Properties

Label 3150.2.bf.e.1151.1
Level 3150
Weight 2
Character 3150.1151
Analytic conductor 25.153
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1151.1
Character \(\chi\) = 3150.1151
Dual form 3150.2.bf.e.1601.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.52781 - 2.16005i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.52781 - 2.16005i) q^{7} +1.00000i q^{8} +(4.29783 + 2.48135i) q^{11} +5.49388i q^{13} +(-0.243099 + 2.63456i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.53712 + 2.66237i) q^{17} +(-2.68622 + 1.55089i) q^{19} -4.96270 q^{22} +(-5.34875 + 3.08810i) q^{23} +(-2.74694 - 4.75784i) q^{26} +(-1.10675 - 2.40314i) q^{28} +6.67885i q^{29} +(-1.01653 - 0.586893i) q^{31} +(0.866025 + 0.500000i) q^{32} -3.07424i q^{34} +(-5.35400 - 9.27339i) q^{37} +(1.55089 - 2.68622i) q^{38} -8.39427 q^{41} -8.81025 q^{43} +(4.29783 - 2.48135i) q^{44} +(3.08810 - 5.34875i) q^{46} +(2.07312 + 3.59075i) q^{47} +(-2.33160 - 6.60028i) q^{49} +(4.75784 + 2.74694i) q^{52} +(3.85443 + 2.22536i) q^{53} +(2.16005 + 1.52781i) q^{56} +(-3.33943 - 5.78405i) q^{58} +(3.00381 - 5.20275i) q^{59} +(9.05018 - 5.22512i) q^{61} +1.17379 q^{62} -1.00000 q^{64} +(-5.97727 + 10.3529i) q^{67} +(1.53712 + 2.66237i) q^{68} +0.973522i q^{71} +(-14.4612 - 8.34916i) q^{73} +(9.27339 + 5.35400i) q^{74} +3.10178i q^{76} +(11.9261 - 5.49247i) q^{77} +(2.12328 + 3.67763i) q^{79} +(7.26965 - 4.19713i) q^{82} -14.2841 q^{83} +(7.62990 - 4.40513i) q^{86} +(-2.48135 + 4.29783i) q^{88} +(7.38517 + 12.7915i) q^{89} +(11.8670 + 8.39360i) q^{91} +6.17620i q^{92} +(-3.59075 - 2.07312i) q^{94} -4.41643i q^{97} +(5.31936 + 4.55021i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 12q^{4} + 4q^{7} + O(q^{10}) \) \( 24q + 12q^{4} + 4q^{7} - 12q^{16} + 12q^{19} - 4q^{28} - 28q^{37} - 96q^{43} - 8q^{46} - 52q^{49} + 12q^{52} - 8q^{58} - 12q^{61} - 24q^{64} + 4q^{67} + 12q^{73} + 4q^{79} + 68q^{91} - 24q^{94} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) 1.52781 2.16005i 0.577458 0.816421i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) 4.29783 + 2.48135i 1.29584 + 0.748156i 0.979683 0.200550i \(-0.0642729\pi\)
0.316160 + 0.948706i \(0.397606\pi\)
\(12\) 0 0
\(13\) 5.49388i 1.52373i 0.647737 + 0.761864i \(0.275715\pi\)
−0.647737 + 0.761864i \(0.724285\pi\)
\(14\) −0.243099 + 2.63456i −0.0649709 + 0.704116i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.53712 + 2.66237i −0.372806 + 0.645719i −0.989996 0.141095i \(-0.954938\pi\)
0.617190 + 0.786814i \(0.288271\pi\)
\(18\) 0 0
\(19\) −2.68622 + 1.55089i −0.616261 + 0.355798i −0.775412 0.631456i \(-0.782458\pi\)
0.159151 + 0.987254i \(0.449124\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −4.96270 −1.05805
\(23\) −5.34875 + 3.08810i −1.11529 + 0.643914i −0.940195 0.340638i \(-0.889357\pi\)
−0.175097 + 0.984551i \(0.556024\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −2.74694 4.75784i −0.538719 0.933089i
\(27\) 0 0
\(28\) −1.10675 2.40314i −0.209156 0.454152i
\(29\) 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 \(0.700282\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 3.07424i 0.527228i
\(35\) 0 0
\(36\) 0 0
\(37\) −5.35400 9.27339i −0.880192 1.52454i −0.851128 0.524959i \(-0.824081\pi\)
−0.0290640 0.999578i \(-0.509253\pi\)
\(38\) 1.55089 2.68622i 0.251587 0.435762i
\(39\) 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
\(43\) −8.81025 −1.34355 −0.671776 0.740755i \(-0.734468\pi\)
−0.671776 + 0.740755i \(0.734468\pi\)
\(44\) 4.29783 2.48135i 0.647922 0.374078i
\(45\) 0 0
\(46\) 3.08810 5.34875i 0.455316 0.788630i
\(47\) 2.07312 + 3.59075i 0.302396 + 0.523765i 0.976678 0.214709i \(-0.0688803\pi\)
−0.674282 + 0.738474i \(0.735547\pi\)
\(48\) 0 0
\(49\) −2.33160 6.60028i −0.333085 0.942897i
\(50\) 0 0
\(51\) 0 0
\(52\) 4.75784 + 2.74694i 0.659793 + 0.380932i
