Properties

Label 403.2.c.b.311.9
Level 403
Weight 2
Character 403.311
Analytic conductor 3.218
Analytic rank 0
Dimension 32
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 311.9
Character \(\chi\) = 403.311
Dual form 403.2.c.b.311.24

$q$-expansion

\(f(q)\) \(=\) \(q-1.44935i q^{2} +0.0382575 q^{3} -0.100611 q^{4} +3.85977i q^{5} -0.0554484i q^{6} +1.66255i q^{7} -2.75288i q^{8} -2.99854 q^{9} +O(q^{10})\) \(q-1.44935i q^{2} +0.0382575 q^{3} -0.100611 q^{4} +3.85977i q^{5} -0.0554484i q^{6} +1.66255i q^{7} -2.75288i q^{8} -2.99854 q^{9} +5.59415 q^{10} +1.88038i q^{11} -0.00384914 q^{12} +(1.08571 + 3.43820i) q^{13} +2.40961 q^{14} +0.147665i q^{15} -4.19110 q^{16} +3.75015 q^{17} +4.34592i q^{18} +3.26949i q^{19} -0.388337i q^{20} +0.0636049i q^{21} +2.72532 q^{22} +5.31401 q^{23} -0.105318i q^{24} -9.89783 q^{25} +(4.98315 - 1.57358i) q^{26} -0.229489 q^{27} -0.167271i q^{28} +3.11168 q^{29} +0.214018 q^{30} +1.00000i q^{31} +0.568613i q^{32} +0.0719384i q^{33} -5.43528i q^{34} -6.41705 q^{35} +0.301687 q^{36} -11.5806i q^{37} +4.73863 q^{38} +(0.0415366 + 0.131537i) q^{39} +10.6255 q^{40} -7.94532i q^{41} +0.0921856 q^{42} -9.24319 q^{43} -0.189187i q^{44} -11.5737i q^{45} -7.70185i q^{46} +6.97995i q^{47} -0.160341 q^{48} +4.23593 q^{49} +14.3454i q^{50} +0.143471 q^{51} +(-0.109235 - 0.345923i) q^{52} +6.11470 q^{53} +0.332609i q^{54} -7.25782 q^{55} +4.57679 q^{56} +0.125082i q^{57} -4.50991i q^{58} -12.1104i q^{59} -0.0148568i q^{60} +1.75416 q^{61} +1.44935 q^{62} -4.98521i q^{63} -7.55808 q^{64} +(-13.2707 + 4.19060i) q^{65} +0.104264 q^{66} +7.94479i q^{67} -0.377308 q^{68} +0.203300 q^{69} +9.30055i q^{70} +0.735383i q^{71} +8.25460i q^{72} +13.5423i q^{73} -16.7843 q^{74} -0.378666 q^{75} -0.328948i q^{76} -3.12622 q^{77} +(0.190643 - 0.0602010i) q^{78} -5.66333 q^{79} -16.1767i q^{80} +8.98683 q^{81} -11.5155 q^{82} -13.7729i q^{83} -0.00639938i q^{84} +14.4747i q^{85} +13.3966i q^{86} +0.119045 q^{87} +5.17644 q^{88} +10.2781i q^{89} -16.7743 q^{90} +(-5.71618 + 1.80505i) q^{91} -0.534650 q^{92} +0.0382575i q^{93} +10.1164 q^{94} -12.6195 q^{95} +0.0217537i q^{96} -8.34364i q^{97} -6.13935i q^{98} -5.63838i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + 4q^{10} - 16q^{12} + 10q^{13} - 16q^{14} + 28q^{16} - 8q^{17} - 16q^{22} - 8q^{23} + 4q^{25} + 18q^{26} + 20q^{27} - 16q^{29} + 40q^{30} - 4q^{35} - 44q^{36} + 12q^{38} + 4q^{39} + 28q^{40} + 28q^{42} - 32q^{43} - 64q^{49} - 64q^{52} - 12q^{53} + 44q^{55} + 8q^{56} + 16q^{61} + 8q^{62} - 76q^{64} - 66q^{65} - 68q^{66} + 64q^{68} + 20q^{69} + 16q^{74} - 32q^{77} - 20q^{78} + 64q^{79} - 16q^{81} + 12q^{82} - 72q^{87} + 80q^{88} + 68q^{90} + 22q^{91} + 28q^{92} + 88q^{94} + 4q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.44935i 1.02484i −0.858734 0.512422i \(-0.828748\pi\)
0.858734 0.512422i \(-0.171252\pi\)
\(3\) 0.0382575 0.0220880 0.0110440 0.999939i \(-0.496485\pi\)
0.0110440 + 0.999939i \(0.496485\pi\)
\(4\) −0.100611 −0.0503057
\(5\) 3.85977i 1.72614i 0.505083 + 0.863071i \(0.331462\pi\)
−0.505083 + 0.863071i \(0.668538\pi\)
\(6\) 0.0554484i 0.0226367i
\(7\) 1.66255i 0.628384i 0.949359 + 0.314192i \(0.101734\pi\)
−0.949359 + 0.314192i \(0.898266\pi\)
\(8\) 2.75288i 0.973289i
\(9\) −2.99854 −0.999512
\(10\) 5.59415 1.76903
\(11\) 1.88038i 0.566955i 0.958979 + 0.283477i \(0.0914881\pi\)
−0.958979 + 0.283477i \(0.908512\pi\)
\(12\) −0.00384914 −0.00111115
\(13\) 1.08571 + 3.43820i 0.301122 + 0.953586i
\(14\) 2.40961 0.643996
\(15\) 0.147665i 0.0381270i
\(16\) −4.19110 −1.04778
\(17\) 3.75015 0.909546 0.454773 0.890607i \(-0.349720\pi\)
0.454773 + 0.890607i \(0.349720\pi\)
\(18\) 4.34592i 1.02434i
\(19\) 3.26949i 0.750073i 0.927010 + 0.375036i \(0.122370\pi\)
−0.927010 + 0.375036i \(0.877630\pi\)
\(20\) 0.388337i 0.0868349i
\(21\) 0.0636049i 0.0138797i
\(22\) 2.72532 0.581040
\(23\) 5.31401 1.10805 0.554023 0.832501i \(-0.313092\pi\)
0.554023 + 0.832501i \(0.313092\pi\)
\(24\) 0.105318i 0.0214980i
\(25\) −9.89783 −1.97957
\(26\) 4.98315 1.57358i 0.977277 0.308603i
\(27\) −0.229489 −0.0441651
\(28\) 0.167271i 0.0316113i
\(29\) 3.11168 0.577824 0.288912 0.957356i \(-0.406706\pi\)
0.288912 + 0.957356i \(0.406706\pi\)
\(30\) 0.214018 0.0390742
\(31\) 1.00000i 0.179605i
\(32\) 0.568613i 0.100518i
\(33\) 0.0719384i 0.0125229i
\(34\) 5.43528i 0.932143i
\(35\) −6.41705 −1.08468
\(36\) 0.301687 0.0502812
