Properties

Label 456.2.bf.a.449.2
Level $456$
Weight $2$
Character 456.449
Analytic conductor $3.641$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 456.bf (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.64117833217\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
Defining polynomial: \(x^{4} - x^{3} - 2 x^{2} - 3 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 449.2
Root \(1.68614 + 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 456.449
Dual form 456.2.bf.a.65.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.68614 + 0.396143i) q^{3} +(-2.18614 + 1.26217i) q^{5} +3.37228 q^{7} +(2.68614 + 1.33591i) q^{9} +O(q^{10})\) \(q+(1.68614 + 0.396143i) q^{3} +(-2.18614 + 1.26217i) q^{5} +3.37228 q^{7} +(2.68614 + 1.33591i) q^{9} -3.46410i q^{11} +(2.87228 + 1.65831i) q^{13} +(-4.18614 + 1.26217i) q^{15} +(-2.18614 + 1.26217i) q^{17} +(-4.00000 + 1.73205i) q^{19} +(5.68614 + 1.33591i) q^{21} +(7.93070 + 4.57879i) q^{23} +(0.686141 - 1.18843i) q^{25} +(4.00000 + 3.31662i) q^{27} +(0.186141 - 0.322405i) q^{29} +7.72049i q^{31} +(1.37228 - 5.84096i) q^{33} +(-7.37228 + 4.25639i) q^{35} -11.1846i q^{37} +(4.18614 + 3.93398i) q^{39} +(-3.18614 - 5.51856i) q^{41} +(-5.87228 - 10.1711i) q^{43} +(-7.55842 + 0.469882i) q^{45} +(-0.813859 - 0.469882i) q^{47} +4.37228 q^{49} +(-4.18614 + 1.26217i) q^{51} +(2.81386 - 4.87375i) q^{53} +(4.37228 + 7.57301i) q^{55} +(-7.43070 + 1.33591i) q^{57} +(-0.813859 - 1.40965i) q^{59} +(0.500000 - 0.866025i) q^{61} +(9.05842 + 4.50506i) q^{63} -8.37228 q^{65} +(-1.24456 - 0.718549i) q^{67} +(11.5584 + 10.8622i) q^{69} +(-6.18614 - 10.7147i) q^{71} +(-2.87228 - 4.97494i) q^{73} +(1.62772 - 1.73205i) q^{75} -11.6819i q^{77} +(-12.9891 + 7.49927i) q^{79} +(5.43070 + 7.17687i) q^{81} +3.46410i q^{83} +(3.18614 - 5.51856i) q^{85} +(0.441578 - 0.469882i) q^{87} +(0.813859 - 1.40965i) q^{89} +(9.68614 + 5.59230i) q^{91} +(-3.05842 + 13.0178i) q^{93} +(6.55842 - 8.83518i) q^{95} +(2.44158 - 1.40965i) q^{97} +(4.62772 - 9.30506i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + q^{3} - 3q^{5} + 2q^{7} + 5q^{9} + O(q^{10}) \) \( 4q + q^{3} - 3q^{5} + 2q^{7} + 5q^{9} - 11q^{15} - 3q^{17} - 16q^{19} + 17q^{21} + 3q^{23} - 3q^{25} + 16q^{27} - 5q^{29} - 6q^{33} - 18q^{35} + 11q^{39} - 7q^{41} - 12q^{43} - 13q^{45} - 9q^{47} + 6q^{49} - 11q^{51} + 17q^{53} + 6q^{55} - q^{57} - 9q^{59} + 2q^{61} + 19q^{63} - 22q^{65} + 18q^{67} + 29q^{69} - 19q^{71} + 18q^{75} - 6q^{79} - 7q^{81} + 7q^{85} + 19q^{87} + 9q^{89} + 33q^{91} + 5q^{93} + 9q^{95} + 27q^{97} + 30q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/456\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(343\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.68614 + 0.396143i 0.973494 + 0.228714i
\(4\) 0 0
\(5\) −2.18614 + 1.26217i −0.977672 + 0.564459i −0.901566 0.432641i \(-0.857582\pi\)
−0.0761054 + 0.997100i \(0.524249\pi\)
\(6\) 0 0
\(7\) 3.37228 1.27460 0.637301 0.770615i \(-0.280051\pi\)
0.637301 + 0.770615i \(0.280051\pi\)
\(8\) 0 0
\(9\) 2.68614 + 1.33591i 0.895380 + 0.445302i
\(10\) 0 0
\(11\) 3.46410i 1.04447i −0.852803 0.522233i \(-0.825099\pi\)
0.852803 0.522233i \(-0.174901\pi\)
\(12\) 0 0
\(13\) 2.87228 + 1.65831i 0.796628 + 0.459933i 0.842291 0.539024i \(-0.181207\pi\)
−0.0456630 + 0.998957i \(0.514540\pi\)
\(14\) 0 0
\(15\) −4.18614 + 1.26217i −1.08086 + 0.325891i
\(16\) 0 0
\(17\) −2.18614 + 1.26217i −0.530217 + 0.306121i −0.741105 0.671389i \(-0.765698\pi\)
0.210888 + 0.977510i \(0.432365\pi\)
\(18\) 0 0
\(19\) −4.00000 + 1.73205i −0.917663 + 0.397360i
\(20\) 0 0
\(21\) 5.68614 + 1.33591i 1.24082 + 0.291519i
\(22\) 0 0
\(23\) 7.93070 + 4.57879i 1.65367 + 0.954744i 0.975547 + 0.219793i \(0.0705381\pi\)
0.678119 + 0.734952i \(0.262795\pi\)
\(24\) 0 0
\(25\) 0.686141 1.18843i 0.137228 0.237686i
\(26\) 0 0
\(27\) 4.00000 + 3.31662i 0.769800 + 0.638285i
\(28\) 0 0
\(29\) 0.186141 0.322405i 0.0345655 0.0598691i −0.848225 0.529636i \(-0.822329\pi\)
0.882791 + 0.469767i \(0.155662\pi\)
\(30\) 0 0
\(31\) 7.72049i 1.38664i 0.720629 + 0.693320i \(0.243853\pi\)
−0.720629 + 0.693320i \(0.756147\pi\)
\(32\) 0 0
\(33\) 1.37228 5.84096i 0.238884 1.01678i
\(34\) 0 0
\(35\) −7.37228 + 4.25639i −1.24614 + 0.719461i
\(36\) 0 0
\(37\) 11.1846i 1.83874i −0.393399 0.919368i \(-0.628701\pi\)
