Properties

Label 588.4.i.l.361.3
Level $588$
Weight $4$
Character 588.361
Analytic conductor $34.693$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(34.6931230834\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - 2 x^{7} + 27 x^{6} + 10 x^{5} + 446 x^{4} + 62 x^{3} + 3061 x^{2} + 2142 x + 14161\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.3
Root \(-1.65506 + 2.86665i\) of defining polynomial
Character \(\chi\) \(=\) 588.361
Dual form 588.4.i.l.373.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 2.59808i) q^{3} +(4.08470 + 7.07491i) q^{5} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(1.50000 - 2.59808i) q^{3} +(4.08470 + 7.07491i) q^{5} +(-4.50000 - 7.79423i) q^{9} +(-18.9094 + 32.7521i) q^{11} -39.9319 q^{13} +24.5082 q^{15} +(4.96798 - 8.60480i) q^{17} +(-45.2229 - 78.3284i) q^{19} +(-59.2973 - 102.706i) q^{23} +(29.1304 - 50.4554i) q^{25} -27.0000 q^{27} -78.4061 q^{29} +(46.0055 - 79.6838i) q^{31} +(56.7283 + 98.2563i) q^{33} +(-166.218 - 287.897i) q^{37} +(-59.8979 + 103.746i) q^{39} -71.7451 q^{41} -115.947 q^{43} +(36.7623 - 63.6742i) q^{45} +(153.964 + 266.673i) q^{47} +(-14.9039 - 25.8144i) q^{51} +(201.575 - 349.138i) q^{53} -308.958 q^{55} -271.337 q^{57} +(296.855 - 514.168i) q^{59} +(166.585 + 288.534i) q^{61} +(-163.110 - 282.515i) q^{65} +(371.756 - 643.900i) q^{67} -355.784 q^{69} -728.272 q^{71} +(-400.874 + 694.335i) q^{73} +(-87.3912 - 151.366i) q^{75} +(-533.953 - 924.833i) q^{79} +(-40.5000 + 70.1481i) q^{81} -906.756 q^{83} +81.1709 q^{85} +(-117.609 + 203.705i) q^{87} +(556.634 + 964.119i) q^{89} +(-138.016 - 239.051i) q^{93} +(369.444 - 639.896i) q^{95} -1480.94 q^{97} +340.370 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 12q^{3} - 36q^{9} + O(q^{10}) \) \( 8q + 12q^{3} - 36q^{9} + 48q^{17} + 192q^{19} - 192q^{23} - 324q^{25} - 216q^{27} + 192q^{29} + 48q^{31} - 256q^{37} - 2016q^{41} - 224q^{43} + 864q^{47} - 144q^{51} + 648q^{53} - 4704q^{55} + 1152q^{57} + 336q^{59} + 960q^{61} + 360q^{65} - 720q^{67} - 1152q^{69} - 2688q^{71} + 672q^{73} + 972q^{75} + 1984q^{79} - 324q^{81} - 6240q^{83} + 1360q^{85} + 288q^{87} + 2160q^{89} - 144q^{93} + 3744q^{95} - 4032q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 1.50000 2.59808i 0.288675 0.500000i
\(4\) 0 0
\(5\) 4.08470 + 7.07491i 0.365347 + 0.632799i 0.988832 0.149036i \(-0.0476170\pi\)
−0.623485 + 0.781835i \(0.714284\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 0 0
\(11\) −18.9094 + 32.7521i −0.518310 + 0.897739i 0.481464 + 0.876466i \(0.340105\pi\)
−0.999774 + 0.0212729i \(0.993228\pi\)
\(12\) 0 0
\(13\) −39.9319 −0.851933 −0.425966 0.904739i \(-0.640066\pi\)
−0.425966 + 0.904739i \(0.640066\pi\)
\(14\) 0 0
\(15\) 24.5082 0.421866
\(16\) 0 0
\(17\) 4.96798 8.60480i 0.0708772 0.122763i −0.828409 0.560124i \(-0.810753\pi\)
0.899286 + 0.437361i \(0.144087\pi\)
\(18\) 0 0
\(19\) −45.2229 78.3284i −0.546045 0.945777i −0.998540 0.0540105i \(-0.982800\pi\)
0.452496 0.891767i \(-0.350534\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −59.2973 102.706i −0.537580 0.931116i −0.999034 0.0439513i \(-0.986005\pi\)
0.461454 0.887164i \(-0.347328\pi\)
\(24\) 0 0
\(25\) 29.1304 50.4554i 0.233043 0.403643i
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −78.4061 −0.502057 −0.251028 0.967980i \(-0.580769\pi\)
−0.251028 + 0.967980i \(0.580769\pi\)
\(30\) 0 0
\(31\) 46.0055 79.6838i 0.266543 0.461666i −0.701424 0.712744i \(-0.747452\pi\)
0.967967 + 0.251079i \(0.0807853\pi\)
\(32\) 0 0
\(33\) 56.7283 + 98.2563i 0.299246 + 0.518310i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −166.218 287.897i −0.738541 1.27919i −0.953152 0.302491i \(-0.902182\pi\)
0.214611 0.976700i \(-0.431152\pi\)
\(38\) 0 0
\(39\) −59.8979 + 103.746i −0.245932 + 0.425966i
\(40\) 0 0
\(41\) −71.7451 −0.273285 −0.136643 0.990620i \(-0.543631\pi\)
−0.136643 + 0.990620i \(0.543631\pi\)
\(42\) 0 0
\(43\) −115.947 −0.411202 −0.205601 0.978636i \(-0.565915\pi\)
−0.205601 + 0.978636i \(0.565915\pi\)
