Properties

Label 99.2.f.b.64.1
Level 99
Weight 2
Character 99.64
Analytic conductor 0.791
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 99.f (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.790518980011\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 64.1
Root \(-0.309017 - 0.951057i\)
Character \(\chi\) = 99.64
Dual form 99.2.f.b.82.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.190983 - 0.587785i) q^{2} +(1.30902 + 0.951057i) q^{4} +(0.809017 + 2.48990i) q^{5} +(-2.42705 - 1.76336i) q^{7} +(1.80902 - 1.31433i) q^{8} +O(q^{10})\) \(q+(0.190983 - 0.587785i) q^{2} +(1.30902 + 0.951057i) q^{4} +(0.809017 + 2.48990i) q^{5} +(-2.42705 - 1.76336i) q^{7} +(1.80902 - 1.31433i) q^{8} +1.61803 q^{10} +(-1.69098 - 2.85317i) q^{11} +(0.545085 - 1.67760i) q^{13} +(-1.50000 + 1.08981i) q^{14} +(0.572949 + 1.76336i) q^{16} +(-0.500000 - 1.53884i) q^{17} +(-4.73607 + 3.44095i) q^{19} +(-1.30902 + 4.02874i) q^{20} +(-2.00000 + 0.449028i) q^{22} -3.47214 q^{23} +(-1.50000 + 1.08981i) q^{25} +(-0.881966 - 0.640786i) q^{26} +(-1.50000 - 4.61653i) q^{28} +(3.61803 + 2.62866i) q^{29} +(0.881966 - 2.71441i) q^{31} +5.61803 q^{32} -1.00000 q^{34} +(2.42705 - 7.46969i) q^{35} +(-0.190983 - 0.138757i) q^{37} +(1.11803 + 3.44095i) q^{38} +(4.73607 + 3.44095i) q^{40} +(-9.66312 + 7.02067i) q^{41} +6.23607 q^{43} +(0.500000 - 5.34307i) q^{44} +(-0.663119 + 2.04087i) q^{46} +(1.30902 - 0.951057i) q^{47} +(0.618034 + 1.90211i) q^{49} +(0.354102 + 1.08981i) q^{50} +(2.30902 - 1.67760i) q^{52} +(2.97214 - 9.14729i) q^{53} +(5.73607 - 6.51864i) q^{55} -6.70820 q^{56} +(2.23607 - 1.62460i) q^{58} +(8.35410 + 6.06961i) q^{59} +(2.42705 + 7.46969i) q^{61} +(-1.42705 - 1.03681i) q^{62} +(-0.0729490 + 0.224514i) q^{64} +4.61803 q^{65} -9.56231 q^{67} +(0.809017 - 2.48990i) q^{68} +(-3.92705 - 2.85317i) q^{70} +(1.71885 + 5.29007i) q^{71} +(2.61803 + 1.90211i) q^{73} +(-0.118034 + 0.0857567i) q^{74} -9.47214 q^{76} +(-0.927051 + 9.90659i) q^{77} +(2.92705 - 9.00854i) q^{79} +(-3.92705 + 2.85317i) q^{80} +(2.28115 + 7.02067i) q^{82} +(-0.218847 - 0.673542i) q^{83} +(3.42705 - 2.48990i) q^{85} +(1.19098 - 3.66547i) q^{86} +(-6.80902 - 2.93893i) q^{88} -0.527864 q^{89} +(-4.28115 + 3.11044i) q^{91} +(-4.54508 - 3.30220i) q^{92} +(-0.309017 - 0.951057i) q^{94} +(-12.3992 - 9.00854i) q^{95} +(-4.33688 + 13.3475i) q^{97} +1.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 3q^{2} + 3q^{4} + q^{5} - 3q^{7} + 5q^{8} + O(q^{10}) \) \( 4q + 3q^{2} + 3q^{4} + q^{5} - 3q^{7} + 5q^{8} + 2q^{10} - 9q^{11} - 9q^{13} - 6q^{14} + 9q^{16} - 2q^{17} - 10q^{19} - 3q^{20} - 8q^{22} + 4q^{23} - 6q^{25} - 8q^{26} - 6q^{28} + 10q^{29} + 8q^{31} + 18q^{32} - 4q^{34} + 3q^{35} - 3q^{37} + 10q^{40} - 23q^{41} + 16q^{43} + 2q^{44} + 13q^{46} + 3q^{47} - 2q^{49} - 12q^{50} + 7q^{52} - 6q^{53} + 14q^{55} + 20q^{59} + 3q^{61} + q^{62} - 7q^{64} + 14q^{65} + 2q^{67} + q^{68} - 9q^{70} + 27q^{71} + 6q^{73} + 4q^{74} - 20q^{76} + 3q^{77} + 5q^{79} - 9q^{80} - 11q^{82} - 21q^{83} + 7q^{85} + 7q^{86} - 25q^{88} - 20q^{89} + 3q^{91} - 7q^{92} + q^{94} - 25q^{95} - 33q^{97} - 4q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.190983 0.587785i 0.135045 0.415627i −0.860552 0.509363i \(-0.829881\pi\)
0.995597 + 0.0937362i \(0.0298810\pi\)
\(3\) 0 0
\(4\) 1.30902 + 0.951057i 0.654508 + 0.475528i
\(5\) 0.809017 + 2.48990i 0.361803 + 1.11352i 0.951959 + 0.306227i \(0.0990665\pi\)
−0.590155 + 0.807290i \(0.700933\pi\)
\(6\) 0 0
\(7\) −2.42705 1.76336i −0.917339 0.666486i 0.0255212 0.999674i \(-0.491875\pi\)
−0.942860 + 0.333188i \(0.891875\pi\)
\(8\) 1.80902 1.31433i 0.639584 0.464685i
\(9\) 0 0
\(10\) 1.61803 0.511667
\(11\) −1.69098 2.85317i −0.509851 0.860263i
\(12\) 0 0
\(13\) 0.545085 1.67760i 0.151179 0.465282i −0.846574 0.532270i \(-0.821339\pi\)
0.997754 + 0.0669881i \(0.0213390\pi\)
\(14\) −1.50000 + 1.08981i −0.400892 + 0.291265i
\(15\) 0 0
\(16\) 0.572949 + 1.76336i 0.143237 + 0.440839i
\(17\) −0.500000 1.53884i −0.121268 0.373224i 0.871935 0.489622i \(-0.162865\pi\)
−0.993203 + 0.116398i \(0.962865\pi\)
\(18\) 0 0
\(19\) −4.73607 + 3.44095i −1.08653 + 0.789409i −0.978810 0.204772i \(-0.934355\pi\)
−0.107719 + 0.994181i \(0.534355\pi\)
\(20\) −1.30902 + 4.02874i −0.292705 + 0.900854i
\(21\) 0 0
\(22\) −2.00000 + 0.449028i −0.426401 + 0.0957331i
\(23\) −3.47214 −0.723990 −0.361995 0.932180i \(-0.617904\pi\)
−0.361995 + 0.932180i \(0.617904\pi\)
\(24\) 0 0
\(25\) −1.50000 + 1.08981i −0.300000 + 0.217963i
\(26\) −0.881966 0.640786i −0.172968 0.125668i
\(27\) 0 0
\(28\) −1.50000 4.61653i −0.283473 0.872441i
\(29\) 3.61803 + 2.62866i 0.671852 + 0.488129i 0.870645 0.491912i \(-0.163702\pi\)
−0.198793 + 0.980042i \(0.563702\pi\)
\(30\) 0 0
\(31\) 0.881966 2.71441i 0.158406 0.487523i −0.840084 0.542456i \(-0.817495\pi\)
0.998490 + 0.0549331i \(0.0174946\pi\)
\(32\) 5.61803 0.993137
\(33\) 0 0
\(34\) −1.00000 −0.171499
\(35\) 2.42705 7.46969i 0.410246 1.26261i
