Properties

Label 72.3.m.b.41.4
Level $72$
Weight $3$
Character 72.41
Analytic conductor $1.962$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 72.m (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.96185790339\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.19269881856.9
Defining polynomial: \( x^{8} - 2x^{7} + 15x^{6} - 2x^{5} + 133x^{4} - 84x^{3} + 276x^{2} + 144x + 144 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.4
Root \(-1.41950 + 2.45865i\) of defining polynomial
Character \(\chi\) \(=\) 72.41
Dual form 72.3.m.b.65.4

$q$-expansion

\(f(q)\) \(=\) \(q+(2.91950 + 0.690286i) q^{3} +(1.80902 + 1.04444i) q^{5} +(-0.781452 - 1.35351i) q^{7} +(8.04701 + 4.03058i) q^{9} +O(q^{10})\) \(q+(2.91950 + 0.690286i) q^{3} +(1.80902 + 1.04444i) q^{5} +(-0.781452 - 1.35351i) q^{7} +(8.04701 + 4.03058i) q^{9} +(-10.8302 + 6.25280i) q^{11} +(11.0441 - 19.1289i) q^{13} +(4.56049 + 4.29799i) q^{15} +12.6991i q^{17} -21.7686 q^{19} +(-1.34714 - 4.49102i) q^{21} +(-28.7989 - 16.6271i) q^{23} +(-10.3183 - 17.8718i) q^{25} +(20.7110 + 17.3220i) q^{27} +(-25.7787 + 14.8833i) q^{29} +(6.91549 - 11.9780i) q^{31} +(-35.9349 + 10.7792i) q^{33} -3.26472i q^{35} -8.26807 q^{37} +(45.4476 - 48.2234i) q^{39} +(43.8453 + 25.3141i) q^{41} +(35.5364 + 61.5508i) q^{43} +(10.3475 + 15.6960i) q^{45} +(57.2470 - 33.0516i) q^{47} +(23.2787 - 40.3198i) q^{49} +(-8.76600 + 37.0750i) q^{51} -6.04384i q^{53} -26.1227 q^{55} +(-63.5536 - 15.0266i) q^{57} +(-8.01575 - 4.62789i) q^{59} +(51.9009 + 89.8950i) q^{61} +(-0.832899 - 14.0415i) q^{63} +(39.9580 - 23.0698i) q^{65} +(-19.8853 + 34.4424i) q^{67} +(-72.6012 - 68.4223i) q^{69} -18.3599i q^{71} -68.5777 q^{73} +(-17.7876 - 59.2994i) q^{75} +(16.9265 + 9.77252i) q^{77} +(13.3130 + 23.0587i) q^{79} +(48.5088 + 64.8683i) q^{81} +(21.0376 - 12.1461i) q^{83} +(-13.2634 + 22.9729i) q^{85} +(-85.5347 + 25.6573i) q^{87} -111.730i q^{89} -34.5217 q^{91} +(28.4580 - 30.1961i) q^{93} +(-39.3800 - 22.7360i) q^{95} +(-2.51182 - 4.35061i) q^{97} +(-112.353 + 6.66446i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 10 q^{3} - 6 q^{5} + 6 q^{7} - 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 10 q^{3} - 6 q^{5} + 6 q^{7} - 22 q^{9} + 36 q^{11} + 14 q^{13} + 10 q^{15} + 4 q^{19} - 54 q^{21} - 102 q^{23} + 10 q^{25} - 20 q^{27} - 114 q^{29} - 50 q^{31} - 104 q^{33} + 120 q^{37} + 82 q^{39} + 264 q^{41} - 28 q^{43} + 206 q^{45} + 150 q^{47} + 94 q^{49} + 170 q^{51} - 244 q^{55} - 178 q^{57} - 108 q^{59} + 14 q^{61} - 210 q^{63} - 198 q^{65} - 20 q^{67} - 14 q^{69} - 76 q^{73} + 326 q^{75} + 66 q^{77} + 26 q^{79} + 194 q^{81} + 246 q^{83} - 224 q^{85} - 18 q^{87} + 108 q^{91} - 130 q^{93} - 456 q^{95} - 236 q^{97} - 634 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.91950 + 0.690286i 0.973168 + 0.230095i
\(4\) 0 0
\(5\) 1.80902 + 1.04444i 0.361805 + 0.208888i 0.669872 0.742476i \(-0.266349\pi\)
−0.308067 + 0.951365i \(0.599682\pi\)
\(6\) 0 0
\(7\) −0.781452 1.35351i −0.111636 0.193359i 0.804794 0.593554i \(-0.202276\pi\)
−0.916430 + 0.400195i \(0.868942\pi\)
\(8\) 0 0
\(9\) 8.04701 + 4.03058i 0.894112 + 0.447843i
\(10\) 0 0
\(11\) −10.8302 + 6.25280i −0.984560 + 0.568436i −0.903644 0.428285i \(-0.859118\pi\)
−0.0809165 + 0.996721i \(0.525785\pi\)
\(12\) 0 0
\(13\) 11.0441 19.1289i 0.849545 1.47145i −0.0320708 0.999486i \(-0.510210\pi\)
0.881615 0.471969i \(-0.156456\pi\)
\(14\) 0 0
\(15\) 4.56049 + 4.29799i 0.304033 + 0.286533i
\(16\) 0 0
\(17\) 12.6991i 0.747005i 0.927629 + 0.373503i \(0.121843\pi\)
−0.927629 + 0.373503i \(0.878157\pi\)
\(18\) 0 0
\(19\) −21.7686 −1.14572 −0.572859 0.819654i \(-0.694166\pi\)
−0.572859 + 0.819654i \(0.694166\pi\)
\(20\) 0 0
\(21\) −1.34714 4.49102i −0.0641495 0.213858i
\(22\) 0 0
\(23\) −28.7989 16.6271i −1.25213 0.722916i −0.280596 0.959826i \(-0.590532\pi\)
−0.971532 + 0.236909i \(0.923866\pi\)
\(24\) 0 0
\(25\) −10.3183 17.8718i −0.412732 0.714872i
\(26\) 0 0
\(27\) 20.7110 + 17.3220i 0.767075 + 0.641557i
\(28\) 0 0
\(29\) −25.7787 + 14.8833i −0.888920 + 0.513218i −0.873589 0.486665i \(-0.838213\pi\)
−0.0153306 + 0.999882i \(0.504880\pi\)
\(30\) 0 0
\(31\) 6.91549 11.9780i 0.223080 0.386386i −0.732662 0.680593i \(-0.761722\pi\)
0.955742 + 0.294207i \(0.0950555\pi\)
\(32\) 0 0
\(33\) −35.9349 + 10.7792i −1.08894 + 0.326641i
\(34\) 0 0
