Properties

Label 1400.2.bh.f.849.1
Level $1400$
Weight $2$
Character 1400.849
Analytic conductor $11.179$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.bh (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 849.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1400.849
Dual form 1400.2.bh.f.249.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.59808 + 1.50000i) q^{3} +(-1.73205 + 2.00000i) q^{7} +(3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(q+(-2.59808 + 1.50000i) q^{3} +(-1.73205 + 2.00000i) q^{7} +(3.00000 - 5.19615i) q^{9} +(0.500000 + 0.866025i) q^{11} -2.00000i q^{13} +(2.59808 - 1.50000i) q^{17} +(2.50000 - 4.33013i) q^{19} +(1.50000 - 7.79423i) q^{21} +(-2.59808 - 1.50000i) q^{23} +9.00000i q^{27} +6.00000 q^{29} +(0.500000 + 0.866025i) q^{31} +(-2.59808 - 1.50000i) q^{33} +(4.33013 + 2.50000i) q^{37} +(3.00000 + 5.19615i) q^{39} -10.0000 q^{41} +4.00000i q^{43} +(-0.866025 - 0.500000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-4.50000 + 7.79423i) q^{51} +(7.79423 - 4.50000i) q^{53} +15.0000i q^{57} +(1.50000 + 2.59808i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(5.19615 + 15.0000i) q^{63} +(9.52628 - 5.50000i) q^{67} +9.00000 q^{69} +16.0000 q^{71} +(-6.06218 + 3.50000i) q^{73} +(-2.59808 - 0.500000i) q^{77} +(-5.50000 + 9.52628i) q^{79} +(-4.50000 - 7.79423i) q^{81} +4.00000i q^{83} +(-15.5885 + 9.00000i) q^{87} +(-4.50000 + 7.79423i) q^{89} +(4.00000 + 3.46410i) q^{91} +(-2.59808 - 1.50000i) q^{93} +6.00000i q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 12q^{9} + O(q^{10}) \) \( 4q + 12q^{9} + 2q^{11} + 10q^{19} + 6q^{21} + 24q^{29} + 2q^{31} + 12q^{39} - 40q^{41} - 4q^{49} - 18q^{51} + 6q^{59} - 6q^{61} + 36q^{69} + 64q^{71} - 22q^{79} - 18q^{81} - 18q^{89} + 16q^{91} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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
\(3\) −2.59808 + 1.50000i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.73205 + 2.00000i −0.654654 + 0.755929i
\(8\) 0 0
\(9\) 3.00000 5.19615i 1.00000 1.73205i
\(10\) 0 0
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i 0.931505 0.363727i \(-0.118496\pi\)
−0.780750 + 0.624844i \(0.785163\pi\)
\(12\) 0 0
\(13\) 2.00000i 0.554700i −0.960769 0.277350i \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.59808 1.50000i 0.630126 0.363803i −0.150675 0.988583i \(-0.548145\pi\)
0.780801 + 0.624780i \(0.214811\pi\)
\(18\) 0 0
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) 0 0
\(21\) 1.50000 7.79423i 0.327327 1.70084i
\(22\) 0 0
\(23\) −2.59808 1.50000i −0.541736 0.312772i 0.204046 0.978961i \(-0.434591\pi\)
−0.745782 + 0.666190i \(0.767924\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 9.00000i 1.73205i
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) 0 0
\(33\) −2.59808 1.50000i −0.452267 0.261116i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.33013 + 2.50000i 0.711868 + 0.410997i 0.811752 0.584002i \(-0.198514\pi\)
−0.0998840 + 0.994999i \(0.531847\pi\)
\(38\) 0 0
\(39\) 3.00000 + 5.19615i 0.480384 + 0.832050i
\(40\) 0 0
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i 0.952353 + 0.304997i \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.866025 0.500000i −0.126323 0.0729325i 0.435507 0.900185i \(-0.356569\pi\)
−0.561830 + 0.827253i \(0.689902\pi\)
\(48\) 0 0
\(49\) −1.00000 6.92820i −0.142857 0.989743i
\(50\) 0 0
\(51\) −4.50000 + 7.79423i −0.630126 + 1.09141i
\(52\) 0 0
\(53\) 7.79423 4.50000i 1.07062 0.618123i 0.142269 0.989828i \(-0.454560\pi\)
0.928351 + 0.371706i \(0.121227\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 15.0000i 1.98680i
\(58\) 0 0
\(59\) 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i \(-0.104104\pi\)
