Properties

Label 48.3.i.b.5.2
Level $48$
Weight $3$
Character 48.5
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 5.2
Root \(-1.85381 - 0.750590i\) of defining polynomial
Character \(\chi\) \(=\) 48.5
Dual form 48.3.i.b.29.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.85381 + 0.750590i) q^{2} +(1.50491 + 2.59524i) q^{3} +(2.87323 - 2.78290i) q^{4} +(-2.59897 + 2.59897i) q^{5} +(-4.73777 - 3.68151i) q^{6} +7.30027i q^{7} +(-3.23761 + 7.31559i) q^{8} +(-4.47050 + 7.81118i) q^{9} +O(q^{10})\) \(q+(-1.85381 + 0.750590i) q^{2} +(1.50491 + 2.59524i) q^{3} +(2.87323 - 2.78290i) q^{4} +(-2.59897 + 2.59897i) q^{5} +(-4.73777 - 3.68151i) q^{6} +7.30027i q^{7} +(-3.23761 + 7.31559i) q^{8} +(-4.47050 + 7.81118i) q^{9} +(2.86723 - 6.76875i) q^{10} +(11.3161 - 11.3161i) q^{11} +(11.5462 + 3.26870i) q^{12} +(-0.746462 + 0.746462i) q^{13} +(-5.47951 - 13.5333i) q^{14} +(-10.6561 - 2.83373i) q^{15} +(0.510910 - 15.9918i) q^{16} -6.67452i q^{17} +(2.42448 - 17.8360i) q^{18} +(22.1936 - 22.1936i) q^{19} +(-0.234761 + 14.7001i) q^{20} +(-18.9459 + 10.9862i) q^{21} +(-12.4841 + 29.4716i) q^{22} +21.4389 q^{23} +(-23.8580 + 2.60693i) q^{24} +11.4908i q^{25} +(0.823512 - 1.94408i) q^{26} +(-26.9996 + 0.153096i) q^{27} +(20.3159 + 20.9754i) q^{28} +(1.54272 + 1.54272i) q^{29} +(21.8814 - 2.74519i) q^{30} -14.6082 q^{31} +(11.0562 + 30.0293i) q^{32} +(46.3976 + 12.3382i) q^{33} +(5.00983 + 12.3733i) q^{34} +(-18.9732 - 18.9732i) q^{35} +(8.89297 + 34.8843i) q^{36} +(-50.1010 - 50.1010i) q^{37} +(-24.4845 + 57.8011i) q^{38} +(-3.06060 - 0.813888i) q^{39} +(-10.5985 - 27.4274i) q^{40} -15.0731 q^{41} +(26.8760 - 34.5870i) q^{42} +(26.3634 + 26.3634i) q^{43} +(1.02217 - 64.0053i) q^{44} +(-8.68231 - 31.9197i) q^{45} +(-39.7438 + 16.0918i) q^{46} +36.6067i q^{47} +(42.2715 - 22.7403i) q^{48} -4.29399 q^{49} +(-8.62484 - 21.3017i) q^{50} +(17.3220 - 10.0445i) q^{51} +(-0.0674268 + 4.22209i) q^{52} +(50.9270 - 50.9270i) q^{53} +(49.9372 - 20.5494i) q^{54} +58.8202i q^{55} +(-53.4058 - 23.6354i) q^{56} +(90.9971 + 24.1983i) q^{57} +(-4.01787 - 1.70196i) q^{58} +(-12.1683 + 12.1683i) q^{59} +(-38.5035 + 21.5130i) q^{60} +(-27.5789 + 27.5789i) q^{61} +(27.0809 - 10.9648i) q^{62} +(-57.0238 - 32.6359i) q^{63} +(-43.0358 - 47.3701i) q^{64} -3.88006i q^{65} +(-95.2733 + 11.9528i) q^{66} +(-4.84214 + 4.84214i) q^{67} +(-18.5745 - 19.1774i) q^{68} +(32.2636 + 55.6391i) q^{69} +(49.4137 + 20.9316i) q^{70} -74.9072 q^{71} +(-42.6697 - 57.9939i) q^{72} -3.47110i q^{73} +(130.483 + 55.2725i) q^{74} +(-29.8212 + 17.2925i) q^{75} +(2.00472 - 125.530i) q^{76} +(82.6105 + 82.6105i) q^{77} +(6.28467 - 0.788459i) q^{78} +103.463 q^{79} +(40.2344 + 42.8901i) q^{80} +(-41.0292 - 69.8399i) q^{81} +(27.9427 - 11.3137i) q^{82} +(-31.7254 - 31.7254i) q^{83} +(-23.8624 + 84.2907i) q^{84} +(17.3469 + 17.3469i) q^{85} +(-68.6608 - 29.0846i) q^{86} +(-1.68207 + 6.32538i) q^{87} +(46.1468 + 119.421i) q^{88} -78.2605 q^{89} +(40.0539 + 52.6562i) q^{90} +(-5.44937 - 5.44937i) q^{91} +(61.5990 - 59.6625i) q^{92} +(-21.9840 - 37.9118i) q^{93} +(-27.4766 - 67.8619i) q^{94} +115.361i q^{95} +(-61.2947 + 73.8848i) q^{96} -61.5651 q^{97} +(7.96025 - 3.22303i) q^{98} +(37.8034 + 138.981i) 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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.85381 + 0.750590i −0.926906 + 0.375295i
\(3\) 1.50491 + 2.59524i 0.501636 + 0.865079i
\(4\) 2.87323 2.78290i 0.718308 0.695726i
\(5\) −2.59897 + 2.59897i −0.519793 + 0.519793i −0.917509 0.397716i \(-0.869803\pi\)
0.397716 + 0.917509i \(0.369803\pi\)
\(6\) −4.73777 3.68151i −0.789629 0.613585i
\(7\) 7.30027i 1.04290i 0.853283 + 0.521448i \(0.174608\pi\)
−0.853283 + 0.521448i \(0.825392\pi\)
\(8\) −3.23761 + 7.31559i −0.404701 + 0.914449i
\(9\) −4.47050 + 7.81118i −0.496723 + 0.867909i
\(10\) 2.86723 6.76875i 0.286723 0.676875i
\(11\) 11.3161 11.3161i 1.02873 1.02873i 0.0291601 0.999575i \(-0.490717\pi\)
0.999575 0.0291601i \(-0.00928328\pi\)
\(12\) 11.5462 + 3.26870i 0.962186 + 0.272392i
\(13\) −0.746462 + 0.746462i −0.0574201 + 0.0574201i −0.735234 0.677814i \(-0.762928\pi\)
0.677814 + 0.735234i \(0.262928\pi\)
\(14\) −5.47951 13.5333i −0.391393 0.966666i
\(15\) −10.6561 2.83373i −0.710409 0.188915i
\(16\) 0.510910 15.9918i 0.0319319 0.999490i
\(17\) 6.67452i 0.392619i −0.980542 0.196310i \(-0.937104\pi\)
0.980542 0.196310i \(-0.0628957\pi\)
\(18\) 2.42448 17.8360i 0.134693 0.990887i
\(19\) 22.1936 22.1936i 1.16809 1.16809i 0.185428 0.982658i \(-0.440633\pi\)
0.982658 0.185428i \(-0.0593670\pi\)
\(20\) −0.234761 + 14.7001i −0.0117380 + 0.735005i
\(21\) −18.9459 + 10.9862i −0.902187 + 0.523154i
\(22\) −12.4841 + 29.4716i −0.567461 + 1.33962i
\(23\) 21.4389 0.932128 0.466064 0.884751i \(-0.345672\pi\)
0.466064 + 0.884751i \(0.345672\pi\)
\(24\) −23.8580 + 2.60693i −0.994083 + 0.108622i
\(25\) 11.4908i 0.459630i
\(26\) 0.823512 1.94408i 0.0316736 0.0747725i
\(27\) −26.9996 + 0.153096i −0.999984 + 0.00567024i
\(28\) 20.3159 + 20.9754i 0.725570 + 0.749120i
\(29\) 1.54272 + 1.54272i 0.0531973 + 0.0531973i 0.733205 0.680008i \(-0.238024\pi\)
−0.680008 + 0.733205i \(0.738024\pi\)
\(30\) 21.8814 2.74519i 0.729381 0.0915063i
\(31\) −14.6082 −0.471233 −0.235616 0.971846i \(-0.575711\pi\)
−0.235616 + 0.971846i \(0.575711\pi\)
\(32\) 11.0562 + 30.0293i 0.345506 + 0.938417i
\(33\) 46.3976 + 12.3382i 1.40599 + 0.373886i
\(34\) 5.00983 + 12.3733i 0.147348 + 0.363921i
\(35\) −18.9732 18.9732i −0.542090 0.542090i
\(36\) 8.89297 + 34.8843i 0.247027 + 0.969009i
\(37\) −50.1010 50.1010i −1.35408 1.35408i −0.881041 0.473039i \(-0.843157\pi\)
−0.473039 0.881041i \(-0.656843\pi\)
\(38\) −24.4845 + 57.8011i −0.644329 + 1.52108i
\(39\) −3.06060 0.813888i −0.0784769 0.0208689i
\(40\) −10.5985 27.4274i −0.264963 0.685685i
\(41\) −15.0731 −0.367637 −0.183819 0.982960i \(-0.558846\pi\)
−0.183819 + 0.982960i \(0.558846\pi\)
