Properties

Label 120.3.c.a.89.5
Level $120$
Weight $3$
Character 120.89
Analytic conductor $3.270$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 120.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.26976317232\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \( x^{12} + 34x^{10} + 305x^{8} + 616x^{6} + 305x^{4} + 34x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{15}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 89.5
Root \(-0.723561i\) of defining polynomial
Character \(\chi\) \(=\) 120.89
Dual form 120.3.c.a.89.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.938195 - 2.84952i) q^{3} +(4.88807 + 1.05205i) q^{5} -6.81219i q^{7} +(-7.23958 + 5.34682i) q^{9} +O(q^{10})\) \(q+(-0.938195 - 2.84952i) q^{3} +(4.88807 + 1.05205i) q^{5} -6.81219i q^{7} +(-7.23958 + 5.34682i) q^{9} -7.52980i q^{11} -16.2362i q^{13} +(-1.58813 - 14.9157i) q^{15} +4.11928 q^{17} +7.86469 q^{19} +(-19.4115 + 6.39117i) q^{21} -19.5246 q^{23} +(22.7864 + 10.2850i) q^{25} +(22.0280 + 15.6130i) q^{27} +55.8878i q^{29} +43.4375 q^{31} +(-21.4563 + 7.06442i) q^{33} +(7.16675 - 33.2984i) q^{35} +31.5824i q^{37} +(-46.2655 + 15.2328i) q^{39} -51.3487i q^{41} +51.2914i q^{43} +(-41.0127 + 18.5192i) q^{45} -61.7596 q^{47} +2.59407 q^{49} +(-3.86469 - 11.7380i) q^{51} +82.7111 q^{53} +(7.92170 - 36.8061i) q^{55} +(-7.37861 - 22.4106i) q^{57} +97.6026i q^{59} +4.13531 q^{61} +(36.4236 + 49.3174i) q^{63} +(17.0813 - 79.3638i) q^{65} -63.1940i q^{67} +(18.3179 + 55.6358i) q^{69} +40.3087i q^{71} -78.5111i q^{73} +(7.92915 - 74.5797i) q^{75} -51.2944 q^{77} -51.0103 q^{79} +(23.8230 - 77.4175i) q^{81} +2.72011 q^{83} +(20.1353 + 4.33368i) q^{85} +(159.254 - 52.4337i) q^{87} -70.4279i q^{89} -110.604 q^{91} +(-40.7528 - 123.776i) q^{93} +(38.4431 + 8.27403i) q^{95} -3.44364i q^{97} +(40.2605 + 54.5126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 8 q^{9} + 16 q^{15} + 4 q^{21} + 36 q^{25} - 48 q^{31} - 128 q^{39} - 68 q^{45} - 252 q^{49} + 48 q^{51} - 48 q^{55} + 144 q^{61} + 268 q^{69} + 304 q^{75} + 432 q^{79} - 188 q^{81} + 336 q^{85} - 560 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(41\) \(61\) \(97\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.938195 2.84952i −0.312732 0.949841i
\(4\) 0 0
\(5\) 4.88807 + 1.05205i 0.977613 + 0.210409i
\(6\) 0 0
\(7\) 6.81219i 0.973170i −0.873633 0.486585i \(-0.838242\pi\)
0.873633 0.486585i \(-0.161758\pi\)
\(8\) 0 0
\(9\) −7.23958 + 5.34682i −0.804398 + 0.594091i
\(10\) 0 0
\(11\) 7.52980i 0.684527i −0.939604 0.342263i \(-0.888806\pi\)
0.939604 0.342263i \(-0.111194\pi\)
\(12\) 0 0
\(13\) 16.2362i 1.24894i −0.781048 0.624471i \(-0.785315\pi\)
0.781048 0.624471i \(-0.214685\pi\)
\(14\) 0 0
\(15\) −1.58813 14.9157i −0.105875 0.994379i
\(16\) 0 0
\(17\) 4.11928 0.242311 0.121155 0.992634i \(-0.461340\pi\)
0.121155 + 0.992634i \(0.461340\pi\)
\(18\) 0 0
\(19\) 7.86469 0.413931 0.206965 0.978348i \(-0.433641\pi\)
0.206965 + 0.978348i \(0.433641\pi\)
\(20\) 0 0
\(21\) −19.4115 + 6.39117i −0.924357 + 0.304341i
\(22\) 0 0
\(23\) −19.5246 −0.848895 −0.424447 0.905453i \(-0.639532\pi\)
−0.424447 + 0.905453i \(0.639532\pi\)
\(24\) 0 0
\(25\) 22.7864 + 10.2850i 0.911456 + 0.411398i
\(26\) 0 0
\(27\) 22.0280 + 15.6130i 0.815853 + 0.578259i
\(28\) 0 0
\(29\) 55.8878i 1.92717i 0.267408 + 0.963583i \(0.413833\pi\)
−0.267408 + 0.963583i \(0.586167\pi\)
\(30\) 0 0
\(31\) 43.4375 1.40121 0.700604 0.713550i \(-0.252914\pi\)
0.700604 + 0.713550i \(0.252914\pi\)
\(32\) 0 0
\(33\) −21.4563 + 7.06442i −0.650192 + 0.214073i
\(34\) 0 0
\(35\) 7.16675 33.2984i 0.204764 0.951384i
\(36\) 0 0
\(37\) 31.5824i 0.853579i 0.904351 + 0.426790i \(0.140356\pi\)
−0.904351 + 0.426790i \(0.859644\pi\)
\(38\) 0 0
\(39\) −46.2655 + 15.2328i −1.18630 + 0.390584i
\(40\) 0 0
\(41\) 51.3487i 1.25241i −0.779659 0.626204i \(-0.784608\pi\)
0.779659 0.626204i \(-0.215392\pi\)
\(42\) 0 0
\(43\) 51.2914i 1.19282i 0.802678 + 0.596412i \(0.203408\pi\)
