Properties

Label 729.2.i.a.685.20
Level $729$
Weight $2$
Character 729.685
Analytic conductor $5.821$
Analytic rank $0$
Dimension $1404$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.i (of order \(81\), degree \(54\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(1404\)
Relative dimension: \(26\) over \(\Q(\zeta_{81})\)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label 685.20
Character \(\chi\) \(=\) 729.685
Dual form 729.2.i.a.613.20

$q$-expansion

\(f(q)\) \(=\) \(q+(1.39265 + 0.387670i) q^{2} +(0.0768505 + 0.0463795i) q^{4} +(-1.01971 + 0.0395696i) q^{5} +(-0.161658 - 0.0252828i) q^{7} +(-1.89502 - 2.00860i) q^{8} +O(q^{10})\) \(q+(1.39265 + 0.387670i) q^{2} +(0.0768505 + 0.0463795i) q^{4} +(-1.01971 + 0.0395696i) q^{5} +(-0.161658 - 0.0252828i) q^{7} +(-1.89502 - 2.00860i) q^{8} +(-1.43545 - 0.340207i) q^{10} +(-0.568431 - 4.16165i) q^{11} +(1.68656 - 2.45906i) q^{13} +(-0.215331 - 0.0978801i) q^{14} +(-1.94408 - 3.69075i) q^{16} +(6.87645 - 3.45348i) q^{17} +(0.307437 + 5.27850i) q^{19} +(-0.0802008 - 0.0442529i) q^{20} +(0.821725 - 6.01609i) q^{22} +(2.81598 - 7.29357i) q^{23} +(-3.94671 + 0.306763i) q^{25} +(3.30209 - 2.77079i) q^{26} +(-0.0112509 - 0.00944061i) q^{28} +(-7.18377 - 5.13465i) q^{29} +(1.77271 - 2.03130i) q^{31} +(-0.107416 - 0.495887i) q^{32} +(10.9153 - 2.14369i) q^{34} +(0.165845 + 0.0193845i) q^{35} +(2.96555 + 3.98343i) q^{37} +(-1.61816 + 7.47028i) q^{38} +(2.01186 + 1.97321i) q^{40} +(-2.73505 + 10.6181i) q^{41} +(0.972771 + 0.882743i) q^{43} +(0.149331 - 0.346189i) q^{44} +(6.74917 - 9.06571i) q^{46} +(2.91535 + 3.34063i) q^{47} +(-6.64024 - 2.12911i) q^{49} +(-5.61531 - 1.10281i) q^{50} +(0.243663 - 0.110759i) q^{52} +(1.30702 - 7.41249i) q^{53} +(0.744313 + 4.22121i) q^{55} +(0.255561 + 0.372617i) q^{56} +(-8.01392 - 9.93570i) q^{58} +(-9.14555 + 3.73637i) q^{59} +(-1.32732 + 0.801042i) q^{61} +(3.25624 - 2.14166i) q^{62} +(-0.442450 + 7.59658i) q^{64} +(-1.62251 + 2.57428i) q^{65} +(5.87992 - 4.20272i) q^{67} +(0.688629 + 0.0535245i) q^{68} +(0.223450 + 0.0912892i) q^{70} +(1.31059 + 4.37768i) q^{71} +(3.87220 - 0.917728i) q^{73} +(2.58572 + 6.69718i) q^{74} +(-0.221187 + 0.419914i) q^{76} +(-0.0133270 + 0.687135i) q^{77} +(7.95096 - 7.79825i) q^{79} +(2.12845 + 3.68659i) q^{80} +(-7.92530 + 13.7270i) q^{82} +(-1.44424 - 5.60690i) q^{83} +(-6.87536 + 3.79367i) q^{85} +(1.01252 + 1.60647i) q^{86} +(-7.28191 + 9.02815i) q^{88} +(-1.18082 + 3.94420i) q^{89} +(-0.334818 + 0.354886i) q^{91} +(0.554681 - 0.429910i) q^{92} +(2.76500 + 5.78252i) q^{94} +(-0.522366 - 5.37039i) q^{95} +(5.41592 + 0.210162i) q^{97} +(-8.42214 - 5.53933i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{81}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.39265 + 0.387670i 0.984752 + 0.274124i 0.722877 0.690977i \(-0.242820\pi\)
0.261875 + 0.965102i \(0.415659\pi\)
\(3\) 0 0
\(4\) 0.0768505 + 0.0463795i 0.0384253 + 0.0231898i
\(5\) −1.01971 + 0.0395696i −0.456030 + 0.0176961i −0.265768 0.964037i \(-0.585625\pi\)
−0.190263 + 0.981733i \(0.560934\pi\)
\(6\) 0 0
\(7\) −0.161658 0.0252828i −0.0611009 0.00955601i 0.123894 0.992295i \(-0.460462\pi\)
−0.184995 + 0.982739i \(0.559227\pi\)
\(8\) −1.89502 2.00860i −0.669990 0.710148i
\(9\) 0 0
\(10\) −1.43545 0.340207i −0.453928 0.107583i
\(11\) −0.568431 4.16165i −0.171388 1.25479i −0.852547 0.522650i \(-0.824943\pi\)
0.681159 0.732136i \(-0.261476\pi\)
\(12\) 0 0
\(13\) 1.68656 2.45906i 0.467768 0.682022i −0.516983 0.855996i \(-0.672945\pi\)
0.984750 + 0.173974i \(0.0556609\pi\)
\(14\) −0.215331 0.0978801i −0.0575497 0.0261595i
\(15\) 0 0
\(16\) −1.94408 3.69075i −0.486021 0.922688i
\(17\) 6.87645 3.45348i 1.66778 0.837593i 0.672553 0.740049i \(-0.265198\pi\)
0.995231 0.0975436i \(-0.0310985\pi\)
\(18\) 0 0
\(19\) 0.307437 + 5.27850i 0.0705310 + 1.21097i 0.828995 + 0.559255i \(0.188913\pi\)
−0.758464 + 0.651714i \(0.774050\pi\)
\(20\) −0.0802008 0.0442529i −0.0179334 0.00989526i
\(21\) 0 0
\(22\) 0.821725 6.01609i 0.175192 1.28263i
\(23\) 2.81598 7.29357i 0.587172 1.52081i −0.246834 0.969058i \(-0.579390\pi\)
0.834006 0.551756i \(-0.186042\pi\)
\(24\) 0 0
\(25\) −3.94671 + 0.306763i −0.789342 + 0.0613525i
\(26\) 3.30209 2.77079i 0.647594 0.543396i
\(27\) 0 0
\(28\) −0.0112509 0.00944061i −0.00212622 0.00178411i
\(29\) −7.18377 5.13465i −1.33399 0.953481i −0.999940 0.0109259i \(-0.996522\pi\)
−0.334052 0.942555i \(-0.608416\pi\)
\(30\) 0 0
\(31\) 1.77271 2.03130i 0.318388 0.364832i −0.571826 0.820375i \(-0.693765\pi\)
0.890214 + 0.455543i \(0.150555\pi\)
\(32\) −0.107416 0.495887i −0.0189886 0.0876613i
\(33\) 0 0
\(34\) 10.9153 2.14369i 1.87196 0.367641i
\(35\) 0.165845 + 0.0193845i 0.0280330 + 0.00327658i
\(36\) 0 0
\(37\) 2.96555 + 3.98343i 0.487534 + 0.654871i 0.976015 0.217703i \(-0.0698564\pi\)
−0.488481 + 0.872574i \(0.662449\pi\)
\(38\) −1.61816 + 7.47028i −0.262501 + 1.21184i
\(39\) 0 0
\(40\) 2.01186 + 1.97321i 0.318102 + 0.311993i
\(41\) −2.73505 + 10.6181i −0.427143 + 1.65827i 0.286741 + 0.958008i \(0.407428\pi\)
−0.713884 + 0.700264i \(0.753066\pi\)
\(42\) 0 0
\(43\) 0.972771 + 0.882743i 0.148346 + 0.134617i 0.742802 0.669512i \(-0.233497\pi\)