\(42\) 26.8760 34.5870i 0.639905 0.823501i
\(43\) 26.3634 + 26.3634i 0.613102 + 0.613102i 0.943753 0.330651i \(-0.107268\pi\)
−0.330651 + 0.943753i \(0.607268\pi\)
\(44\) 1.02217 64.0053i 0.0232310 1.45467i
\(45\) −8.68231 31.9197i −0.192940 0.709326i
\(46\) −39.7438 + 16.0918i −0.863995 + 0.349823i
\(47\) 36.6067i 0.778866i 0.921055 + 0.389433i \(0.127329\pi\)
−0.921055 + 0.389433i \(0.872671\pi\)
\(48\) 42.2715 22.7403i 0.880656 0.473757i
\(49\) −4.29399 −0.0876325
\(50\) −8.62484 21.3017i −0.172497 0.426034i
\(51\) 17.3220 10.0445i 0.339646 0.196952i
\(52\) −0.0674268 + 4.22209i −0.00129667 + 0.0811940i
\(53\) 50.9270 50.9270i 0.960887 0.960887i −0.0383765 0.999263i \(-0.512219\pi\)
0.999263 + 0.0383765i \(0.0122186\pi\)
\(54\) 49.9372 20.5494i 0.924763 0.380544i
\(55\) 58.8202i 1.06946i
\(56\) −53.4058 23.6354i −0.953675 0.422061i
\(57\) 90.9971 + 24.1983i 1.59644 + 0.424532i
\(58\) −4.01787 1.70196i −0.0692736 0.0293442i
\(59\) −12.1683 + 12.1683i −0.206242 + 0.206242i −0.802668 0.596426i \(-0.796587\pi\)
0.596426 + 0.802668i \(0.296587\pi\)
\(60\) −38.5035 + 21.5130i −0.641725 + 0.358550i
\(61\) −27.5789 + 27.5789i −0.452113 + 0.452113i −0.896055 0.443943i \(-0.853579\pi\)
0.443943 + 0.896055i \(0.353579\pi\)
\(62\) 27.0809 10.9648i 0.436788 0.176851i
\(63\) −57.0238 32.6359i −0.905139 0.518030i
\(64\) −43.0358 47.3701i −0.672434 0.740157i
\(65\) 3.88006i 0.0596932i
\(66\) −95.2733 + 11.9528i −1.44353 + 0.181102i
\(67\) −4.84214 + 4.84214i −0.0722707 + 0.0722707i −0.742318 0.670047i \(-0.766274\pi\)
0.670047 + 0.742318i \(0.266274\pi\)
\(68\) −18.5745 19.1774i −0.273155 0.282021i
\(69\) 32.2636 + 55.6391i 0.467589 + 0.806364i
\(70\) 49.4137 + 20.9316i 0.705910 + 0.299023i
\(71\) −74.9072 −1.05503 −0.527515 0.849546i \(-0.676876\pi\)
−0.527515 + 0.849546i \(0.676876\pi\)
\(72\) −42.6697 57.9939i −0.592634 0.805472i
\(73\) 3.47110i 0.0475494i −0.999717 0.0237747i \(-0.992432\pi\)
0.999717 0.0237747i \(-0.00756843\pi\)
\(74\) 130.483 + 55.2725i 1.76328 + 0.746925i
\(75\) −29.8212 + 17.2925i −0.397616 + 0.230567i
\(76\) 2.00472 125.530i 0.0263779 1.65171i
\(77\) 82.6105 + 82.6105i 1.07286 + 1.07286i
\(78\) 6.28467 0.788459i 0.0805727 0.0101085i
\(79\) 103.463 1.30966 0.654831 0.755775i \(-0.272740\pi\)
0.654831 + 0.755775i \(0.272740\pi\)
\(80\) 40.2344 + 42.8901i 0.502930 + 0.536126i
\(81\) −41.0292 69.8399i −0.506533 0.862221i
\(82\) 27.9427 11.3137i 0.340765 0.137972i
\(83\) −31.7254 31.7254i −0.382233 0.382233i 0.489673 0.871906i \(-0.337116\pi\)
−0.871906 + 0.489673i \(0.837116\pi\)
\(84\) −23.8624 + 84.2907i −0.284076 + 1.00346i
\(85\) 17.3469 + 17.3469i 0.204081 + 0.204081i
\(86\) −68.6608 29.0846i −0.798381 0.338194i
\(87\) −1.68207 + 6.32538i −0.0193342 + 0.0727056i
\(88\) 46.1468 + 119.421i 0.524395 + 1.35706i
\(89\) −78.2605 −0.879331 −0.439666 0.898162i \(-0.644903\pi\)
−0.439666 + 0.898162i \(0.644903\pi\)
\(90\) 40.0539 + 52.6562i 0.445044 + 0.585069i
\(91\) −5.44937 5.44937i −0.0598832 0.0598832i
\(92\) 61.5990 59.6625i 0.669555 0.648505i
\(93\) −21.9840 37.9118i −0.236387 0.407653i
\(94\) −27.4766 67.8619i −0.292304 0.721935i
\(95\) 115.361i 1.21433i
\(96\) −61.2947 + 73.8848i −0.638486 + 0.769633i
\(97\) −61.5651 −0.634692 −0.317346 0.948310i \(-0.602792\pi\)
−0.317346 + 0.948310i \(0.602792\pi\)
\(98\) 7.96025 3.22303i 0.0812271 0.0328880i
\(99\) 37.8034 + 138.981i 0.381853 + 1.40384i
\(100\) 31.9777 + 33.0156i 0.319777 + 0.330156i
\(101\) −56.9675 + 56.9675i −0.564034 + 0.564034i −0.930451 0.366417i \(-0.880585\pi\)
0.366417 + 0.930451i \(0.380585\pi\)
\(102\) −24.5723 + 31.6224i −0.240905 + 0.310023i
\(103\) 153.944i 1.49460i −0.664485 0.747301i \(-0.731349\pi\)
0.664485 0.747301i \(-0.268651\pi\)
\(104\) −3.04406 7.87756i −0.0292698 0.0757458i
\(105\) 20.6870 77.7927i 0.197019 0.740883i
\(106\) −56.1838 + 132.634i −0.530036 + 1.25127i
\(107\) 76.9344 76.9344i 0.719013 0.719013i −0.249390 0.968403i \(-0.580230\pi\)
0.968403 + 0.249390i \(0.0802300\pi\)
\(108\) −77.1499 + 75.5770i −0.714351 + 0.699787i
\(109\) 74.1271 74.1271i 0.680065 0.680065i −0.279949 0.960015i \(-0.590318\pi\)
0.960015 + 0.279949i \(0.0903177\pi\)
\(110\) −44.1498 109.042i −0.401362 0.991287i
\(111\) 54.6265 205.421i 0.492131 1.85064i
\(112\) 116.745 + 3.72978i 1.04236 + 0.0333016i
\(113\) 38.3909i 0.339742i 0.985466 + 0.169871i \(0.0543352\pi\)
−0.985466 + 0.169871i \(0.945665\pi\)
\(114\) −186.854 + 23.4423i −1.63907 + 0.205634i
\(115\) −55.7191 + 55.7191i −0.484514 + 0.484514i
\(116\) 8.72584 + 0.139352i 0.0752228 + 0.00120131i
\(117\) −2.49369 9.16781i −0.0213136 0.0783573i
\(118\) 13.4243 31.6911i 0.113766 0.268569i
\(119\) 48.7259 0.409461
\(120\) 55.2308 68.7814i 0.460257 0.573179i
\(121\) 135.108i 1.11659i
\(122\) 30.4256 71.8264i 0.249390 0.588741i
\(123\) −22.6837 39.1184i −0.184420 0.318035i
\(124\) −41.9728 + 40.6532i −0.338490 + 0.327849i
\(125\) −94.8382 94.8382i −0.758706 0.758706i
\(126\) 130.207 + 17.6994i 1.03339 + 0.140471i
\(127\) −43.3417 −0.341273 −0.170636 0.985334i \(-0.554582\pi\)
−0.170636 + 0.985334i \(0.554582\pi\)
\(128\) 115.336 + 55.5129i 0.901060 + 0.433695i
\(129\) −28.7447 + 108.094i −0.222827 + 0.837935i
\(130\) 2.91233 + 7.19289i 0.0224025 + 0.0553299i
\(131\) 1.21414 + 1.21414i 0.00926827 + 0.00926827i 0.711726 0.702457i \(-0.247914\pi\)
−0.702457 + 0.711726i \(0.747914\pi\)
\(132\) 167.647 93.6693i 1.27005 0.709616i
\(133\) 162.020 + 162.020i 1.21819 + 1.21819i
\(134\) 5.34195 12.6109i 0.0398653 0.0941110i
\(135\) 69.7730 70.5688i 0.516837 0.522732i
\(136\) 48.8281 + 21.6095i 0.359030 + 0.158893i
\(137\) −238.227 −1.73889 −0.869443 0.494033i \(-0.835522\pi\)
−0.869443 + 0.494033i \(0.835522\pi\)
\(138\) −101.573 78.9277i −0.736035 0.571940i
\(139\) −26.5704 26.5704i −0.191154 0.191154i 0.605041 0.796195i \(-0.293157\pi\)
−0.796195 + 0.605041i \(0.793157\pi\)
\(140\) −107.315 1.71382i −0.766534 0.0122416i
\(141\) −95.0030 + 55.0897i −0.673780 + 0.390707i
