Properties

Label 370.2.b.d.149.5
Level $370$
Weight $2$
Character 370.149
Analytic conductor $2.954$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - 2 x^{9} + 2 x^{8} - 4 x^{7} + 51 x^{6} - 124 x^{5} + 154 x^{4} - 46 x^{3} + x^{2} + 4 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 149.5
Root \(-0.282359 + 0.282359i\) of defining polynomial
Character \(\chi\) \(=\) 370.149
Dual form 370.2.b.d.149.6

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +2.62545i q^{3} -1.00000 q^{4} +(1.70518 - 1.44650i) q^{5} +2.62545 q^{6} +1.83227i q^{7} +1.00000i q^{8} -3.89300 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +2.62545i q^{3} -1.00000 q^{4} +(1.70518 - 1.44650i) q^{5} +2.62545 q^{6} +1.83227i q^{7} +1.00000i q^{8} -3.89300 q^{9} +(-1.44650 - 1.70518i) q^{10} +4.19017 q^{11} -2.62545i q^{12} -0.369454i q^{13} +1.83227 q^{14} +(3.79772 + 4.47687i) q^{15} +1.00000 q^{16} +5.08317i q^{17} +3.89300i q^{18} -3.55963 q^{19} +(-1.70518 + 1.44650i) q^{20} -4.81053 q^{21} -4.19017i q^{22} +5.62036i q^{23} -2.62545 q^{24} +(0.815273 - 4.93309i) q^{25} -0.369454 q^{26} -2.34453i q^{27} -1.83227i q^{28} -1.20681 q^{29} +(4.47687 - 3.79772i) q^{30} +10.1030 q^{31} -1.00000i q^{32} +11.0011i q^{33} +5.08317 q^{34} +(2.65038 + 3.12434i) q^{35} +3.89300 q^{36} -1.00000i q^{37} +3.55963i q^{38} +0.969984 q^{39} +(1.44650 + 1.70518i) q^{40} -8.01447 q^{41} +4.81053i q^{42} -2.27264i q^{43} -4.19017 q^{44} +(-6.63826 + 5.63123i) q^{45} +5.62036 q^{46} -10.9154i q^{47} +2.62545i q^{48} +3.64280 q^{49} +(-4.93309 - 0.815273i) q^{50} -13.3456 q^{51} +0.369454i q^{52} -9.94355i q^{53} -2.34453 q^{54} +(7.14499 - 6.06108i) q^{55} -1.83227 q^{56} -9.34563i q^{57} +1.20681i q^{58} +5.34563 q^{59} +(-3.79772 - 4.47687i) q^{60} -9.79428 q^{61} -10.1030i q^{62} -7.13302i q^{63} -1.00000 q^{64} +(-0.534415 - 0.629985i) q^{65} +11.0011 q^{66} -1.85073i q^{67} -5.08317i q^{68} -14.7560 q^{69} +(3.12434 - 2.65038i) q^{70} +2.86038 q^{71} -3.89300i q^{72} -8.09942i q^{73} -1.00000 q^{74} +(12.9516 + 2.14046i) q^{75} +3.55963 q^{76} +7.67751i q^{77} -0.969984i q^{78} -6.06361 q^{79} +(1.70518 - 1.44650i) q^{80} -5.52355 q^{81} +8.01447i q^{82} -8.93200i q^{83} +4.81053 q^{84} +(7.35281 + 8.66772i) q^{85} -2.27264 q^{86} -3.16843i q^{87} +4.19017i q^{88} -11.4773 q^{89} +(5.63123 + 6.63826i) q^{90} +0.676938 q^{91} -5.62036i q^{92} +26.5249i q^{93} -10.9154 q^{94} +(-6.06980 + 5.14900i) q^{95} +2.62545 q^{96} -6.05864i q^{97} -3.64280i q^{98} -16.3123 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 10 q^{4} + 6 q^{5} - 6 q^{9} + O(q^{10}) \) \( 10 q - 10 q^{4} + 6 q^{5} - 6 q^{9} + 2 q^{10} + 6 q^{11} + 2 q^{14} + 10 q^{16} - 8 q^{19} - 6 q^{20} + 32 q^{21} + 4 q^{25} - 12 q^{26} - 22 q^{29} + 20 q^{30} + 46 q^{31} - 18 q^{34} + 32 q^{35} + 6 q^{36} - 40 q^{39} - 2 q^{40} - 14 q^{41} - 6 q^{44} + 2 q^{45} + 12 q^{46} - 60 q^{49} + 8 q^{50} - 40 q^{51} + 42 q^{55} - 2 q^{56} - 40 q^{59} - 18 q^{61} - 10 q^{64} + 4 q^{65} + 40 q^{66} - 32 q^{69} - 6 q^{70} + 12 q^{71} - 10 q^{74} + 50 q^{75} + 8 q^{76} - 40 q^{79} + 6 q^{80} - 14 q^{81} - 32 q^{84} + 36 q^{85} - 34 q^{86} - 24 q^{89} + 44 q^{90} + 32 q^{91} - 24 q^{94} + 12 q^{95} + 22 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 2.62545i 1.51581i 0.652367 + 0.757903i \(0.273776\pi\)
−0.652367 + 0.757903i \(0.726224\pi\)
\(4\) −1.00000 −0.500000
\(5\) 1.70518 1.44650i 0.762579 0.646895i
\(6\) 2.62545 1.07184
\(7\) 1.83227i 0.692532i 0.938136 + 0.346266i \(0.112551\pi\)
−0.938136 + 0.346266i \(0.887449\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −3.89300 −1.29767
\(10\) −1.44650 1.70518i −0.457424 0.539225i
\(11\) 4.19017 1.26338 0.631692 0.775219i \(-0.282361\pi\)
0.631692 + 0.775219i \(0.282361\pi\)
\(12\) 2.62545i 0.757903i
\(13\) 0.369454i 0.102468i −0.998687 0.0512340i \(-0.983685\pi\)
0.998687 0.0512340i \(-0.0163154\pi\)
\(14\) 1.83227 0.489694
\(15\) 3.79772 + 4.47687i 0.980567 + 1.15592i
\(16\) 1.00000 0.250000
\(17\) 5.08317i 1.23285i 0.787414 + 0.616425i \(0.211420\pi\)
−0.787414 + 0.616425i \(0.788580\pi\)
\(18\) 3.89300i 0.917589i
\(19\) −3.55963 −0.816634 −0.408317 0.912840i \(-0.633884\pi\)
−0.408317 + 0.912840i \(0.633884\pi\)
\(20\) −1.70518 + 1.44650i −0.381290 + 0.323447i
\(21\) −4.81053 −1.04974
\(22\) 4.19017i 0.893348i
\(23\) 5.62036i 1.17193i 0.810338 + 0.585963i \(0.199284\pi\)
−0.810338 + 0.585963i \(0.800716\pi\)
\(24\) −2.62545 −0.535918
\(25\) 0.815273 4.93309i 0.163055 0.986617i
\(26\) −0.369454 −0.0724559
\(27\) 2.34453i 0.451205i
\(28\) 1.83227i 0.346266i
\(29\) −1.20681 −0.224100 −0.112050 0.993703i \(-0.535742\pi\)
−0.112050 + 0.993703i \(0.535742\pi\)
\(30\) 4.47687 3.79772i 0.817360 0.693365i
