Properties

Label 819.2.j.c.352.2
Level $819$
Weight $2$
Character 819.352
Analytic conductor $6.540$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.j (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(1\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 352.2
Root \(-0.309017 + 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 819.352
Dual form 819.2.j.c.235.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.190983 + 0.330792i) q^{2} +(0.927051 + 1.60570i) q^{4} +(-1.11803 + 1.93649i) q^{5} +(-2.00000 - 1.73205i) q^{7} -1.47214 q^{8} +O(q^{10})\) \(q+(-0.190983 + 0.330792i) q^{2} +(0.927051 + 1.60570i) q^{4} +(-1.11803 + 1.93649i) q^{5} +(-2.00000 - 1.73205i) q^{7} -1.47214 q^{8} +(-0.427051 - 0.739674i) q^{10} +(-1.50000 - 2.59808i) q^{11} -1.00000 q^{13} +(0.954915 - 0.330792i) q^{14} +(-1.57295 + 2.72443i) q^{16} +(-3.73607 - 6.47106i) q^{17} +(-1.50000 + 2.59808i) q^{19} -4.14590 q^{20} +1.14590 q^{22} +(-1.88197 + 3.25966i) q^{23} +(0.190983 - 0.330792i) q^{26} +(0.927051 - 4.81710i) q^{28} +4.47214 q^{29} +(-2.50000 - 4.33013i) q^{31} +(-2.07295 - 3.59045i) q^{32} +2.85410 q^{34} +(5.59017 - 1.93649i) q^{35} +(4.35410 - 7.54153i) q^{37} +(-0.572949 - 0.992377i) q^{38} +(1.64590 - 2.85078i) q^{40} -4.47214 q^{41} -8.00000 q^{43} +(2.78115 - 4.81710i) q^{44} +(-0.718847 - 1.24508i) q^{46} +(0.736068 - 1.27491i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-0.927051 - 1.60570i) q^{52} +(0.736068 + 1.27491i) q^{53} +6.70820 q^{55} +(2.94427 + 2.54981i) q^{56} +(-0.854102 + 1.47935i) q^{58} +(3.73607 + 6.47106i) q^{59} +(-1.50000 + 2.59808i) q^{61} +1.90983 q^{62} -4.70820 q^{64} +(1.11803 - 1.93649i) q^{65} +(1.50000 + 2.59808i) q^{67} +(6.92705 - 11.9980i) q^{68} +(-0.427051 + 2.21902i) q^{70} -8.94427 q^{71} +(-5.35410 - 9.27358i) q^{73} +(1.66312 + 2.88061i) q^{74} -5.56231 q^{76} +(-1.50000 + 7.79423i) q^{77} +(-5.35410 + 9.27358i) q^{79} +(-3.51722 - 6.09201i) q^{80} +(0.854102 - 1.47935i) q^{82} +16.7082 q^{85} +(1.52786 - 2.64634i) q^{86} +(2.20820 + 3.82472i) q^{88} +(-1.11803 + 1.93649i) q^{89} +(2.00000 + 1.73205i) q^{91} -6.97871 q^{92} +(0.281153 + 0.486971i) q^{94} +(-3.35410 - 5.80948i) q^{95} -17.4164 q^{97} +(-2.48278 - 0.992377i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 3 q^{2} - 3 q^{4} - 8 q^{7} + 12 q^{8} + O(q^{10}) \) \( 4 q - 3 q^{2} - 3 q^{4} - 8 q^{7} + 12 q^{8} + 5 q^{10} - 6 q^{11} - 4 q^{13} + 15 q^{14} - 13 q^{16} - 6 q^{17} - 6 q^{19} - 30 q^{20} + 18 q^{22} - 12 q^{23} + 3 q^{26} - 3 q^{28} - 10 q^{31} - 15 q^{32} - 2 q^{34} + 4 q^{37} - 9 q^{38} + 20 q^{40} - 32 q^{43} - 9 q^{44} - 23 q^{46} - 6 q^{47} + 4 q^{49} + 3 q^{52} - 6 q^{53} - 24 q^{56} + 10 q^{58} + 6 q^{59} - 6 q^{61} + 30 q^{62} + 8 q^{64} + 6 q^{67} + 21 q^{68} + 5 q^{70} - 8 q^{73} - 9 q^{74} + 18 q^{76} - 6 q^{77} - 8 q^{79} + 15 q^{80} - 10 q^{82} + 40 q^{85} + 24 q^{86} - 18 q^{88} + 8 q^{91} + 66 q^{92} - 19 q^{94} - 16 q^{97} - 39 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.190983 + 0.330792i −0.135045 + 0.233905i −0.925615 0.378467i \(-0.876451\pi\)
0.790569 + 0.612372i \(0.209785\pi\)
\(3\) 0 0
\(4\) 0.927051 + 1.60570i 0.463525 + 0.802850i
\(5\) −1.11803 + 1.93649i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(6\) 0 0
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) −1.47214 −0.520479
\(9\) 0 0
\(10\) −0.427051 0.739674i −0.135045 0.233905i
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0.954915 0.330792i 0.255212 0.0884080i
\(15\) 0 0
\(16\) −1.57295 + 2.72443i −0.393237 + 0.681107i
\(17\) −3.73607 6.47106i −0.906130 1.56946i −0.819394 0.573231i \(-0.805690\pi\)
−0.0867359 0.996231i \(-0.527644\pi\)
\(18\) 0 0
\(19\) −1.50000 + 2.59808i −0.344124 + 0.596040i −0.985194 0.171442i \(-0.945157\pi\)
0.641071 + 0.767482i \(0.278491\pi\)
\(20\) −4.14590 −0.927051
\(21\) 0 0
\(22\) 1.14590 0.244306
\(23\) −1.88197 + 3.25966i −0.392417 + 0.679686i −0.992768 0.120051i \(-0.961694\pi\)
0.600351 + 0.799737i \(0.295028\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0.190983 0.330792i 0.0374548 0.0648737i
\(27\) 0 0
\(28\) 0.927051 4.81710i 0.175196 0.910346i
\(29\) 4.47214 0.830455 0.415227 0.909718i \(-0.363702\pi\)
0.415227 + 0.909718i \(0.363702\pi\)
\(30\) 0 0
\(31\) −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i \(-0.314891\pi\)
−0.998322 + 0.0579057i \(0.981558\pi\)
\(32\) −2.07295 3.59045i −0.366449 0.634708i
\(33\) 0 0
\(34\) 2.85410 0.489474
\(35\) 5.59017 1.93649i 0.944911 0.327327i
\(36\) 0 0
\(37\) 4.35410 7.54153i 0.715810 1.23982i −0.246836 0.969057i \(-0.579391\pi\)
0.962646 0.270762i \(-0.0872757\pi\)
