Properties

Label 855.2.c.d.514.1
Level $855$
Weight $2$
Character 855.514
Analytic conductor $6.827$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.16516096.1
Defining polynomial: \(x^{6} + 9 x^{4} + 13 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 514.1
Root \(1.30397i\) of defining polynomial
Character \(\chi\) \(=\) 855.514
Dual form 855.2.c.d.514.6

$q$-expansion

\(f(q)\) \(=\) \(q-2.41987i q^{2} -3.85577 q^{4} +(2.07772 + 0.826491i) q^{5} +3.18676i q^{7} +4.49073i q^{8} +O(q^{10})\) \(q-2.41987i q^{2} -3.85577 q^{4} +(2.07772 + 0.826491i) q^{5} +3.18676i q^{7} +4.49073i q^{8} +(2.00000 - 5.02781i) q^{10} -4.15544 q^{11} +2.07086i q^{13} +7.71155 q^{14} +3.15544 q^{16} +5.79470i q^{17} +1.00000 q^{19} +(-8.01121 - 3.18676i) q^{20} +10.0556i q^{22} +2.60794i q^{23} +(3.63383 + 3.43443i) q^{25} +5.01121 q^{26} -12.2874i q^{28} +6.00000 q^{29} +2.59933 q^{31} +1.34571i q^{32} +14.0224 q^{34} +(-2.63383 + 6.62119i) q^{35} -4.30266i q^{37} -2.41987i q^{38} +(-3.71155 + 9.33047i) q^{40} +0.599328 q^{41} +3.18676i q^{43} +16.0224 q^{44} +6.31087 q^{46} +11.7086i q^{47} -3.15544 q^{49} +(8.31087 - 8.79339i) q^{50} -7.98476i q^{52} -11.7503i q^{53} +(-8.63383 - 3.43443i) q^{55} -14.3109 q^{56} -14.5192i q^{58} -1.71155 q^{59} -8.75476 q^{61} -6.29004i q^{62} +9.56732 q^{64} +(-1.71155 + 4.30266i) q^{65} -4.76228i q^{67} -22.3430i q^{68} +(16.0224 + 6.37352i) q^{70} -13.7115 q^{71} -2.72714i q^{73} -10.4119 q^{74} -3.85577 q^{76} -13.2424i q^{77} +1.40067 q^{79} +(6.55611 + 2.60794i) q^{80} -1.45030i q^{82} +7.07154i q^{83} +(-4.78926 + 12.0398i) q^{85} +7.71155 q^{86} -18.6609i q^{88} +16.5353 q^{89} -6.59933 q^{91} -10.0556i q^{92} +28.3333 q^{94} +(2.07772 + 0.826491i) q^{95} -2.07086i q^{97} +7.63575i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 8 q^{4} + q^{5} + O(q^{10}) \) \( 6 q - 8 q^{4} + q^{5} + 12 q^{10} - 2 q^{11} + 16 q^{14} - 4 q^{16} + 6 q^{19} - 10 q^{20} + 3 q^{25} - 8 q^{26} + 36 q^{29} + 8 q^{34} + 3 q^{35} + 8 q^{40} - 12 q^{41} + 20 q^{44} - 8 q^{46} + 4 q^{49} + 4 q^{50} - 33 q^{55} - 40 q^{56} + 20 q^{59} - 14 q^{61} + 12 q^{64} + 20 q^{65} + 20 q^{70} - 52 q^{71} - 40 q^{74} - 8 q^{76} + 24 q^{79} + 32 q^{80} + 13 q^{85} + 16 q^{86} + 24 q^{89} - 24 q^{91} + 48 q^{94} + q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.41987i 1.71111i −0.517715 0.855553i \(-0.673217\pi\)
0.517715 0.855553i \(-0.326783\pi\)
\(3\) 0 0
\(4\) −3.85577 −1.92789
\(5\) 2.07772 + 0.826491i 0.929184 + 0.369618i
\(6\) 0 0
\(7\) 3.18676i 1.20448i 0.798314 + 0.602241i \(0.205725\pi\)
−0.798314 + 0.602241i \(0.794275\pi\)
\(8\) 4.49073i 1.58771i
\(9\) 0 0
\(10\) 2.00000 5.02781i 0.632456 1.58993i
\(11\) −4.15544 −1.25291 −0.626456 0.779457i \(-0.715495\pi\)
−0.626456 + 0.779457i \(0.715495\pi\)
\(12\) 0 0
\(13\) 2.07086i 0.574353i 0.957878 + 0.287176i \(0.0927166\pi\)
−0.957878 + 0.287176i \(0.907283\pi\)
\(14\) 7.71155 2.06100
\(15\) 0 0
\(16\) 3.15544 0.788859
\(17\) 5.79470i 1.40542i 0.711476 + 0.702710i \(0.248027\pi\)
−0.711476 + 0.702710i \(0.751973\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) −8.01121 3.18676i −1.79136 0.712581i
\(21\) 0 0
\(22\) 10.0556i 2.14386i
\(23\) 2.60794i 0.543793i 0.962327 + 0.271896i \(0.0876508\pi\)
−0.962327 + 0.271896i \(0.912349\pi\)
\(24\) 0 0
\(25\) 3.63383 + 3.43443i 0.726765 + 0.686886i
\(26\) 5.01121 0.982779
\(27\) 0 0
\(28\) 12.2874i 2.32210i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 2.59933 0.466853 0.233427 0.972374i \(-0.425006\pi\)
0.233427 + 0.972374i \(0.425006\pi\)
\(32\) 1.34571i 0.237890i
\(33\) 0 0
\(34\) 14.0224 2.40482
\(35\) −2.63383 + 6.62119i −0.445198 + 1.11919i
\(36\) 0 0
\(37\) 4.30266i 0.707353i −0.935368 0.353677i \(-0.884931\pi\)
0.935368 0.353677i \(-0.115069\pi\)
\(38\) 2.41987i 0.392555i
\(39\) 0 0
\(40\) −3.71155 + 9.33047i −0.586847 + 1.47528i
\(41\) 0.599328 0.0935993 0.0467997 0.998904i \(-0.485098\pi\)
0.0467997 + 0.998904i \(0.485098\pi\)
