Properties

Label 154.2.c.a.153.6
Level $154$
Weight $2$
Character 154.153
Analytic conductor $1.230$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.22969619113\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.12745506816.1
Defining polynomial: \( x^{8} + 23x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 153.6
Root \(0.323042 + 0.323042i\) of defining polynomial
Character \(\chi\) \(=\) 154.153
Dual form 154.2.c.a.153.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -0.646084i q^{3} -1.00000 q^{4} -3.09557i q^{5} +0.646084 q^{6} +(2.44949 - 1.00000i) q^{7} -1.00000i q^{8} +2.58258 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -0.646084i q^{3} -1.00000 q^{4} -3.09557i q^{5} +0.646084 q^{6} +(2.44949 - 1.00000i) q^{7} -1.00000i q^{8} +2.58258 q^{9} +3.09557 q^{10} +(-1.79129 + 2.79129i) q^{11} +0.646084i q^{12} +0.646084 q^{13} +(1.00000 + 2.44949i) q^{14} -2.00000 q^{15} +1.00000 q^{16} -3.74166 q^{17} +2.58258i q^{18} -1.80341 q^{19} +3.09557i q^{20} +(-0.646084 - 1.58258i) q^{21} +(-2.79129 - 1.79129i) q^{22} +4.00000 q^{23} -0.646084 q^{24} -4.58258 q^{25} +0.646084i q^{26} -3.60681i q^{27} +(-2.44949 + 1.00000i) q^{28} -1.58258i q^{29} -2.00000i q^{30} +8.64064i q^{31} +1.00000i q^{32} +(1.80341 + 1.15732i) q^{33} -3.74166i q^{34} +(-3.09557 - 7.58258i) q^{35} -2.58258 q^{36} +3.58258 q^{37} -1.80341i q^{38} -0.417424i q^{39} -3.09557 q^{40} -9.93280 q^{41} +(1.58258 - 0.646084i) q^{42} +7.16515i q^{43} +(1.79129 - 2.79129i) q^{44} -7.99455i q^{45} +4.00000i q^{46} +9.93280i q^{47} -0.646084i q^{48} +(5.00000 - 4.89898i) q^{49} -4.58258i q^{50} +2.41742i q^{51} -0.646084 q^{52} -11.5826 q^{53} +3.60681 q^{54} +(8.64064 + 5.54506i) q^{55} +(-1.00000 - 2.44949i) q^{56} +1.16515i q^{57} +1.58258 q^{58} +0.646084i q^{59} +2.00000 q^{60} +1.93825 q^{61} -8.64064 q^{62} +(6.32599 - 2.58258i) q^{63} -1.00000 q^{64} -2.00000i q^{65} +(-1.15732 + 1.80341i) q^{66} -7.58258 q^{67} +3.74166 q^{68} -2.58434i q^{69} +(7.58258 - 3.09557i) q^{70} +2.00000 q^{71} -2.58258i q^{72} +16.1240 q^{73} +3.58258i q^{74} +2.96073i q^{75} +1.80341 q^{76} +(-1.59645 + 8.62852i) q^{77} +0.417424 q^{78} +4.00000i q^{79} -3.09557i q^{80} +5.41742 q^{81} -9.93280i q^{82} +12.8935 q^{83} +(0.646084 + 1.58258i) q^{84} +11.5826i q^{85} -7.16515 q^{86} -1.02248 q^{87} +(2.79129 + 1.79129i) q^{88} -9.79796i q^{89} +7.99455 q^{90} +(1.58258 - 0.646084i) q^{91} -4.00000 q^{92} +5.58258 q^{93} -9.93280 q^{94} +5.58258i q^{95} +0.646084 q^{96} +8.50579i q^{97} +(4.89898 + 5.00000i) q^{98} +(-4.62614 + 7.20871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{4} - 16 q^{9} + 4 q^{11} + 8 q^{14} - 16 q^{15} + 8 q^{16} - 4 q^{22} + 32 q^{23} + 16 q^{36} - 8 q^{37} - 24 q^{42} - 4 q^{44} + 40 q^{49} - 56 q^{53} - 8 q^{56} - 24 q^{58} + 16 q^{60} - 8 q^{64} - 24 q^{67} + 24 q^{70} + 16 q^{71} + 4 q^{77} + 40 q^{78} + 80 q^{81} + 16 q^{86} + 4 q^{88} - 24 q^{91} - 32 q^{92} + 8 q^{93} - 92 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/154\mathbb{Z}\right)^\times\).

\(n\) \(45\) \(57\)
\(\chi(n)\) \(-1\) \(-1\)

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
\(3\) 0.646084i 0.373017i −0.982453 0.186508i \(-0.940283\pi\)
0.982453 0.186508i \(-0.0597171\pi\)
\(4\) −1.00000 −0.500000
\(5\) 3.09557i 1.38438i −0.721714 0.692191i \(-0.756645\pi\)
0.721714 0.692191i \(-0.243355\pi\)
\(6\) 0.646084 0.263763
\(7\) 2.44949 1.00000i 0.925820 0.377964i
\(8\) 1.00000i 0.353553i
\(9\) 2.58258 0.860859
\(10\) 3.09557 0.978906
\(11\) −1.79129 + 2.79129i −0.540094 + 0.841605i
\(12\) 0.646084i 0.186508i
\(13\) 0.646084 0.179191 0.0895957 0.995978i \(-0.471443\pi\)
0.0895957 + 0.995978i \(0.471443\pi\)
\(14\) 1.00000 + 2.44949i 0.267261 + 0.654654i
\(15\) −2.00000 −0.516398
\(16\) 1.00000 0.250000
\(17\) −3.74166 −0.907485 −0.453743 0.891133i \(-0.649911\pi\)
−0.453743 + 0.891133i \(0.649911\pi\)
\(18\) 2.58258i 0.608719i
\(19\) −1.80341 −0.413730 −0.206865 0.978370i \(-0.566326\pi\)
−0.206865 + 0.978370i \(0.566326\pi\)
\(20\) 3.09557i 0.692191i
\(21\) −0.646084 1.58258i −0.140987 0.345346i
\(22\) −2.79129 1.79129i −0.595105 0.381904i
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) −0.646084 −0.131881
\(25\) −4.58258 −0.916515
\(26\) 0.646084i 0.126707i
\(27\) 3.60681i 0.694131i
\(28\) −2.44949 + 1.00000i −0.462910 + 0.188982i
\(29\) 1.58258i 0.293877i −0.989146 0.146938i \(-0.953058\pi\)
0.989146 0.146938i \(-0.0469419\pi\)
\(30\) 2.00000i 0.365148i
\(31\) 8.64064i 1.55190i 0.630792 + 0.775952i \(0.282730\pi\)
−0.630792 + 0.775952i \(0.717270\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.80341 + 1.15732i 0.313933 + 0.201464i
\(34\) 3.74166i 0.641689i
