Properties

Label 154.2.c.a.153.1
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 153.1
Root \(-1.54779 + 1.54779i\) of defining polynomial
Character \(\chi\) \(=\) 154.153
Dual form 154.2.c.a.153.8

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -3.09557i q^{3} -1.00000 q^{4} -0.646084i q^{5} -3.09557 q^{6} +(2.44949 + 1.00000i) q^{7} +1.00000i q^{8} -6.58258 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -3.09557i q^{3} -1.00000 q^{4} -0.646084i q^{5} -3.09557 q^{6} +(2.44949 + 1.00000i) q^{7} +1.00000i q^{8} -6.58258 q^{9} -0.646084 q^{10} +(2.79129 + 1.79129i) q^{11} +3.09557i q^{12} -3.09557 q^{13} +(1.00000 - 2.44949i) q^{14} -2.00000 q^{15} +1.00000 q^{16} +3.74166 q^{17} +6.58258i q^{18} -5.54506 q^{19} +0.646084i q^{20} +(3.09557 - 7.58258i) q^{21} +(1.79129 - 2.79129i) q^{22} +4.00000 q^{23} +3.09557 q^{24} +4.58258 q^{25} +3.09557i q^{26} +11.0901i q^{27} +(-2.44949 - 1.00000i) q^{28} -7.58258i q^{29} +2.00000i q^{30} -1.15732i q^{31} -1.00000i q^{32} +(5.54506 - 8.64064i) q^{33} -3.74166i q^{34} +(0.646084 - 1.58258i) q^{35} +6.58258 q^{36} -5.58258 q^{37} +5.54506i q^{38} +9.58258i q^{39} +0.646084 q^{40} +5.03383 q^{41} +(-7.58258 - 3.09557i) q^{42} +11.1652i q^{43} +(-2.79129 - 1.79129i) q^{44} +4.25290i q^{45} -4.00000i q^{46} +5.03383i q^{47} -3.09557i q^{48} +(5.00000 + 4.89898i) q^{49} -4.58258i q^{50} -11.5826i q^{51} +3.09557 q^{52} -2.41742 q^{53} +11.0901 q^{54} +(1.15732 - 1.80341i) q^{55} +(-1.00000 + 2.44949i) q^{56} +17.1652i q^{57} -7.58258 q^{58} +3.09557i q^{59} +2.00000 q^{60} -9.28672 q^{61} -1.15732 q^{62} +(-16.1240 - 6.58258i) q^{63} -1.00000 q^{64} +2.00000i q^{65} +(-8.64064 - 5.54506i) q^{66} +1.58258 q^{67} -3.74166 q^{68} -12.3823i q^{69} +(-1.58258 - 0.646084i) q^{70} +2.00000 q^{71} -6.58258i q^{72} -6.32599 q^{73} +5.58258i q^{74} -14.1857i q^{75} +5.54506 q^{76} +(5.04594 + 7.17903i) q^{77} +9.58258 q^{78} -4.00000i q^{79} -0.646084i q^{80} +14.5826 q^{81} -5.03383i q^{82} +9.15188 q^{83} +(-3.09557 + 7.58258i) q^{84} -2.41742i q^{85} +11.1652 q^{86} -23.4724 q^{87} +(-1.79129 + 2.79129i) q^{88} +9.79796i q^{89} +4.25290 q^{90} +(-7.58258 - 3.09557i) q^{91} -4.00000 q^{92} -3.58258 q^{93} +5.03383 q^{94} +3.58258i q^{95} -3.09557 q^{96} -15.9891i q^{97} +(4.89898 - 5.00000i) q^{98} +(-18.3739 - 11.7913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4} - 16 q^{9}+O(q^{10}) \) 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
\(3\) 3.09557i 1.78723i −0.448834 0.893615i \(-0.648161\pi\)
0.448834 0.893615i \(-0.351839\pi\)
\(4\) −1.00000 −0.500000
\(5\) 0.646084i 0.288937i −0.989509 0.144469i \(-0.953853\pi\)
0.989509 0.144469i \(-0.0461473\pi\)
\(6\) −3.09557 −1.26376
\(7\) 2.44949 + 1.00000i 0.925820 + 0.377964i
\(8\) 1.00000i 0.353553i
\(9\) −6.58258 −2.19419
\(10\) −0.646084 −0.204310
\(11\) 2.79129 + 1.79129i 0.841605 + 0.540094i
\(12\) 3.09557i 0.893615i
\(13\) −3.09557 −0.858558 −0.429279 0.903172i \(-0.641232\pi\)
−0.429279 + 0.903172i \(0.641232\pi\)
\(14\) 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 \(-0.350089\pi\)
0.453743 + 0.891133i \(0.350089\pi\)
\(18\) 6.58258i 1.55153i
\(19\) −5.54506 −1.27212 −0.636062 0.771638i \(-0.719438\pi\)
−0.636062 + 0.771638i \(0.719438\pi\)
\(20\) 0.646084i 0.144469i
\(21\) 3.09557 7.58258i 0.675510 1.65465i
\(22\) 1.79129 2.79129i 0.381904 0.595105i
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 3.09557 0.631881
\(25\) 4.58258 0.916515
\(26\) 3.09557i 0.607092i
\(27\) 11.0901i 2.13430i
\(28\) −2.44949 1.00000i −0.462910 0.188982i
\(29\) 7.58258i 1.40805i −0.710176 0.704024i \(-0.751385\pi\)
0.710176 0.704024i \(-0.248615\pi\)
\(30\) 2.00000i 0.365148i
\(31\) 1.15732i 0.207861i −0.994585 0.103931i \(-0.966858\pi\)
0.994585 0.103931i \(-0.0331420\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 5.54506 8.64064i 0.965272 1.50414i
\(34\) 3.74166i 0.641689i
\(35\) 0.646084 1.58258i 0.109208 0.267504i
\(36\) 6.58258 1.09710
\(37\) −5.58258 −0.917770 −0.458885 0.888496i \(-0.651751\pi\)
−0.458885 + 0.888496i \(0.651751\pi\)
\(38\) 5.54506i 0.899528i
\(39\) 9.58258i 1.53444i
\(40\) 0.646084 0.102155
\(41\) 5.03383 0.786151 0.393076 0.919506i \(-0.371411\pi\)
0.393076 + 0.919506i \(0.371411\pi\)
\(42\) −7.58258 3.09557i −1.17002 0.477657i
\(43\) 11.1652i 1.70267i 0.524623 + 0.851335i \(0.324206\pi\)
−0.524623 + 0.851335i \(0.675794\pi\)
\(44\) −2.79129 1.79129i −0.420802 0.270047i
\(45\) 4.25290i 0.633984i
\(46\) 4.00000i 0.589768i
\(47\) 5.03383i 0.734259i 0.930170 + 0.367129i \(0.119659\pi\)
−0.930170 + 0.367129i \(0.880341\pi\)
