Properties

Label 441.2.w.a.251.10
Level $441$
Weight $2$
Character 441.251
Analytic conductor $3.521$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.w (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 251.10
Character \(\chi\) \(=\) 441.251
Dual form 441.2.w.a.188.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.00441089 - 0.00351757i) q^{2} +(-0.445035 - 1.94982i) q^{4} +(-1.95912 - 0.943460i) q^{5} +(2.55289 + 0.694800i) q^{7} +(-0.00979136 + 0.0203320i) q^{8} +O(q^{10})\) \(q+(-0.00441089 - 0.00351757i) q^{2} +(-0.445035 - 1.94982i) q^{4} +(-1.95912 - 0.943460i) q^{5} +(2.55289 + 0.694800i) q^{7} +(-0.00979136 + 0.0203320i) q^{8} +(0.00532276 + 0.0110528i) q^{10} +(-1.56142 - 1.24519i) q^{11} +(-1.10775 - 0.883399i) q^{13} +(-0.00881652 - 0.0120447i) q^{14} +(-3.60370 + 1.73545i) q^{16} +(0.751799 - 3.29385i) q^{17} -6.30461i q^{19} +(-0.967708 + 4.23980i) q^{20} +(0.00250721 + 0.0109848i) q^{22} +(-7.96285 + 1.81747i) q^{23} +(-0.169433 - 0.212462i) q^{25} +(0.00177874 + 0.00779316i) q^{26} +(0.218614 - 5.28690i) q^{28} +(-5.47364 - 1.24932i) q^{29} +5.21141i q^{31} +(0.0660021 + 0.0150646i) q^{32} +(-0.0149024 + 0.0118843i) q^{34} +(-4.34589 - 3.76975i) q^{35} +(1.55054 - 6.79337i) q^{37} +(-0.0221769 + 0.0278090i) q^{38} +(0.0383648 - 0.0305949i) q^{40} +(9.97587 + 4.80413i) q^{41} +(0.0684189 - 0.0329488i) q^{43} +(-1.73302 + 3.59865i) q^{44} +(0.0415164 + 0.0199932i) q^{46} +(3.46380 - 4.34347i) q^{47} +(6.03450 + 3.54750i) q^{49} +0.00153314i q^{50} +(-1.22949 + 2.55306i) q^{52} +(0.739555 - 0.168799i) q^{53} +(1.88422 + 3.91261i) q^{55} +(-0.0391230 + 0.0451023i) q^{56} +(0.0197491 + 0.0247646i) q^{58} +(9.30068 - 4.47897i) q^{59} +(7.51004 + 1.71412i) q^{61} +(0.0183315 - 0.0229870i) q^{62} +(4.98744 + 6.25405i) q^{64} +(1.33675 + 2.77580i) q^{65} -8.97651 q^{67} -6.75700 q^{68} +(0.00590892 + 0.0319149i) q^{70} +(14.3180 - 3.26798i) q^{71} +(2.21540 - 1.76672i) q^{73} +(-0.0307354 + 0.0245107i) q^{74} +(-12.2929 + 2.80577i) q^{76} +(-3.12098 - 4.26371i) q^{77} -5.29436 q^{79} +8.69740 q^{80} +(-0.0271036 - 0.0562813i) q^{82} +(1.21293 + 1.52097i) q^{83} +(-4.58047 + 5.74373i) q^{85} +(-0.000417688 - 9.53346e-5i) q^{86} +(0.0406057 - 0.0195547i) q^{88} +(-4.85674 - 6.09016i) q^{89} +(-2.21417 - 3.02489i) q^{91} +(7.08749 + 14.7173i) q^{92} +(-0.0305569 + 0.00697441i) q^{94} +(-5.94815 + 12.3515i) q^{95} +0.0843849i q^{97} +(-0.0141390 - 0.0368744i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 24q^{4} + O(q^{10}) \) \( 120q + 24q^{4} - 32q^{16} - 44q^{22} - 4q^{25} - 56q^{28} + 112q^{34} - 76q^{37} + 28q^{40} + 8q^{43} - 40q^{46} - 84q^{49} - 140q^{52} + 12q^{58} - 84q^{61} + 24q^{64} + 16q^{67} + 112q^{70} - 84q^{76} - 24q^{79} + 140q^{82} - 96q^{85} - 24q^{88} - 112q^{91} - 112q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{9}{14}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.00441089 0.00351757i −0.00311897 0.00248730i 0.621929 0.783074i \(-0.286349\pi\)
−0.625048 + 0.780586i \(0.714921\pi\)
\(3\) 0 0
\(4\) −0.445035 1.94982i −0.222517 0.974912i
\(5\) −1.95912 0.943460i −0.876143 0.421928i −0.0589288 0.998262i \(-0.518768\pi\)
−0.817214 + 0.576334i \(0.804483\pi\)
\(6\) 0 0
\(7\) 2.55289 + 0.694800i 0.964902 + 0.262610i
\(8\) −0.00979136 + 0.0203320i −0.00346177 + 0.00718844i
\(9\) 0 0
\(10\) 0.00532276 + 0.0110528i 0.00168320 + 0.00349521i
\(11\) −1.56142 1.24519i −0.470786 0.375439i 0.359166 0.933274i \(-0.383061\pi\)
−0.829952 + 0.557834i \(0.811633\pi\)
\(12\) 0 0
\(13\) −1.10775 0.883399i −0.307234 0.245011i 0.457719 0.889097i \(-0.348667\pi\)
−0.764953 + 0.644086i \(0.777238\pi\)
\(14\) −0.00881652 0.0120447i −0.00235631 0.00321907i
\(15\) 0 0
\(16\) −3.60370 + 1.73545i −0.900926 + 0.433863i
\(17\) 0.751799 3.29385i 0.182338 0.798875i −0.798176 0.602425i \(-0.794201\pi\)
0.980514 0.196450i \(-0.0629414\pi\)
\(18\) 0 0
\(19\) 6.30461i 1.44638i −0.690651 0.723188i \(-0.742676\pi\)
0.690651 0.723188i \(-0.257324\pi\)
\(20\) −0.967708 + 4.23980i −0.216386 + 0.948049i
\(21\) 0 0
\(22\) 0.00250721 + 0.0109848i 0.000534539 + 0.00234197i
\(23\) −7.96285 + 1.81747i −1.66037 + 0.378969i −0.946852 0.321669i \(-0.895756\pi\)
−0.713517 + 0.700637i \(0.752899\pi\)
\(24\) 0 0
\(25\) −0.169433 0.212462i −0.0338865 0.0424924i
\(26\) 0.00177874 + 0.00779316i 0.000348839 + 0.00152836i
\(27\) 0 0
\(28\) 0.218614 5.28690i 0.0413141 0.999130i
\(29\) −5.47364 1.24932i −1.01643 0.231994i −0.318320 0.947983i \(-0.603118\pi\)
−0.698111 + 0.715990i \(0.745976\pi\)
\(30\) 0 0
\(31\) 5.21141i 0.935998i 0.883729 + 0.467999i \(0.155025\pi\)
−0.883729 + 0.467999i \(0.844975\pi\)
\(32\) 0.0660021 + 0.0150646i 0.0116676 + 0.00266306i
\(33\) 0 0
\(34\) −0.0149024 + 0.0118843i −0.00255575 + 0.00203814i
\(35\) −4.34589 3.76975i −0.734590 0.637203i
\(36\) 0 0
\(37\) 1.55054 6.79337i 0.254907 1.11682i −0.671709 0.740815i \(-0.734440\pi\)
0.926617 0.376007i \(-0.122703\pi\)
\(38\) −0.0221769 + 0.0278090i −0.00359757 + 0.00451121i
\(39\) 0 0
\(40\) 0.0383648 0.0305949i 0.00606601 0.00483748i
\(41\) 9.97587 + 4.80413i 1.55797 + 0.750278i 0.996988 0.0775505i \(-0.0247099\pi\)
0.560981 + 0.827829i \(0.310424\pi\)