\(36\) 0 0
\(37\) −0.190983 0.138757i −0.0313974 0.0228116i 0.571976 0.820270i \(-0.306177\pi\)
−0.603373 + 0.797459i \(0.706177\pi\)
\(38\) 1.11803 + 3.44095i 0.181369 + 0.558197i
\(39\) 0 0
\(40\) 4.73607 + 3.44095i 0.748838 + 0.544063i
\(41\) −9.66312 + 7.02067i −1.50913 + 1.09644i −0.542562 + 0.840015i \(0.682546\pi\)
−0.966563 + 0.256428i \(0.917454\pi\)
\(42\) 0 0
\(43\) 6.23607 0.950991 0.475496 0.879718i \(-0.342269\pi\)
0.475496 + 0.879718i \(0.342269\pi\)
\(44\) 0.500000 5.34307i 0.0753778 0.805498i
\(45\) 0 0
\(46\) −0.663119 + 2.04087i −0.0977716 + 0.300910i
\(47\) 1.30902 0.951057i 0.190940 0.138726i −0.488208 0.872727i \(-0.662349\pi\)
0.679148 + 0.734001i \(0.262349\pi\)
\(48\) 0 0
\(49\) 0.618034 + 1.90211i 0.0882906 + 0.271730i
\(50\) 0.354102 + 1.08981i 0.0500776 + 0.154123i
\(51\) 0 0
\(52\) 2.30902 1.67760i 0.320203 0.232641i
\(53\) 2.97214 9.14729i 0.408254 1.25648i −0.509893 0.860238i \(-0.670315\pi\)
0.918147 0.396240i \(-0.129685\pi\)
\(54\) 0 0
\(55\) 5.73607 6.51864i 0.773451 0.878973i
\(56\) −6.70820 −0.896421
\(57\) 0 0
\(58\) 2.23607 1.62460i 0.293610 0.213320i
\(59\) 8.35410 + 6.06961i 1.08761 + 0.790196i 0.978994 0.203888i \(-0.0653577\pi\)
0.108617 + 0.994084i \(0.465358\pi\)
\(60\) 0 0
\(61\) 2.42705 + 7.46969i 0.310752 + 0.956396i 0.977468 + 0.211084i \(0.0676995\pi\)
−0.666716 + 0.745312i \(0.732301\pi\)
\(62\) −1.42705 1.03681i −0.181236 0.131675i
\(63\) 0 0
\(64\) −0.0729490 + 0.224514i −0.00911863 + 0.0280642i
\(65\) 4.61803 0.572797
\(66\) 0 0
\(67\) −9.56231 −1.16822 −0.584111 0.811674i \(-0.698557\pi\)
−0.584111 + 0.811674i \(0.698557\pi\)
\(68\) 0.809017 2.48990i 0.0981077 0.301945i
\(69\) 0 0
\(70\) −3.92705 2.85317i −0.469372 0.341019i
\(71\) 1.71885 + 5.29007i 0.203990 + 0.627815i 0.999753 + 0.0222083i \(0.00706970\pi\)
−0.795764 + 0.605607i \(0.792930\pi\)
\(72\) 0 0
\(73\) 2.61803 + 1.90211i 0.306418 + 0.222625i 0.730358 0.683065i \(-0.239353\pi\)
−0.423940 + 0.905690i \(0.639353\pi\)
\(74\) −0.118034 + 0.0857567i −0.0137212 + 0.00996902i
\(75\) 0 0
\(76\) −9.47214 −1.08653
\(77\) −0.927051 + 9.90659i −0.105647 + 1.12896i
\(78\) 0 0
\(79\) 2.92705 9.00854i 0.329319 1.01354i −0.640134 0.768263i \(-0.721121\pi\)
0.969453 0.245276i \(-0.0788787\pi\)
\(80\) −3.92705 + 2.85317i −0.439058 + 0.318994i
\(81\) 0 0
\(82\) 2.28115 + 7.02067i 0.251911 + 0.775303i
\(83\) −0.218847 0.673542i −0.0240216 0.0739308i 0.938327 0.345749i \(-0.112375\pi\)
−0.962349 + 0.271818i \(0.912375\pi\)
\(84\) 0 0
\(85\) 3.42705 2.48990i 0.371716 0.270067i
\(86\) 1.19098 3.66547i 0.128427 0.395258i
\(87\) 0 0
\(88\) −6.80902 2.93893i −0.725844 0.313291i
\(89\) −0.527864 −0.0559535 −0.0279767 0.999609i \(-0.508906\pi\)
−0.0279767 + 0.999609i \(0.508906\pi\)
\(90\) 0 0
\(91\) −4.28115 + 3.11044i −0.448787 + 0.326063i
\(92\) −4.54508 3.30220i −0.473858 0.344278i
\(93\) 0 0
\(94\) −0.309017 0.951057i −0.0318727 0.0980940i
\(95\) −12.3992 9.00854i −1.27213 0.924256i
\(96\) 0 0
\(97\) −4.33688 + 13.3475i −0.440344 + 1.35524i 0.447167 + 0.894451i \(0.352433\pi\)
−0.887510 + 0.460788i \(0.847567\pi\)
\(98\) 1.23607 0.124862
\(99\) 0 0
\(100\) −3.00000 −0.300000
\(101\) 0.927051 2.85317i 0.0922450 0.283901i −0.894281 0.447506i \(-0.852312\pi\)
0.986526 + 0.163605i \(0.0523123\pi\)
\(102\) 0 0
\(103\) 4.85410 + 3.52671i 0.478289 + 0.347497i 0.800663 0.599115i \(-0.204481\pi\)
−0.322374 + 0.946612i \(0.604481\pi\)
\(104\) −1.21885 3.75123i −0.119518 0.367838i
\(105\) 0 0
\(106\) −4.80902 3.49396i −0.467093 0.339363i
\(107\) −3.42705 + 2.48990i −0.331306 + 0.240708i −0.740984 0.671522i \(-0.765641\pi\)
0.409679 + 0.912230i \(0.365641\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) −2.73607 4.61653i −0.260874 0.440168i
\(111\) 0 0
\(112\) 1.71885 5.29007i 0.162416 0.499864i
\(113\) 0.572949 0.416272i 0.0538985 0.0391596i −0.560510 0.828148i \(-0.689395\pi\)
0.614408 + 0.788988i \(0.289395\pi\)
\(114\) 0 0
\(115\) −2.80902 8.64527i −0.261942 0.806175i
\(116\) 2.23607 + 6.88191i 0.207614 + 0.638969i
\(117\) 0 0
\(118\) 5.16312 3.75123i 0.475304 0.345328i
\(119\) −1.50000 + 4.61653i −0.137505 + 0.423196i
\(120\) 0 0
\(121\) −5.28115 + 9.64932i −0.480105 + 0.877211i
\(122\) 4.85410 0.439470
\(123\) 0 0
\(124\) 3.73607 2.71441i 0.335509 0.243761i
\(125\) 6.66312 + 4.84104i 0.595967 + 0.432996i
\(126\) 0 0
\(127\) −1.14590 3.52671i −0.101682 0.312945i 0.887255 0.461279i \(-0.152609\pi\)
−0.988937 + 0.148333i \(0.952609\pi\)
\(128\) 9.20820 + 6.69015i 0.813898 + 0.591331i
\(129\) 0 0
\(130\) 0.881966 2.71441i 0.0773535 0.238070i
\(131\) 7.14590 0.624340 0.312170 0.950026i \(-0.398944\pi\)
0.312170 + 0.950026i \(0.398944\pi\)
\(132\) 0 0
\(133\) 17.5623 1.52285
\(134\) −1.82624 + 5.62058i −0.157763 + 0.485544i
\(135\) 0 0
\(136\) −2.92705 2.12663i −0.250993 0.182357i
\(137\) −2.30902 7.10642i −0.197273 0.607143i −0.999943 0.0107192i \(-0.996588\pi\)
0.802670 0.596424i \(-0.203412\pi\)
\(138\) 0 0
