Properties

Label 819.2.fm.e.370.7
Level $819$
Weight $2$
Character 819.370
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
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.fm (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 370.7
Character \(\chi\) \(=\) 819.370
Dual form 819.2.fm.e.622.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500642 + 1.86842i) q^{2} +(-1.50830 + 0.870817i) q^{4} +(-2.44068 - 2.44068i) q^{5} +(2.02526 + 1.70244i) q^{7} +(0.353388 + 0.353388i) q^{8} +O(q^{10})\) \(q+(0.500642 + 1.86842i) q^{2} +(-1.50830 + 0.870817i) q^{4} +(-2.44068 - 2.44068i) q^{5} +(2.02526 + 1.70244i) q^{7} +(0.353388 + 0.353388i) q^{8} +(3.33831 - 5.78213i) q^{10} +(-2.85290 + 0.764433i) q^{11} +(3.60488 - 0.0697642i) q^{13} +(-2.16695 + 4.63635i) q^{14} +(-2.22499 + 3.85380i) q^{16} +(0.667729 + 1.15654i) q^{17} +(-1.32547 + 4.94673i) q^{19} +(5.80667 + 1.55589i) q^{20} +(-2.85656 - 4.94771i) q^{22} +(7.61450 + 4.39623i) q^{23} +6.91386i q^{25} +(1.93510 + 6.70049i) q^{26} +(-4.53722 - 0.804162i) q^{28} +(-3.97913 + 6.89205i) q^{29} +(-2.04259 - 2.04259i) q^{31} +(-7.34896 - 1.96915i) q^{32} +(-1.82661 + 1.82661i) q^{34} +(-0.787896 - 9.09815i) q^{35} +(4.73577 - 1.26895i) q^{37} -9.90616 q^{38} -1.72501i q^{40} +(1.45657 - 0.390287i) q^{41} +(-0.212417 + 0.122639i) q^{43} +(3.63735 - 3.63735i) q^{44} +(-4.40187 + 16.4280i) q^{46} +(1.13049 - 1.13049i) q^{47} +(1.20337 + 6.89579i) q^{49} +(-12.9180 + 3.46137i) q^{50} +(-5.37648 + 3.24441i) q^{52} -2.62146 q^{53} +(8.82877 + 5.09729i) q^{55} +(0.114080 + 1.31732i) q^{56} +(-14.8694 - 3.98423i) q^{58} +(-3.96915 - 1.06353i) q^{59} +(-7.82911 + 4.52014i) q^{61} +(2.79382 - 4.83903i) q^{62} -5.81681i q^{64} +(-8.96863 - 8.62809i) q^{65} +(-2.97553 - 11.1048i) q^{67} +(-2.01427 - 1.16294i) q^{68} +(16.6047 - 6.02703i) q^{70} +(11.0479 + 2.96028i) q^{71} +(1.06136 - 1.06136i) q^{73} +(4.74184 + 8.21311i) q^{74} +(-2.30849 - 8.61540i) q^{76} +(-7.07928 - 3.30873i) q^{77} +7.65266 q^{79} +(14.8364 - 3.97540i) q^{80} +(1.45844 + 2.52609i) q^{82} +(10.1314 + 10.1314i) q^{83} +(1.19303 - 4.45246i) q^{85} +(-0.335486 - 0.335486i) q^{86} +(-1.27832 - 0.738039i) q^{88} +(-4.11486 - 15.3569i) q^{89} +(7.41959 + 5.99581i) q^{91} -15.3133 q^{92} +(2.67819 + 1.54626i) q^{94} +(15.3085 - 8.83835i) q^{95} +(3.28484 - 12.2592i) q^{97} +(-12.2818 + 5.70072i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + O(q^{10}) \) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + 2q^{10} + 4q^{11} + 6q^{13} - 34q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 44q^{20} - 4q^{22} + 18q^{23} + 28q^{26} - 32q^{28} + 18q^{29} - 14q^{31} + 8q^{32} - 66q^{34} - 22q^{35} - 24q^{37} - 24q^{38} - 6q^{43} + 20q^{44} - 58q^{46} + 28q^{47} + 8q^{49} - 70q^{50} + 28q^{52} + 80q^{53} + 60q^{55} + 54q^{56} - 4q^{58} + 42q^{59} + 36q^{61} - 52q^{62} - 14q^{65} + 26q^{67} + 72q^{68} - 116q^{70} + 4q^{71} + 12q^{73} + 18q^{74} - 48q^{76} - 28q^{77} - 4q^{79} + 98q^{80} + 20q^{82} + 36q^{83} - 10q^{85} + 40q^{86} + 96q^{88} + 54q^{89} + 148q^{91} + 4q^{92} - 60q^{95} - 40q^{97} - 36q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500642 + 1.86842i 0.354007 + 1.32117i 0.881729 + 0.471755i \(0.156379\pi\)
−0.527722 + 0.849417i \(0.676954\pi\)
\(3\) 0 0
\(4\) −1.50830 + 0.870817i −0.754150 + 0.435408i
\(5\) −2.44068 2.44068i −1.09151 1.09151i −0.995368 0.0961385i \(-0.969351\pi\)
−0.0961385 0.995368i \(-0.530649\pi\)
\(6\) 0 0
\(7\) 2.02526 + 1.70244i 0.765477 + 0.643463i
\(8\) 0.353388 + 0.353388i 0.124941 + 0.124941i
\(9\) 0 0
\(10\) 3.33831 5.78213i 1.05567 1.82847i
\(11\) −2.85290 + 0.764433i −0.860183 + 0.230485i −0.661838 0.749647i \(-0.730223\pi\)
−0.198345 + 0.980132i \(0.563557\pi\)
\(12\) 0 0
\(13\) 3.60488 0.0697642i 0.999813 0.0193491i
\(14\) −2.16695 + 4.63635i −0.579142 + 1.23912i
\(15\) 0 0
\(16\) −2.22499 + 3.85380i −0.556247 + 0.963449i
\(17\) 0.667729 + 1.15654i 0.161948 + 0.280502i 0.935567 0.353149i \(-0.114889\pi\)
−0.773619 + 0.633651i \(0.781556\pi\)
\(18\) 0 0
\(19\) −1.32547 + 4.94673i −0.304084 + 1.13486i 0.629646 + 0.776882i \(0.283200\pi\)
−0.933731 + 0.357977i \(0.883467\pi\)
\(20\) 5.80667 + 1.55589i 1.29841 + 0.347908i
\(21\) 0 0
\(22\) −2.85656 4.94771i −0.609022 1.05486i
\(23\) 7.61450 + 4.39623i 1.58773 + 0.916678i 0.993680 + 0.112253i \(0.0358066\pi\)
0.594053 + 0.804426i \(0.297527\pi\)
\(24\) 0 0
\(25\) 6.91386i 1.38277i
\(26\) 1.93510 + 6.70049i 0.379504 + 1.31408i
\(27\) 0 0
\(28\) −4.53722 0.804162i −0.857454 0.151972i
\(29\) −3.97913 + 6.89205i −0.738905 + 1.27982i 0.214084 + 0.976815i \(0.431323\pi\)
−0.952989 + 0.303006i \(0.902010\pi\)
\(30\) 0 0
\(31\) −2.04259 2.04259i −0.366861 0.366861i 0.499470 0.866331i \(-0.333528\pi\)
−0.866331 + 0.499470i \(0.833528\pi\)
\(32\) −7.34896 1.96915i −1.29912 0.348099i
\(33\) 0 0
\(34\) −1.82661 + 1.82661i −0.313261 + 0.313261i
\(35\) −0.787896 9.09815i −0.133179 1.53787i
\(36\) 0 0