\(42\) 0 0
\(43\) 3.18676i 0.485976i 0.970029 + 0.242988i \(0.0781276\pi\)
−0.970029 + 0.242988i \(0.921872\pi\)
\(44\) 16.0224 2.41547
\(45\) 0 0
\(46\) 6.31087 0.930487
\(47\) 11.7086i 1.70787i 0.520376 + 0.853937i \(0.325792\pi\)
−0.520376 + 0.853937i \(0.674208\pi\)
\(48\) 0 0
\(49\) −3.15544 −0.450777
\(50\) 8.31087 8.79339i 1.17533 1.24357i
\(51\) 0 0
\(52\) 7.98476i 1.10729i
\(53\) 11.7503i 1.61403i −0.590529 0.807017i \(-0.701081\pi\)
0.590529 0.807017i \(-0.298919\pi\)
\(54\) 0 0
\(55\) −8.63383 3.43443i −1.16418 0.463098i
\(56\) −14.3109 −1.91237
\(57\) 0 0
\(58\) 14.5192i 1.90647i
\(59\) −1.71155 −0.222824 −0.111412 0.993774i \(-0.535537\pi\)
−0.111412 + 0.993774i \(0.535537\pi\)
\(60\) 0 0
\(61\) −8.75476 −1.12093 −0.560466 0.828177i \(-0.689378\pi\)
−0.560466 + 0.828177i \(0.689378\pi\)
\(62\) 6.29004i 0.798836i
\(63\) 0 0
\(64\) 9.56732 1.19591
\(65\) −1.71155 + 4.30266i −0.212291 + 0.533679i
\(66\) 0 0
\(67\) 4.76228i 0.581805i −0.956753 0.290902i \(-0.906044\pi\)
0.956753 0.290902i \(-0.0939555\pi\)
\(68\) 22.3430i 2.70949i
\(69\) 0 0
\(70\) 16.0224 + 6.37352i 1.91505 + 0.761781i
\(71\) −13.7115 −1.62726 −0.813631 0.581382i \(-0.802512\pi\)
−0.813631 + 0.581382i \(0.802512\pi\)
\(72\) 0 0
\(73\) 2.72714i 0.319188i −0.987183 0.159594i \(-0.948982\pi\)
0.987183 0.159594i \(-0.0510185\pi\)
\(74\) −10.4119 −1.21036
\(75\) 0 0
\(76\) −3.85577 −0.442287
\(77\) 13.2424i 1.50911i
\(78\) 0 0
\(79\) 1.40067 0.157588 0.0787939 0.996891i \(-0.474893\pi\)
0.0787939 + 0.996891i \(0.474893\pi\)
\(80\) 6.55611 + 2.60794i 0.732995 + 0.291576i
\(81\) 0 0
\(82\) 1.45030i 0.160158i
\(83\) 7.07154i 0.776203i 0.921617 + 0.388101i \(0.126869\pi\)
−0.921617 + 0.388101i \(0.873131\pi\)
\(84\) 0 0
\(85\) −4.78926 + 12.0398i −0.519469 + 1.30589i
\(86\) 7.71155 0.831557
\(87\) 0 0
\(88\) 18.6609i 1.98926i
\(89\) 16.5353 1.75274 0.876370 0.481639i \(-0.159958\pi\)
0.876370 + 0.481639i \(0.159958\pi\)
\(90\) 0 0
\(91\) −6.59933 −0.691798
\(92\) 10.0556i 1.04837i
\(93\) 0 0
\(94\) 28.3333 2.92236
\(95\) 2.07772 + 0.826491i 0.213169 + 0.0847961i
\(96\) 0 0
\(97\) 2.07086i 0.210264i −0.994458 0.105132i \(-0.966474\pi\)
0.994458 0.105132i \(-0.0335265\pi\)
\(98\) 7.63575i 0.771327i
\(99\) 0 0
\(100\) −14.0112 13.2424i −1.40112 1.32424i
\(101\) 1.71155 0.170305 0.0851525 0.996368i \(-0.472862\pi\)
0.0851525 + 0.996368i \(0.472862\pi\)
\(102\) 0 0
\(103\) 5.75296i 0.566856i 0.958994 + 0.283428i \(0.0914716\pi\)
−0.958994 + 0.283428i \(0.908528\pi\)
\(104\) −9.29966 −0.911907
\(105\) 0 0
\(106\) −28.4343 −2.76178
\(107\) 15.4324i 1.49191i −0.665996 0.745955i \(-0.731993\pi\)
0.665996 0.745955i \(-0.268007\pi\)
\(108\) 0 0
\(109\) −11.7115 −1.12176 −0.560881 0.827896i \(-0.689538\pi\)
−0.560881 + 0.827896i \(0.689538\pi\)
\(110\) −8.31087 + 20.8927i −0.792411 + 1.99204i
\(111\) 0 0
\(112\) 10.0556i 0.950167i
\(113\) 10.5927i 0.996477i 0.867040 + 0.498239i \(0.166020\pi\)
−0.867040 + 0.498239i \(0.833980\pi\)
\(114\) 0 0
\(115\) −2.15544 + 5.41856i −0.200996 + 0.505283i
\(116\) −23.1346 −2.14800
\(117\) 0 0
\(118\) 4.14172i 0.381276i
\(119\) −18.4663 −1.69280
\(120\) 0 0
\(121\) 6.26765 0.569787
\(122\) 21.1854i 1.91804i
\(123\) 0 0
\(124\) −10.0224 −0.900040
\(125\) 4.71155 + 10.1391i 0.421413 + 0.906869i
\(126\) 0 0
\(127\) 6.07484i 0.539055i 0.962993 + 0.269528i \(0.0868676\pi\)
−0.962993 + 0.269528i \(0.913132\pi\)
\(128\) 20.4602i 1.80845i
\(129\) 0 0
\(130\) 10.4119 + 4.14172i 0.913182 + 0.363253i
\(131\) 13.5785 1.18636 0.593181 0.805069i \(-0.297872\pi\)
0.593181 + 0.805069i \(0.297872\pi\)
\(132\) 0 0
\(133\) 3.18676i 0.276327i
\(134\) −11.5241 −0.995530
\(135\) 0 0
\(136\) −26.0224 −2.23140
\(137\) 7.94302i 0.678618i −0.940675 0.339309i \(-0.889807\pi\)
0.940675 0.339309i \(-0.110193\pi\)
\(138\) 0 0
\(139\) −3.26765 −0.277159 −0.138579 0.990351i \(-0.544254\pi\)
−0.138579 + 0.990351i \(0.544254\pi\)
\(140\) 10.1554 25.5298i 0.858291 2.15766i
\(141\) 0 0
