Properties

Label 78.3.l.a.37.1
Level $78$
Weight $3$
Character 78.37
Analytic conductor $2.125$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 78.l (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.12534606201\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 78.37
Dual form 78.3.l.a.19.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.366025 - 1.36603i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-1.26795 - 1.26795i) q^{5} +(-2.36603 + 0.633975i) q^{6} +(-2.50000 - 9.33013i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.366025 - 1.36603i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-1.26795 - 1.26795i) q^{5} +(-2.36603 + 0.633975i) q^{6} +(-2.50000 - 9.33013i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(-2.19615 + 1.26795i) q^{10} +(9.92820 + 2.66025i) q^{11} +3.46410i q^{12} +(-11.2583 - 6.50000i) q^{13} -13.6603 q^{14} +(-0.803848 + 3.00000i) q^{15} +(2.00000 + 3.46410i) q^{16} +(16.3923 + 9.46410i) q^{17} +(3.00000 + 3.00000i) q^{18} +(31.9545 - 8.56218i) q^{19} +(0.928203 + 3.46410i) q^{20} +(-11.8301 + 11.8301i) q^{21} +(7.26795 - 12.5885i) q^{22} +(-3.58846 + 2.07180i) q^{23} +(4.73205 + 1.26795i) q^{24} -21.7846i q^{25} +(-13.0000 + 13.0000i) q^{26} +5.19615 q^{27} +(-5.00000 + 18.6603i) q^{28} +(8.66025 + 15.0000i) q^{29} +(3.80385 + 2.19615i) q^{30} +(22.1699 + 22.1699i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-4.60770 - 17.1962i) q^{33} +(18.9282 - 18.9282i) q^{34} +(-8.66025 + 15.0000i) q^{35} +(5.19615 - 3.00000i) q^{36} +(-35.7583 - 9.58142i) q^{37} -46.7846i q^{38} +22.5167i q^{39} +5.07180 q^{40} +(-6.67949 + 24.9282i) q^{41} +(11.8301 + 20.4904i) q^{42} +(-13.2846 - 7.66987i) q^{43} +(-14.5359 - 14.5359i) q^{44} +(5.19615 - 1.39230i) q^{45} +(1.51666 + 5.66025i) q^{46} +(7.01924 - 7.01924i) q^{47} +(3.46410 - 6.00000i) q^{48} +(-38.3660 + 22.1506i) q^{49} +(-29.7583 - 7.97372i) q^{50} -32.7846i q^{51} +(13.0000 + 22.5167i) q^{52} -61.6743 q^{53} +(1.90192 - 7.09808i) q^{54} +(-9.21539 - 15.9615i) q^{55} +(23.6603 + 13.6603i) q^{56} +(-40.5167 - 40.5167i) q^{57} +(23.6603 - 6.33975i) q^{58} +(-17.1051 - 63.8372i) q^{59} +(4.39230 - 4.39230i) q^{60} +(3.65064 - 6.32309i) q^{61} +(38.3993 - 22.1699i) q^{62} +(27.9904 + 7.50000i) q^{63} -8.00000i q^{64} +(6.03332 + 22.5167i) q^{65} -25.1769 q^{66} +(-10.1532 + 37.8923i) q^{67} +(-18.9282 - 32.7846i) q^{68} +(6.21539 + 3.58846i) q^{69} +(17.3205 + 17.3205i) q^{70} +(103.890 - 27.8372i) q^{71} +(-2.19615 - 8.19615i) q^{72} +(-67.4186 + 67.4186i) q^{73} +(-26.1769 + 45.3397i) q^{74} +(-32.6769 + 18.8660i) q^{75} +(-63.9090 - 17.1244i) q^{76} -99.2820i q^{77} +(30.7583 + 8.24167i) q^{78} +11.8756 q^{79} +(1.85641 - 6.92820i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(31.6077 + 18.2487i) q^{82} +(111.033 + 111.033i) q^{83} +(32.3205 - 8.66025i) q^{84} +(-8.78461 - 32.7846i) q^{85} +(-15.3397 + 15.3397i) q^{86} +(15.0000 - 25.9808i) q^{87} +(-25.1769 + 14.5359i) q^{88} +(162.067 + 43.4256i) q^{89} -7.60770i q^{90} +(-32.5000 + 121.292i) q^{91} +8.28719 q^{92} +(14.0551 - 52.4545i) q^{93} +(-7.01924 - 12.1577i) q^{94} +(-51.3731 - 29.6603i) q^{95} +(-6.92820 - 6.92820i) q^{96} +(150.246 - 40.2583i) q^{97} +(16.2154 + 60.5167i) q^{98} +(-21.8038 + 21.8038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 12 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 12 q^{5} - 6 q^{6} - 10 q^{7} - 8 q^{8} - 6 q^{9} + 12 q^{10} + 12 q^{11} - 20 q^{14} - 24 q^{15} + 8 q^{16} + 24 q^{17} + 12 q^{18} + 62 q^{19} - 24 q^{20} - 30 q^{21} + 36 q^{22} + 48 q^{23} + 12 q^{24} - 52 q^{26} - 20 q^{28} + 36 q^{30} + 106 q^{31} + 8 q^{32} - 60 q^{33} + 48 q^{34} - 98 q^{37} + 48 q^{40} - 96 q^{41} + 30 q^{42} + 30 q^{43} - 72 q^{44} - 84 q^{46} + 132 q^{47} - 150 q^{49} - 74 q^{50} + 52 q^{52} + 72 q^{53} + 18 q^{54} - 120 q^{55} + 60 q^{56} - 72 q^{57} + 60 q^{58} + 84 q^{59} - 24 q^{60} - 72 q^{61} - 30 q^{62} + 60 q^{63} - 156 q^{65} + 24 q^{66} - 148 q^{67} - 48 q^{68} + 108 q^{69} + 180 q^{71} + 12 q^{72} - 190 q^{73} + 20 q^{74} - 6 q^{75} - 124 q^{76} + 78 q^{78} + 96 q^{79} - 48 q^{80} - 18 q^{81} + 168 q^{82} + 264 q^{83} + 60 q^{84} + 48 q^{85} - 96 q^{86} + 60 q^{87} + 24 q^{88} + 288 q^{89} - 130 q^{91} + 144 q^{92} + 174 q^{93} - 132 q^{94} - 60 q^{95} + 310 q^{97} + 148 q^{98} - 108 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(67\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.366025 1.36603i 0.183013 0.683013i
\(3\) −0.866025 1.50000i −0.288675 0.500000i
\(4\) −1.73205 1.00000i −0.433013 0.250000i
\(5\) −1.26795 1.26795i −0.253590 0.253590i 0.568851 0.822441i \(-0.307388\pi\)
−0.822441 + 0.568851i \(0.807388\pi\)
\(6\) −2.36603 + 0.633975i −0.394338 + 0.105662i
\(7\) −2.50000 9.33013i −0.357143 1.33288i −0.877766 0.479089i \(-0.840967\pi\)
0.520624 0.853786i \(-0.325700\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) −1.50000 + 2.59808i −0.166667 + 0.288675i
\(10\) −2.19615 + 1.26795i −0.219615 + 0.126795i
\(11\) 9.92820 + 2.66025i 0.902564 + 0.241841i 0.680117 0.733104i \(-0.261929\pi\)
0.222447 + 0.974945i \(0.428596\pi\)
\(12\) 3.46410i 0.288675i
\(13\) −11.2583 6.50000i −0.866025 0.500000i
\(14\) −13.6603 −0.975732
\(15\) −0.803848 + 3.00000i −0.0535898 + 0.200000i
\(16\) 2.00000 + 3.46410i 0.125000 + 0.216506i
\(17\) 16.3923 + 9.46410i 0.964253 + 0.556712i 0.897479 0.441056i \(-0.145396\pi\)
0.0667738 + 0.997768i \(0.478729\pi\)
\(18\) 3.00000 + 3.00000i 0.166667 + 0.166667i
\(19\) 31.9545 8.56218i 1.68181 0.450641i 0.713558 0.700597i \(-0.247083\pi\)
0.968257 + 0.249956i \(0.0804160\pi\)
\(20\) 0.928203 + 3.46410i 0.0464102 + 0.173205i
\(21\) −11.8301 + 11.8301i −0.563339 + 0.563339i
\(22\) 7.26795 12.5885i 0.330361 0.572203i
\(23\) −3.58846 + 2.07180i −0.156020 + 0.0900781i −0.575977 0.817466i \(-0.695378\pi\)
0.419957 + 0.907544i \(0.362045\pi\)
\(24\) 4.73205 + 1.26795i 0.197169 + 0.0528312i
\(25\) 21.7846i 0.871384i
\(26\) −13.0000 + 13.0000i −0.500000 + 0.500000i
\(27\) 5.19615 0.192450
\(28\) −5.00000 + 18.6603i −0.178571 + 0.666438i
