Properties

Label 819.2.y.h.811.4
Level $819$
Weight $2$
Character 819.811
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.y (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \( x^{12} + 35x^{8} + 295x^{4} + 169 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 811.4
Root \(1.52891 - 1.52891i\) of defining polynomial
Character \(\chi\) \(=\) 819.811
Dual form 819.2.y.h.307.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.403032 - 0.403032i) q^{2} +1.67513i q^{4} +(1.03221 + 1.03221i) q^{5} +(-0.450747 + 2.60707i) q^{7} +(1.48119 + 1.48119i) q^{8} +O(q^{10})\) \(q+(0.403032 - 0.403032i) q^{2} +1.67513i q^{4} +(1.03221 + 1.03221i) q^{5} +(-0.450747 + 2.60707i) q^{7} +(1.48119 + 1.48119i) q^{8} +0.832030 q^{10} +(0.596968 + 0.596968i) q^{11} +(3.59334 + 0.296512i) q^{13} +(0.869067 + 1.23240i) q^{14} -2.15633 q^{16} -7.34804 q^{17} +(-3.59334 - 3.59334i) q^{19} +(-1.72909 + 1.72909i) q^{20} +0.481194 q^{22} +4.44358i q^{23} -2.86907i q^{25} +(1.56773 - 1.32873i) q^{26} +(-4.36719 - 0.755061i) q^{28} +3.54420 q^{29} +(1.27122 + 1.27122i) q^{31} +(-3.83146 + 3.83146i) q^{32} +(-2.96149 + 2.96149i) q^{34} +(-3.15633 + 2.22579i) q^{35} +(2.88423 + 2.88423i) q^{37} -2.89646 q^{38} +3.05782i q^{40} +(1.23240 + 1.23240i) q^{41} +8.66291i q^{43} +(-1.00000 + 1.00000i) q^{44} +(1.79090 + 1.79090i) q^{46} +(2.52230 - 2.52230i) q^{47} +(-6.59365 - 2.35026i) q^{49} +(-1.15633 - 1.15633i) q^{50} +(-0.496696 + 6.01931i) q^{52} +9.79384 q^{53} +1.23240i q^{55} +(-4.52923 + 3.19394i) q^{56} +(1.42842 - 1.42842i) q^{58} +(-1.08972 + 1.08972i) q^{59} -7.10903i q^{61} +1.02469 q^{62} -1.22425i q^{64} +(3.40303 + 4.01516i) q^{65} +(8.76845 - 8.76845i) q^{67} -12.3089i q^{68} +(-0.375035 + 2.16916i) q^{70} +(1.46604 - 1.46604i) q^{71} +(0.103857 - 0.103857i) q^{73} +2.32487 q^{74} +(6.01931 - 6.01931i) q^{76} +(-1.82542 + 1.28726i) q^{77} -4.79877 q^{79} +(-2.22579 - 2.22579i) q^{80} +0.993391 q^{82} +(12.3165 + 12.3165i) q^{83} +(-7.58475 - 7.58475i) q^{85} +(3.49143 + 3.49143i) q^{86} +1.76845i q^{88} +(-6.89017 + 6.89017i) q^{89} +(-2.39271 + 9.23444i) q^{91} -7.44358 q^{92} -2.03313i q^{94} -7.41819i q^{95} +(6.05814 + 6.05814i) q^{97} +(-3.60468 + 1.71022i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{2} - 8 q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{2} - 8 q^{7} - 4 q^{8} + 8 q^{11} - 8 q^{14} + 16 q^{16} - 16 q^{22} - 20 q^{28} + 4 q^{29} + 16 q^{32} + 4 q^{35} + 12 q^{37} - 12 q^{44} + 24 q^{46} + 28 q^{50} + 12 q^{53} - 44 q^{58} + 40 q^{65} + 60 q^{67} + 4 q^{70} + 48 q^{74} - 4 q^{79} + 12 q^{85} - 36 q^{86} - 32 q^{91} - 24 q^{92} + 28 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.403032 0.403032i 0.284986 0.284986i −0.550107 0.835094i \(-0.685413\pi\)
0.835094 + 0.550107i \(0.185413\pi\)
\(3\) 0 0
\(4\) 1.67513i 0.837565i
\(5\) 1.03221 + 1.03221i 0.461620 + 0.461620i 0.899186 0.437566i \(-0.144159\pi\)
−0.437566 + 0.899186i \(0.644159\pi\)
\(6\) 0 0
\(7\) −0.450747 + 2.60707i −0.170366 + 0.985381i
\(8\) 1.48119 + 1.48119i 0.523681 + 0.523681i
\(9\) 0 0
\(10\) 0.832030 0.263111
\(11\) 0.596968 + 0.596968i 0.179993 + 0.179993i 0.791353 0.611360i \(-0.209377\pi\)
−0.611360 + 0.791353i \(0.709377\pi\)
\(12\) 0 0
\(13\) 3.59334 + 0.296512i 0.996613 + 0.0822375i
\(14\) 0.869067 + 1.23240i 0.232268 + 0.329372i
\(15\) 0 0
\(16\) −2.15633 −0.539081
\(17\) −7.34804 −1.78216 −0.891080 0.453845i \(-0.850052\pi\)
−0.891080 + 0.453845i \(0.850052\pi\)
\(18\) 0 0
\(19\) −3.59334 3.59334i −0.824368 0.824368i 0.162363 0.986731i \(-0.448089\pi\)
−0.986731 + 0.162363i \(0.948089\pi\)
\(20\) −1.72909 + 1.72909i −0.386637 + 0.386637i
\(21\) 0 0
\(22\) 0.481194 0.102591
\(23\) 4.44358i 0.926551i 0.886214 + 0.463276i \(0.153326\pi\)
−0.886214 + 0.463276i \(0.846674\pi\)
\(24\) 0 0
\(25\) 2.86907i 0.573813i
\(26\) 1.56773 1.32873i 0.307458 0.260585i
\(27\) 0 0
\(28\) −4.36719 0.755061i −0.825321 0.142693i
\(29\) 3.54420 0.658141 0.329071 0.944305i \(-0.393265\pi\)
0.329071 + 0.944305i \(0.393265\pi\)
\(30\) 0 0
\(31\) 1.27122 + 1.27122i 0.228318 + 0.228318i 0.811990 0.583672i \(-0.198384\pi\)
−0.583672 + 0.811990i \(0.698384\pi\)
\(32\) −3.83146 + 3.83146i −0.677312 + 0.677312i
\(33\) 0 0
\(34\) −2.96149 + 2.96149i −0.507892 + 0.507892i
\(35\) −3.15633 + 2.22579i −0.533516 + 0.376227i
\(36\) 0 0
\(37\) 2.88423 + 2.88423i 0.474164 + 0.474164i 0.903259 0.429095i \(-0.141168\pi\)
−0.429095 + 0.903259i \(0.641168\pi\)
\(38\) −2.89646 −0.469868
\(39\) 0 0
\(40\) 3.05782i 0.483484i
\(41\) 1.23240 + 1.23240i 0.192468 + 0.192468i 0.796762 0.604294i \(-0.206545\pi\)
