Properties

Label 48.3.i.b.29.10
Level $48$
Weight $3$
Character 48.29
Analytic conductor $1.308$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 48.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.30790526893\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + 24576 x^{4} - 131072 x^{2} + 1048576\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 29.10
Root \(1.96139 - 0.391068i\) of defining polynomial
Character \(\chi\) \(=\) 48.29
Dual form 48.3.i.b.5.10

$q$-expansion

\(f(q)\) \(=\) \(q+(1.96139 + 0.391068i) q^{2} +(-0.164573 - 2.99548i) q^{3} +(3.69413 + 1.53408i) q^{4} +(-3.61305 - 3.61305i) q^{5} +(0.848646 - 5.93968i) q^{6} +12.2792i q^{7} +(6.64572 + 4.45358i) q^{8} +(-8.94583 + 0.985948i) q^{9} +O(q^{10})\) \(q+(1.96139 + 0.391068i) q^{2} +(-0.164573 - 2.99548i) q^{3} +(3.69413 + 1.53408i) q^{4} +(-3.61305 - 3.61305i) q^{5} +(0.848646 - 5.93968i) q^{6} +12.2792i q^{7} +(6.64572 + 4.45358i) q^{8} +(-8.94583 + 0.985948i) q^{9} +(-5.67366 - 8.49955i) q^{10} +(1.76932 + 1.76932i) q^{11} +(3.98735 - 11.3182i) q^{12} +(-2.38826 - 2.38826i) q^{13} +(-4.80199 + 24.0843i) q^{14} +(-10.2282 + 11.4174i) q^{15} +(11.2932 + 11.3342i) q^{16} -20.0754i q^{17} +(-17.9319 - 1.56460i) q^{18} +(-8.77090 - 8.77090i) q^{19} +(-7.80438 - 18.8898i) q^{20} +(36.7820 - 2.02081i) q^{21} +(2.77840 + 4.16225i) q^{22} -13.1821 q^{23} +(12.2469 - 20.6401i) q^{24} +1.10820i q^{25} +(-3.75035 - 5.61830i) q^{26} +(4.42563 + 26.6348i) q^{27} +(-18.8372 + 45.3609i) q^{28} +(-6.51544 + 6.51544i) q^{29} +(-24.5265 + 18.3941i) q^{30} +37.5922 q^{31} +(17.7180 + 26.6472i) q^{32} +(5.00877 - 5.59113i) q^{33} +(7.85085 - 39.3758i) q^{34} +(44.3652 - 44.3652i) q^{35} +(-34.5596 - 10.0814i) q^{36} +(10.0057 - 10.0057i) q^{37} +(-13.7732 - 20.6332i) q^{38} +(-6.76096 + 7.54704i) q^{39} +(-7.92028 - 40.1023i) q^{40} -4.57407 q^{41} +(72.9343 + 10.4207i) q^{42} +(21.2835 - 21.2835i) q^{43} +(3.82182 + 9.25035i) q^{44} +(35.8840 + 28.7594i) q^{45} +(-25.8553 - 5.15509i) q^{46} +54.8366i q^{47} +(32.0927 - 35.6939i) q^{48} -101.778 q^{49} +(-0.433383 + 2.17362i) q^{50} +(-60.1356 + 3.30386i) q^{51} +(-5.15878 - 12.4863i) q^{52} +(21.5215 + 21.5215i) q^{53} +(-1.73563 + 53.9721i) q^{54} -12.7852i q^{55} +(-54.6863 + 81.6039i) q^{56} +(-24.8296 + 27.7165i) q^{57} +(-15.3273 + 10.2314i) q^{58} +(-53.6617 - 53.6617i) q^{59} +(-55.2996 + 26.4866i) q^{60} +(-19.2186 - 19.2186i) q^{61} +(73.7331 + 14.7011i) q^{62} +(-12.1066 - 109.847i) q^{63} +(24.3312 + 59.1945i) q^{64} +17.2578i q^{65} +(12.0107 - 9.00765i) q^{66} +(31.5603 + 31.5603i) q^{67} +(30.7972 - 74.1612i) q^{68} +(2.16941 + 39.4867i) q^{69} +(104.367 - 69.6678i) q^{70} -65.1220 q^{71} +(-63.8425 - 33.2887i) q^{72} +50.2451i q^{73} +(23.5379 - 15.7121i) q^{74} +(3.31960 - 0.182380i) q^{75} +(-18.9456 - 45.8561i) q^{76} +(-21.7257 + 21.7257i) q^{77} +(-16.2123 + 12.1587i) q^{78} +20.9299 q^{79} +(0.147933 - 81.7538i) q^{80} +(79.0558 - 17.6403i) q^{81} +(-8.97156 - 1.78877i) q^{82} +(-6.35791 + 6.35791i) q^{83} +(138.978 + 48.9613i) q^{84} +(-72.5334 + 72.5334i) q^{85} +(50.0687 - 33.4221i) q^{86} +(20.5891 + 18.4446i) q^{87} +(3.87858 + 19.6382i) q^{88} +166.399 q^{89} +(59.1357 + 70.4416i) q^{90} +(29.3259 - 29.3259i) q^{91} +(-48.6964 - 20.2223i) q^{92} +(-6.18664 - 112.607i) q^{93} +(-21.4449 + 107.556i) q^{94} +63.3793i q^{95} +(76.9052 - 57.4594i) q^{96} +139.213 q^{97} +(-199.627 - 39.8021i) q^{98} +(-17.5725 - 14.0835i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 6q^{3} + 4q^{4} - 12q^{6} + O(q^{10}) \) \( 20q - 6q^{3} + 4q^{4} - 12q^{6} + 32q^{10} - 88q^{12} + 92q^{13} - 116q^{15} - 16q^{16} + 4q^{18} - 52q^{19} + 48q^{21} + 24q^{22} - 8q^{24} + 18q^{27} + 56q^{28} + 28q^{30} - 80q^{31} + 60q^{33} + 104q^{34} + 92q^{36} - 116q^{37} + 88q^{40} + 304q^{42} + 172q^{43} + 60q^{45} - 424q^{46} + 176q^{48} - 364q^{49} + 128q^{51} - 208q^{52} + 40q^{54} - 512q^{58} - 240q^{60} - 244q^{61} + 296q^{63} + 88q^{64} - 492q^{66} + 356q^{67} - 20q^{69} + 200q^{70} - 472q^{72} - 146q^{75} + 328q^{76} + 84q^{78} + 384q^{79} - 188q^{81} + 560q^{82} + 816q^{84} + 48q^{85} + 416q^{88} + 616q^{90} + 136q^{91} - 132q^{93} + 32q^{94} - 24q^{96} + 472q^{97} - 452q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.96139 + 0.391068i 0.980697 + 0.195534i
\(3\) −0.164573 2.99548i −0.0548575 0.998494i
\(4\) 3.69413 + 1.53408i 0.923533 + 0.383519i
\(5\) −3.61305 3.61305i −0.722609 0.722609i 0.246527 0.969136i \(-0.420711\pi\)
−0.969136 + 0.246527i \(0.920711\pi\)
\(6\) 0.848646 5.93968i 0.141441 0.989947i
\(7\) 12.2792i 1.75417i 0.480338 + 0.877083i \(0.340514\pi\)
−0.480338 + 0.877083i \(0.659486\pi\)
\(8\) 6.64572 + 4.45358i 0.830715 + 0.556698i
\(9\) −8.94583 + 0.985948i −0.993981 + 0.109550i
\(10\) −5.67366 8.49955i −0.567366 0.849955i
\(11\) 1.76932 + 1.76932i 0.160847 + 0.160847i 0.782942 0.622095i \(-0.213718\pi\)
−0.622095 + 0.782942i \(0.713718\pi\)
\(12\) 3.98735 11.3182i 0.332279 0.943181i
\(13\) −2.38826 2.38826i −0.183713 0.183713i 0.609259 0.792971i \(-0.291467\pi\)
−0.792971 + 0.609259i \(0.791467\pi\)
\(14\) −4.80199 + 24.0843i −0.342999 + 1.72031i
\(15\) −10.2282 + 11.4174i −0.681881 + 0.761162i
\(16\) 11.2932 + 11.3342i 0.705826 + 0.708385i
\(17\) 20.0754i 1.18091i −0.807072 0.590453i \(-0.798949\pi\)
0.807072 0.590453i \(-0.201051\pi\)
\(18\) −17.9319 1.56460i −0.996215 0.0869220i
\(19\) −8.77090 8.77090i −0.461626 0.461626i 0.437562 0.899188i \(-0.355842\pi\)
−0.899188 + 0.437562i \(0.855842\pi\)
\(20\) −7.80438 18.8898i −0.390219 0.944488i
\(21\) 36.7820 2.02081i 1.75153 0.0962292i
\(22\) 2.77840 + 4.16225i 0.126291 + 0.189193i
\(23\) −13.1821 −0.573134 −0.286567 0.958060i \(-0.592514\pi\)
−0.286567 + 0.958060i \(0.592514\pi\)
\(24\) 12.2469 20.6401i 0.510289 0.860003i
\(25\) 1.10820i 0.0443281i
\(26\) −3.75035 5.61830i −0.144244 0.216088i
\(27\) 4.42563 + 26.6348i 0.163912 + 0.986475i
\(28\) −18.8372 + 45.3609i −0.672756 + 1.62003i
\(29\) −6.51544 + 6.51544i −0.224670 + 0.224670i −0.810462 0.585792i \(-0.800784\pi\)
