Properties

Label 441.2.w.a.188.5
Level $441$
Weight $2$
Character 441.188
Analytic conductor $3.521$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.w (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 188.5
Character \(\chi\) \(=\) 441.188
Dual form 441.2.w.a.251.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.42590 + 1.13712i) q^{2} +(0.295114 - 1.29298i) q^{4} +(0.0720329 - 0.0346892i) q^{5} +(2.51149 + 0.832121i) q^{7} +(-0.533164 - 1.10713i) q^{8} +O(q^{10})\) \(q+(-1.42590 + 1.13712i) q^{2} +(0.295114 - 1.29298i) q^{4} +(0.0720329 - 0.0346892i) q^{5} +(2.51149 + 0.832121i) q^{7} +(-0.533164 - 1.10713i) q^{8} +(-0.0632661 + 0.131373i) q^{10} +(0.0489389 - 0.0390274i) q^{11} +(3.06781 - 2.44650i) q^{13} +(-4.52735 + 1.66934i) q^{14} +(4.40896 + 2.12324i) q^{16} +(0.399548 + 1.75053i) q^{17} -5.46553i q^{19} +(-0.0235945 - 0.103374i) q^{20} +(-0.0254032 + 0.111299i) q^{22} +(4.14363 + 0.945756i) q^{23} +(-3.11346 + 3.90416i) q^{25} +(-1.59244 + 6.97692i) q^{26} +(1.81709 - 3.00173i) q^{28} +(8.80774 - 2.01031i) q^{29} +6.38885i q^{31} +(-6.30510 + 1.43910i) q^{32} +(-2.56028 - 2.04175i) q^{34} +(0.209775 - 0.0271815i) q^{35} +(0.385319 + 1.68819i) q^{37} +(6.21495 + 7.79331i) q^{38} +(-0.0768107 - 0.0612545i) q^{40} +(-6.08257 + 2.92921i) q^{41} +(1.79918 + 0.866440i) q^{43} +(-0.0360191 - 0.0747945i) q^{44} +(-6.98384 + 3.36324i) q^{46} +(2.99901 + 3.76064i) q^{47} +(5.61515 + 4.17972i) q^{49} -9.10732i q^{50} +(-2.25792 - 4.68861i) q^{52} +(-0.0985022 - 0.0224825i) q^{53} +(0.00217138 - 0.00450891i) q^{55} +(-0.417772 - 3.22419i) q^{56} +(-10.2730 + 12.8819i) q^{58} +(3.52530 + 1.69769i) q^{59} +(-3.20273 + 0.731001i) q^{61} +(-7.26488 - 9.10987i) q^{62} +(1.25183 - 1.56975i) q^{64} +(0.136116 - 0.282648i) q^{65} -13.0206 q^{67} +2.38132 q^{68} +(-0.268210 + 0.277298i) q^{70} +(2.96758 + 0.677330i) q^{71} +(0.291084 + 0.232132i) q^{73} +(-2.46910 - 1.96904i) q^{74} +(-7.06682 - 1.61296i) q^{76} +(0.155385 - 0.0572939i) q^{77} +10.2856 q^{79} +0.391244 q^{80} +(5.34228 - 11.0934i) q^{82} +(10.5324 - 13.2072i) q^{83} +(0.0895053 + 0.112236i) q^{85} +(-3.55070 + 0.810424i) q^{86} +(-0.0693007 - 0.0333735i) q^{88} +(-3.24641 + 4.07086i) q^{89} +(9.74055 - 3.59156i) q^{91} +(2.44569 - 5.07852i) q^{92} +(-8.55259 - 1.95207i) q^{94} +(-0.189595 - 0.393698i) q^{95} -13.6406i q^{97} +(-12.7595 + 0.425217i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 24 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{14}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.42590 + 1.13712i −1.00826 + 0.804064i −0.980693 0.195556i \(-0.937349\pi\)
−0.0275717 + 0.999620i \(0.508777\pi\)
\(3\) 0 0
\(4\) 0.295114 1.29298i 0.147557 0.646490i
\(5\) 0.0720329 0.0346892i 0.0322141 0.0155135i −0.417707 0.908582i \(-0.637166\pi\)
0.449921 + 0.893068i \(0.351452\pi\)
\(6\) 0 0
\(7\) 2.51149 + 0.832121i 0.949253 + 0.314512i
\(8\) −0.533164 1.10713i −0.188502 0.391428i
\(9\) 0 0
\(10\) −0.0632661 + 0.131373i −0.0200065 + 0.0415439i
\(11\) 0.0489389 0.0390274i 0.0147556 0.0117672i −0.616084 0.787680i \(-0.711282\pi\)
0.630840 + 0.775913i \(0.282710\pi\)
\(12\) 0 0
\(13\) 3.06781 2.44650i 0.850857 0.678536i −0.0976743 0.995218i \(-0.531140\pi\)
0.948532 + 0.316682i \(0.102569\pi\)
\(14\) −4.52735 + 1.66934i −1.20999 + 0.446149i
\(15\) 0 0
\(16\) 4.40896 + 2.12324i 1.10224 + 0.530810i
\(17\) 0.399548 + 1.75053i 0.0969046 + 0.424567i 0.999988 0.00489839i \(-0.00155921\pi\)
−0.903083 + 0.429465i \(0.858702\pi\)
\(18\) 0 0
\(19\) 5.46553i 1.25388i −0.779068 0.626939i \(-0.784307\pi\)
0.779068 0.626939i \(-0.215693\pi\)
\(20\) −0.0235945 0.103374i −0.00527590 0.0231152i
\(21\) 0 0
\(22\) −0.0254032 + 0.111299i −0.00541597 + 0.0237289i
\(23\) 4.14363 + 0.945756i 0.864006 + 0.197204i 0.631485 0.775388i \(-0.282446\pi\)
0.232520 + 0.972592i \(0.425303\pi\)
\(24\) 0 0
\(25\) −3.11346 + 3.90416i −0.622693 + 0.780832i
\(26\) −1.59244 + 6.97692i −0.312303 + 1.36829i
\(27\) 0 0
\(28\) 1.81709 3.00173i 0.343398 0.567274i
\(29\) 8.80774 2.01031i 1.63556 0.373305i 0.696632 0.717429i \(-0.254681\pi\)
0.938924 + 0.344124i \(0.111824\pi\)
\(30\) 0 0
\(31\) 6.38885i 1.14747i 0.819040 + 0.573736i \(0.194506\pi\)
−0.819040 + 0.573736i \(0.805494\pi\)
\(32\) −6.30510 + 1.43910i −1.11459 + 0.254399i
\(33\) 0 0
\(34\) −2.56028 2.04175i −0.439084 0.350158i
\(35\) 0.209775 0.0271815i 0.0354585 0.00459451i
\(36\) 0 0
\(37\) 0.385319 + 1.68819i 0.0633461 + 0.277537i 0.996674 0.0814866i \(-0.0259668\pi\)
−0.933328 + 0.359024i \(0.883110\pi\)
\(38\) 6.21495 + 7.79331i 1.00820 + 1.26424i
\(39\) 0 0
\(40\) −0.0768107 0.0612545i −0.0121448 0.00968518i
\(41\) −6.08257 + 2.92921i −0.949938 + 0.457466i −0.843664 0.536871i \(-0.819606\pi\)
−0.106274 + 0.994337i \(0.533892\pi\)
\(42\) 0 0
\(43\) 1.79918 + 0.866440i 0.274373 + 0.132131i 0.566011 0.824398i \(-0.308486\pi\)
−0.291638 + 0.956529i \(0.594200\pi\)
\(44\) −0.0360191 0.0747945i −0.00543009 0.0112757i
\(45\) 0 0
\(46\) −6.98384 + 3.36324i −1.02971 + 0.495882i
