Properties

Label 600.2.k.f.301.4
Level 600
Weight 2
Character 600.301
Analytic conductor 4.791
Analytic rank 0
Dimension 12
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 600.k (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.79102412128\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: 12.0.180227832610816.1
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 301.4
Root \(-0.806504 + 1.16170i\) of \(x^{12} + x^{10} - 8 x^{6} + 16 x^{2} + 64\)
Character \(\chi\) \(=\) 600.301
Dual form 600.2.k.f.301.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.806504 + 1.16170i) q^{2} -1.00000i q^{3} +(-0.699104 - 1.87383i) q^{4} +(1.16170 + 0.806504i) q^{6} -0.746175 q^{7} +(2.74067 + 0.699104i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.806504 + 1.16170i) q^{2} -1.00000i q^{3} +(-0.699104 - 1.87383i) q^{4} +(1.16170 + 0.806504i) q^{6} -0.746175 q^{7} +(2.74067 + 0.699104i) q^{8} -1.00000 q^{9} -5.36068i q^{11} +(-1.87383 + 0.699104i) q^{12} +2.92520i q^{13} +(0.601793 - 0.866833i) q^{14} +(-3.02251 + 2.62001i) q^{16} -2.13466 q^{17} +(0.806504 - 1.16170i) q^{18} -1.73367i q^{19} +0.746175i q^{21} +(6.22751 + 4.32340i) q^{22} -7.49534 q^{23} +(0.699104 - 2.74067i) q^{24} +(-3.39821 - 2.35918i) q^{26} +1.00000i q^{27} +(0.521653 + 1.39821i) q^{28} -6.74916i q^{29} +2.64681 q^{31} +(-0.606006 - 5.62430i) q^{32} -5.36068 q^{33} +(1.72161 - 2.47984i) q^{34} +(0.699104 + 1.87383i) q^{36} -1.07480i q^{37} +(2.01400 + 1.39821i) q^{38} +2.92520 q^{39} -11.2936 q^{41} +(-0.866833 - 0.601793i) q^{42} -7.44322i q^{43} +(-10.0450 + 3.74767i) q^{44} +(6.04502 - 8.70735i) q^{46} -1.73367 q^{47} +(2.62001 + 3.02251i) q^{48} -6.44322 q^{49} +2.13466i q^{51} +(5.48133 - 2.04502i) q^{52} -7.72161i q^{53} +(-1.16170 - 0.806504i) q^{54} +(-2.04502 - 0.521653i) q^{56} -1.73367 q^{57} +(7.84052 + 5.44322i) q^{58} -6.85302i q^{59} +6.45203i q^{61} +(-2.13466 + 3.07480i) q^{62} +0.746175 q^{63} +(7.02251 + 3.83202i) q^{64} +(4.32340 - 6.22751i) q^{66} -7.44322i q^{67} +(1.49235 + 4.00000i) q^{68} +7.49534i q^{69} +13.2936 q^{71} +(-2.74067 - 0.699104i) q^{72} +0.690358 q^{73} +(1.24860 + 0.866833i) q^{74} +(-3.24860 + 1.21201i) q^{76} +4.00000i q^{77} +(-2.35918 + 3.39821i) q^{78} +2.64681 q^{79} +1.00000 q^{81} +(9.10834 - 13.1198i) q^{82} +5.85039i q^{83} +(1.39821 - 0.521653i) q^{84} +(8.64681 + 6.00299i) q^{86} -6.74916 q^{87} +(3.74767 - 14.6918i) q^{88} +7.59283 q^{89} -2.18271i q^{91} +(5.24002 + 14.0450i) q^{92} -2.64681i q^{93} +(1.39821 - 2.01400i) q^{94} +(-5.62430 + 0.606006i) q^{96} +14.1887 q^{97} +(5.19648 - 7.48511i) q^{98} +5.36068i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{4} - 2q^{6} - 12q^{9} + O(q^{10}) \) \( 12q - 2q^{4} - 2q^{6} - 12q^{9} + 20q^{14} + 2q^{16} + 2q^{24} - 28q^{26} - 32q^{31} - 24q^{34} + 2q^{36} + 16q^{39} - 8q^{41} - 44q^{44} - 4q^{46} + 12q^{49} + 2q^{54} + 52q^{56} + 46q^{64} + 20q^{66} + 32q^{71} - 36q^{74} + 12q^{76} - 32q^{79} + 12q^{81} + 4q^{84} + 40q^{86} + 40q^{89} + 4q^{94} - 42q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).

\(n\) \(151\) \(301\) \(401\) \(577\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.806504 + 1.16170i −0.570284 + 0.821447i
\(3\) 1.00000i 0.577350i
\(4\) −0.699104 1.87383i −0.349552 0.936917i
\(5\) 0 0
\(6\) 1.16170 + 0.806504i 0.474263 + 0.329254i
\(7\) −0.746175 −0.282028 −0.141014 0.990008i \(-0.545036\pi\)
−0.141014 + 0.990008i \(0.545036\pi\)
\(8\) 2.74067 + 0.699104i 0.968972 + 0.247170i
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 5.36068i 1.61630i −0.588974 0.808152i \(-0.700468\pi\)
0.588974 0.808152i \(-0.299532\pi\)
\(12\) −1.87383 + 0.699104i −0.540929 + 0.201814i
\(13\) 2.92520i 0.811304i 0.914028 + 0.405652i \(0.132955\pi\)
−0.914028 + 0.405652i \(0.867045\pi\)
\(14\) 0.601793 0.866833i 0.160836 0.231671i
\(15\) 0 0
\(16\) −3.02251 + 2.62001i −0.755627 + 0.655002i
\(17\) −2.13466 −0.517731 −0.258866 0.965913i \(-0.583349\pi\)
−0.258866 + 0.965913i \(0.583349\pi\)
\(18\) 0.806504 1.16170i 0.190095 0.273816i
\(19\) 1.73367i 0.397730i −0.980027 0.198865i \(-0.936274\pi\)
0.980027 0.198865i \(-0.0637255\pi\)
\(20\) 0 0
\(21\) 0.746175i 0.162829i
\(22\) 6.22751 + 4.32340i 1.32771 + 0.921753i
\(23\) −7.49534 −1.56289 −0.781443 0.623977i \(-0.785516\pi\)
−0.781443 + 0.623977i \(0.785516\pi\)
\(24\) 0.699104 2.74067i 0.142704 0.559436i
\(25\) 0 0
\(26\) −3.39821 2.35918i −0.666443 0.462674i
\(27\) 1.00000i 0.192450i
\(28\) 0.521653 + 1.39821i 0.0985832 + 0.264236i
\(29\) 6.74916i 1.25329i −0.779306 0.626644i \(-0.784428\pi\)
0.779306 0.626644i \(-0.215572\pi\)
\(30\) 0 0
\(31\) 2.64681 0.475381 0.237690 0.971341i \(-0.423610\pi\)
0.237690 + 0.971341i \(0.423610\pi\)
\(32\) −0.606006 5.62430i −0.107128 0.994245i
\(33\) −5.36068 −0.933174
