Properties

Label 1148.2.k.b.337.18
Level $1148$
Weight $2$
Character 1148.337
Analytic conductor $9.167$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 337.18
Character \(\chi\) \(=\) 1148.337
Dual form 1148.2.k.b.729.18

$q$-expansion

\(f(q)\) \(=\) \(q+(2.38527 + 2.38527i) q^{3} +0.515487i q^{5} +(0.707107 + 0.707107i) q^{7} +8.37900i q^{9} +O(q^{10})\) \(q+(2.38527 + 2.38527i) q^{3} +0.515487i q^{5} +(0.707107 + 0.707107i) q^{7} +8.37900i q^{9} +(-3.73270 - 3.73270i) q^{11} +(0.0725409 + 0.0725409i) q^{13} +(-1.22958 + 1.22958i) q^{15} +(-4.03186 + 4.03186i) q^{17} +(-2.33728 + 2.33728i) q^{19} +3.37328i q^{21} +4.66571 q^{23} +4.73427 q^{25} +(-12.8303 + 12.8303i) q^{27} +(6.22153 + 6.22153i) q^{29} -2.93310 q^{31} -17.8070i q^{33} +(-0.364505 + 0.364505i) q^{35} -10.6326 q^{37} +0.346059i q^{39} +(5.72814 + 2.86154i) q^{41} -1.10612i q^{43} -4.31927 q^{45} +(8.99324 - 8.99324i) q^{47} +1.00000i q^{49} -19.2341 q^{51} +(3.20712 + 3.20712i) q^{53} +(1.92416 - 1.92416i) q^{55} -11.1501 q^{57} +12.6830 q^{59} -9.12150i q^{61} +(-5.92485 + 5.92485i) q^{63} +(-0.0373939 + 0.0373939i) q^{65} +(1.97135 - 1.97135i) q^{67} +(11.1290 + 11.1290i) q^{69} +(8.02127 + 8.02127i) q^{71} -11.8259i q^{73} +(11.2925 + 11.2925i) q^{75} -5.27883i q^{77} +(1.52258 + 1.52258i) q^{79} -36.0706 q^{81} +5.12597 q^{83} +(-2.07837 - 2.07837i) q^{85} +29.6800i q^{87} +(-11.3538 - 11.3538i) q^{89} +0.102588i q^{91} +(-6.99623 - 6.99623i) q^{93} +(-1.20484 - 1.20484i) q^{95} +(10.0266 - 10.0266i) q^{97} +(31.2763 - 31.2763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + O(q^{10}) \) \( 36q - 12q^{11} - 16q^{17} - 4q^{19} - 36q^{23} - 64q^{25} + 12q^{27} + 16q^{29} - 28q^{31} + 12q^{35} + 48q^{37} + 4q^{41} + 36q^{45} + 12q^{47} - 12q^{51} - 12q^{53} + 12q^{55} + 76q^{57} + 20q^{59} - 4q^{65} - 44q^{67} + 72q^{69} - 20q^{71} + 72q^{75} - 8q^{79} - 100q^{81} - 40q^{83} - 8q^{85} - 16q^{89} + 20q^{93} + 76q^{95} - 16q^{97} + 56q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 2.38527 + 2.38527i 1.37713 + 1.37713i 0.849425 + 0.527710i \(0.176949\pi\)
0.527710 + 0.849425i \(0.323051\pi\)
\(4\) 0 0
\(5\) 0.515487i 0.230533i 0.993335 + 0.115266i \(0.0367722\pi\)
−0.993335 + 0.115266i \(0.963228\pi\)
\(6\) 0 0
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) 0 0
\(9\) 8.37900i 2.79300i
\(10\) 0 0
\(11\) −3.73270 3.73270i −1.12545 1.12545i −0.990908 0.134543i \(-0.957043\pi\)
−0.134543 0.990908i \(-0.542957\pi\)
\(12\) 0 0
\(13\) 0.0725409 + 0.0725409i 0.0201192 + 0.0201192i 0.717095 0.696976i \(-0.245471\pi\)
−0.696976 + 0.717095i \(0.745471\pi\)
\(14\) 0 0
\(15\) −1.22958 + 1.22958i −0.317475 + 0.317475i
\(16\) 0 0
\(17\) −4.03186 + 4.03186i −0.977871 + 0.977871i −0.999760 0.0218898i \(-0.993032\pi\)
0.0218898 + 0.999760i \(0.493032\pi\)
\(18\) 0 0
\(19\) −2.33728 + 2.33728i −0.536208 + 0.536208i −0.922413 0.386205i \(-0.873786\pi\)
0.386205 + 0.922413i \(0.373786\pi\)
\(20\) 0 0
\(21\) 3.37328i 0.736109i
\(22\) 0 0
\(23\) 4.66571 0.972868 0.486434 0.873717i \(-0.338297\pi\)
0.486434 + 0.873717i \(0.338297\pi\)
\(24\) 0 0
\(25\) 4.73427 0.946855
\(26\) 0 0
\(27\) −12.8303 + 12.8303i −2.46920 + 2.46920i
\(28\) 0 0
\(29\) 6.22153 + 6.22153i 1.15531 + 1.15531i 0.985472 + 0.169838i \(0.0543243\pi\)
0.169838 + 0.985472i \(0.445676\pi\)
\(30\) 0 0
\(31\) −2.93310 −0.526800 −0.263400 0.964687i \(-0.584844\pi\)
−0.263400 + 0.964687i \(0.584844\pi\)
\(32\) 0 0
\(33\) 17.8070i 3.09980i
\(34\) 0 0
\(35\) −0.364505 + 0.364505i −0.0616125 + 0.0616125i
\(36\) 0 0
\(37\) −10.6326 −1.74799 −0.873994 0.485937i \(-0.838478\pi\)
−0.873994 + 0.485937i \(0.838478\pi\)
\(38\) 0 0
\(39\) 0.346059i 0.0554138i
\(40\) 0 0
\(41\) 5.72814 + 2.86154i 0.894585 + 0.446898i
\(42\) 0 0
\(43\) 1.10612i 0.168681i −0.996437 0.0843406i \(-0.973122\pi\)
0.996437 0.0843406i \(-0.0268784\pi\)
\(44\) 0 0
\(45\) −4.31927 −0.643878
\(46\) 0 0
\(47\) 8.99324 8.99324i 1.31180 1.31180i 0.391711 0.920088i \(-0.371883\pi\)
