Properties

Label 1148.2.ba.a.113.14
Level $1148$
Weight $2$
Character 1148.113
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
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.ba (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 113.14
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.7

$q$-expansion

\(f(q)\) \(=\) \(q+1.48167i q^{3} +(-0.0508728 - 0.156570i) q^{5} +(0.587785 + 0.809017i) q^{7} +0.804648 q^{9} +O(q^{10})\) \(q+1.48167i q^{3} +(-0.0508728 - 0.156570i) q^{5} +(0.587785 + 0.809017i) q^{7} +0.804648 q^{9} +(-2.04392 - 0.664111i) q^{11} +(3.59771 - 4.95183i) q^{13} +(0.231986 - 0.0753767i) q^{15} +(5.92096 + 1.92384i) q^{17} +(-1.77638 - 2.44498i) q^{19} +(-1.19870 + 0.870905i) q^{21} +(3.15951 + 2.29552i) q^{23} +(4.02316 - 2.92300i) q^{25} +5.63724i q^{27} +(-3.99249 + 1.29724i) q^{29} +(1.08076 - 3.32623i) q^{31} +(0.983995 - 3.02843i) q^{33} +(0.0967657 - 0.133187i) q^{35} +(2.70765 + 8.33329i) q^{37} +(7.33698 + 5.33063i) q^{39} +(3.89499 + 5.08223i) q^{41} +(-5.52617 - 4.01500i) q^{43} +(-0.0409347 - 0.125984i) q^{45} +(-3.11819 + 4.29183i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-2.85049 + 8.77292i) q^{51} +(8.19061 - 2.66129i) q^{53} +0.353803i q^{55} +(3.62265 - 2.63201i) q^{57} +(-5.75201 - 4.17908i) q^{59} +(-9.32691 + 6.77640i) q^{61} +(0.472960 + 0.650974i) q^{63} +(-0.958334 - 0.311382i) q^{65} +(2.44934 - 0.795837i) q^{67} +(-3.40121 + 4.68136i) q^{69} +(4.83900 + 1.57229i) q^{71} +6.80054 q^{73} +(4.33092 + 5.96100i) q^{75} +(-0.664111 - 2.04392i) q^{77} -9.73908i q^{79} -5.93860 q^{81} +8.20719 q^{83} -1.02492i q^{85} +(-1.92208 - 5.91556i) q^{87} +(4.69741 + 6.46543i) q^{89} +6.12079 q^{91} +(4.92838 + 1.60133i) q^{93} +(-0.292441 + 0.402511i) q^{95} +(-7.52542 + 2.44516i) q^{97} +(-1.64464 - 0.534376i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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
\(3\) 1.48167i 0.855444i 0.903910 + 0.427722i \(0.140684\pi\)
−0.903910 + 0.427722i \(0.859316\pi\)
\(4\) 0 0
\(5\) −0.0508728 0.156570i −0.0227510 0.0700203i 0.939036 0.343818i \(-0.111720\pi\)
−0.961787 + 0.273797i \(0.911720\pi\)
\(6\) 0 0
\(7\) 0.587785 + 0.809017i 0.222162 + 0.305780i
\(8\) 0 0
\(9\) 0.804648 0.268216
\(10\) 0 0
\(11\) −2.04392 0.664111i −0.616267 0.200237i −0.0157845 0.999875i \(-0.505025\pi\)
−0.600482 + 0.799638i \(0.705025\pi\)
\(12\) 0 0
\(13\) 3.59771 4.95183i 0.997826 1.37339i 0.0711761 0.997464i \(-0.477325\pi\)
0.926650 0.375926i \(-0.122675\pi\)
\(14\) 0 0
\(15\) 0.231986 0.0753767i 0.0598985 0.0194622i
\(16\) 0 0
\(17\) 5.92096 + 1.92384i 1.43604 + 0.466599i 0.920661 0.390362i \(-0.127650\pi\)
0.515382 + 0.856961i \(0.327650\pi\)
\(18\) 0 0
\(19\) −1.77638 2.44498i −0.407530 0.560916i 0.555084 0.831794i \(-0.312686\pi\)
−0.962614 + 0.270878i \(0.912686\pi\)
\(20\) 0 0
\(21\) −1.19870 + 0.870905i −0.261577 + 0.190047i
\(22\) 0 0
\(23\) 3.15951 + 2.29552i 0.658804 + 0.478649i 0.866259 0.499595i \(-0.166518\pi\)
−0.207455 + 0.978245i \(0.566518\pi\)
\(24\) 0 0
\(25\) 4.02316 2.92300i 0.804632 0.584599i
\(26\) 0 0
\(27\) 5.63724i 1.08489i
\(28\) 0 0
\(29\) −3.99249 + 1.29724i −0.741387 + 0.240891i −0.655271 0.755394i \(-0.727445\pi\)
−0.0861157 + 0.996285i \(0.527445\pi\)
\(30\) 0 0
\(31\) 1.08076 3.32623i 0.194110 0.597409i −0.805876 0.592084i \(-0.798305\pi\)
0.999986 0.00532434i \(-0.00169480\pi\)
\(32\) 0 0
\(33\) 0.983995 3.02843i 0.171292 0.527181i
\(34\) 0 0
\(35\) 0.0967657 0.133187i 0.0163564 0.0225126i
\(36\) 0 0
\(37\) 2.70765 + 8.33329i 0.445135 + 1.36998i 0.882336 + 0.470621i \(0.155970\pi\)
−0.437200 + 0.899364i \(0.644030\pi\)
\(38\) 0 0
\(39\) 7.33698 + 5.33063i 1.17486 + 0.853584i
\(40\) 0 0
\(41\) 3.89499 + 5.08223i 0.608296 + 0.793711i
\(42\) 0 0
\(43\) −5.52617 4.01500i −0.842733 0.612281i 0.0803999 0.996763i \(-0.474380\pi\)
−0.923133 + 0.384481i \(0.874380\pi\)
\(44\) 0 0
\(45\) −0.0409347 0.125984i −0.00610218 0.0187806i
\(46\) 0 0
\(47\) −3.11819 + 4.29183i −0.454835 + 0.626027i −0.973428 0.228994i \(-0.926456\pi\)
0.518592 + 0.855022i \(0.326456\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) −2.85049 + 8.77292i −0.399149 + 1.22845i
\(52\) 0 0
\(53\) 8.19061 2.66129i 1.12507 0.365556i 0.313367 0.949632i \(-0.398543\pi\)
