Properties

Label 45.4.b.b.19.2
Level $45$
Weight $4$
Character 45.19
Analytic conductor $2.655$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 45.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.65508595026\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{41})\)
Defining polynomial: \( x^{4} + 21x^{2} + 100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 19.2
Root \(-2.70156i\) of defining polynomial
Character \(\chi\) \(=\) 45.19
Dual form 45.4.b.b.19.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.70156i q^{2} +5.10469 q^{4} +(8.10469 + 7.70156i) q^{5} -22.2094i q^{7} -22.2984i q^{8} +O(q^{10})\) \(q-1.70156i q^{2} +5.10469 q^{4} +(8.10469 + 7.70156i) q^{5} -22.2094i q^{7} -22.2984i q^{8} +(13.1047 - 13.7906i) q^{10} +1.79063 q^{11} +58.2094i q^{13} -37.7906 q^{14} +2.89531 q^{16} +18.9844i q^{17} -104.837 q^{19} +(41.3719 + 39.3141i) q^{20} -3.04686i q^{22} +49.6125i q^{23} +(6.37188 + 124.837i) q^{25} +99.0469 q^{26} -113.372i q^{28} -293.466 q^{29} +64.4187 q^{31} -183.314i q^{32} +32.3031 q^{34} +(171.047 - 180.000i) q^{35} +19.8844i q^{37} +178.388i q^{38} +(171.733 - 180.722i) q^{40} +165.581 q^{41} -247.350i q^{43} +9.14059 q^{44} +84.4187 q^{46} +384.544i q^{47} -150.256 q^{49} +(212.419 - 10.8422i) q^{50} +297.141i q^{52} -463.528i q^{53} +(14.5125 + 13.7906i) q^{55} -495.234 q^{56} +499.350i q^{58} -73.7906 q^{59} -137.350 q^{61} -109.612i q^{62} -288.758 q^{64} +(-448.303 + 471.769i) q^{65} -173.906i q^{67} +96.9093i q^{68} +(-306.281 - 291.047i) q^{70} +594.281 q^{71} +320.231i q^{73} +33.8345 q^{74} -535.163 q^{76} -39.7687i q^{77} +770.469 q^{79} +(23.4656 + 22.2984i) q^{80} -281.747i q^{82} -173.925i q^{83} +(-146.209 + 153.862i) q^{85} -420.881 q^{86} -39.9282i q^{88} +1019.02 q^{89} +1292.79 q^{91} +253.256i q^{92} +654.325 q^{94} +(-849.675 - 807.412i) q^{95} -384.375i q^{97} +255.670i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 18 q^{4} - 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 18 q^{4} - 6 q^{5} + 14 q^{10} + 84 q^{11} - 228 q^{14} + 50 q^{16} - 112 q^{19} + 396 q^{20} + 256 q^{25} + 12 q^{26} - 636 q^{29} + 104 q^{31} - 716 q^{34} + 300 q^{35} + 418 q^{40} + 816 q^{41} - 1116 q^{44} + 184 q^{46} - 140 q^{49} + 696 q^{50} - 864 q^{55} - 60 q^{56} - 372 q^{59} + 680 q^{61} + 958 q^{64} - 948 q^{65} + 1080 q^{70} + 72 q^{71} + 3132 q^{74} - 2448 q^{76} - 760 q^{79} - 444 q^{80} - 508 q^{85} - 4296 q^{86} + 2232 q^{89} + 1944 q^{91} + 3232 q^{94} - 2784 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.70156i 0.601593i −0.953688 0.300797i \(-0.902747\pi\)
0.953688 0.300797i \(-0.0972525\pi\)
\(3\) 0 0
\(4\) 5.10469 0.638086
\(5\) 8.10469 + 7.70156i 0.724905 + 0.688849i
\(6\) 0 0
\(7\) 22.2094i 1.19919i −0.800302 0.599597i \(-0.795328\pi\)
0.800302 0.599597i \(-0.204672\pi\)
\(8\) 22.2984i 0.985461i
\(9\) 0 0
\(10\) 13.1047 13.7906i 0.414407 0.436098i
\(11\) 1.79063 0.0490813 0.0245407 0.999699i \(-0.492188\pi\)
0.0245407 + 0.999699i \(0.492188\pi\)
\(12\) 0 0
\(13\) 58.2094i 1.24188i 0.783860 + 0.620938i \(0.213248\pi\)
−0.783860 + 0.620938i \(0.786752\pi\)
\(14\) −37.7906 −0.721426
\(15\) 0 0
\(16\) 2.89531 0.0452393
\(17\) 18.9844i 0.270846i 0.990788 + 0.135423i \(0.0432394\pi\)
−0.990788 + 0.135423i \(0.956761\pi\)
\(18\) 0 0
\(19\) −104.837 −1.26586 −0.632931 0.774208i \(-0.718148\pi\)
−0.632931 + 0.774208i \(0.718148\pi\)
\(20\) 41.3719 + 39.3141i 0.462552 + 0.439545i
\(21\) 0 0
\(22\) 3.04686i 0.0295270i
\(23\) 49.6125i 0.449779i 0.974384 + 0.224890i \(0.0722021\pi\)
−0.974384 + 0.224890i \(0.927798\pi\)
\(24\) 0 0
\(25\) 6.37188 + 124.837i 0.0509751 + 0.998700i
\(26\) 99.0469 0.747103
\(27\) 0 0
\(28\) 113.372i 0.765188i
\(29\) −293.466 −1.87914 −0.939572 0.342350i \(-0.888777\pi\)
−0.939572 + 0.342350i \(0.888777\pi\)
\(30\) 0 0
\(31\) 64.4187 0.373224 0.186612 0.982434i \(-0.440249\pi\)
0.186612 + 0.982434i \(0.440249\pi\)
\(32\) 183.314i 1.01268i
\(33\) 0 0
\(34\) 32.3031 0.162939
\(35\) 171.047 180.000i 0.826063 0.869302i
