Properties

Label 950.2.u.g.149.1
Level $950$
Weight $2$
Character 950.149
Analytic conductor $7.586$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.u (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 149.1
Character \(\chi\) \(=\) 950.149
Dual form 950.2.u.g.899.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.642788 + 0.766044i) q^{2} +(-0.613893 - 1.68666i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.68666 + 0.613893i) q^{6} +(-1.17907 + 0.680736i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.169813 + 0.142490i) q^{9} +O(q^{10})\) \(q+(-0.642788 + 0.766044i) q^{2} +(-0.613893 - 1.68666i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.68666 + 0.613893i) q^{6} +(-1.17907 + 0.680736i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.169813 + 0.142490i) q^{9} +(-3.22960 + 5.59384i) q^{11} +(-1.55443 + 0.897451i) q^{12} +(2.01005 - 5.52256i) q^{13} +(0.236417 - 1.34079i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-1.64480 + 1.96020i) q^{17} -0.221676i q^{18} +(3.83851 + 2.06538i) q^{19} +(1.87199 + 1.57079i) q^{21} +(-2.20918 - 6.06967i) q^{22} +(-8.29626 + 1.46285i) q^{23} +(0.311682 - 1.76763i) q^{24} +(2.93849 + 5.08962i) q^{26} +(-4.31871 - 2.49341i) q^{27} +(0.875137 + 1.04295i) q^{28} +(-3.41558 + 2.86601i) q^{29} +(0.701264 + 1.21462i) q^{31} +(0.342020 - 0.939693i) q^{32} +(11.4175 + 2.01322i) q^{33} +(-0.444341 - 2.51998i) q^{34} +(0.169813 + 0.142490i) q^{36} +4.42962i q^{37} +(-4.04953 + 1.61287i) q^{38} -10.5486 q^{39} +(5.15407 - 1.87593i) q^{41} +(-2.40658 + 0.424346i) q^{42} +(6.74986 + 1.19018i) q^{43} +(6.06967 + 2.20918i) q^{44} +(4.21212 - 7.29560i) q^{46} +(6.11821 + 7.29140i) q^{47} +(1.15374 + 1.37498i) q^{48} +(-2.57320 + 4.45691i) q^{49} +(4.31591 + 1.57086i) q^{51} +(-5.78770 - 1.02053i) q^{52} +(-4.35841 + 0.768506i) q^{53} +(4.68608 - 1.70559i) q^{54} -1.36147 q^{56} +(1.12716 - 7.74218i) q^{57} -4.45872i q^{58} +(7.87687 + 6.60948i) q^{59} +(1.12233 + 6.36503i) q^{61} +(-1.38122 - 0.243546i) q^{62} +(0.103223 - 0.283604i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-8.88125 + 7.45226i) q^{66} +(4.31929 + 5.14753i) q^{67} +(2.21604 + 1.27943i) q^{68} +(7.56034 + 13.0949i) q^{69} +(0.336459 - 1.90815i) q^{71} +(-0.218308 + 0.0384936i) q^{72} +(2.14907 + 5.90451i) q^{73} +(-3.39328 - 2.84730i) q^{74} +(1.36746 - 4.13885i) q^{76} -8.79403i q^{77} +(6.78052 - 8.08071i) q^{78} +(-3.37355 + 1.22787i) q^{79} +(-1.66978 + 9.46980i) q^{81} +(-1.87593 + 5.15407i) q^{82} +(-11.6908 + 6.74970i) q^{83} +(1.22185 - 2.11631i) q^{84} +(-5.25046 + 4.40566i) q^{86} +(6.93077 + 4.00148i) q^{87} +(-5.59384 + 3.22960i) q^{88} +(-1.78165 - 0.648469i) q^{89} +(1.38942 + 7.87979i) q^{91} +(2.88126 + 7.91619i) q^{92} +(1.61815 - 1.92844i) q^{93} -9.51825 q^{94} -1.79490 q^{96} +(-0.0793596 + 0.0945771i) q^{97} +(-1.76017 - 4.83603i) q^{98} +(-0.248638 - 1.41010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 36q^{9} + O(q^{10}) \) \( 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{9}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.642788 + 0.766044i −0.454519 + 0.541675i
\(3\) −0.613893 1.68666i −0.354431 0.973792i −0.980929 0.194368i \(-0.937734\pi\)
0.626497 0.779423i \(-0.284488\pi\)
\(4\) −0.173648 0.984808i −0.0868241 0.492404i
\(5\) 0 0
\(6\) 1.68666 + 0.613893i 0.688575 + 0.250621i
\(7\) −1.17907 + 0.680736i −0.445646 + 0.257294i −0.705990 0.708222i \(-0.749498\pi\)
0.260343 + 0.965516i \(0.416164\pi\)
\(8\) 0.866025 + 0.500000i 0.306186 + 0.176777i
\(9\) −0.169813 + 0.142490i −0.0566045 + 0.0474968i
\(10\) 0 0
\(11\) −3.22960 + 5.59384i −0.973762 + 1.68661i −0.289803 + 0.957086i \(0.593590\pi\)
−0.683960 + 0.729520i \(0.739744\pi\)
\(12\) −1.55443 + 0.897451i −0.448726 + 0.259072i
\(13\) 2.01005 5.52256i 0.557487 1.53168i −0.265784 0.964033i \(-0.585631\pi\)
0.823270 0.567650i \(-0.192147\pi\)
\(14\) 0.236417 1.34079i 0.0631851 0.358341i
\(15\) 0 0
\(16\) −0.939693 + 0.342020i −0.234923 + 0.0855050i
\(17\) −1.64480 + 1.96020i −0.398923 + 0.475418i −0.927691 0.373348i \(-0.878210\pi\)
0.528768 + 0.848766i \(0.322654\pi\)
\(18\) 0.221676i 0.0522494i
\(19\) 3.83851 + 2.06538i 0.880615 + 0.473832i
\(20\) 0 0
\(21\) 1.87199 + 1.57079i 0.408502 + 0.342774i
\(22\) −2.20918 6.06967i −0.470999 1.29406i
\(23\) −8.29626 + 1.46285i −1.72989 + 0.305026i −0.947971 0.318356i \(-0.896869\pi\)
−0.781918 + 0.623382i \(0.785758\pi\)
\(24\) 0.311682 1.76763i 0.0636217 0.360817i
\(25\) 0 0
\(26\) 2.93849 + 5.08962i 0.576286 + 0.998156i
\(27\) −4.31871 2.49341i −0.831137 0.479857i
\(28\) 0.875137 + 1.04295i 0.165385 + 0.197099i
\(29\) −3.41558 + 2.86601i −0.634257 + 0.532205i −0.902248 0.431217i \(-0.858084\pi\)
0.267992 + 0.963421i \(0.413640\pi\)
\(30\) 0 0
\(31\) 0.701264 + 1.21462i 0.125951 + 0.218153i 0.922104 0.386942i \(-0.126469\pi\)
−0.796153 + 0.605095i \(0.793135\pi\)
\(32\) 0.342020 0.939693i 0.0604612 0.166116i
\(33\) 11.4175 + 2.01322i 1.98753 + 0.350456i
\(34\) −0.444341 2.51998i −0.0762038 0.432173i
\(35\) 0 0
\(36\) 0.169813 + 0.142490i 0.0283022 + 0.0237484i
\(37\) 4.42962i 0.728225i 0.931355 + 0.364112i \(0.118628\pi\)
−0.931355 + 0.364112i \(0.881372\pi\)
\(38\) −4.04953 + 1.61287i −0.656920 + 0.261642i
\(39\) −10.5486 −1.68913
\(40\) 0 0
\(41\) 5.15407 1.87593i 0.804931 0.292971i 0.0934025 0.995628i \(-0.470226\pi\)
0.711528 + 0.702658i \(0.248003\pi\)
\(42\) −2.40658 + 0.424346i −0.371344 + 0.0654780i
