Properties

Label 2100.2.q.j.1201.1
Level $2100$
Weight $2$
Character 2100.1201
Analytic conductor $16.769$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(16.7685844245\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1201.1
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 2100.1201
Dual form 2100.2.q.j.1801.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.62132 - 2.09077i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.62132 - 2.09077i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.12132 - 3.67423i) q^{11} -5.00000 q^{13} +(-2.12132 + 3.67423i) q^{17} +(-1.62132 - 2.80821i) q^{19} +(-2.62132 + 0.358719i) q^{21} +(3.00000 + 5.19615i) q^{23} -1.00000 q^{27} -8.48528 q^{29} +(2.00000 - 3.46410i) q^{31} +(-2.12132 - 3.67423i) q^{33} +(2.50000 + 4.33013i) q^{37} +(-2.50000 + 4.33013i) q^{39} -1.75736 q^{41} -4.48528 q^{43} +(0.878680 + 1.52192i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(2.12132 + 3.67423i) q^{51} +(-2.12132 + 3.67423i) q^{53} -3.24264 q^{57} +(-0.878680 + 1.52192i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-1.00000 + 2.44949i) q^{63} +(-6.86396 + 11.8887i) q^{67} +6.00000 q^{69} +8.48528 q^{71} +(6.74264 - 11.6786i) q^{73} +(-11.1213 + 1.52192i) q^{77} +(-0.378680 - 0.655892i) q^{79} +(-0.500000 + 0.866025i) q^{81} -10.2426 q^{83} +(-4.24264 + 7.34847i) q^{87} +(-8.12132 - 14.0665i) q^{89} +(8.10660 + 10.4539i) q^{91} +(-2.00000 - 3.46410i) q^{93} -15.9706 q^{97} -4.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} + 2q^{7} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{3} + 2q^{7} - 2q^{9} - 20q^{13} + 2q^{19} - 2q^{21} + 12q^{23} - 4q^{27} + 8q^{31} + 10q^{37} - 10q^{39} - 24q^{41} + 16q^{43} + 12q^{47} + 10q^{49} + 4q^{57} - 12q^{59} + 2q^{61} - 4q^{63} - 2q^{67} + 24q^{69} + 10q^{73} - 36q^{77} - 10q^{79} - 2q^{81} - 24q^{83} - 24q^{89} - 10q^{91} - 8q^{93} + 4q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).

\(n\) \(701\) \(1051\) \(1177\) \(1501\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.62132 2.09077i −0.612801 0.790237i
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 2.12132 3.67423i 0.639602 1.10782i −0.345918 0.938265i \(-0.612432\pi\)
0.985520 0.169559i \(-0.0542342\pi\)
\(12\) 0 0
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.12132 + 3.67423i −0.514496 + 0.891133i 0.485363 + 0.874313i \(0.338688\pi\)
−0.999859 + 0.0168199i \(0.994646\pi\)
\(18\) 0 0
\(19\) −1.62132 2.80821i −0.371956 0.644247i 0.617910 0.786249i \(-0.287980\pi\)
−0.989866 + 0.142001i \(0.954646\pi\)
\(20\) 0 0
\(21\) −2.62132 + 0.358719i −0.572019 + 0.0782790i
\(22\) 0 0
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −8.48528 −1.57568 −0.787839 0.615882i \(-0.788800\pi\)
−0.787839 + 0.615882i \(0.788800\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) 0 0
\(33\) −2.12132 3.67423i −0.369274 0.639602i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.50000 + 4.33013i 0.410997 + 0.711868i 0.994999 0.0998840i \(-0.0318472\pi\)
−0.584002 + 0.811752i \(0.698514\pi\)
\(38\) 0 0
\(39\) −2.50000 + 4.33013i −0.400320 + 0.693375i
\(40\) 0 0
\(41\) −1.75736 −0.274453 −0.137227 0.990540i \(-0.543819\pi\)
−0.137227 + 0.990540i \(0.543819\pi\)
\(42\) 0 0
\(43\) −4.48528 −0.683999 −0.341999 0.939700i \(-0.611104\pi\)
−0.341999 + 0.939700i \(0.611104\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.878680 + 1.52192i 0.128169 + 0.221995i 0.922967 0.384879i \(-0.125757\pi\)
−0.794798 + 0.606873i \(0.792423\pi\)
\(48\) 0 0
\(49\) −1.74264 + 6.77962i −0.248949 + 0.968517i
\(50\) 0 0
\(51\) 2.12132 + 3.67423i 0.297044 + 0.514496i
\(52\) 0 0
\(53\) −2.12132 + 3.67423i −0.291386 + 0.504695i −0.974138 0.225955i \(-0.927450\pi\)
0.682752 + 0.730650i \(0.260783\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −3.24264 −0.429498
\(58\) 0 0
