Properties

Label 570.2.k.a.77.4
Level $570$
Weight $2$
Character 570.77
Analytic conductor $4.551$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 77.4
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.a.533.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.752859 + 1.55987i) q^{3} -1.00000i q^{4} +(1.50962 + 1.64956i) q^{5} +(-0.570645 - 1.63535i) q^{6} +(0.306664 + 0.306664i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.86641 - 2.34873i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.752859 + 1.55987i) q^{3} -1.00000i q^{4} +(1.50962 + 1.64956i) q^{5} +(-0.570645 - 1.63535i) q^{6} +(0.306664 + 0.306664i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.86641 - 2.34873i) q^{9} +(-2.23388 - 0.0989549i) q^{10} +0.944248i q^{11} +(1.55987 + 0.752859i) q^{12} +(-4.86057 + 4.86057i) q^{13} -0.433689 q^{14} +(-3.70964 + 1.11292i) q^{15} -1.00000 q^{16} +(2.18295 - 2.18295i) q^{17} +(2.98055 + 0.341054i) q^{18} +1.00000i q^{19} +(1.64956 - 1.50962i) q^{20} +(-0.709233 + 0.247482i) q^{21} +(-0.667684 - 0.667684i) q^{22} +(5.00219 + 5.00219i) q^{23} +(-1.63535 + 0.570645i) q^{24} +(-0.442106 + 4.98042i) q^{25} -6.87388i q^{26} +(5.06886 - 1.14309i) q^{27} +(0.306664 - 0.306664i) q^{28} -1.77850 q^{29} +(1.83615 - 3.41007i) q^{30} -10.9563 q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.47291 - 0.710886i) q^{33} +3.08715i q^{34} +(-0.0429156 + 0.968808i) q^{35} +(-2.34873 + 1.86641i) q^{36} +(-3.09818 - 3.09818i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(-3.92254 - 11.2412i) q^{39} +(-0.0989549 + 2.23388i) q^{40} -6.08532i q^{41} +(0.326507 - 0.676500i) q^{42} +(-3.19643 + 3.19643i) q^{43} +0.944248 q^{44} +(1.05681 - 6.62444i) q^{45} -7.07416 q^{46} +(-4.22008 + 4.22008i) q^{47} +(0.752859 - 1.55987i) q^{48} -6.81191i q^{49} +(-3.20907 - 3.83430i) q^{50} +(1.76167 + 5.04857i) q^{51} +(4.86057 + 4.86057i) q^{52} +(-5.08232 - 5.08232i) q^{53} +(-2.77594 + 4.39251i) q^{54} +(-1.55759 + 1.42545i) q^{55} +0.433689i q^{56} +(-1.55987 - 0.752859i) q^{57} +(1.25759 - 1.25759i) q^{58} +7.52893 q^{59} +(1.11292 + 3.70964i) q^{60} +4.53489 q^{61} +(7.74725 - 7.74725i) q^{62} +(0.147911 - 1.29263i) q^{63} +1.00000i q^{64} +(-15.3554 - 0.680204i) q^{65} +(1.54417 - 0.538830i) q^{66} +(7.65067 + 7.65067i) q^{67} +(-2.18295 - 2.18295i) q^{68} +(-11.5687 + 4.03683i) q^{69} +(-0.654705 - 0.715397i) q^{70} +12.9834i q^{71} +(0.341054 - 2.98055i) q^{72} +(2.53764 - 2.53764i) q^{73} +4.38149 q^{74} +(-7.43597 - 4.43918i) q^{75} +1.00000 q^{76} +(-0.289567 + 0.289567i) q^{77} +(10.7224 + 5.17507i) q^{78} -9.50297i q^{79} +(-1.50962 - 1.64956i) q^{80} +(-2.03306 + 8.76736i) q^{81} +(4.30297 + 4.30297i) q^{82} +(7.84806 + 7.84806i) q^{83} +(0.247482 + 0.709233i) q^{84} +(6.89632 + 0.305489i) q^{85} -4.52043i q^{86} +(1.33896 - 2.77424i) q^{87} +(-0.667684 + 0.667684i) q^{88} -8.88554 q^{89} +(3.93690 + 5.43146i) q^{90} -2.98113 q^{91} +(5.00219 - 5.00219i) q^{92} +(8.24852 - 17.0904i) q^{93} -5.96810i q^{94} +(-1.64956 + 1.50962i) q^{95} +(0.570645 + 1.63535i) q^{96} +(-0.722973 - 0.722973i) q^{97} +(4.81675 + 4.81675i) q^{98} +(2.21778 - 1.76235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 4q^{6} - 12q^{7} + O(q^{10}) \) \( 36q + 4q^{3} + 4q^{6} - 12q^{7} - 4q^{10} - 4q^{12} + 8q^{13} + 4q^{15} - 36q^{16} - 32q^{21} - 4q^{22} + 32q^{25} + 28q^{27} - 12q^{28} - 8q^{30} + 8q^{31} + 36q^{33} + 4q^{36} - 32q^{37} - 8q^{40} + 12q^{42} - 24q^{43} - 28q^{45} - 16q^{46} - 4q^{48} - 40q^{51} - 8q^{52} - 4q^{55} + 4q^{57} - 4q^{58} - 24q^{60} + 200q^{61} + 28q^{63} + 12q^{70} - 68q^{73} - 36q^{75} + 36q^{76} + 24q^{78} - 92q^{81} + 24q^{82} + 24q^{85} + 28q^{87} - 4q^{88} - 68q^{90} + 64q^{91} + 16q^{93} - 4q^{96} - 148q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −0.752859 + 1.55987i −0.434663 + 0.900593i
\(4\) 1.00000i 0.500000i
\(5\) 1.50962 + 1.64956i 0.675122 + 0.737706i
\(6\) −0.570645 1.63535i −0.232965 0.667628i
\(7\) 0.306664 + 0.306664i 0.115908 + 0.115908i 0.762682 0.646774i \(-0.223882\pi\)
−0.646774 + 0.762682i \(0.723882\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −1.86641 2.34873i −0.622135 0.782910i
\(10\) −2.23388 0.0989549i −0.706414 0.0312923i
\(11\) 0.944248i 0.284701i 0.989816 + 0.142351i \(0.0454661\pi\)
−0.989816 + 0.142351i \(0.954534\pi\)
\(12\) 1.55987 + 0.752859i 0.450296 + 0.217332i
\(13\) −4.86057 + 4.86057i −1.34808 + 1.34808i −0.460332 + 0.887747i \(0.652270\pi\)
−0.887747 + 0.460332i \(0.847730\pi\)
\(14\) −0.433689 −0.115908
\(15\) −3.70964 + 1.11292i −0.957824 + 0.287356i
\(16\) −1.00000 −0.250000
\(17\) 2.18295 2.18295i 0.529443 0.529443i −0.390964 0.920406i \(-0.627858\pi\)
0.920406 + 0.390964i \(0.127858\pi\)
\(18\) 2.98055 + 0.341054i 0.702523 + 0.0803872i
\(19\) 1.00000i 0.229416i
\(20\) 1.64956 1.50962i 0.368853 0.337561i
\(21\) −0.709233 + 0.247482i −0.154767 + 0.0540051i
\(22\) −0.667684 0.667684i −0.142351 0.142351i
\(23\) 5.00219 + 5.00219i 1.04303 + 1.04303i 0.999032 + 0.0439961i \(0.0140089\pi\)
0.0439961 + 0.999032i \(0.485991\pi\)
\(24\) −1.63535 + 0.570645i −0.333814 + 0.116482i
\(25\) −0.442106 + 4.98042i −0.0884212 + 0.996083i
\(26\) 6.87388i 1.34808i
\(27\) 5.06886 1.14309i 0.975502 0.219988i
\(28\) 0.306664 0.306664i 0.0579541 0.0579541i
\(29\) −1.77850 −0.330260 −0.165130 0.986272i \(-0.552804\pi\)
−0.165130 + 0.986272i \(0.552804\pi\)
\(30\) 1.83615 3.41007i 0.335234 0.622590i
\(31\) −10.9563 −1.96780 −0.983901 0.178714i \(-0.942806\pi\)
−0.983901 + 0.178714i \(0.942806\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −1.47291 0.710886i −0.256400 0.123749i
\(34\) 3.08715i 0.529443i
\(35\) −0.0429156 + 0.968808i −0.00725407 + 0.163758i
\(36\) −2.34873 + 1.86641i −0.391455 + 0.311068i
\(37\) −3.09818 3.09818i −0.509338 0.509338i 0.404985 0.914323i \(-0.367277\pi\)