\(35\) −3.09557 7.58258i −0.523247 1.28169i
\(36\) −2.58258 −0.430429
\(37\) 3.58258 0.588972 0.294486 0.955656i \(-0.404852\pi\)
0.294486 + 0.955656i \(0.404852\pi\)
\(38\) 1.80341i 0.292551i
\(39\) 0.417424i 0.0668414i
\(40\) −3.09557 −0.489453
\(41\) −9.93280 −1.55124 −0.775622 0.631198i \(-0.782564\pi\)
−0.775622 + 0.631198i \(0.782564\pi\)
\(42\) 1.58258 0.646084i 0.244197 0.0996929i
\(43\) 7.16515i 1.09268i 0.837565 + 0.546338i \(0.183978\pi\)
−0.837565 + 0.546338i \(0.816022\pi\)
\(44\) 1.79129 2.79129i 0.270047 0.420802i
\(45\) 7.99455i 1.19176i
\(46\) 4.00000i 0.589768i
\(47\) 9.93280i 1.44885i 0.689354 + 0.724424i \(0.257894\pi\)
−0.689354 + 0.724424i \(0.742106\pi\)
\(48\) 0.646084i 0.0932542i
\(49\) 5.00000 4.89898i 0.714286 0.699854i
\(50\) 4.58258i 0.648074i
\(51\) 2.41742i 0.338507i
\(52\) −0.646084 −0.0895957
\(53\) −11.5826 −1.59099 −0.795495 0.605961i \(-0.792789\pi\)
−0.795495 + 0.605961i \(0.792789\pi\)
\(54\) 3.60681 0.490825
\(55\) 8.64064 + 5.54506i 1.16510 + 0.747696i
\(56\) −1.00000 2.44949i −0.133631 0.327327i
\(57\) 1.16515i 0.154328i
\(58\) 1.58258 0.207802
\(59\) 0.646084i 0.0841129i 0.999115 + 0.0420565i \(0.0133909\pi\)
−0.999115 + 0.0420565i \(0.986609\pi\)
\(60\) 2.00000 0.258199
\(61\) 1.93825 0.248168 0.124084 0.992272i \(-0.460401\pi\)
0.124084 + 0.992272i \(0.460401\pi\)
\(62\) −8.64064 −1.09736
\(63\) 6.32599 2.58258i 0.797000 0.325374i
\(64\) −1.00000 −0.125000
\(65\) 2.00000i 0.248069i
\(66\) −1.15732 + 1.80341i −0.142457 + 0.221984i
\(67\) −7.58258 −0.926359 −0.463180 0.886264i \(-0.653291\pi\)
−0.463180 + 0.886264i \(0.653291\pi\)
\(68\) 3.74166 0.453743
\(69\) 2.58434i 0.311117i
\(70\) 7.58258 3.09557i 0.906291 0.369992i
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 2.58258i 0.304359i
\(73\) 16.1240 1.88717 0.943583 0.331136i \(-0.107432\pi\)
0.943583 + 0.331136i \(0.107432\pi\)
\(74\) 3.58258i 0.416466i
\(75\) 2.96073i 0.341875i
\(76\) 1.80341 0.206865
\(77\) −1.59645 + 8.62852i −0.181933 + 0.983311i
\(78\) 0.417424 0.0472640
\(79\) 4.00000i 0.450035i 0.974355 + 0.225018i \(0.0722440\pi\)
−0.974355 + 0.225018i \(0.927756\pi\)
\(80\) 3.09557i 0.346096i
\(81\) 5.41742 0.601936
\(82\) 9.93280i 1.09689i
\(83\) 12.8935 1.41525 0.707625 0.706589i \(-0.249767\pi\)
0.707625 + 0.706589i \(0.249767\pi\)
\(84\) 0.646084 + 1.58258i 0.0704935 + 0.172673i
\(85\) 11.5826i 1.25631i
\(86\) −7.16515 −0.772638
\(87\) −1.02248 −0.109621
\(88\) 2.79129 + 1.79129i 0.297552 + 0.190952i
\(89\) 9.79796i 1.03858i −0.854598 0.519291i \(-0.826196\pi\)
0.854598 0.519291i \(-0.173804\pi\)
\(90\) 7.99455 0.842700
\(91\) 1.58258 0.646084i 0.165899 0.0677280i
\(92\) −4.00000 −0.417029
\(93\) 5.58258 0.578886
\(94\) −9.93280 −1.02449
\(95\) 5.58258i 0.572760i
\(96\) 0.646084 0.0659407
\(97\) 8.50579i 0.863632i 0.901962 + 0.431816i \(0.142127\pi\)
−0.901962 + 0.431816i \(0.857873\pi\)
\(98\) 4.89898 + 5.00000i 0.494872 + 0.505076i
\(99\) −4.62614 + 7.20871i −0.464944 + 0.724503i
\(100\) 4.58258 0.458258
\(101\) −11.7362 −1.16780 −0.583898 0.811827i \(-0.698473\pi\)
−0.583898 + 0.811827i \(0.698473\pi\)
\(102\) −2.41742 −0.239361
\(103\) 6.05630i 0.596745i −0.954449 0.298373i \(-0.903556\pi\)
0.954449 0.298373i \(-0.0964438\pi\)
\(104\) 0.646084i 0.0633537i
\(105\) −4.89898 + 2.00000i −0.478091 + 0.195180i
\(106\) 11.5826i 1.12500i
\(107\) 17.5826i 1.69977i −0.526967 0.849886i \(-0.676671\pi\)
0.526967 0.849886i \(-0.323329\pi\)
\(108\) 3.60681i 0.347066i
\(109\) 17.1652i 1.64412i −0.569398 0.822062i \(-0.692824\pi\)
0.569398 0.822062i \(-0.307176\pi\)
\(110\) −5.54506 + 8.64064i −0.528701 + 0.823852i
\(111\) 2.31464i 0.219696i
\(112\) 2.44949 1.00000i 0.231455 0.0944911i
\(113\) 10.7477 1.01106 0.505531 0.862809i \(-0.331297\pi\)
0.505531 + 0.862809i \(0.331297\pi\)
\(114\) −1.16515 −0.109126
\(115\) 12.3823i 1.15465i
\(116\) 1.58258i 0.146938i
\(117\) 1.66856 0.154258
\(118\) −0.646084 −0.0594768
\(119\) −9.16515 + 3.74166i −0.840168 + 0.342997i
\(120\) 2.00000i 0.182574i
\(121\) −4.58258 10.0000i −0.416598 0.909091i
\(122\) 1.93825i 0.175481i
\(123\) 6.41742i 0.578640i
\(124\) 8.64064i 0.775952i
\(125\) 1.29217i 0.115575i
\(126\) 2.58258 + 6.32599i 0.230074 + 0.563564i
\(127\) 3.58258i 0.317902i 0.987286 + 0.158951i \(0.0508112\pi\)
−0.987286 + 0.158951i \(0.949189\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 4.62929 0.407586
\(130\) 2.00000 0.175412
\(131\) −16.7700 −1.46520 −0.732602 0.680657i \(-0.761694\pi\)
−0.732602 + 0.680657i \(0.761694\pi\)
\(132\) −1.80341 1.15732i −0.156966 0.100732i
\(133\) −4.41742 + 1.80341i −0.383039 + 0.156375i
\(134\) 7.58258i 0.655035i
\(135\) −11.1652 −0.960943
\(136\) 3.74166i 0.320844i
