Properties

Label 570.2.k.a.77.10
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 77.10
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.a.533.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.55987 + 0.752859i) q^{3} -1.00000i q^{4} +(-1.50962 - 1.64956i) q^{5} +(-0.570645 + 1.63535i) q^{6} +(0.306664 + 0.306664i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.86641 - 2.34873i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.55987 + 0.752859i) 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} +(0.752859 + 1.55987i) q^{12} +(-4.86057 + 4.86057i) q^{13} +0.433689 q^{14} +(3.59670 + 1.43658i) q^{15} -1.00000 q^{16} +(-2.18295 + 2.18295i) q^{17} +(-0.341054 - 2.98055i) 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} +(-1.14309 + 5.06886i) q^{27} +(0.306664 - 0.306664i) q^{28} +1.77850 q^{29} +(3.55906 - 1.52744i) q^{30} -10.9563 q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.710886 + 1.47291i) 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} +(-0.676500 + 0.326507i) q^{42} +(-3.19643 + 3.19643i) q^{43} -0.944248 q^{44} +(-6.69193 + 0.466933i) q^{45} -7.07416 q^{46} +(4.22008 - 4.22008i) q^{47} +(1.55987 - 0.752859i) 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} +(-0.752859 - 1.55987i) q^{57} +(1.25759 - 1.25759i) q^{58} -7.52893 q^{59} +(1.43658 - 3.59670i) q^{60} +4.53489 q^{61} +(-7.74725 + 7.74725i) q^{62} +(1.29263 - 0.147911i) 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} +(-2.98055 + 0.341054i) q^{72} +(2.53764 - 2.53764i) q^{73} -4.38149 q^{74} +(-3.05992 - 8.10166i) q^{75} +1.00000 q^{76} +(0.289567 - 0.289567i) q^{77} +(-5.17507 - 10.7224i) 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} +(-2.77424 + 1.33896i) q^{87} +(-0.667684 + 0.667684i) q^{88} +8.88554 q^{89} +(-4.40174 + 5.06208i) q^{90} -2.98113 q^{91} +(-5.00219 + 5.00219i) q^{92} +(17.0904 - 8.24852i) 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
\(3\) −1.55987 + 0.752859i −0.900593 + 0.434663i
\(4\) 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 \(-0.954534\pi\)
0.989816 0.142351i \(-0.0454661\pi\)
\(12\) 0.752859 + 1.55987i 0.217332 + 0.450296i
\(13\) −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
\(15\) 3.59670 + 1.43658i 0.928664 + 0.370922i
\(16\) −1.00000 −0.250000
\(17\) −2.18295 + 2.18295i −0.529443 + 0.529443i −0.920406 0.390964i \(-0.872142\pi\)
0.390964 + 0.920406i \(0.372142\pi\)
\(18\) −0.341054 2.98055i −0.0803872 0.702523i
\(19\) 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 \(-0.985991\pi\)
−0.0439961 0.999032i \(-0.514009\pi\)
\(24\) 1.63535 + 0.570645i 0.333814 + 0.116482i
\(25\) −0.442106 + 4.98042i −0.0884212 + 0.996083i
\(26\) 6.87388i 1.34808i
\(27\) −1.14309 + 5.06886i −0.219988 + 0.975502i
\(28\) 0.306664 0.306664i 0.0579541 0.0579541i
\(29\) 1.77850 0.330260 0.165130 0.986272i \(-0.447196\pi\)
0.165130 + 0.986272i \(0.447196\pi\)
\(30\) 3.55906 1.52744i 0.649793 0.278871i
\(31\) −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
\(33\) 0.710886 + 1.47291i 0.123749 + 0.256400i
\(34\) 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 \(0.157618\pi\)
−0.879886 + 0.475184i \(0.842382\pi\)
