Properties

Label 912.2.bn.g.449.1
Level $912$
Weight $2$
Character 912.449
Analytic conductor $7.282$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 449.1
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 912.449
Dual form 912.2.bn.g.65.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.41421i) q^{3} +(-1.22474 + 0.707107i) q^{5} -4.44949 q^{7} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.41421i) q^{3} +(-1.22474 + 0.707107i) q^{5} -4.44949 q^{7} +(-1.00000 + 2.82843i) q^{9} -0.317837i q^{11} +(-3.00000 - 1.73205i) q^{13} +(2.22474 + 1.02494i) q^{15} +(5.44949 - 3.14626i) q^{17} +(4.17423 + 1.25529i) q^{19} +(4.44949 + 6.29253i) q^{21} +(6.12372 + 3.53553i) q^{23} +(-1.50000 + 2.59808i) q^{25} +(5.00000 - 1.41421i) q^{27} +(1.22474 - 2.12132i) q^{29} +4.24264i q^{31} +(-0.449490 + 0.317837i) q^{33} +(5.44949 - 3.14626i) q^{35} +0.778539i q^{37} +(0.550510 + 5.97469i) q^{39} +(1.50000 + 2.59808i) q^{41} +(0.449490 + 0.778539i) q^{43} +(-0.775255 - 4.17121i) q^{45} +(-5.57321 - 3.21770i) q^{47} +12.7980 q^{49} +(-9.89898 - 4.56048i) q^{51} +(0.550510 - 0.953512i) q^{53} +(0.224745 + 0.389270i) q^{55} +(-2.39898 - 7.15855i) q^{57} +(3.27526 + 5.67291i) q^{59} +(3.22474 - 5.58542i) q^{61} +(4.44949 - 12.5851i) q^{63} +4.89898 q^{65} +(5.17423 + 2.98735i) q^{67} +(-1.12372 - 12.1958i) q^{69} +(3.00000 + 5.19615i) q^{71} +(5.39898 + 9.35131i) q^{73} +(5.17423 - 0.476756i) q^{75} +1.41421i q^{77} +(-7.34847 + 4.24264i) q^{79} +(-7.00000 - 5.65685i) q^{81} -14.1742i q^{83} +(-4.44949 + 7.70674i) q^{85} +(-4.22474 + 0.389270i) q^{87} +(-8.44949 + 14.6349i) q^{89} +(13.3485 + 7.70674i) q^{91} +(6.00000 - 4.24264i) q^{93} +(-6.00000 + 1.41421i) q^{95} +(-11.8485 + 6.84072i) q^{97} +(0.898979 + 0.317837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} - 8 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} - 8 q^{7} - 4 q^{9} - 12 q^{13} + 4 q^{15} + 12 q^{17} + 2 q^{19} + 8 q^{21} - 6 q^{25} + 20 q^{27} + 8 q^{33} + 12 q^{35} + 12 q^{39} + 6 q^{41} - 8 q^{43} - 8 q^{45} + 12 q^{47} + 12 q^{49} - 20 q^{51} + 12 q^{53} - 4 q^{55} + 10 q^{57} + 18 q^{59} + 8 q^{61} + 8 q^{63} + 6 q^{67} + 20 q^{69} + 12 q^{71} + 2 q^{73} + 6 q^{75} - 28 q^{81} - 8 q^{85} - 12 q^{87} - 24 q^{89} + 24 q^{91} + 24 q^{93} - 24 q^{95} - 18 q^{97} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(1\)

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
\(3\) −1.00000 1.41421i −0.577350 0.816497i
\(4\) 0 0
\(5\) −1.22474 + 0.707107i −0.547723 + 0.316228i −0.748203 0.663470i \(-0.769083\pi\)
0.200480 + 0.979698i \(0.435750\pi\)
\(6\) 0 0
\(7\) −4.44949 −1.68175 −0.840875 0.541230i \(-0.817959\pi\)
−0.840875 + 0.541230i \(0.817959\pi\)
\(8\) 0 0
\(9\) −1.00000 + 2.82843i −0.333333 + 0.942809i
\(10\) 0 0
\(11\) 0.317837i 0.0958315i −0.998851 0.0479158i \(-0.984742\pi\)
0.998851 0.0479158i \(-0.0152579\pi\)
\(12\) 0 0
\(13\) −3.00000 1.73205i −0.832050 0.480384i 0.0225039 0.999747i \(-0.492836\pi\)
−0.854554 + 0.519362i \(0.826170\pi\)
\(14\) 0 0
\(15\) 2.22474 + 1.02494i 0.574427 + 0.264639i
\(16\) 0 0
\(17\) 5.44949 3.14626i 1.32170 0.763081i 0.337696 0.941255i \(-0.390352\pi\)
0.983999 + 0.178174i \(0.0570190\pi\)
\(18\) 0 0
\(19\) 4.17423 + 1.25529i 0.957635 + 0.287984i
\(20\) 0 0
\(21\) 4.44949 + 6.29253i 0.970958 + 1.37314i
\(22\) 0 0
\(23\) 6.12372 + 3.53553i 1.27688 + 0.737210i 0.976274 0.216537i \(-0.0694763\pi\)
0.300610 + 0.953747i \(0.402810\pi\)
\(24\) 0 0
\(25\) −1.50000 + 2.59808i −0.300000 + 0.519615i
\(26\) 0 0
\(27\) 5.00000 1.41421i 0.962250 0.272166i
\(28\) 0 0
\(29\) 1.22474 2.12132i 0.227429 0.393919i −0.729616 0.683857i \(-0.760301\pi\)
0.957046 + 0.289938i \(0.0936346\pi\)
\(30\) 0 0
\(31\) 4.24264i 0.762001i 0.924575 + 0.381000i \(0.124420\pi\)
−0.924575 + 0.381000i \(0.875580\pi\)
\(32\) 0 0
\(33\) −0.449490 + 0.317837i −0.0782461 + 0.0553284i
\(34\) 0 0
\(35\) 5.44949 3.14626i 0.921132 0.531816i
\(36\) 0 0
\(37\) 0.778539i 0.127991i 0.997950 + 0.0639955i \(0.0203843\pi\)
−0.997950 + 0.0639955i \(0.979616\pi\)
\(38\) 0 0
\(39\) 0.550510 + 5.97469i 0.0881522 + 0.956716i
\(40\) 0 0
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) 0 0
\(43\) 0.449490 + 0.778539i 0.0685465 + 0.118726i 0.898262 0.439461i \(-0.144831\pi\)
