Properties

Label 78.2.g.a.5.5
Level $78$
Weight $2$
Character 78.5
Analytic conductor $0.623$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 78.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.622833135766\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.58498535041007616.52
Defining polynomial: \( x^{12} - 12x^{9} + 72x^{6} - 324x^{3} + 729 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.5
Root \(-0.949550 + 1.44857i\) of defining polynomial
Character \(\chi\) \(=\) 78.5
Dual form 78.2.g.a.47.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(0.352860 - 1.69573i) q^{3} +1.00000i q^{4} +(-0.499019 - 0.499019i) q^{5} +(1.44857 - 0.949550i) q^{6} +(1.39812 + 1.39812i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.75098 - 1.19671i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(0.352860 - 1.69573i) q^{3} +1.00000i q^{4} +(-0.499019 - 0.499019i) q^{5} +(1.44857 - 0.949550i) q^{6} +(1.39812 + 1.39812i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.75098 - 1.19671i) q^{9} -0.705720i q^{10} +(-3.39145 + 3.39145i) q^{11} +(1.69573 + 0.352860i) q^{12} +(-2.39812 - 2.69240i) q^{13} +1.97724i q^{14} +(-1.02228 + 0.670116i) q^{15} -1.00000 q^{16} +4.38949 q^{17} +(-1.09904 - 2.79144i) q^{18} +(-1.70572 + 1.70572i) q^{19} +(0.499019 - 0.499019i) q^{20} +(2.86417 - 1.87749i) q^{21} -4.79624 q^{22} -0.998038 q^{23} +(0.949550 + 1.44857i) q^{24} -4.50196i q^{25} +(0.208088 - 3.59954i) q^{26} +(-3.00000 + 4.24264i) q^{27} +(-1.39812 + 1.39812i) q^{28} -0.998038i q^{29} +(-1.19671 - 0.249020i) q^{30} +(6.50196 - 6.50196i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.55427 + 6.94769i) q^{33} +(3.10384 + 3.10384i) q^{34} -1.39538i q^{35} +(1.19671 - 2.75098i) q^{36} +(4.10384 + 4.10384i) q^{37} -2.41225 q^{38} +(-5.41178 + 3.11652i) q^{39} +0.705720 q^{40} +(5.24068 + 5.24068i) q^{41} +(3.35286 + 0.697689i) q^{42} +8.88676i q^{43} +(-3.39145 - 3.39145i) q^{44} +(0.775612 + 1.96997i) q^{45} +(-0.705720 - 0.705720i) q^{46} +(-0.352168 + 0.352168i) q^{47} +(-0.352860 + 1.69573i) q^{48} -3.09052i q^{49} +(3.18337 - 3.18337i) q^{50} +(1.54888 - 7.44338i) q^{51} +(2.69240 - 2.39812i) q^{52} -14.2702i q^{53} +(-5.12132 + 0.878680i) q^{54} +3.38480 q^{55} -1.97724 q^{56} +(2.29055 + 3.49431i) q^{57} +(0.705720 - 0.705720i) q^{58} +(0.998038 - 0.998038i) q^{59} +(-0.670116 - 1.02228i) q^{60} -9.59248 q^{61} +9.19516 q^{62} +(-2.17306 - 5.51934i) q^{63} -1.00000i q^{64} +(-0.146852 + 2.54027i) q^{65} +(-1.69240 + 8.13311i) q^{66} +(-5.79624 + 5.79624i) q^{67} +4.38949i q^{68} +(-0.352168 + 1.69240i) q^{69} +(0.986681 - 0.986681i) q^{70} +(-7.13508 - 7.13508i) q^{71} +(2.79144 - 1.09904i) q^{72} +(-1.70572 - 1.70572i) q^{73} +5.80371i q^{74} +(-7.63409 - 1.58856i) q^{75} +(-1.70572 - 1.70572i) q^{76} -9.48332 q^{77} +(-6.03041 - 1.62299i) q^{78} -0.207679 q^{79} +(0.499019 + 0.499019i) q^{80} +(6.13578 + 6.58424i) q^{81} +7.41144i q^{82} +(9.17632 + 9.17632i) q^{83} +(1.87749 + 2.86417i) q^{84} +(-2.19044 - 2.19044i) q^{85} +(-6.28389 + 6.28389i) q^{86} +(-1.69240 - 0.352168i) q^{87} -4.79624i q^{88} +(2.54027 - 2.54027i) q^{89} +(-0.844540 + 1.94142i) q^{90} +(0.411439 - 7.11716i) q^{91} -0.998038i q^{92} +(-8.73127 - 13.3198i) q^{93} -0.498040 q^{94} +1.70237 q^{95} +(-1.44857 + 0.949550i) q^{96} +(-3.58856 + 3.58856i) q^{97} +(2.18533 - 2.18533i) q^{98} +(13.3884 - 5.27124i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 12 q^{7} - 12 q^{16} - 12 q^{19} - 36 q^{27} + 12 q^{28} + 12 q^{31} + 36 q^{33} + 12 q^{37} + 36 q^{42} + 36 q^{45} + 12 q^{52} - 36 q^{54} - 36 q^{57} - 36 q^{63} - 12 q^{67} - 12 q^{73} - 12 q^{76} - 36 q^{78} + 72 q^{79} - 72 q^{85} - 12 q^{91} + 36 q^{93} - 72 q^{94} - 60 q^{97} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(67\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0.352860 1.69573i 0.203724 0.979028i
\(4\) 1.00000i 0.500000i
\(5\) −0.499019 0.499019i −0.223168 0.223168i 0.586663 0.809831i \(-0.300441\pi\)
−0.809831 + 0.586663i \(0.800441\pi\)
\(6\) 1.44857 0.949550i 0.591376 0.387652i
\(7\) 1.39812 + 1.39812i 0.528440 + 0.528440i 0.920107 0.391667i \(-0.128102\pi\)
−0.391667 + 0.920107i \(0.628102\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) −2.75098 1.19671i −0.916993 0.398903i
\(10\) 0.705720i 0.223168i
\(11\) −3.39145 + 3.39145i −1.02256 + 1.02256i −0.0228223 + 0.999740i \(0.507265\pi\)
−0.999740 + 0.0228223i \(0.992735\pi\)
\(12\) 1.69573 + 0.352860i 0.489514 + 0.101862i
\(13\) −2.39812 2.69240i −0.665119 0.746738i
\(14\) 1.97724i 0.528440i
\(15\) −1.02228 + 0.670116i −0.263953 + 0.173023i
\(16\) −1.00000 −0.250000
\(17\) 4.38949 1.06461 0.532304 0.846553i \(-0.321326\pi\)
0.532304 + 0.846553i \(0.321326\pi\)
\(18\) −1.09904 2.79144i −0.259045 0.657948i
\(19\) −1.70572 + 1.70572i −0.391319 + 0.391319i −0.875157 0.483838i \(-0.839242\pi\)
0.483838 + 0.875157i \(0.339242\pi\)
\(20\) 0.499019 0.499019i 0.111584 0.111584i
\(21\) 2.86417 1.87749i 0.625013 0.409702i
\(22\) −4.79624 −1.02256
\(23\) −0.998038 −0.208105 −0.104053 0.994572i \(-0.533181\pi\)
−0.104053 + 0.994572i \(0.533181\pi\)
\(24\) 0.949550 + 1.44857i 0.193826 + 0.295688i
\(25\) 4.50196i 0.900392i
\(26\) 0.208088 3.59954i 0.0408093 0.705928i
\(27\) −3.00000 + 4.24264i −0.577350 + 0.816497i
\(28\) −1.39812 + 1.39812i −0.264220 + 0.264220i
\(29\) 0.998038i 0.185331i −0.995697 0.0926655i \(-0.970461\pi\)
0.995697 0.0926655i \(-0.0295387\pi\)
\(30\) −1.19671 0.249020i −0.218488 0.0454646i
\(31\) 6.50196 6.50196i 1.16779 1.16779i 0.185059 0.982727i \(-0.440752\pi\)
0.982727 0.185059i \(-0.0592476\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 4.55427 + 6.94769i 0.792797 + 1.20944i
\(34\) 3.10384 + 3.10384i 0.532304 + 0.532304i
