Properties

Label 48.3.i.b.5.7
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 5.7
Root \(1.21144 + 1.59136i\) of defining polynomial
Character \(\chi\) \(=\) 48.5
Dual form 48.3.i.b.29.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.21144 - 1.59136i) q^{2} +(2.77106 - 1.14944i) q^{3} +(-1.06484 - 3.85566i) q^{4} +(-4.80434 + 4.80434i) q^{5} +(1.52779 - 5.80223i) q^{6} +7.36187i q^{7} +(-7.42573 - 2.97634i) q^{8} +(6.35757 - 6.37035i) q^{9} +O(q^{10})\) \(q+(1.21144 - 1.59136i) q^{2} +(2.77106 - 1.14944i) q^{3} +(-1.06484 - 3.85566i) q^{4} +(-4.80434 + 4.80434i) q^{5} +(1.52779 - 5.80223i) q^{6} +7.36187i q^{7} +(-7.42573 - 2.97634i) q^{8} +(6.35757 - 6.37035i) q^{9} +(1.82527 + 13.4656i) q^{10} +(0.514693 - 0.514693i) q^{11} +(-7.38260 - 9.46029i) q^{12} +(7.12969 - 7.12969i) q^{13} +(11.7154 + 8.91843i) q^{14} +(-7.79081 + 18.8354i) q^{15} +(-13.7322 + 8.21135i) q^{16} -11.1126i q^{17} +(-2.43571 - 17.8344i) q^{18} +(-21.1403 + 21.1403i) q^{19} +(23.6398 + 13.4080i) q^{20} +(8.46203 + 20.4002i) q^{21} +(-0.195543 - 1.44258i) q^{22} +7.80231 q^{23} +(-23.9983 + 0.287823i) q^{24} -21.1633i q^{25} +(-2.70873 - 19.9831i) q^{26} +(10.2949 - 24.9603i) q^{27} +(28.3849 - 7.83924i) q^{28} +(-34.6058 - 34.6058i) q^{29} +(20.5358 + 35.2159i) q^{30} +24.8644 q^{31} +(-3.56850 + 31.8004i) q^{32} +(0.834637 - 2.01786i) q^{33} +(-17.6842 - 13.4623i) q^{34} +(-35.3689 - 35.3689i) q^{35} +(-31.3317 - 17.7292i) q^{36} +(-18.2760 - 18.2760i) q^{37} +(8.03168 + 59.2520i) q^{38} +(11.5617 - 27.9520i) q^{39} +(49.9750 - 21.3764i) q^{40} +64.2448 q^{41} +(42.7152 + 11.2474i) q^{42} +(7.24058 + 7.24058i) q^{43} +(-2.53255 - 1.43641i) q^{44} +(0.0613789 + 61.1492i) q^{45} +(9.45200 - 12.4163i) q^{46} +23.0508i q^{47} +(-28.6144 + 38.5385i) q^{48} -5.19710 q^{49} +(-33.6784 - 25.6380i) q^{50} +(-12.7733 - 30.7938i) q^{51} +(-35.0817 - 19.8976i) q^{52} +(-31.9199 + 31.9199i) q^{53} +(-27.2492 - 46.6206i) q^{54} +4.94552i q^{55} +(21.9114 - 54.6672i) q^{56} +(-34.2816 + 82.8807i) q^{57} +(-96.9929 + 13.1475i) q^{58} +(-17.6272 + 17.6272i) q^{59} +(80.9190 + 9.98194i) q^{60} +(-12.3933 + 12.3933i) q^{61} +(30.1216 - 39.5682i) q^{62} +(46.8976 + 46.8036i) q^{63} +(46.2828 + 44.2029i) q^{64} +68.5069i q^{65} +(-2.20002 - 3.77271i) q^{66} +(41.1425 - 41.1425i) q^{67} +(-42.8465 + 11.8332i) q^{68} +(21.6207 - 8.96830i) q^{69} +(-99.1318 + 13.4374i) q^{70} +25.6785 q^{71} +(-66.1699 + 28.3822i) q^{72} -56.1845i q^{73} +(-51.2239 + 6.94346i) q^{74} +(-24.3260 - 58.6449i) q^{75} +(104.021 + 58.9988i) q^{76} +(3.78910 + 3.78910i) q^{77} +(-30.4754 - 52.2608i) q^{78} -35.7013 q^{79} +(26.5241 - 105.424i) q^{80} +(-0.162608 - 80.9998i) q^{81} +(77.8285 - 102.236i) q^{82} +(94.9424 + 94.9424i) q^{83} +(69.6454 - 54.3497i) q^{84} +(53.3889 + 53.3889i) q^{85} +(20.2939 - 2.75086i) q^{86} +(-135.672 - 56.1175i) q^{87} +(-5.35387 + 2.29007i) q^{88} +44.8713 q^{89} +(97.3847 + 73.9807i) q^{90} +(52.4878 + 52.4878i) q^{91} +(-8.30824 - 30.0830i) q^{92} +(68.9008 - 28.5802i) q^{93} +(36.6821 + 27.9246i) q^{94} -203.131i q^{95} +(26.6642 + 92.2227i) q^{96} -82.3636 q^{97} +(-6.29596 + 8.27045i) q^{98} +(-0.00657558 - 6.55097i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6} + O(q^{10}) \) \( 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6} + 32 q^{10} - 88 q^{12} + 92 q^{13} - 116 q^{15} - 16 q^{16} + 4 q^{18} - 52 q^{19} + 48 q^{21} + 24 q^{22} - 8 q^{24} + 18 q^{27} + 56 q^{28} + 28 q^{30} - 80 q^{31} + 60 q^{33} + 104 q^{34} + 92 q^{36} - 116 q^{37} + 88 q^{40} + 304 q^{42} + 172 q^{43} + 60 q^{45} - 424 q^{46} + 176 q^{48} - 364 q^{49} + 128 q^{51} - 208 q^{52} + 40 q^{54} - 512 q^{58} - 240 q^{60} - 244 q^{61} + 296 q^{63} + 88 q^{64} - 492 q^{66} + 356 q^{67} - 20 q^{69} + 200 q^{70} - 472 q^{72} - 146 q^{75} + 328 q^{76} + 84 q^{78} + 384 q^{79} - 188 q^{81} + 560 q^{82} + 816 q^{84} + 48 q^{85} + 416 q^{88} + 616 q^{90} + 136 q^{91} - 132 q^{93} + 32 q^{94} - 24 q^{96} + 472 q^{97} - 452 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.21144 1.59136i 0.605718 0.795679i
\(3\) 2.77106 1.14944i 0.923687 0.383147i
\(4\) −1.06484 3.85566i −0.266211 0.963915i
\(5\) −4.80434 + 4.80434i −0.960868 + 0.960868i −0.999263 0.0383950i \(-0.987775\pi\)
0.0383950 + 0.999263i \(0.487775\pi\)
\(6\) 1.52779 5.80223i 0.254632 0.967038i
\(7\) 7.36187i 1.05170i 0.850579 + 0.525848i \(0.176252\pi\)
−0.850579 + 0.525848i \(0.823748\pi\)
\(8\) −7.42573 2.97634i −0.928216 0.372042i
\(9\) 6.35757 6.37035i 0.706397 0.707816i
\(10\) 1.82527 + 13.4656i 0.182527 + 1.34656i
\(11\) 0.514693 0.514693i 0.0467903 0.0467903i −0.683325 0.730115i \(-0.739467\pi\)
0.730115 + 0.683325i \(0.239467\pi\)
\(12\) −7.38260 9.46029i −0.615217 0.788358i
\(13\) 7.12969 7.12969i 0.548438 0.548438i −0.377551 0.925989i \(-0.623234\pi\)
0.925989 + 0.377551i \(0.123234\pi\)
\(14\) 11.7154 + 8.91843i 0.836812 + 0.637031i
\(15\) −7.79081 + 18.8354i −0.519388 + 1.25569i
\(16\) −13.7322 + 8.21135i −0.858263 + 0.513210i
\(17\) 11.1126i 0.653684i −0.945079 0.326842i \(-0.894015\pi\)
0.945079 0.326842i \(-0.105985\pi\)
\(18\) −2.43571 17.8344i −0.135317 0.990802i
\(19\) −21.1403 + 21.1403i −1.11265 + 1.11265i −0.119858 + 0.992791i \(0.538244\pi\)
−0.992791 + 0.119858i \(0.961756\pi\)
\(20\) 23.6398 + 13.4080i 1.18199 + 0.670401i
\(21\) 8.46203 + 20.4002i 0.402954 + 0.971438i
\(22\) −0.195543 1.44258i −0.00888834 0.0655718i
\(23\) 7.80231 0.339231 0.169615 0.985510i \(-0.445747\pi\)
0.169615 + 0.985510i \(0.445747\pi\)
\(24\) −23.9983 + 0.287823i −0.999928 + 0.0119926i
\(25\) 21.1633i 0.846533i
\(26\) −2.70873 19.9831i −0.104182 0.768579i
\(27\) 10.2949 24.9603i 0.381292 0.924455i
\(28\) 28.3849 7.83924i 1.01374 0.279973i
\(29\) −34.6058 34.6058i −1.19330 1.19330i −0.976134 0.217169i \(-0.930318\pi\)
−0.217169 0.976134i \(-0.569682\pi\)
\(30\) 20.5358 + 35.2159i 0.684528 + 1.17386i
\(31\) 24.8644 0.802078 0.401039 0.916061i \(-0.368649\pi\)
0.401039 + 0.916061i \(0.368649\pi\)
