + 0.387032i
\(183\) 0 0
\(184\) −6.02718 + 3.47980i −0.444330 + 0.256534i
\(185\) 7.61527 + 4.39668i 0.559885 + 0.323250i
\(186\) 0 0
\(187\) 0.166993 0.0839183i 0.0122117 0.00613671i
\(188\) 2.98222i 0.217501i
\(189\) 0 0
\(190\) −7.46950 −0.541895
\(191\) 10.5752 6.10561i 0.765197 0.441787i −0.0659616 0.997822i \(-0.521011\pi\)
0.831159 + 0.556035i \(0.187678\pi\)
\(192\) 0 0
\(193\) −6.93577 4.00437i −0.499248 0.288241i 0.229155 0.973390i \(-0.426404\pi\)
−0.728403 + 0.685149i \(0.759737\pi\)
\(194\) −3.12858 5.41886i −0.224619 0.389052i
\(195\) 0 0
\(196\) 4.46538 5.39076i 0.318956 0.385055i
\(197\) −6.14148 −0.437562 −0.218781 0.975774i \(-0.570208\pi\)
−0.218781 + 0.975774i \(0.570208\pi\)
\(198\) 0 0
\(199\) −5.93851 + 10.2858i −0.420970 + 0.729141i −0.996035 0.0889669i \(-0.971643\pi\)
0.575065 + 0.818108i \(0.304977\pi\)
\(200\) 1.17651 2.03778i 0.0831920 0.144093i
\(201\) 0 0
\(202\) −15.7359 −1.10717
\(203\) 1.42957 16.9599i 0.100336 1.19035i
\(204\) 0 0
\(205\) −6.37337 + 3.67967i −0.445136 + 0.256999i
\(206\) −4.13406 + 7.16040i −0.288034 + 0.498889i
\(207\) 0 0
\(208\) −1.88857 + 1.09037i −0.130949 + 0.0756034i
\(209\) −9.12065 0.528971i −0.630888 0.0365897i
\(210\) 0 0
\(211\) 19.9499i 1.37341i 0.726936 + 0.686706i \(0.240944\pi\)
−0.726936 + 0.686706i \(0.759056\pi\)
\(212\) 10.1931 5.88497i 0.700062 0.404181i
\(213\) 0 0
\(214\) −5.86711 + 10.1621i −0.401067 + 0.694669i
\(215\) 14.4185 + 24.9736i 0.983334 + 1.70318i
\(216\) 0 0
\(217\) −15.8625 11.0322i −1.07682 0.748915i
\(218\) 6.65378i 0.450651i
\(219\) 0 0
\(220\) 4.94017 7.51518i 0.333066 0.506674i
\(221\) −0.106421 0.0614425i −0.00715868 0.00413307i
\(222\) 0 0
\(223\) −13.6887 −0.916665 −0.458333 0.888781i \(-0.651553\pi\)
−0.458333 + 0.888781i \(0.651553\pi\)
\(224\) 2.17208 + 1.51065i 0.145128 + 0.100935i
\(225\) 0 0
\(226\) 11.0856 6.40030i 0.737406 0.425742i
\(227\) −3.18180 + 5.51104i −0.211184 + 0.365781i −0.952085 0.305833i \(-0.901065\pi\)
0.740902 + 0.671614i \(0.234398\pi\)
\(228\) 0 0
\(229\) −5.17077 8.95604i −0.341694 0.591832i 0.643053 0.765822i \(-0.277667\pi\)
−0.984747 + 0.173990i \(0.944334\pi\)
\(230\) −18.8719 −1.24438
\(231\) 0 0
\(232\) 6.43297 0.422345
\(233\) −4.45228 7.71157i −0.291678 0.505202i 0.682528 0.730859i \(-0.260880\pi\)
−0.974207 + 0.225657i \(0.927547\pi\)
\(234\) 0 0
\(235\) −4.04336 + 7.00331i −0.263760 + 0.456846i
\(236\) 12.2489 7.07189i 0.797333 0.460341i
\(237\) 0 0
\(238\) −0.0125225 + 0.148562i −0.000811712 + 0.00962984i
\(239\) 22.6090 1.46246 0.731228 0.682133i \(-0.238947\pi\)
0.731228 + 0.682133i \(0.238947\pi\)
\(240\) 0 0
\(241\) −8.06528 4.65649i −0.519530 0.299951i 0.217212 0.976124i \(-0.430304\pi\)
−0.736742 + 0.676173i \(0.763637\pi\)
\(242\) 6.56441 8.82658i 0.421976 0.567394i
\(243\) 0 0
\(244\) 11.8611i 0.759331i
\(245\) 17.7952 6.60516i 1.13690 0.421988i
\(246\) 0 0
\(247\) 3.00353 + 5.20226i 0.191110 + 0.331012i
\(248\) 3.65147 6.32453i 0.231868 0.401608i
\(249\) 0 0
\(250\) −6.21604 + 3.58883i −0.393137 + 0.226978i
\(251\) 4.12748i 0.260524i −0.991480 0.130262i \(-0.958418\pi\)
0.991480 0.130262i \(-0.0415819\pi\)
\(252\) 0 0
\(253\) −23.0436 1.33646i −1.44874 0.0840227i
\(254\) −5.02879 + 2.90337i −0.315534 + 0.182174i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 13.1583 7.59695i 0.820792 0.473885i −0.0298973 0.999553i \(-0.509518\pi\)