\(31\) 10.1030 1.81455 0.907276 0.420535i \(-0.138158\pi\)
0.907276 + 0.420535i \(0.138158\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 11.0011i 1.91504i
\(34\) 5.08317 0.871757
\(35\) 2.65038 + 3.12434i 0.447995 + 0.528111i
\(36\) 3.89300 0.648833
\(37\) 1.00000i 0.164399i
\(38\) 3.55963i 0.577447i
\(39\) 0.969984 0.155322
\(40\) 1.44650 + 1.70518i 0.228712 + 0.269613i
\(41\) −8.01447 −1.25165 −0.625825 0.779964i \(-0.715238\pi\)
−0.625825 + 0.779964i \(0.715238\pi\)
\(42\) 4.81053i 0.742281i
\(43\) 2.27264i 0.346575i −0.984871 0.173287i \(-0.944561\pi\)
0.984871 0.173287i \(-0.0554389\pi\)
\(44\) −4.19017 −0.631692
\(45\) −6.63826 + 5.63123i −0.989574 + 0.839454i
\(46\) 5.62036 0.828677
\(47\) 10.9154i 1.59218i −0.605178 0.796090i \(-0.706898\pi\)
0.605178 0.796090i \(-0.293102\pi\)
\(48\) 2.62545i 0.378951i
\(49\) 3.64280 0.520400
\(50\) −4.93309 0.815273i −0.697644 0.115297i
\(51\) −13.3456 −1.86876
\(52\) 0.369454i 0.0512340i
\(53\) 9.94355i 1.36585i −0.730488 0.682926i \(-0.760707\pi\)
0.730488 0.682926i \(-0.239293\pi\)
\(54\) −2.34453 −0.319050
\(55\) 7.14499 6.06108i 0.963431 0.817276i
\(56\) −1.83227 −0.244847
\(57\) 9.34563i 1.23786i
\(58\) 1.20681i 0.158463i
\(59\) 5.34563 0.695941 0.347971 0.937505i \(-0.386871\pi\)
0.347971 + 0.937505i \(0.386871\pi\)
\(60\) −3.79772 4.47687i −0.490283 0.577961i
\(61\) −9.79428 −1.25403 −0.627015 0.779008i \(-0.715723\pi\)
−0.627015 + 0.779008i \(0.715723\pi\)
\(62\) 10.1030i 1.28308i
\(63\) 7.13302i 0.898676i
\(64\) −1.00000 −0.125000
\(65\) −0.534415 0.629985i −0.0662861 0.0781401i
\(66\) 11.0011 1.35414
\(67\) 1.85073i 0.226103i −0.993589 0.113052i \(-0.963937\pi\)
0.993589 0.113052i \(-0.0360625\pi\)
\(68\) 5.08317i 0.616425i
\(69\) −14.7560 −1.77641
\(70\) 3.12434 2.65038i 0.373431 0.316780i
\(71\) 2.86038 0.339464 0.169732 0.985490i \(-0.445710\pi\)
0.169732 + 0.985490i \(0.445710\pi\)
\(72\) 3.89300i 0.458795i
\(73\) 8.09942i 0.947966i −0.880534 0.473983i \(-0.842816\pi\)
0.880534 0.473983i \(-0.157184\pi\)
\(74\) −1.00000 −0.116248
\(75\) 12.9516 + 2.14046i 1.49552 + 0.247159i
\(76\) 3.55963 0.408317
\(77\) 7.67751i 0.874934i
\(78\) 0.969984i 0.109829i
\(79\) −6.06361 −0.682209 −0.341105 0.940025i \(-0.610801\pi\)
−0.341105 + 0.940025i \(0.610801\pi\)
\(80\) 1.70518 1.44650i 0.190645 0.161724i
\(81\) −5.52355 −0.613727
\(82\) 8.01447i 0.885050i
\(83\) 8.93200i 0.980414i −0.871606 0.490207i \(-0.836921\pi\)
0.871606 0.490207i \(-0.163079\pi\)
\(84\) 4.81053 0.524872
\(85\) 7.35281 + 8.66772i 0.797524 + 0.940146i
\(86\) −2.27264 −0.245065
\(87\) 3.16843i 0.339692i
\(88\) 4.19017i 0.446674i
\(89\) −11.4773 −1.21659 −0.608295 0.793711i \(-0.708146\pi\)
−0.608295 + 0.793711i \(0.708146\pi\)
\(90\) 5.63123 + 6.63826i 0.593583 + 0.699735i
\(91\) 0.676938 0.0709624
\(92\) 5.62036i 0.585963i
\(93\) 26.5249i 2.75051i
\(94\) −10.9154 −1.12584
\(95\) −6.06980 + 5.14900i −0.622748 + 0.528276i
\(96\) 2.62545 0.267959
\(97\) 6.05864i 0.615162i −0.951522 0.307581i \(-0.900480\pi\)
0.951522 0.307581i \(-0.0995195\pi\)
\(98\) 3.64280i 0.367978i
\(99\) −16.3123 −1.63945
\(100\) −0.815273 + 4.93309i −0.0815273 + 0.493309i
\(101\) 4.96528 0.494064 0.247032 0.969007i \(-0.420545\pi\)
0.247032 + 0.969007i \(0.420545\pi\)
\(102\) 13.3456i 1.32141i
\(103\) 7.33338i 0.722579i −0.932454 0.361289i \(-0.882337\pi\)
0.932454 0.361289i \(-0.117663\pi\)
\(104\) 0.369454 0.0362279
\(105\) −8.20282 + 6.95843i −0.800513 + 0.679074i
\(106\) −9.94355 −0.965803
\(107\) 8.21182i 0.793867i 0.917847 + 0.396933i \(0.129926\pi\)
−0.917847 + 0.396933i \(0.870074\pi\)
\(108\) 2.34453i 0.225603i
\(109\) 20.5503 1.96836 0.984179 0.177175i \(-0.0566960\pi\)
0.984179 + 0.177175i \(0.0566960\pi\)
\(110\) −6.06108 7.14499i −0.577902 0.681248i
\(111\) 2.62545 0.249197
\(112\) 1.83227i 0.173133i
\(113\) 0.652984i 0.0614276i −0.999528 0.0307138i \(-0.990222\pi\)
0.999528 0.0307138i \(-0.00977804\pi\)
\(114\) −9.34563 −0.875298
\(115\) 8.12985 + 9.58372i 0.758113 + 0.893686i
\(116\) 1.20681 0.112050
\(117\) 1.43828i 0.132969i
\(118\) 5.34563i 0.492105i
\(119\) −9.31373 −0.853788
\(120\) −4.47687 + 3.79772i −0.408680 + 0.346683i
\(121\) 6.55754 0.596140
\(122\) 9.79428i 0.886733i
\(123\) 21.0416i 1.89726i
\(124\) −10.1030 −0.907276
\(125\) −5.74552 9.59109i −0.513895 0.857853i
\(126\) −7.13302 −0.635460
\(127\) 19.2856i 1.71132i 0.517539 + 0.855660i \(0.326848\pi\)
−0.517539 + 0.855660i \(0.673152\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 5.96671 0.525340
\(130\) −0.629985 + 0.534415i −0.0552534 + 0.0468713i
\(131\) −8.82072 −0.770670 −0.385335 0.922777i \(-0.625914\pi\)
−0.385335 + 0.922777i \(0.625914\pi\)
\(132\) 11.0011i 0.957522i