−0.751710 + 0.659494i \(0.770771\pi\)
\(60\) 0 0
\(61\) −1.50000 + 2.59808i −0.192055 + 0.332650i −0.945931 0.324367i \(-0.894849\pi\)
0.753876 + 0.657017i \(0.228182\pi\)
\(62\) 0 0
\(63\) 5.19615 + 15.0000i 0.654654 + 1.88982i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 9.52628 5.50000i 1.16382 0.671932i 0.211604 0.977356i \(-0.432131\pi\)
0.952217 + 0.305424i \(0.0987981\pi\)
\(68\) 0 0
\(69\) 9.00000 1.08347
\(70\) 0 0
\(71\) 16.0000 1.89885 0.949425 0.313993i \(-0.101667\pi\)
0.949425 + 0.313993i \(0.101667\pi\)
\(72\) 0 0
\(73\) −6.06218 + 3.50000i −0.709524 + 0.409644i −0.810885 0.585206i \(-0.801014\pi\)
0.101361 + 0.994850i \(0.467680\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.59808 0.500000i −0.296078 0.0569803i
\(78\) 0 0
\(79\) −5.50000 + 9.52628i −0.618798 + 1.07179i 0.370907 + 0.928670i \(0.379047\pi\)
−0.989705 + 0.143120i \(0.954286\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) 4.00000i 0.439057i 0.975606 + 0.219529i \(0.0704519\pi\)
−0.975606 + 0.219529i \(0.929548\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −15.5885 + 9.00000i −1.67126 + 0.964901i
\(88\) 0 0
\(89\) −4.50000 + 7.79423i −0.476999 + 0.826187i −0.999653 0.0263586i \(-0.991609\pi\)
0.522654 + 0.852545i \(0.324942\pi\)
\(90\) 0 0
\(91\) 4.00000 + 3.46410i 0.419314 + 0.363137i
\(92\) 0 0
\(93\) −2.59808 1.50000i −0.269408 0.155543i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.00000i 0.609208i 0.952479 + 0.304604i \(0.0985241\pi\)
−0.952479 + 0.304604i \(0.901476\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) 6.50000 + 11.2583i 0.646774 + 1.12025i 0.983889 + 0.178782i \(0.0572157\pi\)
−0.337115 + 0.941464i \(0.609451\pi\)
\(102\) 0 0
\(103\) 4.33013 + 2.50000i 0.426660 + 0.246332i 0.697923 0.716173i \(-0.254108\pi\)
−0.271263 + 0.962505i \(0.587441\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.59808 + 1.50000i 0.251166 + 0.145010i 0.620298 0.784366i \(-0.287012\pi\)
−0.369132 + 0.929377i \(0.620345\pi\)
\(108\) 0 0
\(109\) 5.50000 + 9.52628i 0.526804 + 0.912452i 0.999512 + 0.0312328i \(0.00994332\pi\)
−0.472708 + 0.881219i \(0.656723\pi\)
\(110\) 0 0
\(111\) −15.0000 −1.42374
\(112\) 0 0
\(113\) 10.0000i 0.940721i 0.882474 + 0.470360i \(0.155876\pi\)
−0.882474 + 0.470360i \(0.844124\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −10.3923 6.00000i −0.960769 0.554700i
\(118\) 0 0
\(119\) −1.50000 + 7.79423i −0.137505 + 0.714496i
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 0 0
\(123\) 25.9808 15.0000i 2.34261 1.35250i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 8.00000i 0.709885i −0.934888 0.354943i \(-0.884500\pi\)
0.934888 0.354943i \(-0.115500\pi\)
\(128\) 0 0
\(129\) −6.00000 10.3923i −0.528271 0.914991i
\(130\) 0 0
\(131\) −8.50000 + 14.7224i −0.742648 + 1.28630i 0.208637 + 0.977993i \(0.433097\pi\)
−0.951285 + 0.308312i \(0.900236\pi\)
\(132\) 0 0
\(133\) 4.33013 + 12.5000i 0.375470 + 1.08389i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.59808 1.50000i 0.221969 0.128154i −0.384893 0.922961i \(-0.625762\pi\)
0.606861 + 0.794808i \(0.292428\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 3.00000 0.252646
\(142\) 0 0
\(143\) 1.73205 1.00000i 0.144841 0.0836242i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 12.9904 + 16.5000i 1.07143 + 1.36090i
\(148\) 0 0
\(149\) 7.50000 12.9904i 0.614424 1.06421i −0.376061 0.926595i \(-0.622722\pi\)
0.990485 0.137619i \(-0.0439449\pi\)
\(150\) 0 0
\(151\) −7.50000 12.9904i −0.610341 1.05714i −0.991183 0.132502i \(-0.957699\pi\)
0.380841 0.924640i \(-0.375634\pi\)
\(152\) 0 0
