Properties

Label 912.2.bo.e.481.1
Level $912$
Weight $2$
Character 912.481
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bo (of order \(9\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 228)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 481.1
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 912.481
Dual form 912.2.bo.e.529.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.939693 + 0.342020i) q^{3} +(0.233956 + 1.32683i) q^{5} +(1.20574 - 2.08840i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\) \(q+(0.939693 + 0.342020i) q^{3} +(0.233956 + 1.32683i) q^{5} +(1.20574 - 2.08840i) q^{7} +(0.766044 + 0.642788i) q^{9} +(-2.97178 - 5.14728i) q^{11} +(3.47178 - 1.26363i) q^{13} +(-0.233956 + 1.32683i) q^{15} +(-0.124485 + 0.104455i) q^{17} +(4.11721 + 1.43128i) q^{19} +(1.84730 - 1.55007i) q^{21} +(1.14156 - 6.47410i) q^{23} +(2.99273 - 1.08926i) q^{25} +(0.500000 + 0.866025i) q^{27} +(1.83022 + 1.53574i) q^{29} +(-1.29813 + 2.24843i) q^{31} +(-1.03209 - 5.85327i) q^{33} +(3.05303 + 1.11121i) q^{35} -6.94356 q^{37} +3.69459 q^{39} +(0.340022 + 0.123758i) q^{41} +(1.98886 + 11.2794i) q^{43} +(-0.673648 + 1.16679i) q^{45} +(5.26991 + 4.42198i) q^{47} +(0.592396 + 1.02606i) q^{49} +(-0.152704 + 0.0555796i) q^{51} +(0.698463 - 3.96118i) q^{53} +(6.13429 - 5.14728i) q^{55} +(3.37939 + 2.75314i) q^{57} +(-9.23055 + 7.74535i) q^{59} +(1.07398 - 6.09083i) q^{61} +(2.26604 - 0.824773i) q^{63} +(2.48886 + 4.31082i) q^{65} +(4.41147 + 3.70167i) q^{67} +(3.28699 - 5.69323i) q^{69} +(-2.11721 - 12.0073i) q^{71} +(8.61721 + 3.13641i) q^{73} +3.18479 q^{75} -14.3327 q^{77} +(-9.10994 - 3.31575i) q^{79} +(0.173648 + 0.984808i) q^{81} +(1.01367 - 1.75573i) q^{83} +(-0.167718 - 0.140732i) q^{85} +(1.19459 + 2.06910i) q^{87} +(-3.24035 + 1.17939i) q^{89} +(1.54710 - 8.77406i) q^{91} +(-1.98886 + 1.66885i) q^{93} +(-0.935822 + 5.79769i) q^{95} +(9.26264 - 7.77228i) q^{97} +(1.03209 - 5.85327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{5} - 3 q^{7} + O(q^{10}) \) \( 6 q + 6 q^{5} - 3 q^{7} - 3 q^{11} + 6 q^{13} - 6 q^{15} + 12 q^{17} - 6 q^{19} + 9 q^{21} + 15 q^{23} + 3 q^{27} - 12 q^{29} + 6 q^{31} + 3 q^{33} + 6 q^{35} - 12 q^{37} + 18 q^{39} - 18 q^{41} + 18 q^{43} - 3 q^{45} + 3 q^{47} - 3 q^{51} - 24 q^{53} + 27 q^{55} + 9 q^{57} - 18 q^{59} - 9 q^{61} + 9 q^{63} + 21 q^{65} + 6 q^{67} + 12 q^{69} + 18 q^{71} + 21 q^{73} + 12 q^{75} - 48 q^{77} - 6 q^{79} - 15 q^{83} + 27 q^{85} + 3 q^{87} + 15 q^{89} - 30 q^{91} - 18 q^{93} - 24 q^{95} + 9 q^{97} - 3 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.939693 + 0.342020i 0.542532 + 0.197465i
\(4\) 0 0
\(5\) 0.233956 + 1.32683i 0.104628 + 0.593375i 0.991368 + 0.131107i \(0.0418532\pi\)
−0.886740 + 0.462268i \(0.847036\pi\)
\(6\) 0 0
\(7\) 1.20574 2.08840i 0.455726 0.789340i −0.543004 0.839730i \(-0.682713\pi\)
0.998730 + 0.0503900i \(0.0160464\pi\)
\(8\) 0 0
\(9\) 0.766044 + 0.642788i 0.255348 + 0.214263i
\(10\) 0 0
\(11\) −2.97178 5.14728i −0.896026 1.55196i −0.832530 0.553980i \(-0.813108\pi\)
−0.0634960 0.997982i \(-0.520225\pi\)
\(12\) 0 0
\(13\) 3.47178 1.26363i 0.962899 0.350467i 0.187730 0.982221i \(-0.439887\pi\)
0.775169 + 0.631754i \(0.217665\pi\)
\(14\) 0 0
\(15\) −0.233956 + 1.32683i −0.0604071 + 0.342585i
\(16\) 0 0
\(17\) −0.124485 + 0.104455i −0.0301921 + 0.0253342i −0.657759 0.753229i \(-0.728495\pi\)
0.627567 + 0.778563i \(0.284051\pi\)
\(18\) 0 0
\(19\) 4.11721 + 1.43128i 0.944553 + 0.328359i
\(20\) 0 0
\(21\) 1.84730 1.55007i 0.403113 0.338252i
\(22\) 0 0
\(23\) 1.14156 6.47410i 0.238032 1.34994i −0.598103 0.801419i \(-0.704079\pi\)
0.836134 0.548525i \(-0.184810\pi\)
\(24\) 0 0
\(25\) 2.99273 1.08926i 0.598545 0.217853i
\(26\) 0 0
\(27\) 0.500000 + 0.866025i 0.0962250 + 0.166667i
\(28\) 0 0
\(29\) 1.83022 + 1.53574i 0.339864 + 0.285180i 0.796705 0.604369i \(-0.206575\pi\)
−0.456841 + 0.889548i \(0.651019\pi\)
\(30\) 0 0
\(31\) −1.29813 + 2.24843i −0.233152 + 0.403830i −0.958734 0.284305i \(-0.908237\pi\)
0.725582 + 0.688135i \(0.241571\pi\)
\(32\) 0 0
\(33\) −1.03209 5.85327i −0.179664 1.01892i
\(34\) 0 0
\(35\) 3.05303 + 1.11121i 0.516057 + 0.187829i
\(36\) 0 0
\(37\) −6.94356 −1.14151 −0.570757 0.821119i \(-0.693350\pi\)
−0.570757 + 0.821119i \(0.693350\pi\)
\(38\) 0 0
\(39\) 3.69459 0.591608
\(40\) 0 0
\(41\) 0.340022 + 0.123758i 0.0531026 + 0.0193278i 0.368435 0.929654i \(-0.379894\pi\)
−0.315332 + 0.948981i \(0.602116\pi\)
\(42\) 0 0