−0.914323 + 0.404985i \(0.867277\pi\)
\(38\) −0.707107 0.707107i −0.114708 0.114708i
\(39\) −3.92254 11.2412i −0.628110 1.80003i
\(40\) −0.0989549 + 2.23388i −0.0156461 + 0.353207i
\(41\) 6.08532i 0.950368i −0.879886 0.475184i \(-0.842382\pi\)
0.879886 0.475184i \(-0.157618\pi\)
\(42\) 0.326507 0.676500i 0.0503811 0.104386i
\(43\) −3.19643 + 3.19643i −0.487451 + 0.487451i −0.907501 0.420050i \(-0.862013\pi\)
0.420050 + 0.907501i \(0.362013\pi\)
\(44\) 0.944248 0.142351
\(45\) 1.05681 6.62444i 0.157540 0.987513i
\(46\) −7.07416 −1.04303
\(47\) −4.22008 + 4.22008i −0.615562 + 0.615562i −0.944390 0.328828i \(-0.893346\pi\)
0.328828 + 0.944390i \(0.393346\pi\)
\(48\) 0.752859 1.55987i 0.108666 0.225148i
\(49\) 6.81191i 0.973131i
\(50\) −3.20907 3.83430i −0.453831 0.542252i
\(51\) 1.76167 + 5.04857i 0.246683 + 0.706942i
\(52\) 4.86057 + 4.86057i 0.674040 + 0.674040i
\(53\) −5.08232 5.08232i −0.698110 0.698110i 0.265893 0.964003i \(-0.414333\pi\)
−0.964003 + 0.265893i \(0.914333\pi\)
\(54\) −2.77594 + 4.39251i −0.377757 + 0.597745i
\(55\) −1.55759 + 1.42545i −0.210026 + 0.192208i
\(56\) 0.433689i 0.0579541i
\(57\) −1.55987 0.752859i −0.206610 0.0997186i
\(58\) 1.25759 1.25759i 0.165130 0.165130i
\(59\) 7.52893 0.980183 0.490092 0.871671i \(-0.336963\pi\)
0.490092 + 0.871671i \(0.336963\pi\)
\(60\) 1.11292 + 3.70964i 0.143678 + 0.478912i
\(61\) 4.53489 0.580633 0.290316 0.956931i \(-0.406239\pi\)
0.290316 + 0.956931i \(0.406239\pi\)
\(62\) 7.74725 7.74725i 0.983901 0.983901i
\(63\) 0.147911 1.29263i 0.0186351 0.162856i
\(64\) 1.00000i 0.125000i
\(65\) −15.3554 0.680204i −1.90460 0.0843689i
\(66\) 1.54417 0.538830i 0.190075 0.0663254i
\(67\) 7.65067 + 7.65067i 0.934678 + 0.934678i 0.997994 0.0633153i \(-0.0201674\pi\)
−0.0633153 + 0.997994i \(0.520167\pi\)
\(68\) −2.18295 2.18295i −0.264721 0.264721i
\(69\) −11.5687 + 4.03683i −1.39271 + 0.485977i
\(70\) −0.654705 0.715397i −0.0782522 0.0855062i
\(71\) 12.9834i 1.54085i 0.637531 + 0.770425i \(0.279956\pi\)
−0.637531 + 0.770425i \(0.720044\pi\)
\(72\) 0.341054 2.98055i 0.0401936 0.351261i
\(73\) 2.53764 2.53764i 0.297009 0.297009i −0.542832 0.839841i \(-0.682648\pi\)
0.839841 + 0.542832i \(0.182648\pi\)
\(74\) 4.38149 0.509338
\(75\) −7.43597 4.43918i −0.858632 0.512593i
\(76\) 1.00000 0.114708
\(77\) −0.289567 + 0.289567i −0.0329992 + 0.0329992i
\(78\) 10.7224 + 5.17507i 1.21407 + 0.585961i
\(79\) 9.50297i 1.06917i −0.845115 0.534584i \(-0.820468\pi\)
0.845115 0.534584i \(-0.179532\pi\)
\(80\) −1.50962 1.64956i −0.168780 0.184427i
\(81\) −2.03306 + 8.76736i −0.225895 + 0.974152i
\(82\) 4.30297 + 4.30297i 0.475184 + 0.475184i
\(83\) 7.84806 + 7.84806i 0.861436 + 0.861436i 0.991505 0.130069i \(-0.0415197\pi\)
−0.130069 + 0.991505i \(0.541520\pi\)
\(84\) 0.247482 + 0.709233i 0.0270025 + 0.0773836i
\(85\) 6.89632 + 0.305489i 0.748011 + 0.0331349i
\(86\) 4.52043i 0.487451i
\(87\) 1.33896 2.77424i 0.143552 0.297430i
\(88\) −0.667684 + 0.667684i −0.0711753 + 0.0711753i
\(89\) −8.88554 −0.941866 −0.470933 0.882169i \(-0.656083\pi\)
−0.470933 + 0.882169i \(0.656083\pi\)
\(90\) 3.93690 + 5.43146i 0.414986 + 0.572526i
\(91\) −2.98113 −0.312507
\(92\) 5.00219 5.00219i 0.521514 0.521514i
\(93\) 8.24852 17.0904i 0.855332 1.77219i
\(94\) 5.96810i 0.615562i
\(95\) −1.64956 + 1.50962i −0.169241 + 0.154884i
\(96\) 0.570645 + 1.63535i 0.0582412 + 0.166907i
\(97\) −0.722973 0.722973i −0.0734067 0.0734067i 0.669450 0.742857i \(-0.266530\pi\)
−0.742857 + 0.669450i \(0.766530\pi\)
\(98\) 4.81675 + 4.81675i 0.486565 + 0.486565i
\(99\) 2.21778 1.76235i 0.222895 0.177123i
\(100\) 4.98042 + 0.442106i 0.498042 + 0.0442106i
\(101\) 1.65814i 0.164991i −0.996591 0.0824956i \(-0.973711\pi\)
0.996591 0.0824956i \(-0.0262890\pi\)
\(102\) −4.81557 2.32419i −0.476812 0.230129i
\(103\) −1.69267 + 1.69267i −0.166784 + 0.166784i −0.785564 0.618780i \(-0.787627\pi\)
0.618780 + 0.785564i \(0.287627\pi\)
\(104\) −6.87388 −0.674040
\(105\) −1.47891 0.796319i −0.144327 0.0777128i
\(106\) 7.18748 0.698110
\(107\) 7.42775 7.42775i 0.718067 0.718067i −0.250142 0.968209i \(-0.580477\pi\)
0.968209 + 0.250142i \(0.0804773\pi\)
\(108\) −1.14309 5.06886i −0.109994 0.487751i
\(109\) 7.49186i 0.717590i 0.933416 + 0.358795i \(0.116812\pi\)
−0.933416 + 0.358795i \(0.883188\pi\)
\(110\) 0.0934379 2.10933i 0.00890895 0.201117i
\(111\) 7.16526 2.50027i 0.680097 0.237315i
\(112\) −0.306664 0.306664i −0.0289771 0.0289771i
\(113\) 11.8230 + 11.8230i 1.11222 + 1.11222i 0.992850 + 0.119367i \(0.0380865\pi\)
0.119367 + 0.992850i \(0.461913\pi\)
\(114\) 1.63535 0.570645i 0.153164 0.0534458i
\(115\) −0.700022 + 15.8028i −0.0652774 + 1.47362i
\(116\) 1.77850i 0.165130i
\(117\) 20.4880 + 2.34436i 1.89411 + 0.216737i
\(118\) −5.32376 + 5.32376i −0.490092 + 0.490092i
\(119\) 1.33886 0.122734
\(120\) −3.41007 1.83615i −0.311295 0.167617i
\(121\) 10.1084 0.918945
\(122\) −3.20665 + 3.20665i −0.290316 + 0.290316i
\(123\) 9.49233 + 4.58139i 0.855895 + 0.413090i
\(124\) 10.9563i 0.983901i
\(125\) −8.88291 + 6.78925i −0.794512 + 0.607249i
\(126\) 0.809440 + 1.01862i 0.0721106 + 0.0907457i
\(127\) 1.42736 + 1.42736i 0.126658 + 0.126658i 0.767594 0.640936i \(-0.221454\pi\)
−0.640936 + 0.767594i \(0.721454\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −2.57956 7.39249i −0.227118 0.650872i
\(130\) 11.3389 10.3769i 0.994486 0.910117i
\(131\) 18.5477i 1.62052i 0.586073 + 0.810258i \(0.300673\pi\)
−0.586073 + 0.810258i \(0.699327\pi\)
\(132\) −0.710886 + 1.47291i −0.0618746 + 0.128200i
\(133\) −0.306664 + 0.306664i −0.0265912 + 0.0265912i
\(134\) −10.8197 −0.934678
\(135\) 9.53765 + 6.63576i 0.820870 + 0.571115i
\(136\) 3.08715 0.264721
\(137\) 2.22249 2.22249i 0.189880 0.189880i −0.605764 0.795644i \(-0.707132\pi\)
0.795644 + 0.605764i \(0.207132\pi\)
\(138\) 5.32585 11.0348i 0.453366 0.939343i