\(37\) 4.73577 1.26895i 0.778555 0.208613i 0.152408 0.988318i \(-0.451297\pi\)
0.626148 + 0.779704i \(0.284631\pi\)
\(38\) −9.90616 −1.60699
\(39\) 0 0
\(40\) 1.72501i 0.272749i
\(41\) 1.45657 0.390287i 0.227478 0.0609527i −0.143279 0.989682i \(-0.545765\pi\)
0.370758 + 0.928730i \(0.379098\pi\)
\(42\) 0 0
\(43\) −0.212417 + 0.122639i −0.0323933 + 0.0187023i −0.516109 0.856523i \(-0.672620\pi\)
0.483716 + 0.875225i \(0.339287\pi\)
\(44\) 3.63735 3.63735i 0.548351 0.548351i
\(45\) 0 0
\(46\) −4.40187 + 16.4280i −0.649021 + 2.42218i
\(47\) 1.13049 1.13049i 0.164899 0.164899i −0.619834 0.784733i \(-0.712800\pi\)
0.784733 + 0.619834i \(0.212800\pi\)
\(48\) 0 0
\(49\) 1.20337 + 6.89579i 0.171910 + 0.985113i
\(50\) −12.9180 + 3.46137i −1.82688 + 0.489511i
\(51\) 0 0
\(52\) −5.37648 + 3.24441i −0.745584 + 0.449919i
\(53\) −2.62146 −0.360085 −0.180043 0.983659i \(-0.557624\pi\)
−0.180043 + 0.983659i \(0.557624\pi\)
\(54\) 0 0
\(55\) 8.82877 + 5.09729i 1.19047 + 0.687319i
\(56\) 0.114080 + 1.31732i 0.0152446 + 0.176035i
\(57\) 0 0
\(58\) −14.8694 3.98423i −1.95244 0.523155i
\(59\) −3.96915 1.06353i −0.516739 0.138460i −0.00898130 0.999960i \(-0.502859\pi\)
−0.507758 + 0.861500i \(0.669526\pi\)
\(60\) 0 0
\(61\) −7.82911 + 4.52014i −1.00241 + 0.578744i −0.908962 0.416879i \(-0.863124\pi\)
−0.0934527 + 0.995624i \(0.529790\pi\)
\(62\) 2.79382 4.83903i 0.354815 0.614558i
\(63\) 0 0
\(64\) 5.81681i 0.727101i
\(65\) −8.96863 8.62809i −1.11242 1.07018i
\(66\) 0 0
\(67\) −2.97553 11.1048i −0.363519 1.35667i −0.869417 0.494079i \(-0.835505\pi\)
0.505898 0.862593i \(-0.331161\pi\)
\(68\) −2.01427 1.16294i −0.244266 0.141027i
\(69\) 0 0
\(70\) 16.6047 6.02703i 1.98464 0.720368i
\(71\) 11.0479 + 2.96028i 1.31115 + 0.351320i 0.845654 0.533732i \(-0.179211\pi\)
0.465492 + 0.885052i \(0.345877\pi\)
\(72\) 0 0
\(73\) 1.06136 1.06136i 0.124222 0.124222i −0.642262 0.766485i \(-0.722004\pi\)
0.766485 + 0.642262i \(0.222004\pi\)
\(74\) 4.74184 + 8.21311i 0.551228 + 0.954755i
\(75\) 0 0
\(76\) −2.30849 8.61540i −0.264802 0.988254i
\(77\) −7.07928 3.30873i −0.806759 0.377065i
\(78\) 0 0
\(79\) 7.65266 0.860992 0.430496 0.902593i \(-0.358339\pi\)
0.430496 + 0.902593i \(0.358339\pi\)
\(80\) 14.8364 3.97540i 1.65876 0.444463i
\(81\) 0 0
\(82\) 1.45844 + 2.52609i 0.161058 + 0.278960i
\(83\) 10.1314 + 10.1314i 1.11207 + 1.11207i 0.992871 + 0.119194i \(0.0380311\pi\)
0.119194 + 0.992871i \(0.461969\pi\)
\(84\) 0 0
\(85\) 1.19303 4.45246i 0.129403 0.482937i
\(86\) −0.335486 0.335486i −0.0361763 0.0361763i
\(87\) 0 0
\(88\) −1.27832 0.738039i −0.136270 0.0786753i
\(89\) −4.11486 15.3569i −0.436174 1.62782i −0.738241 0.674537i \(-0.764343\pi\)
0.302067 0.953287i \(-0.402323\pi\)
\(90\) 0 0
\(91\) 7.41959 + 5.99581i 0.777784 + 0.628531i
\(92\) −15.3133 −1.59652
\(93\) 0 0
\(94\) 2.67819 + 1.54626i 0.276235 + 0.159484i
\(95\) 15.3085 8.83835i 1.57062 0.906795i
\(96\) 0 0
\(97\) 3.28484 12.2592i 0.333525 1.24473i −0.571934 0.820300i \(-0.693807\pi\)
0.905459 0.424433i \(-0.139527\pi\)
\(98\) −12.2818 + 5.70072i −1.24065 + 0.575860i
\(99\) 0 0
\(100\) −6.02071 10.4282i −0.602071 1.04282i
\(101\) 4.49790 7.79059i 0.447558 0.775192i −0.550669 0.834724i \(-0.685627\pi\)
0.998226 + 0.0595314i \(0.0189606\pi\)
\(102\) 0 0
\(103\) −6.31734 −0.622466 −0.311233 0.950334i \(-0.600742\pi\)
−0.311233 + 0.950334i \(0.600742\pi\)
\(104\) 1.29857 + 1.24926i 0.127335 + 0.122500i
\(105\) 0 0
\(106\) −1.31241 4.89799i −0.127473 0.475735i
\(107\) 9.52494 16.4977i 0.920810 1.59489i 0.122646 0.992450i \(-0.460862\pi\)
0.798164 0.602440i \(-0.205805\pi\)
\(108\) 0 0
\(109\) −9.27465 + 9.27465i −0.888351 + 0.888351i −0.994365 0.106014i \(-0.966191\pi\)
0.106014 + 0.994365i \(0.466191\pi\)
\(110\) −5.10383 + 19.0478i −0.486631 + 1.81613i
\(111\) 0 0
\(112\) −11.0671 + 4.01702i −1.04574 + 0.379573i
\(113\) 3.53376 + 6.12066i 0.332429 + 0.575783i 0.982987 0.183673i \(-0.0587986\pi\)
−0.650559 + 0.759456i \(0.725465\pi\)
\(114\) 0 0
\(115\) −7.85477 29.3144i −0.732461 2.73358i
\(116\) 13.8604i 1.28690i
\(117\) 0 0
\(118\) 7.94848i 0.731717i
\(119\) −0.616619 + 3.47907i −0.0565254 + 0.318925i
\(120\) 0 0
\(121\) −1.97158 + 1.13829i −0.179234 + 0.103481i
\(122\) −12.3651 12.3651i −1.11948 1.11948i
\(123\) 0 0
\(124\) 4.85957 + 1.30212i 0.436402 + 0.116934i
\(125\) 4.67113 4.67113i 0.417799 0.417799i
\(126\) 0 0
\(127\) 12.2515 + 7.07343i 1.08715 + 0.627665i 0.932816 0.360354i \(-0.117344\pi\)
0.154332 + 0.988019i \(0.450677\pi\)
\(128\) −3.82967 + 1.02616i −0.338498 + 0.0907002i
\(129\) 0 0
\(130\) 11.6308 21.0767i 1.02009 1.84855i
\(131\) 9.97987i 0.871945i 0.899960 + 0.435973i \(0.143596\pi\)
−0.899960 + 0.435973i \(0.856404\pi\)
\(132\) 0 0
\(133\) −11.1060 + 7.76189i −0.963009 + 0.673041i
\(134\) 19.2588 11.1191i 1.66371 0.960543i
\(135\) 0 0
\(136\) −0.172740 + 0.644674i −0.0148123 + 0.0552803i
\(137\) 0.141310 0.527376i 0.0120729 0.0450567i −0.959627 0.281277i \(-0.909242\pi\)
0.971700 + 0.236220i \(0.0759087\pi\)
\(138\) 0 0
