Properties

Label 325.2.e.e.126.3
Level $325$
Weight $2$
Character 325.126
Analytic conductor $2.595$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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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: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 8 x^{10} + 54 x^{8} + 78 x^{6} + 92 x^{4} + 10 x^{2} + 1\)
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 126.3
Root \(-0.165418 - 0.286513i\) of defining polynomial
Character \(\chi\) \(=\) 325.126
Dual form 325.2.e.e.276.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.165418 + 0.286513i) q^{2} +(1.34590 - 2.33117i) q^{3} +(0.945274 + 1.63726i) q^{4} +(0.445274 + 0.771236i) q^{6} +(-1.67674 - 2.90420i) q^{7} -1.28714 q^{8} +(-2.12291 - 3.67698i) q^{9} +O(q^{10})\) \(q+(-0.165418 + 0.286513i) q^{2} +(1.34590 - 2.33117i) q^{3} +(0.945274 + 1.63726i) q^{4} +(0.445274 + 0.771236i) q^{6} +(-1.67674 - 2.90420i) q^{7} -1.28714 q^{8} +(-2.12291 - 3.67698i) q^{9} +(1.62291 - 2.81095i) q^{11} +5.08898 q^{12} +(3.39414 - 1.21648i) q^{13} +1.10945 q^{14} +(-1.67763 + 2.90574i) q^{16} +(0.974404 + 1.68772i) q^{17} +1.40467 q^{18} +(0.622905 + 1.07890i) q^{19} -9.02690 q^{21} +(0.536916 + 0.929966i) q^{22} +(-1.34590 + 2.33117i) q^{23} +(-1.73236 + 3.00053i) q^{24} +(-0.212916 + 1.17369i) q^{26} -3.35348 q^{27} +(3.16995 - 5.49052i) q^{28} +(-1.50000 + 2.59808i) q^{29} +3.78109 q^{31} +(-1.84216 - 3.19071i) q^{32} +(-4.36854 - 7.56654i) q^{33} -0.644737 q^{34} +(4.01345 - 6.95150i) q^{36} +(-0.974404 + 1.68772i) q^{37} -0.412160 q^{38} +(1.73236 - 9.54958i) q^{39} +(-1.39055 + 2.40850i) q^{41} +(1.49321 - 2.58632i) q^{42} +(4.36854 + 7.56654i) q^{43} +6.13636 q^{44} +(-0.445274 - 0.771236i) q^{46} -6.86960 q^{47} +(4.51586 + 7.82169i) q^{48} +(-2.12291 + 3.67698i) q^{49} +5.24581 q^{51} +(5.20008 + 4.40719i) q^{52} -12.8336 q^{53} +(0.554726 - 0.960814i) q^{54} +(2.15819 + 3.73809i) q^{56} +3.35348 q^{57} +(-0.496255 - 0.859539i) q^{58} +(1.26764 + 2.19562i) q^{59} +(3.74581 + 6.48793i) q^{61} +(-0.625462 + 1.08333i) q^{62} +(-7.11911 + 12.3307i) q^{63} -5.49162 q^{64} +2.89055 q^{66} +(2.00758 - 3.47722i) q^{67} +(-1.84216 + 3.19071i) q^{68} +(3.62291 + 6.27506i) q^{69} +(-2.62291 - 4.54300i) q^{71} +(2.73247 + 4.73277i) q^{72} -5.46493 q^{73} +(-0.322368 - 0.558359i) q^{74} +(-1.17763 + 2.03972i) q^{76} -10.8848 q^{77} +(2.44951 + 2.07602i) q^{78} +13.7811 q^{79} +(1.85526 - 3.21341i) q^{81} +(-0.460044 - 0.796819i) q^{82} +8.61955 q^{83} +(-8.53289 - 14.7794i) q^{84} -2.89055 q^{86} +(4.03771 + 6.99351i) q^{87} +(-2.08890 + 3.61808i) q^{88} +(-5.15819 + 8.93425i) q^{89} +(-9.22398 - 7.81753i) q^{91} -5.08898 q^{92} +(5.08898 - 8.81438i) q^{93} +(1.13636 - 1.96823i) q^{94} -9.91745 q^{96} +(2.63304 + 4.56055i) q^{97} +(-0.702335 - 1.21648i) q^{98} -13.7811 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{4} - 10 q^{6} - 6 q^{9} + O(q^{10}) \) \( 12 q - 4 q^{4} - 10 q^{6} - 6 q^{9} + 44 q^{14} - 16 q^{16} - 12 q^{19} - 8 q^{21} - 32 q^{24} + 24 q^{26} - 18 q^{29} - 16 q^{31} - 16 q^{34} - 2 q^{36} + 32 q^{39} + 14 q^{41} + 4 q^{44} + 10 q^{46} - 6 q^{49} + 24 q^{51} + 22 q^{54} - 16 q^{56} + 4 q^{59} + 6 q^{61} + 12 q^{64} + 4 q^{66} + 24 q^{69} - 12 q^{71} - 8 q^{74} - 10 q^{76} + 104 q^{79} + 14 q^{81} - 90 q^{84} - 4 q^{86} - 20 q^{89} - 44 q^{91} - 56 q^{94} + 12 q^{96} - 104 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(27\) \(301\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.165418 + 0.286513i −0.116968 + 0.202595i −0.918565 0.395270i \(-0.870651\pi\)
0.801597 + 0.597865i \(0.203984\pi\)
\(3\) 1.34590 2.33117i 0.777057 1.34590i −0.156574 0.987666i \(-0.550045\pi\)
0.933631 0.358236i \(-0.116622\pi\)
\(4\) 0.945274 + 1.63726i 0.472637 + 0.818631i
\(5\) 0 0
\(6\) 0.445274 + 0.771236i 0.181782 + 0.314856i
\(7\) −1.67674 2.90420i −0.633748 1.09768i −0.986779 0.162072i \(-0.948182\pi\)
0.353031 0.935611i \(-0.385151\pi\)
\(8\) −1.28714 −0.455071
\(9\) −2.12291 3.67698i −0.707635 1.22566i
\(10\) 0 0
\(11\) 1.62291 2.81095i 0.489324 0.847535i −0.510600 0.859818i \(-0.670577\pi\)
0.999925 + 0.0122837i \(0.00391011\pi\)
\(12\) 5.08898 1.46906
\(13\) 3.39414 1.21648i 0.941365 0.337391i
\(14\) 1.10945 0.296514
\(15\) 0 0
\(16\) −1.67763 + 2.90574i −0.419408 + 0.726436i
\(17\) 0.974404 + 1.68772i 0.236328 + 0.409332i 0.959658 0.281171i \(-0.0907228\pi\)
−0.723330 + 0.690503i \(0.757389\pi\)
\(18\) 1.40467 0.331084
\(19\) 0.622905 + 1.07890i 0.142904 + 0.247517i 0.928589 0.371110i \(-0.121023\pi\)
−0.785685 + 0.618627i \(0.787689\pi\)
\(20\) 0 0
\(21\) −9.02690 −1.96983
\(22\) 0.536916 + 0.929966i 0.114471 + 0.198269i
\(23\) −1.34590 + 2.33117i −0.280640 + 0.486083i −0.971543 0.236865i \(-0.923880\pi\)
0.690903 + 0.722948i \(0.257213\pi\)
\(24\) −1.73236 + 3.00053i −0.353616 + 0.612481i
\(25\) 0 0
\(26\) −0.212916 + 1.17369i −0.0417562 + 0.230180i
\(27\) −3.35348 −0.645377
\(28\) 3.16995 5.49052i 0.599065 1.03761i
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 0 0
\(31\) 3.78109 0.679105 0.339552 0.940587i \(-0.389724\pi\)
0.339552 + 0.940587i \(0.389724\pi\)