−0.594455 + 0.804129i \(0.702632\pi\)
\(44\) 0.149331 0.346189i 0.0225125 0.0521899i
\(45\) 0 0
\(46\) 6.74917 9.06571i 0.995111 1.33667i
\(47\) 2.91535 + 3.34063i 0.425248 + 0.487280i 0.925579 0.378554i \(-0.123579\pi\)
−0.500331 + 0.865834i \(0.666788\pi\)
\(48\) 0 0
\(49\) −6.64024 2.12911i −0.948606 0.304158i
\(50\) −5.61531 1.10281i −0.794125 0.155961i
\(51\) 0 0
\(52\) 0.243663 0.110759i 0.0337900 0.0153594i
\(53\) 1.30702 7.41249i 0.179533 1.01818i −0.753247 0.657738i \(-0.771514\pi\)
0.932780 0.360446i \(-0.117375\pi\)
\(54\) 0 0
\(55\) 0.744313 + 4.22121i 0.100363 + 0.569187i
\(56\) 0.255561 + 0.372617i 0.0341508 + 0.0497931i
\(57\) 0 0
\(58\) −8.01392 9.93570i −1.05228 1.30462i
\(59\) −9.14555 + 3.73637i −1.19065 + 0.486434i −0.884946 0.465693i \(-0.845805\pi\)
−0.305703 + 0.952127i \(0.598892\pi\)
\(60\) 0 0
\(61\) −1.32732 + 0.801042i −0.169946 + 0.102563i −0.599121 0.800658i \(-0.704483\pi\)
0.429175 + 0.903221i \(0.358804\pi\)
\(62\) 3.25624 2.14166i 0.413542 0.271991i
\(63\) 0 0
\(64\) −0.442450 + 7.59658i −0.0553063 + 0.949572i
\(65\) −1.62251 + 2.57428i −0.201247 + 0.319300i
\(66\) 0 0
\(67\) 5.87992 4.20272i 0.718347 0.513443i −0.162580 0.986695i \(-0.551982\pi\)
0.880927 + 0.473252i \(0.156920\pi\)
\(68\) 0.688629 + 0.0535245i 0.0835086 + 0.00649080i
\(69\) 0 0
\(70\) 0.223450 + 0.0912892i 0.0267073 + 0.0109111i
\(71\) 1.31059 + 4.37768i 0.155539 + 0.519535i 0.999867 0.0162905i \(-0.00518564\pi\)
−0.844329 + 0.535826i \(0.820000\pi\)
\(72\) 0 0
\(73\) 3.87220 0.917728i 0.453207 0.107412i 0.00232814 0.999997i \(-0.499259\pi\)
0.450878 + 0.892585i \(0.351111\pi\)
\(74\) 2.58572 + 6.69718i 0.300584 + 0.778531i
\(75\) 0 0
\(76\) −0.221187 + 0.419914i −0.0253719 + 0.0481674i
\(77\) −0.0133270 + 0.687135i −0.00151875 + 0.0783063i
\(78\) 0 0
\(79\) 7.95096 7.79825i 0.894553 0.877372i −0.0984881 0.995138i \(-0.531401\pi\)
0.993041 + 0.117767i \(0.0375735\pi\)
\(80\) 2.12845 + 3.68659i 0.237968 + 0.412173i
\(81\) 0 0
\(82\) −7.92530 + 13.7270i −0.875203 + 1.51590i
\(83\) −1.44424 5.60690i −0.158526 0.615437i −0.997462 0.0712058i \(-0.977315\pi\)
0.838935 0.544231i \(-0.183179\pi\)
\(84\) 0 0
\(85\) −6.87536 + 3.79367i −0.745738 + 0.411481i
\(86\) 1.01252 + 1.60647i 0.109182 + 0.173230i
\(87\) 0 0
\(88\) −7.28191 + 9.02815i −0.776254 + 0.962404i
\(89\) −1.18082 + 3.94420i −0.125166 + 0.418084i −0.997487 0.0708497i \(-0.977429\pi\)
0.872321 + 0.488934i \(0.162614\pi\)
\(90\) 0 0
\(91\) −0.334818 + 0.354886i −0.0350984 + 0.0372022i
\(92\) 0.554681 0.429910i 0.0578295 0.0448213i
\(93\) 0 0
\(94\) 2.76500 + 5.78252i 0.285188 + 0.596421i
\(95\) −0.522366 5.37039i −0.0535936 0.550991i
\(96\) 0 0
\(97\) 5.41592 + 0.210162i 0.549903 + 0.0213388i 0.312230 0.950006i \(-0.398924\pi\)
0.237673 + 0.971345i \(0.423615\pi\)
\(98\) −8.42214 5.53933i −0.850764 0.559556i
\(99\) 0 0
\(100\) −0.317534 0.159472i −0.0317534 0.0159472i
\(101\) 0.0115083 + 0.593364i 0.00114512 + 0.0590420i 0.999949 + 0.0101381i \(0.00322711\pi\)
−0.998803 + 0.0489039i \(0.984427\pi\)
\(102\) 0 0
\(103\) 10.7641 + 8.34284i 1.06062 + 0.822045i 0.984558 0.175058i \(-0.0560113\pi\)
0.0760649 + 0.997103i \(0.475764\pi\)
\(104\) −8.13534 + 1.27234i −0.797735 + 0.124764i
\(105\) 0 0
\(106\) 4.69383 9.81630i 0.455905 0.953444i
\(107\) 7.79161 + 2.83591i 0.753243 + 0.274158i 0.689970 0.723838i \(-0.257624\pi\)
0.0632735 + 0.997996i \(0.479846\pi\)
\(108\) 0 0
\(109\) −2.51418 + 0.915087i −0.240815 + 0.0876494i −0.459608 0.888122i \(-0.652010\pi\)
0.218793 + 0.975771i \(0.429788\pi\)
\(110\) −0.599871 + 6.16721i −0.0571954 + 0.588020i
\(111\) 0 0
\(112\) 0.220964 + 0.645791i 0.0208791 + 0.0610215i
\(113\) 4.14789 3.76401i 0.390201 0.354088i −0.453166 0.891426i \(-0.649706\pi\)
0.843367 + 0.537338i \(0.180570\pi\)
\(114\) 0 0
\(115\) −2.58289 + 7.54878i −0.240856 + 0.703928i
\(116\) −0.313934 0.727780i −0.0291480 0.0675727i
\(117\) 0 0
\(118\) −14.1850 + 1.65799i −1.30584 + 0.152631i
\(119\) −1.19895 + 0.384426i −0.109907 + 0.0352403i
\(120\) 0 0
\(121\) −6.39916 + 1.78133i −0.581742 + 0.161939i
\(122\) −2.15903 + 0.601008i −0.195470 + 0.0544127i
\(123\) 0 0
\(124\) 0.230444 0.0738889i 0.0206945 0.00663542i
\(125\) 9.08029 1.06133i 0.812166 0.0949286i
\(126\) 0 0
\(127\) 4.23580 + 9.81969i 0.375866 + 0.871356i 0.996206 + 0.0870232i \(0.0277354\pi\)
−0.620340 + 0.784333i \(0.713005\pi\)
\(128\) −3.88966 + 11.3680i −0.343801 + 1.00480i
\(129\) 0 0
\(130\) −3.25755 + 2.95607i −0.285706 + 0.259265i
\(131\) −2.05573 6.00810i −0.179610 0.524930i 0.819210 0.573494i \(-0.194412\pi\)
−0.998820 + 0.0485634i \(0.984536\pi\)
\(132\) 0 0
\(133\) 0.0837556 0.861083i 0.00726253 0.0746653i
\(134\) 9.81794 3.57344i 0.848141 0.308698i
\(135\) 0 0
\(136\) −19.9677 7.26763i −1.71221 0.623194i
\(137\) −2.27819 + 4.76442i −0.194639 + 0.407052i −0.976230 0.216739i \(-0.930458\pi\)
0.781591 + 0.623791i \(0.214408\pi\)
\(138\) 0 0
\(139\) −2.26702 + 0.354556i −0.192286 + 0.0300730i −0.249929 0.968264i \(-0.580407\pi\)
0.0576423 + 0.998337i \(0.481642\pi\)
\(140\) 0.0118462 + 0.00918153i 0.00100119 + 0.000775981i
\(141\) 0 0
\(142\) 0.128097 + 6.60465i 0.0107497 + 0.554250i
\(143\) −11.1925 5.62107i −0.935961 0.470057i
