Properties

Label 3150.2.bf.e.1601.4
Level 3150
Weight 2
Character 3150.1601
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 \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1601.4
Character \(\chi\) = 3150.1601
Dual form 3150.2.bf.e.1151.4

$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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 \(-0.690507\pi\)
0.433795 + 0.901011i \(0.357174\pi\)
\(12\) 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 0.997969 0.0636974i \(-0.0202893\pi\)
−0.554148 + 0.832418i \(0.686956\pi\)
\(18\) 0 0
\(19\) 3.12125 + 1.80205i 0.716064 + 0.413420i 0.813302 0.581841i \(-0.197668\pi\)
−0.0972384 + 0.995261i \(0.531001\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.496352 0.105823
\(23\) 5.56351 + 3.21210i 1.16007 + 0.669768i 0.951321 0.308200i \(-0.0997267\pi\)
0.208751 + 0.977969i \(0.433060\pi\)
\(24\) 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 −0.969216 0.246211i \(-0.920814\pi\)
−0.271383 + 0.962472i \(0.587481\pi\)
\(32\) 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 \(-0.893634\pi\)
0.756377 + 0.654136i \(0.226968\pi\)
\(38\) −1.80205 3.12125i −0.292332 0.506334i
\(39\) 0 0
\(40\) 0 0
\(41\) 2.22816 0.347980 0.173990 0.984747i \(-0.444334\pi\)
0.173990 + 0.984747i \(0.444334\pi\)
\(42\) 0 0
\(43\) 2.22575 0.339424 0.169712 0.985494i \(-0.445716\pi\)
0.169712 + 0.985494i \(0.445716\pi\)
\(44\) −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 −0.999661 0.0260292i \(-0.991714\pi\)
0.522373 + 0.852717i \(0.325047\pi\)
\(48\) 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 0.0390085 0.999239i \(-0.487580\pi\)
0.884870 + 0.465837i \(0.154247\pi\)
\(54\) 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 \(-0.0366040\pi\)
−0.596067 + 0.802935i \(0.703271\pi\)
\(60\) 0 0
\(61\) 3.24271 + 1.87218i 0.415187 + 0.239708i 0.693016 0.720922i \(-0.256282\pi\)
−0.277829 + 0.960630i \(0.589615\pi\)
\(62\) 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 \(-0.333163\pi\)
−1.00000 0.000534152i \(0.999830\pi\)
\(68\) −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 \(-0.389553\pi\)
0.984443 + 0.175704i \(0.0562201\pi\)
\(74\) 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 −0.500074 0.865983i \(-0.666694\pi\)
1.00000 8.52501e-5i \(2.71360e-5\pi\)
\(80\) 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 \(-0.858449\pi\)
0.823921 + 0.566704i \(0.191782\pi\)
\(90\) 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 \(-0.214412\pi\)
−0.931019 + 0.364972i \(0.881079\pi\)
\(102\) 0 0
\(103\) 12.4491 + 7.18752i 1.22665 + 0.708207i 0.966328 0.257314i \(-0.0828376\pi\)
0.260323 + 0.965522i \(0.416171\pi\)
\(104\) −2.74440 −0.269111
\(105\) 0 0
\(106\) −7.76645 −0.754344
\(107\) 1.84141 + 1.06314i 0.178016 + 0.102778i 0.586360 0.810050i \(-0.300560\pi\)
−0.408344 + 0.912828i \(0.633894\pi\)
\(108\) 0 0
\(109\) −3.95181 6.84474i −0.378515 0.655607i 0.612331 0.790601i \(-0.290232\pi\)
−0.990846 + 0.134994i \(0.956899\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.06672 + 1.65187i 0.195287 + 0.156087i
\(113\) 12.2968i 1.15678i 0.815760 + 0.578391i \(0.196319\pi\)
−0.815760 + 0.578391i \(0.803681\pi\)
\(114\) 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 \(-0.489357\pi\)
0.0334287 + 0.999441i \(0.489357\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) −6.35624 + 11.0093i −0.555347 + 0.961890i 0.442529 + 0.896754i \(0.354081\pi\)
−0.997876 + 0.0651355i \(0.979252\pi\)
\(132\) 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 −0.331808 0.943347i \(-0.607659\pi\)
0.651058 + 0.759028i \(0.274325\pi\)
\(138\) 0 0
\(139\) 0.0681276i 0.00577851i −0.999996 0.00288926i \(-0.999080\pi\)
0.999996 0.00288926i \(-0.000919680\pi\)
\(140\) 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 \(-0.0935783\pi\)