0.585792 + 0.810462i \(0.300784\pi\)
\(30\) −24.5265 + 18.3941i −0.817551 + 0.613138i
\(31\) 37.5922 1.21265 0.606326 0.795216i \(-0.292643\pi\)
0.606326 + 0.795216i \(0.292643\pi\)
\(32\) 17.7180 + 26.6472i 0.553688 + 0.832724i
\(33\) 5.00877 5.59113i 0.151781 0.169428i
\(34\) 7.85085 39.3758i 0.230907 1.15811i
\(35\) 44.3652 44.3652i 1.26758 1.26758i
\(36\) −34.5596 10.0814i −0.959989 0.280038i
\(37\) 10.0057 10.0057i 0.270423 0.270423i −0.558847 0.829271i \(-0.688756\pi\)
0.829271 + 0.558847i \(0.188756\pi\)
\(38\) −13.7732 20.6332i −0.362452 0.542979i
\(39\) −6.76096 + 7.54704i −0.173358 + 0.193514i
\(40\) −7.92028 40.1023i −0.198007 1.00256i
\(41\) −4.57407 −0.111563 −0.0557814 0.998443i \(-0.517765\pi\)
−0.0557814 + 0.998443i \(0.517765\pi\)
\(42\) 72.9343 + 10.4207i 1.73653 + 0.248111i
\(43\) 21.2835 21.2835i 0.494966 0.494966i −0.414901 0.909867i \(-0.636184\pi\)
0.909867 + 0.414901i \(0.136184\pi\)
\(44\) 3.82182 + 9.25035i 0.0868595 + 0.210235i
\(45\) 35.8840 + 28.7594i 0.797422 + 0.639098i
\(46\) −25.8553 5.15509i −0.562071 0.112067i
\(47\) 54.8366i 1.16674i 0.812208 + 0.583368i \(0.198266\pi\)
−0.812208 + 0.583368i \(0.801734\pi\)
\(48\) 32.0927 35.6939i 0.668599 0.743624i
\(49\) −101.778 −2.07710
\(50\) −0.433383 + 2.17362i −0.00866765 + 0.0434724i
\(51\) −60.1356 + 3.30386i −1.17913 + 0.0647816i
\(52\) −5.15878 12.4863i −0.0992073 0.240122i
\(53\) 21.5215 + 21.5215i 0.406065 + 0.406065i 0.880364 0.474299i \(-0.157298\pi\)
−0.474299 + 0.880364i \(0.657298\pi\)
\(54\) −1.73563 + 53.9721i −0.0321412 + 0.999483i
\(55\) 12.7852i 0.232459i
\(56\) −54.6863 + 81.6039i −0.976541 + 1.45721i
\(57\) −24.8296 + 27.7165i −0.435607 + 0.486255i
\(58\) −15.3273 + 10.2314i −0.264264 + 0.176403i
\(59\) −53.6617 53.6617i −0.909520 0.909520i 0.0867132 0.996233i \(-0.472364\pi\)
−0.996233 + 0.0867132i \(0.972364\pi\)
\(60\) −55.2996 + 26.4866i −0.921659 + 0.441444i
\(61\) −19.2186 19.2186i −0.315059 0.315059i 0.531807 0.846866i \(-0.321513\pi\)
−0.846866 + 0.531807i \(0.821513\pi\)
\(62\) 73.7331 + 14.7011i 1.18924 + 0.237115i
\(63\) −12.1066 109.847i −0.192169 1.74361i
\(64\) 24.3312 + 59.1945i 0.380174 + 0.924915i
\(65\) 17.2578i 0.265505i
\(66\) 12.0107 9.00765i 0.181980 0.136479i
\(67\) 31.5603 + 31.5603i 0.471049 + 0.471049i 0.902254 0.431205i \(-0.141911\pi\)
−0.431205 + 0.902254i \(0.641911\pi\)
\(68\) 30.7972 74.1612i 0.452900 1.09061i
\(69\) 2.16941 + 39.4867i 0.0314407 + 0.572271i
\(70\) 104.367 69.6678i 1.49096 0.995254i
\(71\) −65.1220 −0.917211 −0.458606 0.888640i \(-0.651651\pi\)
−0.458606 + 0.888640i \(0.651651\pi\)
\(72\) −63.8425 33.2887i −0.886701 0.462343i
\(73\) 50.2451i 0.688290i 0.938917 + 0.344145i \(0.111831\pi\)
−0.938917 + 0.344145i \(0.888169\pi\)
\(74\) 23.5379 15.7121i 0.318080 0.212326i
\(75\) 3.31960 0.182380i 0.0442614 0.00243173i
\(76\) −18.9456 45.8561i −0.249284 0.603369i
\(77\) −21.7257 + 21.7257i −0.282152 + 0.282152i
\(78\) −16.2123 + 12.1587i −0.207850 + 0.155881i
\(79\) 20.9299 0.264935 0.132468 0.991187i \(-0.457710\pi\)
0.132468 + 0.991187i \(0.457710\pi\)
\(80\) 0.147933 81.7538i 0.00184916 1.02192i
\(81\) 79.0558 17.6403i 0.975998 0.217781i
\(82\) −8.97156 1.78877i −0.109409 0.0218143i
\(83\) −6.35791 + 6.35791i −0.0766013 + 0.0766013i −0.744369 0.667768i \(-0.767250\pi\)
0.667768 + 0.744369i \(0.267250\pi\)
\(84\) 138.978 + 48.9613i 1.65450 + 0.582873i
\(85\) −72.5334 + 72.5334i −0.853334 + 0.853334i
\(86\) 50.0687 33.4221i 0.582194 0.388629i
\(87\) 20.5891 + 18.4446i 0.236657 + 0.212007i
\(88\) 3.87858 + 19.6382i 0.0440747 + 0.223161i
\(89\) 166.399 1.86966 0.934828 0.355102i \(-0.115554\pi\)
0.934828 + 0.355102i \(0.115554\pi\)
\(90\) 59.1357 + 70.4416i 0.657064 + 0.782685i
\(91\) 29.3259 29.3259i 0.322262 0.322262i
\(92\) −48.6964 20.2223i −0.529308 0.219808i
\(93\) −6.18664 112.607i −0.0665231 1.21083i
\(94\) −21.4449 + 107.556i −0.228137 + 1.14422i
\(95\) 63.3793i 0.667151i
\(96\) 76.9052 57.4594i 0.801096 0.598536i
\(97\) 139.213 1.43519 0.717593 0.696463i \(-0.245244\pi\)
0.717593 + 0.696463i \(0.245244\pi\)
\(98\) −199.627 39.8021i −2.03701 0.406144i
\(99\) −17.5725 14.0835i −0.177500 0.142258i
\(100\) −1.70007 + 4.09385i −0.0170007 + 0.0409385i
\(101\) −125.879 125.879i −1.24632 1.24632i −0.957331 0.288994i \(-0.906679\pi\)
−0.288994 0.957331i \(-0.593321\pi\)
\(102\) −119.242 17.0369i −1.16903 0.167029i
\(103\) 26.3937i 0.256250i −0.991758 0.128125i \(-0.959104\pi\)
0.991758 0.128125i \(-0.0408958\pi\)
\(104\) −5.23539 26.5081i −0.0503403 0.254885i
\(105\) −140.196 125.594i −1.33520 1.19613i
\(106\) 33.7957 + 50.6284i 0.318828 + 0.477627i
\(107\) 83.9534 + 83.9534i 0.784611 + 0.784611i 0.980605 0.195994i \(-0.0627933\pi\)
−0.195994 + 0.980605i \(0.562793\pi\)
\(108\) −24.5110 + 105.182i −0.226954 + 0.973906i
\(109\) 2.29518 + 2.29518i 0.0210567 + 0.0210567i 0.717557 0.696500i \(-0.245260\pi\)
−0.696500 + 0.717557i \(0.745260\pi\)
\(110\) 4.99990 25.0769i 0.0454536 0.227972i
\(111\) −31.6184 28.3251i −0.284851 0.255181i
\(112\) −139.174 + 138.671i −1.24263 + 1.23814i
\(113\) 177.630i 1.57195i 0.618260 + 0.785974i \(0.287838\pi\)
−0.618260 + 0.785974i \(0.712162\pi\)
\(114\) −59.5397 + 44.6529i −0.522278 + 0.391692i
\(115\) 47.6275 + 47.6275i 0.414152 + 0.414152i
\(116\) −34.0641 + 14.0737i −0.293656 + 0.121325i
\(117\) 23.7197 + 19.0103i 0.202733 + 0.162481i
\(118\) −84.2663 126.237i −0.714122 1.06981i
\(119\) 246.509 2.07151
\(120\) −118.822 + 30.3248i −0.990186 + 0.252707i
\(121\) 114.739i 0.948257i
\(122\) −30.1794 45.2110i −0.247372 0.370582i
\(123\) 0.752766 + 13.7016i 0.00612005 + 0.111395i
\(124\) 138.871 + 57.6693i 1.11992 + 0.465075i
\(125\) −86.3222 + 86.3222i −0.690577 + 0.690577i
\(126\) 19.2119 220.188i 0.152476 1.74753i
\(127\) −152.167 −1.19816 −0.599082 0.800687i \(-0.704468\pi\)
−0.599082 + 0.800687i \(0.704468\pi\)
\(128\) 24.5739 + 125.619i 0.191984 + 0.981398i
\(129\) −67.2571 60.2517i −0.521373 0.467068i
\(130\) −6.74898 + 33.8494i −0.0519152 + 0.260380i