\(59\) −0.878680 + 1.52192i −0.114394 + 0.198137i −0.917537 0.397649i \(-0.869826\pi\)
0.803143 + 0.595786i \(0.203159\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 0 0
\(63\) −1.00000 + 2.44949i −0.125988 + 0.308607i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −6.86396 + 11.8887i −0.838566 + 1.45244i 0.0525271 + 0.998619i \(0.483272\pi\)
−0.891093 + 0.453820i \(0.850061\pi\)
\(68\) 0 0
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 8.48528 1.00702 0.503509 0.863990i \(-0.332042\pi\)
0.503509 + 0.863990i \(0.332042\pi\)
\(72\) 0 0
\(73\) 6.74264 11.6786i 0.789166 1.36688i −0.137312 0.990528i \(-0.543846\pi\)
0.926478 0.376348i \(-0.122820\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −11.1213 + 1.52192i −1.26739 + 0.173439i
\(78\) 0 0
\(79\) −0.378680 0.655892i −0.0426048 0.0737937i 0.843937 0.536443i \(-0.180232\pi\)
−0.886541 + 0.462649i \(0.846899\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −10.2426 −1.12428 −0.562138 0.827043i \(-0.690021\pi\)
−0.562138 + 0.827043i \(0.690021\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −4.24264 + 7.34847i −0.454859 + 0.787839i
\(88\) 0 0
\(89\) −8.12132 14.0665i −0.860858 1.49105i −0.871102 0.491103i \(-0.836594\pi\)
0.0102435 0.999948i \(-0.496739\pi\)
\(90\) 0 0
\(91\) 8.10660 + 10.4539i 0.849803 + 1.09586i
\(92\) 0 0
\(93\) −2.00000 3.46410i −0.207390 0.359211i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −15.9706 −1.62156 −0.810782 0.585348i \(-0.800958\pi\)
−0.810782 + 0.585348i \(0.800958\pi\)
\(98\) 0 0
\(99\) −4.24264 −0.426401
\(100\) 0 0
\(101\) 9.36396 16.2189i 0.931749 1.61384i 0.151418 0.988470i \(-0.451616\pi\)
0.780331 0.625367i \(-0.215051\pi\)
\(102\) 0 0
\(103\) 4.62132 + 8.00436i 0.455352 + 0.788693i 0.998708 0.0508091i \(-0.0161800\pi\)
−0.543356 + 0.839502i \(0.682847\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −9.36396 16.2189i −0.905248 1.56794i −0.820584 0.571527i \(-0.806351\pi\)
−0.0846647 0.996409i \(-0.526982\pi\)
\(108\) 0 0
\(109\) −9.74264 + 16.8747i −0.933176 + 1.61631i −0.155321 + 0.987864i \(0.549641\pi\)
−0.777855 + 0.628444i \(0.783692\pi\)
\(110\) 0 0
\(111\) 5.00000 0.474579
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 2.50000 + 4.33013i 0.231125 + 0.400320i
\(118\) 0 0
\(119\) 11.1213 1.52192i 1.01949 0.139514i
\(120\) 0 0
\(121\) −3.50000 6.06218i −0.318182 0.551107i
\(122\) 0 0
\(123\) −0.878680 + 1.52192i −0.0792279 + 0.137227i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −9.24264 −0.820152 −0.410076 0.912051i \(-0.634498\pi\)
−0.410076 + 0.912051i \(0.634498\pi\)
\(128\) 0 0
\(129\) −2.24264 + 3.88437i −0.197454 + 0.341999i
\(130\) 0 0
\(131\) −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i \(-0.251085\pi\)
−0.966803 + 0.255524i \(0.917752\pi\)
\(132\) 0 0
\(133\) −3.24264 + 7.94282i −0.281173 + 0.688729i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 7.24264 12.5446i 0.618781 1.07176i −0.370928 0.928662i \(-0.620960\pi\)
0.989709 0.143098i \(-0.0457063\pi\)
\(138\) 0 0
\(139\) −13.7279 −1.16439 −0.582194 0.813050i \(-0.697805\pi\)
−0.582194 + 0.813050i \(0.697805\pi\)
\(140\) 0 0
\(141\) 1.75736 0.147996
\(142\) 0 0
\(143\) −10.6066 + 18.3712i −0.886969 + 1.53627i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 5.00000 + 4.89898i 0.412393 + 0.404061i
\(148\) 0 0
\(149\) 6.87868 + 11.9142i 0.563523 + 0.976051i 0.997185 + 0.0749755i \(0.0238879\pi\)
−0.433662 + 0.901076i \(0.642779\pi\)
\(150\) 0 0
\(151\) −5.86396 + 10.1567i −0.477202 + 0.826539i −0.999659 0.0261273i \(-0.991682\pi\)
0.522456 + 0.852666i \(0.325016\pi\)
\(152\) 0 0
\(153\) 4.24264 0.342997
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.742641 1.28629i 0.0592692 0.102657i −0.834868 0.550450i \(-0.814456\pi\)
0.894138 + 0.447792i \(0.147790\pi\)
\(158\) 0 0
