Properties

Label 1386.2.k.v.991.3
Level $1386$
Weight $2$
Character 1386.991
Analytic conductor $11.067$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.21870000.1
Defining polynomial: \(x^{6} - 3 x^{5} + 24 x^{4} - 43 x^{3} + 138 x^{2} - 117 x + 73\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 462)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.3
Root \(0.500000 + 3.23735i\) of defining polynomial
Character \(\chi\) \(=\) 1386.991
Dual form 1386.2.k.v.793.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.20942 + 3.82682i) q^{5} +(2.20942 - 1.45550i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.20942 + 3.82682i) q^{5} +(2.20942 - 1.45550i) q^{7} -1.00000 q^{8} +(-2.20942 + 3.82682i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(2.36521 + 1.18566i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.18842 - 2.05840i) q^{17} +(1.84421 + 3.19426i) q^{19} -4.41883 q^{20} -1.00000 q^{22} +(2.36521 + 4.09666i) q^{23} +(-7.26304 + 12.5800i) q^{25} +(0.155792 + 2.64116i) q^{28} +6.52608 q^{29} +(1.68842 - 2.92442i) q^{31} +(0.500000 - 0.866025i) q^{32} +2.37683 q^{34} +(10.4515 + 5.23924i) q^{35} +(-3.84421 - 6.65836i) q^{37} +(-1.84421 + 3.19426i) q^{38} +(-2.20942 - 3.82682i) q^{40} -12.1492 q^{41} +3.06525 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-2.36521 + 4.09666i) q^{46} +(-2.05362 - 3.55698i) q^{47} +(2.76304 - 6.43161i) q^{49} -14.5261 q^{50} +(4.00000 - 6.92820i) q^{53} -4.41883 q^{55} +(-2.20942 + 1.45550i) q^{56} +(3.26304 + 5.65175i) q^{58} +(-6.26304 + 10.8479i) q^{59} +(-1.89783 - 3.28714i) q^{61} +3.37683 q^{62} +1.00000 q^{64} +(-5.07462 + 8.78951i) q^{67} +(1.18842 + 2.05840i) q^{68} +(0.688417 + 11.6708i) q^{70} -0.934749 q^{71} +(3.73042 - 6.46127i) q^{73} +(3.84421 - 6.65836i) q^{74} -3.68842 q^{76} +(0.155792 + 2.64116i) q^{77} +(0.209416 + 0.362720i) q^{79} +(2.20942 - 3.82682i) q^{80} +(-6.07462 - 10.5216i) q^{82} +2.14925 q^{83} +10.5028 q^{85} +(1.53263 + 2.65458i) q^{86} +(0.500000 - 0.866025i) q^{88} +(-6.41883 - 11.1177i) q^{89} -4.73042 q^{92} +(2.05362 - 3.55698i) q^{94} +(-8.14925 + 14.1149i) q^{95} +7.00000 q^{97} +(6.95146 - 0.822941i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{2} - 3q^{4} - 6q^{8} + O(q^{10}) \) \( 6q + 3q^{2} - 3q^{4} - 6q^{8} - 3q^{11} + 3q^{14} - 3q^{16} + 3q^{17} + 9q^{19} - 6q^{22} + 3q^{23} - 15q^{25} + 3q^{28} - 18q^{29} + 6q^{31} + 3q^{32} + 6q^{34} + 30q^{35} - 21q^{37} - 9q^{38} - 24q^{41} + 6q^{43} - 3q^{44} - 3q^{46} + 3q^{47} - 12q^{49} - 30q^{50} + 24q^{53} - 9q^{58} - 9q^{59} + 6q^{61} + 12q^{62} + 6q^{64} - 6q^{67} + 3q^{68} - 18q^{71} + 21q^{74} - 18q^{76} + 3q^{77} - 12q^{79} - 12q^{82} - 36q^{83} + 3q^{86} + 3q^{88} - 12q^{89} - 6q^{92} - 3q^{94} + 42q^{97} + 9q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 2.20942 + 3.82682i 0.988081 + 1.71141i 0.627352 + 0.778736i \(0.284139\pi\)
0.360729 + 0.932671i \(0.382528\pi\)
\(6\) 0 0
\(7\) 2.20942 1.45550i 0.835081 0.550127i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −2.20942 + 3.82682i −0.698679 + 1.21015i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 2.36521 + 1.18566i 0.632128 + 0.316881i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.18842 2.05840i 0.288233 0.499235i −0.685155 0.728398i \(-0.740265\pi\)
0.973388 + 0.229163i \(0.0735988\pi\)
\(18\) 0 0
\(19\) 1.84421 + 3.19426i 0.423090 + 0.732814i 0.996240 0.0866367i \(-0.0276119\pi\)
−0.573150 + 0.819451i \(0.694279\pi\)
\(20\) −4.41883 −0.988081
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 2.36521 + 4.09666i 0.493180 + 0.854213i 0.999969 0.00785730i \(-0.00250108\pi\)
−0.506789 + 0.862070i \(0.669168\pi\)
\(24\) 0 0
\(25\) −7.26304 + 12.5800i −1.45261 + 2.51599i
\(26\) 0 0
\(27\) 0 0
\(28\) 0.155792 + 2.64116i 0.0294418 + 0.499132i
\(29\) 6.52608 1.21186 0.605932 0.795517i \(-0.292801\pi\)
0.605932 + 0.795517i \(0.292801\pi\)
\(30\) 0 0
\(31\) 1.68842 2.92442i 0.303249 0.525242i −0.673621 0.739077i \(-0.735262\pi\)
0.976870 + 0.213835i \(0.0685954\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 2.37683 0.407624
\(35\) 10.4515 + 5.23924i 1.76662 + 0.885593i
\(36\) 0 0
\(37\) −3.84421 6.65836i −0.631984 1.09463i −0.987146 0.159823i \(-0.948908\pi\)
0.355162 0.934805i \(-0.384426\pi\)
\(38\) −1.84421 + 3.19426i −0.299170 + 0.518178i
\(39\) 0 0
\(40\) −2.20942 3.82682i −0.349339 0.605074i
\(41\) −12.1492 −1.89739 −0.948697 0.316187i \(-0.897597\pi\)
−0.948697 + 0.316187i \(0.897597\pi\)
\(42\) 0 0
\(43\) 3.06525 0.467446 0.233723 0.972303i \(-0.424909\pi\)