\(131\) −65.6955 + 65.6955i −0.501492 + 0.501492i −0.911901 0.410409i \(-0.865386\pi\)
0.410409 + 0.911901i \(0.365386\pi\)
\(132\) 27.0803 12.9705i 0.205154 0.0982617i
\(133\) 107.699 107.699i 0.809769 0.809769i
\(134\) 49.5599 + 74.2443i 0.369850 + 0.554062i
\(135\) 80.2428 112.223i 0.594391 0.831280i
\(136\) 89.4076 133.416i 0.657409 0.980997i
\(137\) 53.1509 0.387963 0.193982 0.981005i \(-0.437860\pi\)
0.193982 + 0.981005i \(0.437860\pi\)
\(138\) −11.1869 + 78.2974i −0.0810647 + 0.567372i
\(139\) −161.324 + 161.324i −1.16060 + 1.16060i −0.176261 + 0.984343i \(0.556400\pi\)
−0.984343 + 0.176261i \(0.943600\pi\)
\(140\) 231.950 95.8313i 1.65679 0.684509i
\(141\) 164.262 9.02460i 1.16498 0.0640043i
\(142\) −127.730 25.4671i −0.899506 0.179346i
\(143\) 8.45118i 0.0590992i
\(144\) −112.202 90.2590i −0.779181 0.626798i
\(145\) 47.0811 0.324698
\(146\) −19.6493 + 98.5505i −0.134584 + 0.675004i
\(147\) 16.7498 + 304.874i 0.113945 + 2.07397i
\(148\) 52.3117 21.6128i 0.353457 0.146032i
\(149\) −116.911 116.911i −0.784638 0.784638i 0.195971 0.980610i \(-0.437214\pi\)
−0.980610 + 0.195971i \(0.937214\pi\)
\(150\) 6.58237 + 0.940472i 0.0438825 + 0.00626981i
\(151\) 10.9723i 0.0726643i −0.999340 0.0363321i \(-0.988433\pi\)
0.999340 0.0363321i \(-0.0115674\pi\)
\(152\) −19.2270 97.3509i −0.126493 0.640466i
\(153\) 19.7933 + 179.591i 0.129368 + 1.17380i
\(154\) −51.1089 + 34.1165i −0.331876 + 0.221535i
\(155\) −135.822 135.822i −0.876273 0.876273i
\(156\) −36.5536 + 17.5079i −0.234318 + 0.112230i
\(157\) 49.8246 + 49.8246i 0.317354 + 0.317354i 0.847750 0.530396i \(-0.177957\pi\)
−0.530396 + 0.847750i \(0.677957\pi\)
\(158\) 41.0517 + 8.18501i 0.259821 + 0.0518038i
\(159\) 60.9253 68.0090i 0.383178 0.427730i
\(160\) 32.2614 160.293i 0.201634 1.00183i
\(161\) 161.865i 1.00537i
\(162\) 161.958 3.68329i 0.999741 0.0227363i
\(163\) −66.4240 66.4240i −0.407509 0.407509i 0.473360 0.880869i \(-0.343041\pi\)
−0.880869 + 0.473360i \(0.843041\pi\)
\(164\) −16.8972 7.01698i −0.103032 0.0427864i
\(165\) −38.2980 + 2.10410i −0.232109 + 0.0127521i
\(166\) −14.9567 + 9.98399i −0.0901008 + 0.0601445i
\(167\) −182.851 −1.09492 −0.547459 0.836832i \(-0.684405\pi\)
−0.547459 + 0.836832i \(0.684405\pi\)
\(168\) 253.443 + 150.382i 1.50859 + 0.895132i
\(169\) 157.592i 0.932499i
\(170\) −170.632 + 113.901i −1.00372 + 0.670006i
\(171\) 87.1106 + 69.8153i 0.509419 + 0.408277i
\(172\) 111.275 45.9736i 0.646946 0.267288i
\(173\) 123.809 123.809i 0.715661 0.715661i −0.252052 0.967714i \(-0.581106\pi\)
0.967714 + 0.252052i \(0.0811056\pi\)
\(174\) 33.1703 + 44.2289i 0.190634 + 0.254189i
\(175\) −13.6078 −0.0777589
\(176\) −0.0724429 + 40.0350i −0.000411608 + 0.227471i
\(177\) −151.911 + 169.574i −0.858257 + 0.958045i
\(178\) 326.375 + 65.0734i 1.83357 + 0.365581i
\(179\) 168.642 168.642i 0.942134 0.942134i −0.0562807 0.998415i \(-0.517924\pi\)
0.998415 + 0.0562807i \(0.0179242\pi\)
\(180\) 88.4410 + 161.290i 0.491339 + 0.896055i
\(181\) −162.162 + 162.162i −0.895920 + 0.895920i −0.995072 0.0991520i \(-0.968387\pi\)
0.0991520 + 0.995072i \(0.468387\pi\)
\(182\) 68.9880 46.0512i 0.379055 0.253029i
\(183\) −54.4061 + 60.7318i −0.297301 + 0.331868i
\(184\) −87.6045 58.7076i −0.476111 0.319063i
\(185\) −72.3018 −0.390821
\(186\) 31.9025 223.286i 0.171519 1.20046i
\(187\) 35.5198 35.5198i 0.189945 0.189945i
\(188\) −84.1236 + 202.574i −0.447466 + 1.07752i
\(189\) −327.053 + 54.3430i −1.73044 + 0.287529i
\(190\) −24.7856 + 124.312i −0.130451 + 0.654273i
\(191\) 60.8777i 0.318731i 0.987220 + 0.159366i \(0.0509449\pi\)
−0.987220 + 0.159366i \(0.949055\pi\)
\(192\) 173.312 82.6254i 0.902667 0.430340i
\(193\) 177.871 0.921611 0.460806 0.887501i \(-0.347561\pi\)
0.460806 + 0.887501i \(0.347561\pi\)
\(194\) 273.052 + 54.4418i 1.40748 + 0.280628i
\(195\) 51.6955 2.84016i 0.265105 0.0145649i
\(196\) −375.981 156.135i −1.91827 0.796608i
\(197\) 66.9411 + 66.9411i 0.339803 + 0.339803i 0.856293 0.516490i \(-0.172762\pi\)
−0.516490 + 0.856293i \(0.672762\pi\)
\(198\) −28.9589 34.4954i −0.146257 0.174219i
\(199\) 0.826328i 0.00415240i −0.999998 0.00207620i \(-0.999339\pi\)
0.999998 0.00207620i \(-0.000660875\pi\)
\(200\) −4.93548 + 7.36480i −0.0246774 + 0.0368240i
\(201\) 89.3443 99.7322i 0.444499 0.496180i
\(202\) −197.671 296.125i −0.978568 1.46597i
\(203\) −80.0041 80.0041i −0.394109 0.394109i
\(204\) −227.217 80.0477i −1.11381 0.392391i
\(205\) 16.5263 + 16.5263i 0.0806162 + 0.0806162i
\(206\) 10.3217 51.7685i 0.0501055 0.251303i
\(207\) 117.925 12.9969i 0.569685 0.0627868i
\(208\) 0.0977852 54.0401i 0.000470121 0.259808i
\(209\) 31.0370i 0.148502i
\(210\) −225.865 301.165i −1.07555 1.43412i
\(211\) −181.344 181.344i −0.859448 0.859448i 0.131825 0.991273i \(-0.457916\pi\)
−0.991273 + 0.131825i \(0.957916\pi\)
\(212\) 46.4876 + 112.519i 0.219281 + 0.530749i
\(213\) 10.7173 + 195.072i 0.0503159 + 0.915830i
\(214\) 131.834 + 197.497i 0.616048 + 0.922884i
\(215\) −153.797 −0.715333
\(216\) −89.2090 + 196.717i −0.413004 + 0.910729i
\(217\) 461.601i 2.12719i
\(218\) 3.60419 + 5.39933i 0.0165330 + 0.0247676i
\(219\) 150.508 8.26897i 0.687253 0.0377579i
\(220\) 19.6135 47.2303i 0.0891524 0.214683i
\(221\) −47.9454 + 47.9454i −0.216947 + 0.216947i
\(222\) −50.9392 67.9217i −0.229456 0.305953i
\(223\) −17.7339 −0.0795241 −0.0397621 0.999209i \(-0.512660\pi\)
−0.0397621 + 0.999209i \(0.512660\pi\)
\(224\) −327.205 + 217.563i −1.46074 + 0.971261i
\(225\) −1.09263 9.91380i −0.00485614 0.0440613i
\(226\) −69.4654 + 348.402i −0.307369 + 1.54160i
\(227\) 7.53766 7.53766i 0.0332055 0.0332055i −0.690309 0.723515i \(-0.742525\pi\)
0.723515 + 0.690309i \(0.242525\pi\)
\(228\) −134.243 + 64.2979i −0.588786 + 0.282008i
\(229\) 223.748 223.748i 0.977063 0.977063i −0.0226794 0.999743i \(-0.507220\pi\)
0.999743 + 0.0226794i \(0.00721971\pi\)
\(230\) 74.7907 + 112.042i 0.325177 + 0.487139i
\(231\) 68.6545 + 61.5036i 0.297205 + 0.266249i
\(232\) −72.3168 + 14.2827i −0.311710 + 0.0615634i
\(233\) −123.585 −0.530406 −0.265203 0.964193i \(-0.585439\pi\)