\(38\) −0.572949 0.992377i −0.0929446 0.160985i
\(39\) 0 0
\(40\) 1.64590 2.85078i 0.260239 0.450748i
\(41\) −4.47214 −0.698430 −0.349215 0.937043i \(-0.613552\pi\)
−0.349215 + 0.937043i \(0.613552\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 2.78115 4.81710i 0.419275 0.726205i
\(45\) 0 0
\(46\) −0.718847 1.24508i −0.105988 0.183577i
\(47\) 0.736068 1.27491i 0.107367 0.185964i −0.807336 0.590092i \(-0.799091\pi\)
0.914703 + 0.404128i \(0.132425\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.927051 1.60570i −0.128559 0.222670i
\(53\) 0.736068 + 1.27491i 0.101107 + 0.175122i 0.912141 0.409877i \(-0.134428\pi\)
−0.811034 + 0.584999i \(0.801095\pi\)
\(54\) 0 0
\(55\) 6.70820 0.904534
\(56\) 2.94427 + 2.54981i 0.393445 + 0.340733i
\(57\) 0 0
\(58\) −0.854102 + 1.47935i −0.112149 + 0.194248i
\(59\) 3.73607 + 6.47106i 0.486395 + 0.842460i 0.999878 0.0156395i \(-0.00497842\pi\)
−0.513483 + 0.858100i \(0.671645\pi\)
\(60\) 0 0
\(61\) −1.50000 + 2.59808i −0.192055 + 0.332650i −0.945931 0.324367i \(-0.894849\pi\)
0.753876 + 0.657017i \(0.228182\pi\)
\(62\) 1.90983 0.242549
\(63\) 0 0
\(64\) −4.70820 −0.588525
\(65\) 1.11803 1.93649i 0.138675 0.240192i
\(66\) 0 0
\(67\) 1.50000 + 2.59808i 0.183254 + 0.317406i 0.942987 0.332830i \(-0.108004\pi\)
−0.759733 + 0.650236i \(0.774670\pi\)
\(68\) 6.92705 11.9980i 0.840028 1.45497i
\(69\) 0 0
\(70\) −0.427051 + 2.21902i −0.0510424 + 0.265224i
\(71\) −8.94427 −1.06149 −0.530745 0.847532i \(-0.678088\pi\)
−0.530745 + 0.847532i \(0.678088\pi\)
\(72\) 0 0
\(73\) −5.35410 9.27358i −0.626650 1.08539i −0.988219 0.153045i \(-0.951092\pi\)
0.361569 0.932345i \(-0.382241\pi\)
\(74\) 1.66312 + 2.88061i 0.193334 + 0.334864i
\(75\) 0 0
\(76\) −5.56231 −0.638040
\(77\) −1.50000 + 7.79423i −0.170941 + 0.888235i
\(78\) 0 0
\(79\) −5.35410 + 9.27358i −0.602384 + 1.04336i 0.390076 + 0.920783i \(0.372449\pi\)
−0.992459 + 0.122576i \(0.960884\pi\)
\(80\) −3.51722 6.09201i −0.393237 0.681107i
\(81\) 0 0
\(82\) 0.854102 1.47935i 0.0943198 0.163367i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 16.7082 1.81226
\(86\) 1.52786 2.64634i 0.164754 0.285362i
\(87\) 0 0
\(88\) 2.20820 + 3.82472i 0.235395 + 0.407717i
\(89\) −1.11803 + 1.93649i −0.118511 + 0.205268i −0.919178 0.393842i \(-0.871146\pi\)
0.800667 + 0.599110i \(0.204479\pi\)
\(90\) 0 0
\(91\) 2.00000 + 1.73205i 0.209657 + 0.181568i
\(92\) −6.97871 −0.727581
\(93\) 0 0
\(94\) 0.281153 + 0.486971i 0.0289987 + 0.0502272i
\(95\) −3.35410 5.80948i −0.344124 0.596040i
\(96\) 0 0
\(97\) −17.4164 −1.76837 −0.884184 0.467139i \(-0.845285\pi\)
−0.884184 + 0.467139i \(0.845285\pi\)
\(98\) −2.48278 0.992377i −0.250799 0.100245i
\(99\) 0 0
\(100\) 0 0
\(101\) −4.50000 7.79423i −0.447767 0.775555i 0.550474 0.834853i \(-0.314447\pi\)
−0.998240 + 0.0592978i \(0.981114\pi\)
\(102\) 0 0
\(103\) −5.35410 + 9.27358i −0.527555 + 0.913753i 0.471929 + 0.881637i \(0.343558\pi\)
−0.999484 + 0.0321160i \(0.989775\pi\)
\(104\) 1.47214 0.144355
\(105\) 0 0
\(106\) −0.562306 −0.0546160
\(107\) −7.11803 + 12.3288i −0.688126 + 1.19187i 0.284317 + 0.958730i \(0.408233\pi\)
−0.972443 + 0.233139i \(0.925100\pi\)
\(108\) 0 0
\(109\) −5.35410 9.27358i −0.512830 0.888248i −0.999889 0.0148787i \(-0.995264\pi\)
0.487059 0.873369i \(-0.338070\pi\)
\(110\) −1.28115 + 2.21902i −0.122153 + 0.211575i
\(111\) 0 0
\(112\) 7.86475 2.72443i 0.743149 0.257434i
\(113\) 14.9443 1.40584 0.702919 0.711269i \(-0.251879\pi\)
0.702919 + 0.711269i \(0.251879\pi\)
\(114\) 0 0
\(115\) −4.20820 7.28882i −0.392417 0.679686i
\(116\) 4.14590 + 7.18091i 0.384937 + 0.666730i
\(117\) 0 0
\(118\) −2.85410 −0.262741
\(119\) −3.73607 + 19.4132i −0.342485 + 1.77960i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) −0.572949 0.992377i −0.0518724 0.0898456i
\(123\) 0 0
\(124\) 4.63525 8.02850i 0.416258 0.720980i
\(125\) −11.1803 −1.00000
\(126\) 0 0
\(127\) 15.4164 1.36798 0.683992 0.729489i \(-0.260242\pi\)
0.683992 + 0.729489i \(0.260242\pi\)
\(128\) 5.04508 8.73834i 0.445927 0.772368i
\(129\) 0 0
\(130\) 0.427051 + 0.739674i 0.0374548 + 0.0648737i
\(131\) −1.88197 + 3.25966i −0.164428 + 0.284798i −0.936452 0.350796i \(-0.885911\pi\)
0.772024 + 0.635593i \(0.219245\pi\)
\(132\) 0 0
\(133\) 7.50000 2.59808i 0.650332 0.225282i
\(134\) −1.14590 −0.0989905
\(135\) 0 0
\(136\) 5.50000 + 9.52628i 0.471621 + 0.816872i
\(137\) −1.88197 3.25966i −0.160787 0.278492i 0.774364 0.632740i \(-0.218070\pi\)
−0.935151 + 0.354249i \(0.884737\pi\)
\(138\) 0 0
\(139\) 3.41641 0.289776 0.144888 0.989448i \(-0.453718\pi\)
0.144888 + 0.989448i \(0.453718\pi\)
\(140\) 8.29180 + 7.18091i 0.700785 + 0.606897i