\(43\) 1.98886 + 11.2794i 0.303298 + 1.72009i 0.631411 + 0.775448i \(0.282476\pi\)
−0.328114 + 0.944638i \(0.606413\pi\)
\(44\) 0 0
\(45\) −0.673648 + 1.16679i −0.100422 + 0.173935i
\(46\) 0 0
\(47\) 5.26991 + 4.42198i 0.768696 + 0.645013i 0.940375 0.340140i \(-0.110475\pi\)
−0.171679 + 0.985153i \(0.554919\pi\)
\(48\) 0 0
\(49\) 0.592396 + 1.02606i 0.0846280 + 0.146580i
\(50\) 0 0
\(51\) −0.152704 + 0.0555796i −0.0213828 + 0.00778270i
\(52\) 0 0
\(53\) 0.698463 3.96118i 0.0959413 0.544110i −0.898514 0.438946i \(-0.855352\pi\)
0.994455 0.105164i \(-0.0335369\pi\)
\(54\) 0 0
\(55\) 6.13429 5.14728i 0.827147 0.694059i
\(56\) 0 0
\(57\) 3.37939 + 2.75314i 0.447611 + 0.364662i
\(58\) 0 0
\(59\) −9.23055 + 7.74535i −1.20172 + 1.00836i −0.202136 + 0.979357i \(0.564788\pi\)
−0.999579 + 0.0290016i \(0.990767\pi\)
\(60\) 0 0
\(61\) 1.07398 6.09083i 0.137509 0.779851i −0.835571 0.549383i \(-0.814863\pi\)
0.973080 0.230469i \(-0.0740259\pi\)
\(62\) 0 0
\(63\) 2.26604 0.824773i 0.285495 0.103912i
\(64\) 0 0
\(65\) 2.48886 + 4.31082i 0.308705 + 0.534692i
\(66\) 0 0
\(67\) 4.41147 + 3.70167i 0.538947 + 0.452231i 0.871178 0.490968i \(-0.163357\pi\)
−0.332230 + 0.943198i \(0.607801\pi\)
\(68\) 0 0
\(69\) 3.28699 5.69323i 0.395707 0.685385i
\(70\) 0 0
\(71\) −2.11721 12.0073i −0.251267 1.42500i −0.805477 0.592628i \(-0.798091\pi\)
0.554210 0.832377i \(-0.313020\pi\)
\(72\) 0 0
\(73\) 8.61721 + 3.13641i 1.00857 + 0.367089i 0.792883 0.609374i \(-0.208579\pi\)
0.215685 + 0.976463i \(0.430801\pi\)
\(74\) 0 0
\(75\) 3.18479 0.367748
\(76\) 0 0
\(77\) −14.3327 −1.63337
\(78\) 0 0
\(79\) −9.10994 3.31575i −1.02495 0.373051i −0.225793 0.974175i \(-0.572497\pi\)
−0.799155 + 0.601125i \(0.794719\pi\)
\(80\) 0 0
\(81\) 0.173648 + 0.984808i 0.0192942 + 0.109423i
\(82\) 0 0
\(83\) 1.01367 1.75573i 0.111265 0.192716i −0.805016 0.593254i \(-0.797843\pi\)
0.916280 + 0.400537i \(0.131176\pi\)
\(84\) 0 0
\(85\) −0.167718 0.140732i −0.0181916 0.0152646i
\(86\) 0 0
\(87\) 1.19459 + 2.06910i 0.128074 + 0.221830i
\(88\) 0 0
\(89\) −3.24035 + 1.17939i −0.343477 + 0.125015i −0.507998 0.861358i \(-0.669614\pi\)
0.164521 + 0.986374i \(0.447392\pi\)
\(90\) 0 0
\(91\) 1.54710 8.77406i 0.162181 0.919771i
\(92\) 0 0
\(93\) −1.98886 + 1.66885i −0.206235 + 0.173051i
\(94\) 0 0
\(95\) −0.935822 + 5.79769i −0.0960133 + 0.594830i
\(96\) 0 0
\(97\) 9.26264 7.77228i 0.940479 0.789155i −0.0371898 0.999308i \(-0.511841\pi\)
0.977669 + 0.210153i \(0.0673962\pi\)
\(98\) 0 0
\(99\) 1.03209 5.85327i 0.103729 0.588275i
\(100\) 0 0
\(101\) 3.69846 1.34613i 0.368011 0.133945i −0.151394 0.988474i \(-0.548376\pi\)
0.519404 + 0.854529i \(0.326154\pi\)
\(102\) 0 0
\(103\) −6.15657 10.6635i −0.606625 1.05071i −0.991792 0.127859i \(-0.959190\pi\)
0.385167 0.922847i \(-0.374144\pi\)
\(104\) 0 0
\(105\) 2.48886 + 2.08840i 0.242887 + 0.203807i
\(106\) 0 0
\(107\) −6.71688 + 11.6340i −0.649345 + 1.12470i 0.333934 + 0.942596i \(0.391624\pi\)
−0.983279 + 0.182103i \(0.941710\pi\)
\(108\) 0 0
\(109\) 0.393933 + 2.23411i 0.0377320 + 0.213989i 0.997844 0.0656260i \(-0.0209044\pi\)
−0.960112 + 0.279615i \(0.909793\pi\)
\(110\) 0 0
\(111\) −6.52481 2.37484i −0.619308 0.225410i
\(112\) 0 0
\(113\) −12.7101 −1.19566 −0.597832 0.801622i \(-0.703971\pi\)
−0.597832 + 0.801622i \(0.703971\pi\)
\(114\) 0 0
\(115\) 8.85710 0.825929
\(116\) 0 0
\(117\) 3.47178 + 1.26363i 0.320966 + 0.116822i
\(118\) 0 0
\(119\) 0.0680482 + 0.385920i 0.00623797 + 0.0353773i
\(120\) 0 0
\(121\) −12.1630 + 21.0669i −1.10572 + 1.91517i
\(122\) 0 0
\(123\) 0.277189 + 0.232589i 0.0249933 + 0.0209718i
\(124\) 0 0
\(125\) 5.51367 + 9.54996i 0.493158 + 0.854174i
\(126\) 0 0
\(127\) 7.26517 2.64430i 0.644679 0.234644i 0.00107137 0.999999i \(-0.499659\pi\)
0.643608 + 0.765355i \(0.277437\pi\)
\(128\) 0 0
\(129\) −1.98886 + 11.2794i −0.175109 + 0.993092i
\(130\) 0 0
\(131\) −9.62701 + 8.07802i −0.841116 + 0.705780i −0.957814 0.287387i \(-0.907213\pi\)
0.116699 + 0.993167i \(0.462769\pi\)
\(132\) 0 0
\(133\) 7.95336 6.87262i 0.689644 0.595932i
\(134\) 0 0
\(135\) −1.03209 + 0.866025i −0.0888281 + 0.0745356i
\(136\) 0 0
\(137\) 2.72803 15.4714i 0.233071 1.32181i −0.613567 0.789642i \(-0.710266\pi\)
0.846638 0.532169i \(-0.178623\pi\)
\(138\) 0 0
\(139\) 3.03936 1.10624i 0.257795 0.0938298i −0.209890 0.977725i \(-0.567310\pi\)
0.467685 + 0.883895i \(0.345088\pi\)
\(140\) 0 0
\(141\) 3.43969 + 5.95772i 0.289674 + 0.501731i
\(142\) 0 0