\(44\) 0 0
\(45\) 36.7623 63.6742i 0.121782 0.210933i
\(46\) 0 0
\(47\) 153.964 + 266.673i 0.477828 + 0.827623i 0.999677 0.0254154i \(-0.00809085\pi\)
−0.521849 + 0.853038i \(0.674758\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −14.9039 25.8144i −0.0409210 0.0708772i
\(52\) 0 0
\(53\) 201.575 349.138i 0.522424 0.904865i −0.477236 0.878775i \(-0.658361\pi\)
0.999660 0.0260895i \(-0.00830548\pi\)
\(54\) 0 0
\(55\) −308.958 −0.757451
\(56\) 0 0
\(57\) −271.337 −0.630518
\(58\) 0 0
\(59\) 296.855 514.168i 0.655038 1.13456i −0.326847 0.945077i \(-0.605986\pi\)
0.981884 0.189481i \(-0.0606806\pi\)
\(60\) 0 0
\(61\) 166.585 + 288.534i 0.349657 + 0.605623i 0.986188 0.165628i \(-0.0529649\pi\)
−0.636532 + 0.771250i \(0.719632\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −163.110 282.515i −0.311251 0.539102i
\(66\) 0 0
\(67\) 371.756 643.900i 0.677869 1.17410i −0.297753 0.954643i \(-0.596237\pi\)
0.975622 0.219460i \(-0.0704295\pi\)
\(68\) 0 0
\(69\) −355.784 −0.620744
\(70\) 0 0
\(71\) −728.272 −1.21732 −0.608662 0.793429i \(-0.708294\pi\)
−0.608662 + 0.793429i \(0.708294\pi\)
\(72\) 0 0
\(73\) −400.874 + 694.335i −0.642723 + 1.11323i 0.342099 + 0.939664i \(0.388862\pi\)
−0.984822 + 0.173566i \(0.944471\pi\)
\(74\) 0 0
\(75\) −87.3912 151.366i −0.134548 0.233043i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −533.953 924.833i −0.760435 1.31711i −0.942626 0.333849i \(-0.891652\pi\)
0.182191 0.983263i \(-0.441681\pi\)
\(80\) 0 0
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −906.756 −1.19915 −0.599575 0.800319i \(-0.704664\pi\)
−0.599575 + 0.800319i \(0.704664\pi\)
\(84\) 0 0
\(85\) 81.1709 0.103579
\(86\) 0 0
\(87\) −117.609 + 203.705i −0.144931 + 0.251028i
\(88\) 0 0
\(89\) 556.634 + 964.119i 0.662957 + 1.14827i 0.979835 + 0.199808i \(0.0640320\pi\)
−0.316878 + 0.948466i \(0.602635\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −138.016 239.051i −0.153889 0.266543i
\(94\) 0 0
\(95\) 369.444 639.896i 0.398991 0.691073i
\(96\) 0 0
\(97\) −1480.94 −1.55017 −0.775084 0.631858i \(-0.782293\pi\)
−0.775084 + 0.631858i \(0.782293\pi\)
\(98\) 0 0
\(99\) 340.370 0.345540
\(100\) 0 0
\(101\) −278.158 + 481.784i −0.274037 + 0.474647i −0.969892 0.243536i \(-0.921693\pi\)
0.695854 + 0.718183i \(0.255026\pi\)
\(102\) 0 0
\(103\) 276.217 + 478.423i 0.264238 + 0.457674i 0.967364 0.253392i \(-0.0815462\pi\)
−0.703126 + 0.711066i \(0.748213\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −266.902 462.288i −0.241144 0.417674i 0.719896 0.694082i \(-0.244189\pi\)
−0.961040 + 0.276408i \(0.910856\pi\)
\(108\) 0 0
\(109\) −547.314 + 947.976i −0.480947 + 0.833025i −0.999761 0.0218626i \(-0.993040\pi\)
0.518814 + 0.854887i \(0.326374\pi\)
\(110\) 0 0
\(111\) −997.306 −0.852794
\(112\) 0 0
\(113\) −1425.18 −1.18646 −0.593228 0.805035i \(-0.702147\pi\)
−0.593228 + 0.805035i \(0.702147\pi\)
\(114\) 0 0
\(115\) 484.423 839.046i 0.392806 0.680360i
\(116\) 0 0
\(117\) 179.694 + 311.239i 0.141989 + 0.245932i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −49.6330 85.9668i −0.0372900 0.0645882i
\(122\) 0 0
\(123\) −107.618 + 186.399i −0.0788907 + 0.136643i
\(124\) 0 0
\(125\) 1497.13 1.07126
\(126\) 0 0
\(127\) −786.485 −0.549522 −0.274761 0.961513i \(-0.588599\pi\)
−0.274761 + 0.961513i \(0.588599\pi\)
\(128\) 0 0
\(129\) −173.920 + 301.238i −0.118704 + 0.205601i
\(130\) 0 0
\(131\) −13.8651 24.0151i −0.00924735 0.0160169i 0.861365 0.507987i \(-0.169610\pi\)
−0.870612 + 0.491970i \(0.836277\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −110.287 191.023i −0.0703110 0.121782i
\(136\) 0 0
\(137\) 1181.49 2046.40i 0.736798 1.27617i −0.217132 0.976142i \(-0.569670\pi\)
0.953930 0.300029i \(-0.0969964\pi\)
\(138\) 0 0
\(139\) −2513.28 −1.53362 −0.766811 0.641873i \(-0.778158\pi\)
−0.766811 + 0.641873i \(0.778158\pi\)
\(140\) 0 0
\(141\) 923.782 0.551748
\(142\) 0 0
\(143\) 755.090 1307.85i 0.441565 0.764813i
\(144\) 0 0
