Properties

Label 288.2.w.a.251.5
Level $288$
Weight $2$
Character 288.251
Analytic conductor $2.300$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 251.5
Character \(\chi\) \(=\) 288.251
Dual form 288.2.w.a.179.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.290763 - 1.38400i) q^{2} +(-1.83091 + 0.804831i) q^{4} +(-1.12344 + 2.71222i) q^{5} +(3.03150 - 3.03150i) q^{7} +(1.64625 + 2.29997i) q^{8} +O(q^{10})\) \(q+(-0.290763 - 1.38400i) q^{2} +(-1.83091 + 0.804831i) q^{4} +(-1.12344 + 2.71222i) q^{5} +(3.03150 - 3.03150i) q^{7} +(1.64625 + 2.29997i) q^{8} +(4.08037 + 0.766228i) q^{10} +(0.616847 - 1.48920i) q^{11} +(3.35133 - 1.38816i) q^{13} +(-5.07705 - 3.31415i) q^{14} +(2.70449 - 2.94715i) q^{16} +4.76709 q^{17} +(1.13264 + 2.73444i) q^{19} +(-0.125961 - 5.87003i) q^{20} +(-2.24041 - 0.420712i) q^{22} +(4.11192 - 4.11192i) q^{23} +(-2.55851 - 2.55851i) q^{25} +(-2.89566 - 4.23461i) q^{26} +(-3.11057 + 7.99027i) q^{28} +(-8.16664 + 3.38273i) q^{29} +6.16305i q^{31} +(-4.86523 - 2.88610i) q^{32} +(-1.38609 - 6.59765i) q^{34} +(4.81640 + 11.6278i) q^{35} +(-9.38963 - 3.88931i) q^{37} +(3.45513 - 2.36265i) q^{38} +(-8.08750 + 1.88112i) q^{40} +(-0.169917 - 0.169917i) q^{41} +(7.57687 + 3.13844i) q^{43} +(0.0691613 + 3.22306i) q^{44} +(-6.88649 - 4.49531i) q^{46} -2.44049i q^{47} -11.3800i q^{49} +(-2.79706 + 4.28490i) q^{50} +(-5.01875 + 5.23886i) q^{52} +(1.99073 + 0.824586i) q^{53} +(3.34605 + 3.34605i) q^{55} +(11.9630 + 1.98176i) q^{56} +(7.05626 + 10.3191i) q^{58} +(1.21488 + 0.503218i) q^{59} +(1.04489 + 2.52258i) q^{61} +(8.52966 - 1.79198i) q^{62} +(-2.57973 + 7.57265i) q^{64} +10.6491i q^{65} +(3.91551 - 1.62186i) q^{67} +(-8.72813 + 3.83670i) q^{68} +(14.6925 - 10.0468i) q^{70} +(-5.28919 - 5.28919i) q^{71} +(-1.57482 + 1.57482i) q^{73} +(-2.65266 + 14.1261i) q^{74} +(-4.27453 - 4.09494i) q^{76} +(-2.64454 - 6.38449i) q^{77} -13.7711 q^{79} +(4.95501 + 10.6461i) q^{80} +(-0.185759 + 0.284570i) q^{82} +(3.31934 - 1.37492i) q^{83} +(-5.35554 + 12.9294i) q^{85} +(2.14053 - 11.3989i) q^{86} +(4.44060 - 1.03286i) q^{88} +(6.99010 - 6.99010i) q^{89} +(5.95133 - 14.3678i) q^{91} +(-4.21917 + 10.8380i) q^{92} +(-3.37763 + 0.709602i) q^{94} -8.68886 q^{95} -13.5584 q^{97} +(-15.7499 + 3.30888i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.290763 1.38400i −0.205600 0.978636i
\(3\) 0 0
\(4\) −1.83091 + 0.804831i −0.915457 + 0.402416i
\(5\) −1.12344 + 2.71222i −0.502418 + 1.21294i 0.445745 + 0.895160i \(0.352939\pi\)
−0.948163 + 0.317784i \(0.897061\pi\)
\(6\) 0 0
\(7\) 3.03150 3.03150i 1.14580 1.14580i 0.158430 0.987370i \(-0.449357\pi\)
0.987370 0.158430i \(-0.0506433\pi\)
\(8\) 1.64625 + 2.29997i 0.582037 + 0.813163i
\(9\) 0 0
\(10\) 4.08037 + 0.766228i 1.29033 + 0.242303i
\(11\) 0.616847 1.48920i 0.185986 0.449011i −0.803194 0.595718i \(-0.796868\pi\)
0.989180 + 0.146707i \(0.0468676\pi\)
\(12\) 0 0
\(13\) 3.35133 1.38816i 0.929490 0.385008i 0.134005 0.990981i \(-0.457216\pi\)
0.795485 + 0.605973i \(0.207216\pi\)
\(14\) −5.07705 3.31415i −1.35690 0.885745i
\(15\) 0 0
\(16\) 2.70449 2.94715i 0.676123 0.736789i
\(17\) 4.76709 1.15619 0.578094 0.815970i \(-0.303797\pi\)
0.578094 + 0.815970i \(0.303797\pi\)
\(18\) 0 0
\(19\) 1.13264 + 2.73444i 0.259846 + 0.627323i 0.998928 0.0462921i \(-0.0147405\pi\)
−0.739082 + 0.673615i \(0.764741\pi\)
\(20\) −0.125961 5.87003i −0.0281657 1.31258i
\(21\) 0 0
\(22\) −2.24041 0.420712i −0.477657 0.0896962i
\(23\) 4.11192 4.11192i 0.857395 0.857395i −0.133636 0.991031i \(-0.542665\pi\)
0.991031 + 0.133636i \(0.0426652\pi\)
\(24\) 0 0
\(25\) −2.55851 2.55851i −0.511702 0.511702i
\(26\) −2.89566 4.23461i −0.567886 0.830475i
\(27\) 0 0
\(28\) −3.11057 + 7.99027i −0.587843 + 1.51002i
\(29\) −8.16664 + 3.38273i −1.51651 + 0.628158i −0.976888 0.213751i \(-0.931432\pi\)
−0.539620 + 0.841909i \(0.681432\pi\)
\(30\) 0 0
\(31\) 6.16305i 1.10692i 0.832877 + 0.553458i \(0.186692\pi\)
−0.832877 + 0.553458i \(0.813308\pi\)
\(32\) −4.86523 2.88610i −0.860059 0.510195i
\(33\) 0 0
\(34\) −1.38609 6.59765i −0.237713 1.13149i
\(35\) 4.81640 + 11.6278i 0.814121 + 1.96546i
\(36\) 0 0
\(37\) −9.38963 3.88931i −1.54365 0.639399i −0.561493 0.827482i \(-0.689773\pi\)
−0.982153 + 0.188083i \(0.939773\pi\)
\(38\) 3.45513 2.36265i 0.560497 0.383272i
\(39\) 0 0
\(40\) −8.08750 + 1.88112i −1.27875 + 0.297431i
\(41\) −0.169917 0.169917i −0.0265365 0.0265365i 0.693714 0.720251i \(-0.255973\pi\)
−0.720251 + 0.693714i \(0.755973\pi\)
\(42\) 0 0
\(43\) 7.57687 + 3.13844i 1.15546 + 0.478608i 0.876361 0.481654i \(-0.159964\pi\)
0.279100 + 0.960262i \(0.409964\pi\)
\(44\) 0.0691613 + 3.22306i 0.0104265 + 0.485894i
\(45\) 0 0
\(46\) −6.88649 4.49531i −1.01536 0.662797i
\(47\) 2.44049i 0.355981i −0.984032 0.177991i \(-0.943040\pi\)
0.984032 0.177991i \(-0.0569597\pi\)
\(48\) 0 0
\(49\) 11.3800i 1.62572i
\(50\) −2.79706 + 4.28490i −0.395564 + 0.605976i