0.811699 + 0.584076i \(0.198543\pi\)
\(54\) 0 0
\(55\) 0.353803i 0.0477068i
\(56\) 0 0
\(57\) 3.62265 2.63201i 0.479832 0.348619i
\(58\) 0 0
\(59\) −5.75201 4.17908i −0.748848 0.544070i 0.146622 0.989193i \(-0.453160\pi\)
−0.895469 + 0.445123i \(0.853160\pi\)
\(60\) 0 0
\(61\) −9.32691 + 6.77640i −1.19419 + 0.867629i −0.993701 0.112067i \(-0.964253\pi\)
−0.200488 + 0.979696i \(0.564253\pi\)
\(62\) 0 0
\(63\) 0.472960 + 0.650974i 0.0595874 + 0.0820150i
\(64\) 0 0
\(65\) −0.958334 0.311382i −0.118867 0.0386221i
\(66\) 0 0
\(67\) 2.44934 0.795837i 0.299234 0.0972270i −0.155552 0.987828i \(-0.549716\pi\)
0.454786 + 0.890601i \(0.349716\pi\)
\(68\) 0 0
\(69\) −3.40121 + 4.68136i −0.409458 + 0.563570i
\(70\) 0 0
\(71\) 4.83900 + 1.57229i 0.574284 + 0.186596i 0.581738 0.813376i \(-0.302373\pi\)
−0.00745420 + 0.999972i \(0.502373\pi\)
\(72\) 0 0
\(73\) 6.80054 0.795943 0.397971 0.917398i \(-0.369714\pi\)
0.397971 + 0.917398i \(0.369714\pi\)
\(74\) 0 0
\(75\) 4.33092 + 5.96100i 0.500092 + 0.688317i
\(76\) 0 0
\(77\) −0.664111 2.04392i −0.0756825 0.232927i
\(78\) 0 0
\(79\) 9.73908i 1.09573i −0.836566 0.547866i \(-0.815440\pi\)
0.836566 0.547866i \(-0.184560\pi\)
\(80\) 0 0
\(81\) −5.93860 −0.659844
\(82\) 0 0
\(83\) 8.20719 0.900856 0.450428 0.892813i \(-0.351271\pi\)
0.450428 + 0.892813i \(0.351271\pi\)
\(84\) 0 0
\(85\) 1.02492i 0.111168i
\(86\) 0 0
\(87\) −1.92208 5.91556i −0.206069 0.634214i
\(88\) 0 0
\(89\) 4.69741 + 6.46543i 0.497925 + 0.685334i 0.981825 0.189789i \(-0.0607803\pi\)
−0.483900 + 0.875123i \(0.660780\pi\)
\(90\) 0 0
\(91\) 6.12079 0.641634
\(92\) 0 0
\(93\) 4.92838 + 1.60133i 0.511050 + 0.166050i
\(94\) 0 0
\(95\) −0.292441 + 0.402511i −0.0300039 + 0.0412968i
\(96\) 0 0
\(97\) −7.52542 + 2.44516i −0.764091 + 0.248268i −0.665033 0.746814i \(-0.731583\pi\)
−0.0990574 + 0.995082i \(0.531583\pi\)
\(98\) 0 0
\(99\) −1.64464 0.534376i −0.165293 0.0537068i
\(100\) 0 0
\(101\) 8.73078 + 12.0169i 0.868745 + 1.19572i 0.979413 + 0.201868i \(0.0647010\pi\)
−0.110668 + 0.993857i \(0.535299\pi\)
\(102\) 0 0
\(103\) −14.1197 + 10.2586i −1.39125 + 1.01081i −0.395528 + 0.918454i \(0.629438\pi\)
−0.995726 + 0.0923517i \(0.970562\pi\)
\(104\) 0 0
\(105\) 0.197339 + 0.143375i 0.0192583 + 0.0139920i
\(106\) 0 0
\(107\) 4.47795 3.25342i 0.432900 0.314520i −0.349908 0.936784i \(-0.613787\pi\)
0.782807 + 0.622264i \(0.213787\pi\)
\(108\) 0 0
\(109\) 3.31768i 0.317776i 0.987297 + 0.158888i \(0.0507909\pi\)
−0.987297 + 0.158888i \(0.949209\pi\)
\(110\) 0 0
\(111\) −12.3472 + 4.01185i −1.17194 + 0.380788i
\(112\) 0 0
\(113\) 4.65535 14.3277i 0.437939 1.34784i −0.452107 0.891964i \(-0.649327\pi\)
0.890045 0.455872i \(-0.150673\pi\)
\(114\) 0 0
\(115\) 0.198677 0.611465i 0.0185267 0.0570195i
\(116\) 0 0
\(117\) 2.89489 3.98448i 0.267633 0.368365i
\(118\) 0 0
\(119\) 1.92384 + 5.92096i 0.176358 + 0.542773i
\(120\) 0 0
\(121\) −5.16260 3.75085i −0.469327 0.340986i
\(122\) 0 0
\(123\) −7.53019 + 5.77110i −0.678975 + 0.520363i
\(124\) 0 0
\(125\) −1.32826 0.965035i −0.118803 0.0863153i
\(126\) 0 0
\(127\) 5.02260 + 15.4580i 0.445684 + 1.37167i 0.881732 + 0.471750i \(0.156378\pi\)
−0.436049 + 0.899923i \(0.643622\pi\)
\(128\) 0 0
\(129\) 5.94891 8.18797i 0.523772 0.720911i
\(130\) 0 0
\(131\) 2.58003 7.94052i 0.225419 0.693767i −0.772830 0.634613i \(-0.781160\pi\)
0.998249 0.0591542i \(-0.0188404\pi\)
\(132\) 0 0
\(133\) 0.933898 2.87424i 0.0809793 0.249229i
\(134\) 0 0
\(135\) 0.882624 0.286782i 0.0759642 0.0246823i
\(136\) 0 0
\(137\) 7.29628i 0.623363i −0.950187 0.311681i \(-0.899108\pi\)
0.950187 0.311681i \(-0.100892\pi\)
\(138\) 0 0
\(139\) −14.7518 + 10.7178i −1.25123 + 0.909072i −0.998293 0.0584106i \(-0.981397\pi\)
−0.252938 + 0.967483i \(0.581397\pi\)
\(140\) 0 0
\(141\) −6.35908 4.62014i −0.535531 0.389086i
\(142\) 0 0
\(143\) −10.6420 + 7.73188i −0.889930 + 0.646572i
\(144\) 0 0
\(145\) 0.406218 + 0.559111i 0.0337346 + 0.0464316i
\(146\) 0 0
\(147\) −1.40915 0.457862i −0.116225 0.0377638i
\(148\) 0 0
\(149\) 8.30494 2.69844i 0.680367 0.221065i 0.0516111 0.998667i \(-0.483564\pi\)
0.628756 + 0.777603i \(0.283564\pi\)
\(150\) 0 0
\(151\) 5.65924 7.78928i 0.460543 0.633882i −0.514079 0.857743i \(-0.671866\pi\)
0.974621 + 0.223861i \(0.0718660\pi\)
\(152\) 0 0
\(153\) 4.76429 + 1.54801i 0.385170 + 0.125149i
