Properties

Label 825.2.n.c.301.1
Level $825$
Weight $2$
Character 825.301
Analytic conductor $6.588$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.n (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \(x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 301.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 825.301
Dual form 825.2.n.c.751.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.309017 - 0.224514i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.572949 - 1.76336i) q^{4} +(-0.309017 + 0.224514i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.454915 + 1.40008i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.309017 - 0.224514i) q^{2} +(0.309017 - 0.951057i) q^{3} +(-0.572949 - 1.76336i) q^{4} +(-0.309017 + 0.224514i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.454915 + 1.40008i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-2.19098 + 2.48990i) q^{11} -1.85410 q^{12} +(-3.42705 - 2.48990i) q^{13} +(0.118034 - 0.363271i) q^{14} +(-2.54508 + 1.84911i) q^{16} +(-6.35410 + 4.61653i) q^{17} +(0.118034 + 0.363271i) q^{18} +(-0.263932 + 0.812299i) q^{19} +1.00000 q^{21} +(1.23607 - 0.277515i) q^{22} +4.23607 q^{23} +(1.19098 + 0.865300i) q^{24} +(0.500000 + 1.53884i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(1.50000 - 1.08981i) q^{28} +(-1.85410 - 5.70634i) q^{29} +(-4.11803 - 2.99193i) q^{31} +4.14590 q^{32} +(1.69098 + 2.85317i) q^{33} +3.00000 q^{34} +(-0.572949 + 1.76336i) q^{36} +(0.545085 + 1.67760i) q^{37} +(0.263932 - 0.191758i) q^{38} +(-3.42705 + 2.48990i) q^{39} +(-1.30902 + 4.02874i) q^{41} +(-0.309017 - 0.224514i) q^{42} -6.70820 q^{43} +(5.64590 + 2.43690i) q^{44} +(-1.30902 - 0.951057i) q^{46} +(-0.336881 + 1.03681i) q^{47} +(0.972136 + 2.99193i) q^{48} +(4.85410 - 3.52671i) q^{49} +(2.42705 + 7.46969i) q^{51} +(-2.42705 + 7.46969i) q^{52} +(-2.11803 - 1.53884i) q^{53} +0.381966 q^{54} -1.47214 q^{56} +(0.690983 + 0.502029i) q^{57} +(-0.708204 + 2.17963i) q^{58} +(2.97214 + 9.14729i) q^{59} +(-6.92705 + 5.03280i) q^{61} +(0.600813 + 1.84911i) q^{62} +(0.309017 - 0.951057i) q^{63} +(3.80902 + 2.76741i) q^{64} +(0.118034 - 1.26133i) q^{66} +4.85410 q^{67} +(11.7812 + 8.55951i) q^{68} +(1.30902 - 4.02874i) q^{69} +(4.30902 - 3.13068i) q^{71} +(1.19098 - 0.865300i) q^{72} +(-2.38197 - 7.33094i) q^{73} +(0.208204 - 0.640786i) q^{74} +1.58359 q^{76} +(-3.04508 - 1.31433i) q^{77} +1.61803 q^{78} +(-8.89919 - 6.46564i) q^{79} +(0.309017 + 0.951057i) q^{81} +(1.30902 - 0.951057i) q^{82} +(-6.04508 + 4.39201i) q^{83} +(-0.572949 - 1.76336i) q^{84} +(2.07295 + 1.50609i) q^{86} -6.00000 q^{87} +(-2.48936 - 4.20025i) q^{88} -3.76393 q^{89} +(1.30902 - 4.02874i) q^{91} +(-2.42705 - 7.46969i) q^{92} +(-4.11803 + 2.99193i) q^{93} +(0.336881 - 0.244758i) q^{94} +(1.28115 - 3.94298i) q^{96} +(0.927051 + 0.673542i) q^{97} -2.29180 q^{98} +(3.23607 - 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} - q^{3} - 9 q^{4} + q^{6} - q^{7} - 13 q^{8} - q^{9} + O(q^{10}) \) \( 4 q + q^{2} - q^{3} - 9 q^{4} + q^{6} - q^{7} - 13 q^{8} - q^{9} - 11 q^{11} + 6 q^{12} - 7 q^{13} - 4 q^{14} + q^{16} - 12 q^{17} - 4 q^{18} - 10 q^{19} + 4 q^{21} - 4 q^{22} + 8 q^{23} + 7 q^{24} + 2 q^{26} - q^{27} + 6 q^{28} + 6 q^{29} - 12 q^{31} + 30 q^{32} + 9 q^{33} + 12 q^{34} - 9 q^{36} - 9 q^{37} + 10 q^{38} - 7 q^{39} - 3 q^{41} + q^{42} + 36 q^{44} - 3 q^{46} - 17 q^{47} - 14 q^{48} + 6 q^{49} + 3 q^{51} - 3 q^{52} - 4 q^{53} + 6 q^{54} + 12 q^{56} + 5 q^{57} + 24 q^{58} - 6 q^{59} - 21 q^{61} + 27 q^{62} - q^{63} + 13 q^{64} - 4 q^{66} + 6 q^{67} + 27 q^{68} + 3 q^{69} + 15 q^{71} + 7 q^{72} - 14 q^{73} - 26 q^{74} + 60 q^{76} - q^{77} + 2 q^{78} - 11 q^{79} - q^{81} + 3 q^{82} - 13 q^{83} - 9 q^{84} + 15 q^{86} - 24 q^{87} + 37 q^{88} - 24 q^{89} + 3 q^{91} - 3 q^{92} - 12 q^{93} + 17 q^{94} - 15 q^{96} - 3 q^{97} - 36 q^{98} + 4 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 0.224514i −0.218508 0.158755i 0.473147 0.880984i \(-0.343118\pi\)
−0.691655 + 0.722228i \(0.743118\pi\)
\(3\) 0.309017 0.951057i 0.178411 0.549093i
\(4\) −0.572949 1.76336i −0.286475 0.881678i
\(5\) 0 0
\(6\) −0.309017 + 0.224514i −0.126156 + 0.0916575i
\(7\) 0.309017 + 0.951057i 0.116797 + 0.359466i 0.992318 0.123716i \(-0.0394811\pi\)
−0.875520 + 0.483181i \(0.839481\pi\)
\(8\) −0.454915 + 1.40008i −0.160837 + 0.495005i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 0 0
\(11\) −2.19098 + 2.48990i −0.660606 + 0.750733i
\(12\) −1.85410 −0.535233
\(13\) −3.42705 2.48990i −0.950493 0.690574i 0.000430477 1.00000i \(-0.499863\pi\)
−0.950923 + 0.309426i \(0.899863\pi\)
\(14\) 0.118034 0.363271i 0.0315459 0.0970883i
\(15\) 0 0
\(16\) −2.54508 + 1.84911i −0.636271 + 0.462278i
\(17\) −6.35410 + 4.61653i −1.54110 + 1.11967i −0.591452 + 0.806340i \(0.701445\pi\)
−0.949644 + 0.313332i \(0.898555\pi\)
\(18\) 0.118034 + 0.363271i 0.0278209 + 0.0856239i
\(19\) −0.263932 + 0.812299i −0.0605502 + 0.186354i −0.976756 0.214353i \(-0.931236\pi\)
0.916206 + 0.400707i \(0.131236\pi\)
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) 1.23607 0.277515i 0.263531 0.0591663i
\(23\) 4.23607 0.883281 0.441641 0.897192i \(-0.354397\pi\)
0.441641 + 0.897192i \(0.354397\pi\)
\(24\) 1.19098 + 0.865300i 0.243108 + 0.176629i
\(25\) 0 0
\(26\) 0.500000 + 1.53884i 0.0980581 + 0.301792i
\(27\) −0.809017 + 0.587785i −0.155695 + 0.113119i
\(28\) 1.50000 1.08981i 0.283473 0.205955i
