Properties

Label 378.2.k.d.269.4
Level $378$
Weight $2$
Character 378.269
Analytic conductor $3.018$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.k (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.4
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 378.269
Dual form 378.2.k.d.215.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.22474 + 2.12132i) q^{5} +(-1.00000 + 2.44949i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.22474 + 2.12132i) q^{5} +(-1.00000 + 2.44949i) q^{7} -1.00000i q^{8} +(2.12132 + 1.22474i) q^{10} +(3.67423 + 2.12132i) q^{11} -0.717439i q^{13} +(0.358719 + 2.62132i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.22474 - 2.12132i) q^{17} +(-4.24264 + 2.44949i) q^{19} +2.44949 q^{20} +4.24264 q^{22} +(5.19615 - 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.358719 - 0.621320i) q^{26} +(1.62132 + 2.09077i) q^{28} -1.75736i q^{29} +(-7.86396 - 4.54026i) q^{31} +(-0.866025 - 0.500000i) q^{32} -2.44949i q^{34} +(-6.42090 + 0.878680i) q^{35} +(-2.62132 - 4.54026i) q^{37} +(-2.44949 + 4.24264i) q^{38} +(2.12132 - 1.22474i) q^{40} +2.44949 q^{41} +7.00000 q^{43} +(3.67423 - 2.12132i) q^{44} +(3.00000 - 5.19615i) q^{46} +(6.42090 + 11.1213i) q^{47} +(-5.00000 - 4.89898i) q^{49} +1.00000i q^{50} +(-0.621320 - 0.358719i) q^{52} +(-12.5446 - 7.24264i) q^{53} +10.3923i q^{55} +(2.44949 + 1.00000i) q^{56} +(-0.878680 - 1.52192i) q^{58} +(-1.22474 + 2.12132i) q^{59} +(3.62132 - 2.09077i) q^{61} -9.08052 q^{62} -1.00000 q^{64} +(1.52192 - 0.878680i) q^{65} +(-6.74264 + 11.6786i) q^{67} +(-1.22474 - 2.12132i) q^{68} +(-5.12132 + 3.97141i) q^{70} -12.7279i q^{71} +(-4.75736 - 2.74666i) q^{73} +(-4.54026 - 2.62132i) q^{74} +4.89898i q^{76} +(-8.87039 + 6.87868i) q^{77} +(-0.378680 - 0.655892i) q^{79} +(1.22474 - 2.12132i) q^{80} +(2.12132 - 1.22474i) q^{82} -15.2913 q^{83} +6.00000 q^{85} +(6.06218 - 3.50000i) q^{86} +(2.12132 - 3.67423i) q^{88} +(1.52192 + 2.63604i) q^{89} +(1.75736 + 0.717439i) q^{91} -6.00000i q^{92} +(11.1213 + 6.42090i) q^{94} +(-10.3923 - 6.00000i) q^{95} +3.16693i q^{97} +(-6.77962 - 1.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} - 8 q^{7} - 4 q^{16} - 4 q^{25} - 4 q^{28} - 12 q^{31} - 4 q^{37} + 56 q^{43} + 24 q^{46} - 40 q^{49} + 12 q^{52} - 24 q^{58} + 12 q^{61} - 8 q^{64} - 20 q^{67} - 24 q^{70} - 72 q^{73} - 20 q^{79} + 48 q^{85} + 48 q^{91} + 72 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.22474 + 2.12132i 0.547723 + 0.948683i 0.998430 + 0.0560116i \(0.0178384\pi\)
−0.450708 + 0.892672i \(0.648828\pi\)
\(6\) 0 0
\(7\) −1.00000 + 2.44949i −0.377964 + 0.925820i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.12132 + 1.22474i 0.670820 + 0.387298i
\(11\) 3.67423 + 2.12132i 1.10782 + 0.639602i 0.938265 0.345918i \(-0.112432\pi\)
0.169559 + 0.985520i \(0.445766\pi\)
\(12\) 0 0
\(13\) 0.717439i 0.198982i −0.995038 0.0994909i \(-0.968279\pi\)
0.995038 0.0994909i \(-0.0317214\pi\)
\(14\) 0.358719 + 2.62132i 0.0958718 + 0.700577i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.22474 2.12132i 0.297044 0.514496i −0.678414 0.734680i \(-0.737332\pi\)
0.975458 + 0.220184i \(0.0706658\pi\)
\(18\) 0 0
\(19\) −4.24264 + 2.44949i −0.973329 + 0.561951i −0.900249 0.435375i \(-0.856616\pi\)
−0.0730792 + 0.997326i \(0.523283\pi\)
\(20\) 2.44949 0.547723
\(21\) 0 0
\(22\) 4.24264 0.904534
\(23\) 5.19615 3.00000i 1.08347 0.625543i 0.151642 0.988436i \(-0.451544\pi\)
0.931831 + 0.362892i \(0.118211\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −0.358719 0.621320i −0.0703507 0.121851i
\(27\) 0 0
\(28\) 1.62132 + 2.09077i 0.306401 + 0.395118i
\(29\) 1.75736i 0.326333i −0.986599 0.163167i \(-0.947829\pi\)
0.986599 0.163167i \(-0.0521708\pi\)
\(30\) 0 0
\(31\) −7.86396 4.54026i −1.41241 0.815455i −0.416794 0.909001i \(-0.636846\pi\)
−0.995615 + 0.0935461i \(0.970180\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 2.44949i 0.420084i
\(35\) −6.42090 + 0.878680i −1.08533 + 0.148524i
\(36\) 0 0
\(37\) −2.62132 4.54026i −0.430942 0.746414i 0.566012 0.824397i \(-0.308485\pi\)
−0.996955 + 0.0779826i \(0.975152\pi\)
\(38\) −2.44949 + 4.24264i −0.397360 + 0.688247i
\(39\) 0 0
\(40\) 2.12132 1.22474i 0.335410 0.193649i
\(41\) 2.44949 0.382546 0.191273 0.981537i \(-0.438738\pi\)
0.191273 + 0.981537i \(0.438738\pi\)
\(42\) 0 0
\(43\) 7.00000 1.06749 0.533745 0.845645i \(-0.320784\pi\)
0.533745 + 0.845645i \(0.320784\pi\)
\(44\) 3.67423 2.12132i 0.553912 0.319801i
\(45\) 0 0
\(46\) 3.00000 5.19615i 0.442326 0.766131i
\(47\) 6.42090 + 11.1213i 0.936584 + 1.62221i 0.771784 + 0.635884i \(0.219364\pi\)
0.164800 + 0.986327i \(0.447302\pi\)
\(48\) 0 0