0.920088 0.391711i \(-0.128117\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) −19.2341 −2.69332
\(52\) 0 0
\(53\) 3.20712 + 3.20712i 0.440532 + 0.440532i 0.892191 0.451659i \(-0.149167\pi\)
−0.451659 + 0.892191i \(0.649167\pi\)
\(54\) 0 0
\(55\) 1.92416 1.92416i 0.259454 0.259454i
\(56\) 0 0
\(57\) −11.1501 −1.47686
\(58\) 0 0
\(59\) 12.6830 1.65119 0.825593 0.564266i \(-0.190841\pi\)
0.825593 + 0.564266i \(0.190841\pi\)
\(60\) 0 0
\(61\) 9.12150i 1.16789i −0.811794 0.583944i \(-0.801509\pi\)
0.811794 0.583944i \(-0.198491\pi\)
\(62\) 0 0
\(63\) −5.92485 + 5.92485i −0.746460 + 0.746460i
\(64\) 0 0
\(65\) −0.0373939 + 0.0373939i −0.00463815 + 0.00463815i
\(66\) 0 0
\(67\) 1.97135 1.97135i 0.240839 0.240839i −0.576358 0.817197i \(-0.695527\pi\)
0.817197 + 0.576358i \(0.195527\pi\)
\(68\) 0 0
\(69\) 11.1290 + 11.1290i 1.33977 + 1.33977i
\(70\) 0 0
\(71\) 8.02127 + 8.02127i 0.951950 + 0.951950i 0.998897 0.0469473i \(-0.0149493\pi\)
−0.0469473 + 0.998897i \(0.514949\pi\)
\(72\) 0 0
\(73\) 11.8259i 1.38412i −0.721840 0.692060i \(-0.756703\pi\)
0.721840 0.692060i \(-0.243297\pi\)
\(74\) 0 0
\(75\) 11.2925 + 11.2925i 1.30395 + 1.30395i
\(76\) 0 0
\(77\) 5.27883i 0.601579i
\(78\) 0 0
\(79\) 1.52258 + 1.52258i 0.171303 + 0.171303i 0.787552 0.616248i \(-0.211348\pi\)
−0.616248 + 0.787552i \(0.711348\pi\)
\(80\) 0 0
\(81\) −36.0706 −4.00785
\(82\) 0 0
\(83\) 5.12597 0.562648 0.281324 0.959613i \(-0.409226\pi\)
0.281324 + 0.959613i \(0.409226\pi\)
\(84\) 0 0
\(85\) −2.07837 2.07837i −0.225431 0.225431i
\(86\) 0 0
\(87\) 29.6800i 3.18203i
\(88\) 0 0
\(89\) −11.3538 11.3538i −1.20350 1.20350i −0.973093 0.230412i \(-0.925993\pi\)
−0.230412 0.973093i \(-0.574007\pi\)
\(90\) 0 0
\(91\) 0.102588i 0.0107542i
\(92\) 0 0
\(93\) −6.99623 6.99623i −0.725475 0.725475i
\(94\) 0 0
\(95\) −1.20484 1.20484i −0.123614 0.123614i
\(96\) 0 0
\(97\) 10.0266 10.0266i 1.01805 1.01805i 0.0182154 0.999834i \(-0.494202\pi\)
0.999834 0.0182154i \(-0.00579848\pi\)
\(98\) 0 0
\(99\) 31.2763 31.2763i 3.14338 3.14338i
\(100\) 0 0
\(101\) 0.283665 0.283665i 0.0282257 0.0282257i −0.692853 0.721079i \(-0.743647\pi\)
0.721079 + 0.692853i \(0.243647\pi\)
\(102\) 0 0
\(103\) 3.29717i 0.324880i 0.986718 + 0.162440i \(0.0519364\pi\)
−0.986718 + 0.162440i \(0.948064\pi\)
\(104\) 0 0
\(105\) −1.73888 −0.169697
\(106\) 0 0
\(107\) 4.92775 0.476384 0.238192 0.971218i \(-0.423445\pi\)
0.238192 + 0.971218i \(0.423445\pi\)
\(108\) 0 0
\(109\) −1.63794 + 1.63794i −0.156886 + 0.156886i −0.781185 0.624299i \(-0.785385\pi\)
0.624299 + 0.781185i \(0.285385\pi\)
\(110\) 0 0
\(111\) −25.3616 25.3616i −2.40721 2.40721i
\(112\) 0 0
\(113\) −9.28969 −0.873901 −0.436950 0.899486i \(-0.643941\pi\)
−0.436950 + 0.899486i \(0.643941\pi\)
\(114\) 0 0
\(115\) 2.40511i 0.224278i
\(116\) 0 0
\(117\) −0.607820 + 0.607820i −0.0561930 + 0.0561930i
\(118\) 0 0
\(119\) −5.70192 −0.522694
\(120\) 0 0
\(121\) 16.8661i 1.53328i
\(122\) 0 0
\(123\) 6.83760 + 20.4887i 0.616526 + 1.84740i
\(124\) 0 0
\(125\) 5.01789i 0.448814i
\(126\) 0 0
\(127\) −4.19701 −0.372425 −0.186212 0.982510i \(-0.559621\pi\)
−0.186212 + 0.982510i \(0.559621\pi\)
\(128\) 0 0
\(129\) 2.63838 2.63838i 0.232297 0.232297i
\(130\) 0 0
\(131\) 16.0114i 1.39892i −0.714670 0.699462i \(-0.753423\pi\)
0.714670 0.699462i \(-0.246577\pi\)
\(132\) 0 0
\(133\) −3.30541 −0.286615
\(134\) 0 0
\(135\) −6.61388 6.61388i −0.569232 0.569232i
\(136\) 0 0
\(137\) 1.82944 1.82944i 0.156300 0.156300i −0.624625 0.780925i \(-0.714748\pi\)
0.780925 + 0.624625i \(0.214748\pi\)
\(138\) 0 0
\(139\) −6.73374 −0.571148 −0.285574 0.958357i \(-0.592184\pi\)
−0.285574 + 0.958357i \(0.592184\pi\)
\(140\) 0 0
\(141\) 42.9026 3.61305
\(142\) 0 0
\(143\) 0.541547i 0.0452864i
\(144\) 0 0
\(145\) −3.20712 + 3.20712i −0.266337 + 0.266337i
\(146\) 0 0
\(147\) −2.38527 + 2.38527i −0.196734 + 0.196734i
\(148\) 0 0
\(149\) −7.34646 + 7.34646i −0.601845 + 0.601845i −0.940802 0.338957i \(-0.889926\pi\)
0.338957 + 0.940802i \(0.389926\pi\)