\(34\) 1.72161 2.47984i 0.295254 0.425289i
\(35\) 0 0
\(36\) 0.699104 + 1.87383i 0.116517 + 0.312306i
\(37\) 1.07480i 0.176697i −0.996090 0.0883483i \(-0.971841\pi\)
0.996090 0.0883483i \(-0.0281588\pi\)
\(38\) 2.01400 + 1.39821i 0.326714 + 0.226819i
\(39\) 2.92520 0.468406
\(40\) 0 0
\(41\) −11.2936 −1.76377 −0.881883 0.471468i \(-0.843724\pi\)
−0.881883 + 0.471468i \(0.843724\pi\)
\(42\) −0.866833 0.601793i −0.133755 0.0928586i
\(43\) 7.44322i 1.13508i −0.823346 0.567540i \(-0.807895\pi\)
0.823346 0.567540i \(-0.192105\pi\)
\(44\) −10.0450 + 3.74767i −1.51434 + 0.564982i
\(45\) 0 0
\(46\) 6.04502 8.70735i 0.891289 1.28383i
\(47\) −1.73367 −0.252881 −0.126441 0.991974i \(-0.540355\pi\)
−0.126441 + 0.991974i \(0.540355\pi\)
\(48\) 2.62001 + 3.02251i 0.378166 + 0.436261i
\(49\) −6.44322 −0.920460
\(50\) 0 0
\(51\) 2.13466i 0.298912i
\(52\) 5.48133 2.04502i 0.760124 0.283593i
\(53\) 7.72161i 1.06064i −0.847796 0.530322i \(-0.822071\pi\)
0.847796 0.530322i \(-0.177929\pi\)
\(54\) −1.16170 0.806504i −0.158088 0.109751i
\(55\) 0 0
\(56\) −2.04502 0.521653i −0.273277 0.0697089i
\(57\) −1.73367 −0.229630
\(58\) 7.84052 + 5.44322i 1.02951 + 0.714730i
\(59\) 6.85302i 0.892188i −0.894986 0.446094i \(-0.852815\pi\)
0.894986 0.446094i \(-0.147185\pi\)
\(60\) 0 0
\(61\) 6.45203i 0.826098i 0.910709 + 0.413049i \(0.135536\pi\)
−0.910709 + 0.413049i \(0.864464\pi\)
\(62\) −2.13466 + 3.07480i −0.271102 + 0.390500i
\(63\) 0.746175 0.0940092
\(64\) 7.02251 + 3.83202i 0.877813 + 0.479003i
\(65\) 0 0
\(66\) 4.32340 6.22751i 0.532174 0.766553i
\(67\) 7.44322i 0.909334i −0.890661 0.454667i \(-0.849758\pi\)
0.890661 0.454667i \(-0.150242\pi\)
\(68\) 1.49235 + 4.00000i 0.180974 + 0.485071i
\(69\) 7.49534i 0.902332i
\(70\) 0 0
\(71\) 13.2936 1.57766 0.788831 0.614610i \(-0.210687\pi\)
0.788831 + 0.614610i \(0.210687\pi\)
\(72\) −2.74067 0.699104i −0.322991 0.0823902i
\(73\) 0.690358 0.0808003 0.0404002 0.999184i \(-0.487137\pi\)
0.0404002 + 0.999184i \(0.487137\pi\)
\(74\) 1.24860 + 0.866833i 0.145147 + 0.100767i
\(75\) 0 0
\(76\) −3.24860 + 1.21201i −0.372640 + 0.139027i
\(77\) 4.00000i 0.455842i
\(78\) −2.35918 + 3.39821i −0.267125 + 0.384771i
\(79\) 2.64681 0.297789 0.148895 0.988853i \(-0.452428\pi\)
0.148895 + 0.988853i \(0.452428\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 9.10834 13.1198i 1.00585 1.44884i
\(83\) 5.85039i 0.642164i 0.947051 + 0.321082i \(0.104047\pi\)
−0.947051 + 0.321082i \(0.895953\pi\)
\(84\) 1.39821 0.521653i 0.152557 0.0569171i
\(85\) 0 0
\(86\) 8.64681 + 6.00299i 0.932409 + 0.647319i
\(87\) −6.74916 −0.723586
\(88\) 3.74767 14.6918i 0.399503 1.56615i
\(89\) 7.59283 0.804838 0.402419 0.915456i \(-0.368169\pi\)
0.402419 + 0.915456i \(0.368169\pi\)
\(90\) 0 0
\(91\) 2.18271i 0.228810i
\(92\) 5.24002 + 14.0450i 0.546310 + 1.46429i
\(93\) 2.64681i 0.274461i
\(94\) 1.39821 2.01400i 0.144214 0.207729i
\(95\) 0 0
\(96\) −5.62430 + 0.606006i −0.574028 + 0.0618502i
\(97\) 14.1887 1.44064 0.720321 0.693641i \(-0.243994\pi\)
0.720321 + 0.693641i \(0.243994\pi\)
\(98\) 5.19648 7.48511i 0.524924 0.756110i
\(99\) 5.36068i 0.538768i
\(100\) 0 0
\(101\) 7.43952i 0.740260i 0.928980 + 0.370130i \(0.120687\pi\)
−0.928980 + 0.370130i \(0.879313\pi\)
\(102\) −2.47984 1.72161i −0.245541 0.170465i
\(103\) −7.19820 −0.709260 −0.354630 0.935007i \(-0.615393\pi\)
−0.354630 + 0.935007i \(0.615393\pi\)
\(104\) −2.04502 + 8.01699i −0.200530 + 0.786131i
\(105\) 0 0
\(106\) 8.97021 + 6.22751i 0.871264 + 0.604869i
\(107\) 4.00000i 0.386695i −0.981130 0.193347i \(-0.938066\pi\)
0.981130 0.193347i \(-0.0619344\pi\)
\(108\) 1.87383 0.699104i 0.180310 0.0672713i
\(109\) 19.9504i 1.91090i 0.295158 + 0.955449i \(0.404628\pi\)
−0.295158 + 0.955449i \(0.595372\pi\)
\(110\) 0 0
\(111\) −1.07480 −0.102016
\(112\) 2.25532 1.95498i 0.213108 0.184729i
\(113\) −12.0540 −1.13395 −0.566973 0.823736i \(-0.691886\pi\)
−0.566973 + 0.823736i \(0.691886\pi\)
\(114\) 1.39821 2.01400i 0.130954 0.188629i
\(115\) 0 0
\(116\) −12.6468 + 4.71836i −1.17423 + 0.438089i
\(117\) 2.92520i 0.270435i
\(118\) 7.96117 + 5.52699i 0.732885 + 0.508801i
\(119\) 1.59283 0.146014
\(120\) 0 0
\(121\) −17.7368 −1.61244
\(122\) −7.49534 5.20359i −0.678596 0.471110i
\(123\) 11.2936i 1.01831i
\(124\) −1.85039 4.95968i −0.166170 0.445392i
\(125\) 0 0
\(126\) −0.601793 + 0.866833i −0.0536119 + 0.0772236i
\(127\) 4.21351 0.373888 0.186944 0.982371i \(-0.440142\pi\)
0.186944 + 0.982371i \(0.440142\pi\)
\(128\) −10.1153 + 5.06752i −0.894079 + 0.447910i
\(129\) −7.44322 −0.655339
\(130\) 0 0
\(131\) 10.3204i 0.901694i −0.892601 0.450847i \(-0.851122\pi\)
0.892601 0.450847i \(-0.148878\pi\)
\(132\) 3.74767 + 10.0450i 0.326193 + 0.874306i
\(133\) 1.29362i 0.112171i
\(134\) 8.64681 + 6.00299i 0.746970 + 0.518579i
\(135\) 0 0
\(136\) −5.85039 1.49235i −0.501667 0.127968i