\(47\) 2.99901 + 3.76064i 0.437451 + 0.548546i 0.950869 0.309592i \(-0.100193\pi\)
−0.513419 + 0.858138i \(0.671621\pi\)
\(48\) 0 0
\(49\) 5.61515 + 4.17972i 0.802164 + 0.597103i
\(50\) 9.10732i 1.28797i
\(51\) 0 0
\(52\) −2.25792 4.68861i −0.313117 0.650193i
\(53\) −0.0985022 0.0224825i −0.0135303 0.00308821i 0.215750 0.976449i \(-0.430780\pi\)
−0.229281 + 0.973360i \(0.573637\pi\)
\(54\) 0 0
\(55\) 0.00217138 0.00450891i 0.000292788 0.000607981i
\(56\) −0.417772 3.22419i −0.0558272 0.430851i
\(57\) 0 0
\(58\) −10.2730 + 12.8819i −1.34891 + 1.69148i
\(59\) 3.52530 + 1.69769i 0.458955 + 0.221021i 0.649052 0.760744i \(-0.275166\pi\)
−0.190097 + 0.981765i \(0.560880\pi\)
\(60\) 0 0
\(61\) −3.20273 + 0.731001i −0.410067 + 0.0935951i −0.422578 0.906327i \(-0.638875\pi\)
0.0125108 + 0.999922i \(0.496018\pi\)
\(62\) −7.26488 9.10987i −0.922641 1.15695i
\(63\) 0 0
\(64\) 1.25183 1.56975i 0.156479 0.196219i
\(65\) 0.136116 0.282648i 0.0168831 0.0350582i
\(66\) 0 0
\(67\) −13.0206 −1.59072 −0.795361 0.606135i \(-0.792719\pi\)
−0.795361 + 0.606135i \(0.792719\pi\)
\(68\) 2.38132 0.288777
\(69\) 0 0
\(70\) −0.268210 + 0.277298i −0.0320573 + 0.0331434i
\(71\) 2.96758 + 0.677330i 0.352187 + 0.0803843i 0.394954 0.918701i \(-0.370760\pi\)
−0.0427678 + 0.999085i \(0.513618\pi\)
\(72\) 0 0
\(73\) 0.291084 + 0.232132i 0.0340688 + 0.0271690i 0.640376 0.768061i \(-0.278778\pi\)
−0.606307 + 0.795230i \(0.707350\pi\)
\(74\) −2.46910 1.96904i −0.287027 0.228897i
\(75\) 0 0
\(76\) −7.06682 1.61296i −0.810620 0.185019i
\(77\) 0.155385 0.0572939i 0.0177078 0.00652925i
\(78\) 0 0
\(79\) 10.2856 1.15722 0.578609 0.815605i \(-0.303596\pi\)
0.578609 + 0.815605i \(0.303596\pi\)
\(80\) 0.391244 0.0437424
\(81\) 0 0
\(82\) 5.34228 11.0934i 0.589957 1.22506i
\(83\) 10.5324 13.2072i 1.15608 1.44968i 0.285006 0.958526i \(-0.408004\pi\)
0.871074 0.491153i \(-0.163424\pi\)
\(84\) 0 0
\(85\) 0.0895053 + 0.112236i 0.00970821 + 0.0121737i
\(86\) −3.55070 + 0.810424i −0.382882 + 0.0873903i
\(87\) 0 0
\(88\) −0.0693007 0.0333735i −0.00738748 0.00355762i
\(89\) −3.24641 + 4.07086i −0.344118 + 0.431511i −0.923531 0.383523i \(-0.874711\pi\)
0.579413 + 0.815034i \(0.303282\pi\)
\(90\) 0 0
\(91\) 9.74055 3.59156i 1.02109 0.376498i
\(92\) 2.44569 5.07852i 0.254980 0.529472i
\(93\) 0 0
\(94\) −8.55259 1.95207i −0.882132 0.201341i
\(95\) −0.189595 0.393698i −0.0194520 0.0403926i
\(96\) 0 0
\(97\) 13.6406i 1.38499i −0.721422 0.692496i \(-0.756511\pi\)
0.721422 0.692496i \(-0.243489\pi\)
\(98\) −12.7595 + 0.425217i −1.28890 + 0.0429534i
\(99\) 0 0
\(100\) 4.12917 + 5.17782i 0.412917 + 0.517782i
\(101\) 14.6900 7.07432i 1.46171 0.703921i 0.477124 0.878836i \(-0.341679\pi\)
0.984584 + 0.174915i \(0.0559650\pi\)
\(102\) 0 0
\(103\) −6.01021 12.4803i −0.592204 1.22972i −0.954653 0.297720i \(-0.903774\pi\)
0.362449 0.932004i \(-0.381941\pi\)
\(104\) −4.34422 2.09207i −0.425986 0.205144i
\(105\) 0 0
\(106\) 0.166020 0.0799508i 0.0161252 0.00776551i
\(107\) −4.53315 3.61507i −0.438236 0.349482i 0.379384 0.925239i \(-0.376136\pi\)
−0.817620 + 0.575758i \(0.804707\pi\)
\(108\) 0 0
\(109\) −1.20144 1.50656i −0.115077 0.144302i 0.720957 0.692980i \(-0.243703\pi\)
−0.836034 + 0.548678i \(0.815131\pi\)
\(110\) 0.00203100 + 0.00889837i 0.000193648 + 0.000848427i
\(111\) 0 0
\(112\) 9.30625 + 9.00128i 0.879358 + 0.850541i
\(113\) −4.97507 3.96749i −0.468015 0.373230i 0.360900 0.932605i \(-0.382470\pi\)
−0.828915 + 0.559375i \(0.811041\pi\)
\(114\) 0 0
\(115\) 0.331285 0.0756136i 0.0308925 0.00705101i
\(116\) 11.9815i 1.11245i
\(117\) 0 0
\(118\) −6.95721 + 1.58794i −0.640463 + 0.146181i
\(119\) −0.453195 + 4.72892i −0.0415444 + 0.433499i
\(120\) 0 0
\(121\) −2.44686 + 10.7204i −0.222442 + 0.974581i
\(122\) 3.73554 4.68421i 0.338200 0.424089i
\(123\) 0 0
\(124\) 8.26066 + 1.88544i 0.741829 + 0.169318i
\(125\) −0.177793 + 0.778961i −0.0159023 + 0.0696724i
\(126\) 0 0
\(127\) −2.40561 10.5397i −0.213463 0.935244i −0.962193 0.272369i \(-0.912193\pi\)
0.748730 0.662876i \(-0.230664\pi\)
\(128\) 9.27270i 0.819598i
\(129\) 0 0
\(130\) 0.127316 + 0.557808i 0.0111664 + 0.0489230i
\(131\) −2.76634 1.33220i −0.241697 0.116395i 0.309115 0.951025i \(-0.399967\pi\)
−0.550811 + 0.834630i \(0.685682\pi\)
\(132\) 0 0
\(133\) 4.54798 13.7266i 0.394360 1.19025i
\(134\) 18.5661 14.8060i 1.60387 1.27904i
\(135\) 0 0
\(136\) 1.72504 1.37567i 0.147921 0.117963i
\(137\) −0.739039 + 1.53463i −0.0631404 + 0.131112i −0.930151 0.367178i \(-0.880324\pi\)
0.867011 + 0.498290i \(0.166038\pi\)
\(138\) 0 0
\(139\) −4.50183 9.34815i −0.381840 0.792900i −0.999977 0.00682869i \(-0.997826\pi\)
0.618136 0.786071i \(-0.287888\pi\)
\(140\) 0.0267626 0.279257i 0.00226185 0.0236015i
\(141\) 0 0
\(142\) −5.00167 + 2.40868i −0.419731 + 0.202132i
\(143\) 0.0546546 0.239458i 0.00457045 0.0200244i
\(144\) 0 0
\(145\) 0.564711 0.450342i 0.0468967 0.0373989i
\(146\) −0.679018 −0.0561959
\(147\) 0 0
\(148\) 2.29651 0.188772
\(149\) −15.6797 + 12.5041i −1.28453 + 1.02438i −0.286732 + 0.958011i \(0.592569\pi\)