−0.829715 + 0.558187i \(0.811497\pi\)
\(44\) 0 0
\(45\) −0.775255 4.17121i −0.115568 0.621807i
\(46\) 0 0
\(47\) −5.57321 3.21770i −0.812937 0.469349i 0.0350379 0.999386i \(-0.488845\pi\)
−0.847975 + 0.530037i \(0.822178\pi\)
\(48\) 0 0
\(49\) 12.7980 1.82828
\(50\) 0 0
\(51\) −9.89898 4.56048i −1.38613 0.638595i
\(52\) 0 0
\(53\) 0.550510 0.953512i 0.0756184 0.130975i −0.825737 0.564056i \(-0.809240\pi\)
0.901355 + 0.433081i \(0.142574\pi\)
\(54\) 0 0
\(55\) 0.224745 + 0.389270i 0.0303046 + 0.0524891i
\(56\) 0 0
\(57\) −2.39898 7.15855i −0.317753 0.948174i
\(58\) 0 0
\(59\) 3.27526 + 5.67291i 0.426402 + 0.738550i 0.996550 0.0829920i \(-0.0264476\pi\)
−0.570148 + 0.821542i \(0.693114\pi\)
\(60\) 0 0
\(61\) 3.22474 5.58542i 0.412886 0.715140i −0.582318 0.812961i \(-0.697854\pi\)
0.995204 + 0.0978213i \(0.0311874\pi\)
\(62\) 0 0
\(63\) 4.44949 12.5851i 0.560583 1.58557i
\(64\) 0 0
\(65\) 4.89898 0.607644
\(66\) 0 0
\(67\) 5.17423 + 2.98735i 0.632133 + 0.364962i 0.781578 0.623808i \(-0.214415\pi\)
−0.149444 + 0.988770i \(0.547749\pi\)
\(68\) 0 0
\(69\) −1.12372 12.1958i −0.135281 1.46820i
\(70\) 0 0
\(71\) 3.00000 + 5.19615i 0.356034 + 0.616670i 0.987294 0.158901i \(-0.0507952\pi\)
−0.631260 + 0.775571i \(0.717462\pi\)
\(72\) 0 0
\(73\) 5.39898 + 9.35131i 0.631903 + 1.09449i 0.987162 + 0.159720i \(0.0510591\pi\)
−0.355260 + 0.934768i \(0.615608\pi\)
\(74\) 0 0
\(75\) 5.17423 0.476756i 0.597469 0.0550510i
\(76\) 0 0
\(77\) 1.41421i 0.161165i
\(78\) 0 0
\(79\) −7.34847 + 4.24264i −0.826767 + 0.477334i −0.852745 0.522328i \(-0.825064\pi\)
0.0259772 + 0.999663i \(0.491730\pi\)
\(80\) 0 0
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) 0 0
\(83\) 14.1742i 1.55583i −0.628372 0.777913i \(-0.716279\pi\)
0.628372 0.777913i \(-0.283721\pi\)
\(84\) 0 0
\(85\) −4.44949 + 7.70674i −0.482615 + 0.835914i
\(86\) 0 0
\(87\) −4.22474 + 0.389270i −0.452940 + 0.0417341i
\(88\) 0 0
\(89\) −8.44949 + 14.6349i −0.895644 + 1.55130i −0.0626387 + 0.998036i \(0.519952\pi\)
−0.833005 + 0.553265i \(0.813382\pi\)
\(90\) 0 0
\(91\) 13.3485 + 7.70674i 1.39930 + 0.807886i
\(92\) 0 0
\(93\) 6.00000 4.24264i 0.622171 0.439941i
\(94\) 0 0
\(95\) −6.00000 + 1.41421i −0.615587 + 0.145095i
\(96\) 0 0
\(97\) −11.8485 + 6.84072i −1.20303 + 0.694570i −0.961228 0.275756i \(-0.911072\pi\)
−0.241802 + 0.970326i \(0.577738\pi\)
\(98\) 0 0
\(99\) 0.898979 + 0.317837i 0.0903508 + 0.0319438i
\(100\) 0 0
\(101\) 8.57321 + 4.94975i 0.853067 + 0.492518i 0.861684 0.507445i \(-0.169410\pi\)
−0.00861771 + 0.999963i \(0.502743\pi\)
\(102\) 0 0
\(103\) 11.9494i 1.17741i −0.808349 0.588704i \(-0.799638\pi\)
0.808349 0.588704i \(-0.200362\pi\)
\(104\) 0 0
\(105\) −9.89898 4.56048i −0.966041 0.445057i
\(106\) 0 0
\(107\) 4.89898 0.473602 0.236801 0.971558i \(-0.423901\pi\)
0.236801 + 0.971558i \(0.423901\pi\)
\(108\) 0 0
\(109\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 0 0
\(111\) 1.10102 0.778539i 0.104504 0.0738957i
\(112\) 0 0
\(113\) −0.797959 −0.0750657 −0.0375328 0.999295i \(-0.511950\pi\)
−0.0375328 + 0.999295i \(0.511950\pi\)
\(114\) 0 0
\(115\) −10.0000 −0.932505
\(116\) 0 0
\(117\) 7.89898 6.75323i 0.730261 0.624336i
\(118\) 0 0
\(119\) −24.2474 + 13.9993i −2.22276 + 1.28331i
\(120\) 0 0
\(121\) 10.8990 0.990816
\(122\) 0 0
\(123\) 2.17423 4.71940i 0.196044 0.425534i
\(124\) 0 0
\(125\) 11.3137i 1.01193i
\(126\) 0 0
\(127\) 9.00000 + 5.19615i 0.798621 + 0.461084i 0.842989 0.537931i \(-0.180794\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) 0 0
\(129\) 0.651531 1.41421i 0.0573641 0.124515i
\(130\) 0 0
\(131\) 19.0732 11.0119i 1.66643 0.962116i 0.696898 0.717171i \(-0.254563\pi\)
0.969537 0.244946i \(-0.0787702\pi\)
\(132\) 0 0
\(133\) −18.5732 5.58542i −1.61050 0.484318i
\(134\) 0 0
\(135\) −5.12372 + 5.26758i −0.440980 + 0.453362i
\(136\) 0 0
\(137\) 6.39898 + 3.69445i 0.546702 + 0.315638i 0.747791 0.663935i \(-0.231115\pi\)
−0.201089 + 0.979573i \(0.564448\pi\)
\(138\) 0 0
\(139\) 0.174235 0.301783i 0.0147784 0.0255969i −0.858542 0.512744i \(-0.828629\pi\)
0.873320 + 0.487147i \(0.161962\pi\)
\(140\) 0 0
\(141\) 1.02270 + 11.0994i 0.0861272 + 0.934739i
\(142\) 0 0
\(143\) −0.550510 + 0.953512i −0.0460360 + 0.0797367i
\(144\) 0 0
\(145\) 3.46410i 0.287678i
\(146\) 0 0
\(147\) −12.7980 18.0990i −1.05556 1.49278i