\(29\) −1.85410 5.70634i −0.344298 1.05964i −0.961958 0.273196i \(-0.911919\pi\)
0.617660 0.786445i \(-0.288081\pi\)
\(30\) 0 0
\(31\) −4.11803 2.99193i −0.739621 0.537366i 0.152972 0.988231i \(-0.451116\pi\)
−0.892592 + 0.450865i \(0.851116\pi\)
\(32\) 4.14590 0.732898
\(33\) 1.69098 + 2.85317i 0.294362 + 0.496673i
\(34\) 3.00000 0.514496
\(35\) 0 0
\(36\) −0.572949 + 1.76336i −0.0954915 + 0.293893i
\(37\) 0.545085 + 1.67760i 0.0896114 + 0.275796i 0.985812 0.167854i \(-0.0536836\pi\)
−0.896201 + 0.443649i \(0.853684\pi\)
\(38\) 0.263932 0.191758i 0.0428154 0.0311072i
\(39\) −3.42705 + 2.48990i −0.548767 + 0.398703i
\(40\) 0 0
\(41\) −1.30902 + 4.02874i −0.204434 + 0.629183i 0.795302 + 0.606213i \(0.207312\pi\)
−0.999736 + 0.0229701i \(0.992688\pi\)
\(42\) −0.309017 0.224514i −0.0476824 0.0346433i
\(43\) −6.70820 −1.02299 −0.511496 0.859286i \(-0.670908\pi\)
−0.511496 + 0.859286i \(0.670908\pi\)
\(44\) 5.64590 + 2.43690i 0.851151 + 0.367376i
\(45\) 0 0
\(46\) −1.30902 0.951057i −0.193004 0.140226i
\(47\) −0.336881 + 1.03681i −0.0491391 + 0.151235i −0.972615 0.232421i \(-0.925335\pi\)
0.923476 + 0.383656i \(0.125335\pi\)
\(48\) 0.972136 + 2.99193i 0.140316 + 0.431847i
\(49\) 4.85410 3.52671i 0.693443 0.503816i
\(50\) 0 0
\(51\) 2.42705 + 7.46969i 0.339855 + 1.04597i
\(52\) −2.42705 + 7.46969i −0.336571 + 1.03586i
\(53\) −2.11803 1.53884i −0.290934 0.211376i 0.432738 0.901520i \(-0.357547\pi\)
−0.723673 + 0.690143i \(0.757547\pi\)
\(54\) 0.381966 0.0519790
\(55\) 0 0
\(56\) −1.47214 −0.196722
\(57\) 0.690983 + 0.502029i 0.0915229 + 0.0664953i
\(58\) −0.708204 + 2.17963i −0.0929917 + 0.286199i
\(59\) 2.97214 + 9.14729i 0.386939 + 1.19088i 0.935064 + 0.354480i \(0.115342\pi\)
−0.548125 + 0.836397i \(0.684658\pi\)
\(60\) 0 0
\(61\) −6.92705 + 5.03280i −0.886918 + 0.644384i −0.935073 0.354456i \(-0.884666\pi\)
0.0481546 + 0.998840i \(0.484666\pi\)
\(62\) 0.600813 + 1.84911i 0.0763033 + 0.234838i
\(63\) 0.309017 0.951057i 0.0389325 0.119822i
\(64\) 3.80902 + 2.76741i 0.476127 + 0.345927i
\(65\) 0 0
\(66\) 0.118034 1.26133i 0.0145290 0.155259i
\(67\) 4.85410 0.593023 0.296511 0.955029i \(-0.404177\pi\)
0.296511 + 0.955029i \(0.404177\pi\)
\(68\) 11.7812 + 8.55951i 1.42867 + 1.03799i
\(69\) 1.30902 4.02874i 0.157587 0.485003i
\(70\) 0 0
\(71\) 4.30902 3.13068i 0.511386 0.371544i −0.301963 0.953320i \(-0.597642\pi\)
0.813349 + 0.581776i \(0.197642\pi\)
\(72\) 1.19098 0.865300i 0.140359 0.101977i
\(73\) −2.38197 7.33094i −0.278788 0.858021i −0.988192 0.153219i \(-0.951036\pi\)
0.709404 0.704802i \(-0.248964\pi\)
\(74\) 0.208204 0.640786i 0.0242032 0.0744898i
\(75\) 0 0
\(76\) 1.58359 0.181650
\(77\) −3.04508 1.31433i −0.347020 0.149782i
\(78\) 1.61803 0.183206
\(79\) −8.89919 6.46564i −1.00124 0.727441i −0.0388837 0.999244i \(-0.512380\pi\)
−0.962353 + 0.271803i \(0.912380\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 1.30902 0.951057i 0.144557 0.105027i
\(83\) −6.04508 + 4.39201i −0.663534 + 0.482086i −0.867855 0.496818i \(-0.834502\pi\)
0.204320 + 0.978904i \(0.434502\pi\)
\(84\) −0.572949 1.76336i −0.0625139 0.192398i
\(85\) 0 0
\(86\) 2.07295 + 1.50609i 0.223532 + 0.162405i
\(87\) −6.00000 −0.643268
\(88\) −2.48936 4.20025i −0.265366 0.447749i
\(89\) −3.76393 −0.398976 −0.199488 0.979900i \(-0.563928\pi\)
−0.199488 + 0.979900i \(0.563928\pi\)
\(90\) 0 0
\(91\) 1.30902 4.02874i 0.137222 0.422327i
\(92\) −2.42705 7.46969i −0.253038 0.778770i
\(93\) −4.11803 + 2.99193i −0.427020 + 0.310248i
\(94\) 0.336881 0.244758i 0.0347466 0.0252449i
\(95\) 0 0
\(96\) 1.28115 3.94298i 0.130757 0.402429i
\(97\) 0.927051 + 0.673542i 0.0941278 + 0.0683878i 0.633854 0.773453i \(-0.281472\pi\)
−0.539726 + 0.841841i \(0.681472\pi\)
\(98\) −2.29180 −0.231506
\(99\) 3.23607 0.726543i 0.325237 0.0730203i
\(100\) 0 0
\(101\) 4.66312 + 3.38795i 0.463998 + 0.337114i 0.795097 0.606482i \(-0.207420\pi\)
−0.331100 + 0.943596i \(0.607420\pi\)
\(102\) 0.927051 2.85317i 0.0917917 0.282506i
\(103\) −2.14590 6.60440i −0.211442 0.650750i −0.999387 0.0350054i \(-0.988855\pi\)
0.787946 0.615745i \(-0.211145\pi\)
\(104\) 5.04508 3.66547i 0.494711 0.359429i
\(105\) 0 0
\(106\) 0.309017 + 0.951057i 0.0300144 + 0.0923748i
\(107\) 0.781153 2.40414i 0.0755169 0.232417i −0.906172 0.422910i \(-0.861009\pi\)
0.981689 + 0.190493i \(0.0610086\pi\)
\(108\) 1.50000 + 1.08981i 0.144338 + 0.104867i
\(109\) −12.0000 −1.14939 −0.574696 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(110\) 0 0
\(111\) 1.76393 0.167425
\(112\) −2.54508 1.84911i −0.240488 0.174725i
\(113\) −1.39919 + 4.30625i −0.131624 + 0.405098i −0.995050 0.0993784i \(-0.968315\pi\)
0.863425 + 0.504477i \(0.168315\pi\)
\(114\) −0.100813 0.310271i −0.00944201 0.0290595i
\(115\) 0 0
\(116\) −9.00000 + 6.53888i −0.835629 + 0.607120i
\(117\) 1.30902 + 4.02874i 0.121019 + 0.372457i
\(118\) 1.13525 3.49396i 0.104509 0.321645i
\(119\) −6.35410 4.61653i −0.582480 0.423196i
\(120\) 0 0
\(121\) −1.39919 10.9106i −0.127199 0.991877i
\(122\) 3.27051 0.296098
\(123\) 3.42705 + 2.48990i 0.309007 + 0.224507i
\(124\) −2.91641 + 8.97578i −0.261901 + 0.806049i
\(125\) 0 0
\(126\) −0.309017 + 0.224514i −0.0275294 + 0.0200013i
\(127\) −4.61803 + 3.35520i −0.409784 + 0.297726i −0.773514 0.633779i \(-0.781503\pi\)
0.363730 + 0.931504i \(0.381503\pi\)
\(128\) −3.11803 9.59632i −0.275598 0.848203i
\(129\) −2.07295 + 6.37988i −0.182513 + 0.561717i
\(130\) 0 0