\(159\) 2.12132 + 3.67423i 0.168232 + 0.291386i
\(160\) 0 0
\(161\) 6.00000 14.6969i 0.472866 1.15828i
\(162\) 0 0
\(163\) −4.37868 7.58410i −0.342965 0.594032i 0.642017 0.766690i \(-0.278098\pi\)
−0.984982 + 0.172658i \(0.944764\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.75736 0.135989 0.0679943 0.997686i \(-0.478340\pi\)
0.0679943 + 0.997686i \(0.478340\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) −1.62132 + 2.80821i −0.123985 + 0.214749i
\(172\) 0 0
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0.878680 + 1.52192i 0.0660456 + 0.114394i
\(178\) 0 0
\(179\) −1.75736 + 3.04384i −0.131351 + 0.227507i −0.924198 0.381914i \(-0.875265\pi\)
0.792846 + 0.609421i \(0.208598\pi\)
\(180\) 0 0
\(181\) 4.48528 0.333388 0.166694 0.986009i \(-0.446691\pi\)
0.166694 + 0.986009i \(0.446691\pi\)
\(182\) 0 0
\(183\) 1.00000 0.0739221
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 9.00000 + 15.5885i 0.658145 + 1.13994i
\(188\) 0 0
\(189\) 1.62132 + 2.09077i 0.117934 + 0.152081i
\(190\) 0 0
\(191\) −8.12132 14.0665i −0.587638 1.01782i −0.994541 0.104348i \(-0.966725\pi\)
0.406903 0.913471i \(-0.366609\pi\)
\(192\) 0 0
\(193\) 2.24264 3.88437i 0.161429 0.279603i −0.773953 0.633244i \(-0.781723\pi\)
0.935381 + 0.353641i \(0.115056\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −8.48528 −0.604551 −0.302276 0.953221i \(-0.597746\pi\)
−0.302276 + 0.953221i \(0.597746\pi\)
\(198\) 0 0
\(199\) 8.62132 14.9326i 0.611149 1.05854i −0.379898 0.925028i \(-0.624041\pi\)
0.991047 0.133513i \(-0.0426258\pi\)
\(200\) 0 0
\(201\) 6.86396 + 11.8887i 0.484146 + 0.838566i
\(202\) 0 0
\(203\) 13.7574 + 17.7408i 0.965577 + 1.24516i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 3.00000 5.19615i 0.208514 0.361158i
\(208\) 0 0
\(209\) −13.7574 −0.951616
\(210\) 0 0
\(211\) 12.7574 0.878253 0.439126 0.898425i \(-0.355288\pi\)
0.439126 + 0.898425i \(0.355288\pi\)
\(212\) 0 0
\(213\) 4.24264 7.34847i 0.290701 0.503509i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −10.4853 + 1.43488i −0.711787 + 0.0974059i
\(218\) 0 0
\(219\) −6.74264 11.6786i −0.455625 0.789166i
\(220\) 0 0
\(221\) 10.6066 18.3712i 0.713477 1.23578i
\(222\) 0 0
\(223\) −9.24264 −0.618933 −0.309466 0.950910i \(-0.600150\pi\)
−0.309466 + 0.950910i \(0.600150\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.75736 + 3.04384i −0.116640 + 0.202026i −0.918434 0.395574i \(-0.870546\pi\)
0.801794 + 0.597600i \(0.203879\pi\)
\(228\) 0 0
\(229\) 2.98528 + 5.17066i 0.197273 + 0.341687i 0.947643 0.319331i \(-0.103458\pi\)
−0.750370 + 0.661018i \(0.770125\pi\)
\(230\) 0 0
\(231\) −4.24264 + 10.3923i −0.279145 + 0.683763i
\(232\) 0 0
\(233\) −5.12132 8.87039i −0.335509 0.581118i 0.648074 0.761578i \(-0.275575\pi\)
−0.983582 + 0.180459i \(0.942242\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −0.757359 −0.0491958
\(238\) 0 0
\(239\) 28.9706 1.87395 0.936975 0.349397i \(-0.113613\pi\)
0.936975 + 0.349397i \(0.113613\pi\)
\(240\) 0 0
\(241\) −13.9853 + 24.2232i −0.900871 + 1.56035i −0.0745056 + 0.997221i \(0.523738\pi\)
−0.826366 + 0.563134i \(0.809595\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 8.10660 + 14.0410i 0.515811 + 0.893410i
\(248\) 0 0
\(249\) −5.12132 + 8.87039i −0.324550 + 0.562138i
\(250\) 0 0
\(251\) −7.75736 −0.489640 −0.244820 0.969569i \(-0.578729\pi\)
−0.244820 + 0.969569i \(0.578729\pi\)
\(252\) 0 0
\(253\) 25.4558 1.60040
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.87868 11.9142i −0.429080 0.743189i 0.567712 0.823228i \(-0.307829\pi\)
−0.996792 + 0.0800388i \(0.974496\pi\)
\(258\) 0 0
\(259\) 5.00000 12.2474i 0.310685 0.761019i
\(260\) 0 0
\(261\) 4.24264 + 7.34847i 0.262613 + 0.454859i
\(262\) 0 0
\(263\) −2.48528 + 4.30463i −0.153249 + 0.265435i −0.932420 0.361376i \(-0.882307\pi\)