\(153\) 18.0000i 1.45521i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 12.9904 7.50000i 1.03675 0.598565i 0.117836 0.993033i \(-0.462404\pi\)
0.918910 + 0.394468i \(0.129071\pi\)
\(158\) 0 0
\(159\) −13.5000 + 23.3827i −1.07062 + 1.85437i
\(160\) 0 0
\(161\) 7.50000 2.59808i 0.591083 0.204757i
\(162\) 0 0
\(163\) 7.79423 + 4.50000i 0.610491 + 0.352467i 0.773158 0.634214i \(-0.218676\pi\)
−0.162667 + 0.986681i \(0.552009\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 20.0000i 1.54765i −0.633402 0.773823i \(-0.718342\pi\)
0.633402 0.773823i \(-0.281658\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) 0 0
\(171\) −15.0000 25.9808i −1.14708 1.98680i
\(172\) 0 0
\(173\) −18.1865 10.5000i −1.38270 0.798300i −0.390218 0.920722i \(-0.627601\pi\)
−0.992478 + 0.122422i \(0.960934\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −7.79423 4.50000i −0.585850 0.338241i
\(178\) 0 0
\(179\) −0.500000 0.866025i −0.0373718 0.0647298i 0.846735 0.532016i \(-0.178565\pi\)
−0.884106 + 0.467286i \(0.845232\pi\)
\(180\) 0 0
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 0 0
\(183\) 9.00000i 0.665299i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 2.59808 + 1.50000i 0.189990 + 0.109691i
\(188\) 0 0
\(189\) −18.0000 15.5885i −1.30931 1.13389i
\(190\) 0 0
\(191\) −8.50000 + 14.7224i −0.615038 + 1.06528i 0.375339 + 0.926887i \(0.377526\pi\)
−0.990378 + 0.138390i \(0.955807\pi\)
\(192\) 0 0
\(193\) 4.33013 2.50000i 0.311689 0.179954i −0.335993 0.941865i \(-0.609072\pi\)
0.647682 + 0.761911i \(0.275738\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.0000i 1.28245i 0.767354 + 0.641223i \(0.221573\pi\)
−0.767354 + 0.641223i \(0.778427\pi\)
\(198\) 0 0
\(199\) −4.50000 7.79423i −0.318997 0.552518i 0.661282 0.750137i \(-0.270013\pi\)
−0.980279 + 0.197619i \(0.936679\pi\)
\(200\) 0 0
\(201\) −16.5000 + 28.5788i −1.16382 + 2.01580i
\(202\) 0 0
\(203\) −10.3923 + 12.0000i −0.729397 + 0.842235i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −15.5885 + 9.00000i −1.08347 + 0.625543i
\(208\) 0 0
\(209\) 5.00000 0.345857
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 0 0
\(213\) −41.5692 + 24.0000i −2.84828 + 1.64445i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −2.59808 0.500000i −0.176369 0.0339422i
\(218\) 0 0
\(219\) 10.5000 18.1865i 0.709524 1.22893i
\(220\) 0 0
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) 0 0
\(223\) 24.0000i 1.60716i −0.595198 0.803579i \(-0.702926\pi\)
0.595198 0.803579i \(-0.297074\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.06218 3.50000i 0.402361 0.232303i −0.285141 0.958485i \(-0.592041\pi\)
0.687502 + 0.726182i \(0.258707\pi\)
\(228\) 0 0
\(229\) 3.50000 6.06218i 0.231287 0.400600i −0.726900 0.686743i \(-0.759040\pi\)
0.958187 + 0.286143i \(0.0923732\pi\)
\(230\) 0 0
\(231\) 7.50000 2.59808i 0.493464 0.170941i
\(232\) 0 0
\(233\) −11.2583 6.50000i −0.737558 0.425829i 0.0836229 0.996497i \(-0.473351\pi\)
−0.821181 + 0.570668i \(0.806684\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 33.0000i 2.14358i
\(238\) 0 0
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 0 0
\(241\) 8.50000 + 14.7224i 0.547533 + 0.948355i 0.998443 + 0.0557856i \(0.0177663\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −8.66025 5.00000i −0.551039 0.318142i
\(248\) 0 0
\(249\) −6.00000 10.3923i −0.380235 0.658586i
\(250\) 0 0
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) 3.00000i 0.188608i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 11.2583 + 6.50000i 0.702275 + 0.405459i 0.808194 0.588916i \(-0.200445\pi\)
−0.105919 + 0.994375i \(0.533778\pi\)
\(258\) 0 0
\(259\) −12.5000 + 4.33013i −0.776712 + 0.269061i
\(260\) 0 0
\(261\) 18.0000 31.1769i 1.11417 1.92980i
\(262\) 0 0
