Properties

Label 400.2.y.c.369.2
Level $400$
Weight $2$
Character 400.369
Analytic conductor $3.194$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.y (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.19401608085\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: 8.0.58140625.2
Defining polynomial: \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 25)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 369.2
Root \(-0.983224 + 0.644389i\) of defining polynomial
Character \(\chi\) \(=\) 400.369
Dual form 400.2.y.c.129.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.865190 + 1.19083i) q^{3} +(0.107666 + 2.23347i) q^{5} +3.26086i q^{7} +(0.257524 - 0.792578i) q^{9} +O(q^{10})\) \(q+(0.865190 + 1.19083i) q^{3} +(0.107666 + 2.23347i) q^{5} +3.26086i q^{7} +(0.257524 - 0.792578i) q^{9} +(-0.618034 - 1.90211i) q^{11} +(0.281873 + 0.0915860i) q^{13} +(-2.56654 + 2.06059i) q^{15} +(-3.03472 + 4.17693i) q^{17} +(-1.39991 - 1.01709i) q^{19} +(-3.88313 + 2.82126i) q^{21} +(-0.836161 + 0.271685i) q^{23} +(-4.97682 + 0.480938i) q^{25} +(5.36635 - 1.74363i) q^{27} +(4.78304 - 3.47508i) q^{29} +(4.93462 + 3.58521i) q^{31} +(1.73038 - 2.38166i) q^{33} +(-7.28304 + 0.351083i) q^{35} +(7.69215 + 2.49933i) q^{37} +(0.134810 + 0.414902i) q^{39} +(-0.313697 + 0.965461i) q^{41} -3.24199i q^{43} +(1.79793 + 0.489840i) q^{45} +(2.48043 + 3.41402i) q^{47} -3.63318 q^{49} -7.59963 q^{51} +(-4.76148 - 6.55362i) q^{53} +(4.18178 - 1.58516i) q^{55} -2.54703i q^{57} +(1.83443 - 5.64581i) q^{59} +(0.282941 + 0.870802i) q^{61} +(2.58448 + 0.839749i) q^{63} +(-0.174207 + 0.639416i) q^{65} +(-4.04870 + 5.57255i) q^{67} +(-1.04697 - 0.760668i) q^{69} +(-4.82884 + 3.50836i) q^{71} +(8.40107 - 2.72967i) q^{73} +(-4.87861 - 5.51045i) q^{75} +(6.20252 - 2.01532i) q^{77} +(6.27851 - 4.56161i) q^{79} +(4.69667 + 3.41233i) q^{81} +(8.53192 - 11.7432i) q^{83} +(-9.65580 - 6.32825i) q^{85} +(8.27647 + 2.68919i) q^{87} +(-2.32579 - 7.15805i) q^{89} +(-0.298649 + 0.919147i) q^{91} +8.97820i q^{93} +(2.12093 - 3.23616i) q^{95} +(3.95373 + 5.44184i) q^{97} -1.66673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 5 q^{3} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 5 q^{3} + q^{9} + 4 q^{11} - 5 q^{13} - 15 q^{15} - 10 q^{17} + 5 q^{19} - 4 q^{21} - 5 q^{23} - 10 q^{25} + 5 q^{27} - 5 q^{29} + 9 q^{31} + 10 q^{33} - 15 q^{35} + 30 q^{37} + 3 q^{39} - 4 q^{41} - 15 q^{45} + 14 q^{49} + 4 q^{51} - 10 q^{53} + 10 q^{55} - 9 q^{61} - 10 q^{63} + 5 q^{65} - 20 q^{67} + 17 q^{69} - 6 q^{71} + 15 q^{73} + 10 q^{75} + 10 q^{77} - 15 q^{79} + 28 q^{81} + 45 q^{83} - 15 q^{85} + 20 q^{87} - 25 q^{89} - 6 q^{91} - 15 q^{95} - 60 q^{97} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(1\) \(e\left(\frac{9}{10}\right)\) \(1\)

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 0
\(3\) 0.865190 + 1.19083i 0.499518 + 0.687527i 0.982108 0.188319i \(-0.0603039\pi\)
−0.482590 + 0.875846i \(0.660304\pi\)
\(4\) 0 0
\(5\) 0.107666 + 2.23347i 0.0481496 + 0.998840i
\(6\) 0 0
\(7\) 3.26086i 1.23249i 0.787555 + 0.616244i \(0.211346\pi\)
−0.787555 + 0.616244i \(0.788654\pi\)
\(8\) 0 0
\(9\) 0.257524 0.792578i 0.0858414 0.264193i
\(10\) 0 0
\(11\) −0.618034 1.90211i −0.186344 0.573509i 0.813625 0.581390i \(-0.197491\pi\)
−0.999969 + 0.00788181i \(0.997491\pi\)
\(12\) 0 0
\(13\) 0.281873 + 0.0915860i 0.0781775 + 0.0254014i 0.347845 0.937552i \(-0.386914\pi\)
−0.269667 + 0.962954i \(0.586914\pi\)
\(14\) 0 0
\(15\) −2.56654 + 2.06059i −0.662678 + 0.532042i
\(16\) 0 0
\(17\) −3.03472 + 4.17693i −0.736027 + 1.01305i 0.262810 + 0.964847i \(0.415351\pi\)
−0.998837 + 0.0482067i \(0.984649\pi\)
\(18\) 0 0
\(19\) −1.39991 1.01709i −0.321161 0.233337i 0.415510 0.909589i \(-0.363603\pi\)
−0.736671 + 0.676252i \(0.763603\pi\)
\(20\) 0 0
\(21\) −3.88313 + 2.82126i −0.847369 + 0.615649i
\(22\) 0 0
\(23\) −0.836161 + 0.271685i −0.174352 + 0.0566503i −0.394892 0.918728i \(-0.629218\pi\)
0.220540 + 0.975378i \(0.429218\pi\)
\(24\) 0 0
\(25\) −4.97682 + 0.480938i −0.995363 + 0.0961876i
\(26\) 0 0
\(27\) 5.36635 1.74363i 1.03276 0.335563i
\(28\) 0 0
\(29\) 4.78304 3.47508i 0.888188 0.645306i −0.0472171 0.998885i \(-0.515035\pi\)
0.935405 + 0.353578i \(0.115035\pi\)
\(30\) 0 0
\(31\) 4.93462 + 3.58521i 0.886285 + 0.643923i 0.934907 0.354894i \(-0.115483\pi\)
−0.0486220 + 0.998817i \(0.515483\pi\)
\(32\) 0 0
\(33\) 1.73038 2.38166i 0.301220 0.414594i