\(51\) 0 0
\(52\) −5.01875 + 5.23886i −0.695976 + 0.726499i
\(53\) 1.99073 + 0.824586i 0.273447 + 0.113266i 0.515193 0.857074i \(-0.327720\pi\)
−0.241746 + 0.970340i \(0.577720\pi\)
\(54\) 0 0
\(55\) 3.34605 + 3.34605i 0.451182 + 0.451182i
\(56\) 11.9630 + 1.98176i 1.59862 + 0.264824i
\(57\) 0 0
\(58\) 7.05626 + 10.3191i 0.926533 + 1.35496i
\(59\) 1.21488 + 0.503218i 0.158163 + 0.0655134i 0.460361 0.887732i \(-0.347720\pi\)
−0.302197 + 0.953245i \(0.597720\pi\)
\(60\) 0 0
\(61\) 1.04489 + 2.52258i 0.133784 + 0.322983i 0.976548 0.215300i \(-0.0690731\pi\)
−0.842764 + 0.538283i \(0.819073\pi\)
\(62\) 8.52966 1.79198i 1.08327 0.227582i
\(63\) 0 0
\(64\) −2.57973 + 7.57265i −0.322467 + 0.946581i
\(65\) 10.6491i 1.32085i
\(66\) 0 0
\(67\) 3.91551 1.62186i 0.478355 0.198141i −0.130459 0.991454i \(-0.541645\pi\)
0.608815 + 0.793312i \(0.291645\pi\)
\(68\) −8.72813 + 3.83670i −1.05844 + 0.465268i
\(69\) 0 0
\(70\) 14.6925 10.0468i 1.75609 1.20083i
\(71\) −5.28919 5.28919i −0.627711 0.627711i 0.319781 0.947492i \(-0.396391\pi\)
−0.947492 + 0.319781i \(0.896391\pi\)
\(72\) 0 0
\(73\) −1.57482 + 1.57482i −0.184319 + 0.184319i −0.793235 0.608916i \(-0.791605\pi\)
0.608916 + 0.793235i \(0.291605\pi\)
\(74\) −2.65266 + 14.1261i −0.308365 + 1.64213i
\(75\) 0 0
\(76\) −4.27453 4.09494i −0.490322 0.469721i
\(77\) −2.64454 6.38449i −0.301373 0.727580i
\(78\) 0 0
\(79\) −13.7711 −1.54937 −0.774684 0.632348i \(-0.782091\pi\)
−0.774684 + 0.632348i \(0.782091\pi\)
\(80\) 4.95501 + 10.6461i 0.553987 + 1.19028i
\(81\) 0 0
\(82\) −0.185759 + 0.284570i −0.0205137 + 0.0314255i
\(83\) 3.31934 1.37492i 0.364345 0.150917i −0.192997 0.981199i \(-0.561821\pi\)
0.557343 + 0.830282i \(0.311821\pi\)
\(84\) 0 0
\(85\) −5.35554 + 12.9294i −0.580890 + 1.40239i
\(86\) 2.14053 11.3989i 0.230820 1.22918i
\(87\) 0 0
\(88\) 4.44060 1.03286i 0.473370 0.110104i
\(89\) 6.99010 6.99010i 0.740949 0.740949i −0.231811 0.972761i \(-0.574465\pi\)
0.972761 + 0.231811i \(0.0744652\pi\)
\(90\) 0 0
\(91\) 5.95133 14.3678i 0.623869 1.50615i
\(92\) −4.21917 + 10.8380i −0.439879 + 1.12994i
\(93\) 0 0
\(94\) −3.37763 + 0.709602i −0.348376 + 0.0731899i
\(95\) −8.68886 −0.891459
\(96\) 0 0
\(97\) −13.5584 −1.37665 −0.688323 0.725404i \(-0.741653\pi\)
−0.688323 + 0.725404i \(0.741653\pi\)
\(98\) −15.7499 + 3.30888i −1.59099 + 0.334248i
\(99\) 0 0
\(100\) 6.74358 + 2.62524i 0.674358 + 0.262524i
\(101\) −1.10479 + 2.66720i −0.109931 + 0.265396i −0.969265 0.246018i \(-0.920878\pi\)
0.859335 + 0.511413i \(0.170878\pi\)
\(102\) 0 0
\(103\) −12.8009 + 12.8009i −1.26131 + 1.26131i −0.310851 + 0.950459i \(0.600614\pi\)
−0.950459 + 0.310851i \(0.899386\pi\)
\(104\) 8.70985 + 5.42269i 0.854071 + 0.531738i
\(105\) 0 0
\(106\) 0.562398 2.99492i 0.0546249 0.290893i
\(107\) −0.720677 + 1.73987i −0.0696704 + 0.168199i −0.954879 0.296995i \(-0.904016\pi\)
0.885209 + 0.465194i \(0.154016\pi\)
\(108\) 0 0
\(109\) 4.45017 1.84332i 0.426249 0.176558i −0.159238 0.987240i \(-0.550904\pi\)
0.585486 + 0.810682i \(0.300904\pi\)
\(110\) 3.65803 5.60385i 0.348780 0.534306i
\(111\) 0 0
\(112\) −0.735628 17.1330i −0.0695104 1.61891i
\(113\) −13.6612 −1.28514 −0.642568 0.766229i \(-0.722131\pi\)
−0.642568 + 0.766229i \(0.722131\pi\)
\(114\) 0 0
\(115\) 6.53296 + 15.7720i 0.609201 + 1.47074i
\(116\) 12.2299 12.7663i 1.13552 1.18532i
\(117\) 0 0
\(118\) 0.343213 1.82771i 0.0315954 0.168254i
\(119\) 14.4514 14.4514i 1.32476 1.32476i
\(120\) 0 0
\(121\) 5.94096 + 5.94096i 0.540087 + 0.540087i
\(122\) 3.18743 2.17959i 0.288577 0.197331i
\(123\) 0 0
\(124\) −4.96021 11.2840i −0.445440 1.01333i
\(125\) −3.74754 + 1.55228i −0.335190 + 0.138840i
\(126\) 0 0
\(127\) 13.2014i 1.17143i −0.810515 0.585717i \(-0.800813\pi\)
0.810515 0.585717i \(-0.199187\pi\)
\(128\) 11.2306 + 1.36851i 0.992657 + 0.120960i
\(129\) 0 0
\(130\) 14.7383 3.09635i 1.29264 0.271568i
\(131\) −2.56553 6.19375i −0.224152 0.541150i 0.771294 0.636479i \(-0.219610\pi\)
−0.995446 + 0.0953287i \(0.969610\pi\)
\(132\) 0 0
\(133\) 11.7231 + 4.85585i 1.01652 + 0.421056i
\(134\) −3.38313 4.94749i −0.292258 0.427398i
\(135\) 0 0
\(136\) 7.84781 + 10.9642i 0.672944 + 0.940169i
\(137\) 9.77333 + 9.77333i 0.834992 + 0.834992i 0.988195 0.153203i \(-0.0489587\pi\)
−0.153203 + 0.988195i \(0.548959\pi\)
\(138\) 0 0
\(139\) −8.26616 3.42396i −0.701127 0.290416i 0.00350050 0.999994i \(-0.498886\pi\)
−0.704627 + 0.709578i \(0.748886\pi\)
\(140\) −18.1769 17.4132i −1.53623 1.47168i
\(141\) 0 0
\(142\) −5.78234 + 8.85814i −0.485243 + 0.743358i
\(143\) 5.84708i 0.488957i
\(144\) 0 0
\(145\) 25.9501i 2.15504i
\(146\) 2.63745 + 1.72165i 0.218277 + 0.142485i
\(147\) 0 0
\(148\) 20.3219 0.436073i 1.67045 0.0358449i
\(149\) −18.9803 7.86190i −1.55493 0.644072i −0.570729 0.821139i \(-0.693339\pi\)
−0.984199 + 0.177066i \(0.943339\pi\)
\(150\) 0 0