\(35\) 1.39538i 0.235862i
\(36\) 1.19671 2.75098i 0.199451 0.458497i
\(37\) 4.10384 + 4.10384i 0.674667 + 0.674667i 0.958788 0.284121i \(-0.0917018\pi\)
−0.284121 + 0.958788i \(0.591702\pi\)
\(38\) −2.41225 −0.391319
\(39\) −5.41178 + 3.11652i −0.866578 + 0.499042i
\(40\) 0.705720 0.111584
\(41\) 5.24068 + 5.24068i 0.818457 + 0.818457i 0.985884 0.167428i \(-0.0535461\pi\)
−0.167428 + 0.985884i \(0.553546\pi\)
\(42\) 3.35286 + 0.697689i 0.517358 + 0.107656i
\(43\) 8.88676i 1.35522i 0.735422 + 0.677609i \(0.236984\pi\)
−0.735422 + 0.677609i \(0.763016\pi\)
\(44\) −3.39145 3.39145i −0.511281 0.511281i
\(45\) 0.775612 + 1.96997i 0.115621 + 0.293666i
\(46\) −0.705720 0.705720i −0.104053 0.104053i
\(47\) −0.352168 + 0.352168i −0.0513689 + 0.0513689i −0.732325 0.680956i \(-0.761565\pi\)
0.680956 + 0.732325i \(0.261565\pi\)
\(48\) −0.352860 + 1.69573i −0.0509309 + 0.244757i
\(49\) 3.09052i 0.441503i
\(50\) 3.18337 3.18337i 0.450196 0.450196i
\(51\) 1.54888 7.44338i 0.216886 1.04228i
\(52\) 2.69240 2.39812i 0.373369 0.332559i
\(53\) 14.2702i 1.96016i −0.198613 0.980078i \(-0.563644\pi\)
0.198613 0.980078i \(-0.436356\pi\)
\(54\) −5.12132 + 0.878680i −0.696923 + 0.119573i
\(55\) 3.38480 0.456406
\(56\) −1.97724 −0.264220
\(57\) 2.29055 + 3.49431i 0.303391 + 0.462833i
\(58\) 0.705720 0.705720i 0.0926655 0.0926655i
\(59\) 0.998038 0.998038i 0.129934 0.129934i −0.639149 0.769083i \(-0.720713\pi\)
0.769083 + 0.639149i \(0.220713\pi\)
\(60\) −0.670116 1.02228i −0.0865117 0.131976i
\(61\) −9.59248 −1.22819 −0.614096 0.789232i \(-0.710479\pi\)
−0.614096 + 0.789232i \(0.710479\pi\)
\(62\) 9.19516 1.16779
\(63\) −2.17306 5.51934i −0.273780 0.695372i
\(64\) 1.00000i 0.125000i
\(65\) −0.146852 + 2.54027i −0.0182147 + 0.315081i
\(66\) −1.69240 + 8.13311i −0.208320 + 1.00112i
\(67\) −5.79624 + 5.79624i −0.708123 + 0.708123i −0.966140 0.258017i \(-0.916931\pi\)
0.258017 + 0.966140i \(0.416931\pi\)
\(68\) 4.38949i 0.532304i
\(69\) −0.352168 + 1.69240i −0.0423960 + 0.203741i
\(70\) 0.986681 0.986681i 0.117931 0.117931i
\(71\) −7.13508 7.13508i −0.846778 0.846778i 0.142952 0.989730i \(-0.454341\pi\)
−0.989730 + 0.142952i \(0.954341\pi\)
\(72\) 2.79144 1.09904i 0.328974 0.129523i
\(73\) −1.70572 1.70572i −0.199639 0.199639i 0.600206 0.799845i \(-0.295085\pi\)
−0.799845 + 0.600206i \(0.795085\pi\)
\(74\) 5.80371i 0.674667i
\(75\) −7.63409 1.58856i −0.881509 0.183431i
\(76\) −1.70572 1.70572i −0.195659 0.195659i
\(77\) −9.48332 −1.08072
\(78\) −6.03041 1.62299i −0.682810 0.183768i
\(79\) −0.207679 −0.0233658 −0.0116829 0.999932i \(-0.503719\pi\)
−0.0116829 + 0.999932i \(0.503719\pi\)
\(80\) 0.499019 + 0.499019i 0.0557920 + 0.0557920i
\(81\) 6.13578 + 6.58424i 0.681753 + 0.731582i
\(82\) 7.41144i 0.818457i
\(83\) 9.17632 + 9.17632i 1.00723 + 1.00723i 0.999974 + 0.00725871i \(0.00231054\pi\)
0.00725871 + 0.999974i \(0.497689\pi\)
\(84\) 1.87749 + 2.86417i 0.204851 + 0.312507i
\(85\) −2.19044 2.19044i −0.237587 0.237587i
\(86\) −6.28389 + 6.28389i −0.677609 + 0.677609i
\(87\) −1.69240 0.352168i −0.181444 0.0377563i
\(88\) 4.79624i 0.511281i
\(89\) 2.54027 2.54027i 0.269268 0.269268i −0.559537 0.828805i \(-0.689021\pi\)
0.828805 + 0.559537i \(0.189021\pi\)
\(90\) −0.844540 + 1.94142i −0.0890224 + 0.204644i
\(91\) 0.411439 7.11716i 0.0431306 0.746081i
\(92\) 0.998038i 0.104053i
\(93\) −8.73127 13.3198i −0.905390 1.38120i
\(94\) −0.498040 −0.0513689
\(95\) 1.70237 0.174660
\(96\) −1.44857 + 0.949550i −0.147844 + 0.0969131i
\(97\) −3.58856 + 3.58856i −0.364363 + 0.364363i −0.865416 0.501053i \(-0.832946\pi\)
0.501053 + 0.865416i \(0.332946\pi\)
\(98\) 2.18533 2.18533i 0.220751 0.220751i
\(99\) 13.3884 5.27124i 1.34558 0.529780i
\(100\) 4.50196 0.450196
\(101\) −5.08053 −0.505532 −0.252766 0.967527i \(-0.581340\pi\)
−0.252766 + 0.967527i \(0.581340\pi\)
\(102\) 6.35849 4.16804i 0.629584 0.412698i
\(103\) 12.2077i 1.20286i 0.798926 + 0.601429i \(0.205402\pi\)
−0.798926 + 0.601429i \(0.794598\pi\)
\(104\) 3.59954 + 0.208088i 0.352964 + 0.0204047i
\(105\) −2.36618 0.492373i −0.230915 0.0480506i
\(106\) 10.0905 10.0905i 0.980078 0.980078i
\(107\) 6.78291i 0.655728i −0.944725 0.327864i \(-0.893671\pi\)
0.944725 0.327864i \(-0.106329\pi\)
\(108\) −4.24264 3.00000i −0.408248 0.288675i
\(109\) 3.30760 3.30760i 0.316811 0.316811i −0.530730 0.847541i \(-0.678082\pi\)
0.847541 + 0.530730i \(0.178082\pi\)
\(110\) 2.39342 + 2.39342i 0.228203 + 0.228203i
\(111\) 8.40707 5.51091i 0.797964 0.523073i
\(112\) −1.39812 1.39812i −0.132110 0.132110i
\(113\) 13.2721i 1.24854i 0.781211 + 0.624268i \(0.214603\pi\)
−0.781211 + 0.624268i \(0.785397\pi\)
\(114\) −0.851187 + 4.09052i −0.0797209 + 0.383112i
\(115\) 0.498040 + 0.498040i 0.0464425 + 0.0464425i
\(116\) 0.998038 0.0926655
\(117\) 3.37516 + 10.2766i 0.312034 + 0.950071i
\(118\) 1.41144 0.129934
\(119\) 6.13704 + 6.13704i 0.562581 + 0.562581i
\(120\) 0.249020 1.19671i 0.0227323 0.109244i
\(121\) 12.0039i 1.09127i
\(122\) −6.78291 6.78291i −0.614096 0.614096i
\(123\) 10.7360 7.03754i 0.968031 0.634553i
\(124\) 6.50196 + 6.50196i 0.583893 + 0.583893i
\(125\) −4.74166 + 4.74166i −0.424107 + 0.424107i
\(126\) 2.36618 5.43935i 0.210796 0.484576i
\(127\) 11.6191i 1.03103i 0.856881 + 0.515515i \(0.172399\pi\)
−0.856881 + 0.515515i \(0.827601\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 15.0695 + 3.13578i 1.32680 + 0.276090i
\(130\) −1.90008 + 1.69240i −0.166648 + 0.148433i
\(131\) 7.08990i 0.619448i −0.950827 0.309724i \(-0.899763\pi\)
0.950827 0.309724i \(-0.100237\pi\)
\(132\) −6.94769 + 4.55427i −0.604719 + 0.396399i
\(133\) −4.76960 −0.413577
\(134\) −8.19712 −0.708123
\(135\) 3.61422 0.620101i 0.311062 0.0533698i
\(136\) −3.10384 + 3.10384i −0.266152 + 0.266152i