\(141\) 0 0
\(142\) 1.70820 2.95870i 0.143349 0.248288i
\(143\) 1.50000 + 2.59808i 0.125436 + 0.217262i
\(144\) 0 0
\(145\) −5.00000 + 8.66025i −0.415227 + 0.719195i
\(146\) 4.09017 0.338505
\(147\) 0 0
\(148\) 16.1459 1.32718
\(149\) −6.35410 + 11.0056i −0.520548 + 0.901616i 0.479166 + 0.877724i \(0.340939\pi\)
−0.999715 + 0.0238920i \(0.992394\pi\)
\(150\) 0 0
\(151\) 3.20820 + 5.55677i 0.261080 + 0.452204i 0.966529 0.256557i \(-0.0825880\pi\)
−0.705449 + 0.708760i \(0.749255\pi\)
\(152\) 2.20820 3.82472i 0.179109 0.310226i
\(153\) 0 0
\(154\) −2.29180 1.98475i −0.184678 0.159936i
\(155\) 11.1803 0.898027
\(156\) 0 0
\(157\) −3.50000 6.06218i −0.279330 0.483814i 0.691888 0.722005i \(-0.256779\pi\)
−0.971219 + 0.238190i \(0.923446\pi\)
\(158\) −2.04508 3.54219i −0.162698 0.281802i
\(159\) 0 0
\(160\) 9.27051 0.732898
\(161\) 9.40983 3.25966i 0.741598 0.256897i
\(162\) 0 0
\(163\) −5.20820 + 9.02087i −0.407938 + 0.706569i −0.994659 0.103220i \(-0.967085\pi\)
0.586721 + 0.809789i \(0.300419\pi\)
\(164\) −4.14590 7.18091i −0.323740 0.560735i
\(165\) 0 0
\(166\) 0 0
\(167\) −13.5279 −1.04682 −0.523409 0.852082i \(-0.675340\pi\)
−0.523409 + 0.852082i \(0.675340\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −3.19098 + 5.52694i −0.244737 + 0.423897i
\(171\) 0 0
\(172\) −7.41641 12.8456i −0.565496 0.979467i
\(173\) 5.20820 9.02087i 0.395972 0.685844i −0.597252 0.802053i \(-0.703741\pi\)
0.993225 + 0.116209i \(0.0370743\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 9.43769 0.711393
\(177\) 0 0
\(178\) −0.427051 0.739674i −0.0320088 0.0554409i
\(179\) 10.0623 + 17.4284i 0.752092 + 1.30266i 0.946807 + 0.321802i \(0.104288\pi\)
−0.194715 + 0.980860i \(0.562378\pi\)
\(180\) 0 0
\(181\) 1.41641 0.105281 0.0526404 0.998614i \(-0.483236\pi\)
0.0526404 + 0.998614i \(0.483236\pi\)
\(182\) −0.954915 + 0.330792i −0.0707830 + 0.0245200i
\(183\) 0 0
\(184\) 2.77051 4.79866i 0.204245 0.353762i
\(185\) 9.73607 + 16.8634i 0.715810 + 1.23982i
\(186\) 0 0
\(187\) −11.2082 + 19.4132i −0.819625 + 1.41963i
\(188\) 2.72949 0.199069
\(189\) 0 0
\(190\) 2.56231 0.185889
\(191\) −5.59017 + 9.68246i −0.404491 + 0.700598i −0.994262 0.106972i \(-0.965884\pi\)
0.589772 + 0.807570i \(0.299218\pi\)
\(192\) 0 0
\(193\) 6.35410 + 11.0056i 0.457378 + 0.792202i 0.998821 0.0485349i \(-0.0154552\pi\)
−0.541443 + 0.840737i \(0.682122\pi\)
\(194\) 3.32624 5.76121i 0.238810 0.413631i
\(195\) 0 0
\(196\) −10.1976 + 8.02850i −0.728397 + 0.573464i
\(197\) 26.9443 1.91970 0.959850 0.280514i \(-0.0905049\pi\)
0.959850 + 0.280514i \(0.0905049\pi\)
\(198\) 0 0
\(199\) 3.64590 + 6.31488i 0.258451 + 0.447650i 0.965827 0.259187i \(-0.0834547\pi\)
−0.707376 + 0.706837i \(0.750121\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 3.43769 0.241875
\(203\) −8.94427 7.74597i −0.627765 0.543660i
\(204\) 0 0
\(205\) 5.00000 8.66025i 0.349215 0.604858i
\(206\) −2.04508 3.54219i −0.142488 0.246796i
\(207\) 0 0
\(208\) 1.57295 2.72443i 0.109064 0.188905i
\(209\) 9.00000 0.622543
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) −1.36475 + 2.36381i −0.0937311 + 0.162347i
\(213\) 0 0
\(214\) −2.71885 4.70918i −0.185857 0.321913i
\(215\) 8.94427 15.4919i 0.609994 1.05654i
\(216\) 0 0
\(217\) −2.50000 + 12.9904i −0.169711 + 0.881845i
\(218\) 4.09017 0.277021
\(219\) 0 0
\(220\) 6.21885 + 10.7714i 0.419275 + 0.726205i
\(221\) 3.73607 + 6.47106i 0.251315 + 0.435291i
\(222\) 0 0
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) −2.07295 + 10.7714i −0.138505 + 0.719692i
\(225\) 0 0
\(226\) −2.85410 + 4.94345i −0.189852 + 0.328833i
\(227\) −5.97214 10.3440i −0.396385 0.686558i 0.596892 0.802321i \(-0.296402\pi\)
−0.993277 + 0.115763i \(0.963069\pi\)
\(228\) 0 0
\(229\) 8.06231 13.9643i 0.532772 0.922788i −0.466495 0.884524i \(-0.654484\pi\)
0.999268 0.0382649i \(-0.0121831\pi\)
\(230\) 3.21478 0.211976
\(231\) 0 0
\(232\) −6.58359 −0.432234
\(233\) −2.97214 + 5.14789i −0.194711 + 0.337250i −0.946806 0.321806i \(-0.895710\pi\)
0.752095 + 0.659055i \(0.229044\pi\)
\(234\) 0 0
\(235\) 1.64590 + 2.85078i 0.107367 + 0.185964i
\(236\) −6.92705 + 11.9980i −0.450913 + 0.781004i
\(237\) 0 0
\(238\) −5.70820 4.94345i −0.370008 0.320436i
\(239\) 7.41641 0.479728 0.239864 0.970807i \(-0.422897\pi\)
0.239864 + 0.970807i \(0.422897\pi\)
\(240\) 0 0
\(241\) 4.35410 + 7.54153i 0.280472 + 0.485792i 0.971501 0.237035i \(-0.0761756\pi\)
−0.691029 + 0.722827i \(0.742842\pi\)
\(242\) 0.381966 + 0.661585i 0.0245537 + 0.0425283i
\(243\) 0 0
\(244\) −5.56231 −0.356090
\(245\) −14.5344 5.80948i −0.928571 0.371154i
\(246\) 0 0
