Properties

Label 1110.2.h.f.961.6
Level $1110$
Weight $2$
Character 1110.961
Analytic conductor $8.863$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.279290944.1
Defining polynomial: \(x^{6} + 26 x^{4} + 169 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{37}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 961.6
Root \(-3.75054i\) of defining polynomial
Character \(\chi\) \(=\) 1110.961
Dual form 1110.2.h.f.961.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{5} +1.00000i q^{6} +2.75054 q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{5} +1.00000i q^{6} +2.75054 q^{7} -1.00000i q^{8} +1.00000 q^{9} -1.00000 q^{10} +4.75054 q^{11} -1.00000 q^{12} -6.75054i q^{13} +2.75054i q^{14} +1.00000i q^{15} +1.00000 q^{16} -7.06651i q^{17} +1.00000i q^{18} +6.75054i q^{19} -1.00000i q^{20} +2.75054 q^{21} +4.75054i q^{22} -5.06651i q^{23} -1.00000i q^{24} -1.00000 q^{25} +6.75054 q^{26} +1.00000 q^{27} -2.75054 q^{28} -2.00000i q^{29} -1.00000 q^{30} -0.315979i q^{31} +1.00000i q^{32} +4.75054 q^{33} +7.06651 q^{34} +2.75054i q^{35} -1.00000 q^{36} +(-4.90852 + 3.59255i) q^{37} -6.75054 q^{38} -6.75054i q^{39} +1.00000 q^{40} -2.00000 q^{41} +2.75054i q^{42} +9.81705i q^{43} -4.75054 q^{44} +1.00000i q^{45} +5.06651 q^{46} +3.50107 q^{47} +1.00000 q^{48} +0.565444 q^{49} -1.00000i q^{50} -7.06651i q^{51} +6.75054i q^{52} +4.75054 q^{53} +1.00000i q^{54} +4.75054i q^{55} -2.75054i q^{56} +6.75054i q^{57} +2.00000 q^{58} +11.8170i q^{59} -1.00000i q^{60} -2.00000i q^{61} +0.315979 q^{62} +2.75054 q^{63} -1.00000 q^{64} +6.75054 q^{65} +4.75054i q^{66} +15.0021 q^{67} +7.06651i q^{68} -5.06651i q^{69} -2.75054 q^{70} -14.1330 q^{71} -1.00000i q^{72} -6.43456 q^{73} +(-3.59255 - 4.90852i) q^{74} -1.00000 q^{75} -6.75054i q^{76} +13.0665 q^{77} +6.75054 q^{78} +8.31598i q^{79} +1.00000i q^{80} +1.00000 q^{81} -2.00000i q^{82} +4.43456 q^{83} -2.75054 q^{84} +7.06651 q^{85} -9.81705 q^{86} -2.00000i q^{87} -4.75054i q^{88} -6.25161i q^{89} -1.00000 q^{90} -18.5676i q^{91} +5.06651i q^{92} -0.315979i q^{93} +3.50107i q^{94} -6.75054 q^{95} +1.00000i q^{96} +11.5011i q^{97} +0.565444i q^{98} +4.75054 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{3} - 6q^{4} - 6q^{7} + 6q^{9} + O(q^{10}) \) \( 6q + 6q^{3} - 6q^{4} - 6q^{7} + 6q^{9} - 6q^{10} + 6q^{11} - 6q^{12} + 6q^{16} - 6q^{21} - 6q^{25} + 18q^{26} + 6q^{27} + 6q^{28} - 6q^{30} + 6q^{33} + 10q^{34} - 6q^{36} - 2q^{37} - 18q^{38} + 6q^{40} - 12q^{41} - 6q^{44} - 2q^{46} - 24q^{47} + 6q^{48} + 16q^{49} + 6q^{53} + 12q^{58} - 8q^{62} - 6q^{63} - 6q^{64} + 18q^{65} + 6q^{70} - 20q^{71} - 26q^{73} - 4q^{74} - 6q^{75} + 46q^{77} + 18q^{78} + 6q^{81} + 14q^{83} + 6q^{84} + 10q^{85} - 4q^{86} - 6q^{90} - 18q^{95} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000 0.577350
\(4\) −1.00000 −0.500000
\(5\) 1.00000i 0.447214i
\(6\) 1.00000i 0.408248i
\(7\) 2.75054 1.03960 0.519802 0.854287i \(-0.326006\pi\)
0.519802 + 0.854287i \(0.326006\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 4.75054 1.43234 0.716170 0.697926i \(-0.245893\pi\)
0.716170 + 0.697926i \(0.245893\pi\)
\(12\) −1.00000 −0.288675
\(13\) 6.75054i 1.87226i −0.351652 0.936131i \(-0.614380\pi\)
0.351652 0.936131i \(-0.385620\pi\)
\(14\) 2.75054i 0.735111i
\(15\) 1.00000i 0.258199i
\(16\) 1.00000 0.250000
\(17\) 7.06651i 1.71388i −0.515415 0.856941i \(-0.672362\pi\)
0.515415 0.856941i \(-0.327638\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 6.75054i 1.54868i 0.632770 + 0.774339i \(0.281918\pi\)
−0.632770 + 0.774339i \(0.718082\pi\)
\(20\) 1.00000i 0.223607i
\(21\) 2.75054 0.600216
\(22\) 4.75054i 1.01282i
\(23\) 5.06651i 1.05644i −0.849107 0.528221i \(-0.822859\pi\)
0.849107 0.528221i \(-0.177141\pi\)
\(24\) 1.00000i 0.204124i
\(25\) −1.00000 −0.200000
\(26\) 6.75054 1.32389
\(27\) 1.00000 0.192450
\(28\) −2.75054 −0.519802
\(29\) 2.00000i 0.371391i −0.982607 0.185695i \(-0.940546\pi\)
0.982607 0.185695i \(-0.0594537\pi\)
\(30\) −1.00000 −0.182574
\(31\) 0.315979i 0.0567515i −0.999597 0.0283758i \(-0.990966\pi\)
0.999597 0.0283758i \(-0.00903350\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 4.75054 0.826962
\(34\) 7.06651 1.21190
\(35\) 2.75054i 0.464925i
\(36\) −1.00000 −0.166667
\(37\) −4.90852 + 3.59255i −0.806957 + 0.590611i