\(148\) 0 0
\(149\) −4.22474 + 2.43916i −0.346105 + 0.199824i −0.662968 0.748648i \(-0.730704\pi\)
0.316864 + 0.948471i \(0.397370\pi\)
\(150\) 0 0
\(151\) 18.0990i 1.47288i 0.676503 + 0.736440i \(0.263495\pi\)
−0.676503 + 0.736440i \(0.736505\pi\)
\(152\) 0 0
\(153\) 3.44949 + 18.5597i 0.278875 + 1.50047i
\(154\) 0 0
\(155\) −3.00000 5.19615i −0.240966 0.417365i
\(156\) 0 0
\(157\) 9.34847 + 16.1920i 0.746089 + 1.29226i 0.949684 + 0.313209i \(0.101404\pi\)
−0.203595 + 0.979055i \(0.565263\pi\)
\(158\) 0 0
\(159\) −1.89898 + 0.174973i −0.150599 + 0.0138762i
\(160\) 0 0
\(161\) −27.2474 15.7313i −2.14740 1.23980i
\(162\) 0 0
\(163\) −3.65153 −0.286010 −0.143005 0.989722i \(-0.545676\pi\)
−0.143005 + 0.989722i \(0.545676\pi\)
\(164\) 0 0
\(165\) 0.325765 0.707107i 0.0253608 0.0550482i
\(166\) 0 0
\(167\) 2.44949 4.24264i 0.189547 0.328305i −0.755552 0.655089i \(-0.772631\pi\)
0.945099 + 0.326783i \(0.105965\pi\)
\(168\) 0 0
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) 0 0
\(171\) −7.72474 + 10.5512i −0.590726 + 0.806872i
\(172\) 0 0
\(173\) −5.44949 9.43879i −0.414317 0.717618i 0.581039 0.813875i \(-0.302646\pi\)
−0.995356 + 0.0962572i \(0.969313\pi\)
\(174\) 0 0
\(175\) 6.67423 11.5601i 0.504525 0.873862i
\(176\) 0 0
\(177\) 4.74745 10.3048i 0.356840 0.774558i
\(178\) 0 0
\(179\) −22.3485 −1.67040 −0.835202 0.549944i \(-0.814649\pi\)
−0.835202 + 0.549944i \(0.814649\pi\)
\(180\) 0 0
\(181\) 11.3258 + 6.53893i 0.841838 + 0.486035i 0.857888 0.513836i \(-0.171776\pi\)
−0.0160509 + 0.999871i \(0.505109\pi\)
\(182\) 0 0
\(183\) −11.1237 + 1.02494i −0.822289 + 0.0757660i
\(184\) 0 0
\(185\) −0.550510 0.953512i −0.0404743 0.0701036i
\(186\) 0 0
\(187\) −1.00000 1.73205i −0.0731272 0.126660i
\(188\) 0 0
\(189\) −22.2474 + 6.29253i −1.61826 + 0.457714i
\(190\) 0 0
\(191\) 19.5133i 1.41193i 0.708247 + 0.705965i \(0.249486\pi\)
−0.708247 + 0.705965i \(0.750514\pi\)
\(192\) 0 0
\(193\) −7.65153 + 4.41761i −0.550769 + 0.317987i −0.749432 0.662081i \(-0.769673\pi\)
0.198663 + 0.980068i \(0.436340\pi\)
\(194\) 0 0
\(195\) −4.89898 6.92820i −0.350823 0.496139i
\(196\) 0 0
\(197\) 0.492810i 0.0351113i 0.999846 + 0.0175556i \(0.00558842\pi\)
−0.999846 + 0.0175556i \(0.994412\pi\)
\(198\) 0 0
\(199\) 3.44949 5.97469i 0.244528 0.423535i −0.717471 0.696588i \(-0.754700\pi\)
0.961999 + 0.273054i \(0.0880337\pi\)
\(200\) 0 0
\(201\) −0.949490 10.3048i −0.0669718 0.726846i
\(202\) 0 0
\(203\) −5.44949 + 9.43879i −0.382479 + 0.662473i
\(204\) 0 0
\(205\) −3.67423 2.12132i −0.256620 0.148159i
\(206\) 0 0
\(207\) −16.1237 + 13.7850i −1.12068 + 0.958122i
\(208\) 0 0
\(209\) 0.398979 1.32673i 0.0275980 0.0917716i
\(210\) 0 0
\(211\) −13.3485 + 7.70674i −0.918947 + 0.530554i −0.883299 0.468810i \(-0.844683\pi\)
−0.0356477 + 0.999364i \(0.511349\pi\)
\(212\) 0 0
\(213\) 4.34847 9.43879i 0.297952 0.646735i
\(214\) 0 0
\(215\) −1.10102 0.635674i −0.0750890 0.0433526i
\(216\) 0 0
\(217\) 18.8776i 1.28149i
\(218\) 0 0
\(219\) 7.82577 16.9866i 0.528816 1.14785i
\(220\) 0 0
\(221\) −21.7980 −1.46629
\(222\) 0 0
\(223\) 8.32577 4.80688i 0.557534 0.321893i −0.194621 0.980879i \(-0.562348\pi\)
0.752155 + 0.658986i \(0.229014\pi\)
\(224\) 0 0
\(225\) −5.84847 6.84072i −0.389898 0.456048i
\(226\) 0 0
\(227\) 5.44949 0.361695 0.180848 0.983511i \(-0.442116\pi\)
0.180848 + 0.983511i \(0.442116\pi\)
\(228\) 0 0
\(229\) −8.89898 −0.588061 −0.294031 0.955796i \(-0.594997\pi\)
−0.294031 + 0.955796i \(0.594997\pi\)
\(230\) 0 0
\(231\) 2.00000 1.41421i 0.131590 0.0930484i
\(232\) 0 0
\(233\) 5.60102 3.23375i 0.366935 0.211850i −0.305184 0.952294i \(-0.598718\pi\)
0.672119 + 0.740443i \(0.265384\pi\)
\(234\) 0 0
\(235\) 9.10102 0.593685
\(236\) 0 0
\(237\) 13.3485 + 6.14966i 0.867076 + 0.399464i
\(238\) 0 0
\(239\) 7.21393i 0.466630i 0.972401 + 0.233315i \(0.0749574\pi\)
−0.972401 + 0.233315i \(0.925043\pi\)
\(240\) 0 0
\(241\) 8.84847 + 5.10867i 0.569980 + 0.329078i 0.757141 0.653251i \(-0.226595\pi\)
−0.187161 + 0.982329i \(0.559929\pi\)
\(242\) 0 0
\(243\) −1.00000 + 15.5563i −0.0641500 + 0.997940i
\(244\) 0 0
\(245\) −15.6742 + 9.04952i −1.00139 + 0.578153i
\(246\) 0 0
\(247\) −10.3485 10.9959i −0.658457 0.699651i
\(248\) 0 0
\(249\) −20.0454 + 14.1742i −1.27033 + 0.898256i