0.850690 + 0.525668i \(0.176185\pi\)
\(258\) 0 0
\(259\) −7.76427 + 3.65058i −0.482448 + 0.226836i
\(260\) −5.91338 −0.366732
\(261\) 0 0
\(262\) 0.981044 1.69922i 0.0606091 0.104978i
\(263\) 8.24623 14.2829i 0.508484 0.880720i −0.491468 0.870896i \(-0.663539\pi\)
0.999952 0.00982443i \(-0.00312726\pi\)
\(264\) 0 0
\(265\) 31.9159 1.96058
\(266\) 4.16125 5.98321i 0.255143 0.366854i
\(267\) 0 0
\(268\) 0.749028 + 1.29735i 0.0457541 + 0.0792485i
\(269\) 12.6371 + 7.29606i 0.770500 + 0.444848i 0.833053 0.553193i \(-0.186591\pi\)
−0.0625529 + 0.998042i \(0.519924\pi\)
\(270\) 0 0
\(271\) 21.0688 12.1641i 1.27984 0.738914i 0.303018 0.952985i \(-0.402006\pi\)
0.976818 + 0.214071i \(0.0686723\pi\)
\(272\) −0.0563502 −0.00341674
\(273\) 0 0
\(274\) 6.37094i 0.384883i
\(275\) 6.97314 3.50419i 0.420496 0.211310i
\(276\) 0 0
\(277\) −2.92994 1.69160i −0.176043 0.101638i 0.409389 0.912360i \(-0.365742\pi\)
−0.585432 + 0.810721i \(0.699075\pi\)
\(278\) −9.70368 + 5.60242i −0.581988 + 0.336011i
\(279\) 0 0
\(280\) 3.05263 + 6.49251i 0.182430 + 0.388001i
\(281\) −7.92539 −0.472789 −0.236395 0.971657i \(-0.575966\pi\)
−0.236395 + 0.971657i \(0.575966\pi\)
\(282\) 0 0
\(283\) 20.8485 + 12.0369i 1.23931 + 0.715518i 0.968954 0.247241i \(-0.0795240\pi\)
0.270360 + 0.962759i \(0.412857\pi\)
\(284\) 1.57831 + 0.911240i 0.0936557 + 0.0540721i
\(285\) 0 0
\(286\) −7.22055 0.418770i −0.426960 0.0247624i
\(287\) 0.603115 7.15513i 0.0356008 0.422354i
\(288\) 0 0
\(289\) 8.49841 + 14.7197i 0.499907 + 0.865864i
\(290\) 15.1069 + 8.72197i 0.887108 + 0.512172i
\(291\) 0 0
\(292\) 6.82420 3.93995i 0.399356 0.230568i
\(293\) −16.6528 −0.972864 −0.486432 0.873718i \(-0.661702\pi\)
−0.486432 + 0.873718i \(0.661702\pi\)
\(294\) 0 0
\(295\) 38.3529 2.23299
\(296\) −1.62140 2.80836i −0.0942422 0.163232i
\(297\) 0 0
\(298\) −8.08008 + 13.9951i −0.468067 + 0.810715i
\(299\) 7.58851 + 13.1437i 0.438855 + 0.760119i
\(300\) 0 0
\(301\) −28.0368 2.36326i −1.61602 0.136216i
\(302\) 13.2348i 0.761574i
\(303\) 0 0
\(304\) 2.38555 + 1.37730i 0.136821 + 0.0789936i
\(305\) 16.0816 27.8541i 0.920829 1.59492i
\(306\) 0 0
\(307\) 29.4599i 1.68137i −0.541528 0.840683i \(-0.682154\pi\)
0.541528 0.840683i \(-0.317846\pi\)
\(308\) 3.26764 + 8.14387i 0.186191 + 0.464040i
\(309\) 0 0
\(310\) 17.1499 9.90149i 0.974048 0.562367i
\(311\) −0.466034 0.269065i −0.0264263 0.0152573i 0.486729 0.873553i \(-0.338190\pi\)
−0.513155 + 0.858296i \(0.671523\pi\)
\(312\) 0 0
\(313\) −6.81418 11.8025i −0.385160 0.667117i 0.606631 0.794984i \(-0.292521\pi\)
−0.991791 + 0.127866i \(0.959187\pi\)
\(314\) 1.34293 0.0757860
\(315\) 0 0
\(316\) 9.03048i 0.508004i
\(317\) −0.730381 + 0.421686i −0.0410223 + 0.0236842i −0.520371 0.853940i \(-0.674206\pi\)
0.479349 + 0.877625i \(0.340873\pi\)
\(318\) 0 0
\(319\) 17.8286 + 11.7198i 0.998212 + 0.656184i
\(320\) −2.34835 + 1.35582i −0.131277 + 0.0757928i
\(321\) 0 0
\(322\) 10.5135 15.1168i 0.585896 0.842425i
\(323\) 0.155222i 0.00863681i
\(324\) 0 0
\(325\) −4.44386 2.56566i −0.246501 0.142317i
\(326\) 9.16486 15.8740i 0.507595 0.879180i
\(327\) 0 0
\(328\) 2.71397 0.149854
\(329\) −3.35723 7.14034i −0.185090 0.393660i
\(330\) 0 0
\(331\) 5.79849 + 10.0433i 0.318714 + 0.552028i 0.980220 0.197911i \(-0.0634158\pi\)
−0.661506 + 0.749940i \(0.730082\pi\)
\(332\) 8.61496 14.9216i 0.472808 0.818927i
