Properties

Label 48.3.i.b.29.2
Level $48$
Weight $3$
Character 48.29
Analytic conductor $1.308$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 29.2
Root \(-1.85381 + 0.750590i\) of defining polynomial
Character \(\chi\) \(=\) 48.29
Dual form 48.3.i.b.5.2

$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.85381 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 0.397716 0.917509i \(-0.369803\pi\)
−0.917509 + 0.397716i \(0.869803\pi\)
\(6\) −4.73777 + 3.68151i −0.789629 + 0.613585i
\(7\) 7.30027i 1.04290i −0.853283 0.521448i \(-0.825392\pi\)
0.853283 0.521448i \(-0.174608\pi\)
\(8\) −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 0.999575 + 0.0291601i \(0.00928328\pi\)
0.0291601 + 0.999575i \(0.490717\pi\)
\(12\) 11.5462 3.26870i 0.962186 0.272392i
\(13\) −0.746462 0.746462i −0.0574201 0.0574201i 0.677814 0.735234i \(-0.262928\pi\)
−0.735234 + 0.677814i \(0.762928\pi\)
\(14\) −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 \(0.0628957\pi\)
−0.980542 + 0.196310i \(0.937104\pi\)
\(18\) 2.42448 + 17.8360i 0.134693 + 0.990887i
\(19\) 22.1936 + 22.1936i 1.16809 + 1.16809i 0.982658 + 0.185428i \(0.0593670\pi\)
0.185428 + 0.982658i \(0.440633\pi\)
\(20\) −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 −0.680008 0.733205i \(-0.738024\pi\)
0.733205 + 0.680008i \(0.238024\pi\)
\(30\) 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 −0.473039 + 0.881041i \(0.656843\pi\)
−0.881041 + 0.473039i \(0.843157\pi\)
\(38\) −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 −0.330651 0.943753i \(-0.607268\pi\)
0.943753 + 0.330651i \(0.107268\pi\)
\(44\) 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 \(-0.872671\pi\)
0.921055 0.389433i \(-0.127329\pi\)
\(48\) 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 0.999263 0.0383765i \(-0.0122186\pi\)
−0.0383765 + 0.999263i \(0.512219\pi\)
\(54\) 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 0.596426 0.802668i \(-0.296587\pi\)
−0.802668 + 0.596426i \(0.796587\pi\)
\(60\) −38.5035 21.5130i −0.641725 0.358550i
\(61\) −27.5789 27.5789i −0.452113 0.452113i 0.443943 0.896055i \(-0.353579\pi\)
−0.896055 + 0.443943i \(0.853579\pi\)
\(62\) 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 0.670047 0.742318i \(-0.266274\pi\)
−0.742318 + 0.670047i \(0.766274\pi\)
\(68\) −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 \(0.00756843\pi\)
−0.999717 + 0.0237747i \(0.992432\pi\)
\(74\) 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 −0.871906 0.489673i \(-0.837116\pi\)
0.489673 + 0.871906i \(0.337116\pi\)
\(84\) −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 0.366417 0.930451i \(-0.380585\pi\)
−0.930451 + 0.366417i \(0.880585\pi\)
\(102\) −24.5723 31.6224i −0.240905 0.310023i
\(103\) 153.944i 1.49460i 0.664485 + 0.747301i \(0.268651\pi\)
−0.664485 + 0.747301i \(0.731349\pi\)
\(104\) −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 0.968403 0.249390i \(-0.0802300\pi\)
−0.249390 + 0.968403i \(0.580230\pi\)
\(108\) −77.1499 75.5770i −0.714351 0.699787i
\(109\) 74.1271 + 74.1271i 0.680065 + 0.680065i 0.960015 0.279949i \(-0.0903177\pi\)
−0.279949 + 0.960015i \(0.590318\pi\)
\(110\) −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 \(-0.945665\pi\)
0.985466 0.169871i \(-0.0543352\pi\)
\(114\) −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 −0.702457 0.711726i \(-0.747914\pi\)
0.711726 + 0.702457i \(0.247914\pi\)
\(132\) 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 −0.796195 0.605041i \(-0.793157\pi\)
0.605041 + 0.796195i \(0.293157\pi\)
\(140\) −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 0.994926 0.100605i \(-0.0320779\pi\)
−0.100605 + 0.994926i \(0.532078\pi\)
\(150\) 42.3033 + 54.4406i 0.282022 + 0.362937i
\(151\) 23.3716i 0.154779i 0.997001 + 0.0773895i \(0.0246585\pi\)
−0.997001 + 0.0773895i \(0.975342\pi\)
\(152\) 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 0.332438 0.943125i \(-0.392129\pi\)
−0.943125 + 0.332438i \(0.892129\pi\)
\(158\) −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 0.314896 0.949126i \(-0.398030\pi\)
−0.949126 + 0.314896i \(0.898030\pi\)
\(164\) −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 −0.154147 0.988048i \(-0.549263\pi\)
0.988048 + 0.154147i \(0.0492630\pi\)
\(174\) −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 −0.752538 0.658549i \(-0.771171\pi\)
0.658549 + 0.752538i \(0.271171\pi\)
\(180\) −113.776 + 67.5506i −0.632087 + 0.375281i
\(181\) 34.2037 34.2037i 0.188971 0.188971i −0.606280 0.795251i \(-0.707339\pi\)
0.795251 + 0.606280i \(0.207339\pi\)