\(137\) −15.4150 + 15.4150i −1.31700 + 1.31700i −0.400854 + 0.916142i \(0.631286\pi\)
−0.916142 + 0.400854i \(0.868714\pi\)
\(138\) −1.44573 + 0.947688i −0.123069 + 0.0806725i
\(139\) 10.8868 0.923403 0.461701 0.887035i \(-0.347239\pi\)
0.461701 + 0.887035i \(0.347239\pi\)
\(140\) 1.39538 0.117931
\(141\) 0.472914 + 0.721446i 0.0398266 + 0.0607567i
\(142\) 10.0905i 0.846778i
\(143\) 17.2643 + 0.998038i 1.44371 + 0.0834602i
\(144\) 2.75098 + 1.19671i 0.229248 + 0.0997257i
\(145\) −0.498040 + 0.498040i −0.0413600 + 0.0413600i
\(146\) 2.41225i 0.199639i
\(147\) −5.24068 1.09052i −0.432244 0.0899446i
\(148\) −4.10384 + 4.10384i −0.337334 + 0.337334i
\(149\) 2.54027 + 2.54027i 0.208107 + 0.208107i 0.803462 0.595356i \(-0.202989\pi\)
−0.595356 + 0.803462i \(0.702989\pi\)
\(150\) −4.27484 6.52140i −0.349039 0.532470i
\(151\) −4.01332 4.01332i −0.326599 0.326599i 0.524693 0.851292i \(-0.324180\pi\)
−0.851292 + 0.524693i \(0.824180\pi\)
\(152\) 2.41225i 0.195659i
\(153\) −12.0754 5.25294i −0.976239 0.424675i
\(154\) −6.70572 6.70572i −0.540362 0.540362i
\(155\) −6.48920 −0.521225
\(156\) −3.11652 5.41178i −0.249521 0.433289i
\(157\) 4.76960 0.380656 0.190328 0.981721i \(-0.439045\pi\)
0.190328 + 0.981721i \(0.439045\pi\)
\(158\) −0.146852 0.146852i −0.0116829 0.0116829i
\(159\) −24.1983 5.03536i −1.91905 0.399330i
\(160\) 0.705720i 0.0557920i
\(161\) −1.39538 1.39538i −0.109971 0.109971i
\(162\) −0.317107 + 8.99441i −0.0249143 + 0.706668i
\(163\) −11.4154 11.4154i −0.894120 0.894120i 0.100788 0.994908i \(-0.467864\pi\)
−0.994908 + 0.100788i \(0.967864\pi\)
\(164\) −5.24068 + 5.24068i −0.409228 + 0.409228i
\(165\) 1.19436 5.73970i 0.0929808 0.446835i
\(166\) 12.9773i 1.00723i
\(167\) −7.78095 + 7.78095i −0.602108 + 0.602108i −0.940871 0.338764i \(-0.889991\pi\)
0.338764 + 0.940871i \(0.389991\pi\)
\(168\) −0.697689 + 3.35286i −0.0538279 + 0.258679i
\(169\) −1.49804 + 12.9134i −0.115234 + 0.993338i
\(170\) 3.09775i 0.237587i
\(171\) 6.73365 2.65115i 0.514935 0.202739i
\(172\) −8.88676 −0.677609
\(173\) 19.3507 1.47121 0.735603 0.677413i \(-0.236899\pi\)
0.735603 + 0.677413i \(0.236899\pi\)
\(174\) −0.947688 1.44573i −0.0718440 0.109600i
\(175\) 6.29428 6.29428i 0.475803 0.475803i
\(176\) 3.39145 3.39145i 0.255640 0.255640i
\(177\) −1.34023 2.04457i −0.100738 0.153679i
\(178\) 3.59248 0.269268
\(179\) 7.08990 0.529924 0.264962 0.964259i \(-0.414641\pi\)
0.264962 + 0.964259i \(0.414641\pi\)
\(180\) −1.96997 + 0.775612i −0.146833 + 0.0578107i
\(181\) 6.20768i 0.461413i 0.973023 + 0.230707i \(0.0741038\pi\)
−0.973023 + 0.230707i \(0.925896\pi\)
\(182\) 5.32352 4.74166i 0.394606 0.351475i
\(183\) −3.38480 + 16.2662i −0.250212 + 1.20243i
\(184\) 0.705720 0.705720i 0.0520263 0.0520263i
\(185\) 4.09579i 0.301128i
\(186\) 3.24460 15.5925i 0.237906 1.14330i
\(187\) −14.8868 + 14.8868i −1.08863 + 1.08863i
\(188\) −0.352168 0.352168i −0.0256845 0.0256845i
\(189\) −10.1261 + 1.73736i −0.736564 + 0.126374i
\(190\) 1.20376 + 1.20376i 0.0873299 + 0.0873299i
\(191\) 9.77702i 0.707441i −0.935351 0.353720i \(-0.884916\pi\)
0.935351 0.353720i \(-0.115084\pi\)
\(192\) −1.69573 0.352860i −0.122379 0.0254655i
\(193\) 3.79624 + 3.79624i 0.273259 + 0.273259i 0.830411 0.557152i \(-0.188106\pi\)
−0.557152 + 0.830411i \(0.688106\pi\)
\(194\) −5.07499 −0.364363
\(195\) 4.25578 + 1.14538i 0.304763 + 0.0820222i
\(196\) 3.09052 0.220751
\(197\) −7.28193 7.28193i −0.518816 0.518816i 0.398397 0.917213i \(-0.369567\pi\)
−0.917213 + 0.398397i \(0.869567\pi\)
\(198\) 13.1944 + 5.73970i 0.937682 + 0.407903i
\(199\) 18.1544i 1.28693i −0.765475 0.643466i \(-0.777496\pi\)
0.765475 0.643466i \(-0.222504\pi\)
\(200\) 3.18337 + 3.18337i 0.225098 + 0.225098i
\(201\) 7.78358 + 11.8741i 0.549011 + 0.837535i
\(202\) −3.59248 3.59248i −0.252766 0.252766i
\(203\) 1.39538 1.39538i 0.0979363 0.0979363i
\(204\) 7.44338 + 1.54888i 0.521141 + 0.108443i
\(205\) 5.23040i 0.365307i
\(206\) −8.63213 + 8.63213i −0.601429 + 0.601429i
\(207\) 2.74558 + 1.19436i 0.190831 + 0.0830138i
\(208\) 2.39812 + 2.69240i 0.166280 + 0.186684i
\(209\) 11.5697i 0.800296i
\(210\) −1.32498 2.02130i −0.0914324 0.139483i
\(211\) 11.2943 0.777530 0.388765 0.921337i \(-0.372902\pi\)
0.388765 + 0.921337i \(0.372902\pi\)
\(212\) 14.2702 0.980078
\(213\) −14.6168 + 9.58146i −1.00153 + 0.656511i
\(214\) 4.79624 4.79624i 0.327864 0.327864i
\(215\) 4.43466 4.43466i 0.302442 0.302442i
\(216\) −0.878680 5.12132i −0.0597866 0.348462i
\(217\) 18.1810 1.23421
\(218\) 4.67765 0.316811
\(219\) −3.49431 + 2.29055i −0.236124 + 0.154781i
\(220\) 3.38480i 0.228203i
\(221\) −10.5265 11.8183i −0.708091 0.794983i
\(222\) 9.84150 + 2.04789i 0.660518 + 0.137446i
\(223\) 6.19436 6.19436i 0.414805 0.414805i −0.468604 0.883409i \(-0.655243\pi\)
0.883409 + 0.468604i \(0.155243\pi\)
\(224\) 1.97724i 0.132110i
\(225\) −5.38753 + 12.3848i −0.359169 + 0.825653i
\(226\) −9.38480 + 9.38480i −0.624268 + 0.624268i
\(227\) −13.5658 13.5658i −0.900395 0.900395i 0.0950753 0.995470i \(-0.469691\pi\)
−0.995470 + 0.0950753i \(0.969691\pi\)
\(228\) −3.49431 + 2.29055i −0.231417 + 0.151696i
\(229\) 3.30760 + 3.30760i 0.218572 + 0.218572i 0.807897 0.589324i \(-0.200606\pi\)
−0.589324 + 0.807897i \(0.700606\pi\)
\(230\) 0.704335i 0.0464425i
\(231\) −3.34628 + 16.0811i −0.220169 + 1.05806i
\(232\) 0.705720 + 0.705720i 0.0463328 + 0.0463328i
\(233\) 10.8787 0.712687 0.356344 0.934355i \(-0.384023\pi\)
0.356344 + 0.934355i \(0.384023\pi\)
\(234\) −4.88004 + 9.65325i −0.319018 + 0.631052i
\(235\) 0.351477 0.0229278
\(236\) 0.998038 + 0.998038i 0.0649668 + 0.0649668i
\(237\) −0.0732817 + 0.352168i −0.00476016 + 0.0228757i
\(238\) 8.67908i 0.562581i
\(239\) −5.13900 5.13900i −0.332414 0.332414i 0.521088 0.853503i \(-0.325526\pi\)
