Properties

Label 975.2.h.f.649.3
Level $975$
Weight $2$
Character 975.649
Analytic conductor $7.785$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 975.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.78541419707\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 649.3
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 975.649
Dual form 975.2.h.f.649.4

$q$-expansion

\(f(q)\) \(=\) \(q+1.73205 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.73205i q^{6} -3.46410 q^{7} -1.73205 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.73205 q^{2} -1.00000i q^{3} +1.00000 q^{4} -1.73205i q^{6} -3.46410 q^{7} -1.73205 q^{8} -1.00000 q^{9} -3.46410i q^{11} -1.00000i q^{12} +(-3.46410 - 1.00000i) q^{13} -6.00000 q^{14} -5.00000 q^{16} +6.00000i q^{17} -1.73205 q^{18} -3.46410i q^{19} +3.46410i q^{21} -6.00000i q^{22} +1.73205i q^{24} +(-6.00000 - 1.73205i) q^{26} +1.00000i q^{27} -3.46410 q^{28} -6.00000 q^{29} -3.46410i q^{31} -5.19615 q^{32} -3.46410 q^{33} +10.3923i q^{34} -1.00000 q^{36} +6.92820 q^{37} -6.00000i q^{38} +(-1.00000 + 3.46410i) q^{39} -6.92820i q^{41} +6.00000i q^{42} -4.00000i q^{43} -3.46410i q^{44} +3.46410 q^{47} +5.00000i q^{48} +5.00000 q^{49} +6.00000 q^{51} +(-3.46410 - 1.00000i) q^{52} +6.00000i q^{53} +1.73205i q^{54} +6.00000 q^{56} -3.46410 q^{57} -10.3923 q^{58} -10.3923i q^{59} -2.00000 q^{61} -6.00000i q^{62} +3.46410 q^{63} +1.00000 q^{64} -6.00000 q^{66} -10.3923 q^{67} +6.00000i q^{68} +3.46410i q^{71} +1.73205 q^{72} +12.0000 q^{74} -3.46410i q^{76} +12.0000i q^{77} +(-1.73205 + 6.00000i) q^{78} +8.00000 q^{79} +1.00000 q^{81} -12.0000i q^{82} +3.46410 q^{83} +3.46410i q^{84} -6.92820i q^{86} +6.00000i q^{87} +6.00000i q^{88} +6.92820i q^{89} +(12.0000 + 3.46410i) q^{91} -3.46410 q^{93} +6.00000 q^{94} +5.19615i q^{96} -13.8564 q^{97} +8.66025 q^{98} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{4} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{4} - 4 q^{9} - 24 q^{14} - 20 q^{16} - 24 q^{26} - 24 q^{29} - 4 q^{36} - 4 q^{39} + 20 q^{49} + 24 q^{51} + 24 q^{56} - 8 q^{61} + 4 q^{64} - 24 q^{66} + 48 q^{74} + 32 q^{79} + 4 q^{81} + 48 q^{91} + 24 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(326\) \(352\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205 1.22474 0.612372 0.790569i \(-0.290215\pi\)
0.612372 + 0.790569i \(0.290215\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 1.73205i 0.707107i
\(7\) −3.46410 −1.30931 −0.654654 0.755929i \(-0.727186\pi\)
−0.654654 + 0.755929i \(0.727186\pi\)
\(8\) −1.73205 −0.612372
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 3.46410i 1.04447i −0.852803 0.522233i \(-0.825099\pi\)
0.852803 0.522233i \(-0.174901\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −3.46410 1.00000i −0.960769 0.277350i
\(14\) −6.00000 −1.60357
\(15\) 0 0
\(16\) −5.00000 −1.25000
\(17\) 6.00000i 1.45521i 0.685994 + 0.727607i \(0.259367\pi\)
−0.685994 + 0.727607i \(0.740633\pi\)
\(18\) −1.73205 −0.408248
\(19\) 3.46410i 0.794719i −0.917663 0.397360i \(-0.869927\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) 0 0
\(21\) 3.46410i 0.755929i
\(22\) 6.00000i 1.27920i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 1.73205i 0.353553i
\(25\) 0 0
\(26\) −6.00000 1.73205i −1.17670 0.339683i
\(27\) 1.00000i 0.192450i
\(28\) −3.46410 −0.654654
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 3.46410i 0.622171i −0.950382 0.311086i \(-0.899307\pi\)
0.950382 0.311086i \(-0.100693\pi\)
\(32\) −5.19615 −0.918559
\(33\) −3.46410 −0.603023
\(34\) 10.3923i 1.78227i
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 6.92820 1.13899 0.569495 0.821995i \(-0.307139\pi\)
0.569495 + 0.821995i \(0.307139\pi\)