\(53\) 3.85443 + 2.22536i 0.529446 + 0.305676i 0.740791 0.671736i \(-0.234451\pi\)
−0.211345 + 0.977412i \(0.567784\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.16005 + 1.52781i 0.288648 + 0.204162i
\(57\) 0 0
\(58\) −3.33943 5.78405i −0.438488 0.759484i
\(59\) 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 \(0.100052\pi\)
\(62\) 1.17379 0.149071
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −5.97727 + 10.3529i −0.730240 + 1.26481i 0.226540 + 0.974002i \(0.427259\pi\)
−0.956780 + 0.290811i \(0.906075\pi\)
\(68\) 1.53712 + 2.66237i 0.186403 + 0.322860i
\(69\) 0 0
\(70\) 0 0
\(71\) 0.973522i 0.115536i 0.998330 + 0.0577679i \(0.0183983\pi\)
−0.998330 + 0.0577679i \(0.981602\pi\)
\(72\) 0 0
\(73\) −14.4612 8.34916i −1.69255 0.977196i −0.952446 0.304706i \(-0.901442\pi\)
−0.740106 0.672490i \(-0.765225\pi\)
\(74\) 9.27339 + 5.35400i 1.07801 + 0.622389i
\(75\) 0 0
\(76\) 3.10178i 0.355798i
\(77\) 11.9261 5.49247i 1.35910 0.625925i
\(78\) 0 0
\(79\) 2.12328 + 3.67763i 0.238887 + 0.413765i 0.960395 0.278641i \(-0.0898840\pi\)
−0.721508 + 0.692406i \(0.756551\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 7.26965 4.19713i 0.802798 0.463496i
\(83\) −14.2841 −1.56789 −0.783944 0.620831i \(-0.786795\pi\)
−0.783944 + 0.620831i \(0.786795\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 7.62990 4.40513i 0.822754 0.475017i
\(87\) 0 0
\(88\) −2.48135 + 4.29783i −0.264513 + 0.458150i
\(89\) 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
\(92\) 6.17620i 0.643914i
\(93\) 0 0
\(94\) −3.59075 2.07312i −0.370358 0.213826i
\(95\) 0 0
\(96\) 0 0
\(97\) 4.41643i 0.448420i −0.974541 0.224210i \(-0.928020\pi\)
0.974541 0.224210i \(-0.0719802\pi\)
\(98\) 5.31936 + 4.55021i 0.537336 + 0.459641i
\(99\) 0 0
\(100\) 0 0
\(101\) 5.19825 9.00364i 0.517245 0.895895i −0.482554 0.875866i \(-0.660291\pi\)
0.999799 0.0200290i \(-0.00637586\pi\)
\(102\) 0 0
\(103\) −8.86709 + 5.11942i −0.873701 + 0.504431i −0.868576 0.495556i \(-0.834965\pi\)
−0.00512447 + 0.999987i \(0.501631\pi\)
\(104\) −5.49388 −0.538719
\(105\) 0 0
\(106\) −4.45071 −0.432291
\(107\) −5.69797 + 3.28972i −0.550844 + 0.318030i −0.749462 0.662047i \(-0.769688\pi\)
0.198619 + 0.980077i \(0.436355\pi\)
\(108\) 0 0
\(109\) −1.34219 + 2.32474i −0.128558 + 0.222669i −0.923118 0.384516i \(-0.874368\pi\)
0.794560 + 0.607186i \(0.207702\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.63456 0.243099i −0.248942 0.0229707i
\(113\) 3.55031i 0.333985i 0.985958 + 0.166992i \(0.0534056\pi\)
−0.985958 + 0.166992i \(0.946594\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 5.78405 + 3.33943i 0.537036 + 0.310058i
\(117\) 0 0
\(118\) 6.00761i 0.553046i
\(119\) 3.40241 + 7.38784i 0.311899 + 0.677242i
\(120\) 0 0
\(121\) 6.81421 + 11.8026i 0.619474 + 1.07296i
\(122\) −5.22512 + 9.05018i −0.473060 + 0.819365i
\(123\) 0 0
\(124\) −1.01653 + 0.586893i −0.0912869 + 0.0527045i
\(125\) 0 0
\(126\) 0 0
\(127\) 5.51567 0.489437 0.244719 0.969594i \(-0.421304\pi\)
0.244719 + 0.969594i \(0.421304\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) −10.3068 17.8519i −0.900510 1.55973i −0.826833 0.562447i \(-0.809860\pi\)
−0.0736773 0.997282i \(-0.523473\pi\)
\(132\) 0 0
\(133\) −0.754039 + 8.17182i −0.0653835 + 0.708586i
\(134\) 11.9545i 1.03272i
\(135\) 0 0
\(136\) −2.66237 1.53712i −0.228296 0.131807i
\(137\) 9.92131 + 5.72807i 0.847635 + 0.489382i 0.859852 0.510543i \(-0.170556\pi\)
−0.0122175 + 0.999925i \(0.503889\pi\)
\(138\) 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
\(142\) −0.486761 0.843095i −0.0408481 0.0707509i
\(143\) −13.6322 + 23.6117i −1.13999 + 1.97451i
\(144\) 0 0
\(145\) 0 0
\(146\) 16.6983 1.38196
\(147\) 0 0
\(148\) −10.7080 −0.880192
\(149\) −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 \(0.179915\pi\)
\(152\) −1.55089 2.68622i −0.125794 0.217881i
\(153\) 0 0
