Properties

Label 441.2.w.a.188.14
Level $441$
Weight $2$
Character 441.188
Analytic conductor $3.521$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.w (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 188.14
Character \(\chi\) \(=\) 441.188
Dual form 441.2.w.a.251.14

$q$-expansion

\(f(q)\) \(=\) \(q+(0.947442 - 0.755560i) q^{2} +(-0.118266 + 0.518156i) q^{4} +(3.15639 - 1.52004i) q^{5} +(1.53392 + 2.15571i) q^{7} +(1.33103 + 2.76391i) q^{8} +O(q^{10})\) \(q+(0.947442 - 0.755560i) q^{2} +(-0.118266 + 0.518156i) q^{4} +(3.15639 - 1.52004i) q^{5} +(1.53392 + 2.15571i) q^{7} +(1.33103 + 2.76391i) q^{8} +(1.84202 - 3.82499i) q^{10} +(-0.959544 + 0.765211i) q^{11} +(-4.81566 + 3.84036i) q^{13} +(3.08207 + 0.883437i) q^{14} +(2.39168 + 1.15177i) q^{16} +(-0.101589 - 0.445092i) q^{17} -8.04235i q^{19} +(0.414324 + 1.81527i) q^{20} +(-0.330950 + 1.44999i) q^{22} +(-1.94273 - 0.443416i) q^{23} +(4.53483 - 5.68650i) q^{25} +(-1.66094 + 7.27704i) q^{26} +(-1.29840 + 0.539866i) q^{28} +(6.85693 - 1.56505i) q^{29} -6.87818i q^{31} +(-2.84538 + 0.649440i) q^{32} +(-0.432544 - 0.344943i) q^{34} +(8.11842 + 4.47263i) q^{35} +(0.226997 + 0.994537i) q^{37} +(-6.07648 - 7.61967i) q^{38} +(8.40250 + 6.70077i) q^{40} +(5.35226 - 2.57751i) q^{41} +(-8.06594 - 3.88435i) q^{43} +(-0.283018 - 0.587692i) q^{44} +(-2.17566 + 1.04774i) q^{46} +(-0.922167 - 1.15636i) q^{47} +(-2.29415 + 6.61339i) q^{49} -8.81397i q^{50} +(-1.42038 - 2.94945i) q^{52} +(-7.14540 - 1.63089i) q^{53} +(-1.86555 + 3.87385i) q^{55} +(-3.91649 + 7.10894i) q^{56} +(5.31406 - 6.66362i) q^{58} +(6.83339 + 3.29079i) q^{59} +(-6.28213 + 1.43385i) q^{61} +(-5.19688 - 6.51668i) q^{62} +(-5.51533 + 6.91601i) q^{64} +(-9.36261 + 19.4417i) q^{65} +1.41606 q^{67} +0.242642 q^{68} +(11.0711 - 1.89639i) q^{70} +(-14.0112 - 3.19797i) q^{71} +(-1.23210 - 0.982563i) q^{73} +(0.966498 + 0.770757i) q^{74} +(4.16720 + 0.951136i) q^{76} +(-3.12144 - 0.894721i) q^{77} -6.59140 q^{79} +9.29981 q^{80} +(3.12349 - 6.48600i) q^{82} +(3.24033 - 4.06324i) q^{83} +(-0.997213 - 1.25047i) q^{85} +(-10.5769 + 2.41410i) q^{86} +(-3.39216 - 1.63358i) q^{88} +(8.27979 - 10.3825i) q^{89} +(-15.6656 - 4.49033i) q^{91} +(0.459518 - 0.954199i) q^{92} +(-1.74740 - 0.398833i) q^{94} +(-12.2247 - 25.3848i) q^{95} +11.9798i q^{97} +(2.82323 + 7.99917i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 24 q^{4} + O(q^{10}) \) \( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{14}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.947442 0.755560i 0.669943 0.534262i −0.228394 0.973569i \(-0.573347\pi\)
0.898337 + 0.439307i \(0.144776\pi\)
\(3\) 0 0
\(4\) −0.118266 + 0.518156i −0.0591329 + 0.259078i
\(5\) 3.15639 1.52004i 1.41158 0.679781i 0.436106 0.899895i \(-0.356357\pi\)
0.975474 + 0.220114i \(0.0706429\pi\)
\(6\) 0 0
\(7\) 1.53392 + 2.15571i 0.579769 + 0.814781i
\(8\) 1.33103 + 2.76391i 0.470590 + 0.977191i
\(9\) 0 0
\(10\) 1.84202 3.82499i 0.582497 1.20957i
\(11\) −0.959544 + 0.765211i −0.289313 + 0.230720i −0.757381 0.652973i \(-0.773522\pi\)
0.468068 + 0.883692i \(0.344950\pi\)
\(12\) 0 0
\(13\) −4.81566 + 3.84036i −1.33562 + 1.06512i −0.343595 + 0.939118i \(0.611645\pi\)
−0.992029 + 0.126006i \(0.959784\pi\)
\(14\) 3.08207 + 0.883437i 0.823718 + 0.236108i
\(15\) 0 0
\(16\) 2.39168 + 1.15177i 0.597920 + 0.287943i
\(17\) −0.101589 0.445092i −0.0246391 0.107951i 0.961113 0.276155i \(-0.0890603\pi\)
−0.985752 + 0.168204i \(0.946203\pi\)
\(18\) 0 0
\(19\) 8.04235i 1.84504i −0.385946 0.922521i \(-0.626125\pi\)
0.385946 0.922521i \(-0.373875\pi\)
\(20\) 0.414324 + 1.81527i 0.0926457 + 0.405907i
\(21\) 0 0
\(22\) −0.330950 + 1.44999i −0.0705588 + 0.309138i
\(23\) −1.94273 0.443416i −0.405088 0.0924587i 0.0151218 0.999886i \(-0.495186\pi\)
−0.420210 + 0.907427i \(0.638044\pi\)
\(24\) 0 0
\(25\) 4.53483 5.68650i 0.906967 1.13730i
\(26\) −1.66094 + 7.27704i −0.325737 + 1.42715i
\(27\) 0 0
\(28\) −1.29840 + 0.539866i −0.245375 + 0.102025i
\(29\) 6.85693 1.56505i 1.27330 0.290623i 0.468127 0.883661i \(-0.344929\pi\)
0.805174 + 0.593039i \(0.202072\pi\)
\(30\) 0 0
\(31\) 6.87818i 1.23536i −0.786430 0.617679i \(-0.788073\pi\)
0.786430 0.617679i \(-0.211927\pi\)
\(32\) −2.84538 + 0.649440i −0.502998 + 0.114806i
\(33\) 0 0
\(34\) −0.432544 0.344943i −0.0741807 0.0591572i
\(35\) 8.11842 + 4.47263i 1.37226 + 0.756013i
\(36\) 0 0
\(37\) 0.226997 + 0.994537i 0.0373180 + 0.163501i 0.990153 0.139987i \(-0.0447060\pi\)
−0.952835 + 0.303488i \(0.901849\pi\)
\(38\) −6.07648 7.61967i −0.985736 1.23607i
\(39\) 0 0
\(40\) 8.40250 + 6.70077i 1.32855 + 1.05948i
\(41\) 5.35226 2.57751i 0.835882 0.402540i 0.0335644 0.999437i \(-0.489314\pi\)
0.802318 + 0.596897i \(0.203600\pi\)
\(42\) 0 0
\(43\) −8.06594 3.88435i −1.23004 0.592358i −0.297953 0.954581i \(-0.596304\pi\)
−0.932092 + 0.362223i \(0.882018\pi\)
\(44\) −0.283018 0.587692i −0.0426665 0.0885979i
\(45\) 0 0
\(46\) −2.17566 + 1.04774i −0.320783 + 0.154481i