\(43\) 6.74986 + 1.19018i 1.02934 + 0.181501i 0.662719 0.748868i \(-0.269402\pi\)
0.366625 + 0.930369i \(0.380513\pi\)
\(44\) 6.06967 + 2.20918i 0.915037 + 0.333046i
\(45\) 0 0
\(46\) 4.21212 7.29560i 0.621043 1.07568i
\(47\) 6.11821 + 7.29140i 0.892433 + 1.06356i 0.997609 + 0.0691065i \(0.0220148\pi\)
−0.105176 + 0.994454i \(0.533541\pi\)
\(48\) 1.15374 + 1.37498i 0.166528 + 0.198461i
\(49\) −2.57320 + 4.45691i −0.367600 + 0.636701i
\(50\) 0 0
\(51\) 4.31591 + 1.57086i 0.604349 + 0.219965i
\(52\) −5.78770 1.02053i −0.802610 0.141522i
\(53\) −4.35841 + 0.768506i −0.598674 + 0.105562i −0.464769 0.885432i \(-0.653863\pi\)
−0.133905 + 0.990994i \(0.542752\pi\)
\(54\) 4.68608 1.70559i 0.637695 0.232102i
\(55\) 0 0
\(56\) −1.36147 −0.181934
\(57\) 1.12716 7.74218i 0.149296 1.02548i
\(58\) 4.45872i 0.585458i
\(59\) 7.87687 + 6.60948i 1.02548 + 0.860481i 0.990306 0.138900i \(-0.0443566\pi\)
0.0351753 + 0.999381i \(0.488801\pi\)
\(60\) 0 0
\(61\) 1.12233 + 6.36503i 0.143699 + 0.814958i 0.968402 + 0.249393i \(0.0802310\pi\)
−0.824703 + 0.565566i \(0.808658\pi\)
\(62\) −1.38122 0.243546i −0.175415 0.0309304i
\(63\) 0.103223 0.283604i 0.0130049 0.0357307i
\(64\) 0.500000 + 0.866025i 0.0625000 + 0.108253i
\(65\) 0 0
\(66\) −8.88125 + 7.45226i −1.09321 + 0.917309i
\(67\) 4.31929 + 5.14753i 0.527685 + 0.628871i 0.962380 0.271707i \(-0.0875882\pi\)
−0.434695 + 0.900578i \(0.643144\pi\)
\(68\) 2.21604 + 1.27943i 0.268734 + 0.155153i
\(69\) 7.56034 + 13.0949i 0.910158 + 1.57644i
\(70\) 0 0
\(71\) 0.336459 1.90815i 0.0399303 0.226456i −0.958312 0.285725i \(-0.907766\pi\)
0.998242 + 0.0592685i \(0.0188768\pi\)
\(72\) −0.218308 + 0.0384936i −0.0257278 + 0.00453651i
\(73\) 2.14907 + 5.90451i 0.251529 + 0.691071i 0.999622 + 0.0274772i \(0.00874737\pi\)
−0.748093 + 0.663594i \(0.769030\pi\)
\(74\) −3.39328 2.84730i −0.394461 0.330992i
\(75\) 0 0
\(76\) 1.36746 4.13885i 0.156858 0.474758i
\(77\) 8.79403i 1.00217i
\(78\) 6.78052 8.08071i 0.767743 0.914960i
\(79\) −3.37355 + 1.22787i −0.379554 + 0.138146i −0.524750 0.851257i \(-0.675841\pi\)
0.145195 + 0.989403i \(0.453619\pi\)
\(80\) 0 0
\(81\) −1.66978 + 9.46980i −0.185531 + 1.05220i
\(82\) −1.87593 + 5.15407i −0.207162 + 0.569172i
\(83\) −11.6908 + 6.74970i −1.28323 + 0.740876i −0.977438 0.211221i \(-0.932256\pi\)
−0.305797 + 0.952097i \(0.598923\pi\)
\(84\) 1.22185 2.11631i 0.133315 0.230909i
\(85\) 0 0
\(86\) −5.25046 + 4.40566i −0.566172 + 0.475074i
\(87\) 6.93077 + 4.00148i 0.743057 + 0.429004i
\(88\) −5.59384 + 3.22960i −0.596305 + 0.344277i
\(89\) −1.78165 0.648469i −0.188855 0.0687376i 0.245861 0.969305i \(-0.420929\pi\)
−0.434716 + 0.900567i \(0.643151\pi\)
\(90\) 0 0
\(91\) 1.38942 + 7.87979i 0.145651 + 0.826026i
\(92\) 2.88126 + 7.91619i 0.300392 + 0.825320i
\(93\) 1.61815 1.92844i 0.167795 0.199970i
\(94\) −9.51825 −0.981732
\(95\) 0 0
\(96\) −1.79490 −0.183191
\(97\) −0.0793596 + 0.0945771i −0.00805774 + 0.00960285i −0.770058 0.637974i \(-0.779773\pi\)
0.762001 + 0.647576i \(0.224217\pi\)
\(98\) −1.76017 4.83603i −0.177804 0.488513i
\(99\) −0.248638 1.41010i −0.0249891 0.141720i
\(100\) 0 0
\(101\) −12.8307 4.66998i −1.27670 0.464680i −0.387359 0.921929i \(-0.626613\pi\)
−0.889339 + 0.457249i \(0.848835\pi\)
\(102\) −3.97757 + 2.29645i −0.393838 + 0.227382i
\(103\) 5.95330 + 3.43714i 0.586596 + 0.338672i 0.763751 0.645512i \(-0.223356\pi\)
−0.177154 + 0.984183i \(0.556689\pi\)
\(104\) 4.50203 3.77765i 0.441460 0.370429i
\(105\) 0 0
\(106\) 2.21282 3.83272i 0.214929 0.372267i
\(107\) −7.65580 + 4.42008i −0.740114 + 0.427305i −0.822111 0.569328i \(-0.807204\pi\)
0.0819969 + 0.996633i \(0.473870\pi\)
\(108\) −1.70559 + 4.68608i −0.164121 + 0.450918i
\(109\) 1.65245 9.37152i 0.158276 0.897629i −0.797453 0.603381i \(-0.793820\pi\)
0.955729 0.294248i \(-0.0950691\pi\)
\(110\) 0 0
\(111\) 7.47124 2.71931i 0.709139 0.258106i
\(112\) 0.875137 1.04295i 0.0826927 0.0985493i
\(113\) 11.0799i 1.04231i −0.853462 0.521154i \(-0.825502\pi\)
0.853462 0.521154i \(-0.174498\pi\)
\(114\) 5.20633 + 5.84003i 0.487617 + 0.546969i
\(115\) 0 0
\(116\) 3.41558 + 2.86601i 0.317128 + 0.266102i
\(117\) 0.445578 + 1.22422i 0.0411937 + 0.113179i
\(118\) −10.1263 + 1.78554i −0.932203 + 0.164373i
\(119\) 0.604958 3.43088i 0.0554564 0.314509i
\(120\) 0 0
\(121\) −15.3607 26.6055i −1.39643 2.41868i
\(122\) −5.59731 3.23161i −0.506757 0.292576i
\(123\) −6.32809 7.54153i −0.570585 0.679997i
\(124\) 1.07440 0.901527i 0.0964838 0.0809595i
\(125\) 0 0
\(126\) 0.150903 + 0.261371i 0.0134435 + 0.0232848i
\(127\) −3.14395 + 8.63792i −0.278980 + 0.766491i 0.718499 + 0.695528i \(0.244830\pi\)
−0.997479 + 0.0709633i \(0.977393\pi\)
\(128\) −0.984808 0.173648i −0.0870455 0.0153485i
\(129\) −2.13626 12.1153i −0.188087 1.06670i
\(130\) 0 0
\(131\) 0.0847217 + 0.0710900i 0.00740217 + 0.00621116i 0.646481 0.762930i \(-0.276240\pi\)
−0.639079 + 0.769141i \(0.720684\pi\)
\(132\) 11.5937i 1.00910i
\(133\) −5.93185 + 0.177782i −0.514357 + 0.0154157i
\(134\) −6.71962 −0.580487
\(135\) 0 0
\(136\) −2.40454 + 0.875181i −0.206188 + 0.0750461i
\(137\) 13.4434 2.37043i 1.14855 0.202520i 0.433205 0.901295i \(-0.357383\pi\)
0.715341 + 0.698776i \(0.246271\pi\)
\(138\) −14.8910 2.62568i −1.26760 0.223513i
\(139\) 2.27126 + 0.826670i 0.192645 + 0.0701172i 0.436541 0.899684i \(-0.356203\pi\)
−0.243896 + 0.969801i \(0.578425\pi\)
\(140\) 0 0
\(141\) 8.54216 14.7955i 0.719380 1.24600i
\(142\) 1.24546 + 1.48428i 0.104517 + 0.124558i