\(263\) −2.59808 + 1.50000i −0.160204 + 0.0924940i −0.577959 0.816066i \(-0.696151\pi\)
0.417755 + 0.908560i \(0.362817\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 27.0000i 1.65237i
\(268\) 0 0
\(269\) −8.50000 14.7224i −0.518254 0.897643i −0.999775 0.0212079i \(-0.993249\pi\)
0.481521 0.876435i \(-0.340085\pi\)
\(270\) 0 0
\(271\) 1.50000 2.59808i 0.0911185 0.157822i −0.816864 0.576831i \(-0.804289\pi\)
0.907982 + 0.419009i \(0.137622\pi\)
\(272\) 0 0
\(273\) −15.5885 3.00000i −0.943456 0.181568i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 6.06218 3.50000i 0.364241 0.210295i −0.306699 0.951807i \(-0.599224\pi\)
0.670940 + 0.741512i \(0.265891\pi\)
\(278\) 0 0
\(279\) 6.00000 0.359211
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 0 0
\(283\) 14.7224 8.50000i 0.875158 0.505273i 0.00609896 0.999981i \(-0.498059\pi\)
0.869059 + 0.494709i \(0.164725\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 17.3205 20.0000i 1.02240 1.18056i
\(288\) 0 0
\(289\) −4.00000 + 6.92820i −0.235294 + 0.407541i
\(290\) 0 0
\(291\) −9.00000 15.5885i −0.527589 0.913812i
\(292\) 0 0
\(293\) 6.00000i 0.350524i −0.984522 0.175262i \(-0.943923\pi\)
0.984522 0.175262i \(-0.0560772\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −7.79423 + 4.50000i −0.452267 + 0.261116i
\(298\) 0 0
\(299\) −3.00000 + 5.19615i −0.173494 + 0.300501i
\(300\) 0 0
\(301\) −8.00000 6.92820i −0.461112 0.399335i
\(302\) 0 0
\(303\) −33.7750 19.5000i −1.94032 1.12025i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 4.00000i 0.228292i 0.993464 + 0.114146i \(0.0364132\pi\)
−0.993464 + 0.114146i \(0.963587\pi\)
\(308\) 0 0
\(309\) −15.0000 −0.853320
\(310\) 0 0
\(311\) −5.50000 9.52628i −0.311876 0.540186i 0.666892 0.745154i \(-0.267624\pi\)
−0.978769 + 0.204968i \(0.934291\pi\)
\(312\) 0 0
\(313\) 26.8468 + 15.5000i 1.51747 + 0.876112i 0.999789 + 0.0205381i \(0.00653795\pi\)
0.517681 + 0.855574i \(0.326795\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −23.3827 13.5000i −1.31330 0.758236i −0.330661 0.943750i \(-0.607272\pi\)
−0.982642 + 0.185514i \(0.940605\pi\)
\(318\) 0 0
\(319\) 3.00000 + 5.19615i 0.167968 + 0.290929i
\(320\) 0 0
\(321\) −9.00000 −0.502331
\(322\) 0 0
\(323\) 15.0000i 0.834622i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −28.5788 16.5000i −1.58041 0.912452i
\(328\) 0 0
\(329\) 2.50000 0.866025i 0.137829 0.0477455i
\(330\) 0 0
\(331\) 3.50000 6.06218i 0.192377 0.333207i −0.753660 0.657264i \(-0.771714\pi\)
0.946038 + 0.324057i \(0.105047\pi\)
\(332\) 0 0
\(333\) 25.9808 15.0000i 1.42374 0.821995i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 14.0000i 0.762629i 0.924445 + 0.381314i \(0.124528\pi\)
−0.924445 + 0.381314i \(0.875472\pi\)
\(338\) 0 0
\(339\) −15.0000 25.9808i −0.814688 1.41108i
\(340\) 0 0
\(341\) −0.500000 + 0.866025i −0.0270765 + 0.0468979i
\(342\) 0 0
\(343\) 15.5885 + 10.0000i 0.841698 + 0.539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.59808 1.50000i 0.139472 0.0805242i −0.428640 0.903475i \(-0.641007\pi\)
0.568112 + 0.822951i \(0.307674\pi\)
\(348\) 0 0
\(349\) 6.00000 0.321173 0.160586 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(350\) 0 0
\(351\) 18.0000 0.960769
\(352\) 0 0
\(353\) 4.33013 2.50000i 0.230469 0.133062i −0.380319 0.924855i \(-0.624186\pi\)
0.610789 + 0.791794i \(0.290853\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −7.79423 22.5000i −0.412514 1.19083i
\(358\) 0 0
\(359\) −7.50000 + 12.9904i −0.395835 + 0.685606i −0.993207 0.116358i \(-0.962878\pi\)
0.597372 + 0.801964i \(0.296211\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 0 0