\(36\) 0 0
\(37\) 19.8844i 0.0883505i 0.999024 + 0.0441752i \(0.0140660\pi\)
−0.999024 + 0.0441752i \(0.985934\pi\)
\(38\) 178.388i 0.761534i
\(39\) 0 0
\(40\) 171.733 180.722i 0.678834 0.714366i
\(41\) 165.581 0.630718 0.315359 0.948972i \(-0.397875\pi\)
0.315359 + 0.948972i \(0.397875\pi\)
\(42\) 0 0
\(43\) 247.350i 0.877221i −0.898677 0.438611i \(-0.855471\pi\)
0.898677 0.438611i \(-0.144529\pi\)
\(44\) 9.14059 0.0313181
\(45\) 0 0
\(46\) 84.4187 0.270584
\(47\) 384.544i 1.19344i 0.802451 + 0.596718i \(0.203529\pi\)
−0.802451 + 0.596718i \(0.796471\pi\)
\(48\) 0 0
\(49\) −150.256 −0.438065
\(50\) 212.419 10.8422i 0.600811 0.0306662i
\(51\) 0 0
\(52\) 297.141i 0.792423i
\(53\) 463.528i 1.20133i −0.799501 0.600665i \(-0.794903\pi\)
0.799501 0.600665i \(-0.205097\pi\)
\(54\) 0 0
\(55\) 14.5125 + 13.7906i 0.0355793 + 0.0338096i
\(56\) −495.234 −1.18176
\(57\) 0 0
\(58\) 499.350i 1.13048i
\(59\) −73.7906 −0.162826 −0.0814129 0.996680i \(-0.525943\pi\)
−0.0814129 + 0.996680i \(0.525943\pi\)
\(60\) 0 0
\(61\) −137.350 −0.288293 −0.144146 0.989556i \(-0.546044\pi\)
−0.144146 + 0.989556i \(0.546044\pi\)
\(62\) 109.612i 0.224529i
\(63\) 0 0
\(64\) −288.758 −0.563980
\(65\) −448.303 + 471.769i −0.855464 + 0.900242i
\(66\) 0 0
\(67\) 173.906i 0.317105i −0.987351 0.158552i \(-0.949317\pi\)
0.987351 0.158552i \(-0.0506827\pi\)
\(68\) 96.9093i 0.172823i
\(69\) 0 0
\(70\) −306.281 291.047i −0.522966 0.496954i
\(71\) 594.281 0.993355 0.496677 0.867935i \(-0.334553\pi\)
0.496677 + 0.867935i \(0.334553\pi\)
\(72\) 0 0
\(73\) 320.231i 0.513428i 0.966487 + 0.256714i \(0.0826398\pi\)
−0.966487 + 0.256714i \(0.917360\pi\)
\(74\) 33.8345 0.0531510
\(75\) 0 0
\(76\) −535.163 −0.807728
\(77\) 39.7687i 0.0588580i
\(78\) 0 0
\(79\) 770.469 1.09727 0.548636 0.836061i \(-0.315147\pi\)
0.548636 + 0.836061i \(0.315147\pi\)
\(80\) 23.4656 + 22.2984i 0.0327942 + 0.0311630i
\(81\) 0 0
\(82\) 281.747i 0.379436i
\(83\) 173.925i 0.230009i −0.993365 0.115004i \(-0.963312\pi\)
0.993365 0.115004i \(-0.0366882\pi\)
\(84\) 0 0
\(85\) −146.209 + 153.862i −0.186572 + 0.196338i
\(86\) −420.881 −0.527730
\(87\) 0 0
\(88\) 39.9282i 0.0483677i
\(89\) 1019.02 1.21367 0.606834 0.794829i \(-0.292439\pi\)
0.606834 + 0.794829i \(0.292439\pi\)
\(90\) 0 0
\(91\) 1292.79 1.48925
\(92\) 253.256i 0.286998i
\(93\) 0 0
\(94\) 654.325 0.717962
\(95\) −849.675 807.412i −0.917630 0.871987i
\(96\) 0 0
\(97\) 384.375i 0.402344i −0.979556 0.201172i \(-0.935525\pi\)
0.979556 0.201172i \(-0.0644750\pi\)
\(98\) 255.670i 0.263537i
\(99\) 0 0
\(100\) 32.5265 + 637.256i 0.0325265 + 0.637256i
\(101\) −34.4906 −0.0339796 −0.0169898 0.999856i \(-0.505408\pi\)
−0.0169898 + 0.999856i \(0.505408\pi\)
\(102\) 0 0
\(103\) 1756.30i 1.68013i −0.542484 0.840066i \(-0.682516\pi\)
0.542484 0.840066i \(-0.317484\pi\)
\(104\) 1297.98 1.22382
\(105\) 0 0
\(106\) −788.722 −0.722712
\(107\) 1361.74i 1.23032i −0.788403 0.615159i \(-0.789092\pi\)
0.788403 0.615159i \(-0.210908\pi\)
\(108\) 0 0
\(109\) −321.119 −0.282180 −0.141090 0.989997i \(-0.545061\pi\)
−0.141090 + 0.989997i \(0.545061\pi\)
\(110\) 23.4656 24.6939i 0.0203396 0.0214043i
\(111\) 0 0
\(112\) 64.3031i 0.0542506i
\(113\) 1582.25i 1.31721i 0.752487 + 0.658607i \(0.228854\pi\)
−0.752487 + 0.658607i \(0.771146\pi\)
\(114\) 0 0
\(115\) −382.094 + 402.094i −0.309830 + 0.326047i
\(116\) −1498.05 −1.19906
\(117\) 0 0
\(118\) 125.559i 0.0979549i
\(119\) 421.631 0.324797
\(120\) 0 0
\(121\) −1327.79 −0.997591
\(122\) 233.709i 0.173435i
\(123\) 0 0
\(124\) 328.837 0.238149
\(125\) −909.802 + 1060.84i −0.651001 + 0.759077i
\(126\) 0 0
\(127\) 1197.14i 0.836449i 0.908344 + 0.418225i \(0.137348\pi\)
−0.908344 + 0.418225i \(0.862652\pi\)
\(128\) 975.173i 0.673390i
\(129\) 0 0
\(130\) 802.744 + 762.816i 0.541579 + 0.514641i
\(131\) 321.647 0.214522 0.107261 0.994231i \(-0.465792\pi\)
0.107261 + 0.994231i \(0.465792\pi\)
\(132\) 0 0
\(133\) 2328.37i 1.51801i
\(134\) −295.912 −0.190768
\(135\) 0 0
\(136\) 423.322 0.266909
