Properties

Label 120.2.d.a.109.5
Level 120
Weight 2
Character 120.109
Analytic conductor 0.958
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.958204824255\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.839056.1
Defining polynomial: \(x^{6} + 6 x^{4} + 8 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 109.5
Root \(0.373087i\) of defining polynomial
Character \(\chi\) \(=\) 120.109
Dual form 120.2.d.a.109.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.16170 - 0.806504i) q^{2} +1.00000 q^{3} +(0.699104 - 1.87383i) q^{4} +(-1.86081 + 1.23992i) q^{5} +(1.16170 - 0.806504i) q^{6} -0.746175i q^{7} +(-0.699104 - 2.74067i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(1.16170 - 0.806504i) q^{2} +1.00000 q^{3} +(0.699104 - 1.87383i) q^{4} +(-1.86081 + 1.23992i) q^{5} +(1.16170 - 0.806504i) q^{6} -0.746175i q^{7} +(-0.699104 - 2.74067i) q^{8} +1.00000 q^{9} +(-1.16170 + 2.94116i) q^{10} +5.36068i q^{11} +(0.699104 - 1.87383i) q^{12} -2.92520 q^{13} +(-0.601793 - 0.866833i) q^{14} +(-1.86081 + 1.23992i) q^{15} +(-3.02251 - 2.62001i) q^{16} -2.13466i q^{17} +(1.16170 - 0.806504i) q^{18} -1.73367i q^{19} +(1.02251 + 4.35367i) q^{20} -0.746175i q^{21} +(4.32340 + 6.22751i) q^{22} +7.49534i q^{23} +(-0.699104 - 2.74067i) q^{24} +(1.92520 - 4.61450i) q^{25} +(-3.39821 + 2.35918i) q^{26} +1.00000 q^{27} +(-1.39821 - 0.521653i) q^{28} -6.74916i q^{29} +(-1.16170 + 2.94116i) q^{30} +2.64681 q^{31} +(-5.62430 - 0.606006i) q^{32} +5.36068i q^{33} +(-1.72161 - 2.47984i) q^{34} +(0.925197 + 1.38849i) q^{35} +(0.699104 - 1.87383i) q^{36} -1.07480 q^{37} +(-1.39821 - 2.01400i) q^{38} -2.92520 q^{39} +(4.69910 + 4.23302i) q^{40} -11.2936 q^{41} +(-0.601793 - 0.866833i) q^{42} +7.44322 q^{43} +(10.0450 + 3.74767i) q^{44} +(-1.86081 + 1.23992i) q^{45} +(6.04502 + 8.70735i) q^{46} -1.73367i q^{47} +(-3.02251 - 2.62001i) q^{48} +6.44322 q^{49} +(-1.48511 - 6.91335i) q^{50} -2.13466i q^{51} +(-2.04502 + 5.48133i) q^{52} +7.72161 q^{53} +(1.16170 - 0.806504i) q^{54} +(-6.64681 - 9.97518i) q^{55} +(-2.04502 + 0.521653i) q^{56} -1.73367i q^{57} +(-5.44322 - 7.84052i) q^{58} -6.85302i q^{59} +(1.02251 + 4.35367i) q^{60} -6.45203i q^{61} +(3.07480 - 2.13466i) q^{62} -0.746175i q^{63} +(-7.02251 + 3.83202i) q^{64} +(5.44322 - 3.62701i) q^{65} +(4.32340 + 6.22751i) q^{66} -7.44322 q^{67} +(-4.00000 - 1.49235i) q^{68} +7.49534i q^{69} +(2.19462 + 0.866833i) q^{70} +13.2936 q^{71} +(-0.699104 - 2.74067i) q^{72} -0.690358i q^{73} +(-1.24860 + 0.866833i) q^{74} +(1.92520 - 4.61450i) q^{75} +(-3.24860 - 1.21201i) q^{76} +4.00000 q^{77} +(-3.39821 + 2.35918i) q^{78} -2.64681 q^{79} +(8.87290 + 1.12766i) q^{80} +1.00000 q^{81} +(-13.1198 + 9.10834i) q^{82} -5.85039 q^{83} +(-1.39821 - 0.521653i) q^{84} +(2.64681 + 3.97219i) q^{85} +(8.64681 - 6.00299i) q^{86} -6.74916i q^{87} +(14.6918 - 3.74767i) q^{88} -7.59283 q^{89} +(-1.16170 + 2.94116i) q^{90} +2.18271i q^{91} +(14.0450 + 5.24002i) q^{92} +2.64681 q^{93} +(-1.39821 - 2.01400i) q^{94} +(2.14961 + 3.22601i) q^{95} +(-5.62430 - 0.606006i) q^{96} +14.1887i q^{97} +(7.48511 - 5.19648i) q^{98} +5.36068i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} + 6q^{3} + q^{4} - q^{6} - q^{8} + 6q^{9} + O(q^{10}) \) \( 6q - q^{2} + 6q^{3} + q^{4} - q^{6} - q^{8} + 6q^{9} + q^{10} + q^{12} - 8q^{13} - 10q^{14} + q^{16} - q^{18} - 13q^{20} + 10q^{22} - q^{24} + 2q^{25} - 14q^{26} + 6q^{27} - 2q^{28} + q^{30} - 16q^{31} - 21q^{32} + 12q^{34} - 4q^{35} + q^{36} - 16q^{37} - 2q^{38} - 8q^{39} + 25q^{40} - 4q^{41} - 10q^{42} + 22q^{44} - 2q^{46} + q^{48} - 6q^{49} + 15q^{50} + 26q^{52} + 24q^{53} - q^{54} - 8q^{55} + 26q^{56} + 12q^{58} - 13q^{60} + 28q^{62} - 23q^{64} - 12q^{65} + 10q^{66} - 24q^{68} - 6q^{70} + 16q^{71} - q^{72} + 18q^{74} + 2q^{75} + 6q^{76} + 24q^{77} - 14q^{78} + 16q^{79} + 15q^{80} + 6q^{81} - 50q^{82} - 16q^{83} - 2q^{84} - 16q^{85} + 20q^{86} + 18q^{88} - 20q^{89} + q^{90} + 46q^{92} - 16q^{93} - 2q^{94} + 32q^{95} - 21q^{96} + 21q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.16170 0.806504i 0.821447 0.570284i
\(3\) 1.00000 0.577350
\(4\) 0.699104 1.87383i 0.349552 0.936917i
\(5\) −1.86081 + 1.23992i −0.832178 + 0.554509i
\(6\) 1.16170 0.806504i 0.474263 0.329254i
\(7\) 0.746175i 0.282028i −0.990008 0.141014i \(-0.954964\pi\)
0.990008 0.141014i \(-0.0450362\pi\)
\(8\) −0.699104 2.74067i −0.247170 0.968972i
\(9\) 1.00000 0.333333
\(10\) −1.16170 + 2.94116i −0.367362 + 0.930078i
\(11\) 5.36068i 1.61630i 0.588974 + 0.808152i \(0.299532\pi\)
−0.588974 + 0.808152i \(0.700468\pi\)
\(12\) 0.699104 1.87383i 0.201814 0.540929i
\(13\) −2.92520 −0.811304 −0.405652 0.914028i \(-0.632955\pi\)
−0.405652 + 0.914028i \(0.632955\pi\)
\(14\) −0.601793 0.866833i −0.160836 0.231671i
\(15\) −1.86081 + 1.23992i −0.480458 + 0.320146i
\(16\) −3.02251 2.62001i −0.755627 0.655002i
\(17\) 2.13466i 0.517731i −0.965913 0.258866i \(-0.916651\pi\)
0.965913 0.258866i \(-0.0833487\pi\)
\(18\) 1.16170 0.806504i 0.273816 0.190095i
\(19\) 1.73367i 0.397730i −0.980027 0.198865i \(-0.936274\pi\)
0.980027 0.198865i \(-0.0637255\pi\)
\(20\) 1.02251 + 4.35367i 0.228640 + 0.973511i
\(21\) 0.746175i 0.162829i
\(22\) 4.32340 + 6.22751i 0.921753 + 1.32771i
\(23\) 7.49534i 1.56289i 0.623977 + 0.781443i \(0.285516\pi\)
−0.623977 + 0.781443i \(0.714484\pi\)
\(24\) −0.699104 2.74067i −0.142704 0.559436i
\(25\) 1.92520 4.61450i 0.385039 0.922900i
\(26\) −3.39821 + 2.35918i −0.666443 + 0.462674i
\(27\) 1.00000 0.192450
\(28\) −1.39821 0.521653i −0.264236 0.0985832i
\(29\) 6.74916i 1.25329i −0.779306 0.626644i \(-0.784428\pi\)
