Properties

Label 349.2.e.a.123.12
Level 349
Weight 2
Character 349.123
Analytic conductor 2.787
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.78677903054\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 123.12
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.788972 + 0.455513i) q^{2} +(-1.46240 + 2.53295i) q^{3} +(-0.585016 + 1.01328i) q^{4} +(1.45267 - 2.51610i) q^{5} -2.66457i q^{6} +(3.29342 - 1.90146i) q^{7} -2.88798i q^{8} +(-2.77724 - 4.81032i) q^{9} +O(q^{10})\) \(q+(-0.788972 + 0.455513i) q^{2} +(-1.46240 + 2.53295i) q^{3} +(-0.585016 + 1.01328i) q^{4} +(1.45267 - 2.51610i) q^{5} -2.66457i q^{6} +(3.29342 - 1.90146i) q^{7} -2.88798i q^{8} +(-2.77724 - 4.81032i) q^{9} +2.64684i q^{10} -3.72216i q^{11} +(-1.71106 - 2.96364i) q^{12} +(3.22785 - 1.86360i) q^{13} +(-1.73228 + 3.00039i) q^{14} +(4.24877 + 7.35909i) q^{15} +(0.145481 + 0.251980i) q^{16} -5.36165 q^{17} +(4.38232 + 2.53014i) q^{18} +(1.62062 - 2.80699i) q^{19} +(1.69967 + 2.94391i) q^{20} +11.1228i q^{21} +(1.69549 + 2.93667i) q^{22} +(-2.39400 - 4.14653i) q^{23} +(7.31512 + 4.22339i) q^{24} +(-1.72049 - 2.97998i) q^{25} +(-1.69779 + 2.94065i) q^{26} +7.47134 q^{27} +4.44953i q^{28} +(-2.19135 + 3.79553i) q^{29} +(-6.70432 - 3.87074i) q^{30} +6.79620 q^{31} +(4.77257 + 2.75544i) q^{32} +(9.42805 + 5.44329i) q^{33} +(4.23019 - 2.44230i) q^{34} -11.0488i q^{35} +6.49892 q^{36} -7.48368 q^{37} +2.95285i q^{38} +10.9013i q^{39} +(-7.26644 - 4.19528i) q^{40} -2.38606 q^{41} +(-5.06657 - 8.77556i) q^{42} +(-1.70678 - 0.985410i) q^{43} +(3.77158 + 2.17752i) q^{44} -16.1376 q^{45} +(3.77759 + 2.18099i) q^{46} -7.30944i q^{47} -0.851005 q^{48} +(3.73109 - 6.46243i) q^{49} +(2.71484 + 1.56741i) q^{50} +(7.84088 - 13.5808i) q^{51} +4.36094i q^{52} +12.2676i q^{53} +(-5.89468 + 3.40329i) q^{54} +(-9.36530 - 5.40706i) q^{55} +(-5.49137 - 9.51134i) q^{56} +(4.73998 + 8.20989i) q^{57} -3.99275i q^{58} +(-7.06848 - 4.08099i) q^{59} -9.94240 q^{60} -4.05102i q^{61} +(-5.36201 + 3.09576i) q^{62} +(-18.2932 - 10.5616i) q^{63} -5.60248 q^{64} -10.8288i q^{65} -9.91795 q^{66} +15.3725 q^{67} +(3.13665 - 5.43284i) q^{68} +14.0039 q^{69} +(5.03285 + 8.71715i) q^{70} +(6.81338 - 3.93371i) q^{71} +(-13.8921 + 8.02061i) q^{72} +(-3.57439 + 6.19102i) q^{73} +(5.90441 - 3.40891i) q^{74} +10.0642 q^{75} +(1.89617 + 3.28427i) q^{76} +(-7.07752 - 12.2586i) q^{77} +(-4.96569 - 8.60082i) q^{78} +11.6997i q^{79} +0.845341 q^{80} +(-2.59439 + 4.49362i) q^{81} +(1.88253 - 1.08688i) q^{82} +(7.11627 + 12.3257i) q^{83} +(-11.2705 - 6.50701i) q^{84} +(-7.78870 + 13.4904i) q^{85} +1.79547 q^{86} +(-6.40927 - 11.1012i) q^{87} -10.7495 q^{88} +(12.8584 + 7.42383i) q^{89} +(12.7321 - 7.35090i) q^{90} +(7.08710 - 12.2752i) q^{91} +5.60211 q^{92} +(-9.93877 + 17.2145i) q^{93} +(3.32955 + 5.76694i) q^{94} +(-4.70844 - 8.15525i) q^{95} +(-13.9588 + 8.05913i) q^{96} +(-5.04200 + 2.91100i) q^{97} +6.79823i q^{98} +(-17.9048 + 10.3373i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} + O(q^{10}) \) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} - q^{12} - 3q^{13} - 10q^{14} + q^{15} - 29q^{16} - 10q^{17} + 15q^{18} - 9q^{19} - 3q^{22} - 17q^{23} - 48q^{24} - 29q^{25} - 4q^{26} + 18q^{27} - 2q^{29} + 9q^{30} + 32q^{31} + 9q^{32} - 12q^{33} - 63q^{34} + 24q^{36} - 16q^{37} + 54q^{40} - 10q^{41} - 15q^{42} - 45q^{43} + 18q^{44} - 2q^{45} + 27q^{46} + 6q^{48} + 35q^{49} + 6q^{50} - 14q^{51} + 27q^{54} + 24q^{55} + 11q^{56} - 29q^{57} - 18q^{59} + 116q^{60} - 9q^{62} - 21q^{63} - 132q^{64} + 130q^{66} + 58q^{67} + 42q^{69} + 40q^{70} - 24q^{71} + 72q^{72} - 6q^{73} + 30q^{74} - 58q^{75} + 37q^{76} - 4q^{77} - 33q^{78} - 40q^{80} - 81q^{81} + 21q^{82} + 12q^{83} + 18q^{84} - 11q^{85} - 126q^{86} - 42q^{87} - 50q^{88} + 3q^{89} - 12q^{90} - 28q^{91} - 120q^{92} + 31q^{93} + 29q^{94} + 60q^{95} - 120q^{96} - 15q^{97} + 39q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.788972 + 0.455513i −0.557887 + 0.322096i −0.752297 0.658824i \(-0.771054\pi\)
0.194410 + 0.980920i \(0.437721\pi\)
\(3\) −1.46240 + 2.53295i −0.844318 + 1.46240i 0.0418940 + 0.999122i \(0.486661\pi\)
−0.886212 + 0.463280i \(0.846673\pi\)
\(4\) −0.585016 + 1.01328i −0.292508 + 0.506639i
\(5\) 1.45267 2.51610i 0.649653 1.12523i −0.333552 0.942732i \(-0.608247\pi\)
0.983206 0.182501i \(-0.0584193\pi\)
\(6\) 2.66457i 1.08781i
\(7\) 3.29342 1.90146i 1.24480 0.718684i 0.274730 0.961522i \(-0.411412\pi\)
0.970067 + 0.242838i \(0.0780783\pi\)
\(8\) 2.88798i 1.02106i
\(9\) −2.77724 4.81032i −0.925746 1.60344i
\(10\) 2.64684i 0.837004i
\(11\) 3.72216i 1.12227i −0.827724 0.561136i \(-0.810364\pi\)
0.827724 0.561136i \(-0.189636\pi\)
\(12\) −1.71106 2.96364i −0.493940 0.855528i
\(13\) 3.22785 1.86360i 0.895243 0.516869i 0.0195893 0.999808i \(-0.493764\pi\)
0.875654 + 0.482939i \(0.160431\pi\)
\(14\) −1.73228 + 3.00039i −0.462971 + 0.801889i
\(15\) 4.24877 + 7.35909i 1.09703 + 1.90011i
\(16\) 0.145481 + 0.251980i 0.0363702 + 0.0629950i
\(17\) −5.36165 −1.30039 −0.650195 0.759767i \(-0.725313\pi\)
−0.650195 + 0.759767i \(0.725313\pi\)
\(18\) 4.38232 + 2.53014i 1.03292 + 0.596359i
\(19\) 1.62062 2.80699i 0.371795 0.643968i −0.618047 0.786141i \(-0.712076\pi\)
0.989842 + 0.142174i \(0.0454091\pi\)
\(20\) 1.69967 + 2.94391i 0.380058 + 0.658279i
\(21\) 11.1228i 2.42719i
\(22\) 1.69549 + 2.93667i 0.361480 + 0.626101i
\(23\) −2.39400 4.14653i −0.499183 0.864610i 0.500817 0.865553i \(-0.333033\pi\)
−1.00000 0.000943088i \(0.999700\pi\)
\(24\) 7.31512 + 4.22339i 1.49319 + 0.862096i
\(25\) −1.72049 2.97998i −0.344099 0.595997i