\(32\) −1.84216 3.19071i −0.325650 0.564043i
\(33\) −4.36854 7.56654i −0.760466 1.31717i
\(34\) −0.644737 −0.110571
\(35\) 0 0
\(36\) 4.01345 6.95150i 0.668909 1.15858i
\(37\) −0.974404 + 1.68772i −0.160191 + 0.277459i −0.934937 0.354813i \(-0.884544\pi\)
0.774746 + 0.632273i \(0.217878\pi\)
\(38\) −0.412160 −0.0668611
\(39\) 1.73236 9.54958i 0.277399 1.52916i
\(40\) 0 0
\(41\) −1.39055 + 2.40850i −0.217167 + 0.376144i −0.953941 0.299995i \(-0.903015\pi\)
0.736774 + 0.676139i \(0.236348\pi\)
\(42\) 1.49321 2.58632i 0.230408 0.399078i
\(43\) 4.36854 + 7.56654i 0.666197 + 1.15389i 0.978959 + 0.204055i \(0.0654122\pi\)
−0.312763 + 0.949831i \(0.601255\pi\)
\(44\) 6.13636 0.925091
\(45\) 0 0
\(46\) −0.445274 0.771236i −0.0656520 0.113713i
\(47\) −6.86960 −1.00203 −0.501017 0.865437i \(-0.667041\pi\)
−0.501017 + 0.865437i \(0.667041\pi\)
\(48\) 4.51586 + 7.82169i 0.651808 + 1.12896i
\(49\) −2.12291 + 3.67698i −0.303272 + 0.525283i
\(50\) 0 0
\(51\) 5.24581 0.734560
\(52\) 5.20008 + 4.40719i 0.721122 + 0.611167i
\(53\) −12.8336 −1.76282 −0.881412 0.472347i \(-0.843407\pi\)
−0.881412 + 0.472347i \(0.843407\pi\)
\(54\) 0.554726 0.960814i 0.0754887 0.130750i
\(55\) 0 0
\(56\) 2.15819 + 3.73809i 0.288400 + 0.499524i
\(57\) 3.35348 0.444179
\(58\) −0.496255 0.859539i −0.0651614 0.112863i
\(59\) 1.26764 + 2.19562i 0.165033 + 0.285845i 0.936667 0.350221i \(-0.113894\pi\)
−0.771634 + 0.636067i \(0.780560\pi\)
\(60\) 0 0
\(61\) 3.74581 + 6.48793i 0.479602 + 0.830695i 0.999726 0.0233957i \(-0.00744777\pi\)
−0.520124 + 0.854090i \(0.674114\pi\)
\(62\) −0.625462 + 1.08333i −0.0794338 + 0.137583i
\(63\) −7.11911 + 12.3307i −0.896924 + 1.55352i
\(64\) −5.49162 −0.686453
\(65\) 0 0
\(66\) 2.89055 0.355802
\(67\) 2.00758 3.47722i 0.245264 0.424810i −0.716942 0.697133i \(-0.754459\pi\)
0.962206 + 0.272323i \(0.0877919\pi\)
\(68\) −1.84216 + 3.19071i −0.223394 + 0.386930i
\(69\) 3.62291 + 6.27506i 0.436147 + 0.755428i
\(70\) 0 0
\(71\) −2.62291 4.54300i −0.311282 0.539155i 0.667359 0.744737i \(-0.267425\pi\)
−0.978640 + 0.205581i \(0.934092\pi\)
\(72\) 2.73247 + 4.73277i 0.322024 + 0.557762i
\(73\) −5.46493 −0.639622 −0.319811 0.947481i \(-0.603619\pi\)
−0.319811 + 0.947481i \(0.603619\pi\)
\(74\) −0.322368 0.558359i −0.0374746 0.0649079i
\(75\) 0 0
\(76\) −1.17763 + 2.03972i −0.135084 + 0.233972i
\(77\) −10.8848 −1.24043
\(78\) 2.44951 + 2.07602i 0.277353 + 0.235063i
\(79\) 13.7811 1.55049 0.775247 0.631658i \(-0.217625\pi\)
0.775247 + 0.631658i \(0.217625\pi\)
\(80\) 0 0
\(81\) 1.85526 3.21341i 0.206140 0.357046i
\(82\) −0.460044 0.796819i −0.0508033 0.0879940i
\(83\) 8.61955 0.946119 0.473059 0.881031i \(-0.343150\pi\)
0.473059 + 0.881031i \(0.343150\pi\)
\(84\) −8.53289 14.7794i −0.931015 1.61257i
\(85\) 0 0
\(86\) −2.89055 −0.311696
\(87\) 4.03771 + 6.99351i 0.432888 + 0.749783i
\(88\) −2.08890 + 3.61808i −0.222677 + 0.385688i
\(89\) −5.15819 + 8.93425i −0.546767 + 0.947028i 0.451726 + 0.892156i \(0.350808\pi\)
−0.998493 + 0.0548717i \(0.982525\pi\)
\(90\) 0 0
\(91\) −9.22398 7.81753i −0.966936 0.819500i
\(92\) −5.08898 −0.530563
\(93\) 5.08898 8.81438i 0.527703 0.914008i
\(94\) 1.13636 1.96823i 0.117206 0.203007i
\(95\) 0 0
\(96\) −9.91745 −1.01220
\(97\) 2.63304 + 4.56055i 0.267344 + 0.463054i 0.968175 0.250273i \(-0.0805205\pi\)
−0.700831 + 0.713328i \(0.747187\pi\)
\(98\) −0.702335 1.21648i −0.0709465 0.122883i
\(99\) −13.7811 −1.38505
\(100\) 0 0
\(101\) −2.85526 + 4.94546i −0.284109 + 0.492092i −0.972393 0.233350i \(-0.925031\pi\)
0.688283 + 0.725442i \(0.258365\pi\)
\(102\) −0.867753 + 1.50299i −0.0859203 + 0.148818i
\(103\) −7.36863 −0.726052 −0.363026 0.931779i \(-0.618256\pi\)
−0.363026 + 0.931779i \(0.618256\pi\)
\(104\) −4.36872 + 1.56577i −0.428388 + 0.153537i
\(105\) 0 0
\(106\) 2.12291 3.67698i 0.206195 0.357140i
\(107\) −4.28722 + 7.42568i −0.414461 + 0.717868i −0.995372 0.0960996i \(-0.969363\pi\)
0.580911 + 0.813967i \(0.302697\pi\)
\(108\) −3.16995 5.49052i −0.305029 0.528326i
\(109\) −8.49162 −0.813350 −0.406675 0.913573i \(-0.633312\pi\)
−0.406675 + 0.913573i \(0.633312\pi\)
\(110\) 0 0
\(111\) 2.62291 + 4.54300i 0.248955 + 0.431203i
\(112\) 11.2518 1.06320
\(113\) 3.66621 + 6.35006i 0.344888 + 0.597363i 0.985333 0.170640i \(-0.0545836\pi\)
−0.640446 + 0.768004i \(0.721250\pi\)
\(114\) −0.554726 + 0.960814i −0.0519549 + 0.0899885i
\(115\) 0 0
\(116\) −5.67164 −0.526599
\(117\) −11.6784 9.89771i −1.07967 0.915044i
\(118\) −0.838765 −0.0772145
\(119\) 3.26764 5.65972i 0.299544 0.518826i
\(120\) 0 0
\(121\) 0.232358 + 0.402456i 0.0211234 + 0.0365869i
\(122\) −2.47850 −0.224393
\(123\) 3.74308 + 6.48321i 0.337502 + 0.584571i
\(124\) 3.57417 + 6.19064i 0.320970 + 0.555936i
\(125\) 0 0
\(126\) −2.35526 4.07944i −0.209824 0.363425i
\(127\) 4.58185 7.93599i 0.406573 0.704205i −0.587930 0.808912i \(-0.700057\pi\)
0.994503 + 0.104707i \(0.0333903\pi\)
\(128\) 4.59273 7.95484i 0.405944 0.703115i
\(129\) 23.5185 2.07069
\(130\) 0 0
\(131\) 10.0000 0.873704 0.436852 0.899533i \(-0.356093\pi\)
0.436852 + 0.899533i \(0.356093\pi\)
\(132\) 8.25894 14.3049i 0.718848 1.24508i
\(133\) 2.08890 3.61808i 0.181130 0.313727i