\(137\) 354.291i 0.220942i 0.993879 + 0.110471i \(0.0352360\pi\)
−0.993879 + 0.110471i \(0.964764\pi\)
\(138\) 0 0
\(139\) −77.2562 −0.0471424 −0.0235712 0.999722i \(-0.507504\pi\)
−0.0235712 + 0.999722i \(0.507504\pi\)
\(140\) 873.141 918.844i 0.527099 0.554689i
\(141\) 0 0
\(142\) 1011.21i 0.597595i
\(143\) 104.231i 0.0609529i
\(144\) 0 0
\(145\) −2378.45 2260.14i −1.36220 1.29445i
\(146\) 544.893 0.308875
\(147\) 0 0
\(148\) 101.503i 0.0563752i
\(149\) −1705.38 −0.937651 −0.468826 0.883291i \(-0.655323\pi\)
−0.468826 + 0.883291i \(0.655323\pi\)
\(150\) 0 0
\(151\) 758.281 0.408663 0.204331 0.978902i \(-0.434498\pi\)
0.204331 + 0.978902i \(0.434498\pi\)
\(152\) 2337.71i 1.24746i
\(153\) 0 0
\(154\) −67.6689 −0.0354086
\(155\) 522.094 + 496.125i 0.270552 + 0.257095i
\(156\) 0 0
\(157\) 1769.05i 0.899273i 0.893212 + 0.449636i \(0.148446\pi\)
−0.893212 + 0.449636i \(0.851554\pi\)
\(158\) 1311.00i 0.660111i
\(159\) 0 0
\(160\) 1411.80 1485.70i 0.697581 0.734095i
\(161\) 1101.86 0.539372
\(162\) 0 0
\(163\) 881.719i 0.423690i −0.977303 0.211845i \(-0.932053\pi\)
0.977303 0.211845i \(-0.0679473\pi\)
\(164\) 845.240 0.402452
\(165\) 0 0
\(166\) −295.944 −0.138372
\(167\) 216.900i 0.100504i −0.998737 0.0502522i \(-0.983997\pi\)
0.998737 0.0502522i \(-0.0160025\pi\)
\(168\) 0 0
\(169\) −1191.33 −0.542254
\(170\) 261.806 + 248.784i 0.118116 + 0.112241i
\(171\) 0 0
\(172\) 1262.64i 0.559742i
\(173\) 4125.91i 1.81322i −0.421970 0.906610i \(-0.638661\pi\)
0.421970 0.906610i \(-0.361339\pi\)
\(174\) 0 0
\(175\) 2772.56 141.515i 1.19763 0.0611289i
\(176\) 5.18443 0.00222040
\(177\) 0 0
\(178\) 1733.93i 0.730134i
\(179\) −3213.14 −1.34168 −0.670842 0.741600i \(-0.734067\pi\)
−0.670842 + 0.741600i \(0.734067\pi\)
\(180\) 0 0
\(181\) 3394.42 1.39395 0.696976 0.717095i \(-0.254529\pi\)
0.696976 + 0.717095i \(0.254529\pi\)
\(182\) 2199.77i 0.895921i
\(183\) 0 0
\(184\) 1106.28 0.443240
\(185\) −153.141 + 161.156i −0.0608601 + 0.0640457i
\(186\) 0 0
\(187\) 33.9939i 0.0132935i
\(188\) 1962.98i 0.761514i
\(189\) 0 0
\(190\) −1373.86 + 1445.77i −0.524581 + 0.552040i
\(191\) 3467.49 1.31361 0.656804 0.754062i \(-0.271908\pi\)
0.656804 + 0.754062i \(0.271908\pi\)
\(192\) 0 0
\(193\) 1792.14i 0.668401i 0.942502 + 0.334200i \(0.108466\pi\)
−0.942502 + 0.334200i \(0.891534\pi\)
\(194\) −654.038 −0.242047
\(195\) 0 0
\(196\) −767.011 −0.279523
\(197\) 1678.19i 0.606935i 0.952842 + 0.303467i \(0.0981443\pi\)
−0.952842 + 0.303467i \(0.901856\pi\)
\(198\) 0 0
\(199\) −3108.23 −1.10722 −0.553610 0.832776i \(-0.686750\pi\)
−0.553610 + 0.832776i \(0.686750\pi\)
\(200\) 2783.68 142.083i 0.984180 0.0502339i
\(201\) 0 0
\(202\) 58.6878i 0.0204419i
\(203\) 6517.69i 2.25346i
\(204\) 0 0
\(205\) 1341.98 + 1275.23i 0.457211 + 0.434469i
\(206\) −2988.46 −1.01076
\(207\) 0 0
\(208\) 168.534i 0.0561815i
\(209\) −187.725 −0.0621301
\(210\) 0 0
\(211\) −4473.27 −1.45949 −0.729745 0.683719i \(-0.760361\pi\)
−0.729745 + 0.683719i \(0.760361\pi\)
\(212\) 2366.17i 0.766551i
\(213\) 0 0
\(214\) −2317.08 −0.740151
\(215\) 1904.98 2004.69i 0.604273 0.635902i
\(216\) 0 0
\(217\) 1430.70i 0.447568i
\(218\) 546.403i 0.169757i
\(219\) 0 0
\(220\) 74.0816 + 70.3968i 0.0227026 + 0.0215734i
\(221\) −1105.07 −0.336357
\(222\) 0 0
\(223\) 1753.42i 0.526535i −0.964723 0.263268i \(-0.915200\pi\)
0.964723 0.263268i \(-0.0848003\pi\)
\(224\) −4071.29 −1.21440
\(225\) 0 0
\(226\) 2692.29 0.792427
\(227\) 936.900i 0.273939i −0.990575 0.136970i \(-0.956264\pi\)
0.990575 0.136970i \(-0.0437363\pi\)
\(228\) 0 0
\(229\) 2582.06 0.745096 0.372548 0.928013i \(-0.378484\pi\)
0.372548 + 0.928013i \(0.378484\pi\)
\(230\) 684.187 + 650.156i 0.196148 + 0.186391i
\(231\) 0 0
\(232\) 6543.82i 1.85182i
\(233\) 2295.01i 0.645284i −0.946521 0.322642i \(-0.895429\pi\)
0.946521 0.322642i \(-0.104571\pi\)
\(234\) 0 0
\(235\) −2961.59 + 3116.61i −0.822096 + 0.865128i
\(236\) −376.678 −0.103897
\(237\) 0 0
\(238\) 717.432i 0.195396i
\(239\) −2294.01 −0.620866 −0.310433 0.950595i \(-0.600474\pi\)
−0.310433 + 0.950595i \(0.600474\pi\)