\(250\) 0 0
\(251\) −5.72474 3.30518i −0.361343 0.208621i 0.308327 0.951280i \(-0.400231\pi\)
−0.669670 + 0.742659i \(0.733564\pi\)
\(252\) 0 0
\(253\) 1.12372 1.94635i 0.0706479 0.122366i
\(254\) 0 0
\(255\) 15.3485 1.41421i 0.961158 0.0885615i
\(256\) 0 0
\(257\) 7.50000 12.9904i 0.467837 0.810318i −0.531487 0.847066i \(-0.678367\pi\)
0.999325 + 0.0367485i \(0.0117000\pi\)
\(258\) 0 0
\(259\) 3.46410i 0.215249i
\(260\) 0 0
\(261\) 4.77526 + 5.58542i 0.295581 + 0.345729i
\(262\) 0 0
\(263\) 10.2247 5.90326i 0.630485 0.364011i −0.150455 0.988617i \(-0.548074\pi\)
0.780940 + 0.624606i \(0.214741\pi\)
\(264\) 0 0
\(265\) 1.55708i 0.0956506i
\(266\) 0 0
\(267\) 29.1464 2.68556i 1.78373 0.164354i
\(268\) 0 0
\(269\) 12.2474 + 21.2132i 0.746740 + 1.29339i 0.949377 + 0.314138i \(0.101715\pi\)
−0.202637 + 0.979254i \(0.564951\pi\)
\(270\) 0 0
\(271\) 12.0227 + 20.8239i 0.730327 + 1.26496i 0.956743 + 0.290933i \(0.0939658\pi\)
−0.226416 + 0.974031i \(0.572701\pi\)
\(272\) 0 0
\(273\) −2.44949 26.5843i −0.148250 1.60896i
\(274\) 0 0
\(275\) 0.825765 + 0.476756i 0.0497955 + 0.0287495i
\(276\) 0 0
\(277\) −4.24745 −0.255204 −0.127602 0.991825i \(-0.540728\pi\)
−0.127602 + 0.991825i \(0.540728\pi\)
\(278\) 0 0
\(279\) −12.0000 4.24264i −0.718421 0.254000i
\(280\) 0 0
\(281\) 8.29796 14.3725i 0.495015 0.857391i −0.504969 0.863138i \(-0.668496\pi\)
0.999983 + 0.00574696i \(0.00182932\pi\)
\(282\) 0 0
\(283\) −2.27526 3.94086i −0.135250 0.234260i 0.790443 0.612536i \(-0.209850\pi\)
−0.925693 + 0.378276i \(0.876517\pi\)
\(284\) 0 0
\(285\) 8.00000 + 7.07107i 0.473879 + 0.418854i
\(286\) 0 0
\(287\) −6.67423 11.5601i −0.393968 0.682372i
\(288\) 0 0
\(289\) 11.2980 19.5686i 0.664586 1.15110i
\(290\) 0 0
\(291\) 21.5227 + 9.91555i 1.26168 + 0.581260i
\(292\) 0 0
\(293\) 4.65153 0.271745 0.135873 0.990726i \(-0.456616\pi\)
0.135873 + 0.990726i \(0.456616\pi\)
\(294\) 0 0
\(295\) −8.02270 4.63191i −0.467100 0.269680i
\(296\) 0 0
\(297\) −0.449490 1.58919i −0.0260820 0.0922139i
\(298\) 0 0
\(299\) −12.2474 21.2132i −0.708288 1.22679i
\(300\) 0 0
\(301\) −2.00000 3.46410i −0.115278 0.199667i
\(302\) 0 0
\(303\) −1.57321 17.0741i −0.0903788 0.980882i
\(304\) 0 0
\(305\) 9.12096i 0.522264i
\(306\) 0 0
\(307\) 3.52270 2.03383i 0.201051 0.116077i −0.396094 0.918210i \(-0.629635\pi\)
0.597146 + 0.802133i \(0.296301\pi\)
\(308\) 0 0
\(309\) −16.8990 + 11.9494i −0.961349 + 0.679777i
\(310\) 0 0
\(311\) 15.5563i 0.882120i −0.897478 0.441060i \(-0.854603\pi\)
0.897478 0.441060i \(-0.145397\pi\)
\(312\) 0 0
\(313\) 9.50000 16.4545i 0.536972 0.930062i −0.462093 0.886831i \(-0.652902\pi\)
0.999065 0.0432311i \(-0.0137652\pi\)
\(314\) 0 0
\(315\) 3.44949 + 18.5597i 0.194357 + 1.04572i
\(316\) 0 0
\(317\) 3.00000 5.19615i 0.168497 0.291845i −0.769395 0.638774i \(-0.779442\pi\)
0.937892 + 0.346929i \(0.112775\pi\)
\(318\) 0 0
\(319\) −0.674235 0.389270i −0.0377499 0.0217949i
\(320\) 0 0
\(321\) −4.89898 6.92820i −0.273434 0.386695i
\(322\) 0 0
\(323\) 26.6969 6.29253i 1.48546 0.350126i
\(324\) 0 0
\(325\) 9.00000 5.19615i 0.499230 0.288231i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 24.7980 + 14.3171i 1.36716 + 0.789328i
\(330\) 0 0
\(331\) 14.8099i 0.814027i −0.913422 0.407013i \(-0.866570\pi\)
0.913422 0.407013i \(-0.133430\pi\)
\(332\) 0 0
\(333\) −2.20204 0.778539i −0.120671 0.0426637i
\(334\) 0 0
\(335\) −8.44949 −0.461645
\(336\) 0 0
\(337\) −3.15153 + 1.81954i −0.171675 + 0.0991165i −0.583375 0.812203i \(-0.698268\pi\)
0.411701 + 0.911319i \(0.364935\pi\)
\(338\) 0 0
\(339\) 0.797959 + 1.12848i 0.0433392 + 0.0612909i
\(340\) 0 0
\(341\) 1.34847 0.0730237
\(342\) 0 0
\(343\) −25.7980 −1.39296
\(344\) 0 0
\(345\) 10.0000 + 14.1421i 0.538382 + 0.761387i
\(346\) 0 0
\(347\) 5.72474 3.30518i 0.307320 0.177432i −0.338406 0.941000i \(-0.609888\pi\)
0.645727 + 0.763569i \(0.276555\pi\)
\(348\) 0 0
\(349\) −16.4949 −0.882952 −0.441476 0.897273i \(-0.645545\pi\)
−0.441476 + 0.897273i \(0.645545\pi\)
\(350\) 0 0
\(351\) −17.4495 4.41761i −0.931385 0.235795i
\(352\) 0 0
\(353\) 14.6028i 0.777231i 0.921400 + 0.388615i \(0.127046\pi\)
−0.921400 + 0.388615i \(0.872954\pi\)
\(354\) 0 0
\(355\) −7.34847 4.24264i −0.390016 0.225176i
\(356\) 0 0
\(357\) 44.0454 + 20.2918i 2.33113 + 1.07396i