\(37\) 11.5806i 1.90383i −0.306361 0.951915i \(-0.599112\pi\)
0.306361 0.951915i \(-0.400888\pi\)
\(38\) 4.73863 0.768708
\(39\) 0.0415366 + 0.131537i 0.00665118 + 0.0210628i
\(40\) 10.6255 1.68003
\(41\) 7.94532i 1.24085i −0.784266 0.620425i \(-0.786960\pi\)
0.784266 0.620425i \(-0.213040\pi\)
\(42\) 0.0921856 0.0142246
\(43\) −9.24319 −1.40957 −0.704786 0.709420i \(-0.748957\pi\)
−0.704786 + 0.709420i \(0.748957\pi\)
\(44\) 0.189187i 0.0285211i
\(45\) 11.5737i 1.72530i
\(46\) 7.70185i 1.13558i
\(47\) 6.97995i 1.01813i 0.860728 + 0.509065i \(0.170009\pi\)
−0.860728 + 0.509065i \(0.829991\pi\)
\(48\) −0.160341 −0.0231432
\(49\) 4.23593 0.605133
\(50\) 14.3454i 2.02875i
\(51\) 0.143471 0.0200900
\(52\) −0.109235 0.345923i −0.0151482 0.0479708i
\(53\) 6.11470 0.839918 0.419959 0.907543i \(-0.362044\pi\)
0.419959 + 0.907543i \(0.362044\pi\)
\(54\) 0.332609i 0.0452624i
\(55\) −7.25782 −0.978644
\(56\) 4.57679 0.611599
\(57\) 0.125082i 0.0165676i
\(58\) 4.50991i 0.592180i
\(59\) 12.1104i 1.57664i −0.615268 0.788318i \(-0.710952\pi\)
0.615268 0.788318i \(-0.289048\pi\)
\(60\) 0.0148568i 0.00191801i
\(61\) 1.75416 0.224598 0.112299 0.993674i \(-0.464179\pi\)
0.112299 + 0.993674i \(0.464179\pi\)
\(62\) 1.44935 0.184067
\(63\) 4.98521i 0.628078i
\(64\) −7.55808 −0.944760
\(65\) −13.2707 + 4.19060i −1.64602 + 0.519780i
\(66\) 0.104264 0.0128340
\(67\) 7.94479i 0.970611i 0.874345 + 0.485306i \(0.161292\pi\)
−0.874345 + 0.485306i \(0.838708\pi\)
\(68\) −0.377308 −0.0457554
\(69\) 0.203300 0.0244745
\(70\) 9.30055i 1.11163i
\(71\) 0.735383i 0.0872739i 0.999047 + 0.0436369i \(0.0138945\pi\)
−0.999047 + 0.0436369i \(0.986106\pi\)
\(72\) 8.25460i 0.972814i
\(73\) 13.5423i 1.58500i 0.609870 + 0.792501i \(0.291222\pi\)
−0.609870 + 0.792501i \(0.708778\pi\)
\(74\) −16.7843 −1.95113
\(75\) −0.378666 −0.0437246
\(76\) 0.328948i 0.0377330i
\(77\) −3.12622 −0.356265
\(78\) 0.190643 0.0602010i 0.0215860 0.00681642i
\(79\) −5.66333 −0.637174 −0.318587 0.947894i \(-0.603208\pi\)
−0.318587 + 0.947894i \(0.603208\pi\)
\(80\) 16.1767i 1.80861i
\(81\) 8.98683 0.998537
\(82\) −11.5155 −1.27168
\(83\) 13.7729i 1.51177i −0.654704 0.755886i \(-0.727207\pi\)
0.654704 0.755886i \(-0.272793\pi\)
\(84\) 0.00639938i 0.000698230i
\(85\) 14.4747i 1.57001i
\(86\) 13.3966i 1.44459i
\(87\) 0.119045 0.0127630
\(88\) 5.17644 0.551811
\(89\) 10.2781i 1.08948i 0.838606 + 0.544738i \(0.183371\pi\)
−0.838606 + 0.544738i \(0.816629\pi\)
\(90\) −16.7743 −1.76816
\(91\) −5.71618 + 1.80505i −0.599218 + 0.189220i
\(92\) −0.534650 −0.0557411
\(93\) 0.0382575i 0.00396711i
\(94\) 10.1164 1.04342
\(95\) −12.6195 −1.29473
\(96\) 0.0217537i 0.00222023i
\(97\) 8.34364i 0.847169i −0.905857 0.423584i \(-0.860772\pi\)
0.905857 0.423584i \(-0.139228\pi\)
\(98\) 6.13935i 0.620168i
\(99\) 5.63838i 0.566678i
\(100\) 0.995836 0.0995836
\(101\) 8.36630 0.832478 0.416239 0.909255i \(-0.363348\pi\)
0.416239 + 0.909255i \(0.363348\pi\)
\(102\) 0.207940i 0.0205891i
\(103\) 14.0180 1.38123 0.690616 0.723222i \(-0.257340\pi\)
0.690616 + 0.723222i \(0.257340\pi\)
\(104\) 9.46494 2.98883i 0.928114 0.293079i
\(105\) −0.245500 −0.0239584
\(106\) 8.86233i 0.860785i
\(107\) −0.569178 −0.0550245 −0.0275122 0.999621i \(-0.508759\pi\)
−0.0275122 + 0.999621i \(0.508759\pi\)
\(108\) 0.0230892 0.00222176
\(109\) 10.7415i 1.02885i −0.857537 0.514423i \(-0.828006\pi\)
0.857537 0.514423i \(-0.171994\pi\)
\(110\) 10.5191i 1.00296i
\(111\) 0.443043i 0.0420517i
\(112\) 6.96791i 0.658405i
\(113\) −7.41542 −0.697584 −0.348792 0.937200i \(-0.613408\pi\)
−0.348792 + 0.937200i \(0.613408\pi\)
\(114\) 0.181288 0.0169792
\(115\) 20.5108i 1.91265i
\(116\) −0.313071 −0.0290679
\(117\) −3.25555 10.3096i −0.300975 0.953120i
\(118\) −17.5522 −1.61581
\(119\) 6.23481i 0.571544i
\(120\) 0.406504 0.0371085
\(121\) 7.46419 0.678562
\(122\) 2.54240i 0.230178i
\(123\) 0.303968i 0.0274079i
\(124\) 0.100611i 0.00903518i
\(125\) 18.9045i 1.69087i
\(126\) −7.22531 −0.643682
\(127\) −18.2144 −1.61627 −0.808133 0.589000i \(-0.799522\pi\)
−0.808133 + 0.589000i \(0.799522\pi\)
\(128\) 12.0915i 1.06875i
\(129\) −0.353621 −0.0311346
\(130\) 6.07364 + 19.2338i 0.532693 + 1.68692i
\(131\) 18.5465 1.62042 0.810209 0.586141i \(-0.199354\pi\)
0.810209 + 0.586141i \(0.199354\pi\)
\(132\) 0.00723783i 0.000629972i
\(133\) −5.43568 −0.471334
\(134\) 11.5148 0.994725
\(135\) 0.885774i 0.0762353i
\(136\) 10.3237i 0.885251i
\(137\) 3.12119i 0.266661i 0.991072 + 0.133331i \(0.0425672\pi\)