0.779171 + 0.626811i \(0.215640\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −16.2426 −0.994033
\(268\) 0 0
\(269\) −3.36396 + 5.82655i −0.205104 + 0.355251i −0.950166 0.311745i \(-0.899087\pi\)
0.745062 + 0.666996i \(0.232420\pi\)
\(270\) 0 0
\(271\) −1.00000 1.73205i −0.0607457 0.105215i 0.834053 0.551684i \(-0.186015\pi\)
−0.894799 + 0.446469i \(0.852681\pi\)
\(272\) 0 0
\(273\) 13.1066 1.79360i 0.793248 0.108553i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 15.7426 27.2671i 0.945884 1.63832i 0.191911 0.981412i \(-0.438531\pi\)
0.753972 0.656906i \(-0.228135\pi\)
\(278\) 0 0
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) −19.7574 −1.17863 −0.589313 0.807905i \(-0.700601\pi\)
−0.589313 + 0.807905i \(0.700601\pi\)
\(282\) 0 0
\(283\) −5.62132 + 9.73641i −0.334153 + 0.578770i −0.983322 0.181875i \(-0.941783\pi\)
0.649169 + 0.760644i \(0.275117\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.84924 + 3.67423i 0.168185 + 0.216883i
\(288\) 0 0
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) 0 0
\(291\) −7.98528 + 13.8309i −0.468105 + 0.810782i
\(292\) 0 0
\(293\) −20.4853 −1.19676 −0.598381 0.801211i \(-0.704189\pi\)
−0.598381 + 0.801211i \(0.704189\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −2.12132 + 3.67423i −0.123091 + 0.213201i
\(298\) 0 0
\(299\) −15.0000 25.9808i −0.867472 1.50251i
\(300\) 0 0
\(301\) 7.27208 + 9.37769i 0.419156 + 0.540521i
\(302\) 0 0
\(303\) −9.36396 16.2189i −0.537946 0.931749i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 12.4853 0.712573 0.356286 0.934377i \(-0.384043\pi\)
0.356286 + 0.934377i \(0.384043\pi\)
\(308\) 0 0
\(309\) 9.24264 0.525795
\(310\) 0 0
\(311\) 1.24264 2.15232i 0.0704637 0.122047i −0.828641 0.559781i \(-0.810885\pi\)
0.899105 + 0.437734i \(0.144219\pi\)
\(312\) 0 0
\(313\) −16.4853 28.5533i −0.931803 1.61393i −0.780238 0.625483i \(-0.784902\pi\)
−0.151566 0.988447i \(-0.548431\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i \(-0.112775\pi\)
−0.769395 + 0.638774i \(0.779442\pi\)
\(318\) 0 0
\(319\) −18.0000 + 31.1769i −1.00781 + 1.74557i
\(320\) 0 0
\(321\) −18.7279 −1.04529
\(322\) 0 0
\(323\) 13.7574 0.765480
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 9.74264 + 16.8747i 0.538769 + 0.933176i
\(328\) 0 0
\(329\) 1.75736 4.30463i 0.0968864 0.237322i
\(330\) 0 0
\(331\) 4.37868 + 7.58410i 0.240674 + 0.416860i 0.960906 0.276873i \(-0.0892982\pi\)
−0.720232 + 0.693733i \(0.755965\pi\)
\(332\) 0 0
\(333\) 2.50000 4.33013i 0.136999 0.237289i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 8.97056 0.488658 0.244329 0.969692i \(-0.421432\pi\)
0.244329 + 0.969692i \(0.421432\pi\)
\(338\) 0 0
\(339\) 3.00000 5.19615i 0.162938 0.282216i
\(340\) 0 0
\(341\) −8.48528 14.6969i −0.459504 0.795884i
\(342\) 0 0
\(343\) 17.0000 7.34847i 0.917914 0.396780i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 15.3640 26.6112i 0.824781 1.42856i −0.0773062 0.997007i \(-0.524632\pi\)
0.902087 0.431555i \(-0.142035\pi\)
\(348\) 0 0
\(349\) 8.00000 0.428230 0.214115 0.976808i \(-0.431313\pi\)
0.214115 + 0.976808i \(0.431313\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) 3.36396 5.82655i 0.179046 0.310116i −0.762508 0.646978i \(-0.776032\pi\)
0.941554 + 0.336862i \(0.109366\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 4.24264 10.3923i 0.224544 0.550019i
\(358\) 0 0
\(359\) −15.3640 26.6112i −0.810879 1.40448i −0.912250 0.409635i \(-0.865656\pi\)
0.101371 0.994849i \(-0.467677\pi\)
\(360\) 0 0
\(361\) 4.24264 7.34847i 0.223297 0.386762i
\(362\) 0 0
\(363\) −7.00000 −0.367405
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 7.00000 12.1244i 0.365397 0.632886i −0.623443 0.781869i \(-0.714267\pi\)
0.988840 + 0.148983i \(0.0475999\pi\)
\(368\) 0 0
\(369\) 0.878680 + 1.52192i 0.0457422 + 0.0792279i
\(370\) 0 0
\(371\) 11.1213 1.52192i 0.577390 0.0790140i