\(154\) −7.58207 + 10.7197i −0.610980 + 0.863815i
\(155\) 0 0
\(156\) 0 0
\(157\) −4.64699 2.68294i −0.370871 0.214122i 0.302968 0.953001i \(-0.402022\pi\)
−0.673839 + 0.738878i \(0.735356\pi\)
\(158\) −3.67763 2.12328i −0.292576 0.168919i
\(159\) 0 0
\(160\) 0 0
\(161\) −1.50143 + 16.2716i −0.118329 + 1.28238i
\(162\) 0 0
\(163\) 5.02108 + 8.69677i 0.393282 + 0.681184i 0.992880 0.119117i \(-0.0380064\pi\)
−0.599599 + 0.800301i \(0.704673\pi\)
\(164\) −4.19713 + 7.26965i −0.327741 + 0.567664i
\(165\) 0 0
\(166\) 12.3704 7.14207i 0.960131 0.554332i
\(167\) 2.46005 0.190364 0.0951822 0.995460i \(-0.469657\pi\)
0.0951822 + 0.995460i \(0.469657\pi\)
\(168\) 0 0
\(169\) −17.1827 −1.32175
\(170\) 0 0
\(171\) 0 0
\(172\) −4.40513 + 7.62990i −0.335888 + 0.581775i
\(173\) 1.50042 + 2.59880i 0.114075 + 0.197583i 0.917410 0.397944i \(-0.130276\pi\)
−0.803335 + 0.595528i \(0.796943\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 4.96270i 0.374078i
\(177\) 0 0
\(178\) −12.7915 7.38517i −0.958763 0.553542i
\(179\) 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 \(-0.0732278\pi\)
\(182\) −14.4739 1.33556i −1.07288 0.0989980i
\(183\) 0 0
\(184\) −3.08810 5.34875i −0.227658 0.394315i
\(185\) 0 0
\(186\) 0 0
\(187\) −13.2125 + 7.62827i −0.966197 + 0.557834i
\(188\) 4.14624 0.302396
\(189\) 0 0
\(190\) 0 0
\(191\) −4.95227 + 2.85920i −0.358334 + 0.206884i −0.668350 0.743847i \(-0.732999\pi\)
0.310016 + 0.950731i \(0.399666\pi\)
\(192\) 0 0
\(193\) 3.11665 5.39819i 0.224341 0.388570i −0.731780 0.681541i \(-0.761310\pi\)
0.956122 + 0.292970i \(0.0946437\pi\)
\(194\) 2.20821 + 3.82474i 0.158540 + 0.274600i
\(195\) 0 0
\(196\) −6.88181 1.28092i −0.491558 0.0914941i
\(197\) 1.32234i 0.0942128i −0.998890 0.0471064i \(-0.985000\pi\)
0.998890 0.0471064i \(-0.0150000\pi\)
\(198\) 0 0
\(199\) −8.27163 4.77563i −0.586360 0.338535i 0.177297 0.984157i \(-0.443265\pi\)
−0.763657 + 0.645622i \(0.776598\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 10.3965i 0.731495i
\(203\) 14.4266 + 10.2040i 1.01255 + 0.716181i
\(204\) 0 0
\(205\) 0 0
\(206\) 5.11942 8.86709i 0.356687 0.617800i
\(207\) 0 0
\(208\) 4.75784 2.74694i 0.329897 0.190466i
\(209\) −15.3932 −1.06477
\(210\) 0 0
\(211\) 26.0219 1.79142 0.895711 0.444636i \(-0.146667\pi\)
0.895711 + 0.444636i \(0.146667\pi\)
\(212\) 3.85443 2.22536i 0.264723 0.152838i
\(213\) 0 0
\(214\) 3.28972 5.69797i 0.224881 0.389505i
\(215\) 0 0
\(216\) 0 0
\(217\) −2.82078 + 1.29909i −0.191487 + 0.0881878i
\(218\) 2.68437i 0.181809i
\(219\) 0 0
\(220\) 0 0
\(221\) −14.6267 8.44475i −0.983900 0.568055i
\(222\) 0 0
\(223\) 7.25222i 0.485644i −0.970071 0.242822i \(-0.921927\pi\)
0.970071 0.242822i \(-0.0780731\pi\)
\(224\) 2.40314 1.10675i 0.160567 0.0739478i
\(225\) 0 0
\(226\) −1.77515 3.07466i −0.118081 0.204523i
\(227\) 13.3604 23.1409i 0.886762 1.53592i 0.0430820 0.999072i \(-0.486282\pi\)
0.843680 0.536846i \(-0.180384\pi\)
\(228\) 0 0
\(229\) 21.0473 12.1517i 1.39085 0.803006i 0.397439 0.917629i \(-0.369899\pi\)
0.993409 + 0.114622i \(0.0365658\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.67885 −0.438488
\(233\) 8.01573 4.62788i 0.525128 0.303183i −0.213902 0.976855i \(-0.568617\pi\)
0.739030 + 0.673672i \(0.235284\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −3.00381 5.20275i −0.195531 0.338670i
\(237\) 0 0
\(238\) −6.64050 4.69685i −0.430439 0.304452i
\(239\) 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 \(0.636132\pi\)
\(242\) −11.8026 6.81421i −0.758698 0.438034i
\(243\) 0 0
\(244\) 10.4502i 0.669008i
\(245\) 0 0
\(246\) 0 0
\(247\) −8.52039 14.7578i −0.542140 0.939013i
\(248\) 0.586893 1.01653i 0.0372677 0.0645496i
\(249\) 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
\(253\) −30.6507 −1.92699
\(254\) −4.77671 + 2.75784i −0.299718 + 0.173042i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.29797 + 10.9084i 0.392856 + 0.680447i 0.992825 0.119576i \(-0.0381536\pi\)