\(131\) 12.7984 1.11820 0.559100 0.829101i \(-0.311147\pi\)
0.559100 + 0.829101i \(0.311147\pi\)
\(132\) 4.06231 4.61653i 0.353578 0.401817i
\(133\) −0.854102 −0.0740600
\(134\) −1.50000 1.08981i −0.129580 0.0941456i
\(135\) 0 0
\(136\) −3.57295 10.9964i −0.306378 0.942934i
\(137\) 11.5172 8.36775i 0.983983 0.714905i 0.0253875 0.999678i \(-0.491918\pi\)
0.958595 + 0.284772i \(0.0919181\pi\)
\(138\) −1.30902 + 0.951057i −0.111431 + 0.0809593i
\(139\) −1.71885 5.29007i −0.145791 0.448698i 0.851321 0.524645i \(-0.175802\pi\)
−0.997112 + 0.0759473i \(0.975802\pi\)
\(140\) 0 0
\(141\) 0.881966 + 0.640786i 0.0742749 + 0.0539639i
\(142\) −2.03444 −0.170727
\(143\) 13.7082 3.07768i 1.14634 0.257369i
\(144\) 3.14590 0.262158
\(145\) 0 0
\(146\) −0.909830 + 2.80017i −0.0752981 + 0.231744i
\(147\) −1.85410 5.70634i −0.152924 0.470651i
\(148\) 2.64590 1.92236i 0.217491 0.158017i
\(149\) −0.190983 + 0.138757i −0.0156459 + 0.0113674i −0.595581 0.803295i \(-0.703078\pi\)
0.579935 + 0.814663i \(0.303078\pi\)
\(150\) 0 0
\(151\) 5.85410 18.0171i 0.476400 1.46621i −0.367660 0.929960i \(-0.619841\pi\)
0.844060 0.536248i \(-0.180159\pi\)
\(152\) −1.01722 0.739054i −0.0825075 0.0599452i
\(153\) 7.85410 0.634967
\(154\) 0.645898 + 1.08981i 0.0520479 + 0.0878197i
\(155\) 0 0
\(156\) 6.35410 + 4.61653i 0.508735 + 0.369618i
\(157\) −0.708204 + 2.17963i −0.0565208 + 0.173953i −0.975331 0.220745i \(-0.929151\pi\)
0.918811 + 0.394699i \(0.129151\pi\)
\(158\) 1.29837 + 3.99598i 0.103293 + 0.317903i
\(159\) −2.11803 + 1.53884i −0.167971 + 0.122038i
\(160\) 0 0
\(161\) 1.30902 + 4.02874i 0.103165 + 0.317509i
\(162\) 0.118034 0.363271i 0.00927363 0.0285413i
\(163\) −9.59017 6.96767i −0.751160 0.545750i 0.145026 0.989428i \(-0.453673\pi\)
−0.896186 + 0.443678i \(0.853673\pi\)
\(164\) 7.85410 0.613302
\(165\) 0 0
\(166\) 2.85410 0.221521
\(167\) −13.7812 10.0126i −1.06642 0.774798i −0.0911527 0.995837i \(-0.529055\pi\)
−0.975265 + 0.221039i \(0.929055\pi\)
\(168\) −0.454915 + 1.40008i −0.0350975 + 0.108019i
\(169\) 1.52786 + 4.70228i 0.117528 + 0.361714i
\(170\) 0 0
\(171\) 0.690983 0.502029i 0.0528408 0.0383911i
\(172\) 3.84346 + 11.8290i 0.293061 + 0.901949i
\(173\) −3.40983 + 10.4944i −0.259245 + 0.797873i 0.733719 + 0.679453i \(0.237783\pi\)
−0.992964 + 0.118420i \(0.962217\pi\)
\(174\) 1.85410 + 1.34708i 0.140559 + 0.102122i
\(175\) 0 0
\(176\) 0.972136 10.3884i 0.0732775 0.783053i
\(177\) 9.61803 0.722936
\(178\) 1.16312 + 0.845055i 0.0871795 + 0.0633396i
\(179\) −5.39919 + 16.6170i −0.403554 + 1.24201i 0.518542 + 0.855052i \(0.326475\pi\)
−0.922096 + 0.386960i \(0.873525\pi\)
\(180\) 0 0
\(181\) −9.28115 + 6.74315i −0.689863 + 0.501215i −0.876615 0.481192i \(-0.840204\pi\)
0.186752 + 0.982407i \(0.440204\pi\)
\(182\) −1.30902 + 0.951057i −0.0970308 + 0.0704970i
\(183\) 2.64590 + 8.14324i 0.195590 + 0.601965i
\(184\) −1.92705 + 5.93085i −0.142064 + 0.437228i
\(185\) 0 0
\(186\) 1.94427 0.142561
\(187\) 2.42705 25.9358i 0.177484 1.89661i
\(188\) 2.02129 0.147417
\(189\) −0.809017 0.587785i −0.0588473 0.0427551i
\(190\) 0 0
\(191\) −7.16312 22.0458i −0.518305 1.59518i −0.777187 0.629270i \(-0.783354\pi\)
0.258882 0.965909i \(-0.416646\pi\)
\(192\) 3.80902 2.76741i 0.274892 0.199721i
\(193\) −7.97214 + 5.79210i −0.573847 + 0.416924i −0.836501 0.547966i \(-0.815402\pi\)
0.262654 + 0.964890i \(0.415402\pi\)
\(194\) −0.135255 0.416272i −0.00971074 0.0298866i
\(195\) 0 0
\(196\) −9.00000 6.53888i −0.642857 0.467063i
\(197\) 16.0344 1.14241 0.571203 0.820809i \(-0.306477\pi\)
0.571203 + 0.820809i \(0.306477\pi\)
\(198\) −1.16312 0.502029i −0.0826593 0.0356776i
\(199\) −6.70820 −0.475532 −0.237766 0.971322i \(-0.576415\pi\)
−0.237766 + 0.971322i \(0.576415\pi\)
\(200\) 0 0
\(201\) 1.50000 4.61653i 0.105802 0.325625i
\(202\) −0.680340 2.09387i −0.0478685 0.147324i
\(203\) 4.85410 3.52671i 0.340691 0.247527i
\(204\) 11.7812 8.55951i 0.824846 0.599285i
\(205\) 0 0
\(206\) −0.819660 + 2.52265i −0.0571084 + 0.175762i
\(207\) −3.42705 2.48990i −0.238197 0.173060i
\(208\) 13.3262 0.924008
\(209\) −1.44427 2.43690i −0.0999024 0.168564i
\(210\) 0 0
\(211\) −1.11803 0.812299i −0.0769686 0.0559210i 0.548636 0.836062i \(-0.315147\pi\)
−0.625604 + 0.780141i \(0.715147\pi\)
\(212\) −1.50000 + 4.61653i −0.103020 + 0.317064i
\(213\) −1.64590 5.06555i −0.112775 0.347086i
\(214\) −0.781153 + 0.567541i −0.0533985 + 0.0387963i
\(215\) 0 0
\(216\) −0.454915 1.40008i −0.0309530 0.0952637i
\(217\) 1.57295 4.84104i 0.106779 0.328631i
\(218\) 3.70820 + 2.69417i 0.251151 + 0.182472i
\(219\) −7.70820 −0.520872
\(220\) 0 0
\(221\) 33.2705 2.23802
\(222\) −0.545085 0.396027i −0.0365837 0.0265796i
\(223\) 4.69098 14.4374i 0.314131 0.966797i −0.661979 0.749522i \(-0.730283\pi\)
0.976110 0.217275i \(-0.0697168\pi\)
\(224\) 1.28115 + 3.94298i 0.0856006 + 0.263452i
\(225\) 0 0
\(226\) 1.39919 1.01657i 0.0930725 0.0676212i
\(227\) 2.83688 + 8.73102i 0.188290 + 0.579498i 0.999990 0.00457752i \(-0.00145707\pi\)
−0.811699 + 0.584076i \(0.801457\pi\)
\(228\) 0.489357 1.50609i 0.0324085 0.0997430i
\(229\) 6.85410 + 4.97980i 0.452932 + 0.329074i 0.790752 0.612136i \(-0.209690\pi\)
−0.337820 + 0.941211i \(0.609690\pi\)
\(230\) 0 0
\(231\) −2.19098 + 2.48990i −0.144156 + 0.163823i
\(232\) 8.83282 0.579903
\(233\) −8.78115 6.37988i −0.575272 0.417960i 0.261744 0.965137i \(-0.415702\pi\)
−0.837017 + 0.547177i \(0.815702\pi\)
\(234\) 0.500000 1.53884i 0.0326860 0.100597i
