Properties

Label 3150.2.bf.d.1151.4
Level 3150
Weight 2
Character 3150.1151
Analytic conductor 25.153
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3150.bf (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1151.4
Character \(\chi\) \(=\) 3150.1151
Dual form 3150.2.bf.d.1601.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.397202 - 2.61577i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.397202 - 2.61577i) q^{7} +1.00000i q^{8} +(0.429853 + 0.248176i) q^{11} -2.74440i q^{13} +(1.65187 + 2.06672i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.82992 - 3.16952i) q^{17} +(3.12125 - 1.80205i) q^{19} -0.496352 q^{22} +(5.56351 - 3.21210i) q^{23} +(1.37220 + 2.37672i) q^{26} +(-2.46392 - 0.963896i) q^{28} +8.87959i q^{29} +(-6.90736 - 3.98797i) q^{31} +(0.866025 + 0.500000i) q^{32} +3.65984i q^{34} +(1.14545 + 1.98397i) q^{37} +(-1.80205 + 3.12125i) q^{38} -2.22816 q^{41} -2.22575 q^{43} +(0.429853 - 0.248176i) q^{44} +(-3.21210 + 5.56351i) q^{46} +(-3.27213 - 5.66749i) q^{47} +(-6.68446 + 2.07798i) q^{49} +(-2.37672 - 1.37220i) q^{52} +(6.72594 + 3.88322i) q^{53} +(2.61577 - 0.397202i) q^{56} +(-4.43979 - 7.68995i) q^{58} +(-3.05194 + 5.28611i) q^{59} +(3.24271 - 1.87218i) q^{61} +7.97593 q^{62} -1.00000 q^{64} +(4.08889 - 7.08216i) q^{67} +(-1.82992 - 3.16952i) q^{68} -10.3761i q^{71} +(-11.3165 - 6.53361i) q^{73} +(-1.98397 - 1.14545i) q^{74} -3.60411i q^{76} +(0.478431 - 1.22297i) q^{77} +(4.44344 + 7.69627i) q^{79} +(1.92964 - 1.11408i) q^{82} +4.79091 q^{83} +(1.92756 - 1.11288i) q^{86} +(-0.248176 + 0.429853i) q^{88} +(0.743586 + 1.28793i) q^{89} +(-7.17871 + 1.09008i) q^{91} -6.42419i q^{92} +(5.66749 + 3.27213i) q^{94} -9.05174i q^{97} +(4.74992 - 5.14181i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 12q^{4} - 4q^{7} + O(q^{10}) \) \( 24q + 12q^{4} - 4q^{7} - 12q^{16} + 12q^{19} + 4q^{28} + 28q^{37} + 96q^{43} - 8q^{46} - 52q^{49} - 12q^{52} + 8q^{58} - 12q^{61} - 24q^{64} - 4q^{67} - 12q^{73} + 4q^{79} + 68q^{91} - 24q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −0.397202 2.61577i −0.150128 0.988667i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) 0.429853 + 0.248176i 0.129606 + 0.0748278i 0.563401 0.826184i \(-0.309493\pi\)
−0.433795 + 0.901011i \(0.642826\pi\)
\(12\) 0 0
\(13\) 2.74440i 0.761160i −0.924748 0.380580i \(-0.875724\pi\)
0.924748 0.380580i \(-0.124276\pi\)
\(14\) 1.65187 + 2.06672i 0.441481 + 0.552354i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.82992 3.16952i 0.443821 0.768721i −0.554148 0.832418i \(-0.686956\pi\)
0.997969 + 0.0636974i \(0.0202893\pi\)
\(18\) 0 0
\(19\) 3.12125 1.80205i 0.716064 0.413420i −0.0972384 0.995261i \(-0.531001\pi\)
0.813302 + 0.581841i \(0.197668\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.496352 −0.105823
\(23\) 5.56351 3.21210i 1.16007 0.669768i 0.208751 0.977969i \(-0.433060\pi\)
0.951321 + 0.308200i \(0.0997267\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 1.37220 + 2.37672i 0.269111 + 0.466114i
\(27\) 0 0
\(28\) −2.46392 0.963896i −0.465637 0.182159i
\(29\) 8.87959i 1.64890i 0.565937 + 0.824449i \(0.308515\pi\)
−0.565937 + 0.824449i \(0.691485\pi\)
\(30\) 0 0
\(31\) −6.90736 3.98797i −1.24060 0.716260i −0.271383 0.962472i \(-0.587481\pi\)
−0.969216 + 0.246211i \(0.920814\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 3.65984i 0.627658i
\(35\) 0 0
\(36\) 0 0
\(37\) 1.14545 + 1.98397i 0.188311 + 0.326163i 0.944687 0.327973i \(-0.106366\pi\)
−0.756377 + 0.654136i \(0.773032\pi\)
\(38\) −1.80205 + 3.12125i −0.292332 + 0.506334i
\(39\) 0 0
\(40\) 0 0
\(41\) −2.22816 −0.347980 −0.173990 0.984747i \(-0.555666\pi\)
−0.173990 + 0.984747i \(0.555666\pi\)
\(42\) 0 0
\(43\) −2.22575 −0.339424 −0.169712 0.985494i \(-0.554284\pi\)
−0.169712 + 0.985494i \(0.554284\pi\)
\(44\) 0.429853 0.248176i 0.0648028 0.0374139i
\(45\) 0 0
\(46\) −3.21210 + 5.56351i −0.473598 + 0.820295i
\(47\) −3.27213 5.66749i −0.477289 0.826688i 0.522373 0.852717i \(-0.325047\pi\)
−0.999661 + 0.0260292i \(0.991714\pi\)
\(48\) 0 0
\(49\) −6.68446 + 2.07798i −0.954923 + 0.296854i
\(50\) 0 0
\(51\) 0 0
\(52\) −2.37672 1.37220i −0.329592 0.190290i
\(53\) 6.72594 + 3.88322i 0.923879 + 0.533402i 0.884870 0.465837i \(-0.154247\pi\)
0.0390085 + 0.999239i \(0.487580\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.61577 0.397202i 0.349546 0.0530784i