\(144\) 0 0
\(145\) 7.52857 + 4.95162i 0.625214 + 0.411210i
\(146\) 5.74839 + 0.223064i 0.475740 + 0.0184609i
\(147\) 0 0
\(148\) 0.0431547 + 0.443669i 0.00354730 + 0.0364694i
\(149\) 4.16744 + 8.71547i 0.341410 + 0.713999i 0.999232 0.0391743i \(-0.0124728\pi\)
−0.657822 + 0.753173i \(0.728522\pi\)
\(150\) 0 0
\(151\) 3.54973 2.75125i 0.288873 0.223894i −0.457848 0.889030i \(-0.651380\pi\)
0.746722 + 0.665137i \(0.231627\pi\)
\(152\) 10.0198 10.6204i 0.812712 0.861425i
\(153\) 0 0
\(154\) −0.284942 + 0.951772i −0.0229613 + 0.0766960i
\(155\) −1.72728 + 2.14149i −0.138738 + 0.172009i
\(156\) 0 0
\(157\) −6.04980 9.59867i −0.482827 0.766057i 0.512896 0.858451i \(-0.328573\pi\)
−0.995723 + 0.0923939i \(0.970548\pi\)
\(158\) 14.0961 7.77787i 1.12142 0.618774i
\(159\) 0 0
\(160\) 0.129156 + 0.501413i 0.0102107 + 0.0396402i
\(161\) −0.639627 + 1.10787i −0.0504096 + 0.0873121i
\(162\) 0 0
\(163\) 5.36363 + 9.29008i 0.420112 + 0.727656i 0.995950 0.0899083i \(-0.0286574\pi\)
−0.575838 + 0.817564i \(0.695324\pi\)
\(164\) −0.702653 + 0.689158i −0.0548680 + 0.0538142i
\(165\) 0 0
\(166\) 0.162304 8.36833i 0.0125972 0.649509i
\(167\) 2.38746 4.53248i 0.184747 0.350734i −0.774835 0.632164i \(-0.782167\pi\)
0.959582 + 0.281430i \(0.0908088\pi\)
\(168\) 0 0
\(169\) 1.47980 + 3.83277i 0.113831 + 0.294828i
\(170\) −11.0457 + 2.61787i −0.847164 + 0.200782i
\(171\) 0 0
\(172\) 0.0338168 + 0.112956i 0.00257850 + 0.00861281i
\(173\) 18.0422 + 7.37104i 1.37172 + 0.560410i 0.939869 0.341535i \(-0.110947\pi\)
0.431852 + 0.901945i \(0.357860\pi\)
\(174\) 0 0
\(175\) 0.645773 + 0.0501934i 0.0488158 + 0.00379427i
\(176\) −14.2546 + 10.1885i −1.07448 + 0.767990i
\(177\) 0 0
\(178\) −3.17351 + 5.03512i −0.237865 + 0.377398i
\(179\) 0.113114 1.94209i 0.00845452 0.145159i −0.991439 0.130570i \(-0.958319\pi\)
0.999894 0.0145883i \(-0.00464376\pi\)
\(180\) 0 0
\(181\) 13.2848 8.73752i 0.987449 0.649455i 0.0504274 0.998728i \(-0.483942\pi\)
0.937021 + 0.349273i \(0.113571\pi\)
\(182\) −0.603862 + 0.364433i −0.0447613 + 0.0270136i
\(183\) 0 0
\(184\) −19.9862 + 8.16526i −1.47340 + 0.601951i
\(185\) −3.18164 3.94461i −0.233919 0.290014i
\(186\) 0 0
\(187\) −18.2810 26.6543i −1.33684 1.94916i
\(188\) 0.0691098 + 0.391941i 0.00504035 + 0.0285853i
\(189\) 0 0
\(190\) 1.35447 7.68158i 0.0982636 0.557281i
\(191\) −5.41212 + 2.46011i −0.391607 + 0.178007i −0.599929 0.800053i \(-0.704805\pi\)
0.208322 + 0.978060i \(0.433200\pi\)
\(192\) 0 0
\(193\) −23.9668 4.70693i −1.72517 0.338812i −0.770717 0.637178i \(-0.780102\pi\)
−0.954452 + 0.298366i \(0.903559\pi\)
\(194\) 7.46101 + 2.39228i 0.535669 + 0.171755i
\(195\) 0 0
\(196\) −0.411559 0.471594i −0.0293971 0.0336853i
\(197\) −16.1596 + 21.7060i −1.15132 + 1.54649i −0.362371 + 0.932034i \(0.618033\pi\)
−0.788949 + 0.614458i \(0.789375\pi\)
\(198\) 0 0
\(199\) 1.00671 2.33383i 0.0713641 0.165440i −0.878800 0.477189i \(-0.841656\pi\)
0.950164 + 0.311749i \(0.100915\pi\)
\(200\) 8.09525 + 7.34605i 0.572421 + 0.519444i
\(201\) 0 0
\(202\) −0.214003 + 0.830810i −0.0150572 + 0.0584556i
\(203\) 1.03149 + 1.01168i 0.0723967 + 0.0710062i
\(204\) 0 0
\(205\) 2.36882 10.9357i 0.165445 0.763781i
\(206\) 11.7564 + 15.7916i 0.819108 + 1.10025i
\(207\) 0 0
\(208\) −12.3546 1.44405i −0.856638 0.100127i
\(209\) 21.7925 4.27991i 1.50742 0.296047i
\(210\) 0 0
\(211\) −5.07006 23.4060i −0.349038 1.61134i −0.727763 0.685828i \(-0.759440\pi\)
0.378726 0.925509i \(-0.376362\pi\)
\(212\) 0.444233 0.509034i 0.0305100 0.0349606i
\(213\) 0 0
\(214\) 9.75158 + 6.97001i 0.666604 + 0.476460i
\(215\) −1.02688 0.861654i −0.0700326 0.0587643i
\(216\) 0 0
\(217\) −0.337929 + 0.283556i −0.0229401 + 0.0192490i
\(218\) −3.85612 + 0.299722i −0.261170 + 0.0202997i
\(219\) 0 0
\(220\) −0.138577 + 0.358923i −0.00934284 + 0.0241986i
\(221\) 3.10521 22.7341i 0.208879 1.52926i
\(222\) 0 0
\(223\) 15.1723 + 8.37173i 1.01601 + 0.560612i 0.901486 0.432808i \(-0.142477\pi\)
0.114527 + 0.993420i \(0.463465\pi\)
\(224\) 0.00482720 + 0.0828798i 0.000322531 + 0.00553764i
\(225\) 0 0
\(226\) 7.23576 3.63393i 0.481315 0.241726i
\(227\) −7.95218 15.0968i −0.527805 1.00201i −0.993146 0.116881i \(-0.962710\pi\)
0.465341 0.885131i \(-0.345932\pi\)
\(228\) 0 0
\(229\) 19.3311 + 8.78705i 1.27743 + 0.580664i 0.933583 0.358360i \(-0.116664\pi\)
0.343849 + 0.939025i \(0.388269\pi\)
\(230\) −6.52350 + 9.51150i −0.430147 + 0.627170i
\(231\) 0 0
\(232\) 3.29990 + 24.1596i 0.216649 + 1.58615i
\(233\) 6.53641 + 1.54916i 0.428214 + 0.101489i 0.439071 0.898452i \(-0.355308\pi\)
−0.0108566 + 0.999941i \(0.503456\pi\)
\(234\) 0 0
\(235\) −3.10502 3.29113i −0.202549 0.214689i
\(236\) −0.876131 0.137024i −0.0570313 0.00891953i
\(237\) 0 0
\(238\) −1.81874 + 0.0705755i −0.117892 + 0.00457473i
\(239\) −0.468903 0.282985i −0.0303308 0.0183048i 0.501453 0.865185i \(-0.332799\pi\)
−0.531784 + 0.846880i \(0.678478\pi\)
\(240\) 0 0
\(241\) 7.70182 + 2.14395i 0.496118 + 0.138104i 0.507189 0.861835i \(-0.330685\pi\)
−0.0110712 + 0.999939i \(0.503524\pi\)
\(242\) −9.60236 −0.617263
\(243\) 0 0
\(244\) −0.139157 −0.00890863
\(245\) 6.85540 + 1.90833i 0.437975 + 0.121919i
\(246\) 0 0
