Properties

Label 819.2.y.h.811.3
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 811.3
Root \(-1.52891 + 1.52891i\) of defining polynomial
Character \(\chi\) \(=\) 819.811
Dual form 819.2.y.h.307.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.403032 - 0.403032i) q^{2} +1.67513i q^{4} +(-1.03221 - 1.03221i) q^{5} +(2.60707 - 0.450747i) q^{7} +(1.48119 + 1.48119i) q^{8} +O(q^{10})\) \(q+(0.403032 - 0.403032i) q^{2} +1.67513i q^{4} +(-1.03221 - 1.03221i) q^{5} +(2.60707 - 0.450747i) q^{7} +(1.48119 + 1.48119i) q^{8} -0.832030 q^{10} +(0.596968 + 0.596968i) q^{11} +(-3.59334 - 0.296512i) q^{13} +(0.869067 - 1.23240i) q^{14} -2.15633 q^{16} +7.34804 q^{17} +(3.59334 + 3.59334i) q^{19} +(1.72909 - 1.72909i) q^{20} +0.481194 q^{22} +4.44358i q^{23} -2.86907i q^{25} +(-1.56773 + 1.32873i) q^{26} +(0.755061 + 4.36719i) q^{28} +3.54420 q^{29} +(-1.27122 - 1.27122i) q^{31} +(-3.83146 + 3.83146i) q^{32} +(2.96149 - 2.96149i) q^{34} +(-3.15633 - 2.22579i) q^{35} +(2.88423 + 2.88423i) q^{37} +2.89646 q^{38} -3.05782i q^{40} +(-1.23240 - 1.23240i) q^{41} +8.66291i q^{43} +(-1.00000 + 1.00000i) q^{44} +(1.79090 + 1.79090i) q^{46} +(-2.52230 + 2.52230i) q^{47} +(6.59365 - 2.35026i) q^{49} +(-1.15633 - 1.15633i) q^{50} +(0.496696 - 6.01931i) q^{52} +9.79384 q^{53} -1.23240i q^{55} +(4.52923 + 3.19394i) q^{56} +(1.42842 - 1.42842i) q^{58} +(1.08972 - 1.08972i) q^{59} +7.10903i q^{61} -1.02469 q^{62} -1.22425i q^{64} +(3.40303 + 4.01516i) q^{65} +(8.76845 - 8.76845i) q^{67} +12.3089i q^{68} +(-2.16916 + 0.375035i) q^{70} +(1.46604 - 1.46604i) q^{71} +(-0.103857 + 0.103857i) q^{73} +2.32487 q^{74} +(-6.01931 + 6.01931i) q^{76} +(1.82542 + 1.28726i) q^{77} -4.79877 q^{79} +(2.22579 + 2.22579i) q^{80} -0.993391 q^{82} +(-12.3165 - 12.3165i) q^{83} +(-7.58475 - 7.58475i) q^{85} +(3.49143 + 3.49143i) q^{86} +1.76845i q^{88} +(6.89017 - 6.89017i) q^{89} +(-9.50175 + 0.846661i) q^{91} -7.44358 q^{92} +2.03313i q^{94} -7.41819i q^{95} +(-6.05814 - 6.05814i) q^{97} +(1.71022 - 3.60468i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{2} - 8 q^{7} - 4 q^{8}+O(q^{10}) \) 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 0.437566 0.899186i \(-0.355841\pi\)
−0.899186 + 0.437566i \(0.855841\pi\)
\(6\) 0 0
\(7\) 2.60707 0.450747i 0.985381 0.170366i
\(8\) 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 \(-0.149948\pi\)
0.891080 + 0.453845i \(0.149948\pi\)
\(18\) 0 0
\(19\) 3.59334 + 3.59334i 0.824368 + 0.824368i 0.986731 0.162363i \(-0.0519115\pi\)
−0.162363 + 0.986731i \(0.551911\pi\)
\(20\) 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
\(28\) 0.755061 + 4.36719i 0.142693 + 0.825321i
\(29\) 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 0.583672 0.811990i \(-0.301616\pi\)
−0.811990 + 0.583672i \(0.801616\pi\)
\(32\) −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 0.604294 0.796762i \(-0.293455\pi\)
−0.796762 + 0.604294i \(0.793455\pi\)
\(42\) 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 −0.866717 0.498801i \(-0.833774\pi\)
0.498801 + 0.866717i \(0.333774\pi\)
\(48\) 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 −0.632605 0.774474i \(-0.718014\pi\)
0.774474 + 0.632605i \(0.218014\pi\)
\(60\) 0 0
\(61\) 7.10903i 0.910218i 0.890436 + 0.455109i \(0.150400\pi\)
−0.890436 + 0.455109i \(0.849600\pi\)
\(62\) −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
\(70\) −2.16916 + 0.375035i −0.259265 + 0.0448253i
\(71\) 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 −0.713158 0.701003i \(-0.752736\pi\)
0.701003 + 0.713158i \(0.252736\pi\)
\(74\) 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 \(-0.844838\pi\)
−0.468379 0.883528i \(-0.655162\pi\)
\(84\) 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 −0.240334 0.970690i \(-0.577257\pi\)