\(38\) −6.75054 −1.09508
\(39\) 6.75054i 1.08095i
\(40\) 1.00000 0.158114
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 2.75054i 0.424417i
\(43\) 9.81705i 1.49709i 0.663086 + 0.748543i \(0.269246\pi\)
−0.663086 + 0.748543i \(0.730754\pi\)
\(44\) −4.75054 −0.716170
\(45\) 1.00000i 0.149071i
\(46\) 5.06651 0.747017
\(47\) 3.50107 0.510684 0.255342 0.966851i \(-0.417812\pi\)
0.255342 + 0.966851i \(0.417812\pi\)
\(48\) 1.00000 0.144338
\(49\) 0.565444 0.0807777
\(50\) 1.00000i 0.141421i
\(51\) 7.06651i 0.989510i
\(52\) 6.75054i 0.936131i
\(53\) 4.75054 0.652536 0.326268 0.945277i \(-0.394209\pi\)
0.326268 + 0.945277i \(0.394209\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 4.75054i 0.640562i
\(56\) 2.75054i 0.367556i
\(57\) 6.75054i 0.894130i
\(58\) 2.00000 0.262613
\(59\) 11.8170i 1.53845i 0.638979 + 0.769224i \(0.279357\pi\)
−0.638979 + 0.769224i \(0.720643\pi\)
\(60\) 1.00000i 0.129099i
\(61\) 2.00000i 0.256074i −0.991769 0.128037i \(-0.959132\pi\)
0.991769 0.128037i \(-0.0408676\pi\)
\(62\) 0.315979 0.0401294
\(63\) 2.75054 0.346535
\(64\) −1.00000 −0.125000
\(65\) 6.75054 0.837301
\(66\) 4.75054i 0.584750i
\(67\) 15.0021 1.83280 0.916402 0.400260i \(-0.131080\pi\)
0.916402 + 0.400260i \(0.131080\pi\)
\(68\) 7.06651i 0.856941i
\(69\) 5.06651i 0.609937i
\(70\) −2.75054 −0.328752
\(71\) −14.1330 −1.67728 −0.838641 0.544685i \(-0.816649\pi\)
−0.838641 + 0.544685i \(0.816649\pi\)
\(72\) 1.00000i 0.117851i
\(73\) −6.43456 −0.753108 −0.376554 0.926395i \(-0.622891\pi\)
−0.376554 + 0.926395i \(0.622891\pi\)
\(74\) −3.59255 4.90852i −0.417625 0.570604i
\(75\) −1.00000 −0.115470
\(76\) 6.75054i 0.774339i
\(77\) 13.0665 1.48907
\(78\) 6.75054 0.764348
\(79\) 8.31598i 0.935621i 0.883829 + 0.467810i \(0.154957\pi\)
−0.883829 + 0.467810i \(0.845043\pi\)
\(80\) 1.00000i 0.111803i
\(81\) 1.00000 0.111111
\(82\) 2.00000i 0.220863i
\(83\) 4.43456 0.486756 0.243378 0.969932i \(-0.421744\pi\)
0.243378 + 0.969932i \(0.421744\pi\)
\(84\) −2.75054 −0.300108
\(85\) 7.06651 0.766471
\(86\) −9.81705 −1.05860
\(87\) 2.00000i 0.214423i
\(88\) 4.75054i 0.506409i
\(89\) 6.25161i 0.662669i −0.943513 0.331334i \(-0.892501\pi\)
0.943513 0.331334i \(-0.107499\pi\)
\(90\) −1.00000 −0.105409
\(91\) 18.5676i 1.94641i
\(92\) 5.06651i 0.528221i
\(93\) 0.315979i 0.0327655i
\(94\) 3.50107i 0.361108i
\(95\) −6.75054 −0.692590
\(96\) 1.00000i 0.102062i
\(97\) 11.5011i 1.16776i 0.811841 + 0.583878i \(0.198466\pi\)
−0.811841 + 0.583878i \(0.801534\pi\)
\(98\) 0.565444i 0.0571185i
\(99\) 4.75054 0.477447
\(100\) 1.00000 0.100000
\(101\) 7.18509 0.714943 0.357472 0.933924i \(-0.383639\pi\)
0.357472 + 0.933924i \(0.383639\pi\)
\(102\) 7.06651 0.699689
\(103\) 0.631958i 0.0622687i −0.999515 0.0311344i \(-0.990088\pi\)
0.999515 0.0311344i \(-0.00991198\pi\)
\(104\) −6.75054 −0.661944
\(105\) 2.75054i 0.268425i
\(106\) 4.75054i 0.461413i
\(107\) −12.0687 −1.16672 −0.583360 0.812213i \(-0.698262\pi\)
−0.583360 + 0.812213i \(0.698262\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 4.56758i 0.437495i 0.975781 + 0.218748i \(0.0701971\pi\)
−0.975781 + 0.218748i \(0.929803\pi\)
\(110\) −4.75054 −0.452946
\(111\) −4.90852 + 3.59255i −0.465897 + 0.340989i
\(112\) 2.75054 0.259901
\(113\) 2.00000i 0.188144i 0.995565 + 0.0940721i \(0.0299884\pi\)
−0.995565 + 0.0940721i \(0.970012\pi\)
\(114\) −6.75054 −0.632246
\(115\) 5.06651 0.472455
\(116\) 2.00000i 0.185695i
\(117\) 6.75054i 0.624087i
\(118\) −11.8170 −1.08785
\(119\) 19.4367i 1.78176i
\(120\) 1.00000 0.0912871
\(121\) 11.5676 1.05160
\(122\) 2.00000 0.181071
\(123\) −2.00000 −0.180334
\(124\) 0.315979i 0.0283758i
\(125\) 1.00000i 0.0894427i
\(126\) 2.75054i 0.245037i
\(127\) −14.7505 −1.30890 −0.654449 0.756106i \(-0.727099\pi\)
−0.654449 + 0.756106i \(0.727099\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 9.81705i 0.864343i
\(130\) 6.75054i 0.592061i
\(131\) 7.18509i 0.627764i −0.949462 0.313882i \(-0.898370\pi\)
0.949462 0.313882i \(-0.101630\pi\)
\(132\) −4.75054 −0.413481
\(133\) 18.5676i 1.61001i
\(134\) 15.0021i 1.29599i
\(135\) 1.00000i 0.0860663i
\(136\) −7.06651 −0.605949
\(137\) −1.68402 −0.143876 −0.0719378 0.997409i \(-0.522918\pi\)
−0.0719378 + 0.997409i \(0.522918\pi\)
\(138\) 5.06651 0.431290
\(139\) −23.0021 −1.95102 −0.975508 0.219964i \(-0.929406\pi\)