\(137\) −15.0387 −1.28484 −0.642422 0.766351i \(-0.722070\pi\)
−0.642422 + 0.766351i \(0.722070\pi\)
\(138\) −8.70735 6.04502i −0.741219 0.514586i
\(139\) 9.47032i 0.803262i 0.915802 + 0.401631i \(0.131557\pi\)
−0.915802 + 0.401631i \(0.868443\pi\)
\(140\) 0 0
\(141\) 1.73367i 0.146001i
\(142\) −10.7214 + 15.4432i −0.899716 + 1.29597i
\(143\) 15.6810 1.31131
\(144\) 3.02251 2.62001i 0.251876 0.218334i
\(145\) 0 0
\(146\) −0.556777 + 0.801991i −0.0460792 + 0.0663732i
\(147\) 6.44322i 0.531428i
\(148\) −2.01400 + 0.751399i −0.165550 + 0.0617646i
\(149\) 1.78948i 0.146600i −0.997310 0.0733000i \(-0.976647\pi\)
0.997310 0.0733000i \(-0.0233531\pi\)
\(150\) 0 0
\(151\) 10.6468 0.866425 0.433212 0.901292i \(-0.357380\pi\)
0.433212 + 0.901292i \(0.357380\pi\)
\(152\) 1.21201 4.75140i 0.0983071 0.385389i
\(153\) 2.13466 0.172577
\(154\) −4.64681 3.22601i −0.374451 0.259960i
\(155\) 0 0
\(156\) −2.04502 5.48133i −0.163732 0.438858i
\(157\) 6.92520i 0.552691i 0.961058 + 0.276345i \(0.0891234\pi\)
−0.961058 + 0.276345i \(0.910877\pi\)
\(158\) −2.13466 + 3.07480i −0.169824 + 0.244618i
\(159\) −7.72161 −0.612364
\(160\) 0 0
\(161\) 5.59283 0.440777
\(162\) −0.806504 + 1.16170i −0.0633649 + 0.0912719i
\(163\) 7.70079i 0.603172i −0.953439 0.301586i \(-0.902484\pi\)
0.953439 0.301586i \(-0.0975161\pi\)
\(164\) 7.89541 + 21.1624i 0.616528 + 1.65250i
\(165\) 0 0
\(166\) −6.79641 4.71836i −0.527504 0.366216i
\(167\) 3.22601 0.249637 0.124818 0.992180i \(-0.460165\pi\)
0.124818 + 0.992180i \(0.460165\pi\)
\(168\) −0.521653 + 2.04502i −0.0402464 + 0.157776i
\(169\) 4.44322 0.341786
\(170\) 0 0
\(171\) 1.73367i 0.132577i
\(172\) −13.9474 + 5.20359i −1.06348 + 0.396770i
\(173\) 6.42799i 0.488711i 0.969686 + 0.244356i \(0.0785764\pi\)
−0.969686 + 0.244356i \(0.921424\pi\)
\(174\) 5.44322 7.84052i 0.412650 0.594388i
\(175\) 0 0
\(176\) 14.0450 + 16.2027i 1.05868 + 1.22132i
\(177\) −6.85302 −0.515105
\(178\) −6.12364 + 8.82061i −0.458987 + 0.661132i
\(179\) 8.13765i 0.608236i −0.952634 0.304118i \(-0.901638\pi\)
0.952634 0.304118i \(-0.0983618\pi\)
\(180\) 0 0
\(181\) 1.49235i 0.110925i 0.998461 + 0.0554627i \(0.0176634\pi\)
−0.998461 + 0.0554627i \(0.982337\pi\)
\(182\) 2.53566 + 1.76036i 0.187955 + 0.130487i
\(183\) 6.45203 0.476948
\(184\) −20.5422 5.24002i −1.51439 0.386299i
\(185\) 0 0
\(186\) 3.07480 + 2.13466i 0.225456 + 0.156521i
\(187\) 11.4432i 0.836811i
\(188\) 1.21201 + 3.24860i 0.0883951 + 0.236929i
\(189\) 0.746175i 0.0542762i
\(190\) 0 0
\(191\) 6.88645 0.498286 0.249143 0.968467i \(-0.419851\pi\)
0.249143 + 0.968467i \(0.419851\pi\)
\(192\) 3.83202 7.02251i 0.276552 0.506806i
\(193\) 16.4830 1.18647 0.593237 0.805028i \(-0.297850\pi\)
0.593237 + 0.805028i \(0.297850\pi\)
\(194\) −11.4432 + 16.4830i −0.821576 + 1.18341i
\(195\) 0 0
\(196\) 4.50448 + 12.0735i 0.321749 + 0.862395i
\(197\) 13.5720i 0.966965i −0.875354 0.483483i \(-0.839372\pi\)
0.875354 0.483483i \(-0.160628\pi\)
\(198\) −6.22751 4.32340i −0.442570 0.307251i
\(199\) 9.05398 0.641820 0.320910 0.947110i \(-0.396011\pi\)
0.320910 + 0.947110i \(0.396011\pi\)
\(200\) 0 0
\(201\) −7.44322 −0.525005
\(202\) −8.64251 6.00000i −0.608085 0.422159i
\(203\) 5.03605i 0.353462i
\(204\) 4.00000 1.49235i 0.280056 0.104485i
\(205\) 0 0
\(206\) 5.80538 8.36217i 0.404480 0.582620i
\(207\) 7.49534 0.520962
\(208\) −7.66404 8.84143i −0.531406 0.613043i
\(209\) −9.29362 −0.642853
\(210\) 0 0
\(211\) 2.53566i 0.174562i −0.996184 0.0872809i \(-0.972182\pi\)
0.996184 0.0872809i \(-0.0278178\pi\)
\(212\) −14.4690 + 5.39821i −0.993736 + 0.370750i
\(213\) 13.2936i 0.910864i
\(214\) 4.64681 + 3.22601i 0.317649 + 0.220526i
\(215\) 0 0
\(216\) −0.699104 + 2.74067i −0.0475680 + 0.186479i
\(217\) −1.97498 −0.134070
\(218\) −23.1764 16.0900i −1.56970 1.08975i
\(219\) 0.690358i 0.0466501i
\(220\) 0 0
\(221\) 6.24430i 0.420037i
\(222\) 0.866833 1.24860i 0.0581780 0.0838006i
\(223\) −12.1579 −0.814152 −0.407076 0.913394i \(-0.633452\pi\)
−0.407076 + 0.913394i \(0.633452\pi\)
\(224\) 0.452186 + 4.19671i 0.0302130 + 0.280405i
\(225\) 0 0
\(226\) 9.72161 14.0032i 0.646672 0.931478i
\(227\) 20.7368i 1.37635i 0.725544 + 0.688176i \(0.241588\pi\)
−0.725544 + 0.688176i \(0.758412\pi\)
\(228\) 1.21201 + 3.24860i 0.0802674 + 0.215144i
\(229\) 19.9504i 1.31836i −0.751987 0.659178i \(-0.770904\pi\)
0.751987 0.659178i \(-0.229096\pi\)
\(230\) 0 0
\(231\) 4.00000 0.263181
\(232\) 4.71836 18.4972i 0.309776 1.21440i
\(233\) 13.3386 0.873844 0.436922 0.899499i \(-0.356069\pi\)
0.436922 + 0.899499i \(0.356069\pi\)
\(234\) 3.39821 + 2.35918i 0.222148 + 0.154225i
\(235\) 0 0
\(236\) −12.8414 + 4.79097i −0.835906 + 0.311866i
\(237\) 2.64681i 0.171929i
\(238\) −1.28462 + 1.85039i −0.0832697 + 0.119943i
\(239\) 22.8864 1.48040 0.740201 0.672386i \(-0.234731\pi\)