\(154\) 0 0
\(155\) −0.575770 −0.0462470
\(156\) 0 0
\(157\) −10.6281 14.6283i −0.848216 1.16747i −0.984253 0.176765i \(-0.943437\pi\)
0.136038 0.990704i \(-0.456563\pi\)
\(158\) 0 0
\(159\) 3.94316 + 12.1358i 0.312713 + 0.962431i
\(160\) 0 0
\(161\) 3.90537i 0.307787i
\(162\) 0 0
\(163\) 10.7123 0.839055 0.419528 0.907743i \(-0.362196\pi\)
0.419528 + 0.907743i \(0.362196\pi\)
\(164\) 0 0
\(165\) −0.524220 −0.0408105
\(166\) 0 0
\(167\) 1.55628i 0.120429i −0.998185 0.0602143i \(-0.980822\pi\)
0.998185 0.0602143i \(-0.0191784\pi\)
\(168\) 0 0
\(169\) −7.55983 23.2668i −0.581525 1.78975i
\(170\) 0 0
\(171\) −1.42936 1.96735i −0.109306 0.150447i
\(172\) 0 0
\(173\) −3.20051 −0.243331 −0.121665 0.992571i \(-0.538823\pi\)
−0.121665 + 0.992571i \(0.538823\pi\)
\(174\) 0 0
\(175\) 4.72951 + 1.53671i 0.357517 + 0.116164i
\(176\) 0 0
\(177\) 6.19202 8.52259i 0.465421 0.640597i
\(178\) 0 0
\(179\) −16.0452 + 5.21339i −1.19927 + 0.389667i −0.839493 0.543370i \(-0.817148\pi\)
−0.359780 + 0.933037i \(0.617148\pi\)
\(180\) 0 0
\(181\) −13.6442 4.43327i −1.01417 0.329522i −0.245654 0.969358i \(-0.579003\pi\)
−0.768512 + 0.639835i \(0.779003\pi\)
\(182\) 0 0
\(183\) −10.0404 13.8194i −0.742208 1.02156i
\(184\) 0 0
\(185\) 1.16700 0.847875i 0.0857995 0.0623370i
\(186\) 0 0
\(187\) −10.8244 7.86435i −0.791555 0.575098i
\(188\) 0 0
\(189\) −4.56062 + 3.31349i −0.331737 + 0.241021i
\(190\) 0 0
\(191\) 5.79551i 0.419349i 0.977771 + 0.209674i \(0.0672404\pi\)
−0.977771 + 0.209674i \(0.932760\pi\)
\(192\) 0 0
\(193\) −1.26442 + 0.410835i −0.0910150 + 0.0295726i −0.354171 0.935181i \(-0.615237\pi\)
0.263156 + 0.964753i \(0.415237\pi\)
\(194\) 0 0
\(195\) 0.461365 1.41994i 0.0330391 0.101684i
\(196\) 0 0
\(197\) 7.35070 22.6231i 0.523715 1.61183i −0.243127 0.969995i \(-0.578173\pi\)
0.766842 0.641836i \(-0.221827\pi\)
\(198\) 0 0
\(199\) 9.53263 13.1205i 0.675750 0.930090i −0.324123 0.946015i \(-0.605069\pi\)
0.999873 + 0.0159249i \(0.00506926\pi\)
\(200\) 0 0
\(201\) 1.17917 + 3.62911i 0.0831722 + 0.255978i
\(202\) 0 0
\(203\) −3.39621 2.46749i −0.238367 0.173184i
\(204\) 0 0
\(205\) 0.597577 0.868387i 0.0417366 0.0606508i
\(206\) 0 0
\(207\) 2.54230 + 1.84709i 0.176702 + 0.128381i
\(208\) 0 0
\(209\) 2.00705 + 6.17707i 0.138831 + 0.427277i
\(210\) 0 0
\(211\) 12.2597 16.8741i 0.843994 1.16166i −0.141160 0.989987i \(-0.545083\pi\)
0.985154 0.171672i \(-0.0549169\pi\)
\(212\) 0 0
\(213\) −2.32961 + 7.16982i −0.159623 + 0.491268i
\(214\) 0 0
\(215\) −0.347498 + 1.06949i −0.0236991 + 0.0729384i
\(216\) 0 0
\(217\) 3.32623 1.08076i 0.225799 0.0733666i
\(218\) 0 0
\(219\) 10.0762i 0.680884i
\(220\) 0 0
\(221\) 30.8284 22.3981i 2.07374 1.50666i
\(222\) 0 0
\(223\) 10.7940 + 7.84227i 0.722817 + 0.525157i 0.887283 0.461226i \(-0.152590\pi\)
−0.164466 + 0.986383i \(0.552590\pi\)
\(224\) 0 0
\(225\) 3.23723 2.35198i 0.215815 0.156799i
\(226\) 0 0
\(227\) 12.5068 + 17.2141i 0.830104 + 1.14254i 0.987904 + 0.155069i \(0.0495599\pi\)
−0.157800 + 0.987471i \(0.550440\pi\)
\(228\) 0 0
\(229\) −12.5263 4.07004i −0.827760 0.268956i −0.135659 0.990756i \(-0.543315\pi\)
−0.692102 + 0.721800i \(0.743315\pi\)
\(230\) 0 0
\(231\) 3.02843 0.983995i 0.199256 0.0647421i
\(232\) 0 0
\(233\) −3.30671 + 4.55129i −0.216630 + 0.298165i −0.903477 0.428637i \(-0.858994\pi\)
0.686847 + 0.726802i \(0.258994\pi\)
\(234\) 0 0
\(235\) 0.830603 + 0.269879i 0.0541826 + 0.0176050i
\(236\) 0 0
\(237\) 14.4301 0.937337
\(238\) 0 0
\(239\) −4.82031 6.63459i −0.311800 0.429156i 0.624141 0.781311i \(-0.285449\pi\)
−0.935942 + 0.352155i \(0.885449\pi\)
\(240\) 0 0
\(241\) −2.65228 8.16287i −0.170848 0.525817i 0.828571 0.559883i \(-0.189154\pi\)
−0.999420 + 0.0340668i \(0.989154\pi\)
\(242\) 0 0
\(243\) 8.11267i 0.520428i
\(244\) 0 0
\(245\) 0.164628 0.0105177
\(246\) 0 0
\(247\) −18.4980 −1.17700
\(248\) 0 0
\(249\) 12.1604i 0.770631i
\(250\) 0 0
\(251\) −8.07469 24.8513i −0.509670 1.56860i −0.792776 0.609513i \(-0.791365\pi\)
0.283106 0.959089i \(-0.408635\pi\)
\(252\) 0 0
\(253\) −4.93333 6.79014i −0.310156 0.426893i
\(254\) 0 0
\(255\) 1.51859 0.0950978
\(256\) 0 0
\(257\) −22.5474 7.32609i −1.40647 0.456989i −0.495191 0.868784i \(-0.664902\pi\)
−0.911277 + 0.411795i \(0.864902\pi\)
\(258\) 0 0