\(57\) 0 0
\(58\) −4.43979 7.68995i −0.582973 1.00974i
\(59\) −3.05194 + 5.28611i −0.397328 + 0.688193i −0.993395 0.114742i \(-0.963396\pi\)
0.596067 + 0.802935i \(0.296729\pi\)
\(60\) 0 0
\(61\) 3.24271 1.87218i 0.415187 0.239708i −0.277829 0.960630i \(-0.589615\pi\)
0.693016 + 0.720922i \(0.256282\pi\)
\(62\) 7.97593 1.01294
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 4.08889 7.08216i 0.499537 0.865224i −0.500463 0.865758i \(-0.666837\pi\)
1.00000 0.000534152i \(0.000170026\pi\)
\(68\) −1.82992 3.16952i −0.221911 0.384360i
\(69\) 0 0
\(70\) 0 0
\(71\) 10.3761i 1.23141i −0.787975 0.615707i \(-0.788871\pi\)
0.787975 0.615707i \(-0.211129\pi\)
\(72\) 0 0
\(73\) −11.3165 6.53361i −1.32450 0.764701i −0.340058 0.940405i \(-0.610447\pi\)
−0.984443 + 0.175704i \(0.943780\pi\)
\(74\) −1.98397 1.14545i −0.230632 0.133156i
\(75\) 0 0
\(76\) 3.60411i 0.413420i
\(77\) 0.478431 1.22297i 0.0545223 0.139370i
\(78\) 0 0
\(79\) 4.44344 + 7.69627i 0.499926 + 0.865898i 1.00000 8.52501e-5i \(-2.71360e-5\pi\)
−0.500074 + 0.865983i \(0.666694\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 1.92964 1.11408i 0.213093 0.123030i
\(83\) 4.79091 0.525871 0.262935 0.964813i \(-0.415309\pi\)
0.262935 + 0.964813i \(0.415309\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.92756 1.11288i 0.207854 0.120005i
\(87\) 0 0
\(88\) −0.248176 + 0.429853i −0.0264556 + 0.0458225i
\(89\) 0.743586 + 1.28793i 0.0788199 + 0.136520i 0.902741 0.430184i \(-0.141551\pi\)
−0.823921 + 0.566704i \(0.808218\pi\)
\(90\) 0 0
\(91\) −7.17871 + 1.09008i −0.752534 + 0.114272i
\(92\) 6.42419i 0.669768i
\(93\) 0 0
\(94\) 5.66749 + 3.27213i 0.584557 + 0.337494i
\(95\) 0 0
\(96\) 0 0
\(97\) 9.05174i 0.919064i −0.888161 0.459532i \(-0.848017\pi\)
0.888161 0.459532i \(-0.151983\pi\)
\(98\) 4.74992 5.14181i 0.479815 0.519401i
\(99\) 0 0
\(100\) 0 0
\(101\) 1.50180 2.60119i 0.149434 0.258828i −0.781584 0.623800i \(-0.785588\pi\)
0.931019 + 0.364972i \(0.118921\pi\)
\(102\) 0 0
\(103\) −12.4491 + 7.18752i −1.22665 + 0.708207i −0.966328 0.257314i \(-0.917162\pi\)
−0.260323 + 0.965522i \(0.583829\pi\)
\(104\) 2.74440 0.269111
\(105\) 0 0
\(106\) −7.76645 −0.754344
\(107\) 1.84141 1.06314i 0.178016 0.102778i −0.408344 0.912828i \(-0.633894\pi\)
0.586360 + 0.810050i \(0.300560\pi\)
\(108\) 0 0
\(109\) −3.95181 + 6.84474i −0.378515 + 0.655607i −0.990846 0.134994i \(-0.956899\pi\)
0.612331 + 0.790601i \(0.290232\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.06672 + 1.65187i −0.195287 + 0.156087i
\(113\) 12.2968i 1.15678i −0.815760 0.578391i \(-0.803681\pi\)
0.815760 0.578391i \(-0.196319\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 7.68995 + 4.43979i 0.713994 + 0.412224i
\(117\) 0 0
\(118\) 6.10388i 0.561907i
\(119\) −9.01756 3.52771i −0.826638 0.323384i
\(120\) 0 0
\(121\) −5.37682 9.31292i −0.488802 0.846629i
\(122\) −1.87218 + 3.24271i −0.169499 + 0.293581i
\(123\) 0 0
\(124\) −6.90736 + 3.98797i −0.620299 + 0.358130i
\(125\) 0 0
\(126\) 0 0
\(127\) −0.753445 −0.0668574 −0.0334287 0.999441i \(-0.510643\pi\)
−0.0334287 + 0.999441i \(0.510643\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) 6.35624 + 11.0093i 0.555347 + 0.961890i 0.997876 + 0.0651355i \(0.0207479\pi\)
−0.442529 + 0.896754i \(0.645919\pi\)
\(132\) 0 0
\(133\) −5.95352 7.44868i −0.516236 0.645882i
\(134\) 8.17778i 0.706452i
\(135\) 0 0
\(136\) 3.16952 + 1.82992i 0.271784 + 0.156914i
\(137\) 3.73673 + 2.15740i 0.319250 + 0.184319i 0.651058 0.759028i \(-0.274325\pi\)
−0.331808 + 0.943347i \(0.607659\pi\)
\(138\) 0 0
\(139\) 0.0681276i 0.00577851i 0.999996 + 0.00288926i \(0.000919680\pi\)
−0.999996 + 0.00288926i \(0.999080\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 5.18804 + 8.98595i 0.435371 + 0.754084i
\(143\) 0.681094 1.17969i 0.0569560 0.0986507i
\(144\) 0 0
\(145\) 0 0
\(146\) 13.0672 1.08145
\(147\) 0 0
\(148\) 2.29090 0.188311
\(149\) −14.4611 + 8.34911i −1.18470 + 0.683986i −0.957097 0.289768i \(-0.906422\pi\)
−0.227602 + 0.973754i \(0.573088\pi\)
\(150\) 0 0
\(151\) 6.51016 11.2759i 0.529789 0.917622i −0.469607 0.882876i \(-0.655604\pi\)
0.999396 0.0347463i \(-0.0110623\pi\)
\(152\) 1.80205 + 3.12125i 0.146166 + 0.253167i
\(153\) 0 0
\(154\) 0.197152 + 1.29834i 0.0158870 + 0.104623i