\(145\) −320.266 554.716i −0.183425 0.317701i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1132.92 1962.27i −0.622900 1.07889i −0.988943 0.148296i \(-0.952621\pi\)
0.366043 0.930598i \(-0.380712\pi\)
\(150\) 0 0
\(151\) −141.573 + 245.212i −0.0762984 + 0.132153i −0.901650 0.432466i \(-0.857644\pi\)
0.825352 + 0.564619i \(0.190977\pi\)
\(152\) 0 0
\(153\) −89.4237 −0.0472515
\(154\) 0 0
\(155\) 751.675 0.389522
\(156\) 0 0
\(157\) 96.2904 166.780i 0.0489478 0.0847801i −0.840513 0.541791i \(-0.817747\pi\)
0.889461 + 0.457011i \(0.151080\pi\)
\(158\) 0 0
\(159\) −604.725 1047.41i −0.301622 0.522424i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 421.417 + 729.915i 0.202502 + 0.350744i 0.949334 0.314269i \(-0.101759\pi\)
−0.746832 + 0.665013i \(0.768426\pi\)
\(164\) 0 0
\(165\) −463.436 + 802.695i −0.218657 + 0.378726i
\(166\) 0 0
\(167\) 3859.21 1.78823 0.894116 0.447836i \(-0.147805\pi\)
0.894116 + 0.447836i \(0.147805\pi\)
\(168\) 0 0
\(169\) −602.441 −0.274211
\(170\) 0 0
\(171\) −407.006 + 704.955i −0.182015 + 0.315259i
\(172\) 0 0
\(173\) 755.329 + 1308.27i 0.331946 + 0.574947i 0.982893 0.184176i \(-0.0589616\pi\)
−0.650948 + 0.759123i \(0.725628\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −890.565 1542.50i −0.378186 0.655038i
\(178\) 0 0
\(179\) 1232.31 2134.43i 0.514566 0.891255i −0.485291 0.874353i \(-0.661286\pi\)
0.999857 0.0169022i \(-0.00538039\pi\)
\(180\) 0 0
\(181\) 3297.36 1.35409 0.677047 0.735940i \(-0.263259\pi\)
0.677047 + 0.735940i \(0.263259\pi\)
\(182\) 0 0
\(183\) 999.511 0.403749
\(184\) 0 0
\(185\) 1357.90 2351.95i 0.539647 0.934696i
\(186\) 0 0
\(187\) 187.883 + 325.424i 0.0734727 + 0.127258i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2364.85 + 4096.05i 0.895889 + 1.55173i 0.832700 + 0.553724i \(0.186794\pi\)
0.0631890 + 0.998002i \(0.479873\pi\)
\(192\) 0 0
\(193\) −2276.59 + 3943.17i −0.849080 + 1.47065i 0.0329498 + 0.999457i \(0.489510\pi\)
−0.882030 + 0.471193i \(0.843823\pi\)
\(194\) 0 0
\(195\) −978.660 −0.359402
\(196\) 0 0
\(197\) −3109.06 −1.12442 −0.562212 0.826993i \(-0.690050\pi\)
−0.562212 + 0.826993i \(0.690050\pi\)
\(198\) 0 0
\(199\) −221.756 + 384.092i −0.0789943 + 0.136822i −0.902816 0.430027i \(-0.858504\pi\)
0.823822 + 0.566849i \(0.191838\pi\)
\(200\) 0 0
\(201\) −1115.27 1931.70i −0.391368 0.677869i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −293.057 507.590i −0.0998439 0.172935i
\(206\) 0 0
\(207\) −533.675 + 924.353i −0.179193 + 0.310372i
\(208\) 0 0
\(209\) 3420.56 1.13208
\(210\) 0 0
\(211\) 4653.28 1.51822 0.759112 0.650960i \(-0.225633\pi\)
0.759112 + 0.650960i \(0.225633\pi\)
\(212\) 0 0
\(213\) −1092.41 + 1892.11i −0.351411 + 0.608662i
\(214\) 0 0
\(215\) −473.607 820.311i −0.150231 0.260208i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 1202.62 + 2083.00i 0.371077 + 0.642723i
\(220\) 0 0
\(221\) −198.381 + 343.606i −0.0603826 + 0.104586i
\(222\) 0 0
\(223\) −2778.90 −0.834481 −0.417240 0.908796i \(-0.637003\pi\)
−0.417240 + 0.908796i \(0.637003\pi\)
\(224\) 0 0
\(225\) −524.347 −0.155362
\(226\) 0 0
\(227\) 1608.61 2786.20i 0.470340 0.814653i −0.529084 0.848569i \(-0.677464\pi\)
0.999425 + 0.0339159i \(0.0107978\pi\)
\(228\) 0 0
\(229\) −1864.01 3228.56i −0.537891 0.931655i −0.999017 0.0443203i \(-0.985888\pi\)
0.461126 0.887335i \(-0.347446\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1801.76 + 3120.73i 0.506596 + 0.877451i 0.999971 + 0.00763377i \(0.00242993\pi\)
−0.493374 + 0.869817i \(0.664237\pi\)
\(234\) 0 0
\(235\) −1257.79 + 2178.56i −0.349146 + 0.604739i
\(236\) 0 0
\(237\) −3203.72 −0.878075
\(238\) 0 0
\(239\) 2348.76 0.635684 0.317842 0.948144i \(-0.397042\pi\)
0.317842 + 0.948144i \(0.397042\pi\)
\(240\) 0 0
\(241\) −2546.70 + 4411.01i −0.680693 + 1.17900i 0.294076 + 0.955782i \(0.404988\pi\)
−0.974770 + 0.223213i \(0.928345\pi\)
\(242\) 0 0
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1805.84 + 3127.80i 0.465193 + 0.805738i
\(248\) 0 0
\(249\) −1360.13 + 2355.82i −0.346165 + 0.599575i
\(250\) 0 0