0.740201 + 0.672386i \(0.234731\pi\)
\(240\) 0 0
\(241\) 3.59283 0.231435 0.115717 0.993282i \(-0.463083\pi\)
0.115717 + 0.993282i \(0.463083\pi\)
\(242\) 14.3048 20.6049i 0.919549 1.32453i
\(243\) 1.00000i 0.0641500i
\(244\) 12.0900 4.51064i 0.773985 0.288764i
\(245\) 0 0
\(246\) −13.1198 9.10834i −0.836489 0.580727i
\(247\) 5.07131 0.322680
\(248\) 7.25402 + 1.85039i 0.460631 + 0.117500i
\(249\) 5.85039 0.370754
\(250\) 0 0
\(251\) 8.82801i 0.557219i 0.960404 + 0.278609i \(0.0898735\pi\)
−0.960404 + 0.278609i \(0.910127\pi\)
\(252\) −0.521653 1.39821i −0.0328611 0.0880788i
\(253\) 40.1801i 2.52610i
\(254\) −3.39821 + 4.89484i −0.213222 + 0.307129i
\(255\) 0 0
\(256\) 2.27111 15.8380i 0.141944 0.989875i
\(257\) 22.2927 1.39058 0.695291 0.718728i \(-0.255275\pi\)
0.695291 + 0.718728i \(0.255275\pi\)
\(258\) 6.00299 8.64681i 0.373730 0.538327i
\(259\) 0.801991i 0.0498333i
\(260\) 0 0
\(261\) 6.74916i 0.417763i
\(262\) 11.9892 + 8.32340i 0.740694 + 0.514222i
\(263\) 21.2014 1.30733 0.653667 0.756783i \(-0.273230\pi\)
0.653667 + 0.756783i \(0.273230\pi\)
\(264\) −14.6918 3.74767i −0.904219 0.230653i
\(265\) 0 0
\(266\) −1.50280 1.04331i −0.0921424 0.0639693i
\(267\) 7.59283i 0.464674i
\(268\) −13.9474 + 5.20359i −0.851971 + 0.317860i
\(269\) 14.6935i 0.895881i −0.894063 0.447940i \(-0.852158\pi\)
0.894063 0.447940i \(-0.147842\pi\)
\(270\) 0 0
\(271\) −20.2396 −1.22947 −0.614735 0.788734i \(-0.710737\pi\)
−0.614735 + 0.788734i \(0.710737\pi\)
\(272\) 6.45203 5.59283i 0.391212 0.339115i
\(273\) −2.18271 −0.132103
\(274\) 12.1288 17.4705i 0.732727 1.05543i
\(275\) 0 0
\(276\) 14.0450 5.24002i 0.845411 0.315412i
\(277\) 0.518027i 0.0311252i 0.999879 + 0.0155626i \(0.00495393\pi\)
−0.999879 + 0.0155626i \(0.995046\pi\)
\(278\) −11.0017 7.63785i −0.659837 0.458088i
\(279\) −2.64681 −0.158460
\(280\) 0 0
\(281\) 13.7008 0.817320 0.408660 0.912687i \(-0.365996\pi\)
0.408660 + 0.912687i \(0.365996\pi\)
\(282\) −2.01400 1.39821i −0.119932 0.0832620i
\(283\) 18.0305i 1.07180i −0.844282 0.535900i \(-0.819973\pi\)
0.844282 0.535900i \(-0.180027\pi\)
\(284\) −9.29362 24.9100i −0.551475 1.47814i
\(285\) 0 0
\(286\) −12.6468 + 18.2167i −0.747821 + 1.07718i
\(287\) 8.42701 0.497431
\(288\) 0.606006 + 5.62430i 0.0357092 + 0.331415i
\(289\) −12.4432 −0.731954
\(290\) 0 0
\(291\) 14.1887i 0.831755i
\(292\) −0.482632 1.29362i −0.0282439 0.0757032i
\(293\) 15.9792i 0.933513i −0.884386 0.466757i \(-0.845422\pi\)
0.884386 0.466757i \(-0.154578\pi\)
\(294\) −7.48511 5.19648i −0.436540 0.303065i
\(295\) 0 0
\(296\) 0.751399 2.94568i 0.0436742 0.171214i
\(297\) 5.36068 0.311058
\(298\) 2.07884 + 1.44322i 0.120424 + 0.0836037i
\(299\) 21.9253i 1.26797i
\(300\) 0 0
\(301\) 5.55394i 0.320124i
\(302\) −8.58669 + 12.3684i −0.494108 + 0.711723i
\(303\) 7.43952 0.427389
\(304\) 4.54222 + 5.24002i 0.260514 + 0.300536i
\(305\) 0 0
\(306\) −1.72161 + 2.47984i −0.0984180 + 0.141763i
\(307\) 22.5872i 1.28912i −0.764553 0.644561i \(-0.777040\pi\)
0.764553 0.644561i \(-0.222960\pi\)
\(308\) 7.49534 2.79641i 0.427086 0.159341i
\(309\) 7.19820i 0.409492i
\(310\) 0 0
\(311\) −18.5872 −1.05399 −0.526993 0.849870i \(-0.676680\pi\)
−0.526993 + 0.849870i \(0.676680\pi\)
\(312\) 8.01699 + 2.04502i 0.453873 + 0.115776i
\(313\) 29.3871 1.66106 0.830528 0.556977i \(-0.188039\pi\)
0.830528 + 0.556977i \(0.188039\pi\)
\(314\) −8.04502 5.58520i −0.454007 0.315191i
\(315\) 0 0
\(316\) −1.85039 4.95968i −0.104093 0.279004i
\(317\) 5.57201i 0.312955i −0.987682 0.156478i \(-0.949986\pi\)
0.987682 0.156478i \(-0.0500139\pi\)
\(318\) 6.22751 8.97021i 0.349221 0.503025i
\(319\) −36.1801 −2.02569
\(320\) 0 0
\(321\) −4.00000 −0.223258
\(322\) −4.51064 + 6.49720i −0.251368 + 0.362075i
\(323\) 3.70079i 0.205917i
\(324\) −0.699104 1.87383i −0.0388391 0.104102i
\(325\) 0 0
\(326\) 8.94602 + 6.21071i 0.495474 + 0.343980i
\(327\) 19.9504 1.10326
\(328\) −30.9520 7.89541i −1.70904 0.435951i
\(329\) 1.29362 0.0713194
\(330\) 0 0
\(331\) 13.7396i 0.755199i −0.925969 0.377599i \(-0.876750\pi\)
0.925969 0.377599i \(-0.123250\pi\)
\(332\) 10.9627 4.09003i 0.601655 0.224470i
\(333\) 1.07480i 0.0588989i
\(334\) −2.60179 + 3.74767i −0.142364 + 0.205063i
\(335\) 0 0
\(336\) −1.95498 2.25532i −0.106653 0.123038i
\(337\) −20.7523 −1.13045 −0.565226 0.824936i \(-0.691211\pi\)
−0.565226 + 0.824936i \(0.691211\pi\)
\(338\) −3.58348 + 5.16170i −0.194915 + 0.280760i
\(339\) 12.0540i 0.654685i
\(340\) 0 0
\(341\) 14.1887i 0.768360i
\(342\) −2.01400 1.39821i −0.108905 0.0756064i
\(343\) 10.0310 0.541623
\(344\) 5.20359 20.3994i 0.280559 1.09986i
\(345\) 0 0
\(346\) −7.46742 5.18420i −0.401451 0.278704i
\(347\) 4.73684i 0.254287i −0.991884 0.127143i \(-0.959419\pi\)
0.991884 0.127143i \(-0.0405809\pi\)
\(348\) 4.71836 + 12.6468i 0.252931 + 0.677940i