\(134\) 0.664179 + 1.15039i 0.0573763 + 0.0993787i
\(135\) 0 0
\(136\) −1.25419 2.17232i −0.107546 0.186275i
\(137\) −8.42435 14.5914i −0.719741 1.24663i −0.961102 0.276193i \(-0.910927\pi\)
0.241361 0.970435i \(-0.422406\pi\)
\(138\) −2.39718 −0.204061
\(139\) 0.513452 + 0.889325i 0.0435505 + 0.0754316i 0.886979 0.461810i \(-0.152800\pi\)
−0.843429 + 0.537241i \(0.819466\pi\)
\(140\) 0 0
\(141\) −9.24581 + 16.0142i −0.778638 + 1.34864i
\(142\) 1.73551 0.145640
\(143\) 2.08890 11.5150i 0.174682 0.962933i
\(144\) 14.2458 1.18715
\(145\) 0 0
\(146\) 0.904000 1.56577i 0.0748155 0.129584i
\(147\) 5.71445 + 9.89771i 0.471319 + 0.816349i
\(148\) −3.68431 −0.302849
\(149\) −7.92583 13.7279i −0.649309 1.12464i −0.983288 0.182056i \(-0.941725\pi\)
0.333979 0.942581i \(-0.391609\pi\)
\(150\) 0 0
\(151\) 14.5454 1.18369 0.591845 0.806052i \(-0.298400\pi\)
0.591845 + 0.806052i \(0.298400\pi\)
\(152\) −0.801763 1.38869i −0.0650316 0.112638i
\(153\) 4.13713 7.16573i 0.334468 0.579315i
\(154\) 1.80054 3.11862i 0.145091 0.251306i
\(155\) 0 0
\(156\) 17.2727 6.19064i 1.38292 0.495648i
\(157\) 10.9210 0.871588 0.435794 0.900047i \(-0.356468\pi\)
0.435794 + 0.900047i \(0.356468\pi\)
\(158\) −2.27964 + 3.94846i −0.181359 + 0.314123i
\(159\) −17.2727 + 29.9172i −1.36982 + 2.37259i
\(160\) 0 0
\(161\) 9.02690 0.711420
\(162\) 0.613789 + 1.06311i 0.0482238 + 0.0835261i
\(163\) 2.08890 + 3.61808i 0.163615 + 0.283390i 0.936163 0.351567i \(-0.114351\pi\)
−0.772547 + 0.634957i \(0.781018\pi\)
\(164\) −5.25779 −0.410564
\(165\) 0 0
\(166\) −1.42583 + 2.46961i −0.110666 + 0.191679i
\(167\) 1.67674 2.90420i 0.129750 0.224733i −0.793830 0.608140i \(-0.791916\pi\)
0.923580 + 0.383407i \(0.125249\pi\)
\(168\) 11.6188 0.896413
\(169\) 10.0404 8.25780i 0.772335 0.635215i
\(170\) 0 0
\(171\) 2.64474 4.58082i 0.202248 0.350304i
\(172\) −8.25894 + 14.3049i −0.629738 + 1.09074i
\(173\) −4.36854 7.56654i −0.332134 0.575273i 0.650796 0.759253i \(-0.274435\pi\)
−0.982930 + 0.183979i \(0.941102\pi\)
\(174\) −2.67164 −0.202537
\(175\) 0 0
\(176\) 5.44527 + 9.43149i 0.410453 + 0.710925i
\(177\) 6.82449 0.512960
\(178\) −1.70652 2.95577i −0.127909 0.221545i
\(179\) 9.00507 15.5972i 0.673071 1.16579i −0.303958 0.952685i \(-0.598308\pi\)
0.977029 0.213107i \(-0.0683584\pi\)
\(180\) 0 0
\(181\) 1.04366 0.0775749 0.0387875 0.999247i \(-0.487650\pi\)
0.0387875 + 0.999247i \(0.487650\pi\)
\(182\) 3.76564 1.34963i 0.279128 0.100041i
\(183\) 20.1660 1.49071
\(184\) 1.73236 3.00053i 0.127711 0.221202i
\(185\) 0 0
\(186\) 1.68362 + 2.91612i 0.123449 + 0.213820i
\(187\) 6.32546 0.462564
\(188\) −6.49365 11.2473i −0.473598 0.820296i
\(189\) 5.62291 + 9.73916i 0.409006 + 0.708419i
\(190\) 0 0
\(191\) −12.7593 22.0997i −0.923228 1.59908i −0.794387 0.607412i \(-0.792208\pi\)
−0.128841 0.991665i \(-0.541126\pi\)
\(192\) −7.39118 + 12.8019i −0.533413 + 0.923898i
\(193\) 9.91035 17.1652i 0.713362 1.23558i −0.250225 0.968188i \(-0.580505\pi\)
0.963588 0.267392i \(-0.0861619\pi\)
\(194\) −1.74221 −0.125083
\(195\) 0 0
\(196\) −8.02690 −0.573350
\(197\) −10.8260 + 18.7512i −0.771319 + 1.33596i 0.165521 + 0.986206i \(0.447070\pi\)
−0.936840 + 0.349758i \(0.886264\pi\)
\(198\) 2.27964 3.94846i 0.162007 0.280605i
\(199\) −9.11453 15.7868i −0.646112 1.11910i −0.984044 0.177928i \(-0.943061\pi\)
0.337932 0.941171i \(-0.390273\pi\)
\(200\) 0 0
\(201\) −5.40400 9.36000i −0.381169 0.660204i
\(202\) −0.944625 1.63614i −0.0664636 0.115118i
\(203\) 10.0604 0.706104
\(204\) 4.95873 + 8.58877i 0.347180 + 0.601334i
\(205\) 0 0
\(206\) 1.21891 2.11121i 0.0849252 0.147095i
\(207\) 11.4289 0.794363
\(208\) −2.15934 + 11.9033i −0.149723 + 0.825345i
\(209\) 4.04366 0.279706
\(210\) 0 0
\(211\) −9.64981 + 16.7140i −0.664320 + 1.15064i 0.315149 + 0.949042i \(0.397946\pi\)
−0.979469 + 0.201594i \(0.935388\pi\)
\(212\) −12.1312 21.0119i −0.833176 1.44310i
\(213\) −14.1207 −0.967534
\(214\) −1.41837 2.45669i −0.0969577 0.167936i
\(215\) 0 0
\(216\) 4.31638 0.293692
\(217\) −6.33991 10.9810i −0.430381 0.745442i
\(218\) 1.40467 2.43296i 0.0951362 0.164781i
\(219\) −7.35526 + 12.7397i −0.497023 + 0.860868i
\(220\) 0 0
\(221\) 5.36034 + 4.54300i 0.360575 + 0.305596i
\(222\) −1.73551 −0.116480
\(223\) −6.18537 + 10.7134i −0.414203 + 0.717421i −0.995344 0.0963818i \(-0.969273\pi\)
0.581141 + 0.813803i \(0.302606\pi\)
\(224\) −6.17763 + 10.7000i −0.412760 + 0.714922i
\(225\) 0 0
\(226\) −2.42583 −0.161364
\(227\) 3.08141 + 5.33715i 0.204520 + 0.354239i 0.949980 0.312311i \(-0.101103\pi\)
−0.745460 + 0.666551i \(0.767770\pi\)
\(228\) 3.16995 + 5.49052i 0.209935 + 0.363619i
\(229\) −26.9832 −1.78310 −0.891551 0.452920i \(-0.850382\pi\)
−0.891551 + 0.452920i \(0.850382\pi\)
\(230\) 0 0
\(231\) −14.6498 + 25.3742i −0.963887 + 1.66950i
\(232\) 1.93070 3.34408i 0.126757 0.219549i
\(233\) 0.824319 0.0540029 0.0270015 0.999635i \(-0.491404\pi\)
0.0270015 + 0.999635i \(0.491404\pi\)
\(234\) 4.76764 1.70875i 0.311671 0.111705i
\(235\) 0 0
\(236\) −2.39654 + 4.15092i −0.156001 + 0.270202i
\(237\) 18.5480 32.1261i 1.20482 2.08681i
\(238\) 1.08106 + 1.87244i 0.0700744 + 0.121372i
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 0 0