0.233723 + 0.972303i \(0.424909\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) 0 0
\(46\) −2.36521 + 4.09666i −0.348731 + 0.604020i
\(47\) −2.05362 3.55698i −0.299552 0.518839i 0.676482 0.736460i \(-0.263504\pi\)
−0.976033 + 0.217620i \(0.930171\pi\)
\(48\) 0 0
\(49\) 2.76304 6.43161i 0.394720 0.918801i
\(50\) −14.5261 −2.05430
\(51\) 0 0
\(52\) 0 0
\(53\) 4.00000 6.92820i 0.549442 0.951662i −0.448871 0.893597i \(-0.648174\pi\)
0.998313 0.0580651i \(-0.0184931\pi\)
\(54\) 0 0
\(55\) −4.41883 −0.595835
\(56\) −2.20942 + 1.45550i −0.295246 + 0.194499i
\(57\) 0 0
\(58\) 3.26304 + 5.65175i 0.428458 + 0.742112i
\(59\) −6.26304 + 10.8479i −0.815379 + 1.41228i 0.0936773 + 0.995603i \(0.470138\pi\)
−0.909056 + 0.416674i \(0.863196\pi\)
\(60\) 0 0
\(61\) −1.89783 3.28714i −0.242993 0.420876i 0.718573 0.695452i \(-0.244796\pi\)
−0.961565 + 0.274576i \(0.911462\pi\)
\(62\) 3.37683 0.428858
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −5.07462 + 8.78951i −0.619964 + 1.07381i 0.369528 + 0.929220i \(0.379519\pi\)
−0.989492 + 0.144589i \(0.953814\pi\)
\(68\) 1.18842 + 2.05840i 0.144117 + 0.249617i
\(69\) 0 0
\(70\) 0.688417 + 11.6708i 0.0822816 + 1.39493i
\(71\) −0.934749 −0.110934 −0.0554672 0.998461i \(-0.517665\pi\)
−0.0554672 + 0.998461i \(0.517665\pi\)
\(72\) 0 0
\(73\) 3.73042 6.46127i 0.436612 0.756234i −0.560814 0.827942i \(-0.689512\pi\)
0.997426 + 0.0717077i \(0.0228449\pi\)
\(74\) 3.84421 6.65836i 0.446880 0.774019i
\(75\) 0 0
\(76\) −3.68842 −0.423090
\(77\) 0.155792 + 2.64116i 0.0177541 + 0.300988i
\(78\) 0 0
\(79\) 0.209416 + 0.362720i 0.0235612 + 0.0408092i 0.877566 0.479457i \(-0.159166\pi\)
−0.854004 + 0.520266i \(0.825833\pi\)
\(80\) 2.20942 3.82682i 0.247020 0.427852i
\(81\) 0 0
\(82\) −6.07462 10.5216i −0.670830 1.16191i
\(83\) 2.14925 0.235911 0.117955 0.993019i \(-0.462366\pi\)
0.117955 + 0.993019i \(0.462366\pi\)
\(84\) 0 0
\(85\) 10.5028 1.13919
\(86\) 1.53263 + 2.65458i 0.165267 + 0.286251i
\(87\) 0 0
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) −6.41883 11.1177i −0.680395 1.17848i −0.974860 0.222816i \(-0.928475\pi\)
0.294466 0.955662i \(-0.404858\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −4.73042 −0.493180
\(93\) 0 0
\(94\) 2.05362 3.55698i 0.211815 0.366875i
\(95\) −8.14925 + 14.1149i −0.836095 + 1.44816i
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 6.95146 0.822941i 0.702203 0.0831296i
\(99\) 0 0
\(100\) −7.26304 12.5800i −0.726304 1.25800i
\(101\) −7.68187 + 13.3054i −0.764375 + 1.32394i 0.176201 + 0.984354i \(0.443619\pi\)
−0.940576 + 0.339582i \(0.889714\pi\)
\(102\) 0 0
\(103\) 1.31158 + 2.27173i 0.129234 + 0.223840i 0.923380 0.383887i \(-0.125415\pi\)
−0.794146 + 0.607727i \(0.792081\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 8.00000 0.777029
\(107\) 5.45146 + 9.44220i 0.527012 + 0.912812i 0.999504 + 0.0314773i \(0.0100212\pi\)
−0.472492 + 0.881335i \(0.656645\pi\)
\(108\) 0 0
\(109\) 5.89783 10.2153i 0.564910 0.978453i −0.432148 0.901803i \(-0.642244\pi\)
0.997058 0.0766501i \(-0.0244224\pi\)
\(110\) −2.20942 3.82682i −0.210660 0.364873i
\(111\) 0 0
\(112\) −2.36521 1.18566i −0.223491 0.112034i
\(113\) −5.37683 −0.505810 −0.252905 0.967491i \(-0.581386\pi\)
−0.252905 + 0.967491i \(0.581386\pi\)
\(114\) 0 0
\(115\) −10.4515 + 18.1025i −0.974603 + 1.68806i
\(116\) −3.26304 + 5.65175i −0.302966 + 0.524752i
\(117\) 0 0
\(118\) −12.5261 −1.15312
\(119\) −0.370291 6.27760i −0.0339445 0.575467i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 1.89783 3.28714i 0.171822 0.297604i
\(123\) 0 0
\(124\) 1.68842 + 2.92442i 0.151624 + 0.262621i
\(125\) −42.0942 −3.76502
\(126\) 0 0
\(127\) 0.730416 0.0648139 0.0324070 0.999475i \(-0.489683\pi\)
0.0324070 + 0.999475i \(0.489683\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 3.68842 + 6.38853i 0.322258 + 0.558168i 0.980954 0.194242i \(-0.0622246\pi\)
−0.658695 + 0.752410i \(0.728891\pi\)
\(132\) 0 0
\(133\) 8.72387 + 4.37321i 0.756456 + 0.379206i
\(134\) −10.1492 −0.876762
\(135\) 0 0
\(136\) −1.18842 + 2.05840i −0.101906 + 0.176506i
\(137\) −4.41883 + 7.65364i −0.377526 + 0.653895i −0.990702 0.136052i \(-0.956559\pi\)
0.613175 + 0.789947i \(0.289892\pi\)
\(138\) 0 0
\(139\) 1.47392 0.125016 0.0625080 0.998044i \(-0.480090\pi\)
0.0625080 + 0.998044i \(0.480090\pi\)
\(140\) −9.76304 + 6.43161i −0.825128 + 0.543570i
\(141\) 0 0
\(142\) −0.467375 0.809517i −0.0392212 0.0679331i
\(143\) 0 0
\(144\) 0 0
\(145\) 14.4188 + 24.9742i 1.19742 + 2.07399i
\(146\) 7.46083 0.617463
\(147\) 0 0
\(148\) 7.68842 0.631984
\(149\) −4.68187 8.10924i −0.383554 0.664335i 0.608013 0.793927i \(-0.291967\pi\)