\(42\) −0.676500 + 0.326507i −0.104386 + 0.0503811i
\(43\) −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
\(45\) −6.69193 + 0.466933i −0.997575 + 0.0696062i
\(46\) −7.07416 −1.04303
\(47\) 4.22008 4.22008i 0.615562 0.615562i −0.328828 0.944390i \(-0.606654\pi\)
0.944390 + 0.328828i \(0.106654\pi\)
\(48\) 1.55987 0.752859i 0.225148 0.108666i
\(49\) 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 0.964003 0.265893i \(-0.0856667\pi\)
−0.265893 + 0.964003i \(0.585667\pi\)
\(54\) 2.77594 + 4.39251i 0.377757 + 0.597745i
\(55\) −1.55759 + 1.42545i −0.210026 + 0.192208i
\(56\) 0.433689i 0.0579541i
\(57\) −0.752859 1.55987i −0.0997186 0.206610i
\(58\) 1.25759 1.25759i 0.165130 0.165130i
\(59\) −7.52893 −0.980183 −0.490092 0.871671i \(-0.663037\pi\)
−0.490092 + 0.871671i \(0.663037\pi\)
\(60\) 1.43658 3.59670i 0.185461 0.464332i
\(61\) 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
\(63\) 1.29263 0.147911i 0.162856 0.0186351i
\(64\) 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 \(-0.720044\pi\)
0.637531 0.770425i \(-0.279956\pi\)
\(72\) −2.98055 + 0.341054i −0.351261 + 0.0401936i
\(73\) 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
\(75\) −3.05992 8.10166i −0.353329 0.935499i
\(76\) 1.00000 0.114708
\(77\) 0.289567 0.289567i 0.0329992 0.0329992i
\(78\) −5.17507 10.7224i −0.585961 1.21407i
\(79\) 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 0.130069 0.991505i \(-0.458480\pi\)
−0.991505 + 0.130069i \(0.958480\pi\)
\(84\) −0.247482 + 0.709233i −0.0270025 + 0.0773836i
\(85\) 6.89632 + 0.305489i 0.748011 + 0.0331349i
\(86\) 4.52043i 0.487451i
\(87\) −2.77424 + 1.33896i −0.297430 + 0.143552i
\(88\) −0.667684 + 0.667684i −0.0711753 + 0.0711753i
\(89\) 8.88554 0.941866 0.470933 0.882169i \(-0.343917\pi\)
0.470933 + 0.882169i \(0.343917\pi\)
\(90\) −4.40174 + 5.06208i −0.463984 + 0.533590i
\(91\) −2.98113 −0.312507
\(92\) −5.00219 + 5.00219i −0.521514 + 0.521514i
\(93\) 17.0904 8.24852i 1.77219 0.855332i
\(94\) 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 \(0.0262890\pi\)
−0.996591 + 0.0824956i \(0.973711\pi\)
\(102\) −2.32419 4.81557i −0.230129 0.476812i
\(103\) −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
\(105\) 0.662433 + 1.54353i 0.0646468 + 0.150633i
\(106\) 7.18748 0.698110
\(107\) −7.42775 + 7.42775i −0.718067 + 0.718067i −0.968209 0.250142i \(-0.919523\pi\)
0.250142 + 0.968209i \(0.419523\pi\)
\(108\) 5.06886 + 1.14309i 0.487751 + 0.109994i
\(109\) 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 \(-0.961913\pi\)
−0.119367 0.992850i \(-0.538087\pi\)
\(114\) −1.63535 0.570645i −0.153164 0.0534458i
\(115\) −0.700022 + 15.8028i −0.0652774 + 1.47362i
\(116\) 1.77850i 0.165130i
\(117\) 2.34436 + 20.4880i 0.216737 + 1.89411i
\(118\) −5.32376 + 5.32376i −0.490092 + 0.490092i
\(119\) −1.33886 −0.122734
\(120\) −1.52744 3.55906i −0.139435 0.324897i
\(121\) 10.1084 0.918945
\(122\) 3.20665 3.20665i 0.290316 0.290316i
\(123\) −4.58139 9.49233i −0.413090 0.855895i
\(124\) 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 \(-0.699327\pi\)
0.586073 0.810258i \(-0.300673\pi\)
\(132\) 1.47291 0.710886i 0.128200 0.0618746i
