Properties

Label 405.4.b.f.244.1
Level $405$
Weight $4$
Character 405.244
Analytic conductor $23.896$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 91 x^{14} + 3268 x^{12} + 59128 x^{10} + 571975 x^{8} + 2881141 x^{6} + 6555196 x^{4} + 4069504 x^{2} + 614656\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{12}\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 244.1
Root \(-5.05435i\) of defining polynomial
Character \(\chi\) \(=\) 405.244
Dual form 405.4.b.f.244.16

$q$-expansion

\(f(q)\) \(=\) \(q-5.05435i q^{2} -17.5465 q^{4} +(7.77185 + 8.03731i) q^{5} -21.0117i q^{7} +48.2513i q^{8} +O(q^{10})\) \(q-5.05435i q^{2} -17.5465 q^{4} +(7.77185 + 8.03731i) q^{5} -21.0117i q^{7} +48.2513i q^{8} +(40.6234 - 39.2817i) q^{10} +28.5629 q^{11} -10.0704i q^{13} -106.201 q^{14} +103.507 q^{16} -82.7541i q^{17} -1.91981 q^{19} +(-136.369 - 141.026i) q^{20} -144.367i q^{22} -170.564i q^{23} +(-4.19662 + 124.930i) q^{25} -50.8993 q^{26} +368.682i q^{28} -256.428 q^{29} +48.0525 q^{31} -137.151i q^{32} -418.268 q^{34} +(168.878 - 163.300i) q^{35} -161.834i q^{37} +9.70338i q^{38} +(-387.810 + 375.002i) q^{40} -279.348 q^{41} +269.073i q^{43} -501.179 q^{44} -862.088 q^{46} -9.58841i q^{47} -98.4924 q^{49} +(631.438 + 21.2112i) q^{50} +176.700i q^{52} -35.7716i q^{53} +(221.987 + 229.569i) q^{55} +1013.84 q^{56} +1296.08i q^{58} -562.771 q^{59} -79.3242 q^{61} -242.874i q^{62} +134.846 q^{64} +(80.9389 - 78.2656i) q^{65} -466.752i q^{67} +1452.04i q^{68} +(-825.376 - 853.567i) q^{70} -316.854 q^{71} -633.515i q^{73} -817.968 q^{74} +33.6858 q^{76} -600.156i q^{77} +791.315 q^{79} +(804.442 + 831.918i) q^{80} +1411.92i q^{82} -228.078i q^{83} +(665.120 - 643.152i) q^{85} +1359.99 q^{86} +1378.20i q^{88} +53.9091 q^{89} -211.596 q^{91} +2992.79i q^{92} -48.4632 q^{94} +(-14.9205 - 15.4301i) q^{95} +96.6940i q^{97} +497.815i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 54 q^{4} + 3 q^{5} + O(q^{10}) \) \( 16 q - 54 q^{4} + 3 q^{5} - 10 q^{10} + 90 q^{11} - 102 q^{14} + 146 q^{16} - 4 q^{19} - 6 q^{20} - 71 q^{25} + 468 q^{26} - 516 q^{29} + 38 q^{31} - 212 q^{34} + 267 q^{35} - 44 q^{40} + 576 q^{41} - 1644 q^{44} - 290 q^{46} + 4 q^{49} + 558 q^{50} + 15 q^{55} + 2430 q^{56} - 2202 q^{59} + 20 q^{61} + 322 q^{64} + 339 q^{65} - 636 q^{70} + 2952 q^{71} - 4080 q^{74} - 396 q^{76} + 218 q^{79} - 1266 q^{80} + 704 q^{85} + 6108 q^{86} - 4074 q^{89} - 942 q^{91} + 1078 q^{94} - 1692 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.05435i 1.78698i −0.449080 0.893492i \(-0.648248\pi\)
0.449080 0.893492i \(-0.351752\pi\)
\(3\) 0 0
\(4\) −17.5465 −2.19331
\(5\) 7.77185 + 8.03731i 0.695136 + 0.718879i
\(6\) 0 0
\(7\) 21.0117i 1.13453i −0.823537 0.567263i \(-0.808002\pi\)
0.823537 0.567263i \(-0.191998\pi\)
\(8\) 48.2513i 2.13243i
\(9\) 0 0
\(10\) 40.6234 39.2817i 1.28462 1.24220i
\(11\) 28.5629 0.782914 0.391457 0.920196i \(-0.371971\pi\)
0.391457 + 0.920196i \(0.371971\pi\)
\(12\) 0 0
\(13\) 10.0704i 0.214848i −0.994213 0.107424i \(-0.965740\pi\)
0.994213 0.107424i \(-0.0342603\pi\)
\(14\) −106.201 −2.02738
\(15\) 0 0
\(16\) 103.507 1.61730
\(17\) 82.7541i 1.18064i −0.807171 0.590318i \(-0.799002\pi\)
0.807171 0.590318i \(-0.200998\pi\)
\(18\) 0 0
\(19\) −1.91981 −0.0231807 −0.0115904 0.999933i \(-0.503689\pi\)
−0.0115904 + 0.999933i \(0.503689\pi\)
\(20\) −136.369 141.026i −1.52465 1.57672i
\(21\) 0 0
\(22\) 144.367i 1.39905i
\(23\) 170.564i 1.54630i −0.634222 0.773151i \(-0.718679\pi\)
0.634222 0.773151i \(-0.281321\pi\)
\(24\) 0 0
\(25\) −4.19662 + 124.930i −0.0335730 + 0.999436i
\(26\) −50.8993 −0.383930
\(27\) 0 0
\(28\) 368.682i 2.48837i
\(29\) −256.428 −1.64199 −0.820993 0.570939i \(-0.806579\pi\)
−0.820993 + 0.570939i \(0.806579\pi\)
\(30\) 0 0
\(31\) 48.0525 0.278403 0.139201 0.990264i \(-0.455546\pi\)
0.139201 + 0.990264i \(0.455546\pi\)
\(32\) 137.151i 0.757660i
\(33\) 0 0
\(34\) −418.268 −2.10978
\(35\) 168.878 163.300i 0.815587 0.788650i
\(36\) 0 0
