Properties

Label 1008.2.r.l.337.3
Level 1008
Weight 2
Character 1008.337
Analytic conductor 8.049
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.2091141441.1
Defining polynomial: \(x^{8} - x^{7} + x^{6} + 3 x^{5} - 15 x^{4} + 9 x^{3} + 9 x^{2} - 27 x + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 337.3
Root \(-1.69047 - 0.377226i\) of defining polynomial
Character \(\chi\) \(=\) 1008.337
Dual form 1008.2.r.l.673.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.17192 - 1.27538i) q^{3} +(-2.19047 + 3.79401i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.253189 - 2.98930i) q^{9} +O(q^{10})\) \(q+(1.17192 - 1.27538i) q^{3} +(-2.19047 + 3.79401i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.253189 - 2.98930i) q^{9} +(-2.69047 - 4.66004i) q^{11} +(1.27174 - 2.20272i) q^{13} +(2.27174 + 7.23998i) q^{15} -2.58058 q^{17} +6.72479 q^{19} +(-1.69047 - 0.377226i) q^{21} +(-0.400185 + 0.693141i) q^{23} +(-7.09635 - 12.2912i) q^{25} +(-4.10921 - 3.18032i) q^{27} +(-1.87155 - 3.24163i) q^{29} +(1.69685 - 2.93903i) q^{31} +(-9.09635 - 2.02983i) q^{33} +4.38095 q^{35} +4.38095 q^{37} +(-1.31892 - 4.20337i) q^{39} +(3.19685 - 5.53711i) q^{41} +(-0.381635 - 0.661012i) q^{43} +(11.8960 + 5.58737i) q^{45} +(-4.13414 - 7.16053i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-3.02424 + 3.29122i) q^{51} -4.94877 q^{53} +23.5736 q^{55} +(7.88095 - 8.57667i) q^{57} +(2.78751 - 4.82811i) q^{59} +(4.14329 + 7.17639i) q^{61} +(-2.46221 + 1.71392i) q^{63} +(5.57142 + 9.64998i) q^{65} +(-0.946441 + 1.63928i) q^{67} +(0.415032 + 1.32270i) q^{69} -1.34385 q^{71} -8.65060 q^{73} +(-23.9924 - 5.35385i) q^{75} +(-2.69047 + 4.66004i) q^{77} +(-6.64051 - 11.5017i) q^{79} +(-8.87179 + 1.51371i) q^{81} +(1.86240 + 3.22577i) q^{83} +(5.65269 - 9.79074i) q^{85} +(-6.32762 - 1.41200i) q^{87} -6.99862 q^{89} -2.54348 q^{91} +(-1.75980 - 5.60845i) q^{93} +(-14.7305 + 25.5139i) q^{95} +(-1.48076 - 2.56476i) q^{97} +(-13.2490 + 9.22249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + q^{3} - 3q^{5} - 4q^{7} - q^{9} + O(q^{10}) \) \( 8q + q^{3} - 3q^{5} - 4q^{7} - q^{9} - 7q^{11} + 3q^{13} + 11q^{15} + 6q^{17} + 8q^{19} + q^{21} - 2q^{23} - 5q^{25} - 11q^{27} - 9q^{29} - 3q^{31} - 21q^{33} + 6q^{35} + 6q^{37} - 2q^{39} + 9q^{41} - 8q^{43} + 7q^{45} - 3q^{47} - 4q^{49} + 18q^{51} + 12q^{53} + 56q^{55} + 34q^{57} - 10q^{59} + 20q^{61} + 2q^{63} + q^{65} - 11q^{67} - 17q^{69} + 6q^{71} - 48q^{73} - 52q^{75} - 7q^{77} - 21q^{79} - 25q^{81} - 8q^{83} + 9q^{85} + 15q^{87} + 12q^{89} - 6q^{91} + 29q^{93} - 36q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(3\) 1.17192 1.27538i 0.676611 0.736341i
\(4\) 0 0
\(5\) −2.19047 + 3.79401i −0.979610 + 1.69673i −0.315811 + 0.948822i \(0.602277\pi\)
−0.663799 + 0.747911i \(0.731057\pi\)
\(6\) 0 0
\(7\) −0.500000 0.866025i −0.188982 0.327327i
\(8\) 0 0
\(9\) −0.253189 2.98930i −0.0843964 0.996432i
\(10\) 0 0
\(11\) −2.69047 4.66004i −0.811208 1.40505i −0.912019 0.410148i \(-0.865477\pi\)
0.100811 0.994906i \(-0.467856\pi\)
\(12\) 0 0
\(13\) 1.27174 2.20272i 0.352717 0.610924i −0.634008 0.773327i \(-0.718591\pi\)
0.986724 + 0.162403i \(0.0519245\pi\)
\(14\) 0 0
\(15\) 2.27174 + 7.23998i 0.586560 + 1.86935i
\(16\) 0 0
\(17\) −2.58058 −0.625882 −0.312941 0.949773i \(-0.601314\pi\)
−0.312941 + 0.949773i \(0.601314\pi\)
\(18\) 0 0
\(19\) 6.72479 1.54277 0.771387 0.636366i \(-0.219563\pi\)
0.771387 + 0.636366i \(0.219563\pi\)
\(20\) 0 0
\(21\) −1.69047 0.377226i −0.368892 0.0823174i
\(22\) 0 0
\(23\) −0.400185 + 0.693141i −0.0834443 + 0.144530i −0.904727 0.425991i \(-0.859925\pi\)
0.821283 + 0.570521i \(0.193259\pi\)
\(24\) 0 0
\(25\) −7.09635 12.2912i −1.41927 2.45825i
\(26\) 0 0
\(27\) −4.10921 3.18032i −0.790817 0.612052i
\(28\) 0 0
\(29\) −1.87155 3.24163i −0.347539 0.601955i 0.638273 0.769810i \(-0.279649\pi\)
−0.985812 + 0.167855i \(0.946316\pi\)
\(30\) 0 0
\(31\) 1.69685 2.93903i 0.304764 0.527866i −0.672445 0.740147i \(-0.734756\pi\)
0.977209 + 0.212281i \(0.0680892\pi\)
\(32\) 0 0
\(33\) −9.09635 2.02983i −1.58347 0.353348i
\(34\) 0 0
\(35\) 4.38095 0.740515
\(36\) 0 0
\(37\) 4.38095 0.720223 0.360112 0.932909i \(-0.382739\pi\)
0.360112 + 0.932909i \(0.382739\pi\)
\(38\) 0 0
\(39\) −1.31892 4.20337i −0.211196 0.673077i
\(40\) 0 0
