Properties

Label 315.2.bz.a.208.1
Level 315
Weight 2
Character 315.208
Analytic conductor 2.515
Analytic rank 1
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 315.bz (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.51528766367\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 208.1
Root \(0.866025 - 0.500000i\)
Character \(\chi\) = 315.208
Dual form 315.2.bz.a.262.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 1.86603i) q^{2} +(-1.50000 + 0.866025i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(-0.366025 - 0.366025i) q^{8} +O(q^{10})\) \(q+(-0.500000 - 1.86603i) q^{2} +(-1.50000 + 0.866025i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(3.23205 + 2.86603i) q^{10} +(0.366025 + 0.633975i) q^{11} +(-2.00000 + 2.00000i) q^{13} +(-0.366025 + 5.09808i) q^{14} +(-2.23205 + 3.86603i) q^{16} +(-0.267949 + 1.00000i) q^{17} +(-1.36603 + 2.36603i) q^{19} +(1.73205 - 3.46410i) q^{20} +(1.00000 - 1.00000i) q^{22} +(-6.96410 + 1.86603i) q^{23} +(1.96410 - 4.59808i) q^{25} +(4.73205 + 2.73205i) q^{26} +(4.50000 - 0.866025i) q^{28} -3.00000i q^{29} +(0.464102 - 0.267949i) q^{31} +(7.33013 + 1.96410i) q^{32} +2.00000 q^{34} +(5.73205 - 1.46410i) q^{35} +(-1.26795 - 4.73205i) q^{37} +(5.09808 + 1.36603i) q^{38} +(1.13397 + 0.232051i) q^{40} +0.464102i q^{41} +(-5.83013 - 5.83013i) q^{43} +(-1.09808 - 0.633975i) q^{44} +(6.96410 + 12.0622i) q^{46} +(-0.633975 + 0.169873i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-9.56218 - 1.36603i) q^{50} +(1.26795 - 4.73205i) q^{52} +(1.83013 - 6.83013i) q^{53} +(-1.46410 - 0.732051i) q^{55} +(0.598076 + 1.23205i) q^{56} +(-5.59808 + 1.50000i) q^{58} +(-1.09808 - 1.90192i) q^{59} +(-7.33013 - 4.23205i) q^{61} +(-0.732051 - 0.732051i) q^{62} -5.73205i q^{64} +(1.26795 - 6.19615i) q^{65} +(1.13397 + 0.303848i) q^{67} +(-0.464102 - 1.73205i) q^{68} +(-5.59808 - 9.96410i) q^{70} -4.73205 q^{71} +(3.46410 + 0.928203i) q^{73} +(-8.19615 + 4.73205i) q^{74} -4.73205i q^{76} +(-0.366025 - 1.90192i) q^{77} +(-5.83013 - 3.36603i) q^{79} +(-0.598076 - 9.96410i) q^{80} +(0.866025 - 0.232051i) q^{82} +(-3.09808 + 3.09808i) q^{83} +(-0.732051 - 2.19615i) q^{85} +(-7.96410 + 13.7942i) q^{86} +(0.0980762 - 0.366025i) q^{88} +(-8.33013 + 14.4282i) q^{89} +(6.73205 - 3.26795i) q^{91} +(8.83013 - 8.83013i) q^{92} +(0.633975 + 1.09808i) q^{94} +(-0.366025 - 6.09808i) q^{95} +(7.92820 + 7.92820i) q^{97} +(5.33013 - 12.4282i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 6q^{4} - 4q^{5} - 10q^{7} + 2q^{8} + O(q^{10}) \) \( 4q - 2q^{2} - 6q^{4} - 4q^{5} - 10q^{7} + 2q^{8} + 6q^{10} - 2q^{11} - 8q^{13} + 2q^{14} - 2q^{16} - 8q^{17} - 2q^{19} + 4q^{22} - 14q^{23} - 6q^{25} + 12q^{26} + 18q^{28} - 12q^{31} + 12q^{32} + 8q^{34} + 16q^{35} - 12q^{37} + 10q^{38} + 8q^{40} - 6q^{43} + 6q^{44} + 14q^{46} - 6q^{47} + 22q^{49} - 14q^{50} + 12q^{52} - 10q^{53} + 8q^{55} - 8q^{56} - 12q^{58} + 6q^{59} - 12q^{61} + 4q^{62} + 12q^{65} + 8q^{67} + 12q^{68} - 12q^{70} - 12q^{71} - 12q^{74} + 2q^{77} - 6q^{79} + 8q^{80} - 2q^{83} + 4q^{85} - 18q^{86} - 10q^{88} - 16q^{89} + 20q^{91} + 18q^{92} + 6q^{94} + 2q^{95} + 4q^{97} + 4q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 1.86603i −0.353553 1.31948i −0.882295 0.470696i \(-0.844003\pi\)
0.528742 0.848783i \(-0.322664\pi\)
\(3\) 0 0
\(4\) −1.50000 + 0.866025i −0.750000 + 0.433013i
\(5\) −1.86603 + 1.23205i −0.834512 + 0.550990i
\(6\) 0 0
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) −0.366025 0.366025i −0.129410 0.129410i
\(9\) 0 0
\(10\) 3.23205 + 2.86603i 1.02206 + 0.906317i
\(11\) 0.366025 + 0.633975i 0.110361 + 0.191151i 0.915916 0.401371i \(-0.131466\pi\)
−0.805555 + 0.592521i \(0.798133\pi\)
\(12\) 0 0
\(13\) −2.00000 + 2.00000i −0.554700 + 0.554700i −0.927794 0.373094i \(-0.878297\pi\)
0.373094 + 0.927794i \(0.378297\pi\)
\(14\) −0.366025 + 5.09808i −0.0978244 + 1.36252i
\(15\) 0 0
\(16\) −2.23205 + 3.86603i −0.558013 + 0.966506i
\(17\) −0.267949 + 1.00000i −0.0649872 + 0.242536i −0.990777 0.135503i \(-0.956735\pi\)
0.925790 + 0.378039i \(0.123401\pi\)
\(18\) 0 0
\(19\) −1.36603 + 2.36603i −0.313388 + 0.542803i −0.979093 0.203411i \(-0.934797\pi\)
0.665706 + 0.746214i \(0.268131\pi\)
\(20\) 1.73205 3.46410i 0.387298 0.774597i
\(21\) 0 0
\(22\) 1.00000 1.00000i 0.213201 0.213201i
\(23\) −6.96410 + 1.86603i −1.45212 + 0.389093i −0.896759 0.442519i \(-0.854085\pi\)
−0.555357 + 0.831612i \(0.687418\pi\)
\(24\) 0 0
\(25\) 1.96410 4.59808i 0.392820 0.919615i
\(26\) 4.73205 + 2.73205i 0.928032 + 0.535799i
\(27\) 0 0
\(28\) 4.50000 0.866025i 0.850420 0.163663i
\(29\) 3.00000i 0.557086i −0.960424 0.278543i \(-0.910149\pi\)
0.960424 0.278543i \(-0.0898515\pi\)
\(30\) 0 0
\(31\) 0.464102 0.267949i 0.0833551 0.0481251i −0.457743 0.889085i \(-0.651342\pi\)
0.541098 + 0.840959i \(0.318009\pi\)
\(32\) 7.33013 + 1.96410i 1.29580 + 0.347207i
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) 5.73205 1.46410i 0.968893 0.247478i
\(36\) 0 0
\(37\) −1.26795 4.73205i −0.208450 0.777944i −0.988370 0.152066i \(-0.951407\pi\)