\(42\) 0 0
\(43\) 0.0684189 0.0329488i 0.0104338 0.00502465i −0.428660 0.903466i \(-0.641014\pi\)
0.439093 + 0.898441i \(0.355300\pi\)
\(44\) −1.73302 + 3.59865i −0.261262 + 0.542517i
\(45\) 0 0
\(46\) 0.0415164 + 0.0199932i 0.00612125 + 0.00294784i
\(47\) 3.46380 4.34347i 0.505247 0.633559i −0.462157 0.886798i \(-0.652924\pi\)
0.967404 + 0.253239i \(0.0814958\pi\)
\(48\) 0 0
\(49\) 6.03450 + 3.54750i 0.862072 + 0.506786i
\(50\) 0.00153314i 0.000216818i
\(51\) 0 0
\(52\) −1.22949 + 2.55306i −0.170499 + 0.354045i
\(53\) 0.739555 0.168799i 0.101586 0.0231863i −0.171426 0.985197i \(-0.554837\pi\)
0.273012 + 0.962011i \(0.411980\pi\)
\(54\) 0 0
\(55\) 1.88422 + 3.91261i 0.254068 + 0.527577i
\(56\) −0.0391230 + 0.0451023i −0.00522802 + 0.00602705i
\(57\) 0 0
\(58\) 0.0197491 + 0.0247646i 0.00259318 + 0.00325175i
\(59\) 9.30068 4.47897i 1.21084 0.583112i 0.284097 0.958796i \(-0.408306\pi\)
0.926748 + 0.375683i \(0.122592\pi\)
\(60\) 0 0
\(61\) 7.51004 + 1.71412i 0.961562 + 0.219470i 0.674362 0.738401i \(-0.264419\pi\)
0.287199 + 0.957871i \(0.407276\pi\)
\(62\) 0.0183315 0.0229870i 0.00232810 0.00291935i
\(63\) 0 0
\(64\) 4.98744 + 6.25405i 0.623430 + 0.781757i
\(65\) 1.33675 + 2.77580i 0.165804 + 0.344295i
\(66\) 0 0
\(67\) −8.97651 −1.09666 −0.548328 0.836263i \(-0.684735\pi\)
−0.548328 + 0.836263i \(0.684735\pi\)
\(68\) −6.75700 −0.819406
\(69\) 0 0
\(70\) 0.00590892 + 0.0319149i 0.000706251 + 0.00381456i
\(71\) 14.3180 3.26798i 1.69923 0.387838i 0.740478 0.672080i \(-0.234599\pi\)
0.958753 + 0.284242i \(0.0917419\pi\)
\(72\) 0 0
\(73\) 2.21540 1.76672i 0.259293 0.206779i −0.485211 0.874397i \(-0.661257\pi\)
0.744504 + 0.667618i \(0.232686\pi\)
\(74\) −0.0307354 + 0.0245107i −0.00357292 + 0.00284931i
\(75\) 0 0
\(76\) −12.2929 + 2.80577i −1.41009 + 0.321844i
\(77\) −3.12098 4.26371i −0.355668 0.485895i
\(78\) 0 0
\(79\) −5.29436 −0.595662 −0.297831 0.954619i \(-0.596263\pi\)
−0.297831 + 0.954619i \(0.596263\pi\)
\(80\) 8.69740 0.972399
\(81\) 0 0
\(82\) −0.0271036 0.0562813i −0.00299310 0.00621523i
\(83\) 1.21293 + 1.52097i 0.133136 + 0.166948i 0.843931 0.536452i \(-0.180236\pi\)
−0.710794 + 0.703400i \(0.751664\pi\)
\(84\) 0 0
\(85\) −4.58047 + 5.74373i −0.496822 + 0.622995i
\(86\) −0.000417688 0 9.53346e-5i −4.50405e−5 0 1.02802e-5i
\(87\) 0 0
\(88\) 0.0406057 0.0195547i 0.00432858 0.00208453i
\(89\) −4.85674 6.09016i −0.514814 0.645556i 0.454685 0.890652i \(-0.349752\pi\)
−0.969499 + 0.245096i \(0.921180\pi\)
\(90\) 0 0
\(91\) −2.21417 3.02489i −0.232108 0.317094i
\(92\) 7.08749 + 14.7173i 0.738922 + 1.53439i
\(93\) 0 0
\(94\) −0.0305569 + 0.00697441i −0.00315170 + 0.000719355i
\(95\) −5.94815 + 12.3515i −0.610267 + 1.26723i
\(96\) 0 0
\(97\) 0.0843849i 0.00856799i 0.999991 + 0.00428399i \(0.00136364\pi\)
−0.999991 + 0.00428399i \(0.998636\pi\)
\(98\) −0.0141390 0.0368744i −0.00142825 0.00372488i
\(99\) 0 0
\(100\) −0.338860 + 0.424917i −0.0338860 + 0.0424917i
\(101\) −5.10630 2.45906i −0.508096 0.244686i 0.162230 0.986753i \(-0.448131\pi\)
−0.670326 + 0.742067i \(0.733846\pi\)
\(102\) 0 0
\(103\) −3.75711 + 7.80172i −0.370199 + 0.768726i −0.999968 0.00805686i \(-0.997435\pi\)
0.629769 + 0.776783i \(0.283150\pi\)
\(104\) 0.0288076 0.0138730i 0.00282482 0.00136036i
\(105\) 0 0
\(106\) −0.00385586 0.00185688i −0.000374514 0.000180357i
\(107\) −0.719156 + 0.573508i −0.0695234 + 0.0554431i −0.657635 0.753337i \(-0.728443\pi\)
0.588111 + 0.808780i \(0.299872\pi\)
\(108\) 0 0
\(109\) 0.286342 0.359062i 0.0274266 0.0343919i −0.767929 0.640535i \(-0.778713\pi\)
0.795356 + 0.606143i \(0.207284\pi\)
\(110\) 0.00545182 0.0238860i 0.000519810 0.00227744i
\(111\) 0 0
\(112\) −10.4057 + 1.92657i −0.983242 + 0.182043i
\(113\) 10.8556 8.65707i 1.02121 0.814389i 0.0384487 0.999261i \(-0.487758\pi\)
0.982763 + 0.184872i \(0.0591869\pi\)
\(114\) 0 0
\(115\) 17.3149 + 3.95200i 1.61462 + 0.368526i
\(116\) 11.2286i 1.04255i
\(117\) 0 0
\(118\) −0.0567794 0.0129595i −0.00522697 0.00119302i
\(119\) 4.20782 7.88648i 0.385731 0.722952i
\(120\) 0 0
\(121\) −1.56020 6.83567i −0.141836 0.621425i
\(122\) −0.0270964 0.0339779i −0.00245320 0.00307621i
\(123\) 0 0
\(124\) 10.1613 2.31926i 0.912516 0.208276i
\(125\) 2.55080 + 11.1758i 0.228150 + 0.999591i
\(126\) 0 0
\(127\) −1.48826 + 6.52048i −0.132061 + 0.578599i 0.864985 + 0.501798i \(0.167328\pi\)
−0.997046 + 0.0768013i \(0.975529\pi\)
\(128\) 0.180529i 0.0159566i
\(129\) 0 0
\(130\) 0.00386778 0.0169459i 0.000339227 0.00148625i
\(131\) 17.0656 8.21835i 1.49103 0.718040i 0.501875 0.864940i \(-0.332644\pi\)
0.989151 + 0.146900i \(0.0469295\pi\)
\(132\) 0 0
\(133\) 4.38044 16.0950i 0.379833 1.39561i
\(134\) 0.0395944 + 0.0315755i 0.00342044 + 0.00272771i
\(135\) 0 0
\(136\) 0.0596093 + 0.0475368i 0.00511145 + 0.00407625i
\(137\) 7.35687 + 15.2767i 0.628540 + 1.30518i 0.935457 + 0.353440i \(0.114988\pi\)
−0.306918 + 0.951736i \(0.599298\pi\)
\(138\) 0 0
\(139\) −6.52132 + 13.5417i −0.553131 + 1.14859i 0.417647 + 0.908609i \(0.362855\pi\)
−0.970778 + 0.239979i \(0.922859\pi\)
\(140\) −5.41627 + 10.1514i −0.457758 + 0.857950i
\(141\) 0 0
\(142\) −0.0746504 0.0359497i −0.00626452 0.00301684i