\(150\) 0 0
\(151\) 5.47921 + 5.47921i 0.445892 + 0.445892i 0.893986 0.448094i \(-0.147897\pi\)
−0.448094 + 0.893986i \(0.647897\pi\)
\(152\) 0 0
\(153\) −33.7830 33.7830i −2.73119 2.73119i
\(154\) 0 0
\(155\) 1.51198i 0.121445i
\(156\) 0 0
\(157\) −6.21037 6.21037i −0.495641 0.495641i 0.414437 0.910078i \(-0.363979\pi\)
−0.910078 + 0.414437i \(0.863979\pi\)
\(158\) 0 0
\(159\) 15.2997i 1.21334i
\(160\) 0 0
\(161\) 3.29916 + 3.29916i 0.260010 + 0.260010i
\(162\) 0 0
\(163\) −3.81284 −0.298645 −0.149322 0.988789i \(-0.547709\pi\)
−0.149322 + 0.988789i \(0.547709\pi\)
\(164\) 0 0
\(165\) 9.17927 0.714605
\(166\) 0 0
\(167\) 9.57625 + 9.57625i 0.741033 + 0.741033i 0.972777 0.231744i \(-0.0744432\pi\)
−0.231744 + 0.972777i \(0.574443\pi\)
\(168\) 0 0
\(169\) 12.9895i 0.999190i
\(170\) 0 0
\(171\) −19.5840 19.5840i −1.49763 1.49763i
\(172\) 0 0
\(173\) 20.5259i 1.56056i 0.625433 + 0.780278i \(0.284922\pi\)
−0.625433 + 0.780278i \(0.715078\pi\)
\(174\) 0 0
\(175\) 3.34764 + 3.34764i 0.253058 + 0.253058i
\(176\) 0 0
\(177\) 30.2523 + 30.2523i 2.27391 + 2.27391i
\(178\) 0 0
\(179\) −9.85685 + 9.85685i −0.736735 + 0.736735i −0.971945 0.235209i \(-0.924422\pi\)
0.235209 + 0.971945i \(0.424422\pi\)
\(180\) 0 0
\(181\) 4.50389 4.50389i 0.334772 0.334772i −0.519624 0.854395i \(-0.673928\pi\)
0.854395 + 0.519624i \(0.173928\pi\)
\(182\) 0 0
\(183\) 21.7572 21.7572i 1.60834 1.60834i
\(184\) 0 0
\(185\) 5.48097i 0.402969i
\(186\) 0 0
\(187\) 30.0995 2.20109
\(188\) 0 0
\(189\) −18.1449 −1.31984
\(190\) 0 0
\(191\) 9.82974 9.82974i 0.711255 0.711255i −0.255542 0.966798i \(-0.582254\pi\)
0.966798 + 0.255542i \(0.0822541\pi\)
\(192\) 0 0
\(193\) 17.0716 + 17.0716i 1.22884 + 1.22884i 0.964402 + 0.264442i \(0.0851878\pi\)
0.264442 + 0.964402i \(0.414812\pi\)
\(194\) 0 0
\(195\) −0.178389 −0.0127747
\(196\) 0 0
\(197\) 15.7804i 1.12431i 0.827032 + 0.562155i \(0.190027\pi\)
−0.827032 + 0.562155i \(0.809973\pi\)
\(198\) 0 0
\(199\) 3.06105 3.06105i 0.216992 0.216992i −0.590238 0.807230i \(-0.700966\pi\)
0.807230 + 0.590238i \(0.200966\pi\)
\(200\) 0 0
\(201\) 9.40439 0.663335
\(202\) 0 0
\(203\) 8.79858i 0.617539i
\(204\) 0 0
\(205\) −1.47509 + 2.95278i −0.103025 + 0.206231i
\(206\) 0 0
\(207\) 39.0940i 2.71722i
\(208\) 0 0
\(209\) 17.4487 1.20695
\(210\) 0 0
\(211\) 10.2542 10.2542i 0.705928 0.705928i −0.259748 0.965676i \(-0.583640\pi\)
0.965676 + 0.259748i \(0.0836395\pi\)
\(212\) 0 0
\(213\) 38.2658i 2.62193i
\(214\) 0 0
\(215\) 0.570189 0.0388866
\(216\) 0 0
\(217\) −2.07401 2.07401i −0.140793 0.140793i
\(218\) 0 0
\(219\) 28.2080 28.2080i 1.90612 1.90612i
\(220\) 0 0
\(221\) −0.584950 −0.0393480
\(222\) 0 0
\(223\) 2.63590 0.176513 0.0882564 0.996098i \(-0.471871\pi\)
0.0882564 + 0.996098i \(0.471871\pi\)
\(224\) 0 0
\(225\) 39.6685i 2.64456i
\(226\) 0 0
\(227\) 5.05013 5.05013i 0.335189 0.335189i −0.519364 0.854553i \(-0.673831\pi\)
0.854553 + 0.519364i \(0.173831\pi\)
\(228\) 0 0
\(229\) −4.14203 + 4.14203i −0.273713 + 0.273713i −0.830593 0.556880i \(-0.811998\pi\)
0.556880 + 0.830593i \(0.311998\pi\)
\(230\) 0 0
\(231\) 12.5914 12.5914i 0.828455 0.828455i
\(232\) 0 0
\(233\) −14.2789 14.2789i −0.935442 0.935442i 0.0625965 0.998039i \(-0.480062\pi\)
−0.998039 + 0.0625965i \(0.980062\pi\)
\(234\) 0 0
\(235\) 4.63590 + 4.63590i 0.302413 + 0.302413i
\(236\) 0 0
\(237\) 7.26350i 0.471815i
\(238\) 0 0
\(239\) 7.87813 + 7.87813i 0.509594 + 0.509594i 0.914402 0.404808i \(-0.132662\pi\)
−0.404808 + 0.914402i \(0.632662\pi\)
\(240\) 0 0
\(241\) 22.7596i 1.46607i −0.680189 0.733036i \(-0.738103\pi\)
0.680189 0.733036i \(-0.261897\pi\)
\(242\) 0 0
\(243\) −47.5470 47.5470i −3.05014 3.05014i
\(244\) 0 0
\(245\) −0.515487 −0.0329333
\(246\) 0 0
\(247\) −0.339097 −0.0215762
\(248\) 0 0
\(249\) 12.2268 + 12.2268i 0.774842 + 0.774842i
\(250\) 0 0
\(251\) 3.84367i 0.242611i 0.992615 + 0.121305i \(0.0387080\pi\)
−0.992615 + 0.121305i \(0.961292\pi\)
\(252\) 0 0
\(253\) −17.4157 17.4157i −1.09492 1.09492i
\(254\) 0 0