\(38\) 6.00000i 0.973329i
\(39\) −1.00000 + 3.46410i −0.160128 + 0.554700i
\(40\) 0 0
\(41\) 6.92820i 1.08200i −0.841021 0.541002i \(-0.818045\pi\)
0.841021 0.541002i \(-0.181955\pi\)
\(42\) 6.00000i 0.925820i
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 3.46410i 0.522233i
\(45\) 0 0
\(46\) 0 0
\(47\) 3.46410 0.505291 0.252646 0.967559i \(-0.418699\pi\)
0.252646 + 0.967559i \(0.418699\pi\)
\(48\) 5.00000i 0.721688i
\(49\) 5.00000 0.714286
\(50\) 0 0
\(51\) 6.00000 0.840168
\(52\) −3.46410 1.00000i −0.480384 0.138675i
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 1.73205i 0.235702i
\(55\) 0 0
\(56\) 6.00000 0.801784
\(57\) −3.46410 −0.458831
\(58\) −10.3923 −1.36458
\(59\) 10.3923i 1.35296i −0.736460 0.676481i \(-0.763504\pi\)
0.736460 0.676481i \(-0.236496\pi\)
\(60\) 0 0
\(61\) −2.00000 −0.256074 −0.128037 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 6.00000i 0.762001i
\(63\) 3.46410 0.436436
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −6.00000 −0.738549
\(67\) −10.3923 −1.26962 −0.634811 0.772667i \(-0.718922\pi\)
−0.634811 + 0.772667i \(0.718922\pi\)
\(68\) 6.00000i 0.727607i
\(69\) 0 0
\(70\) 0 0
\(71\) 3.46410i 0.411113i 0.978645 + 0.205557i \(0.0659005\pi\)
−0.978645 + 0.205557i \(0.934100\pi\)
\(72\) 1.73205 0.204124
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 12.0000 1.39497
\(75\) 0 0
\(76\) 3.46410i 0.397360i
\(77\) 12.0000i 1.36753i
\(78\) −1.73205 + 6.00000i −0.196116 + 0.679366i
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 12.0000i 1.32518i
\(83\) 3.46410 0.380235 0.190117 0.981761i \(-0.439113\pi\)
0.190117 + 0.981761i \(0.439113\pi\)
\(84\) 3.46410i 0.377964i
\(85\) 0 0
\(86\) 6.92820i 0.747087i
\(87\) 6.00000i 0.643268i
\(88\) 6.00000i 0.639602i
\(89\) 6.92820i 0.734388i 0.930144 + 0.367194i \(0.119682\pi\)
−0.930144 + 0.367194i \(0.880318\pi\)
\(90\) 0 0
\(91\) 12.0000 + 3.46410i 1.25794 + 0.363137i
\(92\) 0 0
\(93\) −3.46410 −0.359211
\(94\) 6.00000 0.618853
\(95\) 0 0
\(96\) 5.19615i 0.530330i
\(97\) −13.8564 −1.40690 −0.703452 0.710742i \(-0.748359\pi\)
−0.703452 + 0.710742i \(0.748359\pi\)
\(98\) 8.66025 0.874818
\(99\) 3.46410i 0.348155i
\(100\) 0 0
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 10.3923 1.02899
\(103\) 8.00000i 0.788263i 0.919054 + 0.394132i \(0.128955\pi\)
−0.919054 + 0.394132i \(0.871045\pi\)
\(104\) 6.00000 + 1.73205i 0.588348 + 0.169842i
\(105\) 0 0
\(106\) 10.3923i 1.00939i
\(107\) 12.0000i 1.16008i −0.814587 0.580042i \(-0.803036\pi\)
0.814587 0.580042i \(-0.196964\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 6.92820i 0.663602i −0.943349 0.331801i \(-0.892344\pi\)
0.943349 0.331801i \(-0.107656\pi\)
\(110\) 0 0
\(111\) 6.92820i 0.657596i
\(112\) 17.3205 1.63663
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) −6.00000 −0.561951
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 3.46410 + 1.00000i 0.320256 + 0.0924500i
\(118\) 18.0000i 1.65703i
\(119\) 20.7846i 1.90532i
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) −3.46410 −0.313625
\(123\) −6.92820 −0.624695
\(124\) 3.46410i 0.311086i
\(125\) 0 0
\(126\) 6.00000 0.534522
\(127\) 8.00000i 0.709885i 0.934888 + 0.354943i \(0.115500\pi\)
−0.934888 + 0.354943i \(0.884500\pi\)
\(128\) 12.1244 1.07165
\(129\) −4.00000 −0.352180
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) −3.46410 −0.301511
\(133\) 12.0000i 1.04053i
\(134\) −18.0000 −1.55496
\(135\) 0 0
\(136\) 10.3923i 0.891133i
\(137\) −20.7846 −1.77575 −0.887875 0.460086i \(-0.847819\pi\)
−0.887875 + 0.460086i \(0.847819\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 3.46410i 0.291730i
\(142\) 6.00000i 0.503509i
\(143\) −3.46410 + 12.0000i −0.289683 + 1.00349i
