Properties

Label 48.3.i.b.29.1
Level $48$
Weight $3$
Character 48.29
Analytic conductor $1.308$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 29.1
Root \(-1.96139 + 0.391068i\) of defining polynomial
Character \(\chi\) \(=\) 48.29
Dual form 48.3.i.b.5.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.96139 - 0.391068i) q^{2} +(-2.99548 - 0.164573i) q^{3} +(3.69413 + 1.53408i) q^{4} +(3.61305 + 3.61305i) q^{5} +(5.81096 + 1.49423i) q^{6} +12.2792i q^{7} +(-6.64572 - 4.45358i) q^{8} +(8.94583 + 0.985948i) q^{9} +O(q^{10})\) \(q+(-1.96139 - 0.391068i) q^{2} +(-2.99548 - 0.164573i) q^{3} +(3.69413 + 1.53408i) q^{4} +(3.61305 + 3.61305i) q^{5} +(5.81096 + 1.49423i) 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} +(-10.8132 - 5.20325i) 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} +(-17.1607 - 5.43226i) q^{18} +(-8.77090 - 8.77090i) q^{19} +(7.80438 + 18.8898i) q^{20} +(2.02081 - 36.7820i) q^{21} +(2.77840 + 4.16225i) q^{22} +13.1821 q^{23} +(19.1742 + 14.4343i) q^{24} +1.10820i q^{25} +(3.75035 + 5.61830i) q^{26} +(-26.6348 - 4.42563i) q^{27} +(-18.8372 + 45.3609i) q^{28} +(6.51544 - 6.51544i) q^{29} +(15.5966 + 26.3940i) 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} +(31.5346 + 17.3658i) 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} +(-18.3479 + 71.3538i) q^{42} +(21.2835 - 21.2835i) q^{43} +(-3.82182 - 9.25035i) q^{44} +(28.7594 + 35.8840i) q^{45} +(-25.8553 - 5.15509i) q^{46} -54.8366i q^{47} +(-31.9633 - 35.8098i) q^{48} -101.778 q^{49} +(0.433383 - 2.17362i) q^{50} +(3.30386 - 60.1356i) q^{51} +(-5.15878 - 12.4863i) q^{52} +(-21.5215 - 21.5215i) q^{53} +(50.5107 + 19.0964i) 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} +(-20.2691 - 57.8683i) 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} +(-7.63766 - 12.9252i) q^{66} +(31.5603 + 31.5603i) q^{67} +(-30.7972 + 74.1612i) q^{68} +(-39.4867 - 2.16941i) q^{69} +(104.367 - 69.6678i) q^{70} +65.1220 q^{71} +(-55.0605 - 46.3934i) q^{72} +50.2451i q^{73} +(-23.5379 + 15.7121i) q^{74} +(0.182380 - 3.31960i) q^{75} +(-18.9456 - 45.8561i) q^{76} +(21.7257 - 21.7257i) q^{77} +(-10.3095 - 17.4467i) 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} +(63.8916 - 132.778i) 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} +(-42.3755 - 81.6295i) q^{90} +(29.3259 - 29.3259i) q^{91} +(48.6964 + 20.2223i) q^{92} +(-112.607 - 6.18664i) q^{93} +(-21.4449 + 107.556i) q^{94} -63.3793i q^{95} +(48.6886 + 82.7370i) q^{96} +139.213 q^{97} +(199.627 + 39.8021i) q^{98} +(-14.0835 - 17.5725i) 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
\(3\) −2.99548 0.164573i −0.998494 0.0548575i
\(4\) 3.69413 + 1.53408i 0.923533 + 0.383519i
\(5\) 3.61305 + 3.61305i 0.722609 + 0.722609i 0.969136 0.246527i \(-0.0792893\pi\)
−0.246527 + 0.969136i \(0.579289\pi\)
\(6\) 5.81096 + 1.49423i 0.968494 + 0.249038i
\(7\) 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 0.622095 0.782942i \(-0.286282\pi\)
−0.782942 + 0.622095i \(0.786282\pi\)
\(12\) −10.8132 5.20325i −0.901103 0.433604i
\(13\) −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 \(0.201051\pi\)
−0.807072 + 0.590453i \(0.798949\pi\)
\(18\) −17.1607 5.43226i −0.953374 0.301792i
\(19\) −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
\(21\) 2.02081 36.7820i 0.0962292 1.75153i
\(22\) 2.77840 + 4.16225i 0.126291 + 0.189193i
\(23\) 13.1821 0.573134 0.286567 0.958060i \(-0.407486\pi\)
0.286567 + 0.958060i \(0.407486\pi\)
\(24\) 19.1742 + 14.4343i 0.798925 + 0.601431i
\(25\) 1.10820i 0.0443281i
\(26\) 3.75035 + 5.61830i 0.144244 + 0.216088i
\(27\) −26.6348 4.42563i −0.986475 0.163912i
\(28\) −18.8372 + 45.3609i −0.672756 + 1.62003i
\(29\) 6.51544 6.51544i 0.224670 0.224670i −0.585792 0.810462i \(-0.699216\pi\)
0.810462 + 0.585792i \(0.199216\pi\)