\(49\) −5.00000 4.89898i −0.714286 0.699854i
\(50\) 1.00000i 0.141421i
\(51\) 0 0
\(52\) −0.621320 0.358719i −0.0861616 0.0497454i
\(53\) −12.5446 7.24264i −1.72314 0.994853i −0.912231 0.409675i \(-0.865642\pi\)
−0.810905 0.585178i \(-0.801025\pi\)
\(54\) 0 0
\(55\) 10.3923i 1.40130i
\(56\) 2.44949 + 1.00000i 0.327327 + 0.133631i
\(57\) 0 0
\(58\) −0.878680 1.52192i −0.115376 0.199838i
\(59\) −1.22474 + 2.12132i −0.159448 + 0.276172i −0.934670 0.355517i \(-0.884305\pi\)
0.775222 + 0.631689i \(0.217638\pi\)
\(60\) 0 0
\(61\) 3.62132 2.09077i 0.463663 0.267696i −0.249920 0.968266i \(-0.580404\pi\)
0.713583 + 0.700571i \(0.247071\pi\)
\(62\) −9.08052 −1.15323
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.52192 0.878680i 0.188771 0.108987i
\(66\) 0 0
\(67\) −6.74264 + 11.6786i −0.823745 + 1.42677i 0.0791303 + 0.996864i \(0.474786\pi\)
−0.902875 + 0.429903i \(0.858548\pi\)
\(68\) −1.22474 2.12132i −0.148522 0.257248i
\(69\) 0 0
\(70\) −5.12132 + 3.97141i −0.612115 + 0.474674i
\(71\) 12.7279i 1.51053i −0.655422 0.755263i \(-0.727509\pi\)
0.655422 0.755263i \(-0.272491\pi\)
\(72\) 0 0
\(73\) −4.75736 2.74666i −0.556807 0.321473i 0.195056 0.980792i \(-0.437511\pi\)
−0.751863 + 0.659320i \(0.770844\pi\)
\(74\) −4.54026 2.62132i −0.527795 0.304722i
\(75\) 0 0
\(76\) 4.89898i 0.561951i
\(77\) −8.87039 + 6.87868i −1.01087 + 0.783898i
\(78\) 0 0
\(79\) −0.378680 0.655892i −0.0426048 0.0737937i 0.843937 0.536443i \(-0.180232\pi\)
−0.886541 + 0.462649i \(0.846899\pi\)
\(80\) 1.22474 2.12132i 0.136931 0.237171i
\(81\) 0 0
\(82\) 2.12132 1.22474i 0.234261 0.135250i
\(83\) −15.2913 −1.67844 −0.839218 0.543795i \(-0.816987\pi\)
−0.839218 + 0.543795i \(0.816987\pi\)
\(84\) 0 0
\(85\) 6.00000 0.650791
\(86\) 6.06218 3.50000i 0.653701 0.377415i
\(87\) 0 0
\(88\) 2.12132 3.67423i 0.226134 0.391675i
\(89\) 1.52192 + 2.63604i 0.161323 + 0.279420i 0.935343 0.353741i \(-0.115091\pi\)
−0.774020 + 0.633161i \(0.781757\pi\)
\(90\) 0 0
\(91\) 1.75736 + 0.717439i 0.184221 + 0.0752080i
\(92\) 6.00000i 0.625543i
\(93\) 0 0
\(94\) 11.1213 + 6.42090i 1.14708 + 0.662265i
\(95\) −10.3923 6.00000i −1.06623 0.615587i
\(96\) 0 0
\(97\) 3.16693i 0.321553i 0.986991 + 0.160776i \(0.0513998\pi\)
−0.986991 + 0.160776i \(0.948600\pi\)
\(98\) −6.77962 1.74264i −0.684845 0.176033i
\(99\) 0 0
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) 3.67423 6.36396i 0.365600 0.633238i −0.623272 0.782005i \(-0.714197\pi\)
0.988872 + 0.148767i \(0.0475305\pi\)
\(102\) 0 0
\(103\) 9.62132 5.55487i 0.948017 0.547338i 0.0555525 0.998456i \(-0.482308\pi\)
0.892464 + 0.451118i \(0.148975\pi\)
\(104\) −0.717439 −0.0703507
\(105\) 0 0
\(106\) −14.4853 −1.40693
\(107\) −2.15232 + 1.24264i −0.208072 + 0.120131i −0.600415 0.799688i \(-0.704998\pi\)
0.392343 + 0.919819i \(0.371665\pi\)
\(108\) 0 0
\(109\) 8.86396 15.3528i 0.849013 1.47053i −0.0330761 0.999453i \(-0.510530\pi\)
0.882090 0.471082i \(-0.156136\pi\)
\(110\) 5.19615 + 9.00000i 0.495434 + 0.858116i
\(111\) 0 0
\(112\) 2.62132 0.358719i 0.247691 0.0338958i
\(113\) 10.2426i 0.963547i 0.876296 + 0.481773i \(0.160007\pi\)
−0.876296 + 0.481773i \(0.839993\pi\)
\(114\) 0 0
\(115\) 12.7279 + 7.34847i 1.18688 + 0.685248i
\(116\) −1.52192 0.878680i −0.141307 0.0815834i
\(117\) 0 0
\(118\) 2.44949i 0.225494i
\(119\) 3.97141 + 5.12132i 0.364058 + 0.469471i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 2.09077 3.62132i 0.189289 0.327859i
\(123\) 0 0
\(124\) −7.86396 + 4.54026i −0.706205 + 0.407727i
\(125\) 9.79796 0.876356
\(126\) 0 0
\(127\) −7.72792 −0.685742 −0.342871 0.939382i \(-0.611399\pi\)
−0.342871 + 0.939382i \(0.611399\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 0.878680 1.52192i 0.0770653 0.133481i
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) −1.75736 12.8418i −0.152382 1.11352i
\(134\) 13.4853i 1.16495i
\(135\) 0 0
\(136\) −2.12132 1.22474i −0.181902 0.105021i
\(137\) −5.19615 3.00000i −0.443937 0.256307i 0.261329 0.965250i \(-0.415839\pi\)
−0.705266 + 0.708942i \(0.749173\pi\)
\(138\) 0 0
\(139\) 8.06591i 0.684141i 0.939674 + 0.342071i \(0.111128\pi\)
−0.939674 + 0.342071i \(0.888872\pi\)
\(140\) −2.44949 + 6.00000i −0.207020 + 0.507093i
\(141\) 0 0
\(142\) −6.36396 11.0227i −0.534052 0.925005i
\(143\) 1.52192 2.63604i 0.127269 0.220437i
\(144\) 0 0
\(145\) 3.72792 2.15232i 0.309587 0.178740i
\(146\) −5.49333 −0.454631
\(147\) 0 0
\(148\) −5.24264 −0.430942
\(149\) 14.0665 8.12132i 1.15238 0.665324i 0.202911 0.979197i \(-0.434960\pi\)
0.949465 + 0.313873i \(0.101627\pi\)
\(150\) 0 0
\(151\) −4.37868 + 7.58410i −0.356332 + 0.617185i −0.987345 0.158587i \(-0.949306\pi\)
0.631013 + 0.775772i \(0.282639\pi\)
