Properties

Label 325.2.e.b.276.1
Level $325$
Weight $2$
Character 325.276
Analytic conductor $2.595$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.59513806569\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \( x^{4} - x^{3} + 2x^{2} + x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 276.1
Root \(-0.309017 - 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 325.276
Dual form 325.2.e.b.126.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.309017 - 0.535233i) q^{2} +(1.11803 + 1.93649i) q^{3} +(0.809017 - 1.40126i) q^{4} +(0.690983 - 1.19682i) q^{6} +(2.11803 - 3.66854i) q^{7} -2.23607 q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.309017 - 0.535233i) q^{2} +(1.11803 + 1.93649i) q^{3} +(0.809017 - 1.40126i) q^{4} +(0.690983 - 1.19682i) q^{6} +(2.11803 - 3.66854i) q^{7} -2.23607 q^{8} +(-1.00000 + 1.73205i) q^{9} +(0.118034 + 0.204441i) q^{11} +3.61803 q^{12} +(1.00000 - 3.46410i) q^{13} -2.61803 q^{14} +(-0.927051 - 1.60570i) q^{16} +(-1.73607 + 3.00696i) q^{17} +1.23607 q^{18} +(-2.11803 + 3.66854i) q^{19} +9.47214 q^{21} +(0.0729490 - 0.126351i) q^{22} +(1.88197 + 3.25966i) q^{23} +(-2.50000 - 4.33013i) q^{24} +(-2.16312 + 0.535233i) q^{26} +2.23607 q^{27} +(-3.42705 - 5.93583i) q^{28} +(3.73607 + 6.47106i) q^{29} +(-2.80902 + 4.86536i) q^{32} +(-0.263932 + 0.457144i) q^{33} +2.14590 q^{34} +(1.61803 + 2.80252i) q^{36} +(1.50000 + 2.59808i) q^{37} +2.61803 q^{38} +(7.82624 - 1.93649i) q^{39} +(-5.97214 - 10.3440i) q^{41} +(-2.92705 - 5.06980i) q^{42} +(-3.11803 + 5.40059i) q^{43} +0.381966 q^{44} +(1.16312 - 2.01458i) q^{46} +4.94427 q^{47} +(2.07295 - 3.59045i) q^{48} +(-5.47214 - 9.47802i) q^{49} -7.76393 q^{51} +(-4.04508 - 4.20378i) q^{52} -6.00000 q^{53} +(-0.690983 - 1.19682i) q^{54} +(-4.73607 + 8.20311i) q^{56} -9.47214 q^{57} +(2.30902 - 3.99933i) q^{58} +(0.354102 - 0.613323i) q^{59} +(-7.20820 + 12.4850i) q^{61} +(4.23607 + 7.33708i) q^{63} -0.236068 q^{64} +0.326238 q^{66} +(-1.35410 - 2.34537i) q^{67} +(2.80902 + 4.86536i) q^{68} +(-4.20820 + 7.28882i) q^{69} +(3.11803 - 5.40059i) q^{71} +(2.23607 - 3.87298i) q^{72} +6.00000 q^{73} +(0.927051 - 1.60570i) q^{74} +(3.42705 + 5.93583i) q^{76} +1.00000 q^{77} +(-3.45492 - 3.59045i) q^{78} +(5.50000 + 9.52628i) q^{81} +(-3.69098 + 6.39297i) q^{82} -8.94427 q^{83} +(7.66312 - 13.2729i) q^{84} +3.85410 q^{86} +(-8.35410 + 14.4697i) q^{87} +(-0.263932 - 0.457144i) q^{88} +(4.50000 + 7.79423i) q^{89} +(-10.5902 - 11.0056i) q^{91} +6.09017 q^{92} +(-1.52786 - 2.64634i) q^{94} -12.5623 q^{96} +(-1.73607 + 3.00696i) q^{97} +(-3.38197 + 5.85774i) q^{98} -0.472136 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} + q^{4} + 5 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + q^{2} + q^{4} + 5 q^{6} + 4 q^{7} - 4 q^{9} - 4 q^{11} + 10 q^{12} + 4 q^{13} - 6 q^{14} + 3 q^{16} + 2 q^{17} - 4 q^{18} - 4 q^{19} + 20 q^{21} + 7 q^{22} + 12 q^{23} - 10 q^{24} + 7 q^{26} - 7 q^{28} + 6 q^{29} - 9 q^{32} - 10 q^{33} + 22 q^{34} + 2 q^{36} + 6 q^{37} + 6 q^{38} - 6 q^{41} - 5 q^{42} - 8 q^{43} + 6 q^{44} - 11 q^{46} - 16 q^{47} + 15 q^{48} - 4 q^{49} - 40 q^{51} - 5 q^{52} - 24 q^{53} - 5 q^{54} - 10 q^{56} - 20 q^{57} + 7 q^{58} - 12 q^{59} - 2 q^{61} + 8 q^{63} + 8 q^{64} - 30 q^{66} + 8 q^{67} + 9 q^{68} + 10 q^{69} + 8 q^{71} + 24 q^{73} - 3 q^{74} + 7 q^{76} + 4 q^{77} - 25 q^{78} + 22 q^{81} - 17 q^{82} + 15 q^{84} + 2 q^{86} - 20 q^{87} - 10 q^{88} + 18 q^{89} - 20 q^{91} + 2 q^{92} - 24 q^{94} - 10 q^{96} + 2 q^{97} - 18 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 0.535233i −0.218508 0.378467i 0.735844 0.677151i \(-0.236786\pi\)
−0.954352 + 0.298684i \(0.903452\pi\)
\(3\) 1.11803 + 1.93649i 0.645497 + 1.11803i 0.984186 + 0.177136i \(0.0566831\pi\)
−0.338689 + 0.940898i \(0.609984\pi\)
\(4\) 0.809017 1.40126i 0.404508 0.700629i
\(5\) 0 0
\(6\) 0.690983 1.19682i 0.282093 0.488599i
\(7\) 2.11803 3.66854i 0.800542 1.38658i −0.118718 0.992928i \(-0.537879\pi\)
0.919260 0.393651i \(-0.128788\pi\)
\(8\) −2.23607 −0.790569
\(9\) −1.00000 + 1.73205i −0.333333 + 0.577350i
\(10\) 0 0
\(11\) 0.118034 + 0.204441i 0.0355886 + 0.0616412i 0.883271 0.468863i \(-0.155336\pi\)
−0.847683 + 0.530504i \(0.822003\pi\)
\(12\) 3.61803 1.04444
\(13\) 1.00000 3.46410i 0.277350 0.960769i
\(14\) −2.61803 −0.699699
\(15\) 0 0
\(16\) −0.927051 1.60570i −0.231763 0.401425i
\(17\) −1.73607 + 3.00696i −0.421058 + 0.729294i −0.996043 0.0888696i \(-0.971675\pi\)
0.574985 + 0.818164i \(0.305008\pi\)
\(18\) 1.23607 0.291344
\(19\) −2.11803 + 3.66854i −0.485910 + 0.841621i −0.999869 0.0161937i \(-0.994845\pi\)
0.513959 + 0.857815i \(0.328179\pi\)
\(20\) 0 0
\(21\) 9.47214 2.06699
\(22\) 0.0729490 0.126351i 0.0155528 0.0269382i
\(23\) 1.88197 + 3.25966i 0.392417 + 0.679686i 0.992768 0.120051i \(-0.0383057\pi\)
−0.600351 + 0.799737i \(0.704972\pi\)
\(24\) −2.50000 4.33013i −0.510310 0.883883i
\(25\) 0 0
\(26\) −2.16312 + 0.535233i −0.424223 + 0.104968i
\(27\) 2.23607 0.430331