\(241\) −11.3469 19.6534i −0.730917 1.26599i −0.956492 0.291760i \(-0.905759\pi\)
0.225575 0.974226i \(-0.427574\pi\)
\(242\) −0.153745 −0.00988310
\(243\) −10.0242 17.3625i −0.643054 1.11380i
\(244\) −7.08163 + 12.2657i −0.453355 + 0.785234i
\(245\) 0 0
\(246\) −2.47670 −0.157908
\(247\) 3.42669 + 2.90420i 0.218035 + 0.184790i
\(248\) −4.86678 −0.309041
\(249\) 11.6011 20.0936i 0.735188 1.27338i
\(250\) 0 0
\(251\) −9.51345 16.4778i −0.600484 1.04007i −0.992748 0.120216i \(-0.961641\pi\)
0.392264 0.919853i \(-0.371692\pi\)
\(252\) −26.9180 −1.69568
\(253\) 4.36854 + 7.56654i 0.274648 + 0.475704i
\(254\) 1.51584 + 2.62552i 0.0951124 + 0.164739i
\(255\) 0 0
\(256\) −3.97218 6.88001i −0.248261 0.430001i
\(257\) 1.05573 1.82857i 0.0658544 0.114063i −0.831218 0.555946i \(-0.812356\pi\)
0.897073 + 0.441883i \(0.145689\pi\)
\(258\) −3.89039 + 6.73836i −0.242205 + 0.419512i
\(259\) 6.53528 0.406083
\(260\) 0 0
\(261\) 12.7374 0.788427
\(262\) −1.65418 + 2.86513i −0.102196 + 0.177008i
\(263\) −14.9587 + 25.9092i −0.922391 + 1.59763i −0.126687 + 0.991943i \(0.540434\pi\)
−0.795704 + 0.605685i \(0.792899\pi\)
\(264\) 5.62291 + 9.73916i 0.346066 + 0.599404i
\(265\) 0 0
\(266\) 0.691084 + 1.19699i 0.0423731 + 0.0733923i
\(267\) 13.8848 + 24.0492i 0.849738 + 1.47179i
\(268\) 7.59083 0.463684
\(269\) −9.29455 16.0986i −0.566699 0.981551i −0.996889 0.0788127i \(-0.974887\pi\)
0.430191 0.902738i \(-0.358446\pi\)
\(270\) 0 0
\(271\) −2.91238 + 5.04439i −0.176914 + 0.306425i −0.940822 0.338901i \(-0.889945\pi\)
0.763908 + 0.645326i \(0.223278\pi\)
\(272\) −6.53876 −0.396471
\(273\) −30.6386 + 10.9810i −1.85433 + 0.664603i
\(274\) 5.57417 0.336748
\(275\) 0 0
\(276\) −6.84927 + 11.8633i −0.412278 + 0.714086i
\(277\) 6.77017 + 11.7263i 0.406780 + 0.704564i 0.994527 0.104481i \(-0.0333181\pi\)
−0.587747 + 0.809045i \(0.699985\pi\)
\(278\) −0.339738 −0.0203761
\(279\) −8.02690 13.9030i −0.480558 0.832351i
\(280\) 0 0
\(281\) −0.464716 −0.0277226 −0.0138613 0.999904i \(-0.504412\pi\)
−0.0138613 + 0.999904i \(0.504412\pi\)
\(282\) −3.05885 5.29809i −0.182152 0.315496i
\(283\) 5.03022 8.71259i 0.299015 0.517910i −0.676896 0.736079i \(-0.736675\pi\)
0.975911 + 0.218169i \(0.0700085\pi\)
\(284\) 4.95873 8.58877i 0.294246 0.509649i
\(285\) 0 0
\(286\) 2.95365 + 2.50329i 0.174653 + 0.148022i
\(287\) 9.32634 0.550516
\(288\) −7.82145 + 13.5471i −0.460883 + 0.798273i
\(289\) 6.60107 11.4334i 0.388298 0.672553i
\(290\) 0 0
\(291\) 14.1752 0.830967
\(292\) −5.16586 8.94752i −0.302309 0.523614i
\(293\) 6.72506 + 11.6481i 0.392882 + 0.680492i 0.992828 0.119548i \(-0.0381447\pi\)
−0.599946 + 0.800040i \(0.704811\pi\)
\(294\) −3.78109 −0.220518
\(295\) 0 0
\(296\) 1.25419 2.17232i 0.0728983 0.126264i
\(297\) −5.44238 + 9.42647i −0.315799 + 0.546979i
\(298\) 5.24431 0.303795
\(299\) −1.73236 + 9.54958i −0.100185 + 0.552266i
\(300\) 0 0
\(301\) 14.6498 25.3742i 0.844401 1.46255i
\(302\) −2.40608 + 4.16745i −0.138454 + 0.239810i
\(303\) 7.68581 + 13.3122i 0.441538 + 0.764767i
\(304\) −4.18002 −0.239741
\(305\) 0 0
\(306\) 1.36872 + 2.37068i 0.0782442 + 0.135523i
\(307\) −24.6077 −1.40444 −0.702219 0.711961i \(-0.747807\pi\)
−0.702219 + 0.711961i \(0.747807\pi\)
\(308\) −10.2891 17.8212i −0.586274 1.01546i
\(309\) −9.91745 + 17.1775i −0.564184 + 0.977196i
\(310\) 0 0
\(311\) 2.43781 0.138236 0.0691178 0.997609i \(-0.477982\pi\)
0.0691178 + 0.997609i \(0.477982\pi\)
\(312\) −2.22978 + 12.2916i −0.126236 + 0.695875i
\(313\) 19.2965 1.09071 0.545353 0.838207i \(-0.316396\pi\)
0.545353 + 0.838207i \(0.316396\pi\)
\(314\) −1.80653 + 3.12900i −0.101948 + 0.176579i
\(315\) 0 0
\(316\) 13.0269 + 22.5633i 0.732821 + 1.26928i
\(317\) 28.8217 1.61879 0.809395 0.587265i \(-0.199795\pi\)
0.809395 + 0.587265i \(0.199795\pi\)
\(318\) −5.71445 9.89771i −0.320450 0.555036i
\(319\) 4.86872 + 8.43286i 0.272596 + 0.472150i
\(320\) 0 0
\(321\) 11.5404 + 19.9885i 0.644120 + 1.11565i
\(322\) −1.49321 + 2.58632i −0.0832136 + 0.144130i
\(323\) −1.21392 + 2.10258i −0.0675445 + 0.116990i
\(324\) 7.01492 0.389718
\(325\) 0 0
\(326\) −1.38217 −0.0765512
\(327\) −11.4289 + 19.7954i −0.632019 + 1.09469i
\(328\) 1.78982 3.10006i 0.0988264 0.171172i
\(329\) 11.5185 + 19.9507i 0.635037 + 1.09992i
\(330\) 0 0
\(331\) 1.48655 + 2.57478i 0.0817081 + 0.141522i 0.903984 0.427567i \(-0.140629\pi\)
−0.822276 + 0.569089i \(0.807296\pi\)
\(332\) 8.14783 + 14.1125i 0.447171 + 0.774522i
\(333\) 8.27427 0.453427
\(334\) 0.554726 + 0.960814i 0.0303533 + 0.0525734i
\(335\) 0 0
\(336\) 15.1438 26.2299i 0.826163 1.43096i
\(337\) −1.90370 −0.103701 −0.0518505 0.998655i \(-0.516512\pi\)
−0.0518505 + 0.998655i \(0.516512\pi\)
\(338\) 0.705107 + 4.24268i 0.0383528 + 0.230771i
\(339\) 19.7374 1.07199
\(340\) 0 0
\(341\) 6.13636 10.6285i 0.332302 0.575565i
\(342\) 0.874976 + 1.51550i 0.0473133 + 0.0819490i
\(343\) −9.23611 −0.498703
\(344\) −5.62291 9.73916i −0.303167 0.525100i
\(345\) 0 0
\(346\) 2.89055 0.155397
\(347\) −6.31735 10.9420i −0.339133 0.587396i 0.645137 0.764067i \(-0.276800\pi\)
−0.984270 + 0.176671i \(0.943467\pi\)
\(348\) −7.63347 + 13.2216i −0.409197 + 0.708750i