\(41\) 3.19685 5.53711i 0.499264 0.864751i −0.500735 0.865600i \(-0.666937\pi\)
1.00000 0.000849221i \(0.000270315\pi\)
\(42\) 0 0
\(43\) −0.381635 0.661012i −0.0581988 0.100803i 0.835458 0.549554i \(-0.185202\pi\)
−0.893657 + 0.448751i \(0.851869\pi\)
\(44\) 0 0
\(45\) 11.8960 + 5.58737i 1.77336 + 0.832916i
\(46\) 0 0
\(47\) −4.13414 7.16053i −0.603026 1.04447i −0.992360 0.123375i \(-0.960628\pi\)
0.389334 0.921096i \(-0.372705\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 0 0
\(51\) −3.02424 + 3.29122i −0.423478 + 0.460863i
\(52\) 0 0
\(53\) −4.94877 −0.679766 −0.339883 0.940468i \(-0.610387\pi\)
−0.339883 + 0.940468i \(0.610387\pi\)
\(54\) 0 0
\(55\) 23.5736 3.17867
\(56\) 0 0
\(57\) 7.88095 8.57667i 1.04386 1.13601i
\(58\) 0 0
\(59\) 2.78751 4.82811i 0.362903 0.628566i −0.625534 0.780197i \(-0.715119\pi\)
0.988437 + 0.151630i \(0.0484523\pi\)
\(60\) 0 0
\(61\) 4.14329 + 7.17639i 0.530494 + 0.918843i 0.999367 + 0.0355773i \(0.0113270\pi\)
−0.468873 + 0.883266i \(0.655340\pi\)
\(62\) 0 0
\(63\) −2.46221 + 1.71392i −0.310210 + 0.215933i
\(64\) 0 0
\(65\) 5.57142 + 9.64998i 0.691050 + 1.19693i
\(66\) 0 0
\(67\) −0.946441 + 1.63928i −0.115626 + 0.200270i −0.918030 0.396511i \(-0.870221\pi\)
0.802404 + 0.596782i \(0.203554\pi\)
\(68\) 0 0
\(69\) 0.415032 + 1.32270i 0.0499639 + 0.159234i
\(70\) 0 0
\(71\) −1.34385 −0.159485 −0.0797427 0.996815i \(-0.525410\pi\)
−0.0797427 + 0.996815i \(0.525410\pi\)
\(72\) 0 0
\(73\) −8.65060 −1.01248 −0.506238 0.862394i \(-0.668964\pi\)
−0.506238 + 0.862394i \(0.668964\pi\)
\(74\) 0 0
\(75\) −23.9924 5.35385i −2.77040 0.618209i
\(76\) 0 0
\(77\) −2.69047 + 4.66004i −0.306608 + 0.531060i
\(78\) 0 0
\(79\) −6.64051 11.5017i −0.747116 1.29404i −0.949199 0.314675i \(-0.898104\pi\)
0.202083 0.979368i \(-0.435229\pi\)
\(80\) 0 0
\(81\) −8.87179 + 1.51371i −0.985755 + 0.168191i
\(82\) 0 0
\(83\) 1.86240 + 3.22577i 0.204425 + 0.354074i 0.949949 0.312404i \(-0.101134\pi\)
−0.745525 + 0.666478i \(0.767801\pi\)
\(84\) 0 0
\(85\) 5.65269 9.79074i 0.613120 1.06195i
\(86\) 0 0
\(87\) −6.32762 1.41200i −0.678393 0.151382i
\(88\) 0 0
\(89\) −6.99862 −0.741853 −0.370926 0.928662i \(-0.620960\pi\)
−0.370926 + 0.928662i \(0.620960\pi\)
\(90\) 0 0
\(91\) −2.54348 −0.266629
\(92\) 0 0
\(93\) −1.75980 5.60845i −0.182483 0.581570i
\(94\) 0 0
\(95\) −14.7305 + 25.5139i −1.51132 + 2.61768i
\(96\) 0 0
\(97\) −1.48076 2.56476i −0.150349 0.260411i 0.781007 0.624522i \(-0.214706\pi\)
−0.931356 + 0.364111i \(0.881373\pi\)
\(98\) 0 0
\(99\) −13.2490 + 9.22249i −1.33158 + 0.926896i
\(100\) 0 0
\(101\) 8.56494 + 14.8349i 0.852243 + 1.47613i 0.879179 + 0.476492i \(0.158092\pi\)
−0.0269357 + 0.999637i \(0.508575\pi\)
\(102\) 0 0
\(103\) −6.01786 + 10.4232i −0.592958 + 1.02703i 0.400874 + 0.916133i \(0.368706\pi\)
−0.993832 + 0.110899i \(0.964627\pi\)
\(104\) 0 0
\(105\) 5.13414 5.58737i 0.501040 0.545272i
\(106\) 0 0
\(107\) 6.92580 0.669542 0.334771 0.942299i \(-0.391341\pi\)
0.334771 + 0.942299i \(0.391341\pi\)
\(108\) 0 0
\(109\) −4.41942 −0.423304 −0.211652 0.977345i \(-0.567884\pi\)
−0.211652 + 0.977345i \(0.567884\pi\)
\(110\) 0 0
\(111\) 5.13414 5.58737i 0.487311 0.530330i
\(112\) 0 0
\(113\) −6.41805 + 11.1164i −0.603759 + 1.04574i 0.388487 + 0.921454i \(0.372998\pi\)
−0.992246 + 0.124287i \(0.960336\pi\)
\(114\) 0 0
\(115\) −1.75319 3.03661i −0.163486 0.283166i
\(116\) 0 0
\(117\) −6.90656 3.24390i −0.638512 0.299899i
\(118\) 0 0
\(119\) 1.29029 + 2.23485i 0.118281 + 0.204868i
\(120\) 0 0
\(121\) −8.97730 + 15.5491i −0.816118 + 1.41356i
\(122\) 0 0
\(123\) −3.31545 10.5663i −0.298944 0.952729i
\(124\) 0 0
\(125\) 40.2727 3.60210
\(126\) 0 0
\(127\) 2.82471 0.250653 0.125326 0.992116i \(-0.460002\pi\)
0.125326 + 0.992116i \(0.460002\pi\)
\(128\) 0 0
\(129\) −1.29029 0.287925i −0.113604 0.0253504i
\(130\) 0 0
\(131\) 8.55925 14.8251i 0.747825 1.29527i −0.201038 0.979583i \(-0.564432\pi\)
0.948863 0.315688i \(-0.102235\pi\)
\(132\) 0 0
\(133\) −3.36240 5.82384i −0.291557 0.504991i
\(134\) 0 0
\(135\) 21.0673 8.62399i 1.81318 0.742235i
\(136\) 0 0
\(137\) 7.10643 + 12.3087i 0.607143 + 1.05160i 0.991709 + 0.128505i \(0.0410179\pi\)
−0.384566 + 0.923098i \(0.625649\pi\)
\(138\) 0 0
\(139\) −1.60050 + 2.77215i −0.135753 + 0.235131i −0.925885 0.377806i \(-0.876679\pi\)
0.790132 + 0.612937i \(0.210012\pi\)
\(140\) 0 0