\(37\) 161.834i 0.719065i −0.933132 0.359533i \(-0.882936\pi\)
0.933132 0.359533i \(-0.117064\pi\)
\(38\) 9.70338i 0.0414236i
\(39\) 0 0
\(40\) −387.810 + 375.002i −1.53295 + 1.48232i
\(41\) −279.348 −1.06407 −0.532034 0.846723i \(-0.678572\pi\)
−0.532034 + 0.846723i \(0.678572\pi\)
\(42\) 0 0
\(43\) 269.073i 0.954261i 0.878833 + 0.477130i \(0.158323\pi\)
−0.878833 + 0.477130i \(0.841677\pi\)
\(44\) −501.179 −1.71717
\(45\) 0 0
\(46\) −862.088 −2.76322
\(47\) 9.58841i 0.0297577i −0.999889 0.0148789i \(-0.995264\pi\)
0.999889 0.0148789i \(-0.00473626\pi\)
\(48\) 0 0
\(49\) −98.4924 −0.287150
\(50\) 631.438 + 21.2112i 1.78598 + 0.0599944i
\(51\) 0 0
\(52\) 176.700i 0.471229i
\(53\) 35.7716i 0.0927095i −0.998925 0.0463547i \(-0.985240\pi\)
0.998925 0.0463547i \(-0.0147605\pi\)
\(54\) 0 0
\(55\) 221.987 + 229.569i 0.544231 + 0.562820i
\(56\) 1013.84 2.41929
\(57\) 0 0
\(58\) 1296.08i 2.93420i
\(59\) −562.771 −1.24181 −0.620903 0.783888i \(-0.713234\pi\)
−0.620903 + 0.783888i \(0.713234\pi\)
\(60\) 0 0
\(61\) −79.3242 −0.166499 −0.0832494 0.996529i \(-0.526530\pi\)
−0.0832494 + 0.996529i \(0.526530\pi\)
\(62\) 242.874i 0.497501i
\(63\) 0 0
\(64\) 134.846 0.263372
\(65\) 80.9389 78.2656i 0.154450 0.149349i
\(66\) 0 0
\(67\) 466.752i 0.851087i −0.904938 0.425544i \(-0.860083\pi\)
0.904938 0.425544i \(-0.139917\pi\)
\(68\) 1452.04i 2.58950i
\(69\) 0 0
\(70\) −825.376 853.567i −1.40930 1.45744i
\(71\) −316.854 −0.529628 −0.264814 0.964299i \(-0.585311\pi\)
−0.264814 + 0.964299i \(0.585311\pi\)
\(72\) 0 0
\(73\) 633.515i 1.01572i −0.861440 0.507859i \(-0.830437\pi\)
0.861440 0.507859i \(-0.169563\pi\)
\(74\) −817.968 −1.28496
\(75\) 0 0
\(76\) 33.6858 0.0508425
\(77\) 600.156i 0.888236i
\(78\) 0 0
\(79\) 791.315 1.12696 0.563481 0.826129i \(-0.309462\pi\)
0.563481 + 0.826129i \(0.309462\pi\)
\(80\) 804.442 + 831.918i 1.12424 + 1.16264i
\(81\) 0 0
\(82\) 1411.92i 1.90147i
\(83\) 228.078i 0.301624i −0.988562 0.150812i \(-0.951811\pi\)
0.988562 0.150812i \(-0.0481888\pi\)
\(84\) 0 0
\(85\) 665.120 643.152i 0.848734 0.820702i
\(86\) 1359.99 1.70525
\(87\) 0 0
\(88\) 1378.20i 1.66950i
\(89\) 53.9091 0.0642062 0.0321031 0.999485i \(-0.489780\pi\)
0.0321031 + 0.999485i \(0.489780\pi\)
\(90\) 0 0
\(91\) −211.596 −0.243751
\(92\) 2992.79i 3.39152i
\(93\) 0 0
\(94\) −48.4632 −0.0531766
\(95\) −14.9205 15.4301i −0.0161137 0.0166641i
\(96\) 0 0
\(97\) 96.6940i 0.101214i 0.998719 + 0.0506071i \(0.0161156\pi\)
−0.998719 + 0.0506071i \(0.983884\pi\)
\(98\) 497.815i 0.513132i
\(99\) 0 0
\(100\) 73.6360 2192.07i 0.0736360 2.19207i
\(101\) 1083.42 1.06737 0.533686 0.845683i \(-0.320807\pi\)
0.533686 + 0.845683i \(0.320807\pi\)
\(102\) 0 0
\(103\) 430.322i 0.411659i 0.978588 + 0.205830i \(0.0659892\pi\)
−0.978588 + 0.205830i \(0.934011\pi\)
\(104\) 485.909 0.458148
\(105\) 0 0
\(106\) −180.802 −0.165670
\(107\) 12.9348i 0.0116865i 0.999983 + 0.00584323i \(0.00185997\pi\)
−0.999983 + 0.00584323i \(0.998140\pi\)
\(108\) 0 0
\(109\) 20.1087 0.0176703 0.00883517 0.999961i \(-0.497188\pi\)
0.00883517 + 0.999961i \(0.497188\pi\)
\(110\) 1160.32 1122.00i 1.00575 0.972532i
\(111\) 0 0
\(112\) 2174.86i 1.83487i
\(113\) 1130.64i 0.941254i −0.882332 0.470627i \(-0.844028\pi\)
0.882332 0.470627i \(-0.155972\pi\)
\(114\) 0 0
\(115\) 1370.87 1325.59i 1.11160 1.07489i
\(116\) 4499.42 3.60138
\(117\) 0 0
\(118\) 2844.44i 2.21909i
\(119\) −1738.81 −1.33946
\(120\) 0 0
\(121\) −515.159 −0.387046
\(122\) 400.933i 0.297531i
\(123\) 0 0
\(124\) −843.152 −0.610623
\(125\) −1036.71 + 937.204i −0.741811 + 0.670609i
\(126\) 0 0
\(127\) 277.149i 0.193646i 0.995302 + 0.0968228i \(0.0308680\pi\)
−0.995302 + 0.0968228i \(0.969132\pi\)
\(128\) 1778.77i 1.22830i
\(129\) 0 0
\(130\) −395.582 409.094i −0.266883 0.275999i
\(131\) 502.599 0.335208 0.167604 0.985854i \(-0.446397\pi\)
0.167604 + 0.985854i \(0.446397\pi\)
\(132\) 0 0
\(133\) 40.3384i 0.0262991i
\(134\) −2359.13 −1.52088
\(135\) 0 0
\(136\) 3992.99 2.51762
\(137\) 2221.12i 1.38513i −0.721354 0.692566i \(-0.756480\pi\)