\(247\) 1.50000 2.59808i 0.0954427 0.165312i
\(248\) 3.68034 + 6.37454i 0.233702 + 0.404783i
\(249\) 0 0
\(250\) 2.13525 3.69837i 0.135045 0.233905i
\(251\) −10.4721 −0.660995 −0.330498 0.943807i \(-0.607217\pi\)
−0.330498 + 0.943807i \(0.607217\pi\)
\(252\) 0 0
\(253\) 11.2918 0.709909
\(254\) −2.94427 + 5.09963i −0.184740 + 0.319979i
\(255\) 0 0
\(256\) −2.78115 4.81710i −0.173822 0.301069i
\(257\) −8.97214 + 15.5402i −0.559666 + 0.969371i 0.437858 + 0.899044i \(0.355737\pi\)
−0.997524 + 0.0703264i \(0.977596\pi\)
\(258\) 0 0
\(259\) −21.7705 + 7.54153i −1.35275 + 0.468608i
\(260\) 4.14590 0.257118
\(261\) 0 0
\(262\) −0.718847 1.24508i −0.0444105 0.0769213i
\(263\) −7.06231 12.2323i −0.435480 0.754274i 0.561854 0.827236i \(-0.310088\pi\)
−0.997335 + 0.0729620i \(0.976755\pi\)
\(264\) 0 0
\(265\) −3.29180 −0.202213
\(266\) −0.572949 + 2.97713i −0.0351298 + 0.182540i
\(267\) 0 0
\(268\) −2.78115 + 4.81710i −0.169886 + 0.294251i
\(269\) 2.26393 + 3.92125i 0.138034 + 0.239083i 0.926753 0.375672i \(-0.122588\pi\)
−0.788718 + 0.614755i \(0.789255\pi\)
\(270\) 0 0
\(271\) −3.20820 + 5.55677i −0.194885 + 0.337550i −0.946863 0.321638i \(-0.895767\pi\)
0.751978 + 0.659188i \(0.229100\pi\)
\(272\) 23.5066 1.42530
\(273\) 0 0
\(274\) 1.43769 0.0868543
\(275\) 0 0
\(276\) 0 0
\(277\) −13.2082 22.8773i −0.793604 1.37456i −0.923722 0.383064i \(-0.874869\pi\)
0.130118 0.991499i \(-0.458464\pi\)
\(278\) −0.652476 + 1.13012i −0.0391329 + 0.0677802i
\(279\) 0 0
\(280\) −8.22949 + 2.85078i −0.491806 + 0.170367i
\(281\) −9.05573 −0.540219 −0.270110 0.962830i \(-0.587060\pi\)
−0.270110 + 0.962830i \(0.587060\pi\)
\(282\) 0 0
\(283\) 7.06231 + 12.2323i 0.419811 + 0.727133i 0.995920 0.0902393i \(-0.0287632\pi\)
−0.576110 + 0.817372i \(0.695430\pi\)
\(284\) −8.29180 14.3618i −0.492028 0.852217i
\(285\) 0 0
\(286\) −1.14590 −0.0677584
\(287\) 8.94427 + 7.74597i 0.527964 + 0.457230i
\(288\) 0 0
\(289\) −19.4164 + 33.6302i −1.14214 + 1.97825i
\(290\) −1.90983 3.30792i −0.112149 0.194248i
\(291\) 0 0
\(292\) 9.92705 17.1942i 0.580937 1.00621i
\(293\) −2.94427 −0.172006 −0.0860031 0.996295i \(-0.527409\pi\)
−0.0860031 + 0.996295i \(0.527409\pi\)
\(294\) 0 0
\(295\) −16.7082 −0.972789
\(296\) −6.40983 + 11.1022i −0.372564 + 0.645299i
\(297\) 0 0
\(298\) −2.42705 4.20378i −0.140595 0.243518i
\(299\) 1.88197 3.25966i 0.108837 0.188511i
\(300\) 0 0
\(301\) 16.0000 + 13.8564i 0.922225 + 0.798670i
\(302\) −2.45085 −0.141031
\(303\) 0 0
\(304\) −4.71885 8.17328i −0.270644 0.468770i
\(305\) −3.35410 5.80948i −0.192055 0.332650i
\(306\) 0 0
\(307\) −7.41641 −0.423277 −0.211638 0.977348i \(-0.567880\pi\)
−0.211638 + 0.977348i \(0.567880\pi\)
\(308\) −13.9058 + 4.81710i −0.792354 + 0.274480i
\(309\) 0 0
\(310\) −2.13525 + 3.69837i −0.121274 + 0.210053i
\(311\) −16.1180 27.9173i −0.913970 1.58304i −0.808403 0.588630i \(-0.799667\pi\)
−0.105567 0.994412i \(-0.533666\pi\)
\(312\) 0 0
\(313\) 16.2082 28.0734i 0.916142 1.58680i 0.110921 0.993829i \(-0.464620\pi\)
0.805221 0.592975i \(-0.202047\pi\)
\(314\) 2.67376 0.150889
\(315\) 0 0
\(316\) −19.8541 −1.11688
\(317\) −1.88197 + 3.25966i −0.105702 + 0.183081i −0.914025 0.405659i \(-0.867042\pi\)
0.808323 + 0.588739i \(0.200376\pi\)
\(318\) 0 0
\(319\) −6.70820 11.6190i −0.375587 0.650536i
\(320\) 5.26393 9.11740i 0.294263 0.509678i
\(321\) 0 0
\(322\) −0.718847 + 3.73524i −0.0400598 + 0.208157i
\(323\) 22.4164 1.24728
\(324\) 0 0
\(325\) 0 0
\(326\) −1.98936 3.44567i −0.110180 0.190838i
\(327\) 0 0
\(328\) 6.58359 0.363518
\(329\) −3.68034 + 1.27491i −0.202904 + 0.0702879i
\(330\) 0 0
\(331\) 14.2082 24.6093i 0.780954 1.35265i −0.150433 0.988620i \(-0.548067\pi\)
0.931387 0.364031i \(-0.118600\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 2.58359 4.47491i 0.141368 0.244856i
\(335\) −6.70820 −0.366508
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) −0.190983 + 0.330792i −0.0103881 + 0.0179927i
\(339\) 0 0
\(340\) 15.4894 + 26.8284i 0.840028 + 1.45497i
\(341\) −7.50000 + 12.9904i −0.406148 + 0.703469i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 11.7771 0.634978
\(345\) 0 0
\(346\) 1.98936 + 3.44567i 0.106948 + 0.185240i
\(347\) −17.5344 30.3705i −0.941298 1.63038i −0.762999 0.646400i \(-0.776274\pi\)
−0.178299 0.983976i \(-0.557060\pi\)
\(348\) 0 0
\(349\) −2.58359 −0.138297 −0.0691483 0.997606i \(-0.522028\pi\)
−0.0691483 + 0.997606i \(0.522028\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −6.21885 + 10.7714i −0.331466 + 0.574115i
\(353\) 15.3541 + 26.5941i 0.817216 + 1.41546i 0.907725 + 0.419565i \(0.137817\pi\)
−0.0905091 + 0.995896i \(0.528849\pi\)
\(354\) 0 0