\(142\) 138.864 56.2245i 0.977914 0.395947i
\(143\) 16.8940i 0.118140i
\(144\) 122.631 + 75.4824i 0.851605 + 0.524183i
\(145\) −8.01896 −0.0553032
\(146\) 2.60537 + 6.43477i 0.0178450 + 0.0440738i
\(147\) −6.46207 11.1439i −0.0439596 0.0758090i
\(148\) −283.378 4.52555i −1.91472 0.0305780i
\(149\) 133.254 133.254i 0.894321 0.894321i −0.100605 0.994926i \(-0.532078\pi\)
0.994926 + 0.100605i \(0.0320779\pi\)
\(150\) 42.3033 54.4406i 0.282022 0.362937i
\(151\) 23.3716i 0.154779i −0.997001 0.0773895i \(-0.975342\pi\)
0.997001 0.0773895i \(-0.0246585\pi\)
\(152\) 90.5052 + 234.214i 0.595429 + 1.54088i
\(153\) 52.1359 + 29.8385i 0.340758 + 0.195023i
\(154\) −215.151 91.1377i −1.39708 0.591803i
\(155\) 37.9662 37.9662i 0.244943 0.244943i
\(156\) −11.0588 + 6.17886i −0.0708896 + 0.0396081i
\(157\) −95.8780 + 95.8780i −0.610688 + 0.610688i −0.943125 0.332438i \(-0.892129\pi\)
0.332438 + 0.943125i \(0.392129\pi\)
\(158\) −191.801 + 77.6585i −1.21393 + 0.491509i
\(159\) 208.808 + 55.5272i 1.31326 + 0.349227i
\(160\) −106.780 49.3106i −0.667374 0.308191i
\(161\) 156.510i 0.972113i
\(162\) 128.481 + 98.6738i 0.793095 + 0.609098i
\(163\) −103.379 + 103.379i −0.634230 + 0.634230i −0.949126 0.314896i \(-0.898030\pi\)
0.314896 + 0.949126i \(0.398030\pi\)
\(164\) −43.3086 + 41.9471i −0.264077 + 0.255775i
\(165\) −152.652 + 88.5190i −0.925166 + 0.536479i
\(166\) 82.6256 + 35.0001i 0.497744 + 0.210844i
\(167\) 113.980 0.682515 0.341258 0.939970i \(-0.389147\pi\)
0.341258 + 0.939970i \(0.389147\pi\)
\(168\) −19.0313 174.170i −0.113282 1.03673i
\(169\) 167.886i 0.993406i
\(170\) −45.1782 19.1374i −0.265754 0.112573i
\(171\) 74.1418 + 272.575i 0.433578 + 1.59401i
\(172\) 149.115 + 2.38136i 0.866946 + 0.0138451i
\(173\) 144.265 + 144.265i 0.833901 + 0.833901i 0.988048 0.154147i \(-0.0492630\pi\)
−0.154147 + 0.988048i \(0.549263\pi\)
\(174\) −1.62952 12.9886i −0.00936505 0.0746472i
\(175\) −83.8857 −0.479347
\(176\) −175.184 186.747i −0.995361 1.06106i
\(177\) −49.8918 13.2674i −0.281875 0.0749573i
\(178\) 145.080 58.7415i 0.815057 0.330008i
\(179\) −16.8240 16.8240i −0.0939888 0.0939888i 0.658549 0.752538i \(-0.271171\pi\)
−0.752538 + 0.658549i \(0.771171\pi\)
\(180\) −113.776 67.5506i −0.632087 0.375281i
\(181\) 34.2037 + 34.2037i 0.188971 + 0.188971i 0.795251 0.606280i \(-0.207339\pi\)
−0.606280 + 0.795251i \(0.707339\pi\)
\(182\) 14.1924 + 6.01187i 0.0779800 + 0.0330322i
\(183\) −113.077 30.0700i −0.617909 0.164317i
\(184\) −69.4109 + 156.839i −0.377233 + 0.852384i
\(185\) 260.421 1.40768
\(186\) 69.2104 + 53.7803i 0.372099 + 0.289141i
\(187\) −75.5295 75.5295i −0.403901 0.403901i
\(188\) 101.873 + 105.179i 0.541877 + 0.559465i
\(189\) −1.11765 197.104i −0.00591347 1.04288i
\(190\) −86.5887 213.857i −0.455730 1.12557i
\(191\) 150.160i 0.786177i −0.919501 0.393088i \(-0.871407\pi\)
0.919501 0.393088i \(-0.128593\pi\)
\(192\) 58.1716 182.976i 0.302977 0.952998i
\(193\) 117.637 0.609518 0.304759 0.952429i \(-0.401424\pi\)
0.304759 + 0.952429i \(0.401424\pi\)
\(194\) 114.130 46.2102i 0.588300 0.238197i
\(195\) 10.0697 5.83913i 0.0516393 0.0299442i
\(196\) −12.3376 + 11.9498i −0.0629471 + 0.0609682i
\(197\) 31.8524 31.8524i 0.161688 0.161688i −0.621626 0.783314i \(-0.713528\pi\)
0.783314 + 0.621626i \(0.213528\pi\)
\(198\) −174.398 229.269i −0.880797 1.15792i
\(199\) 128.347i 0.644959i 0.946576 + 0.322480i \(0.104516\pi\)
−0.946576 + 0.322480i \(0.895484\pi\)
\(200\) −84.0617 37.2026i −0.420308 0.186013i
\(201\) −19.8535 5.27952i −0.0987735 0.0262663i
\(202\) 62.8477 148.366i 0.311127 0.734486i
\(203\) −11.2623 + 11.2623i −0.0554793 + 0.0554793i
\(204\) 21.8170 77.0656i 0.106946 0.377773i
\(205\) 39.1746 39.1746i 0.191095 0.191095i
\(206\) 115.549 + 285.383i 0.560916 + 1.38536i
\(207\) −95.8429 + 167.464i −0.463009 + 0.809003i
\(208\) 11.5559 + 12.3187i 0.0555573 + 0.0592244i
\(209\) 502.290i 2.40330i
\(210\) 20.0406 + 159.740i 0.0954316 + 0.760668i
\(211\) 78.8045 78.8045i 0.373481 0.373481i −0.495262 0.868743i \(-0.664928\pi\)
0.868743 + 0.495262i \(0.164928\pi\)
\(212\) 4.60016 288.050i 0.0216989 1.35873i
\(213\) −112.728 194.402i −0.529241 0.912685i
\(214\) −84.8757 + 200.368i −0.396616 + 0.936299i
\(215\) −137.035 −0.637372
\(216\) 86.2941 198.013i 0.399510 0.916729i
\(217\) 106.644i 0.491447i
\(218\) −81.7786 + 193.057i −0.375131 + 0.885581i
\(219\) 9.00834 5.22369i 0.0411340 0.0238525i
\(220\) 163.691 + 169.004i 0.744050 + 0.768200i
\(221\) 4.98228 + 4.98228i 0.0225442 + 0.0225442i
\(222\) 52.9198 + 421.814i 0.238377 + 1.90006i
\(223\) −153.748 −0.689455 −0.344727 0.938703i \(-0.612029\pi\)
−0.344727 + 0.938703i \(0.612029\pi\)
\(224\) −219.222 + 80.7131i −0.978671 + 0.360326i
\(225\) −89.7564 51.3695i −0.398917 0.228309i
\(226\) −28.8158 71.1695i −0.127504 0.314909i
\(227\) −43.6518 43.6518i −0.192299 0.192299i 0.604390 0.796689i \(-0.293417\pi\)
−0.796689 + 0.604390i \(0.793417\pi\)
\(228\) 328.797 183.709i 1.44209 0.805739i
\(229\) −111.882 111.882i −0.488566 0.488566i 0.419288 0.907853i \(-0.362280\pi\)
−0.907853 + 0.419288i \(0.862280\pi\)
\(230\) 61.4705 145.115i 0.267263 0.630934i
\(231\) −90.0726 + 338.715i −0.389925 + 1.46630i
\(232\) −16.2807 + 6.29119i −0.0701753 + 0.0271172i
\(233\) −32.4793 −0.139396 −0.0696980 0.997568i \(-0.522204\pi\)
−0.0696980 + 0.997568i \(0.522204\pi\)
\(234\) 11.5041 + 15.1236i 0.0491628 + 0.0646310i
\(235\) −95.1395 95.1395i −0.404849 0.404849i
\(236\) −1.09914 + 68.8255i −0.00465739 + 0.291634i
\(237\) 155.703 + 268.512i 0.656974 + 1.13296i
\(238\) −90.3285 + 36.5731i −0.379532 + 0.153669i
\(239\) 133.305i 0.557762i 0.960326 + 0.278881i \(0.0899636\pi\)
−0.960326 + 0.278881i \(0.910036\pi\)
\(240\) −50.7608 + 168.963i −0.211503 + 0.704014i
\(241\) 159.670 0.662532 0.331266 0.943537i \(-0.392524\pi\)
0.331266 + 0.943537i \(0.392524\pi\)
\(242\) 101.410 + 250.464i 0.419051 + 1.03497i
\(243\) 119.506 211.583i 0.491793 0.870712i