0.779921 0.625878i \(-0.215259\pi\)
\(38\) 5.09808 + 1.36603i 0.827017 + 0.221599i
\(39\) 0 0
\(40\) 1.13397 + 0.232051i 0.179297 + 0.0366905i
\(41\) 0.464102i 0.0724805i 0.999343 + 0.0362402i \(0.0115382\pi\)
−0.999343 + 0.0362402i \(0.988462\pi\)
\(42\) 0 0
\(43\) −5.83013 5.83013i −0.889086 0.889086i 0.105349 0.994435i \(-0.466404\pi\)
−0.994435 + 0.105349i \(0.966404\pi\)
\(44\) −1.09808 0.633975i −0.165541 0.0955753i
\(45\) 0 0
\(46\) 6.96410 + 12.0622i 1.02680 + 1.77847i
\(47\) −0.633975 + 0.169873i −0.0924747 + 0.0247785i −0.304760 0.952429i \(-0.598576\pi\)
0.212285 + 0.977208i \(0.431909\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) −9.56218 1.36603i −1.35230 0.193185i
\(51\) 0 0
\(52\) 1.26795 4.73205i 0.175833 0.656217i
\(53\) 1.83013 6.83013i 0.251387 0.938190i −0.718677 0.695344i \(-0.755252\pi\)
0.970065 0.242846i \(-0.0780811\pi\)
\(54\) 0 0
\(55\) −1.46410 0.732051i −0.197419 0.0987097i
\(56\) 0.598076 + 1.23205i 0.0799213 + 0.164640i
\(57\) 0 0
\(58\) −5.59808 + 1.50000i −0.735063 + 0.196960i
\(59\) −1.09808 1.90192i −0.142957 0.247609i 0.785652 0.618669i \(-0.212328\pi\)
−0.928609 + 0.371060i \(0.878995\pi\)
\(60\) 0 0
\(61\) −7.33013 4.23205i −0.938527 0.541859i −0.0490285 0.998797i \(-0.515613\pi\)
−0.889498 + 0.456939i \(0.848946\pi\)
\(62\) −0.732051 0.732051i −0.0929705 0.0929705i
\(63\) 0 0
\(64\) 5.73205i 0.716506i
\(65\) 1.26795 6.19615i 0.157270 0.768538i
\(66\) 0 0
\(67\) 1.13397 + 0.303848i 0.138537 + 0.0371209i 0.327421 0.944878i \(-0.393820\pi\)
−0.188884 + 0.981999i \(0.560487\pi\)
\(68\) −0.464102 1.73205i −0.0562806 0.210042i
\(69\) 0 0
\(70\) −5.59808 9.96410i −0.669098 1.19094i
\(71\) −4.73205 −0.561591 −0.280796 0.959768i \(-0.590598\pi\)
−0.280796 + 0.959768i \(0.590598\pi\)
\(72\) 0 0
\(73\) 3.46410 + 0.928203i 0.405442 + 0.108638i 0.455776 0.890094i \(-0.349362\pi\)
−0.0503336 + 0.998732i \(0.516028\pi\)
\(74\) −8.19615 + 4.73205i −0.952783 + 0.550090i
\(75\) 0 0
\(76\) 4.73205i 0.542803i
\(77\) −0.366025 1.90192i −0.0417125 0.216744i
\(78\) 0 0
\(79\) −5.83013 3.36603i −0.655941 0.378707i 0.134788 0.990874i \(-0.456965\pi\)
−0.790728 + 0.612167i \(0.790298\pi\)
\(80\) −0.598076 9.96410i −0.0668670 1.11402i
\(81\) 0 0
\(82\) 0.866025 0.232051i 0.0956365 0.0256257i
\(83\) −3.09808 + 3.09808i −0.340058 + 0.340058i −0.856389 0.516331i \(-0.827297\pi\)
0.516331 + 0.856389i \(0.327297\pi\)
\(84\) 0 0
\(85\) −0.732051 2.19615i −0.0794021 0.238206i
\(86\) −7.96410 + 13.7942i −0.858791 + 1.48747i
\(87\) 0 0
\(88\) 0.0980762 0.366025i 0.0104550 0.0390184i
\(89\) −8.33013 + 14.4282i −0.882992 + 1.52939i −0.0349934 + 0.999388i \(0.511141\pi\)
−0.847998 + 0.529999i \(0.822192\pi\)
\(90\) 0 0
\(91\) 6.73205 3.26795i 0.705711 0.342574i
\(92\) 8.83013 8.83013i 0.920604 0.920604i
\(93\) 0 0
\(94\) 0.633975 + 1.09808i 0.0653895 + 0.113258i
\(95\) −0.366025 6.09808i −0.0375534 0.625649i
\(96\) 0 0
\(97\) 7.92820 + 7.92820i 0.804987 + 0.804987i 0.983870 0.178883i \(-0.0572484\pi\)
−0.178883 + 0.983870i \(0.557248\pi\)
\(98\) 5.33013 12.4282i 0.538424 1.25544i
\(99\) 0 0
\(100\) 1.03590 + 8.59808i 0.103590 + 0.859808i
\(101\) 10.1603 5.86603i 1.01098 0.583691i 0.0995037 0.995037i \(-0.468274\pi\)
0.911479 + 0.411346i \(0.134941\pi\)
\(102\) 0 0
\(103\) −0.598076 2.23205i −0.0589302 0.219931i 0.930181 0.367102i \(-0.119650\pi\)
−0.989111 + 0.147171i \(0.952983\pi\)
\(104\) 1.46410 0.143567
\(105\) 0 0
\(106\) −13.6603 −1.32680
\(107\) −2.30385 8.59808i −0.222721 0.831207i −0.983305 0.181967i \(-0.941754\pi\)
0.760583 0.649240i \(-0.224913\pi\)
\(108\) 0 0
\(109\) −12.2321 + 7.06218i −1.17162 + 0.676434i −0.954061 0.299614i \(-0.903142\pi\)
−0.217557 + 0.976048i \(0.569809\pi\)
\(110\) −0.633975 + 3.09808i −0.0604471 + 0.295390i
\(111\) 0 0
\(112\) 8.92820 7.73205i 0.843636 0.730610i
\(113\) 4.26795 + 4.26795i 0.401495 + 0.401495i 0.878760 0.477265i \(-0.158372\pi\)
−0.477265 + 0.878760i \(0.658372\pi\)
\(114\) 0 0
\(115\) 10.6962 12.0622i 0.997421 1.12480i
\(116\) 2.59808 + 4.50000i 0.241225 + 0.417815i
\(117\) 0 0
\(118\) −3.00000 + 3.00000i −0.276172 + 0.276172i
\(119\) 1.53590 2.26795i 0.140796 0.207903i
\(120\) 0 0
\(121\) 5.23205 9.06218i 0.475641 0.823834i
\(122\) −4.23205 + 15.7942i −0.383152 + 1.42994i
\(123\) 0 0
\(124\) −0.464102 + 0.803848i −0.0416776 + 0.0721876i
\(125\) 2.00000 + 11.0000i 0.178885 + 0.983870i
\(126\) 0 0
\(127\) −6.46410 + 6.46410i −0.573596 + 0.573596i −0.933132 0.359535i \(-0.882935\pi\)
0.359535 + 0.933132i \(0.382935\pi\)
\(128\) 3.96410 1.06218i 0.350380 0.0938841i
\(129\) 0 0
\(130\) −12.1962 + 0.732051i −1.06967 + 0.0642051i
\(131\) −7.39230 4.26795i −0.645869 0.372892i 0.141003 0.990009i \(-0.454967\pi\)
−0.786872 + 0.617117i \(0.788301\pi\)
\(132\) 0 0
\(133\) 5.46410 4.73205i 0.473798 0.410321i
\(134\) 2.26795i 0.195921i
\(135\) 0 0
\(136\) 0.464102 0.267949i 0.0397964 0.0229765i
\(137\) 10.4641 + 2.80385i 0.894009 + 0.239549i 0.676441 0.736496i \(-0.263521\pi\)
0.217567 + 0.976045i \(0.430188\pi\)
\(138\) 0 0
\(139\) 11.6603 0.989010 0.494505 0.869175i \(-0.335349\pi\)