\(26\) −1.69779 + 2.94065i −0.332963 + 0.576709i
\(27\) 7.47134 1.43786
\(28\) 4.44953i 0.840883i
\(29\) −2.19135 + 3.79553i −0.406924 + 0.704812i −0.994543 0.104325i \(-0.966732\pi\)
0.587620 + 0.809137i \(0.300065\pi\)
\(30\) −6.70432 3.87074i −1.22404 0.706697i
\(31\) 6.79620 1.22063 0.610317 0.792158i \(-0.291042\pi\)
0.610317 + 0.792158i \(0.291042\pi\)
\(32\) 4.77257 + 2.75544i 0.843679 + 0.487098i
\(33\) 9.42805 + 5.44329i 1.64121 + 0.947555i
\(34\) 4.23019 2.44230i 0.725471 0.418851i
\(35\) 11.0488i 1.86758i
\(36\) 6.49892 1.08315
\(37\) −7.48368 −1.23031 −0.615155 0.788407i \(-0.710906\pi\)
−0.615155 + 0.788407i \(0.710906\pi\)
\(38\) 2.95285i 0.479015i
\(39\) 10.9013i 1.74561i
\(40\) −7.26644 4.19528i −1.14892 0.663332i
\(41\) −2.38606 −0.372640 −0.186320 0.982489i \(-0.559656\pi\)
−0.186320 + 0.982489i \(0.559656\pi\)
\(42\) −5.06657 8.77556i −0.781789 1.35410i
\(43\) −1.70678 0.985410i −0.260282 0.150274i 0.364181 0.931328i \(-0.381349\pi\)
−0.624463 + 0.781054i \(0.714682\pi\)
\(44\) 3.77158 + 2.17752i 0.568587 + 0.328274i
\(45\) −16.1376 −2.40566
\(46\) 3.77759 + 2.18099i 0.556976 + 0.321570i
\(47\) 7.30944i 1.06619i −0.846055 0.533096i \(-0.821028\pi\)
0.846055 0.533096i \(-0.178972\pi\)
\(48\) −0.851005 −0.122832
\(49\) 3.73109 6.46243i 0.533012 0.923204i
\(50\) 2.71484 + 1.56741i 0.383937 + 0.221666i
\(51\) 7.84088 13.5808i 1.09794 1.90169i
\(52\) 4.36094i 0.604753i
\(53\) 12.2676i 1.68508i 0.538634 + 0.842540i \(0.318941\pi\)
−0.538634 + 0.842540i \(0.681059\pi\)
\(54\) −5.89468 + 3.40329i −0.802164 + 0.463130i
\(55\) −9.36530 5.40706i −1.26282 0.729088i
\(56\) −5.49137 9.51134i −0.733816 1.27101i
\(57\) 4.73998 + 8.20989i 0.627826 + 1.08743i
\(58\) 3.99275i 0.524274i
\(59\) −7.06848 4.08099i −0.920238 0.531300i −0.0365271 0.999333i \(-0.511630\pi\)
−0.883711 + 0.468033i \(0.844963\pi\)
\(60\) −9.94240 −1.28356
\(61\) 4.05102i 0.518680i −0.965786 0.259340i \(-0.916495\pi\)
0.965786 0.259340i \(-0.0835050\pi\)
\(62\) −5.36201 + 3.09576i −0.680976 + 0.393161i
\(63\) −18.2932 10.5616i −2.30473 1.33064i
\(64\) −5.60248 −0.700311
\(65\) 10.8288i 1.34314i
\(66\) −9.91795 −1.22082
\(67\) 15.3725 1.87805 0.939025 0.343849i \(-0.111731\pi\)
0.939025 + 0.343849i \(0.111731\pi\)
\(68\) 3.13665 5.43284i 0.380375 0.658828i
\(69\) 14.0039 1.68588
\(70\) 5.03285 + 8.71715i 0.601541 + 1.04190i
\(71\) 6.81338 3.93371i 0.808599 0.466845i −0.0378699 0.999283i \(-0.512057\pi\)
0.846469 + 0.532438i \(0.178724\pi\)
\(72\) −13.8921 + 8.02061i −1.63720 + 0.945238i
\(73\) −3.57439 + 6.19102i −0.418350 + 0.724604i −0.995774 0.0918407i \(-0.970725\pi\)
0.577423 + 0.816445i \(0.304058\pi\)
\(74\) 5.90441 3.40891i 0.686374 0.396278i
\(75\) 10.0642 1.16212
\(76\) 1.89617 + 3.28427i 0.217506 + 0.376731i
\(77\) −7.07752 12.2586i −0.806559 1.39700i
\(78\) −4.96569 8.60082i −0.562254 0.973852i
\(79\) 11.6997i 1.31632i 0.752877 + 0.658162i \(0.228666\pi\)
−0.752877 + 0.658162i \(0.771334\pi\)
\(80\) 0.845341 0.0945120
\(81\) −2.59439 + 4.49362i −0.288266 + 0.499291i
\(82\) 1.88253 1.08688i 0.207891 0.120026i
\(83\) 7.11627 + 12.3257i 0.781112 + 1.35293i 0.931294 + 0.364267i \(0.118681\pi\)
−0.150182 + 0.988658i \(0.547986\pi\)
\(84\) −11.2705 6.50701i −1.22971 0.709973i
\(85\) −7.78870 + 13.4904i −0.844803 + 1.46324i
\(86\) 1.79547 0.193610
\(87\) −6.40927 11.1012i −0.687146 1.19017i
\(88\) −10.7495 −1.14590
\(89\) 12.8584 + 7.42383i 1.36299 + 0.786924i 0.990021 0.140919i \(-0.0450056\pi\)
0.372971 + 0.927843i \(0.378339\pi\)
\(90\) 12.7321 7.35090i 1.34208 0.774853i
\(91\) 7.08710 12.2752i 0.742930 1.28679i
\(92\) 5.60211 0.584060
\(93\) −9.93877 + 17.2145i −1.03060 + 1.78506i
\(94\) 3.32955 + 5.76694i 0.343417 + 0.594815i
\(95\) −4.70844 8.15525i −0.483076 0.836711i
\(96\) −13.9588 + 8.05913i −1.42467 + 0.822532i
\(97\) −5.04200 + 2.91100i −0.511938 + 0.295568i −0.733630 0.679549i \(-0.762175\pi\)
0.221692 + 0.975117i \(0.428842\pi\)
\(98\) 6.79823i 0.686725i
\(99\) −17.9048 + 10.3373i −1.79950 + 1.03894i
\(100\) 4.02607 0.402607
\(101\) 16.0750i 1.59952i −0.600320 0.799760i \(-0.704960\pi\)
0.600320 0.799760i \(-0.295040\pi\)
\(102\) 14.2865i 1.41457i
\(103\) 19.7867i 1.94964i 0.222999 + 0.974819i \(0.428415\pi\)
−0.222999 + 0.974819i \(0.571585\pi\)
\(104\) −5.38203 9.32196i −0.527752 0.914093i
\(105\) 27.9860 + 16.1577i 2.73115 + 1.57683i
\(106\) −5.58804 9.67876i −0.542758 0.940084i
\(107\) 0.976050 0.563523i 0.0943583 0.0544778i −0.452078 0.891978i \(-0.649317\pi\)
0.546437 + 0.837500i \(0.315984\pi\)
\(108\) −4.37085 + 7.57054i −0.420586 + 0.728476i
\(109\) 2.35788 4.08396i 0.225844 0.391173i −0.730728 0.682668i \(-0.760819\pi\)
0.956572 + 0.291495i \(0.0941528\pi\)
\(110\) 9.85194 0.939346
\(111\) 10.9441 18.9558i 1.03877 1.79921i
\(112\) 0.958259 + 0.553251i 0.0905469 + 0.0522773i
\(113\) 0.355888 0.205472i 0.0334791 0.0193292i −0.483167 0.875528i \(-0.660514\pi\)
0.516646 + 0.856199i \(0.327180\pi\)
\(114\) −7.47943 4.31825i −0.700512 0.404441i
\(115\) −13.9107 −1.29718
\(116\) −2.56395 4.44089i −0.238057 0.412326i
\(117\) −17.9290 10.3513i −1.65754 0.956979i
\(118\) 7.43578 0.684519
\(119\) −17.6582 + 10.1950i −1.61872 + 0.934570i
\(120\) 21.2529 12.2704i 1.94012 1.12013i
\(121\) −2.85444 −0.259495
\(122\) 1.84529 + 3.19614i 0.167065 + 0.289365i
\(123\) 3.48938 6.04378i 0.314626 0.544949i
\(124\) −3.97588 + 6.88643i −0.357045 + 0.618420i
\(125\) 4.52946 0.405127
\(126\) 19.2438 1.71437
\(127\) 3.07777i 0.273108i −0.990633 0.136554i \(-0.956397\pi\)
0.990633 0.136554i \(-0.0436027\pi\)
\(128\) −5.12494 + 2.95888i −0.452985 + 0.261531i