\(133\) 6.52218i 0.565545i
\(134\) −1.85073 −0.159879
\(135\) −3.39137 3.99785i −0.291882 0.344080i
\(136\) −5.08317 −0.435878
\(137\) 4.66126i 0.398239i −0.979975 0.199119i \(-0.936192\pi\)
0.979975 0.199119i \(-0.0638081\pi\)
\(138\) 14.7560i 1.25611i
\(139\) −16.4050 −1.39145 −0.695727 0.718306i \(-0.744918\pi\)
−0.695727 + 0.718306i \(0.744918\pi\)
\(140\) −2.65038 3.12434i −0.223998 0.264055i
\(141\) 28.6580 2.41344
\(142\) 2.86038i 0.240037i
\(143\) 1.54808i 0.129457i
\(144\) −3.89300 −0.324417
\(145\) −2.05784 + 1.74566i −0.170894 + 0.144969i
\(146\) −8.09942 −0.670313
\(147\) 9.56399i 0.788825i
\(148\) 1.00000i 0.0821995i
\(149\) 5.86259 0.480282 0.240141 0.970738i \(-0.422806\pi\)
0.240141 + 0.970738i \(0.422806\pi\)
\(150\) 2.14046 12.9516i 0.174768 1.05749i
\(151\) 13.1460 1.06981 0.534903 0.844913i \(-0.320348\pi\)
0.534903 + 0.844913i \(0.320348\pi\)
\(152\) 3.55963i 0.288724i
\(153\) 19.7888i 1.59983i
\(154\) 7.67751 0.618672
\(155\) 17.2274 14.6140i 1.38374 1.17382i
\(156\) −0.969984 −0.0776609
\(157\) 7.33629i 0.585500i 0.956189 + 0.292750i \(0.0945704\pi\)
−0.956189 + 0.292750i \(0.905430\pi\)
\(158\) 6.06361i 0.482395i
\(159\) 26.1063 2.07037
\(160\) −1.44650 1.70518i −0.114356 0.134806i
\(161\) −10.2980 −0.811596
\(162\) 5.52355i 0.433971i
\(163\) 18.7968i 1.47228i −0.676831 0.736138i \(-0.736647\pi\)
0.676831 0.736138i \(-0.263353\pi\)
\(164\) 8.01447 0.625825
\(165\) 15.9131 + 18.7588i 1.23883 + 1.46037i
\(166\) −8.93200 −0.693257
\(167\) 5.92772i 0.458700i 0.973344 + 0.229350i \(0.0736601\pi\)
−0.973344 + 0.229350i \(0.926340\pi\)
\(168\) 4.81053i 0.371140i
\(169\) 12.8635 0.989500
\(170\) 8.66772 7.35281i 0.664784 0.563935i
\(171\) 13.8576 1.05972
\(172\) 2.27264i 0.173287i
\(173\) 5.78242i 0.439629i 0.975542 + 0.219815i \(0.0705453\pi\)
−0.975542 + 0.219815i \(0.929455\pi\)
\(174\) −3.16843 −0.240198
\(175\) 9.03873 + 1.49380i 0.683264 + 0.112921i
\(176\) 4.19017 0.315846
\(177\) 14.0347i 1.05491i
\(178\) 11.4773i 0.860259i
\(179\) −7.13581 −0.533355 −0.266678 0.963786i \(-0.585926\pi\)
−0.266678 + 0.963786i \(0.585926\pi\)
\(180\) 6.63826 5.63123i 0.494787 0.419727i
\(181\) 11.5365 0.857503 0.428752 0.903422i \(-0.358954\pi\)
0.428752 + 0.903422i \(0.358954\pi\)
\(182\) 0.676938i 0.0501780i
\(183\) 25.7144i 1.90086i
\(184\) −5.62036 −0.414338
\(185\) −1.44650 1.70518i −0.106349 0.125367i
\(186\) 26.5249 1.94490
\(187\) 21.2994i 1.55756i
\(188\) 10.9154i 0.796090i
\(189\) 4.29581 0.312474
\(190\) 5.14900 + 6.06980i 0.373548 + 0.440350i
\(191\) −20.6048 −1.49091 −0.745456 0.666555i \(-0.767768\pi\)
−0.745456 + 0.666555i \(0.767768\pi\)
\(192\) 2.62545i 0.189476i
\(193\) 26.1663i 1.88349i −0.336321 0.941747i \(-0.609183\pi\)
0.336321 0.941747i \(-0.390817\pi\)
\(194\) −6.05864 −0.434985
\(195\) 1.65400 1.40308i 0.118445 0.100477i
\(196\) −3.64280 −0.260200
\(197\) 14.6067i 1.04069i −0.853957 0.520343i \(-0.825804\pi\)
0.853957 0.520343i \(-0.174196\pi\)
\(198\) 16.3123i 1.15927i
\(199\) −5.81275 −0.412055 −0.206027 0.978546i \(-0.566054\pi\)
−0.206027 + 0.978546i \(0.566054\pi\)
\(200\) 4.93309 + 0.815273i 0.348822 + 0.0576485i
\(201\) 4.85901 0.342728
\(202\) 4.96528i 0.349356i
\(203\) 2.21121i 0.155196i
\(204\) 13.3456 0.934381
\(205\) −13.6661 + 11.5929i −0.954482 + 0.809685i
\(206\) −7.33338 −0.510940
\(207\) 21.8801i 1.52077i
\(208\) 0.369454i 0.0256170i
\(209\) −14.9154 −1.03172
\(210\) 6.95843 + 8.20282i 0.480178 + 0.566048i
\(211\) 16.0976 1.10821 0.554104 0.832448i \(-0.313061\pi\)
0.554104 + 0.832448i \(0.313061\pi\)
\(212\) 9.94355i 0.682926i
\(213\) 7.50978i 0.514562i
\(214\) 8.21182 0.561349
\(215\) −3.28738 3.87526i −0.224197 0.264291i
\(216\) 2.34453 0.159525
\(217\) 18.5114i 1.25664i
\(218\) 20.5503i 1.39184i
\(219\) 21.2646 1.43693
\(220\) −7.14499 + 6.06108i −0.481715 + 0.408638i
\(221\) 1.87800 0.126328
\(222\) 2.62545i 0.176209i
\(223\) 25.3608i 1.69828i 0.528164 + 0.849142i \(0.322881\pi\)
−0.528164 + 0.849142i \(0.677119\pi\)
\(224\) 1.83227 0.122423
\(225\) −3.17386 + 19.2045i −0.211591 + 1.28030i
\(226\) −0.652984 −0.0434359
\(227\) 5.57339i 0.369919i 0.982746 + 0.184960i \(0.0592154\pi\)
−0.982746 + 0.184960i \(0.940785\pi\)
\(228\) 9.34563i 0.618929i
\(229\) −9.02035 −0.596081 −0.298041 0.954553i \(-0.596333\pi\)
−0.298041 + 0.954553i \(0.596333\pi\)
\(230\) 9.58372 8.12985i 0.631932 0.536067i
\(231\) −20.1569 −1.32623
\(232\) 1.20681i 0.0792313i
\(233\) 11.8100i 0.773696i 0.922144 + 0.386848i \(0.126436\pi\)
−0.922144 + 0.386848i \(0.873564\pi\)
\(234\) 1.43828 0.0940236
\(235\) −15.7892 18.6128i −1.02997 1.21416i
\(236\) −5.34563 −0.347971
\(237\) 15.9197i 1.03410i
\(238\) 9.31373i 0.603719i