0.393399 0.919368i \(-0.371299\pi\)
\(38\) 0 0
\(39\) 4.18614 + 3.93398i 0.670319 + 0.629942i
\(40\) 0 0
\(41\) −3.18614 5.51856i −0.497592 0.861854i 0.502405 0.864633i \(-0.332449\pi\)
−0.999996 + 0.00277878i \(0.999115\pi\)
\(42\) 0 0
\(43\) −5.87228 10.1711i −0.895515 1.55108i −0.833167 0.553022i \(-0.813474\pi\)
−0.0623480 0.998054i \(-0.519859\pi\)
\(44\) 0 0
\(45\) −7.55842 + 0.469882i −1.12674 + 0.0700459i
\(46\) 0 0
\(47\) −0.813859 0.469882i −0.118714 0.0685393i 0.439467 0.898259i \(-0.355167\pi\)
−0.558181 + 0.829719i \(0.688501\pi\)
\(48\) 0 0
\(49\) 4.37228 0.624612
\(50\) 0 0
\(51\) −4.18614 + 1.26217i −0.586177 + 0.176739i
\(52\) 0 0
\(53\) 2.81386 4.87375i 0.386513 0.669461i −0.605465 0.795872i \(-0.707013\pi\)
0.991978 + 0.126412i \(0.0403460\pi\)
\(54\) 0 0
\(55\) 4.37228 + 7.57301i 0.589558 + 1.02114i
\(56\) 0 0
\(57\) −7.43070 + 1.33591i −0.984221 + 0.176945i
\(58\) 0 0
\(59\) −0.813859 1.40965i −0.105955 0.183520i 0.808173 0.588946i \(-0.200457\pi\)
−0.914128 + 0.405425i \(0.867123\pi\)
\(60\) 0 0
\(61\) 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i \(-0.812942\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 0 0
\(63\) 9.05842 + 4.50506i 1.14125 + 0.567584i
\(64\) 0 0
\(65\) −8.37228 −1.03845
\(66\) 0 0
\(67\) −1.24456 0.718549i −0.152048 0.0877847i 0.422046 0.906574i \(-0.361312\pi\)
−0.574094 + 0.818790i \(0.694645\pi\)
\(68\) 0 0
\(69\) 11.5584 + 10.8622i 1.39147 + 1.30765i
\(70\) 0 0
\(71\) −6.18614 10.7147i −0.734160 1.27160i −0.955091 0.296313i \(-0.904243\pi\)
0.220931 0.975289i \(-0.429090\pi\)
\(72\) 0 0
\(73\) −2.87228 4.97494i −0.336175 0.582272i 0.647535 0.762036i \(-0.275800\pi\)
−0.983710 + 0.179764i \(0.942467\pi\)
\(74\) 0 0
\(75\) 1.62772 1.73205i 0.187953 0.200000i
\(76\) 0 0
\(77\) 11.6819i 1.33128i
\(78\) 0 0
\(79\) −12.9891 + 7.49927i −1.46139 + 0.843734i −0.999076 0.0429815i \(-0.986314\pi\)
−0.462315 + 0.886716i \(0.652981\pi\)
\(80\) 0 0
\(81\) 5.43070 + 7.17687i 0.603411 + 0.797430i
\(82\) 0 0
\(83\) 3.46410i 0.380235i 0.981761 + 0.190117i \(0.0608868\pi\)
−0.981761 + 0.190117i \(0.939113\pi\)
\(84\) 0 0
\(85\) 3.18614 5.51856i 0.345585 0.598572i
\(86\) 0 0
\(87\) 0.441578 0.469882i 0.0473421 0.0503766i
\(88\) 0 0
\(89\) 0.813859 1.40965i 0.0862689 0.149422i −0.819662 0.572847i \(-0.805839\pi\)
0.905931 + 0.423425i \(0.139172\pi\)
\(90\) 0 0
\(91\) 9.68614 + 5.59230i 1.01538 + 0.586232i
\(92\) 0 0
\(93\) −3.05842 + 13.0178i −0.317144 + 1.34989i
\(94\) 0 0
\(95\) 6.55842 8.83518i 0.672880 0.906471i
\(96\) 0 0
\(97\) 2.44158 1.40965i 0.247905 0.143128i −0.370900 0.928673i \(-0.620951\pi\)
0.618804 + 0.785545i \(0.287617\pi\)
\(98\) 0 0
\(99\) 4.62772 9.30506i 0.465103 0.935194i
\(100\) 0 0
\(101\) −2.18614 1.26217i −0.217529 0.125590i 0.387277 0.921964i \(-0.373416\pi\)
−0.604806 + 0.796373i \(0.706749\pi\)
\(102\) 0 0
\(103\) 9.30506i 0.916855i 0.888732 + 0.458428i \(0.151587\pi\)
−0.888732 + 0.458428i \(0.848413\pi\)
\(104\) 0 0
\(105\) −14.1168 + 4.25639i −1.37766 + 0.415381i
\(106\) 0 0
\(107\) 5.25544 0.508062 0.254031 0.967196i \(-0.418243\pi\)
0.254031 + 0.967196i \(0.418243\pi\)
\(108\) 0 0
\(109\) −3.55842 + 2.05446i −0.340835 + 0.196781i −0.660641 0.750702i \(-0.729716\pi\)
0.319806 + 0.947483i \(0.396382\pi\)
\(110\) 0 0
\(111\) 4.43070 18.8588i 0.420544 1.79000i
\(112\) 0 0
\(113\) −3.25544 −0.306246 −0.153123 0.988207i \(-0.548933\pi\)
−0.153123 + 0.988207i \(0.548933\pi\)
\(114\) 0 0
\(115\) −23.1168 −2.15566
\(116\) 0 0
\(117\) 5.50000 + 8.29156i 0.508475 + 0.766555i
\(118\) 0 0
\(119\) −7.37228 + 4.25639i −0.675816 + 0.390183i
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) 0 0
\(123\) −3.18614 10.5672i −0.287285 0.952815i
\(124\) 0 0
\(125\) 9.15759i 0.819080i
\(126\) 0 0
\(127\) 3.30298 + 1.90698i 0.293092 + 0.169217i 0.639336 0.768928i \(-0.279209\pi\)
−0.346243 + 0.938145i \(0.612543\pi\)
\(128\) 0 0
\(129\) −5.87228 19.4762i −0.517026 1.71478i
\(130\) 0 0
\(131\) −15.3030 + 8.83518i −1.33703 + 0.771933i −0.986366 0.164569i \(-0.947377\pi\)
−0.350662 + 0.936502i \(0.614044\pi\)
\(132\) 0 0
\(133\) −13.4891 + 5.84096i −1.16966 + 0.506476i
\(134\) 0 0
\(135\) −12.9307 2.20193i −1.11290 0.189512i
\(136\) 0 0
\(137\) −14.1861 8.19037i −1.21200 0.699751i −0.248808 0.968553i \(-0.580039\pi\)
−0.963195 + 0.268802i \(0.913372\pi\)
\(138\) 0 0