−0.604294 + 0.796762i \(0.706545\pi\)
\(42\) 0 0
\(43\) 8.66291i 1.32108i 0.750790 + 0.660541i \(0.229673\pi\)
−0.750790 + 0.660541i \(0.770327\pi\)
\(44\) −1.00000 + 1.00000i −0.150756 + 0.150756i
\(45\) 0 0
\(46\) 1.79090 + 1.79090i 0.264055 + 0.264055i
\(47\) 2.52230 2.52230i 0.367915 0.367915i −0.498801 0.866717i \(-0.666226\pi\)
0.866717 + 0.498801i \(0.166226\pi\)
\(48\) 0 0
\(49\) −6.59365 2.35026i −0.941951 0.335752i
\(50\) −1.15633 1.15633i −0.163529 0.163529i
\(51\) 0 0
\(52\) −0.496696 + 6.01931i −0.0688793 + 0.834728i
\(53\) 9.79384 1.34529 0.672644 0.739966i \(-0.265159\pi\)
0.672644 + 0.739966i \(0.265159\pi\)
\(54\) 0 0
\(55\) 1.23240i 0.166177i
\(56\) −4.52923 + 3.19394i −0.605243 + 0.426808i
\(57\) 0 0
\(58\) 1.42842 1.42842i 0.187561 0.187561i
\(59\) −1.08972 + 1.08972i −0.141869 + 0.141869i −0.774474 0.632605i \(-0.781986\pi\)
0.632605 + 0.774474i \(0.281986\pi\)
\(60\) 0 0
\(61\) 7.10903i 0.910218i −0.890436 0.455109i \(-0.849600\pi\)
0.890436 0.455109i \(-0.150400\pi\)
\(62\) 1.02469 0.130135
\(63\) 0 0
\(64\) 1.22425i 0.153032i
\(65\) 3.40303 + 4.01516i 0.422094 + 0.498019i
\(66\) 0 0
\(67\) 8.76845 8.76845i 1.07124 1.07124i 0.0739770 0.997260i \(-0.476431\pi\)
0.997260 0.0739770i \(-0.0235691\pi\)
\(68\) 12.3089i 1.49268i
\(69\) 0 0
\(70\) −0.375035 + 2.16916i −0.0448253 + 0.259265i
\(71\) 1.46604 1.46604i 0.173986 0.173986i −0.614742 0.788728i \(-0.710740\pi\)
0.788728 + 0.614742i \(0.210740\pi\)
\(72\) 0 0
\(73\) 0.103857 0.103857i 0.0121555 0.0121555i −0.701003 0.713158i \(-0.747264\pi\)
0.713158 + 0.701003i \(0.247264\pi\)
\(74\) 2.32487 0.270261
\(75\) 0 0
\(76\) 6.01931 6.01931i 0.690462 0.690462i
\(77\) −1.82542 + 1.28726i −0.208026 + 0.146697i
\(78\) 0 0
\(79\) −4.79877 −0.539904 −0.269952 0.962874i \(-0.587008\pi\)
−0.269952 + 0.962874i \(0.587008\pi\)
\(80\) −2.22579 2.22579i −0.248851 0.248851i
\(81\) 0 0
\(82\) 0.993391 0.109702
\(83\) 12.3165 + 12.3165i 1.35191 + 1.35191i 0.883528 + 0.468379i \(0.155162\pi\)
0.468379 + 0.883528i \(0.344838\pi\)
\(84\) 0 0
\(85\) −7.58475 7.58475i −0.822682 0.822682i
\(86\) 3.49143 + 3.49143i 0.376490 + 0.376490i
\(87\) 0 0
\(88\) 1.76845i 0.188518i
\(89\) −6.89017 + 6.89017i −0.730356 + 0.730356i −0.970690 0.240334i \(-0.922743\pi\)
0.240334 + 0.970690i \(0.422743\pi\)
\(90\) 0 0
\(91\) −2.39271 + 9.23444i −0.250825 + 0.968033i
\(92\) −7.44358 −0.776047
\(93\) 0 0
\(94\) 2.03313i 0.209702i
\(95\) 7.41819i 0.761090i
\(96\) 0 0
\(97\) 6.05814 + 6.05814i 0.615110 + 0.615110i 0.944273 0.329163i \(-0.106766\pi\)
−0.329163 + 0.944273i \(0.606766\pi\)
\(98\) −3.60468 + 1.71022i −0.364128 + 0.172758i
\(99\) 0 0
\(100\) 4.80606 0.480606
\(101\) 12.8707 1.28068 0.640339 0.768092i \(-0.278794\pi\)
0.640339 + 0.768092i \(0.278794\pi\)
\(102\) 0 0
\(103\) 6.11564 0.602592 0.301296 0.953531i \(-0.402581\pi\)
0.301296 + 0.953531i \(0.402581\pi\)
\(104\) 4.88324 + 5.76162i 0.478841 + 0.564974i
\(105\) 0 0
\(106\) 3.94723 3.94723i 0.383389 0.383389i
\(107\) −8.86907 −0.857405 −0.428703 0.903446i \(-0.641029\pi\)
−0.428703 + 0.903446i \(0.641029\pi\)
\(108\) 0 0
\(109\) −4.59697 + 4.59697i −0.440310 + 0.440310i −0.892116 0.451806i \(-0.850780\pi\)
0.451806 + 0.892116i \(0.350780\pi\)
\(110\) 0.496696 + 0.496696i 0.0473581 + 0.0473581i
\(111\) 0 0
\(112\) 0.971958 5.62170i 0.0918414 0.531200i
\(113\) −1.60720 −0.151193 −0.0755964 0.997138i \(-0.524086\pi\)
−0.0755964 + 0.997138i \(0.524086\pi\)
\(114\) 0 0
\(115\) −4.58673 + 4.58673i −0.427715 + 0.427715i
\(116\) 5.93700i 0.551236i
\(117\) 0 0
\(118\) 0.878382i 0.0808617i
\(119\) 3.31211 19.1569i 0.303620 1.75611i
\(120\) 0 0
\(121\) 10.2873i 0.935205i
\(122\) −2.86516 2.86516i −0.259400 0.259400i
\(123\) 0 0
\(124\) −2.12946 + 2.12946i −0.191231 + 0.191231i
\(125\) 8.12256 8.12256i 0.726504 0.726504i
\(126\) 0 0
\(127\) 1.54912i 0.137462i 0.997635 + 0.0687312i \(0.0218951\pi\)
−0.997635 + 0.0687312i \(0.978105\pi\)
\(128\) −8.15633 8.15633i −0.720924 0.720924i
\(129\) 0 0
\(130\) 2.98977 + 0.246707i 0.262220 + 0.0216376i
\(131\) 5.31490i 0.464365i 0.972672 + 0.232183i \(0.0745867\pi\)
−0.972672 + 0.232183i \(0.925413\pi\)
\(132\) 0 0
\(133\) 10.9878 7.74841i 0.952761 0.671872i
\(134\) 7.06793i 0.610576i
\(135\) 0 0
\(136\) −10.8839 10.8839i −0.933284 0.933284i
\(137\) −12.7157 12.7157i −1.08637 1.08637i −0.995899 0.0904753i \(-0.971161\pi\)
−0.0904753 0.995899i \(-0.528839\pi\)
\(138\) 0 0
\(139\) 6.94767i 0.589294i 0.955606 + 0.294647i \(0.0952020\pi\)
−0.955606 + 0.294647i \(0.904798\pi\)
\(140\) −3.72849 5.28726i −0.315115 0.446855i
\(141\) 0 0