\(235\) 0 0
\(236\) 14.4271 10.4819i 0.939121 0.682311i
\(237\) −8.89919 + 6.46564i −0.578064 + 0.419988i
\(238\) 0.927051 + 2.85317i 0.0600918 + 0.184944i
\(239\) 0.809017 2.48990i 0.0523310 0.161058i −0.921476 0.388436i \(-0.873015\pi\)
0.973807 + 0.227378i \(0.0730154\pi\)
\(240\) 0 0
\(241\) 21.7082 1.39835 0.699174 0.714951i \(-0.253551\pi\)
0.699174 + 0.714951i \(0.253551\pi\)
\(242\) −2.01722 + 3.68571i −0.129672 + 0.236927i
\(243\) 1.00000 0.0641500
\(244\) 12.8435 + 9.33132i 0.822218 + 0.597376i
\(245\) 0 0
\(246\) −0.500000 1.53884i −0.0318788 0.0981130i
\(247\) 2.92705 2.12663i 0.186244 0.135314i
\(248\) 6.06231 4.40452i 0.384957 0.279687i
\(249\) 2.30902 + 7.10642i 0.146328 + 0.450351i
\(250\) 0 0
\(251\) −20.2082 14.6821i −1.27553 0.926727i −0.276122 0.961123i \(-0.589049\pi\)
−0.999408 + 0.0343954i \(0.989049\pi\)
\(252\) −1.85410 −0.116797
\(253\) −9.28115 + 10.5474i −0.583501 + 0.663108i
\(254\) 2.18034 0.136807
\(255\) 0 0
\(256\) 1.71885 5.29007i 0.107428 0.330629i
\(257\) 3.93769 + 12.1190i 0.245627 + 0.755961i 0.995533 + 0.0944167i \(0.0300986\pi\)
−0.749906 + 0.661544i \(0.769901\pi\)
\(258\) 2.07295 1.50609i 0.129056 0.0937648i
\(259\) −1.42705 + 1.03681i −0.0886726 + 0.0644244i
\(260\) 0 0
\(261\) −1.85410 + 5.70634i −0.114766 + 0.353214i
\(262\) −3.95492 2.87341i −0.244335 0.177520i
\(263\) −18.2705 −1.12661 −0.563304 0.826250i \(-0.690470\pi\)
−0.563304 + 0.826250i \(0.690470\pi\)
\(264\) −4.76393 + 1.06957i −0.293200 + 0.0658274i
\(265\) 0 0
\(266\) 0.263932 + 0.191758i 0.0161827 + 0.0117574i
\(267\) −1.16312 + 3.57971i −0.0711817 + 0.219075i
\(268\) −2.78115 8.55951i −0.169886 0.522855i
\(269\) −1.14590 + 0.832544i −0.0698666 + 0.0507611i −0.622170 0.782882i \(-0.713749\pi\)
0.552304 + 0.833643i \(0.313749\pi\)
\(270\) 0 0
\(271\) 5.06231 + 15.5802i 0.307513 + 0.946428i 0.978727 + 0.205165i \(0.0657731\pi\)
−0.671214 + 0.741263i \(0.734227\pi\)
\(272\) 7.63525 23.4989i 0.462955 1.42483i
\(273\) −3.42705 2.48990i −0.207415 0.150695i
\(274\) −5.43769 −0.328503
\(275\) 0 0
\(276\) −7.85410 −0.472761
\(277\) 17.9721 + 13.0575i 1.07984 + 0.784550i 0.977655 0.210215i \(-0.0674164\pi\)
0.102186 + 0.994765i \(0.467416\pi\)
\(278\) −0.656541 + 2.02063i −0.0393767 + 0.121189i
\(279\) 1.57295 + 4.84104i 0.0941700 + 0.289825i
\(280\) 0 0
\(281\) −23.6525 + 17.1845i −1.41099 + 1.02514i −0.417811 + 0.908534i \(0.637202\pi\)
−0.993178 + 0.116609i \(0.962798\pi\)
\(282\) −0.128677 0.396027i −0.00766261 0.0235831i
\(283\) −2.38197 + 7.33094i −0.141593 + 0.435779i −0.996557 0.0829083i \(-0.973579\pi\)
0.854964 + 0.518687i \(0.173579\pi\)
\(284\) −7.98936 5.80461i −0.474081 0.344440i
\(285\) 0 0
\(286\) −4.92705 2.12663i −0.291343 0.125750i
\(287\) −4.23607 −0.250047
\(288\) −3.35410 2.43690i −0.197642 0.143596i
\(289\) 13.8090 42.4998i 0.812295 2.49999i
\(290\) 0 0
\(291\) 0.927051 0.673542i 0.0543447 0.0394837i
\(292\) −11.5623 + 8.40051i −0.676633 + 0.491602i
\(293\) −2.98278 9.18005i −0.174256 0.536304i 0.825343 0.564632i \(-0.190982\pi\)
−0.999599 + 0.0283276i \(0.990982\pi\)
\(294\) −0.708204 + 2.17963i −0.0413033 + 0.127118i
\(295\) 0 0
\(296\) −2.59675 −0.150933
\(297\) 0.309017 3.30220i 0.0179310 0.191613i
\(298\) 0.0901699 0.00522340
\(299\) −14.5172 10.5474i −0.839553 0.609971i
\(300\) 0 0
\(301\) −2.07295 6.37988i −0.119483 0.367730i
\(302\) −5.85410 + 4.25325i −0.336866 + 0.244747i
\(303\) 4.66312 3.38795i 0.267889 0.194633i
\(304\) −0.830303 2.55541i −0.0476212 0.146563i
\(305\) 0 0
\(306\) −2.42705 1.76336i −0.138745 0.100804i
\(307\) 18.9787 1.08317 0.541586 0.840645i \(-0.317824\pi\)
0.541586 + 0.840645i \(0.317824\pi\)
\(308\) −0.572949 + 6.12261i −0.0326468 + 0.348868i
\(309\) −6.94427 −0.395046
\(310\) 0 0
\(311\) −6.07295 + 18.6906i −0.344365 + 1.05985i 0.617557 + 0.786526i \(0.288122\pi\)
−0.961923 + 0.273322i \(0.911878\pi\)
\(312\) −1.92705 5.93085i −0.109098 0.335768i
\(313\) −9.28115 + 6.74315i −0.524602 + 0.381146i −0.818335 0.574742i \(-0.805102\pi\)
0.293733 + 0.955888i \(0.405102\pi\)
\(314\) 0.708204 0.514540i 0.0399663 0.0290372i
\(315\) 0 0
\(316\) −6.30244 + 19.3969i −0.354540 + 1.09116i
\(317\) −23.6074 17.1518i −1.32592 0.963340i −0.999838 0.0179992i \(-0.994270\pi\)
−0.326085 0.945340i \(-0.605730\pi\)
\(318\) 1.00000 0.0560772
\(319\) 18.2705 + 7.88597i 1.02295 + 0.441529i
\(320\) 0 0
\(321\) −2.04508 1.48584i −0.114146 0.0829316i
\(322\) 0.500000 1.53884i 0.0278639 0.0857563i
\(323\) −2.07295 6.37988i −0.115342 0.354986i
\(324\) 1.50000 1.08981i 0.0833333 0.0605452i
\(325\) 0 0
\(326\) 1.39919 + 4.30625i 0.0774938 + 0.238501i
\(327\) −3.70820 + 11.4127i −0.205064 + 0.631123i
\(328\) −5.04508 3.66547i −0.278568 0.202392i
\(329\) −1.09017 −0.0601030
\(330\) 0 0
\(331\) 3.29180 0.180933 0.0904667 0.995899i \(-0.471164\pi\)
0.0904667 + 0.995899i \(0.471164\pi\)
\(332\) 11.2082 + 8.14324i 0.615130 + 0.446918i
\(333\) 0.545085 1.67760i 0.0298705 0.0919319i
\(334\) 2.01064 + 6.18812i 0.110017 + 0.338599i
\(335\) 0 0
\(336\) −2.54508 + 1.84911i −0.138846 + 0.100877i
\(337\) −1.29180 3.97574i −0.0703686 0.216572i 0.909687 0.415294i \(-0.136321\pi\)
−0.980056 + 0.198721i \(0.936321\pi\)
\(338\) 0.583592 1.79611i 0.0317432 0.0976956i
\(339\) 3.66312 + 2.66141i 0.198953 + 0.144548i
\(340\) 0 0
\(341\) 16.4721 3.69822i 0.892016 0.200270i
\(342\) −0.326238 −0.0176409
\(343\) 10.5172 + 7.64121i 0.567877 + 0.412586i