\(139\) 3.24456 5.61975i 0.275200 0.476661i −0.694985 0.719024i \(-0.744589\pi\)
0.970186 + 0.242363i \(0.0779225\pi\)
\(140\) 0 0
\(141\) −1.18614 1.11469i −0.0998911 0.0938740i
\(142\) 0 0
\(143\) 5.74456 9.94987i 0.480384 0.832050i
\(144\) 0 0
\(145\) 0.939764i 0.0780431i
\(146\) 0 0
\(147\) 7.37228 + 1.73205i 0.608056 + 0.142857i
\(148\) 0 0
\(149\) 6.55842 3.78651i 0.537287 0.310203i −0.206692 0.978406i \(-0.566270\pi\)
0.743979 + 0.668203i \(0.232936\pi\)
\(150\) 0 0
\(151\) 0.294954i 0.0240030i 0.999928 + 0.0120015i \(0.00382029\pi\)
−0.999928 + 0.0120015i \(0.996180\pi\)
\(152\) 0 0
\(153\) −7.55842 + 0.469882i −0.611062 + 0.0379877i
\(154\) 0 0
\(155\) −9.74456 16.8781i −0.782702 1.35568i
\(156\) 0 0
\(157\) 1.24456 + 2.15565i 0.0993269 + 0.172039i 0.911406 0.411508i \(-0.134998\pi\)
−0.812079 + 0.583547i \(0.801664\pi\)
\(158\) 0 0
\(159\) 6.67527 7.10313i 0.529383 0.563315i
\(160\) 0 0
\(161\) 26.7446 + 15.4410i 2.10777 + 1.21692i
\(162\) 0 0
\(163\) 15.3723 1.20405 0.602025 0.798477i \(-0.294361\pi\)
0.602025 + 0.798477i \(0.294361\pi\)
\(164\) 0 0
\(165\) 4.37228 + 14.5012i 0.340382 + 1.12892i
\(166\) 0 0
\(167\) −0.441578 + 0.764836i −0.0341703 + 0.0591848i −0.882605 0.470116i \(-0.844212\pi\)
0.848434 + 0.529300i \(0.177546\pi\)
\(168\) 0 0
\(169\) −1.00000 1.73205i −0.0769231 0.133235i
\(170\) 0 0
\(171\) −13.0584 0.691097i −0.998602 0.0528495i
\(172\) 0 0
\(173\) 6.93070 + 12.0043i 0.526932 + 0.912672i 0.999507 + 0.0313823i \(0.00999094\pi\)
−0.472576 + 0.881290i \(0.656676\pi\)
\(174\) 0 0
\(175\) 2.31386 4.00772i 0.174911 0.302955i
\(176\) 0 0
\(177\) −0.813859 2.69927i −0.0611734 0.202889i
\(178\) 0 0
\(179\) −1.48913 −0.111302 −0.0556512 0.998450i \(-0.517723\pi\)
−0.0556512 + 0.998450i \(0.517723\pi\)
\(180\) 0 0
\(181\) −18.3030 10.5672i −1.36045 0.785456i −0.370766 0.928726i \(-0.620905\pi\)
−0.989684 + 0.143270i \(0.954238\pi\)
\(182\) 0 0
\(183\) 1.18614 1.26217i 0.0876820 0.0933022i
\(184\) 0 0
\(185\) 14.1168 + 24.4511i 1.03789 + 1.79768i
\(186\) 0 0
\(187\) 4.37228 + 7.57301i 0.319733 + 0.553794i
\(188\) 0 0
\(189\) 13.4891 + 11.1846i 0.981189 + 0.813559i
\(190\) 0 0
\(191\) 6.63325i 0.479965i 0.970777 + 0.239983i \(0.0771417\pi\)
−0.970777 + 0.239983i \(0.922858\pi\)
\(192\) 0 0
\(193\) 13.5000 7.79423i 0.971751 0.561041i 0.0719816 0.997406i \(-0.477068\pi\)
0.899770 + 0.436365i \(0.143734\pi\)
\(194\) 0 0
\(195\) −14.1168 3.31662i −1.01093 0.237508i
\(196\) 0 0
\(197\) 23.3639i 1.66461i 0.554321 + 0.832303i \(0.312978\pi\)
−0.554321 + 0.832303i \(0.687022\pi\)
\(198\) 0 0
\(199\) 1.24456 2.15565i 0.0882247 0.152810i −0.818536 0.574455i \(-0.805214\pi\)
0.906761 + 0.421645i \(0.138547\pi\)
\(200\) 0 0
\(201\) −1.81386 1.70460i −0.127940 0.120233i
\(202\) 0 0
\(203\) 0.627719 1.08724i 0.0440572 0.0763093i
\(204\) 0 0
\(205\) 13.9307 + 8.04290i 0.972963 + 0.561740i
\(206\) 0 0
\(207\) 15.1861 + 22.8940i 1.05551 + 1.59124i
\(208\) 0 0
\(209\) 6.00000 + 13.8564i 0.415029 + 0.958468i
\(210\) 0 0
\(211\) 9.98913 5.76722i 0.687680 0.397032i −0.115062 0.993358i \(-0.536707\pi\)
0.802742 + 0.596326i \(0.203373\pi\)
\(212\) 0 0
\(213\) −6.18614 20.5171i −0.423867 1.40581i
\(214\) 0 0
\(215\) 25.6753 + 14.8236i 1.75104 + 1.01096i
\(216\) 0 0
\(217\) 26.0357i 1.76742i
\(218\) 0 0
\(219\) −2.87228 9.52628i −0.194091 0.643726i
\(220\) 0 0
\(221\) −8.37228 −0.563181
\(222\) 0 0
\(223\) 18.7337 10.8159i 1.25450 0.724286i 0.282501 0.959267i \(-0.408836\pi\)
0.972000 + 0.234981i \(0.0755028\pi\)
\(224\) 0 0
\(225\) 3.43070 2.27567i 0.228714 0.151711i
\(226\) 0 0
\(227\) −18.7446 −1.24412 −0.622060 0.782969i \(-0.713704\pi\)
−0.622060 + 0.782969i \(0.713704\pi\)
\(228\) 0 0
\(229\) −3.88316 −0.256606 −0.128303 0.991735i \(-0.540953\pi\)
−0.128303 + 0.991735i \(0.540953\pi\)
\(230\) 0 0
\(231\) 4.62772 19.6974i 0.304482 1.29599i
\(232\) 0 0
\(233\) 12.5584 7.25061i 0.822730 0.475003i −0.0286273 0.999590i \(-0.509114\pi\)
0.851357 + 0.524587i \(0.175780\pi\)
\(234\) 0 0
\(235\) 2.37228 0.154751
\(236\) 0 0
\(237\) −24.8723 + 7.49927i −1.61563 + 0.487130i
\(238\) 0 0
\(239\) 10.3923i 0.672222i 0.941822 + 0.336111i \(0.109112\pi\)
−0.941822 + 0.336111i \(0.890888\pi\)
\(240\) 0 0
\(241\) 17.6168 + 10.1711i 1.13480 + 0.655177i 0.945138 0.326672i \(-0.105927\pi\)
0.189663 + 0.981849i \(0.439261\pi\)