\(255\) 9.91496i 0.620899i
\(256\) 0 0
\(257\) −3.78522 3.78522i −0.236115 0.236115i 0.579124 0.815239i \(-0.303395\pi\)
−0.815239 + 0.579124i \(0.803395\pi\)
\(258\) 0 0
\(259\) −7.51838 7.51838i −0.467169 0.467169i
\(260\) 0 0
\(261\) −52.1302 + 52.1302i −3.22678 + 3.22678i
\(262\) 0 0
\(263\) −15.0562 + 15.0562i −0.928403 + 0.928403i −0.997603 0.0691998i \(-0.977955\pi\)
0.0691998 + 0.997603i \(0.477955\pi\)
\(264\) 0 0
\(265\) −1.65323 + 1.65323i −0.101557 + 0.101557i
\(266\) 0 0
\(267\) 54.1639i 3.31478i
\(268\) 0 0
\(269\) 8.47699 0.516852 0.258426 0.966031i \(-0.416796\pi\)
0.258426 + 0.966031i \(0.416796\pi\)
\(270\) 0 0
\(271\) −14.3815 −0.873615 −0.436808 0.899555i \(-0.643891\pi\)
−0.436808 + 0.899555i \(0.643891\pi\)
\(272\) 0 0
\(273\) −0.244701 + 0.244701i −0.0148100 + 0.0148100i
\(274\) 0 0
\(275\) −17.6716 17.6716i −1.06564 1.06564i
\(276\) 0 0
\(277\) −17.0460 −1.02420 −0.512099 0.858926i \(-0.671132\pi\)
−0.512099 + 0.858926i \(0.671132\pi\)
\(278\) 0 0
\(279\) 24.5764i 1.47135i
\(280\) 0 0
\(281\) 4.30611 4.30611i 0.256881 0.256881i −0.566903 0.823784i \(-0.691859\pi\)
0.823784 + 0.566903i \(0.191859\pi\)
\(282\) 0 0
\(283\) −16.5412 −0.983272 −0.491636 0.870801i \(-0.663601\pi\)
−0.491636 + 0.870801i \(0.663601\pi\)
\(284\) 0 0
\(285\) 5.74772i 0.340465i
\(286\) 0 0
\(287\) 2.02699 + 6.07382i 0.119649 + 0.358526i
\(288\) 0 0
\(289\) 15.5118i 0.912462i
\(290\) 0 0
\(291\) 47.8324 2.80398
\(292\) 0 0
\(293\) −0.781612 + 0.781612i −0.0456622 + 0.0456622i −0.729569 0.683907i \(-0.760279\pi\)
0.683907 + 0.729569i \(0.260279\pi\)
\(294\) 0 0
\(295\) 6.53793i 0.380653i
\(296\) 0 0
\(297\) 95.7836 5.55793
\(298\) 0 0
\(299\) 0.338455 + 0.338455i 0.0195734 + 0.0195734i
\(300\) 0 0
\(301\) 0.782143 0.782143i 0.0450820 0.0450820i
\(302\) 0 0
\(303\) 1.35323 0.0777412
\(304\) 0 0
\(305\) 4.70202 0.269237
\(306\) 0 0
\(307\) 9.83325i 0.561213i −0.959823 0.280607i \(-0.909464\pi\)
0.959823 0.280607i \(-0.0905356\pi\)
\(308\) 0 0
\(309\) −7.86464 + 7.86464i −0.447404 + 0.447404i
\(310\) 0 0
\(311\) 10.1168 10.1168i 0.573670 0.573670i −0.359482 0.933152i \(-0.617046\pi\)
0.933152 + 0.359482i \(0.117046\pi\)
\(312\) 0 0
\(313\) 5.32121 5.32121i 0.300773 0.300773i −0.540543 0.841316i \(-0.681781\pi\)
0.841316 + 0.540543i \(0.181781\pi\)
\(314\) 0 0
\(315\) −3.05418 3.05418i −0.172084 0.172084i
\(316\) 0 0
\(317\) −3.29102 3.29102i −0.184842 0.184842i 0.608620 0.793462i \(-0.291723\pi\)
−0.793462 + 0.608620i \(0.791723\pi\)
\(318\) 0 0
\(319\) 46.4462i 2.60049i
\(320\) 0 0
\(321\) 11.7540 + 11.7540i 0.656044 + 0.656044i
\(322\) 0 0
\(323\) 18.8472i 1.04868i
\(324\) 0 0
\(325\) 0.343429 + 0.343429i 0.0190500 + 0.0190500i
\(326\) 0 0
\(327\) −7.81385 −0.432107
\(328\) 0 0
\(329\) 12.7184 0.701186
\(330\) 0 0
\(331\) −7.94459 7.94459i −0.436674 0.436674i 0.454217 0.890891i \(-0.349919\pi\)
−0.890891 + 0.454217i \(0.849919\pi\)
\(332\) 0 0
\(333\) 89.0905i 4.88213i
\(334\) 0 0
\(335\) 1.01621 + 1.01621i 0.0555213 + 0.0555213i
\(336\) 0 0
\(337\) 20.7976i 1.13292i 0.824091 + 0.566458i \(0.191687\pi\)
−0.824091 + 0.566458i \(0.808313\pi\)
\(338\) 0 0
\(339\) −22.1584 22.1584i −1.20348 1.20348i
\(340\) 0 0
\(341\) 10.9484 + 10.9484i 0.592888 + 0.592888i
\(342\) 0 0
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) 0 0
\(345\) −5.73684 + 5.73684i −0.308861 + 0.308861i
\(346\) 0 0
\(347\) 8.98959 8.98959i 0.482587 0.482587i −0.423370 0.905957i \(-0.639153\pi\)
0.905957 + 0.423370i \(0.139153\pi\)
\(348\) 0 0
\(349\) 3.68188i 0.197087i −0.995133 0.0985434i \(-0.968582\pi\)
0.995133 0.0985434i \(-0.0314183\pi\)
\(350\) 0 0
\(351\) −1.86145 −0.0993569
\(352\) 0 0
\(353\) 5.31309 0.282787 0.141394 0.989953i \(-0.454842\pi\)
0.141394 + 0.989953i \(0.454842\pi\)
\(354\) 0 0
\(355\) −4.13487 + 4.13487i −0.219456 + 0.219456i
\(356\) 0 0
\(357\) −13.6006 13.6006i −0.719820 0.719820i
\(358\) 0 0
\(359\) 12.2528 0.646678 0.323339 0.946283i \(-0.395195\pi\)
0.323339 + 0.946283i \(0.395195\pi\)