\(155\) 0 0
\(156\) 0 0
\(157\) −12.8242 7.40408i −1.02349 0.590910i −0.108374 0.994110i \(-0.534564\pi\)
−0.915112 + 0.403200i \(0.867898\pi\)
\(158\) −7.69627 4.44344i −0.612282 0.353501i
\(159\) 0 0
\(160\) 0 0
\(161\) −10.6119 13.2770i −0.836337 1.04637i
\(162\) 0 0
\(163\) −7.68966 13.3189i −0.602301 1.04322i −0.992472 0.122473i \(-0.960918\pi\)
0.390171 0.920742i \(-0.372416\pi\)
\(164\) −1.11408 + 1.92964i −0.0869950 + 0.150680i
\(165\) 0 0
\(166\) −4.14905 + 2.39546i −0.322029 + 0.185923i
\(167\) −24.5161 −1.89712 −0.948558 0.316603i \(-0.897458\pi\)
−0.948558 + 0.316603i \(0.897458\pi\)
\(168\) 0 0
\(169\) 5.46825 0.420635
\(170\) 0 0
\(171\) 0 0
\(172\) −1.11288 + 1.92756i −0.0848561 + 0.146975i
\(173\) 6.26213 + 10.8463i 0.476101 + 0.824631i 0.999625 0.0273795i \(-0.00871625\pi\)
−0.523524 + 0.852011i \(0.675383\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.496352i 0.0374139i
\(177\) 0 0
\(178\) −1.28793 0.743586i −0.0965343 0.0557341i
\(179\) 1.58961 + 0.917762i 0.118813 + 0.0685968i 0.558229 0.829687i \(-0.311481\pi\)
−0.439416 + 0.898284i \(0.644814\pi\)
\(180\) 0 0
\(181\) 23.6564i 1.75837i −0.476481 0.879185i \(-0.658088\pi\)
0.476481 0.879185i \(-0.341912\pi\)
\(182\) 5.67191 4.53340i 0.420430 0.336038i
\(183\) 0 0
\(184\) 3.21210 + 5.56351i 0.236799 + 0.410148i
\(185\) 0 0
\(186\) 0 0
\(187\) 1.57319 0.908284i 0.115043 0.0664203i
\(188\) −6.54425 −0.477289
\(189\) 0 0
\(190\) 0 0
\(191\) −7.02253 + 4.05446i −0.508133 + 0.293371i −0.732066 0.681234i \(-0.761444\pi\)
0.223933 + 0.974605i \(0.428110\pi\)
\(192\) 0 0
\(193\) −6.02502 + 10.4356i −0.433691 + 0.751174i −0.997188 0.0749438i \(-0.976122\pi\)
0.563497 + 0.826118i \(0.309456\pi\)
\(194\) 4.52587 + 7.83903i 0.324938 + 0.562810i
\(195\) 0 0
\(196\) −1.54265 + 6.82790i −0.110189 + 0.487707i
\(197\) 12.7463i 0.908137i −0.890967 0.454068i \(-0.849972\pi\)
0.890967 0.454068i \(-0.150028\pi\)
\(198\) 0 0
\(199\) 16.4954 + 9.52361i 1.16933 + 0.675111i 0.953521 0.301325i \(-0.0974290\pi\)
0.215805 + 0.976436i \(0.430762\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 3.00359i 0.211332i
\(203\) 23.2269 3.52699i 1.63021 0.247546i
\(204\) 0 0
\(205\) 0 0
\(206\) 7.18752 12.4491i 0.500778 0.867373i
\(207\) 0 0
\(208\) −2.37672 + 1.37220i −0.164796 + 0.0951450i
\(209\) 1.78891 0.123741
\(210\) 0 0
\(211\) −8.92057 −0.614117 −0.307059 0.951691i \(-0.599345\pi\)
−0.307059 + 0.951691i \(0.599345\pi\)
\(212\) 6.72594 3.88322i 0.461939 0.266701i
\(213\) 0 0
\(214\) −1.06314 + 1.84141i −0.0726748 + 0.125876i
\(215\) 0 0
\(216\) 0 0
\(217\) −7.68797 + 19.6521i −0.521893 + 1.33407i
\(218\) 7.90363i 0.535301i
\(219\) 0 0
\(220\) 0 0
\(221\) −8.69843 5.02204i −0.585120 0.337819i
\(222\) 0 0
\(223\) 23.5443i 1.57664i −0.615265 0.788320i \(-0.710951\pi\)
0.615265 0.788320i \(-0.289049\pi\)
\(224\) 0.963896 2.46392i 0.0644030 0.164628i
\(225\) 0 0
\(226\) 6.14838 + 10.6493i 0.408984 + 0.708382i
\(227\) 4.66223 8.07522i 0.309443 0.535971i −0.668797 0.743445i \(-0.733191\pi\)
0.978241 + 0.207473i \(0.0665240\pi\)
\(228\) 0 0
\(229\) 20.1545 11.6362i 1.33185 0.768944i 0.346266 0.938136i \(-0.387449\pi\)
0.985583 + 0.169193i \(0.0541160\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −8.87959 −0.582973
\(233\) 10.9295 6.31017i 0.716018 0.413393i −0.0972676 0.995258i \(-0.531010\pi\)
0.813285 + 0.581865i \(0.197677\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 3.05194 + 5.28611i 0.198664 + 0.344097i
\(237\) 0 0
\(238\) 9.57329 1.45370i 0.620544 0.0942292i
\(239\) 16.1198i 1.04270i −0.853342 0.521351i \(-0.825428\pi\)
0.853342 0.521351i \(-0.174572\pi\)
\(240\) 0 0
\(241\) −18.3222 10.5783i −1.18024 0.681411i −0.224168 0.974550i \(-0.571966\pi\)
−0.956070 + 0.293140i \(0.905300\pi\)
\(242\) 9.31292 + 5.37682i 0.598657 + 0.345635i
\(243\) 0 0
\(244\) 3.74436i 0.239708i
\(245\) 0 0
\(246\) 0 0
\(247\) −4.94556 8.56597i −0.314679 0.545039i
\(248\) 3.98797 6.90736i 0.253236 0.438618i
\(249\) 0 0
\(250\) 0 0
\(251\) −6.06317 −0.382704 −0.191352 0.981522i \(-0.561287\pi\)
−0.191352 + 0.981522i \(0.561287\pi\)
\(252\) 0 0
\(253\) 3.18866 0.200469
\(254\) 0.652503 0.376723i 0.0409416 0.0236377i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 5.49266 + 9.51357i 0.342623 + 0.593440i 0.984919 0.173016i \(-0.0553513\pi\)