\(242\) 0 0
\(243\) 6.31386 + 14.2525i 0.405034 + 0.914302i
\(244\) 0 0
\(245\) −9.55842 + 5.51856i −0.610665 + 0.352568i
\(246\) 0 0
\(247\) −14.3614 1.65831i −0.913794 0.105516i
\(248\) 0 0
\(249\) −1.37228 + 5.84096i −0.0869648 + 0.370156i
\(250\) 0 0
\(251\) 19.9307 + 11.5070i 1.25801 + 0.726315i 0.972688 0.232115i \(-0.0745646\pi\)
0.285327 + 0.958430i \(0.407898\pi\)
\(252\) 0 0
\(253\) 15.8614 27.4728i 0.997198 1.72720i
\(254\) 0 0
\(255\) 7.55842 8.04290i 0.473327 0.503666i
\(256\) 0 0
\(257\) 9.55842 16.5557i 0.596238 1.03271i −0.397133 0.917761i \(-0.629995\pi\)
0.993371 0.114953i \(-0.0366719\pi\)
\(258\) 0 0
\(259\) 37.7176i 2.34366i
\(260\) 0 0
\(261\) 0.930703 0.617359i 0.0576091 0.0382135i
\(262\) 0 0
\(263\) 10.9307 6.31084i 0.674016 0.389143i −0.123581 0.992335i \(-0.539438\pi\)
0.797597 + 0.603191i \(0.206104\pi\)
\(264\) 0 0
\(265\) 14.2063i 0.872684i
\(266\) 0 0
\(267\) 1.93070 2.05446i 0.118157 0.125731i
\(268\) 0 0
\(269\) −7.93070 13.7364i −0.483544 0.837522i 0.516278 0.856421i \(-0.327317\pi\)
−0.999821 + 0.0188992i \(0.993984\pi\)
\(270\) 0 0
\(271\) 9.93070 + 17.2005i 0.603247 + 1.04485i 0.992326 + 0.123650i \(0.0394601\pi\)
−0.389079 + 0.921205i \(0.627207\pi\)
\(272\) 0 0
\(273\) 14.1168 + 13.2665i 0.854390 + 0.802925i
\(274\) 0 0
\(275\) −4.11684 2.37686i −0.248255 0.143330i
\(276\) 0 0
\(277\) −19.4891 −1.17099 −0.585494 0.810677i \(-0.699099\pi\)
−0.585494 + 0.810677i \(0.699099\pi\)
\(278\) 0 0
\(279\) −10.3139 + 20.7383i −0.617475 + 1.24157i
\(280\) 0 0
\(281\) −7.30298 + 12.6491i −0.435660 + 0.754584i −0.997349 0.0727635i \(-0.976818\pi\)
0.561690 + 0.827348i \(0.310151\pi\)
\(282\) 0 0
\(283\) −0.0692967 0.120025i −0.00411926 0.00713477i 0.863958 0.503563i \(-0.167978\pi\)
−0.868078 + 0.496428i \(0.834645\pi\)
\(284\) 0 0
\(285\) 14.5584 12.2993i 0.862366 0.728547i
\(286\) 0 0
\(287\) −10.7446 18.6101i −0.634231 1.09852i
\(288\) 0 0
\(289\) −5.31386 + 9.20387i −0.312580 + 0.541404i
\(290\) 0 0
\(291\) 4.67527 1.40965i 0.274069 0.0826349i
\(292\) 0 0
\(293\) −20.7446 −1.21191 −0.605955 0.795499i \(-0.707209\pi\)
−0.605955 + 0.795499i \(0.707209\pi\)
\(294\) 0 0
\(295\) 3.55842 + 2.05446i 0.207179 + 0.119615i
\(296\) 0 0
\(297\) 11.4891 13.8564i 0.666667 0.804030i
\(298\) 0 0
\(299\) 15.1861 + 26.3032i 0.878237 + 1.52115i
\(300\) 0 0
\(301\) −19.8030 34.2998i −1.14143 1.97701i
\(302\) 0 0
\(303\) −3.18614 2.99422i −0.183039 0.172013i
\(304\) 0 0
\(305\) 2.52434i 0.144543i
\(306\) 0 0
\(307\) −26.7921 + 15.4684i −1.52911 + 0.882830i −0.529707 + 0.848181i \(0.677698\pi\)
−0.999400 + 0.0346493i \(0.988969\pi\)
\(308\) 0 0
\(309\) −3.68614 + 15.6896i −0.209697 + 0.892553i
\(310\) 0 0
\(311\) 18.9051i 1.07201i 0.844215 + 0.536004i \(0.180067\pi\)
−0.844215 + 0.536004i \(0.819933\pi\)
\(312\) 0 0
\(313\) 9.67527 16.7581i 0.546878 0.947221i −0.451608 0.892217i \(-0.649149\pi\)
0.998486 0.0550045i \(-0.0175173\pi\)
\(314\) 0 0
\(315\) −25.4891 + 1.58457i −1.43615 + 0.0892806i
\(316\) 0 0
\(317\) −7.81386 + 13.5340i −0.438870 + 0.760145i −0.997603 0.0692026i \(-0.977954\pi\)
0.558733 + 0.829348i \(0.311288\pi\)
\(318\) 0 0
\(319\) −1.11684 0.644810i −0.0625313 0.0361024i
\(320\) 0 0
\(321\) 8.86141 + 2.08191i 0.494595 + 0.116201i
\(322\) 0 0
\(323\) 6.55842 8.83518i 0.364920 0.491603i
\(324\) 0 0
\(325\) 3.94158 2.27567i 0.218639 0.126232i
\(326\) 0 0
\(327\) −6.81386 + 2.05446i −0.376807 + 0.113612i
\(328\) 0 0
\(329\) −2.74456 1.58457i −0.151313 0.0873604i
\(330\) 0 0
\(331\) 2.96677i 0.163068i −0.996671 0.0815342i \(-0.974018\pi\)
0.996671 0.0815342i \(-0.0259820\pi\)
\(332\) 0 0
\(333\) 14.9416 30.0434i 0.818793 1.64637i
\(334\) 0 0
\(335\) 3.62772 0.198203
\(336\) 0 0
\(337\) −24.7337 + 14.2800i −1.34733 + 0.777881i −0.987871 0.155280i \(-0.950372\pi\)
−0.359459 + 0.933161i \(0.617039\pi\)
\(338\) 0 0
\(339\) −5.48913 1.28962i −0.298128 0.0700426i
\(340\) 0 0
\(341\) 26.7446 1.44830
\(342\) 0 0
\(343\) −8.86141 −0.478471
\(344\) 0 0
\(345\) −38.9783 9.15759i −2.09852 0.493028i
\(346\) 0 0
\(347\) −24.0475 + 13.8839i −1.29094 + 0.745325i −0.978821 0.204718i \(-0.934372\pi\)
−0.312119 + 0.950043i \(0.601039\pi\)
\(348\) 0 0
\(349\) 9.60597 0.514196 0.257098 0.966385i \(-0.417234\pi\)
0.257098 + 0.966385i \(0.417234\pi\)
\(350\) 0 0
\(351\) 5.98913 + 16.1595i 0.319676 + 0.862532i