\(344\) 3.05166 9.39205i 0.164535 0.506386i
\(345\) 0 0
\(346\) 3.40983 2.47739i 0.183314 0.133185i
\(347\) −8.47214 + 6.15537i −0.454808 + 0.330437i −0.791491 0.611181i \(-0.790695\pi\)
0.336683 + 0.941618i \(0.390695\pi\)
\(348\) 3.43769 + 10.5801i 0.184280 + 0.567155i
\(349\) −0.218847 + 0.673542i −0.0117146 + 0.0360539i −0.956743 0.290935i \(-0.906034\pi\)
0.945028 + 0.326988i \(0.106034\pi\)
\(350\) 0 0
\(351\) 4.23607 0.226105
\(352\) −9.08359 + 10.3229i −0.484157 + 0.550211i
\(353\) 12.0000 0.638696 0.319348 0.947638i \(-0.396536\pi\)
0.319348 + 0.947638i \(0.396536\pi\)
\(354\) −2.97214 2.15938i −0.157967 0.114770i
\(355\) 0 0
\(356\) 2.15654 + 6.63715i 0.114296 + 0.351768i
\(357\) −6.35410 + 4.61653i −0.336295 + 0.244332i
\(358\) 5.39919 3.92274i 0.285356 0.207323i
\(359\) 1.14590 + 3.52671i 0.0604782 + 0.186133i 0.976731 0.214468i \(-0.0688016\pi\)
−0.916253 + 0.400600i \(0.868802\pi\)
\(360\) 0 0
\(361\) 14.7812 + 10.7391i 0.777955 + 0.565218i
\(362\) 4.38197 0.230311
\(363\) −10.8090 2.04087i −0.567326 0.107118i
\(364\) −7.85410 −0.411667
\(365\) 0 0
\(366\) 1.01064 3.11044i 0.0528272 0.162585i
\(367\) −8.91641 27.4419i −0.465433 1.43245i −0.858438 0.512918i \(-0.828564\pi\)
0.393005 0.919536i \(-0.371436\pi\)
\(368\) −10.7812 + 7.83297i −0.562006 + 0.408322i
\(369\) 3.42705 2.48990i 0.178405 0.129619i
\(370\) 0 0
\(371\) 0.809017 2.48990i 0.0420021 0.129269i
\(372\) 7.63525 + 5.54734i 0.395870 + 0.287616i
\(373\) 34.8885 1.80646 0.903230 0.429156i \(-0.141189\pi\)
0.903230 + 0.429156i \(0.141189\pi\)
\(374\) −6.57295 + 7.46969i −0.339879 + 0.386249i
\(375\) 0 0
\(376\) −1.29837 0.943324i −0.0669585 0.0486482i
\(377\) −7.85410 + 24.1724i −0.404507 + 1.24494i
\(378\) 0.118034 + 0.363271i 0.00607101 + 0.0186847i
\(379\) −8.80902 + 6.40013i −0.452489 + 0.328752i −0.790578 0.612362i \(-0.790220\pi\)
0.338089 + 0.941114i \(0.390220\pi\)
\(380\) 0 0
\(381\) 1.76393 + 5.42882i 0.0903690 + 0.278127i
\(382\) −2.73607 + 8.42075i −0.139989 + 0.430843i
\(383\) 0.572949 + 0.416272i 0.0292763 + 0.0212705i 0.602327 0.798249i \(-0.294240\pi\)
−0.573051 + 0.819520i \(0.694240\pi\)
\(384\) −10.0902 −0.514912
\(385\) 0 0
\(386\) 3.76393 0.191579
\(387\) 5.42705 + 3.94298i 0.275873 + 0.200433i
\(388\) 0.656541 2.02063i 0.0333308 0.102582i
\(389\) 1.77458 + 5.46158i 0.0899745 + 0.276913i 0.985911 0.167268i \(-0.0534946\pi\)
−0.895937 + 0.444181i \(0.853495\pi\)
\(390\) 0 0
\(391\) −26.9164 + 19.5559i −1.36122 + 0.988985i
\(392\) 2.72949 + 8.40051i 0.137860 + 0.424290i
\(393\) 3.95492 12.1720i 0.199499 0.613995i
\(394\) −4.95492 3.59996i −0.249625 0.181363i
\(395\) 0 0
\(396\) −3.13525 5.29007i −0.157552 0.265836i
\(397\) 5.29180 0.265588 0.132794 0.991144i \(-0.457605\pi\)
0.132794 + 0.991144i \(0.457605\pi\)
\(398\) 2.07295 + 1.50609i 0.103908 + 0.0754933i
\(399\) −0.263932 + 0.812299i −0.0132131 + 0.0406658i
\(400\) 0 0
\(401\) −23.2082 + 16.8617i −1.15896 + 0.842035i −0.989646 0.143526i \(-0.954156\pi\)
−0.169316 + 0.985562i \(0.554156\pi\)
\(402\) −1.50000 + 1.08981i −0.0748132 + 0.0543550i
\(403\) 6.66312 + 20.5070i 0.331914 + 1.02153i
\(404\) 3.30244 10.1639i 0.164302 0.505671i
\(405\) 0 0
\(406\) −2.29180 −0.113740
\(407\) −5.37132 2.31838i −0.266247 0.114918i
\(408\) −11.5623 −0.572419
\(409\) −2.00000 1.45309i −0.0988936 0.0718504i 0.537240 0.843430i \(-0.319467\pi\)
−0.636133 + 0.771579i \(0.719467\pi\)
\(410\) 0 0
\(411\) −4.39919 13.5393i −0.216996 0.667845i
\(412\) −10.4164 + 7.56796i −0.513180 + 0.372847i
\(413\) −7.78115 + 5.65334i −0.382886 + 0.278183i
\(414\) 0.500000 + 1.53884i 0.0245737 + 0.0756299i
\(415\) 0 0
\(416\) −14.2082 10.3229i −0.696615 0.506120i
\(417\) −5.56231 −0.272387
\(418\) −0.100813 + 1.07730i −0.00493093 + 0.0526926i
\(419\) −24.4508 −1.19450 −0.597251 0.802054i \(-0.703740\pi\)
−0.597251 + 0.802054i \(0.703740\pi\)
\(420\) 0 0
\(421\) −8.50000 + 26.1603i −0.414265 + 1.27498i 0.498642 + 0.866808i \(0.333832\pi\)
−0.912907 + 0.408168i \(0.866168\pi\)
\(422\) 0.163119 + 0.502029i 0.00794051 + 0.0244384i
\(423\) 0.881966 0.640786i 0.0428827 0.0311561i
\(424\) 3.11803 2.26538i 0.151425 0.110017i
\(425\) 0 0
\(426\) −0.628677 + 1.93487i −0.0304595 + 0.0937447i
\(427\) −6.92705 5.03280i −0.335223 0.243554i
\(428\) −4.68692 −0.226551
\(429\) 1.30902 13.9883i 0.0631999 0.675363i
\(430\) 0 0
\(431\) 13.8262 + 10.0453i 0.665986 + 0.483867i 0.868679 0.495375i \(-0.164969\pi\)
−0.202693 + 0.979242i \(0.564969\pi\)
\(432\) 0.972136 2.99193i 0.0467719 0.143949i
\(433\) 8.43769 + 25.9686i 0.405490 + 1.24797i 0.920486 + 0.390776i \(0.127793\pi\)
−0.514996 + 0.857193i \(0.672207\pi\)
\(434\) −1.57295 + 1.14281i −0.0755040 + 0.0548568i
\(435\) 0 0
\(436\) 6.87539 + 21.1603i 0.329271 + 1.01339i
\(437\) −1.11803 + 3.44095i −0.0534828 + 0.164603i
\(438\) 2.38197 + 1.73060i 0.113815 + 0.0826912i
\(439\) 36.7082 1.75199 0.875993 0.482323i \(-0.160207\pi\)
0.875993 + 0.482323i \(0.160207\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) −10.2812 7.46969i −0.489025 0.355297i
\(443\) −5.43769 + 16.7355i −0.258353 + 0.795128i 0.734798 + 0.678286i \(0.237277\pi\)
−0.993151 + 0.116842i \(0.962723\pi\)
\(444\) −1.01064 3.11044i −0.0479630 0.147615i
\(445\) 0 0
\(446\) −4.69098 + 3.40820i −0.222124 + 0.161383i
\(447\) 0.0729490 + 0.224514i 0.00345037 + 0.0106191i
\(448\) −1.45492 + 4.47777i −0.0687383 + 0.211555i
\(449\) 21.7984 + 15.8374i 1.02873 + 0.747415i 0.968054 0.250742i \(-0.0806747\pi\)