\(142\) 1.18172i 0.0991676i
\(143\) 1.96810 + 2.32212i 0.164581 + 0.194185i
\(144\) 0 0
\(145\) 3.65837 + 3.65837i 0.303811 + 0.303811i
\(146\) 0.0837150i 0.00692831i
\(147\) 0 0
\(148\) −4.83146 + 4.83146i −0.397143 + 0.397143i
\(149\) 10.9653 10.9653i 0.898315 0.898315i −0.0969724 0.995287i \(-0.530916\pi\)
0.995287 + 0.0969724i \(0.0309158\pi\)
\(150\) 0 0
\(151\) 6.14117 + 6.14117i 0.499761 + 0.499761i 0.911363 0.411602i \(-0.135031\pi\)
−0.411602 + 0.911363i \(0.635031\pi\)
\(152\) 10.6449i 0.863413i
\(153\) 0 0
\(154\) −0.216897 + 1.25451i −0.0174781 + 0.101091i
\(155\) 2.62435i 0.210793i
\(156\) 0 0
\(157\) 9.69783i 0.773971i −0.922086 0.386985i \(-0.873516\pi\)
0.922086 0.386985i \(-0.126484\pi\)
\(158\) −1.93406 + 1.93406i −0.153865 + 0.153865i
\(159\) 0 0
\(160\) −7.90977 −0.625322
\(161\) −11.5847 2.00293i −0.913006 0.157853i
\(162\) 0 0
\(163\) −5.41327 5.41327i −0.424000 0.424000i 0.462579 0.886578i \(-0.346924\pi\)
−0.886578 + 0.462579i \(0.846924\pi\)
\(164\) −2.06443 + 2.06443i −0.161205 + 0.161205i
\(165\) 0 0
\(166\) 9.92784 0.770550
\(167\) 8.90824 8.90824i 0.689340 0.689340i −0.272746 0.962086i \(-0.587932\pi\)
0.962086 + 0.272746i \(0.0879318\pi\)
\(168\) 0 0
\(169\) 12.8242 + 2.13093i 0.986474 + 0.163918i
\(170\) −6.11379 −0.468906
\(171\) 0 0
\(172\) −14.5115 −1.10649
\(173\) 7.15538 0.544014 0.272007 0.962295i \(-0.412313\pi\)
0.272007 + 0.962295i \(0.412313\pi\)
\(174\) 0 0
\(175\) 7.47987 + 1.29322i 0.565425 + 0.0977586i
\(176\) −1.28726 1.28726i −0.0970307 0.0970307i
\(177\) 0 0
\(178\) 5.55391i 0.416283i
\(179\) 13.8119i 1.03235i 0.856482 + 0.516177i \(0.172645\pi\)
−0.856482 + 0.516177i \(0.827355\pi\)
\(180\) 0 0
\(181\) 4.56052 0.338981 0.169490 0.985532i \(-0.445788\pi\)
0.169490 + 0.985532i \(0.445788\pi\)
\(182\) 2.75743 + 4.68611i 0.204395 + 0.347358i
\(183\) 0 0
\(184\) −6.58181 + 6.58181i −0.485217 + 0.485217i
\(185\) 5.95428i 0.437767i
\(186\) 0 0
\(187\) −4.38655 4.38655i −0.320776 0.320776i
\(188\) 4.22518 + 4.22518i 0.308153 + 0.308153i
\(189\) 0 0
\(190\) −2.98977 2.98977i −0.216900 0.216900i
\(191\) −3.70545 −0.268117 −0.134058 0.990973i \(-0.542801\pi\)
−0.134058 + 0.990973i \(0.542801\pi\)
\(192\) 0 0
\(193\) −17.0508 17.0508i −1.22734 1.22734i −0.964965 0.262377i \(-0.915494\pi\)
−0.262377 0.964965i \(-0.584506\pi\)
\(194\) 4.88324 0.350596
\(195\) 0 0
\(196\) 3.93700 11.0452i 0.281214 0.788945i
\(197\) 8.01810 8.01810i 0.571266 0.571266i −0.361216 0.932482i \(-0.617638\pi\)
0.932482 + 0.361216i \(0.117638\pi\)
\(198\) 0 0
\(199\) 4.57558 0.324354 0.162177 0.986762i \(-0.448148\pi\)
0.162177 + 0.986762i \(0.448148\pi\)
\(200\) 4.24965 4.24965i 0.300495 0.300495i
\(201\) 0 0
\(202\) 5.18728 5.18728i 0.364976 0.364976i
\(203\) −1.59754 + 9.23998i −0.112125 + 0.648520i
\(204\) 0 0
\(205\) 2.54420i 0.177695i
\(206\) 2.46480 2.46480i 0.171731 0.171731i
\(207\) 0 0
\(208\) −7.74841 0.639375i −0.537255 0.0443327i
\(209\) 4.29022i 0.296761i
\(210\) 0 0
\(211\) −0.594028 −0.0408946 −0.0204473 0.999791i \(-0.506509\pi\)
−0.0204473 + 0.999791i \(0.506509\pi\)
\(212\) 16.4060i 1.12677i
\(213\) 0 0
\(214\) −3.57452 + 3.57452i −0.244349 + 0.244349i
\(215\) −8.94198 + 8.94198i −0.609838 + 0.609838i
\(216\) 0 0
\(217\) −3.88717 + 2.74117i −0.263878 + 0.186083i
\(218\) 3.70545i 0.250965i
\(219\) 0 0
\(220\) −2.06443 −0.139184
\(221\) −26.4040 2.17878i −1.77612 0.146560i
\(222\) 0 0
\(223\) −2.85764 2.85764i −0.191361 0.191361i 0.604923 0.796284i \(-0.293204\pi\)
−0.796284 + 0.604923i \(0.793204\pi\)
\(224\) −8.26187 11.7159i −0.552019 0.782802i
\(225\) 0 0
\(226\) −0.647754 + 0.647754i −0.0430879 + 0.0430879i
\(227\) −19.6570 19.6570i −1.30468 1.30468i −0.925201 0.379477i \(-0.876104\pi\)
−0.379477 0.925201i \(-0.623896\pi\)
\(228\) 0 0
\(229\) 13.2060 13.2060i 0.872676 0.872676i −0.120087 0.992763i \(-0.538317\pi\)
0.992763 + 0.120087i \(0.0383174\pi\)
\(230\) 3.69720i 0.243786i
\(231\) 0 0
\(232\) 5.24965 + 5.24965i 0.344656 + 0.344656i
\(233\) 16.2243i 1.06289i −0.847094 0.531443i \(-0.821650\pi\)
0.847094 0.531443i \(-0.178350\pi\)
\(234\) 0 0
\(235\) 5.20711 0.339674
\(236\) −1.82542 1.82542i −0.118825 0.118825i
\(237\) 0 0
\(238\) −6.38594 9.05571i −0.413939 0.586994i
\(239\) 0.843675 0.843675i 0.0545728 0.0545728i −0.679294 0.733867i \(-0.737714\pi\)
0.733867 + 0.679294i \(0.237714\pi\)
\(240\) 0 0
\(241\) −15.2966 + 15.2966i −0.985342 + 0.985342i −0.999894 0.0145517i \(-0.995368\pi\)
0.0145517 + 0.999894i \(0.495368\pi\)
\(242\) −4.14609 4.14609i −0.266521 0.266521i
\(243\) 0 0
\(244\) 11.9086 0.762367