\(137\) −3.16515 −0.270417 −0.135209 0.990817i \(-0.543170\pi\)
−0.135209 + 0.990817i \(0.543170\pi\)
\(138\) 2.58434 0.219993
\(139\) −15.4779 −1.31282 −0.656408 0.754406i \(-0.727925\pi\)
−0.656408 + 0.754406i \(0.727925\pi\)
\(140\) 3.09557 + 7.58258i 0.261624 + 0.640845i
\(141\) 6.41742 0.540445
\(142\) 2.00000i 0.167836i
\(143\) −1.15732 + 1.80341i −0.0967801 + 0.150808i
\(144\) 2.58258 0.215215
\(145\) −4.89898 −0.406838
\(146\) 16.1240i 1.33443i
\(147\) −3.16515 3.23042i −0.261057 0.266440i
\(148\) −3.58258 −0.294486
\(149\) 14.0000i 1.14692i 0.819232 + 0.573462i \(0.194400\pi\)
−0.819232 + 0.573462i \(0.805600\pi\)
\(150\) −2.96073 −0.241742
\(151\) 5.58258i 0.454304i −0.973859 0.227152i \(-0.927059\pi\)
0.973859 0.227152i \(-0.0729414\pi\)
\(152\) 1.80341i 0.146276i
\(153\) −9.66311 −0.781216
\(154\) −8.62852 1.59645i −0.695306 0.128646i
\(155\) 26.7477 2.14843
\(156\) 0.417424i 0.0334207i
\(157\) 13.1632i 1.05054i 0.850936 + 0.525270i \(0.176036\pi\)
−0.850936 + 0.525270i \(0.823964\pi\)
\(158\) −4.00000 −0.318223
\(159\) 7.48331i 0.593465i
\(160\) 3.09557 0.244727
\(161\) 9.79796 4.00000i 0.772187 0.315244i
\(162\) 5.41742i 0.425633i
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 9.93280 0.775622
\(165\) 3.58258 5.58258i 0.278903 0.434603i
\(166\) 12.8935i 1.00073i
\(167\) 1.29217 0.0999909 0.0499955 0.998749i \(-0.484079\pi\)
0.0499955 + 0.998749i \(0.484079\pi\)
\(168\) −1.58258 + 0.646084i −0.122098 + 0.0498464i
\(169\) −12.5826 −0.967890
\(170\) −11.5826 −0.888343
\(171\) −4.65743 −0.356163
\(172\) 7.16515i 0.546338i
\(173\) 10.7137 0.814550 0.407275 0.913306i \(-0.366479\pi\)
0.407275 + 0.913306i \(0.366479\pi\)
\(174\) 1.02248i 0.0775137i
\(175\) −11.2250 + 4.58258i −0.848528 + 0.346410i
\(176\) −1.79129 + 2.79129i −0.135023 + 0.210401i
\(177\) 0.417424 0.0313755
\(178\) 9.79796 0.734388
\(179\) 11.1652 0.834523 0.417261 0.908787i \(-0.362990\pi\)
0.417261 + 0.908787i \(0.362990\pi\)
\(180\) 7.99455i 0.595879i
\(181\) 5.41022i 0.402138i −0.979577 0.201069i \(-0.935558\pi\)
0.979577 0.201069i \(-0.0644416\pi\)
\(182\) 0.646084 + 1.58258i 0.0478909 + 0.117308i
\(183\) 1.25227i 0.0925707i
\(184\) 4.00000i 0.294884i
\(185\) 11.0901i 0.815362i
\(186\) 5.58258i 0.409334i
\(187\) 6.70239 10.4440i 0.490127 0.763744i
\(188\) 9.93280i 0.724424i
\(189\) −3.60681 8.83485i −0.262357 0.642641i
\(190\) −5.58258 −0.405003
\(191\) −18.0000 −1.30243 −0.651217 0.758891i \(-0.725741\pi\)
−0.651217 + 0.758891i \(0.725741\pi\)
\(192\) 0.646084i 0.0466271i
\(193\) 16.3303i 1.17548i −0.809050 0.587740i \(-0.800018\pi\)
0.809050 0.587740i \(-0.199982\pi\)
\(194\) −8.50579 −0.610680
\(195\) −1.29217 −0.0925340
\(196\) −5.00000 + 4.89898i −0.357143 + 0.349927i
\(197\) 8.74773i 0.623250i −0.950205 0.311625i \(-0.899127\pi\)
0.950205 0.311625i \(-0.100873\pi\)
\(198\) −7.20871 4.62614i −0.512301 0.328765i
\(199\) 9.66311i 0.685000i 0.939518 + 0.342500i \(0.111274\pi\)
−0.939518 + 0.342500i \(0.888726\pi\)
\(200\) 4.58258i 0.324037i
\(201\) 4.89898i 0.345547i
\(202\) 11.7362i 0.825757i
\(203\) −1.58258 3.87650i −0.111075 0.272077i
\(204\) 2.41742i 0.169254i
\(205\) 30.7477i 2.14751i
\(206\) 6.05630 0.421963
\(207\) 10.3303 0.718006
\(208\) 0.646084 0.0447979
\(209\) 3.23042 5.03383i 0.223453 0.348197i
\(210\) −2.00000 4.89898i −0.138013 0.338062i
\(211\) 16.7477i 1.15296i −0.817111 0.576481i \(-0.804426\pi\)
0.817111 0.576481i \(-0.195574\pi\)
\(212\) 11.5826 0.795495
\(213\) 1.29217i 0.0885379i
\(214\) 17.5826 1.20192
\(215\) 22.1803 1.51268
\(216\) −3.60681 −0.245412
\(217\) 8.64064 + 21.1652i 0.586565 + 1.43678i
\(218\) 17.1652 1.16257
\(219\) 10.4174i 0.703944i
\(220\) −8.64064 5.54506i −0.582552 0.373848i
\(221\) −2.41742 −0.162614
\(222\) 2.31464 0.155349
\(223\) 16.1240i 1.07974i −0.841749 0.539870i \(-0.818473\pi\)
0.841749 0.539870i \(-0.181527\pi\)
\(224\) 1.00000 + 2.44949i 0.0668153 + 0.163663i
\(225\) −11.8348 −0.788990
\(226\) 10.7477i 0.714928i
\(227\) −0.511238 −0.0339321 −0.0169660 0.999856i \(-0.505401\pi\)
−0.0169660 + 0.999856i \(0.505401\pi\)
\(228\) 1.16515i 0.0771640i
\(229\) 5.67991i 0.375339i 0.982232 + 0.187669i \(0.0600934\pi\)
−0.982232 + 0.187669i \(0.939907\pi\)
\(230\) 12.3823 0.816464
\(231\) 5.57475 + 1.03144i 0.366791 + 0.0678639i
\(232\) −1.58258 −0.103901
\(233\) 27.1652i 1.77965i 0.456304 + 0.889824i \(0.349173\pi\)
−0.456304 + 0.889824i \(0.650827\pi\)
\(234\) 1.66856i 0.109077i
\(235\) 30.7477 2.00576
\(236\) 0.646084i 0.0420565i
\(237\) 2.58434 0.167871
\(238\) −3.74166 9.16515i −0.242536 0.594089i
\(239\) 8.41742i 0.544478i 0.962230 + 0.272239i \(0.0877641\pi\)
−0.962230 + 0.272239i \(0.912236\pi\)
\(240\) −2.00000 −0.129099