\(352\) 0 0
\(353\) 11.0920i 0.590369i −0.955440 0.295184i \(-0.904619\pi\)
0.955440 0.295184i \(-0.0953810\pi\)
\(354\) 0 0
\(355\) 27.0475 + 15.6159i 1.43553 + 0.828806i
\(356\) 0 0
\(357\) −14.1168 + 4.25639i −0.747143 + 0.225272i
\(358\) 0 0
\(359\) 18.3030 10.5672i 0.965995 0.557717i 0.0679818 0.997687i \(-0.478344\pi\)
0.898013 + 0.439969i \(0.145011\pi\)
\(360\) 0 0
\(361\) 13.0000 13.8564i 0.684211 0.729285i
\(362\) 0 0
\(363\) −1.68614 0.396143i −0.0884994 0.0207921i
\(364\) 0 0
\(365\) 12.5584 + 7.25061i 0.657338 + 0.379514i
\(366\) 0 0
\(367\) −7.61684 + 13.1928i −0.397596 + 0.688657i −0.993429 0.114452i \(-0.963489\pi\)
0.595833 + 0.803109i \(0.296822\pi\)
\(368\) 0 0
\(369\) −1.18614 19.0800i −0.0617480 0.993266i
\(370\) 0 0
\(371\) 9.48913 16.4356i 0.492651 0.853296i
\(372\) 0 0
\(373\) 6.92820i 0.358729i 0.983783 + 0.179364i \(0.0574041\pi\)
−0.983783 + 0.179364i \(0.942596\pi\)
\(374\) 0 0
\(375\) 3.62772 15.4410i 0.187335 0.797369i
\(376\) 0 0
\(377\) 1.06930 0.617359i 0.0550716 0.0317956i
\(378\) 0 0
\(379\) 12.4742i 0.640757i −0.947290 0.320379i \(-0.896190\pi\)
0.947290 0.320379i \(-0.103810\pi\)
\(380\) 0 0
\(381\) 4.81386 + 4.52389i 0.246621 + 0.231766i
\(382\) 0 0
\(383\) 15.3030 + 26.5055i 0.781946 + 1.35437i 0.930807 + 0.365512i \(0.119106\pi\)
−0.148861 + 0.988858i \(0.547561\pi\)
\(384\) 0 0
\(385\) 14.7446 + 25.5383i 0.751452 + 1.30155i
\(386\) 0 0
\(387\) −2.18614 35.1658i −0.111128 1.78758i
\(388\) 0 0
\(389\) 22.1644 + 12.7966i 1.12378 + 0.648814i 0.942363 0.334592i \(-0.108599\pi\)
0.181416 + 0.983406i \(0.441932\pi\)
\(390\) 0 0
\(391\) −23.1168 −1.16907
\(392\) 0 0
\(393\) −29.3030 + 8.83518i −1.47814 + 0.445676i
\(394\) 0 0
\(395\) 18.9307 32.7889i 0.952507 1.64979i
\(396\) 0 0
\(397\) 12.6168 + 21.8530i 0.633221 + 1.09677i 0.986889 + 0.161400i \(0.0516010\pi\)
−0.353668 + 0.935371i \(0.615066\pi\)
\(398\) 0 0
\(399\) −25.0584 + 4.50506i −1.25449 + 0.225535i
\(400\) 0 0
\(401\) −16.6753 28.8824i −0.832723 1.44232i −0.895871 0.444314i \(-0.853447\pi\)
0.0631479 0.998004i \(-0.479886\pi\)
\(402\) 0 0
\(403\) −12.8030 + 22.1754i −0.637762 + 1.10464i
\(404\) 0 0
\(405\) −20.9307 8.83518i −1.04006 0.439024i
\(406\) 0 0
\(407\) −38.7446 −1.92050
\(408\) 0 0
\(409\) −11.7921 6.80818i −0.583082 0.336643i 0.179275 0.983799i \(-0.442625\pi\)
−0.762357 + 0.647156i \(0.775958\pi\)
\(410\) 0 0
\(411\) −20.6753 19.4299i −1.01984 0.958405i
\(412\) 0 0
\(413\) −2.74456 4.75372i −0.135051 0.233915i
\(414\) 0 0
\(415\) −4.37228 7.57301i −0.214627 0.371745i
\(416\) 0 0
\(417\) 7.69702 8.19037i 0.376924 0.401084i
\(418\) 0 0
\(419\) 10.9822i 0.536516i −0.963347 0.268258i \(-0.913552\pi\)
0.963347 0.268258i \(-0.0864480\pi\)
\(420\) 0 0
\(421\) −17.7921 + 10.2723i −0.867134 + 0.500640i −0.866395 0.499359i \(-0.833569\pi\)
−0.000739475 1.00000i \(0.500235\pi\)
\(422\) 0 0
\(423\) −1.55842 2.34941i −0.0757731 0.114232i
\(424\) 0 0
\(425\) 3.46410i 0.168034i
\(426\) 0 0
\(427\) 1.68614 2.92048i 0.0815981 0.141332i
\(428\) 0 0
\(429\) 13.6277 14.5012i 0.657952 0.700125i
\(430\) 0 0
\(431\) 4.06930 7.04823i 0.196011 0.339501i −0.751220 0.660051i \(-0.770534\pi\)
0.947232 + 0.320550i \(0.103868\pi\)
\(432\) 0 0
\(433\) −30.7337 17.7441i −1.47697 0.852727i −0.477305 0.878738i \(-0.658386\pi\)
−0.999662 + 0.0260105i \(0.991720\pi\)
\(434\) 0 0
\(435\) −0.372281 + 1.58457i −0.0178495 + 0.0759745i
\(436\) 0 0
\(437\) −39.6535 4.57879i −1.89688 0.219033i
\(438\) 0 0
\(439\) 4.50000 2.59808i 0.214773 0.123999i −0.388755 0.921341i \(-0.627095\pi\)
0.603528 + 0.797342i \(0.293761\pi\)
\(440\) 0 0
\(441\) 11.7446 + 5.84096i 0.559265 + 0.278141i
\(442\) 0 0
\(443\) 23.5367 + 13.5889i 1.11826 + 0.645628i 0.940956 0.338528i \(-0.109929\pi\)
0.177305 + 0.984156i \(0.443262\pi\)
\(444\) 0 0
\(445\) 4.10891i 0.194781i
\(446\) 0 0
\(447\) 12.5584 3.78651i 0.593993 0.179096i
\(448\) 0 0
\(449\) 30.4674 1.43784 0.718922 0.695091i \(-0.244636\pi\)
0.718922 + 0.695091i \(0.244636\pi\)
\(450\) 0 0
\(451\) −19.1168 + 11.0371i −0.900177 + 0.519717i
\(452\) 0 0
\(453\) −0.116844 + 0.497333i −0.00548981 + 0.0233668i
\(454\) 0 0
\(455\) −28.2337 −1.32362
\(456\) 0 0
\(457\) 30.6277 1.43270 0.716352 0.697739i \(-0.245810\pi\)
0.716352 + 0.697739i \(0.245810\pi\)
\(458\) 0 0
\(459\) −12.9307 2.20193i −0.603554 0.102777i