\(143\) 0.629659 + 2.75872i 0.0526547 + 0.230696i
\(144\) 0 0
\(145\) 9.54481 + 7.61173i 0.792654 + 0.632120i
\(146\) −0.0159864 −0.00132305
\(147\) 0 0
\(148\) −13.9359 −1.14553
\(149\) −7.96334 6.35056i −0.652383 0.520258i 0.240441 0.970664i \(-0.422708\pi\)
−0.892824 + 0.450406i \(0.851279\pi\)
\(150\) 0 0
\(151\) 1.86646 + 8.17748i 0.151890 + 0.665474i 0.992335 + 0.123577i \(0.0394366\pi\)
−0.840445 + 0.541897i \(0.817706\pi\)
\(152\) 0.128185 + 0.0617307i 0.0103972 + 0.00500702i
\(153\) 0 0
\(154\) −0.00123161 + 0.0297850i −9.92463e−5 + 0.00240015i
\(155\) 4.91676 10.2098i 0.394924 0.820068i
\(156\) 0 0
\(157\) 1.92513 + 3.99758i 0.153642 + 0.319041i 0.963556 0.267508i \(-0.0862002\pi\)
−0.809913 + 0.586550i \(0.800486\pi\)
\(158\) 0.0233528 + 0.0186233i 0.00185785 + 0.00148159i
\(159\) 0 0
\(160\) −0.115093 0.0917836i −0.00909890 0.00725613i
\(161\) −21.5911 0.892792i −1.70162 0.0703619i
\(162\) 0 0
\(163\) 19.5157 9.39829i 1.52859 0.736131i 0.534550 0.845137i \(-0.320481\pi\)
0.994041 + 0.109006i \(0.0347669\pi\)
\(164\) 4.92759 21.5892i 0.384780 1.68583i
\(165\) 0 0
\(166\) 0.0109754i 0.000851855i
\(167\) 2.41521 10.5817i 0.186895 0.818839i −0.791347 0.611368i \(-0.790620\pi\)
0.978241 0.207471i \(-0.0665233\pi\)
\(168\) 0 0
\(169\) −2.44606 10.7169i −0.188159 0.824377i
\(170\) 0.0404079 0.00922285i 0.00309915 0.000707360i
\(171\) 0 0
\(172\) −0.0946932 0.118742i −0.00722029 0.00905396i
\(173\) −4.19091 18.3616i −0.318629 1.39600i −0.839960 0.542649i \(-0.817421\pi\)
0.521331 0.853355i \(-0.325436\pi\)
\(174\) 0 0
\(175\) −0.284925 0.660114i −0.0215383 0.0498999i
\(176\) 7.78787 + 1.77753i 0.587033 + 0.133986i
\(177\) 0 0
\(178\) 0.0439470i 0.00329397i
\(179\) −7.92157 1.80805i −0.592086 0.135140i −0.0840291 0.996463i \(-0.526779\pi\)
−0.508057 + 0.861324i \(0.669636\pi\)
\(180\) 0 0
\(181\) 0.621193 0.495385i 0.0461729 0.0368217i −0.600131 0.799901i \(-0.704885\pi\)
0.646304 + 0.763080i \(0.276314\pi\)
\(182\) −0.000873767 0.0211310i −6.47679e−5 0.00156633i
\(183\) 0 0
\(184\) 0.0410145 0.179696i 0.00302363 0.0132474i
\(185\) −9.44696 + 11.8461i −0.694554 + 0.870944i
\(186\) 0 0
\(187\) −5.27534 + 4.20695i −0.385771 + 0.307642i
\(188\) −10.0105 4.82081i −0.730091 0.351593i
\(189\) 0 0
\(190\) 0.0696837 0.0335579i 0.00505539 0.00243455i
\(191\) −2.97564 + 6.17897i −0.215310 + 0.447095i −0.980450 0.196769i \(-0.936955\pi\)
0.765140 + 0.643863i \(0.222670\pi\)
\(192\) 0 0
\(193\) −21.8437 10.5194i −1.57234 0.757200i −0.574234 0.818691i \(-0.694700\pi\)
−0.998108 + 0.0614911i \(0.980414\pi\)
\(194\) 0.000296830 0 0.000372213i 2.13111e−5 0 2.67233e-5i
\(195\) 0 0
\(196\) 4.23144 13.3450i 0.302246 0.953213i
\(197\) 13.1835i 0.939284i 0.882857 + 0.469642i \(0.155617\pi\)
−0.882857 + 0.469642i \(0.844383\pi\)
\(198\) 0 0
\(199\) 5.36518 11.1409i 0.380328 0.789759i −0.619660 0.784870i \(-0.712730\pi\)
0.999988 0.00488858i \(-0.00155609\pi\)
\(200\) 0.00597875 0.00136461i 0.000422761 9.64925e-5i
\(201\) 0 0
\(202\) 0.0138734 + 0.0288084i 0.000976130 + 0.00202695i
\(203\) −13.1056 6.99248i −0.919832 0.490776i
\(204\) 0 0
\(205\) −15.0114 18.8237i −1.04844 1.31470i
\(206\) 0.0440153 0.0211966i 0.00306669 0.00147684i
\(207\) 0 0
\(208\) 5.52509 + 1.26107i 0.383096 + 0.0874392i
\(209\) −7.85045 + 9.84415i −0.543027 + 0.680934i
\(210\) 0 0
\(211\) 12.6490 + 15.8613i 0.870793 + 1.09194i 0.995019 + 0.0996861i \(0.0317839\pi\)
−0.124226 + 0.992254i \(0.539645\pi\)
\(212\) −0.658256 1.36688i −0.0452092 0.0938778i
\(213\) 0 0
\(214\) 0.00518947 0.000354745
\(215\) −0.165126 −0.0112615
\(216\) 0 0
\(217\) −3.62089 + 13.3042i −0.245802 + 0.903146i
\(218\) −0.00252605 0.000576554i −0.000171086 3.90492e-5i
\(219\) 0 0
\(220\) 6.79037 5.41514i 0.457807 0.365089i
\(221\) −3.74258 + 2.98461i −0.251753 + 0.200767i
\(222\) 0 0
\(223\) 9.56540 2.18324i 0.640547 0.146201i 0.110102 0.993920i \(-0.464882\pi\)
0.530444 + 0.847720i \(0.322025\pi\)
\(224\) 0.158029 + 0.0843165i 0.0105588 + 0.00563363i
\(225\) 0 0
\(226\) −0.0783349 −0.00521076
\(227\) 0.229766 0.0152501 0.00762505 0.999971i \(-0.497573\pi\)
0.00762505 + 0.999971i \(0.497573\pi\)
\(228\) 0 0
\(229\) −5.92639 12.3063i −0.391627 0.813222i −0.999811 0.0194260i \(-0.993816\pi\)
0.608184 0.793796i \(-0.291898\pi\)
\(230\) −0.0624725 0.0783381i −0.00411932 0.00516546i
\(231\) 0 0
\(232\) 0.0789957 0.0990574i 0.00518632 0.00650344i
\(233\) −17.3937 3.96999i −1.13950 0.260083i −0.389180 0.921162i \(-0.627242\pi\)
−0.750316 + 0.661079i \(0.770099\pi\)
\(234\) 0 0
\(235\) −10.8839 + 5.24139i −0.709985 + 0.341911i
\(236\) −12.8723 16.1414i −0.837917 1.05072i
\(237\) 0 0
\(238\) −0.0463015 + 0.0199851i −0.00300128 + 0.00129544i
\(239\) 4.82970 + 10.0290i 0.312408 + 0.648721i 0.996760 0.0804301i \(-0.0256294\pi\)
−0.684353 + 0.729151i \(0.739915\pi\)
\(240\) 0 0
\(241\) −16.8259 + 3.84041i −1.08385 + 0.247382i −0.726902 0.686741i \(-0.759041\pi\)
−0.356951 + 0.934123i \(0.616184\pi\)
\(242\) −0.0171631 + 0.0356395i −0.00110328 + 0.00229099i
\(243\) 0 0
\(244\) 15.4061i 0.986274i
\(245\) −8.47537 12.6433i −0.541471 0.807749i
\(246\) 0 0
\(247\) −5.56949 + 6.98392i −0.354378 + 0.444376i
