Properties

Label 3150.2.bp.g.899.4
Level 3150
Weight 2
Character 3150.899
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 \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 899.4
Character \(\chi\) \(=\) 3150.899
Dual form 3150.2.bp.g.1349.4

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 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 \(-0.602394\pi\)
−0.979683 + 0.200550i \(0.935727\pi\)
\(12\) 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 \(-0.454938\pi\)
−0.786814 + 0.617190i \(0.788271\pi\)
\(18\) 0 0
\(19\) 2.68622 1.55089i 0.616261 0.355798i −0.159151 0.987254i \(-0.550876\pi\)
0.775412 + 0.631456i \(0.217542\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 4.96270i 1.05805i
\(23\) 3.08810 + 5.34875i 0.643914 + 1.11529i 0.984551 + 0.175097i \(0.0560238\pi\)
−0.340638 + 0.940195i \(0.610643\pi\)
\(24\) 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 0.405928 0.913905i \(-0.366949\pi\)
−0.588501 + 0.808496i \(0.700282\pi\)
\(32\) −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 −0.524959 + 0.851128i \(0.675919\pi\)
−0.999578 + 0.0290640i \(0.990747\pi\)
\(38\) −2.68622 1.55089i −0.435762 0.251587i
\(39\) 0 0
\(40\) 0 0
\(41\) 8.39427 1.31096 0.655482 0.755211i \(-0.272466\pi\)
0.655482 + 0.755211i \(0.272466\pi\)
\(42\) 0 0
\(43\) 8.81025i 1.34355i −0.740755 0.671776i \(-0.765532\pi\)
0.740755 0.671776i \(-0.234468\pi\)
\(44\) 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 \(-0.764453\pi\)
0.214709 + 0.976678i \(0.431120\pi\)
\(48\) 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 \(-0.734451\pi\)
0.977412 + 0.211345i \(0.0677842\pi\)
\(54\) 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 \(-0.705441\pi\)
0.992590 + 0.121512i \(0.0387743\pi\)
\(60\) 0 0
\(61\) 9.05018 5.22512i 1.15876 0.669008i 0.207751 0.978182i \(-0.433386\pi\)
0.951006 + 0.309173i \(0.100052\pi\)
\(62\) 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 0.974002 0.226540i \(-0.0727414\pi\)
0.290811 + 0.956780i \(0.406075\pi\)
\(68\) 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 0.304706 0.952446i \(-0.401442\pi\)
0.672490 0.740106i \(-0.265225\pi\)
\(74\) 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 0.721508 0.692406i \(-0.243449\pi\)
−0.960395 + 0.278641i \(0.910116\pi\)
\(80\) 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 0.930289 + 0.366827i \(0.119556\pi\)
−0.147463 + 0.989068i \(0.547111\pi\)
\(90\) 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 0.482554 + 0.875866i \(0.339709\pi\)
−0.999799 + 0.0200290i \(0.993624\pi\)
\(102\) 0 0
\(103\) −5.11942 8.86709i −0.504431 0.873701i −0.999987 0.00512447i \(-0.998369\pi\)
0.495556 0.868576i \(-0.334965\pi\)
\(104\) −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 \(-0.269688\pi\)
−0.980077 + 0.198619i \(0.936355\pi\)
\(108\) 0 0
\(109\) 1.34219 2.32474i 0.128558 0.222669i −0.794560 0.607186i \(-0.792298\pi\)
0.923118 + 0.384516i \(0.125632\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.243099 + 2.63456i −0.0229707 + 0.248942i
\(113\) 3.55031 0.333985 0.166992 0.985958i \(-0.446594\pi\)
0.166992 + 0.985958i \(0.446594\pi\)
\(114\) 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 \(-0.921304\pi\)
0.969594 0.244719i \(-0.0786955\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 10.3068 + 17.8519i 0.900510 + 1.55973i 0.826833 + 0.562447i \(0.190140\pi\)
0.0736773 + 0.997282i \(0.476527\pi\)
\(132\) 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 \(-0.996111\pi\)
0.510543 + 0.859852i \(0.329444\pi\)
\(138\) 0 0
\(139\) 1.16700i 0.0989840i 0.998775 + 0.0494920i \(0.0157602\pi\)
−0.998775 + 0.0494920i \(0.984240\pi\)
\(140\) 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 \(-0.884012\pi\)