\(372\) 0 0
\(373\) −7.74264 13.4106i −0.400899 0.694377i 0.592936 0.805250i \(-0.297969\pi\)
−0.993835 + 0.110873i \(0.964635\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 42.4264 2.18507
\(378\) 0 0
\(379\) 11.7279 0.602423 0.301211 0.953557i \(-0.402609\pi\)
0.301211 + 0.953557i \(0.402609\pi\)
\(380\) 0 0
\(381\) −4.62132 + 8.00436i −0.236757 + 0.410076i
\(382\) 0 0
\(383\) 9.72792 + 16.8493i 0.497074 + 0.860957i 0.999994 0.00337583i \(-0.00107456\pi\)
−0.502921 + 0.864333i \(0.667741\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.24264 + 3.88437i 0.114000 + 0.197454i
\(388\) 0 0
\(389\) −2.63604 + 4.56575i −0.133652 + 0.231493i −0.925082 0.379768i \(-0.876004\pi\)
0.791429 + 0.611261i \(0.209337\pi\)
\(390\) 0 0
\(391\) −25.4558 −1.28736
\(392\) 0 0
\(393\) −6.00000 −0.302660
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 10.0000 + 17.3205i 0.501886 + 0.869291i 0.999998 + 0.00217869i \(0.000693499\pi\)
−0.498112 + 0.867113i \(0.665973\pi\)
\(398\) 0 0
\(399\) 5.25736 + 6.77962i 0.263197 + 0.339405i
\(400\) 0 0
\(401\) −7.60660 13.1750i −0.379856 0.657929i 0.611185 0.791487i \(-0.290693\pi\)
−0.991041 + 0.133558i \(0.957360\pi\)
\(402\) 0 0
\(403\) −10.0000 + 17.3205i −0.498135 + 0.862796i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 21.2132 1.05150
\(408\) 0 0
\(409\) 3.50000 6.06218i 0.173064 0.299755i −0.766426 0.642333i \(-0.777967\pi\)
0.939490 + 0.342578i \(0.111300\pi\)
\(410\) 0 0
\(411\) −7.24264 12.5446i −0.357253 0.618781i
\(412\) 0 0
\(413\) 4.60660 0.630399i 0.226676 0.0310199i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −6.86396 + 11.8887i −0.336130 + 0.582194i
\(418\) 0 0
\(419\) 12.7279 0.621800 0.310900 0.950443i \(-0.399370\pi\)
0.310900 + 0.950443i \(0.399370\pi\)
\(420\) 0 0
\(421\) −1.00000 −0.0487370 −0.0243685 0.999703i \(-0.507758\pi\)
−0.0243685 + 0.999703i \(0.507758\pi\)
\(422\) 0 0
\(423\) 0.878680 1.52192i 0.0427229 0.0739982i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.00000 2.44949i 0.0483934 0.118539i
\(428\) 0 0
\(429\) 10.6066 + 18.3712i 0.512092 + 0.886969i
\(430\) 0 0
\(431\) −13.2426 + 22.9369i −0.637876 + 1.10483i 0.348023 + 0.937486i \(0.386853\pi\)
−0.985898 + 0.167347i \(0.946480\pi\)
\(432\) 0 0
\(433\) 8.97056 0.431098 0.215549 0.976493i \(-0.430846\pi\)
0.215549 + 0.976493i \(0.430846\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 9.72792 16.8493i 0.465350 0.806009i
\(438\) 0 0
\(439\) −17.8640 30.9413i −0.852600 1.47675i −0.878853 0.477092i \(-0.841691\pi\)
0.0262531 0.999655i \(-0.491642\pi\)
\(440\) 0 0
\(441\) 6.74264 1.88064i 0.321078 0.0895542i
\(442\) 0 0
\(443\) 15.7279 + 27.2416i 0.747256 + 1.29429i 0.949133 + 0.314875i \(0.101963\pi\)
−0.201877 + 0.979411i \(0.564704\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 13.7574 0.650701
\(448\) 0 0
\(449\) 36.7279 1.73330 0.866649 0.498919i \(-0.166269\pi\)
0.866649 + 0.498919i \(0.166269\pi\)
\(450\) 0 0
\(451\) −3.72792 + 6.45695i −0.175541 + 0.304046i
\(452\) 0 0
\(453\) 5.86396 + 10.1567i 0.275513 + 0.477202i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 3.74264 + 6.48244i 0.175073 + 0.303236i 0.940187 0.340660i \(-0.110650\pi\)
−0.765113 + 0.643896i \(0.777317\pi\)
\(458\) 0 0
\(459\) 2.12132 3.67423i 0.0990148 0.171499i
\(460\) 0 0
\(461\) −26.4853 −1.23354 −0.616771 0.787142i \(-0.711560\pi\)
−0.616771 + 0.787142i \(0.711560\pi\)
\(462\) 0 0
\(463\) 2.75736 0.128145 0.0640727 0.997945i \(-0.479591\pi\)
0.0640727 + 0.997945i \(0.479591\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −15.7279 27.2416i −0.727801 1.26059i −0.957810 0.287401i \(-0.907209\pi\)
0.230009 0.973188i \(-0.426124\pi\)
\(468\) 0 0
\(469\) 35.9853 4.92447i 1.66165 0.227391i
\(470\) 0 0
\(471\) −0.742641 1.28629i −0.0342191 0.0592692i
\(472\) 0 0