\(28\) −3.42705 5.93583i −0.647652 1.12177i
\(29\) 3.73607 + 6.47106i 0.693770 + 1.20165i 0.970593 + 0.240725i \(0.0773851\pi\)
−0.276823 + 0.960921i \(0.589282\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −2.80902 + 4.86536i −0.496569 + 0.860082i
\(33\) −0.263932 + 0.457144i −0.0459447 + 0.0795785i
\(34\) 2.14590 0.368018
\(35\) 0 0
\(36\) 1.61803 + 2.80252i 0.269672 + 0.467086i
\(37\) 1.50000 + 2.59808i 0.246598 + 0.427121i 0.962580 0.270998i \(-0.0873538\pi\)
−0.715981 + 0.698119i \(0.754020\pi\)
\(38\) 2.61803 0.424701
\(39\) 7.82624 1.93649i 1.25320 0.310087i
\(40\) 0 0
\(41\) −5.97214 10.3440i −0.932691 1.61547i −0.778701 0.627396i \(-0.784121\pi\)
−0.153990 0.988072i \(-0.549212\pi\)
\(42\) −2.92705 5.06980i −0.451654 0.782287i
\(43\) −3.11803 + 5.40059i −0.475496 + 0.823583i −0.999606 0.0280676i \(-0.991065\pi\)
0.524110 + 0.851650i \(0.324398\pi\)
\(44\) 0.381966 0.0575835
\(45\) 0 0
\(46\) 1.16312 2.01458i 0.171493 0.297034i
\(47\) 4.94427 0.721196 0.360598 0.932721i \(-0.382573\pi\)
0.360598 + 0.932721i \(0.382573\pi\)
\(48\) 2.07295 3.59045i 0.299204 0.518237i
\(49\) −5.47214 9.47802i −0.781734 1.35400i
\(50\) 0 0
\(51\) −7.76393 −1.08717
\(52\) −4.04508 4.20378i −0.560952 0.582959i
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) −0.690983 1.19682i −0.0940309 0.162866i
\(55\) 0 0
\(56\) −4.73607 + 8.20311i −0.632884 + 1.09619i
\(57\) −9.47214 −1.25462
\(58\) 2.30902 3.99933i 0.303189 0.525138i
\(59\) 0.354102 0.613323i 0.0461001 0.0798478i −0.842055 0.539392i \(-0.818654\pi\)
0.888155 + 0.459545i \(0.151987\pi\)
\(60\) 0 0
\(61\) −7.20820 + 12.4850i −0.922916 + 1.59854i −0.128037 + 0.991769i \(0.540868\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 0 0
\(63\) 4.23607 + 7.33708i 0.533694 + 0.924386i
\(64\) −0.236068 −0.0295085
\(65\) 0 0
\(66\) 0.326238 0.0401571
\(67\) −1.35410 2.34537i −0.165430 0.286533i 0.771378 0.636377i \(-0.219568\pi\)
−0.936808 + 0.349844i \(0.886234\pi\)
\(68\) 2.80902 + 4.86536i 0.340643 + 0.590012i
\(69\) −4.20820 + 7.28882i −0.506608 + 0.877471i
\(70\) 0 0
\(71\) 3.11803 5.40059i 0.370043 0.640933i −0.619529 0.784974i \(-0.712676\pi\)
0.989572 + 0.144041i \(0.0460098\pi\)
\(72\) 2.23607 3.87298i 0.263523 0.456435i
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 0.927051 1.60570i 0.107767 0.186659i
\(75\) 0 0
\(76\) 3.42705 + 5.93583i 0.393110 + 0.680886i
\(77\) 1.00000 0.113961
\(78\) −3.45492 3.59045i −0.391192 0.406539i
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) −3.69098 + 6.39297i −0.407601 + 0.705985i
\(83\) −8.94427 −0.981761 −0.490881 0.871227i \(-0.663325\pi\)
−0.490881 + 0.871227i \(0.663325\pi\)
\(84\) 7.66312 13.2729i 0.836115 1.44819i
\(85\) 0 0
\(86\) 3.85410 0.415599
\(87\) −8.35410 + 14.4697i −0.895654 + 1.55132i
\(88\) −0.263932 0.457144i −0.0281352 0.0487317i
\(89\) 4.50000 + 7.79423i 0.476999 + 0.826187i 0.999653 0.0263586i \(-0.00839118\pi\)
−0.522654 + 0.852545i \(0.675058\pi\)
\(90\) 0 0
\(91\) −10.5902 11.0056i −1.11015 1.15370i
\(92\) 6.09017 0.634944
\(93\) 0 0
\(94\) −1.52786 2.64634i −0.157587 0.272949i
\(95\) 0 0
\(96\) −12.5623 −1.28213
\(97\) −1.73607 + 3.00696i −0.176271 + 0.305310i −0.940600 0.339516i \(-0.889737\pi\)
0.764329 + 0.644826i \(0.223070\pi\)
\(98\) −3.38197 + 5.85774i −0.341630 + 0.591721i
\(99\) −0.472136 −0.0474514
\(100\) 0 0
\(101\) −0.263932 0.457144i −0.0262622 0.0454875i 0.852596 0.522571i \(-0.175027\pi\)
−0.878858 + 0.477084i \(0.841694\pi\)
\(102\) 2.39919 + 4.15551i 0.237555 + 0.411457i
\(103\) −12.9443 −1.27544 −0.637719 0.770270i \(-0.720122\pi\)
−0.637719 + 0.770270i \(0.720122\pi\)
\(104\) −2.23607 + 7.74597i −0.219265 + 0.759555i
\(105\) 0 0
\(106\) 1.85410 + 3.21140i 0.180086 + 0.311919i
\(107\) −2.88197 4.99171i −0.278610 0.482567i 0.692429 0.721486i \(-0.256540\pi\)
−0.971040 + 0.238919i \(0.923207\pi\)
\(108\) 1.80902 3.13331i 0.174073 0.301503i
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 0 0
\(111\) −3.35410 + 5.80948i −0.318357 + 0.551411i
\(112\) −7.85410 −0.742143
\(113\) 0.736068 1.27491i 0.0692435 0.119933i −0.829325 0.558766i \(-0.811275\pi\)
0.898568 + 0.438833i \(0.144608\pi\)
\(114\) 2.92705 + 5.06980i 0.274143 + 0.474830i
\(115\) 0 0
\(116\) 12.0902 1.12254
\(117\) 5.00000 + 5.19615i 0.462250 + 0.480384i
\(118\) −0.437694 −0.0402930
\(119\) 7.35410 + 12.7377i 0.674149 + 1.16766i
\(120\) 0 0
\(121\) 5.47214 9.47802i 0.497467 0.861638i
\(122\) 8.90983 0.806658
\(123\) 13.3541 23.1300i 1.20410 2.08556i
\(124\) 0 0
\(125\) 0 0
\(126\) 2.61803 4.53457i 0.233233 0.403971i
\(127\) −2.11803 3.66854i −0.187945 0.325531i 0.756620 0.653855i \(-0.226849\pi\)
−0.944565 + 0.328325i \(0.893516\pi\)
\(128\) 5.69098 + 9.85707i 0.503017 + 0.871250i
\(129\) −13.9443 −1.22772
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0.427051 + 0.739674i 0.0371700 + 0.0643804i
\(133\) 8.97214 + 15.5402i 0.777983 + 1.34751i
\(134\) −0.836881 + 1.44952i −0.0722955 + 0.125219i
\(135\) 0 0
\(136\) 3.88197 6.72376i 0.332876 0.576558i