\(245\) −4.38009 9.23204i −0.279834 0.589813i
\(246\) 0 0
\(247\) −11.8466 13.9775i −0.753782 0.889370i
\(248\) 3.76585i 0.239132i
\(249\) 0 0
\(250\) 6.54730i 0.414088i
\(251\) 27.4367 1.73179 0.865893 0.500229i \(-0.166751\pi\)
0.865893 + 0.500229i \(0.166751\pi\)
\(252\) 0 0
\(253\) −2.65268 + 2.65268i −0.166772 + 0.166772i
\(254\) 0.624346 + 0.624346i 0.0391749 + 0.0391749i
\(255\) 0 0
\(256\) −4.12601 −0.257876
\(257\) 20.5727 1.28329 0.641645 0.767002i \(-0.278252\pi\)
0.641645 + 0.767002i \(0.278252\pi\)
\(258\) 0 0
\(259\) −8.81944 + 6.21933i −0.548014 + 0.386450i
\(260\) −6.72592 + 5.70052i −0.417124 + 0.353531i
\(261\) 0 0
\(262\) 2.14207 + 2.14207i 0.132338 + 0.132338i
\(263\) 23.8568 1.47108 0.735538 0.677483i \(-0.236929\pi\)
0.735538 + 0.677483i \(0.236929\pi\)
\(264\) 0 0
\(265\) 10.1093 + 10.1093i 0.621012 + 0.621012i
\(266\) 1.30557 7.55128i 0.0800497 0.462999i
\(267\) 0 0
\(268\) 14.6883 + 14.6883i 0.897231 + 0.897231i
\(269\) 1.10840i 0.0675803i 0.999429 + 0.0337902i \(0.0107578\pi\)
−0.999429 + 0.0337902i \(0.989242\pi\)
\(270\) 0 0
\(271\) −20.8894 + 20.8894i −1.26894 + 1.26894i −0.322301 + 0.946637i \(0.604456\pi\)
−0.946637 + 0.322301i \(0.895544\pi\)
\(272\) 15.8448 0.960730
\(273\) 0 0
\(274\) −10.2496 −0.619204
\(275\) 1.71274 1.71274i 0.103282 0.103282i
\(276\) 0 0
\(277\) 25.8265i 1.55177i 0.630877 + 0.775883i \(0.282695\pi\)
−0.630877 + 0.775883i \(0.717305\pi\)
\(278\) 2.80013 + 2.80013i 0.167941 + 0.167941i
\(279\) 0 0
\(280\) −7.97196 1.37830i −0.476416 0.0823694i
\(281\) −12.0782 12.0782i −0.720523 0.720523i 0.248189 0.968712i \(-0.420165\pi\)
−0.968712 + 0.248189i \(0.920165\pi\)
\(282\) 0 0
\(283\) 15.3667 0.913458 0.456729 0.889606i \(-0.349021\pi\)
0.456729 + 0.889606i \(0.349021\pi\)
\(284\) 2.45580 + 2.45580i 0.145725 + 0.145725i
\(285\) 0 0
\(286\) 1.72909 + 0.142680i 0.102243 + 0.00843683i
\(287\) −3.76845 + 2.65745i −0.222445 + 0.156864i
\(288\) 0 0
\(289\) 36.9937 2.17610
\(290\) 2.94888 0.173164
\(291\) 0 0
\(292\) 0.173973 + 0.173973i 0.0101810 + 0.0101810i
\(293\) −9.78662 + 9.78662i −0.571741 + 0.571741i −0.932615 0.360874i \(-0.882478\pi\)
0.360874 + 0.932615i \(0.382478\pi\)
\(294\) 0 0
\(295\) −2.24965 −0.130979
\(296\) 8.54420i 0.496621i
\(297\) 0 0
\(298\) 8.83875i 0.512015i
\(299\) −1.31757 + 15.9673i −0.0761972 + 0.923413i
\(300\) 0 0
\(301\) −22.5848 3.90478i −1.30177 0.225068i
\(302\) 4.95017 0.284850
\(303\) 0 0
\(304\) 7.74841 + 7.74841i 0.444402 + 0.444402i
\(305\) 7.33804 7.33804i 0.420175 0.420175i
\(306\) 0 0
\(307\) 8.14125 8.14125i 0.464645 0.464645i −0.435529 0.900175i \(-0.643439\pi\)
0.900175 + 0.435529i \(0.143439\pi\)
\(308\) −2.15633 3.05782i −0.122868 0.174235i
\(309\) 0 0
\(310\) 1.05769 + 1.05769i 0.0600730 + 0.0600730i
\(311\) −32.4813 −1.84184 −0.920922 0.389747i \(-0.872562\pi\)
−0.920922 + 0.389747i \(0.872562\pi\)
\(312\) 0 0
\(313\) 19.7346i 1.11547i 0.830020 + 0.557733i \(0.188329\pi\)
−0.830020 + 0.557733i \(0.811671\pi\)
\(314\) −3.90853 3.90853i −0.220571 0.220571i
\(315\) 0 0
\(316\) 8.03857i 0.452205i
\(317\) 8.11871 8.11871i 0.455992 0.455992i −0.441345 0.897337i \(-0.645499\pi\)
0.897337 + 0.441345i \(0.145499\pi\)
\(318\) 0 0
\(319\) 2.11577 + 2.11577i 0.118461 + 0.118461i
\(320\) 1.26369 1.26369i 0.0706425 0.0706425i
\(321\) 0 0
\(322\) −5.47626 + 3.86177i −0.305180 + 0.215208i
\(323\) 26.4040 + 26.4040i 1.46916 + 1.46916i
\(324\) 0 0
\(325\) 0.850712 10.3095i 0.0471890 0.571870i
\(326\) −4.36344 −0.241668
\(327\) 0 0
\(328\) 3.65084i 0.201584i
\(329\) 5.43890 + 7.71274i 0.299856 + 0.425217i
\(330\) 0 0
\(331\) −0.806063 + 0.806063i −0.0443053 + 0.0443053i −0.728912 0.684607i \(-0.759974\pi\)
0.684607 + 0.728912i \(0.259974\pi\)
\(332\) −20.6317 + 20.6317i −1.13231 + 1.13231i
\(333\) 0 0
\(334\) 7.18061i 0.392905i
\(335\) 18.1018 0.989009
\(336\) 0 0
\(337\) 26.6058i 1.44931i −0.689112 0.724655i \(-0.741999\pi\)
0.689112 0.724655i \(-0.258001\pi\)
\(338\) 6.02738 4.30971i 0.327846 0.234417i
\(339\) 0 0
\(340\) 12.7054 12.7054i 0.689050 0.689050i
\(341\) 1.51776i 0.0821912i
\(342\) 0 0
\(343\) 9.09937 16.1308i 0.491320 0.870979i
\(344\) −12.8315 + 12.8315i −0.691826 + 0.691826i
\(345\) 0 0
\(346\) 2.88385 2.88385i 0.155037 0.155037i
\(347\) 20.2071 1.08477 0.542387 0.840129i \(-0.317521\pi\)
0.542387 + 0.840129i \(0.317521\pi\)
\(348\) 0 0
\(349\) 2.31459 2.31459i 0.123897 0.123897i −0.642439 0.766336i \(-0.722078\pi\)
0.766336 + 0.642439i \(0.222078\pi\)
\(350\) 3.53583 2.49341i 0.188998 0.133279i
\(351\) 0 0
\(352\) −4.57452 −0.243822
\(353\) −10.7412 10.7412i −0.571696 0.571696i 0.360906 0.932602i \(-0.382467\pi\)