\(251\) 5939.02 1.49350 0.746749 0.665106i \(-0.231614\pi\)
0.746749 + 0.665106i \(0.231614\pi\)
\(252\) 0 0
\(253\) 4485.11 1.11453
\(254\) 0 0
\(255\) 121.756 210.888i 0.0299007 0.0517895i
\(256\) 0 0
\(257\) −757.944 1312.80i −0.183966 0.318638i 0.759262 0.650785i \(-0.225560\pi\)
−0.943228 + 0.332147i \(0.892227\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 352.827 + 611.115i 0.0836761 + 0.144931i
\(262\) 0 0
\(263\) 3216.96 5571.94i 0.754244 1.30639i −0.191505 0.981492i \(-0.561337\pi\)
0.945749 0.324898i \(-0.105330\pi\)
\(264\) 0 0
\(265\) 3293.50 0.763464
\(266\) 0 0
\(267\) 3339.81 0.765516
\(268\) 0 0
\(269\) −3474.90 + 6018.69i −0.787614 + 1.36419i 0.139811 + 0.990178i \(0.455350\pi\)
−0.927425 + 0.374009i \(0.877983\pi\)
\(270\) 0 0
\(271\) −480.997 833.111i −0.107817 0.186745i 0.807068 0.590458i \(-0.201053\pi\)
−0.914886 + 0.403713i \(0.867719\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1101.68 + 1908.16i 0.241577 + 0.418424i
\(276\) 0 0
\(277\) −380.005 + 658.188i −0.0824271 + 0.142768i −0.904292 0.426915i \(-0.859600\pi\)
0.821865 + 0.569682i \(0.192934\pi\)
\(278\) 0 0
\(279\) −828.099 −0.177695
\(280\) 0 0
\(281\) −4412.07 −0.936662 −0.468331 0.883553i \(-0.655145\pi\)
−0.468331 + 0.883553i \(0.655145\pi\)
\(282\) 0 0
\(283\) −1301.07 + 2253.53i −0.273289 + 0.473351i −0.969702 0.244291i \(-0.921445\pi\)
0.696413 + 0.717641i \(0.254778\pi\)
\(284\) 0 0
\(285\) −1108.33 1919.69i −0.230358 0.398991i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2407.14 + 4169.29i 0.489953 + 0.848623i
\(290\) 0 0
\(291\) −2221.41 + 3847.59i −0.447495 + 0.775084i
\(292\) 0 0
\(293\) 9332.18 1.86072 0.930361 0.366644i \(-0.119493\pi\)
0.930361 + 0.366644i \(0.119493\pi\)
\(294\) 0 0
\(295\) 4850.26 0.957264
\(296\) 0 0
\(297\) 510.555 884.306i 0.0997488 0.172770i
\(298\) 0 0
\(299\) 2367.85 + 4101.24i 0.457982 + 0.793248i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 834.474 + 1445.35i 0.158216 + 0.274037i
\(304\) 0 0
\(305\) −1360.90 + 2357.15i −0.255492 + 0.442525i
\(306\) 0 0
\(307\) −4895.51 −0.910103 −0.455051 0.890465i \(-0.650379\pi\)
−0.455051 + 0.890465i \(0.650379\pi\)
\(308\) 0 0
\(309\) 1657.30 0.305116
\(310\) 0 0
\(311\) 3752.64 6499.77i 0.684221 1.18511i −0.289460 0.957190i \(-0.593476\pi\)
0.973681 0.227916i \(-0.0731910\pi\)
\(312\) 0 0
\(313\) −3174.64 5498.63i −0.573294 0.992974i −0.996225 0.0868124i \(-0.972332\pi\)
0.422931 0.906162i \(-0.361001\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3999.80 + 6927.86i 0.708679 + 1.22747i 0.965347 + 0.260968i \(0.0840417\pi\)
−0.256669 + 0.966499i \(0.582625\pi\)
\(318\) 0 0
\(319\) 1482.61 2567.96i 0.260221 0.450716i
\(320\) 0 0
\(321\) −1601.41 −0.278449
\(322\) 0 0
\(323\) −898.666 −0.154808
\(324\) 0 0
\(325\) −1163.23 + 2014.78i −0.198537 + 0.343876i
\(326\) 0 0
\(327\) 1641.94 + 2843.93i 0.277675 + 0.480947i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1060.78 + 1837.32i 0.176150 + 0.305101i 0.940559 0.339631i \(-0.110302\pi\)
−0.764409 + 0.644732i \(0.776969\pi\)
\(332\) 0 0
\(333\) −1495.96 + 2591.08i −0.246180 + 0.426397i
\(334\) 0 0
\(335\) 6074.05 0.990629
\(336\) 0 0
\(337\) −9114.19 −1.47324 −0.736620 0.676307i \(-0.763579\pi\)
−0.736620 + 0.676307i \(0.763579\pi\)
\(338\) 0 0
\(339\) −2137.77 + 3702.72i −0.342500 + 0.593228i
\(340\) 0 0
\(341\) 1739.87 + 3013.55i 0.276303 + 0.478572i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −1453.27 2517.14i −0.226787 0.392806i
\(346\) 0 0
\(347\) 836.534 1448.92i 0.129416 0.224156i −0.794034 0.607873i \(-0.792023\pi\)
0.923451 + 0.383717i \(0.125356\pi\)
\(348\) 0 0
\(349\) 3467.56 0.531845 0.265923 0.963994i \(-0.414323\pi\)
0.265923 + 0.963994i \(0.414323\pi\)
\(350\) 0 0
\(351\) 1078.16 0.163955
\(352\) 0 0
\(353\) 1992.12 3450.45i 0.300368 0.520252i −0.675851 0.737038i \(-0.736224\pi\)
0.976219 + 0.216785i \(0.0695572\pi\)
\(354\) 0 0
\(355\) −2974.78 5152.46i −0.444746 0.770322i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1085.47 1880.08i −0.159579 0.276398i 0.775138 0.631792i \(-0.217680\pi\)