\(137\) 0.736068 1.27491i 0.0628865 0.108923i −0.832868 0.553472i \(-0.813303\pi\)
0.895755 + 0.444549i \(0.146636\pi\)
\(138\) 5.20163 0.442792
\(139\) 8.35410 14.4697i 0.708586 1.22731i −0.256796 0.966466i \(-0.582667\pi\)
0.965382 0.260841i \(-0.0839998\pi\)
\(140\) 0 0
\(141\) 5.52786 + 9.57454i 0.465530 + 0.806322i
\(142\) −3.85410 −0.323429
\(143\) 0.826238 0.204441i 0.0690935 0.0170962i
\(144\) 3.70820 0.309017
\(145\) 0 0
\(146\) −1.85410 3.21140i −0.153447 0.265777i
\(147\) 12.2361 21.1935i 1.00921 1.74801i
\(148\) 4.85410 0.399005
\(149\) −2.26393 + 3.92125i −0.185469 + 0.321241i −0.943734 0.330705i \(-0.892714\pi\)
0.758266 + 0.651946i \(0.226047\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 4.73607 8.20311i 0.384146 0.665360i
\(153\) −3.47214 6.01392i −0.280706 0.486196i
\(154\) −0.309017 0.535233i −0.0249013 0.0431303i
\(155\) 0 0
\(156\) 3.61803 12.5332i 0.289675 1.00346i
\(157\) 18.0000 1.43656 0.718278 0.695756i \(-0.244931\pi\)
0.718278 + 0.695756i \(0.244931\pi\)
\(158\) 0 0
\(159\) −6.70820 11.6190i −0.531995 0.921443i
\(160\) 0 0
\(161\) 15.9443 1.25658
\(162\) 3.39919 5.88756i 0.267065 0.462571i
\(163\) 7.35410 12.7377i 0.576018 0.997692i −0.419913 0.907565i \(-0.637939\pi\)
0.995930 0.0901274i \(-0.0287274\pi\)
\(164\) −19.3262 −1.50913
\(165\) 0 0
\(166\) 2.76393 + 4.78727i 0.214523 + 0.371564i
\(167\) −8.59017 14.8786i −0.664727 1.15134i −0.979359 0.202128i \(-0.935214\pi\)
0.314632 0.949214i \(-0.398119\pi\)
\(168\) −21.1803 −1.63410
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) 0 0
\(171\) −4.23607 7.33708i −0.323940 0.561081i
\(172\) 5.04508 + 8.73834i 0.384684 + 0.666292i
\(173\) −9.44427 + 16.3580i −0.718035 + 1.24367i 0.243743 + 0.969840i \(0.421625\pi\)
−0.961777 + 0.273833i \(0.911709\pi\)
\(174\) 10.3262 0.782830
\(175\) 0 0
\(176\) 0.218847 0.379054i 0.0164962 0.0285723i
\(177\) 1.58359 0.119030
\(178\) 2.78115 4.81710i 0.208456 0.361057i
\(179\) 4.11803 + 7.13264i 0.307796 + 0.533119i 0.977880 0.209167i \(-0.0670751\pi\)
−0.670084 + 0.742286i \(0.733742\pi\)
\(180\) 0 0
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) −2.61803 + 9.06914i −0.194062 + 0.672249i
\(183\) −32.2361 −2.38296
\(184\) −4.20820 7.28882i −0.310233 0.537339i
\(185\) 0 0
\(186\) 0 0
\(187\) −0.819660 −0.0599395
\(188\) 4.00000 6.92820i 0.291730 0.505291i
\(189\) 4.73607 8.20311i 0.344498 0.596688i
\(190\) 0 0
\(191\) 13.5902 23.5389i 0.983350 1.70321i 0.334300 0.942467i \(-0.391500\pi\)
0.649050 0.760746i \(-0.275167\pi\)
\(192\) −0.263932 0.457144i −0.0190477 0.0329915i
\(193\) −1.73607 3.00696i −0.124965 0.216446i 0.796754 0.604303i \(-0.206548\pi\)
−0.921719 + 0.387858i \(0.873215\pi\)
\(194\) 2.14590 0.154067
\(195\) 0 0
\(196\) −17.7082 −1.26487
\(197\) 1.50000 + 2.59808i 0.106871 + 0.185105i 0.914501 0.404584i \(-0.132584\pi\)
−0.807630 + 0.589689i \(0.799250\pi\)
\(198\) 0.145898 + 0.252703i 0.0103685 + 0.0179588i
\(199\) 0.645898 1.11873i 0.0457865 0.0793045i −0.842224 0.539128i \(-0.818754\pi\)
0.888010 + 0.459823i \(0.152087\pi\)
\(200\) 0 0
\(201\) 3.02786 5.24441i 0.213569 0.369912i
\(202\) −0.163119 + 0.282530i −0.0114770 + 0.0198788i
\(203\) 31.6525 2.22157
\(204\) −6.28115 + 10.8793i −0.439769 + 0.761702i
\(205\) 0 0
\(206\) 4.00000 + 6.92820i 0.278693 + 0.482711i
\(207\) −7.52786 −0.523223
\(208\) −6.48936 + 1.60570i −0.449956 + 0.111335i
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) 6.59017 + 11.4145i 0.453686 + 0.785807i 0.998612 0.0526772i \(-0.0167754\pi\)
−0.544926 + 0.838484i \(0.683442\pi\)
\(212\) −4.85410 + 8.40755i −0.333381 + 0.577433i
\(213\) 13.9443 0.955446
\(214\) −1.78115 + 3.08505i −0.121757 + 0.210889i
\(215\) 0 0
\(216\) −5.00000 −0.340207
\(217\) 0 0
\(218\) 0.618034 + 1.07047i 0.0418585 + 0.0725011i
\(219\) 6.70820 + 11.6190i 0.453298 + 0.785136i
\(220\) 0 0
\(221\) 8.68034 + 9.02087i 0.583903 + 0.606810i
\(222\) 4.14590 0.278254
\(223\) 0.354102 + 0.613323i 0.0237124 + 0.0410711i 0.877638 0.479324i \(-0.159118\pi\)
−0.853926 + 0.520395i \(0.825785\pi\)
\(224\) 11.8992 + 20.6100i 0.795048 + 1.37706i
\(225\) 0 0
\(226\) −0.909830 −0.0605210
\(227\) −3.11803 + 5.40059i −0.206951 + 0.358450i −0.950753 0.309951i \(-0.899687\pi\)
0.743801 + 0.668401i \(0.233021\pi\)
\(228\) −7.66312 + 13.2729i −0.507502 + 0.879020i
\(229\) 15.8885 1.04994 0.524972 0.851119i \(-0.324076\pi\)
0.524972 + 0.851119i \(0.324076\pi\)
\(230\) 0 0
\(231\) 1.11803 + 1.93649i 0.0735612 + 0.127412i
\(232\) −8.35410 14.4697i −0.548474 0.949984i
\(233\) 15.8885 1.04089 0.520447 0.853894i \(-0.325765\pi\)
0.520447 + 0.853894i \(0.325765\pi\)
\(234\) 1.23607 4.28187i 0.0808043 0.279914i
\(235\) 0 0
\(236\) −0.572949 0.992377i −0.0372958 0.0645982i
\(237\) 0 0
\(238\) 4.54508 7.87232i 0.294614 0.510287i
\(239\) −25.8885 −1.67459 −0.837295 0.546751i \(-0.815864\pi\)
−0.837295 + 0.546751i \(0.815864\pi\)
\(240\) 0 0
\(241\) −7.50000 + 12.9904i −0.483117 + 0.836784i −0.999812 0.0193858i \(-0.993829\pi\)