\(144\) 5.00000 0.416667
\(145\) 0 0
\(146\) 0 0
\(147\) 5.00000i 0.412393i
\(148\) 6.92820 0.569495
\(149\) 13.8564i 1.13516i −0.823318 0.567581i \(-0.807880\pi\)
0.823318 0.567581i \(-0.192120\pi\)
\(150\) 0 0
\(151\) 10.3923i 0.845714i 0.906196 + 0.422857i \(0.138973\pi\)
−0.906196 + 0.422857i \(0.861027\pi\)
\(152\) 6.00000i 0.486664i
\(153\) 6.00000i 0.485071i
\(154\) 20.7846i 1.67487i
\(155\) 0 0
\(156\) −1.00000 + 3.46410i −0.0800641 + 0.277350i
\(157\) 14.0000i 1.11732i −0.829396 0.558661i \(-0.811315\pi\)
0.829396 0.558661i \(-0.188685\pi\)
\(158\) 13.8564 1.10236
\(159\) 6.00000 0.475831
\(160\) 0 0
\(161\) 0 0
\(162\) 1.73205 0.136083
\(163\) −3.46410 −0.271329 −0.135665 0.990755i \(-0.543317\pi\)
−0.135665 + 0.990755i \(0.543317\pi\)
\(164\) 6.92820i 0.541002i
\(165\) 0 0
\(166\) 6.00000 0.465690
\(167\) 17.3205 1.34030 0.670151 0.742225i \(-0.266230\pi\)
0.670151 + 0.742225i \(0.266230\pi\)
\(168\) 6.00000i 0.462910i
\(169\) 11.0000 + 6.92820i 0.846154 + 0.532939i
\(170\) 0 0
\(171\) 3.46410i 0.264906i
\(172\) 4.00000i 0.304997i
\(173\) 18.0000i 1.36851i −0.729241 0.684257i \(-0.760127\pi\)
0.729241 0.684257i \(-0.239873\pi\)
\(174\) 10.3923i 0.787839i
\(175\) 0 0
\(176\) 17.3205i 1.30558i
\(177\) −10.3923 −0.781133
\(178\) 12.0000i 0.899438i
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 20.7846 + 6.00000i 1.54066 + 0.444750i
\(183\) 2.00000i 0.147844i
\(184\) 0 0
\(185\) 0 0
\(186\) −6.00000 −0.439941
\(187\) 20.7846 1.51992
\(188\) 3.46410 0.252646
\(189\) 3.46410i 0.251976i
\(190\) 0 0
\(191\) 24.0000 1.73658 0.868290 0.496058i \(-0.165220\pi\)
0.868290 + 0.496058i \(0.165220\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) −24.0000 −1.72310
\(195\) 0 0
\(196\) 5.00000 0.357143
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 6.00000i 0.426401i
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 0 0
\(201\) 10.3923i 0.733017i
\(202\) 10.3923 0.731200
\(203\) 20.7846 1.45879
\(204\) 6.00000 0.420084
\(205\) 0 0
\(206\) 13.8564i 0.965422i
\(207\) 0 0
\(208\) 17.3205 + 5.00000i 1.20096 + 0.346688i
\(209\) −12.0000 −0.830057
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 3.46410 0.237356
\(214\) 20.7846i 1.42081i
\(215\) 0 0
\(216\) 1.73205i 0.117851i
\(217\) 12.0000i 0.814613i
\(218\) 12.0000i 0.812743i
\(219\) 0 0
\(220\) 0 0
\(221\) 6.00000 20.7846i 0.403604 1.39812i
\(222\) 12.0000i 0.805387i
\(223\) 3.46410 0.231973 0.115987 0.993251i \(-0.462997\pi\)
0.115987 + 0.993251i \(0.462997\pi\)
\(224\) 18.0000 1.20268
\(225\) 0 0
\(226\) 10.3923i 0.691286i
\(227\) −17.3205 −1.14960 −0.574801 0.818293i \(-0.694921\pi\)
−0.574801 + 0.818293i \(0.694921\pi\)
\(228\) −3.46410 −0.229416
\(229\) 6.92820i 0.457829i 0.973447 + 0.228914i \(0.0735176\pi\)
−0.973447 + 0.228914i \(0.926482\pi\)
\(230\) 0 0
\(231\) 12.0000 0.789542
\(232\) 10.3923 0.682288
\(233\) 6.00000i 0.393073i −0.980497 0.196537i \(-0.937031\pi\)
0.980497 0.196537i \(-0.0629694\pi\)
\(234\) 6.00000 + 1.73205i 0.392232 + 0.113228i
\(235\) 0 0
\(236\) 10.3923i 0.676481i
\(237\) 8.00000i 0.519656i
\(238\) 36.0000i 2.33353i
\(239\) 10.3923i 0.672222i 0.941822 + 0.336111i \(0.109112\pi\)
−0.941822 + 0.336111i \(0.890888\pi\)
\(240\) 0 0
\(241\) 13.8564i 0.892570i 0.894891 + 0.446285i \(0.147253\pi\)
−0.894891 + 0.446285i \(0.852747\pi\)
\(242\) −1.73205 −0.111340
\(243\) 1.00000i 0.0641500i
\(244\) −2.00000 −0.128037
\(245\) 0 0
\(246\) −12.0000 −0.765092
\(247\) −3.46410 + 12.0000i −0.220416 + 0.763542i
\(248\) 6.00000i 0.381000i
\(249\) 3.46410i 0.219529i
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 3.46410 0.218218
\(253\) 0 0
\(254\) 13.8564i 0.869428i
\(255\) 0 0
\(256\) 19.0000 1.18750