\(141\) −13.9773 3.11900i −1.17710 0.262668i
\(142\) 0 0
\(143\) −13.6863 −1.14451
\(144\) 0 0
\(145\) 16.3984 1.36181
\(146\) 0 0
\(147\) 0.518550 + 1.65261i 0.0427693 + 0.136305i
\(148\) 0 0
\(149\) −8.54917 + 14.8076i −0.700375 + 1.21309i 0.267960 + 0.963430i \(0.413651\pi\)
−0.968335 + 0.249655i \(0.919683\pi\)
\(150\) 0 0
\(151\) 0.0528709 + 0.0915750i 0.00430257 + 0.00745227i 0.868169 0.496269i \(-0.165297\pi\)
−0.863866 + 0.503722i \(0.831964\pi\)
\(152\) 0 0
\(153\) 0.653374 + 7.71411i 0.0528222 + 0.623649i
\(154\) 0 0
\(155\) 7.43382 + 12.8758i 0.597099 + 1.03421i
\(156\) 0 0
\(157\) 10.5023 18.1906i 0.838177 1.45177i −0.0532404 0.998582i \(-0.516955\pi\)
0.891417 0.453183i \(-0.149712\pi\)
\(158\) 0 0
\(159\) −5.79958 + 6.31156i −0.459937 + 0.500539i
\(160\) 0 0
\(161\) 0.800370 0.0630780
\(162\) 0 0
\(163\) −2.58915 −0.202798 −0.101399 0.994846i \(-0.532332\pi\)
−0.101399 + 0.994846i \(0.532332\pi\)
\(164\) 0 0
\(165\) 27.6265 30.0654i 2.15072 2.34058i
\(166\) 0 0
\(167\) 1.30884 2.26697i 0.101281 0.175424i −0.810932 0.585141i \(-0.801039\pi\)
0.912213 + 0.409717i \(0.134373\pi\)
\(168\) 0 0
\(169\) 3.26536 + 5.65577i 0.251182 + 0.435059i
\(170\) 0 0
\(171\) −1.70264 20.1024i −0.130205 1.53727i
\(172\) 0 0
\(173\) −7.22757 12.5185i −0.549502 0.951766i −0.998309 0.0581367i \(-0.981484\pi\)
0.448806 0.893629i \(-0.351849\pi\)
\(174\) 0 0
\(175\) −7.09635 + 12.2912i −0.536434 + 0.929130i
\(176\) 0 0
\(177\) −2.89093 9.21331i −0.217295 0.692515i
\(178\) 0 0
\(179\) 23.7179 1.77276 0.886378 0.462962i \(-0.153213\pi\)
0.886378 + 0.462962i \(0.153213\pi\)
\(180\) 0 0
\(181\) −6.60630 −0.491042 −0.245521 0.969391i \(-0.578959\pi\)
−0.245521 + 0.969391i \(0.578959\pi\)
\(182\) 0 0
\(183\) 14.0083 + 3.12591i 1.03552 + 0.231074i
\(184\) 0 0
\(185\) −9.59635 + 16.6214i −0.705538 + 1.22203i
\(186\) 0 0
\(187\) 6.94297 + 12.0256i 0.507721 + 0.879398i
\(188\) 0 0
\(189\) −0.699630 + 5.14884i −0.0508906 + 0.374523i
\(190\) 0 0
\(191\) −2.08336 3.60848i −0.150746 0.261100i 0.780756 0.624836i \(-0.214834\pi\)
−0.931502 + 0.363736i \(0.881501\pi\)
\(192\) 0 0
\(193\) 8.09426 14.0197i 0.582637 1.00916i −0.412528 0.910945i \(-0.635354\pi\)
0.995165 0.0982128i \(-0.0313126\pi\)
\(194\) 0 0
\(195\) 18.8367 + 4.20337i 1.34892 + 0.301009i
\(196\) 0 0
\(197\) 4.33109 0.308577 0.154289 0.988026i \(-0.450691\pi\)
0.154289 + 0.988026i \(0.450691\pi\)
\(198\) 0 0
\(199\) −13.7849 −0.977183 −0.488591 0.872513i \(-0.662489\pi\)
−0.488591 + 0.872513i \(0.662489\pi\)
\(200\) 0 0
\(201\) 0.981553 + 3.12819i 0.0692334 + 0.220645i
\(202\) 0 0
\(203\) −1.87155 + 3.24163i −0.131357 + 0.227518i
\(204\) 0 0
\(205\) 14.0052 + 24.2578i 0.978168 + 1.69424i
\(206\) 0 0
\(207\) 2.17333 + 1.02078i 0.151057 + 0.0709488i
\(208\) 0 0
\(209\) −18.0929 31.3378i −1.25151 2.16768i
\(210\) 0 0
\(211\) 6.18341 10.7100i 0.425683 0.737305i −0.570801 0.821089i \(-0.693367\pi\)
0.996484 + 0.0837836i \(0.0267004\pi\)
\(212\) 0 0
\(213\) −1.57489 + 1.71392i −0.107909 + 0.117436i
\(214\) 0 0
\(215\) 3.34385 0.228049
\(216\) 0 0
\(217\) −3.39370 −0.230380
\(218\) 0 0
\(219\) −10.1378 + 11.0328i −0.685052 + 0.745527i
\(220\) 0 0
\(221\) −3.28182 + 5.68428i −0.220759 + 0.382366i
\(222\) 0 0
\(223\) −7.40320 12.8227i −0.495755 0.858673i 0.504233 0.863568i \(-0.331775\pi\)
−0.999988 + 0.00489487i \(0.998442\pi\)
\(224\) 0 0
\(225\) −34.9454 + 24.3251i −2.32970 + 1.62167i
\(226\) 0 0
\(227\) 6.89881 + 11.9491i 0.457890 + 0.793089i 0.998849 0.0479600i \(-0.0152720\pi\)
−0.540959 + 0.841049i \(0.681939\pi\)
\(228\) 0 0
\(229\) −0.471369 + 0.816435i −0.0311489 + 0.0539515i −0.881180 0.472782i \(-0.843250\pi\)
0.850031 + 0.526733i \(0.176583\pi\)
\(230\) 0 0
\(231\) 2.79029 + 8.89258i 0.183588 + 0.585089i
\(232\) 0 0
\(233\) 16.6608 1.09149 0.545743 0.837953i \(-0.316248\pi\)
0.545743 + 0.837953i \(0.316248\pi\)
\(234\) 0 0
\(235\) 36.2229 2.36292
\(236\) 0 0
\(237\) −22.4512 5.00995i −1.45836 0.325431i
\(238\) 0 0
\(239\) 0.678405 1.17503i 0.0438824 0.0760065i −0.843250 0.537522i \(-0.819361\pi\)
0.887132 + 0.461515i \(0.152694\pi\)
\(240\) 0 0
\(241\) 4.60828 + 7.98178i 0.296846 + 0.514152i 0.975413 0.220387i \(-0.0707320\pi\)
−0.678567 + 0.734539i \(0.737399\pi\)
\(242\) 0 0
\(243\) −8.46650 + 13.0889i −0.543126 + 0.839651i
\(244\) 0 0