\(333\) 0 0
\(334\) 2.52226 + 4.36868i 0.138012 + 0.239044i
\(335\) 4.06220i 0.221941i
\(336\) 0 0
\(337\) 0.863660i 0.0470466i 0.999723 + 0.0235233i \(0.00748838\pi\)
−0.999723 + 0.0235233i \(0.992512\pi\)
\(338\) −4.12220 7.13986i −0.224218 0.388357i
\(339\) 0 0
\(340\) −0.132330 0.0764010i −0.00717662 0.00414342i
\(341\) 21.6421 10.8757i 1.17199 0.588953i
\(342\) 0 0
\(343\) −4.62285 + 17.9340i −0.249610 + 0.968346i
\(344\) 10.6345i 0.573374i
\(345\) 0 0
\(346\) 0.459832 0.796453i 0.0247207 0.0428176i
\(347\) −3.69571 + 6.40116i −0.198396 + 0.343632i −0.948009 0.318245i \(-0.896907\pi\)
0.749612 + 0.661877i \(0.230240\pi\)
\(348\) 0 0
\(349\) 31.5777i 1.69032i −0.534515 0.845159i \(-0.679506\pi\)
0.534515 0.845159i \(-0.320494\pi\)
\(350\) −0.522903 + 6.20352i −0.0279503 + 0.331592i
\(351\) 0 0
\(352\) −2.96348 + 1.48923i −0.157954 + 0.0793760i
\(353\) 3.85186 + 2.22387i 0.205014 + 0.118365i 0.598992 0.800755i \(-0.295568\pi\)
−0.393978 + 0.919120i \(0.628901\pi\)
\(354\) 0 0
\(355\) 2.47096 + 4.27983i 0.131145 + 0.227150i
\(356\) 8.58825i 0.455176i
\(357\) 0 0
\(358\) 17.2813i 0.913343i
\(359\) 10.0548 + 17.4154i 0.530673 + 0.919152i 0.999359 + 0.0357874i \(0.0113939\pi\)
−0.468687 + 0.883364i \(0.655273\pi\)
\(360\) 0 0
\(361\) −5.70609 + 9.88324i −0.300320 + 0.520170i
\(362\) 4.84310 + 8.38850i 0.254548 + 0.440890i
\(363\) 0 0
\(364\) 3.29434 4.73673i 0.172670 0.248272i
\(365\) 21.3675 1.11843
\(366\) 0 0
\(367\) −6.39813 + 11.0819i −0.333980 + 0.578470i −0.983288 0.182055i \(-0.941725\pi\)
0.649309 + 0.760525i \(0.275058\pi\)
\(368\) 6.02718 + 3.47980i 0.314189 + 0.181397i
\(369\) 0 0
\(370\) 8.79335i 0.457145i
\(371\) −17.7803 + 25.5652i −0.923107 + 1.32728i
\(372\) 0 0
\(373\) −6.97826 + 4.02890i −0.361321 + 0.208609i −0.669660 0.742668i \(-0.733560\pi\)
0.308339 + 0.951276i \(0.400227\pi\)
\(374\) −0.156172 0.102661i −0.00807545 0.00530847i
\(375\) 0 0
\(376\) 2.58268 1.49111i 0.133192 0.0768982i
\(377\) 14.0286i 0.722510i
\(378\) 0 0
\(379\) −30.6120 −1.57244 −0.786218 0.617950i \(-0.787964\pi\)
−0.786218 + 0.617950i \(0.787964\pi\)
\(380\) 3.73475 + 6.46878i 0.191589 + 0.331841i
\(381\) 0 0
\(382\) −10.5752 6.10561i −0.541076 0.312390i
\(383\) −0.763632 + 0.440883i −0.0390198 + 0.0225281i −0.519383 0.854542i \(-0.673838\pi\)
0.480363 + 0.877070i \(0.340505\pi\)
\(384\) 0 0
\(385\) −3.36807 + 23.5550i −0.171653 + 1.20048i
\(386\) 8.00874i 0.407634i
\(387\) 0 0
\(388\) −3.12858 + 5.41886i −0.158830 + 0.275101i
\(389\) −5.35275 3.09041i −0.271395 0.156690i 0.358126 0.933673i \(-0.383416\pi\)
−0.629522 + 0.776983i \(0.716749\pi\)
\(390\) 0 0
\(391\) 0.392175i 0.0198331i
\(392\) −6.90123 1.17175i −0.348565 0.0591825i
\(393\) 0 0
\(394\) 3.07074 + 5.31868i 0.154702 + 0.267951i
\(395\) −12.2437 + 21.2068i −0.616049 + 1.06703i
\(396\) 0 0
\(397\) 13.4710 + 23.3325i 0.676091 + 1.17102i 0.976149 + 0.217103i \(0.0696608\pi\)
−0.300058 + 0.953921i \(0.597006\pi\)
\(398\) 11.8770 0.595341
\(399\) 0 0
\(400\) −2.35302 −0.117651
\(401\) −3.85186 + 2.22387i −0.192353 + 0.111055i −0.593083 0.805141i \(-0.702090\pi\)
0.400731 + 0.916196i \(0.368756\pi\)
\(402\) 0 0
\(403\) −13.7921 7.96288i −0.687034 0.396659i
\(404\) 7.86795 + 13.6277i 0.391445 + 0.678003i
\(405\) 0 0
\(406\) −15.4025 + 7.24190i −0.764413 + 0.359410i
\(407\) 0.622722 10.7371i 0.0308672 0.532220i
\(408\) 0 0