\(32\) −3.56850 + 31.8004i −0.111516 + 0.993763i
\(33\) 0.834637 2.01786i 0.0252920 0.0611472i
\(34\) −17.6842 13.4623i −0.520123 0.395949i
\(35\) −35.3689 35.3689i −1.01054 1.01054i
\(36\) −31.3317 17.7292i −0.870325 0.492478i
\(37\) −18.2760 18.2760i −0.493946 0.493946i 0.415601 0.909547i \(-0.363571\pi\)
−0.909547 + 0.415601i \(0.863571\pi\)
\(38\) 8.03168 + 59.2520i 0.211360 + 1.55926i
\(39\) 11.5617 27.9520i 0.296453 0.716717i
\(40\) 49.9750 21.3764i 1.24938 0.534409i
\(41\) 64.2448 1.56695 0.783473 0.621426i \(-0.213446\pi\)
0.783473 + 0.621426i \(0.213446\pi\)
\(42\) 42.7152 + 11.2474i 1.01703 + 0.267795i
\(43\) 7.24058 + 7.24058i 0.168386 + 0.168386i 0.786269 0.617884i \(-0.212010\pi\)
−0.617884 + 0.786269i \(0.712010\pi\)
\(44\) −2.53255 1.43641i −0.0575579 0.0326458i
\(45\) 0.0613789 + 61.1492i 0.00136398 + 1.35887i
\(46\) 9.45200 12.4163i 0.205478 0.269919i
\(47\) 23.0508i 0.490442i 0.969467 + 0.245221i \(0.0788606\pi\)
−0.969467 + 0.245221i \(0.921139\pi\)
\(48\) −28.6144 + 38.5385i −0.596132 + 0.802886i
\(49\) −5.19710 −0.106063
\(50\) −33.6784 25.6380i −0.673569 0.512760i
\(51\) −12.7733 30.7938i −0.250457 0.603800i
\(52\) −35.0817 19.8976i −0.674647 0.382647i
\(53\) −31.9199 + 31.9199i −0.602263 + 0.602263i −0.940913 0.338650i \(-0.890030\pi\)
0.338650 + 0.940913i \(0.390030\pi\)
\(54\) −27.2492 46.6206i −0.504614 0.863345i
\(55\) 4.94552i 0.0899185i
\(56\) 21.9114 54.6672i 0.391275 0.976200i
\(57\) −34.2816 + 82.8807i −0.601432 + 1.45405i
\(58\) −96.9929 + 13.1475i −1.67229 + 0.226681i
\(59\) −17.6272 + 17.6272i −0.298766 + 0.298766i −0.840530 0.541764i \(-0.817756\pi\)
0.541764 + 0.840530i \(0.317756\pi\)
\(60\) 80.9190 + 9.98194i 1.34865 + 0.166366i
\(61\) −12.3933 + 12.3933i −0.203170 + 0.203170i −0.801357 0.598187i \(-0.795888\pi\)
0.598187 + 0.801357i \(0.295888\pi\)
\(62\) 30.1216 39.5682i 0.485833 0.638196i
\(63\) 46.8976 + 46.8036i 0.744407 + 0.742914i
\(64\) 46.2828 + 44.2029i 0.723169 + 0.690671i
\(65\) 68.5069i 1.05395i
\(66\) −2.20002 3.77271i −0.0333337 0.0571623i
\(67\) 41.1425 41.1425i 0.614067 0.614067i −0.329936 0.944003i \(-0.607027\pi\)
0.944003 + 0.329936i \(0.107027\pi\)
\(68\) −42.8465 + 11.8332i −0.630096 + 0.174018i
\(69\) 21.6207 8.96830i 0.313343 0.129975i
\(70\) −99.1318 + 13.4374i −1.41617 + 0.191963i
\(71\) 25.6785 0.361669 0.180834 0.983514i \(-0.442120\pi\)
0.180834 + 0.983514i \(0.442120\pi\)
\(72\) −66.1699 + 28.3822i −0.919026 + 0.394197i
\(73\) 56.1845i 0.769650i −0.922990 0.384825i \(-0.874262\pi\)
0.922990 0.384825i \(-0.125738\pi\)
\(74\) −51.2239 + 6.94346i −0.692214 + 0.0938305i
\(75\) −24.3260 58.6449i −0.324347 0.781932i
\(76\) 104.021 + 58.9988i 1.36870 + 0.776299i
\(77\) 3.78910 + 3.78910i 0.0492091 + 0.0492091i
\(78\) −30.4754 52.2608i −0.390710 0.670010i
\(79\) −35.7013 −0.451915 −0.225957 0.974137i \(-0.572551\pi\)
−0.225957 + 0.974137i \(0.572551\pi\)
\(80\) 26.5241 105.424i 0.331551 1.31780i
\(81\) −0.162608 80.9998i −0.00200751 0.999998i
\(82\) 77.8285 102.236i 0.949128 1.24679i
\(83\) 94.9424 + 94.9424i 1.14388 + 1.14388i 0.987733 + 0.156151i \(0.0499086\pi\)
0.156151 + 0.987733i \(0.450091\pi\)
\(84\) 69.6454 54.3497i 0.829112 0.647021i
\(85\) 53.3889 + 53.3889i 0.628104 + 0.628104i
\(86\) 20.2939 2.75086i 0.235975 0.0319867i
\(87\) −135.672 56.1175i −1.55945 0.645028i
\(88\) −5.35387 + 2.29007i −0.0608394 + 0.0260235i
\(89\) 44.8713 0.504172 0.252086 0.967705i \(-0.418883\pi\)
0.252086 + 0.967705i \(0.418883\pi\)
\(90\) 97.3847 + 73.9807i 1.08205 + 0.822008i
\(91\) 52.4878 + 52.4878i 0.576789 + 0.576789i
\(92\) −8.30824 30.0830i −0.0903070 0.326990i
\(93\) 68.9008 28.5802i 0.740869 0.307314i
\(94\) 36.6821 + 27.9246i 0.390235 + 0.297070i
\(95\) 203.131i 2.13822i
\(96\) 26.6642 + 92.2227i 0.277752 + 0.960653i
\(97\) −82.3636 −0.849109 −0.424554 0.905402i \(-0.639569\pi\)
−0.424554 + 0.905402i \(0.639569\pi\)
\(98\) −6.29596 + 8.27045i −0.0642445 + 0.0843924i
\(99\) −0.00657558 6.55097i −6.64200e−5 0.0661714i
\(100\) −81.5986 + 22.5356i −0.815986 + 0.225356i
\(101\) 36.3420 36.3420i 0.359822 0.359822i −0.503925 0.863747i \(-0.668111\pi\)
0.863747 + 0.503925i \(0.168111\pi\)
\(102\) −64.4781 16.9778i −0.632138 0.166449i
\(103\) 87.5176i 0.849685i 0.905267 + 0.424843i \(0.139671\pi\)
−0.905267 + 0.424843i \(0.860329\pi\)
\(104\) −74.1635 + 31.7228i −0.713110 + 0.305027i
\(105\) −138.664 57.3550i −1.32061 0.546238i
\(106\) 12.1271 + 89.4650i 0.114407 + 0.844010i
\(107\) −104.866 + 104.866i −0.980058 + 0.980058i −0.999805 0.0197471i \(-0.993714\pi\)
0.0197471 + 0.999805i \(0.493714\pi\)
\(108\) −107.201 13.1148i −0.992600 0.121433i
\(109\) 7.64006 7.64006i 0.0700923 0.0700923i −0.671192 0.741284i \(-0.734217\pi\)
0.741284 + 0.671192i \(0.234217\pi\)
\(110\) 7.87010 + 5.99118i 0.0715463 + 0.0544653i
\(111\) −71.6511 29.6367i −0.645505 0.266998i
\(112\) −60.4509 101.095i −0.539740 0.902632i
\(113\) 13.1273i 0.116171i 0.998312 + 0.0580853i \(0.0184995\pi\)
−0.998312 + 0.0580853i \(0.981500\pi\)
\(114\) 90.3630 + 154.959i 0.792658 + 1.35929i
\(115\) −37.4849 + 37.4849i −0.325956 + 0.325956i
\(116\) −96.5784 + 170.278i −0.832572 + 1.46791i
\(117\) −0.0910869 90.7461i −0.000778521 0.775607i
\(118\) 6.69696 + 49.4054i 0.0567539 + 0.418690i
\(119\) 81.8098 0.687477
\(120\) 113.913 116.679i 0.949275 0.972322i
\(121\) 120.470i 0.995621i
\(122\) 4.70851 + 34.7360i 0.0385943 + 0.284721i
\(123\) 178.026 73.8456i 1.44737 0.600371i
\(124\) −26.4767 95.8687i −0.213522 0.773134i
\(125\) −18.4327 18.4327i −0.147461 0.147461i
\(126\) 131.295 17.9314i 1.04202 0.142313i
\(127\) −88.2707 −0.695045 −0.347523 0.937672i \(-0.612977\pi\)
−0.347523 + 0.937672i \(0.612977\pi\)
\(128\) 126.411 20.1036i 0.987589 0.157059i
\(129\) 28.3867 + 11.7415i 0.220052 + 0.0910192i
\(130\) 109.019 + 82.9917i 0.838608 + 0.638398i
\(131\) 57.0518 + 57.0518i 0.435510 + 0.435510i 0.890498 0.454988i \(-0.150356\pi\)
−0.454988 + 0.890498i \(0.650356\pi\)
\(132\) −8.66892 1.06937i −0.0656737 0.00810132i
\(133\) −155.632 155.632i −1.17017 1.17017i