\(460\) 0 0
\(461\) 25.9307 14.9711i 1.20771 0.697274i 0.245454 0.969408i \(-0.421063\pi\)
0.962259 + 0.272135i \(0.0877296\pi\)
\(462\) 0 0
\(463\) 23.3723 1.08620 0.543101 0.839667i \(-0.317250\pi\)
0.543101 + 0.839667i \(0.317250\pi\)
\(464\) 0 0
\(465\) −9.74456 32.3191i −0.451893 1.49876i
\(466\) 0 0
\(467\) 42.2689i 1.95597i 0.208668 + 0.977986i \(0.433087\pi\)
−0.208668 + 0.977986i \(0.566913\pi\)
\(468\) 0 0
\(469\) −4.19702 2.42315i −0.193800 0.111891i
\(470\) 0 0
\(471\) 1.24456 + 4.12775i 0.0573464 + 0.190197i
\(472\) 0 0
\(473\) −35.2337 + 20.3422i −1.62005 + 0.935334i
\(474\) 0 0
\(475\) −0.686141 + 5.94215i −0.0314823 + 0.272645i
\(476\) 0 0
\(477\) 14.0693 9.33252i 0.644189 0.427307i
\(478\) 0 0
\(479\) −22.9307 13.2390i −1.04773 0.604908i −0.125717 0.992066i \(-0.540123\pi\)
−0.922013 + 0.387159i \(0.873457\pi\)
\(480\) 0 0
\(481\) 18.5475 32.1253i 0.845695 1.46479i
\(482\) 0 0
\(483\) 38.9783 + 36.6303i 1.77357 + 1.66674i
\(484\) 0 0
\(485\) −3.55842 + 6.16337i −0.161580 + 0.279864i
\(486\) 0 0
\(487\) 13.5615i 0.614528i −0.951624 0.307264i \(-0.900587\pi\)
0.951624 0.307264i \(-0.0994135\pi\)
\(488\) 0 0
\(489\) 25.9198 + 6.08963i 1.17214 + 0.275383i
\(490\) 0 0
\(491\) 7.67527 4.43132i 0.346380 0.199983i −0.316710 0.948522i \(-0.602578\pi\)
0.663090 + 0.748540i \(0.269245\pi\)
\(492\) 0 0
\(493\) 0.939764i 0.0423248i
\(494\) 0 0
\(495\) 1.62772 + 26.1831i 0.0731605 + 1.17684i
\(496\) 0 0
\(497\) −20.8614 36.1330i −0.935762 1.62079i
\(498\) 0 0
\(499\) 6.12772 + 10.6135i 0.274314 + 0.475126i 0.969962 0.243257i \(-0.0782158\pi\)
−0.695648 + 0.718383i \(0.744882\pi\)
\(500\) 0 0
\(501\) −1.04755 + 1.11469i −0.0468010 + 0.0498008i
\(502\) 0 0
\(503\) 33.8139 + 19.5224i 1.50769 + 0.870463i 0.999960 + 0.00894369i \(0.00284690\pi\)
0.507725 + 0.861519i \(0.330486\pi\)
\(504\) 0 0
\(505\) 6.37228 0.283563
\(506\) 0 0
\(507\) −1.00000 3.31662i −0.0444116 0.147296i
\(508\) 0 0
\(509\) 3.55842 6.16337i 0.157724 0.273186i −0.776323 0.630335i \(-0.782918\pi\)
0.934048 + 0.357148i \(0.116251\pi\)
\(510\) 0 0
\(511\) −9.68614 16.7769i −0.428490 0.742166i
\(512\) 0 0
\(513\) −21.7446 6.33830i −0.960046 0.279843i
\(514\) 0 0
\(515\) −11.7446 20.3422i −0.517527 0.896384i
\(516\) 0 0
\(517\) −1.62772 + 2.81929i −0.0715870 + 0.123992i
\(518\) 0 0
\(519\) 6.93070 + 22.9865i 0.304224 + 1.00900i
\(520\) 0 0
\(521\) 10.0000 0.438108 0.219054 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) 0 0
\(523\) −1.24456 0.718549i −0.0544209 0.0314199i 0.472543 0.881308i \(-0.343336\pi\)
−0.526964 + 0.849888i \(0.676670\pi\)
\(524\) 0 0
\(525\) 5.48913 5.84096i 0.239565 0.254921i
\(526\) 0 0
\(527\) −9.74456 16.8781i −0.424480 0.735221i
\(528\) 0 0
\(529\) 30.4307 + 52.7075i 1.32307 + 2.29163i
\(530\) 0 0
\(531\) −0.302985 4.87375i −0.0131484 0.211503i
\(532\) 0 0
\(533\) 21.1345i 0.915435i
\(534\) 0 0
\(535\) −11.4891 + 6.63325i −0.496718 + 0.286780i
\(536\) 0 0
\(537\) −2.51087 0.589907i −0.108352 0.0254564i
\(538\) 0 0
\(539\) 15.1460i 0.652386i
\(540\) 0 0
\(541\) −14.9891 + 25.9619i −0.644433 + 1.11619i 0.339999 + 0.940426i \(0.389573\pi\)
−0.984432 + 0.175765i \(0.943760\pi\)
\(542\) 0 0
\(543\) −26.6753 25.0684i −1.14475 1.07579i
\(544\) 0 0
\(545\) 5.18614 8.98266i 0.222150 0.384775i
\(546\) 0 0
\(547\) −18.3832 10.6135i −0.786007 0.453801i 0.0525479 0.998618i \(-0.483266\pi\)
−0.838555 + 0.544817i \(0.816599\pi\)
\(548\) 0 0
\(549\) 2.50000 1.65831i 0.106697 0.0707750i
\(550\) 0 0
\(551\) −0.186141 + 1.61203i −0.00792986 + 0.0686746i
\(552\) 0 0
\(553\) −43.8030 + 25.2897i −1.86269 + 1.07543i
\(554\) 0 0
\(555\) 14.1168 + 46.8203i 0.599227 + 1.98741i
\(556\) 0 0
\(557\) 13.0693 + 7.54556i 0.553764 + 0.319716i 0.750639 0.660713i \(-0.229746\pi\)
−0.196875 + 0.980429i \(0.563079\pi\)
\(558\) 0 0
\(559\) 38.9523i 1.64751i
\(560\) 0 0
\(561\) 4.37228 + 14.5012i 0.184598 + 0.612242i
\(562\) 0 0
\(563\) 13.7228 0.578348 0.289174 0.957277i \(-0.406619\pi\)
0.289174 + 0.957277i \(0.406619\pi\)
\(564\) 0 0
\(565\) 7.11684 4.10891i 0.299408 0.172863i
\(566\) 0 0
\(567\) 18.3139 + 24.2024i 0.769110 + 1.01641i
\(568\) 0 0
\(569\) −27.2554 −1.14261 −0.571304 0.820739i \(-0.693562\pi\)
−0.571304 + 0.820739i \(0.693562\pi\)
\(570\) 0 0
\(571\) 15.3723 0.643310 0.321655 0.946857i \(-0.395761\pi\)
0.321655 + 0.946857i \(0.395761\pi\)