\(143\) −16.8216 14.1150i −1.40669 1.18036i
\(144\) 0 0
\(145\) −1.60947 + 2.78768i −0.133659 + 0.231505i
\(146\) 0 0
\(147\) 0.205737 + 1.16679i 0.0169689 + 0.0962355i
\(148\) 0 0
\(149\) −4.19119 1.52547i −0.343356 0.124971i 0.164586 0.986363i \(-0.447371\pi\)
−0.507942 + 0.861392i \(0.669593\pi\)
\(150\) 0 0
\(151\) −8.94862 −0.728228 −0.364114 0.931354i \(-0.618628\pi\)
−0.364114 + 0.931354i \(0.618628\pi\)
\(152\) 0 0
\(153\) −0.162504 −0.0131377
\(154\) 0 0
\(155\) −3.28699 1.19637i −0.264017 0.0960944i
\(156\) 0 0
\(157\) −2.00047 11.3452i −0.159655 0.905446i −0.954406 0.298511i \(-0.903510\pi\)
0.794751 0.606935i \(-0.207601\pi\)
\(158\) 0 0
\(159\) 2.01114 3.48340i 0.159494 0.276252i
\(160\) 0 0
\(161\) −12.1441 10.1901i −0.957088 0.803092i
\(162\) 0 0
\(163\) −5.26217 9.11435i −0.412165 0.713891i 0.582961 0.812500i \(-0.301894\pi\)
−0.995126 + 0.0986089i \(0.968561\pi\)
\(164\) 0 0
\(165\) 7.52481 2.73881i 0.585806 0.213216i
\(166\) 0 0
\(167\) −1.86484 + 10.5760i −0.144305 + 0.818397i 0.823617 + 0.567147i \(0.191953\pi\)
−0.967922 + 0.251250i \(0.919158\pi\)
\(168\) 0 0
\(169\) 0.497941 0.417822i 0.0383031 0.0321401i
\(170\) 0 0
\(171\) 2.23396 + 3.74292i 0.170835 + 0.286228i
\(172\) 0 0
\(173\) −5.77584 + 4.84651i −0.439129 + 0.368473i −0.835383 0.549668i \(-0.814754\pi\)
0.396254 + 0.918141i \(0.370310\pi\)
\(174\) 0 0
\(175\) 1.33363 7.56337i 0.100813 0.571737i
\(176\) 0 0
\(177\) −11.3229 + 4.12122i −0.851085 + 0.309770i
\(178\) 0 0
\(179\) 13.1814 + 22.8308i 0.985223 + 1.70646i 0.640940 + 0.767591i \(0.278545\pi\)
0.344283 + 0.938866i \(0.388122\pi\)
\(180\) 0 0
\(181\) 16.1570 + 13.5574i 1.20094 + 1.00771i 0.999603 + 0.0281899i \(0.00897431\pi\)
0.201341 + 0.979521i \(0.435470\pi\)
\(182\) 0 0
\(183\) 3.09240 5.35619i 0.228597 0.395941i
\(184\) 0 0
\(185\) −1.62449 9.21291i −0.119435 0.677347i
\(186\) 0 0
\(187\) 0.907604 + 0.330341i 0.0663706 + 0.0241569i
\(188\) 0 0
\(189\) 2.41147 0.175409
\(190\) 0 0
\(191\) 0.255777 0.0185074 0.00925370 0.999957i \(-0.497054\pi\)
0.00925370 + 0.999957i \(0.497054\pi\)
\(192\) 0 0
\(193\) −13.4829 4.90738i −0.970522 0.353241i −0.192374 0.981322i \(-0.561619\pi\)
−0.778148 + 0.628081i \(0.783841\pi\)
\(194\) 0 0
\(195\) 0.864370 + 4.90209i 0.0618989 + 0.351046i
\(196\) 0 0
\(197\) −11.8405 + 20.5083i −0.843600 + 1.46116i 0.0432316 + 0.999065i \(0.486235\pi\)
−0.886832 + 0.462093i \(0.847099\pi\)
\(198\) 0 0
\(199\) 9.03596 + 7.58207i 0.640542 + 0.537479i 0.904185 0.427142i \(-0.140479\pi\)
−0.263642 + 0.964620i \(0.584924\pi\)
\(200\) 0 0
\(201\) 2.87939 + 4.98724i 0.203096 + 0.351773i
\(202\) 0 0
\(203\) 5.41400 1.97053i 0.379988 0.138304i
\(204\) 0 0
\(205\) −0.0846555 + 0.480105i −0.00591260 + 0.0335320i
\(206\) 0 0
\(207\) 5.03596 4.22567i 0.350023 0.293704i
\(208\) 0 0
\(209\) −4.86824 25.4459i −0.336743 1.76013i
\(210\) 0 0
\(211\) −21.3405 + 17.9068i −1.46914 + 1.23275i −0.552211 + 0.833705i \(0.686216\pi\)
−0.916929 + 0.399050i \(0.869340\pi\)
\(212\) 0 0
\(213\) 2.11721 12.0073i 0.145069 0.822727i
\(214\) 0 0
\(215\) −14.5005 + 5.27774i −0.988924 + 0.359939i
\(216\) 0 0
\(217\) 3.13041 + 5.42204i 0.212506 + 0.368072i
\(218\) 0 0
\(219\) 7.02481 + 5.89452i 0.474693 + 0.398315i
\(220\) 0 0
\(221\) −0.300193 + 0.519949i −0.0201931 + 0.0349756i
\(222\) 0 0
\(223\) 4.29561 + 24.3616i 0.287655 + 1.63137i 0.695644 + 0.718386i \(0.255119\pi\)
−0.407989 + 0.912987i \(0.633770\pi\)
\(224\) 0 0
\(225\) 2.99273 + 1.08926i 0.199515 + 0.0726175i
\(226\) 0 0
\(227\) 22.0155 1.46122 0.730609 0.682796i \(-0.239236\pi\)
0.730609 + 0.682796i \(0.239236\pi\)
\(228\) 0 0
\(229\) −9.29591 −0.614291 −0.307146 0.951663i \(-0.599374\pi\)
−0.307146 + 0.951663i \(0.599374\pi\)
\(230\) 0 0
\(231\) −13.4684 4.90209i −0.886154 0.322534i
\(232\) 0 0
\(233\) −1.38713 7.86678i −0.0908736 0.515370i −0.995934 0.0900867i \(-0.971286\pi\)
0.905060 0.425283i \(-0.139826\pi\)
\(234\) 0 0
\(235\) −4.63429 + 8.02682i −0.302307 + 0.523612i
\(236\) 0 0
\(237\) −7.42649 6.23156i −0.482402 0.404784i
\(238\) 0 0
\(239\) −13.2246 22.9057i −0.855430 1.48165i −0.876246 0.481864i \(-0.839960\pi\)
0.0208161 0.999783i \(-0.493374\pi\)
\(240\) 0 0
\(241\) 2.57398 0.936851i 0.165804 0.0603479i −0.257784 0.966202i \(-0.582992\pi\)
0.423589 + 0.905855i \(0.360770\pi\)
\(242\) 0 0
\(243\) −0.173648 + 0.984808i −0.0111395 + 0.0631754i
\(244\) 0 0
\(245\) −1.22281 + 1.02606i −0.0781225 + 0.0655526i
\(246\) 0 0