0.779306 0.626644i \(-0.215572\pi\)
\(30\) −1.16170 + 2.94116i −0.212097 + 0.536981i
\(31\) 2.64681 0.475381 0.237690 0.971341i \(-0.423610\pi\)
0.237690 + 0.971341i \(0.423610\pi\)
\(32\) −5.62430 0.606006i −0.994245 0.107128i
\(33\) 5.36068i 0.933174i
\(34\) −1.72161 2.47984i −0.295254 0.425289i
\(35\) 0.925197 + 1.38849i 0.156387 + 0.234697i
\(36\) 0.699104 1.87383i 0.116517 0.312306i
\(37\) −1.07480 −0.176697 −0.0883483 0.996090i \(-0.528159\pi\)
−0.0883483 + 0.996090i \(0.528159\pi\)
\(38\) −1.39821 2.01400i −0.226819 0.326714i
\(39\) −2.92520 −0.468406
\(40\) 4.69910 + 4.23302i 0.742994 + 0.669299i
\(41\) −11.2936 −1.76377 −0.881883 0.471468i \(-0.843724\pi\)
−0.881883 + 0.471468i \(0.843724\pi\)
\(42\) −0.601793 0.866833i −0.0928586 0.133755i
\(43\) 7.44322 1.13508 0.567540 0.823346i \(-0.307895\pi\)
0.567540 + 0.823346i \(0.307895\pi\)
\(44\) 10.0450 + 3.74767i 1.51434 + 0.564982i
\(45\) −1.86081 + 1.23992i −0.277393 + 0.184836i
\(46\) 6.04502 + 8.70735i 0.891289 + 1.28383i
\(47\) 1.73367i 0.252881i −0.991974 0.126441i \(-0.959645\pi\)
0.991974 0.126441i \(-0.0403553\pi\)
\(48\) −3.02251 2.62001i −0.436261 0.378166i
\(49\) 6.44322 0.920460
\(50\) −1.48511 6.91335i −0.210026 0.977696i
\(51\) 2.13466i 0.298912i
\(52\) −2.04502 + 5.48133i −0.283593 + 0.760124i
\(53\) 7.72161 1.06064 0.530322 0.847796i \(-0.322071\pi\)
0.530322 + 0.847796i \(0.322071\pi\)
\(54\) 1.16170 0.806504i 0.158088 0.109751i
\(55\) −6.64681 9.97518i −0.896255 1.34505i
\(56\) −2.04502 + 0.521653i −0.273277 + 0.0697089i
\(57\) 1.73367i 0.229630i
\(58\) −5.44322 7.84052i −0.714730 1.02951i
\(59\) 6.85302i 0.892188i −0.894986 0.446094i \(-0.852815\pi\)
0.894986 0.446094i \(-0.147185\pi\)
\(60\) 1.02251 + 4.35367i 0.132005 + 0.562057i
\(61\) 6.45203i 0.826098i −0.910709 0.413049i \(-0.864464\pi\)
0.910709 0.413049i \(-0.135536\pi\)
\(62\) 3.07480 2.13466i 0.390500 0.271102i
\(63\) 0.746175i 0.0940092i
\(64\) −7.02251 + 3.83202i −0.877813 + 0.479003i
\(65\) 5.44322 3.62701i 0.675149 0.449875i
\(66\) 4.32340 + 6.22751i 0.532174 + 0.766553i
\(67\) −7.44322 −0.909334 −0.454667 0.890661i \(-0.650242\pi\)
−0.454667 + 0.890661i \(0.650242\pi\)
\(68\) −4.00000 1.49235i −0.485071 0.180974i
\(69\) 7.49534i 0.902332i
\(70\) 2.19462 + 0.866833i 0.262308 + 0.103606i
\(71\) 13.2936 1.57766 0.788831 0.614610i \(-0.210687\pi\)
0.788831 + 0.614610i \(0.210687\pi\)
\(72\) −0.699104 2.74067i −0.0823902 0.322991i
\(73\) 0.690358i 0.0808003i −0.999184 0.0404002i \(-0.987137\pi\)
0.999184 0.0404002i \(-0.0128633\pi\)
\(74\) −1.24860 + 0.866833i −0.145147 + 0.100767i
\(75\) 1.92520 4.61450i 0.222303 0.532837i
\(76\) −3.24860 1.21201i −0.372640 0.139027i
\(77\) 4.00000 0.455842
\(78\) −3.39821 + 2.35918i −0.384771 + 0.267125i
\(79\) −2.64681 −0.297789 −0.148895 0.988853i \(-0.547572\pi\)
−0.148895 + 0.988853i \(0.547572\pi\)
\(80\) 8.87290 + 1.12766i 0.992021 + 0.126076i
\(81\) 1.00000 0.111111
\(82\) −13.1198 + 9.10834i −1.44884 + 1.00585i
\(83\) −5.85039 −0.642164 −0.321082 0.947051i \(-0.604047\pi\)
−0.321082 + 0.947051i \(0.604047\pi\)
\(84\) −1.39821 0.521653i −0.152557 0.0569171i
\(85\) 2.64681 + 3.97219i 0.287087 + 0.430844i
\(86\) 8.64681 6.00299i 0.932409 0.647319i
\(87\) 6.74916i 0.723586i
\(88\) 14.6918 3.74767i 1.56615 0.399503i
\(89\) −7.59283 −0.804838 −0.402419 0.915456i \(-0.631831\pi\)
−0.402419 + 0.915456i \(0.631831\pi\)
\(90\) −1.16170 + 2.94116i −0.122454 + 0.310026i
\(91\) 2.18271i 0.228810i
\(92\) 14.0450 + 5.24002i 1.46429 + 0.546310i
\(93\) 2.64681 0.274461
\(94\) −1.39821 2.01400i −0.144214 0.207729i
\(95\) 2.14961 + 3.22601i 0.220545 + 0.330982i
\(96\) −5.62430 0.606006i −0.574028 0.0618502i
\(97\) 14.1887i 1.44064i 0.693641 + 0.720321i \(0.256006\pi\)
−0.693641 + 0.720321i \(0.743994\pi\)
\(98\) 7.48511 5.19648i 0.756110 0.524924i
\(99\) 5.36068i 0.538768i
\(100\) −7.30090 6.83351i −0.730090 0.683351i
\(101\) 7.43952i 0.740260i −0.928980 0.370130i \(-0.879313\pi\)
0.928980 0.370130i \(-0.120687\pi\)
\(102\) −1.72161 2.47984i −0.170465 0.245541i
\(103\) 7.19820i 0.709260i 0.935007 + 0.354630i \(0.115393\pi\)
−0.935007 + 0.354630i \(0.884607\pi\)
\(104\) 2.04502 + 8.01699i 0.200530 + 0.786131i
\(105\) 0.925197 + 1.38849i 0.0902900 + 0.135502i
\(106\) 8.97021 6.22751i 0.871264 0.604869i
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 0.699104 1.87383i 0.0672713 0.180310i
\(109\) 19.9504i 1.91090i 0.295158 + 0.955449i \(0.404628\pi\)
−0.295158 + 0.955449i \(0.595372\pi\)
\(110\) −15.7666 6.22751i −1.50329 0.593770i
\(111\) −1.07480 −0.102016
\(112\) −1.95498 + 2.25532i −0.184729 + 0.213108i
\(113\) 12.0540i 1.13395i 0.823736 + 0.566973i \(0.191886\pi\)
−0.823736 + 0.566973i \(0.808114\pi\)
\(114\) −1.39821 2.01400i −0.130954 0.188629i
\(115\) −9.29362 13.9474i −0.866634 1.30060i
\(116\) −12.6468 4.71836i −1.17423 0.438089i
\(117\) −2.92520 −0.270435
\(118\) −5.52699 7.96117i −0.508801 0.732885i
\(119\) −1.59283 −0.146014
\(120\) 4.69910 + 4.23302i 0.428968 + 0.386420i
\(121\) −17.7368 −1.61244
\(122\) −5.20359 7.49534i −0.471110 0.678596i
\(123\) −11.2936 −1.01831
\(124\) 1.85039 4.95968i 0.166170 0.445392i
\(125\) 2.13919 + 10.9738i 0.191335 + 0.981525i
\(126\) −0.601793 0.866833i −0.0536119 0.0772236i
\(127\) 4.21351i 0.373888i 0.982371 + 0.186944i \(0.0598583\pi\)
−0.982371 + 0.186944i \(0.940142\pi\)
\(128\) −5.06752 + 10.1153i −0.447910 + 0.894079i
\(129\) 7.44322 0.655339
\(130\) 3.39821 8.60348i 0.298043 0.754576i
\(131\) 10.3204i 0.901694i 0.892601 + 0.450847i \(0.148878\pi\)
−0.892601 + 0.450847i \(0.851122\pi\)