\(48\) 3.09557i 0.446808i
\(49\) 5.00000 + 4.89898i 0.714286 + 0.699854i
\(50\) 4.58258i 0.648074i
\(51\) 11.5826i 1.62189i
\(52\) 3.09557 0.429279
\(53\) −2.41742 −0.332059 −0.166029 0.986121i \(-0.553095\pi\)
−0.166029 + 0.986121i \(0.553095\pi\)
\(54\) 11.0901 1.50918
\(55\) 1.15732 1.80341i 0.156053 0.243171i
\(56\) −1.00000 + 2.44949i −0.133631 + 0.327327i
\(57\) 17.1652i 2.27358i
\(58\) −7.58258 −0.995641
\(59\) 3.09557i 0.403009i 0.979488 + 0.201505i \(0.0645831\pi\)
−0.979488 + 0.201505i \(0.935417\pi\)
\(60\) 2.00000 0.258199
\(61\) −9.28672 −1.18904 −0.594521 0.804080i \(-0.702658\pi\)
−0.594521 + 0.804080i \(0.702658\pi\)
\(62\) −1.15732 −0.146980
\(63\) −16.1240 6.58258i −2.03143 0.829327i
\(64\) −1.00000 −0.125000
\(65\) 2.00000i 0.248069i
\(66\) −8.64064 5.54506i −1.06359 0.682550i
\(67\) 1.58258 0.193342 0.0966712 0.995316i \(-0.469180\pi\)
0.0966712 + 0.995316i \(0.469180\pi\)
\(68\) −3.74166 −0.453743
\(69\) 12.3823i 1.49065i
\(70\) −1.58258 0.646084i −0.189154 0.0772218i
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 6.58258i 0.775764i
\(73\) −6.32599 −0.740401 −0.370201 0.928952i \(-0.620711\pi\)
−0.370201 + 0.928952i \(0.620711\pi\)
\(74\) 5.58258i 0.648961i
\(75\) 14.1857i 1.63802i
\(76\) 5.54506 0.636062
\(77\) 5.04594 + 7.17903i 0.575039 + 0.818126i
\(78\) 9.58258 1.08501
\(79\) 4.00000i 0.450035i −0.974355 0.225018i \(-0.927756\pi\)
0.974355 0.225018i \(-0.0722440\pi\)
\(80\) 0.646084i 0.0722344i
\(81\) 14.5826 1.62029
\(82\) 5.03383i 0.555893i
\(83\) 9.15188 1.00455 0.502274 0.864708i \(-0.332497\pi\)
0.502274 + 0.864708i \(0.332497\pi\)
\(84\) −3.09557 + 7.58258i −0.337755 + 0.827327i
\(85\) 2.41742i 0.262206i
\(86\) 11.1652 1.20397
\(87\) −23.4724 −2.51651
\(88\) −1.79129 + 2.79129i −0.190952 + 0.297552i
\(89\) 9.79796i 1.03858i 0.854598 + 0.519291i \(0.173804\pi\)
−0.854598 + 0.519291i \(0.826196\pi\)
\(90\) 4.25290 0.448295
\(91\) −7.58258 3.09557i −0.794870 0.324504i
\(92\) −4.00000 −0.417029
\(93\) −3.58258 −0.371496
\(94\) 5.03383 0.519199
\(95\) 3.58258i 0.367565i
\(96\) −3.09557 −0.315941
\(97\) 15.9891i 1.62345i −0.584041 0.811724i \(-0.698529\pi\)
0.584041 0.811724i \(-0.301471\pi\)
\(98\) 4.89898 5.00000i 0.494872 0.505076i
\(99\) −18.3739 11.7913i −1.84664 1.18507i
\(100\) −4.58258 −0.458258
\(101\) −0.511238 −0.0508701 −0.0254351 0.999676i \(-0.508097\pi\)
−0.0254351 + 0.999676i \(0.508097\pi\)
\(102\) −11.5826 −1.14685
\(103\) 13.5396i 1.33410i 0.745014 + 0.667049i \(0.232443\pi\)
−0.745014 + 0.667049i \(0.767557\pi\)
\(104\) 3.09557i 0.303546i
\(105\) −4.89898 2.00000i −0.478091 0.195180i
\(106\) 2.41742i 0.234801i
\(107\) 8.41742i 0.813743i 0.913485 + 0.406872i \(0.133380\pi\)
−0.913485 + 0.406872i \(0.866620\pi\)
\(108\) 11.0901i 1.06715i
\(109\) 1.16515i 0.111601i −0.998442 0.0558006i \(-0.982229\pi\)
0.998442 0.0558006i \(-0.0177711\pi\)
\(110\) −1.80341 1.15732i −0.171948 0.110346i
\(111\) 17.2813i 1.64027i
\(112\) 2.44949 + 1.00000i 0.231455 + 0.0944911i
\(113\) −16.7477 −1.57549 −0.787747 0.615999i \(-0.788752\pi\)
−0.787747 + 0.615999i \(0.788752\pi\)
\(114\) 17.1652 1.60766
\(115\) 2.58434i 0.240991i
\(116\) 7.58258i 0.704024i
\(117\) 20.3768 1.88384
\(118\) 3.09557 0.284971
\(119\) 9.16515 + 3.74166i 0.840168 + 0.342997i
\(120\) 2.00000i 0.182574i
\(121\) 4.58258 + 10.0000i 0.416598 + 0.909091i
\(122\) 9.28672i 0.840780i
\(123\) 15.5826i 1.40503i
\(124\) 1.15732i 0.103931i
\(125\) 6.19115i 0.553753i
\(126\) −6.58258 + 16.1240i −0.586422 + 1.43644i
\(127\) 5.58258i 0.495373i 0.968840 + 0.247687i \(0.0796704\pi\)
−0.968840 + 0.247687i \(0.920330\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 34.5625 3.04306
\(130\) 2.00000 0.175412
\(131\) 9.42157 0.823166 0.411583 0.911372i \(-0.364976\pi\)
0.411583 + 0.911372i \(0.364976\pi\)
\(132\) −5.54506 + 8.64064i −0.482636 + 0.752071i
\(133\) −13.5826 5.54506i −1.17776 0.480818i
\(134\) 1.58258i 0.136714i
\(135\) 7.16515 0.616678
\(136\) 3.74166i 0.320844i
\(137\) 15.1652 1.29565 0.647823 0.761791i \(-0.275680\pi\)
0.647823 + 0.761791i \(0.275680\pi\)
\(138\) −12.3823 −1.05405
\(139\) 3.23042 0.274001 0.137000 0.990571i \(-0.456254\pi\)
0.137000 + 0.990571i \(0.456254\pi\)
\(140\) −0.646084 + 1.58258i −0.0546040 + 0.133752i
\(141\) 15.5826 1.31229
\(142\) 2.00000i 0.167836i
\(143\) −8.64064 5.54506i −0.722566 0.463701i
\(144\) −6.58258 −0.548548
\(145\) −4.89898 −0.406838
\(146\) 6.32599i 0.523543i
\(147\) 15.1652 15.4779i 1.25080 1.27659i
\(148\) 5.58258 0.458885
\(149\) 14.0000i 1.14692i −0.819232 0.573462i \(-0.805600\pi\)
0.819232 0.573462i \(-0.194400\pi\)