0.721354 0.692566i \(-0.243520\pi\)
\(138\) 0 0
\(139\) −2632.79 −1.60655 −0.803273 0.595611i \(-0.796910\pi\)
−0.803273 + 0.595611i \(0.796910\pi\)
\(140\) −2963.21 + 2865.34i −1.78883 + 1.72975i
\(141\) 0 0
\(142\) 1601.49i 0.946437i
\(143\) 287.640i 0.168208i
\(144\) 0 0
\(145\) −1992.92 2060.99i −1.14140 1.18039i
\(146\) −3202.01 −1.81507
\(147\) 0 0
\(148\) 2839.62i 1.57713i
\(149\) −2565.71 −1.41068 −0.705340 0.708869i \(-0.749206\pi\)
−0.705340 + 0.708869i \(0.749206\pi\)
\(150\) 0 0
\(151\) −1504.49 −0.810818 −0.405409 0.914135i \(-0.632871\pi\)
−0.405409 + 0.914135i \(0.632871\pi\)
\(152\) 92.6331i 0.0494312i
\(153\) 0 0
\(154\) −3033.40 −1.58726
\(155\) 373.457 + 386.213i 0.193528 + 0.200138i
\(156\) 0 0
\(157\) 1198.19i 0.609082i 0.952499 + 0.304541i \(0.0985031\pi\)
−0.952499 + 0.304541i \(0.901497\pi\)
\(158\) 3999.59i 2.01386i
\(159\) 0 0
\(160\) 1102.33 1065.92i 0.544666 0.526677i
\(161\) −3583.83 −1.75432
\(162\) 0 0
\(163\) 2204.91i 1.05952i 0.848148 + 0.529760i \(0.177718\pi\)
−0.848148 + 0.529760i \(0.822282\pi\)
\(164\) 4901.57 2.33383
\(165\) 0 0
\(166\) −1152.78 −0.538997
\(167\) 1132.11i 0.524584i −0.964989 0.262292i \(-0.915522\pi\)
0.964989 0.262292i \(-0.0844784\pi\)
\(168\) 0 0
\(169\) 2095.59 0.953840
\(170\) −3250.72 3361.75i −1.46658 1.51667i
\(171\) 0 0
\(172\) 4721.28i 2.09299i
\(173\) 1854.00i 0.814778i 0.913255 + 0.407389i \(0.133561\pi\)
−0.913255 + 0.407389i \(0.866439\pi\)
\(174\) 0 0
\(175\) 2624.98 + 88.1783i 1.13389 + 0.0380894i
\(176\) 2956.47 1.26620
\(177\) 0 0
\(178\) 272.476i 0.114735i
\(179\) 3205.81 1.33862 0.669312 0.742981i \(-0.266589\pi\)
0.669312 + 0.742981i \(0.266589\pi\)
\(180\) 0 0
\(181\) 2278.79 0.935806 0.467903 0.883780i \(-0.345010\pi\)
0.467903 + 0.883780i \(0.345010\pi\)
\(182\) 1069.48i 0.435579i
\(183\) 0 0
\(184\) 8229.91 3.29737
\(185\) 1300.71 1257.75i 0.516921 0.499848i
\(186\) 0 0
\(187\) 2363.70i 0.924336i
\(188\) 168.243i 0.0652679i
\(189\) 0 0
\(190\) −77.9890 + 75.4132i −0.0297785 + 0.0287950i
\(191\) −3388.65 −1.28374 −0.641870 0.766814i \(-0.721841\pi\)
−0.641870 + 0.766814i \(0.721841\pi\)
\(192\) 0 0
\(193\) 2778.22i 1.03617i −0.855329 0.518085i \(-0.826645\pi\)
0.855329 0.518085i \(-0.173355\pi\)
\(194\) 488.725 0.180868
\(195\) 0 0
\(196\) 1728.19 0.629808
\(197\) 2941.71i 1.06390i −0.846776 0.531950i \(-0.821459\pi\)
0.846776 0.531950i \(-0.178541\pi\)
\(198\) 0 0
\(199\) 4929.28 1.75592 0.877959 0.478737i \(-0.158905\pi\)
0.877959 + 0.478737i \(0.158905\pi\)
\(200\) −6028.01 202.492i −2.13122 0.0715919i
\(201\) 0 0
\(202\) 5475.99i 1.90737i
\(203\) 5388.00i 1.86288i
\(204\) 0 0
\(205\) −2171.05 2245.20i −0.739672 0.764936i
\(206\) 2175.00 0.735628
\(207\) 0 0
\(208\) 1042.36i 0.347474i
\(209\) −54.8353 −0.0181485
\(210\) 0 0
\(211\) 5418.51 1.76789 0.883947 0.467587i \(-0.154877\pi\)
0.883947 + 0.467587i \(0.154877\pi\)
\(212\) 627.665i 0.203341i
\(213\) 0 0
\(214\) 65.3768 0.0208835
\(215\) −2162.62 + 2091.19i −0.685998 + 0.663341i
\(216\) 0 0
\(217\) 1009.67i 0.315855i
\(218\) 101.637i 0.0315766i
\(219\) 0 0
\(220\) −3895.09 4028.13i −1.19367 1.23444i
\(221\) −833.366 −0.253657
\(222\) 0 0
\(223\) 4084.35i 1.22650i 0.789891 + 0.613248i \(0.210137\pi\)
−0.789891 + 0.613248i \(0.789863\pi\)
\(224\) −2881.78 −0.859586
\(225\) 0 0
\(226\) −5714.65 −1.68201
\(227\) 221.829i 0.0648604i −0.999474 0.0324302i \(-0.989675\pi\)
0.999474 0.0324302i \(-0.0103247\pi\)
\(228\) 0 0
\(229\) 1598.07 0.461152 0.230576 0.973054i \(-0.425939\pi\)
0.230576 + 0.973054i \(0.425939\pi\)
\(230\) −6700.02 6928.87i −1.92081 1.98642i
\(231\) 0 0
\(232\) 12373.0i 3.50141i
\(233\) 6620.40i 1.86144i −0.365727 0.930722i \(-0.619180\pi\)
0.365727 0.930722i \(-0.380820\pi\)
\(234\) 0 0
\(235\) 77.0650 74.5197i 0.0213922 0.0206857i
\(236\) 9874.65 2.72366
\(237\) 0 0
\(238\) 8788.53i 2.39360i
\(239\) 3557.20 0.962744 0.481372 0.876516i \(-0.340139\pi\)
0.481372 + 0.876516i \(0.340139\pi\)
\(240\) 0 0
\(241\) 2967.34 0.793126 0.396563 0.918007i \(-0.370203\pi\)