\(248\) −0.105958 0.0510269i −0.00672836 0.00324021i
\(249\) 0 0
\(250\) 0.0280603 0.0582677i 0.00177469 0.00368517i
\(251\) 16.8505 8.11476i 1.06359 0.512199i 0.181556 0.983381i \(-0.441887\pi\)
0.882036 + 0.471181i \(0.156172\pi\)
\(252\) 0 0
\(253\) 14.6965 + 7.07744i 0.923959 + 0.444955i
\(254\) 0.0295008 0.0235261i 0.00185104 0.00147616i
\(255\) 0 0
\(256\) 9.97425 12.5073i 0.623391 0.781707i
\(257\) −6.48011 + 28.3912i −0.404218 + 1.77099i 0.205787 + 0.978597i \(0.434024\pi\)
−0.610005 + 0.792397i \(0.708833\pi\)
\(258\) 0 0
\(259\) 8.67840 16.2654i 0.539249 1.01068i
\(260\) 4.81742 3.84176i 0.298764 0.238256i
\(261\) 0 0
\(262\) −0.104183 0.0237791i −0.00643645 0.00146908i
\(263\) 26.8737i 1.65710i 0.559912 + 0.828552i \(0.310835\pi\)
−0.559912 + 0.828552i \(0.689165\pi\)
\(264\) 0 0
\(265\) −1.60813 0.367045i −0.0987866 0.0225474i
\(266\) −0.0759369 + 0.0555847i −0.00465599 + 0.00340812i
\(267\) 0 0
\(268\) 3.99486 + 17.5026i 0.244025 + 1.06914i
\(269\) −2.49263 3.12566i −0.151979 0.190575i 0.700014 0.714129i \(-0.253177\pi\)
−0.851992 + 0.523554i \(0.824606\pi\)
\(270\) 0 0
\(271\) 25.7952 5.88759i 1.56695 0.357646i 0.651043 0.759041i \(-0.274332\pi\)
0.915905 + 0.401395i \(0.131475\pi\)
\(272\) 3.00705 + 13.1748i 0.182329 + 0.798837i
\(273\) 0 0
\(274\) 0.0212865 0.0932621i 0.00128596 0.00563417i
\(275\) 0.542719i 0.0327272i
\(276\) 0 0
\(277\) 2.05960 9.02368i 0.123749 0.542180i −0.874605 0.484836i \(-0.838879\pi\)
0.998354 0.0573448i \(-0.0182634\pi\)
\(278\) 0.0763985 0.0367916i 0.00458208 0.00220661i
\(279\) 0 0
\(280\) 0.119199 0.0514496i 0.00712348 0.00307470i
\(281\) −12.0953 9.64571i −0.721547 0.575415i 0.192367 0.981323i \(-0.438384\pi\)
−0.913914 + 0.405908i \(0.866955\pi\)
\(282\) 0 0
\(283\) −10.6669 8.50654i −0.634079 0.505661i 0.252887 0.967496i \(-0.418620\pi\)
−0.886966 + 0.461835i \(0.847191\pi\)
\(284\) −12.7440 26.4632i −0.756217 1.57030i
\(285\) 0 0
\(286\) 0.00692662 0.0143833i 0.000409580 0.000850501i
\(287\) 22.1294 + 19.1956i 1.30626 + 1.13308i
\(288\) 0 0
\(289\) 5.03226 + 2.42341i 0.296015 + 0.142553i
\(290\) −0.0153263 0.0671491i −0.000899994 0.00394313i
\(291\) 0 0
\(292\) −4.43073 3.53339i −0.259289 0.206776i
\(293\) −2.88801 −0.168720 −0.0843598 0.996435i \(-0.526885\pi\)
−0.0843598 + 0.996435i \(0.526885\pi\)
\(294\) 0 0
\(295\) −22.4468 −1.30691
\(296\) 0.122941 + 0.0980419i 0.00714578 + 0.00569857i
\(297\) 0 0
\(298\) 0.0127869 + 0.0560232i 0.000740727 + 0.00324534i
\(299\) 10.4264 + 5.02108i 0.602973 + 0.290377i
\(300\) 0 0
\(301\) 0.197559 0.0365772i 0.0113871 0.00210828i
\(302\) 0.0205321 0.0426354i 0.00118149 0.00245339i
\(303\) 0 0
\(304\) 10.9413 + 22.7199i 0.627529 + 1.30308i
\(305\) −13.0958 10.4436i −0.749865 0.597997i
\(306\) 0 0
\(307\) −13.0948 10.4428i −0.747361 0.596001i 0.173983 0.984749i \(-0.444336\pi\)
−0.921344 + 0.388748i \(0.872908\pi\)
\(308\) −6.92455 + 7.98286i −0.394563 + 0.454866i
\(309\) 0 0
\(310\) −0.0576009 + 0.0277391i −0.00327151 + 0.00157548i
\(311\) 4.95676 21.7170i 0.281072 1.23146i −0.615349 0.788254i \(-0.710985\pi\)
0.896421 0.443203i \(-0.146158\pi\)
\(312\) 0 0
\(313\) 11.6294i 0.657335i −0.944446 0.328667i \(-0.893400\pi\)
0.944446 0.328667i \(-0.106600\pi\)
\(314\) 0.00557021 0.0244047i 0.000314345 0.00137724i
\(315\) 0 0
\(316\) 2.35617 + 10.3231i 0.132545 + 0.580718i
\(317\) −3.39782 + 0.775530i −0.190841 + 0.0435581i −0.316873 0.948468i \(-0.602633\pi\)
0.126032 + 0.992026i \(0.459776\pi\)
\(318\) 0 0
\(319\) 6.99102 + 8.76646i 0.391422 + 0.490827i
\(320\) −3.87052 16.9579i −0.216369 0.947974i
\(321\) 0 0
\(322\) 0.0920955 + 0.0798861i 0.00513228 + 0.00445188i
\(323\) −20.7664 4.73980i −1.15547 0.263729i
\(324\) 0 0
\(325\) 0.385031i 0.0213577i
\(326\) −0.119141 0.0271931i −0.00659861 0.00150609i
\(327\) 0 0
\(328\) −0.195355 + 0.155790i −0.0107867 + 0.00860208i
\(329\) 11.8605 8.68174i 0.653893 0.478640i
\(330\) 0 0
\(331\) −0.637151 + 2.79154i −0.0350210 + 0.153437i −0.989415 0.145112i \(-0.953646\pi\)
0.954394 + 0.298549i \(0.0965028\pi\)
\(332\) 2.42582 3.04188i 0.133134 0.166945i
\(333\) 0 0
\(334\) −0.0478752 + 0.0381792i −0.00261962 + 0.00208907i
\(335\) 17.5860 + 8.46898i 0.960827 + 0.462710i
\(336\) 0 0
\(337\) 12.0356 5.79603i 0.655620 0.315730i −0.0763357 0.997082i \(-0.524322\pi\)
0.731956 + 0.681352i \(0.238608\pi\)
\(338\) −0.0269081 + 0.0558753i −0.00146361 + 0.00303921i
\(339\) 0 0
\(340\) 13.2377 + 6.37496i 0.717917 + 0.345731i
\(341\) 6.48921 8.13721i 0.351410 0.440655i
\(342\) 0 0
\(343\) 12.9406 + 13.2492i 0.698728 + 0.715387i
\(344\) 0.00171371i 9.23968e-5i
\(345\) 0 0
\(346\) −0.0461024 + 0.0957327i −0.00247848 + 0.00514662i
\(347\) 28.8400 6.58255i 1.54821 0.353370i 0.638837 0.769342i \(-0.279416\pi\)
0.909377 + 0.415973i \(0.136559\pi\)
\(348\) 0 0
\(349\) 3.66406 + 7.60850i 0.196133 + 0.407273i 0.975721 0.219019i \(-0.0702858\pi\)
−0.779588 + 0.626293i \(0.784571\pi\)
\(350\) −0.00106522 + 0.00391393i −5.69386e−5 + 0.000209209i
\(351\) 0 0
\(352\) −0.0842988 0.105707i −0.00449314 0.00563422i
\(353\) 3.11324 1.49926i 0.165701 0.0797975i −0.349195 0.937050i \(-0.613545\pi\)
0.514896 + 0.857253i \(0.327831\pi\)
