Properties

Label 546.2.o.b.265.1
Level $546$
Weight $2$
Character 546.265
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.836829184.2
Defining polynomial: \(x^{8} + 14 x^{6} + 61 x^{4} + 84 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 265.1
Root \(-2.06644i\) of defining polynomial
Character \(\chi\) \(=\) 546.265
Dual form 546.2.o.b.307.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(-2.16830 - 2.16830i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.62949 - 0.292893i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(-2.16830 - 2.16830i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.62949 - 0.292893i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +3.06644 q^{10} +(0.516075 + 0.516075i) q^{11} -1.00000 q^{12} +(3.60525 - 0.0469777i) q^{13} +(-1.65222 + 2.06644i) q^{14} +(-2.16830 + 2.16830i) q^{15} -1.00000 q^{16} -2.57461 q^{17} +(0.707107 - 0.707107i) q^{18} +(-3.82052 - 3.82052i) q^{19} +(-2.16830 + 2.16830i) q^{20} +(-0.292893 - 2.62949i) q^{21} -0.729840 q^{22} -6.97248i q^{23} +(0.707107 - 0.707107i) q^{24} +4.40303i q^{25} +(-2.51608 + 2.58251i) q^{26} +1.00000i q^{27} +(-0.292893 - 2.62949i) q^{28} -6.32541 q^{29} -3.06644i q^{30} +(-4.33660 - 4.33660i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.516075 - 0.516075i) q^{33} +(1.82052 - 1.82052i) q^{34} +(-6.33660 - 5.06644i) q^{35} +1.00000i q^{36} +(-3.58251 - 3.58251i) q^{37} +5.40303 q^{38} +(-0.0469777 - 3.60525i) q^{39} -3.06644i q^{40} +(-0.176204 - 0.176204i) q^{41} +(2.06644 + 1.65222i) q^{42} +7.89486i q^{43} +(0.516075 - 0.516075i) q^{44} +(2.16830 + 2.16830i) q^{45} +(4.93029 + 4.93029i) q^{46} +(1.41421 - 1.41421i) q^{47} +1.00000i q^{48} +(6.82843 - 1.54032i) q^{49} +(-3.11341 - 3.11341i) q^{50} +2.57461i q^{51} +(-0.0469777 - 3.60525i) q^{52} -0.514936 q^{53} +(-0.707107 - 0.707107i) q^{54} -2.23801i q^{55} +(2.06644 + 1.65222i) q^{56} +(-3.82052 + 3.82052i) q^{57} +(4.47274 - 4.47274i) q^{58} +(-3.17834 + 3.17834i) q^{59} +(2.16830 + 2.16830i) q^{60} +6.41208i q^{61} +6.13287 q^{62} +(-2.62949 + 0.292893i) q^{63} +1.00000i q^{64} +(-7.91911 - 7.71538i) q^{65} +0.729840i q^{66} +(-3.96130 + 3.96130i) q^{67} +2.57461i q^{68} -6.97248 q^{69} +(8.06316 - 0.898138i) q^{70} +(8.12169 - 8.12169i) q^{71} +(-0.707107 - 0.707107i) q^{72} +(11.6056 - 11.6056i) q^{73} +5.06644 q^{74} +4.40303 q^{75} +(-3.82052 + 3.82052i) q^{76} +(1.50817 + 1.20586i) q^{77} +(2.58251 + 2.51608i) q^{78} +10.9455 q^{79} +(2.16830 + 2.16830i) q^{80} +1.00000 q^{81} +0.249190 q^{82} +(1.01118 + 1.01118i) q^{83} +(-2.62949 + 0.292893i) q^{84} +(5.58251 + 5.58251i) q^{85} +(-5.58251 - 5.58251i) q^{86} +6.32541i q^{87} +0.729840i q^{88} +(1.10977 - 1.10977i) q^{89} -3.06644 q^{90} +(9.46619 - 1.17948i) q^{91} -6.97248 q^{92} +(-4.33660 + 4.33660i) q^{93} +2.00000i q^{94} +16.5681i q^{95} +(-0.707107 - 0.707107i) q^{96} +(-9.34336 - 9.34336i) q^{97} +(-3.73926 + 5.91760i) q^{98} +(-0.516075 - 0.516075i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{5} - 8q^{9} + O(q^{10}) \) \( 8q - 4q^{5} - 8q^{9} + 4q^{10} - 8q^{12} + 16q^{13} - 4q^{14} - 4q^{15} - 8q^{16} + 4q^{17} - 8q^{19} - 4q^{20} - 8q^{21} - 12q^{22} - 16q^{26} - 8q^{28} + 12q^{29} - 8q^{31} - 8q^{34} - 24q^{35} - 4q^{37} - 4q^{38} - 4q^{39} + 12q^{41} - 4q^{42} + 4q^{45} + 24q^{46} + 32q^{49} - 8q^{50} - 4q^{52} + 40q^{53} - 4q^{56} - 8q^{57} + 4q^{58} - 8q^{59} + 4q^{60} + 8q^{62} - 12q^{65} + 32q^{67} - 28q^{69} + 8q^{70} - 12q^{71} + 20q^{73} + 20q^{74} - 12q^{75} - 8q^{76} + 8q^{77} - 4q^{78} + 24q^{79} + 4q^{80} + 8q^{81} + 40q^{82} + 44q^{83} + 20q^{85} - 20q^{86} + 16q^{89} - 4q^{90} - 28q^{91} - 28q^{92} - 8q^{93} - 8q^{97} - 16q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 1.00000i 0.577350i
\(4\) 1.00000i 0.500000i
\(5\) −2.16830 2.16830i −0.969692 0.969692i 0.0298617 0.999554i \(-0.490493\pi\)
−0.999554 + 0.0298617i \(0.990493\pi\)
\(6\) 0.707107 + 0.707107i 0.288675 + 0.288675i
\(7\) 2.62949 0.292893i 0.993854 0.110703i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −1.00000 −0.333333
\(10\) 3.06644 0.969692
\(11\) 0.516075 + 0.516075i 0.155603 + 0.155603i 0.780615 0.625012i \(-0.214906\pi\)
−0.625012 + 0.780615i \(0.714906\pi\)
\(12\) −1.00000 −0.288675
\(13\) 3.60525 0.0469777i 0.999915 0.0130293i
\(14\) −1.65222 + 2.06644i −0.441575 + 0.552278i
\(15\) −2.16830 + 2.16830i −0.559852 + 0.559852i
\(16\) −1.00000 −0.250000
\(17\) −2.57461 −0.624434 −0.312217 0.950011i \(-0.601072\pi\)
−0.312217 + 0.950011i \(0.601072\pi\)
\(18\) 0.707107 0.707107i 0.166667 0.166667i
\(19\) −3.82052 3.82052i −0.876488 0.876488i 0.116682 0.993169i \(-0.462774\pi\)
−0.993169 + 0.116682i \(0.962774\pi\)
\(20\) −2.16830 + 2.16830i −0.484846 + 0.484846i
\(21\) −0.292893 2.62949i −0.0639145 0.573802i
\(22\) −0.729840 −0.155603
\(23\) 6.97248i 1.45386i −0.686710 0.726931i \(-0.740946\pi\)
0.686710 0.726931i \(-0.259054\pi\)
\(24\) 0.707107 0.707107i 0.144338 0.144338i
\(25\) 4.40303i 0.880606i
\(26\) −2.51608 + 2.58251i −0.493443 + 0.506472i
\(27\) 1.00000i 0.192450i
\(28\) −0.292893 2.62949i −0.0553516 0.496927i
\(29\) −6.32541 −1.17460 −0.587300 0.809369i \(-0.699809\pi\)
−0.587300 + 0.809369i \(0.699809\pi\)
\(30\) 3.06644i 0.559852i
\(31\) −4.33660 4.33660i −0.778876 0.778876i 0.200764 0.979640i \(-0.435658\pi\)
−0.979640 + 0.200764i \(0.935658\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 0.516075 0.516075i 0.0898371 0.0898371i
\(34\) 1.82052 1.82052i 0.312217 0.312217i
\(35\) −6.33660 5.06644i −1.07108 0.856384i
\(36\) 1.00000i 0.166667i