\(244\) −2.49116 + 155.990i −0.0102097 + 0.639302i
\(245\) 11.1599 11.1599i 0.0455508 0.0455508i
\(246\) 71.4131 + 55.4919i 0.290297 + 0.225577i
\(247\) 33.1334i 0.134143i
\(248\) 47.2957 106.868i 0.190708 0.430918i
\(249\) 34.5911 130.079i 0.138920 0.522404i
\(250\) 246.997 + 104.628i 0.987987 + 0.418510i
\(251\) −106.711 + 106.711i −0.425141 + 0.425141i −0.886969 0.461828i \(-0.847194\pi\)
0.461828 + 0.886969i \(0.347194\pi\)
\(252\) −254.665 + 64.9211i −1.01058 + 0.257623i
\(253\) 242.605 242.605i 0.958913 0.958913i
\(254\) 80.3473 32.5318i 0.316328 0.128078i
\(255\) −18.9138 + 71.1246i −0.0741717 + 0.278920i
\(256\) −255.478 16.3408i −0.997961 0.0638312i
\(257\) 343.816i 1.33781i 0.743350 + 0.668903i \(0.233236\pi\)
−0.743350 + 0.668903i \(0.766764\pi\)
\(258\) −27.8466 221.961i −0.107933 0.860313i
\(259\) 365.751 365.751i 1.41217 1.41217i
\(260\) −10.7978 11.1483i −0.0415301 0.0428781i
\(261\) −18.9472 + 5.15374i −0.0725948 + 0.0197461i
\(262\) −3.16212 1.33947i −0.0120691 0.00511248i
\(263\) −266.255 −1.01238 −0.506188 0.862423i \(-0.668946\pi\)
−0.506188 + 0.862423i \(0.668946\pi\)
\(264\) −240.479 + 299.479i −0.910905 + 1.13439i
\(265\) 264.715i 0.998925i
\(266\) −421.964 178.743i −1.58633 0.671968i
\(267\) −117.775 203.104i −0.441104 0.760691i
\(268\) −0.437383 + 27.3878i −0.00163203 + 0.102193i
\(269\) −102.194 102.194i −0.379904 0.379904i 0.491164 0.871067i \(-0.336572\pi\)
−0.871067 + 0.491164i \(0.836572\pi\)
\(270\) −76.3778 + 183.192i −0.282881 + 0.678490i
\(271\) −38.5636 −0.142301 −0.0711505 0.997466i \(-0.522667\pi\)
−0.0711505 + 0.997466i \(0.522667\pi\)
\(272\) −106.738 3.41008i −0.392419 0.0125371i
\(273\) 5.94161 22.3432i 0.0217641 0.0818433i
\(274\) 441.629 178.811i 1.61178 0.652595i
\(275\) 130.030 + 130.030i 0.472838 + 0.472838i
\(276\) 247.539 + 70.0775i 0.896881 + 0.253904i
\(277\) −277.306 277.306i −1.00111 1.00111i −0.999999 0.00110593i \(-0.999648\pi\)
−0.00110593 0.999999i \(-0.500352\pi\)
\(278\) 69.1999 + 29.3130i 0.248921 + 0.105443i
\(279\) 65.3061 114.107i 0.234072 0.408987i
\(280\) 200.228 77.3722i 0.715098 0.276329i
\(281\) 458.765 1.63262 0.816308 0.577617i \(-0.196017\pi\)
0.816308 + 0.577617i \(0.196017\pi\)
\(282\) 134.768 173.434i 0.477900 0.615015i
\(283\) 276.746 + 276.746i 0.977900 + 0.977900i 0.999761 0.0218614i \(-0.00695927\pi\)
−0.0218614 + 0.999761i \(0.506959\pi\)
\(284\) −215.226 + 208.459i −0.757837 + 0.734012i
\(285\) −299.389 + 173.608i −1.05049 + 0.609149i
\(286\) −12.6805 31.3184i −0.0443374 0.109505i
\(287\) 110.038i 0.383408i
\(288\) −283.991 47.8844i −0.986081 0.166265i
\(289\) 244.451 0.845850
\(290\) 14.8656 6.01895i 0.0512608 0.0207550i
\(291\) −92.6499 159.776i −0.318384 0.549059i
\(292\) −9.65974 9.97328i −0.0330813 0.0341551i
\(293\) −306.513 + 306.513i −1.04612 + 1.04612i −0.0472370 + 0.998884i \(0.515042\pi\)
−0.998884 + 0.0472370i \(0.984958\pi\)
\(294\) 20.3440 + 15.8084i 0.0691972 + 0.0537700i
\(295\) 63.2500i 0.214407i
\(296\) 528.726 204.311i 1.78624 0.690240i
\(297\) −303.797 + 307.262i −1.02289 + 1.03455i
\(298\) −147.009 + 347.046i −0.493317 + 1.16459i
\(299\) −16.0033 + 16.0033i −0.0535229 + 0.0535229i
\(300\) −37.5599 + 132.675i −0.125200 + 0.442250i
\(301\) −192.460 + 192.460i −0.639401 + 0.639401i
\(302\) 17.5425 + 43.3266i 0.0580877 + 0.143466i
\(303\) −233.575 62.1133i −0.770874 0.204994i
\(304\) −343.578 366.256i −1.13019 1.20479i
\(305\) 143.353i 0.470010i
\(306\) −119.047 16.1822i −0.389041 0.0528831i
\(307\) −359.692 + 359.692i −1.17163 + 1.17163i −0.189814 + 0.981820i \(0.560789\pi\)
−0.981820 + 0.189814i \(0.939211\pi\)
\(308\) 467.256 + 7.46209i 1.51706 + 0.0242276i
\(309\) 399.521 231.672i 1.29295 0.749746i
\(310\) −41.8852 + 98.8793i −0.135113 + 0.318965i
\(311\) 572.008 1.83925 0.919626 0.392794i \(-0.128492\pi\)
0.919626 + 0.392794i \(0.128492\pi\)
\(312\) 15.8631 19.7550i 0.0508433 0.0633175i
\(313\) 333.314i 1.06490i 0.846461 + 0.532450i \(0.178729\pi\)
−0.846461 + 0.532450i \(0.821271\pi\)
\(314\) 105.775 249.705i 0.336862 0.795238i
\(315\) 233.022 63.3832i 0.739754 0.201217i
\(316\) 297.274 287.928i 0.940741 0.911166i
\(317\) −266.382 266.382i −0.840322 0.840322i 0.148578 0.988901i \(-0.452530\pi\)
−0.988901 + 0.148578i \(0.952530\pi\)
\(318\) −428.769 + 53.7923i −1.34833 + 0.169158i
\(319\) 34.9151 0.109452
\(320\) 234.962 + 11.2647i 0.734255 + 0.0352021i
\(321\) 315.442 + 83.8838i 0.982686 + 0.261320i
\(322\) −117.475 290.140i −0.364829 0.901057i
\(323\) −148.132 148.132i −0.458613 0.458613i
\(324\) −312.244 86.4858i −0.963715 0.266932i
\(325\) −8.57741 8.57741i −0.0263920 0.0263920i
\(326\) 114.050 269.242i 0.349848 0.825894i
\(327\) 303.932 + 80.8229i 0.929455 + 0.247165i
\(328\) 48.8009 110.269i 0.148783 0.336186i
\(329\) −267.239 −0.812276
\(330\) 216.547 278.677i 0.656204 0.844475i
\(331\) −212.431 212.431i −0.641787 0.641787i 0.309208 0.950995i \(-0.399936\pi\)
−0.950995 + 0.309208i \(0.899936\pi\)
\(332\) −179.443 2.86571i −0.540491 0.00863165i
\(333\) 615.325 167.371i 1.84782 0.502617i
\(334\) −211.298 + 85.5522i −0.632627 + 0.256144i
\(335\) 25.1691i 0.0751317i
\(336\) 166.011 + 308.593i 0.494079 + 0.918433i
\(337\) −207.477 −0.615658 −0.307829 0.951442i \(-0.599602\pi\)
−0.307829 + 0.951442i \(0.599602\pi\)
\(338\) −126.013 311.228i −0.372820 0.920793i
\(339\) −99.6335 + 57.7748i −0.293904 + 0.170427i
\(340\) 98.1161 + 1.56692i 0.288577 + 0.00460858i
\(341\) −165.308 + 165.308i −0.484773 + 0.484773i
\(342\) −342.037 449.653i −1.00011 1.31477i
\(343\) 326.366i 0.951505i
\(344\) −278.218 + 107.509i −0.808773 + 0.312527i
\(345\) −228.456 60.7521i −0.662192 0.176093i
\(346\) −375.723 159.156i −1.08591 0.459989i
\(347\) −98.4692 + 98.4692i −0.283773 + 0.283773i −0.834612 0.550839i \(-0.814308\pi\)
0.550839 + 0.834612i \(0.314308\pi\)
\(348\) 12.7699 + 22.8553i 0.0366952 + 0.0656763i
\(349\) −337.382 + 337.382i −0.966711 + 0.966711i −0.999463 0.0327527i \(-0.989573\pi\)