\(142\) 33.1802i 2.78442i
\(143\) 8.60532i 0.719613i
\(144\) 0 0
\(145\) 12.4663 + 4.95894i 1.03527 + 0.411818i
\(146\) −6.59933 −0.546164
\(147\) 0 0
\(148\) 16.5901i 1.36370i
\(149\) 8.44389 0.691751 0.345875 0.938280i \(-0.387582\pi\)
0.345875 + 0.938280i \(0.387582\pi\)
\(150\) 0 0
\(151\) 0.887783 0.0722468 0.0361234 0.999347i \(-0.488499\pi\)
0.0361234 + 0.999347i \(0.488499\pi\)
\(152\) 4.49073i 0.364246i
\(153\) 0 0
\(154\) −32.0448 −2.58225
\(155\) 5.40067 + 2.14832i 0.433792 + 0.172557i
\(156\) 0 0
\(157\) 4.14172i 0.330545i −0.986248 0.165273i \(-0.947150\pi\)
0.986248 0.165273i \(-0.0528504\pi\)
\(158\) 3.38944i 0.269650i
\(159\) 0 0
\(160\) −1.11222 + 2.79601i −0.0879285 + 0.221044i
\(161\) −8.31087 −0.654989
\(162\) 0 0
\(163\) 24.7126i 1.93564i −0.251647 0.967819i \(-0.580972\pi\)
0.251647 0.967819i \(-0.419028\pi\)
\(164\) −2.31087 −0.180449
\(165\) 0 0
\(166\) 17.1122 1.32817
\(167\) 3.60464i 0.278935i −0.990227 0.139468i \(-0.955461\pi\)
0.990227 0.139468i \(-0.0445391\pi\)
\(168\) 0 0
\(169\) 8.71155 0.670119
\(170\) 29.1346 + 11.5894i 2.23452 + 0.888866i
\(171\) 0 0
\(172\) 12.2874i 0.936907i
\(173\) 22.4205i 1.70460i 0.523054 + 0.852300i \(0.324793\pi\)
−0.523054 + 0.852300i \(0.675207\pi\)
\(174\) 0 0
\(175\) −10.9447 + 11.5801i −0.827342 + 0.875376i
\(176\) −13.1122 −0.988371
\(177\) 0 0
\(178\) 40.0133i 2.99912i
\(179\) −5.13464 −0.383781 −0.191890 0.981416i \(-0.561462\pi\)
−0.191890 + 0.981416i \(0.561462\pi\)
\(180\) 0 0
\(181\) 20.8462 1.54948 0.774742 0.632277i \(-0.217880\pi\)
0.774742 + 0.632277i \(0.217880\pi\)
\(182\) 15.9695i 1.18374i
\(183\) 0 0
\(184\) −11.7115 −0.863387
\(185\) 3.55611 8.93972i 0.261450 0.657261i
\(186\) 0 0
\(187\) 24.0795i 1.76087i
\(188\) 45.1457i 3.29259i
\(189\) 0 0
\(190\) 2.00000 5.02781i 0.145095 0.364756i
\(191\) 5.26765 0.381154 0.190577 0.981672i \(-0.438964\pi\)
0.190577 + 0.981672i \(0.438964\pi\)
\(192\) 0 0
\(193\) 2.07086i 0.149064i 0.997219 + 0.0745318i \(0.0237462\pi\)
−0.997219 + 0.0745318i \(0.976254\pi\)
\(194\) −5.01121 −0.359784
\(195\) 0 0
\(196\) 12.1666 0.869046
\(197\) 10.4318i 0.743232i 0.928387 + 0.371616i \(0.121196\pi\)
−0.928387 + 0.371616i \(0.878804\pi\)
\(198\) 0 0
\(199\) 2.73235 0.193691 0.0968455 0.995299i \(-0.469125\pi\)
0.0968455 + 0.995299i \(0.469125\pi\)
\(200\) −15.4231 + 16.3185i −1.09058 + 1.15389i
\(201\) 0 0
\(202\) 4.14172i 0.291410i
\(203\) 19.1206i 1.34200i
\(204\) 0 0
\(205\) 1.24524 + 0.495339i 0.0869710 + 0.0345960i
\(206\) 13.9214 0.969951
\(207\) 0 0
\(208\) 6.53446i 0.453083i
\(209\) −4.15544 −0.287438
\(210\) 0 0
\(211\) −15.7340 −1.08317 −0.541585 0.840646i \(-0.682176\pi\)
−0.541585 + 0.840646i \(0.682176\pi\)
\(212\) 45.3066i 3.11167i
\(213\) 0 0
\(214\) −37.3445 −2.55282
\(215\) −2.63383 + 6.62119i −0.179625 + 0.451561i
\(216\) 0 0
\(217\) 8.28343i 0.562316i
\(218\) 28.3404i 1.91946i
\(219\) 0 0
\(220\) 33.2901 + 13.2424i 2.24442 + 0.892801i
\(221\) −12.0000 −0.807207
\(222\) 0 0
\(223\) 18.8219i 1.26041i 0.776430 + 0.630203i \(0.217028\pi\)
−0.776430 + 0.630203i \(0.782972\pi\)
\(224\) −4.28845 −0.286534
\(225\) 0 0
\(226\) 25.6330 1.70508
\(227\) 14.4418i 0.958533i −0.877669 0.479267i \(-0.840903\pi\)
0.877669 0.479267i \(-0.159097\pi\)
\(228\) 0 0
\(229\) 4.17785 0.276080 0.138040 0.990427i \(-0.455920\pi\)
0.138040 + 0.990427i \(0.455920\pi\)
\(230\) 13.1122 + 5.21588i 0.864594 + 0.343925i
\(231\) 0 0
\(232\) 26.9444i 1.76898i
\(233\) 12.0847i 0.791697i −0.918316 0.395849i \(-0.870450\pi\)
0.918316 0.395849i \(-0.129550\pi\)
\(234\) 0 0
\(235\) −9.67705 + 24.3272i −0.631261 + 1.58693i
\(236\) 6.59933 0.429580
\(237\) 0 0
\(238\) 44.6861i 2.89657i
\(239\) −11.3541 −0.734435 −0.367218 0.930135i \(-0.619690\pi\)
−0.367218 + 0.930135i \(0.619690\pi\)
\(240\) 0 0
\(241\) −3.40067 −0.219057 −0.109528 0.993984i \(-0.534934\pi\)
−0.109528 + 0.993984i \(0.534934\pi\)
\(242\) 15.1669i 0.974966i
\(243\) 0 0
\(244\) 33.7564 2.16103
\(245\) −6.55611 2.60794i −0.418854 0.166615i