0.516695 + 0.856170i \(0.327162\pi\)
\(242\) −6.76393 −0.434802
\(243\) −8.94427 + 15.4919i −0.573775 + 0.993808i
\(244\) 11.6631 + 20.2011i 0.746655 + 1.29324i
\(245\) 0 0
\(246\) −16.5066 −1.05242
\(247\) 10.5902 + 11.0056i 0.673836 + 0.700271i
\(248\) 0 0
\(249\) −10.0000 17.3205i −0.633724 1.09764i
\(250\) 0 0
\(251\) −10.1180 + 17.5249i −0.638645 + 1.10616i 0.347086 + 0.937833i \(0.387171\pi\)
−0.985730 + 0.168332i \(0.946162\pi\)
\(252\) 13.7082 0.863536
\(253\) −0.444272 + 0.769502i −0.0279311 + 0.0483781i
\(254\) −1.30902 + 2.26728i −0.0821350 + 0.142262i
\(255\) 0 0
\(256\) 3.28115 5.68312i 0.205072 0.355195i
\(257\) 8.73607 + 15.1313i 0.544941 + 0.943865i 0.998611 + 0.0526955i \(0.0167813\pi\)
−0.453670 + 0.891170i \(0.649885\pi\)
\(258\) 4.30902 + 7.46344i 0.268268 + 0.464653i
\(259\) 12.7082 0.789649
\(260\) 0 0
\(261\) −14.9443 −0.925027
\(262\) 3.70820 + 6.42280i 0.229094 + 0.396802i
\(263\) 1.88197 + 3.25966i 0.116047 + 0.200999i 0.918198 0.396122i \(-0.129644\pi\)
−0.802151 + 0.597122i \(0.796311\pi\)
\(264\) 0.590170 1.02220i 0.0363224 0.0629123i
\(265\) 0 0
\(266\) 5.54508 9.60437i 0.339991 0.588882i
\(267\) −10.0623 + 17.4284i −0.615803 + 1.06660i
\(268\) −4.38197 −0.267671
\(269\) 3.26393 5.65330i 0.199005 0.344688i −0.749201 0.662343i \(-0.769562\pi\)
0.948206 + 0.317655i \(0.102896\pi\)
\(270\) 0 0
\(271\) −0.645898 1.11873i −0.0392355 0.0679579i 0.845741 0.533594i \(-0.179159\pi\)
−0.884976 + 0.465636i \(0.845826\pi\)
\(272\) 6.43769 0.390343
\(273\) 9.47214 32.8124i 0.573280 1.98590i
\(274\) −0.909830 −0.0549648
\(275\) 0 0
\(276\) 6.80902 + 11.7936i 0.409855 + 0.709889i
\(277\) 8.44427 14.6259i 0.507367 0.878786i −0.492597 0.870258i \(-0.663952\pi\)
0.999964 0.00852782i \(-0.00271452\pi\)
\(278\) −10.3262 −0.619327
\(279\) 0 0
\(280\) 0 0
\(281\) −15.8885 −0.947831 −0.473916 0.880570i \(-0.657160\pi\)
−0.473916 + 0.880570i \(0.657160\pi\)
\(282\) 3.41641 5.91739i 0.203444 0.352376i
\(283\) −5.35410 9.27358i −0.318268 0.551257i 0.661859 0.749629i \(-0.269768\pi\)
−0.980127 + 0.198372i \(0.936435\pi\)
\(284\) −5.04508 8.73834i −0.299371 0.518525i
\(285\) 0 0
\(286\) −0.364745 0.379054i −0.0215678 0.0224139i
\(287\) −50.5967 −2.98663
\(288\) −5.61803 9.73072i −0.331046 0.573388i
\(289\) 2.47214 + 4.28187i 0.145420 + 0.251874i
\(290\) 0 0
\(291\) −7.76393 −0.455130
\(292\) 4.85410 8.40755i 0.284065 0.492015i
\(293\) −14.9721 + 25.9325i −0.874682 + 1.51499i −0.0175799 + 0.999845i \(0.505596\pi\)
−0.857102 + 0.515147i \(0.827737\pi\)
\(294\) −15.1246 −0.882085
\(295\) 0 0
\(296\) −3.35410 5.80948i −0.194953 0.337669i
\(297\) 0.263932 + 0.457144i 0.0153149 + 0.0265262i
\(298\) 2.79837 0.162105
\(299\) 13.1738 3.25966i 0.761858 0.188511i
\(300\) 0 0
\(301\) 13.2082 + 22.8773i 0.761308 + 1.31862i
\(302\) −2.47214 4.28187i −0.142255 0.246394i
\(303\) 0.590170 1.02220i 0.0339044 0.0587241i
\(304\) 7.85410 0.450464
\(305\) 0 0
\(306\) −2.14590 + 3.71680i −0.122673 + 0.212476i
\(307\) −24.9443 −1.42364 −0.711822 0.702360i \(-0.752130\pi\)
−0.711822 + 0.702360i \(0.752130\pi\)
\(308\) 0.809017 1.40126i 0.0460980 0.0798441i
\(309\) −14.4721 25.0665i −0.823291 1.42598i
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) −17.5000 + 4.33013i −0.990742 + 0.245145i
\(313\) −3.88854 −0.219793 −0.109897 0.993943i \(-0.535052\pi\)
−0.109897 + 0.993943i \(0.535052\pi\)
\(314\) −5.56231 9.63420i −0.313899 0.543689i
\(315\) 0 0
\(316\) 0 0
\(317\) 11.8885 0.667727 0.333864 0.942621i \(-0.391648\pi\)
0.333864 + 0.942621i \(0.391648\pi\)
\(318\) −4.14590 + 7.18091i −0.232490 + 0.402685i
\(319\) −0.881966 + 1.52761i −0.0493806 + 0.0855297i
\(320\) 0 0
\(321\) 6.44427 11.1618i 0.359684 0.622991i
\(322\) −4.92705 8.53390i −0.274574 0.475576i
\(323\) −7.35410 12.7377i −0.409193 0.708743i
\(324\) 17.7984 0.988799
\(325\) 0 0
\(326\) −9.09017 −0.503458
\(327\) −2.23607 3.87298i −0.123655 0.214176i
\(328\) 13.3541 + 23.1300i 0.737357 + 1.27714i
\(329\) 10.4721 18.1383i 0.577348 0.999995i
\(330\) 0 0
\(331\) 2.82624 4.89519i 0.155344 0.269064i −0.777840 0.628462i \(-0.783685\pi\)
0.933184 + 0.359398i \(0.117018\pi\)
\(332\) −7.23607 + 12.5332i −0.397131 + 0.687851i
\(333\) −6.00000 −0.328798
\(334\) −5.30902 + 9.19549i −0.290496 + 0.503155i
\(335\) 0 0
\(336\) −8.78115 15.2094i −0.479051 0.829741i
\(337\) 7.88854 0.429716 0.214858 0.976645i \(-0.431071\pi\)
0.214858 + 0.976645i \(0.431071\pi\)
\(338\) −0.309017 + 8.02850i −0.0168083 + 0.436693i
\(339\) 3.29180 0.178786
\(340\) 0 0
\(341\) 0 0
\(342\) −2.61803 + 4.53457i −0.141567 + 0.245201i
\(343\) −16.7082 −0.902158
\(344\) 6.97214 12.0761i 0.375912 0.651099i
\(345\) 0 0
\(346\) 11.6738 0.627585
\(347\) 15.3541 26.5941i 0.824251 1.42765i −0.0782387 0.996935i \(-0.524930\pi\)
0.902490 0.430711i \(-0.141737\pi\)
\(348\) 13.5172 + 23.4125i 0.724599 + 1.25504i
\(349\) −1.20820 2.09267i −0.0646737 0.112018i 0.831876 0.554962i \(-0.187267\pi\)
−0.896549 + 0.442944i \(0.853934\pi\)
\(350\) 0 0
