Properties

Label 3150.2.bp.h.1349.4
Level 3150
Weight 2
Character 3150.1349
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.bp (of order \(6\), degree \(2\), not 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 1349.4
Character \(\chi\) = 3150.1349
Dual form 3150.2.bp.h.899.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.16005 + 1.52781i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.16005 + 1.52781i) q^{7} -1.00000 q^{8} +(4.29783 - 2.48135i) q^{11} -5.49388 q^{13} +(0.243099 + 2.63456i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.66237 - 1.53712i) q^{17} +(2.68622 + 1.55089i) q^{19} -4.96270i q^{22} +(-3.08810 + 5.34875i) q^{23} +(-2.74694 + 4.75784i) q^{26} +(2.40314 + 1.10675i) q^{28} +6.67885i q^{29} +(-1.01653 + 0.586893i) q^{31} +(0.500000 + 0.866025i) q^{32} -3.07424i q^{34} +(-9.27339 - 5.35400i) q^{37} +(2.68622 - 1.55089i) q^{38} -8.39427 q^{41} +8.81025i q^{43} +(-4.29783 - 2.48135i) q^{44} +(3.08810 + 5.34875i) q^{46} +(3.59075 + 2.07312i) q^{47} +(2.33160 - 6.60028i) q^{49} +(2.74694 + 4.75784i) q^{52} +(-2.22536 - 3.85443i) q^{53} +(2.16005 - 1.52781i) q^{56} +(5.78405 + 3.33943i) q^{58} +(-3.00381 - 5.20275i) q^{59} +(9.05018 + 5.22512i) q^{61} +1.17379i q^{62} +1.00000 q^{64} +(10.3529 - 5.97727i) q^{67} +(-2.66237 - 1.53712i) q^{68} -0.973522i q^{71} +(8.34916 + 14.4612i) q^{73} +(-9.27339 + 5.35400i) q^{74} -3.10178i q^{76} +(-5.49247 + 11.9261i) q^{77} +(-2.12328 + 3.67763i) q^{79} +(-4.19713 + 7.26965i) q^{82} +14.2841i q^{83} +(7.62990 + 4.40513i) q^{86} +(-4.29783 + 2.48135i) q^{88} +(-7.38517 + 12.7915i) q^{89} +(11.8670 - 8.39360i) q^{91} +6.17620 q^{92} +(3.59075 - 2.07312i) q^{94} -4.41643 q^{97} +(-4.55021 - 5.31936i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 12q^{2} - 12q^{4} - 24q^{8} + O(q^{10}) \) \( 24q + 12q^{2} - 12q^{4} - 24q^{8} - 12q^{16} - 24q^{17} - 12q^{19} + 8q^{23} + 12q^{32} - 12q^{38} - 8q^{46} + 24q^{47} + 52q^{49} + 32q^{53} - 12q^{61} + 24q^{64} + 24q^{68} + 16q^{77} - 4q^{79} + 68q^{91} - 16q^{92} + 24q^{94} + 20q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −2.16005 + 1.52781i −0.816421 + 0.577458i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) 4.29783 2.48135i 1.29584 0.748156i 0.316160 0.948706i \(-0.397606\pi\)
0.979683 + 0.200550i \(0.0642729\pi\)
\(12\) 0 0
\(13\) −5.49388 −1.52373 −0.761864 0.647737i \(-0.775715\pi\)
−0.761864 + 0.647737i \(0.775715\pi\)
\(14\) 0.243099 + 2.63456i 0.0649709 + 0.704116i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.66237 1.53712i 0.645719 0.372806i −0.141095 0.989996i \(-0.545062\pi\)
0.786814 + 0.617190i \(0.211729\pi\)
\(18\) 0 0
\(19\) 2.68622 + 1.55089i 0.616261 + 0.355798i 0.775412 0.631456i \(-0.217542\pi\)
−0.159151 + 0.987254i \(0.550876\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 4.96270i 1.05805i
\(23\) −3.08810 + 5.34875i −0.643914 + 1.11529i 0.340638 + 0.940195i \(0.389357\pi\)
−0.984551 + 0.175097i \(0.943976\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −2.74694 + 4.75784i −0.538719 + 0.933089i
\(27\) 0 0
\(28\) 2.40314 + 1.10675i 0.454152 + 0.209156i
\(29\) 6.67885i 1.24023i 0.784510 + 0.620116i \(0.212914\pi\)
−0.784510 + 0.620116i \(0.787086\pi\)
\(30\) 0 0
\(31\) −1.01653 + 0.586893i −0.182574 + 0.105409i −0.588501 0.808496i \(-0.700282\pi\)
0.405928 + 0.913905i \(0.366949\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 3.07424i 0.527228i
\(35\) 0 0
\(36\) 0 0
\(37\) −9.27339 5.35400i −1.52454 0.880192i −0.999578 0.0290640i \(-0.990747\pi\)
−0.524959 0.851128i \(-0.675919\pi\)
\(38\) 2.68622 1.55089i 0.435762 0.251587i
\(39\) 0 0
\(40\) 0 0
\(41\) −8.39427 −1.31096 −0.655482 0.755211i \(-0.727534\pi\)
−0.655482 + 0.755211i \(0.727534\pi\)
\(42\) 0 0
\(43\) 8.81025i 1.34355i 0.740755 + 0.671776i \(0.234468\pi\)
−0.740755 + 0.671776i \(0.765532\pi\)
\(44\) −4.29783 2.48135i −0.647922 0.374078i
\(45\) 0 0
\(46\) 3.08810 + 5.34875i 0.455316 + 0.788630i
\(47\) 3.59075 + 2.07312i 0.523765 + 0.302396i 0.738474 0.674282i \(-0.235547\pi\)
−0.214709 + 0.976678i \(0.568880\pi\)
\(48\) 0 0
\(49\) 2.33160 6.60028i 0.333085 0.942897i
\(50\) 0 0
\(51\) 0 0
\(52\) 2.74694 + 4.75784i 0.380932 + 0.659793i
\(53\) −2.22536 3.85443i −0.305676 0.529446i 0.671736 0.740791i \(-0.265549\pi\)