\(30\) 15.5966 + 26.3940i 0.519885 + 0.879800i
\(31\) 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
\(36\) 31.5346 + 17.3658i 0.875960 + 0.482384i
\(37\) 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 \(-0.482235\pi\)
0.0557814 + 0.998443i \(0.482235\pi\)
\(42\) −18.3479 + 71.3538i −0.436854 + 1.69890i
\(43\) 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
\(45\) 28.7594 + 35.8840i 0.639098 + 0.797422i
\(46\) −25.8553 5.15509i −0.562071 0.112067i
\(47\) 54.8366i 1.16674i −0.812208 0.583368i \(-0.801734\pi\)
0.812208 0.583368i \(-0.198266\pi\)
\(48\) −31.9633 35.8098i −0.665903 0.746038i
\(49\) −101.778 −2.07710
\(50\) 0.433383 2.17362i 0.00866765 0.0434724i
\(51\) 3.30386 60.1356i 0.0647816 1.17913i
\(52\) −5.15878 12.4863i −0.0992073 0.240122i
\(53\) −21.5215 21.5215i −0.406065 0.406065i 0.474299 0.880364i \(-0.342702\pi\)
−0.880364 + 0.474299i \(0.842702\pi\)
\(54\) 50.5107 + 19.0964i 0.935383 + 0.353638i
\(55\) 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 0.996233 0.0867132i \(-0.0276364\pi\)
−0.0867132 + 0.996233i \(0.527636\pi\)
\(60\) −20.2691 57.8683i −0.337819 0.964472i
\(61\) −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
\(66\) −7.63766 12.9252i −0.115722 0.195836i
\(67\) 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
\(69\) −39.4867 2.16941i −0.572271 0.0314407i
\(70\) 104.367 69.6678i 1.49096 0.995254i
\(71\) 65.1220 0.917211 0.458606 0.888640i \(-0.348349\pi\)
0.458606 + 0.888640i \(0.348349\pi\)
\(72\) −55.0605 46.3934i −0.764729 0.644352i
\(73\) 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
\(75\) 0.182380 3.31960i 0.00243173 0.0442614i
\(76\) −18.9456 45.8561i −0.249284 0.603369i
\(77\) 21.7257 21.7257i 0.282152 0.282152i
\(78\) −10.3095 17.4467i −0.132173 0.223676i
\(79\) 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 −0.667768 0.744369i \(-0.732750\pi\)
0.744369 + 0.667768i \(0.232750\pi\)
\(84\) 63.8916 132.778i 0.760614 1.58069i
\(85\) −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 \(-0.884446\pi\)
−0.934828 + 0.355102i \(0.884446\pi\)
\(90\) −42.3755 81.6295i −0.470839 0.906994i
\(91\) 29.3259 29.3259i 0.322262 0.322262i
\(92\) 48.6964 + 20.2223i 0.529308 + 0.219808i
\(93\) −112.607 6.18664i −1.21083 0.0665231i
\(94\) −21.4449 + 107.556i −0.228137 + 1.14422i
\(95\) 63.3793i 0.667151i
\(96\) 48.6886 + 82.7370i 0.507173 + 0.861844i
\(97\) 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
\(99\) −14.0835 17.5725i −0.142258 0.177500i
\(100\) −1.70007 + 4.09385i −0.0170007 + 0.0409385i
\(101\) 125.879 + 125.879i 1.24632 + 1.24632i 0.957331 + 0.288994i \(0.0933207\pi\)
0.288994 + 0.957331i \(0.406679\pi\)
\(102\) −29.9973 + 116.657i −0.294091 + 1.14370i
\(103\) 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 0.195994 0.980605i \(-0.437207\pi\)
−0.980605 + 0.195994i \(0.937207\pi\)
\(108\) −91.6033 57.2087i −0.848179 0.529710i
\(109\) 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 \(-0.712162\pi\)
0.618260 0.785974i \(-0.287838\pi\)
\(114\) −37.8616 64.0731i −0.332120 0.562045i
\(115\) 47.6275 + 47.6275i 0.414152 + 0.414152i
\(116\) 34.0641 14.0737i 0.293656 0.121325i
\(117\) −19.0103 23.7197i −0.162481 0.202733i
\(118\) −84.2663 126.237i −0.714122 1.06981i
\(119\) −246.509 −2.07151
\(120\) 17.1253 + 121.429i 0.142711 + 1.01191i
\(121\) 114.739i 0.948257i
\(122\) 30.1794 + 45.2110i 0.247372 + 0.370582i
\(123\) −13.7016 0.752766i −0.111395 0.00612005i
\(124\) 138.871 + 57.6693i 1.11992 + 0.465075i
\(125\) 86.3222 86.3222i 0.690577 0.690577i
\(126\) 66.7036 210.719i 0.529394 1.67238i
\(127\) −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 −0.410409 0.911901i \(-0.634614\pi\)
0.911901 + 0.410409i \(0.134614\pi\)
\(132\) 9.92584 + 28.3382i 0.0751957 + 0.214684i
\(133\) 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 \(-0.562140\pi\)