0.494505 + 0.869175i \(0.335349\pi\)
\(140\) −7.33013 + 7.16025i −0.619509 + 0.605152i
\(141\) 0 0
\(142\) 2.36603 + 8.83013i 0.198552 + 0.741008i
\(143\) −2.00000 0.535898i −0.167248 0.0448141i
\(144\) 0 0
\(145\) 3.69615 + 5.59808i 0.306949 + 0.464895i
\(146\) 6.92820i 0.573382i
\(147\) 0 0
\(148\) 6.00000 + 6.00000i 0.493197 + 0.493197i
\(149\) 9.69615 + 5.59808i 0.794340 + 0.458612i 0.841488 0.540276i \(-0.181680\pi\)
−0.0471484 + 0.998888i \(0.515013\pi\)
\(150\) 0 0
\(151\) 6.92820 + 12.0000i 0.563809 + 0.976546i 0.997159 + 0.0753205i \(0.0239980\pi\)
−0.433350 + 0.901226i \(0.642669\pi\)
\(152\) 1.36603 0.366025i 0.110799 0.0296886i
\(153\) 0 0
\(154\) −3.36603 + 1.63397i −0.271242 + 0.131669i
\(155\) −0.535898 + 1.07180i −0.0430444 + 0.0860888i
\(156\) 0 0
\(157\) −6.36603 + 23.7583i −0.508064 + 1.89612i −0.0691164 + 0.997609i \(0.522018\pi\)
−0.438948 + 0.898513i \(0.644649\pi\)
\(158\) −3.36603 + 12.5622i −0.267787 + 0.999393i
\(159\) 0 0
\(160\) −16.0981 + 5.36603i −1.27266 + 0.424222i
\(161\) 19.0263 + 1.36603i 1.49948 + 0.107658i
\(162\) 0 0
\(163\) −5.36603 + 1.43782i −0.420300 + 0.112619i −0.462769 0.886479i \(-0.653144\pi\)
0.0424696 + 0.999098i \(0.486477\pi\)
\(164\) −0.401924 0.696152i −0.0313850 0.0543604i
\(165\) 0 0
\(166\) 7.33013 + 4.23205i 0.568928 + 0.328471i
\(167\) 10.7583 + 10.7583i 0.832505 + 0.832505i 0.987859 0.155354i \(-0.0496519\pi\)
−0.155354 + 0.987859i \(0.549652\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) −3.73205 + 2.46410i −0.286235 + 0.188988i
\(171\) 0 0
\(172\) 13.7942 + 3.69615i 1.05180 + 0.281829i
\(173\) −6.07180 22.6603i −0.461630 1.72283i −0.667827 0.744317i \(-0.732775\pi\)
0.206197 0.978511i \(-0.433891\pi\)
\(174\) 0 0
\(175\) −8.89230 + 9.79423i −0.672195 + 0.740374i
\(176\) −3.26795 −0.246331
\(177\) 0 0
\(178\) 31.0885 + 8.33013i 2.33018 + 0.624369i
\(179\) −17.1962 + 9.92820i −1.28530 + 0.742069i −0.977812 0.209483i \(-0.932822\pi\)
−0.307488 + 0.951552i \(0.599489\pi\)
\(180\) 0 0
\(181\) 9.19615i 0.683545i −0.939783 0.341772i \(-0.888973\pi\)
0.939783 0.341772i \(-0.111027\pi\)
\(182\) −9.46410 10.9282i −0.701526 0.810052i
\(183\) 0 0
\(184\) 3.23205 + 1.86603i 0.238270 + 0.137565i
\(185\) 8.19615 + 7.26795i 0.602593 + 0.534350i
\(186\) 0 0
\(187\) −0.732051 + 0.196152i −0.0535329 + 0.0143441i
\(188\) 0.803848 0.803848i 0.0586266 0.0586266i
\(189\) 0 0
\(190\) −11.1962 + 3.73205i −0.812254 + 0.270751i
\(191\) 8.36603 14.4904i 0.605344 1.04849i −0.386653 0.922225i \(-0.626369\pi\)
0.991997 0.126262i \(-0.0402979\pi\)
\(192\) 0 0
\(193\) 0.830127 3.09808i 0.0597539 0.223004i −0.929592 0.368591i \(-0.879840\pi\)
0.989346 + 0.145587i \(0.0465070\pi\)
\(194\) 10.8301 18.7583i 0.777558 1.34677i
\(195\) 0 0
\(196\) −12.0000 1.73205i −0.857143 0.123718i
\(197\) −14.1244 + 14.1244i −1.00632 + 1.00632i −0.00633876 + 0.999980i \(0.502018\pi\)
−0.999980 + 0.00633876i \(0.997982\pi\)
\(198\) 0 0
\(199\) −12.4641 21.5885i −0.883557 1.53037i −0.847359 0.531021i \(-0.821809\pi\)
−0.0361978 0.999345i \(-0.511525\pi\)
\(200\) −2.40192 + 0.964102i −0.169842 + 0.0681723i
\(201\) 0 0
\(202\) −16.0263 16.0263i −1.12761 1.12761i
\(203\) −2.59808 + 7.50000i −0.182349 + 0.526397i
\(204\) 0 0
\(205\) −0.571797 0.866025i −0.0399360 0.0604858i
\(206\) −3.86603 + 2.23205i −0.269359 + 0.155514i
\(207\) 0 0
\(208\) −3.26795 12.1962i −0.226592 0.845651i
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) 10.1962 0.701932 0.350966 0.936388i \(-0.385853\pi\)
0.350966 + 0.936388i \(0.385853\pi\)
\(212\) 3.16987 + 11.8301i 0.217708 + 0.812496i
\(213\) 0 0
\(214\) −14.8923 + 8.59808i −1.01802 + 0.587752i
\(215\) 18.0622 + 3.69615i 1.23183 + 0.252076i
\(216\) 0 0
\(217\) −1.39230 + 0.267949i −0.0945158 + 0.0181896i
\(218\) 19.2942 + 19.2942i 1.30677 + 1.30677i
\(219\) 0 0
\(220\) 2.83013 0.169873i 0.190807 0.0114528i
\(221\) −1.46410 2.53590i −0.0984861 0.170583i
\(222\) 0 0
\(223\) −6.12436 + 6.12436i −0.410117 + 0.410117i −0.881779 0.471662i \(-0.843654\pi\)
0.471662 + 0.881779i \(0.343654\pi\)
\(224\) −16.6244 11.2583i −1.11076 0.752229i
\(225\) 0 0
\(226\) 5.83013 10.0981i 0.387814 0.671714i
\(227\) −0.0262794 + 0.0980762i −0.00174423 + 0.00650955i −0.966792 0.255563i \(-0.917739\pi\)
0.965048 + 0.262072i \(0.0844059\pi\)
\(228\) 0 0
\(229\) 1.19615 2.07180i 0.0790440 0.136908i −0.823794 0.566890i \(-0.808147\pi\)
0.902838 + 0.429981i \(0.141480\pi\)
\(230\) −27.8564 13.9282i −1.83680 0.918399i
\(231\) 0 0
\(232\) −1.09808 + 1.09808i −0.0720922 + 0.0720922i
\(233\) −1.73205 + 0.464102i −0.113470 + 0.0304043i −0.315107 0.949056i \(-0.602041\pi\)
0.201637 + 0.979460i \(0.435374\pi\)
\(234\) 0 0
\(235\) 0.973721 1.09808i 0.0635185 0.0716306i
\(236\) 3.29423 + 1.90192i 0.214436 + 0.123805i
\(237\) 0 0
\(238\) −5.00000 1.73205i −0.324102 0.112272i
\(239\) 18.3923i 1.18970i −0.803837 0.594850i \(-0.797212\pi\)
0.803837 0.594850i \(-0.202788\pi\)
\(240\) 0 0
\(241\) 14.5359 8.39230i 0.936340 0.540596i 0.0475286 0.998870i \(-0.484865\pi\)