\(245\) −2.19047 3.79401i −0.139944 0.242391i
\(246\) 0 0
\(247\) 8.55218 14.8128i 0.544162 0.942517i
\(248\) 0 0
\(249\) 6.29667 + 1.40509i 0.399035 + 0.0890439i
\(250\) 0 0
\(251\) 2.53189 0.159812 0.0799058 0.996802i \(-0.474538\pi\)
0.0799058 + 0.996802i \(0.474538\pi\)
\(252\) 0 0
\(253\) 4.30675 0.270763
\(254\) 0 0
\(255\) −5.86240 18.6833i −0.367118 1.17000i
\(256\) 0 0
\(257\) 3.08404 5.34172i 0.192377 0.333207i −0.753660 0.657264i \(-0.771714\pi\)
0.946038 + 0.324057i \(0.105047\pi\)
\(258\) 0 0
\(259\) −2.19047 3.79401i −0.136109 0.235748i
\(260\) 0 0
\(261\) −9.21633 + 6.41537i −0.570476 + 0.397102i
\(262\) 0 0
\(263\) 5.49074 + 9.51024i 0.338574 + 0.586427i 0.984165 0.177257i \(-0.0567223\pi\)
−0.645591 + 0.763683i \(0.723389\pi\)
\(264\) 0 0
\(265\) 10.8401 18.7757i 0.665905 1.15338i
\(266\) 0 0
\(267\) −8.20185 + 8.92591i −0.501945 + 0.546257i
\(268\) 0 0
\(269\) 4.73035 0.288415 0.144207 0.989547i \(-0.453937\pi\)
0.144207 + 0.989547i \(0.453937\pi\)
\(270\) 0 0
\(271\) 13.5379 0.822370 0.411185 0.911552i \(-0.365115\pi\)
0.411185 + 0.911552i \(0.365115\pi\)
\(272\) 0 0
\(273\) −2.98076 + 3.24390i −0.180404 + 0.196330i
\(274\) 0 0
\(275\) −38.1851 + 66.1385i −2.30265 + 3.98830i
\(276\) 0 0
\(277\) 14.6614 + 25.3943i 0.880918 + 1.52579i 0.850322 + 0.526262i \(0.176407\pi\)
0.0305952 + 0.999532i \(0.490260\pi\)
\(278\) 0 0
\(279\) −9.21527 4.32826i −0.551704 0.259126i
\(280\) 0 0
\(281\) −7.31336 12.6671i −0.436279 0.755657i 0.561120 0.827734i \(-0.310370\pi\)
−0.997399 + 0.0720774i \(0.977037\pi\)
\(282\) 0 0
\(283\) 7.64562 13.2426i 0.454485 0.787191i −0.544174 0.838973i \(-0.683157\pi\)
0.998658 + 0.0517817i \(0.0164900\pi\)
\(284\) 0 0
\(285\) 15.2770 + 48.6874i 0.904930 + 2.88399i
\(286\) 0 0
\(287\) −6.39370 −0.377408
\(288\) 0 0
\(289\) −10.3406 −0.608272
\(290\) 0 0
\(291\) −5.00638 1.11716i −0.293479 0.0654893i
\(292\) 0 0
\(293\) 0.940196 1.62847i 0.0549268 0.0951361i −0.837255 0.546813i \(-0.815841\pi\)
0.892181 + 0.451677i \(0.149174\pi\)
\(294\) 0 0
\(295\) 12.2119 + 21.1517i 0.711006 + 1.23150i
\(296\) 0 0
\(297\) −3.76467 + 27.7056i −0.218448 + 1.60764i
\(298\) 0 0
\(299\) 1.01786 + 1.76299i 0.0588645 + 0.101956i
\(300\) 0 0
\(301\) −0.381635 + 0.661012i −0.0219971 + 0.0381001i
\(302\) 0 0
\(303\) 28.9576 + 6.46183i 1.66357 + 0.371222i
\(304\) 0 0
\(305\) −36.3031 −2.07871
\(306\) 0 0
\(307\) −11.8451 −0.676038 −0.338019 0.941139i \(-0.609757\pi\)
−0.338019 + 0.941139i \(0.609757\pi\)
\(308\) 0 0
\(309\) 6.24112 + 19.8903i 0.355045 + 1.13152i
\(310\) 0 0
\(311\) 17.5422 30.3840i 0.994729 1.72292i 0.408562 0.912730i \(-0.366030\pi\)
0.586167 0.810190i \(-0.300636\pi\)
\(312\) 0 0
\(313\) 0.430906 + 0.746351i 0.0243563 + 0.0421863i 0.877947 0.478759i \(-0.158913\pi\)
−0.853590 + 0.520945i \(0.825580\pi\)
\(314\) 0 0
\(315\) −1.10921 13.0960i −0.0624968 0.737873i
\(316\) 0 0
\(317\) −4.31381 7.47175i −0.242288 0.419655i 0.719078 0.694930i \(-0.244565\pi\)
−0.961366 + 0.275275i \(0.911231\pi\)
\(318\) 0 0
\(319\) −10.0707 + 17.4430i −0.563853 + 0.976622i
\(320\) 0 0
\(321\) 8.11651 8.83303i 0.453019 0.493012i
\(322\) 0 0
\(323\) −17.3539 −0.965594
\(324\) 0 0
\(325\) −36.0988 −2.00240
\(326\) 0 0
\(327\) −5.17923 + 5.63644i −0.286412 + 0.311696i
\(328\) 0 0
\(329\) −4.13414 + 7.16053i −0.227922 + 0.394773i
\(330\) 0 0
\(331\) −8.76851 15.1875i −0.481961 0.834781i 0.517825 0.855487i \(-0.326742\pi\)
−0.999786 + 0.0207060i \(0.993409\pi\)
\(332\) 0 0
\(333\) −1.10921 13.0960i −0.0607842 0.717654i
\(334\) 0 0
\(335\) −4.14631 7.18162i −0.226537 0.392374i
\(336\) 0 0
\(337\) −16.7861 + 29.0744i −0.914399 + 1.58379i −0.106620 + 0.994300i \(0.534003\pi\)
−0.807779 + 0.589486i \(0.799330\pi\)
\(338\) 0 0
\(339\) 6.65615 + 21.2130i 0.361513 + 1.15213i
\(340\) 0 0
\(341\) −18.2613 −0.988907
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −5.92744 1.32270i −0.319123 0.0712116i
\(346\) 0 0
\(347\) −1.80616 + 3.12837i −0.0969599 + 0.167939i −0.910425 0.413674i \(-0.864245\pi\)
0.813465 + 0.581614i \(0.197579\pi\)
\(348\) 0 0
\(349\) 4.66891 + 8.08679i 0.249921 + 0.432876i 0.963504 0.267695i \(-0.0862620\pi\)
−0.713583 + 0.700571i \(0.752929\pi\)
\(350\) 0 0
\(351\) −12.2312 + 5.00689i −0.652852 + 0.267248i
\(352\) 0 0
\(353\) −9.67693 16.7609i −0.515051 0.892094i −0.999847 0.0174672i \(-0.994440\pi\)