\(239\) −0.907160 −0.0586793 −0.0293396 0.999569i \(-0.509340\pi\)
−0.0293396 + 0.999569i \(0.509340\pi\)
\(240\) 3.79772 + 4.47687i 0.245142 + 0.288981i
\(241\) −4.15616 −0.267722 −0.133861 0.991000i \(-0.542738\pi\)
−0.133861 + 0.991000i \(0.542738\pi\)
\(242\) 6.55754i 0.421534i
\(243\) 21.5354i 1.38150i
\(244\) 9.79428 0.627015
\(245\) 6.21162 5.26931i 0.396846 0.336644i
\(246\) −21.0416 −1.34156
\(247\) 1.31512i 0.0836789i
\(248\) 10.1030i 0.641541i
\(249\) 23.4505 1.48612
\(250\) −9.59109 + 5.74552i −0.606594 + 0.363379i
\(251\) 9.31888 0.588203 0.294101 0.955774i \(-0.404980\pi\)
0.294101 + 0.955774i \(0.404980\pi\)
\(252\) 7.13302i 0.449338i
\(253\) 23.5503i 1.48059i
\(254\) 19.2856 1.21009
\(255\) −22.7567 + 19.3045i −1.42508 + 1.20889i
\(256\) 1.00000 0.0625000
\(257\) 13.6312i 0.850294i 0.905124 + 0.425147i \(0.139778\pi\)
−0.905124 + 0.425147i \(0.860222\pi\)
\(258\) 5.96671i 0.371471i
\(259\) 1.83227 0.113852
\(260\) 0.534415 + 0.629985i 0.0331430 + 0.0390700i
\(261\) 4.69813 0.290807
\(262\) 8.82072i 0.544946i
\(263\) 27.2170i 1.67827i 0.543921 + 0.839137i \(0.316939\pi\)
−0.543921 + 0.839137i \(0.683061\pi\)
\(264\) −11.0011 −0.677071
\(265\) −14.3833 16.9555i −0.883562 1.04157i
\(266\) −6.52218 −0.399901
\(267\) 30.1331i 1.84411i
\(268\) 1.85073i 0.113052i
\(269\) −23.0550 −1.40569 −0.702845 0.711343i \(-0.748087\pi\)
−0.702845 + 0.711343i \(0.748087\pi\)
\(270\) −3.99785 + 3.39137i −0.243301 + 0.206392i
\(271\) 22.9320 1.39302 0.696510 0.717547i \(-0.254735\pi\)
0.696510 + 0.717547i \(0.254735\pi\)
\(272\) 5.08317i 0.308213i
\(273\) 1.77727i 0.107565i
\(274\) −4.66126 −0.281597
\(275\) 3.41613 20.6705i 0.206001 1.24648i
\(276\) 14.7560 0.888206
\(277\) 11.7534i 0.706192i 0.935587 + 0.353096i \(0.114871\pi\)
−0.935587 + 0.353096i \(0.885129\pi\)
\(278\) 16.4050i 0.983906i
\(279\) −39.3310 −2.35468
\(280\) −3.12434 + 2.65038i −0.186715 + 0.158390i
\(281\) −29.0962 −1.73573 −0.867865 0.496799i \(-0.834508\pi\)
−0.867865 + 0.496799i \(0.834508\pi\)
\(282\) 28.6580i 1.70656i
\(283\) 10.1829i 0.605311i −0.953100 0.302655i \(-0.902127\pi\)
0.953100 0.302655i \(-0.0978731\pi\)
\(284\) −2.86038 −0.169732
\(285\) −13.5185 15.9360i −0.800764 0.943965i
\(286\) −1.54808 −0.0915396
\(287\) 14.6846i 0.866807i
\(288\) 3.89300i 0.229397i
\(289\) −8.83864 −0.519920
\(290\) 1.74566 + 2.05784i 0.102509 + 0.120840i
\(291\) 15.9067 0.932466
\(292\) 8.09942i 0.473983i
\(293\) 18.1243i 1.05883i 0.848363 + 0.529415i \(0.177589\pi\)
−0.848363 + 0.529415i \(0.822411\pi\)
\(294\) 9.56399 0.557783
\(295\) 9.11525 7.73245i 0.530711 0.450201i
\(296\) 1.00000 0.0581238
\(297\) 9.82399i 0.570046i
\(298\) 5.86259i 0.339611i
\(299\) 2.07646 0.120085
\(300\) −12.9516 2.14046i −0.747760 0.123580i
\(301\) 4.16409 0.240014
\(302\) 13.1460i 0.756467i
\(303\) 13.0361i 0.748905i
\(304\) −3.55963 −0.204159
\(305\) −16.7010 + 14.1674i −0.956297 + 0.811225i
\(306\) −19.7888 −1.13125
\(307\) 6.15561i 0.351319i 0.984451 + 0.175660i \(0.0562058\pi\)
−0.984451 + 0.175660i \(0.943794\pi\)
\(308\) 7.67751i 0.437467i
\(309\) 19.2534 1.09529
\(310\) −14.6140 17.2274i −0.830019 0.978452i
\(311\) −29.4512 −1.67002 −0.835011 0.550234i \(-0.814539\pi\)
−0.835011 + 0.550234i \(0.814539\pi\)
\(312\) 0.969984i 0.0549145i
\(313\) 13.0102i 0.735378i 0.929949 + 0.367689i \(0.119851\pi\)
−0.929949 + 0.367689i \(0.880149\pi\)
\(314\) 7.33629 0.414011
\(315\) −10.3179 12.1631i −0.581349 0.685312i
\(316\) 6.06361 0.341105
\(317\) 7.39826i 0.415528i 0.978179 + 0.207764i \(0.0666186\pi\)
−0.978179 + 0.207764i \(0.933381\pi\)
\(318\) 26.1063i 1.46397i
\(319\) −5.05676 −0.283124
\(320\) −1.70518 + 1.44650i −0.0953224 + 0.0808618i
\(321\) −21.5598 −1.20335
\(322\) 10.2980i 0.573885i
\(323\) 18.0942i 1.00679i
\(324\) 5.52355 0.306864
\(325\) −1.82255 0.301206i −0.101097 0.0167079i
\(326\) −18.7968 −1.04106
\(327\) 53.9537i 2.98365i
\(328\) 8.01447i 0.442525i
\(329\) 20.0000 1.10264
\(330\) 18.7588 15.9131i 1.03264 0.875987i
\(331\) 33.2545 1.82783 0.913916 0.405903i \(-0.133043\pi\)
0.913916 + 0.405903i \(0.133043\pi\)
\(332\) 8.93200i 0.490207i
\(333\) 3.89300i 0.213335i
\(334\) 5.92772 0.324350
\(335\) −2.67709 3.15583i −0.146265 0.172422i
\(336\) −4.81053 −0.262436
\(337\) 22.6288i 1.23267i −0.787485 0.616334i \(-0.788617\pi\)
0.787485 0.616334i \(-0.211383\pi\)
\(338\) 12.8635i 0.699682i
\(339\) 1.71438 0.0931123
\(340\) −7.35281 8.66772i −0.398762 0.470073i
\(341\) 42.3333 2.29248
\(342\) 13.8576i 0.749334i
\(343\) 19.5004i 1.05293i
\(344\) 2.27264 0.122533
\(345\) −25.1616 + 21.3445i −1.35466 + 1.14915i
\(346\) 5.78242 0.310865
\(347\) 24.1396i 1.29588i 0.761691 + 0.647941i \(0.224370\pi\)
−0.761691 + 0.647941i \(0.775630\pi\)