\(132\) 10.0450 + 3.74767i 0.874306 + 0.326193i
\(133\) −1.29362 −0.112171
\(134\) −8.64681 + 6.00299i −0.746970 + 0.518579i
\(135\) −1.86081 + 1.23992i −0.160153 + 0.106715i
\(136\) −5.85039 + 1.49235i −0.501667 + 0.127968i
\(137\) 15.0387i 1.28484i −0.766351 0.642422i \(-0.777930\pi\)
0.766351 0.642422i \(-0.222070\pi\)
\(138\) 6.04502 + 8.70735i 0.514586 + 0.741219i
\(139\) 9.47032i 0.803262i 0.915802 + 0.401631i \(0.131557\pi\)
−0.915802 + 0.401631i \(0.868443\pi\)
\(140\) 3.24860 0.762970i 0.274557 0.0644827i
\(141\) 1.73367i 0.146001i
\(142\) 15.4432 10.7214i 1.29597 0.899716i
\(143\) 15.6810i 1.31131i
\(144\) −3.02251 2.62001i −0.251876 0.218334i
\(145\) 8.36842 + 12.5589i 0.694959 + 1.04296i
\(146\) −0.556777 0.801991i −0.0460792 0.0663732i
\(147\) 6.44322 0.531428
\(148\) −0.751399 + 2.01400i −0.0617646 + 0.165550i
\(149\) 1.78948i 0.146600i −0.997310 0.0733000i \(-0.976647\pi\)
0.997310 0.0733000i \(-0.0233531\pi\)
\(150\) −1.48511 6.91335i −0.121258 0.564473i
\(151\) 10.6468 0.866425 0.433212 0.901292i \(-0.357380\pi\)
0.433212 + 0.901292i \(0.357380\pi\)
\(152\) −4.75140 + 1.21201i −0.385389 + 0.0983071i
\(153\) 2.13466i 0.172577i
\(154\) 4.64681 3.22601i 0.374451 0.259960i
\(155\) −4.92520 + 3.28183i −0.395601 + 0.263603i
\(156\) −2.04502 + 5.48133i −0.163732 + 0.438858i
\(157\) 6.92520 0.552691 0.276345 0.961058i \(-0.410877\pi\)
0.276345 + 0.961058i \(0.410877\pi\)
\(158\) −3.07480 + 2.13466i −0.244618 + 0.169824i
\(159\) 7.72161 0.612364
\(160\) 11.2171 5.84602i 0.886792 0.462169i
\(161\) 5.59283 0.440777
\(162\) 1.16170 0.806504i 0.0912719 0.0633649i
\(163\) 7.70079 0.603172 0.301586 0.953439i \(-0.402484\pi\)
0.301586 + 0.953439i \(0.402484\pi\)
\(164\) −7.89541 + 21.1624i −0.616528 + 1.65250i
\(165\) −6.64681 9.97518i −0.517453 0.776566i
\(166\) −6.79641 + 4.71836i −0.527504 + 0.366216i
\(167\) 3.22601i 0.249637i 0.992180 + 0.124818i \(0.0398348\pi\)
−0.992180 + 0.124818i \(0.960165\pi\)
\(168\) −2.04502 + 0.521653i −0.157776 + 0.0402464i
\(169\) −4.44322 −0.341786
\(170\) 6.27839 + 2.47984i 0.481530 + 0.190195i
\(171\) 1.73367i 0.132577i
\(172\) 5.20359 13.9474i 0.396770 1.06348i
\(173\) −6.42799 −0.488711 −0.244356 0.969686i \(-0.578576\pi\)
−0.244356 + 0.969686i \(0.578576\pi\)
\(174\) −5.44322 7.84052i −0.412650 0.594388i
\(175\) −3.44322 1.43653i −0.260283 0.108592i
\(176\) 14.0450 16.2027i 1.05868 1.22132i
\(177\) 6.85302i 0.515105i
\(178\) −8.82061 + 6.12364i −0.661132 + 0.458987i
\(179\) 8.13765i 0.608236i −0.952634 0.304118i \(-0.901638\pi\)
0.952634 0.304118i \(-0.0983618\pi\)
\(180\) 1.02251 + 4.35367i 0.0762132 + 0.324504i
\(181\) 1.49235i 0.110925i −0.998461 0.0554627i \(-0.982337\pi\)
0.998461 0.0554627i \(-0.0176634\pi\)
\(182\) 1.76036 + 2.53566i 0.130487 + 0.187955i
\(183\) 6.45203i 0.476948i
\(184\) 20.5422 5.24002i 1.51439 0.386299i
\(185\) 2.00000 1.33267i 0.147043 0.0979798i
\(186\) 3.07480 2.13466i 0.225456 0.156521i
\(187\) 11.4432 0.836811
\(188\) −3.24860 1.21201i −0.236929 0.0883951i
\(189\) 0.746175i 0.0542762i
\(190\) 5.09899 + 2.01400i 0.369920 + 0.146111i
\(191\) 6.88645 0.498286 0.249143 0.968467i \(-0.419851\pi\)
0.249143 + 0.968467i \(0.419851\pi\)
\(192\) −7.02251 + 3.83202i −0.506806 + 0.276552i
\(193\) 16.4830i 1.18647i −0.805028 0.593237i \(-0.797850\pi\)
0.805028 0.593237i \(-0.202150\pi\)
\(194\) 11.4432 + 16.4830i 0.821576 + 1.18341i
\(195\) 5.44322 3.62701i 0.389797 0.259736i
\(196\) 4.50448 12.0735i 0.321749 0.862395i
\(197\) −13.5720 −0.966965 −0.483483 0.875354i \(-0.660628\pi\)
−0.483483 + 0.875354i \(0.660628\pi\)
\(198\) 4.32340 + 6.22751i 0.307251 + 0.442570i
\(199\) −9.05398 −0.641820 −0.320910 0.947110i \(-0.603989\pi\)
−0.320910 + 0.947110i \(0.603989\pi\)
\(200\) −13.9927 2.05031i −0.989435 0.144979i
\(201\) −7.44322 −0.525005
\(202\) −6.00000 8.64251i −0.422159 0.608085i
\(203\) −5.03605 −0.353462
\(204\) −4.00000 1.49235i −0.280056 0.104485i
\(205\) 21.0152 14.0032i 1.46777 0.978025i
\(206\) 5.80538 + 8.36217i 0.404480 + 0.582620i
\(207\) 7.49534i 0.520962i
\(208\) 8.84143 + 7.66404i 0.613043 + 0.531406i
\(209\) 9.29362 0.642853
\(210\) 2.19462 + 0.866833i 0.151443 + 0.0598171i
\(211\) 2.53566i 0.174562i 0.996184 + 0.0872809i \(0.0278178\pi\)
−0.996184 + 0.0872809i \(0.972182\pi\)
\(212\) 5.39821 14.4690i 0.370750 0.993736i
\(213\) 13.2936 0.910864
\(214\) −4.64681 + 3.22601i −0.317649 + 0.220526i
\(215\) −13.8504 + 9.22900i −0.944589 + 0.629413i
\(216\) −0.699104 2.74067i −0.0475680 0.186479i
\(217\) 1.97498i 0.134070i
\(218\) 16.0900 + 23.1764i 1.08975 + 1.56970i
\(219\) 0.690358i 0.0466501i
\(220\) −23.3386 + 5.48133i −1.57349 + 0.369551i
\(221\) 6.24430i 0.420037i
\(222\) −1.24860 + 0.866833i −0.0838006 + 0.0581780i
\(223\) 12.1579i 0.814152i 0.913394 + 0.407076i \(0.133452\pi\)
−0.913394 + 0.407076i \(0.866548\pi\)
\(224\) −0.452186 + 4.19671i −0.0302130 + 0.280405i
\(225\) 1.92520 4.61450i 0.128346 0.307633i
\(226\) 9.72161 + 14.0032i 0.646672 + 0.931478i
\(227\) 20.7368 1.37635 0.688176 0.725544i \(-0.258412\pi\)
0.688176 + 0.725544i \(0.258412\pi\)
\(228\) −3.24860 1.21201i −0.215144 0.0802674i
\(229\) 19.9504i 1.31836i −0.751987 0.659178i \(-0.770904\pi\)
0.751987 0.659178i \(-0.229096\pi\)
\(230\) −22.0450 8.70735i −1.45361 0.574146i
\(231\) 4.00000 0.263181
\(232\) −18.4972 + 4.71836i −1.21440 + 0.309776i
\(233\) 13.3386i 0.873844i −0.899499 0.436922i \(-0.856069\pi\)
0.899499 0.436922i \(-0.143931\pi\)
\(234\) −3.39821 + 2.35918i −0.222148 + 0.154225i
\(235\) 2.14961 + 3.22601i 0.140225 + 0.210442i
\(236\) −12.8414 4.79097i −0.835906 0.311866i