\(257\) 18.0000i 1.12281i −0.827541 0.561405i \(-0.810261\pi\)
0.827541 0.561405i \(-0.189739\pi\)
\(258\) −6.92820 −0.431331
\(259\) −24.0000 −1.49129
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) −20.7846 −1.28408
\(263\) 24.0000i 1.47990i −0.672660 0.739952i \(-0.734848\pi\)
0.672660 0.739952i \(-0.265152\pi\)
\(264\) 6.00000 0.369274
\(265\) 0 0
\(266\) 20.7846i 1.27439i
\(267\) 6.92820 0.423999
\(268\) −10.3923 −0.634811
\(269\) −6.00000 −0.365826 −0.182913 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 0 0
\(271\) 10.3923i 0.631288i 0.948878 + 0.315644i \(0.102220\pi\)
−0.948878 + 0.315644i \(0.897780\pi\)
\(272\) 30.0000i 1.81902i
\(273\) 3.46410 12.0000i 0.209657 0.726273i
\(274\) −36.0000 −2.17484
\(275\) 0 0
\(276\) 0 0
\(277\) 10.0000i 0.600842i 0.953807 + 0.300421i \(0.0971271\pi\)
−0.953807 + 0.300421i \(0.902873\pi\)
\(278\) 6.92820 0.415526
\(279\) 3.46410i 0.207390i
\(280\) 0 0
\(281\) 6.92820i 0.413302i 0.978415 + 0.206651i \(0.0662565\pi\)
−0.978415 + 0.206651i \(0.933744\pi\)
\(282\) 6.00000i 0.357295i
\(283\) 4.00000i 0.237775i 0.992908 + 0.118888i \(0.0379328\pi\)
−0.992908 + 0.118888i \(0.962067\pi\)
\(284\) 3.46410i 0.205557i
\(285\) 0 0
\(286\) −6.00000 + 20.7846i −0.354787 + 1.22902i
\(287\) 24.0000i 1.41668i
\(288\) 5.19615 0.306186
\(289\) −19.0000 −1.11765
\(290\) 0 0
\(291\) 13.8564i 0.812277i
\(292\) 0 0
\(293\) −27.7128 −1.61900 −0.809500 0.587120i \(-0.800262\pi\)
−0.809500 + 0.587120i \(0.800262\pi\)
\(294\) 8.66025i 0.505076i
\(295\) 0 0
\(296\) −12.0000 −0.697486
\(297\) 3.46410 0.201008
\(298\) 24.0000i 1.39028i
\(299\) 0 0
\(300\) 0 0
\(301\) 13.8564i 0.798670i
\(302\) 18.0000i 1.03578i
\(303\) 6.00000i 0.344691i
\(304\) 17.3205i 0.993399i
\(305\) 0 0
\(306\) 10.3923i 0.594089i
\(307\) −10.3923 −0.593120 −0.296560 0.955014i \(-0.595840\pi\)
−0.296560 + 0.955014i \(0.595840\pi\)
\(308\) 12.0000i 0.683763i
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 1.73205 6.00000i 0.0980581 0.339683i
\(313\) 10.0000i 0.565233i 0.959233 + 0.282617i \(0.0912024\pi\)
−0.959233 + 0.282617i \(0.908798\pi\)
\(314\) 24.2487i 1.36843i
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) 13.8564 0.778253 0.389127 0.921184i \(-0.372777\pi\)
0.389127 + 0.921184i \(0.372777\pi\)
\(318\) 10.3923 0.582772
\(319\) 20.7846i 1.16371i
\(320\) 0 0
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) 20.7846 1.15649
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −6.00000 −0.332309
\(327\) −6.92820 −0.383131
\(328\) 12.0000i 0.662589i
\(329\) −12.0000 −0.661581
\(330\) 0 0
\(331\) 3.46410i 0.190404i 0.995458 + 0.0952021i \(0.0303497\pi\)
−0.995458 + 0.0952021i \(0.969650\pi\)
\(332\) 3.46410 0.190117
\(333\) −6.92820 −0.379663
\(334\) 30.0000 1.64153
\(335\) 0 0
\(336\) 17.3205i 0.944911i
\(337\) 14.0000i 0.762629i 0.924445 + 0.381314i \(0.124528\pi\)
−0.924445 + 0.381314i \(0.875472\pi\)
\(338\) 19.0526 + 12.0000i 1.03632 + 0.652714i
\(339\) −6.00000 −0.325875
\(340\) 0 0
\(341\) −12.0000 −0.649836
\(342\) 6.00000i 0.324443i
\(343\) 6.92820 0.374088
\(344\) 6.92820i 0.373544i
\(345\) 0 0
\(346\) 31.1769i 1.67608i
\(347\) 36.0000i 1.93258i −0.257454 0.966291i \(-0.582883\pi\)
0.257454 0.966291i \(-0.417117\pi\)
\(348\) 6.00000i 0.321634i
\(349\) 6.92820i 0.370858i 0.982658 + 0.185429i \(0.0593675\pi\)
−0.982658 + 0.185429i \(0.940632\pi\)
\(350\) 0 0
\(351\) 1.00000 3.46410i 0.0533761 0.184900i
\(352\) 18.0000i 0.959403i
\(353\) −34.6410 −1.84376 −0.921878 0.387481i \(-0.873345\pi\)
−0.921878 + 0.387481i \(0.873345\pi\)
\(354\) −18.0000 −0.956689
\(355\) 0 0
\(356\) 6.92820i 0.367194i
\(357\) −20.7846 −1.10004
\(358\) 20.7846 1.09850
\(359\) 17.3205i 0.914141i −0.889430 0.457071i \(-0.848899\pi\)