−0.265203 + 0.964193i \(0.585439\pi\)
\(234\) 39.0894 + 46.5627i 0.167049 + 0.198986i
\(235\) 198.127 198.127i 0.843095 0.843095i
\(236\) −115.912 280.554i −0.491153 1.18879i
\(237\) −3.44448 62.6951i −0.0145337 0.264536i
\(238\) 483.502 + 96.4019i 2.03152 + 0.405050i
\(239\) 118.501i 0.495820i −0.968783 0.247910i \(-0.920256\pi\)
0.968783 0.247910i \(-0.0797437\pi\)
\(240\) −244.916 + 13.0113i −1.02048 + 0.0542137i
\(241\) −264.162 −1.09611 −0.548053 0.836443i \(-0.684631\pi\)
−0.548053 + 0.836443i \(0.684631\pi\)
\(242\) 44.8708 225.048i 0.185416 0.929952i
\(243\) −65.8515 233.907i −0.270994 0.962581i
\(244\) −41.5132 100.479i −0.170136 0.411798i
\(245\) 367.728 + 367.728i 1.50093 + 1.50093i
\(246\) −3.88177 + 27.1685i −0.0157795 + 0.110441i
\(247\) 41.8944i 0.169613i
\(248\) 249.827 + 167.420i 1.00737 + 0.675081i
\(249\) 20.0913 + 17.9987i 0.0806881 + 0.0722838i
\(250\) −203.070 + 135.554i −0.812278 + 0.542216i
\(251\) 152.477 + 152.477i 0.607478 + 0.607478i 0.942286 0.334808i \(-0.108672\pi\)
−0.334808 + 0.942286i \(0.608672\pi\)
\(252\) 123.791 424.363i 0.491233 1.68398i
\(253\) −23.3233 23.3233i −0.0921869 0.0921869i
\(254\) −298.459 59.5076i −1.17504 0.234282i
\(255\) 229.210 + 205.336i 0.898861 + 0.805238i
\(256\) −0.926457 + 255.998i −0.00361897 + 0.999993i
\(257\) 113.118i 0.440147i −0.975483 0.220074i \(-0.929370\pi\)
0.975483 0.220074i \(-0.0706298\pi\)
\(258\) −108.355 144.479i −0.419981 0.559998i
\(259\) 122.861 + 122.861i 0.474367 + 0.474367i
\(260\) −26.4748 + 63.7526i −0.101826 + 0.245202i
\(261\) 51.8621 64.7099i 0.198705 0.247931i
\(262\) −154.546 + 103.163i −0.589871 + 0.393753i
\(263\) 129.324 0.491727 0.245864 0.969304i \(-0.420928\pi\)
0.245864 + 0.969304i \(0.420928\pi\)
\(264\) 58.1875 14.8501i 0.220407 0.0562504i
\(265\) 155.516i 0.586853i
\(266\) 253.359 169.123i 0.952476 0.635801i
\(267\) −27.3848 498.446i −0.102565 1.86684i
\(268\) 68.1719 + 165.004i 0.254373 + 0.615685i
\(269\) 129.457 129.457i 0.481253 0.481253i −0.424278 0.905532i \(-0.639472\pi\)
0.905532 + 0.424278i \(0.139472\pi\)
\(270\) 201.275 188.733i 0.745461 0.699010i
\(271\) 170.727 0.629990 0.314995 0.949093i \(-0.397997\pi\)
0.314995 + 0.949093i \(0.397997\pi\)
\(272\) 227.538 226.716i 0.836537 0.833515i
\(273\) −92.6714 83.0189i −0.339456 0.304099i
\(274\) 104.250 + 20.7856i 0.380474 + 0.0758600i
\(275\) −1.96076 + 1.96076i −0.00713004 + 0.00713004i
\(276\) −52.5616 + 149.197i −0.190440 + 0.540570i
\(277\) 114.051 114.051i 0.411737 0.411737i −0.470606 0.882343i \(-0.655965\pi\)
0.882343 + 0.470606i \(0.155965\pi\)
\(278\) −379.509 + 253.331i −1.36514 + 0.911264i
\(279\) −336.294 + 37.0640i −1.20535 + 0.132846i
\(280\) 492.423 97.2544i 1.75865 0.347337i
\(281\) 136.468 0.485650 0.242825 0.970070i \(-0.421926\pi\)
0.242825 + 0.970070i \(0.421926\pi\)
\(282\) 325.712 + 46.5369i 1.15501 + 0.165024i
\(283\) −132.657 + 132.657i −0.468752 + 0.468752i −0.901510 0.432758i \(-0.857540\pi\)
0.432758 + 0.901510i \(0.357540\pi\)
\(284\) −240.569 99.9021i −0.847075 0.351768i
\(285\) 189.852 10.4305i 0.666146 0.0365982i
\(286\) 3.30499 16.5761i 0.0115559 0.0579584i
\(287\) 56.1658i 0.195700i
\(288\) −184.775 220.912i −0.641580 0.767056i
\(289\) −114.022 −0.394541
\(290\) 92.3447 + 18.4119i 0.318430 + 0.0634894i
\(291\) −22.9106 417.010i −0.0787307 1.43303i
\(292\) −77.0799 + 185.612i −0.263972 + 0.635658i
\(293\) −143.968 143.968i −0.491360 0.491360i 0.417375 0.908735i \(-0.362950\pi\)
−0.908735 + 0.417375i \(0.862950\pi\)
\(294\) −86.3734 + 604.528i −0.293787 + 2.05622i
\(295\) 387.764i 1.31446i
\(296\) 111.056 21.9337i 0.375189 0.0741005i
\(297\) −39.2951 + 54.9557i −0.132307 + 0.185036i
\(298\) −183.589 275.029i −0.616069 0.922916i
\(299\) 31.4823 + 31.4823i 0.105292 + 0.105292i
\(300\) 12.5428 + 4.41879i 0.0418094 + 0.0147293i
\(301\) 261.344 + 261.344i 0.868252 + 0.868252i
\(302\) 4.29092 21.5210i 0.0142083 0.0712617i
\(303\) −356.352 + 397.784i −1.17608 + 1.31282i
\(304\) 0.359116 198.462i 0.00118130 0.652837i
\(305\) 138.875i 0.455328i
\(306\) −31.4099 + 359.990i −0.102647 + 1.17644i
\(307\) −89.3258 89.3258i −0.290964 0.290964i 0.546497 0.837461i \(-0.315961\pi\)
−0.837461 + 0.546497i \(0.815961\pi\)
\(308\) −113.587 + 46.9288i −0.368788 + 0.152366i
\(309\) −79.0619 + 4.34368i −0.255864 + 0.0140572i
\(310\) −213.285 319.517i −0.688017 1.03070i
\(311\) −314.507 −1.01128 −0.505638 0.862746i \(-0.668743\pi\)
−0.505638 + 0.862746i \(0.668743\pi\)
\(312\) −78.5428 + 20.0450i −0.251740 + 0.0642469i
\(313\) 103.874i 0.331867i 0.986137 + 0.165934i \(0.0530638\pi\)
−0.986137 + 0.165934i \(0.946936\pi\)
\(314\) 78.2408 + 117.210i 0.249175 + 0.373281i
\(315\) −353.142 + 440.625i −1.12108 + 1.39881i
\(316\) 77.3178 + 32.1080i 0.244676 + 0.101608i
\(317\) −321.109 + 321.109i −1.01296 + 1.01296i −0.0130482 + 0.999915i \(0.504153\pi\)
−0.999915 + 0.0130482i \(0.995847\pi\)
\(318\) 146.095 109.567i 0.459417 0.344549i
\(319\) −23.0557 −0.0722750
\(320\) 125.963 301.782i 0.393634 0.943069i
\(321\) 237.665 265.297i 0.740388 0.826472i
\(322\) 63.3002 317.481i 0.196585 0.985966i
\(323\) −176.079 + 176.079i −0.545138 + 0.545138i
\(324\) 319.104 + 56.1123i 0.984889 + 0.173186i
\(325\) 2.64668 2.64668i 0.00814363 0.00814363i
\(326\) −104.307 156.260i −0.319961 0.479325i
\(327\) 6.49746 7.25291i 0.0198699 0.0221801i
\(328\) −30.3980 20.3710i −0.0926768 0.0621068i
\(329\) −673.348 −2.04665
\(330\) −75.9402 10.8501i −0.230122 0.0328792i
\(331\) −313.858 + 313.858i −0.948213 + 0.948213i −0.998724 0.0505107i \(-0.983915\pi\)
0.0505107 + 0.998724i \(0.483915\pi\)
\(332\) −33.2405 + 13.7334i −0.100122 + 0.0413658i
\(333\) −79.6439 + 99.3740i −0.239171 + 0.298420i
\(334\) −358.643 71.5073i −1.07378 0.214094i
\(335\) 228.057i 0.680768i
\(336\) 438.292 + 394.072i 1.30444 + 1.17283i
\(337\) −236.028 −0.700380 −0.350190 0.936679i \(-0.613883\pi\)
−0.350190 + 0.936679i \(0.613883\pi\)
\(338\) 61.6293 309.101i 0.182335 0.914499i
\(339\) 532.088 29.2330i 1.56958 0.0862331i
\(340\) −379.220 + 156.676i −1.11535 + 0.460812i