−0.997795 + 0.0663657i \(0.978860\pi\)
\(150\) 0 0
\(151\) −2.43375 + 10.6629i −0.198056 + 0.867738i 0.774037 + 0.633140i \(0.218234\pi\)
−0.972093 + 0.234598i \(0.924623\pi\)
\(152\) −6.05103 + 2.91402i −0.490803 + 0.236358i
\(153\) 0 0
\(154\) −0.156414 + 0.258386i −0.0126042 + 0.0208214i
\(155\) 0.221624 + 0.460208i 0.0178013 + 0.0369648i
\(156\) 0 0
\(157\) 2.34186 4.86291i 0.186900 0.388103i −0.786373 0.617752i \(-0.788044\pi\)
0.973273 + 0.229649i \(0.0737579\pi\)
\(158\) −14.6662 + 11.6959i −1.16678 + 0.930476i
\(159\) 0 0
\(160\) −0.404253 + 0.322381i −0.0319590 + 0.0254865i
\(161\) 9.61969 + 5.82325i 0.758137 + 0.458936i
\(162\) 0 0
\(163\) 1.10485 + 0.532066i 0.0865382 + 0.0416746i 0.476652 0.879092i \(-0.341850\pi\)
−0.390114 + 0.920767i \(0.627564\pi\)
\(164\) 1.99236 + 8.72909i 0.155577 + 0.681628i
\(165\) 0 0
\(166\) 30.8087i 2.39122i
\(167\) −4.81868 21.1120i −0.372881 1.63370i −0.718645 0.695377i \(-0.755237\pi\)
0.345764 0.938321i \(-0.387620\pi\)
\(168\) 0 0
\(169\) 0.533339 2.33671i 0.0410260 0.179747i
\(170\) −0.255251 0.0582594i −0.0195769 0.00446829i
\(171\) 0 0
\(172\) 1.65125 2.07061i 0.125907 0.157882i
\(173\) −3.33599 + 14.6159i −0.253630 + 1.11123i 0.674295 + 0.738462i \(0.264447\pi\)
−0.927926 + 0.372765i \(0.878410\pi\)
\(174\) 0 0
\(175\) −11.0682 + 7.21448i −0.836674 + 0.545363i
\(176\) 0.298634 0.0681613i 0.0225104 0.00513785i
\(177\) 0 0
\(178\) 9.49620i 0.711770i
\(179\) −3.72363 + 0.849895i −0.278317 + 0.0635241i −0.359401 0.933183i \(-0.617019\pi\)
0.0810837 + 0.996707i \(0.474162\pi\)
\(180\) 0 0
\(181\) 14.2509 + 11.3647i 1.05926 + 0.844730i 0.988265 0.152747i \(-0.0488120\pi\)
0.0709924 + 0.997477i \(0.477383\pi\)
\(182\) −9.80503 + 16.1974i −0.726797 + 1.20063i
\(183\) 0 0
\(184\) −1.16216 5.09176i −0.0856756 0.375369i
\(185\) 0.0863178 + 0.108239i 0.00634621 + 0.00795790i
\(186\) 0 0
\(187\) 0.0878723 + 0.0700758i 0.00642586 + 0.00512445i
\(188\) 5.74749 2.76784i 0.419178 0.201866i
\(189\) 0 0
\(190\) 0.718025 + 0.345783i 0.0520910 + 0.0250857i
\(191\) −2.12895 4.42080i −0.154045 0.319878i 0.809637 0.586932i \(-0.199664\pi\)
−0.963682 + 0.267054i \(0.913950\pi\)
\(192\) 0 0
\(193\) −0.0963446 + 0.0463971i −0.00693503 + 0.00333974i −0.437348 0.899292i \(-0.644082\pi\)
0.430413 + 0.902632i \(0.358368\pi\)
\(194\) 15.5110 + 19.4501i 1.11362 + 1.39644i
\(195\) 0 0
\(196\) 7.06141 6.02678i 0.504386 0.430484i
\(197\) 27.0265i 1.92556i 0.270294 + 0.962778i \(0.412879\pi\)
−0.270294 + 0.962778i \(0.587121\pi\)
\(198\) 0 0
\(199\) −3.33989 6.93534i −0.236758 0.491633i 0.748408 0.663239i \(-0.230819\pi\)
−0.985166 + 0.171606i \(0.945104\pi\)
\(200\) 5.98238 + 1.36544i 0.423018 + 0.0965512i
\(201\) 0 0
\(202\) −12.9021 + 26.7915i −0.907790 + 1.88504i
\(203\) 23.7934 + 2.28023i 1.66997 + 0.160041i
\(204\) 0 0
\(205\) −0.336533 + 0.421999i −0.0235045 + 0.0294737i
\(206\) 22.7616 + 10.9614i 1.58587 + 0.763717i
\(207\) 0 0
\(208\) 18.7203 4.27280i 1.29802 0.296265i
\(209\) −0.213306 0.267477i −0.0147547 0.0185018i
\(210\) 0 0
\(211\) −10.5551 + 13.2356i −0.726641 + 0.911179i −0.998693 0.0511032i \(-0.983726\pi\)
0.272052 + 0.962283i \(0.412298\pi\)
\(212\) −0.0581388 + 0.120726i −0.00399299 + 0.00829152i
\(213\) 0 0
\(214\) 10.5746 0.722863
\(215\) 0.159656 0.0108885
\(216\) 0 0
\(217\) −5.31630 + 16.0455i −0.360894 + 1.08924i
\(218\) 3.42627 + 0.782023i 0.232056 + 0.0529653i
\(219\) 0 0
\(220\) −0.00518913 0.00413819i −0.000349851 0.000278997i
\(221\) 5.50841 + 4.39281i 0.370536 + 0.295493i
\(222\) 0 0
\(223\) −18.1221 4.13624i −1.21354 0.276983i −0.432600 0.901586i \(-0.642404\pi\)
−0.780943 + 0.624602i \(0.785261\pi\)
\(224\) −17.0327 1.63233i −1.13804 0.109064i
\(225\) 0 0
\(226\) 11.6055 0.771983
\(227\) −10.6354 −0.705899 −0.352950 0.935642i \(-0.614821\pi\)
−0.352950 + 0.935642i \(0.614821\pi\)
\(228\) 0 0
\(229\) 6.60218 13.7096i 0.436285 0.905954i −0.560675 0.828036i \(-0.689458\pi\)
0.996960 0.0779185i \(-0.0248274\pi\)
\(230\) −0.386398 + 0.484528i −0.0254783 + 0.0319488i
\(231\) 0 0
\(232\) −6.92163 8.67945i −0.454427 0.569834i
\(233\) −27.6145 + 6.30283i −1.80908 + 0.412912i −0.987558 0.157258i \(-0.949735\pi\)
−0.821527 + 0.570169i \(0.806878\pi\)
\(234\) 0 0
\(235\) 0.346481 + 0.166857i 0.0226019 + 0.0108845i
\(236\) 3.23545 4.05713i 0.210610 0.264096i
\(237\) 0 0
\(238\) −4.73113 7.25831i −0.306673 0.470486i
\(239\) −4.08821 + 8.48926i −0.264444 + 0.549125i −0.990337 0.138684i \(-0.955713\pi\)
0.725892 + 0.687808i \(0.241427\pi\)
\(240\) 0 0
\(241\) 17.7669 + 4.05517i 1.14446 + 0.261216i 0.752390 0.658717i \(-0.228901\pi\)
0.392074 + 0.919934i \(0.371758\pi\)
\(242\) −8.70137 18.0686i −0.559345 1.16149i
\(243\) 0 0
\(244\) 4.35679i 0.278915i
\(245\) 0.549467 + 0.106292i 0.0351042 + 0.00679078i
\(246\) 0 0
\(247\) −13.3714 16.7672i −0.850802 1.06687i
\(248\) 7.07326 3.40630i 0.449153 0.216301i
\(249\) 0 0
\(250\) −0.632256 1.31289i −0.0399874 0.0830347i
\(251\) 18.9959 + 9.14794i 1.19901 + 0.577413i 0.923393 0.383855i \(-0.125404\pi\)