\(473\) −9.51472 + 16.4800i −0.437487 + 0.757750i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 4.24264 0.194257
\(478\) 0 0
\(479\) 13.6066 23.5673i 0.621702 1.07682i −0.367467 0.930036i \(-0.619775\pi\)
0.989169 0.146782i \(-0.0468916\pi\)
\(480\) 0 0
\(481\) −12.5000 21.6506i −0.569951 0.987184i
\(482\) 0 0
\(483\) −9.72792 12.5446i −0.442636 0.570800i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 5.75736 9.97204i 0.260891 0.451876i −0.705588 0.708622i \(-0.749317\pi\)
0.966479 + 0.256746i \(0.0826504\pi\)
\(488\) 0 0
\(489\) −8.75736 −0.396021
\(490\) 0 0
\(491\) 21.5147 0.970946 0.485473 0.874252i \(-0.338647\pi\)
0.485473 + 0.874252i \(0.338647\pi\)
\(492\) 0 0
\(493\) 18.0000 31.1769i 0.810679 1.40414i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −13.7574 17.7408i −0.617102 0.795782i
\(498\) 0 0
\(499\) 2.62132 + 4.54026i 0.117346 + 0.203250i 0.918715 0.394921i \(-0.129228\pi\)
−0.801369 + 0.598170i \(0.795895\pi\)
\(500\) 0 0
\(501\) 0.878680 1.52192i 0.0392565 0.0679943i
\(502\) 0 0
\(503\) 25.4558 1.13502 0.567510 0.823367i \(-0.307907\pi\)
0.567510 + 0.823367i \(0.307907\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 6.00000 10.3923i 0.266469 0.461538i
\(508\) 0 0
\(509\) −22.2426 38.5254i −0.985888 1.70761i −0.637923 0.770100i \(-0.720206\pi\)
−0.347964 0.937508i \(-0.613127\pi\)
\(510\) 0 0
\(511\) −35.3492 + 4.83743i −1.56376 + 0.213995i
\(512\) 0 0
\(513\) 1.62132 + 2.80821i 0.0715830 + 0.123985i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 7.45584 0.327908
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 21.7279 37.6339i 0.951918 1.64877i 0.210648 0.977562i \(-0.432443\pi\)
0.741269 0.671208i \(-0.234224\pi\)
\(522\) 0 0
\(523\) −3.75736 6.50794i −0.164298 0.284572i 0.772108 0.635492i \(-0.219202\pi\)
−0.936406 + 0.350919i \(0.885869\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.48528 + 14.6969i 0.369625 + 0.640209i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) 1.75736 0.0762629
\(532\) 0 0
\(533\) 8.78680 0.380598
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1.75736 + 3.04384i 0.0758357 + 0.131351i
\(538\) 0 0
\(539\) 21.2132 + 20.7846i 0.913717 + 0.895257i
\(540\) 0 0
\(541\) 7.74264 + 13.4106i 0.332882 + 0.576569i 0.983076 0.183200i \(-0.0586455\pi\)
−0.650194 + 0.759769i \(0.725312\pi\)
\(542\) 0 0
\(543\) 2.24264 3.88437i 0.0962409 0.166694i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −26.0000 −1.11168 −0.555840 0.831289i \(-0.687603\pi\)
−0.555840 + 0.831289i \(0.687603\pi\)
\(548\) 0 0
\(549\) 0.500000 0.866025i 0.0213395 0.0369611i
\(550\) 0 0
\(551\) 13.7574 + 23.8284i 0.586083 + 1.01513i
\(552\) 0 0
\(553\) −0.757359 + 1.85514i −0.0322062 + 0.0788887i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22.2426 38.5254i 0.942451 1.63237i 0.181675 0.983359i \(-0.441848\pi\)
0.760776 0.649014i \(-0.224818\pi\)
\(558\) 0 0
\(559\) 22.4264 0.948536
\(560\) 0 0
\(561\) 18.0000 0.759961
\(562\) 0 0
\(563\) 14.1213 24.4588i 0.595143 1.03082i −0.398384 0.917219i \(-0.630429\pi\)
0.993527 0.113599i \(-0.0362378\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 2.62132 0.358719i 0.110085 0.0150648i
\(568\) 0 0
\(569\) −2.63604 4.56575i −0.110509 0.191406i 0.805467 0.592641i \(-0.201915\pi\)
−0.915975 + 0.401234i \(0.868581\pi\)
\(570\) 0 0
\(571\) −22.6213 + 39.1813i −0.946673 + 1.63969i −0.194306 + 0.980941i \(0.562245\pi\)
−0.752367 + 0.658744i \(0.771088\pi\)
\(572\) 0 0
\(573\) −16.2426 −0.678546
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −7.48528 + 12.9649i −0.311616 + 0.539735i −0.978712 0.205236i \(-0.934204\pi\)
0.667096 + 0.744972i \(0.267537\pi\)
\(578\) 0 0
\(579\) −2.24264 3.88437i −0.0932010 0.161429i
\(580\) 0 0
\(581\) 16.6066 + 21.4150i 0.688958 + 0.888444i
\(582\) 0 0
