Properties

Label 950.2.u.g.149.6
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 149.6
Character \(\chi\) \(=\) 950.149
Dual form 950.2.u.g.899.6

$q$-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 \(0.0622657\pi\)
−0.626497 + 0.779423i \(0.715512\pi\)
\(4\) −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 −0.260343 0.965516i \(-0.583836\pi\)
0.705990 + 0.708222i \(0.250502\pi\)
\(8\) −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 \(0.414369\pi\)
−0.823270 + 0.567650i \(0.807853\pi\)
\(14\) 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 −0.528768 0.848766i \(-0.677346\pi\)
0.927691 + 0.373348i \(0.121790\pi\)
\(18\) 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 0.781918 0.623382i \(-0.214242\pi\)
0.947971 + 0.318356i \(0.103131\pi\)
\(24\) 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 \(-0.881372\pi\)
0.931355 0.364112i \(-0.118628\pi\)
\(38\) 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 −0.366625 0.930369i \(-0.619487\pi\)
−0.662719 + 0.748868i \(0.730598\pi\)
\(44\) 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 \(-0.977985\pi\)
0.105176 0.994454i \(-0.466459\pi\)
\(48\) −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 0.133905 0.990994i \(-0.457248\pi\)
0.464769 + 0.885432i \(0.346137\pi\)
\(54\) 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 0.434695 0.900578i \(-0.356856\pi\)
−0.962380 + 0.271707i \(0.912412\pi\)
\(68\) −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 \(-0.991253\pi\)
0.748093 0.663594i \(-0.230970\pi\)
\(74\) −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 0.305797 0.952097i \(-0.401077\pi\)
0.977438 + 0.211221i \(0.0677439\pi\)
\(84\) 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 −0.762001 0.647576i \(-0.775783\pi\)
0.770058 + 0.637974i \(0.220227\pi\)
\(98\) 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 0.177154 0.984183i \(-0.443311\pi\)
−0.763751 + 0.645512i \(0.776644\pi\)
\(104\) 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 −0.0819969 0.996633i \(-0.526130\pi\)
0.822111 + 0.569328i \(0.192796\pi\)
\(108\) 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 \(0.174498\pi\)
−0.853462 + 0.521154i \(0.825502\pi\)
\(114\) 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 \(-0.755170\pi\)
0.997479 0.0709633i \(-0.0226073\pi\)
\(128\) 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 −0.715341 0.698776i \(-0.753729\pi\)
−0.433205 + 0.901295i \(0.642617\pi\)
\(138\) 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 0.00762562 0.999971i \(-0.497573\pi\)
−0.334844 + 0.942273i \(0.608684\pi\)
\(158\) −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 0.653954 0.756534i \(-0.273109\pi\)
−0.328201 + 0.944608i \(0.606442\pi\)
\(164\) −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 −0.0243418 0.999704i \(-0.507749\pi\)
0.319045 + 0.947740i \(0.396638\pi\)
\(168\) −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 −0.406461 0.913668i \(-0.633237\pi\)
0.970369 + 0.241629i \(0.0776818\pi\)
\(174\) −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 0.961243 0.275704i \(-0.0889109\pi\)
−0.913574 + 0.406674i \(0.866689\pi\)
\(194\) −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 −0.0718004 0.997419i \(-0.522874\pi\)
0.827890 + 0.560890i \(0.189541\pi\)
\(198\) −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 0.856497 0.516151i \(-0.172636\pi\)
0.628310 + 0.777963i \(0.283747\pi\)
\(224\) 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 \(-0.785002\pi\)
0.780433 0.625239i \(-0.214998\pi\)
\(228\) 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 0.509701 0.860351i \(-0.329756\pi\)
0.184705 + 0.982794i \(0.440867\pi\)
\(234\) −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 0.756195 0.654346i \(-0.227056\pi\)
−0.775717 + 0.631081i \(0.782612\pi\)
\(258\) −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 \(-0.872918\pi\)
0.455936 0.890013i \(-0.349305\pi\)
\(264\) 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 0.245417 0.969418i \(-0.421075\pi\)
−0.716832 + 0.697246i \(0.754408\pi\)
\(278\) 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 −0.920667 0.390349i \(-0.872354\pi\)
0.544291 + 0.838897i \(0.316799\pi\)
\(284\) −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 0.692418 0.721497i \(-0.256545\pi\)
−0.278625 + 0.960400i \(0.589879\pi\)
\(294\) −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 0.984612 0.174753i \(-0.0559128\pi\)
−0.866586 + 0.499028i \(0.833691\pi\)
\(308\) 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 0.866423 0.499312i \(-0.166414\pi\)
−0.642179 + 0.766555i \(0.721969\pi\)
\(314\) −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 \(0.263527\pi\)