\(37\) −3.58251 3.58251i −0.588961 0.588961i 0.348389 0.937350i \(-0.386729\pi\)
−0.937350 + 0.348389i \(0.886729\pi\)
\(38\) 5.40303 0.876488
\(39\) −0.0469777 3.60525i −0.00752245 0.577301i
\(40\) 3.06644i 0.484846i
\(41\) −0.176204 0.176204i −0.0275185 0.0275185i 0.693214 0.720732i \(-0.256194\pi\)
−0.720732 + 0.693214i \(0.756194\pi\)
\(42\) 2.06644 + 1.65222i 0.318858 + 0.254944i
\(43\) 7.89486i 1.20396i 0.798513 + 0.601978i \(0.205620\pi\)
−0.798513 + 0.601978i \(0.794380\pi\)
\(44\) 0.516075 0.516075i 0.0778013 0.0778013i
\(45\) 2.16830 + 2.16830i 0.323231 + 0.323231i
\(46\) 4.93029 + 4.93029i 0.726931 + 0.726931i
\(47\) 1.41421 1.41421i 0.206284 0.206284i −0.596402 0.802686i \(-0.703403\pi\)
0.802686 + 0.596402i \(0.203403\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 6.82843 1.54032i 0.975490 0.220046i
\(50\) −3.11341 3.11341i −0.440303 0.440303i
\(51\) 2.57461i 0.360517i
\(52\) −0.0469777 3.60525i −0.00651463 0.499958i
\(53\) −0.514936 −0.0707319 −0.0353660 0.999374i \(-0.511260\pi\)
−0.0353660 + 0.999374i \(0.511260\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) 2.23801i 0.301773i
\(56\) 2.06644 + 1.65222i 0.276139 + 0.220788i
\(57\) −3.82052 + 3.82052i −0.506040 + 0.506040i
\(58\) 4.47274 4.47274i 0.587300 0.587300i
\(59\) −3.17834 + 3.17834i −0.413785 + 0.413785i −0.883055 0.469270i \(-0.844517\pi\)
0.469270 + 0.883055i \(0.344517\pi\)
\(60\) 2.16830 + 2.16830i 0.279926 + 0.279926i
\(61\) 6.41208i 0.820982i 0.911865 + 0.410491i \(0.134643\pi\)
−0.911865 + 0.410491i \(0.865357\pi\)
\(62\) 6.13287 0.778876
\(63\) −2.62949 + 0.292893i −0.331285 + 0.0369011i
\(64\) 1.00000i 0.125000i
\(65\) −7.91911 7.71538i −0.982244 0.956976i
\(66\) 0.729840i 0.0898371i
\(67\) −3.96130 + 3.96130i −0.483950 + 0.483950i −0.906391 0.422441i \(-0.861173\pi\)
0.422441 + 0.906391i \(0.361173\pi\)
\(68\) 2.57461i 0.312217i
\(69\) −6.97248 −0.839388
\(70\) 8.06316 0.898138i 0.963732 0.107348i
\(71\) 8.12169 8.12169i 0.963867 0.963867i −0.0355021 0.999370i \(-0.511303\pi\)
0.999370 + 0.0355021i \(0.0113031\pi\)
\(72\) −0.707107 0.707107i −0.0833333 0.0833333i
\(73\) 11.6056 11.6056i 1.35833 1.35833i 0.482364 0.875971i \(-0.339778\pi\)
0.875971 0.482364i \(-0.160222\pi\)
\(74\) 5.06644 0.588961
\(75\) 4.40303 0.508418
\(76\) −3.82052 + 3.82052i −0.438244 + 0.438244i
\(77\) 1.50817 + 1.20586i 0.171872 + 0.137420i
\(78\) 2.58251 + 2.51608i 0.292412 + 0.284889i
\(79\) 10.9455 1.23146 0.615732 0.787956i \(-0.288860\pi\)
0.615732 + 0.787956i \(0.288860\pi\)
\(80\) 2.16830 + 2.16830i 0.242423 + 0.242423i
\(81\) 1.00000 0.111111
\(82\) 0.249190 0.0275185
\(83\) 1.01118 + 1.01118i 0.110992 + 0.110992i 0.760421 0.649430i \(-0.224992\pi\)
−0.649430 + 0.760421i \(0.724992\pi\)
\(84\) −2.62949 + 0.292893i −0.286901 + 0.0319573i
\(85\) 5.58251 + 5.58251i 0.605508 + 0.605508i
\(86\) −5.58251 5.58251i −0.601978 0.601978i
\(87\) 6.32541i 0.678156i
\(88\) 0.729840i 0.0778013i
\(89\) 1.10977 1.10977i 0.117635 0.117635i −0.645839 0.763474i \(-0.723492\pi\)
0.763474 + 0.645839i \(0.223492\pi\)
\(90\) −3.06644 −0.323231
\(91\) 9.46619 1.17948i 0.992327 0.123643i
\(92\) −6.97248 −0.726931
\(93\) −4.33660 + 4.33660i −0.449684 + 0.449684i
\(94\) 2.00000i 0.206284i
\(95\) 16.5681i 1.69985i
\(96\) −0.707107 0.707107i −0.0721688 0.0721688i
\(97\) −9.34336 9.34336i −0.948675 0.948675i 0.0500709 0.998746i \(-0.484055\pi\)
−0.998746 + 0.0500709i \(0.984055\pi\)
\(98\) −3.73926 + 5.91760i −0.377722 + 0.597768i
\(99\) −0.516075 0.516075i −0.0518675 0.0518675i
\(100\) 4.40303 0.440303
\(101\) −5.86058 −0.583149 −0.291575 0.956548i \(-0.594179\pi\)
−0.291575 + 0.956548i \(0.594179\pi\)
\(102\) −1.82052 1.82052i −0.180258 0.180258i
\(103\) −9.16965 −0.903513 −0.451756 0.892141i \(-0.649202\pi\)
−0.451756 + 0.892141i \(0.649202\pi\)
\(104\) 2.58251 + 2.51608i 0.253236 + 0.246721i
\(105\) −5.06644 + 6.33660i −0.494434 + 0.618388i
\(106\) 0.364115 0.364115i 0.0353660 0.0353660i
\(107\) 7.91334 0.765011 0.382506 0.923953i \(-0.375061\pi\)
0.382506 + 0.923953i \(0.375061\pi\)
\(108\) 1.00000 0.0962250
\(109\) 9.90330 9.90330i 0.948564 0.948564i −0.0501767 0.998740i \(-0.515978\pi\)
0.998740 + 0.0501767i \(0.0159785\pi\)
\(110\) 1.58251 + 1.58251i 0.150887 + 0.150887i
\(111\) −3.58251 + 3.58251i −0.340037 + 0.340037i
\(112\) −2.62949 + 0.292893i −0.248463 + 0.0276758i
\(113\) 11.9450 1.12369 0.561844 0.827243i \(-0.310092\pi\)
0.561844 + 0.827243i \(0.310092\pi\)
\(114\) 5.40303i 0.506040i
\(115\) −15.1184 + 15.1184i −1.40980 + 1.40980i
\(116\) 6.32541i 0.587300i
\(117\) −3.60525 + 0.0469777i −0.333305 + 0.00434309i
\(118\) 4.49485i 0.413785i
\(119\) −6.76990 + 0.754084i −0.620595 + 0.0691268i
\(120\) −3.06644 −0.279926
\(121\) 10.4673i 0.951576i
\(122\) −4.53402 4.53402i −0.410491 0.410491i
\(123\) −0.176204 + 0.176204i −0.0158878 + 0.0158878i
\(124\) −4.33660 + 4.33660i −0.389438 + 0.389438i
\(125\) −1.29440 + 1.29440i −0.115775 + 0.115775i
\(126\) 1.65222 2.06644i 0.147192 0.184093i
\(127\) 19.2112i 1.70472i 0.522954 + 0.852361i \(0.324830\pi\)
−0.522954 + 0.852361i \(0.675170\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 7.89486 0.695104
\(130\) 11.0553 0.144054i 0.969610 0.0126344i
\(131\) 9.83056i 0.858900i 0.903091 + 0.429450i \(0.141293\pi\)
−0.903091 + 0.429450i \(0.858707\pi\)
\(132\) −0.516075 0.516075i −0.0449186 0.0449186i
\(133\) −11.1650 8.92701i −0.968130 0.774070i
\(134\) 5.60212i 0.483950i
\(135\) 2.16830 2.16830i 0.186617 0.186617i
\(136\) −1.82052 1.82052i −0.156108 0.156108i
\(137\) 3.88019 + 3.88019i 0.331507 + 0.331507i 0.853159 0.521652i \(-0.174684\pi\)