\(349\) −4.48655 + 7.77093i −0.240159 + 0.415968i −0.960760 0.277383i \(-0.910533\pi\)
0.720600 + 0.693351i \(0.243866\pi\)
\(350\) 0 0
\(351\) −11.3822 + 4.07944i −0.607535 + 0.217744i
\(352\) −11.9586 −0.637395
\(353\) −17.1252 + 29.6618i −0.911484 + 1.57874i −0.0995150 + 0.995036i \(0.531729\pi\)
−0.811969 + 0.583701i \(0.801604\pi\)
\(354\) −1.12890 + 1.95530i −0.0600001 + 0.103923i
\(355\) 0 0
\(356\) −19.5036 −1.03369
\(357\) −8.79585 15.2349i −0.465526 0.806315i
\(358\) 2.97921 + 5.16014i 0.157456 + 0.272722i
\(359\) 22.4043 1.18245 0.591227 0.806505i \(-0.298644\pi\)
0.591227 + 0.806505i \(0.298644\pi\)
\(360\) 0 0
\(361\) 8.72398 15.1104i 0.459157 0.795283i
\(362\) −0.172641 + 0.299023i −0.00907381 + 0.0157163i
\(363\) 1.25092 0.0656565
\(364\) 4.08016 22.4918i 0.213858 1.17889i
\(365\) 0 0
\(366\) −3.33582 + 5.77781i −0.174366 + 0.302011i
\(367\) −6.59753 + 11.4273i −0.344388 + 0.596498i −0.985242 0.171165i \(-0.945247\pi\)
0.640854 + 0.767663i \(0.278580\pi\)
\(368\) −4.51586 7.82169i −0.235405 0.407734i
\(369\) 11.8080 0.614700
\(370\) 0 0
\(371\) 21.5185 + 37.2712i 1.11719 + 1.93502i
\(372\) 19.2419 0.997647
\(373\) −7.63070 13.2168i −0.395103 0.684338i 0.598012 0.801488i \(-0.295958\pi\)
−0.993114 + 0.117149i \(0.962624\pi\)
\(374\) −1.04635 + 1.81233i −0.0541053 + 0.0937131i
\(375\) 0 0
\(376\) 8.84210 0.455997
\(377\) −1.93070 + 10.6430i −0.0994362 + 0.548140i
\(378\) −3.72052 −0.191363
\(379\) −9.11453 + 15.7868i −0.468182 + 0.810915i −0.999339 0.0363588i \(-0.988424\pi\)
0.531157 + 0.847273i \(0.321757\pi\)
\(380\) 0 0
\(381\) −12.3334 21.3621i −0.631861 1.09442i
\(382\) 8.44246 0.431954
\(383\) 0.720440 + 1.24784i 0.0368128 + 0.0637616i 0.883845 0.467780i \(-0.154946\pi\)
−0.847032 + 0.531542i \(0.821613\pi\)
\(384\) −12.3627 21.4129i −0.630883 1.09272i
\(385\) 0 0
\(386\) 3.27870 + 5.67888i 0.166882 + 0.289048i
\(387\) 18.5480 32.1261i 0.942848 1.63306i
\(388\) −4.97788 + 8.62194i −0.252714 + 0.437713i
\(389\) −18.7912 −0.952754 −0.476377 0.879241i \(-0.658050\pi\)
−0.476377 + 0.879241i \(0.658050\pi\)
\(390\) 0 0
\(391\) −5.24581 −0.265292
\(392\) 2.73247 4.73277i 0.138010 0.239041i
\(393\) 13.4590 23.3117i 0.678918 1.17592i
\(394\) −3.58163 6.20357i −0.180440 0.312531i
\(395\) 0 0
\(396\) −13.0269 22.5633i −0.654627 1.13385i
\(397\) −8.54634 14.8027i −0.428928 0.742926i 0.567850 0.823132i \(-0.307775\pi\)
−0.996778 + 0.0802063i \(0.974442\pi\)
\(398\) 6.03084 0.302298
\(399\) −5.62291 9.73916i −0.281497 0.487568i
\(400\) 0 0
\(401\) −11.1011 + 19.2276i −0.554361 + 0.960182i 0.443592 + 0.896229i \(0.353704\pi\)
−0.997953 + 0.0639527i \(0.979629\pi\)
\(402\) 3.57568 0.178339
\(403\) 12.8336 4.59962i 0.639285 0.229124i
\(404\) −10.7960 −0.537122
\(405\) 0 0
\(406\) −1.66418 + 2.88244i −0.0825918 + 0.143053i
\(407\) 3.16273 + 5.47801i 0.156771 + 0.271535i
\(408\) −6.75207 −0.334277
\(409\) 4.81638 + 8.34221i 0.238155 + 0.412496i 0.960185 0.279366i \(-0.0901242\pi\)
−0.722030 + 0.691862i \(0.756791\pi\)
\(410\) 0 0
\(411\) −45.3534 −2.23712
\(412\) −6.96537 12.0644i −0.343159 0.594369i
\(413\) 4.25101 7.36296i 0.209178 0.362308i
\(414\) −1.89055 + 3.27452i −0.0929153 + 0.160934i
\(415\) 0 0
\(416\) −10.1340 8.58877i −0.496859 0.421099i
\(417\) 2.76423 0.135365
\(418\) −0.668896 + 1.15856i −0.0327168 + 0.0566671i
\(419\) 0.978168 1.69424i 0.0477866 0.0827689i −0.841143 0.540813i \(-0.818117\pi\)
0.888929 + 0.458044i \(0.151450\pi\)
\(420\) 0 0
\(421\) −12.0807 −0.588778 −0.294389 0.955686i \(-0.595116\pi\)
−0.294389 + 0.955686i \(0.595116\pi\)
\(422\) −3.19251 5.52959i −0.155409 0.269176i
\(423\) 14.5835 + 25.2594i 0.709075 + 1.22815i
\(424\) 16.5185 0.802210
\(425\) 0 0
\(426\) 2.33582 4.04576i 0.113171 0.196018i
\(427\) 12.5615 21.7571i 0.607893 1.05290i
\(428\) −16.2104 −0.783558
\(429\) −24.0320 20.3676i −1.16027 0.983359i
\(430\) 0 0
\(431\) −12.2945 + 21.2948i −0.592207 + 1.02573i 0.401727 + 0.915759i \(0.368410\pi\)
−0.993934 + 0.109974i \(0.964923\pi\)
\(432\) 5.62590 9.74434i 0.270676 0.468825i
\(433\) −18.0364 31.2400i −0.866775 1.50130i −0.865274 0.501299i \(-0.832856\pi\)
−0.00150085 0.999999i \(-0.500478\pi\)
\(434\) 4.19495 0.201364
\(435\) 0 0
\(436\) −8.02690 13.9030i −0.384419 0.665833i
\(437\) −3.35348 −0.160419
\(438\) −2.43339 4.21475i −0.116272 0.201389i
\(439\) −1.26764 + 2.19562i −0.0605013 + 0.104791i −0.894690 0.446688i \(-0.852603\pi\)
0.834188 + 0.551480i \(0.185937\pi\)
\(440\) 0 0
\(441\) 18.0269 0.858424
\(442\) −2.18833 + 0.784309i −0.104088 + 0.0373058i
\(443\) 19.3579 0.919721 0.459860 0.887991i \(-0.347899\pi\)
0.459860 + 0.887991i \(0.347899\pi\)
\(444\) −4.95873 + 8.58877i −0.235331 + 0.407605i
\(445\) 0 0
\(446\) −2.04635 3.54438i −0.0968973 0.167831i
\(447\) −42.6696 −2.01820
\(448\) 9.20801 + 15.9487i 0.435038 + 0.753507i
\(449\) 12.4040 + 21.4844i 0.585381 + 1.01391i 0.994828 + 0.101576i \(0.0323884\pi\)
−0.409447 + 0.912334i \(0.634278\pi\)
\(450\) 0 0
\(451\) 4.51345 + 7.81753i 0.212530 + 0.368113i
\(452\) −6.93114 + 12.0051i −0.326013 + 0.564672i
\(453\) 19.5767 33.9079i 0.919795 1.59313i
\(454\) −2.03888 −0.0956896
\(455\) 0 0