\(133\) −0.306664 + 0.306664i −0.0265912 + 0.0265912i
\(134\) 10.8197 0.934678
\(135\) 10.0870 5.76644i 0.868153 0.496296i
\(136\) 3.08715 0.264721
\(137\) −2.22249 + 2.22249i −0.189880 + 0.189880i −0.795644 0.605764i \(-0.792868\pi\)
0.605764 + 0.795644i \(0.292868\pi\)
\(138\) 11.0348 5.32585i 0.939343 0.453366i
\(139\) 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
\(147\) 5.12841 + 10.6257i 0.422984 + 0.876395i
\(148\) −3.09818 + 3.09818i −0.254669 + 0.254669i
\(149\) −12.9585 −1.06160 −0.530799 0.847498i \(-0.678108\pi\)
−0.530799 + 0.847498i \(0.678108\pi\)
\(150\) −7.89243 3.56505i −0.644414 0.291085i
\(151\) 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
\(153\) 1.05289 + 9.20142i 0.0851208 + 0.743891i
\(154\) 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
\(162\) −7.63705 4.76187i −0.600023 0.374128i
\(163\) −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
\(165\) 1.35648 3.39618i 0.105602 0.264392i
\(166\) −11.0988 −0.861436
\(167\) 3.33084 3.33084i 0.257749 0.257749i −0.566389 0.824138i \(-0.691660\pi\)
0.824138 + 0.566389i \(0.191660\pi\)
\(168\) 0.326507 + 0.676500i 0.0251905 + 0.0521931i
\(169\) 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 0.239902 0.970797i \(-0.422885\pi\)
−0.970797 + 0.239902i \(0.922885\pi\)
\(174\) −1.01489 + 2.90847i −0.0769389 + 0.220491i
\(175\) −1.66289 + 1.39174i −0.125703 + 0.105206i
\(176\) 0.944248i 0.0711753i
\(177\) 11.7442 5.66823i 0.882746 0.426050i
\(178\) 6.28303 6.28303i 0.470933 0.470933i
\(179\) −22.6680 −1.69429 −0.847143 0.531365i \(-0.821679\pi\)
−0.847143 + 0.531365i \(0.821679\pi\)
\(180\) 0.466933 + 6.69193i 0.0348031 + 0.498787i
\(181\) 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
\(183\) −7.07384 + 3.41413i −0.522914 + 0.252380i
\(184\) 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 \(-0.962837\pi\)
0.993192 0.116487i \(-0.0371635\pi\)
\(192\) −0.752859 1.55987i −0.0543329 0.112574i
\(193\) −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
\(195\) −24.4646 + 10.4994i −1.75194 + 0.751880i
\(196\) −6.81191 −0.486565
\(197\) −6.36112 + 6.36112i −0.453211 + 0.453211i −0.896419 0.443208i \(-0.853840\pi\)
0.443208 + 0.896419i \(0.353840\pi\)
\(198\) −2.81438 + 0.322039i −0.200009 + 0.0228863i
\(199\) 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
\(207\) −21.0849 + 2.41267i −1.46550 + 0.167692i
\(208\) 4.86057 4.86057i 0.337020 0.337020i
\(209\) 0.944248 0.0653150
\(210\) 1.55985 + 0.623027i 0.107640 + 0.0429930i
\(211\) −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
\(213\) 9.77470 + 20.2525i 0.669751 + 1.38768i
\(214\) 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
\(222\) 6.83457 3.29864i 0.458706 0.221391i
\(223\) −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
\(225\) 10.8725 + 10.3339i 0.724833 + 0.688924i
\(226\) −16.7203 −1.11222
\(227\) 8.83516 8.83516i 0.586410 0.586410i −0.350247 0.936657i \(-0.613902\pi\)
0.936657 + 0.350247i \(0.113902\pi\)
\(228\) −1.55987 + 0.752859i −0.103305 + 0.0498593i
\(229\) 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 0.963127 0.269048i \(-0.0867089\pi\)
−0.269048 + 0.963127i \(0.586709\pi\)