−0.975508 + 0.219964i \(0.929406\pi\)
\(140\) 2.75054i 0.232463i
\(141\) 3.50107 0.294843
\(142\) 14.1330i 1.18602i
\(143\) 32.0687i 2.68172i
\(144\) 1.00000 0.0833333
\(145\) 2.00000 0.166091
\(146\) 6.43456i 0.532528i
\(147\) 0.565444 0.0466370
\(148\) 4.90852 3.59255i 0.403478 0.295305i
\(149\) −7.81705 −0.640398 −0.320199 0.947350i \(-0.603750\pi\)
−0.320199 + 0.947350i \(0.603750\pi\)
\(150\) 1.00000i 0.0816497i
\(151\) 16.4346 1.33743 0.668713 0.743521i \(-0.266846\pi\)
0.668713 + 0.743521i \(0.266846\pi\)
\(152\) 6.75054 0.547541
\(153\) 7.06651i 0.571294i
\(154\) 13.0665i 1.05293i
\(155\) 0.315979 0.0253801
\(156\) 6.75054i 0.540475i
\(157\) −5.81705 −0.464251 −0.232126 0.972686i \(-0.574568\pi\)
−0.232126 + 0.972686i \(0.574568\pi\)
\(158\) −8.31598 −0.661584
\(159\) 4.75054 0.376742
\(160\) −1.00000 −0.0790569
\(161\) 13.9356i 1.09828i
\(162\) 1.00000i 0.0785674i
\(163\) 18.2516i 1.42958i 0.699341 + 0.714788i \(0.253477\pi\)
−0.699341 + 0.714788i \(0.746523\pi\)
\(164\) 2.00000 0.156174
\(165\) 4.75054i 0.369829i
\(166\) 4.43456i 0.344188i
\(167\) 5.06651i 0.392059i 0.980598 + 0.196029i \(0.0628048\pi\)
−0.980598 + 0.196029i \(0.937195\pi\)
\(168\) 2.75054i 0.212208i
\(169\) −32.5697 −2.50536
\(170\) 7.06651i 0.541977i
\(171\) 6.75054i 0.516226i
\(172\) 9.81705i 0.748543i
\(173\) 4.11858 0.313130 0.156565 0.987668i \(-0.449958\pi\)
0.156565 + 0.987668i \(0.449958\pi\)
\(174\) 2.00000 0.151620
\(175\) −2.75054 −0.207921
\(176\) 4.75054 0.358085
\(177\) 11.8170i 0.888224i
\(178\) 6.25161 0.468578
\(179\) 9.68402i 0.723818i −0.932213 0.361909i \(-0.882125\pi\)
0.932213 0.361909i \(-0.117875\pi\)
\(180\) 1.00000i 0.0745356i
\(181\) 10.6320 0.790267 0.395134 0.918624i \(-0.370698\pi\)
0.395134 + 0.918624i \(0.370698\pi\)
\(182\) 18.5676 1.37632
\(183\) 2.00000i 0.147844i
\(184\) −5.06651 −0.373508
\(185\) −3.59255 4.90852i −0.264129 0.360882i
\(186\) 0.315979 0.0231687
\(187\) 33.5697i 2.45486i
\(188\) −3.50107 −0.255342
\(189\) 2.75054 0.200072
\(190\) 6.75054i 0.489735i
\(191\) 6.93349i 0.501689i 0.968027 + 0.250845i \(0.0807084\pi\)
−0.968027 + 0.250845i \(0.919292\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 0.498930i 0.0359137i −0.999839 0.0179569i \(-0.994284\pi\)
0.999839 0.0179569i \(-0.00571616\pi\)
\(194\) −11.5011 −0.825729
\(195\) 6.75054 0.483416
\(196\) −0.565444 −0.0403889
\(197\) −16.7505 −1.19343 −0.596713 0.802455i \(-0.703527\pi\)
−0.596713 + 0.802455i \(0.703527\pi\)
\(198\) 4.75054i 0.337606i
\(199\) 3.31812i 0.235215i 0.993060 + 0.117608i \(0.0375225\pi\)
−0.993060 + 0.117608i \(0.962477\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 15.0021 1.05817
\(202\) 7.18509i 0.505541i
\(203\) 5.50107i 0.386099i
\(204\) 7.06651i 0.494755i
\(205\) 2.00000i 0.139686i
\(206\) 0.631958 0.0440306
\(207\) 5.06651i 0.352147i
\(208\) 6.75054i 0.468065i
\(209\) 32.0687i 2.21824i
\(210\) −2.75054 −0.189805
\(211\) −13.5011 −0.929452 −0.464726 0.885455i \(-0.653847\pi\)
−0.464726 + 0.885455i \(0.653847\pi\)
\(212\) −4.75054 −0.326268
\(213\) −14.1330 −0.968379
\(214\) 12.0687i 0.824996i
\(215\) −9.81705 −0.669517
\(216\) 1.00000i 0.0680414i
\(217\) 0.869112i 0.0589992i
\(218\) −4.56758 −0.309356
\(219\) −6.43456 −0.434807
\(220\) 4.75054i 0.320281i
\(221\) −47.7028 −3.20883
\(222\) −3.59255 4.90852i −0.241116 0.329439i
\(223\) 25.3181 1.69543 0.847713 0.530455i \(-0.177979\pi\)
0.847713 + 0.530455i \(0.177979\pi\)
\(224\) 2.75054i 0.183778i
\(225\) −1.00000 −0.0666667
\(226\) −2.00000 −0.133038
\(227\) 4.63196i 0.307434i −0.988115 0.153717i \(-0.950876\pi\)
0.988115 0.153717i \(-0.0491244\pi\)
\(228\) 6.75054i 0.447065i
\(229\) 20.1330 1.33043 0.665214 0.746653i \(-0.268340\pi\)
0.665214 + 0.746653i \(0.268340\pi\)
\(230\) 5.06651i 0.334076i
\(231\) 13.0665 0.859714
\(232\) −2.00000 −0.131306
\(233\) −6.31598 −0.413774 −0.206887 0.978365i \(-0.566333\pi\)
−0.206887 + 0.978365i \(0.566333\pi\)
\(234\) 6.75054 0.441296
\(235\) 3.50107i 0.228385i
\(236\) 11.8170i 0.769224i
\(237\) 8.31598i 0.540181i
\(238\) 19.4367 1.25989
\(239\) 12.6320i 0.817093i 0.912737 + 0.408547i \(0.133964\pi\)
−0.912737 + 0.408547i \(0.866036\pi\)
\(240\) 1.00000i 0.0645497i
\(241\) 16.6320i 1.07136i 0.844422 + 0.535679i \(0.179944\pi\)
−0.844422 + 0.535679i \(0.820056\pi\)
\(242\) 11.5676i 0.743593i