−0.977412 + 0.211345i \(0.932216\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.16005 1.52781i 0.288648 0.204162i
\(57\) 0 0
\(58\) 5.78405 + 3.33943i 0.759484 + 0.438488i
\(59\) −3.00381 5.20275i −0.391062 0.677340i 0.601528 0.798852i \(-0.294559\pi\)
−0.992590 + 0.121512i \(0.961226\pi\)
\(60\) 0 0
\(61\) 9.05018 + 5.22512i 1.15876 + 0.669008i 0.951006 0.309173i \(-0.100052\pi\)
0.207751 + 0.978182i \(0.433386\pi\)
\(62\) 1.17379i 0.149071i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 10.3529 5.97727i 1.26481 0.730240i 0.290811 0.956780i \(-0.406075\pi\)
0.974002 + 0.226540i \(0.0727414\pi\)
\(68\) −2.66237 1.53712i −0.322860 0.186403i
\(69\) 0 0
\(70\) 0 0
\(71\) 0.973522i 0.115536i −0.998330 0.0577679i \(-0.981602\pi\)
0.998330 0.0577679i \(-0.0183983\pi\)
\(72\) 0 0
\(73\) 8.34916 + 14.4612i 0.977196 + 1.69255i 0.672490 + 0.740106i \(0.265225\pi\)
0.304706 + 0.952446i \(0.401442\pi\)
\(74\) −9.27339 + 5.35400i −1.07801 + 0.622389i
\(75\) 0 0
\(76\) 3.10178i 0.355798i
\(77\) −5.49247 + 11.9261i −0.625925 + 1.35910i
\(78\) 0 0
\(79\) −2.12328 + 3.67763i −0.238887 + 0.413765i −0.960395 0.278641i \(-0.910116\pi\)
0.721508 + 0.692406i \(0.243449\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −4.19713 + 7.26965i −0.463496 + 0.802798i
\(83\) 14.2841i 1.56789i 0.620831 + 0.783944i \(0.286795\pi\)
−0.620831 + 0.783944i \(0.713205\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 7.62990 + 4.40513i 0.822754 + 0.475017i
\(87\) 0 0
\(88\) −4.29783 + 2.48135i −0.458150 + 0.264513i
\(89\) −7.38517 + 12.7915i −0.782826 + 1.35590i 0.147463 + 0.989068i \(0.452889\pi\)
−0.930289 + 0.366827i \(0.880444\pi\)
\(90\) 0 0
\(91\) 11.8670 8.39360i 1.24400 0.879888i
\(92\) 6.17620 0.643914
\(93\) 0 0
\(94\) 3.59075 2.07312i 0.370358 0.213826i
\(95\) 0 0
\(96\) 0 0
\(97\) −4.41643 −0.448420 −0.224210 0.974541i \(-0.571980\pi\)
−0.224210 + 0.974541i \(0.571980\pi\)
\(98\) −4.55021 5.31936i −0.459641 0.537336i
\(99\) 0 0
\(100\) 0 0
\(101\) 5.19825 + 9.00364i 0.517245 + 0.895895i 0.999799 + 0.0200290i \(0.00637586\pi\)
−0.482554 + 0.875866i \(0.660291\pi\)
\(102\) 0 0
\(103\) −5.11942 + 8.86709i −0.504431 + 0.873701i 0.495556 + 0.868576i \(0.334965\pi\)
−0.999987 + 0.00512447i \(0.998369\pi\)
\(104\) 5.49388 0.538719
\(105\) 0 0
\(106\) −4.45071 −0.432291
\(107\) 3.28972 5.69797i 0.318030 0.550844i −0.662047 0.749462i \(-0.730312\pi\)
0.980077 + 0.198619i \(0.0636455\pi\)
\(108\) 0 0
\(109\) 1.34219 + 2.32474i 0.128558 + 0.222669i 0.923118 0.384516i \(-0.125632\pi\)
−0.794560 + 0.607186i \(0.792298\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.243099 2.63456i −0.0229707 0.248942i
\(113\) −3.55031 −0.333985 −0.166992 0.985958i \(-0.553406\pi\)
−0.166992 + 0.985958i \(0.553406\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 5.78405 3.33943i 0.537036 0.310058i
\(117\) 0 0
\(118\) −6.00761 −0.553046
\(119\) −3.40241 + 7.38784i −0.311899 + 0.677242i
\(120\) 0 0
\(121\) 6.81421 11.8026i 0.619474 1.07296i
\(122\) 9.05018 5.22512i 0.819365 0.473060i
\(123\) 0 0
\(124\) 1.01653 + 0.586893i 0.0912869 + 0.0527045i
\(125\) 0 0
\(126\) 0 0
\(127\) 5.51567i 0.489437i 0.969594 + 0.244719i \(0.0786955\pi\)
−0.969594 + 0.244719i \(0.921304\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −10.3068 + 17.8519i −0.900510 + 1.55973i −0.0736773 + 0.997282i \(0.523473\pi\)
−0.826833 + 0.562447i \(0.809860\pi\)
\(132\) 0 0
\(133\) −8.17182 + 0.754039i −0.708586 + 0.0653835i
\(134\) 11.9545i 1.03272i
\(135\) 0 0
\(136\) −2.66237 + 1.53712i −0.228296 + 0.131807i
\(137\) 5.72807 + 9.92131i 0.489382 + 0.847635i 0.999925 0.0122175i \(-0.00388903\pi\)
−0.510543 + 0.859852i \(0.670556\pi\)
\(138\) 0 0
\(139\) 1.16700i 0.0989840i −0.998775 0.0494920i \(-0.984240\pi\)
0.998775 0.0494920i \(-0.0157602\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.843095 0.486761i −0.0707509 0.0408481i
\(143\) −23.6117 + 13.6322i −1.97451 + 1.13999i
\(144\) 0 0
\(145\) 0 0
\(146\) 16.6983 1.38196
\(147\) 0 0
\(148\) 10.7080i 0.880192i
\(149\) 13.3404 + 7.70205i 1.09288 + 0.630977i 0.934343 0.356375i \(-0.115988\pi\)
0.158541 + 0.987352i \(0.449321\pi\)
\(150\) 0 0
\(151\) −0.511281 0.885565i −0.0416075 0.0720663i 0.844472 0.535600i \(-0.179915\pi\)
−0.886079 + 0.463534i \(0.846581\pi\)