0.970690 + 0.240334i \(0.0772570\pi\)
\(90\) 0 0
\(91\) −9.50175 + 0.846661i −0.996054 + 0.0887541i
\(92\) −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 0.329163 0.944273i \(-0.393234\pi\)
−0.944273 + 0.329163i \(0.893234\pi\)
\(98\) 1.71022 3.60468i 0.172758 0.364128i
\(99\) 0 0
\(100\) 4.80606 0.480606
\(101\) −12.8707 −1.28068 −0.640339 0.768092i \(-0.721206\pi\)
−0.640339 + 0.768092i \(0.721206\pi\)
\(102\) 0 0
\(103\) −6.11564 −0.602592 −0.301296 0.953531i \(-0.597419\pi\)
−0.301296 + 0.953531i \(0.597419\pi\)
\(104\) −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
\(112\) −5.62170 + 0.971958i −0.531200 + 0.0918414i
\(113\) −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
\(119\) 19.1569 3.31211i 1.75611 0.303620i
\(120\) 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 \(-0.925413\pi\)
0.972672 0.232183i \(-0.0745867\pi\)
\(132\) 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 \(-0.904798\pi\)
0.955606 0.294647i \(-0.0952020\pi\)
\(140\) 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
\(154\) 1.25451 0.216897i 0.101091 0.0174781i
\(155\) 2.62435i 0.210793i
\(156\) 0 0
\(157\) 9.69783i 0.773971i 0.922086 + 0.386985i \(0.126484\pi\)
−0.922086 + 0.386985i \(0.873516\pi\)
\(158\) −1.93406 + 1.93406i −0.153865 + 0.153865i
\(159\) 0 0
\(160\) 7.90977 0.625322
\(161\) 2.00293 + 11.5847i 0.157853 + 0.913006i
\(162\) 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 −0.962086 0.272746i \(-0.912068\pi\)
0.272746 + 0.962086i \(0.412068\pi\)
\(168\) 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 \(-0.587687\pi\)
−0.272007 + 0.962295i \(0.587687\pi\)
\(174\) 0 0
\(175\) −1.29322 7.47987i −0.0977586 0.565425i
\(176\) −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 \(-0.554212\pi\)
−0.169490 + 0.985532i \(0.554212\pi\)
\(182\) −3.48827 + 4.17074i −0.258568 + 0.309156i
\(183\) 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 \(-0.551852\pi\)
−0.162177 + 0.986762i \(0.551852\pi\)
\(200\) 4.24965 4.24965i 0.300495 0.300495i
\(201\) 0 0
\(202\) −5.18728 + 5.18728i −0.364976 + 0.364976i
\(203\) 9.23998 1.59754i 0.648520 0.112125i
\(204\) 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 0.796284 0.604923i \(-0.206796\pi\)
−0.604923 + 0.796284i \(0.706796\pi\)
\(224\) −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 \(0.123896\pi\)
0.379477 + 0.925201i \(0.376104\pi\)
\(228\) 0 0
\(229\) −13.2060 + 13.2060i −0.872676 + 0.872676i −0.992763 0.120087i \(-0.961683\pi\)
0.120087 + 0.992763i \(0.461683\pi\)
\(230\) 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 −0.0145517 0.999894i \(-0.504632\pi\)
0.999894 + 0.0145517i \(0.00463211\pi\)
\(242\) −4.14609 4.14609i −0.266521 0.266521i
\(243\) 0 0
\(244\) −11.9086 −0.762367
\(245\) −9.23204 4.38009i −0.589813 0.279834i
\(246\) 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 \(-0.833249\pi\)
−0.865893 + 0.500229i \(0.833249\pi\)
\(252\) 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 \(-0.721748\pi\)
−0.641645 + 0.767002i \(0.721748\pi\)
\(258\) 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
\(266\) 7.55128 1.30557i 0.462999 0.0800497i
\(267\) 0 0
\(268\) 14.6883 + 14.6883i 0.897231 + 0.897231i
\(269\) 1.10840i 0.0675803i −0.999429 0.0337902i \(-0.989242\pi\)
0.999429 0.0337902i \(-0.0107578\pi\)
\(270\) 0 0
\(271\) 20.8894 20.8894i 1.26894 1.26894i 0.322301 0.946637i \(-0.395544\pi\)
0.946637 0.322301i \(-0.104456\pi\)
\(272\) −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
\(280\) −1.37830 7.97196i −0.0823694 0.476416i
\(281\) −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 \(-0.650979\pi\)
−0.456729 + 0.889606i \(0.650979\pi\)
\(284\) 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 −0.360874 0.932615i \(-0.617522\pi\)