\(240\) 0 0
\(241\) 382.287 0.102180 0.0510898 0.998694i \(-0.483731\pi\)
0.0510898 + 0.998694i \(0.483731\pi\)
\(242\) 2259.32i 0.600144i
\(243\) 0 0
\(244\) −701.128 −0.183956
\(245\) −1217.78 1157.21i −0.317555 0.301760i
\(246\) 0 0
\(247\) 6102.52i 1.57204i
\(248\) 1436.44i 0.367798i
\(249\) 0 0
\(250\) 1805.09 + 1548.08i 0.456655 + 0.391638i
\(251\) 2259.98 0.568322 0.284161 0.958777i \(-0.408285\pi\)
0.284161 + 0.958777i \(0.408285\pi\)
\(252\) 0 0
\(253\) 88.8375i 0.0220758i
\(254\) 2037.01 0.503202
\(255\) 0 0
\(256\) −3969.38 −0.969087
\(257\) 92.7843i 0.0225203i −0.999937 0.0112602i \(-0.996416\pi\)
0.999937 0.0112602i \(-0.00358430\pi\)
\(258\) 0 0
\(259\) 441.619 0.105949
\(260\) −2288.45 + 2408.23i −0.545859 + 0.574431i
\(261\) 0 0
\(262\) 547.302i 0.129055i
\(263\) 568.312i 0.133246i 0.997778 + 0.0666229i \(0.0212224\pi\)
−0.997778 + 0.0666229i \(0.978778\pi\)
\(264\) 0 0
\(265\) 3569.89 3756.75i 0.827534 0.870850i
\(266\) 3961.87 0.913226
\(267\) 0 0
\(268\) 887.737i 0.202340i
\(269\) 7582.41 1.71862 0.859309 0.511458i \(-0.170894\pi\)
0.859309 + 0.511458i \(0.170894\pi\)
\(270\) 0 0
\(271\) 7943.69 1.78061 0.890304 0.455366i \(-0.150492\pi\)
0.890304 + 0.455366i \(0.150492\pi\)
\(272\) 54.9657i 0.0122529i
\(273\) 0 0
\(274\) 602.847 0.132917
\(275\) 11.4097 + 223.537i 0.00250192 + 0.0490175i
\(276\) 0 0
\(277\) 6823.00i 1.47998i −0.672618 0.739990i \(-0.734830\pi\)
0.672618 0.739990i \(-0.265170\pi\)
\(278\) 131.456i 0.0283605i
\(279\) 0 0
\(280\) −4013.72 3814.08i −0.856663 0.814053i
\(281\) −3315.86 −0.703942 −0.351971 0.936011i \(-0.614488\pi\)
−0.351971 + 0.936011i \(0.614488\pi\)
\(282\) 0 0
\(283\) 6602.76i 1.38690i 0.720504 + 0.693451i \(0.243910\pi\)
−0.720504 + 0.693451i \(0.756090\pi\)
\(284\) 3033.62 0.633846
\(285\) 0 0
\(286\) 177.356 0.0366688
\(287\) 3677.46i 0.756353i
\(288\) 0 0
\(289\) 4552.59 0.926642
\(290\) −3845.77 + 4047.07i −0.778730 + 0.819491i
\(291\) 0 0
\(292\) 1634.68i 0.327611i
\(293\) 5814.14i 1.15927i −0.814877 0.579634i \(-0.803195\pi\)
0.814877 0.579634i \(-0.196805\pi\)
\(294\) 0 0
\(295\) −598.050 568.303i −0.118033 0.112162i
\(296\) 443.390 0.0870660
\(297\) 0 0
\(298\) 2901.81i 0.564084i
\(299\) −2887.91 −0.558570
\(300\) 0 0
\(301\) −5493.49 −1.05196
\(302\) 1290.26i 0.245849i
\(303\) 0 0
\(304\) −303.537 −0.0572667
\(305\) −1113.18 1057.81i −0.208985 0.198590i
\(306\) 0 0
\(307\) 8124.86i 1.51046i 0.655462 + 0.755229i \(0.272474\pi\)
−0.655462 + 0.755229i \(0.727526\pi\)
\(308\) 203.007i 0.0375564i
\(309\) 0 0
\(310\) 844.187 888.375i 0.154667 0.162762i
\(311\) −7336.26 −1.33762 −0.668812 0.743432i \(-0.733197\pi\)
−0.668812 + 0.743432i \(0.733197\pi\)
\(312\) 0 0
\(313\) 2202.66i 0.397768i −0.980023 0.198884i \(-0.936268\pi\)
0.980023 0.198884i \(-0.0637318\pi\)
\(314\) 3010.15 0.540996
\(315\) 0 0
\(316\) 3933.00 0.700154
\(317\) 10008.9i 1.77336i 0.462386 + 0.886679i \(0.346993\pi\)
−0.462386 + 0.886679i \(0.653007\pi\)
\(318\) 0 0
\(319\) −525.488 −0.0922309
\(320\) −2340.29 2223.89i −0.408832 0.388497i
\(321\) 0 0
\(322\) 1874.89i 0.324483i
\(323\) 1990.27i 0.342854i
\(324\) 0 0
\(325\) −7266.71 + 370.903i −1.24026 + 0.0633046i
\(326\) −1500.30 −0.254889
\(327\) 0 0
\(328\) 3692.20i 0.621548i
\(329\) 8540.47 1.43116
\(330\) 0 0
\(331\) −8695.94 −1.44402 −0.722012 0.691881i \(-0.756782\pi\)
−0.722012 + 0.691881i \(0.756782\pi\)
\(332\) 887.832i 0.146765i
\(333\) 0 0
\(334\) −369.069 −0.0604627
\(335\) 1339.35 1409.46i 0.218437 0.229871i
\(336\) 0 0
\(337\) 7400.61i 1.19625i 0.801402 + 0.598126i \(0.204088\pi\)
−0.801402 + 0.598126i \(0.795912\pi\)
\(338\) 2027.12i 0.326216i
\(339\) 0 0
\(340\) −746.353 + 785.419i −0.119049 + 0.125280i
\(341\) 115.350 0.0183183
\(342\) 0 0
\(343\) 4280.72i 0.673869i
\(344\) −5515.52 −0.864467
\(345\) 0 0
\(346\) −7020.49 −1.09082
\(347\) 7841.44i 1.21311i 0.795040 + 0.606557i \(0.207450\pi\)
−0.795040 + 0.606557i \(0.792550\pi\)
\(348\) 0 0
\(349\) 4961.26 0.760946 0.380473 0.924792i \(-0.375761\pi\)