−0.193982 + 0.981005i \(0.562140\pi\)
\(138\) 76.6006 + 19.6971i 0.555077 + 0.142732i
\(139\) −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
\(141\) −9.02460 + 164.262i −0.0640043 + 1.16498i
\(142\) −127.730 25.4671i −0.899506 0.179346i
\(143\) 8.45118i 0.0590992i
\(144\) 89.8523 + 112.528i 0.623975 + 0.781445i
\(145\) 47.0811 0.324698
\(146\) 19.6493 98.5505i 0.134584 0.675004i
\(147\) 304.874 + 16.7498i 2.07397 + 0.113945i
\(148\) 52.3117 21.6128i 0.353457 0.146032i
\(149\) 116.911 + 116.911i 0.784638 + 0.784638i 0.980610 0.195971i \(-0.0627859\pi\)
−0.195971 + 0.980610i \(0.562786\pi\)
\(150\) −1.65591 + 6.43972i −0.0110394 + 0.0429315i
\(151\) 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
\(156\) 13.3981 + 38.2516i 0.0858854 + 0.245203i
\(157\) 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
\(162\) −148.161 65.5157i −0.914574 0.404418i
\(163\) −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
\(165\) −2.10410 + 38.2980i −0.0127521 + 0.232109i
\(166\) −14.9567 + 9.98399i −0.0901008 + 0.0601445i
\(167\) 182.851 1.09492 0.547459 0.836832i \(-0.315595\pi\)
0.547459 + 0.836832i \(0.315595\pi\)
\(168\) −177.242 + 235.443i −1.05501 + 1.40145i
\(169\) 157.592i 0.932499i
\(170\) 170.632 113.901i 1.00372 0.670006i
\(171\) −69.8153 87.1106i −0.408277 0.509419i
\(172\) 111.275 45.9736i 0.646946 0.267288i
\(173\) −123.809 + 123.809i −0.715661 + 0.715661i −0.967714 0.252052i \(-0.918894\pi\)
0.252052 + 0.967714i \(0.418894\pi\)
\(174\) 47.5965 28.1254i 0.273543 0.161640i
\(175\) −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 −0.998415 0.0562807i \(-0.982076\pi\)
0.0562807 + 0.998415i \(0.482076\pi\)
\(180\) 51.1923 + 176.679i 0.284402 + 0.981552i
\(181\) −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
\(186\) 218.447 + 56.1714i 1.17445 + 0.301997i
\(187\) 35.5198 35.5198i 0.189945 0.189945i
\(188\) 84.1236 202.574i 0.447466 1.07752i
\(189\) 54.3430 327.053i 0.287529 1.73044i
\(190\) −24.7856 + 124.312i −0.130451 + 0.654273i
\(191\) 60.8777i 0.318731i −0.987220 0.159366i \(-0.949055\pi\)
0.987220 0.159366i \(-0.0509449\pi\)
\(192\) −63.1418 181.320i −0.328863 0.944377i
\(193\) 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
\(195\) −2.84016 + 51.6955i −0.0145649 + 0.265105i
\(196\) −375.981 156.135i −1.91827 0.796608i
\(197\) −66.9411 66.9411i −0.339803 0.339803i 0.516490 0.856293i \(-0.327238\pi\)
−0.856293 + 0.516490i \(0.827238\pi\)
\(198\) 20.7514 + 39.9741i 0.104805 + 0.201890i
\(199\) 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
\(204\) 104.457 217.080i 0.512046 1.06412i
\(205\) 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
\(210\) −324.096 + 191.513i −1.54332 + 0.911965i
\(211\) −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
\(213\) −195.072 10.7173i −0.915830 0.0503159i
\(214\) 131.834 + 197.497i 0.616048 + 0.922884i
\(215\) 153.797 0.715333
\(216\) 157.298 + 148.032i 0.728230 + 0.685333i
\(217\) 461.601i 2.12719i
\(218\) −3.60419 5.39933i −0.0165330 0.0247676i
\(219\) 8.26897 150.508i 0.0377579 0.687253i
\(220\) 19.6135 47.2303i 0.0891524 0.214683i
\(221\) 47.9454 47.9454i 0.216947 0.216947i
\(222\) 73.0932 43.1918i 0.329249 0.194557i
\(223\) −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 −0.723515 0.690309i \(-0.757475\pi\)
0.690309 + 0.723515i \(0.257475\pi\)
\(228\) 49.2046 + 140.479i 0.215810 + 0.616136i
\(229\) 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 \(-0.414561\pi\)
0.265203 + 0.964193i \(0.414561\pi\)
\(234\) 28.0107 + 53.9580i 0.119704 + 0.230590i
\(235\) 198.127 198.127i 0.843095 0.843095i
\(236\) 115.912 + 280.554i 0.491153 + 1.18879i
\(237\) −62.6951 3.44448i −0.264536 0.0145337i
\(238\) 483.502 + 96.4019i 2.03152 + 0.405050i
\(239\) 118.501i 0.495820i 0.968783 + 0.247910i \(0.0797437\pi\)