\(182\) 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 \(0.128593\pi\)
−0.919501 + 0.393088i \(0.871407\pi\)
\(192\) 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 0.783314 0.621626i \(-0.213528\pi\)
−0.621626 + 0.783314i \(0.713528\pi\)
\(198\) −174.398 + 229.269i −0.880797 + 1.15792i
\(199\) 128.347i 0.644959i −0.946576 0.322480i \(-0.895484\pi\)
0.946576 0.322480i \(-0.104516\pi\)
\(200\) −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 0.868743 0.495262i \(-0.164928\pi\)
−0.495262 + 0.868743i \(0.664928\pi\)
\(212\) 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 −0.796689 0.604390i \(-0.793417\pi\)
0.604390 + 0.796689i \(0.293417\pi\)
\(228\) 328.797 + 183.709i 1.44209 + 0.805739i
\(229\) −111.882 + 111.882i −0.488566 + 0.488566i −0.907853 0.419288i \(-0.862280\pi\)
0.419288 + 0.907853i \(0.362280\pi\)
\(230\) 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 \(-0.910036\pi\)
0.960326 0.278881i \(-0.0899636\pi\)
\(240\) −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 0.461828 0.886969i \(-0.347194\pi\)
−0.886969 + 0.461828i \(0.847194\pi\)
\(252\) −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 \(-0.766764\pi\)
0.743350 0.668903i \(-0.233236\pi\)
\(258\) −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 −0.871067 0.491164i \(-0.836572\pi\)
0.491164 + 0.871067i \(0.336572\pi\)
\(270\) −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 −0.00110593 + 0.999999i \(0.500352\pi\)
−0.999999 + 0.00110593i \(0.999648\pi\)
\(278\) 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 −0.0218614 0.999761i \(-0.506959\pi\)
0.999761 + 0.0218614i \(0.00695927\pi\)
\(284\) −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 −0.998884 0.0472370i \(-0.984958\pi\)
−0.0472370 0.998884i \(-0.515042\pi\)
\(294\) 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 −0.981820 0.189814i \(-0.939211\pi\)
−0.189814 0.981820i \(-0.560789\pi\)
\(308\) 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 \(-0.821271\pi\)
0.846461 0.532450i \(-0.178729\pi\)
\(314\) 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 −0.988901 0.148578i \(-0.952530\pi\)
0.148578 + 0.988901i \(0.452530\pi\)
\(318\) −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 −0.950995 0.309208i \(-0.899936\pi\)
0.309208 + 0.950995i \(0.399936\pi\)
\(332\) −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 0.550839 0.834612i \(-0.314308\pi\)
−0.834612 + 0.550839i \(0.814308\pi\)
\(348\) 12.7699 22.8553i 0.0366952 0.0656763i
\(349\) −337.382 337.382i −0.966711 0.966711i 0.0327527 0.999463i \(-0.489573\pi\)
−0.999463 + 0.0327527i \(0.989573\pi\)
\(350\) 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 \(-0.863613\pi\)
0.909601 0.415482i \(-0.136387\pi\)
\(354\) 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 −0.481671 0.876352i \(-0.659970\pi\)
0.876352 + 0.481671i \(0.159970\pi\)
\(374\) 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 −0.193342 0.981131i \(-0.561933\pi\)
0.981131 + 0.193342i \(0.0619326\pi\)
\(380\) 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 \(0.188380\pi\)
−0.829931 + 0.557866i \(0.811620\pi\)
\(384\) 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 0.176847 0.984238i \(-0.443410\pi\)
−0.984238 + 0.176847i \(0.943410\pi\)
\(390\) −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 0.904551 0.426366i \(-0.140206\pi\)
−0.426366 + 0.904551i \(0.640206\pi\)
\(398\) −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 \(-0.891452\pi\)
0.942416 0.334443i \(-0.108548\pi\)
\(402\) 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 \(0.0100599\pi\)
−0.999501 + 0.0315988i \(0.989940\pi\)
\(410\) −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 −0.354313 0.935127i \(-0.615285\pi\)
0.935127 + 0.354313i \(0.115285\pi\)
\(420\) −157.051 + 281.086i −0.373931 + 0.669253i
\(421\) 115.847 115.847i 0.275171 0.275171i −0.556007 0.831178i \(-0.687667\pi\)
0.831178 + 0.556007i \(0.187667\pi\)
\(422\) −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 \(0.229010\pi\)
−0.752165 + 0.658975i \(0.770990\pi\)
\(432\) −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 \(0.186889\pi\)
−0.832534 + 0.553973i \(0.813111\pi\)
\(440\) −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 0.935850 0.352399i \(-0.114634\pi\)
−0.352399 + 0.935850i \(0.614634\pi\)
\(444\) −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 \(0.187122\pi\)
−0.832129 + 0.554582i \(0.812878\pi\)
\(450\) 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 \(0.170487\pi\)
−0.859961 + 0.510359i \(0.829513\pi\)
\(458\) 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 −0.145061 0.989423i \(-0.546338\pi\)