\(237\) −2.64681 −0.171929
\(238\) −1.85039 + 1.28462i −0.119943 + 0.0832697i
\(239\) −22.8864 −1.48040 −0.740201 0.672386i \(-0.765269\pi\)
−0.740201 + 0.672386i \(0.765269\pi\)
\(240\) 8.87290 + 1.12766i 0.572743 + 0.0727901i
\(241\) 3.59283 0.231435 0.115717 0.993282i \(-0.463083\pi\)
0.115717 + 0.993282i \(0.463083\pi\)
\(242\) −20.6049 + 14.3048i −1.32453 + 0.919549i
\(243\) 1.00000 0.0641500
\(244\) −12.0900 4.51064i −0.773985 0.288764i
\(245\) −11.9896 + 7.98908i −0.765987 + 0.510404i
\(246\) −13.1198 + 9.10834i −0.836489 + 0.580727i
\(247\) 5.07131i 0.322680i
\(248\) −1.85039 7.25402i −0.117500 0.460631i
\(249\) −5.85039 −0.370754
\(250\) 11.3355 + 11.0230i 0.716920 + 0.697155i
\(251\) 8.82801i 0.557219i −0.960404 0.278609i \(-0.910127\pi\)
0.960404 0.278609i \(-0.0898735\pi\)
\(252\) −1.39821 0.521653i −0.0880788 0.0328611i
\(253\) −40.1801 −2.52610
\(254\) 3.39821 + 4.89484i 0.213222 + 0.307129i
\(255\) 2.64681 + 3.97219i 0.165750 + 0.248748i
\(256\) 2.27111 + 15.8380i 0.141944 + 0.989875i
\(257\) 22.2927i 1.39058i 0.718728 + 0.695291i \(0.244725\pi\)
−0.718728 + 0.695291i \(0.755275\pi\)
\(258\) 8.64681 6.00299i 0.538327 0.373730i
\(259\) 0.801991i 0.0498333i
\(260\) −2.99104 12.7354i −0.185496 0.789813i
\(261\) 6.74916i 0.417763i
\(262\) 8.32340 + 11.9892i 0.514222 + 0.740694i
\(263\) 21.2014i 1.30733i −0.756783 0.653667i \(-0.773230\pi\)
0.756783 0.653667i \(-0.226770\pi\)
\(264\) 14.6918 3.74767i 0.904219 0.230653i
\(265\) −14.3684 + 9.57418i −0.882645 + 0.588137i
\(266\) −1.50280 + 1.04331i −0.0921424 + 0.0639693i
\(267\) −7.59283 −0.464674
\(268\) −5.20359 + 13.9474i −0.317860 + 0.851971i
\(269\) 14.6935i 0.895881i −0.894063 0.447940i \(-0.852158\pi\)
0.894063 0.447940i \(-0.147842\pi\)
\(270\) −1.16170 + 2.94116i −0.0706989 + 0.178994i
\(271\) −20.2396 −1.22947 −0.614735 0.788734i \(-0.710737\pi\)
−0.614735 + 0.788734i \(0.710737\pi\)
\(272\) −5.59283 + 6.45203i −0.339115 + 0.391212i
\(273\) 2.18271i 0.132103i
\(274\) −12.1288 17.4705i −0.732727 1.05543i
\(275\) 24.7368 + 10.3204i 1.49169 + 0.622341i
\(276\) 14.0450 + 5.24002i 0.845411 + 0.315412i
\(277\) 0.518027 0.0311252 0.0155626 0.999879i \(-0.495046\pi\)
0.0155626 + 0.999879i \(0.495046\pi\)
\(278\) 7.63785 + 11.0017i 0.458088 + 0.659837i
\(279\) 2.64681 0.158460
\(280\) 3.15857 3.50635i 0.188761 0.209545i
\(281\) 13.7008 0.817320 0.408660 0.912687i \(-0.365996\pi\)
0.408660 + 0.912687i \(0.365996\pi\)
\(282\) −1.39821 2.01400i −0.0832620 0.119932i
\(283\) 18.0305 1.07180 0.535900 0.844282i \(-0.319973\pi\)
0.535900 + 0.844282i \(0.319973\pi\)
\(284\) 9.29362 24.9100i 0.551475 1.47814i
\(285\) 2.14961 + 3.22601i 0.127332 + 0.191093i
\(286\) −12.6468 18.2167i −0.747821 1.07718i
\(287\) 8.42701i 0.497431i
\(288\) −5.62430 0.606006i −0.331415 0.0357092i
\(289\) 12.4432 0.731954
\(290\) 19.8504 + 7.84052i 1.16566 + 0.460411i
\(291\) 14.1887i 0.831755i
\(292\) −1.29362 0.482632i −0.0757032 0.0282439i
\(293\) 15.9792 0.933513 0.466757 0.884386i \(-0.345422\pi\)
0.466757 + 0.884386i \(0.345422\pi\)
\(294\) 7.48511 5.19648i 0.436540 0.303065i
\(295\) 8.49720 + 12.7521i 0.494726 + 0.742459i
\(296\) 0.751399 + 2.94568i 0.0436742 + 0.171214i
\(297\) 5.36068i 0.311058i
\(298\) −1.44322 2.07884i −0.0836037 0.120424i
\(299\) 21.9253i 1.26797i
\(300\) −7.30090 6.83351i −0.421517 0.394533i
\(301\) 5.55394i 0.320124i
\(302\) 12.3684 8.58669i 0.711723 0.494108i
\(303\) 7.43952i 0.427389i
\(304\) −4.54222 + 5.24002i −0.260514 + 0.300536i
\(305\) 8.00000 + 12.0060i 0.458079 + 0.687460i
\(306\) −1.72161 2.47984i −0.0984180 0.141763i
\(307\) −22.5872 −1.28912 −0.644561 0.764553i \(-0.722960\pi\)
−0.644561 + 0.764553i \(0.722960\pi\)
\(308\) 2.79641 7.49534i 0.159341 0.427086i
\(309\) 7.19820i 0.409492i
\(310\) −3.07480 + 7.78470i −0.174637 + 0.442141i
\(311\) −18.5872 −1.05399 −0.526993 0.849870i \(-0.676680\pi\)
−0.526993 + 0.849870i \(0.676680\pi\)
\(312\) 2.04502 + 8.01699i 0.115776 + 0.453873i
\(313\) 29.3871i 1.66106i −0.556977 0.830528i \(-0.688039\pi\)
0.556977 0.830528i \(-0.311961\pi\)
\(314\) 8.04502 5.58520i 0.454007 0.315191i
\(315\) 0.925197 + 1.38849i 0.0521289 + 0.0782323i
\(316\) −1.85039 + 4.95968i −0.104093 + 0.279004i
\(317\) −5.57201 −0.312955 −0.156478 0.987682i \(-0.550014\pi\)
−0.156478 + 0.987682i \(0.550014\pi\)
\(318\) 8.97021 6.22751i 0.503025 0.349221i
\(319\) 36.1801 2.02569
\(320\) 8.31613 15.8380i 0.464886 0.885371i
\(321\) −4.00000 −0.223258
\(322\) 6.49720 4.51064i 0.362075 0.251368i
\(323\) −3.70079 −0.205917
\(324\) 0.699104 1.87383i 0.0388391 0.104102i
\(325\) −5.63158 + 13.4983i −0.312384 + 0.748752i
\(326\) 8.94602 6.21071i 0.495474 0.343980i
\(327\) 19.9504i 1.10326i
\(328\) 7.89541 + 30.9520i 0.435951 + 1.70904i
\(329\) −1.29362 −0.0713194
\(330\) −15.7666 6.22751i −0.867924 0.342813i
\(331\) 13.7396i 0.755199i 0.925969 + 0.377599i \(0.123250\pi\)
−0.925969 + 0.377599i \(0.876750\pi\)
\(332\) −4.09003 + 10.9627i −0.224470 + 0.601655i
\(333\) −1.07480 −0.0588989
\(334\) 2.60179 + 3.74767i 0.142364 + 0.205063i
\(335\) 13.8504 9.22900i 0.756728 0.504234i
\(336\) −1.95498 + 2.25532i −0.106653 + 0.123038i
\(337\) 20.7523i 1.13045i −0.824936 0.565226i \(-0.808789\pi\)
0.824936 0.565226i \(-0.191211\pi\)
\(338\) −5.16170 + 3.58348i −0.280760 + 0.194915i
\(339\) 12.0540i 0.654685i
\(340\) 9.29362 2.18271i 0.504017 0.118374i
\(341\) 14.1887i 0.768360i
\(342\) −1.39821 2.01400i −0.0756064 0.108905i
\(343\) 10.0310i 0.541623i
\(344\) −5.20359 20.3994i −0.280559 1.09986i
\(345\) −9.29362 13.9474i −0.500352 0.750901i
\(346\) −7.46742 + 5.18420i −0.401451 + 0.278704i