\(150\) −14.1857 −1.15826
\(151\) 3.58258i 0.291546i −0.989318 0.145773i \(-0.953433\pi\)
0.989318 0.145773i \(-0.0465669\pi\)
\(152\) 5.54506i 0.449764i
\(153\) −24.6297 −1.99120
\(154\) 7.17903 5.04594i 0.578503 0.406614i
\(155\) −0.747727 −0.0600589
\(156\) 9.58258i 0.767220i
\(157\) 20.5117i 1.63701i 0.574498 + 0.818506i \(0.305197\pi\)
−0.574498 + 0.818506i \(0.694803\pi\)
\(158\) −4.00000 −0.318223
\(159\) 7.48331i 0.593465i
\(160\) −0.646084 −0.0510774
\(161\) 9.79796 + 4.00000i 0.772187 + 0.315244i
\(162\) 14.5826i 1.14572i
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) −5.03383 −0.393076
\(165\) −5.58258 3.58258i −0.434603 0.278903i
\(166\) 9.15188i 0.710323i
\(167\) −6.19115 −0.479085 −0.239543 0.970886i \(-0.576998\pi\)
−0.239543 + 0.970886i \(0.576998\pi\)
\(168\) 7.58258 + 3.09557i 0.585008 + 0.238829i
\(169\) −3.41742 −0.262879
\(170\) −2.41742 −0.185408
\(171\) 36.5008 2.79129
\(172\) 11.1652i 0.851335i
\(173\) −22.9612 −1.74571 −0.872853 0.487983i \(-0.837733\pi\)
−0.872853 + 0.487983i \(0.837733\pi\)
\(174\) 23.4724i 1.77944i
\(175\) 11.2250 + 4.58258i 0.848528 + 0.346410i
\(176\) 2.79129 + 1.79129i 0.210401 + 0.135023i
\(177\) 9.58258 0.720270
\(178\) 9.79796 0.734388
\(179\) −7.16515 −0.535549 −0.267774 0.963482i \(-0.586288\pi\)
−0.267774 + 0.963482i \(0.586288\pi\)
\(180\) 4.25290i 0.316992i
\(181\) 16.6352i 1.23648i 0.785988 + 0.618242i \(0.212155\pi\)
−0.785988 + 0.618242i \(0.787845\pi\)
\(182\) −3.09557 + 7.58258i −0.229459 + 0.562058i
\(183\) 28.7477i 2.12509i
\(184\) 4.00000i 0.294884i
\(185\) 3.60681i 0.265178i
\(186\) 3.58258i 0.262687i
\(187\) 10.4440 + 6.70239i 0.763744 + 0.490127i
\(188\) 5.03383i 0.367129i
\(189\) −11.0901 + 27.1652i −0.806688 + 1.97597i
\(190\) 3.58258 0.259907
\(191\) −18.0000 −1.30243 −0.651217 0.758891i \(-0.725741\pi\)
−0.651217 + 0.758891i \(0.725741\pi\)
\(192\) 3.09557i 0.223404i
\(193\) 20.3303i 1.46341i −0.681623 0.731704i \(-0.738726\pi\)
0.681623 0.731704i \(-0.261274\pi\)
\(194\) −15.9891 −1.14795
\(195\) 6.19115 0.443357
\(196\) −5.00000 4.89898i −0.357143 0.349927i
\(197\) 18.7477i 1.33572i −0.744287 0.667860i \(-0.767210\pi\)
0.744287 0.667860i \(-0.232790\pi\)
\(198\) −11.7913 + 18.3739i −0.837970 + 1.30577i
\(199\) 24.6297i 1.74596i −0.487759 0.872978i \(-0.662186\pi\)
0.487759 0.872978i \(-0.337814\pi\)
\(200\) 4.58258i 0.324037i
\(201\) 4.89898i 0.345547i
\(202\) 0.511238i 0.0359706i
\(203\) 7.58258 18.5734i 0.532192 1.30360i
\(204\) 11.5826i 0.810943i
\(205\) 3.25227i 0.227149i
\(206\) 13.5396 0.943350
\(207\) −26.3303 −1.83008
\(208\) −3.09557 −0.214639
\(209\) −15.4779 9.93280i −1.07063 0.687066i
\(210\) −2.00000 + 4.89898i −0.138013 + 0.338062i
\(211\) 10.7477i 0.739904i −0.929051 0.369952i \(-0.879374\pi\)
0.929051 0.369952i \(-0.120626\pi\)
\(212\) 2.41742 0.166029
\(213\) 6.19115i 0.424210i
\(214\) 8.41742 0.575403
\(215\) 7.21362 0.491965
\(216\) −11.0901 −0.754588
\(217\) 1.15732 2.83485i 0.0785641 0.192442i
\(218\) −1.16515 −0.0789140
\(219\) 19.5826i 1.32327i
\(220\) −1.15732 + 1.80341i −0.0780266 + 0.121586i
\(221\) −11.5826 −0.779128
\(222\) 17.2813 1.15984
\(223\) 6.32599i 0.423620i −0.977311 0.211810i \(-0.932064\pi\)
0.977311 0.211810i \(-0.0679358\pi\)
\(224\) 1.00000 2.44949i 0.0668153 0.163663i
\(225\) −30.1652 −2.01101
\(226\) 16.7477i 1.11404i
\(227\) −11.7362 −0.778960 −0.389480 0.921035i \(-0.627345\pi\)
−0.389480 + 0.921035i \(0.627345\pi\)
\(228\) 17.1652i 1.13679i
\(229\) 13.0284i 0.860939i 0.902605 + 0.430470i \(0.141652\pi\)
−0.902605 + 0.430470i \(0.858348\pi\)
\(230\) −2.58434 −0.170406
\(231\) 22.2232 15.6201i 1.46218 1.02773i
\(232\) 7.58258 0.497820
\(233\) 8.83485i 0.578790i −0.957210 0.289395i \(-0.906546\pi\)
0.957210 0.289395i \(-0.0934541\pi\)
\(234\) 20.3768i 1.33208i
\(235\) 3.25227 0.212155
\(236\) 3.09557i 0.201505i
\(237\) −12.3823 −0.804316
\(238\) 3.74166 9.16515i 0.242536 0.594089i
\(239\) 17.5826i 1.13732i −0.822572 0.568661i \(-0.807462\pi\)
0.822572 0.568661i \(-0.192538\pi\)
\(240\) −2.00000 −0.129099
\(241\) −25.9219 −1.66978 −0.834889 0.550419i \(-0.814468\pi\)
−0.834889 + 0.550419i \(0.814468\pi\)
\(242\) 10.0000 4.58258i 0.642824 0.294579i
\(243\) 11.8711i 0.761529i
\(244\) 9.28672 0.594521
\(245\) 3.16515 3.23042i 0.202214 0.206384i
\(246\) −15.5826 −0.993509
\(247\) 17.1652 1.09219
\(248\) 1.15732 0.0734900
\(249\) 28.3303i 1.79536i
\(250\) −6.19115 −0.391563
\(251\) 2.07310i 0.130853i −0.997857 0.0654264i \(-0.979159\pi\)
0.997857 0.0654264i \(-0.0208407\pi\)
\(252\) 16.1240 + 6.58258i 1.01571 + 0.414663i