\(139\) −2.89550 + 1.67172i −0.245593 + 0.141793i −0.617745 0.786379i \(-0.711953\pi\)
0.372152 + 0.928172i \(0.378620\pi\)
\(140\) 9.11120 + 13.0366i 0.770037 + 1.10179i
\(141\) 0 0
\(142\) 22.1242i 1.85662i
\(143\) −10.2310 + 2.95472i −0.855562 + 0.247086i
\(144\) 0 0
\(145\) 26.5331 7.10952i 2.20345 0.590413i
\(146\) 2.51442 + 1.45170i 0.208095 + 0.120144i
\(147\) 0 0
\(148\) −6.03794 + 6.03794i −0.496315 + 0.496315i
\(149\) 8.56339 + 2.29455i 0.701540 + 0.187977i 0.591920 0.805996i \(-0.298370\pi\)
0.109620 + 0.993974i \(0.465037\pi\)
\(150\) 0 0
\(151\) −10.4345 10.4345i −0.849144 0.849144i 0.140882 0.990026i \(-0.455006\pi\)
−0.990026 + 0.140882i \(0.955006\pi\)
\(152\) −2.21652 + 1.27971i −0.179784 + 0.103798i
\(153\) 0 0
\(154\) 2.63792 14.8836i 0.212569 1.19935i
\(155\) 9.97065i 0.800862i
\(156\) 0 0
\(157\) 1.05925i 0.0845376i 0.999106 + 0.0422688i \(0.0134586\pi\)
−0.999106 + 0.0422688i \(0.986541\pi\)
\(158\) 3.83124 + 14.2984i 0.304797 + 1.13752i
\(159\) 0 0
\(160\) 13.1304 + 22.7425i 1.03805 + 1.79795i
\(161\) 7.93702 + 21.8668i 0.625525 + 1.72334i
\(162\) 0 0
\(163\) 2.76615 10.3234i 0.216661 0.808591i −0.768914 0.639353i \(-0.779202\pi\)
0.985575 0.169239i \(-0.0541309\pi\)
\(164\) −1.85708 + 1.85708i −0.145013 + 0.145013i
\(165\) 0 0
\(166\) −13.8575 + 24.0019i −1.07555 + 1.86291i
\(167\) 0.203527 + 0.759573i 0.0157494 + 0.0587775i 0.973353 0.229310i \(-0.0736471\pi\)
−0.957604 + 0.288088i \(0.906980\pi\)
\(168\) 0 0
\(169\) 12.9903 0.502983i 0.999251 0.0386910i
\(170\) 8.91635 0.683853
\(171\) 0 0
\(172\) 0.213592 0.369952i 0.0162862 0.0282086i
\(173\) −2.78559 4.82478i −0.211784 0.366821i 0.740489 0.672069i \(-0.234594\pi\)
−0.952273 + 0.305248i \(0.901261\pi\)
\(174\) 0 0
\(175\) −11.7705 + 14.0024i −0.889763 + 1.05848i
\(176\) 3.40171 12.6954i 0.256414 0.956949i
\(177\) 0 0
\(178\) 26.6330 15.3766i 1.99623 1.15252i
\(179\) 3.04329 + 1.75705i 0.227466 + 0.131328i 0.609403 0.792861i \(-0.291409\pi\)
−0.381936 + 0.924189i \(0.624743\pi\)
\(180\) 0 0
\(181\) −23.3185 −1.73325 −0.866624 0.498961i \(-0.833715\pi\)
−0.866624 + 0.498961i \(0.833715\pi\)
\(182\) −7.48813 + 16.8647i −0.555057 + 1.25009i
\(183\) 0 0
\(184\) 1.13730 + 4.24444i 0.0838425 + 0.312905i
\(185\) −14.6556 8.46141i −1.07750 0.622096i
\(186\) 0 0
\(187\) −2.78906 2.78906i −0.203956 0.203956i
\(188\) −0.720666 + 2.68956i −0.0525599 + 0.196156i
\(189\) 0 0
\(190\) 24.1778 + 24.1778i 1.75404 + 1.75404i
\(191\) −6.95240 12.0419i −0.503058 0.871322i −0.999994 0.00353445i \(-0.998875\pi\)
0.496936 0.867787i \(-0.334458\pi\)
\(192\) 0 0
\(193\) 2.80644 0.751984i 0.202012 0.0541290i −0.156394 0.987695i \(-0.549987\pi\)
0.358406 + 0.933566i \(0.383320\pi\)
\(194\) 24.5499 1.76258
\(195\) 0 0
\(196\) −7.82001 9.35300i −0.558572 0.668071i
\(197\) −0.210804 0.786731i −0.0150192 0.0560523i 0.958010 0.286736i \(-0.0925703\pi\)
−0.973029 + 0.230684i \(0.925904\pi\)
\(198\) 0 0
\(199\) 0.861092 + 1.49145i 0.0610412 + 0.105726i 0.894931 0.446204i \(-0.147225\pi\)
−0.833890 + 0.551931i \(0.813891\pi\)
\(200\) −2.44327 + 2.44327i −0.172766 + 0.172766i
\(201\) 0 0
\(202\) 16.8079 + 4.50367i 1.18260 + 0.316877i
\(203\) −19.7921 + 7.18396i −1.38913 + 0.504215i
\(204\) 0 0
\(205\) −4.50760 2.60246i −0.314824 0.181764i
\(206\) −3.16272 11.8034i −0.220357 0.822385i
\(207\) 0 0
\(208\) −7.75196 + 14.0477i −0.537501 + 0.974031i
\(209\) 15.1258i 1.04627i
\(210\) 0 0
\(211\) −1.84269 + 3.19163i −0.126856 + 0.219721i −0.922457 0.386100i \(-0.873822\pi\)
0.795601 + 0.605821i \(0.207155\pi\)
\(212\) 3.95395 2.28281i 0.271558 0.156784i
\(213\) 0 0
\(214\) 35.5932 + 9.53716i 2.43310 + 0.651947i
\(215\) 0.817765 + 0.219119i 0.0557711 + 0.0149438i
\(216\) 0 0
\(217\) −0.659386 7.61419i −0.0447621 0.516885i
\(218\) −21.9722 12.6857i −1.48815 0.859182i
\(219\) 0 0
\(220\) −17.7552 −1.19706
\(221\) 2.48776 + 4.12260i 0.167345 + 0.277316i
\(222\) 0 0
\(223\) 18.0743 4.84300i 1.21035 0.324311i 0.403449 0.915002i \(-0.367811\pi\)
0.806898 + 0.590691i \(0.201145\pi\)
\(224\) −11.5312 16.4992i −0.770461 1.10240i
\(225\) 0 0
\(226\) −9.66681 + 9.66681i −0.643027 + 0.643027i
\(227\) 0.339915 1.26858i 0.0225609 0.0841985i −0.953727 0.300672i \(-0.902789\pi\)
0.976288 + 0.216474i \(0.0694556\pi\)
\(228\) 0 0
\(229\) 6.99659 6.99659i 0.462348 0.462348i −0.437077 0.899424i \(-0.643986\pi\)
0.899424 + 0.437077i \(0.143986\pi\)
\(230\) 50.8392 29.3520i 3.35224 1.93541i
\(231\) 0 0
\(232\) −3.84174 + 1.02939i −0.252222 + 0.0675828i
\(233\) 24.7335i 1.62035i 0.586189 + 0.810174i \(0.300627\pi\)
−0.586189 + 0.810174i \(0.699373\pi\)
\(234\) 0 0
\(235\) −5.51832 −0.359976
\(236\) 6.91280 1.85228i 0.449985 0.120573i
\(237\) 0 0
\(238\) −6.80906 + 0.589662i −0.441366 + 0.0382221i
\(239\) 7.30351 7.30351i 0.472425 0.472425i −0.430274 0.902698i \(-0.641583\pi\)
0.902698 + 0.430274i \(0.141583\pi\)
\(240\) 0 0
\(241\) −8.63024 2.31247i −0.555923 0.148959i −0.0300903 0.999547i \(-0.509579\pi\)
−0.525833 + 0.850588i \(0.676246\pi\)