−0.991072 + 0.133331i \(0.957433\pi\)
\(138\) 0.294653i 0.0250825i
\(139\) −16.0910 −1.36482 −0.682410 0.730970i \(-0.739068\pi\)
−0.682410 + 0.730970i \(0.739068\pi\)
\(140\) 0.645629 0.0545657
\(141\) 0.267035i 0.0224884i
\(142\) 1.06583 0.0894421
\(143\) −6.46511 + 2.04155i −0.540640 + 0.170723i
\(144\) 12.5672 1.04726
\(145\) 12.0104i 0.997407i
\(146\) 19.6275 1.62438
\(147\) 0.162056 0.0133662
\(148\) 1.16514i 0.0957736i
\(149\) 18.8430i 1.54368i −0.635820 0.771838i \(-0.719338\pi\)
0.635820 0.771838i \(-0.280662\pi\)
\(150\) 0.548819i 0.0448109i
\(151\) 0.726888i 0.0591533i −0.999563 0.0295767i \(-0.990584\pi\)
0.999563 0.0295767i \(-0.00941591\pi\)
\(152\) 9.00050 0.730037
\(153\) −11.2450 −0.909102
\(154\) 4.53098i 0.365116i
\(155\) −3.85977 −0.310024
\(156\) −0.00417906 0.0132341i −0.000334592 0.00105958i
\(157\) −5.75901 −0.459619 −0.229809 0.973236i \(-0.573810\pi\)
−0.229809 + 0.973236i \(0.573810\pi\)
\(158\) 8.20814i 0.653004i
\(159\) 0.233933 0.0185521
\(160\) −2.19472 −0.173508
\(161\) 8.83479i 0.696279i
\(162\) 13.0250i 1.02334i
\(163\) 3.17279i 0.248512i −0.992250 0.124256i \(-0.960346\pi\)
0.992250 0.124256i \(-0.0396544\pi\)
\(164\) 0.799390i 0.0624219i
\(165\) −0.277666 −0.0216163
\(166\) −19.9617 −1.54933
\(167\) 4.97051i 0.384630i 0.981333 + 0.192315i \(0.0615995\pi\)
−0.981333 + 0.192315i \(0.938400\pi\)
\(168\) 0.175096 0.0135090
\(169\) −10.6425 + 7.46579i −0.818651 + 0.574292i
\(170\) 20.9789 1.60901
\(171\) 9.80369i 0.749707i
\(172\) 0.929971 0.0709096
\(173\) −1.97560 −0.150202 −0.0751009 0.997176i \(-0.523928\pi\)
−0.0751009 + 0.997176i \(0.523928\pi\)
\(174\) 0.172538i 0.0130800i
\(175\) 16.4556i 1.24393i
\(176\) 7.88084i 0.594041i
\(177\) 0.463312i 0.0348247i
\(178\) 14.8965 1.11654
\(179\) 6.07427 0.454012 0.227006 0.973893i \(-0.427106\pi\)
0.227006 + 0.973893i \(0.427106\pi\)
\(180\) 1.16444i 0.0867925i
\(181\) 20.6084 1.53181 0.765906 0.642953i \(-0.222291\pi\)
0.765906 + 0.642953i \(0.222291\pi\)
\(182\) 2.61614 + 8.28473i 0.193922 + 0.614105i
\(183\) 0.0671099 0.00496091
\(184\) 14.6288i 1.07845i
\(185\) 44.6983 3.28628
\(186\) 0.0554484 0.00406567
\(187\) 7.05170i 0.515671i
\(188\) 0.702263i 0.0512178i
\(189\) 0.381536i 0.0277527i
\(190\) 18.2900i 1.32690i
\(191\) 6.78433 0.490897 0.245448 0.969410i \(-0.421065\pi\)
0.245448 + 0.969410i \(0.421065\pi\)
\(192\) −0.289153 −0.0208678
\(193\) 22.3446i 1.60840i 0.594361 + 0.804198i \(0.297405\pi\)
−0.594361 + 0.804198i \(0.702595\pi\)
\(194\) −12.0928 −0.868216
\(195\) −0.507702 + 0.160322i −0.0363573 + 0.0114809i
\(196\) −0.426184 −0.0304417
\(197\) 6.85560i 0.488441i −0.969720 0.244221i \(-0.921468\pi\)
0.969720 0.244221i \(-0.0785321\pi\)
\(198\) −8.17197 −0.580757
\(199\) −6.55363 −0.464575 −0.232287 0.972647i \(-0.574621\pi\)
−0.232287 + 0.972647i \(0.574621\pi\)
\(200\) 27.2475i 1.92669i
\(201\) 0.303948i 0.0214388i
\(202\) 12.1257i 0.853160i
\(203\) 5.17332i 0.363096i
\(204\) −0.0144349 −0.00101064
\(205\) 30.6671 2.14188
\(206\) 20.3169i 1.41555i
\(207\) −15.9342 −1.10751
\(208\) −4.55033 14.4098i −0.315508 0.999143i
\(209\) −6.14787 −0.425257
\(210\) 0.355815i 0.0245536i
\(211\) 21.8282 1.50271 0.751356 0.659897i \(-0.229400\pi\)
0.751356 + 0.659897i \(0.229400\pi\)
\(212\) −0.615209 −0.0422527
\(213\) 0.0281339i 0.00192770i
\(214\) 0.824937i 0.0563915i
\(215\) 35.6766i 2.43312i
\(216\) 0.631754i 0.0429854i
\(217\) −1.66255 −0.112861
\(218\) −15.5681 −1.05441
\(219\) 0.518093i 0.0350095i
\(220\) 0.730220 0.0492314
\(221\) 4.07159 + 12.8938i 0.273884 + 0.867330i
\(222\) −0.642123 −0.0430965
\(223\) 1.22551i 0.0820659i −0.999158 0.0410330i \(-0.986935\pi\)
0.999158 0.0410330i \(-0.0130649\pi\)
\(224\) −0.945347 −0.0631636
\(225\) 29.6790 1.97860
\(226\) 10.7475i 0.714915i
\(227\) 9.82473i 0.652090i −0.945354 0.326045i \(-0.894284\pi\)
0.945354 0.326045i \(-0.105716\pi\)
\(228\) 0.0125847i 0.000833444i
\(229\) 1.46932i 0.0970954i −0.998821 0.0485477i \(-0.984541\pi\)
0.998821 0.0485477i \(-0.0154593\pi\)
\(230\) 29.7274 1.96016
\(231\) −0.119601 −0.00786917
\(232\) 8.56607i 0.562390i
\(233\) 14.1766 0.928737 0.464369 0.885642i \(-0.346281\pi\)
0.464369 + 0.885642i \(0.346281\pi\)
\(234\) −14.9422 + 4.71842i −0.976800 + 0.308453i
\(235\) −26.9410 −1.75744
\(236\) 1.21844i 0.0793139i
\(237\) −0.216665 −0.0140739
\(238\) 9.03641 0.585744
\(239\) 12.4101i 0.802745i −0.915915 0.401372i \(-0.868533\pi\)