−0.642296 + 0.766457i \(0.722018\pi\)
\(258\) 0 0
\(259\) 4.73464 3.78426i 0.294196 0.235143i
\(260\) 0 0
\(261\) 0 0
\(262\) −11.0093 6.35624i −0.680159 0.392690i
\(263\) −1.15937 0.669365i −0.0714901 0.0412748i 0.463829 0.885925i \(-0.346475\pi\)
−0.535319 + 0.844650i \(0.679809\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 8.88024 + 3.47399i 0.544482 + 0.213004i
\(267\) 0 0
\(268\) −4.08889 7.08216i −0.249769 0.432612i
\(269\) −0.311161 + 0.538946i −0.0189718 + 0.0328601i −0.875355 0.483480i \(-0.839373\pi\)
0.856384 + 0.516340i \(0.172706\pi\)
\(270\) 0 0
\(271\) 18.4634 10.6598i 1.12157 0.647539i 0.179769 0.983709i \(-0.442465\pi\)
0.941801 + 0.336170i \(0.109132\pi\)
\(272\) −3.65984 −0.221911
\(273\) 0 0
\(274\) −4.31480 −0.260667
\(275\) 0 0
\(276\) 0 0
\(277\) 0.593544 1.02805i 0.0356626 0.0617694i −0.847643 0.530567i \(-0.821979\pi\)
0.883306 + 0.468797i \(0.155312\pi\)
\(278\) −0.0340638 0.0590003i −0.00204301 0.00353860i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.97593i 0.117874i −0.998262 0.0589370i \(-0.981229\pi\)
0.998262 0.0589370i \(-0.0187711\pi\)
\(282\) 0 0
\(283\) 23.4960 + 13.5654i 1.39669 + 0.806382i 0.994045 0.108972i \(-0.0347560\pi\)
0.402650 + 0.915354i \(0.368089\pi\)
\(284\) −8.98595 5.18804i −0.533218 0.307853i
\(285\) 0 0
\(286\) 1.36219i 0.0805479i
\(287\) 0.885030 + 5.82835i 0.0522417 + 0.344036i
\(288\) 0 0
\(289\) 1.80278 + 3.12250i 0.106046 + 0.183677i
\(290\) 0 0
\(291\) 0 0
\(292\) −11.3165 + 6.53361i −0.662250 + 0.382350i
\(293\) −10.3808 −0.606456 −0.303228 0.952918i \(-0.598064\pi\)
−0.303228 + 0.952918i \(0.598064\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.98397 + 1.14545i −0.115316 + 0.0665778i
\(297\) 0 0
\(298\) 8.34911 14.4611i 0.483651 0.837708i
\(299\) −8.81529 15.2685i −0.509801 0.883002i
\(300\) 0 0
\(301\) 0.884074 + 5.82205i 0.0509572 + 0.335577i
\(302\) 13.0203i 0.749235i
\(303\) 0 0
\(304\) −3.12125 1.80205i −0.179016 0.103355i
\(305\) 0 0
\(306\) 0 0
\(307\) 14.1364i 0.806808i −0.915022 0.403404i \(-0.867827\pi\)
0.915022 0.403404i \(-0.132173\pi\)
\(308\) −0.819908 1.02582i −0.0467186 0.0584515i
\(309\) 0 0
\(310\) 0 0
\(311\) 3.32643 5.76155i 0.188625 0.326708i −0.756167 0.654378i \(-0.772930\pi\)
0.944792 + 0.327671i \(0.106264\pi\)
\(312\) 0 0
\(313\) −10.5184 + 6.07282i −0.594537 + 0.343256i −0.766890 0.641779i \(-0.778197\pi\)
0.172352 + 0.985035i \(0.444863\pi\)
\(314\) 14.8082 0.835673
\(315\) 0 0
\(316\) 8.88688 0.499926
\(317\) −26.6051 + 15.3605i −1.49429 + 0.862730i −0.999979 0.00655283i \(-0.997914\pi\)
−0.494314 + 0.869283i \(0.664581\pi\)
\(318\) 0 0
\(319\) −2.20370 + 3.81692i −0.123383 + 0.213706i
\(320\) 0 0
\(321\) 0 0
\(322\) 15.8287 + 6.19225i 0.882099 + 0.345081i
\(323\) 13.1905i 0.733937i
\(324\) 0 0
\(325\) 0 0
\(326\) 13.3189 + 7.68966i 0.737665 + 0.425891i
\(327\) 0 0
\(328\) 2.22816i 0.123030i
\(329\) −13.5251 + 10.8103i −0.745664 + 0.595989i
\(330\) 0 0
\(331\) 15.5140 + 26.8710i 0.852724 + 1.47696i 0.878741 + 0.477300i \(0.158384\pi\)
−0.0260166 + 0.999662i \(0.508282\pi\)
\(332\) 2.39546 4.14905i 0.131468 0.227709i
\(333\) 0 0
\(334\) 21.2316 12.2581i 1.16174 0.670732i
\(335\) 0 0
\(336\) 0 0
\(337\) 6.91470 0.376668 0.188334 0.982105i \(-0.439691\pi\)
0.188334 + 0.982105i \(0.439691\pi\)
\(338\) −4.73565 + 2.73413i −0.257585 + 0.148717i
\(339\) 0 0
\(340\) 0 0
\(341\) −1.97943 3.42848i −0.107192 0.185663i
\(342\) 0 0
\(343\) 8.09058 + 16.6596i 0.436850 + 0.899534i
\(344\) 2.22575i 0.120005i
\(345\) 0 0
\(346\) −10.8463 6.26213i −0.583103 0.336654i
\(347\) −6.49006 3.74704i −0.348405 0.201152i 0.315578 0.948900i \(-0.397802\pi\)
−0.663982 + 0.747748i \(0.731135\pi\)
\(348\) 0 0
\(349\) 12.4552i 0.666714i −0.942801 0.333357i \(-0.891819\pi\)
0.942801 0.333357i \(-0.108181\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.248176 + 0.429853i 0.0132278 + 0.0229113i
\(353\) −9.47011 + 16.4027i −0.504043 + 0.873028i 0.495946 + 0.868353i \(0.334821\pi\)
−0.999989 + 0.00467471i \(0.998512\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.48717 0.0788199
\(357\) 0 0
\(358\) −1.83552 −0.0970105
\(359\) 23.0590 13.3131i 1.21701 0.702639i 0.252730 0.967537i \(-0.418671\pi\)
0.964277 + 0.264898i \(0.0853381\pi\)
\(360\) 0 0
\(361\) −3.00520 + 5.20516i −0.158168 + 0.273956i