\(152\) −2.68622 1.55089i −0.217881 0.125794i
\(153\) 0 0
\(154\) 7.58207 + 10.7197i 0.610980 + 0.863815i
\(155\) 0 0
\(156\) 0 0
\(157\) −2.68294 4.64699i −0.214122 0.370871i 0.738878 0.673839i \(-0.235356\pi\)
−0.953001 + 0.302968i \(0.902022\pi\)
\(158\) 2.12328 + 3.67763i 0.168919 + 0.292576i
\(159\) 0 0
\(160\) 0 0
\(161\) −1.50143 16.2716i −0.118329 1.28238i
\(162\) 0 0
\(163\) −8.69677 5.02108i −0.681184 0.393282i 0.119117 0.992880i \(-0.461994\pi\)
−0.800301 + 0.599599i \(0.795327\pi\)
\(164\) 4.19713 + 7.26965i 0.327741 + 0.567664i
\(165\) 0 0
\(166\) 12.3704 + 7.14207i 0.960131 + 0.554332i
\(167\) 2.46005i 0.190364i 0.995460 + 0.0951822i \(0.0303434\pi\)
−0.995460 + 0.0951822i \(0.969657\pi\)
\(168\) 0 0
\(169\) 17.1827 1.32175
\(170\) 0 0
\(171\) 0 0
\(172\) 7.62990 4.40513i 0.581775 0.335888i
\(173\) −2.59880 1.50042i −0.197583 0.114075i 0.397944 0.917410i \(-0.369724\pi\)
−0.595528 + 0.803335i \(0.703057\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 4.96270i 0.374078i
\(177\) 0 0
\(178\) 7.38517 + 12.7915i 0.553542 + 0.958763i
\(179\) −3.18036 + 1.83618i −0.237711 + 0.137243i −0.614124 0.789209i \(-0.710491\pi\)
0.376413 + 0.926452i \(0.377157\pi\)
\(180\) 0 0
\(181\) 6.13560i 0.456056i 0.973655 + 0.228028i \(0.0732278\pi\)
−0.973655 + 0.228028i \(0.926772\pi\)
\(182\) −1.33556 14.4739i −0.0989980 1.07288i
\(183\) 0 0
\(184\) 3.08810 5.34875i 0.227658 0.394315i
\(185\) 0 0
\(186\) 0 0
\(187\) 7.62827 13.2125i 0.557834 0.966197i
\(188\) 4.14624i 0.302396i
\(189\) 0 0
\(190\) 0 0
\(191\) −4.95227 2.85920i −0.358334 0.206884i 0.310016 0.950731i \(-0.399666\pi\)
−0.668350 + 0.743847i \(0.732999\pi\)
\(192\) 0 0
\(193\) 5.39819 3.11665i 0.388570 0.224341i −0.292970 0.956122i \(-0.594644\pi\)
0.681541 + 0.731780i \(0.261310\pi\)
\(194\) −2.20821 + 3.82474i −0.158540 + 0.274600i
\(195\) 0 0
\(196\) −6.88181 + 1.28092i −0.491558 + 0.0914941i
\(197\) −1.32234 −0.0942128 −0.0471064 0.998890i \(-0.515000\pi\)
−0.0471064 + 0.998890i \(0.515000\pi\)
\(198\) 0 0
\(199\) 8.27163 4.77563i 0.586360 0.338535i −0.177297 0.984157i \(-0.556735\pi\)
0.763657 + 0.645622i \(0.223402\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 10.3965 0.731495
\(203\) −10.2040 14.4266i −0.716181 1.01255i
\(204\) 0 0
\(205\) 0 0
\(206\) 5.11942 + 8.86709i 0.356687 + 0.617800i
\(207\) 0 0
\(208\) 2.74694 4.75784i 0.190466 0.329897i
\(209\) 15.3932 1.06477
\(210\) 0 0
\(211\) 26.0219 1.79142 0.895711 0.444636i \(-0.146667\pi\)
0.895711 + 0.444636i \(0.146667\pi\)
\(212\) −2.22536 + 3.85443i −0.152838 + 0.264723i
\(213\) 0 0
\(214\) −3.28972 5.69797i −0.224881 0.389505i
\(215\) 0 0
\(216\) 0 0
\(217\) 1.29909 2.82078i 0.0881878 0.191487i
\(218\) 2.68437 0.181809
\(219\) 0 0
\(220\) 0 0
\(221\) −14.6267 + 8.44475i −0.983900 + 0.568055i
\(222\) 0 0
\(223\) 7.25222 0.485644 0.242822 0.970071i \(-0.421927\pi\)
0.242822 + 0.970071i \(0.421927\pi\)
\(224\) −2.40314 1.10675i −0.160567 0.0739478i
\(225\) 0 0
\(226\) −1.77515 + 3.07466i −0.118081 + 0.204523i
\(227\) −23.1409 + 13.3604i −1.53592 + 0.886762i −0.536846 + 0.843680i \(0.680384\pi\)
−0.999072 + 0.0430820i \(0.986282\pi\)
\(228\) 0 0
\(229\) −21.0473 12.1517i −1.39085 0.803006i −0.397439 0.917629i \(-0.630101\pi\)
−0.993409 + 0.114622i \(0.963434\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.67885i 0.438488i
\(233\) 4.62788 8.01573i 0.303183 0.525128i −0.673672 0.739030i \(-0.735284\pi\)
0.976855 + 0.213902i \(0.0686174\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −3.00381 + 5.20275i −0.195531 + 0.338670i
\(237\) 0 0
\(238\) 4.69685 + 6.64050i 0.304452 + 0.430439i
\(239\) 0.253367i 0.0163889i −0.999966 0.00819446i \(-0.997392\pi\)
0.999966 0.00819446i \(-0.00260841\pi\)
\(240\) 0 0
\(241\) 2.57538 1.48689i 0.165895 0.0957792i −0.414754 0.909934i \(-0.636132\pi\)
0.580649 + 0.814154i \(0.302799\pi\)
\(242\) −6.81421 11.8026i −0.438034 0.758698i
\(243\) 0 0
\(244\) 10.4502i 0.669008i
\(245\) 0 0
\(246\) 0 0
\(247\) −14.7578 8.52039i −0.939013 0.542140i
\(248\) 1.01653 0.586893i 0.0645496 0.0372677i
\(249\) 0 0
\(250\) 0 0
\(251\) −13.0800 −0.825599 −0.412800 0.910822i \(-0.635449\pi\)
−0.412800 + 0.910822i \(0.635449\pi\)
\(252\) 0 0
\(253\) 30.6507i 1.92699i