0.0327527 + 0.999463i \(0.489573\pi\)
\(350\) 155.508 62.9637i 0.444309 0.179896i
\(351\) 20.0399 20.2684i 0.0570936 0.0577448i
\(352\) 464.927 + 214.702i 1.32082 + 0.609948i
\(353\) 293.330i 0.830964i 0.909601 + 0.415482i \(0.136387\pi\)
−0.909601 + 0.415482i \(0.863613\pi\)
\(354\) 102.448 12.8529i 0.289402 0.0363077i
\(355\) 194.681 194.681i 0.548398 0.548398i
\(356\) −224.860 + 217.791i −0.631630 + 0.611773i
\(357\) 73.3279 + 126.455i 0.205400 + 0.354216i
\(358\) 43.8164 + 18.5606i 0.122392 + 0.0518452i
\(359\) 305.954 0.852239 0.426119 0.904667i \(-0.359880\pi\)
0.426119 + 0.904667i \(0.359880\pi\)
\(360\) 261.621 + 39.8272i 0.726726 + 0.110631i
\(361\) 624.114i 1.72885i
\(362\) −89.0801 37.7342i −0.246078 0.104238i
\(363\) 350.636 203.324i 0.965939 0.560122i
\(364\) −30.8224 0.492234i −0.0846769 0.00135229i
\(365\) 9.02128 + 9.02128i 0.0247158 + 0.0247158i
\(366\) 232.194 29.1305i 0.634411 0.0795916i
\(367\) 221.149 0.602585 0.301292 0.953532i \(-0.402582\pi\)
0.301292 + 0.953532i \(0.402582\pi\)
\(368\) 10.9534 342.848i 0.0297646 0.931653i
\(369\) 67.3845 117.739i 0.182614 0.319076i
\(370\) −482.772 + 195.470i −1.30479 + 0.528296i
\(371\) 371.781 + 371.781i 1.00211 + 1.00211i
\(372\) −168.670 47.7499i −0.453414 0.128360i
\(373\) 147.216 + 147.216i 0.394682 + 0.394682i 0.876352 0.481671i \(-0.159970\pi\)
−0.481671 + 0.876352i \(0.659970\pi\)
\(374\) 196.709 + 83.3257i 0.525960 + 0.222796i
\(375\) 103.405 388.850i 0.275746 1.03693i
\(376\) −267.800 118.518i −0.712233 0.315208i
\(377\) −2.30317 −0.00610919
\(378\) 150.016 + 364.555i 0.396868 + 0.964431i
\(379\) 298.572 + 298.572i 0.787790 + 0.787790i 0.981131 0.193342i \(-0.0619326\pi\)
−0.193342 + 0.981131i \(0.561933\pi\)
\(380\) 321.038 + 331.459i 0.844837 + 0.872259i
\(381\) −65.2252 112.482i −0.171195 0.295228i
\(382\) 112.708 + 278.368i 0.295048 + 0.728712i
\(383\) 427.326i 1.11573i −0.829931 0.557866i \(-0.811620\pi\)
0.829931 0.557866i \(-0.188380\pi\)
\(384\) 29.5003 + 382.865i 0.0768237 + 0.997045i
\(385\) −429.404 −1.11533
\(386\) −218.077 + 88.2971i −0.564966 + 0.228749i
\(387\) −323.787 + 88.0716i −0.836658 + 0.227575i
\(388\) −176.891 + 171.330i −0.455904 + 0.441572i
\(389\) −314.075 + 314.075i −0.807391 + 0.807391i −0.984238 0.176847i \(-0.943410\pi\)
0.176847 + 0.984238i \(0.443410\pi\)
\(390\) −14.2845 + 18.3828i −0.0366268 + 0.0471354i
\(391\) 143.095i 0.365971i
\(392\) 13.9023 31.4131i 0.0354650 0.0801355i
\(393\) −1.32382 + 4.97816i −0.00336849 + 0.0126671i
\(394\) −35.1403 + 82.9565i −0.0891886 + 0.210550i
\(395\) −268.898 + 268.898i −0.680753 + 0.680753i
\(396\) 495.387 + 294.120i 1.25098 + 0.742728i
\(397\) 189.839 189.839i 0.478185 0.478185i −0.426366 0.904551i \(-0.640206\pi\)
0.904551 + 0.426366i \(0.140206\pi\)
\(398\) −96.3358 237.931i −0.242050 0.597816i
\(399\) −176.655 + 664.304i −0.442743 + 1.66492i
\(400\) 183.758 + 5.87075i 0.459396 + 0.0146769i
\(401\) 268.223i 0.668886i 0.942416 + 0.334443i \(0.108548\pi\)
−0.942416 + 0.334443i \(0.891452\pi\)
\(402\) 40.7673 5.11457i 0.101411 0.0127228i
\(403\) 10.9045 10.9045i 0.0270582 0.0270582i
\(404\) −5.14579 + 322.216i −0.0127371 + 0.797563i
\(405\) 288.145 + 74.8780i 0.711469 + 0.184884i
\(406\) 12.4248 29.3315i 0.0306030 0.0722451i
\(407\) −1133.89 −2.78598
\(408\) 17.4000 + 159.241i 0.0426471 + 0.390296i
\(409\) 25.8478i 0.0631976i −0.999501 0.0315988i \(-0.989940\pi\)
0.999501 0.0315988i \(-0.0100599\pi\)
\(410\) −43.2182 + 102.026i −0.105410 + 0.248844i
\(411\) −358.510 618.257i −0.872288 1.50427i
\(412\) −428.411 442.317i −1.03983 1.07358i
\(413\) −88.8319 88.8319i −0.215089 0.215089i
\(414\) 51.9783 382.384i 0.125551 0.923634i
\(415\) 164.906 0.397365
\(416\) −30.6688 14.1627i −0.0737230 0.0340450i
\(417\) 28.9705 108.942i 0.0694735 0.261253i
\(418\) 377.014 + 931.151i 0.901946 + 2.22763i
\(419\) 243.361 + 243.361i 0.580813 + 0.580813i 0.935127 0.354313i \(-0.115285\pi\)
−0.354313 + 0.935127i \(0.615285\pi\)
\(420\) −157.051 281.086i −0.373931 0.669253i
\(421\) 115.847 + 115.847i 0.275171 + 0.275171i 0.831178 0.556007i \(-0.187667\pi\)
−0.556007 + 0.831178i \(0.687667\pi\)
\(422\) −86.9388 + 205.238i −0.206016 + 0.486347i
\(423\) −285.942 163.650i −0.675985 0.386880i
\(424\) 207.679 + 537.443i 0.489810 + 1.26755i
\(425\) 76.6953 0.180460
\(426\) 354.893 + 275.771i 0.833082 + 0.647351i
\(427\) −201.333 201.333i −0.471507 0.471507i
\(428\) 6.94937 435.151i 0.0162369 1.01671i
\(429\) −43.8440 + 25.4240i −0.102201 + 0.0592634i
\(430\) 254.037 102.857i 0.590784 0.239202i
\(431\) 568.037i 1.31795i −0.752165 0.658975i \(-0.770990\pi\)
0.752165 0.658975i \(-0.229010\pi\)
\(432\) −11.3461 + 431.851i −0.0262640 + 0.999655i
\(433\) −647.222 −1.49474 −0.747370 0.664408i \(-0.768684\pi\)
−0.747370 + 0.664408i \(0.768684\pi\)
\(434\) 80.0458 + 197.698i 0.184437 + 0.455525i
\(435\) −12.0678 20.8111i −0.0277421 0.0478416i
\(436\) 6.69579 419.273i 0.0153573 0.961635i
\(437\) 475.808 475.808i 1.08881 1.08881i
\(438\) −12.7789 + 16.4453i −0.0291756 + 0.0375464i
\(439\) 486.389i 1.10795i −0.832534 0.553973i \(-0.813111\pi\)
0.832534 0.553973i \(-0.186889\pi\)
\(440\) −430.305 190.437i −0.977965 0.432811i
\(441\) 19.1963 33.5412i 0.0435291 0.0760571i
\(442\) −12.9758 5.49655i −0.0293571 0.0124356i
\(443\) 258.469 258.469i 0.583451 0.583451i −0.352399 0.935850i \(-0.614634\pi\)
0.935850 + 0.352399i \(0.114634\pi\)
\(444\) −414.713 742.243i −0.934038 1.67172i
\(445\) 203.396 203.396i 0.457070 0.457070i
\(446\) 285.020 115.402i 0.639059 0.258749i
\(447\) 546.360 + 145.290i 1.22228 + 0.325035i
\(448\) 345.814 314.173i 0.771907 0.701279i
\(449\) 498.015i 1.10916i −0.832129 0.554582i \(-0.812878\pi\)
0.832129 0.554582i \(-0.187122\pi\)
\(450\) 204.949 + 27.8591i 0.455442 + 0.0619091i
\(451\) −170.569 + 170.569i −0.378201 + 0.378201i
\(452\) 106.838 + 110.306i 0.236368 + 0.244040i
\(453\) 60.6549 35.1721i 0.133896 0.0776427i