\(349\) 0.482632i 0.0258347i −0.999917 0.0129174i \(-0.995888\pi\)
0.999917 0.0129174i \(-0.00411184\pi\)
\(350\) 0 0
\(351\) −2.92520 −0.156135
\(352\) −30.1500 + 3.24860i −1.60700 + 0.173151i
\(353\) 2.13466 0.113617 0.0568083 0.998385i \(-0.481908\pi\)
0.0568083 + 0.998385i \(0.481908\pi\)
\(354\) 5.52699 7.96117i 0.293756 0.423132i
\(355\) 0 0
\(356\) −5.30818 14.2277i −0.281333 0.754067i
\(357\) 1.59283i 0.0843015i
\(358\) 9.45352 + 6.56304i 0.499634 + 0.346868i
\(359\) −9.59283 −0.506290 −0.253145 0.967428i \(-0.581465\pi\)
−0.253145 + 0.967428i \(0.581465\pi\)
\(360\) 0 0
\(361\) 15.9944 0.841811
\(362\) −1.73367 1.20359i −0.0911194 0.0632590i
\(363\) 17.7368i 0.930943i
\(364\) −4.09003 + 1.52594i −0.214376 + 0.0799809i
\(365\) 0 0
\(366\) −5.20359 + 7.49534i −0.271996 + 0.391787i
\(367\) −34.0832 −1.77913 −0.889565 0.456809i \(-0.848992\pi\)
−0.889565 + 0.456809i \(0.848992\pi\)
\(368\) 22.6547 19.6378i 1.18096 1.02369i
\(369\) 11.2936 0.587922
\(370\) 0 0
\(371\) 5.76167i 0.299131i
\(372\) −4.95968 + 1.85039i −0.257147 + 0.0959384i
\(373\) 4.33796i 0.224611i −0.993674 0.112306i \(-0.964176\pi\)
0.993674 0.112306i \(-0.0358236\pi\)
\(374\) −13.2936 9.22900i −0.687397 0.477220i
\(375\) 0 0
\(376\) −4.75140 1.21201i −0.245035 0.0625047i
\(377\) 19.7426 1.01680
\(378\) 0.866833 + 0.601793i 0.0445851 + 0.0309529i
\(379\) 6.90107i 0.354484i 0.984167 + 0.177242i \(0.0567176\pi\)
−0.984167 + 0.177242i \(0.943282\pi\)
\(380\) 0 0
\(381\) 4.21351i 0.215864i
\(382\) −5.55394 + 8.00000i −0.284165 + 0.409316i
\(383\) −22.3744 −1.14328 −0.571639 0.820506i \(-0.693692\pi\)
−0.571639 + 0.820506i \(0.693692\pi\)
\(384\) 5.06752 + 10.1153i 0.258601 + 0.516197i
\(385\) 0 0
\(386\) −13.2936 + 19.1484i −0.676627 + 0.974626i
\(387\) 7.44322i 0.378360i
\(388\) −9.91936 26.5872i −0.503579 1.34976i
\(389\) 11.0185i 0.558659i 0.960195 + 0.279330i \(0.0901122\pi\)
−0.960195 + 0.279330i \(0.909888\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) −17.6587 4.50448i −0.891900 0.227511i
\(393\) −10.3204 −0.520593
\(394\) 15.7666 + 10.9459i 0.794311 + 0.551445i
\(395\) 0 0
\(396\) 10.0450 3.74767i 0.504781 0.188327i
\(397\) 25.2549i 1.26751i 0.773536 + 0.633753i \(0.218486\pi\)
−0.773536 + 0.633753i \(0.781514\pi\)
\(398\) −7.30207 + 10.5180i −0.366020 + 0.527221i
\(399\) 1.29362 0.0647619
\(400\) 0 0
\(401\) 7.29362 0.364226 0.182113 0.983278i \(-0.441706\pi\)
0.182113 + 0.983278i \(0.441706\pi\)
\(402\) 6.00299 8.64681i 0.299402 0.431264i
\(403\) 7.74244i 0.385678i
\(404\) 13.9404 5.20100i 0.693562 0.258759i
\(405\) 0 0
\(406\) −5.85039 4.06160i −0.290350 0.201574i
\(407\) −5.76167 −0.285595
\(408\) −1.49235 + 5.85039i −0.0738823 + 0.289638i
\(409\) 15.8504 0.783752 0.391876 0.920018i \(-0.371826\pi\)
0.391876 + 0.920018i \(0.371826\pi\)
\(410\) 0 0
\(411\) 15.0387i 0.741805i
\(412\) 5.03229 + 13.4882i 0.247923 + 0.664518i
\(413\) 5.11355i 0.251622i
\(414\) −6.04502 + 8.70735i −0.297096 + 0.427943i
\(415\) 0 0
\(416\) 16.4522 1.77269i 0.806635 0.0869131i
\(417\) 9.47032 0.463763
\(418\) 7.49534 10.7964i 0.366609 0.528070i
\(419\) 8.02602i 0.392097i 0.980594 + 0.196048i \(0.0628109\pi\)
−0.980594 + 0.196048i \(0.937189\pi\)
\(420\) 0 0
\(421\) 22.9351i 1.11779i −0.829240 0.558893i \(-0.811226\pi\)
0.829240 0.558893i \(-0.188774\pi\)
\(422\) 2.94568 + 2.04502i 0.143393 + 0.0995498i
\(423\) 1.73367 0.0842937
\(424\) 5.39821 21.1624i 0.262160 1.02774i
\(425\) 0 0
\(426\) 15.4432 + 10.7214i 0.748227 + 0.519451i
\(427\) 4.81434i 0.232982i
\(428\) −7.49534 + 2.79641i −0.362301 + 0.135170i
\(429\) 15.6810i 0.757087i
\(430\) 0 0
\(431\) −35.0665 −1.68909 −0.844547 0.535481i \(-0.820130\pi\)
−0.844547 + 0.535481i \(0.820130\pi\)
\(432\) −2.62001 3.02251i −0.126055 0.145420i
\(433\) −17.0773 −0.820682 −0.410341 0.911932i \(-0.634590\pi\)
−0.410341 + 0.911932i \(0.634590\pi\)
\(434\) 1.59283 2.29434i 0.0764583 0.110132i
\(435\) 0 0
\(436\) 37.3836 13.9474i 1.79035 0.667958i
\(437\) 12.9944i 0.621607i
\(438\) 0.801991 + 0.556777i 0.0383206 + 0.0266038i
\(439\) 8.53885 0.407537 0.203769 0.979019i \(-0.434681\pi\)
0.203769 + 0.979019i \(0.434681\pi\)
\(440\) 0 0
\(441\) 6.44322 0.306820
\(442\) 7.25402 + 5.03605i 0.345039 + 0.239541i
\(443\) 20.7368i 0.985237i 0.870245 + 0.492619i \(0.163960\pi\)
−0.870245 + 0.492619i \(0.836040\pi\)
\(444\) 0.751399 + 2.01400i 0.0356598 + 0.0955803i
\(445\) 0 0
\(446\) 9.80538 14.1238i 0.464298 0.668783i
\(447\) −1.78948 −0.0846396
\(448\) −5.24002 2.85936i −0.247568 0.135092i
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 0 0
\(451\) 60.5414i 2.85078i
\(452\) 8.42701 + 22.5872i 0.396373 + 1.06241i
\(453\) 10.6468i 0.500231i
\(454\) −24.0900 16.7243i −1.13060 0.784912i
\(455\) 0 0
\(456\) −4.75140 1.21201i −0.222505 0.0567577i