−0.158541 + 0.987352i \(0.550679\pi\)
\(150\) 0 0
\(151\) −0.511281 + 0.885565i −0.0416075 + 0.0720663i −0.886079 0.463534i \(-0.846581\pi\)
0.844472 + 0.535600i \(0.179915\pi\)
\(152\) 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 −0.953001 0.302968i \(-0.902022\pi\)
0.738878 + 0.673839i \(0.235356\pi\)
\(158\) −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 −0.800301 0.599599i \(-0.795327\pi\)
0.119117 + 0.992880i \(0.461994\pi\)
\(164\) −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 \(-0.630276\pi\)
0.595528 + 0.803335i \(0.296943\pi\)
\(174\) 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 \(-0.289509\pi\)
−0.376413 + 0.926452i \(0.622843\pi\)
\(180\) 0 0
\(181\) 6.13560i 0.456056i −0.973655 0.228028i \(-0.926772\pi\)
0.973655 0.228028i \(-0.0732278\pi\)
\(182\) 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 \(-0.600334\pi\)
0.668350 + 0.743847i \(0.267001\pi\)
\(192\) 0 0
\(193\) 5.39819 + 3.11665i 0.388570 + 0.224341i 0.681541 0.731780i \(-0.261310\pi\)
−0.292970 + 0.956122i \(0.594644\pi\)
\(194\) 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 \(-0.485000\pi\)
0.0471064 + 0.998890i \(0.485000\pi\)
\(198\) 0 0
\(199\) 8.27163 + 4.77563i 0.586360 + 0.338535i 0.763657 0.645622i \(-0.223402\pi\)
−0.177297 + 0.984157i \(0.556735\pi\)
\(200\) 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 0.999072 + 0.0430820i \(0.0137177\pi\)
0.536846 + 0.843680i \(0.319616\pi\)
\(228\) 0 0
\(229\) −21.0473 + 12.1517i −1.39085 + 0.803006i −0.993409 0.114622i \(-0.963434\pi\)
−0.397439 + 0.917629i \(0.630101\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.67885i 0.438488i
\(233\) −4.62788 8.01573i −0.303183 0.525128i 0.673672 0.739030i \(-0.264716\pi\)
−0.976855 + 0.213902i \(0.931383\pi\)
\(234\) 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 0.580649 0.814154i \(-0.302799\pi\)
−0.414754 + 0.909934i \(0.636132\pi\)
\(242\) 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 \(-0.364551\pi\)
0.412800 + 0.910822i \(0.364551\pi\)
\(252\) 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 \(-0.795180\pi\)
0.119576 + 0.992825i \(0.461846\pi\)
\(258\) 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 −0.485852 0.874041i \(-0.661490\pi\)
0.999868 0.0162609i \(-0.00517625\pi\)
\(264\) 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 0.381330 + 0.924439i \(0.375466\pi\)
−0.991253 + 0.131978i \(0.957867\pi\)
\(270\) 0 0
\(271\) −15.4684 + 8.93068i −0.939638 + 0.542500i −0.889847 0.456259i \(-0.849189\pi\)
−0.0497914 + 0.998760i \(0.515856\pi\)
\(272\) 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 −0.0530128 0.998594i \(-0.516882\pi\)
−0.891314 + 0.453386i \(0.850216\pi\)
\(278\) 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 0.475141 + 0.879910i \(0.342397\pi\)
−0.999595 + 0.0284708i \(0.990936\pi\)
\(284\) 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 −0.118268 0.992982i \(-0.537734\pi\)
0.919081 0.394068i \(-0.128932\pi\)
\(312\) 0 0
\(313\) 10.2651 + 17.7797i 0.580218 + 1.00497i 0.995453 + 0.0952528i \(0.0303659\pi\)
−0.415235 + 0.909714i \(0.636301\pi\)
\(314\) 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 \(-0.187003\pi\)
−0.896181 + 0.443688i \(0.853670\pi\)
\(318\) 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 0.599317 + 0.800512i \(0.295439\pi\)
0.393605 + 0.919280i \(0.371228\pi\)
\(332\) −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 \(-0.967313\pi\)
0.994732 0.102508i \(-0.0326869\pi\)
\(338\) −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 \(-0.867986\pi\)
0.806575 + 0.591132i \(0.201319\pi\)
\(348\) 0 0
\(349\) 23.9364i 1.28129i −0.767838 0.640644i \(-0.778667\pi\)
0.767838 0.640644i \(-0.221333\pi\)