\(454\) 113.687 + 48.1576i 0.250411 + 0.106074i
\(455\) 28.3255 0.0622538
\(456\) −471.638 + 587.353i −1.03429 + 1.28805i
\(457\) 466.468i 1.02072i −0.859961 0.510359i \(-0.829513\pi\)
0.859961 0.510359i \(-0.170487\pi\)
\(458\) 291.384 + 123.430i 0.636210 + 0.269498i
\(459\) 1.02185 + 180.209i 0.00222624 + 0.392613i
\(460\) −5.03302 + 315.155i −0.0109414 + 0.685119i
\(461\) 389.251 + 389.251i 0.844362 + 0.844362i 0.989423 0.145061i \(-0.0463378\pi\)
−0.145061 + 0.989423i \(0.546338\pi\)
\(462\) −87.2584 695.521i −0.188871 1.50546i
\(463\) 500.857 1.08177 0.540883 0.841098i \(-0.318090\pi\)
0.540883 + 0.841098i \(0.318090\pi\)
\(464\) 25.4592 23.8828i 0.0548689 0.0514715i
\(465\) 155.667 + 41.3957i 0.334768 + 0.0890229i
\(466\) 60.2104 24.3786i 0.129207 0.0523146i
\(467\) −188.836 188.836i −0.404359 0.404359i 0.475407 0.879766i \(-0.342301\pi\)
−0.879766 + 0.475407i \(0.842301\pi\)
\(468\) −32.6781 19.4015i −0.0698249 0.0414563i
\(469\) −35.3489 35.3489i −0.0753709 0.0753709i
\(470\) 247.781 + 104.960i 0.527195 + 0.223319i
\(471\) −393.113 104.538i −0.834636 0.221950i
\(472\) −49.6221 128.415i −0.105132 0.272065i
\(473\) 596.660 1.26144
\(474\) −490.186 380.901i −1.03415 0.803589i
\(475\) 255.022 + 255.022i 0.536888 + 0.536888i
\(476\) 140.001 135.599i 0.294119 0.284872i
\(477\) 170.131 + 625.470i 0.356668 + 1.31126i
\(478\) −100.058 247.123i −0.209325 0.516993i
\(479\) 326.344i 0.681303i 0.940190 + 0.340652i \(0.110648\pi\)
−0.940190 + 0.340652i \(0.889352\pi\)
\(480\) −32.7212 351.327i −0.0681691 0.731931i
\(481\) 74.7969 0.155503
\(482\) −295.998 + 119.847i −0.614104 + 0.248645i
\(483\) −406.181 + 235.533i −0.840954 + 0.487647i
\(484\) −375.991 388.195i −0.776841 0.802056i
\(485\) 160.006 160.006i 0.329909 0.329909i
\(486\) −62.7292 + 481.935i −0.129072 + 0.991635i
\(487\) 196.238i 0.402952i 0.979493 + 0.201476i \(0.0645739\pi\)
−0.979493 + 0.201476i \(0.935426\pi\)
\(488\) −112.466 291.045i −0.230463 0.596405i
\(489\) −423.871 112.718i −0.866812 0.230506i
\(490\) −12.3119 + 29.0650i −0.0251263 + 0.0593162i
\(491\) −349.172 + 349.172i −0.711144 + 0.711144i −0.966774 0.255631i \(-0.917717\pi\)
0.255631 + 0.966774i \(0.417717\pi\)
\(492\) −174.038 49.2696i −0.353736 0.100141i
\(493\) 10.2969 10.2969i 0.0208863 0.0208863i
\(494\) −24.8696 61.4230i −0.0503433 0.124338i
\(495\) −459.456 262.956i −0.928193 0.531224i
\(496\) −7.46348 + 233.612i −0.0150473 + 0.470992i
\(497\) 546.843i 1.10029i
\(498\) 33.5103 + 267.105i 0.0672898 + 0.536355i
\(499\) −321.326 + 321.326i −0.643940 + 0.643940i −0.951522 0.307582i \(-0.900480\pi\)
0.307582 + 0.951522i \(0.400480\pi\)
\(500\) −536.418 8.56660i −1.07284 0.0171332i
\(501\) 171.530 + 295.805i 0.342374 + 0.590430i
\(502\) 117.725 277.917i 0.234513 0.553619i
\(503\) 623.698 1.23996 0.619978 0.784619i \(-0.287142\pi\)
0.619978 + 0.784619i \(0.287142\pi\)
\(504\) 423.372 311.500i 0.840023 0.618056i
\(505\) 296.113i 0.586362i
\(506\) −267.647 + 631.840i −0.528947 + 1.24870i
\(507\) −435.703 + 252.652i −0.859374 + 0.498328i
\(508\) −124.531 + 120.616i −0.245139 + 0.237432i
\(509\) −452.448 452.448i −0.888897 0.888897i 0.105520 0.994417i \(-0.466349\pi\)
−0.994417 + 0.105520i \(0.966349\pi\)
\(510\) −18.3228 146.048i −0.0359271 0.286369i
\(511\) 25.3400 0.0495891
\(512\) 485.873 161.466i 0.948971 0.315364i
\(513\) −595.821 + 602.616i −1.16144 + 1.17469i
\(514\) −258.065 637.370i −0.502071 1.24002i
\(515\) 400.095 + 400.095i 0.776884 + 0.776884i
\(516\) 218.224 + 390.572i 0.422914 + 0.756922i
\(517\) 414.244 + 414.244i 0.801247 + 0.801247i
\(518\) −403.504 + 952.562i −0.778966 + 1.83892i
\(519\) −157.296 + 591.506i −0.303075 + 1.13970i
\(520\) 28.3849 + 12.5621i 0.0545863 + 0.0241579i
\(521\) 444.986 0.854100 0.427050 0.904228i \(-0.359553\pi\)
0.427050 + 0.904228i \(0.359553\pi\)
\(522\) 31.2562 23.7757i 0.0598779 0.0455472i
\(523\) 399.942 + 399.942i 0.764707 + 0.764707i 0.977169 0.212462i \(-0.0681483\pi\)
−0.212462 + 0.977169i \(0.568148\pi\)
\(524\) 6.86736 + 0.109672i 0.0131056 + 0.000209297i
\(525\) −126.240 217.703i −0.240458 0.414673i
\(526\) 493.586 199.848i 0.938377 0.379939i
\(527\) 97.5029i 0.185015i
\(528\) 221.016 735.679i 0.418591 1.39333i
\(529\) −69.3715 −0.131137
\(530\) −198.692 490.732i −0.374891 0.925909i
\(531\) −40.6504 149.447i −0.0765544 0.281445i
\(532\) 916.404 + 14.6350i 1.72256 + 0.0275094i
\(533\) 11.2515 11.2515i 0.0211098 0.0211098i
\(534\) 370.780 + 288.117i 0.694345 + 0.539545i
\(535\) 399.900i 0.747476i
\(536\) −19.7462 51.1001i −0.0368399 0.0953360i
\(537\) 18.3437 68.9808i 0.0341595 0.128456i
\(538\) 266.154 + 112.743i 0.494711 + 0.209559i
\(539\) −48.5912 + 48.5912i −0.0901506 + 0.0901506i
\(540\) 4.08791 396.932i 0.00757020 0.735059i
\(541\) −116.940 + 116.940i −0.216155 + 0.216155i −0.806876 0.590721i \(-0.798844\pi\)
0.590721 + 0.806876i \(0.298844\pi\)
\(542\) 71.4895 28.9454i 0.131900 0.0534048i
\(543\) −37.2932 + 140.240i −0.0686800 + 0.258269i
\(544\) 200.432 73.7947i 0.368440 0.135652i
\(545\) 385.308i 0.706987i
\(546\) 5.75597 + 45.8798i 0.0105421 + 0.0840290i
\(547\) 85.6914 85.6914i 0.156657 0.156657i −0.624427 0.781084i \(-0.714667\pi\)
0.781084 + 0.624427i \(0.214667\pi\)
\(548\) −684.483 + 662.964i −1.24906 + 1.20979i
\(549\) −92.1322 338.715i −0.167818 0.616968i
\(550\) −338.651 143.452i −0.615729 0.260822i
\(551\) 68.4772 0.124278
\(552\) −511.490 + 55.8898i −0.926613 + 0.101250i
\(553\) 755.311i 1.36584i
\(554\) 722.216 + 305.930i 1.30364 + 0.552220i
\(555\) 391.910 + 675.855i 0.706145 + 1.21776i
\(556\) −150.286 2.40006i −0.270298 0.00431666i
\(557\) −104.194 104.194i −0.187062 0.187062i 0.607363 0.794425i \(-0.292228\pi\)
−0.794425 + 0.607363i \(0.792228\pi\)
\(558\) −35.4173 + 260.552i −0.0634718 + 0.466938i
\(559\) −39.3585 −0.0704087
\(560\) −313.109 + 293.722i −0.559124 + 0.524504i
\(561\) 82.3519 309.682i 0.146795 0.552017i