\(34\) 0 0
\(35\) −7.28304 + 0.351083i −1.23106 + 0.0593438i
\(36\) 0 0
\(37\) 7.69215 + 2.49933i 1.26458 + 0.410887i 0.863125 0.504991i \(-0.168504\pi\)
0.401457 + 0.915878i \(0.368504\pi\)
\(38\) 0 0
\(39\) 0.134810 + 0.414902i 0.0215869 + 0.0664376i
\(40\) 0 0
\(41\) −0.313697 + 0.965461i −0.0489913 + 0.150780i −0.972559 0.232655i \(-0.925259\pi\)
0.923568 + 0.383434i \(0.125259\pi\)
\(42\) 0 0
\(43\) 3.24199i 0.494399i −0.968965 0.247200i \(-0.920490\pi\)
0.968965 0.247200i \(-0.0795103\pi\)
\(44\) 0 0
\(45\) 1.79793 + 0.489840i 0.268019 + 0.0730210i
\(46\) 0 0
\(47\) 2.48043 + 3.41402i 0.361808 + 0.497986i 0.950651 0.310261i \(-0.100417\pi\)
−0.588844 + 0.808247i \(0.700417\pi\)
\(48\) 0 0
\(49\) −3.63318 −0.519026
\(50\) 0 0
\(51\) −7.59963 −1.06416
\(52\) 0 0
\(53\) −4.76148 6.55362i −0.654040 0.900209i 0.345226 0.938520i \(-0.387802\pi\)
−0.999266 + 0.0383106i \(0.987802\pi\)
\(54\) 0 0
\(55\) 4.18178 1.58516i 0.563871 0.213742i
\(56\) 0 0
\(57\) 2.54703i 0.337363i
\(58\) 0 0
\(59\) 1.83443 5.64581i 0.238823 0.735021i −0.757768 0.652524i \(-0.773710\pi\)
0.996591 0.0824976i \(-0.0262897\pi\)
\(60\) 0 0
\(61\) 0.282941 + 0.870802i 0.0362268 + 0.111495i 0.967535 0.252738i \(-0.0813312\pi\)
−0.931308 + 0.364233i \(0.881331\pi\)
\(62\) 0 0
\(63\) 2.58448 + 0.839749i 0.325614 + 0.105798i
\(64\) 0 0
\(65\) −0.174207 + 0.639416i −0.0216077 + 0.0793099i
\(66\) 0 0
\(67\) −4.04870 + 5.57255i −0.494627 + 0.680796i −0.981233 0.192826i \(-0.938235\pi\)
0.486606 + 0.873622i \(0.338235\pi\)
\(68\) 0 0
\(69\) −1.04697 0.760668i −0.126040 0.0915737i
\(70\) 0 0
\(71\) −4.82884 + 3.50836i −0.573078 + 0.416366i −0.836222 0.548391i \(-0.815241\pi\)
0.263144 + 0.964757i \(0.415241\pi\)
\(72\) 0 0
\(73\) 8.40107 2.72967i 0.983271 0.319484i 0.227110 0.973869i \(-0.427072\pi\)
0.756161 + 0.654385i \(0.227072\pi\)
\(74\) 0 0
\(75\) −4.87861 5.51045i −0.563333 0.636292i
\(76\) 0 0
\(77\) 6.20252 2.01532i 0.706842 0.229667i
\(78\) 0 0
\(79\) 6.27851 4.56161i 0.706388 0.513221i −0.175618 0.984458i \(-0.556192\pi\)
0.882006 + 0.471237i \(0.156192\pi\)
\(80\) 0 0
\(81\) 4.69667 + 3.41233i 0.521852 + 0.379148i
\(82\) 0 0
\(83\) 8.53192 11.7432i 0.936500 1.28898i −0.0207694 0.999784i \(-0.506612\pi\)
0.957269 0.289197i \(-0.0933884\pi\)
\(84\) 0 0
\(85\) −9.65580 6.32825i −1.04732 0.686395i
\(86\) 0 0
\(87\) 8.27647 + 2.68919i 0.887331 + 0.288311i
\(88\) 0 0
\(89\) −2.32579 7.15805i −0.246534 0.758752i −0.995380 0.0960092i \(-0.969392\pi\)
0.748847 0.662743i \(-0.230608\pi\)
\(90\) 0 0
\(91\) −0.298649 + 0.919147i −0.0313069 + 0.0963528i
\(92\) 0 0
\(93\) 8.97820i 0.930996i
\(94\) 0 0
\(95\) 2.12093 3.23616i 0.217602 0.332023i
\(96\) 0 0
\(97\) 3.95373 + 5.44184i 0.401440 + 0.552535i 0.961105 0.276184i \(-0.0890699\pi\)
−0.559664 + 0.828719i \(0.689070\pi\)
\(98\) 0 0
\(99\) −1.66673 −0.167513
\(100\) 0 0
\(101\) −12.1955 −1.21350 −0.606748 0.794894i \(-0.707526\pi\)
−0.606748 + 0.794894i \(0.707526\pi\)
\(102\) 0 0
\(103\) −0.811969 1.11758i −0.0800057 0.110118i 0.767138 0.641482i \(-0.221680\pi\)
−0.847144 + 0.531363i \(0.821680\pi\)
\(104\) 0 0
\(105\) −6.71929 8.36912i −0.655736 0.816742i
\(106\) 0 0
\(107\) 15.8285i 1.53020i −0.643911 0.765101i \(-0.722689\pi\)
0.643911 0.765101i \(-0.277311\pi\)
\(108\) 0 0
\(109\) 0.619199 1.90570i 0.0593085 0.182533i −0.917013 0.398857i \(-0.869407\pi\)
0.976322 + 0.216324i \(0.0694069\pi\)
\(110\) 0 0
\(111\) 3.67889 + 11.3225i 0.349185 + 1.07468i
\(112\) 0 0
\(113\) 9.91713 + 3.22227i 0.932925 + 0.303126i 0.735758 0.677244i \(-0.236826\pi\)
0.197167 + 0.980370i \(0.436826\pi\)
\(114\) 0 0
\(115\) −0.696828 1.83829i −0.0649795 0.171422i
\(116\) 0 0
\(117\) 0.145178 0.199821i 0.0134217 0.0184734i
\(118\) 0 0
\(119\) −13.6204 9.89577i −1.24858 0.907144i
\(120\) 0 0
\(121\) 5.66312 4.11450i 0.514829 0.374045i
\(122\) 0 0
\(123\) −1.42111 + 0.461746i −0.128137 + 0.0416343i
\(124\) 0 0
\(125\) −1.61000 11.0638i −0.144002 0.989577i
\(126\) 0 0
\(127\) −5.56375 + 1.80777i −0.493703 + 0.160414i −0.545278 0.838255i \(-0.683576\pi\)
0.0515752 + 0.998669i \(0.483576\pi\)
\(128\) 0 0
\(129\) 3.86067 2.80494i 0.339913 0.246961i
\(130\) 0 0
\(131\) −1.21081 0.879704i −0.105789 0.0768601i 0.533633 0.845716i \(-0.320826\pi\)
−0.639422 + 0.768856i \(0.720826\pi\)
\(132\) 0 0
\(133\) 3.31659 4.56489i 0.287585 0.395827i
\(134\) 0 0
\(135\) 4.47214 + 11.7979i 0.384900 + 1.01540i
\(136\) 0 0