0.915915 0.401372i \(-0.131467\pi\)
\(240\) 0.618879i 0.0399485i
\(241\) 9.96203i 0.641711i −0.947128 0.320855i \(-0.896030\pi\)
0.947128 0.320855i \(-0.103970\pi\)
\(242\) 10.8182i 0.695421i
\(243\) 1.03228 0.0662208
\(244\) −0.176489 −0.0112986
\(245\) 16.3497i 1.04455i
\(246\) −0.440555 −0.0280888
\(247\) −11.2412 + 3.54972i −0.715258 + 0.225864i
\(248\) 2.75288 0.174808
\(249\) 0.526916i 0.0333919i
\(250\) −27.3992 −1.73288
\(251\) −2.57983 −0.162837 −0.0814187 0.996680i \(-0.525945\pi\)
−0.0814187 + 0.996680i \(0.525945\pi\)
\(252\) 0.501570i 0.0315959i
\(253\) 9.99233i 0.628212i
\(254\) 26.3990i 1.65642i
\(255\) 0.553767i 0.0346782i
\(256\) 2.40867 0.150542
\(257\) 8.69963 0.542668 0.271334 0.962485i \(-0.412535\pi\)
0.271334 + 0.962485i \(0.412535\pi\)
\(258\) 0.512520i 0.0319081i
\(259\) 19.2532 1.19634
\(260\) 1.33518 0.421622i 0.0828045 0.0261479i
\(261\) −9.33048 −0.577542
\(262\) 26.8804i 1.66068i
\(263\) 4.64597 0.286483 0.143241 0.989688i \(-0.454248\pi\)
0.143241 + 0.989688i \(0.454248\pi\)
\(264\) 0.198038 0.0121884
\(265\) 23.6013i 1.44982i
\(266\) 7.87820i 0.483044i
\(267\) 0.393214i 0.0240643i
\(268\) 0.799338i 0.0488273i
\(269\) −1.50231 −0.0915976 −0.0457988 0.998951i \(-0.514583\pi\)
−0.0457988 + 0.998951i \(0.514583\pi\)
\(270\) −1.28380 −0.0781293
\(271\) 8.71423i 0.529352i −0.964337 0.264676i \(-0.914735\pi\)
0.964337 0.264676i \(-0.0852650\pi\)
\(272\) −15.7173 −0.952999
\(273\) −0.218686 + 0.0690566i −0.0132355 + 0.00417949i
\(274\) 4.52369 0.273286
\(275\) 18.6116i 1.12232i
\(276\) −0.0204544 −0.00123121
\(277\) 4.24495 0.255054 0.127527 0.991835i \(-0.459296\pi\)
0.127527 + 0.991835i \(0.459296\pi\)
\(278\) 23.3214i 1.39873i
\(279\) 2.99854i 0.179518i
\(280\) 17.6654i 1.05571i
\(281\) 5.08775i 0.303510i −0.988418 0.151755i \(-0.951508\pi\)
0.988418 0.151755i \(-0.0484924\pi\)
\(282\) 0.387027 0.0230471
\(283\) −32.6740 −1.94227 −0.971134 0.238533i \(-0.923334\pi\)
−0.971134 + 0.238533i \(0.923334\pi\)
\(284\) 0.0739880i 0.00439038i
\(285\) −0.482789 −0.0285980
\(286\) 2.95891 + 9.37020i 0.174964 + 0.554072i
\(287\) 13.2095 0.779731
\(288\) 1.70501i 0.100469i
\(289\) −2.93635 −0.172727
\(290\) 17.4072 1.02219
\(291\) 0.319207i 0.0187122i
\(292\) 1.36251i 0.0797347i
\(293\) 10.6513i 0.622254i 0.950368 + 0.311127i \(0.100707\pi\)
−0.950368 + 0.311127i \(0.899293\pi\)
\(294\) 0.234876i 0.0136982i
\(295\) 46.7433 2.72150
\(296\) −31.8798 −1.85298
\(297\) 0.431525i 0.0250396i
\(298\) −27.3100 −1.58203
\(299\) 5.76948 + 18.2706i 0.333658 + 1.05662i
\(300\) 0.0380982 0.00219960
\(301\) 15.3672i 0.885753i
\(302\) −1.05351 −0.0606229
\(303\) 0.320073 0.0183877
\(304\) 13.7028i 0.785907i
\(305\) 6.77067i 0.387688i
\(306\) 16.2979i 0.931688i
\(307\) 11.4536i 0.653691i 0.945078 + 0.326845i \(0.105986\pi\)
−0.945078 + 0.326845i \(0.894014\pi\)
\(308\) 0.314533 0.0179222
\(309\) 0.536292 0.0305086
\(310\) 5.59415i 0.317727i
\(311\) −14.2666 −0.808983 −0.404492 0.914542i \(-0.632552\pi\)
−0.404492 + 0.914542i \(0.632552\pi\)
\(312\) 0.362105 0.114345i 0.0205001 0.00647352i
\(313\) 10.3671 0.585983 0.292991 0.956115i \(-0.405349\pi\)
0.292991 + 0.956115i \(0.405349\pi\)
\(314\) 8.34681i 0.471038i
\(315\) 19.2418 1.08415
\(316\) 0.569796 0.0320535
\(317\) 5.67935i 0.318984i 0.987199 + 0.159492i \(0.0509857\pi\)
−0.987199 + 0.159492i \(0.949014\pi\)
\(318\) 0.339050i 0.0190130i
\(319\) 5.85113i 0.327600i
\(320\) 29.1725i 1.63079i
\(321\) −0.0217753 −0.00121538
\(322\) 12.8047 0.713577
\(323\) 12.2611i 0.682225i
\(324\) −0.904178 −0.0502321
\(325\) −10.7462 34.0307i −0.596092 1.88769i
\(326\) −4.59848 −0.254686
\(327\) 0.410941i 0.0227251i
\(328\) −21.8725 −1.20771
\(329\) −11.6045 −0.639777
\(330\) 0.402435i 0.0221533i
\(331\) 0.676975i 0.0372099i 0.999827 + 0.0186050i \(0.00592248\pi\)
−0.999827 + 0.0186050i \(0.994078\pi\)
\(332\) 1.38571i 0.0760508i
\(333\) 34.7247i 1.90290i
\(334\) 7.20401 0.394186
\(335\) −30.6651 −1.67541
\(336\) 0.266574i 0.0145428i
\(337\) 4.73721 0.258052 0.129026 0.991641i \(-0.458815\pi\)
0.129026 + 0.991641i \(0.458815\pi\)
\(338\) 10.8205 + 15.4246i 0.588560 + 0.838989i
\(339\) −0.283695 −0.0154082
\(340\) 1.45632i 0.0789803i
\(341\) −1.88038 −0.101828
\(342\) −14.2090 −0.768332
\(343\) 18.6803i 1.00864i
\(344\) 25.4453i 1.37192i
\(345\) 0.784693i 0.0422464i
\(346\) 2.86333i 0.153933i
\(347\) −31.6786 −1.70059 −0.850297 0.526303i \(-0.823578\pi\)
−0.850297 + 0.526303i \(0.823578\pi\)