\(129\) 4.99200 2.88213i 0.439521 0.253757i
\(130\) 4.93264 + 8.54358i 0.432621 + 0.749322i
\(131\) 9.13364i 0.798010i −0.916949 0.399005i \(-0.869356\pi\)
0.916949 0.399005i \(-0.130644\pi\)
\(132\) −11.0311 + 6.36882i −0.960136 + 0.554335i
\(133\) 12.3261i 1.06881i
\(134\) −12.1285 + 7.00237i −1.04774 + 0.604913i
\(135\) 10.8534 18.7986i 0.934111 1.61793i
\(136\) 15.4843i 1.32777i
\(137\) 6.66936 + 3.85056i 0.569802 + 0.328975i 0.757070 0.653334i \(-0.226630\pi\)
−0.187268 + 0.982309i \(0.559963\pi\)
\(138\) −11.0487 + 6.37898i −0.940529 + 0.543015i
\(139\) 11.6995 0.992341 0.496170 0.868225i \(-0.334739\pi\)
0.496170 + 0.868225i \(0.334739\pi\)
\(140\) 11.1955 + 6.46370i 0.946189 + 0.546282i
\(141\) 18.5145 + 10.6893i 1.55920 + 0.900205i
\(142\) −3.58371 + 6.20716i −0.300738 + 0.520894i
\(143\) −6.93660 12.0145i −0.580068 1.00471i
\(144\) 0.808069 1.39962i 0.0673391 0.116635i
\(145\) 6.36661 + 11.0273i 0.528718 + 0.915767i
\(146\) 6.51272i 0.538997i
\(147\) 10.9127 + 18.9013i 0.900064 + 1.55896i
\(148\) 4.37807 7.58304i 0.359875 0.623322i
\(149\) −2.15443 + 1.24386i −0.176498 + 0.101901i −0.585646 0.810567i \(-0.699159\pi\)
0.409149 + 0.912468i \(0.365826\pi\)
\(150\) −7.94038 + 4.58438i −0.648329 + 0.374313i
\(151\) 2.53021 4.38245i 0.205905 0.356638i −0.744516 0.667605i \(-0.767319\pi\)
0.950421 + 0.310967i \(0.100653\pi\)
\(152\) −8.10653 4.68031i −0.657527 0.379623i
\(153\) 14.8906 + 25.7912i 1.20383 + 2.08510i
\(154\) 11.1679 + 6.44781i 0.899937 + 0.519579i
\(155\) 9.87263 17.0999i 0.792988 1.37350i
\(156\) −11.0461 6.37744i −0.884392 0.510604i
\(157\) −4.39296 + 7.60883i −0.350597 + 0.607251i −0.986354 0.164638i \(-0.947354\pi\)
0.635758 + 0.771889i \(0.280688\pi\)
\(158\) −5.32938 9.23076i −0.423983 0.734360i
\(159\) −31.0732 17.9401i −2.46426 1.42274i
\(160\) 13.8659 8.00550i 1.09620 0.632890i
\(161\) −15.7689 9.10417i −1.24276 0.717509i
\(162\) 4.72711i 0.371397i
\(163\) 4.03054i 0.315697i −0.987463 0.157848i \(-0.949544\pi\)
0.987463 0.157848i \(-0.0504557\pi\)
\(164\) 1.39588 2.41774i 0.109000 0.188794i
\(165\) 27.3917 15.8146i 2.13244 1.23116i
\(166\) −11.2291 6.48311i −0.871545 0.503187i
\(167\) 9.36911i 0.725003i 0.931983 + 0.362502i \(0.118077\pi\)
−0.931983 + 0.362502i \(0.881923\pi\)
\(168\) 32.1224 2.47830
\(169\) 0.445989 0.772476i 0.0343069 0.0594213i
\(170\) 14.1914i 1.08843i
\(171\) −18.0034 −1.37675
\(172\) 1.99699 1.15296i 0.152269 0.0879125i
\(173\) −1.70254 + 0.982963i −0.129442 + 0.0747333i −0.563323 0.826237i \(-0.690477\pi\)
0.433881 + 0.900970i \(0.357144\pi\)
\(174\) 10.1135 + 5.83901i 0.766700 + 0.442654i
\(175\) −11.3326 6.54289i −0.856666 0.494596i
\(176\) 0.937909 0.541502i 0.0706975 0.0408172i
\(177\) 20.6739 11.9361i 1.55395 0.897172i
\(178\) −13.5266 −1.01386
\(179\) 8.05262i 0.601881i −0.953643 0.300941i \(-0.902699\pi\)
0.953643 0.300941i \(-0.0973006\pi\)
\(180\) 9.44077 16.3519i 0.703674 1.21880i
\(181\) −15.5706 −1.15736 −0.578679 0.815556i \(-0.696431\pi\)
−0.578679 + 0.815556i \(0.696431\pi\)
\(182\) 12.9131i 0.957180i
\(183\) 10.2610 + 5.92422i 0.758518 + 0.437931i
\(184\) −11.9751 + 6.91382i −0.882815 + 0.509694i
\(185\) −10.8713 + 18.8297i −0.799274 + 1.38438i
\(186\) 18.1090i 1.32781i
\(187\) 19.9569i 1.45939i
\(188\) 7.40650 + 4.27614i 0.540174 + 0.311870i
\(189\) 24.6063 14.2064i 1.78984 1.03337i
\(190\) 7.42965 + 4.28951i 0.539003 + 0.311194i
\(191\) 7.60898 + 13.1791i 0.550566 + 0.953609i 0.998234 + 0.0594087i \(0.0189215\pi\)
−0.447667 + 0.894200i \(0.647745\pi\)
\(192\) 8.19308 14.1908i 0.591285 1.02414i
\(193\) −12.2940 7.09792i −0.884938 0.510919i −0.0126549 0.999920i \(-0.504028\pi\)
−0.872284 + 0.489000i \(0.837362\pi\)
\(194\) 2.65200 4.59340i 0.190402 0.329787i
\(195\) 27.4288 + 15.8360i 1.96421 + 1.13404i
\(196\) 4.36549 + 7.56125i 0.311821 + 0.540089i
\(197\) −8.79258 5.07640i −0.626445 0.361678i 0.152929 0.988237i \(-0.451130\pi\)
−0.779374 + 0.626559i \(0.784463\pi\)
\(198\) 9.41756 16.3117i 0.669277 1.15922i
\(199\) 7.14996 4.12803i 0.506847 0.292628i −0.224690 0.974430i \(-0.572137\pi\)
0.731537 + 0.681802i \(0.238803\pi\)
\(200\) −8.60613 + 4.96875i −0.608546 + 0.351344i
\(201\) −22.4808 + 38.9378i −1.58567 + 2.74646i
\(202\) 7.32236 + 12.6827i 0.515199 + 0.892351i
\(203\) 16.6670i 1.16980i
\(204\) 9.17409 + 15.8900i 0.642314 + 1.11252i
\(205\) −3.46615 + 6.00355i −0.242087 + 0.419306i
\(206\) −9.01308 15.6111i −0.627971 1.08768i
\(207\) −13.2974 + 23.0318i −0.924234 + 1.60082i
\(208\) 0.939178 + 0.542235i 0.0651203 + 0.0375972i
\(209\) −10.4481 6.03219i −0.722707 0.417255i
\(210\) −29.4402 −2.03157
\(211\) 1.51078 0.872252i 0.104007 0.0600483i −0.447094 0.894487i \(-0.647541\pi\)
0.551101 + 0.834438i \(0.314208\pi\)
\(212\) −12.4304 7.17672i −0.853727 0.492899i
\(213\) 23.0106i 1.57666i
\(214\) −0.513384 + 0.889207i −0.0350942 + 0.0607849i
\(215\) −4.95877 + 2.86295i −0.338186 + 0.195252i
\(216\) 21.5771i 1.46814i
\(217\) 22.3828 12.9227i 1.51944 0.877249i
\(218\) 4.29618i 0.290974i
\(219\) −10.4544 18.1075i −0.706442 1.22359i
\(220\) 10.9577 6.32643i 0.738768 0.426528i
\(221\) −17.3066 + 9.99195i −1.16417 + 0.672132i
\(222\) 19.9408i 1.33834i
\(223\) 9.41521 0.630489 0.315245 0.949010i \(-0.397913\pi\)
0.315245 + 0.949010i \(0.397913\pi\)
\(224\) 20.9574 1.40028
\(225\) −9.55644 + 16.5522i −0.637096 + 1.10348i
\(226\) −0.187190 + 0.324223i −0.0124517 + 0.0215670i
\(227\) −0.760430 1.31710i −0.0504715 0.0874193i 0.839686 0.543072i \(-0.182739\pi\)
−0.890157 + 0.455653i \(0.849406\pi\)
\(228\) −11.0919 −0.734577