\(29\) 8.66025 + 15.0000i 0.298629 + 0.517241i 0.975823 0.218564i \(-0.0701372\pi\)
−0.677193 + 0.735805i \(0.736804\pi\)
\(30\) 3.80385 + 2.19615i 0.126795 + 0.0732051i
\(31\) 22.1699 + 22.1699i 0.715157 + 0.715157i 0.967609 0.252452i \(-0.0812370\pi\)
−0.252452 + 0.967609i \(0.581237\pi\)
\(32\) 5.46410 1.46410i 0.170753 0.0457532i
\(33\) −4.60770 17.1962i −0.139627 0.521096i
\(34\) 18.9282 18.9282i 0.556712 0.556712i
\(35\) −8.66025 + 15.0000i −0.247436 + 0.428571i
\(36\) 5.19615 3.00000i 0.144338 0.0833333i
\(37\) −35.7583 9.58142i −0.966441 0.258957i −0.259117 0.965846i \(-0.583431\pi\)
−0.707325 + 0.706889i \(0.750098\pi\)
\(38\) 46.7846i 1.23117i
\(39\) 22.5167i 0.577350i
\(40\) 5.07180 0.126795
\(41\) −6.67949 + 24.9282i −0.162914 + 0.608005i 0.835383 + 0.549669i \(0.185246\pi\)
−0.998297 + 0.0583360i \(0.981421\pi\)
\(42\) 11.8301 + 20.4904i 0.281670 + 0.487866i
\(43\) −13.2846 7.66987i −0.308944 0.178369i 0.337510 0.941322i \(-0.390415\pi\)
−0.646454 + 0.762953i \(0.723749\pi\)
\(44\) −14.5359 14.5359i −0.330361 0.330361i
\(45\) 5.19615 1.39230i 0.115470 0.0309401i
\(46\) 1.51666 + 5.66025i 0.0329709 + 0.123049i
\(47\) 7.01924 7.01924i 0.149345 0.149345i −0.628480 0.777826i \(-0.716323\pi\)
0.777826 + 0.628480i \(0.216323\pi\)
\(48\) 3.46410 6.00000i 0.0721688 0.125000i
\(49\) −38.3660 + 22.1506i −0.782980 + 0.452054i
\(50\) −29.7583 7.97372i −0.595167 0.159474i
\(51\) 32.7846i 0.642835i
\(52\) 13.0000 + 22.5167i 0.250000 + 0.433013i
\(53\) −61.6743 −1.16367 −0.581833 0.813308i \(-0.697664\pi\)
−0.581833 + 0.813308i \(0.697664\pi\)
\(54\) 1.90192 7.09808i 0.0352208 0.131446i
\(55\) −9.21539 15.9615i −0.167553 0.290210i
\(56\) 23.6603 + 13.6603i 0.422505 + 0.243933i
\(57\) −40.5167 40.5167i −0.710819 0.710819i
\(58\) 23.6603 6.33975i 0.407935 0.109306i
\(59\) −17.1051 63.8372i −0.289917 1.08199i −0.945171 0.326577i \(-0.894105\pi\)
0.655253 0.755409i \(-0.272562\pi\)
\(60\) 4.39230 4.39230i 0.0732051 0.0732051i
\(61\) 3.65064 6.32309i 0.0598465 0.103657i −0.834550 0.550932i \(-0.814272\pi\)
0.894396 + 0.447275i \(0.147606\pi\)
\(62\) 38.3993 22.1699i 0.619344 0.357579i
\(63\) 27.9904 + 7.50000i 0.444292 + 0.119048i
\(64\) 8.00000i 0.125000i
\(65\) 6.03332 + 22.5167i 0.0928203 + 0.346410i
\(66\) −25.1769 −0.381468
\(67\) −10.1532 + 37.8923i −0.151540 + 0.565557i 0.847836 + 0.530258i \(0.177905\pi\)
−0.999377 + 0.0352988i \(0.988762\pi\)
\(68\) −18.9282 32.7846i −0.278356 0.482127i
\(69\) 6.21539 + 3.58846i 0.0900781 + 0.0520066i
\(70\) 17.3205 + 17.3205i 0.247436 + 0.247436i
\(71\) 103.890 27.8372i 1.46324 0.392073i 0.562630 0.826709i \(-0.309790\pi\)
0.900606 + 0.434636i \(0.143123\pi\)
\(72\) −2.19615 8.19615i −0.0305021 0.113835i
\(73\) −67.4186 + 67.4186i −0.923542 + 0.923542i −0.997278 0.0737356i \(-0.976508\pi\)
0.0737356 + 0.997278i \(0.476508\pi\)
\(74\) −26.1769 + 45.3397i −0.353742 + 0.612699i
\(75\) −32.6769 + 18.8660i −0.435692 + 0.251547i
\(76\) −63.9090 17.1244i −0.840907 0.225320i
\(77\) 99.2820i 1.28938i
\(78\) 30.7583 + 8.24167i 0.394338 + 0.105662i
\(79\) 11.8756 0.150325 0.0751623 0.997171i \(-0.476053\pi\)
0.0751623 + 0.997171i \(0.476053\pi\)
\(80\) 1.85641 6.92820i 0.0232051 0.0866025i
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 31.6077 + 18.2487i 0.385460 + 0.222545i
\(83\) 111.033 + 111.033i 1.33775 + 1.33775i 0.898235 + 0.439516i \(0.144850\pi\)
0.439516 + 0.898235i \(0.355150\pi\)
\(84\) 32.3205 8.66025i 0.384768 0.103098i
\(85\) −8.78461 32.7846i −0.103348 0.385701i
\(86\) −15.3397 + 15.3397i −0.178369 + 0.178369i
\(87\) 15.0000 25.9808i 0.172414 0.298629i
\(88\) −25.1769 + 14.5359i −0.286101 + 0.165181i
\(89\) 162.067 + 43.4256i 1.82097 + 0.487928i 0.996909 0.0785673i \(-0.0250346\pi\)
0.824065 + 0.566496i \(0.191701\pi\)
\(90\) 7.60770i 0.0845299i
\(91\) −32.5000 + 121.292i −0.357143 + 1.33288i
\(92\) 8.28719 0.0900781
\(93\) 14.0551 52.4545i 0.151130 0.564027i
\(94\) −7.01924 12.1577i −0.0746727 0.129337i
\(95\) −51.3731 29.6603i −0.540769 0.312213i
\(96\) −6.92820 6.92820i −0.0721688 0.0721688i
\(97\) 150.246 40.2583i 1.54893 0.415034i 0.619791 0.784767i \(-0.287217\pi\)
0.929138 + 0.369733i \(0.120551\pi\)
\(98\) 16.2154 + 60.5167i 0.165463 + 0.617517i
\(99\) −21.8038 + 21.8038i −0.220241 + 0.220241i
\(100\) −21.7846 + 37.7321i −0.217846 + 0.377321i
\(101\) −161.785 + 93.4064i −1.60183 + 0.924816i −0.610706 + 0.791857i \(0.709114\pi\)
−0.991122 + 0.132958i \(0.957552\pi\)
\(102\) −44.7846 12.0000i −0.439065 0.117647i
\(103\) 83.2628i 0.808377i 0.914676 + 0.404188i \(0.132446\pi\)
−0.914676 + 0.404188i \(0.867554\pi\)
\(104\) 35.5167 9.51666i 0.341506 0.0915064i
\(105\) 30.0000 0.285714
\(106\) −22.5744 + 84.2487i −0.212966 + 0.794799i
\(107\) −51.2487 88.7654i −0.478960 0.829583i 0.520749 0.853710i \(-0.325653\pi\)
−0.999709 + 0.0241269i \(0.992319\pi\)
\(108\) −9.00000 5.19615i −0.0833333 0.0481125i
\(109\) 48.1891 + 48.1891i 0.442102 + 0.442102i 0.892718 0.450616i \(-0.148796\pi\)
−0.450616 + 0.892718i \(0.648796\pi\)
\(110\) −25.1769 + 6.74613i −0.228881 + 0.0613285i
\(111\) 16.5955 + 61.9352i 0.149509 + 0.557975i
\(112\) 27.3205 27.3205i 0.243933 0.243933i
\(113\) 22.6077 39.1577i 0.200068 0.346528i −0.748482 0.663155i \(-0.769217\pi\)
0.948550 + 0.316627i \(0.102550\pi\)
\(114\) −70.1769 + 40.5167i −0.615587 + 0.355409i
\(115\) 7.17691 + 1.92305i 0.0624080 + 0.0167222i
\(116\) 34.6410i 0.298629i
\(117\) 33.7750 19.5000i 0.288675 0.166667i
\(118\) −93.4641 −0.792069
\(119\) 47.3205 176.603i 0.397651 1.48405i
\(120\) −4.39230 7.60770i −0.0366025 0.0633975i
\(121\) −13.2968 7.67691i −0.109891 0.0634456i
\(122\) −7.30127 7.30127i −0.0598465 0.0598465i
\(123\) 43.1769 11.5692i 0.351032 0.0940587i
\(124\) −16.2295 60.5692i −0.130883 0.488461i
\(125\) −59.3205 + 59.3205i −0.474564 + 0.474564i
\(126\) 20.4904 35.4904i 0.162622 0.281670i
\(127\) 205.115 118.423i 1.61508 0.932465i 0.626908 0.779093i \(-0.284320\pi\)
0.988169 0.153372i \(-0.0490132\pi\)
\(128\) −10.9282 2.92820i −0.0853766 0.0228766i