0.484797 0.874627i \(-0.338894\pi\)
\(354\) 0 0
\(355\) 2.94366 5.09857i 0.156233 0.270604i
\(356\) 0 0
\(357\) 4.36240 + 0.973460i 0.230883 + 0.0515210i
\(358\) 0 0
\(359\) −31.1716 −1.64518 −0.822588 0.568638i \(-0.807471\pi\)
−0.822588 + 0.568638i \(0.807471\pi\)
\(360\) 0 0
\(361\) 26.2229 1.38015
\(362\) 0 0
\(363\) 9.31035 + 29.6719i 0.488667 + 1.55737i
\(364\) 0 0
\(365\) 18.9489 32.8205i 0.991831 1.71790i
\(366\) 0 0
\(367\) 2.75411 + 4.77027i 0.143764 + 0.249006i 0.928911 0.370303i \(-0.120746\pi\)
−0.785147 + 0.619309i \(0.787413\pi\)
\(368\) 0 0
\(369\) −17.3615 8.15440i −0.903802 0.424501i
\(370\) 0 0
\(371\) 2.47438 + 4.28576i 0.128464 + 0.222505i
\(372\) 0 0
\(373\) 5.76687 9.98851i 0.298597 0.517186i −0.677218 0.735782i \(-0.736815\pi\)
0.975815 + 0.218597i \(0.0701479\pi\)
\(374\) 0 0
\(375\) 47.1966 51.3630i 2.43722 2.65238i
\(376\) 0 0
\(377\) −9.52051 −0.490331
\(378\) 0 0
\(379\) −35.4614 −1.82153 −0.910766 0.412923i \(-0.864508\pi\)
−0.910766 + 0.412923i \(0.864508\pi\)
\(380\) 0 0
\(381\) 3.31035 3.60258i 0.169594 0.184566i
\(382\) 0 0
\(383\) −14.6401 + 25.3573i −0.748072 + 1.29570i 0.200673 + 0.979658i \(0.435687\pi\)
−0.948746 + 0.316041i \(0.897646\pi\)
\(384\) 0 0
\(385\) −11.7868 20.4154i −0.600712 1.04046i
\(386\) 0 0
\(387\) −1.87933 + 1.30818i −0.0955319 + 0.0664986i
\(388\) 0 0
\(389\) 3.45364 + 5.98188i 0.175107 + 0.303293i 0.940198 0.340628i \(-0.110640\pi\)
−0.765092 + 0.643921i \(0.777306\pi\)
\(390\) 0 0
\(391\) 1.03271 1.78870i 0.0522263 0.0904586i
\(392\) 0 0
\(393\) −8.87679 28.2901i −0.447775 1.42705i
\(394\) 0 0
\(395\) 58.1835 2.92753
\(396\) 0 0
\(397\) 24.6291 1.23610 0.618048 0.786140i \(-0.287924\pi\)
0.618048 + 0.786140i \(0.287924\pi\)
\(398\) 0 0
\(399\) −11.3681 2.53677i −0.569116 0.126997i
\(400\) 0 0
\(401\) 16.9020 29.2750i 0.844043 1.46193i −0.0424059 0.999100i \(-0.513502\pi\)
0.886449 0.462826i \(-0.153164\pi\)
\(402\) 0 0
\(403\) −4.31590 7.47537i −0.214991 0.372375i
\(404\) 0 0
\(405\) 13.6904 36.9754i 0.680280 1.83732i
\(406\) 0 0
\(407\) −11.7868 20.4154i −0.584251 1.01195i
\(408\) 0 0
\(409\) 12.1513 21.0467i 0.600844 1.04069i −0.391850 0.920029i \(-0.628165\pi\)
0.992694 0.120663i \(-0.0385019\pi\)
\(410\) 0 0
\(411\) 24.0265 + 5.36146i 1.18514 + 0.264461i
\(412\) 0 0
\(413\) −5.57502 −0.274329
\(414\) 0 0
\(415\) −16.3181 −0.801025
\(416\) 0 0
\(417\) 1.65988 + 5.29000i 0.0812847 + 0.259053i
\(418\) 0 0
\(419\) 9.51868 16.4868i 0.465018 0.805435i −0.534184 0.845368i \(-0.679381\pi\)
0.999202 + 0.0399331i \(0.0127145\pi\)
\(420\) 0 0
\(421\) 5.85893 + 10.1480i 0.285547 + 0.494582i 0.972742 0.231892i \(-0.0744915\pi\)
−0.687195 + 0.726473i \(0.741158\pi\)
\(422\) 0 0
\(423\) −20.3582 + 14.1711i −0.989852 + 0.689024i
\(424\) 0 0
\(425\) 18.3127 + 31.7185i 0.888295 + 1.53857i
\(426\) 0 0
\(427\) 4.14329 7.17639i 0.200508 0.347290i
\(428\) 0 0
\(429\) −16.0393 + 17.4553i −0.774386 + 0.842748i
\(430\) 0 0
\(431\) 9.89426 0.476590 0.238295 0.971193i \(-0.423412\pi\)
0.238295 + 0.971193i \(0.423412\pi\)
\(432\) 0 0
\(433\) 38.0986 1.83090 0.915451 0.402429i \(-0.131834\pi\)
0.915451 + 0.402429i \(0.131834\pi\)
\(434\) 0 0
\(435\) 19.2176 20.9141i 0.921415 1.00276i
\(436\) 0 0
\(437\) −2.69116 + 4.66123i −0.128736 + 0.222977i
\(438\) 0 0
\(439\) 9.99746 + 17.3161i 0.477153 + 0.826453i 0.999657 0.0261839i \(-0.00833554\pi\)
−0.522504 + 0.852637i \(0.675002\pi\)
\(440\) 0 0
\(441\) 2.71540 + 1.27538i 0.129305 + 0.0607324i
\(442\) 0 0
\(443\) −4.15824 7.20229i −0.197564 0.342191i 0.750174 0.661240i \(-0.229970\pi\)
−0.947738 + 0.319049i \(0.896636\pi\)
\(444\) 0 0
\(445\) 15.3303 26.5529i 0.726726 1.25873i
\(446\) 0 0
\(447\) 8.86634 + 28.2568i 0.419363 + 1.33650i
\(448\) 0 0
\(449\) 22.5036 1.06201 0.531006 0.847368i \(-0.321814\pi\)
0.531006 + 0.847368i \(0.321814\pi\)
\(450\) 0 0
\(451\) −34.4042 −1.62003
\(452\) 0 0
\(453\) 0.178754 + 0.0398885i 0.00839858 + 0.00187413i
\(454\) 0 0
\(455\) 5.57142 9.64998i 0.261192 0.452398i
\(456\) 0 0
\(457\) −7.91143 13.7030i −0.370081 0.640999i 0.619497 0.784999i \(-0.287337\pi\)
−0.989578 + 0.144000i \(0.954003\pi\)
\(458\) 0 0
\(459\) 10.6041 + 8.20705i 0.494958 + 0.383072i
\(460\) 0 0
\(461\) 7.87933 + 13.6474i 0.366977 + 0.635623i 0.989091 0.147303i \(-0.0470594\pi\)
−0.622114 + 0.782927i \(0.713726\pi\)