\(363\) 30.0000i 1.57459i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 16.4545 9.50000i 0.858917 0.495896i −0.00473247 0.999989i \(-0.501506\pi\)
0.863649 + 0.504093i \(0.168173\pi\)
\(368\) 0 0
\(369\) −30.0000 + 51.9615i −1.56174 + 2.70501i
\(370\) 0 0
\(371\) −4.50000 + 23.3827i −0.233628 + 1.21397i
\(372\) 0 0
\(373\) 16.4545 + 9.50000i 0.851981 + 0.491891i 0.861319 0.508065i \(-0.169639\pi\)
−0.00933789 + 0.999956i \(0.502972\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.0000i 0.618031i
\(378\) 0 0
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 0 0
\(381\) 12.0000 + 20.7846i 0.614779 + 1.06483i
\(382\) 0 0
\(383\) 7.79423 + 4.50000i 0.398266 + 0.229939i 0.685736 0.727851i \(-0.259481\pi\)
−0.287469 + 0.957790i \(0.592814\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 20.7846 + 12.0000i 1.05654 + 0.609994i
\(388\) 0 0
\(389\) 9.50000 + 16.4545i 0.481669 + 0.834275i 0.999779 0.0210389i \(-0.00669738\pi\)
−0.518110 + 0.855314i \(0.673364\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 0 0
\(393\) 51.0000i 2.57261i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 14.7224 + 8.50000i 0.738898 + 0.426603i 0.821668 0.569966i \(-0.193044\pi\)
−0.0827707 + 0.996569i \(0.526377\pi\)
\(398\) 0 0
\(399\) −30.0000 25.9808i −1.50188 1.30066i
\(400\) 0 0
\(401\) −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i \(-0.857199\pi\)
0.826139 + 0.563466i \(0.190532\pi\)
\(402\) 0 0
\(403\) 1.73205 1.00000i 0.0862796 0.0498135i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.00000i 0.247841i
\(408\) 0 0
\(409\) 9.50000 + 16.4545i 0.469745 + 0.813622i 0.999402 0.0345902i \(-0.0110126\pi\)
−0.529657 + 0.848212i \(0.677679\pi\)
\(410\) 0 0
\(411\) −4.50000 + 7.79423i −0.221969 + 0.384461i
\(412\) 0 0
\(413\) −7.79423 1.50000i −0.383529 0.0738102i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 10.3923 6.00000i 0.508913 0.293821i
\(418\) 0 0
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 0 0
\(423\) −5.19615 + 3.00000i −0.252646 + 0.145865i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −2.59808 7.50000i −0.125730 0.362950i
\(428\) 0 0
\(429\) −3.00000 + 5.19615i −0.144841 + 0.250873i
\(430\) 0 0
\(431\) 20.5000 + 35.5070i 0.987450 + 1.71031i 0.630497 + 0.776192i \(0.282851\pi\)
0.356953 + 0.934122i \(0.383815\pi\)
\(432\) 0 0
\(433\) 26.0000i 1.24948i 0.780833 + 0.624740i \(0.214795\pi\)
−0.780833 + 0.624740i \(0.785205\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −12.9904 + 7.50000i −0.621414 + 0.358774i
\(438\) 0 0
\(439\) −7.50000 + 12.9904i −0.357955 + 0.619997i −0.987619 0.156871i \(-0.949859\pi\)
0.629664 + 0.776868i \(0.283193\pi\)
\(440\) 0 0
\(441\) −39.0000 15.5885i −1.85714 0.742307i
\(442\) 0 0
\(443\) −23.3827 13.5000i −1.11094 0.641404i −0.171871 0.985119i \(-0.554981\pi\)
−0.939074 + 0.343715i \(0.888315\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 45.0000i 2.12843i
\(448\) 0 0
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 0 0
\(451\) −5.00000 8.66025i −0.235441 0.407795i
\(452\) 0 0
\(453\) 38.9711 + 22.5000i 1.83102 + 1.05714i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 14.7224 + 8.50000i 0.688686 + 0.397613i 0.803120 0.595818i \(-0.203172\pi\)
−0.114433 + 0.993431i \(0.536505\pi\)
\(458\) 0 0
\(459\) 13.5000 + 23.3827i 0.630126 + 1.09141i
\(460\) 0 0
\(461\) −6.00000 −0.279448 −0.139724 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) 0 0
\(463\) 16.0000i 0.743583i 0.928316 + 0.371792i \(0.121256\pi\)
−0.928316 + 0.371792i \(0.878744\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −21.6506 12.5000i −1.00187 0.578431i −0.0930703 0.995660i \(-0.529668\pi\)
−0.908802 + 0.417229i \(0.863001\pi\)
\(468\) 0 0
\(469\) −5.50000 + 28.5788i −0.253966 + 1.31965i