\(355\) 10.0000 17.3205i 0.530745 0.919277i
\(356\) −4.14590 −0.219732
\(357\) 0 0
\(358\) −7.68692 −0.406266
\(359\) −2.97214 + 5.14789i −0.156863 + 0.271695i −0.933736 0.357963i \(-0.883472\pi\)
0.776873 + 0.629658i \(0.216805\pi\)
\(360\) 0 0
\(361\) 5.00000 + 8.66025i 0.263158 + 0.455803i
\(362\) −0.270510 + 0.468537i −0.0142177 + 0.0246257i
\(363\) 0 0
\(364\) −0.927051 + 4.81710i −0.0485907 + 0.252485i
\(365\) 23.9443 1.25330
\(366\) 0 0
\(367\) −0.354102 0.613323i −0.0184840 0.0320152i 0.856635 0.515922i \(-0.172551\pi\)
−0.875119 + 0.483907i \(0.839217\pi\)
\(368\) −5.92047 10.2546i −0.308626 0.534556i
\(369\) 0 0
\(370\) −7.43769 −0.386667
\(371\) 0.736068 3.82472i 0.0382147 0.198570i
\(372\) 0 0
\(373\) 14.2082 24.6093i 0.735673 1.27422i −0.218755 0.975780i \(-0.570199\pi\)
0.954427 0.298443i \(-0.0964673\pi\)
\(374\) −4.28115 7.41517i −0.221373 0.383430i
\(375\) 0 0
\(376\) −1.08359 + 1.87684i −0.0558820 + 0.0967905i
\(377\) −4.47214 −0.230327
\(378\) 0 0
\(379\) 11.4164 0.586421 0.293211 0.956048i \(-0.405276\pi\)
0.293211 + 0.956048i \(0.405276\pi\)
\(380\) 6.21885 10.7714i 0.319020 0.552559i
\(381\) 0 0
\(382\) −2.13525 3.69837i −0.109249 0.189225i
\(383\) 7.50000 12.9904i 0.383232 0.663777i −0.608290 0.793715i \(-0.708144\pi\)
0.991522 + 0.129937i \(0.0414776\pi\)
\(384\) 0 0
\(385\) −13.4164 11.6190i −0.683763 0.592157i
\(386\) −4.85410 −0.247067
\(387\) 0 0
\(388\) −16.1459 27.9655i −0.819684 1.41973i
\(389\) −3.73607 6.47106i −0.189426 0.328096i 0.755633 0.654995i \(-0.227329\pi\)
−0.945059 + 0.326900i \(0.893996\pi\)
\(390\) 0 0
\(391\) 28.1246 1.42232
\(392\) −1.47214 10.1993i −0.0743541 0.515140i
\(393\) 0 0
\(394\) −5.14590 + 8.91296i −0.259247 + 0.449028i
\(395\) −11.9721 20.7363i −0.602384 1.04336i
\(396\) 0 0
\(397\) −7.06231 + 12.2323i −0.354447 + 0.613920i −0.987023 0.160578i \(-0.948664\pi\)
0.632576 + 0.774498i \(0.281998\pi\)
\(398\) −2.78522 −0.139610
\(399\) 0 0
\(400\) 0 0
\(401\) 4.88197 8.45581i 0.243794 0.422263i −0.717998 0.696045i \(-0.754941\pi\)
0.961792 + 0.273782i \(0.0882747\pi\)
\(402\) 0 0
\(403\) 2.50000 + 4.33013i 0.124534 + 0.215699i
\(404\) 8.34346 14.4513i 0.415103 0.718979i
\(405\) 0 0
\(406\) 4.27051 1.47935i 0.211942 0.0734188i
\(407\) −26.1246 −1.29495
\(408\) 0 0
\(409\) 2.35410 + 4.07742i 0.116403 + 0.201616i 0.918340 0.395793i \(-0.129530\pi\)
−0.801937 + 0.597409i \(0.796197\pi\)
\(410\) 1.90983 + 3.30792i 0.0943198 + 0.163367i
\(411\) 0 0
\(412\) −19.8541 −0.978141
\(413\) 3.73607 19.4132i 0.183840 0.955260i
\(414\) 0 0
\(415\) 0 0
\(416\) 2.07295 + 3.59045i 0.101635 + 0.176036i
\(417\) 0 0
\(418\) −1.71885 + 2.97713i −0.0840716 + 0.145616i
\(419\) −15.0557 −0.735520 −0.367760 0.929921i \(-0.619875\pi\)
−0.367760 + 0.929921i \(0.619875\pi\)
\(420\) 0 0
\(421\) −13.4164 −0.653876 −0.326938 0.945046i \(-0.606017\pi\)
−0.326938 + 0.945046i \(0.606017\pi\)
\(422\) −0.763932 + 1.32317i −0.0371876 + 0.0644109i
\(423\) 0 0
\(424\) −1.08359 1.87684i −0.0526239 0.0911472i
\(425\) 0 0
\(426\) 0 0
\(427\) 7.50000 2.59808i 0.362950 0.125730i
\(428\) −26.3951 −1.27586
\(429\) 0 0
\(430\) 3.41641 + 5.91739i 0.164754 + 0.285362i
\(431\) 6.68034 + 11.5707i 0.321781 + 0.557340i 0.980856 0.194737i \(-0.0623853\pi\)
−0.659075 + 0.752077i \(0.729052\pi\)
\(432\) 0 0
\(433\) 2.58359 0.124160 0.0620798 0.998071i \(-0.480227\pi\)
0.0620798 + 0.998071i \(0.480227\pi\)
\(434\) −3.81966 3.30792i −0.183350 0.158785i
\(435\) 0 0
\(436\) 9.92705 17.1942i 0.475420 0.823451i
\(437\) −5.64590 9.77898i −0.270080 0.467792i
\(438\) 0 0
\(439\) 8.06231 13.9643i 0.384793 0.666481i −0.606948 0.794742i \(-0.707606\pi\)
0.991740 + 0.128261i \(0.0409395\pi\)
\(440\) −9.87539 −0.470791
\(441\) 0 0
\(442\) −2.85410 −0.135756
\(443\) −1.11803 + 1.93649i −0.0531194 + 0.0920055i −0.891362 0.453291i \(-0.850250\pi\)
0.838243 + 0.545297i \(0.183583\pi\)
\(444\) 0 0
\(445\) −2.50000 4.33013i −0.118511 0.205268i
\(446\) 0.763932 1.32317i 0.0361732 0.0626539i
\(447\) 0 0
\(448\) 9.41641 + 8.15485i 0.444883 + 0.385280i
\(449\) −10.3607 −0.488951 −0.244475 0.969656i \(-0.578616\pi\)
−0.244475 + 0.969656i \(0.578616\pi\)
\(450\) 0 0
\(451\) 6.70820 + 11.6190i 0.315877 + 0.547115i
\(452\) 13.8541 + 23.9960i 0.651642 + 1.12868i
\(453\) 0 0
\(454\) 4.56231 0.214120
\(455\) −5.59017 + 1.93649i −0.262071 + 0.0907841i
\(456\) 0 0
\(457\) −17.0623 + 29.5528i −0.798141 + 1.38242i 0.122684 + 0.992446i \(0.460850\pi\)
−0.920825 + 0.389975i \(0.872484\pi\)
\(458\) 3.07953 + 5.33390i 0.143897 + 0.249237i
\(459\) 0 0
\(460\) 7.80244 13.5142i 0.363791 0.630104i
\(461\) 10.3607 0.482545 0.241272 0.970457i \(-0.422435\pi\)