\(253\) 11.1652 + 7.16515i 0.701947 + 0.450469i
\(254\) 5.58258 0.350282
\(255\) −7.48331 −0.468623
\(256\) 1.00000 0.0625000
\(257\) 4.89898i 0.305590i −0.988258 0.152795i \(-0.951173\pi\)
0.988258 0.152795i \(-0.0488274\pi\)
\(258\) 34.5625i 2.15177i
\(259\) −13.6745 5.58258i −0.849690 0.346884i
\(260\) 2.00000i 0.124035i
\(261\) 49.9129i 3.08953i
\(262\) 9.42157i 0.582066i
\(263\) 28.3303i 1.74692i 0.486895 + 0.873461i \(0.338130\pi\)
−0.486895 + 0.873461i \(0.661870\pi\)
\(264\) 8.64064 + 5.54506i 0.531794 + 0.341275i
\(265\) 1.56186i 0.0959442i
\(266\) −5.54506 + 13.5826i −0.339990 + 0.832801i
\(267\) 30.3303 1.85618
\(268\) −1.58258 −0.0966712
\(269\) 20.2420i 1.23418i −0.786894 0.617088i \(-0.788312\pi\)
0.786894 0.617088i \(-0.211688\pi\)
\(270\) 7.16515i 0.436057i
\(271\) −4.89898 −0.297592 −0.148796 0.988868i \(-0.547540\pi\)
−0.148796 + 0.988868i \(0.547540\pi\)
\(272\) 3.74166 0.226871
\(273\) −9.58258 + 23.4724i −0.579964 + 1.42062i
\(274\) 15.1652i 0.916160i
\(275\) 12.7913 + 8.20871i 0.771344 + 0.495004i
\(276\) 12.3823i 0.745327i
\(277\) 2.00000i 0.120168i 0.998193 + 0.0600842i \(0.0191369\pi\)
−0.998193 + 0.0600842i \(0.980863\pi\)
\(278\) 3.23042i 0.193748i
\(279\) 7.61816i 0.456087i
\(280\) 1.58258 + 0.646084i 0.0945770 + 0.0386109i
\(281\) 7.16515i 0.427437i −0.976895 0.213719i \(-0.931442\pi\)
0.976895 0.213719i \(-0.0685575\pi\)
\(282\) 15.5826i 0.927929i
\(283\) 15.6127 0.928079 0.464040 0.885814i \(-0.346399\pi\)
0.464040 + 0.885814i \(0.346399\pi\)
\(284\) −2.00000 −0.118678
\(285\) 11.0901 0.656922
\(286\) −5.54506 + 8.64064i −0.327886 + 0.510932i
\(287\) 12.3303 + 5.03383i 0.727835 + 0.297137i
\(288\) 6.58258i 0.387882i
\(289\) −3.00000 −0.176471
\(290\) 4.89898i 0.287678i
\(291\) −49.4955 −2.90147
\(292\) 6.32599 0.370201
\(293\) 21.3993 1.25016 0.625081 0.780560i \(-0.285066\pi\)
0.625081 + 0.780560i \(0.285066\pi\)
\(294\) −15.4779 15.1652i −0.902688 0.884450i
\(295\) 2.00000 0.116445
\(296\) 5.58258i 0.324481i
\(297\) −19.8656 + 30.9557i −1.15272 + 1.79623i
\(298\) −14.0000 −0.810998
\(299\) −12.3823 −0.716087
\(300\) 14.1857i 0.819012i
\(301\) −11.1652 + 27.3489i −0.643549 + 1.57637i
\(302\) −3.58258 −0.206154
\(303\) 1.58258i 0.0909166i
\(304\) −5.54506 −0.318031
\(305\) 6.00000i 0.343559i
\(306\) 24.6297i 1.40799i
\(307\) 8.12940 0.463969 0.231985 0.972719i \(-0.425478\pi\)
0.231985 + 0.972719i \(0.425478\pi\)
\(308\) −5.04594 7.17903i −0.287519 0.409063i
\(309\) 41.9129 2.38434
\(310\) 0.747727i 0.0424680i
\(311\) 9.93280i 0.563238i −0.959526 0.281619i \(-0.909129\pi\)
0.959526 0.281619i \(-0.0908714\pi\)
\(312\) −9.58258 −0.542507
\(313\) 1.02248i 0.0577938i −0.999582 0.0288969i \(-0.990801\pi\)
0.999582 0.0288969i \(-0.00919945\pi\)
\(314\) 20.5117 1.15754
\(315\) −4.25290 + 10.4174i −0.239624 + 0.586955i
\(316\) 4.00000i 0.225018i
\(317\) −9.16515 −0.514766 −0.257383 0.966309i \(-0.582860\pi\)
−0.257383 + 0.966309i \(0.582860\pi\)
\(318\) 7.48331 0.419643
\(319\) 13.5826 21.1652i 0.760478 1.18502i
\(320\) 0.646084i 0.0361172i
\(321\) 26.0568 1.45435
\(322\) 4.00000 9.79796i 0.222911 0.546019i
\(323\) −20.7477 −1.15443
\(324\) −14.5826 −0.810143
\(325\) −14.1857 −0.786881
\(326\) 4.00000i 0.221540i
\(327\) −3.60681 −0.199457
\(328\) 5.03383i 0.277946i
\(329\) −5.03383 + 12.3303i −0.277524 + 0.679792i
\(330\) −3.58258 + 5.58258i −0.197214 + 0.307311i
\(331\) −14.4174 −0.792453 −0.396227 0.918153i \(-0.629681\pi\)
−0.396227 + 0.918153i \(0.629681\pi\)
\(332\) −9.15188 −0.502274
\(333\) 36.7477 2.01376
\(334\) 6.19115i 0.338764i
\(335\) 1.02248i 0.0558639i
\(336\) 3.09557 7.58258i 0.168877 0.413663i
\(337\) 29.1652i 1.58873i 0.607443 + 0.794364i \(0.292195\pi\)
−0.607443 + 0.794364i \(0.707805\pi\)
\(338\) 3.41742i 0.185883i
\(339\) 51.8438i 2.81577i
\(340\) 2.41742i 0.131103i
\(341\) 2.07310 3.23042i 0.112264 0.174937i
\(342\) 36.5008i 1.97374i
\(343\) 7.34847 + 17.0000i 0.396780 + 0.917914i
\(344\) −11.1652 −0.601985
\(345\) −8.00000 −0.430706
\(346\) 22.9612i 1.23440i
\(347\) 0.834849i 0.0448170i −0.999749 0.0224085i \(-0.992867\pi\)
0.999749 0.0224085i \(-0.00713345\pi\)
\(348\) 23.4724 1.25825
\(349\) −2.07310 −0.110970 −0.0554852 0.998460i \(-0.517671\pi\)
−0.0554852 + 0.998460i \(0.517671\pi\)
\(350\) 4.58258 11.2250i 0.244949 0.600000i
\(351\) 34.3303i 1.83242i
\(352\) 1.79129 2.79129i 0.0954760 0.148776i
\(353\) 7.48331i 0.398297i −0.979969 0.199148i \(-0.936182\pi\)
0.979969 0.199148i \(-0.0638176\pi\)
\(354\) 9.58258i 0.509308i
\(355\) 1.29217i 0.0685811i
\(356\) 9.79796i 0.519291i
\(357\) 11.5826 28.3714i 0.613015 1.50157i