−0.599969 + 0.800023i \(0.704820\pi\)
\(258\) 0 0
\(259\) −28.2108 2.60310i −1.75294 0.161749i
\(260\) 0 0
\(261\) 0 0
\(262\) 17.8519 + 10.3068i 1.10290 + 0.636757i
\(263\) 14.4383 + 8.33594i 0.890302 + 0.514016i 0.874041 0.485852i \(-0.161490\pi\)
0.0162609 + 0.999868i \(0.494824\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −3.43289 7.45402i −0.210484 0.457035i
\(267\) 0 0
\(268\) 5.97727 + 10.3529i 0.365120 + 0.632407i
\(269\) −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 \(0.515856\pi\)
\(272\) 3.07424 0.186403
\(273\) 0 0
\(274\) −11.4561 −0.692091
\(275\) 0 0
\(276\) 0 0
\(277\) 9.07406 15.7167i 0.545207 0.944327i −0.453386 0.891314i \(-0.649784\pi\)
0.998594 0.0530128i \(-0.0168824\pi\)
\(278\) 0.583502 + 1.01066i 0.0349961 + 0.0606151i
\(279\) 0 0
\(280\) 0 0
\(281\) 15.5129i 0.925425i 0.886508 + 0.462713i \(0.153124\pi\)
−0.886508 + 0.462713i \(0.846876\pi\)
\(282\) 0 0
\(283\) 15.2813 + 8.82268i 0.908381 + 0.524454i 0.879910 0.475141i \(-0.157603\pi\)
0.0284708 + 0.999595i \(0.490936\pi\)
\(284\) 0.843095 + 0.486761i 0.0500285 + 0.0288840i
\(285\) 0 0
\(286\) 27.2645i 1.61218i
\(287\) −12.8248 + 18.1320i −0.757026 + 1.07030i
\(288\) 0 0
\(289\) 3.77453 + 6.53767i 0.222031 + 0.384569i
\(290\) 0 0
\(291\) 0 0
\(292\) −14.4612 + 8.34916i −0.846276 + 0.488598i
\(293\) −10.4489 −0.610432 −0.305216 0.952283i \(-0.598729\pi\)
−0.305216 + 0.952283i \(0.598729\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 9.27339 5.35400i 0.539005 0.311195i
\(297\) 0 0
\(298\) 7.70205 13.3404i 0.446168 0.772786i
\(299\) −16.9657 29.3854i −0.981149 1.69940i
\(300\) 0 0
\(301\) −13.4604 + 19.0306i −0.775844 + 1.09690i
\(302\) 1.02256i 0.0588419i
\(303\) 0 0
\(304\) 2.68622 + 1.55089i 0.154065 + 0.0889496i
\(305\) 0 0
\(306\) 0 0
\(307\) 0.724648i 0.0413579i 0.999786 + 0.0206789i \(0.00658278\pi\)
−0.999786 + 0.0206789i \(0.993417\pi\)
\(308\) 1.20643 13.0745i 0.0687426 0.744991i
\(309\) 0 0
\(310\) 0 0
\(311\) −14.1225 + 24.4609i −0.800813 + 1.38705i 0.118268 + 0.992982i \(0.462266\pi\)
−0.919081 + 0.394068i \(0.871068\pi\)
\(312\) 0 0
\(313\) 17.7797 10.2651i 1.00497 0.580218i 0.0952528 0.995453i \(-0.469634\pi\)
0.909714 + 0.415235i \(0.136301\pi\)
\(314\) 5.36589 0.302815
\(315\) 0 0
\(316\) 4.24656 0.238887
\(317\) −1.96890 + 1.13674i −0.110584 + 0.0638459i −0.554272 0.832336i \(-0.687003\pi\)
0.443688 + 0.896181i \(0.353670\pi\)
\(318\) 0 0
\(319\) −16.5726 + 28.7045i −0.927886 + 1.60715i
\(320\) 0 0
\(321\) 0 0
\(322\) −6.83551 14.8423i −0.380928 0.827130i
\(323\) 9.53560i 0.530575i
\(324\) 0 0
\(325\) 0 0
\(326\) −8.69677 5.02108i −0.481670 0.278092i
\(327\) 0 0
\(328\) 8.39427i 0.463496i
\(329\) 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 \(0.371228\pi\)
\(332\) −7.14207 + 12.3704i −0.391972 + 0.678915i
\(333\) 0 0
\(334\) −2.13047 + 1.23003i −0.116574 + 0.0673040i
\(335\) 0 0
\(336\) 0 0
\(337\) 3.76361 0.205017 0.102508 0.994732i \(-0.467313\pi\)
0.102508 + 0.994732i \(0.467313\pi\)
\(338\) 14.8806 8.59134i 0.809400 0.467308i
\(339\) 0 0
\(340\) 0 0
\(341\) −2.91258 5.04473i −0.157725 0.273187i
\(342\) 0 0
\(343\) −17.8191 5.04761i −0.962143 0.272546i
\(344\) 8.81025i 0.475017i
\(345\) 0 0
\(346\) −2.59880 1.50042i −0.139713 0.0806631i
\(347\) 3.50549 + 2.02389i 0.188184 + 0.108648i 0.591132 0.806575i \(-0.298681\pi\)
−0.402948 + 0.915223i \(0.632014\pi\)
\(348\) 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
\(352\) 2.48135 + 4.29783i 0.132256 + 0.229075i
\(353\) −12.7409 + 22.0679i −0.678129 + 1.17455i 0.297415 + 0.954748i \(0.403876\pi\)
−0.975544 + 0.219805i \(0.929458\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 14.7703 0.782826
\(357\) 0 0
\(358\) −3.67236 −0.194091
\(359\) 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