\(241\) −3.47197 −0.223649 −0.111825 0.993728i \(-0.535669\pi\)
−0.111825 + 0.993728i \(0.535669\pi\)
\(242\) 10.0000 4.58258i 0.642824 0.294579i
\(243\) 14.3205i 0.918663i
\(244\) −1.93825 −0.124084
\(245\) −15.1652 15.4779i −0.968866 0.988845i
\(246\) −6.41742 −0.409160
\(247\) −1.16515 −0.0741368
\(248\) 8.64064 0.548681
\(249\) 8.33030i 0.527911i
\(250\) 1.29217 0.0817239
\(251\) 24.1185i 1.52235i −0.648549 0.761173i \(-0.724624\pi\)
0.648549 0.761173i \(-0.275376\pi\)
\(252\) −6.32599 + 2.58258i −0.398500 + 0.162687i
\(253\) −7.16515 + 11.1652i −0.450469 + 0.701947i
\(254\) −3.58258 −0.224791
\(255\) 7.48331 0.468623
\(256\) 1.00000 0.0625000
\(257\) 4.89898i 0.305590i 0.988258 + 0.152795i \(0.0488274\pi\)
−0.988258 + 0.152795i \(0.951173\pi\)
\(258\) 4.62929i 0.288207i
\(259\) 8.77548 3.58258i 0.545282 0.222610i
\(260\) 2.00000i 0.124035i
\(261\) 4.08712i 0.252986i
\(262\) 16.7700i 1.03606i
\(263\) 8.33030i 0.513668i 0.966455 + 0.256834i \(0.0826794\pi\)
−0.966455 + 0.256834i \(0.917321\pi\)
\(264\) 1.15732 1.80341i 0.0712283 0.110992i
\(265\) 35.8547i 2.20254i
\(266\) −1.80341 4.41742i −0.110574 0.270850i
\(267\) −6.33030 −0.387408
\(268\) 7.58258 0.463180
\(269\) 16.5003i 1.00604i 0.864274 + 0.503022i \(0.167778\pi\)
−0.864274 + 0.503022i \(0.832222\pi\)
\(270\) 11.1652i 0.679489i
\(271\) −4.89898 −0.297592 −0.148796 0.988868i \(-0.547540\pi\)
−0.148796 + 0.988868i \(0.547540\pi\)
\(272\) −3.74166 −0.226871
\(273\) −0.417424 1.02248i −0.0252637 0.0618831i
\(274\) 3.16515i 0.191214i
\(275\) 8.20871 12.7913i 0.495004 0.771344i
\(276\) 2.58434i 0.155559i
\(277\) 2.00000i 0.120168i −0.998193 0.0600842i \(-0.980863\pi\)
0.998193 0.0600842i \(-0.0191369\pi\)
\(278\) 15.4779i 0.928301i
\(279\) 22.3151i 1.33597i
\(280\) −7.58258 + 3.09557i −0.453146 + 0.184996i
\(281\) 11.1652i 0.666057i −0.942917 0.333029i \(-0.891929\pi\)
0.942917 0.333029i \(-0.108071\pi\)
\(282\) 6.41742i 0.382152i
\(283\) −18.0622 −1.07369 −0.536843 0.843682i \(-0.680383\pi\)
−0.536843 + 0.843682i \(0.680383\pi\)
\(284\) −2.00000 −0.118678
\(285\) 3.60681 0.213649
\(286\) −1.80341 1.15732i −0.106638 0.0684339i
\(287\) −24.3303 + 9.93280i −1.43617 + 0.586315i
\(288\) 2.58258i 0.152180i
\(289\) −3.00000 −0.176471
\(290\) 4.89898i 0.287678i
\(291\) 5.49545 0.322149
\(292\) −16.1240 −0.943583
\(293\) 25.1410 1.46875 0.734376 0.678743i \(-0.237475\pi\)
0.734376 + 0.678743i \(0.237475\pi\)
\(294\) 3.23042 3.16515i 0.188402 0.184595i
\(295\) 2.00000 0.116445
\(296\) 3.58258i 0.208233i
\(297\) 10.0677 + 6.46084i 0.584184 + 0.374896i
\(298\) −14.0000 −0.810998
\(299\) 2.58434 0.149456
\(300\) 2.96073i 0.170938i
\(301\) 7.16515 + 17.5510i 0.412992 + 1.01162i
\(302\) 5.58258 0.321241
\(303\) 7.58258i 0.435608i
\(304\) −1.80341 −0.103432
\(305\) 6.00000i 0.343559i
\(306\) 9.66311i 0.552403i
\(307\) −10.5789 −0.603769 −0.301885 0.953344i \(-0.597616\pi\)
−0.301885 + 0.953344i \(0.597616\pi\)
\(308\) 1.59645 8.62852i 0.0909664 0.491655i
\(309\) −3.91288 −0.222596
\(310\) 26.7477i 1.51917i
\(311\) 5.03383i 0.285442i −0.989763 0.142721i \(-0.954415\pi\)
0.989763 0.142721i \(-0.0455852\pi\)
\(312\) −0.417424 −0.0236320
\(313\) 23.4724i 1.32674i 0.748292 + 0.663370i \(0.230874\pi\)
−0.748292 + 0.663370i \(0.769126\pi\)
\(314\) −13.1632 −0.742844
\(315\) −7.99455 19.5826i −0.450442 1.10335i
\(316\) 4.00000i 0.225018i
\(317\) 9.16515 0.514766 0.257383 0.966309i \(-0.417140\pi\)
0.257383 + 0.966309i \(0.417140\pi\)
\(318\) −7.48331 −0.419643
\(319\) 4.41742 + 2.83485i 0.247328 + 0.158721i
\(320\) 3.09557i 0.173048i
\(321\) −11.3598 −0.634043
\(322\) 4.00000 + 9.79796i 0.222911 + 0.546019i
\(323\) 6.74773 0.375454
\(324\) −5.41742 −0.300968
\(325\) −2.96073 −0.164232
\(326\) 4.00000i 0.221540i
\(327\) −11.0901 −0.613285
\(328\) 9.93280i 0.548447i
\(329\) 9.93280 + 24.3303i 0.547613 + 1.34137i
\(330\) 5.58258 + 3.58258i 0.307311 + 0.197214i
\(331\) −23.5826 −1.29622 −0.648108 0.761549i \(-0.724439\pi\)
−0.648108 + 0.761549i \(0.724439\pi\)
\(332\) −12.8935 −0.707625
\(333\) 9.25227 0.507021
\(334\) 1.29217i 0.0707043i
\(335\) 23.4724i 1.28244i
\(336\) −0.646084 1.58258i −0.0352468 0.0863366i
\(337\) 10.8348i 0.590212i −0.955465 0.295106i \(-0.904645\pi\)
0.955465 0.295106i \(-0.0953549\pi\)
\(338\) 12.5826i 0.684402i
\(339\) 6.94393i 0.377143i
\(340\) 11.5826i 0.628153i
\(341\) −24.1185 15.4779i −1.30609 0.838174i
\(342\) 4.65743i 0.251845i
\(343\) 7.34847 17.0000i 0.396780 0.917914i
\(344\) 7.16515 0.386319
\(345\) −8.00000 −0.430706
\(346\) 10.7137i 0.575974i
\(347\) 19.1652i 1.02884i 0.857539 + 0.514420i \(0.171993\pi\)
−0.857539 + 0.514420i \(0.828007\pi\)
\(348\) 1.02248 0.0548105
\(349\) 24.1185 1.29103 0.645517 0.763746i \(-0.276642\pi\)