\(347\) −4.73684 −0.254287 −0.127143 0.991884i \(-0.540581\pi\)
−0.127143 + 0.991884i \(0.540581\pi\)
\(348\) −12.6468 4.71836i −0.677940 0.252931i
\(349\) 0.482632i 0.0258347i −0.999917 0.0129174i \(-0.995888\pi\)
0.999917 0.0129174i \(-0.00411184\pi\)
\(350\) −5.15857 + 1.10815i −0.275737 + 0.0592330i
\(351\) −2.92520 −0.156135
\(352\) 3.24860 30.1500i 0.173151 1.60700i
\(353\) 2.13466i 0.113617i −0.998385 0.0568083i \(-0.981908\pi\)
0.998385 0.0568083i \(-0.0180924\pi\)
\(354\) −5.52699 7.96117i −0.293756 0.423132i
\(355\) −24.7368 + 16.4830i −1.31290 + 0.874828i
\(356\) −5.30818 + 14.2277i −0.281333 + 0.754067i
\(357\) −1.59283 −0.0843015
\(358\) −6.56304 9.45352i −0.346868 0.499634i
\(359\) 9.59283 0.506290 0.253145 0.967428i \(-0.418535\pi\)
0.253145 + 0.967428i \(0.418535\pi\)
\(360\) 4.69910 + 4.23302i 0.247665 + 0.223100i
\(361\) 15.9944 0.841811
\(362\) −1.20359 1.73367i −0.0632590 0.0911194i
\(363\) −17.7368 −0.930943
\(364\) 4.09003 + 1.52594i 0.214376 + 0.0799809i
\(365\) 0.855989 + 1.28462i 0.0448045 + 0.0672402i
\(366\) −5.20359 7.49534i −0.271996 0.391787i
\(367\) 34.0832i 1.77913i −0.456809 0.889565i \(-0.651008\pi\)
0.456809 0.889565i \(-0.348992\pi\)
\(368\) 19.6378 22.6547i 1.02369 1.18096i
\(369\) −11.2936 −0.587922
\(370\) 1.24860 3.16117i 0.0649117 0.164342i
\(371\) 5.76167i 0.299131i
\(372\) 1.85039 4.95968i 0.0959384 0.257147i
\(373\) 4.33796 0.224611 0.112306 0.993674i \(-0.464176\pi\)
0.112306 + 0.993674i \(0.464176\pi\)
\(374\) 13.2936 9.22900i 0.687397 0.477220i
\(375\) 2.13919 + 10.9738i 0.110468 + 0.566684i
\(376\) −4.75140 + 1.21201i −0.245035 + 0.0625047i
\(377\) 19.7426i 1.01680i
\(378\) −0.601793 0.866833i −0.0309529 0.0445851i
\(379\) 6.90107i 0.354484i 0.984167 + 0.177242i \(0.0567176\pi\)
−0.984167 + 0.177242i \(0.943282\pi\)
\(380\) 7.54781 1.77269i 0.387195 0.0909369i
\(381\) 4.21351i 0.215864i
\(382\) 8.00000 5.55394i 0.409316 0.284165i
\(383\) 22.3744i 1.14328i 0.820506 + 0.571639i \(0.193692\pi\)
−0.820506 + 0.571639i \(0.806308\pi\)
\(384\) −5.06752 + 10.1153i −0.258601 + 0.516197i
\(385\) −7.44322 + 4.95968i −0.379342 + 0.252769i
\(386\) −13.2936 19.1484i −0.676627 0.974626i
\(387\) 7.44322 0.378360
\(388\) 26.5872 + 9.91936i 1.34976 + 0.503579i
\(389\) 11.0185i 0.558659i 0.960195 + 0.279330i \(0.0901122\pi\)
−0.960195 + 0.279330i \(0.909888\pi\)
\(390\) 3.39821 8.60348i 0.172075 0.435654i
\(391\) 16.0000 0.809155
\(392\) −4.50448 17.6587i −0.227511 0.891900i
\(393\) 10.3204i 0.520593i
\(394\) −15.7666 + 10.9459i −0.794311 + 0.551445i
\(395\) 4.92520 3.28183i 0.247814 0.165127i
\(396\) 10.0450 + 3.74767i 0.504781 + 0.188327i
\(397\) 25.2549 1.26751 0.633753 0.773536i \(-0.281514\pi\)
0.633753 + 0.773536i \(0.281514\pi\)
\(398\) −10.5180 + 7.30207i −0.527221 + 0.366020i
\(399\) −1.29362 −0.0647619
\(400\) −17.9090 + 8.90333i −0.895448 + 0.445167i
\(401\) 7.29362 0.364226 0.182113 0.983278i \(-0.441706\pi\)
0.182113 + 0.983278i \(0.441706\pi\)
\(402\) −8.64681 + 6.00299i −0.431264 + 0.299402i
\(403\) −7.74244 −0.385678
\(404\) −13.9404 5.20100i −0.693562 0.258759i
\(405\) −1.86081 + 1.23992i −0.0924642 + 0.0616121i
\(406\) −5.85039 + 4.06160i −0.290350 + 0.201574i
\(407\) 5.76167i 0.285595i
\(408\) −5.85039 + 1.49235i −0.289638 + 0.0738823i
\(409\) −15.8504 −0.783752 −0.391876 0.920018i \(-0.628174\pi\)
−0.391876 + 0.920018i \(0.628174\pi\)
\(410\) 13.1198 33.2164i 0.647942 1.64044i
\(411\) 15.0387i 0.741805i
\(412\) 13.4882 + 5.03229i 0.664518 + 0.247923i
\(413\) −5.11355 −0.251622
\(414\) 6.04502 + 8.70735i 0.297096 + 0.427943i
\(415\) 10.8864 7.25402i 0.534395 0.356086i
\(416\) 16.4522 + 1.77269i 0.806635 + 0.0869131i
\(417\) 9.47032i 0.463763i
\(418\) 10.7964 7.49534i 0.528070 0.366609i
\(419\) 8.02602i 0.392097i 0.980594 + 0.196048i \(0.0628109\pi\)
−0.980594 + 0.196048i \(0.937189\pi\)
\(420\) 3.24860 0.762970i 0.158516 0.0372291i
\(421\) 22.9351i 1.11779i 0.829240 + 0.558893i \(0.188774\pi\)
−0.829240 + 0.558893i \(0.811226\pi\)
\(422\) 2.04502 + 2.94568i 0.0995498 + 0.143393i
\(423\) 1.73367i 0.0842937i
\(424\) −5.39821 21.1624i −0.262160 1.02774i
\(425\) −9.85039 4.10964i −0.477814 0.199347i
\(426\) 15.4432 10.7214i 0.748227 0.519451i
\(427\) −4.81434 −0.232982
\(428\) −2.79641 + 7.49534i −0.135170 + 0.362301i
\(429\) 15.6810i 0.757087i
\(430\) −8.64681 + 21.8917i −0.416986 + 1.05571i
\(431\) −35.0665 −1.68909 −0.844547 0.535481i \(-0.820130\pi\)
−0.844547 + 0.535481i \(0.820130\pi\)
\(432\) −3.02251 2.62001i −0.145420 0.126055i
\(433\) 17.0773i 0.820682i 0.911932 + 0.410341i \(0.134590\pi\)
−0.911932 + 0.410341i \(0.865410\pi\)
\(434\) −1.59283 2.29434i −0.0764583 0.110132i
\(435\) 8.36842 + 12.5589i 0.401235 + 0.602152i
\(436\) 37.3836 + 13.9474i 1.79035 + 0.667958i
\(437\) 12.9944 0.621607
\(438\) −0.556777 0.801991i −0.0266038 0.0383206i
\(439\) −8.53885 −0.407537 −0.203769 0.979019i \(-0.565319\pi\)
−0.203769 + 0.979019i \(0.565319\pi\)
\(440\) −22.6918 + 25.1904i −1.08179 + 1.20090i
\(441\) 6.44322 0.306820
\(442\) 5.03605 + 7.25402i 0.239541 + 0.345039i
\(443\) −20.7368 −0.985237 −0.492619 0.870245i \(-0.663960\pi\)
−0.492619 + 0.870245i \(0.663960\pi\)
\(444\) −0.751399 + 2.01400i −0.0356598 + 0.0955803i
\(445\) 14.1288 9.41450i 0.669769 0.446290i
\(446\) 9.80538 + 14.1238i 0.464298 + 0.668783i
\(447\) 1.78948i 0.0846396i
\(448\) 2.85936 + 5.24002i 0.135092 + 0.247568i
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) −1.48511 6.91335i −0.0700086 0.325899i
\(451\) 60.5414i 2.85078i
\(452\) 22.5872 + 8.42701i 1.06241 + 0.396373i
\(453\) 10.6468 0.500231