\(35\) 3.26472i 0.0932777i
\(36\) 0 0
\(37\) −8.26807 −0.223461 −0.111731 0.993739i \(-0.535639\pi\)
−0.111731 + 0.993739i \(0.535639\pi\)
\(38\) 0 0
\(39\) 45.4476 48.2234i 1.16532 1.23650i
\(40\) 0 0
\(41\) 43.8453 + 25.3141i 1.06940 + 0.617418i 0.928017 0.372538i \(-0.121512\pi\)
0.141382 + 0.989955i \(0.454846\pi\)
\(42\) 0 0
\(43\) 35.5364 + 61.5508i 0.826427 + 1.43141i 0.900824 + 0.434185i \(0.142964\pi\)
−0.0743965 + 0.997229i \(0.523703\pi\)
\(44\) 0 0
\(45\) 10.3475 + 15.6960i 0.229945 + 0.348801i
\(46\) 0 0
\(47\) 57.2470 33.0516i 1.21802 0.703225i 0.253527 0.967328i \(-0.418409\pi\)
0.964495 + 0.264103i \(0.0850759\pi\)
\(48\) 0 0
\(49\) 23.2787 40.3198i 0.475075 0.822854i
\(50\) 0 0
\(51\) −8.76600 + 37.0750i −0.171882 + 0.726962i
\(52\) 0 0
\(53\) 6.04384i 0.114035i −0.998373 0.0570174i \(-0.981841\pi\)
0.998373 0.0570174i \(-0.0181590\pi\)
\(54\) 0 0
\(55\) −26.1227 −0.474958
\(56\) 0 0
\(57\) −63.5536 15.0266i −1.11498 0.263624i
\(58\) 0 0
\(59\) −8.01575 4.62789i −0.135860 0.0784389i 0.430529 0.902577i \(-0.358327\pi\)
−0.566390 + 0.824138i \(0.691660\pi\)
\(60\) 0 0
\(61\) 51.9009 + 89.8950i 0.850834 + 1.47369i 0.880457 + 0.474127i \(0.157236\pi\)
−0.0296226 + 0.999561i \(0.509431\pi\)
\(62\) 0 0
\(63\) −0.832899 14.0415i −0.0132206 0.222880i
\(64\) 0 0
\(65\) 39.9580 23.0698i 0.614738 0.354919i
\(66\) 0 0
\(67\) −19.8853 + 34.4424i −0.296796 + 0.514065i −0.975401 0.220438i \(-0.929251\pi\)
0.678605 + 0.734503i \(0.262585\pi\)
\(68\) 0 0
\(69\) −72.6012 68.4223i −1.05219 0.991628i
\(70\) 0 0
\(71\) 18.3599i 0.258590i −0.991606 0.129295i \(-0.958729\pi\)
0.991606 0.129295i \(-0.0412714\pi\)
\(72\) 0 0
\(73\) −68.5777 −0.939421 −0.469711 0.882820i \(-0.655642\pi\)
−0.469711 + 0.882820i \(0.655642\pi\)
\(74\) 0 0
\(75\) −17.7876 59.2994i −0.237169 0.790658i
\(76\) 0 0
\(77\) 16.9265 + 9.77252i 0.219825 + 0.126916i
\(78\) 0 0
\(79\) 13.3130 + 23.0587i 0.168518 + 0.291883i 0.937899 0.346908i \(-0.112768\pi\)
−0.769381 + 0.638791i \(0.779435\pi\)
\(80\) 0 0
\(81\) 48.5088 + 64.8683i 0.598874 + 0.800843i
\(82\) 0 0
\(83\) 21.0376 12.1461i 0.253465 0.146338i −0.367885 0.929871i \(-0.619918\pi\)
0.621350 + 0.783533i \(0.286585\pi\)
\(84\) 0 0
\(85\) −13.2634 + 22.9729i −0.156040 + 0.270270i
\(86\) 0 0
\(87\) −85.5347 + 25.6573i −0.983157 + 0.294911i
\(88\) 0 0
\(89\) 111.730i 1.25539i −0.778459 0.627695i \(-0.783999\pi\)
0.778459 0.627695i \(-0.216001\pi\)
\(90\) 0 0
\(91\) −34.5217 −0.379359
\(92\) 0 0
\(93\) 28.4580 30.1961i 0.306000 0.324689i
\(94\) 0 0
\(95\) −39.3800 22.7360i −0.414526 0.239327i
\(96\) 0 0
\(97\) −2.51182 4.35061i −0.0258951 0.0448516i 0.852787 0.522258i \(-0.174910\pi\)
−0.878683 + 0.477407i \(0.841577\pi\)
\(98\) 0 0
\(99\) −112.353 + 6.66446i −1.13488 + 0.0673178i
\(100\) 0 0
\(101\) −86.1052 + 49.7129i −0.852527 + 0.492207i −0.861503 0.507753i \(-0.830476\pi\)
0.00897555 + 0.999960i \(0.497143\pi\)
\(102\) 0 0
\(103\) 13.6160 23.5836i 0.132194 0.228967i −0.792328 0.610096i \(-0.791131\pi\)
0.924522 + 0.381128i \(0.124464\pi\)
\(104\) 0 0
\(105\) 2.25359 9.53136i 0.0214627 0.0907748i
\(106\) 0 0
\(107\) 127.242i 1.18918i 0.804030 + 0.594588i \(0.202685\pi\)
−0.804030 + 0.594588i \(0.797315\pi\)
\(108\) 0 0
\(109\) 55.3100 0.507431 0.253716 0.967279i \(-0.418347\pi\)
0.253716 + 0.967279i \(0.418347\pi\)
\(110\) 0 0
\(111\) −24.1387 5.70733i −0.217465 0.0514174i
\(112\) 0 0
\(113\) 102.845 + 59.3775i 0.910131 + 0.525464i 0.880473 0.474096i \(-0.157225\pi\)
0.0296577 + 0.999560i \(0.490558\pi\)
\(114\) 0 0
\(115\) −34.7320 60.1576i −0.302017 0.523109i
\(116\) 0 0
\(117\) 165.972 109.416i 1.41857 0.935183i
\(118\) 0 0
\(119\) 17.1884 9.92372i 0.144440 0.0833926i
\(120\) 0 0
\(121\) 17.6950 30.6486i 0.146239 0.253294i
\(122\) 0 0
\(123\) 110.533 + 104.170i 0.898640 + 0.846915i
\(124\) 0 0
\(125\) 95.3294i 0.762635i
\(126\) 0 0
\(127\) 74.4516 0.586233 0.293116 0.956077i \(-0.405308\pi\)
0.293116 + 0.956077i \(0.405308\pi\)
\(128\) 0 0
\(129\) 61.2610 + 204.228i 0.474891 + 1.58316i
\(130\) 0 0
\(131\) −7.08499 4.09052i −0.0540839 0.0312254i 0.472714 0.881216i \(-0.343274\pi\)
−0.526798 + 0.849990i \(0.676608\pi\)
\(132\) 0 0
\(133\) 17.0111 + 29.4642i 0.127903 + 0.221535i
\(134\) 0 0
\(135\) 19.3749 + 52.9674i 0.143518 + 0.392351i
\(136\) 0 0