\(348\) −0.0119773 −0.000642050
\(349\) 8.64433i 0.462720i −0.972868 0.231360i \(-0.925682\pi\)
0.972868 0.231360i \(-0.0743176\pi\)
\(350\) −23.8499 −1.27483
\(351\) −0.249159 0.789029i −0.0132991 0.0421152i
\(352\) −1.06921 −0.0569889
\(353\) 11.6266i 0.618820i −0.950929 0.309410i \(-0.899869\pi\)
0.950929 0.309410i \(-0.100131\pi\)
\(354\) −0.671501 −0.0356899
\(355\) −2.83841 −0.150647
\(356\) 1.03409i 0.0548069i
\(357\) 0.238528i 0.0126242i
\(358\) 8.80373i 0.465292i
\(359\) 5.12526i 0.270501i −0.990811 0.135250i \(-0.956816\pi\)
0.990811 0.135250i \(-0.0431839\pi\)
\(360\) −31.8609 −1.67921
\(361\) 8.31043 0.437391
\(362\) 29.8688i 1.56987i
\(363\) 0.285561 0.0149881
\(364\) 0.575113 0.181609i 0.0301441 0.00951888i
\(365\) −52.2701 −2.73594
\(366\) 0.0972656i 0.00508416i
\(367\) −35.1284 −1.83369 −0.916844 0.399246i \(-0.869272\pi\)
−0.916844 + 0.399246i \(0.869272\pi\)
\(368\) −22.2715 −1.16098
\(369\) 23.8243i 1.24024i
\(370\) 64.7834i 3.36793i
\(371\) 10.1660i 0.527791i
\(372\) 0.00384914i 0.000199569i
\(373\) 3.37056 0.174521 0.0872604 0.996186i \(-0.472189\pi\)
0.0872604 + 0.996186i \(0.472189\pi\)
\(374\) 10.2204 0.528483
\(375\) 0.723239i 0.0373479i
\(376\) 19.2149 0.990934
\(377\) 3.37839 + 10.6986i 0.173996 + 0.551005i
\(378\) −0.552979 −0.0284422
\(379\) 15.5733i 0.799945i −0.916527 0.399972i \(-0.869020\pi\)
0.916527 0.399972i \(-0.130980\pi\)
\(380\) 1.26967 0.0651324
\(381\) −0.696837 −0.0357000
\(382\) 9.83285i 0.503092i
\(383\) 14.2746i 0.729396i 0.931126 + 0.364698i \(0.118828\pi\)
−0.931126 + 0.364698i \(0.881172\pi\)
\(384\) 0.462591i 0.0236065i
\(385\) 12.0665i 0.614964i
\(386\) 32.3851 1.64836
\(387\) 27.7160 1.40888
\(388\) 0.839467i 0.0426175i
\(389\) 10.3188 0.523185 0.261592 0.965178i \(-0.415752\pi\)
0.261592 + 0.965178i \(0.415752\pi\)
\(390\) 0.232362 + 0.735838i 0.0117661 + 0.0372606i
\(391\) 19.9283 1.00782
\(392\) 11.6610i 0.588970i
\(393\) 0.709543 0.0357917
\(394\) −9.93615 −0.500576
\(395\) 21.8591i 1.09985i
\(396\) 0.567285i 0.0285072i
\(397\) 24.3801i 1.22360i −0.791012 0.611801i \(-0.790446\pi\)
0.791012 0.611801i \(-0.209554\pi\)
\(398\) 9.49850i 0.476117i
\(399\) −0.207956 −0.0104108
\(400\) 41.4828 2.07414
\(401\) 15.7425i 0.786141i 0.919508 + 0.393071i \(0.128587\pi\)
−0.919508 + 0.393071i \(0.871413\pi\)
\(402\) 0.440526 0.0219714
\(403\) −3.43820 + 1.08571i −0.171269 + 0.0540832i
\(404\) −0.841746 −0.0418784
\(405\) 34.6871i 1.72362i
\(406\) 7.49794 0.372116
\(407\) 21.7758 1.07939
\(408\) 0.394959i 0.0195534i
\(409\) 13.4932i 0.667196i −0.942716 0.333598i \(-0.891737\pi\)
0.942716 0.333598i \(-0.108263\pi\)
\(410\) 44.4473i 2.19510i
\(411\) 0.119409i 0.00589000i
\(412\) −1.41037 −0.0694839
\(413\) 20.1341 0.990733
\(414\) 23.0943i 1.13502i
\(415\) 53.1602 2.60953
\(416\) −1.95501 + 0.617350i −0.0958521 + 0.0302681i
\(417\) −0.615600 −0.0301461
\(418\) 8.91041i 0.435822i
\(419\) −30.1496 −1.47290 −0.736451 0.676491i \(-0.763500\pi\)
−0.736451 + 0.676491i \(0.763500\pi\)
\(420\) 0.0247001 0.00120524
\(421\) 29.2902i 1.42752i −0.700393 0.713758i \(-0.746992\pi\)
0.700393 0.713758i \(-0.253008\pi\)
\(422\) 31.6366i 1.54005i
\(423\) 20.9296i 1.01763i
\(424\) 16.8330i 0.817483i
\(425\) −37.1184 −1.80051
\(426\) 0.0407758 0.00197559
\(427\) 2.91638i 0.141134i
\(428\) 0.0572658 0.00276805
\(429\) −0.247339 + 0.0781044i −0.0119416 + 0.00377092i
\(430\) −51.7078 −2.49357
\(431\) 35.3794i 1.70416i −0.523408 0.852082i \(-0.675340\pi\)
0.523408 0.852082i \(-0.324660\pi\)
\(432\) 0.961811 0.0462751
\(433\) 12.7072 0.610671 0.305335 0.952245i \(-0.401231\pi\)
0.305335 + 0.952245i \(0.401231\pi\)
\(434\) 2.40961i 0.115665i
\(435\) 0.459486i 0.0220307i
\(436\) 1.08071i 0.0517568i
\(437\) 17.3741i 0.831115i
\(438\) 0.750897 0.0358793
\(439\) 18.4508 0.880609 0.440305 0.897849i \(-0.354870\pi\)
0.440305 + 0.897849i \(0.354870\pi\)
\(440\) 19.9799i 0.952503i
\(441\) −12.7016 −0.604838
\(442\) 18.6876 5.90115i 0.888878 0.280689i
\(443\) 10.8749 0.516680 0.258340 0.966054i \(-0.416824\pi\)
0.258340 + 0.966054i \(0.416824\pi\)
\(444\) 0.0445752i 0.00211544i
\(445\) −39.6711 −1.88059
\(446\) −1.77619 −0.0841048
\(447\) 0.720884i 0.0340966i
\(448\) 12.5657i 0.593672i
\(449\) 11.8359i 0.558569i 0.960208 + 0.279284i \(0.0900972\pi\)
−0.960208 + 0.279284i \(0.909903\pi\)
\(450\) 43.0152i 2.02776i
\(451\) 14.9402 0.703506
\(452\) 0.746076 0.0350925
\(453\) 0.0278089i 0.00130658i