\(454\) 24.0900 16.7243i 1.13060 0.784912i
\(455\) −2.70638 4.06160i −0.126877 0.190411i
\(456\) −4.75140 + 1.21201i −0.222505 + 0.0567577i
\(457\) 1.28462i 0.0600921i −0.999549 0.0300461i \(-0.990435\pi\)
0.999549 0.0300461i \(-0.00956540\pi\)
\(458\) −16.0900 23.1764i −0.751838 1.08296i
\(459\) 2.13466i 0.0996374i
\(460\) −32.6323 + 7.66404i −1.52149 + 0.357338i
\(461\) 15.7033i 0.731374i 0.930738 + 0.365687i \(0.119166\pi\)
−0.930738 + 0.365687i \(0.880834\pi\)
\(462\) 4.64681 3.22601i 0.216189 0.150088i
\(463\) 18.7215i 0.870064i 0.900415 + 0.435032i \(0.143263\pi\)
−0.900415 + 0.435032i \(0.856737\pi\)
\(464\) −17.6829 + 20.3994i −0.820906 + 0.947018i
\(465\) −4.92520 + 3.28183i −0.228401 + 0.152191i
\(466\) −10.7577 15.4955i −0.498339 0.717817i
\(467\) −2.14961 −0.0994719 −0.0497360 0.998762i \(-0.515838\pi\)
−0.0497360 + 0.998762i \(0.515838\pi\)
\(468\) −2.04502 + 5.48133i −0.0945309 + 0.253375i
\(469\) 5.55394i 0.256457i
\(470\) 5.09899 + 2.01400i 0.235199 + 0.0928990i
\(471\) 6.92520 0.319096
\(472\) −18.7819 + 4.79097i −0.864505 + 0.220522i
\(473\) 39.9007i 1.83464i
\(474\) −3.07480 + 2.13466i −0.141230 + 0.0980482i
\(475\) −8.00000 3.33765i −0.367065 0.153142i
\(476\) −1.11355 + 2.98470i −0.0510396 + 0.136803i
\(477\) 7.72161 0.353548
\(478\) −26.5872 + 18.4580i −1.21607 + 0.844249i
\(479\) 12.1801 0.556521 0.278261 0.960506i \(-0.410242\pi\)
0.278261 + 0.960506i \(0.410242\pi\)
\(480\) 11.2171 5.84602i 0.511990 0.266833i
\(481\) 3.14401 0.143355
\(482\) 4.17380 2.89763i 0.190111 0.131983i
\(483\) 5.59283 0.254483
\(484\) −12.3999 + 33.2359i −0.563631 + 1.51072i
\(485\) −17.5928 26.4024i −0.798849 1.19887i
\(486\) 1.16170 0.806504i 0.0526959 0.0365837i
\(487\) 25.7678i 1.16765i −0.811879 0.583826i \(-0.801555\pi\)
0.811879 0.583826i \(-0.198445\pi\)
\(488\) −17.6829 + 4.51064i −0.800466 + 0.204187i
\(489\) 7.70079 0.348242
\(490\) −7.48511 + 18.9506i −0.338143 + 0.856100i
\(491\) 16.7724i 0.756927i −0.925616 0.378464i \(-0.876453\pi\)
0.925616 0.378464i \(-0.123547\pi\)
\(492\) −7.89541 + 21.1624i −0.355953 + 0.954073i
\(493\) −14.4072 −0.648866
\(494\) 4.09003 + 5.89135i 0.184019 + 0.265065i
\(495\) −6.64681 9.97518i −0.298752 0.448351i
\(496\) −8.00000 6.93466i −0.359211 0.311375i
\(497\) 9.91936i 0.444944i
\(498\) −6.79641 + 4.71836i −0.304555 + 0.211435i
\(499\) 17.6224i 0.788888i −0.918920 0.394444i \(-0.870937\pi\)
0.918920 0.394444i \(-0.129063\pi\)
\(500\) 22.0586 + 3.66332i 0.986489 + 0.163828i
\(501\) 3.22601i 0.144128i
\(502\) −7.11982 10.2555i −0.317773 0.457726i
\(503\) 27.1263i 1.20950i −0.796414 0.604752i \(-0.793272\pi\)
0.796414 0.604752i \(-0.206728\pi\)
\(504\) −2.04502 + 0.521653i −0.0910923 + 0.0232363i
\(505\) 9.22441 + 13.8435i 0.410481 + 0.616028i
\(506\) −46.6773 + 32.4054i −2.07506 + 1.44059i
\(507\) −4.44322 −0.197330
\(508\) 7.89541 + 2.94568i 0.350302 + 0.130693i
\(509\) 15.9782i 0.708220i 0.935204 + 0.354110i \(0.115216\pi\)
−0.935204 + 0.354110i \(0.884784\pi\)
\(510\) 6.27839 + 2.47984i 0.278012 + 0.109809i
\(511\) −0.515128 −0.0227879
\(512\) 15.4118 + 16.5674i 0.681110 + 0.732181i
\(513\) 1.73367i 0.0765432i
\(514\) 17.9792 + 25.8975i 0.793027 + 1.14229i
\(515\) −8.92520 13.3945i −0.393291 0.590230i
\(516\) 5.20359 13.9474i 0.229075 0.613999i
\(517\) 9.29362 0.408733
\(518\) 0.646809 + 0.931674i 0.0284191 + 0.0409354i
\(519\) −6.42799 −0.282158
\(520\) −13.7458 12.3824i −0.602793 0.543004i
\(521\) 0.886447 0.0388359 0.0194180 0.999811i \(-0.493819\pi\)
0.0194180 + 0.999811i \(0.493819\pi\)
\(522\) −5.44322 7.84052i −0.238243 0.343170i
\(523\) 41.7729 1.82660 0.913301 0.407286i \(-0.133525\pi\)
0.913301 + 0.407286i \(0.133525\pi\)
\(524\) 19.3386 + 7.21500i 0.844812 + 0.315189i
\(525\) −3.44322 1.43653i −0.150275 0.0626954i
\(526\) −17.0990 24.6297i −0.745552 1.07391i
\(527\) 5.65004i 0.246120i
\(528\) 14.0450 16.2027i 0.611231 0.705131i
\(529\) −33.1801 −1.44261
\(530\) −8.97021 + 22.7105i −0.389641 + 0.986482i
\(531\) 6.85302i 0.297396i
\(532\) −0.904373 + 2.42402i −0.0392095 + 0.105095i
\(533\) 33.0361 1.43095
\(534\) −8.82061 + 6.12364i −0.381705 + 0.264996i
\(535\) 7.44322 4.95968i 0.321799 0.214426i
\(536\) 5.20359 + 20.3994i 0.224761 + 0.881120i
\(537\) 8.13765i 0.351165i
\(538\) −11.8504 17.0695i −0.510907 0.735919i
\(539\) 34.5400i 1.48774i
\(540\) 1.02251 + 4.35367i 0.0440017 + 0.187352i
\(541\) 4.47705i 0.192483i −0.995358 0.0962417i \(-0.969318\pi\)
0.995358 0.0962417i \(-0.0306822\pi\)
\(542\) −23.5124 + 16.3233i −1.00995 + 0.701148i
\(543\) 1.49235i 0.0640428i
\(544\) −1.29362 + 12.0060i −0.0554634 + 0.514752i
\(545\) −24.7368 37.1237i −1.05961 1.59021i
\(546\) 1.76036 + 2.53566i 0.0753365 + 0.108516i
\(547\) −14.3297 −0.612692 −0.306346 0.951920i \(-0.599107\pi\)
−0.306346 + 0.951920i \(0.599107\pi\)
\(548\) −28.1801 10.5136i −1.20379 0.449120i
\(549\) 6.45203i 0.275366i
\(550\) 37.0602 7.96117i 1.58025 0.339466i
\(551\) −11.7008 −0.498470
\(552\) 20.5422 5.24002i 0.874335 0.223030i
\(553\) 1.97498i 0.0839848i
\(554\) 0.601793 0.417790i 0.0255677 0.0177502i
\(555\) 2.00000 1.33267i 0.0848953 0.0565687i
\(556\) 17.7458 + 6.62073i 0.752590 + 0.280782i
\(557\) 2.68556 0.113791 0.0568954 0.998380i \(-0.481880\pi\)
0.0568954 + 0.998380i \(0.481880\pi\)
\(558\) 3.07480 2.13466i 0.130167 0.0903674i
\(559\) −21.7729 −0.920895
\(560\) 0.841431 6.62073i 0.0355569 0.279777i
\(561\) 11.4432 0.483133
\(562\) 15.9162 11.0497i 0.671386 0.466105i
\(563\) 20.7368 0.873954 0.436977 0.899473i \(-0.356049\pi\)
0.436977 + 0.899473i \(0.356049\pi\)
\(564\) −3.24860 1.21201i −0.136791 0.0510349i
