Properties

Label 819.2.y.h.307.3
Level $819$
Weight $2$
Character 819.307
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 307.3
Root \(-1.52891 - 1.52891i\) of defining polynomial
Character \(\chi\) \(=\) 819.307
Dual form 819.2.y.h.811.3

$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

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

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 0.835094 0.550107i \(-0.185413\pi\)
−0.550107 + 0.835094i \(0.685413\pi\)
\(3\) 0 0
\(4\) 1.67513i 0.837565i
\(5\) −1.03221 + 1.03221i −0.461620 + 0.461620i −0.899186 0.437566i \(-0.855841\pi\)
0.437566 + 0.899186i \(0.355841\pi\)
\(6\) 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 −0.611360 0.791353i \(-0.709377\pi\)
0.791353 + 0.611360i \(0.209377\pi\)
\(12\) 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 −0.162363 0.986731i \(-0.551911\pi\)
0.986731 + 0.162363i \(0.0519115\pi\)
\(20\) 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 \(-0.846674\pi\)
0.886214 0.463276i \(-0.153326\pi\)
\(24\) 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 −0.811990 0.583672i \(-0.801616\pi\)
0.583672 + 0.811990i \(0.301616\pi\)
\(32\) −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 −0.429095 0.903259i \(-0.641168\pi\)
0.903259 + 0.429095i \(0.141168\pi\)
\(38\) 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 \(-0.793455\pi\)
0.604294 + 0.796762i \(0.293455\pi\)
\(42\) 0 0
\(43\) 8.66291i 1.32108i −0.750790 0.660541i \(-0.770327\pi\)
0.750790 0.660541i \(-0.229673\pi\)
\(44\) −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 \(-0.333774\pi\)
−0.866717 + 0.498801i \(0.833774\pi\)
\(48\) 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 \(-0.218014\pi\)
−0.632605 + 0.774474i \(0.718014\pi\)
\(60\) 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 0.997260 + 0.0739770i \(0.0235691\pi\)
0.0739770 + 0.997260i \(0.476431\pi\)
\(68\) 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 0.788728 0.614742i \(-0.210740\pi\)
−0.614742 + 0.788728i \(0.710740\pi\)
\(72\) 0 0
\(73\) −0.103857 0.103857i −0.0121555 0.0121555i 0.701003 0.713158i \(-0.252736\pi\)
−0.713158 + 0.701003i \(0.752736\pi\)
\(74\) 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 −0.468379 + 0.883528i \(0.655162\pi\)
−0.883528 + 0.468379i \(0.844838\pi\)
\(84\) 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 \(-0.0772570\pi\)
−0.240334 + 0.970690i \(0.577257\pi\)
\(90\) 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 −0.944273 0.329163i \(-0.893234\pi\)
0.329163 + 0.944273i \(0.393234\pi\)
\(98\) 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 0.451806 0.892116i \(-0.350780\pi\)
−0.892116 + 0.451806i \(0.850780\pi\)
\(110\) −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 \(-0.978105\pi\)
0.997635 0.0687312i \(-0.0218951\pi\)
\(128\) −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 −0.0904753 + 0.995899i \(0.528839\pi\)
−0.995899 + 0.0904753i \(0.971161\pi\)
\(138\) 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 0.995287 0.0969724i \(-0.0309158\pi\)
−0.0969724 + 0.995287i \(0.530916\pi\)
\(150\) 0 0
\(151\) 6.14117 6.14117i 0.499761 0.499761i −0.411602 0.911363i \(-0.635031\pi\)
0.911363 + 0.411602i \(0.135031\pi\)
\(152\) 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 \(-0.873516\pi\)
0.922086 0.386985i \(-0.126484\pi\)
\(158\) −1.93406 1.93406i −0.153865 0.153865i
\(159\) 0 0
\(160\) 7.90977 0.625322
\(161\) 2.00293 11.5847i 0.157853 0.913006i
\(162\) 0 0
\(163\) −5.41327 + 5.41327i −0.424000 + 0.424000i −0.886578 0.462579i \(-0.846924\pi\)
0.462579 + 0.886578i \(0.346924\pi\)
\(164\) 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 \(-0.412068\pi\)
−0.962086 + 0.272746i \(0.912068\pi\)
\(168\) 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 \(-0.827355\pi\)
0.856482 0.516177i \(-0.172645\pi\)
\(180\) 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 −0.262377 + 0.964965i \(0.584506\pi\)
−0.964965 + 0.262377i \(0.915494\pi\)
\(194\) −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 0.932482 0.361216i \(-0.117638\pi\)
−0.361216 + 0.932482i \(0.617638\pi\)
\(198\) 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 −0.604923 0.796284i \(-0.706796\pi\)