0.889430 0.457071i \(-0.151101\pi\)
\(360\) 0 0
\(361\) 7.00000 0.368421
\(362\) −17.3205 −0.910346
\(363\) 1.00000i 0.0524864i
\(364\) 12.0000 + 3.46410i 0.628971 + 0.181568i
\(365\) 0 0
\(366\) 3.46410i 0.181071i
\(367\) 16.0000i 0.835193i 0.908633 + 0.417597i \(0.137127\pi\)
−0.908633 + 0.417597i \(0.862873\pi\)
\(368\) 0 0
\(369\) 6.92820i 0.360668i
\(370\) 0 0
\(371\) 20.7846i 1.07908i
\(372\) −3.46410 −0.179605
\(373\) 22.0000i 1.13912i 0.821951 + 0.569558i \(0.192886\pi\)
−0.821951 + 0.569558i \(0.807114\pi\)
\(374\) 36.0000 1.86152
\(375\) 0 0
\(376\) −6.00000 −0.309426
\(377\) 20.7846 + 6.00000i 1.07046 + 0.309016i
\(378\) 6.00000i 0.308607i
\(379\) 17.3205i 0.889695i −0.895606 0.444847i \(-0.853258\pi\)
0.895606 0.444847i \(-0.146742\pi\)
\(380\) 0 0
\(381\) 8.00000 0.409852
\(382\) 41.5692 2.12687
\(383\) −3.46410 −0.177007 −0.0885037 0.996076i \(-0.528208\pi\)
−0.0885037 + 0.996076i \(0.528208\pi\)
\(384\) 12.1244i 0.618718i
\(385\) 0 0
\(386\) 0 0
\(387\) 4.00000i 0.203331i
\(388\) −13.8564 −0.703452
\(389\) 18.0000 0.912636 0.456318 0.889817i \(-0.349168\pi\)
0.456318 + 0.889817i \(0.349168\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −8.66025 −0.437409
\(393\) 12.0000i 0.605320i
\(394\) 0 0
\(395\) 0 0
\(396\) 3.46410i 0.174078i
\(397\) −34.6410 −1.73858 −0.869291 0.494300i \(-0.835424\pi\)
−0.869291 + 0.494300i \(0.835424\pi\)
\(398\) −27.7128 −1.38912
\(399\) 12.0000 0.600751
\(400\) 0 0
\(401\) 6.92820i 0.345978i 0.984924 + 0.172989i \(0.0553425\pi\)
−0.984924 + 0.172989i \(0.944657\pi\)
\(402\) 18.0000i 0.897758i
\(403\) −3.46410 + 12.0000i −0.172559 + 0.597763i
\(404\) 6.00000 0.298511
\(405\) 0 0
\(406\) 36.0000 1.78665
\(407\) 24.0000i 1.18964i
\(408\) −10.3923 −0.514496
\(409\) 27.7128i 1.37031i −0.728397 0.685155i \(-0.759734\pi\)
0.728397 0.685155i \(-0.240266\pi\)
\(410\) 0 0
\(411\) 20.7846i 1.02523i
\(412\) 8.00000i 0.394132i
\(413\) 36.0000i 1.77144i
\(414\) 0 0
\(415\) 0 0
\(416\) 18.0000 + 5.19615i 0.882523 + 0.254762i
\(417\) 4.00000i 0.195881i
\(418\) −20.7846 −1.01661
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) 34.6410i 1.68830i −0.536107 0.844150i \(-0.680106\pi\)
0.536107 0.844150i \(-0.319894\pi\)
\(422\) −34.6410 −1.68630
\(423\) −3.46410 −0.168430
\(424\) 10.3923i 0.504695i
\(425\) 0 0
\(426\) 6.00000 0.290701
\(427\) 6.92820 0.335279
\(428\) 12.0000i 0.580042i
\(429\) 12.0000 + 3.46410i 0.579365 + 0.167248i
\(430\) 0 0
\(431\) 24.2487i 1.16802i −0.811747 0.584010i \(-0.801483\pi\)
0.811747 0.584010i \(-0.198517\pi\)
\(432\) 5.00000i 0.240563i
\(433\) 34.0000i 1.63394i 0.576683 + 0.816968i \(0.304347\pi\)
−0.576683 + 0.816968i \(0.695653\pi\)
\(434\) 20.7846i 0.997693i
\(435\) 0 0
\(436\) 6.92820i 0.331801i
\(437\) 0 0
\(438\) 0 0
\(439\) −8.00000 −0.381819 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) 0 0
\(441\) −5.00000 −0.238095
\(442\) 10.3923 36.0000i 0.494312 1.71235i
\(443\) 36.0000i 1.71041i −0.518289 0.855206i \(-0.673431\pi\)
0.518289 0.855206i \(-0.326569\pi\)
\(444\) 6.92820i 0.328798i
\(445\) 0 0
\(446\) 6.00000 0.284108
\(447\) −13.8564 −0.655386
\(448\) −3.46410 −0.163663
\(449\) 6.92820i 0.326962i −0.986546 0.163481i \(-0.947728\pi\)
0.986546 0.163481i \(-0.0522723\pi\)
\(450\) 0 0
\(451\) −24.0000 −1.13012
\(452\) 6.00000i 0.282216i
\(453\) 10.3923 0.488273
\(454\) −30.0000 −1.40797
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) −27.7128 −1.29635 −0.648175 0.761491i \(-0.724468\pi\)
−0.648175 + 0.761491i \(0.724468\pi\)
\(458\) 12.0000i 0.560723i
\(459\) −6.00000 −0.280056
\(460\) 0 0
\(461\) 13.8564i 0.645357i −0.946509 0.322679i \(-0.895417\pi\)
0.946509 0.322679i \(-0.104583\pi\)
\(462\) 20.7846 0.966988