\(139\) 18.9629i 1.60841i 0.594350 + 0.804206i \(0.297409\pi\)
−0.594350 + 0.804206i \(0.702591\pi\)
\(140\) 0.968808 + 0.0429156i 0.0818792 + 0.00362703i
\(141\) −3.40566 9.75992i −0.286809 0.821933i
\(142\) −9.18067 9.18067i −0.770425 0.770425i
\(143\) −4.58958 4.58958i −0.383800 0.383800i
\(144\) 1.86641 + 2.34873i 0.155534 + 0.195727i
\(145\) −2.68486 2.93375i −0.222966 0.243635i
\(146\) 3.58877i 0.297009i
\(147\) 10.6257 + 5.12841i 0.876395 + 0.422984i
\(148\) −3.09818 + 3.09818i −0.254669 + 0.254669i
\(149\) 12.9585 1.06160 0.530799 0.847498i \(-0.321892\pi\)
0.530799 + 0.847498i \(0.321892\pi\)
\(150\) 8.39700 2.11905i 0.685612 0.173020i
\(151\) 4.35166 0.354133 0.177067 0.984199i \(-0.443339\pi\)
0.177067 + 0.984199i \(0.443339\pi\)
\(152\) −0.707107 + 0.707107i −0.0573539 + 0.0573539i
\(153\) −9.20142 1.05289i −0.743891 0.0851208i
\(154\) 0.409510i 0.0329992i
\(155\) −16.5398 18.0730i −1.32851 1.45166i
\(156\) −11.2412 + 3.92254i −0.900016 + 0.314055i
\(157\) −5.26086 5.26086i −0.419863 0.419863i 0.465294 0.885156i \(-0.345949\pi\)
−0.885156 + 0.465294i \(0.845949\pi\)
\(158\) 6.71962 + 6.71962i 0.534584 + 0.534584i
\(159\) 11.7540 4.10150i 0.932156 0.325270i
\(160\) 2.23388 + 0.0989549i 0.176604 + 0.00782307i
\(161\) 3.06798i 0.241791i
\(162\) −4.76187 7.63705i −0.374128 0.600023i
\(163\) −2.53089 + 2.53089i −0.198234 + 0.198234i −0.799243 0.601008i \(-0.794766\pi\)
0.601008 + 0.799243i \(0.294766\pi\)
\(164\) −6.08532 −0.475184
\(165\) −1.05088 3.50281i −0.0818106 0.272694i
\(166\) −11.0988 −0.861436
\(167\) −3.33084 + 3.33084i −0.257749 + 0.257749i −0.824138 0.566389i \(-0.808340\pi\)
0.566389 + 0.824138i \(0.308340\pi\)
\(168\) −0.676500 0.326507i −0.0521931 0.0251905i
\(169\) 34.2502i 2.63463i
\(170\) −5.09245 + 4.66042i −0.390573 + 0.357438i
\(171\) 2.34873 1.86641i 0.179612 0.142728i
\(172\) 3.19643 + 3.19643i 0.243725 + 0.243725i
\(173\) 9.61343 + 9.61343i 0.730896 + 0.730896i 0.970797 0.239902i \(-0.0771152\pi\)
−0.239902 + 0.970797i \(0.577115\pi\)
\(174\) 1.01489 + 2.90847i 0.0769389 + 0.220491i
\(175\) −1.66289 + 1.39174i −0.125703 + 0.105206i
\(176\) 0.944248i 0.0711753i
\(177\) −5.66823 + 11.7442i −0.426050 + 0.882746i
\(178\) 6.28303 6.28303i 0.470933 0.470933i
\(179\) 22.6680 1.69429 0.847143 0.531365i \(-0.178321\pi\)
0.847143 + 0.531365i \(0.178321\pi\)
\(180\) −6.62444 1.05681i −0.493756 0.0787702i
\(181\) 3.95190 0.293743 0.146871 0.989156i \(-0.453080\pi\)
0.146871 + 0.989156i \(0.453080\pi\)
\(182\) 2.10797 2.10797i 0.156253 0.156253i
\(183\) −3.41413 + 7.07384i −0.252380 + 0.522914i
\(184\) 7.07416i 0.521514i
\(185\) 0.433570 9.78771i 0.0318767 0.719607i
\(186\) 6.25213 + 17.9173i 0.458429 + 1.31376i
\(187\) 2.06124 + 2.06124i 0.150733 + 0.150733i
\(188\) 4.22008 + 4.22008i 0.307781 + 0.307781i
\(189\) 1.90498 + 1.20389i 0.138567 + 0.0875703i
\(190\) 0.0989549 2.23388i 0.00717894 0.162062i
\(191\) 3.21978i 0.232975i 0.993192 + 0.116487i \(0.0371635\pi\)
−0.993192 + 0.116487i \(0.962837\pi\)
\(192\) −1.55987 0.752859i −0.112574 0.0543329i
\(193\) −8.96414 + 8.96414i −0.645253 + 0.645253i −0.951842 0.306589i \(-0.900812\pi\)
0.306589 + 0.951842i \(0.400812\pi\)
\(194\) 1.02244 0.0734067
\(195\) 12.6215 23.4404i 0.903844 1.67860i
\(196\) −6.81191 −0.486565
\(197\) 6.36112 6.36112i 0.453211 0.453211i −0.443208 0.896419i \(-0.646160\pi\)
0.896419 + 0.443208i \(0.146160\pi\)
\(198\) −0.322039 + 2.81438i −0.0228863 + 0.200009i
\(199\) 21.5251i 1.52588i −0.646472 0.762938i \(-0.723756\pi\)
0.646472 0.762938i \(-0.276244\pi\)
\(200\) −3.83430 + 3.20907i −0.271126 + 0.226915i
\(201\) −17.6940 + 6.17419i −1.24804 + 0.435494i
\(202\) 1.17248 + 1.17248i 0.0824956 + 0.0824956i
\(203\) −0.545404 0.545404i −0.0382798 0.0382798i
\(204\) 5.04857 1.76167i 0.353471 0.123341i
\(205\) 10.0381 9.18652i 0.701092 0.641614i
\(206\) 2.39380i 0.166784i
\(207\) 2.41267 21.0849i 0.167692 1.46550i
\(208\) 4.86057 4.86057i 0.337020 0.337020i
\(209\) −0.944248 −0.0653150
\(210\) 1.60883 0.482663i 0.111020 0.0333069i
\(211\) −1.03406 −0.0711877 −0.0355938 0.999366i \(-0.511332\pi\)
−0.0355938 + 0.999366i \(0.511332\pi\)
\(212\) −5.08232 + 5.08232i −0.349055 + 0.349055i
\(213\) −20.2525 9.77470i −1.38768 0.669751i
\(214\) 10.5044i 0.718067i
\(215\) −10.0981 0.447319i −0.688684 0.0305069i
\(216\) 4.39251 + 2.77594i 0.298873 + 0.188879i
\(217\) −3.35989 3.35989i −0.228085 0.228085i
\(218\) −5.29755 5.29755i −0.358795 0.358795i
\(219\) 2.04791 + 5.86889i 0.138385 + 0.396583i
\(220\) 1.42545 + 1.55759i 0.0961040 + 0.105013i
\(221\) 21.2207i 1.42746i
\(222\) −3.29864 + 6.83457i −0.221391 + 0.458706i
\(223\) −4.32004 + 4.32004i −0.289291 + 0.289291i −0.836800 0.547509i \(-0.815576\pi\)
0.547509 + 0.836800i \(0.315576\pi\)
\(224\) 0.433689 0.0289771
\(225\) 12.5228 8.25709i 0.834853 0.550473i
\(226\) −16.7203 −1.11222
\(227\) −8.83516 + 8.83516i −0.586410 + 0.586410i −0.936657 0.350247i \(-0.886098\pi\)
0.350247 + 0.936657i \(0.386098\pi\)
\(228\) −0.752859 + 1.55987i −0.0498593 + 0.103305i
\(229\) 21.6673i 1.43182i 0.698194 + 0.715908i \(0.253987\pi\)
−0.698194 + 0.715908i \(0.746013\pi\)
\(230\) −10.6793 11.6693i −0.704171 0.769448i
\(231\) −0.233685 0.669691i −0.0153753 0.0440624i
\(232\) −1.25759 1.25759i −0.0825649 0.0825649i
\(233\) −10.5947 10.5947i −0.694079 0.694079i 0.269048 0.963127i \(-0.413291\pi\)
−0.963127 + 0.269048i \(0.913291\pi\)
\(234\) −16.1449 + 12.8295i −1.05542 + 0.838688i
\(235\) −13.3320 0.590572i −0.869683 0.0385247i
\(236\) 7.52893i 0.490092i
\(237\) 14.8234 + 7.15440i 0.962885 + 0.464728i
\(238\) −0.946720 + 0.946720i −0.0613668 + 0.0613668i
\(239\) 11.6073 0.750812 0.375406 0.926860i \(-0.377503\pi\)
0.375406 + 0.926860i \(0.377503\pi\)
\(240\) 3.70964 1.11292i 0.239456 0.0718390i
\(241\) 20.6897 1.33274 0.666369 0.745622i \(-0.267848\pi\)