\(152\) 2.44949 + 4.24264i 0.198680 + 0.344124i
\(153\) 0 0
\(154\) −4.24264 + 10.3923i −0.341882 + 0.837436i
\(155\) 22.2426i 1.78657i
\(156\) 0 0
\(157\) −9.00000 5.19615i −0.718278 0.414698i 0.0958404 0.995397i \(-0.469446\pi\)
−0.814119 + 0.580699i \(0.802779\pi\)
\(158\) −0.655892 0.378680i −0.0521800 0.0301261i
\(159\) 0 0
\(160\) 2.44949i 0.193649i
\(161\) 2.15232 + 15.7279i 0.169626 + 1.23953i
\(162\) 0 0
\(163\) 4.74264 + 8.21449i 0.371472 + 0.643409i 0.989792 0.142518i \(-0.0455197\pi\)
−0.618320 + 0.785926i \(0.712186\pi\)
\(164\) 1.22474 2.12132i 0.0956365 0.165647i
\(165\) 0 0
\(166\) −13.2426 + 7.64564i −1.02783 + 0.593417i
\(167\) 0.594346 0.0459919 0.0229959 0.999736i \(-0.492680\pi\)
0.0229959 + 0.999736i \(0.492680\pi\)
\(168\) 0 0
\(169\) 12.4853 0.960406
\(170\) 5.19615 3.00000i 0.398527 0.230089i
\(171\) 0 0
\(172\) 3.50000 6.06218i 0.266872 0.462237i
\(173\) 10.3923 + 18.0000i 0.790112 + 1.36851i 0.925897 + 0.377776i \(0.123311\pi\)
−0.135785 + 0.990738i \(0.543356\pi\)
\(174\) 0 0
\(175\) −1.62132 2.09077i −0.122560 0.158047i
\(176\) 4.24264i 0.319801i
\(177\) 0 0
\(178\) 2.63604 + 1.52192i 0.197579 + 0.114073i
\(179\) 5.82655 + 3.36396i 0.435497 + 0.251434i 0.701686 0.712487i \(-0.252431\pi\)
−0.266189 + 0.963921i \(0.585764\pi\)
\(180\) 0 0
\(181\) 9.79796i 0.728277i −0.931345 0.364138i \(-0.881364\pi\)
0.931345 0.364138i \(-0.118636\pi\)
\(182\) 1.88064 0.257359i 0.139402 0.0190767i
\(183\) 0 0
\(184\) −3.00000 5.19615i −0.221163 0.383065i
\(185\) 6.42090 11.1213i 0.472074 0.817656i
\(186\) 0 0
\(187\) 9.00000 5.19615i 0.658145 0.379980i
\(188\) 12.8418 0.936584
\(189\) 0 0
\(190\) −12.0000 −0.870572
\(191\) 18.3712 10.6066i 1.32929 0.767467i 0.344101 0.938933i \(-0.388184\pi\)
0.985190 + 0.171466i \(0.0548503\pi\)
\(192\) 0 0
\(193\) 0.742641 1.28629i 0.0534564 0.0925893i −0.838059 0.545580i \(-0.816310\pi\)
0.891515 + 0.452990i \(0.149643\pi\)
\(194\) 1.58346 + 2.74264i 0.113686 + 0.196910i
\(195\) 0 0
\(196\) −6.74264 + 1.88064i −0.481617 + 0.134331i
\(197\) 16.9706i 1.20910i 0.796566 + 0.604551i \(0.206648\pi\)
−0.796566 + 0.604551i \(0.793352\pi\)
\(198\) 0 0
\(199\) −18.1066 10.4539i −1.28354 0.741054i −0.306049 0.952016i \(-0.599007\pi\)
−0.977494 + 0.210962i \(0.932340\pi\)
\(200\) 0.866025 + 0.500000i 0.0612372 + 0.0353553i
\(201\) 0 0
\(202\) 7.34847i 0.517036i
\(203\) 4.30463 + 1.75736i 0.302126 + 0.123342i
\(204\) 0 0
\(205\) 3.00000 + 5.19615i 0.209529 + 0.362915i
\(206\) 5.55487 9.62132i 0.387026 0.670349i
\(207\) 0 0
\(208\) −0.621320 + 0.358719i −0.0430808 + 0.0248727i
\(209\) −20.7846 −1.43770
\(210\) 0 0
\(211\) 3.48528 0.239937 0.119968 0.992778i \(-0.461721\pi\)
0.119968 + 0.992778i \(0.461721\pi\)
\(212\) −12.5446 + 7.24264i −0.861568 + 0.497427i
\(213\) 0 0
\(214\) −1.24264 + 2.15232i −0.0849452 + 0.147129i
\(215\) 8.57321 + 14.8492i 0.584688 + 1.01271i
\(216\) 0 0
\(217\) 18.9853 14.7224i 1.28880 0.999424i
\(218\) 17.7279i 1.20069i
\(219\) 0 0
\(220\) 9.00000 + 5.19615i 0.606780 + 0.350325i
\(221\) −1.52192 0.878680i −0.102375 0.0591064i
\(222\) 0 0
\(223\) 10.3923i 0.695920i −0.937509 0.347960i \(-0.886874\pi\)
0.937509 0.347960i \(-0.113126\pi\)
\(224\) 2.09077 1.62132i 0.139695 0.108329i
\(225\) 0 0
\(226\) 5.12132 + 8.87039i 0.340665 + 0.590049i
\(227\) −12.5446 + 21.7279i −0.832616 + 1.44213i 0.0633412 + 0.997992i \(0.479824\pi\)
−0.895957 + 0.444141i \(0.853509\pi\)
\(228\) 0 0
\(229\) −4.86396 + 2.80821i −0.321420 + 0.185572i −0.652025 0.758197i \(-0.726080\pi\)
0.330606 + 0.943769i \(0.392747\pi\)
\(230\) 14.6969 0.969087
\(231\) 0 0
\(232\) −1.75736 −0.115376
\(233\) 17.7408 10.2426i 1.16224 0.671018i 0.210398 0.977616i \(-0.432524\pi\)
0.951839 + 0.306598i \(0.0991908\pi\)
\(234\) 0 0
\(235\) −15.7279 + 27.2416i −1.02598 + 1.77704i
\(236\) 1.22474 + 2.12132i 0.0797241 + 0.138086i
\(237\) 0 0
\(238\) 6.00000 + 2.44949i 0.388922 + 0.158777i
\(239\) 16.2426i 1.05065i 0.850902 + 0.525325i \(0.176056\pi\)
−0.850902 + 0.525325i \(0.823944\pi\)
\(240\) 0 0
\(241\) −0.985281 0.568852i −0.0634676 0.0366430i 0.467930 0.883765i \(-0.345000\pi\)
−0.531398 + 0.847122i \(0.678333\pi\)
\(242\) 6.06218 + 3.50000i 0.389692 + 0.224989i
\(243\) 0 0
\(244\) 4.18154i 0.267696i
\(245\) 4.26858 16.6066i 0.272710 1.06096i
\(246\) 0 0
\(247\) 1.75736 + 3.04384i 0.111818 + 0.193675i
\(248\) −4.54026 + 7.86396i −0.288307 + 0.499362i
\(249\) 0 0
\(250\) 8.48528 4.89898i 0.536656 0.309839i
\(251\) 15.2913 0.965177 0.482589 0.875847i \(-0.339697\pi\)
0.482589 + 0.875847i \(0.339697\pi\)
\(252\) 0 0
\(253\) 25.4558 1.60040