0.396563 + 0.918007i \(0.370203\pi\)
\(242\) 2603.79i 0.691645i
\(243\) 0 0
\(244\) 1391.86 0.365183
\(245\) −765.468 791.613i −0.199608 0.206426i
\(246\) 0 0
\(247\) 19.3332i 0.00498034i
\(248\) 2318.59i 0.593673i
\(249\) 0 0
\(250\) 4736.96 + 5239.91i 1.19837 + 1.32560i
\(251\) 903.562 0.227220 0.113610 0.993525i \(-0.463759\pi\)
0.113610 + 0.993525i \(0.463759\pi\)
\(252\) 0 0
\(253\) 4871.79i 1.21062i
\(254\) 1400.81 0.346041
\(255\) 0 0
\(256\) −7911.76 −1.93158
\(257\) 1484.49i 0.360312i −0.983638 0.180156i \(-0.942340\pi\)
0.983638 0.180156i \(-0.0576602\pi\)
\(258\) 0 0
\(259\) −3400.42 −0.815799
\(260\) −1420.19 + 1373.29i −0.338756 + 0.327568i
\(261\) 0 0
\(262\) 2540.31i 0.599011i
\(263\) 2716.65i 0.636943i −0.947932 0.318472i \(-0.896830\pi\)
0.947932 0.318472i \(-0.103170\pi\)
\(264\) 0 0
\(265\) 287.507 278.011i 0.0666469 0.0644456i
\(266\) 203.885 0.0469961
\(267\) 0 0
\(268\) 8189.85i 1.86670i
\(269\) 7492.51 1.69824 0.849120 0.528201i \(-0.177133\pi\)
0.849120 + 0.528201i \(0.177133\pi\)
\(270\) 0 0
\(271\) 2013.02 0.451226 0.225613 0.974217i \(-0.427561\pi\)
0.225613 + 0.974217i \(0.427561\pi\)
\(272\) 8565.63i 1.90944i
\(273\) 0 0
\(274\) −11226.3 −2.47521
\(275\) −119.868 + 3568.35i −0.0262848 + 0.782472i
\(276\) 0 0
\(277\) 3570.97i 0.774580i 0.921958 + 0.387290i \(0.126589\pi\)
−0.921958 + 0.387290i \(0.873411\pi\)
\(278\) 13307.0i 2.87087i
\(279\) 0 0
\(280\) 7879.43 + 8148.56i 1.68174 + 1.73918i
\(281\) 6761.40 1.43541 0.717707 0.696346i \(-0.245192\pi\)
0.717707 + 0.696346i \(0.245192\pi\)
\(282\) 0 0
\(283\) 4012.29i 0.842776i −0.906880 0.421388i \(-0.861543\pi\)
0.906880 0.421388i \(-0.138457\pi\)
\(284\) 5559.66 1.16164
\(285\) 0 0
\(286\) −1453.83 −0.300584
\(287\) 5869.58i 1.20721i
\(288\) 0 0
\(289\) −1935.23 −0.393901
\(290\) −10417.0 + 10072.9i −2.10933 + 2.03967i
\(291\) 0 0
\(292\) 11116.0i 2.22778i
\(293\) 2446.05i 0.487712i 0.969811 + 0.243856i \(0.0784125\pi\)
−0.969811 + 0.243856i \(0.921588\pi\)
\(294\) 0 0
\(295\) −4373.77 4523.16i −0.863223 0.892707i
\(296\) 7808.72 1.53335
\(297\) 0 0
\(298\) 12968.0i 2.52086i
\(299\) −1717.64 −0.332220
\(300\) 0 0
\(301\) 5653.68 1.08263
\(302\) 7604.22i 1.44892i
\(303\) 0 0
\(304\) −198.714 −0.0374902
\(305\) −616.496 637.553i −0.115739 0.119692i
\(306\) 0 0
\(307\) 5539.06i 1.02974i 0.857268 + 0.514871i \(0.172160\pi\)
−0.857268 + 0.514871i \(0.827840\pi\)
\(308\) 10530.6i 1.94818i
\(309\) 0 0
\(310\) 1952.05 1887.58i 0.357643 0.345831i
\(311\) 3525.20 0.642752 0.321376 0.946952i \(-0.395855\pi\)
0.321376 + 0.946952i \(0.395855\pi\)
\(312\) 0 0
\(313\) 6910.59i 1.24795i −0.781443 0.623977i \(-0.785516\pi\)
0.781443 0.623977i \(-0.214484\pi\)
\(314\) 6056.07 1.08842
\(315\) 0 0
\(316\) −13884.8 −2.47177
\(317\) 4209.66i 0.745861i 0.927859 + 0.372930i \(0.121647\pi\)
−0.927859 + 0.372930i \(0.878353\pi\)
\(318\) 0 0
\(319\) −7324.35 −1.28553
\(320\) 1048.01 + 1083.80i 0.183079 + 0.189332i
\(321\) 0 0
\(322\) 18114.0i 3.13494i
\(323\) 158.872i 0.0273680i
\(324\) 0 0
\(325\) 1258.09 + 42.2617i 0.214727 + 0.00721310i
\(326\) 11144.4 1.89334
\(327\) 0 0
\(328\) 13478.9i 2.26905i
\(329\) −201.469 −0.0337609
\(330\) 0 0
\(331\) −1696.24 −0.281673 −0.140836 0.990033i \(-0.544979\pi\)
−0.140836 + 0.990033i \(0.544979\pi\)
\(332\) 4001.96i 0.661554i
\(333\) 0 0
\(334\) −5722.10 −0.937423
\(335\) 3751.43 3627.53i 0.611828 0.591621i
\(336\) 0 0
\(337\) 7205.22i 1.16467i 0.812950 + 0.582334i \(0.197860\pi\)
−0.812950 + 0.582334i \(0.802140\pi\)
\(338\) 10591.8i 1.70450i
\(339\) 0 0
\(340\) −11670.5 + 11285.1i −1.86154 + 1.80005i
\(341\) 1372.52 0.217965
\(342\) 0 0
\(343\) 5137.53i 0.808747i
\(344\) −12983.1 −2.03489
\(345\) 0 0
\(346\) 9370.75 1.45600
\(347\) 6496.64i 1.00507i 0.864558 + 0.502533i \(0.167599\pi\)
−0.864558 + 0.502533i \(0.832401\pi\)
\(348\) 0 0
\(349\) 6464.51 0.991510 0.495755 0.868462i \(-0.334891\pi\)
0.495755 + 0.868462i \(0.334891\pi\)
\(350\) 445.684 13267.6i 0.0680652 2.02624i