0.380473 + 0.924792i \(0.375761\pi\)
\(350\) −240.797 4717.69i −0.0367748 0.720489i
\(351\) 0 0
\(352\) 328.247i 0.0497035i
\(353\) 12163.0i 1.83392i 0.398981 + 0.916959i \(0.369364\pi\)
−0.398981 + 0.916959i \(0.630636\pi\)
\(354\) 0 0
\(355\) 4816.46 + 4576.89i 0.720088 + 0.684271i
\(356\) 5201.80 0.774424
\(357\) 0 0
\(358\) 5467.36i 0.807148i
\(359\) 5193.79 0.763559 0.381779 0.924253i \(-0.375311\pi\)
0.381779 + 0.924253i \(0.375311\pi\)
\(360\) 0 0
\(361\) 4131.90 0.602406
\(362\) 5775.81i 0.838591i
\(363\) 0 0
\(364\) 6599.31 0.950268
\(365\) −2466.28 + 2595.37i −0.353674 + 0.372187i
\(366\) 0 0
\(367\) 6086.09i 0.865644i 0.901479 + 0.432822i \(0.142482\pi\)
−0.901479 + 0.432822i \(0.857518\pi\)
\(368\) 143.644i 0.0203477i
\(369\) 0 0
\(370\) 274.218 + 260.578i 0.0385295 + 0.0366130i
\(371\) −10294.7 −1.44063
\(372\) 0 0
\(373\) 10581.9i 1.46893i −0.678646 0.734466i \(-0.737433\pi\)
0.678646 0.734466i \(-0.262567\pi\)
\(374\) 57.8428 0.00799727
\(375\) 0 0
\(376\) 8574.72 1.17608
\(377\) 17082.4i 2.33366i
\(378\) 0 0
\(379\) −11655.2 −1.57964 −0.789822 0.613336i \(-0.789827\pi\)
−0.789822 + 0.613336i \(0.789827\pi\)
\(380\) −4337.32 4121.59i −0.585526 0.556403i
\(381\) 0 0
\(382\) 5900.16i 0.790257i
\(383\) 6364.97i 0.849177i −0.905387 0.424588i \(-0.860419\pi\)
0.905387 0.424588i \(-0.139581\pi\)
\(384\) 0 0
\(385\) 306.281 322.313i 0.0405442 0.0426665i
\(386\) 3049.44 0.402105
\(387\) 0 0
\(388\) 1962.11i 0.256730i
\(389\) 6134.33 0.799545 0.399773 0.916614i \(-0.369089\pi\)
0.399773 + 0.916614i \(0.369089\pi\)
\(390\) 0 0
\(391\) −941.862 −0.121821
\(392\) 3350.48i 0.431696i
\(393\) 0 0
\(394\) 2855.55 0.365128
\(395\) 6244.41 + 5933.81i 0.795418 + 0.755854i
\(396\) 0 0
\(397\) 9746.46i 1.23214i −0.787690 0.616072i \(-0.788723\pi\)
0.787690 0.616072i \(-0.211277\pi\)
\(398\) 5288.85i 0.666096i
\(399\) 0 0
\(400\) 18.4486 + 361.444i 0.00230607 + 0.0451805i
\(401\) 1306.44 0.162695 0.0813474 0.996686i \(-0.474078\pi\)
0.0813474 + 0.996686i \(0.474078\pi\)
\(402\) 0 0
\(403\) 3749.77i 0.463498i
\(404\) −176.063 −0.0216819
\(405\) 0 0
\(406\) 11090.2 1.35566
\(407\) 35.6055i 0.00433636i
\(408\) 0 0
\(409\) 3876.93 0.468709 0.234354 0.972151i \(-0.424702\pi\)
0.234354 + 0.972151i \(0.424702\pi\)
\(410\) 2169.89 2283.47i 0.261374 0.275055i
\(411\) 0 0
\(412\) 8965.38i 1.07207i
\(413\) 1638.84i 0.195260i
\(414\) 0 0
\(415\) 1339.49 1409.61i 0.158441 0.166735i
\(416\) 10670.6 1.25762
\(417\) 0 0
\(418\) 319.426i 0.0373771i
\(419\) −16022.5 −1.86814 −0.934071 0.357088i \(-0.883770\pi\)
−0.934071 + 0.357088i \(0.883770\pi\)
\(420\) 0 0
\(421\) −8119.73 −0.939980 −0.469990 0.882672i \(-0.655742\pi\)
−0.469990 + 0.882672i \(0.655742\pi\)
\(422\) 7611.54i 0.878019i
\(423\) 0 0
\(424\) −10336.0 −1.18386
\(425\) −2369.96 + 120.966i −0.270494 + 0.0138064i
\(426\) 0 0
\(427\) 3050.46i 0.345719i
\(428\) 6951.24i 0.785049i
\(429\) 0 0
\(430\) −3411.11 3241.44i −0.382554 0.363526i
\(431\) 5713.99 0.638592 0.319296 0.947655i \(-0.396554\pi\)
0.319296 + 0.947655i \(0.396554\pi\)
\(432\) 0 0
\(433\) 6251.34i 0.693811i 0.937900 + 0.346906i \(0.112768\pi\)
−0.937900 + 0.346906i \(0.887232\pi\)
\(434\) −2434.42 −0.269254
\(435\) 0 0
\(436\) −1639.21 −0.180055
\(437\) 5201.25i 0.569358i
\(438\) 0 0
\(439\) 4230.97 0.459984 0.229992 0.973192i \(-0.426130\pi\)
0.229992 + 0.973192i \(0.426130\pi\)
\(440\) 307.509 323.605i 0.0333180 0.0350620i
\(441\) 0 0
\(442\) 1880.34i 0.202350i
\(443\) 6314.29i 0.677203i −0.940930 0.338601i \(-0.890046\pi\)
0.940930 0.338601i \(-0.109954\pi\)
\(444\) 0 0
\(445\) 8258.88 + 7848.08i 0.879794 + 0.836033i
\(446\) −2983.55 −0.316760
\(447\) 0 0
\(448\) 6413.13i 0.676321i
\(449\) −9349.71 −0.982717 −0.491358 0.870957i \(-0.663499\pi\)
−0.491358 + 0.870957i \(0.663499\pi\)
\(450\) 0 0
\(451\) 296.494 0.0309565
\(452\) 8076.87i 0.840496i
\(453\) 0 0
\(454\) −1594.19 −0.164800
\(455\) 10477.7 + 9956.53i 1.07956 + 1.02587i
\(456\) 0 0
\(457\) 9547.46i 0.977268i 0.872489 + 0.488634i \(0.162505\pi\)