\(358\) 7.16515i 0.378690i
\(359\) 0.417424i 0.0220308i −0.999939 0.0110154i \(-0.996494\pi\)
0.999939 0.0110154i \(-0.00350638\pi\)
\(360\) −4.25290 −0.224147
\(361\) 11.7477 0.618301
\(362\) 16.6352 0.874326
\(363\) 30.9557 14.1857i 1.62475 0.744556i
\(364\) 7.58258 + 3.09557i 0.397435 + 0.162252i
\(365\) 4.08712i 0.213930i
\(366\) 28.7477 1.50267
\(367\) 1.42701i 0.0744895i −0.999306 0.0372447i \(-0.988142\pi\)
0.999306 0.0372447i \(-0.0118581\pi\)
\(368\) 4.00000 0.208514
\(369\) −33.1355 −1.72497
\(370\) 3.60681 0.187509
\(371\) −5.92146 2.41742i −0.307427 0.125506i
\(372\) 3.58258 0.185748
\(373\) 0.417424i 0.0216134i 0.999942 + 0.0108067i \(0.00343995\pi\)
−0.999942 + 0.0108067i \(0.996560\pi\)
\(374\) 6.70239 10.4440i 0.346572 0.540049i
\(375\) −19.1652 −0.989684
\(376\) −5.03383 −0.259600
\(377\) 23.4724i 1.20889i
\(378\) 27.1652 + 11.0901i 1.39722 + 0.570415i
\(379\) 14.3303 0.736098 0.368049 0.929806i \(-0.380026\pi\)
0.368049 + 0.929806i \(0.380026\pi\)
\(380\) 3.58258i 0.183782i
\(381\) 17.2813 0.885346
\(382\) 18.0000i 0.920960i
\(383\) 4.76413i 0.243436i 0.992565 + 0.121718i \(0.0388403\pi\)
−0.992565 + 0.121718i \(0.961160\pi\)
\(384\) 3.09557 0.157970
\(385\) 4.63825 3.26010i 0.236387 0.166150i
\(386\) −20.3303 −1.03479
\(387\) 73.4955i 3.73598i
\(388\) 15.9891i 0.811724i
\(389\) 10.0000 0.507020 0.253510 0.967333i \(-0.418415\pi\)
0.253510 + 0.967333i \(0.418415\pi\)
\(390\) 6.19115i 0.313501i
\(391\) 14.9666 0.756895
\(392\) −4.89898 + 5.00000i −0.247436 + 0.252538i
\(393\) 29.1652i 1.47119i
\(394\) −18.7477 −0.944497
\(395\) −2.58434 −0.130032
\(396\) 18.3739 + 11.7913i 0.923321 + 0.592535i
\(397\) 23.8488i 1.19694i −0.801146 0.598469i \(-0.795776\pi\)
0.801146 0.598469i \(-0.204224\pi\)
\(398\) −24.6297 −1.23458
\(399\) −17.1652 + 42.0459i −0.859332 + 2.10493i
\(400\) 4.58258 0.229129
\(401\) −1.58258 −0.0790301 −0.0395150 0.999219i \(-0.512581\pi\)
−0.0395150 + 0.999219i \(0.512581\pi\)
\(402\) −4.89898 −0.244339
\(403\) 3.58258i 0.178461i
\(404\) 0.511238 0.0254351
\(405\) 9.42157i 0.468161i
\(406\) −18.5734 7.58258i −0.921784 0.376317i
\(407\) −15.5826 10.0000i −0.772400 0.495682i
\(408\) 11.5826 0.573423
\(409\) 9.93280 0.491146 0.245573 0.969378i \(-0.421024\pi\)
0.245573 + 0.969378i \(0.421024\pi\)
\(410\) −3.25227 −0.160618
\(411\) 46.9448i 2.31562i
\(412\) 13.5396i 0.667049i
\(413\) −3.09557 + 7.58258i −0.152323 + 0.373114i
\(414\) 26.3303i 1.29406i
\(415\) 5.91288i 0.290252i
\(416\) 3.09557i 0.151773i
\(417\) 10.0000i 0.489702i
\(418\) −9.93280 + 15.4779i −0.485829 + 0.757047i
\(419\) 5.67991i 0.277482i −0.990329 0.138741i \(-0.955694\pi\)
0.990329 0.138741i \(-0.0443055\pi\)
\(420\) 4.89898 + 2.00000i 0.239046 + 0.0975900i
\(421\) −1.58258 −0.0771300 −0.0385650 0.999256i \(-0.512279\pi\)
−0.0385650 + 0.999256i \(0.512279\pi\)
\(422\) −10.7477 −0.523191
\(423\) 33.1355i 1.61110i
\(424\) 2.41742i 0.117401i
\(425\) 17.1464 0.831724
\(426\) −6.19115 −0.299962
\(427\) −22.7477 9.28672i −1.10084 0.449416i
\(428\) 8.41742i 0.406872i
\(429\) −17.1652 + 26.7477i −0.828741 + 1.29139i
\(430\) 7.21362i 0.347872i
\(431\) 17.9129i 0.862833i 0.902153 + 0.431416i \(0.141986\pi\)
−0.902153 + 0.431416i \(0.858014\pi\)
\(432\) 11.0901i 0.533574i
\(433\) 28.1017i 1.35048i 0.737597 + 0.675241i \(0.235960\pi\)
−0.737597 + 0.675241i \(0.764040\pi\)
\(434\) −2.83485 1.15732i −0.136077 0.0555532i
\(435\) 15.1652i 0.727113i
\(436\) 1.16515i 0.0558006i
\(437\) −22.1803 −1.06103
\(438\) 19.5826 0.935692
\(439\) 2.31464 0.110472 0.0552360 0.998473i \(-0.482409\pi\)
0.0552360 + 0.998473i \(0.482409\pi\)
\(440\) 1.80341 + 1.15732i 0.0859740 + 0.0551732i
\(441\) −32.9129 32.2479i −1.56728 1.53561i
\(442\) 11.5826i 0.550927i
\(443\) −3.16515 −0.150381 −0.0751904 0.997169i \(-0.523956\pi\)
−0.0751904 + 0.997169i \(0.523956\pi\)
\(444\) 17.2813i 0.820133i
\(445\) 6.33030 0.300085
\(446\) −6.32599 −0.299544
\(447\) −43.3380 −2.04982
\(448\) −2.44949 1.00000i −0.115728 0.0472456i
\(449\) 12.8348 0.605714 0.302857 0.953036i \(-0.402060\pi\)
0.302857 + 0.953036i \(0.402060\pi\)
\(450\) 30.1652i 1.42200i
\(451\) 14.0509 + 9.01703i 0.661629 + 0.424595i
\(452\) 16.7477 0.787747
\(453\) −11.0901 −0.521060
\(454\) 11.7362i 0.550808i
\(455\) −2.00000 + 4.89898i −0.0937614 + 0.229668i
\(456\) −17.1652 −0.803832
\(457\) 14.8348i 0.693945i 0.937875 + 0.346972i \(0.112790\pi\)
−0.937875 + 0.346972i \(0.887210\pi\)
\(458\) 13.0284 0.608776
\(459\) 41.4955i 1.93684i
\(460\) 2.58434i 0.120495i
\(461\) 26.2983 1.22483 0.612417 0.790535i \(-0.290197\pi\)
0.612417 + 0.790535i \(0.290197\pi\)