0.645517 + 0.763746i \(0.276642\pi\)
\(350\) −4.58258 11.2250i −0.244949 0.600000i
\(351\) 2.33030i 0.124382i
\(352\) −2.79129 1.79129i −0.148776 0.0954760i
\(353\) 7.48331i 0.398297i −0.979969 0.199148i \(-0.936182\pi\)
0.979969 0.199148i \(-0.0638176\pi\)
\(354\) 0.417424i 0.0221859i
\(355\) 6.19115i 0.328592i
\(356\) 9.79796i 0.519291i
\(357\) 2.41742 + 5.92146i 0.127944 + 0.313397i
\(358\) 11.1652i 0.590097i
\(359\) 9.58258i 0.505749i 0.967499 + 0.252875i \(0.0813760\pi\)
−0.967499 + 0.252875i \(0.918624\pi\)
\(360\) −7.99455 −0.421350
\(361\) −15.7477 −0.828828
\(362\) 5.41022 0.284355
\(363\) −6.46084 + 2.96073i −0.339106 + 0.155398i
\(364\) −1.58258 + 0.646084i −0.0829495 + 0.0338640i
\(365\) 49.9129i 2.61256i
\(366\) 1.25227 0.0654574
\(367\) 21.0229i 1.09739i −0.836023 0.548694i \(-0.815125\pi\)
0.836023 0.548694i \(-0.184875\pi\)
\(368\) 4.00000 0.208514
\(369\) −25.6522 −1.33540
\(370\) 11.0901 0.576548
\(371\) −28.3714 + 11.5826i −1.47297 + 0.601337i
\(372\) −5.58258 −0.289443
\(373\) 9.58258i 0.496167i −0.968739 0.248083i \(-0.920199\pi\)
0.968739 0.248083i \(-0.0798007\pi\)
\(374\) 10.4440 + 6.70239i 0.540049 + 0.346572i
\(375\) −0.834849 −0.0431114
\(376\) 9.93280 0.512245
\(377\) 1.02248i 0.0526602i
\(378\) 8.83485 3.60681i 0.454416 0.185514i
\(379\) −22.3303 −1.14703 −0.573515 0.819195i \(-0.694421\pi\)
−0.573515 + 0.819195i \(0.694421\pi\)
\(380\) 5.58258i 0.286380i
\(381\) 2.31464 0.118583
\(382\) 18.0000i 0.920960i
\(383\) 19.7308i 1.00819i −0.863647 0.504097i \(-0.831825\pi\)
0.863647 0.504097i \(-0.168175\pi\)
\(384\) −0.646084 −0.0329703
\(385\) 26.7102 + 4.94194i 1.36128 + 0.251865i
\(386\) 16.3303 0.831191
\(387\) 18.5045i 0.940639i
\(388\) 8.50579i 0.431816i
\(389\) 10.0000 0.507020 0.253510 0.967333i \(-0.418415\pi\)
0.253510 + 0.967333i \(0.418415\pi\)
\(390\) 1.29217i 0.0654315i
\(391\) −14.9666 −0.756895
\(392\) −4.89898 5.00000i −0.247436 0.252538i
\(393\) 10.8348i 0.546546i
\(394\) 8.74773 0.440704
\(395\) 12.3823 0.623021
\(396\) 4.62614 7.20871i 0.232472 0.362251i
\(397\) 27.5905i 1.38473i 0.721549 + 0.692363i \(0.243430\pi\)
−0.721549 + 0.692363i \(0.756570\pi\)
\(398\) −9.66311 −0.484368
\(399\) 1.16515 + 2.85403i 0.0583305 + 0.142880i
\(400\) −4.58258 −0.229129
\(401\) 7.58258 0.378656 0.189328 0.981914i \(-0.439369\pi\)
0.189328 + 0.981914i \(0.439369\pi\)
\(402\) −4.89898 −0.244339
\(403\) 5.58258i 0.278088i
\(404\) 11.7362 0.583898
\(405\) 16.7700i 0.833310i
\(406\) 3.87650 1.58258i 0.192388 0.0785419i
\(407\) −6.41742 + 10.0000i −0.318100 + 0.495682i
\(408\) 2.41742 0.119680
\(409\) −5.03383 −0.248907 −0.124453 0.992225i \(-0.539718\pi\)
−0.124453 + 0.992225i \(0.539718\pi\)
\(410\) −30.7477 −1.51852
\(411\) 2.04495i 0.100870i
\(412\) 6.05630i 0.298373i
\(413\) 0.646084 + 1.58258i 0.0317917 + 0.0778735i
\(414\) 10.3303i 0.507707i
\(415\) 39.9129i 1.95925i
\(416\) 0.646084i 0.0316769i
\(417\) 10.0000i 0.489702i
\(418\) 5.03383 + 3.23042i 0.246212 + 0.158005i
\(419\) 13.0284i 0.636478i −0.948011 0.318239i \(-0.896909\pi\)
0.948011 0.318239i \(-0.103091\pi\)
\(420\) 4.89898 2.00000i 0.239046 0.0975900i
\(421\) 7.58258 0.369552 0.184776 0.982781i \(-0.440844\pi\)
0.184776 + 0.982781i \(0.440844\pi\)
\(422\) 16.7477 0.815267
\(423\) 25.6522i 1.24725i
\(424\) 11.5826i 0.562500i
\(425\) 17.1464 0.831724
\(426\) 1.29217 0.0626057
\(427\) 4.74773 1.93825i 0.229759 0.0937986i
\(428\) 17.5826i 0.849886i
\(429\) 1.16515 + 0.747727i 0.0562540 + 0.0361006i
\(430\) 22.1803i 1.06963i
\(431\) 27.9129i 1.34452i 0.740317 + 0.672258i \(0.234675\pi\)
−0.740317 + 0.672258i \(0.765325\pi\)
\(432\) 3.60681i 0.173533i
\(433\) 35.5850i 1.71011i −0.518540 0.855054i \(-0.673524\pi\)
0.518540 0.855054i \(-0.326476\pi\)
\(434\) −21.1652 + 8.64064i −1.01596 + 0.414764i
\(435\) 3.16515i 0.151757i
\(436\) 17.1652i 0.822062i
\(437\) −7.21362 −0.345074
\(438\) 10.4174 0.497764
\(439\) 17.2813 0.824790 0.412395 0.911005i \(-0.364692\pi\)
0.412395 + 0.911005i \(0.364692\pi\)
\(440\) 5.54506 8.64064i 0.264351 0.411926i
\(441\) 12.9129 12.6520i 0.614899 0.602475i
\(442\) 2.41742i 0.114985i
\(443\) 15.1652 0.720518 0.360259 0.932852i \(-0.382688\pi\)
0.360259 + 0.932852i \(0.382688\pi\)
\(444\) 2.31464i 0.109848i
\(445\) −30.3303 −1.43779
\(446\) 16.1240 0.763491
\(447\) 9.04517 0.427822
\(448\) −2.44949 + 1.00000i −0.115728 + 0.0472456i
\(449\) 31.1652 1.47077 0.735387 0.677647i \(-0.237000\pi\)
0.735387 + 0.677647i \(0.237000\pi\)
\(450\) 11.8348i 0.557900i
\(451\) 17.7925 27.7253i 0.837817 1.30553i
\(452\) −10.7477 −0.505531
\(453\) −3.60681 −0.169463
\(454\) 0.511238i 0.0239936i
\(455\) −2.00000 4.89898i −0.0937614 0.229668i
\(456\) 1.16515 0.0545632