\(583\) 9.00000 + 15.5885i 0.372742 + 0.645608i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −10.9706 −0.452804 −0.226402 0.974034i \(-0.572696\pi\)
−0.226402 + 0.974034i \(0.572696\pi\)
\(588\) 0 0
\(589\) −12.9706 −0.534443
\(590\) 0 0
\(591\) −4.24264 + 7.34847i −0.174519 + 0.302276i
\(592\) 0 0
\(593\) −17.4853 30.2854i −0.718034 1.24367i −0.961777 0.273832i \(-0.911709\pi\)
0.243743 0.969840i \(-0.421625\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −8.62132 14.9326i −0.352847 0.611149i
\(598\) 0 0
\(599\) −17.8492 + 30.9158i −0.729300 + 1.26319i 0.227879 + 0.973689i \(0.426821\pi\)
−0.957179 + 0.289496i \(0.906512\pi\)
\(600\) 0 0
\(601\) 7.48528 0.305331 0.152665 0.988278i \(-0.451214\pi\)
0.152665 + 0.988278i \(0.451214\pi\)
\(602\) 0 0
\(603\) 13.7279 0.559044
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 21.5919 + 37.3982i 0.876388 + 1.51795i 0.855277 + 0.518171i \(0.173387\pi\)
0.0211102 + 0.999777i \(0.493280\pi\)
\(608\) 0 0
\(609\) 22.2426 3.04384i 0.901317 0.123342i
\(610\) 0 0
\(611\) −4.39340 7.60959i −0.177738 0.307851i
\(612\) 0 0
\(613\) −8.00000 + 13.8564i −0.323117 + 0.559655i −0.981129 0.193352i \(-0.938064\pi\)
0.658012 + 0.753007i \(0.271397\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 37.4558 1.50792 0.753958 0.656923i \(-0.228142\pi\)
0.753958 + 0.656923i \(0.228142\pi\)
\(618\) 0 0
\(619\) −8.24264 + 14.2767i −0.331300 + 0.573828i −0.982767 0.184849i \(-0.940820\pi\)
0.651467 + 0.758677i \(0.274154\pi\)
\(620\) 0 0
\(621\) −3.00000 5.19615i −0.120386 0.208514i
\(622\) 0 0
\(623\) −16.2426 + 39.7862i −0.650748 + 1.59400i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −6.87868 + 11.9142i −0.274708 + 0.475808i
\(628\) 0 0
\(629\) −21.2132 −0.845826
\(630\) 0 0
\(631\) −16.2132 −0.645437 −0.322719 0.946495i \(-0.604597\pi\)
−0.322719 + 0.946495i \(0.604597\pi\)
\(632\) 0 0
\(633\) 6.37868 11.0482i 0.253530 0.439126i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 8.71320 33.8981i 0.345230 1.34309i
\(638\) 0 0
\(639\) −4.24264 7.34847i −0.167836 0.290701i
\(640\) 0 0
\(641\) −12.0000 + 20.7846i −0.473972 + 0.820943i −0.999556 0.0297987i \(-0.990513\pi\)
0.525584 + 0.850741i \(0.323847\pi\)
\(642\) 0 0
\(643\) −23.7279 −0.935738 −0.467869 0.883798i \(-0.654978\pi\)
−0.467869 + 0.883798i \(0.654978\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −20.1213 + 34.8511i −0.791051 + 1.37014i 0.134266 + 0.990945i \(0.457132\pi\)
−0.925317 + 0.379195i \(0.876201\pi\)
\(648\) 0 0
\(649\) 3.72792 + 6.45695i 0.146334 + 0.253457i
\(650\) 0 0
\(651\) −4.00000 + 9.79796i −0.156772 + 0.384012i
\(652\) 0 0
\(653\) −11.1213 19.2627i −0.435211 0.753807i 0.562102 0.827068i \(-0.309993\pi\)
−0.997313 + 0.0732606i \(0.976660\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −13.4853 −0.526111
\(658\) 0 0
\(659\) 23.2721 0.906551 0.453276 0.891370i \(-0.350255\pi\)
0.453276 + 0.891370i \(0.350255\pi\)
\(660\) 0 0
\(661\) −0.0147186 + 0.0254934i −0.000572488 + 0.000991579i −0.866312 0.499504i \(-0.833516\pi\)
0.865739 + 0.500496i \(0.166849\pi\)
\(662\) 0 0
\(663\) −10.6066 18.3712i −0.411926 0.713477i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −25.4558 44.0908i −0.985654 1.70720i
\(668\) 0 0
\(669\) −4.62132 + 8.00436i −0.178671 + 0.309466i
\(670\) 0 0
\(671\) 4.24264 0.163785
\(672\) 0 0
\(673\) 21.4853 0.828197 0.414098 0.910232i \(-0.364097\pi\)
0.414098 + 0.910232i \(0.364097\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 9.72792 + 16.8493i 0.373874 + 0.647569i 0.990158 0.139955i \(-0.0446958\pi\)
−0.616283 + 0.787524i \(0.711362\pi\)
\(678\) 0 0
\(679\) 25.8934 + 33.3908i 0.993697 + 1.28142i
\(680\) 0 0
\(681\) 1.75736 + 3.04384i 0.0673422 + 0.116640i
\(682\) 0 0
\(683\) −12.3640 + 21.4150i −0.473094 + 0.819423i −0.999526 0.0307948i \(-0.990196\pi\)
0.526432 + 0.850217i \(0.323530\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 5.97056 0.227791