\(129\) 26.5692i 0.205963i
\(130\) 32.9667 0.253590
\(131\) −209.636 −1.60027 −0.800137 0.599817i \(-0.795240\pi\)
−0.800137 + 0.599817i \(0.795240\pi\)
\(132\) −9.21539 + 34.3923i −0.0698136 + 0.260548i
\(133\) −159.772 276.734i −1.20130 2.08071i
\(134\) 48.0455 + 27.7391i 0.358549 + 0.207008i
\(135\) −6.58846 6.58846i −0.0488034 0.0488034i
\(136\) −51.7128 + 13.8564i −0.380241 + 0.101885i
\(137\) 29.4782 + 110.014i 0.215169 + 0.803023i 0.986107 + 0.166112i \(0.0531213\pi\)
−0.770938 + 0.636911i \(0.780212\pi\)
\(138\) 7.17691 7.17691i 0.0520066 0.0520066i
\(139\) 47.8538 82.8853i 0.344272 0.596297i −0.640949 0.767583i \(-0.721459\pi\)
0.985221 + 0.171287i \(0.0547924\pi\)
\(140\) 30.0000 17.3205i 0.214286 0.123718i
\(141\) −16.6077 4.45002i −0.117785 0.0315604i
\(142\) 152.105i 1.07116i
\(143\) −94.4833 94.4833i −0.660723 0.660723i
\(144\) −12.0000 −0.0833333
\(145\) 8.03848 30.0000i 0.0554378 0.206897i
\(146\) 67.4186 + 116.772i 0.461771 + 0.799811i
\(147\) 66.4519 + 38.3660i 0.452054 + 0.260993i
\(148\) 52.3538 + 52.3538i 0.353742 + 0.353742i
\(149\) −54.9282 + 14.7180i −0.368646 + 0.0987783i −0.438386 0.898787i \(-0.644450\pi\)
0.0697402 + 0.997565i \(0.477783\pi\)
\(150\) 13.8109 + 51.5429i 0.0920726 + 0.343620i
\(151\) −55.0385 + 55.0385i −0.364493 + 0.364493i −0.865464 0.500971i \(-0.832976\pi\)
0.500971 + 0.865464i \(0.332976\pi\)
\(152\) −46.7846 + 81.0333i −0.307793 + 0.533114i
\(153\) −49.1769 + 28.3923i −0.321418 + 0.185571i
\(154\) −135.622 36.3397i −0.880661 0.235972i
\(155\) 56.2205i 0.362713i
\(156\) 22.5167 39.0000i 0.144338 0.250000i
\(157\) 55.4308 0.353062 0.176531 0.984295i \(-0.443512\pi\)
0.176531 + 0.984295i \(0.443512\pi\)
\(158\) 4.34679 16.2224i 0.0275113 0.102674i
\(159\) 53.4115 + 92.5115i 0.335922 + 0.581833i
\(160\) −8.78461 5.07180i −0.0549038 0.0316987i
\(161\) 28.3013 + 28.3013i 0.175784 + 0.175784i
\(162\) −12.2942 + 3.29423i −0.0758903 + 0.0203347i
\(163\) −52.9468 197.600i −0.324827 1.21227i −0.914486 0.404618i \(-0.867405\pi\)
0.589659 0.807652i \(-0.299262\pi\)
\(164\) 36.4974 36.4974i 0.222545 0.222545i
\(165\) −15.9615 + 27.6462i −0.0967365 + 0.167553i
\(166\) 192.315 111.033i 1.15853 0.668875i
\(167\) −156.315 41.8846i −0.936020 0.250806i −0.241600 0.970376i \(-0.577672\pi\)
−0.694420 + 0.719570i \(0.744339\pi\)
\(168\) 47.3205i 0.281670i
\(169\) 84.5000 + 146.358i 0.500000 + 0.866025i
\(170\) −48.0000 −0.282353
\(171\) −25.6865 + 95.8634i −0.150214 + 0.560605i
\(172\) 15.3397 + 26.5692i 0.0891846 + 0.154472i
\(173\) 232.492 + 134.229i 1.34389 + 0.775893i 0.987375 0.158398i \(-0.0506330\pi\)
0.356511 + 0.934291i \(0.383966\pi\)
\(174\) −30.0000 30.0000i −0.172414 0.172414i
\(175\) −203.253 + 54.4615i −1.16145 + 0.311209i
\(176\) 10.6410 + 39.7128i 0.0604603 + 0.225641i
\(177\) −80.9423 + 80.9423i −0.457301 + 0.457301i
\(178\) 118.641 205.492i 0.666523 1.15445i
\(179\) −247.492 + 142.890i −1.38264 + 0.798267i −0.992471 0.122477i \(-0.960916\pi\)
−0.390167 + 0.920744i \(0.627583\pi\)
\(180\) −10.3923 2.78461i −0.0577350 0.0154701i
\(181\) 177.646i 0.981471i 0.871309 + 0.490735i \(0.163272\pi\)
−0.871309 + 0.490735i \(0.836728\pi\)
\(182\) 153.792 + 88.7917i 0.845009 + 0.487866i
\(183\) −12.6462 −0.0691048
\(184\) 3.03332 11.3205i 0.0164854 0.0615245i
\(185\) 33.1910 + 57.4885i 0.179411 + 0.310749i
\(186\) −66.5096 38.3993i −0.357579 0.206448i
\(187\) 137.569 + 137.569i 0.735664 + 0.735664i
\(188\) −19.1769 + 5.13844i −0.102005 + 0.0273321i
\(189\) −12.9904 48.4808i −0.0687322 0.256512i
\(190\) −59.3205 + 59.3205i −0.312213 + 0.312213i
\(191\) −98.6603 + 170.885i −0.516546 + 0.894684i 0.483270 + 0.875472i \(0.339449\pi\)
−0.999815 + 0.0192120i \(0.993884\pi\)
\(192\) −12.0000 + 6.92820i −0.0625000 + 0.0360844i
\(193\) −20.2846 5.43524i −0.105102 0.0281619i 0.205885 0.978576i \(-0.433993\pi\)
−0.310987 + 0.950414i \(0.600659\pi\)
\(194\) 219.976i 1.13389i
\(195\) 28.5500 28.5500i 0.146410 0.146410i
\(196\) 88.6025 0.452054
\(197\) 39.1487 146.105i 0.198725 0.741650i −0.792547 0.609811i \(-0.791245\pi\)
0.991271 0.131839i \(-0.0420882\pi\)
\(198\) 21.8038 + 37.7654i 0.110120 + 0.190734i
\(199\) 19.2391 + 11.1077i 0.0966789 + 0.0558176i 0.547560 0.836766i \(-0.315557\pi\)
−0.450881 + 0.892584i \(0.648890\pi\)
\(200\) 43.5692 + 43.5692i 0.217846 + 0.217846i
\(201\) 65.6314 17.5859i 0.326524 0.0874919i
\(202\) 68.3782 + 255.191i 0.338506 + 1.26332i
\(203\) 118.301 118.301i 0.582765 0.582765i
\(204\) −32.7846 + 56.7846i −0.160709 + 0.278356i
\(205\) 40.0770 23.1384i 0.195497 0.112870i
\(206\) 113.739 + 30.4763i 0.552132 + 0.147943i
\(207\) 12.4308i 0.0600521i
\(208\) 52.0000i 0.250000i
\(209\) 340.028 1.62693
\(210\) 10.9808 40.9808i 0.0522893 0.195146i
\(211\) −32.1007 55.6000i −0.152136 0.263507i 0.779877 0.625933i \(-0.215282\pi\)
−0.932012 + 0.362426i \(0.881948\pi\)
\(212\) 106.823 + 61.6743i 0.503882 + 0.290917i
\(213\) −131.727 131.727i −0.618436 0.618436i
\(214\) −140.014 + 37.5167i −0.654271 + 0.175311i
\(215\) 7.11920 + 26.5692i 0.0331126 + 0.123578i
\(216\) −10.3923 + 10.3923i −0.0481125 + 0.0481125i
\(217\) 151.423 262.272i 0.697802 1.20863i
\(218\) 83.4660 48.1891i 0.382872 0.221051i
\(219\) 159.514 + 42.7417i 0.728375 + 0.195167i
\(220\) 36.8616i 0.167553i
\(221\) −123.033 213.100i −0.556712 0.964253i
\(222\) 90.6795 0.408466
\(223\) −56.5622 + 211.093i −0.253642 + 0.946605i 0.715199 + 0.698921i \(0.246336\pi\)
−0.968841 + 0.247684i \(0.920331\pi\)
\(224\) −27.3205 47.3205i −0.121967 0.211252i
\(225\) 56.5981 + 32.6769i 0.251547 + 0.145231i
\(226\) −45.2154 45.2154i −0.200068 0.200068i
\(227\) 62.4449 16.7321i 0.275088 0.0737095i −0.118638 0.992938i \(-0.537853\pi\)
0.393725 + 0.919228i \(0.371186\pi\)
\(228\) 29.6603 + 110.694i 0.130089 + 0.485498i
\(229\) 58.6846 58.6846i 0.256265 0.256265i −0.567268 0.823533i \(-0.692000\pi\)
0.823533 + 0.567268i \(0.192000\pi\)
\(230\) 5.25387 9.09996i 0.0228429 0.0395651i
\(231\) −148.923 + 85.9808i −0.644689 + 0.372211i
\(232\) −47.3205 12.6795i −0.203968 0.0546530i