\(457\) 33.1652i 1.55140i −0.631102 0.775700i \(-0.717397\pi\)
0.631102 0.775700i \(-0.282603\pi\)
\(458\) −5.67991 −0.265405
\(459\) 13.4955i 0.629914i
\(460\) 12.3823i 0.577327i
\(461\) 30.0400 1.39910 0.699550 0.714583i \(-0.253384\pi\)
0.699550 + 0.714583i \(0.253384\pi\)
\(462\) −1.03144 + 5.57475i −0.0479871 + 0.259361i
\(463\) 5.16515 0.240045 0.120022 0.992771i \(-0.461703\pi\)
0.120022 + 0.992771i \(0.461703\pi\)
\(464\) 1.58258i 0.0734692i
\(465\) 17.2813i 0.801400i
\(466\) −27.1652 −1.25840
\(467\) 11.7362i 0.543087i 0.962426 + 0.271544i \(0.0875341\pi\)
−0.962426 + 0.271544i \(0.912466\pi\)
\(468\) −1.66856 −0.0771292
\(469\) −18.5734 + 7.58258i −0.857642 + 0.350131i
\(470\) 30.7477i 1.41829i
\(471\) 8.50455 0.391869
\(472\) 0.646084 0.0297384
\(473\) −20.0000 12.8348i −0.919601 0.590147i
\(474\) 2.58434i 0.118702i
\(475\) 8.26424 0.379190
\(476\) 9.16515 3.74166i 0.420084 0.171499i
\(477\) −29.9129 −1.36962
\(478\) −8.41742 −0.385004
\(479\) 30.9557 1.41440 0.707202 0.707012i \(-0.249957\pi\)
0.707202 + 0.707012i \(0.249957\pi\)
\(480\) 2.00000i 0.0912871i
\(481\) 2.31464 0.105539
\(482\) 3.47197i 0.158144i
\(483\) −2.58434 6.33030i −0.117591 0.288039i
\(484\) 4.58258 + 10.0000i 0.208299 + 0.454545i
\(485\) 26.3303 1.19560
\(486\) 14.3205 0.649593
\(487\) 21.4955 0.974052 0.487026 0.873387i \(-0.338082\pi\)
0.487026 + 0.873387i \(0.338082\pi\)
\(488\) 1.93825i 0.0877405i
\(489\) 2.58434i 0.116868i
\(490\) 15.4779 15.1652i 0.699219 0.685092i
\(491\) 33.4955i 1.51163i −0.654786 0.755814i \(-0.727241\pi\)
0.654786 0.755814i \(-0.272759\pi\)
\(492\) 6.41742i 0.289320i
\(493\) 5.92146i 0.266689i
\(494\) 1.16515i 0.0524226i
\(495\) 22.3151 + 14.3205i 1.00299 + 0.643661i
\(496\) 8.64064i 0.387976i
\(497\) 4.89898 2.00000i 0.219749 0.0897123i
\(498\) 8.33030 0.373290
\(499\) −17.9129 −0.801891 −0.400945 0.916102i \(-0.631318\pi\)
−0.400945 + 0.916102i \(0.631318\pi\)
\(500\) 1.29217i 0.0577875i
\(501\) 0.834849i 0.0372983i
\(502\) 24.1185 1.07646
\(503\) −17.0116 −0.758509 −0.379254 0.925292i \(-0.623820\pi\)
−0.379254 + 0.925292i \(0.623820\pi\)
\(504\) −2.58258 6.32599i −0.115037 0.281782i
\(505\) 36.3303i 1.61668i
\(506\) −11.1652 7.16515i −0.496352 0.318530i
\(507\) 8.12940i 0.361039i
\(508\) 3.58258i 0.158951i
\(509\) 0.780929i 0.0346141i −0.999850 0.0173070i \(-0.994491\pi\)
0.999850 0.0173070i \(-0.00550928\pi\)
\(510\) 7.48331i 0.331367i
\(511\) 39.4955 16.1240i 1.74718 0.713282i
\(512\) 1.00000i 0.0441942i
\(513\) 6.50455i 0.287183i
\(514\) −4.89898 −0.216085
\(515\) −18.7477 −0.826124
\(516\) −4.62929 −0.203793
\(517\) −27.7253 17.7925i −1.21936 0.782514i
\(518\) 3.58258 + 8.77548i 0.157409 + 0.385573i
\(519\) 6.92197i 0.303841i
\(520\) −2.00000 −0.0877058
\(521\) 28.1017i 1.23116i 0.788075 + 0.615579i \(0.211078\pi\)
−0.788075 + 0.615579i \(0.788922\pi\)
\(522\) 4.08712 0.178888
\(523\) −14.4554 −0.632090 −0.316045 0.948744i \(-0.602355\pi\)
−0.316045 + 0.948744i \(0.602355\pi\)
\(524\) 16.7700 0.732602
\(525\) 2.96073 + 7.25227i 0.129217 + 0.316515i
\(526\) −8.33030 −0.363218
\(527\) 32.3303i 1.40833i
\(528\) 1.80341 + 1.15732i 0.0784832 + 0.0503660i
\(529\) −7.00000 −0.304348
\(530\) −35.8547 −1.55743
\(531\) 1.66856i 0.0724094i
\(532\) 4.41742 1.80341i 0.191520 0.0781876i
\(533\) −6.41742 −0.277970
\(534\) 6.33030i 0.273939i
\(535\) −54.4282 −2.35313
\(536\) 7.58258i 0.327517i
\(537\) 7.21362i 0.311291i
\(538\) −16.5003 −0.711380
\(539\) 4.71802 + 22.7319i 0.203220 + 0.979133i
\(540\) 11.1652 0.480472
\(541\) 36.7477i 1.57991i 0.613166 + 0.789954i \(0.289896\pi\)
−0.613166 + 0.789954i \(0.710104\pi\)
\(542\) 4.89898i 0.210429i
\(543\) −3.49545 −0.150004
\(544\) 3.74166i 0.160422i
\(545\) −53.1360 −2.27610
\(546\) 1.02248 0.417424i 0.0437580 0.0178641i
\(547\) 24.7477i 1.05814i 0.848579 + 0.529068i \(0.177458\pi\)
−0.848579 + 0.529068i \(0.822542\pi\)
\(548\) 3.16515 0.135209
\(549\) 5.00568 0.213637
\(550\) 12.7913 + 8.20871i 0.545422 + 0.350021i
\(551\) 2.85403i 0.121586i
\(552\) −2.58434 −0.109997
\(553\) 4.00000 + 9.79796i 0.170097 + 0.416652i
\(554\) 2.00000 0.0849719
\(555\) −7.16515 −0.304144
\(556\) 15.4779 0.656408
\(557\) 35.9129i 1.52168i 0.648941 + 0.760839i \(0.275212\pi\)
−0.648941 + 0.760839i \(0.724788\pi\)
\(558\) −22.3151 −0.944673
\(559\) 4.62929i 0.195798i
\(560\) −3.09557 7.58258i −0.130812 0.320422i
\(561\) −6.74773 4.33030i −0.284889 0.182826i
\(562\) 11.1652 0.470973
\(563\) 23.7140 0.999425 0.499712 0.866191i \(-0.333439\pi\)
0.499712 + 0.866191i \(0.333439\pi\)
\(564\) −6.41742 −0.270222
\(565\) 33.2704i 1.39970i
\(566\) 18.0622i 0.759211i
\(567\) 13.2699 5.41742i 0.557284 0.227510i
\(568\) 2.00000i 0.0839181i