\(143\) 24.4007 + 29.0796i 2.04048 + 2.43176i
\(144\) 0.110838 0.191977i 0.00923648 0.0159981i
\(145\) 0 0
\(146\) −5.90451 2.14907i −0.488661 0.177858i
\(147\) 9.09694 + 1.60404i 0.750303 + 0.132299i
\(148\) 4.36232 0.769195i 0.358581 0.0632274i
\(149\) −2.08531 + 0.758990i −0.170835 + 0.0621789i −0.426022 0.904713i \(-0.640085\pi\)
0.255187 + 0.966892i \(0.417863\pi\)
\(150\) 0 0
\(151\) −11.6771 −0.950267 −0.475133 0.879914i \(-0.657600\pi\)
−0.475133 + 0.879914i \(0.657600\pi\)
\(152\) 2.29156 + 3.70793i 0.185870 + 0.300753i
\(153\) 0.567236i 0.0458583i
\(154\) 6.73662 + 5.65269i 0.542852 + 0.455507i
\(155\) 0 0
\(156\) 1.83175 + 10.3884i 0.146657 + 0.831734i
\(157\) 4.10004 + 0.722948i 0.327219 + 0.0576975i 0.334844 0.942273i \(-0.391316\pi\)
−0.00762562 + 0.999971i \(0.502427\pi\)
\(158\) 1.22787 3.37355i 0.0976843 0.268385i
\(159\) 3.97181 + 6.87937i 0.314985 + 0.545569i
\(160\) 0 0
\(161\) 8.78604 7.37236i 0.692437 0.581024i
\(162\) −6.18097 7.36620i −0.485623 0.578743i
\(163\) −4.15894 2.40117i −0.325753 0.188074i 0.328201 0.944608i \(-0.393558\pi\)
−0.653954 + 0.756534i \(0.726891\pi\)
\(164\) −2.74242 4.75002i −0.214147 0.370914i
\(165\) 0 0
\(166\) 2.34415 13.2943i 0.181941 1.03184i
\(167\) −3.80840 + 0.671525i −0.294703 + 0.0519641i −0.319045 0.947740i \(-0.603362\pi\)
0.0243418 + 0.999704i \(0.492251\pi\)
\(168\) 0.835798 + 2.29634i 0.0644832 + 0.177166i
\(169\) −16.4998 13.8450i −1.26921 1.06500i
\(170\) 0 0
\(171\) −0.946128 + 0.196221i −0.0723522 + 0.0150054i
\(172\) 6.85399i 0.522612i
\(173\) −7.41704 + 8.83929i −0.563907 + 0.672039i −0.970369 0.241629i \(-0.922318\pi\)
0.406461 + 0.913668i \(0.366763\pi\)
\(174\) −7.52033 + 2.73718i −0.570115 + 0.207505i
\(175\) 0 0
\(176\) 1.12163 6.36108i 0.0845460 0.479484i
\(177\) 6.31237 17.3431i 0.474467 1.30359i
\(178\) 1.64198 0.947998i 0.123072 0.0710555i
\(179\) 4.18981 7.25696i 0.313161 0.542411i −0.665884 0.746055i \(-0.731945\pi\)
0.979045 + 0.203645i \(0.0652788\pi\)
\(180\) 0 0
\(181\) −8.13969 + 6.83001i −0.605018 + 0.507671i −0.893054 0.449949i \(-0.851442\pi\)
0.288036 + 0.957620i \(0.406998\pi\)
\(182\) −6.92937 4.00067i −0.513639 0.296550i
\(183\) 10.0466 5.80042i 0.742668 0.428780i
\(184\) −7.91619 2.88126i −0.583590 0.212409i
\(185\) 0 0
\(186\) 0.437142 + 2.47915i 0.0320528 + 0.181780i
\(187\) −5.65298 15.5314i −0.413386 1.13577i
\(188\) 6.11821 7.29140i 0.446216 0.531780i
\(189\) 6.78942 0.493857
\(190\) 0 0
\(191\) 10.8514 0.785179 0.392589 0.919714i \(-0.371579\pi\)
0.392589 + 0.919714i \(0.371579\pi\)
\(192\) 1.15374 1.37498i 0.0832641 0.0992303i
\(193\) −0.662240 1.81949i −0.0476691 0.130970i 0.913574 0.406674i \(-0.133311\pi\)
−0.961243 + 0.275704i \(0.911089\pi\)
\(194\) −0.0214389 0.121586i −0.00153922 0.00872936i
\(195\) 0 0
\(196\) 4.83603 + 1.76017i 0.345431 + 0.125726i
\(197\) −10.6122 + 6.12697i −0.756090 + 0.436529i −0.827890 0.560890i \(-0.810459\pi\)
0.0718004 + 0.997419i \(0.477126\pi\)
\(198\) 1.24002 + 0.715925i 0.0881242 + 0.0508785i
\(199\) 0.331678 0.278311i 0.0235121 0.0197290i −0.630956 0.775819i \(-0.717337\pi\)
0.654468 + 0.756090i \(0.272893\pi\)
\(200\) 0 0
\(201\) 6.03053 10.4452i 0.425361 0.736747i
\(202\) 11.8248 6.82705i 0.831990 0.480350i
\(203\) 2.07621 5.70433i 0.145721 0.400365i
\(204\) 0.797549 4.52312i 0.0558396 0.316682i
\(205\) 0 0
\(206\) −6.45971 + 2.35114i −0.450070 + 0.163812i
\(207\) 1.20037 1.43055i 0.0834317 0.0994300i
\(208\) 5.87698i 0.407496i
\(209\) −23.9503 + 14.8017i −1.65668 + 1.02385i
\(210\) 0 0
\(211\) −10.5293 8.83513i −0.724867 0.608235i 0.203860 0.979000i \(-0.434651\pi\)
−0.928727 + 0.370765i \(0.879096\pi\)
\(212\) 1.51366 + 4.15875i 0.103959 + 0.285624i
\(213\) −3.42495 + 0.603911i −0.234674 + 0.0413793i
\(214\) 1.53508 8.70585i 0.104936 0.595120i
\(215\) 0 0
\(216\) −2.49341 4.31871i −0.169655 0.293851i
\(217\) −1.65368 0.954751i −0.112259 0.0648127i
\(218\) 6.11683 + 7.28975i 0.414284 + 0.493724i
\(219\) 8.63959 7.24948i 0.583809 0.489874i
\(220\) 0 0
\(221\) 7.51918 + 13.0236i 0.505795 + 0.876062i
\(222\) −2.71931 + 7.47124i −0.182508 + 0.501437i
\(223\) −22.1729 3.90968i −1.48481 0.261812i −0.628310 0.777963i \(-0.716253\pi\)
−0.856497 + 0.516151i \(0.827364\pi\)
\(224\) 0.236417 + 1.34079i 0.0157963 + 0.0895852i
\(225\) 0 0
\(226\) 8.48769 + 7.12202i 0.564593 + 0.473750i
\(227\) 18.8403i 1.25048i 0.780433 + 0.625239i \(0.214998\pi\)
−0.780433 + 0.625239i \(0.785002\pi\)
\(228\) −7.82029 + 0.234380i −0.517911 + 0.0155222i
\(229\) 4.51829 0.298577 0.149289 0.988794i \(-0.452302\pi\)
0.149289 + 0.988794i \(0.452302\pi\)
\(230\) 0 0
\(231\) −14.8325 + 5.39859i −0.975908 + 0.355201i
\(232\) −4.39098 + 0.774248i −0.288282 + 0.0508319i
\(233\) −10.5997 1.86901i −0.694406 0.122443i −0.184705 0.982794i \(-0.559133\pi\)
−0.509701 + 0.860351i \(0.670244\pi\)
\(234\) −1.22422 0.445578i −0.0800295 0.0291284i
\(235\) 0 0
\(236\) 5.14126 8.90493i 0.334668 0.579662i
\(237\) 4.14200 + 4.93624i 0.269052 + 0.320643i
\(238\) 2.23935 + 2.66875i 0.145156 + 0.172990i
\(239\) 11.7010 20.2668i 0.756876 1.31095i −0.187560 0.982253i \(-0.560058\pi\)
0.944436 0.328695i \(-0.106609\pi\)
\(240\) 0 0
\(241\) 19.6353 + 7.14665i 1.26482 + 0.460356i 0.885383 0.464862i \(-0.153896\pi\)
0.379435 + 0.925218i \(0.376118\pi\)
\(242\) 30.2547 + 5.33471i 1.94484 + 0.342928i
\(243\) 2.26419 0.399237i 0.145248 0.0256111i
\(244\) 6.07344 2.21055i 0.388812 0.141516i
\(245\) 0 0
\(246\) 9.84477 0.627679