\(462\) 0 0
\(463\) −8.57410 + 14.8508i −0.398472 + 0.690174i −0.993538 0.113503i \(-0.963793\pi\)
0.595066 + 0.803677i \(0.297126\pi\)
\(464\) 0 0
\(465\) 25.1333 + 5.60845i 1.16553 + 0.260086i
\(466\) 0 0
\(467\) 2.41270 0.111646 0.0558231 0.998441i \(-0.482222\pi\)
0.0558231 + 0.998441i \(0.482222\pi\)
\(468\) 0 0
\(469\) 1.89288 0.0874052
\(470\) 0 0
\(471\) −10.8920 34.7124i −0.501875 1.59946i
\(472\) 0 0
\(473\) −2.05356 + 3.55687i −0.0944227 + 0.163545i
\(474\) 0 0
\(475\) −47.7215 82.6560i −2.18961 3.79252i
\(476\) 0 0
\(477\) 1.25297 + 14.7933i 0.0573697 + 0.677340i
\(478\) 0 0
\(479\) −13.1784 22.8257i −0.602138 1.04293i −0.992497 0.122271i \(-0.960982\pi\)
0.390359 0.920663i \(-0.372351\pi\)
\(480\) 0 0
\(481\) 5.57142 9.64998i 0.254035 0.440001i
\(482\) 0 0
\(483\) 0.937973 1.02078i 0.0426792 0.0464469i
\(484\) 0 0
\(485\) 12.9743 0.589132
\(486\) 0 0
\(487\) −16.1141 −0.730200 −0.365100 0.930968i \(-0.618965\pi\)
−0.365100 + 0.930968i \(0.618965\pi\)
\(488\) 0 0
\(489\) −3.03429 + 3.30216i −0.137215 + 0.149329i
\(490\) 0 0
\(491\) 3.66266 6.34392i 0.165294 0.286297i −0.771466 0.636271i \(-0.780476\pi\)
0.936760 + 0.349974i \(0.113809\pi\)
\(492\) 0 0
\(493\) 4.82969 + 8.36527i 0.217518 + 0.376753i
\(494\) 0 0
\(495\) −5.96859 70.4686i −0.268268 3.16733i
\(496\) 0 0
\(497\) 0.671924 + 1.16381i 0.0301399 + 0.0522038i
\(498\) 0 0
\(499\) 3.01587 5.22365i 0.135009 0.233843i −0.790592 0.612343i \(-0.790227\pi\)
0.925601 + 0.378501i \(0.123560\pi\)
\(500\) 0 0
\(501\) −1.35740 4.32599i −0.0606440 0.193271i
\(502\) 0 0
\(503\) 16.4106 0.731714 0.365857 0.930671i \(-0.380776\pi\)
0.365857 + 0.930671i \(0.380776\pi\)
\(504\) 0 0
\(505\) −75.0451 −3.33946
\(506\) 0 0
\(507\) 11.0400 + 2.46356i 0.490304 + 0.109410i
\(508\) 0 0
\(509\) −5.70693 + 9.88470i −0.252955 + 0.438132i −0.964338 0.264673i \(-0.914736\pi\)
0.711383 + 0.702805i \(0.248069\pi\)
\(510\) 0 0
\(511\) 4.32530 + 7.49164i 0.191340 + 0.331410i
\(512\) 0 0
\(513\) −27.6336 21.3870i −1.22005 0.944258i
\(514\) 0 0
\(515\) −26.3639 45.6637i −1.16173 2.01218i
\(516\) 0 0
\(517\) −22.2456 + 38.5305i −0.978359 + 1.69457i
\(518\) 0 0
\(519\) −24.4360 5.45285i −1.07262 0.239354i
\(520\) 0 0
\(521\) 41.1600 1.80325 0.901627 0.432514i \(-0.142373\pi\)
0.901627 + 0.432514i \(0.142373\pi\)
\(522\) 0 0
\(523\) 29.2303 1.27815 0.639075 0.769144i \(-0.279317\pi\)
0.639075 + 0.769144i \(0.279317\pi\)
\(524\) 0 0
\(525\) 7.35962 + 23.4549i 0.321200 + 1.02366i
\(526\) 0 0
\(527\) −4.37886 + 7.58440i −0.190746 + 0.330382i
\(528\) 0 0
\(529\) 11.1797 + 19.3638i 0.486074 + 0.841905i
\(530\) 0 0
\(531\) −15.1384 7.11027i −0.656951 0.308559i
\(532\) 0 0
\(533\) −8.13112 14.0835i −0.352198 0.610025i
\(534\) 0 0
\(535\) −15.1708 + 26.2766i −0.655890 + 1.13604i
\(536\) 0 0
\(537\) 27.7955 30.2493i 1.19947 1.30535i
\(538\) 0 0
\(539\) 5.38095 0.231774
\(540\) 0 0
\(541\) −6.44101 −0.276921 −0.138460 0.990368i \(-0.544215\pi\)
−0.138460 + 0.990368i \(0.544215\pi\)
\(542\) 0 0
\(543\) −7.74208 + 8.42554i −0.332244 + 0.361575i
\(544\) 0 0
\(545\) 9.68063 16.7673i 0.414673 0.718234i
\(546\) 0 0
\(547\) −0.689682 1.19456i −0.0294887 0.0510759i 0.850904 0.525321i \(-0.176055\pi\)
−0.880393 + 0.474245i \(0.842721\pi\)
\(548\) 0 0
\(549\) 20.4033 14.2025i 0.870793 0.606149i
\(550\) 0 0
\(551\) −12.5858 21.7993i −0.536174 0.928680i
\(552\) 0 0
\(553\) −6.64051 + 11.5017i −0.282383 + 0.489102i
\(554\) 0 0
\(555\) 9.95237 + 31.7180i 0.422454 + 1.34635i
\(556\) 0 0
\(557\) 25.5692 1.08340 0.541701 0.840571i \(-0.317781\pi\)
0.541701 + 0.840571i \(0.317781\pi\)
\(558\) 0 0
\(559\) −1.94136 −0.0821108
\(560\) 0 0
\(561\) 23.4738 + 5.23814i 0.991066 + 0.221154i
\(562\) 0 0
\(563\) −7.53329 + 13.0480i −0.317490 + 0.549910i −0.979964 0.199176i \(-0.936173\pi\)
0.662473 + 0.749086i \(0.269507\pi\)
\(564\) 0 0
\(565\) −28.1171 48.7003i −1.18290 2.04884i
\(566\) 0 0
\(567\) 5.74681 + 6.92634i 0.241343 + 0.290879i
\(568\) 0 0
\(569\) −7.16938 12.4177i −0.300556 0.520578i 0.675706 0.737171i \(-0.263839\pi\)
−0.976262 + 0.216593i \(0.930506\pi\)
\(570\) 0 0
\(571\) −1.29409 + 2.24144i −0.0541562 + 0.0938013i −0.891833 0.452366i \(-0.850580\pi\)
0.837676 + 0.546167i \(0.183914\pi\)
\(572\) 0 0
\(573\) −7.04371 1.57179i −0.294255 0.0656625i
\(574\) 0 0
\(575\) 11.3594 0.473720