\(137\) −41.7273 + 24.0913i −0.304579 + 0.175849i −0.644498 0.764606i \(-0.722934\pi\)
0.339919 + 0.940455i \(0.389600\pi\)
\(138\) 0 0
\(139\) 119.023 206.155i 0.856284 1.48313i −0.0191645 0.999816i \(-0.506101\pi\)
0.875449 0.483311i \(-0.160566\pi\)
\(140\) 0 0
\(141\) 189.948 56.9775i 1.34715 0.404095i
\(142\) 0 0
\(143\) 276.226i 1.93165i
\(144\) 0 0
\(145\) −62.1789 −0.428820
\(146\) 0 0
\(147\) 95.7944 101.645i 0.651662 0.691463i
\(148\) 0 0
\(149\) −246.854 142.521i −1.65674 0.956517i −0.974207 0.225658i \(-0.927547\pi\)
−0.682529 0.730859i \(-0.739120\pi\)
\(150\) 0 0
\(151\) −77.2434 133.790i −0.511546 0.886024i −0.999910 0.0133838i \(-0.995740\pi\)
0.488365 0.872640i \(-0.337594\pi\)
\(152\) 0 0
\(153\) −51.1847 + 102.190i −0.334541 + 0.667907i
\(154\) 0 0
\(155\) 25.0206 14.4456i 0.161423 0.0931976i
\(156\) 0 0
\(157\) −119.947 + 207.754i −0.763993 + 1.32328i 0.176784 + 0.984250i \(0.443431\pi\)
−0.940777 + 0.339026i \(0.889903\pi\)
\(158\) 0 0
\(159\) 4.17198 17.6450i 0.0262388 0.110975i
\(160\) 0 0
\(161\) 51.9730i 0.322814i
\(162\) 0 0
\(163\) 111.245 0.682483 0.341241 0.939976i \(-0.389153\pi\)
0.341241 + 0.939976i \(0.389153\pi\)
\(164\) 0 0
\(165\) −76.2653 18.0321i −0.462214 0.109286i
\(166\) 0 0
\(167\) 37.9116 + 21.8883i 0.227016 + 0.131068i 0.609195 0.793021i \(-0.291493\pi\)
−0.382179 + 0.924088i \(0.624826\pi\)
\(168\) 0 0
\(169\) −159.443 276.164i −0.943452 1.63411i
\(170\) 0 0
\(171\) −175.172 87.7403i −1.02440 0.513101i
\(172\) 0 0
\(173\) −253.383 + 146.291i −1.46464 + 0.845611i −0.999220 0.0394795i \(-0.987430\pi\)
−0.465420 + 0.885090i \(0.654097\pi\)
\(174\) 0 0
\(175\) −16.1265 + 27.9319i −0.0921514 + 0.159611i
\(176\) 0 0
\(177\) −20.2074 19.0443i −0.114166 0.107595i
\(178\) 0 0
\(179\) 194.612i 1.08722i −0.839338 0.543610i \(-0.817057\pi\)
0.839338 0.543610i \(-0.182943\pi\)
\(180\) 0 0
\(181\) 89.3906 0.493871 0.246935 0.969032i \(-0.420576\pi\)
0.246935 + 0.969032i \(0.420576\pi\)
\(182\) 0 0
\(183\) 89.4716 + 298.275i 0.488916 + 1.62992i
\(184\) 0 0
\(185\) −14.9571 8.63550i −0.0808494 0.0466784i
\(186\) 0 0
\(187\) −79.4048 137.533i −0.424625 0.735472i
\(188\) 0 0
\(189\) 7.26096 41.5690i 0.0384178 0.219942i
\(190\) 0 0
\(191\) −44.9085 + 25.9279i −0.235123 + 0.135748i −0.612933 0.790135i \(-0.710011\pi\)
0.377810 + 0.925883i \(0.376677\pi\)
\(192\) 0 0
\(193\) −29.7763 + 51.5741i −0.154281 + 0.267223i −0.932797 0.360402i \(-0.882640\pi\)
0.778516 + 0.627625i \(0.215973\pi\)
\(194\) 0 0
\(195\) 132.582 39.7698i 0.679909 0.203948i
\(196\) 0 0
\(197\) 47.4968i 0.241100i −0.992707 0.120550i \(-0.961534\pi\)
0.992707 0.120550i \(-0.0384659\pi\)
\(198\) 0 0
\(199\) 29.5239 0.148361 0.0741805 0.997245i \(-0.476366\pi\)
0.0741805 + 0.997245i \(0.476366\pi\)
\(200\) 0 0
\(201\) −81.8303 + 86.8281i −0.407116 + 0.431981i
\(202\) 0 0
\(203\) 40.2896 + 23.2612i 0.198471 + 0.114587i
\(204\) 0 0
\(205\) 52.8782 + 91.5877i 0.257942 + 0.446769i
\(206\) 0 0
\(207\) −164.729 249.875i −0.795790 1.20712i
\(208\) 0 0
\(209\) 235.758 136.115i 1.12803 0.651268i
\(210\) 0 0
\(211\) −81.0561 + 140.393i −0.384152 + 0.665371i −0.991651 0.128949i \(-0.958840\pi\)
0.607499 + 0.794320i \(0.292173\pi\)
\(212\) 0 0
\(213\) 12.6736 53.6017i 0.0595003 0.251651i
\(214\) 0 0
\(215\) 148.462i 0.690523i
\(216\) 0 0
\(217\) −21.6165 −0.0996151
\(218\) 0 0
\(219\) −200.213 47.3382i −0.914215 0.216156i
\(220\) 0 0
\(221\) 242.920 + 140.250i 1.09918 + 0.634614i
\(222\) 0 0
\(223\) 102.706 + 177.891i 0.460564 + 0.797719i 0.998989 0.0449536i \(-0.0143140\pi\)
−0.538426 + 0.842673i \(0.680981\pi\)
\(224\) 0 0
\(225\) −10.9976 185.403i −0.0488782 0.824015i
\(226\) 0 0
\(227\) 54.0416 31.2009i 0.238069 0.137449i −0.376220 0.926530i \(-0.622776\pi\)
0.614289 + 0.789081i \(0.289443\pi\)
\(228\) 0 0
\(229\) −5.73790 + 9.93834i −0.0250563 + 0.0433989i −0.878282 0.478144i \(-0.841310\pi\)
0.853225 + 0.521542i \(0.174643\pi\)
\(230\) 0 0
\(231\) 42.6712 + 40.2150i 0.184724 + 0.174091i
\(232\) 0 0
\(233\) 177.096i 0.760069i −0.924972 0.380035i \(-0.875912\pi\)
0.924972 0.380035i \(-0.124088\pi\)
\(234\) 0 0
\(235\) 138.082 0.587581
\(236\) 0 0
\(237\) 22.9501 + 76.5098i 0.0968360 + 0.322826i
\(238\) 0 0
\(239\) −231.234 133.503i −0.967505 0.558589i −0.0690305 0.997615i \(-0.521991\pi\)
−0.898475 + 0.439025i \(0.855324\pi\)
\(240\) 0 0