\(350\) 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 \(-0.0961244\pi\)
0.219805 + 0.975544i \(0.429458\pi\)
\(354\) 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 \(-0.510206\pi\)
0.849552 + 0.527505i \(0.176872\pi\)
\(360\) 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 −0.788907 0.614512i \(-0.789353\pi\)
0.926637 + 0.375958i \(0.122686\pi\)
\(368\) 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 −0.789352 0.613941i \(-0.789583\pi\)
0.137013 + 0.990569i \(0.456250\pi\)
\(374\) 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 \(-0.500427\pi\)
0.865355 + 0.501160i \(0.167093\pi\)
\(384\) 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 \(-0.477733\pi\)
−0.828960 + 0.559309i \(0.811067\pi\)
\(390\) 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 0.970274 + 0.242011i \(0.0778069\pi\)
−0.275549 + 0.961287i \(0.588860\pi\)
\(398\) 9.55125i 0.478761i
\(399\) 0 0
\(400\) 0 0
\(401\) −32.7521 + 18.9095i −1.63556 + 0.944293i −0.653229 + 0.757161i \(0.726586\pi\)
−0.982335 + 0.187132i \(0.940081\pi\)
\(402\) 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 −0.996987 0.0775719i \(-0.975283\pi\)
−0.565673 0.824630i \(-0.691383\pi\)
\(410\) 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 \(-0.677526\pi\)
−0.529249 + 0.848466i \(0.677526\pi\)
\(420\) 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 \(-0.0792802\pi\)
0.271097 + 0.962552i \(0.412614\pi\)
\(432\) 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 −0.802711 0.596368i \(-0.796610\pi\)
0.115114 + 0.993352i \(0.463277\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 16.8895i 0.803351i
\(443\) 1.63637 + 2.83428i 0.0777464 + 0.134661i 0.902277 0.431156i \(-0.141894\pi\)
−0.824531 + 0.565817i \(0.808561\pi\)
\(444\) 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 0.353238 0.935533i \(-0.385080\pi\)
0.986815 + 0.161853i \(0.0517471\pi\)
\(458\) 21.0473 + 12.1517i 0.983478 + 0.567811i
\(459\) 0 0
\(460\) 0 0
\(461\) 11.5639 0.538585 0.269293 0.963058i \(-0.413210\pi\)
0.269293 + 0.963058i \(0.413210\pi\)
\(462\) 0 0
\(463\) 38.6061i 1.79418i 0.441848 + 0.897090i \(0.354323\pi\)
−0.441848 + 0.897090i \(0.645677\pi\)
\(464\) 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 \(-0.701452\pi\)
0.402564 + 0.915392i \(0.368119\pi\)
\(468\) 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 \(-0.984534\pi\)
0.541471 + 0.840720i \(0.317868\pi\)
\(480\) 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 0.404292 0.914630i \(-0.367518\pi\)
−0.589947 + 0.807442i \(0.700851\pi\)
\(488\) 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 0.928400 0.371583i \(-0.121185\pi\)
−0.786000 + 0.618227i \(0.787851\pi\)
\(500\) 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 \(-0.0428905\pi\)
−0.611807 + 0.791007i \(0.709557\pi\)
\(510\) 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 0.0427789 0.999085i \(-0.486379\pi\)
0.843843 0.536590i \(-0.180288\pi\)
\(522\) 0 0
\(523\) 21.8420 + 37.8314i 0.955083 + 1.65425i 0.734178 + 0.678957i \(0.237568\pi\)
0.220905 + 0.975295i \(0.429099\pi\)
\(524\) −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 0.964013 0.265855i \(-0.0856541\pi\)
−0.712243 + 0.701933i \(0.752321\pi\)
\(542\) 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 \(0.265537\pi\)
−0.671764 + 0.740765i \(0.734463\pi\)
\(548\) −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 0.200578 + 0.979678i \(0.435718\pi\)
−0.948715 + 0.316134i \(0.897615\pi\)
\(558\) 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 \(-0.636862\pi\)
−0.995620 + 0.0934975i \(0.970195\pi\)
\(564\) 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 \(-0.618657\pi\)
0.624450 + 0.781065i \(0.285323\pi\)