−0.932602 + 0.360906i \(0.882467\pi\)
\(354\) 0 0
\(355\) 3.02653 0.160631
\(356\) −11.5419 11.5419i −0.611721 0.611721i
\(357\) 0 0
\(358\) 5.56665 + 5.56665i 0.294207 + 0.294207i
\(359\) 16.9726 + 16.9726i 0.895781 + 0.895781i 0.995060 0.0992789i \(-0.0316536\pi\)
−0.0992789 + 0.995060i \(0.531654\pi\)
\(360\) 0 0
\(361\) 6.82416i 0.359166i
\(362\) 1.83803 1.83803i 0.0966049 0.0966049i
\(363\) 0 0
\(364\) −15.4689 4.00811i −0.810791 0.210082i
\(365\) 0.214405 0.0112225
\(366\) 0 0
\(367\) 9.79778i 0.511440i −0.966751 0.255720i \(-0.917688\pi\)
0.966751 0.255720i \(-0.0823125\pi\)
\(368\) 9.58181i 0.499486i
\(369\) 0 0
\(370\) 2.39976 + 2.39976i 0.124758 + 0.124758i
\(371\) −4.41455 + 25.5333i −0.229192 + 1.32562i
\(372\) 0 0
\(373\) −5.96731 −0.308976 −0.154488 0.987995i \(-0.549373\pi\)
−0.154488 + 0.987995i \(0.549373\pi\)
\(374\) −3.53583 −0.182834
\(375\) 0 0
\(376\) 7.47204 0.385341
\(377\) 12.7355 + 1.05090i 0.655912 + 0.0541239i
\(378\) 0 0
\(379\) 2.14117 2.14117i 0.109984 0.109984i −0.649973 0.759957i \(-0.725220\pi\)
0.759957 + 0.649973i \(0.225220\pi\)
\(380\) 12.4264 0.637463
\(381\) 0 0
\(382\) −1.49341 + 1.49341i −0.0764097 + 0.0764097i
\(383\) 2.91152 + 2.91152i 0.148772 + 0.148772i 0.777569 0.628798i \(-0.216453\pi\)
−0.628798 + 0.777569i \(0.716453\pi\)
\(384\) 0 0
\(385\) −3.21295 0.555500i −0.163747 0.0283109i
\(386\) −13.7440 −0.699552
\(387\) 0 0
\(388\) −10.1482 + 10.1482i −0.515195 + 0.515195i
\(389\) 17.4436i 0.884425i 0.896910 + 0.442212i \(0.145806\pi\)
−0.896910 + 0.442212i \(0.854194\pi\)
\(390\) 0 0
\(391\) 32.6516i 1.65126i
\(392\) −6.28529 13.2477i −0.317455 0.669109i
\(393\) 0 0
\(394\) 6.46310i 0.325606i
\(395\) −4.95336 4.95336i −0.249230 0.249230i
\(396\) 0 0
\(397\) −10.1870 + 10.1870i −0.511270 + 0.511270i −0.914916 0.403645i \(-0.867743\pi\)
0.403645 + 0.914916i \(0.367743\pi\)
\(398\) 1.84410 1.84410i 0.0924365 0.0924365i
\(399\) 0 0
\(400\) 6.18664i 0.309332i
\(401\) −15.5950 15.5950i −0.778776 0.778776i 0.200846 0.979623i \(-0.435631\pi\)
−0.979623 + 0.200846i \(0.935631\pi\)
\(402\) 0 0
\(403\) 4.19100 + 4.94486i 0.208768 + 0.246321i
\(404\) 21.5600i 1.07265i
\(405\) 0 0
\(406\) 3.08015 + 4.36786i 0.152865 + 0.216773i
\(407\) 3.44358i 0.170692i
\(408\) 0 0
\(409\) −1.79921 1.79921i −0.0889652 0.0889652i 0.661224 0.750189i \(-0.270037\pi\)
−0.750189 + 0.661224i \(0.770037\pi\)
\(410\) 1.02539 + 1.02539i 0.0506405 + 0.0506405i
\(411\) 0 0
\(412\) 10.2445i 0.504710i
\(413\) −2.34979 3.33216i −0.115626 0.163965i
\(414\) 0 0
\(415\) 25.4264i 1.24813i
\(416\) −14.9038 + 12.6316i −0.730718 + 0.619317i
\(417\) 0 0
\(418\) −1.72909 1.72909i −0.0845728 0.0845728i
\(419\) 16.5064i 0.806392i −0.915114 0.403196i \(-0.867899\pi\)
0.915114 0.403196i \(-0.132101\pi\)
\(420\) 0 0
\(421\) −8.53492 + 8.53492i −0.415967 + 0.415967i −0.883811 0.467844i \(-0.845031\pi\)
0.467844 + 0.883811i \(0.345031\pi\)
\(422\) −0.239412 + 0.239412i −0.0116544 + 0.0116544i
\(423\) 0 0
\(424\) 14.5066 + 14.5066i 0.704502 + 0.704502i
\(425\) 21.0820i 1.02263i
\(426\) 0 0
\(427\) 18.5338 + 3.20438i 0.896911 + 0.155071i
\(428\) 14.8568i 0.718133i
\(429\) 0 0
\(430\) 7.20780i 0.347591i
\(431\) −24.2071 + 24.2071i −1.16602 + 1.16602i −0.182880 + 0.983135i \(0.558542\pi\)
−0.983135 + 0.182880i \(0.941458\pi\)
\(432\) 0 0
\(433\) 35.8708 1.72384 0.861920 0.507044i \(-0.169262\pi\)
0.861920 + 0.507044i \(0.169262\pi\)
\(434\) −0.461874 + 2.67143i −0.0221707 + 0.128233i
\(435\) 0 0
\(436\) −7.70052 7.70052i −0.368788 0.368788i
\(437\) 15.9673 15.9673i 0.763819 0.763819i
\(438\) 0 0
\(439\) −10.5299 −0.502563 −0.251281 0.967914i \(-0.580852\pi\)
−0.251281 + 0.967914i \(0.580852\pi\)
\(440\) −1.82542 + 1.82542i −0.0870236 + 0.0870236i
\(441\) 0 0
\(442\) −11.5198 + 9.76353i −0.547939 + 0.464404i
\(443\) −12.8618 −0.611081 −0.305541 0.952179i \(-0.598837\pi\)
−0.305541 + 0.952179i \(0.598837\pi\)
\(444\) 0 0
\(445\) −14.2243 −0.674294
\(446\) −2.30344 −0.109071
\(447\) 0 0
\(448\) 3.19172 + 0.551829i 0.150795 + 0.0260715i
\(449\) −9.65069 9.65069i −0.455444 0.455444i 0.441712 0.897157i \(-0.354371\pi\)
−0.897157 + 0.441712i \(0.854371\pi\)
\(450\) 0 0
\(451\) 1.47141i 0.0692858i
\(452\) 2.69227i 0.126634i
\(453\) 0 0
\(454\) −15.8448 −0.743631
\(455\) −12.0017 + 7.06213i −0.562649 + 0.331078i
\(456\) 0 0
\(457\) −22.1217 + 22.1217i −1.03481 + 1.03481i −0.0354353 + 0.999372i \(0.511282\pi\)
−0.999372 + 0.0354353i \(0.988718\pi\)
\(458\) 10.6449i 0.497402i
\(459\) 0 0
\(460\) −7.68337 7.68337i −0.358239 0.358239i