0.241272 + 0.970457i \(0.422435\pi\)
\(462\) 0 0
\(463\) −24.0000 −1.11537 −0.557687 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) −7.03444 + 12.1840i −0.326566 + 0.565628i
\(465\) 0 0
\(466\) −1.13525 1.96632i −0.0525897 0.0910880i
\(467\) −10.8262 + 18.7516i −0.500979 + 0.867720i 0.499021 + 0.866590i \(0.333693\pi\)
−0.999999 + 0.00113029i \(0.999640\pi\)
\(468\) 0 0
\(469\) 1.50000 7.79423i 0.0692636 0.359904i
\(470\) −1.25735 −0.0579974
\(471\) 0 0
\(472\) −5.50000 9.52628i −0.253158 0.438483i
\(473\) 12.0000 + 20.7846i 0.551761 + 0.955677i
\(474\) 0 0
\(475\) 0 0
\(476\) −34.6353 + 11.9980i −1.58750 + 0.549928i
\(477\) 0 0
\(478\) −1.41641 + 2.45329i −0.0647850 + 0.112211i
\(479\) −14.9164 25.8360i −0.681548 1.18048i −0.974508 0.224351i \(-0.927974\pi\)
0.292960 0.956125i \(-0.405360\pi\)
\(480\) 0 0
\(481\) −4.35410 + 7.54153i −0.198530 + 0.343864i
\(482\) −3.32624 −0.151506
\(483\) 0 0
\(484\) 3.70820 0.168555
\(485\) 19.4721 33.7267i 0.884184 1.53145i
\(486\) 0 0
\(487\) −15.9164 27.5680i −0.721241 1.24923i −0.960503 0.278271i \(-0.910239\pi\)
0.239261 0.970955i \(-0.423095\pi\)
\(488\) 2.20820 3.82472i 0.0999607 0.173137i
\(489\) 0 0
\(490\) 4.69756 3.69837i 0.212214 0.167075i
\(491\) 34.4721 1.55571 0.777853 0.628446i \(-0.216309\pi\)
0.777853 + 0.628446i \(0.216309\pi\)
\(492\) 0 0
\(493\) −16.7082 28.9395i −0.752500 1.30337i
\(494\) 0.572949 + 0.992377i 0.0257782 + 0.0446491i
\(495\) 0 0
\(496\) 15.7295 0.706275
\(497\) 17.8885 + 15.4919i 0.802411 + 0.694908i
\(498\) 0 0
\(499\) 0.208204 0.360620i 0.00932049 0.0161436i −0.861328 0.508050i \(-0.830366\pi\)
0.870648 + 0.491907i \(0.163700\pi\)
\(500\) −10.3647 17.9523i −0.463525 0.802850i
\(501\) 0 0
\(502\) 2.00000 3.46410i 0.0892644 0.154610i
\(503\) −3.05573 −0.136248 −0.0681241 0.997677i \(-0.521701\pi\)
−0.0681241 + 0.997677i \(0.521701\pi\)
\(504\) 0 0
\(505\) 20.1246 0.895533
\(506\) −2.15654 + 3.73524i −0.0958699 + 0.166052i
\(507\) 0 0
\(508\) 14.2918 + 24.7541i 0.634096 + 1.09829i
\(509\) −7.88197 + 13.6520i −0.349362 + 0.605113i −0.986136 0.165938i \(-0.946935\pi\)
0.636774 + 0.771050i \(0.280268\pi\)
\(510\) 0 0
\(511\) −5.35410 + 27.8207i −0.236852 + 1.23072i
\(512\) 22.3050 0.985749
\(513\) 0 0
\(514\) −3.42705 5.93583i −0.151161 0.261818i
\(515\) −11.9721 20.7363i −0.527555 0.913753i
\(516\) 0 0
\(517\) −4.41641 −0.194233
\(518\) 1.66312 8.64182i 0.0730733 0.379700i
\(519\) 0 0
\(520\) −1.64590 + 2.85078i −0.0721774 + 0.125015i
\(521\) −0.0278640 0.0482619i −0.00122075 0.00211439i 0.865414 0.501057i \(-0.167055\pi\)
−0.866635 + 0.498942i \(0.833722\pi\)
\(522\) 0 0
\(523\) −9.64590 + 16.7072i −0.421786 + 0.730554i −0.996114 0.0880707i \(-0.971930\pi\)
0.574329 + 0.818625i \(0.305263\pi\)
\(524\) −6.97871 −0.304867
\(525\) 0 0
\(526\) 5.39512 0.235238
\(527\) −18.6803 + 32.3553i −0.813728 + 1.40942i
\(528\) 0 0
\(529\) 4.41641 + 7.64944i 0.192018 + 0.332584i
\(530\) 0.628677 1.08890i 0.0273080 0.0472988i
\(531\) 0 0
\(532\) 11.1246 + 9.63420i 0.482313 + 0.417695i
\(533\) 4.47214 0.193710
\(534\) 0 0
\(535\) −15.9164 27.5680i −0.688126 1.19187i
\(536\) −2.20820 3.82472i −0.0953799 0.165203i
\(537\) 0 0
\(538\) −1.72949 −0.0745636
\(539\) 16.5000 12.9904i 0.710705 0.559535i
\(540\) 0 0
\(541\) −7.35410 + 12.7377i −0.316178 + 0.547636i −0.979687 0.200532i \(-0.935733\pi\)
0.663510 + 0.748168i \(0.269066\pi\)
\(542\) −1.22542 2.12250i −0.0526365 0.0911691i
\(543\) 0 0
\(544\) −15.4894 + 26.8284i −0.664101 + 1.15026i
\(545\) 23.9443 1.02566
\(546\) 0 0
\(547\) −31.4164 −1.34327 −0.671634 0.740883i \(-0.734407\pi\)
−0.671634 + 0.740883i \(0.734407\pi\)
\(548\) 3.48936 6.04374i 0.149058 0.258176i
\(549\) 0 0
\(550\) 0 0
\(551\) −6.70820 + 11.6190i −0.285779 + 0.494984i
\(552\) 0 0
\(553\) 26.7705 9.27358i 1.13840 0.394353i
\(554\) 10.0902 0.428690
\(555\) 0 0
\(556\) 3.16718 + 5.48572i 0.134319 + 0.232647i
\(557\) −2.64590 4.58283i −0.112110 0.194181i 0.804511 0.593938i \(-0.202428\pi\)
−0.916621 + 0.399758i \(0.869094\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) −3.51722 + 18.2760i −0.148630 + 0.772303i
\(561\) 0 0
\(562\) 1.72949 2.99556i 0.0729541 0.126360i
\(563\) −18.2984 31.6937i −0.771185 1.33573i −0.936914 0.349560i \(-0.886331\pi\)
0.165730 0.986171i \(-0.447002\pi\)
\(564\) 0 0
\(565\) −16.7082 + 28.9395i −0.702919 + 1.21749i
\(566\) −5.39512 −0.226774
\(567\) 0 0
\(568\) 13.1672 0.552483
\(569\) 8.26393 14.3136i 0.346442 0.600055i −0.639173 0.769063i \(-0.720723\pi\)
0.985615 + 0.169008i \(0.0540564\pi\)
\(570\) 0 0
\(571\) −2.06231 3.57202i −0.0863048 0.149484i 0.819642 0.572877i \(-0.194173\pi\)