−0.934717 + 0.355394i \(0.884347\pi\)
\(360\) 0 0
\(361\) −660.724 + 1144.41i −0.0963295 + 0.166848i
\(362\) 0 0
\(363\) −297.798 −0.0430588
\(364\) 0 0
\(365\) −6549.81 −0.939268
\(366\) 0 0
\(367\) 1796.06 3110.86i 0.255459 0.442468i −0.709561 0.704644i \(-0.751107\pi\)
0.965020 + 0.262176i \(0.0844400\pi\)
\(368\) 0 0
\(369\) 322.853 + 559.197i 0.0455475 + 0.0788907i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −3719.90 6443.05i −0.516378 0.894393i −0.999819 0.0190163i \(-0.993947\pi\)
0.483441 0.875377i \(-0.339387\pi\)
\(374\) 0 0
\(375\) 2245.70 3889.66i 0.309246 0.535630i
\(376\) 0 0
\(377\) 3130.91 0.427719
\(378\) 0 0
\(379\) 11243.9 1.52390 0.761951 0.647635i \(-0.224242\pi\)
0.761951 + 0.647635i \(0.224242\pi\)
\(380\) 0 0
\(381\) −1179.73 + 2043.35i −0.158633 + 0.274761i
\(382\) 0 0
\(383\) 1770.62 + 3066.81i 0.236226 + 0.409156i 0.959628 0.281271i \(-0.0907561\pi\)
−0.723402 + 0.690427i \(0.757423\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 521.759 + 903.714i 0.0685336 + 0.118704i
\(388\) 0 0
\(389\) 5279.10 9143.66i 0.688074 1.19178i −0.284386 0.958710i \(-0.591790\pi\)
0.972460 0.233070i \(-0.0748770\pi\)
\(390\) 0 0
\(391\) −1178.35 −0.152409
\(392\) 0 0
\(393\) −83.1908 −0.0106779
\(394\) 0 0
\(395\) 4362.08 7555.34i 0.555645 0.962406i
\(396\) 0 0
\(397\) −270.287 468.151i −0.0341696 0.0591834i 0.848435 0.529300i \(-0.177545\pi\)
−0.882604 + 0.470116i \(0.844212\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1083.52 1876.70i −0.134933 0.233711i 0.790639 0.612283i \(-0.209749\pi\)
−0.925572 + 0.378572i \(0.876415\pi\)
\(402\) 0 0
\(403\) −1837.09 + 3181.93i −0.227077 + 0.393308i
\(404\) 0 0
\(405\) −661.722 −0.0811882
\(406\) 0 0
\(407\) 12572.3 1.53117
\(408\) 0 0
\(409\) −478.845 + 829.384i −0.0578908 + 0.100270i −0.893518 0.449027i \(-0.851771\pi\)
0.835628 + 0.549296i \(0.185104\pi\)
\(410\) 0 0
\(411\) −3544.46 6139.19i −0.425390 0.736798i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −3703.83 6415.22i −0.438105 0.758821i
\(416\) 0 0
\(417\) −3769.92 + 6529.69i −0.442719 + 0.766811i
\(418\) 0 0
\(419\) −6464.42 −0.753718 −0.376859 0.926271i \(-0.622996\pi\)
−0.376859 + 0.926271i \(0.622996\pi\)
\(420\) 0 0
\(421\) −6201.23 −0.717885 −0.358943 0.933360i \(-0.616863\pi\)
−0.358943 + 0.933360i \(0.616863\pi\)
\(422\) 0 0
\(423\) 1385.67 2400.06i 0.159276 0.275874i
\(424\) 0 0
\(425\) −289.439 501.322i −0.0330349 0.0572181i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −2265.27 3923.56i −0.254938 0.441565i
\(430\) 0 0
\(431\) −707.796 + 1225.94i −0.0791029 + 0.137010i −0.902863 0.429928i \(-0.858539\pi\)
0.823760 + 0.566938i \(0.191872\pi\)
\(432\) 0 0
\(433\) −8905.73 −0.988411 −0.494206 0.869345i \(-0.664541\pi\)
−0.494206 + 0.869345i \(0.664541\pi\)
\(434\) 0 0
\(435\) −1921.59 −0.211801
\(436\) 0 0
\(437\) −5363.19 + 9289.32i −0.587085 + 1.01686i
\(438\) 0 0
\(439\) 5438.25 + 9419.33i 0.591238 + 1.02405i 0.994066 + 0.108779i \(0.0346940\pi\)
−0.402828 + 0.915276i \(0.631973\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5701.48 9875.25i −0.611479 1.05911i −0.990991 0.133927i \(-0.957241\pi\)
0.379512 0.925187i \(-0.376092\pi\)
\(444\) 0 0
\(445\) −4547.37 + 7876.28i −0.484418 + 0.839037i
\(446\) 0 0
\(447\) −6797.49 −0.719262
\(448\) 0 0
\(449\) −12689.0 −1.33370 −0.666852 0.745190i \(-0.732359\pi\)
−0.666852 + 0.745190i \(0.732359\pi\)
\(450\) 0 0
\(451\) 1356.66 2349.80i 0.141646 0.245339i
\(452\) 0 0
\(453\) 424.720 + 735.636i 0.0440509 + 0.0762984i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1135.02 1965.92i −0.116180 0.201229i 0.802071 0.597229i \(-0.203732\pi\)
−0.918251 + 0.395999i \(0.870398\pi\)
\(458\) 0 0
\(459\) −134.135 + 232.329i −0.0136403 + 0.0236257i
\(460\) 0 0
\(461\) −10731.2 −1.08417 −0.542085 0.840324i \(-0.682365\pi\)
−0.542085 + 0.840324i \(0.682365\pi\)
\(462\) 0 0
\(463\) −3307.74 −0.332017 −0.166008 0.986124i \(-0.553088\pi\)