\(454\) −14.2395 −0.668291
\(455\) −6.96707 22.0631i −0.326621 1.03434i
\(456\) 0.344336 0.0161250
\(457\) 32.9139i 1.53965i 0.638258 + 0.769823i \(0.279655\pi\)
−0.638258 + 0.769823i \(0.720345\pi\)
\(458\) −2.12956 −0.0995077
\(459\) −0.860618 −0.0401702
\(460\) 2.06363i 0.0962171i
\(461\) 25.2638i 1.17665i 0.808625 + 0.588325i \(0.200212\pi\)
−0.808625 + 0.588325i \(0.799788\pi\)
\(462\) 0.173344i 0.00806468i
\(463\) 19.8975i 0.924714i 0.886694 + 0.462357i \(0.152996\pi\)
−0.886694 + 0.462357i \(0.847004\pi\)
\(464\) −13.0414 −0.605430
\(465\) −0.147665 −0.00684780
\(466\) 20.5468i 0.951811i
\(467\) −19.7000 −0.911608 −0.455804 0.890080i \(-0.650648\pi\)
−0.455804 + 0.890080i \(0.650648\pi\)
\(468\) 0.327545 + 1.03726i 0.0151408 + 0.0479474i
\(469\) −13.2086 −0.609917
\(470\) 39.0469i 1.80110i
\(471\) −0.220325 −0.0101520
\(472\) −33.3384 −1.53452
\(473\) 17.3807i 0.799164i
\(474\) 0.314022i 0.0144235i
\(475\) 32.3609i 1.48482i
\(476\) 0.627294i 0.0287520i
\(477\) −18.3351 −0.839508
\(478\) −17.9866 −0.822688
\(479\) 24.1566i 1.10374i 0.833929 + 0.551872i \(0.186086\pi\)
−0.833929 + 0.551872i \(0.813914\pi\)
\(480\) −0.0839643 −0.00383243
\(481\) 39.8163 12.5731i 1.81547 0.573286i
\(482\) −14.4385 −0.657653
\(483\) 0.337997i 0.0153794i
\(484\) −0.750983 −0.0341356
\(485\) 32.2046 1.46233
\(486\) 1.49613i 0.0678660i
\(487\) 21.5211i 0.975213i 0.873063 + 0.487607i \(0.162130\pi\)
−0.873063 + 0.487607i \(0.837870\pi\)
\(488\) 4.82900i 0.218598i
\(489\) 0.121383i 0.00548913i
\(490\) 23.6965 1.07050
\(491\) 1.06521 0.0480723 0.0240361 0.999711i \(-0.492348\pi\)
0.0240361 + 0.999711i \(0.492348\pi\)
\(492\) 0.0305827i 0.00137877i
\(493\) 11.6693 0.525558
\(494\) 5.14479 + 16.2924i 0.231475 + 0.733028i
\(495\) 21.7628 0.978167
\(496\) 4.19110i 0.188186i
\(497\) −1.22261 −0.0548415
\(498\) −0.763685 −0.0342215
\(499\) 21.7718i 0.974641i −0.873223 0.487321i \(-0.837974\pi\)
0.873223 0.487321i \(-0.162026\pi\)
\(500\) 1.90201i 0.0850605i
\(501\) 0.190159i 0.00849569i
\(502\) 3.73907i 0.166883i
\(503\) −19.9950 −0.891531 −0.445766 0.895150i \(-0.647068\pi\)
−0.445766 + 0.895150i \(0.647068\pi\)
\(504\) −13.7237 −0.611301
\(505\) 32.2920i 1.43697i
\(506\) 14.4824 0.643820
\(507\) −0.407154 + 0.285622i −0.0180823 + 0.0126849i
\(508\) 1.83258 0.0813075
\(509\) 18.7005i 0.828883i 0.910076 + 0.414442i \(0.136023\pi\)
−0.910076 + 0.414442i \(0.863977\pi\)
\(510\) 0.802601 0.0355398
\(511\) −22.5147 −0.995990
\(512\) 20.6920i 0.914468i
\(513\) 0.750311i 0.0331271i
\(514\) 12.6088i 0.556150i
\(515\) 54.1062i 2.38420i
\(516\) 0.0355783 0.00156625
\(517\) −13.1249 −0.577234
\(518\) 27.9046i 1.22606i
\(519\) −0.0755813 −0.00331765
\(520\) 11.5362 + 36.5325i 0.505896 + 1.60206i
\(521\) 21.5470 0.943992 0.471996 0.881601i \(-0.343534\pi\)
0.471996 + 0.881601i \(0.343534\pi\)
\(522\) 13.5231i 0.591891i
\(523\) −35.8946 −1.56956 −0.784781 0.619773i \(-0.787225\pi\)
−0.784781 + 0.619773i \(0.787225\pi\)
\(524\) −1.86599 −0.0815163
\(525\) 0.629550i 0.0274758i
\(526\) 6.73363i 0.293600i
\(527\) 3.75015i 0.163359i
\(528\) 0.301501i 0.0131212i
\(529\) 5.23865 0.227768
\(530\) 34.2065 1.48584
\(531\) 36.3134i 1.57587i
\(532\) 0.546892 0.0237108
\(533\) 27.3176 8.62633i 1.18326 0.373648i
\(534\) 0.569904 0.0246622
\(535\) 2.19690i 0.0949801i
\(536\) 21.8710 0.944685
\(537\) 0.232386 0.0100282
\(538\) 2.17737i 0.0938733i
\(539\) 7.96515i 0.343083i
\(540\) 0.0891191i 0.00383507i
\(541\) 12.8955i 0.554420i −0.960809 0.277210i \(-0.910590\pi\)
0.960809 0.277210i \(-0.0894097\pi\)
\(542\) −12.6300 −0.542503
\(543\) 0.788426 0.0338346
\(544\) 2.13239i 0.0914253i
\(545\) 41.4596 1.77593
\(546\) 0.100087 + 0.316953i 0.00428333 + 0.0135643i
\(547\) 28.8880 1.23516 0.617582 0.786507i \(-0.288113\pi\)
0.617582 + 0.786507i \(0.288113\pi\)
\(548\) 0.314027i 0.0134146i
\(549\) −5.25993 −0.224488
\(550\) −26.9748 −1.15021
\(551\) 10.1736i 0.433410i
\(552\) 0.559661i 0.0238207i
\(553\) 9.41555i 0.400390i
\(554\) 6.15241i 0.261391i
\(555\) 1.71004 0.0725873
\(556\) 1.61894 0.0686583
\(557\) 8.61442i 0.365005i 0.983205 + 0.182502i \(0.0584197\pi\)
−0.983205 + 0.182502i \(0.941580\pi\)
\(558\) −4.34592 −0.183978
\(559\) −10.0354 31.7799i −0.424454 1.34415i
\(560\) 26.8945 1.13650
\(561\) 0.269780i 0.0113901i
\(562\) −7.37392 −0.311050
\(563\) 5.36118 0.225947 0.112973 0.993598i \(-0.463963\pi\)
0.112973 + 0.993598i \(0.463963\pi\)
\(564\) 0.0268668i 0.00113130i