\(243\) 1.00000 0.0641500
\(244\) 2.00000i 0.128037i
\(245\) 0.565444i 0.0361249i
\(246\) 2.00000i 0.127515i
\(247\) 45.5697 2.89953
\(248\) −0.315979 −0.0200647
\(249\) 4.43456 0.281029
\(250\) 1.00000 0.0632456
\(251\) 1.68402i 0.106294i −0.998587 0.0531472i \(-0.983075\pi\)
0.998587 0.0531472i \(-0.0169253\pi\)
\(252\) −2.75054 −0.173267
\(253\) 24.0687i 1.51318i
\(254\) 14.7505i 0.925531i
\(255\) 7.06651 0.442522
\(256\) 1.00000 0.0625000
\(257\) 3.43242i 0.214108i −0.994253 0.107054i \(-0.965858\pi\)
0.994253 0.107054i \(-0.0341418\pi\)
\(258\) −9.81705 −0.611183
\(259\) −13.5011 + 9.88142i −0.838916 + 0.614002i
\(260\) −6.75054 −0.418650
\(261\) 2.00000i 0.123797i
\(262\) 7.18509 0.443896
\(263\) 6.86911 0.423568 0.211784 0.977317i \(-0.432073\pi\)
0.211784 + 0.977317i \(0.432073\pi\)
\(264\) 4.75054i 0.292375i
\(265\) 4.75054i 0.291823i
\(266\) −18.5676 −1.13845
\(267\) 6.25161i 0.382592i
\(268\) −15.0021 −0.916402
\(269\) −9.24946 −0.563950 −0.281975 0.959422i \(-0.590989\pi\)
−0.281975 + 0.959422i \(0.590989\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 14.3702 0.872926 0.436463 0.899722i \(-0.356231\pi\)
0.436463 + 0.899722i \(0.356231\pi\)
\(272\) 7.06651i 0.428470i
\(273\) 18.5676i 1.12376i
\(274\) 1.68402i 0.101735i
\(275\) −4.75054 −0.286468
\(276\) 5.06651i 0.304968i
\(277\) 26.3846i 1.58530i −0.609678 0.792650i \(-0.708701\pi\)
0.609678 0.792650i \(-0.291299\pi\)
\(278\) 23.0021i 1.37958i
\(279\) 0.315979i 0.0189172i
\(280\) 2.75054 0.164376
\(281\) 15.7527i 0.939726i −0.882739 0.469863i \(-0.844303\pi\)
0.882739 0.469863i \(-0.155697\pi\)
\(282\) 3.50107i 0.208486i
\(283\) 12.3846i 0.736190i −0.929788 0.368095i \(-0.880010\pi\)
0.929788 0.368095i \(-0.119990\pi\)
\(284\) 14.1330 0.838641
\(285\) −6.75054 −0.399867
\(286\) 32.0687 1.89626
\(287\) −5.50107 −0.324718
\(288\) 1.00000i 0.0589256i
\(289\) −32.9356 −1.93739
\(290\) 2.00000i 0.117444i
\(291\) 11.5011i 0.674205i
\(292\) 6.43456 0.376554
\(293\) 0.750535 0.0438467 0.0219234 0.999760i \(-0.493021\pi\)
0.0219234 + 0.999760i \(0.493021\pi\)
\(294\) 0.565444i 0.0329774i
\(295\) −11.8170 −0.688015
\(296\) 3.59255 + 4.90852i 0.208812 + 0.285302i
\(297\) 4.75054 0.275654
\(298\) 7.81705i 0.452830i
\(299\) −34.2017 −1.97793
\(300\) 1.00000 0.0577350
\(301\) 27.0021i 1.55638i
\(302\) 16.4346i 0.945702i
\(303\) 7.18509 0.412773
\(304\) 6.75054i 0.387170i
\(305\) 2.00000 0.114520
\(306\) 7.06651 0.403966
\(307\) 18.3702 1.04844 0.524221 0.851582i \(-0.324357\pi\)
0.524221 + 0.851582i \(0.324357\pi\)
\(308\) −13.0665 −0.744534
\(309\) 0.631958i 0.0359509i
\(310\) 0.315979i 0.0179464i
\(311\) 35.0021i 1.98479i −0.123097 0.992395i \(-0.539283\pi\)
0.123097 0.992395i \(-0.460717\pi\)
\(312\) −6.75054 −0.382174
\(313\) 1.36804i 0.0773263i −0.999252 0.0386631i \(-0.987690\pi\)
0.999252 0.0386631i \(-0.0123099\pi\)
\(314\) 5.81705i 0.328275i
\(315\) 2.75054i 0.154975i
\(316\) 8.31598i 0.467810i
\(317\) 10.0542 0.564700 0.282350 0.959311i \(-0.408886\pi\)
0.282350 + 0.959311i \(0.408886\pi\)
\(318\) 4.75054i 0.266397i
\(319\) 9.50107i 0.531958i
\(320\) 1.00000i 0.0559017i
\(321\) −12.0687 −0.673607
\(322\) 13.9356 0.776602
\(323\) 47.7028 2.65425
\(324\) −1.00000 −0.0555556
\(325\) 6.75054i 0.374452i
\(326\) −18.2516 −1.01086
\(327\) 4.56758i 0.252588i
\(328\) 2.00000i 0.110432i
\(329\) 9.62982 0.530909
\(330\) −4.75054 −0.261508
\(331\) 26.3160i 1.44646i −0.690609 0.723229i \(-0.742657\pi\)
0.690609 0.723229i \(-0.257343\pi\)
\(332\) −4.43456 −0.243378
\(333\) −4.90852 + 3.59255i −0.268986 + 0.196870i
\(334\) −5.06651 −0.277227
\(335\) 15.0021i 0.819655i
\(336\) 2.75054 0.150054
\(337\) −26.7006 −1.45448 −0.727238 0.686386i \(-0.759196\pi\)
−0.727238 + 0.686386i \(0.759196\pi\)
\(338\) 32.5697i 1.77156i
\(339\) 2.00000i 0.108625i
\(340\) −7.06651 −0.383236
\(341\) 1.50107i 0.0812875i
\(342\) −6.75054 −0.365027
\(343\) −17.6985 −0.955628
\(344\) 9.81705 0.529300
\(345\) 5.06651 0.272772
\(346\) 4.11858i 0.221416i
\(347\) 13.5011i 0.724775i 0.932027 + 0.362388i \(0.118038\pi\)
−0.932027 + 0.362388i \(0.881962\pi\)
\(348\) 2.00000i 0.107211i
\(349\) −9.36804 −0.501460 −0.250730 0.968057i \(-0.580671\pi\)
−0.250730 + 0.968057i \(0.580671\pi\)
\(350\) 2.75054i 0.147022i
\(351\) 6.75054i 0.360317i
\(352\) 4.75054i 0.253204i