\(247\) 19.1218 17.0469i 1.21669 1.08467i
\(248\) 1.40253i 0.0890606i
\(249\) 18.5613 + 15.5748i 1.17628 + 0.987014i
\(250\) 0 0
\(251\) −3.10917 17.6330i −0.196249 1.11298i −0.910628 0.413226i \(-0.864402\pi\)
0.714379 0.699759i \(-0.246709\pi\)
\(252\) −0.297220 0.0524079i −0.0187231 0.00330139i
\(253\) 18.6107 51.1324i 1.17004 3.21466i
\(254\) −4.59614 7.96075i −0.288388 0.499502i
\(255\) 0 0
\(256\) 0.766044 0.642788i 0.0478778 0.0401742i
\(257\) 0.312965 + 0.372978i 0.0195222 + 0.0232657i 0.775717 0.631081i \(-0.217388\pi\)
−0.756195 + 0.654346i \(0.772944\pi\)
\(258\) 10.6541 + 6.15112i 0.663292 + 0.382952i
\(259\) −3.01540 5.22282i −0.187368 0.324531i
\(260\) 0 0
\(261\) 0.171632 0.973373i 0.0106238 0.0602503i
\(262\) −0.108916 + 0.0192049i −0.00672886 + 0.00118648i
\(263\) 7.54785 + 20.7375i 0.465420 + 1.27873i 0.921356 + 0.388719i \(0.127082\pi\)
−0.455936 + 0.890013i \(0.650695\pi\)
\(264\) 8.88125 + 7.45226i 0.546603 + 0.458655i
\(265\) 0 0
\(266\) 3.67673 4.65834i 0.225435 0.285621i
\(267\) 3.40313i 0.208268i
\(268\) 4.31929 5.14753i 0.263843 0.314435i
\(269\) 16.6789 6.07061i 1.01693 0.370131i 0.220838 0.975310i \(-0.429121\pi\)
0.796089 + 0.605179i \(0.206899\pi\)
\(270\) 0 0
\(271\) 1.89657 10.7560i 0.115208 0.653380i −0.871438 0.490505i \(-0.836812\pi\)
0.986647 0.162875i \(-0.0520766\pi\)
\(272\) 0.875181 2.40454i 0.0530656 0.145797i
\(273\) 12.4375 7.18082i 0.752755 0.434603i
\(274\) −6.82538 + 11.8219i −0.412337 + 0.714188i
\(275\) 0 0
\(276\) 11.5831 9.71939i 0.697222 0.585039i
\(277\) 7.84590 + 4.52983i 0.471414 + 0.272171i 0.716832 0.697246i \(-0.245592\pi\)
−0.245417 + 0.969418i \(0.578925\pi\)
\(278\) −2.09320 + 1.20851i −0.125542 + 0.0724816i
\(279\) −0.292156 0.106336i −0.0174909 0.00636618i
\(280\) 0 0
\(281\) 2.65688 + 15.0679i 0.158496 + 0.898876i 0.955520 + 0.294928i \(0.0952956\pi\)
−0.797023 + 0.603948i \(0.793593\pi\)
\(282\) 5.84318 + 16.0540i 0.347957 + 0.956003i
\(283\) 6.33163 7.54574i 0.376376 0.448548i −0.544291 0.838897i \(-0.683201\pi\)
0.920667 + 0.390349i \(0.127646\pi\)
\(284\) −1.93759 −0.114975
\(285\) 0 0
\(286\) −37.9607 −2.24466
\(287\) −4.79999 + 5.72041i −0.283335 + 0.337665i
\(288\) 0.0758175 + 0.208307i 0.00446759 + 0.0122746i
\(289\) 1.81501 + 10.2935i 0.106766 + 0.605498i
\(290\) 0 0
\(291\) 0.208237 + 0.0757922i 0.0122071 + 0.00444302i
\(292\) 5.44163 3.14173i 0.318447 0.183856i
\(293\) −7.08299 4.08936i −0.413792 0.238903i 0.278625 0.960400i \(-0.410121\pi\)
−0.692418 + 0.721497i \(0.743455\pi\)
\(294\) −7.07617 + 5.93761i −0.412690 + 0.346288i
\(295\) 0 0
\(296\) −2.21481 + 3.83616i −0.128733 + 0.222972i
\(297\) 27.8955 16.1055i 1.61866 0.934534i
\(298\) 0.758990 2.08531i 0.0439671 0.120799i
\(299\) −8.59717 + 48.7570i −0.497187 + 2.81969i
\(300\) 0 0
\(301\) −8.76875 + 3.19157i −0.505423 + 0.183959i
\(302\) 7.50588 8.94516i 0.431915 0.514736i
\(303\) 24.5078i 1.40794i
\(304\) −4.31343 0.627978i −0.247392 0.0360170i
\(305\) 0 0
\(306\) 0.434528 + 0.364612i 0.0248403 + 0.0208435i
\(307\) −2.06799 5.68175i −0.118026 0.324275i 0.866586 0.499028i \(-0.166309\pi\)
−0.984612 + 0.174753i \(0.944087\pi\)
\(308\) −8.66043 + 1.52707i −0.493474 + 0.0870127i
\(309\) 2.14259 12.1512i 0.121888 0.691259i
\(310\) 0 0
\(311\) −16.5582 28.6797i −0.938932 1.62628i −0.767468 0.641087i \(-0.778484\pi\)
−0.171463 0.985191i \(-0.554849\pi\)
\(312\) −9.13537 5.27431i −0.517188 0.298599i
\(313\) −3.96728 4.72802i −0.224244 0.267244i 0.642179 0.766555i \(-0.278031\pi\)
−0.866423 + 0.499312i \(0.833586\pi\)
\(314\) −3.18927 + 2.67611i −0.179981 + 0.151022i
\(315\) 0 0
\(316\) 1.79503 + 3.10908i 0.100978 + 0.174900i
\(317\) 5.61135 15.4171i 0.315165 0.865908i −0.676428 0.736509i \(-0.736473\pi\)
0.991593 0.129399i \(-0.0413049\pi\)
\(318\) −7.82293 1.37939i −0.438688 0.0773525i
\(319\) −5.00103 28.3623i −0.280004 1.58798i
\(320\) 0 0
\(321\) 12.1550 + 10.1992i 0.678425 + 0.569266i
\(322\) 11.4694i 0.639163i
\(323\) −10.3622 + 4.12710i −0.576566 + 0.229638i
\(324\) 9.61589 0.534216
\(325\) 0 0
\(326\) 4.51272 1.64249i 0.249936 0.0909694i
\(327\) −16.8210 + 2.96599i −0.930202 + 0.164020i
\(328\) 5.40152 + 0.952434i 0.298249 + 0.0525894i
\(329\) −12.1773 4.43218i −0.671357 0.244354i
\(330\) 0 0
\(331\) −8.53392 + 14.7812i −0.469066 + 0.812447i −0.999375 0.0353579i \(-0.988743\pi\)
0.530308 + 0.847805i \(0.322076\pi\)
\(332\) 8.67725 + 10.3411i 0.476226 + 0.567544i
\(333\) −0.631178 0.752208i −0.0345883 0.0412208i
\(334\) 1.93358 3.34906i 0.105801 0.183252i
\(335\) 0 0
\(336\) −2.29634 0.835798i −0.125275 0.0455965i
\(337\) −18.5701 3.27441i −1.01158 0.178368i −0.356792 0.934184i \(-0.616130\pi\)
−0.654785 + 0.755816i \(0.727241\pi\)
\(338\) 21.2117 3.74020i 1.15377 0.203440i
\(339\) −18.6880 + 6.80187i −1.01499 + 0.369427i
\(340\) 0 0
\(341\) −9.05922 −0.490584
\(342\) 0.457845 0.850905i 0.0247574 0.0460117i
\(343\) 16.5370i 0.892913i
\(344\) 5.25046 + 4.40566i 0.283086 + 0.237537i
\(345\) 0 0
\(346\) −2.00370 11.3636i −0.107720 0.610909i
\(347\) −5.32560 0.939047i −0.285893 0.0504107i 0.0288626 0.999583i \(-0.490811\pi\)
−0.314756 + 0.949173i \(0.601923\pi\)
\(348\) 2.73718 7.52033i 0.146728 0.403132i
\(349\) −18.1540 31.4436i −0.971761 1.68314i −0.690235 0.723586i \(-0.742493\pi\)
−0.281526 0.959554i \(-0.590841\pi\)
\(350\) 0 0
\(351\) −22.4508 + 18.8385i −1.19834 + 1.00552i
\(352\) 4.15190 + 4.94804i 0.221297 + 0.263731i
\(353\) 1.06514 + 0.614958i 0.0566916 + 0.0327309i 0.528078 0.849196i \(-0.322913\pi\)