−0.802678 + 0.596412i \(0.796592\pi\)
\(44\) 0 0
\(45\) −41.0127 + 18.5192i −0.911392 + 0.411539i
\(46\) 0 0
\(47\) −61.7596 −1.31403 −0.657017 0.753875i \(-0.728182\pi\)
−0.657017 + 0.753875i \(0.728182\pi\)
\(48\) 0 0
\(49\) 2.59407 0.0529401
\(50\) 0 0
\(51\) −3.86469 11.7380i −0.0757782 0.230157i
\(52\) 0 0
\(53\) 82.7111 1.56059 0.780293 0.625414i \(-0.215070\pi\)
0.780293 + 0.625414i \(0.215070\pi\)
\(54\) 0 0
\(55\) 7.92170 36.8061i 0.144031 0.669203i
\(56\) 0 0
\(57\) −7.37861 22.4106i −0.129449 0.393169i
\(58\) 0 0
\(59\) 97.6026i 1.65428i 0.561994 + 0.827141i \(0.310034\pi\)
−0.561994 + 0.827141i \(0.689966\pi\)
\(60\) 0 0
\(61\) 4.13531 0.0677920 0.0338960 0.999425i \(-0.489209\pi\)
0.0338960 + 0.999425i \(0.489209\pi\)
\(62\) 0 0
\(63\) 36.4236 + 49.3174i 0.578152 + 0.782816i
\(64\) 0 0
\(65\) 17.0813 79.3638i 0.262789 1.22098i
\(66\) 0 0
\(67\) 63.1940i 0.943194i −0.881814 0.471597i \(-0.843678\pi\)
0.881814 0.471597i \(-0.156322\pi\)
\(68\) 0 0
\(69\) 18.3179 + 55.6358i 0.265476 + 0.806316i
\(70\) 0 0
\(71\) 40.3087i 0.567729i 0.958864 + 0.283864i \(0.0916165\pi\)
−0.958864 + 0.283864i \(0.908383\pi\)
\(72\) 0 0
\(73\) 78.5111i 1.07549i −0.843106 0.537747i \(-0.819276\pi\)
0.843106 0.537747i \(-0.180724\pi\)
\(74\) 0 0
\(75\) 7.92915 74.5797i 0.105722 0.994396i
\(76\) 0 0
\(77\) −51.2944 −0.666161
\(78\) 0 0
\(79\) −51.0103 −0.645699 −0.322850 0.946450i \(-0.604641\pi\)
−0.322850 + 0.946450i \(0.604641\pi\)
\(80\) 0 0
\(81\) 23.8230 77.4175i 0.294111 0.955771i
\(82\) 0 0
\(83\) 2.72011 0.0327725 0.0163862 0.999866i \(-0.494784\pi\)
0.0163862 + 0.999866i \(0.494784\pi\)
\(84\) 0 0
\(85\) 20.1353 + 4.33368i 0.236886 + 0.0509844i
\(86\) 0 0
\(87\) 159.254 52.4337i 1.83050 0.602686i
\(88\) 0 0
\(89\) 70.4279i 0.791325i −0.918396 0.395662i \(-0.870515\pi\)
0.918396 0.395662i \(-0.129485\pi\)
\(90\) 0 0
\(91\) −110.604 −1.21543
\(92\) 0 0
\(93\) −40.7528 123.776i −0.438203 1.33093i
\(94\) 0 0
\(95\) 38.4431 + 8.27403i 0.404664 + 0.0870950i
\(96\) 0 0
\(97\) 3.44364i 0.0355015i −0.999842 0.0177507i \(-0.994349\pi\)
0.999842 0.0177507i \(-0.00565053\pi\)
\(98\) 0 0
\(99\) 40.2605 + 54.5126i 0.406671 + 0.550632i
\(100\) 0 0
\(101\) 49.2446i 0.487570i 0.969829 + 0.243785i \(0.0783892\pi\)
−0.969829 + 0.243785i \(0.921611\pi\)
\(102\) 0 0
\(103\) 90.5470i 0.879097i 0.898219 + 0.439548i \(0.144862\pi\)
−0.898219 + 0.439548i \(0.855138\pi\)
\(104\) 0 0
\(105\) −101.609 + 10.8186i −0.967700 + 0.103034i
\(106\) 0 0
\(107\) −65.3836 −0.611062 −0.305531 0.952182i \(-0.598834\pi\)
−0.305531 + 0.952182i \(0.598834\pi\)
\(108\) 0 0
\(109\) −170.469 −1.56394 −0.781968 0.623319i \(-0.785784\pi\)
−0.781968 + 0.623319i \(0.785784\pi\)
\(110\) 0 0
\(111\) 89.9949 29.6305i 0.810765 0.266941i
\(112\) 0 0
\(113\) 55.4137 0.490387 0.245193 0.969474i \(-0.421149\pi\)
0.245193 + 0.969474i \(0.421149\pi\)
\(114\) 0 0
\(115\) −95.4375 20.5408i −0.829891 0.178616i
\(116\) 0 0
\(117\) 86.8123 + 117.544i 0.741985 + 1.00465i
\(118\) 0 0
\(119\) 28.0613i 0.235809i
\(120\) 0 0
\(121\) 64.3022 0.531423
\(122\) 0 0
\(123\) −146.319 + 48.1751i −1.18959 + 0.391668i
\(124\) 0 0
\(125\) 100.561 + 74.2459i 0.804489 + 0.593967i
\(126\) 0 0
\(127\) 74.9923i 0.590491i 0.955421 + 0.295245i \(0.0954014\pi\)
−0.955421 + 0.295245i \(0.904599\pi\)
\(128\) 0 0
\(129\) 146.156 48.1214i 1.13299 0.373034i
\(130\) 0 0
\(131\) 101.149i 0.772130i −0.922472 0.386065i \(-0.873834\pi\)
0.922472 0.386065i \(-0.126166\pi\)
\(132\) 0 0
\(133\) 53.5758i 0.402825i
\(134\) 0 0
\(135\) 91.2489 + 99.4919i 0.675918 + 0.736977i
\(136\) 0 0
\(137\) −114.292 −0.834248 −0.417124 0.908850i \(-0.636962\pi\)
−0.417124 + 0.908850i \(0.636962\pi\)
\(138\) 0 0
\(139\) 230.156 1.65580 0.827899 0.560878i \(-0.189536\pi\)
0.827899 + 0.560878i \(0.189536\pi\)
\(140\) 0 0
\(141\) 57.9426 + 175.986i 0.410940 + 1.24812i
\(142\) 0 0
\(143\) −122.256 −0.854934
\(144\) 0 0
\(145\) −58.7966 + 273.183i −0.405494 + 1.88402i