\(254\) 4.77671 + 2.75784i 0.299718 + 0.173042i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 10.9084 + 6.29797i 0.680447 + 0.392856i 0.800023 0.599969i \(-0.204820\pi\)
−0.119576 + 0.992825i \(0.538154\pi\)
\(258\) 0 0
\(259\) 28.2108 2.60310i 1.75294 0.161749i
\(260\) 0 0
\(261\) 0 0
\(262\) 10.3068 + 17.8519i 0.636757 + 1.10290i
\(263\) −8.33594 14.4383i −0.514016 0.890302i −0.999868 0.0162609i \(-0.994824\pi\)
0.485852 0.874041i \(-0.338510\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −3.43289 + 7.45402i −0.210484 + 0.457035i
\(267\) 0 0
\(268\) −10.3529 5.97727i −0.632407 0.365120i
\(269\) 10.0035 + 17.3265i 0.609923 + 1.05642i 0.991253 + 0.131978i \(0.0421328\pi\)
−0.381330 + 0.924439i \(0.624534\pi\)
\(270\) 0 0
\(271\) −15.4684 8.93068i −0.939638 0.542500i −0.0497914 0.998760i \(-0.515856\pi\)
−0.889847 + 0.456259i \(0.849189\pi\)
\(272\) 3.07424i 0.186403i
\(273\) 0 0
\(274\) 11.4561 0.692091
\(275\) 0 0
\(276\) 0 0
\(277\) −15.7167 + 9.07406i −0.944327 + 0.545207i −0.891314 0.453386i \(-0.850216\pi\)
−0.0530128 + 0.998594i \(0.516882\pi\)
\(278\) −1.01066 0.583502i −0.0606151 0.0349961i
\(279\) 0 0
\(280\) 0 0
\(281\) 15.5129i 0.925425i −0.886508 0.462713i \(-0.846876\pi\)
0.886508 0.462713i \(-0.153124\pi\)
\(282\) 0 0
\(283\) −8.82268 15.2813i −0.524454 0.908381i −0.999595 0.0284708i \(-0.990936\pi\)
0.475141 0.879910i \(-0.342397\pi\)
\(284\) −0.843095 + 0.486761i −0.0500285 + 0.0288840i
\(285\) 0 0
\(286\) 27.2645i 1.61218i
\(287\) 18.1320 12.8248i 1.07030 0.757026i
\(288\) 0 0
\(289\) −3.77453 + 6.53767i −0.222031 + 0.384569i
\(290\) 0 0
\(291\) 0 0
\(292\) 8.34916 14.4612i 0.488598 0.846276i
\(293\) 10.4489i 0.610432i 0.952283 + 0.305216i \(0.0987287\pi\)
−0.952283 + 0.305216i \(0.901271\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 9.27339 + 5.35400i 0.539005 + 0.311195i
\(297\) 0 0
\(298\) 13.3404 7.70205i 0.772786 0.446168i
\(299\) 16.9657 29.3854i 0.981149 1.69940i
\(300\) 0 0
\(301\) −13.4604 19.0306i −0.775844 1.09690i
\(302\) −1.02256 −0.0588419
\(303\) 0 0
\(304\) −2.68622 + 1.55089i −0.154065 + 0.0889496i
\(305\) 0 0
\(306\) 0 0
\(307\) 0.724648 0.0413579 0.0206789 0.999786i \(-0.493417\pi\)
0.0206789 + 0.999786i \(0.493417\pi\)
\(308\) 13.0745 1.20643i 0.744991 0.0687426i
\(309\) 0 0
\(310\) 0 0
\(311\) −14.1225 24.4609i −0.800813 1.38705i −0.919081 0.394068i \(-0.871068\pi\)
0.118268 0.992982i \(-0.462266\pi\)
\(312\) 0 0
\(313\) 10.2651 17.7797i 0.580218 1.00497i −0.415235 0.909714i \(-0.636301\pi\)
0.995453 0.0952528i \(-0.0303659\pi\)
\(314\) −5.36589 −0.302815
\(315\) 0 0
\(316\) 4.24656 0.238887
\(317\) 1.13674 1.96890i 0.0638459 0.110584i −0.832336 0.554272i \(-0.812997\pi\)
0.896181 + 0.443688i \(0.146330\pi\)
\(318\) 0 0
\(319\) 16.5726 + 28.7045i 0.927886 + 1.60715i
\(320\) 0 0
\(321\) 0 0
\(322\) −14.8423 6.83551i −0.827130 0.380928i
\(323\) 9.53560 0.530575
\(324\) 0 0
\(325\) 0 0
\(326\) −8.69677 + 5.02108i −0.481670 + 0.278092i
\(327\) 0 0
\(328\) 8.39427 0.463496
\(329\) −10.9235 + 1.00795i −0.602233 + 0.0555699i
\(330\) 0 0
\(331\) 18.0646 31.2889i 0.992922 1.71979i 0.393605 0.919280i \(-0.371228\pi\)
0.599317 0.800512i \(-0.295439\pi\)
\(332\) 12.3704 7.14207i 0.678915 0.391972i
\(333\) 0 0
\(334\) 2.13047 + 1.23003i 0.116574 + 0.0673040i
\(335\) 0 0
\(336\) 0 0
\(337\) 3.76361i 0.205017i 0.994732 + 0.102508i \(0.0326869\pi\)
−0.994732 + 0.102508i \(0.967313\pi\)
\(338\) 8.59134 14.8806i 0.467308 0.809400i
\(339\) 0 0
\(340\) 0 0
\(341\) −2.91258 + 5.04473i −0.157725 + 0.273187i
\(342\) 0 0
\(343\) 5.04761 + 17.8191i 0.272546 + 0.962143i
\(344\) 8.81025i 0.475017i
\(345\) 0 0
\(346\) −2.59880 + 1.50042i −0.139713 + 0.0806631i
\(347\) 2.02389 + 3.50549i 0.108648 + 0.188184i 0.915223 0.402948i \(-0.132014\pi\)
−0.806575 + 0.591132i \(0.798681\pi\)
\(348\) 0 0
\(349\) 23.9364i 1.28129i 0.767838 + 0.640644i \(0.221333\pi\)
−0.767838 + 0.640644i \(0.778667\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 4.29783 + 2.48135i 0.229075 + 0.132256i
\(353\) −22.0679 + 12.7409i −1.17455 + 0.678129i −0.954748 0.297415i \(-0.903876\pi\)
−0.219805 + 0.975544i \(0.570542\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 14.7703 0.782826
\(357\) 0 0
\(358\) 3.67236i 0.194091i
\(359\) −15.4893 8.94277i −0.817496 0.471981i 0.0320565 0.999486i \(-0.489794\pi\)
−0.849552 + 0.527505i \(0.823128\pi\)