\(462\) −15.6201 22.2232i −0.726712 1.03392i
\(463\) −13.1652 −0.611836 −0.305918 0.952058i \(-0.598963\pi\)
−0.305918 + 0.952058i \(0.598963\pi\)
\(464\) 7.58258i 0.352012i
\(465\) 2.31464i 0.107339i
\(466\) −8.83485 −0.409266
\(467\) 0.511238i 0.0236573i −0.999930 0.0118286i \(-0.996235\pi\)
0.999930 0.0118286i \(-0.00376526\pi\)
\(468\) −20.3768 −0.941920
\(469\) 3.87650 + 1.58258i 0.179000 + 0.0730766i
\(470\) 3.25227i 0.150016i
\(471\) 63.4955 2.92572
\(472\) −3.09557 −0.142485
\(473\) −20.0000 + 31.1652i −0.919601 + 1.43298i
\(474\) 12.3823i 0.568738i
\(475\) −25.4107 −1.16592
\(476\) −9.16515 3.74166i −0.420084 0.171499i
\(477\) 15.9129 0.728601
\(478\) −17.5826 −0.804208
\(479\) −6.46084 −0.295203 −0.147602 0.989047i \(-0.547155\pi\)
−0.147602 + 0.989047i \(0.547155\pi\)
\(480\) 2.00000i 0.0912871i
\(481\) 17.2813 0.787958
\(482\) 25.9219i 1.18071i
\(483\) 12.3823 30.3303i 0.563414 1.38008i
\(484\) −4.58258 10.0000i −0.208299 0.454545i
\(485\) −10.3303 −0.469075
\(486\) −11.8711 −0.538482
\(487\) −33.4955 −1.51782 −0.758912 0.651193i \(-0.774269\pi\)
−0.758912 + 0.651193i \(0.774269\pi\)
\(488\) 9.28672i 0.420390i
\(489\) 12.3823i 0.559947i
\(490\) −3.23042 3.16515i −0.145935 0.142987i
\(491\) 21.4955i 0.970076i −0.874493 0.485038i \(-0.838806\pi\)
0.874493 0.485038i \(-0.161194\pi\)
\(492\) 15.5826i 0.702517i
\(493\) 28.3714i 1.27778i
\(494\) 17.1652i 0.772297i
\(495\) −7.61816 + 11.8711i −0.342411 + 0.533564i
\(496\) 1.15732i 0.0519653i
\(497\) 4.89898 + 2.00000i 0.219749 + 0.0897123i
\(498\) −28.3303 −1.26951
\(499\) 27.9129 1.24955 0.624776 0.780804i \(-0.285190\pi\)
0.624776 + 0.780804i \(0.285190\pi\)
\(500\) 6.19115i 0.276877i
\(501\) 19.1652i 0.856236i
\(502\) −2.07310 −0.0925268
\(503\) −31.9782 −1.42584 −0.712919 0.701246i \(-0.752627\pi\)
−0.712919 + 0.701246i \(0.752627\pi\)
\(504\) 6.58258 16.1240i 0.293211 0.718218i
\(505\) 0.330303i 0.0146983i
\(506\) 7.16515 11.1652i 0.318530 0.496352i
\(507\) 10.5789i 0.469825i
\(508\) 5.58258i 0.247687i
\(509\) 17.9274i 0.794616i −0.917685 0.397308i \(-0.869944\pi\)
0.917685 0.397308i \(-0.130056\pi\)
\(510\) 7.48331i 0.331367i
\(511\) −15.4955 6.32599i −0.685479 0.279845i
\(512\) 1.00000i 0.0441942i
\(513\) 61.4955i 2.71509i
\(514\) −4.89898 −0.216085
\(515\) 8.74773 0.385471
\(516\) −34.5625 −1.52153
\(517\) −9.01703 + 14.0509i −0.396569 + 0.617956i
\(518\) −5.58258 + 13.6745i −0.245284 + 0.600821i
\(519\) 71.0780i 3.11998i
\(520\) −2.00000 −0.0877058
\(521\) 35.5850i 1.55901i −0.626397 0.779504i \(-0.715471\pi\)
0.626397 0.779504i \(-0.284529\pi\)
\(522\) 49.9129 2.18463
\(523\) 26.7028 1.16763 0.583817 0.811885i \(-0.301559\pi\)
0.583817 + 0.811885i \(0.301559\pi\)
\(524\) −9.42157 −0.411583
\(525\) 14.1857 34.7477i 0.619115 1.51652i
\(526\) 28.3303 1.23526
\(527\) 4.33030i 0.188631i
\(528\) 5.54506 8.64064i 0.241318 0.376035i
\(529\) −7.00000 −0.304348
\(530\) 1.56186 0.0678428
\(531\) 20.3768i 0.884280i
\(532\) 13.5826 + 5.54506i 0.588879 + 0.240409i
\(533\) −15.5826 −0.674956
\(534\) 30.3303i 1.31252i
\(535\) 5.43836 0.235121
\(536\) 1.58258i 0.0683569i
\(537\) 22.1803i 0.957149i
\(538\) −20.2420 −0.872695
\(539\) 5.18096 + 22.6309i 0.223160 + 0.974782i
\(540\) −7.16515 −0.308339
\(541\) 9.25227i 0.397786i −0.980021 0.198893i \(-0.936265\pi\)
0.980021 0.198893i \(-0.0637347\pi\)
\(542\) 4.89898i 0.210429i
\(543\) 51.4955 2.20988
\(544\) 3.74166i 0.160422i
\(545\) −0.752785 −0.0322458
\(546\) 23.4724 + 9.58258i 1.00453 + 0.410096i
\(547\) 2.74773i 0.117484i 0.998273 + 0.0587422i \(0.0187090\pi\)
−0.998273 + 0.0587422i \(0.981291\pi\)
\(548\) −15.1652 −0.647823
\(549\) 61.1305 2.60899
\(550\) 8.20871 12.7913i 0.350021 0.545422i
\(551\) 42.0459i 1.79121i
\(552\) 12.3823 0.527025
\(553\) 4.00000 9.79796i 0.170097 0.416652i
\(554\) 2.00000 0.0849719
\(555\) 11.1652 0.473934
\(556\) −3.23042 −0.137000
\(557\) 9.91288i 0.420022i 0.977699 + 0.210011i \(0.0673500\pi\)
−0.977699 + 0.210011i \(0.932650\pi\)
\(558\) 7.61816 0.322502
\(559\) 34.5625i 1.46184i
\(560\) 0.646084 1.58258i 0.0273020 0.0668760i
\(561\) 20.7477 32.3303i 0.875970 1.36499i
\(562\) −7.16515 −0.302244
\(563\) 42.4223 1.78788 0.893942 0.448182i \(-0.147928\pi\)
0.893942 + 0.448182i \(0.147928\pi\)
\(564\) −15.5826 −0.656145
\(565\) 10.8204i 0.455219i
\(566\) 15.6127i 0.656251i
\(567\) 35.7199 + 14.5826i 1.50009 + 0.612411i
\(568\) 2.00000i 0.0839181i
\(569\) 15.4955i 0.649603i −0.945782 0.324802i \(-0.894702\pi\)
0.945782 0.324802i \(-0.105298\pi\)
\(570\) 11.0901i 0.464514i
\(571\) 3.58258i 0.149926i 0.997186 + 0.0749631i \(0.0238839\pi\)