\(134\) −15.6310 115.314i −0.116649 0.860552i
\(135\) 70.4575 + 169.378i 0.521907 + 1.25465i
\(136\) −33.0749 + 82.5194i −0.243198 + 0.606760i
\(137\) −165.112 −1.20520 −0.602599 0.798045i \(-0.705868\pi\)
−0.602599 + 0.798045i \(0.705868\pi\)
\(138\) 11.9203 45.2708i 0.0863790 0.328049i
\(139\) −95.0802 95.0802i −0.684030 0.684030i 0.276875 0.960906i \(-0.410701\pi\)
−0.960906 + 0.276875i \(0.910701\pi\)
\(140\) −98.7081 + 174.033i −0.705058 + 1.24309i
\(141\) 26.4955 + 63.8752i 0.187912 + 0.453015i
\(142\) 31.1078 40.8637i 0.219069 0.287772i
\(143\) 7.33920i 0.0513231i
\(144\) −34.9944 + 139.683i −0.243016 + 0.970022i
\(145\) 332.516 2.29321
\(146\) −89.4096 68.0639i −0.612395 0.466191i
\(147\) −14.4015 + 5.97376i −0.0979693 + 0.0406378i
\(148\) −51.0049 + 89.9271i −0.344628 + 0.607615i
\(149\) 131.077 131.077i 0.879709 0.879709i −0.113795 0.993504i \(-0.536301\pi\)
0.993504 + 0.113795i \(0.0363006\pi\)
\(150\) −122.794 32.3332i −0.818630 0.215554i
\(151\) 123.070i 0.815031i −0.913198 0.407515i \(-0.866395\pi\)
0.913198 0.407515i \(-0.133605\pi\)
\(152\) 219.903 94.0616i 1.44673 0.618826i
\(153\) −70.7913 70.6494i −0.462688 0.461761i
\(154\) 10.6201 1.43956i 0.0689615 0.00934782i
\(155\) −119.457 + 119.457i −0.770690 + 0.770690i
\(156\) −120.085 14.8133i −0.769773 0.0949570i
\(157\) 139.181 139.181i 0.886503 0.886503i −0.107683 0.994185i \(-0.534343\pi\)
0.994185 + 0.107683i \(0.0343430\pi\)
\(158\) −43.2498 + 56.8135i −0.273733 + 0.359579i
\(159\) −51.7620 + 125.142i −0.325547 + 0.787058i
\(160\) −135.636 169.924i −0.847723 1.06203i
\(161\) 57.4396i 0.356768i
\(162\) −129.097 97.8674i −0.796894 0.604120i
\(163\) −19.9311 + 19.9311i −0.122277 + 0.122277i −0.765597 0.643320i \(-0.777556\pi\)
0.643320 + 0.765597i \(0.277556\pi\)
\(164\) −68.4107 247.706i −0.417138 1.51040i
\(165\) 5.68458 + 13.7043i 0.0344520 + 0.0830566i
\(166\) 266.104 36.0707i 1.60304 0.217294i
\(167\) −60.3220 −0.361210 −0.180605 0.983556i \(-0.557806\pi\)
−0.180605 + 0.983556i \(0.557806\pi\)
\(168\) −2.11892 176.672i −0.0126126 1.05162i
\(169\) 67.3351i 0.398432i
\(170\) 149.638 20.2836i 0.880224 0.119315i
\(171\) 0.270083 + 269.072i 0.00157943 + 1.57352i
\(172\) 20.2071 35.6273i 0.117483 0.207135i
\(173\) −74.8292 74.8292i −0.432539 0.432539i 0.456952 0.889491i \(-0.348941\pi\)
−0.889491 + 0.456952i \(0.848941\pi\)
\(174\) −253.661 + 147.920i −1.45782 + 0.850116i
\(175\) 155.802 0.890295
\(176\) −2.84155 + 11.2942i −0.0161452 + 0.0641716i
\(177\) −28.5846 + 69.1074i −0.161495 + 0.390438i
\(178\) 54.3587 71.4063i 0.305386 0.401159i
\(179\) −3.96558 3.96558i −0.0221541 0.0221541i 0.695943 0.718097i \(-0.254987\pi\)
−0.718097 + 0.695943i \(0.754987\pi\)
\(180\) 235.705 65.3510i 1.30947 0.363061i
\(181\) 158.820 + 158.820i 0.877457 + 0.877457i 0.993271 0.115814i \(-0.0369475\pi\)
−0.115814 + 0.993271i \(0.536948\pi\)
\(182\) 147.113 19.9413i 0.808311 0.109568i
\(183\) −20.0973 + 48.5882i −0.109821 + 0.265509i
\(184\) −57.9378 23.2223i −0.314879 0.126208i
\(185\) 175.608 0.949233
\(186\) 37.9876 144.269i 0.204235 0.775639i
\(187\) −5.71960 5.71960i −0.0305861 0.0305861i
\(188\) 88.8760 24.5455i 0.472745 0.130561i
\(189\) 183.754 + 75.7896i 0.972245 + 0.401003i
\(190\) −323.254 246.080i −1.70133 1.29516i
\(191\) 68.8639i 0.360544i −0.983617 0.180272i \(-0.942302\pi\)
0.983617 0.180272i \(-0.0576978\pi\)
\(192\) 179.061 + 69.2896i 0.932611 + 0.360884i
\(193\) −366.645 −1.89971 −0.949856 0.312686i \(-0.898771\pi\)
−0.949856 + 0.312686i \(0.898771\pi\)
\(194\) −99.7782 + 131.070i −0.514321 + 0.675618i
\(195\) 78.7446 + 189.837i 0.403819 + 0.973522i
\(196\) 5.53410 + 20.0383i 0.0282352 + 0.102236i
\(197\) −246.744 + 246.744i −1.25251 + 1.25251i −0.297912 + 0.954593i \(0.596290\pi\)
−0.954593 + 0.297912i \(0.903710\pi\)
\(198\) −10.4329 7.92562i −0.0526915 0.0400284i
\(199\) 287.802i 1.44624i −0.690722 0.723120i \(-0.742707\pi\)
0.690722 0.723120i \(-0.257293\pi\)
\(200\) −62.9892 + 157.153i −0.314946 + 0.785765i
\(201\) 66.7176 161.299i 0.331928 0.802484i
\(202\) −13.8071 101.859i −0.0683521 0.504253i
\(203\) 254.763 254.763i 1.25499 1.25499i
\(204\) −105.129 + 82.0402i −0.515337 + 0.402158i
\(205\) −308.654 + 308.654i −1.50563 + 1.50563i
\(206\) 139.272 + 106.022i 0.676077 + 0.514670i
\(207\) 49.6037 49.7034i 0.239632 0.240113i
\(208\) −39.3620 + 156.451i −0.189240 + 0.752167i
\(209\) 21.7616i 0.104122i
\(210\) −259.255 + 151.182i −1.23455 + 0.719915i
\(211\) 156.146 156.146i 0.740027 0.740027i −0.232556 0.972583i \(-0.574709\pi\)
0.972583 + 0.232556i \(0.0747089\pi\)
\(212\) 157.062 + 89.0826i 0.740859 + 0.420201i
\(213\) 71.1567 29.5159i 0.334069 0.138572i
\(214\) 39.8410 + 293.918i 0.186173 + 1.37345i
\(215\) −69.5724 −0.323593
\(216\) −150.737 + 154.707i −0.697857 + 0.716237i
\(217\) 183.048i 0.843541i
\(218\) −2.90263 21.4135i −0.0133148 0.0982271i
\(219\) −64.5807 155.691i −0.294889 0.710916i
\(220\) 19.0682 5.26621i 0.0866738 0.0239373i
\(221\) −79.2296 79.2296i −0.358505 0.358505i
\(222\) −133.963 + 78.1196i −0.603439 + 0.351890i
\(223\) 45.2998 0.203138 0.101569 0.994828i \(-0.467614\pi\)
0.101569 + 0.994828i \(0.467614\pi\)
\(224\) −234.110 26.2708i −1.04514 0.117280i
\(225\) −134.818 134.547i −0.599190 0.597988i
\(226\) 20.8902 + 15.9029i 0.0924345 + 0.0703666i
\(227\) −300.757 300.757i −1.32492 1.32492i −0.909737 0.415186i \(-0.863717\pi\)
−0.415186 0.909737i \(-0.636283\pi\)
\(228\) 356.064 + 43.9231i 1.56169 + 0.192645i
\(229\) 65.7088 + 65.7088i 0.286938 + 0.286938i 0.835868 0.548930i \(-0.184965\pi\)
−0.548930 + 0.835868i \(0.684965\pi\)
\(230\) 14.2414 + 105.063i 0.0619190 + 0.456794i
\(231\) 14.8552 + 6.14449i 0.0643082 + 0.0265995i
\(232\) 153.975 + 359.972i 0.663684 + 1.55160i
\(233\) 42.8218 0.183785 0.0918923 0.995769i \(-0.470708\pi\)
0.0918923 + 0.995769i \(0.470708\pi\)
\(234\) −144.520 109.788i −0.617606 0.469180i
\(235\) −110.744 110.744i −0.471250 0.471250i
\(236\) 86.7346 + 49.1942i 0.367520 + 0.208450i