\(351\) 2.23607 7.74597i 0.119352 0.413449i
\(352\) −1.32624 −0.0706887
\(353\) −9.73607 16.8634i −0.518199 0.897546i −0.999776 0.0211430i \(-0.993269\pi\)
0.481578 0.876403i \(-0.340064\pi\)
\(354\) −0.489357 0.847591i −0.0260090 0.0450490i
\(355\) 0 0
\(356\) 14.5623 0.771801
\(357\) −16.4443 + 28.4823i −0.870323 + 1.50744i
\(358\) 2.54508 4.40822i 0.134512 0.232981i
\(359\) 17.8885 0.944121 0.472061 0.881566i \(-0.343510\pi\)
0.472061 + 0.881566i \(0.343510\pi\)
\(360\) 0 0
\(361\) 0.527864 + 0.914287i 0.0277823 + 0.0481204i
\(362\) −1.85410 3.21140i −0.0974494 0.168787i
\(363\) 24.4721 1.28445
\(364\) −23.9894 + 5.93583i −1.25738 + 0.311122i
\(365\) 0 0
\(366\) 9.96149 + 17.2538i 0.520696 + 0.901871i
\(367\) 2.82624 + 4.89519i 0.147528 + 0.255527i 0.930313 0.366766i \(-0.119535\pi\)
−0.782785 + 0.622292i \(0.786202\pi\)
\(368\) 3.48936 6.04374i 0.181895 0.315052i
\(369\) 23.8885 1.24359
\(370\) 0 0
\(371\) −12.7082 + 22.0113i −0.659777 + 1.14277i
\(372\) 0 0
\(373\) 13.9721 24.2004i 0.723450 1.25305i −0.236159 0.971714i \(-0.575889\pi\)
0.959609 0.281337i \(-0.0907780\pi\)
\(374\) 0.253289 + 0.438709i 0.0130973 + 0.0226851i
\(375\) 0 0
\(376\) −11.0557 −0.570156
\(377\) 26.1525 6.47106i 1.34692 0.333277i
\(378\) −5.85410 −0.301103
\(379\) −5.40983 9.37010i −0.277884 0.481310i 0.692974 0.720962i \(-0.256300\pi\)
−0.970859 + 0.239652i \(0.922967\pi\)
\(380\) 0 0
\(381\) 4.73607 8.20311i 0.242636 0.420258i
\(382\) −16.7984 −0.859480
\(383\) 2.11803 3.66854i 0.108226 0.187454i −0.806825 0.590790i \(-0.798816\pi\)
0.915052 + 0.403336i \(0.132149\pi\)
\(384\) −12.7254 + 22.0411i −0.649392 + 1.12478i
\(385\) 0 0
\(386\) −1.07295 + 1.85840i −0.0546117 + 0.0945902i
\(387\) −6.23607 10.8012i −0.316997 0.549055i
\(388\) 2.80902 + 4.86536i 0.142606 + 0.247001i
\(389\) −0.111456 −0.00565105 −0.00282553 0.999996i \(-0.500899\pi\)
−0.00282553 + 0.999996i \(0.500899\pi\)
\(390\) 0 0
\(391\) −13.0689 −0.660922
\(392\) 12.2361 + 21.1935i 0.618015 + 1.07043i
\(393\) −13.4164 23.2379i −0.676768 1.17220i
\(394\) 0.927051 1.60570i 0.0467042 0.0808940i
\(395\) 0 0
\(396\) −0.381966 + 0.661585i −0.0191945 + 0.0332459i
\(397\) 13.9721 24.2004i 0.701241 1.21459i −0.266790 0.963755i \(-0.585963\pi\)
0.968031 0.250831i \(-0.0807038\pi\)
\(398\) −0.798374 −0.0400189
\(399\) −20.0623 + 34.7489i −1.00437 + 1.73962i
\(400\) 0 0
\(401\) −4.44427 7.69770i −0.221936 0.384405i 0.733460 0.679733i \(-0.237904\pi\)
−0.955396 + 0.295328i \(0.904571\pi\)
\(402\) −3.74265 −0.186666
\(403\) 0 0
\(404\) −0.854102 −0.0424932
\(405\) 0 0
\(406\) −9.78115 16.9415i −0.485430 0.840790i
\(407\) −0.354102 + 0.613323i −0.0175522 + 0.0304013i
\(408\) 17.3607 0.859482
\(409\) −12.4443 + 21.5541i −0.615330 + 1.06578i 0.374997 + 0.927026i \(0.377644\pi\)
−0.990327 + 0.138756i \(0.955690\pi\)
\(410\) 0 0
\(411\) 3.29180 0.162372
\(412\) −10.4721 + 18.1383i −0.515925 + 0.893609i
\(413\) −1.50000 2.59808i −0.0738102 0.127843i
\(414\) 2.32624 + 4.02916i 0.114328 + 0.198023i
\(415\) 0 0
\(416\) 14.0451 + 14.5961i 0.688617 + 0.715632i
\(417\) 37.3607 1.82956
\(418\) 0.309017 + 0.535233i 0.0151145 + 0.0261791i
\(419\) −8.82624 15.2875i −0.431190 0.746843i 0.565786 0.824552i \(-0.308573\pi\)
−0.996976 + 0.0777091i \(0.975239\pi\)
\(420\) 0 0
\(421\) 6.00000 0.292422 0.146211 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) 4.07295 7.05455i 0.198268 0.343410i
\(423\) −4.94427 + 8.56373i −0.240399 + 0.416383i
\(424\) 13.4164 0.651558
\(425\) 0 0
\(426\) −4.30902 7.46344i −0.208773 0.361605i
\(427\) 30.5344 + 52.8872i 1.47767 + 2.55939i
\(428\) −9.32624 −0.450801
\(429\) 1.31966 + 1.37143i 0.0637138 + 0.0662133i
\(430\) 0 0
\(431\) −13.5902 23.5389i −0.654615 1.13383i −0.981990 0.188933i \(-0.939497\pi\)
0.327375 0.944895i \(-0.393836\pi\)
\(432\) −2.07295 3.59045i −0.0997348 0.172746i
\(433\) −7.26393 + 12.5815i −0.349082 + 0.604628i −0.986087 0.166232i \(-0.946840\pi\)
0.637004 + 0.770860i \(0.280173\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.61803 + 2.80252i −0.0774898 + 0.134216i
\(437\) −15.9443 −0.762718
\(438\) 4.14590 7.18091i 0.198099 0.343117i
\(439\) 11.3541 + 19.6659i 0.541902 + 0.938601i 0.998795 + 0.0490797i \(0.0156288\pi\)
−0.456893 + 0.889522i \(0.651038\pi\)
\(440\) 0 0
\(441\) 21.8885 1.04231
\(442\) 2.14590 7.43361i 0.102070 0.353581i
\(443\) −0.944272 −0.0448637 −0.0224319 0.999748i \(-0.507141\pi\)
−0.0224319 + 0.999748i \(0.507141\pi\)
\(444\) 5.42705 + 9.39993i 0.257556 + 0.446101i
\(445\) 0 0
\(446\) 0.218847 0.379054i 0.0103627 0.0179487i
\(447\) −10.1246 −0.478878
\(448\) −0.500000 + 0.866025i −0.0236228 + 0.0409159i
\(449\) −1.97214 + 3.41584i −0.0930709 + 0.161203i −0.908802 0.417228i \(-0.863002\pi\)
0.815731 + 0.578431i \(0.196335\pi\)
\(450\) 0 0
\(451\) 1.40983 2.44190i 0.0663863 0.114984i
\(452\) −1.19098 2.06284i −0.0560191 0.0970280i
\(453\) 8.94427 + 15.4919i 0.420239 + 0.727875i
\(454\) 3.85410 0.180882
\(455\) 0 0
\(456\) 21.1803 0.991860