\(146\) 0 0
\(147\) −2.43374 7.39185i −0.0165561 0.0502847i
\(148\) 0 0
\(149\) 9.12446i 0.0612380i −0.999531 0.0306190i \(-0.990252\pi\)
0.999531 0.0306190i \(-0.00974785\pi\)
\(150\) 0 0
\(151\) −163.010 −1.07954 −0.539769 0.841813i \(-0.681488\pi\)
−0.539769 + 0.841813i \(0.681488\pi\)
\(152\) 0 0
\(153\) −29.8218 + 22.0250i −0.194914 + 0.143955i
\(154\) 0 0
\(155\) 212.325 + 45.6983i 1.36984 + 0.294828i
\(156\) 0 0
\(157\) 122.529i 0.780442i 0.920721 + 0.390221i \(0.127601\pi\)
−0.920721 + 0.390221i \(0.872399\pi\)
\(158\) 0 0
\(159\) −77.5991 235.687i −0.488045 1.48231i
\(160\) 0 0
\(161\) 133.005i 0.826119i
\(162\) 0 0
\(163\) 66.6959i 0.409177i 0.978848 + 0.204589i \(0.0655857\pi\)
−0.978848 + 0.204589i \(0.934414\pi\)
\(164\) 0 0
\(165\) −112.312 + 11.9583i −0.680680 + 0.0724744i
\(166\) 0 0
\(167\) −163.583 −0.979539 −0.489769 0.871852i \(-0.662919\pi\)
−0.489769 + 0.871852i \(0.662919\pi\)
\(168\) 0 0
\(169\) −94.6153 −0.559854
\(170\) 0 0
\(171\) −56.9370 + 42.0511i −0.332965 + 0.245913i
\(172\) 0 0
\(173\) −34.7133 −0.200655 −0.100327 0.994954i \(-0.531989\pi\)
−0.100327 + 0.994954i \(0.531989\pi\)
\(174\) 0 0
\(175\) 70.0631 155.225i 0.400360 0.887001i
\(176\) 0 0
\(177\) 278.121 91.5704i 1.57131 0.517347i
\(178\) 0 0
\(179\) 273.448i 1.52764i −0.645429 0.763820i \(-0.723321\pi\)
0.645429 0.763820i \(-0.276679\pi\)
\(180\) 0 0
\(181\) −40.8749 −0.225828 −0.112914 0.993605i \(-0.536019\pi\)
−0.112914 + 0.993605i \(0.536019\pi\)
\(182\) 0 0
\(183\) −3.87973 11.7837i −0.0212007 0.0643916i
\(184\) 0 0
\(185\) −33.2262 + 154.377i −0.179601 + 0.834471i
\(186\) 0 0
\(187\) 31.0173i 0.165868i
\(188\) 0 0
\(189\) 106.359 150.059i 0.562744 0.793964i
\(190\) 0 0
\(191\) 40.5934i 0.212531i −0.994338 0.106266i \(-0.966111\pi\)
0.994338 0.106266i \(-0.0338894\pi\)
\(192\) 0 0
\(193\) 141.259i 0.731912i −0.930632 0.365956i \(-0.880742\pi\)
0.930632 0.365956i \(-0.119258\pi\)
\(194\) 0 0
\(195\) −242.175 + 25.7852i −1.24192 + 0.132232i
\(196\) 0 0
\(197\) −232.643 −1.18093 −0.590464 0.807064i \(-0.701055\pi\)
−0.590464 + 0.807064i \(0.701055\pi\)
\(198\) 0 0
\(199\) 85.3744 0.429017 0.214509 0.976722i \(-0.431185\pi\)
0.214509 + 0.976722i \(0.431185\pi\)
\(200\) 0 0
\(201\) −180.073 + 59.2883i −0.895885 + 0.294967i
\(202\) 0 0
\(203\) 380.719 1.87546
\(204\) 0 0
\(205\) 54.0213 250.996i 0.263518 1.22437i
\(206\) 0 0
\(207\) 141.350 104.394i 0.682849 0.504321i
\(208\) 0 0
\(209\) 59.2195i 0.283347i
\(210\) 0 0
\(211\) 284.532 1.34849 0.674247 0.738506i \(-0.264468\pi\)
0.674247 + 0.738506i \(0.264468\pi\)
\(212\) 0 0
\(213\) 114.861 37.8175i 0.539252 0.177547i
\(214\) 0 0
\(215\) −53.9610 + 250.716i −0.250982 + 1.16612i
\(216\) 0 0
\(217\) 295.904i 1.36361i
\(218\) 0 0
\(219\) −223.719 + 73.6587i −1.02155 + 0.336341i
\(220\) 0 0
\(221\) 66.8816i 0.302632i
\(222\) 0 0
\(223\) 30.2924i 0.135840i −0.997691 0.0679201i \(-0.978364\pi\)
0.997691 0.0679201i \(-0.0216363\pi\)
\(224\) 0 0
\(225\) −219.956 + 47.3760i −0.977581 + 0.210560i
\(226\) 0 0
\(227\) 239.380 1.05454 0.527269 0.849698i \(-0.323216\pi\)
0.527269 + 0.849698i \(0.323216\pi\)
\(228\) 0 0
\(229\) 284.959 1.24436 0.622180 0.782874i \(-0.286247\pi\)
0.622180 + 0.782874i \(0.286247\pi\)
\(230\) 0 0
\(231\) 48.1242 + 146.165i 0.208330 + 0.632747i
\(232\) 0 0
\(233\) 93.8635 0.402848 0.201424 0.979504i \(-0.435443\pi\)
0.201424 + 0.979504i \(0.435443\pi\)
\(234\) 0 0
\(235\) −301.885 64.9741i −1.28462 0.276485i
\(236\) 0 0
\(237\) 47.8576 + 145.355i 0.201931 + 0.613312i
\(238\) 0 0
\(239\) 238.326i 0.997181i −0.866838 0.498590i \(-0.833851\pi\)
0.866838 0.498590i \(-0.166149\pi\)
\(240\) 0 0
\(241\) 44.2919 0.183784 0.0918919 0.995769i \(-0.470709\pi\)
0.0918919 + 0.995769i \(0.470709\pi\)
\(242\) 0 0
\(243\) −242.954 + 4.74848i −0.999809 + 0.0195411i
\(244\) 0 0
\(245\) 12.6800 + 2.72908i 0.0517550 + 0.0111391i
\(246\) 0 0
\(247\) 127.693i 0.516975i
\(248\) 0 0