−0.968783 + 0.247910i \(0.920256\pi\)
\(240\) 13.8976 244.868i 0.0579065 1.02028i
\(241\) −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
\(243\) −233.907 65.8515i −0.962581 0.270994i
\(244\) −41.5132 100.479i −0.170136 0.411798i
\(245\) −367.728 367.728i −1.50093 1.50093i
\(246\) 26.5798 + 6.83471i 0.108048 + 0.0277834i
\(247\) 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 0.334808 0.942286i \(-0.391328\pi\)
−0.942286 + 0.334808i \(0.891328\pi\)
\(252\) −213.238 + 387.218i −0.846181 + 1.53658i
\(253\) −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 \(0.0706298\pi\)
−0.975483 + 0.220074i \(0.929370\pi\)
\(258\) 155.480 91.8753i 0.602636 0.356106i
\(259\) 122.861 + 122.861i 0.474367 + 0.474367i
\(260\) 26.4748 63.7526i 0.101826 0.245202i
\(261\) 64.7099 51.8621i 0.247931 0.198705i
\(262\) −154.546 + 103.163i −0.589871 + 0.393753i
\(263\) −129.324 −0.491727 −0.245864 0.969304i \(-0.579072\pi\)
−0.245864 + 0.969304i \(0.579072\pi\)
\(264\) −8.38631 59.4641i −0.0317663 0.225243i
\(265\) 155.516i 0.586853i
\(266\) −253.359 + 169.123i −0.952476 + 0.635801i
\(267\) 498.446 + 27.3848i 1.86684 + 0.102565i
\(268\) 68.1719 + 165.004i 0.254373 + 0.615685i
\(269\) −129.457 + 129.457i −0.481253 + 0.481253i −0.905532 0.424278i \(-0.860528\pi\)
0.424278 + 0.905532i \(0.360528\pi\)
\(270\) 113.501 + 251.494i 0.420374 + 0.931458i
\(271\) 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
\(276\) −142.541 68.5897i −0.516453 0.248514i
\(277\) 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 \(-0.578074\pi\)
−0.242825 + 0.970070i \(0.578074\pi\)
\(282\) 81.9385 318.654i 0.290562 1.12998i
\(283\) −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
\(285\) −10.4305 + 189.852i −0.0365982 + 0.666146i
\(286\) 3.30499 16.5761i 0.0115559 0.0579584i
\(287\) 56.1658i 0.195700i
\(288\) −132.230 255.850i −0.459131 0.888369i
\(289\) −114.022 −0.394541
\(290\) −92.3447 18.4119i −0.318430 0.0634894i
\(291\) −417.010 22.9106i −1.43303 0.0787307i
\(292\) −77.0799 + 185.612i −0.263972 + 0.635658i
\(293\) 143.968 + 143.968i 0.491360 + 0.491360i 0.908735 0.417375i \(-0.137050\pi\)
−0.417375 + 0.908735i \(0.637050\pi\)
\(294\) −591.428 152.079i −2.01166 0.517277i
\(295\) 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
\(300\) 5.76626 11.9833i 0.0192209 0.0399442i
\(301\) 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
\(306\) 109.055 344.509i 0.356389 1.12585i
\(307\) −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
\(309\) −4.34368 + 79.0619i −0.0140572 + 0.255864i
\(310\) −213.285 319.517i −0.688017 1.03070i
\(311\) 314.507 1.01128 0.505638 0.862746i \(-0.331257\pi\)
0.505638 + 0.862746i \(0.331257\pi\)
\(312\) −11.3200 80.2660i −0.0362822 0.257263i
\(313\) 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
\(315\) −440.625 + 353.142i −1.39881 + 1.12108i
\(316\) 77.3178 + 32.1080i 0.244676 + 0.101608i
\(317\) 321.109 321.109i 1.01296 1.01296i 0.0130482 0.999915i \(-0.495847\pi\)
0.999915 0.0130482i \(-0.00415349\pi\)
\(318\) −92.9024 157.218i −0.292146 0.494398i
\(319\) −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
\(324\) 264.981 + 186.443i 0.817843 + 0.575442i
\(325\) 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
\(330\) 19.1041 74.2945i 0.0578911 0.225135i
\(331\) −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
\(333\) 99.3740 79.6439i 0.298420 0.239171i
\(334\) −358.643 71.5073i −1.07378 0.214094i
\(335\) 228.057i 0.680768i
\(336\) 439.715 392.483i 1.30868 1.16810i
\(337\) −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
\(339\) −29.2330 + 532.088i −0.0862331 + 1.56958i
\(340\) −379.220 + 156.676i −1.11535 + 0.460812i
\(341\) −66.5125 66.5125i −0.195051 0.195051i
\(342\) 102.869 + 198.161i 0.300787 + 0.579417i
\(343\) 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 \(-0.893138\pi\)