\(358\) 0 0
\(359\) −20.8207 + 12.0208i −1.09887 + 0.634434i −0.935925 0.352200i \(-0.885434\pi\)
−0.162948 + 0.986635i \(0.552100\pi\)
\(360\) 0 0
\(361\) 15.8485 + 10.4798i 0.834130 + 0.551568i
\(362\) 0 0
\(363\) −10.8990 15.4135i −0.572048 0.808998i
\(364\) 0 0
\(365\) −13.2247 7.63531i −0.692215 0.399650i
\(366\) 0 0
\(367\) −11.6742 + 20.2204i −0.609390 + 1.05549i 0.381951 + 0.924183i \(0.375252\pi\)
−0.991341 + 0.131312i \(0.958081\pi\)
\(368\) 0 0
\(369\) −8.84847 + 1.64456i −0.460633 + 0.0856126i
\(370\) 0 0
\(371\) −2.44949 + 4.24264i −0.127171 + 0.220267i
\(372\) 0 0
\(373\) 25.4558i 1.31805i 0.752119 + 0.659027i \(0.229032\pi\)
−0.752119 + 0.659027i \(0.770968\pi\)
\(374\) 0 0
\(375\) −16.0000 + 11.3137i −0.826236 + 0.584237i
\(376\) 0 0
\(377\) −7.34847 + 4.24264i −0.378465 + 0.218507i
\(378\) 0 0
\(379\) 15.4135i 0.791738i 0.918307 + 0.395869i \(0.129556\pi\)
−0.918307 + 0.395869i \(0.870444\pi\)
\(380\) 0 0
\(381\) −1.65153 17.9241i −0.0846105 0.918278i
\(382\) 0 0
\(383\) 7.77526 + 13.4671i 0.397297 + 0.688139i 0.993391 0.114776i \(-0.0366150\pi\)
−0.596094 + 0.802914i \(0.703282\pi\)
\(384\) 0 0
\(385\) −1.00000 1.73205i −0.0509647 0.0882735i
\(386\) 0 0
\(387\) −2.65153 + 0.492810i −0.134785 + 0.0250509i
\(388\) 0 0
\(389\) 22.8990 + 13.2207i 1.16102 + 0.670318i 0.951549 0.307496i \(-0.0994912\pi\)
0.209475 + 0.977814i \(0.432824\pi\)
\(390\) 0 0
\(391\) 44.4949 2.25020
\(392\) 0 0
\(393\) −34.6464 15.9617i −1.74768 0.805160i
\(394\) 0 0
\(395\) 6.00000 10.3923i 0.301893 0.522894i
\(396\) 0 0
\(397\) −4.67423 8.09601i −0.234593 0.406327i 0.724561 0.689210i \(-0.242042\pi\)
−0.959154 + 0.282883i \(0.908709\pi\)
\(398\) 0 0
\(399\) 10.6742 + 31.8519i 0.534380 + 1.59459i
\(400\) 0 0
\(401\) −6.39898 11.0834i −0.319550 0.553476i 0.660844 0.750523i \(-0.270198\pi\)
−0.980394 + 0.197047i \(0.936865\pi\)
\(402\) 0 0
\(403\) 7.34847 12.7279i 0.366053 0.634023i
\(404\) 0 0
\(405\) 12.5732 + 1.97846i 0.624768 + 0.0983103i
\(406\) 0 0
\(407\) 0.247449 0.0122656
\(408\) 0 0
\(409\) 17.8485 + 10.3048i 0.882550 + 0.509540i 0.871498 0.490398i \(-0.163149\pi\)
0.0110517 + 0.999939i \(0.496482\pi\)
\(410\) 0 0
\(411\) −1.17423 12.7440i −0.0579207 0.628614i
\(412\) 0 0
\(413\) −14.5732 25.2415i −0.717101 1.24206i
\(414\) 0 0
\(415\) 10.0227 + 17.3598i 0.491995 + 0.852161i
\(416\) 0 0
\(417\) −0.601021 + 0.0553782i −0.0294321 + 0.00271188i
\(418\) 0 0
\(419\) 3.74983i 0.183191i 0.995796 + 0.0915956i \(0.0291967\pi\)
−0.995796 + 0.0915956i \(0.970803\pi\)
\(420\) 0 0
\(421\) −26.0227 + 15.0242i −1.26827 + 0.732235i −0.974660 0.223690i \(-0.928190\pi\)
−0.293609 + 0.955926i \(0.594856\pi\)
\(422\) 0 0
\(423\) 14.6742 12.5457i 0.713486 0.609994i
\(424\) 0 0
\(425\) 18.8776i 0.915697i
\(426\) 0 0
\(427\) −14.3485 + 24.8523i −0.694371 + 1.20269i
\(428\) 0 0
\(429\) 1.89898 0.174973i 0.0916836 0.00844776i
\(430\) 0 0
\(431\) 16.3485 28.3164i 0.787478 1.36395i −0.140029 0.990147i \(-0.544720\pi\)
0.927507 0.373805i \(-0.121947\pi\)
\(432\) 0 0
\(433\) 11.6969 + 6.75323i 0.562119 + 0.324540i 0.753996 0.656880i \(-0.228124\pi\)
−0.191877 + 0.981419i \(0.561457\pi\)
\(434\) 0 0
\(435\) 4.89898 3.46410i 0.234888 0.166091i
\(436\) 0 0
\(437\) 21.1237 + 22.4452i 1.01048 + 1.07370i
\(438\) 0 0
\(439\) 2.32577 1.34278i 0.111003 0.0640875i −0.443471 0.896289i \(-0.646253\pi\)
0.554474 + 0.832201i \(0.312920\pi\)
\(440\) 0 0
\(441\) −12.7980 + 36.1981i −0.609427 + 1.72372i
\(442\) 0 0
\(443\) 25.3207 + 14.6189i 1.20302 + 0.694564i 0.961226 0.275763i \(-0.0889304\pi\)
0.241795 + 0.970327i \(0.422264\pi\)
\(444\) 0 0
\(445\) 23.8988i 1.13291i
\(446\) 0 0
\(447\) 7.67423 + 3.53553i 0.362979 + 0.167225i
\(448\) 0 0
\(449\) −11.2020 −0.528657 −0.264329 0.964433i \(-0.585150\pi\)
−0.264329 + 0.964433i \(0.585150\pi\)
\(450\) 0 0
\(451\) 0.825765 0.476756i 0.0388838 0.0224496i
\(452\) 0 0
\(453\) 25.5959 18.0990i 1.20260 0.850367i
\(454\) 0 0
\(455\) −21.7980 −1.02190
\(456\) 0 0
\(457\) −13.0000 −0.608114 −0.304057 0.952654i \(-0.598341\pi\)
−0.304057 + 0.952654i \(0.598341\pi\)
\(458\) 0 0
\(459\) 22.7980 23.4381i 1.06412 1.09400i
\(460\) 0 0
\(461\) 8.75255 5.05329i 0.407647 0.235355i −0.282131 0.959376i \(-0.591041\pi\)
0.689778 + 0.724021i \(0.257708\pi\)
\(462\) 0 0