\(341\) 66.5125 + 66.5125i 0.195051 + 0.195051i
\(342\) 143.556 + 171.002i 0.419754 + 0.500004i
\(343\) 648.069i 1.88941i
\(344\) 236.232 46.6563i 0.686722 0.135629i
\(345\) 134.829 150.506i 0.390809 0.436248i
\(346\) 291.257 194.421i 0.841783 0.561911i
\(347\) 441.946 + 441.946i 1.27362 + 1.27362i 0.944175 + 0.329445i \(0.106862\pi\)
0.329445 + 0.944175i \(0.393138\pi\)
\(348\) 47.7635 + 99.7221i 0.137252 + 0.286558i
\(349\) −476.643 476.643i −1.36574 1.36574i −0.866417 0.499321i \(-0.833583\pi\)
−0.499321 0.866417i \(-0.666417\pi\)
\(350\) −26.6903 5.32158i −0.0762579 0.0152045i
\(351\) 53.0414 74.1805i 0.151115 0.211341i
\(352\) −15.7985 + 78.4960i −0.0448821 + 0.223000i
\(353\) 452.246i 1.28115i −0.767895 0.640575i \(-0.778696\pi\)
0.767895 0.640575i \(-0.221304\pi\)
\(354\) −364.273 + 273.194i −1.02902 + 0.771733i
\(355\) 235.289 + 235.289i 0.662785 + 0.662785i
\(356\) 614.701 + 255.269i 1.72669 + 0.717049i
\(357\) −40.5687 738.415i −0.113638 2.06839i
\(358\) 396.724 264.823i 1.10817 0.739729i
\(359\) 617.295 1.71948 0.859742 0.510728i \(-0.170624\pi\)
0.859742 + 0.510728i \(0.170624\pi\)
\(360\) 110.392 + 350.939i 0.306645 + 0.974832i
\(361\) 207.143i 0.573803i
\(362\) −381.479 + 254.647i −1.05381 + 0.703443i
\(363\) −343.699 + 18.8829i −0.946829 + 0.0520190i
\(364\) 153.322 63.3455i 0.421214 0.174026i
\(365\) 181.538 181.538i 0.497364 0.497364i
\(366\) −130.462 + 97.8424i −0.356453 + 0.267329i
\(367\) −11.3588 −0.0309505 −0.0154753 0.999880i \(-0.504926\pi\)
−0.0154753 + 0.999880i \(0.504926\pi\)
\(368\) −148.868 149.408i −0.404533 0.406000i
\(369\) 40.9189 4.50980i 0.110891 0.0122217i
\(370\) −141.812 28.2749i −0.383277 0.0764187i
\(371\) −264.266 + 264.266i −0.712306 + 0.712306i
\(372\) 149.893 425.475i 0.402939 1.14375i
\(373\) −59.4092 + 59.4092i −0.159274 + 0.159274i −0.782245 0.622971i \(-0.785925\pi\)
0.622971 + 0.782245i \(0.285925\pi\)
\(374\) 83.5589 55.7776i 0.223419 0.149138i
\(375\) 272.783 + 244.370i 0.727421 + 0.651654i
\(376\) −244.220 + 364.429i −0.649520 + 0.969226i
\(377\) 31.1212 0.0825495
\(378\) −662.732 21.3120i −1.75326 0.0563810i
\(379\) 435.432 435.432i 1.14890 1.14890i 0.162129 0.986770i \(-0.448164\pi\)
0.986770 0.162129i \(-0.0518359\pi\)
\(380\) −97.2287 + 234.132i −0.255865 + 0.616136i
\(381\) 25.0425 + 455.813i 0.0657283 + 1.19636i
\(382\) −23.8073 + 119.405i −0.0623228 + 0.312579i
\(383\) 272.117i 0.710488i 0.934774 + 0.355244i \(0.115602\pi\)
−0.934774 + 0.355244i \(0.884398\pi\)
\(384\) 372.245 94.2841i 0.969389 0.245532i
\(385\) 156.992 0.407772
\(386\) 348.875 + 69.5596i 0.903821 + 0.180206i
\(387\) −169.414 + 211.383i −0.437763 + 0.546210i
\(388\) 514.271 + 213.563i 1.32544 + 0.550421i
\(389\) 260.985 + 260.985i 0.670913 + 0.670913i 0.957927 0.287013i \(-0.0926623\pi\)
−0.287013 + 0.957927i \(0.592662\pi\)
\(390\) 102.506 + 14.6458i 0.262836 + 0.0375533i
\(391\) 264.636i 0.676818i
\(392\) −676.387 453.277i −1.72548 1.15632i
\(393\) 207.601 + 185.978i 0.528248 + 0.473226i
\(394\) 105.119 + 157.476i 0.266800 + 0.399686i
\(395\) −75.6206 75.6206i −0.191445 0.191445i
\(396\) −43.3097 78.9840i −0.109368 0.199454i
\(397\) 258.248 + 258.248i 0.650500 + 0.650500i 0.953113 0.302614i \(-0.0978592\pi\)
−0.302614 + 0.953113i \(0.597859\pi\)
\(398\) 0.323150 1.62075i 0.000811935 0.00407225i
\(399\) −340.336 304.887i −0.852972 0.764128i
\(400\) −12.5605 + 12.5152i −0.0314014 + 0.0312879i
\(401\) 430.073i 1.07250i 0.844059 + 0.536250i \(0.180160\pi\)
−0.844059 + 0.536250i \(0.819840\pi\)
\(402\) 214.241 160.674i 0.532939 0.399688i
\(403\) −89.7801 89.7801i −0.222779 0.222779i
\(404\) −271.905 658.121i −0.673033 1.62901i
\(405\) −349.367 221.897i −0.862635 0.547894i
\(406\) −125.633 188.207i −0.309440 0.463563i
\(407\) 35.4063 0.0869935
\(408\) −414.358 245.862i −1.01558 0.602604i
\(409\) 207.501i 0.507337i −0.967291 0.253668i \(-0.918363\pi\)
0.967291 0.253668i \(-0.0816372\pi\)
\(410\) 25.9517 + 38.8776i 0.0632969 + 0.0948233i
\(411\) −8.74718 159.213i −0.0212827 0.387379i
\(412\) 40.4900 97.5019i 0.0982767 0.236655i
\(413\) 658.921 658.921i 1.59545 1.59545i
\(414\) 236.380 + 20.6246i 0.570965 + 0.0498180i
\(415\) 45.9428 0.110706
\(416\) 21.3252 105.956i 0.0512624 0.254701i
\(417\) 509.793 + 456.694i 1.22253 + 1.09519i
\(418\) 12.1376 60.8757i 0.0290372 0.145636i
\(419\) −108.717 + 108.717i −0.259467 + 0.259467i −0.824837 0.565370i \(-0.808733\pi\)
0.565370 + 0.824837i \(0.308733\pi\)
\(420\) −325.234 679.032i −0.774366 1.61674i
\(421\) −484.985 + 484.985i −1.15198 + 1.15198i −0.165829 + 0.986155i \(0.553030\pi\)
−0.986155 + 0.165829i \(0.946970\pi\)
\(422\) −284.768 426.604i −0.674807 1.01091i
\(423\) −54.0661 490.559i −0.127816 1.15971i
\(424\) 47.1779 + 238.873i 0.111269 + 0.563380i
\(425\) 22.2476 0.0523474
\(426\) −55.2655 + 386.804i −0.129731 + 0.907990i
\(427\) 235.988 235.988i 0.552665 0.552665i
\(428\) 181.344 + 438.926i 0.423701 + 1.02553i
\(429\) −25.3154 + 1.39083i −0.0590102 + 0.00324203i
\(430\) −301.656 60.1450i −0.701525 0.139872i
\(431\) 213.570i 0.495522i −0.968821 0.247761i \(-0.920305\pi\)
0.968821 0.247761i \(-0.0796947\pi\)
\(432\) −251.904 + 350.954i −0.583111 + 0.812393i
\(433\) 440.669 1.01771 0.508856 0.860852i \(-0.330069\pi\)
0.508856 + 0.860852i \(0.330069\pi\)
\(434\) −180.517 + 905.381i −0.415939 + 2.08613i
\(435\) −7.74826 141.031i −0.0178121 0.324209i
\(436\) 4.95772 + 11.9997i 0.0113709 + 0.0275222i
\(437\) 115.619 + 115.619i 0.264574 + 0.264574i
\(438\) 298.440 + 42.6403i 0.681370 + 0.0973523i
\(439\) 400.367i 0.911998i 0.889980 + 0.455999i \(0.150718\pi\)
−0.889980 + 0.455999i \(0.849282\pi\)
\(440\) 56.9401 84.9671i 0.129409 0.193107i
\(441\) 910.488 100.348i 2.06460 0.227546i
\(442\) −112.790 + 75.2899i −0.255180 + 0.170339i
\(443\) −324.076 324.076i −0.731549 0.731549i 0.239378 0.970926i \(-0.423057\pi\)
−0.970926 + 0.239378i \(0.923057\pi\)
\(444\) −73.3498 153.142i −0.165202 0.344914i
\(445\) −601.208 601.208i −1.35103 1.35103i
\(446\) −34.7831 6.93515i −0.0779891 0.0155497i