\(247\) 13.4987 + 8.14649i 0.858900 + 0.518349i
\(248\) −7.43938 + 0.288682i −0.472401 + 0.0183313i
\(249\) 0 0
\(250\) 13.0571 + 2.04210i 0.825804 + 0.129153i
\(251\) −1.78971 1.89698i −0.112966 0.119737i 0.668423 0.743781i \(-0.266970\pi\)
−0.781388 + 0.624045i \(0.785488\pi\)
\(252\) 0 0
\(253\) −31.9540 7.57323i −2.00893 0.476125i
\(254\) 2.09218 + 15.3175i 0.131275 + 0.961104i
\(255\) 0 0
\(256\) −1.21605 + 1.77305i −0.0760032 + 0.110815i
\(257\) −27.3862 12.4485i −1.70830 0.776519i −0.997308 0.0733207i \(-0.976640\pi\)
−0.710994 0.703198i \(-0.751755\pi\)
\(258\) 0 0
\(259\) −0.378692 0.718930i −0.0235308 0.0446721i
\(260\) −0.244084 + 0.122584i −0.0151375 + 0.00760232i
\(261\) 0 0
\(262\) −0.533749 9.16412i −0.0329752 0.566161i
\(263\) 14.2684 + 7.87295i 0.879825 + 0.485467i 0.857619 0.514286i \(-0.171943\pi\)
0.0222067 + 0.999753i \(0.492931\pi\)
\(264\) 0 0
\(265\) −1.03948 + 7.61034i −0.0638548 + 0.467499i
\(266\) 0.450459 1.16672i 0.0276194 0.0715360i
\(267\) 0 0
\(268\) 0.646795 0.0502729i 0.0395093 0.00307090i
\(269\) −7.73321 + 6.48893i −0.471502 + 0.395637i −0.847342 0.531047i \(-0.821799\pi\)
0.375840 + 0.926685i \(0.377354\pi\)
\(270\) 0 0
\(271\) 5.17989 + 4.34645i 0.314656 + 0.264028i 0.786413 0.617701i \(-0.211936\pi\)
−0.471757 + 0.881729i \(0.656380\pi\)
\(272\) −26.1144 18.6654i −1.58342 1.13176i
\(273\) 0 0
\(274\) −5.01974 + 5.75198i −0.303254 + 0.347490i
\(275\) 3.52007 + 16.2505i 0.212268 + 0.979940i
\(276\) 0 0
\(277\) −20.0846 + 3.94449i −1.20677 + 0.237001i −0.755356 0.655314i \(-0.772536\pi\)
−0.451412 + 0.892316i \(0.649079\pi\)
\(278\) −3.29462 0.385086i −0.197598 0.0230959i
\(279\) 0 0
\(280\) −0.275344 0.369851i −0.0164549 0.0221028i
\(281\) 4.06776 18.7789i 0.242662 1.12025i −0.679568 0.733613i \(-0.737833\pi\)
0.922230 0.386641i \(-0.126365\pi\)
\(282\) 0 0
\(283\) 17.0525 + 16.7250i 1.01367 + 0.994197i 0.999984 0.00570916i \(-0.00181729\pi\)
0.0136829 + 0.999906i \(0.495644\pi\)
\(284\) −0.102315 + 0.397212i −0.00607128 + 0.0235702i
\(285\) 0 0
\(286\) −13.4081 12.1672i −0.792835 0.719460i
\(287\) 0.710598 1.64735i 0.0419453 0.0972401i
\(288\) 0 0
\(289\) 25.2073 33.8593i 1.48278 1.99172i
\(290\) 8.56506 + 9.81448i 0.502958 + 0.576326i
\(291\) 0 0
\(292\) 0.340144 + 0.109063i 0.0199054 + 0.00638242i
\(293\) 1.23529 + 0.242602i 0.0721662 + 0.0141730i 0.228665 0.973505i \(-0.426564\pi\)
−0.156499 + 0.987678i \(0.550021\pi\)
\(294\) 0 0
\(295\) 9.17801 4.17192i 0.534364 0.242898i
\(296\) 2.38134 13.5053i 0.138413 0.784978i
\(297\) 0 0
\(298\) 2.42506 + 13.7532i 0.140480 + 0.796701i
\(299\) −13.1860 19.2257i −0.762568 1.11185i
\(300\) 0 0
\(301\) −0.134938 0.167297i −0.00777769 0.00964282i
\(302\) 6.01011 2.45540i 0.345843 0.141293i
\(303\) 0 0
\(304\) 18.8839 11.3965i 1.08307 0.653635i
\(305\) 1.32179 0.869356i 0.0756856 0.0497792i
\(306\) 0 0
\(307\) 1.18915 20.4169i 0.0678682 1.16525i −0.776724 0.629842i \(-0.783120\pi\)
0.844592 0.535411i \(-0.179843\pi\)
\(308\) −0.0328932 + 0.0521886i −0.00187426 + 0.00297372i
\(309\) 0 0
\(310\) −3.23569 + 2.31273i −0.183775 + 0.131354i
\(311\) 26.4427 + 2.05529i 1.49943 + 0.116545i 0.800795 0.598938i \(-0.204411\pi\)
0.698630 + 0.715483i \(0.253793\pi\)
\(312\) 0 0
\(313\) −5.58110 2.28013i −0.315463 0.128881i 0.214938 0.976628i \(-0.431045\pi\)
−0.530401 + 0.847747i \(0.677959\pi\)
\(314\) −4.70414 15.7129i −0.265470 0.886731i
\(315\) 0 0
\(316\) 0.972714 0.230538i 0.0547195 0.0129688i
\(317\) −2.02480 5.24435i −0.113724 0.294552i 0.864323 0.502937i \(-0.167747\pi\)
−0.978047 + 0.208385i \(0.933179\pi\)
\(318\) 0 0
\(319\) −17.2852 + 32.8150i −0.967783 + 1.83729i
\(320\) 0.150580 7.76385i 0.00841766 0.434012i
\(321\) 0 0
\(322\) −1.32026 + 1.29490i −0.0735754 + 0.0721622i
\(323\) 20.3433 + 35.2356i 1.13193 + 1.96056i
\(324\) 0 0
\(325\) −5.90202 + 10.2226i −0.327385 + 0.567047i
\(326\) 3.86817 + 15.0172i 0.214238 + 0.831723i
\(327\) 0 0
\(328\) 26.5105 14.6279i 1.46380 0.807690i
\(329\) −0.386829 0.613746i −0.0213266 0.0338369i
\(330\) 0 0
\(331\) −6.62023 + 8.20779i −0.363881 + 0.451141i −0.926903 0.375300i \(-0.877540\pi\)
0.563023 + 0.826441i \(0.309638\pi\)
\(332\) 0.149054 0.497876i 0.00818042 0.0273245i
\(333\) 0 0
\(334\) 5.08200 5.38661i 0.278075 0.294742i
\(335\) −5.82954 + 4.51824i −0.318502 + 0.246858i
\(336\) 0 0
\(337\) 1.94346 + 4.06439i 0.105867 + 0.221402i 0.948283 0.317425i \(-0.102818\pi\)
−0.842416 + 0.538827i \(0.818868\pi\)
\(338\) 0.574986 + 5.91138i 0.0312751 + 0.321537i
\(339\) 0 0
\(340\) −0.704324 0.0273310i −0.0381973 0.00148223i
\(341\) −9.46122 6.22274i −0.512354 0.336980i
\(342\) 0 0
\(343\) 2.04315 + 1.02611i 0.110320 + 0.0554046i
\(344\) −0.0703402 3.62672i −0.00379249 0.195540i
\(345\) 0 0
\(346\) 22.2689 + 17.2597i 1.19718 + 0.927887i
\(347\) 17.1174 2.67711i 0.918908 0.143715i 0.322660 0.946515i \(-0.395423\pi\)
0.596248 + 0.802800i \(0.296658\pi\)
\(348\) 0 0
\(349\) −4.88284 + 10.2116i −0.261372 + 0.546614i −0.990459 0.137807i \(-0.955995\pi\)
0.729087 + 0.684421i \(0.239945\pi\)
\(350\) 0.879876 + 0.320249i 0.0470314 + 0.0171180i
\(351\) 0 0
\(352\) −2.00265 + 0.728906i −0.106742 + 0.0388508i