\(570\) 0 0
\(571\) 10.7717 18.6571i 0.450781 0.780776i −0.547653 0.836705i \(-0.684479\pi\)
0.998435 + 0.0559290i \(0.0178121\pi\)
\(572\) −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 −0.654666 0.755919i \(-0.727191\pi\)
0.981978 + 0.188998i \(0.0605239\pi\)
\(578\) −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 \(-0.641637\pi\)
0.566483 + 0.824074i \(0.308304\pi\)
\(594\) 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 \(-0.437760\pi\)
−0.752378 + 0.658731i \(0.771093\pi\)
\(600\) 0 0
\(601\) 1.39673i 0.0569740i −0.999594 0.0284870i \(-0.990931\pi\)
0.999594 0.0284870i \(-0.00906892\pi\)
\(602\) 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 0.741910 0.670500i \(-0.233920\pi\)
−0.951625 + 0.307263i \(0.900587\pi\)
\(608\) 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 0.699379 0.714751i \(-0.253460\pi\)
−0.269303 + 0.963055i \(0.586793\pi\)
\(614\) −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 \(-0.552193\pi\)
−0.163235 + 0.986587i \(0.552193\pi\)
\(618\) 0 0
\(619\) −7.03506 4.06170i −0.282763 0.163253i 0.351911 0.936034i \(-0.385532\pi\)
−0.634674 + 0.772780i \(0.718865\pi\)
\(620\) 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 \(-0.593962\pi\)
−0.974028 + 0.226427i \(0.927295\pi\)
\(642\) 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 \(-0.170049\pi\)
−0.0106266 + 0.999944i \(0.503383\pi\)
\(648\) 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 \(-0.258818\pi\)
−0.972724 + 0.231966i \(0.925484\pi\)
\(654\) 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 0.181285 0.983431i \(-0.441974\pi\)
−0.761034 + 0.648713i \(0.775308\pi\)
\(662\) 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 \(0.00907922\pi\)
−0.999593 + 0.0285193i \(0.990921\pi\)
\(674\) −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 \(-0.739799\pi\)
0.289637 + 0.957136i \(0.406465\pi\)
\(678\) 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 \(-0.768779\pi\)
0.948985 + 0.315320i \(0.102112\pi\)
\(684\) 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 −0.368845 0.929491i \(-0.620247\pi\)
0.620540 + 0.784175i \(0.286913\pi\)
\(692\) 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 −0.974081 0.226201i \(-0.927369\pi\)
0.291145 0.956679i \(-0.405964\pi\)
\(710\) 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 \(-0.157494\pi\)
−0.851260 + 0.524744i \(0.824161\pi\)
\(720\) 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 0.913386 + 0.407095i \(0.133458\pi\)
−0.104138 + 0.994563i \(0.533208\pi\)
\(734\) −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 −0.964213 0.265130i \(-0.914585\pi\)
0.711715 + 0.702468i \(0.247919\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 9.61374 + 6.79984i 0.352931 + 0.249630i
\(743\) 20.8393 0.764520 0.382260 0.924055i \(-0.375146\pi\)
0.382260 + 0.924055i \(0.375146\pi\)
\(744\) 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 0.921719 + 0.387859i \(0.126785\pi\)
−0.124964 + 0.992161i \(0.539881\pi\)
\(752\) 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 \(-0.737468\pi\)
0.678727 0.734391i \(-0.262532\pi\)
\(758\) 1.83335 + 3.17545i 0.0665901 + 0.115337i
\(759\) 0 0
\(760\) 0 0
\(761\) 18.3292 + 31.7471i 0.664432 + 1.15083i 0.979439 + 0.201741i \(0.0646598\pi\)
−0.315007 + 0.949089i \(0.602007\pi\)
\(762\) 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 \(0.120084\pi\)
−0.929680 + 0.368369i \(0.879916\pi\)
\(770\) 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 \(-0.412533\pi\)
−0.697865 + 0.716229i \(0.745866\pi\)
\(774\) 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 −0.721371 0.692549i \(-0.756488\pi\)
0.960450 + 0.278451i \(0.0898211\pi\)
\(788\) −0.661170 + 1.14518i −0.0235532 +