−0.166008 + 0.986124i \(0.553088\pi\)
\(464\) 0 0
\(465\) 1127.51 1952.91i 0.112445 0.194761i
\(466\) 0 0
\(467\) −4623.35 8007.87i −0.458122 0.793490i 0.540740 0.841190i \(-0.318144\pi\)
−0.998862 + 0.0476996i \(0.984811\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −288.871 500.339i −0.0282600 0.0489478i
\(472\) 0 0
\(473\) 2192.48 3797.49i 0.213130 0.369152i
\(474\) 0 0
\(475\) −5269.45 −0.509008
\(476\) 0 0
\(477\) −3628.35 −0.348283
\(478\) 0 0
\(479\) 7611.66 13183.8i 0.726066 1.25758i −0.232468 0.972604i \(-0.574680\pi\)
0.958534 0.284978i \(-0.0919865\pi\)
\(480\) 0 0
\(481\) 6637.39 + 11496.3i 0.629187 + 1.08978i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6049.19 10477.5i −0.566349 0.980946i
\(486\) 0 0
\(487\) 3879.36 6719.25i 0.360966 0.625212i −0.627154 0.778895i \(-0.715780\pi\)
0.988120 + 0.153683i \(0.0491136\pi\)
\(488\) 0 0
\(489\) 2528.50 0.233830
\(490\) 0 0
\(491\) −8342.30 −0.766767 −0.383384 0.923589i \(-0.625241\pi\)
−0.383384 + 0.923589i \(0.625241\pi\)
\(492\) 0 0
\(493\) −389.520 + 674.668i −0.0355844 + 0.0616340i
\(494\) 0 0
\(495\) 1390.31 + 2408.09i 0.126242 + 0.218657i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 1293.47 + 2240.36i 0.116040 + 0.200987i 0.918195 0.396129i \(-0.129647\pi\)
−0.802155 + 0.597116i \(0.796313\pi\)
\(500\) 0 0
\(501\) 5788.82 10026.5i 0.516218 0.894116i
\(502\) 0 0
\(503\) −409.682 −0.0363157 −0.0181578 0.999835i \(-0.505780\pi\)
−0.0181578 + 0.999835i \(0.505780\pi\)
\(504\) 0 0
\(505\) −4544.77 −0.400475
\(506\) 0 0
\(507\) −903.662 + 1565.19i −0.0791578 + 0.137105i
\(508\) 0 0
\(509\) 2195.25 + 3802.29i 0.191165 + 0.331107i 0.945637 0.325225i \(-0.105440\pi\)
−0.754472 + 0.656333i \(0.772107\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 1221.02 + 2114.87i 0.105086 + 0.182015i
\(514\) 0 0
\(515\) −2256.53 + 3908.43i −0.193077 + 0.334419i
\(516\) 0 0
\(517\) −11645.5 −0.990652
\(518\) 0 0
\(519\) 4531.98 0.383298
\(520\) 0 0
\(521\) −9714.76 + 16826.5i −0.816912 + 1.41493i 0.0910341 + 0.995848i \(0.470983\pi\)
−0.907947 + 0.419086i \(0.862351\pi\)
\(522\) 0 0
\(523\) 8974.35 + 15544.0i 0.750326 + 1.29960i 0.947664 + 0.319268i \(0.103437\pi\)
−0.197338 + 0.980336i \(0.563230\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −457.109 791.735i −0.0377836 0.0654431i
\(528\) 0 0
\(529\) −948.833 + 1643.43i −0.0779841 + 0.135072i
\(530\) 0 0
\(531\) −5343.39 −0.436692
\(532\) 0 0
\(533\) 2864.92 0.232821
\(534\) 0 0
\(535\) 2180.43 3776.62i 0.176202 0.305192i
\(536\) 0 0
\(537\) −3696.94 6403.28i −0.297085 0.514566i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −11547.0 20000.0i −0.917641 1.58940i −0.802989 0.595994i \(-0.796758\pi\)
−0.114652 0.993406i \(-0.536575\pi\)
\(542\) 0 0
\(543\) 4946.04 8566.80i 0.390893 0.677047i
\(544\) 0 0
\(545\) −8942.47 −0.702850
\(546\) 0 0
\(547\) −2266.68 −0.177178 −0.0885889 0.996068i \(-0.528236\pi\)
−0.0885889 + 0.996068i \(0.528236\pi\)
\(548\) 0 0
\(549\) 1499.27 2596.81i 0.116552 0.201874i
\(550\) 0 0
\(551\) 3545.75 + 6141.42i 0.274145 + 0.474834i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −4073.70 7055.85i −0.311565 0.539647i
\(556\) 0 0
\(557\) 5519.27 9559.65i 0.419854 0.727209i −0.576070 0.817400i \(-0.695415\pi\)
0.995924 + 0.0901913i \(0.0287478\pi\)
\(558\) 0 0
\(559\) 4629.97 0.350316
\(560\) 0 0
\(561\) 1127.30 0.0848390
\(562\) 0 0
\(563\) −3529.68 + 6113.58i −0.264224 + 0.457650i −0.967360 0.253406i \(-0.918449\pi\)
0.703136 + 0.711055i \(0.251783\pi\)
\(564\) 0 0
\(565\) −5821.43 10083.0i −0.433468 0.750788i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 676.403 + 1171.56i 0.0498353 + 0.0863172i 0.889867 0.456220i \(-0.150797\pi\)
−0.840032 + 0.542537i \(0.817464\pi\)
\(570\) 0 0
\(571\) 10419.6 18047.3i 0.763655 1.32269i −0.177300 0.984157i \(-0.556736\pi\)
0.940955 0.338532i \(-0.109930\pi\)
\(572\) 0 0
\(573\) 14189.1 1.03448
\(574\) 0 0
\(575\) −6909.42 −0.501117
\(576\) 0 0