\(247\) 16.1027 0.233508i 1.02459 0.0148578i
\(248\) 0 0
\(249\) 1.55303 1.30315i 0.0984195 0.0825838i
\(250\) 0 0
\(251\) −2.64455 + 14.9980i −0.166923 + 0.946665i 0.780137 + 0.625608i \(0.215149\pi\)
−0.947060 + 0.321057i \(0.895962\pi\)
\(252\) 0 0
\(253\) −36.7165 + 13.3637i −2.30834 + 0.840169i
\(254\) 0 0
\(255\) −0.109470 0.189608i −0.00685530 0.0118737i
\(256\) 0 0
\(257\) 9.98545 + 8.37879i 0.622875 + 0.522655i 0.898706 0.438552i \(-0.144508\pi\)
−0.275831 + 0.961206i \(0.588953\pi\)
\(258\) 0 0
\(259\) −8.37211 + 14.5009i −0.520218 + 0.901043i
\(260\) 0 0
\(261\) 0.414878 + 2.35289i 0.0256803 + 0.145640i
\(262\) 0 0
\(263\) −11.2071 4.07904i −0.691058 0.251525i −0.0274700 0.999623i \(-0.508745\pi\)
−0.663588 + 0.748098i \(0.730967\pi\)
\(264\) 0 0
\(265\) 5.41921 0.332900
\(266\) 0 0
\(267\) −3.44831 −0.211033
\(268\) 0 0
\(269\) −24.2986 8.84397i −1.48151 0.539226i −0.530312 0.847802i \(-0.677925\pi\)
−0.951200 + 0.308576i \(0.900148\pi\)
\(270\) 0 0
\(271\) −2.06165 11.6922i −0.125236 0.710251i −0.981167 0.193161i \(-0.938126\pi\)
0.855931 0.517090i \(-0.172985\pi\)
\(272\) 0 0
\(273\) 4.45471 7.71578i 0.269611 0.466980i
\(274\) 0 0
\(275\) −14.5005 12.1673i −0.874411 0.733718i
\(276\) 0 0
\(277\) −7.20574 12.4807i −0.432951 0.749893i 0.564175 0.825655i \(-0.309194\pi\)
−0.997126 + 0.0757624i \(0.975861\pi\)
\(278\) 0 0
\(279\) −2.43969 + 0.887975i −0.146061 + 0.0531617i
\(280\) 0 0
\(281\) −0.456929 + 2.59137i −0.0272581 + 0.154588i −0.995399 0.0958183i \(-0.969453\pi\)
0.968141 + 0.250407i \(0.0805643\pi\)
\(282\) 0 0
\(283\) −4.66637 + 3.91555i −0.277387 + 0.232755i −0.770858 0.637007i \(-0.780172\pi\)
0.493471 + 0.869762i \(0.335728\pi\)
\(284\) 0 0
\(285\) −2.86231 + 5.12797i −0.169549 + 0.303755i
\(286\) 0 0
\(287\) 0.668434 0.560882i 0.0394564 0.0331078i
\(288\) 0 0
\(289\) −2.94743 + 16.7157i −0.173378 + 0.983278i
\(290\) 0 0
\(291\) 11.3623 4.13554i 0.666070 0.242430i
\(292\) 0 0
\(293\) 16.3653 + 28.3455i 0.956071 + 1.65596i 0.731897 + 0.681415i \(0.238635\pi\)
0.224174 + 0.974549i \(0.428032\pi\)
\(294\) 0 0
\(295\) −12.4363 10.4353i −0.724069 0.607566i
\(296\) 0 0
\(297\) 2.97178 5.14728i 0.172440 0.298675i
\(298\) 0 0
\(299\) −4.21760 23.9192i −0.243910 1.38328i
\(300\) 0 0
\(301\) 25.9538 + 9.44642i 1.49595 + 0.544483i
\(302\) 0 0
\(303\) 3.93582 0.226107
\(304\) 0 0
\(305\) 8.33275 0.477132
\(306\) 0 0
\(307\) −5.83497 2.12376i −0.333019 0.121209i 0.170098 0.985427i \(-0.445592\pi\)
−0.503118 + 0.864218i \(0.667814\pi\)
\(308\) 0 0
\(309\) −2.13816 12.1261i −0.121635 0.689829i
\(310\) 0 0
\(311\) 1.55303 2.68993i 0.0880644 0.152532i −0.818628 0.574323i \(-0.805265\pi\)
0.906693 + 0.421791i \(0.138599\pi\)
\(312\) 0 0
\(313\) −12.9251 10.8455i −0.730572 0.613023i 0.199715 0.979854i \(-0.435998\pi\)
−0.930288 + 0.366831i \(0.880443\pi\)
\(314\) 0 0
\(315\) 1.62449 + 2.81369i 0.0915294 + 0.158534i
\(316\) 0 0
\(317\) −13.5560 + 4.93399i −0.761382 + 0.277120i −0.693387 0.720565i \(-0.743882\pi\)
−0.0679951 + 0.997686i \(0.521660\pi\)
\(318\) 0 0
\(319\) 2.46585 13.9845i 0.138061 0.782984i
\(320\) 0 0
\(321\) −10.2909 + 8.63506i −0.574380 + 0.481962i
\(322\) 0 0
\(323\) −0.662037 + 0.251892i −0.0368367 + 0.0140156i
\(324\) 0 0
\(325\) 9.01367 7.56337i 0.499988 0.419540i
\(326\) 0 0
\(327\) −0.393933 + 2.23411i −0.0217846 + 0.123546i
\(328\) 0 0
\(329\) 15.5890 5.67393i 0.859449 0.312814i
\(330\) 0 0
\(331\) −4.49866 7.79190i −0.247268 0.428282i 0.715498 0.698614i \(-0.246200\pi\)
−0.962767 + 0.270333i \(0.912866\pi\)
\(332\) 0 0
\(333\) −5.31908 4.46324i −0.291484 0.244584i
\(334\) 0 0
\(335\) −3.87939 + 6.71929i −0.211953 + 0.367114i
\(336\) 0 0
\(337\) −0.395582 2.24346i −0.0215487 0.122209i 0.972136 0.234418i \(-0.0753185\pi\)
−0.993685 + 0.112209i \(0.964207\pi\)
\(338\) 0 0
\(339\) −11.9436 4.34710i −0.648685 0.236102i
\(340\) 0 0
\(341\) 15.4311 0.835640
\(342\) 0 0
\(343\) 19.7374 1.06572
\(344\) 0 0
\(345\) 8.32295 + 3.02931i 0.448092 + 0.163092i
\(346\) 0 0
\(347\) −1.30288 7.38901i −0.0699423 0.396663i −0.999601 0.0282410i \(-0.991009\pi\)
0.929659 0.368422i \(-0.120102\pi\)
\(348\) 0 0
\(349\) 14.5175 25.1451i 0.777106 1.34599i −0.156497 0.987678i \(-0.550020\pi\)
0.933603 0.358309i \(-0.116647\pi\)
\(350\) 0 0
\(351\) 2.83022 + 2.37484i 0.151066 + 0.126759i
\(352\) 0 0
\(353\) 11.7096 + 20.2816i 0.623240 + 1.07948i 0.988878 + 0.148726i \(0.0475172\pi\)
−0.365639 + 0.930757i \(0.619150\pi\)
\(354\) 0 0