\(353\) 2.60842 26.8169i 0.138832 1.42732i −0.624355 0.781140i \(-0.714638\pi\)
0.763187 0.646177i \(-0.223633\pi\)
\(354\) 0 0
\(355\) −1.50965 4.41213i −0.0801240 0.234171i
\(356\) −0.273676 + 0.248348i −0.0145048 + 0.0131624i
\(357\) 0 0
\(358\) 0.910418 2.66080i 0.0481171 0.140628i
\(359\) 9.25644 + 21.4588i 0.488536 + 1.13255i 0.967076 + 0.254488i \(0.0819070\pi\)
−0.478540 + 0.878066i \(0.658834\pi\)
\(360\) 0 0
\(361\) −8.89647 + 1.03985i −0.468235 + 0.0547288i
\(362\) 21.8883 7.01820i 1.15042 0.368868i
\(363\) 0 0
\(364\) −0.0421903 + 0.0117445i −0.00221137 + 0.000615578i
\(365\) −3.91222 + 1.08904i −0.204775 + 0.0570031i
\(366\) 0 0
\(367\) 16.3887 5.25483i 0.855484 0.274300i 0.154953 0.987922i \(-0.450477\pi\)
0.700531 + 0.713622i \(0.252947\pi\)
\(368\) −32.3932 + 3.78623i −1.68861 + 0.197371i
\(369\) 0 0
\(370\) −2.90170 6.72689i −0.150852 0.349715i
\(371\) −0.398699 + 1.16524i −0.0206994 + 0.0604963i
\(372\) 0 0
\(373\) −2.69016 + 2.44119i −0.139291 + 0.126400i −0.738675 0.674062i \(-0.764548\pi\)
0.599384 + 0.800462i \(0.295412\pi\)
\(374\) −15.1259 44.2071i −0.782142 2.28590i
\(375\) 0 0
\(376\) 1.18534 12.1863i 0.0611291 0.628462i
\(377\) −24.7423 + 9.00546i −1.27429 + 0.463805i
\(378\) 0 0
\(379\) 29.5533 + 10.7565i 1.51805 + 0.552526i 0.960661 0.277724i \(-0.0895802\pi\)
0.557391 + 0.830250i \(0.311802\pi\)
\(380\) 0.208932 0.436945i 0.0107180 0.0224148i
\(381\) 0 0
\(382\) −8.49090 + 1.32795i −0.434432 + 0.0679439i
\(383\) 0.0366957 + 0.0284413i 0.00187506 + 0.00145328i 0.613538 0.789665i \(-0.289746\pi\)
−0.611663 + 0.791119i \(0.709499\pi\)
\(384\) 0 0
\(385\) −0.0135999 0.701209i −0.000693117 0.0357369i
\(386\) −31.5526 15.8463i −1.60599 0.806557i
\(387\) 0 0
\(388\) 0.406469 + 0.267339i 0.0206353 + 0.0135721i
\(389\) −27.4190 1.06398i −1.39020 0.0539461i −0.667243 0.744840i \(-0.732526\pi\)
−0.722956 + 0.690894i \(0.757217\pi\)
\(390\) 0 0
\(391\) −5.82427 59.8788i −0.294546 3.02820i
\(392\) 8.30684 + 17.3723i 0.419559 + 0.877433i
\(393\) 0 0
\(394\) −30.9194 + 23.9643i −1.55770 + 1.20731i
\(395\) −7.79914 + 8.26661i −0.392417 + 0.415938i
\(396\) 0 0
\(397\) −6.43740 + 21.5024i −0.323084 + 1.07918i 0.630032 + 0.776569i \(0.283042\pi\)
−0.953116 + 0.302606i \(0.902143\pi\)
\(398\) 2.30675 2.85993i 0.115627 0.143355i
\(399\) 0 0
\(400\) 8.80493 + 13.9700i 0.440246 + 0.698498i
\(401\) −4.97522 + 2.74521i −0.248451 + 0.137089i −0.602451 0.798156i \(-0.705809\pi\)
0.354000 + 0.935245i \(0.384821\pi\)
\(402\) 0 0
\(403\) −2.00531 7.78511i −0.0998919 0.387804i
\(404\) −0.0266355 + 0.0461341i −0.00132517 + 0.00229526i
\(405\) 0 0
\(406\) 1.04431 + 1.80880i 0.0518282 + 0.0897691i
\(407\) 14.8919 14.6059i 0.738166 0.723988i
\(408\) 0 0
\(409\) 0.117282 6.04703i 0.00579922 0.299006i −0.985671 0.168677i \(-0.946051\pi\)
0.991471 0.130330i \(-0.0416036\pi\)
\(410\) 7.53837 14.3112i 0.372294 0.706782i
\(411\) 0 0
\(412\) 0.440293 + 1.14039i 0.0216917 + 0.0561829i
\(413\) 1.57292 0.372788i 0.0773981 0.0183437i
\(414\) 0 0
\(415\) 1.69458 + 5.66029i 0.0831836 + 0.277853i
\(416\) −1.40058 0.572201i −0.0686692 0.0280544i
\(417\) 0 0
\(418\) 32.0085 + 2.48790i 1.56559 + 0.121687i
\(419\) 6.05958 4.33113i 0.296030 0.211589i −0.423772 0.905769i \(-0.639294\pi\)
0.719802 + 0.694179i \(0.244233\pi\)
\(420\) 0 0
\(421\) −8.47127 + 13.4406i −0.412864 + 0.655054i −0.986444 0.164095i \(-0.947529\pi\)
0.573580 + 0.819150i \(0.305554\pi\)
\(422\) 2.01300 34.5619i 0.0979914 1.68245i
\(423\) 0 0
\(424\) −17.3656 + 11.4215i −0.843346 + 0.554677i
\(425\) −26.0800 + 15.7393i −1.26506 + 0.763470i
\(426\) 0 0
\(427\) 0.234824 0.0959363i 0.0113639 0.00464268i
\(428\) 0.467261 + 0.579313i 0.0225859 + 0.0280021i
\(429\) 0 0
\(430\) −1.09604 1.59807i −0.0528560 0.0770659i
\(431\) −4.23951 24.0435i −0.204210 1.15813i −0.898678 0.438609i \(-0.855471\pi\)
0.694468 0.719524i \(-0.255640\pi\)
\(432\) 0 0
\(433\) 3.18938 18.0879i 0.153272 0.869249i −0.807077 0.590447i \(-0.798952\pi\)
0.960349 0.278802i \(-0.0899373\pi\)
\(434\) −0.580543 + 0.263889i −0.0278670 + 0.0126671i
\(435\) 0 0
\(436\) −0.235657 0.0462816i −0.0112859 0.00221649i
\(437\) 39.3648 + 12.6218i 1.88307 + 0.603783i
\(438\) 0 0
\(439\) 18.1744 + 20.8256i 0.867419 + 0.993952i 0.999996 + 0.00277887i \(0.000884543\pi\)
−0.132577 + 0.991173i \(0.542325\pi\)
\(440\) 7.06823 9.49428i 0.336965 0.452622i
\(441\) 0 0
\(442\) 13.1378 30.4569i 0.624902 1.44869i
\(443\) −3.08554 2.79998i −0.146599 0.133031i 0.595409 0.803423i \(-0.296990\pi\)
−0.742007 + 0.670392i \(0.766126\pi\)
\(444\) 0 0
\(445\) 1.04803 4.06868i 0.0496812 0.192874i
\(446\) 17.8842 + 17.5407i 0.846843 + 0.830578i
\(447\) 0 0
\(448\) 0.263588 1.21686i 0.0124534 0.0574912i
\(449\) 2.94564 + 3.95668i 0.139013 + 0.186727i 0.866178 0.499736i \(-0.166570\pi\)
−0.727165 + 0.686463i \(0.759162\pi\)
\(450\) 0 0
\(451\) 45.7436 + 5.34666i 2.15398 + 0.251765i
\(452\) 0.493341 0.0968889i 0.0232048 0.00455727i
\(453\) 0 0
\(454\) −5.22200 24.1074i −0.245081 1.13142i
\(455\) 0.327376 0.375131i 0.0153476 0.0175864i
\(456\) 0 0
\(457\) −1.77444 1.26829i −0.0830049 0.0593283i 0.539232 0.842157i \(-0.318714\pi\)
−0.622237 + 0.782829i \(0.713776\pi\)
\(458\) 23.5149 + 19.7314i 1.09878 + 0.921986i