−0.991567 + 0.129592i \(0.958633\pi\)
\(150\) 0 0
\(151\) 6.78404 11.7503i 0.552077 0.956226i −0.446047 0.895009i \(-0.647169\pi\)
0.998125 0.0612166i \(-0.0194980\pi\)
\(152\) −1.84421 3.19426i −0.149585 0.259089i
\(153\) 0 0
\(154\) −2.20942 + 1.45550i −0.178040 + 0.117288i
\(155\) 14.9217 1.19854
\(156\) 0 0
\(157\) 9.37029 16.2298i 0.747831 1.29528i −0.201030 0.979585i \(-0.564429\pi\)
0.948861 0.315696i \(-0.102238\pi\)
\(158\) −0.209416 + 0.362720i −0.0166603 + 0.0288564i
\(159\) 0 0
\(160\) 4.41883 0.349339
\(161\) 11.1884 + 5.60867i 0.881771 + 0.442025i
\(162\) 0 0
\(163\) −9.38621 16.2574i −0.735185 1.27338i −0.954642 0.297755i \(-0.903762\pi\)
0.219458 0.975622i \(-0.429571\pi\)
\(164\) 6.07462 10.5216i 0.474348 0.821596i
\(165\) 0 0
\(166\) 1.07462 + 1.86130i 0.0834070 + 0.144465i
\(167\) 23.8898 1.84865 0.924325 0.381606i \(-0.124629\pi\)
0.924325 + 0.381606i \(0.124629\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 5.25142 + 9.09572i 0.402765 + 0.697610i
\(171\) 0 0
\(172\) −1.53263 + 2.65458i −0.116862 + 0.202410i
\(173\) 5.68842 + 9.85263i 0.432482 + 0.749081i 0.997086 0.0762805i \(-0.0243045\pi\)
−0.564604 + 0.825362i \(0.690971\pi\)
\(174\) 0 0
\(175\) 2.26304 + 38.3657i 0.171070 + 2.90018i
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) 6.41883 11.1177i 0.481112 0.833310i
\(179\) 12.3050 21.3130i 0.919722 1.59301i 0.119885 0.992788i \(-0.461747\pi\)
0.799837 0.600217i \(-0.204919\pi\)
\(180\) 0 0
\(181\) 17.4608 1.29785 0.648927 0.760851i \(-0.275218\pi\)
0.648927 + 0.760851i \(0.275218\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −2.36521 4.09666i −0.174365 0.302010i
\(185\) 16.9869 29.4222i 1.24890 2.16316i
\(186\) 0 0
\(187\) 1.18842 + 2.05840i 0.0869056 + 0.150525i
\(188\) 4.10725 0.299552
\(189\) 0 0
\(190\) −16.2985 −1.18242
\(191\) −8.41883 14.5818i −0.609165 1.05511i −0.991378 0.131031i \(-0.958171\pi\)
0.382213 0.924074i \(-0.375162\pi\)
\(192\) 0 0
\(193\) −2.73042 + 4.72922i −0.196540 + 0.340417i −0.947404 0.320040i \(-0.896304\pi\)
0.750865 + 0.660456i \(0.229637\pi\)
\(194\) 3.50000 + 6.06218i 0.251285 + 0.435239i
\(195\) 0 0
\(196\) 4.18842 + 5.60867i 0.299173 + 0.400619i
\(197\) 9.68842 0.690271 0.345136 0.938553i \(-0.387833\pi\)
0.345136 + 0.938553i \(0.387833\pi\)
\(198\) 0 0
\(199\) −10.1492 + 17.5790i −0.719461 + 1.24614i 0.241752 + 0.970338i \(0.422278\pi\)
−0.961214 + 0.275805i \(0.911056\pi\)
\(200\) 7.26304 12.5800i 0.513575 0.889537i
\(201\) 0 0
\(202\) −15.3637 −1.08099
\(203\) 14.4188 9.49871i 1.01200 0.666679i
\(204\) 0 0
\(205\) −26.8427 46.4930i −1.87478 3.24721i
\(206\) −1.31158 + 2.27173i −0.0913823 + 0.158279i
\(207\) 0 0
\(208\) 0 0
\(209\) −3.68842 −0.255133
\(210\) 0 0
\(211\) 22.5130 1.54986 0.774929 0.632048i \(-0.217785\pi\)
0.774929 + 0.632048i \(0.217785\pi\)
\(212\) 4.00000 + 6.92820i 0.274721 + 0.475831i
\(213\) 0 0
\(214\) −5.45146 + 9.44220i −0.372654 + 0.645456i
\(215\) 6.77241 + 11.7302i 0.461875 + 0.799991i
\(216\) 0 0
\(217\) −0.526082 8.91876i −0.0357128 0.605445i
\(218\) 11.7957 0.798903
\(219\) 0 0
\(220\) 2.20942 3.82682i 0.148959 0.258004i
\(221\) 0 0
\(222\) 0 0
\(223\) −7.46083 −0.499614 −0.249807 0.968296i \(-0.580367\pi\)
−0.249807 + 0.968296i \(0.580367\pi\)
\(224\) −0.155792 2.64116i −0.0104093 0.176470i
\(225\) 0 0
\(226\) −2.68842 4.65647i −0.178831 0.309744i
\(227\) −1.38621 + 2.40098i −0.0920058 + 0.159359i −0.908355 0.418200i \(-0.862661\pi\)
0.816349 + 0.577559i \(0.195995\pi\)
\(228\) 0 0
\(229\) 1.26958 + 2.19898i 0.0838965 + 0.145313i 0.904920 0.425581i \(-0.139930\pi\)
−0.821024 + 0.570894i \(0.806597\pi\)
\(230\) −20.9029 −1.37830
\(231\) 0 0
\(232\) −6.52608 −0.428458
\(233\) −12.0261 20.8298i −0.787855 1.36460i −0.927279 0.374372i \(-0.877858\pi\)
0.139424 0.990233i \(-0.455475\pi\)
\(234\) 0 0
\(235\) 9.07462 15.7177i 0.591963 1.02531i
\(236\) −6.26304 10.8479i −0.407689 0.706138i
\(237\) 0 0
\(238\) 5.25142 3.45948i 0.340399 0.224245i
\(239\) −7.59133 −0.491042 −0.245521 0.969391i \(-0.578959\pi\)
−0.245521 + 0.969391i \(0.578959\pi\)
\(240\) 0 0
\(241\) −8.14925 + 14.1149i −0.524939 + 0.909221i 0.474639 + 0.880181i \(0.342579\pi\)
−0.999578 + 0.0290409i \(0.990755\pi\)
\(242\) 0.500000 0.866025i 0.0321412 0.0556702i
\(243\) 0 0
\(244\) 3.79567 0.242993
\(245\) 30.7173 3.63644i 1.96246 0.232324i
\(246\) 0 0
\(247\) 0 0
\(248\) −1.68842 + 2.92442i −0.107215 + 0.185701i
\(249\) 0 0
\(250\) −21.0471 36.4546i −1.33113 2.30559i
\(251\) 8.61008 0.543463 0.271732 0.962373i \(-0.412404\pi\)