\(151\) 7.83326 + 7.83326i 0.637462 + 0.637462i 0.949929 0.312467i \(-0.101155\pi\)
−0.312467 + 0.949929i \(0.601155\pi\)
\(152\) −4.42452 + 7.10661i −0.358876 + 0.576422i
\(153\) 0 0
\(154\) −8.06720 + 5.51642i −0.650073 + 0.444526i
\(155\) −16.7156 6.92381i −1.34263 0.556134i
\(156\) 0 0
\(157\) 3.58014 + 8.64323i 0.285727 + 0.689805i 0.999949 0.0101140i \(-0.00321944\pi\)
−0.714222 + 0.699919i \(0.753219\pi\)
\(158\) 4.00412 + 19.0592i 0.318551 + 1.51627i
\(159\) 0 0
\(160\) 13.2935 9.95323i 1.05095 0.786872i
\(161\) 24.9306i 1.96481i
\(162\) 0 0
\(163\) −4.73693 + 1.96210i −0.371025 + 0.153684i −0.560402 0.828221i \(-0.689353\pi\)
0.189377 + 0.981904i \(0.439353\pi\)
\(164\) 0.447857 + 0.174349i 0.0349718 + 0.0136143i
\(165\) 0 0
\(166\) −2.86803 4.19420i −0.222602 0.325533i
\(167\) −4.55199 4.55199i −0.352244 0.352244i 0.508700 0.860944i \(-0.330126\pi\)
−0.860944 + 0.508700i \(0.830126\pi\)
\(168\) 0 0
\(169\) 0.111994 0.111994i 0.00861490 0.00861490i
\(170\) 19.4515 + 3.65268i 1.49186 + 0.280147i
\(171\) 0 0
\(172\) −16.3985 + 0.351884i −1.25037 + 0.0268309i
\(173\) −4.28444 10.3436i −0.325740 0.786406i −0.998899 0.0469083i \(-0.985063\pi\)
0.673159 0.739498i \(-0.264937\pi\)
\(174\) 0 0
\(175\) −15.5123 −1.17262
\(176\) −2.72064 5.84547i −0.205076 0.440619i
\(177\) 0 0
\(178\) −11.7068 7.64184i −0.877459 0.572780i
\(179\) 10.2246 4.23519i 0.764226 0.316553i 0.0336946 0.999432i \(-0.489273\pi\)
0.730531 + 0.682880i \(0.239273\pi\)
\(180\) 0 0
\(181\) −1.33358 + 3.21956i −0.0991246 + 0.239308i −0.965661 0.259806i \(-0.916341\pi\)
0.866536 + 0.499114i \(0.166341\pi\)
\(182\) −21.6154 4.05903i −1.60224 0.300875i
\(183\) 0 0
\(184\) 16.2265 + 2.68806i 1.19624 + 0.198166i
\(185\) 21.0974 21.0974i 1.55111 1.55111i
\(186\) 0 0
\(187\) 2.94056 7.09915i 0.215035 0.519141i
\(188\) 1.96418 + 4.46832i 0.143253 + 0.325886i
\(189\) 0 0
\(190\) 2.52640 + 12.0254i 0.183284 + 0.872414i
\(191\) 4.82446 0.349085 0.174543 0.984650i \(-0.444155\pi\)
0.174543 + 0.984650i \(0.444155\pi\)
\(192\) 0 0
\(193\) 0.222878 0.0160431 0.00802155 0.999968i \(-0.497447\pi\)
0.00802155 + 0.999968i \(0.497447\pi\)
\(194\) 3.94228 + 18.7648i 0.283039 + 1.34724i
\(195\) 0 0
\(196\) 9.15899 + 20.8358i 0.654214 + 1.48827i
\(197\) −9.44160 + 22.7940i −0.672686 + 1.62401i 0.104341 + 0.994542i \(0.466727\pi\)
−0.777028 + 0.629467i \(0.783273\pi\)
\(198\) 0 0
\(199\) 14.8710 14.8710i 1.05418 1.05418i 0.0557310 0.998446i \(-0.482251\pi\)
0.998446 0.0557310i \(-0.0177489\pi\)
\(200\) 1.67256 10.0964i 0.118268 0.713926i
\(201\) 0 0
\(202\) 4.01263 + 0.753507i 0.282328 + 0.0530165i
\(203\) −14.5024 + 35.0120i −1.01787 + 2.45736i
\(204\) 0 0
\(205\) 0.651743 0.269961i 0.0455197 0.0188549i
\(206\) 21.4385 + 13.9944i 1.49369 + 0.975037i
\(207\) 0 0
\(208\) 4.97250 13.6312i 0.344781 0.945150i
\(209\) 4.77079 0.330003
\(210\) 0 0
\(211\) −0.644000 1.55475i −0.0443348 0.107034i 0.900161 0.435558i \(-0.143449\pi\)
−0.944496 + 0.328524i \(0.893449\pi\)
\(212\) −4.30850 + 0.0924532i −0.295909 + 0.00634971i
\(213\) 0 0
\(214\) 2.61752 + 0.491528i 0.178930 + 0.0336002i
\(215\) −17.0243 + 17.0243i −1.16105 + 1.16105i
\(216\) 0 0
\(217\) 18.6833 + 18.6833i 1.26830 + 1.26830i
\(218\) −3.84510 5.62306i −0.260423 0.380842i
\(219\) 0 0
\(220\) −8.81935 3.43333i −0.594600 0.231475i
\(221\) 15.9761 6.61750i 1.07467 0.445141i
\(222\) 0 0
\(223\) 23.4280i 1.56885i −0.620221 0.784427i \(-0.712957\pi\)
0.620221 0.784427i \(-0.287043\pi\)
\(224\) −23.4982 + 5.99974i −1.57004 + 0.400875i
\(225\) 0 0
\(226\) 3.97216 + 18.9071i 0.264224 + 1.25768i
\(227\) 5.10690 + 12.3292i 0.338957 + 0.818315i 0.997816 + 0.0660486i \(0.0210392\pi\)
−0.658859 + 0.752266i \(0.728961\pi\)
\(228\) 0 0
\(229\) −7.82666 3.24191i −0.517200 0.214231i 0.108786 0.994065i \(-0.465304\pi\)
−0.625987 + 0.779834i \(0.715304\pi\)
\(230\) 19.9288 13.6275i 1.31407 0.898571i
\(231\) 0 0
\(232\) −21.2245 13.2142i −1.39346 0.867556i
\(233\) 9.66805 + 9.66805i 0.633375 + 0.633375i 0.948913 0.315538i \(-0.102185\pi\)
−0.315538 + 0.948913i \(0.602185\pi\)
\(234\) 0 0
\(235\) 6.61915 + 2.74174i 0.431785 + 0.178851i
\(236\) −2.62934 + 0.0564212i −0.171155 + 0.00367270i
\(237\) 0 0
\(238\) −24.2027 15.7989i −1.56883 1.02409i
\(239\) 25.8579i 1.67261i 0.548268 + 0.836303i \(0.315287\pi\)
−0.548268 + 0.836303i \(0.684713\pi\)
\(240\) 0 0
\(241\) 24.9358i 1.60626i 0.595805 + 0.803129i \(0.296833\pi\)
−0.595805 + 0.803129i \(0.703167\pi\)
\(242\) 6.49488 9.94970i 0.417507 0.639591i
\(243\) 0 0
\(244\) −3.94334 3.77766i −0.252447 0.241840i
\(245\) 30.8652 + 12.7848i 1.97190 + 0.816789i
\(246\) 0 0
\(247\) 7.59170 + 7.59170i 0.483048 + 0.483048i
\(248\) −14.1748 + 10.1459i −0.900102 + 0.644266i
\(249\) 0 0
\(250\) 3.23800 + 4.73525i 0.204789 + 0.299483i
\(251\) 11.5486 + 4.78358i 0.728939 + 0.301937i 0.716116 0.697981i \(-0.245918\pi\)
0.0128233 + 0.999918i \(0.495918\pi\)
\(252\) 0 0