\(569\) 39.4955i 1.65574i −0.560923 0.827868i \(-0.689554\pi\)
0.560923 0.827868i \(-0.310446\pi\)
\(570\) 3.60681i 0.151073i
\(571\) 5.58258i 0.233624i 0.993154 + 0.116812i \(0.0372674\pi\)
−0.993154 + 0.116812i \(0.962733\pi\)
\(572\) 1.15732 1.80341i 0.0483901 0.0754042i
\(573\) 11.6295i 0.485830i
\(574\) −9.93280 24.3303i −0.414587 1.01553i
\(575\) −18.3303 −0.764426
\(576\) −2.58258 −0.107607
\(577\) 29.6636i 1.23491i −0.786606 0.617455i \(-0.788164\pi\)
0.786606 0.617455i \(-0.211836\pi\)
\(578\) 3.00000i 0.124784i
\(579\) −10.5507 −0.438474
\(580\) 4.89898 0.203419
\(581\) 31.5826 12.8935i 1.31027 0.534914i
\(582\) 5.49545i 0.227794i
\(583\) 20.7477 32.3303i 0.859283 1.33898i
\(584\) 16.1240i 0.667214i
\(585\) 5.16515i 0.213553i
\(586\) 25.1410i 1.03856i
\(587\) 39.0851i 1.61322i 0.591087 + 0.806608i \(0.298699\pi\)
−0.591087 + 0.806608i \(0.701301\pi\)
\(588\) 3.16515 + 3.23042i 0.130529 + 0.133220i
\(589\) 15.5826i 0.642069i
\(590\) 2.00000i 0.0823387i
\(591\) −5.65176 −0.232483
\(592\) 3.58258 0.147243
\(593\) −14.8318 −0.609068 −0.304534 0.952501i \(-0.598501\pi\)
−0.304534 + 0.952501i \(0.598501\pi\)
\(594\) −6.46084 + 10.0677i −0.265091 + 0.413081i
\(595\) 11.5826 + 28.3714i 0.474839 + 1.16311i
\(596\) 14.0000i 0.573462i
\(597\) 6.24318 0.255516
\(598\) 2.58434i 0.105681i
\(599\) −21.1652 −0.864785 −0.432392 0.901686i \(-0.642330\pi\)
−0.432392 + 0.901686i \(0.642330\pi\)
\(600\) 2.96073 0.120871
\(601\) 21.0229 0.857543 0.428772 0.903413i \(-0.358947\pi\)
0.428772 + 0.903413i \(0.358947\pi\)
\(602\) −17.5510 + 7.16515i −0.715324 + 0.292030i
\(603\) −19.5826 −0.797464
\(604\) 5.58258i 0.227152i
\(605\) −30.9557 + 14.1857i −1.25853 + 0.576731i
\(606\) −7.58258 −0.308021
\(607\) 2.04495 0.0830021 0.0415010 0.999138i \(-0.486786\pi\)
0.0415010 + 0.999138i \(0.486786\pi\)
\(608\) 1.80341i 0.0731378i
\(609\) −2.50455 + 1.02248i −0.101489 + 0.0414328i
\(610\) 6.00000 0.242933
\(611\) 6.41742i 0.259621i
\(612\) 9.66311 0.390608
\(613\) 31.9129i 1.28895i −0.764626 0.644475i \(-0.777076\pi\)
0.764626 0.644475i \(-0.222924\pi\)
\(614\) 10.5789i 0.426929i
\(615\) 19.8656 0.801059
\(616\) 8.62852 + 1.59645i 0.347653 + 0.0643229i
\(617\) −19.9129 −0.801662 −0.400831 0.916152i \(-0.631279\pi\)
−0.400831 + 0.916152i \(0.631279\pi\)
\(618\) 3.91288i 0.157399i
\(619\) 17.9274i 0.720561i 0.932844 + 0.360281i \(0.117319\pi\)
−0.932844 + 0.360281i \(0.882681\pi\)
\(620\) −26.7477 −1.07421
\(621\) 14.4272i 0.578945i
\(622\) 5.03383 0.201838
\(623\) −9.79796 24.0000i −0.392547 0.961540i
\(624\) 0.417424i 0.0167103i
\(625\) −26.9129 −1.07652
\(626\) −23.4724 −0.938147
\(627\) −3.25227 2.08712i −0.129883 0.0833516i
\(628\) 13.1632i 0.525270i
\(629\) −13.4048 −0.534483
\(630\) 19.5826 7.99455i 0.780188 0.318511i
\(631\) 13.1652 0.524096 0.262048 0.965055i \(-0.415602\pi\)
0.262048 + 0.965055i \(0.415602\pi\)
\(632\) 4.00000 0.159111
\(633\) −10.8204 −0.430074
\(634\) 9.16515i 0.363995i
\(635\) 11.0901 0.440098
\(636\) 7.48331i 0.296733i
\(637\) 3.23042 3.16515i 0.127994 0.125408i
\(638\) −2.83485 + 4.41742i −0.112233 + 0.174888i
\(639\) 5.16515 0.204330
\(640\) −3.09557 −0.122363
\(641\) −15.9129 −0.628521 −0.314260 0.949337i \(-0.601757\pi\)
−0.314260 + 0.949337i \(0.601757\pi\)
\(642\) 11.3598i 0.448336i
\(643\) 9.42157i 0.371550i 0.982592 + 0.185775i \(0.0594796\pi\)
−0.982592 + 0.185775i \(0.940520\pi\)
\(644\) −9.79796 + 4.00000i −0.386094 + 0.157622i
\(645\) 14.3303i 0.564255i
\(646\) 6.74773i 0.265486i
\(647\) 30.0681i 1.18210i 0.806635 + 0.591050i \(0.201286\pi\)
−0.806635 + 0.591050i \(0.798714\pi\)
\(648\) 5.41742i 0.212817i
\(649\) −1.80341 1.15732i −0.0707899 0.0454289i
\(650\) 2.96073i 0.116129i
\(651\) 13.6745 5.58258i 0.535944 0.218798i
\(652\) −4.00000 −0.156652
\(653\) −6.00000 −0.234798 −0.117399 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) 11.0901i 0.433658i
\(655\) 51.9129i 2.02840i
\(656\) −9.93280 −0.387811
\(657\) 41.6413 1.62458
\(658\) −24.3303 + 9.93280i −0.948494 + 0.387221i
\(659\) 6.33030i 0.246594i 0.992370 + 0.123297i \(0.0393467\pi\)
−0.992370 + 0.123297i \(0.960653\pi\)
\(660\) −3.58258 + 5.58258i −0.139452 + 0.217301i
\(661\) 8.26424i 0.321442i −0.987000 0.160721i \(-0.948618\pi\)
0.987000 0.160721i \(-0.0513819\pi\)
\(662\) 23.5826i 0.916563i
\(663\) 1.56186i 0.0606576i
\(664\) 12.8935i 0.500366i
\(665\) 5.58258 + 13.6745i 0.216483 + 0.530273i
\(666\) 9.25227i 0.358518i
\(667\) 6.33030i 0.245110i
\(668\) −1.29217 −0.0499955
\(669\) −10.4174 −0.402761
\(670\) −23.4724 −0.906819
\(671\) −3.47197 + 5.41022i −0.134034 + 0.208859i
\(672\) 1.58258 0.646084i 0.0610492 0.0249232i
\(673\) 18.3303i 0.706581i 0.935514 + 0.353291i \(0.114937\pi\)