\(470\) 0 0
\(471\) −22.5000 + 38.9711i −1.03675 + 1.79570i
\(472\) 0 0
\(473\) −3.46410 + 2.00000i −0.159280 + 0.0919601i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 54.0000i 2.47249i
\(478\) 0 0
\(479\) −10.5000 18.1865i −0.479757 0.830964i 0.519973 0.854183i \(-0.325942\pi\)
−0.999730 + 0.0232187i \(0.992609\pi\)
\(480\) 0 0
\(481\) 5.00000 8.66025i 0.227980 0.394874i
\(482\) 0 0
\(483\) −15.5885 + 18.0000i −0.709299 + 0.819028i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −11.2583 + 6.50000i −0.510164 + 0.294543i −0.732901 0.680335i \(-0.761834\pi\)
0.222737 + 0.974879i \(0.428501\pi\)
\(488\) 0 0
\(489\) −27.0000 −1.22098
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 15.5885 9.00000i 0.702069 0.405340i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −27.7128 + 32.0000i −1.24309 + 1.43540i
\(498\) 0 0
\(499\) −3.50000 + 6.06218i −0.156682 + 0.271380i −0.933670 0.358134i \(-0.883413\pi\)
0.776989 + 0.629515i \(0.216746\pi\)
\(500\) 0 0
\(501\) 30.0000 + 51.9615i 1.34030 + 2.32147i
\(502\) 0 0
\(503\) 16.0000i 0.713405i −0.934218 0.356702i \(-0.883901\pi\)
0.934218 0.356702i \(-0.116099\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −23.3827 + 13.5000i −1.03846 + 0.599556i
\(508\) 0 0
\(509\) 3.50000 6.06218i 0.155135 0.268701i −0.777973 0.628297i \(-0.783752\pi\)
0.933108 + 0.359596i \(0.117085\pi\)
\(510\) 0 0
\(511\) 3.50000 18.1865i 0.154831 0.804525i
\(512\) 0 0
\(513\) 38.9711 + 22.5000i 1.72062 + 0.993399i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 1.00000i 0.0439799i
\(518\) 0 0
\(519\) 63.0000 2.76539
\(520\) 0 0
\(521\) −7.50000 12.9904i −0.328581 0.569119i 0.653650 0.756797i \(-0.273237\pi\)
−0.982231 + 0.187678i \(0.939904\pi\)
\(522\) 0 0
\(523\) 11.2583 + 6.50000i 0.492292 + 0.284225i 0.725525 0.688196i \(-0.241597\pi\)
−0.233233 + 0.972421i \(0.574930\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.59808 + 1.50000i 0.113174 + 0.0653410i
\(528\) 0 0
\(529\) −7.00000 12.1244i −0.304348 0.527146i
\(530\) 0 0
\(531\) 18.0000 0.781133
\(532\) 0 0
\(533\) 20.0000i 0.866296i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 2.59808 + 1.50000i 0.112115 + 0.0647298i
\(538\) 0 0
\(539\) 5.50000 4.33013i 0.236902 0.186512i
\(540\) 0 0
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) 0 0
\(543\) −57.1577 + 33.0000i −2.45287 + 1.41617i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 9.00000 + 15.5885i 0.384111 + 0.665299i
\(550\) 0 0
\(551\) 15.0000 25.9808i 0.639021 1.10682i
\(552\) 0 0
\(553\) −9.52628 27.5000i −0.405099 1.16942i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9.52628 5.50000i 0.403641 0.233042i −0.284413 0.958702i \(-0.591799\pi\)
0.688054 + 0.725660i \(0.258465\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) −9.00000 −0.379980
\(562\) 0 0
\(563\) −9.52628 + 5.50000i −0.401485 + 0.231797i −0.687124 0.726540i \(-0.741127\pi\)
0.285640 + 0.958337i \(0.407794\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 23.3827 + 4.50000i 0.981981 + 0.188982i
\(568\) 0 0
\(569\) −0.500000 + 0.866025i −0.0209611 + 0.0363057i −0.876316 0.481737i \(-0.840006\pi\)
0.855355 + 0.518043i \(0.173339\pi\)
\(570\) 0 0
\(571\) 8.50000 + 14.7224i 0.355714 + 0.616115i 0.987240 0.159240i \(-0.0509044\pi\)
−0.631526 + 0.775355i \(0.717571\pi\)
\(572\) 0 0
\(573\) 51.0000i 2.13056i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 26.8468 15.5000i 1.11765 0.645273i 0.176847 0.984238i \(-0.443410\pi\)
0.940799 + 0.338965i \(0.110077\pi\)
\(578\) 0 0
\(579\) −7.50000 + 12.9904i −0.311689 + 0.539862i
\(580\) 0 0
\(581\) −8.00000 6.92820i −0.331896 0.287430i
\(582\) 0 0