0.275617 + 0.961268i \(0.411118\pi\)
\(252\) 0 0
\(253\) 0.239695 0.115431i 0.0150695 0.00725708i
\(254\) 15.4150 + 12.2931i 0.967224 + 0.771335i
\(255\) 0 0
\(256\) 13.0478 + 16.3614i 0.815489 + 1.02259i
\(257\) −4.03415 17.6748i −0.251644 1.10252i −0.929933 0.367728i \(-0.880136\pi\)
0.678290 0.734794i \(-0.262721\pi\)
\(258\) 0 0
\(259\) −0.437056 + 4.56051i −0.0271574 + 0.283376i
\(260\) −0.325289 0.259409i −0.0201735 0.0160879i
\(261\) 0 0
\(262\) 5.45940 1.24607i 0.337283 0.0769826i
\(263\) 19.8437i 1.22361i −0.791007 0.611807i \(-0.790443\pi\)
0.791007 0.611807i \(-0.209557\pi\)
\(264\) 0 0
\(265\) −0.00787530 + 0.00179749i −0.000483776 + 0.000110419i
\(266\) 9.12382 + 24.7444i 0.559417 + 1.51718i
\(267\) 0 0
\(268\) −3.84257 + 16.8354i −0.234722 + 1.02839i
\(269\) −12.2821 + 15.4012i −0.748852 + 0.939030i −0.999579 0.0290276i \(-0.990759\pi\)
0.250727 + 0.968058i \(0.419330\pi\)
\(270\) 0 0
\(271\) −10.3442 2.36100i −0.628365 0.143420i −0.103533 0.994626i \(-0.533015\pi\)
−0.524832 + 0.851206i \(0.675872\pi\)
\(272\) −1.95522 + 8.56637i −0.118552 + 0.519412i
\(273\) 0 0
\(274\) −0.691259 3.02861i −0.0417605 0.182965i
\(275\) 0.312576i 0.0188490i
\(276\) 0 0
\(277\) 2.67833 + 11.7345i 0.160925 + 0.705059i 0.989422 + 0.145066i \(0.0463393\pi\)
−0.828497 + 0.559994i \(0.810804\pi\)
\(278\) 17.0491 + 8.21042i 1.02254 + 0.492428i
\(279\) 0 0
\(280\) −0.141938 0.217756i −0.00848242 0.0130134i
\(281\) −12.8009 + 10.2084i −0.763638 + 0.608981i −0.925901 0.377766i \(-0.876692\pi\)
0.162263 + 0.986748i \(0.448121\pi\)
\(282\) 0 0
\(283\) 4.21849 3.36413i 0.250763 0.199977i −0.490038 0.871701i \(-0.663017\pi\)
0.740802 + 0.671724i \(0.234446\pi\)
\(284\) 1.75155 3.63713i 0.103935 0.215824i
\(285\) 0 0
\(286\) 0.194359 + 0.403591i 0.0114927 + 0.0238649i
\(287\) −17.7138 + 2.29525i −1.04561 + 0.135484i
\(288\) 0 0
\(289\) 12.4117 5.97718i 0.730102 0.351599i
\(290\) −0.293130 + 1.28429i −0.0172132 + 0.0754159i
\(291\) 0 0
\(292\) 0.386044 0.307860i 0.0225915 0.0180162i
\(293\) −5.02608 −0.293627 −0.146813 0.989164i \(-0.546902\pi\)
−0.146813 + 0.989164i \(0.546902\pi\)
\(294\) 0 0
\(295\) 0.312829 0.0182136
\(296\) 1.66360 1.32668i 0.0966951 0.0771117i
\(297\) 0 0
\(298\) 8.13899 35.6592i 0.471479 2.06568i
\(299\) 15.0256 7.23597i 0.868955 0.418467i
\(300\) 0 0
\(301\) 3.79764 + 3.67319i 0.218892 + 0.211719i
\(302\) −8.65475 17.9718i −0.498025 1.03416i
\(303\) 0 0
\(304\) 11.6046 24.0973i 0.665572 1.38207i
\(305\) −0.205344 + 0.163756i −0.0117580 + 0.00937666i
\(306\) 0 0
\(307\) 21.7077 17.3113i 1.23892 0.988007i 0.239066 0.971003i \(-0.423159\pi\)
0.999855 0.0170033i \(-0.00541258\pi\)
\(308\) −0.0282236 0.217818i −0.00160819 0.0124113i
\(309\) 0 0
\(310\) −0.839325 0.404198i −0.0476704 0.0229569i
\(311\) −7.38544 32.3577i −0.418790 1.83484i −0.539282 0.842125i \(-0.681304\pi\)
0.120492 0.992714i \(-0.461553\pi\)
\(312\) 0 0
\(313\) 21.9941i 1.24318i 0.783344 + 0.621589i \(0.213512\pi\)
−0.783344 + 0.621589i \(0.786488\pi\)
\(314\) 2.19045 + 9.59700i 0.123614 + 0.541590i
\(315\) 0 0
\(316\) 3.03542 13.2990i 0.170756 0.748129i
\(317\) −32.1185 7.33084i −1.80395 0.411741i −0.817520 0.575900i \(-0.804652\pi\)
−0.986434 + 0.164159i \(0.947509\pi\)
\(318\) 0 0
\(319\) 0.352584 0.442126i 0.0197409 0.0247543i
\(320\) 0.0357198 0.156499i 0.00199680 0.00874855i
\(321\) 0 0
\(322\) −20.3384 + 2.63534i −1.13342 + 0.146862i
\(323\) 9.56760 2.18374i 0.532355 0.121507i
\(324\) 0 0
\(325\) 19.5943i 1.08690i
\(326\) −2.18042 + 0.497667i −0.120762 + 0.0275632i
\(327\) 0 0
\(328\) 6.48601 + 5.17242i 0.358130 + 0.285599i
\(329\) 4.40268 + 11.9404i 0.242727 + 0.658293i
\(330\) 0 0
\(331\) −6.11936 26.8107i −0.336350 1.47365i −0.806591 0.591109i \(-0.798690\pi\)
0.470241 0.882538i \(-0.344167\pi\)
\(332\) −13.9684 17.5158i −0.766614 0.961304i
\(333\) 0 0
\(334\) 30.8778 + 24.6243i 1.68956 + 1.34738i
\(335\) −0.937914 + 0.451675i −0.0512437 + 0.0246777i
\(336\) 0 0
\(337\) −16.9593 8.16718i −0.923834 0.444895i −0.0893953 0.995996i \(-0.528493\pi\)
−0.834438 + 0.551101i \(0.814208\pi\)
\(338\) 1.89663 + 3.93838i 0.103163 + 0.214220i
\(339\) 0 0
\(340\) 0.171533 0.0826060i 0.00930269 0.00447994i
\(341\) 0.249341 + 0.312663i 0.0135025 + 0.0169317i
\(342\) 0 0
\(343\) 10.6244 + 15.1698i 0.573661 + 0.819093i
\(344\) 2.45388i 0.132304i
\(345\) 0 0
\(346\) −11.8632 24.6342i −0.637771 1.32435i
\(347\) −6.86589 1.56709i −0.368580 0.0841260i 0.0342191 0.999414i \(-0.489106\pi\)
−0.402799 + 0.915288i \(0.631963\pi\)
\(348\) 0 0
\(349\) −12.1607 + 25.2520i −0.650947 + 1.35171i 0.270318 + 0.962771i \(0.412871\pi\)
−0.921265 + 0.388935i \(0.872843\pi\)
\(350\) 7.57839 22.8729i 0.405082 1.22261i
\(351\) 0 0
\(352\) −0.252400 + 0.316500i −0.0134530 + 0.0168695i
\(353\) −22.4618 10.8170i −1.19552 0.575732i −0.273124 0.961979i \(-0.588057\pi\)
−0.922395 + 0.386247i \(0.873771\pi\)
\(354\) 0 0
\(355\) 0.237259 0.0541529i 0.0125924 0.00287414i
\(356\) 4.30548 + 5.39891i 0.228190 + 0.286141i