−0.853503 + 0.521088i \(0.825526\pi\)
\(240\) 1.02228 0.670116i 0.0659881 0.0432558i
\(241\) −5.06388 5.06388i −0.326193 0.326193i 0.524944 0.851137i \(-0.324086\pi\)
−0.851137 + 0.524944i \(0.824086\pi\)
\(242\) 8.48805 8.48805i 0.545633 0.545633i
\(243\) 13.3301 8.08130i 0.855129 0.518415i
\(244\) 9.59248i 0.614096i
\(245\) −1.54223 + 1.54223i −0.0985294 + 0.0985294i
\(246\) 12.5678 + 2.61520i 0.801292 + 0.166739i
\(247\) 8.68300 + 0.501960i 0.552486 + 0.0319389i
\(248\) 9.19516i 0.583893i
\(249\) 18.7985 12.3226i 1.19131 0.780912i
\(250\) −6.70572 −0.424107
\(251\) −19.2603 −1.21570 −0.607851 0.794051i \(-0.707968\pi\)
−0.607851 + 0.794051i \(0.707968\pi\)
\(252\) 5.51934 2.17306i 0.347686 0.136890i
\(253\) 3.38480 3.38480i 0.212801 0.212801i
\(254\) −8.21596 + 8.21596i −0.515515 + 0.515515i
\(255\) −4.48731 + 2.94147i −0.281006 + 0.184202i
\(256\) 1.00000 0.0625000
\(257\) 18.2490 1.13834 0.569171 0.822219i \(-0.307264\pi\)
0.569171 + 0.822219i \(0.307264\pi\)
\(258\) 8.43843 + 12.8731i 0.525354 + 0.801444i
\(259\) 11.4753i 0.713042i
\(260\) −2.54027 0.146852i −0.157541 0.00910735i
\(261\) −1.19436 + 2.74558i −0.0739290 + 0.169947i
\(262\) 5.01332 5.01332i 0.309724 0.309724i
\(263\) 3.99215i 0.246167i 0.992396 + 0.123083i \(0.0392783\pi\)
−0.992396 + 0.123083i \(0.960722\pi\)
\(264\) −8.13311 1.69240i −0.500559 0.104160i
\(265\) −7.12108 + 7.12108i −0.437444 + 0.437444i
\(266\) −3.37262 3.37262i −0.206788 0.206788i
\(267\) −3.41124 5.20396i −0.208765 0.318477i
\(268\) −5.79624 5.79624i −0.354062 0.354062i
\(269\) 10.4814i 0.639060i −0.947576 0.319530i \(-0.896475\pi\)
0.947576 0.319530i \(-0.103525\pi\)
\(270\) 2.99411 + 2.11716i 0.182216 + 0.128846i
\(271\) −3.37148 3.37148i −0.204803 0.204803i 0.597251 0.802054i \(-0.296260\pi\)
−0.802054 + 0.597251i \(0.796260\pi\)
\(272\) −4.38949 −0.266152
\(273\) −11.9236 3.20905i −0.721648 0.194220i
\(274\) −21.8002 −1.31700
\(275\) 15.2682 + 15.2682i 0.920706 + 0.920706i
\(276\) −1.69240 0.352168i −0.101871 0.0211980i
\(277\) 27.2382i 1.63659i −0.574801 0.818294i \(-0.694920\pi\)
0.574801 0.818294i \(-0.305080\pi\)
\(278\) 7.69810 + 7.69810i 0.461701 + 0.461701i
\(279\) −25.6677 + 10.1058i −1.53669 + 0.605019i
\(280\) 0.986681 + 0.986681i 0.0589655 + 0.0589655i
\(281\) −2.24656 + 2.24656i −0.134019 + 0.134019i −0.770934 0.636915i \(-0.780210\pi\)
0.636915 + 0.770934i \(0.280210\pi\)
\(282\) −0.175738 + 0.844540i −0.0104651 + 0.0502916i
\(283\) 3.00392i 0.178564i −0.996006 0.0892822i \(-0.971543\pi\)
0.996006 0.0892822i \(-0.0284573\pi\)
\(284\) 7.13508 7.13508i 0.423389 0.423389i
\(285\) 0.600699 2.88676i 0.0355824 0.170997i
\(286\) 11.5020 + 12.9134i 0.680125 + 0.763585i
\(287\) 14.6542i 0.865010i
\(288\) 1.09904 + 2.79144i 0.0647613 + 0.164487i
\(289\) 2.26764 0.133391
\(290\) −0.704335 −0.0413600
\(291\) 4.81896 + 7.35148i 0.282492 + 0.430951i
\(292\) 1.70572 1.70572i 0.0998197 0.0998197i
\(293\) 6.98822 6.98822i 0.408256 0.408256i −0.472874 0.881130i \(-0.656783\pi\)
0.881130 + 0.472874i \(0.156783\pi\)
\(294\) −2.93461 4.47683i −0.171150 0.261094i
\(295\) −0.996080 −0.0579940
\(296\) −5.80371 −0.337334
\(297\) −4.21436 24.5631i −0.244542 1.42529i
\(298\) 3.59248i 0.208107i
\(299\) 2.39342 + 2.68712i 0.138415 + 0.155400i
\(300\) 1.58856 7.63409i 0.0917156 0.440755i
\(301\) −12.4248 + 12.4248i −0.716151 + 0.716151i
\(302\) 5.67569i 0.326599i
\(303\) −1.79272 + 8.61520i −0.102989 + 0.494930i
\(304\) 1.70572 1.70572i 0.0978297 0.0978297i
\(305\) 4.78683 + 4.78683i 0.274093 + 0.274093i
\(306\) −4.82421 12.2530i −0.275782 0.700457i
\(307\) −8.88284 8.88284i −0.506971 0.506971i 0.406625 0.913595i \(-0.366706\pi\)
−0.913595 + 0.406625i \(0.866706\pi\)
\(308\) 9.48332i 0.540362i
\(309\) 20.7009 + 4.30760i 1.17763 + 0.245051i
\(310\) −4.58856 4.58856i −0.260613 0.260613i
\(311\) −13.2721 −0.752592 −0.376296 0.926499i \(-0.622803\pi\)
−0.376296 + 0.926499i \(0.622803\pi\)
\(312\) 1.62299 6.03041i 0.0918839 0.341405i
\(313\) −0.913399 −0.0516284 −0.0258142 0.999667i \(-0.508218\pi\)
−0.0258142 + 0.999667i \(0.508218\pi\)
\(314\) 3.37262 + 3.37262i 0.190328 + 0.190328i
\(315\) −1.66986 + 3.83866i −0.0940859 + 0.216284i
\(316\) 0.207679i 0.0116829i
\(317\) −0.544191 0.544191i −0.0305648 0.0305648i 0.691659 0.722224i \(-0.256880\pi\)
−0.722224 + 0.691659i \(0.756880\pi\)
\(318\) −13.5502 20.6713i −0.759859 1.15919i
\(319\) 3.38480 + 3.38480i 0.189512 + 0.189512i
\(320\) −0.499019 + 0.499019i −0.0278960 + 0.0278960i
\(321\) −11.5020 2.39342i −0.641977 0.133587i
\(322\) 1.97336i 0.109971i
\(323\) −7.48724 + 7.48724i −0.416601 + 0.416601i
\(324\) −6.58424 + 6.13578i −0.365791 + 0.340877i
\(325\) −12.1211 + 10.7962i −0.672356 + 0.598868i
\(326\) 16.1438i 0.894120i
\(327\) −4.44167 6.77590i −0.245625 0.374708i
\(328\) −7.41144 −0.409228
\(329\) −0.984745 −0.0542908
\(330\) 4.90312 3.21404i 0.269908 0.176927i
\(331\) −10.5925 + 10.5925i −0.582215 + 0.582215i −0.935512 0.353296i \(-0.885061\pi\)
0.353296 + 0.935512i \(0.385061\pi\)
\(332\) −9.17632 + 9.17632i −0.503616 + 0.503616i
\(333\) −6.37848 16.2007i −0.349539 0.887792i
\(334\) −11.0039 −0.602108
\(335\) 5.78487 0.316061
\(336\) −2.86417 + 1.87749i −0.156253 + 0.102425i
\(337\) 13.7363i 0.748263i −0.927376 0.374131i \(-0.877941\pi\)
0.927376 0.374131i \(-0.122059\pi\)
\(338\) −10.1904 + 8.07188i −0.554286 + 0.439052i
\(339\) 22.5059 + 4.68320i 1.22235 + 0.254356i
\(340\) 2.19044 2.19044i 0.118793 0.118793i
\(341\) 44.1022i 2.38827i
\(342\) 6.63606 + 2.88676i 0.358837 + 0.156098i
\(343\) 14.1078 14.1078i 0.761747 0.761747i
\(344\) −6.28389 6.28389i −0.338805 0.338805i
\(345\) 1.02028 0.668802i 0.0549300 0.0360071i
\(346\) 13.6830 + 13.6830i 0.735603 + 0.735603i