\(233\) 380.669i 1.63377i 0.576798 + 0.816887i \(0.304302\pi\)
−0.576798 + 0.816887i \(0.695698\pi\)
\(234\) −14.2750 53.2750i −0.0610042 0.227671i
\(235\) −17.8001 −0.0757450
\(236\) −34.2102 + 127.674i −0.144959 + 0.540993i
\(237\) −10.2846 17.8135i −0.0433950 0.0751623i
\(238\) −223.923 129.282i −0.940853 0.543202i
\(239\) −167.138 167.138i −0.699324 0.699324i 0.264941 0.964265i \(-0.414648\pi\)
−0.964265 + 0.264941i \(0.914648\pi\)
\(240\) −12.0000 + 3.21539i −0.0500000 + 0.0133975i
\(241\) 0.796806 + 2.97372i 0.00330625 + 0.0123391i 0.967559 0.252644i \(-0.0813002\pi\)
−0.964253 + 0.264983i \(0.914634\pi\)
\(242\) −15.3538 + 15.3538i −0.0634456 + 0.0634456i
\(243\) −7.79423 + 13.5000i −0.0320750 + 0.0555556i
\(244\) −12.6462 + 7.30127i −0.0518286 + 0.0299232i
\(245\) 76.7321 + 20.5603i 0.313192 + 0.0839196i
\(246\) 63.2154i 0.256973i
\(247\) −415.408 111.308i −1.68181 0.450641i
\(248\) −88.6795 −0.357579
\(249\) 70.3923 262.708i 0.282700 1.05505i
\(250\) 59.3205 + 102.746i 0.237282 + 0.410985i
\(251\) −180.746 104.354i −0.720104 0.415752i 0.0946869 0.995507i \(-0.469815\pi\)
−0.814791 + 0.579755i \(0.803148\pi\)
\(252\) −40.9808 40.9808i −0.162622 0.162622i
\(253\) −41.1384 + 11.0230i −0.162603 + 0.0435692i
\(254\) −86.6917 323.538i −0.341306 1.27377i
\(255\) −41.5692 + 41.5692i −0.163017 + 0.163017i
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 64.2769 37.1103i 0.250105 0.144398i −0.369708 0.929148i \(-0.620542\pi\)
0.619812 + 0.784750i \(0.287209\pi\)
\(258\) 36.2942 + 9.72501i 0.140675 + 0.0376938i
\(259\) 357.583i 1.38063i
\(260\) 12.0666 45.0333i 0.0464102 0.173205i
\(261\) −51.9615 −0.199086
\(262\) −76.7321 + 286.368i −0.292870 + 1.09301i
\(263\) 12.1821 + 21.1000i 0.0463197 + 0.0802280i 0.888256 0.459349i \(-0.151917\pi\)
−0.841936 + 0.539577i \(0.818584\pi\)
\(264\) 43.6077 + 25.1769i 0.165181 + 0.0953671i
\(265\) 78.1999 + 78.1999i 0.295094 + 0.295094i
\(266\) −436.506 + 116.962i −1.64100 + 0.439705i
\(267\) −75.2154 280.708i −0.281706 1.05134i
\(268\) 55.4782 55.4782i 0.207008 0.207008i
\(269\) 87.8705 152.196i 0.326656 0.565785i −0.655190 0.755464i \(-0.727411\pi\)
0.981846 + 0.189679i \(0.0607448\pi\)
\(270\) −11.4115 + 6.58846i −0.0422650 + 0.0244017i
\(271\) 269.169 + 72.1237i 0.993244 + 0.266139i 0.718613 0.695411i \(-0.244777\pi\)
0.274632 + 0.961550i \(0.411444\pi\)
\(272\) 75.7128i 0.278356i
\(273\) 210.083 56.2917i 0.769536 0.206197i
\(274\) 161.072 0.587853
\(275\) 57.9526 216.282i 0.210737 0.786480i
\(276\) −7.17691 12.4308i −0.0260033 0.0450391i
\(277\) −387.100 223.492i −1.39747 0.806831i −0.403345 0.915048i \(-0.632153\pi\)
−0.994127 + 0.108216i \(0.965486\pi\)
\(278\) −95.7077 95.7077i −0.344272 0.344272i
\(279\) −90.8538 + 24.3442i −0.325641 + 0.0872552i
\(280\) −12.6795 47.3205i −0.0452839 0.169002i
\(281\) −5.54483 + 5.54483i −0.0197325 + 0.0197325i −0.716904 0.697172i \(-0.754442\pi\)
0.697172 + 0.716904i \(0.254442\pi\)
\(282\) −12.1577 + 21.0577i −0.0431123 + 0.0746727i
\(283\) 14.4160 8.32309i 0.0509400 0.0294102i −0.474314 0.880356i \(-0.657304\pi\)
0.525254 + 0.850946i \(0.323970\pi\)
\(284\) −207.779 55.6743i −0.731618 0.196036i
\(285\) 102.746i 0.360513i
\(286\) −163.650 + 94.4833i −0.572203 + 0.330361i
\(287\) 249.282 0.868579
\(288\) −4.39230 + 16.3923i −0.0152511 + 0.0569177i
\(289\) 34.6384 + 59.9955i 0.119856 + 0.207597i
\(290\) −38.0385 21.9615i −0.131167 0.0757294i
\(291\) −190.504 190.504i −0.654655 0.654655i
\(292\) 184.191 49.3538i 0.630791 0.169020i
\(293\) 48.4885 + 180.962i 0.165490 + 0.617616i 0.997977 + 0.0635723i \(0.0202493\pi\)
−0.832487 + 0.554044i \(0.813084\pi\)
\(294\) 76.7321 76.7321i 0.260993 0.260993i
\(295\) −59.2539 + 102.631i −0.200861 + 0.347901i
\(296\) 90.6795 52.3538i 0.306350 0.176871i
\(297\) 51.5885 + 13.8231i 0.173699 + 0.0465424i
\(298\) 80.4205i 0.269867i
\(299\) 53.8667 0.180156
\(300\) 75.4641 0.251547
\(301\) −38.3494 + 143.122i −0.127407 + 0.475488i
\(302\) 55.0385 + 95.3294i 0.182247 + 0.315660i
\(303\) 280.219 + 161.785i 0.924816 + 0.533943i
\(304\) 93.5692 + 93.5692i 0.307793 + 0.307793i
\(305\) −12.6462 + 3.38853i −0.0414629 + 0.0111099i
\(306\) 20.7846 + 77.5692i 0.0679236 + 0.253494i
\(307\) 375.069 375.069i 1.22172 1.22172i 0.254702 0.967020i \(-0.418023\pi\)
0.967020 0.254702i \(-0.0819774\pi\)
\(308\) −99.2820 + 171.962i −0.322344 + 0.558317i
\(309\) 124.894 72.1077i 0.404188 0.233358i
\(310\) −76.7987 20.5781i −0.247738 0.0663811i
\(311\) 296.238i 0.952535i −0.879300 0.476268i \(-0.841989\pi\)
0.879300 0.476268i \(-0.158011\pi\)
\(312\) −45.0333 45.0333i −0.144338 0.144338i
\(313\) 118.286 0.377910 0.188955 0.981986i \(-0.439490\pi\)
0.188955 + 0.981986i \(0.439490\pi\)
\(314\) 20.2891 75.7199i 0.0646149 0.241146i
\(315\) −25.9808 45.0000i −0.0824786 0.142857i
\(316\) −20.5692 11.8756i −0.0650925 0.0375812i
\(317\) −280.708 280.708i −0.885513 0.885513i 0.108575 0.994088i \(-0.465371\pi\)
−0.994088 + 0.108575i \(0.965371\pi\)
\(318\) 145.923 39.1000i 0.458878 0.122956i
\(319\) 46.0770 + 171.962i 0.144442 + 0.539064i
\(320\) −10.1436 + 10.1436i −0.0316987 + 0.0316987i
\(321\) −88.7654 + 153.746i −0.276528 + 0.478960i
\(322\) 49.0192 28.3013i 0.152234 0.0878921i
\(323\) 604.841 + 162.067i 1.87257 + 0.501754i
\(324\) 18.0000i 0.0555556i
\(325\) −141.600 + 245.258i −0.435692 + 0.754641i
\(326\) −289.306 −0.887443
\(327\) 30.5507 114.017i 0.0934271 0.348675i
\(328\) −36.4974 63.2154i −0.111273 0.192730i
\(329\) −83.0385 47.9423i −0.252397 0.145721i
\(330\) 31.9230 + 31.9230i 0.0967365 + 0.0967365i
\(331\) −137.454 + 36.8308i −0.415270 + 0.111271i −0.460404 0.887710i \(-0.652295\pi\)
0.0451334 + 0.998981i \(0.485629\pi\)
\(332\) −81.2820 303.349i −0.244825 0.913701i
\(333\) 78.5307 78.5307i 0.235828 0.235828i
\(334\) −114.431 + 198.200i −0.342607 + 0.593413i
\(335\) 60.9193 35.1718i 0.181849 0.104990i
\(336\) −64.6410 17.3205i −0.192384 0.0515491i
\(337\) 347.508i 1.03118i 0.856835 + 0.515590i \(0.172427\pi\)
−0.856835 + 0.515590i \(0.827573\pi\)
\(338\) 230.858 61.8583i 0.683013 0.183013i
\(339\) −78.3154 −0.231019