\(354\) 0 0
\(355\) −31.1338 7.10608i −1.65241 0.377152i
\(356\) −9.71333 + 12.1801i −0.514805 + 0.645546i
\(357\) 0 0
\(358\) 0.0285813 + 0.0358398i 0.00151057 + 0.00189419i
\(359\) 0.761364 + 1.58099i 0.0401832 + 0.0834414i 0.920094 0.391698i \(-0.128112\pi\)
−0.879911 + 0.475139i \(0.842398\pi\)
\(360\) 0 0
\(361\) −20.7481 −1.09200
\(362\) −0.00448257 −0.000235599
\(363\) 0 0
\(364\) −4.91261 + 5.66343i −0.257491 + 0.296844i
\(365\) −6.00705 + 1.37107i −0.314423 + 0.0717651i
\(366\) 0 0
\(367\) −18.1667 + 14.4874i −0.948292 + 0.756237i −0.969894 0.243529i \(-0.921695\pi\)
0.0216020 + 0.999767i \(0.493123\pi\)
\(368\) 25.5416 20.3688i 1.33145 1.06180i
\(369\) 0 0
\(370\) 0.0833390 0.0190216i 0.00433259 0.000988886i
\(371\) 2.00529 + 0.0829187i 0.104109 + 0.00430492i
\(372\) 0 0
\(373\) −11.8862 −0.615444 −0.307722 0.951476i \(-0.599567\pi\)
−0.307722 + 0.951476i \(0.599567\pi\)
\(374\) 0.0380672 0.00196841
\(375\) 0 0
\(376\) 0.0543959 + 0.112954i 0.00280526 + 0.00582517i
\(377\) 4.95977 + 6.21935i 0.255441 + 0.320313i
\(378\) 0 0
\(379\) 5.68424 7.12782i 0.291980 0.366131i −0.614107 0.789223i \(-0.710484\pi\)
0.906087 + 0.423091i \(0.139055\pi\)
\(380\) 26.7303 + 6.10102i 1.37124 + 0.312976i
\(381\) 0 0
\(382\) 0.0348602 0.0167878i 0.00178360 0.000858938i
\(383\) 17.3778 + 21.7911i 0.887967 + 1.11347i 0.992895 + 0.118995i \(0.0379672\pi\)
−0.104928 + 0.994480i \(0.533461\pi\)
\(384\) 0 0
\(385\) 2.09171 + 11.2976i 0.106603 + 0.575780i
\(386\) 0.0593475 + 0.123236i 0.00302071 + 0.00627257i
\(387\) 0 0
\(388\) 0.164536 0.0375542i 0.00835304 0.00190653i
\(389\) −0.260129 + 0.540163i −0.0131891 + 0.0273873i −0.907459 0.420140i \(-0.861981\pi\)
0.894270 + 0.447527i \(0.147695\pi\)
\(390\) 0 0
\(391\) 27.5948i 1.39553i
\(392\) −0.131214 + 0.0879586i −0.00662729 + 0.00444258i
\(393\) 0 0
\(394\) 0.0463738 0.0581509i 0.00233628 0.00292960i
\(395\) 10.3723 + 4.99502i 0.521885 + 0.251327i
\(396\) 0 0
\(397\) −11.9753 + 24.8669i −0.601021 + 1.24803i 0.349373 + 0.936984i \(0.386395\pi\)
−0.950394 + 0.311049i \(0.899320\pi\)
\(398\) −0.0628542 + 0.0302690i −0.00315060 + 0.00151725i
\(399\) 0 0
\(400\) 0.979302 + 0.471607i 0.0489651 + 0.0235804i
\(401\) −19.0713 + 15.2089i −0.952376 + 0.759495i −0.970689 0.240338i \(-0.922742\pi\)
0.0183131 + 0.999832i \(0.494170\pi\)
\(402\) 0 0
\(403\) 4.60376 5.77293i 0.229330 0.287570i
\(404\) −2.52226 + 11.0508i −0.125487 + 0.549796i
\(405\) 0 0
\(406\) 0.0332108 + 0.0769429i 0.00164822 + 0.00381861i
\(407\) −10.8801 + 8.67658i −0.539306 + 0.430082i
\(408\) 0 0
\(409\) 9.36470 + 2.13743i 0.463055 + 0.105689i 0.447682 0.894193i \(-0.352250\pi\)
0.0153722 + 0.999882i \(0.495107\pi\)
\(410\) 0.135833i 0.00670830i
\(411\) 0 0
\(412\) 16.8840 + 3.85367i 0.831816 + 0.189857i
\(413\) 26.8556 4.97221i 1.32148 0.244666i
\(414\) 0 0
\(415\) −0.941299 4.12410i −0.0462065 0.202444i
\(416\) −0.0598057 0.0749940i −0.00293222 0.00367688i
\(417\) 0 0
\(418\) 0.0692550 0.0158070i 0.00338737 0.000773145i
\(419\) −2.86994 12.5740i −0.140206 0.614282i −0.995386 0.0959514i \(-0.969411\pi\)
0.855180 0.518331i \(-0.173446\pi\)
\(420\) 0 0
\(421\) 6.87283 30.1118i 0.334961 1.46756i −0.474431 0.880293i \(-0.657346\pi\)
0.809392 0.587268i \(-0.199797\pi\)
\(422\) 0.114456i 0.00557165i
\(423\) 0 0
\(424\) −0.00380924 + 0.0166894i −0.000184993 + 0.000810508i
\(425\) −0.827196 + 0.398356i −0.0401249 + 0.0193231i
\(426\) 0 0
\(427\) 17.9813 + 9.59393i 0.870178 + 0.464283i
\(428\) 1.43829 + 1.14700i 0.0695223 + 0.0554422i
\(429\) 0 0
\(430\) 0.000728355 0 0.000580844i 3.51244e−5 0 2.80108e-5i
\(431\) 2.74151 + 5.69280i 0.132054 + 0.274213i 0.956503 0.291724i \(-0.0942289\pi\)
−0.824449 + 0.565937i \(0.808515\pi\)
\(432\) 0 0
\(433\) 3.96743 8.23846i 0.190663 0.395915i −0.783621 0.621239i \(-0.786630\pi\)
0.974284 + 0.225324i \(0.0723440\pi\)
\(434\) 0.0627697 0.0459465i 0.00301304 0.00220550i
\(435\) 0 0
\(436\) −0.827539 0.398522i −0.0396319 0.0190857i
\(437\) 11.4584 + 50.2027i 0.548131 + 2.40152i
\(438\) 0 0
\(439\) 2.36090 + 1.88276i 0.112680 + 0.0898590i 0.678209 0.734869i \(-0.262757\pi\)
−0.565529 + 0.824728i \(0.691328\pi\)
\(440\) −0.0980002 −0.00467198
\(441\) 0 0
\(442\) 0.0270067 0.00128458
\(443\) 4.28966 + 3.42089i 0.203808 + 0.162531i 0.720075 0.693896i \(-0.244107\pi\)
−0.516267 + 0.856428i \(0.672679\pi\)
\(444\) 0 0
\(445\) 3.76909 + 16.5135i 0.178672 + 0.782814i
\(446\) −0.0498717 0.0240169i −0.00236149 0.00113723i
\(447\) 0 0
\(448\) 8.38708 + 19.4312i 0.396252 + 0.918038i
\(449\) 1.88400 3.91217i 0.0889115 0.184627i −0.851771 0.523914i \(-0.824471\pi\)
0.940683 + 0.339287i \(0.110186\pi\)
\(450\) 0 0
\(451\) −9.59448 19.9231i −0.451786 0.938144i
\(452\) −21.7109 17.3139i −1.02120 0.814376i
\(453\) 0 0
\(454\) −0.00101347 0.000808218i −4.75646e−5 3.79315e-5i
\(455\) 1.48396 + 8.01509i 0.0695692 + 0.375753i
\(456\) 0 0
\(457\) −28.7245 + 13.8330i −1.34368 + 0.647080i −0.960935 0.276776i \(-0.910734\pi\)
−0.382741 + 0.923856i \(0.625020\pi\)
\(458\) −0.0171475 + 0.0751282i −0.000801251 + 0.00351051i
\(459\) 0 0
\(460\) 35.5197i 1.65612i
\(461\) 0.764762 3.35064i 0.0356185 0.156055i −0.953991 0.299835i \(-0.903069\pi\)