\(362\) 11.8282 + 20.4871i 0.621677 + 1.07678i
\(363\) 0 0
\(364\) −2.64532 + 6.76199i −0.138652 + 0.354425i
\(365\) 0 0
\(366\) 0 0
\(367\) −9.45017 5.45606i −0.493295 0.284804i 0.232646 0.972562i \(-0.425262\pi\)
−0.725940 + 0.687758i \(0.758595\pi\)
\(368\) −5.56351 3.21210i −0.290018 0.167442i
\(369\) 0 0
\(370\) 0 0
\(371\) 7.48604 19.1359i 0.388656 0.993487i
\(372\) 0 0
\(373\) −11.2539 19.4924i −0.582707 1.00928i −0.995157 0.0982976i \(-0.968660\pi\)
0.412450 0.910980i \(-0.364673\pi\)
\(374\) −0.908284 + 1.57319i −0.0469663 + 0.0813480i
\(375\) 0 0
\(376\) 5.66749 3.27213i 0.292278 0.168747i
\(377\) 24.3692 1.25508
\(378\) 0 0
\(379\) −3.25909 −0.167408 −0.0837040 0.996491i \(-0.526675\pi\)
−0.0837040 + 0.996491i \(0.526675\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 4.05446 7.02253i 0.207444 0.359304i
\(383\) −8.66098 15.0013i −0.442555 0.766528i 0.555323 0.831635i \(-0.312595\pi\)
−0.997878 + 0.0651064i \(0.979261\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 12.0500i 0.613331i
\(387\) 0 0
\(388\) −7.83903 4.52587i −0.397967 0.229766i
\(389\) −27.4515 15.8491i −1.39185 0.803582i −0.398326 0.917244i \(-0.630409\pi\)
−0.993520 + 0.113662i \(0.963742\pi\)
\(390\) 0 0
\(391\) 23.5115i 1.18903i
\(392\) −2.07798 6.68446i −0.104954 0.337616i
\(393\) 0 0
\(394\) 6.37315 + 11.0386i 0.321075 + 0.556118i
\(395\) 0 0
\(396\) 0 0
\(397\) 29.0224 16.7561i 1.45659 0.840964i 0.457750 0.889081i \(-0.348655\pi\)
0.998842 + 0.0481170i \(0.0153220\pi\)
\(398\) −19.0472 −0.954751
\(399\) 0 0
\(400\) 0 0
\(401\) −31.0404 + 17.9212i −1.55008 + 0.894940i −0.551947 + 0.833879i \(0.686115\pi\)
−0.998134 + 0.0610611i \(0.980552\pi\)
\(402\) 0 0
\(403\) −10.9446 + 18.9566i −0.545189 + 0.944295i
\(404\) −1.50180 2.60119i −0.0747171 0.129414i
\(405\) 0 0
\(406\) −18.3516 + 14.6679i −0.910775 + 0.727957i
\(407\) 1.13709i 0.0563635i
\(408\) 0 0
\(409\) −21.3474 12.3249i −1.05556 0.609429i −0.131361 0.991335i \(-0.541935\pi\)
−0.924201 + 0.381905i \(0.875268\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 14.3750i 0.708207i
\(413\) 15.0395 + 5.88350i 0.740044 + 0.289508i
\(414\) 0 0
\(415\) 0 0
\(416\) 1.37220 2.37672i 0.0672777 0.116528i
\(417\) 0 0
\(418\) −1.54924 + 0.894453i −0.0757757 + 0.0437491i
\(419\) 10.6574 0.520646 0.260323 0.965522i \(-0.416171\pi\)
0.260323 + 0.965522i \(0.416171\pi\)
\(420\) 0 0
\(421\) 22.6815 1.10543 0.552714 0.833371i \(-0.313592\pi\)
0.552714 + 0.833371i \(0.313592\pi\)
\(422\) 7.72544 4.46028i 0.376068 0.217123i
\(423\) 0 0
\(424\) −3.88322 + 6.72594i −0.188586 + 0.326641i
\(425\) 0 0
\(426\) 0 0
\(427\) −6.18520 7.73854i −0.299323 0.374494i
\(428\) 2.12628i 0.102778i
\(429\) 0 0
\(430\) 0 0
\(431\) −26.0439 15.0364i −1.25449 0.724279i −0.282491 0.959270i \(-0.591161\pi\)
−0.971998 + 0.234991i \(0.924494\pi\)
\(432\) 0 0
\(433\) 14.9203i 0.717025i 0.933525 + 0.358512i \(0.116716\pi\)
−0.933525 + 0.358512i \(0.883284\pi\)
\(434\) −3.16806 20.8632i −0.152072 1.00146i
\(435\) 0 0
\(436\) 3.95181 + 6.84474i 0.189258 + 0.327804i
\(437\) 11.5767 20.0515i 0.553791 0.959194i
\(438\) 0 0
\(439\) 11.1126 6.41586i 0.530375 0.306212i −0.210794 0.977530i \(-0.567605\pi\)
0.741169 + 0.671318i \(0.234272\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 10.0441 0.477748
\(443\) 17.6792 10.2071i 0.839963 0.484953i −0.0172887 0.999851i \(-0.505503\pi\)
0.857252 + 0.514898i \(0.172170\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 11.7721 + 20.3899i 0.557426 + 0.965491i
\(447\) 0 0
\(448\) 0.397202 + 2.61577i 0.0187660 + 0.123583i
\(449\) 20.8404i 0.983519i 0.870731 + 0.491760i \(0.163646\pi\)
−0.870731 + 0.491760i \(0.836354\pi\)
\(450\) 0 0
\(451\) −0.957782 0.552976i −0.0451002 0.0260386i
\(452\) −10.6493 6.14838i −0.500901 0.289196i
\(453\) 0 0
\(454\) 9.32446i 0.437619i
\(455\) 0 0
\(456\) 0 0
\(457\) 8.01424 + 13.8811i 0.374890 + 0.649329i 0.990311 0.138870i \(-0.0443470\pi\)
−0.615420 + 0.788199i \(0.711014\pi\)
\(458\) −11.6362 + 20.1545i −0.543725 + 0.941760i
\(459\) 0 0
\(460\) 0 0
\(461\) −1.98400 −0.0924039 −0.0462020 0.998932i \(-0.514712\pi\)
−0.0462020 + 0.998932i \(0.514712\pi\)
\(462\) 0 0
\(463\) 36.3987 1.69159 0.845796 0.533506i \(-0.179126\pi\)
0.845796 + 0.533506i \(0.179126\pi\)
\(464\) 7.68995 4.43979i 0.356997 0.206112i
\(465\) 0 0