\(249\) −2.55200 7.75103i −0.0102490 0.0311286i
\(250\) 0 0
\(251\) 293.093i 1.16770i 0.811862 + 0.583850i \(0.198454\pi\)
−0.811862 + 0.583850i \(0.801546\pi\)
\(252\) 0 0
\(253\) 147.016i 0.581092i
\(254\) 0 0
\(255\) −6.54194 61.4419i −0.0256547 0.240949i
\(256\) 0 0
\(257\) −169.330 −0.658870 −0.329435 0.944178i \(-0.606858\pi\)
−0.329435 + 0.944178i \(0.606858\pi\)
\(258\) 0 0
\(259\) 215.146 0.830678
\(260\) 0 0
\(261\) −298.822 404.604i −1.14491 1.55021i
\(262\) 0 0
\(263\) 91.1958 0.346752 0.173376 0.984856i \(-0.444532\pi\)
0.173376 + 0.984856i \(0.444532\pi\)
\(264\) 0 0
\(265\) 404.297 + 87.0160i 1.52565 + 0.328362i
\(266\) 0 0
\(267\) −200.686 + 66.0751i −0.751633 + 0.247472i
\(268\) 0 0
\(269\) 325.164i 1.20879i −0.796686 0.604393i \(-0.793416\pi\)
0.796686 0.604393i \(-0.206584\pi\)
\(270\) 0 0
\(271\) −132.719 −0.489738 −0.244869 0.969556i \(-0.578745\pi\)
−0.244869 + 0.969556i \(0.578745\pi\)
\(272\) 0 0
\(273\) 103.768 + 315.170i 0.380104 + 1.15447i
\(274\) 0 0
\(275\) 77.4436 171.577i 0.281613 0.623916i
\(276\) 0 0
\(277\) 254.199i 0.917687i 0.888517 + 0.458844i \(0.151736\pi\)
−0.888517 + 0.458844i \(0.848264\pi\)
\(278\) 0 0
\(279\) −314.469 + 232.252i −1.12713 + 0.832446i
\(280\) 0 0
\(281\) 19.5488i 0.0695687i −0.999395 0.0347843i \(-0.988926\pi\)
0.999395 0.0347843i \(-0.0110744\pi\)
\(282\) 0 0
\(283\) 109.674i 0.387541i −0.981047 0.193770i \(-0.937928\pi\)
0.981047 0.193770i \(-0.0620717\pi\)
\(284\) 0 0
\(285\) −12.4901 117.307i −0.0438250 0.411604i
\(286\) 0 0
\(287\) −349.797 −1.21881
\(288\) 0 0
\(289\) −272.032 −0.941286
\(290\) 0 0
\(291\) −9.81275 + 3.23081i −0.0337208 + 0.0111024i
\(292\) 0 0
\(293\) −178.388 −0.608832 −0.304416 0.952539i \(-0.598461\pi\)
−0.304416 + 0.952539i \(0.598461\pi\)
\(294\) 0 0
\(295\) −102.683 + 477.088i −0.348077 + 1.61725i
\(296\) 0 0
\(297\) 117.563 165.867i 0.395834 0.558474i
\(298\) 0 0
\(299\) 317.006i 1.06022i
\(300\) 0 0
\(301\) 349.407 1.16082
\(302\) 0 0
\(303\) 140.324 46.2011i 0.463115 0.152479i
\(304\) 0 0
\(305\) 20.2137 + 4.35054i 0.0662744 + 0.0142641i
\(306\) 0 0
\(307\) 289.046i 0.941518i 0.882262 + 0.470759i \(0.156020\pi\)
−0.882262 + 0.470759i \(0.843980\pi\)
\(308\) 0 0
\(309\) 258.016 84.9508i 0.835003 0.274922i
\(310\) 0 0
\(311\) 336.061i 1.08058i 0.841478 + 0.540291i \(0.181686\pi\)
−0.841478 + 0.540291i \(0.818314\pi\)
\(312\) 0 0
\(313\) 563.702i 1.80096i 0.434894 + 0.900482i \(0.356786\pi\)
−0.434894 + 0.900482i \(0.643214\pi\)
\(314\) 0 0
\(315\) 126.157 + 279.386i 0.400497 + 0.886940i
\(316\) 0 0
\(317\) −139.938 −0.441445 −0.220722 0.975337i \(-0.570842\pi\)
−0.220722 + 0.975337i \(0.570842\pi\)
\(318\) 0 0
\(319\) 420.824 1.31920
\(320\) 0 0
\(321\) 61.3426 + 186.312i 0.191098 + 0.580412i
\(322\) 0 0
\(323\) 32.3968 0.100300
\(324\) 0 0
\(325\) 166.989 369.965i 0.513812 1.13835i
\(326\) 0 0
\(327\) 159.933 + 485.756i 0.489092 + 1.48549i
\(328\) 0 0
\(329\) 420.718i 1.27878i
\(330\) 0 0
\(331\) −14.5116 −0.0438416 −0.0219208 0.999760i \(-0.506978\pi\)
−0.0219208 + 0.999760i \(0.506978\pi\)
\(332\) 0 0
\(333\) −168.866 228.644i −0.507104 0.686617i
\(334\) 0 0
\(335\) 66.4831 308.896i 0.198457 0.922079i
\(336\) 0 0
\(337\) 347.492i 1.03113i −0.856850 0.515566i \(-0.827582\pi\)
0.856850 0.515566i \(-0.172418\pi\)
\(338\) 0 0
\(339\) −51.9889 157.903i −0.153359 0.465790i
\(340\) 0 0
\(341\) 327.075i 0.959165i
\(342\) 0 0
\(343\) 351.469i 1.02469i
\(344\) 0 0
\(345\) 31.0075 + 291.223i 0.0898769 + 0.844124i
\(346\) 0 0
\(347\) 273.321 0.787670 0.393835 0.919181i \(-0.371148\pi\)
0.393835 + 0.919181i \(0.371148\pi\)
\(348\) 0 0
\(349\) −550.853 −1.57838 −0.789188 0.614152i \(-0.789498\pi\)
−0.789188 + 0.614152i \(0.789498\pi\)
\(350\) 0 0
\(351\) 253.496 357.652i 0.722212 1.01895i
\(352\) 0 0
\(353\) −643.177 −1.82203 −0.911015 0.412373i \(-0.864700\pi\)
−0.911015 + 0.412373i \(0.864700\pi\)
\(354\) 0 0
\(355\) −42.4067 + 197.032i −0.119455 + 0.555019i
\(356\) 0 0