\(688\) 0 0
\(689\) 10.6066 18.3712i 0.404079 0.699886i
\(690\) 0 0
\(691\) 15.3492 + 26.5857i 0.583913 + 1.01137i 0.995010 + 0.0997750i \(0.0318123\pi\)
−0.411097 + 0.911591i \(0.634854\pi\)
\(692\) 0 0
\(693\) 6.87868 + 8.87039i 0.261299 + 0.336958i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 3.72792 6.45695i 0.141205 0.244574i
\(698\) 0 0
\(699\) −10.2426 −0.387412
\(700\) 0 0
\(701\) −36.7279 −1.38719 −0.693597 0.720363i \(-0.743975\pi\)
−0.693597 + 0.720363i \(0.743975\pi\)
\(702\) 0 0
\(703\) 8.10660 14.0410i 0.305746 0.529568i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −49.0919 + 6.71807i −1.84629 + 0.252659i
\(708\) 0 0
\(709\) 4.74264 + 8.21449i 0.178114 + 0.308502i 0.941234 0.337754i \(-0.109667\pi\)
−0.763121 + 0.646256i \(0.776334\pi\)
\(710\) 0 0
\(711\) −0.378680 + 0.655892i −0.0142016 + 0.0245979i
\(712\) 0 0
\(713\) 24.0000 0.898807
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 14.4853 25.0892i 0.540963 0.936975i
\(718\) 0 0
\(719\) 13.0919 + 22.6758i 0.488245 + 0.845665i 0.999909 0.0135209i \(-0.00430397\pi\)
−0.511664 + 0.859186i \(0.670971\pi\)
\(720\) 0 0
\(721\) 9.24264 22.6398i 0.344214 0.843148i
\(722\) 0 0
\(723\) 13.9853 + 24.2232i 0.520118 + 0.900871i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 47.2426 1.75213 0.876066 0.482191i \(-0.160159\pi\)
0.876066 + 0.482191i \(0.160159\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 9.51472 16.4800i 0.351915 0.609534i
\(732\) 0 0
\(733\) 4.25736 + 7.37396i 0.157249 + 0.272364i 0.933876 0.357598i \(-0.116404\pi\)
−0.776627 + 0.629961i \(0.783071\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 29.1213 + 50.4396i 1.07270 + 1.85797i
\(738\) 0 0
\(739\) 20.8345 36.0865i 0.766410 1.32746i −0.173087 0.984906i \(-0.555374\pi\)
0.939498 0.342555i \(-0.111292\pi\)
\(740\) 0 0
\(741\) 16.2132 0.595607
\(742\) 0 0
\(743\) 22.9706 0.842708 0.421354 0.906896i \(-0.361555\pi\)
0.421354 + 0.906896i \(0.361555\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 5.12132 + 8.87039i 0.187379 + 0.324550i
\(748\) 0 0
\(749\) −18.7279 + 45.8739i −0.684303 + 1.67619i
\(750\) 0 0
\(751\) 3.86396 + 6.69258i 0.140998 + 0.244216i 0.927873 0.372897i \(-0.121636\pi\)
−0.786875 + 0.617113i \(0.788302\pi\)
\(752\) 0 0
\(753\) −3.87868 + 6.71807i −0.141347 + 0.244820i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −36.4558 −1.32501 −0.662505 0.749057i \(-0.730507\pi\)
−0.662505 + 0.749057i \(0.730507\pi\)
\(758\) 0 0
\(759\) 12.7279 22.0454i 0.461994 0.800198i
\(760\) 0 0
\(761\) −15.8787 27.5027i −0.575602 0.996971i −0.995976 0.0896206i \(-0.971435\pi\)
0.420374 0.907351i \(-0.361899\pi\)
\(762\) 0 0
\(763\) 51.0772 6.98975i 1.84912 0.253046i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.39340 7.60959i 0.158636 0.274766i
\(768\) 0 0
\(769\) −48.4853 −1.74842 −0.874212 0.485544i \(-0.838621\pi\)
−0.874212 + 0.485544i \(0.838621\pi\)
\(770\) 0 0
\(771\) −13.7574 −0.495459
\(772\) 0 0
\(773\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −8.10660 10.4539i −0.290823 0.375030i
\(778\) 0 0
\(779\) 2.84924 + 4.93503i 0.102085 + 0.176816i
\(780\) 0 0
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) 0 0
\(783\) 8.48528 0.303239
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −3.86396 + 6.69258i −0.137735 + 0.238565i −0.926639 0.375952i \(-0.877316\pi\)
0.788904 + 0.614517i \(0.210649\pi\)
\(788\) 0 0
\(789\) 2.48528 + 4.30463i 0.0884784 + 0.153249i
\(790\) 0 0
\(791\) −9.72792 12.5446i −0.345885 0.446035i
\(792\) 0 0
\(793\) −2.50000 4.33013i −0.0887776 0.153767i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −36.4264 −1.29029 −0.645145 0.764060i \(-0.723203\pi\)
−0.645145 + 0.764060i \(0.723203\pi\)
\(798\) 0 0
\(799\) −7.45584 −0.263769
\(800\) 0 0
\(801\) −8.12132