\(347\) 24.3542i 1.30740i 0.756754 + 0.653700i \(0.226784\pi\)
−0.756754 + 0.653700i \(0.773216\pi\)
\(348\) 0.352168 1.69240i 0.0188782 0.0907222i
\(349\) 6.48472 + 6.48472i 0.347119 + 0.347119i 0.859035 0.511916i \(-0.171064\pi\)
−0.511916 + 0.859035i \(0.671064\pi\)
\(350\) 8.90146 0.475803
\(351\) 18.6172 2.09716i 0.993715 0.111938i
\(352\) 4.79624 0.255640
\(353\) −8.63213 8.63213i −0.459442 0.459442i 0.439030 0.898472i \(-0.355322\pi\)
−0.898472 + 0.439030i \(0.855322\pi\)
\(354\) 0.498040 2.39342i 0.0264705 0.127209i
\(355\) 7.12108i 0.377948i
\(356\) 2.54027 + 2.54027i 0.134634 + 0.134634i
\(357\) 12.5723 8.24123i 0.665394 0.436172i
\(358\) 5.01332 + 5.01332i 0.264962 + 0.264962i
\(359\) −12.5678 + 12.5678i −0.663302 + 0.663302i −0.956157 0.292855i \(-0.905395\pi\)
0.292855 + 0.956157i \(0.405395\pi\)
\(360\) −1.94142 0.844540i −0.102322 0.0445112i
\(361\) 13.1810i 0.693739i
\(362\) −4.38949 + 4.38949i −0.230707 + 0.230707i
\(363\) −20.3554 4.23570i −1.06838 0.222317i
\(364\) 7.11716 + 0.411439i 0.373040 + 0.0215653i
\(365\) 1.70237i 0.0891063i
\(366\) −13.8954 + 9.10854i −0.726323 + 0.476111i
\(367\) 19.3848 1.01188 0.505939 0.862569i \(-0.331146\pi\)
0.505939 + 0.862569i \(0.331146\pi\)
\(368\) 0.998038 0.0520263
\(369\) −8.14544 20.6886i −0.424035 1.07700i
\(370\) 2.89616 2.89616i 0.150564 0.150564i
\(371\) 19.9514 19.9514i 1.03582 1.03582i
\(372\) 13.3198 8.73127i 0.690601 0.452695i
\(373\) 24.4154 1.26418 0.632090 0.774895i \(-0.282197\pi\)
0.632090 + 0.774895i \(0.282197\pi\)
\(374\) −21.0531 −1.08863
\(375\) 6.36742 + 9.71370i 0.328812 + 0.501613i
\(376\) 0.498040i 0.0256845i
\(377\) −2.68712 + 2.39342i −0.138394 + 0.123267i
\(378\) −8.38872 5.93172i −0.431469 0.305095i
\(379\) −2.17712 + 2.17712i −0.111831 + 0.111831i −0.760808 0.648977i \(-0.775197\pi\)
0.648977 + 0.760808i \(0.275197\pi\)
\(380\) 1.70237i 0.0873299i
\(381\) 19.7029 + 4.09992i 1.00941 + 0.210045i
\(382\) 6.91340 6.91340i 0.353720 0.353720i
\(383\) 4.14096 + 4.14096i 0.211593 + 0.211593i 0.804944 0.593351i \(-0.202195\pi\)
−0.593351 + 0.804944i \(0.702195\pi\)
\(384\) −0.949550 1.44857i −0.0484565 0.0739220i
\(385\) 4.73236 + 4.73236i 0.241183 + 0.241183i
\(386\) 5.36869i 0.273259i
\(387\) 10.6349 24.4473i 0.540600 1.24273i
\(388\) −3.58856 3.58856i −0.182182 0.182182i
\(389\) 6.78291 0.343907 0.171954 0.985105i \(-0.444992\pi\)
0.171954 + 0.985105i \(0.444992\pi\)
\(390\) 2.19939 + 3.81920i 0.111370 + 0.193393i
\(391\) −4.38088 −0.221551
\(392\) 2.18533 + 2.18533i 0.110376 + 0.110376i
\(393\) −12.0225 2.50174i −0.606457 0.126196i
\(394\) 10.2982i 0.518816i
\(395\) 0.103636 + 0.103636i 0.00521449 + 0.00521449i
\(396\) 5.27124 + 13.3884i 0.264890 + 0.672792i
\(397\) 17.2716 + 17.2716i 0.866835 + 0.866835i 0.992121 0.125286i \(-0.0399848\pi\)
−0.125286 + 0.992121i \(0.539985\pi\)
\(398\) 12.8371 12.8371i 0.643466 0.643466i
\(399\) −1.68300 + 8.08794i −0.0842554 + 0.404904i
\(400\) 4.50196i 0.225098i
\(401\) 22.1979 22.1979i 1.10851 1.10851i 0.115166 0.993346i \(-0.463260\pi\)
0.993346 0.115166i \(-0.0367401\pi\)
\(402\) −2.89243 + 13.9001i −0.144262 + 0.693273i
\(403\) −33.0984 1.91340i −1.64875 0.0953132i
\(404\) 5.08053i 0.252766i
\(405\) 0.223789 6.34753i 0.0111202 0.315411i
\(406\) 1.97336 0.0979363
\(407\) −27.8360 −1.37978
\(408\) 4.16804 + 6.35849i 0.206349 + 0.314792i
\(409\) 3.02664 3.02664i 0.149658 0.149658i −0.628307 0.777965i \(-0.716252\pi\)
0.777965 + 0.628307i \(0.216252\pi\)
\(410\) 3.69845 3.69845i 0.182653 0.182653i
\(411\) 20.7004 + 31.5790i 1.02107 + 1.55768i
\(412\) −12.2077 −0.601429
\(413\) 2.79075 0.137324
\(414\) 1.09688 + 2.78596i 0.0539087 + 0.136923i
\(415\) 9.15832i 0.449564i
\(416\) −0.208088 + 3.59954i −0.0102023 + 0.176482i
\(417\) 3.84150 18.4610i 0.188119 0.904038i
\(418\) 8.18104 8.18104i 0.400148 0.400148i
\(419\) 34.2215i 1.67183i −0.548858 0.835916i \(-0.684937\pi\)
0.548858 0.835916i \(-0.315063\pi\)
\(420\) 0.492373 2.36618i 0.0240253 0.115458i
\(421\) 2.87344 2.87344i 0.140043 0.140043i −0.633610 0.773653i \(-0.718428\pi\)
0.773653 + 0.633610i \(0.218428\pi\)
\(422\) 7.98626 + 7.98626i 0.388765 + 0.388765i
\(423\) 1.39025 0.547364i 0.0675962 0.0266138i
\(424\) 10.0905 + 10.0905i 0.490039 + 0.490039i
\(425\) 19.7613i 0.958565i
\(426\) −17.1108 3.56054i −0.829019 0.172509i
\(427\) −13.4114 13.4114i −0.649025 0.649025i
\(428\) 6.78291 0.327864
\(429\) 7.78427 28.9233i 0.375828 1.39643i
\(430\) 6.27156 0.302442
\(431\) −6.84137 6.84137i −0.329537 0.329537i 0.522873 0.852410i \(-0.324860\pi\)
−0.852410 + 0.522873i \(0.824860\pi\)
\(432\) 3.00000 4.24264i 0.144338 0.204124i
\(433\) 29.2833i 1.40727i 0.710563 + 0.703633i \(0.248440\pi\)
−0.710563 + 0.703633i \(0.751560\pi\)
\(434\) 12.8559 + 12.8559i 0.617105 + 0.617105i
\(435\) 0.668802 + 1.02028i 0.0320666 + 0.0489186i
\(436\) 3.30760 + 3.30760i 0.158405 + 0.158405i
\(437\) 1.70237 1.70237i 0.0814356 0.0814356i
\(438\) −4.09052 0.851187i −0.195453 0.0406713i
\(439\) 18.0000i 0.859093i −0.903045 0.429547i \(-0.858673\pi\)
0.903045 0.429547i \(-0.141327\pi\)
\(440\) −2.39342 + 2.39342i −0.114102 + 0.114102i
\(441\) −3.69845 + 8.50196i −0.176117 + 0.404855i
\(442\) 0.913399 15.8002i 0.0434460 0.751537i
\(443\) 26.6439i 1.26589i 0.774196 + 0.632946i \(0.218155\pi\)
−0.774196 + 0.632946i \(0.781845\pi\)
\(444\) 5.51091 + 8.40707i 0.261536 + 0.398982i
\(445\) −2.53528 −0.120184
\(446\) 8.76015 0.414805
\(447\) 5.20396 3.41124i 0.246139 0.161346i
\(448\) 1.39812 1.39812i 0.0660550 0.0660550i
\(449\) −25.9867 + 25.9867i −1.22639 + 1.22639i −0.261070 + 0.965320i \(0.584075\pi\)
−0.965320 + 0.261070i \(0.915925\pi\)
\(450\) −12.5669 + 4.94782i −0.592411 + 0.233242i
\(451\) −35.5470 −1.67384
\(452\) −13.2721 −0.624268