\(137\) −7.46472 2.42543i −0.637754 0.207219i −0.0277472 0.999615i \(-0.508833\pi\)
−0.610007 + 0.792396i \(0.708833\pi\)
\(138\) 0 0
\(139\) 1.66607 + 5.12764i 0.141314 + 0.434921i 0.996519 0.0833702i \(-0.0265684\pi\)
−0.855204 + 0.518291i \(0.826568\pi\)
\(140\) 0 0
\(141\) −1.91948 + 5.90755i −0.161649 + 0.497505i
\(142\) 0 0
\(143\) 0.592757i 0.0495689i
\(144\) 0 0
\(145\) 8.27647 + 10.3086i 0.687324 + 0.856086i
\(146\) 0 0
\(147\) −3.14339 4.32651i −0.259262 0.356844i
\(148\) 0 0
\(149\) −18.8229 −1.54203 −0.771015 0.636817i \(-0.780251\pi\)
−0.771015 + 0.636817i \(0.780251\pi\)
\(150\) 0 0
\(151\) 3.88797 0.316398 0.158199 0.987407i \(-0.449431\pi\)
0.158199 + 0.987407i \(0.449431\pi\)
\(152\) 0 0
\(153\) 2.52903 + 3.48091i 0.204460 + 0.281415i
\(154\) 0 0
\(155\) −7.47619 + 11.4074i −0.600502 + 0.916261i
\(156\) 0 0
\(157\) 4.28378i 0.341883i 0.985281 + 0.170941i \(0.0546808\pi\)
−0.985281 + 0.170941i \(0.945319\pi\)
\(158\) 0 0
\(159\) 3.68467 11.3403i 0.292214 0.899341i
\(160\) 0 0
\(161\) −0.885926 2.72660i −0.0698208 0.214886i
\(162\) 0 0
\(163\) 14.9566 + 4.85970i 1.17149 + 0.380641i 0.829200 0.558952i \(-0.188796\pi\)
0.342293 + 0.939593i \(0.388796\pi\)
\(164\) 0 0
\(165\) 5.50569 + 3.60834i 0.428617 + 0.280909i
\(166\) 0 0
\(167\) −12.3629 + 17.0161i −0.956670 + 1.31674i −0.00816967 + 0.999967i \(0.502601\pi\)
−0.948500 + 0.316777i \(0.897399\pi\)
\(168\) 0 0
\(169\) −10.4462 7.58958i −0.803551 0.583814i
\(170\) 0 0
\(171\) −1.16663 + 0.847609i −0.0892148 + 0.0648183i
\(172\) 0 0
\(173\) 6.81587 2.21461i 0.518201 0.168374i −0.0382277 0.999269i \(-0.512171\pi\)
0.556429 + 0.830895i \(0.312171\pi\)
\(174\) 0 0
\(175\) −1.56827 16.2287i −0.118550 1.22677i
\(176\) 0 0
\(177\) 8.31034 2.70019i 0.624643 0.202959i
\(178\) 0 0
\(179\) −6.50396 + 4.72540i −0.486129 + 0.353193i −0.803694 0.595043i \(-0.797135\pi\)
0.317565 + 0.948237i \(0.397135\pi\)
\(180\) 0 0
\(181\) 16.6796 + 12.1184i 1.23978 + 0.900756i 0.997584 0.0694707i \(-0.0221310\pi\)
0.242200 + 0.970226i \(0.422131\pi\)
\(182\) 0 0
\(183\) −0.792181 + 1.09034i −0.0585597 + 0.0806005i
\(184\) 0 0
\(185\) −4.75401 + 17.4493i −0.349522 + 1.28290i
\(186\) 0 0
\(187\) 9.82055 + 3.19089i 0.718150 + 0.233341i
\(188\) 0 0
\(189\) 5.68574 + 17.4989i 0.413577 + 1.27286i
\(190\) 0 0
\(191\) −5.57167 + 17.1478i −0.403152 + 1.24077i 0.519277 + 0.854606i \(0.326201\pi\)
−0.922429 + 0.386167i \(0.873799\pi\)
\(192\) 0 0
\(193\) 6.78859i 0.488653i −0.969693 0.244327i \(-0.921433\pi\)
0.969693 0.244327i \(-0.0785669\pi\)
\(194\) 0 0
\(195\) −0.912160 + 0.345766i −0.0653211 + 0.0247608i
\(196\) 0 0
\(197\) −4.69956 6.46839i −0.334830 0.460854i 0.608092 0.793866i \(-0.291935\pi\)
−0.942923 + 0.333012i \(0.891935\pi\)
\(198\) 0 0
\(199\) −5.20485 −0.368962 −0.184481 0.982836i \(-0.559060\pi\)
−0.184481 + 0.982836i \(0.559060\pi\)
\(200\) 0 0
\(201\) −10.1389 −0.715141
\(202\) 0 0
\(203\) 11.3317 + 15.5968i 0.795332 + 1.09468i
\(204\) 0 0
\(205\) −2.19011 0.596687i −0.152964 0.0416745i
\(206\) 0 0
\(207\) 0.732688i 0.0509254i
\(208\) 0 0
\(209\) −1.06943 + 3.29138i −0.0739743 + 0.227669i
\(210\) 0 0
\(211\) −5.13029 15.7894i −0.353184 1.08699i −0.957055 0.289906i \(-0.906376\pi\)
0.603872 0.797082i \(-0.293624\pi\)
\(212\) 0 0
\(213\) −8.35573 2.71494i −0.572525 0.186025i
\(214\) 0 0
\(215\) 7.24091 0.349052i 0.493826 0.0238051i
\(216\) 0 0
\(217\) −11.6909 + 16.0911i −0.793628 + 1.09233i
\(218\) 0 0
\(219\) 10.5191 + 7.64258i 0.710815 + 0.516438i
\(220\) 0 0
\(221\) −1.23795 + 0.899425i −0.0832737 + 0.0605019i
\(222\) 0 0
\(223\) −6.30368 + 2.04819i −0.422126 + 0.137157i −0.512374 0.858762i \(-0.671234\pi\)
0.0902485 + 0.995919i \(0.471234\pi\)
\(224\) 0 0
\(225\) −0.900470 + 4.06837i −0.0600313 + 0.271224i
\(226\) 0 0
\(227\) 12.7365 4.13833i 0.845350 0.274671i 0.145853 0.989306i \(-0.453407\pi\)
0.699497 + 0.714636i \(0.253407\pi\)
\(228\) 0 0
\(229\) 8.16032 5.92882i 0.539249 0.391788i −0.284557 0.958659i \(-0.591846\pi\)
0.823806 + 0.566872i \(0.191846\pi\)
\(230\) 0 0
\(231\) 7.76626 + 5.64252i 0.510983 + 0.371251i
\(232\) 0 0
\(233\) −12.9345 + 17.8028i −0.847368 + 1.16630i 0.137069 + 0.990562i \(0.456232\pi\)
−0.984437 + 0.175740i \(0.943768\pi\)
\(234\) 0 0
\(235\) −7.35806 + 5.90755i −0.479987 + 0.385366i
\(236\) 0 0
\(237\) 10.8642 + 3.53000i 0.705707 + 0.229298i
\(238\) 0 0
\(239\) 2.33626 + 7.19026i 0.151120 + 0.465099i 0.997747 0.0670870i \(-0.0213705\pi\)