−0.905946 + 0.423392i \(0.860839\pi\)
\(572\) −2.78115 + 4.81710i −0.116286 + 0.201413i
\(573\) 0 0
\(574\) −4.27051 + 1.47935i −0.178248 + 0.0617468i
\(575\) 0 0
\(576\) 0 0
\(577\) 16.3541 + 28.3261i 0.680830 + 1.17923i 0.974728 + 0.223396i \(0.0717142\pi\)
−0.293898 + 0.955837i \(0.594953\pi\)
\(578\) −7.41641 12.8456i −0.308482 0.534306i
\(579\) 0 0
\(580\) −18.5410 −0.769874
\(581\) 0 0
\(582\) 0 0
\(583\) 2.20820 3.82472i 0.0914545 0.158404i
\(584\) 7.88197 + 13.6520i 0.326158 + 0.564922i
\(585\) 0 0
\(586\) 0.562306 0.973942i 0.0232286 0.0402332i
\(587\) 41.8885 1.72893 0.864463 0.502697i \(-0.167659\pi\)
0.864463 + 0.502697i \(0.167659\pi\)
\(588\) 0 0
\(589\) 15.0000 0.618064
\(590\) 3.19098 5.52694i 0.131371 0.227541i
\(591\) 0 0
\(592\) 13.6976 + 23.7249i 0.562966 + 0.975086i
\(593\) 16.1180 27.9173i 0.661888 1.14642i −0.318231 0.948013i \(-0.603089\pi\)
0.980119 0.198411i \(-0.0635780\pi\)
\(594\) 0 0
\(595\) −33.4164 28.9395i −1.36994 1.18640i
\(596\) −23.5623 −0.965150
\(597\) 0 0
\(598\) 0.718847 + 1.24508i 0.0293958 + 0.0509151i
\(599\) 20.5344 + 35.5667i 0.839015 + 1.45322i 0.890719 + 0.454553i \(0.150201\pi\)
−0.0517049 + 0.998662i \(0.516466\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) −7.63932 + 2.64634i −0.311355 + 0.107857i
\(603\) 0 0
\(604\) −5.94834 + 10.3028i −0.242034 + 0.419216i
\(605\) 2.23607 + 3.87298i 0.0909091 + 0.157459i
\(606\) 0 0
\(607\) 8.06231 13.9643i 0.327239 0.566794i −0.654724 0.755868i \(-0.727215\pi\)
0.981963 + 0.189074i \(0.0605485\pi\)
\(608\) 12.4377 0.504415
\(609\) 0 0
\(610\) 2.56231 0.103745
\(611\) −0.736068 + 1.27491i −0.0297781 + 0.0515772i
\(612\) 0 0
\(613\) −11.0623 19.1605i −0.446802 0.773884i 0.551373 0.834259i \(-0.314104\pi\)
−0.998176 + 0.0603742i \(0.980771\pi\)
\(614\) 1.41641 2.45329i 0.0571616 0.0990067i
\(615\) 0 0
\(616\) 2.20820 11.4742i 0.0889711 0.462307i
\(617\) −4.47214 −0.180041 −0.0900207 0.995940i \(-0.528693\pi\)
−0.0900207 + 0.995940i \(0.528693\pi\)
\(618\) 0 0
\(619\) −8.50000 14.7224i −0.341644 0.591744i 0.643094 0.765787i \(-0.277650\pi\)
−0.984738 + 0.174042i \(0.944317\pi\)
\(620\) 10.3647 + 17.9523i 0.416258 + 0.720980i
\(621\) 0 0
\(622\) 12.3131 0.493710
\(623\) 5.59017 1.93649i 0.223965 0.0775839i
\(624\) 0 0
\(625\) 12.5000 21.6506i 0.500000 0.866025i
\(626\) 6.19098 + 10.7231i 0.247441 + 0.428581i
\(627\) 0 0
\(628\) 6.48936 11.2399i 0.258954 0.448521i
\(629\) −65.0689 −2.59447
\(630\) 0 0
\(631\) −30.8328 −1.22744 −0.613718 0.789526i \(-0.710327\pi\)
−0.613718 + 0.789526i \(0.710327\pi\)
\(632\) 7.88197 13.6520i 0.313528 0.543046i
\(633\) 0 0
\(634\) −0.718847 1.24508i −0.0285491 0.0494484i
\(635\) −17.2361 + 29.8537i −0.683992 + 1.18471i
\(636\) 0 0
\(637\) −1.00000 6.92820i −0.0396214 0.274505i
\(638\) 5.12461 0.202885
\(639\) 0 0
\(640\) 11.2812 + 19.5395i 0.445927 + 0.772368i
\(641\) −2.97214 5.14789i −0.117392 0.203329i 0.801341 0.598208i \(-0.204120\pi\)
−0.918734 + 0.394878i \(0.870787\pi\)
\(642\) 0 0
\(643\) −18.8328 −0.742694 −0.371347 0.928494i \(-0.621104\pi\)
−0.371347 + 0.928494i \(0.621104\pi\)
\(644\) 13.9574 + 12.0875i 0.550000 + 0.476314i
\(645\) 0 0
\(646\) −4.28115 + 7.41517i −0.168440 + 0.291746i
\(647\) 7.88197 + 13.6520i 0.309872 + 0.536714i 0.978334 0.207032i \(-0.0663804\pi\)
−0.668462 + 0.743746i \(0.733047\pi\)
\(648\) 0 0
\(649\) 11.2082 19.4132i 0.439960 0.762034i
\(650\) 0 0
\(651\) 0 0
\(652\) −19.3131 −0.756359
\(653\) 6.73607 11.6672i 0.263603 0.456573i −0.703594 0.710602i \(-0.748423\pi\)
0.967197 + 0.254029i \(0.0817559\pi\)
\(654\) 0 0
\(655\) −4.20820 7.28882i −0.164428 0.284798i
\(656\) 7.03444 12.1840i 0.274649 0.475706i
\(657\) 0 0
\(658\) 0.281153 1.46091i 0.0109605 0.0569523i
\(659\) −8.94427 −0.348419 −0.174210 0.984709i \(-0.555737\pi\)
−0.174210 + 0.984709i \(0.555737\pi\)
\(660\) 0 0
\(661\) −3.35410 5.80948i −0.130459 0.225962i 0.793394 0.608708i \(-0.208312\pi\)
−0.923854 + 0.382746i \(0.874979\pi\)
\(662\) 5.42705 + 9.39993i 0.210928 + 0.365339i
\(663\) 0 0
\(664\) 0 0
\(665\) −3.35410 + 17.4284i −0.130066 + 0.675845i
\(666\) 0 0
\(667\) −8.41641 + 14.5776i −0.325885 + 0.564449i
\(668\) −12.5410 21.7217i −0.485227 0.840437i
\(669\) 0 0
\(670\) 1.28115 2.21902i 0.0494953 0.0857283i
\(671\) 9.00000 0.347441
\(672\) 0 0
\(673\) 17.4164 0.671353 0.335677 0.941977i \(-0.391035\pi\)
0.335677 + 0.941977i \(0.391035\pi\)
\(674\) −3.43769 + 5.95426i −0.132415 + 0.229350i
\(675\) 0 0
\(676\) 0.927051 + 1.60570i 0.0356558 + 0.0617577i
\(677\) 16.4443 28.4823i 0.632005 1.09466i −0.355137 0.934814i \(-0.615566\pi\)