\(348\) 3.16843i 0.169846i
\(349\) 10.3702 0.555102 0.277551 0.960711i \(-0.410477\pi\)
0.277551 + 0.960711i \(0.410477\pi\)
\(350\) 1.49380 9.03873i 0.0798469 0.483140i
\(351\) −0.866196 −0.0462341
\(352\) 4.19017i 0.223337i
\(353\) 3.92699i 0.209013i −0.994524 0.104506i \(-0.966674\pi\)
0.994524 0.104506i \(-0.0333262\pi\)
\(354\) 14.0347 0.745935
\(355\) 4.87745 4.13753i 0.258868 0.219598i
\(356\) 11.4773 0.608295
\(357\) 24.4528i 1.29418i
\(358\) 7.13581i 0.377139i
\(359\) 9.85179 0.519957 0.259979 0.965614i \(-0.416284\pi\)
0.259979 + 0.965614i \(0.416284\pi\)
\(360\) −5.63123 6.63826i −0.296792 0.349867i
\(361\) −6.32907 −0.333109
\(362\) 11.5365i 0.606346i
\(363\) 17.2165i 0.903632i
\(364\) −0.676938 −0.0354812
\(365\) −11.7158 13.8110i −0.613234 0.722899i
\(366\) −25.7144 −1.34411
\(367\) 33.2559i 1.73594i −0.496614 0.867972i \(-0.665423\pi\)
0.496614 0.867972i \(-0.334577\pi\)
\(368\) 5.62036i 0.292981i
\(369\) 31.2003 1.62422
\(370\) −1.70518 + 1.44650i −0.0886481 + 0.0752000i
\(371\) 18.2192 0.945896
\(372\) 26.5249i 1.37525i
\(373\) 28.5387i 1.47768i −0.673882 0.738839i \(-0.735375\pi\)
0.673882 0.738839i \(-0.264625\pi\)
\(374\) 21.2994 1.10136
\(375\) 25.1809 15.0846i 1.30034 0.778965i
\(376\) 10.9154 0.562921
\(377\) 0.445862i 0.0229631i
\(378\) 4.29581i 0.220953i
\(379\) −0.476554 −0.0244789 −0.0122395 0.999925i \(-0.503896\pi\)
−0.0122395 + 0.999925i \(0.503896\pi\)
\(380\) 6.06980 5.14900i 0.311374 0.264138i
\(381\) −50.6334 −2.59403
\(382\) 20.6048i 1.05423i
\(383\) 7.13962i 0.364818i 0.983223 + 0.182409i \(0.0583895\pi\)
−0.983223 + 0.182409i \(0.941611\pi\)
\(384\) −2.62545 −0.133980
\(385\) 11.1055 + 13.0915i 0.565990 + 0.667206i
\(386\) −26.1663 −1.33183
\(387\) 8.84740i 0.449738i
\(388\) 6.05864i 0.307581i
\(389\) 24.2060 1.22729 0.613646 0.789581i \(-0.289702\pi\)
0.613646 + 0.789581i \(0.289702\pi\)
\(390\) −1.40308 1.65400i −0.0710478 0.0837534i
\(391\) −28.5693 −1.44481
\(392\) 3.64280i 0.183989i
\(393\) 23.1584i 1.16819i
\(394\) −14.6067 −0.735876
\(395\) −10.3395 + 8.77101i −0.520239 + 0.441318i
\(396\) 16.3123 0.819726
\(397\) 20.7491i 1.04137i −0.853750 0.520684i \(-0.825677\pi\)
0.853750 0.520684i \(-0.174323\pi\)
\(398\) 5.81275i 0.291367i
\(399\) 17.1237 0.857256
\(400\) 0.815273 4.93309i 0.0407637 0.246654i
\(401\) −34.8410 −1.73988 −0.869939 0.493159i \(-0.835842\pi\)
−0.869939 + 0.493159i \(0.835842\pi\)
\(402\) 4.85901i 0.242346i
\(403\) 3.73259i 0.185934i
\(404\) −4.96528 −0.247032
\(405\) −9.41864 + 7.98981i −0.468016 + 0.397017i
\(406\) −2.21121 −0.109740
\(407\) 4.19017i 0.207699i
\(408\) 13.3456i 0.660707i
\(409\) −25.2132 −1.24671 −0.623356 0.781938i \(-0.714231\pi\)
−0.623356 + 0.781938i \(0.714231\pi\)
\(410\) 11.5929 + 13.6661i 0.572534 + 0.674921i
\(411\) 12.2379 0.603652
\(412\) 7.33338i 0.361289i
\(413\) 9.79462i 0.481962i
\(414\) −21.8801 −1.07535
\(415\) −12.9201 15.2307i −0.634225 0.747644i
\(416\) −0.369454 −0.0181140
\(417\) 43.0705i 2.10917i
\(418\) 14.9154i 0.729538i
\(419\) −5.69695 −0.278314 −0.139157 0.990270i \(-0.544439\pi\)
−0.139157 + 0.990270i \(0.544439\pi\)
\(420\) 8.20282 6.95843i 0.400256 0.339537i
\(421\) 3.38092 0.164776 0.0823880 0.996600i \(-0.473745\pi\)
0.0823880 + 0.996600i \(0.473745\pi\)
\(422\) 16.0976i 0.783621i
\(423\) 42.4938i 2.06612i
\(424\) 9.94355 0.482901
\(425\) 25.0757 + 4.14417i 1.21635 + 0.201022i
\(426\) 7.50978 0.363850
\(427\) 17.9457i 0.868455i
\(428\) 8.21182i 0.396933i
\(429\) 4.06440 0.196231
\(430\) −3.87526 + 3.28738i −0.186882 + 0.158531i
\(431\) −0.381731 −0.0183873 −0.00919367 0.999958i \(-0.502926\pi\)
−0.00919367 + 0.999958i \(0.502926\pi\)
\(432\) 2.34453i 0.112801i
\(433\) 21.6393i 1.03992i −0.854192 0.519958i \(-0.825948\pi\)
0.854192 0.519958i \(-0.174052\pi\)
\(434\) 18.5114 0.888575
\(435\) −4.58314 5.40275i −0.219745 0.259042i
\(436\) −20.5503 −0.984179
\(437\) 20.0064i 0.957035i
\(438\) 21.2646i 1.01606i
\(439\) −26.4663 −1.26317 −0.631583 0.775308i \(-0.717595\pi\)
−0.631583 + 0.775308i \(0.717595\pi\)
\(440\) 6.06108 + 7.14499i 0.288951 + 0.340624i
\(441\) −14.1814 −0.675305
\(442\) 1.87800i 0.0893273i
\(443\) 4.65489i 0.221161i −0.993867 0.110580i \(-0.964729\pi\)
0.993867 0.110580i \(-0.0352709\pi\)
\(444\) −2.62545 −0.124598
\(445\) −19.5708 + 16.6019i −0.927746 + 0.787005i
\(446\) 25.3608 1.20087
\(447\) 15.3920i 0.728015i
\(448\) 1.83227i 0.0865665i
\(449\) 26.5531 1.25312 0.626558 0.779375i \(-0.284463\pi\)
0.626558 + 0.779375i \(0.284463\pi\)
\(450\) 19.2045 + 3.17386i 0.905309 + 0.149617i
\(451\) −33.5820 −1.58131
\(452\) 0.652984i 0.0307138i
\(453\) 34.5142i 1.62162i
\(454\) 5.57339 0.261572
\(455\) 1.15430 0.979192i 0.0541145 0.0459052i