\(253\) −3.58705 8.65990i −0.225516 0.544443i
\(254\) −18.2707 + 3.83848i −1.14641 + 0.240847i
\(255\) 0 0
\(256\) −1.37144 15.9411i −0.0857148 0.996320i
\(257\) 17.0780i 1.06530i 0.846337 + 0.532648i \(0.178803\pi\)
−0.846337 + 0.532648i \(0.821197\pi\)
\(258\) 0 0
\(259\) −40.2552 + 16.6742i −2.50133 + 1.03609i
\(260\) −8.57070 19.4975i −0.531532 1.20919i
\(261\) 0 0
\(262\) −7.82619 + 5.35161i −0.483503 + 0.330624i
\(263\) −10.4595 10.4595i −0.644963 0.644963i 0.306809 0.951771i \(-0.400739\pi\)
−0.951771 + 0.306809i \(0.900739\pi\)
\(264\) 0 0
\(265\) −4.47292 + 4.47292i −0.274770 + 0.274770i
\(266\) 3.31187 17.6366i 0.203064 1.08137i
\(267\) 0 0
\(268\) −5.86364 + 6.12080i −0.358179 + 0.373888i
\(269\) −3.47587 8.39150i −0.211928 0.511639i 0.781792 0.623540i \(-0.214306\pi\)
−0.993719 + 0.111901i \(0.964306\pi\)
\(270\) 0 0
\(271\) −5.66173 −0.343925 −0.171963 0.985103i \(-0.555011\pi\)
−0.171963 + 0.985103i \(0.555011\pi\)
\(272\) 12.8926 14.0493i 0.781726 0.851866i
\(273\) 0 0
\(274\) 10.6846 16.3680i 0.645479 0.988828i
\(275\) −5.38834 + 2.23192i −0.324929 + 0.134590i
\(276\) 0 0
\(277\) −5.27625 + 12.7380i −0.317019 + 0.765352i 0.682390 + 0.730988i \(0.260940\pi\)
−0.999409 + 0.0343637i \(0.989060\pi\)
\(278\) −2.33527 + 12.4359i −0.140060 + 0.745858i
\(279\) 0 0
\(280\) −18.8147 + 30.2199i −1.12439 + 1.80598i
\(281\) −5.75892 + 5.75892i −0.343548 + 0.343548i −0.857700 0.514151i \(-0.828107\pi\)
0.514151 + 0.857700i \(0.328107\pi\)
\(282\) 0 0
\(283\) 10.4136 25.1407i 0.619025 1.49446i −0.233812 0.972282i \(-0.575120\pi\)
0.852837 0.522177i \(-0.174880\pi\)
\(284\) 13.9410 + 5.42714i 0.827243 + 0.322042i
\(285\) 0 0
\(286\) −8.09236 + 1.70011i −0.478511 + 0.100530i
\(287\) −1.03021 −0.0608111
\(288\) 0 0
\(289\) 5.72512 0.336772
\(290\) −35.9149 + 7.54531i −2.10900 + 0.443076i
\(291\) 0 0
\(292\) 1.61590 4.15083i 0.0945632 0.242909i
\(293\) 5.21345 12.5864i 0.304573 0.735304i −0.695290 0.718729i \(-0.744724\pi\)
0.999863 0.0165743i \(-0.00527600\pi\)
\(294\) 0 0
\(295\) −2.72968 + 2.72968i −0.158928 + 0.158928i
\(296\) −6.51236 27.9987i −0.378523 1.62739i
\(297\) 0 0
\(298\) −5.36211 + 28.5547i −0.310619 + 1.65413i
\(299\) 8.07236 19.4884i 0.466837 1.12704i
\(300\) 0 0
\(301\) 32.4835 13.4551i 1.87232 0.775539i
\(302\) 8.56362 13.1189i 0.492781 0.754905i
\(303\) 0 0
\(304\) 11.1220 + 4.05720i 0.637892 + 0.232696i
\(305\) −8.01566 −0.458975
\(306\) 0 0
\(307\) −8.98052 21.6809i −0.512545 1.23739i −0.942398 0.334495i \(-0.891434\pi\)
0.429852 0.902899i \(-0.358566\pi\)
\(308\) 9.98036 + 9.56104i 0.568684 + 0.544791i
\(309\) 0 0
\(310\) −4.72230 + 25.1475i −0.268208 + 1.42828i
\(311\) 12.7177 12.7177i 0.721157 0.721157i −0.247684 0.968841i \(-0.579670\pi\)
0.968841 + 0.247684i \(0.0796695\pi\)
\(312\) 0 0
\(313\) 10.1388 + 10.1388i 0.573081 + 0.573081i 0.932988 0.359907i \(-0.117192\pi\)
−0.359907 + 0.932988i \(0.617192\pi\)
\(314\) 10.9213 7.46805i 0.616323 0.421446i
\(315\) 0 0
\(316\) 25.2137 11.0834i 1.41838 0.623490i
\(317\) 2.52668 1.04659i 0.141913 0.0587822i −0.310597 0.950542i \(-0.600529\pi\)
0.452509 + 0.891760i \(0.350529\pi\)
\(318\) 0 0
\(319\) 14.2484i 0.797757i
\(320\) −17.6405 15.5042i −0.986136 0.866713i
\(321\) 0 0
\(322\) −34.5040 + 7.24889i −1.92283 + 0.403965i
\(323\) 5.39940 + 13.0353i 0.300431 + 0.725304i
\(324\) 0 0
\(325\) −12.1260 5.02277i −0.672631 0.278613i
\(326\) 4.09287 + 5.98540i 0.226683 + 0.331501i
\(327\) 0 0
\(328\) 0.111078 0.670528i 0.00613327 0.0370237i
\(329\) −7.39834 7.39834i −0.407884 0.407884i
\(330\) 0 0
\(331\) −5.49794 2.27732i −0.302194 0.125173i 0.226434 0.974027i \(-0.427293\pi\)
−0.528628 + 0.848854i \(0.677293\pi\)
\(332\) −4.97086 + 5.18887i −0.272811 + 0.284776i
\(333\) 0 0
\(334\) −4.97641 + 7.62351i −0.272297 + 0.417140i
\(335\) 12.4418i 0.679768i
\(336\) 0 0
\(337\) 5.85273i 0.318818i −0.987213 0.159409i \(-0.949041\pi\)
0.987213 0.159409i \(-0.0509589\pi\)
\(338\) −0.187563 0.122436i −0.0102021 0.00665963i
\(339\) 0 0
\(340\) −0.600467 27.9829i −0.0325649 1.51759i
\(341\) 9.17801 + 3.80166i 0.497017 + 0.205871i
\(342\) 0 0
\(343\) −13.2780 13.2780i −0.716946 0.716946i
\(344\) 5.25508 + 22.5932i 0.283335 + 1.21815i
\(345\) 0 0
\(346\) −13.0697 + 8.93719i −0.702633 + 0.480466i
\(347\) −7.23994 2.99888i −0.388660 0.160988i 0.179792 0.983705i \(-0.442458\pi\)
−0.568452 + 0.822716i \(0.692458\pi\)
\(348\) 0 0
\(349\) −4.01973 9.70449i −0.215171 0.519469i 0.779032 0.626984i \(-0.215711\pi\)
−0.994204 + 0.107515i \(0.965711\pi\)
\(350\) 4.51039 + 21.4690i 0.241090 + 1.14756i
\(351\) 0 0
\(352\) −7.29908 + 5.46502i −0.389042 + 0.291286i
\(353\) 16.6657i 0.887026i 0.896268 + 0.443513i \(0.146268\pi\)
−0.896268 + 0.443513i \(0.853732\pi\)
\(354\) 0 0
\(355\) 20.2875 8.40338i 1.07675 0.446005i
\(356\) −7.17242 + 18.4241i −0.380138 + 0.976477i
\(357\) 0 0
\(358\) −8.83444 12.9195i −0.466915 0.682815i