\(565\) 28.6218i 1.20413i
\(566\) 47.3560i 1.99052i
\(567\) 14.9410i 0.627465i
\(568\) 2.02442 0.0849427
\(569\) −13.1854 −0.552760 −0.276380 0.961048i \(-0.589135\pi\)
−0.276380 + 0.961048i \(0.589135\pi\)
\(570\) 0.699730i 0.0293085i
\(571\) 36.6258 1.53274 0.766372 0.642397i \(-0.222060\pi\)
0.766372 + 0.642397i \(0.222060\pi\)
\(572\) 0.650464 0.205403i 0.0271973 0.00858833i
\(573\) 0.259551 0.0108429
\(574\) 19.1451i 0.799102i
\(575\) −52.5971 −2.19345
\(576\) 22.6632 0.944299
\(577\) 26.2411i 1.09243i 0.837645 + 0.546215i \(0.183932\pi\)
−0.837645 + 0.546215i \(0.816068\pi\)
\(578\) 4.25580i 0.177018i
\(579\) 0.854846i 0.0355262i
\(580\) 1.20838i 0.0501753i
\(581\) 22.8981 0.949973
\(582\) −0.462642 −0.0191771
\(583\) 11.4979i 0.476195i
\(584\) 37.2802 1.54267
\(585\) 39.7926 12.5657i 1.64522 0.519526i
\(586\) 15.4374 0.637714
\(587\) 15.9650i 0.658945i −0.944165 0.329472i \(-0.893129\pi\)
0.944165 0.329472i \(-0.106871\pi\)
\(588\) −0.0163047 −0.000672395
\(589\) −3.26949 −0.134717
\(590\) 67.7473i 2.78911i
\(591\) 0.262278i 0.0107887i
\(592\) 48.5352i 1.99479i
\(593\) 20.7033i 0.850181i −0.905151 0.425091i \(-0.860242\pi\)
0.905151 0.425091i \(-0.139758\pi\)
\(594\) −0.625430 −0.0256617
\(595\) −24.0649 −0.986566
\(596\) 1.89582i 0.0776558i
\(597\) −0.250725 −0.0102615
\(598\) 26.4805 8.36199i 1.08287 0.341947i
\(599\) −31.4587 −1.28537 −0.642685 0.766131i \(-0.722179\pi\)
−0.642685 + 0.766131i \(0.722179\pi\)
\(600\) 1.04242i 0.0425566i
\(601\) 14.5688 0.594274 0.297137 0.954835i \(-0.403968\pi\)
0.297137 + 0.954835i \(0.403968\pi\)
\(602\) −22.2725 −0.907759
\(603\) 23.8228i 0.970137i
\(604\) 0.0731333i 0.00297575i
\(605\) 28.8101i 1.17130i
\(606\) 0.463898i 0.0188446i
\(607\) −8.19708 −0.332709 −0.166355 0.986066i \(-0.553200\pi\)
−0.166355 + 0.986066i \(0.553200\pi\)
\(608\) −1.85908 −0.0753955
\(609\) 0.197918i 0.00802004i
\(610\) 9.81307 0.397319
\(611\) −23.9985 + 7.57821i −0.970874 + 0.306582i
\(612\) 1.13137 0.0457331
\(613\) 5.02425i 0.202927i 0.994839 + 0.101464i \(0.0323526\pi\)
−0.994839 + 0.101464i \(0.967647\pi\)
\(614\) 16.6002 0.669931
\(615\) 1.17325 0.0473098
\(616\) 8.60608i 0.346749i
\(617\) 20.3301i 0.818460i −0.912431 0.409230i \(-0.865797\pi\)
0.912431 0.409230i \(-0.134203\pi\)
\(618\) 0.777274i 0.0312666i
\(619\) 9.73194i 0.391160i −0.980688 0.195580i \(-0.937341\pi\)
0.980688 0.195580i \(-0.0626589\pi\)
\(620\) 0.388337 0.0155960
\(621\) −1.21950 −0.0489370
\(622\) 20.6772i 0.829082i
\(623\) −17.0878 −0.684609
\(624\) −0.174084 0.551284i −0.00696894 0.0220690i
\(625\) 23.4779 0.939117
\(626\) 15.0255i 0.600541i
\(627\) −0.235202 −0.00939306
\(628\) 0.579422 0.0231215
\(629\) 43.4288i 1.73162i
\(630\) 27.8880i 1.11109i
\(631\) 46.9356i 1.86848i 0.356651 + 0.934238i \(0.383919\pi\)
−0.356651 + 0.934238i \(0.616081\pi\)
\(632\) 15.5904i 0.620154i
\(633\) 0.835090 0.0331919
\(634\) 8.23136 0.326909
\(635\) 70.3034i 2.78991i
\(636\) −0.0235363 −0.000933276
\(637\) 4.59900 + 14.5640i 0.182219 + 0.577046i
\(638\) 8.48032 0.335739
\(639\) 2.20507i 0.0872313i
\(640\) −46.6705 −1.84481
\(641\) −27.2007 −1.07436 −0.537181 0.843467i \(-0.680511\pi\)
−0.537181 + 0.843467i \(0.680511\pi\)
\(642\) 0.0315600i 0.00124557i
\(643\) 41.5545i 1.63875i 0.573257 + 0.819375i \(0.305680\pi\)
−0.573257 + 0.819375i \(0.694320\pi\)
\(644\) 0.888881i 0.0350268i
\(645\) 1.36490i 0.0537427i
\(646\) 17.7706 0.699175
\(647\) −12.4684 −0.490184 −0.245092 0.969500i \(-0.578818\pi\)
−0.245092 + 0.969500i \(0.578818\pi\)
\(648\) 24.7396i 0.971864i
\(649\) 22.7720 0.893881
\(650\) −49.3224 + 15.5750i −1.93458 + 0.610901i
\(651\) −0.0636049 −0.00249287
\(652\) 0.319219i 0.0125016i
\(653\) 48.1876 1.88572 0.942862 0.333182i \(-0.108122\pi\)
0.942862 + 0.333182i \(0.108122\pi\)
\(654\) −0.595597 −0.0232897
\(655\) 71.5854i 2.79707i
\(656\) 33.2996i 1.30013i
\(657\) 40.6070i 1.58423i
\(658\) 16.8190i 0.655672i
\(659\) −8.64394 −0.336720 −0.168360 0.985726i \(-0.553847\pi\)
−0.168360 + 0.985726i \(0.553847\pi\)
\(660\) 0.0279364 0.00108742
\(661\) 25.8464i 1.00531i 0.864487 + 0.502654i \(0.167643\pi\)
−0.864487 + 0.502654i \(0.832357\pi\)
\(662\) 0.981173 0.0381344
\(663\) 0.155769 + 0.493283i 0.00604955 + 0.0191575i
\(664\) −37.9151 −1.47139
\(665\) 20.9805i 0.813589i
\(666\) 50.3282 1.95018
\(667\) 16.5355 0.640256
\(668\) 0.500091i 0.0193491i
\(669\) 0.0468847i 0.00181267i
\(670\) 44.4444i 1.71704i
\(671\) 3.29849i 0.127337i