\(463\) 17.3205 0.804952 0.402476 0.915430i \(-0.368150\pi\)
0.402476 + 0.915430i \(0.368150\pi\)
\(464\) 30.0000 1.39272
\(465\) 0 0
\(466\) 10.3923i 0.481414i
\(467\) 12.0000i 0.555294i −0.960683 0.277647i \(-0.910445\pi\)
0.960683 0.277647i \(-0.0895545\pi\)
\(468\) 3.46410 + 1.00000i 0.160128 + 0.0462250i
\(469\) 36.0000 1.66233
\(470\) 0 0
\(471\) −14.0000 −0.645086
\(472\) 18.0000i 0.828517i
\(473\) −13.8564 −0.637118
\(474\) 13.8564i 0.636446i
\(475\) 0 0
\(476\) 20.7846i 0.952661i
\(477\) 6.00000i 0.274721i
\(478\) 18.0000i 0.823301i
\(479\) 10.3923i 0.474837i 0.971408 + 0.237418i \(0.0763012\pi\)
−0.971408 + 0.237418i \(0.923699\pi\)
\(480\) 0 0
\(481\) −24.0000 6.92820i −1.09431 0.315899i
\(482\) 24.0000i 1.09317i
\(483\) 0 0
\(484\) −1.00000 −0.0454545
\(485\) 0 0
\(486\) 1.73205i 0.0785674i
\(487\) 38.1051 1.72671 0.863354 0.504599i \(-0.168360\pi\)
0.863354 + 0.504599i \(0.168360\pi\)
\(488\) 3.46410 0.156813
\(489\) 3.46410i 0.156652i
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) −6.92820 −0.312348
\(493\) 36.0000i 1.62136i
\(494\) −6.00000 + 20.7846i −0.269953 + 0.935144i
\(495\) 0 0
\(496\) 17.3205i 0.777714i
\(497\) 12.0000i 0.538274i
\(498\) 6.00000i 0.268866i
\(499\) 10.3923i 0.465223i 0.972570 + 0.232612i \(0.0747271\pi\)
−0.972570 + 0.232612i \(0.925273\pi\)
\(500\) 0 0
\(501\) 17.3205i 0.773823i
\(502\) −20.7846 −0.927663
\(503\) 24.0000i 1.07011i 0.844818 + 0.535054i \(0.179709\pi\)
−0.844818 + 0.535054i \(0.820291\pi\)
\(504\) −6.00000 −0.267261
\(505\) 0 0
\(506\) 0 0
\(507\) 6.92820 11.0000i 0.307692 0.488527i
\(508\) 8.00000i 0.354943i
\(509\) 41.5692i 1.84252i 0.388943 + 0.921262i \(0.372840\pi\)
−0.388943 + 0.921262i \(0.627160\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 8.66025 0.382733
\(513\) 3.46410 0.152944
\(514\) 31.1769i 1.37515i
\(515\) 0 0
\(516\) −4.00000 −0.176090
\(517\) 12.0000i 0.527759i
\(518\) −41.5692 −1.82645
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 10.3923 0.454859
\(523\) 4.00000i 0.174908i −0.996169 0.0874539i \(-0.972127\pi\)
0.996169 0.0874539i \(-0.0278730\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 41.5692i 1.81250i
\(527\) 20.7846 0.905392
\(528\) 17.3205 0.753778
\(529\) 23.0000 1.00000
\(530\) 0 0
\(531\) 10.3923i 0.450988i
\(532\) 12.0000i 0.520266i
\(533\) −6.92820 + 24.0000i −0.300094 + 1.03956i
\(534\) 12.0000 0.519291
\(535\) 0 0
\(536\) 18.0000 0.777482
\(537\) 12.0000i 0.517838i
\(538\) −10.3923 −0.448044
\(539\) 17.3205i 0.746047i
\(540\) 0 0
\(541\) 6.92820i 0.297867i 0.988847 + 0.148933i \(0.0475840\pi\)
−0.988847 + 0.148933i \(0.952416\pi\)
\(542\) 18.0000i 0.773166i
\(543\) 10.0000i 0.429141i
\(544\) 31.1769i 1.33670i
\(545\) 0 0
\(546\) 6.00000 20.7846i 0.256776 0.889499i
\(547\) 20.0000i 0.855138i −0.903983 0.427569i \(-0.859370\pi\)
0.903983 0.427569i \(-0.140630\pi\)
\(548\) −20.7846 −0.887875
\(549\) 2.00000 0.0853579
\(550\) 0 0
\(551\) 20.7846i 0.885454i
\(552\) 0 0
\(553\) −27.7128 −1.17847
\(554\) 17.3205i 0.735878i
\(555\) 0 0
\(556\) 4.00000 0.169638
\(557\) 13.8564 0.587115 0.293557 0.955941i \(-0.405161\pi\)
0.293557 + 0.955941i \(0.405161\pi\)
\(558\) 6.00000i 0.254000i
\(559\) −4.00000 + 13.8564i −0.169182 + 0.586064i
\(560\) 0 0
\(561\) 20.7846i 0.877527i
\(562\) 12.0000i 0.506189i
\(563\) 12.0000i 0.505740i −0.967500 0.252870i \(-0.918626\pi\)
0.967500 0.252870i \(-0.0813744\pi\)
\(564\) 3.46410i 0.145865i
\(565\) 0 0
\(566\) 6.92820i 0.291214i
\(567\) −3.46410 −0.145479
\(568\) 6.00000i 0.251754i
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) 0 0
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) −3.46410 + 12.0000i −0.144841 + 0.501745i
\(573\) 24.0000i 1.00261i