\(447\) −330.965 + 369.446i −0.740414 + 0.826500i
\(448\) −726.860 + 298.766i −1.62245 + 0.666889i
\(449\) 691.918i 1.54102i 0.637427 + 0.770510i \(0.279999\pi\)
−0.637427 + 0.770510i \(0.720001\pi\)
\(450\) 1.73389 19.8722i 0.00385309 0.0441603i
\(451\) −8.09298 8.09298i −0.0179445 0.0179445i
\(452\) −272.498 + 656.189i −0.602872 + 1.45174i
\(453\) −32.8674 + 1.80574i −0.0725549 + 0.00398618i
\(454\) 17.7321 11.8366i 0.0390574 0.0260718i
\(455\) −211.912 −0.465740
\(456\) −288.449 + 73.6154i −0.632563 + 0.161437i
\(457\) 385.436i 0.843404i −0.906734 0.421702i \(-0.861433\pi\)
0.906734 0.421702i \(-0.138567\pi\)
\(458\) 526.357 351.357i 1.14925 0.767154i
\(459\) 534.705 88.8463i 1.16494 0.193565i
\(460\) 102.878 + 249.006i 0.223648 + 0.541318i
\(461\) −312.070 + 312.070i −0.676942 + 0.676942i −0.959307 0.282365i \(-0.908881\pi\)
0.282365 + 0.959307i \(0.408881\pi\)
\(462\) 110.606 + 147.481i 0.239408 + 0.319224i
\(463\) 718.961 1.55283 0.776416 0.630220i \(-0.217035\pi\)
0.776416 + 0.630220i \(0.217035\pi\)
\(464\) −147.427 0.266768i −0.317731 0.000574932i
\(465\) −384.501 + 429.206i −0.826884 + 0.923024i
\(466\) −242.398 48.3300i −0.520168 0.103712i
\(467\) −82.7894 + 82.7894i −0.177279 + 0.177279i −0.790169 0.612889i \(-0.790007\pi\)
0.612889 + 0.790169i \(0.290007\pi\)
\(468\) 58.4605 + 106.614i 0.124916 + 0.227809i
\(469\) −387.534 + 387.534i −0.826298 + 0.826298i
\(470\) 466.087 311.124i 0.991674 0.661967i
\(471\) 141.049 157.448i 0.299467 0.334285i
\(472\) −117.634 595.607i −0.249224 1.26188i
\(473\) 75.3145 0.159227
\(474\) 17.7621 124.317i 0.0374727 0.262272i
\(475\) 9.71993 9.71993i 0.0204630 0.0204630i
\(476\) 910.638 + 378.164i 1.91311 + 0.794463i
\(477\) −213.746 171.308i −0.448106 0.359137i
\(478\) 46.3419 232.427i 0.0969497 0.486249i
\(479\) 749.099i 1.56388i −0.623353 0.781941i \(-0.714230\pi\)
0.623353 0.781941i \(-0.285770\pi\)
\(480\) −485.466 70.2587i −1.01139 0.146372i
\(481\) −47.7923 −0.0993603
\(482\) −518.125 103.305i −1.07495 0.214326i
\(483\) −484.864 + 26.6385i −1.00386 + 0.0551523i
\(484\) 176.018 423.861i 0.363675 0.875746i
\(485\) −502.983 502.983i −1.03708 1.03708i
\(486\) −37.6871 484.537i −0.0775454 0.996989i
\(487\) 533.210i 1.09489i −0.836843 0.547443i \(-0.815601\pi\)
0.836843 0.547443i \(-0.184399\pi\)
\(488\) −42.1297 213.313i −0.0863313 0.437116i
\(489\) −188.040 + 209.904i −0.384541 + 0.429251i
\(490\) 577.453 + 865.067i 1.17848 + 1.76544i
\(491\) −6.75013 6.75013i −0.0137477 0.0137477i 0.700200 0.713947i \(-0.253094\pi\)
−0.713947 + 0.700200i \(0.753094\pi\)
\(492\) −18.2384 + 51.7701i −0.0370699 + 0.105224i
\(493\) 130.800 + 130.800i 0.265315 + 0.265315i
\(494\) −16.3836 + 82.1715i −0.0331651 + 0.166339i
\(495\) 12.6056 + 114.375i 0.0254658 + 0.231060i
\(496\) 424.537 + 426.076i 0.855921 + 0.859025i
\(497\) 799.644i 1.60894i
\(498\) 32.3683 + 43.1596i 0.0649967 + 0.0866658i
\(499\) 556.347 + 556.347i 1.11492 + 1.11492i 0.992475 + 0.122448i \(0.0390746\pi\)
0.122448 + 0.992475i \(0.460925\pi\)
\(500\) −451.310 + 186.461i −0.902620 + 0.372921i
\(501\) 30.0923 + 547.728i 0.0600645 + 1.09327i
\(502\) 239.439 + 358.696i 0.476969 + 0.714534i
\(503\) 304.892 0.606147 0.303074 0.952967i \(-0.401987\pi\)
0.303074 + 0.952967i \(0.401987\pi\)
\(504\) 408.757 783.933i 0.811026 1.55542i
\(505\) 909.612i 1.80121i
\(506\) −36.6251 54.8671i −0.0723817 0.108433i
\(507\) −472.065 + 25.9354i −0.931095 + 0.0511546i
\(508\) −562.125 233.436i −1.10654 0.459519i
\(509\) −118.591 + 118.591i −0.232988 + 0.232988i −0.813939 0.580951i \(-0.802681\pi\)
0.580951 + 0.813939i \(0.302681\pi\)
\(510\) 369.270 + 492.380i 0.724059 + 0.965452i
\(511\) −616.968 −1.20737
\(512\) −101.930 + 501.751i −0.199082 + 0.979983i
\(513\) 194.795 272.428i 0.379716 0.531049i
\(514\) 44.2368 221.869i 0.0860638 0.431651i
\(515\) −95.3617 + 95.3617i −0.185168 + 0.185168i
\(516\) −156.026 325.755i −0.302376 0.631309i
\(517\) −97.0233 + 97.0233i −0.187666 + 0.187666i
\(518\) 192.932 + 289.026i 0.372456 + 0.557966i
\(519\) −391.244 350.493i −0.753843 0.675324i
\(520\) −76.8591 + 114.691i −0.147806 + 0.220559i
\(521\) −105.077 −0.201683 −0.100842 0.994902i \(-0.532154\pi\)
−0.100842 + 0.994902i \(0.532154\pi\)
\(522\) 127.028 106.640i 0.243349 0.204291i
\(523\) −479.455 + 479.455i −0.916740 + 0.916740i −0.996791 0.0800507i \(-0.974492\pi\)
0.0800507 + 0.996791i \(0.474492\pi\)
\(524\) −343.470 + 141.906i −0.655476 + 0.270813i
\(525\) 2.23947 + 40.7619i 0.00426566 + 0.0776418i
\(526\) 253.656 + 50.5746i 0.482235 + 0.0961494i
\(527\) 754.679i 1.43203i
\(528\) 119.936 6.37165i 0.227151 0.0120675i
\(529\) −355.232 −0.671517
\(530\) 60.8174 305.028i 0.114750 0.575525i
\(531\) 532.956 + 427.141i 1.00368 + 0.804408i
\(532\) 563.074 232.636i 1.05841 0.437287i
\(533\) 10.9241 + 10.9241i 0.0204955 + 0.0204955i
\(534\) 141.214 988.359i 0.264446 1.85086i
\(535\) 606.655i 1.13393i
\(536\) 69.1843 + 350.297i 0.129075 + 0.653539i
\(537\) −532.918 477.410i −0.992399 0.889032i
\(538\) 304.543 203.290i 0.566065 0.377862i
\(539\) −180.077 180.077i −0.334095 0.334095i
\(540\) 468.586 291.467i 0.867752 0.539754i
\(541\) 726.230 + 726.230i 1.34238 + 1.34238i 0.893680 + 0.448704i \(0.148114\pi\)
0.448704 + 0.893680i \(0.351886\pi\)
\(542\) 334.864 + 66.7660i 0.617829 + 0.123184i
\(543\) 512.439 + 459.065i 0.943719 + 0.845423i
\(544\) 534.953 355.697i 0.983370 0.653854i
\(545\) 16.5852i 0.0304316i
\(546\) −149.299 199.074i −0.273442 0.364604i
\(547\) 314.507 + 314.507i 0.574966 + 0.574966i 0.933512 0.358546i \(-0.116727\pi\)
−0.358546 + 0.933512i \(0.616727\pi\)
\(548\) 196.347 + 81.5376i 0.358297 + 0.148791i
\(549\) 190.875 + 152.978i 0.347677 + 0.278648i
\(550\) −4.61261 + 3.07903i −0.00838657 + 0.00559824i
\(551\) 114.292 0.207427
\(552\) −161.440 + 272.079i −0.292464 + 0.492897i
\(553\) 257.002i 0.464741i
\(554\) 268.301 179.097i 0.484298 0.323281i
\(555\) 11.8989 + 216.579i 0.0214394 + 0.390232i
\(556\) −843.436 + 348.469i −1.51697 + 0.626743i
\(557\) 134.274 134.274i 0.241066 0.241066i −0.576225 0.817291i \(-0.695475\pi\)