\(241\) 40.7178 + 70.5252i 0.168953 + 0.292636i 0.938052 0.346494i \(-0.112628\pi\)
−0.769099 + 0.639130i \(0.779295\pi\)
\(242\) 0 0
\(243\) 96.8440 + 222.868i 0.398535 + 0.917153i
\(244\) 0 0
\(245\) 84.2233 48.6263i 0.343769 0.198475i
\(246\) 0 0
\(247\) −240.415 + 416.410i −0.973338 + 1.68587i
\(248\) 0 0
\(249\) 69.8036 20.9385i 0.280336 0.0840905i
\(250\) 0 0
\(251\) 311.819i 1.24231i −0.783689 0.621153i \(-0.786664\pi\)
0.783689 0.621153i \(-0.213336\pi\)
\(252\) 0 0
\(253\) 415.863 1.64373
\(254\) 0 0
\(255\) −54.5806 + 57.9141i −0.214041 + 0.227114i
\(256\) 0 0
\(257\) 335.121 + 193.482i 1.30397 + 0.752849i 0.981083 0.193588i \(-0.0620125\pi\)
0.322889 + 0.946437i \(0.395346\pi\)
\(258\) 0 0
\(259\) 6.46110 + 11.1909i 0.0249463 + 0.0432083i
\(260\) 0 0
\(261\) −267.430 + 15.8632i −1.02463 + 0.0607785i
\(262\) 0 0
\(263\) 417.095 240.810i 1.58591 0.915627i 0.591942 0.805981i \(-0.298362\pi\)
0.993971 0.109646i \(-0.0349718\pi\)
\(264\) 0 0
\(265\) 6.31243 10.9334i 0.0238205 0.0412583i
\(266\) 0 0
\(267\) 77.1254 326.195i 0.288859 1.22171i
\(268\) 0 0
\(269\) 225.818i 0.839474i 0.907646 + 0.419737i \(0.137878\pi\)
−0.907646 + 0.419737i \(0.862122\pi\)
\(270\) 0 0
\(271\) −23.6619 −0.0873135 −0.0436567 0.999047i \(-0.513901\pi\)
−0.0436567 + 0.999047i \(0.513901\pi\)
\(272\) 0 0
\(273\) −100.786 23.8298i −0.369180 0.0872887i
\(274\) 0 0
\(275\) 223.498 + 129.036i 0.812718 + 0.469223i
\(276\) 0 0
\(277\) −27.9969 48.4920i −0.101072 0.175061i 0.811055 0.584970i \(-0.198894\pi\)
−0.912126 + 0.409909i \(0.865560\pi\)
\(278\) 0 0
\(279\) 103.927 68.5135i 0.372499 0.245568i
\(280\) 0 0
\(281\) 122.023 70.4498i 0.434244 0.250711i −0.266909 0.963722i \(-0.586002\pi\)
0.701153 + 0.713011i \(0.252669\pi\)
\(282\) 0 0
\(283\) −155.690 + 269.663i −0.550141 + 0.952872i 0.448123 + 0.893972i \(0.352093\pi\)
−0.998264 + 0.0589002i \(0.981241\pi\)
\(284\) 0 0
\(285\) −99.2757 93.5614i −0.348336 0.328286i
\(286\) 0 0
\(287\) 79.1271i 0.275704i
\(288\) 0 0
\(289\) 127.733 0.441983
\(290\) 0 0
\(291\) −4.33012 14.4355i −0.0148801 0.0496065i
\(292\) 0 0
\(293\) −273.621 157.975i −0.933859 0.539164i −0.0458290 0.998949i \(-0.514593\pi\)
−0.888030 + 0.459786i \(0.847926\pi\)
\(294\) 0 0
\(295\) −9.66712 16.7439i −0.0327699 0.0567591i
\(296\) 0 0
\(297\) −332.615 58.0987i −1.11992 0.195618i
\(298\) 0 0
\(299\) −636.116 + 367.262i −2.12748 + 1.22830i
\(300\) 0 0
\(301\) 55.5399 96.1980i 0.184518 0.319595i
\(302\) 0 0
\(303\) −285.701 + 85.6998i −0.942907 + 0.282838i
\(304\) 0 0
\(305\) 216.829i 0.710916i
\(306\) 0 0
\(307\) −379.819 −1.23720 −0.618598 0.785707i \(-0.712299\pi\)
−0.618598 + 0.785707i \(0.712299\pi\)
\(308\) 0 0
\(309\) 56.0315 59.4536i 0.181332 0.192406i
\(310\) 0 0
\(311\) −335.497 193.699i −1.07877 0.622827i −0.148204 0.988957i \(-0.547349\pi\)
−0.930564 + 0.366130i \(0.880683\pi\)
\(312\) 0 0
\(313\) −100.742 174.491i −0.321860 0.557479i 0.659011 0.752133i \(-0.270975\pi\)
−0.980872 + 0.194654i \(0.937642\pi\)
\(314\) 0 0
\(315\) 13.1587 26.2712i 0.0417737 0.0834007i
\(316\) 0 0
\(317\) 319.046 184.201i 1.00645 0.581077i 0.0963027 0.995352i \(-0.469298\pi\)
0.910152 + 0.414275i \(0.135965\pi\)
\(318\) 0 0
\(319\) 186.125 322.378i 0.583463 1.01059i
\(320\) 0 0
\(321\) −87.8332 + 371.483i −0.273624 + 1.15727i
\(322\) 0 0
\(323\) 276.442i 0.855857i
\(324\) 0 0
\(325\) −455.824 −1.40254
\(326\) 0 0
\(327\) 161.478 + 38.1797i 0.493816 + 0.116758i
\(328\) 0 0
\(329\) −89.4716 51.6564i −0.271950 0.157010i
\(330\) 0 0
\(331\) 150.832 + 261.248i 0.455684 + 0.789268i 0.998727 0.0504365i \(-0.0160613\pi\)
−0.543043 + 0.839705i \(0.682728\pi\)
\(332\) 0 0
\(333\) −66.5333 33.3251i −0.199800 0.100076i
\(334\) 0 0
\(335\) −71.9460 + 41.5380i −0.214764 + 0.123994i
\(336\) 0 0
\(337\) 85.5075 148.103i 0.253732 0.439476i −0.710819 0.703375i \(-0.751675\pi\)
0.964550 + 0.263899i \(0.0850087\pi\)
\(338\) 0 0
\(339\) 259.268 + 244.345i 0.764804 + 0.720782i
\(340\) 0 0
\(341\) 172.965i 0.507227i
\(342\) 0 0
\(343\) −149.347 −0.435414
\(344\) 0 0
\(345\) −59.8743 199.605i −0.173549 0.578566i
\(346\) 0 0
\(347\) 264.744 + 152.850i 0.762950 + 0.440489i 0.830354 0.557237i \(-0.188138\pi\)
−0.0674041 + 0.997726i \(0.521472\pi\)
\(348\) 0 0
\(349\) −11.1944 19.3893i −0.0320756 0.0555566i 0.849542 0.527521i \(-0.176878\pi\)