0.271732 + 0.962373i \(0.412404\pi\)
\(252\) 0 0
\(253\) −4.73042 −0.297399
\(254\) 0.365208 + 0.632559i 0.0229152 + 0.0396903i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0.418833 + 0.725439i 0.0261261 + 0.0452517i 0.878793 0.477203i \(-0.158350\pi\)
−0.852667 + 0.522455i \(0.825016\pi\)
\(258\) 0 0
\(259\) −18.1847 9.11585i −1.12994 0.566432i
\(260\) 0 0
\(261\) 0 0
\(262\) −3.68842 + 6.38853i −0.227871 + 0.394684i
\(263\) 5.41883 9.38569i 0.334140 0.578747i −0.649180 0.760635i \(-0.724888\pi\)
0.983319 + 0.181888i \(0.0582210\pi\)
\(264\) 0 0
\(265\) 35.3507 2.17157
\(266\) 0.574624 + 9.74170i 0.0352325 + 0.597302i
\(267\) 0 0
\(268\) −5.07462 8.78951i −0.309982 0.536905i
\(269\) 8.93983 15.4842i 0.545071 0.944091i −0.453531 0.891240i \(-0.649836\pi\)
0.998602 0.0528506i \(-0.0168307\pi\)
\(270\) 0 0
\(271\) 4.41883 + 7.65364i 0.268425 + 0.464926i 0.968455 0.249187i \(-0.0801635\pi\)
−0.700030 + 0.714113i \(0.746830\pi\)
\(272\) −2.37683 −0.144117
\(273\) 0 0
\(274\) −8.83767 −0.533903
\(275\) −7.26304 12.5800i −0.437978 0.758600i
\(276\) 0 0
\(277\) 8.00000 13.8564i 0.480673 0.832551i −0.519081 0.854725i \(-0.673726\pi\)
0.999754 + 0.0221745i \(0.00705893\pi\)
\(278\) 0.736959 + 1.27645i 0.0441999 + 0.0765564i
\(279\) 0 0
\(280\) −10.4515 5.23924i −0.624594 0.313104i
\(281\) 15.9217 0.949807 0.474903 0.880038i \(-0.342483\pi\)
0.474903 + 0.880038i \(0.342483\pi\)
\(282\) 0 0
\(283\) 9.04200 15.6612i 0.537491 0.930962i −0.461547 0.887116i \(-0.652706\pi\)
0.999038 0.0438462i \(-0.0139611\pi\)
\(284\) 0.467375 0.809517i 0.0277336 0.0480360i
\(285\) 0 0
\(286\) 0 0
\(287\) −26.8427 + 17.6832i −1.58448 + 1.04381i
\(288\) 0 0
\(289\) 5.67533 + 9.82996i 0.333843 + 0.578233i
\(290\) −14.4188 + 24.9742i −0.846703 + 1.46653i
\(291\) 0 0
\(292\) 3.73042 + 6.46127i 0.218306 + 0.378117i
\(293\) −25.1492 −1.46923 −0.734617 0.678482i \(-0.762638\pi\)
−0.734617 + 0.678482i \(0.762638\pi\)
\(294\) 0 0
\(295\) −55.3507 −3.22264
\(296\) 3.84421 + 6.65836i 0.223440 + 0.387010i
\(297\) 0 0
\(298\) 4.68187 8.10924i 0.271214 0.469756i
\(299\) 0 0
\(300\) 0 0
\(301\) 6.77241 4.46147i 0.390355 0.257155i
\(302\) 13.5681 0.780755
\(303\) 0 0
\(304\) 1.84421 3.19426i 0.105773 0.183204i
\(305\) 8.38621 14.5253i 0.480193 0.831718i
\(306\) 0 0
\(307\) −3.86950 −0.220844 −0.110422 0.993885i \(-0.535220\pi\)
−0.110422 + 0.993885i \(0.535220\pi\)
\(308\) −2.36521 1.18566i −0.134770 0.0675593i
\(309\) 0 0
\(310\) 7.46083 + 12.9225i 0.423747 + 0.733951i
\(311\) −6.78404 + 11.7503i −0.384688 + 0.666299i −0.991726 0.128374i \(-0.959024\pi\)
0.607038 + 0.794673i \(0.292358\pi\)
\(312\) 0 0
\(313\) −1.26304 2.18765i −0.0713913 0.123653i 0.828120 0.560551i \(-0.189411\pi\)
−0.899511 + 0.436898i \(0.856077\pi\)
\(314\) 18.7406 1.05759
\(315\) 0 0
\(316\) −0.418833 −0.0235612
\(317\) −10.0051 17.3293i −0.561941 0.973311i −0.997327 0.0730670i \(-0.976721\pi\)
0.435386 0.900244i \(-0.356612\pi\)
\(318\) 0 0
\(319\) −3.26304 + 5.65175i −0.182695 + 0.316437i
\(320\) 2.20942 + 3.82682i 0.123510 + 0.213926i
\(321\) 0 0
\(322\) 0.736959 + 12.4938i 0.0410691 + 0.696252i
\(323\) 8.76675 0.487795
\(324\) 0 0
\(325\) 0 0
\(326\) 9.38621 16.2574i 0.519854 0.900413i
\(327\) 0 0
\(328\) 12.1492 0.670830
\(329\) −9.71450 4.86980i −0.535578 0.268481i
\(330\) 0 0
\(331\) 8.07462 + 13.9857i 0.443821 + 0.768721i 0.997969 0.0636969i \(-0.0202891\pi\)
−0.554148 + 0.832418i \(0.686956\pi\)
\(332\) −1.07462 + 1.86130i −0.0589777 + 0.102152i
\(333\) 0 0
\(334\) 11.9449 + 20.6892i 0.653597 + 1.13206i
\(335\) −44.8478 −2.45030
\(336\) 0 0
\(337\) 23.1362 1.26031 0.630154 0.776471i \(-0.282992\pi\)
0.630154 + 0.776471i \(0.282992\pi\)
\(338\) −6.50000 11.2583i −0.353553 0.612372i
\(339\) 0 0
\(340\) −5.25142 + 9.09572i −0.284798 + 0.493285i
\(341\) 1.68842 + 2.92442i 0.0914329 + 0.158366i
\(342\) 0 0
\(343\) −3.25650 18.2317i −0.175834 0.984420i
\(344\) −3.06525 −0.165267
\(345\) 0 0
\(346\) −5.68842 + 9.85263i −0.305811 + 0.529681i
\(347\) 7.82829 13.5590i 0.420245 0.727885i −0.575718 0.817648i \(-0.695278\pi\)
0.995963 + 0.0897628i \(0.0286109\pi\)
\(348\) 0 0
\(349\) −20.0102 −1.07112 −0.535560 0.844497i \(-0.679899\pi\)
−0.535560 + 0.844497i \(0.679899\pi\)
\(350\) −32.0942 + 21.1427i −1.71551 + 1.13013i
\(351\) 0 0
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) 3.73042 6.46127i 0.198550 0.343899i −0.749508 0.661995i \(-0.769710\pi\)
0.948058 + 0.318096i \(0.103043\pi\)
\(354\) 0 0
\(355\) −2.06525 3.57712i −0.109612 0.189854i
\(356\) 12.8377 0.680395
\(357\) 0 0
\(358\) 24.6101 1.30068