\(461\) 0.593023 + 0.593023i 0.0276198 + 0.0276198i 0.720782 0.693162i \(-0.243783\pi\)
−0.693162 + 0.720782i \(0.743783\pi\)
\(462\) 0 0
\(463\) 2.47096 + 2.47096i 0.114835 + 0.114835i 0.762189 0.647354i \(-0.224124\pi\)
−0.647354 + 0.762189i \(0.724124\pi\)
\(464\) −7.64244 −0.354792
\(465\) 0 0
\(466\) −6.53889 6.53889i −0.302908 0.302908i
\(467\) −13.3860 −0.619432 −0.309716 0.950829i \(-0.600234\pi\)
−0.309716 + 0.950829i \(0.600234\pi\)
\(468\) 0 0
\(469\) 18.9076 + 26.8123i 0.873073 + 1.23808i
\(470\) 2.09863 2.09863i 0.0968026 0.0968026i
\(471\) 0 0
\(472\) −3.22817 −0.148589
\(473\) −5.17148 + 5.17148i −0.237785 + 0.237785i
\(474\) 0 0
\(475\) −10.3095 + 10.3095i −0.473034 + 0.473034i
\(476\) 32.0903 + 5.54821i 1.47085 + 0.254302i
\(477\) 0 0
\(478\) 0.680055i 0.0311050i
\(479\) −8.85827 + 8.85827i −0.404745 + 0.404745i −0.879901 0.475157i \(-0.842391\pi\)
0.475157 + 0.879901i \(0.342391\pi\)
\(480\) 0 0
\(481\) 9.50879 + 11.2192i 0.433564 + 0.511552i
\(482\) 12.3301i 0.561619i
\(483\) 0 0
\(484\) 17.2325 0.783296
\(485\) 12.5066i 0.567895i
\(486\) 0 0
\(487\) 17.9805 17.9805i 0.814774 0.814774i −0.170572 0.985345i \(-0.554561\pi\)
0.985345 + 0.170572i \(0.0545614\pi\)
\(488\) 10.5299 10.5299i 0.476664 0.476664i
\(489\) 0 0
\(490\) −5.48612 1.95549i −0.247838 0.0883400i
\(491\) 19.4944i 0.879769i 0.898054 + 0.439884i \(0.144981\pi\)
−0.898054 + 0.439884i \(0.855019\pi\)
\(492\) 0 0
\(493\) −26.0429 −1.17291
\(494\) −10.4080 0.858833i −0.468276 0.0386407i
\(495\) 0 0
\(496\) −2.74117 2.74117i −0.123082 0.123082i
\(497\) 3.16125 + 4.48287i 0.141801 + 0.201084i
\(498\) 0 0
\(499\) 10.2150 10.2150i 0.457285 0.457285i −0.440478 0.897763i \(-0.645191\pi\)
0.897763 + 0.440478i \(0.145191\pi\)
\(500\) 13.6064 + 13.6064i 0.608495 + 0.608495i
\(501\) 0 0
\(502\) 11.0578 11.0578i 0.493536 0.493536i
\(503\) 31.8196i 1.41877i 0.704824 + 0.709383i \(0.251026\pi\)
−0.704824 + 0.709383i \(0.748974\pi\)
\(504\) 0 0
\(505\) 13.2853 + 13.2853i 0.591187 + 0.591187i
\(506\) 2.13823i 0.0950558i
\(507\) 0 0
\(508\) −2.59498 −0.115134
\(509\) −13.6139 13.6139i −0.603425 0.603425i 0.337795 0.941220i \(-0.390319\pi\)
−0.941220 + 0.337795i \(0.890319\pi\)
\(510\) 0 0
\(511\) 0.223949 + 0.317575i 0.00990691 + 0.0140487i
\(512\) 14.6497 14.6497i 0.647433 0.647433i
\(513\) 0 0
\(514\) 8.29145 8.29145i 0.365720 0.365720i
\(515\) 6.31265 + 6.31265i 0.278169 + 0.278169i
\(516\) 0 0
\(517\) 3.01147 0.132444
\(518\) −1.04793 + 6.06110i −0.0460433 + 0.266310i
\(519\) 0 0
\(520\) −0.906679 + 10.9878i −0.0397605 + 0.481846i
\(521\) 21.6750i 0.949601i −0.880094 0.474800i \(-0.842520\pi\)
0.880094 0.474800i \(-0.157480\pi\)
\(522\) 0 0
\(523\) 8.77309i 0.383620i 0.981432 + 0.191810i \(0.0614358\pi\)
−0.981432 + 0.191810i \(0.938564\pi\)
\(524\) −8.90316 −0.388936
\(525\) 0 0
\(526\) 9.61507 9.61507i 0.419237 0.419237i
\(527\) −9.34098 9.34098i −0.406900 0.406900i
\(528\) 0 0
\(529\) 3.25457 0.141503
\(530\) 8.14877 0.353960
\(531\) 0 0
\(532\) 12.9796 + 18.4060i 0.562737 + 0.798000i
\(533\) 4.06300 + 4.79384i 0.175988 + 0.207644i
\(534\) 0 0
\(535\) −9.15478 9.15478i −0.395796 0.395796i
\(536\) 25.9756 1.12197
\(537\) 0 0
\(538\) 0.446720 + 0.446720i 0.0192595 + 0.0192595i
\(539\) −2.53317 5.33923i −0.109111 0.229977i
\(540\) 0 0
\(541\) −23.2853 23.2853i −1.00111 1.00111i −0.999999 0.00111270i \(-0.999646\pi\)
−0.00111270 0.999999i \(-0.500354\pi\)
\(542\) 16.8382i 0.723260i
\(543\) 0 0
\(544\) 28.1537 28.1537i 1.20708 1.20708i
\(545\) −9.49011 −0.406512
\(546\) 0 0
\(547\) −15.1744 −0.648812 −0.324406 0.945918i \(-0.605164\pi\)
−0.324406 + 0.945918i \(0.605164\pi\)
\(548\) 21.3004 21.3004i 0.909909 0.909909i
\(549\) 0 0
\(550\) 1.38058i 0.0588681i
\(551\) −12.7355 12.7355i −0.542551 0.542551i
\(552\) 0 0
\(553\) 2.16303 12.5107i 0.0919815 0.532011i
\(554\) 10.4089 + 10.4089i 0.442232 + 0.442232i
\(555\) 0 0
\(556\) −11.6383 −0.493572
\(557\) −8.45676 8.45676i −0.358324 0.358324i 0.504871 0.863195i \(-0.331540\pi\)
−0.863195 + 0.504871i \(0.831540\pi\)
\(558\) 0 0
\(559\) −2.56865 + 31.1288i −0.108642 + 1.31661i
\(560\) 6.80606 4.79953i 0.287609 0.202817i
\(561\) 0 0
\(562\) −9.73577 −0.410678
\(563\) 6.34858 0.267561 0.133780 0.991011i \(-0.457288\pi\)
0.133780 + 0.991011i \(0.457288\pi\)
\(564\) 0 0
\(565\) −1.65898 1.65898i −0.0697937 0.0697937i
\(566\) 6.19329 6.19329i 0.260323 0.260323i
\(567\) 0 0
\(568\) 4.34297 0.182227
\(569\) 36.6140i 1.53494i 0.641085 + 0.767470i \(0.278485\pi\)
−0.641085 + 0.767470i \(0.721515\pi\)
\(570\) 0 0
\(571\) 18.8070i 0.787049i 0.919314 + 0.393525i \(0.128744\pi\)