\(351\) 0 0
\(352\) 3917.44i 0.593183i
\(353\) 11849.0i 1.78657i 0.449493 + 0.893284i \(0.351605\pi\)
−0.449493 + 0.893284i \(0.648395\pi\)
\(354\) 0 0
\(355\) −2462.54 2546.65i −0.368163 0.380738i
\(356\) −945.915 −0.140824
\(357\) 0 0
\(358\) 16203.3i 2.39210i
\(359\) −11702.9 −1.72048 −0.860242 0.509886i \(-0.829688\pi\)
−0.860242 + 0.509886i \(0.829688\pi\)
\(360\) 0 0
\(361\) −6855.31 −0.999463
\(362\) 11517.8i 1.67227i
\(363\) 0 0
\(364\) 3712.77 0.534621
\(365\) 5091.76 4923.59i 0.730177 0.706061i
\(366\) 0 0
\(367\) 2580.51i 0.367034i −0.983017 0.183517i \(-0.941252\pi\)
0.983017 0.183517i \(-0.0587483\pi\)
\(368\) 17654.5i 2.50083i
\(369\) 0 0
\(370\) −6357.13 6574.26i −0.893220 0.923729i
\(371\) −751.622 −0.105181
\(372\) 0 0
\(373\) 4499.56i 0.624607i −0.949982 0.312304i \(-0.898899\pi\)
0.949982 0.312304i \(-0.101101\pi\)
\(374\) −11947.0 −1.65177
\(375\) 0 0
\(376\) 462.653 0.0634561
\(377\) 2582.34i 0.352777i
\(378\) 0 0
\(379\) 5888.24 0.798044 0.399022 0.916941i \(-0.369350\pi\)
0.399022 + 0.916941i \(0.369350\pi\)
\(380\) 261.801 + 270.743i 0.0353424 + 0.0365496i
\(381\) 0 0
\(382\) 17127.4i 2.29402i
\(383\) 8020.16i 1.07000i −0.844851 0.535001i \(-0.820311\pi\)
0.844851 0.535001i \(-0.179689\pi\)
\(384\) 0 0
\(385\) 4823.64 4664.33i 0.638534 0.617444i
\(386\) −14042.1 −1.85162
\(387\) 0 0
\(388\) 1696.64i 0.221994i
\(389\) −167.380 −0.0218162 −0.0109081 0.999941i \(-0.503472\pi\)
−0.0109081 + 0.999941i \(0.503472\pi\)
\(390\) 0 0
\(391\) −14114.8 −1.82562
\(392\) 4752.38i 0.612325i
\(393\) 0 0
\(394\) −14868.4 −1.90117
\(395\) 6149.99 + 6360.04i 0.783391 + 0.810148i
\(396\) 0 0
\(397\) 5893.09i 0.745002i 0.928032 + 0.372501i \(0.121500\pi\)
−0.928032 + 0.372501i \(0.878500\pi\)
\(398\) 24914.3i 3.13779i
\(399\) 0 0
\(400\) −434.380 + 12931.1i −0.0542975 + 1.61639i
\(401\) 2632.86 0.327877 0.163938 0.986471i \(-0.447580\pi\)
0.163938 + 0.986471i \(0.447580\pi\)
\(402\) 0 0
\(403\) 483.908i 0.0598143i
\(404\) −19010.2 −2.34108
\(405\) 0 0
\(406\) 27232.9 3.32893
\(407\) 4622.47i 0.562966i
\(408\) 0 0
\(409\) 13690.3 1.65512 0.827558 0.561381i \(-0.189730\pi\)
0.827558 + 0.561381i \(0.189730\pi\)
\(410\) −11348.1 + 10973.3i −1.36693 + 1.32178i
\(411\) 0 0
\(412\) 7550.64i 0.902896i
\(413\) 11824.8i 1.40886i
\(414\) 0 0
\(415\) 1833.13 1772.59i 0.216831 0.209669i
\(416\) −1381.17 −0.162782
\(417\) 0 0
\(418\) 277.157i 0.0324311i
\(419\) 258.973 0.0301949 0.0150974 0.999886i \(-0.495194\pi\)
0.0150974 + 0.999886i \(0.495194\pi\)
\(420\) 0 0
\(421\) 13643.1 1.57939 0.789696 0.613499i \(-0.210238\pi\)
0.789696 + 0.613499i \(0.210238\pi\)
\(422\) 27387.1i 3.15920i
\(423\) 0 0
\(424\) 1726.02 0.197696
\(425\) 10338.4 + 347.288i 1.17997 + 0.0396375i
\(426\) 0 0
\(427\) 1666.74i 0.188897i
\(428\) 226.959i 0.0256320i
\(429\) 0 0
\(430\) 10569.6 + 10930.6i 1.18538 + 1.22587i
\(431\) 13258.5 1.48176 0.740881 0.671636i \(-0.234408\pi\)
0.740881 + 0.671636i \(0.234408\pi\)
\(432\) 0 0
\(433\) 14980.2i 1.66259i −0.555832 0.831295i \(-0.687600\pi\)
0.555832 0.831295i \(-0.312400\pi\)
\(434\) −5103.20 −0.564428
\(435\) 0 0
\(436\) −352.837 −0.0387565
\(437\) 327.449i 0.0358444i
\(438\) 0 0
\(439\) 7362.59 0.800450 0.400225 0.916417i \(-0.368932\pi\)
0.400225 + 0.916417i \(0.368932\pi\)
\(440\) −11077.0 + 10711.2i −1.20017 + 1.16053i
\(441\) 0 0
\(442\) 4212.13i 0.453282i
\(443\) 1587.81i 0.170291i −0.996369 0.0851456i \(-0.972864\pi\)
0.996369 0.0851456i \(-0.0271355\pi\)
\(444\) 0 0
\(445\) 418.974 + 433.284i 0.0446320 + 0.0461565i
\(446\) 20643.8 2.19173
\(447\) 0 0
\(448\) 2833.35i 0.298802i
\(449\) −7331.63 −0.770604 −0.385302 0.922791i \(-0.625903\pi\)
−0.385302 + 0.922791i \(0.625903\pi\)
\(450\) 0 0
\(451\) −7978.99 −0.833074
\(452\) 19838.8i 2.06446i
\(453\) 0 0
\(454\) −1121.20 −0.115905
\(455\) −1644.50 1700.67i −0.169440 0.175227i
\(456\) 0 0
\(457\) 6296.83i 0.644537i 0.946648 + 0.322268i \(0.104445\pi\)
−0.946648 + 0.322268i \(0.895555\pi\)
\(458\) 8077.23i 0.824070i