−0.329445 0.944175i \(-0.606862\pi\)
\(348\) −104.354 + 36.5515i −0.299869 + 0.105033i
\(349\) −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 \(0.221304\pi\)
−0.767895 + 0.640575i \(0.778696\pi\)
\(354\) 231.643 + 392.009i 0.654359 + 1.10737i
\(355\) 235.289 + 235.289i 0.662785 + 0.662785i
\(356\) −614.701 255.269i −1.72669 0.717049i
\(357\) 738.415 + 40.5687i 2.06839 + 0.113638i
\(358\) 396.724 264.823i 1.10817 0.739729i
\(359\) −617.295 −1.71948 −0.859742 0.510728i \(-0.829376\pi\)
−0.859742 + 0.510728i \(0.829376\pi\)
\(360\) −31.3147 366.557i −0.0869853 1.01821i
\(361\) 207.143i 0.573803i
\(362\) 381.479 254.647i 1.05381 0.703443i
\(363\) −18.8829 + 343.699i −0.0520190 + 0.946829i
\(364\) 153.322 63.3455i 0.421214 0.174026i
\(365\) −181.538 + 181.538i −0.497364 + 0.497364i
\(366\) −82.9615 140.395i −0.226671 0.383594i
\(367\) −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
\(372\) −406.494 195.602i −1.09272 0.525811i
\(373\) −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
\(378\) −234.488 + 620.229i −0.620339 + 1.64082i
\(379\) 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
\(381\) 455.813 + 25.0425i 1.19636 + 0.0657283i
\(382\) −23.8073 + 119.405i −0.0623228 + 0.312579i
\(383\) 272.117i 0.710488i −0.934774 0.355244i \(-0.884398\pi\)
0.934774 0.355244i \(-0.115602\pi\)
\(384\) 52.9373 + 380.334i 0.137857 + 0.990452i
\(385\) 156.992 0.407772
\(386\) −348.875 69.5596i −0.903821 0.180206i
\(387\) 211.383 169.414i 0.546210 0.437763i
\(388\) 514.271 + 213.563i 1.32544 + 0.550421i
\(389\) −260.985 260.985i −0.670913 0.670913i 0.287013 0.957927i \(-0.407338\pi\)
−0.957927 + 0.287013i \(0.907338\pi\)
\(390\) 25.7871 100.284i 0.0661208 0.257140i
\(391\) 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
\(396\) −25.0690 86.5202i −0.0633055 0.218485i
\(397\) 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 \(-0.819840\pi\)
0.844059 0.536250i \(-0.180160\pi\)
\(402\) 136.237 + 230.554i 0.338899 + 0.573517i
\(403\) −89.7801 89.7801i −0.222779 0.222779i
\(404\) 271.905 + 658.121i 0.673033 + 1.62901i
\(405\) 221.897 + 349.367i 0.547894 + 0.862635i
\(406\) −125.633 188.207i −0.309440 0.463563i
\(407\) −35.4063 −0.0869935
\(408\) −289.775 + 384.930i −0.710234 + 0.943456i
\(409\) 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
\(411\) 159.213 + 8.74718i 0.387379 + 0.0212827i
\(412\) 40.4900 97.5019i 0.0982767 0.236655i
\(413\) −658.921 + 658.921i −1.59545 + 1.59545i
\(414\) −226.214 71.6086i −0.546411 0.172968i
\(415\) 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 −0.565370 0.824837i \(-0.691267\pi\)
0.824837 + 0.565370i \(0.191267\pi\)
\(420\) 710.575 248.888i 1.69184 0.592591i
\(421\) −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
\(426\) 378.421 + 97.3072i 0.888313 + 0.228421i
\(427\) 235.988 235.988i 0.552665 0.552665i
\(428\) −181.344 438.926i −0.423701 1.02553i
\(429\) 1.39083 25.3154i 0.00324203 0.0590102i
\(430\) −301.656 60.1450i −0.701525 0.139872i
\(431\) 213.570i 0.495522i 0.968821 + 0.247761i \(0.0796947\pi\)
−0.968821 + 0.247761i \(0.920305\pi\)
\(432\) −250.632 351.863i −0.580167 0.814498i
\(433\) 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
\(435\) −141.031 7.74826i −0.324209 0.0178121i
\(436\) 4.95772 + 11.9997i 0.0113709 + 0.0275222i
\(437\) −115.619 115.619i −0.264574 0.264574i
\(438\) −75.0777 + 291.973i −0.171410 + 0.666604i
\(439\) 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 0.970926 0.239378i \(-0.0769435\pi\)
−0.239378 + 0.970926i \(0.576943\pi\)
\(444\) −160.256 + 56.1316i −0.360936 + 0.126423i
\(445\) −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 \(-0.720001\pi\)
0.637427 0.770510i \(-0.279999\pi\)
\(450\) 6.02005 19.0176i 0.0133779 0.0422613i
\(451\) −8.09298 8.09298i −0.0179445 0.0179445i