\(409\) −1.50956 0.871544i −0.0746428 0.0430951i 0.462214 0.886768i \(-0.347055\pi\)
−0.536857 + 0.843673i \(0.680388\pi\)
\(410\) 6.37337 + 3.67967i 0.314758 + 0.181726i
\(411\) 0 0
\(412\) 8.26812 0.407341
\(413\) −21.3663 + 30.7214i −1.05137 + 1.51170i
\(414\) 0 0
\(415\) 40.4620 23.3607i 1.98620 1.14673i
\(416\) 1.88857 + 1.09037i 0.0925949 + 0.0534597i
\(417\) 0 0
\(418\) 4.10222 + 8.16320i 0.200646 + 0.399275i
\(419\) 22.8877i 1.11814i 0.829121 + 0.559069i \(0.188841\pi\)
−0.829121 + 0.559069i \(0.811159\pi\)
\(420\) 0 0
\(421\) 29.7817 1.45147 0.725735 0.687975i \(-0.241500\pi\)
0.725735 + 0.687975i \(0.241500\pi\)
\(422\) 17.2772 9.97497i 0.841039 0.485574i
\(423\) 0 0
\(424\) −10.1931 5.88497i −0.495019 0.285799i
\(425\) −0.0662968 0.114829i −0.00321587 0.00557004i
\(426\) 0 0
\(427\) 13.3526 + 28.3991i 0.646179 + 1.37433i
\(428\) 11.7342 0.567195
\(429\) 0 0
\(430\) 14.4185 24.9736i 0.695322 1.20433i
\(431\) 5.29786 9.17616i 0.255189 0.442000i −0.709758 0.704446i \(-0.751196\pi\)
0.964947 + 0.262446i \(0.0845290\pi\)
\(432\) 0 0
\(433\) −23.5494 −1.13171 −0.565856 0.824504i \(-0.691454\pi\)
−0.565856 + 0.824504i \(0.691454\pi\)
\(434\) −1.62290 + 19.2535i −0.0779018 + 0.924196i
\(435\) 0 0
\(436\) −5.76234 + 3.32689i −0.275966 + 0.159329i
\(437\) 9.58544 16.6025i 0.458534 0.794204i
\(438\) 0 0
\(439\) −10.0258 + 5.78842i −0.478507 + 0.276266i −0.719794 0.694188i \(-0.755764\pi\)
0.241287 + 0.970454i \(0.422430\pi\)
\(440\) −8.97843 0.520722i −0.428030 0.0248245i
\(441\) 0 0
\(442\) 0.122885i 0.00584504i
\(443\) −32.4006 + 18.7065i −1.53940 + 0.888771i −0.540523 + 0.841329i \(0.681774\pi\)
−0.998874 + 0.0474425i \(0.984893\pi\)
\(444\) 0 0
\(445\) 11.6441 20.1682i 0.551985 0.956067i
\(446\) 6.84437 + 11.8548i 0.324090 + 0.561340i
\(447\) 0 0
\(448\) 0.222226 2.63640i 0.0104992 0.124558i
\(449\) 19.4749i 0.919075i 0.888158 + 0.459538i \(0.151985\pi\)
−0.888158 + 0.459538i \(0.848015\pi\)
\(450\) 0 0
\(451\) 7.52164 + 4.94441i 0.354180 + 0.232823i
\(452\) −11.0856 6.40030i −0.521425 0.301045i
\(453\) 0 0
\(454\) 6.36360 0.298659
\(455\) 14.1584 6.65698i 0.663758 0.312084i
\(456\) 0 0
\(457\) 23.7421 13.7075i 1.11061 0.641212i 0.171623 0.985163i \(-0.445099\pi\)
0.938988 + 0.343951i \(0.111765\pi\)
\(458\) −5.17077 + 8.95604i −0.241614 + 0.418488i
\(459\) 0 0
\(460\) 9.43597 + 16.3436i 0.439955 + 0.762024i
\(461\) −38.6594 −1.80055 −0.900273 0.435325i \(-0.856634\pi\)
−0.900273 + 0.435325i \(0.856634\pi\)
\(462\) 0 0
\(463\) 35.4956 1.64962 0.824810 0.565409i \(-0.191282\pi\)
0.824810 + 0.565409i \(0.191282\pi\)
\(464\) −3.21649 5.57112i −0.149322 0.258633i
\(465\) 0 0
\(466\) −4.45228 + 7.71157i −0.206248 + 0.357232i
\(467\) 9.49408 5.48141i 0.439334 0.253649i −0.263981 0.964528i \(-0.585036\pi\)
0.703315 + 0.710878i \(0.251702\pi\)
\(468\) 0 0
\(469\) −3.25389 2.26304i −0.150251 0.104498i
\(470\) 8.08673 0.373013
\(471\) 0 0
\(472\) −12.2489 7.07189i −0.563800 0.325510i
\(473\) 19.3743 29.4730i 0.890832 1.35517i
\(474\) 0 0
\(475\) 6.48164i 0.297398i
\(476\) 0.134920 0.0634362i 0.00618403 0.00290759i
\(477\) 0 0
\(478\) −11.3045 19.5800i −0.517057 0.895568i
\(479\) 6.08034 10.5315i 0.277818 0.481195i −0.693024 0.720914i \(-0.743722\pi\)
0.970842 + 0.239719i \(0.0770554\pi\)
\(480\) 0 0
\(481\) −6.12428 + 3.53585i −0.279243 + 0.161221i
\(482\) 9.31298i 0.424195i