\(139\) 0.690983 + 0.502029i 0.0586084 + 0.0425815i 0.616704 0.787195i \(-0.288468\pi\)
−0.558095 + 0.829777i \(0.688468\pi\)
\(140\) 10.2812 7.46969i 0.868916 0.631304i
\(141\) 0 0
\(142\) 3.43769 0.288485
\(143\) −5.70820 + 1.28157i −0.477344 + 0.107170i
\(144\) 0 0
\(145\) −3.61803 + 11.1352i −0.300461 + 0.924725i
\(146\) 1.61803 1.17557i 0.133909 0.0972909i
\(147\) 0 0
\(148\) −0.118034 0.363271i −0.00970233 0.0298607i
\(149\) −4.63525 14.2658i −0.379735 1.16870i −0.940228 0.340545i \(-0.889388\pi\)
0.560493 0.828159i \(-0.310612\pi\)
\(150\) 0 0
\(151\) −1.61803 + 1.17557i −0.131674 + 0.0956666i −0.651673 0.758500i \(-0.725932\pi\)
0.519999 + 0.854167i \(0.325932\pi\)
\(152\) −4.04508 + 12.4495i −0.328100 + 1.00979i
\(153\) 0 0
\(154\) 5.64590 + 2.43690i 0.454959 + 0.196371i
\(155\) 7.47214 0.600176
\(156\) 0 0
\(157\) 3.00000 2.17963i 0.239426 0.173953i −0.461601 0.887087i \(-0.652725\pi\)
0.701028 + 0.713134i \(0.252725\pi\)
\(158\) −4.73607 3.44095i −0.376781 0.273748i
\(159\) 0 0
\(160\) 4.54508 + 13.9883i 0.359321 + 1.10587i
\(161\) 8.42705 + 6.12261i 0.664145 + 0.482529i
\(162\) 0 0
\(163\) 5.64590 17.3763i 0.442221 1.36102i −0.443282 0.896382i \(-0.646186\pi\)
0.885503 0.464634i \(-0.153814\pi\)
\(164\) −19.3262 −1.50913
\(165\) 0 0
\(166\) −0.437694 −0.0339717
\(167\) −3.10081 + 9.54332i −0.239948 + 0.738484i 0.756478 + 0.654019i \(0.226918\pi\)
−0.996426 + 0.0844656i \(0.973082\pi\)
\(168\) 0 0
\(169\) 8.00000 + 5.81234i 0.615385 + 0.447103i
\(170\) −0.809017 2.48990i −0.0620488 0.190966i
\(171\) 0 0
\(172\) 8.16312 + 5.93085i 0.622432 + 0.452223i
\(173\) 12.4443 9.04129i 0.946120 0.687397i −0.00376565 0.999993i \(-0.501199\pi\)
0.949886 + 0.312596i \(0.101199\pi\)
\(174\) 0 0
\(175\) 5.56231 0.420471
\(176\) 4.06231 4.61653i 0.306208 0.347984i
\(177\) 0 0
\(178\) −0.100813 + 0.310271i −0.00755626 + 0.0232558i
\(179\) −1.80902 + 1.31433i −0.135212 + 0.0982375i −0.653335 0.757069i \(-0.726631\pi\)
0.518123 + 0.855306i \(0.326631\pi\)
\(180\) 0 0
\(181\) −5.39919 16.6170i −0.401318 1.23513i −0.923930 0.382560i \(-0.875042\pi\)
0.522612 0.852571i \(-0.324958\pi\)
\(182\) 1.01064 + 3.11044i 0.0749139 + 0.230561i
\(183\) 0 0
\(184\) −6.28115 + 4.56352i −0.463053 + 0.336428i
\(185\) 0.190983 0.587785i 0.0140413 0.0432148i
\(186\) 0 0
\(187\) −3.54508 + 4.02874i −0.259242 + 0.294611i
\(188\) 2.61803 0.190940
\(189\) 0 0
\(190\) −7.66312 + 5.56758i −0.555941 + 0.403915i
\(191\) −6.04508 4.39201i −0.437407 0.317795i 0.347197 0.937792i \(-0.387134\pi\)
−0.784604 + 0.619998i \(0.787134\pi\)
\(192\) 0 0
\(193\) −5.73607 17.6538i −0.412891 1.27075i −0.914124 0.405436i \(-0.867120\pi\)
0.501232 0.865313i \(-0.332880\pi\)
\(194\) 7.01722 + 5.09831i 0.503807 + 0.366037i
\(195\) 0 0
\(196\) −1.00000 + 3.07768i −0.0714286 + 0.219835i
\(197\) −24.3820 −1.73714 −0.868572 0.495564i \(-0.834961\pi\)
−0.868572 + 0.495564i \(0.834961\pi\)
\(198\) 0 0
\(199\) −16.7082 −1.18441 −0.592207 0.805786i \(-0.701743\pi\)
−0.592207 + 0.805786i \(0.701743\pi\)
\(200\) −1.28115 + 3.94298i −0.0905912 + 0.278811i
\(201\) 0 0
\(202\) −1.50000 1.08981i −0.105540 0.0766790i
\(203\) −4.14590 12.7598i −0.290985 0.895560i
\(204\) 0 0
\(205\) −25.2984 18.3803i −1.76692 1.28374i
\(206\) 3.00000 2.17963i 0.209020 0.151862i
\(207\) 0 0
\(208\) 3.27051 0.226769
\(209\) 17.8262 + 7.69421i 1.23307 + 0.532220i
\(210\) 0 0
\(211\) −6.88197 + 21.1805i −0.473774 + 1.45813i 0.373830 + 0.927497i \(0.378044\pi\)
−0.847604 + 0.530629i \(0.821956\pi\)
\(212\) 12.5902 9.14729i 0.864696 0.628239i
\(213\) 0 0
\(214\) 0.809017 + 2.48990i 0.0553033 + 0.170206i
\(215\) 5.04508 + 15.5272i 0.344072 + 1.05894i
\(216\) 0 0
\(217\) −6.92705 + 5.03280i −0.470239 + 0.341649i
\(218\) 0 0
\(219\) 0 0
\(220\) 13.7082 3.07768i 0.924207 0.207497i
\(221\) −2.85410 −0.191988
\(222\) 0 0
\(223\) −0.572949 + 0.416272i −0.0383675 + 0.0278756i −0.606804 0.794852i \(-0.707549\pi\)
0.568436 + 0.822727i \(0.307549\pi\)
\(224\) −13.6353 9.90659i −0.911044 0.661912i
\(225\) 0 0
\(226\) −0.135255 0.416272i −0.00899702 0.0276900i
\(227\) −20.1353 14.6291i −1.33642 0.970969i −0.999567 0.0294127i \(-0.990636\pi\)
−0.336856 0.941556i \(-0.609364\pi\)
\(228\) 0 0
\(229\) 3.09017 9.51057i 0.204204 0.628476i −0.795541 0.605900i \(-0.792813\pi\)
0.999745 0.0225760i \(-0.00718678\pi\)
\(230\) −5.61803 −0.370442
\(231\) 0 0
\(232\) 10.0000 0.656532
\(233\) −7.51722 + 23.1356i −0.492470 + 1.51567i 0.328394 + 0.944541i \(0.393493\pi\)
−0.820863 + 0.571124i \(0.806507\pi\)
\(234\) 0 0
\(235\) 3.42705 + 2.48990i 0.223556 + 0.162423i
\(236\) 5.16312 + 15.8904i 0.336090 + 1.03438i
\(237\) 0 0
\(238\) 2.42705 + 1.76336i 0.157322 + 0.114301i
\(239\) 2.07295 1.50609i 0.134088 0.0974206i −0.518719 0.854945i \(-0.673591\pi\)
0.652807 + 0.757524i \(0.273591\pi\)
\(240\) 0 0
\(241\) −23.1246 −1.48959 −0.744794 0.667295i \(-0.767452\pi\)
−0.744794 + 0.667295i \(0.767452\pi\)
\(242\) 4.66312 + 4.94704i 0.299757 + 0.318008i