0.932615 + 0.360874i \(0.117522\pi\)
\(294\) 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
\(301\) 3.90478 + 22.5848i 0.225068 + 1.30177i
\(302\) 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 −0.900175 0.435529i \(-0.856561\pi\)
0.435529 + 0.900175i \(0.356561\pi\)
\(308\) −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 \(-0.127438\pi\)
0.920922 + 0.389747i \(0.127438\pi\)
\(312\) 0 0
\(313\) 19.7346i 1.11547i −0.830020 0.557733i \(-0.811671\pi\)
0.830020 0.557733i \(-0.188329\pi\)
\(314\) 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
\(343\) 16.1308 9.09937i 0.870979 0.491320i
\(344\) −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 −0.766336 0.642439i \(-0.777922\pi\)
0.642439 + 0.766336i \(0.277922\pi\)
\(350\) −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 0.932602 0.360906i \(-0.117533\pi\)
−0.360906 + 0.932602i \(0.617533\pi\)
\(354\) 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
\(364\) −1.41827 15.9167i −0.0743374 0.834260i
\(365\) 0.214405 0.0112225
\(366\) 0 0
\(367\) 9.79778i 0.511440i 0.966751 + 0.255720i \(0.0823125\pi\)
−0.966751 + 0.255720i \(0.917688\pi\)
\(368\) 9.58181i 0.499486i
\(369\) 0 0
\(370\) −2.39976 2.39976i −0.124758 0.124758i
\(371\) 25.5333 4.41455i 1.32562 0.229192i
\(372\) 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 0.628798 0.777569i \(-0.283547\pi\)
−0.777569 + 0.628798i \(0.783547\pi\)
\(384\) 0 0
\(385\) −0.555500 3.21295i −0.0283109 0.163747i
\(386\) −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
\(392\) 13.2477 + 6.28529i 0.669109 + 0.317455i
\(393\) 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 −0.403645 0.914916i \(-0.632257\pi\)
0.914916 + 0.403645i \(0.132257\pi\)
\(398\) −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 0.750189 0.661224i \(-0.229963\pi\)
−0.661224 + 0.750189i \(0.729963\pi\)
\(410\) 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 \(0.132101\pi\)
−0.915114 + 0.403196i \(0.867899\pi\)
\(420\) 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
\(427\) 3.20438 + 18.5338i 0.155071 + 0.896911i
\(428\) 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 \(-0.830738\pi\)
−0.861920 + 0.507044i \(0.830738\pi\)
\(434\) −2.67143 + 0.461874i −0.128233 + 0.0221707i
\(435\) 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 \(-0.419148\pi\)
0.251281 + 0.967914i \(0.419148\pi\)
\(440\) 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
\(448\) −0.551829 3.19172i −0.0260715 0.150795i
\(449\) −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
\(455\) 10.6818 + 8.93390i 0.500769 + 0.418828i
\(456\) 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 0.693162 0.720782i \(-0.256217\pi\)
−0.720782 + 0.693162i \(0.756217\pi\)
\(462\) 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 \(-0.399766\pi\)
0.309716 + 0.950829i \(0.399766\pi\)
\(468\) 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
\(476\) 5.54821 + 32.0903i 0.254302 + 1.47085i
\(477\) 0 0
\(478\) 0.680055i 0.0311050i
\(479\) 8.85827 8.85827i 0.404745 0.404745i −0.475157 0.879901i \(-0.657609\pi\)
0.879901 + 0.475157i \(0.157609\pi\)
\(480\) 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 \(-0.748974\pi\)
0.704824 0.709383i \(-0.251026\pi\)
\(504\) 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 0.941220 0.337795i \(-0.109681\pi\)
−0.337795 + 0.941220i \(0.609681\pi\)
\(510\) 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
\(518\) 6.06110 1.04793i 0.266310 0.0460433i
\(519\) 0 0
\(520\) −0.906679 + 10.9878i −0.0397605 + 0.481846i
\(521\) 21.6750i 0.949601i 0.880094 + 0.474800i \(0.157480\pi\)
−0.880094 + 0.474800i \(0.842520\pi\)
\(522\) 0 0
\(523\) 8.77309i 0.383620i −0.981432 0.191810i \(-0.938564\pi\)
0.981432 0.191810i \(-0.0614358\pi\)