−0.881618 + 0.471964i \(0.843545\pi\)
\(350\) 0 0
\(351\) 560.086 204.873i 1.59569 0.583685i
\(352\) 0 0
\(353\) −462.657 + 267.115i −1.31064 + 0.756700i −0.982203 0.187825i \(-0.939856\pi\)
−0.328440 + 0.944525i \(0.606523\pi\)
\(354\) 0 0
\(355\) 19.1758 33.2134i 0.0540163 0.0935590i
\(356\) 0 0
\(357\) 57.0318 17.1075i 0.159753 0.0479200i
\(358\) 0 0
\(359\) 217.172i 0.604936i −0.953159 0.302468i \(-0.902189\pi\)
0.953159 0.302468i \(-0.0978106\pi\)
\(360\) 0 0
\(361\) 112.874 0.312669
\(362\) 0 0
\(363\) 72.8168 77.2641i 0.200597 0.212849i
\(364\) 0 0
\(365\) −124.059 71.6253i −0.339887 0.196234i
\(366\) 0 0
\(367\) −51.1847 88.6546i −0.139468 0.241566i 0.787827 0.615896i \(-0.211206\pi\)
−0.927295 + 0.374330i \(0.877873\pi\)
\(368\) 0 0
\(369\) 250.793 + 380.425i 0.679657 + 1.03096i
\(370\) 0 0
\(371\) −8.18042 + 4.72297i −0.0220497 + 0.0127304i
\(372\) 0 0
\(373\) 243.458 421.682i 0.652702 1.13051i −0.329762 0.944064i \(-0.606969\pi\)
0.982464 0.186450i \(-0.0596982\pi\)
\(374\) 0 0
\(375\) 65.8045 278.314i 0.175479 0.742172i
\(376\) 0 0
\(377\) 657.490i 1.74401i
\(378\) 0 0
\(379\) 553.727 1.46102 0.730510 0.682901i \(-0.239282\pi\)
0.730510 + 0.682901i \(0.239282\pi\)
\(380\) 0 0
\(381\) 217.362 + 51.3929i 0.570503 + 0.134889i
\(382\) 0 0
\(383\) 184.612 + 106.586i 0.482016 + 0.278292i 0.721256 0.692668i \(-0.243565\pi\)
−0.239240 + 0.970960i \(0.576898\pi\)
\(384\) 0 0
\(385\) 20.4136 + 35.3574i 0.0530224 + 0.0918375i
\(386\) 0 0
\(387\) 37.8759 + 638.532i 0.0978707 + 1.64995i
\(388\) 0 0
\(389\) −82.4958 + 47.6290i −0.212071 + 0.122439i −0.602274 0.798290i \(-0.705738\pi\)
0.390202 + 0.920729i \(0.372405\pi\)
\(390\) 0 0
\(391\) 211.149 365.720i 0.540022 0.935346i
\(392\) 0 0
\(393\) −17.8610 16.8330i −0.0454479 0.0428320i
\(394\) 0 0
\(395\) 55.6184i 0.140806i
\(396\) 0 0
\(397\) −481.407 −1.21261 −0.606306 0.795231i \(-0.707349\pi\)
−0.606306 + 0.795231i \(0.707349\pi\)
\(398\) 0 0
\(399\) 29.3254 + 97.7633i 0.0734973 + 0.245021i
\(400\) 0 0
\(401\) −517.354 298.694i −1.29016 0.744874i −0.311477 0.950254i \(-0.600824\pi\)
−0.978682 + 0.205380i \(0.934157\pi\)
\(402\) 0 0
\(403\) −152.750 264.571i −0.379033 0.656505i
\(404\) 0 0
\(405\) 20.0025 + 168.013i 0.0493888 + 0.414846i
\(406\) 0 0
\(407\) 89.5446 51.6986i 0.220011 0.127024i
\(408\) 0 0
\(409\) −53.7260 + 93.0562i −0.131359 + 0.227521i −0.924201 0.381907i \(-0.875268\pi\)
0.792841 + 0.609428i \(0.208601\pi\)
\(410\) 0 0
\(411\) −138.453 + 41.5308i −0.336868 + 0.101048i
\(412\) 0 0
\(413\) 14.4659i 0.0350264i
\(414\) 0 0
\(415\) 50.7433 0.122273
\(416\) 0 0
\(417\) 489.795 519.709i 1.17457 1.24631i
\(418\) 0 0
\(419\) 39.6993 + 22.9204i 0.0947477 + 0.0547026i 0.546625 0.837377i \(-0.315912\pi\)
−0.451878 + 0.892080i \(0.649246\pi\)
\(420\) 0 0
\(421\) −5.53062 9.57932i −0.0131369 0.0227537i 0.859382 0.511334i \(-0.170848\pi\)
−0.872519 + 0.488580i \(0.837515\pi\)
\(422\) 0 0
\(423\) 593.885 35.2276i 1.40398 0.0832803i
\(424\) 0 0
\(425\) 226.956 131.033i 0.534013 0.308313i
\(426\) 0 0
\(427\) 81.1161 140.497i 0.189967 0.329033i
\(428\) 0 0
\(429\) −190.675 + 806.442i −0.444463 + 1.87982i
\(430\) 0 0
\(431\) 590.788i 1.37074i 0.728196 + 0.685369i \(0.240359\pi\)
−0.728196 + 0.685369i \(0.759641\pi\)
\(432\) 0 0
\(433\) −13.9683 −0.0322594 −0.0161297 0.999870i \(-0.505134\pi\)
−0.0161297 + 0.999870i \(0.505134\pi\)
\(434\) 0 0
\(435\) −181.532 42.9212i −0.417314 0.0986695i
\(436\) 0 0
\(437\) 626.914 + 361.949i 1.43459 + 0.828258i
\(438\) 0 0
\(439\) 35.9051 + 62.1894i 0.0817883 + 0.141662i 0.904018 0.427494i \(-0.140604\pi\)
−0.822230 + 0.569156i \(0.807270\pi\)
\(440\) 0 0
\(441\) 349.836 230.628i 0.793279 0.522965i
\(442\) 0 0
\(443\) −581.028 + 335.457i −1.31158 + 0.757239i −0.982357 0.187015i \(-0.940119\pi\)
−0.329219 + 0.944254i \(0.606786\pi\)
\(444\) 0 0
\(445\) 116.695 202.122i 0.262236 0.454206i
\(446\) 0 0
\(447\) −622.310 586.490i −1.39219 1.31206i
\(448\) 0 0
\(449\) 830.401i 1.84945i −0.380642 0.924723i \(-0.624297\pi\)
0.380642 0.924723i \(-0.375703\pi\)
\(450\) 0 0
\(451\) −633.136 −1.40385
\(452\) 0 0
\(453\) −133.160 443.919i −0.293950 0.979954i
\(454\) 0 0
\(455\) −62.4505 36.0558i −0.137254 0.0792435i
\(456\) 0 0
\(457\) 423.113 + 732.854i 0.925850 + 1.60362i 0.790188 + 0.612864i \(0.209983\pi\)
0.135661 + 0.990755i \(0.456684\pi\)