0.989610 + 0.143780i \(0.0459256\pi\)
\(462\) 0 0
\(463\) −2.98438 13.0754i −0.138696 0.607667i −0.995722 0.0923947i \(-0.970548\pi\)
0.857026 0.515273i \(-0.172309\pi\)
\(464\) 21.8935 4.99706i 1.01638 0.231982i
\(465\) 0 0
\(466\) 0.0627569 + 0.0786946i 0.00290716 + 0.00364546i
\(467\) 2.77375 + 12.1526i 0.128354 + 0.562356i 0.997678 + 0.0681125i \(0.0216977\pi\)
−0.869324 + 0.494243i \(0.835445\pi\)
\(468\) 0 0
\(469\) −22.9161 6.23689i −1.05817 0.287993i
\(470\) 0.0664445 + 0.0151655i 0.00306486 + 0.000699534i
\(471\) 0 0
\(472\) 0.232956i 0.0107227i
\(473\) −0.147858 0.0337477i −0.00679853 0.00155172i
\(474\) 0 0
\(475\) −1.33949 + 1.06821i −0.0614600 + 0.0490127i
\(476\) −17.2499 4.69476i −0.790647 0.215184i
\(477\) 0 0
\(478\) 0.0139743 0.0612256i 0.000639172 0.00280039i
\(479\) −20.1015 + 25.2064i −0.918460 + 1.15171i 0.0695899 + 0.997576i \(0.477831\pi\)
−0.988050 + 0.154136i \(0.950740\pi\)
\(480\) 0 0
\(481\) −7.71886 + 6.15559i −0.351950 + 0.280671i
\(482\) 0.0877262 + 0.0422467i 0.00399582 + 0.00192429i
\(483\) 0 0
\(484\) −12.6340 + 6.08422i −0.574273 + 0.276556i
\(485\) 0.0796138 0.165320i 0.00361508 0.00750678i
\(486\) 0 0
\(487\) 6.02530 + 2.90163i 0.273032 + 0.131485i 0.565390 0.824824i \(-0.308726\pi\)
−0.292358 + 0.956309i \(0.594440\pi\)
\(488\) −0.108385 + 0.135910i −0.00490635 + 0.00615237i
\(489\) 0 0
\(490\) −0.00708967 + 0.0855808i −0.000320279 + 0.00386615i
\(491\) 13.6184i 0.614588i −0.951615 0.307294i \(-0.900577\pi\)
0.951615 0.307294i \(-0.0994235\pi\)
\(492\) 0 0
\(493\) −8.23016 + 17.0901i −0.370668 + 0.769699i
\(494\) 0.0491328 0.0112142i 0.00221059 0.000504553i
\(495\) 0 0
\(496\) −9.04416 18.7804i −0.406095 0.843264i
\(497\) 38.8228 + 1.60533i 1.74144 + 0.0720087i
\(498\) 0 0
\(499\) 26.4561 + 33.1748i 1.18434 + 1.48511i 0.836856 + 0.547422i \(0.184391\pi\)
0.347479 + 0.937688i \(0.387038\pi\)
\(500\) 20.6556 9.94721i 0.923747 0.444853i
\(501\) 0 0
\(502\) −0.102870 0.0234794i −0.00459131 0.00104794i
\(503\) 15.7566 19.7581i 0.702550 0.880970i −0.294661 0.955602i \(-0.595207\pi\)
0.997211 + 0.0746320i \(0.0237782\pi\)
\(504\) 0 0
\(505\) 7.68380 + 9.63518i 0.341925 + 0.428760i
\(506\) −0.0399291 0.0829137i −0.00177507 0.00368596i
\(507\) 0 0
\(508\) 13.3761 0.593469
\(509\) −44.4455 −1.97001 −0.985006 0.172523i \(-0.944808\pi\)
−0.985006 + 0.172523i \(0.944808\pi\)
\(510\) 0 0
\(511\) 6.88319 2.97099i 0.304494 0.131429i
\(512\) −0.439995 + 0.100426i −0.0194452 + 0.00443825i
\(513\) 0 0
\(514\) 0.128451 0.102436i 0.00566573 0.00451827i
\(515\) 14.7212 11.7398i 0.648694 0.517317i
\(516\) 0 0
\(517\) −10.8169 + 2.46889i −0.475726 + 0.108581i
\(518\) −0.0954942 + 0.0412181i −0.00419577 + 0.00181102i
\(519\) 0 0
\(520\) −0.0695261 −0.00304892
\(521\) −20.3446 −0.891314 −0.445657 0.895204i \(-0.647030\pi\)
−0.445657 + 0.895204i \(0.647030\pi\)
\(522\) 0 0
\(523\) 17.8019 + 36.9660i 0.778421 + 1.61641i 0.787395 + 0.616449i \(0.211429\pi\)
−0.00897326 + 0.999960i \(0.502856\pi\)
\(524\) −23.6191 29.6174i −1.03181 1.29384i
\(525\) 0 0
\(526\) 0.0945302 0.118537i 0.00412171 0.00516846i
\(527\) 17.1656 + 3.91793i 0.747745 + 0.170668i
\(528\) 0 0
\(529\) 39.3816 18.9652i 1.71224 0.824572i
\(530\) 0.00580218 + 0.00727570i 0.000252031 + 0.000316036i
\(531\) 0 0
\(532\) −33.3318 1.37827i −1.44512 0.0597557i
\(533\) −6.80679 14.1344i −0.294835 0.612231i
\(534\) 0 0
\(535\) 1.94999 0.445073i 0.0843055 0.0192422i
\(536\) 0.0878923 0.182510i 0.00379637 0.00788324i
\(537\) 0 0
\(538\) 0.0225550i 0.000972414i
\(539\) −5.00509 13.0533i −0.215584 0.562244i
\(540\) 0 0
\(541\) 11.8503 14.8599i 0.509486 0.638875i −0.458854 0.888512i \(-0.651740\pi\)
0.968340 + 0.249637i \(0.0803112\pi\)
\(542\) −0.134490 0.0647669i −0.00577684 0.00278198i
\(543\) 0 0
\(544\) 0.0992406 0.206075i 0.00425491 0.00883540i
\(545\) −0.899738 + 0.433291i −0.0385405 + 0.0185601i
\(546\) 0 0
\(547\) −29.3752 14.1463i −1.25599 0.604853i −0.316879 0.948466i \(-0.602635\pi\)
−0.939111 + 0.343613i \(0.888349\pi\)
\(548\) 26.5128 21.1433i 1.13257 0.903195i
\(549\) 0 0
\(550\) 0.00190905 0.00239387i 8.14022e−5 0.000102075i
\(551\) −7.87650 + 34.5092i −0.335550 + 1.47014i
\(552\) 0 0
\(553\) −13.5159 3.67852i −0.574755 0.156427i
\(554\) −0.0408261 + 0.0325577i −0.00173453 + 0.00138324i
\(555\) 0 0
\(556\) 29.3061 + 6.68892i 1.24285 + 0.283673i
\(557\) 7.44376i 0.315402i 0.987487 + 0.157701i \(0.0504082\pi\)
−0.987487 + 0.157701i \(0.949592\pi\)
\(558\) 0 0
\(559\) −0.104898 0.0239423i −0.00443671 0.00101265i
\(560\) 22.2035 + 6.04296i 0.938270 + 0.255362i
\(561\) 0 0
\(562\) 0.0194218 + 0.0850924i 0.000819258 + 0.00358940i
\(563\) −16.5053 20.6970i −0.695617 0.872276i 0.301071 0.953602i \(-0.402656\pi\)
−0.996688 + 0.0813261i \(0.974084\pi\)
\(564\) 0 0
\(565\) −29.4350 + 6.71835i −1.23834 + 0.282643i
\(566\) 0.0171280 + 0.0750428i 0.000719945 + 0.00315429i
\(567\) 0 0
\(568\) −0.0737479 + 0.323111i −0.00309439 + 0.0135574i
\(569\) 23.8408i 0.999457i −0.866182 0.499729i \(-0.833433\pi\)
0.866182 0.499729i \(-0.166567\pi\)
\(570\) 0 0
\(571\) 3.87073 16.9588i 0.161985 0.709702i −0.827063 0.562109i \(-0.809990\pi\)