\(246\) 0 0
\(247\) 2.07086i 0.131766i
\(248\) 11.6729i 0.741229i
\(249\) 0 0
\(250\) 24.5353 11.4013i 1.55175 0.721083i
\(251\) −3.04322 −0.192086 −0.0960432 0.995377i \(-0.530619\pi\)
−0.0960432 + 0.995377i \(0.530619\pi\)
\(252\) 0 0
\(253\) 10.8371i 0.681324i
\(254\) 14.7003 0.922381
\(255\) 0 0
\(256\) −30.3765 −1.89853
\(257\) 17.2881i 1.07840i 0.842177 + 0.539201i \(0.181274\pi\)
−0.842177 + 0.539201i \(0.818726\pi\)
\(258\) 0 0
\(259\) 13.7115 0.851994
\(260\) 6.59933 16.5901i 0.409273 1.02887i
\(261\) 0 0
\(262\) 32.8583i 2.02999i
\(263\) 1.19336i 0.0735859i 0.999323 + 0.0367930i \(0.0117142\pi\)
−0.999323 + 0.0367930i \(0.988286\pi\)
\(264\) 0 0
\(265\) 9.71155 24.4139i 0.596575 1.49973i
\(266\) 7.71155 0.472825
\(267\) 0 0
\(268\) 18.3623i 1.12165i
\(269\) 22.1089 1.34800 0.674000 0.738731i \(-0.264575\pi\)
0.674000 + 0.738731i \(0.264575\pi\)
\(270\) 0 0
\(271\) −4.08644 −0.248234 −0.124117 0.992268i \(-0.539610\pi\)
−0.124117 + 0.992268i \(0.539610\pi\)
\(272\) 18.2848i 1.10868i
\(273\) 0 0
\(274\) −19.2211 −1.16119
\(275\) −15.1001 14.2716i −0.910572 0.860607i
\(276\) 0 0
\(277\) 10.0199i 0.602037i 0.953618 + 0.301019i \(0.0973266\pi\)
−0.953618 + 0.301019i \(0.902673\pi\)
\(278\) 7.90730i 0.474248i
\(279\) 0 0
\(280\) −29.7340 11.8278i −1.77694 0.706846i
\(281\) −0.599328 −0.0357529 −0.0178765 0.999840i \(-0.505691\pi\)
−0.0178765 + 0.999840i \(0.505691\pi\)
\(282\) 0 0
\(283\) 5.41856i 0.322100i 0.986946 + 0.161050i \(0.0514880\pi\)
−0.986946 + 0.161050i \(0.948512\pi\)
\(284\) 52.8686 3.13717
\(285\) 0 0
\(286\) −20.8238 −1.23133
\(287\) 1.90991i 0.112739i
\(288\) 0 0
\(289\) −16.5785 −0.975207
\(290\) 12.0000 30.1669i 0.704664 1.77146i
\(291\) 0 0
\(292\) 10.5152i 0.615358i
\(293\) 3.46691i 0.202539i −0.994859 0.101269i \(-0.967710\pi\)
0.994859 0.101269i \(-0.0322904\pi\)
\(294\) 0 0
\(295\) −3.55611 1.41458i −0.207045 0.0823598i
\(296\) 19.3221 1.12307
\(297\) 0 0
\(298\) 20.4331i 1.18366i
\(299\) −5.40067 −0.312329
\(300\) 0 0
\(301\) −10.1554 −0.585350
\(302\) 2.14832i 0.123622i
\(303\) 0 0
\(304\) 3.15544 0.180977
\(305\) −18.1899 7.23573i −1.04155 0.414317i
\(306\) 0 0
\(307\) 16.5901i 0.946846i 0.880835 + 0.473423i \(0.156982\pi\)
−0.880835 + 0.473423i \(0.843018\pi\)
\(308\) 51.0596i 2.90939i
\(309\) 0 0
\(310\) 5.19866 13.0689i 0.295264 0.742265i
\(311\) 4.15544 0.235633 0.117817 0.993035i \(-0.462411\pi\)
0.117817 + 0.993035i \(0.462411\pi\)
\(312\) 0 0
\(313\) 0.919237i 0.0519583i −0.999662 0.0259792i \(-0.991730\pi\)
0.999662 0.0259792i \(-0.00827036\pi\)
\(314\) −10.0224 −0.565598
\(315\) 0 0
\(316\) −5.40067 −0.303812
\(317\) 26.7292i 1.50126i −0.660723 0.750630i \(-0.729750\pi\)
0.660723 0.750630i \(-0.270250\pi\)
\(318\) 0 0
\(319\) −24.9326 −1.39596
\(320\) 19.8782 + 7.90730i 1.11122 + 0.442031i
\(321\) 0 0
\(322\) 20.1112i 1.12076i
\(323\) 5.79470i 0.322426i
\(324\) 0 0
\(325\) −7.11222 + 7.52514i −0.394515 + 0.417420i
\(326\) −59.8012 −3.31208
\(327\) 0 0
\(328\) 2.69142i 0.148609i
\(329\) −37.3125 −2.05710
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 27.2663i 1.49643i
\(333\) 0 0
\(334\) −8.72275 −0.477288
\(335\) 3.93598 9.89467i 0.215045 0.540604i
\(336\) 0 0
\(337\) 22.5040i 1.22587i −0.790133 0.612935i \(-0.789989\pi\)
0.790133 0.612935i \(-0.210011\pi\)
\(338\) 21.0808i 1.14664i
\(339\) 0 0
\(340\) 18.4663 46.4225i 1.00148 2.51762i
\(341\) −10.8013 −0.584926
\(342\) 0 0
\(343\) 12.2517i 0.661530i
\(344\) −14.3109 −0.771591
\(345\) 0 0
\(346\) 54.2547 2.91675
\(347\) 14.4543i 0.775946i −0.921671 0.387973i \(-0.873175\pi\)
0.921671 0.387973i \(-0.126825\pi\)
\(348\) 0 0
\(349\) 13.3541 0.714828 0.357414 0.933946i \(-0.383658\pi\)
0.357414 + 0.933946i \(0.383658\pi\)
\(350\) 28.0224 + 26.4848i 1.49786 + 1.41567i
\(351\) 0 0
\(352\) 5.59201i 0.298055i
\(353\) 17.6410i 0.938937i −0.882949 0.469469i \(-0.844446\pi\)
0.882949 0.469469i \(-0.155554\pi\)
\(354\) 0 0
\(355\) −28.4887 11.3325i −1.51202 0.601465i