\(483\) 0 0
\(484\) −10.9262 1.27166i −0.496648 0.0578026i
\(485\) −14.6940 + 8.48360i −0.667222 + 0.385221i
\(486\) 0 0
\(487\) −1.22436 + 2.12066i −0.0554813 + 0.0960964i −0.892432 0.451182i \(-0.851003\pi\)
0.836951 + 0.547278i \(0.184336\pi\)
\(488\) −10.2720 + 5.93056i −0.464993 + 0.268464i
\(489\) 0 0
\(490\) −14.6178 12.1085i −0.660367 0.547008i
\(491\) 0.134894 0.00608767 0.00304383 0.999995i \(-0.499031\pi\)
0.00304383 + 0.999995i \(0.499031\pi\)
\(492\) 0 0
\(493\) 0.181250 0.313934i 0.00816308 0.0141389i
\(494\) 3.00353 5.20226i 0.135135 0.234061i
\(495\) 0 0
\(496\) −7.30294 −0.327911
\(497\) −4.80479 0.405002i −0.215524 0.0181668i
\(498\) 0 0
\(499\) −18.6333 32.2738i −0.834140 1.44477i −0.894729 0.446610i \(-0.852631\pi\)
0.0605888 0.998163i \(-0.480702\pi\)
\(500\) 6.21604 + 3.58883i 0.277990 + 0.160497i
\(501\) 0 0
\(502\) −3.57450 + 2.06374i −0.159538 + 0.0921092i
\(503\) 22.4935 1.00294 0.501469 0.865176i \(-0.332793\pi\)
0.501469 + 0.865176i \(0.332793\pi\)
\(504\) 0 0
\(505\) 42.6702i 1.89880i
\(506\) 10.3644 + 20.6246i 0.460754 + 0.916875i
\(507\) 0 0
\(508\) 5.02879 + 2.90337i 0.223116 + 0.128816i
\(509\) 20.3512 11.7498i 0.902053 0.520801i 0.0241874 0.999707i \(-0.492300\pi\)
0.877866 + 0.478907i \(0.158967\pi\)
\(510\) 0 0
\(511\) −11.9038 + 17.1158i −0.526594 + 0.757157i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −13.1583 7.59695i −0.580388 0.335087i
\(515\) 19.4165 + 11.2101i 0.855592 + 0.493976i
\(516\) 0 0
\(517\) 9.87432 + 0.572681i 0.434272 + 0.0251865i
\(518\) 7.04363 + 4.89876i 0.309480 + 0.215239i
\(519\) 0 0
\(520\) 2.95669 + 5.12114i 0.129659 + 0.224577i
\(521\) 4.95557 + 2.86110i 0.217107 + 0.125347i 0.604610 0.796522i \(-0.293329\pi\)
−0.387503 + 0.921869i \(0.626662\pi\)
\(522\) 0 0
\(523\) −1.75580 + 1.01371i −0.0767758 + 0.0443265i −0.537896 0.843011i \(-0.680781\pi\)
0.461121 + 0.887337i \(0.347448\pi\)
\(524\) −1.96209 −0.0857142
\(525\) 0 0
\(526\) −16.4925 −0.719105
\(527\) −0.205761 0.356389i −0.00896309 0.0155245i
\(528\) 0 0
\(529\) 12.7179 22.0281i 0.552954 0.957745i
\(530\) −15.9579 27.6400i −0.693169 1.20060i
\(531\) 0 0
\(532\) −7.26223 0.612144i −0.314858 0.0265398i
\(533\) 5.91846i 0.256357i
\(534\) 0 0
\(535\) 27.5561 + 15.9095i 1.19135 + 0.687829i
\(536\) 0.749028 1.29735i 0.0323531 0.0560371i
\(537\) 0 0
\(538\) 14.5921i 0.629111i
\(539\) −16.9917 15.8204i −0.731882 0.681431i
\(540\) 0 0
\(541\) −12.1688 + 7.02567i −0.523179 + 0.302057i −0.738234 0.674544i \(-0.764340\pi\)
0.215056 + 0.976602i \(0.431007\pi\)
\(542\) −21.0688 12.1641i −0.904981 0.522491i
\(543\) 0 0
\(544\) 0.0281751 + 0.0488007i 0.00120800 + 0.00209231i
\(545\) −18.0427 −0.772864
\(546\) 0 0
\(547\) 14.9517i 0.639290i 0.947537 + 0.319645i \(0.103564\pi\)
−0.947537 + 0.319645i \(0.896436\pi\)
\(548\) 5.51740 3.18547i 0.235692 0.136077i
\(549\) 0 0
\(550\) −6.52128 4.28682i −0.278068 0.182791i
\(551\) −15.3462 + 8.86013i −0.653770 + 0.377454i
\(552\) 0 0
\(553\) −10.1660 21.6217i −0.432304 0.919449i
\(554\) 3.38320i 0.143738i
\(555\) 0 0
\(556\) 9.70368 + 5.60242i 0.411528 + 0.237596i
\(557\) 8.41830 14.5809i 0.356695 0.617813i −0.630712 0.776017i \(-0.717237\pi\)
0.987406 + 0.158204i \(0.0505703\pi\)
\(558\) 0 0
\(559\) −23.1910 −0.980876
\(560\) 4.09636 5.88991i 0.173103 0.248894i
\(561\) 0 0
\(562\) 3.96270 + 6.86359i 0.167156 + 0.289523i