−0.872489 + 0.488634i \(0.837495\pi\)
\(458\) 4393.53i 0.448245i
\(459\) 0 0
\(460\) −1950.47 + 2052.56i −0.197698 + 0.208046i
\(461\) −6237.23 −0.630145 −0.315073 0.949068i \(-0.602029\pi\)
−0.315073 + 0.949068i \(0.602029\pi\)
\(462\) 0 0
\(463\) 6469.98i 0.649428i 0.945812 + 0.324714i \(0.105268\pi\)
−0.945812 + 0.324714i \(0.894732\pi\)
\(464\) −849.675 −0.0850111
\(465\) 0 0
\(466\) −3905.10 −0.388198
\(467\) 7206.64i 0.714097i 0.934086 + 0.357049i \(0.116217\pi\)
−0.934086 + 0.357049i \(0.883783\pi\)
\(468\) 0 0
\(469\) −3862.35 −0.380270
\(470\) 5303.10 + 5039.32i 0.520455 + 0.494567i
\(471\) 0 0
\(472\) 1645.42i 0.160458i
\(473\) 442.912i 0.0430552i
\(474\) 0 0
\(475\) −668.012 13087.6i −0.0645274 1.26422i
\(476\) 2152.29 0.207248
\(477\) 0 0
\(478\) 3903.39i 0.373509i
\(479\) −10851.8 −1.03514 −0.517571 0.855640i \(-0.673164\pi\)
−0.517571 + 0.855640i \(0.673164\pi\)
\(480\) 0 0
\(481\) −1157.46 −0.109720
\(482\) 650.485i 0.0614705i
\(483\) 0 0
\(484\) −6777.97 −0.636549
\(485\) 2960.29 3115.24i 0.277154 0.291661i
\(486\) 0 0
\(487\) 12757.1i 1.18702i −0.804827 0.593510i \(-0.797742\pi\)
0.804827 0.593510i \(-0.202258\pi\)
\(488\) 3062.69i 0.284101i
\(489\) 0 0
\(490\) −1969.06 + 2072.13i −0.181537 + 0.191039i
\(491\) 7016.52 0.644911 0.322455 0.946585i \(-0.395492\pi\)
0.322455 + 0.946585i \(0.395492\pi\)
\(492\) 0 0
\(493\) 5571.26i 0.508960i
\(494\) −10383.8 −0.945729
\(495\) 0 0
\(496\) 186.512 0.0168844
\(497\) 13198.6i 1.19122i
\(498\) 0 0
\(499\) −11372.3 −1.02023 −0.510113 0.860107i \(-0.670396\pi\)
−0.510113 + 0.860107i \(0.670396\pi\)
\(500\) −4644.25 + 5415.27i −0.415395 + 0.484356i
\(501\) 0 0
\(502\) 3845.50i 0.341899i
\(503\) 5587.37i 0.495285i 0.968851 + 0.247643i \(0.0796559\pi\)
−0.968851 + 0.247643i \(0.920344\pi\)
\(504\) 0 0
\(505\) −279.535 265.631i −0.0246320 0.0234068i
\(506\) 151.163 0.0132806
\(507\) 0 0
\(508\) 6111.03i 0.533726i
\(509\) 16256.7 1.41565 0.707825 0.706388i \(-0.249676\pi\)
0.707825 + 0.706388i \(0.249676\pi\)
\(510\) 0 0
\(511\) 7112.14 0.615699
\(512\) 1047.24i 0.0903943i
\(513\) 0 0
\(514\) −157.878 −0.0135481
\(515\) 13526.3 14234.3i 1.15736 1.21794i
\(516\) 0 0
\(517\) 688.574i 0.0585754i
\(518\) 751.442i 0.0637384i
\(519\) 0 0
\(520\) 10519.7 + 9996.46i 0.887153 + 0.843026i
\(521\) −19748.4 −1.66064 −0.830320 0.557286i \(-0.811843\pi\)
−0.830320 + 0.557286i \(0.811843\pi\)
\(522\) 0 0
\(523\) 7843.44i 0.655774i −0.944717 0.327887i \(-0.893663\pi\)
0.944717 0.327887i \(-0.106337\pi\)
\(524\) 1641.91 0.136884
\(525\) 0 0
\(526\) 967.019 0.0801597
\(527\) 1222.95i 0.101086i
\(528\) 0 0
\(529\) 9705.60 0.797699
\(530\) −6392.34 6074.39i −0.523897 0.497839i
\(531\) 0 0
\(532\) 11885.6i 0.968622i
\(533\) 9638.38i 0.783273i
\(534\) 0 0
\(535\) 10487.5 11036.5i 0.847504 0.891865i
\(536\) −3877.84 −0.312495
\(537\) 0 0
\(538\) 12902.0i 1.03391i
\(539\) −269.053 −0.0215008
\(540\) 0 0
\(541\) 7383.29 0.586751 0.293376 0.955997i \(-0.405221\pi\)
0.293376 + 0.955997i \(0.405221\pi\)
\(542\) 13516.7i 1.07120i
\(543\) 0 0
\(544\) 3480.10 0.274280
\(545\) −2602.57 2473.12i −0.204554 0.194379i
\(546\) 0 0
\(547\) 3354.90i 0.262240i 0.991367 + 0.131120i \(0.0418573\pi\)
−0.991367 + 0.131120i \(0.958143\pi\)
\(548\) 1808.54i 0.140980i
\(549\) 0 0
\(550\) 380.363 19.4143i 0.0294886 0.00150514i
\(551\) 30766.2 2.37874
\(552\) 0 0
\(553\) 17111.6i 1.31584i
\(554\) −11609.8 −0.890346
\(555\) 0 0
\(556\) −394.369 −0.0300809
\(557\) 20771.8i 1.58012i 0.613028 + 0.790061i \(0.289951\pi\)
−0.613028 + 0.790061i \(0.710049\pi\)
\(558\) 0 0
\(559\) 14398.1 1.08940
\(560\) 495.234 521.156i 0.0373705 0.0393266i
\(561\) 0 0
\(562\) 5642.15i 0.423487i
\(563\) 7194.86i 0.538592i −0.963057 0.269296i \(-0.913209\pi\)
0.963057 0.269296i \(-0.0867910\pi\)
\(564\) 0 0
\(565\) −12185.8 + 12823.6i −0.907361 + 0.954856i
\(566\) 11235.0 0.834350
\(567\) 0 0
\(568\) 13251.5i 0.978913i
\(569\) 11549.5 0.850931 0.425466 0.904975i \(-0.360110\pi\)
0.425466 + 0.904975i \(0.360110\pi\)
\(570\) 0 0