\(356\) −63.7564 −3.37908
\(357\) 0 0
\(358\) 12.4252i 0.656690i
\(359\) 12.4663 0.657947 0.328973 0.944339i \(-0.393297\pi\)
0.328973 + 0.944339i \(0.393297\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 50.4451i 2.65133i
\(363\) 0 0
\(364\) 25.4455 1.33371
\(365\) 2.25396 5.66623i 0.117977 0.296584i
\(366\) 0 0
\(367\) 16.4291i 0.857594i 0.903401 + 0.428797i \(0.141062\pi\)
−0.903401 + 0.428797i \(0.858938\pi\)
\(368\) 8.22918i 0.428976i
\(369\) 0 0
\(370\) −21.6330 8.60532i −1.12464 0.447369i
\(371\) 37.4455 1.94407
\(372\) 0 0
\(373\) 5.29334i 0.274079i −0.990566 0.137039i \(-0.956241\pi\)
0.990566 0.137039i \(-0.0437587\pi\)
\(374\) −58.2693 −3.01303
\(375\) 0 0
\(376\) −52.5801 −2.71161
\(377\) 12.4252i 0.639928i
\(378\) 0 0
\(379\) −14.5353 −0.746629 −0.373314 0.927705i \(-0.621779\pi\)
−0.373314 + 0.927705i \(0.621779\pi\)
\(380\) −8.01121 3.18676i −0.410966 0.163477i
\(381\) 0 0
\(382\) 12.7470i 0.652195i
\(383\) 0.453598i 0.0231778i −0.999933 0.0115889i \(-0.996311\pi\)
0.999933 0.0115889i \(-0.00368894\pi\)
\(384\) 0 0
\(385\) 10.9447 27.5139i 0.557794 1.40224i
\(386\) 5.01121 0.255064
\(387\) 0 0
\(388\) 7.98476i 0.405365i
\(389\) 16.1554 0.819113 0.409557 0.912285i \(-0.365683\pi\)
0.409557 + 0.912285i \(0.365683\pi\)
\(390\) 0 0
\(391\) −15.1122 −0.764258
\(392\) 14.1702i 0.715704i
\(393\) 0 0
\(394\) 25.2435 1.27175
\(395\) 2.91020 + 1.15764i 0.146428 + 0.0582473i
\(396\) 0 0
\(397\) 32.7563i 1.64399i −0.569495 0.821995i \(-0.692861\pi\)
0.569495 0.821995i \(-0.307139\pi\)
\(398\) 6.61192i 0.331426i
\(399\) 0 0
\(400\) 11.4663 + 10.8371i 0.573315 + 0.541856i
\(401\) −12.0864 −0.603568 −0.301784 0.953376i \(-0.597582\pi\)
−0.301784 + 0.953376i \(0.597582\pi\)
\(402\) 0 0
\(403\) 5.38284i 0.268138i
\(404\) −6.59933 −0.328329
\(405\) 0 0
\(406\) 46.2693 2.29631
\(407\) 17.8794i 0.886251i
\(408\) 0 0
\(409\) 19.1346 0.946147 0.473073 0.881023i \(-0.343145\pi\)
0.473073 + 0.881023i \(0.343145\pi\)
\(410\) 1.19866 3.01331i 0.0591974 0.148817i
\(411\) 0 0
\(412\) 22.1821i 1.09283i
\(413\) 5.45428i 0.268388i
\(414\) 0 0
\(415\) −5.84456 + 14.6927i −0.286898 + 0.721235i
\(416\) −2.78678 −0.136633
\(417\) 0 0
\(418\) 10.0556i 0.491836i
\(419\) 8.04484 0.393016 0.196508 0.980502i \(-0.437040\pi\)
0.196508 + 0.980502i \(0.437040\pi\)
\(420\) 0 0
\(421\) −29.3591 −1.43087 −0.715437 0.698678i \(-0.753772\pi\)
−0.715437 + 0.698678i \(0.753772\pi\)
\(422\) 38.0742i 1.85342i
\(423\) 0 0
\(424\) 52.7676 2.56262
\(425\) −19.9015 + 21.0569i −0.965364 + 1.02141i
\(426\) 0 0
\(427\) 27.8993i 1.35014i
\(428\) 59.5040i 2.87623i
\(429\) 0 0
\(430\) 16.0224 + 6.37352i 0.772670 + 0.307358i
\(431\) 32.0448 1.54355 0.771773 0.635898i \(-0.219370\pi\)
0.771773 + 0.635898i \(0.219370\pi\)
\(432\) 0 0
\(433\) 0.482831i 0.0232034i 0.999933 + 0.0116017i \(0.00369301\pi\)
−0.999933 + 0.0116017i \(0.996307\pi\)
\(434\) 20.0448 0.962183
\(435\) 0 0
\(436\) 45.1571 2.16263
\(437\) 2.60794i 0.124755i
\(438\) 0 0
\(439\) 27.3591 1.30578 0.652889 0.757454i \(-0.273557\pi\)
0.652889 + 0.757454i \(0.273557\pi\)
\(440\) 15.4231 38.7722i 0.735267 1.84839i
\(441\) 0 0
\(442\) 29.0384i 1.38122i
\(443\) 23.3815i 1.11089i −0.831554 0.555444i \(-0.812548\pi\)
0.831554 0.555444i \(-0.187452\pi\)
\(444\) 0 0
\(445\) 34.3557 + 13.6663i 1.62862 + 0.647844i
\(446\) 45.5465 2.15669
\(447\) 0 0
\(448\) 30.4887i 1.44046i
\(449\) 23.1346 1.09179 0.545895 0.837853i \(-0.316190\pi\)
0.545895 + 0.837853i \(0.316190\pi\)
\(450\) 0 0
\(451\) −2.49047 −0.117272
\(452\) 40.8430i 1.92109i
\(453\) 0 0
\(454\) −34.9472 −1.64015
\(455\) −13.7115 5.45428i −0.642807 0.255701i
\(456\) 0 0
\(457\) 21.2503i 0.994049i −0.867736 0.497025i \(-0.834426\pi\)
0.867736 0.497025i \(-0.165574\pi\)
\(458\) 10.1099i 0.472403i
\(459\) 0 0
\(460\) 8.31087 20.8927i 0.387496 0.974129i
\(461\) −31.5785 −1.47076 −0.735379 0.677656i \(-0.762996\pi\)
−0.735379 + 0.677656i \(0.762996\pi\)
\(462\) 0 0