\(583\) 7.79423 + 4.50000i 0.322804 + 0.186371i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.0000i 0.495293i 0.968850 + 0.247647i \(0.0796572\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(588\) 0 0
\(589\) 5.00000 0.206021
\(590\) 0 0
\(591\) −27.0000 46.7654i −1.11063 1.92367i
\(592\) 0 0
\(593\) 37.2391 + 21.5000i 1.52923 + 0.882899i 0.999394 + 0.0347964i \(0.0110783\pi\)
0.529832 + 0.848103i \(0.322255\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 23.3827 + 13.5000i 0.956990 + 0.552518i
\(598\) 0 0
\(599\) −10.5000 18.1865i −0.429018 0.743082i 0.567768 0.823189i \(-0.307807\pi\)
−0.996786 + 0.0801071i \(0.974474\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) 0 0
\(603\) 66.0000i 2.68773i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 6.06218 + 3.50000i 0.246056 + 0.142061i 0.617957 0.786212i \(-0.287961\pi\)
−0.371901 + 0.928272i \(0.621294\pi\)
\(608\) 0 0
\(609\) 9.00000 46.7654i 0.364698 1.89503i
\(610\) 0 0
\(611\) −1.00000 + 1.73205i −0.0404557 + 0.0700713i
\(612\) 0 0
\(613\) 18.1865 10.5000i 0.734547 0.424091i −0.0855362 0.996335i \(-0.527260\pi\)
0.820083 + 0.572244i \(0.193927\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 22.0000i 0.885687i 0.896599 + 0.442843i \(0.146030\pi\)
−0.896599 + 0.442843i \(0.853970\pi\)
\(618\) 0 0
\(619\) −2.50000 4.33013i −0.100483 0.174042i 0.811400 0.584491i \(-0.198706\pi\)
−0.911884 + 0.410448i \(0.865372\pi\)
\(620\) 0 0
\(621\) 13.5000 23.3827i 0.541736 0.938315i
\(622\) 0 0
\(623\) −7.79423 22.5000i −0.312269 0.901443i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −12.9904 + 7.50000i −0.518786 + 0.299521i
\(628\) 0 0
\(629\) 15.0000 0.598089
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) −31.1769 + 18.0000i −1.23917 + 0.715436i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −13.8564 + 2.00000i −0.549011 + 0.0792429i
\(638\) 0 0
\(639\) 48.0000 83.1384i 1.89885 3.28891i
\(640\) 0 0
\(641\) −7.50000 12.9904i −0.296232 0.513089i 0.679039 0.734103i \(-0.262397\pi\)
−0.975271 + 0.221013i \(0.929064\pi\)
\(642\) 0 0
\(643\) 44.0000i 1.73519i 0.497271 + 0.867595i \(0.334335\pi\)
−0.497271 + 0.867595i \(0.665665\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 37.2391 21.5000i 1.46402 0.845252i 0.464826 0.885402i \(-0.346117\pi\)
0.999194 + 0.0401498i \(0.0127835\pi\)
\(648\) 0 0
\(649\) −1.50000 + 2.59808i −0.0588802 + 0.101983i
\(650\) 0 0
\(651\) 7.50000 2.59808i 0.293948 0.101827i
\(652\) 0 0
\(653\) −4.33013 2.50000i −0.169451 0.0978326i 0.412876 0.910787i \(-0.364524\pi\)
−0.582327 + 0.812955i \(0.697858\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 42.0000i 1.63858i
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) 0.500000 + 0.866025i 0.0194477 + 0.0336845i 0.875585 0.483063i \(-0.160476\pi\)
−0.856138 + 0.516748i \(0.827143\pi\)
\(662\) 0 0
\(663\) 15.5885 + 9.00000i 0.605406 + 0.349531i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −15.5885 9.00000i −0.603587 0.348481i
\(668\) 0 0
\(669\) 36.0000 + 62.3538i 1.39184 + 2.41074i
\(670\) 0 0
\(671\) −3.00000 −0.115814
\(672\) 0 0
\(673\) 2.00000i 0.0770943i 0.999257 + 0.0385472i \(0.0122730\pi\)
−0.999257 + 0.0385472i \(0.987727\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7.79423 + 4.50000i 0.299557 + 0.172949i 0.642244 0.766501i \(-0.278004\pi\)
−0.342687 + 0.939450i \(0.611337\pi\)
\(678\) 0 0
\(679\) −12.0000 10.3923i −0.460518 0.398820i
\(680\) 0 0
\(681\) −10.5000 + 18.1865i −0.402361 + 0.696909i
\(682\) 0 0
\(683\) −33.7750 + 19.5000i −1.29236 + 0.746147i −0.979073 0.203510i \(-0.934765\pi\)
−0.313291 + 0.949657i \(0.601432\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 21.0000i 0.801200i
\(688\) 0 0