\(360\) 0 0
\(361\) 8.07427i 0.424962i
\(362\) 0 0
\(363\) −40.2301 + 40.2301i −2.11153 + 2.11153i
\(364\) 0 0
\(365\) 6.09612 0.319085
\(366\) 0 0
\(367\) 19.9220i 1.03992i 0.854191 + 0.519960i \(0.174053\pi\)
−0.854191 + 0.519960i \(0.825947\pi\)
\(368\) 0 0
\(369\) −23.9769 + 47.9961i −1.24818 + 2.49858i
\(370\) 0 0
\(371\) 4.53556i 0.235474i
\(372\) 0 0
\(373\) 4.62160 0.239297 0.119649 0.992816i \(-0.461823\pi\)
0.119649 + 0.992816i \(0.461823\pi\)
\(374\) 0 0
\(375\) −11.9690 + 11.9690i −0.618077 + 0.618077i
\(376\) 0 0
\(377\) 0.902632i 0.0464879i
\(378\) 0 0
\(379\) 20.8730 1.07217 0.536087 0.844163i \(-0.319902\pi\)
0.536087 + 0.844163i \(0.319902\pi\)
\(380\) 0 0
\(381\) −10.0110 10.0110i −0.512879 0.512879i
\(382\) 0 0
\(383\) 19.3933 19.3933i 0.990951 0.990951i −0.00900803 0.999959i \(-0.502867\pi\)
0.999959 + 0.00900803i \(0.00286738\pi\)
\(384\) 0 0
\(385\) 2.72117 0.138684
\(386\) 0 0
\(387\) 9.26815 0.471127
\(388\) 0 0
\(389\) 26.7041i 1.35395i −0.736006 0.676975i \(-0.763290\pi\)
0.736006 0.676975i \(-0.236710\pi\)
\(390\) 0 0
\(391\) −18.8115 + 18.8115i −0.951339 + 0.951339i
\(392\) 0 0
\(393\) 38.1915 38.1915i 1.92651 1.92651i
\(394\) 0 0
\(395\) −0.784869 + 0.784869i −0.0394911 + 0.0394911i
\(396\) 0 0
\(397\) −17.1112 17.1112i −0.858785 0.858785i 0.132410 0.991195i \(-0.457728\pi\)
−0.991195 + 0.132410i \(0.957728\pi\)
\(398\) 0 0
\(399\) −7.88428 7.88428i −0.394708 0.394708i
\(400\) 0 0
\(401\) 13.6710i 0.682699i 0.939936 + 0.341350i \(0.110884\pi\)
−0.939936 + 0.341350i \(0.889116\pi\)
\(402\) 0 0
\(403\) −0.212770 0.212770i −0.0105988 0.0105988i
\(404\) 0 0
\(405\) 18.5939i 0.923941i
\(406\) 0 0
\(407\) 39.6883 + 39.6883i 1.96727 + 1.96727i
\(408\) 0 0
\(409\) −16.9515 −0.838198 −0.419099 0.907941i \(-0.637654\pi\)
−0.419099 + 0.907941i \(0.637654\pi\)
\(410\) 0 0
\(411\) 8.72743 0.430492
\(412\) 0 0
\(413\) 8.96823 + 8.96823i 0.441298 + 0.441298i
\(414\) 0 0
\(415\) 2.64237i 0.129709i
\(416\) 0 0
\(417\) −16.0618 16.0618i −0.786548 0.786548i
\(418\) 0 0
\(419\) 2.49951i 0.122109i 0.998134 + 0.0610545i \(0.0194464\pi\)
−0.998134 + 0.0610545i \(0.980554\pi\)
\(420\) 0 0
\(421\) 18.1546 + 18.1546i 0.884803 + 0.884803i 0.994018 0.109215i \(-0.0348339\pi\)
−0.109215 + 0.994018i \(0.534834\pi\)
\(422\) 0 0
\(423\) 75.3544 + 75.3544i 3.66386 + 3.66386i
\(424\) 0 0
\(425\) −19.0879 + 19.0879i −0.925901 + 0.925901i
\(426\) 0 0
\(427\) 6.44987 6.44987i 0.312131 0.312131i
\(428\) 0 0
\(429\) 1.29173 1.29173i 0.0623655 0.0623655i
\(430\) 0 0
\(431\) 1.10325i 0.0531418i 0.999647 + 0.0265709i \(0.00845878\pi\)
−0.999647 + 0.0265709i \(0.991541\pi\)
\(432\) 0 0
\(433\) 13.0897 0.629052 0.314526 0.949249i \(-0.398154\pi\)
0.314526 + 0.949249i \(0.398154\pi\)
\(434\) 0 0
\(435\) −15.2997 −0.733564
\(436\) 0 0
\(437\) −10.9051 + 10.9051i −0.521660 + 0.521660i
\(438\) 0 0
\(439\) −12.8182 12.8182i −0.611781 0.611781i 0.331629 0.943410i \(-0.392402\pi\)
−0.943410 + 0.331629i \(0.892402\pi\)
\(440\) 0 0
\(441\) −8.37900 −0.399000
\(442\) 0 0
\(443\) 15.1642i 0.720475i 0.932861 + 0.360238i \(0.117304\pi\)
−0.932861 + 0.360238i \(0.882696\pi\)
\(444\) 0 0
\(445\) 5.85276 5.85276i 0.277448 0.277448i
\(446\) 0 0
\(447\) −35.0465 −1.65764
\(448\) 0 0
\(449\) 12.2083i 0.576147i −0.957608 0.288074i \(-0.906985\pi\)
0.957608 0.288074i \(-0.0930148\pi\)
\(450\) 0 0
\(451\) −10.7001 32.0627i −0.503850 1.50977i
\(452\) 0 0
\(453\) 26.1388i 1.22811i
\(454\) 0 0
\(455\) −0.0528830 −0.00247919
\(456\) 0 0
\(457\) −12.6069 + 12.6069i −0.589724 + 0.589724i −0.937557 0.347832i \(-0.886918\pi\)
0.347832 + 0.937557i \(0.386918\pi\)
\(458\) 0 0
\(459\) 103.460i 4.82912i
\(460\) 0 0
\(461\) −22.1545 −1.03184 −0.515918 0.856638i \(-0.672549\pi\)
−0.515918 + 0.856638i \(0.672549\pi\)
\(462\) 0 0
\(463\) 15.5112 + 15.5112i 0.720867 + 0.720867i 0.968782 0.247915i \(-0.0797453\pi\)
−0.247915 + 0.968782i \(0.579745\pi\)
\(464\) 0 0
\(465\) 3.60647 3.60647i 0.167246 0.167246i
\(466\) 0 0