\(463\) 15.6119i 0.725547i −0.931877 0.362774i \(-0.881830\pi\)
0.931877 0.362774i \(-0.118170\pi\)
\(464\) 18.9326 0.878925
\(465\) 0 0
\(466\) −29.2435 −1.35468
\(467\) 29.8264i 1.38020i −0.723713 0.690101i \(-0.757566\pi\)
0.723713 0.690101i \(-0.242434\pi\)
\(468\) 0 0
\(469\) 15.1762 0.700774
\(470\) 58.8686 + 23.4172i 2.71541 + 1.08015i
\(471\) 0 0
\(472\) 7.68608i 0.353781i
\(473\) 13.2424i 0.608885i
\(474\) 0 0
\(475\) 3.63383 + 3.43443i 0.166731 + 0.157582i
\(476\) 71.2019 3.26353
\(477\) 0 0
\(478\) 27.4754i 1.25670i
\(479\) 4.53531 0.207223 0.103612 0.994618i \(-0.466960\pi\)
0.103612 + 0.994618i \(0.466960\pi\)
\(480\) 0 0
\(481\) 8.91020 0.406270
\(482\) 8.22918i 0.374829i
\(483\) 0 0
\(484\) −24.1666 −1.09848
\(485\) 1.71155 4.30266i 0.0777173 0.195374i
\(486\) 0 0
\(487\) 39.2550i 1.77881i −0.457116 0.889407i \(-0.651118\pi\)
0.457116 0.889407i \(-0.348882\pi\)
\(488\) 39.3153i 1.77972i
\(489\) 0 0
\(490\) −6.31087 + 15.8649i −0.285096 + 0.716705i
\(491\) −38.8910 −1.75513 −0.877564 0.479460i \(-0.840832\pi\)
−0.877564 + 0.479460i \(0.840832\pi\)
\(492\) 0 0
\(493\) 34.7682i 1.56588i
\(494\) 5.01121 0.225465
\(495\) 0 0
\(496\) 8.20202 0.368281
\(497\) 43.6954i 1.96001i
\(498\) 0 0
\(499\) −4.73235 −0.211849 −0.105924 0.994374i \(-0.533780\pi\)
−0.105924 + 0.994374i \(0.533780\pi\)
\(500\) −18.1666 39.0941i −0.812437 1.74834i
\(501\) 0 0
\(502\) 7.36420i 0.328680i
\(503\) 1.85567i 0.0827400i −0.999144 0.0413700i \(-0.986828\pi\)
0.999144 0.0413700i \(-0.0131722\pi\)
\(504\) 0 0
\(505\) 3.55611 + 1.41458i 0.158245 + 0.0629478i
\(506\) −26.2244 −1.16582
\(507\) 0 0
\(508\) 23.4232i 1.03924i
\(509\) 22.8878 1.01448 0.507242 0.861804i \(-0.330665\pi\)
0.507242 + 0.861804i \(0.330665\pi\)
\(510\) 0 0
\(511\) 8.69074 0.384456
\(512\) 32.5867i 1.44014i
\(513\) 0 0
\(514\) 41.8350 1.84526
\(515\) −4.75476 + 11.9530i −0.209520 + 0.526713i
\(516\) 0 0
\(517\) 48.6543i 2.13982i
\(518\) 33.1802i 1.45785i
\(519\) 0 0
\(520\) −19.3221 7.68608i −0.847329 0.337057i
\(521\) 29.7340 1.30267 0.651334 0.758791i \(-0.274210\pi\)
0.651334 + 0.758791i \(0.274210\pi\)
\(522\) 0 0
\(523\) 30.6497i 1.34022i 0.742263 + 0.670109i \(0.233752\pi\)
−0.742263 + 0.670109i \(0.766248\pi\)
\(524\) −52.3557 −2.28717
\(525\) 0 0
\(526\) 2.88778 0.125913
\(527\) 15.0623i 0.656125i
\(528\) 0 0
\(529\) 16.1987 0.704289
\(530\) −59.0785 23.5007i −2.56620 1.02080i
\(531\) 0 0
\(532\) 12.2874i 0.532727i
\(533\) 1.24112i 0.0537590i
\(534\) 0 0
\(535\) 12.7548 32.0643i 0.551437 1.38626i
\(536\) 21.3861 0.923739
\(537\) 0 0
\(538\) 53.5006i 2.30657i
\(539\) 13.1122 0.564783
\(540\) 0 0
\(541\) 2.21946 0.0954220 0.0477110 0.998861i \(-0.484807\pi\)
0.0477110 + 0.998861i \(0.484807\pi\)
\(542\) 9.88865i 0.424754i
\(543\) 0 0
\(544\) −7.79798 −0.334336
\(545\) −24.3333 9.67948i −1.04232 0.414623i
\(546\) 0 0
\(547\) 14.4297i 0.616970i 0.951229 + 0.308485i \(0.0998220\pi\)
−0.951229 + 0.308485i \(0.900178\pi\)
\(548\) 30.6265i 1.30830i
\(549\) 0 0
\(550\) −34.5353 + 36.5404i −1.47259 + 1.55809i
\(551\) 6.00000 0.255609
\(552\) 0 0
\(553\) 4.46360i 0.189812i
\(554\) 24.2469 1.03015
\(555\) 0 0
\(556\) 12.5993 0.534331
\(557\) 19.4610i 0.824588i 0.911051 + 0.412294i \(0.135272\pi\)
−0.911051 + 0.412294i \(0.864728\pi\)
\(558\) 0 0
\(559\) −6.59933 −0.279122
\(560\) −8.31087 + 20.8927i −0.351198 + 0.882879i
\(561\) 0 0
\(562\) 1.45030i 0.0611771i
\(563\) 12.3649i 0.521118i 0.965458 + 0.260559i \(0.0839068\pi\)
−0.965458 + 0.260559i \(0.916093\pi\)
\(564\) 0 0
\(565\) −8.75476 + 22.0086i −0.368316 + 0.925911i
\(566\) 13.1122 0.551148
\(567\) 0 0
\(568\) 61.5748i 2.58362i
\(569\) 15.0898 0.632597 0.316299 0.948660i \(-0.397560\pi\)
0.316299 + 0.948660i \(0.397560\pi\)
\(570\) 0 0
\(571\) 17.1571 0.718000 0.359000 0.933337i \(-0.383118\pi\)
0.359000 + 0.933337i \(0.383118\pi\)
\(572\) 33.1802i 1.38733i
\(573\) 0 0
\(574\) 4.62175 0.192908
\(575\) −8.95678 + 9.47680i −0.373524 + 0.395210i
\(576\) 0 0