\(459\) 0 0
\(460\) −0.548605 + 0.460335i −0.0255789 + 0.0214632i
\(461\) −5.22069 + 0.405784i −0.243152 + 0.0188992i −0.198490 0.980103i \(-0.563604\pi\)
−0.0446617 + 0.999002i \(0.514221\pi\)
\(462\) 0 0
\(463\) −8.37633 + 21.6952i −0.389281 + 1.00826i 0.590294 + 0.807188i \(0.299012\pi\)
−0.979576 + 0.201076i \(0.935556\pi\)
\(464\) −4.98487 + 36.4957i −0.231417 + 1.69427i
\(465\) 0 0
\(466\) 8.50236 + 4.69140i 0.393864 + 0.217325i
\(467\) −1.60319 27.5257i −0.0741869 1.27374i −0.805869 0.592094i \(-0.798302\pi\)
0.731682 0.681646i \(-0.238736\pi\)
\(468\) 0 0
\(469\) −1.05679 + 0.530741i −0.0487981 + 0.0245073i
\(470\) −3.04833 5.78711i −0.140609 0.266939i
\(471\) 0 0
\(472\) 24.8359 + 11.2893i 1.14316 + 0.519631i
\(473\) 3.12072 4.55011i 0.143491 0.209214i
\(474\) 0 0
\(475\) −2.83261 20.7384i −0.129969 0.951543i
\(476\) −0.109969 0.0260631i −0.00504042 0.00119460i
\(477\) 0 0
\(478\) −0.543313 0.575878i −0.0248506 0.0263401i
\(479\) −19.5183 3.05261i −0.891815 0.139477i −0.308021 0.951379i \(-0.599667\pi\)
−0.583793 + 0.811902i \(0.698432\pi\)
\(480\) 0 0
\(481\) 14.7971 0.574194i 0.674689 0.0261810i
\(482\) 9.89479 + 5.97153i 0.450695 + 0.271996i
\(483\) 0 0
\(484\) −0.574396 0.159894i −0.0261089 0.00726791i
\(485\) −5.53101 −0.251150
\(486\) 0 0
\(487\) 7.01353 0.317813 0.158907 0.987294i \(-0.449203\pi\)
0.158907 + 0.987294i \(0.449203\pi\)
\(488\) 4.12427 + 1.14807i 0.186697 + 0.0519706i
\(489\) 0 0
\(490\) 8.80737 + 5.31527i 0.397876 + 0.240120i
\(491\) 4.77417 0.185259i 0.215455 0.00836064i 0.0691782 0.997604i \(-0.477962\pi\)
0.146277 + 0.989244i \(0.453271\pi\)
\(492\) 0 0
\(493\) −67.1313 10.4991i −3.02344 0.472857i
\(494\) 15.6408 + 16.5782i 0.703711 + 0.745890i
\(495\) 0 0
\(496\) −10.9433 2.59361i −0.491369 0.116457i
\(497\) −0.101187 0.740822i −0.00453887 0.0332304i
\(498\) 0 0
\(499\) −17.1968 + 25.0735i −0.769833 + 1.12244i 0.219334 + 0.975650i \(0.429612\pi\)
−0.989167 + 0.146795i \(0.953104\pi\)
\(500\) 0.747049 + 0.339576i 0.0334091 + 0.0151863i
\(501\) 0 0
\(502\) −1.75704 3.33565i −0.0784204 0.148877i
\(503\) 34.8506 17.5026i 1.55391 0.780403i 0.555227 0.831699i \(-0.312631\pi\)
0.998684 + 0.0512958i \(0.0163351\pi\)
\(504\) 0 0
\(505\) −0.0352144 0.604607i −0.00156702 0.0269047i
\(506\) −41.5648 22.9345i −1.84778 1.01956i
\(507\) 0 0
\(508\) −0.129909 + 0.951102i −0.00576378 + 0.0421983i
\(509\) −11.4930 + 29.7675i −0.509417 + 1.31942i 0.404877 + 0.914371i \(0.367314\pi\)
−0.914294 + 0.405051i \(0.867254\pi\)
\(510\) 0 0
\(511\) −0.649174 + 0.0504578i −0.0287178 + 0.00223212i
\(512\) 16.0272 13.4484i 0.708307 0.594340i
\(513\) 0 0
\(514\) −33.3134 27.9533i −1.46939 1.23297i
\(515\) −11.3065 8.08139i −0.498223 0.356109i
\(516\) 0 0
\(517\) 12.2453 14.0316i 0.538550 0.617109i
\(518\) −0.248678 1.14802i −0.0109263 0.0504413i
\(519\) 0 0
\(520\) 8.24538 1.61934i 0.361584 0.0710127i
\(521\) −19.7568 2.30923i −0.865559 0.101169i −0.328287 0.944578i \(-0.606471\pi\)
−0.537272 + 0.843409i \(0.680545\pi\)
\(522\) 0 0
\(523\) −12.1586 16.3319i −0.531660 0.714143i 0.452433 0.891798i \(-0.350556\pi\)
−0.984093 + 0.177655i \(0.943149\pi\)
\(524\) 0.120669 0.557069i 0.00527144 0.0243357i
\(525\) 0 0
\(526\) 16.8187 + 16.4957i 0.733331 + 0.719246i
\(527\) 5.17489 20.0901i 0.225422 0.875140i
\(528\) 0 0
\(529\) −28.2339 25.6209i −1.22756 1.11395i
\(530\) −4.39794 + 10.1956i −0.191034 + 0.442867i
\(531\) 0 0
\(532\) 0.0463733 0.0622901i 0.00201054 0.00270062i
\(533\) 21.4978 + 24.6338i 0.931174 + 1.06701i
\(534\) 0 0
\(535\) −8.05744 2.58351i −0.348353 0.111695i
\(536\) −19.5841 3.84620i −0.845905 0.166130i
\(537\) 0 0
\(538\) −13.2852 + 6.03887i −0.572766 + 0.260354i
\(539\) −5.08609 + 28.8446i −0.219073 + 1.24243i
\(540\) 0 0
\(541\) −4.09510 23.2245i −0.176062 0.998497i −0.936911 0.349568i \(-0.886328\pi\)
0.760849 0.648929i \(-0.224783\pi\)
\(542\) 5.52879 + 8.06117i 0.237482 + 0.346257i
\(543\) 0 0
\(544\) −2.45118 3.03898i −0.105093 0.130295i
\(545\) 2.52754 1.03261i 0.108268 0.0442323i
\(546\) 0 0
\(547\) 12.0551 7.27526i 0.515437 0.311068i −0.235016 0.971991i \(-0.575514\pi\)
0.750453 + 0.660924i \(0.229835\pi\)
\(548\) −0.396051 + 0.260487i −0.0169185 + 0.0111275i
\(549\) 0 0
\(550\) −1.39760 + 23.9958i −0.0595938 + 1.02319i
\(551\) 24.8947 39.4981i 1.06055 1.68267i
\(552\) 0 0
\(553\) −1.48250 + 1.05962i −0.0630422 + 0.0450598i
\(554\) −29.5000 2.29292i −1.25333 0.0974169i
\(555\) 0 0
\(556\) −0.190666 0.0778956i −0.00808604 0.00330351i
\(557\) −5.12433 17.1165i −0.217125 0.725248i −0.995269 0.0971615i \(-0.969024\pi\)
0.778144 0.628086i \(-0.216162\pi\)
\(558\) 0 0
\(559\) 3.81136 0.903309i 0.161203 0.0382059i
\(560\) −0.250874 0.649779i −0.0106013 0.0274582i
\(561\) 0 0
\(562\) 12.9450 24.5754i 0.546051 1.03665i
\(563\) −0.595337 + 30.6954i −0.0250905 + 1.29366i 0.749843 + 0.661616i \(0.230129\pi\)
−0.774934 + 0.632043i \(0.782217\pi\)
\(564\) 0 0
\(565\) −4.08073 + 4.00235i −0.171677 + 0.168380i
\(566\) 17.2644 + 29.9028i 0.725676 + 1.25691i
\(567\) 0 0
\(568\) 6.30942 10.9282i 0.264737 0.458538i
\(569\) 3.90030 + 15.1419i 0.163509 + 0.634781i 0.996655 + 0.0817272i \(0.0260436\pi\)