\(254\) −6.69258 + 3.86396i −0.419930 + 0.242446i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −12.5446 21.7279i −0.782512 1.35535i −0.930474 0.366358i \(-0.880605\pi\)
0.147962 0.988993i \(-0.452729\pi\)
\(258\) 0 0
\(259\) 13.7426 1.88064i 0.853926 0.116857i
\(260\) 1.75736i 0.108987i
\(261\) 0 0
\(262\) 0 0
\(263\) −5.82655 3.36396i −0.359281 0.207431i 0.309485 0.950904i \(-0.399843\pi\)
−0.668765 + 0.743474i \(0.733177\pi\)
\(264\) 0 0
\(265\) 35.4815i 2.17961i
\(266\) −7.94282 10.2426i −0.487005 0.628017i
\(267\) 0 0
\(268\) 6.74264 + 11.6786i 0.411872 + 0.713384i
\(269\) −4.89898 + 8.48528i −0.298696 + 0.517357i −0.975838 0.218496i \(-0.929885\pi\)
0.677142 + 0.735853i \(0.263218\pi\)
\(270\) 0 0
\(271\) −16.3492 + 9.43924i −0.993146 + 0.573393i −0.906213 0.422821i \(-0.861040\pi\)
−0.0869326 + 0.996214i \(0.527706\pi\)
\(272\) −2.44949 −0.148522
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) −3.67423 + 2.12132i −0.221565 + 0.127920i
\(276\) 0 0
\(277\) −11.8640 + 20.5490i −0.712836 + 1.23467i 0.250952 + 0.968000i \(0.419256\pi\)
−0.963788 + 0.266669i \(0.914077\pi\)
\(278\) 4.03295 + 6.98528i 0.241881 + 0.418949i
\(279\) 0 0
\(280\) 0.878680 + 6.42090i 0.0525112 + 0.383722i
\(281\) 13.7574i 0.820695i −0.911929 0.410348i \(-0.865407\pi\)
0.911929 0.410348i \(-0.134593\pi\)
\(282\) 0 0
\(283\) 5.22792 + 3.01834i 0.310768 + 0.179422i 0.647270 0.762261i \(-0.275911\pi\)
−0.336502 + 0.941683i \(0.609244\pi\)
\(284\) −11.0227 6.36396i −0.654077 0.377632i
\(285\) 0 0
\(286\) 3.04384i 0.179986i
\(287\) −2.44949 + 6.00000i −0.144589 + 0.354169i
\(288\) 0 0
\(289\) 5.50000 + 9.52628i 0.323529 + 0.560369i
\(290\) 2.15232 3.72792i 0.126388 0.218911i
\(291\) 0 0
\(292\) −4.75736 + 2.74666i −0.278403 + 0.160736i
\(293\) 12.8418 0.750226 0.375113 0.926979i \(-0.377604\pi\)
0.375113 + 0.926979i \(0.377604\pi\)
\(294\) 0 0
\(295\) −6.00000 −0.349334
\(296\) −4.54026 + 2.62132i −0.263897 + 0.152361i
\(297\) 0 0
\(298\) 8.12132 14.0665i 0.470455 0.814853i
\(299\) −2.15232 3.72792i −0.124472 0.215591i
\(300\) 0 0
\(301\) −7.00000 + 17.1464i −0.403473 + 0.988304i
\(302\) 8.75736i 0.503929i
\(303\) 0 0
\(304\) 4.24264 + 2.44949i 0.243332 + 0.140488i
\(305\) 8.87039 + 5.12132i 0.507917 + 0.293246i
\(306\) 0 0
\(307\) 26.8213i 1.53077i 0.643571 + 0.765386i \(0.277452\pi\)
−0.643571 + 0.765386i \(0.722548\pi\)
\(308\) 1.52192 + 11.1213i 0.0867193 + 0.633696i
\(309\) 0 0
\(310\) −11.1213 19.2627i −0.631649 1.09405i
\(311\) 8.57321 14.8492i 0.486142 0.842023i −0.513731 0.857951i \(-0.671737\pi\)
0.999873 + 0.0159282i \(0.00507031\pi\)
\(312\) 0 0
\(313\) −17.4853 + 10.0951i −0.988327 + 0.570611i −0.904774 0.425893i \(-0.859960\pi\)
−0.0835529 + 0.996503i \(0.526627\pi\)
\(314\) −10.3923 −0.586472
\(315\) 0 0
\(316\) −0.757359 −0.0426048
\(317\) −19.2627 + 11.1213i −1.08190 + 0.624636i −0.931408 0.363976i \(-0.881419\pi\)
−0.150492 + 0.988611i \(0.548086\pi\)
\(318\) 0 0
\(319\) 3.72792 6.45695i 0.208724 0.361520i
\(320\) −1.22474 2.12132i −0.0684653 0.118585i
\(321\) 0 0
\(322\) 9.72792 + 12.5446i 0.542116 + 0.699084i
\(323\) 12.0000i 0.667698i
\(324\) 0 0
\(325\) 0.621320 + 0.358719i 0.0344647 + 0.0198982i
\(326\) 8.21449 + 4.74264i 0.454959 + 0.262671i
\(327\) 0 0
\(328\) 2.44949i 0.135250i
\(329\) −33.6625 + 4.60660i −1.85587 + 0.253970i
\(330\) 0 0
\(331\) −5.00000 8.66025i −0.274825 0.476011i 0.695266 0.718752i \(-0.255287\pi\)
−0.970091 + 0.242742i \(0.921953\pi\)
\(332\) −7.64564 + 13.2426i −0.419609 + 0.726784i
\(333\) 0 0
\(334\) 0.514719 0.297173i 0.0281642 0.0162606i
\(335\) −33.0321 −1.80473
\(336\) 0 0
\(337\) −21.4558 −1.16877 −0.584387 0.811475i \(-0.698665\pi\)
−0.584387 + 0.811475i \(0.698665\pi\)
\(338\) 10.8126 6.24264i 0.588126 0.339555i
\(339\) 0 0
\(340\) 3.00000 5.19615i 0.162698 0.281801i
\(341\) −19.2627 33.3640i −1.04313 1.80676i
\(342\) 0 0
\(343\) 17.0000 7.34847i 0.917914 0.396780i
\(344\) 7.00000i 0.377415i
\(345\) 0 0
\(346\) 18.0000 + 10.3923i 0.967686 + 0.558694i
\(347\) −4.30463 2.48528i −0.231085 0.133417i 0.379988 0.924992i \(-0.375928\pi\)
−0.611072 + 0.791575i \(0.709262\pi\)
\(348\) 0 0
\(349\) 0.123093i 0.00658902i −0.999995 0.00329451i \(-0.998951\pi\)
0.999995 0.00329451i \(-0.00104868\pi\)
\(350\) −2.44949 1.00000i −0.130931 0.0534522i
\(351\) 0 0
\(352\) −2.12132 3.67423i −0.113067 0.195837i
\(353\) −5.49333 + 9.51472i −0.292380 + 0.506417i −0.974372 0.224942i \(-0.927781\pi\)
0.681992 + 0.731360i \(0.261114\pi\)
\(354\) 0 0
\(355\) 27.0000 15.5885i 1.43301 0.827349i
\(356\) 3.04384 0.161323
\(357\) 0 0
\(358\) 6.72792 0.355582
\(359\) −12.5446 + 7.24264i −0.662080 + 0.382252i −0.793069 0.609132i \(-0.791518\pi\)
0.130989 + 0.991384i \(0.458185\pi\)
\(360\) 0 0