\(459\) 0 0
\(460\) −24054.0 + 23259.5i −2.43809 + 2.35757i
\(461\) −6335.46 −0.640068 −0.320034 0.947406i \(-0.603694\pi\)
−0.320034 + 0.947406i \(0.603694\pi\)
\(462\) 0 0
\(463\) 2295.72i 0.230435i 0.993340 + 0.115217i \(0.0367565\pi\)
−0.993340 + 0.115217i \(0.963244\pi\)
\(464\) −26542.2 −2.65558
\(465\) 0 0
\(466\) −33461.8 −3.32637
\(467\) 6182.82i 0.612648i 0.951927 + 0.306324i \(0.0990991\pi\)
−0.951927 + 0.306324i \(0.900901\pi\)
\(468\) 0 0
\(469\) −9807.26 −0.965581
\(470\) −376.649 389.514i −0.0369649 0.0382275i
\(471\) 0 0
\(472\) 27154.4i 2.64806i
\(473\) 7685.51i 0.747104i
\(474\) 0 0
\(475\) 8.05671 239.841i 0.000778246 0.0231677i
\(476\) 30509.9 2.93786
\(477\) 0 0
\(478\) 17979.3i 1.72041i
\(479\) 3898.36 0.371860 0.185930 0.982563i \(-0.440470\pi\)
0.185930 + 0.982563i \(0.440470\pi\)
\(480\) 0 0
\(481\) −1629.74 −0.154490
\(482\) 14998.0i 1.41730i
\(483\) 0 0
\(484\) 9039.22 0.848913
\(485\) −777.159 + 751.491i −0.0727608 + 0.0703576i
\(486\) 0 0
\(487\) 14776.3i 1.37490i 0.726232 + 0.687450i \(0.241270\pi\)
−0.726232 + 0.687450i \(0.758730\pi\)
\(488\) 3827.49i 0.355046i
\(489\) 0 0
\(490\) −4001.09 + 3868.95i −0.368879 + 0.356696i
\(491\) −3637.24 −0.334310 −0.167155 0.985931i \(-0.553458\pi\)
−0.167155 + 0.985931i \(0.553458\pi\)
\(492\) 0 0
\(493\) 21220.5i 1.93859i
\(494\) 97.7169 0.00889978
\(495\) 0 0
\(496\) 4973.77 0.450260
\(497\) 6657.64i 0.600877i
\(498\) 0 0
\(499\) 3257.75 0.292258 0.146129 0.989266i \(-0.453319\pi\)
0.146129 + 0.989266i \(0.453319\pi\)
\(500\) 18190.7 16444.6i 1.62702 1.47085i
\(501\) 0 0
\(502\) 4566.92i 0.406039i
\(503\) 20857.4i 1.84888i −0.381327 0.924440i \(-0.624533\pi\)
0.381327 0.924440i \(-0.375467\pi\)
\(504\) 0 0
\(505\) 8420.19 + 8707.79i 0.741968 + 0.767310i
\(506\) −24623.8 −2.16336
\(507\) 0 0
\(508\) 4862.99i 0.424725i
\(509\) −19907.5 −1.73356 −0.866781 0.498688i \(-0.833815\pi\)
−0.866781 + 0.498688i \(0.833815\pi\)
\(510\) 0 0
\(511\) −13311.2 −1.15236
\(512\) 25758.7i 2.22340i
\(513\) 0 0
\(514\) −7503.15 −0.643871
\(515\) −3458.63 + 3344.40i −0.295933 + 0.286159i
\(516\) 0 0
\(517\) 273.873i 0.0232977i
\(518\) 17186.9i 1.45782i
\(519\) 0 0
\(520\) 3776.42 + 3905.40i 0.318475 + 0.329352i
\(521\) 4264.69 0.358617 0.179308 0.983793i \(-0.442614\pi\)
0.179308 + 0.983793i \(0.442614\pi\)
\(522\) 0 0
\(523\) 3687.86i 0.308334i 0.988045 + 0.154167i \(0.0492694\pi\)
−0.988045 + 0.154167i \(0.950731\pi\)
\(524\) −8818.84 −0.735215
\(525\) 0 0
\(526\) −13730.9 −1.13821
\(527\) 3976.54i 0.328692i
\(528\) 0 0
\(529\) −16924.9 −1.39105
\(530\) −1405.17 1453.16i −0.115163 0.119097i
\(531\) 0 0
\(532\) 707.798i 0.0576822i
\(533\) 2813.14i 0.228613i
\(534\) 0 0
\(535\) −103.961 + 100.527i −0.00840114 + 0.00812367i
\(536\) 22521.4 1.81488
\(537\) 0 0
\(538\) 37869.8i 3.03473i
\(539\) −2813.23 −0.224813
\(540\) 0 0
\(541\) 21551.0 1.71266 0.856331 0.516428i \(-0.172739\pi\)
0.856331 + 0.516428i \(0.172739\pi\)
\(542\) 10174.5i 0.806334i
\(543\) 0 0
\(544\) −11349.8 −0.894521
\(545\) 156.282 + 161.620i 0.0122833 + 0.0127028i
\(546\) 0 0
\(547\) 19907.0i 1.55606i 0.628229 + 0.778029i \(0.283780\pi\)
−0.628229 + 0.778029i \(0.716220\pi\)
\(548\) 38972.8i 3.03802i
\(549\) 0 0
\(550\) 18035.7 + 605.855i 1.39826 + 0.0469704i
\(551\) 492.293 0.0380624
\(552\) 0 0
\(553\) 16626.9i 1.27857i
\(554\) 18048.9 1.38416
\(555\) 0 0
\(556\) 46196.1 3.52365
\(557\) 1747.00i 0.132896i 0.997790 + 0.0664479i \(0.0211666\pi\)
−0.997790 + 0.0664479i \(0.978833\pi\)
\(558\) 0 0
\(559\) 2709.67 0.205021
\(560\) 17480.0 16902.7i 1.31905 1.27548i
\(561\) 0 0
\(562\) 34174.5i 2.56506i
\(563\) 2122.04i 0.158851i 0.996841 + 0.0794257i \(0.0253086\pi\)
−0.996841 + 0.0794257i \(0.974691\pi\)
\(564\) 0 0
\(565\) 9087.30 8787.17i 0.676647 0.654299i
\(566\) −20279.5 −1.50603
\(567\) 0 0
\(568\) 15288.6i 1.12939i
\(569\) 10753.1 0.792254 0.396127 0.918196i \(-0.370354\pi\)
0.396127 + 0.918196i \(0.370354\pi\)
\(570\) 0 0
\(571\) 725.745 0.0531900 0.0265950 0.999646i \(-0.491534\pi\)