\(457\) −0.791796 1.37143i −0.0370387 0.0641528i 0.846912 0.531733i \(-0.178459\pi\)
−0.883950 + 0.467580i \(0.845126\pi\)
\(458\) −4.90983 8.50408i −0.229421 0.397369i
\(459\) −3.88197 + 6.72376i −0.181195 + 0.313838i
\(460\) 0 0
\(461\) 0.791796 1.37143i 0.0368776 0.0638739i −0.846998 0.531597i \(-0.821592\pi\)
0.883875 + 0.467723i \(0.154925\pi\)
\(462\) 0.690983 1.19682i 0.0321474 0.0556810i
\(463\) −11.0557 −0.513803 −0.256902 0.966438i \(-0.582702\pi\)
−0.256902 + 0.966438i \(0.582702\pi\)
\(464\) 6.92705 11.9980i 0.321580 0.556993i
\(465\) 0 0
\(466\) −4.90983 8.50408i −0.227443 0.393944i
\(467\) −8.94427 −0.413892 −0.206946 0.978352i \(-0.566352\pi\)
−0.206946 + 0.978352i \(0.566352\pi\)
\(468\) 11.3262 2.80252i 0.523556 0.129546i
\(469\) −11.4721 −0.529734
\(470\) 0 0
\(471\) 20.1246 + 34.8569i 0.927293 + 1.60612i
\(472\) −0.791796 + 1.37143i −0.0364454 + 0.0631252i
\(473\) −1.47214 −0.0676889
\(474\) 0 0
\(475\) 0 0
\(476\) 23.7984 1.09080
\(477\) 6.00000 10.3923i 0.274721 0.475831i
\(478\) 8.00000 + 13.8564i 0.365911 + 0.633777i
\(479\) −16.0623 27.8207i −0.733905 1.27116i −0.955202 0.295955i \(-0.904362\pi\)
0.221296 0.975207i \(-0.428971\pi\)
\(480\) 0 0
\(481\) 10.5000 2.59808i 0.478759 0.118462i
\(482\) 9.27051 0.422260
\(483\) 17.8262 + 30.8759i 0.811122 + 1.40490i
\(484\) −8.85410 15.3358i −0.402459 0.697080i
\(485\) 0 0
\(486\) 11.0557 0.501498
\(487\) 7.06231 12.2323i 0.320024 0.554297i −0.660469 0.750853i \(-0.729642\pi\)
0.980493 + 0.196556i \(0.0629758\pi\)
\(488\) 16.1180 27.9173i 0.729629 1.26375i
\(489\) 32.8885 1.48727
\(490\) 0 0
\(491\) 0.118034 + 0.204441i 0.00532680 + 0.00922629i 0.868677 0.495380i \(-0.164971\pi\)
−0.863350 + 0.504606i \(0.831638\pi\)
\(492\) −21.6074 37.4251i −0.974136 1.68725i
\(493\) −25.9443 −1.16847
\(494\) 2.61803 9.06914i 0.117791 0.408040i
\(495\) 0 0
\(496\) 0 0
\(497\) −13.2082 22.8773i −0.592469 1.02619i
\(498\) −6.18034 + 10.7047i −0.276948 + 0.479687i
\(499\) −21.8885 −0.979866 −0.489933 0.871760i \(-0.662979\pi\)
−0.489933 + 0.871760i \(0.662979\pi\)
\(500\) 0 0
\(501\) 19.2082 33.2696i 0.858159 1.48638i
\(502\) 12.5066 0.558196
\(503\) 4.59017 7.95041i 0.204666 0.354491i −0.745361 0.666662i \(-0.767723\pi\)
0.950026 + 0.312170i \(0.101056\pi\)
\(504\) −9.47214 16.4062i −0.421922 0.730791i
\(505\) 0 0
\(506\) 0.549150 0.0244127
\(507\) 1.11803 29.0474i 0.0496536 1.29004i
\(508\) −6.85410 −0.304102
\(509\) 16.6803 + 28.8912i 0.739343 + 1.28058i 0.952791 + 0.303625i \(0.0981971\pi\)
−0.213448 + 0.976954i \(0.568470\pi\)
\(510\) 0 0
\(511\) 12.7082 22.0113i 0.562178 0.973721i
\(512\) 18.7082 0.826794
\(513\) −4.73607 + 8.20311i −0.209103 + 0.362176i
\(514\) 5.39919 9.35167i 0.238148 0.412484i
\(515\) 0 0
\(516\) −11.2812 + 19.5395i −0.496625 + 0.860180i
\(517\) 0.583592 + 1.01081i 0.0256664 + 0.0444554i
\(518\) −3.92705 6.80185i −0.172545 0.298856i
\(519\) −42.2361 −1.85396
\(520\) 0 0
\(521\) 29.7771 1.30456 0.652279 0.757979i \(-0.273813\pi\)
0.652279 + 0.757979i \(0.273813\pi\)
\(522\) 4.61803 + 7.99867i 0.202126 + 0.350092i
\(523\) 2.64590 + 4.58283i 0.115697 + 0.200393i 0.918058 0.396446i \(-0.129756\pi\)
−0.802361 + 0.596839i \(0.796423\pi\)
\(524\) −9.70820 + 16.8151i −0.424105 + 0.734571i
\(525\) 0 0
\(526\) 1.16312 2.01458i 0.0507144 0.0878399i
\(527\) 0 0
\(528\) 0.978714 0.0425930
\(529\) 4.41641 7.64944i 0.192018 0.332584i
\(530\) 0 0
\(531\) 0.708204 + 1.22665i 0.0307334 + 0.0532319i
\(532\) 29.0344 1.25880
\(533\) −41.8050 + 10.3440i −1.81077 + 0.448050i
\(534\) 12.4377 0.538232
\(535\) 0 0
\(536\) 3.02786 + 5.24441i 0.130784 + 0.226524i
\(537\) −9.20820 + 15.9491i −0.397363 + 0.688253i
\(538\) −4.03444 −0.173937
\(539\) 1.29180 2.23746i 0.0556416 0.0963741i
\(540\) 0 0
\(541\) −27.8885 −1.19902 −0.599511 0.800366i \(-0.704638\pi\)
−0.599511 + 0.800366i \(0.704638\pi\)
\(542\) −0.399187 + 0.691412i −0.0171465 + 0.0296987i
\(543\) 6.70820 + 11.6190i 0.287877 + 0.498617i
\(544\) −9.75329 16.8932i −0.418169 0.724290i
\(545\) 0 0
\(546\) −20.4894 + 5.06980i −0.876864 + 0.216967i
\(547\) −18.8328 −0.805233 −0.402617 0.915369i \(-0.631899\pi\)
−0.402617 + 0.915369i \(0.631899\pi\)
\(548\) −1.19098 2.06284i −0.0508763 0.0881203i
\(549\) −14.4164 24.9700i −0.615277 1.06569i
\(550\) 0 0
\(551\) −31.6525 −1.34844
\(552\) 9.40983 16.2983i 0.400509 0.693702i
\(553\) 0 0
\(554\) −10.4377 −0.443455
\(555\) 0 0
\(556\) −13.5172 23.4125i −0.573258 0.992912i
\(557\) −4.97214 8.61199i −0.210676 0.364902i 0.741250 0.671229i \(-0.234233\pi\)
−0.951926 + 0.306327i \(0.900900\pi\)
\(558\) 0 0
\(559\) 15.5902 + 16.2018i 0.659394 + 0.685262i
\(560\) 0 0
\(561\) −0.916408 1.58726i −0.0386908 0.0670144i
\(562\) 4.90983 + 8.50408i 0.207109 + 0.358723i
\(563\) 15.3541 26.5941i 0.647098 1.12081i −0.336714 0.941607i \(-0.609316\pi\)
0.983813 0.179200i \(-0.0573510\pi\)
\(564\) 17.8885 0.753244
\(565\) 0 0
\(566\) −3.30902 + 5.73139i −0.139088 + 0.240908i
\(567\) 46.5967 1.95688
\(568\) −6.97214 + 12.0761i −0.292544 + 0.506702i