\(456\) −4.31638 −0.202133
\(457\) 3.78374 6.55363i 0.176996 0.306566i −0.763854 0.645389i \(-0.776695\pi\)
0.940850 + 0.338823i \(0.110029\pi\)
\(458\) 4.46352 7.73105i 0.208567 0.361248i
\(459\) −3.26764 5.65972i −0.152520 0.264173i
\(460\) 0 0
\(461\) 6.17164 + 10.6896i 0.287442 + 0.497864i 0.973198 0.229967i \(-0.0738618\pi\)
−0.685756 + 0.727831i \(0.740528\pi\)
\(462\) −4.84669 8.39472i −0.225489 0.390558i
\(463\) −22.8578 −1.06229 −0.531146 0.847281i \(-0.678238\pi\)
−0.531146 + 0.847281i \(0.678238\pi\)
\(464\) −5.03289 8.71723i −0.233646 0.404687i
\(465\) 0 0
\(466\) −0.136357 + 0.236178i −0.00631664 + 0.0109407i
\(467\) 15.2976 0.707889 0.353945 0.935266i \(-0.384840\pi\)
0.353945 + 0.935266i \(0.384840\pi\)
\(468\) 5.16586 28.4766i 0.238792 1.31633i
\(469\) −13.4647 −0.621743
\(470\) 0 0
\(471\) 14.6985 25.4586i 0.677273 1.17307i
\(472\) −1.63163 2.82606i −0.0751017 0.130080i
\(473\) 28.3589 1.30394
\(474\) 6.13636 + 10.6285i 0.281852 + 0.488182i
\(475\) 0 0
\(476\) 12.3553 0.566303
\(477\) 27.2444 + 47.1887i 1.24744 + 2.16062i
\(478\) −0.661673 + 1.14605i −0.0302642 + 0.0524192i
\(479\) −12.1414 + 21.0296i −0.554756 + 0.960866i 0.443166 + 0.896439i \(0.353855\pi\)
−0.997922 + 0.0644264i \(0.979478\pi\)
\(480\) 0 0
\(481\) −1.25419 + 6.91369i −0.0571861 + 0.315237i
\(482\) 7.50793 0.341977
\(483\) 12.1493 21.0433i 0.552814 0.957501i
\(484\) −0.439284 + 0.760862i −0.0199674 + 0.0345846i
\(485\) 0 0
\(486\) 6.63276 0.300868
\(487\) 18.4441 + 31.9462i 0.835783 + 1.44762i 0.893391 + 0.449280i \(0.148319\pi\)
−0.0576081 + 0.998339i \(0.518347\pi\)
\(488\) −4.82136 8.35085i −0.218253 0.378025i
\(489\) 11.2458 0.508553
\(490\) 0 0
\(491\) 17.6767 30.6170i 0.797739 1.38172i −0.123346 0.992364i \(-0.539363\pi\)
0.921085 0.389361i \(-0.127304\pi\)
\(492\) −7.07647 + 12.2568i −0.319032 + 0.552580i
\(493\) −5.84642 −0.263310
\(494\) −1.39893 + 0.501383i −0.0629407 + 0.0225583i
\(495\) 0 0
\(496\) −6.34328 + 10.9869i −0.284822 + 0.493326i
\(497\) −8.79585 + 15.2349i −0.394548 + 0.683377i
\(498\) 3.83806 + 6.64771i 0.171988 + 0.297891i
\(499\) 16.2189 0.726058 0.363029 0.931778i \(-0.381743\pi\)
0.363029 + 0.931778i \(0.381743\pi\)
\(500\) 0 0
\(501\) −4.51345 7.81753i −0.201646 0.349261i
\(502\) 6.29480 0.280950
\(503\) 10.1192 + 17.5270i 0.451193 + 0.781489i 0.998460 0.0554688i \(-0.0176653\pi\)
−0.547268 + 0.836958i \(0.684332\pi\)
\(504\) 9.16326 15.8712i 0.408164 0.706961i
\(505\) 0 0
\(506\) −2.89055 −0.128500
\(507\) −5.73700 34.5200i −0.254789 1.53309i
\(508\) 17.3244 0.768646
\(509\) 10.0185 17.3526i 0.444063 0.769140i −0.553923 0.832568i \(-0.686870\pi\)
0.997986 + 0.0634276i \(0.0202032\pi\)
\(510\) 0 0
\(511\) 9.16326 + 15.8712i 0.405359 + 0.702102i
\(512\) 20.9992 0.928042
\(513\) −2.08890 3.61808i −0.0922271 0.159742i
\(514\) 0.349273 + 0.604959i 0.0154058 + 0.0266836i
\(515\) 0 0
\(516\) 22.2314 + 38.5060i 0.978685 + 1.69513i
\(517\) −11.1487 + 19.3101i −0.490320 + 0.849259i
\(518\) −1.08106 + 1.87244i −0.0474988 + 0.0822704i
\(519\) −23.5185 −1.03235
\(520\) 0 0
\(521\) 16.0269 0.702151 0.351076 0.936347i \(-0.385816\pi\)
0.351076 + 0.936347i \(0.385816\pi\)
\(522\) −2.10700 + 3.64944i −0.0922210 + 0.159732i
\(523\) −5.86898 + 10.1654i −0.256633 + 0.444501i −0.965338 0.261004i \(-0.915946\pi\)
0.708705 + 0.705505i \(0.249280\pi\)
\(524\) 9.45274 + 16.3726i 0.412945 + 0.715241i
\(525\) 0 0
\(526\) −4.94887 8.57170i −0.215781 0.373744i
\(527\) 3.68431 + 6.38142i 0.160491 + 0.277979i
\(528\) 29.3152 1.27578
\(529\) 7.87709 + 13.6435i 0.342482 + 0.593197i
\(530\) 0 0
\(531\) 5.38217 9.32219i 0.233566 0.404548i
\(532\) 7.89832 0.342436
\(533\) −1.78982 + 9.86635i −0.0775258 + 0.427359i
\(534\) −9.18722 −0.397570
\(535\) 0 0
\(536\) −2.58402 + 4.47565i −0.111613 + 0.193319i
\(537\) −24.2399 41.9847i −1.04603 1.81177i
\(538\) 6.14995 0.265143
\(539\) 6.89055 + 11.9348i 0.296797 + 0.514067i
\(540\) 0 0
\(541\) −21.8080 −0.937599 −0.468800 0.883305i \(-0.655313\pi\)
−0.468800 + 0.883305i \(0.655313\pi\)
\(542\) −0.963521 1.66887i −0.0413868 0.0716840i
\(543\) 1.40467 2.43296i 0.0602801 0.104408i
\(544\) 3.59001 6.21808i 0.153920 0.266598i
\(545\) 0 0
\(546\) 1.92197 10.5948i 0.0822527 0.453416i
\(547\) 6.30924 0.269764 0.134882 0.990862i \(-0.456935\pi\)
0.134882 + 0.990862i \(0.456935\pi\)
\(548\) 15.9266 27.5858i 0.680352 1.17840i
\(549\) 15.9040 27.5465i 0.678766 1.17566i
\(550\) 0 0
\(551\) −3.73743 −0.159220
\(552\) −4.66317 8.07684i −0.198478 0.343773i
\(553\) −23.1073 40.0230i −0.982622 1.70195i
\(554\) −4.47964 −0.190322
\(555\) 0 0
\(556\) −0.970706 + 1.68131i −0.0411671 + 0.0713035i
\(557\) 17.9189 31.0364i 0.759247 1.31506i −0.183987 0.982929i \(-0.558901\pi\)
0.943235 0.332126i \(-0.107766\pi\)
\(558\) 5.31119 0.224840
\(559\) 24.0320 + 20.3676i 1.01644 + 0.861459i
\(560\) 0 0
\(561\) 8.51345 14.7457i 0.359438 0.622565i
\(562\) 0.0768725 0.133147i 0.00324267 0.00561647i
\(563\) 2.50106 + 4.33196i 0.105407 + 0.182570i 0.913904 0.405929i \(-0.133052\pi\)
−0.808497 + 0.588500i \(0.799719\pi\)
\(564\) −34.9593 −1.47205
\(565\) 0 0
\(566\) 1.66418 + 2.88244i 0.0699507 + 0.121158i