0.666369 + 0.745622i \(0.267848\pi\)
\(242\) −7.14772 + 7.14772i −0.459473 + 0.459473i
\(243\) −12.1454 9.77190i −0.779126 0.626868i
\(244\) 4.53489i 0.290316i
\(245\) 11.2367 10.2834i 0.717885 0.656982i
\(246\) −9.95162 + 3.47256i −0.634492 + 0.221402i
\(247\) −4.86057 4.86057i −0.309271 0.309271i
\(248\) −7.74725 7.74725i −0.491951 0.491951i
\(249\) −18.1505 + 6.33349i −1.15024 + 0.401369i
\(250\) 1.48045 11.0819i 0.0936317 0.700880i
\(251\) 15.5598i 0.982128i −0.871123 0.491064i \(-0.836608\pi\)
0.871123 0.491064i \(-0.163392\pi\)
\(252\) −1.29263 0.147911i −0.0814282 0.00931754i
\(253\) −4.72330 + 4.72330i −0.296951 + 0.296951i
\(254\) −2.01860 −0.126658
\(255\) −5.66848 + 10.5274i −0.354974 + 0.659251i
\(256\) 1.00000 0.0625000
\(257\) −2.98574 + 2.98574i −0.186245 + 0.186245i −0.794071 0.607825i \(-0.792042\pi\)
0.607825 + 0.794071i \(0.292042\pi\)
\(258\) 7.05130 + 3.40325i 0.438995 + 0.211877i
\(259\) 1.90020i 0.118073i
\(260\) −0.680204 + 15.3554i −0.0421845 + 0.952302i
\(261\) 3.31941 + 4.17722i 0.205466 + 0.258564i
\(262\) −13.1152 13.1152i −0.810258 0.810258i
\(263\) 8.55701 + 8.55701i 0.527648 + 0.527648i 0.919870 0.392222i \(-0.128294\pi\)
−0.392222 + 0.919870i \(0.628294\pi\)
\(264\) −0.538830 1.54417i −0.0331627 0.0950373i
\(265\) 0.711236 16.0560i 0.0436909 0.986309i
\(266\) 0.433689i 0.0265912i
\(267\) 6.68956 13.8603i 0.409395 0.848237i
\(268\) 7.65067 7.65067i 0.467339 0.467339i
\(269\) 11.0350 0.672814 0.336407 0.941717i \(-0.390788\pi\)
0.336407 + 0.941717i \(0.390788\pi\)
\(270\) −11.4363 + 2.05194i −0.695993 + 0.124877i
\(271\) −12.1851 −0.740190 −0.370095 0.928994i \(-0.620675\pi\)
−0.370095 + 0.928994i \(0.620675\pi\)
\(272\) −2.18295 + 2.18295i −0.132361 + 0.132361i
\(273\) 2.24437 4.65018i 0.135835 0.281442i
\(274\) 3.14308i 0.189880i
\(275\) −4.70275 0.417458i −0.283586 0.0251736i
\(276\) 4.03683 + 11.5687i 0.242989 + 0.696355i
\(277\) 4.80867 + 4.80867i 0.288925 + 0.288925i 0.836655 0.547730i \(-0.184508\pi\)
−0.547730 + 0.836655i \(0.684508\pi\)
\(278\) −13.4088 13.4088i −0.804206 0.804206i
\(279\) 20.4488 + 25.7333i 1.22424 + 1.54061i
\(280\) −0.715397 + 0.654705i −0.0427531 + 0.0391261i
\(281\) 32.0631i 1.91273i −0.292180 0.956363i \(-0.594381\pi\)
0.292180 0.956363i \(-0.405619\pi\)
\(282\) 9.30947 + 4.49314i 0.554371 + 0.267562i
\(283\) 8.65468 8.65468i 0.514467 0.514467i −0.401425 0.915892i \(-0.631485\pi\)
0.915892 + 0.401425i \(0.131485\pi\)
\(284\) 12.9834 0.770425
\(285\) −1.11292 3.70964i −0.0659240 0.219740i
\(286\) 6.49065 0.383800
\(287\) 1.86615 1.86615i 0.110155 0.110155i
\(288\) −2.98055 0.341054i −0.175631 0.0200968i
\(289\) 7.46948i 0.439381i
\(290\) 3.97296 + 0.175992i 0.233300 + 0.0103346i
\(291\) 1.67204 0.583449i 0.0980168 0.0342024i
\(292\) −2.53764 2.53764i −0.148504 0.148504i
\(293\) −7.19596 7.19596i −0.420392 0.420392i 0.464947 0.885339i \(-0.346074\pi\)
−0.885339 + 0.464947i \(0.846074\pi\)
\(294\) −11.1399 + 3.88718i −0.649689 + 0.226705i
\(295\) 11.3658 + 12.4194i 0.661743 + 0.723087i
\(296\) 4.38149i 0.254669i
\(297\) 1.07936 + 4.78626i 0.0626310 + 0.277727i
\(298\) −9.16302 + 9.16302i −0.530799 + 0.530799i
\(299\) −48.6269 −2.81217
\(300\) −4.43918 + 7.43597i −0.256296 + 0.429316i
\(301\) −1.96046 −0.112999
\(302\) −3.07709 + 3.07709i −0.177067 + 0.177067i
\(303\) 2.58649 + 1.24835i 0.148590 + 0.0717156i
\(304\) 1.00000i 0.0573539i
\(305\) 6.84595 + 7.48057i 0.391998 + 0.428336i
\(306\) 7.25089 5.76188i 0.414506 0.329385i
\(307\) −1.61182 1.61182i −0.0919916 0.0919916i 0.659613 0.751605i \(-0.270720\pi\)
−0.751605 + 0.659613i \(0.770720\pi\)
\(308\) 0.289567 + 0.289567i 0.0164996 + 0.0164996i
\(309\) −1.36601 3.91469i −0.0777094 0.222699i
\(310\) 24.4749 + 1.08418i 1.39008 + 0.0615770i
\(311\) 24.1698i 1.37055i −0.728286 0.685273i \(-0.759683\pi\)
0.728286 0.685273i \(-0.240317\pi\)
\(312\) 5.17507 10.7224i 0.292980 0.607035i
\(313\) −20.5330 + 20.5330i −1.16059 + 1.16059i −0.176245 + 0.984346i \(0.556395\pi\)
−0.984346 + 0.176245i \(0.943605\pi\)
\(314\) 7.43999 0.419863
\(315\) 2.35557 1.70739i 0.132721 0.0962006i
\(316\) −9.50297 −0.534584
\(317\) −18.3162 + 18.3162i −1.02874 + 1.02874i −0.0291663 + 0.999575i \(0.509285\pi\)
−0.999575 + 0.0291663i \(0.990715\pi\)
\(318\) −5.41116 + 11.2116i −0.303443 + 0.628713i
\(319\) 1.67935i 0.0940254i
\(320\) −1.64956 + 1.50962i −0.0922133 + 0.0843902i
\(321\) 5.99429 + 17.1784i 0.334569 + 0.958804i
\(322\) −2.16939 2.16939i −0.120896 0.120896i
\(323\) 2.18295 + 2.18295i 0.121462 + 0.121462i
\(324\) 8.76736 + 2.03306i 0.487076 + 0.112948i
\(325\) −22.0588 26.3565i −1.22360 1.46200i
\(326\) 3.57921i 0.198234i
\(327\) −11.6864 5.64032i −0.646257 0.311910i
\(328\) 4.30297 4.30297i 0.237592 0.237592i
\(329\) −2.58830 −0.142697
\(330\) 3.21995 + 1.73378i 0.177252 + 0.0954416i
\(331\) 16.5637 0.910424 0.455212 0.890383i \(-0.349563\pi\)
0.455212 + 0.890383i \(0.349563\pi\)
\(332\) 7.84806 7.84806i 0.430718 0.430718i
\(333\) −1.49432 + 13.0593i −0.0818885 + 0.715643i
\(334\) 4.71053i 0.257749i
\(335\) −1.07066 + 24.1698i −0.0584964 + 1.32054i
\(336\) 0.709233 0.247482i 0.0386918 0.0135013i
\(337\) 25.3948 + 25.3948i 1.38334 + 1.38334i 0.838608 + 0.544735i \(0.183370\pi\)
0.544735 + 0.838608i \(0.316630\pi\)
\(338\) 24.2186 + 24.2186i 1.31732 + 1.31732i
\(339\) −27.3435 + 9.54135i −1.48510 + 0.518215i
\(340\) 0.305489 6.89632i 0.0165675 0.374006i
\(341\) 10.3454i 0.560236i
\(342\) −0.341054 + 2.98055i −0.0184421 + 0.161170i
\(343\) 4.23562 4.23562i 0.228702 0.228702i
\(344\) −4.52043 −0.243725
\(345\) −24.1233 12.9892i −1.29876 0.699317i
\(346\) −13.5954 −0.730896
\(347\) 5.68399 5.68399i 0.305133 0.305133i −0.537885 0.843018i \(-0.680777\pi\)
0.843018 + 0.537885i \(0.180777\pi\)
\(348\) −2.77424 1.33896i −0.148715 0.0717759i