\(359\) 9.54649 + 9.54649i 0.503845 + 0.503845i 0.912630 0.408786i \(-0.134048\pi\)
−0.408786 + 0.912630i \(0.634048\pi\)
\(360\) 0 0
\(361\) 7.24075 7.24075i 0.381092 0.381092i
\(362\) 4.84363 + 0.909554i 0.254575 + 0.0478051i
\(363\) 0 0
\(364\) 0.667267 + 31.0960i 0.0349743 + 1.62987i
\(365\) −2.50205 6.04049i −0.130963 0.316173i
\(366\) 0 0
\(367\) −6.31072 −0.329417 −0.164708 0.986342i \(-0.552668\pi\)
−0.164708 + 0.986342i \(0.552668\pi\)
\(368\) −0.997804 23.2391i −0.0520141 1.21142i
\(369\) 0 0
\(370\) −35.3331 23.0644i −1.83688 1.19906i
\(371\) 8.53463 3.53516i 0.443096 0.183536i
\(372\) 0 0
\(373\) −3.06259 + 7.39375i −0.158575 + 0.382834i −0.983120 0.182963i \(-0.941431\pi\)
0.824545 + 0.565797i \(0.191431\pi\)
\(374\) −10.6802 2.00557i −0.552261 0.103706i
\(375\) 0 0
\(376\) 5.61305 4.01765i 0.289471 0.207194i
\(377\) −22.6733 + 22.6733i −1.16773 + 1.16773i
\(378\) 0 0
\(379\) −8.31838 + 20.0823i −0.427286 + 1.03156i 0.552858 + 0.833275i \(0.313537\pi\)
−0.980144 + 0.198285i \(0.936463\pi\)
\(380\) 15.9086 6.99307i 0.816092 0.358737i
\(381\) 0 0
\(382\) −1.40277 6.67705i −0.0717720 0.341627i
\(383\) −7.95308 −0.406383 −0.203192 0.979139i \(-0.565131\pi\)
−0.203192 + 0.979139i \(0.565131\pi\)
\(384\) 0 0
\(385\) 20.2871 1.03393
\(386\) −0.0648046 0.308463i −0.00329847 0.0157004i
\(387\) 0 0
\(388\) 24.8243 10.9122i 1.26026 0.553984i
\(389\) −2.38215 + 5.75102i −0.120780 + 0.291588i −0.972693 0.232094i \(-0.925442\pi\)
0.851913 + 0.523683i \(0.175442\pi\)
\(390\) 0 0
\(391\) 19.6019 19.6019i 0.991310 0.991310i
\(392\) 26.1737 18.7343i 1.32197 0.946227i
\(393\) 0 0
\(394\) 34.2922 + 6.43952i 1.72762 + 0.324418i
\(395\) 15.4710 37.3503i 0.778430 1.87930i
\(396\) 0 0
\(397\) 25.3118 10.4845i 1.27036 0.526202i 0.357288 0.933994i \(-0.383701\pi\)
0.913075 + 0.407792i \(0.133701\pi\)
\(398\) −24.9054 16.2575i −1.24839 0.814916i
\(399\) 0 0
\(400\) −14.4598 + 0.620851i −0.722990 + 0.0310426i
\(401\) −1.81017 −0.0903954 −0.0451977 0.998978i \(-0.514392\pi\)
−0.0451977 + 0.998978i \(0.514392\pi\)
\(402\) 0 0
\(403\) 8.55532 + 20.6544i 0.426171 + 1.02887i
\(404\) −0.123870 5.77257i −0.00616275 0.287196i
\(405\) 0 0
\(406\) 52.6734 + 9.89120i 2.61413 + 0.490892i
\(407\) −11.5839 + 11.5839i −0.574194 + 0.574194i
\(408\) 0 0
\(409\) −14.4331 14.4331i −0.713672 0.713672i 0.253630 0.967301i \(-0.418376\pi\)
−0.967301 + 0.253630i \(0.918376\pi\)
\(410\) −0.563129 0.823518i −0.0278109 0.0406707i
\(411\) 0 0
\(412\) 13.1348 33.7399i 0.647104 1.66225i
\(413\) 5.20841 2.15739i 0.256289 0.106158i
\(414\) 0 0
\(415\) 10.5474i 0.517754i
\(416\) −20.3113 2.91851i −0.995845 0.143092i
\(417\) 0 0
\(418\) −1.38717 6.60278i −0.0678486 0.322952i
\(419\) −1.33902 3.23269i −0.0654155 0.157927i 0.887791 0.460247i \(-0.152239\pi\)
−0.953207 + 0.302320i \(0.902239\pi\)
\(420\) 0 0
\(421\) −10.5557 4.37232i −0.514454 0.213094i 0.110325 0.993896i \(-0.464811\pi\)
−0.624779 + 0.780802i \(0.714811\pi\)
\(422\) −1.96453 + 1.34336i −0.0956318 + 0.0653938i
\(423\) 0 0
\(424\) 1.38071 + 5.93609i 0.0670530 + 0.288282i
\(425\) −12.1966 12.1966i −0.591624 0.591624i
\(426\) 0 0
\(427\) 10.8148 + 4.47963i 0.523364 + 0.216784i
\(428\) −0.0808028 3.76557i −0.00390575 0.182016i
\(429\) 0 0
\(430\) 28.5117 + 18.6116i 1.37496 + 0.897532i
\(431\) 3.31967i 0.159903i 0.996799 + 0.0799513i \(0.0254765\pi\)
−0.996799 + 0.0799513i \(0.974524\pi\)
\(432\) 0 0
\(433\) 4.53298i 0.217841i 0.994050 + 0.108921i \(0.0347394\pi\)
−0.994050 + 0.108921i \(0.965261\pi\)
\(434\) 20.4253 31.2901i 0.980445 1.50197i
\(435\) 0 0
\(436\) −6.66431 + 6.95659i −0.319163 + 0.333160i
\(437\) 15.9011 + 6.58646i 0.760654 + 0.315073i
\(438\) 0 0
\(439\) 20.9703 + 20.9703i 1.00086 + 1.00086i 1.00000 0.000858061i \(0.000273129\pi\)
0.000858061 1.00000i \(0.499727\pi\)
\(440\) −2.18739 + 13.2043i −0.104280 + 0.629489i
\(441\) 0 0
\(442\) −13.8039 20.1868i −0.656583 0.960186i
\(443\) −31.9708 13.2427i −1.51898 0.629181i −0.541590 0.840643i \(-0.682178\pi\)
−0.977386 + 0.211462i \(0.932178\pi\)
\(444\) 0 0
\(445\) 11.1058 + 26.8117i 0.526464 + 1.27100i
\(446\) −32.4243 + 6.81198i −1.53534 + 0.322557i
\(447\) 0 0
\(448\) 15.1360 + 30.7770i 0.715110 + 1.45407i
\(449\) 21.0485i 0.993340i −0.867940 0.496670i \(-0.834556\pi\)
0.867940 0.496670i \(-0.165444\pi\)
\(450\) 0 0
\(451\) −0.357852 + 0.148227i −0.0168506 + 0.00697975i
\(452\) 25.0125 10.9950i 1.17649 0.517159i
\(453\) 0 0
\(454\) 15.5787 10.6528i 0.731143 0.499961i
\(455\) 32.2827 + 32.2827i 1.51344 + 1.51344i
\(456\) 0 0
\(457\) −4.62656 + 4.62656i −0.216421 + 0.216421i −0.806988 0.590567i \(-0.798904\pi\)
0.590567 + 0.806988i \(0.298904\pi\)
\(458\) −2.21110 + 11.7747i −0.103318 + 0.550197i
\(459\) 0 0
\(460\) −24.6550 23.6192i −1.14955 1.10125i
\(461\) 4.84388 + 11.6942i 0.225602 + 0.544652i 0.995633 0.0933550i \(-0.0297592\pi\)
−0.770031 + 0.638007i \(0.779759\pi\)