\(453\) −8.22163 + 5.38935i −0.386286 + 0.253214i
\(454\) 19.1850i 0.900395i
\(455\) −3.75691 + 3.34628i −0.176127 + 0.156876i
\(456\) −4.09052 0.851187i −0.191556 0.0398605i
\(457\) −18.8907 + 18.8907i −0.883669 + 0.883669i −0.993905 0.110237i \(-0.964839\pi\)
0.110237 + 0.993905i \(0.464839\pi\)
\(458\) 4.67765i 0.218572i
\(459\) −13.1685 + 18.6230i −0.614652 + 0.869249i
\(460\) −0.498040 + 0.498040i −0.0232212 + 0.0232212i
\(461\) 24.8399 + 24.8399i 1.15691 + 1.15691i 0.985137 + 0.171773i \(0.0549495\pi\)
0.171773 + 0.985137i \(0.445051\pi\)
\(462\) −13.7372 + 9.00489i −0.639115 + 0.418945i
\(463\) −14.0944 14.0944i −0.655024 0.655024i 0.299174 0.954198i \(-0.403289\pi\)
−0.954198 + 0.299174i \(0.903289\pi\)
\(464\) 0.998038i 0.0463328i
\(465\) −2.28978 + 11.0039i −0.106186 + 0.510295i
\(466\) 7.69240 + 7.69240i 0.356344 + 0.356344i
\(467\) 16.6769 0.771713 0.385857 0.922559i \(-0.373906\pi\)
0.385857 + 0.922559i \(0.373906\pi\)
\(468\) −10.2766 + 3.37516i −0.475035 + 0.156017i
\(469\) −16.2077 −0.748401
\(470\) 0.248532 + 0.248532i 0.0114639 + 0.0114639i
\(471\) 1.68300 8.08794i 0.0775486 0.372673i
\(472\) 1.41144i 0.0649668i
\(473\) −30.1390 30.1390i −1.38579 1.38579i
\(474\) −0.300838 + 0.197202i −0.0138180 + 0.00905779i
\(475\) 7.67908 + 7.67908i 0.352340 + 0.352340i
\(476\) −6.13704 + 6.13704i −0.281291 + 0.281291i
\(477\) −17.0772 + 39.2569i −0.781911 + 1.79745i
\(478\) 7.26764i 0.332414i
\(479\) 26.4858 26.4858i 1.21017 1.21017i 0.239193 0.970972i \(-0.423117\pi\)
0.970972 0.239193i \(-0.0768830\pi\)
\(480\) 1.19671 + 0.249020i 0.0546220 + 0.0113662i
\(481\) 1.20768 20.8907i 0.0550654 0.952533i
\(482\) 7.16141i 0.326193i
\(483\) −2.85855 + 1.87381i −0.130069 + 0.0852611i
\(484\) 12.0039 0.545633
\(485\) 3.58152 0.162628
\(486\) 15.1402 + 3.71149i 0.686772 + 0.168357i
\(487\) 3.67908 3.67908i 0.166715 0.166715i −0.618819 0.785534i \(-0.712388\pi\)
0.785534 + 0.618819i \(0.212388\pi\)
\(488\) 6.78291 6.78291i 0.307048 0.307048i
\(489\) −23.3854 + 15.3293i −1.05752 + 0.693215i
\(490\) −2.18104 −0.0985294
\(491\) −40.7107 −1.83725 −0.918625 0.395131i \(-0.870699\pi\)
−0.918625 + 0.395131i \(0.870699\pi\)
\(492\) 7.03754 + 10.7360i 0.317277 + 0.484016i
\(493\) 4.38088i 0.197305i
\(494\) 5.78487 + 6.49475i 0.260274 + 0.292213i
\(495\) −9.31152 4.05062i −0.418522 0.182062i
\(496\) −6.50196 + 6.50196i −0.291947 + 0.291947i
\(497\) 19.9514i 0.894942i
\(498\) 22.0059 + 4.57916i 0.986109 + 0.205197i
\(499\) −10.5020 + 10.5020i −0.470132 + 0.470132i −0.901957 0.431825i \(-0.857870\pi\)
0.431825 + 0.901957i \(0.357870\pi\)
\(500\) −4.74166 4.74166i −0.212053 0.212053i
\(501\) 10.4488 + 15.9399i 0.466817 + 0.712144i
\(502\) −13.6191 13.6191i −0.607851 0.607851i
\(503\) 1.38208i 0.0616241i 0.999525 + 0.0308120i \(0.00980933\pi\)
−0.999525 + 0.0308120i \(0.990191\pi\)
\(504\) 5.43935 + 2.36618i 0.242288 + 0.105398i
\(505\) 2.53528 + 2.53528i 0.112819 + 0.112819i
\(506\) 4.78683 0.212801
\(507\) 21.3690 + 7.09689i 0.949031 + 0.315184i
\(508\) −11.6191 −0.515515
\(509\) −7.32710 7.32710i −0.324768 0.324768i 0.525825 0.850593i \(-0.323757\pi\)
−0.850593 + 0.525825i \(0.823757\pi\)
\(510\) −5.25294 1.09307i −0.232604 0.0484020i
\(511\) 4.76960i 0.210995i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −2.11960 12.3539i −0.0935825 0.545439i
\(514\) 12.9040 + 12.9040i 0.569171 + 0.569171i
\(515\) 6.09187 6.09187i 0.268440 0.268440i
\(516\) −3.13578 + 15.0695i −0.138045 + 0.663399i
\(517\) 2.38872i 0.105056i
\(518\) −8.11428 + 8.11428i −0.356521 + 0.356521i
\(519\) 6.82808 32.8135i 0.299719 1.44035i
\(520\) −1.69240 1.90008i −0.0742167 0.0833240i
\(521\) 2.09971i 0.0919901i 0.998942 + 0.0459950i \(0.0146458\pi\)
−0.998942 + 0.0459950i \(0.985354\pi\)
\(522\) −2.78596 + 1.09688i −0.121938 + 0.0480091i
\(523\) −2.76960 −0.121106 −0.0605531 0.998165i \(-0.519286\pi\)
−0.0605531 + 0.998165i \(0.519286\pi\)
\(524\) 7.08990 0.309724
\(525\) −8.45238 12.8944i −0.368892 0.562757i
\(526\) −2.82288 + 2.82288i −0.123083 + 0.123083i
\(527\) 28.5403 28.5403i 1.24324 1.24324i
\(528\) −4.55427 6.94769i −0.198199 0.302359i
\(529\) −22.0039 −0.956692
\(530\) −10.0707 −0.437444
\(531\) −3.93994 + 1.55122i −0.170979 + 0.0673173i
\(532\) 4.76960i 0.206788i
\(533\) 1.54223 26.6778i 0.0668013 1.15554i
\(534\) 1.26764 6.09187i 0.0548562 0.263621i
\(535\) −3.38480 + 3.38480i −0.146338 + 0.146338i
\(536\) 8.19712i 0.354062i
\(537\) 2.50174 12.0225i 0.107958 0.518811i
\(538\) 7.41144 7.41144i 0.319530 0.319530i
\(539\) 10.4814 + 10.4814i 0.451464 + 0.451464i
\(540\) 0.620101 + 3.61422i 0.0266849 + 0.155531i
\(541\) 23.0545 + 23.0545i 0.991190 + 0.991190i 0.999962 0.00877191i \(-0.00279222\pi\)
−0.00877191 + 0.999962i \(0.502792\pi\)
\(542\) 4.76800i 0.204803i
\(543\) 10.5265 + 2.19044i 0.451737 + 0.0940008i
\(544\) −3.10384 3.10384i −0.133076 0.133076i
\(545\) −3.30111 −0.141404
\(546\) −6.16210 10.7004i −0.263714 0.457934i
\(547\) 28.1172 1.20220 0.601101 0.799173i \(-0.294729\pi\)
0.601101 + 0.799173i \(0.294729\pi\)
\(548\) −15.4150 15.4150i −0.658498 0.658498i
\(549\) 26.3887 + 11.4794i 1.12624 + 0.489929i
\(550\) 21.5925i 0.920706i
\(551\) 1.70237 + 1.70237i 0.0725235 + 0.0725235i
\(552\) −0.947688 1.44573i −0.0403363 0.0615343i
\(553\) −0.290361 0.290361i −0.0123474 0.0123474i
\(554\) 19.2603 19.2603i 0.818294 0.818294i
\(555\) −6.94534 1.44524i −0.294813 0.0613470i
\(556\) 10.8868i 0.461701i
\(557\) −14.0648 + 14.0648i −0.595946 + 0.595946i −0.939231 0.343285i \(-0.888460\pi\)
0.343285 + 0.939231i \(0.388460\pi\)
\(558\) −25.2957 11.0039i −1.07085 0.465833i
\(559\) 23.9267 21.3115i 1.01199 0.901381i
\(560\) 1.39538i 0.0589655i
\(561\) 19.9909 + 30.4968i 0.844018 + 1.28758i