\(458\) 0 0
\(459\) −219.974 + 263.011i −0.479247 + 0.573009i
\(460\) 0 0
\(461\) 109.019 62.9423i 0.236484 0.136534i −0.377076 0.926182i \(-0.623070\pi\)
0.613560 + 0.789648i \(0.289737\pi\)
\(462\) 0 0
\(463\) 307.121 531.950i 0.663329 1.14892i −0.316407 0.948624i \(-0.602476\pi\)
0.979735 0.200296i \(-0.0641903\pi\)
\(464\) 0 0
\(465\) 83.0192 24.9027i 0.178536 0.0535543i
\(466\) 0 0
\(467\) 172.270i 0.368887i −0.982843 0.184444i \(-0.940952\pi\)
0.982843 0.184444i \(-0.0590484\pi\)
\(468\) 0 0
\(469\) 62.1576 0.132532
\(470\) 0 0
\(471\) −493.595 + 523.742i −1.04797 + 1.11198i
\(472\) 0 0
\(473\) −769.729 444.403i −1.62733 0.939542i
\(474\) 0 0
\(475\) 224.615 + 389.045i 0.472874 + 0.819042i
\(476\) 0 0
\(477\) 24.3602 48.6349i 0.0510696 0.101960i
\(478\) 0 0
\(479\) −174.532 + 100.766i −0.364367 + 0.210367i −0.670995 0.741462i \(-0.734133\pi\)
0.306628 + 0.951829i \(0.400799\pi\)
\(480\) 0 0
\(481\) −91.3132 + 158.159i −0.189840 + 0.328813i
\(482\) 0 0
\(483\) −35.8762 + 151.736i −0.0742779 + 0.314152i
\(484\) 0 0
\(485\) 10.4938i 0.0216367i
\(486\) 0 0
\(487\) −801.178 −1.64513 −0.822565 0.568671i \(-0.807458\pi\)
−0.822565 + 0.568671i \(0.807458\pi\)
\(488\) 0 0
\(489\) 324.779 + 76.7906i 0.664170 + 0.157036i
\(490\) 0 0
\(491\) 625.711 + 361.255i 1.27436 + 0.735753i 0.975806 0.218640i \(-0.0701619\pi\)
0.298555 + 0.954392i \(0.403495\pi\)
\(492\) 0 0
\(493\) −189.005 327.366i −0.383376 0.664028i
\(494\) 0 0
\(495\) −210.210 105.290i −0.424666 0.212706i
\(496\) 0 0
\(497\) −24.8503 + 14.3474i −0.0500007 + 0.0288679i
\(498\) 0 0
\(499\) −69.4409 + 120.275i −0.139160 + 0.241032i −0.927179 0.374619i \(-0.877774\pi\)
0.788019 + 0.615651i \(0.211107\pi\)
\(500\) 0 0
\(501\) 95.5740 + 90.0728i 0.190766 + 0.179786i
\(502\) 0 0
\(503\) 794.533i 1.57959i −0.613372 0.789794i \(-0.710187\pi\)
0.613372 0.789794i \(-0.289813\pi\)
\(504\) 0 0
\(505\) −207.689 −0.411264
\(506\) 0 0
\(507\) −274.864 916.323i −0.542137 1.80734i
\(508\) 0 0
\(509\) −179.929 103.882i −0.353495 0.204090i 0.312729 0.949843i \(-0.398757\pi\)
−0.666224 + 0.745752i \(0.732090\pi\)
\(510\) 0 0
\(511\) 53.5902 + 92.8209i 0.104873 + 0.181646i
\(512\) 0 0
\(513\) −450.851 377.077i −0.878852 0.735043i
\(514\) 0 0
\(515\) 49.2634 28.4422i 0.0956571 0.0552276i
\(516\) 0 0
\(517\) −413.330 + 715.908i −0.799477 + 1.38474i
\(518\) 0 0
\(519\) −840.734 + 252.190i −1.61991 + 0.485914i
\(520\) 0 0
\(521\) 248.275i 0.476535i 0.971200 + 0.238267i \(0.0765795\pi\)
−0.971200 + 0.238267i \(0.923421\pi\)
\(522\) 0 0
\(523\) −108.678 −0.207797 −0.103898 0.994588i \(-0.533132\pi\)
−0.103898 + 0.994588i \(0.533132\pi\)
\(524\) 0 0
\(525\) −66.3623 + 70.4154i −0.126404 + 0.134125i
\(526\) 0 0
\(527\) 152.109 + 87.8204i 0.288633 + 0.166642i
\(528\) 0 0
\(529\) 288.420 + 499.557i 0.545216 + 0.944343i
\(530\) 0 0
\(531\) −45.8497 69.5489i −0.0863460 0.130977i
\(532\) 0 0
\(533\) 968.463 559.142i 1.81700 1.04905i
\(534\) 0 0
\(535\) −132.896 + 230.183i −0.248405 + 0.430249i
\(536\) 0 0
\(537\) 134.338 568.171i 0.250164 1.05805i
\(538\) 0 0
\(539\) 582.227i 1.08020i
\(540\) 0 0
\(541\) −20.0646 −0.0370880 −0.0185440 0.999828i \(-0.505903\pi\)
−0.0185440 + 0.999828i \(0.505903\pi\)
\(542\) 0 0
\(543\) 260.976 + 61.7051i 0.480619 + 0.113637i
\(544\) 0 0
\(545\) 100.057 + 57.7680i 0.183591 + 0.105996i
\(546\) 0 0
\(547\) 86.6937 + 150.158i 0.158489 + 0.274512i 0.934324 0.356424i \(-0.116004\pi\)
−0.775835 + 0.630936i \(0.782671\pi\)
\(548\) 0 0
\(549\) 55.3178 + 932.577i 0.100761 + 1.69868i
\(550\) 0 0
\(551\) 561.167 323.990i 1.01845 0.588003i
\(552\) 0 0
\(553\) 20.8069 36.0386i 0.0376254 0.0651692i
\(554\) 0 0
\(555\) −37.7064 35.5361i −0.0679395 0.0640290i
\(556\) 0 0
\(557\) 434.666i 0.780370i −0.920737 0.390185i \(-0.872411\pi\)
0.920737 0.390185i \(-0.127589\pi\)
\(558\) 0 0
\(559\) 1569.87 2.80835
\(560\) 0 0
\(561\) −136.886 456.341i −0.244003 0.813442i
\(562\) 0 0
\(563\) 86.8277 + 50.1300i 0.154223 + 0.0890409i 0.575126 0.818065i \(-0.304953\pi\)
−0.420902 + 0.907106i \(0.638286\pi\)
\(564\) 0 0
\(565\) 124.032 + 214.830i 0.219526 + 0.380231i
\(566\) 0 0
\(567\) 49.8929 116.349i 0.0879945 0.205201i
\(568\) 0 0
\(569\) 44.1556 25.4932i 0.0776020 0.0448036i −0.460697 0.887558i \(-0.652400\pi\)
0.538299 + 0.842754i \(0.319067\pi\)
\(570\) 0 0