\(452\) 272.498 656.189i 0.602872 1.45174i
\(453\) −1.80574 + 32.8674i −0.00398618 + 0.0725549i
\(454\) 17.7321 11.8366i 0.0390574 0.0260718i
\(455\) 211.912 0.465740
\(456\) −41.5728 294.777i −0.0911685 0.646441i
\(457\) 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
\(459\) 88.8463 534.705i 0.193565 1.16494i
\(460\) 102.878 + 249.006i 0.223648 + 0.541318i
\(461\) 312.070 312.070i 0.676942 0.676942i −0.282365 0.959307i \(-0.591119\pi\)
0.959307 + 0.282365i \(0.0911190\pi\)
\(462\) 158.711 93.7841i 0.343529 0.202996i
\(463\) 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 −0.612889 0.790169i \(-0.709993\pi\)
0.790169 + 0.612889i \(0.209993\pi\)
\(468\) −33.8387 116.787i −0.0723049 0.249545i
\(469\) −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
\(474\) 121.623 + 31.2740i 0.256588 + 0.0659790i
\(475\) 9.71993 9.71993i 0.0204630 0.0204630i
\(476\) −910.638 378.164i −1.91311 0.794463i
\(477\) −171.308 213.746i −0.359137 0.448106i
\(478\) 46.3419 232.427i 0.0969497 0.486249i
\(479\) 749.099i 1.56388i 0.623353 + 0.781941i \(0.285770\pi\)
−0.623353 + 0.781941i \(0.714230\pi\)
\(480\) −123.018 + 474.847i −0.256288 + 0.989265i
\(481\) −47.7923 −0.0993603
\(482\) 518.125 + 103.305i 1.07495 + 0.214326i
\(483\) 26.6385 484.864i 0.0551523 1.00386i
\(484\) 176.018 423.861i 0.363675 0.875746i
\(485\) 502.983 + 502.983i 1.03708 + 1.03708i
\(486\) 433.032 + 220.634i 0.891012 + 0.453980i
\(487\) 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 0.713947 0.700200i \(-0.246906\pi\)
−0.700200 + 0.713947i \(0.746906\pi\)
\(492\) −49.4605 23.8000i −0.100530 0.0483741i
\(493\) 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
\(498\) 46.4457 27.4454i 0.0932645 0.0551112i
\(499\) 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
\(501\) −547.728 30.0923i −1.09327 0.0600645i
\(502\) 239.439 + 358.696i 0.476969 + 0.714534i
\(503\) −304.892 −0.606147 −0.303074 0.952967i \(-0.598013\pi\)
−0.303074 + 0.952967i \(0.598013\pi\)
\(504\) 569.672 676.097i 1.13030 1.34146i
\(505\) 909.612i 1.80121i
\(506\) 36.6251 + 54.8671i 0.0723817 + 0.108433i
\(507\) −25.9354 + 472.065i −0.0511546 + 0.931095i
\(508\) −562.125 233.436i −1.10654 0.459519i
\(509\) 118.591 118.591i 0.232988 0.232988i −0.580951 0.813939i \(-0.697319\pi\)
0.813939 + 0.580951i \(0.197319\pi\)
\(510\) −529.870 + 313.107i −1.03896 + 0.613936i
\(511\) −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
\(516\) −340.887 + 119.400i −0.660634 + 0.231396i
\(517\) −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 \(-0.467846\pi\)
0.100842 + 0.994902i \(0.467846\pi\)
\(522\) −147.203 + 76.4161i −0.281998 + 0.146391i
\(523\) −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
\(525\) 40.7619 + 2.23947i 0.0776418 + 0.00426566i
\(526\) 253.656 + 50.5746i 0.482235 + 0.0961494i
\(527\) 754.679i 1.43203i
\(528\) −6.80566 + 119.912i −0.0128895 + 0.227106i
\(529\) −355.232 −0.671517
\(530\) −60.8174 + 305.028i −0.114750 + 0.575525i
\(531\) 427.141 + 532.956i 0.804408 + 1.00368i
\(532\) 563.074 232.636i 1.05841 0.437287i
\(533\) −10.9241 10.9241i −0.0204955 0.0204955i
\(534\) −966.940 248.639i −1.81075 0.465615i
\(535\) 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
\(540\) −124.269 537.665i −0.230128 0.995675i
\(541\) 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
\(546\) 214.231 126.592i 0.392365 0.231854i
\(547\) 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
\(549\) −152.978 190.875i −0.278648 0.347677i
\(550\) −4.61261 + 3.07903i −0.00838657 + 0.00559824i
\(551\) −114.292 −0.207427
\(552\) 252.756 + 190.275i 0.457891 + 0.344701i
\(553\) 257.002i 0.464741i
\(554\) −268.301 + 179.097i −0.484298 + 0.323281i
\(555\) −216.579 11.8989i −0.390232 0.0214394i
\(556\) −843.436 + 348.469i −1.51697 + 0.626743i
\(557\) −134.274 + 134.274i −0.241066 + 0.241066i −0.817291 0.576225i \(-0.804525\pi\)