0.888811 + 0.458274i \(0.151532\pi\)
\(242\) −19.5263 5.23205i −1.25520 0.336329i
\(243\) 0 0
\(244\) 14.6603 0.938527
\(245\) −15.5981 1.30385i −0.996525 0.0832998i
\(246\) 0 0
\(247\) −2.00000 7.46410i −0.127257 0.474929i
\(248\) −0.267949 0.0717968i −0.0170148 0.00455910i
\(249\) 0 0
\(250\) 19.5263 9.23205i 1.23495 0.583886i
\(251\) 5.85641i 0.369653i −0.982771 0.184827i \(-0.940828\pi\)
0.982771 0.184827i \(-0.0591723\pi\)
\(252\) 0 0
\(253\) −3.73205 3.73205i −0.234632 0.234632i
\(254\) 15.2942 + 8.83013i 0.959645 + 0.554051i
\(255\) 0 0
\(256\) −9.69615 16.7942i −0.606010 1.04964i
\(257\) −2.73205 + 0.732051i −0.170421 + 0.0456641i −0.343020 0.939328i \(-0.611450\pi\)
0.172600 + 0.984992i \(0.444783\pi\)
\(258\) 0 0
\(259\) −0.928203 + 12.9282i −0.0576757 + 0.803319i
\(260\) 3.46410 + 10.3923i 0.214834 + 0.644503i
\(261\) 0 0
\(262\) −4.26795 + 15.9282i −0.263675 + 0.984048i
\(263\) −2.16025 + 8.06218i −0.133207 + 0.497135i −0.999999 0.00153494i \(-0.999511\pi\)
0.866792 + 0.498670i \(0.166178\pi\)
\(264\) 0 0
\(265\) 5.00000 + 15.0000i 0.307148 + 0.921443i
\(266\) −11.5622 7.83013i −0.708923 0.480096i
\(267\) 0 0
\(268\) −1.96410 + 0.526279i −0.119977 + 0.0321476i
\(269\) 2.42820 + 4.20577i 0.148050 + 0.256430i 0.930507 0.366275i \(-0.119367\pi\)
−0.782457 + 0.622705i \(0.786034\pi\)
\(270\) 0 0
\(271\) −21.4186 12.3660i −1.30109 0.751183i −0.320496 0.947250i \(-0.603850\pi\)
−0.980590 + 0.196067i \(0.937183\pi\)
\(272\) −3.26795 3.26795i −0.198149 0.198149i
\(273\) 0 0
\(274\) 20.9282i 1.26432i
\(275\) 3.63397 0.437822i 0.219137 0.0264017i
\(276\) 0 0
\(277\) 19.3923 + 5.19615i 1.16517 + 0.312207i 0.789029 0.614356i \(-0.210584\pi\)
0.376141 + 0.926562i \(0.377251\pi\)
\(278\) −5.83013 21.7583i −0.349668 1.30498i
\(279\) 0 0
\(280\) −2.63397 1.56218i −0.157410 0.0933580i
\(281\) −12.9282 −0.771232 −0.385616 0.922659i \(-0.626011\pi\)
−0.385616 + 0.922659i \(0.626011\pi\)
\(282\) 0 0
\(283\) −26.4904 7.09808i −1.57469 0.421937i −0.637413 0.770523i \(-0.719995\pi\)
−0.937277 + 0.348586i \(0.886662\pi\)
\(284\) 7.09808 4.09808i 0.421193 0.243176i
\(285\) 0 0
\(286\) 4.00000i 0.236525i
\(287\) 0.401924 1.16025i 0.0237248 0.0684876i
\(288\) 0 0
\(289\) 13.7942 + 7.96410i 0.811425 + 0.468477i
\(290\) 8.59808 9.69615i 0.504896 0.569378i
\(291\) 0 0
\(292\) −6.00000 + 1.60770i −0.351123 + 0.0940832i
\(293\) −18.3923 + 18.3923i −1.07449 + 1.07449i −0.0774974 + 0.996993i \(0.524693\pi\)
−0.996993 + 0.0774974i \(0.975307\pi\)
\(294\) 0 0
\(295\) 4.39230 + 2.19615i 0.255730 + 0.127865i
\(296\) −1.26795 + 2.19615i −0.0736980 + 0.127649i
\(297\) 0 0
\(298\) 5.59808 20.8923i 0.324288 1.21026i
\(299\) 10.1962 17.6603i 0.589659 1.02132i
\(300\) 0 0
\(301\) 9.52628 + 19.6244i 0.549086 + 1.13113i
\(302\) 18.9282 18.9282i 1.08920 1.08920i
\(303\) 0 0
\(304\) −6.09808 10.5622i −0.349749 0.605782i
\(305\) 18.8923 1.13397i 1.08177 0.0649312i
\(306\) 0 0
\(307\) −9.29423 9.29423i −0.530450 0.530450i 0.390257 0.920706i \(-0.372386\pi\)
−0.920706 + 0.390257i \(0.872386\pi\)
\(308\) 2.19615 + 2.53590i 0.125137 + 0.144496i
\(309\) 0 0
\(310\) 2.26795 + 0.464102i 0.128811 + 0.0263592i
\(311\) −16.2224 + 9.36603i −0.919890 + 0.531099i −0.883600 0.468243i \(-0.844887\pi\)
−0.0362898 + 0.999341i \(0.511554\pi\)
\(312\) 0 0
\(313\) 5.19615 + 19.3923i 0.293704 + 1.09612i 0.942241 + 0.334935i \(0.108714\pi\)
−0.648537 + 0.761183i \(0.724619\pi\)
\(314\) 47.5167 2.68152
\(315\) 0 0
\(316\) 11.6603 0.655941
\(317\) 1.19615 + 4.46410i 0.0671826 + 0.250729i 0.991347 0.131265i \(-0.0419040\pi\)
−0.924165 + 0.381994i \(0.875237\pi\)
\(318\) 0 0
\(319\) 1.90192 1.09808i 0.106487 0.0614805i
\(320\) 7.06218 + 10.6962i 0.394788 + 0.597933i
\(321\) 0 0
\(322\) −6.96410 36.1865i −0.388094 2.01660i
\(323\) −2.00000 2.00000i −0.111283 0.111283i
\(324\) 0 0
\(325\) 5.26795 + 13.1244i 0.292213 + 0.728008i
\(326\) 5.36603 + 9.29423i 0.297197 + 0.514760i
\(327\) 0 0
\(328\) 0.169873 0.169873i 0.00937967 0.00937967i
\(329\) 1.73205 + 0.124356i 0.0954911 + 0.00685595i
\(330\) 0 0
\(331\) −12.9282 + 22.3923i −0.710598 + 1.23079i 0.254035 + 0.967195i \(0.418242\pi\)
−0.964633 + 0.263597i \(0.915091\pi\)
\(332\) 1.96410 7.33013i 0.107794 0.402293i
\(333\) 0 0
\(334\) 14.6962 25.4545i 0.804138 1.39281i
\(335\) −2.49038 + 0.830127i −0.136064 + 0.0453547i
\(336\) 0 0
\(337\) 16.4641 16.4641i 0.896857 0.896857i −0.0983001 0.995157i \(-0.531340\pi\)
0.995157 + 0.0983001i \(0.0313405\pi\)
\(338\) 9.33013 2.50000i 0.507492 0.135982i
\(339\) 0 0
\(340\) 3.00000 + 2.66025i 0.162698 + 0.144273i
\(341\) 0.339746 + 0.196152i 0.0183983 + 0.0106222i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 4.26795i 0.230112i
\(345\) 0 0
\(346\) −39.2487 + 22.6603i −2.11002 + 1.21822i
\(347\) −7.79423 2.08846i −0.418416 0.112114i 0.0434674 0.999055i \(-0.486160\pi\)
−0.461884 + 0.886941i \(0.652826\pi\)
\(348\) 0 0
\(349\) 9.73205 0.520945 0.260472 0.965481i \(-0.416122\pi\)
0.260472 + 0.965481i \(0.416122\pi\)
\(350\) 22.7224 + 11.6962i 1.21457 + 0.625186i
\(351\) 0 0
\(352\) 1.43782 + 5.36603i 0.0766362 + 0.286010i