\(462\) 0 0
\(463\) 14.2219 0.660950 0.330475 0.943815i \(-0.392791\pi\)
0.330475 + 0.943815i \(0.392791\pi\)
\(464\) −12.1172 + 33.2169i −0.562526 + 1.54206i
\(465\) 0 0
\(466\) 10.5695 16.1917i 0.489622 0.750066i
\(467\) −34.5241 + 14.3003i −1.59758 + 0.661741i −0.991071 0.133333i \(-0.957432\pi\)
−0.606512 + 0.795074i \(0.707432\pi\)
\(468\) 0 0
\(469\) 6.95321 16.7865i 0.321069 0.775130i
\(470\) 1.86997 9.95809i 0.0862552 0.459333i
\(471\) 0 0
\(472\) 0.842601 + 3.62260i 0.0387838 + 0.166744i
\(473\) 9.34754 9.34754i 0.429800 0.429800i
\(474\) 0 0
\(475\) 4.09821 9.89396i 0.188039 0.453966i
\(476\) −14.8284 + 38.0903i −0.679657 + 1.74587i
\(477\) 0 0
\(478\) 35.7873 7.51850i 1.63687 0.343888i
\(479\) 13.4016 0.612333 0.306167 0.951978i \(-0.400954\pi\)
0.306167 + 0.951978i \(0.400954\pi\)
\(480\) 0 0
\(481\) −36.8667 −1.68098
\(482\) 34.5112 7.25041i 1.57194 0.330247i
\(483\) 0 0
\(484\) −15.6589 6.09591i −0.711766 0.277087i
\(485\) 15.2320 36.7734i 0.691652 1.66979i
\(486\) 0 0
\(487\) 1.26750 1.26750i 0.0574358 0.0574358i −0.677805 0.735241i \(-0.737069\pi\)
0.735241 + 0.677805i \(0.237069\pi\)
\(488\) −4.08171 + 6.55599i −0.184770 + 0.296776i
\(489\) 0 0
\(490\) 8.71969 46.4347i 0.393915 2.09771i
\(491\) 8.81902 21.2910i 0.397997 0.960849i −0.590144 0.807298i \(-0.700929\pi\)
0.988141 0.153551i \(-0.0490710\pi\)
\(492\) 0 0
\(493\) −38.9311 + 16.1258i −1.75337 + 0.726269i
\(494\) 8.29953 12.7143i 0.373414 0.572043i
\(495\) 0 0
\(496\) 18.1634 + 16.6679i 0.815563 + 0.748411i
\(497\) −32.0684 −1.43846
\(498\) 0 0
\(499\) −2.76574 6.67709i −0.123812 0.298908i 0.849805 0.527097i \(-0.176719\pi\)
−0.973617 + 0.228189i \(0.926719\pi\)
\(500\) 5.61209 5.85823i 0.250980 0.261988i
\(501\) 0 0
\(502\) 3.26258 17.3741i 0.145616 0.775445i
\(503\) 17.1789 17.1789i 0.765968 0.765968i −0.211426 0.977394i \(-0.567811\pi\)
0.977394 + 0.211426i \(0.0678108\pi\)
\(504\) 0 0
\(505\) −5.99287 5.99287i −0.266679 0.266679i
\(506\) −10.9423 + 7.48245i −0.486446 + 0.332636i
\(507\) 0 0
\(508\) 10.6249 + 24.1706i 0.471404 + 1.07240i
\(509\) 0.432418 0.179113i 0.0191666 0.00793905i −0.373080 0.927799i \(-0.621698\pi\)
0.392246 + 0.919860i \(0.371698\pi\)
\(510\) 0 0
\(511\) 9.54815i 0.422385i
\(512\) −21.6637 + 6.53315i −0.957411 + 0.288727i
\(513\) 0 0
\(514\) 23.6359 4.96564i 1.04254 0.219025i
\(515\) −20.3379 49.0999i −0.896193 2.16360i
\(516\) 0 0
\(517\) −3.63437 1.50541i −0.159839 0.0662077i
\(518\) 34.7818 + 50.8649i 1.52823 + 2.23488i
\(519\) 0 0
\(520\) −24.4925 + 17.5310i −1.07407 + 0.768786i
\(521\) −20.6495 20.6495i −0.904670 0.904670i 0.0911655 0.995836i \(-0.470941\pi\)
−0.995836 + 0.0911655i \(0.970941\pi\)
\(522\) 0 0
\(523\) −40.6453 16.8358i −1.77729 0.736180i −0.993321 0.115386i \(-0.963190\pi\)
−0.783974 0.620794i \(-0.786810\pi\)
\(524\) 9.68219 + 9.27540i 0.422969 + 0.405198i
\(525\) 0 0
\(526\) −11.4348 + 17.5172i −0.498579 + 0.763788i
\(527\) 29.3798i 1.27980i
\(528\) 0 0
\(529\) 10.8158i 0.470252i
\(530\) 7.49109 + 4.88997i 0.325392 + 0.212407i
\(531\) 0 0
\(532\) −25.3721 + 0.544441i −1.10002 + 0.0236045i
\(533\) −0.805318 0.333574i −0.0348822 0.0144487i
\(534\) 0 0
\(535\) −3.90927 3.90927i −0.169013 0.169013i
\(536\) 10.1761 + 6.33557i 0.439541 + 0.273655i
\(537\) 0 0
\(538\) −10.6032 + 7.25055i −0.457136 + 0.312593i
\(539\) −16.9471 7.01973i −0.729964 0.302361i
\(540\) 0 0
\(541\) −7.26862 17.5480i −0.312502 0.754447i −0.999611 0.0278925i \(-0.991120\pi\)
0.687109 0.726555i \(-0.258880\pi\)
\(542\) 1.64622 + 7.83583i 0.0707111 + 0.336578i
\(543\) 0 0
\(544\) −23.1930 13.7583i −0.994390 0.589881i
\(545\) 14.1407i 0.605721i
\(546\) 0 0
\(547\) −5.22407 + 2.16388i −0.223365 + 0.0925208i −0.491560 0.870844i \(-0.663573\pi\)
0.268195 + 0.963365i \(0.413573\pi\)
\(548\) −25.7600 10.0282i −1.10041 0.428386i
\(549\) 0 0
\(550\) 4.65571 + 6.80851i 0.198520 + 0.290316i
\(551\) −18.4998 18.4998i −0.788116 0.788116i
\(552\) 0 0
\(553\) −41.7471 + 41.7471i −1.77527 + 1.77527i
\(554\) 19.1635 + 3.59860i 0.814180 + 0.152890i
\(555\) 0 0
\(556\) 17.8903 0.383896i 0.758719 0.0162808i
\(557\) 7.20051 + 17.3836i 0.305095 + 0.736565i 0.999850 + 0.0173184i \(0.00551288\pi\)
−0.694755 + 0.719247i \(0.744487\pi\)
\(558\) 0 0
\(559\) 29.7492 1.25826
\(560\) 47.2949 + 17.2527i 1.99858 + 0.729059i
\(561\) 0 0
\(562\) 9.64483 + 6.29587i 0.406843 + 0.265575i
\(563\) 43.4445 17.9953i 1.83097 0.758411i 0.864007 0.503479i \(-0.167947\pi\)
0.966959 0.254932i \(-0.0820530\pi\)
\(564\) 0 0
\(565\) 15.3475 37.0522i 0.645675 1.55880i
\(566\) −37.8226 7.10247i −1.58980 0.298539i
\(567\) 0 0
\(568\) 3.45766 20.8723i 0.145080 0.875782i
\(569\) −5.66061 + 5.66061i −0.237305 + 0.237305i −0.815733 0.578428i \(-0.803666\pi\)
0.578428 + 0.815733i \(0.303666\pi\)
\(570\) 0 0
\(571\) −13.7365 + 33.1629i −0.574856 + 1.38783i 0.322522 + 0.946562i \(0.395469\pi\)
−0.897378 + 0.441263i \(0.854531\pi\)