\(355\) 15.4363 5.61835i 0.819273 0.298191i
\(356\) 0 0
\(357\) −0.0680482 + 0.385920i −0.00360149 + 0.0204251i
\(358\) 0 0
\(359\) 27.3614 22.9590i 1.44408 1.21173i 0.507321 0.861757i \(-0.330636\pi\)
0.936761 0.349971i \(-0.113808\pi\)
\(360\) 0 0
\(361\) 14.9029 + 11.7858i 0.784361 + 0.620305i
\(362\) 0 0
\(363\) −18.6348 + 15.6364i −0.978071 + 0.820699i
\(364\) 0 0
\(365\) −2.14543 + 12.1673i −0.112297 + 0.636867i
\(366\) 0 0
\(367\) −19.6694 + 7.15906i −1.02673 + 0.373700i −0.799836 0.600219i \(-0.795080\pi\)
−0.226897 + 0.973919i \(0.572858\pi\)
\(368\) 0 0
\(369\) 0.180922 + 0.313366i 0.00941843 + 0.0163132i
\(370\) 0 0
\(371\) −7.43036 6.23481i −0.385765 0.323695i
\(372\) 0 0
\(373\) 1.44562 2.50389i 0.0748515 0.129647i −0.826170 0.563421i \(-0.809485\pi\)
0.901022 + 0.433774i \(0.142818\pi\)
\(374\) 0 0
\(375\) 1.91488 + 10.8598i 0.0988839 + 0.560798i
\(376\) 0 0
\(377\) 8.29473 + 3.01903i 0.427200 + 0.155488i
\(378\) 0 0
\(379\) 24.7374 1.27068 0.635338 0.772234i \(-0.280861\pi\)
0.635338 + 0.772234i \(0.280861\pi\)
\(380\) 0 0
\(381\) 7.73143 0.396093
\(382\) 0 0
\(383\) 13.9611 + 5.08143i 0.713379 + 0.259649i 0.673112 0.739540i \(-0.264957\pi\)
0.0402667 + 0.999189i \(0.487179\pi\)
\(384\) 0 0
\(385\) −3.35323 19.0171i −0.170896 0.969201i
\(386\) 0 0
\(387\) −5.72668 + 9.91890i −0.291104 + 0.504206i
\(388\) 0 0
\(389\) 24.3286 + 20.4141i 1.23351 + 1.03504i 0.998003 + 0.0631656i \(0.0201196\pi\)
0.235507 + 0.971873i \(0.424325\pi\)
\(390\) 0 0
\(391\) 0.534148 + 0.925172i 0.0270130 + 0.0467880i
\(392\) 0 0
\(393\) −11.8093 + 4.29823i −0.595699 + 0.216817i
\(394\) 0 0
\(395\) 2.26810 12.8631i 0.114121 0.647211i
\(396\) 0 0
\(397\) −13.6138 + 11.4233i −0.683257 + 0.573321i −0.916956 0.398988i \(-0.869362\pi\)
0.233699 + 0.972309i \(0.424917\pi\)
\(398\) 0 0
\(399\) 9.82429 3.73794i 0.491830 0.187131i
\(400\) 0 0
\(401\) −26.8371 + 22.5190i −1.34018 + 1.12454i −0.358600 + 0.933491i \(0.616746\pi\)
−0.981580 + 0.191053i \(0.938810\pi\)
\(402\) 0 0
\(403\) −1.66566 + 9.44642i −0.0829724 + 0.470560i
\(404\) 0 0
\(405\) −1.26604 + 0.460802i −0.0629103 + 0.0228975i
\(406\) 0 0
\(407\) 20.6348 + 35.7404i 1.02283 + 1.77159i
\(408\) 0 0
\(409\) −8.83203 7.41096i −0.436716 0.366448i 0.397763 0.917488i \(-0.369787\pi\)
−0.834479 + 0.551040i \(0.814231\pi\)
\(410\) 0 0
\(411\) 7.85504 13.6053i 0.387460 0.671101i
\(412\) 0 0
\(413\) 5.04576 + 28.6159i 0.248286 + 1.40810i
\(414\) 0 0
\(415\) 2.56670 + 0.934204i 0.125995 + 0.0458583i
\(416\) 0 0
\(417\) 3.23442 0.158390
\(418\) 0 0
\(419\) 34.7692 1.69859 0.849293 0.527921i \(-0.177028\pi\)
0.849293 + 0.527921i \(0.177028\pi\)
\(420\) 0 0
\(421\) 14.7579 + 5.37143i 0.719256 + 0.261788i 0.675610 0.737259i \(-0.263880\pi\)
0.0436459 + 0.999047i \(0.486103\pi\)
\(422\) 0 0
\(423\) 1.19459 + 6.77487i 0.0580831 + 0.329406i
\(424\) 0 0
\(425\) −0.258770 + 0.448204i −0.0125522 + 0.0217411i
\(426\) 0 0
\(427\) −11.4251 9.58683i −0.552902 0.463939i
\(428\) 0 0
\(429\) −10.9795 19.0171i −0.530096 0.918154i
\(430\) 0 0
\(431\) −12.6604 + 4.60802i −0.609832 + 0.221961i −0.628430 0.777866i \(-0.716302\pi\)
0.0185977 + 0.999827i \(0.494080\pi\)
\(432\) 0 0
\(433\) 2.04442 11.5945i 0.0982483 0.557194i −0.895455 0.445152i \(-0.853150\pi\)
0.993703 0.112042i \(-0.0357392\pi\)
\(434\) 0 0
\(435\) −2.46585 + 2.06910i −0.118229 + 0.0992055i
\(436\) 0 0
\(437\) 13.9663 25.0214i 0.668100 1.19693i
\(438\) 0 0
\(439\) −12.0385 + 10.1015i −0.574566 + 0.482118i −0.883157 0.469077i \(-0.844587\pi\)
0.308592 + 0.951195i \(0.400142\pi\)
\(440\) 0 0
\(441\) −0.205737 + 1.16679i −0.00979700 + 0.0555616i
\(442\) 0 0
\(443\) −14.6998 + 5.35029i −0.698409 + 0.254200i −0.666731 0.745298i \(-0.732307\pi\)
−0.0316775 + 0.999498i \(0.510085\pi\)
\(444\) 0 0
\(445\) −2.32295 4.02346i −0.110118 0.190731i
\(446\) 0 0
\(447\) −3.41669 2.86694i −0.161604 0.135602i
\(448\) 0 0
\(449\) 9.09286 15.7493i 0.429119 0.743255i −0.567676 0.823252i \(-0.692158\pi\)
0.996795 + 0.0799963i \(0.0254909\pi\)
\(450\) 0 0
\(451\) −0.373455 2.11797i −0.0175853 0.0997314i
\(452\) 0 0
\(453\) −8.40895 3.06061i −0.395087 0.143800i
\(454\) 0 0
\(455\) 12.0036 0.562738
\(456\) 0 0
\(457\) 16.8111 0.786390 0.393195 0.919455i \(-0.371370\pi\)
0.393195 + 0.919455i \(0.371370\pi\)
\(458\) 0 0
\(459\) −0.152704 0.0555796i −0.00712760 0.00259423i
\(460\) 0 0
\(461\) −2.19429 12.4444i −0.102198 0.579595i −0.992302 0.123838i \(-0.960480\pi\)
0.890104 0.455757i \(-0.150631\pi\)