\(357\) −79.9614 + 26.3270i −0.223982 + 0.0737451i
\(358\) 0 0
\(359\) 465.873i 1.29770i 0.760918 + 0.648849i \(0.224749\pi\)
−0.760918 + 0.648849i \(0.775251\pi\)
\(360\) 0 0
\(361\) −299.147 −0.828661
\(362\) 0 0
\(363\) −60.3280 183.231i −0.166193 0.504767i
\(364\) 0 0
\(365\) 82.5974 383.767i 0.226294 1.05142i
\(366\) 0 0
\(367\) 44.7168i 0.121844i −0.998143 0.0609221i \(-0.980596\pi\)
0.998143 0.0609221i \(-0.0194041\pi\)
\(368\) 0 0
\(369\) 274.552 + 371.743i 0.744044 + 1.00743i
\(370\) 0 0
\(371\) 563.443i 1.51872i
\(372\) 0 0
\(373\) 275.158i 0.737688i −0.929491 0.368844i \(-0.879754\pi\)
0.929491 0.368844i \(-0.120246\pi\)
\(374\) 0 0
\(375\) 117.220 356.209i 0.312585 0.949890i
\(376\) 0 0
\(377\) 907.408 2.40692
\(378\) 0 0
\(379\) −505.072 −1.33264 −0.666322 0.745664i \(-0.732132\pi\)
−0.666322 + 0.745664i \(0.732132\pi\)
\(380\) 0 0
\(381\) 213.692 70.3575i 0.560873 0.184665i
\(382\) 0 0
\(383\) −193.577 −0.505422 −0.252711 0.967542i \(-0.581322\pi\)
−0.252711 + 0.967542i \(0.581322\pi\)
\(384\) 0 0
\(385\) −250.730 53.9642i −0.651248 0.140167i
\(386\) 0 0
\(387\) −274.246 371.328i −0.708646 0.959505i
\(388\) 0 0
\(389\) 280.077i 0.719993i 0.932954 + 0.359996i \(0.117222\pi\)
−0.932954 + 0.359996i \(0.882778\pi\)
\(390\) 0 0
\(391\) −80.4272 −0.205696
\(392\) 0 0
\(393\) −288.226 + 94.8975i −0.733401 + 0.241469i
\(394\) 0 0
\(395\) −249.342 53.6652i −0.631244 0.135861i
\(396\) 0 0
\(397\) 468.421i 1.17990i 0.807439 + 0.589951i \(0.200853\pi\)
−0.807439 + 0.589951i \(0.799147\pi\)
\(398\) 0 0
\(399\) −152.665 + 50.2645i −0.382620 + 0.125976i
\(400\) 0 0
\(401\) 274.969i 0.685707i 0.939389 + 0.342854i \(0.111394\pi\)
−0.939389 + 0.342854i \(0.888606\pi\)
\(402\) 0 0
\(403\) 705.261i 1.75003i
\(404\) 0 0
\(405\) 197.895 353.359i 0.488630 0.872491i
\(406\) 0 0
\(407\) 237.809 0.584298
\(408\) 0 0
\(409\) −202.697 −0.495592 −0.247796 0.968812i \(-0.579706\pi\)
−0.247796 + 0.968812i \(0.579706\pi\)
\(410\) 0 0
\(411\) 107.228 + 325.678i 0.260896 + 0.792403i
\(412\) 0 0
\(413\) 664.888 1.60990
\(414\) 0 0
\(415\) 13.2961 + 2.86169i 0.0320388 + 0.00689564i
\(416\) 0 0
\(417\) −215.931 655.835i −0.517820 1.57274i
\(418\) 0 0
\(419\) 76.6340i 0.182897i −0.995810 0.0914487i \(-0.970850\pi\)
0.995810 0.0914487i \(-0.0291497\pi\)
\(420\) 0 0
\(421\) −183.991 −0.437033 −0.218516 0.975833i \(-0.570122\pi\)
−0.218516 + 0.975833i \(0.570122\pi\)
\(422\) 0 0
\(423\) 447.114 330.218i 1.05701 0.780657i
\(424\) 0 0
\(425\) 93.8635 + 42.3666i 0.220855 + 0.0996861i
\(426\) 0 0
\(427\) 28.1705i 0.0659731i
\(428\) 0 0
\(429\) 114.700 + 348.370i 0.267365 + 0.812052i
\(430\) 0 0
\(431\) 671.408i 1.55779i −0.627153 0.778896i \(-0.715780\pi\)
0.627153 0.778896i \(-0.284220\pi\)
\(432\) 0 0
\(433\) 399.351i 0.922288i 0.887325 + 0.461144i \(0.152561\pi\)
−0.887325 + 0.461144i \(0.847439\pi\)
\(434\) 0 0
\(435\) 833.606 88.7570i 1.91633 0.204039i
\(436\) 0 0
\(437\) −153.555 −0.351384
\(438\) 0 0
\(439\) 140.833 0.320804 0.160402 0.987052i \(-0.448721\pi\)
0.160402 + 0.987052i \(0.448721\pi\)
\(440\) 0 0
\(441\) −18.7799 + 13.8700i −0.0425849 + 0.0314513i
\(442\) 0 0
\(443\) −211.416 −0.477237 −0.238618 0.971113i \(-0.576694\pi\)
−0.238618 + 0.971113i \(0.576694\pi\)
\(444\) 0 0
\(445\) 74.0935 344.256i 0.166502 0.773610i
\(446\) 0 0
\(447\) −26.0004 + 8.56052i −0.0581664 + 0.0191511i
\(448\) 0 0
\(449\) 455.166i 1.01373i 0.862025 + 0.506866i \(0.169196\pi\)
−0.862025 + 0.506866i \(0.830804\pi\)
\(450\) 0 0
\(451\) −386.645 −0.857307
\(452\) 0 0
\(453\) 152.935 + 464.502i 0.337606 + 1.02539i
\(454\) 0 0
\(455\) −540.641 116.361i −1.18822 0.255738i
\(456\) 0 0
\(457\) 555.776i 1.21614i −0.793883 0.608070i \(-0.791944\pi\)
0.793883 0.608070i \(-0.208056\pi\)
\(458\) 0 0
\(459\) 90.7396 + 64.3143i 0.197690 + 0.140118i
\(460\) 0 0
\(461\) 369.227i 0.800927i 0.916313 + 0.400463i \(0.131151\pi\)
−0.916313 + 0.400463i \(0.868849\pi\)
\(462\) 0 0
\(463\) 360.832i 0.779336i 0.920955 + 0.389668i \(0.127410\pi\)