−0.833146 + 0.553053i \(0.813463\pi\)
\(570\) 0 0
\(571\) 6.30704 3.48007i 0.263941 0.145637i −0.345623 0.938374i \(-0.612332\pi\)
0.609564 + 0.792737i \(0.291345\pi\)
\(572\) −0.599444 0.951083i −0.0250640 0.0397668i
\(573\) 0 0
\(574\) 1.62824 2.01871i 0.0679616 0.0842592i
\(575\) −8.87646 + 29.6494i −0.370174 + 1.23647i
\(576\) 0 0
\(577\) −3.70448 + 3.92651i −0.154219 + 0.163463i −0.799877 0.600164i \(-0.795102\pi\)
0.645657 + 0.763627i \(0.276583\pi\)
\(578\) 48.2312 37.3820i 2.00615 1.55489i
\(579\) 0 0
\(580\) 0.348921 + 0.729706i 0.0144881 + 0.0302994i
\(581\) 0.0917150 + 0.942913i 0.00380498 + 0.0391186i
\(582\) 0 0
\(583\) −31.5911 1.22588i −1.30837 0.0507708i
\(584\) −9.18123 6.03859i −0.379922 0.249879i
\(585\) 0 0
\(586\) 1.62627 + 0.816744i 0.0671807 + 0.0337394i
\(587\) −0.165929 8.55524i −0.00684861 0.353113i −0.987524 0.157470i \(-0.949666\pi\)
0.980675 0.195643i \(-0.0626794\pi\)
\(588\) 0 0
\(589\) 11.2672 + 8.73274i 0.464257 + 0.359826i
\(590\) 14.3991 2.25198i 0.592801 0.0927123i
\(591\) 0 0
\(592\) 8.93656 18.6892i 0.367291 0.768123i
\(593\) −18.5728 6.75993i −0.762691 0.277597i −0.0687553 0.997634i \(-0.521903\pi\)
−0.693936 + 0.720037i \(0.744125\pi\)
\(594\) 0 0
\(595\) 1.20737 0.439447i 0.0494974 0.0180156i
\(596\) −0.0839491 + 0.863072i −0.00343869 + 0.0353528i
\(597\) 0 0
\(598\) −10.9103 31.8865i −0.446155 1.30394i
\(599\) 25.6370 23.2644i 1.04750 0.950556i 0.0486658 0.998815i \(-0.484503\pi\)
0.998835 + 0.0482590i \(0.0153673\pi\)
\(600\) 0 0
\(601\) 6.76430 19.7694i 0.275921 0.806411i −0.717973 0.696071i \(-0.754930\pi\)
0.993894 0.110339i \(-0.0351938\pi\)
\(602\) −0.123065 0.285297i −0.00501576 0.0116278i
\(603\) 0 0
\(604\) 0.400401 0.0468001i 0.0162921 0.00190427i
\(605\) 6.45483 2.06966i 0.262426 0.0841436i
\(606\) 0 0
\(607\) −38.8176 + 10.8056i −1.57556 + 0.438586i −0.942139 0.335224i \(-0.891188\pi\)
−0.633418 + 0.773810i \(0.718349\pi\)
\(608\) 2.58451 0.719449i 0.104816 0.0291775i
\(609\) 0 0
\(610\) 2.17782 0.698289i 0.0881772 0.0282729i
\(611\) 13.1317 1.53488i 0.531253 0.0620946i
\(612\) 0 0
\(613\) −5.08719 11.7934i −0.205470 0.476332i 0.784056 0.620690i \(-0.213148\pi\)
−0.989526 + 0.144358i \(0.953888\pi\)
\(614\) 9.57108 27.9725i 0.386257 1.12888i
\(615\) 0 0
\(616\) 1.40543 1.27536i 0.0566266 0.0513859i
\(617\) 8.49476 + 24.8269i 0.341986 + 0.999493i 0.974392 + 0.224856i \(0.0721910\pi\)
−0.632406 + 0.774637i \(0.717932\pi\)
\(618\) 0 0
\(619\) −2.03774 + 20.9498i −0.0819036 + 0.842043i 0.860918 + 0.508744i \(0.169890\pi\)
−0.942821 + 0.333299i \(0.891838\pi\)
\(620\) −0.232064 + 0.0844642i −0.00931990 + 0.00339216i
\(621\) 0 0
\(622\) 36.0286 + 13.1133i 1.44461 + 0.525797i
\(623\) 0.290609 0.607756i 0.0116430 0.0243492i
\(624\) 0 0
\(625\) 10.3381 1.61684i 0.413522 0.0646737i
\(626\) −6.88858 5.33905i −0.275323 0.213391i
\(627\) 0 0
\(628\) −0.0197489 1.01825i −0.000788068 0.0406326i
\(629\) 34.1492 + 17.1504i 1.36162 + 0.683830i
\(630\) 0 0
\(631\) 7.75911 + 5.10324i 0.308885 + 0.203157i 0.694481 0.719511i \(-0.255634\pi\)
−0.385596 + 0.922668i \(0.626004\pi\)
\(632\) −30.7308 1.19249i −1.22240 0.0474349i
\(633\) 0 0
\(634\) −0.786750 8.08850i −0.0312458 0.321235i
\(635\) −4.70787 9.84567i −0.186826 0.390714i
\(636\) 0 0
\(637\) −16.4348 + 12.7379i −0.651170 + 0.504695i
\(638\) −36.7936 + 38.9989i −1.45667 + 1.54398i
\(639\) 0 0
\(640\) 3.51652 11.7460i 0.139003 0.464301i
\(641\) −14.2164 + 17.6255i −0.561513 + 0.696166i −0.976953 0.213454i \(-0.931529\pi\)
0.415441 + 0.909620i \(0.363627\pi\)
\(642\) 0 0
\(643\) −13.9295 22.1006i −0.549324 0.871562i 0.450450 0.892802i \(-0.351264\pi\)
−0.999774 + 0.0212393i \(0.993239\pi\)
\(644\) −0.100538 + 0.0554745i −0.00396175 + 0.00218600i
\(645\) 0 0
\(646\) 14.6713 + 56.9573i 0.577233 + 2.24095i
\(647\) −11.0603 + 19.1570i −0.434824 + 0.753138i −0.997281 0.0736887i \(-0.976523\pi\)
0.562457 + 0.826827i \(0.309856\pi\)
\(648\) 0 0
\(649\) 20.7481 + 35.9368i 0.814434 + 1.41064i
\(650\) −12.1824 + 11.9485i −0.477835 + 0.468657i
\(651\) 0 0
\(652\) −0.0186717 + 0.962710i −0.000731242 + 0.0377026i
\(653\) −16.2094 + 30.7729i −0.634325 + 1.20424i 0.331110 + 0.943592i \(0.392577\pi\)
−0.965435 + 0.260644i \(0.916065\pi\)
\(654\) 0 0
\(655\) 2.33400 + 6.04520i 0.0911968 + 0.236206i
\(656\) 44.5060 10.5481i 1.73767 0.411835i
\(657\) 0 0
\(658\) −0.300786 1.00470i −0.0117259 0.0391671i
\(659\) −12.8659 5.25631i −0.501185 0.204757i 0.113487 0.993540i \(-0.463798\pi\)
−0.614672 + 0.788783i \(0.710712\pi\)
\(660\) 0 0
\(661\) −29.6294 2.30298i −1.15245 0.0895755i −0.512986 0.858397i \(-0.671461\pi\)
−0.639464 + 0.768821i \(0.720844\pi\)
\(662\) −12.4016 + 8.86411i −0.482001 + 0.344514i
\(663\) 0 0
\(664\) −8.52515 + 13.5261i −0.330840 + 0.524913i
\(665\) −0.0513341 + 0.881373i −0.00199065 + 0.0341782i
\(666\) 0 0
\(667\) −57.6792 + 37.9362i −2.23335 + 1.46890i
\(668\) 0.393692 0.237594i 0.0152324 0.00919279i
\(669\) 0 0
\(670\) −9.87010 + 4.03238i −0.381315 + 0.155784i
\(671\) 4.08815 + 5.06851i 0.157821 + 0.195668i
\(672\) 0 0
\(673\) −6.06444 8.84217i −0.233767 0.340840i 0.689991 0.723818i \(-0.257615\pi\)
−0.923758 + 0.382978i \(0.874899\pi\)