0.227602 + 0.973754i \(0.426912\pi\)
\(150\) 0 0
\(151\) 6.51016 + 11.2759i 0.529789 + 0.917622i 0.999396 + 0.0347463i \(0.0110623\pi\)
−0.469607 + 0.882876i \(0.655604\pi\)
\(152\) 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 \(-0.465436\pi\)
0.915112 + 0.403200i \(0.132102\pi\)
\(158\) −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 −0.390171 0.920742i \(-0.627584\pi\)
0.992472 0.122473i \(-0.0390825\pi\)
\(164\) 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 −0.523524 0.852011i \(-0.675383\pi\)
0.999625 + 0.0273795i \(0.00871625\pi\)
\(174\) 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 \(-0.688519\pi\)
0.439416 + 0.898284i \(0.355186\pi\)
\(180\) 0 0
\(181\) 23.6564i 1.75837i 0.476481 + 0.879185i \(0.341912\pi\)
−0.476481 + 0.879185i \(0.658088\pi\)
\(182\) 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 \(-0.238556\pi\)
−0.223933 + 0.974605i \(0.571890\pi\)
\(192\) 0 0
\(193\) 6.02502 + 10.4356i 0.433691 + 0.751174i 0.997188 0.0749438i \(-0.0238777\pi\)
−0.563497 + 0.826118i \(0.690544\pi\)
\(194\) −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 \(0.150028\pi\)
−0.890967 + 0.454068i \(0.849972\pi\)
\(198\) 0 0
\(199\) 16.4954 9.52361i 1.16933 0.675111i 0.215805 0.976436i \(-0.430762\pi\)
0.953521 + 0.301325i \(0.0974290\pi\)
\(200\) 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 0.978241 0.207473i \(-0.0665240\pi\)
−0.668797 + 0.743445i \(0.733191\pi\)
\(228\) 0 0
\(229\) 20.1545 + 11.6362i 1.33185 + 0.768944i 0.985583 0.169193i \(-0.0541160\pi\)
0.346266 + 0.938136i \(0.387449\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 8.87959 0.582973
\(233\) 10.9295 + 6.31017i 0.716018 + 0.413393i 0.813285 0.581865i \(-0.197677\pi\)
−0.0972676 + 0.995258i \(0.531010\pi\)
\(234\) 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 −0.956070 0.293140i \(-0.905300\pi\)
−0.224168 + 0.974550i \(0.571966\pi\)
\(242\) 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 \(-0.438713\pi\)
0.191352 + 0.981522i \(0.438713\pi\)
\(252\) 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 −0.642296 0.766457i \(-0.722018\pi\)
0.984919 + 0.173016i \(0.0553513\pi\)
\(258\) 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 −0.535319 0.844650i \(-0.679809\pi\)
0.463829 + 0.885925i \(0.346475\pi\)
\(264\) 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 \(-0.160627\pi\)
−0.856384 + 0.516340i \(0.827294\pi\)
\(270\) 0 0
\(271\) 18.4634 + 10.6598i 1.12157 + 0.647539i 0.941801 0.336170i \(-0.109132\pi\)
0.179769 + 0.983709i \(0.442465\pi\)
\(272\) −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 \(-0.178021\pi\)
−0.883306 + 0.468797i \(0.844688\pi\)
\(278\) −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 \(-0.965244\pi\)
−0.402650 + 0.915354i \(0.631911\pi\)
\(284\) 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 \(-0.227070\pi\)
−0.944792 + 0.327671i \(0.893736\pi\)
\(312\) 0 0
\(313\) 10.5184 + 6.07282i 0.594537 + 0.343256i 0.766890 0.641779i \(-0.221803\pi\)
−0.172352 + 0.985035i \(0.555137\pi\)
\(314\) −14.8082 −0.835673
\(315\) 0 0
\(316\) 8.88688 0.499926
\(317\) −26.6051 15.3605i −1.49429 0.862730i −0.494314 0.869283i \(-0.664581\pi\)
−0.999979 + 0.00655283i \(0.997914\pi\)
\(318\) 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 −0.0260166 0.999662i \(-0.508282\pi\)
0.878741 0.477300i \(-0.158384\pi\)
\(332\) 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 \(-0.560309\pi\)
−0.188334 + 0.982105i \(0.560309\pi\)
\(338\) −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 −0.663982 0.747748i \(-0.731135\pi\)
0.315578 + 0.948900i \(0.397802\pi\)
\(348\) 0 0
\(349\) 12.4552i 0.666714i 0.942801 + 0.333357i \(0.108181\pi\)
−0.942801 + 0.333357i \(0.891819\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.248176 + 0.429853i −0.0132278 + 0.0229113i