−0.471386 + 0.881927i \(0.656246\pi\)
\(354\) 9.22807 + 15.9835i 0.490466 + 0.849513i
\(355\) 0 0
\(356\) −0.329236 + 1.86719i −0.0174495 + 0.0989610i
\(357\) −6.15810 + 1.08584i −0.325921 + 0.0574687i
\(358\) 2.86600 + 7.87426i 0.151473 + 0.416168i
\(359\) 11.5897 + 9.72494i 0.611683 + 0.513263i 0.895177 0.445711i \(-0.147049\pi\)
−0.283494 + 0.958974i \(0.591494\pi\)
\(360\) 0 0
\(361\) 10.4684 + 15.8560i 0.550967 + 0.834527i
\(362\) 10.6256i 0.558470i
\(363\) −35.4445 + 42.2411i −1.86036 + 2.21709i
\(364\) 7.51881 2.73662i 0.394093 0.143438i
\(365\) 0 0
\(366\) −2.01447 + 11.4246i −0.105298 + 0.597174i
\(367\) 0.723196 1.98697i 0.0377505 0.103719i −0.919385 0.393358i \(-0.871313\pi\)
0.957136 + 0.289640i \(0.0935354\pi\)
\(368\) 7.29560 4.21212i 0.380310 0.219572i
\(369\) −0.607928 + 1.05296i −0.0316475 + 0.0548151i
\(370\) 0 0
\(371\) 4.61572 3.87305i 0.239636 0.201079i
\(372\) −2.18013 1.25870i −0.113035 0.0652605i
\(373\) 4.36262 2.51876i 0.225888 0.130416i −0.382786 0.923837i \(-0.625035\pi\)
0.608674 + 0.793421i \(0.291702\pi\)
\(374\) 15.5314 + 5.65298i 0.803111 + 0.292308i
\(375\) 0 0
\(376\) 1.65283 + 9.37364i 0.0852380 + 0.483409i
\(377\) 8.96223 + 24.6235i 0.461579 + 1.26818i
\(378\) −4.36415 + 5.20100i −0.224468 + 0.267510i
\(379\) −37.2812 −1.91501 −0.957503 0.288423i \(-0.906869\pi\)
−0.957503 + 0.288423i \(0.906869\pi\)
\(380\) 0 0
\(381\) 16.4993 0.845282
\(382\) −6.97514 + 8.31264i −0.356879 + 0.425312i
\(383\) −5.09082 13.9869i −0.260129 0.714698i −0.999158 0.0410250i \(-0.986938\pi\)
0.739029 0.673673i \(-0.235285\pi\)
\(384\) 0.311682 + 1.76763i 0.0159054 + 0.0902042i
\(385\) 0 0
\(386\) 1.81949 + 0.662240i 0.0926096 + 0.0337071i
\(387\) −1.31581 + 0.759681i −0.0668862 + 0.0386168i
\(388\) 0.106921 + 0.0617308i 0.00542808 + 0.00313391i
\(389\) −23.6259 + 19.8245i −1.19788 + 1.00514i −0.198191 + 0.980163i \(0.563507\pi\)
−0.999688 + 0.0249764i \(0.992049\pi\)
\(390\) 0 0
\(391\) 10.7782 18.6684i 0.545078 0.944102i
\(392\) −4.45691 + 2.57320i −0.225108 + 0.129966i
\(393\) 0.0678943 0.186538i 0.00342482 0.00940960i
\(394\) 2.12787 12.0678i 0.107201 0.607966i
\(395\) 0 0
\(396\) −1.34550 + 0.489721i −0.0676138 + 0.0246094i
\(397\) −14.2405 + 16.9711i −0.714708 + 0.851756i −0.994105 0.108420i \(-0.965421\pi\)
0.279397 + 0.960176i \(0.409865\pi\)
\(398\) 0.432975i 0.0217031i
\(399\) 3.94138 + 9.89586i 0.197316 + 0.495413i
\(400\) 0 0
\(401\) 23.8011 + 19.9715i 1.18857 + 0.997330i 0.999883 + 0.0152927i \(0.00486799\pi\)
0.188688 + 0.982037i \(0.439576\pi\)
\(402\) 4.12513 + 11.3337i 0.205743 + 0.565273i
\(403\) 8.11741 1.43132i 0.404357 0.0712990i
\(404\) −2.37101 + 13.4467i −0.117962 + 0.668997i
\(405\) 0 0
\(406\) 3.03521 + 5.25714i 0.150635 + 0.260907i
\(407\) −24.7786 14.3059i −1.22823 0.709118i
\(408\) 2.95226 + 3.51836i 0.146159 + 0.174185i
\(409\) −1.56037 + 1.30931i −0.0771554 + 0.0647411i −0.680550 0.732702i \(-0.738259\pi\)
0.603394 + 0.797443i \(0.293815\pi\)
\(410\) 0 0
\(411\) −12.2509 21.2192i −0.604292 1.04667i
\(412\) 2.35114 6.45971i 0.115833 0.318247i
\(413\) −13.7867 2.43097i −0.678399 0.119620i
\(414\) 0.324279 + 1.83908i 0.0159374 + 0.0903857i
\(415\) 0 0
\(416\) −4.50203 3.77765i −0.220730 0.185215i
\(417\) 4.33832i 0.212448i
\(418\) 4.05624 27.8613i 0.198397 1.36274i
\(419\) 11.2236 0.548308 0.274154 0.961686i \(-0.411602\pi\)
0.274154 + 0.961686i \(0.411602\pi\)
\(420\) 0 0
\(421\) 9.19144 3.34541i 0.447964 0.163045i −0.108181 0.994131i \(-0.534502\pi\)
0.556144 + 0.831086i \(0.312280\pi\)
\(422\) 13.5362 2.38680i 0.658932 0.116187i
\(423\) −2.07791 0.366391i −0.101031 0.0178146i
\(424\) −4.15875 1.51366i −0.201967 0.0735099i
\(425\) 0 0
\(426\) 1.73889 3.01185i 0.0842496 0.145925i
\(427\) −5.65620 6.74080i −0.273723 0.326210i
\(428\) 5.68234 + 6.77195i 0.274666 + 0.327335i
\(429\) 34.0679 59.0073i 1.64481 2.84890i
\(430\) 0 0
\(431\) 4.58045 + 1.66715i 0.220633 + 0.0803037i 0.449971 0.893043i \(-0.351434\pi\)
−0.229339 + 0.973347i \(0.573656\pi\)
\(432\) 4.91106 + 0.865953i 0.236284 + 0.0416632i
\(433\) 19.6135 3.45838i 0.942563 0.166199i 0.318808 0.947819i \(-0.396717\pi\)
0.623755 + 0.781620i \(0.285606\pi\)
\(434\) 1.79434 0.653088i 0.0861313 0.0313492i
\(435\) 0 0
\(436\) −9.51609 −0.455738
\(437\) −34.8666 11.5198i −1.66790 0.551066i
\(438\) 11.2782i 0.538892i
\(439\) 16.3249 + 13.6982i 0.779145 + 0.653780i 0.943033 0.332699i \(-0.107959\pi\)
−0.163888 + 0.986479i \(0.552404\pi\)
\(440\) 0 0
\(441\) −0.198103 1.12350i −0.00943348 0.0534999i
\(442\) −14.8099 2.61138i −0.704435 0.124211i
\(443\) −2.11541 + 5.81205i −0.100506 + 0.276139i −0.979747 0.200239i \(-0.935828\pi\)
0.879241 + 0.476377i \(0.158050\pi\)
\(444\) −3.97537 6.88554i −0.188662 0.326773i
\(445\) 0 0
\(446\) 17.2475 14.4723i 0.816691 0.685285i
\(447\) 2.56031 + 3.05126i 0.121099 + 0.144320i
\(448\) −1.17907 0.680736i −0.0557058 0.0321617i
\(449\) 20.3687 + 35.2797i 0.961260 + 1.66495i 0.719345 + 0.694653i \(0.244442\pi\)
0.241914 + 0.970298i \(0.422225\pi\)
\(450\) 0 0
\(451\) −6.15197 + 34.8896i −0.289685 + 1.64288i
\(452\) −10.9116 + 1.92400i −0.513237 + 0.0904975i
\(453\) 7.16847 + 19.6952i 0.336804 + 0.925362i
\(454\) −14.4325 12.1103i −0.677353 0.568366i
\(455\) 0 0
\(456\) 4.84724 6.14134i 0.226993 0.287595i
\(457\) 14.7073i 0.687978i −0.938974 0.343989i \(-0.888222\pi\)
0.938974 0.343989i \(-0.111778\pi\)
\(458\) −2.90430 + 3.46121i −0.135709 + 0.161732i