\(563\) −17.2551 + 29.8868i −0.727218 + 1.25958i 0.230837 + 0.972992i \(0.425854\pi\)
−0.958055 + 0.286585i \(0.907480\pi\)
\(564\) 0 0
\(565\) −17.3554 30.0604i −0.730145 1.26465i
\(566\) 24.0738i 1.01190i
\(567\) 0 0
\(568\) 1.82248i 0.0764695i
\(569\) −21.8150 37.7846i −0.914531 1.58401i −0.807587 0.589748i \(-0.799227\pi\)
−0.106944 0.994265i \(-0.534106\pi\)
\(570\) 0 0
\(571\) 33.1381 + 19.1323i 1.38678 + 0.800660i 0.992951 0.118522i \(-0.0378155\pi\)
0.393833 + 0.919182i \(0.371149\pi\)
\(572\) 3.24761 + 6.46256i 0.135789 + 0.270213i
\(573\) 0 0
\(574\) −6.49808 + 3.05525i −0.271225 + 0.127524i
\(575\) 16.3761i 0.682930i
\(576\) 0 0
\(577\) −18.5319 + 32.0982i −0.771492 + 1.33626i 0.165253 + 0.986251i \(0.447156\pi\)
−0.936745 + 0.350013i \(0.886177\pi\)
\(578\) 8.49841 14.7197i 0.353487 0.612258i
\(579\) 0 0
\(580\) 17.4439i 0.724320i
\(581\) −3.82894 + 45.4250i −0.158851 + 1.88455i
\(582\) 0 0
\(583\) −17.5281 34.8799i −0.725939 1.44458i
\(584\) −6.82420 3.93995i −0.282387 0.163036i
\(585\) 0 0
\(586\) 8.32638 + 14.4217i 0.343960 + 0.595755i
\(587\) 40.7527i 1.68204i −0.541002 0.841021i \(-0.681955\pi\)
0.541002 0.841021i \(-0.318045\pi\)
\(588\) 0 0
\(589\) 20.1167i 0.828893i
\(590\) −19.1765 33.2146i −0.789482 1.36742i
\(591\) 0 0
\(592\) −1.62140 + 2.80836i −0.0666393 + 0.115423i
\(593\) −2.07883 3.60063i −0.0853672 0.147860i 0.820180 0.572105i \(-0.193873\pi\)
−0.905548 + 0.424245i \(0.860540\pi\)
\(594\) 0 0
\(595\) 0.402847 + 0.0339565i 0.0165151 + 0.00139208i
\(596\) 16.1602 0.661946
\(597\) 0 0
\(598\) 7.58851 13.1437i 0.310317 0.537485i
\(599\) −1.70659 0.985302i −0.0697295 0.0402584i 0.464730 0.885452i \(-0.346151\pi\)
−0.534459 + 0.845194i \(0.679485\pi\)
\(600\) 0 0
\(601\) 1.40392i 0.0572672i 0.999590 + 0.0286336i \(0.00911560\pi\)
−0.999590 + 0.0286336i \(0.990884\pi\)
\(602\) 11.9718 + 25.4622i 0.487933 + 1.03776i
\(603\) 0 0
\(604\) −11.4616 + 6.61738i −0.466367 + 0.269257i
\(605\) −23.9346 17.8004i −0.973078 0.723688i
\(606\) 0 0
\(607\) 11.4032 6.58367i 0.462843 0.267223i −0.250396 0.968144i \(-0.580561\pi\)
0.713239 + 0.700921i \(0.247227\pi\)
\(608\) 2.75460i 0.111714i
\(609\) 0 0
\(610\) −32.1632 −1.30225
\(611\) −3.25172 5.63214i −0.131550 0.227852i
\(612\) 0 0
\(613\) −0.364197 0.210269i −0.0147098 0.00849270i 0.492627 0.870241i \(-0.336037\pi\)
−0.507337 + 0.861748i \(0.669370\pi\)
\(614\) −25.5130 + 14.7300i −1.02962 + 0.594453i
\(615\) 0 0
\(616\) 5.41898 6.90179i 0.218337 0.278081i
\(617\) 2.85323i 0.114867i −0.998349 0.0574333i \(-0.981708\pi\)
0.998349 0.0574333i \(-0.0182917\pi\)
\(618\) 0 0
\(619\) 12.6081 21.8380i 0.506764 0.877741i −0.493205 0.869913i \(-0.664175\pi\)
0.999969 0.00782835i \(-0.00249187\pi\)
\(620\) −17.1499 9.90149i −0.688756 0.397653i
\(621\) 0 0
\(622\) 0.538129i 0.0215770i
\(623\) 9.66820 + 20.5629i 0.387348 + 0.823834i
\(624\) 0 0
\(625\) 15.6142 + 27.0446i 0.624568 + 1.08178i
\(626\) −6.81418 + 11.8025i −0.272350 + 0.471723i
\(627\) 0 0
\(628\) −0.671466 1.16301i −0.0267944 0.0464092i
\(629\) −0.182733 −0.00728605
\(630\) 0 0
\(631\) −1.15543 −0.0459968 −0.0229984 0.999736i \(-0.507321\pi\)
−0.0229984 + 0.999736i \(0.507321\pi\)
\(632\) 7.82062 4.51524i 0.311088 0.179607i
\(633\) 0 0
\(634\) 0.730381 + 0.421686i 0.0290071 + 0.0167473i
\(635\) 7.87292 + 13.6363i 0.312427 + 0.541140i
\(636\) 0 0