\(242\) −3.11386 3.11386i −0.200166 0.200166i
\(243\) 0 0
\(244\) 7.87242 13.6354i 0.503980 0.872920i
\(245\) 13.8934 19.7675i 0.887616 1.26290i
\(246\) 0 0
\(247\) −4.43306 + 17.9248i −0.282069 + 1.14053i
\(248\) 1.44365i 0.0916722i
\(249\) 0 0
\(250\) 11.0662 + 6.38907i 0.699888 + 0.404081i
\(251\) −6.13739 10.6303i −0.387389 0.670977i 0.604709 0.796447i \(-0.293290\pi\)
−0.992097 + 0.125470i \(0.959956\pi\)
\(252\) 0 0
\(253\) −25.0841 6.72126i −1.57702 0.422562i
\(254\) −7.08250 + 26.4323i −0.444396 + 1.65851i
\(255\) 0 0
\(256\) −9.65139 16.7167i −0.603212 1.04479i
\(257\) 2.78870 4.83017i 0.173954 0.301298i −0.765845 0.643026i \(-0.777679\pi\)
0.939799 + 0.341728i \(0.111012\pi\)
\(258\) 0 0
\(259\) 11.7515 + 5.49243i 0.730201 + 0.341283i
\(260\) 21.0409 + 5.20370i 1.30490 + 0.322720i
\(261\) 0 0
\(262\) −18.6466 + 4.99634i −1.15199 + 0.308675i
\(263\) 0.243621 0.421964i 0.0150223 0.0260194i −0.858417 0.512953i \(-0.828551\pi\)
0.873439 + 0.486934i \(0.161885\pi\)
\(264\) 0 0
\(265\) 6.39815 + 6.39815i 0.393035 + 0.393035i
\(266\) −20.0626 16.8647i −1.23012 1.03404i
\(267\) 0 0
\(268\) 14.1583 + 14.1583i 0.864854 + 0.864854i
\(269\) −14.2503 + 8.22741i −0.868855 + 0.501634i −0.866968 0.498364i \(-0.833934\pi\)
−0.00188759 + 0.999998i \(0.500601\pi\)
\(270\) 0 0
\(271\) −5.62502 20.9928i −0.341695 1.27522i −0.896426 0.443194i \(-0.853845\pi\)
0.554730 0.832030i \(-0.312822\pi\)
\(272\) −5.94276 −0.360333
\(273\) 0 0
\(274\) 1.05610 0.0638016
\(275\) −5.28519 19.7246i −0.318709 1.18944i
\(276\) 0 0
\(277\) 23.9312 13.8167i 1.43789 0.830165i 0.440186 0.897907i \(-0.354913\pi\)
0.997703 + 0.0677412i \(0.0215792\pi\)
\(278\) −4.57307 4.57307i −0.274275 0.274275i
\(279\) 0 0
\(280\) 2.93674 3.49360i 0.175504 0.208783i
\(281\) −15.4703 15.4703i −0.922880 0.922880i 0.0743517 0.997232i \(-0.476311\pi\)
−0.997232 + 0.0743517i \(0.976311\pi\)
\(282\) 0 0
\(283\) 2.67677 4.63631i 0.159118 0.275600i −0.775433 0.631430i \(-0.782468\pi\)
0.934551 + 0.355830i \(0.115802\pi\)
\(284\) −19.2414 + 5.15572i −1.14177 + 0.305936i
\(285\) 0 0
\(286\) −10.6427 17.6366i −0.629318 1.04287i
\(287\) 3.61438 + 1.68930i 0.213350 + 0.0997161i
\(288\) 0 0
\(289\) 7.60828 13.1779i 0.447546 0.775172i
\(290\) 26.5671 + 46.0156i 1.56008 + 2.70213i
\(291\) 0 0
\(292\) −0.676596 + 2.52509i −0.0395948 + 0.147770i
\(293\) 11.8844 + 3.18441i 0.694294 + 0.186035i 0.588673 0.808371i \(-0.299650\pi\)
0.105620 + 0.994407i \(0.466317\pi\)
\(294\) 0 0
\(295\) 7.09169 + 12.2832i 0.412894 + 0.715154i
\(296\) 2.12199 + 1.22513i 0.123338 + 0.0712093i
\(297\) 0 0
\(298\) 17.1488i 0.993401i
\(299\) 27.7560 + 15.3167i 1.60517 + 0.885785i
\(300\) 0 0
\(301\) −0.638985 0.113252i −0.0368305 0.00652772i
\(302\) 14.2720 24.7199i 0.821263 1.42247i
\(303\) 0 0
\(304\) −16.1145 16.1145i −0.924232 0.924232i
\(305\) 30.1406 + 8.07615i 1.72585 + 0.462439i
\(306\) 0 0
\(307\) −8.36730 + 8.36730i −0.477547 + 0.477547i −0.904346 0.426799i \(-0.859641\pi\)
0.426799 + 0.904346i \(0.359641\pi\)
\(308\) 13.5590 1.17420i 0.772594 0.0669064i
\(309\) 0 0
\(310\) −18.6294 + 4.99172i −1.05808 + 0.283511i
\(311\) −2.28494 −0.129567 −0.0647836 0.997899i \(-0.520636\pi\)
−0.0647836 + 0.997899i \(0.520636\pi\)
\(312\) 0 0
\(313\) 24.6656i 1.39418i 0.716982 + 0.697091i \(0.245523\pi\)
−0.716982 + 0.697091i \(0.754477\pi\)
\(314\) −1.97913 + 0.530306i −0.111689 + 0.0299269i
\(315\) 0 0
\(316\) −11.5425 + 6.66407i −0.649317 + 0.374883i
\(317\) −3.55562 + 3.55562i −0.199704 + 0.199704i −0.799873 0.600169i \(-0.795100\pi\)
0.600169 + 0.799873i \(0.295100\pi\)
\(318\) 0 0
\(319\) 6.08355 22.7041i 0.340613 1.27119i
\(320\) −14.1970 + 14.1970i −0.793636 + 0.793636i
\(321\) 0 0
\(322\) −36.8827 + 25.7771i −2.05539 + 1.43650i
\(323\) −6.60615 + 1.77011i −0.367576 + 0.0984917i
\(324\) 0 0
\(325\) 0.482340 + 24.9236i 0.0267554 + 1.38251i
\(326\) 20.6733 1.14499
\(327\) 0 0
\(328\) 0.652657 + 0.376812i 0.0360370 + 0.0208060i
\(329\) 4.21412 0.364942i 0.232332 0.0201199i
\(330\) 0 0
\(331\) 17.6446 + 4.72784i 0.969832 + 0.259866i 0.708757 0.705453i \(-0.249256\pi\)
0.261075 + 0.965318i \(0.415923\pi\)
\(332\) −24.1038 6.45858i −1.32287 0.354461i
\(333\) 0 0
\(334\) −1.31731 + 0.760548i −0.0720798 + 0.0416153i
\(335\) −19.8411 + 34.3657i −1.08403 + 1.87760i
\(336\) 0 0
\(337\) 22.3954i 1.21996i −0.792418 0.609978i \(-0.791178\pi\)
0.792418 0.609978i \(-0.208822\pi\)
\(338\) 7.44325 + 24.0195i 0.404859 + 1.30649i
\(339\) 0 0
\(340\) 2.07783 + 7.75456i 0.112686 + 0.420550i
\(341\) 7.38875 + 4.26590i 0.400123 + 0.231011i
\(342\) 0 0
\(343\) −9.30255 + 16.0144i −0.502291 + 0.864699i
\(344\) −0.118405 0.0317264i −0.00638394 0.00171057i
\(345\) 0 0
\(346\) 7.62013 7.62013i 0.409661 0.409661i
\(347\) −7.01258 12.1461i −0.376455 0.652039i 0.614089 0.789237i \(-0.289524\pi\)
−0.990544 + 0.137198i \(0.956190\pi\)
\(348\) 0 0
\(349\) 2.12038 + 7.91338i 0.113502 + 0.423594i 0.999170 0.0407238i \(-0.0129664\pi\)