\(349\) 18.1493i 0.971512i −0.874094 0.485756i \(-0.838544\pi\)
0.874094 0.485756i \(-0.161456\pi\)
\(350\) 0.191737 2.15995i 0.0102487 0.115454i
\(351\) −19.0815 + 30.1936i −1.01849 + 1.61162i
\(352\) 0.667684 + 0.667684i 0.0355877 + 0.0355877i
\(353\) −8.86486 8.86486i −0.471829 0.471829i 0.430677 0.902506i \(-0.358275\pi\)
−0.902506 + 0.430677i \(0.858275\pi\)
\(354\) −4.29635 12.3124i −0.228348 0.654398i
\(355\) −21.4170 + 19.6000i −1.13669 + 1.04026i
\(356\) 8.88554i 0.470933i
\(357\) −1.00798 + 2.08846i −0.0533478 + 0.110533i
\(358\) −16.0287 + 16.0287i −0.847143 + 0.847143i
\(359\) −10.7838 −0.569150 −0.284575 0.958654i \(-0.591852\pi\)
−0.284575 + 0.958654i \(0.591852\pi\)
\(360\) 5.43146 3.93690i 0.286263 0.207493i
\(361\) −1.00000 −0.0526316
\(362\) −2.79442 + 2.79442i −0.146871 + 0.146871i
\(363\) −7.61020 + 15.7678i −0.399432 + 0.827596i
\(364\) 2.98113i 0.156253i
\(365\) 8.01687 + 0.355126i 0.419622 + 0.0185882i
\(366\) −2.58781 7.41612i −0.135267 0.387647i
\(367\) −9.27545 9.27545i −0.484175 0.484175i 0.422287 0.906462i \(-0.361227\pi\)
−0.906462 + 0.422287i \(0.861227\pi\)
\(368\) −5.00219 5.00219i −0.260757 0.260757i
\(369\) −14.2928 + 11.3577i −0.744052 + 0.591257i
\(370\) 6.61438 + 7.22754i 0.343865 + 0.375742i
\(371\) 3.11713i 0.161833i
\(372\) −17.0904 8.24852i −0.886094 0.427666i
\(373\) −4.66943 + 4.66943i −0.241774 + 0.241774i −0.817584 0.575810i \(-0.804687\pi\)
0.575810 + 0.817584i \(0.304687\pi\)
\(374\) −2.91504 −0.150733
\(375\) −3.90277 18.9676i −0.201538 0.979481i
\(376\) −5.96810 −0.307781
\(377\) 8.64454 8.64454i 0.445216 0.445216i
\(378\) −2.19831 + 0.495747i −0.113069 + 0.0254985i
\(379\) 21.6246i 1.11078i −0.831590 0.555390i \(-0.812569\pi\)
0.831590 0.555390i \(-0.187431\pi\)
\(380\) 1.50962 + 1.64956i 0.0774418 + 0.0846207i
\(381\) −3.30111 + 1.15190i −0.169121 + 0.0590138i
\(382\) −2.27673 2.27673i −0.116487 0.116487i
\(383\) 19.8243 + 19.8243i 1.01297 + 1.01297i 0.999915 + 0.0130600i \(0.00415723\pi\)
0.0130600 + 0.999915i \(0.495843\pi\)
\(384\) 1.63535 0.570645i 0.0834535 0.0291206i
\(385\) −0.914795 0.0405230i −0.0466222 0.00206524i
\(386\) 12.6772i 0.645253i
\(387\) 13.4734 + 1.54171i 0.684891 + 0.0783696i
\(388\) −0.722973 + 0.722973i −0.0367034 + 0.0367034i
\(389\) 18.0320 0.914258 0.457129 0.889400i \(-0.348878\pi\)
0.457129 + 0.889400i \(0.348878\pi\)
\(390\) 7.65011 + 25.4996i 0.387378 + 1.29122i
\(391\) 21.8390 1.10445
\(392\) 4.81675 4.81675i 0.243283 0.243283i
\(393\) −28.9320 13.9638i −1.45943 0.704379i
\(394\) 8.99598i 0.453211i
\(395\) 15.6757 14.3459i 0.788732 0.721819i
\(396\) −1.76235 2.21778i −0.0885614 0.111448i
\(397\) −15.1322 15.1322i −0.759462 0.759462i 0.216763 0.976224i \(-0.430450\pi\)
−0.976224 + 0.216763i \(0.930450\pi\)
\(398\) 15.2206 + 15.2206i 0.762938 + 0.762938i
\(399\) −0.247482 0.709233i −0.0123896 0.0355060i
\(400\) 0.442106 4.98042i 0.0221053 0.249021i
\(401\) 10.1310i 0.505916i −0.967477 0.252958i \(-0.918597\pi\)
0.967477 0.252958i \(-0.0814034\pi\)
\(402\) 8.14570 16.8773i 0.406270 0.841765i
\(403\) 53.2536 53.2536i 2.65275 2.65275i
\(404\) −1.65814 −0.0824956
\(405\) −17.5314 + 9.88172i −0.871145 + 0.491027i
\(406\) 0.771317 0.0382798
\(407\) 2.92545 2.92545i 0.145009 0.145009i
\(408\) −2.32419 + 4.81557i −0.115065 + 0.238406i
\(409\) 8.93136i 0.441627i −0.975316 0.220814i \(-0.929129\pi\)
0.975316 0.220814i \(-0.0708713\pi\)
\(410\) −0.602172 + 13.5939i −0.0297392 + 0.671353i
\(411\) 1.79358 + 5.14003i 0.0884709 + 0.253539i
\(412\) 1.69267 + 1.69267i 0.0833918 + 0.0833918i
\(413\) 2.30886 + 2.30886i 0.113611 + 0.113611i
\(414\) 13.2033 + 16.6153i 0.648904 + 0.816597i
\(415\) −1.09828 + 24.7934i −0.0539126 + 1.21706i
\(416\) 6.87388i 0.337020i
\(417\) −29.5797 14.2764i −1.44853 0.699118i
\(418\) 0.667684 0.667684i 0.0326575 0.0326575i
\(419\) 20.6060 1.00667 0.503333 0.864092i \(-0.332107\pi\)
0.503333 + 0.864092i \(0.332107\pi\)
\(420\) −0.796319 + 1.47891i −0.0388564 + 0.0721633i
\(421\) 15.1039 0.736120 0.368060 0.929802i \(-0.380022\pi\)
0.368060 + 0.929802i \(0.380022\pi\)
\(422\) 0.731191 0.731191i 0.0355938 0.0355938i
\(423\) 17.7882 + 2.03544i 0.864892 + 0.0989666i
\(424\) 7.18748i 0.349055i
\(425\) 9.90689 + 11.8371i 0.480555 + 0.574183i
\(426\) 21.2324 7.40893i 1.02871 0.358964i
\(427\) 1.39069 + 1.39069i 0.0673001 + 0.0673001i
\(428\) −7.42775 7.42775i −0.359034 0.359034i
\(429\) 10.6145 3.70385i 0.512471 0.178824i
\(430\) 7.45673 6.82413i 0.359596 0.329089i
\(431\) 7.39471i 0.356191i −0.984013 0.178095i \(-0.943006\pi\)
0.984013 0.178095i \(-0.0569936\pi\)
\(432\) −5.06886 + 1.14309i −0.243876 + 0.0549971i
\(433\) −6.52218 + 6.52218i −0.313436 + 0.313436i −0.846239 0.532803i \(-0.821139\pi\)
0.532803 + 0.846239i \(0.321139\pi\)
\(434\) 4.75161 0.228085
\(435\) 6.59760 1.97934i 0.316331 0.0949021i
\(436\) 7.49186 0.358795
\(437\) −5.00219 + 5.00219i −0.239287 + 0.239287i
\(438\) −5.59802 2.70184i −0.267484 0.129099i
\(439\) 32.0835i 1.53126i 0.643279 + 0.765632i \(0.277574\pi\)
−0.643279 + 0.765632i \(0.722426\pi\)
\(440\) −2.10933 0.0934379i −0.100559 0.00445448i
\(441\) −15.9993 + 12.7138i −0.761873 + 0.605419i
\(442\) −15.0053 15.0053i −0.713730 0.713730i
\(443\) 5.56755 + 5.56755i 0.264522 + 0.264522i 0.826888 0.562366i \(-0.190109\pi\)
−0.562366 + 0.826888i \(0.690109\pi\)
\(444\) −2.50027 7.16526i −0.118658 0.340048i
\(445\) −13.4138 14.6572i −0.635874 0.694820i
\(446\) 6.10946i 0.289291i
\(447\) −9.75590 + 20.2136i −0.461438 + 0.956068i
\(448\) −0.306664 + 0.306664i −0.0144885 + 0.0144885i
\(449\) 22.1426 1.04497 0.522487 0.852647i \(-0.325004\pi\)
0.522487 + 0.852647i \(0.325004\pi\)
\(450\) −3.01631 + 14.6936i −0.142190 + 0.692663i
\(451\) 5.74605 0.270571
\(452\) 11.8230 11.8230i 0.556109 0.556109i
\(453\) −3.27619 + 6.78804i −0.153929 + 0.318930i