−0.521652 + 0.853159i \(0.674684\pi\)
\(138\) 4.93029 4.93029i 0.419694 0.419694i
\(139\) 3.32681i 0.282176i −0.989997 0.141088i \(-0.954940\pi\)
0.989997 0.141088i \(-0.0450601\pi\)
\(140\) −5.06644 + 6.33660i −0.428192 + 0.535540i
\(141\) −1.41421 1.41421i −0.119098 0.119098i
\(142\) 11.4858i 0.963867i
\(143\) 1.88482 + 1.83633i 0.157617 + 0.153562i
\(144\) 1.00000 0.0833333
\(145\) 13.7154 + 13.7154i 1.13900 + 1.13900i
\(146\) 16.4128i 1.35833i
\(147\) −1.54032 6.82843i −0.127043 0.563199i
\(148\) −3.58251 + 3.58251i −0.294481 + 0.294481i
\(149\) 8.02774 8.02774i 0.657658 0.657658i −0.297168 0.954825i \(-0.596042\pi\)
0.954825 + 0.297168i \(0.0960420\pi\)
\(150\) −3.11341 + 3.11341i −0.254209 + 0.254209i
\(151\) 13.5417 + 13.5417i 1.10201 + 1.10201i 0.994169 + 0.107837i \(0.0343926\pi\)
0.107837 + 0.994169i \(0.465607\pi\)
\(152\) 5.40303i 0.438244i
\(153\) 2.57461 0.208145
\(154\) −1.91911 + 0.213765i −0.154646 + 0.0172257i
\(155\) 18.8061i 1.51054i
\(156\) −3.60525 + 0.0469777i −0.288651 + 0.00376122i
\(157\) 3.14458i 0.250965i 0.992096 + 0.125482i \(0.0400479\pi\)
−0.992096 + 0.125482i \(0.959952\pi\)
\(158\) −7.73963 + 7.73963i −0.615732 + 0.615732i
\(159\) 0.514936i 0.0408371i
\(160\) −3.06644 −0.242423
\(161\) −2.04219 18.3341i −0.160947 1.44493i
\(162\) −0.707107 + 0.707107i −0.0555556 + 0.0555556i
\(163\) −15.2816 15.2816i −1.19694 1.19694i −0.975077 0.221867i \(-0.928785\pi\)
−0.221867 0.975077i \(-0.571215\pi\)
\(164\) −0.176204 + 0.176204i −0.0137592 + 0.0137592i
\(165\) −2.23801 −0.174229
\(166\) −1.43003 −0.110992
\(167\) −9.21892 + 9.21892i −0.713382 + 0.713382i −0.967241 0.253860i \(-0.918300\pi\)
0.253860 + 0.967241i \(0.418300\pi\)
\(168\) 1.65222 2.06644i 0.127472 0.159429i
\(169\) 12.9956 0.338732i 0.999660 0.0260563i
\(170\) −7.89486 −0.605508
\(171\) 3.82052 + 3.82052i 0.292163 + 0.292163i
\(172\) 7.89486 0.601978
\(173\) 17.4793 1.32892 0.664462 0.747322i \(-0.268661\pi\)
0.664462 + 0.747322i \(0.268661\pi\)
\(174\) −4.47274 4.47274i −0.339078 0.339078i
\(175\) 1.28962 + 11.5777i 0.0974860 + 0.875194i
\(176\) −0.516075 0.516075i −0.0389006 0.0389006i
\(177\) 3.17834 + 3.17834i 0.238899 + 0.238899i
\(178\) 1.56945i 0.117635i
\(179\) 18.3235i 1.36956i 0.728749 + 0.684781i \(0.240102\pi\)
−0.728749 + 0.684781i \(0.759898\pi\)
\(180\) 2.16830 2.16830i 0.161615 0.161615i
\(181\) 4.96432 0.368995 0.184498 0.982833i \(-0.440934\pi\)
0.184498 + 0.982833i \(0.440934\pi\)
\(182\) −5.85959 + 7.52763i −0.434342 + 0.557985i
\(183\) 6.41208 0.473994
\(184\) 4.93029 4.93029i 0.363466 0.363466i
\(185\) 15.5359i 1.14222i
\(186\) 6.13287i 0.449684i
\(187\) −1.32869 1.32869i −0.0971634 0.0971634i
\(188\) −1.41421 1.41421i −0.103142 0.103142i
\(189\) 0.292893 + 2.62949i 0.0213048 + 0.191267i
\(190\) −11.7154 11.7154i −0.849923 0.849923i
\(191\) 10.5427 0.762841 0.381421 0.924402i \(-0.375435\pi\)
0.381421 + 0.924402i \(0.375435\pi\)
\(192\) 1.00000 0.0721688
\(193\) −13.6366 13.6366i −0.981586 0.981586i 0.0182475 0.999833i \(-0.494191\pi\)
−0.999833 + 0.0182475i \(0.994191\pi\)
\(194\) 13.2135 0.948675
\(195\) −7.71538 + 7.91911i −0.552510 + 0.567099i
\(196\) −1.54032 6.82843i −0.110023 0.487745i
\(197\) 13.4673 13.4673i 0.959508 0.959508i −0.0397038 0.999211i \(-0.512641\pi\)
0.999211 + 0.0397038i \(0.0126414\pi\)
\(198\) 0.729840 0.0518675
\(199\) 5.92452 0.419978 0.209989 0.977704i \(-0.432657\pi\)
0.209989 + 0.977704i \(0.432657\pi\)
\(200\) −3.11341 + 3.11341i −0.220152 + 0.220152i
\(201\) 3.96130 + 3.96130i 0.279409 + 0.279409i
\(202\) 4.14405 4.14405i 0.291575 0.291575i
\(203\) −16.6326 + 1.85267i −1.16738 + 0.130032i
\(204\) 2.57461 0.180258
\(205\) 0.764127i 0.0533689i
\(206\) 6.48392 6.48392i 0.451756 0.451756i
\(207\) 6.97248i 0.484621i
\(208\) −3.60525 + 0.0469777i −0.249979 + 0.00325731i
\(209\) 3.94335i 0.272767i
\(210\) −0.898138 8.06316i −0.0619774 0.556411i
\(211\) −7.04407 −0.484934 −0.242467 0.970160i \(-0.577957\pi\)
−0.242467 + 0.970160i \(0.577957\pi\)
\(212\) 0.514936i 0.0353660i
\(213\) −8.12169 8.12169i −0.556489 0.556489i
\(214\) −5.59557 + 5.59557i −0.382506 + 0.382506i
\(215\) 17.1184 17.1184i 1.16747 1.16747i
\(216\) −0.707107 + 0.707107i −0.0481125 + 0.0481125i
\(217\) −12.6732 10.1329i −0.860312 0.687864i
\(218\) 14.0054i 0.948564i
\(219\) −11.6056 11.6056i −0.784235 0.784235i
\(220\) −2.23801 −0.150887
\(221\) −9.28208 + 0.120949i −0.624381 + 0.00813591i
\(222\) 5.06644i 0.340037i
\(223\) 9.71425 + 9.71425i 0.650514 + 0.650514i 0.953117 0.302603i \(-0.0978555\pi\)
−0.302603 + 0.953117i \(0.597856\pi\)
\(224\) 1.65222 2.06644i 0.110394 0.138070i
\(225\) 4.40303i 0.293535i
\(226\) −8.44636 + 8.44636i −0.561844 + 0.561844i
\(227\) −13.9000 13.9000i −0.922577 0.922577i 0.0746342 0.997211i \(-0.476221\pi\)
−0.997211 + 0.0746342i \(0.976221\pi\)
\(228\) 3.82052 + 3.82052i 0.253020 + 0.253020i
\(229\) −5.97035 + 5.97035i −0.394532 + 0.394532i −0.876299 0.481768i \(-0.839995\pi\)
0.481768 + 0.876299i \(0.339995\pi\)
\(230\) 21.3807i 1.40980i
\(231\) 1.20586 1.50817i 0.0793397 0.0992302i
\(232\) −4.47274 4.47274i −0.293650 0.293650i
\(233\) 1.35293i 0.0886336i −0.999018 0.0443168i \(-0.985889\pi\)
0.999018 0.0443168i \(-0.0141111\pi\)
\(234\) 2.51608 2.58251i 0.164481 0.168824i
\(235\) −6.13287 −0.400065
\(236\) 3.17834 + 3.17834i 0.206892 + 0.206892i
\(237\) 10.9455i 0.710986i
\(238\) 4.25382 5.32026i 0.275734 0.344861i
\(239\) 20.8904 20.8904i 1.35129 1.35129i 0.467071 0.884220i \(-0.345309\pi\)
0.884220 0.467071i \(-0.154691\pi\)