\(571\) 1482.54 0.108655 0.0543277 0.998523i \(-0.482698\pi\)
0.0543277 + 0.998523i \(0.482698\pi\)
\(572\) 532.068i 0.0388932i
\(573\) 0 0
\(574\) −6257.42 −0.455017
\(575\) −6193.50 + 316.125i −0.449194 + 0.0229275i
\(576\) 0 0
\(577\) 15264.0i 1.10130i 0.834737 + 0.550649i \(0.185620\pi\)
−0.834737 + 0.550649i \(0.814380\pi\)
\(578\) 7746.52i 0.557462i
\(579\) 0 0
\(580\) −12141.2 11537.3i −0.869202 0.825968i
\(581\) −3862.76 −0.275825
\(582\) 0 0
\(583\) 830.006i 0.0589628i
\(584\) 7140.66 0.505963
\(585\) 0 0
\(586\) −9893.12 −0.697408
\(587\) 1736.89i 0.122128i 0.998134 + 0.0610639i \(0.0194493\pi\)
−0.998134 + 0.0610639i \(0.980551\pi\)
\(588\) 0 0
\(589\) −6753.50 −0.472450
\(590\) −967.003 + 1017.62i −0.0674761 + 0.0710080i
\(591\) 0 0
\(592\) 57.5714i 0.00399691i
\(593\) 11764.8i 0.814707i 0.913271 + 0.407353i \(0.133548\pi\)
−0.913271 + 0.407353i \(0.866452\pi\)
\(594\) 0 0
\(595\) 3417.19 + 3247.22i 0.235447 + 0.223736i
\(596\) −8705.42 −0.598302
\(597\) 0 0
\(598\) 4913.96i 0.336032i
\(599\) −9451.99 −0.644737 −0.322369 0.946614i \(-0.604479\pi\)
−0.322369 + 0.946614i \(0.604479\pi\)
\(600\) 0 0
\(601\) −3131.93 −0.212569 −0.106285 0.994336i \(-0.533895\pi\)
−0.106285 + 0.994336i \(0.533895\pi\)
\(602\) 9347.51i 0.632851i
\(603\) 0 0
\(604\) 3870.79 0.260762
\(605\) −10761.4 10226.1i −0.723159 0.687189i
\(606\) 0 0
\(607\) 22700.8i 1.51795i −0.651120 0.758975i \(-0.725700\pi\)
0.651120 0.758975i \(-0.274300\pi\)
\(608\) 19218.2i 1.28191i
\(609\) 0 0
\(610\) −1799.93 + 1894.14i −0.119470 + 0.125724i
\(611\) −22384.0 −1.48210
\(612\) 0 0
\(613\) 28911.6i 1.90494i 0.304629 + 0.952471i \(0.401468\pi\)
−0.304629 + 0.952471i \(0.598532\pi\)
\(614\) 13825.0 0.908681
\(615\) 0 0
\(616\) −886.780 −0.0580023
\(617\) 5566.87i 0.363231i −0.983370 0.181616i \(-0.941867\pi\)
0.983370 0.181616i \(-0.0581326\pi\)
\(618\) 0 0
\(619\) −4150.32 −0.269492 −0.134746 0.990880i \(-0.543022\pi\)
−0.134746 + 0.990880i \(0.543022\pi\)
\(620\) 2665.12 + 2532.56i 0.172635 + 0.164049i
\(621\) 0 0
\(622\) 12483.1i 0.804705i
\(623\) 22631.9i 1.45542i
\(624\) 0 0
\(625\) −15543.8 + 1590.90i −0.994803 + 0.101818i
\(626\) −3747.96 −0.239295
\(627\) 0 0
\(628\) 9030.46i 0.573813i
\(629\) −377.492 −0.0239294
\(630\) 0 0
\(631\) −4090.09 −0.258041 −0.129021 0.991642i \(-0.541183\pi\)
−0.129021 + 0.991642i \(0.541183\pi\)
\(632\) 17180.2i 1.08132i
\(633\) 0 0
\(634\) 17030.7 1.06684
\(635\) −9219.85 + 9702.45i −0.576187 + 0.606346i
\(636\) 0 0
\(637\) 8746.32i 0.544022i
\(638\) 894.150i 0.0554855i
\(639\) 0 0
\(640\) 7510.36 7903.47i 0.463864 0.488144i
\(641\) −3909.35 −0.240890 −0.120445 0.992720i \(-0.538432\pi\)
−0.120445 + 0.992720i \(0.538432\pi\)
\(642\) 0 0
\(643\) 30539.5i 1.87303i 0.350624 + 0.936516i \(0.385969\pi\)
−0.350624 + 0.936516i \(0.614031\pi\)
\(644\) 5624.66 0.344166
\(645\) 0 0
\(646\) −3386.58 −0.206259
\(647\) 12707.7i 0.772167i −0.922464 0.386083i \(-0.873828\pi\)
0.922464 0.386083i \(-0.126172\pi\)
\(648\) 0 0
\(649\) −132.132 −0.00799170
\(650\) 631.115 + 12364.8i 0.0380836 + 0.746132i
\(651\) 0 0
\(652\) 4500.90i 0.270351i
\(653\) 12777.6i 0.765737i −0.923803 0.382869i \(-0.874936\pi\)
0.923803 0.382869i \(-0.125064\pi\)
\(654\) 0 0
\(655\) 2606.85 + 2477.18i 0.155508 + 0.147773i
\(656\) 479.410 0.0285332
\(657\) 0 0
\(658\) 14532.1i 0.860976i
\(659\) 23563.5 1.39287 0.696435 0.717620i \(-0.254768\pi\)
0.696435 + 0.717620i \(0.254768\pi\)
\(660\) 0 0
\(661\) −4361.31 −0.256634 −0.128317 0.991733i \(-0.540958\pi\)
−0.128317 + 0.991733i \(0.540958\pi\)
\(662\) 14796.7i 0.868715i
\(663\) 0 0
\(664\) −3878.25 −0.226665
\(665\) −17932.1 + 18870.7i −1.04568 + 1.10042i
\(666\) 0 0
\(667\) 14559.6i 0.845200i
\(668\) 1107.21i 0.0641304i
\(669\) 0 0
\(670\) −2398.28 2278.99i −0.138289 0.131410i
\(671\) −245.943 −0.0141498
\(672\) 0 0
\(673\) 8203.52i 0.469870i −0.972011 0.234935i \(-0.924512\pi\)
0.972011 0.234935i \(-0.0754877\pi\)
\(674\) 12592.6 0.719657
\(675\) 0 0
\(676\) −6081.37 −0.346004
\(677\) 28057.1i 1.59279i 0.604774 + 0.796397i \(0.293263\pi\)