\(457\) −1.28462 −0.0600921 −0.0300461 0.999549i \(-0.509565\pi\)
−0.0300461 + 0.999549i \(0.509565\pi\)
\(458\) 23.1764 + 16.0900i 1.08296 + 0.751838i
\(459\) 2.13466i 0.0996374i
\(460\) 0 0
\(461\) 15.7033i 0.731374i −0.930738 0.365687i \(-0.880834\pi\)
0.930738 0.365687i \(-0.119166\pi\)
\(462\) −3.22601 + 4.64681i −0.150088 + 0.216189i
\(463\) −18.7215 −0.870064 −0.435032 0.900415i \(-0.643263\pi\)
−0.435032 + 0.900415i \(0.643263\pi\)
\(464\) 17.6829 + 20.3994i 0.820906 + 0.947018i
\(465\) 0 0
\(466\) −10.7577 + 15.4955i −0.498339 + 0.717817i
\(467\) 2.14961i 0.0994719i −0.998762 0.0497360i \(-0.984162\pi\)
0.998762 0.0497360i \(-0.0158380\pi\)
\(468\) −5.48133 + 2.04502i −0.253375 + 0.0945309i
\(469\) 5.55394i 0.256457i
\(470\) 0 0
\(471\) 6.92520 0.319096
\(472\) 4.79097 18.7819i 0.220522 0.864505i
\(473\) −39.9007 −1.83464
\(474\) 3.07480 + 2.13466i 0.141230 + 0.0980482i
\(475\) 0 0
\(476\) −1.11355 2.98470i −0.0510396 0.136803i
\(477\) 7.72161i 0.353548i
\(478\) −18.4580 + 26.5872i −0.844249 + 1.21607i
\(479\) −12.1801 −0.556521 −0.278261 0.960506i \(-0.589758\pi\)
−0.278261 + 0.960506i \(0.589758\pi\)
\(480\) 0 0
\(481\) 3.14401 0.143355
\(482\) −2.89763 + 4.17380i −0.131983 + 0.190111i
\(483\) 5.59283i 0.254483i
\(484\) 12.3999 + 33.2359i 0.563631 + 1.51072i
\(485\) 0 0
\(486\) 1.16170 + 0.806504i 0.0526959 + 0.0365837i
\(487\) −25.7678 −1.16765 −0.583826 0.811879i \(-0.698445\pi\)
−0.583826 + 0.811879i \(0.698445\pi\)
\(488\) −4.51064 + 17.6829i −0.204187 + 0.800466i
\(489\) −7.70079 −0.348242
\(490\) 0 0
\(491\) 16.7724i 0.756927i 0.925616 + 0.378464i \(0.123547\pi\)
−0.925616 + 0.378464i \(0.876453\pi\)
\(492\) 21.1624 7.89541i 0.954073 0.355953i
\(493\) 14.4072i 0.648866i
\(494\) −4.09003 + 5.89135i −0.184019 + 0.265065i
\(495\) 0 0
\(496\) −8.00000 + 6.93466i −0.359211 + 0.311375i
\(497\) −9.91936 −0.444944
\(498\) −4.71836 + 6.79641i −0.211435 + 0.304555i
\(499\) 17.6224i 0.788888i −0.918920 0.394444i \(-0.870937\pi\)
0.918920 0.394444i \(-0.129063\pi\)
\(500\) 0 0
\(501\) 3.22601i 0.144128i
\(502\) −10.2555 7.11982i −0.457726 0.317773i
\(503\) 27.1263 1.20950 0.604752 0.796414i \(-0.293272\pi\)
0.604752 + 0.796414i \(0.293272\pi\)
\(504\) 2.04502 + 0.521653i 0.0910923 + 0.0232363i
\(505\) 0 0
\(506\) −46.6773 32.4054i −2.07506 1.44059i
\(507\) 4.44322i 0.197330i
\(508\) −2.94568 7.89541i −0.130693 0.350302i
\(509\) 15.9782i 0.708220i 0.935204 + 0.354110i \(0.115216\pi\)
−0.935204 + 0.354110i \(0.884784\pi\)
\(510\) 0 0
\(511\) −0.515128 −0.0227879
\(512\) 16.5674 + 15.4118i 0.732181 + 0.681110i
\(513\) 1.73367 0.0765432
\(514\) −17.9792 + 25.8975i −0.793027 + 1.14229i
\(515\) 0 0
\(516\) 5.20359 + 13.9474i 0.229075 + 0.613999i
\(517\) 9.29362i 0.408733i
\(518\) −0.931674 0.646809i −0.0409354 0.0284191i
\(519\) 6.42799 0.282158
\(520\) 0 0
\(521\) 0.886447 0.0388359 0.0194180 0.999811i \(-0.493819\pi\)
0.0194180 + 0.999811i \(0.493819\pi\)
\(522\) −7.84052 5.44322i −0.343170 0.238243i
\(523\) 41.7729i 1.82660i −0.407286 0.913301i \(-0.633525\pi\)
0.407286 0.913301i \(-0.366475\pi\)
\(524\) −19.3386 + 7.21500i −0.844812 + 0.315189i
\(525\) 0 0
\(526\) −17.0990 + 24.6297i −0.745552 + 1.07391i
\(527\) −5.65004 −0.246120
\(528\) 16.2027 14.0450i 0.705131 0.611231i
\(529\) 33.1801 1.44261
\(530\) 0 0
\(531\) 6.85302i 0.297396i
\(532\) 2.42402 0.904373i 0.105095 0.0392095i
\(533\) 33.0361i 1.43095i
\(534\) 8.82061 + 6.12364i 0.381705 + 0.264996i
\(535\) 0 0
\(536\) 5.20359 20.3994i 0.224761 0.881120i
\(537\) −8.13765 −0.351165
\(538\) 17.0695 + 11.8504i 0.735919 + 0.510907i
\(539\) 34.5400i 1.48774i
\(540\) 0 0
\(541\) 4.47705i 0.192483i 0.995358 + 0.0962417i \(0.0306822\pi\)
−0.995358 + 0.0962417i \(0.969318\pi\)
\(542\) 16.3233 23.5124i 0.701148 1.00995i
\(543\) 1.49235 0.0640428
\(544\) 1.29362 + 12.0060i 0.0554634 + 0.514752i
\(545\) 0 0
\(546\) 1.76036 2.53566i 0.0753365 0.108516i
\(547\) 14.3297i 0.612692i −0.951920 0.306346i \(-0.900893\pi\)
0.951920 0.306346i \(-0.0991065\pi\)
\(548\) 10.5136 + 28.1801i 0.449120 + 1.20379i
\(549\) 6.45203i 0.275366i
\(550\) 0 0
\(551\) −11.7008 −0.498470
\(552\) −5.24002 + 20.5422i −0.223030 + 0.874335i
\(553\) −1.97498 −0.0839848
\(554\) −0.601793 0.417790i −0.0255677 0.0177502i
\(555\) 0 0
\(556\) 17.7458 6.62073i 0.752590 0.280782i
\(557\) 2.68556i 0.113791i 0.998380 + 0.0568954i \(0.0181201\pi\)
−0.998380 + 0.0568954i \(0.981880\pi\)
\(558\) 2.13466 3.07480i 0.0903674 0.130167i
\(559\) 21.7729 0.920895
\(560\) 0 0
\(561\) 11.4432 0.483133
\(562\) −11.0497 + 15.9162i −0.466105 + 0.671386i
\(563\) 20.7368i 0.873954i −0.899473 0.436977i \(-0.856049\pi\)
0.899473 0.436977i \(-0.143951\pi\)
\(564\) 3.24860 1.21201i 0.136791 0.0510349i
\(565\) 0 0
\(566\) 20.9460 + 14.5416i 0.880427 + 0.611230i
\(567\) −0.746175 −0.0313364