\(259\) −5.15026 + 7.08872i −0.320021 + 0.440472i
\(260\) 0 0
\(261\) −3.21255 + 1.04382i −0.198852 + 0.0646109i
\(262\) 0 0
\(263\) −14.9562 4.85958i −0.922242 0.299655i −0.190856 0.981618i \(-0.561126\pi\)
−0.731386 + 0.681964i \(0.761126\pi\)
\(264\) 0 0
\(265\) −0.833358 1.14702i −0.0511928 0.0704608i
\(266\) 0 0
\(267\) −9.57965 + 6.96002i −0.586265 + 0.425946i
\(268\) 0 0
\(269\) −8.47867 6.16011i −0.516954 0.375589i 0.298501 0.954409i \(-0.403513\pi\)
−0.815455 + 0.578820i \(0.803513\pi\)
\(270\) 0 0
\(271\) −19.5382 + 14.1954i −1.18686 + 0.862306i −0.992929 0.118708i \(-0.962125\pi\)
−0.193934 + 0.981015i \(0.562125\pi\)
\(272\) 0 0
\(273\) 9.06901i 0.548881i
\(274\) 0 0
\(275\) −10.1642 + 3.30256i −0.612926 + 0.199152i
\(276\) 0 0
\(277\) −0.0626312 + 0.192759i −0.00376314 + 0.0115818i −0.952920 0.303220i \(-0.901938\pi\)
0.949157 + 0.314802i \(0.101938\pi\)
\(278\) 0 0
\(279\) 0.869630 2.67645i 0.0520634 0.160235i
\(280\) 0 0
\(281\) −4.76579 + 6.55955i −0.284303 + 0.391310i −0.927153 0.374682i \(-0.877752\pi\)
0.642850 + 0.765992i \(0.277752\pi\)
\(282\) 0 0
\(283\) −7.29278 22.4449i −0.433511 1.33421i −0.894605 0.446858i \(-0.852543\pi\)
0.461094 0.887351i \(-0.347457\pi\)
\(284\) 0 0
\(285\) −0.596389 0.433302i −0.0353271 0.0256666i
\(286\) 0 0
\(287\) −1.82219 + 6.13837i −0.107560 + 0.362337i
\(288\) 0 0
\(289\) 17.6033 + 12.7896i 1.03549 + 0.752326i
\(290\) 0 0
\(291\) −3.62292 11.1502i −0.212379 0.653637i
\(292\) 0 0
\(293\) −13.4045 + 18.4498i −0.783101 + 1.07785i 0.211832 + 0.977306i \(0.432057\pi\)
−0.994933 + 0.100540i \(0.967943\pi\)
\(294\) 0 0
\(295\) −0.361699 + 1.11319i −0.0210589 + 0.0648127i
\(296\) 0 0
\(297\) 3.74376 11.5221i 0.217235 0.668580i
\(298\) 0 0
\(299\) 22.7340 7.38674i 1.31474 0.427186i
\(300\) 0 0
\(301\) 6.83072i 0.393716i
\(302\) 0 0
\(303\) −17.8051 + 12.9362i −1.02288 + 0.743162i
\(304\) 0 0
\(305\) 1.53547 + 1.11558i 0.0879206 + 0.0638781i
\(306\) 0 0
\(307\) 15.4101 11.1961i 0.879501 0.638995i −0.0536181 0.998562i \(-0.517075\pi\)
0.933120 + 0.359566i \(0.117075\pi\)
\(308\) 0 0
\(309\) −15.1998 20.9208i −0.864687 1.19014i
\(310\) 0 0
\(311\) 10.6313 + 3.45431i 0.602844 + 0.195876i 0.594508 0.804089i \(-0.297347\pi\)
0.00833558 + 0.999965i \(0.497347\pi\)
\(312\) 0 0
\(313\) 18.3889 5.97492i 1.03940 0.337722i 0.260901 0.965365i \(-0.415980\pi\)
0.778501 + 0.627643i \(0.215980\pi\)
\(314\) 0 0
\(315\) 0.0778624 0.107168i 0.00438705 0.00603825i
\(316\) 0 0
\(317\) −32.9940 10.7204i −1.85313 0.602117i −0.996243 0.0866048i \(-0.972398\pi\)
−0.856882 0.515512i \(-0.827602\pi\)
\(318\) 0 0
\(319\) 9.02186 0.505127
\(320\) 0 0
\(321\) 4.82050 + 6.63485i 0.269054 + 0.370321i
\(322\) 0 0
\(323\) −5.81414 17.8941i −0.323507 0.995653i
\(324\) 0 0
\(325\) 30.4381i 1.68840i
\(326\) 0 0
\(327\) −4.91572 −0.271840
\(328\) 0 0
\(329\) −5.30499 −0.292473
\(330\) 0 0
\(331\) 30.9478i 1.70105i 0.525937 + 0.850524i \(0.323715\pi\)
−0.525937 + 0.850524i \(0.676285\pi\)
\(332\) 0 0
\(333\) 2.17871 + 6.70537i 0.119392 + 0.367452i
\(334\) 0 0
\(335\) −0.249209 0.343007i −0.0136157 0.0187405i
\(336\) 0 0
\(337\) −18.4944 −1.00746 −0.503728 0.863862i \(-0.668039\pi\)
−0.503728 + 0.863862i \(0.668039\pi\)
\(338\) 0 0
\(339\) 21.2289 + 6.89770i 1.15300 + 0.374632i
\(340\) 0 0
\(341\) −4.41798 + 6.08082i −0.239247 + 0.329295i
\(342\) 0 0
\(343\) −0.951057 + 0.309017i −0.0513522 + 0.0166853i
\(344\) 0 0
\(345\) 0.905991 + 0.294374i 0.0487769 + 0.0158486i
\(346\) 0 0
\(347\) −2.26279 3.11447i −0.121473 0.167193i 0.743950 0.668236i \(-0.232950\pi\)
−0.865423 + 0.501042i \(0.832950\pi\)
\(348\) 0 0
\(349\) −9.75575 + 7.08797i −0.522213 + 0.379410i −0.817437 0.576018i \(-0.804606\pi\)
0.295224 + 0.955428i \(0.404606\pi\)
\(350\) 0 0
\(351\) 27.9146 + 20.2812i 1.48997 + 1.08253i
\(352\) 0 0
\(353\) −8.93723 + 6.49328i −0.475681 + 0.345602i −0.799651 0.600465i \(-0.794982\pi\)
0.323970 + 0.946067i \(0.394982\pi\)
\(354\) 0 0
\(355\) 0.837631i 0.0444568i
\(356\) 0 0
\(357\) −8.77292 + 2.85049i −0.464312 + 0.150864i
\(358\) 0 0
\(359\) −4.75644 + 14.6388i −0.251035 + 0.772607i 0.743550 + 0.668681i \(0.233141\pi\)
−0.994585 + 0.103926i \(0.966859\pi\)
\(360\) 0 0
\(361\) 3.04893 9.38365i 0.160470 0.493877i
\(362\) 0 0
\(363\) 5.55753 7.64928i 0.291695 0.401483i
\(364\) 0 0