0.987141 0.159850i \(-0.0511010\pi\)
\(678\) 0 0
\(679\) 34.8328 + 30.1661i 1.33676 + 1.15767i
\(680\) −24.5967 −0.943242
\(681\) 0 0
\(682\) −2.86475 4.96188i −0.109697 0.190000i
\(683\) −2.26393 3.92125i −0.0866270 0.150042i 0.819456 0.573142i \(-0.194275\pi\)
−0.906083 + 0.423099i \(0.860942\pi\)
\(684\) 0 0
\(685\) 8.41641 0.321574
\(686\) 3.24671 + 6.28505i 0.123960 + 0.239964i
\(687\) 0 0
\(688\) 12.5836 21.7954i 0.479745 0.830943i
\(689\) −0.736068 1.27491i −0.0280420 0.0485701i
\(690\) 0 0
\(691\) −0.916408 + 1.58726i −0.0348618 + 0.0603824i −0.882930 0.469505i \(-0.844432\pi\)
0.848068 + 0.529887i \(0.177766\pi\)
\(692\) 19.3131 0.734173
\(693\) 0 0
\(694\) 13.3951 0.508472
\(695\) −3.81966 + 6.61585i −0.144888 + 0.250953i
\(696\) 0 0
\(697\) 16.7082 + 28.9395i 0.632868 + 1.09616i
\(698\) 0.493422 0.854632i 0.0186763 0.0323483i
\(699\) 0 0
\(700\) 0 0
\(701\) −22.3607 −0.844551 −0.422276 0.906467i \(-0.638769\pi\)
−0.422276 + 0.906467i \(0.638769\pi\)
\(702\) 0 0
\(703\) 13.0623 + 22.6246i 0.492654 + 0.853302i
\(704\) 7.06231 + 12.2323i 0.266171 + 0.461021i
\(705\) 0 0
\(706\) −11.7295 −0.441445
\(707\) −4.50000 + 23.3827i −0.169240 + 0.879396i
\(708\) 0 0
\(709\) 4.93769 8.55234i 0.185439 0.321190i −0.758285 0.651923i \(-0.773963\pi\)
0.943724 + 0.330733i \(0.107296\pi\)
\(710\) 3.81966 + 6.61585i 0.143349 + 0.248288i
\(711\) 0 0
\(712\) 1.64590 2.85078i 0.0616826 0.106837i
\(713\) 18.8197 0.704802
\(714\) 0 0
\(715\) −6.70820 −0.250873
\(716\) −18.6565 + 32.3141i −0.697228 + 1.20763i
\(717\) 0 0
\(718\) −1.13525 1.96632i −0.0423673 0.0733824i
\(719\) 5.64590 9.77898i 0.210556 0.364694i −0.741332 0.671138i \(-0.765806\pi\)
0.951889 + 0.306444i \(0.0991391\pi\)
\(720\) 0 0
\(721\) 26.7705 9.27358i 0.996986 0.345366i
\(722\) −3.81966 −0.142153
\(723\) 0 0
\(724\) 1.31308 + 2.27433i 0.0488003 + 0.0845246i
\(725\) 0 0
\(726\) 0 0
\(727\) 14.8328 0.550119 0.275059 0.961427i \(-0.411302\pi\)
0.275059 + 0.961427i \(0.411302\pi\)
\(728\) −2.94427 2.54981i −0.109122 0.0945024i
\(729\) 0 0
\(730\) −4.57295 + 7.92058i −0.169252 + 0.293154i
\(731\) 29.8885 + 51.7685i 1.10547 + 1.91473i
\(732\) 0 0
\(733\) −7.64590 + 13.2431i −0.282408 + 0.489144i −0.971977 0.235075i \(-0.924466\pi\)
0.689570 + 0.724219i \(0.257800\pi\)
\(734\) 0.270510 0.00998470
\(735\) 0 0
\(736\) 15.6049 0.575203
\(737\) 4.50000 7.79423i 0.165760 0.287104i
\(738\) 0 0
\(739\) −17.9164 31.0321i −0.659066 1.14154i −0.980858 0.194725i \(-0.937619\pi\)
0.321792 0.946810i \(-0.395715\pi\)
\(740\) −18.0517 + 31.2664i −0.663592 + 1.14938i
\(741\) 0 0
\(742\) 1.12461 + 0.973942i 0.0412858 + 0.0357545i
\(743\) −15.0557 −0.552341 −0.276171 0.961109i \(-0.589065\pi\)
−0.276171 + 0.961109i \(0.589065\pi\)
\(744\) 0 0
\(745\) −14.2082 24.6093i −0.520548 0.901616i
\(746\) 5.42705 + 9.39993i 0.198698 + 0.344156i
\(747\) 0 0
\(748\) −41.5623 −1.51967
\(749\) 35.5902 12.3288i 1.30044 0.450484i
\(750\) 0 0
\(751\) −15.0623 + 26.0887i −0.549631 + 0.951989i 0.448668 + 0.893698i \(0.351898\pi\)
−0.998300 + 0.0582911i \(0.981435\pi\)
\(752\) 2.31559 + 4.01073i 0.0844411 + 0.146256i
\(753\) 0 0
\(754\) 0.854102 1.47935i 0.0311046 0.0538747i
\(755\) −14.3475 −0.522160
\(756\) 0 0
\(757\) 0.832816 0.0302692 0.0151346 0.999885i \(-0.495182\pi\)
0.0151346 + 0.999885i \(0.495182\pi\)
\(758\) −2.18034 + 3.77646i −0.0791935 + 0.137167i
\(759\) 0 0
\(760\) 4.93769 + 8.55234i 0.179109 + 0.310226i
\(761\) 16.7705 29.0474i 0.607931 1.05297i −0.383650 0.923478i \(-0.625333\pi\)
0.991581 0.129488i \(-0.0413334\pi\)
\(762\) 0 0
\(763\) −5.35410 + 27.8207i −0.193832 + 1.00718i
\(764\) −20.7295 −0.749967
\(765\) 0 0
\(766\) 2.86475 + 4.96188i 0.103507 + 0.179280i
\(767\) −3.73607 6.47106i −0.134902 0.233656i
\(768\) 0 0
\(769\) 46.0000 1.65880 0.829401 0.558653i \(-0.188682\pi\)
0.829401 + 0.558653i \(0.188682\pi\)
\(770\) 6.40576 2.21902i 0.230848 0.0799680i
\(771\) 0 0
\(772\) −11.7812 + 20.4056i −0.424013 + 0.734412i
\(773\) 5.53444 + 9.58593i 0.199060 + 0.344782i 0.948224 0.317603i \(-0.102878\pi\)
−0.749164 + 0.662385i \(0.769544\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 25.6393 0.920398
\(777\) 0 0
\(778\) 2.85410 0.102325
\(779\) 6.70820 11.6190i 0.240346 0.416292i
\(780\) 0 0
\(781\) 13.4164 + 23.2379i 0.480077 + 0.831517i
\(782\) −5.37132 + 9.30340i −0.192078 + 0.332689i
\(783\) 0 0
\(784\) −20.4483 8.17328i −0.730298 0.291903i
\(785\) 15.6525 0.558661
\(786\) 0 0
\(787\) 3.20820 + 5.55677i 0.114360 + 0.198078i 0.917524 0.397681i \(-0.130185\pi\)
−0.803164 + 0.595758i \(0.796852\pi\)
\(788\) 24.9787 + 43.2644i 0.889830 + 1.54123i
\(789\) 0