\(637\) −2.55528 + 15.0498i −0.101244 + 0.596293i
\(638\) 1.23534 21.3000i 0.0489074 0.843274i
\(639\) 0 0
\(640\) 2.34835 + 1.35582i 0.0928269 + 0.0535936i
\(641\) −43.5123 25.1218i −1.71863 0.992252i −0.921435 0.388533i \(-0.872982\pi\)
−0.797197 0.603720i \(-0.793685\pi\)
\(642\) 0 0
\(643\) 14.5727 0.574690 0.287345 0.957827i \(-0.407227\pi\)
0.287345 + 0.957827i \(0.407227\pi\)
\(644\) −18.3483 1.54660i −0.723023 0.0609446i
\(645\) 0 0
\(646\) 0.134427 0.0776112i 0.00528894 0.00305357i
\(647\) 3.51582 + 2.02986i 0.138221 + 0.0798020i 0.567516 0.823362i \(-0.307905\pi\)
−0.429295 + 0.903164i \(0.641238\pi\)
\(648\) 0 0
\(649\) −21.0633 41.9148i −0.826806 1.64530i
\(650\) 5.13132i 0.201267i
\(651\) 0 0
\(652\) −18.3297 −0.717847
\(653\) −1.95036 + 1.12604i −0.0763236 + 0.0440654i −0.537676 0.843151i \(-0.680698\pi\)
0.461353 + 0.887217i \(0.347364\pi\)
\(654\) 0 0
\(655\) −4.60768 2.66024i −0.180037 0.103944i
\(656\) −1.35699 2.35037i −0.0529814 0.0917666i
\(657\) 0 0
\(658\) −4.50511 + 6.47762i −0.175627 + 0.252524i
\(659\) −33.8978 −1.32047 −0.660236 0.751058i \(-0.729544\pi\)
−0.660236 + 0.751058i \(0.729544\pi\)
\(660\) 0 0
\(661\) −0.411025 + 0.711916i −0.0159870 + 0.0276903i −0.873908 0.486091i \(-0.838422\pi\)
0.857921 + 0.513781i \(0.171756\pi\)
\(662\) 5.79849 10.0433i 0.225365 0.390343i
\(663\) 0 0
\(664\) −17.2299 −0.668651
\(665\) −16.2243 11.2838i −0.629153 0.437568i
\(666\) 0 0
\(667\) −38.7727 + 22.3854i −1.50128 + 0.866767i
\(668\) 2.52226 4.36868i 0.0975892 0.169029i
\(669\) 0 0
\(670\) 3.51796 2.03110i 0.135911 0.0784682i
\(671\) −39.2729 2.27771i −1.51611 0.0879302i
\(672\) 0 0
\(673\) 22.8706i 0.881596i −0.897606 0.440798i \(-0.854696\pi\)
0.897606 0.440798i \(-0.145304\pi\)
\(674\) 0.747952 0.431830i 0.0288100 0.0166335i
\(675\) 0 0
\(676\) −4.12220 + 7.13986i −0.158546 + 0.274610i
\(677\) −7.34072 12.7145i −0.282127 0.488658i 0.689782 0.724018i \(-0.257707\pi\)
−0.971908 + 0.235360i \(0.924373\pi\)
\(678\) 0 0
\(679\) 1.39050 16.4964i 0.0533626 0.633074i
\(680\) 0.152802i 0.00585969i
\(681\) 0 0
\(682\) −20.2397 13.3047i −0.775018 0.509465i
\(683\) 34.3893 + 19.8546i 1.31587 + 0.759717i 0.983061 0.183278i \(-0.0586708\pi\)
0.332807 + 0.942995i \(0.392004\pi\)
\(684\) 0 0
\(685\) 17.2757 0.660072
\(686\) 17.8427 4.96351i 0.681239 0.189508i
\(687\) 0 0
\(688\) −9.20975 + 5.31725i −0.351119 + 0.202718i
\(689\) −12.8335 + 22.2284i −0.488919 + 0.846833i
\(690\) 0 0
\(691\) −12.6830 21.9677i −0.482486 0.835690i 0.517312 0.855797i \(-0.326933\pi\)
−0.999798 + 0.0201070i \(0.993599\pi\)
\(692\) −0.919665 −0.0349604
\(693\) 0 0
\(694\) 7.39142 0.280574
\(695\) 15.1918 + 26.3129i 0.576257 + 0.998107i
\(696\) 0 0
\(697\) 0.0764666 0.132444i 0.00289638 0.00501667i
\(698\) −27.3471 + 15.7889i −1.03510 + 0.597617i
\(699\) 0 0
\(700\) 5.63386 2.64891i 0.212940 0.100119i
\(701\) −36.3036 −1.37117 −0.685584 0.727994i \(-0.740453\pi\)
−0.685584 + 0.727994i \(0.740453\pi\)
\(702\) 0 0
\(703\) 7.73590 + 4.46632i 0.291765 + 0.168451i
\(704\) 2.77145 + 1.82183i 0.104453 + 0.0686630i
\(705\) 0 0
\(706\) 4.44774i 0.167393i
\(707\) −34.1796 23.7715i −1.28546 0.894020i
\(708\) 0 0
\(709\) −2.73371 4.73492i −0.102667 0.177824i 0.810116 0.586270i \(-0.199404\pi\)
−0.912782 + 0.408446i \(0.866071\pi\)
\(710\) 2.47096 4.27983i 0.0927335 0.160619i
\(711\) 0 0