0.0606750 + 0.998158i \(0.480675\pi\)
\(450\) 0 0
\(451\) −7.16312 12.0862i −0.337298 0.569118i
\(452\) 8.39512 0.394873
\(453\) −15.3262 11.1352i −0.720089 0.523176i
\(454\) 1.08359 3.33495i 0.0508555 0.156517i
\(455\) 0 0
\(456\) −1.01722 + 0.739054i −0.0476357 + 0.0346094i
\(457\) −18.5902 + 13.5065i −0.869611 + 0.631810i −0.930483 0.366336i \(-0.880612\pi\)
0.0608712 + 0.998146i \(0.480612\pi\)
\(458\) −1.00000 3.07768i −0.0467269 0.143811i
\(459\) 2.42705 7.46969i 0.113285 0.348655i
\(460\) 0 0
\(461\) −24.2705 −1.13039 −0.565195 0.824957i \(-0.691199\pi\)
−0.565195 + 0.824957i \(0.691199\pi\)
\(462\) 1.23607 0.277515i 0.0575071 0.0129111i
\(463\) −35.2705 −1.63916 −0.819580 0.572965i \(-0.805793\pi\)
−0.819580 + 0.572965i \(0.805793\pi\)
\(464\) 15.2705 + 11.0947i 0.708916 + 0.515057i
\(465\) 0 0
\(466\) 1.28115 + 3.94298i 0.0593483 + 0.182655i
\(467\) −12.0451 + 8.75127i −0.557380 + 0.404960i −0.830499 0.557020i \(-0.811945\pi\)
0.273119 + 0.961980i \(0.411945\pi\)
\(468\) 6.35410 4.61653i 0.293718 0.213399i
\(469\) 1.50000 + 4.61653i 0.0692636 + 0.213171i
\(470\) 0 0
\(471\) 1.85410 + 1.34708i 0.0854325 + 0.0620704i
\(472\) −14.1591 −0.651723
\(473\) 14.6976 16.7027i 0.675795 0.767993i
\(474\) 4.20163 0.192987
\(475\) 0 0
\(476\) −4.50000 + 13.8496i −0.206257 + 0.634794i
\(477\) 0.809017 + 2.48990i 0.0370423 + 0.114005i
\(478\) −0.809017 + 0.587785i −0.0370036 + 0.0268847i
\(479\) 24.7705 17.9968i 1.13179 0.822296i 0.145839 0.989308i \(-0.453412\pi\)
0.985955 + 0.167012i \(0.0534120\pi\)
\(480\) 0 0
\(481\) 2.30902 7.10642i 0.105282 0.324025i
\(482\) −6.70820 4.87380i −0.305550 0.221995i
\(483\) 4.23607 0.192748
\(484\) −18.4377 + 8.71851i −0.838077 + 0.396296i
\(485\) 0 0
\(486\) −0.309017 0.224514i −0.0140173 0.0101842i
\(487\) −0.218847 + 0.673542i −0.00991691 + 0.0305211i −0.955893 0.293717i \(-0.905108\pi\)
0.945976 + 0.324238i \(0.105108\pi\)
\(488\) −3.89512 11.9880i −0.176324 0.542669i
\(489\) −9.59017 + 6.96767i −0.433682 + 0.315089i
\(490\) 0 0
\(491\) −8.98936 27.6664i −0.405684 1.24857i −0.920323 0.391160i \(-0.872074\pi\)
0.514639 0.857407i \(-0.327926\pi\)
\(492\) 2.42705 7.46969i 0.109420 0.336760i
\(493\) 38.1246 + 27.6992i 1.71705 + 1.24751i
\(494\) −1.38197 −0.0621776
\(495\) 0 0
\(496\) 16.0132 0.719012
\(497\) 4.30902 + 3.13068i 0.193286 + 0.140430i
\(498\) 0.881966 2.71441i 0.0395218 0.121636i
\(499\) −7.68034 23.6377i −0.343819 1.05817i −0.962213 0.272298i \(-0.912216\pi\)
0.618394 0.785868i \(-0.287784\pi\)
\(500\) 0 0
\(501\) −13.7812 + 10.0126i −0.615697 + 0.447330i
\(502\) 2.94834 + 9.07405i 0.131591 + 0.404995i
\(503\) 7.00000 21.5438i 0.312115 0.960590i −0.664811 0.747011i \(-0.731488\pi\)
0.976926 0.213579i \(-0.0685119\pi\)
\(504\) 1.19098 + 0.865300i 0.0530506 + 0.0385435i
\(505\) 0 0
\(506\) 5.23607 1.17557i 0.232772 0.0522605i
\(507\) 4.94427 0.219583
\(508\) 8.56231 + 6.22088i 0.379891 + 0.276007i
\(509\) −1.15654 + 3.55947i −0.0512628 + 0.157771i −0.973411 0.229067i \(-0.926433\pi\)
0.922148 + 0.386837i \(0.126433\pi\)
\(510\) 0 0
\(511\) 6.23607 4.53077i 0.275867 0.200429i
\(512\) −18.0451 + 13.1105i −0.797488 + 0.579409i
\(513\) −0.263932 0.812299i −0.0116529 0.0358639i
\(514\) 1.50407 4.62904i 0.0663415 0.204178i
\(515\) 0 0
\(516\) 12.4377 0.547539
\(517\) −1.84346 3.11044i −0.0810752 0.136797i
\(518\) 0.673762 0.0296034
\(519\) 8.92705 + 6.48588i 0.391854 + 0.284699i
\(520\) 0 0
\(521\) −2.76393 8.50651i −0.121090 0.372677i 0.872078 0.489366i \(-0.162772\pi\)
−0.993168 + 0.116689i \(0.962772\pi\)
\(522\) 1.85410 1.34708i 0.0811518 0.0589603i
\(523\) −12.3541 + 8.97578i −0.540207 + 0.392483i −0.824162 0.566354i \(-0.808353\pi\)
0.283955 + 0.958838i \(0.408353\pi\)
\(524\) −7.33282 22.5681i −0.320336 0.985891i
\(525\) 0 0
\(526\) 5.64590 + 4.10199i 0.246173 + 0.178855i
\(527\) 39.9787 1.74150
\(528\) −9.57953 4.13474i −0.416895 0.179942i
\(529\) −5.05573 −0.219814
\(530\) 0 0
\(531\) 2.97214 9.14729i 0.128980 0.396959i
\(532\) 0.489357 + 1.50609i 0.0212163 + 0.0652971i
\(533\) 14.5172 10.5474i 0.628811 0.456858i
\(534\) 1.16312 0.845055i 0.0503331 0.0365691i
\(535\) 0 0
\(536\) −2.20820 + 6.79615i −0.0953799 + 0.293549i
\(537\) 14.1353 + 10.2699i 0.609981 + 0.443177i
\(538\) 0.541020 0.0233250
\(539\) −1.85410 + 19.8132i −0.0798618 + 0.853414i
\(540\) 0 0
\(541\) 36.8156 + 26.7481i 1.58283 + 1.14999i 0.913364 + 0.407144i \(0.133475\pi\)
0.669462 + 0.742846i \(0.266525\pi\)
\(542\) 1.93363 5.95110i 0.0830565 0.255622i
\(543\) 3.54508 + 10.9106i 0.152134 + 0.468221i
\(544\) −26.3435 + 19.1396i −1.12947 + 0.820605i
\(545\) 0 0
\(546\) 0.500000 + 1.53884i 0.0213980 + 0.0658563i
\(547\) −3.62868 + 11.1679i −0.155151 + 0.477506i −0.998176 0.0603684i \(-0.980772\pi\)
0.843025 + 0.537874i \(0.180772\pi\)
\(548\) −21.3541 15.5147i −0.912202 0.662754i
\(549\) 8.56231 0.365430
\(550\) 0 0
\(551\) 5.12461 0.218316
\(552\) 5.04508 + 3.66547i 0.214733 + 0.156013i
\(553\) 3.39919 10.4616i 0.144548 0.444873i
\(554\) −2.62210 8.06999i −0.111402 0.342861i
\(555\) 0 0
\(556\) −8.34346 + 6.06188i −0.353841 + 0.257081i
\(557\) 12.5557 + 38.6426i 0.532003 + 1.63734i 0.750037 + 0.661396i \(0.230036\pi\)
−0.218033 + 0.975941i \(0.569964\pi\)
\(558\) 0.600813 1.84911i 0.0254344 0.0782792i
\(559\) 22.9894 + 16.7027i 0.972346 + 0.706451i
\(560\) 0 0
\(561\) −23.9164 10.3229i −1.00975 0.435832i
\(562\) 11.1672 0.471059