\(456\) 9.34563 0.437649
\(457\) 4.27264i 0.199866i −0.994994 0.0999329i \(-0.968137\pi\)
0.994994 0.0999329i \(-0.0318628\pi\)
\(458\) 9.02035i 0.421493i
\(459\) 11.9177 0.556269
\(460\) −8.12985 9.58372i −0.379056 0.446843i
\(461\) 32.1873 1.49911 0.749555 0.661942i \(-0.230267\pi\)
0.749555 + 0.661942i \(0.230267\pi\)
\(462\) 20.1569i 0.937786i
\(463\) 18.4014i 0.855186i 0.903971 + 0.427593i \(0.140638\pi\)
−0.903971 + 0.427593i \(0.859362\pi\)
\(464\) −1.20681 −0.0560250
\(465\) 38.3684 + 45.2298i 1.77929 + 2.09748i
\(466\) 11.8100 0.547086
\(467\) 3.06777i 0.141959i 0.997478 + 0.0709797i \(0.0226125\pi\)
−0.997478 + 0.0709797i \(0.977387\pi\)
\(468\) 1.43828i 0.0664847i
\(469\) 3.39104 0.156584
\(470\) −18.6128 + 15.7892i −0.858544 + 0.728301i
\(471\) −19.2611 −0.887504
\(472\) 5.34563i 0.246052i
\(473\) 9.52276i 0.437857i
\(474\) −15.9197 −0.731217
\(475\) −2.90207 + 17.5599i −0.133156 + 0.805705i
\(476\) 9.31373 0.426894
\(477\) 38.7102i 1.77242i
\(478\) 0.907160i 0.0414925i
\(479\) −8.78798 −0.401533 −0.200767 0.979639i \(-0.564343\pi\)
−0.200767 + 0.979639i \(0.564343\pi\)
\(480\) 4.47687 3.79772i 0.204340 0.173341i
\(481\) −0.369454 −0.0168457
\(482\) 4.15616i 0.189308i
\(483\) 27.0369i 1.23022i
\(484\) −6.55754 −0.298070
\(485\) −8.76383 10.3311i −0.397945 0.469110i
\(486\) −21.5354 −0.976866
\(487\) 22.4814i 1.01873i 0.860550 + 0.509366i \(0.170120\pi\)
−0.860550 + 0.509366i \(0.829880\pi\)
\(488\) 9.79428i 0.443366i
\(489\) 49.3500 2.23168
\(490\) −5.26931 6.21162i −0.238043 0.280613i
\(491\) −0.0441752 −0.00199360 −0.000996799 1.00000i \(-0.500317\pi\)
−0.000996799 1.00000i \(0.500317\pi\)
\(492\) 21.0416i 0.948629i
\(493\) 6.13445i 0.276282i
\(494\) 1.31512 0.0591699
\(495\) −27.8155 + 23.5958i −1.25021 + 1.06055i
\(496\) 10.1030 0.453638
\(497\) 5.24097i 0.235090i
\(498\) 23.4505i 1.05084i
\(499\) −28.2445 −1.26440 −0.632199 0.774806i \(-0.717847\pi\)
−0.632199 + 0.774806i \(0.717847\pi\)
\(500\) 5.74552 + 9.59109i 0.256948 + 0.428926i
\(501\) −15.5629 −0.695301
\(502\) 9.31888i 0.415922i
\(503\) 19.7713i 0.881560i −0.897615 0.440780i \(-0.854702\pi\)
0.897615 0.440780i \(-0.145298\pi\)
\(504\) 7.13302 0.317730
\(505\) 8.46670 7.18229i 0.376763 0.319608i
\(506\) 23.5503 1.04694
\(507\) 33.7725i 1.49989i
\(508\) 19.2856i 0.855660i
\(509\) −43.4809 −1.92726 −0.963628 0.267247i \(-0.913886\pi\)
−0.963628 + 0.267247i \(0.913886\pi\)
\(510\) 19.3045 + 22.7567i 0.854816 + 1.00768i
\(511\) 14.8403 0.656496
\(512\) 1.00000i 0.0441942i
\(513\) 8.34565i 0.368470i
\(514\) 13.6312 0.601249
\(515\) −10.6077 12.5047i −0.467432 0.551024i
\(516\) −5.96671 −0.262670
\(517\) 45.7376i 2.01154i
\(518\) 1.83227i 0.0805052i
\(519\) −15.1815 −0.666393
\(520\) 0.629985 0.534415i 0.0276267 0.0234357i
\(521\) −18.0325 −0.790019 −0.395009 0.918677i \(-0.629259\pi\)
−0.395009 + 0.918677i \(0.629259\pi\)
\(522\) 4.69813i 0.205632i
\(523\) 31.6788i 1.38522i 0.721313 + 0.692610i \(0.243539\pi\)
−0.721313 + 0.692610i \(0.756461\pi\)
\(524\) 8.82072 0.385335
\(525\) −3.92190 + 23.7308i −0.171166 + 1.03570i
\(526\) 27.2170 1.18672
\(527\) 51.3553i 2.23707i
\(528\) 11.0011i 0.478761i
\(529\) −8.58844 −0.373410
\(530\) −16.9555 + 14.3833i −0.736501 + 0.624773i
\(531\) −20.8105 −0.903100
\(532\) 6.52218i 0.282773i
\(533\) 2.96098i 0.128254i
\(534\) −30.1331 −1.30398
\(535\) 11.8784 + 14.0026i 0.513548 + 0.605387i
\(536\) 1.85073 0.0799395
\(537\) 18.7347i 0.808463i
\(538\) 23.0550i 0.993973i
\(539\) 15.2639 0.657465
\(540\) 3.39137 + 3.99785i 0.145941 + 0.172040i
\(541\) 9.39442 0.403898 0.201949 0.979396i \(-0.435273\pi\)
0.201949 + 0.979396i \(0.435273\pi\)
\(542\) 22.9320i 0.985014i
\(543\) 30.2886i 1.29981i
\(544\) 5.08317 0.217939
\(545\) 35.0419 29.7260i 1.50103 1.27332i
\(546\) 1.77727 0.0760601
\(547\) 24.7824i 1.05962i −0.848117 0.529809i \(-0.822263\pi\)
0.848117 0.529809i \(-0.177737\pi\)
\(548\) 4.66126i 0.199119i
\(549\) 38.1291 1.62731
\(550\) −20.6705 3.41613i −0.881392 0.145664i
\(551\) 4.29581 0.183008
\(552\) 14.7560i 0.628056i
\(553\) 11.1102i 0.472452i
\(554\) 11.7534 0.499353
\(555\) 4.47687 3.79772i 0.190032 0.161204i
\(556\) 16.4050 0.695727
\(557\) 22.1627i 0.939062i 0.882916 + 0.469531i \(0.155577\pi\)
−0.882916 + 0.469531i \(0.844423\pi\)
\(558\) 39.3310i 1.66501i
\(559\) −0.839637 −0.0355128
\(560\) 2.65038 + 3.12434i 0.111999 + 0.132028i
\(561\) −55.9205 −2.36096
\(562\) 29.0962i 1.22735i
\(563\) 6.46846i 0.272613i 0.990667 + 0.136306i \(0.0435232\pi\)
−0.990667 + 0.136306i \(0.956477\pi\)
\(564\) −28.6580 −1.20672
\(565\) −0.944542 1.11346i −0.0397372 0.0468434i
\(566\) −10.1829 −0.428019
\(567\) 10.1206i 0.425026i
\(568\) 2.86038i 0.120019i