−0.920955 + 0.389668i \(0.872590\pi\)
\(464\) 0 0
\(465\) −68.9842 647.900i −0.148353 1.39333i
\(466\) 0 0
\(467\) −496.306 −1.06275 −0.531377 0.847135i \(-0.678325\pi\)
−0.531377 + 0.847135i \(0.678325\pi\)
\(468\) 0 0
\(469\) −430.490 −0.917888
\(470\) 0 0
\(471\) 349.151 114.957i 0.741296 0.244069i
\(472\) 0 0
\(473\) 386.214 0.816520
\(474\) 0 0
\(475\) 179.208 + 80.8880i 0.377280 + 0.170290i
\(476\) 0 0
\(477\) −598.793 + 442.241i −1.25533 + 0.927131i
\(478\) 0 0
\(479\) 286.032i 0.597145i 0.954387 + 0.298572i \(0.0965105\pi\)
−0.954387 + 0.298572i \(0.903490\pi\)
\(480\) 0 0
\(481\) 512.780 1.06607
\(482\) 0 0
\(483\) 379.002 124.785i 0.784682 0.258354i
\(484\) 0 0
\(485\) 3.62288 16.8328i 0.00746985 0.0347067i
\(486\) 0 0
\(487\) 34.3276i 0.0704880i −0.999379 0.0352440i \(-0.988779\pi\)
0.999379 0.0352440i \(-0.0112208\pi\)
\(488\) 0 0
\(489\) 190.052 62.5738i 0.388653 0.127963i
\(490\) 0 0
\(491\) 26.4204i 0.0538094i −0.999638 0.0269047i \(-0.991435\pi\)
0.999638 0.0269047i \(-0.00856507\pi\)
\(492\) 0 0
\(493\) 230.218i 0.466973i
\(494\) 0 0
\(495\) 139.446 + 308.817i 0.281709 + 0.623873i
\(496\) 0 0
\(497\) 274.591 0.552496
\(498\) 0 0
\(499\) −72.9046 −0.146101 −0.0730507 0.997328i \(-0.523273\pi\)
−0.0730507 + 0.997328i \(0.523273\pi\)
\(500\) 0 0
\(501\) 153.473 + 466.134i 0.306333 + 0.930407i
\(502\) 0 0
\(503\) −228.404 −0.454083 −0.227041 0.973885i \(-0.572905\pi\)
−0.227041 + 0.973885i \(0.572905\pi\)
\(504\) 0 0
\(505\) −51.8077 + 240.711i −0.102589 + 0.476655i
\(506\) 0 0
\(507\) 88.7677 + 269.609i 0.175084 + 0.531773i
\(508\) 0 0
\(509\) 99.1735i 0.194840i −0.995243 0.0974199i \(-0.968941\pi\)
0.995243 0.0974199i \(-0.0310590\pi\)
\(510\) 0 0
\(511\) −534.832 −1.04664
\(512\) 0 0
\(513\) 173.244 + 122.791i 0.337707 + 0.239359i
\(514\) 0 0
\(515\) −95.2597 + 442.600i −0.184970 + 0.859417i
\(516\) 0 0
\(517\) 465.037i 0.899492i
\(518\) 0 0
\(519\) 32.5678 + 98.9163i 0.0627511 + 0.190590i
\(520\) 0 0
\(521\) 691.462i 1.32718i −0.748095 0.663592i \(-0.769031\pi\)
0.748095 0.663592i \(-0.230969\pi\)
\(522\) 0 0
\(523\) 821.405i 1.57056i 0.619138 + 0.785282i \(0.287482\pi\)
−0.619138 + 0.785282i \(0.712518\pi\)
\(524\) 0 0
\(525\) −508.051 54.0149i −0.967716 0.102885i
\(526\) 0 0
\(527\) 178.931 0.339528
\(528\) 0 0
\(529\) −147.791 −0.279377
\(530\) 0 0
\(531\) −521.864 706.602i −0.982795 1.33070i
\(532\) 0 0
\(533\) −833.710 −1.56418
\(534\) 0 0
\(535\) −319.599 68.7866i −0.597382 0.128573i
\(536\) 0 0
\(537\) −779.196 + 256.547i −1.45102 + 0.477742i
\(538\) 0 0
\(539\) 19.5328i 0.0362389i
\(540\) 0 0
\(541\) 446.354 0.825054 0.412527 0.910945i \(-0.364646\pi\)
0.412527 + 0.910945i \(0.364646\pi\)
\(542\) 0 0
\(543\) 38.3487 + 116.474i 0.0706237 + 0.214501i
\(544\) 0 0
\(545\) −833.264 179.341i −1.52892 0.329067i
\(546\) 0 0
\(547\) 485.492i 0.887553i 0.896137 + 0.443777i \(0.146362\pi\)
−0.896137 + 0.443777i \(0.853638\pi\)
\(548\) 0 0
\(549\) −29.9379 + 22.1108i −0.0545317 + 0.0402746i
\(550\) 0 0
\(551\) 439.540i 0.797714i
\(552\) 0 0
\(553\) 347.492i 0.628375i
\(554\) 0 0
\(555\) 471.074 50.1569i 0.848782 0.0903728i
\(556\) 0 0
\(557\) 995.191 1.78670 0.893349 0.449363i \(-0.148349\pi\)
0.893349 + 0.449363i \(0.148349\pi\)
\(558\) 0 0
\(559\) 832.780 1.48977
\(560\) 0 0
\(561\) −88.3847 + 29.1003i −0.157548 + 0.0518722i
\(562\) 0 0
\(563\) 486.571 0.864248 0.432124 0.901814i \(-0.357764\pi\)
0.432124 + 0.901814i \(0.357764\pi\)
\(564\) 0 0
\(565\) 270.866 + 58.2978i 0.479408 + 0.103182i
\(566\) 0 0
\(567\) −527.383 162.287i −0.930128 0.286220i
\(568\) 0 0
\(569\) 737.704i 1.29649i −0.761431 0.648246i \(-0.775503\pi\)
0.761431 0.648246i \(-0.224497\pi\)
\(570\) 0 0
\(571\) 805.843 1.41128 0.705642 0.708569i \(-0.250659\pi\)
0.705642 + 0.708569i \(0.250659\pi\)
\(572\) 0 0
\(573\) −115.672 + 38.0846i −0.201871 + 0.0664652i
\(574\) 0 0
\(575\) −444.895 200.810i −0.773730 0.349234i
\(576\) 0 0