\(562\) −3.17712 −0.134019
\(563\) 28.6400 1.20703 0.603517 0.797350i \(-0.293766\pi\)
0.603517 + 0.797350i \(0.293766\pi\)
\(564\) −0.721446 + 0.472914i −0.0303784 + 0.0199133i
\(565\) 6.62304 6.62304i 0.278633 0.278633i
\(566\) 2.12409 2.12409i 0.0892822 0.0892822i
\(567\) −0.626998 + 17.7841i −0.0263314 + 0.746863i
\(568\) 10.0905 0.423389
\(569\) 3.48180 0.145965 0.0729823 0.997333i \(-0.476748\pi\)
0.0729823 + 0.997333i \(0.476748\pi\)
\(570\) 2.46601 1.61649i 0.103290 0.0677073i
\(571\) 5.34756i 0.223788i 0.993720 + 0.111894i \(0.0356918\pi\)
−0.993720 + 0.111894i \(0.964308\pi\)
\(572\) −0.998038 + 17.2643i −0.0417301 + 0.721855i
\(573\) −16.5792 3.44992i −0.692604 0.144122i
\(574\) −10.3621 + 10.3621i −0.432505 + 0.432505i
\(575\) 4.49313i 0.187376i
\(576\) −1.19671 + 2.75098i −0.0498628 + 0.114624i
\(577\) 26.4753 26.4753i 1.10218 1.10218i 0.108035 0.994147i \(-0.465544\pi\)
0.994147 0.108035i \(-0.0344558\pi\)
\(578\) 1.60347 + 1.60347i 0.0666954 + 0.0666954i
\(579\) 7.77693 5.09785i 0.323198 0.211859i
\(580\) −0.498040 0.498040i −0.0206800 0.0206800i
\(581\) 25.6592i 1.06452i
\(582\) −1.79076 + 8.60580i −0.0742294 + 0.356722i
\(583\) 48.3966 + 48.3966i 2.00438 + 2.00438i
\(584\) 2.41225 0.0998197
\(585\) 3.44394 6.81249i 0.142390 0.281662i
\(586\) 9.88284 0.408256
\(587\) −19.3640 19.3640i −0.799237 0.799237i 0.183738 0.982975i \(-0.441180\pi\)
−0.982975 + 0.183738i \(0.941180\pi\)
\(588\) 1.09052 5.24068i 0.0449723 0.216122i
\(589\) 22.1810i 0.913954i
\(590\) −0.704335 0.704335i −0.0289970 0.0289970i
\(591\) −14.9177 + 9.77866i −0.613631 + 0.402240i
\(592\) −4.10384 4.10384i −0.168667 0.168667i
\(593\) −3.14097 + 3.14097i −0.128984 + 0.128984i −0.768652 0.639668i \(-0.779072\pi\)
0.639668 + 0.768652i \(0.279072\pi\)
\(594\) 14.3887 20.3487i 0.590376 0.834918i
\(595\) 6.12500i 0.251100i
\(596\) −2.54027 + 2.54027i −0.104053 + 0.104053i
\(597\) −30.7849 6.40596i −1.25994 0.262178i
\(598\) −0.207679 + 3.59248i −0.00849264 + 0.146907i
\(599\) 38.7280i 1.58238i 0.611570 + 0.791191i \(0.290538\pi\)
−0.611570 + 0.791191i \(0.709462\pi\)
\(600\) 6.52140 4.27484i 0.266235 0.174520i
\(601\) 16.2794 0.664051 0.332025 0.943270i \(-0.392268\pi\)
0.332025 + 0.943270i \(0.392268\pi\)
\(602\) −17.5713 −0.716151
\(603\) 22.8817 9.00893i 0.931817 0.366872i
\(604\) 4.01332 4.01332i 0.163300 0.163300i
\(605\) −5.99019 + 5.99019i −0.243536 + 0.243536i
\(606\) −7.35951 + 4.82422i −0.298960 + 0.195971i
\(607\) −29.0118 −1.17755 −0.588775 0.808297i \(-0.700390\pi\)
−0.588775 + 0.808297i \(0.700390\pi\)
\(608\) 2.41225 0.0978297
\(609\) −1.87381 2.85855i −0.0759305 0.115834i
\(610\) 6.76960i 0.274093i
\(611\) 1.79272 + 0.103636i 0.0725255 + 0.00419266i
\(612\) 5.25294 12.0754i 0.212338 0.488119i
\(613\) −9.94004 + 9.94004i −0.401474 + 0.401474i −0.878752 0.477278i \(-0.841623\pi\)
0.477278 + 0.878752i \(0.341623\pi\)
\(614\) 12.5622i 0.506971i
\(615\) −8.86933 1.84560i −0.357646 0.0744217i
\(616\) 6.70572 6.70572i 0.270181 0.270181i
\(617\) 2.15622 + 2.15622i 0.0868062 + 0.0868062i 0.749177 0.662370i \(-0.230449\pi\)
−0.662370 + 0.749177i \(0.730449\pi\)
\(618\) 11.5918 + 17.6837i 0.466291 + 0.711342i
\(619\) 0.683001 + 0.683001i 0.0274521 + 0.0274521i 0.720700 0.693247i \(-0.243821\pi\)
−0.693247 + 0.720700i \(0.743821\pi\)
\(620\) 6.48920i 0.260613i
\(621\) 2.99411 4.23432i 0.120150 0.169917i
\(622\) −9.38480 9.38480i −0.376296 0.376296i
\(623\) 7.10320 0.284584
\(624\) 5.41178 3.11652i 0.216644 0.124761i
\(625\) −17.7774 −0.711098
\(626\) −0.645871 0.645871i −0.0258142 0.0258142i
\(627\) −19.6191 4.08250i −0.783512 0.163039i
\(628\) 4.76960i 0.190328i
\(629\) 18.0138 + 18.0138i 0.718256 + 0.718256i
\(630\) −3.89511 + 1.53357i −0.155185 + 0.0610989i
\(631\) −7.98668 7.98668i −0.317945 0.317945i 0.530033 0.847977i \(-0.322180\pi\)
−0.847977 + 0.530033i \(0.822180\pi\)
\(632\) 0.146852 0.146852i 0.00584144 0.00584144i
\(633\) 3.98530 19.1520i 0.158401 0.761224i
\(634\) 0.769602i 0.0305648i
\(635\) 5.79816 5.79816i 0.230093 0.230093i
\(636\) 5.03536 24.1983i 0.199665 0.959524i
\(637\) −8.32092 + 7.41144i −0.329687 + 0.293652i
\(638\) 4.78683i 0.189512i
\(639\) 11.0898 + 28.1670i 0.438708 + 1.11427i
\(640\) −0.705720 −0.0278960
\(641\) −29.7417 −1.17473 −0.587363 0.809323i \(-0.699834\pi\)
−0.587363 + 0.809323i \(0.699834\pi\)
\(642\) −6.44071 9.82551i −0.254195 0.387782i
\(643\) 13.3887 13.3887i 0.528000 0.528000i −0.391976 0.919975i \(-0.628208\pi\)
0.919975 + 0.391976i \(0.128208\pi\)
\(644\) 1.39538 1.39538i 0.0549856 0.0549856i
\(645\) −5.95516 9.08479i −0.234484 0.357713i
\(646\) −10.5886 −0.416601
\(647\) 8.77898 0.345137 0.172569 0.984997i \(-0.444793\pi\)
0.172569 + 0.984997i \(0.444793\pi\)
\(648\) −8.99441 0.317107i −0.353334 0.0124572i
\(649\) 6.76960i 0.265730i
\(650\) −16.2050 0.936802i −0.635612 0.0367444i
\(651\) 6.41536 30.8301i 0.251438 1.20833i
\(652\) 11.4154 11.4154i 0.447060 0.447060i
\(653\) 30.2161i 1.18245i 0.806508 + 0.591223i \(0.201355\pi\)
−0.806508 + 0.591223i \(0.798645\pi\)
\(654\) 1.65056 7.93202i 0.0645418 0.310167i
\(655\) −3.53800 + 3.53800i −0.138241 + 0.138241i
\(656\) −5.24068 5.24068i −0.204614 0.204614i
\(657\) 2.65115 + 6.73365i 0.103431 + 0.262705i
\(658\) −0.696320 0.696320i −0.0271454 0.0271454i
\(659\) 5.10712i 0.198945i −0.995040 0.0994726i \(-0.968284\pi\)
0.995040 0.0994726i \(-0.0317156\pi\)
\(660\) 5.73970 + 1.19436i 0.223417 + 0.0464904i
\(661\) −30.2488 30.2488i −1.17654 1.17654i −0.980619 0.195925i \(-0.937229\pi\)
−0.195925 0.980619i \(-0.562771\pi\)
\(662\) −14.9800 −0.582215
\(663\) −23.7549 + 13.6799i −0.922566 + 0.531284i
\(664\) −12.9773 −0.503616
\(665\) 2.38012 + 2.38012i 0.0922972 + 0.0922972i
\(666\) 6.94534 15.9659i 0.269126 0.618665i