\(237\) −98.9305 + 41.0365i −0.417428 + 0.173150i
\(238\) 99.1073 130.189i 0.416417 0.547011i
\(239\) 100.598i 0.420913i 0.977603 + 0.210456i \(0.0674950\pi\)
−0.977603 + 0.210456i \(0.932505\pi\)
\(240\) −47.6792 322.625i −0.198663 1.34427i
\(241\) −5.23162 −0.0217080 −0.0108540 0.999941i \(-0.503455\pi\)
−0.0108540 + 0.999941i \(0.503455\pi\)
\(242\) 191.711 + 145.942i 0.792195 + 0.603066i
\(243\) −93.5551 224.269i −0.385001 0.922916i
\(244\) 60.9815 + 34.5875i 0.249924 + 0.141752i
\(245\) 24.9686 24.9686i 0.101913 0.101913i
\(246\) 98.1527 372.763i 0.398995 1.51530i
\(247\) 301.448i 1.22044i
\(248\) −184.636 74.0048i −0.744501 0.298407i
\(249\) 372.222 + 153.961i 1.49487 + 0.618315i
\(250\) −51.6630 + 7.00298i −0.206652 + 0.0280119i
\(251\) −17.4381 + 17.4381i −0.0694747 + 0.0694747i −0.740990 0.671516i \(-0.765644\pi\)
0.671516 + 0.740990i \(0.265644\pi\)
\(252\) 130.520 230.660i 0.517937 0.915317i
\(253\) 4.01579 4.01579i 0.0158727 0.0158727i
\(254\) −106.934 + 140.470i −0.421001 + 0.553033i
\(255\) 209.311 + 86.5765i 0.820828 + 0.339516i
\(256\) 121.147 225.520i 0.473232 0.880938i
\(257\) 343.676i 1.33726i −0.743595 0.668630i \(-0.766881\pi\)
0.743595 0.668630i \(-0.233119\pi\)
\(258\) 53.0736 30.9494i 0.205712 0.119959i
\(259\) 134.545 134.545i 0.519480 0.519480i
\(260\) 264.139 72.9491i 1.01592 0.280574i
\(261\) −440.460 + 0.442114i −1.68758 + 0.00169392i
\(262\) 159.904 21.6752i 0.610322 0.0827299i
\(263\) −98.0863 −0.372952 −0.186476 0.982460i \(-0.559707\pi\)
−0.186476 + 0.982460i \(0.559707\pi\)
\(264\) −12.2036 + 12.4999i −0.0462258 + 0.0473481i
\(265\) 306.708i 1.15739i
\(266\) −436.206 + 59.1282i −1.63987 + 0.222286i
\(267\) 124.341 51.5769i 0.465697 0.193172i
\(268\) −202.442 114.821i −0.755380 0.428437i
\(269\) 126.560 + 126.560i 0.470482 + 0.470482i 0.902070 0.431589i \(-0.142047\pi\)
−0.431589 + 0.902070i \(0.642047\pi\)
\(270\) 354.895 + 93.0671i 1.31443 + 0.344693i
\(271\) −206.487 −0.761945 −0.380972 0.924586i \(-0.624411\pi\)
−0.380972 + 0.924586i \(0.624411\pi\)
\(272\) 91.2498 + 152.601i 0.335477 + 0.561033i
\(273\) 205.779 + 85.1154i 0.753768 + 0.311778i
\(274\) −200.023 + 262.752i −0.730010 + 0.958950i
\(275\) −10.8926 10.8926i −0.0396095 0.0396095i
\(276\) −57.6013 73.8121i −0.208701 0.267435i
\(277\) 183.416 + 183.416i 0.662153 + 0.662153i 0.955887 0.293734i \(-0.0948980\pi\)
−0.293734 + 0.955887i \(0.594898\pi\)
\(278\) −266.490 + 36.1231i −0.958598 + 0.129939i
\(279\) 158.077 158.395i 0.566585 0.567723i
\(280\) 157.370 + 367.910i 0.562036 + 1.31396i
\(281\) 109.143 0.388409 0.194204 0.980961i \(-0.437787\pi\)
0.194204 + 0.980961i \(0.437787\pi\)
\(282\) 133.746 + 35.2168i 0.474277 + 0.124882i
\(283\) 60.4623 + 60.4623i 0.213648 + 0.213648i 0.805815 0.592167i \(-0.201728\pi\)
−0.592167 + 0.805815i \(0.701728\pi\)
\(284\) −27.3436 99.0075i −0.0962802 0.348618i
\(285\) −233.487 562.888i −0.819252 1.97504i
\(286\) −11.6793 8.89098i −0.0408367 0.0310873i
\(287\) 472.962i 1.64795i
\(288\) 179.893 + 224.906i 0.624627 + 0.780923i
\(289\) 165.509 0.572697
\(290\) 402.822 529.152i 1.38904 1.82466i
\(291\) −228.235 + 94.6721i −0.784311 + 0.325334i
\(292\) −216.628 + 59.8277i −0.741877 + 0.204889i
\(293\) −19.4639 + 19.4639i −0.0664296 + 0.0664296i −0.739541 0.673111i \(-0.764957\pi\)
0.673111 + 0.739541i \(0.264957\pi\)
\(294\) −7.94009 + 30.1548i −0.0270071 + 0.102567i
\(295\) 169.374i 0.574149i
\(296\) 81.3170 + 190.108i 0.274720 + 0.642257i
\(297\) −7.54818 18.1456i −0.0254147 0.0610963i
\(298\) −49.7990 367.381i −0.167111 1.23282i
\(299\) 55.6280 55.6280i 0.186047 0.186047i
\(300\) −200.211 + 156.240i −0.667371 + 0.520801i
\(301\) −53.3042 + 53.3042i −0.177090 + 0.177090i
\(302\) −195.848 149.091i −0.648503 0.493679i
\(303\) 58.9329 142.479i 0.194498 0.470227i
\(304\) 116.713 463.894i 0.383924 1.52597i
\(305\) 119.084i 0.390438i
\(306\) −198.188 + 27.0672i −0.647672 + 0.0884549i
\(307\) −408.201 + 408.201i −1.32964 + 1.32964i −0.423967 + 0.905677i \(0.639363\pi\)
−0.905677 + 0.423967i \(0.860637\pi\)
\(308\) 10.5747 18.6443i 0.0343334 0.0605334i
\(309\) 100.596 + 242.517i 0.325554 + 0.784844i
\(310\) 45.3844 + 334.813i 0.146401 + 1.08004i
\(311\) 360.965 1.16066 0.580330 0.814381i \(-0.302924\pi\)
0.580330 + 0.814381i \(0.302924\pi\)
\(312\) −169.048 + 173.152i −0.541821 + 0.554975i
\(313\) 73.9217i 0.236172i −0.993003 0.118086i \(-0.962324\pi\)
0.993003 0.118086i \(-0.0376758\pi\)
\(314\) −52.8779 390.096i −0.168401 1.24234i
\(315\) −450.172 + 0.451863i −1.42912 + 0.00143449i
\(316\) 38.0163 + 137.652i 0.120305 + 0.435607i
\(317\) 172.709 + 172.709i 0.544825 + 0.544825i 0.924939 0.380115i \(-0.124116\pi\)
−0.380115 + 0.924939i \(0.624116\pi\)
\(318\) 136.440 + 233.974i 0.429056 + 0.735767i
\(319\) −35.6227 −0.111670
\(320\) −434.724 + 9.99263i −1.35851 + 0.0312270i
\(321\) −170.053 + 411.128i −0.529761 + 1.28077i
\(322\) 91.4070 + 69.5844i 0.283873 + 0.216101i
\(323\) 234.925 + 234.925i 0.727321 + 0.727321i
\(324\) −312.135 + 86.8792i −0.963378 + 0.268146i
\(325\) −150.888 150.888i −0.464271 0.464271i
\(326\) 7.57226 + 55.8627i 0.0232278 + 0.171358i
\(327\) 12.3893 29.9529i 0.0378877 0.0915990i
\(328\) −477.064 191.214i −1.45446 0.582970i
\(329\) −169.697 −0.515796
\(330\) 28.6950 + 7.55573i 0.0869546 + 0.0228961i
\(331\) 261.507 + 261.507i 0.790051 + 0.790051i 0.981502 0.191451i \(-0.0613194\pi\)
−0.191451 + 0.981502i \(0.561319\pi\)
\(332\) 264.967 467.164i 0.798092 1.40712i
\(333\) −232.615 + 0.233489i −0.698544 + 0.000701168i
\(334\) −73.0763 + 95.9940i −0.218791 + 0.287407i
\(335\) 395.325i 1.18007i
\(336\) −283.716 210.655i −0.844392 0.626950i
\(337\) 18.2211 0.0540684 0.0270342 0.999635i \(-0.491394\pi\)
0.0270342 + 0.999635i \(0.491394\pi\)
\(338\) 107.154 + 81.5722i 0.317024 + 0.241338i
\(339\) 15.0890 + 36.3765i 0.0445104 + 0.107305i
\(340\) 148.998 262.700i 0.438231 0.772647i
\(341\) 12.7975 12.7975i 0.0375294 0.0375294i
\(342\) 428.518 + 325.534i 1.25298 + 0.951855i
\(343\) 322.471i 0.940149i