\(454\) 12.4948i 0.586410i
\(455\) −4.50036 4.91755i −0.210980 0.230538i
\(456\) −0.570645 1.63535i −0.0267229 0.0765822i
\(457\) 1.27154 + 1.27154i 0.0594803 + 0.0594803i 0.736221 0.676741i \(-0.236608\pi\)
−0.676741 + 0.736221i \(0.736608\pi\)
\(458\) −15.3211 15.3211i −0.715908 0.715908i
\(459\) 8.56974 13.5604i 0.400001 0.632944i
\(460\) 15.8028 + 0.700022i 0.736809 + 0.0326387i
\(461\) 31.2805i 1.45688i −0.685111 0.728439i \(-0.740246\pi\)
0.685111 0.728439i \(-0.259754\pi\)
\(462\) 0.638783 + 0.308303i 0.0297189 + 0.0143436i
\(463\) 12.3092 12.3092i 0.572056 0.572056i −0.360647 0.932702i \(-0.617444\pi\)
0.932702 + 0.360647i \(0.117444\pi\)
\(464\) 1.77850 0.0825649
\(465\) 40.6437 12.1935i 1.88481 0.565460i
\(466\) 14.9831 0.694079
\(467\) −3.08706 + 3.08706i −0.142852 + 0.142852i −0.774916 0.632064i \(-0.782208\pi\)
0.632064 + 0.774916i \(0.282208\pi\)
\(468\) 2.34436 20.4880i 0.108368 0.947056i
\(469\) 4.69238i 0.216674i
\(470\) 9.84474 9.00955i 0.454104 0.415579i
\(471\) 12.1670 4.24559i 0.560624 0.195626i
\(472\) 5.32376 + 5.32376i 0.245046 + 0.245046i
\(473\) −3.01822 3.01822i −0.138778 0.138778i
\(474\) −15.5407 + 5.42282i −0.713807 + 0.249078i
\(475\) −4.98042 0.442106i −0.228517 0.0202852i
\(476\) 1.33886i 0.0613668i
\(477\) −2.45132 + 21.4227i −0.112238 + 0.980876i
\(478\) −8.20758 + 8.20758i −0.375406 + 0.375406i
\(479\) −3.14915 −0.143888 −0.0719441 0.997409i \(-0.522920\pi\)
−0.0719441 + 0.997409i \(0.522920\pi\)
\(480\) −1.83615 + 3.41007i −0.0838085 + 0.155647i
\(481\) 30.1178 1.37326
\(482\) −14.6298 + 14.6298i −0.666369 + 0.666369i
\(483\) −4.78567 2.30976i −0.217755 0.105098i
\(484\) 10.1084i 0.459473i
\(485\) 0.101175 2.28400i 0.00459413 0.103711i
\(486\) 15.4978 1.67829i 0.702997 0.0761289i
\(487\) −14.2900 14.2900i −0.647541 0.647541i 0.304857 0.952398i \(-0.401391\pi\)
−0.952398 + 0.304857i \(0.901391\pi\)
\(488\) 3.20665 + 3.20665i 0.145158 + 0.145158i
\(489\) −2.04246 5.85326i −0.0923632 0.264694i
\(490\) −0.674072 + 15.2170i −0.0304515 + 0.687433i
\(491\) 3.56231i 0.160765i 0.996764 + 0.0803823i \(0.0256141\pi\)
−0.996764 + 0.0803823i \(0.974386\pi\)
\(492\) 4.58139 9.49233i 0.206545 0.427947i
\(493\) −3.88238 + 3.88238i −0.174854 + 0.174854i
\(494\) 6.87388 0.309271
\(495\) 6.25511 + 0.997893i 0.281146 + 0.0448520i
\(496\) 10.9563 0.491951
\(497\) −3.98156 + 3.98156i −0.178597 + 0.178597i
\(498\) 8.35586 17.3128i 0.374435 0.775804i
\(499\) 22.7927i 1.02034i −0.860074 0.510170i \(-0.829583\pi\)
0.860074 0.510170i \(-0.170417\pi\)
\(500\) 6.78925 + 8.88291i 0.303624 + 0.397256i
\(501\) −2.68804 7.70335i −0.120093 0.344160i
\(502\) 11.0025 + 11.0025i 0.491064 + 0.491064i
\(503\) 2.87058 + 2.87058i 0.127993 + 0.127993i 0.768201 0.640208i \(-0.221152\pi\)
−0.640208 + 0.768201i \(0.721152\pi\)
\(504\) 1.01862 0.809440i 0.0453728 0.0360553i
\(505\) 2.73521 2.50316i 0.121715 0.111389i
\(506\) 6.67976i 0.296951i
\(507\) 53.4260 + 25.7856i 2.37273 + 1.14518i
\(508\) 1.42736 1.42736i 0.0633291 0.0633291i
\(509\) −12.2215 −0.541709 −0.270854 0.962620i \(-0.587306\pi\)
−0.270854 + 0.962620i \(0.587306\pi\)
\(510\) −3.43577 11.4522i −0.152138 0.507113i
\(511\) 1.55641 0.0688515
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 1.14309 + 5.06886i 0.0504688 + 0.223796i
\(514\) 4.22247i 0.186245i
\(515\) −5.34745 0.236878i −0.235637 0.0104381i
\(516\) −7.39249 + 2.57956i −0.325436 + 0.113559i
\(517\) −3.98480 3.98480i −0.175251 0.175251i
\(518\) 1.34365 + 1.34365i 0.0590365 + 0.0590365i
\(519\) −22.2333 + 7.75817i −0.975933 + 0.340546i
\(520\) −10.3769 11.3389i −0.455059 0.497243i
\(521\) 41.4157i 1.81446i 0.420639 + 0.907228i \(0.361806\pi\)
−0.420639 + 0.907228i \(0.638194\pi\)
\(522\) −5.30092 0.606566i −0.232015 0.0265487i
\(523\) −0.411090 + 0.411090i −0.0179757 + 0.0179757i −0.716038 0.698062i \(-0.754046\pi\)
0.698062 + 0.716038i \(0.254046\pi\)
\(524\) 18.5477 0.810258
\(525\) −0.919009 3.64169i −0.0401088 0.158936i
\(526\) −12.1014 −0.527648
\(527\) −23.9169 + 23.9169i −1.04184 + 1.04184i
\(528\) 1.47291 + 0.710886i 0.0641000 + 0.0309373i
\(529\) 27.0437i 1.17581i
\(530\) 10.8504 + 11.8562i 0.471309 + 0.515000i
\(531\) −14.0520 17.6834i −0.609807 0.767395i
\(532\) 0.306664 + 0.306664i 0.0132956 + 0.0132956i
\(533\) 29.5781 + 29.5781i 1.28117 + 1.28117i
\(534\) 5.07049 + 14.5310i 0.219421 + 0.628816i
\(535\) 23.4656 + 1.03946i 1.01451 + 0.0449399i
\(536\) 10.8197i 0.467339i
\(537\) −17.0658 + 35.3592i −0.736444 + 1.52586i
\(538\) −7.80290 + 7.80290i −0.336407 + 0.336407i
\(539\) 6.43213 0.277052
\(540\) 6.63576 9.53765i 0.285558 0.410435i
\(541\) −0.975280 −0.0419306 −0.0209653 0.999780i \(-0.506674\pi\)
−0.0209653 + 0.999780i \(0.506674\pi\)
\(542\) 8.61614 8.61614i 0.370095 0.370095i
\(543\) −2.97523 + 6.16447i −0.127679 + 0.264543i
\(544\) 3.08715i 0.132361i
\(545\) −12.3583 + 11.3099i −0.529371 + 0.484461i
\(546\) 1.70116 + 4.87518i 0.0728031 + 0.208638i
\(547\) −8.86543 8.86543i −0.379058 0.379058i 0.491704 0.870762i \(-0.336374\pi\)
−0.870762 + 0.491704i \(0.836374\pi\)
\(548\) −2.22249 2.22249i −0.0949402 0.0949402i
\(549\) −8.46394 10.6512i −0.361232 0.454583i
\(550\) 3.62053 3.03016i 0.154380 0.129206i
\(551\) 1.77850i 0.0757668i
\(552\) −11.0348 5.32585i −0.469672 0.226683i
\(553\) 2.91422 2.91422i 0.123925 0.123925i
\(554\) −6.80049 −0.288925
\(555\) 14.9412 + 8.04508i 0.634217 + 0.341495i
\(556\) 18.9629 0.804206
\(557\) −18.8971 + 18.8971i −0.800694 + 0.800694i −0.983204 0.182510i \(-0.941578\pi\)
0.182510 + 0.983204i \(0.441578\pi\)
\(558\) −32.6557 3.73668i −1.38243 0.158186i
\(559\) 31.0729i 1.31424i
\(560\) 0.0429156 0.968808i 0.00181352 0.0409396i
\(561\) −4.76710 + 1.66345i −0.201267 + 0.0702310i
\(562\) 22.6721 + 22.6721i 0.956363 + 0.956363i
\(563\) −1.06006 1.06006i −0.0446761 0.0446761i 0.684416 0.729092i \(-0.260057\pi\)