0.796284 + 0.604923i \(0.206796\pi\)
\(224\) −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 0.379477 0.925201i \(-0.376104\pi\)
0.925201 0.379477i \(-0.123896\pi\)
\(228\) 0 0
\(229\) −13.2060 13.2060i −0.872676 0.872676i 0.120087 0.992763i \(-0.461683\pi\)
−0.992763 + 0.120087i \(0.961683\pi\)
\(230\) 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 \(0.178350\pi\)
−0.847094 + 0.531443i \(0.821650\pi\)
\(234\) 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 0.733867 0.679294i \(-0.237714\pi\)
−0.679294 + 0.733867i \(0.737714\pi\)
\(240\) 0 0
\(241\) 15.2966 + 15.2966i 0.985342 + 0.985342i 0.999894 0.0145517i \(-0.00463211\pi\)
−0.0145517 + 0.999894i \(0.504632\pi\)
\(242\) −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 \(0.0107578\pi\)
−0.999429 + 0.0337902i \(0.989242\pi\)
\(270\) 0 0
\(271\) 20.8894 + 20.8894i 1.26894 + 1.26894i 0.946637 + 0.322301i \(0.104456\pi\)
0.322301 + 0.946637i \(0.395544\pi\)
\(272\) −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 \(-0.717305\pi\)
0.630877 0.775883i \(-0.282695\pi\)
\(278\) −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 −0.968712 0.248189i \(-0.920165\pi\)
0.248189 + 0.968712i \(0.420165\pi\)
\(282\) 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 0.932615 0.360874i \(-0.117522\pi\)
−0.360874 + 0.932615i \(0.617522\pi\)
\(294\) 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 0.435529 0.900175i \(-0.356561\pi\)
−0.900175 + 0.435529i \(0.856561\pi\)
\(308\) −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 \(0.188329\pi\)
−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 0.897337 0.441345i \(-0.145499\pi\)
−0.441345 + 0.897337i \(0.645499\pi\)
\(318\) 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 0.684607 0.728912i \(-0.259974\pi\)
−0.728912 + 0.684607i \(0.759974\pi\)
\(332\) 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 \(0.258001\pi\)
−0.689112 + 0.724655i \(0.741999\pi\)
\(338\) 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 0.642439 0.766336i \(-0.277922\pi\)
−0.766336 + 0.642439i \(0.777922\pi\)
\(350\) −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 \(-0.617533\pi\)
0.932602 + 0.360906i \(0.117533\pi\)
\(354\) 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 −0.0992789 0.995060i \(-0.531654\pi\)
0.995060 + 0.0992789i \(0.0316536\pi\)
\(360\) 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 \(-0.917688\pi\)
0.966751 0.255720i \(-0.0823125\pi\)
\(368\) 9.58181i 0.499486i
\(369\) 0 0
\(370\) −2.39976 + 2.39976i −0.124758 + 0.124758i
\(371\) 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 0.759957 0.649973i \(-0.225220\pi\)
−0.649973 + 0.759957i \(0.725220\pi\)
\(380\) 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 \(-0.783547\pi\)
0.628798 + 0.777569i \(0.283547\pi\)
\(384\) 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 \(-0.854194\pi\)
0.896910 0.442212i \(-0.145806\pi\)
\(390\) 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 0.914916 0.403645i \(-0.132257\pi\)
−0.403645 + 0.914916i \(0.632257\pi\)
\(398\) −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 −0.979623 0.200846i \(-0.935631\pi\)
0.200846 + 0.979623i \(0.435631\pi\)
\(402\) 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 \(-0.729963\pi\)
0.750189 + 0.661224i \(0.229963\pi\)
\(410\) 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 0.467844 0.883811i \(-0.345031\pi\)
−0.883811 + 0.467844i \(0.845031\pi\)
\(422\) −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 −0.983135 0.182880i \(-0.941458\pi\)
−0.182880 0.983135i \(-0.558542\pi\)
\(432\) 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 −0.897157 0.441712i \(-0.854371\pi\)
0.441712 + 0.897157i \(0.354371\pi\)
\(450\) 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 −0.999372 0.0354353i \(-0.988718\pi\)
−0.0354353 0.999372i \(-0.511282\pi\)
\(458\) 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 \(-0.756217\pi\)
0.693162 + 0.720782i \(0.256217\pi\)
\(462\) 0 0
\(463\) 2.47096 2.47096i 0.114835 0.114835i −0.647354 0.762189i \(-0.724124\pi\)
0.762189 + 0.647354i \(0.224124\pi\)
\(464\) −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 0.879901 0.475157i \(-0.157609\pi\)