\(229\) 11.9185 6.88117i 0.787599 0.454721i −0.0515176 0.998672i \(-0.516406\pi\)
0.839117 + 0.543952i \(0.183072\pi\)
\(230\) 10.9752 6.33652i 0.723682 0.417818i
\(231\) 41.4007 2.72397
\(232\) 10.9614 + 6.32858i 0.719652 + 0.415492i
\(233\) 10.3133 + 17.8632i 0.675646 + 1.17025i 0.976280 + 0.216514i \(0.0694687\pi\)
−0.300633 + 0.953740i \(0.597198\pi\)
\(234\) 18.8606 1.23296
\(235\) −18.3913 10.6182i −1.19971 0.692655i
\(236\) 8.27035 4.77489i 0.538354 0.310819i
\(237\) −29.6349 17.1097i −1.92499 1.11140i
\(238\) 9.28786 16.0871i 0.602043 1.04277i
\(239\) 22.7370 1.47073 0.735367 0.677669i \(-0.237010\pi\)
0.735367 + 0.677669i \(0.237010\pi\)
\(240\) −1.23623 + 2.14121i −0.0797982 + 0.138215i
\(241\) −0.999927 + 1.73192i −0.0644110 + 0.111563i −0.896433 0.443180i \(-0.853850\pi\)
0.832022 + 0.554743i \(0.187184\pi\)
\(242\) 2.25208 1.30024i 0.144769 0.0835823i
\(243\) 3.61893 + 6.26817i 0.232155 + 0.402103i
\(244\) 4.10480 + 2.36991i 0.262783 + 0.151718i
\(245\) −10.8401 18.7755i −0.692546 1.19953i
\(246\) 6.35782i 0.405360i
\(247\) 12.0807i 0.768677i
\(248\) 19.6273i 1.24633i
\(249\) −41.6274 −2.63803
\(250\) −3.57361 + 2.06323i −0.226015 + 0.130490i
\(251\) 4.54845i 0.287096i −0.989643 0.143548i \(-0.954149\pi\)
0.989643 0.143548i \(-0.0458511\pi\)
\(252\) 21.4037 12.3574i 1.34830 0.778444i
\(253\) −15.4340 + 8.91083i −0.970328 + 0.560219i
\(254\) 1.40196 + 2.42827i 0.0879670 + 0.152363i
\(255\) −22.7804 39.4568i −1.42657 2.47088i
\(256\) 8.29810 14.3727i 0.518632 0.898296i
\(257\) 9.79450 0.610964 0.305482 0.952198i \(-0.401182\pi\)
0.305482 + 0.952198i \(0.401182\pi\)
\(258\) −2.62570 + 4.54784i −0.163469 + 0.283136i
\(259\) −24.6469 + 14.2299i −1.53148 + 0.884203i
\(260\) 10.9725 + 6.33500i 0.680488 + 0.392880i
\(261\) 24.3436 1.50683
\(262\) 4.16049 + 7.20618i 0.257036 + 0.445199i
\(263\) 5.11317 0.315291 0.157646 0.987496i \(-0.449610\pi\)
0.157646 + 0.987496i \(0.449610\pi\)
\(264\) 15.7201 27.2280i 0.967506 1.67577i
\(265\) 30.8664 + 17.8207i 1.89611 + 1.09472i
\(266\) 5.61471 + 9.72497i 0.344260 + 0.596276i
\(267\) −37.6084 + 21.7132i −2.30160 + 1.32883i
\(268\) −8.99316 + 15.5766i −0.549345 + 0.951493i
\(269\) −15.8725 −0.967765 −0.483883 0.875133i \(-0.660774\pi\)
−0.483883 + 0.875133i \(0.660774\pi\)
\(270\) 19.7754i 1.20349i
\(271\) −4.48554 7.76919i −0.272477 0.471945i 0.697018 0.717053i \(-0.254510\pi\)
−0.969496 + 0.245109i \(0.921176\pi\)
\(272\) −0.780016 1.35103i −0.0472954 0.0819181i
\(273\) 20.7284 + 35.9026i 1.25454 + 2.17293i
\(274\) −7.01591 −0.423847
\(275\) −11.0920 + 6.40395i −0.668870 + 0.386173i
\(276\) −8.19253 + 14.1899i −0.493133 + 0.854131i
\(277\) −1.36761 + 0.789591i −0.0821719 + 0.0474419i −0.540523 0.841329i \(-0.681774\pi\)
0.458351 + 0.888771i \(0.348440\pi\)
\(278\) −9.23059 + 5.32928i −0.553614 + 0.319629i
\(279\) −18.8747 32.6919i −1.13000 1.95721i
\(280\) −31.9086 −1.90690
\(281\) 10.7532 18.6250i 0.641480 1.11108i −0.343622 0.939108i \(-0.611654\pi\)
0.985102 0.171968i \(-0.0550127\pi\)
\(282\) −19.4765 −1.15981
\(283\) −23.4411 −1.39343 −0.696715 0.717348i \(-0.745356\pi\)
−0.696715 + 0.717348i \(0.745356\pi\)
\(284\) 9.20512i 0.546224i
\(285\) 27.5425 1.63148
\(286\) 10.9456 + 6.31942i 0.647224 + 0.373675i
\(287\) −7.85830 + 4.53699i −0.463861 + 0.267810i
\(288\) 30.6101i 1.80372i
\(289\) 11.7473 0.691016
\(290\) −10.0462 5.80015i −0.589930 0.340597i
\(291\) 17.0282i 0.998212i
\(292\) −4.18215 7.24369i −0.244742 0.423905i
\(293\) 0.124522 + 0.215679i 0.00727467 + 0.0126001i 0.869640 0.493687i \(-0.164351\pi\)
−0.862365 + 0.506287i \(0.831018\pi\)
\(294\) −17.2196 9.94175i −1.00427 0.579814i
\(295\) −20.5363 + 11.8567i −1.19567 + 0.690321i
\(296\) 21.6127i 1.25621i
\(297\) 27.8095i 1.61367i
\(298\) 1.13319 1.96274i 0.0656438 0.113698i
\(299\) −15.4549 8.92290i −0.893780 0.516024i
\(300\) −5.88773 + 10.1978i −0.339928 + 0.588773i
\(301\) −7.49486 −0.431997
\(302\) 4.61017i 0.265285i
\(303\) 40.7172 + 23.5081i 2.33914 + 1.35050i
\(304\) 0.943074 0.0540890
\(305\) −10.1928 5.88479i −0.583635 0.336962i
\(306\) −23.4965 13.5657i −1.34320 0.775499i
\(307\) −4.15492 7.19653i −0.237134 0.410728i 0.722757 0.691102i \(-0.242875\pi\)
−0.959891 + 0.280375i \(0.909541\pi\)
\(308\) 16.5619 0.943699
\(309\) −50.1187 28.9360i −2.85115 1.64611i
\(310\) 17.9884i 1.02167i
\(311\) 32.5143i 1.84372i 0.387528 + 0.921858i \(0.373329\pi\)
−0.387528 + 0.921858i \(0.626671\pi\)
\(312\) 31.4828 1.78236
\(313\) 26.1994 1.48088 0.740440 0.672123i \(-0.234617\pi\)
0.740440 + 0.672123i \(0.234617\pi\)
\(314\) 8.00420i 0.451703i
\(315\) −53.1480 + 30.6850i −2.99455 + 1.72891i
\(316\) −11.8551 6.84453i −0.666900 0.385035i
\(317\) −1.93003 1.11430i −0.108401 0.0625854i 0.444819 0.895620i \(-0.353268\pi\)
−0.553220 + 0.833035i \(0.686601\pi\)
\(318\) 32.6878 1.83304
\(319\) 14.1276 + 8.15655i 0.790991 + 0.456679i
\(320\) −8.13856 + 14.0964i −0.454959 + 0.788012i
\(321\) 3.29639i 0.183986i
\(322\) 16.5883 0.924428
\(323\) −8.68918 + 15.0501i −0.483479 + 0.837410i
\(324\) −3.03552 5.25767i −0.168640 0.292093i
\(325\) −11.1070 6.41262i −0.616104 0.355708i
\(326\) 1.83596 + 3.17998i 0.101685 + 0.176123i
\(327\) 6.89633 + 11.9448i 0.381368 + 0.660549i
\(328\) 6.89089i 0.380486i
\(329\) −13.8986 24.0731i −0.766255 1.32719i
\(330\) −14.4075 + 24.9545i −0.793107 + 1.37370i
\(331\) −14.5319 8.39000i −0.798745 0.461156i 0.0442869 0.999019i \(-0.485898\pi\)
−0.843032 + 0.537863i \(0.819232\pi\)
\(332\) −16.6525 −0.913926
\(333\) 20.7840 + 35.9989i 1.13895 + 1.97273i
\(334\) −4.26775 7.39196i −0.233521 0.404470i
\(335\) 22.3312 38.6787i 1.22008 2.11324i