\(572\) 0 0
\(573\) −2.62772 + 11.1846i −0.109775 + 0.467243i
\(574\) 0 0
\(575\) 10.8832 6.28339i 0.453859 0.262036i
\(576\) 0 0
\(577\) −4.51087 −0.187790 −0.0938951 0.995582i \(-0.529932\pi\)
−0.0938951 + 0.995582i \(0.529932\pi\)
\(578\) 0 0
\(579\) 25.8505 7.79423i 1.07431 0.323917i
\(580\) 0 0
\(581\) 11.6819i 0.484648i
\(582\) 0 0
\(583\) −16.8832 9.74749i −0.699229 0.403700i
\(584\) 0 0
\(585\) −22.4891 11.1846i −0.929811 0.462426i
\(586\) 0 0
\(587\) −41.1861 + 23.7788i −1.69993 + 0.981457i −0.754127 + 0.656729i \(0.771940\pi\)
−0.945807 + 0.324728i \(0.894727\pi\)
\(588\) 0 0
\(589\) −13.3723 30.8820i −0.550995 1.27247i
\(590\) 0 0
\(591\) −9.25544 + 39.3947i −0.380718 + 1.62048i
\(592\) 0 0
\(593\) −27.0475 15.6159i −1.11071 0.641269i −0.171697 0.985150i \(-0.554925\pi\)
−0.939013 + 0.343881i \(0.888258\pi\)
\(594\) 0 0
\(595\) 10.7446 18.6101i 0.440484 0.762941i
\(596\) 0 0
\(597\) 2.95245 3.14170i 0.120836 0.128581i
\(598\) 0 0
\(599\) −8.55842 + 14.8236i −0.349688 + 0.605677i −0.986194 0.165595i \(-0.947046\pi\)
0.636506 + 0.771272i \(0.280379\pi\)
\(600\) 0 0
\(601\) 22.2766i 0.908682i −0.890828 0.454341i \(-0.849875\pi\)
0.890828 0.454341i \(-0.150125\pi\)
\(602\) 0 0
\(603\) −2.38316 3.59274i −0.0970496 0.146308i
\(604\) 0 0
\(605\) 2.18614 1.26217i 0.0888793 0.0513145i
\(606\) 0 0
\(607\) 0.792287i 0.0321579i 0.999871 + 0.0160790i \(0.00511832\pi\)
−0.999871 + 0.0160790i \(0.994882\pi\)
\(608\) 0 0
\(609\) 1.48913 1.58457i 0.0603424 0.0642102i
\(610\) 0 0
\(611\) −1.55842 2.69927i −0.0630470 0.109201i
\(612\) 0 0
\(613\) −12.5584 21.7518i −0.507230 0.878548i −0.999965 0.00836857i \(-0.997336\pi\)
0.492735 0.870179i \(-0.335997\pi\)
\(614\) 0 0
\(615\) 20.3030 + 19.0800i 0.818695 + 0.769380i
\(616\) 0 0
\(617\) 12.5584 + 7.25061i 0.505583 + 0.291898i 0.731016 0.682360i \(-0.239046\pi\)
−0.225433 + 0.974259i \(0.572380\pi\)
\(618\) 0 0
\(619\) 3.13859 0.126151 0.0630754 0.998009i \(-0.479909\pi\)
0.0630754 + 0.998009i \(0.479909\pi\)
\(620\) 0 0
\(621\) 16.5367 + 44.6183i 0.663594 + 1.79047i
\(622\) 0 0
\(623\) 2.74456 4.75372i 0.109959 0.190454i
\(624\) 0 0
\(625\) 14.9891 + 25.9619i 0.599565 + 1.03848i
\(626\) 0 0
\(627\) 4.62772 + 25.7407i 0.184813 + 1.02798i
\(628\) 0 0
\(629\) 14.1168 + 24.4511i 0.562875 + 0.974929i
\(630\) 0 0
\(631\) 12.6168 21.8530i 0.502269 0.869955i −0.497728 0.867333i \(-0.665832\pi\)
0.999997 0.00262157i \(-0.000834473\pi\)
\(632\) 0 0
\(633\) 19.1277 5.76722i 0.760259 0.229227i
\(634\) 0 0
\(635\) −9.62772 −0.382064
\(636\) 0 0
\(637\) 12.5584 + 7.25061i 0.497583 + 0.287280i
\(638\) 0 0
\(639\) −2.30298 37.0453i −0.0911047 1.46549i
\(640\) 0 0
\(641\) −13.1861 22.8391i −0.520821 0.902089i −0.999707 0.0242115i \(-0.992292\pi\)
0.478886 0.877877i \(-0.341041\pi\)
\(642\) 0 0
\(643\) 1.50000 + 2.59808i 0.0591542 + 0.102458i 0.894086 0.447895i \(-0.147826\pi\)
−0.834932 + 0.550353i \(0.814493\pi\)
\(644\) 0 0
\(645\) 37.4198 + 35.1658i 1.47340 + 1.38465i
\(646\) 0 0
\(647\) 17.9104i 0.704131i −0.935975 0.352066i \(-0.885479\pi\)
0.935975 0.352066i \(-0.114521\pi\)
\(648\) 0 0
\(649\) −4.88316 + 2.81929i −0.191681 + 0.110667i
\(650\) 0 0
\(651\) −10.3139 + 43.8998i −0.404232 + 1.72057i
\(652\) 0 0
\(653\) 2.17448i 0.0850940i −0.999094 0.0425470i \(-0.986453\pi\)
0.999094 0.0425470i \(-0.0135472\pi\)
\(654\) 0 0
\(655\) 22.3030 38.6299i 0.871450 1.50940i
\(656\) 0 0
\(657\) −1.06930 17.2005i −0.0417172 0.671055i
\(658\) 0 0
\(659\) −12.0475 + 20.8670i −0.469306 + 0.812862i −0.999384 0.0350871i \(-0.988829\pi\)
0.530078 + 0.847949i \(0.322162\pi\)
\(660\) 0 0
\(661\) −24.3030 14.0313i −0.945277 0.545756i −0.0536661 0.998559i \(-0.517091\pi\)
−0.891610 + 0.452803i \(0.850424\pi\)
\(662\) 0 0
\(663\) −14.1168 3.31662i −0.548253 0.128807i
\(664\) 0 0
\(665\) 22.1168 29.7947i 0.857654 1.15539i
\(666\) 0 0
\(667\) 2.95245 1.70460i 0.114319 0.0660024i
\(668\) 0 0
\(669\) 35.8723 10.8159i 1.38690 0.418167i
\(670\) 0 0
\(671\) −3.00000 1.73205i −0.115814 0.0668651i
\(672\) 0 0
\(673\) 2.08191i 0.0802516i −0.999195 0.0401258i \(-0.987224\pi\)
0.999195 0.0401258i \(-0.0127759\pi\)
\(674\) 0 0
\(675\) 6.68614 2.47805i 0.257350 0.0953802i
\(676\) 0 0
\(677\) −15.2554 −0.586314 −0.293157 0.956064i \(-0.594706\pi\)
−0.293157 + 0.956064i \(0.594706\pi\)
\(678\) 0 0