\(359\) −5.62317 9.73961i −0.296779 0.514037i 0.678618 0.734492i \(-0.262579\pi\)
−0.975397 + 0.220455i \(0.929246\pi\)
\(360\) 0 0
\(361\) 2.69779 4.67271i 0.141989 0.245932i
\(362\) 8.73042 + 15.1215i 0.458860 + 0.794770i
\(363\) 0 0
\(364\) 0 0
\(365\) 32.9682 1.72563
\(366\) 0 0
\(367\) 2.95800 5.12341i 0.154406 0.267440i −0.778436 0.627724i \(-0.783987\pi\)
0.932843 + 0.360284i \(0.117320\pi\)
\(368\) 2.36521 4.09666i 0.123295 0.213553i
\(369\) 0 0
\(370\) 33.9738 1.76622
\(371\) −1.24633 21.1293i −0.0647064 1.09698i
\(372\) 0 0
\(373\) 11.5630 + 20.0277i 0.598709 + 1.03700i 0.993012 + 0.118014i \(0.0376529\pi\)
−0.394303 + 0.918981i \(0.629014\pi\)
\(374\) −1.18842 + 2.05840i −0.0614516 + 0.106437i
\(375\) 0 0
\(376\) 2.05362 + 3.55698i 0.105908 + 0.183437i
\(377\) 0 0
\(378\) 0 0
\(379\) −6.77241 −0.347876 −0.173938 0.984757i \(-0.555649\pi\)
−0.173938 + 0.984757i \(0.555649\pi\)
\(380\) −8.14925 14.1149i −0.418048 0.724080i
\(381\) 0 0
\(382\) 8.41883 14.5818i 0.430745 0.746072i
\(383\) 12.6819 + 21.9656i 0.648013 + 1.12239i 0.983597 + 0.180382i \(0.0577333\pi\)
−0.335583 + 0.942011i \(0.608933\pi\)
\(384\) 0 0
\(385\) −9.76304 + 6.43161i −0.497571 + 0.327785i
\(386\) −5.46083 −0.277949
\(387\) 0 0
\(388\) −3.50000 + 6.06218i −0.177686 + 0.307760i
\(389\) 12.6282 21.8728i 0.640278 1.10899i −0.345093 0.938568i \(-0.612153\pi\)
0.985371 0.170425i \(-0.0545140\pi\)
\(390\) 0 0
\(391\) 11.2434 0.568604
\(392\) −2.76304 + 6.43161i −0.139555 + 0.324845i
\(393\) 0 0
\(394\) 4.84421 + 8.39042i 0.244048 + 0.422703i
\(395\) −0.925376 + 1.60280i −0.0465607 + 0.0806455i
\(396\) 0 0
\(397\) 6.73696 + 11.6688i 0.338118 + 0.585638i 0.984079 0.177733i \(-0.0568763\pi\)
−0.645961 + 0.763371i \(0.723543\pi\)
\(398\) −20.2985 −1.01747
\(399\) 0 0
\(400\) 14.5261 0.726304
\(401\) 16.9449 + 29.3495i 0.846189 + 1.46564i 0.884585 + 0.466379i \(0.154442\pi\)
−0.0383962 + 0.999263i \(0.512225\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −7.68187 13.3054i −0.382188 0.661968i
\(405\) 0 0
\(406\) 15.4355 + 7.73772i 0.766053 + 0.384017i
\(407\) 7.68842 0.381101
\(408\) 0 0
\(409\) 2.10725 3.64986i 0.104197 0.180474i −0.809213 0.587515i \(-0.800106\pi\)
0.913410 + 0.407041i \(0.133439\pi\)
\(410\) 26.8427 46.4930i 1.32567 2.29613i
\(411\) 0 0
\(412\) −2.62317 −0.129234
\(413\) 1.95146 + 33.0834i 0.0960250 + 1.62793i
\(414\) 0 0
\(415\) 4.74858 + 8.22479i 0.233099 + 0.403739i
\(416\) 0 0
\(417\) 0 0
\(418\) −1.84421 3.19426i −0.0902032 0.156236i
\(419\) 22.3116 1.08999 0.544996 0.838439i \(-0.316531\pi\)
0.544996 + 0.838439i \(0.316531\pi\)
\(420\) 0 0
\(421\) 18.3116 0.892452 0.446226 0.894920i \(-0.352768\pi\)
0.446226 + 0.894920i \(0.352768\pi\)
\(422\) 11.2565 + 19.4968i 0.547958 + 0.949091i
\(423\) 0 0
\(424\) −4.00000 + 6.92820i −0.194257 + 0.336463i
\(425\) 17.2630 + 29.9005i 0.837380 + 1.45039i
\(426\) 0 0
\(427\) −8.97754 4.50037i −0.434454 0.217788i
\(428\) −10.9029 −0.527012
\(429\) 0 0
\(430\) −6.77241 + 11.7302i −0.326595 + 0.565679i
\(431\) −14.4188 + 24.9742i −0.694531 + 1.20296i 0.275808 + 0.961213i \(0.411055\pi\)
−0.970339 + 0.241750i \(0.922279\pi\)
\(432\) 0 0
\(433\) 7.62317 0.366346 0.183173 0.983081i \(-0.441363\pi\)
0.183173 + 0.983081i \(0.441363\pi\)
\(434\) 7.46083 4.91498i 0.358131 0.235927i
\(435\) 0 0
\(436\) 5.89783 + 10.2153i 0.282455 + 0.489226i
\(437\) −8.72387 + 15.1102i −0.417319 + 0.722818i
\(438\) 0 0
\(439\) 16.6870 + 28.9027i 0.796425 + 1.37945i 0.921930 + 0.387356i \(0.126611\pi\)
−0.125505 + 0.992093i \(0.540055\pi\)
\(440\) 4.41883 0.210660
\(441\) 0 0
\(442\) 0 0
\(443\) −2.42538 4.20087i −0.115233 0.199590i 0.802640 0.596464i \(-0.203428\pi\)
−0.917873 + 0.396874i \(0.870095\pi\)
\(444\) 0 0
\(445\) 28.3637 49.1275i 1.34457 2.32886i
\(446\) −3.73042 6.46127i −0.176640 0.305950i
\(447\) 0 0
\(448\) 2.20942 1.45550i 0.104385 0.0687659i
\(449\) −14.3450 −0.676982 −0.338491 0.940970i \(-0.609917\pi\)
−0.338491 + 0.940970i \(0.609917\pi\)
\(450\) 0 0
\(451\) 6.07462 10.5216i 0.286043 0.495441i
\(452\) 2.68842 4.65647i 0.126452 0.219022i
\(453\) 0 0
\(454\) −2.77241 −0.130116
\(455\) 0 0
\(456\) 0 0
\(457\) 12.5913 + 21.8088i 0.588998 + 1.02017i 0.994364 + 0.106020i \(0.0338106\pi\)
−0.405366 + 0.914154i \(0.632856\pi\)
\(458\) −1.26958 + 2.19898i −0.0593238 + 0.102752i
\(459\) 0 0
\(460\) −10.4515 18.1025i −0.487302 0.844031i
\(461\) −13.0187 −0.606344 −0.303172 0.952936i \(-0.598046\pi\)
−0.303172 + 0.952936i \(0.598046\pi\)
\(462\) 0 0
\(463\) −14.2145 −0.660604 −0.330302 0.943875i \(-0.607151\pi\)
−0.330302 + 0.943875i \(0.607151\pi\)