\(336\) −2.80272 + 1.61815i −0.152901 + 0.0882773i
\(337\) 5.63262 + 9.75598i 0.306828 + 0.531442i 0.977667 0.210162i \(-0.0673990\pi\)
−0.670839 + 0.741603i \(0.734066\pi\)
\(338\) 0.812616i 0.0442005i
\(339\) 1.20193i 0.0652798i
\(340\) −9.11303 15.7842i −0.494223 0.856020i
\(341\) 25.2965i 1.36988i
\(342\) 14.2041 8.20076i 0.768071 0.443446i
\(343\) 1.75760i 0.0949016i
\(344\) −2.84585 + 4.92915i −0.153438 + 0.265762i
\(345\) 20.3431 35.2353i 1.09524 1.89700i
\(346\) 0.895504 1.55106i 0.0481426 0.0833855i
\(347\) −20.0250 + 11.5615i −1.07500 + 0.620651i −0.929543 0.368713i \(-0.879798\pi\)
−0.145457 + 0.989365i \(0.546465\pi\)
\(348\) 14.9981 0.803983
\(349\) 6.70238 17.4378i 0.358770 0.933426i
\(350\) 11.9215 0.637231
\(351\) 24.1163 13.9236i 1.28723 0.743185i
\(352\) 10.2562 17.7642i 0.546657 0.946838i
\(353\) 1.81411 3.14213i 0.0965552 0.167239i −0.813701 0.581283i \(-0.802551\pi\)
0.910257 + 0.414045i \(0.135884\pi\)
\(354\) −10.8741 + 18.8345i −0.577951 + 1.00104i
\(355\) 22.8575i 1.21315i
\(356\) −15.0448 + 8.68612i −0.797372 + 0.460363i
\(357\) 59.6365i 3.15630i
\(358\) 3.66807 + 6.35329i 0.193864 + 0.335782i
\(359\) 18.9391i 0.999569i −0.866150 0.499784i \(-0.833413\pi\)
0.866150 0.499784i \(-0.166587\pi\)
\(360\) 46.6052i 2.45631i
\(361\) 4.24721 + 7.35638i 0.223537 + 0.387178i
\(362\) 12.2848 7.09263i 0.645675 0.372780i
\(363\) 4.17434 7.23018i 0.219096 0.379486i
\(364\) 8.29214 + 14.3624i 0.434626 + 0.752795i
\(365\) 10.3848 + 17.9870i 0.543566 + 0.941483i
\(366\) −10.7942 −0.564223
\(367\) −6.67162 3.85186i −0.348256 0.201066i 0.315661 0.948872i \(-0.397774\pi\)
−0.663917 + 0.747806i \(0.731107\pi\)
\(368\) 0.696561 1.20648i 0.0363108 0.0628921i
\(369\) 6.62665 + 11.4777i 0.344970 + 0.597505i
\(370\) 19.8081i 1.02977i
\(371\) 23.3263 + 40.4023i 1.21104 + 2.09758i
\(372\) −11.6287 20.1415i −0.602919 1.04429i
\(373\) −27.1246 15.6604i −1.40446 0.810865i −0.409613 0.912259i \(-0.634336\pi\)
−0.994846 + 0.101395i \(0.967670\pi\)
\(374\) −9.09062 15.7454i −0.470065 0.814176i
\(375\) −6.62389 + 11.4729i −0.342056 + 0.592458i
\(376\) −21.1095 −1.08864
\(377\) 16.3352i 0.841305i
\(378\) −12.9424 + 22.4170i −0.665687 + 1.15300i
\(379\) −3.25384 1.87860i −0.167138 0.0964974i 0.414097 0.910233i \(-0.364097\pi\)
−0.581236 + 0.813735i \(0.697431\pi\)
\(380\) 11.0180 0.565214
\(381\) 7.79585 + 4.50094i 0.399394 + 0.230590i
\(382\) −12.0065 6.93198i −0.614308 0.354671i
\(383\) −27.7702 + 16.0331i −1.41899 + 0.819255i −0.996210 0.0869769i \(-0.972279\pi\)
−0.422781 + 0.906232i \(0.638946\pi\)
\(384\) 17.3083i 0.883261i
\(385\) −41.1252 −2.09593
\(386\) 12.9328 0.658261
\(387\) 10.9469i 0.556461i
\(388\) 6.81193i 0.345823i
\(389\) 2.35547 + 1.35993i 0.119427 + 0.0689514i 0.558524 0.829489i \(-0.311368\pi\)
−0.439096 + 0.898440i \(0.644701\pi\)
\(390\) −28.8540 −1.46108
\(391\) 12.8358 + 22.2322i 0.649133 + 1.12433i
\(392\) −18.6634 10.7753i −0.942643 0.544235i
\(393\) 23.1351 + 13.3571i 1.16701 + 0.673774i
\(394\) 9.24946 0.465981
\(395\) 29.4377 + 16.9958i 1.48117 + 0.855154i
\(396\) 24.1900i 1.21559i
\(397\) 36.7920 1.84654 0.923269 0.384154i \(-0.125507\pi\)
0.923269 + 0.384154i \(0.125507\pi\)
\(398\) −3.76074 + 6.51380i −0.188509 + 0.326507i
\(399\) 31.2215 + 18.0258i 1.56303 + 0.902417i
\(400\) 0.500597 0.867060i 0.0250299 0.0433530i
\(401\) 10.6153i 0.530101i 0.964234 + 0.265051i \(0.0853887\pi\)
−0.964234 + 0.265051i \(0.914611\pi\)
\(402\) 40.9611i 2.04296i
\(403\) 21.9371 12.6654i 1.09276 0.630907i
\(404\) 16.2884 + 9.40412i 0.810378 + 0.467872i
\(405\) 7.53758 + 13.0555i 0.374545 + 0.648732i
\(406\) −7.59205 13.1498i −0.376787 0.652615i
\(407\) 27.8554i 1.38074i
\(408\) −39.2211 22.6443i −1.94173 1.12106i
\(409\) −2.39326 −0.118339 −0.0591696 0.998248i \(-0.518845\pi\)
−0.0591696 + 0.998248i \(0.518845\pi\)
\(410\) 6.31551i 0.311901i
\(411\) −19.5066 + 11.2621i −0.962188 + 0.555520i
\(412\) −20.0494 11.5755i −0.987762 0.570284i
\(413\) −31.0393 −1.52735
\(414\) 24.2286i 1.19077i
\(415\) 41.3503 2.02981
\(416\) 20.5402 1.00706
\(417\) −17.1094 + 29.6344i −0.837851 + 1.45120i
\(418\) 10.9910 0.537585
\(419\) 13.9701 + 24.1970i 0.682486 + 1.18210i 0.974220 + 0.225601i \(0.0724347\pi\)
−0.291733 + 0.956500i \(0.594232\pi\)
\(420\) −32.7445 + 18.9051i −1.59777 + 0.922472i
\(421\) 16.7426 9.66633i 0.815983 0.471108i −0.0330460 0.999454i \(-0.510521\pi\)
0.849029 + 0.528346i \(0.177187\pi\)
\(422\) −0.794644 + 1.37636i −0.0386827 + 0.0670003i
\(423\) −35.1608 + 20.3001i −1.70957 + 0.987023i
\(424\) 35.4285 1.72056
\(425\) 9.22468 + 15.9776i 0.447463 + 0.775028i
\(426\) −10.4816 18.1547i −0.507837 0.879600i
\(427\) −7.70284 13.3417i −0.372767 0.645651i
\(428\) 1.31868i 0.0637408i
\(429\) 40.5764 1.95905
\(430\) 2.60822 4.51757i 0.125780 0.217857i
\(431\) 30.3276 17.5096i 1.46083 0.843410i 0.461779 0.886995i \(-0.347211\pi\)
0.999050 + 0.0435847i \(0.0138778\pi\)
\(432\) 1.08694 + 1.88263i 0.0522952 + 0.0905780i
\(433\) 3.33449 + 1.92517i 0.160245 + 0.0925177i 0.577978 0.816052i \(-0.303842\pi\)
−0.417733 + 0.908570i \(0.637175\pi\)
\(434\) −11.7729 + 20.3913i −0.565117 + 0.978812i
\(435\) −37.2422 −1.78563
\(436\) 2.75879 + 4.77837i 0.132122 + 0.228842i
\(437\) −15.5190 −0.742375
\(438\) 16.4964 + 9.52421i 0.788230 + 0.455085i
\(439\) −13.2961 + 7.67652i −0.634589 + 0.366380i −0.782527 0.622617i \(-0.786070\pi\)
0.147938 + 0.988997i \(0.452736\pi\)
\(440\) −15.6155 + 27.0468i −0.744439 + 1.28941i
\(441\) −41.4485 −1.97374
\(442\) 9.10293 15.7667i 0.432982 0.749947i
\(443\) −3.49833 6.05929i −0.166211 0.287886i 0.770874 0.636988i \(-0.219820\pi\)