\(462\) 0 0
\(463\) −2.94743 + 5.10510i −0.136979 + 0.237254i −0.926352 0.376660i \(-0.877073\pi\)
0.789373 + 0.613914i \(0.210406\pi\)
\(464\) 0 0
\(465\) −2.67958 2.24843i −0.124262 0.104269i
\(466\) 0 0
\(467\) −2.68479 4.65020i −0.124237 0.215185i 0.797197 0.603719i \(-0.206315\pi\)
−0.921435 + 0.388534i \(0.872982\pi\)
\(468\) 0 0
\(469\) 13.0496 4.74968i 0.602576 0.219320i
\(470\) 0 0
\(471\) 2.00047 11.3452i 0.0921766 0.522760i
\(472\) 0 0
\(473\) 52.1475 43.7570i 2.39775 2.01195i
\(474\) 0 0
\(475\) 13.8807 0.201288i 0.636892 0.00923571i
\(476\) 0 0
\(477\) 3.08125 2.58548i 0.141081 0.118381i
\(478\) 0 0
\(479\) 3.44650 19.5461i 0.157475 0.893083i −0.799014 0.601313i \(-0.794645\pi\)
0.956488 0.291770i \(-0.0942442\pi\)
\(480\) 0 0
\(481\) −24.1065 + 8.77406i −1.09916 + 0.400063i
\(482\) 0 0
\(483\) −7.92649 13.7291i −0.360668 0.624695i
\(484\) 0 0
\(485\) 12.4795 + 10.4716i 0.566666 + 0.475489i
\(486\) 0 0
\(487\) 6.50387 11.2650i 0.294718 0.510467i −0.680201 0.733026i \(-0.738107\pi\)
0.974919 + 0.222558i \(0.0714408\pi\)
\(488\) 0 0
\(489\) −1.82753 10.3645i −0.0826439 0.468697i
\(490\) 0 0
\(491\) 27.9538 + 10.1744i 1.26154 + 0.459163i 0.884285 0.466947i \(-0.154646\pi\)
0.377254 + 0.926110i \(0.376869\pi\)
\(492\) 0 0
\(493\) −0.388252 −0.0174860
\(494\) 0 0
\(495\) 8.00774 0.359921
\(496\) 0 0
\(497\) −27.6288 10.0561i −1.23932 0.451076i
\(498\) 0 0
\(499\) −2.60220 14.7578i −0.116490 0.660649i −0.986002 0.166736i \(-0.946677\pi\)
0.869511 0.493913i \(-0.164434\pi\)
\(500\) 0 0
\(501\) −5.36959 + 9.30039i −0.239895 + 0.415511i
\(502\) 0 0
\(503\) 13.5646 + 11.3821i 0.604818 + 0.507502i 0.892990 0.450076i \(-0.148603\pi\)
−0.288173 + 0.957579i \(0.593048\pi\)
\(504\) 0 0
\(505\) 2.65136 + 4.59229i 0.117984 + 0.204354i
\(506\) 0 0
\(507\) 0.610815 0.222318i 0.0271272 0.00987350i
\(508\) 0 0
\(509\) 4.72715 26.8090i 0.209527 1.18829i −0.680628 0.732629i \(-0.738293\pi\)
0.890155 0.455658i \(-0.150596\pi\)
\(510\) 0 0
\(511\) 16.9402 14.2145i 0.749389 0.628812i
\(512\) 0 0
\(513\) 0.819078 + 4.28125i 0.0361632 + 0.189022i
\(514\) 0 0
\(515\) 12.7083 10.6635i 0.559993 0.469890i
\(516\) 0 0
\(517\) 7.10014 40.2669i 0.312264 1.77094i
\(518\) 0 0
\(519\) −7.08512 + 2.57877i −0.311002 + 0.113196i
\(520\) 0 0
\(521\) −10.2130 17.6895i −0.447440 0.774989i 0.550778 0.834651i \(-0.314331\pi\)
−0.998219 + 0.0596624i \(0.980998\pi\)
\(522\) 0 0
\(523\) 31.4957 + 26.4280i 1.37721 + 1.15562i 0.970231 + 0.242181i \(0.0778628\pi\)
0.406981 + 0.913437i \(0.366582\pi\)
\(524\) 0 0
\(525\) 3.84002 6.65111i 0.167592 0.290278i
\(526\) 0 0
\(527\) −0.0732627 0.415494i −0.00319137 0.0180992i
\(528\) 0 0
\(529\) −18.9979 6.91468i −0.825997 0.300638i
\(530\) 0 0
\(531\) −12.0496 −0.522909
\(532\) 0 0
\(533\) 1.33687 0.0579061
\(534\) 0 0
\(535\) −17.0077 6.19031i −0.735309 0.267630i
\(536\) 0 0
\(537\) 4.57785 + 25.9623i 0.197549 + 1.12035i
\(538\) 0 0
\(539\) 3.52094 6.09845i 0.151658 0.262679i
\(540\) 0 0
\(541\) −4.65064 3.90235i −0.199947 0.167775i 0.537317 0.843381i \(-0.319438\pi\)
−0.737264 + 0.675605i \(0.763882\pi\)
\(542\) 0 0
\(543\) 10.5458 + 18.2658i 0.452562 + 0.783860i
\(544\) 0 0
\(545\) −2.87211 + 1.04536i −0.123028 + 0.0447784i
\(546\) 0 0
\(547\) 4.13547 23.4534i 0.176820 1.00280i −0.759203 0.650854i \(-0.774411\pi\)
0.936022 0.351941i \(-0.114478\pi\)
\(548\) 0 0
\(549\) 4.73783 3.97551i 0.202205 0.169671i
\(550\) 0 0
\(551\) 5.33733 + 8.94253i 0.227378 + 0.380964i
\(552\) 0 0
\(553\) −17.9088 + 15.0273i −0.761559 + 0.639024i
\(554\) 0 0
\(555\) 1.62449 9.21291i 0.0689556 0.391066i
\(556\) 0 0
\(557\) 21.9094 7.97437i 0.928332 0.337885i 0.166784 0.985994i \(-0.446662\pi\)
0.761548 + 0.648108i \(0.224440\pi\)
\(558\) 0 0
\(559\) 21.1578 + 36.6463i 0.894878 + 1.54997i
\(560\) 0 0
\(561\) 0.739885 + 0.620838i 0.0312380 + 0.0262118i
\(562\) 0 0
\(563\) 7.35369 12.7370i 0.309921 0.536799i −0.668424 0.743781i \(-0.733031\pi\)
0.978345 + 0.206981i \(0.0663640\pi\)
\(564\) 0 0
\(565\) −2.97359 16.8641i −0.125100 0.709477i
\(566\) 0 0
\(567\) 2.26604 + 0.824773i 0.0951649 + 0.0346372i
\(568\) 0 0
\(569\) 32.6750 1.36981 0.684903 0.728634i \(-0.259844\pi\)
0.684903 + 0.728634i \(0.259844\pi\)
\(570\) 0 0
\(571\) −30.3901 −1.27179 −0.635893 0.771777i \(-0.719368\pi\)
−0.635893 + 0.771777i \(0.719368\pi\)
\(572\) 0 0
\(573\) 0.240352 + 0.0874810i 0.0100409 + 0.00365457i
\(574\) 0 0
\(575\) −3.63563 20.6187i −0.151616 0.859858i