\(47\) −0.922167 1.15636i −0.134512 0.168672i 0.710014 0.704188i \(-0.248689\pi\)
−0.844525 + 0.535515i \(0.820117\pi\)
\(48\) 0 0
\(49\) −2.29415 + 6.61339i −0.327736 + 0.944769i
\(50\) 8.81397i 1.24648i
\(51\) 0 0
\(52\) −1.42038 2.94945i −0.196971 0.409015i
\(53\) −7.14540 1.63089i −0.981496 0.224020i −0.298474 0.954418i \(-0.596478\pi\)
−0.683022 + 0.730398i \(0.739335\pi\)
\(54\) 0 0
\(55\) −1.86555 + 3.87385i −0.251550 + 0.522349i
\(56\) −3.91649 + 7.10894i −0.523363 + 0.949973i
\(57\) 0 0
\(58\) 5.31406 6.66362i 0.697770 0.874976i
\(59\) 6.83339 + 3.29079i 0.889631 + 0.428424i 0.822133 0.569296i \(-0.192784\pi\)
0.0674982 + 0.997719i \(0.478498\pi\)
\(60\) 0 0
\(61\) −6.28213 + 1.43385i −0.804344 + 0.183586i −0.604878 0.796318i \(-0.706778\pi\)
−0.199466 + 0.979905i \(0.563921\pi\)
\(62\) −5.19688 6.51668i −0.660004 0.827619i
\(63\) 0 0
\(64\) −5.51533 + 6.91601i −0.689417 + 0.864501i
\(65\) −9.36261 + 19.4417i −1.16129 + 2.41144i
\(66\) 0 0
\(67\) 1.41606 0.172999 0.0864996 0.996252i \(-0.472432\pi\)
0.0864996 + 0.996252i \(0.472432\pi\)
\(68\) 0.242642 0.0294247
\(69\) 0 0
\(70\) 11.0711 1.89639i 1.32325 0.226662i
\(71\) −14.0112 3.19797i −1.66283 0.379529i −0.715202 0.698918i \(-0.753665\pi\)
−0.947624 + 0.319388i \(0.896523\pi\)
\(72\) 0 0
\(73\) −1.23210 0.982563i −0.144206 0.115000i 0.548730 0.836000i \(-0.315112\pi\)
−0.692936 + 0.720999i \(0.743683\pi\)
\(74\) 0.966498 + 0.770757i 0.112353 + 0.0895987i
\(75\) 0 0
\(76\) 4.16720 + 0.951136i 0.478010 + 0.109103i
\(77\) −3.12144 0.894721i −0.355721 0.101963i
\(78\) 0 0
\(79\) −6.59140 −0.741591 −0.370795 0.928715i \(-0.620915\pi\)
−0.370795 + 0.928715i \(0.620915\pi\)
\(80\) 9.29981 1.03975
\(81\) 0 0
\(82\) 3.12349 6.48600i 0.344932 0.716259i
\(83\) 3.24033 4.06324i 0.355672 0.445999i −0.571518 0.820589i \(-0.693645\pi\)
0.927190 + 0.374591i \(0.122217\pi\)
\(84\) 0 0
\(85\) −0.997213 1.25047i −0.108163 0.135632i
\(86\) −10.5769 + 2.41410i −1.14053 + 0.260319i
\(87\) 0 0
\(88\) −3.39216 1.63358i −0.361605 0.174140i
\(89\) 8.27979 10.3825i 0.877656 1.10055i −0.116564 0.993183i \(-0.537188\pi\)
0.994220 0.107362i \(-0.0342405\pi\)
\(90\) 0 0
\(91\) −15.6656 4.49033i −1.64220 0.470715i
\(92\) 0.459518 0.954199i 0.0479081 0.0994821i
\(93\) 0 0
\(94\) −1.74740 0.398833i −0.180230 0.0411364i
\(95\) −12.2247 25.3848i −1.25423 2.60443i
\(96\) 0 0
\(97\) 11.9798i 1.21636i 0.793798 + 0.608182i \(0.208101\pi\)
−0.793798 + 0.608182i \(0.791899\pi\)
\(98\) 2.82323 + 7.99917i 0.285190 + 0.808038i
\(99\) 0 0
\(100\) 2.41018 + 3.02227i 0.241018 + 0.302227i
\(101\) 6.88920 3.31766i 0.685501 0.330120i −0.0585104 0.998287i \(-0.518635\pi\)
0.744011 + 0.668167i \(0.232921\pi\)
\(102\) 0 0
\(103\) 5.15066 + 10.6955i 0.507509 + 1.05385i 0.984571 + 0.174984i \(0.0559875\pi\)
−0.477062 + 0.878870i \(0.658298\pi\)
\(104\) −17.0242 8.19843i −1.66936 0.803922i
\(105\) 0 0
\(106\) −8.00209 + 3.85360i −0.777232 + 0.374295i
\(107\) −5.08805 4.05759i −0.491881 0.392262i 0.345898 0.938272i \(-0.387574\pi\)
−0.837778 + 0.546010i \(0.816146\pi\)
\(108\) 0 0
\(109\) 6.58122 + 8.25259i 0.630366 + 0.790454i 0.989762 0.142731i \(-0.0455884\pi\)
−0.359395 + 0.933185i \(0.617017\pi\)
\(110\) 1.15943 + 5.07978i 0.110547 + 0.484338i
\(111\) 0 0
\(112\) 1.18577 + 6.92249i 0.112045 + 0.654114i
\(113\) 15.7697 + 12.5759i 1.48348 + 1.18304i 0.938831 + 0.344379i \(0.111911\pi\)
0.544654 + 0.838661i \(0.316661\pi\)
\(114\) 0 0
\(115\) −6.80603 + 1.55343i −0.634666 + 0.144858i
\(116\) 3.73806i 0.347070i
\(117\) 0 0
\(118\) 8.96063 2.04520i 0.824892 0.188276i
\(119\) 0.803659 0.901735i 0.0736713 0.0826619i
\(120\) 0 0
\(121\) −2.11255 + 9.25570i −0.192050 + 0.841427i
\(122\) −4.86859 + 6.10502i −0.440781 + 0.552722i
\(123\) 0 0
\(124\) 3.56397 + 0.813454i 0.320054 + 0.0730503i
\(125\) 1.77219 7.76447i 0.158510 0.694476i
\(126\) 0 0
\(127\) −1.06065 4.64701i −0.0941174 0.412355i 0.905819 0.423666i \(-0.139257\pi\)
−0.999936 + 0.0113103i \(0.996400\pi\)
\(128\) 4.88257i 0.431562i
\(129\) 0 0
\(130\) 5.81881 + 25.4939i 0.510343 + 2.23596i
\(131\) 10.8445 + 5.22244i 0.947489 + 0.456287i 0.842805 0.538219i \(-0.180903\pi\)
0.104684 + 0.994506i \(0.466617\pi\)
\(132\) 0 0
\(133\) 17.3370 12.3364i 1.50331 1.06970i
\(134\) 1.34163 1.06992i 0.115900 0.0924268i
\(135\) 0 0
\(136\) 1.09498 0.873216i 0.0938936 0.0748776i
\(137\) −5.84780 + 12.1431i −0.499611 + 1.03745i 0.486854 + 0.873483i \(0.338144\pi\)
−0.986465 + 0.163970i \(0.947570\pi\)
\(138\) 0 0
\(139\) 1.37251 + 2.85004i 0.116415 + 0.241737i 0.951032 0.309093i \(-0.100025\pi\)
−0.834617 + 0.550830i \(0.814311\pi\)
\(140\) −3.27765 + 3.67765i −0.277012 + 0.310818i
\(141\) 0 0
\(142\) −15.6911 + 7.55643i −1.31677 + 0.634121i
\(143\) 1.68215 7.36999i 0.140669 0.616310i
\(144\) 0 0
\(145\) 19.2642 15.3627i 1.59981 1.27580i
\(146\) −1.90973 −0.158050
\(147\) 0 0
\(148\) −0.542172 −0.0445662
\(149\) 4.48031 3.57293i 0.367041 0.292706i −0.422549 0.906340i \(-0.638865\pi\)