\(365\) −0.345962 1.06476i −0.0181085 0.0557322i
\(366\) 0 0
\(367\) −13.4120 9.74437i −0.700100 0.508652i 0.179865 0.983691i \(-0.442434\pi\)
−0.879965 + 0.475039i \(0.842434\pi\)
\(368\) 0 0
\(369\) 3.13410 + 4.08941i 0.163155 + 0.212886i
\(370\) 0 0
\(371\) 6.96735 + 5.06207i 0.361727 + 0.262810i
\(372\) 0 0
\(373\) −7.33117 22.5630i −0.379594 1.16827i −0.940327 0.340272i \(-0.889481\pi\)
0.560733 0.827996i \(-0.310519\pi\)
\(374\) 0 0
\(375\) 1.42986 1.96804i 0.0738379 0.101629i
\(376\) 0 0
\(377\) −7.94013 + 24.4372i −0.408937 + 1.25858i
\(378\) 0 0
\(379\) 5.07824 15.6292i 0.260852 0.802818i −0.731769 0.681553i \(-0.761305\pi\)
0.992620 0.121265i \(-0.0386952\pi\)
\(380\) 0 0
\(381\) −22.9036 + 7.44185i −1.17339 + 0.381257i
\(382\) 0 0
\(383\) 36.2821i 1.85393i 0.375149 + 0.926964i \(0.377591\pi\)
−0.375149 + 0.926964i \(0.622409\pi\)
\(384\) 0 0
\(385\) −0.286233 + 0.207960i −0.0145878 + 0.0105986i
\(386\) 0 0
\(387\) −4.44662 3.23066i −0.226035 0.164224i
\(388\) 0 0
\(389\) −6.88628 + 5.00318i −0.349149 + 0.253671i −0.748512 0.663122i \(-0.769231\pi\)
0.399363 + 0.916793i \(0.369231\pi\)
\(390\) 0 0
\(391\) 14.2911 + 19.6701i 0.722734 + 0.994758i
\(392\) 0 0
\(393\) 11.7653 + 3.82276i 0.593478 + 0.192833i
\(394\) 0 0
\(395\) −1.52485 + 0.495454i −0.0767235 + 0.0249290i
\(396\) 0 0
\(397\) −14.7560 + 20.3098i −0.740581 + 1.01932i 0.258004 + 0.966144i \(0.416935\pi\)
−0.998585 + 0.0531783i \(0.983065\pi\)
\(398\) 0 0
\(399\) 4.25869 + 1.38373i 0.213201 + 0.0692732i
\(400\) 0 0
\(401\) 35.8171 1.78862 0.894309 0.447449i \(-0.147667\pi\)
0.894309 + 0.447449i \(0.147667\pi\)
\(402\) 0 0
\(403\) −12.5827 17.3185i −0.626787 0.862698i
\(404\) 0 0
\(405\) 0.302113 + 0.929807i 0.0150121 + 0.0462025i
\(406\) 0 0
\(407\) 18.8308i 0.933408i
\(408\) 0 0
\(409\) −7.39908 −0.365861 −0.182931 0.983126i \(-0.558558\pi\)
−0.182931 + 0.983126i \(0.558558\pi\)
\(410\) 0 0
\(411\) 10.8107 0.533252
\(412\) 0 0
\(413\) 7.10987i 0.349854i
\(414\) 0 0
\(415\) −0.417522 1.28500i −0.0204954 0.0630782i
\(416\) 0 0
\(417\) −15.8803 21.8573i −0.777660 1.07036i
\(418\) 0 0
\(419\) 19.9432 0.974290 0.487145 0.873321i \(-0.338038\pi\)
0.487145 + 0.873321i \(0.338038\pi\)
\(420\) 0 0
\(421\) −0.897797 0.291712i −0.0437559 0.0142172i 0.287057 0.957913i \(-0.407323\pi\)
−0.330813 + 0.943696i \(0.607323\pi\)
\(422\) 0 0
\(423\) −2.50905 + 3.45341i −0.121994 + 0.167911i
\(424\) 0 0
\(425\) 29.4443 9.56704i 1.42826 0.464070i
\(426\) 0 0
\(427\) −10.9644 3.56256i −0.530606 0.172405i
\(428\) 0 0
\(429\) −11.4561 15.7680i −0.553106 0.761285i
\(430\) 0 0
\(431\) 1.89042 1.37347i 0.0910584 0.0661578i −0.541324 0.840814i \(-0.682077\pi\)
0.632383 + 0.774656i \(0.282077\pi\)
\(432\) 0 0
\(433\) 0.458230 + 0.332923i 0.0220211 + 0.0159993i 0.598741 0.800942i \(-0.295668\pi\)
−0.576720 + 0.816942i \(0.695668\pi\)
\(434\) 0 0
\(435\) −0.828419 + 0.601882i −0.0397196 + 0.0288580i
\(436\) 0 0
\(437\) 11.8027i 0.564598i
\(438\) 0 0
\(439\) −8.94065 + 2.90499i −0.426714 + 0.138648i −0.514498 0.857492i \(-0.672022\pi\)
0.0877836 + 0.996140i \(0.472022\pi\)
\(440\) 0 0
\(441\) −0.248650 + 0.765266i −0.0118405 + 0.0364412i
\(442\) 0 0
\(443\) −10.6864 + 32.8893i −0.507726 + 1.56262i 0.288414 + 0.957506i \(0.406872\pi\)
−0.796140 + 0.605113i \(0.793128\pi\)
\(444\) 0 0
\(445\) 0.773324 1.06439i 0.0366591 0.0504569i
\(446\) 0 0
\(447\) 3.99820 + 12.3052i 0.189108 + 0.582016i
\(448\) 0 0
\(449\) 26.8676 + 19.5204i 1.26796 + 0.921226i 0.999119 0.0419586i \(-0.0133597\pi\)
0.268840 + 0.963185i \(0.413360\pi\)
\(450\) 0 0
\(451\) −4.58591 12.9744i −0.215942 0.610941i
\(452\) 0 0
\(453\) 11.5412 + 8.38514i 0.542251 + 0.393968i
\(454\) 0 0
\(455\) −0.311382 0.958334i −0.0145978 0.0449274i
\(456\) 0 0
\(457\) −3.92520 + 5.40258i −0.183613 + 0.252722i −0.890895 0.454210i \(-0.849921\pi\)
0.707281 + 0.706932i \(0.249921\pi\)
\(458\) 0 0
\(459\) −10.8451 + 33.3779i −0.506207 + 1.55795i
\(460\) 0 0
\(461\) −4.13378 + 12.7225i −0.192529 + 0.592544i 0.807467 + 0.589912i \(0.200838\pi\)
−0.999997 + 0.00263170i \(0.999162\pi\)
\(462\) 0 0
\(463\) −24.8668 + 8.07973i −1.15566 + 0.375497i −0.823273 0.567646i \(-0.807854\pi\)
−0.332388 + 0.943143i \(0.607854\pi\)
\(464\) 0 0
\(465\) 0.853102i 0.0395617i
\(466\) 0 0