\(361\) 2.50000 4.33013i 0.131579 0.227901i
\(362\) −4.89898 8.48528i −0.257485 0.445976i
\(363\) 0 0
\(364\) 1.50000 1.16320i 0.0786214 0.0609682i
\(365\) 13.4558i 0.704311i
\(366\) 0 0
\(367\) −25.9706 14.9941i −1.35565 0.782686i −0.366618 0.930372i \(-0.619484\pi\)
−0.989034 + 0.147685i \(0.952818\pi\)
\(368\) −5.19615 3.00000i −0.270868 0.156386i
\(369\) 0 0
\(370\) 12.8418i 0.667613i
\(371\) 30.2854 23.4853i 1.57234 1.21930i
\(372\) 0 0
\(373\) 11.0000 + 19.0526i 0.569558 + 0.986504i 0.996610 + 0.0822766i \(0.0262191\pi\)
−0.427051 + 0.904227i \(0.640448\pi\)
\(374\) 5.19615 9.00000i 0.268687 0.465379i
\(375\) 0 0
\(376\) 11.1213 6.42090i 0.573538 0.331132i
\(377\) −1.26080 −0.0649344
\(378\) 0 0
\(379\) −7.48528 −0.384493 −0.192247 0.981347i \(-0.561577\pi\)
−0.192247 + 0.981347i \(0.561577\pi\)
\(380\) −10.3923 + 6.00000i −0.533114 + 0.307794i
\(381\) 0 0
\(382\) 10.6066 18.3712i 0.542681 0.939951i
\(383\) −2.74666 4.75736i −0.140348 0.243090i 0.787280 0.616596i \(-0.211489\pi\)
−0.927628 + 0.373506i \(0.878155\pi\)
\(384\) 0 0
\(385\) −25.4558 10.3923i −1.29735 0.529641i
\(386\) 1.48528i 0.0755988i
\(387\) 0 0
\(388\) 2.74264 + 1.58346i 0.139236 + 0.0803882i
\(389\) 13.4361 + 7.75736i 0.681239 + 0.393314i 0.800322 0.599571i \(-0.204662\pi\)
−0.119082 + 0.992884i \(0.537995\pi\)
\(390\) 0 0
\(391\) 14.6969i 0.743256i
\(392\) −4.89898 + 5.00000i −0.247436 + 0.252538i
\(393\) 0 0
\(394\) 8.48528 + 14.6969i 0.427482 + 0.740421i
\(395\) 0.927572 1.60660i 0.0466712 0.0808369i
\(396\) 0 0
\(397\) −13.1360 + 7.58410i −0.659279 + 0.380635i −0.792002 0.610518i \(-0.790961\pi\)
0.132723 + 0.991153i \(0.457628\pi\)
\(398\) −20.9077 −1.04801
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −17.1104 + 9.87868i −0.854451 + 0.493318i −0.862150 0.506653i \(-0.830883\pi\)
0.00769892 + 0.999970i \(0.497549\pi\)
\(402\) 0 0
\(403\) −3.25736 + 5.64191i −0.162261 + 0.281044i
\(404\) −3.67423 6.36396i −0.182800 0.316619i
\(405\) 0 0
\(406\) 4.60660 0.630399i 0.228622 0.0312862i
\(407\) 22.2426i 1.10253i
\(408\) 0 0
\(409\) −3.25736 1.88064i −0.161066 0.0929915i 0.417300 0.908769i \(-0.362976\pi\)
−0.578366 + 0.815777i \(0.696310\pi\)
\(410\) 5.19615 + 3.00000i 0.256620 + 0.148159i
\(411\) 0 0
\(412\) 11.1097i 0.547338i
\(413\) −3.97141 5.12132i −0.195420 0.252004i
\(414\) 0 0
\(415\) −18.7279 32.4377i −0.919318 1.59230i
\(416\) −0.358719 + 0.621320i −0.0175877 + 0.0304627i
\(417\) 0 0
\(418\) −18.0000 + 10.3923i −0.880409 + 0.508304i
\(419\) 7.94282 0.388032 0.194016 0.980998i \(-0.437849\pi\)
0.194016 + 0.980998i \(0.437849\pi\)
\(420\) 0 0
\(421\) −23.4558 −1.14317 −0.571584 0.820544i \(-0.693671\pi\)
−0.571584 + 0.820544i \(0.693671\pi\)
\(422\) 3.01834 1.74264i 0.146931 0.0848304i
\(423\) 0 0
\(424\) −7.24264 + 12.5446i −0.351734 + 0.609221i
\(425\) 1.22474 + 2.12132i 0.0594089 + 0.102899i
\(426\) 0 0
\(427\) 1.50000 + 10.9612i 0.0725901 + 0.530448i
\(428\) 2.48528i 0.120131i
\(429\) 0 0
\(430\) 14.8492 + 8.57321i 0.716094 + 0.413437i
\(431\) 1.52192 + 0.878680i 0.0733082 + 0.0423245i 0.536206 0.844087i \(-0.319857\pi\)
−0.462898 + 0.886412i \(0.653190\pi\)
\(432\) 0 0
\(433\) 2.57258i 0.123630i 0.998088 + 0.0618152i \(0.0196889\pi\)
−0.998088 + 0.0618152i \(0.980311\pi\)
\(434\) 9.08052 22.2426i 0.435879 1.06768i
\(435\) 0 0
\(436\) −8.86396 15.3528i −0.424507 0.735267i
\(437\) −14.6969 + 25.4558i −0.703050 + 1.21772i
\(438\) 0 0
\(439\) 3.72792 2.15232i 0.177924 0.102724i −0.408393 0.912806i \(-0.633911\pi\)
0.586317 + 0.810082i \(0.300577\pi\)
\(440\) 10.3923 0.495434
\(441\) 0 0
\(442\) −1.75736 −0.0835891
\(443\) −22.0454 + 12.7279i −1.04741 + 0.604722i −0.921923 0.387374i \(-0.873382\pi\)
−0.125486 + 0.992095i \(0.540049\pi\)
\(444\) 0 0
\(445\) −3.72792 + 6.45695i −0.176720 + 0.306089i
\(446\) −5.19615 9.00000i −0.246045 0.426162i
\(447\) 0 0
\(448\) 1.00000 2.44949i 0.0472456 0.115728i
\(449\) 5.27208i 0.248805i 0.992232 + 0.124402i \(0.0397014\pi\)
−0.992232 + 0.124402i \(0.960299\pi\)
\(450\) 0 0
\(451\) 9.00000 + 5.19615i 0.423793 + 0.244677i
\(452\) 8.87039 + 5.12132i 0.417228 + 0.240887i
\(453\) 0 0
\(454\) 25.0892i 1.17750i
\(455\) 0.630399 + 4.60660i 0.0295536 + 0.215961i
\(456\) 0 0
\(457\) 11.5000 + 19.9186i 0.537947 + 0.931752i 0.999014 + 0.0443868i \(0.0141334\pi\)
−0.461067 + 0.887365i \(0.652533\pi\)
\(458\) −2.80821 + 4.86396i −0.131219 + 0.227278i
\(459\) 0 0
\(460\) 12.7279 7.34847i 0.593442 0.342624i
\(461\) 21.4511 0.999076 0.499538 0.866292i \(-0.333503\pi\)
0.499538 + 0.866292i \(0.333503\pi\)
\(462\) 0 0
\(463\) −22.0000 −1.02243 −0.511213 0.859454i \(-0.670804\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(464\) −1.52192 + 0.878680i −0.0706533 + 0.0407917i