0.576225 + 0.817291i \(0.304525\pi\)
\(558\) −645.110 204.211i −1.15611 0.365969i
\(559\) −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 −0.792493 0.609881i \(-0.791217\pi\)
0.609881 + 0.792493i \(0.291217\pi\)
\(564\) −285.329 + 592.962i −0.505902 + 1.05135i
\(565\) 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 \(-0.521963\pi\)
−0.0689430 + 0.997621i \(0.521963\pi\)
\(570\) 94.7032 368.295i 0.166146 0.646131i
\(571\) 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
\(573\) −10.0188 + 182.358i −0.0174848 + 0.318251i
\(574\) 21.9646 110.163i 0.0382659 0.191922i
\(575\) 14.6084i 0.0254060i
\(576\) 159.300 + 553.534i 0.276562 + 0.960996i
\(577\) −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
\(579\) −532.809 29.2727i −0.920223 0.0505573i
\(580\) 173.924 + 72.2261i 0.299869 + 0.124528i
\(581\) 78.0698 + 78.0698i 0.134371 + 0.134371i
\(582\) 808.962 + 208.016i 1.38997 + 0.357416i
\(583\) 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 0.641845 0.766835i \(-0.278169\pi\)
−0.766835 + 0.641845i \(0.778169\pi\)
\(588\) 1100.55 + 529.576i 1.87168 + 0.900640i
\(589\) −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 \(-0.873591\pi\)
0.922177 0.386769i \(-0.126409\pi\)
\(594\) −55.5817 123.157i −0.0935719 0.207335i
\(595\) −890.650 890.650i −1.49689 1.49689i
\(596\) 252.534 + 611.236i 0.423716 + 1.02556i
\(597\) −0.135991 + 2.47525i −0.000227790 + 0.00414615i
\(598\) 49.4375 + 74.0609i 0.0826714 + 0.123848i
\(599\) 423.611 0.707197 0.353599 0.935397i \(-0.384958\pi\)
0.353599 + 0.935397i \(0.384958\pi\)
\(600\) −15.9962 + 21.2489i −0.0266603 + 0.0354148i
\(601\) 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
\(603\) 251.216 + 313.450i 0.416610 + 0.519817i
\(604\) 16.8324 40.5332i 0.0278682 0.0671079i
\(605\) 414.557 414.557i 0.685219 0.685219i
\(606\) 543.385 + 919.569i 0.896675 + 1.51744i
\(607\) −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
\(612\) −348.626 + 633.070i −0.569650 + 1.03443i
\(613\) 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 \(-0.781022\pi\)
−0.772555 + 0.634947i \(0.781022\pi\)
\(618\) 39.4382 153.373i 0.0638159 0.248176i
\(619\) −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
\(621\) −351.103 58.3390i −0.565383 0.0939437i
\(622\) −616.872 122.994i −0.991755 0.197739i
\(623\) 2043.24i 3.27969i
\(624\) −9.18644 + 161.860i −0.0147219 + 0.259391i
\(625\) 651.477 1.04236
\(626\) 40.6220 203.739i 0.0648914 0.325461i
\(627\) 5.10783 92.9707i 0.00814646 0.148279i
\(628\) 107.624 + 260.493i 0.171375 + 0.414798i
\(629\) 200.868 + 200.868i 0.319345 + 0.319345i
\(630\) 1002.34 520.336i 1.59102 0.825930i
\(631\) 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
\(636\) 120.735 + 344.698i 0.189835 + 0.541979i
\(637\) 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 \(0.209731\pi\)
−0.790673 + 0.612238i \(0.790269\pi\)
\(642\) −362.404 613.296i −0.564493 0.955289i
\(643\) −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
\(645\) −460.695 25.3107i −0.714256 0.0392414i
\(646\) −414.220 + 276.502i −0.641208 + 0.428022i
\(647\) 681.751 1.05371 0.526855 0.849955i \(-0.323371\pi\)
0.526855 + 0.849955i \(0.323371\pi\)
\(648\) −446.820 469.314i −0.689538 0.724250i
\(649\) 189.889i 0.292587i
\(650\) −6.22621 + 4.15615i −0.00957879 + 0.00639408i
\(651\) 75.9668 1382.72i 0.116693 2.12399i
\(652\) −143.480 347.279i −0.220061 0.532636i
\(653\) −636.071 + 636.071i −0.974075 + 0.974075i −0.999672 0.0255977i \(-0.991851\pi\)
0.0255977 + 0.999672i \(0.491851\pi\)
\(654\) 9.90770 + 16.7668i 0.0151494 + 0.0256372i
\(655\) 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 −0.634179 0.773186i \(-0.718662\pi\)
0.773186 + 0.634179i \(0.218662\pi\)
\(660\) −66.5248 + 138.250i −0.100795 + 0.209469i