\(466\) −6.31017 + 10.9295i −0.292313 + 0.506301i
\(467\) 15.5372 + 26.9113i 0.718977 + 1.24530i 0.961405 + 0.275136i \(0.0887227\pi\)
−0.242428 + 0.970169i \(0.577944\pi\)
\(468\) 0 0
\(469\) −20.1494 7.88253i −0.930413 0.363981i
\(470\) 0 0
\(471\) 0 0
\(472\) −5.28611 3.05194i −0.243313 0.140477i
\(473\) −0.956747 0.552378i −0.0439913 0.0253984i
\(474\) 0 0
\(475\) 0 0
\(476\) −7.56386 + 6.04558i −0.346689 + 0.277099i
\(477\) 0 0
\(478\) 8.05990 + 13.9601i 0.368651 + 0.638522i
\(479\) 18.2404 31.5933i 0.833426 1.44354i −0.0618788 0.998084i \(-0.519709\pi\)
0.895305 0.445453i \(-0.146957\pi\)
\(480\) 0 0
\(481\) 5.44483 3.14357i 0.248263 0.143335i
\(482\) 21.1567 0.963660
\(483\) 0 0
\(484\) −10.7536 −0.488802
\(485\) 0 0
\(486\) 0 0
\(487\) −7.06672 + 12.2399i −0.320224 + 0.554644i −0.980534 0.196349i \(-0.937091\pi\)
0.660310 + 0.750993i \(0.270425\pi\)
\(488\) 1.87218 + 3.24271i 0.0847496 + 0.146791i
\(489\) 0 0
\(490\) 0 0
\(491\) 32.5466i 1.46881i −0.678714 0.734403i \(-0.737462\pi\)
0.678714 0.734403i \(-0.262538\pi\)
\(492\) 0 0
\(493\) 28.1440 + 16.2489i 1.26754 + 0.731815i
\(494\) 8.56597 + 4.94556i 0.385401 + 0.222511i
\(495\) 0 0
\(496\) 7.97593i 0.358130i
\(497\) −27.1414 + 4.12140i −1.21746 + 0.184870i
\(498\) 0 0
\(499\) −5.87396 10.1740i −0.262955 0.455451i 0.704071 0.710130i \(-0.251364\pi\)
−0.967026 + 0.254679i \(0.918030\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 5.25086 3.03158i 0.234357 0.135306i
\(503\) −24.5250 −1.09352 −0.546758 0.837291i \(-0.684138\pi\)
−0.546758 + 0.837291i \(0.684138\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −2.76146 + 1.59433i −0.122762 + 0.0708766i
\(507\) 0 0
\(508\) −0.376723 + 0.652503i −0.0167144 + 0.0289501i
\(509\) −5.84634 10.1262i −0.259135 0.448834i 0.706876 0.707338i \(-0.250104\pi\)
−0.966010 + 0.258503i \(0.916771\pi\)
\(510\) 0 0
\(511\) −12.5954 + 32.1966i −0.557189 + 1.42429i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −9.51357 5.49266i −0.419626 0.242271i
\(515\) 0 0
\(516\) 0 0
\(517\) 3.24825i 0.142858i
\(518\) −2.20819 + 5.64459i −0.0970221 + 0.248009i
\(519\) 0 0
\(520\) 0 0
\(521\) −14.8674 + 25.7511i −0.651354 + 1.12818i 0.331441 + 0.943476i \(0.392465\pi\)
−0.982795 + 0.184702i \(0.940868\pi\)
\(522\) 0 0
\(523\) −4.90024 + 2.82915i −0.214272 + 0.123710i −0.603295 0.797518i \(-0.706146\pi\)
0.389023 + 0.921228i \(0.372813\pi\)
\(524\) 12.7125 0.555347
\(525\) 0 0
\(526\) 1.33873 0.0583714
\(527\) −25.2799 + 14.5953i −1.10121 + 0.635783i
\(528\) 0 0
\(529\) 9.13513 15.8225i 0.397179 0.687935i
\(530\) 0 0
\(531\) 0 0
\(532\) −9.42751 + 1.43156i −0.408734 + 0.0620660i
\(533\) 6.11497i 0.264869i
\(534\) 0 0
\(535\) 0 0
\(536\) 7.08216 + 4.08889i 0.305903 + 0.176613i
\(537\) 0 0
\(538\) 0.622322i 0.0268302i
\(539\) −3.38904 0.765697i −0.145976 0.0329809i
\(540\) 0 0
\(541\) 17.6742 + 30.6126i 0.759874 + 1.31614i 0.942915 + 0.333035i \(0.108073\pi\)
−0.183041 + 0.983105i \(0.558594\pi\)
\(542\) −10.6598 + 18.4634i −0.457879 + 0.793070i
\(543\) 0 0
\(544\) 3.16952 1.82992i 0.135892 0.0784572i
\(545\) 0 0
\(546\) 0 0
\(547\) −21.4806 −0.918445 −0.459223 0.888321i \(-0.651872\pi\)
−0.459223 + 0.888321i \(0.651872\pi\)
\(548\) 3.73673 2.15740i 0.159625 0.0921595i
\(549\) 0 0
\(550\) 0 0
\(551\) 16.0015 + 27.7154i 0.681687 + 1.18072i
\(552\) 0 0
\(553\) 18.3667 14.6800i 0.781031 0.624256i
\(554\) 1.18709i 0.0504345i
\(555\) 0 0
\(556\) 0.0590003 + 0.0340638i 0.00250217 + 0.00144463i
\(557\) 34.4939 + 19.9150i 1.46155 + 0.843828i 0.999083 0.0428076i \(-0.0136303\pi\)
0.462469 + 0.886635i \(0.346964\pi\)
\(558\) 0 0
\(559\) 6.10836i 0.258356i
\(560\) 0 0
\(561\) 0 0
\(562\) 0.987964 + 1.71120i 0.0416747 + 0.0721828i
\(563\) −5.17056 + 8.95567i −0.217913 + 0.377437i −0.954170 0.299266i \(-0.903258\pi\)
0.736257 + 0.676702i \(0.236592\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −27.1309 −1.14040
\(567\) 0 0
\(568\) 10.3761 0.435371
\(569\) −24.3464 + 14.0564i −1.02065 + 0.589275i −0.914293 0.405053i \(-0.867253\pi\)
−0.106361 + 0.994328i \(0.533920\pi\)
\(570\) 0 0
\(571\) 13.7146 23.7544i 0.573938 0.994090i −0.422218 0.906494i \(-0.638748\pi\)
0.996156 0.0875958i \(-0.0279184\pi\)
\(572\) −0.681094 1.17969i −0.0284780 0.0493253i
\(573\) 0 0
\(574\) −3.68063 4.60498i −0.153627 0.192208i
\(575\) 0 0