0.789590 + 0.613634i \(0.210293\pi\)
\(150\) 0 0
\(151\) −1.58064 + 6.92523i −0.128631 + 0.563567i 0.869003 + 0.494807i \(0.164761\pi\)
−0.997633 + 0.0687598i \(0.978096\pi\)
\(152\) 22.2284 10.7046i 1.80296 0.868259i
\(153\) 0 0
\(154\) −3.63340 + 1.51074i −0.292788 + 0.121739i
\(155\) −10.4551 21.7102i −0.839773 1.74381i
\(156\) 0 0
\(157\) −4.34877 + 9.03031i −0.347069 + 0.720697i −0.999303 0.0373208i \(-0.988118\pi\)
0.652234 + 0.758018i \(0.273832\pi\)
\(158\) −6.24497 + 4.98020i −0.496823 + 0.396203i
\(159\) 0 0
\(160\) −7.99397 + 6.37498i −0.631979 + 0.503986i
\(161\) −2.02413 4.86813i −0.159524 0.383663i
\(162\) 0 0
\(163\) −7.55622 3.63888i −0.591849 0.285019i 0.113888 0.993494i \(-0.463670\pi\)
−0.705737 + 0.708474i \(0.749384\pi\)
\(164\) 0.702565 + 3.07814i 0.0548611 + 0.240362i
\(165\) 0 0
\(166\) 6.29795i 0.488816i
\(167\) −2.03637 8.92191i −0.157579 0.690398i −0.990558 0.137094i \(-0.956224\pi\)
0.832979 0.553304i \(-0.186633\pi\)
\(168\) 0 0
\(169\) 5.54944 24.3137i 0.426880 1.87028i
\(170\) −1.88960 0.431290i −0.144926 0.0330784i
\(171\) 0 0
\(172\) 2.96663 3.72003i 0.226203 0.283650i
\(173\) 0.0716983 0.314131i 0.00545112 0.0238829i −0.972129 0.234446i \(-0.924672\pi\)
0.977580 + 0.210563i \(0.0675296\pi\)
\(174\) 0 0
\(175\) 19.2145 + 1.05311i 1.45248 + 0.0796078i
\(176\) −3.17627 + 0.724963i −0.239420 + 0.0546461i
\(177\) 0 0
\(178\) 16.0927i 1.20620i
\(179\) −7.72502 + 1.76319i −0.577395 + 0.131787i −0.501238 0.865309i \(-0.667122\pi\)
−0.0761567 + 0.997096i \(0.524265\pi\)
\(180\) 0 0
\(181\) −17.3051 13.8004i −1.28628 1.02577i −0.997663 0.0683268i \(-0.978234\pi\)
−0.288615 0.957445i \(-0.593195\pi\)
\(182\) −18.2349 + 7.58194i −1.35166 + 0.562011i
\(183\) 0 0
\(184\) −1.36027 5.95975i −0.100281 0.439358i
\(185\) 2.22822 + 2.79410i 0.163822 + 0.205427i
\(186\) 0 0
\(187\) 0.438069 + 0.349348i 0.0320348 + 0.0255469i
\(188\) 0.708236 0.341069i 0.0516534 0.0248750i
\(189\) 0 0
\(190\) −30.7619 14.8142i −2.23170 1.07473i
\(191\) 10.0965 + 20.9655i 0.730555 + 1.51701i 0.851500 + 0.524354i \(0.175693\pi\)
−0.120945 + 0.992659i \(0.538593\pi\)
\(192\) 0 0
\(193\) −3.10991 + 1.49765i −0.223856 + 0.107803i −0.542451 0.840088i \(-0.682503\pi\)
0.318595 + 0.947891i \(0.396789\pi\)
\(194\) 9.05146 + 11.3502i 0.649857 + 0.814894i
\(195\) 0 0
\(196\) −3.15545 1.97087i −0.225389 0.140776i
\(197\) 2.77362i 0.197612i −0.995107 0.0988062i \(-0.968498\pi\)
0.995107 0.0988062i \(-0.0315024\pi\)
\(198\) 0 0
\(199\) −1.14907 2.38608i −0.0814557 0.169145i 0.856263 0.516540i \(-0.172780\pi\)
−0.937719 + 0.347396i \(0.887066\pi\)
\(200\) 21.7530 + 4.96498i 1.53817 + 0.351077i
\(201\) 0 0
\(202\) 4.02043 8.34850i 0.282876 0.587398i
\(203\) 13.8918 + 12.3809i 0.975014 + 0.868967i
\(204\) 0 0
\(205\) 12.9759 16.2713i 0.906276 1.13643i
\(206\) 12.9610 + 6.24169i 0.903036 + 0.434879i
\(207\) 0 0
\(208\) −15.9407 + 3.63837i −1.10529 + 0.252275i
\(209\) 6.15410 + 7.71699i 0.425688 + 0.533796i
\(210\) 0 0
\(211\) −2.79124 + 3.50010i −0.192157 + 0.240957i −0.868571 0.495564i \(-0.834961\pi\)
0.676415 + 0.736521i \(0.263533\pi\)
\(212\) 1.69011 3.50956i 0.116077 0.241037i
\(213\) 0 0
\(214\) −7.88639 −0.539102
\(215\) −31.3636 −2.13898
\(216\) 0 0
\(217\) 14.8273 10.5506i 1.00655 0.716222i
\(218\) 12.4707 + 2.84634i 0.844619 + 0.192779i
\(219\) 0 0
\(220\) −1.78663 1.42479i −0.120454 0.0960592i
\(221\) 2.19854 + 1.75327i 0.147890 + 0.117938i
\(222\) 0 0
\(223\) 3.45202 + 0.787902i 0.231165 + 0.0527618i 0.336534 0.941671i \(-0.390745\pi\)
−0.105369 + 0.994433i \(0.533602\pi\)
\(224\) −5.76461 5.13762i −0.385164 0.343272i
\(225\) 0 0
\(226\) 24.4427 1.62590
\(227\) −14.9921 −0.995061 −0.497530 0.867447i \(-0.665760\pi\)
−0.497530 + 0.867447i \(0.665760\pi\)
\(228\) 0 0
\(229\) 4.82346 10.0160i 0.318743 0.661877i −0.678617 0.734492i \(-0.737420\pi\)
0.997360 + 0.0726156i \(0.0231346\pi\)
\(230\) −5.27461 + 6.61416i −0.347798 + 0.436125i
\(231\) 0 0
\(232\) 13.4524 + 16.8688i 0.883196 + 1.10749i
\(233\) 7.35458 1.67864i 0.481815 0.109971i 0.0252870 0.999680i \(-0.491950\pi\)
0.456528 + 0.889709i \(0.349093\pi\)
\(234\) 0 0
\(235\) −4.66843 2.24820i −0.304535 0.146656i
\(236\) −2.51330 + 3.15158i −0.163602 + 0.205150i
\(237\) 0 0
\(238\) 0.0801051 1.46155i 0.00519244 0.0947385i
\(239\) 1.14542 2.37849i 0.0740912 0.153852i −0.860633 0.509225i \(-0.829932\pi\)
0.934724 + 0.355373i \(0.115646\pi\)
\(240\) 0 0
\(241\) −4.91058 1.12081i −0.316318 0.0721976i 0.0614142 0.998112i \(-0.480439\pi\)
−0.377732 + 0.925915i \(0.623296\pi\)
\(242\) 4.99172 + 10.3654i 0.320880 + 0.666313i
\(243\) 0 0
\(244\) 3.42470i 0.219244i
\(245\) 2.81136 + 24.3616i 0.179611 + 1.55641i
\(246\) 0 0
\(247\) 30.8855 + 38.7292i 1.96520 + 2.46428i
\(248\) 19.0107 9.15506i 1.20718 0.581347i
\(249\) 0 0
\(250\) −4.18748 8.69539i −0.264839 0.549945i
\(251\) −2.02229 0.973881i −0.127646 0.0614708i 0.368971 0.929441i \(-0.379710\pi\)