\(463\) 0.202041 0.00938964 0.00469482 0.999989i \(-0.498506\pi\)
0.00469482 + 0.999989i \(0.498506\pi\)
\(464\) 0 0
\(465\) −4.34847 + 9.43879i −0.201655 + 0.437714i
\(466\) 0 0
\(467\) 32.4162i 1.50004i 0.661415 + 0.750020i \(0.269956\pi\)
−0.661415 + 0.750020i \(0.730044\pi\)
\(468\) 0 0
\(469\) −23.0227 13.2922i −1.06309 0.613775i
\(470\) 0 0
\(471\) 13.5505 29.4128i 0.624375 1.35527i
\(472\) 0 0
\(473\) 0.247449 0.142865i 0.0113777 0.00656892i
\(474\) 0 0
\(475\) −9.52270 + 8.96204i −0.436932 + 0.411206i
\(476\) 0 0
\(477\) 2.14643 + 2.51059i 0.0982782 + 0.114952i
\(478\) 0 0
\(479\) 35.1464 + 20.2918i 1.60588 + 0.927156i 0.990278 + 0.139099i \(0.0444208\pi\)
0.615603 + 0.788057i \(0.288913\pi\)
\(480\) 0 0
\(481\) 1.34847 2.33562i 0.0614849 0.106495i
\(482\) 0 0
\(483\) 5.00000 + 54.2650i 0.227508 + 2.46914i
\(484\) 0 0
\(485\) 9.67423 16.7563i 0.439284 0.760863i
\(486\) 0 0
\(487\) 16.5420i 0.749588i −0.927108 0.374794i \(-0.877713\pi\)
0.927108 0.374794i \(-0.122287\pi\)
\(488\) 0 0
\(489\) 3.65153 + 5.16404i 0.165128 + 0.233526i
\(490\) 0 0
\(491\) −4.10102 + 2.36773i −0.185076 + 0.106854i −0.589676 0.807640i \(-0.700744\pi\)
0.404599 + 0.914494i \(0.367411\pi\)
\(492\) 0 0
\(493\) 15.4135i 0.694188i
\(494\) 0 0
\(495\) −1.32577 + 0.246405i −0.0595887 + 0.0110751i
\(496\) 0 0
\(497\) −13.3485 23.1202i −0.598761 1.03708i
\(498\) 0 0
\(499\) 1.27526 + 2.20881i 0.0570883 + 0.0988798i 0.893157 0.449745i \(-0.148485\pi\)
−0.836069 + 0.548624i \(0.815152\pi\)
\(500\) 0 0
\(501\) −8.44949 + 0.778539i −0.377495 + 0.0347826i
\(502\) 0 0
\(503\) 13.4722 + 7.77817i 0.600695 + 0.346812i 0.769315 0.638870i \(-0.220598\pi\)
−0.168620 + 0.985681i \(0.553931\pi\)
\(504\) 0 0
\(505\) −14.0000 −0.622992
\(506\) 0 0
\(507\) −0.724745 + 1.57313i −0.0321870 + 0.0698653i
\(508\) 0 0
\(509\) 20.6969 35.8481i 0.917376 1.58894i 0.113990 0.993482i \(-0.463637\pi\)
0.803385 0.595459i \(-0.203030\pi\)
\(510\) 0 0
\(511\) −24.0227 41.6085i −1.06270 1.84065i
\(512\) 0 0
\(513\) 22.6464 + 0.373215i 0.999864 + 0.0164779i
\(514\) 0 0
\(515\) 8.44949 + 14.6349i 0.372329 + 0.644893i
\(516\) 0 0
\(517\) −1.02270 + 1.77138i −0.0449785 + 0.0779050i
\(518\) 0 0
\(519\) −7.89898 + 17.1455i −0.346727 + 0.752605i
\(520\) 0 0
\(521\) 16.1010 0.705399 0.352699 0.935737i \(-0.385264\pi\)
0.352699 + 0.935737i \(0.385264\pi\)
\(522\) 0 0
\(523\) −23.6969 13.6814i −1.03619 0.598247i −0.117442 0.993080i \(-0.537469\pi\)
−0.918753 + 0.394832i \(0.870803\pi\)
\(524\) 0 0
\(525\) −23.0227 + 2.12132i −1.00479 + 0.0925820i
\(526\) 0 0
\(527\) 13.3485 + 23.1202i 0.581468 + 1.00713i
\(528\) 0 0
\(529\) 13.5000 + 23.3827i 0.586957 + 1.01664i
\(530\) 0 0
\(531\) −19.3207 + 3.59091i −0.838445 + 0.155832i
\(532\) 0 0
\(533\) 10.3923i 0.450141i
\(534\) 0 0
\(535\) −6.00000 + 3.46410i −0.259403 + 0.149766i
\(536\) 0 0
\(537\) 22.3485 + 31.6055i 0.964408 + 1.36388i
\(538\) 0 0
\(539\) 4.06767i 0.175207i
\(540\) 0 0
\(541\) 9.34847 16.1920i 0.401922 0.696149i −0.592036 0.805912i \(-0.701676\pi\)
0.993958 + 0.109762i \(0.0350089\pi\)
\(542\) 0 0
\(543\) −2.07832 22.5560i −0.0891891 0.967970i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −26.3939 15.2385i −1.12852 0.651552i −0.184958 0.982746i \(-0.559215\pi\)
−0.943562 + 0.331195i \(0.892548\pi\)
\(548\) 0 0
\(549\) 12.5732 + 14.7064i 0.536612 + 0.627653i
\(550\) 0 0
\(551\) 7.77526 7.31747i 0.331237 0.311735i
\(552\) 0 0
\(553\) 32.6969 18.8776i 1.39042 0.802757i
\(554\) 0 0
\(555\) −0.797959 + 1.73205i −0.0338715 + 0.0735215i
\(556\) 0 0
\(557\) 24.2474 + 13.9993i 1.02740 + 0.593168i 0.916238 0.400634i \(-0.131210\pi\)
0.111159 + 0.993803i \(0.464544\pi\)
\(558\) 0 0
\(559\) 3.11416i 0.131715i
\(560\) 0 0
\(561\) −1.44949 + 3.14626i −0.0611975 + 0.132835i
\(562\) 0 0
\(563\) −22.8434 −0.962733 −0.481367 0.876519i \(-0.659859\pi\)
−0.481367 + 0.876519i \(0.659859\pi\)
\(564\) 0 0
\(565\) 0.977296 0.564242i 0.0411152 0.0237378i
\(566\) 0 0
\(567\) 31.1464 + 25.1701i 1.30803 + 1.05705i
\(568\) 0 0
\(569\) −34.2929 −1.43763 −0.718816 0.695201i \(-0.755315\pi\)
−0.718816 + 0.695201i \(0.755315\pi\)
\(570\) 0 0
\(571\) 11.0454 0.462236 0.231118 0.972926i \(-0.425762\pi\)
0.231118 + 0.972926i \(0.425762\pi\)
\(572\) 0 0
\(573\) 27.5959 19.5133i 1.15284 0.815178i