\(565\) −14.9460 22.4302i −0.628784 0.943645i
\(566\) 20.9460 14.5416i 0.880427 0.611230i
\(567\) 0.746175i 0.0313364i
\(568\) −9.29362 36.4334i −0.389952 1.52871i
\(569\) −4.40717 −0.184758 −0.0923791 0.995724i \(-0.529447\pi\)
−0.0923791 + 0.995724i \(0.529447\pi\)
\(570\) 5.09899 + 2.01400i 0.213573 + 0.0843573i
\(571\) 23.6590i 0.990098i 0.868865 + 0.495049i \(0.164850\pi\)
−0.868865 + 0.495049i \(0.835150\pi\)
\(572\) −29.3836 10.9627i −1.22859 0.458372i
\(573\) 6.88645 0.287685
\(574\) 6.79641 + 9.78968i 0.283677 + 0.408613i
\(575\) 34.5872 + 14.4300i 1.44239 + 0.601772i
\(576\) −7.02251 + 3.83202i −0.292604 + 0.159668i
\(577\) 6.56366i 0.273249i 0.990623 + 0.136624i \(0.0436253\pi\)
−0.990623 + 0.136624i \(0.956375\pi\)
\(578\) 14.4553 10.0355i 0.601262 0.417422i
\(579\) 16.4830i 0.685011i
\(580\) 29.3836 6.90107i 1.22009 0.286551i
\(581\) 4.36542i 0.181108i
\(582\) 11.4432 + 16.4830i 0.474337 + 0.683243i
\(583\) 41.3931i 1.71433i
\(584\) −1.89204 + 0.482632i −0.0782933 + 0.0199715i
\(585\) 5.44322 3.62701i 0.225050 0.149958i
\(586\) 18.5630 12.8873i 0.766832 0.532368i
\(587\) −16.2992 −0.672741 −0.336370 0.941730i \(-0.609199\pi\)
−0.336370 + 0.941730i \(0.609199\pi\)
\(588\) 4.50448 12.0735i 0.185762 0.497904i
\(589\) 4.58868i 0.189073i
\(590\) 20.1559 + 7.96117i 0.829804 + 0.327756i
\(591\) −13.5720 −0.558278
\(592\) 3.24860 + 2.81599i 0.133517 + 0.115737i
\(593\) 16.3233i 0.670319i −0.942161 0.335160i \(-0.891210\pi\)
0.942161 0.335160i \(-0.108790\pi\)
\(594\) 4.32340 + 6.22751i 0.177391 + 0.255518i
\(595\) 2.96395 1.97498i 0.121510 0.0809663i
\(596\) −3.35319 1.25103i −0.137352 0.0512443i
\(597\) −9.05398 −0.370555
\(598\) −17.6829 25.4707i −0.723106 1.04157i
\(599\) 25.5928 1.04569 0.522847 0.852426i \(-0.324870\pi\)
0.522847 + 0.852426i \(0.324870\pi\)
\(600\) −13.9927 2.05031i −0.571250 0.0837035i
\(601\) 29.9225 1.22056 0.610282 0.792184i \(-0.291056\pi\)
0.610282 + 0.792184i \(0.291056\pi\)
\(602\) −4.47928 6.45203i −0.182562 0.262965i
\(603\) −7.44322 −0.303111
\(604\) 7.44322 19.9504i 0.302860 0.811768i
\(605\) 33.0048 21.9923i 1.34184 0.894113i
\(606\) −6.00000 8.64251i −0.243733 0.351078i
\(607\) 20.6965i 0.840046i 0.907513 + 0.420023i \(0.137978\pi\)
−0.907513 + 0.420023i \(0.862022\pi\)
\(608\) −1.05061 + 9.75065i −0.0426079 + 0.395441i
\(609\) −5.03605 −0.204071
\(610\) 18.9765 + 7.49534i 0.768335 + 0.303477i
\(611\) 5.07131i 0.205163i
\(612\) −4.00000 1.49235i −0.161690 0.0603246i
\(613\) 22.6676 0.915537 0.457769 0.889071i \(-0.348649\pi\)
0.457769 + 0.889071i \(0.348649\pi\)
\(614\) −26.2396 + 18.2167i −1.05895 + 0.735166i
\(615\) 21.0152 14.0032i 0.847416 0.564663i
\(616\) −2.79641 10.9627i −0.112671 0.441698i
\(617\) 22.1966i 0.893603i −0.894633 0.446802i \(-0.852563\pi\)
0.894633 0.446802i \(-0.147437\pi\)
\(618\) 5.80538 + 8.36217i 0.233527 + 0.336376i
\(619\) 16.8204i 0.676070i 0.941133 + 0.338035i \(0.109762\pi\)
−0.941133 + 0.338035i \(0.890238\pi\)
\(620\) 2.70638 + 11.5233i 0.108691 + 0.462789i
\(621\) 7.49534i 0.300777i
\(622\) −21.5928 + 14.9907i −0.865794 + 0.601071i
\(623\) 5.66558i 0.226987i
\(624\) 8.84143 + 7.66404i 0.353940 + 0.306807i
\(625\) −17.5872 17.7676i −0.703489 0.710706i
\(626\) −23.7008 34.1390i −0.947274 1.36447i
\(627\) 9.29362 0.371151
\(628\) 4.84143 12.9767i 0.193194 0.517825i
\(629\) 2.29434i 0.0914813i
\(630\) 2.19462 + 0.866833i 0.0874358 + 0.0345354i
\(631\) −44.1205 −1.75641 −0.878204 0.478285i \(-0.841258\pi\)
−0.878204 + 0.478285i \(0.841258\pi\)
\(632\) 1.85039 + 7.25402i 0.0736047 + 0.288549i
\(633\) 2.53566i 0.100783i
\(634\) −6.47301 + 4.49384i −0.257076 + 0.178473i
\(635\) −5.22441 7.84052i −0.207324 0.311141i
\(636\) 5.39821 14.4690i 0.214053 0.573734i
\(637\) −18.8477 −0.746773
\(638\) 42.0305 29.1794i 1.66400 1.15522i
\(639\) 13.2936 0.525887
\(640\) −3.11254 25.1060i −0.123034 0.992402i
\(641\) −1.18566 −0.0468307 −0.0234154 0.999726i \(-0.507454\pi\)
−0.0234154 + 0.999726i \(0.507454\pi\)
\(642\) −4.64681 + 3.22601i −0.183395 + 0.127321i
\(643\) −22.5872 −0.890754 −0.445377 0.895343i \(-0.646930\pi\)
−0.445377 + 0.895343i \(0.646930\pi\)
\(644\) 3.90997 10.4800i 0.154074 0.412971i
\(645\) −13.8504 + 9.22900i −0.545359 + 0.363392i
\(646\) −4.29921 + 2.98470i −0.169150 + 0.117431i
\(647\) 19.7090i 0.774842i 0.921903 + 0.387421i \(0.126634\pi\)
−0.921903 + 0.387421i \(0.873366\pi\)
\(648\) −0.699104 2.74067i −0.0274634 0.107664i
\(649\) 36.7368 1.44205
\(650\) 4.34423 + 20.2229i 0.170395 + 0.793208i
\(651\) 1.97498i 0.0774056i
\(652\) 5.38365 14.4300i 0.210840 0.565122i
\(653\) −44.4585 −1.73979 −0.869897 0.493234i \(-0.835815\pi\)
−0.869897 + 0.493234i \(0.835815\pi\)
\(654\) 16.0900 + 23.1764i 0.629170 + 0.906268i
\(655\) −12.7964 19.2042i −0.499997 0.750369i
\(656\) 34.1350 + 29.5894i 1.33275 + 1.15527i
\(657\) 0.690358i 0.0269334i
\(658\) −1.50280 + 1.04331i −0.0585852 + 0.0406723i
\(659\) 41.5863i 1.61997i 0.586448 + 0.809987i \(0.300526\pi\)
−0.586448 + 0.809987i \(0.699474\pi\)
\(660\) −23.3386 + 5.48133i −0.908455 + 0.213361i
\(661\) 12.0060i 0.466978i −0.972359 0.233489i \(-0.924986\pi\)
0.972359 0.233489i \(-0.0750143\pi\)
\(662\) 11.0811 + 15.9614i 0.430678 + 0.620356i
\(663\) 6.24430i 0.242509i
\(664\) 4.09003 + 16.0340i 0.158724 + 0.622239i
\(665\) 2.40717 1.60398i 0.0933461 0.0621997i
\(666\) −1.24860 + 0.866833i −0.0483823 + 0.0335891i
\(667\) 50.5872 1.95875
\(668\) 6.04502 + 2.25532i 0.233889 + 0.0872609i
\(669\) 12.1579i 0.470051i
\(670\) 8.64681 21.8917i 0.334055 0.845752i
\(671\) 34.5872 1.33523