−0.846627 + 0.532187i \(0.821371\pi\)
\(240\) 0 0
\(241\) −6.30226 + 19.3964i −0.405964 + 1.24943i 0.514123 + 0.857716i \(0.328117\pi\)
−0.920087 + 0.391713i \(0.871883\pi\)
\(242\) 0 0
\(243\) 8.38230i 0.537725i
\(244\) 0 0
\(245\) −0.391169 8.11461i −0.0249909 0.518424i
\(246\) 0 0
\(247\) −0.301444 0.414902i −0.0191804 0.0263996i
\(248\) 0 0
\(249\) 21.3659 1.35401
\(250\) 0 0
\(251\) −10.5717 −0.667278 −0.333639 0.942701i \(-0.608277\pi\)
−0.333639 + 0.942701i \(0.608277\pi\)
\(252\) 0 0
\(253\) 1.03355 + 1.42256i 0.0649789 + 0.0894357i
\(254\) 0 0
\(255\) −0.818220 16.9736i −0.0512389 1.06293i
\(256\) 0 0
\(257\) 20.2700i 1.26441i −0.774801 0.632205i \(-0.782150\pi\)
0.774801 0.632205i \(-0.217850\pi\)
\(258\) 0 0
\(259\) −8.14996 + 25.0830i −0.506414 + 1.55858i
\(260\) 0 0
\(261\) −1.52252 4.68585i −0.0942419 0.290047i
\(262\) 0 0
\(263\) −26.7160 8.68056i −1.64738 0.535267i −0.669211 0.743072i \(-0.733368\pi\)
−0.978170 + 0.207806i \(0.933368\pi\)
\(264\) 0 0
\(265\) 14.1247 11.3403i 0.867673 0.696626i
\(266\) 0 0
\(267\) 6.51179 8.96271i 0.398515 0.548509i
\(268\) 0 0
\(269\) 16.4416 + 11.9455i 1.00246 + 0.728333i 0.962615 0.270873i \(-0.0873123\pi\)
0.0398490 + 0.999206i \(0.487312\pi\)
\(270\) 0 0
\(271\) 25.4409 18.4839i 1.54543 1.12282i 0.598610 0.801041i \(-0.295720\pi\)
0.946816 0.321777i \(-0.104280\pi\)
\(272\) 0 0
\(273\) −1.35294 + 0.439596i −0.0818835 + 0.0266056i
\(274\) 0 0
\(275\) 3.99064 + 9.16923i 0.240645 + 0.552925i
\(276\) 0 0
\(277\) −13.2487 + 4.30475i −0.796035 + 0.258648i −0.678672 0.734441i \(-0.737444\pi\)
−0.117363 + 0.993089i \(0.537444\pi\)
\(278\) 0 0
\(279\) 4.11235 2.98779i 0.246200 0.178875i
\(280\) 0 0
\(281\) −20.9355 15.2105i −1.24891 0.907383i −0.250748 0.968052i \(-0.580677\pi\)
−0.998158 + 0.0606690i \(0.980677\pi\)
\(282\) 0 0
\(283\) −13.9491 + 19.1993i −0.829188 + 1.14128i 0.158885 + 0.987297i \(0.449210\pi\)
−0.988074 + 0.153983i \(0.950790\pi\)
\(284\) 0 0
\(285\) 5.68873 0.274228i 0.336971 0.0162439i
\(286\) 0 0
\(287\) −3.14823 1.02292i −0.185834 0.0603811i
\(288\) 0 0
\(289\) −2.98394 9.18363i −0.175526 0.540214i
\(290\) 0 0
\(291\) −3.05959 + 9.41645i −0.179356 + 0.552002i
\(292\) 0 0
\(293\) 12.3029i 0.718742i −0.933195 0.359371i \(-0.882991\pi\)
0.933195 0.359371i \(-0.117009\pi\)
\(294\) 0 0
\(295\) 12.8073 + 3.48930i 0.745668 + 0.203155i
\(296\) 0 0
\(297\) −6.63318 9.12979i −0.384896 0.529764i
\(298\) 0 0
\(299\) −0.260574 −0.0150694
\(300\) 0 0
\(301\) 10.5717 0.609341
\(302\) 0 0
\(303\) −10.5514 14.5228i −0.606163 0.834311i
\(304\) 0 0
\(305\) −1.91445 + 0.725696i −0.109621 + 0.0415532i
\(306\) 0 0
\(307\) 4.28249i 0.244415i 0.992505 + 0.122207i \(0.0389973\pi\)
−0.992505 + 0.122207i \(0.961003\pi\)
\(308\) 0 0
\(309\) 0.628342 1.93384i 0.0357451 0.110012i
\(310\) 0 0
\(311\) −7.92526 24.3915i −0.449400 1.38311i −0.877585 0.479421i \(-0.840847\pi\)
0.428185 0.903691i \(-0.359153\pi\)
\(312\) 0 0
\(313\) −21.2573 6.90692i −1.20153 0.390402i −0.361209 0.932485i \(-0.617636\pi\)
−0.840325 + 0.542083i \(0.817636\pi\)
\(314\) 0 0
\(315\) −1.59730 + 5.86279i −0.0899975 + 0.330331i
\(316\) 0 0
\(317\) −12.8859 + 17.7360i −0.723746 + 0.996151i 0.275645 + 0.961259i \(0.411108\pi\)
−0.999391 + 0.0348911i \(0.988892\pi\)
\(318\) 0 0
\(319\) −9.56608 6.95016i −0.535597 0.389134i
\(320\) 0 0
\(321\) 18.8491 13.6947i 1.05205 0.764363i
\(322\) 0 0
\(323\) 8.49664 2.76073i 0.472766 0.153611i
\(324\) 0 0
\(325\) −1.44688 0.320244i −0.0802583 0.0177639i
\(326\) 0 0
\(327\) 2.80509 0.911429i 0.155122 0.0504021i
\(328\) 0 0
\(329\) −11.1326 + 8.08832i −0.613761 + 0.445923i
\(330\) 0 0
\(331\) −7.25121 5.26831i −0.398563 0.289573i 0.370393 0.928875i \(-0.379223\pi\)
−0.768955 + 0.639303i \(0.779223\pi\)
\(332\) 0 0
\(333\) 3.96183 5.45299i 0.217107 0.298822i
\(334\) 0 0
\(335\) −12.8821 8.44269i −0.703822 0.461273i
\(336\) 0 0
\(337\) 27.6601 + 8.98731i 1.50674 + 0.489570i 0.941976 0.335681i \(-0.108966\pi\)
0.564766 + 0.825251i \(0.308966\pi\)
\(338\) 0 0
\(339\) 4.74302 + 14.5975i 0.257605 + 0.792828i
\(340\) 0 0
\(341\) 3.76972 11.6020i 0.204142 0.628283i
\(342\) 0 0
\(343\) 10.9787i 0.592795i
\(344\) 0 0
\(345\) 1.58621 2.42028i 0.0853987 0.130303i
\(346\) 0 0
\(347\) −8.40368 11.5667i −0.451133 0.620931i 0.521508 0.853247i \(-0.325370\pi\)
−0.972641 + 0.232315i \(0.925370\pi\)
\(348\) 0 0
\(349\) −5.62382 −0.301036 −0.150518 0.988607i \(-0.548094\pi\)