\(568\) 36.4334 + 9.29362i 1.52871 + 0.389952i
\(569\) 4.40717 0.184758 0.0923791 0.995724i \(-0.470553\pi\)
0.0923791 + 0.995724i \(0.470553\pi\)
\(570\) 0 0
\(571\) 23.6590i 0.990098i −0.868865 0.495049i \(-0.835150\pi\)
0.868865 0.495049i \(-0.164850\pi\)
\(572\) −10.9627 29.3836i −0.458372 1.22859i
\(573\) 6.88645i 0.287685i
\(574\) −6.79641 + 9.78968i −0.283677 + 0.408613i
\(575\) 0 0
\(576\) −7.02251 3.83202i −0.292604 0.159668i
\(577\) 6.56366 0.273249 0.136624 0.990623i \(-0.456375\pi\)
0.136624 + 0.990623i \(0.456375\pi\)
\(578\) 10.0355 14.4553i 0.417422 0.601262i
\(579\) 16.4830i 0.685011i
\(580\) 0 0
\(581\) 4.36542i 0.181108i
\(582\) 16.4830 + 11.4432i 0.683243 + 0.474337i
\(583\) −41.3931 −1.71433
\(584\) 1.89204 + 0.482632i 0.0782933 + 0.0199715i
\(585\) 0 0
\(586\) 18.5630 + 12.8873i 0.766832 + 0.532368i
\(587\) 16.2992i 0.672741i −0.941730 0.336370i \(-0.890801\pi\)
0.941730 0.336370i \(-0.109199\pi\)
\(588\) 12.0735 4.50448i 0.497904 0.185762i
\(589\) 4.58868i 0.189073i
\(590\) 0 0
\(591\) −13.5720 −0.558278
\(592\) 2.81599 + 3.24860i 0.115737 + 0.133517i
\(593\) 16.3233 0.670319 0.335160 0.942161i \(-0.391210\pi\)
0.335160 + 0.942161i \(0.391210\pi\)
\(594\) −4.32340 + 6.22751i −0.177391 + 0.255518i
\(595\) 0 0
\(596\) −3.35319 + 1.25103i −0.137352 + 0.0512443i
\(597\) 9.05398i 0.370555i
\(598\) 25.4707 + 17.6829i 1.04157 + 0.723106i
\(599\) −25.5928 −1.04569 −0.522847 0.852426i \(-0.675130\pi\)
−0.522847 + 0.852426i \(0.675130\pi\)
\(600\) 0 0
\(601\) 29.9225 1.22056 0.610282 0.792184i \(-0.291056\pi\)
0.610282 + 0.792184i \(0.291056\pi\)
\(602\) −6.45203 4.47928i −0.262965 0.182562i
\(603\) 7.44322i 0.303111i
\(604\) −7.44322 19.9504i −0.302860 0.811768i
\(605\) 0 0
\(606\) −6.00000 + 8.64251i −0.243733 + 0.351078i
\(607\) 20.6965 0.840046 0.420023 0.907513i \(-0.362022\pi\)
0.420023 + 0.907513i \(0.362022\pi\)
\(608\) −9.75065 + 1.05061i −0.395441 + 0.0426079i
\(609\) 5.03605 0.204071
\(610\) 0 0
\(611\) 5.07131i 0.205163i
\(612\) −1.49235 4.00000i −0.0603246 0.161690i
\(613\) 22.6676i 0.915537i −0.889071 0.457769i \(-0.848649\pi\)
0.889071 0.457769i \(-0.151351\pi\)
\(614\) 26.2396 + 18.2167i 1.05895 + 0.735166i
\(615\) 0 0
\(616\) −2.79641 + 10.9627i −0.112671 + 0.441698i
\(617\) −22.1966 −0.893603 −0.446802 0.894633i \(-0.647437\pi\)
−0.446802 + 0.894633i \(0.647437\pi\)
\(618\) −8.36217 5.80538i −0.336376 0.233527i
\(619\) 16.8204i 0.676070i 0.941133 + 0.338035i \(0.109762\pi\)
−0.941133 + 0.338035i \(0.890238\pi\)
\(620\) 0 0
\(621\) 7.49534i 0.300777i
\(622\) 14.9907 21.5928i 0.601071 0.865794i
\(623\) −5.66558 −0.226987
\(624\) −8.84143 + 7.66404i −0.353940 + 0.306807i
\(625\) 0 0
\(626\) −23.7008 + 34.1390i −0.947274 + 1.36447i
\(627\) 9.29362i 0.371151i
\(628\) 12.9767 4.84143i 0.517825 0.193194i
\(629\) 2.29434i 0.0914813i
\(630\) 0 0
\(631\) −44.1205 −1.75641 −0.878204 0.478285i \(-0.841258\pi\)
−0.878204 + 0.478285i \(0.841258\pi\)
\(632\) 7.25402 + 1.85039i 0.288549 + 0.0736047i
\(633\) −2.53566 −0.100783
\(634\) 6.47301 + 4.49384i 0.257076 + 0.178473i
\(635\) 0 0
\(636\) 5.39821 + 14.4690i 0.214053 + 0.573734i
\(637\) 18.8477i 0.746773i
\(638\) 29.1794 42.0305i 1.15522 1.66400i
\(639\) −13.2936 −0.525887
\(640\) 0 0
\(641\) −1.18566 −0.0468307 −0.0234154 0.999726i \(-0.507454\pi\)
−0.0234154 + 0.999726i \(0.507454\pi\)
\(642\) 3.22601 4.64681i 0.127321 0.183395i
\(643\) 22.5872i 0.890754i 0.895343 + 0.445377i \(0.146930\pi\)
−0.895343 + 0.445377i \(0.853070\pi\)
\(644\) −3.90997 10.4800i −0.154074 0.412971i
\(645\) 0 0
\(646\) −4.29921 2.98470i −0.169150 0.117431i
\(647\) 19.7090 0.774842 0.387421 0.921903i \(-0.373366\pi\)
0.387421 + 0.921903i \(0.373366\pi\)
\(648\) 2.74067 + 0.699104i 0.107664 + 0.0274634i
\(649\) −36.7368 −1.44205
\(650\) 0 0
\(651\) 1.97498i 0.0774056i
\(652\) −14.4300 + 5.38365i −0.565122 + 0.210840i
\(653\) 44.4585i 1.73979i 0.493234 + 0.869897i \(0.335815\pi\)
−0.493234 + 0.869897i \(0.664185\pi\)
\(654\) −16.0900 + 23.1764i −0.629170 + 0.906268i
\(655\) 0 0
\(656\) 34.1350 29.5894i 1.33275 1.15527i
\(657\) −0.690358 −0.0269334
\(658\) −1.04331 + 1.50280i −0.0406723 + 0.0585852i
\(659\) 41.5863i 1.61997i 0.586448 + 0.809987i \(0.300526\pi\)
−0.586448 + 0.809987i \(0.699474\pi\)
\(660\) 0 0
\(661\) 12.0060i 0.466978i 0.972359 + 0.233489i \(0.0750143\pi\)
−0.972359 + 0.233489i \(0.924986\pi\)
\(662\) 15.9614 + 11.0811i 0.620356 + 0.430678i
\(663\) −6.24430 −0.242509
\(664\) −4.09003 + 16.0340i −0.158724 + 0.622239i
\(665\) 0 0
\(666\) −1.24860 0.866833i −0.0483823 0.0335891i
\(667\) 50.5872i 1.95875i
\(668\) −2.25532 6.04502i −0.0872609 0.233889i
\(669\) 12.1579i 0.470051i
\(670\) 0 0
\(671\) 34.5872 1.33523
\(672\) 4.19671 0.452186i 0.161892 0.0174435i
\(673\) −14.5080 −0.559244 −0.279622 0.960110i \(-0.590209\pi\)