\(465\) 0 0
\(466\) 10.2426 17.7408i 0.474481 0.821825i
\(467\) −8.87039 15.3640i −0.410473 0.710959i 0.584469 0.811416i \(-0.301303\pi\)
−0.994941 + 0.100457i \(0.967970\pi\)
\(468\) 0 0
\(469\) −21.8640 28.1946i −1.00958 1.30191i
\(470\) 31.4558i 1.45095i
\(471\) 0 0
\(472\) 2.12132 + 1.22474i 0.0976417 + 0.0563735i
\(473\) 25.7196 + 14.8492i 1.18259 + 0.682769i
\(474\) 0 0
\(475\) 4.89898i 0.224781i
\(476\) 6.42090 0.878680i 0.294301 0.0402742i
\(477\) 0 0
\(478\) 8.12132 + 14.0665i 0.371461 + 0.643389i
\(479\) −1.22474 + 2.12132i −0.0559600 + 0.0969256i −0.892648 0.450754i \(-0.851155\pi\)
0.836688 + 0.547679i \(0.184489\pi\)
\(480\) 0 0
\(481\) −3.25736 + 1.88064i −0.148523 + 0.0857497i
\(482\) −1.13770 −0.0518210
\(483\) 0 0
\(484\) 7.00000 0.318182
\(485\) −6.71807 + 3.87868i −0.305052 + 0.176122i
\(486\) 0 0
\(487\) −11.0000 + 19.0526i −0.498458 + 0.863354i −0.999998 0.00178012i \(-0.999433\pi\)
0.501541 + 0.865134i \(0.332767\pi\)
\(488\) −2.09077 3.62132i −0.0946447 0.163929i
\(489\) 0 0
\(490\) −4.60660 16.5160i −0.208105 0.746118i
\(491\) 34.9706i 1.57820i 0.614265 + 0.789100i \(0.289453\pi\)
−0.614265 + 0.789100i \(0.710547\pi\)
\(492\) 0 0
\(493\) −3.72792 2.15232i −0.167897 0.0969355i
\(494\) 3.04384 + 1.75736i 0.136949 + 0.0790673i
\(495\) 0 0
\(496\) 9.08052i 0.407727i
\(497\) 31.1769 + 12.7279i 1.39848 + 0.570925i
\(498\) 0 0
\(499\) 12.2279 + 21.1794i 0.547397 + 0.948119i 0.998452 + 0.0556231i \(0.0177145\pi\)
−0.451055 + 0.892496i \(0.648952\pi\)
\(500\) 4.89898 8.48528i 0.219089 0.379473i
\(501\) 0 0
\(502\) 13.2426 7.64564i 0.591048 0.341242i
\(503\) −0.594346 −0.0265006 −0.0132503 0.999912i \(-0.504218\pi\)
−0.0132503 + 0.999912i \(0.504218\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 22.0454 12.7279i 0.980038 0.565825i
\(507\) 0 0
\(508\) −3.86396 + 6.69258i −0.171436 + 0.296935i
\(509\) 4.60181 + 7.97056i 0.203971 + 0.353289i 0.949805 0.312844i \(-0.101282\pi\)
−0.745833 + 0.666133i \(0.767948\pi\)
\(510\) 0 0
\(511\) 11.4853 8.90644i 0.508079 0.393998i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −21.7279 12.5446i −0.958378 0.553320i
\(515\) 23.5673 + 13.6066i 1.03850 + 0.599579i
\(516\) 0 0
\(517\) 54.4831i 2.39616i
\(518\) 10.9612 8.50000i 0.481606 0.373469i
\(519\) 0 0
\(520\) −0.878680 1.52192i −0.0385327 0.0667405i
\(521\) 14.9941 25.9706i 0.656904 1.13779i −0.324509 0.945883i \(-0.605199\pi\)
0.981413 0.191908i \(-0.0614676\pi\)
\(522\) 0 0
\(523\) 23.7426 13.7078i 1.03819 0.599401i 0.118872 0.992910i \(-0.462072\pi\)
0.919321 + 0.393508i \(0.128739\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −6.72792 −0.293351
\(527\) −19.2627 + 11.1213i −0.839096 + 0.484452i
\(528\) 0 0
\(529\) 6.50000 11.2583i 0.282609 0.489493i
\(530\) −17.7408 30.7279i −0.770610 1.33474i
\(531\) 0 0
\(532\) −12.0000 4.89898i −0.520266 0.212398i
\(533\) 1.75736i 0.0761197i
\(534\) 0 0
\(535\) −5.27208 3.04384i −0.227932 0.131596i
\(536\) 11.6786 + 6.74264i 0.504439 + 0.291238i
\(537\) 0 0
\(538\) 9.79796i 0.422420i
\(539\) −7.97887 28.6066i −0.343674 1.23217i
\(540\) 0 0
\(541\) 2.72792 + 4.72490i 0.117283 + 0.203139i 0.918690 0.394980i \(-0.129248\pi\)
−0.801407 + 0.598119i \(0.795915\pi\)
\(542\) −9.43924 + 16.3492i −0.405450 + 0.702260i
\(543\) 0 0
\(544\) −2.12132 + 1.22474i −0.0909509 + 0.0525105i
\(545\) 43.4244 1.86010
\(546\) 0 0
\(547\) 39.9706 1.70902 0.854509 0.519437i \(-0.173858\pi\)
0.854509 + 0.519437i \(0.173858\pi\)
\(548\) −5.19615 + 3.00000i −0.221969 + 0.128154i
\(549\) 0 0
\(550\) −2.12132 + 3.67423i −0.0904534 + 0.156670i
\(551\) 4.30463 + 7.45584i 0.183384 + 0.317630i
\(552\) 0 0
\(553\) 1.98528 0.271680i 0.0844228 0.0115530i
\(554\) 23.7279i 1.00810i
\(555\) 0 0
\(556\) 6.98528 + 4.03295i 0.296242 + 0.171035i
\(557\) −18.3712 10.6066i −0.778412 0.449416i 0.0574555 0.998348i \(-0.481701\pi\)
−0.835867 + 0.548932i \(0.815035\pi\)
\(558\) 0 0
\(559\) 5.02207i 0.212411i
\(560\) 3.97141 + 5.12132i 0.167823 + 0.216415i
\(561\) 0 0
\(562\) −6.87868 11.9142i −0.290160 0.502571i
\(563\) 22.9369 39.7279i 0.966676 1.67433i 0.261634 0.965167i \(-0.415739\pi\)
0.705043 0.709165i \(-0.250928\pi\)
\(564\) 0 0
\(565\) −21.7279 + 12.5446i −0.914101 + 0.527756i
\(566\) 6.03668 0.253741
\(567\) 0 0
\(568\) −12.7279 −0.534052
\(569\) −8.87039 + 5.12132i −0.371866 + 0.214697i −0.674273 0.738482i \(-0.735543\pi\)
0.302407 + 0.953179i \(0.402210\pi\)
\(570\) 0 0
\(571\) 11.0000 19.0526i 0.460336 0.797325i −0.538642 0.842535i \(-0.681062\pi\)
0.998978 + 0.0452101i \(0.0143957\pi\)
\(572\) −1.52192 2.63604i −0.0636346 0.110218i
\(573\) 0 0