\(362\) 3.06780 + 5.31359i 0.161240 + 0.279276i
\(363\) 0 0
\(364\) 13.2026 6.08035i 0.692003 0.318697i
\(365\) 0 0
\(366\) 0 0
\(367\) 4.57004 + 2.63851i 0.238554 + 0.137729i 0.614512 0.788907i \(-0.289353\pi\)
−0.375958 + 0.926637i \(0.622686\pi\)
\(368\) 5.34875 + 3.08810i 0.278823 + 0.160978i
\(369\) 0 0
\(370\) 0 0
\(371\) 10.6957 4.92582i 0.555293 0.255736i
\(372\) 0 0
\(373\) 7.27390 + 12.5988i 0.376628 + 0.652339i 0.990569 0.137013i \(-0.0437501\pi\)
−0.613941 + 0.789352i \(0.710417\pi\)
\(374\) 7.62827 13.2125i 0.394448 0.683205i
\(375\) 0 0
\(376\) −3.59075 + 2.07312i −0.185179 + 0.106913i
\(377\) −36.6928 −1.88977
\(378\) 0 0
\(379\) 3.66669 0.188345 0.0941726 0.995556i \(-0.469979\pi\)
0.0941726 + 0.995556i \(0.469979\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 2.85920 4.95227i 0.146289 0.253380i
\(383\) 9.76247 + 16.9091i 0.498839 + 0.864015i 0.999999 0.00134002i \(-0.000426542\pi\)
−0.501160 + 0.865355i \(0.667093\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 6.23330i 0.317266i
\(387\) 0 0
\(388\) −3.82474 2.20821i −0.194172 0.112105i
\(389\) −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
\(392\) 6.60028 2.33160i 0.333364 0.117763i
\(393\) 0 0
\(394\) 0.661170 + 1.14518i 0.0333092 + 0.0576933i
\(395\) 0 0
\(396\) 0 0
\(397\) −23.9755 + 13.8423i −1.20330 + 0.694724i −0.961287 0.275549i \(-0.911140\pi\)
−0.242011 + 0.970274i \(0.577807\pi\)
\(398\) 9.55125 0.478761
\(399\) 0 0
\(400\) 0 0
\(401\) 32.7521 18.9095i 1.63556 0.944293i 0.653229 0.757161i \(-0.273414\pi\)
0.982335 0.187132i \(-0.0599194\pi\)
\(402\) 0 0
\(403\) 3.22432 5.58468i 0.160615 0.278193i
\(404\) −5.19825 9.00364i −0.258623 0.447948i
\(405\) 0 0
\(406\) −17.5958 1.62362i −0.873266 0.0805790i
\(407\) 53.1406i 2.63408i
\(408\) 0 0
\(409\) 31.6028 + 18.2459i 1.56266 + 0.902202i 0.996987 + 0.0775719i \(0.0247167\pi\)
0.565673 + 0.824630i \(0.308617\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 10.2388i 0.504431i
\(413\) −6.64893 14.4372i −0.327172 0.710407i
\(414\) 0 0
\(415\) 0 0
\(416\) −2.74694 + 4.75784i −0.134680 + 0.233272i
\(417\) 0 0
\(418\) 13.3309 7.69660i 0.652036 0.376453i
\(419\) −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 \(0.569127\pi\)
\(422\) −22.5356 + 13.0110i −1.09702 + 0.633363i
\(423\) 0 0
\(424\) −2.22536 + 3.85443i −0.108073 + 0.187188i
\(425\) 0 0
\(426\) 0 0
\(427\) 2.54044 27.5318i 0.122941 1.33236i
\(428\) 6.57945i 0.318030i
\(429\) 0 0
\(430\) 0 0
\(431\) −25.7481 14.8656i −1.24024 0.716053i −0.271097 0.962552i \(-0.587386\pi\)
−0.969143 + 0.246499i \(0.920720\pi\)
\(432\) 0 0
\(433\) 26.5666i 1.27671i 0.769741 + 0.638356i \(0.220385\pi\)
−0.769741 + 0.638356i \(0.779615\pi\)
\(434\) 1.79332 2.53543i 0.0860822 0.121705i
\(435\) 0 0
\(436\) 1.34219 + 2.32474i 0.0642791 + 0.111335i
\(437\) 9.57860 16.5906i 0.458207 0.793637i
\(438\) 0 0
\(439\) 14.4067 8.31774i 0.687597 0.396984i −0.115114 0.993352i \(-0.536723\pi\)
0.802711 + 0.596368i \(0.203390\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 16.8895 0.803351
\(443\) −2.83428 + 1.63637i −0.134661 + 0.0777464i −0.565817 0.824531i \(-0.691439\pi\)
0.431156 + 0.902277i \(0.358106\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 3.62611 + 6.28060i 0.171701 + 0.297395i
\(447\) 0 0
\(448\) −1.52781 + 2.16005i −0.0721822 + 0.102053i
\(449\) 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
\(452\) 3.07466 + 1.77515i 0.144620 + 0.0834962i
\(453\) 0 0
\(454\) 26.7208i 1.25407i
\(455\) 0 0
\(456\) 0 0
\(457\) 16.5394 + 28.6471i 0.773680 + 1.34005i 0.935533 + 0.353238i \(0.114920\pi\)
−0.161853 + 0.986815i \(0.551747\pi\)
\(458\) −12.1517 + 21.0473i −0.567811 + 0.983478i
\(459\) 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
\(463\) 38.6061 1.79418 0.897090 0.441848i \(-0.145677\pi\)
0.897090 + 0.441848i \(0.145677\pi\)
\(464\) 5.78405 3.33943i 0.268518 0.155029i