\(467\) −20.9608 + 15.2289i −0.969950 + 0.704710i −0.955440 0.295185i \(-0.904619\pi\)
−0.0145098 + 0.999895i \(0.504619\pi\)
\(468\) 0 0
\(469\) 2.08353 + 1.51377i 0.0962084 + 0.0698995i
\(470\) 0 0
\(471\) 21.6744 15.7474i 0.998704 0.725601i
\(472\) 0 0
\(473\) 8.62867 + 11.8763i 0.396747 + 0.546075i
\(474\) 0 0
\(475\) −14.2933 4.64418i −0.655822 0.213090i
\(476\) 0 0
\(477\) 6.59056 2.14140i 0.301761 0.0980481i
\(478\) 0 0
\(479\) 2.98035 4.10210i 0.136176 0.187430i −0.735483 0.677543i \(-0.763045\pi\)
0.871659 + 0.490114i \(0.163045\pi\)
\(480\) 0 0
\(481\) 51.0064 + 16.5730i 2.32569 + 0.755663i
\(482\) 0 0
\(483\) −5.78648 −0.263294
\(484\) 0 0
\(485\) 0.765678 + 1.05387i 0.0347676 + 0.0478536i
\(486\) 0 0
\(487\) −10.1544 31.2522i −0.460142 1.41617i −0.864991 0.501787i \(-0.832676\pi\)
0.404849 0.914383i \(-0.367324\pi\)
\(488\) 0 0
\(489\) 15.8722i 0.717764i
\(490\) 0 0
\(491\) 32.7495 1.47797 0.738983 0.673724i \(-0.235306\pi\)
0.738983 + 0.673724i \(0.235306\pi\)
\(492\) 0 0
\(493\) −26.1350 −1.17706
\(494\) 0 0
\(495\) 0.284687i 0.0127957i
\(496\) 0 0
\(497\) 1.57229 + 4.83900i 0.0705267 + 0.217059i
\(498\) 0 0
\(499\) 8.34358 + 11.4840i 0.373510 + 0.514093i 0.953851 0.300281i \(-0.0970806\pi\)
−0.580341 + 0.814374i \(0.697081\pi\)
\(500\) 0 0
\(501\) 2.30590 0.103020
\(502\) 0 0
\(503\) 12.4927 + 4.05914i 0.557024 + 0.180988i 0.573982 0.818868i \(-0.305398\pi\)
−0.0169576 + 0.999856i \(0.505398\pi\)
\(504\) 0 0
\(505\) 1.43733 1.97831i 0.0639603 0.0880338i
\(506\) 0 0
\(507\) 34.4737 11.2012i 1.53103 0.497462i
\(508\) 0 0
\(509\) 15.2239 + 4.94654i 0.674786 + 0.219251i 0.626311 0.779573i \(-0.284564\pi\)
0.0484751 + 0.998824i \(0.484564\pi\)
\(510\) 0 0
\(511\) 3.99726 + 5.50175i 0.176828 + 0.243383i
\(512\) 0 0
\(513\) 13.7829 10.0139i 0.608531 0.442124i
\(514\) 0 0
\(515\) 2.32449 + 1.68884i 0.102429 + 0.0744193i
\(516\) 0 0
\(517\) 9.22361 6.70134i 0.405654 0.294725i
\(518\) 0 0
\(519\) 4.74211i 0.208156i
\(520\) 0 0
\(521\) −9.80436 + 3.18563i −0.429537 + 0.139565i −0.515803 0.856707i \(-0.672506\pi\)
0.0862663 + 0.996272i \(0.472506\pi\)
\(522\) 0 0
\(523\) 1.32934 4.09128i 0.0581279 0.178899i −0.917777 0.397097i \(-0.870018\pi\)
0.975905 + 0.218197i \(0.0700177\pi\)
\(524\) 0 0
\(525\) −2.27690 + 7.00758i −0.0993721 + 0.305836i
\(526\) 0 0
\(527\) 12.7982 17.6153i 0.557500 0.767333i
\(528\) 0 0
\(529\) −2.39428 7.36883i −0.104099 0.320384i
\(530\) 0 0
\(531\) −4.62834 3.36269i −0.200853 0.145928i
\(532\) 0 0
\(533\) 39.1794 1.00293i 1.69705 0.0434418i
\(534\) 0 0
\(535\) −0.737194 0.535603i −0.0318717 0.0231561i
\(536\) 0 0
\(537\) −7.72454 23.7737i −0.333339 1.02591i
\(538\) 0 0
\(539\) 1.26322 1.73867i 0.0544105 0.0748897i
\(540\) 0 0
\(541\) −3.29337 + 10.1360i −0.141593 + 0.435779i −0.996557 0.0829084i \(-0.973579\pi\)
0.854964 + 0.518687i \(0.173579\pi\)
\(542\) 0 0
\(543\) 6.56865 20.2162i 0.281888 0.867562i
\(544\) 0 0
\(545\) 0.519450 0.168780i 0.0222508 0.00722972i
\(546\) 0 0
\(547\) 38.1179i 1.62980i −0.579598 0.814902i \(-0.696790\pi\)
0.579598 0.814902i \(-0.303210\pi\)
\(548\) 0 0
\(549\) −7.50488 + 5.45262i −0.320301 + 0.232712i
\(550\) 0 0
\(551\) 10.2639 + 7.45716i 0.437257 + 0.317686i
\(552\) 0 0
\(553\) 7.87908 5.72449i 0.335053 0.243430i
\(554\) 0 0
\(555\) 1.25627 + 1.72911i 0.0533258 + 0.0733967i
\(556\) 0 0
\(557\) 26.6890 + 8.67180i 1.13085 + 0.367436i 0.813899 0.581006i \(-0.197341\pi\)
0.316952 + 0.948442i \(0.397341\pi\)
\(558\) 0 0
\(559\) −39.7631 + 12.9198i −1.68180 + 0.546450i
\(560\) 0 0
\(561\) 11.6524 16.0381i 0.491964 0.677131i
\(562\) 0 0
\(563\) 1.70343 + 0.553477i 0.0717909 + 0.0233263i 0.344692 0.938716i \(-0.387983\pi\)
−0.272901 + 0.962042i \(0.587983\pi\)
\(564\) 0 0
\(565\) −2.48012 −0.104339
\(566\) 0 0
\(567\) −3.49062 4.80443i −0.146592 0.201767i
\(568\) 0 0
\(569\) −13.1437 40.4521i −0.551012 1.69584i −0.706249 0.707964i \(-0.749614\pi\)
0.155237 0.987877i \(-0.450386\pi\)
\(570\) 0 0
\(571\) 2.63954i 0.110462i 0.998474 + 0.0552308i \(0.0175894\pi\)
−0.998474 + 0.0552308i \(0.982411\pi\)
\(572\) 0 0
\(573\) −8.58705 −0.358729
\(574\) 0 0
\(575\) 19.4210 0.809913
\(576\) 0 0
\(577\) 27.3681i 1.13935i 0.821871 + 0.569674i \(0.192931\pi\)
−0.821871 + 0.569674i \(0.807069\pi\)
\(578\) 0 0
\(579\) −0.608723 1.87346i −0.0252977 0.0778582i