\(353\) −5.36603 1.43782i −0.285605 0.0765276i 0.113173 0.993575i \(-0.463899\pi\)
−0.398777 + 0.917048i \(0.630565\pi\)
\(354\) 0 0
\(355\) 8.83013 5.83013i 0.468654 0.309431i
\(356\) 28.8564i 1.52939i
\(357\) 0 0
\(358\) 27.1244 + 27.1244i 1.43357 + 1.43357i
\(359\) −12.3397 7.12436i −0.651267 0.376009i 0.137675 0.990478i \(-0.456037\pi\)
−0.788941 + 0.614468i \(0.789371\pi\)
\(360\) 0 0
\(361\) 5.76795 + 9.99038i 0.303576 + 0.525810i
\(362\) −17.1603 + 4.59808i −0.901923 + 0.241670i
\(363\) 0 0
\(364\) −7.26795 + 10.7321i −0.380944 + 0.562512i
\(365\) −7.60770 + 2.53590i −0.398205 + 0.132735i
\(366\) 0 0
\(367\) 0.500000 1.86603i 0.0260998 0.0974057i −0.951647 0.307193i \(-0.900610\pi\)
0.977747 + 0.209787i \(0.0672770\pi\)
\(368\) 8.33013 31.0885i 0.434238 1.62060i
\(369\) 0 0
\(370\) 9.46410 18.9282i 0.492015 0.984030i
\(371\) −10.4904 + 15.4904i −0.544633 + 0.804221i
\(372\) 0 0
\(373\) 15.9282 4.26795i 0.824731 0.220986i 0.178317 0.983973i \(-0.442935\pi\)
0.646414 + 0.762987i \(0.276268\pi\)
\(374\) 0.732051 + 1.26795i 0.0378534 + 0.0655641i
\(375\) 0 0
\(376\) 0.294229 + 0.169873i 0.0151737 + 0.00876053i
\(377\) 6.00000 + 6.00000i 0.309016 + 0.309016i
\(378\) 0 0
\(379\) 19.6603i 1.00988i −0.863155 0.504940i \(-0.831515\pi\)
0.863155 0.504940i \(-0.168485\pi\)
\(380\) 5.83013 + 8.83013i 0.299079 + 0.452976i
\(381\) 0 0
\(382\) −31.2224 8.36603i −1.59748 0.428043i
\(383\) 7.55256 + 28.1865i 0.385918 + 1.44026i 0.836715 + 0.547638i \(0.184473\pi\)
−0.450797 + 0.892626i \(0.648860\pi\)
\(384\) 0 0
\(385\) 3.02628 + 3.09808i 0.154233 + 0.157893i
\(386\) −6.19615 −0.315376
\(387\) 0 0
\(388\) −18.7583 5.02628i −0.952310 0.255171i
\(389\) 7.73205 4.46410i 0.392031 0.226339i −0.291009 0.956720i \(-0.593991\pi\)
0.683040 + 0.730381i \(0.260658\pi\)
\(390\) 0 0
\(391\) 7.46410i 0.377476i
\(392\) −0.428203 3.59808i −0.0216275 0.181730i
\(393\) 0 0
\(394\) 33.4186 + 19.2942i 1.68360 + 0.972029i
\(395\) 15.0263 0.901924i 0.756054 0.0453807i
\(396\) 0 0
\(397\) −20.0263 + 5.36603i −1.00509 + 0.269313i −0.723577 0.690244i \(-0.757503\pi\)
−0.281514 + 0.959557i \(0.590836\pi\)
\(398\) −34.0526 + 34.0526i −1.70690 + 1.70690i
\(399\) 0 0
\(400\) 13.3923 + 17.8564i 0.669615 + 0.892820i
\(401\) 5.50000 9.52628i 0.274657 0.475720i −0.695392 0.718631i \(-0.744769\pi\)
0.970049 + 0.242911i \(0.0781024\pi\)
\(402\) 0 0
\(403\) −0.392305 + 1.46410i −0.0195421 + 0.0729321i
\(404\) −10.1603 + 17.5981i −0.505492 + 0.875537i
\(405\) 0 0
\(406\) 15.2942 + 1.09808i 0.759040 + 0.0544966i
\(407\) 2.53590 2.53590i 0.125700 0.125700i
\(408\) 0 0
\(409\) 3.42820 + 5.93782i 0.169514 + 0.293606i 0.938249 0.345961i \(-0.112447\pi\)
−0.768735 + 0.639567i \(0.779114\pi\)
\(410\) −1.33013 + 1.50000i −0.0656903 + 0.0740797i
\(411\) 0 0
\(412\) 2.83013 + 2.83013i 0.139430 + 0.139430i
\(413\) 1.09808 + 5.70577i 0.0540328 + 0.280763i
\(414\) 0 0
\(415\) 1.96410 9.59808i 0.0964140 0.471151i
\(416\) −18.5885 + 10.7321i −0.911374 + 0.526182i
\(417\) 0 0
\(418\) 1.00000 + 3.73205i 0.0489116 + 0.182541i
\(419\) 3.85641 0.188398 0.0941989 0.995553i \(-0.469971\pi\)
0.0941989 + 0.995553i \(0.469971\pi\)
\(420\) 0 0
\(421\) −34.6603 −1.68924 −0.844619 0.535368i \(-0.820173\pi\)
−0.844619 + 0.535368i \(0.820173\pi\)
\(422\) −5.09808 19.0263i −0.248170 0.926185i
\(423\) 0 0
\(424\) −3.16987 + 1.83013i −0.153943 + 0.0888788i
\(425\) 4.07180 + 3.19615i 0.197511 + 0.155036i
\(426\) 0 0
\(427\) 14.6603 + 16.9282i 0.709459 + 0.819213i
\(428\) 10.9019 + 10.9019i 0.526964 + 0.526964i
\(429\) 0 0
\(430\) −2.13397 35.5526i −0.102909 1.71450i
\(431\) −2.09808 3.63397i −0.101061 0.175042i 0.811061 0.584961i \(-0.198890\pi\)
−0.912122 + 0.409919i \(0.865557\pi\)
\(432\) 0 0
\(433\) −24.4641 + 24.4641i −1.17567 + 1.17567i −0.194833 + 0.980836i \(0.562417\pi\)
−0.980836 + 0.194833i \(0.937583\pi\)
\(434\) 1.19615 + 2.46410i 0.0574172 + 0.118281i
\(435\) 0 0
\(436\) 12.2321 21.1865i 0.585809 1.01465i
\(437\) 5.09808 19.0263i 0.243874 0.910150i
\(438\) 0 0
\(439\) −15.6603 + 27.1244i −0.747423 + 1.29457i 0.201631 + 0.979462i \(0.435376\pi\)
−0.949054 + 0.315113i \(0.897957\pi\)
\(440\) 0.267949 + 0.803848i 0.0127740 + 0.0383219i
\(441\) 0 0
\(442\) −4.00000 + 4.00000i −0.190261 + 0.190261i
\(443\) 3.50000 0.937822i 0.166290 0.0445573i −0.174713 0.984619i \(-0.555900\pi\)
0.341003 + 0.940062i \(0.389233\pi\)
\(444\) 0 0
\(445\) −2.23205 37.1865i −0.105809 1.76281i
\(446\) 14.4904 + 8.36603i 0.686139 + 0.396143i
\(447\) 0 0
\(448\) −4.96410 + 14.3301i −0.234532 + 0.677035i
\(449\) 5.05256i 0.238445i 0.992868 + 0.119222i \(0.0380402\pi\)
−0.992868 + 0.119222i \(0.961960\pi\)
\(450\) 0 0
\(451\) −0.294229 + 0.169873i −0.0138547 + 0.00799901i
\(452\) −10.0981 2.70577i −0.474974 0.127269i
\(453\) 0 0
\(454\) 0.196152 0.00920589
\(455\) −8.53590 + 14.3923i −0.400169 + 0.674722i
\(456\) 0 0
\(457\) −8.26795 30.8564i −0.386758 1.44340i −0.835376 0.549678i \(-0.814750\pi\)
0.448618 0.893724i \(-0.351916\pi\)
\(458\) −4.46410 1.19615i −0.208594 0.0558925i