\(571\) 430.481 745.615i 0.753907 1.30581i −0.192009 0.981393i \(-0.561500\pi\)
0.945916 0.324412i \(-0.105166\pi\)
\(572\) 0 0
\(573\) −149.008 + 44.6970i −0.260049 + 0.0780053i
\(574\) 0 0
\(575\) 686.252i 1.19348i
\(576\) 0 0
\(577\) 59.3431 0.102848 0.0514239 0.998677i \(-0.483624\pi\)
0.0514239 + 0.998677i \(0.483624\pi\)
\(578\) 0 0
\(579\) −122.533 + 130.017i −0.211628 + 0.224554i
\(580\) 0 0
\(581\) −32.8797 18.9831i −0.0565916 0.0326732i
\(582\) 0 0
\(583\) 37.7909 + 65.4558i 0.0648215 + 0.112274i
\(584\) 0 0
\(585\) 414.527 24.5886i 0.708593 0.0420318i
\(586\) 0 0
\(587\) 534.777 308.754i 0.911034 0.525986i 0.0302706 0.999542i \(-0.490363\pi\)
0.880764 + 0.473556i \(0.157030\pi\)
\(588\) 0 0
\(589\) −150.541 + 260.744i −0.255587 + 0.442690i
\(590\) 0 0
\(591\) 32.7863 138.667i 0.0554760 0.234631i
\(592\) 0 0
\(593\) 342.310i 0.577251i 0.957442 + 0.288626i \(0.0931983\pi\)
−0.957442 + 0.288626i \(0.906802\pi\)
\(594\) 0 0
\(595\) 41.4589 0.0696789
\(596\) 0 0
\(597\) 86.1950 + 20.3799i 0.144380 + 0.0341372i
\(598\) 0 0
\(599\) 379.292 + 218.984i 0.633209 + 0.365583i 0.781994 0.623286i \(-0.214203\pi\)
−0.148785 + 0.988870i \(0.547536\pi\)
\(600\) 0 0
\(601\) 304.452 + 527.327i 0.506576 + 0.877416i 0.999971 + 0.00761053i \(0.00242253\pi\)
−0.493395 + 0.869806i \(0.664244\pi\)
\(602\) 0 0
\(603\) −298.840 + 197.009i −0.495589 + 0.326714i
\(604\) 0 0
\(605\) 64.0212 36.9627i 0.105820 0.0610953i
\(606\) 0 0
\(607\) −540.751 + 936.608i −0.890858 + 1.54301i −0.0520102 + 0.998647i \(0.516563\pi\)
−0.838848 + 0.544365i \(0.816770\pi\)
\(608\) 0 0
\(609\) 101.569 + 95.7225i 0.166779 + 0.157180i
\(610\) 0 0
\(611\) 1460.10i 2.38968i
\(612\) 0 0
\(613\) −222.279 −0.362609 −0.181304 0.983427i \(-0.558032\pi\)
−0.181304 + 0.983427i \(0.558032\pi\)
\(614\) 0 0
\(615\) 91.1564 + 303.892i 0.148222 + 0.494133i
\(616\) 0 0
\(617\) −31.0310 17.9158i −0.0502934 0.0290369i 0.474642 0.880179i \(-0.342577\pi\)
−0.524936 + 0.851142i \(0.675911\pi\)
\(618\) 0 0
\(619\) −161.494 279.717i −0.260896 0.451885i 0.705584 0.708626i \(-0.250685\pi\)
−0.966480 + 0.256741i \(0.917351\pi\)
\(620\) 0 0
\(621\) −308.441 843.221i −0.496684 1.35784i
\(622\) 0 0
\(623\) −151.228 + 87.3114i −0.242741 + 0.140147i
\(624\) 0 0
\(625\) −158.391 + 274.342i −0.253426 + 0.438947i
\(626\) 0 0
\(627\) 782.254 234.648i 1.24761 0.374239i
\(628\) 0 0
\(629\) 104.997i 0.166927i
\(630\) 0 0
\(631\) −794.037 −1.25838 −0.629189 0.777252i \(-0.716613\pi\)
−0.629189 + 0.777252i \(0.716613\pi\)
\(632\) 0 0
\(633\) −333.555 + 353.927i −0.526943 + 0.559126i
\(634\) 0 0
\(635\) 134.685 + 77.7602i 0.212102 + 0.122457i
\(636\) 0 0
\(637\) −514.183 890.591i −0.807194 1.39810i
\(638\) 0 0
\(639\) 74.0010 147.742i 0.115808 0.231208i
\(640\) 0 0
\(641\) −753.063 + 434.781i −1.17483 + 0.678286i −0.954812 0.297211i \(-0.903943\pi\)
−0.220013 + 0.975497i \(0.570610\pi\)
\(642\) 0 0
\(643\) 31.2519 54.1299i 0.0486033 0.0841834i −0.840700 0.541501i \(-0.817856\pi\)
0.889304 + 0.457317i \(0.151190\pi\)
\(644\) 0 0
\(645\) −102.481 + 433.437i −0.158886 + 0.671995i
\(646\) 0 0
\(647\) 761.439i 1.17688i 0.808542 + 0.588438i \(0.200257\pi\)
−0.808542 + 0.588438i \(0.799743\pi\)
\(648\) 0 0
\(649\) 115.749 0.178350
\(650\) 0 0
\(651\) −63.1094 14.9215i −0.0969422 0.0229210i
\(652\) 0 0
\(653\) 129.622 + 74.8371i 0.198502 + 0.114605i 0.595956 0.803017i \(-0.296773\pi\)
−0.397455 + 0.917622i \(0.630106\pi\)
\(654\) 0 0
\(655\) −8.54461 14.7997i −0.0130452 0.0225950i
\(656\) 0 0
\(657\) −551.846 276.408i −0.839948 0.420713i
\(658\) 0 0
\(659\) −564.273 + 325.783i −0.856256 + 0.494360i −0.862757 0.505619i \(-0.831264\pi\)
0.00650063 + 0.999979i \(0.497931\pi\)
\(660\) 0 0
\(661\) 596.672 1033.47i 0.902681 1.56349i 0.0786818 0.996900i \(-0.474929\pi\)
0.824000 0.566590i \(-0.191738\pi\)
\(662\) 0 0
\(663\) 612.393 + 577.144i 0.923669 + 0.870503i
\(664\) 0 0
\(665\) 71.0685i 0.106870i
\(666\) 0 0
\(667\) 989.865 1.48405
\(668\) 0 0
\(669\) 177.054 + 590.251i 0.264654 + 0.882289i
\(670\) 0 0
\(671\) −1124.19 649.051i −1.67539 0.967290i
\(672\) 0 0
\(673\) −74.7771 129.518i −0.111110 0.192448i 0.805108 0.593128i \(-0.202107\pi\)
−0.916218 + 0.400680i \(0.868774\pi\)
\(674\) 0 0
\(675\) 95.8737 548.877i 0.142035 0.813152i
\(676\) 0 0
\(677\) −607.487 + 350.733i −0.897322 + 0.518069i −0.876331 0.481710i \(-0.840016\pi\)