\(577\) 690.512i 1.19673i −0.801225 0.598364i \(-0.795818\pi\)
0.801225 0.598364i \(-0.204182\pi\)
\(578\) 0 0
\(579\) −402.521 + 132.529i −0.695201 + 0.228892i
\(580\) 0 0
\(581\) 18.5299i 0.0318932i
\(582\) 0 0
\(583\) 622.798i 1.06826i
\(584\) 0 0
\(585\) 300.683 + 665.891i 0.513988 + 1.13828i
\(586\) 0 0
\(587\) 670.611 1.14244 0.571219 0.820798i \(-0.306471\pi\)
0.571219 + 0.820798i \(0.306471\pi\)
\(588\) 0 0
\(589\) 341.622 0.580004
\(590\) 0 0
\(591\) 218.265 + 662.922i 0.369314 + 1.12170i
\(592\) 0 0
\(593\) 214.249 0.361296 0.180648 0.983548i \(-0.442181\pi\)
0.180648 + 0.983548i \(0.442181\pi\)
\(594\) 0 0
\(595\) 29.5218 137.166i 0.0496165 0.230530i
\(596\) 0 0
\(597\) −80.0979 243.276i −0.134167 0.407498i
\(598\) 0 0
\(599\) 303.315i 0.506368i 0.967418 + 0.253184i \(0.0814779\pi\)
−0.967418 + 0.253184i \(0.918522\pi\)
\(600\) 0 0
\(601\) 66.0555 0.109909 0.0549546 0.998489i \(-0.482499\pi\)
0.0549546 + 0.998489i \(0.482499\pi\)
\(602\) 0 0
\(603\) 337.887 + 457.498i 0.560343 + 0.758703i
\(604\) 0 0
\(605\) 314.313 + 67.6489i 0.519526 + 0.111816i
\(606\) 0 0
\(607\) 178.972i 0.294847i 0.989073 + 0.147423i \(0.0470980\pi\)
−0.989073 + 0.147423i \(0.952902\pi\)
\(608\) 0 0
\(609\) −357.188 1084.87i −0.586516 1.78139i
\(610\) 0 0
\(611\) 1002.74i 1.64115i
\(612\) 0 0
\(613\) 728.201i 1.18793i −0.804491 0.593965i \(-0.797562\pi\)
0.804491 0.593965i \(-0.202438\pi\)
\(614\) 0 0
\(615\) −765.902 + 81.5483i −1.24537 + 0.132599i
\(616\) 0 0
\(617\) 198.426 0.321598 0.160799 0.986987i \(-0.448593\pi\)
0.160799 + 0.986987i \(0.448593\pi\)
\(618\) 0 0
\(619\) 17.1752 0.0277468 0.0138734 0.999904i \(-0.495584\pi\)
0.0138734 + 0.999904i \(0.495584\pi\)
\(620\) 0 0
\(621\) −430.088 304.837i −0.692574 0.490881i
\(622\) 0 0
\(623\) −479.768 −0.770094
\(624\) 0 0
\(625\) 413.439 + 468.714i 0.661503 + 0.749943i
\(626\) 0 0
\(627\) −168.747 + 55.5595i −0.269135 + 0.0886116i
\(628\) 0 0
\(629\) 130.097i 0.206831i
\(630\) 0 0
\(631\) −388.876 −0.616285 −0.308142 0.951340i \(-0.599707\pi\)
−0.308142 + 0.951340i \(0.599707\pi\)
\(632\) 0 0
\(633\) −266.947 810.781i −0.421717 1.28085i
\(634\) 0 0
\(635\) −78.8955 + 366.568i −0.124245 + 0.577272i
\(636\) 0 0
\(637\) 42.1179i 0.0661191i
\(638\) 0 0
\(639\) −215.524 291.818i −0.337283 0.456680i
\(640\) 0 0
\(641\) 180.547i 0.281664i −0.990034 0.140832i \(-0.955022\pi\)
0.990034 0.140832i \(-0.0449778\pi\)
\(642\) 0 0
\(643\) 701.008i 1.09021i −0.838367 0.545107i \(-0.816489\pi\)
0.838367 0.545107i \(-0.183511\pi\)
\(644\) 0 0
\(645\) 765.047 81.4573i 1.18612 0.126290i
\(646\) 0 0
\(647\) 114.266 0.176609 0.0883046 0.996094i \(-0.471855\pi\)
0.0883046 + 0.996094i \(0.471855\pi\)
\(648\) 0 0
\(649\) 734.928 1.13240
\(650\) 0 0
\(651\) −843.187 + 277.616i −1.29522 + 0.426446i
\(652\) 0 0
\(653\) 240.882 0.368884 0.184442 0.982843i \(-0.440952\pi\)
0.184442 + 0.982843i \(0.440952\pi\)
\(654\) 0 0
\(655\) 106.414 494.423i 0.162463 0.754844i
\(656\) 0 0
\(657\) 419.785 + 568.387i 0.638942 + 0.865125i
\(658\) 0 0
\(659\) 1218.15i 1.84848i −0.381807 0.924242i \(-0.624698\pi\)
0.381807 0.924242i \(-0.375302\pi\)
\(660\) 0 0
\(661\) −1075.32 −1.62681 −0.813404 0.581699i \(-0.802388\pi\)
−0.813404 + 0.581699i \(0.802388\pi\)
\(662\) 0 0
\(663\) −190.581 + 62.7480i −0.287452 + 0.0946425i
\(664\) 0 0
\(665\) 56.3642 261.882i 0.0847583 0.393807i
\(666\) 0 0
\(667\) 1091.19i 1.63596i
\(668\) 0 0
\(669\) −86.3189 + 28.4202i −0.129027 + 0.0424816i
\(670\) 0 0
\(671\) 31.1381i 0.0464054i
\(672\) 0 0
\(673\) 356.367i 0.529521i −0.964314 0.264760i \(-0.914707\pi\)
0.964314 0.264760i \(-0.0852928\pi\)
\(674\) 0 0
\(675\) 341.361 + 582.321i 0.505719 + 0.862698i
\(676\) 0 0
\(677\) −79.8649 −0.117969 −0.0589844 0.998259i \(-0.518786\pi\)
−0.0589844 + 0.998259i \(0.518786\pi\)
\(678\) 0 0
\(679\) −23.4588 −0.0345490
\(680\) 0 0
\(681\) −224.585 682.120i −0.329788 1.00164i
\(682\) 0 0
\(683\) −1270.41 −1.86004 −0.930021 0.367507i \(-0.880211\pi\)