0.0265950 + 0.999646i \(0.491534\pi\)
\(572\) 5047.07i 0.368931i
\(573\) 0 0
\(574\) 29666.9 2.15727
\(575\) 21308.4 + 715.791i 1.54543 + 0.0519140i
\(576\) 0 0
\(577\) 23839.3i 1.72001i −0.510290 0.860003i \(-0.670462\pi\)
0.510290 0.860003i \(-0.329538\pi\)
\(578\) 9781.36i 0.703894i
\(579\) 0 0
\(580\) 34968.8 + 36163.2i 2.50345 + 2.58896i
\(581\) −4792.30 −0.342200
\(582\) 0 0
\(583\) 1021.74i 0.0725835i
\(584\) 30567.9 2.16594
\(585\) 0 0
\(586\) 12363.2 0.871534
\(587\) 7777.68i 0.546881i 0.961889 + 0.273440i \(0.0881616\pi\)
−0.961889 + 0.273440i \(0.911838\pi\)
\(588\) 0 0
\(589\) −92.2515 −0.00645357
\(590\) −22861.7 + 22106.6i −1.59525 + 1.54257i
\(591\) 0 0
\(592\) 16751.0i 1.16294i
\(593\) 6677.79i 0.462435i −0.972902 0.231217i \(-0.925729\pi\)
0.972902 0.231217i \(-0.0742709\pi\)
\(594\) 0 0
\(595\) −13513.7 13975.3i −0.931108 0.962911i
\(596\) 45019.2 3.09406
\(597\) 0 0
\(598\) 8681.57i 0.593672i
\(599\) 12946.9 0.883132 0.441566 0.897229i \(-0.354423\pi\)
0.441566 + 0.897229i \(0.354423\pi\)
\(600\) 0 0
\(601\) −4366.09 −0.296334 −0.148167 0.988962i \(-0.547337\pi\)
−0.148167 + 0.988962i \(0.547337\pi\)
\(602\) 28575.7i 1.93465i
\(603\) 0 0
\(604\) 26398.5 1.77838
\(605\) −4003.74 4140.49i −0.269050 0.278239i
\(606\) 0 0
\(607\) 24177.5i 1.61669i 0.588706 + 0.808347i \(0.299638\pi\)
−0.588706 + 0.808347i \(0.700362\pi\)
\(608\) 263.304i 0.0175631i
\(609\) 0 0
\(610\) −3222.42 + 3115.99i −0.213888 + 0.206824i
\(611\) −96.5591 −0.00639339
\(612\) 0 0
\(613\) 7772.63i 0.512127i 0.966660 + 0.256063i \(0.0824256\pi\)
−0.966660 + 0.256063i \(0.917574\pi\)
\(614\) 27996.3 1.84013
\(615\) 0 0
\(616\) 28958.3 1.89410
\(617\) 626.260i 0.0408627i 0.999791 + 0.0204313i \(0.00650395\pi\)
−0.999791 + 0.0204313i \(0.993496\pi\)
\(618\) 0 0
\(619\) −22835.1 −1.48275 −0.741373 0.671093i \(-0.765825\pi\)
−0.741373 + 0.671093i \(0.765825\pi\)
\(620\) −6552.85 6776.67i −0.424466 0.438964i
\(621\) 0 0
\(622\) 17817.6i 1.14859i
\(623\) 1132.72i 0.0728436i
\(624\) 0 0
\(625\) −15589.8 1048.56i −0.997746 0.0671081i
\(626\) −34928.6 −2.23007
\(627\) 0 0
\(628\) 21024.0i 1.33591i
\(629\) −13392.5 −0.848954
\(630\) 0 0
\(631\) −26862.1 −1.69471 −0.847355 0.531027i \(-0.821806\pi\)
−0.847355 + 0.531027i \(0.821806\pi\)
\(632\) 38182.0i 2.40316i
\(633\) 0 0
\(634\) 21277.1 1.33284
\(635\) −2227.53 + 2153.96i −0.139208 + 0.134610i
\(636\) 0 0
\(637\) 991.857i 0.0616936i
\(638\) 37019.8i 2.29723i
\(639\) 0 0
\(640\) 14296.5 13824.3i 0.883000 0.853836i
\(641\) −8609.98 −0.530536 −0.265268 0.964175i \(-0.585460\pi\)
−0.265268 + 0.964175i \(0.585460\pi\)
\(642\) 0 0
\(643\) 17173.4i 1.05327i −0.850091 0.526636i \(-0.823453\pi\)
0.850091 0.526636i \(-0.176547\pi\)
\(644\) 62883.6 3.84777
\(645\) 0 0
\(646\) 802.994 0.0489062
\(647\) 1258.94i 0.0764978i 0.999268 + 0.0382489i \(0.0121780\pi\)
−0.999268 + 0.0382489i \(0.987822\pi\)
\(648\) 0 0
\(649\) −16074.4 −0.972226
\(650\) 213.605 6358.83i 0.0128897 0.383714i
\(651\) 0 0
\(652\) 38688.4i 2.32386i
\(653\) 2540.41i 0.152242i 0.997099 + 0.0761209i \(0.0242535\pi\)
−0.997099 + 0.0761209i \(0.975746\pi\)
\(654\) 0 0
\(655\) 3906.12 + 4039.54i 0.233015 + 0.240974i
\(656\) −28914.5 −1.72092
\(657\) 0 0
\(658\) 1018.29i 0.0603302i
\(659\) −26199.8 −1.54871 −0.774356 0.632750i \(-0.781926\pi\)
−0.774356 + 0.632750i \(0.781926\pi\)
\(660\) 0 0
\(661\) −5443.77 −0.320330 −0.160165 0.987090i \(-0.551203\pi\)
−0.160165 + 0.987090i \(0.551203\pi\)
\(662\) 8573.39i 0.503345i
\(663\) 0 0
\(664\) 11005.0 0.643190
\(665\) −324.212 + 313.504i −0.0189059 + 0.0182815i
\(666\) 0 0
\(667\) 43737.3i 2.53901i
\(668\) 19864.6i 1.15058i
\(669\) 0 0
\(670\) −18334.8 18961.0i −1.05722 1.09333i
\(671\) −2265.73 −0.130354
\(672\) 0 0
\(673\) 16820.8i 0.963440i −0.876325 0.481720i \(-0.840012\pi\)
0.876325 0.481720i \(-0.159988\pi\)
\(674\) 36417.7 2.08124
\(675\) 0 0
\(676\) −36770.2 −2.09207
\(677\) 23199.5i 1.31703i −0.752568 0.658515i \(-0.771185\pi\)