\(569\) −8.44427 14.6259i −0.354002 0.613150i 0.632944 0.774197i \(-0.281846\pi\)
−0.986947 + 0.161047i \(0.948513\pi\)
\(570\) 0 0
\(571\) 28.0000 1.17176 0.585882 0.810397i \(-0.300748\pi\)
0.585882 + 0.810397i \(0.300748\pi\)
\(572\) 0.381966 1.32317i 0.0159708 0.0553245i
\(573\) 60.7771 2.53900
\(574\) 15.6353 + 27.0811i 0.652603 + 1.13034i
\(575\) 0 0
\(576\) 0.236068 0.408882i 0.00983617 0.0170367i
\(577\) −27.8885 −1.16102 −0.580508 0.814255i \(-0.697146\pi\)
−0.580508 + 0.814255i \(0.697146\pi\)
\(578\) 1.52786 2.64634i 0.0635508 0.110073i
\(579\) 3.88197 6.72376i 0.161329 0.279430i
\(580\) 0 0
\(581\) −18.9443 + 32.8124i −0.785941 + 1.36129i
\(582\) 2.39919 + 4.15551i 0.0994495 + 0.172252i
\(583\) −0.708204 1.22665i −0.0293308 0.0508025i
\(584\) −13.4164 −0.555175
\(585\) 0 0
\(586\) 18.5066 0.764500
\(587\) 5.11803 + 8.86469i 0.211244 + 0.365885i 0.952104 0.305774i \(-0.0989152\pi\)
−0.740860 + 0.671659i \(0.765582\pi\)
\(588\) −19.7984 34.2918i −0.816471 1.41417i
\(589\) 0 0
\(590\) 0 0
\(591\) −3.35410 + 5.80948i −0.137969 + 0.238970i
\(592\) 2.78115 4.81710i 0.114305 0.197982i
\(593\) 7.88854 0.323944 0.161972 0.986795i \(-0.448215\pi\)
0.161972 + 0.986795i \(0.448215\pi\)
\(594\) 0.163119 0.282530i 0.00669285 0.0115924i
\(595\) 0 0
\(596\) 3.66312 + 6.34471i 0.150047 + 0.259889i
\(597\) 2.88854 0.118220
\(598\) −5.81559 6.04374i −0.237817 0.247147i
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) −21.9721 38.0569i −0.896262 1.55237i −0.832235 0.554423i \(-0.812939\pi\)
−0.0640274 0.997948i \(-0.520394\pi\)
\(602\) 8.16312 14.1389i 0.332704 0.576260i
\(603\) 5.41641 0.220573
\(604\) 6.47214 11.2101i 0.263347 0.456131i
\(605\) 0 0
\(606\) −0.729490 −0.0296335
\(607\) −0.354102 + 0.613323i −0.0143726 + 0.0248940i −0.873122 0.487501i \(-0.837908\pi\)
0.858750 + 0.512395i \(0.171242\pi\)
\(608\) −11.8992 20.6100i −0.482576 0.835846i
\(609\) 35.3885 + 61.2948i 1.43402 + 2.48379i
\(610\) 0 0
\(611\) 4.94427 17.1275i 0.200024 0.692903i
\(612\) −11.2361 −0.454191
\(613\) 19.9721 + 34.5928i 0.806667 + 1.39719i 0.915160 + 0.403091i \(0.132064\pi\)
−0.108493 + 0.994097i \(0.534602\pi\)
\(614\) 7.70820 + 13.3510i 0.311078 + 0.538803i
\(615\) 0 0
\(616\) −2.23607 −0.0900937
\(617\) −20.2082 + 35.0016i −0.813552 + 1.40911i 0.0968116 + 0.995303i \(0.469136\pi\)
−0.910363 + 0.413810i \(0.864198\pi\)
\(618\) −8.94427 + 15.4919i −0.359791 + 0.623177i
\(619\) 12.0000 0.482321 0.241160 0.970485i \(-0.422472\pi\)
0.241160 + 0.970485i \(0.422472\pi\)
\(620\) 0 0
\(621\) 4.20820 + 7.28882i 0.168869 + 0.292490i
\(622\) 7.41641 + 12.8456i 0.297371 + 0.515061i
\(623\) 38.1246 1.52743
\(624\) −10.3647 10.7714i −0.414922 0.431199i
\(625\) 0 0
\(626\) 1.20163 + 2.08128i 0.0480266 + 0.0831846i
\(627\) −1.11803 1.93649i −0.0446500 0.0773360i
\(628\) 14.5623 25.2227i 0.581099 1.00649i
\(629\) −10.4164 −0.415329
\(630\) 0 0
\(631\) 8.06231 13.9643i 0.320955 0.555911i −0.659730 0.751503i \(-0.729329\pi\)
0.980685 + 0.195592i \(0.0626627\pi\)
\(632\) 0 0
\(633\) −14.7361 + 25.5236i −0.585706 + 1.01447i
\(634\) −3.67376 6.36314i −0.145904 0.252713i
\(635\) 0 0
\(636\) −21.7082 −0.860786
\(637\) −38.3050 + 9.47802i −1.51770 + 0.375533i
\(638\) 1.09017 0.0431602
\(639\) 6.23607 + 10.8012i 0.246695 + 0.427288i
\(640\) 0 0
\(641\) −4.44427 + 7.69770i −0.175538 + 0.304041i −0.940347 0.340216i \(-0.889500\pi\)
0.764809 + 0.644257i \(0.222833\pi\)
\(642\) −7.96556 −0.314376
\(643\) −8.64590 + 14.9751i −0.340961 + 0.590562i −0.984611 0.174758i \(-0.944086\pi\)
0.643650 + 0.765320i \(0.277419\pi\)
\(644\) 12.8992 22.3420i 0.508299 0.880400i
\(645\) 0 0
\(646\) −4.54508 + 7.87232i −0.178824 + 0.309732i
\(647\) 1.29837 + 2.24885i 0.0510443 + 0.0884114i 0.890419 0.455142i \(-0.150412\pi\)
−0.839374 + 0.543554i \(0.817078\pi\)
\(648\) −12.2984 21.3014i −0.483126 0.836798i
\(649\) 0.167184 0.00656256
\(650\) 0 0
\(651\) 0 0
\(652\) −11.8992 20.6100i −0.466008 0.807150i
\(653\) −10.5000 18.1865i −0.410897 0.711694i 0.584091 0.811688i \(-0.301451\pi\)
−0.994988 + 0.0999939i \(0.968118\pi\)
\(654\) −1.38197 + 2.39364i −0.0540391 + 0.0935985i
\(655\) 0 0
\(656\) −11.0729 + 19.1789i −0.432326 + 0.748811i
\(657\) −6.00000 + 10.3923i −0.234082 + 0.405442i
\(658\) −12.9443 −0.504620
\(659\) 21.8820 37.9007i 0.852400 1.47640i −0.0266355 0.999645i \(-0.508479\pi\)
0.879036 0.476756i \(-0.158187\pi\)
\(660\) 0 0
\(661\) 20.6803 + 35.8194i 0.804372 + 1.39321i 0.916714 + 0.399544i \(0.130831\pi\)
−0.112342 + 0.993670i \(0.535835\pi\)
\(662\) −3.49342 −0.135776
\(663\) −7.76393 + 26.8950i −0.301526 + 1.04452i
\(664\) 20.0000 0.776151
\(665\) 0 0
\(666\) 1.85410 + 3.21140i 0.0718450 + 0.124439i
\(667\) −14.0623 + 24.3566i −0.544495 + 0.943092i
\(668\) −27.7984 −1.07555
\(669\) −0.791796 + 1.37143i −0.0306126 + 0.0530226i
\(670\) 0 0
\(671\) −3.40325 −0.131381
\(672\) −26.6074 + 46.0854i −1.02640 + 1.77778i
\(673\) −4.79180 8.29963i −0.184710 0.319927i 0.758769 0.651360i \(-0.225801\pi\)