\(563\) −6.95492 5.05304i −0.293115 0.212960i 0.431503 0.902112i \(-0.357984\pi\)
−0.724617 + 0.689151i \(0.757984\pi\)
\(564\) 0.624612 1.92236i 0.0263009 0.0809459i
\(565\) 0 0
\(566\) 2.38197 1.73060i 0.100121 0.0727425i
\(567\) −0.809017 + 0.587785i −0.0339755 + 0.0246847i
\(568\) 2.42299 + 7.45718i 0.101666 + 0.312896i
\(569\) 3.65248 11.2412i 0.153120 0.471254i −0.844846 0.535010i \(-0.820308\pi\)
0.997966 + 0.0637558i \(0.0203079\pi\)
\(570\) 0 0
\(571\) 2.09017 0.0874709 0.0437354 0.999043i \(-0.486074\pi\)
0.0437354 + 0.999043i \(0.486074\pi\)
\(572\) −13.2812 22.4091i −0.555313 0.936971i
\(573\) −23.1803 −0.968373
\(574\) 1.30902 + 0.951057i 0.0546373 + 0.0396963i
\(575\) 0 0
\(576\) −1.45492 4.47777i −0.0606215 0.186574i
\(577\) 14.7984 10.7516i 0.616064 0.447597i −0.235480 0.971879i \(-0.575666\pi\)
0.851545 + 0.524282i \(0.175666\pi\)
\(578\) −13.8090 + 10.0328i −0.574379 + 0.417311i
\(579\) 3.04508 + 9.37181i 0.126549 + 0.389479i
\(580\) 0 0
\(581\) −6.04508 4.39201i −0.250792 0.182211i
\(582\) −0.437694 −0.0181430
\(583\) 8.47214 1.90211i 0.350880 0.0787775i
\(584\) 11.3475 0.469564
\(585\) 0 0
\(586\) −1.13932 + 3.50647i −0.0470649 + 0.144851i
\(587\) −11.7812 36.2587i −0.486260 1.49656i −0.830147 0.557544i \(-0.811744\pi\)
0.343887 0.939011i \(-0.388256\pi\)
\(588\) −9.00000 + 6.53888i −0.371154 + 0.269659i
\(589\) 3.51722 2.55541i 0.144925 0.105294i
\(590\) 0 0
\(591\) 4.95492 15.2497i 0.203818 0.627287i
\(592\) −4.48936 3.26171i −0.184511 0.134055i
\(593\) −15.0344 −0.617391 −0.308695 0.951161i \(-0.599892\pi\)
−0.308695 + 0.951161i \(0.599892\pi\)
\(594\) −0.836881 + 0.951057i −0.0343376 + 0.0390223i
\(595\) 0 0
\(596\) 0.354102 + 0.257270i 0.0145046 + 0.0105382i
\(597\) −2.07295 + 6.37988i −0.0848402 + 0.261111i
\(598\) 2.11803 + 6.51864i 0.0866129 + 0.266567i
\(599\) 15.0902 10.9637i 0.616568 0.447963i −0.235153 0.971958i \(-0.575559\pi\)
0.851721 + 0.523996i \(0.175559\pi\)
\(600\) 0 0
\(601\) 8.92705 + 27.4746i 0.364142 + 1.12071i 0.950517 + 0.310674i \(0.100555\pi\)
−0.586375 + 0.810040i \(0.699445\pi\)
\(602\) −0.791796 + 2.43690i −0.0322712 + 0.0993205i
\(603\) −3.92705 2.85317i −0.159922 0.116190i
\(604\) −35.1246 −1.42920
\(605\) 0 0
\(606\) −2.20163 −0.0894349
\(607\) 2.88197 + 2.09387i 0.116975 + 0.0849876i 0.644735 0.764406i \(-0.276968\pi\)
−0.527760 + 0.849394i \(0.676968\pi\)
\(608\) −1.09424 + 3.36771i −0.0443771 + 0.136579i
\(609\) −1.85410 5.70634i −0.0751320 0.231233i
\(610\) 0 0
\(611\) 3.73607 2.71441i 0.151145 0.109813i
\(612\) −4.50000 13.8496i −0.181902 0.559836i
\(613\) 8.56231 26.3521i 0.345828 1.06435i −0.615311 0.788285i \(-0.710969\pi\)
0.961139 0.276065i \(-0.0890306\pi\)
\(614\) −5.86475 4.26099i −0.236682 0.171959i
\(615\) 0 0
\(616\) 3.22542 3.66547i 0.129956 0.147686i
\(617\) 11.1803 0.450104 0.225052 0.974347i \(-0.427745\pi\)
0.225052 + 0.974347i \(0.427745\pi\)
\(618\) 2.14590 + 1.55909i 0.0863207 + 0.0627156i
\(619\) −4.98278 + 15.3354i −0.200275 + 0.616382i 0.799600 + 0.600533i \(0.205045\pi\)
−0.999874 + 0.0158490i \(0.994955\pi\)
\(620\) 0 0
\(621\) −3.42705 + 2.48990i −0.137523 + 0.0999162i
\(622\) 6.07295 4.41226i 0.243503 0.176915i
\(623\) −1.16312 3.57971i −0.0465994 0.143418i
\(624\) 4.11803 12.6740i 0.164853 0.507366i
\(625\) 0 0
\(626\) 4.38197 0.175139
\(627\) −2.76393 + 0.620541i −0.110381 + 0.0247820i
\(628\) 4.24922 0.169562
\(629\) −11.2082 8.14324i −0.446900 0.324692i
\(630\) 0 0
\(631\) −9.95492 30.6381i −0.396299 1.21968i −0.927945 0.372716i \(-0.878426\pi\)
0.531646 0.846966i \(-0.321574\pi\)
\(632\) 13.1008 9.51830i 0.521122 0.378618i
\(633\) −1.11803 + 0.812299i −0.0444379 + 0.0322860i
\(634\) 3.44427 + 10.6004i 0.136790 + 0.420995i
\(635\) 0 0
\(636\) 3.92705 + 2.85317i 0.155718 + 0.113136i
\(637\) −25.4164 −1.00703
\(638\) −3.87539 6.53888i −0.153428 0.258877i
\(639\) −5.32624 −0.210703
\(640\) 0 0
\(641\) −4.29837 + 13.2290i −0.169776 + 0.522515i −0.999356 0.0358711i \(-0.988579\pi\)
0.829581 + 0.558387i \(0.188579\pi\)
\(642\) 0.298374 + 0.918300i 0.0117759 + 0.0362424i
\(643\) 11.4443 8.31475i 0.451318 0.327902i −0.338798 0.940859i \(-0.610020\pi\)
0.790116 + 0.612957i \(0.210020\pi\)
\(644\) 6.35410 4.61653i 0.250387 0.181917i
\(645\) 0 0
\(646\) −0.791796 + 2.43690i −0.0311528 + 0.0958785i
\(647\) 12.9164 + 9.38432i 0.507796 + 0.368936i 0.811987 0.583676i \(-0.198386\pi\)
−0.304191 + 0.952611i \(0.598386\pi\)
\(648\) −1.47214 −0.0578310
\(649\) −29.2877 12.6412i −1.14964 0.496212i
\(650\) 0 0
\(651\) −4.11803 2.99193i −0.161398 0.117263i
\(652\) −6.79180 + 20.9030i −0.265987 + 0.818625i
\(653\) 1.04508 + 3.21644i 0.0408973 + 0.125869i 0.969421 0.245405i \(-0.0789210\pi\)
−0.928523 + 0.371274i \(0.878921\pi\)
\(654\) 3.70820 2.69417i 0.145002 0.105350i
\(655\) 0 0
\(656\) −4.11803 12.6740i −0.160782 0.494837i
\(657\) −2.38197 + 7.33094i −0.0929293 + 0.286007i
\(658\) 0.336881 + 0.244758i 0.0131330 + 0.00954168i
\(659\) −0.875388 −0.0341003 −0.0170501 0.999855i \(-0.505427\pi\)
−0.0170501 + 0.999855i \(0.505427\pi\)
\(660\) 0 0
\(661\) 16.4377 0.639352 0.319676 0.947527i \(-0.396426\pi\)
0.319676 + 0.947527i \(0.396426\pi\)
\(662\) −1.01722 0.739054i −0.0395354 0.0287242i
\(663\) 10.2812 31.6421i 0.399287 1.22888i
\(664\) −3.39919 10.4616i −0.131914 0.405990i
\(665\) 0 0
\(666\) −0.545085 + 0.396027i −0.0211216 + 0.0153458i
\(667\) −7.85410 24.1724i −0.304112 0.935961i