0.817291 + 0.576225i \(0.195475\pi\)
\(558\) −674.099 58.8166i −1.20806 0.105406i
\(559\) −101.661 −0.181863
\(560\) 1003.87 + 1.81649i 1.79262 + 0.00324373i
\(561\) −112.244 100.553i −0.200079 0.179239i
\(562\) 267.667 + 53.3681i 0.476275 + 0.0949610i
\(563\) 102.810 102.810i 0.182612 0.182612i −0.609881 0.792493i \(-0.708783\pi\)
0.792493 + 0.609881i \(0.208783\pi\)
\(564\) 620.651 + 218.653i 1.10044 + 0.387682i
\(565\) 641.785 641.785i 1.13590 1.13590i
\(566\) −312.070 + 208.315i −0.551361 + 0.368047i
\(567\) 216.608 + 970.739i 0.382024 + 1.71206i
\(568\) −432.783 290.026i −0.761941 0.510610i
\(569\) 78.4572 0.137886 0.0689430 0.997621i \(-0.478037\pi\)
0.0689430 + 0.997621i \(0.478037\pi\)
\(570\) 376.453 + 53.7866i 0.660444 + 0.0943624i
\(571\) 363.164 363.164i 0.636013 0.636013i −0.313556 0.949570i \(-0.601520\pi\)
0.949570 + 0.313556i \(0.101520\pi\)
\(572\) 12.9648 31.2198i 0.0226657 0.0545800i
\(573\) 182.358 10.0188i 0.318251 0.0174848i
\(574\) 21.9646 110.163i 0.0382659 0.191922i
\(575\) 14.6084i 0.0254060i
\(576\) −276.025 505.555i −0.479210 0.877700i
\(577\) −566.880 −0.982460 −0.491230 0.871030i \(-0.663453\pi\)
−0.491230 + 0.871030i \(0.663453\pi\)
\(578\) −223.643 44.5905i −0.386925 0.0771462i
\(579\) −29.2727 532.809i −0.0505573 0.920223i
\(580\) 173.924 + 72.2261i 0.299869 + 0.124528i
\(581\) −78.0698 78.0698i −0.134371 0.134371i
\(582\) 118.143 826.881i 0.202994 1.42076i
\(583\) 76.1565i 0.130629i
\(584\) −223.771 + 333.915i −0.383170 + 0.571772i
\(585\) −17.0153 154.385i −0.0290860 0.263907i
\(586\) −226.077 338.680i −0.385798 0.577953i
\(587\) 73.3693 + 73.3693i 0.124990 + 0.124990i 0.766835 0.641845i \(-0.221831\pi\)
−0.641845 + 0.766835i \(0.721831\pi\)
\(588\) −405.824 + 1151.94i −0.690177 + 1.95908i
\(589\) −329.717 329.717i −0.559792 0.559792i
\(590\) −151.642 + 760.559i −0.257021 + 1.28908i
\(591\) 189.504 211.538i 0.320650 0.357932i
\(592\) 226.402 + 0.409672i 0.382436 + 0.000692014i
\(593\) 458.708i 0.773538i 0.922177 + 0.386769i \(0.126409\pi\)
−0.922177 + 0.386769i \(0.873591\pi\)
\(594\) −98.5645 + 92.4228i −0.165934 + 0.155594i
\(595\) −890.650 890.650i −1.49689 1.49689i
\(596\) −252.534 611.236i −0.423716 1.02556i
\(597\) −2.47525 + 0.135991i −0.00414615 + 0.000227790i
\(598\) 49.4375 + 74.0609i 0.0826714 + 0.123848i
\(599\) −423.611 −0.707197 −0.353599 0.935397i \(-0.615042\pi\)
−0.353599 + 0.935397i \(0.615042\pi\)
\(600\) 22.8734 + 13.5721i 0.0381223 + 0.0226201i
\(601\) 795.376i 1.32342i −0.749759 0.661711i \(-0.769831\pi\)
0.749759 0.661711i \(-0.230169\pi\)
\(602\) 410.395 + 614.802i 0.681719 + 1.02126i
\(603\) −313.450 251.216i −0.519817 0.416610i
\(604\) 16.8324 40.5332i 0.0278682 0.0671079i
\(605\) −414.557 + 414.557i −0.685219 + 0.685219i
\(606\) −854.506 + 640.853i −1.41008 + 1.05751i
\(607\) −631.699 −1.04069 −0.520345 0.853956i \(-0.674197\pi\)
−0.520345 + 0.853956i \(0.674197\pi\)
\(608\) 78.3167 389.123i 0.128810 0.640004i
\(609\) −226.484 + 252.817i −0.371896 + 0.415135i
\(610\) −54.3096 + 272.389i −0.0890322 + 0.446539i
\(611\) 130.964 130.964i 0.214344 0.214344i
\(612\) −202.388 + 693.798i −0.330699 + 1.13366i
\(613\) 385.264 385.264i 0.628490 0.628490i −0.319198 0.947688i \(-0.603414\pi\)
0.947688 + 0.319198i \(0.103414\pi\)
\(614\) −140.271 210.136i −0.228454 0.342240i
\(615\) 46.7846 52.2241i 0.0760724 0.0849173i
\(616\) −241.140 + 47.6257i −0.391462 + 0.0773144i
\(617\) 953.333 1.54511 0.772555 0.634947i \(-0.218978\pi\)
0.772555 + 0.634947i \(0.218978\pi\)
\(618\) −156.770 22.3989i −0.253673 0.0362442i
\(619\) −574.046 + 574.046i −0.927377 + 0.927377i −0.997536 0.0701591i \(-0.977649\pi\)
0.0701591 + 0.997536i \(0.477649\pi\)
\(620\) −293.384 710.108i −0.473200 1.14533i
\(621\) −58.3390 351.103i −0.0939437 0.565383i
\(622\) −616.872 122.994i −0.991755 0.197739i
\(623\) 2043.24i 3.27969i
\(624\) −161.892 + 8.60061i −0.259443 + 0.0137830i
\(625\) 651.477 1.04236
\(626\) −40.6220 + 203.739i −0.0648914 + 0.325461i
\(627\) −92.9707 + 5.10783i −0.148279 + 0.00814646i
\(628\) 107.624 + 260.493i 0.171375 + 0.414798i
\(629\) −200.868 200.868i −0.319345 0.319345i
\(630\) −864.965 + 726.137i −1.37296 + 1.15260i
\(631\) 138.048i 0.218777i 0.993999 + 0.109389i \(0.0348893\pi\)
−0.993999 + 0.109389i \(0.965111\pi\)
\(632\) 139.094 + 93.2130i 0.220086 + 0.147489i
\(633\) −513.367 + 573.056i −0.811007 + 0.905301i
\(634\) −755.397 + 504.246i −1.19148 + 0.795341i
\(635\) 549.786 + 549.786i 0.865805 + 0.865805i
\(636\) 329.397 157.770i 0.517920 0.248066i
\(637\) 243.072 + 243.072i 0.381589 + 0.381589i
\(638\) −45.2214 9.01636i −0.0708799 0.0141322i
\(639\) 582.570 64.2069i 0.911691 0.100480i
\(640\) 365.080 542.654i 0.570438 0.847896i
\(641\) 784.889i 1.22448i −0.790673 0.612238i \(-0.790269\pi\)
0.790673 0.612238i \(-0.209731\pi\)
\(642\) 569.903 427.410i 0.887700 0.665747i
\(643\) −238.456 238.456i −0.370850 0.370850i 0.496937 0.867787i \(-0.334458\pi\)
−0.867787 + 0.496937i \(0.834458\pi\)
\(644\) 248.313 597.951i 0.385580 0.928495i
\(645\) 25.3107 + 460.695i 0.0392414 + 0.714256i
\(646\) −414.220 + 276.502i −0.641208 + 0.428022i
\(647\) −681.751 −1.05371 −0.526855 0.849955i \(-0.676629\pi\)
−0.526855 + 0.849955i \(0.676629\pi\)
\(648\) 603.945 + 234.850i 0.932014 + 0.362422i
\(649\) 189.889i 0.292587i
\(650\) 6.22621 4.15615i 0.00957879 0.00639408i
\(651\) 1382.72 75.9668i 2.12399 0.116693i
\(652\) −143.480 347.279i −0.220061 0.532636i
\(653\) 636.071 636.071i 0.974075 0.974075i −0.0255977 0.999672i \(-0.508149\pi\)
0.999672 + 0.0255977i \(0.00814890\pi\)
\(654\) 15.5805 11.6849i 0.0238233 0.0178668i
\(655\) 474.721 0.724766
\(656\) −51.6560 51.8433i −0.0787439 0.0790294i
\(657\) −49.5391 449.485i −0.0754020 0.684147i
\(658\) −1320.70 263.325i −2.00714 0.400190i
\(659\) −91.6052 + 91.6052i −0.139006 + 0.139006i −0.773186 0.634179i \(-0.781338\pi\)
0.634179 + 0.773186i \(0.281338\pi\)
\(660\) −144.706 50.9792i −0.219251 0.0772412i
\(661\) 721.715 721.715i 1.09185 1.09185i 0.0965216 0.995331i \(-0.469228\pi\)