\(240\) 2.16830 2.16830i 0.139963 0.139963i
\(241\) 11.1816 11.1816i 0.720269 0.720269i −0.248391 0.968660i \(-0.579902\pi\)
0.968660 + 0.248391i \(0.0799018\pi\)
\(242\) 7.40152 + 7.40152i 0.475788 + 0.475788i
\(243\) 1.00000i 0.0641500i
\(244\) 6.41208 0.410491
\(245\) −18.1459 11.4662i −1.15930 0.732548i
\(246\) 0.249190i 0.0158878i
\(247\) −13.9534 13.5944i −0.887833 0.864993i
\(248\) 6.13287i 0.389438i
\(249\) 1.01118 1.01118i 0.0640810 0.0640810i
\(250\) 1.83056i 0.115775i
\(251\) 20.6366 1.30257 0.651286 0.758832i \(-0.274230\pi\)
0.651286 + 0.758832i \(0.274230\pi\)
\(252\) 0.292893 + 2.62949i 0.0184505 + 0.165642i
\(253\) 3.59832 3.59832i 0.226225 0.226225i
\(254\) −13.5844 13.5844i −0.852361 0.852361i
\(255\) 5.58251 5.58251i 0.349590 0.349590i
\(256\) 1.00000 0.0625000
\(257\) −9.21351 −0.574723 −0.287362 0.957822i \(-0.592778\pi\)
−0.287362 + 0.957822i \(0.592778\pi\)
\(258\) −5.58251 + 5.58251i −0.347552 + 0.347552i
\(259\) −10.4695 8.37088i −0.650541 0.520141i
\(260\) −7.71538 + 7.91911i −0.478488 + 0.491122i
\(261\) 6.32541 0.391533
\(262\) −6.95126 6.95126i −0.429450 0.429450i
\(263\) 9.50464 0.586081 0.293041 0.956100i \(-0.405333\pi\)
0.293041 + 0.956100i \(0.405333\pi\)
\(264\) 0.729840 0.0449186
\(265\) 1.11654 + 1.11654i 0.0685882 + 0.0685882i
\(266\) 14.2072 1.58251i 0.871100 0.0970300i
\(267\) −1.10977 1.10977i −0.0679167 0.0679167i
\(268\) 3.96130 + 3.96130i 0.241975 + 0.241975i
\(269\) 15.7423i 0.959824i −0.877317 0.479912i \(-0.840669\pi\)
0.877317 0.479912i \(-0.159331\pi\)
\(270\) 3.06644i 0.186617i
\(271\) −17.4746 + 17.4746i −1.06151 + 1.06151i −0.0635278 + 0.997980i \(0.520235\pi\)
−0.997980 + 0.0635278i \(0.979765\pi\)
\(272\) 2.57461 0.156108
\(273\) −1.17948 9.46619i −0.0713853 0.572920i
\(274\) −5.48742 −0.331507
\(275\) −2.27230 + 2.27230i −0.137025 + 0.137025i
\(276\) 6.97248i 0.419694i
\(277\) 21.3991i 1.28575i 0.765971 + 0.642875i \(0.222259\pi\)
−0.765971 + 0.642875i \(0.777741\pi\)
\(278\) 2.35241 + 2.35241i 0.141088 + 0.141088i
\(279\) 4.33660 + 4.33660i 0.259625 + 0.259625i
\(280\) −0.898138 8.06316i −0.0536740 0.481866i
\(281\) 0.634274 + 0.634274i 0.0378376 + 0.0378376i 0.725772 0.687935i \(-0.241483\pi\)
−0.687935 + 0.725772i \(0.741483\pi\)
\(282\) 2.00000 0.119098
\(283\) −11.6503 −0.692539 −0.346269 0.938135i \(-0.612552\pi\)
−0.346269 + 0.938135i \(0.612552\pi\)
\(284\) −8.12169 8.12169i −0.481934 0.481934i
\(285\) 16.5681 0.981407
\(286\) −2.63125 + 0.0342862i −0.155589 + 0.00202739i
\(287\) −0.514936 0.411718i −0.0303957 0.0243030i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) −10.3714 −0.610083
\(290\) −19.3965 −1.13900
\(291\) −9.34336 + 9.34336i −0.547718 + 0.547718i
\(292\) −11.6056 11.6056i −0.679167 0.679167i
\(293\) 16.3755 16.3755i 0.956668 0.956668i −0.0424317 0.999099i \(-0.513510\pi\)
0.999099 + 0.0424317i \(0.0135105\pi\)
\(294\) 5.91760 + 3.73926i 0.345121 + 0.218078i
\(295\) 13.7832 0.802488
\(296\) 5.06644i 0.294481i
\(297\) −0.516075 + 0.516075i −0.0299457 + 0.0299457i
\(298\) 11.3529i 0.657658i
\(299\) −0.327551 25.1375i −0.0189428 1.45374i
\(300\) 4.40303i 0.254209i
\(301\) 2.31235 + 20.7595i 0.133282 + 1.19656i
\(302\) −19.1508 −1.10201
\(303\) 5.86058i 0.336681i
\(304\) 3.82052 + 3.82052i 0.219122 + 0.219122i
\(305\) 13.9033 13.9033i 0.796100 0.796100i
\(306\) −1.82052 + 1.82052i −0.104072 + 0.104072i
\(307\) 14.8704 14.8704i 0.848697 0.848697i −0.141274 0.989971i \(-0.545120\pi\)
0.989971 + 0.141274i \(0.0451198\pi\)
\(308\) 1.20586 1.50817i 0.0687102 0.0859359i
\(309\) 9.16965i 0.521643i
\(310\) −13.2979 13.2979i −0.755270 0.755270i
\(311\) 26.0489 1.47710 0.738549 0.674199i \(-0.235511\pi\)
0.738549 + 0.674199i \(0.235511\pi\)
\(312\) 2.51608 2.58251i 0.142445 0.146206i
\(313\) 13.1007i 0.740497i 0.928933 + 0.370248i \(0.120727\pi\)
−0.928933 + 0.370248i \(0.879273\pi\)
\(314\) −2.22355 2.22355i −0.125482 0.125482i
\(315\) 6.33660 + 5.06644i 0.357027 + 0.285461i
\(316\) 10.9455i 0.615732i
\(317\) −15.6157 + 15.6157i −0.877063 + 0.877063i −0.993230 0.116167i \(-0.962939\pi\)
0.116167 + 0.993230i \(0.462939\pi\)
\(318\) −0.364115 0.364115i −0.0204185 0.0204185i
\(319\) −3.26439 3.26439i −0.182771 0.182771i
\(320\) 2.16830 2.16830i 0.121212 0.121212i
\(321\) 7.91334i 0.441679i
\(322\) 14.4082 + 11.5201i 0.802937 + 0.641990i
\(323\) 9.83633 + 9.83633i 0.547308 + 0.547308i
\(324\) 1.00000i 0.0555556i
\(325\) 0.206844 + 15.8740i 0.0114736 + 0.880532i
\(326\) 21.6114 1.19694
\(327\) −9.90330 9.90330i −0.547653 0.547653i
\(328\) 0.249190i 0.0137592i
\(329\) 3.30445 4.13287i 0.182180 0.227853i
\(330\) 1.58251 1.58251i 0.0871144 0.0871144i
\(331\) −6.01634 + 6.01634i −0.330688 + 0.330688i −0.852848 0.522160i \(-0.825126\pi\)
0.522160 + 0.852848i \(0.325126\pi\)
\(332\) 1.01118 1.01118i 0.0554958 0.0554958i
\(333\) 3.58251 + 3.58251i 0.196320 + 0.196320i
\(334\) 13.0375i 0.713382i
\(335\) 17.1786 0.938565
\(336\) 0.292893 + 2.62949i 0.0159786 + 0.143450i
\(337\) 1.23748i 0.0674101i −0.999432 0.0337050i \(-0.989269\pi\)
0.999432 0.0337050i \(-0.0107307\pi\)
\(338\) −8.94975 + 9.42879i −0.486802 + 0.512858i
\(339\) 11.9450i 0.648761i
\(340\) 5.58251 5.58251i 0.302754 0.302754i
\(341\) 4.47602i 0.242390i
\(342\) −5.40303 −0.292163
\(343\) 17.5041 6.05025i 0.945134 0.326683i
\(344\) −5.58251 + 5.58251i −0.300989 + 0.300989i
\(345\) 15.1184 + 15.1184i 0.813948 + 0.813948i
\(346\) −12.3597 + 12.3597i −0.664462 + 0.664462i
\(347\) −12.1613 −0.652852 −0.326426 0.945223i \(-0.605844\pi\)
−0.326426 + 0.945223i \(0.605844\pi\)
\(348\) 6.32541 0.339078