−0.496617 + 0.867970i \(0.665424\pi\)
\(252\) 0 0
\(253\) 2.20345 1.06112i 0.138529 0.0667123i
\(254\) −4.51600 3.60139i −0.283359 0.225971i
\(255\) 0 0
\(256\) −7.34159 9.20606i −0.458849 0.575379i
\(257\) 1.76621 + 7.73825i 0.110173 + 0.482699i 0.999668 + 0.0257548i \(0.00819892\pi\)
−0.889495 + 0.456944i \(0.848944\pi\)
\(258\) 0 0
\(259\) −1.79574 + 2.01488i −0.111582 + 0.125199i
\(260\) −8.96655 7.15058i −0.556082 0.443460i
\(261\) 0 0
\(262\) 14.2204 3.24572i 0.878540 0.200521i
\(263\) 20.6681i 1.27445i −0.770678 0.637225i \(-0.780082\pi\)
0.770678 0.637225i \(-0.219918\pi\)
\(264\) 0 0
\(265\) −25.0327 + 5.71355i −1.53775 + 0.350980i
\(266\) 7.10491 24.7871i 0.435630 1.51980i
\(267\) 0 0
\(268\) −0.167471 + 0.733740i −0.0102299 + 0.0448203i
\(269\) 5.27129 6.60999i 0.321396 0.403018i −0.594719 0.803934i \(-0.702737\pi\)
0.916115 + 0.400916i \(0.131308\pi\)
\(270\) 0 0
\(271\) −8.94561 2.04178i −0.543407 0.124029i −0.0579988 0.998317i \(-0.518472\pi\)
−0.485408 + 0.874287i \(0.661329\pi\)
\(272\) 0.269676 1.18153i 0.0163515 0.0716405i
\(273\) 0 0
\(274\) 3.63438 + 15.9232i 0.219561 + 0.961958i
\(275\) 8.92655i 0.538291i
\(276\) 0 0
\(277\) −1.96408 8.60518i −0.118010 0.517035i −0.999033 0.0439623i \(-0.986002\pi\)
0.881023 0.473073i \(-0.156855\pi\)
\(278\) 3.45375 + 1.66324i 0.207142 + 0.0997544i
\(279\) 0 0
\(280\) −1.55610 + 28.3918i −0.0929949 + 1.69673i
\(281\) 14.4181 11.4980i 0.860110 0.685915i −0.0906366 0.995884i \(-0.528890\pi\)
0.950747 + 0.309969i \(0.100319\pi\)
\(282\) 0 0
\(283\) 3.08371 2.45917i 0.183307 0.146183i −0.527537 0.849532i \(-0.676884\pi\)
0.710844 + 0.703349i \(0.248313\pi\)
\(284\) 3.31410 6.88180i 0.196656 0.408359i
\(285\) 0 0
\(286\) −3.97473 8.25361i −0.235031 0.488046i
\(287\) 13.7663 + 7.58420i 0.812600 + 0.447681i
\(288\) 0 0
\(289\) 15.1287 7.28559i 0.889923 0.428564i
\(290\) 6.64429 29.1106i 0.390166 1.70943i
\(291\) 0 0
\(292\) 0.654836 0.522215i 0.0383214 0.0305603i
\(293\) 0.602753 0.0352132 0.0176066 0.999845i \(-0.494395\pi\)
0.0176066 + 0.999845i \(0.494395\pi\)
\(294\) 0 0
\(295\) 26.5709 1.54702
\(296\) −2.44667 + 1.95116i −0.142210 + 0.113409i
\(297\) 0 0
\(298\) 1.54527 6.77029i 0.0895153 0.392192i
\(299\) 11.0584 5.32546i 0.639525 0.307979i
\(300\) 0 0
\(301\) −3.99901 23.3461i −0.230499 1.34565i
\(302\) 3.73486 + 7.75552i 0.214917 + 0.446280i
\(303\) 0 0
\(304\) 9.26296 19.2347i 0.531267 1.10319i
\(305\) −17.6493 + 14.0749i −1.01060 + 0.805925i
\(306\) 0 0
\(307\) −2.84674 + 2.27020i −0.162472 + 0.129567i −0.701351 0.712816i \(-0.747419\pi\)
0.538879 + 0.842383i \(0.318848\pi\)
\(308\) 0.832765 1.51158i 0.0474512 0.0861302i
\(309\) 0 0
\(310\) −26.3090 12.6697i −1.49425 0.719592i
\(311\) 7.31324 + 32.0414i 0.414696 + 1.81690i 0.561186 + 0.827689i \(0.310345\pi\)
−0.146491 + 0.989212i \(0.546798\pi\)
\(312\) 0 0
\(313\) 4.97171i 0.281018i 0.990079 + 0.140509i \(0.0448739\pi\)
−0.990079 + 0.140509i \(0.955126\pi\)
\(314\) 2.70273 + 11.8414i 0.152524 + 0.668252i
\(315\) 0 0
\(316\) 0.779538 3.41538i 0.0438524 0.192130i
\(317\) −5.13426 1.17186i −0.288369 0.0658183i 0.0758895 0.997116i \(-0.475820\pi\)
−0.364258 + 0.931298i \(0.618678\pi\)
\(318\) 0 0
\(319\) −5.38194 + 6.74873i −0.301331 + 0.377857i
\(320\) −6.89595 + 30.2131i −0.385495 + 1.68897i
\(321\) 0 0
\(322\) −5.59591 3.08292i −0.311848 0.171805i
\(323\) −3.57959 + 0.817018i −0.199174 + 0.0454601i
\(324\) 0 0
\(325\) 44.7997i 2.48504i
\(326\) −9.90848 + 2.26155i −0.548780 + 0.125255i
\(327\) 0 0
\(328\) 14.2480 + 11.3624i 0.786716 + 0.627385i
\(329\) 1.07824 3.76169i 0.0594454 0.207389i
\(330\) 0 0
\(331\) 6.80413 + 29.8108i 0.373989 + 1.63855i 0.715456 + 0.698658i \(0.246219\pi\)
−0.341467 + 0.939894i \(0.610924\pi\)
\(332\) 1.72217 + 2.15954i 0.0945166 + 0.118520i
\(333\) 0 0
\(334\) −8.67038 6.91440i −0.474422 0.378339i
\(335\) 4.46963 2.15246i 0.244202 0.117602i
\(336\) 0 0
\(337\) 24.4093 + 11.7549i 1.32966 + 0.640330i 0.957660 0.287903i \(-0.0929581\pi\)
0.371999 + 0.928233i \(0.378672\pi\)
\(338\) −13.1127 27.2288i −0.713236 1.48105i
\(339\) 0 0
\(340\) 0.765873 0.368825i 0.0415353 0.0200023i
\(341\) 5.26326 + 6.59992i 0.285021 + 0.357406i
\(342\) 0 0
\(343\) −17.7756 + 5.19891i −0.959791 + 0.280715i
\(344\) 27.4637i 1.48075i
\(345\) 0 0
\(346\) −0.169415 0.351793i −0.00910779 0.0189125i
\(347\) −11.7839 2.68961i −0.632596 0.144386i −0.105813 0.994386i \(-0.533745\pi\)
−0.526782 + 0.850000i \(0.676602\pi\)
\(348\) 0 0
\(349\) 10.3760 21.5459i 0.555413 1.15333i −0.414539 0.910032i \(-0.636057\pi\)
0.969952 0.243296i \(-0.0782285\pi\)
\(350\) 19.0004 13.5200i 1.01561 0.722673i
\(351\) 0 0
\(352\) 2.23331 2.80048i 0.119036 0.149266i
\(353\) −11.6343 5.60277i −0.619230 0.298205i 0.0978448 0.995202i \(-0.468805\pi\)
−0.717075 + 0.696996i \(0.754519\pi\)
\(354\) 0 0
\(355\) −49.0859 + 11.2035i −2.60521 + 0.594622i
\(356\) 4.40056 + 5.51812i 0.233229 + 0.292460i
\(357\) 0 0