\(574\) 0 0
\(575\) −18.3712 + 10.6066i −0.766131 + 0.442326i
\(576\) 0 0
\(577\) −20.5959 −0.857419 −0.428710 0.903442i \(-0.641032\pi\)
−0.428710 + 0.903442i \(0.641032\pi\)
\(578\) 0 0
\(579\) 13.8990 + 6.40329i 0.577622 + 0.266111i
\(580\) 0 0
\(581\) 63.0682i 2.61651i
\(582\) 0 0
\(583\) −0.303062 0.174973i −0.0125515 0.00724663i
\(584\) 0 0
\(585\) −4.89898 + 13.8564i −0.202548 + 0.572892i
\(586\) 0 0
\(587\) −4.10102 + 2.36773i −0.169267 + 0.0977265i −0.582240 0.813017i \(-0.697824\pi\)
0.412973 + 0.910743i \(0.364490\pi\)
\(588\) 0 0
\(589\) −5.32577 + 17.7098i −0.219444 + 0.729719i
\(590\) 0 0
\(591\) 0.696938 0.492810i 0.0286682 0.0202715i
\(592\) 0 0
\(593\) 24.0959 + 13.9118i 0.989501 + 0.571289i 0.905125 0.425145i \(-0.139777\pi\)
0.0843757 + 0.996434i \(0.473110\pi\)
\(594\) 0 0
\(595\) 19.7980 34.2911i 0.811637 1.40580i
\(596\) 0 0
\(597\) −11.8990 + 1.09638i −0.486993 + 0.0448717i
\(598\) 0 0
\(599\) 14.5732 25.2415i 0.595445 1.03134i −0.398038 0.917369i \(-0.630309\pi\)
0.993484 0.113973i \(-0.0363577\pi\)
\(600\) 0 0
\(601\) 31.0019i 1.26460i −0.774725 0.632298i \(-0.782112\pi\)
0.774725 0.632298i \(-0.217888\pi\)
\(602\) 0 0
\(603\) −13.6237 + 11.6476i −0.554801 + 0.474327i
\(604\) 0 0
\(605\) −13.3485 + 7.70674i −0.542692 + 0.313324i
\(606\) 0 0
\(607\) 36.9766i 1.50084i −0.660964 0.750418i \(-0.729852\pi\)
0.660964 0.750418i \(-0.270148\pi\)
\(608\) 0 0
\(609\) 18.7980 1.73205i 0.761732 0.0701862i
\(610\) 0 0
\(611\) 11.1464 + 19.3062i 0.450936 + 0.781044i
\(612\) 0 0
\(613\) −14.1010 24.4237i −0.569535 0.986463i −0.996612 0.0822481i \(-0.973790\pi\)
0.427077 0.904215i \(-0.359543\pi\)
\(614\) 0 0
\(615\) 0.674235 + 7.31747i 0.0271878 + 0.295069i
\(616\) 0 0
\(617\) −12.9495 7.47639i −0.521327 0.300988i 0.216151 0.976360i \(-0.430650\pi\)
−0.737477 + 0.675372i \(0.763983\pi\)
\(618\) 0 0
\(619\) 1.30306 0.0523745 0.0261872 0.999657i \(-0.491663\pi\)
0.0261872 + 0.999657i \(0.491663\pi\)
\(620\) 0 0
\(621\) 35.6186 + 9.01742i 1.42933 + 0.361856i
\(622\) 0 0
\(623\) 37.5959 65.1180i 1.50625 2.60890i
\(624\) 0 0
\(625\) 0.500000 + 0.866025i 0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −2.27526 + 0.762485i −0.0908649 + 0.0304507i
\(628\) 0 0
\(629\) 2.44949 + 4.24264i 0.0976676 + 0.169165i
\(630\) 0 0
\(631\) −4.87628 + 8.44596i −0.194121 + 0.336228i −0.946612 0.322375i \(-0.895519\pi\)
0.752491 + 0.658603i \(0.228852\pi\)
\(632\) 0 0
\(633\) 24.2474 + 11.1708i 0.963750 + 0.444001i
\(634\) 0 0
\(635\) −14.6969 −0.583230
\(636\) 0 0
\(637\) −38.3939 22.1667i −1.52122 0.878277i
\(638\) 0 0
\(639\) −17.6969 + 3.28913i −0.700080 + 0.130116i
\(640\) 0 0
\(641\) −16.1969 28.0539i −0.639741 1.10806i −0.985490 0.169736i \(-0.945708\pi\)
0.345749 0.938327i \(-0.387625\pi\)
\(642\) 0 0
\(643\) −12.0732 20.9114i −0.476121 0.824666i 0.523505 0.852023i \(-0.324624\pi\)
−0.999626 + 0.0273569i \(0.991291\pi\)
\(644\) 0 0
\(645\) 0.202041 + 2.19275i 0.00795536 + 0.0863396i
\(646\) 0 0
\(647\) 7.84961i 0.308600i −0.988024 0.154300i \(-0.950688\pi\)
0.988024 0.154300i \(-0.0493122\pi\)
\(648\) 0 0
\(649\) 1.80306 1.04100i 0.0707764 0.0408627i
\(650\) 0 0
\(651\) −26.6969 + 18.8776i −1.04634 + 0.739871i
\(652\) 0 0
\(653\) 19.5133i 0.763613i −0.924242 0.381806i \(-0.875302\pi\)
0.924242 0.381806i \(-0.124698\pi\)
\(654\) 0 0
\(655\) −15.5732 + 26.9736i −0.608496 + 1.05395i
\(656\) 0 0
\(657\) −31.8485 + 5.91931i −1.24253 + 0.230934i
\(658\) 0 0
\(659\) −12.0000 + 20.7846i −0.467454 + 0.809653i −0.999309 0.0371821i \(-0.988162\pi\)
0.531855 + 0.846836i \(0.321495\pi\)
\(660\) 0 0
\(661\) −25.7196 14.8492i −1.00038 0.577569i −0.0920180 0.995757i \(-0.529332\pi\)
−0.908360 + 0.418189i \(0.862665\pi\)
\(662\) 0 0
\(663\) 21.7980 + 30.8270i 0.846563 + 1.19722i
\(664\) 0 0
\(665\) 26.6969 6.29253i 1.03526 0.244014i
\(666\) 0 0
\(667\) 15.0000 8.66025i 0.580802 0.335326i
\(668\) 0 0
\(669\) −15.1237 6.96753i −0.584717 0.269380i
\(670\) 0 0
\(671\) −1.77526 1.02494i −0.0685330 0.0395675i
\(672\) 0 0
\(673\) 3.46410i 0.133531i 0.997769 + 0.0667657i \(0.0212680\pi\)
−0.997769 + 0.0667657i \(0.978732\pi\)
\(674\) 0 0
\(675\) −3.82577 + 15.1117i −0.147254 + 0.581650i
\(676\) 0 0
\(677\) 3.30306 0.126947 0.0634735 0.997984i \(-0.479782\pi\)