\(344\) −32.2162 75.3170i −0.0936517 0.218945i
\(345\) −60.7863 + 146.960i −0.176192 + 0.425970i
\(346\) −209.731 + 28.4293i −0.606159 + 0.0821656i
\(347\) 173.710 173.710i 0.500605 0.500605i −0.411021 0.911626i \(-0.634828\pi\)
0.911626 + 0.411021i \(0.134828\pi\)
\(348\) −71.9002 + 582.862i −0.206610 + 1.67489i
\(349\) 387.899 387.899i 1.11146 1.11146i 0.118506 0.992953i \(-0.462189\pi\)
0.992953 0.118506i \(-0.0378106\pi\)
\(350\) 188.744 247.936i 0.539268 0.708389i
\(351\) −104.560 251.358i −0.297891 0.716121i
\(352\) 14.5308 + 18.2041i 0.0412806 + 0.0517163i
\(353\) 676.812i 1.91732i 0.284561 + 0.958658i \(0.408152\pi\)
−0.284561 + 0.958658i \(0.591848\pi\)
\(354\) 75.3463 + 129.208i 0.212843 + 0.364993i
\(355\) −123.368 + 123.368i −0.347516 + 0.347516i
\(356\) −47.7809 173.008i −0.134216 0.485979i
\(357\) 226.700 94.0355i 0.635014 0.263405i
\(358\) −11.1147 + 1.50661i −0.0310467 + 0.00420842i
\(359\) −240.896 −0.671020 −0.335510 0.942037i \(-0.608909\pi\)
−0.335510 + 0.942037i \(0.608909\pi\)
\(360\) 181.545 454.260i 0.504291 1.26183i
\(361\) 532.827i 1.47598i
\(362\) 445.139 60.3392i 1.22967 0.166683i
\(363\) 138.473 + 333.830i 0.381469 + 0.919643i
\(364\) 146.484 258.267i 0.402428 0.709523i
\(365\) 269.929 + 269.929i 0.739532 + 0.739532i
\(366\) 52.9746 + 90.8435i 0.144739 + 0.248206i
\(367\) 666.702 1.81663 0.908313 0.418291i \(-0.137371\pi\)
0.908313 + 0.418291i \(0.137371\pi\)
\(368\) −107.143 + 64.0675i −0.291149 + 0.174096i
\(369\) 408.441 409.261i 1.10689 1.10911i
\(370\) 212.738 279.455i 0.574968 0.755285i
\(371\) −234.990 234.990i −0.633397 0.633397i
\(372\) −183.564 235.225i −0.493452 0.632324i
\(373\) −358.513 358.513i −0.961160 0.961160i 0.0381137 0.999273i \(-0.487865\pi\)
−0.999273 + 0.0381137i \(0.987865\pi\)
\(374\) −16.0309 + 2.17300i −0.0428633 + 0.00581017i
\(375\) −72.2653 29.8908i −0.192708 0.0797088i
\(376\) 68.6069 171.169i 0.182465 0.455236i
\(377\) −493.457 −1.30890
\(378\) 343.215 200.605i 0.907976 0.530700i
\(379\) −140.959 140.959i −0.371925 0.371925i 0.496253 0.868178i \(-0.334709\pi\)
−0.868178 + 0.496253i \(0.834709\pi\)
\(380\) −783.202 + 216.302i −2.06106 + 0.569217i
\(381\) −244.604 + 101.462i −0.642004 + 0.266305i
\(382\) −109.587 83.4242i −0.286877 0.218388i
\(383\) 69.4683i 0.181379i −0.995879 0.0906897i \(-0.971093\pi\)
0.995879 0.0906897i \(-0.0289071\pi\)
\(384\) 327.186 201.011i 0.852047 0.523465i
\(385\) −36.4083 −0.0945669
\(386\) −444.167 + 583.463i −1.15069 + 1.51156i
\(387\) 92.1575 0.0925037i 0.238133 0.000239028i
\(388\) 87.7043 + 317.566i 0.226042 + 0.818468i
\(389\) 265.362 265.362i 0.682165 0.682165i −0.278322 0.960488i \(-0.589778\pi\)
0.960488 + 0.278322i \(0.0897783\pi\)
\(390\) 397.492 + 104.664i 1.01921 + 0.268370i
\(391\) 86.7042i 0.221750i
\(392\) 38.5923 + 15.4683i 0.0984496 + 0.0394600i
\(393\) 223.672 + 92.5164i 0.569139 + 0.235411i
\(394\) 93.7434 + 691.571i 0.237927 + 1.75526i
\(395\) 171.521 171.521i 0.434230 0.434230i
\(396\) −25.2513 + 7.00112i −0.0637659 + 0.0176796i
\(397\) 259.123 259.123i 0.652703 0.652703i −0.300940 0.953643i \(-0.597300\pi\)
0.953643 + 0.300940i \(0.0973004\pi\)
\(398\) −457.996 348.654i −1.15074 0.876014i
\(399\) −610.157 252.377i −1.52922 0.632523i
\(400\) 173.780 + 290.619i 0.434449 + 0.726548i
\(401\) 664.163i 1.65627i −0.560531 0.828133i \(-0.689403\pi\)
0.560531 0.828133i \(-0.310597\pi\)
\(402\) −175.861 301.575i −0.437465 0.750188i
\(403\) 177.275 177.275i 0.439889 0.439889i
\(404\) −178.821 101.424i −0.442626 0.251049i
\(405\) 389.932 + 388.369i 0.962795 + 0.958937i
\(406\) −96.7902 714.049i −0.238400 1.75874i
\(407\) −18.8131 −0.0462237
\(408\) 3.19847 + 266.684i 0.00783940 + 0.653637i
\(409\) 530.421i 1.29687i 0.761269 + 0.648437i \(0.224577\pi\)
−0.761269 + 0.648437i \(0.775423\pi\)
\(410\) 117.264 + 865.093i 0.286011 + 2.10998i
\(411\) −457.536 + 189.787i −1.11323 + 0.461768i
\(412\) 337.438 93.1926i 0.819024 0.226196i
\(413\) −129.769 129.769i −0.314211 0.314211i
\(414\) −19.0042 139.150i −0.0459038 0.336111i
\(415\) −912.271 −2.19824
\(416\) 201.285 + 252.169i 0.483857 + 0.606176i
\(417\) −372.762 154.184i −0.893914 0.369746i
\(418\) 34.6305 + 26.3628i 0.0828480 + 0.0630688i
\(419\) 404.149 + 404.149i 0.964556 + 0.964556i 0.999393 0.0348367i \(-0.0110911\pi\)
−0.0348367 + 0.999393i \(0.511091\pi\)
\(420\) −73.4857 + 595.715i −0.174966 + 1.41837i
\(421\) −264.630 264.630i −0.628575 0.628575i 0.319134 0.947710i \(-0.396608\pi\)
−0.947710 + 0.319134i \(0.896608\pi\)
\(422\) −59.3232 437.644i −0.140576 1.03707i
\(423\) 146.842 + 146.547i 0.347143 + 0.346447i
\(424\) 332.033 142.024i 0.783097 0.334963i
\(425\) −235.180 −0.553366
\(426\) 39.2314 148.992i 0.0920925 0.349747i
\(427\) −91.2382 91.2382i −0.213673 0.213673i
\(428\) 515.994 + 292.662i 1.20559 + 0.683790i
\(429\) −8.43598 20.3374i −0.0196643 0.0474065i
\(430\) −84.2825 + 110.715i −0.196006 + 0.257476i
\(431\) 766.652i 1.77877i −0.457155 0.889387i \(-0.651132\pi\)
0.457155 0.889387i \(-0.348868\pi\)
\(432\) 63.5861 + 427.295i 0.147190 + 0.989108i
\(433\) 151.222 0.349243 0.174622 0.984636i \(-0.444130\pi\)
0.174622 + 0.984636i \(0.444130\pi\)
\(434\) 291.296 + 221.752i 0.671188 + 0.510948i
\(435\) 921.422 382.207i 2.11821 0.878638i
\(436\) −37.5929 21.3220i −0.0862223 0.0489036i
\(437\) −164.943 + 164.943i −0.377445 + 0.377445i
\(438\) −325.995 85.8382i −0.744281 0.195978i
\(439\) 565.007i 1.28703i 0.765433 + 0.643516i \(0.222525\pi\)
−0.765433 + 0.643516i \(0.777475\pi\)
\(440\) 14.7195 36.7241i 0.0334535 0.0834638i
\(441\) −33.0409 + 33.1073i −0.0749228 + 0.0750733i
\(442\) −222.064 + 30.1011i −0.502408 + 0.0681020i
\(443\) 100.963 100.963i 0.227907 0.227907i −0.583911 0.811818i \(-0.698478\pi\)
0.811818 + 0.583911i \(0.198478\pi\)
\(444\) −37.9719 + 307.821i −0.0855223 + 0.693290i
\(445\) −215.577 + 215.577i −0.484442 + 0.484442i
\(446\) 54.8779 72.0883i 0.123045 0.161633i
\(447\) 212.557 513.887i 0.475518 1.14963i
\(448\) −325.416 + 340.728i −0.726375 + 0.760554i