\(567\) −12.4432 −0.522564
\(568\) 3.37603 + 5.84746i 0.141655 + 0.245354i
\(569\) 6.58402 11.4039i 0.276017 0.478075i −0.694375 0.719614i \(-0.744319\pi\)
0.970391 + 0.241539i \(0.0776522\pi\)
\(570\) 0 0
\(571\) 19.8349 0.830065 0.415032 0.909807i \(-0.363770\pi\)
0.415032 + 0.909807i \(0.363770\pi\)
\(572\) 20.8276 7.46475i 0.870848 0.312117i
\(573\) −68.6909 −2.86960
\(574\) −1.54275 + 2.67212i −0.0643930 + 0.111532i
\(575\) 0 0
\(576\) 11.6582 + 20.1926i 0.485758 + 0.841357i
\(577\) −10.9210 −0.454646 −0.227323 0.973819i \(-0.572997\pi\)
−0.227323 + 0.973819i \(0.572997\pi\)
\(578\) 2.18388 + 3.78258i 0.0908373 + 0.157335i
\(579\) −26.6767 46.2054i −1.10865 1.92023i
\(580\) 0 0
\(581\) −14.4527 25.0329i −0.599601 1.03854i
\(582\) −2.34484 + 4.06139i −0.0971969 + 0.168350i
\(583\) −20.8276 + 36.0745i −0.862593 + 1.49406i
\(584\) 7.03411 0.291073
\(585\) 0 0
\(586\) −4.44979 −0.183819
\(587\) 20.2247 35.0303i 0.834764 1.44585i −0.0594576 0.998231i \(-0.518937\pi\)
0.894222 0.447624i \(-0.147730\pi\)
\(588\) −10.8034 + 18.7121i −0.445526 + 0.771673i
\(589\) 2.35526 + 4.07944i 0.0970469 + 0.168090i
\(590\) 0 0
\(591\) 29.1414 + 50.4744i 1.19872 + 2.07624i
\(592\) −3.26938 5.66274i −0.134371 0.232737i
\(593\) −1.47709 −0.0606569 −0.0303284 0.999540i \(-0.509655\pi\)
−0.0303284 + 0.999540i \(0.509655\pi\)
\(594\) −1.80054 3.11862i −0.0738769 0.127959i
\(595\) 0 0
\(596\) 14.9842 25.9533i 0.613775 1.06309i
\(597\) −49.0690 −2.00826
\(598\) −2.44951 2.07602i −0.100168 0.0848947i
\(599\) 2.27271 0.0928606 0.0464303 0.998922i \(-0.485215\pi\)
0.0464303 + 0.998922i \(0.485215\pi\)
\(600\) 0 0
\(601\) −3.70215 + 6.41231i −0.151014 + 0.261563i −0.931600 0.363484i \(-0.881587\pi\)
0.780587 + 0.625048i \(0.214920\pi\)
\(602\) 4.84669 + 8.39472i 0.197536 + 0.342143i
\(603\) −17.0476 −0.694231
\(604\) 13.7494 + 23.8147i 0.559456 + 0.969005i
\(605\) 0 0
\(606\) −5.08549 −0.206584
\(607\) −5.34661 9.26059i −0.217012 0.375876i 0.736881 0.676022i \(-0.236298\pi\)
−0.953893 + 0.300146i \(0.902964\pi\)
\(608\) 2.29498 3.97502i 0.0930736 0.161208i
\(609\) 13.5404 23.4526i 0.548683 0.950347i
\(610\) 0 0
\(611\) −23.3164 + 8.35673i −0.943280 + 0.338077i
\(612\) 15.6429 0.632327
\(613\) 3.04075 5.26673i 0.122815 0.212721i −0.798062 0.602575i \(-0.794141\pi\)
0.920877 + 0.389854i \(0.127475\pi\)
\(614\) 4.07057 7.05043i 0.164275 0.284532i
\(615\) 0 0
\(616\) 14.0101 0.564485
\(617\) 15.9194 + 27.5732i 0.640892 + 1.11006i 0.985234 + 0.171213i \(0.0547685\pi\)
−0.344342 + 0.938844i \(0.611898\pi\)
\(618\) −3.28106 5.68295i −0.131983 0.228602i
\(619\) −26.4043 −1.06128 −0.530639 0.847598i \(-0.678048\pi\)
−0.530639 + 0.847598i \(0.678048\pi\)
\(620\) 0 0
\(621\) 4.51345 7.81753i 0.181119 0.313707i
\(622\) −0.403259 + 0.698464i −0.0161692 + 0.0280059i
\(623\) 34.5957 1.38605
\(624\) 24.8424 + 21.0545i 0.994491 + 0.842853i
\(625\) 0 0
\(626\) −3.19200 + 5.52871i −0.127578 + 0.220972i
\(627\) 5.44238 9.42647i 0.217348 0.376457i
\(628\) 10.3233 + 17.8805i 0.411944 + 0.713509i
\(629\) −3.79785 −0.151430
\(630\) 0 0
\(631\) −17.5840 30.4564i −0.700009 1.21245i −0.968463 0.249158i \(-0.919846\pi\)
0.268454 0.963293i \(-0.413487\pi\)
\(632\) −17.7381 −0.705585
\(633\) 25.9754 + 44.9907i 1.03243 + 1.78822i
\(634\) −4.76764 + 8.25780i −0.189347 + 0.327959i
\(635\) 0 0
\(636\) −65.3098 −2.58970
\(637\) −2.73247 + 15.0626i −0.108264 + 0.596804i
\(638\) −3.22150 −0.127540
\(639\) −11.1364 + 19.2887i −0.440547 + 0.763051i
\(640\) 0 0
\(641\) −2.76257 4.78491i −0.109115 0.188993i 0.806297 0.591511i \(-0.201468\pi\)
−0.915412 + 0.402518i \(0.868135\pi\)
\(642\) −7.63594 −0.301367
\(643\) −16.0776 27.8472i −0.634039 1.09819i −0.986718 0.162444i \(-0.948062\pi\)
0.352679 0.935744i \(-0.385271\pi\)
\(644\) 8.53289 + 14.7794i 0.336243 + 0.582390i
\(645\) 0 0
\(646\) −0.401610 0.695609i −0.0158011 0.0273684i
\(647\) −6.89216 + 11.9376i −0.270959 + 0.469314i −0.969108 0.246638i \(-0.920674\pi\)
0.698149 + 0.715953i \(0.254007\pi\)
\(648\) −2.38797 + 4.13609i −0.0938085 + 0.162481i
\(649\) 8.22905 0.323019
\(650\) 0 0
\(651\) −34.1316 −1.33772
\(652\) −3.94916 + 6.84015i −0.154661 + 0.267881i
\(653\) 4.25101 7.36296i 0.166355 0.288135i −0.770781 0.637100i \(-0.780134\pi\)
0.937136 + 0.348965i \(0.113467\pi\)
\(654\) −3.78109 6.54905i −0.147852 0.256088i
\(655\) 0 0
\(656\) −4.66565 8.08115i −0.182163 0.315516i
\(657\) 11.6015 + 20.0944i 0.452619 + 0.783959i
\(658\) −7.62150 −0.297117
\(659\) −2.02183 3.50192i −0.0787594 0.136415i 0.823956 0.566654i \(-0.191763\pi\)
−0.902715 + 0.430239i \(0.858429\pi\)
\(660\) 0 0
\(661\) −15.6364 + 27.0830i −0.608184 + 1.05341i 0.383356 + 0.923601i \(0.374768\pi\)
−0.991540 + 0.129805i \(0.958565\pi\)
\(662\) −0.983609 −0.0382290
\(663\) 17.8050 6.38142i 0.691489 0.247834i
\(664\) −11.0945 −0.430551
\(665\) 0 0
\(666\) −1.36872 + 2.37068i −0.0530366 + 0.0918622i
\(667\) −4.03771 6.99351i −0.156341 0.270790i
\(668\) 6.33991 0.245298
\(669\) 16.6498 + 28.8383i 0.643719 + 1.11495i
\(670\) 0 0
\(671\) 24.3164 0.938723
\(672\) 16.6290 + 28.8022i 0.641477 + 1.11107i
\(673\) −16.0370 + 27.7768i −0.618179 + 1.07072i 0.371639 + 0.928377i \(0.378796\pi\)