\(668\) −9.75987 + 30.0378i −0.377621 + 1.16220i
\(669\) −12.2812 8.92278i −0.474817 0.344975i
\(670\) 0 0
\(671\) 2.64590 28.2744i 0.102144 1.09152i
\(672\) 4.14590 0.159931
\(673\) −14.4271 10.4819i −0.556122 0.404046i 0.273916 0.961754i \(-0.411681\pi\)
−0.830038 + 0.557707i \(0.811681\pi\)
\(674\) −0.493422 + 1.51860i −0.0190059 + 0.0584942i
\(675\) 0 0
\(676\) 7.41641 5.38834i 0.285246 0.207244i
\(677\) 18.1803 13.2088i 0.698727 0.507655i −0.180790 0.983522i \(-0.557866\pi\)
0.879517 + 0.475867i \(0.157866\pi\)
\(678\) −0.534442 1.64484i −0.0205251 0.0631698i
\(679\) −0.354102 + 1.08981i −0.0135892 + 0.0418232i
\(680\) 0 0
\(681\) 9.18034 0.351791
\(682\) −5.92047 2.55541i −0.226707 0.0978517i
\(683\) 49.0689 1.87757 0.938784 0.344505i \(-0.111953\pi\)
0.938784 + 0.344505i \(0.111953\pi\)
\(684\) −1.28115 0.930812i −0.0489861 0.0355905i
\(685\) 0 0
\(686\) −1.53444 4.72253i −0.0585853 0.180307i
\(687\) 6.85410 4.97980i 0.261500 0.189991i
\(688\) 17.0729 12.4042i 0.650900 0.472907i
\(689\) 3.42705 + 10.5474i 0.130560 + 0.401823i
\(690\) 0 0
\(691\) −26.4164 19.1926i −1.00493 0.730123i −0.0417884 0.999126i \(-0.513306\pi\)
−0.963139 + 0.269004i \(0.913306\pi\)
\(692\) 20.4590 0.777734
\(693\) 1.69098 + 2.85317i 0.0642351 + 0.108383i
\(694\) 4.00000 0.151838
\(695\) 0 0
\(696\) 2.72949 8.40051i 0.103461 0.318420i
\(697\) −10.2812 31.6421i −0.389426 1.19853i
\(698\) 0.218847 0.159002i 0.00828348 0.00601830i
\(699\) −8.78115 + 6.37988i −0.332134 + 0.241309i
\(700\) 0 0
\(701\) −3.15248 + 9.70232i −0.119067 + 0.366452i −0.992774 0.120002i \(-0.961710\pi\)
0.873706 + 0.486454i \(0.161710\pi\)
\(702\) −1.30902 0.951057i −0.0494057 0.0358953i
\(703\) −1.50658 −0.0568217
\(704\) −15.2361 + 3.42071i −0.574231 + 0.128923i
\(705\) 0 0
\(706\) −3.70820 2.69417i −0.139560 0.101396i
\(707\) −1.78115 + 5.48183i −0.0669872 + 0.206165i
\(708\) −5.51064 16.9600i −0.207103 0.637396i
\(709\) 32.5344 23.6377i 1.22186 0.887731i 0.225604 0.974219i \(-0.427565\pi\)
0.996253 + 0.0864884i \(0.0275645\pi\)
\(710\) 0 0
\(711\) 3.39919 + 10.4616i 0.127479 + 0.392341i
\(712\) 1.71227 5.26982i 0.0641700 0.197495i
\(713\) −17.4443 12.6740i −0.653293 0.474645i
\(714\) 3.00000 0.112272
\(715\) 0 0
\(716\) 32.3951 1.21066
\(717\) −2.11803 1.53884i −0.0790994 0.0574691i
\(718\) 0.437694 1.34708i 0.0163346 0.0502727i
\(719\) 14.3647 + 44.2101i 0.535715 + 1.64876i 0.742100 + 0.670289i \(0.233830\pi\)
−0.206385 + 0.978471i \(0.566170\pi\)
\(720\) 0 0
\(721\) 5.61803 4.08174i 0.209227 0.152012i
\(722\) −2.15654 6.63715i −0.0802582 0.247009i
\(723\) 6.70820 20.6457i 0.249481 0.767823i
\(724\) 17.2082 + 12.5025i 0.639538 + 0.464651i
\(725\) 0 0
\(726\) 2.88197 + 3.05744i 0.106960 + 0.113472i
\(727\) 15.8541 0.587996 0.293998 0.955806i \(-0.405014\pi\)
0.293998 + 0.955806i \(0.405014\pi\)
\(728\) 5.04508 + 3.66547i 0.186983 + 0.135851i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 0 0
\(731\) 42.6246 30.9686i 1.57653 1.14541i
\(732\) 12.8435 9.33132i 0.474708 0.344895i
\(733\) 15.3262 + 47.1693i 0.566088 + 1.74224i 0.664698 + 0.747112i \(0.268560\pi\)
−0.0986105 + 0.995126i \(0.531440\pi\)
\(734\) −3.40576 + 10.4819i −0.125709 + 0.386893i
\(735\) 0 0
\(736\) 17.5623 0.647355
\(737\) −10.6353 + 12.0862i −0.391755 + 0.445202i
\(738\) −1.61803 −0.0595607
\(739\) −2.42705 1.76336i −0.0892805 0.0648661i 0.542250 0.840218i \(-0.317573\pi\)
−0.631530 + 0.775351i \(0.717573\pi\)
\(740\) 0 0
\(741\) −1.11803 3.44095i −0.0410720 0.126407i
\(742\) −0.809017 + 0.587785i −0.0296999 + 0.0215783i
\(743\) −5.75329 + 4.18001i −0.211068 + 0.153350i −0.688297 0.725429i \(-0.741641\pi\)
0.477229 + 0.878779i \(0.341641\pi\)
\(744\) −2.31559 7.12667i −0.0848938 0.261276i
\(745\) 0 0
\(746\) −10.7812 7.83297i −0.394726 0.286785i
\(747\) 7.47214 0.273391
\(748\) −47.1246 + 10.5801i −1.72305 + 0.386848i
\(749\) 2.52786 0.0923661
\(750\) 0 0
\(751\) 7.06231 21.7355i 0.257707 0.793141i −0.735577 0.677441i \(-0.763089\pi\)
0.993284 0.115700i \(-0.0369111\pi\)
\(752\) −1.05979 3.26171i −0.0386467 0.118942i
\(753\) −20.2082 + 14.6821i −0.736428 + 0.535046i
\(754\) 7.85410 5.70634i 0.286030 0.207813i
\(755\) 0 0
\(756\) −0.572949 + 1.76336i −0.0208380 + 0.0641326i
\(757\) 4.04508 + 2.93893i 0.147021 + 0.106817i 0.658864 0.752262i \(-0.271037\pi\)
−0.511843 + 0.859079i \(0.671037\pi\)
\(758\) 4.15905 0.151064
\(759\) 7.16312 + 12.0862i 0.260005 + 0.438702i
\(760\) 0 0
\(761\) −34.5517 25.1033i −1.25250 0.909992i −0.254133 0.967169i \(-0.581790\pi\)
−0.998364 + 0.0571772i \(0.981790\pi\)
\(762\) 0.673762 2.07363i 0.0244078 0.0751196i
\(763\) −3.70820 11.4127i −0.134246 0.413167i
\(764\) −34.7705 + 25.2623i −1.25795 + 0.913956i
\(765\) 0 0
\(766\) −0.0835921 0.257270i −0.00302031 0.00929555i
\(767\) 12.5902 38.7486i 0.454605 1.39913i
\(768\) −4.50000 3.26944i −0.162380 0.117976i
\(769\) 3.50658 0.126450 0.0632252 0.997999i \(-0.479861\pi\)
0.0632252 + 0.997999i \(0.479861\pi\)
\(770\) 0 0
\(771\) 12.7426 0.458915
\(772\) 14.7812 + 10.7391i 0.531985 + 0.386510i
\(773\) −1.48936 + 4.58377i −0.0535684 + 0.164867i −0.974262 0.225421i \(-0.927624\pi\)
0.920693 + 0.390287i \(0.127624\pi\)
\(774\) −0.791796 2.43690i −0.0284605 0.0875925i
\(775\) 0 0
\(776\) −1.36475 + 0.991545i −0.0489915 + 0.0355944i
\(777\) 0.545085 + 1.67760i 0.0195548 + 0.0601835i
\(778\) 0.677827 2.08614i 0.0243013 0.0747917i
\(779\) −2.92705 2.12663i −0.104872 0.0761943i
\(780\) 0 0