\(661\) 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
\(666\) −226.058 + 117.351i −0.339426 + 0.176203i
\(667\) 85.8871 85.8871i 0.128766 0.128766i
\(668\) 675.477 + 280.508i 1.01119 + 0.419922i
\(669\) 53.1215 + 2.91851i 0.0794044 + 0.00436250i
\(670\) 89.1859 447.310i 0.133113 0.667627i
\(671\) 68.0074i 0.101352i
\(672\) −1015.94 + 597.856i −1.51182 + 0.889666i
\(673\) 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
\(675\) 4.90449 29.5168i 0.00726592 0.0437286i
\(676\) 241.759 582.167i 0.357631 0.861194i
\(677\) −585.326 585.326i −0.864587 0.864587i 0.127280 0.991867i \(-0.459375\pi\)
−0.991867 + 0.127280i \(0.959375\pi\)
\(678\) 265.420 1032.20i 0.391475 1.52242i
\(679\) 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 0.779301 0.626650i \(-0.215574\pi\)
−0.626650 + 0.779301i \(0.715574\pi\)
\(684\) −124.273 428.900i −0.181685 0.627047i
\(685\) −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
\(690\) 205.595 + 347.928i 0.297964 + 0.504243i
\(691\) −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
\(693\) 215.775 172.934i 0.311364 0.249544i
\(694\) 693.999 + 1039.66i 0.999999 + 1.49807i
\(695\) −1165.74 −1.67733
\(696\) 218.974 30.8822i 0.314618 0.0443710i
\(697\) 91.8264i 0.131745i
\(698\) 748.484 + 1121.28i 1.07233 + 1.60642i
\(699\) −370.196 20.3386i −0.529608 0.0290968i
\(700\) −50.2690 20.8754i −0.0718129 0.0298220i
\(701\) 490.458 490.458i 0.699655 0.699655i −0.264681 0.964336i \(-0.585267\pi\)
0.964336 + 0.264681i \(0.0852666\pi\)
\(702\) −75.0255 166.240i −0.106874 0.236809i
\(703\) −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
\(708\) −301.041 859.472i −0.425200 1.21394i
\(709\) 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
\(714\) −1432.46 368.341i −2.00624 0.515884i
\(715\) −30.5345 + 30.5345i −0.0427056 + 0.0427056i
\(716\) −881.696 + 364.276i −1.23142 + 0.508765i
\(717\) 19.5020 354.968i 0.0271994 0.495073i
\(718\) 1210.76 + 241.404i 1.68629 + 0.336218i
\(719\) 1083.05i 1.50633i −0.657831 0.753166i \(-0.728526\pi\)
0.657831 0.753166i \(-0.271474\pi\)
\(720\) −81.9284 + 731.210i −0.113789 + 1.01557i
\(721\) 324.093 0.449505
\(722\) −81.0069 + 406.288i −0.112198 + 0.562726i
\(723\) 791.292 + 43.4738i 1.09446 + 0.0601297i
\(724\) −847.814 + 350.278i −1.17101 + 0.483809i
\(725\) 7.22042 + 7.22042i 0.00995921 + 0.00995921i
\(726\) 171.446 666.744i 0.236152 0.918380i
\(727\) 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
\(732\) 107.816 + 307.814i 0.147290 + 0.420511i
\(733\) 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
\(738\) −78.4944 24.8475i −0.106361 0.0336688i
\(739\) 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
\(741\) 6.89467 125.494i 0.00930455 0.169358i
\(742\) −621.675 + 414.983i −0.837837 + 0.559277i
\(743\) 574.044 0.772603 0.386302 0.922373i \(-0.373752\pi\)
0.386302 + 0.922373i \(0.373752\pi\)
\(744\) 720.800 + 542.619i 0.968818 + 0.729326i
\(745\) 844.811i 1.13397i
\(746\) 139.758 93.2919i 0.187343 0.125056i
\(747\) 63.1454 50.6082i 0.0845319 0.0677486i
\(748\) 185.705 76.7246i 0.248268 0.102573i
\(749\) 1030.88 1030.88i 1.37634 1.37634i
\(750\) 630.600 372.630i 0.840800 0.496840i
\(751\) −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
\(756\) 702.475 1124.81i 0.929200 1.48785i
\(757\) −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 \(-0.511318\pi\)
−0.0355499 + 0.999368i \(0.511318\pi\)
\(762\) −884.236 227.372i −1.16042 0.298389i
\(763\) −28.1829 + 28.1829i −0.0369370 + 0.0369370i
\(764\) 93.3911 224.890i 0.122240 0.294359i
\(765\) −720.386 + 577.358i −0.941681 + 0.754716i
\(766\) −106.416 + 533.728i −0.138925 + 0.696773i
\(767\) 256.316i 0.334181i
\(768\) 44.9055 766.686i 0.0584707 0.998289i
\(769\) 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
\(771\) 18.6161 338.843i 0.0241454 0.439485i
\(772\) 657.079 + 272.868i 0.851