\(465\) 0 0
\(466\) −4.62788 + 8.01573i −0.214383 + 0.371322i
\(467\) 2.35692 + 4.08230i 0.109065 + 0.188906i 0.915392 0.402564i \(-0.131881\pi\)
−0.806327 + 0.591471i \(0.798548\pi\)
\(468\) 0 0
\(469\) 13.2307 + 28.7285i 0.610937 + 1.32656i
\(470\) 0 0
\(471\) 0 0
\(472\) 5.20275 + 3.00381i 0.239476 + 0.138261i
\(473\) −37.8649 21.8613i −1.74103 1.00519i
\(474\) 0 0
\(475\) 0 0
\(476\) 8.09926 + 0.747344i 0.371229 + 0.0342545i
\(477\) 0 0
\(478\) 0.126683 + 0.219422i 0.00579436 + 0.0100361i
\(479\) −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
\(482\) −2.97379 −0.135452
\(483\) 0 0
\(484\) 13.6284 0.619474
\(485\) 0 0
\(486\) 0 0
\(487\) 2.36544 4.09706i 0.107188 0.185656i −0.807442 0.589947i \(-0.799149\pi\)
0.914630 + 0.404292i \(0.132482\pi\)
\(488\) 5.22512 + 9.05018i 0.236530 + 0.409682i
\(489\) 0 0
\(490\) 0 0
\(491\) 16.0027i 0.722190i 0.932529 + 0.361095i \(0.117597\pi\)
−0.932529 + 0.361095i \(0.882403\pi\)
\(492\) 0 0
\(493\) −17.7816 10.2662i −0.800841 0.462366i
\(494\) 14.7578 + 8.52039i 0.663983 + 0.383351i
\(495\) 0 0
\(496\) 1.17379i 0.0527045i
\(497\) 2.10285 + 1.48736i 0.0943258 + 0.0667170i
\(498\) 0 0
\(499\) −3.18097 5.50961i −0.142400 0.246644i 0.786000 0.618227i \(-0.212149\pi\)
−0.928400 + 0.371583i \(0.878815\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 11.3276 6.53998i 0.505574 0.291893i
\(503\) −36.3826 −1.62222 −0.811109 0.584895i \(-0.801136\pi\)
−0.811109 + 0.584895i \(0.801136\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 26.5443 15.3253i 1.18004 0.681294i
\(507\) 0 0
\(508\) 2.75784 4.77671i 0.122359 0.211932i
\(509\) 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
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −10.9084 6.29797i −0.481149 0.277791i
\(515\) 0 0
\(516\) 0 0
\(517\) 20.5766i 0.904956i
\(518\) 25.7329 11.8511i 1.13064 0.520706i
\(519\) 0 0
\(520\) 0 0
\(521\) −20.2375 + 35.0524i −0.886622 + 1.53567i −0.0427789 + 0.999085i \(0.513621\pi\)
−0.843843 + 0.536590i \(0.819712\pi\)
\(522\) 0 0
\(523\) 37.8314 21.8420i 1.65425 0.955083i 0.678957 0.734178i \(-0.262432\pi\)
0.975295 0.220905i \(-0.0709010\pi\)
\(524\) −20.6136 −0.900510
\(525\) 0 0
\(526\) −16.6719 −0.726929
\(527\) 3.12505 1.80425i 0.136129 0.0785943i
\(528\) 0 0
\(529\) 7.57274 13.1164i 0.329250 0.570277i
\(530\) 0 0
\(531\) 0 0
\(532\) 6.69998 + 4.73893i 0.290481 + 0.205458i
\(533\) 46.1171i 1.99755i
\(534\) 0 0
\(535\) 0 0
\(536\) −10.3529 5.97727i −0.447179 0.258179i
\(537\) 0 0
\(538\) 20.0069i 0.862561i
\(539\) 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 \(0.752321\pi\)
\(542\) 8.93068 15.4684i 0.383606 0.664425i
\(543\) 0 0
\(544\) −2.66237 + 1.53712i −0.114148 + 0.0659035i
\(545\) 0 0
\(546\) 0 0
\(547\) −34.6501 −1.48153 −0.740765 0.671764i \(-0.765537\pi\)
−0.740765 + 0.671764i \(0.765537\pi\)
\(548\) 9.92131 5.72807i 0.423817 0.244691i
\(549\) 0 0
\(550\) 0 0
\(551\) −10.3582 17.9409i −0.441272 0.764306i
\(552\) 0 0
\(553\) 11.1878 + 1.03233i 0.475754 + 0.0438993i
\(554\) 18.1481i 0.771040i
\(555\) 0 0
\(556\) −1.01066 0.583502i −0.0428613 0.0247460i
\(557\) 30.5822 + 17.6567i 1.29581 + 0.748137i 0.979678 0.200578i \(-0.0642819\pi\)
0.316134 + 0.948715i \(0.397615\pi\)
\(558\) 0 0
\(559\) 48.4025i 2.04721i
\(560\) 0 0
\(561\) 0 0
\(562\) −7.75647 13.4346i −0.327187 0.566705i
\(563\) 19.3495 33.5143i 0.815483 1.41246i −0.0934975 0.995620i \(-0.529805\pi\)
0.908981 0.416839i \(-0.136862\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −17.6454 −0.741690
\(567\) 0 0
\(568\) −0.973522 −0.0408481
\(569\) 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 \(0.0178121\pi\)
\(572\) 13.6322 + 23.6117i 0.569993 + 0.987256i
\(573\) 0 0
\(574\) 2.04064 22.1152i 0.0851746 0.923070i
\(575\) 0 0
\(576\) 0 0
\(577\) 13.6179 + 7.86230i 0.566921 + 0.327312i 0.755919 0.654666i \(-0.227191\pi\)