\(577\) 22.5165i 0.937374i 0.883364 + 0.468687i \(0.155273\pi\)
−0.883364 + 0.468687i \(0.844727\pi\)
\(578\) 40.1179i 1.66868i
\(579\) 0 0
\(580\) −48.0673 19.1206i −1.99588 0.793938i
\(581\) −22.5353 −0.934922
\(582\) 0 0
\(583\) 48.8278i 2.02224i
\(584\) 12.2469 0.506778
\(585\) 0 0
\(586\) −8.38946 −0.346566
\(587\) 7.49544i 0.309370i 0.987964 + 0.154685i \(0.0494363\pi\)
−0.987964 + 0.154685i \(0.950564\pi\)
\(588\) 0 0
\(589\) 2.59933 0.107103
\(590\) −3.42309 + 8.60532i −0.140926 + 0.354275i
\(591\) 0 0
\(592\) 13.5768i 0.558002i
\(593\) 27.8094i 1.14199i −0.820952 0.570997i \(-0.806557\pi\)
0.820952 0.570997i \(-0.193443\pi\)
\(594\) 0 0
\(595\) −38.3678 15.2622i −1.57293 0.625690i
\(596\) −32.5577 −1.33362
\(597\) 0 0
\(598\) 13.0689i 0.534428i
\(599\) −45.4903 −1.85869 −0.929343 0.369219i \(-0.879625\pi\)
−0.929343 + 0.369219i \(0.879625\pi\)
\(600\) 0 0
\(601\) −16.5993 −0.677101 −0.338550 0.940948i \(-0.609937\pi\)
−0.338550 + 0.940948i \(0.609937\pi\)
\(602\) 24.5748i 1.00160i
\(603\) 0 0
\(604\) −3.42309 −0.139284
\(605\) 13.0224 + 5.18016i 0.529437 + 0.210603i
\(606\) 0 0
\(607\) 5.08417i 0.206360i 0.994663 + 0.103180i \(0.0329018\pi\)
−0.994663 + 0.103180i \(0.967098\pi\)
\(608\) 1.34571i 0.0545758i
\(609\) 0 0
\(610\) −17.5095 + 44.0173i −0.708940 + 1.78221i
\(611\) −24.2469 −0.980923
\(612\) 0 0
\(613\) 4.63706i 0.187289i 0.995606 + 0.0936445i \(0.0298517\pi\)
−0.995606 + 0.0936445i \(0.970148\pi\)
\(614\) 40.1458 1.62015
\(615\) 0 0
\(616\) 59.4679 2.39603
\(617\) 40.2874i 1.62191i 0.585108 + 0.810955i \(0.301052\pi\)
−0.585108 + 0.810955i \(0.698948\pi\)
\(618\) 0 0
\(619\) 43.3815 1.74365 0.871825 0.489818i \(-0.162937\pi\)
0.871825 + 0.489818i \(0.162937\pi\)
\(620\) −20.8238 8.28343i −0.836302 0.332671i
\(621\) 0 0
\(622\) 10.0556i 0.403194i
\(623\) 52.6940i 2.11114i
\(624\) 0 0
\(625\) 1.40939 + 24.9602i 0.0563757 + 0.998410i
\(626\) −2.22443 −0.0889062
\(627\) 0 0
\(628\) 15.9695i 0.637253i
\(629\) 24.9326 0.994129
\(630\) 0 0
\(631\) 7.53369 0.299911 0.149956 0.988693i \(-0.452087\pi\)
0.149956 + 0.988693i \(0.452087\pi\)
\(632\) 6.29004i 0.250204i
\(633\) 0 0
\(634\) −64.6812 −2.56882
\(635\) −5.02080 + 12.6218i −0.199244 + 0.500881i
\(636\) 0 0
\(637\) 6.53446i 0.258905i
\(638\) 60.3337i 2.38863i
\(639\) 0 0
\(640\) 16.9102 42.5106i 0.668434 1.68038i
\(641\) 23.3075 0.920591 0.460296 0.887766i \(-0.347743\pi\)
0.460296 + 0.887766i \(0.347743\pi\)
\(642\) 0 0
\(643\) 1.87419i 0.0739110i 0.999317 + 0.0369555i \(0.0117660\pi\)
−0.999317 + 0.0369555i \(0.988234\pi\)
\(644\) 32.0448 1.26274
\(645\) 0 0
\(646\) 14.0224 0.551705
\(647\) 47.0371i 1.84922i −0.380917 0.924609i \(-0.624392\pi\)
0.380917 0.924609i \(-0.375608\pi\)
\(648\) 0 0
\(649\) 7.11222 0.279179
\(650\) 18.2099 + 17.2106i 0.714250 + 0.675057i
\(651\) 0 0
\(652\) 95.2861i 3.73169i
\(653\) 24.1630i 0.945571i −0.881178 0.472785i \(-0.843249\pi\)
0.881178 0.472785i \(-0.156751\pi\)
\(654\) 0 0
\(655\) 28.2124 + 11.2225i 1.10235 + 0.438500i
\(656\) 1.89114 0.0738367
\(657\) 0 0
\(658\) 90.2914i 3.51992i
\(659\) 10.2885 0.400781 0.200391 0.979716i \(-0.435779\pi\)
0.200391 + 0.979716i \(0.435779\pi\)
\(660\) 0 0
\(661\) 5.93598 0.230883 0.115441 0.993314i \(-0.463172\pi\)
0.115441 + 0.993314i \(0.463172\pi\)
\(662\) 19.3590i 0.752407i
\(663\) 0 0
\(664\) −31.7564 −1.23239
\(665\) −2.63383 + 6.62119i −0.102135 + 0.256759i
\(666\) 0 0
\(667\) 15.6476i 0.605879i
\(668\) 13.8987i 0.537755i
\(669\) 0 0
\(670\) −23.9438 9.52456i −0.925031 0.367966i
\(671\) 36.3799 1.40443
\(672\) 0 0
\(673\) 40.7053i 1.56907i −0.620082 0.784537i \(-0.712901\pi\)
0.620082 0.784537i \(-0.287099\pi\)
\(674\) −54.4567 −2.09759
\(675\) 0 0
\(676\) −33.5897 −1.29191
\(677\) 18.8761i 0.725469i 0.931893 + 0.362734i \(0.118157\pi\)
−0.931893 + 0.362734i \(0.881843\pi\)
\(678\) 0 0
\(679\) 6.59933 0.253259
\(680\) −54.0673 21.5073i −2.07338 0.824767i
\(681\) 0 0
\(682\) 26.1379i 1.00087i