\(349\) 17.9622 17.9622i 0.961494 0.961494i −0.0377919 0.999286i \(-0.512032\pi\)
0.999286 + 0.0377919i \(0.0120324\pi\)
\(350\) −9.09859 7.27479i −0.486340 0.388854i
\(351\) 0.0469777 + 3.60525i 0.00250748 + 0.192434i
\(352\) 0.729840 0.0389006
\(353\) 21.2045 + 21.2045i 1.12860 + 1.12860i 0.990405 + 0.138195i \(0.0441300\pi\)
0.138195 + 0.990405i \(0.455870\pi\)
\(354\) −4.49485 −0.238899
\(355\) −35.2205 −1.86931
\(356\) −1.10977 1.10977i −0.0588176 0.0588176i
\(357\) 0.754084 + 6.76990i 0.0399104 + 0.358301i
\(358\) −12.9567 12.9567i −0.684781 0.684781i
\(359\) 20.4359 + 20.4359i 1.07857 + 1.07857i 0.996638 + 0.0819287i \(0.0261080\pi\)
0.0819287 + 0.996638i \(0.473892\pi\)
\(360\) 3.06644i 0.161615i
\(361\) 10.1928i 0.536461i
\(362\) −3.51030 + 3.51030i −0.184498 + 0.184498i
\(363\) −10.4673 −0.549392
\(364\) −1.17948 9.46619i −0.0618215 0.496163i
\(365\) −50.3289 −2.63433
\(366\) −4.53402 + 4.53402i −0.236997 + 0.236997i
\(367\) 1.09998i 0.0574185i 0.999588 + 0.0287092i \(0.00913969\pi\)
−0.999588 + 0.0287092i \(0.990860\pi\)
\(368\) 6.97248i 0.363466i
\(369\) 0.176204 + 0.176204i 0.00917283 + 0.00917283i
\(370\) −10.9855 10.9855i −0.571111 0.571111i
\(371\) −1.35402 + 0.150821i −0.0702972 + 0.00783025i
\(372\) 4.33660 + 4.33660i 0.224842 + 0.224842i
\(373\) 20.6382 1.06861 0.534304 0.845293i \(-0.320574\pi\)
0.534304 + 0.845293i \(0.320574\pi\)
\(374\) 1.87905 0.0971634
\(375\) 1.29440 + 1.29440i 0.0668427 + 0.0668427i
\(376\) 2.00000 0.103142
\(377\) −22.8047 + 0.297153i −1.17450 + 0.0153042i
\(378\) −2.06644 1.65222i −0.106286 0.0849812i
\(379\) −5.82027 + 5.82027i −0.298967 + 0.298967i −0.840609 0.541642i \(-0.817803\pi\)
0.541642 + 0.840609i \(0.317803\pi\)
\(380\) 16.5681 0.849923
\(381\) 19.2112 0.984221
\(382\) −7.45480 + 7.45480i −0.381421 + 0.381421i
\(383\) −9.25710 9.25710i −0.473016 0.473016i 0.429874 0.902889i \(-0.358558\pi\)
−0.902889 + 0.429874i \(0.858558\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) −0.655498 5.88482i −0.0334073 0.299918i
\(386\) 19.2851 0.981586
\(387\) 7.89486i 0.401318i
\(388\) −9.34336 + 9.34336i −0.474337 + 0.474337i
\(389\) 33.6641i 1.70684i −0.521224 0.853420i \(-0.674524\pi\)
0.521224 0.853420i \(-0.325476\pi\)
\(390\) −0.144054 11.0553i −0.00729446 0.559805i
\(391\) 17.9514i 0.907841i
\(392\) 5.91760 + 3.73926i 0.298884 + 0.188861i
\(393\) 9.83056 0.495886
\(394\) 19.0457i 0.959508i
\(395\) −23.7331 23.7331i −1.19414 1.19414i
\(396\) −0.516075 + 0.516075i −0.0259338 + 0.0259338i
\(397\) −24.1629 + 24.1629i −1.21270 + 1.21270i −0.242566 + 0.970135i \(0.577989\pi\)
−0.970135 + 0.242566i \(0.922011\pi\)
\(398\) −4.18927 + 4.18927i −0.209989 + 0.209989i
\(399\) −8.92701 + 11.1650i −0.446910 + 0.558950i
\(400\) 4.40303i 0.220152i
\(401\) −8.28885 8.28885i −0.413925 0.413925i 0.469178 0.883104i \(-0.344550\pi\)
−0.883104 + 0.469178i \(0.844550\pi\)
\(402\) −5.60212 −0.279409
\(403\) −15.8382 15.4308i −0.788958 0.768661i
\(404\) 5.86058i 0.291575i
\(405\) −2.16830 2.16830i −0.107744 0.107744i
\(406\) 10.4510 13.0711i 0.518674 0.648706i
\(407\) 3.69769i 0.183288i
\(408\) −1.82052 + 1.82052i −0.0901292 + 0.0901292i
\(409\) 7.74077 + 7.74077i 0.382756 + 0.382756i 0.872094 0.489338i \(-0.162762\pi\)
−0.489338 + 0.872094i \(0.662762\pi\)
\(410\) −0.540319 0.540319i −0.0266845 0.0266845i
\(411\) 3.88019 3.88019i 0.191396 0.191396i
\(412\) 9.16965i 0.451756i
\(413\) −7.42650 + 9.28833i −0.365434 + 0.457049i
\(414\) −4.93029 4.93029i −0.242310 0.242310i
\(415\) 4.38508i 0.215255i
\(416\) 2.51608 2.58251i 0.123361 0.126618i
\(417\) −3.32681 −0.162914
\(418\) 2.78837 + 2.78837i 0.136384 + 0.136384i
\(419\) 37.2548i 1.82002i 0.414592 + 0.910008i \(0.363924\pi\)
−0.414592 + 0.910008i \(0.636076\pi\)
\(420\) 6.33660 + 5.06644i 0.309194 + 0.247217i
\(421\) 26.1725 26.1725i 1.27557 1.27557i 0.332451 0.943121i \(-0.392125\pi\)
0.943121 0.332451i \(-0.107875\pi\)
\(422\) 4.98091 4.98091i 0.242467 0.242467i
\(423\) −1.41421 + 1.41421i −0.0687614 + 0.0687614i
\(424\) −0.364115 0.364115i −0.0176830 0.0176830i
\(425\) 11.3361i 0.549880i
\(426\) 11.4858 0.556489
\(427\) 1.87805 + 16.8605i 0.0908854 + 0.815936i
\(428\) 7.91334i 0.382506i
\(429\) 1.83633 1.88482i 0.0886590 0.0910000i
\(430\) 24.2091i 1.16747i
\(431\) 2.05151 2.05151i 0.0988177 0.0988177i −0.655970 0.754787i \(-0.727740\pi\)
0.754787 + 0.655970i \(0.227740\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) −15.7613 −0.757441 −0.378720 0.925511i \(-0.623636\pi\)
−0.378720 + 0.925511i \(0.623636\pi\)
\(434\) 16.1263 1.79628i 0.774088 0.0862240i
\(435\) 13.7154 13.7154i 0.657602 0.657602i
\(436\) −9.90330 9.90330i −0.474282 0.474282i
\(437\) −26.6385 + 26.6385i −1.27429 + 1.27429i
\(438\) 16.4128 0.784235
\(439\) −10.8489 −0.517788 −0.258894 0.965906i \(-0.583358\pi\)
−0.258894 + 0.965906i \(0.583358\pi\)
\(440\) 1.58251 1.58251i 0.0754433 0.0754433i
\(441\) −6.82843 + 1.54032i −0.325163 + 0.0733485i
\(442\) 6.47790 6.64895i 0.308122 0.316258i
\(443\) −9.19115 −0.436685 −0.218342 0.975872i \(-0.570065\pi\)
−0.218342 + 0.975872i \(0.570065\pi\)
\(444\) 3.58251 + 3.58251i 0.170018 + 0.170018i
\(445\) −4.81261 −0.228140
\(446\) −13.7380 −0.650514
\(447\) −8.02774 8.02774i −0.379699 0.379699i
\(448\) 0.292893 + 2.62949i 0.0138379 + 0.124232i
\(449\) 15.6122 + 15.6122i 0.736784 + 0.736784i 0.971954 0.235170i \(-0.0755648\pi\)
−0.235170 + 0.971954i \(0.575565\pi\)
\(450\) 3.11341 + 3.11341i 0.146768 + 0.146768i
\(451\) 0.181869i 0.00856389i
\(452\) 11.9450i 0.561844i
\(453\) 13.5417 13.5417i 0.636243 0.636243i
\(454\) 19.6576 0.922577