\(449\) 131.725i 0.293375i −0.989183 0.146687i \(-0.953139\pi\)
0.989183 0.146687i \(-0.0468611\pi\)
\(450\) −377.436 + 51.5478i −0.838747 + 0.114551i
\(451\) 33.0663 33.0663i 0.0733178 0.0733178i
\(452\) 50.6143 13.9785i 0.111979 0.0309259i
\(453\) −141.461 341.034i −0.312277 0.752833i
\(454\) −842.961 + 114.264i −1.85674 + 0.251684i
\(455\) −504.339 −1.10844
\(456\) 501.247 513.416i 1.09923 1.12591i
\(457\) 137.963i 0.301888i 0.988542 + 0.150944i \(0.0482313\pi\)
−0.988542 + 0.150944i \(0.951769\pi\)
\(458\) 184.168 24.9642i 0.402114 0.0545071i
\(459\) −277.374 114.403i −0.604302 0.249245i
\(460\) 184.445 + 104.613i 0.400967 + 0.227421i
\(461\) 303.536 + 303.536i 0.658430 + 0.658430i 0.955008 0.296579i \(-0.0958457\pi\)
−0.296579 + 0.955008i \(0.595846\pi\)
\(462\) 27.7742 16.1963i 0.0601173 0.0350569i
\(463\) 280.379 0.605570 0.302785 0.953059i \(-0.402084\pi\)
0.302785 + 0.953059i \(0.402084\pi\)
\(464\) 759.374 + 191.054i 1.63658 + 0.411754i
\(465\) −193.714 + 468.332i −0.416589 + 1.00716i
\(466\) 51.8759 68.1449i 0.111322 0.146234i
\(467\) 65.6355 + 65.6355i 0.140547 + 0.140547i 0.773880 0.633333i \(-0.218313\pi\)
−0.633333 + 0.773880i \(0.718313\pi\)
\(468\) −349.789 + 96.9816i −0.747412 + 0.207226i
\(469\) 302.886 + 302.886i 0.645812 + 0.645812i
\(470\) −310.392 + 42.0740i −0.660409 + 0.0895192i
\(471\) 225.699 545.659i 0.479190 1.15851i
\(472\) 183.359 78.4302i 0.388473 0.166166i
\(473\) 7.45335 0.0157576
\(474\) −54.5441 + 207.147i −0.115072 + 0.437019i
\(475\) 447.400 + 447.400i 0.941894 + 0.941894i
\(476\) −87.1147 315.431i −0.183014 0.662669i
\(477\) 0.407800 + 406.274i 0.000854927 + 0.851728i
\(478\) 160.088 + 121.868i 0.334912 + 0.254955i
\(479\) 373.272i 0.779273i 0.920969 + 0.389636i \(0.127399\pi\)
−0.920969 + 0.389636i \(0.872601\pi\)
\(480\) −571.173 314.965i −1.18994 0.656178i
\(481\) −260.604 −0.541797
\(482\) −6.33778 + 8.32539i −0.0131489 + 0.0172726i
\(483\) 66.0234 + 159.169i 0.136694 + 0.329542i
\(484\) 464.492 128.282i 0.959694 0.265045i
\(485\) 395.702 395.702i 0.815881 0.815881i
\(486\) −470.228 122.807i −0.967547 0.252690i
\(487\) 0.0470526i 9.66171e-5i 1.00000 4.83086e-5i \(1.53771e-5\pi\)
−1.00000 4.83086e-5i \(0.999985\pi\)
\(488\) 128.916 55.1429i 0.264173 0.112998i
\(489\) −32.3206 + 78.1398i −0.0660954 + 0.159795i
\(490\) −9.48614 69.9820i −0.0193595 0.142820i
\(491\) −273.442 + 273.442i −0.556908 + 0.556908i −0.928426 0.371518i \(-0.878837\pi\)
0.371518 + 0.928426i \(0.378837\pi\)
\(492\) −474.294 607.775i −0.964012 1.23531i
\(493\) −384.562 + 384.562i −0.780044 + 0.780044i
\(494\) 479.712 + 365.185i 0.971077 + 0.739241i
\(495\) 31.5047 + 31.4415i 0.0636458 + 0.0635182i
\(496\) −341.443 + 204.170i −0.688394 + 0.411634i
\(497\) 189.042i 0.380365i
\(498\) 695.930 405.825i 1.39745 0.814910i
\(499\) −46.2637 + 46.2637i −0.0927129 + 0.0927129i −0.751942 0.659229i \(-0.770883\pi\)
0.659229 + 0.751942i \(0.270883\pi\)
\(500\) −51.4422 + 90.6980i −0.102884 + 0.181396i
\(501\) −167.156 + 69.3366i −0.333645 + 0.138396i
\(502\) 6.62514 + 48.8755i 0.0131975 + 0.0973616i
\(503\) −864.426 −1.71854 −0.859270 0.511522i \(-0.829082\pi\)
−0.859270 + 0.511522i \(0.829082\pi\)
\(504\) −208.946 487.134i −0.414575 0.966535i
\(505\) 349.198i 0.691482i
\(506\) −1.52569 11.2554i −0.00301520 0.0222440i
\(507\) 77.3977 + 186.590i 0.152658 + 0.368027i
\(508\) 93.9946 + 340.342i 0.185029 + 0.669964i
\(509\) 171.041 + 171.041i 0.336033 + 0.336033i 0.854872 0.518839i \(-0.173635\pi\)
−0.518839 + 0.854872i \(0.673635\pi\)
\(510\) 391.341 228.207i 0.767336 0.447465i
\(511\) 413.623 0.809438
\(512\) −212.121 465.992i −0.414299 0.910141i
\(513\) 310.031 + 745.306i 0.604349 + 1.45284i
\(514\) −546.911 416.341i −1.06403 0.810002i
\(515\) −420.464 420.464i −0.816435 0.816435i
\(516\) 15.0437 121.952i 0.0291545 0.236342i
\(517\) 11.8641 + 11.8641i 0.0229479 + 0.0229479i
\(518\) −51.1168 377.103i −0.0986811 0.727999i
\(519\) −293.368 121.345i −0.565257 0.233805i
\(520\) 203.899 508.713i 0.392114 0.978295i
\(521\) −351.572 −0.674802 −0.337401 0.941361i \(-0.609548\pi\)
−0.337401 + 0.941361i \(0.609548\pi\)
\(522\) −532.885 + 701.465i −1.02085 + 1.34380i
\(523\) −287.638 287.638i −0.549977 0.549977i 0.376457 0.926434i \(-0.377142\pi\)
−0.926434 + 0.376457i \(0.877142\pi\)
\(524\) 159.221 280.724i 0.303857 0.535732i
\(525\) 431.736 179.085i 0.822354 0.341114i
\(526\) −118.825 + 156.090i −0.225904 + 0.296750i
\(527\) 276.309i 0.524306i
\(528\) 5.10791 + 34.5631i 0.00967407 + 0.0654605i
\(529\) −468.124 −0.884922
\(530\) −488.083 371.558i −0.920911 0.701052i
\(531\) 0.225200 + 224.357i 0.000424106 + 0.422519i
\(532\) −434.341 + 765.789i −0.816431 + 1.43945i
\(533\) 458.045 458.045i 0.859372 0.859372i
\(534\) 68.5540 260.353i 0.128378 0.487553i
\(535\) 1007.63i 1.88341i
\(536\) −427.967 + 183.059i −0.798446 + 0.341528i
\(537\) −15.5471 6.43067i −0.0289517 0.0119752i
\(538\) 354.721 48.0828i 0.659332 0.0893732i
\(539\) −2.67491 + 2.67491i −0.00496273 + 0.00496273i
\(540\) 578.036 452.021i 1.07044 0.837076i
\(541\) 419.846 419.846i 0.776056 0.776056i −0.203102 0.979158i \(-0.565102\pi\)
0.979158 + 0.203102i \(0.0651021\pi\)
\(542\) −250.146 + 328.595i −0.461524 + 0.606264i
\(543\) 622.654 + 257.545i 1.14669 + 0.474301i
\(544\) 353.386 + 39.6554i 0.649607 + 0.0728960i
\(545\) 73.4108i 0.134699i
\(546\) 384.737 224.356i 0.704646 0.410908i
\(547\) 517.346 517.346i 0.945789 0.945789i −0.0528155 0.998604i \(-0.516820\pi\)
0.998604 + 0.0528155i \(0.0168195\pi\)
\(548\) 175.819 + 636.616i 0.320837 + 1.16171i
\(549\) 0.158334 + 157.742i 0.000288404 + 0.287325i
\(550\) −30.5298 + 4.13835i −0.0555087 + 0.00752427i
\(551\) 1463.16 2.65546
\(552\) −187.242 + 2.24569i −0.339206 + 0.00406827i
\(553\) 262.828i 0.475277i
\(554\) 514.079 69.6840i 0.927940 0.125783i
\(555\) 486.621 201.851i 0.876794 0.363696i
\(556\) −265.351 + 467.843i −0.477251 + 0.841443i
\(557\) −31.8976 31.8976i −0.0572667 0.0572667i 0.677893 0.735160i \(-0.262893\pi\)
−0.735160 + 0.677893i \(0.762893\pi\)