\(576\) 0 0
\(577\) 11.2914 + 6.51910i 0.470068 + 0.271394i 0.716268 0.697825i \(-0.245849\pi\)
−0.246200 + 0.969219i \(0.579182\pi\)
\(578\) −3.12250 1.80278i −0.129879 0.0749857i
\(579\) 0 0
\(580\) 0 0
\(581\) −1.90296 12.5319i −0.0789481 0.519911i
\(582\) 0 0
\(583\) 1.92744 + 3.33843i 0.0798266 + 0.138264i
\(584\) 6.53361 11.3165i 0.270363 0.468282i
\(585\) 0 0
\(586\) 8.99008 5.19042i 0.371377 0.214414i
\(587\) −35.0223 −1.44553 −0.722763 0.691096i \(-0.757128\pi\)
−0.722763 + 0.691096i \(0.757128\pi\)
\(588\) 0 0
\(589\) −28.7461 −1.18446
\(590\) 0 0
\(591\) 0 0
\(592\) 1.14545 1.98397i 0.0470776 0.0815409i
\(593\) 8.19370 + 14.1919i 0.336475 + 0.582792i 0.983767 0.179450i \(-0.0574319\pi\)
−0.647292 + 0.762242i \(0.724099\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 16.6982i 0.683986i
\(597\) 0 0
\(598\) 15.2685 + 8.81529i 0.624376 + 0.360484i
\(599\) 26.0718 + 15.0526i 1.06527 + 0.615032i 0.926884 0.375347i \(-0.122476\pi\)
0.138382 + 0.990379i \(0.455810\pi\)
\(600\) 0 0
\(601\) 1.75569i 0.0716162i −0.999359 0.0358081i \(-0.988599\pi\)
0.999359 0.0358081i \(-0.0114005\pi\)
\(602\) −3.67666 4.60001i −0.149849 0.187482i
\(603\) 0 0
\(604\) −6.51016 11.2759i −0.264895 0.458811i
\(605\) 0 0
\(606\) 0 0
\(607\) 15.6511 9.03616i 0.635258 0.366766i −0.147528 0.989058i \(-0.547132\pi\)
0.782785 + 0.622292i \(0.213798\pi\)
\(608\) 3.60411 0.146166
\(609\) 0 0
\(610\) 0 0
\(611\) −15.5539 + 8.98003i −0.629242 + 0.363293i
\(612\) 0 0
\(613\) −6.42507 + 11.1285i −0.259506 + 0.449478i −0.966110 0.258132i \(-0.916893\pi\)
0.706604 + 0.707610i \(0.250226\pi\)
\(614\) 7.06821 + 12.2425i 0.285250 + 0.494067i
\(615\) 0 0
\(616\) 1.22297 + 0.478431i 0.0492749 + 0.0192765i
\(617\) 37.3633i 1.50419i −0.659055 0.752094i \(-0.729044\pi\)
0.659055 0.752094i \(-0.270956\pi\)
\(618\) 0 0
\(619\) 23.7213 + 13.6955i 0.953439 + 0.550468i 0.894147 0.447773i \(-0.147783\pi\)
0.0592911 + 0.998241i \(0.481116\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 6.65287i 0.266756i
\(623\) 3.07356 2.45661i 0.123140 0.0984222i
\(624\) 0 0
\(625\) 0 0
\(626\) 6.07282 10.5184i 0.242719 0.420401i
\(627\) 0 0
\(628\) −12.8242 + 7.40408i −0.511743 + 0.295455i
\(629\) 8.38432 0.334305
\(630\) 0 0
\(631\) −4.09420 −0.162987 −0.0814937 0.996674i \(-0.525969\pi\)
−0.0814937 + 0.996674i \(0.525969\pi\)
\(632\) −7.69627 + 4.44344i −0.306141 + 0.176751i
\(633\) 0 0
\(634\) 15.3605 26.6051i 0.610043 1.05662i
\(635\) 0 0
\(636\) 0 0
\(637\) 5.70280 + 18.3449i 0.225953 + 0.726850i
\(638\) 4.40740i 0.174491i
\(639\) 0 0
\(640\) 0 0
\(641\) 28.4700 + 16.4371i 1.12450 + 0.649228i 0.942545 0.334080i \(-0.108426\pi\)
0.181951 + 0.983308i \(0.441759\pi\)
\(642\) 0 0
\(643\) 48.1790i 1.89999i 0.312261 + 0.949996i \(0.398914\pi\)
−0.312261 + 0.949996i \(0.601086\pi\)
\(644\) −16.8042 + 2.55170i −0.662178 + 0.100551i
\(645\) 0 0
\(646\) 6.59524 + 11.4233i 0.259486 + 0.449443i
\(647\) −2.64703 + 4.58478i −0.104065 + 0.180246i −0.913356 0.407162i \(-0.866518\pi\)
0.809291 + 0.587408i \(0.199852\pi\)
\(648\) 0 0
\(649\) −2.62377 + 1.51483i −0.102992 + 0.0594625i
\(650\) 0 0
\(651\) 0 0
\(652\) −15.3793 −0.602301
\(653\) −43.4057 + 25.0603i −1.69860 + 0.980686i −0.751503 + 0.659729i \(0.770671\pi\)
−0.947094 + 0.320956i \(0.895996\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.11408 + 1.92964i 0.0434975 + 0.0753399i
\(657\) 0 0
\(658\) 6.30798 16.1245i 0.245911 0.628599i
\(659\) 2.20149i 0.0857579i 0.999080 + 0.0428790i \(0.0136530\pi\)
−0.999080 + 0.0428790i \(0.986347\pi\)
\(660\) 0 0
\(661\) −33.7612 19.4921i −1.31316 0.758153i −0.330542 0.943791i \(-0.607231\pi\)
−0.982618 + 0.185638i \(0.940565\pi\)
\(662\) −26.8710 15.5140i −1.04437 0.602967i
\(663\) 0 0
\(664\) 4.79091i 0.185923i
\(665\) 0 0
\(666\) 0 0
\(667\) 28.5221 + 49.4017i 1.10438 + 1.91284i
\(668\) −12.2581 + 21.2316i −0.474279 + 0.821475i
\(669\) 0 0
\(670\) 0 0
\(671\) 1.85852 0.0717473
\(672\) 0 0
\(673\) 43.4830 1.67615 0.838074 0.545556i \(-0.183682\pi\)
0.838074 + 0.545556i \(0.183682\pi\)
\(674\) −5.98830 + 3.45735i −0.230661 + 0.133172i
\(675\) 0 0
\(676\) 2.73413 4.73565i 0.105159 0.182140i
\(677\) −20.8309 36.0802i −0.800597 1.38668i −0.919223 0.393736i \(-0.871182\pi\)
0.118626 0.992939i \(-0.462151\pi\)
\(678\) 0 0
\(679\) −23.6772 + 3.59537i −0.908648 + 0.137978i