\(562\) −850.464 + 344.344i −1.51328 + 0.612712i
\(563\) −776.673 776.673i −1.37953 1.37953i −0.845414 0.534111i \(-0.820646\pi\)
−0.534111 0.845414i \(-0.679354\pi\)
\(564\) −119.656 + 422.670i −0.212157 + 0.749414i
\(565\) −99.7766 99.7766i −0.176596 0.176596i
\(566\) −720.756 305.312i −1.27342 0.539420i
\(567\) 509.850 299.524i 0.899207 0.528261i
\(568\) 242.520 547.990i 0.426972 0.964772i
\(569\) −456.546 −0.802366 −0.401183 0.915998i \(-0.631401\pi\)
−0.401183 + 0.915998i \(0.631401\pi\)
\(570\) 424.702 546.554i 0.745092 0.958866i
\(571\) −475.108 475.108i −0.832062 0.832062i 0.155736 0.987799i \(-0.450225\pi\)
−0.987799 + 0.155736i \(0.950225\pi\)
\(572\) 47.0145 + 48.5405i 0.0821931 + 0.0848610i
\(573\) 389.700 225.977i 0.680105 0.394375i
\(574\) 82.5934 + 203.990i 0.143891 + 0.355383i
\(575\) 246.350i 0.428434i
\(576\) 562.408 124.392i 0.976402 0.215959i
\(577\) 1127.70 1.95443 0.977213 0.212262i \(-0.0680832\pi\)
0.977213 + 0.212262i \(0.0680832\pi\)
\(578\) −453.165 + 183.482i −0.784023 + 0.317443i
\(579\) 177.033 + 305.296i 0.305756 + 0.527281i
\(580\) −23.0403 + 22.3160i −0.0397247 + 0.0384758i
\(581\) 231.604 231.604i 0.398630 0.398630i
\(582\) 291.682 + 226.653i 0.501171 + 0.389438i
\(583\) 1152.59i 1.97700i
\(584\) 25.3932 + 11.2381i 0.0434815 + 0.0192433i
\(585\) 30.3078 + 17.3458i 0.0518082 + 0.0296509i
\(586\) 338.152 798.284i 0.577051 1.36226i
\(587\) 584.236 584.236i 0.995292 0.995292i −0.00469688 0.999989i \(-0.501495\pi\)
0.999989 + 0.00469688i \(0.00149507\pi\)
\(588\) −49.5795 14.0358i −0.0843188 0.0238704i
\(589\) −324.209 + 324.209i −0.550440 + 0.550440i
\(590\) 47.4748 + 117.254i 0.0804657 + 0.198735i
\(591\) 130.600 + 34.7296i 0.220981 + 0.0587642i
\(592\) −826.804 + 775.610i −1.39663 + 1.31015i
\(593\) 870.906i 1.46864i 0.678801 + 0.734322i \(0.262500\pi\)
−0.678801 + 0.734322i \(0.737500\pi\)
\(594\) 332.555 797.632i 0.559856 1.34281i
\(595\) −126.637 + 126.637i −0.212835 + 0.212835i
\(596\) 12.0366 753.702i 0.0201957 1.26460i
\(597\) −333.090 + 193.150i −0.557940 + 0.323535i
\(598\) 17.6552 41.6791i 0.0295238 0.0696975i
\(599\) −224.305 −0.374466 −0.187233 0.982316i \(-0.559952\pi\)
−0.187233 + 0.982316i \(0.559952\pi\)
\(600\) −29.9556 274.146i −0.0499260 0.456911i
\(601\) 234.358i 0.389946i 0.980809 + 0.194973i \(0.0624620\pi\)
−0.980809 + 0.194973i \(0.937538\pi\)
\(602\) 212.326 501.243i 0.352701 0.832629i
\(603\) −16.1760 59.4697i −0.0268259 0.0986230i
\(604\) −65.0410 67.1521i −0.107684 0.111179i
\(605\) 351.140 + 351.140i 0.580396 + 0.580396i
\(606\) 479.625 60.1726i 0.791461 0.0992947i
\(607\) −620.755 −1.02266 −0.511330 0.859384i \(-0.670847\pi\)
−0.511330 + 0.859384i \(0.670847\pi\)
\(608\) 911.837 + 421.083i 1.49973 + 0.692571i
\(609\) −46.1770 12.2796i −0.0758244 0.0201635i
\(610\) 107.599 + 265.750i 0.176392 + 0.435655i
\(611\) −27.3255 27.3255i −0.0447226 0.0447226i
\(612\) 232.836 59.3563i 0.380451 0.0969875i
\(613\) −645.945 645.945i −1.05374 1.05374i −0.998471 0.0552724i \(-0.982397\pi\)
−0.0552724 0.998471i \(-0.517603\pi\)
\(614\) 396.820 936.781i 0.646286 1.52570i
\(615\) 160.621 + 42.7131i 0.261173 + 0.0694523i
\(616\) −871.805 + 336.884i −1.41527 + 0.546890i
\(617\) −169.883 −0.275337 −0.137669 0.990478i \(-0.543961\pi\)
−0.137669 + 0.990478i \(0.543961\pi\)
\(618\) −566.747 + 729.352i −0.917066 + 1.18018i
\(619\) −647.603 647.603i −1.04621 1.04621i −0.998879 0.0473286i \(-0.984929\pi\)
−0.0473286 0.998879i \(-0.515071\pi\)
\(620\) 3.42943 214.742i 0.00553134 0.346358i
\(621\) −578.842 + 3.28222i −0.932113 + 0.00528539i
\(622\) −1060.39 + 429.343i −1.70481 + 0.690262i
\(623\) 571.323i 0.917051i
\(624\) −14.5793 + 48.5288i −0.0233642 + 0.0777705i
\(625\) 205.694 0.329110
\(626\) −250.182 617.901i −0.399652 0.987062i
\(627\) 1303.56 755.900i 2.07904 1.20558i
\(628\) −8.66051 + 542.298i −0.0137906 + 0.863533i
\(629\) −334.400 + 334.400i −0.531638 + 0.531638i
\(630\) −384.405 + 292.405i −0.610166 + 0.464134i
\(631\) 975.374i 1.54576i 0.634553 + 0.772880i \(0.281184\pi\)
−0.634553 + 0.772880i \(0.718816\pi\)
\(632\) −334.974 + 756.895i −0.530022 + 1.19762i
\(633\) 323.110 + 85.9228i 0.510442 + 0.135739i
\(634\) 693.766 + 293.879i 1.09427 + 0.463531i
\(635\) 112.643 112.643i 0.177391 0.177391i
\(636\) 754.480 421.550i 1.18629 0.662815i
\(637\) 3.20530 3.20530i 0.00503187 0.00503187i
\(638\) −64.7261 + 26.2069i −0.101452 + 0.0410767i
\(639\) 334.873 585.114i 0.524058 0.915671i
\(640\) −444.030 + 155.477i −0.693796 + 0.242933i
\(641\) 771.555i 1.20367i −0.798619 0.601837i \(-0.794436\pi\)
0.798619 0.601837i \(-0.205564\pi\)
\(642\) −647.733 + 81.2629i −1.00893 + 0.126578i
\(643\) 319.214 319.214i 0.496445 0.496445i −0.413884 0.910330i \(-0.635828\pi\)
0.910330 + 0.413884i \(0.135828\pi\)
\(644\) 435.553 + 449.690i 0.676324 + 0.698276i
\(645\) −206.225 355.638i −0.319729 0.551377i
\(646\) 385.795 + 163.422i 0.597206 + 0.252976i
\(647\) 360.720 0.557527 0.278764 0.960360i \(-0.410075\pi\)
0.278764 + 0.960360i \(0.410075\pi\)
\(648\) 643.756 74.0385i 0.993451 0.114257i
\(649\) 275.395i 0.424338i
\(650\) 22.3390 + 9.46278i 0.0343677 + 0.0145581i
\(651\) 276.766 160.489i 0.425140 0.246527i
\(652\) −9.33812 + 584.728i −0.0143223 + 0.896822i
\(653\) −415.043 415.043i −0.635595 0.635595i 0.313871 0.949466i \(-0.398374\pi\)
−0.949466 + 0.313871i \(0.898374\pi\)
\(654\) −624.097 + 78.2977i −0.954277 + 0.119721i
\(655\) −6.31104 −0.00963517
\(656\) −7.70102 + 241.047i −0.0117394 + 0.367450i
\(657\) 27.1134 + 15.5176i 0.0412685 + 0.0236189i
\(658\) 495.410 200.587i 0.752903 0.304843i
\(659\) 363.535 + 363.535i 0.551646 + 0.551646i 0.926916 0.375269i \(-0.122450\pi\)
−0.375269 + 0.926916i \(0.622450\pi\)
\(660\) −192.266 + 679.152i −0.291312 + 1.02902i
\(661\) −151.997 151.997i −0.229951 0.229951i 0.582721 0.812672i \(-0.301988\pi\)
−0.812672 + 0.582721i \(0.801988\pi\)
\(662\) 553.257 + 234.359i 0.835735 + 0.354017i