\(558\) −60.5626 443.443i −0.108535 0.794700i
\(559\) 103.246 0.184698
\(560\) 776.120 + 195.267i 1.38593 + 0.348691i
\(561\) −22.4237 9.27502i −0.0399709 0.0165330i
\(562\) 132.220 173.685i 0.235266 0.309049i
\(563\) 32.9214 + 32.9214i 0.0584750 + 0.0584750i 0.735740 0.677265i \(-0.236835\pi\)
−0.677265 + 0.735740i \(0.736835\pi\)
\(564\) 218.067 170.175i 0.386644 0.301728i
\(565\) −63.0679 63.0679i −0.111625 0.111625i
\(566\) 169.464 22.9710i 0.299406 0.0405848i
\(567\) 596.310 1.19710i 1.05169 0.00211129i
\(568\) −190.681 76.4278i −0.335707 0.134556i
\(569\) −647.095 −1.13725 −0.568624 0.822597i \(-0.692524\pi\)
−0.568624 + 0.822597i \(0.692524\pi\)
\(570\) −1178.61 310.341i −2.06774 0.544459i
\(571\) 451.861 + 451.861i 0.791350 + 0.791350i 0.981714 0.190363i \(-0.0609666\pi\)
−0.190363 + 0.981714i \(0.560967\pi\)
\(572\) −28.2975 + 7.81511i −0.0494711 + 0.0136628i
\(573\) −79.1550 190.826i −0.138141 0.333030i
\(574\) 752.652 + 572.963i 1.31124 + 0.998193i
\(575\) 165.123i 0.287170i
\(576\) 575.834 13.8145i 0.999712 0.0239835i
\(577\) 532.176 0.922315 0.461157 0.887318i \(-0.347434\pi\)
0.461157 + 0.887318i \(0.347434\pi\)
\(578\) 200.504 263.385i 0.346893 0.455683i
\(579\) −1015.99 + 421.436i −1.75474 + 0.727869i
\(580\) −354.078 1282.07i −0.610478 2.21046i
\(581\) −698.953 + 698.953i −1.20302 + 1.20302i
\(582\) −125.834 + 477.892i −0.216210 + 0.821120i
\(583\) 32.8579i 0.0563601i
\(584\) −167.224 + 417.210i −0.286342 + 0.714402i
\(585\) 436.412 + 435.537i 0.746004 + 0.744508i
\(586\) 7.39475 + 54.5532i 0.0126190 + 0.0930942i
\(587\) −532.393 + 532.393i −0.906973 + 0.906973i −0.996027 0.0890534i \(-0.971616\pi\)
0.0890534 + 0.996027i \(0.471616\pi\)
\(588\) 38.3681 + 49.1661i 0.0652519 + 0.0836158i
\(589\) −525.642 + 525.642i −0.892431 + 0.892431i
\(590\) −269.535 205.186i −0.456838 0.347772i
\(591\) −400.124 + 967.359i −0.677029 + 1.63682i
\(592\) 401.040 + 100.899i 0.677433 + 0.170438i
\(593\) 254.750i 0.429595i 0.976659 + 0.214798i \(0.0689092\pi\)
−0.976659 + 0.214798i \(0.931091\pi\)
\(594\) −38.0203 9.97037i −0.0640072 0.0167851i
\(595\) −393.042 + 393.042i −0.660574 + 0.660574i
\(596\) −644.963 365.811i −1.08215 0.613777i
\(597\) −330.811 797.517i −0.554123 1.33587i
\(598\) −21.1343 155.914i −0.0353417 0.260726i
\(599\) −624.772 −1.04303 −0.521513 0.853244i \(-0.674632\pi\)
−0.521513 + 0.853244i \(0.674632\pi\)
\(600\) 6.09130 + 507.883i 0.0101522 + 0.846472i
\(601\) 386.910i 0.643777i −0.946778 0.321889i \(-0.895682\pi\)
0.946778 0.321889i \(-0.104318\pi\)
\(602\) 20.2515 + 149.401i 0.0336403 + 0.248174i
\(603\) −0.525625 523.658i −0.000871684 0.868422i
\(604\) −474.514 + 131.050i −0.785620 + 0.216970i
\(605\) −578.779 578.779i −0.956660 0.956660i
\(606\) −155.341 266.387i −0.256339 0.439583i
\(607\) −951.141 −1.56695 −0.783477 0.621421i \(-0.786556\pi\)
−0.783477 + 0.621421i \(0.786556\pi\)
\(608\) −596.832 747.710i −0.981632 1.22979i
\(609\) 413.129 998.800i 0.678373 1.64007i
\(610\) −189.505 144.262i −0.310664 0.236496i
\(611\) 164.345 + 164.345i 0.268977 + 0.268977i
\(612\) −197.018 + 348.178i −0.321925 + 0.568918i
\(613\) 387.896 + 387.896i 0.632783 + 0.632783i 0.948765 0.315982i \(-0.102334\pi\)
−0.315982 + 0.948765i \(0.602334\pi\)
\(614\) 155.085 + 1144.10i 0.252581 + 1.86336i
\(615\) −500.519 + 1210.08i −0.813852 + 1.96761i
\(616\) −16.8592 39.4145i −0.0273688 0.0639846i
\(617\) 882.945 1.43103 0.715514 0.698598i \(-0.246192\pi\)
0.715514 + 0.698598i \(0.246192\pi\)
\(618\) 507.797 + 133.709i 0.821678 + 0.216357i
\(619\) −694.731 694.731i −1.12234 1.12234i −0.991388 0.130955i \(-0.958196\pi\)
−0.130955 0.991388i \(-0.541804\pi\)
\(620\) 587.789 + 333.382i 0.948046 + 0.537714i
\(621\) 80.3239 194.748i 0.129346 0.313604i
\(622\) 437.286 574.425i 0.703033 0.923513i
\(623\) 330.337i 0.530235i
\(624\) 70.7564 + 478.779i 0.113392 + 0.767274i
\(625\) 706.197 1.12991
\(626\) −117.636 89.5515i −0.187917 0.143053i
\(627\) 25.0136 + 60.3027i 0.0398942 + 0.0961765i
\(628\) −684.840 388.428i −1.09051 0.618516i
\(629\) −203.094 + 203.094i −0.322885 + 0.322885i
\(630\) −544.636 + 716.933i −0.864502 + 1.13799i
\(631\) 927.845i 1.47044i 0.677831 + 0.735218i \(0.262920\pi\)
−0.677831 + 0.735218i \(0.737080\pi\)
\(632\) 265.108 + 106.259i 0.419475 + 0.168131i
\(633\) 253.209 612.170i 0.400014 0.967093i
\(634\) 484.069 65.6161i 0.763516 0.103495i
\(635\) 424.082 424.082i 0.667846 0.667846i
\(636\) 537.624 + 66.3198i 0.845321 + 0.104276i
\(637\) −37.0537 + 37.0537i −0.0581691 + 0.0581691i
\(638\) −43.1547 + 56.6885i −0.0676405 + 0.0888535i
\(639\) 163.253 163.581i 0.255482 0.255995i
\(640\) −510.739 + 703.908i −0.798029 + 1.09986i
\(641\) 759.287i 1.18453i −0.805741 0.592267i \(-0.798233\pi\)
0.805741 0.592267i \(-0.201767\pi\)
\(642\) 448.244 + 768.671i 0.698199 + 1.19731i
\(643\) 274.424 274.424i 0.426787 0.426787i −0.460746 0.887532i \(-0.652418\pi\)
0.887532 + 0.460746i \(0.152418\pi\)
\(644\) 221.467 61.1642i 0.343893 0.0949755i
\(645\) −192.789 + 79.9694i −0.298898 + 0.123984i
\(646\) 658.446 89.2532i 1.01927 0.138163i
\(647\) 747.683 1.15561 0.577807 0.816173i \(-0.303908\pi\)
0.577807 + 0.816173i \(0.303908\pi\)
\(648\) −239.875 + 601.967i −0.370178 + 0.928961i
\(649\) 18.1452i 0.0279587i
\(650\) −422.908 + 57.3257i −0.650628 + 0.0881934i
\(651\) 210.403 + 507.239i 0.323200 + 0.779168i
\(652\) 98.0709 + 55.6239i 0.150416 + 0.0853128i
\(653\) −605.127 605.127i −0.926688 0.926688i 0.0708022 0.997490i \(-0.477444\pi\)
−0.997490 + 0.0708022i \(0.977444\pi\)
\(654\) −32.6569 56.0018i −0.0499341 0.0856296i
\(655\) −548.192 −0.836935
\(656\) −882.223 + 527.537i −1.34485 + 0.804172i
\(657\) −357.914 357.197i −0.544771 0.543678i
\(658\) −205.577 + 270.049i −0.312427 + 0.410408i
\(659\) −588.767 588.767i −0.893425 0.893425i 0.101418 0.994844i \(-0.467662\pi\)
−0.994844 + 0.101418i \(0.967662\pi\)
\(660\) 46.7861 36.5108i 0.0708880 0.0553194i
\(661\) 3.60334 + 3.60334i 0.00545135 + 0.00545135i 0.709827 0.704376i \(-0.248773\pi\)