−0.930021 + 0.367507i \(0.880211\pi\)
\(684\) 0 0
\(685\) −558.667 120.241i −0.815572 0.175534i
\(686\) 0 0
\(687\) −267.347 811.996i −0.389151 1.18195i
\(688\) 0 0
\(689\) 1342.92i 1.94908i
\(690\) 0 0
\(691\) 1244.39 1.80085 0.900424 0.435013i \(-0.143256\pi\)
0.900424 + 0.435013i \(0.143256\pi\)
\(692\) 0 0
\(693\) 371.350 274.262i 0.535858 0.395760i
\(694\) 0 0
\(695\) 1125.02 + 242.135i 1.61873 + 0.348395i
\(696\) 0 0
\(697\) 211.520i 0.303472i
\(698\) 0 0
\(699\) −88.0623 267.466i −0.125983 0.382641i
\(700\) 0 0
\(701\) 1034.47i 1.47570i 0.674965 + 0.737850i \(0.264159\pi\)
−0.674965 + 0.737850i \(0.735841\pi\)
\(702\) 0 0
\(703\) 248.386i 0.353323i
\(704\) 0 0
\(705\) 98.0821 + 921.188i 0.139124 + 1.30665i
\(706\) 0 0
\(707\) 335.464 0.474489
\(708\) 0 0
\(709\) 659.081 0.929592 0.464796 0.885418i \(-0.346128\pi\)
0.464796 + 0.885418i \(0.346128\pi\)
\(710\) 0 0
\(711\) 369.293 272.743i 0.519399 0.383604i
\(712\) 0 0
\(713\) −848.099 −1.18948
\(714\) 0 0
\(715\) −597.593 128.619i −0.835795 0.179886i
\(716\) 0 0
\(717\) −679.116 + 223.597i −0.947164 + 0.311850i
\(718\) 0 0
\(719\) 471.213i 0.655373i −0.944787 0.327686i \(-0.893731\pi\)
0.944787 0.327686i \(-0.106269\pi\)
\(720\) 0 0
\(721\) 616.823 0.855511
\(722\) 0 0
\(723\) −41.5545 126.211i −0.0574750 0.174566i
\(724\) 0 0
\(725\) −574.804 + 1273.48i −0.792833 + 1.75653i
\(726\) 0 0
\(727\) 640.411i 0.880895i 0.897778 + 0.440447i \(0.145180\pi\)
−0.897778 + 0.440447i \(0.854820\pi\)
\(728\) 0 0
\(729\) 241.469 + 687.847i 0.331233 + 0.943549i
\(730\) 0 0
\(731\) 211.284i 0.289034i
\(732\) 0 0
\(733\) 619.831i 0.845608i −0.906221 0.422804i \(-0.861046\pi\)
0.906221 0.422804i \(-0.138954\pi\)
\(734\) 0 0
\(735\) −4.11971 38.6923i −0.00560504 0.0526426i
\(736\) 0 0
\(737\) −475.838 −0.645642
\(738\) 0 0
\(739\) −135.992 −0.184022 −0.0920111 0.995758i \(-0.529330\pi\)
−0.0920111 + 0.995758i \(0.529330\pi\)
\(740\) 0 0
\(741\) −363.864 + 119.801i −0.491045 + 0.161675i
\(742\) 0 0
\(743\) 986.468 1.32768 0.663841 0.747874i \(-0.268925\pi\)
0.663841 + 0.747874i \(0.268925\pi\)
\(744\) 0 0
\(745\) 9.59936 44.6010i 0.0128851 0.0598671i
\(746\) 0 0
\(747\) −19.6925 + 14.5440i −0.0263621 + 0.0194698i
\(748\) 0 0
\(749\) 445.405i 0.594667i
\(750\) 0 0
\(751\) −551.977 −0.734990 −0.367495 0.930026i \(-0.619784\pi\)
−0.367495 + 0.930026i \(0.619784\pi\)
\(752\) 0 0
\(753\) 835.175 274.978i 1.10913 0.365177i
\(754\) 0 0
\(755\) −796.805 171.495i −1.05537 0.227145i
\(756\) 0 0
\(757\) 1143.91i 1.51111i 0.655084 + 0.755556i \(0.272633\pi\)
−0.655084 + 0.755556i \(0.727367\pi\)
\(758\) 0 0
\(759\) 418.926 137.930i 0.551945 0.181726i
\(760\) 0 0
\(761\) 29.3201i 0.0385284i 0.999814 + 0.0192642i \(0.00613236\pi\)
−0.999814 + 0.0192642i \(0.993868\pi\)
\(762\) 0 0
\(763\) 1161.27i 1.52198i
\(764\) 0 0
\(765\) −168.943 + 76.2859i −0.220840 + 0.0997201i
\(766\) 0 0
\(767\) 1584.70 2.06610
\(768\) 0 0
\(769\) −61.7841 −0.0803434 −0.0401717 0.999193i \(-0.512790\pi\)
−0.0401717 + 0.999193i \(0.512790\pi\)
\(770\) 0 0
\(771\) 158.864 + 482.509i 0.206050 + 0.625822i
\(772\) 0 0
\(773\) 444.408 0.574913 0.287457 0.957794i \(-0.407190\pi\)
0.287457 + 0.957794i \(0.407190\pi\)
\(774\) 0 0
\(775\) 989.783 + 446.753i 1.27714 + 0.576455i
\(776\) 0 0
\(777\) −201.849 613.063i −0.259779 0.789012i
\(778\) 0 0
\(779\) 403.842i 0.518410i
\(780\) 0 0
\(781\) 303.517 0.388626
\(782\) 0 0
\(783\) −872.576 + 1231.10i −1.11440 + 1.57229i
\(784\) 0 0
\(785\) −128.907 + 598.932i −0.164212 + 0.762971i
\(786\) 0 0
\(787\) 206.738i 0.262691i 0.991337 + 0.131346i \(0.0419298\pi\)
−0.991337 + 0.131346i \(0.958070\pi\)
\(788\) 0 0
\(789\) −85.5595 259.865i −0.108440 0.329360i
\(790\) 0 0
\(791\) 377.489i 0.477230i
\(792\) 0 0
\(793\) 67.1419i 0.0846682i
\(794\) 0 0
\(795\) −131.356 1233.69i −0.165227 1.55181i
\(796\) 0 0
\(797\) −235.281 −0.295208 −0.147604 0.989047i \(-0.547156\pi\)
−0.147604 + 0.989047i \(0.547156\pi\)