\(672\) −0.452186 + 4.19671i −0.0174435 + 0.161892i
\(673\) 14.5080i 0.559244i 0.960110 + 0.279622i \(0.0902091\pi\)
−0.960110 + 0.279622i \(0.909791\pi\)
\(674\) −16.7368 24.1080i −0.644679 0.928607i
\(675\) 1.92520 4.61450i 0.0741009 0.177612i
\(676\) −3.10627 + 8.32586i −0.119472 + 0.320226i
\(677\) −43.8600 −1.68568 −0.842839 0.538166i \(-0.819117\pi\)
−0.842839 + 0.538166i \(0.819117\pi\)
\(678\) 9.72161 + 14.0032i 0.373356 + 0.537789i
\(679\) 10.5872 0.406301
\(680\) 9.03605 10.0310i 0.346517 0.384671i
\(681\) 20.7368 0.794637
\(682\) 11.4432 + 16.4830i 0.438184 + 0.631168i
\(683\) 5.33527 0.204148 0.102074 0.994777i \(-0.467452\pi\)
0.102074 + 0.994777i \(0.467452\pi\)
\(684\) −3.24860 1.21201i −0.124213 0.0463424i
\(685\) 18.6468 + 27.9841i 0.712458 + 1.06922i
\(686\) −8.09003 11.6530i −0.308879 0.444915i
\(687\) 19.9504i 0.761153i
\(688\) −22.4972 19.5013i −0.857698 0.743480i
\(689\) −22.5872 −0.860505
\(690\) −22.0450 8.70735i −0.839239 0.331483i
\(691\) 39.7710i 1.51296i 0.654016 + 0.756480i \(0.273083\pi\)
−0.654016 + 0.756480i \(0.726917\pi\)
\(692\) −4.49383 + 12.0450i −0.170830 + 0.457882i
\(693\) 4.00000 0.151947
\(694\) −5.50280 + 3.82028i −0.208883 + 0.145016i
\(695\) −11.7424 17.6224i −0.445416 0.668457i
\(696\) −18.4972 + 4.71836i −0.701135 + 0.178849i
\(697\) 24.1080i 0.913157i
\(698\) −0.389245 0.560675i −0.0147331 0.0212219i
\(699\) 13.3386i 0.504514i
\(700\) −5.09899 + 5.44774i −0.192724 + 0.205905i
\(701\) 27.5015i 1.03872i −0.854556 0.519359i \(-0.826171\pi\)
0.854556 0.519359i \(-0.173829\pi\)
\(702\) −3.39821 + 2.35918i −0.128257 + 0.0890416i
\(703\) 1.86335i 0.0702775i
\(704\) −20.5422 37.6454i −0.774214 1.41881i
\(705\) 2.14961 + 3.22601i 0.0809589 + 0.121499i
\(706\) −1.72161 2.47984i −0.0647937 0.0933300i
\(707\) −5.55118 −0.208774
\(708\) −12.8414 4.79097i −0.482611 0.180056i
\(709\) 0.111632i 0.00419244i −0.999998 0.00209622i \(-0.999333\pi\)
0.999998 0.00209622i \(-0.000667249\pi\)
\(710\) −15.4432 + 39.0987i −0.579574 + 1.46735i
\(711\) −2.64681 −0.0992631
\(712\) 5.30818 + 20.8094i 0.198932 + 0.779866i
\(713\) 19.8387i 0.742966i
\(714\) −1.85039 + 1.28462i −0.0692492 + 0.0480758i
\(715\) 19.4432 + 29.1794i 0.727135 + 1.09125i
\(716\) −15.2486 5.68906i −0.569867 0.212610i
\(717\) −22.8864 −0.854710
\(718\) 11.1440 7.73665i 0.415891 0.288729i
\(719\) −10.7064 −0.399281 −0.199640 0.979869i \(-0.563977\pi\)
−0.199640 + 0.979869i \(0.563977\pi\)
\(720\) 8.87290 + 1.12766i 0.330674 + 0.0420254i
\(721\) 5.37112 0.200031
\(722\) 18.5807 12.8995i 0.691503 0.480071i
\(723\) 3.59283 0.133619
\(724\) −2.79641 1.04331i −0.103928 0.0387742i
\(725\) −31.1440 12.9935i −1.15666 0.482565i
\(726\) −20.6049 + 14.3048i −0.764721 + 0.530902i
\(727\) 25.6562i 0.951536i 0.879571 + 0.475768i \(0.157830\pi\)
−0.879571 + 0.475768i \(0.842170\pi\)
\(728\) 5.98207 1.52594i 0.221710 0.0565551i
\(729\) 1.00000 0.0370370
\(730\) 2.03046 + 0.801991i 0.0751506 + 0.0296830i
\(731\) 15.8888i 0.587667i
\(732\) −12.0900 4.51064i −0.446860 0.166718i
\(733\) −30.3684 −1.12168 −0.560842 0.827923i \(-0.689522\pi\)
−0.560842 + 0.827923i \(0.689522\pi\)
\(734\) −27.4882 39.5945i −1.01461 1.46146i
\(735\) −11.9896 + 7.98908i −0.442243 + 0.294682i
\(736\) 4.54222 42.1560i 0.167428 1.55389i
\(737\) 39.9007i 1.46976i
\(738\) −13.1198 + 9.10834i −0.482947 + 0.335283i
\(739\) 20.1917i 0.742763i −0.928480 0.371381i \(-0.878884\pi\)
0.928480 0.371381i \(-0.121116\pi\)
\(740\) −1.09899 4.67934i −0.0403999 0.172016i
\(741\) 5.07131i 0.186299i
\(742\) −4.64681 6.69335i −0.170590 0.245720i
\(743\) 46.3863i 1.70175i 0.525369 + 0.850875i \(0.323927\pi\)
−0.525369 + 0.850875i \(0.676073\pi\)
\(744\) −1.85039 7.25402i −0.0678387 0.265945i
\(745\) 2.21881 + 3.32988i 0.0812911 + 0.121997i
\(746\) 5.03942 3.49858i 0.184506 0.128092i
\(747\) −5.85039 −0.214055
\(748\) 8.00000 21.4427i 0.292509 0.784023i
\(749\) 2.98470i 0.109059i
\(750\) 11.3355 + 11.0230i 0.413914 + 0.402503i
\(751\) −27.1261 −0.989845 −0.494922 0.868937i \(-0.664804\pi\)
−0.494922 + 0.868937i \(0.664804\pi\)
\(752\) −4.54222 + 5.24002i −0.165638 + 0.191084i
\(753\) 8.82801i 0.321710i
\(754\) 15.9225 + 22.9351i 0.579863 + 0.835245i
\(755\) −19.8116 + 13.2012i −0.721020 + 0.480441i
\(756\) −1.39821 0.521653i −0.0508523 0.0189724i
\(757\) −45.2549 −1.64482 −0.822408 0.568898i \(-0.807370\pi\)
−0.822408 + 0.568898i \(0.807370\pi\)
\(758\) 5.56574 + 8.01699i 0.202157 + 0.291190i
\(759\) −40.1801 −1.45844
\(760\) 7.33863 8.14667i 0.266200 0.295511i
\(761\) 16.8864 0.612133 0.306067 0.952010i \(-0.400987\pi\)
0.306067 + 0.952010i \(0.400987\pi\)
\(762\) 3.39821 + 4.89484i 0.123104 + 0.177321i
\(763\) 14.8864 0.538926
\(764\) 4.81434 12.9041i 0.174177 0.466852i
\(765\) 2.64681 + 3.97219i 0.0956956 + 0.143615i
\(766\) 18.0450 + 25.9924i 0.651993 + 0.939142i
\(767\) 20.0464i 0.723835i
\(768\) 2.27111 + 15.8380i 0.0819516 + 0.571504i
\(769\) −16.3297 −0.588863 −0.294431 0.955673i \(-0.595130\pi\)
−0.294431 + 0.955673i \(0.595130\pi\)
\(770\) −4.64681 + 11.7647i −0.167459 + 0.423969i
\(771\) 22.2927i 0.802853i
\(772\) −30.8864 11.5233i −1.11163 0.414734i
\(773\) 41.3144 1.48598 0.742989 0.669304i \(-0.233408\pi\)
0.742989 + 0.669304i \(0.233408\pi\)
\(774\) 8.64681 6.00299i 0.310803 0.215773i
\(775\) 5.09563 12.2137i 0.183040 0.438729i
\(776\) 38.8864 9.91936i 1.39594 0.356084i
\(777\) 0.801991i 0.0287713i
\(778\) 8.88645 + 12.8002i 0.318595 + 0.458909i
\(779\) 19.5794i 0.701503i
\(780\) −2.99104 12.7354i −0.107096 0.455999i
\(781\) 71.2628i 2.54998i
\(782\) 18.5872 12.9041i 0.664678 0.461448i
\(783\) 6.74916i 0.241195i