\(580\) 0 0
\(581\) 4.82406 + 6.63975i 0.200136 + 0.275463i
\(582\) 0 0
\(583\) −18.5084 −0.766539
\(584\) 0 0
\(585\) −0.771122 0.250553i −0.0318820 0.0103591i
\(586\) 0 0
\(587\) 3.92980 5.40890i 0.162200 0.223249i −0.720179 0.693788i \(-0.755940\pi\)
0.882379 + 0.470539i \(0.155940\pi\)
\(588\) 0 0
\(589\) −10.0524 + 3.26622i −0.414202 + 0.134582i
\(590\) 0 0
\(591\) 33.5200 + 10.8913i 1.37883 + 0.448009i
\(592\) 0 0
\(593\) 10.8035 + 14.8697i 0.443646 + 0.610626i 0.971017 0.239009i \(-0.0768224\pi\)
−0.527372 + 0.849635i \(0.676822\pi\)
\(594\) 0 0
\(595\) 0.829175 0.602431i 0.0339929 0.0246973i
\(596\) 0 0
\(597\) 19.4403 + 14.1242i 0.795640 + 0.578066i
\(598\) 0 0
\(599\) −31.0820 + 22.5824i −1.26998 + 0.922691i −0.999202 0.0399522i \(-0.987279\pi\)
−0.270773 + 0.962643i \(0.587279\pi\)
\(600\) 0 0
\(601\) 0.134811i 0.00549905i 0.999996 + 0.00274953i \(0.000875203\pi\)
−0.999996 + 0.00274953i \(0.999125\pi\)
\(602\) 0 0
\(603\) 1.97085 0.640369i 0.0802594 0.0260778i
\(604\) 0 0
\(605\) −0.324636 + 0.999126i −0.0131983 + 0.0406202i
\(606\) 0 0
\(607\) 12.9545 39.8700i 0.525809 1.61827i −0.236902 0.971534i \(-0.576132\pi\)
0.762711 0.646740i \(-0.223868\pi\)
\(608\) 0 0
\(609\) 3.65602 5.03207i 0.148149 0.203910i
\(610\) 0 0
\(611\) 10.0340 + 30.8815i 0.405933 + 1.24933i
\(612\) 0 0
\(613\) −10.0530 7.30393i −0.406037 0.295003i 0.365959 0.930631i \(-0.380741\pi\)
−0.771995 + 0.635628i \(0.780741\pi\)
\(614\) 0 0
\(615\) 1.28666 + 0.885413i 0.0518833 + 0.0357033i
\(616\) 0 0
\(617\) −35.3489 25.6825i −1.42309 1.03394i −0.991251 0.131987i \(-0.957864\pi\)
−0.431841 0.901950i \(-0.642136\pi\)
\(618\) 0 0
\(619\) 1.21533 + 3.74041i 0.0488484 + 0.150340i 0.972505 0.232880i \(-0.0748150\pi\)
−0.923657 + 0.383220i \(0.874815\pi\)
\(620\) 0 0
\(621\) −12.9404 + 17.8109i −0.519281 + 0.714729i
\(622\) 0 0
\(623\) −2.46958 + 7.60057i −0.0989414 + 0.304510i
\(624\) 0 0
\(625\) 7.60003 23.3905i 0.304001 0.935619i
\(626\) 0 0
\(627\) −9.15238 + 2.97379i −0.365511 + 0.118762i
\(628\) 0 0
\(629\) 54.5501i 2.17506i
\(630\) 0 0
\(631\) 10.5711 7.68035i 0.420828 0.305750i −0.357143 0.934050i \(-0.616249\pi\)
0.777971 + 0.628300i \(0.216249\pi\)
\(632\) 0 0
\(633\) 25.0018 + 18.1649i 0.993734 + 0.721990i
\(634\) 0 0
\(635\) 2.16475 1.57278i 0.0859053 0.0624138i
\(636\) 0 0
\(637\) 3.59771 + 4.95183i 0.142547 + 0.196198i
\(638\) 0 0
\(639\) 3.89370 + 1.26514i 0.154032 + 0.0500481i
\(640\) 0 0
\(641\) 11.8356 3.84561i 0.467477 0.151892i −0.0658008 0.997833i \(-0.520960\pi\)
0.533277 + 0.845940i \(0.320960\pi\)
\(642\) 0 0
\(643\) 3.24843 4.47108i 0.128106 0.176322i −0.740146 0.672446i \(-0.765244\pi\)
0.868252 + 0.496124i \(0.165244\pi\)
\(644\) 0 0
\(645\) −1.58463 0.514877i −0.0623947 0.0202733i
\(646\) 0 0
\(647\) −35.3366 −1.38923 −0.694613 0.719384i \(-0.744424\pi\)
−0.694613 + 0.719384i \(0.744424\pi\)
\(648\) 0 0
\(649\) 8.98130 + 12.3617i 0.352547 + 0.485239i
\(650\) 0 0
\(651\) 1.60133 + 4.92838i 0.0627610 + 0.193159i
\(652\) 0 0
\(653\) 25.0020i 0.978405i 0.872170 + 0.489202i \(0.162712\pi\)
−0.872170 + 0.489202i \(0.837288\pi\)
\(654\) 0 0
\(655\) −1.37450 −0.0537063
\(656\) 0 0
\(657\) 5.47204 0.213485
\(658\) 0 0
\(659\) 30.0961i 1.17238i 0.810175 + 0.586188i \(0.199372\pi\)
−0.810175 + 0.586188i \(0.800628\pi\)
\(660\) 0 0
\(661\) 10.8568 + 33.4139i 0.422281 + 1.29965i 0.905573 + 0.424189i \(0.139441\pi\)
−0.483292 + 0.875459i \(0.660559\pi\)
\(662\) 0 0
\(663\) 33.1867 + 45.6776i 1.28886 + 1.77397i
\(664\) 0 0
\(665\) −0.497531 −0.0192934
\(666\) 0 0
\(667\) −15.5922 5.06620i −0.603731 0.196164i
\(668\) 0 0
\(669\) −11.6197 + 15.9931i −0.449242 + 0.618329i
\(670\) 0 0
\(671\) 23.5638 7.65634i 0.909670 0.295570i
\(672\) 0 0
\(673\) 30.8489 + 10.0234i 1.18914 + 0.386374i 0.835754 0.549105i \(-0.185031\pi\)
0.353383 + 0.935479i \(0.385031\pi\)
\(674\) 0 0
\(675\) 16.4776 + 22.6795i 0.634224 + 0.872935i
\(676\) 0 0
\(677\) 20.4388 14.8497i 0.785529 0.570720i −0.121105 0.992640i \(-0.538644\pi\)
0.906633 + 0.421920i \(0.138644\pi\)
\(678\) 0 0
\(679\) −6.40151 4.65097i −0.245667 0.178488i
\(680\) 0 0
\(681\) −25.5056 + 18.5309i −0.977379 + 0.710107i
\(682\) 0 0
\(683\) 19.1333i 0.732116i −0.930592 0.366058i \(-0.880707\pi\)
0.930592 0.366058i \(-0.119293\pi\)