\(467\) −4.38169 −0.202761 −0.101380 0.994848i \(-0.532326\pi\)
−0.101380 + 0.994848i \(0.532326\pi\)
\(468\) 0 0
\(469\) 2.78791 0.128734
\(470\) 0 0
\(471\) 29.6268i 1.36513i
\(472\) 0 0
\(473\) −4.12880 + 4.12880i −0.189842 + 0.189842i
\(474\) 0 0
\(475\) −11.0653 + 11.0653i −0.507711 + 0.507711i
\(476\) 0 0
\(477\) −26.8725 + 26.8725i −1.23041 + 1.23041i
\(478\) 0 0
\(479\) −4.99918 4.99918i −0.228418 0.228418i 0.583613 0.812032i \(-0.301638\pi\)
−0.812032 + 0.583613i \(0.801638\pi\)
\(480\) 0 0
\(481\) −0.771298 0.771298i −0.0351682 0.0351682i
\(482\) 0 0
\(483\) 15.7387i 0.716137i
\(484\) 0 0
\(485\) 5.16860 + 5.16860i 0.234694 + 0.234694i
\(486\) 0 0
\(487\) 19.8721i 0.900493i −0.892904 0.450247i \(-0.851336\pi\)
0.892904 0.450247i \(-0.148664\pi\)
\(488\) 0 0
\(489\) −9.09464 9.09464i −0.411274 0.411274i
\(490\) 0 0
\(491\) −25.5055 −1.15105 −0.575524 0.817785i \(-0.695202\pi\)
−0.575524 + 0.817785i \(0.695202\pi\)
\(492\) 0 0
\(493\) −50.1687 −2.25949
\(494\) 0 0
\(495\) 16.1225 + 16.1225i 0.724654 + 0.724654i
\(496\) 0 0
\(497\) 11.3438i 0.508839i
\(498\) 0 0
\(499\) −1.88376 1.88376i −0.0843286 0.0843286i 0.663684 0.748013i \(-0.268992\pi\)
−0.748013 + 0.663684i \(0.768992\pi\)
\(500\) 0 0
\(501\) 45.6839i 2.04100i
\(502\) 0 0
\(503\) 14.4448 + 14.4448i 0.644063 + 0.644063i 0.951552 0.307489i \(-0.0994886\pi\)
−0.307489 + 0.951552i \(0.599489\pi\)
\(504\) 0 0
\(505\) 0.146226 + 0.146226i 0.00650696 + 0.00650696i
\(506\) 0 0
\(507\) 30.9834 30.9834i 1.37602 1.37602i
\(508\) 0 0
\(509\) −16.3552 + 16.3552i −0.724933 + 0.724933i −0.969606 0.244673i \(-0.921319\pi\)
0.244673 + 0.969606i \(0.421319\pi\)
\(510\) 0 0
\(511\) 8.36219 8.36219i 0.369922 0.369922i
\(512\) 0 0
\(513\) 59.9762i 2.64801i
\(514\) 0 0
\(515\) −1.69965 −0.0748956
\(516\) 0 0
\(517\) −67.1381 −2.95273
\(518\) 0 0
\(519\) −48.9598 + 48.9598i −2.14910 + 2.14910i
\(520\) 0 0
\(521\) −21.7776 21.7776i −0.954092 0.954092i 0.0448992 0.998992i \(-0.485703\pi\)
−0.998992 + 0.0448992i \(0.985703\pi\)
\(522\) 0 0
\(523\) −8.93717 −0.390795 −0.195398 0.980724i \(-0.562600\pi\)
−0.195398 + 0.980724i \(0.562600\pi\)
\(524\) 0 0
\(525\) 15.9700i 0.696989i
\(526\) 0 0
\(527\) 11.8259 11.8259i 0.515143 0.515143i
\(528\) 0 0
\(529\) −1.23115 −0.0535283
\(530\) 0 0
\(531\) 106.271i 4.61176i
\(532\) 0 0
\(533\) 0.207946 + 0.623103i 0.00900713 + 0.0269896i
\(534\) 0 0
\(535\) 2.54019i 0.109822i
\(536\) 0 0
\(537\) −47.0224 −2.02917
\(538\) 0 0
\(539\) 3.73270 3.73270i 0.160779 0.160779i
\(540\) 0 0
\(541\) 8.68014i 0.373189i 0.982437 + 0.186594i \(0.0597450\pi\)
−0.982437 + 0.186594i \(0.940255\pi\)
\(542\) 0 0
\(543\) 21.4860 0.922052
\(544\) 0 0
\(545\) −0.844338 0.844338i −0.0361675 0.0361675i
\(546\) 0 0
\(547\) −16.2596 + 16.2596i −0.695210 + 0.695210i −0.963373 0.268163i \(-0.913583\pi\)
0.268163 + 0.963373i \(0.413583\pi\)
\(548\) 0 0
\(549\) 76.4290 3.26191
\(550\) 0 0
\(551\) −29.0829 −1.23897
\(552\) 0 0
\(553\) 2.15325i 0.0915655i
\(554\) 0 0
\(555\) 13.0736 13.0736i 0.554942 0.554942i
\(556\) 0 0
\(557\) 11.3822 11.3822i 0.482280 0.482280i −0.423579 0.905859i \(-0.639226\pi\)
0.905859 + 0.423579i \(0.139226\pi\)
\(558\) 0 0
\(559\) 0.0802388 0.0802388i 0.00339374 0.00339374i
\(560\) 0 0
\(561\) 71.7953 + 71.7953i 3.03120 + 3.03120i
\(562\) 0 0
\(563\) 14.2376 + 14.2376i 0.600043 + 0.600043i 0.940324 0.340281i \(-0.110522\pi\)
−0.340281 + 0.940324i \(0.610522\pi\)
\(564\) 0 0
\(565\) 4.78872i 0.201463i
\(566\) 0 0
\(567\) −25.5058 25.5058i −1.07114 1.07114i
\(568\) 0 0
\(569\) 2.77716i 0.116425i 0.998304 + 0.0582123i \(0.0185400\pi\)
−0.998304 + 0.0582123i \(0.981460\pi\)
\(570\) 0 0
\(571\) 0.0948741 + 0.0948741i 0.00397036 + 0.00397036i 0.709089 0.705119i \(-0.249106\pi\)
−0.705119 + 0.709089i \(0.749106\pi\)
\(572\) 0 0
\(573\) 46.8931 1.95899
\(574\) 0 0
\(575\) 22.0887 0.921164
\(576\) 0 0
\(577\) −18.1781 18.1781i −0.756763 0.756763i 0.218969 0.975732i \(-0.429731\pi\)
−0.975732 + 0.218969i \(0.929731\pi\)