0.989423 + 0.145061i \(0.0463378\pi\)
\(462\) −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 −0.879766 0.475407i \(-0.842301\pi\)
0.475407 + 0.879766i \(0.342301\pi\)
\(468\) −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 \(-0.889352\pi\)
0.940190 0.340652i \(-0.110648\pi\)
\(480\) −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 \(-0.935426\pi\)
0.979493 0.201476i \(-0.0645739\pi\)
\(488\) −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 0.255631 0.966774i \(-0.417717\pi\)
−0.966774 + 0.255631i \(0.917717\pi\)
\(492\) −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 0.307582 0.951522i \(-0.400480\pi\)
−0.951522 + 0.307582i \(0.900480\pi\)
\(500\) −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 −0.994417 0.105520i \(-0.966349\pi\)
0.105520 + 0.994417i \(0.466349\pi\)
\(510\) −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 −0.212462 0.977169i \(-0.568148\pi\)
0.977169 + 0.212462i \(0.0681483\pi\)
\(524\) 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 0.590721 0.806876i \(-0.298844\pi\)
−0.806876 + 0.590721i \(0.798844\pi\)
\(542\) 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 0.781084 0.624427i \(-0.214667\pi\)
−0.624427 + 0.781084i \(0.714667\pi\)
\(548\) −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 −0.794425 0.607363i \(-0.792228\pi\)
0.607363 + 0.794425i \(0.292228\pi\)
\(558\) −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 −0.534111 + 0.845414i \(0.679354\pi\)
−0.845414 + 0.534111i \(0.820646\pi\)
\(564\) −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 −0.987799 0.155736i \(-0.950225\pi\)
0.155736 + 0.987799i \(0.450225\pi\)
\(572\) 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 0.999989 0.00469688i \(-0.00149507\pi\)
−0.00469688 + 0.999989i \(0.501495\pi\)
\(588\) −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 \(-0.737500\pi\)
0.678801 0.734322i \(-0.262500\pi\)
\(594\) 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 \(-0.937538\pi\)
0.980809 0.194973i \(-0.0624620\pi\)
\(602\) 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 −0.0552724 + 0.998471i \(0.517603\pi\)
−0.998471 + 0.0552724i \(0.982397\pi\)
\(614\) 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 −0.0473286 + 0.998879i \(0.515071\pi\)
−0.998879 + 0.0473286i \(0.984929\pi\)
\(620\) 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 \(-0.718816\pi\)
0.634553 0.772880i \(-0.281184\pi\)
\(632\) −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 \(0.205564\pi\)
−0.798619 + 0.601837i \(0.794436\pi\)
\(642\) −647.733 81.2629i −1.00893 0.126578i
\(643\) 319.214 + 319.214i 0.496445 + 0.496445i 0.910330 0.413884i \(-0.135828\pi\)
−0.413884 + 0.910330i \(0.635828\pi\)
\(644\) 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 −0.949466 0.313871i \(-0.898374\pi\)
0.313871 + 0.949466i \(0.398374\pi\)
\(654\) −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 −0.375269 0.926916i \(-0.622450\pi\)
0.926916 + 0.375269i \(0.122450\pi\)
\(660\) −192.266 679.152i −0.291312 1.02902i
\(661\) −151.997 + 151.997i −0.229951 + 0.229951i −0.812672 0.582721i \(-0.801988\pi\)
0.582721 + 0.812672i \(0.301988\pi\)
\(662\) 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 0.0535849 0.998563i \(-0.482935\pi\)
−0.998563 + 0.0535849i \(0.982935\pi\)
\(678\) 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 0.772018 0.635601i \(-0.219248\pi\)
−0.635601 + 0.772018i \(0.719248\pi\)
\(684\) 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 0.891916 0.452200i \(-0.149361\pi\)
−0.452200 + 0.891916i \(0.649361\pi\)
\(692\) 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 0.148238 0.988952i \(-0.452640\pi\)
0.988952 0.148238i \(-0.0473601\pi\)
\(702\) −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 −0.152178 0.988353i \(-0.548629\pi\)
0.988353 + 0.152178i \(0.0486286\pi\)
\(710\) −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 \(-0.663295\pi\)
0.490799 0.871273i \(-0.336705\pi\)
\(720\) −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 \(-0.697530\pi\)
0.581490 0.813553i \(-0.302470\pi\)
\(728\) 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 0.997469 0.0711072i \(-0.0226532\pi\)
−0.0711072 + 0.997469i \(0.522653\pi\)
\(734\) −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 0.927274 0.374383i \(-0.122145\pi\)
−0.374383 + 0.927274i \(0.622145\pi\)
\(740\) 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 −0.605556 0.795803i \(-0.707049\pi\)
0.795803 + 0.605556i \(0.207049\pi\)
\(758\) −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