\(360\) 0 0
\(361\) −4.68949 8.12243i −0.246815 0.427496i
\(362\) 5.31359 + 3.06780i 0.279276 + 0.161240i
\(363\) 0 0
\(364\) −13.2026 6.08035i −0.692003 0.318697i
\(365\) 0 0
\(366\) 0 0
\(367\) 2.63851 + 4.57004i 0.137729 + 0.238554i 0.926637 0.375958i \(-0.122686\pi\)
−0.788907 + 0.614512i \(0.789353\pi\)
\(368\) −3.08810 5.34875i −0.160978 0.278823i
\(369\) 0 0
\(370\) 0 0
\(371\) 10.6957 + 4.92582i 0.555293 + 0.255736i
\(372\) 0 0
\(373\) −12.5988 7.27390i −0.652339 0.376628i 0.137013 0.990569i \(-0.456250\pi\)
−0.789352 + 0.613941i \(0.789583\pi\)
\(374\) −7.62827 13.2125i −0.394448 0.683205i
\(375\) 0 0
\(376\) −3.59075 2.07312i −0.185179 0.106913i
\(377\) 36.6928i 1.88977i
\(378\) 0 0
\(379\) −3.66669 −0.188345 −0.0941726 0.995556i \(-0.530021\pi\)
−0.0941726 + 0.995556i \(0.530021\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −4.95227 + 2.85920i −0.253380 + 0.146289i
\(383\) −16.9091 9.76247i −0.864015 0.498839i 0.00134002 0.999999i \(-0.499573\pi\)
−0.865355 + 0.501160i \(0.832907\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 6.23330i 0.317266i
\(387\) 0 0
\(388\) 2.20821 + 3.82474i 0.112105 + 0.194172i
\(389\) 14.9711 8.64356i 0.759064 0.438246i −0.0698956 0.997554i \(-0.522267\pi\)
0.828960 + 0.559309i \(0.188933\pi\)
\(390\) 0 0
\(391\) 18.9871i 0.960220i
\(392\) −2.33160 + 6.60028i −0.117763 + 0.333364i
\(393\) 0 0
\(394\) −0.661170 + 1.14518i −0.0333092 + 0.0576933i
\(395\) 0 0
\(396\) 0 0
\(397\) 13.8423 23.9755i 0.694724 1.20330i −0.275549 0.961287i \(-0.588860\pi\)
0.970274 0.242011i \(-0.0778069\pi\)
\(398\) 9.55125i 0.478761i
\(399\) 0 0
\(400\) 0 0
\(401\) 32.7521 + 18.9095i 1.63556 + 0.944293i 0.982335 + 0.187132i \(0.0599194\pi\)
0.653229 + 0.757161i \(0.273414\pi\)
\(402\) 0 0
\(403\) 5.58468 3.22432i 0.278193 0.160615i
\(404\) 5.19825 9.00364i 0.258623 0.447948i
\(405\) 0 0
\(406\) −17.5958 + 1.62362i −0.873266 + 0.0805790i
\(407\) −53.1406 −2.63408
\(408\) 0 0
\(409\) −31.6028 + 18.2459i −1.56266 + 0.902202i −0.565673 + 0.824630i \(0.691383\pi\)
−0.996987 + 0.0775719i \(0.975283\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 10.2388 0.504431
\(413\) 14.4372 + 6.64893i 0.710407 + 0.327172i
\(414\) 0 0
\(415\) 0 0
\(416\) −2.74694 4.75784i −0.134680 0.233272i
\(417\) 0 0
\(418\) 7.69660 13.3309i 0.376453 0.652036i
\(419\) 21.6669 1.05850 0.529249 0.848466i \(-0.322474\pi\)
0.529249 + 0.848466i \(0.322474\pi\)
\(420\) 0 0
\(421\) −8.84193 −0.430929 −0.215465 0.976512i \(-0.569127\pi\)
−0.215465 + 0.976512i \(0.569127\pi\)
\(422\) 13.0110 22.5356i 0.633363 1.09702i
\(423\) 0 0
\(424\) 2.22536 + 3.85443i 0.108073 + 0.187188i
\(425\) 0 0
\(426\) 0 0
\(427\) −27.5318 + 2.54044i −1.33236 + 0.122941i
\(428\) −6.57945 −0.318030
\(429\) 0 0
\(430\) 0 0
\(431\) −25.7481 + 14.8656i −1.24024 + 0.716053i −0.969143 0.246499i \(-0.920720\pi\)
−0.271097 + 0.962552i \(0.587386\pi\)
\(432\) 0 0
\(433\) −26.5666 −1.27671 −0.638356 0.769741i \(-0.720385\pi\)
−0.638356 + 0.769741i \(0.720385\pi\)
\(434\) −1.79332 2.53543i −0.0860822 0.121705i
\(435\) 0 0
\(436\) 1.34219 2.32474i 0.0642791 0.111335i
\(437\) −16.5906 + 9.57860i −0.793637 + 0.458207i
\(438\) 0 0
\(439\) −14.4067 8.31774i −0.687597 0.396984i 0.115114 0.993352i \(-0.463277\pi\)
−0.802711 + 0.596368i \(0.796610\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 16.8895i 0.803351i
\(443\) −1.63637 + 2.83428i −0.0777464 + 0.134661i −0.902277 0.431156i \(-0.858106\pi\)
0.824531 + 0.565817i \(0.191439\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 3.62611 6.28060i 0.171701 0.297395i
\(447\) 0 0
\(448\) −2.16005 + 1.52781i −0.102053 + 0.0721822i
\(449\) 10.4322i 0.492324i −0.969229 0.246162i \(-0.920831\pi\)
0.969229 0.246162i \(-0.0791695\pi\)
\(450\) 0 0
\(451\) −36.0771 + 20.8291i −1.69880 + 0.980805i
\(452\) 1.77515 + 3.07466i 0.0834962 + 0.144620i
\(453\) 0 0
\(454\) 26.7208i 1.25407i
\(455\) 0 0
\(456\) 0 0
\(457\) 28.6471 + 16.5394i 1.34005 + 0.773680i 0.986815 0.161853i \(-0.0517471\pi\)
0.353238 + 0.935533i \(0.385080\pi\)
\(458\) −21.0473 + 12.1517i −0.983478 + 0.567811i
\(459\) 0 0
\(460\) 0 0
\(461\) −11.5639 −0.538585 −0.269293 0.963058i \(-0.586790\pi\)
−0.269293 + 0.963058i \(0.586790\pi\)
\(462\) 0 0
\(463\) 38.6061i 1.79418i −0.441848 0.897090i \(-0.645677\pi\)