\(464\) −3.26304 5.65175i −0.151483 0.262376i
\(465\) 0 0
\(466\) 12.0261 20.8298i 0.557098 0.964921i
\(467\) −1.19779 2.07463i −0.0554271 0.0960026i 0.836981 0.547233i \(-0.184319\pi\)
−0.892408 + 0.451230i \(0.850985\pi\)
\(468\) 0 0
\(469\) 1.58117 + 26.8058i 0.0730115 + 1.23778i
\(470\) 18.1492 0.837162
\(471\) 0 0
\(472\) 6.26304 10.8479i 0.288280 0.499315i
\(473\) −1.53263 + 2.65458i −0.0704702 + 0.122058i
\(474\) 0 0
\(475\) −53.5782 −2.45834
\(476\) 5.62171 + 2.81812i 0.257670 + 0.129168i
\(477\) 0 0
\(478\) −3.79567 6.57429i −0.173610 0.300701i
\(479\) 5.41883 9.38569i 0.247593 0.428843i −0.715265 0.698854i \(-0.753694\pi\)
0.962857 + 0.270010i \(0.0870272\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −16.2985 −0.742376
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 15.4659 + 26.7877i 0.702271 + 1.21637i
\(486\) 0 0
\(487\) 17.3217 30.0021i 0.784923 1.35953i −0.144121 0.989560i \(-0.546036\pi\)
0.929045 0.369967i \(-0.120631\pi\)
\(488\) 1.89783 + 3.28714i 0.0859109 + 0.148802i
\(489\) 0 0
\(490\) 18.5079 + 24.7838i 0.836102 + 1.11962i
\(491\) −38.1492 −1.72165 −0.860826 0.508900i \(-0.830052\pi\)
−0.860826 + 0.508900i \(0.830052\pi\)
\(492\) 0 0
\(493\) 7.75571 13.4333i 0.349299 0.605004i
\(494\) 0 0
\(495\) 0 0
\(496\) −3.37683 −0.151624
\(497\) −2.06525 + 1.36053i −0.0926392 + 0.0610280i
\(498\) 0 0
\(499\) 0.311583 + 0.539678i 0.0139484 + 0.0241593i 0.872915 0.487872i \(-0.162227\pi\)
−0.858967 + 0.512031i \(0.828893\pi\)
\(500\) 21.0471 36.4546i 0.941254 1.63030i
\(501\) 0 0
\(502\) 4.30504 + 7.45655i 0.192143 + 0.332802i
\(503\) −31.1362 −1.38829 −0.694146 0.719834i \(-0.744218\pi\)
−0.694146 + 0.719834i \(0.744218\pi\)
\(504\) 0 0
\(505\) −67.8898 −3.02106
\(506\) −2.36521 4.09666i −0.105146 0.182119i
\(507\) 0 0
\(508\) −0.365208 + 0.632559i −0.0162035 + 0.0280653i
\(509\) −21.0522 36.4634i −0.933121 1.61621i −0.777951 0.628325i \(-0.783741\pi\)
−0.155170 0.987888i \(-0.549592\pi\)
\(510\) 0 0
\(511\) −1.16233 19.7053i −0.0514187 0.871709i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −0.418833 + 0.725439i −0.0184739 + 0.0319978i
\(515\) −5.79567 + 10.0384i −0.255388 + 0.442344i
\(516\) 0 0
\(517\) 4.10725 0.180637
\(518\) −1.19779 20.3063i −0.0526279 0.892209i
\(519\) 0 0
\(520\) 0 0
\(521\) −9.00000 + 15.5885i −0.394297 + 0.682943i −0.993011 0.118020i \(-0.962345\pi\)
0.598714 + 0.800963i \(0.295679\pi\)
\(522\) 0 0
\(523\) 12.6333 + 21.8816i 0.552417 + 0.956814i 0.998099 + 0.0616232i \(0.0196277\pi\)
−0.445682 + 0.895191i \(0.647039\pi\)
\(524\) −7.37683 −0.322258
\(525\) 0 0
\(526\) 10.8377 0.472545
\(527\) −4.01309 6.95087i −0.174813 0.302785i
\(528\) 0 0
\(529\) 0.311583 0.539678i 0.0135471 0.0234643i
\(530\) 17.6753 + 30.6146i 0.767767 + 1.32981i
\(531\) 0 0
\(532\) −8.14925 + 5.36849i −0.353315 + 0.232754i
\(533\) 0 0
\(534\) 0 0
\(535\) −24.0891 + 41.7235i −1.04146 + 1.80386i
\(536\) 5.07462 8.78951i 0.219190 0.379649i
\(537\) 0 0
\(538\) 17.8797 0.770847
\(539\) 4.18842 + 5.60867i 0.180408 + 0.241582i
\(540\) 0 0
\(541\) 2.20942 + 3.82682i 0.0949902 + 0.164528i 0.909605 0.415475i \(-0.136385\pi\)
−0.814614 + 0.580003i \(0.803051\pi\)
\(542\) −4.41883 + 7.65364i −0.189805 + 0.328752i
\(543\) 0 0
\(544\) −1.18842 2.05840i −0.0509530 0.0882531i
\(545\) 52.1231 2.23271
\(546\) 0 0
\(547\) −27.6622 −1.18275 −0.591376 0.806396i \(-0.701415\pi\)
−0.591376 + 0.806396i \(0.701415\pi\)
\(548\) −4.41883 7.65364i −0.188763 0.326947i
\(549\) 0 0
\(550\) 7.26304 12.5800i 0.309697 0.536411i
\(551\) 12.0355 + 20.8460i 0.512728 + 0.888070i
\(552\) 0 0
\(553\) 0.990626 + 0.496593i 0.0421257 + 0.0211173i
\(554\) 16.0000 0.679775
\(555\) 0 0
\(556\) −0.736959 + 1.27645i −0.0312540 + 0.0541335i
\(557\) −3.99346 + 6.91687i −0.169208 + 0.293077i −0.938142 0.346252i \(-0.887454\pi\)
0.768934 + 0.639329i \(0.220788\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −0.688417 11.6708i −0.0290909 0.493183i
\(561\) 0 0
\(562\) 7.96083 + 13.7886i 0.335807 + 0.581636i
\(563\) −13.6753 + 23.6864i −0.576346 + 0.998261i 0.419547 + 0.907733i \(0.362189\pi\)
−0.995894 + 0.0905280i \(0.971145\pi\)
\(564\) 0 0
\(565\) −11.8797 20.5762i −0.499781 0.865646i
\(566\) 18.0840 0.760127
\(567\) 0 0
\(568\) 0.934749 0.0392212
\(569\) −14.7239 25.5025i −0.617257 1.06912i −0.989984 0.141179i \(-0.954911\pi\)
0.372727 0.927941i \(-0.378423\pi\)
\(570\) 0 0
\(571\) 7.26304 12.5800i 0.303949 0.526455i −0.673078 0.739572i \(-0.735028\pi\)
0.977027 + 0.213117i \(0.0683615\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −28.7355 14.4049i −1.19940 0.601248i