\(577\) 5007.32 8672.92i 0.361278 0.625751i −0.626894 0.779105i \(-0.715674\pi\)
0.988171 + 0.153353i \(0.0490073\pi\)
\(578\) 0 0
\(579\) 6829.77 + 11829.5i 0.490217 + 0.849080i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 7623.34 + 13204.0i 0.541555 + 0.938001i
\(584\) 0 0
\(585\) −1467.99 + 2542.63i −0.103750 + 0.179701i
\(586\) 0 0
\(587\) −20864.8 −1.46709 −0.733546 0.679640i \(-0.762136\pi\)
−0.733546 + 0.679640i \(0.762136\pi\)
\(588\) 0 0
\(589\) −8322.01 −0.582177
\(590\) 0 0
\(591\) −4663.60 + 8077.59i −0.324593 + 0.562212i
\(592\) 0 0
\(593\) 8773.84 + 15196.7i 0.607586 + 1.05237i 0.991637 + 0.129058i \(0.0411952\pi\)
−0.384051 + 0.923312i \(0.625471\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 665.268 + 1152.28i 0.0456074 + 0.0789943i
\(598\) 0 0
\(599\) 65.3409 113.174i 0.00445703 0.00771980i −0.863788 0.503855i \(-0.831915\pi\)
0.868245 + 0.496135i \(0.165248\pi\)
\(600\) 0 0
\(601\) 5964.47 0.404818 0.202409 0.979301i \(-0.435123\pi\)
0.202409 + 0.979301i \(0.435123\pi\)
\(602\) 0 0
\(603\) −6691.60 −0.451912
\(604\) 0 0
\(605\) 405.472 702.298i 0.0272476 0.0471942i
\(606\) 0 0
\(607\) −4955.82 8583.73i −0.331384 0.573975i 0.651399 0.758735i \(-0.274182\pi\)
−0.982784 + 0.184761i \(0.940849\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6148.07 10648.8i −0.407077 0.705079i
\(612\) 0 0
\(613\) 3241.26 5614.03i 0.213562 0.369900i −0.739265 0.673415i \(-0.764827\pi\)
0.952827 + 0.303515i \(0.0981602\pi\)
\(614\) 0 0
\(615\) −1758.34 −0.115290
\(616\) 0 0
\(617\) 7189.36 0.469097 0.234548 0.972104i \(-0.424639\pi\)
0.234548 + 0.972104i \(0.424639\pi\)
\(618\) 0 0
\(619\) 930.696 1612.01i 0.0604327 0.104672i −0.834226 0.551422i \(-0.814085\pi\)
0.894659 + 0.446750i \(0.147419\pi\)
\(620\) 0 0
\(621\) 1601.03 + 2773.06i 0.103457 + 0.179193i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 2474.04 + 4285.16i 0.158338 + 0.274250i
\(626\) 0 0
\(627\) 5130.84 8886.87i 0.326804 0.566041i
\(628\) 0 0
\(629\) −3303.06 −0.209383
\(630\) 0 0
\(631\) −29032.0 −1.83161 −0.915803 0.401627i \(-0.868445\pi\)
−0.915803 + 0.401627i \(0.868445\pi\)
\(632\) 0 0
\(633\) 6979.93 12089.6i 0.438274 0.759112i
\(634\) 0 0
\(635\) −3212.56 5564.32i −0.200766 0.347737i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 3277.23 + 5676.32i 0.202887 + 0.351411i
\(640\) 0 0
\(641\) −12228.9 + 21181.0i −0.753527 + 1.30515i 0.192576 + 0.981282i \(0.438316\pi\)
−0.946103 + 0.323866i \(0.895017\pi\)
\(642\) 0 0
\(643\) −10968.2 −0.672695 −0.336348 0.941738i \(-0.609192\pi\)
−0.336348 + 0.941738i \(0.609192\pi\)
\(644\) 0 0
\(645\) −2841.64 −0.173472
\(646\) 0 0
\(647\) 2742.37 4749.92i 0.166636 0.288622i −0.770599 0.637320i \(-0.780043\pi\)
0.937235 + 0.348698i \(0.113376\pi\)
\(648\) 0 0
\(649\) 11226.7 + 19445.2i 0.679025 + 1.17611i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 5164.98 + 8946.01i 0.309527 + 0.536117i 0.978259 0.207387i \(-0.0664959\pi\)
−0.668732 + 0.743504i \(0.733163\pi\)
\(654\) 0 0
\(655\) 113.270 196.189i 0.00675698 0.0117034i
\(656\) 0 0
\(657\) 7215.74 0.428482
\(658\) 0 0
\(659\) 26822.2 1.58550 0.792751 0.609546i \(-0.208648\pi\)
0.792751 + 0.609546i \(0.208648\pi\)
\(660\) 0 0
\(661\) 1249.38 2163.99i 0.0735177 0.127336i −0.826923 0.562315i \(-0.809911\pi\)
0.900441 + 0.434979i \(0.143244\pi\)
\(662\) 0 0
\(663\) 595.143 + 1030.82i 0.0348619 + 0.0603826i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 4649.27 + 8052.77i 0.269896 + 0.467473i
\(668\) 0 0
\(669\) −4168.36 + 7219.81i −0.240894 + 0.417240i
\(670\) 0 0
\(671\) −12600.1 −0.724922
\(672\) 0 0
\(673\) 10092.1 0.578044 0.289022 0.957322i \(-0.406670\pi\)
0.289022 + 0.957322i \(0.406670\pi\)
\(674\) 0 0
\(675\) −786.521 + 1362.29i −0.0448492 + 0.0776811i
\(676\) 0 0
\(677\) −13183.2 22833.9i −0.748406 1.29628i −0.948586 0.316518i \(-0.897486\pi\)
0.200181 0.979759i \(-0.435847\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −4825.83 8358.59i −0.271551 0.470340i
\(682\) 0 0