−0.885669 + 0.464317i \(0.846300\pi\)
\(350\) −32.0551 14.9820i −1.71342 0.800821i
\(351\) 0 0
\(352\) 22.4711 1.19772
\(353\) 25.1216 6.73131i 1.33709 0.358271i 0.481734 0.876318i \(-0.340007\pi\)
0.855353 + 0.518046i \(0.173341\pi\)
\(354\) 0 0
\(355\) −19.7393 34.1895i −1.04766 1.81459i
\(356\) 19.5794 + 19.5794i 1.03771 + 1.03771i
\(357\) 0 0
\(358\) −1.75930 + 6.56579i −0.0929819 + 0.347013i
\(359\) −3.71625 3.71625i −0.196136 0.196136i 0.602205 0.798341i \(-0.294289\pi\)
−0.798341 + 0.602205i \(0.794289\pi\)
\(360\) 0 0
\(361\) −6.25881 3.61353i −0.329411 0.190186i
\(362\) −11.6742 43.5687i −0.613582 2.28992i
\(363\) 0 0
\(364\) −16.4122 2.58237i −0.860234 0.135353i
\(365\) −5.18087 −0.271179
\(366\) 0 0
\(367\) 26.8907 + 15.5253i 1.40368 + 0.810416i 0.994768 0.102157i \(-0.0325744\pi\)
0.408913 + 0.912573i \(0.365908\pi\)
\(368\) −33.8844 + 19.5632i −1.76634 + 1.01980i
\(369\) 0 0
\(370\) 8.47227 31.6189i 0.440452 1.64379i
\(371\) −5.30914 4.46289i −0.275637 0.231702i
\(372\) 0 0
\(373\) −6.35916 11.0144i −0.329265 0.570304i 0.653101 0.757271i \(-0.273468\pi\)
−0.982366 + 0.186967i \(0.940134\pi\)
\(374\) 3.81482 6.60746i 0.197260 0.341664i
\(375\) 0 0
\(376\) 0.799000 0.0412053
\(377\) −13.8634 + 25.1226i −0.714003 + 1.29388i
\(378\) 0 0
\(379\) −5.03747 18.8001i −0.258757 0.965696i −0.965961 0.258686i \(-0.916710\pi\)
0.707204 0.707010i \(-0.249956\pi\)
\(380\) −15.3932 + 26.6617i −0.789653 + 1.36772i
\(381\) 0 0
\(382\) 19.0187 19.0187i 0.973080 0.973080i
\(383\) 1.38240 5.15917i 0.0706372 0.263621i −0.921572 0.388209i \(-0.873094\pi\)
0.992209 + 0.124587i \(0.0397607\pi\)
\(384\) 0 0
\(385\) 9.20272 + 25.3538i 0.469014 + 1.29215i
\(386\) 2.81004 + 4.86714i 0.143028 + 0.247731i
\(387\) 0 0
\(388\) 5.72099 + 21.3510i 0.290439 + 1.08393i
\(389\) 3.01128i 0.152678i −0.997082 0.0763390i \(-0.975677\pi\)
0.997082 0.0763390i \(-0.0243231\pi\)
\(390\) 0 0
\(391\) 11.7420i 0.593817i
\(392\) −2.01163 + 2.86214i −0.101603 + 0.144560i
\(393\) 0 0
\(394\) 1.36441 0.787740i 0.0687378 0.0396858i
\(395\) −18.6777 18.6777i −0.939778 0.939778i
\(396\) 0 0
\(397\) −13.7845 3.69353i −0.691822 0.185373i −0.104257 0.994550i \(-0.533247\pi\)
−0.587565 + 0.809177i \(0.699913\pi\)
\(398\) −2.35556 + 2.35556i −0.118074 + 0.118074i
\(399\) 0 0
\(400\) −26.6446 15.3833i −1.33223 0.769164i
\(401\) −29.6397 + 7.94193i −1.48014 + 0.396601i −0.906393 0.422435i \(-0.861176\pi\)
−0.573742 + 0.819036i \(0.694509\pi\)
\(402\) 0 0
\(403\) −7.50580 7.22080i −0.373891 0.359694i
\(404\) 15.6674i 0.779481i
\(405\) 0 0
\(406\) −23.3314 33.3833i −1.15792 1.65679i
\(407\) −12.5407 + 7.24036i −0.621618 + 0.358891i
\(408\) 0 0
\(409\) −2.88987 + 10.7851i −0.142895 + 0.533291i 0.856945 + 0.515408i \(0.172359\pi\)
−0.999840 + 0.0178834i \(0.994307\pi\)
\(410\) 2.60580 9.72499i 0.128691 0.480283i
\(411\) 0 0
\(412\) 9.52844 5.50125i 0.469433 0.271027i
\(413\) −6.22797 8.91118i −0.306458 0.438490i
\(414\) 0 0
\(415\) 49.4550i 2.42765i
\(416\) −26.6295 6.58584i −1.30562 0.322897i
\(417\) 0 0
\(418\) 28.2613 7.57260i 1.38231 0.370388i
\(419\) −9.49737 5.48331i −0.463977 0.267877i 0.249738 0.968313i \(-0.419655\pi\)
−0.713715 + 0.700436i \(0.752989\pi\)
\(420\) 0 0
\(421\) 6.63694 6.63694i 0.323465 0.323465i −0.526630 0.850095i \(-0.676545\pi\)
0.850095 + 0.526630i \(0.176545\pi\)
\(422\) −6.88584 1.84505i −0.335197 0.0898159i
\(423\) 0 0
\(424\) −0.926392 0.926392i −0.0449895 0.0449895i
\(425\) −7.99616 + 4.61658i −0.387871 + 0.223937i
\(426\) 0 0
\(427\) −23.5513 4.17415i −1.13973 0.202001i
\(428\) 33.1779i 1.60371i
\(429\) 0 0
\(430\) 1.63763i 0.0789734i
\(431\) −8.92021 33.2907i −0.429671 1.60355i −0.753506 0.657441i \(-0.771639\pi\)
0.323835 0.946114i \(-0.395028\pi\)
\(432\) 0 0
\(433\) 19.6718 + 34.0725i 0.945365 + 1.63742i 0.755019 + 0.655703i \(0.227628\pi\)
0.190346 + 0.981717i \(0.439039\pi\)
\(434\) 13.8964 5.04399i 0.667048 0.242119i
\(435\) 0 0
\(436\) 5.91243 22.0655i 0.283154 1.05674i
\(437\) −31.8398 + 31.8398i −1.52311 + 1.52311i
\(438\) 0 0
\(439\) −0.862363 + 1.49366i −0.0411583 + 0.0712883i −0.885871 0.463932i \(-0.846438\pi\)
0.844712 + 0.535220i \(0.179771\pi\)
\(440\) 1.31866 + 4.92130i 0.0628645 + 0.234614i
\(441\) 0 0
\(442\) −6.45727 + 6.71213i −0.307141 + 0.319264i
\(443\) 3.62484 0.172221 0.0861107 0.996286i \(-0.472556\pi\)
0.0861107 + 0.996286i \(0.472556\pi\)
\(444\) 0 0
\(445\) −27.4382 + 47.5243i −1.30069 + 2.25287i
\(446\) 18.0975 + 31.3458i 0.856943 + 1.48427i
\(447\) 0 0
\(448\) 9.90279 11.7806i 0.467863 0.556579i
\(449\) −3.15356 + 11.7692i −0.148826 + 0.555425i 0.850730 + 0.525604i \(0.176160\pi\)
−0.999555 + 0.0298212i \(0.990506\pi\)
\(450\) 0 0
\(451\) −3.85711 + 2.22690i −0.181624 + 0.104861i
\(452\) −10.6599 6.15452i −0.501402 0.289484i
\(453\) 0 0
\(454\) 2.54041 0.119227
\(455\) −3.47499 32.7427i −0.162910 1.53500i
\(456\) 0 0
\(457\) −4.20527 15.6943i −0.196714 0.734147i −0.991816 0.127672i \(-0.959250\pi\)
0.795102 0.606475i \(-0.207417\pi\)