\(575\) −68.7144 −2.86559
\(576\) 0 0
\(577\) −6.69779 + 11.6009i −0.278833 + 0.482952i −0.971095 0.238694i \(-0.923281\pi\)
0.692262 + 0.721646i \(0.256614\pi\)
\(578\) −5.67533 + 9.82996i −0.236063 + 0.408872i
\(579\) 0 0
\(580\) −28.8377 −1.19742
\(581\) 4.74858 3.12823i 0.197004 0.129781i
\(582\) 0 0
\(583\) 4.00000 + 6.92820i 0.165663 + 0.286937i
\(584\) −3.73042 + 6.46127i −0.154366 + 0.267369i
\(585\) 0 0
\(586\) −12.5746 21.7799i −0.519453 0.899719i
\(587\) 11.2928 0.466105 0.233053 0.972464i \(-0.425129\pi\)
0.233053 + 0.972464i \(0.425129\pi\)
\(588\) 0 0
\(589\) 12.4552 0.513206
\(590\) −27.6753 47.9351i −1.13938 1.97346i
\(591\) 0 0
\(592\) −3.84421 + 6.65836i −0.157996 + 0.273657i
\(593\) −9.78912 16.9553i −0.401991 0.696269i 0.591975 0.805956i \(-0.298348\pi\)
−0.993966 + 0.109687i \(0.965015\pi\)
\(594\) 0 0
\(595\) 23.2051 15.2869i 0.951317 0.626700i
\(596\) 9.36375 0.383554
\(597\) 0 0
\(598\) 0 0
\(599\) 5.46591 9.46724i 0.223331 0.386821i −0.732486 0.680782i \(-0.761640\pi\)
0.955817 + 0.293961i \(0.0949735\pi\)
\(600\) 0 0
\(601\) −41.2202 −1.68141 −0.840703 0.541497i \(-0.817858\pi\)
−0.840703 + 0.541497i \(0.817858\pi\)
\(602\) 7.24995 + 3.63435i 0.295486 + 0.148125i
\(603\) 0 0
\(604\) 6.78404 + 11.7503i 0.276039 + 0.478113i
\(605\) 2.20942 3.82682i 0.0898255 0.155582i
\(606\) 0 0
\(607\) 15.6702 + 27.1417i 0.636036 + 1.10165i 0.986295 + 0.164993i \(0.0527603\pi\)
−0.350259 + 0.936653i \(0.613906\pi\)
\(608\) 3.68842 0.149585
\(609\) 0 0
\(610\) 16.7724 0.679095
\(611\) 0 0
\(612\) 0 0
\(613\) −8.54425 + 14.7991i −0.345099 + 0.597729i −0.985372 0.170419i \(-0.945488\pi\)
0.640273 + 0.768148i \(0.278821\pi\)
\(614\) −1.93475 3.35108i −0.0780801 0.135239i
\(615\) 0 0
\(616\) −0.155792 2.64116i −0.00627702 0.106415i
\(617\) 6.96817 0.280528 0.140264 0.990114i \(-0.455205\pi\)
0.140264 + 0.990114i \(0.455205\pi\)
\(618\) 0 0
\(619\) 0.00937364 0.0162356i 0.000376759 0.000652565i −0.865837 0.500326i \(-0.833213\pi\)
0.866214 + 0.499674i \(0.166547\pi\)
\(620\) −7.46083 + 12.9225i −0.299634 + 0.518982i
\(621\) 0 0
\(622\) −13.5681 −0.544030
\(623\) −30.3637 15.2211i −1.21650 0.609821i
\(624\) 0 0
\(625\) −56.6883 98.1871i −2.26753 3.92748i
\(626\) 1.26304 2.18765i 0.0504813 0.0874361i
\(627\) 0 0
\(628\) 9.37029 + 16.2298i 0.373915 + 0.647640i
\(629\) −18.2741 −0.728636
\(630\) 0 0
\(631\) −5.78550 −0.230317 −0.115159 0.993347i \(-0.536738\pi\)
−0.115159 + 0.993347i \(0.536738\pi\)
\(632\) −0.209416 0.362720i −0.00833013 0.0144282i
\(633\) 0 0
\(634\) 10.0051 17.3293i 0.397353 0.688235i
\(635\) 1.61379 + 2.79517i 0.0640414 + 0.110923i
\(636\) 0 0
\(637\) 0 0
\(638\) −6.52608 −0.258370
\(639\) 0 0
\(640\) −2.20942 + 3.82682i −0.0873348 + 0.151268i
\(641\) 7.68842 13.3167i 0.303674 0.525979i −0.673291 0.739378i \(-0.735120\pi\)
0.976965 + 0.213398i \(0.0684532\pi\)
\(642\) 0 0
\(643\) −35.8058 −1.41204 −0.706022 0.708190i \(-0.749512\pi\)
−0.706022 + 0.708190i \(0.749512\pi\)
\(644\) −10.4515 + 6.88512i −0.411845 + 0.271312i
\(645\) 0 0
\(646\) 4.38338 + 7.59223i 0.172462 + 0.298712i
\(647\) 4.62825 8.01636i 0.181955 0.315156i −0.760591 0.649231i \(-0.775091\pi\)
0.942546 + 0.334076i \(0.108424\pi\)
\(648\) 0 0
\(649\) −6.26304 10.8479i −0.245846 0.425818i
\(650\) 0 0
\(651\) 0 0
\(652\) 18.7724 0.735185
\(653\) 12.4239 + 21.5189i 0.486185 + 0.842098i 0.999874 0.0158790i \(-0.00505464\pi\)
−0.513689 + 0.857977i \(0.671721\pi\)
\(654\) 0 0
\(655\) −16.2985 + 28.2298i −0.636835 + 1.10303i
\(656\) 6.07462 + 10.5216i 0.237174 + 0.410798i
\(657\) 0 0
\(658\) −0.639875 10.8479i −0.0249449 0.422895i
\(659\) 6.60442 0.257272 0.128636 0.991692i \(-0.458940\pi\)
0.128636 + 0.991692i \(0.458940\pi\)
\(660\) 0 0
\(661\) 6.61662 11.4603i 0.257357 0.445755i −0.708176 0.706036i \(-0.750482\pi\)
0.965533 + 0.260281i \(0.0838151\pi\)
\(662\) −8.07462 + 13.9857i −0.313829 + 0.543568i
\(663\) 0 0
\(664\) −2.14925 −0.0834070
\(665\) 2.53917 + 43.0469i 0.0984647 + 1.66929i
\(666\) 0 0
\(667\) 15.4355 + 26.7351i 0.597667 + 1.03519i
\(668\) −11.9449 + 20.6892i −0.462163 + 0.800489i
\(669\) 0 0
\(670\) −22.4239 38.8394i −0.866311 1.50050i
\(671\) 3.79567 0.146530
\(672\) 0 0
\(673\) 0.130501 0.00503045 0.00251523 0.999997i \(-0.499199\pi\)
0.00251523 + 0.999997i \(0.499199\pi\)
\(674\) 11.5681 + 20.0365i 0.445586 + 0.771777i
\(675\) 0 0
\(676\) 6.50000 11.2583i 0.250000 0.433013i
\(677\) 14.0587 + 24.3504i 0.540320 + 0.935862i 0.998885 + 0.0472011i \(0.0150301\pi\)
−0.458565 + 0.888661i \(0.651637\pi\)
\(678\) 0 0