\(459\) 0 0
\(460\) −5.59808 + 27.3564i −0.261012 + 1.27550i
\(461\) 26.3923i 1.22921i −0.788834 0.614606i \(-0.789315\pi\)
0.788834 0.614606i \(-0.210685\pi\)
\(462\) 0 0
\(463\) 17.7583 + 17.7583i 0.825300 + 0.825300i 0.986862 0.161563i \(-0.0516534\pi\)
−0.161563 + 0.986862i \(0.551653\pi\)
\(464\) 11.5981 + 6.69615i 0.538427 + 0.310861i
\(465\) 0 0
\(466\) 1.73205 + 3.00000i 0.0802357 + 0.138972i
\(467\) −31.3564 + 8.40192i −1.45100 + 0.388795i −0.896372 0.443303i \(-0.853807\pi\)
−0.554629 + 0.832097i \(0.687140\pi\)
\(468\) 0 0
\(469\) −2.57180 1.74167i −0.118755 0.0804228i
\(470\) −2.53590 1.26795i −0.116972 0.0584861i
\(471\) 0 0
\(472\) −0.294229 + 1.09808i −0.0135430 + 0.0505431i
\(473\) 1.56218 5.83013i 0.0718290 0.268070i
\(474\) 0 0
\(475\) 8.19615 + 10.9282i 0.376065 + 0.501420i
\(476\) −0.339746 + 4.73205i −0.0155722 + 0.216893i
\(477\) 0 0
\(478\) −34.3205 + 9.19615i −1.56978 + 0.420622i
\(479\) −13.4641 23.3205i −0.615191 1.06554i −0.990351 0.138581i \(-0.955746\pi\)
0.375161 0.926960i \(-0.377588\pi\)
\(480\) 0 0
\(481\) 12.0000 + 6.92820i 0.547153 + 0.315899i
\(482\) −22.9282 22.9282i −1.04435 1.04435i
\(483\) 0 0
\(484\) 18.1244i 0.823834i
\(485\) −24.5622 5.02628i −1.11531 0.228232i
\(486\) 0 0
\(487\) −8.29423 2.22243i −0.375847 0.100708i 0.0659498 0.997823i \(-0.478992\pi\)
−0.441797 + 0.897115i \(0.645659\pi\)
\(488\) 1.13397 + 4.23205i 0.0513326 + 0.191576i
\(489\) 0 0
\(490\) 5.36603 + 29.7583i 0.242412 + 1.34434i
\(491\) 17.7128 0.799368 0.399684 0.916653i \(-0.369120\pi\)
0.399684 + 0.916653i \(0.369120\pi\)
\(492\) 0 0
\(493\) 3.00000 + 0.803848i 0.135113 + 0.0362035i
\(494\) −12.9282 + 7.46410i −0.581667 + 0.335826i
\(495\) 0 0
\(496\) 2.39230i 0.107418i
\(497\) 11.8301 + 4.09808i 0.530654 + 0.183824i
\(498\) 0 0
\(499\) −29.0263 16.7583i −1.29939 0.750206i −0.319095 0.947723i \(-0.603379\pi\)
−0.980300 + 0.197517i \(0.936712\pi\)
\(500\) −12.5263 14.7679i −0.560192 0.660443i
\(501\) 0 0
\(502\) −10.9282 + 2.92820i −0.487750 + 0.130692i
\(503\) 19.3660 19.3660i 0.863488 0.863488i −0.128253 0.991741i \(-0.540937\pi\)
0.991741 + 0.128253i \(0.0409370\pi\)
\(504\) 0 0
\(505\) −11.7321 + 23.4641i −0.522069 + 1.04414i
\(506\) −5.09808 + 8.83013i −0.226637 + 0.392547i
\(507\) 0 0
\(508\) 4.09808 15.2942i 0.181823 0.678572i
\(509\) −13.4545 + 23.3038i −0.596359 + 1.03292i 0.396994 + 0.917821i \(0.370053\pi\)
−0.993353 + 0.115104i \(0.963280\pi\)
\(510\) 0 0
\(511\) −7.85641 5.32051i −0.347547 0.235365i
\(512\) −20.6865 + 20.6865i −0.914224 + 0.914224i
\(513\) 0 0
\(514\) 2.73205 + 4.73205i 0.120506 + 0.208722i
\(515\) 3.86603 + 3.42820i 0.170357 + 0.151065i
\(516\) 0 0
\(517\) −0.339746 0.339746i −0.0149420 0.0149420i
\(518\) 24.5885 4.73205i 1.08035 0.207914i
\(519\) 0 0
\(520\) −2.73205 + 1.80385i −0.119808 + 0.0791039i
\(521\) 3.33975 1.92820i 0.146317 0.0844761i −0.425054 0.905168i \(-0.639745\pi\)
0.571371 + 0.820692i \(0.306412\pi\)
\(522\) 0 0
\(523\) 3.88269 + 14.4904i 0.169778 + 0.633620i 0.997382 + 0.0723082i \(0.0230365\pi\)
−0.827604 + 0.561312i \(0.810297\pi\)
\(524\) 14.7846 0.645869
\(525\) 0 0
\(526\) 16.1244 0.703055
\(527\) 0.143594 + 0.535898i 0.00625503 + 0.0233441i
\(528\) 0 0
\(529\) 25.0981 14.4904i 1.09122 0.630017i
\(530\) 25.4904 16.8301i 1.10723 0.731054i
\(531\) 0 0
\(532\) −4.09808 + 11.8301i −0.177674 + 0.512901i
\(533\) −0.928203 0.928203i −0.0402049 0.0402049i
\(534\) 0 0
\(535\) 14.8923 + 13.2058i 0.643850 + 0.570935i
\(536\) −0.303848 0.526279i −0.0131242 0.0227318i
\(537\) 0 0
\(538\) 6.63397 6.63397i 0.286011 0.286011i
\(539\) −0.732051 + 5.07180i −0.0315317 + 0.218458i
\(540\) 0 0
\(541\) 9.35641 16.2058i 0.402263 0.696741i −0.591735 0.806132i \(-0.701557\pi\)
0.993999 + 0.109392i \(0.0348903\pi\)
\(542\) −12.3660 + 46.1506i −0.531166 + 1.98234i
\(543\) 0 0
\(544\) −3.92820 + 6.80385i −0.168420 + 0.291713i
\(545\) 14.1244 28.2487i 0.605021 1.21004i
\(546\) 0 0
\(547\) 5.75833 5.75833i 0.246208 0.246208i −0.573204 0.819413i \(-0.694300\pi\)
0.819413 + 0.573204i \(0.194300\pi\)
\(548\) −18.1244 + 4.85641i −0.774234 + 0.207455i
\(549\) 0 0
\(550\) −2.63397 6.56218i −0.112313 0.279812i
\(551\) 7.09808 + 4.09808i 0.302388 + 0.174584i
\(552\) 0 0
\(553\) 11.6603 + 13.4641i 0.495844 + 0.572552i
\(554\) 38.7846i 1.64780i
\(555\) 0 0
\(556\) −17.4904 + 10.0981i −0.741757 + 0.428254i
\(557\) −6.63397 1.77757i −0.281091 0.0753180i 0.115519 0.993305i \(-0.463147\pi\)
−0.396610 + 0.917987i \(0.629813\pi\)
\(558\) 0 0
\(559\) 23.3205 0.986352
\(560\) −7.13397 + 25.4282i −0.301465 + 1.07454i
\(561\) 0 0
\(562\) 6.46410 + 24.1244i 0.272672 + 1.01762i
\(563\) −21.3564 5.72243i −0.900065 0.241172i −0.221021 0.975269i \(-0.570939\pi\)
−0.679044 + 0.734097i \(0.737606\pi\)
\(564\) 0 0
\(565\) −13.2224 2.70577i −0.556272 0.113833i
\(566\) 52.9808i 2.22695i
\(567\) 0 0
\(568\) 1.73205 + 1.73205i 0.0726752 + 0.0726752i
\(569\) −13.0526 7.53590i −0.547192 0.315921i 0.200797 0.979633i \(-0.435647\pi\)
−0.747989 + 0.663712i \(0.768980\pi\)
\(570\) 0 0