\(574\) 41.5692i 1.73507i
\(575\) 0 0
\(576\) −1.00000 −0.0416667
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) −32.9090 −1.36883
\(579\) 0 0
\(580\) 0 0
\(581\) −12.0000 −0.497844
\(582\) 24.0000i 0.994832i
\(583\) 20.7846 0.860811
\(584\) 0 0
\(585\) 0 0
\(586\) −48.0000 −1.98286
\(587\) 10.3923 0.428936 0.214468 0.976731i \(-0.431198\pi\)
0.214468 + 0.976731i \(0.431198\pi\)
\(588\) 5.00000i 0.206197i
\(589\) −12.0000 −0.494451
\(590\) 0 0
\(591\) 0 0
\(592\) −34.6410 −1.42374
\(593\) −6.92820 −0.284507 −0.142254 0.989830i \(-0.545435\pi\)
−0.142254 + 0.989830i \(0.545435\pi\)
\(594\) 6.00000 0.246183
\(595\) 0 0
\(596\) 13.8564i 0.567581i
\(597\) 16.0000i 0.654836i
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 24.0000i 0.978167i
\(603\) 10.3923 0.423207
\(604\) 10.3923i 0.422857i
\(605\) 0 0
\(606\) 10.3923i 0.422159i
\(607\) 32.0000i 1.29884i −0.760430 0.649420i \(-0.775012\pi\)
0.760430 0.649420i \(-0.224988\pi\)
\(608\) 18.0000i 0.729996i
\(609\) 20.7846i 0.842235i
\(610\) 0 0
\(611\) −12.0000 3.46410i −0.485468 0.140143i
\(612\) 6.00000i 0.242536i
\(613\) 20.7846 0.839482 0.419741 0.907644i \(-0.362121\pi\)
0.419741 + 0.907644i \(0.362121\pi\)
\(614\) −18.0000 −0.726421
\(615\) 0 0
\(616\) 20.7846i 0.837436i
\(617\) −6.92820 −0.278919 −0.139459 0.990228i \(-0.544536\pi\)
−0.139459 + 0.990228i \(0.544536\pi\)
\(618\) 13.8564 0.557386
\(619\) 31.1769i 1.25311i −0.779379 0.626553i \(-0.784465\pi\)
0.779379 0.626553i \(-0.215535\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 24.0000i 0.961540i
\(624\) 5.00000 17.3205i 0.200160 0.693375i
\(625\) 0 0
\(626\) 17.3205i 0.692267i
\(627\) 12.0000i 0.479234i
\(628\) 14.0000i 0.558661i
\(629\) 41.5692i 1.65747i
\(630\) 0 0
\(631\) 38.1051i 1.51694i 0.651707 + 0.758470i \(0.274053\pi\)
−0.651707 + 0.758470i \(0.725947\pi\)
\(632\) −13.8564 −0.551178
\(633\) 20.0000i 0.794929i
\(634\) 24.0000 0.953162
\(635\) 0 0
\(636\) 6.00000 0.237915
\(637\) −17.3205 5.00000i −0.686264 0.198107i
\(638\) 36.0000i 1.42525i
\(639\) 3.46410i 0.137038i
\(640\) 0 0
\(641\) −6.00000 −0.236986 −0.118493 0.992955i \(-0.537806\pi\)
−0.118493 + 0.992955i \(0.537806\pi\)
\(642\) −20.7846 −0.820303
\(643\) 10.3923 0.409832 0.204916 0.978780i \(-0.434308\pi\)
0.204916 + 0.978780i \(0.434308\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 36.0000 1.41640
\(647\) 24.0000i 0.943537i 0.881722 + 0.471769i \(0.156384\pi\)
−0.881722 + 0.471769i \(0.843616\pi\)
\(648\) −1.73205 −0.0680414
\(649\) −36.0000 −1.41312
\(650\) 0 0
\(651\) 12.0000 0.470317
\(652\) −3.46410 −0.135665
\(653\) 6.00000i 0.234798i 0.993085 + 0.117399i \(0.0374557\pi\)
−0.993085 + 0.117399i \(0.962544\pi\)
\(654\) −12.0000 −0.469237
\(655\) 0 0
\(656\) 34.6410i 1.35250i
\(657\) 0 0
\(658\) −20.7846 −0.810268
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) 20.7846i 0.808428i −0.914665 0.404214i \(-0.867545\pi\)
0.914665 0.404214i \(-0.132455\pi\)
\(662\) 6.00000i 0.233197i
\(663\) −20.7846 6.00000i −0.807207 0.233021i
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) −12.0000 −0.464991
\(667\) 0 0
\(668\) 17.3205 0.670151
\(669\) 3.46410i 0.133930i
\(670\) 0 0
\(671\) 6.92820i 0.267460i
\(672\) 18.0000i 0.694365i
\(673\) 46.0000i 1.77317i −0.462566 0.886585i \(-0.653071\pi\)
0.462566 0.886585i \(-0.346929\pi\)
\(674\) 24.2487i 0.934025i
\(675\) 0 0
\(676\) 11.0000 + 6.92820i 0.423077 + 0.266469i
\(677\) 6.00000i 0.230599i −0.993331 0.115299i \(-0.963217\pi\)
0.993331 0.115299i \(-0.0367827\pi\)
\(678\) −10.3923 −0.399114
\(679\) 48.0000 1.84207
\(680\) 0 0
\(681\) 17.3205i 0.663723i
\(682\) −20.7846 −0.795884
\(683\) 31.1769 1.19295 0.596476 0.802631i \(-0.296567\pi\)
0.596476 + 0.802631i \(0.296567\pi\)