\(340\) −17.5692 + 65.5692i −0.0516742 + 0.192851i
\(341\) 161.130 + 279.084i 0.472521 + 0.818430i
\(342\) 121.550 + 70.1769i 0.355409 + 0.205196i
\(343\) −32.0929 32.0929i −0.0935654 0.0935654i
\(344\) 41.9090 11.2295i 0.121828 0.0326438i
\(345\) −3.33082 12.4308i −0.00965454 0.0360312i
\(346\) 268.459 268.459i 0.775893 0.775893i
\(347\) −218.851 + 379.061i −0.630695 + 1.09240i 0.356715 + 0.934213i \(0.383897\pi\)
−0.987410 + 0.158183i \(0.949436\pi\)
\(348\) −51.9615 + 30.0000i −0.149315 + 0.0862069i
\(349\) −432.889 115.992i −1.24037 0.332356i −0.421761 0.906707i \(-0.638588\pi\)
−0.818609 + 0.574351i \(0.805254\pi\)
\(350\) 297.583i 0.850238i
\(351\) −58.5000 33.7750i −0.166667 0.0962250i
\(352\) 58.1436 0.165181
\(353\) −151.914 + 566.951i −0.430352 + 1.60609i 0.321600 + 0.946876i \(0.395779\pi\)
−0.751951 + 0.659218i \(0.770887\pi\)
\(354\) 80.9423 + 140.196i 0.228651 + 0.396034i
\(355\) −167.023 96.4308i −0.470487 0.271636i
\(356\) −237.282 237.282i −0.666523 0.666523i
\(357\) −305.885 + 81.9615i −0.856820 + 0.229584i
\(358\) 104.603 + 390.382i 0.292186 + 1.09045i
\(359\) 64.2769 64.2769i 0.179044 0.179044i −0.611895 0.790939i \(-0.709592\pi\)
0.790939 + 0.611895i \(0.209592\pi\)
\(360\) −7.60770 + 13.1769i −0.0211325 + 0.0366025i
\(361\) 635.143 366.700i 1.75940 1.01579i
\(362\) 242.669 + 65.0230i 0.670357 + 0.179622i
\(363\) 26.5936i 0.0732606i
\(364\) 177.583 177.583i 0.487866 0.487866i
\(365\) 170.967 0.468402
\(366\) −4.62882 + 17.2750i −0.0126470 + 0.0471994i
\(367\) 108.892 + 188.607i 0.296709 + 0.513916i 0.975381 0.220526i \(-0.0707774\pi\)
−0.678672 + 0.734442i \(0.737444\pi\)
\(368\) −14.3538 8.28719i −0.0390050 0.0225195i
\(369\) −54.7461 54.7461i −0.148364 0.148364i
\(370\) 90.6795 24.2975i 0.245080 0.0656689i
\(371\) 154.186 + 575.429i 0.415595 + 1.55102i
\(372\) −76.7987 + 76.7987i −0.206448 + 0.206448i
\(373\) 109.803 190.185i 0.294378 0.509878i −0.680462 0.732784i \(-0.738221\pi\)
0.974840 + 0.222905i \(0.0715541\pi\)
\(374\) 238.277 137.569i 0.637104 0.367832i
\(375\) 140.354 + 37.6077i 0.374277 + 0.100287i
\(376\) 28.0770i 0.0746727i
\(377\) 225.167i 0.597259i
\(378\) −70.9808 −0.187780
\(379\) 50.1846 187.292i 0.132413 0.494173i −0.867582 0.497294i \(-0.834327\pi\)
0.999995 + 0.00312126i \(0.000993528\pi\)
\(380\) 59.3205 + 102.746i 0.156107 + 0.270385i
\(381\) −355.269 205.115i −0.932465 0.538359i
\(382\) 197.321 + 197.321i 0.516546 + 0.516546i
\(383\) 188.172 50.4205i 0.491310 0.131646i −0.00465401 0.999989i \(-0.501481\pi\)
0.495964 + 0.868343i \(0.334815\pi\)
\(384\) 5.07180 + 18.9282i 0.0132078 + 0.0492922i
\(385\) −125.885 + 125.885i −0.326973 + 0.326973i
\(386\) −14.8494 + 25.7199i −0.0384699 + 0.0666317i
\(387\) 39.8538 23.0096i 0.102981 0.0594564i
\(388\) −300.492 80.5167i −0.774465 0.207517i
\(389\) 17.7513i 0.0456331i −0.999740 0.0228166i \(-0.992737\pi\)
0.999740 0.0228166i \(-0.00726337\pi\)
\(390\) −28.5500 49.4500i −0.0732051 0.126795i
\(391\) −78.4308 −0.200590
\(392\) 32.4308 121.033i 0.0827316 0.308758i
\(393\) 181.550 + 314.454i 0.461959 + 0.800137i
\(394\) −185.254 106.956i −0.470187 0.271463i
\(395\) −15.0577 15.0577i −0.0381208 0.0381208i
\(396\) 59.5692 15.9615i 0.150427 0.0403069i
\(397\) −87.3494 325.992i −0.220024 0.821139i −0.984337 0.176295i \(-0.943589\pi\)
0.764314 0.644844i \(-0.223078\pi\)
\(398\) 22.2154 22.2154i 0.0558176 0.0558176i
\(399\) −276.734 + 479.317i −0.693569 + 1.20130i
\(400\) 75.4641 43.5692i 0.188660 0.108923i
\(401\) −496.435 133.019i −1.23799 0.331719i −0.420305 0.907383i \(-0.638077\pi\)
−0.817686 + 0.575664i \(0.804744\pi\)
\(402\) 96.0910i 0.239032i
\(403\) −105.492 393.700i −0.261766 0.976923i
\(404\) 373.626 0.924816
\(405\) −4.17691 + 15.5885i −0.0103134 + 0.0384900i
\(406\) −118.301 204.904i −0.291382 0.504689i
\(407\) −329.527 190.252i −0.809649 0.467451i
\(408\) 65.5692 + 65.5692i 0.160709 + 0.160709i
\(409\) −562.838 + 150.812i −1.37613 + 0.368734i −0.869715 0.493554i \(-0.835697\pi\)
−0.506418 + 0.862288i \(0.669031\pi\)
\(410\) −16.9385 63.2154i −0.0413134 0.154184i
\(411\) 139.492 139.492i 0.339397 0.339397i
\(412\) 83.2628 144.215i 0.202094 0.350037i
\(413\) −552.846 + 319.186i −1.33861 + 0.772847i
\(414\) −16.9808 4.54998i −0.0410163 0.0109903i
\(415\) 281.569i 0.678480i
\(416\) −71.0333 19.0333i −0.170753 0.0457532i
\(417\) −165.771 −0.397531
\(418\) 124.459 464.487i 0.297749 1.11121i
\(419\) 391.177 + 677.538i 0.933596 + 1.61704i 0.777118 + 0.629355i \(0.216681\pi\)
0.156479 + 0.987681i \(0.449986\pi\)
\(420\) −51.9615 30.0000i −0.123718 0.0714286i
\(421\) −27.0352 27.0352i −0.0642166 0.0642166i 0.674269 0.738486i \(-0.264459\pi\)
−0.738486 + 0.674269i \(0.764459\pi\)
\(422\) −87.7006 + 23.4993i −0.207821 + 0.0556856i
\(423\) 7.70766 + 28.7654i 0.0182214 + 0.0680032i
\(424\) 123.349 123.349i 0.290917 0.290917i
\(425\) 206.172 357.100i 0.485110 0.840235i
\(426\) −228.158 + 131.727i −0.535581 + 0.309218i
\(427\) −68.1218 18.2532i −0.159536 0.0427475i
\(428\) 204.995i 0.478960i
\(429\) −59.9000 + 223.550i −0.139627 + 0.521096i
\(430\) 38.9000 0.0904652
\(431\) 162.995 608.305i 0.378178 1.41138i −0.470467 0.882418i \(-0.655914\pi\)
0.848645 0.528963i \(-0.177419\pi\)
\(432\) 10.3923 + 18.0000i 0.0240563 + 0.0416667i
\(433\) −205.928 118.892i −0.475583 0.274578i 0.242991 0.970029i \(-0.421872\pi\)
−0.718574 + 0.695451i \(0.755205\pi\)
\(434\) −302.846 302.846i −0.697802 0.697802i
\(435\) −51.9615 + 13.9230i −0.119452 + 0.0320070i
\(436\) −35.2769 131.655i −0.0809103 0.301961i
\(437\) −96.9282 + 96.9282i −0.221804 + 0.221804i
\(438\) 116.772 202.256i 0.266604 0.461771i
\(439\) 597.092 344.731i 1.36012 0.785265i 0.370480 0.928841i \(-0.379193\pi\)
0.989639 + 0.143576i \(0.0458600\pi\)
\(440\) 50.3538 + 13.4923i 0.114441 + 0.0306642i
\(441\) 132.904i 0.301369i
\(442\) −336.133 + 90.0666i −0.760483 + 0.203771i
\(443\) −304.028 −0.686294 −0.343147 0.939282i \(-0.611493\pi\)
−0.343147 + 0.939282i \(0.611493\pi\)
\(444\) 33.1910 123.870i 0.0747545 0.278988i