−0.991593 + 0.129399i \(0.958695\pi\)
\(318\) 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 0.654785 0.755816i \(-0.272759\pi\)
0.356792 + 0.934184i \(0.383870\pi\)
\(338\) −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 0.314756 0.949173i \(-0.398077\pi\)
−0.0288626 + 0.999583i \(0.509189\pi\)
\(348\) −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 0.471386 0.881927i \(-0.343754\pi\)
−0.528078 + 0.849196i \(0.677087\pi\)
\(354\) 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 −0.957136 0.289640i \(-0.906465\pi\)
0.919385 + 0.393358i \(0.128687\pi\)
\(368\) −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 −0.608674 0.793421i \(-0.708298\pi\)
0.382786 + 0.923837i \(0.374965\pi\)
\(374\) 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 \(0.0130623\pi\)
−0.739029 + 0.673673i \(0.764715\pi\)
\(384\) 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 −0.279397 0.960176i \(-0.590135\pi\)
0.994105 + 0.108420i \(0.0345790\pi\)
\(398\) 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 −0.623755 0.781620i \(-0.714394\pi\)
−0.318808 + 0.947819i \(0.603283\pi\)
\(434\) 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 −0.879241 0.476377i \(-0.841950\pi\)
0.979747 + 0.200239i \(0.0641718\pi\)
\(444\) −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 \(0.111778\pi\)
−0.938974 + 0.343989i \(0.888222\pi\)
\(458\) 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 −0.545062 0.838396i \(-0.683494\pi\)
0.453541 + 0.891235i \(0.350160\pi\)
\(464\) 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 0.956205 0.292698i \(-0.0945531\pi\)
0.224618 + 0.974447i \(0.427886\pi\)
\(468\) −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 0.195637 0.980676i \(-0.437323\pi\)
0.947109 + 0.320912i \(0.103989\pi\)
\(488\) 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 0.655258 0.755405i \(-0.272560\pi\)
−0.857713 + 0.514128i \(0.828116\pi\)
\(504\) 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 \(-0.828386\pi\)
−0.356583 0.934263i \(-0.616058\pi\)
\(524\) 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 −0.654836 0.755771i \(-0.727262\pi\)
−0.356855 + 0.934160i \(0.616151\pi\)
\(548\) 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 −0.902288 0.431135i \(-0.858113\pi\)
0.968320 + 0.249711i \(0.0803356\pi\)
\(558\) −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 −0.0174729 0.999847i \(-0.505562\pi\)
0.857157 + 0.515056i \(0.172229\pi\)
\(564\) −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 −0.841906 0.539624i \(-0.818566\pi\)
0.0463754 + 0.998924i \(0.485233\pi\)
\(578\) 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 −0.727107 0.686524i \(-0.759136\pi\)
0.802355 + 0.596847i \(0.203580\pi\)
\(588\) 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 −0.936557 0.350515i \(-0.886006\pi\)
−0.760192 + 0.649698i \(0.774895\pi\)
\(594\) −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 \(-0.954157\pi\)
0.989647 0.143522i \(-0.0458428\pi\)
\(608\) −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 0.576840 0.816857i \(-0.304286\pi\)
0.262670 + 0.964886i \(0.415397\pi\)
\(614\) 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 0.240472 0.970656i \(-0.422698\pi\)
−0.997667 + 0.0682659i \(0.978253\pi\)
\(618\) −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 0.859236 0.511579i \(-0.170939\pi\)
−0.987050 + 0.160414i \(0.948717\pi\)
\(644\) −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 \(0.107523\pi\)
−0.943489 + 0.331405i \(0.892477\pi\)
\(648\) 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 −0.671534 0.740974i \(-0.734364\pi\)
0.305936 + 0.952052i \(0.401031\pi\)
\(654\) 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 0.0861200 0.996285i \(-0.472553\pi\)
−0.819748 + 0.572724i \(0.805887\pi\)
\(674\) 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 \(0.684536\pi\)
−0.998425 + 0.0561091i \(0.982131\pi\)
\(678\) −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 \(0.0826511\pi\)
−0.966478 + 0.256748i \(0.917349\pi\)
\(684\) 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 −0.163284 0.986579i \(-0.552209\pi\)
−0.490866 + 0.871235i \(0.663320\pi\)
\(728\) 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 \(-0.988835\pi\)
−0.530063 0.847958i \(-0.677832\pi\)
\(734\) 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 −0.801467 0.598039i \(-0.795947\pi\)
0.728127 + 0.685443i \(0.240391\pi\)
\(744\) 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 \(0.140425\pi\)
−0.418239 + 0.908337i \(0.637353\pi\)
\(758\) −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 −0.961248 0.275684i \(-0.911096\pi\)
0.913565 + 0.406693i \(0.133318\pi\)
\(774\) 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 +