\(571\) −10.0263 17.3660i −0.419587 0.726746i 0.576311 0.817230i \(-0.304492\pi\)
−0.995898 + 0.0904849i \(0.971158\pi\)
\(572\) 3.46410 0.928203i 0.144841 0.0388101i
\(573\) 0 0
\(574\) −2.36603 0.169873i −0.0987560 0.00709036i
\(575\) −5.09808 + 35.6865i −0.212604 + 1.48823i
\(576\) 0 0
\(577\) 7.36603 27.4904i 0.306652 1.14444i −0.624863 0.780735i \(-0.714845\pi\)
0.931514 0.363705i \(-0.118488\pi\)
\(578\) 7.96410 29.7224i 0.331263 1.23629i
\(579\) 0 0
\(580\) −10.3923 5.19615i −0.431517 0.215758i
\(581\) 10.4282 5.06218i 0.432635 0.210015i
\(582\) 0 0
\(583\) 5.00000 1.33975i 0.207079 0.0554866i
\(584\) −0.928203 1.60770i −0.0384093 0.0665269i
\(585\) 0 0
\(586\) 43.5167 + 25.1244i 1.79766 + 1.03788i
\(587\) 25.7846 + 25.7846i 1.06424 + 1.06424i 0.997789 + 0.0664553i \(0.0211690\pi\)
0.0664553 + 0.997789i \(0.478831\pi\)
\(588\) 0 0
\(589\) 1.46410i 0.0603273i
\(590\) 1.90192 9.29423i 0.0783010 0.382637i
\(591\) 0 0
\(592\) 21.1244 + 5.66025i 0.868206 + 0.232635i
\(593\) 1.75833 + 6.56218i 0.0722060 + 0.269476i 0.992585 0.121550i \(-0.0387866\pi\)
−0.920379 + 0.391027i \(0.872120\pi\)
\(594\) 0 0
\(595\) −0.0717968 + 6.12436i −0.00294338 + 0.251074i
\(596\) −19.3923 −0.794340
\(597\) 0 0
\(598\) −38.0526 10.1962i −1.55608 0.416952i
\(599\) 32.6603 18.8564i 1.33446 0.770452i 0.348482 0.937316i \(-0.386697\pi\)
0.985980 + 0.166864i \(0.0533640\pi\)
\(600\) 0 0
\(601\) 21.1769i 0.863824i −0.901916 0.431912i \(-0.857839\pi\)
0.901916 0.431912i \(-0.142161\pi\)
\(602\) 31.8564 27.5885i 1.29837 1.12442i
\(603\) 0 0
\(604\) −20.7846 12.0000i −0.845714 0.488273i
\(605\) 1.40192 + 23.3564i 0.0569963 + 0.949573i
\(606\) 0 0
\(607\) 8.59808 2.30385i 0.348985 0.0935103i −0.0800683 0.996789i \(-0.525514\pi\)
0.429053 + 0.903279i \(0.358847\pi\)
\(608\) −14.6603 + 14.6603i −0.594552 + 0.594552i
\(609\) 0 0
\(610\) −11.5622 34.6865i −0.468139 1.40442i
\(611\) 0.928203 1.60770i 0.0375511 0.0650404i
\(612\) 0 0
\(613\) 3.60770 13.4641i 0.145713 0.543810i −0.854009 0.520258i \(-0.825836\pi\)
0.999723 0.0235520i \(-0.00749753\pi\)
\(614\) −12.6962 + 21.9904i −0.512375 + 0.887460i
\(615\) 0 0
\(616\) −0.562178 + 0.830127i −0.0226508 + 0.0334468i
\(617\) 31.9090 31.9090i 1.28461 1.28461i 0.346590 0.938017i \(-0.387340\pi\)
0.938017 0.346590i \(-0.112660\pi\)
\(618\) 0 0
\(619\) −0.0980762 0.169873i −0.00394202 0.00682777i 0.864048 0.503410i \(-0.167921\pi\)
−0.867990 + 0.496582i \(0.834588\pi\)
\(620\) −0.124356 2.07180i −0.00499424 0.0832054i
\(621\) 0 0
\(622\) 25.5885 + 25.5885i 1.02600 + 1.02600i
\(623\) 33.3205 28.8564i 1.33496 1.15611i
\(624\) 0 0
\(625\) −17.2846 18.0622i −0.691384 0.722487i
\(626\) 33.5885 19.3923i 1.34246 0.775072i
\(627\) 0 0
\(628\) −11.0263 41.1506i −0.439996 1.64209i
\(629\) 5.07180 0.202226
\(630\) 0 0
\(631\) 26.5885 1.05847 0.529235 0.848475i \(-0.322479\pi\)
0.529235 + 0.848475i \(0.322479\pi\)
\(632\) 0.901924 + 3.36603i 0.0358766 + 0.133893i
\(633\) 0 0
\(634\) 7.73205 4.46410i 0.307079 0.177292i
\(635\) 4.09808 20.0263i 0.162627 0.794719i
\(636\) 0 0
\(637\) −19.6603 + 2.33975i −0.778968 + 0.0927041i
\(638\) −3.00000 3.00000i −0.118771 0.118771i
\(639\) 0 0
\(640\) −6.08846 + 6.86603i −0.240667 + 0.271403i
\(641\) −3.33013 5.76795i −0.131532 0.227820i 0.792735 0.609566i \(-0.208656\pi\)
−0.924267 + 0.381746i \(0.875323\pi\)
\(642\) 0 0
\(643\) 24.4641 24.4641i 0.964770 0.964770i −0.0346302 0.999400i \(-0.511025\pi\)
0.999400 + 0.0346302i \(0.0110253\pi\)
\(644\) −29.7224 + 14.4282i −1.17123 + 0.568551i
\(645\) 0 0
\(646\) −2.73205 + 4.73205i −0.107491 + 0.186180i
\(647\) −1.44744 + 5.40192i −0.0569048 + 0.212372i −0.988524 0.151065i \(-0.951730\pi\)
0.931619 + 0.363436i \(0.118397\pi\)
\(648\) 0 0
\(649\) 0.803848 1.39230i 0.0315538 0.0546527i
\(650\) 21.8564 16.3923i 0.857279 0.642959i
\(651\) 0 0
\(652\) 6.80385 6.80385i 0.266459 0.266459i
\(653\) 8.73205 2.33975i 0.341712 0.0915613i −0.0838822 0.996476i \(-0.526732\pi\)
0.425594 + 0.904914i \(0.360065\pi\)
\(654\) 0 0
\(655\) 19.0526 1.14359i 0.744445 0.0446839i
\(656\) −1.79423 1.03590i −0.0700529 0.0404450i
\(657\) 0 0
\(658\) −0.633975 3.29423i −0.0247149 0.128422i
\(659\) 10.3397i 0.402779i −0.979511 0.201390i \(-0.935454\pi\)
0.979511 0.201390i \(-0.0645457\pi\)
\(660\) 0 0
\(661\) −12.2776 + 7.08846i −0.477542 + 0.275709i −0.719392 0.694605i \(-0.755579\pi\)
0.241850 + 0.970314i \(0.422246\pi\)
\(662\) 48.2487 + 12.9282i 1.87524 + 0.502469i
\(663\) 0 0
\(664\) 2.26795 0.0880135
\(665\) −4.36603 + 15.5622i −0.169307 + 0.603475i
\(666\) 0 0
\(667\) 5.59808 + 20.8923i 0.216758 + 0.808953i
\(668\) −25.4545 6.82051i −0.984864 0.263893i
\(669\) 0 0
\(670\) 2.79423 + 4.23205i 0.107950 + 0.163498i
\(671\) 6.19615i 0.239200i
\(672\) 0 0
\(673\) −16.3923 16.3923i −0.631877 0.631877i 0.316662 0.948539i \(-0.397438\pi\)
−0.948539 + 0.316662i \(0.897438\pi\)
\(674\) −38.9545 22.4904i −1.50047 0.866297i
\(675\) 0 0
\(676\) −4.33013 7.50000i −0.166543 0.288462i
\(677\) −6.92820 + 1.85641i −0.266272 + 0.0713475i −0.389485 0.921033i \(-0.627347\pi\)
0.123213 + 0.992380i \(0.460680\pi\)