\(674\) 1.13091 + 6.41370i 0.0435609 + 0.247046i
\(675\) 0 0
\(676\) −0.0640389 + 0.363183i −0.00246303 + 0.0139686i
\(677\) −44.5865 + 20.2671i −1.71360 + 0.778926i −0.716951 + 0.697124i \(0.754463\pi\)
−0.996649 + 0.0818027i \(0.973932\pi\)
\(678\) 0 0
\(679\) −0.870212 0.170904i −0.0333957 0.00655870i
\(680\) 20.6489 + 6.62080i 0.791849 + 0.253896i
\(681\) 0 0
\(682\) −10.7638 12.3339i −0.412167 0.472291i
\(683\) 0.762977 1.02486i 0.0291945 0.0392150i −0.787286 0.616588i \(-0.788515\pi\)
0.816481 + 0.577373i \(0.195922\pi\)
\(684\) 0 0
\(685\) 2.13457 4.94850i 0.0815579 0.189072i
\(686\) 2.44760 + 2.22108i 0.0934497 + 0.0848011i
\(687\) 0 0
\(688\) 1.36684 5.30638i 0.0521102 0.202304i
\(689\) −16.0234 15.7157i −0.610443 0.598719i
\(690\) 0 0
\(691\) −3.28010 + 15.1426i −0.124781 + 0.576053i 0.871538 + 0.490328i \(0.163123\pi\)
−0.996319 + 0.0857249i \(0.972679\pi\)
\(692\) 1.04468 + 1.40325i 0.0397129 + 0.0533437i
\(693\) 0 0
\(694\) 24.8763 + 2.90762i 0.944292 + 0.110372i
\(695\) 2.29769 0.451251i 0.0871562 0.0171169i
\(696\) 0 0
\(697\) 17.8621 + 82.4604i 0.676574 + 3.12341i
\(698\) −10.7588 + 12.3282i −0.407227 + 0.466631i
\(699\) 0 0
\(700\) 0.0473000 + 0.0338080i 0.00178777 + 0.00127782i
\(701\) −9.42749 7.91060i −0.356071 0.298779i 0.447151 0.894458i \(-0.352439\pi\)
−0.803223 + 0.595679i \(0.796883\pi\)
\(702\) 0 0
\(703\) −20.1148 + 16.8783i −0.758643 + 0.636577i
\(704\) 31.8658 2.47681i 1.20099 0.0933482i
\(705\) 0 0
\(706\) 14.0287 36.3353i 0.527978 1.36750i
\(707\) 0.0131415 0.0962129i 0.000494238 0.00361846i
\(708\) 0 0
\(709\) 6.49473 + 3.58364i 0.243915 + 0.134586i 0.600360 0.799730i \(-0.295024\pi\)
−0.356446 + 0.934316i \(0.616011\pi\)
\(710\) −0.391966 6.72979i −0.0147102 0.252565i
\(711\) 0 0
\(712\) 10.1600 5.10254i 0.380762 0.191226i
\(713\) −9.82350 18.6495i −0.367893 0.698428i
\(714\) 0 0
\(715\) 11.6355 + 5.28900i 0.435145 + 0.197798i
\(716\) 0.0987660 0.144004i 0.00369106 0.00538169i
\(717\) 0 0
\(718\) 4.57202 + 33.4731i 0.170626 + 1.24920i
\(719\) 11.9143 + 2.82373i 0.444327 + 0.105307i 0.446688 0.894690i \(-0.352603\pi\)
−0.00236092 + 0.999997i \(0.500752\pi\)
\(720\) 0 0
\(721\) −1.52918 1.62083i −0.0569496 0.0603630i
\(722\) −12.7928 2.00075i −0.476098 0.0744604i
\(723\) 0 0
\(724\) 1.42618 0.0553424i 0.0530037 0.00205678i
\(725\) 29.9274 + 18.0613i 1.11148 + 0.670779i
\(726\) 0 0
\(727\) −1.89340 0.527063i −0.0702222 0.0195477i 0.232883 0.972505i \(-0.425184\pi\)
−0.303106 + 0.952957i \(0.598023\pi\)
\(728\) 1.34731 0.0499346
\(729\) 0 0
\(730\) −5.87055 −0.217279
\(731\) 9.73775 + 2.71069i 0.360164 + 0.100258i
\(732\) 0 0
\(733\) 27.6454 + 16.6841i 1.02111 + 0.616240i 0.925330 0.379163i \(-0.123788\pi\)
0.0957752 + 0.995403i \(0.469467\pi\)
\(734\) 24.8609 0.964715i 0.917632 0.0356083i
\(735\) 0 0
\(736\) −3.91927 0.612962i −0.144466 0.0225941i
\(737\) −20.8326 22.0812i −0.767378 0.813373i
\(738\) 0 0
\(739\) −19.1572 4.54034i −0.704709 0.167019i −0.137390 0.990517i \(-0.543871\pi\)
−0.567319 + 0.823498i \(0.692019\pi\)
\(740\) −0.0615613 0.450709i −0.00226304 0.0165684i
\(741\) 0 0
\(742\) −1.00698 + 1.46821i −0.0369673 + 0.0538996i
\(743\) 24.0075 + 10.9127i 0.880749 + 0.400350i 0.802548 0.596588i \(-0.203477\pi\)
0.0782014 + 0.996938i \(0.475082\pi\)
\(744\) 0 0
\(745\) −4.59447 8.72239i −0.168328 0.319564i
\(746\) −4.69282 + 2.35683i −0.171817 + 0.0862895i
\(747\) 0 0
\(748\) −0.168688 2.89626i −0.00616785 0.105898i
\(749\) −1.18787 0.655441i −0.0434040 0.0239493i
\(750\) 0 0
\(751\) −4.96942 + 36.3826i −0.181337 + 1.32762i 0.644887 + 0.764278i \(0.276904\pi\)
−0.826224 + 0.563342i \(0.809515\pi\)
\(752\) 6.66173 17.2543i 0.242928 0.629200i
\(753\) 0 0
\(754\) −37.9485 + 2.94959i −1.38200 + 0.107418i
\(755\) −3.51085 + 2.94595i −0.127773 + 0.107214i
\(756\) 0 0
\(757\) 4.11994 + 3.45704i 0.149742 + 0.125648i 0.714581 0.699553i \(-0.246617\pi\)
−0.564839 + 0.825201i \(0.691062\pi\)
\(758\) 36.9874 + 26.4370i 1.34344 + 0.960236i
\(759\) 0 0
\(760\) −9.79708 + 11.2262i −0.355378 + 0.407218i
\(761\) 8.10676 + 37.4250i 0.293870 + 1.35665i 0.850535 + 0.525918i \(0.176278\pi\)
−0.556665 + 0.830737i \(0.687919\pi\)
\(762\) 0 0
\(763\) 0.429573 0.0843653i 0.0155516 0.00305423i
\(764\) −0.530023 0.0619508i −0.0191756 0.00224130i
\(765\) 0 0
\(766\) 0.0400784 + 0.0538346i 0.00144809 + 0.00194512i
\(767\) −6.23655 + 28.7911i −0.225189 + 1.03959i
\(768\) 0 0
\(769\) −5.43973 5.33525i −0.196162 0.192394i 0.595497 0.803357i \(-0.296955\pi\)
−0.791659 + 0.610963i \(0.790782\pi\)
\(770\) 0.252898 0.981811i 0.00911382 0.0353820i
\(771\) 0 0
\(772\) −1.62356 1.47330i −0.0584331 0.0530252i
\(773\) −3.21805 + 7.46027i −0.115745 + 0.268327i −0.966234 0.257665i \(-0.917047\pi\)
0.850489 + 0.525993i \(0.176306\pi\)
\(774\) 0 0
\(775\) −6.37324 + 8.56075i −0.228934 + 0.307511i
\(776\) −9.84113 11.2767i −0.353276 0.404809i
\(777\) 0 0
\(778\) −37.7726 12.1113i −1.35421 0.434211i
\(779\) −56.8886 11.1726i −2.03824 0.400298i
\(780\) 0 0
\(781\) 17.4734 7.94264i 0.625248 0.284210i
\(782\) 15.1021 85.6480i 0.540049 3.06277i
\(783\) 0 0
\(784\) 5.05118 + 28.6467i 0.180399 + 1.02309i
\(785\) 6.54889 + 9.54852i 0.233740 + 0.340801i
\(786\) 0