−0.150518 + 0.988607i \(0.548094\pi\)
\(350\) 0 0
\(351\) 1.67232 0.0892620
\(352\) 0 0
\(353\) −1.12265 1.54520i −0.0597529 0.0822427i 0.778095 0.628147i \(-0.216186\pi\)
−0.837848 + 0.545904i \(0.816186\pi\)
\(354\) 0 0
\(355\) −8.35573 10.4074i −0.443476 0.552366i
\(356\) 0 0
\(357\) 24.7813i 1.31156i
\(358\) 0 0
\(359\) 6.86161 21.1179i 0.362142 1.11456i −0.589609 0.807689i \(-0.700718\pi\)
0.951751 0.306870i \(-0.0992818\pi\)
\(360\) 0 0
\(361\) −4.94606 15.2224i −0.260319 0.801179i
\(362\) 0 0
\(363\) 9.79935 + 3.18400i 0.514332 + 0.167117i
\(364\) 0 0
\(365\) 7.00116 + 18.4697i 0.366458 + 0.966748i
\(366\) 0 0
\(367\) −12.6050 + 17.3493i −0.657978 + 0.905629i −0.999412 0.0342768i \(-0.989087\pi\)
0.341435 + 0.939906i \(0.389087\pi\)
\(368\) 0 0
\(369\) 0.684418 + 0.497259i 0.0356294 + 0.0258863i
\(370\) 0 0
\(371\) 21.3704 15.5265i 1.10950 0.806096i
\(372\) 0 0
\(373\) −22.0074 + 7.15063i −1.13950 + 0.370245i −0.817178 0.576385i \(-0.804463\pi\)
−0.322320 + 0.946631i \(0.604463\pi\)
\(374\) 0 0
\(375\) 11.7822 11.4895i 0.608430 0.593317i
\(376\) 0 0
\(377\) 1.66648 0.541471i 0.0858279 0.0278872i
\(378\) 0 0
\(379\) 17.5153 12.7256i 0.899702 0.653672i −0.0386872 0.999251i \(-0.512318\pi\)
0.938390 + 0.345579i \(0.112318\pi\)
\(380\) 0 0
\(381\) −6.96645 5.06142i −0.356902 0.259304i
\(382\) 0 0
\(383\) −3.32381 + 4.57484i −0.169839 + 0.233763i −0.885449 0.464737i \(-0.846149\pi\)
0.715610 + 0.698500i \(0.246149\pi\)
\(384\) 0 0
\(385\) 5.16896 + 13.6362i 0.263435 + 0.694964i
\(386\) 0 0
\(387\) −2.56953 0.834891i −0.130617 0.0424399i
\(388\) 0 0
\(389\) 2.51109 + 7.72833i 0.127317 + 0.391842i 0.994316 0.106468i \(-0.0339541\pi\)
−0.866999 + 0.498310i \(0.833954\pi\)
\(390\) 0 0
\(391\) 1.40270 4.31707i 0.0709377 0.218324i
\(392\) 0 0
\(393\) 2.20298i 0.111126i
\(394\) 0 0
\(395\) 10.8642 + 13.5318i 0.546638 + 0.680857i
\(396\) 0 0
\(397\) −12.2076 16.8024i −0.612684 0.843287i 0.384111 0.923287i \(-0.374508\pi\)
−0.996795 + 0.0799998i \(0.974508\pi\)
\(398\) 0 0
\(399\) 8.30550 0.415795
\(400\) 0 0
\(401\) 30.1195 1.50410 0.752049 0.659107i \(-0.229066\pi\)
0.752049 + 0.659107i \(0.229066\pi\)
\(402\) 0 0
\(403\) 1.06258 + 1.46252i 0.0529309 + 0.0728532i
\(404\) 0 0
\(405\) −7.11568 + 10.8573i −0.353581 + 0.539503i
\(406\) 0 0
\(407\) 16.1760i 0.801815i
\(408\) 0 0
\(409\) −3.41317 + 10.5046i −0.168770 + 0.519421i −0.999294 0.0375613i \(-0.988041\pi\)
0.830524 + 0.556983i \(0.188041\pi\)
\(410\) 0 0
\(411\) −3.57012 10.9877i −0.176101 0.541983i
\(412\) 0 0
\(413\) 18.4102 + 5.98182i 0.905905 + 0.294346i
\(414\) 0 0
\(415\) 27.1467 + 17.7915i 1.33258 + 0.873350i
\(416\) 0 0
\(417\) −4.66469 + 6.42039i −0.228431 + 0.314408i
\(418\) 0 0
\(419\) 26.6338 + 19.3506i 1.30115 + 0.945337i 0.999966 0.00823011i \(-0.00261975\pi\)
0.301179 + 0.953568i \(0.402620\pi\)
\(420\) 0 0
\(421\) 16.3945 11.9113i 0.799019 0.580522i −0.111607 0.993752i \(-0.535600\pi\)
0.910626 + 0.413231i \(0.135600\pi\)
\(422\) 0 0
\(423\) 3.34464 1.08674i 0.162622 0.0528392i
\(424\) 0 0
\(425\) 13.0944 22.2473i 0.635171 1.07915i
\(426\) 0 0
\(427\) −2.83956 + 0.922629i −0.137416 + 0.0446491i
\(428\) 0 0
\(429\) 0.705874 0.512848i 0.0340799 0.0247605i
\(430\) 0 0
\(431\) 5.78873 + 4.20576i 0.278833 + 0.202584i 0.718408 0.695622i \(-0.244871\pi\)
−0.439575 + 0.898206i \(0.644871\pi\)
\(432\) 0 0
\(433\) −3.22262 + 4.43555i −0.154869 + 0.213159i −0.879400 0.476083i \(-0.842056\pi\)
0.724531 + 0.689242i \(0.242056\pi\)
\(434\) 0 0
\(435\) −5.11514 + 18.7748i −0.245252 + 0.900184i
\(436\) 0 0
\(437\) 1.44688 + 0.470119i 0.0692135 + 0.0224888i
\(438\) 0 0
\(439\) −9.50415 29.2508i −0.453609 1.39606i −0.872761 0.488148i \(-0.837673\pi\)
0.419153 0.907916i \(-0.362327\pi\)
\(440\) 0 0
\(441\) −0.935631 + 2.87958i −0.0445539 + 0.137123i
\(442\) 0 0
\(443\) 11.3527i 0.539381i −0.962947 0.269691i \(-0.913079\pi\)
0.962947 0.269691i \(-0.0869214\pi\)
\(444\) 0 0
\(445\) 15.7369 5.96528i 0.746002 0.282781i
\(446\) 0 0
\(447\) −16.2854 22.4149i −0.770271 1.06019i
\(448\) 0 0
\(449\) 15.7661 0.744050 0.372025 0.928223i \(-0.378664\pi\)
0.372025 + 0.928223i \(0.378664\pi\)
\(450\) 0 0
\(451\) 2.03029 0.0956027
\(452\) 0 0
\(453\) 3.36383 + 4.62992i 0.158047 + 0.217532i
\(454\) 0 0
\(455\) −2.08504 0.568064i −0.0977484 0.0266312i
\(456\) 0 0
\(457\) 4.16714i 0.194931i 0.995239 + 0.0974653i \(0.0310735\pi\)
−0.995239 + 0.0974653i \(0.968926\pi\)
\(458\) 0 0