\(358\) −5.98682 + 7.50723i −0.316413 + 0.396770i
\(359\) 11.4734 23.8248i 0.605544 1.25742i −0.342569 0.939493i \(-0.611297\pi\)
0.948113 0.317932i \(-0.102989\pi\)
\(360\) 0 0
\(361\) −45.6795 −2.40418
\(362\) −26.8226 −1.40976
\(363\) 0 0
\(364\) 4.17940 7.58616i 0.219060 0.397623i
\(365\) −5.38251 1.22852i −0.281733 0.0643038i
\(366\) 0 0
\(367\) 1.33611 + 1.06551i 0.0697442 + 0.0556191i 0.657741 0.753244i \(-0.271512\pi\)
−0.587997 + 0.808863i \(0.700083\pi\)
\(368\) −4.13568 3.29810i −0.215587 0.171925i
\(369\) 0 0
\(370\) 4.22222 + 0.963695i 0.219503 + 0.0501001i
\(371\) −7.44478 17.9051i −0.386514 0.929584i
\(372\) 0 0
\(373\) −11.0506 −0.572178 −0.286089 0.958203i \(-0.592355\pi\)
−0.286089 + 0.958203i \(0.592355\pi\)
\(374\) 0.678999 0.0351102
\(375\) 0 0
\(376\) 1.96865 4.08794i 0.101525 0.210819i
\(377\) −27.0103 + 33.8699i −1.39110 + 1.74439i
\(378\) 0 0
\(379\) −5.73260 7.18846i −0.294464 0.369246i 0.612488 0.790480i \(-0.290169\pi\)
−0.906952 + 0.421234i \(0.861597\pi\)
\(380\) 14.5991 3.33214i 0.748916 0.170935i
\(381\) 0 0
\(382\) 25.4066 + 12.2352i 1.29991 + 0.626005i
\(383\) 1.52822 1.91633i 0.0780883 0.0979196i −0.741253 0.671226i \(-0.765768\pi\)
0.819341 + 0.573306i \(0.194339\pi\)
\(384\) 0 0
\(385\) −11.2125 + 1.92062i −0.571441 + 0.0978836i
\(386\) −1.81489 + 3.76866i −0.0923755 + 0.191820i
\(387\) 0 0
\(388\) −6.20741 1.41680i −0.315133 0.0719272i
\(389\) 11.6682 + 24.2293i 0.591603 + 1.22848i 0.954935 + 0.296816i \(0.0959248\pi\)
−0.363332 + 0.931660i \(0.618361\pi\)
\(390\) 0 0
\(391\) 0.909742i 0.0460077i
\(392\) −21.3324 + 2.46178i −1.07745 + 0.124339i
\(393\) 0 0
\(394\) −2.09564 2.62785i −0.105577 0.132389i
\(395\) −20.8050 + 10.0192i −1.04681 + 0.504119i
\(396\) 0 0
\(397\) 5.53457 + 11.4927i 0.277772 + 0.576800i 0.992449 0.122654i \(-0.0391407\pi\)
−0.714677 + 0.699454i \(0.753426\pi\)
\(398\) −2.89151 1.39248i −0.144938 0.0697985i
\(399\) 0 0
\(400\) 17.3954 8.37719i 0.869771 0.418860i
\(401\) −28.1965 22.4860i −1.40807 1.12290i −0.975171 0.221451i \(-0.928921\pi\)
−0.432895 0.901444i \(-0.642508\pi\)
\(402\) 0 0
\(403\) 26.4147 + 33.1230i 1.31581 + 1.64997i
\(404\) 0.904312 + 3.96205i 0.0449912 + 0.197119i
\(405\) 0 0
\(406\) 22.5162 + 1.23407i 1.11746 + 0.0612459i
\(407\) −0.978843 0.780602i −0.0485195 0.0386930i
\(408\) 0 0
\(409\) 25.5082 5.82209i 1.26130 0.287884i 0.460956 0.887423i \(-0.347507\pi\)
0.800345 + 0.599539i \(0.204649\pi\)
\(410\) 25.2202i 1.24553i
\(411\) 0 0
\(412\) −6.15106 + 1.40394i −0.303041 + 0.0691672i
\(413\) 3.38793 + 19.7786i 0.166709 + 0.973241i
\(414\) 0 0
\(415\) 4.05146 17.7506i 0.198878 0.871342i
\(416\) 11.2083 14.0548i 0.549533 0.689093i
\(417\) 0 0
\(418\) 11.6613 + 2.66162i 0.570373 + 0.130184i
\(419\) 5.59073 24.4946i 0.273125 1.19664i −0.633176 0.774008i \(-0.718249\pi\)
0.906301 0.422632i \(-0.138894\pi\)
\(420\) 0 0
\(421\) 8.50256 + 37.2521i 0.414389 + 1.81556i 0.562753 + 0.826625i \(0.309742\pi\)
−0.148364 + 0.988933i \(0.547401\pi\)
\(422\) 5.42509i 0.264089i
\(423\) 0 0
\(424\) −5.00310 21.9200i −0.242972 1.06453i
\(425\) −2.99171 1.44073i −0.145119 0.0698858i
\(426\) 0 0
\(427\) −12.7273 11.3430i −0.615916 0.548926i
\(428\) 2.70421 2.15653i 0.130713 0.104240i
\(429\) 0 0
\(430\) −29.7152 + 23.6971i −1.43299 + 1.14278i
\(431\) −4.00001 + 8.30611i −0.192674 + 0.400091i −0.974817 0.223008i \(-0.928412\pi\)
0.782143 + 0.623099i \(0.214127\pi\)
\(432\) 0 0
\(433\) 11.6174 + 24.1238i 0.558298 + 1.15932i 0.968888 + 0.247498i \(0.0796083\pi\)
−0.410590 + 0.911820i \(0.634677\pi\)
\(434\) 6.07644 21.1990i 0.291678 1.01759i
\(435\) 0 0
\(436\) −5.05446 + 2.43410i −0.242065 + 0.116572i
\(437\) −3.56611 + 15.6242i −0.170590 + 0.747405i
\(438\) 0 0
\(439\) −10.4707 + 8.35012i −0.499740 + 0.398530i −0.840660 0.541563i \(-0.817833\pi\)
0.340920 + 0.940092i \(0.389261\pi\)
\(440\) −13.1901 −0.628812
\(441\) 0 0
\(442\) 3.40769 0.162087
\(443\) 10.3485 8.25263i 0.491671 0.392094i −0.346030 0.938223i \(-0.612471\pi\)
0.837701 + 0.546129i \(0.183899\pi\)
\(444\) 0 0
\(445\) 10.3524 45.3569i 0.490751 2.15012i
\(446\) 3.86590 1.86172i 0.183056 0.0881550i
\(447\) 0 0
\(448\) −23.3690 1.28081i −1.10408 0.0605126i
\(449\) 14.2954 + 29.6847i 0.674642 + 1.40091i 0.903986 + 0.427562i \(0.140628\pi\)
−0.229344 + 0.973345i \(0.573658\pi\)
\(450\) 0 0
\(451\) −3.16339 + 6.56884i −0.148958 + 0.309315i
\(452\) −8.38129 + 6.68385i −0.394223 + 0.314382i
\(453\) 0 0
\(454\) −14.2042 + 11.3274i −0.666634 + 0.531623i
\(455\) −56.2721 + 9.63899i −2.63808 + 0.451883i
\(456\) 0 0
\(457\) 18.7239 + 9.01697i 0.875869 + 0.421796i 0.817114 0.576476i \(-0.195573\pi\)
0.0587548 + 0.998272i \(0.481287\pi\)
\(458\) −2.99775 13.1340i −0.140076 0.613712i
\(459\) 0 0
\(460\) 3.71031i 0.172994i
\(461\) −6.40585 28.0659i −0.298350 1.30716i −0.872583 0.488465i \(-0.837557\pi\)
0.574233 0.818692i \(-0.305300\pi\)
\(462\) 0 0
\(463\) 1.43641 6.29331i 0.0667554 0.292475i −0.930520 0.366241i \(-0.880645\pi\)