−0.279622 + 0.960110i \(0.590209\pi\)
\(674\) 16.7368 24.1080i 0.644679 0.928607i
\(675\) 0 0
\(676\) −3.10627 8.32586i −0.119472 0.320226i
\(677\) 43.8600i 1.68568i −0.538166 0.842839i \(-0.680883\pi\)
0.538166 0.842839i \(-0.319117\pi\)
\(678\) −14.0032 9.72161i −0.537789 0.373356i
\(679\) −10.5872 −0.406301
\(680\) 0 0
\(681\) 20.7368 0.794637
\(682\) 16.4830 + 11.4432i 0.631168 + 0.438184i
\(683\) 5.33527i 0.204148i −0.994777 0.102074i \(-0.967452\pi\)
0.994777 0.102074i \(-0.0325479\pi\)
\(684\) 3.24860 1.21201i 0.124213 0.0463424i
\(685\) 0 0
\(686\) −8.09003 + 11.6530i −0.308879 + 0.444915i
\(687\) −19.9504 −0.761153
\(688\) 19.5013 + 22.4972i 0.743480 + 0.857698i
\(689\) 22.5872 0.860505
\(690\) 0 0
\(691\) 39.7710i 1.51296i −0.654016 0.756480i \(-0.726917\pi\)
0.654016 0.756480i \(-0.273083\pi\)
\(692\) 12.0450 4.49383i 0.457882 0.170830i
\(693\) 4.00000i 0.151947i
\(694\) 5.50280 + 3.82028i 0.208883 + 0.145016i
\(695\) 0 0
\(696\) −18.4972 4.71836i −0.701135 0.178849i
\(697\) 24.1080 0.913157
\(698\) 0.560675 + 0.389245i 0.0212219 + 0.0147331i
\(699\) 13.3386i 0.504514i
\(700\) 0 0
\(701\) 27.5015i 1.03872i 0.854556 + 0.519359i \(0.173829\pi\)
−0.854556 + 0.519359i \(0.826171\pi\)
\(702\) 2.35918 3.39821i 0.0890416 0.128257i
\(703\) −1.86335 −0.0702775
\(704\) 20.5422 37.6454i 0.774214 1.41881i
\(705\) 0 0
\(706\) −1.72161 + 2.47984i −0.0647937 + 0.0933300i
\(707\) 5.55118i 0.208774i
\(708\) 4.79097 + 12.8414i 0.180056 + 0.482611i
\(709\) 0.111632i 0.00419244i −0.999998 0.00209622i \(-0.999333\pi\)
0.999998 0.00209622i \(-0.000667249\pi\)
\(710\) 0 0
\(711\) −2.64681 −0.0992631
\(712\) 20.8094 + 5.30818i 0.779866 + 0.198932i
\(713\) −19.8387 −0.742966
\(714\) 1.85039 + 1.28462i 0.0692492 + 0.0480758i
\(715\) 0 0
\(716\) −15.2486 + 5.68906i −0.569867 + 0.212610i
\(717\) 22.8864i 0.854710i
\(718\) 7.73665 11.1440i 0.288729 0.415891i
\(719\) 10.7064 0.399281 0.199640 0.979869i \(-0.436023\pi\)
0.199640 + 0.979869i \(0.436023\pi\)
\(720\) 0 0
\(721\) 5.37112 0.200031
\(722\) −12.8995 + 18.5807i −0.480071 + 0.691503i
\(723\) 3.59283i 0.133619i
\(724\) 2.79641 1.04331i 0.103928 0.0387742i
\(725\) 0 0
\(726\) −20.6049 14.3048i −0.764721 0.530902i
\(727\) 25.6562 0.951536 0.475768 0.879571i \(-0.342170\pi\)
0.475768 + 0.879571i \(0.342170\pi\)
\(728\) 1.52594 5.98207i 0.0565551 0.221710i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 15.8888i 0.587667i
\(732\) −4.51064 12.0900i −0.166718 0.446860i
\(733\) 30.3684i 1.12168i 0.827923 + 0.560842i \(0.189522\pi\)
−0.827923 + 0.560842i \(0.810478\pi\)
\(734\) 27.4882 39.5945i 1.01461 1.46146i
\(735\) 0 0
\(736\) 4.54222 + 42.1560i 0.167428 + 1.55389i
\(737\) −39.9007 −1.46976
\(738\) −9.10834 + 13.1198i −0.335283 + 0.482947i
\(739\) 20.1917i 0.742763i −0.928480 0.371381i \(-0.878884\pi\)
0.928480 0.371381i \(-0.121116\pi\)
\(740\) 0 0
\(741\) 5.07131i 0.186299i
\(742\) −6.69335 4.64681i −0.245720 0.170590i
\(743\) −46.3863 −1.70175 −0.850875 0.525369i \(-0.823927\pi\)
−0.850875 + 0.525369i \(0.823927\pi\)
\(744\) 1.85039 7.25402i 0.0678387 0.265945i
\(745\) 0 0
\(746\) 5.03942 + 3.49858i 0.184506 + 0.128092i
\(747\) 5.85039i 0.214055i
\(748\) 21.4427 8.00000i 0.784023 0.292509i
\(749\) 2.98470i 0.109059i
\(750\) 0 0
\(751\) −27.1261 −0.989845 −0.494922 0.868937i \(-0.664804\pi\)
−0.494922 + 0.868937i \(0.664804\pi\)
\(752\) 5.24002 4.54222i 0.191084 0.165638i
\(753\) 8.82801 0.321710
\(754\) −15.9225 + 22.9351i −0.579863 + 0.835245i
\(755\) 0 0
\(756\) −1.39821 + 0.521653i −0.0508523 + 0.0189724i
\(757\) 45.2549i 1.64482i −0.568898 0.822408i \(-0.692630\pi\)
0.568898 0.822408i \(-0.307370\pi\)
\(758\) −8.01699 5.56574i −0.291190 0.202157i
\(759\) 40.1801 1.45844
\(760\) 0 0
\(761\) 16.8864 0.612133 0.306067 0.952010i \(-0.400987\pi\)
0.306067 + 0.952010i \(0.400987\pi\)
\(762\) 4.89484 + 3.39821i 0.177321 + 0.123104i
\(763\) 14.8864i 0.538926i
\(764\) −4.81434 12.9041i −0.174177 0.466852i
\(765\) 0 0
\(766\) 18.0450 25.9924i 0.651993 0.939142i
\(767\) 20.0464 0.723835
\(768\) −15.8380 2.27111i −0.571504 0.0819516i
\(769\) 16.3297 0.588863 0.294431 0.955673i \(-0.404870\pi\)
0.294431 + 0.955673i \(0.404870\pi\)
\(770\) 0 0
\(771\) 22.2927i 0.802853i
\(772\) −11.5233 30.8864i −0.414734 1.11163i
\(773\) 41.3144i 1.48598i −0.669304 0.742989i \(-0.733408\pi\)
0.669304 0.742989i \(-0.266592\pi\)
\(774\) −8.64681 6.00299i −0.310803 0.215773i
\(775\) 0 0
\(776\) 38.8864 + 9.91936i 1.39594 + 0.356084i
\(777\) 0.801991 0.0287713
\(778\) −12.8002 8.88645i −0.458909 0.318595i
\(779\) 19.5794i 0.701503i
\(780\) 0 0
\(781\) 71.2628i 2.54998i
\(782\) −12.9041 + 18.5872i −0.461448 + 0.664678i
\(783\) 6.74916 0.241195
\(784\) 19.4747 16.8813i 0.695525 0.602904i
\(785\) 0 0
\(786\) 8.32340 11.9892i 0.296886