Properties

Label 3150.2.bf.e.1601.12
Level 3150
Weight 2
Character 3150.1601
Analytic conductor 25.153
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1601.12
Character \(\chi\) = 3150.1601
Dual form 3150.2.bf.e.1151.12

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) 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 \(-0.935727\pi\)
−0.316160 + 0.948706i \(0.602394\pi\)
\(12\) 0 0
\(13\) 5.49388i 1.52373i −0.647737 0.761864i \(-0.724285\pi\)
0.647737 0.761864i \(-0.275715\pi\)
\(14\) 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 \(-0.0450623\pi\)
−0.617190 + 0.786814i \(0.711729\pi\)
\(18\) 0 0
\(19\) −2.68622 1.55089i −0.616261 0.355798i 0.159151 0.987254i \(-0.449124\pi\)
−0.775412 + 0.631456i \(0.782458\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −4.96270 −1.05805
\(23\) 5.34875 + 3.08810i 1.11529 + 0.643914i 0.940195 0.340638i \(-0.110643\pi\)
0.175097 + 0.984551i \(0.443976\pi\)
\(24\) 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 −0.588501 0.808496i \(-0.700282\pi\)
0.405928 + 0.913905i \(0.366949\pi\)
\(32\) −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 −0.0290640 + 0.999578i \(0.509253\pi\)
−0.851128 + 0.524959i \(0.824081\pi\)
\(38\) −1.55089 2.68622i −0.251587 0.435762i
\(39\) 0 0
\(40\) 0 0
\(41\) 8.39427 1.31096 0.655482 0.755211i \(-0.272466\pi\)
0.655482 + 0.755211i \(0.272466\pi\)
\(42\) 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 \(-0.931120\pi\)
0.674282 + 0.738474i \(0.264453\pi\)
\(48\) 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 \(-0.765549\pi\)
0.211345 + 0.977412i \(0.432216\pi\)
\(54\) 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 \(-0.294559\pi\)
−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 \(0.433386\pi\)
\(62\) −1.17379 −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 −0.956780 0.290811i \(-0.906075\pi\)
0.226540 0.974002i \(-0.427259\pi\)
\(68\) −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 −0.740106 + 0.672490i \(0.765225\pi\)
−0.952446 + 0.304706i \(0.901442\pi\)
\(74\) −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 −0.721508 0.692406i \(-0.756551\pi\)
0.960395 + 0.278641i \(0.0898840\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 7.26965 + 4.19713i 0.802798 + 0.463496i
\(83\) 14.2841 1.56789 0.783944 0.620831i \(-0.213205\pi\)
0.783944 + 0.620831i \(0.213205\pi\)
\(84\) 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 0.147463 + 0.989068i \(0.452889\pi\)
−0.930289 + 0.366827i \(0.880444\pi\)
\(90\) 0 0
\(91\) 11.8670 8.39360i 1.24400 0.879888i
\(92\) 6.17620i 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 \(0.0719802\pi\)
−0.974541 + 0.224210i \(0.928020\pi\)
\(98\) −5.31936 + 4.55021i −0.537336 + 0.459641i
\(99\) 0 0
\(100\) 0 0
\(101\) −5.19825 9.00364i −0.517245 0.895895i −0.999799 0.0200290i \(-0.993624\pi\)
0.482554 0.875866i \(-0.339709\pi\)
\(102\) 0 0
\(103\) −8.86709 5.11942i −0.873701 0.504431i −0.00512447 0.999987i \(-0.501631\pi\)
−0.868576 + 0.495556i \(0.834965\pi\)
\(104\) 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 \(-0.230312\pi\)
−0.198619 + 0.980077i \(0.563645\pi\)
\(108\) 0 0
\(109\) −1.34219 2.32474i −0.128558 0.222669i 0.794560 0.607186i \(-0.207702\pi\)
−0.923118 + 0.384516i \(0.874368\pi\)
\(110\) 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 0.0736773 0.997282i \(-0.476527\pi\)
0.826833 0.562447i \(-0.190140\pi\)
\(132\) 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 \(-0.829444\pi\)
0.0122175 + 0.999925i \(0.496111\pi\)
\(138\) 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