\(353\) 13.6341i 0.725670i −0.931853 0.362835i \(-0.881809\pi\)
0.931853 0.362835i \(-0.118191\pi\)
\(354\) −11.8170 −0.628069
\(355\) 14.1330i 0.750103i
\(356\) 6.25161i 0.331334i
\(357\) 19.4367i 1.02870i
\(358\) 9.68402 0.511816
\(359\) 8.86911 0.468094 0.234047 0.972225i \(-0.424803\pi\)
0.234047 + 0.972225i \(0.424803\pi\)
\(360\) 1.00000 0.0527046
\(361\) −26.5697 −1.39841
\(362\) 10.6320i 0.558803i
\(363\) 11.5676 0.607141
\(364\) 18.5676i 0.973206i
\(365\) 6.43456i 0.336800i
\(366\) 2.00000 0.104542
\(367\) 2.11858 0.110589 0.0552944 0.998470i \(-0.482390\pi\)
0.0552944 + 0.998470i \(0.482390\pi\)
\(368\) 5.06651i 0.264110i
\(369\) −2.00000 −0.104116
\(370\) 4.90852 3.59255i 0.255182 0.186768i
\(371\) 13.0665 0.678380
\(372\) 0.315979i 0.0163828i
\(373\) 23.0810 1.19509 0.597544 0.801836i \(-0.296143\pi\)
0.597544 + 0.801836i \(0.296143\pi\)
\(374\) 33.5697 1.73585
\(375\) 1.00000i 0.0516398i
\(376\) 3.50107i 0.180554i
\(377\) −13.5011 −0.695341
\(378\) 2.75054i 0.141472i
\(379\) −8.50321 −0.436781 −0.218390 0.975862i \(-0.570081\pi\)
−0.218390 + 0.975862i \(0.570081\pi\)
\(380\) 6.75054 0.346295
\(381\) −14.7505 −0.755693
\(382\) −6.93349 −0.354748
\(383\) 15.1995i 0.776660i −0.921520 0.388330i \(-0.873052\pi\)
0.921520 0.388330i \(-0.126948\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 13.0665i 0.665931i
\(386\) 0.498930 0.0253948
\(387\) 9.81705i 0.499029i
\(388\) 11.5011i 0.583878i
\(389\) 32.1330i 1.62921i −0.580017 0.814605i \(-0.696954\pi\)
0.580017 0.814605i \(-0.303046\pi\)
\(390\) 6.75054i 0.341827i
\(391\) −35.8026 −1.81062
\(392\) 0.565444i 0.0285592i
\(393\) 7.18509i 0.362440i
\(394\) 16.7505i 0.843880i
\(395\) −8.31598 −0.418422
\(396\) −4.75054 −0.238723
\(397\) −28.8192 −1.44639 −0.723197 0.690642i \(-0.757328\pi\)
−0.723197 + 0.690642i \(0.757328\pi\)
\(398\) −3.31812 −0.166322
\(399\) 18.5676i 0.929542i
\(400\) −1.00000 −0.0500000
\(401\) 10.6175i 0.530213i −0.964219 0.265106i \(-0.914593\pi\)
0.964219 0.265106i \(-0.0854071\pi\)
\(402\) 15.0021i 0.748239i
\(403\) −2.13303 −0.106254
\(404\) −7.18509 −0.357472
\(405\) 1.00000i 0.0496904i
\(406\) 5.50107 0.273014
\(407\) −23.3181 + 17.0665i −1.15584 + 0.845956i
\(408\) −7.06651 −0.349845
\(409\) 37.6384i 1.86110i 0.366167 + 0.930549i \(0.380670\pi\)
−0.366167 + 0.930549i \(0.619330\pi\)
\(410\) 2.00000 0.0987730
\(411\) −1.68402 −0.0830666
\(412\) 0.631958i 0.0311344i
\(413\) 32.5032i 1.59938i
\(414\) 5.06651 0.249006
\(415\) 4.43456i 0.217684i
\(416\) 6.75054 0.330972
\(417\) −23.0021 −1.12642
\(418\) −32.0687 −1.56853
\(419\) 22.0145 1.07548 0.537738 0.843112i \(-0.319279\pi\)
0.537738 + 0.843112i \(0.319279\pi\)
\(420\) 2.75054i 0.134212i
\(421\) 3.26392i 0.159074i 0.996832 + 0.0795368i \(0.0253441\pi\)
−0.996832 + 0.0795368i \(0.974656\pi\)
\(422\) 13.5011i 0.657222i
\(423\) 3.50107 0.170228
\(424\) 4.75054i 0.230706i
\(425\) 7.06651i 0.342776i
\(426\) 14.1330i 0.684747i
\(427\) 5.50107i 0.266215i
\(428\) 12.0687 0.583360
\(429\) 32.0687i 1.54829i
\(430\) 9.81705i 0.473420i
\(431\) 26.5676i 1.27972i 0.768493 + 0.639858i \(0.221007\pi\)
−0.768493 + 0.639858i \(0.778993\pi\)
\(432\) 1.00000 0.0481125
\(433\) 8.56758 0.411732 0.205866 0.978580i \(-0.433999\pi\)
0.205866 + 0.978580i \(0.433999\pi\)
\(434\) 0.869112 0.0417187
\(435\) 2.00000 0.0958927
\(436\) 4.56758i 0.218748i
\(437\) 34.2017 1.63609
\(438\) 6.43456i 0.307455i
\(439\) 8.31598i 0.396900i 0.980111 + 0.198450i \(0.0635907\pi\)
−0.980111 + 0.198450i \(0.936409\pi\)
\(440\) 4.75054 0.226473
\(441\) 0.565444 0.0269259
\(442\) 47.7028i 2.26899i
\(443\) 35.2682 1.67564 0.837821 0.545944i \(-0.183829\pi\)
0.837821 + 0.545944i \(0.183829\pi\)
\(444\) 4.90852 3.59255i 0.232948 0.170495i
\(445\) 6.25161 0.296355
\(446\) 25.3181i 1.19885i
\(447\) −7.81705 −0.369734
\(448\) −2.75054 −0.129951
\(449\) 30.3203i 1.43090i 0.698663 + 0.715451i \(0.253779\pi\)
−0.698663 + 0.715451i \(0.746221\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) −9.50107 −0.447388
\(452\) 2.00000i 0.0940721i
\(453\) 16.4346 0.772163
\(454\) 4.63196 0.217389
\(455\) 18.5676 0.870462
\(456\) 6.75054 0.316123
\(457\) 10.6320i 0.497342i 0.968588 + 0.248671i \(0.0799938\pi\)
−0.968588 + 0.248671i \(0.920006\pi\)
\(458\) 20.1330i 0.940755i
\(459\) 7.06651i 0.329837i
\(460\) −5.06651 −0.236227