\(243\) 0 0
\(244\) −3.92705 + 12.0862i −0.251404 + 0.773741i
\(245\) −4.23607 + 3.07768i −0.270632 + 0.196626i
\(246\) 0 0
\(247\) 3.19098 + 9.82084i 0.203037 + 0.624885i
\(248\) −1.97214 6.06961i −0.125231 0.385421i
\(249\) 0 0
\(250\) 4.11803 2.99193i 0.260447 0.189226i
\(251\) 2.40983 7.41669i 0.152107 0.468138i −0.845749 0.533581i \(-0.820846\pi\)
0.997856 + 0.0654431i \(0.0208461\pi\)
\(252\) 0 0
\(253\) 5.87132 + 9.90659i 0.369127 + 0.622822i
\(254\) −2.29180 −0.143800
\(255\) 0 0
\(256\) 5.30902 3.85723i 0.331814 0.241077i
\(257\) −9.44427 6.86167i −0.589117 0.428019i 0.252882 0.967497i \(-0.418622\pi\)
−0.842000 + 0.539478i \(0.818622\pi\)
\(258\) 0 0
\(259\) 0.218847 + 0.673542i 0.0135985 + 0.0418519i
\(260\) 6.04508 + 4.39201i 0.374900 + 0.272381i
\(261\) 0 0
\(262\) 1.36475 4.20025i 0.0843142 0.259493i
\(263\) 16.3262 1.00672 0.503359 0.864077i \(-0.332097\pi\)
0.503359 + 0.864077i \(0.332097\pi\)
\(264\) 0 0
\(265\) 25.1803 1.54682
\(266\) 3.35410 10.3229i 0.205653 0.632935i
\(267\) 0 0
\(268\) −12.5172 9.09429i −0.764611 0.555522i
\(269\) −4.79837 14.7679i −0.292562 0.900413i −0.984029 0.178006i \(-0.943035\pi\)
0.691467 0.722408i \(-0.256965\pi\)
\(270\) 0 0
\(271\) 22.0623 + 16.0292i 1.34019 + 0.973705i 0.999437 + 0.0335518i \(0.0106819\pi\)
0.340753 + 0.940153i \(0.389318\pi\)
\(272\) 2.42705 1.76336i 0.147162 0.106919i
\(273\) 0 0
\(274\) −4.61803 −0.278986
\(275\) 5.64590 + 2.43690i 0.340460 + 0.146950i
\(276\) 0 0
\(277\) 9.44427 29.0665i 0.567451 1.74644i −0.0931022 0.995657i \(-0.529678\pi\)
0.660554 0.750779i \(-0.270322\pi\)
\(278\) 0.427051 0.310271i 0.0256128 0.0186088i
\(279\) 0 0
\(280\) −5.42705 16.7027i −0.324328 0.998180i
\(281\) 0.236068 + 0.726543i 0.0140826 + 0.0433419i 0.957851 0.287266i \(-0.0927463\pi\)
−0.943768 + 0.330608i \(0.892746\pi\)
\(282\) 0 0
\(283\) −0.145898 + 0.106001i −0.00867274 + 0.00630111i −0.592113 0.805855i \(-0.701706\pi\)
0.583440 + 0.812156i \(0.301706\pi\)
\(284\) −2.78115 + 8.55951i −0.165031 + 0.507913i
\(285\) 0 0
\(286\) −0.336881 + 3.59996i −0.0199202 + 0.212870i
\(287\) 35.8328 2.11514
\(288\) 0 0
\(289\) 11.6353 8.45351i 0.684427 0.497265i
\(290\) 5.85410 + 4.25325i 0.343765 + 0.249760i
\(291\) 0 0
\(292\) 1.61803 + 4.97980i 0.0946883 + 0.291421i
\(293\) 0.0450850 + 0.0327561i 0.00263389 + 0.00191363i 0.589101 0.808059i \(-0.299482\pi\)
−0.586468 + 0.809973i \(0.699482\pi\)
\(294\) 0 0
\(295\) −8.35410 + 25.7113i −0.486395 + 1.49697i
\(296\) −0.527864 −0.0306815
\(297\) 0 0
\(298\) −9.27051 −0.537026
\(299\) −1.89261 + 5.82485i −0.109452 + 0.336860i
\(300\) 0 0
\(301\) −15.1353 10.9964i −0.872382 0.633822i
\(302\) 0.381966 + 1.17557i 0.0219797 + 0.0676465i
\(303\) 0 0
\(304\) −8.78115 6.37988i −0.503634 0.365911i
\(305\) −16.6353 + 12.0862i −0.952532 + 0.692055i
\(306\) 0 0
\(307\) 0.562306 0.0320925 0.0160462 0.999871i \(-0.494892\pi\)
0.0160462 + 0.999871i \(0.494892\pi\)
\(308\) −10.6353 + 12.0862i −0.606000 + 0.688676i
\(309\) 0 0
\(310\) 1.42705 4.39201i 0.0810510 0.249449i
\(311\) 2.04508 1.48584i 0.115966 0.0842543i −0.528291 0.849064i \(-0.677167\pi\)
0.644257 + 0.764809i \(0.277167\pi\)
\(312\) 0 0
\(313\) 7.98278 + 24.5685i 0.451213 + 1.38869i 0.875524 + 0.483175i \(0.160517\pi\)
−0.424310 + 0.905517i \(0.639483\pi\)
\(314\) −0.708204 2.17963i −0.0399663 0.123004i
\(315\) 0 0
\(316\) 12.3992 9.00854i 0.697509 0.506770i
\(317\) 5.98278 18.4131i 0.336026 1.03418i −0.630188 0.776443i \(-0.717022\pi\)
0.966214 0.257740i \(-0.0829778\pi\)
\(318\) 0 0
\(319\) 1.38197 14.7679i 0.0773752 0.826842i
\(320\) −0.618034 −0.0345492
\(321\) 0 0
\(322\) 5.20820 3.78398i 0.290242 0.210873i
\(323\) 7.66312 + 5.56758i 0.426387 + 0.309789i
\(324\) 0 0
\(325\) 1.01064 + 3.11044i 0.0560604 + 0.172536i
\(326\) −9.13525 6.63715i −0.505955 0.367598i
\(327\) 0 0
\(328\) −8.25329 + 25.4010i −0.455712 + 1.40254i
\(329\) −4.85410 −0.267615
\(330\) 0 0
\(331\) 26.5967 1.46189 0.730945 0.682437i \(-0.239080\pi\)
0.730945 + 0.682437i \(0.239080\pi\)
\(332\) 0.354102 1.08981i 0.0194339 0.0598113i
\(333\) 0 0
\(334\) 5.01722 + 3.64522i 0.274530 + 0.199458i
\(335\) −7.73607 23.8092i −0.422667 1.30083i
\(336\) 0 0
\(337\) 0.236068 + 0.171513i 0.0128594 + 0.00934293i 0.594196 0.804320i \(-0.297470\pi\)
−0.581337 + 0.813663i \(0.697470\pi\)
\(338\) 4.94427 3.59222i 0.268933 0.195391i
\(339\) 0 0
\(340\) 6.85410 0.371716
\(341\) −9.23607 + 2.07363i −0.500161 + 0.112293i
\(342\) 0 0
\(343\) −4.63525 + 14.2658i −0.250280 + 0.770283i
\(344\) 11.2812 8.19624i 0.608239 0.441912i
\(345\) 0 0
\(346\) −2.93769 9.04129i −0.157931 0.486063i
\(347\) 6.47214 + 19.9192i 0.347442 + 1.06932i 0.960263 + 0.279096i \(0.0900348\pi\)
−0.612821 + 0.790222i \(0.709965\pi\)
\(348\) 0 0
\(349\) 8.19098 5.95110i 0.438453 0.318555i −0.346567 0.938025i \(-0.612653\pi\)
0.785020 + 0.619470i \(0.212653\pi\)
\(350\) 1.06231 3.26944i 0.0567826 0.174759i
\(351\) 0 0
\(352\) −9.50000 16.0292i −0.506352 0.854359i