\(576\) 0 0
\(577\) −15.4324 + 26.7297i −0.642460 + 1.11277i 0.342422 + 0.939546i \(0.388753\pi\)
−0.984882 + 0.173227i \(0.944581\pi\)
\(578\) 0 0
\(579\) −10.9914 9.22286i −0.456786 0.383289i
\(580\) 0 0
\(581\) −2.44444 4.23389i −0.101412 0.175652i
\(582\) 0 0
\(583\) −22.4650 + 8.17658i −0.930404 + 0.338639i
\(584\) 0 0
\(585\) −0.864370 + 4.90209i −0.0357373 + 0.202676i
\(586\) 0 0
\(587\) −21.5804 + 18.1081i −0.890717 + 0.747401i −0.968354 0.249581i \(-0.919707\pi\)
0.0776365 + 0.996982i \(0.475263\pi\)
\(588\) 0 0
\(589\) −8.56283 + 7.39928i −0.352825 + 0.304882i
\(590\) 0 0
\(591\) −18.1407 + 15.2218i −0.746208 + 0.626143i
\(592\) 0 0
\(593\) −1.18438 + 6.71696i −0.0486367 + 0.275833i −0.999421 0.0340206i \(-0.989169\pi\)
0.950784 + 0.309853i \(0.100280\pi\)
\(594\) 0 0
\(595\) −0.496130 + 0.180576i −0.0203393 + 0.00740291i
\(596\) 0 0
\(597\) 5.89780 + 10.2153i 0.241381 + 0.418084i
\(598\) 0 0
\(599\) 27.3562 + 22.9546i 1.11774 + 0.937899i 0.998488 0.0549642i \(-0.0175045\pi\)
0.119256 + 0.992863i \(0.461949\pi\)
\(600\) 0 0
\(601\) −2.76399 + 4.78736i −0.112745 + 0.195281i −0.916876 0.399172i \(-0.869298\pi\)
0.804131 + 0.594452i \(0.202631\pi\)
\(602\) 0 0
\(603\) 1.00000 + 5.67128i 0.0407231 + 0.230952i
\(604\) 0 0
\(605\) −30.7977 11.2095i −1.25211 0.455729i
\(606\) 0 0
\(607\) −19.4953 −0.791288 −0.395644 0.918404i \(-0.629479\pi\)
−0.395644 + 0.918404i \(0.629479\pi\)
\(608\) 0 0
\(609\) 5.76146 0.233466
\(610\) 0 0
\(611\) 23.8837 + 8.69296i 0.966232 + 0.351680i
\(612\) 0 0
\(613\) 6.86262 + 38.9198i 0.277178 + 1.57196i 0.731956 + 0.681352i \(0.238608\pi\)
−0.454777 + 0.890605i \(0.650281\pi\)
\(614\) 0 0
\(615\) −0.243756 + 0.422197i −0.00982918 + 0.0170246i
\(616\) 0 0
\(617\) −0.952648 0.799367i −0.0383522 0.0321813i 0.623410 0.781895i \(-0.285747\pi\)
−0.661762 + 0.749714i \(0.730191\pi\)
\(618\) 0 0
\(619\) −4.20187 7.27785i −0.168887 0.292521i 0.769142 0.639078i \(-0.220684\pi\)
−0.938029 + 0.346557i \(0.887351\pi\)
\(620\) 0 0
\(621\) 6.17752 2.24843i 0.247895 0.0902265i
\(622\) 0 0
\(623\) −1.44397 + 8.18918i −0.0578516 + 0.328093i
\(624\) 0 0
\(625\) 0.817267 0.685768i 0.0326907 0.0274307i
\(626\) 0 0
\(627\) 4.12836 25.5763i 0.164871 1.02142i
\(628\) 0 0
\(629\) 0.864370 0.725293i 0.0344647 0.0289193i
\(630\) 0 0
\(631\) 1.61159 9.13976i 0.0641562 0.363848i −0.935780 0.352584i \(-0.885303\pi\)
0.999937 0.0112645i \(-0.00358567\pi\)
\(632\) 0 0
\(633\) −26.1780 + 9.52801i −1.04048 + 0.378704i
\(634\) 0 0
\(635\) 5.20826 + 9.02098i 0.206684 + 0.357987i
\(636\) 0 0
\(637\) 3.35323 + 2.81369i 0.132860 + 0.111482i
\(638\) 0 0
\(639\) 6.09627 10.5590i 0.241165 0.417709i
\(640\) 0 0
\(641\) −1.51320 8.58180i −0.0597680 0.338961i 0.940231 0.340538i \(-0.110609\pi\)
−0.999999 + 0.00157695i \(0.999498\pi\)
\(642\) 0 0
\(643\) −14.2185 5.17512i −0.560724 0.204087i 0.0460808 0.998938i \(-0.485327\pi\)
−0.606805 + 0.794851i \(0.707549\pi\)
\(644\) 0 0
\(645\) −15.4311 −0.607598
\(646\) 0 0
\(647\) −7.31282 −0.287497 −0.143748 0.989614i \(-0.545916\pi\)
−0.143748 + 0.989614i \(0.545916\pi\)
\(648\) 0 0
\(649\) 67.2987 + 24.4947i 2.64170 + 0.961501i
\(650\) 0 0
\(651\) 1.08718 + 6.16571i 0.0426100 + 0.241653i
\(652\) 0 0
\(653\) −8.76904 + 15.1884i −0.343159 + 0.594369i −0.985018 0.172454i \(-0.944830\pi\)
0.641859 + 0.766823i \(0.278164\pi\)
\(654\) 0 0
\(655\) −12.9704 10.8835i −0.506797 0.425253i
\(656\) 0 0
\(657\) 4.58512 + 7.94166i 0.178883 + 0.309834i
\(658\) 0 0
\(659\) −7.39693 + 2.69226i −0.288143 + 0.104876i −0.482048 0.876145i \(-0.660107\pi\)
0.193905 + 0.981020i \(0.437885\pi\)
\(660\) 0 0
\(661\) 0.167414 0.949450i 0.00651164 0.0369293i −0.981379 0.192082i \(-0.938476\pi\)
0.987890 + 0.155153i \(0.0495871\pi\)
\(662\) 0 0
\(663\) −0.459922 + 0.385920i −0.0178619 + 0.0149879i
\(664\) 0 0
\(665\) 10.9795 + 8.94486i 0.425768 + 0.346867i
\(666\) 0 0
\(667\) 12.0318 10.0959i 0.465875 0.390915i
\(668\) 0 0
\(669\) −4.29561 + 24.3616i −0.166078 + 0.941874i
\(670\) 0 0
\(671\) −34.5428 + 12.5726i −1.33351 + 0.485358i
\(672\) 0 0
\(673\) 12.9265 + 22.3893i 0.498280 + 0.863045i 0.999998 0.00198549i \(-0.000632002\pi\)
−0.501719 + 0.865031i \(0.667299\pi\)
\(674\) 0 0
\(675\) 2.43969 + 2.04715i 0.0939038 + 0.0787947i
\(676\) 0 0
\(677\) −14.9978 + 25.9769i −0.576411 + 0.998374i 0.419475 + 0.907767i \(0.362214\pi\)
−0.995887 + 0.0906072i \(0.971119\pi\)
\(678\) 0 0
\(679\) −5.06330 28.7154i −0.194312 1.10200i