\(353\) −9.47011 16.4027i −0.504043 0.873028i −0.999989 0.00467471i \(-0.998512\pi\)
0.495946 0.868353i \(-0.334821\pi\)
\(354\) 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 \(-0.581329\pi\)
−0.964277 + 0.264898i \(0.914662\pi\)
\(360\) 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 \(-0.574738\pi\)
0.725940 + 0.687758i \(0.241405\pi\)
\(368\) −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 −0.412450 0.910980i \(-0.635327\pi\)
0.995157 0.0982976i \(-0.0313397\pi\)
\(374\) 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 −0.997878 0.0651064i \(-0.979261\pi\)
0.555323 + 0.831635i \(0.312595\pi\)
\(384\) 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 \(-0.369591\pi\)
0.993520 + 0.113662i \(0.0362580\pi\)
\(390\) 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 \(-0.651345\pi\)
−0.998842 + 0.0481170i \(0.984678\pi\)
\(398\) −19.0472 −0.954751
\(399\) 0 0
\(400\) 0 0
\(401\) 31.0404 + 17.9212i 1.55008 + 0.894940i 0.998134 + 0.0610611i \(0.0194485\pi\)
0.551947 + 0.833879i \(0.313885\pi\)
\(402\) 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 −0.924201 0.381905i \(-0.875268\pi\)
−0.131361 + 0.991335i \(0.541935\pi\)
\(410\) 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 \(-0.583829\pi\)
−0.260323 + 0.965522i \(0.583829\pi\)
\(420\) 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 \(-0.408839\pi\)
0.971998 + 0.234991i \(0.0755061\pi\)
\(432\) 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 0.741169 0.671318i \(-0.234272\pi\)
−0.210794 + 0.977530i \(0.567605\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −10.0441 −0.477748
\(443\) 17.6792 + 10.2071i 0.839963 + 0.484953i 0.857252 0.514898i \(-0.172170\pi\)
−0.0172887 + 0.999851i \(0.505503\pi\)
\(444\) 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 \(-0.955653\pi\)
0.615420 + 0.788199i \(0.288986\pi\)
\(458\) −11.6362 20.1545i −0.543725 0.941760i
\(459\) 0 0
\(460\) 0 0
\(461\) 1.98400 0.0924039 0.0462020 0.998932i \(-0.485288\pi\)
0.0462020 + 0.998932i \(0.485288\pi\)
\(462\) 0 0
\(463\) −36.3987 −1.69159 −0.845796 0.533506i \(-0.820874\pi\)
−0.845796 + 0.533506i \(0.820874\pi\)
\(464\) −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 −0.242428 0.970169i \(-0.577944\pi\)
0.961405 0.275136i \(-0.0887227\pi\)
\(468\) 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 −0.895305 0.445453i \(-0.853043\pi\)
0.0618788 0.998084i \(-0.480291\pi\)
\(480\) 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 \(-0.0629086\pi\)
−0.660310 + 0.750993i \(0.729575\pi\)
\(488\) 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 −0.967026 0.254679i \(-0.918030\pi\)
0.704071 + 0.710130i \(0.251364\pi\)
\(500\) 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 \(-0.749896\pi\)
0.966010 + 0.258503i \(0.0832293\pi\)
\(510\) 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 0.982795 + 0.184702i \(0.0591319\pi\)
−0.331441 + 0.943476i \(0.607535\pi\)
\(522\) 0 0
\(523\) 4.90024 + 2.82915i 0.214272 + 0.123710i 0.603295 0.797518i \(-0.293854\pi\)
−0.389023 + 0.921228i \(0.627187\pi\)
\(524\) −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 −0.183041 0.983105i \(-0.558594\pi\)
0.942915 0.333035i \(-0.108073\pi\)
\(542\) −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 \(-0.348128\pi\)
0.459223 + 0.888321i \(0.348128\pi\)
\(548\) 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 0.462469 0.886635i \(-0.346964\pi\)
0.999083 + 0.0428076i \(0.0136303\pi\)
\(558\) 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 0.736257 0.676702i \(-0.236592\pi\)
−0.954170 + 0.299266i \(0.903258\pi\)
\(564\) 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 \(-0.132747\pi\)
0.106361 + 0.994328i \(0.466080\pi\)
\(570\) 0 0