−0.943479 + 0.331433i \(0.892468\pi\)
\(674\) −2.43769 4.22221i −0.0938965 0.162633i
\(675\) 0 0
\(676\) −18.6074 + 9.80881i −0.715669 + 0.377262i
\(677\) −12.1115 −0.465481 −0.232741 0.972539i \(-0.574769\pi\)
−0.232741 + 0.972539i \(0.574769\pi\)
\(678\) −1.01722 1.76188i −0.0390661 0.0676645i
\(679\) 7.35410 + 12.7377i 0.282225 + 0.488827i
\(680\) 0 0
\(681\) −13.9443 −0.534346
\(682\) 0 0
\(683\) 12.8820 22.3122i 0.492915 0.853753i −0.507052 0.861915i \(-0.669265\pi\)
0.999967 + 0.00816213i \(0.00259812\pi\)
\(684\) −13.7082 −0.524146
\(685\) 0 0
\(686\) 5.16312 + 8.94278i 0.197129 + 0.341437i
\(687\) 17.7639 + 30.7680i 0.677736 + 1.17387i
\(688\) 11.5623 0.440809
\(689\) −6.00000 + 20.7846i −0.228582 + 0.791831i
\(690\) 0 0
\(691\) −19.2984 33.4258i −0.734145 1.27158i −0.955098 0.296291i \(-0.904250\pi\)
0.220953 0.975284i \(-0.429083\pi\)
\(692\) 15.2812 + 26.4677i 0.580902 + 1.00615i
\(693\) −1.00000 + 1.73205i −0.0379869 + 0.0657952i
\(694\) −18.9787 −0.720422
\(695\) 0 0
\(696\) 18.6803 32.3553i 0.708076 1.22642i
\(697\) 41.4721 1.57087
\(698\) −0.746711 + 1.29334i −0.0282634 + 0.0489537i
\(699\) 17.7639 + 30.7680i 0.671894 + 1.16375i
\(700\) 0 0
\(701\) 7.88854 0.297946 0.148973 0.988841i \(-0.452403\pi\)
0.148973 + 0.988841i \(0.452403\pi\)
\(702\) −4.83688 + 1.19682i −0.182556 + 0.0451710i
\(703\) −12.7082 −0.479299
\(704\) −0.0278640 0.0482619i −0.00105017 0.00181894i
\(705\) 0 0
\(706\) −6.01722 + 10.4221i −0.226461 + 0.392242i
\(707\) −2.23607 −0.0840960
\(708\) 1.28115 2.21902i 0.0481487 0.0833960i
\(709\) −12.1525 + 21.0487i −0.456396 + 0.790501i −0.998767 0.0496381i \(-0.984193\pi\)
0.542371 + 0.840139i \(0.317527\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −10.0623 17.4284i −0.377101 0.653158i
\(713\) 0 0
\(714\) 20.3262 0.760690
\(715\) 0 0
\(716\) 13.3262 0.498025
\(717\) −28.9443 50.1329i −1.08094 1.87225i
\(718\) −5.52786 9.57454i −0.206298 0.357319i
\(719\) 16.0623 27.8207i 0.599023 1.03754i −0.393943 0.919135i \(-0.628889\pi\)
0.992966 0.118403i \(-0.0377775\pi\)
\(720\) 0 0
\(721\) −27.4164 + 47.4866i −1.02104 + 1.76849i
\(722\) 0.326238 0.565061i 0.0121413 0.0210294i
\(723\) −33.5410 −1.24740
\(724\) 4.85410 8.40755i 0.180401 0.312464i
\(725\) 0 0
\(726\) −7.56231 13.0983i −0.280663 0.486123i
\(727\) −28.9443 −1.07348 −0.536742 0.843747i \(-0.680345\pi\)
−0.536742 + 0.843747i \(0.680345\pi\)
\(728\) 23.6803 + 24.6093i 0.877652 + 0.912082i
\(729\) −7.00000 −0.259259
\(730\) 0 0
\(731\) −10.8262 18.7516i −0.400423 0.693553i
\(732\) −26.0795 + 45.1711i −0.963927 + 1.66957i
\(733\) 43.8885 1.62106 0.810530 0.585697i \(-0.199179\pi\)
0.810530 + 0.585697i \(0.199179\pi\)
\(734\) 1.74671 3.02539i 0.0644723 0.111669i
\(735\) 0 0
\(736\) −21.1459 −0.779448
\(737\) 0.319660 0.553668i 0.0117748 0.0203946i
\(738\) −7.38197 12.7859i −0.271734 0.470657i
\(739\) −13.7705 23.8512i −0.506556 0.877381i −0.999971 0.00758729i \(-0.997585\pi\)
0.493415 0.869794i \(-0.335748\pi\)
\(740\) 0 0
\(741\) −9.47214 + 32.8124i −0.347968 + 1.20540i
\(742\) 15.7082 0.576666
\(743\) −19.0623 33.0169i −0.699328 1.21127i −0.968700 0.248236i \(-0.920149\pi\)
0.269372 0.963036i \(-0.413184\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −17.2705 −0.632318
\(747\) 8.94427 15.4919i 0.327254 0.566820i
\(748\) −0.663119 + 1.14856i −0.0242460 + 0.0419954i
\(749\) −24.4164 −0.892156
\(750\) 0 0
\(751\) 15.3541 + 26.5941i 0.560279 + 0.970432i 0.997472 + 0.0710640i \(0.0226395\pi\)
−0.437193 + 0.899368i \(0.644027\pi\)
\(752\) −4.58359 7.93901i −0.167146 0.289506i
\(753\) −45.2492 −1.64897
\(754\) −11.5451 11.9980i −0.420447 0.436942i
\(755\) 0 0
\(756\) −7.66312 13.2729i −0.278705 0.482731i
\(757\) −3.44427 5.96565i −0.125184 0.216825i 0.796621 0.604479i \(-0.206619\pi\)
−0.921805 + 0.387654i \(0.873286\pi\)
\(758\) −3.34346 + 5.79104i −0.121440 + 0.210340i
\(759\) −1.98684 −0.0721179
\(760\) 0 0
\(761\) 18.9721 32.8607i 0.687739 1.19120i −0.284828 0.958579i \(-0.591937\pi\)
0.972567 0.232621i \(-0.0747302\pi\)
\(762\) −5.85410 −0.212072
\(763\) −4.23607 + 7.33708i −0.153356 + 0.265620i
\(764\) −21.9894 38.0867i −0.795547 1.37793i
\(765\) 0 0
\(766\) −2.61803 −0.0945934
\(767\) −1.77051 1.83997i −0.0639294 0.0664374i
\(768\) 14.6738 0.529494
\(769\) −14.9164 25.8360i −0.537899 0.931669i −0.999017 0.0443301i \(-0.985885\pi\)
0.461118 0.887339i \(-0.347449\pi\)
\(770\) 0 0
\(771\) −19.5344 + 33.8346i −0.703516 + 1.21853i
\(772\) −5.61803 −0.202197
\(773\) −10.0279 + 17.3688i −0.360677 + 0.624711i −0.988072 0.153990i \(-0.950788\pi\)
0.627395 + 0.778701i \(0.284121\pi\)
\(774\) −3.85410 + 6.67550i −0.138533 + 0.239946i
\(775\) 0 0
\(776\) 3.88197 6.72376i 0.139354 0.241369i
\(777\) 14.2082 + 24.6093i 0.509716 + 0.882855i
\(778\) 0.0344419 + 0.0596550i 0.00123480 + 0.00213874i
\(779\) 50.5967 1.81282
\(780\) 0 0
\(781\) 1.47214 0.0526772
\(782\) 4.03851 + 6.99490i 0.144417 + 0.250137i
\(783\) 8.35410 + 14.4697i 0.298551 + 0.517106i
\(784\) −10.1459 + 17.5732i