\(680\) 0 0
\(681\) 20.6878 + 7.52974i 0.792758 + 0.288540i
\(682\) 0 0
\(683\) −33.5084 −1.28216 −0.641081 0.767473i \(-0.721514\pi\)
−0.641081 + 0.767473i \(0.721514\pi\)
\(684\) 0 0
\(685\) 21.1661 0.808716
\(686\) 0 0
\(687\) −8.73530 3.17939i −0.333272 0.121301i
\(688\) 0 0
\(689\) −2.58054 14.6350i −0.0983106 0.557547i
\(690\) 0 0
\(691\) −6.40673 + 11.0968i −0.243723 + 0.422141i −0.961772 0.273852i \(-0.911702\pi\)
0.718049 + 0.695993i \(0.245036\pi\)
\(692\) 0 0
\(693\) −10.9795 9.21291i −0.417078 0.349970i
\(694\) 0 0
\(695\) 2.17886 + 3.77390i 0.0826490 + 0.143152i
\(696\) 0 0
\(697\) −0.0552549 + 0.0201112i −0.00209293 + 0.000761764i
\(698\) 0 0
\(699\) 1.38713 7.86678i 0.0524659 0.297549i
\(700\) 0 0
\(701\) 3.04323 2.55358i 0.114941 0.0964472i −0.583505 0.812109i \(-0.698319\pi\)
0.698447 + 0.715662i \(0.253875\pi\)
\(702\) 0 0
\(703\) −28.5881 9.93821i −1.07822 0.374827i
\(704\) 0 0
\(705\) −7.10014 + 5.95772i −0.267407 + 0.224381i
\(706\) 0 0
\(707\) 1.64812 9.34694i 0.0619839 0.351528i
\(708\) 0 0
\(709\) −30.3572 + 11.0491i −1.14009 + 0.414958i −0.841945 0.539564i \(-0.818589\pi\)
−0.298142 + 0.954521i \(0.596367\pi\)
\(710\) 0 0
\(711\) −4.84730 8.39576i −0.181788 0.314866i
\(712\) 0 0
\(713\) 13.0747 + 10.9710i 0.489651 + 0.410866i
\(714\) 0 0
\(715\) 14.7927 25.6217i 0.553215 0.958196i
\(716\) 0 0
\(717\) −4.59286 26.0474i −0.171524 0.972759i
\(718\) 0 0
\(719\) 42.5385 + 15.4828i 1.58642 + 0.577410i 0.976587 0.215121i \(-0.0690145\pi\)
0.609832 + 0.792530i \(0.291237\pi\)
\(720\) 0 0
\(721\) −29.6928 −1.10582
\(722\) 0 0
\(723\) 2.73917 0.101871
\(724\) 0 0
\(725\) 7.15018 + 2.60245i 0.265551 + 0.0966526i
\(726\) 0 0
\(727\) 3.85188 + 21.8451i 0.142858 + 0.810190i 0.969062 + 0.246818i \(0.0793851\pi\)
−0.826203 + 0.563372i \(0.809504\pi\)
\(728\) 0 0
\(729\) −0.500000 + 0.866025i −0.0185185 + 0.0320750i
\(730\) 0 0
\(731\) −1.42577 1.19637i −0.0527341 0.0442492i
\(732\) 0 0
\(733\) −22.9106 39.6823i −0.846222 1.46570i −0.884556 0.466435i \(-0.845538\pi\)
0.0383334 0.999265i \(-0.487795\pi\)
\(734\) 0 0
\(735\) −1.50000 + 0.545955i −0.0553283 + 0.0201379i
\(736\) 0 0
\(737\) 5.94356 33.7076i 0.218934 1.24164i
\(738\) 0 0
\(739\) 2.89124 2.42604i 0.106356 0.0892434i −0.588059 0.808818i \(-0.700108\pi\)
0.694415 + 0.719575i \(0.255663\pi\)
\(740\) 0 0
\(741\) 15.2114 + 5.28801i 0.558805 + 0.194260i
\(742\) 0 0
\(743\) 17.2251 14.4536i 0.631927 0.530250i −0.269600 0.962972i \(-0.586891\pi\)
0.901527 + 0.432723i \(0.142447\pi\)
\(744\) 0 0
\(745\) 1.04348 5.91788i 0.0382302 0.216814i
\(746\) 0 0
\(747\) 1.90508 0.693392i 0.0697031 0.0253699i
\(748\) 0 0
\(749\) 16.1976 + 28.0550i 0.591847 + 1.02511i
\(750\) 0 0
\(751\) 31.7879 + 26.6732i 1.15996 + 0.973320i 0.999905 0.0137883i \(-0.00438909\pi\)
0.160053 + 0.987108i \(0.448834\pi\)
\(752\) 0 0
\(753\) −7.61468 + 13.1890i −0.277495 + 0.480635i
\(754\) 0 0
\(755\) −2.09358 11.8733i −0.0761931 0.432113i
\(756\) 0 0
\(757\) 16.8037 + 6.11603i 0.610739 + 0.222291i 0.628827 0.777546i \(-0.283536\pi\)
−0.0180875 + 0.999836i \(0.505758\pi\)
\(758\) 0 0
\(759\) −39.0729 −1.41825
\(760\) 0 0
\(761\) 38.0806 1.38042 0.690210 0.723609i \(-0.257518\pi\)
0.690210 + 0.723609i \(0.257518\pi\)
\(762\) 0 0
\(763\) 5.14068 + 1.87106i 0.186105 + 0.0677367i
\(764\) 0 0
\(765\) −0.0380187 0.215615i −0.00137457 0.00779556i
\(766\) 0 0
\(767\) −22.2592 + 38.5541i −0.803734 + 1.39211i
\(768\) 0 0
\(769\) −9.67096 8.11490i −0.348744 0.292631i 0.451542 0.892250i \(-0.350874\pi\)
−0.800285 + 0.599619i \(0.795319\pi\)
\(770\) 0 0
\(771\) 6.51754 + 11.2887i 0.234724 + 0.406553i
\(772\) 0 0
\(773\) −31.7606 + 11.5599i −1.14235 + 0.415781i −0.842761 0.538288i \(-0.819071\pi\)
−0.299588 + 0.954069i \(0.596849\pi\)
\(774\) 0 0
\(775\) −1.43582 + 8.14295i −0.0515763 + 0.292503i
\(776\) 0 0
\(777\) −12.8268 + 10.7630i −0.460160 + 0.386120i
\(778\) 0 0
\(779\) 1.22281 + 0.996206i 0.0438118 + 0.0356928i
\(780\) 0 0
\(781\) −55.5130 + 46.5809i −1.98641 + 1.66680i
\(782\) 0 0
\(783\) −0.414878 + 2.35289i −0.0148265 + 0.0840854i
\(784\) 0 0
\(785\) 14.5851 5.30855i 0.520565 0.189470i
\(786\) 0 0
\(787\) −16.8059 29.1086i −0.599065 1.03761i −0.992959 0.118455i \(-0.962206\pi\)
0.393895 0.919156i \(-0.371127\pi\)
\(788\) 0 0
\(789\) −9.13610 7.66610i −0.325254 0.272920i
\(790\) 0 0
\(791\) −15.3250 + 26.5437i −0.544895 + 0.943785i
\(792\) 0 0
\(793\) −3.96791 22.5031i −0.140905 0.799110i
\(794\) 0