0.995331 0.0965216i \(-0.0307717\pi\)
\(662\) −738.340 + 492.860i −1.11532 + 0.744502i
\(663\) 151.510 + 135.729i 0.228522 + 0.204720i
\(664\) −70.5684 + 13.9374i −0.106278 + 0.0209900i
\(665\) −778.245 −1.17029
\(666\) −195.075 + 163.765i −0.292905 + 0.245894i
\(667\) 85.8871 85.8871i 0.128766 0.128766i
\(668\) −675.477 280.508i −1.01119 0.419922i
\(669\) 2.91851 + 53.1215i 0.00436250 + 0.0794044i
\(670\) 89.1859 447.310i 0.133113 0.667627i
\(671\) 68.0074i 0.101352i
\(672\) 705.554 + 944.332i 1.04993 + 1.40526i
\(673\) 417.305 0.620067 0.310033 0.950726i \(-0.399660\pi\)
0.310033 + 0.950726i \(0.399660\pi\)
\(674\) −462.944 92.3031i −0.686861 0.136948i
\(675\) −29.5168 + 4.90449i −0.0437286 + 0.00726592i
\(676\) 241.759 582.167i 0.357631 0.861194i
\(677\) 585.326 + 585.326i 0.864587 + 0.864587i 0.991867 0.127280i \(-0.0406246\pi\)
−0.127280 + 0.991867i \(0.540625\pi\)
\(678\) 1055.07 + 150.745i 1.55614 + 0.222338i
\(679\) 1709.42i 2.51756i
\(680\) −805.070 + 159.003i −1.18393 + 0.233828i
\(681\) −23.8194 21.3384i −0.0349771 0.0313340i
\(682\) 104.446 + 156.468i 0.153147 + 0.229425i
\(683\) −104.261 104.261i −0.152651 0.152651i 0.626650 0.779301i \(-0.284426\pi\)
−0.779301 + 0.626650i \(0.784426\pi\)
\(684\) 214.696 + 391.541i 0.313883 + 0.572429i
\(685\) −192.037 192.037i −0.280346 0.280346i
\(686\) 253.439 1271.12i 0.369445 1.85294i
\(687\) −707.054 633.409i −1.02919 0.921993i
\(688\) 481.590 + 0.871434i 0.699986 + 0.00126662i
\(689\) 102.798i 0.149199i
\(690\) 323.311 242.473i 0.468567 0.351410i
\(691\) −335.701 335.701i −0.485818 0.485818i 0.421165 0.906984i \(-0.361621\pi\)
−0.906984 + 0.421165i \(0.861621\pi\)
\(692\) 647.301 267.435i 0.935406 0.386467i
\(693\) 172.934 215.775i 0.249544 0.311364i
\(694\) 693.999 + 1039.66i 0.999999 + 1.49807i
\(695\) 1165.74 1.67733
\(696\) 54.6850 + 214.273i 0.0785704 + 0.307864i
\(697\) 91.8264i 0.131745i
\(698\) −748.484 1121.28i −1.07233 1.60642i
\(699\) 20.3386 + 370.196i 0.0290968 + 0.529608i
\(700\) −50.2690 20.8754i −0.0718129 0.0298220i
\(701\) −490.458 + 490.458i −0.699655 + 0.699655i −0.964336 0.264681i \(-0.914733\pi\)
0.264681 + 0.964336i \(0.414733\pi\)
\(702\) 133.045 124.754i 0.189522 0.177713i
\(703\) −175.517 −0.249669
\(704\) −61.6843 + 147.783i −0.0876198 + 0.209920i
\(705\) −626.093 560.881i −0.888075 0.795575i
\(706\) 176.859 887.033i 0.250508 1.25642i
\(707\) 1545.69 1545.69i 2.18626 2.18626i
\(708\) −821.320 + 393.385i −1.16006 + 0.555628i
\(709\) 435.817 435.817i 0.614692 0.614692i −0.329473 0.944165i \(-0.606871\pi\)
0.944165 + 0.329473i \(0.106871\pi\)
\(710\) 369.480 + 553.508i 0.520394 + 0.779589i
\(711\) −187.235 + 20.6358i −0.263341 + 0.0290236i
\(712\) 1105.84 + 741.074i 1.55315 + 1.04083i
\(713\) −495.544 −0.695012
\(714\) 209.199 1464.19i 0.292996 2.05068i
\(715\) −30.5345 + 30.5345i −0.0427056 + 0.0427056i
\(716\) 881.696 364.276i 1.23142 0.508765i
\(717\) −354.968 + 19.5020i −0.495073 + 0.0271994i
\(718\) 1210.76 + 241.404i 1.68629 + 0.336218i
\(719\) 1083.05i 1.50633i 0.657831 + 0.753166i \(0.271474\pi\)
−0.657831 + 0.753166i \(0.728526\pi\)
\(720\) 79.2816 + 731.501i 0.110113 + 1.01597i
\(721\) 324.093 0.449505
\(722\) 81.0069 406.288i 0.112198 0.562726i
\(723\) 43.4738 + 791.292i 0.0601297 + 1.09446i
\(724\) −847.814 + 350.278i −1.17101 + 0.483809i
\(725\) −7.22042 7.22042i −0.00995921 0.00995921i
\(726\) −681.513 97.3728i −0.938723 0.134122i
\(727\) 513.215i 0.705935i −0.935636 0.352968i \(-0.885173\pi\)
0.935636 0.352968i \(-0.114827\pi\)
\(728\) 325.497 64.2863i 0.447111 0.0883053i
\(729\) −689.828 + 235.752i −0.946266 + 0.323390i
\(730\) 427.061 285.074i 0.585015 0.390512i
\(731\) −427.276 427.276i −0.584508 0.584508i
\(732\) −294.150 + 140.888i −0.401845 + 0.192470i
\(733\) 73.6001 + 73.6001i 0.100409 + 0.100409i 0.755527 0.655118i \(-0.227381\pi\)
−0.655118 + 0.755527i \(0.727381\pi\)
\(734\) −22.2791 4.44208i −0.0303531 0.00605188i
\(735\) 1041.01 1162.04i 1.41633 1.58101i
\(736\) −233.561 351.265i −0.317338 0.477263i
\(737\) 111.680i 0.151533i
\(738\) 82.0217 + 7.15657i 0.111140 + 0.00969725i
\(739\) 152.386 + 152.386i 0.206206 + 0.206206i 0.802653 0.596447i \(-0.203421\pi\)
−0.596447 + 0.802653i \(0.703421\pi\)
\(740\) −267.092 110.917i −0.360936 0.149887i
\(741\) 125.494 6.89467i 0.169358 0.00930455i
\(742\) −621.675 + 414.983i −0.837837 + 0.559277i
\(743\) −574.044 −0.772603 −0.386302 0.922373i \(-0.626248\pi\)
−0.386302 + 0.922373i \(0.626248\pi\)
\(744\) 460.389 775.906i 0.618803 1.04288i
\(745\) 844.811i 1.13397i
\(746\) −139.758 + 93.2919i −0.187343 + 0.125056i
\(747\) 50.6082 63.1454i 0.0677486 0.0845319i
\(748\) 185.705 76.7246i 0.248268 0.102573i
\(749\) −1030.88 + 1030.88i −1.37634 + 1.37634i
\(750\) 439.469 + 585.983i 0.585959 + 0.781311i
\(751\) −1014.28 −1.35058 −0.675289 0.737553i \(-0.735981\pi\)
−0.675289 + 0.737553i \(0.735981\pi\)
\(752\) −621.527 + 619.282i −0.826499 + 0.823513i
\(753\) 431.649 481.836i 0.573239 0.639888i
\(754\) 61.0408 + 12.1705i 0.0809560 + 0.0161412i
\(755\) −39.6435 + 39.6435i −0.0525079 + 0.0525079i
\(756\) −1291.54 300.975i −1.70839 0.398115i
\(757\) −1003.73 + 1003.73i −1.32594 + 1.32594i −0.417057 + 0.908880i \(0.636938\pi\)
−0.908880 + 0.417057i \(0.863062\pi\)
\(758\) 1024.34 683.771i 1.35137 0.902072i
\(759\) −66.0261 + 73.7028i −0.0869909 + 0.0971052i
\(760\) −282.265 + 421.201i −0.371402 + 0.554212i
\(761\) 54.1069 0.0710997 0.0355499 0.999368i \(-0.488682\pi\)
0.0355499 + 0.999368i \(0.488682\pi\)
\(762\) −129.136 + 903.823i −0.169470 + 1.18612i
\(763\) −28.1829 + 28.1829i −0.0369370 + 0.0369370i
\(764\) −93.3911 + 224.890i −0.122240 + 0.294359i
\(765\) 577.358 720.386i 0.754716 0.941681i
\(766\) −106.416 + 533.728i −0.138925 + 0.696773i
\(767\) 256.316i 0.334181i
\(768\) 766.991 39.3551i 0.998686 0.0512436i
\(769\) 143.904 0.187132 0.0935659 0.995613i \(-0.470173\pi\)
0.0935659 + 0.995613i \(0.470173\pi\)
\(770\) 307.923 + 61.3946i 0.399900 + 0.0797332i
\(771\) −338.843 + 18.6161i −0.439485 + 0.0241454i