\(445\) −150.431 260.554i −0.338047 0.585514i
\(446\) 267.655 + 154.531i 0.600124 + 0.346481i
\(447\) 69.6462 + 69.6462i 0.155808 + 0.155808i
\(448\) −74.6410 + 20.0000i −0.166609 + 0.0446429i
\(449\) −73.4589 274.153i −0.163606 0.610585i −0.998214 0.0597407i \(-0.980973\pi\)
0.834608 0.550844i \(-0.185694\pi\)
\(450\) 65.3538 65.3538i 0.145231 0.145231i
\(451\) −132.631 + 229.723i −0.294081 + 0.509364i
\(452\) −78.3154 + 45.2154i −0.173264 + 0.100034i
\(453\) 130.222 + 34.8930i 0.287467 + 0.0770265i
\(454\) 91.4256i 0.201378i
\(455\) 195.000 112.583i 0.428571 0.247436i
\(456\) 162.067 0.355409
\(457\) −37.1584 + 138.677i −0.0813093 + 0.303451i −0.994590 0.103881i \(-0.966874\pi\)
0.913280 + 0.407331i \(0.133541\pi\)
\(458\) −58.6846 101.645i −0.128132 0.221932i
\(459\) 85.1769 + 49.1769i 0.185571 + 0.107139i
\(460\) −10.5077 10.5077i −0.0228429 0.0228429i
\(461\) 568.435 152.312i 1.23305 0.330394i 0.417282 0.908777i \(-0.362983\pi\)
0.815765 + 0.578383i \(0.196316\pi\)
\(462\) 62.9423 + 234.904i 0.136239 + 0.508450i
\(463\) −169.599 + 169.599i −0.366305 + 0.366305i −0.866128 0.499823i \(-0.833399\pi\)
0.499823 + 0.866128i \(0.333399\pi\)
\(464\) −34.6410 + 60.0000i −0.0746574 + 0.129310i
\(465\) −84.3308 + 48.6884i −0.181357 + 0.104706i
\(466\) 520.004 + 139.335i 1.11589 + 0.299001i
\(467\) 732.649i 1.56884i 0.620230 + 0.784420i \(0.287039\pi\)
−0.620230 + 0.784420i \(0.712961\pi\)
\(468\) −78.0000 −0.166667
\(469\) 378.923 0.807938
\(470\) −6.51528 + 24.3154i −0.0138623 + 0.0517348i
\(471\) −48.0045 83.1462i −0.101920 0.176531i
\(472\) 161.885 + 93.4641i 0.342976 + 0.198017i
\(473\) −111.488 111.488i −0.235705 0.235705i
\(474\) −28.0981 + 7.52886i −0.0592786 + 0.0158837i
\(475\) −186.524 696.116i −0.392681 1.46551i
\(476\) −258.564 + 258.564i −0.543202 + 0.543202i
\(477\) 92.5115 160.235i 0.193944 0.335922i
\(478\) −289.492 + 167.138i −0.605632 + 0.349662i
\(479\) −357.167 95.7025i −0.745651 0.199796i −0.134063 0.990973i \(-0.542802\pi\)
−0.611588 + 0.791176i \(0.709469\pi\)
\(480\) 17.5692i 0.0366025i
\(481\) 340.300 + 340.300i 0.707484 + 0.707484i
\(482\) 4.35383 0.00903284
\(483\) 17.9423 66.9615i 0.0371476 0.138637i
\(484\) 15.3538 + 26.5936i 0.0317228 + 0.0549455i
\(485\) −241.550 139.459i −0.498041 0.287544i
\(486\) 15.5885 + 15.5885i 0.0320750 + 0.0320750i
\(487\) 187.145 50.1455i 0.384282 0.102968i −0.0615056 0.998107i \(-0.519590\pi\)
0.445788 + 0.895139i \(0.352924\pi\)
\(488\) 5.34490 + 19.9474i 0.0109527 + 0.0408759i
\(489\) −250.547 + 250.547i −0.512365 + 0.512365i
\(490\) 56.1718 97.2923i 0.114636 0.198556i
\(491\) −31.9808 + 18.4641i −0.0651339 + 0.0376051i −0.532213 0.846610i \(-0.678640\pi\)
0.467079 + 0.884215i \(0.345306\pi\)
\(492\) −86.3538 23.1384i −0.175516 0.0470293i
\(493\) 327.846i 0.665002i
\(494\) −304.100 + 526.717i −0.615587 + 1.06623i
\(495\) 55.2923 0.111702
\(496\) −32.4589 + 121.138i −0.0654414 + 0.244231i
\(497\) −519.449 899.711i −1.04517 1.81028i
\(498\) −333.100 192.315i −0.668875 0.386175i
\(499\) 462.769 + 462.769i 0.927393 + 0.927393i 0.997537 0.0701438i \(-0.0223458\pi\)
−0.0701438 + 0.997537i \(0.522346\pi\)
\(500\) 162.067 43.4256i 0.324133 0.0868513i
\(501\) 72.5462 + 270.746i 0.144803 + 0.540411i
\(502\) −208.708 + 208.708i −0.415752 + 0.415752i
\(503\) 179.378 310.692i 0.356617 0.617678i −0.630777 0.775965i \(-0.717264\pi\)
0.987393 + 0.158286i \(0.0505969\pi\)
\(504\) −70.9808 + 40.9808i −0.140835 + 0.0813110i
\(505\) 323.569 + 86.7001i 0.640731 + 0.171683i
\(506\) 60.2309i 0.119033i
\(507\) 146.358 253.500i 0.288675 0.500000i
\(508\) −473.692 −0.932465
\(509\) −190.972 + 712.717i −0.375190 + 1.40023i 0.477876 + 0.878427i \(0.341407\pi\)
−0.853067 + 0.521802i \(0.825260\pi\)
\(510\) 41.5692 + 72.0000i 0.0815083 + 0.141176i
\(511\) 797.570 + 460.477i 1.56080 + 0.901130i
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 166.040 44.4904i 0.323665 0.0867259i
\(514\) −27.1666 101.387i −0.0528533 0.197251i
\(515\) 105.573 105.573i 0.204996 0.204996i
\(516\) 26.5692 46.0192i 0.0514907 0.0891846i
\(517\) 88.3614 51.0155i 0.170912 0.0986759i
\(518\) 488.468 + 130.885i 0.942988 + 0.252673i
\(519\) 464.985i 0.895924i
\(520\) −57.1000 32.9667i −0.109808 0.0633975i
\(521\) 156.049 0.299518 0.149759 0.988723i \(-0.452150\pi\)
0.149759 + 0.988723i \(0.452150\pi\)
\(522\) −19.0192 + 70.9808i −0.0364353 + 0.135978i
\(523\) −20.9615 36.3064i −0.0400794 0.0694196i 0.845290 0.534308i \(-0.179428\pi\)
−0.885369 + 0.464888i \(0.846094\pi\)
\(524\) 363.100 + 209.636i 0.692939 + 0.400068i
\(525\) 257.715 + 257.715i 0.490885 + 0.490885i
\(526\) 33.2820 8.91789i 0.0632738 0.0169542i
\(527\) 153.597 + 573.233i 0.291456 + 1.08773i
\(528\) 50.3538 50.3538i 0.0953671 0.0953671i
\(529\) −255.915 + 443.258i −0.483772 + 0.837917i
\(530\) 135.446 78.1999i 0.255559 0.147547i
\(531\) 191.512 + 51.3154i 0.360662 + 0.0966391i
\(532\) 639.090i 1.20130i
\(533\) 237.233 237.233i 0.445091 0.445091i
\(534\) −410.985 −0.769634
\(535\) −47.5692 + 177.531i −0.0889144 + 0.331833i
\(536\) −55.4782 96.0910i −0.103504 0.179274i
\(537\) 428.669 + 247.492i 0.798267 + 0.460879i
\(538\) −175.741 175.741i −0.326656 0.326656i
\(539\) −439.832 + 117.853i −0.816015 + 0.218651i
\(540\) 4.82309 + 18.0000i 0.00893164 + 0.0333333i
\(541\) −4.44298 + 4.44298i −0.00821253 + 0.00821253i −0.711201 0.702989i \(-0.751848\pi\)
0.702989 + 0.711201i \(0.251848\pi\)
\(542\) 197.046 341.293i 0.363553 0.629692i
\(543\) 266.469 153.846i 0.490735 0.283326i
\(544\) 103.426 + 27.7128i 0.190121 + 0.0509427i
\(545\) 122.203i 0.224225i
\(546\) 307.583i 0.563339i
\(547\) −101.508 −0.185572 −0.0927859 0.995686i \(-0.529577\pi\)
−0.0927859 + 0.995686i \(0.529577\pi\)
\(548\) 58.9564 220.028i 0.107585 0.401511i
\(549\) 10.9519 + 18.9693i 0.0199488 + 0.0345524i
\(550\) −274.235 158.329i −0.498608 0.287872i
\(551\) 405.167 + 405.167i 0.735330 + 0.735330i
\(552\) −19.6077 + 5.25387i −0.0355212 + 0.00951787i
\(553\) −29.6891 110.801i −0.0536874 0.200364i
\(554\) −446.985 + 446.985i −0.806831 + 0.806831i
\(555\) 57.4885 99.5730i 0.103583 0.179411i