\(569\) −8.26550 −0.346508 −0.173254 0.984877i \(-0.555428\pi\)
−0.173254 + 0.984877i \(0.555428\pi\)
\(570\) −15.9360 + 13.5185i −0.667484 + 0.566226i
\(571\) 34.5179 1.44453 0.722264 0.691618i \(-0.243102\pi\)
0.722264 + 0.691618i \(0.243102\pi\)
\(572\) 1.54808i 0.0647283i
\(573\) 54.0970i 2.25993i
\(574\) −14.6846 −0.612925
\(575\) 27.7257 + 4.58213i 1.15624 + 0.191088i
\(576\) 3.89300 0.162208
\(577\) 3.05347i 0.127117i 0.997978 + 0.0635587i \(0.0202450\pi\)
−0.997978 + 0.0635587i \(0.979755\pi\)
\(578\) 8.83864i 0.367639i
\(579\) 68.6985 2.85501
\(580\) 2.05784 1.74566i 0.0854470 0.0724845i
\(581\) 16.3658 0.678968
\(582\) 15.9067i 0.659353i
\(583\) 41.6652i 1.72559i
\(584\) 8.09942 0.335156
\(585\) 2.08048 + 2.45253i 0.0860172 + 0.101400i
\(586\) 18.1243 0.748706
\(587\) 35.1344i 1.45015i 0.688668 + 0.725076i \(0.258196\pi\)
−0.688668 + 0.725076i \(0.741804\pi\)
\(588\) 9.56399i 0.394412i
\(589\) −35.9629 −1.48183
\(590\) −7.73245 9.11525i −0.318340 0.375269i
\(591\) 38.3492 1.57748
\(592\) 1.00000i 0.0410997i
\(593\) 12.0400i 0.494424i −0.968961 0.247212i \(-0.920486\pi\)
0.968961 0.247212i \(-0.0795144\pi\)
\(594\) −9.82399 −0.403083
\(595\) −15.8816 + 13.4723i −0.651081 + 0.552311i
\(596\) −5.86259 −0.240141
\(597\) 15.2611i 0.624595i
\(598\) 2.07646i 0.0849129i
\(599\) 17.4701 0.713810 0.356905 0.934141i \(-0.383832\pi\)
0.356905 + 0.934141i \(0.383832\pi\)
\(600\) −2.14046 + 12.9516i −0.0873839 + 0.528746i
\(601\) 38.7044 1.57878 0.789392 0.613890i \(-0.210396\pi\)
0.789392 + 0.613890i \(0.210396\pi\)
\(602\) 4.16409i 0.169716i
\(603\) 7.20491i 0.293406i
\(604\) −13.1460 −0.534903
\(605\) 11.1818 9.48548i 0.454604 0.385639i
\(606\) 13.0361 0.529556
\(607\) 28.7903i 1.16856i 0.811551 + 0.584282i \(0.198624\pi\)
−0.811551 + 0.584282i \(0.801376\pi\)
\(608\) 3.55963i 0.144362i
\(609\) 5.80542 0.235247
\(610\) 14.1674 + 16.7010i 0.573623 + 0.676204i
\(611\) −4.03275 −0.163148
\(612\) 19.7888i 0.799915i
\(613\) 7.66539i 0.309602i −0.987946 0.154801i \(-0.950526\pi\)
0.987946 0.154801i \(-0.0494737\pi\)
\(614\) 6.15561 0.248420
\(615\) −30.4367 35.8797i −1.22733 1.44681i
\(616\) −7.67751 −0.309336
\(617\) 36.5388i 1.47100i −0.677527 0.735498i \(-0.736948\pi\)
0.677527 0.735498i \(-0.263052\pi\)
\(618\) 19.2534i 0.774487i
\(619\) 45.8085 1.84120 0.920599 0.390510i \(-0.127701\pi\)
0.920599 + 0.390510i \(0.127701\pi\)
\(620\) −17.2274 + 14.6140i −0.691870 + 0.586912i
\(621\) 13.1771 0.528779
\(622\) 29.4512i 1.18088i
\(623\) 21.0294i 0.842527i
\(624\) 0.969984 0.0388304
\(625\) −23.6707 8.04362i −0.946826 0.321745i
\(626\) 13.0102 0.519991
\(627\) 39.1598i 1.56389i
\(628\) 7.33629i 0.292750i
\(629\) 5.08317 0.202679
\(630\) −12.1631 + 10.3179i −0.484588 + 0.411075i
\(631\) 3.42682 0.136420 0.0682098 0.997671i \(-0.478271\pi\)
0.0682098 + 0.997671i \(0.478271\pi\)
\(632\) 6.06361i 0.241197i
\(633\) 42.2636i 1.67983i
\(634\) 7.39826 0.293823
\(635\) 27.8966 + 32.8854i 1.10704 + 1.30502i
\(636\) −26.1063 −1.03518
\(637\) 1.34585i 0.0533244i
\(638\) 5.05676i 0.200199i
\(639\) −11.1354 −0.440511
\(640\) 1.44650 + 1.70518i 0.0571779 + 0.0674031i
\(641\) 38.3241 1.51371 0.756855 0.653583i \(-0.226735\pi\)
0.756855 + 0.653583i \(0.226735\pi\)
\(642\) 21.5598i 0.850896i
\(643\) 1.36660i 0.0538935i 0.999637 + 0.0269468i \(0.00857846\pi\)
−0.999637 + 0.0269468i \(0.991422\pi\)
\(644\) 10.2980 0.405798
\(645\) 10.1743 8.63085i 0.400613 0.339840i
\(646\) −18.0942 −0.711906
\(647\) 11.2690i 0.443028i −0.975157 0.221514i \(-0.928900\pi\)
0.975157 0.221514i \(-0.0710999\pi\)
\(648\) 5.52355i 0.216985i
\(649\) 22.3991 0.879241
\(650\) −0.301206 + 1.82255i −0.0118143 + 0.0714862i
\(651\) −48.6008 −1.90482
\(652\) 18.7968i 0.736138i
\(653\) 29.5439i 1.15614i −0.815987 0.578070i \(-0.803806\pi\)
0.815987 0.578070i \(-0.196194\pi\)
\(654\) 53.9537 2.10976
\(655\) −15.0409 + 12.7592i −0.587697 + 0.498542i
\(656\) −8.01447 −0.312912
\(657\) 31.5311i 1.23014i
\(658\) 20.0000i 0.779681i
\(659\) 49.9126 1.94432 0.972159 0.234324i \(-0.0752877\pi\)
0.972159 + 0.234324i \(0.0752877\pi\)
\(660\) −15.9131 18.7588i −0.619416 0.730187i
\(661\) 25.9950 1.01109 0.505545 0.862800i \(-0.331292\pi\)
0.505545 + 0.862800i \(0.331292\pi\)
\(662\) 33.2545i 1.29247i
\(663\) 4.93059i 0.191488i
\(664\) 8.93200 0.346629
\(665\) −9.43434 11.1215i −0.365848 0.431273i
\(666\) 3.89300 0.150851
\(667\) 6.78273i 0.262628i
\(668\) 5.92772i 0.229350i
\(669\) −66.5836 −2.57427
\(670\) −3.15583 + 2.67709i −0.121920 + 0.103425i
\(671\) −41.0397 −1.58432
\(672\) 4.81053i 0.185570i
\(673\) 6.91054i 0.266382i 0.991090 + 0.133191i \(0.0425223\pi\)
−0.991090 + 0.133191i \(0.957478\pi\)
\(674\) −22.6288 −0.871627
\(675\) −11.5658 1.91143i −0.445167 0.0735711i