\(461\) 30.5032i 1.42068i 0.703861 + 0.710338i \(0.251458\pi\)
−0.703861 + 0.710338i \(0.748542\pi\)
\(462\) 13.0665i 0.607909i
\(463\) 39.5054i 1.83597i 0.396616 + 0.917985i \(0.370185\pi\)
−0.396616 + 0.917985i \(0.629815\pi\)
\(464\) 2.00000i 0.0928477i
\(465\) 0.315979 0.0146532
\(466\) 6.31598i 0.292582i
\(467\) 16.6320i 0.769635i 0.922993 + 0.384818i \(0.125736\pi\)
−0.922993 + 0.384818i \(0.874264\pi\)
\(468\) 6.75054i 0.312044i
\(469\) 41.2639 1.90539
\(470\) −3.50107 −0.161492
\(471\) −5.81705 −0.268036
\(472\) 11.8170 0.543924
\(473\) 46.6362i 2.14434i
\(474\) −8.31598 −0.381966
\(475\) 6.75054i 0.309736i
\(476\) 19.4367i 0.890880i
\(477\) 4.75054 0.217512
\(478\) −12.6320 −0.577772
\(479\) 33.2038i 1.51712i −0.651602 0.758561i \(-0.725903\pi\)
0.651602 0.758561i \(-0.274097\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 24.2516 + 33.1352i 1.10578 + 1.51083i
\(482\) −16.6320 −0.757565
\(483\) 13.9356i 0.634093i
\(484\) −11.5676 −0.525799
\(485\) −11.5011 −0.522237
\(486\) 1.00000i 0.0453609i
\(487\) 11.6341i 0.527191i −0.964633 0.263596i \(-0.915092\pi\)
0.964633 0.263596i \(-0.0849085\pi\)
\(488\) −2.00000 −0.0905357
\(489\) 18.2516i 0.825366i
\(490\) −0.565444 −0.0255442
\(491\) −4.75054 −0.214389 −0.107194 0.994238i \(-0.534187\pi\)
−0.107194 + 0.994238i \(0.534187\pi\)
\(492\) 2.00000 0.0901670
\(493\) −14.1330 −0.636520
\(494\) 45.5697i 2.05028i
\(495\) 4.75054i 0.213521i
\(496\) 0.315979i 0.0141879i
\(497\) −38.8734 −1.74371
\(498\) 4.43456i 0.198717i
\(499\) 9.12072i 0.408299i 0.978940 + 0.204150i \(0.0654429\pi\)
−0.978940 + 0.204150i \(0.934557\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) 5.06651i 0.226355i
\(502\) 1.68402 0.0751615
\(503\) 9.26392i 0.413058i −0.978441 0.206529i \(-0.933783\pi\)
0.978441 0.206529i \(-0.0662167\pi\)
\(504\) 2.75054i 0.122519i
\(505\) 7.18509i 0.319732i
\(506\) 24.0687 1.06998
\(507\) −32.5697 −1.44647
\(508\) 14.7505 0.654449
\(509\) 23.0166 1.02019 0.510096 0.860117i \(-0.329610\pi\)
0.510096 + 0.860117i \(0.329610\pi\)
\(510\) 7.06651i 0.312911i
\(511\) −17.6985 −0.782934
\(512\) 1.00000i 0.0441942i
\(513\) 6.75054i 0.298043i
\(514\) 3.43242 0.151397
\(515\) 0.631958 0.0278474
\(516\) 9.81705i 0.432172i
\(517\) 16.6320 0.731473
\(518\) −9.88142 13.5011i −0.434165 0.593203i
\(519\) 4.11858 0.180785
\(520\) 6.75054i 0.296031i
\(521\) 30.6320 1.34201 0.671005 0.741453i \(-0.265863\pi\)
0.671005 + 0.741453i \(0.265863\pi\)
\(522\) 2.00000 0.0875376
\(523\) 15.5553i 0.680185i −0.940392 0.340092i \(-0.889542\pi\)
0.940392 0.340092i \(-0.110458\pi\)
\(524\) 7.18509i 0.313882i
\(525\) −2.75054 −0.120043
\(526\) 6.86911i 0.299508i
\(527\) −2.23287 −0.0972654
\(528\) 4.75054 0.206741
\(529\) −2.66957 −0.116068
\(530\) −4.75054 −0.206350
\(531\) 11.8170i 0.512816i
\(532\) 18.5676i 0.805007i
\(533\) 13.5011i 0.584796i
\(534\) 6.25161 0.270533
\(535\) 12.0687i 0.521773i
\(536\) 15.0021i 0.647994i
\(537\) 9.68402i 0.417896i
\(538\) 9.24946i 0.398773i
\(539\) 2.68616 0.115701
\(540\) 1.00000i 0.0430331i
\(541\) 3.43242i 0.147571i 0.997274 + 0.0737855i \(0.0235080\pi\)
−0.997274 + 0.0737855i \(0.976492\pi\)
\(542\) 14.3702i 0.617252i
\(543\) 10.6320 0.456261
\(544\) 7.06651 0.302974
\(545\) −4.56758 −0.195654
\(546\) 18.5676 0.794619
\(547\) 17.3825i 0.743222i −0.928389 0.371611i \(-0.878806\pi\)
0.928389 0.371611i \(-0.121194\pi\)
\(548\) 1.68402 0.0719378
\(549\) 2.00000i 0.0853579i
\(550\) 4.75054i 0.202564i
\(551\) 13.5011 0.575165
\(552\) −5.06651 −0.215645
\(553\) 22.8734i 0.972676i
\(554\) 26.3846 1.12098
\(555\) −3.59255 4.90852i −0.152495 0.208355i
\(556\) 23.0021 0.975508
\(557\) 17.0021i 0.720404i 0.932874 + 0.360202i \(0.117292\pi\)
−0.932874 + 0.360202i \(0.882708\pi\)
\(558\) 0.315979 0.0133765
\(559\) 66.2703 2.80294
\(560\) 2.75054i 0.116231i
\(561\) 33.5697i 1.41731i
\(562\) 15.7527 0.664487
\(563\) 38.8734i 1.63832i 0.573566 + 0.819159i \(0.305559\pi\)
−0.573566 + 0.819159i \(0.694441\pi\)
\(564\) −3.50107 −0.147422
\(565\) −2.00000 −0.0841406
\(566\) 12.3846 0.520565
\(567\) 2.75054 0.115512
\(568\) 14.1330i 0.593009i
\(569\) 10.3804i 0.435167i −0.976042 0.217584i \(-0.930183\pi\)
0.976042 0.217584i \(-0.0698174\pi\)
\(570\) 6.75054i 0.282749i
\(571\) −8.99786 −0.376549 −0.188274 0.982116i \(-0.560289\pi\)