\(571\) 13.7146 + 23.7544i 0.573938 + 0.994090i 0.996156 + 0.0875958i \(0.0279184\pi\)
−0.422218 + 0.906494i \(0.638748\pi\)
\(572\) −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 \(-0.754151\pi\)
0.246200 + 0.969219i \(0.420818\pi\)
\(578\) −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 −0.647292 0.762242i \(-0.724099\pi\)
0.983767 + 0.179450i \(0.0574319\pi\)
\(594\) 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 \(-0.877524\pi\)
−0.138382 + 0.990379i \(0.544190\pi\)
\(600\) 0 0
\(601\) 1.75569i 0.0716162i 0.999359 + 0.0358081i \(0.0114005\pi\)
−0.999359 + 0.0358081i \(0.988599\pi\)
\(602\) −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 \(-0.452868\pi\)
−0.782785 + 0.622292i \(0.786202\pi\)
\(608\) 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 \(-0.0831069\pi\)
−0.706604 + 0.707610i \(0.749774\pi\)
\(614\) −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 \(0.270956\pi\)
−0.659055 + 0.752094i \(0.729044\pi\)
\(618\) 0 0
\(619\) 23.7213 13.6955i 0.953439 0.550468i 0.0592911 0.998241i \(-0.481116\pi\)
0.894147 + 0.447773i \(0.147783\pi\)
\(620\) 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 \(-0.891574\pi\)
−0.181951 + 0.983308i \(0.558241\pi\)
\(642\) 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 0.809291 0.587408i \(-0.199852\pi\)
−0.913356 + 0.407162i \(0.866518\pi\)
\(648\) 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 −0.947094 0.320956i \(-0.895996\pi\)
−0.751503 0.659729i \(-0.770671\pi\)
\(654\) 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 −0.982618 0.185638i \(-0.940565\pi\)
−0.330542 + 0.943791i \(0.607231\pi\)
\(662\) −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 \(-0.816318\pi\)
−0.838074 + 0.545556i \(0.816318\pi\)
\(674\) 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 0.118626 + 0.992939i \(0.462151\pi\)
−0.919223 + 0.393736i \(0.871182\pi\)
\(678\) 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 0.586940 0.809630i \(-0.300332\pi\)
0.994631 0.103490i \(-0.0330010\pi\)
\(684\) 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 0.977183 0.212399i \(-0.0681277\pi\)
0.304648 + 0.952465i \(0.401461\pi\)
\(692\) 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 −0.978371 0.206860i \(-0.933676\pi\)
0.668331 + 0.743864i \(0.267009\pi\)
\(710\) 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 0.0476171 + 0.998866i \(0.484837\pi\)
−0.888852 + 0.458195i \(0.848496\pi\)
\(720\) 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 \(-0.00201440\pi\)
0.494509 + 0.869172i \(0.335348\pi\)
\(734\) −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 0.938060 0.346473i \(-0.112621\pi\)
−0.769084 + 0.639147i \(0.779287\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −3.08485 + 20.3152i −0.113248 + 0.745795i
\(743\) 28.5353i 1.04686i −0.852069 0.523430i \(-0.824652\pi\)
0.852069 0.523430i \(-0.175348\pi\)
\(744\) 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 −0.146185 0.989257i \(-0.546700\pi\)
0.929814 0.368029i \(-0.119967\pi\)
\(752\) −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 \(-0.614943\pi\)
−0.353306 + 0.935508i \(0.614943\pi\)
\(758\) 2.82245 + 1.62954i 0.102516 + 0.0591877i
\(759\) 0 0
\(760\) 0 0
\(761\) −24.9154 + 43.1547i −0.903182 + 1.56436i −0.0798434 + 0.996807i \(0.525442\pi\)
−0.823339 + 0.567550i \(0.807891\pi\)
\(762\) 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 \(0.178538\pi\)
−0.846779 + 0.531944i \(0.821462\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −6.02502 + 10.4356i −0.216845 + 0.375587i
\(773\) −12.6641 21.9349i −0.455498 0.788945i 0.543219 0.839591i \(-0.317205\pi\)
−0.998717 + 0.0506458i \(0.983872\pi\)
\(774\) 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 \(-0.627968\pi\)
0.601337 + 0.798996i \(0.294635\pi\)