\(663\) −5.43232 + 20.4280i −0.00819354 + 0.0308115i
\(664\) 334.804 129.376i 0.504223 0.194843i
\(665\) −842.166 −1.26642
\(666\) −1015.07 + 772.131i −1.52413 + 1.15936i
\(667\) 33.0743 + 33.0743i 0.0495867 + 0.0495867i
\(668\) 327.491 317.195i 0.490256 0.474843i
\(669\) −231.377 399.013i −0.345855 0.596433i
\(670\) 18.8917 + 46.6588i 0.0281965 + 0.0696400i
\(671\) 624.170i 0.930208i
\(672\) −539.379 447.468i −0.802647 0.665875i
\(673\) −271.149 −0.402896 −0.201448 0.979499i \(-0.564565\pi\)
−0.201448 + 0.979499i \(0.564565\pi\)
\(674\) 384.622 155.730i 0.570656 0.231053i
\(675\) −1.75919 310.245i −0.00260621 0.459623i
\(676\) 467.209 + 482.374i 0.691138 + 0.713571i
\(677\) −639.750 + 639.750i −0.944978 + 0.944978i −0.998563 0.0535849i \(-0.982935\pi\)
0.0535849 + 0.998563i \(0.482935\pi\)
\(678\) 141.336 181.887i 0.208461 0.268270i
\(679\) 449.442i 0.661918i
\(680\) −183.065 + 70.7402i −0.269213 + 0.104030i
\(681\) 47.5948 178.979i 0.0698895 0.262817i
\(682\) 182.371 430.528i 0.267406 0.631272i
\(683\) 93.1730 93.1730i 0.136417 0.136417i −0.635601 0.772018i \(-0.719248\pi\)
0.772018 + 0.635601i \(0.219248\pi\)
\(684\) 971.577 + 576.842i 1.42043 + 0.843336i
\(685\) 619.145 619.145i 0.903861 0.903861i
\(686\) −244.967 605.021i −0.357095 0.881955i
\(687\) 121.988 458.731i 0.177566 0.667730i
\(688\) 435.068 408.130i 0.632367 0.593212i
\(689\) 76.0301i 0.110348i
\(690\) 469.115 58.8540i 0.679876 0.0852956i
\(691\) 303.844 303.844i 0.439716 0.439716i −0.452200 0.891916i \(-0.649361\pi\)
0.891916 + 0.452200i \(0.149361\pi\)
\(692\) 815.981 + 13.0312i 1.17916 + 0.0188313i
\(693\) −1014.60 + 275.975i −1.46406 + 0.398233i
\(694\) 108.633 256.453i 0.156532 0.369529i
\(695\) 138.111 0.198721
\(696\) −40.8280 32.7845i −0.0586610 0.0471042i
\(697\) 100.606i 0.144341i
\(698\) 372.207 878.678i 0.533248 1.25885i
\(699\) −48.8783 84.2914i −0.0699261 0.120589i
\(700\) −241.023 + 233.446i −0.344318 + 0.333494i
\(701\) 797.170 + 797.170i 1.13719 + 1.13719i 0.988952 + 0.148238i \(0.0473601\pi\)
0.148238 + 0.988952i \(0.452640\pi\)
\(702\) −21.9368 + 52.6155i −0.0312491 + 0.0749509i
\(703\) −2223.85 −3.16336
\(704\) −1023.04 49.0472i −1.45318 0.0696694i
\(705\) 103.733 390.086i 0.147140 0.553313i
\(706\) −220.171 543.779i −0.311857 0.770226i
\(707\) −415.878 415.878i −0.588229 0.588229i
\(708\) −180.273 + 100.724i −0.254622 + 0.142265i
\(709\) 592.848 + 592.848i 0.836176 + 0.836176i 0.988353 0.152178i \(-0.0486286\pi\)
−0.152178 + 0.988353i \(0.548629\pi\)
\(710\) −214.776 + 507.028i −0.302502 + 0.714123i
\(711\) −462.533 + 808.171i −0.650539 + 1.13667i
\(712\) 253.377 572.522i 0.355866 0.804104i
\(713\) −313.185 −0.439249
\(714\) −230.852 179.385i −0.323322 0.251239i
\(715\) −43.9070 43.9070i −0.0614084 0.0614084i
\(716\) −95.1587 1.51969i −0.132903 0.00212247i
\(717\) −345.959 + 200.612i −0.482508 + 0.279794i
\(718\) −567.180 + 229.646i −0.789945 + 0.319841i
\(719\) 1252.89i 1.74255i 0.490799 + 0.871273i \(0.336705\pi\)
−0.490799 + 0.871273i \(0.663295\pi\)
\(720\) −514.890 + 122.538i −0.715125 + 0.170192i
\(721\) 1123.83 1.55872
\(722\) 468.454 + 1156.99i 0.648828 + 1.60248i
\(723\) 240.289 + 414.382i 0.332350 + 0.573142i
\(724\) 193.461 + 3.08957i 0.267211 + 0.00426736i
\(725\) −17.7270 + 17.7270i −0.0244511 + 0.0244511i
\(726\) −497.400 + 640.109i −0.685123 + 0.881692i
\(727\) 1182.91i 1.62711i 0.581490 + 0.813553i \(0.302470\pi\)
−0.581490 + 0.813553i \(0.697530\pi\)
\(728\) 57.5083 22.2224i 0.0789950 0.0305253i
\(729\) 728.953 8.26707i 0.999936 0.0113403i
\(730\) −23.4950 9.95247i −0.0321850 0.0136335i
\(731\) 175.963 175.963i 0.240715 0.240715i
\(732\) −408.579 + 228.285i −0.558169 + 0.311865i
\(733\) 679.023 679.023i 0.926361 0.926361i −0.0711072 0.997469i \(-0.522653\pi\)
0.997469 + 0.0711072i \(0.0226532\pi\)
\(734\) −409.968 + 165.992i −0.558539 + 0.226147i
\(735\) 45.7574 + 12.1680i 0.0622549 + 0.0165551i
\(736\) 237.033 + 643.797i 0.322055 + 0.874725i
\(737\) 109.588i 0.148695i
\(738\) −36.5445 + 268.844i −0.0495183 + 0.364287i
\(739\) 408.587 408.587i 0.552892 0.552892i −0.374383 0.927274i \(-0.622145\pi\)
0.927274 + 0.374383i \(0.122145\pi\)
\(740\) 748.251 724.727i 1.01115 0.979361i
\(741\) −85.9889 + 49.8627i −0.116044 + 0.0672911i
\(742\) −968.267 410.157i −1.30494 0.552772i
\(743\) −228.202 −0.307137 −0.153568 0.988138i \(-0.549077\pi\)
−0.153568 + 0.988138i \(0.549077\pi\)
\(744\) 348.523 38.0826i 0.468444 0.0511863i
\(745\) 692.644i 0.929724i
\(746\) −383.410 162.412i −0.513955 0.217711i
\(747\) 389.641 105.984i 0.521608 0.141880i
\(748\) −427.205 6.82247i −0.571129 0.00912094i
\(749\) 561.642 + 561.642i 0.749856 + 0.749856i
\(750\) 100.174 + 798.470i 0.133565 + 1.06463i
\(751\) 835.943 1.11311 0.556553 0.830812i \(-0.312124\pi\)
0.556553 + 0.830812i \(0.312124\pi\)
\(752\) 585.409 + 18.7027i 0.778469 + 0.0248707i
\(753\) −437.528 116.350i −0.581047 0.154515i
\(754\) 4.26963 1.72873i 0.00566264 0.00229275i
\(755\) 60.7421 + 60.7421i 0.0804530 + 0.0804530i
\(756\) −551.733 563.216i −0.729806 0.744994i
\(757\) 144.017 + 144.017i 0.190247 + 0.190247i 0.795803 0.605556i \(-0.207049\pi\)
−0.605556 + 0.795803i \(0.707049\pi\)
\(758\) −777.602 329.391i −1.02586 0.434553i
\(759\) 994.715 + 264.519i 1.31056 + 0.348510i
\(760\) −843.933 373.494i −1.11044 0.491439i
\(761\) −1238.49 −1.62745 −0.813727 0.581247i \(-0.802565\pi\)
−0.813727 + 0.581247i \(0.802565\pi\)
\(762\) 205.343 + 159.563i 0.269479 + 0.209400i
\(763\) 541.148 + 541.148i 0.709238 + 0.709238i
\(764\) −417.880 431.444i −0.546963 0.564717i
\(765\) −213.049 + 57.9503i −0.278495 + 0.0757520i
\(766\) 320.746 + 792.181i 0.418729 + 1.03418i
\(767\) 18.1663i 0.0236849i
\(768\) −342.063 687.617i −0.445394 0.895335i
\(769\) −906.729 −1.17910 −0.589551 0.807732i \(-0.700695\pi\)
−0.589551 + 0.807732i \(0.700695\pi\)
\(770\) 796.033 322.306i 1.03381 0.418579i
\(771\) −892.284 + 517.411i −1.15731 + 0.671091i
\(772\) 337.998