−0.188274 + 0.982116i \(0.560289\pi\)
\(572\) 32.0687i 1.34086i
\(573\) 6.93349i 0.289651i
\(574\) 5.50107i 0.229610i
\(575\) 5.06651i 0.211288i
\(576\) −1.00000 −0.0416667
\(577\) 26.8691i 1.11858i −0.828973 0.559288i \(-0.811075\pi\)
0.828973 0.559288i \(-0.188925\pi\)
\(578\) 32.9356i 1.36994i
\(579\) 0.498930i 0.0207348i
\(580\) −2.00000 −0.0830455
\(581\) 12.1974 0.506034
\(582\) −11.5011 −0.476735
\(583\) 22.5676 0.934654
\(584\) 6.43456i 0.266264i
\(585\) 6.75054 0.279100
\(586\) 0.750535i 0.0310043i
\(587\) 7.87125i 0.324881i 0.986718 + 0.162441i \(0.0519366\pi\)
−0.986718 + 0.162441i \(0.948063\pi\)
\(588\) −0.565444 −0.0233185
\(589\) 2.13303 0.0878899
\(590\) 11.8170i 0.486500i
\(591\) −16.7505 −0.689025
\(592\) −4.90852 + 3.59255i −0.201739 + 0.147653i
\(593\) 33.0810 1.35847 0.679236 0.733920i \(-0.262311\pi\)
0.679236 + 0.733920i \(0.262311\pi\)
\(594\) 4.75054i 0.194917i
\(595\) 19.4367 0.796827
\(596\) 7.81705 0.320199
\(597\) 3.31812i 0.135802i
\(598\) 34.2017i 1.39861i
\(599\) −16.5032 −0.674303 −0.337151 0.941450i \(-0.609463\pi\)
−0.337151 + 0.941450i \(0.609463\pi\)
\(600\) 1.00000i 0.0408248i
\(601\) −30.0687 −1.22653 −0.613263 0.789879i \(-0.710143\pi\)
−0.613263 + 0.789879i \(0.710143\pi\)
\(602\) −27.0021 −1.10053
\(603\) 15.0021 0.610934
\(604\) −16.4346 −0.668713
\(605\) 11.5676i 0.470289i
\(606\) 7.18509i 0.291874i
\(607\) 7.36804i 0.299060i 0.988757 + 0.149530i \(0.0477760\pi\)
−0.988757 + 0.149530i \(0.952224\pi\)
\(608\) −6.75054 −0.273770
\(609\) 5.50107i 0.222915i
\(610\) 2.00000i 0.0809776i
\(611\) 23.6341i 0.956133i
\(612\) 7.06651i 0.285647i
\(613\) −9.18509 −0.370982 −0.185491 0.982646i \(-0.559388\pi\)
−0.185491 + 0.982646i \(0.559388\pi\)
\(614\) 18.3702i 0.741360i
\(615\) 2.00000i 0.0806478i
\(616\) 13.0665i 0.526465i
\(617\) 7.18509 0.289261 0.144630 0.989486i \(-0.453801\pi\)
0.144630 + 0.989486i \(0.453801\pi\)
\(618\) 0.631958 0.0254211
\(619\) −34.0043 −1.36675 −0.683374 0.730069i \(-0.739488\pi\)
−0.683374 + 0.730069i \(0.739488\pi\)
\(620\) −0.315979 −0.0126900
\(621\) 5.06651i 0.203312i
\(622\) 35.0021 1.40346
\(623\) 17.1953i 0.688914i
\(624\) 6.75054i 0.270238i
\(625\) 1.00000 0.0400000
\(626\) 1.36804 0.0546779
\(627\) 32.0687i 1.28070i
\(628\) 5.81705 0.232126
\(629\) 25.3868 + 34.6862i 1.01224 + 1.38303i
\(630\) −2.75054 −0.109584
\(631\) 5.81705i 0.231573i −0.993274 0.115787i \(-0.963061\pi\)
0.993274 0.115787i \(-0.0369389\pi\)
\(632\) 8.31598 0.330792
\(633\) −13.5011 −0.536619
\(634\) 10.0542i 0.399303i
\(635\) 14.7505i 0.585357i
\(636\) −4.75054 −0.188371
\(637\) 3.81705i 0.151237i
\(638\) 9.50107 0.376151
\(639\) −14.1330 −0.559094
\(640\) 1.00000 0.0395285
\(641\) −13.1309 −0.518639 −0.259319 0.965792i \(-0.583498\pi\)
−0.259319 + 0.965792i \(0.583498\pi\)
\(642\) 12.0687i 0.476312i
\(643\) 22.2516i 0.877518i −0.898605 0.438759i \(-0.855418\pi\)
0.898605 0.438759i \(-0.144582\pi\)
\(644\) 13.9356i 0.549141i
\(645\) −9.81705 −0.386546
\(646\) 47.7028i 1.87684i
\(647\) 24.0687i 0.946236i 0.880999 + 0.473118i \(0.156872\pi\)
−0.880999 + 0.473118i \(0.843128\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 56.1373i 2.20358i
\(650\) −6.75054 −0.264778
\(651\) 0.869112i 0.0340632i
\(652\) 18.2516i 0.714788i
\(653\) 25.3680i 0.992728i 0.868114 + 0.496364i \(0.165332\pi\)
−0.868114 + 0.496364i \(0.834668\pi\)
\(654\) −4.56758 −0.178607
\(655\) 7.18509 0.280745
\(656\) −2.00000 −0.0780869
\(657\) −6.43456 −0.251036
\(658\) 9.62982i 0.375409i
\(659\) −18.4490 −0.718671 −0.359336 0.933208i \(-0.616997\pi\)
−0.359336 + 0.933208i \(0.616997\pi\)
\(660\) 4.75054i 0.184914i
\(661\) 18.9378i 0.736594i 0.929708 + 0.368297i \(0.120059\pi\)
−0.929708 + 0.368297i \(0.879941\pi\)
\(662\) 26.3160 1.02280
\(663\) −47.7028 −1.85262
\(664\) 4.43456i 0.172094i
\(665\) −18.5676 −0.720020
\(666\) −3.59255 4.90852i −0.139208 0.190201i
\(667\) −10.1330 −0.392352
\(668\) 5.06651i 0.196029i
\(669\) 25.3181 0.978855
\(670\) −15.0021 −0.579583
\(671\) 9.50107i 0.366785i
\(672\) 2.75054i 0.106104i
\(673\) −35.5697 −1.37111 −0.685556 0.728020i \(-0.740441\pi\)
−0.685556 + 0.728020i \(0.740441\pi\)
\(674\) 26.7006i 1.02847i
\(675\) −1.00000 −0.0384900
\(676\) 32.5697 1.25268
\(677\) −40.8878 −1.57145 −0.785724 0.618578i \(-0.787709\pi\)
−0.785724 + 0.618578i \(0.787709\pi\)