\(357\) 0 0
\(358\) 4.34310 5.44608i 0.229540 0.287834i
\(359\) 4.16953 8.65812i 0.220059 0.456958i −0.761487 0.648180i \(-0.775531\pi\)
0.981547 + 0.191221i \(0.0612449\pi\)
\(360\) 0 0
\(361\) −10.8720 −0.572212
\(362\) −33.2433 −1.74723
\(363\) 0 0
\(364\) −1.76924 13.6543i −0.0927334 0.715677i
\(365\) 0.0290201 + 0.00662364i 0.00151898 + 0.000346697i
\(366\) 0 0
\(367\) 16.2513 + 12.9600i 0.848310 + 0.676505i 0.947915 0.318522i \(-0.103187\pi\)
−0.0996053 + 0.995027i \(0.531758\pi\)
\(368\) 16.2610 + 12.9677i 0.847663 + 0.675989i
\(369\) 0 0
\(370\) −0.246161 0.0561847i −0.0127973 0.00292090i
\(371\) −0.228679 0.138430i −0.0118724 0.00718694i
\(372\) 0 0
\(373\) 23.7079 1.22755 0.613774 0.789482i \(-0.289650\pi\)
0.613774 + 0.789482i \(0.289650\pi\)
\(374\) −0.204982 −0.0105993
\(375\) 0 0
\(376\) 2.56454 5.32532i 0.132256 0.274633i
\(377\) 22.1023 27.7154i 1.13832 1.42741i
\(378\) 0 0
\(379\) −17.2796 21.6679i −0.887594 1.11301i −0.992945 0.118572i \(-0.962168\pi\)
0.105352 0.994435i \(-0.466403\pi\)
\(380\) −0.564996 + 0.128957i −0.0289837 + 0.00661533i
\(381\) 0 0
\(382\) 8.06264 + 3.88276i 0.412521 + 0.198659i
\(383\) 22.3799 28.0635i 1.14356 1.43398i 0.260033 0.965600i \(-0.416267\pi\)
0.883527 0.468380i \(-0.155162\pi\)
\(384\) 0 0
\(385\) 0.00920535 0.00951723i 0.000469148 0.000485043i
\(386\) 0.0846188 0.175713i 0.00430699 0.00894355i
\(387\) 0 0
\(388\) −17.6370 4.02553i −0.895384 0.204365i
\(389\) −7.63642 15.8572i −0.387182 0.803992i −0.999906 0.0136948i \(-0.995641\pi\)
0.612724 0.790297i \(-0.290074\pi\)
\(390\) 0 0
\(391\) 7.63143i 0.385938i
\(392\) 1.63369 8.44515i 0.0825136 0.426545i
\(393\) 0 0
\(394\) −30.7323 38.5371i −1.54827 1.94147i
\(395\) 0.740899 0.356798i 0.0372787 0.0179525i
\(396\) 0 0
\(397\) −8.96807 18.6224i −0.450094 0.934630i −0.995347 0.0963585i \(-0.969280\pi\)
0.545252 0.838272i \(-0.316434\pi\)
\(398\) 12.6487 + 6.09127i 0.634020 + 0.305328i
\(399\) 0 0
\(400\) −22.0166 + 10.6026i −1.10083 + 0.530132i
\(401\) 29.6733 + 23.6636i 1.48181 + 1.18171i 0.939985 + 0.341216i \(0.110839\pi\)
0.541827 + 0.840490i \(0.317733\pi\)
\(402\) 0 0
\(403\) 15.6303 + 19.5998i 0.778601 + 0.976335i
\(404\) −4.81173 21.0816i −0.239393 1.04885i
\(405\) 0 0
\(406\) −36.5199 + 23.8045i −1.81245 + 1.18140i
\(407\) 0.0847430 + 0.0675803i 0.00420055 + 0.00334983i
\(408\) 0 0
\(409\) 4.32746 0.987715i 0.213979 0.0488394i −0.114187 0.993459i \(-0.536426\pi\)
0.328167 + 0.944620i \(0.393569\pi\)
\(410\) 0.984407i 0.0486164i
\(411\) 0 0
\(412\) −17.9105 + 4.08796i −0.882388 + 0.201399i
\(413\) 7.44106 + 7.19722i 0.366151 + 0.354152i
\(414\) 0 0
\(415\) 0.300531 1.31671i 0.0147525 0.0646349i
\(416\) −15.8221 + 19.8403i −0.775742 + 0.972750i
\(417\) 0 0
\(418\) 0.608306 + 0.138842i 0.0297532 + 0.00679097i
\(419\) −6.17213 + 27.0419i −0.301528 + 1.32108i 0.566292 + 0.824205i \(0.308377\pi\)
−0.867820 + 0.496878i \(0.834480\pi\)
\(420\) 0 0
\(421\) 1.22091 + 5.34915i 0.0595035 + 0.260702i 0.995926 0.0901721i \(-0.0287417\pi\)
−0.936423 + 0.350874i \(0.885885\pi\)
\(422\) 30.8751i 1.50298i
\(423\) 0 0
\(424\) 0.0276269 + 0.121041i 0.00134168 + 0.00587828i
\(425\) −8.07834 3.89032i −0.391857 0.188708i
\(426\) 0 0
\(427\) −8.65189 0.829153i −0.418694 0.0401255i
\(428\) −6.01200 + 4.79441i −0.290601 + 0.231747i
\(429\) 0 0
\(430\) −0.227654 + 0.181548i −0.0109785 + 0.00875503i
\(431\) 9.97595 20.7153i 0.480525 0.997819i −0.509960 0.860198i \(-0.670340\pi\)
0.990485 0.137622i \(-0.0439458\pi\)
\(432\) 0 0
\(433\) −2.52920 5.25193i −0.121545 0.252392i 0.831314 0.555802i \(-0.187589\pi\)
−0.952860 + 0.303411i \(0.901875\pi\)
\(434\) −10.6652 28.9246i −0.511944 1.38843i
\(435\) 0 0
\(436\) −2.30251 + 1.10883i −0.110270 + 0.0531033i
\(437\) 5.16906 22.6471i 0.247270 1.08336i
\(438\) 0 0
\(439\) −21.0324 + 16.7728i −1.00382 + 0.800522i −0.979960 0.199193i \(-0.936168\pi\)
−0.0238631 + 0.999715i \(0.507597\pi\)
\(440\) −0.00614963 −0.000293172
\(441\) 0 0
\(442\) −12.8496 −0.611193
\(443\) −7.69731 + 6.13840i −0.365710 + 0.291644i −0.789053 0.614325i \(-0.789428\pi\)
0.423342 + 0.905970i \(0.360857\pi\)
\(444\) 0 0
\(445\) −0.0926330 + 0.405851i −0.00439122 + 0.0192392i
\(446\) 30.5437 14.7091i 1.44628 0.696494i
\(447\) 0 0
\(448\) 4.45019 2.90073i 0.210252 0.137047i
\(449\) 7.61349 + 15.8096i 0.359303 + 0.746100i 0.999760 0.0218939i \(-0.00696960\pi\)
−0.640458 + 0.767993i \(0.721255\pi\)
\(450\) 0 0
\(451\) −0.183354 + 0.380739i −0.00863383 + 0.0179283i
\(452\) −6.59809 + 5.26180i −0.310348 + 0.247494i
\(453\) 0 0
\(454\) 15.1651 12.0938i 0.711733 0.567588i
\(455\) 0.577052 0.596603i 0.0270526 0.0279692i
\(456\) 0 0
\(457\) 15.7239 + 7.57225i 0.735535 + 0.354215i 0.763858 0.645384i \(-0.223303\pi\)
−0.0283235 + 0.999599i \(0.509017\pi\)
\(458\) 6.17535 + 27.0560i 0.288555 + 1.26424i
\(459\) 0 0
\(460\) 0.450659i 0.0210121i
\(461\) 0.302478 + 1.32524i 0.0140878 + 0.0617227i 0.981483 0.191548i \(-0.0613508\pi\)
−0.967395 + 0.253271i \(0.918494\pi\)
\(462\) 0 0