\(458\) 16.5754 + 9.56978i 0.774515 + 0.447167i
\(459\) 0 0
\(460\) 37.3748 + 37.3748i 1.74261 + 1.74261i
\(461\) 0.972700 3.63017i 0.0453031 0.169074i −0.939568 0.342363i \(-0.888773\pi\)
0.984871 + 0.173289i \(0.0554395\pi\)
\(462\) 0 0
\(463\) −8.26689 8.26689i −0.384195 0.384195i 0.488416 0.872611i \(-0.337575\pi\)
−0.872611 + 0.488416i \(0.837575\pi\)
\(464\) −17.7070 30.6695i −0.822028 1.42379i
\(465\) 0 0
\(466\) −46.2126 + 12.3826i −2.14076 + 0.573615i
\(467\) 32.1951 1.48981 0.744905 0.667170i \(-0.232495\pi\)
0.744905 + 0.667170i \(0.232495\pi\)
\(468\) 0 0
\(469\) 12.8791 27.5559i 0.594703 1.27241i
\(470\) −2.76270 10.3105i −0.127434 0.475590i
\(471\) 0 0
\(472\) −1.02681 1.77849i −0.0472627 0.0818615i
\(473\) 0.512255 0.512255i 0.0235535 0.0235535i
\(474\) 0 0
\(475\) −34.2010 9.16414i −1.56925 0.420480i
\(476\) −2.09958 5.78444i −0.0962343 0.265129i
\(477\) 0 0
\(478\) 17.3025 + 9.98958i 0.791396 + 0.456913i
\(479\) −0.610243 2.27746i −0.0278827 0.104060i 0.950582 0.310473i \(-0.100487\pi\)
−0.978465 + 0.206413i \(0.933821\pi\)
\(480\) 0 0
\(481\) 16.9833 4.90478i 0.774373 0.223639i
\(482\) 17.2826i 0.787202i
\(483\) 0 0
\(484\) 1.98249 3.43377i 0.0901130 0.156080i
\(485\) −37.9381 + 21.9036i −1.72268 + 0.994589i
\(486\) 0 0
\(487\) −13.0172 3.48794i −0.589864 0.158054i −0.0484729 0.998824i \(-0.515435\pi\)
−0.541391 + 0.840771i \(0.682102\pi\)
\(488\) −4.36407 1.16935i −0.197552 0.0529339i
\(489\) 0 0
\(490\) 43.8895 + 16.0623i 1.98273 + 0.725619i
\(491\) 24.0166 + 13.8660i 1.08386 + 0.625764i 0.931934 0.362628i \(-0.118121\pi\)
0.151921 + 0.988393i \(0.451454\pi\)
\(492\) 0 0
\(493\) −10.6279 −0.478657
\(494\) −35.7105 + 0.691095i −1.60669 + 0.0310938i
\(495\) 0 0
\(496\) 12.4165 3.32699i 0.557517 0.149386i
\(497\) 17.3352 + 24.8038i 0.777590 + 1.11260i
\(498\) 0 0
\(499\) −12.5883 + 12.5883i −0.563529 + 0.563529i −0.930308 0.366779i \(-0.880460\pi\)
0.366779 + 0.930308i \(0.380460\pi\)
\(500\) −2.97776 + 11.1132i −0.133170 + 0.496996i
\(501\) 0 0
\(502\) 16.7892 16.7892i 0.749338 0.749338i
\(503\) 35.8460 20.6957i 1.59829 0.922776i 0.606479 0.795100i \(-0.292582\pi\)
0.991816 0.127676i \(-0.0407518\pi\)
\(504\) 0 0
\(505\) −29.9923 + 8.03641i −1.33464 + 0.357616i
\(506\) 50.2325i 2.23311i
\(507\) 0 0
\(508\) −24.6386 −1.09316
\(509\) 3.60857 0.966913i 0.159947 0.0428577i −0.177957 0.984038i \(-0.556949\pi\)
0.337904 + 0.941181i \(0.390282\pi\)
\(510\) 0 0
\(511\) 3.95643 0.342625i 0.175022 0.0151568i
\(512\) 20.7949 20.7949i 0.919014 0.919014i
\(513\) 0 0
\(514\) 10.4209 + 2.79228i 0.459647 + 0.123162i
\(515\) 15.4186 + 15.4186i 0.679426 + 0.679426i
\(516\) 0 0
\(517\) −2.36099 + 4.08935i −0.103836 + 0.179850i
\(518\) −4.37889 + 24.7064i −0.192397 + 1.08554i
\(519\) 0 0
\(520\) −0.120344 6.21846i −0.00527744 0.272698i
\(521\) 38.7341i 1.69697i 0.529219 + 0.848486i \(0.322485\pi\)
−0.529219 + 0.848486i \(0.677515\pi\)
\(522\) 0 0
\(523\) −30.8201 17.7940i −1.34767 0.778077i −0.359749 0.933049i \(-0.617138\pi\)
−0.987919 + 0.154972i \(0.950471\pi\)
\(524\) −8.69064 15.0526i −0.379652 0.657577i
\(525\) 0 0
\(526\) 0.910373 + 0.243934i 0.0396942 + 0.0106360i
\(527\) 0.998443 3.72624i 0.0434929 0.162318i
\(528\) 0 0
\(529\) 27.1537 + 47.0317i 1.18060 + 2.04486i
\(530\) −8.75125 + 15.1576i −0.380130 + 0.658405i
\(531\) 0 0
\(532\) 9.99194 21.3785i 0.433205 0.926876i
\(533\) 5.22354 1.50855i 0.226256 0.0653427i
\(534\) 0 0
\(535\) −63.5129 + 17.0182i −2.74590 + 0.735763i
\(536\) 2.87280 4.97583i 0.124086 0.214923i
\(537\) 0 0
\(538\) −22.5065 22.5065i −0.970326 0.970326i
\(539\) −8.70447 18.7531i −0.374928 0.807754i
\(540\) 0 0
\(541\) 12.2027 + 12.2027i 0.524634 + 0.524634i 0.918967 0.394333i \(-0.129025\pi\)
−0.394333 + 0.918967i \(0.629025\pi\)
\(542\) 36.4073 21.0198i 1.56383 0.902877i
\(543\) 0 0
\(544\) −2.62971 9.81422i −0.112748 0.420781i
\(545\) 45.2730 1.93928
\(546\) 0 0
\(547\) −12.9228 −0.552538 −0.276269 0.961080i \(-0.589098\pi\)
−0.276269 + 0.961080i \(0.589098\pi\)
\(548\) 0.246110 + 0.918495i 0.0105133 + 0.0392362i
\(549\) 0 0
\(550\) 34.2078 19.7499i 1.45863 0.842138i
\(551\) −28.8189 28.8189i −1.22773 1.22773i
\(552\) 0 0
\(553\) 15.4986 + 13.0282i 0.659069 + 0.554017i
\(554\) 37.7964 + 37.7964i 1.60581 + 1.60581i
\(555\) 0 0
\(556\) 2.91152 5.04289i 0.123476 0.213866i
\(557\) −5.77693 + 1.54792i −0.244777 + 0.0655877i −0.379121 0.925347i \(-0.623774\pi\)
0.134345 + 0.990935i \(0.457107\pi\)
\(558\) 0 0
\(559\) −0.757180 + 0.456917i −0.0320253 + 0.0193255i
\(560\) 36.8155 + 17.2069i 1.55574 + 0.727124i
\(561\) 0 0
\(562\) 21.1599 36.6501i 0.892578 1.54599i
\(563\) 3.80484 + 6.59017i 0.160355 + 0.277743i 0.934996 0.354658i \(-0.115403\pi\)
−0.774641 + 0.632401i \(0.782070\pi\)
\(564\) 0 0
\(565\) 6.31379 23.5634i 0.265623 0.991319i
\(566\) 10.0027 + 2.68021i 0.420443 + 0.112657i
\(567\) 0 0
\(568\) 2.85807 + 4.95032i 0.119922 + 0.207711i
\(569\) 23.3969 + 13.5082i 0.980848 + 0.566293i 0.902526 0.430635i \(-0.141711\pi\)