\(572\) 4.70591 + 10.7055i 0.196764 + 0.447619i
\(573\) 0 0
\(574\) 0.299545 + 1.42581i 0.0125028 + 0.0595120i
\(575\) −21.0408 −0.877461
\(576\) 0 0
\(577\) 4.38583 0.182584 0.0912922 0.995824i \(-0.470900\pi\)
0.0912922 + 0.995824i \(0.470900\pi\)
\(578\) −1.66465 7.92357i −0.0692404 0.329577i
\(579\) 0 0
\(580\) 20.8854 + 47.5124i 0.867220 + 1.97284i
\(581\) 5.89454 14.2307i 0.244547 0.590388i
\(582\) 0 0
\(583\) 2.45595 2.45595i 0.101715 0.101715i
\(584\) −6.21459 1.02950i −0.257162 0.0426008i
\(585\) 0 0
\(586\) −18.9354 3.55576i −0.782215 0.146887i
\(587\) −4.24918 + 10.2584i −0.175382 + 0.423411i −0.986988 0.160795i \(-0.948594\pi\)
0.811605 + 0.584206i \(0.198594\pi\)
\(588\) 0 0
\(589\) −16.8525 + 6.98052i −0.694394 + 0.287627i
\(590\) 4.57157 + 2.98419i 0.188208 + 0.122857i
\(591\) 0 0
\(592\) −36.8566 + 17.1541i −1.51480 + 0.705028i
\(593\) 5.76763 0.236848 0.118424 0.992963i \(-0.462216\pi\)
0.118424 + 0.992963i \(0.462216\pi\)
\(594\) 0 0
\(595\) 22.9602 + 55.4309i 0.941277 + 2.27244i
\(596\) 41.0788 0.881482i 1.68265 0.0361069i
\(597\) 0 0
\(598\) −29.3191 5.50565i −1.19895 0.225143i
\(599\) −13.4401 + 13.4401i −0.549149 + 0.549149i −0.926195 0.377045i \(-0.876940\pi\)
0.377045 + 0.926195i \(0.376940\pi\)
\(600\) 0 0
\(601\) 8.58677 + 8.58677i 0.350262 + 0.350262i 0.860207 0.509945i \(-0.170334\pi\)
−0.509945 + 0.860207i \(0.670334\pi\)
\(602\) −28.0669 41.0449i −1.14392 1.67287i
\(603\) 0 0
\(604\) −20.6465 8.03757i −0.840093 0.327044i
\(605\) −22.7875 + 9.43890i −0.926444 + 0.383746i
\(606\) 0 0
\(607\) 13.3743i 0.542847i 0.962460 + 0.271424i \(0.0874944\pi\)
−0.962460 + 0.271424i \(0.912506\pi\)
\(608\) 2.38129 16.5726i 0.0965742 0.672107i
\(609\) 0 0
\(610\) 2.33066 + 11.0937i 0.0943655 + 0.449170i
\(611\) −3.38780 8.17886i −0.137056 0.330881i
\(612\) 0 0
\(613\) −10.6749 4.42168i −0.431154 0.178590i 0.156542 0.987671i \(-0.449965\pi\)
−0.587697 + 0.809081i \(0.699965\pi\)
\(614\) −27.3952 + 18.7330i −1.10558 + 0.756004i
\(615\) 0 0
\(616\) 10.3306 16.5928i 0.416230 0.668544i
\(617\) −14.8713 14.8713i −0.598695 0.598695i 0.341270 0.939965i \(-0.389143\pi\)
−0.939965 + 0.341270i \(0.889143\pi\)
\(618\) 0 0
\(619\) −6.25062 2.58909i −0.251234 0.104064i 0.253513 0.967332i \(-0.418414\pi\)
−0.504746 + 0.863268i \(0.668414\pi\)
\(620\) 36.1773 0.776303i 1.45291 0.0311771i
\(621\) 0 0
\(622\) −21.2992 13.9035i −0.854020 0.557480i
\(623\) 42.3810i 1.69796i
\(624\) 0 0
\(625\) 29.9995i 1.19998i
\(626\) 11.0842 16.9801i 0.443012 0.678663i
\(627\) 0 0
\(628\) −13.5113 12.9436i −0.539159 0.516506i
\(629\) −44.7612 18.5407i −1.78475 0.739266i
\(630\) 0 0
\(631\) −5.78346 5.78346i −0.230236 0.230236i 0.582555 0.812791i \(-0.302053\pi\)
−0.812791 + 0.582555i \(0.802053\pi\)
\(632\) −22.6706 31.6731i −0.901789 1.25989i
\(633\) 0 0
\(634\) −2.18314 3.19262i −0.0867037 0.126795i
\(635\) 35.8052 + 14.8310i 1.42088 + 0.588550i
\(636\) 0 0
\(637\) −15.7973 38.1381i −0.625913 1.51109i
\(638\) 19.7198 4.14290i 0.780714 0.164019i
\(639\) 0 0
\(640\) −16.3286 + 28.9226i −0.645446 + 1.14327i
\(641\) 29.5203i 1.16598i 0.812479 + 0.582990i \(0.198117\pi\)
−0.812479 + 0.582990i \(0.801883\pi\)
\(642\) 0 0
\(643\) 10.0660 4.16947i 0.396964 0.164428i −0.175266 0.984521i \(-0.556079\pi\)
0.572230 + 0.820093i \(0.306079\pi\)
\(644\) 20.0649 + 45.6458i 0.790669 + 1.79870i
\(645\) 0 0
\(646\) 16.4709 11.2630i 0.648040 0.443135i
\(647\) 31.9256 + 31.9256i 1.25512 + 1.25512i 0.953393 + 0.301730i \(0.0975641\pi\)
0.301730 + 0.953393i \(0.402436\pi\)
\(648\) 0 0
\(649\) 1.49878 1.49878i 0.0588324 0.0588324i
\(650\) −3.42571 + 18.2429i −0.134368 + 0.715544i
\(651\) 0 0
\(652\) 7.09375 7.40486i 0.277813 0.289997i
\(653\) 6.05626 + 14.6211i 0.237000 + 0.572168i 0.996970 0.0777900i \(-0.0247864\pi\)
−0.759970 + 0.649958i \(0.774786\pi\)
\(654\) 0 0
\(655\) 19.6811 0.769002
\(656\) −0.960309 + 0.0412322i −0.0374938 + 0.00160985i
\(657\) 0 0
\(658\) −8.08814 + 12.3905i −0.315309 + 0.483031i
\(659\) 28.2612 11.7062i 1.10090 0.456008i 0.243106 0.970000i \(-0.421834\pi\)
0.857795 + 0.513992i \(0.171834\pi\)
\(660\) 0 0
\(661\) 6.64573 16.0442i 0.258489 0.624047i −0.740350 0.672221i \(-0.765340\pi\)
0.998839 + 0.0481743i \(0.0153403\pi\)
\(662\) −1.55322 + 8.27131i −0.0603675 + 0.321474i
\(663\) 0 0
\(664\) 8.62674 + 5.37094i 0.334782 + 0.208433i
\(665\) −26.3403 + 26.3403i −1.02143 + 1.02143i
\(666\) 0 0
\(667\) −19.6711 + 47.4901i −0.761666 + 1.83883i
\(668\) 11.9979 + 4.67072i 0.464212 + 0.180716i
\(669\) 0 0
\(670\) 17.2194 3.61761i 0.665245 0.139760i
\(671\) 4.40116 0.169905
\(672\) 0 0
\(673\) 34.2884 1.32172 0.660860 0.750509i \(-0.270192\pi\)
0.660860 + 0.750509i \(0.270192\pi\)
\(674\) −8.10018 + 1.70176i −0.312007 + 0.0655492i
\(675\) 0 0
\(676\) −0.114915 + 0.295187i −0.00441980 + 0.0113533i
\(677\) −16.6560 + 40.2112i −0.640142 + 1.54544i 0.186345 + 0.982484i \(0.440336\pi\)