\(679\) 15.4659 10.1885i 0.593527 0.390999i
\(680\) −10.5028 −0.402765
\(681\) 0 0
\(682\) −1.68842 + 2.92442i −0.0646528 + 0.111982i
\(683\) 7.95146 13.7723i 0.304254 0.526984i −0.672841 0.739787i \(-0.734926\pi\)
0.977095 + 0.212804i \(0.0682595\pi\)
\(684\) 0 0
\(685\) −39.0522 −1.49211
\(686\) 14.1609 11.9361i 0.540665 0.455721i
\(687\) 0 0
\(688\) −1.53263 2.65458i −0.0584308 0.101205i
\(689\) 0 0
\(690\) 0 0
\(691\) 7.99063 + 13.8402i 0.303978 + 0.526505i 0.977033 0.213087i \(-0.0683518\pi\)
−0.673055 + 0.739592i \(0.735018\pi\)
\(692\) −11.3768 −0.432482
\(693\) 0 0
\(694\) 15.6566 0.594316
\(695\) 3.25650 + 5.64042i 0.123526 + 0.213953i
\(696\) 0 0
\(697\) −14.4384 + 25.0080i −0.546892 + 0.947245i
\(698\) −10.0051 17.3293i −0.378698 0.655924i
\(699\) 0 0
\(700\) −34.3572 17.2230i −1.29858 0.650968i
\(701\) −13.9869 −0.528278 −0.264139 0.964485i \(-0.585088\pi\)
−0.264139 + 0.964485i \(0.585088\pi\)
\(702\) 0 0
\(703\) 14.1790 24.5588i 0.534773 0.926254i
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) 7.46083 0.280792
\(707\) 2.39354 + 40.5781i 0.0900184 + 1.52610i
\(708\) 0 0
\(709\) −3.82096 6.61809i −0.143499 0.248548i 0.785313 0.619099i \(-0.212502\pi\)
−0.928812 + 0.370551i \(0.879169\pi\)
\(710\) 2.06525 3.57712i 0.0775075 0.134247i
\(711\) 0 0
\(712\) 6.41883 + 11.1177i 0.240556 + 0.416655i
\(713\) 15.9738 0.598225
\(714\) 0 0
\(715\) 0 0
\(716\) 12.3050 + 21.3130i 0.459861 + 0.796503i
\(717\) 0 0
\(718\) 5.62317 9.73961i 0.209855 0.363479i
\(719\) −9.71879 16.8334i −0.362450 0.627781i 0.625914 0.779892i \(-0.284726\pi\)
−0.988363 + 0.152111i \(0.951393\pi\)
\(720\) 0 0
\(721\) 6.20433 + 3.11019i 0.231061 + 0.115829i
\(722\) 5.39558 0.200803
\(723\) 0 0
\(724\) −8.73042 + 15.1215i −0.324463 + 0.561987i
\(725\) −47.3992 + 82.0978i −1.76036 + 3.04904i
\(726\) 0 0
\(727\) −44.9217 −1.66605 −0.833026 0.553234i \(-0.813394\pi\)
−0.833026 + 0.553234i \(0.813394\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 16.4841 + 28.5513i 0.610103 + 1.05673i
\(731\) 3.64280 6.30951i 0.134734 0.233366i
\(732\) 0 0
\(733\) −12.5210 21.6870i −0.462474 0.801028i 0.536610 0.843830i \(-0.319705\pi\)
−0.999084 + 0.0428026i \(0.986371\pi\)
\(734\) 5.91600 0.218364
\(735\) 0 0
\(736\) 4.73042 0.174365
\(737\) −5.07462 8.78951i −0.186926 0.323766i
\(738\) 0 0
\(739\) 3.31158 5.73583i 0.121819 0.210996i −0.798666 0.601774i \(-0.794461\pi\)
0.920485 + 0.390778i \(0.127794\pi\)
\(740\) 16.9869 + 29.4222i 0.624451 + 1.08158i
\(741\) 0 0
\(742\) 17.6753 11.6440i 0.648882 0.427465i
\(743\) 39.3972 1.44534 0.722671 0.691192i \(-0.242914\pi\)
0.722671 + 0.691192i \(0.242914\pi\)
\(744\) 0 0
\(745\) 20.6884 35.8334i 0.757965 1.31283i
\(746\) −11.5630 + 20.0277i −0.423351 + 0.733266i
\(747\) 0 0
\(748\) −2.37683 −0.0869056
\(749\) 25.7877 + 12.9272i 0.942261 + 0.472348i
\(750\) 0 0
\(751\) 5.35358 + 9.27268i 0.195355 + 0.338365i 0.947017 0.321184i \(-0.104081\pi\)
−0.751662 + 0.659549i \(0.770747\pi\)
\(752\) −2.05362 + 3.55698i −0.0748880 + 0.129710i
\(753\) 0 0
\(754\) 0 0
\(755\) 59.9551 2.18199
\(756\) 0 0
\(757\) −17.2797 −0.628043 −0.314022 0.949416i \(-0.601676\pi\)
−0.314022 + 0.949416i \(0.601676\pi\)
\(758\) −3.38621 5.86508i −0.122993 0.213029i
\(759\) 0 0
\(760\) 8.14925 14.1149i 0.295604 0.512002i
\(761\) −16.3544 28.3266i −0.592846 1.02684i −0.993847 0.110761i \(-0.964671\pi\)
0.401001 0.916077i \(-0.368662\pi\)
\(762\) 0 0
\(763\) −1.83767 31.1542i −0.0665280 1.12786i
\(764\) 16.8377 0.609165
\(765\) 0 0
\(766\) −12.6819 + 21.9656i −0.458215 + 0.793651i
\(767\) 0 0
\(768\) 0 0
\(769\) 12.2145 0.440466 0.220233 0.975447i \(-0.429318\pi\)
0.220233 + 0.975447i \(0.429318\pi\)
\(770\) −10.4515 5.23924i −0.376644 0.188809i
\(771\) 0 0
\(772\) −2.73042 4.72922i −0.0982698 0.170208i
\(773\) 0.102167 0.176958i 0.00367468 0.00636474i −0.864182 0.503179i \(-0.832164\pi\)
0.867857 + 0.496814i \(0.165497\pi\)
\(774\) 0 0
\(775\) 24.5261 + 42.4804i 0.881003 + 1.52594i
\(776\) −7.00000 −0.251285
\(777\) 0 0
\(778\) 25.2565 0.905489
\(779\) −22.4057 38.8079i −0.802769 1.39044i
\(780\) 0 0
\(781\) 0.467375 0.809517i 0.0167240 0.0289668i
\(782\) 5.62171 + 9.73708i 0.201032 + 0.348197i
\(783\) 0 0
\(784\) −6.95146 + 0.822941i −0.248266 + 0.0293908i
\(785\) 82.8115 2.95567
\(786\) 0 0
\(787\) −12.7790 + 22.1338i −0.455521 + 0.788985i −0.998718 0.0506202i \(-0.983880\pi\)
0.543197 + 0.839605i \(0.317214\pi\)
\(788\) −4.84421 + 8.39042i −0.172568 + 0.298896i
\(789\) 0 0
\(790\) −1.85075 −0.0658468
\(791\) −11.8797 + 7.82598i −0.422392 + 0.278260i
\(792\) 0 0
\(793\)