\(678\) 0 0
\(679\) −12.9545 26.6865i −0.497147 1.02414i
\(680\) −0.535898 + 1.07180i −0.0205508 + 0.0411015i
\(681\) 0 0
\(682\) 0.196152 0.732051i 0.00751106 0.0280317i
\(683\) −4.93782 + 18.4282i −0.188941 + 0.705136i 0.804812 + 0.593530i \(0.202266\pi\)
−0.993753 + 0.111606i \(0.964401\pi\)
\(684\) 0 0
\(685\) −22.9808 + 7.66025i −0.878050 + 0.292683i
\(686\) −24.0885 + 26.4545i −0.919702 + 1.01004i
\(687\) 0 0
\(688\) 35.5526 9.52628i 1.35543 0.363186i
\(689\) 10.0000 + 17.3205i 0.380970 + 0.659859i
\(690\) 0 0
\(691\) −24.9737 14.4186i −0.950045 0.548509i −0.0569502 0.998377i \(-0.518138\pi\)
−0.893095 + 0.449868i \(0.851471\pi\)
\(692\) 28.7321 + 28.7321i 1.09223 + 1.09223i
\(693\) 0 0
\(694\) 15.5885i 0.591730i
\(695\) −21.7583 + 14.3660i −0.825341 + 0.544934i
\(696\) 0 0
\(697\) −0.464102 0.124356i −0.0175791 0.00471031i
\(698\) −4.86603 18.1603i −0.184182 0.687376i
\(699\) 0 0
\(700\) 4.85641 22.3923i 0.183555 0.846350i
\(701\) 23.7321 0.896347 0.448174 0.893947i \(-0.352075\pi\)
0.448174 + 0.893947i \(0.352075\pi\)
\(702\) 0 0
\(703\) 12.9282 + 3.46410i 0.487596 + 0.130651i
\(704\) 3.63397 2.09808i 0.136961 0.0790742i
\(705\) 0 0
\(706\) 10.7321i 0.403906i
\(707\) −30.4808 + 5.86603i −1.14635 + 0.220615i
\(708\) 0 0
\(709\) −6.99038 4.03590i −0.262529 0.151571i 0.362959 0.931805i \(-0.381767\pi\)
−0.625488 + 0.780234i \(0.715100\pi\)
\(710\) −15.2942 13.5622i −0.573982 0.508979i
\(711\) 0 0
\(712\) 8.33013 2.23205i 0.312185 0.0836496i
\(713\) −2.73205 + 2.73205i −0.102316 + 0.102316i
\(714\) 0 0
\(715\) 4.39230 1.46410i 0.164263 0.0547543i
\(716\) 17.1962 29.7846i 0.642650 1.11310i
\(717\) 0 0
\(718\) −7.12436 + 26.5885i −0.265879 + 0.992272i
\(719\) −3.70577 + 6.41858i −0.138202 + 0.239373i −0.926816 0.375516i \(-0.877466\pi\)
0.788614 + 0.614888i \(0.210799\pi\)
\(720\) 0 0
\(721\) −0.437822 + 6.09808i −0.0163053 + 0.227104i
\(722\) 15.7583 15.7583i 0.586464 0.586464i
\(723\) 0 0
\(724\) 7.96410 + 13.7942i 0.295984 + 0.512658i
\(725\) −13.7942 5.89230i −0.512305 0.218835i
\(726\) 0 0
\(727\) −4.90192 4.90192i −0.181802 0.181802i 0.610338 0.792141i \(-0.291033\pi\)
−0.792141 + 0.610338i \(0.791033\pi\)
\(728\) −3.66025 1.26795i −0.135658 0.0469933i
\(729\) 0 0
\(730\) 8.53590 + 12.9282i 0.315928 + 0.478494i
\(731\) 7.39230 4.26795i 0.273414 0.157856i
\(732\) 0 0
\(733\) −2.63397 9.83013i −0.0972881 0.363084i 0.900068 0.435749i \(-0.143516\pi\)
−0.997356 + 0.0726647i \(0.976850\pi\)
\(734\) −3.73205 −0.137753
\(735\) 0 0
\(736\) −54.7128 −2.01674
\(737\) 0.222432 + 0.830127i 0.00819338 + 0.0305781i
\(738\) 0 0
\(739\) −7.43782 + 4.29423i −0.273605 + 0.157966i −0.630525 0.776169i \(-0.717160\pi\)
0.356920 + 0.934135i \(0.383827\pi\)
\(740\) −18.5885 3.80385i −0.683325 0.139832i
\(741\) 0 0
\(742\) 34.1506 + 11.8301i 1.25371 + 0.434298i
\(743\) 14.8301 + 14.8301i 0.544065 + 0.544065i 0.924718 0.380653i \(-0.124301\pi\)
−0.380653 + 0.924718i \(0.624301\pi\)
\(744\) 0 0
\(745\) −24.9904 + 1.50000i −0.915577 + 0.0549557i
\(746\) −15.9282 27.5885i −0.583173 1.01009i
\(747\) 0 0
\(748\) 0.928203 0.928203i 0.0339385 0.0339385i
\(749\) −1.68653 + 23.4904i −0.0616246 + 0.858320i
\(750\) 0 0
\(751\) −7.19615 + 12.4641i −0.262591 + 0.454822i −0.966930 0.255043i \(-0.917910\pi\)
0.704338 + 0.709864i \(0.251244\pi\)
\(752\) 0.758330 2.83013i 0.0276535 0.103204i
\(753\) 0 0
\(754\) 8.19615 14.1962i 0.298486 0.516993i
\(755\) −27.7128 13.8564i −1.00857 0.504286i
\(756\) 0 0
\(757\) 9.26795 9.26795i 0.336849 0.336849i −0.518331 0.855180i \(-0.673446\pi\)
0.855180 + 0.518331i \(0.173446\pi\)
\(758\) −36.6865 + 9.83013i −1.33251 + 0.357046i
\(759\) 0 0
\(760\) −2.09808 + 2.36603i −0.0761052 + 0.0858248i
\(761\) −11.0718 6.39230i −0.401352 0.231721i 0.285715 0.958315i \(-0.407769\pi\)
−0.687067 + 0.726594i \(0.741102\pi\)
\(762\) 0 0
\(763\) 36.6962 7.06218i 1.32849 0.255668i
\(764\) 28.9808i 1.04849i
\(765\) 0 0
\(766\) 48.8205 28.1865i 1.76396 1.01842i
\(767\) 6.00000 + 1.60770i 0.216647 + 0.0580505i
\(768\) 0 0
\(769\) −47.1769 −1.70124 −0.850622 0.525778i \(-0.823774\pi\)
−0.850622 + 0.525778i \(0.823774\pi\)
\(770\) 4.26795 7.19615i 0.153806 0.259331i
\(771\) 0 0
\(772\) 1.43782 + 5.36603i 0.0517484 + 0.193127i
\(773\) −17.9282 4.80385i −0.644833 0.172782i −0.0784412 0.996919i \(-0.524994\pi\)
−0.566391 + 0.824136i \(0.691661\pi\)
\(774\) 0 0
\(775\) −0.320508 2.66025i −0.0115130 0.0955591i
\(776\) 5.80385i 0.208346i
\(777\) 0 0
\(778\) −12.1962 12.1962i −0.437253 0.437253i
\(779\) −1.09808 0.633975i −0.0393427 0.0227145i
\(780\) 0 0
\(781\) −1.73205 3.00000i −0.0619777 0.107348i
\(782\) −13.9282 + 3.73205i −0.498072 + 0.133458i
\(783\) 0 0
\(784\) −29.0167 + 11.5981i −1.03631 + 0.414217i
\(785\) −17.3923 52.1769i −0.620758 1.86227i
\(786\) 0 0
\(787\) −5.18653 + 19.3564i −0.184880 + 0.689981i 0.809776 + 0.586739i \(0.199588\pi\)
−0.994656 + 0.103243i \(0.967078\pi\)
\(788\) 8.95448 33.4186i 0.318990 1.19049i
\(789\) 0 0
\(790\) −9.19615 27.5885i −0.327184 0.981553i
\(791\) −6.97372 14.3660i −0.247957