\(576\) 0 0
\(577\) 17.5050 0.728743 0.364371 0.931254i \(-0.381284\pi\)
0.364371 + 0.931254i \(0.381284\pi\)
\(578\) 0 0
\(579\) −8.39455 26.7532i −0.348866 1.11183i
\(580\) 0 0
\(581\) 1.86240 3.22577i 0.0772653 0.133827i
\(582\) 0 0
\(583\) 13.3145 + 23.0614i 0.551431 + 0.955107i
\(584\) 0 0
\(585\) 27.4360 19.0979i 1.13434 0.789601i
\(586\) 0 0
\(587\) 4.18410 + 7.24707i 0.172696 + 0.299118i 0.939362 0.342928i \(-0.111419\pi\)
−0.766665 + 0.642047i \(0.778085\pi\)
\(588\) 0 0
\(589\) 11.4110 19.7644i 0.470181 0.814378i
\(590\) 0 0
\(591\) 5.07571 5.52379i 0.208787 0.227218i
\(592\) 0 0
\(593\) −38.5284 −1.58217 −0.791087 0.611704i \(-0.790484\pi\)
−0.791087 + 0.611704i \(0.790484\pi\)
\(594\) 0 0
\(595\) −11.3054 −0.463475
\(596\) 0 0
\(597\) −16.1548 + 17.5809i −0.661172 + 0.719540i
\(598\) 0 0
\(599\) 6.57920 11.3955i 0.268819 0.465608i −0.699738 0.714399i \(-0.746700\pi\)
0.968557 + 0.248791i \(0.0800334\pi\)
\(600\) 0 0
\(601\) 5.01135 + 8.67992i 0.204417 + 0.354061i 0.949947 0.312411i \(-0.101137\pi\)
−0.745530 + 0.666473i \(0.767803\pi\)
\(602\) 0 0
\(603\) 5.13993 + 2.41414i 0.209314 + 0.0983115i
\(604\) 0 0
\(605\) −39.3291 68.1199i −1.59895 2.76947i
\(606\) 0 0
\(607\) −18.1380 + 31.4159i −0.736199 + 1.27513i 0.217997 + 0.975949i \(0.430048\pi\)
−0.954195 + 0.299184i \(0.903286\pi\)
\(608\) 0 0
\(609\) 1.94099 + 6.18588i 0.0786528 + 0.250665i
\(610\) 0 0
\(611\) −21.0302 −0.850789
\(612\) 0 0
\(613\) −24.2523 −0.979541 −0.489770 0.871851i \(-0.662919\pi\)
−0.489770 + 0.871851i \(0.662919\pi\)
\(614\) 0 0
\(615\) 47.3510 + 10.5663i 1.90938 + 0.426073i
\(616\) 0 0
\(617\) 6.70926 11.6208i 0.270105 0.467835i −0.698784 0.715333i \(-0.746275\pi\)
0.968888 + 0.247498i \(0.0796084\pi\)
\(618\) 0 0
\(619\) 18.3018 + 31.6997i 0.735612 + 1.27412i 0.954455 + 0.298356i \(0.0964384\pi\)
−0.218843 + 0.975760i \(0.570228\pi\)
\(620\) 0 0
\(621\) 3.84885 1.57554i 0.154449 0.0632244i
\(622\) 0 0
\(623\) 3.49931 + 6.06099i 0.140197 + 0.242828i
\(624\) 0 0
\(625\) −52.7346 + 91.3390i −2.10938 + 3.65356i
\(626\) 0 0
\(627\) −61.1711 13.6502i −2.44294 0.545137i
\(628\) 0 0
\(629\) −11.3054 −0.450775
\(630\) 0 0
\(631\) −26.9365 −1.07232 −0.536162 0.844115i \(-0.680126\pi\)
−0.536162 + 0.844115i \(0.680126\pi\)
\(632\) 0 0
\(633\) −6.41281 20.4375i −0.254886 0.812316i
\(634\) 0 0
\(635\) −6.18746 + 10.7170i −0.245542 + 0.425291i
\(636\) 0 0
\(637\) 1.27174 + 2.20272i 0.0503881 + 0.0872748i
\(638\) 0 0
\(639\) 0.340248 + 4.01716i 0.0134600 + 0.158916i
\(640\) 0 0
\(641\) −10.1390 17.5613i −0.400467 0.693629i 0.593316 0.804970i \(-0.297819\pi\)
−0.993782 + 0.111341i \(0.964485\pi\)
\(642\) 0 0
\(643\) 6.44229 11.1584i 0.254059 0.440043i −0.710581 0.703616i \(-0.751568\pi\)
0.964639 + 0.263573i \(0.0849009\pi\)
\(644\) 0 0
\(645\) 3.91873 4.26468i 0.154300 0.167921i
\(646\) 0 0
\(647\) 41.4633 1.63009 0.815045 0.579397i \(-0.196712\pi\)
0.815045 + 0.579397i \(0.196712\pi\)
\(648\) 0 0
\(649\) −29.9989 −1.17756
\(650\) 0 0
\(651\) −3.97716 + 4.32826i −0.155877 + 0.169638i
\(652\) 0 0
\(653\) −9.38036 + 16.2473i −0.367082 + 0.635805i −0.989108 0.147192i \(-0.952976\pi\)
0.622026 + 0.782997i \(0.286310\pi\)
\(654\) 0 0
\(655\) 37.4976 + 64.9478i 1.46515 + 2.53772i
\(656\) 0 0
\(657\) 2.19024 + 25.8592i 0.0854493 + 1.00886i
\(658\) 0 0
\(659\) 4.33932 + 7.51593i 0.169036 + 0.292779i 0.938081 0.346415i \(-0.112601\pi\)
−0.769045 + 0.639194i \(0.779268\pi\)
\(660\) 0 0
\(661\) 7.19524 12.4625i 0.279862 0.484736i −0.691488 0.722388i \(-0.743045\pi\)
0.971350 + 0.237652i \(0.0763778\pi\)
\(662\) 0 0
\(663\) 3.40357 + 10.8471i 0.132184 + 0.421267i
\(664\) 0 0
\(665\) 29.4610 1.14245
\(666\) 0 0
\(667\) 2.99587 0.116001
\(668\) 0 0
\(669\) −25.0298 5.58535i −0.967709 0.215942i
\(670\) 0 0
\(671\) 22.2948 38.6158i 0.860683 1.49075i
\(672\) 0 0
\(673\) 14.1059 + 24.4321i 0.543742 + 0.941788i 0.998685 + 0.0512676i \(0.0163261\pi\)
−0.454943 + 0.890520i \(0.650341\pi\)
\(674\) 0 0
\(675\) −9.92964 + 73.0759i −0.382192 + 2.81269i
\(676\) 0 0
\(677\) 0.366552 + 0.634887i 0.0140877 + 0.0244007i 0.872983 0.487750i \(-0.162182\pi\)
−0.858896 + 0.512151i \(0.828849\pi\)
\(678\) 0 0
\(679\) −1.48076 + 2.56476i −0.0568264 + 0.0984263i
\(680\) 0 0
\(681\) 23.3245 + 5.20482i 0.893797 + 0.199449i
\(682\) 0 0