\(142\) −0.486761 + 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 \(-0.115988\pi\)
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 \(0.846581\pi\)
\(152\) 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 −0.673839 0.738878i \(-0.735356\pi\)
0.302968 + 0.953001i \(0.402022\pi\)
\(158\) 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 −0.599599 0.800301i \(-0.704673\pi\)
0.992880 + 0.119117i \(0.0380064\pi\)
\(164\) 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 \(-0.530343\pi\)
−0.0951822 + 0.995460i \(0.530343\pi\)
\(168\) 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 \(-0.869724\pi\)
0.803335 + 0.595528i \(0.203057\pi\)
\(174\) 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 \(-0.710491\pi\)
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 \(0.926772\pi\)
\(182\) 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 \(-0.267001\pi\)
−0.310016 + 0.950731i \(0.600334\pi\)
\(192\) 0 0
\(193\) 3.11665 + 5.39819i 0.224341 + 0.388570i 0.956122 0.292970i \(-0.0946437\pi\)
−0.731780 + 0.681541i \(0.761310\pi\)
\(194\) −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 −0.763657 0.645622i \(-0.776598\pi\)
0.177297 + 0.984157i \(0.443265\pi\)
\(200\) 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 \(0.0780731\pi\)
−0.970071 + 0.242822i \(0.921927\pi\)
\(224\) −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 −0.843680 0.536846i \(-0.819616\pi\)
−0.0430820 0.999072i \(-0.513718\pi\)
\(228\) 0 0
\(229\) 21.0473 + 12.1517i 1.39085 + 0.803006i 0.993409 0.114622i \(-0.0365658\pi\)
0.397439 + 0.917629i \(0.369899\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.67885 −0.438488
\(233\) −8.01573 4.62788i −0.525128 0.303183i 0.213902 0.976855i \(-0.431383\pi\)
−0.739030 + 0.673672i \(0.764716\pi\)
\(234\) 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 −0.414754 0.909934i \(-0.636132\pi\)
0.580649 + 0.814154i \(0.302799\pi\)
\(242\) 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 \(-0.364551\pi\)
0.412800 + 0.910822i \(0.364551\pi\)
\(252\) 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 \(-0.961846\pi\)
0.599969 + 0.800023i \(0.295180\pi\)
\(258\) 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 \(-0.838510\pi\)
−0.0162609 + 0.999868i \(0.505176\pi\)
\(264\) 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 0.991253 + 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 \(0.849189\pi\)
\(272\) −3.07424 −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 0.998594 + 0.0530128i \(0.0168824\pi\)
−0.453386 + 0.891314i \(0.649784\pi\)
\(278\) −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 0.0284708 0.999595i \(-0.490936\pi\)
0.879910 + 0.475141i \(0.157603\pi\)
\(284\) −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 \(-0.401271\pi\)
0.305216 + 0.952283i \(0.401271\pi\)
\(294\) 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 \(-0.993417\pi\)
0.999786 0.0206789i \(-0.00658278\pi\)
\(308\) −1.20643 13.0745i −0.0687426 0.744991i
\(309\) 0 0
\(310\) 0 0
\(311\) 14.1225 + 24.4609i 0.800813 + 1.38705i 0.919081 + 0.394068i \(0.128932\pi\)
−0.118268 + 0.992982i \(0.537734\pi\)
\(312\) 0 0
\(313\) 17.7797 + 10.2651i 1.00497 + 0.580218i 0.909714 0.415235i \(-0.136301\pi\)
0.0952528 + 0.995453i \(0.469634\pi\)
\(314\) −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 \(-0.312997\pi\)
−0.443688 + 0.896181i \(0.646330\pi\)
\(318\) 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 0.393605 0.919280i \(-0.371228\pi\)
0.599317 0.800512i \(-0.295439\pi\)
\(332\) 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 \(-0.701319\pi\)