\(578\) 0 0
\(579\) 81.4408i 3.38457i
\(580\) 0 0
\(581\) 3.62461 + 3.62461i 0.150374 + 0.150374i
\(582\) 0 0
\(583\) 23.9424i 0.991595i
\(584\) 0 0
\(585\) −0.313324 0.313324i −0.0129543 0.0129543i
\(586\) 0 0
\(587\) 2.68151 + 2.68151i 0.110678 + 0.110678i 0.760277 0.649599i \(-0.225063\pi\)
−0.649599 + 0.760277i \(0.725063\pi\)
\(588\) 0 0
\(589\) 6.85547 6.85547i 0.282475 0.282475i
\(590\) 0 0
\(591\) −37.6405 + 37.6405i −1.54833 + 1.54833i
\(592\) 0 0
\(593\) 0.981314 0.981314i 0.0402978 0.0402978i −0.686671 0.726969i \(-0.740929\pi\)
0.726969 + 0.686671i \(0.240929\pi\)
\(594\) 0 0
\(595\) 2.93927i 0.120498i
\(596\) 0 0
\(597\) 14.6028 0.597655
\(598\) 0 0
\(599\) 41.7455 1.70568 0.852838 0.522175i \(-0.174879\pi\)
0.852838 + 0.522175i \(0.174879\pi\)
\(600\) 0 0
\(601\) −13.6073 + 13.6073i −0.555052 + 0.555052i −0.927895 0.372843i \(-0.878383\pi\)
0.372843 + 0.927895i \(0.378383\pi\)
\(602\) 0 0
\(603\) 16.5179 + 16.5179i 0.672662 + 0.672662i
\(604\) 0 0
\(605\) −8.69425 −0.353472
\(606\) 0 0
\(607\) 6.69657i 0.271805i −0.990722 0.135903i \(-0.956607\pi\)
0.990722 0.135903i \(-0.0433935\pi\)
\(608\) 0 0
\(609\) −20.9870 + 20.9870i −0.850434 + 0.850434i
\(610\) 0 0
\(611\) 1.30476 0.0527848
\(612\) 0 0
\(613\) 30.8965i 1.24790i 0.781466 + 0.623948i \(0.214472\pi\)
−0.781466 + 0.623948i \(0.785528\pi\)
\(614\) 0 0
\(615\) −10.5617 + 3.52470i −0.425887 + 0.142130i
\(616\) 0 0
\(617\) 4.03203i 0.162323i −0.996701 0.0811616i \(-0.974137\pi\)
0.996701 0.0811616i \(-0.0258630\pi\)
\(618\) 0 0
\(619\) −15.0789 −0.606071 −0.303036 0.952979i \(-0.598000\pi\)
−0.303036 + 0.952979i \(0.598000\pi\)
\(620\) 0 0
\(621\) −59.8627 + 59.8627i −2.40221 + 2.40221i
\(622\) 0 0
\(623\) 16.0568i 0.643300i
\(624\) 0 0
\(625\) 21.0847 0.843388
\(626\) 0 0
\(627\) 41.6198 + 41.6198i 1.66214 + 1.66214i
\(628\) 0 0
\(629\) 42.8692 42.8692i 1.70931 1.70931i
\(630\) 0 0
\(631\) −39.5990 −1.57641 −0.788206 0.615411i \(-0.788990\pi\)
−0.788206 + 0.615411i \(0.788990\pi\)
\(632\) 0 0
\(633\) 48.9180 1.94432
\(634\) 0 0
\(635\) 2.16351i 0.0858562i
\(636\) 0 0
\(637\) −0.0725409 + 0.0725409i −0.00287418 + 0.00287418i
\(638\) 0 0
\(639\) −67.2102 + 67.2102i −2.65880 + 2.65880i
\(640\) 0 0
\(641\) 3.23359 3.23359i 0.127719 0.127719i −0.640358 0.768077i \(-0.721214\pi\)
0.768077 + 0.640358i \(0.221214\pi\)
\(642\) 0 0
\(643\) 4.77331 + 4.77331i 0.188241 + 0.188241i 0.794935 0.606694i \(-0.207505\pi\)
−0.606694 + 0.794935i \(0.707505\pi\)
\(644\) 0 0
\(645\) 1.36005 + 1.36005i 0.0535521 + 0.0535521i
\(646\) 0 0
\(647\) 19.4761i 0.765684i 0.923814 + 0.382842i \(0.125055\pi\)
−0.923814 + 0.382842i \(0.874945\pi\)
\(648\) 0 0
\(649\) −47.3418 47.3418i −1.85833 1.85833i
\(650\) 0 0
\(651\) 9.89416i 0.387783i
\(652\) 0 0
\(653\) −34.6014 34.6014i −1.35406 1.35406i −0.881066 0.472993i \(-0.843173\pi\)
−0.472993 0.881066i \(-0.656827\pi\)
\(654\) 0 0
\(655\) 8.25368 0.322498
\(656\) 0 0
\(657\) 99.0894 3.86585
\(658\) 0 0
\(659\) −21.6336 21.6336i −0.842724 0.842724i 0.146489 0.989212i \(-0.453203\pi\)
−0.989212 + 0.146489i \(0.953203\pi\)
\(660\) 0 0
\(661\) 20.3486i 0.791470i 0.918365 + 0.395735i \(0.129510\pi\)
−0.918365 + 0.395735i \(0.870490\pi\)
\(662\) 0 0
\(663\) −1.39526 1.39526i −0.0541875 0.0541875i
\(664\) 0 0
\(665\) 1.70390i 0.0660743i
\(666\) 0 0
\(667\) 29.0279 + 29.0279i 1.12396 + 1.12396i
\(668\) 0 0
\(669\) 6.28732 + 6.28732i 0.243082 + 0.243082i
\(670\) 0 0
\(671\) −34.0478 + 34.0478i −1.31440 + 1.31440i
\(672\) 0 0
\(673\) −14.2765 + 14.2765i −0.550319 + 0.550319i −0.926533 0.376214i \(-0.877226\pi\)
0.376214 + 0.926533i \(0.377226\pi\)
\(674\) 0 0
\(675\) −60.7424 + 60.7424i −2.33797 + 2.33797i
\(676\) 0 0
\(677\) 33.2769i 1.27894i 0.768818 + 0.639468i \(0.220845\pi\)
−0.768818 + 0.639468i \(0.779155\pi\)
\(678\) 0 0
\(679\) 14.1798 0.544170
\(680\) 0 0
\(681\) 24.0918 0.923200
\(682\) 0 0
\(683\) −11.5598 + 11.5598i −0.442323 + 0.442323i −0.892792 0.450469i \(-0.851257\pi\)
0.450469 + 0.892792i \(0.351257\pi\)