\(574\) 0.878680 + 6.42090i 0.0366754 + 0.268003i
\(575\) 6.00000i 0.250217i
\(576\) 0 0
\(577\) 23.7426 + 13.7078i 0.988419 + 0.570664i 0.904801 0.425834i \(-0.140019\pi\)
0.0836177 + 0.996498i \(0.473353\pi\)
\(578\) 9.52628 + 5.50000i 0.396241 + 0.228770i
\(579\) 0 0
\(580\) 4.30463i 0.178740i
\(581\) 15.2913 37.4558i 0.634389 1.55393i
\(582\) 0 0
\(583\) −30.7279 53.2223i −1.27262 2.20424i
\(584\) −2.74666 + 4.75736i −0.113658 + 0.196861i
\(585\) 0 0
\(586\) 11.1213 6.42090i 0.459418 0.265245i
\(587\) 32.4377 1.33885 0.669424 0.742881i \(-0.266541\pi\)
0.669424 + 0.742881i \(0.266541\pi\)
\(588\) 0 0
\(589\) 44.4853 1.83298
\(590\) −5.19615 + 3.00000i −0.213922 + 0.123508i
\(591\) 0 0
\(592\) −2.62132 + 4.54026i −0.107736 + 0.186604i
\(593\) 0.927572 + 1.60660i 0.0380908 + 0.0659752i 0.884442 0.466650i \(-0.154539\pi\)
−0.846352 + 0.532625i \(0.821206\pi\)
\(594\) 0 0
\(595\) −6.00000 + 14.6969i −0.245976 + 0.602516i
\(596\) 16.2426i 0.665324i
\(597\) 0 0
\(598\) −3.72792 2.15232i −0.152446 0.0880148i
\(599\) 3.04384 + 1.75736i 0.124368 + 0.0718038i 0.560893 0.827888i \(-0.310458\pi\)
−0.436526 + 0.899692i \(0.643791\pi\)
\(600\) 0 0
\(601\) 41.5182i 1.69356i 0.531940 + 0.846782i \(0.321463\pi\)
−0.531940 + 0.846782i \(0.678537\pi\)
\(602\) 2.51104 + 18.3492i 0.102342 + 0.747859i
\(603\) 0 0
\(604\) 4.37868 + 7.58410i 0.178166 + 0.308592i
\(605\) −8.57321 + 14.8492i −0.348551 + 0.603708i
\(606\) 0 0
\(607\) 31.2426 18.0379i 1.26810 0.732138i 0.293471 0.955968i \(-0.405189\pi\)
0.974628 + 0.223830i \(0.0718561\pi\)
\(608\) 4.89898 0.198680
\(609\) 0 0
\(610\) 10.2426 0.414712
\(611\) 7.97887 4.60660i 0.322790 0.186363i
\(612\) 0 0
\(613\) 14.1066 24.4334i 0.569760 0.986854i −0.426829 0.904332i \(-0.640369\pi\)
0.996589 0.0825214i \(-0.0262973\pi\)
\(614\) 13.4106 + 23.2279i 0.541210 + 0.937403i
\(615\) 0 0
\(616\) 6.87868 + 8.87039i 0.277150 + 0.357398i
\(617\) 4.24264i 0.170802i 0.996347 + 0.0854011i \(0.0272172\pi\)
−0.996347 + 0.0854011i \(0.972783\pi\)
\(618\) 0 0
\(619\) −11.0147 6.35935i −0.442719 0.255604i 0.262031 0.965059i \(-0.415608\pi\)
−0.704750 + 0.709455i \(0.748941\pi\)
\(620\) −19.2627 11.1213i −0.773608 0.446643i
\(621\) 0 0
\(622\) 17.1464i 0.687509i
\(623\) −7.97887 + 1.09188i −0.319667 + 0.0437454i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −10.0951 + 17.4853i −0.403483 + 0.698852i
\(627\) 0 0
\(628\) −9.00000 + 5.19615i −0.359139 + 0.207349i
\(629\) −12.8418 −0.512036
\(630\) 0 0
\(631\) −14.7574 −0.587481 −0.293741 0.955885i \(-0.594900\pi\)
−0.293741 + 0.955885i \(0.594900\pi\)
\(632\) −0.655892 + 0.378680i −0.0260900 + 0.0150631i
\(633\) 0 0
\(634\) −11.1213 + 19.2627i −0.441684 + 0.765019i
\(635\) −9.46473 16.3934i −0.375596 0.650552i
\(636\) 0 0
\(637\) −3.51472 + 3.58719i −0.139258 + 0.142130i
\(638\) 7.45584i 0.295180i
\(639\) 0 0
\(640\) −2.12132 1.22474i −0.0838525 0.0484123i
\(641\) 28.7635 + 16.6066i 1.13609 + 0.655921i 0.945459 0.325741i \(-0.105614\pi\)
0.190630 + 0.981662i \(0.438947\pi\)
\(642\) 0 0
\(643\) 1.73205i 0.0683054i −0.999417 0.0341527i \(-0.989127\pi\)
0.999417 0.0341527i \(-0.0108733\pi\)
\(644\) 14.6969 + 6.00000i 0.579141 + 0.236433i
\(645\) 0 0
\(646\) 6.00000 + 10.3923i 0.236067 + 0.408880i
\(647\) −10.3923 + 18.0000i −0.408564 + 0.707653i −0.994729 0.102538i \(-0.967304\pi\)
0.586165 + 0.810191i \(0.300637\pi\)
\(648\) 0 0
\(649\) −9.00000 + 5.19615i −0.353281 + 0.203967i
\(650\) 0.717439 0.0281403
\(651\) 0 0
\(652\) 9.48528 0.371472
\(653\) −2.15232 + 1.24264i −0.0842267 + 0.0486283i −0.541522 0.840687i \(-0.682152\pi\)
0.457295 + 0.889315i \(0.348818\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.22474 2.12132i −0.0478183 0.0828236i
\(657\) 0 0
\(658\) −26.8492 + 20.8207i −1.04669 + 0.811674i
\(659\) 22.2426i 0.866450i 0.901286 + 0.433225i \(0.142624\pi\)
−0.901286 + 0.433225i \(0.857376\pi\)
\(660\) 0 0
\(661\) −4.24264 2.44949i −0.165020 0.0952741i 0.415216 0.909723i \(-0.363706\pi\)
−0.580235 + 0.814449i \(0.697039\pi\)
\(662\) −8.66025 5.00000i −0.336590 0.194331i
\(663\) 0 0
\(664\) 15.2913i 0.593417i
\(665\) 25.0892 19.4558i 0.972919 0.754465i
\(666\) 0 0
\(667\) −5.27208 9.13151i −0.204136 0.353573i
\(668\) 0.297173 0.514719i 0.0114980 0.0199151i
\(669\) 0 0
\(670\) −28.6066 + 16.5160i −1.10517 + 0.638070i
\(671\) 17.7408 0.684875
\(672\) 0 0
\(673\) −45.4558 −1.75219 −0.876097 0.482135i \(-0.839862\pi\)
−0.876097 + 0.482135i \(0.839862\pi\)
\(674\) −18.5813 + 10.7279i −0.715725 + 0.413224i
\(675\) 0 0
\(676\) 6.24264 10.8126i 0.240102 0.415868i
\(677\) 7.34847 + 12.7279i 0.282425 + 0.489174i 0.971981 0.235058i \(-0.0755280\pi\)
−0.689557 + 0.724232i \(0.742195\pi\)