\(556\) −165.771 + 95.7077i −0.298148 + 0.172136i
\(557\) −636.358 170.512i −1.14247 0.306125i −0.362528 0.931973i \(-0.618086\pi\)
−0.779945 + 0.625848i \(0.784753\pi\)
\(558\) 133.019i 0.238386i
\(559\) 99.7083 + 172.700i 0.178369 + 0.308944i
\(560\) −69.2820 −0.123718
\(561\) 87.2154 325.492i 0.155464 0.580200i
\(562\) 5.54483 + 9.60392i 0.00986624 + 0.0170888i
\(563\) 76.8385 + 44.3628i 0.136481 + 0.0787971i 0.566686 0.823934i \(-0.308225\pi\)
−0.430205 + 0.902731i \(0.641559\pi\)
\(564\) 24.3154 + 24.3154i 0.0431123 + 0.0431123i
\(565\) −78.3154 + 20.9845i −0.138611 + 0.0371408i
\(566\) −6.09292 22.7391i −0.0107649 0.0401751i
\(567\) −61.4711 + 61.4711i −0.108415 + 0.108415i
\(568\) −152.105 + 263.454i −0.267791 + 0.463827i
\(569\) −373.750 + 215.785i −0.656854 + 0.379235i −0.791077 0.611716i \(-0.790479\pi\)
0.134223 + 0.990951i \(0.457146\pi\)
\(570\) 140.354 + 37.6077i 0.246235 + 0.0659784i
\(571\) 959.892i 1.68107i −0.541756 0.840536i \(-0.682240\pi\)
0.541756 0.840536i \(-0.317760\pi\)
\(572\) 69.1666 + 258.133i 0.120921 + 0.451282i
\(573\) 341.769 0.596456
\(574\) 91.2436 340.526i 0.158961 0.593250i
\(575\) 45.1333 + 78.1731i 0.0784927 + 0.135953i
\(576\) 20.7846 + 12.0000i 0.0360844 + 0.0208333i
\(577\) −313.669 313.669i −0.543621 0.543621i 0.380968 0.924588i \(-0.375591\pi\)
−0.924588 + 0.380968i \(0.875591\pi\)
\(578\) 94.6340 25.3571i 0.163727 0.0438704i
\(579\) 9.41412 + 35.1340i 0.0162593 + 0.0606804i
\(580\) −43.9230 + 43.9230i −0.0757294 + 0.0757294i
\(581\) 758.372 1313.54i 1.30529 2.26082i
\(582\) −329.963 + 190.504i −0.566947 + 0.327327i
\(583\) −612.315 164.069i −1.05028 0.281423i
\(584\) 269.674i 0.461771i
\(585\) −67.5500 18.1000i −0.115470 0.0309401i
\(586\) 264.946 0.452126
\(587\) −58.5654 + 218.569i −0.0997708 + 0.372350i −0.997700 0.0677912i \(-0.978405\pi\)
0.897929 + 0.440141i \(0.145071\pi\)
\(588\) −76.7321 132.904i −0.130497 0.226027i
\(589\) 898.249 + 518.604i 1.52504 + 0.880483i
\(590\) 118.508 + 118.508i 0.200861 + 0.200861i
\(591\) −253.061 + 67.8076i −0.428192 + 0.114734i
\(592\) −38.3257 143.033i −0.0647393 0.241610i
\(593\) 335.229 335.229i 0.565311 0.565311i −0.365500 0.930811i \(-0.619102\pi\)
0.930811 + 0.365500i \(0.119102\pi\)
\(594\) 37.7654 65.4115i 0.0635781 0.110120i
\(595\) −283.923 + 163.923i −0.477182 + 0.275501i
\(596\) 109.856 + 29.4359i 0.184323 + 0.0493892i
\(597\) 38.4782i 0.0644526i
\(598\) 19.7166 73.5833i 0.0329709 0.123049i
\(599\) 136.908 0.228560 0.114280 0.993449i \(-0.463544\pi\)
0.114280 + 0.993449i \(0.463544\pi\)
\(600\) 27.6218 103.086i 0.0460363 0.171810i
\(601\) 8.78461 + 15.2154i 0.0146167 + 0.0253168i 0.873241 0.487288i \(-0.162014\pi\)
−0.858625 + 0.512605i \(0.828681\pi\)
\(602\) 181.471 + 104.772i 0.301447 + 0.174041i
\(603\) −83.2173 83.2173i −0.138005 0.138005i
\(604\) 150.368 40.2910i 0.248953 0.0667069i
\(605\) 7.12574 + 26.5936i 0.0117781 + 0.0439564i
\(606\) 323.569 323.569i 0.533943 0.533943i
\(607\) −422.300 + 731.445i −0.695716 + 1.20502i 0.274222 + 0.961666i \(0.411580\pi\)
−0.969939 + 0.243350i \(0.921754\pi\)
\(608\) 162.067 93.5692i 0.266557 0.153897i
\(609\) −279.904 75.0000i −0.459612 0.123153i
\(610\) 18.5153i 0.0303529i
\(611\) −124.650 + 33.3999i −0.204010 + 0.0546642i
\(612\) 113.569 0.185571
\(613\) −163.158 + 608.915i −0.266164 + 0.993337i 0.695370 + 0.718651i \(0.255240\pi\)
−0.961534 + 0.274685i \(0.911426\pi\)
\(614\) −375.069 649.638i −0.610861 1.05804i
\(615\) −69.4153 40.0770i −0.112870 0.0651658i
\(616\) 198.564 + 198.564i 0.322344 + 0.322344i
\(617\) 107.014 28.6743i 0.173443 0.0464738i −0.171053 0.985262i \(-0.554717\pi\)
0.344495 + 0.938788i \(0.388050\pi\)
\(618\) −52.7865 197.002i −0.0854150 0.318773i
\(619\) −111.970 + 111.970i −0.180888 + 0.180888i −0.791743 0.610854i \(-0.790826\pi\)
0.610854 + 0.791743i \(0.290826\pi\)
\(620\) −56.2205 + 97.3768i −0.0906783 + 0.157059i
\(621\) −18.6462 + 10.7654i −0.0300260 + 0.0173355i
\(622\) −404.669 108.431i −0.650594 0.174326i
\(623\) 1620.67i 2.60139i
\(624\) −78.0000 + 45.0333i −0.125000 + 0.0721688i
\(625\) −394.184 −0.630695
\(626\) 43.2956 161.581i 0.0691623 0.258117i
\(627\) −294.473 510.042i −0.469654 0.813465i
\(628\) −96.0089 55.4308i −0.152880 0.0882656i
\(629\) −495.482 495.482i −0.787730 0.787730i
\(630\) −70.9808 + 19.0192i −0.112668 + 0.0301893i
\(631\) 283.101 + 1056.55i 0.448654 + 1.67440i 0.706104 + 0.708108i \(0.250451\pi\)
−0.257450 + 0.966292i \(0.582882\pi\)
\(632\) −23.7513 + 23.7513i −0.0375812 + 0.0375812i
\(633\) −55.6000 + 96.3020i −0.0878356 + 0.152136i
\(634\) −486.200 + 280.708i −0.766877 + 0.442757i
\(635\) −410.229 109.921i −0.646031 0.173103i
\(636\) 213.646i 0.335922i
\(637\) 575.917 0.904108
\(638\) 251.769 0.394622
\(639\) −83.5115 + 311.669i −0.130691 + 0.487745i
\(640\) 10.1436 + 17.5692i 0.0158494 + 0.0274519i
\(641\) −353.869 204.306i −0.552058 0.318731i 0.197894 0.980223i \(-0.436590\pi\)
−0.749952 + 0.661493i \(0.769923\pi\)
\(642\) 177.531 + 177.531i 0.276528 + 0.276528i
\(643\) −432.661 + 115.931i −0.672879 + 0.180297i −0.579052 0.815291i \(-0.696577\pi\)
−0.0938279 + 0.995588i \(0.529910\pi\)
\(644\) −20.7180 77.3205i −0.0321708 0.120063i
\(645\) 33.6884 33.6884i 0.0522301 0.0522301i
\(646\) 442.774 766.908i 0.685409 1.18716i
\(647\) −279.588 + 161.420i −0.432131 + 0.249491i −0.700254 0.713894i \(-0.746930\pi\)
0.268123 + 0.963385i \(0.413597\pi\)
\(648\) 24.5885 + 6.58846i 0.0379452 + 0.0101674i
\(649\) 679.292i 1.04668i
\(650\) 283.200 + 283.200i 0.435692 + 0.435692i
\(651\) −524.545 −0.805752
\(652\) −105.894 + 395.200i −0.162413 + 0.606135i
\(653\) 510.424 + 884.081i 0.781660 + 1.35388i 0.930974 + 0.365086i \(0.118960\pi\)
−0.149314 + 0.988790i \(0.547706\pi\)
\(654\) −144.567 83.4660i −0.221051 0.127624i
\(655\) 265.808 + 265.808i 0.405813 + 0.405813i
\(656\) −99.7128 + 26.7180i −0.152001 + 0.0407286i
\(657\) −74.0307 276.286i −0.112680 0.420527i
\(658\) −95.8846 + 95.8846i −0.145721 + 0.145721i
\(659\) −113.842 + 197.181i −0.172750 + 0.299212i −0.939380 0.342877i \(-0.888599\pi\)