\(684\) 0 0
\(685\) 0.943056 + 0.943056i 0.0360323 + 0.0360323i
\(686\) 0 0
\(687\) −19.7597 −0.753880
\(688\) 0 0
\(689\) 0.465295i 0.0177263i
\(690\) 0 0
\(691\) 19.8425 19.8425i 0.754845 0.754845i −0.220534 0.975379i \(-0.570780\pi\)
0.975379 + 0.220534i \(0.0707801\pi\)
\(692\) 0 0
\(693\) 44.2313 1.68021
\(694\) 0 0
\(695\) 3.47116i 0.131669i
\(696\) 0 0
\(697\) −34.6324 + 11.5577i −1.31180 + 0.437780i
\(698\) 0 0
\(699\) 68.1180i 2.57646i
\(700\) 0 0
\(701\) −25.0604 −0.946518 −0.473259 0.880923i \(-0.656923\pi\)
−0.473259 + 0.880923i \(0.656923\pi\)
\(702\) 0 0
\(703\) 24.8513 24.8513i 0.937285 0.937285i
\(704\) 0 0
\(705\) 22.1157i 0.832927i
\(706\) 0 0
\(707\) 0.401163 0.0150873
\(708\) 0 0
\(709\) −29.0627 29.0627i −1.09147 1.09147i −0.995371 0.0961021i \(-0.969362\pi\)
−0.0961021 0.995371i \(-0.530638\pi\)
\(710\) 0 0
\(711\) −12.7577 + 12.7577i −0.478450 + 0.478450i
\(712\) 0 0
\(713\) −13.6850 −0.512507
\(714\) 0 0
\(715\) 0.279161 0.0104400
\(716\) 0 0
\(717\) 37.5829i 1.40356i
\(718\) 0 0
\(719\) 31.8265 31.8265i 1.18693 1.18693i 0.209016 0.977912i \(-0.432974\pi\)
0.977912 0.209016i \(-0.0670260\pi\)
\(720\) 0 0
\(721\) −2.33145 + 2.33145i −0.0868278 + 0.0868278i
\(722\) 0 0
\(723\) 54.2876 54.2876i 2.01898 2.01898i
\(724\) 0 0
\(725\) 29.4544 + 29.4544i 1.09391 + 1.09391i
\(726\) 0 0
\(727\) 31.1328 + 31.1328i 1.15465 + 1.15465i 0.985609 + 0.169043i \(0.0540678\pi\)
0.169043 + 0.985609i \(0.445932\pi\)
\(728\) 0 0
\(729\) 118.613i 4.39307i
\(730\) 0 0
\(731\) 4.45971 + 4.45971i 0.164948 + 0.164948i
\(732\) 0 0
\(733\) 15.1476i 0.559489i 0.960075 + 0.279744i \(0.0902497\pi\)
−0.960075 + 0.279744i \(0.909750\pi\)
\(734\) 0 0
\(735\) −1.22958 1.22958i −0.0453536 0.0453536i
\(736\) 0 0
\(737\) −14.7169 −0.542104
\(738\) 0 0
\(739\) −50.1459 −1.84465 −0.922323 0.386421i \(-0.873711\pi\)
−0.922323 + 0.386421i \(0.873711\pi\)
\(740\) 0 0
\(741\) −0.808836 0.808836i −0.0297133 0.0297133i
\(742\) 0 0
\(743\) 36.9691i 1.35627i −0.734939 0.678133i \(-0.762789\pi\)
0.734939 0.678133i \(-0.237211\pi\)
\(744\) 0 0
\(745\) −3.78701 3.78701i −0.138745 0.138745i
\(746\) 0 0
\(747\) 42.9505i 1.57148i
\(748\) 0 0
\(749\) 3.48445 + 3.48445i 0.127319 + 0.127319i
\(750\) 0 0
\(751\) 5.68062 + 5.68062i 0.207289 + 0.207289i 0.803114 0.595825i \(-0.203175\pi\)
−0.595825 + 0.803114i \(0.703175\pi\)
\(752\) 0 0
\(753\) −9.16819 + 9.16819i −0.334107 + 0.334107i
\(754\) 0 0
\(755\) −2.82446 + 2.82446i −0.102793 + 0.102793i
\(756\) 0 0
\(757\) 29.8059 29.8059i 1.08331 1.08331i 0.0871151 0.996198i \(-0.472235\pi\)
0.996198 0.0871151i \(-0.0277648\pi\)
\(758\) 0 0
\(759\) 83.0821i 3.01569i
\(760\) 0 0
\(761\) 21.9939 0.797279 0.398639 0.917108i \(-0.369483\pi\)
0.398639 + 0.917108i \(0.369483\pi\)
\(762\) 0 0
\(763\) −2.31640 −0.0838593
\(764\) 0 0
\(765\) 17.4147 17.4147i 0.629630 0.629630i
\(766\) 0 0
\(767\) 0.920037 + 0.920037i 0.0332206 + 0.0332206i
\(768\) 0 0
\(769\) −14.4592 −0.521410 −0.260705 0.965418i \(-0.583955\pi\)
−0.260705 + 0.965418i \(0.583955\pi\)
\(770\) 0 0
\(771\) 18.0575i 0.650325i
\(772\) 0 0
\(773\) −6.62782 + 6.62782i −0.238386 + 0.238386i −0.816182 0.577795i \(-0.803913\pi\)
0.577795 + 0.816182i \(0.303913\pi\)
\(774\) 0 0
\(775\) −13.8861 −0.498803
\(776\) 0 0
\(777\) 35.8667i 1.28671i
\(778\) 0 0
\(779\) −20.0765 + 6.70003i −0.719314 + 0.240054i
\(780\) 0 0
\(781\) 59.8820i 2.14275i
\(782\) 0 0
\(783\) −159.649 −5.70538
\(784\) 0 0
\(785\) 3.20137 3.20137i 0.114262 0.114262i
\(786\) 0 0
\(787\) 48.0855i 1.71406i −0.515265 0.857031i \(-0.672306\pi\)
0.515265 0.857031i \(-0.327694\pi\)
\(788\) 0 0
\(789\) −71.8260 −2.55707
\(790\) 0 0
\(791\) −6.56880 6.56880i −0.233560 0.233560i
\(792\) 0 0
\(793\) 0.661682 0.661682i 0.0234970 0.0234970i
\(794\) 0 0
\(795\) −7.88680 −0.279716
\(796\) 0 0
\(797\) −11.0125 −0.390081 −0.195041 0.980795i \(-0.562484\pi\)
−0.195041 + 0.980795i \(0.562484\pi\)
\(798\) 0 0
\(799\) 72.5191i 2.56554i
\(800\) 0 0
\(801\) 95.1338