0.0783217 + 0.996928i \(0.475044\pi\)
\(570\) 0 0
\(571\) 17.2946i 0.723757i 0.932225 + 0.361878i \(0.117864\pi\)
−0.932225 + 0.361878i \(0.882136\pi\)
\(572\) 12.8584 13.3660i 0.537639 0.558859i
\(573\) 0 0
\(574\) −1.34681 + 7.59892i −0.0562147 + 0.317173i
\(575\) −30.3950 + 52.6456i −1.26756 + 2.19547i
\(576\) 0 0
\(577\) −1.06958 1.06958i −0.0445272 0.0445272i 0.684493 0.729020i \(-0.260024\pi\)
−0.729020 + 0.684493i \(0.760024\pi\)
\(578\) 28.4309 + 7.61804i 1.18257 + 0.316869i
\(579\) 0 0
\(580\) −33.8287 + 33.8287i −1.40466 + 1.40466i
\(581\) 3.27060 + 37.7669i 0.135687 + 1.56683i
\(582\) 0 0
\(583\) 7.47878 2.00393i 0.309739 0.0829944i
\(584\) 0.750141 0.0310410
\(585\) 0 0
\(586\) 23.7993i 0.983139i
\(587\) −42.5402 + 11.3986i −1.75582 + 0.470471i −0.985853 0.167613i \(-0.946394\pi\)
−0.769967 + 0.638083i \(0.779728\pi\)
\(588\) 0 0
\(589\) 12.8116 7.39677i 0.527892 0.304778i
\(590\) −19.3997 + 19.3997i −0.798674 + 0.798674i
\(591\) 0 0
\(592\) −5.64678 + 21.0741i −0.232081 + 0.866139i
\(593\) 14.9496 14.9496i 0.613907 0.613907i −0.330055 0.943962i \(-0.607067\pi\)
0.943962 + 0.330055i \(0.107067\pi\)
\(594\) 0 0
\(595\) 9.99627 6.98633i 0.409807 0.286411i
\(596\) −14.9143 + 3.99627i −0.610913 + 0.163694i
\(597\) 0 0
\(598\) −14.7221 + 59.5281i −0.602033 + 2.43428i
\(599\) −22.8397 −0.933203 −0.466601 0.884468i \(-0.654522\pi\)
−0.466601 + 0.884468i \(0.654522\pi\)
\(600\) 0 0
\(601\) 24.7100 + 14.2663i 1.00794 + 0.581936i 0.910589 0.413313i \(-0.135629\pi\)
0.0973547 + 0.995250i \(0.468962\pi\)
\(602\) −0.108301 1.25059i −0.00441401 0.0509703i
\(603\) 0 0
\(604\) 24.8248 + 6.65178i 1.01011 + 0.270657i
\(605\) 7.59020 + 2.03379i 0.308586 + 0.0826852i
\(606\) 0 0
\(607\) 22.6642 13.0852i 0.919913 0.531112i 0.0363055 0.999341i \(-0.488441\pi\)
0.883607 + 0.468229i \(0.155108\pi\)
\(608\) 19.4817 33.7433i 0.790087 1.36847i
\(609\) 0 0
\(610\) 60.3585i 2.44385i
\(611\) 3.99640 4.15413i 0.161677 0.168058i
\(612\) 0 0
\(613\) 7.15174 + 26.6907i 0.288856 + 1.07803i 0.945975 + 0.324239i \(0.105108\pi\)
−0.657119 + 0.753787i \(0.728225\pi\)
\(614\) −19.8226 11.4446i −0.799977 0.461867i
\(615\) 0 0
\(616\) −1.33247 3.67099i −0.0536866 0.147909i
\(617\) −18.4697 4.94894i −0.743562 0.199237i −0.132901 0.991129i \(-0.542429\pi\)
−0.610660 + 0.791893i \(0.709096\pi\)
\(618\) 0 0
\(619\) 5.80624 5.80624i 0.233373 0.233373i −0.580726 0.814099i \(-0.697231\pi\)
0.814099 + 0.580726i \(0.197231\pi\)
\(620\) −8.68261 15.0387i −0.348702 0.603970i
\(621\) 0 0
\(622\) −1.14394 4.26923i −0.0458677 0.171180i
\(623\) 17.8105 38.1070i 0.713563 1.52672i
\(624\) 0 0
\(625\) 11.7678 0.470712
\(626\) −46.0857 + 12.3486i −1.84196 + 0.493550i
\(627\) 0 0
\(628\) −0.922415 1.59767i −0.0368084 0.0637540i
\(629\) 4.62979 + 4.62979i 0.184602 + 0.184602i
\(630\) 0 0
\(631\) 1.64802 6.15049i 0.0656065 0.244847i −0.925333 0.379155i \(-0.876215\pi\)
0.990940 + 0.134308i \(0.0428813\pi\)
\(632\) 2.70436 + 2.70436i 0.107573 + 0.107573i
\(633\) 0 0
\(634\) −8.42348 4.86330i −0.334539 0.193146i
\(635\) −12.6381 47.1661i −0.501529 1.87173i
\(636\) 0 0
\(637\) 4.81908 + 24.7745i 0.190939 + 0.981602i
\(638\) 45.4665 1.80004
\(639\) 0 0
\(640\) 11.8515 + 6.84248i 0.468473 + 0.270473i
\(641\) 12.5318 7.23523i 0.494976 0.285774i −0.231660 0.972797i \(-0.574416\pi\)
0.726636 + 0.687022i \(0.241083\pi\)
\(642\) 0 0
\(643\) −7.35905 + 27.4644i −0.290213 + 1.08309i 0.654733 + 0.755861i \(0.272781\pi\)
−0.944945 + 0.327228i \(0.893885\pi\)
\(644\) −31.0134 26.0700i −1.22210 1.02730i
\(645\) 0 0
\(646\) −6.61463 11.4569i −0.260249 0.450765i
\(647\) 4.83456 8.37370i 0.190066 0.329204i −0.755206 0.655488i \(-0.772463\pi\)
0.945272 + 0.326284i \(0.105796\pi\)
\(648\) 0 0
\(649\) 12.1366 0.476403
\(650\) −46.3263 + 13.3790i −1.81707 + 0.524768i
\(651\) 0 0
\(652\) 4.81762 + 17.9796i 0.188672 + 0.704135i
\(653\) 16.6586 28.8535i 0.651900 1.12912i −0.330762 0.943714i \(-0.607306\pi\)
0.982661 0.185409i \(-0.0593610\pi\)
\(654\) 0 0
\(655\) 24.3577 24.3577i 0.951734 0.951734i
\(656\) −1.73677 + 6.48172i −0.0678095 + 0.253069i
\(657\) 0 0
\(658\) 2.79163 + 7.69105i 0.108829 + 0.299828i
\(659\) −13.4367 23.2730i −0.523418 0.906586i −0.999629 0.0272549i \(-0.991323\pi\)
0.476211 0.879331i \(-0.342010\pi\)
\(660\) 0 0
\(661\) 4.30948 + 16.0832i 0.167619 + 0.625564i 0.997692 + 0.0679081i \(0.0216325\pi\)
−0.830072 + 0.557656i \(0.811701\pi\)
\(662\) 35.3344i 1.37331i
\(663\) 0 0
\(664\) 7.16062i 0.277886i
\(665\) 46.0504 + 8.16184i 1.78576 + 0.316502i
\(666\) 0 0
\(667\) −60.5981 + 34.9863i −2.34637 + 1.35468i
\(668\) −0.968429 0.968429i −0.0374696 0.0374696i
\(669\) 0 0
\(670\) −74.1428 19.8665i −2.86439 0.767510i
\(671\) 18.8803 18.8803i 0.728868 0.728868i
\(672\) 0 0
\(673\) 22.1779 + 12.8044i 0.854896 + 0.493574i 0.862300 0.506398i \(-0.169023\pi\)
−0.00740398 + 0.999973i \(0.502357\pi\)
\(674\) 41.8440 11.2121i 1.61177 0.431873i
\(675\) 0 0
\(676\) −19.1552 + 12.0708i −0.736739 + 0.464261i