0.766630 + 0.642089i \(0.221932\pi\)
\(660\) 55.2923 31.9230i 0.0837763 0.0483683i
\(661\) 146.181 + 39.1692i 0.221152 + 0.0592575i 0.367693 0.929947i \(-0.380148\pi\)
−0.146542 + 0.989205i \(0.546814\pi\)
\(662\) 201.247i 0.303999i
\(663\) −213.100 + 369.100i −0.321418 + 0.556712i
\(664\) −444.133 −0.668875
\(665\) −148.301 + 553.468i −0.223009 + 0.832283i
\(666\) −78.5307 136.019i −0.117914 0.204233i
\(667\) −62.1539 35.8846i −0.0931843 0.0538000i
\(668\) 228.862 + 228.862i 0.342607 + 0.342607i
\(669\) 365.624 97.9686i 0.546523 0.146440i
\(670\) −25.7475 96.0910i −0.0384291 0.143419i
\(671\) 53.0653 53.0653i 0.0790838 0.0790838i
\(672\) −47.3205 + 81.9615i −0.0704174 + 0.121967i
\(673\) −613.138 + 353.996i −0.911052 + 0.525996i −0.880770 0.473545i \(-0.842974\pi\)
−0.0302828 + 0.999541i \(0.509641\pi\)
\(674\) 474.704 + 127.197i 0.704309 + 0.188719i
\(675\) 113.196i 0.167698i
\(676\) 338.000i 0.500000i
\(677\) −754.592 −1.11461 −0.557306 0.830307i \(-0.688165\pi\)
−0.557306 + 0.830307i \(0.688165\pi\)
\(678\) −28.6654 + 106.981i −0.0422794 + 0.157789i
\(679\) −751.231 1301.17i −1.10638 1.91630i
\(680\) 83.1384 + 48.0000i 0.122262 + 0.0705882i
\(681\) −79.1769 79.1769i −0.116266 0.116266i
\(682\) 440.214 117.955i 0.645475 0.172955i
\(683\) −37.2168 138.895i −0.0544901 0.203360i 0.933314 0.359061i \(-0.116903\pi\)
−0.987804 + 0.155701i \(0.950236\pi\)
\(684\) 140.354 140.354i 0.205196 0.205196i
\(685\) 102.115 176.869i 0.149074 0.258203i
\(686\) −55.5866 + 32.0929i −0.0810300 + 0.0467827i
\(687\) −138.849 37.2046i −0.202110 0.0541551i
\(688\) 61.3590i 0.0891846i
\(689\) 694.350 + 400.883i 1.00776 + 0.581833i
\(690\) −18.1999 −0.0263767
\(691\) 140.931 525.961i 0.203952 0.761159i −0.785815 0.618462i \(-0.787756\pi\)
0.989766 0.142697i \(-0.0455774\pi\)
\(692\) −268.459 464.985i −0.387946 0.671943i
\(693\) 257.942 + 148.923i 0.372211 + 0.214896i
\(694\) 437.703 + 437.703i 0.630695 + 0.630695i
\(695\) −165.771 + 44.4181i −0.238519 + 0.0639109i
\(696\) 21.9615 + 81.9615i 0.0315539 + 0.117761i
\(697\) −345.415 + 345.415i −0.495574 + 0.495574i
\(698\) −316.897 + 548.881i −0.454007 + 0.786363i
\(699\) 571.004 329.669i 0.816887 0.471630i
\(700\) 406.506 + 108.923i 0.580723 + 0.155604i
\(701\) 568.344i 0.810761i −0.914148 0.405381i \(-0.867139\pi\)
0.914148 0.405381i \(-0.132861\pi\)
\(702\) −67.5500 + 67.5500i −0.0962250 + 0.0962250i
\(703\) −1224.68 −1.74207
\(704\) 21.2820 79.4256i 0.0302302 0.112820i
\(705\) 15.4153 + 26.7001i 0.0218657 + 0.0378725i
\(706\) 718.865 + 415.037i 1.01822 + 0.587871i
\(707\) 1275.95 + 1275.95i 1.80475 + 1.80475i
\(708\) 221.138 59.2539i 0.312342 0.0836919i
\(709\) 94.9538 + 354.372i 0.133926 + 0.499820i 1.00000 9.64632e-5i \(-3.07052e-5\pi\)
−0.866074 + 0.499916i \(0.833364\pi\)
\(710\) −192.862 + 192.862i −0.271636 + 0.271636i
\(711\) −17.8135 + 30.8538i −0.0250541 + 0.0433950i
\(712\) −410.985 + 237.282i −0.577225 + 0.333261i
\(713\) −125.487 33.6242i −0.175999 0.0471587i
\(714\) 447.846i 0.627235i
\(715\) 239.600i 0.335105i
\(716\) 571.559 0.798267
\(717\) −105.962 + 395.454i −0.147785 + 0.551539i
\(718\) −64.2769 111.331i −0.0895221 0.155057i
\(719\) 228.215 + 131.760i 0.317407 + 0.183255i 0.650236 0.759732i \(-0.274670\pi\)
−0.332829 + 0.942987i \(0.608003\pi\)
\(720\) 15.2154 + 15.2154i 0.0211325 + 0.0211325i
\(721\) 776.852 208.157i 1.07747 0.288706i
\(722\) −268.443 1001.84i −0.371805 1.38759i
\(723\) 3.77053 3.77053i 0.00521511 0.00521511i
\(724\) 177.646 307.692i 0.245368 0.424989i
\(725\) 326.769 188.660i 0.450716 0.260221i
\(726\) 36.3275 + 9.73394i 0.0500379 + 0.0134076i
\(727\) 878.415i 1.20827i −0.796880 0.604137i \(-0.793518\pi\)
0.796880 0.604137i \(-0.206482\pi\)
\(728\) −177.583 307.583i −0.243933 0.422505i
\(729\) 27.0000 0.0370370
\(730\) 62.5781 233.545i 0.0857235 0.319924i
\(731\) −145.177 251.454i −0.198600 0.343986i
\(732\) 21.9038 + 12.6462i 0.0299232 + 0.0172762i
\(733\) −146.627 146.627i −0.200037 0.200037i 0.599979 0.800016i \(-0.295176\pi\)
−0.800016 + 0.599979i \(0.795176\pi\)
\(734\) 297.499 79.7147i 0.405312 0.108603i
\(735\) −35.6115 132.904i −0.0484510 0.180822i
\(736\) −16.5744 + 16.5744i −0.0225195 + 0.0225195i
\(737\) −201.606 + 349.192i −0.273550 + 0.473802i
\(738\) −94.8231 + 54.7461i −0.128487 + 0.0741818i
\(739\) 621.762 + 166.601i 0.841356 + 0.225441i 0.653662 0.756787i \(-0.273232\pi\)
0.187694 + 0.982227i \(0.439899\pi\)
\(740\) 132.764i 0.179411i
\(741\) 192.792 + 719.508i 0.260178 + 0.970996i
\(742\) 842.487 1.13543
\(743\) −3.52835 + 13.1680i −0.00474879 + 0.0177227i −0.968260 0.249947i \(-0.919587\pi\)
0.963511 + 0.267670i \(0.0862535\pi\)
\(744\) 76.7987 + 133.019i 0.103224 + 0.178789i
\(745\) 88.3078 + 50.9845i 0.118534 + 0.0684356i
\(746\) −219.606 219.606i −0.294378 0.294378i
\(747\) −455.023 + 121.923i −0.609134 + 0.163217i
\(748\) −100.708 375.846i −0.134636 0.502468i
\(749\) −700.070 + 700.070i −0.934673 + 0.934673i
\(750\) 102.746 177.962i 0.136995 0.237282i
\(751\) −138.631 + 80.0385i −0.184595 + 0.106576i −0.589450 0.807805i \(-0.700655\pi\)
0.404855 + 0.914381i \(0.367322\pi\)
\(752\) 38.3538 + 10.2769i 0.0510024 + 0.0136661i
\(753\) 361.492i 0.480069i
\(754\) −307.583 82.4167i −0.407935 0.109306i
\(755\) 139.572 0.184864
\(756\) −25.9808 + 96.9615i −0.0343661 + 0.128256i
\(757\) 733.692 + 1270.79i 0.969210 + 1.67872i 0.697850 + 0.716244i \(0.254140\pi\)
0.271360 + 0.962478i \(0.412527\pi\)
\(758\) −237.476 137.107i −0.313293 0.180880i
\(759\) 52.1615 + 52.1615i 0.0687239 + 0.0687239i
\(760\) 162.067 43.4256i 0.213246 0.0571390i
\(761\) 47.3514 + 176.718i 0.0622227 + 0.232218i 0.990033 0.140833i \(-0.0449782\pi\)
−0.927811 + 0.373051i \(0.878312\pi\)
\(762\) −410.229 + 410.229i −0.538359 + 0.538359i
\(763\) 329.138 570.083i 0.431373 0.747160i
\(764\) 341.769 197.321i 0.447342 0.258273i
\(765\) 98.3538 + 26.3538i 0.128567 + 0.0344494i
\(766\) 275.503i 0.359664i
\(767\) −222.367 + 829.883i −0.289917 + 1.08199i
\(768\) 27.7128 0.0360844
\(769\) 351.866 1313.18i