\(455\) −23.0830 17.9681i −1.08215 0.842356i
\(456\) −5.40303 −0.253020
\(457\) −26.7396 + 26.7396i −1.25083 + 1.25083i −0.295477 + 0.955350i \(0.595479\pi\)
−0.955350 + 0.295477i \(0.904521\pi\)
\(458\) 8.44334i 0.394532i
\(459\) 2.57461i 0.120172i
\(460\) 15.1184 + 15.1184i 0.704900 + 0.704900i
\(461\) 17.1846 + 17.1846i 0.800368 + 0.800368i 0.983153 0.182785i \(-0.0585111\pi\)
−0.182785 + 0.983153i \(0.558511\pi\)
\(462\) 0.213765 + 1.91911i 0.00994526 + 0.0892850i
\(463\) −16.9948 16.9948i −0.789816 0.789816i 0.191648 0.981464i \(-0.438617\pi\)
−0.981464 + 0.191648i \(0.938617\pi\)
\(464\) 6.32541 0.293650
\(465\) 18.8061 0.872110
\(466\) 0.956669 + 0.956669i 0.0443168 + 0.0443168i
\(467\) −7.72653 −0.357541 −0.178771 0.983891i \(-0.557212\pi\)
−0.178771 + 0.983891i \(0.557212\pi\)
\(468\) 0.0469777 + 3.60525i 0.00217154 + 0.166653i
\(469\) −9.25596 + 11.5764i −0.427400 + 0.534550i
\(470\) 4.33660 4.33660i 0.200032 0.200032i
\(471\) 3.14458 0.144895
\(472\) −4.49485 −0.206892
\(473\) −4.07434 + 4.07434i −0.187338 + 0.187338i
\(474\) 7.73963 + 7.73963i 0.355493 + 0.355493i
\(475\) 16.8219 16.8219i 0.771841 0.771841i
\(476\) 0.754084 + 6.76990i 0.0345634 + 0.310298i
\(477\) 0.514936 0.0235773
\(478\) 29.5436i 1.35129i
\(479\) −26.0081 + 26.0081i −1.18834 + 1.18834i −0.210816 + 0.977526i \(0.567612\pi\)
−0.977526 + 0.210816i \(0.932388\pi\)
\(480\) 3.06644i 0.139963i
\(481\) −13.0841 12.7475i −0.596585 0.581238i
\(482\) 15.8131i 0.720269i
\(483\) −18.3341 + 2.04219i −0.834229 + 0.0929230i
\(484\) −10.4673 −0.475788
\(485\) 40.5184i 1.83985i
\(486\) 0.707107 + 0.707107i 0.0320750 + 0.0320750i
\(487\) −12.7641 + 12.7641i −0.578398 + 0.578398i −0.934462 0.356064i \(-0.884119\pi\)
0.356064 + 0.934462i \(0.384119\pi\)
\(488\) −4.53402 + 4.53402i −0.205246 + 0.205246i
\(489\) −15.2816 + 15.2816i −0.691056 + 0.691056i
\(490\) 20.9389 4.72329i 0.945925 0.213377i
\(491\) 43.7292i 1.97347i 0.162337 + 0.986735i \(0.448097\pi\)
−0.162337 + 0.986735i \(0.551903\pi\)
\(492\) 0.176204 + 0.176204i 0.00794390 + 0.00794390i
\(493\) 16.2854 0.733460
\(494\) 19.4793 0.253822i 0.876413 0.0114200i
\(495\) 2.23801i 0.100591i
\(496\) 4.33660 + 4.33660i 0.194719 + 0.194719i
\(497\) 18.9771 23.7347i 0.851240 1.06465i
\(498\) 1.43003i 0.0640810i
\(499\) 6.31100 6.31100i 0.282519 0.282519i −0.551594 0.834113i \(-0.685980\pi\)
0.834113 + 0.551594i \(0.185980\pi\)
\(500\) 1.29440 + 1.29440i 0.0578875 + 0.0578875i
\(501\) 9.21892 + 9.21892i 0.411871 + 0.411871i
\(502\) −14.5923 + 14.5923i −0.651286 + 0.651286i
\(503\) 23.4423i 1.04524i 0.852565 + 0.522620i \(0.175046\pi\)
−0.852565 + 0.522620i \(0.824954\pi\)
\(504\) −2.06644 1.65222i −0.0920464 0.0735959i
\(505\) 12.7075 + 12.7075i 0.565475 + 0.565475i
\(506\) 5.08880i 0.226225i
\(507\) −0.338732 12.9956i −0.0150436 0.577154i
\(508\) 19.2112 0.852361
\(509\) 16.5795 + 16.5795i 0.734874 + 0.734874i 0.971581 0.236707i \(-0.0760682\pi\)
−0.236707 + 0.971581i \(0.576068\pi\)
\(510\) 7.89486i 0.349590i
\(511\) 27.1176 33.9161i 1.19961 1.50036i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 3.82052 3.82052i 0.168680 0.168680i
\(514\) 6.51494 6.51494i 0.287362 0.287362i
\(515\) 19.8825 + 19.8825i 0.876130 + 0.876130i
\(516\) 7.89486i 0.347552i
\(517\) 1.45968 0.0641967
\(518\) 13.3221 1.48392i 0.585341 0.0651999i
\(519\) 17.4793i 0.767254i
\(520\) −0.144054 11.0553i −0.00631719 0.484805i
\(521\) 32.3153i 1.41576i −0.706332 0.707880i \(-0.749652\pi\)
0.706332 0.707880i \(-0.250348\pi\)
\(522\) −4.47274 + 4.47274i −0.195767 + 0.195767i
\(523\) 11.3376i 0.495757i −0.968791 0.247878i \(-0.920267\pi\)
0.968791 0.247878i \(-0.0797333\pi\)
\(524\) 9.83056 0.429450
\(525\) 11.5777 1.28962i 0.505293 0.0562836i
\(526\) −6.72080 + 6.72080i −0.293041 + 0.293041i
\(527\) 11.1650 + 11.1650i 0.486356 + 0.486356i
\(528\) −0.516075 + 0.516075i −0.0224593 + 0.0224593i
\(529\) −25.6155 −1.11372
\(530\) −1.57902 −0.0685882
\(531\) 3.17834 3.17834i 0.137928 0.137928i
\(532\) −8.92701 + 11.1650i −0.387035 + 0.484065i
\(533\) −0.643537 0.626982i −0.0278747 0.0271576i
\(534\) 1.56945 0.0679167
\(535\) −17.1585 17.1585i −0.741825 0.741825i
\(536\) −5.60212 −0.241975
\(537\) 18.3235 0.790717
\(538\) 11.1315 + 11.1315i 0.479912 + 0.479912i
\(539\) 4.31890 + 2.72906i 0.186028 + 0.117549i
\(540\) −2.16830 2.16830i −0.0933087 0.0933087i
\(541\) 17.1266 + 17.1266i 0.736329 + 0.736329i 0.971866 0.235536i \(-0.0756847\pi\)
−0.235536 + 0.971866i \(0.575685\pi\)
\(542\) 24.7129i 1.06151i
\(543\) 4.96432i 0.213039i
\(544\) −1.82052 + 1.82052i −0.0780542 + 0.0780542i
\(545\) −42.9466 −1.83963
\(546\) 7.52763 + 5.85959i 0.322153 + 0.250767i
\(547\) 0.145972 0.00624133 0.00312066 0.999995i \(-0.499007\pi\)
0.00312066 + 0.999995i \(0.499007\pi\)
\(548\) 3.88019 3.88019i 0.165754 0.165754i
\(549\) 6.41208i 0.273661i
\(550\) 3.21351i 0.137025i
\(551\) 24.1664 + 24.1664i 1.02952 + 1.02952i
\(552\) −4.93029 4.93029i −0.209847 0.209847i
\(553\) 28.7810 3.20586i 1.22389 0.136327i
\(554\) −15.1315 15.1315i −0.642875 0.642875i
\(555\) 15.5359 0.659462
\(556\) −3.32681 −0.141088
\(557\) −18.1533 18.1533i −0.769181 0.769181i 0.208782 0.977962i \(-0.433050\pi\)
−0.977962 + 0.208782i \(0.933050\pi\)
\(558\) −6.13287 −0.259625
\(559\) 0.370882 + 28.4629i 0.0156866 + 1.20385i
\(560\) 6.33660 + 5.06644i 0.267770 + 0.214096i
\(561\) −1.32869 + 1.32869i −0.0560973 + 0.0560973i
\(562\) −0.897000 −0.0378376
\(563\) 21.4249 0.902951 0.451476 0.892283i \(-0.350898\pi\)
0.451476 + 0.892283i \(0.350898\pi\)
\(564\) −1.41421 + 1.41421i −0.0595491 + 0.0595491i