\(463\) −4.63599 + 20.3116i −0.215453 + 0.943961i 0.745338 + 0.666687i \(0.232288\pi\)
−0.960791 + 0.277274i \(0.910569\pi\)
\(464\) 43.1013 + 9.83760i 2.00093 + 0.456699i
\(465\) 0 0
\(466\) 32.2085 40.3881i 1.49203 1.87094i
\(467\) −4.83052 + 21.1639i −0.223530 + 0.979349i 0.731267 + 0.682091i \(0.238929\pi\)
−0.954797 + 0.297258i \(0.903928\pi\)
\(468\) 0 0
\(469\) −32.7012 10.8347i −1.51000 0.500302i
\(470\) −0.683784 + 0.156069i −0.0315406 + 0.00719893i
\(471\) 0 0
\(472\) 4.80810i 0.221311i
\(473\) 0.121865 0.0278149i 0.00560335 0.00127893i
\(474\) 0 0
\(475\) 21.3383 + 17.0167i 0.979069 + 0.780781i
\(476\) 5.98065 + 1.98154i 0.274123 + 0.0908239i
\(477\) 0 0
\(478\) −3.82390 16.7536i −0.174901 0.766293i
\(479\) 0.615662 + 0.772016i 0.0281303 + 0.0352743i 0.795698 0.605694i \(-0.207104\pi\)
−0.767567 + 0.640968i \(0.778533\pi\)
\(480\) 0 0
\(481\) 5.31225 + 4.23638i 0.242218 + 0.193162i
\(482\) −29.9450 + 14.4207i −1.36396 + 0.656847i
\(483\) 0 0
\(484\) 13.1391 + 6.32748i 0.597234 + 0.287613i
\(485\) −0.473182 0.982572i −0.0214861 0.0446163i
\(486\) 0 0
\(487\) −31.5848 + 15.2104i −1.43124 + 0.689251i −0.979229 0.202759i \(-0.935009\pi\)
−0.452016 + 0.892010i \(0.649295\pi\)
\(488\) 2.51689 + 3.15608i 0.113934 + 0.142869i
\(489\) 0 0
\(490\) −0.904352 + 0.473246i −0.0408545 + 0.0213791i
\(491\) 11.8176i 0.533321i −0.963791 0.266660i \(-0.914080\pi\)
0.963791 0.266660i \(-0.0859202\pi\)
\(492\) 0 0
\(493\) 7.03823 + 14.6150i 0.316986 + 0.658228i
\(494\) 38.1326 + 8.70352i 1.71567 + 0.391590i
\(495\) 0 0
\(496\) −13.5651 + 28.1682i −0.609090 + 1.26479i
\(497\) 6.88942 + 4.17049i 0.309033 + 0.187072i
\(498\) 0 0
\(499\) −24.7503 + 31.0359i −1.10798 + 1.38936i −0.195265 + 0.980751i \(0.562557\pi\)
−0.912711 + 0.408607i \(0.866015\pi\)
\(500\) 0.954712 + 0.459765i 0.0426960 + 0.0205613i
\(501\) 0 0
\(502\) −37.4886 + 8.55652i −1.67320 + 0.381896i
\(503\) 2.94170 + 3.68878i 0.131164 + 0.164474i 0.843076 0.537794i \(-0.180742\pi\)
−0.711912 + 0.702268i \(0.752171\pi\)
\(504\) 0 0
\(505\) 0.812759 1.01917i 0.0361673 0.0453524i
\(506\) −0.210522 + 0.437154i −0.00935886 + 0.0194339i
\(507\) 0 0
\(508\) −14.3375 −0.636124
\(509\) 13.6927 0.606918 0.303459 0.952845i \(-0.401858\pi\)
0.303459 + 0.952845i \(0.401858\pi\)
\(510\) 0 0
\(511\) 0.537892 + 0.825213i 0.0237950 + 0.0365053i
\(512\) −19.1294 4.36616i −0.845407 0.192959i
\(513\) 0 0
\(514\) 25.8506 + 20.6152i 1.14022 + 0.909297i
\(515\) −0.865866 0.690505i −0.0381546 0.0304273i
\(516\) 0 0
\(517\) 0.293536 + 0.0669978i 0.0129097 + 0.00294656i
\(518\) −4.56264 6.99982i −0.200471 0.307555i
\(519\) 0 0
\(520\) −0.385499 −0.0169053
\(521\) −33.0259 −1.44689 −0.723446 0.690381i \(-0.757443\pi\)
−0.723446 + 0.690381i \(0.757443\pi\)
\(522\) 0 0
\(523\) 1.79046 3.71793i 0.0782913 0.162574i −0.858149 0.513401i \(-0.828385\pi\)
0.936440 + 0.350827i \(0.114100\pi\)
\(524\) −2.53890 + 3.18368i −0.110912 + 0.139079i
\(525\) 0 0
\(526\) 22.5646 + 28.2951i 0.983863 + 1.23373i
\(527\) −11.1839 + 2.55265i −0.487179 + 0.111195i
\(528\) 0 0
\(529\) −4.44710 2.14161i −0.193352 0.0931136i
\(530\) 0.00918544 0.0115182i 0.000398990 0.000500318i
\(531\) 0 0
\(532\) −16.4061 9.93137i −0.711293 0.430579i
\(533\) −11.4939 + 23.8673i −0.497855 + 1.03381i
\(534\) 0 0
\(535\) −0.451940 0.103152i −0.0195391 0.00445966i
\(536\) 6.94213 + 14.4155i 0.299854 + 0.622654i
\(537\) 0 0
\(538\) 35.9268i 1.54892i
\(539\) 0.437923 0.0145940i 0.0188627 0.000628609i
\(540\) 0 0
\(541\) −4.69692 5.88975i −0.201936 0.253220i 0.670544 0.741870i \(-0.266061\pi\)
−0.872480 + 0.488650i \(0.837489\pi\)
\(542\) 17.4345 8.39603i 0.748877 0.360640i
\(543\) 0 0
\(544\) −5.03838 10.4623i −0.216019 0.448567i
\(545\) −0.138804 0.0668447i −0.00594573 0.00286331i
\(546\) 0 0
\(547\) 9.81461 4.72647i 0.419642 0.202089i −0.212133 0.977241i \(-0.568041\pi\)
0.631775 + 0.775152i \(0.282327\pi\)
\(548\) 1.76614 + 1.40845i 0.0754460 + 0.0601662i
\(549\) 0 0
\(550\) −0.355435 0.445702i −0.0151558 0.0190048i
\(551\) −10.9874 48.1390i −0.468079 2.05079i
\(552\) 0 0
\(553\) 25.8321 + 8.55884i 1.09849 + 0.363959i
\(554\) −17.1626 13.6867i −0.729168 0.581492i
\(555\) 0 0
\(556\) −13.4155 + 3.06200i −0.568945 + 0.129858i
\(557\) 20.9491i 0.887641i −0.896116 0.443821i \(-0.853623\pi\)
0.896116 0.443821i \(-0.146377\pi\)
\(558\) 0 0
\(559\) 7.63929 1.74362i 0.323108 0.0737472i
\(560\) 0.982604 + 0.325562i 0.0415226 + 0.0137575i
\(561\) 0 0
\(562\) 6.64469 29.1123i 0.280289 1.22803i
\(563\) −7.84657 + 9.83929i −0.330694 + 0.414677i −0.919185 0.393827i \(-0.871151\pi\)
0.588491 + 0.808504i \(0.299722\pi\)
\(564\) 0 0
\(565\) −0.495998 0.113208i −0.0208668 0.00476271i
\(566\) −2.18973 + 9.59384i −0.0920413 + 0.403259i
\(567\) 0 0
\(568\) −0.832315 3.64661i −0.0349231 0.153008i
\(569\) 23.8454i 0.999649i −0.866127 0.499825i \(-0.833398\pi\)
0.866127 0.499825i \(-0.166602\pi\)
\(570\) 0 0
\(571\) −1.44405 6.32680i −0.0604317 0.264769i 0.935682 0.352844i \(-0.114785\pi\)
−0.996114 + 0.0880756i \(0.971928\pi\)