−0.188998 + 0.981978i \(0.560524\pi\)
\(578\) −6.53767 3.77453i −0.271931 0.157000i
\(579\) 0 0
\(580\) 0 0
\(581\) −21.8234 + 30.8544i −0.905389 + 1.28006i
\(582\) 0 0
\(583\) 11.0438 + 19.1284i 0.457387 + 0.792217i
\(584\) 8.34916 14.4612i 0.345491 0.598408i
\(585\) 0 0
\(586\) 9.04902 5.22446i 0.373812 0.215820i
\(587\) −4.59252 −0.189554 −0.0947769 0.995499i \(-0.530214\pi\)
−0.0947769 + 0.995499i \(0.530214\pi\)
\(588\) 0 0
\(589\) 3.64082 0.150017
\(590\) 0 0
\(591\) 0 0
\(592\) −5.35400 + 9.27339i −0.220048 + 0.381134i
\(593\) 1.91286 + 3.31317i 0.0785516 + 0.136055i 0.902625 0.430427i \(-0.141637\pi\)
−0.824074 + 0.566483i \(0.808304\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 15.4041i 0.630977i
\(597\) 0 0
\(598\) 29.3854 + 16.9657i 1.20166 + 0.693777i
\(599\) −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 \(-0.00906892\pi\)
\(602\) 2.14176 23.2111i 0.0872918 0.946015i
\(603\) 0 0
\(604\) 0.511281 + 0.885565i 0.0208037 + 0.0360331i
\(605\) 0 0
\(606\) 0 0
\(607\) 8.94920 5.16682i 0.363237 0.209715i −0.307263 0.951625i \(-0.599413\pi\)
0.670500 + 0.741910i \(0.266080\pi\)
\(608\) −3.10178 −0.125794
\(609\) 0 0
\(610\) 0 0
\(611\) −19.7271 + 11.3895i −0.798075 + 0.460769i
\(612\) 0 0
\(613\) 6.14772 10.6482i 0.248304 0.430075i −0.714751 0.699379i \(-0.753460\pi\)
0.963055 + 0.269303i \(0.0867934\pi\)
\(614\) −0.362324 0.627564i −0.0146222 0.0253264i
\(615\) 0 0
\(616\) 5.49247 + 11.9261i 0.221298 + 0.480516i
\(617\) 8.10935i 0.326470i 0.986587 + 0.163235i \(0.0521929\pi\)
−0.986587 + 0.163235i \(0.947807\pi\)
\(618\) 0 0
\(619\) 7.03506 + 4.06170i 0.282763 + 0.163253i 0.634674 0.772780i \(-0.281135\pi\)
−0.351911 + 0.936034i \(0.614468\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 28.2450i 1.13252i
\(623\) 38.9133 + 3.59065i 1.55903 + 0.143857i
\(624\) 0 0
\(625\) 0 0
\(626\) −10.2651 + 17.7797i −0.410276 + 0.710619i
\(627\) 0 0
\(628\) −4.64699 + 2.68294i −0.185435 + 0.107061i
\(629\) 32.9189 1.31256
\(630\) 0 0
\(631\) −40.6011 −1.61630 −0.808151 0.588975i \(-0.799532\pi\)
−0.808151 + 0.588975i \(0.799532\pi\)
\(632\) −3.67763 + 2.12328i −0.146288 + 0.0844595i
\(633\) 0 0
\(634\) 1.13674 1.96890i 0.0451459 0.0781950i
\(635\) 0 0
\(636\) 0 0
\(637\) 36.2611 12.8095i 1.43672 0.507531i
\(638\) 33.1452i 1.31223i
\(639\) 0 0
\(640\) 0 0
\(641\) 32.0260 + 18.4902i 1.26495 + 0.730319i 0.974028 0.226427i \(-0.0727046\pi\)
0.290922 + 0.956747i \(0.406038\pi\)
\(642\) 0 0
\(643\) 4.86696i 0.191934i 0.995385 + 0.0959671i \(0.0305944\pi\)
−0.995385 + 0.0959671i \(0.969406\pi\)
\(644\) 13.3409 + 9.43606i 0.525704 + 0.371833i
\(645\) 0 0
\(646\) 4.76780 + 8.25808i 0.187587 + 0.324910i
\(647\) 12.4833 21.6217i 0.490769 0.850037i −0.509175 0.860663i \(-0.670049\pi\)
0.999944 + 0.0106266i \(0.00338261\pi\)
\(648\) 0 0
\(649\) 25.8197 14.9070i 1.01351 0.585151i
\(650\) 0 0
\(651\) 0 0
\(652\) 10.0422 0.393282
\(653\) 12.6352 7.29496i 0.494455 0.285474i −0.231966 0.972724i \(-0.574516\pi\)
0.726421 + 0.687250i \(0.241182\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 4.19713 + 7.26965i 0.163870 + 0.283832i
\(657\) 0 0
\(658\) −9.96402 + 4.58885i −0.388438 + 0.178892i
\(659\) 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 \(0.775308\pi\)
\(662\) −31.2889 18.0646i −1.21608 0.702102i
\(663\) 0 0
\(664\) 14.2841i 0.554332i
\(665\) 0 0
\(666\) 0 0
\(667\) −20.6250 35.7235i −0.798602 1.38322i
\(668\) 1.23003 2.13047i 0.0475911 0.0824302i
\(669\) 0 0
\(670\) 0 0
\(671\) 51.8615 2.00209
\(672\) 0 0
\(673\) 1.47971 0.0570387 0.0285193 0.999593i \(-0.490921\pi\)
0.0285193 + 0.999593i \(0.490921\pi\)
\(674\) −3.25938 + 1.88181i −0.125547 + 0.0724844i
\(675\) 0 0
\(676\) −8.59134 + 14.8806i −0.330436 + 0.572333i
\(677\) 5.92549 + 10.2632i 0.227735 + 0.394448i 0.957136 0.289637i \(-0.0935347\pi\)
−0.729402 + 0.684086i \(0.760201\pi\)