\(459\) 11.9910 4.36437i 0.559692 0.203711i
\(460\) 0 0
\(461\) −2.43148 + 13.7896i −0.113245 + 0.642245i 0.874359 + 0.485280i \(0.161282\pi\)
−0.987604 + 0.156966i \(0.949829\pi\)
\(462\) 5.39859 14.8325i 0.251165 0.690071i
\(463\) 1.96929 1.13697i 0.0915206 0.0528394i −0.453541 0.891235i \(-0.649840\pi\)
0.545062 + 0.838396i \(0.316506\pi\)
\(464\) 2.22936 3.86136i 0.103495 0.179259i
\(465\) 0 0
\(466\) 8.24507 6.91843i 0.381945 0.320490i
\(467\) −25.5178 14.7327i −1.18082 0.681749i −0.224618 0.974447i \(-0.572114\pi\)
−0.956205 + 0.292698i \(0.905447\pi\)
\(468\) 1.12824 0.651392i 0.0521531 0.0301106i
\(469\) −8.59685 3.12900i −0.396966 0.144484i
\(470\) 0 0
\(471\) −1.29762 7.35917i −0.0597912 0.339093i
\(472\) 3.51683 + 9.66242i 0.161875 + 0.444749i
\(473\) −28.4571 + 33.9138i −1.30846 + 1.55936i
\(474\) −6.44381 −0.295974
\(475\) 0 0
\(476\) −3.48381 −0.159680
\(477\) 0.630612 0.751534i 0.0288738 0.0344104i
\(478\) 8.00397 + 21.9907i 0.366093 + 1.00583i
\(479\) −3.55187 20.1437i −0.162289 0.920387i −0.951816 0.306671i \(-0.900785\pi\)
0.789527 0.613716i \(-0.210326\pi\)
\(480\) 0 0
\(481\) 24.4628 + 8.90374i 1.11541 + 0.405976i
\(482\) −18.0960 + 10.4477i −0.824248 + 0.475880i
\(483\) −17.8283 10.2932i −0.811217 0.468357i
\(484\) −23.5339 + 19.7473i −1.06972 + 0.897606i
\(485\) 0 0
\(486\) −1.14956 + 1.99109i −0.0521450 + 0.0903178i
\(487\) −25.2182 + 14.5597i −1.14275 + 0.659765i −0.947109 0.320912i \(-0.896011\pi\)
−0.195637 + 0.980676i \(0.562677\pi\)
\(488\) −2.21055 + 6.07344i −0.100067 + 0.274932i
\(489\) −1.49680 + 8.48877i −0.0676876 + 0.383875i
\(490\) 0 0
\(491\) −15.6448 + 5.69426i −0.706042 + 0.256978i −0.669988 0.742372i \(-0.733701\pi\)
−0.0360537 + 0.999350i \(0.511479\pi\)
\(492\) −6.32809 + 7.54153i −0.285293 + 0.339998i
\(493\) 11.4092i 0.513846i
\(494\) 0.767422 + 25.6057i 0.0345279 + 1.15205i
\(495\) 0 0
\(496\) −1.07440 0.901527i −0.0482419 0.0404798i
\(497\) 0.902240 + 2.47888i 0.0404710 + 0.111193i
\(498\) −23.8620 + 4.20752i −1.06928 + 0.188543i
\(499\) −5.09005 + 28.8671i −0.227862 + 1.29227i 0.629276 + 0.777182i \(0.283351\pi\)
−0.857138 + 0.515087i \(0.827760\pi\)
\(500\) 0 0
\(501\) 3.47058 + 6.01123i 0.155054 + 0.268562i
\(502\) 15.5062 + 8.95251i 0.692075 + 0.399570i
\(503\) 4.54061 + 5.41129i 0.202456 + 0.241277i 0.857713 0.514128i \(-0.171884\pi\)
−0.655258 + 0.755405i \(0.727440\pi\)
\(504\) 0.231196 0.193997i 0.0102983 0.00864129i
\(505\) 0 0
\(506\) 27.2070 + 47.1238i 1.20950 + 2.09491i
\(507\) −13.2226 + 36.3288i −0.587237 + 1.61342i
\(508\) 9.05263 + 1.59622i 0.401646 + 0.0708209i
\(509\) −2.11320 11.9846i −0.0936661 0.531207i −0.995148 0.0983900i \(-0.968631\pi\)
0.901482 0.432817i \(-0.142480\pi\)
\(510\) 0 0
\(511\) −6.55331 5.49888i −0.289901 0.243256i
\(512\) 1.00000i 0.0441942i
\(513\) −11.4276 18.4908i −0.504540 0.816389i
\(514\) −0.486888 −0.0214757
\(515\) 0 0
\(516\) −11.5603 + 4.20761i −0.508915 + 0.185230i
\(517\) −60.5463 + 10.6760i −2.66282 + 0.469528i
\(518\) 5.93918 + 1.04724i 0.260952 + 0.0460130i
\(519\) 19.4621 + 7.08363i 0.854292 + 0.310937i
\(520\) 0 0
\(521\) −12.6575 + 21.9234i −0.554535 + 0.960483i 0.443405 + 0.896322i \(0.353770\pi\)
−0.997940 + 0.0641611i \(0.979563\pi\)
\(522\) 0.635324 + 0.757150i 0.0278074 + 0.0331396i
\(523\) 27.7800 + 33.1069i 1.21473 + 1.44766i 0.858150 + 0.513399i \(0.171614\pi\)
0.356583 + 0.934263i \(0.383942\pi\)
\(524\) 0.0552982 0.0957793i 0.00241571 0.00418414i
\(525\) 0 0
\(526\) −20.7375 7.54785i −0.904200 0.329102i
\(527\) −3.53434 0.623200i −0.153958 0.0271470i
\(528\) −11.4175 + 2.01322i −0.496884 + 0.0876140i
\(529\) 45.0750 16.4060i 1.95978 0.713302i
\(530\) 0 0
\(531\) −2.27939 −0.0989169
\(532\) 1.20514 + 5.81086i 0.0522493 + 0.251933i
\(533\) 32.2344i 1.39623i
\(534\) −2.60695 2.18749i −0.112814 0.0946619i
\(535\) 0 0
\(536\) 1.16685 + 6.61753i 0.0504002 + 0.285834i
\(537\) −14.8121 2.61177i −0.639189 0.112706i
\(538\) −6.07061 + 16.6789i −0.261722 + 0.719076i
\(539\) −16.6208 28.7881i −0.715909 1.23999i
\(540\) 0 0
\(541\) −16.8919 + 14.1740i −0.726240 + 0.609388i −0.929104 0.369819i \(-0.879420\pi\)
0.202864 + 0.979207i \(0.434975\pi\)
\(542\) 7.02047 + 8.36667i 0.301555 + 0.359379i
\(543\) 16.5168 + 9.53597i 0.708803 + 0.409228i
\(544\) 1.27943 + 2.21604i 0.0548550 + 0.0950117i
\(545\) 0 0
\(546\) −2.49387 + 14.1435i −0.106728 + 0.605284i
\(547\) 23.6615 4.17215i 1.01169 0.178388i 0.356855 0.934160i \(-0.383849\pi\)
0.654836 + 0.755771i \(0.272738\pi\)
\(548\) −4.66884 12.8275i −0.199443 0.547965i
\(549\) −1.09754 0.920946i −0.0468419 0.0393050i
\(550\) 0 0
\(551\) −19.0301 + 3.94673i −0.810712 + 0.168137i
\(552\) 15.1207i 0.643579i
\(553\) 3.14179 3.74424i 0.133603 0.159221i
\(554\) −8.51330 + 3.09859i −0.361695 + 0.131646i
\(555\) 0 0
\(556\) 0.419711 2.38030i 0.0177997 0.100947i
\(557\) −1.55843 + 4.28175i −0.0660328 + 0.181424i −0.968320 0.249711i \(-0.919664\pi\)
0.902288 + 0.431135i \(0.141887\pi\)
\(558\) 0.269253 0.155453i 0.0113984 0.00658085i
\(559\) 20.1404 34.8842i 0.851848 1.47544i
\(560\) 0 0
\(561\) −22.7259 + 19.0693i −0.959486 + 0.805105i
\(562\) −13.2505 7.65018i −0.558939 0.322703i
\(563\) −19.9237 + 11.5030i −0.839684 + 0.484792i −0.857157 0.515056i \(-0.827771\pi\)
0.0174729 + 0.999847i \(0.494438\pi\)
\(564\) −16.0540 5.84318i −0.675996 0.246042i
\(565\) 0 0
\(566\) 1.71048 + 9.70062i 0.0718969 + 0.407747i
\(567\) −4.47765 12.3022i −0.188043 0.516645i