−0.997186 + 0.0749631i \(0.976116\pi\)
\(572\) 8.64064 + 5.54506i 0.361283 + 0.231851i
\(573\) 55.7203i 2.32775i
\(574\) 5.03383 12.3303i 0.210108 0.514657i
\(575\) 18.3303 0.764426
\(576\) 6.58258 0.274274
\(577\) 0.269691i 0.0112274i −0.999984 0.00561369i \(-0.998213\pi\)
0.999984 0.00561369i \(-0.00178690\pi\)
\(578\) 3.00000i 0.124784i
\(579\) −62.9339 −2.61545
\(580\) 4.89898 0.203419
\(581\) 22.4174 + 9.15188i 0.930031 + 0.379684i
\(582\) 49.4955i 2.05165i
\(583\) −6.74773 4.33030i −0.279462 0.179343i
\(584\) 6.32599i 0.261771i
\(585\) 13.1652i 0.544312i
\(586\) 21.3993i 0.883998i
\(587\) 17.0397i 0.703305i 0.936131 + 0.351652i \(0.114380\pi\)
−0.936131 + 0.351652i \(0.885620\pi\)
\(588\) −15.1652 + 15.4779i −0.625400 + 0.638297i
\(589\) 6.41742i 0.264425i
\(590\) 2.00000i 0.0823387i
\(591\) −58.0350 −2.38724
\(592\) −5.58258 −0.229442
\(593\) 0.134846 0.00553744 0.00276872 0.999996i \(-0.499119\pi\)
0.00276872 + 0.999996i \(0.499119\pi\)
\(594\) 30.9557 + 19.8656i 1.27013 + 0.815096i
\(595\) 2.41742 5.92146i 0.0991047 0.242756i
\(596\) 14.0000i 0.573462i
\(597\) −76.2432 −3.12043
\(598\) 12.3823i 0.506350i
\(599\) −2.83485 −0.115829 −0.0579144 0.998322i \(-0.518445\pi\)
−0.0579144 + 0.998322i \(0.518445\pi\)
\(600\) 14.1857 0.579129
\(601\) −1.42701 −0.0582091 −0.0291045 0.999576i \(-0.509266\pi\)
−0.0291045 + 0.999576i \(0.509266\pi\)
\(602\) 27.3489 + 11.1652i 1.11466 + 0.455058i
\(603\) −10.4174 −0.424230
\(604\) 3.58258i 0.145773i
\(605\) 6.46084 2.96073i 0.262670 0.120371i
\(606\) 1.58258 0.0642877
\(607\) 46.9448 1.90543 0.952716 0.303862i \(-0.0982761\pi\)
0.952716 + 0.303862i \(0.0982761\pi\)
\(608\) 5.54506i 0.224882i
\(609\) −57.4955 23.4724i −2.32983 0.951150i
\(610\) 6.00000 0.242933
\(611\) 15.5826i 0.630404i
\(612\) 24.6297 0.995598
\(613\) 13.9129i 0.561936i −0.959717 0.280968i \(-0.909345\pi\)
0.959717 0.280968i \(-0.0906555\pi\)
\(614\) 8.12940i 0.328076i
\(615\) −10.0677 −0.405967
\(616\) −7.17903 + 5.04594i −0.289251 + 0.203307i
\(617\) 25.9129 1.04321 0.521607 0.853186i \(-0.325333\pi\)
0.521607 + 0.853186i \(0.325333\pi\)
\(618\) 41.9129i 1.68598i
\(619\) 0.780929i 0.0313882i 0.999877 + 0.0156941i \(0.00499579\pi\)
−0.999877 + 0.0156941i \(0.995004\pi\)
\(620\) 0.747727 0.0300294
\(621\) 44.3605i 1.78013i
\(622\) −9.93280 −0.398269
\(623\) −9.79796 + 24.0000i −0.392547 + 0.961540i
\(624\) 9.58258i 0.383610i
\(625\) 18.9129 0.756515
\(626\) −1.02248 −0.0408664
\(627\) −30.7477 + 47.9129i −1.22795 + 1.91346i
\(628\) 20.5117i 0.818506i
\(629\) −20.8881 −0.832863
\(630\) 10.4174 + 4.25290i 0.415040 + 0.169439i
\(631\) −5.16515 −0.205621 −0.102811 0.994701i \(-0.532784\pi\)
−0.102811 + 0.994701i \(0.532784\pi\)
\(632\) 4.00000 0.159111
\(633\) −33.2704 −1.32238
\(634\) 9.16515i 0.363995i
\(635\) 3.60681 0.143132
\(636\) 7.48331i 0.296733i
\(637\) −15.4779 15.1652i −0.613255 0.600865i
\(638\) −21.1652 13.5826i −0.837936 0.537739i
\(639\) −13.1652 −0.520805
\(640\) 0.646084 0.0255387
\(641\) 29.9129 1.18149 0.590744 0.806859i \(-0.298834\pi\)
0.590744 + 0.806859i \(0.298834\pi\)
\(642\) 26.0568i 1.02838i
\(643\) 16.7700i 0.661346i 0.943745 + 0.330673i \(0.107276\pi\)
−0.943745 + 0.330673i \(0.892724\pi\)
\(644\) −9.79796 4.00000i −0.386094 0.157622i
\(645\) 22.3303i 0.879255i
\(646\) 20.7477i 0.816308i
\(647\) 44.7650i 1.75990i 0.475071 + 0.879948i \(0.342423\pi\)
−0.475071 + 0.879948i \(0.657577\pi\)
\(648\) 14.5826i 0.572858i
\(649\) −5.54506 + 8.64064i −0.217663 + 0.339175i
\(650\) 14.1857i 0.556409i
\(651\) −8.77548 3.58258i −0.343938 0.140412i
\(652\) −4.00000 −0.156652
\(653\) −6.00000 −0.234798 −0.117399 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) 3.60681i 0.141038i
\(655\) 6.08712i 0.237844i
\(656\) 5.03383 0.196538
\(657\) 41.6413 1.62458
\(658\) 12.3303 + 5.03383i 0.480685 + 0.196239i
\(659\) 30.3303i 1.18150i 0.806854 + 0.590750i \(0.201168\pi\)
−0.806854 + 0.590750i \(0.798832\pi\)
\(660\) 5.58258 + 3.58258i 0.217301 + 0.139452i
\(661\) 25.4107i 0.988361i −0.869359 0.494180i \(-0.835468\pi\)
0.869359 0.494180i \(-0.164532\pi\)
\(662\) 14.4174i 0.560349i
\(663\) 35.8547i 1.39248i
\(664\) 9.15188i 0.355162i
\(665\) −3.58258 + 8.77548i −0.138926 + 0.340299i
\(666\) 36.7477i 1.42395i
\(667\) 30.3303i 1.17439i
\(668\) 6.19115 0.239543
\(669\) −19.5826 −0.757106
\(670\) −1.02248 −0.0395017
\(671\) −25.9219 16.6352i −1.00070 0.642194i
\(672\) −7.58258 3.09557i −0.292504 0.119414i
\(673\) 18.3303i 0.706581i 0.935514 + 0.353291i \(0.114937\pi\)
−0.935514 + 0.353291i \(0.885063\pi\)
\(674\) 29.1652 1.12340