\(684\) 3.46410i 0.132453i
\(685\) 0 0
\(686\) 12.0000 0.458162
\(687\) 6.92820 0.264327
\(688\) 20.0000i 0.762493i
\(689\) 6.00000 20.7846i 0.228582 0.791831i
\(690\) 0 0
\(691\) 45.0333i 1.71315i 0.516024 + 0.856574i \(0.327412\pi\)
−0.516024 + 0.856574i \(0.672588\pi\)
\(692\) 18.0000i 0.684257i
\(693\) 12.0000i 0.455842i
\(694\) 62.3538i 2.36692i
\(695\) 0 0
\(696\) 10.3923i 0.393919i
\(697\) 41.5692 1.57455
\(698\) 12.0000i 0.454207i
\(699\) −6.00000 −0.226941
\(700\) 0 0
\(701\) −42.0000 −1.58632 −0.793159 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) 1.73205 6.00000i 0.0653720 0.226455i
\(703\) 24.0000i 0.905177i
\(704\) 3.46410i 0.130558i
\(705\) 0 0
\(706\) −60.0000 −2.25813
\(707\) −20.7846 −0.781686
\(708\) −10.3923 −0.390567
\(709\) 6.92820i 0.260194i 0.991501 + 0.130097i \(0.0415289\pi\)
−0.991501 + 0.130097i \(0.958471\pi\)
\(710\) 0 0
\(711\) −8.00000 −0.300023
\(712\) 12.0000i 0.449719i
\(713\) 0 0
\(714\) −36.0000 −1.34727
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 10.3923 0.388108
\(718\) 30.0000i 1.11959i
\(719\) −24.0000 −0.895049 −0.447524 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 0 0
\(721\) 27.7128i 1.03208i
\(722\) 12.1244 0.451222
\(723\) 13.8564 0.515325
\(724\) −10.0000 −0.371647
\(725\) 0 0
\(726\) 1.73205i 0.0642824i
\(727\) 16.0000i 0.593407i −0.954970 0.296704i \(-0.904113\pi\)
0.954970 0.296704i \(-0.0958873\pi\)
\(728\) −20.7846 6.00000i −0.770329 0.222375i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 24.0000 0.887672
\(732\) 2.00000i 0.0739221i
\(733\) −34.6410 −1.27950 −0.639748 0.768585i \(-0.720961\pi\)
−0.639748 + 0.768585i \(0.720961\pi\)
\(734\) 27.7128i 1.02290i
\(735\) 0 0
\(736\) 0 0
\(737\) 36.0000i 1.32608i
\(738\) 12.0000i 0.441726i
\(739\) 38.1051i 1.40172i 0.713299 + 0.700860i \(0.247200\pi\)
−0.713299 + 0.700860i \(0.752800\pi\)
\(740\) 0 0
\(741\) 12.0000 + 3.46410i 0.440831 + 0.127257i
\(742\) 36.0000i 1.32160i
\(743\) −3.46410 −0.127086 −0.0635428 0.997979i \(-0.520240\pi\)
−0.0635428 + 0.997979i \(0.520240\pi\)
\(744\) 6.00000 0.219971
\(745\) 0 0
\(746\) 38.1051i 1.39513i
\(747\) −3.46410 −0.126745
\(748\) 20.7846 0.759961
\(749\) 41.5692i 1.51891i
\(750\) 0 0
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) −17.3205 −0.631614
\(753\) 12.0000i 0.437304i
\(754\) 36.0000 + 10.3923i 1.31104 + 0.378465i
\(755\) 0 0
\(756\) 3.46410i 0.125988i
\(757\) 22.0000i 0.799604i −0.916602 0.399802i \(-0.869079\pi\)
0.916602 0.399802i \(-0.130921\pi\)
\(758\) 30.0000i 1.08965i
\(759\) 0 0
\(760\) 0 0
\(761\) 48.4974i 1.75803i −0.476794 0.879015i \(-0.658201\pi\)
0.476794 0.879015i \(-0.341799\pi\)
\(762\) 13.8564 0.501965
\(763\) 24.0000i 0.868858i
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) −6.00000 −0.216789
\(767\) −10.3923 + 36.0000i −0.375244 + 1.29988i
\(768\) 19.0000i 0.685603i
\(769\) 27.7128i 0.999350i −0.866213 0.499675i \(-0.833453\pi\)
0.866213 0.499675i \(-0.166547\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) 0 0
\(773\) 13.8564 0.498380 0.249190 0.968455i \(-0.419836\pi\)
0.249190 + 0.968455i \(0.419836\pi\)
\(774\) 6.92820i 0.249029i
\(775\) 0 0
\(776\) 24.0000 0.861550
\(777\) 24.0000i 0.860995i
\(778\) 31.1769 1.11775
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) 12.0000 0.429394
\(782\) 0 0
\(783\) 6.00000i 0.214423i
\(784\) −25.0000 −0.892857
\(785\) 0 0
\(786\) 20.7846i 0.741362i
\(787\) −10.3923 −0.370446 −0.185223 0.982697i \(-0.559301\pi\)
−0.185223 + 0.982697i \(0.559301\pi\)
\(788\) 0 0
\(789\) −24.0000 −0.854423
\(790\) 0 0
\(791\) 20.7846i 0.739016i
\(792\) 6.00000i 0.213201i
\(793\) 6.92820 + 2.00000i 0.246028 + 0.0710221i
\(794\) −60.0000 −2.12932
\(795\) 0 0