−0.989818 + 0.142340i \(0.954537\pi\)
\(674\) 0.314906 0.545433i 0.0121297 0.0210093i
\(675\) 0 0
\(676\) 23.0111 + 8.63282i 0.885041 + 0.332031i
\(677\) −14.2382 −0.547220 −0.273610 0.961841i \(-0.588218\pi\)
−0.273610 + 0.961841i \(0.588218\pi\)
\(678\) −3.26493 + 5.65503i −0.125389 + 0.217180i
\(679\) 8.82983 15.2937i 0.338858 0.586919i
\(680\) 0 0
\(681\) 16.5891 0.635695
\(682\) 2.03013 + 3.51629i 0.0777377 + 0.134646i
\(683\) −12.8923 22.3302i −0.493311 0.854440i 0.506659 0.862146i \(-0.330880\pi\)
−0.999970 + 0.00770647i \(0.997547\pi\)
\(684\) 10.0000 0.382360
\(685\) 0 0
\(686\) 1.52782 2.64626i 0.0583325 0.101035i
\(687\) −36.3168 + 62.9025i −1.38557 + 2.39988i
\(688\) −29.3152 −1.11763
\(689\) −43.5589 + 15.6118i −1.65946 + 0.594761i
\(690\) 0 0
\(691\) 0.0218318 0.0378138i 0.000830522 0.00143851i −0.865610 0.500719i \(-0.833069\pi\)
0.866440 + 0.499281i \(0.166402\pi\)
\(692\) 8.25894 14.3049i 0.313958 0.543791i
\(693\) 23.1073 + 40.0230i 0.877774 + 1.52035i
\(694\) 4.18002 0.158671
\(695\) 0 0
\(696\) −5.19707 9.00160i −0.196995 0.341205i
\(697\) −5.41982 −0.205290
\(698\) −1.48431 2.57091i −0.0561821 0.0973103i
\(699\) 1.10945 1.92163i 0.0419634 0.0726827i
\(700\) 0 0
\(701\) −14.5454 −0.549373 −0.274687 0.961534i \(-0.588574\pi\)
−0.274687 + 0.961534i \(0.588574\pi\)
\(702\) 0.714008 3.93595i 0.0269485 0.148553i
\(703\) −2.42785 −0.0915679
\(704\) −8.91238 + 15.4367i −0.335898 + 0.581792i
\(705\) 0 0
\(706\) −5.66565 9.81320i −0.213230 0.369325i
\(707\) 19.1501 0.720214
\(708\) 6.45101 + 11.1735i 0.242444 + 0.419925i
\(709\) −9.81638 17.0025i −0.368662 0.638541i 0.620695 0.784052i \(-0.286851\pi\)
−0.989357 + 0.145511i \(0.953517\pi\)
\(710\) 0 0
\(711\) −29.2560 50.6728i −1.09718 1.90038i
\(712\) 6.63929 11.4996i 0.248818 0.430965i
\(713\) −5.08898 + 8.81438i −0.190584 + 0.330101i
\(714\) 5.81998 0.217807
\(715\) 0 0
\(716\) 34.0490 1.27247
\(717\) 5.38361 9.32468i 0.201055 0.348237i
\(718\) −3.70608 + 6.41912i −0.138310 + 0.239559i
\(719\) −23.7156 41.0766i −0.884443 1.53190i −0.846351 0.532625i \(-0.821206\pi\)
−0.0380914 0.999274i \(-0.512128\pi\)
\(720\) 0 0
\(721\) 12.3553 + 21.3999i 0.460134 + 0.796976i
\(722\) 2.88621 + 4.99906i 0.107414 + 0.186046i
\(723\) −61.0872 −2.27186
\(724\) 0.986548 + 1.70875i 0.0366648 + 0.0635052i
\(725\) 0 0
\(726\) −0.206926 + 0.358406i −0.00767973 + 0.0133017i
\(727\) −34.0951 −1.26452 −0.632259 0.774757i \(-0.717872\pi\)
−0.632259 + 0.774757i \(0.717872\pi\)
\(728\) 11.8725 + 10.0622i 0.440024 + 0.372931i
\(729\) −42.8349 −1.58648
\(730\) 0 0
\(731\) −8.51345 + 14.7457i −0.314881 + 0.545391i
\(732\) 19.0624 + 33.0170i 0.704565 + 1.22034i
\(733\) 14.3920 0.531580 0.265790 0.964031i \(-0.414367\pi\)
0.265790 + 0.964031i \(0.414367\pi\)
\(734\) −2.18270 3.78055i −0.0805651 0.139543i
\(735\) 0 0
\(736\) 9.91745 0.365562
\(737\) −6.51621 11.2864i −0.240028 0.415740i
\(738\) −1.95326 + 3.38314i −0.0719004 + 0.124535i
\(739\) 17.2240 29.8328i 0.633594 1.09742i −0.353217 0.935541i \(-0.614912\pi\)
0.986811 0.161876i \(-0.0517545\pi\)
\(740\) 0 0
\(741\) 11.3822 4.07944i 0.418134 0.149862i
\(742\) −14.2382 −0.522702
\(743\) 20.3567 35.2589i 0.746816 1.29352i −0.202526 0.979277i \(-0.564915\pi\)
0.949342 0.314246i \(-0.101752\pi\)
\(744\) −6.55021 + 11.3453i −0.240142 + 0.415939i
\(745\) 0 0
\(746\) 5.04903 0.184858
\(747\) −18.2985 31.6939i −0.669507 1.15962i
\(748\) 5.97929 + 10.3564i 0.218625 + 0.378669i
\(749\) 28.7542 1.05066
\(750\) 0 0
\(751\) −16.2509 + 28.1474i −0.593003 + 1.02711i 0.400822 + 0.916156i \(0.368725\pi\)
−0.993825 + 0.110956i \(0.964609\pi\)
\(752\) 11.5247 19.9613i 0.420261 0.727914i
\(753\) −51.2167 −1.86644
\(754\) −2.72997 2.31371i −0.0994196 0.0842603i
\(755\) 0 0
\(756\) −10.6304 + 18.4123i −0.386623 + 0.669650i
\(757\) −6.51621 + 11.2864i −0.236836 + 0.410211i −0.959805 0.280669i \(-0.909444\pi\)
0.722969 + 0.690881i \(0.242777\pi\)
\(758\) −3.01542 5.22286i −0.109525 0.189703i
\(759\) 23.5185 0.853668
\(760\) 0 0
\(761\) 1.99493 + 3.45532i 0.0723161 + 0.125255i 0.899916 0.436063i \(-0.143628\pi\)
−0.827600 + 0.561318i \(0.810294\pi\)
\(762\) 8.16070 0.295631
\(763\) 14.2382 + 24.6613i 0.515458 + 0.892800i
\(764\) 24.1220 41.7805i 0.872703 1.51157i
\(765\) 0 0
\(766\) −0.476696 −0.0172237
\(767\) 6.97348 + 5.91018i 0.251798 + 0.213404i
\(768\) −21.3847 −0.771652
\(769\) −3.33343 + 5.77367i −0.120207 + 0.208204i −0.919849 0.392272i \(-0.871689\pi\)
0.799642 + 0.600476i \(0.205022\pi\)
\(770\) 0 0
\(771\) −2.84181 4.92216i −0.102345 0.177267i
\(772\) 37.4720 1.34865
\(773\) 24.1675 + 41.8593i 0.869244 + 1.50557i 0.862771 + 0.505595i \(0.168727\pi\)
0.00647254 + 0.999979i \(0.497940\pi\)
\(774\) 6.13636 + 10.6285i 0.220567 + 0.382033i
\(775\) 0 0
\(776\) −3.38907 5.87005i −0.121661 0.210723i
\(777\) 8.79585 15.2349i 0.315549 0.546548i
\(778\) 3.10841 5.38393i 0.111442 0.193023i
\(779\) −3.46472 −0.124136
\(780\) 0 0
\(781\) −17.0269 −0.609271
\(782\) 0.867753 1.50299i 0.0310308 0.0537469i
\(783\) 5.03022 8.71259i 0.179765 0.311363i
\(784\) −7.12291 12.3372i −0.254389 0.440615i
\(785\) 0 0
\(786\) <