\(353\) 10.4721 0.557376 0.278688 0.960382i \(-0.410101\pi\)
0.278688 + 0.960382i \(0.410101\pi\)
\(354\) 0 0
\(355\) −11.7812 + 8.55951i −0.625279 + 0.454292i
\(356\) −0.690983 0.502029i −0.0366220 0.0266075i
\(357\) 0 0
\(358\) 0.427051 + 1.31433i 0.0225703 + 0.0694644i
\(359\) −10.3262 7.50245i −0.544998 0.395964i 0.280940 0.959725i \(-0.409354\pi\)
−0.825938 + 0.563761i \(0.809354\pi\)
\(360\) 0 0
\(361\) 4.71885 14.5231i 0.248360 0.764375i
\(362\) −10.7984 −0.567550
\(363\) 0 0
\(364\) −8.56231 −0.448787
\(365\) −2.61803 + 8.05748i −0.137034 + 0.421748i
\(366\) 0 0
\(367\) −4.50000 3.26944i −0.234898 0.170663i 0.464109 0.885778i \(-0.346375\pi\)
−0.699007 + 0.715115i \(0.746375\pi\)
\(368\) −1.98936 6.12261i −0.103702 0.319163i
\(369\) 0 0
\(370\) −0.309017 0.224514i −0.0160650 0.0116719i
\(371\) −23.3435 + 16.9600i −1.21193 + 0.880520i
\(372\) 0 0
\(373\) −4.41641 −0.228673 −0.114336 0.993442i \(-0.536474\pi\)
−0.114336 + 0.993442i \(0.536474\pi\)
\(374\) 1.69098 + 2.85317i 0.0874386 + 0.147534i
\(375\) 0 0
\(376\) 1.11803 3.44095i 0.0576582 0.177454i
\(377\) 6.38197 4.63677i 0.328688 0.238806i
\(378\) 0 0
\(379\) 0.489357 + 1.50609i 0.0251366 + 0.0773624i 0.962838 0.270080i \(-0.0870502\pi\)
−0.937701 + 0.347443i \(0.887050\pi\)
\(380\) −7.66312 23.5847i −0.393110 1.20987i
\(381\) 0 0
\(382\) −3.73607 + 2.71441i −0.191154 + 0.138881i
\(383\) −8.30902 + 25.5725i −0.424571 + 1.30669i 0.478834 + 0.877906i \(0.341060\pi\)
−0.903405 + 0.428789i \(0.858940\pi\)
\(384\) 0 0
\(385\) −25.4164 + 5.70634i −1.29534 + 0.290822i
\(386\) −11.4721 −0.583916
\(387\) 0 0
\(388\) −18.3713 + 13.3475i −0.932663 + 0.677619i
\(389\) 19.6353 + 14.2658i 0.995547 + 0.723307i 0.961129 0.276100i \(-0.0890422\pi\)
0.0344181 + 0.999408i \(0.489042\pi\)
\(390\) 0 0
\(391\) 1.73607 + 5.34307i 0.0877967 + 0.270211i
\(392\) 3.61803 + 2.62866i 0.182738 + 0.132767i
\(393\) 0 0
\(394\) −4.65654 + 14.3314i −0.234593 + 0.722003i
\(395\) 24.7984 1.24774
\(396\) 0 0
\(397\) −38.7082 −1.94271 −0.971355 0.237635i \(-0.923628\pi\)
−0.971355 + 0.237635i \(0.923628\pi\)
\(398\) −3.19098 + 9.82084i −0.159950 + 0.492274i
\(399\) 0 0
\(400\) −2.78115 2.02063i −0.139058 0.101031i
\(401\) 8.06231 + 24.8132i 0.402612 + 1.23911i 0.922873 + 0.385106i \(0.125835\pi\)
−0.520260 + 0.854008i \(0.674165\pi\)
\(402\) 0 0
\(403\) −4.07295 2.95917i −0.202888 0.147407i
\(404\) 3.92705 2.85317i 0.195378 0.141950i
\(405\) 0 0
\(406\) −8.29180 −0.411515
\(407\) −0.0729490 + 0.779543i −0.00361595 + 0.0386405i
\(408\) 0 0
\(409\) −3.41641 + 10.5146i −0.168930 + 0.519915i −0.999304 0.0372920i \(-0.988127\pi\)
0.830374 + 0.557207i \(0.188127\pi\)
\(410\) −15.6353 + 11.3597i −0.772170 + 0.561014i
\(411\) 0 0
\(412\) 3.00000 + 9.23305i 0.147799 + 0.454880i
\(413\) −9.57295 29.4625i −0.471054 1.44976i
\(414\) 0 0
\(415\) 1.50000 1.08981i 0.0736321 0.0534969i
\(416\) 3.06231 9.42481i 0.150142 0.462089i
\(417\) 0 0
\(418\) 7.92705 9.00854i 0.387725 0.440622i
\(419\) −16.5066 −0.806399 −0.403200 0.915112i \(-0.632102\pi\)
−0.403200 + 0.915112i \(0.632102\pi\)
\(420\) 0 0
\(421\) 30.1525 21.9071i 1.46954 1.06768i 0.488795 0.872398i \(-0.337436\pi\)
0.980746 0.195286i \(-0.0625636\pi\)
\(422\) 11.1353 + 8.09024i 0.542056 + 0.393827i
\(423\) 0 0
\(424\) −6.64590 20.4540i −0.322753 0.993333i
\(425\) 2.42705 + 1.76336i 0.117729 + 0.0855353i
\(426\) 0 0
\(427\) 7.28115 22.4091i 0.352360 1.08445i
\(428\) −6.85410 −0.331306
\(429\) 0 0
\(430\) 10.0902 0.486591
\(431\) 12.2082 37.5730i 0.588048 1.80983i 0.00138127 0.999999i \(-0.499560\pi\)
0.586667 0.809828i \(-0.300440\pi\)
\(432\) 0 0
\(433\) 4.85410 + 3.52671i 0.233273 + 0.169483i 0.698281 0.715824i \(-0.253949\pi\)
−0.465008 + 0.885307i \(0.653949\pi\)
\(434\) 1.63525 + 5.03280i 0.0784947 + 0.241582i
\(435\) 0 0
\(436\) 0 0
\(437\) 16.4443 11.9475i 0.786636 0.571525i
\(438\) 0 0
\(439\) 3.29180 0.157109 0.0785544 0.996910i \(-0.474970\pi\)
0.0785544 + 0.996910i \(0.474970\pi\)
\(440\) 1.80902 19.3314i 0.0862415 0.921588i
\(441\) 0 0
\(442\) −0.545085 + 1.67760i −0.0259270 + 0.0797952i
\(443\) −33.2705 + 24.1724i −1.58073 + 1.14847i −0.664877 + 0.746953i \(0.731516\pi\)
−0.915853 + 0.401514i \(0.868484\pi\)
\(444\) 0 0
\(445\) −0.427051 1.31433i −0.0202442 0.0623051i
\(446\) 0.135255 + 0.416272i 0.00640451 + 0.0197110i
\(447\) 0 0
\(448\) 0.572949 0.416272i 0.0270693 0.0196670i
\(449\) 7.56231 23.2744i 0.356887 1.09839i −0.598020 0.801481i \(-0.704046\pi\)
0.954907 0.296905i \(-0.0959544\pi\)
\(450\) 0 0
\(451\) 36.3713 + 15.6987i 1.71266 + 0.739222i
\(452\) 1.14590 0.0538985
\(453\) 0 0
\(454\) −12.4443 + 9.04129i −0.584039 + 0.424329i
\(455\) −11.2082 8.14324i −0.525449 0.381761i
\(456\) 0 0
\(457\) 2.53444 + 7.80021i 0.118556 + 0.364878i 0.992672 0.120839i \(-0.0385584\pi\)
−0.874116 + 0.485717i \(0.838558\pi\)
\(458\) −5.00000 3.63271i −0.233635 0.169746i
\(459\) 0 0
\(460\) 4.54508 13.9883i 0.211916 0.652209i