\(568\) 1.24546 1.48428i 0.0522583 0.0622790i
\(569\) 39.2546 1.64564 0.822819 0.568303i \(-0.192400\pi\)
0.822819 + 0.568303i \(0.192400\pi\)
\(570\) 0 0
\(571\) −20.4203 −0.854563 −0.427282 0.904119i \(-0.640529\pi\)
−0.427282 + 0.904119i \(0.640529\pi\)
\(572\) 24.4007 29.0796i 1.02024 1.21588i
\(573\) −6.66159 18.3026i −0.278292 0.764601i
\(574\) −1.29671 7.35402i −0.0541237 0.306951i
\(575\) 0 0
\(576\) −0.208307 0.0758175i −0.00867946 0.00315906i
\(577\) 19.1093 11.0328i 0.795531 0.459300i −0.0463754 0.998924i \(-0.514767\pi\)
0.841906 + 0.539624i \(0.181434\pi\)
\(578\) −9.05191 5.22613i −0.376510 0.217378i
\(579\) −2.66231 + 2.23394i −0.110642 + 0.0928396i
\(580\) 0 0
\(581\) 9.18953 15.9167i 0.381246 0.660337i
\(582\) −0.191913 + 0.110801i −0.00795503 + 0.00459284i
\(583\) 9.77706 26.8622i 0.404924 1.11252i
\(584\) −1.09111 + 6.18799i −0.0451504 + 0.256061i
\(585\) 0 0
\(586\) 7.68549 2.79729i 0.317485 0.115555i
\(587\) −1.82311 + 2.17270i −0.0752478 + 0.0896768i −0.802355 0.596847i \(-0.796420\pi\)
0.727107 + 0.686524i \(0.240864\pi\)
\(588\) 9.23728i 0.380939i
\(589\) 0.183143 + 6.11073i 0.00754629 + 0.251788i
\(590\) 0 0
\(591\) 16.8489 + 14.1379i 0.693070 + 0.581554i
\(592\) −1.51502 4.16248i −0.0622669 0.171077i
\(593\) 41.3185 7.28557i 1.69675 0.299183i 0.760192 0.649698i \(-0.225105\pi\)
0.936557 + 0.350515i \(0.113994\pi\)
\(594\) −5.59337 + 31.7216i −0.229499 + 1.30155i
\(595\) 0 0
\(596\) 1.10957 + 1.92183i 0.0454498 + 0.0787213i
\(597\) −0.673031 0.388574i −0.0275453 0.0159033i
\(598\) −31.8238 37.9262i −1.30137 1.55092i
\(599\) 23.2333 19.4950i 0.949286 0.796546i −0.0298911 0.999553i \(-0.509516\pi\)
0.979177 + 0.203008i \(0.0650716\pi\)
\(600\) 0 0
\(601\) −16.4125 28.4274i −0.669482 1.15958i −0.978049 0.208374i \(-0.933183\pi\)
0.308568 0.951202i \(-0.400150\pi\)
\(602\) 3.19157 8.76875i 0.130078 0.357388i
\(603\) −1.46695 0.258662i −0.0597387 0.0105335i
\(604\) 2.02770 + 11.4997i 0.0825060 + 0.467915i
\(605\) 0 0
\(606\) −18.7741 15.7533i −0.762644 0.639934i
\(607\) 7.07201i 0.287044i 0.989647 + 0.143522i \(0.0458428\pi\)
−0.989647 + 0.143522i \(0.954157\pi\)
\(608\) 3.25368 2.90062i 0.131954 0.117636i
\(609\) −10.8958 −0.441521
\(610\) 0 0
\(611\) 52.5651 19.1321i 2.12656 0.774003i
\(612\) −0.558619 + 0.0984995i −0.0225808 + 0.00398161i
\(613\) −20.7853 3.66501i −0.839510 0.148028i −0.262670 0.964886i \(-0.584603\pi\)
−0.576840 + 0.816857i \(0.695714\pi\)
\(614\) 5.68175 + 2.06799i 0.229297 + 0.0834572i
\(615\) 0 0
\(616\) 4.39702 7.61585i 0.177161 0.306852i
\(617\) 18.8083 + 22.4149i 0.757195 + 0.902390i 0.997667 0.0682659i \(-0.0217466\pi\)
−0.240472 + 0.970656i \(0.577302\pi\)
\(618\) 7.93114 + 9.45197i 0.319037 + 0.380214i
\(619\) −8.81402 + 15.2663i −0.354265 + 0.613606i −0.986992 0.160770i \(-0.948602\pi\)
0.632727 + 0.774375i \(0.281936\pi\)
\(620\) 0 0
\(621\) 39.4767 + 14.3683i 1.58414 + 0.576581i
\(622\) 32.6134 + 5.75062i 1.30768 + 0.230579i
\(623\) 2.54213 0.448246i 0.101848 0.0179586i
\(624\) 9.91246 3.60784i 0.396816 0.144429i
\(625\) 0 0
\(626\) 6.17199 0.246682
\(627\) 39.6682 + 31.3093i 1.58420 + 1.25037i
\(628\) 4.16329i 0.166133i
\(629\) −8.68293 7.28584i −0.346211 0.290505i
\(630\) 0 0
\(631\) 5.98586 + 33.9475i 0.238293 + 1.35143i 0.835566 + 0.549390i \(0.185140\pi\)
−0.597273 + 0.802038i \(0.703749\pi\)
\(632\) −3.53552 0.623407i −0.140635 0.0247978i
\(633\) −8.43797 + 23.1831i −0.335379 + 0.921447i
\(634\) 8.20325 + 14.2084i 0.325793 + 0.564289i
\(635\) 0 0
\(636\) 6.08516 5.10605i 0.241292 0.202468i
\(637\) 19.4413 + 23.1692i 0.770292 + 0.917998i
\(638\) 24.9414 + 14.3999i 0.987438 + 0.570097i
\(639\) 0.214758 + 0.371972i 0.00849570 + 0.0147150i
\(640\) 0 0
\(641\) 8.27820 46.9480i 0.326969 1.85434i −0.168489 0.985704i \(-0.553889\pi\)
0.495458 0.868632i \(-0.335000\pi\)
\(642\) −15.6262 + 2.75531i −0.616715 + 0.108744i
\(643\) 3.24102 + 8.90463i 0.127813 + 0.351164i 0.987050 0.160414i \(-0.0512831\pi\)
−0.859236 + 0.511579i \(0.829061\pi\)
\(644\) −8.78604 7.37236i −0.346219 0.290512i
\(645\) 0 0
\(646\) 3.49912 10.5907i 0.137671 0.416686i
\(647\) 16.8594i 0.662810i −0.943489 0.331405i \(-0.892477\pi\)
0.943489 0.331405i \(-0.107523\pi\)
\(648\) −6.18097 + 7.36620i −0.242812 + 0.289372i
\(649\) −62.4116 + 22.7160i −2.44987 + 0.891679i
\(650\) 0 0
\(651\) −0.595156 + 3.37530i −0.0233260 + 0.132288i
\(652\) −1.64249 + 4.51272i −0.0643250 + 0.176732i
\(653\) 9.34245 5.39386i 0.365598 0.211078i −0.305936 0.952052i \(-0.598969\pi\)
0.671534 + 0.740974i \(0.265636\pi\)
\(654\) 8.54023 14.7921i 0.333949 0.578417i
\(655\) 0 0
\(656\) −4.20164 + 3.52559i −0.164046 + 0.137651i
\(657\) −1.20628 0.696444i −0.0470613 0.0271709i
\(658\) 11.2227 6.47941i 0.437505 0.252594i
\(659\) −18.6209 6.77745i −0.725367 0.264012i −0.0471644 0.998887i \(-0.515018\pi\)
−0.678202 + 0.734875i \(0.737241\pi\)
\(660\) 0 0
\(661\) −4.06094 23.0307i −0.157952 0.895792i −0.956037 0.293247i \(-0.905264\pi\)
0.798084 0.602546i \(-0.205847\pi\)
\(662\) −5.83754 16.0385i −0.226883 0.623355i
\(663\) 17.3504 20.6774i 0.673833 0.803043i
\(664\) −13.4994 −0.523878
\(665\) 0 0
\(666\) 0.981938 0.0380493
\(667\) 24.1439 28.7736i 0.934857 1.11412i
\(668\) 1.32265 + 3.63394i 0.0511747 + 0.140601i
\(669\) 7.01750 + 39.7982i 0.271312 + 1.53869i
\(670\) 0 0
\(671\) −39.2296 14.2784i −1.51444 0.551212i
\(672\) 2.11631 1.22185i 0.0816386 0.0471341i
\(673\) 19.0320 + 10.9881i 0.733628 + 0.423560i 0.819748 0.572724i \(-0.194113\pi\)