0.997276 + 0.0737660i \(0.0235018\pi\)
\(464\) 18.2022 + 4.15453i 0.845014 + 0.192869i
\(465\) 0 0
\(466\) 5.69973 7.14724i 0.264035 0.331090i
\(467\) 4.54647 19.9194i 0.210385 0.921759i −0.753920 0.656966i \(-0.771839\pi\)
0.964305 0.264793i \(-0.0853035\pi\)
\(468\) 0 0
\(469\) 2.17213 + 3.05261i 0.100300 + 0.140956i
\(470\) −6.12171 + 1.39724i −0.282374 + 0.0644499i
\(471\) 0 0
\(472\) 23.2670i 1.07095i
\(473\) 10.7120 2.44494i 0.492537 0.112418i
\(474\) 0 0
\(475\) −45.7329 36.4707i −2.09837 1.67339i
\(476\) 0.372195 + 0.523065i 0.0170595 + 0.0239747i
\(477\) 0 0
\(478\) −0.711873 3.11892i −0.0325603 0.142656i
\(479\) −10.7585 13.4908i −0.491570 0.616409i 0.472735 0.881205i \(-0.343267\pi\)
−0.964305 + 0.264796i \(0.914696\pi\)
\(480\) 0 0
\(481\) −4.91252 3.91760i −0.223992 0.178627i
\(482\) −5.49933 + 2.64834i −0.250488 + 0.120628i
\(483\) 0 0
\(484\) −4.54606 2.18927i −0.206639 0.0995121i
\(485\) 18.2097 + 37.8129i 0.826862 + 1.71700i
\(486\) 0 0
\(487\) −11.7080 + 5.63827i −0.530540 + 0.255495i −0.679921 0.733285i \(-0.737986\pi\)
0.149381 + 0.988780i \(0.452272\pi\)
\(488\) −12.3247 15.4547i −0.557915 0.699603i
\(489\) 0 0
\(490\) 21.0703 + 20.9571i 0.951858 + 0.946744i
\(491\) 23.6167i 1.06581i 0.846176 + 0.532903i \(0.178899\pi\)
−0.846176 + 0.532903i \(0.821101\pi\)
\(492\) 0 0
\(493\) −1.39318 2.89298i −0.0627459 0.130293i
\(494\) 58.5245 + 13.3578i 2.63314 + 0.600998i
\(495\) 0 0
\(496\) 7.92209 16.4504i 0.355713 0.738645i
\(497\) −14.5983 35.1095i −0.654822 1.57488i
\(498\) 0 0
\(499\) −0.765079 + 0.959378i −0.0342496 + 0.0429477i −0.798661 0.601781i \(-0.794458\pi\)
0.764412 + 0.644728i \(0.223030\pi\)
\(500\) 3.81362 + 1.83654i 0.170550 + 0.0821327i
\(501\) 0 0
\(502\) −2.65182 + 0.605262i −0.118357 + 0.0270142i
\(503\) −0.0680914 0.0853839i −0.00303605 0.00380708i 0.780311 0.625391i \(-0.215061\pi\)
−0.783347 + 0.621584i \(0.786489\pi\)
\(504\) 0 0
\(505\) 16.7020 20.9437i 0.743230 0.931982i
\(506\) 1.28590 2.67019i 0.0571650 0.118704i
\(507\) 0 0
\(508\) 2.53332 0.112398
\(509\) −19.6325 −0.870194 −0.435097 0.900384i \(-0.643286\pi\)
−0.435097 + 0.900384i \(0.643286\pi\)
\(510\) 0 0
\(511\) 0.228178 4.16322i 0.0100940 0.184170i
\(512\) −23.4318 5.34815i −1.03555 0.236357i
\(513\) 0 0
\(514\) 7.52009 + 5.99707i 0.331697 + 0.264520i
\(515\) 32.5150 + 25.9298i 1.43278 + 1.14260i
\(516\) 0 0
\(517\) 1.76972 + 0.403927i 0.0778321 + 0.0177647i
\(518\) −0.178991 + 3.26577i −0.00786440 + 0.143490i
\(519\) 0 0
\(520\) −66.1970 −2.90293
\(521\) −34.5444 −1.51342 −0.756709 0.653752i \(-0.773194\pi\)
−0.756709 + 0.653752i \(0.773194\pi\)
\(522\) 0 0
\(523\) −1.36808 + 2.84085i −0.0598219 + 0.124222i −0.928736 0.370741i \(-0.879104\pi\)
0.868914 + 0.494962i \(0.164818\pi\)
\(524\) −3.98858 + 5.00152i −0.174242 + 0.218492i
\(525\) 0 0
\(526\) −15.6160 19.5818i −0.680889 0.853808i
\(527\) −3.06143 + 0.698751i −0.133358 + 0.0304381i
\(528\) 0 0
\(529\) −17.1447 8.25645i −0.745421 0.358976i
\(530\) −19.4001 + 24.3270i −0.842687 + 1.05670i
\(531\) 0 0
\(532\) 4.34180 + 10.4422i 0.188241 + 0.452728i
\(533\) −15.8761 + 32.9670i −0.687670 + 1.42796i
\(534\) 0 0
\(535\) −22.2276 5.07330i −0.960981 0.219338i
\(536\) 1.88482 + 3.91386i 0.0814117 + 0.169053i
\(537\) 0 0
\(538\) 10.2454i 0.441709i
\(539\) −2.85929 8.10134i −0.123159 0.348950i
\(540\) 0 0
\(541\) −5.55764 6.96905i −0.238941 0.299623i 0.647873 0.761748i \(-0.275659\pi\)
−0.886815 + 0.462125i \(0.847087\pi\)
\(542\) −10.0181 + 4.82448i −0.430316 + 0.207229i
\(543\) 0 0
\(544\) 0.578122 + 1.20048i 0.0247868 + 0.0514703i
\(545\) 33.3171 + 16.0447i 1.42715 + 0.687279i
\(546\) 0 0
\(547\) 7.85815 3.78428i 0.335990 0.161804i −0.258279 0.966070i \(-0.583156\pi\)
0.594270 + 0.804266i \(0.297441\pi\)
\(548\) −5.60042 4.46619i −0.239238 0.190786i
\(549\) 0 0
\(550\) 6.74455 + 8.45740i 0.287588 + 0.360625i
\(551\) −12.5867 55.1459i −0.536211 2.34929i
\(552\) 0 0
\(553\) −10.1107 14.2091i −0.429951 0.604234i
\(554\) −8.36258 6.66894i −0.355292 0.283336i
\(555\) 0 0
\(556\) −1.63909 + 0.374111i −0.0695129 + 0.0158659i
\(557\) 37.9448i 1.60777i −0.594783 0.803886i \(-0.702762\pi\)
0.594783 0.803886i \(-0.297238\pi\)
\(558\) 0 0
\(559\) 53.7601 12.2704i 2.27381 0.518983i
\(560\) 14.2652 + 20.0477i 0.602815 + 0.847169i
\(561\) 0 0
\(562\) 4.97284 21.7874i 0.209767 0.919048i
\(563\) −19.0788 + 23.9240i −0.804075 + 1.00828i 0.195544 + 0.980695i \(0.437353\pi\)
−0.999620 + 0.0275835i \(0.991219\pi\)
\(564\) 0 0
\(565\) 68.8910 + 15.7239i 2.89827 + 0.661510i
\(566\) 1.06358 4.65985i 0.0447056 0.195868i
\(567\) 0 0
\(568\) −9.81045 42.9824i −0.411637 1.80350i
\(569\) 6.76360i 0.283545i 0.989899 + 0.141772i \(0.0452801\pi\)
−0.989899 + 0.141772i \(0.954720\pi\)
\(570\) 0 0
\(571\) 3.05357 + 13.3785i 0.127788 + 0.559875i 0.997767 + 0.0667868i \(0.0212747\pi\)
−0.869980 + 0.493088i \(0.835868\pi\)
\(572\) 3.61987 + 1.74324i 0.151354 + 0.0728884i