\(683\) −16.4171 −0.628185 −0.314092 0.949392i \(-0.601700\pi\)
−0.314092 + 0.949392i \(0.601700\pi\)
\(684\) 0 0
\(685\) −62.2658 −2.37905
\(686\) 0 0
\(687\) 0.488856 + 1.55797i 0.0186510 + 0.0594404i
\(688\) 0 0
\(689\) −6.29354 + 10.9007i −0.239765 + 0.415285i
\(690\) 0 0
\(691\) −6.10005 10.5656i −0.232057 0.401934i 0.726356 0.687318i \(-0.241212\pi\)
−0.958413 + 0.285384i \(0.907879\pi\)
\(692\) 0 0
\(693\) 14.6114 + 6.86275i 0.555042 + 0.260694i
\(694\) 0 0
\(695\) −7.01172 12.1447i −0.265970 0.460673i
\(696\) 0 0
\(697\) −8.24972 + 14.2889i −0.312481 + 0.541232i
\(698\) 0 0
\(699\) 19.5252 21.2489i 0.738511 0.803706i
\(700\) 0 0
\(701\) 0.337121 0.0127329 0.00636644 0.999980i \(-0.497973\pi\)
0.00636644 + 0.999980i \(0.497973\pi\)
\(702\) 0 0
\(703\) 29.4610 1.11114
\(704\) 0 0
\(705\) 42.4504 46.1979i 1.59878 1.73991i
\(706\) 0 0
\(707\) 8.56494 14.8349i 0.322118 0.557924i
\(708\) 0 0
\(709\) −10.0315 17.3751i −0.376743 0.652537i 0.613844 0.789428i \(-0.289623\pi\)
−0.990586 + 0.136890i \(0.956289\pi\)
\(710\) 0 0
\(711\) −32.7007 + 22.7626i −1.22637 + 0.853663i
\(712\) 0 0
\(713\) 1.35811 + 2.35231i 0.0508616 + 0.0880949i
\(714\) 0 0
\(715\) 29.9795 51.9261i 1.12117 1.94192i
\(716\) 0 0
\(717\) −0.703574 2.24227i −0.0262754 0.0837392i
\(718\) 0 0
\(719\) −10.7220 −0.399863 −0.199931 0.979810i \(-0.564072\pi\)
−0.199931 + 0.979810i \(0.564072\pi\)
\(720\) 0 0
\(721\) 12.0357 0.448234
\(722\) 0 0
\(723\) 15.5804 + 3.47673i 0.579440 + 0.129301i
\(724\) 0 0
\(725\) −26.5624 + 46.0074i −0.986503 + 1.70867i
\(726\) 0 0
\(727\) −5.22757 9.05442i −0.193880 0.335810i 0.752653 0.658418i \(-0.228774\pi\)
−0.946533 + 0.322608i \(0.895441\pi\)
\(728\) 0 0
\(729\) 6.77118 + 26.1372i 0.250785 + 0.968043i
\(730\) 0 0
\(731\) 0.984839 + 1.70579i 0.0364256 + 0.0630910i
\(732\) 0 0
\(733\) −21.1651 + 36.6590i −0.781751 + 1.35403i 0.149171 + 0.988811i \(0.452340\pi\)
−0.930921 + 0.365220i \(0.880994\pi\)
\(734\) 0 0
\(735\) −7.40588 1.65261i −0.273170 0.0609573i
\(736\) 0 0
\(737\) 10.1855 0.375188
\(738\) 0 0
\(739\) 12.6281 0.464532 0.232266 0.972652i \(-0.425386\pi\)
0.232266 + 0.972652i \(0.425386\pi\)
\(740\) 0 0
\(741\) −8.86946 28.2668i −0.325828 1.03841i
\(742\) 0 0
\(743\) −19.3632 + 33.5381i −0.710368 + 1.23039i 0.254352 + 0.967112i \(0.418138\pi\)
−0.964719 + 0.263281i \(0.915195\pi\)
\(744\) 0 0
\(745\) −37.4535 64.8713i −1.37219 2.37670i
\(746\) 0 0
\(747\) 9.17124 6.38399i 0.335558 0.233578i
\(748\) 0 0
\(749\) −3.46290 5.99792i −0.126532 0.219159i
\(750\) 0 0
\(751\) 10.6405 18.4299i 0.388278 0.672517i −0.603940 0.797030i \(-0.706403\pi\)
0.992218 + 0.124513i \(0.0397367\pi\)
\(752\) 0 0
\(753\) 2.96718 3.22912i 0.108130 0.117676i
\(754\) 0 0
\(755\) −0.463249 −0.0168594
\(756\) 0 0
\(757\) 22.8632 0.830977 0.415488 0.909598i \(-0.363611\pi\)
0.415488 + 0.909598i \(0.363611\pi\)
\(758\) 0 0
\(759\) 5.04718 5.49274i 0.183201 0.199374i
\(760\) 0 0
\(761\) −6.04848 + 10.4763i −0.219257 + 0.379765i −0.954581 0.297951i \(-0.903697\pi\)
0.735324 + 0.677716i \(0.237030\pi\)
\(762\) 0 0
\(763\) 2.20971 + 3.82733i 0.0799969 + 0.138559i
\(764\) 0 0
\(765\) −30.6986 14.4186i −1.10991 0.521307i
\(766\) 0 0
\(767\) −7.08997 12.2802i −0.256004 0.443412i
\(768\) 0 0
\(769\) 20.0921 34.8005i 0.724538 1.25494i −0.234626 0.972086i \(-0.575386\pi\)
0.959164 0.282851i \(-0.0912803\pi\)
\(770\) 0 0
\(771\) −3.19846 10.1934i −0.115190 0.367107i
\(772\) 0 0
\(773\) 34.1442 1.22808 0.614041 0.789274i \(-0.289543\pi\)
0.614041 + 0.789274i \(0.289543\pi\)
\(774\) 0 0
\(775\) −48.1658 −1.73017
\(776\) 0 0
\(777\) −7.40588 1.65261i −0.265684 0.0592869i
\(778\) 0 0
\(779\) 21.4982 37.2359i 0.770252 1.33412i
\(780\) 0 0
\(781\) 3.61559 + 6.26238i 0.129376 + 0.224086i
\(782\) 0 0
\(783\) −2.61879 + 19.2727i −0.0935879 + 0.688748i
\(784\) 0 0
\(785\) 46.0101 + 79.6919i 1.64217 + 2.84433i
\(786\) 0 0
\(787\) −10.0277 + 17.3685i −0.357450 + 0.619122i −0.987534 0.157405i \(-0.949687\pi\)
0.630084 + 0.776527i \(0.283020\pi\)
\(788\) 0 0
\(789\) 18.5639 + 4.14250i 0.660892 + 0.147477i
\(790\) 0 0
\(791\) 12.8361 0.456399
\(792\) 0 0
\(793\) 21.0767 0.748457
\(794\) 0 0
\(795\) −11.2423 35.8290i −0.398724 1.27072i
\(796\) 0 0
\(797\) 6.57026 11.3800i 0.232730 0.403101i −0.725880 0.687821i \(-0.758567\pi\)
0.958611 + 0.284720i \(0.0919007\pi\)
\(798\) 0