\(683\) −11285.4 + 19546.9i −0.632245 + 1.09508i 0.354847 + 0.934924i \(0.384533\pi\)
−0.987092 + 0.160155i \(0.948800\pi\)
\(684\) 0 0
\(685\) 19304.1 1.07675
\(686\) 0 0
\(687\) −11184.0 −0.621103
\(688\) 0 0
\(689\) −8049.28 + 13941.8i −0.445070 + 0.770884i
\(690\) 0 0
\(691\) −5965.75 10333.0i −0.328434 0.568864i 0.653768 0.756695i \(-0.273187\pi\)
−0.982201 + 0.187832i \(0.939854\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −10266.0 17781.2i −0.560304 0.970475i
\(696\) 0 0
\(697\) −356.428 + 617.352i −0.0193697 + 0.0335493i
\(698\) 0 0
\(699\) 10810.5 0.584967
\(700\) 0 0
\(701\) 16592.6 0.893997 0.446999 0.894535i \(-0.352493\pi\)
0.446999 + 0.894535i \(0.352493\pi\)
\(702\) 0 0
\(703\) −15033.7 + 26039.1i −0.806553 + 1.39699i
\(704\) 0 0
\(705\) 3773.38 + 6535.68i 0.201580 + 0.349146i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −9357.00 16206.8i −0.495641 0.858476i 0.504346 0.863502i \(-0.331734\pi\)
−0.999987 + 0.00502575i \(0.998400\pi\)
\(710\) 0 0
\(711\) −4805.57 + 8323.50i −0.253478 + 0.439037i
\(712\) 0 0
\(713\) −10912.0 −0.573152
\(714\) 0 0
\(715\) 12337.3 0.645298
\(716\) 0 0
\(717\) 3523.14 6102.25i 0.183506 0.317842i
\(718\) 0 0
\(719\) −12427.4 21524.9i −0.644594 1.11647i −0.984395 0.175972i \(-0.943693\pi\)
0.339801 0.940497i \(-0.389640\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 7640.09 + 13233.0i 0.392998 + 0.680693i
\(724\) 0 0
\(725\) −2284.00 + 3956.01i −0.117001 + 0.202652i
\(726\) 0 0
\(727\) 22506.0 1.14814 0.574071 0.818805i \(-0.305363\pi\)
0.574071 + 0.818805i \(0.305363\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −576.020 + 997.696i −0.0291448 + 0.0504803i
\(732\) 0 0
\(733\) −11896.0 20604.5i −0.599440 1.03826i −0.992904 0.118920i \(-0.962057\pi\)
0.393464 0.919340i \(-0.371277\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 14059.4 + 24351.6i 0.702692 + 1.21710i
\(738\) 0 0
\(739\) −2401.62 + 4159.72i −0.119547 + 0.207061i −0.919588 0.392884i \(-0.871477\pi\)
0.800041 + 0.599945i \(0.204811\pi\)
\(740\) 0 0
\(741\) 10835.0 0.537159
\(742\) 0 0
\(743\) 5076.10 0.250638 0.125319 0.992116i \(-0.460005\pi\)
0.125319 + 0.992116i \(0.460005\pi\)
\(744\) 0 0
\(745\) 9255.24 16030.6i 0.455149 0.788341i
\(746\) 0 0
\(747\) 4080.40 + 7067.46i 0.199858 + 0.346165i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 4579.36 + 7931.68i 0.222508 + 0.385394i 0.955569 0.294768i \(-0.0952425\pi\)
−0.733061 + 0.680163i \(0.761909\pi\)
\(752\) 0 0
\(753\) 8908.54 15430.0i 0.431136 0.746749i
\(754\) 0 0
\(755\) −2313.14 −0.111502
\(756\) 0 0
\(757\) 33682.2 1.61717 0.808587 0.588377i \(-0.200233\pi\)
0.808587 + 0.588377i \(0.200233\pi\)
\(758\) 0 0
\(759\) 6727.67 11652.7i 0.321738 0.557266i
\(760\) 0 0
\(761\) 6673.14 + 11558.2i 0.317873 + 0.550571i 0.980044 0.198781i \(-0.0636983\pi\)
−0.662171 + 0.749352i \(0.730365\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −365.269 632.665i −0.0172632 0.0299007i
\(766\) 0 0
\(767\) −11854.0 + 20531.7i −0.558048 + 0.966568i
\(768\) 0 0
\(769\) 15530.6 0.728281 0.364140 0.931344i \(-0.381363\pi\)
0.364140 + 0.931344i \(0.381363\pi\)
\(770\) 0 0
\(771\) −4547.66 −0.212425
\(772\) 0 0
\(773\) −5507.62 + 9539.47i −0.256268 + 0.443869i −0.965239 0.261368i \(-0.915826\pi\)
0.708971 + 0.705238i \(0.249160\pi\)
\(774\) 0 0
\(775\) −2680.32 4642.45i −0.124232 0.215176i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3244.52 + 5619.67i 0.149226 + 0.258467i
\(780\) 0 0
\(781\) 13771.2 23852.4i 0.630951 1.09284i
\(782\) 0 0
\(783\) 2116.96 0.0966209
\(784\) 0 0
\(785\) 1573.27 0.0715317
\(786\) 0 0
\(787\) 10596.3 18353.3i 0.479946 0.831291i −0.519789 0.854294i \(-0.673990\pi\)
0.999735 + 0.0230036i \(0.00732292\pi\)
\(788\) 0 0
\(789\) −9650.88 16715.8i −0.435463 0.754244i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −6652.07 11521.7i −0.297884 0.515950i
\(794\) 0 0
\(795\) 4940.25 8556.76i 0.220393 0.381732i
\(796\) 0 0
\(797\) −18189.9 −0.808432 −0.404216 0.914663i \(-0.632456\pi\)
−0.404216 + 0.914663i \(0.632456\pi\)