−0.0209919 + 0.999780i \(0.506682\pi\)
\(678\) 0 0
\(679\) −3.92574 + 6.79958i −0.00578165 + 0.0100141i
\(680\) 0 0
\(681\) 179.312 53.7871i 0.263307 0.0789826i
\(682\) 0 0
\(683\) 503.096i 0.736597i −0.929708 0.368299i \(-0.879940\pi\)
0.929708 0.368299i \(-0.120060\pi\)
\(684\) 0 0
\(685\) −100.648 −0.146931
\(686\) 0 0
\(687\) −23.6121 + 25.0542i −0.0343699 + 0.0364690i
\(688\) 0 0
\(689\) −115.612 66.7487i −0.167797 0.0968776i
\(690\) 0 0
\(691\) −329.413 570.561i −0.476720 0.825703i 0.522924 0.852379i \(-0.324841\pi\)
−0.999644 + 0.0266761i \(0.991508\pi\)
\(692\) 0 0
\(693\) 96.8188 + 146.863i 0.139710 + 0.211924i
\(694\) 0 0
\(695\) 430.633 248.626i 0.619615 0.357735i
\(696\) 0 0
\(697\) −321.466 + 556.796i −0.461214 + 0.798846i
\(698\) 0 0
\(699\) 122.247 517.033i 0.174888 0.739675i
\(700\) 0 0
\(701\) 172.963i 0.246738i 0.992361 + 0.123369i \(0.0393698\pi\)
−0.992361 + 0.123369i \(0.960630\pi\)
\(702\) 0 0
\(703\) 179.985 0.256024
\(704\) 0 0
\(705\) 403.130 + 95.3158i 0.571815 + 0.135200i
\(706\) 0 0
\(707\) 134.574 + 77.6964i 0.190345 + 0.109896i
\(708\) 0 0
\(709\) −527.267 913.254i −0.743677 1.28809i −0.950810 0.309774i \(-0.899747\pi\)
0.207133 0.978313i \(-0.433587\pi\)
\(710\) 0 0
\(711\) 14.1894 + 239.213i 0.0199570 + 0.336446i
\(712\) 0 0
\(713\) −398.317 + 229.969i −0.558650 + 0.322537i
\(714\) 0 0
\(715\) −288.501 + 499.699i −0.403498 + 0.698879i
\(716\) 0 0
\(717\) −582.933 549.380i −0.813017 0.766220i
\(718\) 0 0
\(719\) 1164.78i 1.62000i 0.586432 + 0.809998i \(0.300532\pi\)
−0.586432 + 0.809998i \(0.699468\pi\)
\(720\) 0 0
\(721\) −42.5611 −0.0590306
\(722\) 0 0
\(723\) 70.1931 + 234.006i 0.0970859 + 0.323659i
\(724\) 0 0
\(725\) 531.983 + 307.141i 0.733770 + 0.423642i
\(726\) 0 0
\(727\) −492.209 852.530i −0.677041 1.17267i −0.975868 0.218362i \(-0.929929\pi\)
0.298827 0.954307i \(-0.403405\pi\)
\(728\) 0 0
\(729\) 128.894 + 717.515i 0.176809 + 0.984245i
\(730\) 0 0
\(731\) −781.639 + 451.280i −1.06927 + 0.617345i
\(732\) 0 0
\(733\) 246.459 426.879i 0.336233 0.582372i −0.647488 0.762076i \(-0.724180\pi\)
0.983721 + 0.179703i \(0.0575138\pi\)
\(734\) 0 0
\(735\) 279.456 83.8267i 0.380213 0.114050i
\(736\) 0 0
\(737\) 497.355i 0.674837i
\(738\) 0 0
\(739\) −571.150 −0.772869 −0.386435 0.922317i \(-0.626293\pi\)
−0.386435 + 0.922317i \(0.626293\pi\)
\(740\) 0 0
\(741\) −989.333 + 1049.76i −1.33513 + 1.41668i
\(742\) 0 0
\(743\) −910.255 525.536i −1.22511 0.707316i −0.259105 0.965849i \(-0.583427\pi\)
−0.966002 + 0.258533i \(0.916761\pi\)
\(744\) 0 0
\(745\) −297.709 515.648i −0.399610 0.692144i
\(746\) 0 0
\(747\) 218.246 12.9457i 0.292163 0.0173303i
\(748\) 0 0
\(749\) 172.224 99.4334i 0.229938 0.132755i
\(750\) 0 0
\(751\) −42.3053 + 73.2749i −0.0563319 + 0.0975698i −0.892816 0.450421i \(-0.851274\pi\)
0.836484 + 0.547991i \(0.184607\pi\)
\(752\) 0 0
\(753\) 215.244 910.357i 0.285849 1.20897i
\(754\) 0 0
\(755\) 322.705i 0.427423i
\(756\) 0 0
\(757\) 1007.63 1.33109 0.665543 0.746360i \(-0.268200\pi\)
0.665543 + 0.746360i \(0.268200\pi\)
\(758\) 0 0
\(759\) 1214.11 + 287.064i 1.59962 + 0.378214i
\(760\) 0 0
\(761\) 393.981 + 227.465i 0.517715 + 0.298903i 0.735999 0.676983i \(-0.236713\pi\)
−0.218285 + 0.975885i \(0.570046\pi\)
\(762\) 0 0
\(763\) −43.2221 74.8629i −0.0566476 0.0981165i
\(764\) 0 0
\(765\) −199.325 + 131.404i −0.260556 + 0.171770i
\(766\) 0 0
\(767\) −177.053 + 102.222i −0.230838 + 0.133275i
\(768\) 0 0
\(769\) 352.232 610.084i 0.458039 0.793347i −0.540818 0.841139i \(-0.681885\pi\)
0.998857 + 0.0477927i \(0.0152187\pi\)
\(770\) 0 0
\(771\) 844.829 + 796.201i 1.09576 + 1.03269i
\(772\) 0 0
\(773\) 1021.43i 1.32138i 0.750658 + 0.660691i \(0.229737\pi\)
−0.750658 + 0.660691i \(0.770263\pi\)
\(774\) 0 0
\(775\) −285.424 −0.368289
\(776\) 0 0
\(777\) 11.1383 + 37.1320i 0.0143349 + 0.0477890i
\(778\) 0 0
\(779\) −954.453 551.054i −1.22523 0.707386i
\(780\) 0 0
\(781\) 114.801 + 198.840i 0.146992 + 0.254597i
\(782\) 0 0
\(783\) −791.712 138.290i −1.01113 0.176616i
\(784\) 0 0
\(785\) −433.974 + 250.555i −0.552833 + 0.319178i
\(786\) 0 0
\(787\) −202.007 + 349.886i −0.256680 + 0.444582i −0.965350 0.260957i \(-0.915962\pi\)
0.708671 + 0.705539i \(0.249295\pi\)
\(788\) 0 0
\(789\) 1383.94 415.131i 1.75404 0.526148i
\(790\) 0 0
\(791\) 185.603i 0.234643i