\(524\) 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
\(539\) 5.33923 + 2.53317i 0.229977 + 0.109111i
\(540\) 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
\(553\) −12.5107 + 2.16303i −0.532011 + 0.0919815i
\(554\) 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 \(-0.542712\pi\)
−0.133780 + 0.991011i \(0.542712\pi\)
\(564\) 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
\(574\) −2.58984 + 0.447768i −0.108098 + 0.0186895i
\(575\) 12.7489 0.531668
\(576\) 0 0
\(577\) 31.3416 + 31.3416i 1.30477 + 1.30477i 0.925140 + 0.379627i \(0.123948\pi\)
0.379627 + 0.925140i \(0.376052\pi\)
\(578\) 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 0.634200 0.773169i \(-0.281329\pi\)
−0.773169 + 0.634200i \(0.781329\pi\)
\(588\) 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 −0.891583 0.452857i \(-0.850405\pi\)
0.452857 + 0.891583i \(0.350405\pi\)
\(594\) 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 \(0.130714\pi\)
−0.916862 + 0.399205i \(0.869286\pi\)
\(602\) 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 \(-0.675411\pi\)
0.523598 0.851965i \(-0.324589\pi\)
\(608\) −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
\(616\) 0.797125 + 4.61048i 0.0321171 + 0.185762i
\(617\) −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 \(-0.475803\pi\)
0.997112 0.0759445i \(-0.0241972\pi\)
\(620\) −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
\(637\) −24.3901 + 6.49019i −0.966371 + 0.257151i
\(638\) 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 \(0.0379150\pi\)
0.118832 + 0.992914i \(0.462085\pi\)
\(644\) −19.4060 + 3.35517i −0.764702 + 0.132212i
\(645\) 0 0
\(646\) 21.2833 0.837380
\(647\) −11.1139 −0.436932 −0.218466 0.975845i \(-0.570105\pi\)
−0.218466 + 0.975845i \(0.570105\pi\)
\(648\) 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
\(658\) 0.916430 + 5.30053i 0.0357262 + 0.206636i
\(659\) −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 −0.992140 0.125134i \(-0.960064\pi\)
0.125134 + 0.992140i \(0.460064\pi\)
\(662\) 0.649738i 0.0252528i
\(663\) 0 0
\(664\) 36.4861i 1.41594i
\(665\) −3.34373 19.3398i −0.129664 0.749964i
\(666\) 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 \(0.0878905\pi\)
−0.962122 + 0.272621i \(0.912110\pi\)
\(678\) 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 0.944513 0.328475i \(-0.106535\pi\)
−0.328475 + 0.944513i \(0.606535\pi\)
\(692\) 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
\(700\) 12.5298 2.16632i 0.473580 0.0818792i
\(701\) 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
\(707\) −33.5547 + 5.80141i −1.26196 + 0.218185i
\(708\) 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 \(-0.464345\pi\)
0.111780 + 0.993733i \(0.464345\pi\)
\(720\) 0 0
\(721\) −15.9439 + 2.75661i −0.593782 + 0.102661i
\(722\) 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 \(-0.412618\pi\)
0.271084 + 0.962556i \(0.412618\pi\)
\(728\) −15.3280 12.8199i −0.568093 0.475136i
\(729\) 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 \(-0.988081\pi\)
−0.0374350 0.999299i \(-0.511919\pi\)
\(734\) 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
\(749\) −23.1223 + 3.99771i −0.844871 + 0.146073i
\(750\) 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 −0.875802 0.482670i \(-0.839667\pi\)
0.482670 + 0.875802i \(0.339667\pi\)
\(762\) 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 0.618545 0.785749i \(-0.287722\pi\)
−0.785749 + 0.618545i \(0.787722\pi\)
\(770\) −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 0.801899 0.597460i \(-0.203823\pi\)
−0.597460 + 0.801899i \(0.703823\pi\)
\(774\) 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 −0.844357 0.535781i \(-0.820017\pi\)
0.535781 + 0.844357i \(0.320017\pi\)
\(788\) 13.4314 + 13.4314i 0.478473 + 0.478473i
\(789\)