−0.826487 + 0.562956i \(0.809664\pi\)
\(678\) 0 0
\(679\) −41.1023 + 41.1023i −1.57736 + 1.57736i
\(680\) −38.5538 + 8.96744i −1.47847 + 0.343886i
\(681\) 0 0
\(682\) 2.59287 13.8077i 0.0992861 0.528726i
\(683\) −5.35596 + 12.9304i −0.204940 + 0.494769i −0.992613 0.121325i \(-0.961286\pi\)
0.787673 + 0.616094i \(0.211286\pi\)
\(684\) 0 0
\(685\) −37.4872 + 15.5277i −1.43231 + 0.593284i
\(686\) −14.5160 + 22.2376i −0.554225 + 0.849034i
\(687\) 0 0
\(688\) 29.7411 13.8423i 1.13387 0.527733i
\(689\) 7.81623 0.297775
\(690\) 0 0
\(691\) −19.9998 48.2837i −0.760826 1.83680i −0.480898 0.876777i \(-0.659689\pi\)
−0.279929 0.960021i \(-0.590311\pi\)
\(692\) 16.1693 + 15.4899i 0.614663 + 0.588838i
\(693\) 0 0
\(694\) −2.04535 + 10.8920i −0.0776404 + 0.413456i
\(695\) 18.5731 18.5731i 0.704517 0.704517i
\(696\) 0 0
\(697\) −0.810008 0.810008i −0.0306812 0.0306812i
\(698\) −12.2622 + 8.38501i −0.464132 + 0.317377i
\(699\) 0 0
\(700\) 28.4016 12.4848i 1.07348 0.471879i
\(701\) 22.6661 9.38859i 0.856085 0.354602i 0.0889098 0.996040i \(-0.471662\pi\)
0.767175 + 0.641438i \(0.221662\pi\)
\(702\) 0 0
\(703\) 30.0806i 1.13451i
\(704\) 9.68589 + 8.51290i 0.365051 + 0.320842i
\(705\) 0 0
\(706\) 23.0653 4.84577i 0.868076 0.182373i
\(707\) 4.73644 + 11.4348i 0.178132 + 0.430049i
\(708\) 0 0
\(709\) −6.91323 2.86355i −0.259632 0.107543i 0.249071 0.968485i \(-0.419875\pi\)
−0.508703 + 0.860942i \(0.669875\pi\)
\(710\) −17.5291 25.6346i −0.657857 0.962049i
\(711\) 0 0
\(712\) 27.5845 + 4.56959i 1.03377 + 0.171253i
\(713\) 25.3420 + 25.3420i 0.949064 + 0.949064i
\(714\) 0 0
\(715\) 15.8586 + 6.56884i 0.593078 + 0.245661i
\(716\) −15.3118 + 15.9834i −0.572230 + 0.597327i
\(717\) 0 0
\(718\) 10.4366 15.9881i 0.389490 0.596671i
\(719\) 32.1395i 1.19860i −0.800525 0.599300i \(-0.795446\pi\)
0.800525 0.599300i \(-0.204554\pi\)
\(720\) 0 0
\(721\) 77.6119i 2.89042i
\(722\) −12.1265 7.91587i −0.451303 0.294598i
\(723\) 0 0
\(724\) −0.149522 6.96805i −0.00555696 0.258965i
\(725\) 29.5492 + 12.2397i 1.09743 + 0.454570i
\(726\) 0 0
\(727\) 24.0313 + 24.0313i 0.891271 + 0.891271i 0.994643 0.103372i \(-0.0329632\pi\)
−0.103372 + 0.994643i \(0.532963\pi\)
\(728\) 42.8428 9.96505i 1.58786 0.369329i
\(729\) 0 0
\(730\) −7.63253 + 5.21919i −0.282493 + 0.193171i
\(731\) 36.1196 + 14.9612i 1.33593 + 0.553361i
\(732\) 0 0
\(733\) −3.28110 7.92127i −0.121190 0.292579i 0.851629 0.524145i \(-0.175615\pi\)
−0.972819 + 0.231566i \(0.925615\pi\)
\(734\) 1.83492 + 8.73404i 0.0677282 + 0.322379i
\(735\) 0 0
\(736\) −31.8728 + 8.13803i −1.17485 + 0.299972i
\(737\) 6.83141i 0.251638i
\(738\) 0 0
\(739\) 4.01435 1.66280i 0.147670 0.0611671i −0.307624 0.951508i \(-0.599534\pi\)
0.455295 + 0.890341i \(0.349534\pi\)
\(740\) −21.6477 + 55.6073i −0.795784 + 2.04417i
\(741\) 0 0
\(742\) −7.37421 10.7840i −0.270716 0.395894i
\(743\) −20.6253 20.6253i −0.756669 0.756669i 0.219046 0.975715i \(-0.429706\pi\)
−0.975715 + 0.219046i \(0.929706\pi\)
\(744\) 0 0
\(745\) 42.6465 42.6465i 1.56245 1.56245i
\(746\) 11.1234 + 2.08880i 0.407258 + 0.0764765i
\(747\) 0 0
\(748\) 0.329698 + 15.3646i 0.0120550 + 0.561785i
\(749\) 3.08968 + 7.45915i 0.112894 + 0.272551i
\(750\) 0 0
\(751\) 13.6475 0.498004 0.249002 0.968503i \(-0.419897\pi\)
0.249002 + 0.968503i \(0.419897\pi\)
\(752\) −7.19249 6.60028i −0.262283 0.240687i
\(753\) 0 0
\(754\) 37.9724 + 24.7873i 1.38287 + 0.902700i
\(755\) −30.0458 + 12.4454i −1.09348 + 0.452933i
\(756\) 0 0
\(757\) 1.50145 3.62481i 0.0545710 0.131746i −0.894243 0.447582i \(-0.852285\pi\)
0.948814 + 0.315836i \(0.102285\pi\)
\(758\) 30.2126 + 5.67344i 1.09737 + 0.206069i
\(759\) 0 0
\(760\) −14.3040 19.9841i −0.518862 0.724901i
\(761\) −10.5824 + 10.5824i −0.383612 + 0.383612i −0.872402 0.488790i \(-0.837438\pi\)
0.488790 + 0.872402i \(0.337438\pi\)
\(762\) 0 0
\(763\) 7.90266 19.0787i 0.286096 0.690696i
\(764\) −8.83316 + 3.88287i −0.319573 + 0.140477i
\(765\) 0 0
\(766\) 2.31246 + 11.0071i 0.0835525 + 0.397701i
\(767\) 4.76999 0.172234
\(768\) 0 0
\(769\) −42.6343 −1.53743 −0.768715 0.639591i \(-0.779104\pi\)
−0.768715 + 0.639591i \(0.779104\pi\)
\(770\) −5.89875 28.0774i −0.212576 1.01184i
\(771\) 0 0
\(772\) −0.408070 + 0.179379i −0.0146868 + 0.00645600i
\(773\) 13.5374 32.6822i 0.486906 1.17550i −0.469362 0.883006i \(-0.655516\pi\)
0.956268 0.292490i \(-0.0944839\pi\)
\(774\) 0 0
\(775\) 15.7682 15.7682i 0.566411 0.566411i
\(776\) −22.3205 31.1839i −0.801259 1.11944i
\(777\) 0 0
\(778\) 8.65206 + 1.62472i 0.310191 + 0.0582489i
\(779\) 0.272172 0.657081i 0.00975157 0.0235424i
\(780\) 0 0
\(781\) −11.1393 + 4.61404i −0.398595 + 0.165103i
\(782\) −32.8285 21.4295i −1.17395 0.766318i
\(783\) 0 0
\(784\) −33.5387 30.7772i −1.19781 1.09918i
\(785\) −27.4645 −0.980249
\(786\) 0 0
\(787\) −11.1547 26.9298i −0.397622 0.959945i −0.988228 0.152985i \(-0.951111\pi\)
0.590606