−0.729092 + 0.684416i \(0.760057\pi\)
\(564\) −9.75992 + 3.40566i −0.410967 + 0.143404i
\(565\) −1.65455 + 37.3511i −0.0696076 + 1.57137i
\(566\) 12.2396i 0.514467i
\(567\) −3.31210 + 2.06517i −0.139095 + 0.0867291i
\(568\) −9.18067 + 9.18067i −0.385212 + 0.385212i
\(569\) −5.21442 −0.218600 −0.109300 0.994009i \(-0.534861\pi\)
−0.109300 + 0.994009i \(0.534861\pi\)
\(570\) 3.41007 + 1.83615i 0.142832 + 0.0769080i
\(571\) 27.0533 1.13215 0.566073 0.824355i \(-0.308462\pi\)
0.566073 + 0.824355i \(0.308462\pi\)
\(572\) −4.58958 + 4.58958i −0.191900 + 0.191900i
\(573\) −5.02244 2.42404i −0.209816 0.101266i
\(574\) 2.63914i 0.110155i
\(575\) −27.1245 + 22.7015i −1.13117 + 0.946717i
\(576\) 2.34873 1.86641i 0.0978637 0.0777669i
\(577\) −31.9330 31.9330i −1.32939 1.32939i −0.905903 0.423484i \(-0.860807\pi\)
−0.423484 0.905903i \(-0.639193\pi\)
\(578\) −5.28172 5.28172i −0.219691 0.219691i
\(579\) −7.23419 20.7317i −0.300642 0.861578i
\(580\) −2.93375 + 2.68486i −0.121817 + 0.111483i
\(581\) 4.81344i 0.199695i
\(582\) −0.769752 + 1.59487i −0.0319072 + 0.0661096i
\(583\) 4.79897 4.79897i 0.198753 0.198753i
\(584\) 3.58877 0.148504
\(585\) 27.0618 + 37.3352i 1.11887 + 1.54362i
\(586\) 10.1766 0.420392
\(587\) 4.54157 4.54157i 0.187450 0.187450i −0.607142 0.794593i \(-0.707684\pi\)
0.794593 + 0.607142i \(0.207684\pi\)
\(588\) 5.12841 10.6257i 0.211492 0.438197i
\(589\) 10.9563i 0.451445i
\(590\) −16.8187 0.745024i −0.692415 0.0306722i
\(591\) 5.13351 + 14.7116i 0.211164 + 0.605153i
\(592\) 3.09818 + 3.09818i 0.127334 + 0.127334i
\(593\) 6.70785 + 6.70785i 0.275458 + 0.275458i 0.831293 0.555835i \(-0.187601\pi\)
−0.555835 + 0.831293i \(0.687601\pi\)
\(594\) −4.14762 2.62117i −0.170179 0.107548i
\(595\) 2.02117 + 2.20854i 0.0828601 + 0.0905413i
\(596\) 12.9585i 0.530799i
\(597\) 33.5765 + 16.2054i 1.37419 + 0.663243i
\(598\) 34.3844 34.3844i 1.40608 1.40608i
\(599\) −25.3428 −1.03548 −0.517740 0.855538i \(-0.673226\pi\)
−0.517740 + 0.855538i \(0.673226\pi\)
\(600\) −2.11905 8.39700i −0.0865099 0.342806i
\(601\) 10.1452 0.413833 0.206916 0.978359i \(-0.433657\pi\)
0.206916 + 0.978359i \(0.433657\pi\)
\(602\) 1.38626 1.38626i 0.0564996 0.0564996i
\(603\) 3.69010 32.2486i 0.150272 1.31327i
\(604\) 4.35166i 0.177067i
\(605\) 15.2598 + 16.6744i 0.620400 + 0.677912i
\(606\) −2.71164 + 0.946209i −0.110153 + 0.0384371i
\(607\) 16.7036 + 16.7036i 0.677979 + 0.677979i 0.959543 0.281564i \(-0.0908530\pi\)
−0.281564 + 0.959543i \(0.590853\pi\)
\(608\) 0.707107 + 0.707107i 0.0286770 + 0.0286770i
\(609\) 1.26137 0.440148i 0.0511134 0.0178357i
\(610\) −10.1304 0.448749i −0.410167 0.0181693i
\(611\) 41.0240i 1.65965i
\(612\) −1.05289 + 9.20142i −0.0425604 + 0.371945i
\(613\) 22.7706 22.7706i 0.919695 0.919695i −0.0773118 0.997007i \(-0.524634\pi\)
0.997007 + 0.0773118i \(0.0246337\pi\)
\(614\) 2.27946 0.0919916
\(615\) 6.77251 + 22.5743i 0.273094 + 0.910285i
\(616\) −0.409510 −0.0164996
\(617\) −6.58274 + 6.58274i −0.265011 + 0.265011i −0.827086 0.562075i \(-0.810003\pi\)
0.562075 + 0.827086i \(0.310003\pi\)
\(618\) 3.73402 + 1.80219i 0.150204 + 0.0724948i
\(619\) 27.5771i 1.10842i 0.832378 + 0.554209i \(0.186979\pi\)
−0.832378 + 0.554209i \(0.813021\pi\)
\(620\) −18.0730 + 16.5398i −0.725830 + 0.664253i
\(621\) 31.0733 + 19.6374i 1.24693 + 0.788022i
\(622\) 17.0907 + 17.0907i 0.685273 + 0.685273i
\(623\) −2.72488 2.72488i −0.109170 0.109170i
\(624\) 3.92254 + 11.2412i 0.157027 + 0.450008i
\(625\) −24.6091 4.40374i −0.984363 0.176150i
\(626\) 29.0380i 1.16059i
\(627\) 0.710886 1.47291i 0.0283900 0.0588222i
\(628\) −5.26086 + 5.26086i −0.209931 + 0.209931i
\(629\) −13.5263 −0.539330
\(630\) −0.458328 + 2.87294i −0.0182602 + 0.114461i
\(631\) −30.6726 −1.22106 −0.610529 0.791994i \(-0.709043\pi\)
−0.610529 + 0.791994i \(0.709043\pi\)
\(632\) 6.71962 6.71962i 0.267292 0.267292i
\(633\) 0.778502 1.61300i 0.0309427 0.0641111i
\(634\) 25.9030i 1.02874i
\(635\) −0.199750 + 4.50930i −0.00792684 + 0.178946i
\(636\) −4.10150 11.7540i −0.162635 0.466078i
\(637\) 33.1098 + 33.1098i 1.31186 + 1.31186i
\(638\) 1.18748 + 1.18748i 0.0470127 + 0.0470127i
\(639\) 30.4946 24.2324i 1.20635 0.958617i
\(640\) 0.0989549 2.23388i 0.00391153 0.0883018i
\(641\) 49.7149i 1.96362i −0.189862 0.981811i \(-0.560804\pi\)
0.189862 0.981811i \(-0.439196\pi\)
\(642\) −16.3856 7.90835i −0.646686 0.312118i
\(643\) −2.40899 + 2.40899i −0.0950012 + 0.0950012i −0.753010 0.658009i \(-0.771399\pi\)
0.658009 + 0.753010i \(0.271399\pi\)
\(644\) 3.06798 0.120896
\(645\) 8.30021 15.4150i 0.326820 0.606964i
\(646\) −3.08715 −0.121462
\(647\) −5.87644 + 5.87644i −0.231027 + 0.231027i −0.813121 0.582094i \(-0.802233\pi\)
0.582094 + 0.813121i \(0.302233\pi\)
\(648\) −7.63705 + 4.76187i −0.300012 + 0.187064i
\(649\) 7.10918i 0.279060i
\(650\) 34.2348 + 3.03898i 1.34280 + 0.119199i
\(651\) 7.77054 2.71148i 0.304551 0.106271i
\(652\) 2.53089 + 2.53089i 0.0991172 + 0.0991172i
\(653\) −6.59638 6.59638i −0.258136 0.258136i 0.566159 0.824296i \(-0.308429\pi\)
−0.824296 + 0.566159i \(0.808429\pi\)
\(654\) 12.2518 4.27519i 0.479084 0.167173i
\(655\) −30.5955 + 27.9999i −1.19547 + 1.09405i
\(656\) 6.08532i 0.237592i
\(657\) −10.6965 1.22396i −0.417311 0.0477514i
\(658\) 1.83020 1.83020i 0.0713487 0.0713487i
\(659\) 26.7046 1.04026 0.520132 0.854086i \(-0.325883\pi\)
0.520132 + 0.854086i \(0.325883\pi\)
\(660\) −3.50281 + 1.05088i −0.136347 + 0.0409053i
\(661\) −20.8028 −0.809135 −0.404568 0.914508i \(-0.632578\pi\)
−0.404568 + 0.914508i \(0.632578\pi\)
\(662\) −11.7123 + 11.7123i −0.455212 + 0.455212i
\(663\) −33.1016 15.9762i −1.28556 0.620465i
\(664\) 11.0988i 0.430718i
\(665\) −0.968808 0.0429156i −0.0375688 0.00166420i
\(666\) −8.17764 10.2909i −0.316877 0.398766i
\(667\) −8.89640 8.89640i −0.344470 0.344470i