−0.919314 + 0.393525i \(0.871256\pi\)
\(572\) −3.88985 + 3.29683i −0.162643 + 0.137847i
\(573\) 0 0
\(574\) −0.447768 + 2.58984i −0.0186895 + 0.108098i
\(575\) 12.7489 0.531668
\(576\) 0 0
\(577\) −31.3416 31.3416i −1.30477 1.30477i −0.925140 0.379627i \(-0.876052\pi\)
−0.379627 0.925140i \(-0.623948\pi\)
\(578\) 14.9096 14.9096i 0.620158 0.620158i
\(579\) 0 0
\(580\) −6.12825 + 6.12825i −0.254462 + 0.254462i
\(581\) −37.6615 + 26.5583i −1.56246 + 1.10182i
\(582\) 0 0
\(583\) 5.84661 + 5.84661i 0.242142 + 0.242142i
\(584\) 0.307664 0.0127312
\(585\) 0 0
\(586\) 7.88864i 0.325877i
\(587\) 3.36694 + 3.36694i 0.138969 + 0.138969i 0.773169 0.634200i \(-0.218671\pi\)
−0.634200 + 0.773169i \(0.718671\pi\)
\(588\) 0 0
\(589\) 9.13586i 0.376436i
\(590\) −0.906679 + 0.906679i −0.0373274 + 0.0373274i
\(591\) 0 0
\(592\) −6.21933 6.21933i −0.255613 0.255613i
\(593\) 10.6837 10.6837i 0.438726 0.438726i −0.452857 0.891583i \(-0.649595\pi\)
0.891583 + 0.452857i \(0.149595\pi\)
\(594\) 0 0
\(595\) 23.1928 16.3552i 0.950812 0.670497i
\(596\) 18.3684 + 18.3684i 0.752397 + 0.752397i
\(597\) 0 0
\(598\) 5.90430 + 6.96635i 0.241445 + 0.284875i
\(599\) 12.8437 0.524778 0.262389 0.964962i \(-0.415490\pi\)
0.262389 + 0.964962i \(0.415490\pi\)
\(600\) 0 0
\(601\) 19.5732i 0.798409i −0.916862 0.399205i \(-0.869286\pi\)
0.916862 0.399205i \(-0.130714\pi\)
\(602\) −10.6762 + 7.52865i −0.435128 + 0.306845i
\(603\) 0 0
\(604\) −10.2873 + 10.2873i −0.418583 + 0.418583i
\(605\) 10.6187 10.6187i 0.431710 0.431710i
\(606\) 0 0
\(607\) 41.9804i 1.70393i 0.523598 + 0.851965i \(0.324589\pi\)
−0.523598 + 0.851965i \(0.675411\pi\)
\(608\) 27.5354 1.11671
\(609\) 0 0
\(610\) 5.91493i 0.239488i
\(611\) 9.81137 8.31559i 0.396926 0.336413i
\(612\) 0 0
\(613\) 20.4993 20.4993i 0.827959 0.827959i −0.159276 0.987234i \(-0.550916\pi\)
0.987234 + 0.159276i \(0.0509158\pi\)
\(614\) 6.56236i 0.264835i
\(615\) 0 0
\(616\) −4.61048 0.797125i −0.185762 0.0321171i
\(617\) −8.21440 + 8.21440i −0.330699 + 0.330699i −0.852852 0.522153i \(-0.825129\pi\)
0.522153 + 0.852852i \(0.325129\pi\)
\(618\) 0 0
\(619\) −26.6973 + 26.6973i −1.07306 + 1.07306i −0.0759445 + 0.997112i \(0.524197\pi\)
−0.997112 + 0.0759445i \(0.975803\pi\)
\(620\) −4.39612 −0.176553
\(621\) 0 0
\(622\) −13.0910 + 13.0910i −0.524900 + 0.524900i
\(623\) −14.8574 21.0689i −0.595251 0.844107i
\(624\) 0 0
\(625\) 2.42311 0.0969246
\(626\) 7.95367 + 7.95367i 0.317893 + 0.317893i
\(627\) 0 0
\(628\) 16.2451 0.648251
\(629\) −21.1934 21.1934i −0.845036 0.845036i
\(630\) 0 0
\(631\) 5.13093 + 5.13093i 0.204259 + 0.204259i 0.801822 0.597563i \(-0.203864\pi\)
−0.597563 + 0.801822i \(0.703864\pi\)
\(632\) −7.10791 7.10791i −0.282737 0.282737i
\(633\) 0 0
\(634\) 6.54420i 0.259903i
\(635\) −1.59903 + 1.59903i −0.0634554 + 0.0634554i
\(636\) 0 0
\(637\) −22.9963 10.4004i −0.911149 0.412078i
\(638\) 1.70545 0.0675193
\(639\) 0 0
\(640\) 16.8382i 0.665586i
\(641\) 16.3357i 0.645220i −0.946532 0.322610i \(-0.895440\pi\)
0.946532 0.322610i \(-0.104560\pi\)
\(642\) 0 0
\(643\) −28.1910 28.1910i −1.11175 1.11175i −0.992914 0.118832i \(-0.962085\pi\)
−0.118832 0.992914i \(-0.537915\pi\)
\(644\) 3.35517 19.4060i 0.132212 0.764702i
\(645\) 0 0
\(646\) 21.2833 0.837380
\(647\) 11.1139 0.436932 0.218466 0.975845i \(-0.429895\pi\)
0.218466 + 0.975845i \(0.429895\pi\)
\(648\) 0 0
\(649\) −1.30105 −0.0510709
\(650\) −3.81220 4.49793i −0.149527 0.176423i
\(651\) 0 0
\(652\) 9.06793 9.06793i 0.355127 0.355127i
\(653\) −4.95651 −0.193963 −0.0969816 0.995286i \(-0.530919\pi\)
−0.0969816 + 0.995286i \(0.530919\pi\)
\(654\) 0 0
\(655\) −5.48612 + 5.48612i −0.214360 + 0.214360i
\(656\) −2.65745 2.65745i −0.103756 0.103756i
\(657\) 0 0
\(658\) 5.30053 + 0.916430i 0.206636 + 0.0357262i
\(659\) −26.1514 −1.01871 −0.509357 0.860555i \(-0.670117\pi\)
−0.509357 + 0.860555i \(0.670117\pi\)
\(660\) 0 0
\(661\) 22.2906 22.2906i 0.867006 0.867006i −0.125134 0.992140i \(-0.539936\pi\)
0.992140 + 0.125134i \(0.0399361\pi\)
\(662\) 0.649738i 0.0252528i
\(663\) 0 0
\(664\) 36.4861i 1.41594i
\(665\) 19.3398 + 3.34373i 0.749964 + 0.129664i
\(666\) 0 0
\(667\) 15.7489i 0.609801i
\(668\) 14.9225 + 14.9225i 0.577368 + 0.577368i
\(669\) 0 0
\(670\) 7.29562 7.29562i 0.281854 0.281854i
\(671\) 4.24387 4.24387i 0.163833 0.163833i
\(672\) 0 0
\(673\) 1.38550i 0.0534072i −0.999643 0.0267036i \(-0.991499\pi\)
0.999643 0.0267036i \(-0.00850104\pi\)
\(674\) −10.7230 10.7230i −0.413034 0.413034i
\(675\) 0 0
\(676\) −3.56959 + 21.4821i −0.137292 + 0.826237i
\(677\) 14.1868i 0.545242i −0.962122 0.272621i \(-0.912110\pi\)