\(676\) −12.8635 −0.494750
\(677\) 15.6913i 0.603065i 0.953456 + 0.301532i \(0.0974982\pi\)
−0.953456 + 0.301532i \(0.902502\pi\)
\(678\) 1.71438i 0.0658403i
\(679\) 11.1011 0.426019
\(680\) −8.66772 + 7.35281i −0.332392 + 0.281967i
\(681\) −14.6327 −0.560725
\(682\) 42.3333i 1.62103i
\(683\) 18.2002i 0.696412i −0.937418 0.348206i \(-0.886791\pi\)
0.937418 0.348206i \(-0.113209\pi\)
\(684\) −13.8576 −0.529859
\(685\) −6.74252 7.94829i −0.257618 0.303689i
\(686\) 19.5004 0.744531
\(687\) 23.6825i 0.903544i
\(688\) 2.27264i 0.0866437i
\(689\) −3.67368 −0.139956
\(690\) 21.3445 + 25.1616i 0.812573 + 0.957886i
\(691\) −2.58658 −0.0983982 −0.0491991 0.998789i \(-0.515667\pi\)
−0.0491991 + 0.998789i \(0.515667\pi\)
\(692\) 5.78242i 0.219815i
\(693\) 29.8886i 1.13537i
\(694\) 24.1396 0.916327
\(695\) −27.9735 + 23.7298i −1.06109 + 0.900124i
\(696\) 3.16843 0.120099
\(697\) 40.7389i 1.54310i
\(698\) 10.3702i 0.392516i
\(699\) −31.0065 −1.17277
\(700\) −9.03873 1.49380i −0.341632 0.0564603i
\(701\) −26.5092 −1.00124 −0.500620 0.865667i \(-0.666895\pi\)
−0.500620 + 0.865667i \(0.666895\pi\)
\(702\) 0.866196i 0.0326925i
\(703\) 3.55963i 0.134254i
\(704\) −4.19017 −0.157923
\(705\) 48.8670 41.4538i 1.84044 1.56124i
\(706\) −3.92699 −0.147794
\(707\) 9.09773i 0.342155i
\(708\) 14.0347i 0.527456i
\(709\) 25.0474 0.940674 0.470337 0.882487i \(-0.344132\pi\)
0.470337 + 0.882487i \(0.344132\pi\)
\(710\) −4.13753 4.87745i −0.155279 0.183048i
\(711\) 23.6056 0.885281
\(712\) 11.4773i 0.430129i
\(713\) 56.7825i 2.12652i
\(714\) −24.4528 −0.915121
\(715\) −2.23929 2.63975i −0.0837448 0.0987209i
\(716\) 7.13581 0.266678
\(717\) 2.38171i 0.0889464i
\(718\) 9.85179i 0.367665i
\(719\) −24.9551 −0.930668 −0.465334 0.885135i \(-0.654066\pi\)
−0.465334 + 0.885135i \(0.654066\pi\)
\(720\) −6.63826 + 5.63123i −0.247394 + 0.209863i
\(721\) 13.4367 0.500409
\(722\) 6.32907i 0.235544i
\(723\) 10.9118i 0.405814i
\(724\) −11.5365 −0.428752
\(725\) −0.983883 + 5.95332i −0.0365405 + 0.221101i
\(726\) 17.2165 0.638964
\(727\) 21.6774i 0.803970i 0.915646 + 0.401985i \(0.131680\pi\)
−0.915646 + 0.401985i \(0.868320\pi\)
\(728\) 0.676938i 0.0250890i
\(729\) 39.9695 1.48035
\(730\) −13.8110 + 11.7158i −0.511167 + 0.433622i
\(731\) 11.5522 0.427275
\(732\) 25.7144i 0.950432i
\(733\) 6.33267i 0.233903i 0.993138 + 0.116951i \(0.0373122\pi\)
−0.993138 + 0.116951i \(0.962688\pi\)
\(734\) −33.2559 −1.22750
\(735\) 13.8343 + 16.3083i 0.510286 + 0.601541i
\(736\) 5.62036 0.207169
\(737\) 7.75489i 0.285655i
\(738\) 31.2003i 1.14850i
\(739\) −12.8076 −0.471136 −0.235568 0.971858i \(-0.575695\pi\)
−0.235568 + 0.971858i \(0.575695\pi\)
\(740\) 1.44650 + 1.70518i 0.0531744 + 0.0626836i
\(741\) −3.45278 −0.126841
\(742\) 18.2192i 0.668849i
\(743\) 11.0694i 0.406097i 0.979169 + 0.203048i \(0.0650848\pi\)
−0.979169 + 0.203048i \(0.934915\pi\)
\(744\) −26.5249 −0.972452
\(745\) 9.99677 8.48024i 0.366253 0.310692i
\(746\) −28.5387 −1.04488
\(747\) 34.7723i 1.27225i
\(748\) 21.2994i 0.778782i
\(749\) −15.0463 −0.549778
\(750\) −15.0846 25.1809i −0.550812 0.919478i
\(751\) −46.5316 −1.69796 −0.848981 0.528423i \(-0.822784\pi\)
−0.848981 + 0.528423i \(0.822784\pi\)
\(752\) 10.9154i 0.398045i
\(753\) 24.4663i 0.891601i
\(754\) 0.445862 0.0162374
\(755\) 22.4163 19.0157i 0.815812 0.692052i
\(756\) −4.29581 −0.156237
\(757\) 32.9872i 1.19894i −0.800397 0.599470i \(-0.795378\pi\)
0.800397 0.599470i \(-0.204622\pi\)
\(758\) 0.476554i 0.0173092i
\(759\) −61.8301 −2.24429
\(760\) −5.14900 6.06980i −0.186774 0.220175i
\(761\) 28.7913 1.04369 0.521843 0.853042i \(-0.325245\pi\)
0.521843 + 0.853042i \(0.325245\pi\)
\(762\) 50.6334i 1.83426i
\(763\) 37.6536i 1.36315i
\(764\) 20.6048 0.745456
\(765\) −28.6245 33.7434i −1.03492 1.22000i
\(766\) 7.13962 0.257965
\(767\) 1.97496i 0.0713118i
\(768\) 2.62545i 0.0947379i
\(769\) −41.9025 −1.51104 −0.755521 0.655124i \(-0.772616\pi\)
−0.755521 + 0.655124i \(0.772616\pi\)
\(770\) 13.0915 11.1055i 0.471786 0.400215i
\(771\) −35.7882 −1.28888
\(772\) 26.1663i 0.941747i
\(773\) 31.0931i 1.11834i 0.829052 + 0.559171i \(0.188881\pi\)
−0.829052 + 0.559171i \(0.811119\pi\)
\(774\) 8.84740 0.318013
\(775\) 8.23670 49.8390i 0.295871 1.79027i
\(776\) 6.05864 0.217493
\(777\) 4.81053i 0.172577i
\(778\) 24.2060i 0.867827i
\(779\) 28.5285 1.02214
\(780\) −1.65400 + 1.40308i −0.0592226 + 0.0502384i
\(781\) 11.9855 0.428874
\(782\) 28.5693i 1.02163i
\(783\) 2.82941i 0.101115i
\(784\) 3.64280 0.130100
\(785\) 10.6120 + 12.5097i 0.378757 + 0.446490i
\(786\) −23.1584 −0.826032
\(787\) 18.2842i 0.651760i 0.945411 + 0.325880i \(0.105661\pi\)
−0.945411 + 0.325880i \(0.894339\pi\)
\(788\) 14.6067i