\(677\) 11.4036i 0.438275i 0.975694 + 0.219138i \(0.0703244\pi\)
−0.975694 + 0.219138i \(0.929676\pi\)
\(678\) 0 0
\(679\) 27.5233 19.2358i 1.05625 0.738203i
\(680\) 1.99505 1.15184i 0.0765066 0.0441711i
\(681\) 0 0
\(682\) −4.27137 + 15.9410i −0.163559 + 0.610412i
\(683\) −9.10656 + 33.9861i −0.348453 + 1.30044i 0.540073 + 0.841618i \(0.318396\pi\)
−0.888526 + 0.458826i \(0.848270\pi\)
\(684\) 0 0
\(685\) −1.63205 + 0.942264i −0.0623574 + 0.0360021i
\(686\) −34.5790 9.36357i −1.32023 0.357503i
\(687\) 0 0
\(688\) 1.09148i 0.0416123i
\(689\) −9.45004 + 0.182884i −0.360018 + 0.00696733i
\(690\) 0 0
\(691\) 40.2685 10.7899i 1.53189 0.410468i 0.608252 0.793744i \(-0.291871\pi\)
0.923634 + 0.383276i \(0.125204\pi\)
\(692\) 8.40300 + 4.85147i 0.319434 + 0.184425i
\(693\) 0 0
\(694\) 19.1833 19.1833i 0.728188 0.728188i
\(695\) 11.1471 + 2.98686i 0.422834 + 0.113298i
\(696\) 0 0
\(697\) 1.42398 + 1.42398i 0.0539370 + 0.0539370i
\(698\) −13.7240 + 7.92353i −0.519460 + 0.299910i
\(699\) 0 0
\(700\) 5.55987 31.3697i 0.210143 1.18566i
\(701\) 8.53135i 0.322225i −0.986936 0.161112i \(-0.948492\pi\)
0.986936 0.161112i \(-0.0515081\pi\)
\(702\) 0 0
\(703\) 25.1085i 0.946986i
\(704\) 4.44656 + 16.5948i 0.167586 + 0.625440i
\(705\) 0 0
\(706\) 25.1538 + 43.5677i 0.946676 + 1.63969i
\(707\) 22.3725 8.12056i 0.841403 0.305405i
\(708\) 0 0
\(709\) −0.424499 + 1.58425i −0.0159424 + 0.0594978i −0.973439 0.228947i \(-0.926472\pi\)
0.957496 + 0.288445i \(0.0931383\pi\)
\(710\) 53.9981 53.9981i 2.02651 2.02651i
\(711\) 0 0
\(712\) 3.97278 6.88106i 0.148886 0.257879i
\(713\) −6.57361 24.5331i −0.246184 0.918770i
\(714\) 0 0
\(715\) 32.1822 + 17.7592i 1.20355 + 0.664156i
\(716\) −6.12026 −0.228725
\(717\) 0 0
\(718\) 5.08300 8.80401i 0.189696 0.328563i
\(719\) −7.35184 12.7338i −0.274177 0.474889i 0.695750 0.718284i \(-0.255072\pi\)
−0.969927 + 0.243395i \(0.921739\pi\)
\(720\) 0 0
\(721\) −12.7943 10.7549i −0.476484 0.400534i
\(722\) 3.61816 13.5032i 0.134654 0.502536i
\(723\) 0 0
\(724\) 35.1712 20.3061i 1.30713 0.754671i
\(725\) −47.6507 27.5111i −1.76970 1.02174i
\(726\) 0 0
\(727\) 26.9644 1.00005 0.500026 0.866010i \(-0.333324\pi\)
0.500026 + 0.866010i \(0.333324\pi\)
\(728\) 0.503146 + 4.74083i 0.0186478 + 0.175707i
\(729\) 0 0
\(730\) −2.59376 9.68004i −0.0959993 0.358274i
\(731\) −0.283674 0.163779i −0.0104920 0.00605759i
\(732\) 0 0
\(733\) −27.0088 27.0088i −0.997593 0.997593i 0.00240406 0.999997i \(-0.499235\pi\)
−0.999997 + 0.00240406i \(0.999235\pi\)
\(734\) −15.5453 + 58.0157i −0.573786 + 2.14140i
\(735\) 0 0
\(736\) −47.3018 47.3018i −1.74357 1.74357i
\(737\) 16.9778 + 29.4064i 0.625386 + 1.08320i
\(738\) 0 0
\(739\) 45.4039 12.1659i 1.67021 0.447532i 0.705043 0.709165i \(-0.250928\pi\)
0.965167 + 0.261633i \(0.0842610\pi\)
\(740\) 29.4734 1.08346
\(741\) 0 0
\(742\) 5.68057 12.1540i 0.208540 0.446188i
\(743\) −7.20187 26.8777i −0.264211 0.986049i −0.962732 0.270459i \(-0.912825\pi\)
0.698521 0.715590i \(-0.253842\pi\)
\(744\) 0 0
\(745\) −15.3002 26.5008i −0.560557 0.970914i
\(746\) 17.3958 17.3958i 0.636907 0.636907i
\(747\) 0 0
\(748\) 6.63550 + 1.77798i 0.242618 + 0.0650093i
\(749\) 47.3769 17.1964i 1.73111 0.628344i
\(750\) 0 0
\(751\) 35.2503 + 20.3518i 1.28630 + 0.742647i 0.977993 0.208639i \(-0.0669034\pi\)
0.308310 + 0.951286i \(0.400237\pi\)
\(752\) 1.84134 + 6.87199i 0.0671469 + 0.250596i
\(753\) 0 0
\(754\) −53.8801 13.3253i −1.96220 0.485279i
\(755\) 50.9344i 1.85369i
\(756\) 0 0
\(757\) 6.21461 10.7640i 0.225874 0.391225i −0.730707 0.682691i \(-0.760810\pi\)
0.956581 + 0.291466i \(0.0941430\pi\)
\(758\) 32.6045 18.8242i 1.18425 0.683726i
\(759\) 0 0
\(760\) 8.53318 + 2.28646i 0.309531 + 0.0829386i
\(761\) 9.99508 + 2.67817i 0.362322 + 0.0970838i 0.435387 0.900243i \(-0.356612\pi\)
−0.0730655 + 0.997327i \(0.523278\pi\)
\(762\) 0 0
\(763\) −34.5732 + 2.99403i −1.25163 + 0.108391i
\(764\) 20.9726 + 12.1085i 0.758762 + 0.438071i
\(765\) 0 0
\(766\) 10.3316 0.373295
\(767\) −14.3825 3.55699i −0.519322 0.128435i
\(768\) 0 0
\(769\) 12.9631 3.47345i 0.467461 0.125256i −0.0173970 0.999849i \(-0.505538\pi\)
0.484858 + 0.874593i \(0.338871\pi\)
\(770\) −42.7644 + 29.8877i −1.54112 + 1.07708i
\(771\) 0 0
\(772\) −3.57812 + 3.57812i −0.128779 + 0.128779i
\(773\) −8.80996 + 32.8792i −0.316872 + 1.18258i 0.605362 + 0.795950i \(0.293028\pi\)
−0.922234 + 0.386632i \(0.873638\pi\)
\(774\) 0 0
\(775\) 14.1222 14.1222i 0.507285 0.507285i
\(776\) 5.49307 3.17143i 0.197190 0.113848i
\(777\) 0 0
\(778\) 5.62633 1.50757i 0.201714 0.0540491i
\(779\) 7.72259i 0.276691i
\(780\) 0 0
\(781\) −33.7816 −1.20880
\(782\) −21.9389 + 5.87852i −0.784534 + 0.210215i
\(783\) 0 0
\(784\) −29.2524 10.7055i −1.04473 0.382340i
\(785\) 2.58530 2.58530i 0.0922733 0.0922733i
\(786\) 0 0
\(787\) 44.0881 + 11.8134i 1.57157 + 0.421101i 0.936303 0.351192i \(-0.114224\pi\)
0.635267 + 0.772293i \(0.280890\pi\)
\(788\) 1.00305 + 1.00305i 0.0357323 + 0.0357323i