−0.0861200 + 0.996285i \(0.527447\pi\)
\(674\) 14.4450 12.1208i 0.556399 0.466874i
\(675\) 0 0
\(676\) −10.7695 + 18.6533i −0.414210 + 0.717434i
\(677\) 40.2317 23.2278i 1.54623 0.892716i 0.547804 0.836607i \(-0.315464\pi\)
0.998425 0.0561091i \(-0.0178695\pi\)
\(678\) 6.80187 18.6880i 0.261224 0.717707i
\(679\) 0.0291884 0.165536i 0.00112015 0.00635268i
\(680\) 0 0
\(681\) 31.7772 11.5660i 1.21770 0.443208i
\(682\) 5.82315 6.93976i 0.222980 0.265737i
\(683\) 13.4198i 0.513496i −0.966478 0.256748i \(-0.917349\pi\)
0.966478 0.256748i \(-0.0826511\pi\)
\(684\) 0.357534 + 0.897681i 0.0136706 + 0.0343237i
\(685\) 0 0
\(686\) 12.6681 + 10.6298i 0.483669 + 0.405846i
\(687\) −2.77375 7.62081i −0.105825 0.290752i
\(688\) −6.74986 + 1.19018i −0.257336 + 0.0453753i
\(689\) −4.51650 + 25.6143i −0.172065 + 0.975828i
\(690\) 0 0
\(691\) 20.9252 + 36.2436i 0.796033 + 1.37877i 0.922181 + 0.386759i \(0.126405\pi\)
−0.126148 + 0.992011i \(0.540261\pi\)
\(692\) 9.99296 + 5.76944i 0.379875 + 0.219321i
\(693\) 1.25306 + 1.49334i 0.0476000 + 0.0567275i
\(694\) 4.14258 3.47604i 0.157250 0.131949i
\(695\) 0 0
\(696\) 4.00148 + 6.93077i 0.151676 + 0.262710i
\(697\) −4.80023 + 13.1885i −0.181822 + 0.499551i
\(698\) 35.7564 + 6.30481i 1.35340 + 0.238641i
\(699\) 3.35468 + 19.0253i 0.126886 + 0.719605i
\(700\) 0 0
\(701\) 20.5106 + 17.2104i 0.774674 + 0.650028i 0.941901 0.335890i \(-0.109037\pi\)
−0.167228 + 0.985918i \(0.553481\pi\)
\(702\) 29.3075i 1.10614i
\(703\) −9.14886 + 17.0031i −0.345056 + 0.641286i
\(704\) −6.45921 −0.243441
\(705\) 0 0
\(706\) −1.15574 + 0.420656i −0.0434970 + 0.0158316i
\(707\) 18.3073 3.22806i 0.688515 0.121404i
\(708\) −18.1757 3.20488i −0.683086 0.120447i
\(709\) −17.7455 6.45882i −0.666445 0.242566i −0.0134283 0.999910i \(-0.504274\pi\)
−0.653016 + 0.757344i \(0.726497\pi\)
\(710\) 0 0
\(711\) 0.397914 0.689208i 0.0149230 0.0258473i
\(712\) −1.21872 1.45242i −0.0456736 0.0544317i
\(713\) −7.59468 9.05099i −0.284423 0.338962i
\(714\) 3.12655 5.41535i 0.117008 0.202664i
\(715\) 0 0
\(716\) −7.87426 2.86600i −0.294275 0.107107i
\(717\) −41.3662 7.29398i −1.54485 0.272399i
\(718\) −14.8995 + 2.62718i −0.556044 + 0.0980455i
\(719\) 30.3154 11.0339i 1.13057 0.411496i 0.292074 0.956396i \(-0.405655\pi\)
0.838501 + 0.544900i \(0.183432\pi\)
\(720\) 0 0
\(721\) −9.35914 −0.348553
\(722\) −18.8754 2.17281i −0.702468 0.0808637i
\(723\) 37.5052i 1.39483i
\(724\) 8.13969 + 6.83001i 0.302509 + 0.253835i
\(725\) 0 0
\(726\) −9.57529 54.3042i −0.355372 2.01542i
\(727\) 17.6378 + 3.11002i 0.654150 + 0.115344i 0.490866 0.871235i \(-0.336680\pi\)
0.163284 + 0.986579i \(0.447791\pi\)
\(728\) −2.73662 + 7.51881i −0.101426 + 0.278666i
\(729\) 12.3605 + 21.4090i 0.457796 + 0.792926i
\(730\) 0 0
\(731\) −13.4352 + 11.2735i −0.496918 + 0.416964i
\(732\) −7.45688 8.88676i −0.275614 0.328464i
\(733\) 41.4082 + 23.9071i 1.52945 + 0.883027i 0.999385 + 0.0350693i \(0.0111652\pi\)
0.530063 + 0.847958i \(0.322168\pi\)
\(734\) 1.05724 + 1.83120i 0.0390235 + 0.0675907i
\(735\) 0 0
\(736\) −1.46285 + 8.29626i −0.0539215 + 0.305804i
\(737\) −42.7440 + 7.53693i −1.57450 + 0.277626i
\(738\) −0.415848 1.14253i −0.0153076 0.0420572i
\(739\) 2.75913 + 2.31519i 0.101496 + 0.0851656i 0.692124 0.721779i \(-0.256675\pi\)
−0.590627 + 0.806944i \(0.701120\pi\)
\(740\) 0 0
\(741\) −40.4910 21.7870i −1.48747 0.800364i
\(742\) 6.02540i 0.221199i
\(743\) 1.99911 2.38245i 0.0733403 0.0874036i −0.728127 0.685443i \(-0.759609\pi\)
0.801467 + 0.598039i \(0.204053\pi\)
\(744\) 2.36558 0.861001i 0.0867264 0.0315658i
\(745\) 0 0
\(746\) −0.874756 + 4.96099i −0.0320271 + 0.181635i
\(747\) 1.02349 2.81202i 0.0374476 0.102886i
\(748\) −14.3138 + 8.26410i −0.523366 + 0.302165i
\(749\) 6.01781 10.4231i 0.219886 0.380854i
\(750\) 0 0
\(751\) 15.5562 13.0532i 0.567654 0.476318i −0.313213 0.949683i \(-0.601405\pi\)
0.880866 + 0.473365i \(0.156961\pi\)
\(752\) −8.24304 4.75912i −0.300593 0.173547i
\(753\) −27.8321 + 16.0689i −1.01426 + 0.585582i
\(754\) −24.6235 8.96223i −0.896736 0.326385i
\(755\) 0 0
\(756\) −1.17897 6.68627i −0.0428787 0.243177i
\(757\) −13.3721 36.7396i −0.486018 1.33532i −0.904258 0.426987i \(-0.859575\pi\)
0.418239 0.908337i \(-0.362647\pi\)
\(758\) 23.9639 28.5591i 0.870408 1.03731i
\(759\) −97.6677 −3.54511
\(760\) 0 0
\(761\) 4.22431 0.153131 0.0765656 0.997065i \(-0.475605\pi\)
0.0765656 + 0.997065i \(0.475605\pi\)
\(762\) −10.6055 + 12.6392i −0.384197 + 0.457868i
\(763\) 4.43118 + 12.1746i 0.160419 + 0.440748i
\(764\) −1.88432 10.6865i −0.0681724 0.386625i
\(765\) 0 0
\(766\) 13.9869 + 5.09082i 0.505368 + 0.183939i
\(767\) 52.3341 30.2151i 1.88968 1.09101i
\(768\) −1.55443 0.897451i −0.0560907 0.0323840i
\(769\) −28.9268 + 24.2725i −1.04313 + 0.875288i −0.992354 0.123422i \(-0.960613\pi\)
−0.0507735 + 0.998710i \(0.516169\pi\)
\(770\) 0 0
\(771\) 0.436958 0.756833i 0.0157367 0.0272567i
\(772\) −1.67685 + 0.968131i −0.0603512 + 0.0348438i
\(773\) 1.32574 3.64243i 0.0476834 0.131009i −0.913565 0.406693i \(-0.866682\pi\)
0.961248 + 0.275684i \(0.0889042\pi\)
\(774\) 0.263834 1.49628i 0.00948333 0.0537827i
\(775\) 0 0
\(776\) −0.116016 + 0.0422263i −0.00416473 + 0.00151584i
\(777\) −6.95798 + 8.29220i −0.249616 + 0.297481i
\(778\) 30.8414i 1.10572i
\(779\) 23.6585 + 3.44436i 0.847653 + 0.123407i
\(780\) 0 0
\(781\) 9.58727 + 8.04468i 0.343060 + 0.287861i
\(782\) 7.37273 + 20.2564i 0.263648 + 0.724368i
\(783\) 21.8970 3.86104i