\(565\) −25.9002 25.9002i −1.08963 1.08963i
\(566\) 8.23801 8.23801i 0.346269 0.346269i
\(567\) 2.62949 0.292893i 0.110428 0.0123004i
\(568\) 11.4858 0.481934
\(569\) 26.3627i 1.10518i −0.833452 0.552591i \(-0.813639\pi\)
0.833452 0.552591i \(-0.186361\pi\)
\(570\) −11.7154 + 11.7154i −0.490703 + 0.490703i
\(571\) 21.5077i 0.900068i −0.893012 0.450034i \(-0.851412\pi\)
0.893012 0.450034i \(-0.148588\pi\)
\(572\) 1.83633 1.88482i 0.0767810 0.0788083i
\(573\) 10.5427i 0.440426i
\(574\) 0.655244 0.0729862i 0.0273493 0.00304638i
\(575\) 30.7001 1.28028
\(576\) 1.00000i 0.0416667i
\(577\) −11.5787 11.5787i −0.482028 0.482028i 0.423751 0.905779i \(-0.360713\pi\)
−0.905779 + 0.423751i \(0.860713\pi\)
\(578\) 7.33369 7.33369i 0.305041 0.305041i
\(579\) −13.6366 + 13.6366i −0.566719 + 0.566719i
\(580\) 13.7154 13.7154i 0.569500 0.569500i
\(581\) 2.95506 + 2.36272i 0.122596 + 0.0980222i
\(582\) 13.2135i 0.547718i
\(583\) −0.265746 0.265746i −0.0110061 0.0110061i
\(584\) 16.4128 0.679167
\(585\) 7.91911 + 7.71538i 0.327415 + 0.318992i
\(586\) 23.1585i 0.956668i
\(587\) −27.3890 27.3890i −1.13047 1.13047i −0.990099 0.140368i \(-0.955172\pi\)
−0.140368 0.990099i \(-0.544828\pi\)
\(588\) −6.82843 + 1.54032i −0.281600 + 0.0635217i
\(589\) 33.1361i 1.36535i
\(590\) −9.74618 + 9.74618i −0.401244 + 0.401244i
\(591\) −13.4673 13.4673i −0.553972 0.553972i
\(592\) 3.58251 + 3.58251i 0.147240 + 0.147240i
\(593\) 12.3499 12.3499i 0.507150 0.507150i −0.406500 0.913651i \(-0.633251\pi\)
0.913651 + 0.406500i \(0.133251\pi\)
\(594\) 0.729840i 0.0299457i
\(595\) 16.3142 + 13.0441i 0.668818 + 0.534755i
\(596\) −8.02774 8.02774i −0.328829 0.328829i
\(597\) 5.92452i 0.242474i
\(598\) 18.0065 + 17.5433i 0.736341 + 0.717398i
\(599\) −29.0798 −1.18817 −0.594084 0.804403i \(-0.702485\pi\)
−0.594084 + 0.804403i \(0.702485\pi\)
\(600\) 3.11341 + 3.11341i 0.127105 + 0.127105i
\(601\) 28.7194i 1.17149i −0.810496 0.585744i \(-0.800802\pi\)
0.810496 0.585744i \(-0.199198\pi\)
\(602\) −16.3142 13.0441i −0.664919 0.531637i
\(603\) 3.96130 3.96130i 0.161317 0.161317i
\(604\) 13.5417 13.5417i 0.551003 0.551003i
\(605\) −22.6963 + 22.6963i −0.922736 + 0.922736i
\(606\) −4.14405 4.14405i −0.168341 0.168341i
\(607\) 22.9366i 0.930967i 0.885056 + 0.465484i \(0.154120\pi\)
−0.885056 + 0.465484i \(0.845880\pi\)
\(608\) −5.40303 −0.219122
\(609\) 1.85267 + 16.6326i 0.0750740 + 0.673987i
\(610\) 19.6622i 0.796100i
\(611\) 5.03215 5.16502i 0.203579 0.208954i
\(612\) 2.57461i 0.104072i
\(613\) −5.54006 + 5.54006i −0.223761 + 0.223761i −0.810080 0.586319i \(-0.800576\pi\)
0.586319 + 0.810080i \(0.300576\pi\)
\(614\) 21.0299i 0.848697i
\(615\) 0.764127 0.0308126
\(616\) 0.213765 + 1.91911i 0.00861285 + 0.0773230i
\(617\) −3.86438 + 3.86438i −0.155574 + 0.155574i −0.780602 0.625028i \(-0.785087\pi\)
0.625028 + 0.780602i \(0.285087\pi\)
\(618\) −6.48392 6.48392i −0.260822 0.260822i
\(619\) 25.0182 25.0182i 1.00557 1.00557i 0.00558273 0.999984i \(-0.498223\pi\)
0.999984 0.00558273i \(-0.00177705\pi\)
\(620\) 18.8061 0.755270
\(621\) 6.97248 0.279796
\(622\) −18.4194 + 18.4194i −0.738549 + 0.738549i
\(623\) 2.59308 3.24317i 0.103890 0.129935i
\(624\) 0.0469777 + 3.60525i 0.00188061 + 0.144325i
\(625\) 27.6285 1.10514
\(626\) −9.26361 9.26361i −0.370248 0.370248i
\(627\) −3.94335 −0.157482
\(628\) 3.14458 0.125482
\(629\) 9.22355 + 9.22355i 0.367767 + 0.367767i
\(630\) −8.06316 + 0.898138i −0.321244 + 0.0357827i
\(631\) −8.12549 8.12549i −0.323471 0.323471i 0.526626 0.850097i \(-0.323457\pi\)
−0.850097 + 0.526626i \(0.823457\pi\)
\(632\) 7.73963 + 7.73963i 0.307866 + 0.307866i
\(633\) 7.04407i 0.279977i
\(634\) 22.0839i 0.877063i
\(635\) 41.6557 41.6557i 1.65306 1.65306i
\(636\) 0.514936 0.0204185
\(637\) 24.5458 5.87401i 0.972540 0.232737i
\(638\) 4.61654 0.182771
\(639\) −8.12169 + 8.12169i −0.321289 + 0.321289i
\(640\) 3.06644i 0.121212i
\(641\) 42.7580i 1.68884i −0.535682 0.844420i \(-0.679945\pi\)
0.535682 0.844420i \(-0.320055\pi\)
\(642\) 5.59557 + 5.59557i 0.220840 + 0.220840i
\(643\) 7.37341 + 7.37341i 0.290779 + 0.290779i 0.837388 0.546609i \(-0.184082\pi\)
−0.546609 + 0.837388i \(0.684082\pi\)
\(644\) −18.3341 + 2.04219i −0.722463 + 0.0804737i
\(645\) −17.1184 17.1184i −0.674037 0.674037i
\(646\) −13.9107 −0.547308
\(647\) 22.7445 0.894178 0.447089 0.894490i \(-0.352461\pi\)
0.447089 + 0.894490i \(0.352461\pi\)
\(648\) 0.707107 + 0.707107i 0.0277778 + 0.0277778i
\(649\) −3.28052 −0.128772
\(650\) −11.3709 11.0784i −0.446003 0.434529i
\(651\) −10.1329 + 12.6732i −0.397139 + 0.496702i
\(652\) −15.2816 + 15.2816i −0.598472 + 0.598472i
\(653\) −28.5645 −1.11782 −0.558908 0.829230i \(-0.688780\pi\)
−0.558908 + 0.829230i \(0.688780\pi\)
\(654\) 14.0054 0.547653
\(655\) 21.3156 21.3156i 0.832869 0.832869i
\(656\) 0.176204 + 0.176204i 0.00687962 + 0.00687962i
\(657\) −11.6056 + 11.6056i −0.452778 + 0.452778i
\(658\) 0.585786 + 5.25898i 0.0228363 + 0.205016i
\(659\) −24.6149 −0.958862 −0.479431 0.877580i \(-0.659157\pi\)
−0.479431 + 0.877580i \(0.659157\pi\)
\(660\) 2.23801i 0.0871144i
\(661\) −14.7668 + 14.7668i −0.574363 + 0.574363i −0.933345 0.358981i \(-0.883124\pi\)
0.358981 + 0.933345i \(0.383124\pi\)
\(662\) 8.50839i 0.330688i
\(663\) 0.120949 + 9.28208i 0.00469727 + 0.360486i
\(664\) 1.43003i 0.0554958i
\(665\) 4.85267 + 43.5655i 0.188179 + 1.68940i
\(666\) −5.06644 −0.196320
\(667\) 44.1038i 1.70771i
\(668\) 9.21892 + 9.21892i 0.356691 + 0.356691i
\(669\) 9.71425 9.71425i 0.375574 0.375574i
\(670\) −12.1471 + 12.1471i −0.469282 + 0.469282i