0.752568 0.658515i \(-0.228815\pi\)
\(678\) 0 0
\(679\) 2031.71 0.114830
\(680\) 31032.9 + 32092.9i 1.75009 + 1.80986i
\(681\) 0 0
\(682\) 6937.20i 0.389500i
\(683\) 24902.4i 1.39512i −0.716528 0.697558i \(-0.754270\pi\)
0.716528 0.697558i \(-0.245730\pi\)
\(684\) 0 0
\(685\) 17851.8 17262.2i 0.995742 0.962855i
\(686\) −25966.9 −1.44522
\(687\) 0 0
\(688\) 27850.9i 1.54332i
\(689\) −360.234 −0.0199185
\(690\) 0 0
\(691\) 8467.45 0.466161 0.233080 0.972457i \(-0.425119\pi\)
0.233080 + 0.972457i \(0.425119\pi\)
\(692\) 32531.1i 1.78706i
\(693\) 0 0
\(694\) 32836.3 1.79604
\(695\) −20461.6 21160.5i −1.11677 1.15491i
\(696\) 0 0
\(697\) 23117.2i 1.25628i
\(698\) 32673.9i 1.77181i
\(699\) 0 0
\(700\) −46059.2 1547.22i −2.48696 0.0835419i
\(701\) −5972.30 −0.321784 −0.160892 0.986972i \(-0.551437\pi\)
−0.160892 + 0.986972i \(0.551437\pi\)
\(702\) 0 0
\(703\) 310.691i 0.0166685i
\(704\) 3851.61 0.206197
\(705\) 0 0
\(706\) 59889.0 3.19257
\(707\) 22764.6i 1.21096i
\(708\) 0 0
\(709\) 7549.78 0.399913 0.199956 0.979805i \(-0.435920\pi\)
0.199956 + 0.979805i \(0.435920\pi\)
\(710\) −12871.7 + 12446.5i −0.680373 + 0.657902i
\(711\) 0 0
\(712\) 2601.18i 0.136915i
\(713\) 8196.00i 0.430495i
\(714\) 0 0
\(715\) 2311.85 2235.50i 0.120921 0.116927i
\(716\) −56250.7 −2.93602
\(717\) 0 0
\(718\) 59150.4i 3.07448i
\(719\) −31449.7 −1.63126 −0.815631 0.578573i \(-0.803610\pi\)
−0.815631 + 0.578573i \(0.803610\pi\)
\(720\) 0 0
\(721\) 9041.81 0.467038
\(722\) 34649.2i 1.78602i
\(723\) 0 0
\(724\) −39984.7 −2.05251
\(725\) 1076.13 32035.5i 0.0551264 1.64106i
\(726\) 0 0
\(727\) 7962.03i 0.406183i 0.979160 + 0.203092i \(0.0650990\pi\)
−0.979160 + 0.203092i \(0.934901\pi\)
\(728\) 10209.8i 0.519780i
\(729\) 0 0
\(730\) −24885.5 25735.5i −1.26172 1.30481i
\(731\) 22266.9 1.12663
\(732\) 0 0
\(733\) 11003.2i 0.554451i 0.960805 + 0.277226i \(0.0894150\pi\)
−0.960805 + 0.277226i \(0.910585\pi\)
\(734\) −13042.8 −0.655884
\(735\) 0 0
\(736\) −23393.0 −1.17157
\(737\) 13331.8i 0.666328i
\(738\) 0 0
\(739\) −24719.1 −1.23046 −0.615228 0.788349i \(-0.710936\pi\)
−0.615228 + 0.788349i \(0.710936\pi\)
\(740\) −22822.9 + 22069.1i −1.13377 + 1.09632i
\(741\) 0 0
\(742\) 3798.96i 0.187957i
\(743\) 13326.8i 0.658024i −0.944326 0.329012i \(-0.893284\pi\)
0.944326 0.329012i \(-0.106716\pi\)
\(744\) 0 0
\(745\) −19940.3 20621.4i −0.980614 1.01411i
\(746\) −22742.4 −1.11616
\(747\) 0 0
\(748\) 41474.6i 2.02735i
\(749\) 271.781 0.0132586
\(750\) 0 0
\(751\) −23800.9 −1.15647 −0.578234 0.815871i \(-0.696258\pi\)
−0.578234 + 0.815871i \(0.696258\pi\)
\(752\) 992.468i 0.0481271i
\(753\) 0 0
\(754\) 13052.0 0.630407
\(755\) −11692.7 12092.0i −0.563629 0.582880i
\(756\) 0 0
\(757\) 20867.5i 1.00191i 0.865474 + 0.500953i \(0.167017\pi\)
−0.865474 + 0.500953i \(0.832983\pi\)
\(758\) 29761.2i 1.42609i
\(759\) 0 0
\(760\) 744.521 719.931i 0.0355350 0.0343614i
\(761\) 15487.5 0.737742 0.368871 0.929481i \(-0.379744\pi\)
0.368871 + 0.929481i \(0.379744\pi\)
\(762\) 0 0
\(763\) 422.519i 0.0200475i
\(764\) 59458.9 2.81564
\(765\) 0 0
\(766\) −40536.7 −1.91208
\(767\) 5667.33i 0.266800i
\(768\) 0 0
\(769\) 18468.0 0.866024 0.433012 0.901388i \(-0.357451\pi\)
0.433012 + 0.901388i \(0.357451\pi\)
\(770\) −23575.2 24380.4i −1.10336 1.14105i
\(771\) 0 0
\(772\) 48748.0i 2.27264i
\(773\) 15379.9i 0.715621i 0.933794 + 0.357810i \(0.116477\pi\)
−0.933794 + 0.357810i \(0.883523\pi\)
\(774\) 0 0
\(775\) −201.658 + 6003.17i −0.00934681 + 0.278246i
\(776\) −4665.61 −0.215832
\(777\) 0 0
\(778\) 845.997i 0.0389852i
\(779\) 536.294 0.0246659
\(780\) 0 0
\(781\) −9050.27 −0.414653
\(782\) 71341.3i 3.26235i
\(783\) 0 0
\(784\) −10194.7 −0.464407
\(785\) −9630.21 + 9312.15i −0.437856 + 0.423395i
\(786\) 0 0
\(787\) 38251.8i 1.73257i 0.499552 + 0.866284i \(0.333498\pi\)
−0.499552 + 0.866284i \(0.666502\pi\)
\(788\) 51616.7i 2.33346i
\(789\) 0 0
\(790\) 32145.9 31084.2i 1.44772 1.39991i
\(791\) −23756.7 −1.06788
\(792\) 0 0
\(793\) 798.826i 0.0357720i
\(794\) 29785.8 1.33131