−0.937085 + 0.349102i \(0.886487\pi\)
\(444\) 12.8050 + 22.1789i 0.607698 + 1.05256i
\(445\) 37.3581 21.5687i 1.77095 1.02246i
\(446\) −7.42834 + 4.28875i −0.351742 + 0.203078i
\(447\) 7.27609i 0.344147i
\(448\) −18.4513 + 10.6529i −0.871744 + 0.503302i
\(449\) 15.9271 0.751648 0.375824 0.926691i \(-0.377360\pi\)
0.375824 + 0.926691i \(0.377360\pi\)
\(450\) 17.4123i 0.820825i
\(451\) 8.88128i 0.418203i
\(452\) 0.480817i 0.0226157i
\(453\) 7.40036 + 12.8178i 0.347699 + 0.602232i
\(454\) 1.19992 + 0.692772i 0.0563148 + 0.0325134i
\(455\) −20.5904 35.6637i −0.965294 1.67194i
\(456\) 23.7100 13.6890i 1.11032 0.641045i
\(457\) −0.695814 + 1.20518i −0.0325488 + 0.0563762i −0.881841 0.471547i \(-0.843696\pi\)
0.849292 + 0.527923i \(0.177029\pi\)
\(458\) −6.26892 + 10.8581i −0.292928 + 0.507365i
\(459\) −40.0587 −1.86978
\(460\) 8.13801 14.0954i 0.379437 0.657203i
\(461\) −14.9319 8.62092i −0.695446 0.401516i 0.110203 0.993909i \(-0.464850\pi\)
−0.805649 + 0.592393i \(0.798183\pi\)
\(462\) −32.6640 + 18.8586i −1.51967 + 0.877380i
\(463\) −30.9321 17.8586i −1.43753 0.829961i −0.439856 0.898068i \(-0.644971\pi\)
−0.997678 + 0.0681072i \(0.978304\pi\)
\(464\) −1.27520 −0.0591995
\(465\) 28.8755 + 50.0138i 1.33907 + 2.31934i
\(466\) −16.2738 9.39568i −0.753869 0.435246i
\(467\) 0.753312 0.0348591 0.0174296 0.999848i \(-0.494452\pi\)
0.0174296 + 0.999848i \(0.494452\pi\)
\(468\) 20.9775 12.1114i 0.969685 0.559848i
\(469\) 50.6281 29.2302i 2.33779 1.34972i
\(470\) 19.3469 0.892407
\(471\) −12.8486 22.2543i −0.592030 1.02543i
\(472\) −11.7858 + 20.4136i −0.542486 + 0.939614i
\(473\) −3.66785 + 6.35290i −0.168648 + 0.292107i
\(474\) 31.1748 1.43191
\(475\) −11.1530 −0.511737
\(476\) 23.8568i 1.09348i
\(477\) 59.0109 34.0700i 2.70192 1.55996i
\(478\) −17.9388 + 10.3570i −0.820503 + 0.473718i
\(479\) 15.0579 + 26.0810i 0.688013 + 1.19167i 0.972480 + 0.232987i \(0.0748500\pi\)
−0.284467 + 0.958686i \(0.591817\pi\)
\(480\) 46.8290i 2.13744i
\(481\) −24.1562 + 13.9466i −1.10143 + 0.635909i
\(482\) 1.82192i 0.0829861i
\(483\) 46.1209 26.6279i 2.09857 1.21161i
\(484\) 1.66990 2.89234i 0.0759043 0.131470i
\(485\) 16.9149i 0.768066i
\(486\) −5.71047 3.29694i −0.259032 0.149552i
\(487\) 34.0607 19.6649i 1.54344 0.891104i 0.544819 0.838554i \(-0.316598\pi\)
0.998618 0.0525499i \(-0.0167349\pi\)
\(488\) −11.6993 −0.529601
\(489\) 10.2092 + 5.89428i 0.461675 + 0.266548i
\(490\) 17.1050 + 9.87558i 0.772725 + 0.446133i
\(491\) 4.90674 8.49873i 0.221438 0.383542i −0.733807 0.679358i \(-0.762258\pi\)
0.955245 + 0.295816i \(0.0955916\pi\)
\(492\) 4.08268 + 7.07141i 0.184061 + 0.318804i
\(493\) 11.7493 20.3503i 0.529160 0.916531i
\(494\) 5.50292 + 9.53133i 0.247588 + 0.428835i
\(495\) 60.0668i 2.69980i
\(496\) 0.988716 + 1.71251i 0.0443946 + 0.0768938i
\(497\) 14.9596 25.9107i 0.671028 1.16225i
\(498\) 32.8428 18.9618i 1.47172 0.849699i
\(499\) 34.1585 19.7214i 1.52914 0.882852i 0.529747 0.848156i \(-0.322287\pi\)
0.999398 0.0346962i \(-0.0110464\pi\)
\(500\) −2.64980 + 4.58960i −0.118503 + 0.205253i
\(501\) −23.7315 13.7014i −1.06025 0.612133i
\(502\) 2.07188 + 3.58860i 0.0924725 + 0.160167i
\(503\) −3.36988 1.94560i −0.150255 0.0867500i 0.422987 0.906136i \(-0.360981\pi\)
−0.573243 + 0.819386i \(0.694315\pi\)
\(504\) −30.5017 + 52.8305i −1.35865 + 2.35326i
\(505\) −40.4462 23.3516i −1.79983 1.03913i
\(506\) 8.11800 14.0608i 0.360889 0.625078i
\(507\) 1.30443 + 2.25934i 0.0579318 + 0.100341i
\(508\) 3.11863 + 1.80054i 0.138367 + 0.0798862i
\(509\) −22.2139 + 12.8252i −0.984614 + 0.568467i −0.903660 0.428251i \(-0.859130\pi\)
−0.0809538 + 0.996718i \(0.525797\pi\)
\(510\) 35.9462 + 20.7536i 1.59172 + 0.918983i
\(511\) 27.1862i 1.20265i
\(512\) 3.28404i 0.145135i
\(513\) 12.1082 20.9720i 0.534589 0.925936i
\(514\) −7.72758 + 4.46152i −0.340849 + 0.196789i
\(515\) 49.7851 + 28.7435i 2.19380 + 1.26659i
\(516\) 6.74437i 0.296904i
\(517\) −27.2069 −1.19656
\(518\) 12.9638 22.4540i 0.569597 0.986571i
\(519\) 5.74995i 0.252395i
\(520\) −31.2733 −1.37142
\(521\) 22.2314 12.8353i 0.973976 0.562325i 0.0735299 0.997293i \(-0.476574\pi\)
0.900446 + 0.434968i \(0.143240\pi\)
\(522\) −19.2064 + 11.0888i −0.840642 + 0.485345i
\(523\) 7.06674 + 4.07998i 0.309007 + 0.178405i 0.646482 0.762929i \(-0.276240\pi\)
−0.337475 + 0.941334i \(0.609573\pi\)
\(524\) 9.25491 + 5.34333i 0.404303 + 0.233424i
\(525\) 33.1457 19.1367i 1.44660 0.835193i
\(526\) −4.03414 + 2.32911i −0.175897 + 0.101554i
\(527\) −36.4388 −1.58730
\(528\) 3.16757i 0.137851i
\(529\) 0.0375495 0.0650376i 0.00163259 0.00282772i
\(530\) −32.4703 −1.41042
\(531\) 45.3355i 1.96739i
\(532\) 12.4898 + 7.21099i 0.541501 + 0.312636i
\(533\) −7.70183 + 4.44665i −0.333603 + 0.192606i
\(534\) 19.7813 34.2623i 0.856021 1.48267i
\(535\) 3.27445i 0.141567i
\(536\) 44.3955i 1.91759i
\(537\) 20.3969 + 11.7762i 0.880193 + 0.508179i
\(538\) 12.5230 7.23014i 0.539904 0.311714i
\(539\) −24.0542 13.8877i −1.03609 0.598185i
\(540\) 12.6988 + 21.9950i 0.546470 + 0.946513i
\(541\) −15.2487 + 26.4115i −0.655592 + 1.13552i 0.326153 + 0.945317i \(0.394248\pi\)
−0.981745 + 0.190202i \(0.939086\pi\)
\(542\) 7.07793 + 4.08645i 0.304023 + 0.175528i
\(543\) 22.7705 39.4397i 0.977178 1.69252i
\(544\) −25.5888 14.7737i −1.09711 0.633418i
\(545\) −6.85043 11.8653i −0.293440 0.508253i
\(546\) −32.7082 18.8841i −1.39978 0.808165i
\(547\) 22.3286 38.6743i 0.954702 1.65359i 0.219652 0.975578i \(-0.429508\pi\)
0.735050 0.678013i \(-0.237159\pi\)
\(548\) −7.80336 + 4.50527i −0.333343 + 0.192456i
\(549\) −19.4867 + 11.2506i −0.831671 + 0.480166i