0.441848 0.897090i \(-0.354323\pi\)
\(464\) −5.78405 3.33943i −0.268518 0.155029i
\(465\) 0 0
\(466\) −4.62788 8.01573i −0.214383 0.371322i
\(467\) 4.08230 + 2.35692i 0.188906 + 0.109065i 0.591471 0.806327i \(-0.298548\pi\)
−0.402564 + 0.915392i \(0.631881\pi\)
\(468\) 0 0
\(469\) −13.2307 + 28.7285i −0.610937 + 1.32656i
\(470\) 0 0
\(471\) 0 0
\(472\) 3.00381 + 5.20275i 0.138261 + 0.239476i
\(473\) 21.8613 + 37.8649i 1.00519 + 1.74103i
\(474\) 0 0
\(475\) 0 0
\(476\) 8.09926 0.747344i 0.371229 0.0342545i
\(477\) 0 0
\(478\) −0.219422 0.126683i −0.0100361 0.00579436i
\(479\) 10.0096 + 17.3371i 0.457349 + 0.792152i 0.998820 0.0485678i \(-0.0154657\pi\)
−0.541471 + 0.840720i \(0.682132\pi\)
\(480\) 0 0
\(481\) 50.9469 + 29.4142i 2.32298 + 1.34117i
\(482\) 2.97379i 0.135452i
\(483\) 0 0
\(484\) −13.6284 −0.619474
\(485\) 0 0
\(486\) 0 0
\(487\) −4.09706 + 2.36544i −0.185656 + 0.107188i −0.589947 0.807442i \(-0.700851\pi\)
0.404292 + 0.914630i \(0.367518\pi\)
\(488\) −9.05018 5.22512i −0.409682 0.236530i
\(489\) 0 0
\(490\) 0 0
\(491\) 16.0027i 0.722190i −0.932529 0.361095i \(-0.882403\pi\)
0.932529 0.361095i \(-0.117597\pi\)
\(492\) 0 0
\(493\) 10.2662 + 17.7816i 0.462366 + 0.800841i
\(494\) −14.7578 + 8.52039i −0.663983 + 0.383351i
\(495\) 0 0
\(496\) 1.17379i 0.0527045i
\(497\) 1.48736 + 2.10285i 0.0667170 + 0.0943258i
\(498\) 0 0
\(499\) 3.18097 5.50961i 0.142400 0.246644i −0.786000 0.618227i \(-0.787851\pi\)
0.928400 + 0.371583i \(0.121185\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −6.53998 + 11.3276i −0.291893 + 0.505574i
\(503\) 36.3826i 1.62222i 0.584895 + 0.811109i \(0.301136\pi\)
−0.584895 + 0.811109i \(0.698864\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 26.5443 + 15.3253i 1.18004 + 0.681294i
\(507\) 0 0
\(508\) 4.77671 2.75784i 0.211932 0.122359i
\(509\) −8.55353 + 14.8151i −0.379128 + 0.656670i −0.990936 0.134337i \(-0.957109\pi\)
0.611807 + 0.791007i \(0.290443\pi\)
\(510\) 0 0
\(511\) −40.1285 18.4809i −1.77518 0.817546i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 10.9084 6.29797i 0.481149 0.277791i
\(515\) 0 0
\(516\) 0 0
\(517\) 20.5766 0.904956
\(518\) 11.8511 25.7329i 0.520706 1.13064i
\(519\) 0 0
\(520\) 0 0
\(521\) −20.2375 35.0524i −0.886622 1.53567i −0.843843 0.536590i \(-0.819712\pi\)
−0.0427789 0.999085i \(-0.513621\pi\)
\(522\) 0 0
\(523\) 21.8420 37.8314i 0.955083 1.65425i 0.220905 0.975295i \(-0.429099\pi\)
0.734178 0.678957i \(-0.237568\pi\)
\(524\) 20.6136 0.900510
\(525\) 0 0
\(526\) −16.6719 −0.726929
\(527\) −1.80425 + 3.12505i −0.0785943 + 0.136129i
\(528\) 0 0
\(529\) −7.57274 13.1164i −0.329250 0.570277i
\(530\) 0 0
\(531\) 0 0
\(532\) 4.73893 + 6.69998i 0.205458 + 0.290481i
\(533\) 46.1171 1.99755
\(534\) 0 0
\(535\) 0 0
\(536\) −10.3529 + 5.97727i −0.447179 + 0.258179i
\(537\) 0 0
\(538\) 20.0069 0.862561
\(539\) −6.35681 34.1524i −0.273807 1.47105i
\(540\) 0 0
\(541\) 5.85601 10.1429i 0.251770 0.436078i −0.712243 0.701933i \(-0.752321\pi\)
0.964013 + 0.265855i \(0.0856541\pi\)
\(542\) −15.4684 + 8.93068i −0.664425 + 0.383606i
\(543\) 0 0
\(544\) 2.66237 + 1.53712i 0.114148 + 0.0659035i
\(545\) 0 0
\(546\) 0 0
\(547\) 34.6501i 1.48153i −0.671764 0.740765i \(-0.734463\pi\)
0.671764 0.740765i \(-0.265537\pi\)
\(548\) 5.72807 9.92131i 0.244691 0.423817i
\(549\) 0 0
\(550\) 0 0
\(551\) −10.3582 + 17.9409i −0.441272 + 0.764306i
\(552\) 0 0
\(553\) −1.03233 11.1878i −0.0438993 0.475754i
\(554\) 18.1481i 0.771040i
\(555\) 0 0
\(556\) −1.01066 + 0.583502i −0.0428613 + 0.0247460i
\(557\) 17.6567 + 30.5822i 0.748137 + 1.29581i 0.948715 + 0.316134i \(0.102385\pi\)
−0.200578 + 0.979678i \(0.564282\pi\)
\(558\) 0 0
\(559\) 48.4025i 2.04721i
\(560\) 0 0
\(561\) 0 0
\(562\) −13.4346 7.75647i −0.566705 0.327187i
\(563\) 33.5143 19.3495i 1.41246 0.815483i 0.416839 0.908981i \(-0.363138\pi\)
0.995620 + 0.0934975i \(0.0298047\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −17.6454 −0.741690
\(567\) 0 0
\(568\) 0.973522i 0.0408481i
\(569\) −6.20799 3.58419i −0.260253 0.150257i 0.364197 0.931322i \(-0.381343\pi\)
−0.624450 + 0.781065i \(0.714677\pi\)
\(570\) 0 0
\(571\) 10.7717 + 18.6571i 0.450781 + 0.780776i 0.998435 0.0559290i \(-0.0178121\pi\)
−0.547653 + 0.836705i \(0.684479\pi\)
\(572\) 23.6117 + 13.6322i 0.987256 + 0.569993i