0.989048 0.147593i \(-0.0471526\pi\)
\(572\) 5.09879 2.45545i 0.213191 0.102668i
\(573\) 0 0
\(574\) −0.0300884 0.162512i −0.00125586 0.00678310i
\(575\) 1.73531 + 1.38386i 0.0723674 + 0.0577111i
\(576\) 0 0
\(577\) −36.5255 29.1281i −1.52058 1.21262i −0.905644 0.424038i \(-0.860612\pi\)
−0.614931 0.788581i \(-0.710816\pi\)
\(578\) −0.0136722 0.0283907i −0.000568690 0.00118090i
\(579\) 0 0
\(580\) 10.5938 21.9982i 0.439883 0.913426i
\(581\) 2.03971 + 4.72560i 0.0846214 + 0.196051i
\(582\) 0 0
\(583\) −1.36494 0.657322i −0.0565302 0.0272235i
\(584\) 0.0142292 + 0.0623420i 0.000588807 + 0.00257973i
\(585\) 0 0
\(586\) 0.0127387 + 0.0101588i 0.000526232 + 0.000419656i
\(587\) −29.2649 −1.20789 −0.603946 0.797025i \(-0.706406\pi\)
−0.603946 + 0.797025i \(0.706406\pi\)
\(588\) 0 0
\(589\) 32.8559 1.35380
\(590\) 0.0990106 + 0.0789583i 0.00407620 + 0.00325066i
\(591\) 0 0
\(592\) 6.20187 + 27.1722i 0.254895 + 1.11677i
\(593\) 33.7375 + 16.2471i 1.38543 + 0.667190i 0.970151 0.242502i \(-0.0779680\pi\)
0.415284 + 0.909692i \(0.363682\pi\)
\(594\) 0 0
\(595\) −15.6842 + 11.4806i −0.642989 + 0.470659i
\(596\) −8.83850 + 18.3533i −0.362039 + 0.751782i
\(597\) 0 0
\(598\) −0.0283277 0.0588230i −0.00115840 0.00240545i
\(599\) −22.5664 17.9961i −0.922037 0.735300i 0.0425421 0.999095i \(-0.486454\pi\)
−0.964579 + 0.263795i \(0.915026\pi\)
\(600\) 0 0
\(601\) 17.0095 + 13.5646i 0.693832 + 0.553313i 0.905665 0.423993i \(-0.139372\pi\)
−0.211833 + 0.977306i \(0.567943\pi\)
\(602\) −0.00100007 0.000533589i −4.07600e−5 2.17475e-5i
\(603\) 0 0
\(604\) 15.1140 7.27853i 0.614981 0.296159i
\(605\) −3.39258 + 14.8639i −0.137928 + 0.604301i
\(606\) 0 0
\(607\) 1.99217i 0.0808597i 0.999182 + 0.0404299i \(0.0128727\pi\)
−0.999182 + 0.0404299i \(0.987127\pi\)
\(608\) 0.0949761 0.416118i 0.00385179 0.0168758i
\(609\) 0 0
\(610\) 0.0210283 + 0.0921310i 0.000851411 + 0.00373027i
\(611\) −7.67403 + 1.75155i −0.310458 + 0.0708600i
\(612\) 0 0
\(613\) 27.5141 + 34.5016i 1.11128 + 1.39351i 0.910319 + 0.413907i \(0.135836\pi\)
0.200964 + 0.979599i \(0.435592\pi\)
\(614\) 0.0210267 + 0.0921239i 0.000848568 + 0.00371782i
\(615\) 0 0
\(616\) 0.117248 0.0217081i 0.00472407 0.000874643i
\(617\) −30.1981 6.89252i −1.21573 0.277482i −0.433892 0.900965i \(-0.642860\pi\)
−0.781837 + 0.623483i \(0.785717\pi\)
\(618\) 0 0
\(619\) 46.2835i 1.86029i −0.367191 0.930145i \(-0.619681\pi\)
0.367191 0.930145i \(-0.380319\pi\)
\(620\) −22.0954 5.04313i −0.887372 0.202537i
\(621\) 0 0
\(622\) −0.0982547 + 0.0783555i −0.00393966 + 0.00314177i
\(623\) −8.16729 18.9220i −0.327215 0.758093i
\(624\) 0 0
\(625\) 5.24424 22.9765i 0.209770 0.919061i
\(626\) −0.0409074 + 0.0512962i −0.00163499 + 0.00205021i
\(627\) 0 0
\(628\) 6.93782 5.53273i 0.276849 0.220780i
\(629\) −21.2106 10.2145i −0.845722 0.407278i
\(630\) 0 0
\(631\) −16.5277 + 7.95934i −0.657959 + 0.316856i −0.732905 0.680331i \(-0.761836\pi\)
0.0749456 + 0.997188i \(0.476122\pi\)
\(632\) 0.0518390 0.107645i 0.00206204 0.00428188i
\(633\) 0 0
\(634\) 0.0177154 + 0.00853129i 0.000703568 + 0.000338821i
\(635\) 9.06748 11.3703i 0.359832 0.451215i
\(636\) 0 0
\(637\) −3.55085 9.26061i −0.140690 0.366919i
\(638\) 0.0632593i 0.00250446i
\(639\) 0 0
\(640\) −0.170322 + 0.353676i −0.00673255 + 0.0139803i
\(641\) 35.5468 8.11333i 1.40401 0.320457i 0.547598 0.836742i \(-0.315542\pi\)
0.856417 + 0.516285i \(0.172685\pi\)
\(642\) 0 0
\(643\) 6.23020 + 12.9371i 0.245695 + 0.510191i 0.986949 0.161034i \(-0.0514828\pi\)
−0.741254 + 0.671225i \(0.765769\pi\)
\(644\) 7.86799 + 42.4961i 0.310042 + 1.67458i
\(645\) 0 0
\(646\) 0.0749258 + 0.0939540i 0.00294792 + 0.00369657i
\(647\) −29.3751 + 14.1463i −1.15485 + 0.556148i −0.910488 0.413535i \(-0.864294\pi\)
−0.244365 + 0.969683i \(0.578580\pi\)
\(648\) 0 0
\(649\) −20.0994 4.58757i −0.788972 0.180078i
\(650\) 0.00135437 0.00169833i 5.31229e−5 6.66140e-5i
\(651\) 0 0
\(652\) −27.0102 33.8697i −1.05780 1.32644i
\(653\) 0.582912 + 1.21043i 0.0228111 + 0.0473677i 0.912063 0.410050i \(-0.134489\pi\)
−0.889252 + 0.457418i \(0.848774\pi\)
\(654\) 0 0
\(655\) −41.1871 −1.60931
\(656\) −44.2874 −1.72913
\(657\) 0 0
\(658\) −0.0828542 0.00342603i −0.00322999 0.000133560i
\(659\) −17.0491 + 3.89134i −0.664138 + 0.151585i −0.541284 0.840840i \(-0.682062\pi\)
−0.122854 + 0.992425i \(0.539205\pi\)
\(660\) 0 0
\(661\) 37.0956 29.5827i 1.44285 1.15063i 0.481113 0.876658i \(-0.340233\pi\)
0.961737 0.273976i \(-0.0883389\pi\)
\(662\) 0.0126298 0.0100720i 0.000490873 0.000391458i
\(663\) 0 0
\(664\) −0.0428005 + 0.00976893i −0.00166098 + 0.000379108i
\(665\) −23.7668 + 27.3991i −0.921636 + 1.06249i
\(666\) 0 0
\(667\) 45.8564 1.77557
\(668\) −21.7074 −0.839884
\(669\) 0 0
\(670\) −0.0477798 0.0992159i −0.00184590 0.00383304i
\(671\) −9.59192 12.0279i −0.370292 0.464332i
\(672\) 0 0
\(673\) 29.6815 37.2194i 1.14414 1.43470i 0.261157 0.965296i \(-0.415896\pi\)
0.882981 0.469408i \(-0.155533\pi\)
\(674\) −0.0734756 0.0167703i −0.00283017 0.000645969i
\(675\) 0 0
\(676\) −19.8075 + 9.53878i −0.761826 + 0.366876i
\(677\) 20.2146 + 25.3483i 0.776909 + 0.974214i 1.00000 0.000584095i \(-0.000185923\pi\)