\(459\) −9.00233 + 27.7063i −0.420193 + 1.29322i
\(460\) 0 0
\(461\) −7.40758 22.7982i −0.345005 1.06182i −0.961581 0.274521i \(-0.911481\pi\)
0.616576 0.787296i \(-0.288519\pi\)
\(462\) 0 0
\(463\) −39.3021 12.7700i −1.82652 0.593473i −0.999510 0.0312899i \(-0.990038\pi\)
−0.827013 0.562183i \(-0.809962\pi\)
\(464\) 0 0
\(465\) −20.0526 + 0.966645i −0.929916 + 0.0448271i
\(466\) 0 0
\(467\) −6.11096 + 8.41102i −0.282782 + 0.389216i −0.926653 0.375918i \(-0.877327\pi\)
0.643871 + 0.765134i \(0.277327\pi\)
\(468\) 0 0
\(469\) −18.1713 13.2022i −0.839072 0.609622i
\(470\) 0 0
\(471\) −5.10126 + 3.70628i −0.235054 + 0.170776i
\(472\) 0 0
\(473\) −6.16663 + 2.00366i −0.283542 + 0.0921284i
\(474\) 0 0
\(475\) 7.45624 + 4.38861i 0.342116 + 0.201363i
\(476\) 0 0
\(477\) −6.42045 + 2.08613i −0.293972 + 0.0955174i
\(478\) 0 0
\(479\) −29.1312 + 21.1650i −1.33104 + 0.967055i −0.331314 + 0.943520i \(0.607492\pi\)
−0.999723 + 0.0235349i \(0.992508\pi\)
\(480\) 0 0
\(481\) 1.93930 + 1.40899i 0.0884246 + 0.0642443i
\(482\) 0 0
\(483\) 2.48043 3.41402i 0.112863 0.155343i
\(484\) 0 0
\(485\) −11.7285 + 9.41645i −0.532565 + 0.427579i
\(486\) 0 0
\(487\) 10.1172 + 3.28726i 0.458452 + 0.148960i 0.529133 0.848539i \(-0.322517\pi\)
−0.0706809 + 0.997499i \(0.522517\pi\)
\(488\) 0 0
\(489\) 7.15323 + 22.0154i 0.323480 + 0.995570i
\(490\) 0 0
\(491\) 5.46010 16.8045i 0.246411 0.758375i −0.748990 0.662581i \(-0.769461\pi\)
0.995401 0.0957938i \(-0.0305389\pi\)
\(492\) 0 0
\(493\) 30.5243i 1.37475i
\(494\) 0 0
\(495\) −0.179450 3.72260i −0.00806568 0.167319i
\(496\) 0 0
\(497\) −11.4403 15.7462i −0.513166 0.706312i
\(498\) 0 0
\(499\) −9.41734 −0.421578 −0.210789 0.977532i \(-0.567603\pi\)
−0.210789 + 0.977532i \(0.567603\pi\)
\(500\) 0 0
\(501\) −30.9595 −1.38317
\(502\) 0 0
\(503\) −10.5879 14.5730i −0.472093 0.649780i 0.504869 0.863196i \(-0.331541\pi\)
−0.976961 + 0.213416i \(0.931541\pi\)
\(504\) 0 0
\(505\) −1.31304 27.2383i −0.0584294 1.21209i
\(506\) 0 0
\(507\) 19.0060i 0.844088i
\(508\) 0 0
\(509\) 4.95926 15.2630i 0.219815 0.676522i −0.778961 0.627072i \(-0.784253\pi\)
0.998777 0.0494500i \(-0.0157469\pi\)
\(510\) 0 0
\(511\) 8.90107 + 27.3947i 0.393760 + 1.21187i
\(512\) 0 0
\(513\) −9.28583 3.01715i −0.409980 0.133210i
\(514\) 0 0
\(515\) 2.40867 1.93384i 0.106138 0.0852151i
\(516\) 0 0
\(517\) 4.96086 6.82803i 0.218178 0.300297i
\(518\) 0 0
\(519\) 8.53425 + 6.20050i 0.374612 + 0.272172i
\(520\) 0 0
\(521\) 1.78040 1.29354i 0.0780007 0.0566708i −0.548102 0.836412i \(-0.684649\pi\)
0.626102 + 0.779741i \(0.284649\pi\)
\(522\) 0 0
\(523\) −7.07194 + 2.29781i −0.309234 + 0.100476i −0.459523 0.888166i \(-0.651980\pi\)
0.150289 + 0.988642i \(0.451980\pi\)
\(524\) 0 0
\(525\) 17.9688 15.9084i 0.784222 0.694301i
\(526\) 0 0
\(527\) −29.9504 + 9.73147i −1.30466 + 0.423909i
\(528\) 0 0
\(529\) −17.9820 + 13.0647i −0.781828 + 0.568031i
\(530\) 0 0
\(531\) −4.00233 2.90786i −0.173686 0.126190i
\(532\) 0 0
\(533\) −0.176845 + 0.243407i −0.00766003 + 0.0105431i
\(534\) 0 0
\(535\) 35.3526 1.70419i 1.52843 0.0736786i
\(536\) 0 0
\(537\) −11.2543 3.65675i −0.485660 0.157800i
\(538\) 0 0
\(539\) 2.24543 + 6.91072i 0.0967174 + 0.297666i
\(540\) 0 0
\(541\) 6.38040 19.6368i 0.274315 0.844254i −0.715085 0.699037i \(-0.753612\pi\)
0.989400 0.145216i \(-0.0463878\pi\)
\(542\) 0 0
\(543\) 30.3473i 1.30233i
\(544\) 0 0
\(545\) 4.32299 + 1.17779i 0.185177 + 0.0504508i
\(546\) 0 0
\(547\) −18.4424 25.3839i −0.788542 1.08534i −0.994288 0.106730i \(-0.965962\pi\)
0.205746 0.978605i \(-0.434038\pi\)
\(548\) 0 0
\(549\) 0.763042 0.0325658
\(550\) 0 0
\(551\) −10.2303 −0.435825
\(552\) 0 0
\(553\) 14.8747 + 20.4733i 0.632538 + 0.870615i
\(554\) 0 0
\(555\) −24.8923 + 9.43574i −1.05662 + 0.400525i
\(556\) 0 0
\(557\) 22.3515i 0.947064i 0.880776 + 0.473532i \(0.157021\pi\)
−0.880776 + 0.473532i \(0.842979\pi\)
\(558\) 0 0
\(559\) 0.296921 0.913829i 0.0125584 0.0386509i
\(560\) 0 0
\(561\) 4.69683 + 14.4554i 0.198300 + 0.610305i
\(562\) 0 0
\(563\) 32.6843 + 10.6198i 1.37748 + 0.447570i 0.901840 0.432070i \(-0.142217\pi\)
0.475639 + 0.879640i \(0.342217\pi\)
\(564\) 0 0
\(565\) −6.12912 + 22.4966i −0.257854 + 0.946438i
\(566\) 0 0
\(567\) −11.1271 + 15.3152i −0.467295 + 0.643177i
\(568\) 0 0
\(569\) 26.0230 + 18.9068i 1.09094 + 0.792615i 0.979558 0.201162i \(-0.0644718\pi\)
0.111383 + 0.993778i \(0.464472\pi\)
\(570\) 0 0