\(678\) 0 0
\(679\) −7.75736 3.16693i −0.297700 0.121536i
\(680\) 6.00000i 0.230089i
\(681\) 0 0
\(682\) −33.3640 19.2627i −1.27757 0.737607i
\(683\) 8.87039 + 5.12132i 0.339416 + 0.195962i 0.660014 0.751254i \(-0.270550\pi\)
−0.320598 + 0.947215i \(0.603884\pi\)
\(684\) 0 0
\(685\) 14.6969i 0.561541i
\(686\) 11.0482 14.8640i 0.421822 0.567509i
\(687\) 0 0
\(688\) −3.50000 6.06218i −0.133436 0.231118i
\(689\) −5.19615 + 9.00000i −0.197958 + 0.342873i
\(690\) 0 0
\(691\) 2.22792 1.28629i 0.0847541 0.0489328i −0.457024 0.889454i \(-0.651085\pi\)
0.541778 + 0.840522i \(0.317751\pi\)
\(692\) 20.7846 0.790112
\(693\) 0 0
\(694\) −4.97056 −0.188680
\(695\) −17.1104 + 9.87868i −0.649034 + 0.374720i
\(696\) 0 0
\(697\) 3.00000 5.19615i 0.113633 0.196818i
\(698\) −0.0615465 0.106602i −0.00232957 0.00403493i
\(699\) 0 0
\(700\) −2.62132 + 0.358719i −0.0990766 + 0.0135583i
\(701\) 20.4853i 0.773718i 0.922139 + 0.386859i \(0.126440\pi\)
−0.922139 + 0.386859i \(0.873560\pi\)
\(702\) 0 0
\(703\) 22.2426 + 12.8418i 0.838897 + 0.484337i
\(704\) −3.67423 2.12132i −0.138478 0.0799503i
\(705\) 0 0
\(706\) 10.9867i 0.413488i
\(707\) 11.9142 + 15.3640i 0.448080 + 0.577821i
\(708\) 0 0
\(709\) −8.10660 14.0410i −0.304450 0.527323i 0.672689 0.739925i \(-0.265139\pi\)
−0.977139 + 0.212603i \(0.931806\pi\)
\(710\) 15.5885 27.0000i 0.585024 1.01329i
\(711\) 0 0
\(712\) 2.63604 1.52192i 0.0987897 0.0570363i
\(713\) −54.4831 −2.04041
\(714\) 0 0
\(715\) 7.45584 0.278833
\(716\) 5.82655 3.36396i 0.217748 0.125717i
\(717\) 0 0
\(718\) −7.24264 + 12.5446i −0.270293 + 0.468161i
\(719\) −26.3140 45.5772i −0.981346 1.69974i −0.657166 0.753746i \(-0.728245\pi\)
−0.324181 0.945995i \(-0.605089\pi\)
\(720\) 0 0
\(721\) 3.98528 + 29.1222i 0.148420 + 1.08457i
\(722\) 5.00000i 0.186081i
\(723\) 0 0
\(724\) −8.48528 4.89898i −0.315353 0.182069i
\(725\) 1.52192 + 0.878680i 0.0565226 + 0.0326333i
\(726\) 0 0
\(727\) 28.0821i 1.04151i −0.853707 0.520754i \(-0.825651\pi\)
0.853707 0.520754i \(-0.174349\pi\)
\(728\) 0.717439 1.75736i 0.0265901 0.0651321i
\(729\) 0 0
\(730\) −6.72792 11.6531i −0.249012 0.431301i
\(731\) 8.57321 14.8492i 0.317092 0.549219i
\(732\) 0 0
\(733\) 1.13604 0.655892i 0.0419606 0.0242259i −0.478873 0.877884i \(-0.658955\pi\)
0.520834 + 0.853658i \(0.325621\pi\)
\(734\) −29.9882 −1.10689
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) −49.5481 + 28.6066i −1.82513 + 1.05374i
\(738\) 0 0
\(739\) 4.22792 7.32298i 0.155527 0.269380i −0.777724 0.628606i \(-0.783626\pi\)
0.933251 + 0.359226i \(0.116959\pi\)
\(740\) −6.42090 11.1213i −0.236037 0.408828i
\(741\) 0 0
\(742\) 14.4853 35.4815i 0.531771 1.30257i
\(743\) 18.7279i 0.687061i 0.939142 + 0.343530i \(0.111623\pi\)
−0.939142 + 0.343530i \(0.888377\pi\)
\(744\) 0 0
\(745\) 34.4558 + 19.8931i 1.26236 + 0.728826i
\(746\) 19.0526 + 11.0000i 0.697564 + 0.402739i
\(747\) 0 0
\(748\) 10.3923i 0.379980i
\(749\) −0.891519 6.51472i −0.0325754 0.238043i
\(750\) 0 0
\(751\) −26.7279 46.2941i −0.975316 1.68930i −0.678889 0.734241i \(-0.737538\pi\)
−0.296427 0.955056i \(-0.595795\pi\)
\(752\) 6.42090 11.1213i 0.234146 0.405553i
\(753\) 0 0
\(754\) −1.09188 + 0.630399i −0.0397640 + 0.0229578i
\(755\) −21.4511 −0.780684
\(756\) 0 0
\(757\) 32.7574 1.19059 0.595293 0.803509i \(-0.297036\pi\)
0.595293 + 0.803509i \(0.297036\pi\)
\(758\) −6.48244 + 3.74264i −0.235453 + 0.135939i
\(759\) 0 0
\(760\) −6.00000 + 10.3923i −0.217643 + 0.376969i
\(761\) −12.2474 21.2132i −0.443970 0.768978i 0.554010 0.832510i \(-0.313097\pi\)
−0.997980 + 0.0635319i \(0.979764\pi\)
\(762\) 0 0
\(763\) 28.7426 + 37.0650i 1.04055 + 1.34184i
\(764\) 21.2132i 0.767467i
\(765\) 0 0
\(766\) −4.75736 2.74666i −0.171890 0.0992410i
\(767\) 1.52192 + 0.878680i 0.0549533 + 0.0317273i
\(768\) 0 0
\(769\) 40.3805i 1.45616i −0.685493 0.728080i \(-0.740413\pi\)
0.685493 0.728080i \(-0.259587\pi\)
\(770\) −27.2416 + 3.72792i −0.981718 + 0.134345i
\(771\) 0 0
\(772\) −0.742641 1.28629i −0.0267282 0.0462946i
\(773\) 4.89898 8.48528i 0.176204 0.305194i −0.764373 0.644774i \(-0.776951\pi\)
0.940577 + 0.339580i \(0.110285\pi\)
\(774\) 0 0
\(775\) 7.86396 4.54026i 0.282482 0.163091i
\(776\) 3.16693 0.113686
\(777\) 0 0
\(778\) 15.5147 0.556230
\(779\) −10.3923 + 6.00000i −0.372343 + 0.214972i
\(780\) 0 0
\(781\) 27.0000 46.7654i 0.966136 1.67340i
\(782\) −7.34847 12.7279i −0.262781 0.455150i
\(783\) 0 0
\(784\) −1.74264 + 6.77962i −0.0622372 + 0.242129i
\(785\) 25.4558i 0.908558i
\(786\) 0 0
\(787\) −24.4706 14.1281i −0.872281 0.503612i −0.00417567 0.999991i \(-0.501329\pi\)
−0.868106 + 0.496379i \(0.834662\pi\)
\(788\) 14.6969 + 8.48528i 0.523557