0.402948 + 0.915223i \(0.367986\pi\)
\(348\) 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
\(352\) 2.48135 4.29783i 0.132256 0.229075i
\(353\) 12.7409 + 22.0679i 0.678129 + 1.17455i 0.975544 + 0.219805i \(0.0705422\pi\)
−0.297415 + 0.954748i \(0.596124\pi\)
\(354\) 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 \(-0.489794\pi\)
−0.849552 + 0.527505i \(0.823128\pi\)
\(360\) 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 −0.375958 0.926637i \(-0.622686\pi\)
0.614512 + 0.788907i \(0.289353\pi\)
\(368\) −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 −0.613941 0.789352i \(-0.710417\pi\)
0.990569 + 0.137013i \(0.0437501\pi\)
\(374\) −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 \(-0.999573\pi\)
0.501160 + 0.865355i \(0.332907\pi\)
\(384\) 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 \(-0.522267\pi\)
0.828960 + 0.559309i \(0.188933\pi\)
\(390\) 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 −0.242011 0.970274i \(-0.577807\pi\)
−0.961287 + 0.275549i \(0.911140\pi\)
\(398\) −9.55125 −0.478761
\(399\) 0 0
\(400\) 0 0
\(401\) −32.7521 18.9095i −1.63556 0.944293i −0.982335 0.187132i \(-0.940081\pi\)
−0.653229 0.757161i \(-0.726586\pi\)
\(402\) 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 0.565673 0.824630i \(-0.308617\pi\)
0.996987 0.0775719i \(-0.0247167\pi\)
\(410\) 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 \(-0.322474\pi\)
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 \(0.569127\pi\)
\(422\) 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 \(-0.412614\pi\)
0.969143 + 0.246499i \(0.0792802\pi\)
\(432\) 0 0
\(433\) 26.5666i 1.27671i −0.769741 0.638356i \(-0.779615\pi\)
0.769741 0.638356i \(-0.220385\pi\)
\(434\) −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 0.802711 0.596368i \(-0.203390\pi\)
−0.115114 + 0.993352i \(0.536723\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 16.8895 0.803351
\(443\) 2.83428 + 1.63637i 0.134661 + 0.0777464i 0.565817 0.824531i \(-0.308561\pi\)
−0.431156 + 0.902277i \(0.641894\pi\)
\(444\) 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 −0.161853 0.986815i \(-0.551747\pi\)
0.935533 0.353238i \(-0.114920\pi\)
\(458\) 12.1517 + 21.0473i 0.567811 + 0.983478i
\(459\) 0 0
\(460\) 0 0
\(461\) 11.5639 0.538585 0.269293 0.963058i \(-0.413210\pi\)
0.269293 + 0.963058i \(0.413210\pi\)
\(462\) 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 \(-0.868119\pi\)
0.806327 + 0.591471i \(0.201452\pi\)
\(468\) 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 \(-0.0154657\pi\)
−0.541471 + 0.840720i \(0.682132\pi\)
\(480\) 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 0.914630 0.404292i \(-0.132482\pi\)
−0.807442 + 0.589947i \(0.799149\pi\)
\(488\) −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 −0.928400 0.371583i \(-0.878815\pi\)
0.786000 + 0.618227i \(0.212149\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 11.3276 + 6.53998i 0.505574 + 0.291893i
\(503\) 36.3826 1.62222 0.811109 0.584895i \(-0.198864\pi\)
0.811109 + 0.584895i \(0.198864\pi\)
\(504\) 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 \(-0.957109\pi\)
0.611807 + 0.791007i \(0.290443\pi\)
\(510\) 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 0.843843 + 0.536590i \(0.180288\pi\)
0.0427789 + 0.999085i \(0.486379\pi\)
\(522\) 0 0
\(523\) 37.8314 + 21.8420i 1.65425 + 0.955083i 0.975295 + 0.220905i \(0.0709010\pi\)
0.678957 + 0.734178i \(0.262432\pi\)
\(524\) 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 −0.712243 0.701933i \(-0.752321\pi\)
0.964013 + 0.265855i \(0.0856541\pi\)