\(571\) −21.9784 + 15.9683i −0.919768 + 0.668251i −0.943466 0.331468i \(-0.892456\pi\)
0.0236979 + 0.999719i \(0.492456\pi\)
\(572\) 0 0
\(573\) −25.2407 + 8.20121i −1.05445 + 0.342610i
\(574\) 0 0
\(575\) 4.03076 1.75427i 0.168094 0.0731581i
\(576\) 0 0
\(577\) 13.1724 4.27998i 0.548375 0.178178i −0.0217089 0.999764i \(-0.506911\pi\)
0.570084 + 0.821586i \(0.306911\pi\)
\(578\) 0 0
\(579\) 8.08407 5.87342i 0.335963 0.244091i
\(580\) 0 0
\(581\) 38.2928 + 27.8214i 1.58865 + 1.15422i
\(582\) 0 0
\(583\) −9.52297 + 13.1072i −0.394401 + 0.542847i
\(584\) 0 0
\(585\) 0.461925 + 0.302738i 0.0190982 + 0.0125167i
\(586\) 0 0
\(587\) 41.9890 + 13.6431i 1.73307 + 0.563110i 0.993888 0.110392i \(-0.0352107\pi\)
0.739185 + 0.673502i \(0.235211\pi\)
\(588\) 0 0
\(589\) −3.26152 10.0379i −0.134389 0.413606i
\(590\) 0 0
\(591\) 3.63675 11.1928i 0.149596 0.460409i
\(592\) 0 0
\(593\) 16.2531i 0.667437i −0.942673 0.333718i \(-0.891697\pi\)
0.942673 0.333718i \(-0.108303\pi\)
\(594\) 0 0
\(595\) 20.6355 31.4862i 0.845973 1.29081i
\(596\) 0 0
\(597\) −4.50318 6.19810i −0.184303 0.253671i
\(598\) 0 0
\(599\) 30.4822 1.24547 0.622734 0.782433i \(-0.286022\pi\)
0.622734 + 0.782433i \(0.286022\pi\)
\(600\) 0 0
\(601\) −28.9162 −1.17952 −0.589758 0.807580i \(-0.700777\pi\)
−0.589758 + 0.807580i \(0.700777\pi\)
\(602\) 0 0
\(603\) 3.37405 + 4.64398i 0.137402 + 0.189117i
\(604\) 0 0
\(605\) 9.79935 + 12.2054i 0.398400 + 0.496222i
\(606\) 0 0
\(607\) 8.23276i 0.334157i 0.985944 + 0.167079i \(0.0534334\pi\)
−0.985944 + 0.167079i \(0.946567\pi\)
\(608\) 0 0
\(609\) −8.76906 + 26.9884i −0.355340 + 1.09362i
\(610\) 0 0
\(611\) 0.386489 + 1.18949i 0.0156357 + 0.0481217i
\(612\) 0 0
\(613\) 4.56327 + 1.48270i 0.184309 + 0.0598856i 0.399717 0.916638i \(-0.369108\pi\)
−0.215408 + 0.976524i \(0.569108\pi\)
\(614\) 0 0
\(615\) −1.18430 3.12430i −0.0477557 0.125984i
\(616\) 0 0
\(617\) 1.19428 1.64379i 0.0480800 0.0661765i −0.784300 0.620382i \(-0.786978\pi\)
0.832380 + 0.554205i \(0.186978\pi\)
\(618\) 0 0
\(619\) −6.58621 4.78516i −0.264722 0.192332i 0.447504 0.894282i \(-0.352313\pi\)
−0.712226 + 0.701950i \(0.752313\pi\)
\(620\) 0 0
\(621\) −4.01342 + 2.91592i −0.161053 + 0.117012i
\(622\) 0 0
\(623\) 23.3414 7.58408i 0.935153 0.303850i
\(624\) 0 0
\(625\) 24.5374 4.78708i 0.981496 0.191483i
\(626\) 0 0
\(627\) −4.84474 + 1.57415i −0.193480 + 0.0628656i
\(628\) 0 0
\(629\) −33.7830 + 24.5448i −1.34702 + 0.978665i
\(630\) 0 0
\(631\) 26.9279 + 19.5643i 1.07198 + 0.778841i 0.976268 0.216567i \(-0.0694861\pi\)
0.0957154 + 0.995409i \(0.469486\pi\)
\(632\) 0 0
\(633\) 14.3638 19.7701i 0.570912 0.785793i
\(634\) 0 0
\(635\) −4.63663 12.2318i −0.183999 0.485406i
\(636\) 0 0
\(637\) −1.02409 0.332749i −0.0405761 0.0131840i
\(638\) 0 0
\(639\) 1.53710 + 4.73072i 0.0608069 + 0.187144i
\(640\) 0 0
\(641\) −12.3755 + 38.0880i −0.488804 + 1.50439i 0.337590 + 0.941293i \(0.390388\pi\)
−0.826394 + 0.563092i \(0.809612\pi\)
\(642\) 0 0
\(643\) 11.6870i 0.460890i 0.973085 + 0.230445i \(0.0740182\pi\)
−0.973085 + 0.230445i \(0.925982\pi\)
\(644\) 0 0
\(645\) 6.68042 + 8.32070i 0.263041 + 0.327627i
\(646\) 0 0
\(647\) 4.67252 + 6.43117i 0.183696 + 0.252835i 0.890927 0.454147i \(-0.150056\pi\)
−0.707231 + 0.706982i \(0.750056\pi\)
\(648\) 0 0
\(649\) −11.8727 −0.466044
\(650\) 0 0
\(651\) −29.2766 −1.14744
\(652\) 0 0
\(653\) −1.96165 2.69998i −0.0767653 0.105658i 0.768908 0.639360i \(-0.220801\pi\)
−0.845673 + 0.533702i \(0.820801\pi\)
\(654\) 0 0
\(655\) 1.83443 2.79902i 0.0716772 0.109367i
\(656\) 0 0
\(657\) 7.36146i 0.287198i
\(658\) 0 0
\(659\) −9.28621 + 28.5800i −0.361739 + 1.11332i 0.590259 + 0.807214i \(0.299026\pi\)
−0.951998 + 0.306105i \(0.900974\pi\)
\(660\) 0 0
\(661\) −2.03462 6.26192i −0.0791375 0.243560i 0.903659 0.428253i \(-0.140871\pi\)
−0.982796 + 0.184693i \(0.940871\pi\)
\(662\) 0 0
\(663\) −2.14213 0.696020i −0.0831934 0.0270312i
\(664\) 0 0
\(665\) 10.5527 + 6.91604i 0.409215 + 0.268192i
\(666\) 0 0
\(667\) −3.05526 + 4.20521i −0.118300 + 0.162826i
\(668\) 0 0
\(669\) −7.89293 5.73455i −0.305158 0.221711i
\(670\) 0 0
\(671\) 1.48150 1.07637i 0.0571925 0.0415528i
\(672\) 0 0
\(673\) −6.40194 + 2.08012i −0.246777 + 0.0801826i −0.429794 0.902927i \(-0.641414\pi\)
0.183017 + 0.983110i \(0.441414\pi\)
\(674\) 0 0
\(675\) −25.8688 + 11.2586i −0.995690 + 0.433345i
\(676\) 0 0
\(677\) 12.9799 4.21741i 0.498857 0.162088i −0.0487718 0.998810i \(-0.515531\pi\)
0.547629 + 0.836722i \(0.315531\pi\)