−0.935514 + 0.353291i \(0.885063\pi\)
\(674\) 10.8348 0.417343
\(675\) 16.5285i 0.636182i
\(676\) 12.5826 0.483945
\(677\) 5.27537 0.202749 0.101375 0.994848i \(-0.467676\pi\)
0.101375 + 0.994848i \(0.467676\pi\)
\(678\) 6.94393 0.266680
\(679\) 8.50579 + 20.8348i 0.326422 + 0.799568i
\(680\) 11.5826 0.444172
\(681\) 0.330303i 0.0126572i
\(682\) 15.4779 24.1185i 0.592678 0.923545i
\(683\) −9.49545 −0.363333 −0.181667 0.983360i \(-0.558149\pi\)
−0.181667 + 0.983360i \(0.558149\pi\)
\(684\) 4.65743 0.178081
\(685\) 9.79796i 0.374361i
\(686\) 17.0000 + 7.34847i 0.649063 + 0.280566i
\(687\) 3.66970 0.140008
\(688\) 7.16515i 0.273169i
\(689\) −7.48331 −0.285092
\(690\) 8.00000i 0.304555i
\(691\) 3.98320i 0.151528i 0.997126 + 0.0757641i \(0.0241396\pi\)
−0.997126 + 0.0757641i \(0.975860\pi\)
\(692\) −10.7137 −0.407275
\(693\) −4.12296 + 22.2838i −0.156618 + 0.846492i
\(694\) −19.1652 −0.727499
\(695\) 47.9129i 1.81744i
\(696\) 1.02248i 0.0387569i
\(697\) 37.1652 1.40773
\(698\) 24.1185i 0.912899i
\(699\) 17.5510 0.663838
\(700\) 11.2250 4.58258i 0.424264 0.173205i
\(701\) 12.3303i 0.465709i −0.972512 0.232855i \(-0.925193\pi\)
0.972512 0.232855i \(-0.0748066\pi\)
\(702\) 2.33030 0.0879516
\(703\) −6.46084 −0.243675
\(704\) 1.79129 2.79129i 0.0675117 0.105201i
\(705\) 19.8656i 0.748182i
\(706\) 7.48331 0.281638
\(707\) −28.7477 + 11.7362i −1.08117 + 0.441386i
\(708\) −0.417424 −0.0156878
\(709\) 52.3303 1.96531 0.982653 0.185454i \(-0.0593757\pi\)
0.982653 + 0.185454i \(0.0593757\pi\)
\(710\) 6.19115 0.232350
\(711\) 10.3303i 0.387417i
\(712\) −9.79796 −0.367194
\(713\) 34.5625i 1.29438i
\(714\) −5.92146 + 2.41742i −0.221605 + 0.0904698i
\(715\) 5.58258 + 3.58258i 0.208776 + 0.133981i
\(716\) −11.1652 −0.417261
\(717\) 5.43836 0.203099
\(718\) −9.58258 −0.357619
\(719\) 23.3376i 0.870345i 0.900347 + 0.435172i \(0.143313\pi\)
−0.900347 + 0.435172i \(0.856687\pi\)
\(720\) 7.99455i 0.297939i
\(721\) −6.05630 14.8348i −0.225548 0.552479i
\(722\) 15.7477i 0.586070i
\(723\) 2.24318i 0.0834248i
\(724\) 5.41022i 0.201069i
\(725\) 7.25227i 0.269343i
\(726\) −2.96073 6.46084i −0.109883 0.239784i
\(727\) 37.5514i 1.39271i −0.717700 0.696353i \(-0.754805\pi\)
0.717700 0.696353i \(-0.245195\pi\)
\(728\) −0.646084 1.58258i −0.0239455 0.0586542i
\(729\) 7.00000 0.259259
\(730\) 49.9129 1.84736
\(731\) 26.8095i 0.991587i
\(732\) 1.25227i 0.0462853i
\(733\) 10.7137 0.395721 0.197860 0.980230i \(-0.436601\pi\)
0.197860 + 0.980230i \(0.436601\pi\)
\(734\) 21.0229 0.775971
\(735\) −10.0000 + 9.79796i −0.368856 + 0.361403i
\(736\) 4.00000i 0.147442i
\(737\) 13.5826 21.1652i 0.500321 0.779628i
\(738\) 25.6522i 0.944271i
\(739\) 1.58258i 0.0582160i −0.999576 0.0291080i \(-0.990733\pi\)
0.999576 0.0291080i \(-0.00926667\pi\)
\(740\) 11.0901i 0.407681i
\(741\) 0.752785i 0.0276543i
\(742\) −11.5826 28.3714i −0.425210 1.04155i
\(743\) 1.91288i 0.0701767i −0.999384 0.0350884i \(-0.988829\pi\)
0.999384 0.0350884i \(-0.0111713\pi\)
\(744\) 5.58258i 0.204667i
\(745\) 43.3380 1.58778
\(746\) 9.58258 0.350843
\(747\) 33.2985 1.21833
\(748\) −6.70239 + 10.4440i −0.245063 + 0.381872i
\(749\) −17.5826 43.0683i −0.642453 1.57368i
\(750\) 0.834849i 0.0304844i
\(751\) −41.4955 −1.51419 −0.757095 0.653304i \(-0.773382\pi\)
−0.757095 + 0.653304i \(0.773382\pi\)
\(752\) 9.93280i 0.362212i
\(753\) −15.5826 −0.567861
\(754\) 1.02248 0.0372364
\(755\) −17.2813 −0.628930
\(756\) 3.60681 + 8.83485i 0.131178 + 0.321320i
\(757\) −30.8348 −1.12071 −0.560356 0.828252i \(-0.689336\pi\)
−0.560356 + 0.828252i \(0.689336\pi\)
\(758\) 22.3303i 0.811073i
\(759\) 7.21362 + 4.62929i 0.261838 + 0.168033i
\(760\) 5.58258 0.202501
\(761\) 28.2366 1.02357 0.511787 0.859112i \(-0.328984\pi\)
0.511787 + 0.859112i \(0.328984\pi\)
\(762\) 2.31464i 0.0838507i
\(763\) −17.1652 42.0459i −0.621420 1.52216i
\(764\) 18.0000 0.651217
\(765\) 29.9129i 1.08150i
\(766\) 19.7308 0.712901
\(767\) 0.417424i 0.0150723i
\(768\) 0.646084i 0.0233135i
\(769\) −15.1015 −0.544573 −0.272287 0.962216i \(-0.587780\pi\)
−0.272287 + 0.962216i \(0.587780\pi\)
\(770\) −4.94194 + 26.7102i −0.178095 + 0.962569i
\(771\) 3.16515 0.113990
\(772\) 16.3303i 0.587740i
\(773\) 10.0395i 0.361096i −0.983566 0.180548i \(-0.942213\pi\)
0.983566 0.180548i \(-0.0577871\pi\)
\(774\) −18.5045 −0.665132
\(775\) 39.5964i 1.42234i
\(776\) 8.50579 0.305340
\(777\) −2.31464 5.66970i −0.0830374 0.203399i
\(778\) 10.0000i 0.358517i
\(779\) 17.9129 0.641795
\(780\) 1.29217 0.0462670
\(781\) −3.58258 + 5.58258i −0.128195 + 0.199760i
\(782\) 14.9666i 0.535206i
\(783\) −5.70805 −0.203989
\(784\) 5.00000 4.89898i 0.178571 0.174964i
\(785\) 40.7477 1.45435
\(786\) −10.8348 −0.386466