\(671\) −3.30911 + 3.30911i −0.127747 + 0.127747i
\(672\) −2.06644 1.65222i −0.0797145 0.0637359i
\(673\) 50.9335i 1.96334i −0.190584 0.981671i \(-0.561038\pi\)
0.190584 0.981671i \(-0.438962\pi\)
\(674\) 0.875033 + 0.875033i 0.0337050 + 0.0337050i
\(675\) −4.40303 −0.169473
\(676\) −0.338732 12.9956i −0.0130282 0.499830i
\(677\) 4.02891i 0.154844i −0.996998 0.0774218i \(-0.975331\pi\)
0.996998 0.0774218i \(-0.0246688\pi\)
\(678\) 8.44636 + 8.44636i 0.324381 + 0.324381i
\(679\) −27.3049 21.8317i −1.04787 0.837822i
\(680\) 7.89486i 0.302754i
\(681\) −13.9000 + 13.9000i −0.532650 + 0.532650i
\(682\) 3.16502 + 3.16502i 0.121195 + 0.121195i
\(683\) −17.3021 17.3021i −0.662045 0.662045i 0.293817 0.955862i \(-0.405074\pi\)
−0.955862 + 0.293817i \(0.905074\pi\)
\(684\) 3.82052 3.82052i 0.146081 0.146081i
\(685\) 16.8268i 0.642920i
\(686\) −8.09911 + 16.6555i −0.309226 + 0.635908i
\(687\) 5.97035 + 5.97035i 0.227783 + 0.227783i
\(688\) 7.89486i 0.300989i
\(689\) −1.85647 + 0.0241905i −0.0707259 + 0.000921585i
\(690\) −21.3807 −0.813948
\(691\) 2.49183 + 2.49183i 0.0947937 + 0.0947937i 0.752913 0.658120i \(-0.228648\pi\)
−0.658120 + 0.752913i \(0.728648\pi\)
\(692\) 17.4793i 0.664462i
\(693\) −1.50817 1.20586i −0.0572906 0.0458068i
\(694\) 8.59932 8.59932i 0.326426 0.326426i
\(695\) −7.21351 + 7.21351i −0.273624 + 0.273624i
\(696\) −4.47274 + 4.47274i −0.169539 + 0.169539i
\(697\) 0.453656 + 0.453656i 0.0171835 + 0.0171835i
\(698\) 25.4024i 0.961494i
\(699\) −1.35293 −0.0511727
\(700\) 11.5777 1.28962i 0.437597 0.0487430i
\(701\) 0.236091i 0.00891703i 0.999990 + 0.00445852i \(0.00141919\pi\)
−0.999990 + 0.00445852i \(0.998581\pi\)
\(702\) −2.58251 2.51608i −0.0974706 0.0949631i
\(703\) 27.3741i 1.03243i
\(704\) −0.516075 + 0.516075i −0.0194503 + 0.0194503i
\(705\) 6.13287i 0.230977i
\(706\) −29.9876 −1.12860
\(707\) −15.4103 + 1.71652i −0.579565 + 0.0645565i
\(708\) 3.17834 3.17834i 0.119449 0.119449i
\(709\) 9.68526 + 9.68526i 0.363737 + 0.363737i 0.865187 0.501449i \(-0.167200\pi\)
−0.501449 + 0.865187i \(0.667200\pi\)
\(710\) 24.9047 24.9047i 0.934655 0.934655i
\(711\) −10.9455 −0.410488
\(712\) 1.56945 0.0588176
\(713\) −30.2368 + 30.2368i −1.13238 + 1.13238i
\(714\) −5.32026 4.25382i −0.199106 0.159195i
\(715\) −0.105136 8.06857i −0.00393188 0.301747i
\(716\) 18.3235 0.684781
\(717\) −20.8904 20.8904i −0.780168 0.780168i
\(718\) −28.9008 −1.07857
\(719\) 47.6518 1.77711 0.888556 0.458768i \(-0.151709\pi\)
0.888556 + 0.458768i \(0.151709\pi\)
\(720\) −2.16830 2.16830i −0.0808077 0.0808077i
\(721\) −24.1115 + 2.68573i −0.897959 + 0.100022i
\(722\) −7.20737 7.20737i −0.268231 0.268231i
\(723\) −11.1816 11.1816i −0.415847 0.415847i
\(724\) 4.96432i 0.184498i
\(725\) 27.8510i 1.03436i
\(726\) 7.40152 7.40152i 0.274696 0.274696i
\(727\) −10.6947 −0.396644 −0.198322 0.980137i \(-0.563549\pi\)
−0.198322 + 0.980137i \(0.563549\pi\)
\(728\) 7.52763 + 5.85959i 0.278992 + 0.217171i
\(729\) −1.00000 −0.0370370
\(730\) 35.5879 35.5879i 1.31717 1.31717i
\(731\) 20.3262i 0.751790i
\(732\) 6.41208i 0.236997i
\(733\) 1.22630 + 1.22630i 0.0452945 + 0.0452945i 0.729391 0.684097i \(-0.239803\pi\)
−0.684097 + 0.729391i \(0.739803\pi\)
\(734\) −0.777803 0.777803i −0.0287092 0.0287092i
\(735\) −11.4662 + 18.1459i −0.422937 + 0.669323i
\(736\) −4.93029 4.93029i −0.181733 0.181733i
\(737\) −4.08866 −0.150608
\(738\) −0.249190 −0.00917283
\(739\) 10.0141 + 10.0141i 0.368373 + 0.368373i 0.866884 0.498511i \(-0.166119\pi\)
−0.498511 + 0.866884i \(0.666119\pi\)
\(740\) 15.5359 0.571111
\(741\) −13.5944 + 13.9534i −0.499404 + 0.512591i
\(742\) 0.850789 1.06408i 0.0312335 0.0390637i
\(743\) −17.3229 + 17.3229i −0.635516 + 0.635516i −0.949446 0.313930i \(-0.898354\pi\)
0.313930 + 0.949446i \(0.398354\pi\)
\(744\) −6.13287 −0.224842
\(745\) −34.8130 −1.27545
\(746\) −14.5934 + 14.5934i −0.534304 + 0.534304i
\(747\) −1.01118 1.01118i −0.0369972 0.0369972i
\(748\) −1.32869 + 1.32869i −0.0485817 + 0.0485817i
\(749\) 20.8080 2.31776i 0.760309 0.0846892i
\(750\) −1.83056 −0.0668427
\(751\) 38.8207i 1.41659i −0.705919 0.708293i \(-0.749466\pi\)
0.705919 0.708293i \(-0.250534\pi\)
\(752\) −1.41421 + 1.41421i −0.0515711 + 0.0515711i
\(753\) 20.6366i 0.752041i
\(754\) 15.9152 16.3355i 0.579598 0.594902i
\(755\) 58.7248i 2.13721i
\(756\) 2.62949 0.292893i 0.0956336 0.0106524i
\(757\) −12.6121 −0.458395 −0.229198 0.973380i \(-0.573610\pi\)
−0.229198 + 0.973380i \(0.573610\pi\)
\(758\) 8.23110i 0.298967i
\(759\) −3.59832 3.59832i −0.130611 0.130611i
\(760\) −11.7154 + 11.7154i −0.424962 + 0.424962i
\(761\) −30.3727 + 30.3727i −1.10101 + 1.10101i −0.106721 + 0.994289i \(0.534035\pi\)
−0.994289 + 0.106721i \(0.965965\pi\)
\(762\) −13.5844 + 13.5844i −0.492111 + 0.492111i
\(763\) 23.1400 28.9412i 0.837724 1.04774i
\(764\) 10.5427i 0.381421i
\(765\) −5.58251 5.58251i −0.201836 0.201836i
\(766\) 13.0915 0.473016
\(767\) −11.3094 + 11.6080i −0.408358 + 0.419141i
\(768\) 1.00000i 0.0360844i
\(769\) 0.566917 + 0.566917i 0.0204435 + 0.0204435i 0.717255 0.696811i \(-0.245398\pi\)
−0.696811 + 0.717255i \(0.745398\pi\)
\(770\) 4.62470 + 3.69769i 0.166663 + 0.133256i
\(771\) 9.21351i 0.331816i
\(772\) −13.6366 + 13.6366i −0.490793 + 0.490793i
\(773\) 23.9977 + 23.9977i 0.863137 + 0.863137i 0.991701 0.128564i \(-0.0410369\pi\)
−0.128564 + 0.991701i \(0.541037\pi\)
\(774\) 5.58251 + 5.58251i 0.200659 + 0.200659i
\(775\) 19.0942 19.0942i 0.685883 0.685883i
\(776\) 13.2135i 0.474337i
\(777\) −8.37088 + 10.4695i −0.300304 + 0.375590i
\(778\) 23.8041 + 23.8041i 0.853420 +