−0.704376 + 0.709827i \(0.748773\pi\)
\(662\) 732.950 99.3523i 1.10718 0.150079i
\(663\) −310.620 128.480i −0.468507 0.193786i
\(664\) −422.436 987.597i −0.636198 1.48734i
\(665\) 1495.42 2.24875
\(666\) −281.427 + 370.457i −0.422563 + 0.556242i
\(667\) −270.005 270.005i −0.404805 0.404805i
\(668\) 64.2336 + 232.581i 0.0961581 + 0.348176i
\(669\) 125.529 52.0695i 0.187636 0.0778319i
\(670\) 629.104 + 478.911i 0.938961 + 0.714793i
\(671\) 12.7575i 0.0190127i
\(672\) −678.931 + 196.298i −1.01031 + 0.292110i
\(673\) −460.445 −0.684167 −0.342084 0.939670i \(-0.611133\pi\)
−0.342084 + 0.939670i \(0.611133\pi\)
\(674\) 22.0737 28.9963i 0.0327502 0.0430211i
\(675\) −528.242 217.874i −0.782581 0.322776i
\(676\) 259.621 71.7014i 0.384055 0.106067i
\(677\) −150.713 + 150.713i −0.222618 + 0.222618i −0.809600 0.586982i \(-0.800316\pi\)
0.586982 + 0.809600i \(0.300316\pi\)
\(678\) 76.1674 + 20.0557i 0.112341 + 0.0295807i
\(679\) 606.350i 0.893004i
\(680\) −237.548 555.354i −0.349335 0.816698i
\(681\) −1179.12 487.714i −1.73145 0.716174i
\(682\) −4.86207 35.8689i −0.00712913 0.0525937i
\(683\) 577.893 577.893i 0.846109 0.846109i −0.143536 0.989645i \(-0.545847\pi\)
0.989645 + 0.143536i \(0.0458473\pi\)
\(684\) 1037.16 287.561i 1.51632 0.420412i
\(685\) 793.254 793.254i 1.15803 1.15803i
\(686\) 513.167 + 390.653i 0.748057 + 0.569465i
\(687\) 257.612 + 106.555i 0.374981 + 0.155102i
\(688\) −158.884 39.9742i −0.230936 0.0581021i
\(689\) 455.158i 0.660607i
\(690\) 160.227 + 274.765i 0.232213 + 0.398211i
\(691\) −545.023 + 545.023i −0.788745 + 0.788745i −0.981288 0.192544i \(-0.938326\pi\)
0.192544 + 0.981288i \(0.438326\pi\)
\(692\) −208.834 + 368.197i −0.301784 + 0.532077i
\(693\) 48.2274 0.0484085i 0.0695922 6.98536e-5i
\(694\) −65.9963 486.874i −0.0950956 0.701547i
\(695\) 913.595 1.31453
\(696\) 840.440 + 820.519i 1.20753 + 1.17891i
\(697\) 713.929i 1.02429i
\(698\) −147.372 1087.20i −0.211134 1.55760i
\(699\) 118.662 49.2212i 0.169760 0.0704165i
\(700\) −165.904 600.718i −0.237006 0.858169i
\(701\) 413.745 + 413.745i 0.590221 + 0.590221i 0.937691 0.347470i \(-0.112959\pi\)
−0.347470 + 0.937691i \(0.612959\pi\)
\(702\) −526.669 138.113i −0.750240 0.196742i
\(703\) 772.721 1.09918
\(704\) 46.5724 1.07052i 0.0661540 0.00152062i
\(705\) −434.171 179.584i −0.615846 0.254730i
\(706\) 1077.05 + 819.915i 1.52557 + 1.16135i
\(707\) 267.545 + 267.545i 0.378423 + 0.378423i
\(708\) 296.893 + 36.6239i 0.419340 + 0.0517286i
\(709\) 521.959 + 521.959i 0.736191 + 0.736191i 0.971839 0.235648i \(-0.0757212\pi\)
−0.235648 + 0.971839i \(0.575721\pi\)
\(710\) 46.8703 + 345.776i 0.0660145 + 0.487008i
\(711\) −226.973 + 227.429i −0.319231 + 0.319873i
\(712\) −333.202 133.552i −0.467980 0.187573i
\(713\) 194.000 0.272089
\(714\) 124.988 474.679i 0.175054 0.664816i
\(715\) 35.2600 + 35.2600i 0.0493147 + 0.0493147i
\(716\) −11.0672 + 19.5127i −0.0154570 + 0.0272523i
\(717\) 115.632 + 278.764i 0.161272 + 0.388792i
\(718\) −291.830 + 383.352i −0.406449 + 0.533917i
\(719\) 567.983i 0.789963i 0.918689 + 0.394981i \(0.129249\pi\)
−0.918689 + 0.394981i \(0.870751\pi\)
\(720\) −502.961 839.210i −0.698556 1.16557i
\(721\) −644.293 −0.893610
\(722\) −847.919 645.486i −1.17440 0.894025i
\(723\) −14.4972 + 6.01344i −0.0200514 + 0.00831735i
\(724\) 443.237 781.473i 0.612205 1.07938i
\(725\) −732.374 + 732.374i −1.01017 + 1.01017i
\(726\) 698.995 + 184.053i 0.962804 + 0.253517i
\(727\) 635.396i 0.873998i −0.899462 0.436999i \(-0.856041\pi\)
0.899462 0.436999i \(-0.143959\pi\)
\(728\) −233.539 545.982i −0.320795 0.749975i
\(729\) −517.031 513.926i −0.709233 0.704974i
\(730\) 756.556 102.552i 1.03638 0.140482i
\(731\) 80.4619 80.4619i 0.110071 0.110071i
\(732\) 208.740 + 25.7496i 0.285164 + 0.0351770i
\(733\) −637.378 + 637.378i −0.869547 + 0.869547i −0.992422 0.122875i \(-0.960788\pi\)
0.122875 + 0.992422i \(0.460788\pi\)
\(734\) 807.667 1060.96i 1.10036 1.44545i
\(735\) 40.4897 97.8896i 0.0550880 0.133183i
\(736\) −27.8425 + 248.117i −0.0378295 + 0.337115i
\(737\) 42.3515i 0.0574648i
\(738\) −156.482 1145.77i −0.212035 1.55253i
\(739\) 397.296 397.296i 0.537613 0.537613i −0.385214 0.922827i \(-0.625872\pi\)
0.922827 + 0.385214i \(0.125872\pi\)
\(740\) −186.995 677.085i −0.252696 0.914980i
\(741\) 346.497 + 835.331i 0.467607 + 1.12730i
\(742\) −658.630 + 89.2781i −0.887641 + 0.120321i
\(743\) −1160.78 −1.56229 −0.781145 0.624349i \(-0.785364\pi\)
−0.781145 + 0.624349i \(0.785364\pi\)
\(744\) −596.703 + 7.15655i −0.802020 + 0.00961902i
\(745\) 1259.47i 1.69057i
\(746\) −1004.84 + 136.207i −1.34697 + 0.182583i
\(747\) 1208.42 1.21296i 1.61770 0.00162377i
\(748\) −15.9623 + 28.1433i −0.0213400 + 0.0376247i
\(749\) −772.011 772.011i −1.03072 1.03072i
\(750\) −135.112 + 78.7893i −0.180149 + 0.105052i
\(751\) 1220.14 1.62469 0.812343 0.583181i \(-0.198192\pi\)
0.812343 + 0.583181i \(0.198192\pi\)
\(752\) −189.278 316.538i −0.251700 0.420929i
\(753\) −28.2781 + 68.3663i −0.0375539 + 0.0907919i
\(754\) −597.792 + 785.267i −0.792827 + 1.04147i
\(755\) 591.268 + 591.268i 0.783136 + 0.783136i
\(756\) 96.5491 789.198i 0.127710 1.04391i
\(757\) 202.623 + 202.623i 0.267666 + 0.267666i 0.828159 0.560493i \(-0.189388\pi\)
−0.560493 + 0.828159i \(0.689388\pi\)
\(758\) −395.080 + 53.5536i −0.521214 + 0.0706512i
\(759\) 6.51210 15.7439i 0.00857984 0.0207430i
\(760\) −604.585 + 1508.39i −0.795507 + 1.98473i
\(761\) 694.461 0.912563 0.456282 0.889835i \(-0.349181\pi\)
0.456282 + 0.889835i \(0.349181\pi\)
\(762\) −134.859 + 512.167i −0.176981 + 0.672135i
\(763\) 56.2451 + 56.2451i 0.0737157 + 0.0737157i
\(764\) −265.516 + 73.3293i −0.347534 + 0.0959808i
\(765\) 679.529 0.682081i 0.888273 0.000891610i
\(766\) −110.549 84.1564i −0.144320 0.109865i
\(767\) 251.353i 0.327709i
\(768\) 76.4849 764.182i 0.0995897 0.995029i
\(769\) 405.268 0.527007 0.263503 0.964658i \(-0.415122\pi\)
0.263503 + 0.964658i \(0.415122\pi\)
\(770\) −44.1063 + 57.9386i −0.0572809 + 0.0752449i
\(771\) −395.035 952.347i −0.512367 1.23521i