\(683\) 19.6576i 0.752179i 0.926583 + 0.376089i \(0.122731\pi\)
−0.926583 + 0.376089i \(0.877269\pi\)
\(684\) 0 0
\(685\) 6.56483 16.5034i 0.250829 0.630561i
\(686\) 29.6475 1.13195
\(687\) 0 0
\(688\) 10.0556i 0.383367i
\(689\) 24.3333 0.927025
\(690\) 0 0
\(691\) −48.2451 −1.83533 −0.917665 0.397354i \(-0.869928\pi\)
−0.917665 + 0.397354i \(0.869928\pi\)
\(692\) 86.4483i 3.28627i
\(693\) 0 0
\(694\) −34.9775 −1.32773
\(695\) −6.78926 2.70068i −0.257531 0.102443i
\(696\) 0 0
\(697\) 3.47293i 0.131546i
\(698\) 32.3152i 1.22315i
\(699\) 0 0
\(700\) 42.2003 44.6504i 1.59502 1.68762i
\(701\) −0.512889 −0.0193715 −0.00968577 0.999953i \(-0.503083\pi\)
−0.00968577 + 0.999953i \(0.503083\pi\)
\(702\) 0 0
\(703\) 4.30266i 0.162278i
\(704\) −39.7564 −1.49838
\(705\) 0 0
\(706\) −42.6890 −1.60662
\(707\) 5.45428i 0.205129i
\(708\) 0 0
\(709\) 8.84618 0.332225 0.166113 0.986107i \(-0.446878\pi\)
0.166113 + 0.986107i \(0.446878\pi\)
\(710\) −27.4231 + 68.9390i −1.02917 + 2.58724i
\(711\) 0 0
\(712\) 74.2556i 2.78285i
\(713\) 6.77889i 0.253871i
\(714\) 0 0
\(715\) 7.11222 17.8794i 0.265982 0.668653i
\(716\) 19.7980 0.739885
\(717\) 0 0
\(718\) 30.1669i 1.12582i
\(719\) 7.84456 0.292553 0.146276 0.989244i \(-0.453271\pi\)
0.146276 + 0.989244i \(0.453271\pi\)
\(720\) 0 0
\(721\) −18.3333 −0.682767
\(722\) 2.41987i 0.0900582i
\(723\) 0 0
\(724\) −80.3781 −2.98723
\(725\) 21.8030 + 20.6066i 0.809742 + 0.765309i
\(726\) 0 0
\(727\) 2.91130i 0.107974i 0.998542 + 0.0539870i \(0.0171930\pi\)
−0.998542 + 0.0539870i \(0.982807\pi\)
\(728\) 29.6358i 1.09838i
\(729\) 0 0
\(730\) −13.7115 5.45428i −0.507487 0.201872i
\(731\) −18.4663 −0.683001
\(732\) 0 0
\(733\) 33.7775i 1.24760i −0.781584 0.623800i \(-0.785588\pi\)
0.781584 0.623800i \(-0.214412\pi\)
\(734\) 39.7564 1.46743
\(735\) 0 0
\(736\) −3.50953 −0.129363
\(737\) 19.7893i 0.728950i
\(738\) 0 0
\(739\) 35.8030 1.31703 0.658517 0.752566i \(-0.271184\pi\)
0.658517 + 0.752566i \(0.271184\pi\)
\(740\) −13.7115 + 34.4695i −0.504046 + 1.26712i
\(741\) 0 0
\(742\) 90.6133i 3.32652i
\(743\) 5.66948i 0.207993i 0.994578 + 0.103996i \(0.0331631\pi\)
−0.994578 + 0.103996i \(0.966837\pi\)
\(744\) 0 0
\(745\) 17.5440 + 6.97880i 0.642763 + 0.255683i
\(746\) −12.8092 −0.468978
\(747\) 0 0
\(748\) 92.8451i 3.39475i
\(749\) 49.1795 1.79698
\(750\) 0 0
\(751\) −27.4679 −1.00232 −0.501159 0.865355i \(-0.667093\pi\)
−0.501159 + 0.865355i \(0.667093\pi\)
\(752\) 36.9457i 1.34727i
\(753\) 0 0
\(754\) 30.0673 1.09498
\(755\) 1.84456 + 0.733744i 0.0671305 + 0.0267037i
\(756\) 0 0
\(757\) 41.6370i 1.51332i 0.653806 + 0.756662i \(0.273171\pi\)
−0.653806 + 0.756662i \(0.726829\pi\)
\(758\) 35.1736i 1.27756i
\(759\) 0 0
\(760\) −3.71155 + 9.33047i −0.134632 + 0.338452i
\(761\) 9.46967 0.343275 0.171638 0.985160i \(-0.445094\pi\)
0.171638 + 0.985160i \(0.445094\pi\)
\(762\) 0 0
\(763\) 37.3219i 1.35114i
\(764\) −20.3109 −0.734822
\(765\) 0 0
\(766\) −1.09765 −0.0396597
\(767\) 3.54437i 0.127980i
\(768\) 0 0
\(769\) −1.90858 −0.0688253 −0.0344127 0.999408i \(-0.510956\pi\)
−0.0344127 + 0.999408i \(0.510956\pi\)
\(770\) −66.5801 26.4848i −2.39938 0.954444i
\(771\) 0 0
\(772\) 7.98476i 0.287378i
\(773\) 28.4007i 1.02150i 0.859729 + 0.510751i \(0.170633\pi\)
−0.859729 + 0.510751i \(0.829367\pi\)
\(774\) 0 0
\(775\) 9.44551 + 8.92721i 0.339293 + 0.320675i
\(776\) 9.29966 0.333838
\(777\) 0 0
\(778\) 39.0941i 1.40159i
\(779\) 0.599328 0.0214732
\(780\) 0 0
\(781\) 56.9775 2.03881
\(782\) 36.5696i 1.30773i
\(783\) 0 0
\(784\) −9.95678 −0.355599
\(785\) 3.42309 8.60532i 0.122175 0.307137i
\(786\) 0 0
\(787\) 15.6708i 0.558605i −0.960203 0.279303i \(-0.909897\pi\)
0.960203 0.279303i \(-0.0901033\pi\)
\(788\) 40.2225i 1.43287i
\(789\) 0 0
\(790\) 2.80134 7.04231i 0.0996673 0.250554i
\(791\) −33.7564 −1.20024
\(792\) 0 0
\(793\) 18.1299i 0.643811i
\(794\) −79.2659 −2.81304
\(795\) 0 0
\(796\) −10.5353 −0.373414
\(797\) 36.9225i 1.30786i −0.756554 0.653932i \(-0.773118\pi\)