\(550\) 5.83416 10.1051i 0.248769 0.430881i
\(551\) 7.10268 + 12.3022i 0.302584 + 0.524091i
\(552\) 40.4431i 1.72137i
\(553\) 22.2466 + 38.5322i 0.946020 + 1.63856i
\(554\) 0.719338 1.24593i 0.0305617 0.0529345i
\(555\) −31.7964 55.0730i −1.34968 2.33772i
\(556\) −6.84441 + 11.8549i −0.290268 + 0.502758i
\(557\) −2.01623 1.16407i −0.0854305 0.0493233i 0.456676 0.889633i \(-0.349040\pi\)
−0.542107 + 0.840310i \(0.682373\pi\)
\(558\) 29.7831 + 17.1953i 1.26082 + 0.727935i
\(559\) −7.34563 −0.310687
\(560\) 2.78407 1.60738i 0.117648 0.0679242i
\(561\) −50.5499 29.1850i −2.13422 1.23219i
\(562\) 19.5928i 0.826473i
\(563\) −4.70331 + 8.14636i −0.198221 + 0.343328i −0.947952 0.318415i \(-0.896850\pi\)
0.749731 + 0.661743i \(0.230183\pi\)
\(564\) −21.6625 + 12.5069i −0.912158 + 0.526634i
\(565\) 1.19393i 0.0502290i
\(566\) 18.4944 10.6777i 0.777377 0.448819i
\(567\) 19.7325i 0.828687i
\(568\) −11.3605 19.6769i −0.476675 0.825625i
\(569\) 21.1710 12.2231i 0.887533 0.512418i 0.0143986 0.999896i \(-0.495417\pi\)
0.873135 + 0.487479i \(0.162083\pi\)
\(570\) −21.7303 + 12.5460i −0.910180 + 0.525493i
\(571\) 2.92557i 0.122431i 0.998125 + 0.0612157i \(0.0194978\pi\)
−0.998125 + 0.0612157i \(0.980502\pi\)
\(572\) 16.2321 0.678698
\(573\) −44.5095 −1.85941
\(574\) 4.13331 7.15911i 0.172521 0.298816i
\(575\) −8.23772 + 14.2681i −0.343537 + 0.595023i
\(576\) 15.5594 + 26.9497i 0.648310 + 1.12291i
\(577\) −2.15971 −0.0899101 −0.0449550 0.998989i \(-0.514314\pi\)
−0.0449550 + 0.998989i \(0.514314\pi\)
\(578\) −9.26827 + 5.35104i −0.385509 + 0.222574i
\(579\) 35.9574 20.7600i 1.49434 0.862757i
\(580\) −14.8983 −0.618618
\(581\) 46.8738 + 27.0626i 1.94465 + 1.12274i
\(582\) 7.75657 + 13.4348i 0.321520 + 0.556890i
\(583\) 45.6618 1.89112
\(584\) 17.8796 + 10.3228i 0.739861 + 0.427159i
\(585\) −52.0898 + 30.0740i −2.15365 + 1.24341i
\(586\) −0.196489 0.113443i −0.00811689 0.00468629i
\(587\) −5.29823 + 9.17680i −0.218681 + 0.378767i −0.954405 0.298515i \(-0.903509\pi\)
0.735724 + 0.677282i \(0.236842\pi\)
\(588\) −25.5364 −1.05310
\(589\) 11.0140 19.0769i 0.453825 0.786048i
\(590\) 10.8017 18.7091i 0.444700 0.770243i
\(591\) 25.7166 14.8475i 1.05784 0.610743i
\(592\) −1.08873 1.88574i −0.0447466 0.0775033i
\(593\) −12.3358 7.12210i −0.506572 0.292470i 0.224851 0.974393i \(-0.427810\pi\)
−0.731424 + 0.681923i \(0.761144\pi\)
\(594\) 12.6676 + 21.9409i 0.519757 + 0.900246i
\(595\) 59.2395i 2.42858i
\(596\) 2.91071i 0.119227i
\(597\) 24.1474i 0.988285i
\(598\) 16.2580 0.664838
\(599\) 17.7884 10.2701i 0.726813 0.419626i −0.0904421 0.995902i \(-0.528828\pi\)
0.817255 + 0.576276i \(0.195495\pi\)
\(600\) 29.0653i 1.18658i
\(601\) −35.3644 + 20.4176i −1.44254 + 0.832853i −0.998019 0.0629143i \(-0.979961\pi\)
−0.444524 + 0.895767i \(0.646627\pi\)
\(602\) 5.91323 3.41401i 0.241005 0.139145i
\(603\) −42.6931 73.9466i −1.73860 3.01134i
\(604\) 2.96042 + 5.12760i 0.120458 + 0.208639i
\(605\) −4.14656 + 7.18206i −0.168582 + 0.291992i
\(606\) −42.8329 −1.73997
\(607\) −11.8656 + 20.5518i −0.481609 + 0.834172i −0.999777 0.0211070i \(-0.993281\pi\)
0.518168 + 0.855279i \(0.326614\pi\)
\(608\) 15.4690 8.93104i 0.627351 0.362201i
\(609\) −42.2169 24.3739i −1.71071 0.987681i
\(610\) 10.7224 0.434137
\(611\) −13.6219 23.5938i −0.551082 0.954501i
\(612\) −34.8449 −1.40852
\(613\) 8.86221 15.3498i 0.357941 0.619972i −0.629676 0.776858i \(-0.716812\pi\)
0.987617 + 0.156886i \(0.0501455\pi\)
\(614\) 6.55623 + 3.78524i 0.264588 + 0.152760i
\(615\) −10.1378 17.5592i −0.408796 0.708056i
\(616\) −35.4027 + 20.4398i −1.42642 + 0.823541i
\(617\) −6.80941 + 11.7943i −0.274137 + 0.474819i −0.969917 0.243436i \(-0.921725\pi\)
0.695780 + 0.718255i \(0.255059\pi\)
\(618\) 52.7230 2.12083
\(619\) 0.984228i 0.0395595i 0.999804 + 0.0197797i \(0.00629650\pi\)
−0.999804 + 0.0197797i \(0.993704\pi\)
\(620\) 11.5513 + 20.0074i 0.463911 + 0.803517i
\(621\) −17.8864 30.9801i −0.717756 1.24319i
\(622\) −14.8107 25.6528i −0.593854 1.02859i
\(623\) 56.4644 2.26220
\(624\) −2.74691 + 1.58593i −0.109965 + 0.0634880i
\(625\) 15.1823 26.2965i 0.607291 1.05186i
\(626\) −20.6706 + 11.9342i −0.826164 + 0.476986i
\(627\) 30.5585 17.6430i 1.22039 0.704592i
\(628\) −5.13991 8.90258i −0.205105 0.355252i
\(629\) 40.1249 1.59988
\(630\) 27.9549 48.4192i 1.11375 1.92907i
\(631\) −12.9590 −0.515890 −0.257945 0.966160i \(-0.583045\pi\)
−0.257945 + 0.966160i \(0.583045\pi\)
\(632\) 33.7886 1.34404
\(633\) 5.10233i 0.202799i
\(634\) 2.03032 0.0806342
\(635\) −7.74397 4.47098i −0.307310 0.177425i
\(636\) 36.3566 20.9905i 1.44163 0.832328i
\(637\) 27.8130i 1.10199i
\(638\) −14.8617 −0.588378
\(639\) −37.8448 21.8497i −1.49712 0.864360i
\(640\) 17.1931i 0.679618i
\(641\) −5.80317 10.0514i −0.229211 0.397006i 0.728363 0.685191i \(-0.240281\pi\)
−0.957575 + 0.288186i \(0.906948\pi\)
\(642\) −1.50155 2.60075i −0.0592613 0.102644i
\(643\) 4.72188 + 2.72618i 0.186213 + 0.107510i 0.590208 0.807251i \(-0.299046\pi\)
−0.403996 + 0.914761i \(0.632379\pi\)
\(644\) 18.4501 10.6522i 0.727036 0.419754i
\(645\) 16.7471i 0.659418i
\(646\) 15.8321i 0.622907i
\(647\) 5.53347 9.58426i 0.217543 0.376796i −0.736513 0.676423i \(-0.763529\pi\)
0.954056 + 0.299627i \(0.0968623\pi\)
\(648\) 12.9775 + 7.49255i 0.509803 + 0.294335i
\(649\) −15.1901 + 26.3100i −0.596263 + 1.03276i
\(650\) 11.6841 0.458289
\(651\) 75.5926i 2.96271i
\(652\) 4.08406 + 2.35793i 0.159944 + 0.0923438i
\(653\) −42.9590 −1.68111 −0.840557 0.541723i \(-0.817772\pi\)
−0.840557 + 0.541723i \(0.817772\pi\)
\(654\) −10.8820 6.28273i −0.425521 0.245674i