\(684\) 0 0
\(685\) −1.14238 + 0.371182i −0.0436481 + 0.0141821i
\(686\) 0 0
\(687\) 6.03046 18.5598i 0.230076 0.708102i
\(688\) 0 0
\(689\) 16.2892 50.1330i 0.620569 1.90992i
\(690\) 0 0
\(691\) −0.632753 + 0.870910i −0.0240711 + 0.0331310i −0.820883 0.571097i \(-0.806518\pi\)
0.796812 + 0.604228i \(0.206518\pi\)
\(692\) 0 0
\(693\) −0.534376 1.64464i −0.0202993 0.0624747i
\(694\) 0 0
\(695\) 2.42855 + 1.76445i 0.0921203 + 0.0669293i
\(696\) 0 0
\(697\) 13.2847 + 37.5850i 0.503194 + 1.42363i
\(698\) 0 0
\(699\) −6.74352 4.89945i −0.255063 0.185314i
\(700\) 0 0
\(701\) −5.76507 17.7431i −0.217744 0.670146i −0.998947 0.0458699i \(-0.985394\pi\)
0.781204 0.624276i \(-0.214606\pi\)
\(702\) 0 0
\(703\) 15.5649 21.4232i 0.587041 0.807993i
\(704\) 0 0
\(705\) −0.399873 + 1.23068i −0.0150601 + 0.0463502i
\(706\) 0 0
\(707\) −4.59004 + 14.1267i −0.172626 + 0.531289i
\(708\) 0 0
\(709\) −34.9582 + 11.3586i −1.31288 + 0.426581i −0.880044 0.474892i \(-0.842487\pi\)
−0.432837 + 0.901472i \(0.642487\pi\)
\(710\) 0 0
\(711\) 7.83653i 0.293893i
\(712\) 0 0
\(713\) 11.0501 8.02837i 0.413830 0.300665i
\(714\) 0 0
\(715\) 1.75197 + 1.27288i 0.0655200 + 0.0476031i
\(716\) 0 0
\(717\) 9.83029 7.14212i 0.367119 0.266728i
\(718\) 0 0
\(719\) 25.1679 + 34.6406i 0.938602 + 1.29188i 0.956408 + 0.292034i \(0.0943321\pi\)
−0.0178054 + 0.999841i \(0.505668\pi\)
\(720\) 0 0
\(721\) −16.5987 5.39324i −0.618168 0.200855i
\(722\) 0 0
\(723\) 12.0947 3.92981i 0.449807 0.146151i
\(724\) 0 0
\(725\) −12.2706 + 16.8890i −0.455718 + 0.627243i
\(726\) 0 0
\(727\) 16.8507 + 5.47513i 0.624958 + 0.203061i 0.604340 0.796726i \(-0.293437\pi\)
0.0206178 + 0.999787i \(0.493437\pi\)
\(728\) 0 0
\(729\) −29.8361 −1.10504
\(730\) 0 0
\(731\) −24.9960 34.4041i −0.924511 1.27248i
\(732\) 0 0
\(733\) −7.43392 22.8792i −0.274578 0.845064i −0.989331 0.145687i \(-0.953461\pi\)
0.714753 0.699377i \(-0.246539\pi\)
\(734\) 0 0
\(735\) 0.243924i 0.00899728i
\(736\) 0 0
\(737\) −5.53478 −0.203876
\(738\) 0 0
\(739\) 0.0829569 0.00305162 0.00152581 0.999999i \(-0.499514\pi\)
0.00152581 + 0.999999i \(0.499514\pi\)
\(740\) 0 0
\(741\) 27.4080i 1.00686i
\(742\) 0 0
\(743\) −0.164219 0.505413i −0.00602459 0.0185418i 0.947999 0.318273i \(-0.103103\pi\)
−0.954024 + 0.299731i \(0.903103\pi\)
\(744\) 0 0
\(745\) −0.844990 1.16303i −0.0309581 0.0426101i
\(746\) 0 0
\(747\) 6.60390 0.241624
\(748\) 0 0
\(749\) 5.26414 + 1.71042i 0.192348 + 0.0624975i
\(750\) 0 0
\(751\) 14.6520 20.1667i 0.534659 0.735895i −0.453172 0.891423i \(-0.649708\pi\)
0.987832 + 0.155528i \(0.0497078\pi\)
\(752\) 0 0
\(753\) 36.8215 11.9640i 1.34185 0.435994i
\(754\) 0 0
\(755\) −1.50747 0.489807i −0.0548625 0.0178259i
\(756\) 0 0
\(757\) 5.34474 + 7.35640i 0.194258 + 0.267373i 0.895024 0.446018i \(-0.147158\pi\)
−0.700766 + 0.713391i \(0.747158\pi\)
\(758\) 0 0
\(759\) 10.0608 7.30957i 0.365183 0.265321i
\(760\) 0 0
\(761\) −37.8313 27.4860i −1.37138 0.996368i −0.997628 0.0688410i \(-0.978070\pi\)
−0.373756 0.927527i \(-0.621930\pi\)
\(762\) 0 0
\(763\) −2.68406 + 1.95008i −0.0971695 + 0.0705978i
\(764\) 0 0
\(765\) 0.824697i 0.0298170i
\(766\) 0 0
\(767\) −41.3881 + 13.4478i −1.49444 + 0.485573i
\(768\) 0 0
\(769\) −13.6146 + 41.9013i −0.490954 + 1.51100i 0.332215 + 0.943204i \(0.392204\pi\)
−0.823169 + 0.567797i \(0.807796\pi\)
\(770\) 0 0
\(771\) 10.8549 33.4078i 0.390928 1.20315i
\(772\) 0 0
\(773\) −16.5517 + 22.7815i −0.595323 + 0.819392i −0.995270 0.0971460i \(-0.969029\pi\)
0.399947 + 0.916538i \(0.369029\pi\)
\(774\) 0 0
\(775\) −5.37450 16.5410i −0.193058 0.594171i
\(776\) 0 0
\(777\) −10.5032 7.63099i −0.376799 0.273760i
\(778\) 0 0
\(779\) 5.50695 18.5511i 0.197307 0.664663i
\(780\) 0 0
\(781\) −8.84639 6.42728i −0.316549 0.229986i
\(782\) 0 0
\(783\) −7.31284 22.5066i −0.261340 0.804321i
\(784\) 0 0
\(785\) −1.74968 + 2.40823i −0.0624488 + 0.0859534i
\(786\) 0 0
\(787\) −13.1845 + 40.5778i −0.469977 + 1.44644i 0.382636 + 0.923899i \(0.375016\pi\)
−0.852613 + 0.522542i \(0.824984\pi\)
\(788\) 0 0
\(789\) 7.20030 22.1603i 0.256338 0.788926i
\(790\) 0 0
\(791\) 14.3277 4.65535i 0.509434 0.165525i
\(792\) 0 0
\(793\) 70.5648i 2.50583i
\(794\) 0 0
\(795\) 1.69951 1.23476i 0.0602752 0.0437925i
\(796\) 0 0
\(797\) −24.9938 18.1591i −0.885327