\(712\) −7.43764 + 4.29412i −0.278737 + 0.160929i
\(713\) 50.8254i 1.90343i
\(714\) 0 0
\(715\) −1.13556 + 19.5796i −0.0424674 + 0.732234i
\(716\) −14.9660 + 8.64063i −0.559306 + 0.322915i
\(717\) 0 0
\(718\) 10.0548 17.4154i 0.375242 0.649938i
\(719\) −13.3827 + 7.72650i −0.499090 + 0.288150i −0.728338 0.685218i \(-0.759707\pi\)
0.229248 + 0.973368i \(0.426373\pi\)
\(720\) 0 0
\(721\) −19.7964 + 9.30782i −0.737256 + 0.346641i
\(722\) 11.4122 0.424717
\(723\) 0 0
\(724\) 4.84310 8.38850i 0.179993 0.311756i
\(725\) 7.56847 13.1090i 0.281086 0.486855i
\(726\) 0 0
\(727\) 39.4347 1.46255 0.731276 0.682082i \(-0.238925\pi\)
0.731276 + 0.682082i \(0.238925\pi\)
\(728\) −5.74929 0.484616i −0.213083 0.0179611i
\(729\) 0 0
\(730\) −10.6838 18.5048i −0.395424 0.684894i
\(731\) −0.518972 0.299629i −0.0191949 0.0110822i
\(732\) 0 0
\(733\) −29.2219 + 16.8713i −1.07934 + 0.623156i −0.930717 0.365739i \(-0.880816\pi\)
−0.148620 + 0.988894i \(0.547483\pi\)
\(734\) 12.7963 0.472319
\(735\) 0 0
\(736\) 6.95959i 0.256534i
\(737\) 4.43945 2.23094i 0.163529 0.0821778i
\(738\) 0 0
\(739\) 43.6352 + 25.1928i 1.60515 + 0.926732i 0.990435 + 0.137981i \(0.0440614\pi\)
0.614713 + 0.788751i \(0.289272\pi\)
\(740\) −7.61527 + 4.39668i −0.279943 + 0.161625i
\(741\) 0 0
\(742\) 31.0303 + 2.61558i 1.13916 + 0.0960211i
\(743\) 52.0125 1.90815 0.954077 0.299560i \(-0.0968400\pi\)
0.954077 + 0.299560i \(0.0968400\pi\)
\(744\) 0 0
\(745\) 37.9498 + 21.9103i 1.39037 + 0.802732i
\(746\) 6.97826 + 4.02890i 0.255492 + 0.147509i
\(747\) 0 0
\(748\) −0.0108210 + 0.186579i −0.000395656 + 0.00682201i
\(749\) −28.0953 + 13.2098i −1.02658 + 0.482674i
\(750\) 0 0
\(751\) −12.9264 22.3892i −0.471691 0.816993i 0.527785 0.849378i \(-0.323023\pi\)
−0.999475 + 0.0323857i \(0.989689\pi\)
\(752\) −2.58268 1.49111i −0.0941806 0.0543752i
\(753\) 0 0
\(754\) −12.1491 + 7.01430i −0.442445 + 0.255446i
\(755\) −35.8880 −1.30610
\(756\) 0 0
\(757\) 17.3219 0.629576 0.314788 0.949162i \(-0.398067\pi\)
0.314788 + 0.949162i \(0.398067\pi\)
\(758\) 15.3060 + 26.5108i 0.555940 + 0.962916i
\(759\) 0 0
\(760\) 3.73475 6.46878i 0.135474 0.234647i
\(761\) 20.4262 + 35.3793i 0.740450 + 1.28250i 0.952290 + 0.305193i \(0.0987210\pi\)
−0.211840 + 0.977304i \(0.567946\pi\)
\(762\) 0 0
\(763\) 10.0516 14.4525i 0.363891 0.523217i
\(764\) 12.2112i 0.441787i
\(765\) 0 0
\(766\) 0.763632 + 0.440883i 0.0275912 + 0.0159298i
\(767\) −15.4219 + 26.7115i −0.556853 + 0.964497i
\(768\) 0 0
\(769\) 41.5890i 1.49974i −0.661586 0.749869i \(-0.730116\pi\)
0.661586 0.749869i \(-0.269884\pi\)
\(770\) 22.0833 8.86067i 0.795826 0.319317i
\(771\) 0 0
\(772\) 6.93577 4.00437i 0.249624 0.144120i
\(773\) −42.1450 24.3325i −1.51585 0.875178i −0.999827 0.0186040i \(-0.994078\pi\)
−0.516025 0.856574i \(-0.672589\pi\)
\(774\) 0 0
\(775\) −8.59199 14.8818i −0.308634 0.534569i
\(776\) 6.25716 0.224619
\(777\) 0 0
\(778\) 6.18083i 0.221593i
\(779\) −6.47433 + 3.73796i −0.231967 + 0.133926i
\(780\) 0 0
\(781\) 3.32026 5.05090i 0.118808 0.180736i
\(782\) 0.339633 0.196087i 0.0121453 0.00701207i
\(783\) 0 0
\(784\) 2.43585 + 6.56252i 0.0869945 + 0.234376i
\(785\) 3.64155i 0.129973i
\(786\) 0 0
\(787\) −37.6497 21.7371i −1.34207 0.774842i −0.354956 0.934883i \(-0.615504\pi\)
−0.987110 + 0.160041i \(0.948837\pi\)
\(788\) 3.07074 5.31868i 0.109391 0.189470i
\(789\) 0 0
\(790\) 24.4875 0.871225