−0.604774 + 0.796397i \(0.706737\pi\)
\(678\) 0 0
\(679\) −8536.73 −0.482488
\(680\) 3430.89 + 3260.24i 0.193483 + 0.183860i
\(681\) 0 0
\(682\) 196.275i 0.0110202i
\(683\) 3344.62i 0.187377i 0.995602 + 0.0936885i \(0.0298658\pi\)
−0.995602 + 0.0936885i \(0.970134\pi\)
\(684\) 0 0
\(685\) −2728.59 + 2871.41i −0.152196 + 0.160162i
\(686\) −7283.91 −0.405395
\(687\) 0 0
\(688\) 716.156i 0.0396849i
\(689\) 26981.7 1.49190
\(690\) 0 0
\(691\) 12964.8 0.713757 0.356879 0.934151i \(-0.383841\pi\)
0.356879 + 0.934151i \(0.383841\pi\)
\(692\) 21061.5i 1.15699i
\(693\) 0 0
\(694\) 13342.7 0.729801
\(695\) −626.138 594.994i −0.0341737 0.0324740i
\(696\) 0 0
\(697\) 3143.46i 0.170828i
\(698\) 8441.90i 0.457780i
\(699\) 0 0
\(700\) 14153.1 722.392i 0.764193 0.0390055i
\(701\) 16162.1 0.870806 0.435403 0.900236i \(-0.356606\pi\)
0.435403 + 0.900236i \(0.356606\pi\)
\(702\) 0 0
\(703\) 2084.63i 0.111839i
\(704\) −517.058 −0.0276809
\(705\) 0 0
\(706\) 20696.2 1.10327
\(707\) 766.014i 0.0407481i
\(708\) 0 0
\(709\) 14244.4 0.754529 0.377265 0.926105i \(-0.376865\pi\)
0.377265 + 0.926105i \(0.376865\pi\)
\(710\) 7787.87 8195.51i 0.411653 0.433200i
\(711\) 0 0
\(712\) 22722.7i 1.19602i
\(713\) 3195.97i 0.167868i
\(714\) 0 0
\(715\) −802.744 + 844.762i −0.0419873 + 0.0441850i
\(716\) −16402.1 −0.856109
\(717\) 0 0
\(718\) 8837.55i 0.459352i
\(719\) −27638.5 −1.43358 −0.716790 0.697289i \(-0.754389\pi\)
−0.716790 + 0.697289i \(0.754389\pi\)
\(720\) 0 0
\(721\) −39006.4 −2.01480
\(722\) 7030.68i 0.362403i
\(723\) 0 0
\(724\) 17327.4 0.889460
\(725\) −1869.93 36635.5i −0.0957895 1.87670i
\(726\) 0 0
\(727\) 2525.52i 0.128840i 0.997923 + 0.0644199i \(0.0205197\pi\)
−0.997923 + 0.0644199i \(0.979480\pi\)
\(728\) 28827.3i 1.46760i
\(729\) 0 0
\(730\) 4416.19 + 4196.53i 0.223905 + 0.212768i
\(731\) 4695.79 0.237592
\(732\) 0 0
\(733\) 8400.27i 0.423289i −0.977347 0.211645i \(-0.932118\pi\)
0.977347 0.211645i \(-0.0678820\pi\)
\(734\) 10355.9 0.520765
\(735\) 0 0
\(736\) 9094.67 0.455481
\(737\) 311.401i 0.0155639i
\(738\) 0 0
\(739\) 19689.1 0.980074 0.490037 0.871702i \(-0.336983\pi\)
0.490037 + 0.871702i \(0.336983\pi\)
\(740\) −781.735 + 822.653i −0.0388340 + 0.0408667i
\(741\) 0 0
\(742\) 17517.0i 0.866671i
\(743\) 22526.6i 1.11227i 0.831091 + 0.556137i \(0.187717\pi\)
−0.831091 + 0.556137i \(0.812283\pi\)
\(744\) 0 0
\(745\) −13821.6 13134.1i −0.679708 0.645900i
\(746\) −18005.8 −0.883699
\(747\) 0 0
\(748\) 173.528i 0.00848239i
\(749\) −30243.3 −1.47539
\(750\) 0 0
\(751\) 34691.1 1.68562 0.842808 0.538215i \(-0.180901\pi\)
0.842808 + 0.538215i \(0.180901\pi\)
\(752\) 1113.37i 0.0539902i
\(753\) 0 0
\(754\) −29066.8 −1.40392
\(755\) 6145.63 + 5839.95i 0.296242 + 0.281507i
\(756\) 0 0
\(757\) 6619.98i 0.317843i −0.987291 0.158922i \(-0.949198\pi\)
0.987291 0.158922i \(-0.0508017\pi\)
\(758\) 19832.0i 0.950303i
\(759\) 0 0
\(760\) −18004.0 + 18946.4i −0.859309 + 0.904288i
\(761\) 29368.7 1.39897 0.699483 0.714649i \(-0.253414\pi\)
0.699483 + 0.714649i \(0.253414\pi\)
\(762\) 0 0
\(763\) 7131.84i 0.338388i
\(764\) 17700.5 0.838194
\(765\) 0 0
\(766\) −10830.4 −0.510859
\(767\) 4295.31i 0.202209i
\(768\) 0 0
\(769\) −32677.4 −1.53235 −0.766174 0.642633i \(-0.777842\pi\)
−0.766174 + 0.642633i \(0.777842\pi\)
\(770\) −548.435 521.156i −0.0256678 0.0243911i
\(771\) 0 0
\(772\) 9148.33i 0.426497i
\(773\) 28047.5i 1.30504i 0.757770 + 0.652522i \(0.226289\pi\)
−0.757770 + 0.652522i \(0.773711\pi\)
\(774\) 0 0
\(775\) 410.469 + 8041.87i 0.0190251 + 0.372739i
\(776\) −8570.96 −0.396494
\(777\) 0 0
\(778\) 10438.0i 0.481001i
\(779\) −17359.1 −0.798402
\(780\) 0 0
\(781\) 1064.14 0.0487552
\(782\) 1602.64i 0.0732867i
\(783\) 0 0
\(784\) −435.039 −0.0198177
\(785\) −13624.5 + 14337.6i −0.619463 + 0.651887i
\(786\) 0 0
\(787\) 22172.1i 1.00426i 0.864793 + 0.502128i \(0.167449\pi\)
−0.864793 + 0.502128i \(0.832551\pi\)
\(788\) 8566.64i 0.387276i
\(789\) 0 0
\(790\) 10096.7 10625.2i 0.454717 0.478518i
\(791\) 35140.7 1.57960