\(678\) 0 0
\(679\) −9.53968 6.74746i −0.366099 0.258944i
\(680\) 0 0
\(681\) 0 0
\(682\) 5.04473 + 2.91258i 0.193173 + 0.111528i
\(683\) 9.11732 + 5.26389i 0.348865 + 0.201417i 0.664185 0.747568i \(-0.268779\pi\)
−0.315320 + 0.948985i \(0.602112\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 17.9556 4.53821i 0.685549 0.173270i
\(687\) 0 0
\(688\) 4.40513 + 7.62990i 0.167944 + 0.290887i
\(689\) −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 \(0.286913\pi\)
\(692\) 3.00084 0.114075
\(693\) 0 0
\(694\) −4.04779 −0.153652
\(695\) 0 0
\(696\) 0 0
\(697\) 12.9030 22.3486i 0.488736 0.846515i
\(698\) −11.9682 20.7296i −0.453004 0.784626i
\(699\) 0 0
\(700\) 0 0
\(701\) 35.2007i 1.32951i 0.747060 + 0.664757i \(0.231465\pi\)
−0.747060 + 0.664757i \(0.768535\pi\)
\(702\) 0 0
\(703\) 28.7640 + 16.6069i 1.08485 + 0.626341i
\(704\) −4.29783 2.48135i −0.161980 0.0935195i
\(705\) 0 0
\(706\) 25.4818i 0.959019i
\(707\) −11.5063 24.9843i −0.432740 0.939631i
\(708\) 0 0
\(709\) 18.1846 + 31.4966i 0.682936 + 1.18288i 0.974081 + 0.226201i \(0.0726306\pi\)
−0.291145 + 0.956679i \(0.594036\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −12.7915 + 7.38517i −0.479381 + 0.276771i
\(713\) 7.24954 0.271497
\(714\) 0 0
\(715\) 0 0
\(716\) 3.18036 1.83618i 0.118856 0.0686214i
\(717\) 0 0
\(718\) −8.94277 + 15.4893i −0.333741 + 0.578057i
\(719\) 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
\(722\) 9.37898i 0.349049i
\(723\) 0 0
\(724\) −5.31359 3.06780i −0.197478 0.114014i
\(725\) 0 0
\(726\) 0 0
\(727\) 34.1857i 1.26788i 0.773383 + 0.633939i \(0.218563\pi\)
−0.773383 + 0.633939i \(0.781437\pi\)
\(728\) −8.39360 + 11.8670i −0.311087 + 0.439821i
\(729\) 0 0
\(730\) 0 0
\(731\) 13.5424 23.4561i 0.500884 0.867557i
\(732\) 0 0
\(733\) 37.9485 21.9095i 1.40166 0.809248i 0.407095 0.913386i \(-0.366542\pi\)
0.994563 + 0.104138i \(0.0332084\pi\)
\(734\) −5.27703 −0.194779
\(735\) 0 0
\(736\) −6.17620 −0.227658
\(737\) −51.3786 + 29.6634i −1.89255 + 1.09267i
\(738\) 0 0
\(739\) 6.86403 11.8888i 0.252497 0.437338i −0.711715 0.702468i \(-0.752081\pi\)
0.964213 + 0.265130i \(0.0854148\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −6.79984 + 9.61374i −0.249630 + 0.352931i
\(743\) 20.8393i 0.764520i 0.924055 + 0.382260i \(0.124854\pi\)
−0.924055 + 0.382260i \(0.875146\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −12.5988 7.27390i −0.461274 0.266316i
\(747\) 0 0
\(748\) 15.2565i 0.557834i
\(749\) −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 \(0.539881\pi\)
\(752\) 2.07312 3.59075i 0.0755989 0.130941i
\(753\) 0 0
\(754\) 31.7769 18.3464i 1.15725 0.668136i
\(755\) 0 0
\(756\) 0 0
\(757\) 40.4115 1.46878 0.734391 0.678727i \(-0.237468\pi\)
0.734391 + 0.678727i \(0.237468\pi\)
\(758\) −3.17545 + 1.83335i −0.115337 + 0.0665901i
\(759\) 0 0
\(760\) 0 0
\(761\) −18.3292 31.7471i −0.664432 1.15083i −0.979439 0.201741i \(-0.935340\pi\)
0.315007 0.949089i \(-0.397993\pi\)
\(762\) 0 0
\(763\) 2.97093 + 6.45094i 0.107555 + 0.233540i
\(764\) 5.71839i 0.206884i
\(765\) 0 0
\(766\) −16.9091 9.76247i −0.610951 0.352732i
\(767\) 28.5833 + 16.5025i 1.03208 + 0.595872i
\(768\) 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
\(772\) −3.11665 5.39819i −0.112171 0.194285i
\(773\) 6.84657 11.8586i 0.246254 0.426525i −0.716229 0.697865i \(-0.754134\pi\)
0.962483 + 0.271340i \(0.0874669\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 4.41643 0.158540
\(777\) 0 0
\(778\) 17.2871 0.619773
\(779\) 22.5488 13.0186i 0.807896 0.466439i
\(780\) 0 0
\(781\) −2.41565 + 4.18403i −0.0864388 + 0.149716i
\(782\) 9.49356 + 16.4433i 0.339489 + 0.588012i
\(783\) 0 0
\(784\) −4.55021 + 5.31936i −0.162507 + 0.189977i
\(785\) 0 0
\(786\) 0 0
\(787\) 11.6169 + 6.70701i 0.414097 + 0.239079i 0.692549 0.721371i \(-0.256488\pi\)
−0.278451 + 0.960450i \(0.589821\pi\)