\(680\) 0 0
\(681\) 0 0
\(682\) 3.42848 + 1.97943i 0.131283 + 0.0757965i
\(683\) 41.3332 + 23.8637i 1.58157 + 0.913120i 0.994631 + 0.103490i \(0.0330010\pi\)
0.586940 + 0.809630i \(0.300332\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −15.3365 10.3824i −0.585548 0.396400i
\(687\) 0 0
\(688\) 1.11288 + 1.92756i 0.0424280 + 0.0734875i
\(689\) 10.6571 18.4587i 0.406004 0.703220i
\(690\) 0 0
\(691\) 33.6953 19.4540i 1.28183 0.740066i 0.304648 0.952465i \(-0.401461\pi\)
0.977183 + 0.212399i \(0.0681277\pi\)
\(692\) 12.5243 0.476101
\(693\) 0 0
\(694\) 7.49408 0.284471
\(695\) 0 0
\(696\) 0 0
\(697\) −4.07736 + 7.06219i −0.154441 + 0.267500i
\(698\) 6.22762 + 10.7866i 0.235719 + 0.408277i
\(699\) 0 0
\(700\) 0 0
\(701\) 8.73610i 0.329958i 0.986297 + 0.164979i \(0.0527556\pi\)
−0.986297 + 0.164979i \(0.947244\pi\)
\(702\) 0 0
\(703\) 7.15046 + 4.12832i 0.269685 + 0.155703i
\(704\) −0.429853 0.248176i −0.0162007 0.00935348i
\(705\) 0 0
\(706\) 18.9402i 0.712824i
\(707\) −7.40061 2.89515i −0.278329 0.108883i
\(708\) 0 0
\(709\) −8.25544 14.2988i −0.310039 0.537004i 0.668331 0.743864i \(-0.267009\pi\)
−0.978371 + 0.206860i \(0.933676\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.28793 + 0.743586i −0.0482671 + 0.0278671i
\(713\) −51.2389 −1.91891
\(714\) 0 0
\(715\) 0 0
\(716\) 1.58961 0.917762i 0.0594066 0.0342984i
\(717\) 0 0
\(718\) −13.3131 + 23.0590i −0.496841 + 0.860554i
\(719\) 22.5570 + 39.0699i 0.841234 + 1.45706i 0.888852 + 0.458195i \(0.151504\pi\)
−0.0476171 + 0.998866i \(0.515163\pi\)
\(720\) 0 0
\(721\) 23.7457 + 29.7092i 0.884336 + 1.10643i
\(722\) 6.01040i 0.223684i
\(723\) 0 0
\(724\) −20.4871 11.8282i −0.761396 0.439592i
\(725\) 0 0
\(726\) 0 0
\(727\) 31.9760i 1.18593i −0.805230 0.592963i \(-0.797958\pi\)
0.805230 0.592963i \(-0.202042\pi\)
\(728\) −1.09008 7.17871i −0.0404012 0.266061i
\(729\) 0 0
\(730\) 0 0
\(731\) −4.07295 + 7.05456i −0.150644 + 0.260922i
\(732\) 0 0
\(733\) −40.4618 + 23.3606i −1.49449 + 0.862844i −0.999980 0.00632839i \(-0.997986\pi\)
−0.494509 + 0.869172i \(0.664652\pi\)
\(734\) 10.9121 0.402773
\(735\) 0 0
\(736\) 6.42419 0.236799
\(737\) 3.51524 2.02953i 0.129486 0.0747586i
\(738\) 0 0
\(739\) 4.59353 7.95623i 0.168976 0.292675i −0.769084 0.639147i \(-0.779287\pi\)
0.938060 + 0.346473i \(0.112621\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 3.08485 + 20.3152i 0.113248 + 0.745795i
\(743\) 28.5353i 1.04686i 0.852069 + 0.523430i \(0.175348\pi\)
−0.852069 + 0.523430i \(0.824652\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 19.4924 + 11.2539i 0.713667 + 0.412036i
\(747\) 0 0
\(748\) 1.81657i 0.0664203i
\(749\) −3.51234 4.39442i −0.128338 0.160569i
\(750\) 0 0
\(751\) 21.4749 + 37.1956i 0.783629 + 1.35729i 0.929814 + 0.368029i \(0.119967\pi\)
−0.146185 + 0.989257i \(0.546700\pi\)
\(752\) −3.27213 + 5.66749i −0.119322 + 0.206672i
\(753\) 0 0
\(754\) −21.1043 + 12.1846i −0.768574 + 0.443736i
\(755\) 0 0
\(756\) 0 0
\(757\) 19.4415 0.706612 0.353306 0.935508i \(-0.385057\pi\)
0.353306 + 0.935508i \(0.385057\pi\)
\(758\) 2.82245 1.62954i 0.102516 0.0591877i
\(759\) 0 0
\(760\) 0 0
\(761\) 24.9154 + 43.1547i 0.903182 + 1.56436i 0.823339 + 0.567550i \(0.192109\pi\)
0.0798434 + 0.996807i \(0.474558\pi\)
\(762\) 0 0
\(763\) 19.4739 + 7.61827i 0.705003 + 0.275800i
\(764\) 8.10892i 0.293371i
\(765\) 0 0
\(766\) 15.0013 + 8.66098i 0.542017 + 0.312934i
\(767\) 14.5072 + 8.37575i 0.523825 + 0.302431i
\(768\) 0 0
\(769\) 29.5025i 1.06389i −0.846779 0.531944i \(-0.821462\pi\)
0.846779 0.531944i \(-0.178538\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.02502 + 10.4356i 0.216845 + 0.375587i
\(773\) −12.6641 + 21.9349i −0.455498 + 0.788945i −0.998717 0.0506458i \(-0.983872\pi\)
0.543219 + 0.839591i \(0.317205\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 9.05174 0.324938
\(777\) 0 0
\(778\) 31.6982 1.13644
\(779\) −6.95465 + 4.01527i −0.249176 + 0.143862i
\(780\) 0 0
\(781\) 2.57509 4.46019i 0.0921440 0.159598i
\(782\) 11.7558 + 20.3616i 0.420385 + 0.728129i
\(783\) 0 0
\(784\) 5.14181 + 4.74992i 0.183636 + 0.169640i
\(785\) 0 0
\(786\) 0 0
\(787\) −5.89278 3.40220i −0.210055 0.121275i 0.391282 0.920271i \(-0.372032\pi\)
−0.601337 + 0.798996i \(0.705365\pi\)
\(788\) −11.0386 6.37315i −0.393235 0.227034i
\(789\) 0 0