\(461\) 21.0902 0.982267 0.491134 0.871084i \(-0.336583\pi\)
0.491134 + 0.871084i \(0.336583\pi\)
\(462\) 0 0
\(463\) −15.7984 −0.734213 −0.367106 0.930179i \(-0.619651\pi\)
−0.367106 + 0.930179i \(0.619651\pi\)
\(464\) −2.56231 + 7.88597i −0.118952 + 0.366097i
\(465\) 0 0
\(466\) 12.1631 + 8.83702i 0.563446 + 0.409367i
\(467\) 3.01722 + 9.28605i 0.139620 + 0.429707i 0.996280 0.0861747i \(-0.0274643\pi\)
−0.856660 + 0.515882i \(0.827464\pi\)
\(468\) 0 0
\(469\) 23.2082 + 16.8617i 1.07166 + 0.778603i
\(470\) 2.11803 1.53884i 0.0976976 0.0709815i
\(471\) 0 0
\(472\) 23.0902 1.06281
\(473\) −10.5451 17.7926i −0.484864 0.818103i
\(474\) 0 0
\(475\) 3.35410 10.3229i 0.153897 0.473646i
\(476\) −6.35410 + 4.61653i −0.291240 + 0.211598i
\(477\) 0 0
\(478\) −0.489357 1.50609i −0.0223827 0.0688868i
\(479\) 8.68034 + 26.7153i 0.396615 + 1.22066i 0.927697 + 0.373335i \(0.121786\pi\)
−0.531082 + 0.847320i \(0.678214\pi\)
\(480\) 0 0
\(481\) −0.336881 + 0.244758i −0.0153605 + 0.0111600i
\(482\) −4.41641 + 13.5923i −0.201162 + 0.619113i
\(483\) 0 0
\(484\) −16.0902 + 7.60845i −0.731371 + 0.345839i
\(485\) −36.7426 −1.66840
\(486\) 0 0
\(487\) −13.6074 + 9.88635i −0.616610 + 0.447993i −0.851736 0.523972i \(-0.824450\pi\)
0.235126 + 0.971965i \(0.424450\pi\)
\(488\) 14.2082 + 10.3229i 0.643175 + 0.467294i
\(489\) 0 0
\(490\) 1.00000 + 3.07768i 0.0451754 + 0.139036i
\(491\) 20.3992 + 14.8209i 0.920602 + 0.668857i 0.943674 0.330877i \(-0.107345\pi\)
−0.0230715 + 0.999734i \(0.507345\pi\)
\(492\) 0 0
\(493\) 2.23607 6.88191i 0.100707 0.309946i
\(494\) 6.38197 0.287138
\(495\) 0 0
\(496\) 5.29180 0.237609
\(497\) 5.15654 15.8702i 0.231302 0.711876i
\(498\) 0 0
\(499\) 14.2082 + 10.3229i 0.636047 + 0.462115i 0.858490 0.512831i \(-0.171403\pi\)
−0.222443 + 0.974946i \(0.571403\pi\)
\(500\) 4.11803 + 12.6740i 0.184164 + 0.566799i
\(501\) 0 0
\(502\) −3.89919 2.83293i −0.174029 0.126440i
\(503\) 22.7082 16.4985i 1.01251 0.735631i 0.0477750 0.998858i \(-0.484787\pi\)
0.964734 + 0.263227i \(0.0847870\pi\)
\(504\) 0 0
\(505\) 7.85410 0.349503
\(506\) 6.94427 1.55909i 0.308711 0.0693098i
\(507\) 0 0
\(508\) 1.85410 5.70634i 0.0822625 0.253178i
\(509\) 19.1074 13.8823i 0.846920 0.615324i −0.0773749 0.997002i \(-0.524654\pi\)
0.924295 + 0.381679i \(0.124654\pi\)
\(510\) 0 0
\(511\) −3.00000 9.23305i −0.132712 0.408446i
\(512\) 5.78115 + 17.7926i 0.255493 + 0.786327i
\(513\) 0 0
\(514\) −5.83688 + 4.24074i −0.257454 + 0.187051i
\(515\) −4.85410 + 14.9394i −0.213897 + 0.658308i
\(516\) 0 0
\(517\) −4.92705 2.12663i −0.216691 0.0935289i
\(518\) 0.437694 0.0192312
\(519\) 0 0
\(520\) 8.35410 6.06961i 0.366352 0.266170i
\(521\) −12.0000 8.71851i −0.525730 0.381965i 0.293028 0.956104i \(-0.405337\pi\)
−0.818758 + 0.574139i \(0.805337\pi\)
\(522\) 0 0
\(523\) −3.70163 11.3924i −0.161861 0.498156i 0.836930 0.547309i \(-0.184348\pi\)
−0.998791 + 0.0491529i \(0.984348\pi\)
\(524\) 9.35410 + 6.79615i 0.408636 + 0.296891i
\(525\) 0 0
\(526\) 3.11803 9.59632i 0.135953 0.418420i
\(527\) −4.61803 −0.201165
\(528\) 0 0
\(529\) −10.9443 −0.475838
\(530\) 4.80902 14.8006i 0.208890 0.642898i
\(531\) 0 0
\(532\) 22.9894 + 16.7027i 0.996715 + 0.724156i
\(533\) 6.51064 + 20.0377i 0.282007 + 0.867929i
\(534\) 0 0
\(535\) −8.97214 6.51864i −0.387899 0.281825i
\(536\) −17.2984 + 12.5680i −0.747176 + 0.542855i
\(537\) 0 0
\(538\) −9.59675 −0.413745
\(539\) 4.38197 4.97980i 0.188745 0.214495i
\(540\) 0 0
\(541\) 6.04508 18.6049i 0.259899 0.799885i −0.732926 0.680308i \(-0.761846\pi\)
0.992825 0.119577i \(-0.0381540\pi\)
\(542\) 13.6353 9.90659i 0.585684 0.425525i
\(543\) 0 0
\(544\) −2.80902 8.64527i −0.120436 0.370663i
\(545\) 0 0
\(546\) 0 0
\(547\) −17.4894 + 12.7068i −0.747791 + 0.543302i −0.895141 0.445782i \(-0.852925\pi\)
0.147350 + 0.989084i \(0.452925\pi\)
\(548\) 3.73607 11.4984i 0.159597 0.491189i
\(549\) 0 0
\(550\) 2.51064 2.85317i 0.107054 0.121660i
\(551\) −26.1803 −1.11532
\(552\) 0 0
\(553\) −22.9894 + 16.7027i −0.977607 + 0.710273i
\(554\) −15.2812 11.1024i −0.649234 0.471696i
\(555\) 0 0
\(556\) 0.427051 + 1.31433i 0.0181110 + 0.0557399i
\(557\) 12.0623 + 8.76378i 0.511096 + 0.371333i 0.813239 0.581929i \(-0.197702\pi\)
−0.302143 + 0.953263i \(0.597702\pi\)
\(558\) 0 0
\(559\) 3.39919 10.4616i 0.143770 0.442479i
\(560\) 14.5623 0.615370
\(561\) 0 0
\(562\) 0.472136 0.0199159
\(563\) 2.74671 8.45351i 0.115760 0.356273i −0.876345 0.481684i \(-0.840025\pi\)
0.992105 + 0.125412i \(0.0400251\pi\)
\(564\) 0 0
\(565\) 1.50000 + 1.08981i 0.0631055 + 0.0458488i
\(566\) 0.0344419 + 0.106001i 0.00144770 + 0.00445556i
\(567\) 0 0
\(568\) 10.0623 + 7.31069i 0.422205 + 0.306750i
\(569\) −19.4721 + 14.1473i −0.816314 + 0.593087i −0.915654 0.401966i \(-0.868327\pi\)
0.0993400 + 0.995054i \(0.468327\pi\)
\(570\) 0 0
\(571\) 34.6869 1.45160 0.725801 0.687905i \(-0.241469\pi\)
0.725801 + 0.687905i \(0.241469\pi\)
\(572\) −8.69098 3.75123i −0.363388 0.156847i
\(573\) 0 0
\(574\) 6.84346 21.0620i 0.285640 0.879111i