\(655\) −22.9811 13.2682i −0.897947 0.518430i
\(656\) −0.347125 0.601239i −0.0135530 0.0234744i
\(657\) 39.7077 1.54915
\(658\) 21.9312 + 12.6620i 0.854967 + 0.493616i
\(659\) 27.2028i 1.05967i −0.848101 0.529835i \(-0.822254\pi\)
0.848101 0.529835i \(-0.177746\pi\)
\(660\) 37.0071i 1.44050i
\(661\) −46.1146 −1.79365 −0.896825 0.442386i \(-0.854132\pi\)
−0.896825 + 0.442386i \(0.854132\pi\)
\(662\) 15.2870 0.594146
\(663\) 58.4490i 2.26997i
\(664\) 35.5965 20.5516i 1.38141 0.797559i
\(665\) −31.0137 17.9058i −1.20266 0.694357i
\(666\) −32.7959 18.9347i −1.27082 0.733706i
\(667\) 20.9844 0.812517
\(668\) −9.49351 5.48108i −0.367315 0.212069i
\(669\) −13.7688 + 23.8483i −0.532334 + 0.922029i
\(670\) 40.6885i 1.57193i
\(671\) −15.0785 −0.582100
\(672\) −30.6482 + 53.0843i −1.18228 + 2.04777i
\(673\) 19.0750 + 33.0389i 0.735287 + 1.27355i 0.954597 + 0.297899i \(0.0962860\pi\)
−0.219310 + 0.975655i \(0.570381\pi\)
\(674\) −8.88795 5.13146i −0.342351 0.197656i
\(675\) −12.8544 22.2645i −0.494766 0.856960i
\(676\) 0.521822 + 0.903822i 0.0200701 + 0.0347624i
\(677\) 18.3343i 0.704646i 0.935878 + 0.352323i \(0.114608\pi\)
−0.935878 + 0.352323i \(0.885392\pi\)
\(678\) −0.547494 0.948288i −0.0210264 0.0364188i
\(679\) −11.0703 + 19.1743i −0.424839 + 0.735843i
\(680\) 38.9601 + 22.4936i 1.49405 + 0.862591i
\(681\) 4.44822 0.170456
\(682\) 11.5229 + 19.9582i 0.441234 + 0.764240i
\(683\) −7.10692 12.3095i −0.271939 0.471012i 0.697420 0.716663i \(-0.254331\pi\)
−0.969358 + 0.245651i \(0.920998\pi\)
\(684\) 10.5322 18.2424i 0.402711 0.697515i
\(685\) 19.3767 11.1872i 0.740347 0.427440i
\(686\) 0.800611 + 1.38670i 0.0305675 + 0.0529444i
\(687\) 40.2521i 1.53572i
\(688\) 0.573433i 0.0218619i
\(689\) 22.8618 + 39.5978i 0.870965 + 1.50856i
\(690\) 37.0662i 1.41109i
\(691\) −24.7831 + 14.3085i −0.942794 + 0.544322i −0.890835 0.454327i \(-0.849880\pi\)
−0.0519587 + 0.998649i \(0.516546\pi\)
\(692\) 2.30020i 0.0874403i
\(693\) −39.3119 + 68.0903i −1.49334 + 2.58654i
\(694\) 10.5328 18.2433i 0.399819 0.692507i
\(695\) 16.9955 29.4371i 0.644677 1.11661i
\(696\) −32.0600 + 18.5099i −1.21523 + 0.701614i
\(697\) 12.7932 0.484577
\(698\) 2.65517 + 16.8110i 0.100500 + 0.636305i
\(699\) −60.3287 −2.28184
\(700\) 13.2595 7.65540i 0.501163 0.289347i
\(701\) −7.70203 + 13.3403i −0.290901 + 0.503856i −0.974023 0.226448i \(-0.927289\pi\)
0.683122 + 0.730305i \(0.260622\pi\)
\(702\) −12.6847 + 21.9706i −0.478754 + 0.829227i
\(703\) −12.1282 + 21.0066i −0.457423 + 0.792279i
\(704\) 20.8533i 0.785939i
\(705\) 53.7908 31.0562i 2.02588 1.16964i
\(706\) 3.30540i 0.124400i
\(707\) −30.5659 52.9417i −1.14955 1.99108i
\(708\) 27.9312i 1.04972i
\(709\) 11.6766i 0.438525i 0.975666 + 0.219263i \(0.0703651\pi\)
−0.975666 + 0.219263i \(0.929635\pi\)
\(710\) 10.4119 + 18.0339i 0.390751 + 0.676801i
\(711\) 56.2795 32.4930i 2.11064 1.21858i
\(712\) 21.4399 37.1349i 0.803493 1.39169i
\(713\) −16.2701 28.1806i −0.609319 1.05537i
\(714\) 27.1652 + 47.0515i 1.01663 + 1.76086i
\(715\) −40.3063 −1.50737
\(716\) 8.15954 + 4.71091i 0.304936 + 0.176055i
\(717\) −33.2506 + 57.5918i −1.24177 + 2.15080i
\(718\) 8.62702 + 14.9424i 0.321957 + 0.557646i
\(719\) 41.5665i 1.55017i 0.631859 + 0.775084i \(0.282292\pi\)
−0.631859 + 0.775084i \(0.717708\pi\)
\(720\) −2.34771 4.06636i −0.0874941 0.151544i
\(721\) 37.6235 + 65.1658i 1.40117 + 2.42690i
\(722\) −6.70185 3.86931i −0.249417 0.144001i
\(723\) −2.92459 5.06554i −0.108767 0.188389i
\(724\) 9.10908 15.7774i 0.338536 0.586362i
\(725\) 15.0808 0.560088
\(726\) 7.60587i 0.282280i
\(727\) −13.1180 + 22.7210i −0.486519 + 0.842676i −0.999880 0.0154971i \(-0.995067\pi\)
0.513361 + 0.858173i \(0.328400\pi\)
\(728\) −35.4506 20.4674i −1.31389 0.758573i
\(729\) −36.7357 −1.36058
\(730\) −16.3866 9.46083i −0.606496 0.350161i
\(731\) 9.15116 + 5.28342i 0.338468 + 0.195414i
\(732\) −12.0057 + 6.93152i −0.443745 + 0.256196i
\(733\) 27.5520i 1.01766i 0.860868 + 0.508828i \(0.169921\pi\)
−0.860868 + 0.508828i \(0.830079\pi\)
\(734\) 7.01829 0.259050
\(735\) 63.4101 2.33892
\(736\) 26.3861i 0.972605i
\(737\) 57.2188i 2.10768i
\(738\) −10.4565 6.03705i −0.384908 0.222227i
\(739\) 18.3318 0.674347 0.337173 0.941443i \(-0.390529\pi\)
0.337173 + 0.941443i \(0.390529\pi\)
\(740\) −12.7198 22.0313i −0.467588 0.809887i
\(741\) 30.5999 + 17.6668i 1.12411 + 0.649008i
\(742\) −36.8075 21.2508i −1.35125 0.780143i
\(743\) 19.8630 0.728704 0.364352 0.931261i \(-0.381290\pi\)
0.364352 + 0.931261i \(0.381290\pi\)
\(744\) 49.7150 + 28.7030i 1.82264 + 1.05230i
\(745\) 7.22766i 0.264801i
\(746\) 28.5341 1.04471
\(747\) 39.5272 68.4630i 1.44622 2.50493i
\(748\) −20.2219 11.6751i −0.739385 0.426884i
\(749\) 2.14303 3.71184i 0.0783046 0.135628i
\(750\) 12.0691i 0.440700i
\(751\) 28.9486i 1.05635i 0.849136 + 0.528175i \(0.177123\pi\)
−0.849136 + 0.528175i \(0.822877\pi\)
\(752\) 1.84183 1.06338i 0.0671648 0.0387776i
\(753\) 11.5210 + 6.65167i 0.419850 + 0.242400i
\(754\) −7.44089 12.8880i −0.270981 0.469353i
\(755\) −7.35110 12.7325i −0.267534 0.463383i
\(756\) 33.2440i 1.20907i
\(757\) −1.32465 0.764787i −0.0481452 0.0277967i 0.475734 0.879589i \(-0.342182\pi\)
−0.523879 + 0.851792i \(0.675516\pi\)
\(758\) 3.42291 0.124326
\(759\) 52.1249i 1.89201i
\(760\) −23.5522 + 13.5979i −0.854329 + 0.493247i
\(761\) −3.68255 2.12612i −0.133492 0.0770719i 0.431767 0.901985i \(-0.357890\pi\)
−0.565259 + 0.824914i \(0.691224\pi\)
\(762\) −8.20094 −0.297089
\(763\) 17.9336i 0.649241i
\(764\) −17.8055 −0.644180
\(765\) 86.5243 3.12829
\(766\) 14.6066 25.2994i 0.527758 0.914104i
\(767\) −30.4213