\(573\) 0 0
\(574\) 18.7731 3.21569i 0.783575 0.134221i
\(575\) −11.3315 + 9.03654i −0.472555 + 0.376850i
\(576\) 0 0
\(577\) −7.51312 + 5.99151i −0.312775 + 0.249430i −0.767277 0.641316i \(-0.778389\pi\)
0.454502 + 0.890746i \(0.349817\pi\)
\(578\) 8.82886 18.3333i 0.367232 0.762565i
\(579\) 0 0
\(580\) 5.68199 + 11.7988i 0.235932 + 0.489917i
\(581\) 13.7296 + 0.752492i 0.569599 + 0.0312186i
\(582\) 0 0
\(583\) 8.10430 3.90283i 0.335646 0.161639i
\(584\) 1.07576 4.71323i 0.0445154 0.195035i
\(585\) 0 0
\(586\) 0.571074 0.455416i 0.0235909 0.0188131i
\(587\) 40.3617 1.66591 0.832953 0.553343i \(-0.186648\pi\)
0.832953 + 0.553343i \(0.186648\pi\)
\(588\) 0 0
\(589\) −55.3168 −2.27929
\(590\) 25.1744 20.0759i 1.03642 0.826514i
\(591\) 0 0
\(592\) −0.602577 + 2.64006i −0.0247657 + 0.108506i
\(593\) 24.5780 11.8361i 1.00930 0.486052i 0.145214 0.989400i \(-0.453613\pi\)
0.864083 + 0.503349i \(0.167899\pi\)
\(594\) 0 0
\(595\) 1.16599 4.06782i 0.0478009 0.166764i
\(596\) 1.32147 + 2.74406i 0.0541294 + 0.112401i
\(597\) 0 0
\(598\) 6.45352 13.4009i 0.263904 0.548002i
\(599\) −19.4803 + 15.5350i −0.795945 + 0.634745i −0.934642 0.355590i \(-0.884280\pi\)
0.138697 + 0.990335i \(0.455709\pi\)
\(600\) 0 0
\(601\) 21.3996 17.0656i 0.872908 0.696121i −0.0808401 0.996727i \(-0.525760\pi\)
0.953748 + 0.300606i \(0.0971889\pi\)
\(602\) −21.4282 19.0976i −0.873349 0.778360i
\(603\) 0 0
\(604\) −3.40142 1.63804i −0.138402 0.0666507i
\(605\) 7.40097 + 32.4258i 0.300892 + 1.31829i
\(606\) 0 0
\(607\) 45.4228i 1.84365i 0.387601 + 0.921827i \(0.373304\pi\)
−0.387601 + 0.921827i \(0.626696\pi\)
\(608\) 5.22303 + 22.8836i 0.211822 + 0.928052i
\(609\) 0 0
\(610\) −6.08731 + 26.6703i −0.246468 + 1.07985i
\(611\) 8.88168 + 2.02719i 0.359314 + 0.0820112i
\(612\) 0 0
\(613\) −25.1836 + 31.5792i −1.01716 + 1.27547i −0.0563031 + 0.998414i \(0.517931\pi\)
−0.960853 + 0.277059i \(0.910640\pi\)
\(614\) −0.981849 + 4.30176i −0.0396242 + 0.173605i
\(615\) 0 0
\(616\) −1.68180 9.81828i −0.0677616 0.395590i
\(617\) 7.28753 1.66333i 0.293385 0.0669632i −0.0732951 0.997310i \(-0.523351\pi\)
0.366680 + 0.930347i \(0.380494\pi\)
\(618\) 0 0
\(619\) 7.04484i 0.283156i −0.989927 0.141578i \(-0.954782\pi\)
0.989927 0.141578i \(-0.0452176\pi\)
\(620\) 12.4858 2.84980i 0.501441 0.114451i
\(621\) 0 0
\(622\) 31.1381 + 24.8318i 1.24852 + 0.995664i
\(623\) 35.0823 + 1.92279i 1.40554 + 0.0770351i
\(624\) 0 0
\(625\) 1.88375 + 8.25327i 0.0753502 + 0.330131i
\(626\) 3.75643 + 4.71041i 0.150137 + 0.188266i
\(627\) 0 0
\(628\) −4.16480 3.32132i −0.166194 0.132535i
\(629\) 0.419600 0.202069i 0.0167306 0.00805701i
\(630\) 0 0
\(631\) 29.1127 + 14.0199i 1.15896 + 0.558125i 0.911713 0.410828i \(-0.134760\pi\)
0.247245 + 0.968953i \(0.420475\pi\)
\(632\) −8.77335 18.2181i −0.348985 0.724675i
\(633\) 0 0
\(634\) −5.74983 + 2.76897i −0.228355 + 0.109970i
\(635\) −10.4115 13.0555i −0.413166 0.518094i
\(636\) 0 0
\(637\) −14.3499 40.6582i −0.568565 1.61094i
\(638\) 10.4604i 0.414132i
\(639\) 0 0
\(640\) 7.42169 + 15.4113i 0.293368 + 0.609185i
\(641\) 18.0881 + 4.12849i 0.714437 + 0.163066i 0.564264 0.825594i \(-0.309160\pi\)
0.150173 + 0.988660i \(0.452017\pi\)
\(642\) 0 0
\(643\) 20.8180 43.2289i 0.820980 1.70478i 0.118644 0.992937i \(-0.462145\pi\)
0.702336 0.711845i \(-0.252140\pi\)
\(644\) 2.76184 0.473083i 0.108832 0.0186421i
\(645\) 0 0
\(646\) −2.77415 + 3.47867i −0.109147 + 0.136867i
\(647\) 11.5543 + 5.56424i 0.454245 + 0.218753i 0.646994 0.762495i \(-0.276026\pi\)
−0.192749 + 0.981248i \(0.561740\pi\)
\(648\) 0 0
\(649\) −9.07508 + 2.07133i −0.356228 + 0.0813067i
\(650\) 33.8488 + 42.4451i 1.32766 + 1.66483i
\(651\) 0 0
\(652\) 2.77915 3.48495i 0.108840 0.136481i
\(653\) −12.3764 + 25.6998i −0.484326 + 1.00571i 0.505420 + 0.862873i \(0.331337\pi\)
−0.989746 + 0.142839i \(0.954377\pi\)
\(654\) 0 0
\(655\) 42.1678 1.64763
\(656\) 15.7696 0.615699
\(657\) 0 0
\(658\) −1.82061 4.37866i −0.0709749 0.170698i
\(659\) 9.05005 + 2.06562i 0.352540 + 0.0804650i 0.395124 0.918628i \(-0.370702\pi\)
−0.0425836 + 0.999093i \(0.513559\pi\)
\(660\) 0 0
\(661\) 19.7343 + 15.7376i 0.767574 + 0.612120i 0.926988 0.375092i \(-0.122389\pi\)
−0.159413 + 0.987212i \(0.550960\pi\)
\(662\) 28.9704 + 23.1031i 1.12597 + 0.897928i
\(663\) 0 0
\(664\) 15.5434 + 3.54768i 0.603201 + 0.137677i
\(665\) 35.9705 65.2912i 1.39488 2.53188i
\(666\) 0 0
\(667\) −14.0152 −0.542669
\(668\) 4.86378 0.188185
\(669\) 0 0
\(670\) 2.60841 5.41641i 0.100772 0.209254i
\(671\) 4.93078 6.18300i 0.190350 0.238692i
\(672\) 0 0
\(673\) 16.1270 + 20.2226i 0.621650 + 0.779525i 0.988576 0.150726i \(-0.0481610\pi\)
−0.366926 + 0.930250i \(0.619590\pi\)
\(674\) 32.0079 7.30560i 1.23290 0.281401i
\(675\) 0 0
\(676\) 11.9420 + 5.75096i 0.459307 + 0.221191i
\(677\) −4.15405 + 5.20902i −0.159653 + 0.200199i −0.855224 0.518259i \(-0.826580\pi\)
0.695570 + 0.718458i \(0.255152\pi\)
\(678\) 0 0
\(679\) −25.8249 + 18.3761i −0.991070 + 0.705210i