\(575\) 5.20820 3.78398i 0.217197 0.157803i
\(576\) 0 0
\(577\) 3.32624 + 10.2371i 0.138473 + 0.426176i 0.996114 0.0880726i \(-0.0280707\pi\)
−0.857641 + 0.514249i \(0.828071\pi\)
\(578\) −2.74671 8.45351i −0.114248 0.351620i
\(579\) 0 0
\(580\) −15.3262 + 11.1352i −0.636387 + 0.462363i
\(581\) −0.656541 + 2.02063i −0.0272379 + 0.0838297i
\(582\) 0 0
\(583\) −31.1246 + 6.98791i −1.28905 + 0.289410i
\(584\) 7.23607 0.299431
\(585\) 0 0
\(586\) 0.0278640 0.0202444i 0.00115105 0.000836289i
\(587\) −30.9894 22.5151i −1.27907 0.929297i −0.279543 0.960133i \(-0.590183\pi\)
−0.999524 + 0.0308361i \(0.990183\pi\)
\(588\) 0 0
\(589\) 5.16312 + 15.8904i 0.212743 + 0.654754i
\(590\) 13.5172 + 9.82084i 0.556495 + 0.404317i
\(591\) 0 0
\(592\) 0.135255 0.416272i 0.00555894 0.0171087i
\(593\) −22.2148 −0.912252 −0.456126 0.889915i \(-0.650763\pi\)
−0.456126 + 0.889915i \(0.650763\pi\)
\(594\) 0 0
\(595\) −12.7082 −0.520986
\(596\) 7.50000 23.0826i 0.307212 0.945501i
\(597\) 0 0
\(598\) 3.06231 + 2.22490i 0.125227 + 0.0909827i
\(599\) 2.56231 + 7.88597i 0.104693 + 0.322212i 0.989658 0.143445i \(-0.0458181\pi\)
−0.884965 + 0.465657i \(0.845818\pi\)
\(600\) 0 0
\(601\) −27.3713 19.8864i −1.11650 0.811184i −0.132825 0.991140i \(-0.542405\pi\)
−0.983675 + 0.179955i \(0.942405\pi\)
\(602\) −9.35410 + 6.79615i −0.381245 + 0.276991i
\(603\) 0 0
\(604\) −3.23607 −0.131674
\(605\) −28.2984 5.34307i −1.15049 0.217227i
\(606\) 0 0
\(607\) 4.11803 12.6740i 0.167146 0.514422i −0.832042 0.554712i \(-0.812828\pi\)
0.999188 + 0.0402904i \(0.0128283\pi\)
\(608\) −26.6074 + 19.3314i −1.07907 + 0.783992i
\(609\) 0 0
\(610\) 3.92705 + 12.0862i 0.159002 + 0.489357i
\(611\) −0.881966 2.71441i −0.0356805 0.109813i
\(612\) 0 0
\(613\) −28.0344 + 20.3682i −1.13230 + 0.822664i −0.986028 0.166580i \(-0.946728\pi\)
−0.146272 + 0.989244i \(0.546728\pi\)
\(614\) 0.107391 0.330515i 0.00433394 0.0133385i
\(615\) 0 0
\(616\) 11.3435 + 19.1396i 0.457041 + 0.771158i
\(617\) −19.5836 −0.788406 −0.394203 0.919023i \(-0.628979\pi\)
−0.394203 + 0.919023i \(0.628979\pi\)
\(618\) 0 0
\(619\) 7.13525 5.18407i 0.286790 0.208365i −0.435084 0.900390i \(-0.643281\pi\)
0.721874 + 0.692025i \(0.243281\pi\)
\(620\) 9.78115 + 7.10642i 0.392821 + 0.285401i
\(621\) 0 0
\(622\) −0.482779 1.48584i −0.0193577 0.0595768i
\(623\) 1.28115 + 0.930812i 0.0513283 + 0.0372922i
\(624\) 0 0
\(625\) −9.52786 + 29.3238i −0.381115 + 1.17295i
\(626\) 15.9656 0.638112
\(627\) 0 0
\(628\) 6.00000 0.239426
\(629\) −0.118034 + 0.363271i −0.00470632 + 0.0144846i
\(630\) 0 0
\(631\) −37.4336 27.1971i −1.49021 1.08270i −0.974084 0.226187i \(-0.927374\pi\)
−0.516125 0.856513i \(-0.672626\pi\)
\(632\) −6.54508 20.1437i −0.260350 0.801273i
\(633\) 0 0
\(634\) −9.68034 7.03318i −0.384455 0.279323i
\(635\) 7.85410 5.70634i 0.311681 0.226449i
\(636\) 0 0
\(637\) 3.52786 0.139779
\(638\) −8.41641 3.63271i −0.333209 0.143820i
\(639\) 0 0
\(640\) −9.20820 + 28.3399i −0.363986 + 1.12023i
\(641\) 28.9164 21.0090i 1.14213 0.829806i 0.154715 0.987959i \(-0.450554\pi\)
0.987415 + 0.158154i \(0.0505541\pi\)
\(642\) 0 0
\(643\) −11.9164 36.6749i −0.469937 1.44632i −0.852666 0.522457i \(-0.825015\pi\)
0.382728 0.923861i \(-0.374985\pi\)
\(644\) 5.20820 + 16.0292i 0.205232 + 0.631639i
\(645\) 0 0
\(646\) 4.73607 3.44095i 0.186338 0.135383i
\(647\) −8.59017 + 26.4378i −0.337714 + 1.03938i 0.627655 + 0.778492i \(0.284015\pi\)
−0.965369 + 0.260887i \(0.915985\pi\)
\(648\) 0 0
\(649\) 3.19098 34.0993i 0.125257 1.33851i
\(650\) 2.02129 0.0792814
\(651\) 0 0
\(652\) 23.9164 17.3763i 0.936639 0.680508i
\(653\) 41.2877 + 29.9973i 1.61571 + 1.17388i 0.839323 + 0.543632i \(0.182951\pi\)
0.776390 + 0.630252i \(0.217049\pi\)
\(654\) 0 0
\(655\) 5.78115 + 17.7926i 0.225888 + 0.695213i
\(656\) −17.9164 13.0170i −0.699518 0.508230i
\(657\) 0 0
\(658\) −0.927051 + 2.85317i −0.0361402 + 0.111228i
\(659\) 10.6525 0.414962 0.207481 0.978239i \(-0.433474\pi\)
0.207481 + 0.978239i \(0.433474\pi\)
\(660\) 0 0
\(661\) −9.90983 −0.385448 −0.192724 0.981253i \(-0.561732\pi\)
−0.192724 + 0.981253i \(0.561732\pi\)
\(662\) 5.07953 15.6332i 0.197421 0.607601i
\(663\) 0 0
\(664\) −1.28115 0.930812i −0.0497184 0.0361225i
\(665\) 14.2082 + 43.7284i 0.550971 + 1.69571i
\(666\) 0 0
\(667\) −12.5623 9.12705i −0.486414 0.353401i
\(668\) −13.1353 + 9.54332i −0.508218 + 0.369242i
\(669\) 0 0
\(670\) −15.4721 −0.597741
\(671\) 17.2082 19.5559i 0.664315 0.754948i
\(672\) 0 0
\(673\) 3.83688 11.8087i 0.147901 0.455192i −0.849472 0.527634i \(-0.823079\pi\)
0.997373 + 0.0724420i \(0.0230792\pi\)
\(674\) 0.145898 0.106001i 0.00561978 0.00408301i
\(675\) 0 0
\(676\) 4.94427 + 15.2169i 0.190164 + 0.585266i
\(677\) −4.18034 12.8658i −0.160664 0.494471i 0.838027 0.545629i \(-0.183709\pi\)
−0.998691 + 0.0511572i \(0.983709\pi\)
\(678\) 0 0
\(679\) 34.0623 24.7477i 1.30719 0.949730i
\(680\) 2.92705 9.00854i 0.112247 0.345462i
\(681\) 0 0