\(672\) −0.0361666 −0.00139516
\(673\) −13.1020 −0.505044 −0.252522 0.967591i \(-0.581260\pi\)
−0.252522 + 0.967591i \(0.581260\pi\)
\(674\) 6.86586i 0.264463i
\(675\) 2.27144 0.0874278
\(676\) 1.07075 0.751145i 0.0411828 0.0288902i
\(677\) −44.8541 −1.72388 −0.861941 0.507008i \(-0.830752\pi\)
−0.861941 + 0.507008i \(0.830752\pi\)
\(678\) 0.411173i 0.0157910i
\(679\) 13.8717 0.532347
\(680\) 39.8471 1.52807
\(681\) 0.375869i 0.0144033i
\(682\) 2.72532i 0.104358i
\(683\) 0.979482i 0.0374788i 0.999824 + 0.0187394i \(0.00596529\pi\)
−0.999824 + 0.0187394i \(0.994035\pi\)
\(684\) 0.986363i 0.0377146i
\(685\) −12.0471 −0.460295
\(686\) 27.0742 1.03370
\(687\) 0.0562125i 0.00214464i
\(688\) 38.7391 1.47692
\(689\) 6.63880 + 21.0236i 0.252918 + 0.800934i
\(690\) 1.13729 0.0432960
\(691\) 40.0083i 1.52199i 0.648759 + 0.760994i \(0.275289\pi\)
−0.648759 + 0.760994i \(0.724711\pi\)
\(692\) 0.198768 0.00755602
\(693\) 9.37407 0.356091
\(694\) 45.9133i 1.74284i
\(695\) 62.1075i 2.35587i
\(696\) 0.327716i 0.0124220i
\(697\) 29.7962i 1.12861i
\(698\) −12.5287 −0.474216
\(699\) 0.542359 0.0205139
\(700\) 1.65562i 0.0625767i
\(701\) −37.1969 −1.40491 −0.702454 0.711729i \(-0.747912\pi\)
−0.702454 + 0.711729i \(0.747912\pi\)
\(702\) −1.14358 + 0.361118i −0.0431616 + 0.0136295i
\(703\) 37.8625 1.42801
\(704\) 14.2120i 0.535636i
\(705\) −1.03069 −0.0388182
\(706\) −16.8509 −0.634194
\(707\) 13.9094i 0.523116i
\(708\) 0.0466145i 0.00175188i
\(709\) 33.3437i 1.25225i −0.779722 0.626125i \(-0.784640\pi\)
0.779722 0.626125i \(-0.215360\pi\)
\(710\) 4.11384i 0.154390i
\(711\) 16.9817 0.636863
\(712\) 28.2943 1.06037
\(713\) 5.31401i 0.199011i
\(714\) 0.345710 0.0129379
\(715\) −7.87990 24.9538i −0.294692 0.933221i
\(716\) −0.611141 −0.0228394
\(717\) 0.474780i 0.0177310i
\(718\) −7.42828 −0.277221
\(719\) −23.1357 −0.862815 −0.431407 0.902157i \(-0.641983\pi\)
−0.431407 + 0.902157i \(0.641983\pi\)
\(720\) 48.5064i 1.80773i
\(721\) 23.3056i 0.867944i
\(722\) 12.0447i 0.448258i
\(723\) 0.381122i 0.0141741i
\(724\) −2.07344 −0.0770589
\(725\) −30.7989 −1.14384
\(726\) 0.413877i 0.0153604i
\(727\) −4.47177 −0.165849 −0.0829243 0.996556i \(-0.526426\pi\)
−0.0829243 + 0.996556i \(0.526426\pi\)
\(728\) 4.96907 + 15.7359i 0.184166 + 0.583212i
\(729\) −26.9210 −0.997074
\(730\) 75.7575i 2.80391i
\(731\) −34.6634 −1.28207
\(732\) −0.00675203 −0.000249562
\(733\) 50.4881i 1.86482i −0.361402 0.932410i \(-0.617702\pi\)
0.361402 0.932410i \(-0.382298\pi\)
\(734\) 50.9133i 1.87924i
\(735\) 0.625499i 0.0230719i
\(736\) 3.02161i 0.111378i
\(737\) −14.9392 −0.550292
\(738\) 34.5298 1.27106
\(739\) 51.2533i 1.88538i −0.333666 0.942691i \(-0.608286\pi\)
0.333666 0.942691i \(-0.391714\pi\)
\(740\) −4.49716 −0.165319
\(741\) −0.430059 + 0.135803i −0.0157986 + 0.00498887i
\(742\) 14.7340 0.540904
\(743\) 26.3425i 0.966411i −0.875507 0.483206i \(-0.839472\pi\)
0.875507 0.483206i \(-0.160528\pi\)
\(744\) 0.105318 0.00386115
\(745\) 72.7295 2.66460
\(746\) 4.88511i 0.178857i
\(747\) 41.2985i 1.51103i
\(748\) 0.709482i 0.0259412i
\(749\) 0.946285i 0.0345765i
\(750\) −1.04823 −0.0382758
\(751\) −34.0846 −1.24377 −0.621883 0.783110i \(-0.713632\pi\)
−0.621883 + 0.783110i \(0.713632\pi\)
\(752\) 29.2537i 1.06677i
\(753\) −0.0986978 −0.00359675
\(754\) 15.5060 4.89646i 0.564694 0.178319i
\(755\) 2.80562 0.102107
\(756\) 0.0383869i 0.00139612i
\(757\) −50.7996 −1.84634 −0.923171 0.384389i \(-0.874412\pi\)
−0.923171 + 0.384389i \(0.874412\pi\)
\(758\) −22.5711 −0.819819
\(759\) 0.382281i 0.0138759i
\(760\) 34.7399i 1.26015i
\(761\) 9.08920i 0.329483i 0.986337 + 0.164742i \(0.0526790\pi\)
−0.986337 + 0.164742i \(0.947321\pi\)
\(762\) 1.00996i 0.0365870i
\(763\) 17.8582 0.646510
\(764\) −0.682581 −0.0246949
\(765\) 43.4030i 1.56924i
\(766\) 20.6888 0.747518
\(767\) 41.6379 13.1484i 1.50346 0.474760i
\(768\) 0.0921495 0.00332516
\(769\) 11.9781i 0.431942i −0.976400 0.215971i \(-0.930708\pi\)
0.976400 0.215971i \(-0.0692917\pi\)
\(770\) −17.4885 −0.630243
\(771\) 0.332826 0.0119864
\(772\) 2.24812i 0.0809116i
\(773\) 29.6744i 1.06731i −0.845701 0.533657i \(-0.820817\pi\)
0.845701 0.533657i \(-0.179183\pi\)
\(774\) 40.1702i 1.44389i
\(775\) 9.89783i 0.355541i
\(776\) −22.9690 −0.824540
\(777\) 0.736579 0.0264246
\(778\) 14.9556i 0.536183i
\(779\) 25.9771 0.930728
\(780\) 0.0510807 0.0161302i 0.00182898 0.000577554i
\(781\) −1.38280 −0.0494803
\(782\) 28.8831i