\(678\) 0 0
\(679\) −17.7451 + 12.8925i −0.680993 + 0.494770i
\(680\) 0 0
\(681\) 15.9475 + 11.5866i 0.611111 + 0.443998i
\(682\) 0 0
\(683\) −0.689001 + 0.948329i −0.0263639 + 0.0362868i −0.821995 0.569494i \(-0.807139\pi\)
0.795632 + 0.605781i \(0.207139\pi\)
\(684\) 0 0
\(685\) 4.61345 16.9334i 0.176271 0.646992i
\(686\) 0 0
\(687\) 14.1205 + 4.58802i 0.538729 + 0.175044i
\(688\) 0 0
\(689\) −0.741913 2.28337i −0.0282646 0.0869896i
\(690\) 0 0
\(691\) −3.79083 + 11.6670i −0.144210 + 0.443832i −0.996909 0.0785709i \(-0.974964\pi\)
0.852699 + 0.522403i \(0.174964\pi\)
\(692\) 0 0
\(693\) 5.43497i 0.206457i
\(694\) 0 0
\(695\) −11.2731 + 4.27320i −0.427612 + 0.162092i
\(696\) 0 0
\(697\) −3.08068 4.24019i −0.116689 0.160609i
\(698\) 0 0
\(699\) −32.3910 −1.22514
\(700\) 0 0
\(701\) −20.0271 −0.756415 −0.378207 0.925721i \(-0.623459\pi\)
−0.378207 + 0.925721i \(0.623459\pi\)
\(702\) 0 0
\(703\) −8.22624 11.3225i −0.310259 0.427034i
\(704\) 0 0
\(705\) −13.4010 3.65106i −0.504711 0.137507i
\(706\) 0 0
\(707\) 39.7677i 1.49562i
\(708\) 0 0
\(709\) 1.35816 4.17998i 0.0510067 0.156983i −0.922309 0.386454i \(-0.873700\pi\)
0.973315 + 0.229471i \(0.0736998\pi\)
\(710\) 0 0
\(711\) −1.99856 6.15094i −0.0749519 0.230678i
\(712\) 0 0
\(713\) −5.10019 1.65715i −0.191004 0.0620608i
\(714\) 0 0
\(715\) 1.32391 0.0638197i 0.0495114 0.00238672i
\(716\) 0 0
\(717\) −6.54109 + 9.00303i −0.244281 + 0.336224i
\(718\) 0 0
\(719\) 8.84119 + 6.42350i 0.329721 + 0.239556i 0.740312 0.672263i \(-0.234678\pi\)
−0.410591 + 0.911819i \(0.634678\pi\)
\(720\) 0 0
\(721\) 3.64427 2.64772i 0.135720 0.0986061i
\(722\) 0 0
\(723\) −28.5505 + 9.27661i −1.06180 + 0.345001i
\(724\) 0 0
\(725\) −22.1330 + 19.5952i −0.821999 + 0.727747i
\(726\) 0 0
\(727\) 31.2928 10.1677i 1.16059 0.377097i 0.335465 0.942053i \(-0.391107\pi\)
0.825122 + 0.564955i \(0.191107\pi\)
\(728\) 0 0
\(729\) 24.0719 17.4893i 0.891553 0.647751i
\(730\) 0 0
\(731\) 13.5416 + 9.83853i 0.500853 + 0.363891i
\(732\) 0 0
\(733\) −8.08190 + 11.1238i −0.298512 + 0.410866i −0.931756 0.363086i \(-0.881723\pi\)
0.633244 + 0.773952i \(0.281723\pi\)
\(734\) 0 0
\(735\) 9.32470 7.48650i 0.343947 0.276144i
\(736\) 0 0
\(737\) 13.1019 + 4.25705i 0.482613 + 0.156811i
\(738\) 0 0
\(739\) −13.3462 41.0754i −0.490949 1.51098i −0.823177 0.567785i \(-0.807800\pi\)
0.332228 0.943199i \(-0.392200\pi\)
\(740\) 0 0
\(741\) 0.233273 0.717939i 0.00856948 0.0263741i
\(742\) 0 0
\(743\) 31.8479i 1.16838i 0.811615 + 0.584192i \(0.198589\pi\)
−0.811615 + 0.584192i \(0.801411\pi\)
\(744\) 0 0
\(745\) −2.02658 42.0404i −0.0742482 1.54024i
\(746\) 0 0
\(747\) −7.11021 9.78637i −0.260149 0.358064i
\(748\) 0 0
\(749\) 51.6145 1.88595
\(750\) 0 0
\(751\) 29.5952 1.07995 0.539973 0.841682i \(-0.318435\pi\)
0.539973 + 0.841682i \(0.318435\pi\)
\(752\) 0 0
\(753\) −9.14650 12.5891i −0.333317 0.458771i
\(754\) 0 0
\(755\) 0.418601 + 8.68368i 0.0152345 + 0.316031i
\(756\) 0 0
\(757\) 0.0984401i 0.00357786i −0.999998 0.00178893i \(-0.999431\pi\)
0.999998 0.00178893i \(-0.000569435\pi\)
\(758\) 0 0
\(759\) −0.799814 + 2.46157i −0.0290314 + 0.0893495i
\(760\) 0 0
\(761\) −1.09516 3.37056i −0.0396996 0.122183i 0.929243 0.369470i \(-0.120461\pi\)
−0.968942 + 0.247287i \(0.920461\pi\)
\(762\) 0 0
\(763\) 6.21421 + 2.01912i 0.224969 + 0.0730970i
\(764\) 0 0
\(765\) −7.50223 + 6.02330i −0.271244 + 0.217773i
\(766\) 0 0
\(767\) 1.03415 1.42339i 0.0373411 0.0513957i
\(768\) 0 0
\(769\) 1.15494 + 0.839116i 0.0416484 + 0.0302593i 0.608415 0.793619i \(-0.291806\pi\)
−0.566766 + 0.823879i \(0.691806\pi\)
\(770\) 0 0
\(771\) 24.1382 17.5374i 0.869316 0.631595i
\(772\) 0 0
\(773\) 32.1274 10.4388i 1.15554 0.375458i 0.332313 0.943169i \(-0.392171\pi\)
0.823228 + 0.567711i \(0.192171\pi\)
\(774\) 0 0
\(775\) −26.2830 15.4697i −0.944113 0.555688i
\(776\) 0 0
\(777\) −36.9209 + 11.9963i −1.32453 + 0.430366i
\(778\) 0 0
\(779\) 1.42111 1.03250i 0.0509165 0.0369930i
\(780\) 0 0
\(781\) 9.65769 + 7.01672i 0.345579 + 0.251078i
\(782\) 0 0
\(783\) 19.6082 26.9884i 0.700740 0.964486i
\(784\) 0 0
\(785\) −9.56771 + 0.461216i −0.341486 + 0.0164615i
\(786\) 0 0
\(787\) −2.07358 0.673749i −0.0739153 0.0240165i 0.271826 0.962346i \(-0.412373\pi\)
−0.345741 + 0.938330i \(0.612373\pi\)
\(788\) 0 0
\(789\) −12.7773 39.3246i −0.454886 1.39999i
\(790\) 0 0
\(791\) −10.5074 + 32.3383i −0.373599 + 1.14982i
\(792\) 0 0
\(793\) 0.271369i