\(679\) 8.23369 4.75372i 0.315980 0.182431i
\(680\) 0 0
\(681\) −31.6060 7.42554i −1.21114 0.284547i
\(682\) 0 0
\(683\) 6.74456 0.258074 0.129037 0.991640i \(-0.458811\pi\)
0.129037 + 0.991640i \(0.458811\pi\)
\(684\) 0 0
\(685\) 41.3505 1.57992
\(686\) 0 0
\(687\) −6.54755 1.53829i −0.249805 0.0586893i
\(688\) 0 0
\(689\) 16.1644 9.33252i 0.615814 0.355541i
\(690\) 0 0
\(691\) 49.9565 1.90043 0.950217 0.311588i \(-0.100861\pi\)
0.950217 + 0.311588i \(0.100861\pi\)
\(692\) 0 0
\(693\) 15.6060 31.3793i 0.592822 1.19200i
\(694\) 0 0
\(695\) 16.3807i 0.621357i
\(696\) 0 0
\(697\) 13.9307 + 8.04290i 0.527663 + 0.304646i
\(698\) 0 0
\(699\) 24.0475 7.25061i 0.909562 0.274243i
\(700\) 0 0
\(701\) −5.44158 + 3.14170i −0.205526 + 0.118660i −0.599230 0.800577i \(-0.704527\pi\)
0.393705 + 0.919237i \(0.371193\pi\)
\(702\) 0 0
\(703\) 19.3723 + 44.7384i 0.730639 + 1.68734i
\(704\) 0 0
\(705\) 4.00000 + 0.939764i 0.150649 + 0.0353936i
\(706\) 0 0
\(707\) −7.37228 4.25639i −0.277263 0.160078i
\(708\) 0 0
\(709\) 11.2446 19.4762i 0.422298 0.731442i −0.573865 0.818950i \(-0.694557\pi\)
0.996164 + 0.0875073i \(0.0278901\pi\)
\(710\) 0 0
\(711\) −44.9090 + 2.79184i −1.68422 + 0.104702i
\(712\) 0 0
\(713\) −35.3505 + 61.2289i −1.32389 + 2.29304i
\(714\) 0 0
\(715\) 29.0024i 1.08463i
\(716\) 0 0
\(717\) −4.11684 + 17.5229i −0.153746 + 0.654404i
\(718\) 0 0
\(719\) 0.813859 0.469882i 0.0303518 0.0175236i −0.484747 0.874654i \(-0.661088\pi\)
0.515099 + 0.857131i \(0.327755\pi\)
\(720\) 0 0
\(721\) 31.3793i 1.16863i
\(722\) 0 0
\(723\) 25.6753 + 24.1287i 0.954873 + 0.897355i
\(724\) 0 0
\(725\) −0.255437 0.442430i −0.00948671 0.0164315i
\(726\) 0 0
\(727\) −11.1277 19.2738i −0.412704 0.714825i 0.582480 0.812845i \(-0.302082\pi\)
−0.995184 + 0.0980202i \(0.968749\pi\)
\(728\) 0 0
\(729\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(730\) 0 0
\(731\) 25.6753 + 14.8236i 0.949634 + 0.548271i
\(732\) 0 0
\(733\) 20.9783 0.774849 0.387425 0.921901i \(-0.373365\pi\)
0.387425 + 0.921901i \(0.373365\pi\)
\(734\) 0 0
\(735\) −18.3030 + 5.51856i −0.675116 + 0.203555i
\(736\) 0 0
\(737\) −2.48913 + 4.31129i −0.0916881 + 0.158808i
\(738\) 0 0
\(739\) −3.75544 6.50461i −0.138146 0.239276i 0.788649 0.614844i \(-0.210781\pi\)
−0.926795 + 0.375568i \(0.877448\pi\)
\(740\) 0 0
\(741\) −23.5584 8.48533i −0.865440 0.311716i
\(742\) 0 0
\(743\) −8.18614 14.1788i −0.300320 0.520170i 0.675888 0.737004i \(-0.263760\pi\)
−0.976208 + 0.216834i \(0.930427\pi\)
\(744\) 0 0
\(745\) −9.55842 + 16.5557i −0.350193 + 0.606553i
\(746\) 0 0
\(747\) −4.62772 + 9.30506i −0.169319 + 0.340454i
\(748\) 0 0
\(749\) 17.7228 0.647578
\(750\) 0 0
\(751\) 2.01087 + 1.16098i 0.0733779 + 0.0423647i 0.536240 0.844066i \(-0.319844\pi\)
−0.462862 + 0.886430i \(0.653178\pi\)
\(752\) 0 0
\(753\) 29.0475 + 27.2978i 1.05855 + 0.994788i
\(754\) 0 0
\(755\) −0.372281 0.644810i −0.0135487 0.0234670i
\(756\) 0 0
\(757\) 7.12772 + 12.3456i 0.259061 + 0.448707i 0.965991 0.258577i \(-0.0832535\pi\)
−0.706929 + 0.707284i \(0.749920\pi\)
\(758\) 0 0
\(759\) 37.6277 40.0395i 1.36580 1.45334i
\(760\) 0 0
\(761\) 19.6048i 0.710673i 0.934738 + 0.355337i \(0.115634\pi\)
−0.934738 + 0.355337i \(0.884366\pi\)
\(762\) 0 0
\(763\) −12.0000 + 6.92820i −0.434429 + 0.250818i
\(764\) 0 0
\(765\) 15.9307 10.5672i 0.575976 0.382059i
\(766\) 0 0
\(767\) 5.39853i 0.194930i
\(768\) 0 0
\(769\) 15.8723 27.4916i 0.572369 0.991372i −0.423953 0.905684i \(-0.639358\pi\)
0.996322 0.0856881i \(-0.0273089\pi\)
\(770\) 0 0
\(771\) 22.6753 24.1287i 0.816630 0.868973i
\(772\) 0 0
\(773\) 18.8139 32.5866i 0.676687 1.17206i −0.299285 0.954164i \(-0.596748\pi\)
0.975973 0.217893i \(-0.0699185\pi\)
\(774\) 0 0
\(775\) 9.17527 + 5.29734i 0.329585 + 0.190286i
\(776\) 0 0
\(777\) 14.9416 63.5972i 0.536026 2.28154i
\(778\) 0 0
\(779\) 22.3030 + 16.5557i 0.799087 + 0.593169i
\(780\) 0 0
\(781\) −37.1168 + 21.4294i −1.32815 + 0.766805i
\(782\) 0 0
\(783\) 1.81386 0.672262i 0.0648220 0.0240247i
\(784\) 0 0
\(785\) −5.44158 3.14170i −0.194218 0.112132i
\(786\) 0 0
\(787\) 2.37686i 0.0847259i 0.999102 + 0.0423630i \(0.0134886\pi\)
−0.999102 + 0.0423630i \(0.986511\pi\)
\(788\) 0 0
\(789\) 20.9307 6.31084i 0.745153 0.224672i
\(790\) 0 0
\(791\) −10.9783 −0.390342
\(792\) 0 0
\(793\) 2.87228 1.65831i 0.101998 0.0588884i
\(794\) 0 0