\(680\) 2.12886 4.42062i 0.0816379 0.169523i
\(681\) 0 0
\(682\) 9.97327 + 2.27633i 0.381896 + 0.0871653i
\(683\) −10.2335 21.2501i −0.391574 0.813111i −0.999813 0.0193570i \(-0.993838\pi\)
0.608239 0.793754i \(-0.291876\pi\)
\(684\) 0 0
\(685\) 47.2172i 1.80408i
\(686\) −12.9132 + 18.3562i −0.493030 + 0.700843i
\(687\) 0 0
\(688\) −14.8172 18.5802i −0.564902 0.708365i
\(689\) 40.6730 19.5871i 1.54952 0.746209i
\(690\) 0 0
\(691\) −14.9765 31.0991i −0.569735 1.18307i −0.964451 0.264263i \(-0.914871\pi\)
0.394716 0.918803i \(-0.370843\pi\)
\(692\) 0.154289 + 0.0743019i 0.00586520 + 0.00282453i
\(693\) 0 0
\(694\) −13.1968 + 6.35523i −0.500943 + 0.241241i
\(695\) 8.66434 + 6.90958i 0.328657 + 0.262095i
\(696\) 0 0
\(697\) −1.69096 2.12040i −0.0640498 0.0803160i
\(698\) −6.44861 28.2532i −0.244083 1.06940i
\(699\) 0 0
\(700\) −2.81810 + 9.83159i −0.106514 + 0.371599i
\(701\) 11.8358 + 9.43876i 0.447033 + 0.356497i 0.820984 0.570952i \(-0.193426\pi\)
−0.373951 + 0.927449i \(0.621997\pi\)
\(702\) 0 0
\(703\) 7.99842 1.82559i 0.301666 0.0688533i
\(704\) 10.8566i 0.409174i
\(705\) 0 0
\(706\) −15.2560 + 3.48209i −0.574168 + 0.131050i
\(707\) 17.7194 + 9.76206i 0.666408 + 0.367140i
\(708\) 0 0
\(709\) 1.11533 4.88659i 0.0418872 0.183520i −0.949656 0.313293i \(-0.898568\pi\)
0.991544 + 0.129773i \(0.0414249\pi\)
\(710\) −38.0411 + 47.7021i −1.42766 + 1.79023i
\(711\) 0 0
\(712\) 39.7170 + 9.06515i 1.48846 + 0.339731i
\(713\) −3.04990 + 13.3625i −0.114220 + 0.500429i
\(714\) 0 0
\(715\) −5.89313 25.8195i −0.220391 0.965595i
\(716\) 4.21129i 0.157383i
\(717\) 0 0
\(718\) −7.13067 31.2415i −0.266114 1.16592i
\(719\) −0.983816 0.473781i −0.0366902 0.0176690i 0.415449 0.909617i \(-0.363625\pi\)
−0.452139 + 0.891948i \(0.649339\pi\)
\(720\) 0 0
\(721\) −15.1555 + 27.5093i −0.564422 + 1.02450i
\(722\) −43.2787 + 34.5136i −1.61066 + 1.28446i
\(723\) 0 0
\(724\) 9.19734 7.33464i 0.341817 0.272590i
\(725\) 22.1954 46.0892i 0.824316 1.71171i
\(726\) 0 0
\(727\) 0.203786 + 0.423166i 0.00755800 + 0.0156943i 0.904714 0.426020i \(-0.140085\pi\)
−0.897156 + 0.441714i \(0.854370\pi\)
\(728\) −8.44044 49.2750i −0.312823 1.82625i
\(729\) 0 0
\(730\) −6.02784 + 2.90285i −0.223100 + 0.107439i
\(731\) −0.909481 + 3.98470i −0.0336384 + 0.147379i
\(732\) 0 0
\(733\) 18.9851 15.1401i 0.701231 0.559213i −0.206663 0.978412i \(-0.566261\pi\)
0.907894 + 0.419199i \(0.137689\pi\)
\(734\) 2.07094 0.0764398
\(735\) 0 0
\(736\) 5.81580 0.214373
\(737\) −1.35877 + 1.08358i −0.0500510 + 0.0399143i
\(738\) 0 0
\(739\) 3.50584 15.3601i 0.128964 0.565030i −0.868615 0.495488i \(-0.834989\pi\)
0.997579 0.0695415i \(-0.0221536\pi\)
\(740\) −1.71130 + 0.824121i −0.0629088 + 0.0302953i
\(741\) 0 0
\(742\) −20.5819 11.3390i −0.755584 0.416269i
\(743\) 12.0733 + 25.0705i 0.442928 + 0.919749i 0.996229 + 0.0867673i \(0.0276537\pi\)
−0.553301 + 0.832981i \(0.686632\pi\)
\(744\) 0 0
\(745\) 8.71062 18.0878i 0.319132 0.662685i
\(746\) −10.4698 + 8.34939i −0.383327 + 0.305693i
\(747\) 0 0
\(748\) −0.232826 + 0.185672i −0.00851295 + 0.00678885i
\(749\) 0.942283 17.1924i 0.0344303 0.628196i
\(750\) 0 0
\(751\) −30.9414 14.9006i −1.12907 0.543730i −0.226384 0.974038i \(-0.572691\pi\)
−0.902682 + 0.430308i \(0.858405\pi\)
\(752\) −0.873663 3.82777i −0.0318592 0.139584i
\(753\) 0 0
\(754\) 52.4976i 1.91185i
\(755\) 5.53750 + 24.2614i 0.201530 + 0.882961i
\(756\) 0 0
\(757\) −3.15791 + 13.8357i −0.114776 + 0.502867i 0.884560 + 0.466427i \(0.154459\pi\)
−0.999336 + 0.0364402i \(0.988398\pi\)
\(758\) −10.8626 2.47932i −0.394548 0.0900531i
\(759\) 0 0
\(760\) 53.8900 67.5759i 1.95479 2.45123i
\(761\) −4.34948 + 19.0563i −0.157669 + 0.690792i 0.832860 + 0.553484i \(0.186702\pi\)
−0.990528 + 0.137308i \(0.956155\pi\)
\(762\) 0 0
\(763\) −7.69507 + 26.8460i −0.278580 + 0.971891i
\(764\) −12.0575 + 2.75205i −0.436225 + 0.0995655i
\(765\) 0 0
\(766\) 2.97027i 0.107320i
\(767\) −45.5451 + 10.3954i −1.64454 + 0.375355i
\(768\) 0 0
\(769\) −14.6692 11.6983i −0.528984 0.421851i 0.322236 0.946659i \(-0.395565\pi\)
−0.851220 + 0.524809i \(0.824137\pi\)
\(770\) −9.17204 + 10.2914i −0.330538 + 0.370876i
\(771\) 0 0
\(772\) −0.408222 1.78854i −0.0146922 0.0643709i
\(773\) −29.4407 36.9175i −1.05891 1.32783i −0.942344 0.334645i \(-0.891383\pi\)
−0.116564 0.993183i \(-0.537188\pi\)
\(774\) 0 0
\(775\) −39.1128 31.1914i −1.40497 1.12043i
\(776\) −33.1111 + 15.9455i −1.18862 + 0.572409i
\(777\) 0 0
\(778\) 29.3617 + 14.1398i 1.05267 + 0.506938i
\(779\) −20.7293 43.0448i −0.742703 1.54224i
\(780\) 0 0
\(781\) 15.8915 7.65295i 0.568643 0.273844i
\(782\) 0.687365 + 0.861929i 0.0245801 + 0.0308225i
\(783\) 0 0
\(784\) −13.1040 + 13.1748i −0.467999 + 0.470527i
\(785\) 35.1135i 1.25325i
\(786\) 0 0
\(787\) −20.5290 42.6290i −0.731781 1.51956i −0.850122 0.526585i \(-0.823472\pi\)
0.118342 0.992973i \(-0.462242\pi\)
\(788\) 1.43717 + 0.328025i 0.0511971 + 0.0116854i
\(789\) 0