\(678\) −2.00000 −0.0768095
\(679\) 31.6341i 1.21401i
\(680\) 7.06651i 0.270988i
\(681\) 4.63196i 0.177497i
\(682\) 1.50107 0.0574790
\(683\) 14.3702i 0.549860i 0.961464 + 0.274930i \(0.0886546\pi\)
−0.961464 + 0.274930i \(0.911345\pi\)
\(684\) 6.75054i 0.258113i
\(685\) 1.68402i 0.0643431i
\(686\) 17.6985i 0.675731i
\(687\) 20.1330 0.768123
\(688\) 9.81705i 0.374272i
\(689\) 32.0687i 1.22172i
\(690\) 5.06651i 0.192879i
\(691\) −17.7671 −0.675893 −0.337947 0.941165i \(-0.609732\pi\)
−0.337947 + 0.941165i \(0.609732\pi\)
\(692\) −4.11858 −0.156565
\(693\) 13.0665 0.496356
\(694\) −13.5011 −0.512494
\(695\) 23.0021i 0.872521i
\(696\) −2.00000 −0.0758098
\(697\) 14.1330i 0.535327i
\(698\) 9.36804i 0.354586i
\(699\) −6.31598 −0.238892
\(700\) 2.75054 0.103960
\(701\) 28.1330i 1.06257i −0.847193 0.531285i \(-0.821709\pi\)
0.847193 0.531285i \(-0.178291\pi\)
\(702\) 6.75054 0.254783
\(703\) −24.2516 33.1352i −0.914667 1.24972i
\(704\) −4.75054 −0.179043
\(705\) 3.50107i 0.131858i
\(706\) 13.6341 0.513126
\(707\) 19.7628 0.743258
\(708\) 11.8170i 0.444112i
\(709\) 34.0687i 1.27948i 0.768593 + 0.639738i \(0.220957\pi\)
−0.768593 + 0.639738i \(0.779043\pi\)
\(710\) 14.1330 0.530403
\(711\) 8.31598i 0.311874i
\(712\) −6.25161 −0.234289
\(713\) −1.60091 −0.0599547
\(714\) 19.4367 0.727400
\(715\) 32.0687 1.19930
\(716\) 9.68402i 0.361909i
\(717\) 12.6320i 0.471749i
\(718\) 8.86911i 0.330992i
\(719\) −40.2661 −1.50167 −0.750835 0.660490i \(-0.770349\pi\)
−0.750835 + 0.660490i \(0.770349\pi\)
\(720\) 1.00000i 0.0372678i
\(721\) 1.73822i 0.0647348i
\(722\) 26.5697i 0.988823i
\(723\) 16.6320i 0.618549i
\(724\) −10.6320 −0.395134
\(725\) 2.00000i 0.0742781i
\(726\) 11.5676i 0.429313i
\(727\) 13.1352i 0.487156i 0.969881 + 0.243578i \(0.0783213\pi\)
−0.969881 + 0.243578i \(0.921679\pi\)
\(728\) −18.5676 −0.688160
\(729\) 1.00000 0.0370370
\(730\) 6.43456 0.238154
\(731\) 69.3723 2.56583
\(732\) 2.00000i 0.0739221i
\(733\) −7.05206 −0.260474 −0.130237 0.991483i \(-0.541574\pi\)
−0.130237 + 0.991483i \(0.541574\pi\)
\(734\) 2.11858i 0.0781981i
\(735\) 0.565444i 0.0208567i
\(736\) 5.06651 0.186754
\(737\) 71.2682 2.62520
\(738\) 2.00000i 0.0736210i
\(739\) 24.7404 0.910089 0.455045 0.890469i \(-0.349623\pi\)
0.455045 + 0.890469i \(0.349623\pi\)
\(740\) 3.59255 + 4.90852i 0.132065 + 0.180441i
\(741\) 45.5697 1.67405
\(742\) 13.0665i 0.479687i
\(743\) 1.36804 0.0501886 0.0250943 0.999685i \(-0.492011\pi\)
0.0250943 + 0.999685i \(0.492011\pi\)
\(744\) −0.315979 −0.0115844
\(745\) 7.81705i 0.286395i
\(746\) 23.0810i 0.845054i
\(747\) 4.43456 0.162252
\(748\) 33.5697i 1.22743i
\(749\) −33.1953 −1.21293
\(750\) 1.00000 0.0365148
\(751\) 16.0000 0.583848 0.291924 0.956441i \(-0.405705\pi\)
0.291924 + 0.956441i \(0.405705\pi\)
\(752\) 3.50107 0.127671
\(753\) 1.68402i 0.0613691i
\(754\) 13.5011i 0.491680i
\(755\) 16.4346i 0.598115i
\(756\) −2.75054 −0.100036
\(757\) 49.6239i 1.80361i −0.432141 0.901806i \(-0.642242\pi\)
0.432141 0.901806i \(-0.357758\pi\)
\(758\) 8.50321i 0.308851i
\(759\) 24.0687i 0.873637i
\(760\) 6.75054i 0.244868i
\(761\) −30.6320 −1.11041 −0.555204 0.831714i \(-0.687360\pi\)
−0.555204 + 0.831714i \(0.687360\pi\)
\(762\) 14.7505i 0.534356i
\(763\) 12.5633i 0.454822i
\(764\) 6.93349i 0.250845i
\(765\) 7.06651 0.255490
\(766\) 15.1995 0.549182
\(767\) 79.7714 2.88038
\(768\) 1.00000 0.0360844
\(769\) 29.1352i 1.05064i 0.850904 + 0.525321i \(0.176055\pi\)
−0.850904 + 0.525321i \(0.823945\pi\)
\(770\) −13.0665 −0.470884
\(771\) 3.43242i 0.123615i
\(772\) 0.498930i 0.0179569i
\(773\) 46.2516 1.66355 0.831777 0.555109i \(-0.187324\pi\)
0.831777 + 0.555109i \(0.187324\pi\)
\(774\) −9.81705 −0.352867
\(775\) 0.315979i 0.0113503i
\(776\) 11.5011 0.412864
\(777\) −13.5011 + 9.88142i −0.484348 + 0.354494i
\(778\) 32.1330 1.15202
\(779\) 13.5011i 0.483726i
\(780\) −6.75054 −0.241708
\(781\) −67.1395 −2.40244
\(782\) 35.8026i 1.28030i
\(783\) 2.00000i 0.0714742i
\(784\) 0.565444 0.0201944
\(785\) 5.81705i 0.207619i
\(786\) 7.18509 0.256284
\(787\) 15.8713 0.565749 0.282875 0.959157i \(-0.408712\pi\)
0.282875 + 0.959157i \(0.408712\pi\)
\(788\) 16.7505 0.596713
\(789\) 6.86911 0.244547
\(790\) 8.31598i 0.295869i
\(791\) 5.50107i 0.195596i
\(792\) 4.75054i 0.168803i
\(793\) −13.5011 −0.479437