\(675\) 50.8213i 1.95611i
\(676\) 3.41742 0.131439
\(677\) 31.4670 1.20937 0.604687 0.796463i \(-0.293298\pi\)
0.604687 + 0.796463i \(0.293298\pi\)
\(678\) 51.8438 1.99105
\(679\) 15.9891 39.1652i 0.613606 1.50302i
\(680\) 2.41742 0.0927040
\(681\) 36.3303i 1.39218i
\(682\) −3.23042 2.07310i −0.123699 0.0793830i
\(683\) 45.4955 1.74084 0.870418 0.492314i \(-0.163849\pi\)
0.870418 + 0.492314i \(0.163849\pi\)
\(684\) −36.5008 −1.39564
\(685\) 9.79796i 0.374361i
\(686\) 17.0000 7.34847i 0.649063 0.280566i
\(687\) 40.3303 1.53870
\(688\) 11.1652i 0.425667i
\(689\) 7.48331 0.285092
\(690\) 8.00000i 0.304555i
\(691\) 37.6581i 1.43258i −0.697801 0.716291i \(-0.745838\pi\)
0.697801 0.716291i \(-0.254162\pi\)
\(692\) 22.9612 0.872853
\(693\) −33.2153 47.2565i −1.26175 1.79513i
\(694\) −0.834849 −0.0316904
\(695\) 2.08712i 0.0791690i
\(696\) 23.4724i 0.889720i
\(697\) 18.8348 0.713421
\(698\) 2.07310i 0.0784679i
\(699\) −27.3489 −1.03443
\(700\) −11.2250 4.58258i −0.424264 0.173205i
\(701\) 24.3303i 0.918943i −0.888193 0.459471i \(-0.848039\pi\)
0.888193 0.459471i \(-0.151961\pi\)
\(702\) −34.3303 −1.29571
\(703\) 30.9557 1.16752
\(704\) −2.79129 1.79129i −0.105201 0.0675117i
\(705\) 10.0677i 0.379170i
\(706\) −7.48331 −0.281638
\(707\) −1.25227 0.511238i −0.0470966 0.0192271i
\(708\) −9.58258 −0.360135
\(709\) 15.6697 0.588488 0.294244 0.955730i \(-0.404932\pi\)
0.294244 + 0.955730i \(0.404932\pi\)
\(710\) −1.29217 −0.0484942
\(711\) 26.3303i 0.987464i
\(712\) −9.79796 −0.367194
\(713\) 4.62929i 0.173368i
\(714\) −28.3714 11.5826i −1.06177 0.433467i
\(715\) −3.58258 + 5.58258i −0.133981 + 0.208776i
\(716\) 7.16515 0.267774
\(717\) −54.4282 −2.03266
\(718\) −0.417424 −0.0155781
\(719\) 15.8543i 0.591264i −0.955302 0.295632i \(-0.904470\pi\)
0.955302 0.295632i \(-0.0955302\pi\)
\(720\) 4.25290i 0.158496i
\(721\) −13.5396 + 33.1652i −0.504242 + 1.23513i
\(722\) 11.7477i 0.437205i
\(723\) 80.2432i 2.98428i
\(724\) 16.6352i 0.618242i
\(725\) 34.7477i 1.29050i
\(726\) −14.1857 30.9557i −0.526481 1.14888i
\(727\) 52.2484i 1.93778i −0.247483 0.968892i \(-0.579604\pi\)
0.247483 0.968892i \(-0.420396\pi\)
\(728\) 3.09557 7.58258i 0.114730 0.281029i
\(729\) 7.00000 0.259259
\(730\) 4.08712 0.151271
\(731\) 41.7762i 1.54515i
\(732\) 28.7477i 1.06255i
\(733\) −22.9612 −0.848091 −0.424045 0.905641i \(-0.639390\pi\)
−0.424045 + 0.905641i \(0.639390\pi\)
\(734\) −1.42701 −0.0526720
\(735\) −10.0000 9.79796i −0.368856 0.361403i
\(736\) 4.00000i 0.147442i
\(737\) 4.41742 + 2.83485i 0.162718 + 0.104423i
\(738\) 33.1355i 1.21974i
\(739\) 7.58258i 0.278930i −0.990227 0.139465i \(-0.955462\pi\)
0.990227 0.139465i \(-0.0445382\pi\)
\(740\) 3.60681i 0.132589i
\(741\) 53.1360i 1.95200i
\(742\) −2.41742 + 5.92146i −0.0887464 + 0.217383i
\(743\) 43.9129i 1.61101i −0.592591 0.805504i \(-0.701895\pi\)
0.592591 0.805504i \(-0.298105\pi\)
\(744\) 3.58258i 0.131344i
\(745\) −9.04517 −0.331390
\(746\) 0.417424 0.0152830
\(747\) −60.2429 −2.20417
\(748\) −10.4440 6.70239i −0.381872 0.245063i
\(749\) −8.41742 + 20.6184i −0.307566 + 0.753380i
\(750\) 19.1652i 0.699812i
\(751\) 13.4955 0.492456 0.246228 0.969212i \(-0.420809\pi\)
0.246228 + 0.969212i \(0.420809\pi\)
\(752\) 5.03383i 0.183565i
\(753\) −6.41742 −0.233864
\(754\) 23.4724 0.854815
\(755\) −2.31464 −0.0842385
\(756\) 11.0901 27.1652i 0.403344 0.987987i
\(757\) −49.1652 −1.78694 −0.893469 0.449125i \(-0.851736\pi\)
−0.893469 + 0.449125i \(0.851736\pi\)
\(758\) 14.3303i 0.520500i
\(759\) 22.1803 34.5625i 0.805092 1.25454i
\(760\) −3.58258 −0.129954
\(761\) 20.7532 0.752304 0.376152 0.926558i \(-0.377247\pi\)
0.376152 + 0.926558i \(0.377247\pi\)
\(762\) 17.2813i 0.626034i
\(763\) 1.16515 2.85403i 0.0421813 0.103323i
\(764\) 18.0000 0.651217
\(765\) 15.9129i 0.575331i
\(766\) 4.76413 0.172135
\(767\) 9.58258i 0.346007i
\(768\) 3.09557i 0.111702i
\(769\) 29.7984 1.07456 0.537279 0.843404i \(-0.319452\pi\)
0.537279 + 0.843404i \(0.319452\pi\)
\(770\) −3.26010 4.63825i −0.117486 0.167151i
\(771\) −15.1652 −0.546160
\(772\) 20.3303i 0.731704i
\(773\) 51.1977i 1.84145i 0.390207 + 0.920727i \(0.372404\pi\)
−0.390207 + 0.920727i \(0.627596\pi\)
\(774\) −73.4955 −2.64174
\(775\) 5.30352i 0.190508i
\(776\) 15.9891 0.573975
\(777\) −17.2813 + 42.3303i −0.619962 + 1.51859i
\(778\) 10.0000i 0.358517i
\(779\) −27.9129 −1.00008
\(780\) −6.19115 −0.221679
\(781\) 5.58258 + 3.58258i 0.199760 + 0.128195i
\(782\) 14.9666i 0.535206i
\(783\) 84.0917 3.00519
\(784\) 5.00000 + 4.89898i 0.178571 + 0.174964i
\(785\) 13.2523 0.472994
\(786\) −29.1652 −1.04029