\(542\) −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 \(-0.935718\pi\)
−0.316134 + 0.948715i \(0.602385\pi\)
\(558\) 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 −0.908981 0.416839i \(-0.863138\pi\)
0.0934975 0.995620i \(-0.470195\pi\)
\(564\) 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 \(-0.381343\pi\)
−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 \(0.684479\pi\)
\(572\) −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 −0.188998 0.981978i \(-0.560524\pi\)
0.755919 + 0.654666i \(0.227191\pi\)
\(578\) 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 \(-0.469786\pi\)
0.0947769 + 0.995499i \(0.469786\pi\)
\(588\) 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 \(-0.858363\pi\)
0.824074 + 0.566483i \(0.191696\pi\)
\(594\) 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 \(-0.562240\pi\)
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 \(0.990931\pi\)
\(602\) −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 0.670500 0.741910i \(-0.266080\pi\)
−0.307263 + 0.951625i \(0.599413\pi\)
\(608\) 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 0.963055 0.269303i \(-0.0867934\pi\)
−0.714751 + 0.699379i \(0.753460\pi\)
\(614\) 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 −0.351911 0.936034i \(-0.614468\pi\)
0.634674 + 0.772780i \(0.281135\pi\)
\(620\) 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 \(-0.927295\pi\)
−0.290922 + 0.956747i \(0.593962\pi\)
\(642\) 0 0
\(643\) 4.86696i 0.191934i −0.995385 0.0959671i \(-0.969406\pi\)
0.995385 0.0959671i \(-0.0305944\pi\)
\(644\) −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 \(-0.329951\pi\)
−0.999944 + 0.0106266i \(0.996617\pi\)
\(648\) 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 \(-0.425484\pi\)
−0.726421 + 0.687250i \(0.758818\pi\)
\(654\) 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 −0.761034 0.648713i \(-0.775308\pi\)
0.181285 + 0.983431i \(0.441974\pi\)
\(662\) 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 \(-0.906465\pi\)
0.729402 + 0.684086i \(0.239799\pi\)
\(678\) 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 \(-0.731221\pi\)
0.315320 + 0.948985i \(0.397888\pi\)
\(684\) 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 0.620540 0.784175i \(-0.286913\pi\)
−0.368845 + 0.929491i \(0.620247\pi\)
\(692\) −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 −0.291145 0.956679i \(-0.594036\pi\)
0.974081 0.226201i \(-0.0726306\pi\)
\(710\) 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 \(-0.842506\pi\)
0.851260 + 0.524744i \(0.175839\pi\)
\(720\) 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 \(-0.781437\pi\)
0.773383 0.633939i \(-0.218563\pi\)
\(728\) 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 0.994563 0.104138i \(-0.0332084\pi\)
0.407095 + 0.913386i \(0.366542\pi\)
\(734\) 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 0.964213 0.265130i \(-0.0854148\pi\)
−0.711715 + 0.702468i \(0.752081\pi\)
\(740\) 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 −0.124964 0.992161i \(-0.539881\pi\)
0.921719 0.387859i \(-0.126785\pi\)
\(752\) −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 −0.315007 0.949089i \(-0.602007\pi\)
0.979439 0.201741i \(-0.0646598\pi\)
\(762\) 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 \(0.120084\pi\)
−0.929680 + 0.368369i \(0.879916\pi\)
\(770\) 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 \(-0.245866\pi\)
−0.962483 + 0.271340i \(0.912533\pi\)
\(774\) 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 −0.278451 0.960450i \(-0.589821\pi\)
0.692549 + 0.721371i \(0.256488\pi\)