\(573\) 0 0
\(574\) −2.04064 22.1152i −0.0851746 0.923070i
\(575\) 0 0
\(576\) 0 0
\(577\) 7.86230 + 13.6179i 0.327312 + 0.566921i 0.981978 0.188998i \(-0.0605239\pi\)
−0.654666 + 0.755919i \(0.727191\pi\)
\(578\) 3.77453 + 6.53767i 0.157000 + 0.271931i
\(579\) 0 0
\(580\) 0 0
\(581\) −21.8234 30.8544i −0.905389 1.28006i
\(582\) 0 0
\(583\) −19.1284 11.0438i −0.792217 0.457387i
\(584\) −8.34916 14.4612i −0.345491 0.598408i
\(585\) 0 0
\(586\) 9.04902 + 5.22446i 0.373812 + 0.215820i
\(587\) 4.59252i 0.189554i −0.995499 0.0947769i \(-0.969786\pi\)
0.995499 0.0947769i \(-0.0302138\pi\)
\(588\) 0 0
\(589\) −3.64082 −0.150017
\(590\) 0 0
\(591\) 0 0
\(592\) 9.27339 5.35400i 0.381134 0.220048i
\(593\) −3.31317 1.91286i −0.136055 0.0785516i 0.430427 0.902625i \(-0.358363\pi\)
−0.566483 + 0.824074i \(0.691696\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 15.4041i 0.630977i
\(597\) 0 0
\(598\) −16.9657 29.3854i −0.693777 1.20166i
\(599\) 13.6589 7.88600i 0.558089 0.322213i −0.194289 0.980944i \(-0.562240\pi\)
0.752378 + 0.658731i \(0.228907\pi\)
\(600\) 0 0
\(601\) 1.39673i 0.0569740i 0.999594 + 0.0284870i \(0.00906892\pi\)
−0.999594 + 0.0284870i \(0.990931\pi\)
\(602\) −23.2111 + 2.14176i −0.946015 + 0.0872918i
\(603\) 0 0
\(604\) −0.511281 + 0.885565i −0.0208037 + 0.0360331i
\(605\) 0 0
\(606\) 0 0
\(607\) −5.16682 + 8.94920i −0.209715 + 0.363237i −0.951625 0.307263i \(-0.900587\pi\)
0.741910 + 0.670500i \(0.233920\pi\)
\(608\) 3.10178i 0.125794i
\(609\) 0 0
\(610\) 0 0
\(611\) −19.7271 11.3895i −0.798075 0.460769i
\(612\) 0 0
\(613\) 10.6482 6.14772i 0.430075 0.248304i −0.269303 0.963055i \(-0.586793\pi\)
0.699379 + 0.714751i \(0.253460\pi\)
\(614\) 0.362324 0.627564i 0.0146222 0.0253264i
\(615\) 0 0
\(616\) 5.49247 11.9261i 0.221298 0.480516i
\(617\) 8.10935 0.326470 0.163235 0.986587i \(-0.447807\pi\)
0.163235 + 0.986587i \(0.447807\pi\)
\(618\) 0 0
\(619\) −7.03506 + 4.06170i −0.282763 + 0.163253i −0.634674 0.772780i \(-0.718865\pi\)
0.351911 + 0.936034i \(0.385532\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −28.2450 −1.13252
\(623\) −3.59065 38.9133i −0.143857 1.55903i
\(624\) 0 0
\(625\) 0 0
\(626\) −10.2651 17.7797i −0.410276 0.710619i
\(627\) 0 0
\(628\) −2.68294 + 4.64699i −0.107061 + 0.185435i
\(629\) −32.9189 −1.31256
\(630\) 0 0
\(631\) −40.6011 −1.61630 −0.808151 0.588975i \(-0.799532\pi\)
−0.808151 + 0.588975i \(0.799532\pi\)
\(632\) 2.12328 3.67763i 0.0844595 0.146288i
\(633\) 0 0
\(634\) −1.13674 1.96890i −0.0451459 0.0781950i
\(635\) 0 0
\(636\) 0 0
\(637\) −12.8095 + 36.2611i −0.507531 + 1.43672i
\(638\) 33.1452 1.31223
\(639\) 0 0
\(640\) 0 0
\(641\) 32.0260 18.4902i 1.26495 0.730319i 0.290922 0.956747i \(-0.406038\pi\)
0.974028 + 0.226427i \(0.0727046\pi\)
\(642\) 0 0
\(643\) −4.86696 −0.191934 −0.0959671 0.995385i \(-0.530594\pi\)
−0.0959671 + 0.995385i \(0.530594\pi\)
\(644\) −13.3409 + 9.43606i −0.525704 + 0.371833i
\(645\) 0 0
\(646\) 4.76780 8.25808i 0.187587 0.324910i
\(647\) −21.6217 + 12.4833i −0.850037 + 0.490769i −0.860663 0.509175i \(-0.829951\pi\)
0.0106266 + 0.999944i \(0.496617\pi\)
\(648\) 0 0
\(649\) −25.8197 14.9070i −1.01351 0.585151i
\(650\) 0 0
\(651\) 0 0
\(652\) 10.0422i 0.393282i
\(653\) 7.29496 12.6352i 0.285474 0.494455i −0.687250 0.726421i \(-0.741182\pi\)
0.972724 + 0.231966i \(0.0745158\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 4.19713 7.26965i 0.163870 0.283832i
\(657\) 0 0
\(658\) −4.58885 + 9.96402i −0.178892 + 0.388438i
\(659\) 33.8468i 1.31848i −0.751931 0.659242i \(-0.770877\pi\)
0.751931 0.659242i \(-0.229123\pi\)
\(660\) 0 0
\(661\) −14.9053 + 8.60557i −0.579749 + 0.334718i −0.761034 0.648713i \(-0.775308\pi\)
0.181285 + 0.983431i \(0.441974\pi\)
\(662\) −18.0646 31.2889i −0.702102 1.21608i
\(663\) 0 0
\(664\) 14.2841i 0.554332i
\(665\) 0 0
\(666\) 0 0
\(667\) −35.7235 20.6250i −1.38322 0.798602i
\(668\) 2.13047 1.23003i 0.0824302 0.0475911i
\(669\) 0 0
\(670\) 0 0
\(671\) 51.8615 2.00209
\(672\) 0 0
\(673\) 1.47971i 0.0570387i −0.999593 0.0285193i \(-0.990921\pi\)
0.999593 0.0285193i \(-0.00907922\pi\)
\(674\) 3.25938 + 1.88181i 0.125547 + 0.0724844i
\(675\) 0 0
\(676\) −8.59134 14.8806i −0.330436 0.572333i
\(677\) 10.2632 + 5.92549i 0.394448 + 0.227735i 0.684086 0.729402i \(-0.260201\pi\)