0.0634735 + 0.997984i \(0.479782\pi\)
\(678\) 0 0
\(679\) 52.7196 30.4377i 2.02319 1.16809i
\(680\) 0 0
\(681\) −5.44949 7.70674i −0.208825 0.295323i
\(682\) 0 0
\(683\) −41.3939 −1.58389 −0.791946 0.610591i \(-0.790932\pi\)
−0.791946 + 0.610591i \(0.790932\pi\)
\(684\) 0 0
\(685\) −10.4495 −0.399254
\(686\) 0 0
\(687\) 8.89898 + 12.5851i 0.339517 + 0.480150i
\(688\) 0 0
\(689\) −3.30306 + 1.90702i −0.125837 + 0.0726518i
\(690\) 0 0
\(691\) 40.0000 1.52167 0.760836 0.648944i \(-0.224789\pi\)
0.760836 + 0.648944i \(0.224789\pi\)
\(692\) 0 0
\(693\) −4.00000 1.41421i −0.151947 0.0537215i
\(694\) 0 0
\(695\) 0.492810i 0.0186933i
\(696\) 0 0
\(697\) 16.3485 + 9.43879i 0.619242 + 0.357520i
\(698\) 0 0
\(699\) −10.1742 4.68729i −0.384825 0.177290i
\(700\) 0 0
\(701\) −8.57321 + 4.94975i −0.323806 + 0.186949i −0.653088 0.757282i \(-0.726527\pi\)
0.329282 + 0.944232i \(0.393193\pi\)
\(702\) 0 0
\(703\) −0.977296 + 3.24980i −0.0368594 + 0.122569i
\(704\) 0 0
\(705\) −9.10102 12.8708i −0.342764 0.484742i
\(706\) 0 0
\(707\) −38.1464 22.0239i −1.43464 0.828292i
\(708\) 0 0
\(709\) 1.32577 2.29629i 0.0497902 0.0862391i −0.840056 0.542499i \(-0.817478\pi\)
0.889846 + 0.456260i \(0.150811\pi\)
\(710\) 0 0
\(711\) −4.65153 25.0273i −0.174446 0.938595i
\(712\) 0 0
\(713\) −15.0000 + 25.9808i −0.561754 + 0.972987i
\(714\) 0 0
\(715\) 1.55708i 0.0582314i
\(716\) 0 0
\(717\) 10.2020 7.21393i 0.381002 0.269409i
\(718\) 0 0
\(719\) −8.14643 + 4.70334i −0.303811 + 0.175405i −0.644153 0.764896i \(-0.722790\pi\)
0.340343 + 0.940301i \(0.389457\pi\)
\(720\) 0 0
\(721\) 53.1687i 1.98010i
\(722\) 0 0
\(723\) −1.62372 17.6223i −0.0603870 0.655380i
\(724\) 0 0
\(725\) 3.67423 + 6.36396i 0.136458 + 0.236352i
\(726\) 0 0
\(727\) 4.00000 + 6.92820i 0.148352 + 0.256953i 0.930618 0.365991i \(-0.119270\pi\)
−0.782267 + 0.622944i \(0.785937\pi\)
\(728\) 0 0
\(729\) 23.0000 14.1421i 0.851852 0.523783i
\(730\) 0 0
\(731\) 4.89898 + 2.82843i 0.181195 + 0.104613i
\(732\) 0 0
\(733\) 24.0454 0.888137 0.444069 0.895993i \(-0.353535\pi\)
0.444069 + 0.895993i \(0.353535\pi\)
\(734\) 0 0
\(735\) 28.4722 + 13.1172i 1.05021 + 0.483835i
\(736\) 0 0
\(737\) 0.949490 1.64456i 0.0349749 0.0605783i
\(738\) 0 0
\(739\) 4.82577 + 8.35847i 0.177519 + 0.307471i 0.941030 0.338323i \(-0.109860\pi\)
−0.763511 + 0.645794i \(0.776526\pi\)
\(740\) 0 0
\(741\) −5.20204 + 25.6308i −0.191102 + 0.941572i
\(742\) 0 0
\(743\) −9.67423 16.7563i −0.354913 0.614728i 0.632190 0.774814i \(-0.282156\pi\)
−0.987103 + 0.160086i \(0.948823\pi\)
\(744\) 0 0
\(745\) 3.44949 5.97469i 0.126380 0.218896i
\(746\) 0 0
\(747\) 40.0908 + 14.1742i 1.46685 + 0.518608i
\(748\) 0 0
\(749\) −21.7980 −0.796480
\(750\) 0 0
\(751\) 11.6969 + 6.75323i 0.426827 + 0.246429i 0.697994 0.716103i \(-0.254076\pi\)
−0.271167 + 0.962532i \(0.587409\pi\)
\(752\) 0 0
\(753\) 1.05051 + 11.4012i 0.0382827 + 0.415483i
\(754\) 0 0
\(755\) −12.7980 22.1667i −0.465765 0.806729i
\(756\) 0 0
\(757\) −9.69694 16.7956i −0.352441 0.610446i 0.634235 0.773140i \(-0.281315\pi\)
−0.986677 + 0.162694i \(0.947982\pi\)
\(758\) 0 0
\(759\) −3.87628 + 0.357161i −0.140700 + 0.0129641i
\(760\) 0 0
\(761\) 41.9657i 1.52126i 0.649188 + 0.760628i \(0.275109\pi\)
−0.649188 + 0.760628i \(0.724891\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −17.3485 20.2918i −0.627235 0.733652i
\(766\) 0 0
\(767\) 22.6916i 0.819347i
\(768\) 0 0
\(769\) 17.7980 30.8270i 0.641811 1.11165i −0.343217 0.939256i \(-0.611517\pi\)
0.985028 0.172393i \(-0.0551499\pi\)
\(770\) 0 0
\(771\) −25.8712 + 2.38378i −0.931728 + 0.0858497i
\(772\) 0 0
\(773\) −1.22474 + 2.12132i −0.0440510 + 0.0762986i −0.887210 0.461365i \(-0.847360\pi\)
0.843159 + 0.537664i \(0.180693\pi\)
\(774\) 0 0
\(775\) −11.0227 6.36396i −0.395947 0.228600i
\(776\) 0 0
\(777\) −4.89898 + 3.46410i −0.175750 + 0.124274i
\(778\) 0 0
\(779\) 3.00000 + 12.7279i 0.107486 + 0.456025i
\(780\) 0 0
\(781\) 1.65153 0.953512i 0.0590964 0.0341193i
\(782\) 0 0
\(783\) 3.12372 12.3387i 0.111633 0.440947i
\(784\) 0 0
\(785\) −22.8990 13.2207i −0.817300 0.471868i
\(786\) 0 0
\(787\) 17.9241i 0.638924i 0.947599 + 0.319462i \(0.103502\pi\)
−0.947599 + 0.319462i \(0.896498\pi\)
\(788\) 0 0
\(789\) −18.5732 8.55671i −0.661224 0.304627i
\(790\) 0 0
\(791\) 3.55051 0.126242