−0.223090 + 0.974798i \(0.571614\pi\)
\(678\) 0 0
\(679\) −0.0586307 + 0.215425i −0.00225004 + 0.00826727i
\(680\) −0.0719323 0.149369i −0.00275848 0.00572804i
\(681\) 0 0
\(682\) −0.0572464 + 0.0130661i −0.00219208 + 0.000500328i
\(683\) −11.1029 + 23.0554i −0.424840 + 0.882189i 0.573189 + 0.819423i \(0.305706\pi\)
−0.998028 + 0.0627652i \(0.980008\pi\)
\(684\) 0 0
\(685\) 36.8697i 1.40872i
\(686\) −0.0104749 0.103960i −0.000399934 0.00396922i
\(687\) 0 0
\(688\) −0.189380 + 0.237475i −0.00722006 + 0.00905367i
\(689\) −0.968357 0.466336i −0.0368915 0.0177660i
\(690\) 0 0
\(691\) −7.95316 + 16.5149i −0.302552 + 0.628257i −0.995710 0.0925295i \(-0.970505\pi\)
0.693157 + 0.720786i \(0.256219\pi\)
\(692\) −33.9367 + 16.3431i −1.29008 + 0.621270i
\(693\) 0 0
\(694\) −0.150365 0.0724119i −0.00570777 0.00274872i
\(695\) 25.5520 20.3771i 0.969244 0.772946i
\(696\) 0 0
\(697\) 23.3239 29.2472i 0.883455 1.10782i
\(698\) 0.0106016 0.0464488i 0.000401278 0.00175811i
\(699\) 0 0
\(700\) −1.16031 + 0.849327i −0.0438554 + 0.0321015i
\(701\) −4.02702 + 3.21144i −0.152098 + 0.121294i −0.696582 0.717477i \(-0.745297\pi\)
0.544484 + 0.838771i \(0.316726\pi\)
\(702\) 0 0
\(703\) −42.8295 9.77556i −1.61535 0.368692i
\(704\) 15.9755i 0.602101i
\(705\) 0 0
\(706\) −0.0190059 0.00433798i −0.000715297 0.000163262i
\(707\) −11.3273 9.82558i −0.426006 0.369529i
\(708\) 0 0
\(709\) 1.59463 + 6.98652i 0.0598875 + 0.262384i 0.996004 0.0893049i \(-0.0284646\pi\)
−0.936117 + 0.351689i \(0.885607\pi\)
\(710\) 0.112332 + 0.140859i 0.00421573 + 0.00528636i
\(711\) 0 0
\(712\) 0.171379 0.0391162i 0.00642271 0.00146594i
\(713\) −9.47158 41.4977i −0.354714 1.55410i
\(714\) 0 0
\(715\) 1.36917 5.99870i 0.0512039 0.224339i
\(716\) 16.2503i 0.607303i
\(717\) 0 0
\(718\) 0.00220294 0.00965172i 8.22131e−5 0.000360199i
\(719\) 16.5077 7.94970i 0.615634 0.296474i −0.0999587 0.994992i \(-0.531871\pi\)
0.715593 + 0.698518i \(0.246157\pi\)
\(720\) 0 0
\(721\) −15.0121 + 17.3065i −0.559081 + 0.644527i
\(722\) 0.0915176 + 0.0729828i 0.00340593 + 0.00271614i
\(723\) 0 0
\(724\) −1.24237 0.990754i −0.0461722 0.0368211i
\(725\) 0.661981 + 1.37462i 0.0245853 + 0.0510520i
\(726\) 0 0
\(727\) −0.660640 + 1.37183i −0.0245018 + 0.0508785i −0.912861 0.408272i \(-0.866132\pi\)
0.888359 + 0.459150i \(0.151846\pi\)
\(728\) 0.0831817 0.0154008i 0.00308292 0.000570790i
\(729\) 0 0
\(730\) 0.0313193 + 0.0150826i 0.00115918 + 0.000558231i
\(731\) −0.0570910 0.250132i −0.00211159 0.00925147i
\(732\) 0 0
\(733\) 17.7905 + 14.1874i 0.657106 + 0.524025i 0.894317 0.447434i \(-0.147662\pi\)
−0.237211 + 0.971458i \(0.576233\pi\)
\(734\) 0.131092 0.00483868
\(735\) 0 0
\(736\) −0.552945 −0.0203818
\(737\) 14.0161 + 11.1775i 0.516290 + 0.411728i
\(738\) 0 0
\(739\) 1.29406 + 5.66966i 0.0476029 + 0.208562i 0.993136 0.116963i \(-0.0373160\pi\)
−0.945533 + 0.325525i \(0.894459\pi\)
\(740\) 27.3021 + 13.1480i 1.00364 + 0.483330i
\(741\) 0 0
\(742\) −0.00855343 0.00741948i −0.000314006 0.000272378i
\(743\) −6.53479 + 13.5696i −0.239738 + 0.497821i −0.985772 0.168086i \(-0.946241\pi\)
0.746034 + 0.665908i \(0.231956\pi\)
\(744\) 0 0
\(745\) 9.60961 + 19.9546i 0.352069 + 0.731079i
\(746\) 0.0524288 + 0.0418105i 0.00191955 + 0.00153079i
\(747\) 0 0
\(748\) 10.5505 + 8.41376i 0.385765 + 0.307637i
\(749\) −2.23440 + 0.964433i −0.0816432 + 0.0352396i
\(750\) 0 0
\(751\) −21.3873 + 10.2996i −0.780435 + 0.375838i −0.781295 0.624162i \(-0.785441\pi\)
0.000859983 1.00000i \(0.499726\pi\)
\(752\) −4.94462 + 21.6638i −0.180312 + 0.789998i
\(753\) 0 0
\(754\) 0.0448792i 0.00163440i
\(755\) 4.05852 17.7816i 0.147705 0.647137i
\(756\) 0 0
\(757\) 4.66663 + 20.4458i 0.169612 + 0.743117i 0.986154 + 0.165832i \(0.0530308\pi\)
−0.816543 + 0.577285i \(0.804112\pi\)
\(758\) −0.0501452 + 0.0114453i −0.00182135 + 0.000415712i
\(759\) 0 0
\(760\) −0.192889 0.241875i −0.00699682 0.00877374i
\(761\) −6.54605 28.6801i −0.237294 1.03965i −0.943428 0.331576i \(-0.892420\pi\)
0.706134 0.708078i \(-0.250438\pi\)
\(762\) 0 0
\(763\) 0.980476 0.717695i 0.0354956 0.0259823i
\(764\) 13.3722 + 3.05211i 0.483788 + 0.110422i
\(765\) 0 0
\(766\) 0.157246i 0.00568153i
\(767\) −14.2595 3.25464i −0.514882 0.117518i
\(768\) 0 0
\(769\) 38.7385 30.8929i 1.39695 1.11403i 0.418338 0.908291i \(-0.362613\pi\)
0.978608 0.205735i \(-0.0659586\pi\)
\(770\) 0.0305139 0.0571904i 0.00109964 0.00206100i
\(771\) 0 0
\(772\) −10.7897 + 47.2728i −0.388330 + 1.70139i
\(773\) −22.2514 + 27.9024i −0.800328 + 1.00358i 0.199392 + 0.979920i \(0.436103\pi\)
−0.999720 + 0.0236603i \(0.992468\pi\)
\(774\) 0 0
\(775\) 1.10723 0.882984i 0.0397728 0.0317177i
\(776\) −0.00171571 0.000826243i −6.15905e−5 2.96604e-5i
\(777\) 0 0
\(778\) 0.00304746 0.00146758i 0.000109257 5.26153e-5i
\(779\) 30.2881 62.8940i 1.08518 2.25341i
\(780\) 0 0
\(781\) −26.4257 12.7259i −0.945584 0.455369i
\(782\) 0.0970665 0.121718i 0.00347109 0.00435261i
\(783\) 0 0
\(784\) −27.9031 2.31154i −0.996539 0.0825550i
\(785\) 9.64800i 0.344352i
\(786\) 0 0
\(787\) −6.38240 + 13.2532i −0.227508 + 0.472425i −0.983207 0.182494i \(-0.941583\pi\)
0.755699 + 0.654919i \(0.227297\pi\)
\(788\) 25.7055 5.86711i