\(667\) 0.996080i 0.0385684i
\(668\) −7.78095 7.78095i −0.301054 0.301054i
\(669\) −8.31820 12.6897i −0.321600 0.490612i
\(670\) 4.09052 + 4.09052i 0.158031 + 0.158031i
\(671\) 32.5325 32.5325i 1.25590 1.25590i
\(672\) −3.35286 0.697689i −0.129339 0.0269139i
\(673\) 40.8601i 1.57504i −0.616288 0.787521i \(-0.711364\pi\)
0.616288 0.787521i \(-0.288636\pi\)
\(674\) 9.71302 9.71302i 0.374131 0.374131i
\(675\) 19.1002 + 13.5059i 0.735167 + 0.519842i
\(676\) −12.9134 1.49804i −0.496669 0.0576169i
\(677\) 25.8399i 0.993108i 0.868006 + 0.496554i \(0.165401\pi\)
−0.868006 + 0.496554i \(0.834599\pi\)
\(678\) 12.6025 + 19.2256i 0.483998 + 0.738354i
\(679\) −10.0345 −0.385088
\(680\) 3.09775 0.118793
\(681\) −27.7908 + 18.2171i −1.06494 + 0.698080i
\(682\) −31.1850 + 31.1850i −1.19413 + 1.19413i
\(683\) −2.09971 + 2.09971i −0.0803433 + 0.0803433i −0.746136 0.665793i \(-0.768093\pi\)
0.665793 + 0.746136i \(0.268093\pi\)
\(684\) 2.65115 + 6.73365i 0.101369 + 0.257467i
\(685\) 15.3848 0.587823
\(686\) 19.9514 0.761747
\(687\) 6.77590 4.44167i 0.258517 0.169460i
\(688\) 8.88676i 0.338805i
\(689\) −38.4210 + 34.2215i −1.46372 + 1.30374i
\(690\) 1.19436 + 0.248532i 0.0454685 + 0.00946144i
\(691\) 24.5020 24.5020i 0.932098 0.932098i −0.0657384 0.997837i \(-0.520940\pi\)
0.997837 + 0.0657384i \(0.0209403\pi\)
\(692\) 19.3507i 0.735603i
\(693\) 26.0884 + 11.3488i 0.991017 + 0.431104i
\(694\) −17.2210 + 17.2210i −0.653700 + 0.653700i
\(695\) −5.43270 5.43270i −0.206074 0.206074i
\(696\) 1.44573 0.947688i 0.0548002 0.0359220i
\(697\) 23.0039 + 23.0039i 0.871336 + 0.871336i
\(698\) 9.17078i 0.347119i
\(699\) 3.83866 18.4473i 0.145191 0.697741i
\(700\) 6.29428 + 6.29428i 0.237901 + 0.237901i
\(701\) 19.6710 0.742962 0.371481 0.928440i \(-0.378850\pi\)
0.371481 + 0.928440i \(0.378850\pi\)
\(702\) 14.6473 + 11.6815i 0.552827 + 0.440889i
\(703\) −14.0000 −0.528020
\(704\) 3.39145 + 3.39145i 0.127820 + 0.127820i
\(705\) 0.124022 0.596009i 0.00467094 0.0224470i
\(706\) 12.2077i 0.459442i
\(707\) −7.10320 7.10320i −0.267143 0.267143i
\(708\) 2.04457 1.34023i 0.0768396 0.0503690i
\(709\) −26.0944 26.0944i −0.979997 0.979997i 0.0198066 0.999804i \(-0.493695\pi\)
−0.999804 + 0.0198066i \(0.993695\pi\)
\(710\) −5.03536 + 5.03536i −0.188974 + 0.188974i
\(711\) 0.571322 + 0.248532i 0.0214262 + 0.00932066i
\(712\) 3.59248i 0.134634i
\(713\) −6.48920 + 6.48920i −0.243023 + 0.243023i
\(714\) 14.7174 + 3.06250i 0.550783 + 0.114611i
\(715\) −8.11716 9.11324i −0.303565 0.340816i
\(716\) 7.08990i 0.264962i
\(717\) −10.5277 + 6.90099i −0.393164 + 0.257722i
\(718\) −17.7735 −0.663302
\(719\) −28.7437 −1.07196 −0.535979 0.844231i \(-0.680057\pi\)
−0.535979 + 0.844231i \(0.680057\pi\)
\(720\) −0.775612 1.96997i −0.0289053 0.0734165i
\(721\) −17.0678 + 17.0678i −0.635638 + 0.635638i
\(722\) −9.32040 + 9.32040i −0.346870 + 0.346870i
\(723\) −10.3738 + 6.80012i −0.385806 + 0.252899i
\(724\) −6.20768 −0.230707
\(725\) −4.49313 −0.166871
\(726\) −11.3983 17.3885i −0.423032 0.645348i
\(727\) 11.3848i 0.422239i 0.977460 + 0.211119i \(0.0677109\pi\)
−0.977460 + 0.211119i \(0.932289\pi\)
\(728\) 4.74166 + 5.32352i 0.175738 + 0.197303i
\(729\) −9.00000 25.4558i −0.333333 0.942809i
\(730\) −1.20376 + 1.20376i −0.0445532 + 0.0445532i
\(731\) 39.0084i 1.44278i
\(732\) −16.2662 3.38480i −0.601217 0.125106i
\(733\) 27.3154 27.3154i 1.00892 1.00892i 0.00895888 0.999960i \(-0.497148\pi\)
0.999960 0.00895888i \(-0.00285174\pi\)
\(734\) 13.7071 + 13.7071i 0.505939 + 0.505939i
\(735\) 2.07101 + 3.15939i 0.0763903 + 0.116536i
\(736\) 0.705720 + 0.705720i 0.0260132 + 0.0260132i
\(737\) 39.3154i 1.44820i
\(738\) 8.86933 20.3887i 0.326484 0.750519i
\(739\) −2.26764 2.26764i −0.0834166 0.0834166i 0.664167 0.747584i \(-0.268786\pi\)
−0.747584 + 0.664167i \(0.768786\pi\)
\(740\) 4.09579 0.150564
\(741\) 3.91507 14.5469i 0.143824 0.534393i
\(742\) 28.2155 1.03582
\(743\) −0.645871 0.645871i −0.0236947 0.0236947i 0.695160 0.718855i \(-0.255333\pi\)
−0.718855 + 0.695160i \(0.755333\pi\)
\(744\) 15.5925 + 3.24460i 0.571648 + 0.118953i
\(745\) 2.53528i 0.0928856i
\(746\) 17.2643 + 17.2643i 0.632090 + 0.632090i
\(747\) −14.2625 36.2253i −0.521838 1.32541i
\(748\) −14.8868 14.8868i −0.544314 0.544314i
\(749\) 9.48332 9.48332i 0.346513 0.346513i
\(750\) −2.36618 + 11.3711i −0.0864006 + 0.415213i
\(751\) 26.5964i 0.970516i 0.874371 + 0.485258i \(0.161274\pi\)
−0.874371 + 0.485258i \(0.838726\pi\)
\(752\) 0.352168 0.352168i 0.0128422 0.0128422i
\(753\) −6.79620 + 32.6603i −0.247667 + 1.19021i
\(754\) −3.59248 0.207679i −0.130830 0.00756324i
\(755\) 4.00545i 0.145773i
\(756\) −1.73736 10.1261i −0.0631872 0.368282i
\(757\) −8.19984 −0.298028 −0.149014 0.988835i \(-0.547610\pi\)
−0.149014 + 0.988835i \(0.547610\pi\)
\(758\) −3.07891 −0.111831
\(759\) −4.54534 6.93406i −0.164985 0.251690i
\(760\) −1.20376 + 1.20376i −0.0436650 + 0.0436650i
\(761\) 7.64739 7.64739i 0.277218 0.277218i −0.554780 0.831997i \(-0.687197\pi\)
0.831997 + 0.554780i \(0.187197\pi\)
\(762\) 11.0329 + 16.8311i 0.399681 + 0.609727i
\(763\) 9.24884 0.334831
\(764\) 9.77702 0.353720
\(765\) 3.40454 + 8.64718i 0.123091 + 0.312639i
\(766\) 5.85620i 0.211593i
\(767\) −5.08053 0.293703i −0.183447 0.0106050i
\(768\) 0.352860 1.69573i 0.0127327 0.0611893i
\(769\) 6.14772 6.14772i 0.221692 0.221692i −0.587518 0.809211i \(-0.699895\pi\)
0.809211 + 0.587518i \(0.199895\pi\)
\(770\) 6.69256i 0.241183i
\(771\) 6.43934 30.9453i 0.231907 1.11447i
\(772\) −3.79624 + 3.79624i −0.136630 + 0.136630i
\(773\) −25.8379 25.8379i −0.929326 0.929326i 0.0683364 0.997662i \(-0.478231\pi\)
−0.997662 + 0.0683364i \(0.978231\pi\)
\(774\) 24.8068 9.76687i 0.891663 0.351063i
\(775\) −29.2716 29.2716i −1.05147