\(689\) −9.00000 15.5885i −0.342873 0.593873i
\(690\) 0 0
\(691\) 23.5000 40.7032i 0.893982 1.54842i 0.0589228 0.998263i \(-0.481233\pi\)
0.835059 0.550160i \(-0.185433\pi\)
\(692\) 0 0
\(693\) −10.3923 + 12.0000i −0.394771 + 0.455842i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −25.9808 + 15.0000i −0.984092 + 0.568166i
\(698\) 0 0
\(699\) 39.0000 1.47512
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) 21.6506 12.5000i 0.816569 0.471446i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −33.7750 6.50000i −1.27024 0.244458i
\(708\) 0 0
\(709\) 13.5000 23.3827i 0.507003 0.878155i −0.492964 0.870050i \(-0.664087\pi\)
0.999967 0.00810550i \(-0.00258009\pi\)
\(710\) 0 0
\(711\) 33.0000 + 57.1577i 1.23760 + 2.14358i
\(712\) 0 0
\(713\) 3.00000i 0.112351i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −10.3923 + 6.00000i −0.388108 + 0.224074i
\(718\) 0 0
\(719\) 14.5000 25.1147i 0.540759 0.936622i −0.458102 0.888900i \(-0.651471\pi\)
0.998861 0.0477220i \(-0.0151961\pi\)
\(720\) 0 0
\(721\) −12.5000 + 4.33013i −0.465524 + 0.161262i
\(722\) 0 0
\(723\) −44.1673 25.5000i −1.64260 0.948355i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 16.0000i 0.593407i 0.954970 + 0.296704i \(0.0958873\pi\)
−0.954970 + 0.296704i \(0.904113\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) 6.00000 + 10.3923i 0.221918 + 0.384373i
\(732\) 0 0
\(733\) 9.52628 + 5.50000i 0.351861 + 0.203147i 0.665505 0.746394i \(-0.268216\pi\)
−0.313644 + 0.949541i \(0.601550\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 9.52628 + 5.50000i 0.350905 + 0.202595i
\(738\) 0 0
\(739\) −20.5000 35.5070i −0.754105 1.30615i −0.945818 0.324697i \(-0.894738\pi\)
0.191714 0.981451i \(-0.438596\pi\)
\(740\) 0 0
\(741\) 30.0000 1.10208
\(742\) 0 0
\(743\) 32.0000i 1.17397i −0.809599 0.586983i \(-0.800316\pi\)
0.809599 0.586983i \(-0.199684\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 20.7846 + 12.0000i 0.760469 + 0.439057i
\(748\) 0 0
\(749\) −7.50000 + 2.59808i −0.274044 + 0.0949316i
\(750\) 0 0
\(751\) 23.5000 40.7032i 0.857527 1.48528i −0.0167534 0.999860i \(-0.505333\pi\)
0.874281 0.485421i \(-0.161334\pi\)
\(752\) 0 0
\(753\) −62.3538 + 36.0000i −2.27230 + 1.31191i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 34.0000i 1.23575i 0.786276 + 0.617876i \(0.212006\pi\)
−0.786276 + 0.617876i \(0.787994\pi\)
\(758\) 0 0
\(759\) 4.50000 + 7.79423i 0.163340 + 0.282913i
\(760\) 0 0
\(761\) −13.5000 + 23.3827i −0.489375 + 0.847622i −0.999925 0.0122260i \(-0.996108\pi\)
0.510551 + 0.859848i \(0.329442\pi\)
\(762\) 0 0
\(763\) −28.5788 5.50000i −1.03462 0.199113i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5.19615 3.00000i 0.187622 0.108324i
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) −39.0000 −1.40455
\(772\) 0 0
\(773\) −30.3109 + 17.5000i −1.09021 + 0.629431i −0.933632 0.358235i \(-0.883379\pi\)
−0.156575 + 0.987666i \(0.550045\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 25.9808 30.0000i 0.932055 1.07624i
\(778\) 0 0
\(779\) −25.0000 + 43.3013i −0.895718 + 1.55143i
\(780\) 0 0
\(781\) 8.00000 + 13.8564i 0.286263 + 0.495821i
\(782\) 0 0
\(783\) 54.0000i 1.92980i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −11.2583 + 6.50000i −0.401316 + 0.231700i −0.687052 0.726609i \(-0.741095\pi\)
0.285736 + 0.958308i \(0.407762\pi\)
\(788\) 0 0
\(789\) 4.50000 7.79423i 0.160204 0.277482i
\(790\) 0 0
\(791\) −20.0000 17.3205i −0.711118 0.615846i
\(792\) 0 0
\(793\) 5.19615 + 3.00000i 0.184521 + 0.106533i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 42.0000i 1.48772i 0.668338 + 0.743858i \(0.267006\pi\)
−0.668338 + 0.743858i \(0.732994\pi\)
\(798\) 0 0
\(799\) −3.00000 −0.106132
\(800\)