−0.475157 + 0.879901i \(0.657609\pi\)
\(480\) 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 0.985345 0.170572i \(-0.0545614\pi\)
−0.170572 + 0.985345i \(0.554561\pi\)
\(488\) −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 \(-0.855019\pi\)
0.898054 0.439884i \(-0.144981\pi\)
\(492\) 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 0.897763 0.440478i \(-0.145191\pi\)
−0.440478 + 0.897763i \(0.645191\pi\)
\(500\) −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 \(-0.609681\pi\)
0.941220 + 0.337795i \(0.109681\pi\)
\(510\) 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 \(-0.842520\pi\)
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
\(539\) 5.33923 2.53317i 0.229977 0.109111i
\(540\) 0 0
\(541\) −23.2853 + 23.2853i −1.00111 + 1.00111i −0.00111270 + 0.999999i \(0.500354\pi\)
−0.999999 + 0.00111270i \(0.999646\pi\)
\(542\) 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 −0.863195 0.504871i \(-0.831540\pi\)
0.504871 + 0.863195i \(0.331540\pi\)
\(558\) 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 \(-0.721515\pi\)
0.641085 0.767470i \(-0.278485\pi\)
\(570\) 0 0
\(571\) 18.8070i 0.787049i −0.919314 0.393525i \(-0.871256\pi\)
0.919314 0.393525i \(-0.128744\pi\)
\(572\) 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 0.379627 0.925140i \(-0.376052\pi\)
0.925140 0.379627i \(-0.123948\pi\)
\(578\) 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 \(-0.781329\pi\)
0.634200 + 0.773169i \(0.281329\pi\)
\(588\) 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 \(-0.350405\pi\)
−0.891583 + 0.452857i \(0.850405\pi\)
\(594\) 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 0.987234 0.159276i \(-0.0509158\pi\)
−0.159276 + 0.987234i \(0.550916\pi\)
\(614\) 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 0.522153 0.852852i \(-0.325129\pi\)
−0.852852 + 0.522153i \(0.825129\pi\)
\(618\) 0 0
\(619\) 26.6973 + 26.6973i 1.07306 + 1.07306i 0.997112 + 0.0759445i \(0.0241972\pi\)
0.0759445 + 0.997112i \(0.475803\pi\)
\(620\) −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 −0.597563 0.801822i \(-0.703864\pi\)
0.801822 + 0.597563i \(0.203864\pi\)
\(632\) −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 \(0.104560\pi\)
−0.946532 + 0.322610i \(0.895440\pi\)
\(642\) 0 0
\(643\) 28.1910 28.1910i 1.11175 1.11175i 0.118832 0.992914i \(-0.462085\pi\)
0.992914 0.118832i \(-0.0379150\pi\)
\(644\) −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 0.125134 0.992140i \(-0.460064\pi\)
−0.992140 + 0.125134i \(0.960064\pi\)
\(662\) 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 \(0.00850104\pi\)
−0.999643 + 0.0267036i \(0.991499\pi\)
\(674\) −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 −0.0451754 + 0.998979i \(0.514385\pi\)
−0.998979 + 0.0451754i \(0.985615\pi\)
\(684\) 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 \(-0.606535\pi\)
0.944513 + 0.328475i \(0.106535\pi\)
\(692\) 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 \(0.0932895\pi\)
−0.957359 + 0.288900i \(0.906711\pi\)
\(702\) 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 −0.756703 0.653759i \(-0.773191\pi\)
0.653759 + 0.756703i \(0.273191\pi\)
\(710\) −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 −0.0374350 + 0.999299i \(0.511919\pi\)
−0.999299 + 0.0374350i \(0.988081\pi\)
\(734\) 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 −0.943140 0.332395i \(-0.892143\pi\)
0.332395 + 0.943140i \(0.392143\pi\)
\(740\) 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 0.757897 0.652374i \(-0.226227\pi\)
−0.652374 + 0.757897i \(0.726227\pi\)
\(744\) 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 \(-0.683575\pi\)
0.545275 0.838257i \(-0.316425\pi\)
\(752\) 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 \(-0.339667\pi\)
−0.875802 + 0.482670i \(0.839667\pi\)
\(762\) 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 \(-0.787722\pi\)
0.618545 + 0.785749i \(0.287722\pi\)
\(770\) −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 \(-0.703823\pi\)
0.801899 + 0.597460i \(0.203823\pi\)
\(774\) 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 \(-0.320017\pi\)
−0.844357 + 0.535781i \(0.820017\pi\)
\(788\) 13.4314 13.4314i 0.478473 0.478473i
\(789\) 0