\(668\) 3.33084 + 3.33084i 0.128874 + 0.128874i
\(669\) −3.48633 9.99110i −0.134789 0.386278i
\(670\) −16.3336 17.8477i −0.631022 0.689518i
\(671\) 4.28205i 0.165307i
\(672\) −0.326507 + 0.676500i −0.0125953 + 0.0260965i
\(673\) 29.5002 29.5002i 1.13715 1.13715i 0.148188 0.988959i \(-0.452656\pi\)
0.988959 0.148188i \(-0.0473442\pi\)
\(674\) −35.9137 −1.38334
\(675\) 3.45211 + 25.7504i 0.132872 + 0.991133i
\(676\) −34.2502 −1.31732
\(677\) 35.0885 35.0885i 1.34856 1.34856i 0.461331 0.887228i \(-0.347372\pi\)
0.887228 0.461331i \(-0.152628\pi\)
\(678\) 12.5880 26.0815i 0.483440 1.00165i
\(679\) 0.443420i 0.0170169i
\(680\) 4.66042 + 5.09245i 0.178719 + 0.195287i
\(681\) −7.13009 20.4333i −0.273226 0.783008i
\(682\) 7.31532 + 7.31532i 0.280118 + 0.280118i
\(683\) −16.7946 16.7946i −0.642629 0.642629i 0.308572 0.951201i \(-0.400149\pi\)
−0.951201 + 0.308572i \(0.900149\pi\)
\(684\) −1.86641 2.34873i −0.0713638 0.0898059i
\(685\) 7.02125 + 0.311023i 0.268268 + 0.0118836i
\(686\) 5.99007i 0.228702i
\(687\) −33.7983 16.3124i −1.28948 0.622358i
\(688\) 3.19643 3.19643i 0.121863 0.121863i
\(689\) 49.4059 1.88221
\(690\) 26.2426 7.87301i 0.999037 0.299720i
\(691\) −30.1709 −1.14776 −0.573878 0.818941i \(-0.694562\pi\)
−0.573878 + 0.818941i \(0.694562\pi\)
\(692\) 9.61343 9.61343i 0.365448 0.365448i
\(693\) 1.22056 + 0.139665i 0.0463654 + 0.00530543i
\(694\) 8.03838i 0.305133i
\(695\) −31.2805 + 28.6267i −1.18654 + 1.08587i
\(696\) 2.90847 1.01489i 0.110245 0.0384694i
\(697\) −13.2839 13.2839i −0.503165 0.503165i
\(698\) 12.8335 + 12.8335i 0.485756 + 0.485756i
\(699\) 24.5026 8.55003i 0.926774 0.323392i
\(700\) 1.39174 + 1.66289i 0.0526028 + 0.0628515i
\(701\) 39.5966i 1.49554i −0.663957 0.747771i \(-0.731124\pi\)
0.663957 0.747771i \(-0.268876\pi\)
\(702\) −7.85749 34.8427i −0.296562 1.31505i
\(703\) 3.09818 3.09818i 0.116850 0.116850i
\(704\) −0.944248 −0.0355877
\(705\) 10.9583 20.3516i 0.412715 0.766485i
\(706\) 12.5368 0.471829
\(707\) 0.508493 0.508493i 0.0191238 0.0191238i
\(708\) 11.7442 + 5.66823i 0.441373 + 0.213025i
\(709\) 39.9962i 1.50209i 0.660252 + 0.751044i \(0.270449\pi\)
−0.660252 + 0.751044i \(0.729551\pi\)
\(710\) 1.28477 29.0034i 0.0482167 1.08848i
\(711\) −22.3199 + 17.7364i −0.837062 + 0.665167i
\(712\) −6.28303 6.28303i −0.235466 0.235466i
\(713\) −54.8052 54.8052i −2.05247 2.05247i
\(714\) −0.764016 2.18951i −0.0285926 0.0819404i
\(715\) 0.642281 14.4993i 0.0240199 0.542243i
\(716\) 22.6680i 0.847143i
\(717\) −8.73865 + 18.1059i −0.326351 + 0.676176i
\(718\) 7.62533 7.62533i 0.284575 0.284575i
\(719\) −34.6703 −1.29298 −0.646491 0.762921i \(-0.723764\pi\)
−0.646491 + 0.762921i \(0.723764\pi\)
\(720\) −1.05681 + 6.62444i −0.0393851 + 0.246878i
\(721\) −1.03816 −0.0386632
\(722\) 0.707107 0.707107i 0.0263158 0.0263158i
\(723\) −15.5764 + 32.2732i −0.579293 + 1.20025i
\(724\) 3.95190i 0.146871i
\(725\) 0.786287 8.85768i 0.0292020 0.328966i
\(726\) −5.76830 16.5308i −0.214082 0.613514i
\(727\) 2.33610 + 2.33610i 0.0866412 + 0.0866412i 0.749099 0.662458i \(-0.230487\pi\)
−0.662458 + 0.749099i \(0.730487\pi\)
\(728\) −2.10797 2.10797i −0.0781267 0.0781267i
\(729\) 24.3867 11.5884i 0.903210 0.429198i
\(730\) −5.91990 + 5.41767i −0.219105 + 0.200517i
\(731\) 13.9553i 0.516155i
\(732\) 7.07384 + 3.41413i 0.261457 + 0.126190i
\(733\) −25.5392 + 25.5392i −0.943311 + 0.943311i −0.998477 0.0551665i \(-0.982431\pi\)
0.0551665 + 0.998477i \(0.482431\pi\)
\(734\) 13.1175 0.484175
\(735\) 7.58115 + 25.2697i 0.279635 + 0.932088i
\(736\) 7.07416 0.260757
\(737\) −7.22413 + 7.22413i −0.266104 + 0.266104i
\(738\) 2.07542 18.1376i 0.0763974 0.667655i
\(739\) 6.43422i 0.236686i 0.992973 + 0.118343i \(0.0377583\pi\)
−0.992973 + 0.118343i \(0.962242\pi\)
\(740\) −9.78771 0.433570i −0.359803 0.0159383i
\(741\) 11.2412 3.92254i 0.412955 0.144098i
\(742\) 2.20414 + 2.20414i 0.0809167 + 0.0809167i
\(743\) −2.23501 2.23501i −0.0819944 0.0819944i 0.664920 0.746915i \(-0.268466\pi\)
−0.746915 + 0.664920i \(0.768466\pi\)
\(744\) 17.9173 6.25213i 0.656880 0.229214i
\(745\) 19.5623 + 21.3758i 0.716708 + 0.783148i
\(746\) 6.60357i 0.241774i
\(747\) 3.78530 33.0806i 0.138497 1.21036i
\(748\) 2.06124 2.06124i 0.0753665 0.0753665i
\(749\) 4.55565 0.166460
\(750\) 16.1718 + 10.6524i 0.590510 + 0.388971i
\(751\) −33.0311 −1.20532 −0.602660 0.797998i \(-0.705893\pi\)
−0.602660 + 0.797998i \(0.705893\pi\)
\(752\) 4.22008 4.22008i 0.153891 0.153891i
\(753\) 24.2714 + 11.7144i 0.884498 + 0.426895i
\(754\) 12.2252i 0.445216i
\(755\) 6.56935 + 7.17833i 0.239083 + 0.261246i
\(756\) 1.20389 1.90498i 0.0437852 0.0692836i
\(757\) −22.2750 22.2750i −0.809598 0.809598i 0.174975 0.984573i \(-0.444016\pi\)
−0.984573 + 0.174975i \(0.944016\pi\)
\(758\) 15.2909 + 15.2909i 0.555390 + 0.555390i
\(759\) −3.81177 10.9237i −0.138358 0.396506i
\(760\) −2.23388 0.0989549i −0.0810312 0.00358947i
\(761\) 19.7060i 0.714342i −0.934039 0.357171i \(-0.883741\pi\)
0.934039 0.357171i \(-0.116259\pi\)
\(762\) 1.51972 3.14876i 0.0550537 0.114067i
\(763\) −2.29749 + 2.29749i −0.0831746 + 0.0831746i
\(764\) 3.21978 0.116487
\(765\) −12.1538 16.7678i −0.439423 0.606240i
\(766\) −28.0358 −1.01297
\(767\) −36.5949 + 36.5949i −1.32136 + 1.32136i
\(768\) −0.752859 + 1.55987i −0.0271665 + 0.0562871i
\(769\) 1.48367i 0.0535024i −0.999642 0.0267512i \(-0.991484\pi\)
0.999642 0.0267512i \(-0.00851619\pi\)
\(770\) 0.675512 0.618203i 0.0243437 0.0222785i
\(771\) −2.40953 6.90521i −0.0867771 0.248685i
\(772\) 8.96414 + 8.96414i 0.322627 + 0.322627i
\(773\) 9.99213 + 9.99213i 0.359392 + 0.359392i 0.863589 0.504197i \(-0.168211\pi\)
−0.504197 + 0.863589i \(0.668211\pi\)
\(774\) −10.6173 + 8.43697i −0.381630 + 0.303260i
\(775\) 4.84383 54.5667i 0.173995 1.96009i
\(776\) 1.02244i 0.0367034i
\(777\) 2.96408 + 1.43059i 0.106336 + 0.0513220i