−0.289637 + 0.957136i \(0.593535\pi\)
\(678\) 0 0
\(679\) 9.53968 6.74746i 0.366099 0.258944i
\(680\) 0 0
\(681\) 0 0
\(682\) 2.91258 + 5.04473i 0.111528 + 0.193173i
\(683\) −5.26389 9.11732i −0.201417 0.348865i 0.747568 0.664185i \(-0.231221\pi\)
−0.948985 + 0.315320i \(0.897888\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 17.9556 + 4.53821i 0.685549 + 0.173270i
\(687\) 0 0
\(688\) −7.62990 4.40513i −0.290887 0.167944i
\(689\) 12.2258 + 21.1758i 0.465767 + 0.806732i
\(690\) 0 0
\(691\) 6.61628 + 3.81991i 0.251695 + 0.145316i 0.620540 0.784175i \(-0.286913\pi\)
−0.368845 + 0.929491i \(0.620247\pi\)
\(692\) 3.00084i 0.114075i
\(693\) 0 0
\(694\) 4.04779 0.153652
\(695\) 0 0
\(696\) 0 0
\(697\) −22.3486 + 12.9030i −0.846515 + 0.488736i
\(698\) 20.7296 + 11.9682i 0.784626 + 0.453004i
\(699\) 0 0
\(700\) 0 0
\(701\) 35.2007i 1.32951i −0.747060 0.664757i \(-0.768535\pi\)
0.747060 0.664757i \(-0.231465\pi\)
\(702\) 0 0
\(703\) −16.6069 28.7640i −0.626341 1.08485i
\(704\) 4.29783 2.48135i 0.161980 0.0935195i
\(705\) 0 0
\(706\) 25.4818i 0.959019i
\(707\) −24.9843 11.5063i −0.939631 0.432740i
\(708\) 0 0
\(709\) −18.1846 + 31.4966i −0.682936 + 1.18288i 0.291145 + 0.956679i \(0.405964\pi\)
−0.974081 + 0.226201i \(0.927369\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 7.38517 12.7915i 0.276771 0.479381i
\(713\) 7.24954i 0.271497i
\(714\) 0 0
\(715\) 0 0
\(716\) 3.18036 + 1.83618i 0.118856 + 0.0686214i
\(717\) 0 0
\(718\) −15.4893 + 8.94277i −0.578057 + 0.333741i
\(719\) −0.772550 + 1.33810i −0.0288113 + 0.0499026i −0.880072 0.474841i \(-0.842506\pi\)
0.851260 + 0.524744i \(0.175839\pi\)
\(720\) 0 0
\(721\) −2.48905 26.9748i −0.0926971 1.00460i
\(722\) −9.37898 −0.349049
\(723\) 0 0
\(724\) 5.31359 3.06780i 0.197478 0.114014i
\(725\) 0 0
\(726\) 0 0
\(727\) 34.1857 1.26788 0.633939 0.773383i \(-0.281437\pi\)
0.633939 + 0.773383i \(0.281437\pi\)
\(728\) −11.8670 + 8.39360i −0.439821 + 0.311087i
\(729\) 0 0
\(730\) 0 0
\(731\) 13.5424 + 23.4561i 0.500884 + 0.867557i
\(732\) 0 0
\(733\) 21.9095 37.9485i 0.809248 1.40166i −0.104138 0.994563i \(-0.533208\pi\)
0.913386 0.407095i \(-0.133458\pi\)
\(734\) 5.27703 0.194779
\(735\) 0 0
\(736\) −6.17620 −0.227658
\(737\) 29.6634 51.3786i 1.09267 1.89255i
\(738\) 0 0
\(739\) −6.86403 11.8888i −0.252497 0.437338i 0.711715 0.702468i \(-0.247919\pi\)
−0.964213 + 0.265130i \(0.914585\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 9.61374 6.79984i 0.352931 0.249630i
\(743\) −20.8393 −0.764520 −0.382260 0.924055i \(-0.624854\pi\)
−0.382260 + 0.924055i \(0.624854\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −12.5988 + 7.27390i −0.461274 + 0.266316i
\(747\) 0 0
\(748\) −15.2565 −0.557834
\(749\) 1.59946 + 17.3339i 0.0584429 + 0.633369i
\(750\) 0 0
\(751\) 21.8346 37.8186i 0.796755 1.38002i −0.124964 0.992161i \(-0.539881\pi\)
0.921719 0.387859i \(-0.126785\pi\)
\(752\) −3.59075 + 2.07312i −0.130941 + 0.0755989i
\(753\) 0 0
\(754\) −31.7769 18.3464i −1.15725 0.668136i
\(755\) 0 0
\(756\) 0 0
\(757\) 40.4115i 1.46878i 0.678727 + 0.734391i \(0.262532\pi\)
−0.678727 + 0.734391i \(0.737468\pi\)
\(758\) −1.83335 + 3.17545i −0.0665901 + 0.115337i
\(759\) 0 0
\(760\) 0 0
\(761\) −18.3292 + 31.7471i −0.664432 + 1.15083i 0.315007 + 0.949089i \(0.397993\pi\)
−0.979439 + 0.201741i \(0.935340\pi\)
\(762\) 0 0
\(763\) −6.45094 2.97093i −0.233540 0.107555i
\(764\) 5.71839i 0.206884i
\(765\) 0 0
\(766\) −16.9091 + 9.76247i −0.610951 + 0.352732i
\(767\) 16.5025 + 28.5833i 0.595872 + 1.03208i
\(768\) 0 0
\(769\) 20.4304i 0.736738i −0.929680 0.368369i \(-0.879916\pi\)
0.929680 0.368369i \(-0.120084\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −5.39819 3.11665i −0.194285 0.112171i
\(773\) 11.8586 6.84657i 0.426525 0.246254i −0.271340 0.962483i \(-0.587467\pi\)
0.697865 + 0.716229i \(0.254134\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 4.41643 0.158540
\(777\) 0 0
\(778\) 17.2871i 0.619773i
\(779\) −22.5488 13.0186i −0.807896 0.466439i
\(780\) 0 0
\(781\) −2.41565 4.18403i −0.0864388 0.149716i
\(782\) 16.4433 + 9.49356i 0.588012 + 0.339489i
\(783\) 0 0
\(784\) 4.55021 + 5.31936i 0.162507 + 0.189977i
\(785\) 0 0
\(786\) 0 0
\(787\) 6.70701 + 11.6169i 0.239079 + 0.414097i 0.960450 0.278451i \(-0.0898211\pi\)
−0.721371