\(572\) −0.293484 0.141335i −0.0122712 0.00590950i
\(573\) 0 0
\(574\) 22.6481 23.4154i 0.945314 0.977342i
\(575\) −16.5934 + 13.2328i −0.691993 + 0.551846i
\(576\) 0 0
\(577\) −33.3975 + 26.6336i −1.39036 + 1.10877i −0.409880 + 0.912140i \(0.634429\pi\)
−0.980477 + 0.196633i \(0.936999\pi\)
\(578\) −10.9012 + 22.6365i −0.453428 + 0.941553i
\(579\) 0 0
\(580\) −0.415629 0.863062i −0.0172580 0.0358367i
\(581\) 37.4420 24.4055i 1.55335 1.01251i
\(582\) 0 0
\(583\) −0.00569802 + 0.00274402i −0.000235988 + 0.000113646i
\(584\) 0.101804 0.446031i 0.00421266 0.0184569i
\(585\) 0 0
\(586\) 7.16670 5.71525i 0.296053 0.236095i
\(587\) 15.7350 0.649452 0.324726 0.945808i \(-0.394728\pi\)
0.324726 + 0.945808i \(0.394728\pi\)
\(588\) 0 0
\(589\) 34.9185 1.43879
\(590\) −0.446064 + 0.355724i −0.0183641 + 0.0146449i
\(591\) 0 0
\(592\) −1.88559 + 8.26130i −0.0774972 + 0.339537i
\(593\) −23.1968 + 11.1710i −0.952580 + 0.458738i −0.844590 0.535414i \(-0.820156\pi\)
−0.107990 + 0.994152i \(0.534441\pi\)
\(594\) 0 0
\(595\) 0.131397 + 0.356359i 0.00538677 + 0.0146093i
\(596\) 11.5403 + 23.9636i 0.472708 + 0.981588i
\(597\) 0 0
\(598\) −13.1969 + 27.4037i −0.539663 + 1.12062i
\(599\) −32.7391 + 26.1085i −1.33768 + 1.06677i −0.345975 + 0.938244i \(0.612452\pi\)
−0.991707 + 0.128522i \(0.958977\pi\)
\(600\) 0 0
\(601\) 12.1095 9.65701i 0.493957 0.393918i −0.344584 0.938755i \(-0.611980\pi\)
0.838542 + 0.544838i \(0.183409\pi\)
\(602\) −9.59192 0.919240i −0.390937 0.0374654i
\(603\) 0 0
\(604\) 13.0687 + 6.29357i 0.531759 + 0.256082i
\(605\) 0.195628 + 0.857100i 0.00795339 + 0.0348461i
\(606\) 0 0
\(607\) 6.82644i 0.277077i 0.990357 + 0.138538i \(0.0442404\pi\)
−0.990357 + 0.138538i \(0.955760\pi\)
\(608\) 7.86543 + 34.4607i 0.318985 + 1.39757i
\(609\) 0 0
\(610\) 0.106590 0.467000i 0.00431569 0.0189083i
\(611\) 18.4008 + 4.19986i 0.744417 + 0.169908i
\(612\) 0 0
\(613\) 5.74752 7.20716i 0.232140 0.291095i −0.652094 0.758138i \(-0.726109\pi\)
0.884234 + 0.467043i \(0.154681\pi\)
\(614\) −11.2680 + 49.3683i −0.454739 + 1.99234i
\(615\) 0 0
\(616\) −0.146277 0.141484i −0.00589368 0.00570054i
\(617\) −17.3111 + 3.95114i −0.696918 + 0.159067i −0.556281 0.830994i \(-0.687772\pi\)
−0.140637 + 0.990061i \(0.544915\pi\)
\(618\) 0 0
\(619\) 4.78926i 0.192497i −0.995357 0.0962483i \(-0.969316\pi\)
0.995357 0.0962483i \(-0.0306843\pi\)
\(620\) 0.660444 0.150742i 0.0265241 0.00605394i
\(621\) 0 0
\(622\) 47.3255 + 37.7408i 1.89758 + 1.51327i
\(623\) −11.5408 + 7.52253i −0.462371 + 0.301384i
\(624\) 0 0
\(625\) −5.54170 24.2798i −0.221668 0.971190i
\(626\) −25.0098 31.3613i −0.999594 1.25345i
\(627\) 0 0
\(628\) −5.59653 4.46309i −0.223326 0.178097i
\(629\) −2.80129 + 1.34903i −0.111695 + 0.0537893i
\(630\) 0 0
\(631\) 18.1773 + 8.75372i 0.723626 + 0.348480i 0.759174 0.650888i \(-0.225603\pi\)
−0.0355476 + 0.999368i \(0.511318\pi\)
\(632\) −5.48389 11.3874i −0.218138 0.452967i
\(633\) 0 0
\(634\) 54.1338 26.0695i 2.14993 1.03535i
\(635\) −0.538896 0.675754i −0.0213854 0.0268165i
\(636\) 0 0
\(637\) 27.4519 0.914849i 1.08768 0.0362476i
\(638\) 1.03136i 0.0408318i
\(639\) 0 0
\(640\) −0.321663 0.667939i −0.0127148 0.0264026i
\(641\) 40.9493 + 9.34640i 1.61740 + 0.369161i 0.932980 0.359928i \(-0.117199\pi\)
0.684419 + 0.729089i \(0.260056\pi\)
\(642\) 0 0
\(643\) 19.3615 40.2045i 0.763541 1.58551i −0.0463464 0.998925i \(-0.514758\pi\)
0.809888 0.586585i \(-0.199528\pi\)
\(644\) 10.3683 10.7195i 0.408566 0.422409i
\(645\) 0 0
\(646\) −11.1593 + 13.9933i −0.439056 + 0.550559i
\(647\) 23.4669 + 11.3011i 0.922578 + 0.444290i 0.833991 0.551778i \(-0.186051\pi\)
0.0885873 + 0.996068i \(0.471765\pi\)
\(648\) 0 0
\(649\) 0.238781 0.0545002i 0.00937297 0.00213932i
\(650\) −22.2810 27.9395i −0.873934 1.09588i
\(651\) 0 0
\(652\) 1.01401 1.27152i 0.0397115 0.0497967i
\(653\) −1.66044 + 3.44795i −0.0649782 + 0.134929i −0.930929 0.365201i \(-0.881000\pi\)
0.865950 + 0.500130i \(0.166714\pi\)
\(654\) 0 0
\(655\) −0.245481 −0.00959173
\(656\) −33.0372 −1.28989
\(657\) 0 0
\(658\) −19.8554 12.0194i −0.774043 0.468565i
\(659\) 10.8991 + 2.48764i 0.424567 + 0.0969047i 0.429465 0.903083i \(-0.358702\pi\)
−0.00489821 + 0.999988i \(0.501559\pi\)
\(660\) 0 0
\(661\) −25.5622 20.3852i −0.994256 0.792893i −0.0159108 0.999873i \(-0.505065\pi\)
−0.978345 + 0.206981i \(0.933636\pi\)
\(662\) 39.2125 + 31.2709i 1.52404 + 1.21538i
\(663\) 0 0
\(664\) −20.2375 4.61908i −0.785368 0.179255i
\(665\) −0.148561 1.14653i −0.00576096 0.0444607i
\(666\) 0 0
\(667\) 38.3972 1.48675
\(668\) −28.7195 −1.11119
\(669\) 0 0
\(670\) 0.823764 1.71056i 0.0318248 0.0660848i
\(671\) −0.128209 + 0.160769i −0.00494944 + 0.00620640i
\(672\) 0 0
\(673\) 26.9597 + 33.8063i 1.03922 + 1.30314i 0.951718 + 0.306974i \(0.0993165\pi\)
0.0875005 + 0.996164i \(0.472112\pi\)
\(674\) 33.4694 7.63917i 1.28919 0.294250i
\(675\) 0 0
\(676\) −2.86392 1.37919i −0.110151 0.0530458i
\(677\) −6.81052 + 8.54012i −0.261750 + 0.328224i −0.895288 0.445488i \(-0.853030\pi\)