\(682\) −0.545085 + 5.82485i −0.0208724 + 0.223045i
\(683\) 3.11146 0.119057 0.0595283 0.998227i \(-0.481040\pi\)
0.0595283 + 0.998227i \(0.481040\pi\)
\(684\) 0 0
\(685\) 15.8262 11.4984i 0.604689 0.439333i
\(686\) 7.50000 + 5.44907i 0.286351 + 0.208046i
\(687\) 0 0
\(688\) 3.57295 + 10.9964i 0.136217 + 0.419234i
\(689\) −13.7254 9.97210i −0.522897 0.379907i
\(690\) 0 0
\(691\) −8.12461 + 25.0050i −0.309075 + 0.951234i 0.669050 + 0.743217i \(0.266701\pi\)
−0.978125 + 0.208017i \(0.933299\pi\)
\(692\) 24.8885 0.946120
\(693\) 0 0
\(694\) 12.9443 0.491358
\(695\) −0.690983 + 2.12663i −0.0262105 + 0.0806676i
\(696\) 0 0
\(697\) 15.6353 + 11.3597i 0.592228 + 0.430278i
\(698\) −1.93363 5.95110i −0.0731889 0.225252i
\(699\) 0 0
\(700\) 7.28115 + 5.29007i 0.275202 + 0.199946i
\(701\) −8.64590 + 6.28161i −0.326551 + 0.237253i −0.738966 0.673743i \(-0.764685\pi\)
0.412415 + 0.910996i \(0.364685\pi\)
\(702\) 0 0
\(703\) 1.38197 0.0521218
\(704\) 0.763932 0.171513i 0.0287918 0.00646416i
\(705\) 0 0
\(706\) 2.00000 6.15537i 0.0752710 0.231660i
\(707\) −7.28115 + 5.29007i −0.273836 + 0.198953i
\(708\) 0 0
\(709\) 15.0623 + 46.3570i 0.565677 + 1.74097i 0.665932 + 0.746012i \(0.268034\pi\)
−0.100255 + 0.994962i \(0.531966\pi\)
\(710\) 2.78115 + 8.55951i 0.104375 + 0.321233i
\(711\) 0 0
\(712\) −0.954915 + 0.693786i −0.0357870 + 0.0260007i
\(713\) −3.06231 + 9.42481i −0.114684 + 0.352962i
\(714\) 0 0
\(715\) −7.80902 13.1760i −0.292041 0.492756i
\(716\) −3.61803 −0.135212
\(717\) 0 0
\(718\) −6.38197 + 4.63677i −0.238173 + 0.173043i
\(719\) −1.28115 0.930812i −0.0477789 0.0347134i 0.563639 0.826021i \(-0.309401\pi\)
−0.611418 + 0.791307i \(0.709401\pi\)
\(720\) 0 0
\(721\) −5.56231 17.1190i −0.207151 0.637546i
\(722\) −7.63525 5.54734i −0.284155 0.206451i
\(723\) 0 0
\(724\) 8.73607 26.8869i 0.324673 0.999242i
\(725\) −8.29180 −0.307950
\(726\) 0 0
\(727\) 38.8541 1.44102 0.720509 0.693445i \(-0.243908\pi\)
0.720509 + 0.693445i \(0.243908\pi\)
\(728\) −3.65654 + 11.2537i −0.135520 + 0.417089i
\(729\) 0 0
\(730\) 4.23607 + 3.07768i 0.156784 + 0.113910i
\(731\) −3.11803 9.59632i −0.115325 0.354933i
\(732\) 0 0
\(733\) 30.5066 + 22.1643i 1.12679 + 0.818658i 0.985224 0.171271i \(-0.0547875\pi\)
0.141562 + 0.989929i \(0.454787\pi\)
\(734\) −2.78115 + 2.02063i −0.102654 + 0.0745827i
\(735\) 0 0
\(736\) −19.5066 −0.719022
\(737\) 16.1697 + 27.2829i 0.595618 + 1.00498i
\(738\) 0 0
\(739\) −7.72542 + 23.7764i −0.284184 + 0.874629i 0.702458 + 0.711726i \(0.252086\pi\)
−0.986642 + 0.162904i \(0.947914\pi\)
\(740\) 0.809017 0.587785i 0.0297401 0.0216074i
\(741\) 0 0
\(742\) 5.51064 + 16.9600i 0.202302 + 0.622622i
\(743\) −10.8713 33.4585i −0.398830 1.22747i −0.925938 0.377675i \(-0.876724\pi\)
0.527108 0.849798i \(-0.323276\pi\)
\(744\) 0 0
\(745\) 31.7705 23.0826i 1.16398 0.845682i
\(746\) −0.843459 + 2.59590i −0.0308812 + 0.0950426i
\(747\) 0 0
\(748\) −8.47214 + 1.90211i −0.309772 + 0.0695481i
\(749\) 12.7082 0.464348
\(750\) 0 0
\(751\) −9.64590 + 7.00816i −0.351984 + 0.255731i −0.749701 0.661777i \(-0.769803\pi\)
0.397717 + 0.917508i \(0.369803\pi\)
\(752\) 2.42705 + 1.76336i 0.0885054 + 0.0643030i
\(753\) 0 0
\(754\) −1.50658 4.63677i −0.0548663 0.168861i
\(755\) −4.23607 3.07768i −0.154166 0.112008i
\(756\) 0 0
\(757\) 0.600813 1.84911i 0.0218369 0.0672071i −0.939544 0.342428i \(-0.888751\pi\)
0.961381 + 0.275220i \(0.0887509\pi\)
\(758\) 0.978714 0.0355485
\(759\) 0 0
\(760\) −34.2705 −1.24312
\(761\) 9.54508 29.3768i 0.346009 1.06491i −0.615032 0.788502i \(-0.710857\pi\)
0.961041 0.276404i \(-0.0891429\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −3.73607 11.4984i −0.135166 0.415999i
\(765\) 0 0
\(766\) 13.4443 + 9.76784i 0.485761 + 0.352926i
\(767\) 14.7361 10.7064i 0.532089 0.386585i
\(768\) 0 0
\(769\) 12.6869 0.457502 0.228751 0.973485i \(-0.426536\pi\)
0.228751 + 0.973485i \(0.426536\pi\)
\(770\) −1.50000 + 16.0292i −0.0540562 + 0.577652i
\(771\) 0 0
\(772\) 9.28115 28.5645i 0.334036 1.02806i
\(773\) −25.2812 + 18.3678i −0.909300 + 0.660645i −0.940838 0.338858i \(-0.889960\pi\)
0.0315378 + 0.999503i \(0.489960\pi\)
\(774\) 0 0
\(775\) 1.63525 + 5.03280i 0.0587401 + 0.180783i
\(776\) 9.69756 + 29.8460i 0.348122 + 1.07141i
\(777\) 0 0
\(778\) 12.1353 8.81678i 0.435070 0.316097i
\(779\) 21.6074 66.5007i 0.774165 2.38264i
\(780\) 0 0
\(781\) 12.1869 13.8496i 0.436082 0.495577i
\(782\) 3.47214 0.124163
\(783\) 0 0
\(784\) −3.00000 + 2.17963i −0.107143 + 0.0778438i
\(785\) 7.85410 + 5.70634i 0.280325 + 0.203668i
\(786\) 0 0
\(787\) −3.18034 9.78808i −0.113367 0.348907i 0.878236 0.478227i \(-0.158721\pi\)
−0.991603 + 0.129320i \(0.958721\pi\)
\(788\) −31.9164 23.1886i −1.13697 0.826061i
\(789\) 0 0
\(790\) 4.73607 14.5761i 0.168502 0.518595i
\(791\) −2.12461 −0.0755425
\(792\) 0 0
\(793\) 13.8541 0.491974
\(794\) −7.39261 + 22.7521i −0.262354 + 0.807442i
\(795\) 0 0
\(796\) −21.8713 15.8904i −0.775208 0.563222i
\(797\) −3.32624 10.2371i