0.962122 0.272621i \(-0.0878905\pi\)
\(678\) 0 0
\(679\) −18.5247 + 13.0633i −0.710912 + 0.501324i
\(680\) 22.4690i 0.861646i
\(681\) 0 0
\(682\) 0.611704 + 0.611704i 0.0234234 + 0.0234234i
\(683\) −27.2882 27.2882i −1.04415 1.04415i −0.998979 0.0451754i \(-0.985615\pi\)
−0.0451754 0.998979i \(-0.514385\pi\)
\(684\) 0 0
\(685\) 26.2506i 1.00298i
\(686\) −2.83387 10.1685i −0.108198 0.388237i
\(687\) 0 0
\(688\) 18.6801i 0.712170i
\(689\) 35.1926 + 2.90399i 1.34073 + 0.110633i
\(690\) 0 0
\(691\) −16.1937 16.1937i −0.616037 0.616037i 0.328475 0.944513i \(-0.393465\pi\)
−0.944513 + 0.328475i \(0.893465\pi\)
\(692\) 11.9862i 0.455647i
\(693\) 0 0
\(694\) 8.14411 8.14411i 0.309146 0.309146i
\(695\) −7.17148 + 7.17148i −0.272030 + 0.272030i
\(696\) 0 0
\(697\) −9.05571 9.05571i −0.343009 0.343009i
\(698\) 1.86570i 0.0706180i
\(699\) 0 0
\(700\) −2.16632 + 12.5298i −0.0818792 + 0.473580i
\(701\) 15.2981i 0.577800i −0.957359 0.288900i \(-0.906711\pi\)
0.957359 0.288900i \(-0.0932895\pi\)
\(702\) 0 0
\(703\) 20.7280i 0.781771i
\(704\) 0.730841 0.730841i 0.0275446 0.0275446i
\(705\) 0 0
\(706\) −8.65808 −0.325851
\(707\) −5.80141 + 33.5547i −0.218185 + 1.26196i
\(708\) 0 0
\(709\) −2.74107 2.74107i −0.102943 0.102943i 0.653759 0.756703i \(-0.273191\pi\)
−0.756703 + 0.653759i \(0.773191\pi\)
\(710\) 1.21979 1.21979i 0.0457778 0.0457778i
\(711\) 0 0
\(712\) −20.4113 −0.764948
\(713\) −5.64878 + 5.64878i −0.211548 + 0.211548i
\(714\) 0 0
\(715\) −0.365420 + 4.42842i −0.0136659 + 0.165614i
\(716\) −23.1368 −0.864663
\(717\) 0 0
\(718\) 13.6810 0.510571
\(719\) −5.99456 −0.223559 −0.111780 0.993733i \(-0.535655\pi\)
−0.111780 + 0.993733i \(0.535655\pi\)
\(720\) 0 0
\(721\) −2.75661 + 15.9439i −0.102661 + 0.593782i
\(722\) 2.75035 + 2.75035i 0.102358 + 0.102358i
\(723\) 0 0
\(724\) 7.63947i 0.283919i
\(725\) 10.1685i 0.377650i
\(726\) 0 0
\(727\) −14.6184 −0.542168 −0.271084 0.962556i \(-0.587382\pi\)
−0.271084 + 0.962556i \(0.587382\pi\)
\(728\) −17.2221 + 10.1339i −0.638293 + 0.375588i
\(729\) 0 0
\(730\) 0.0864119 0.0864119i 0.00319825 0.00319825i
\(731\) 63.6554i 2.35438i
\(732\) 0 0
\(733\) 28.0685 + 28.0685i 1.03673 + 1.03673i 0.999299 + 0.0374350i \(0.0119187\pi\)
0.0374350 + 0.999299i \(0.488081\pi\)
\(734\) −3.94881 3.94881i −0.145753 0.145753i
\(735\) 0 0
\(736\) −17.0254 17.0254i −0.627564 0.627564i
\(737\) 10.4690 0.385630
\(738\) 0 0
\(739\) −16.6028 16.6028i −0.610746 0.610746i 0.332395 0.943140i \(-0.392143\pi\)
−0.943140 + 0.332395i \(0.892143\pi\)
\(740\) −9.97420 −0.366659
\(741\) 0 0
\(742\) 8.51151 + 12.0699i 0.312467 + 0.443101i
\(743\) 2.87636 2.87636i 0.105523 0.105523i −0.652374 0.757897i \(-0.726227\pi\)
0.757897 + 0.652374i \(0.226227\pi\)
\(744\) 0 0
\(745\) 22.6371 0.829361
\(746\) −2.40502 + 2.40502i −0.0880539 + 0.0880539i
\(747\) 0 0
\(748\) 7.34804 7.34804i 0.268671 0.268671i
\(749\) 3.99771 23.1223i 0.146073 0.844871i
\(750\) 0 0
\(751\) 45.9438i 1.67651i 0.545275 + 0.838257i \(0.316425\pi\)
−0.545275 + 0.838257i \(0.683575\pi\)
\(752\) −5.43890 + 5.43890i −0.198336 + 0.198336i
\(753\) 0 0
\(754\) 5.55636 4.70927i 0.202351 0.171501i
\(755\) 12.6780i 0.461400i
\(756\) 0 0
\(757\) −24.7889 −0.900969 −0.450484 0.892784i \(-0.648749\pi\)
−0.450484 + 0.892784i \(0.648749\pi\)
\(758\) 1.72592i 0.0626881i
\(759\) 0 0
\(760\) 10.9878 10.9878i 0.398569 0.398569i
\(761\) 10.8450 10.8450i 0.393133 0.393133i −0.482670 0.875802i \(-0.660333\pi\)
0.875802 + 0.482670i \(0.160333\pi\)
\(762\) 0 0
\(763\) −9.91256 14.0567i −0.358859 0.508887i
\(764\) 6.20711i 0.224565i
\(765\) 0 0
\(766\) 2.34687 0.0847958
\(767\) −4.23884 + 3.59261i −0.153056 + 0.129722i
\(768\) 0 0
\(769\) 4.63670 + 4.63670i 0.167204 + 0.167204i 0.785749 0.618545i \(-0.212278\pi\)
−0.618545 + 0.785749i \(0.712278\pi\)
\(770\) −1.51881 + 1.07104i −0.0547340 + 0.0385975i
\(771\) 0 0
\(772\) 28.5623 28.5623i 1.02798 1.02798i
\(773\) −5.68398 5.68398i −0.204438 0.204438i 0.597460 0.801899i \(-0.296177\pi\)
−0.801899 + 0.597460i \(0.796177\pi\)
\(774\) 0 0
\(775\) 3.64722 3.64722i 0.131012 0.131012i
\(776\) 17.9466i 0.644244i
\(777\) 0 0
\(778\) 7.03032 + 7.03032i 0.252049 + 0.252049i
\(779\) 8.85685i 0.317330i
\(780\) 0 0
\(781\) 1.75035 0.0626326
\(782\) −13.1596 13.1596i −0.470588 0.470588i
\(783\) 0 0
\(784\) 14.2181 + 5.06793i 0.507788 + 0.180997i
\(785\) 10.0102 10.0102i 0.357281 0.357281i
\(786\) 0 0
\(787\) 8.65662 8.65662i 0.308575 0.308575i −0.535781 0.844357i \(-0.679983\pi\)
0.844357 + 0.535781i \(0.179983\pi\)
\(788\) 13.4314 + 13.4314i 0.478473 + 0.478473i
\(789\) 0