0.633539 + 0.773711i \(0.281602\pi\)
\(678\) 0 0
\(679\) 11.3506 34.2582i 0.435597 1.31471i
\(680\) 0.0765385 0.158934i 0.00293512 0.00609483i
\(681\) 0 0
\(682\) −0.711070 0.162297i −0.0272283 0.00621468i
\(683\) 0.211166 + 0.438491i 0.00808005 + 0.0167784i 0.904970 0.425476i \(-0.139893\pi\)
−0.896890 + 0.442254i \(0.854179\pi\)
\(684\) 0 0
\(685\) 0.136181i 0.00520319i
\(686\) −32.3991 9.54951i −1.23700 0.364602i
\(687\) 0 0
\(688\) 6.09285 + 7.64020i 0.232288 + 0.291280i
\(689\) −0.357189 + 0.172013i −0.0136078 + 0.00655318i
\(690\) 0 0
\(691\) −13.8343 28.7273i −0.526283 1.09284i −0.979501 0.201438i \(-0.935439\pi\)
0.453219 0.891399i \(-0.350276\pi\)
\(692\) 17.9136 + 8.62672i 0.680972 + 0.327939i
\(693\) 0 0
\(694\) 11.5721 5.57281i 0.439269 0.211541i
\(695\) −0.648560 0.517209i −0.0246013 0.0196189i
\(696\) 0 0
\(697\) −7.55796 9.47739i −0.286278 0.358982i
\(698\) −11.3745 49.8349i −0.430531 1.88628i
\(699\) 0 0
\(700\) 6.06180 + 16.4400i 0.229114 + 0.621374i
\(701\) 18.2624 + 14.5638i 0.689762 + 0.550067i 0.904431 0.426620i \(-0.140296\pi\)
−0.214669 + 0.976687i \(0.568867\pi\)
\(702\) 0 0
\(703\) 9.22688 2.10597i 0.347998 0.0794283i
\(704\) 0.125678i 0.00473666i
\(705\) 0 0
\(706\) 44.3285 10.1177i 1.66832 0.380784i
\(707\) 42.7804 5.54324i 1.60892 0.208475i
\(708\) 0 0
\(709\) −8.46035 + 37.0672i −0.317735 + 1.39209i 0.523779 + 0.851854i \(0.324522\pi\)
−0.841514 + 0.540235i \(0.818336\pi\)
\(710\) −0.276730 + 0.347008i −0.0103855 + 0.0130230i
\(711\) 0 0
\(712\) 6.23782 + 1.42374i 0.233772 + 0.0533570i
\(713\) −6.04229 + 26.4730i −0.226286 + 0.991422i
\(714\) 0 0
\(715\) −0.00436966 0.0191447i −0.000163416 0.000715973i
\(716\) 5.06540i 0.189303i
\(717\) 0 0
\(718\) 3.89997 + 17.0869i 0.145545 + 0.637676i
\(719\) −26.8474 12.9290i −1.00124 0.482171i −0.139880 0.990168i \(-0.544672\pi\)
−0.861359 + 0.507997i \(0.830386\pi\)
\(720\) 0 0
\(721\) −4.70943 36.3454i −0.175389 1.35358i
\(722\) 15.5024 12.3628i 0.576941 0.460095i
\(723\) 0 0
\(724\) 18.8999 15.0722i 0.702410 0.560154i
\(725\) −19.5740 + 40.6458i −0.726960 + 1.50955i
\(726\) 0 0
\(727\) −13.4164 27.8594i −0.497586 1.03325i −0.986929 0.161156i \(-0.948478\pi\)
0.489343 0.872091i \(-0.337237\pi\)
\(728\) −9.16962 8.86912i −0.339849 0.328712i
\(729\) 0 0
\(730\) −0.0489116 + 0.0235546i −0.00181030 + 0.000871795i
\(731\) −0.797874 + 3.49571i −0.0295104 + 0.129294i
\(732\) 0 0
\(733\) −11.7287 + 9.35330i −0.433208 + 0.345472i −0.815688 0.578492i \(-0.803641\pi\)
0.382480 + 0.923964i \(0.375070\pi\)
\(734\) −37.9097 −1.39927
\(735\) 0 0
\(736\) −27.4870 −1.01318
\(737\) −0.637215 + 0.508162i −0.0234721 + 0.0187184i
\(738\) 0 0
\(739\) 7.06950 30.9735i 0.260056 1.13938i −0.661135 0.750267i \(-0.729925\pi\)
0.921191 0.389112i \(-0.127218\pi\)
\(740\) 0.165425 0.0796643i 0.00608113 0.00292852i
\(741\) 0 0
\(742\) 0.483485 0.0626472i 0.0177493 0.00229985i
\(743\) −9.78269 20.3140i −0.358892 0.745247i 0.640857 0.767660i \(-0.278579\pi\)
−0.999749 + 0.0224137i \(0.992865\pi\)
\(744\) 0 0
\(745\) −0.695693 + 1.44462i −0.0254882 + 0.0529269i
\(746\) −33.8051 + 26.9587i −1.23769 + 0.987027i
\(747\) 0 0
\(748\) 0.116539 0.0929367i 0.00426109 0.00339810i
\(749\) −8.37678 12.8513i −0.306081 0.469577i
\(750\) 0 0
\(751\) 3.53737 + 1.70351i 0.129081 + 0.0621620i 0.497309 0.867573i \(-0.334321\pi\)
−0.368229 + 0.929735i \(0.620036\pi\)
\(752\) 5.23776 + 22.9481i 0.191002 + 0.836833i
\(753\) 0 0
\(754\) 64.6522i 2.35450i
\(755\) 0.194579 + 0.852508i 0.00708147 + 0.0310259i
\(756\) 0 0
\(757\) −2.49190 + 10.9177i −0.0905696 + 0.396811i −0.999811 0.0194586i \(-0.993806\pi\)
0.909241 + 0.416270i \(0.136663\pi\)
\(758\) 49.2780 + 11.2474i 1.78986 + 0.408523i
\(759\) 0 0
\(760\) −0.334788 + 0.419811i −0.0121440 + 0.0152281i
\(761\) −0.918025 + 4.02213i −0.0332784 + 0.145802i −0.988838 0.148997i \(-0.952396\pi\)
0.955559 + 0.294799i \(0.0952527\pi\)
\(762\) 0 0
\(763\) −1.76376 4.78344i −0.0638525 0.173172i
\(764\) −6.34429 + 1.44804i −0.229528 + 0.0523883i
\(765\) 0 0
\(766\) 65.4644i 2.36533i
\(767\) 14.9684 3.41643i 0.540476 0.123360i
\(768\) 0 0
\(769\) −33.1561 26.4411i −1.19564 0.953491i −0.196008 0.980602i \(-0.562798\pi\)
−0.999632 + 0.0271112i \(0.991369\pi\)
\(770\) −0.00230370 + 0.0240382i −8.30195e−5 + 0.000866276i
\(771\) 0 0
\(772\) 0.0315579 + 0.138264i 0.00113579 + 0.00497623i
\(773\) −5.38928 6.75794i −0.193839 0.243066i 0.675408 0.737444i \(-0.263967\pi\)
−0.869247 + 0.494378i \(0.835396\pi\)
\(774\) 0 0
\(775\) −24.9431 19.8915i −0.895983 0.714522i
\(776\) −15.1019 + 7.27267i −0.542125 + 0.261074i
\(777\) 0 0
\(778\) 28.9203 + 13.9273i 1.03684 + 0.499317i
\(779\) 16.0097 + 33.2445i 0.573607 + 1.19111i
\(780\) 0 0
\(781\) 0.171664 0.0826692i 0.00614263 0.00295814i
\(782\) −8.67784 10.8817i −0.310319 0.389128i
\(783\) 0 0
\(784\) 15.8824 + 30.3505i 0.567228 + 1.08395i
\(785\) 0.431527i 0.0154019i
\(786\) 0 0
\(787\) 16.5245 + 34.3135i 0.589035 + 1.22314i 0.956125 + 0.292958i \(0.0946397\pi\)
−0.367090 + 0.930185i \(0.619646\pi\)