\(234\) 16.1449 + 12.8295i 1.05542 + 0.838688i
\(235\) −13.3320 0.590572i −0.869683 0.0385247i
\(236\) 7.52893i 0.490092i
\(237\) 7.15440 + 14.8234i 0.464728 + 0.962885i
\(238\) −0.946720 + 0.946720i −0.0613668 + 0.0613668i
\(239\) −11.6073 −0.750812 −0.375406 0.926860i \(-0.622497\pi\)
−0.375406 + 0.926860i \(0.622497\pi\)
\(240\) −3.59670 1.43658i −0.232166 0.0927306i
\(241\) 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
\(243\) 9.77190 + 12.1454i 0.626868 + 0.779126i
\(244\) 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 \(0.163392\pi\)
−0.871123 + 0.491064i \(0.836608\pi\)
\(252\) −0.147911 1.29263i −0.00931754 0.0814282i
\(253\) −4.72330 + 4.72330i −0.296951 + 0.296951i
\(254\) 2.01860 0.126658
\(255\) −10.9874 + 4.71544i −0.688056 + 0.295292i
\(256\) 1.00000 0.0625000
\(257\) 2.98574 2.98574i 0.186245 0.186245i −0.607825 0.794071i \(-0.707958\pi\)
0.794071 + 0.607825i \(0.207958\pi\)
\(258\) −3.40325 7.05130i −0.211877 0.438995i
\(259\) 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 0.392222 0.919870i \(-0.371706\pi\)
−0.919870 + 0.392222i \(0.871706\pi\)
\(264\) 0.538830 1.54417i 0.0331627 0.0950373i
\(265\) 0.711236 16.0560i 0.0436909 0.986309i
\(266\) 0.433689i 0.0265912i
\(267\) −13.8603 + 6.68956i −0.848237 + 0.409395i
\(268\) 7.65067 7.65067i 0.467339 0.467339i
\(269\) −11.0350 −0.672814 −0.336407 0.941717i \(-0.609212\pi\)
−0.336407 + 0.941717i \(0.609212\pi\)
\(270\) 3.05512 11.2101i 0.185929 0.682225i
\(271\) −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
\(273\) 4.65018 2.24437i 0.281442 0.135835i
\(274\) 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 \(0.405619\pi\)
−0.292180 + 0.956363i \(0.594381\pi\)
\(282\) 4.49314 + 9.30947i 0.267562 + 0.554371i
\(283\) 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
\(285\) −1.43658 + 3.59670i −0.0850954 + 0.213050i
\(286\) 6.49065 0.383800
\(287\) −1.86615 + 1.86615i −0.110155 + 0.110155i
\(288\) 0.341054 + 2.98055i 0.0200968 + 0.175631i
\(289\) 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 0.885339 0.464947i \(-0.153926\pi\)
−0.464947 + 0.885339i \(0.653926\pi\)
\(294\) 11.1399 + 3.88718i 0.649689 + 0.226705i
\(295\) 11.3658 + 12.4194i 0.661743 + 0.723087i
\(296\) 4.38149i 0.254669i
\(297\) 4.78626 + 1.07936i 0.277727 + 0.0626310i
\(298\) −9.16302 + 9.16302i −0.530799 + 0.530799i
\(299\) 48.6269 2.81217
\(300\) −8.10166 + 3.05992i −0.467749 + 0.176665i
\(301\) −1.96046 −0.112999
\(302\) 3.07709 3.07709i 0.177067 0.177067i
\(303\) −1.24835 2.58649i −0.0717156 0.148590i
\(304\) 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 \(0.240317\pi\)
−0.728286 + 0.685273i \(0.759683\pi\)
\(312\) −10.7224 + 5.17507i −0.607035 + 0.292980i
\(313\) −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
\(315\) −2.19537 1.90899i −0.123695 0.107559i
\(316\) −9.50297 −0.534584
\(317\) 18.3162 18.3162i 1.02874 1.02874i 0.0291663 0.999575i \(-0.490715\pi\)
0.999575 0.0291663i \(-0.00928523\pi\)
\(318\) −11.2116 + 5.41116i −0.628713 + 0.303443i
\(319\) 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
\(327\) −5.64032 11.6864i −0.311910 0.646257i
\(328\) 4.30297 4.30297i 0.237592 0.237592i
\(329\) 2.58830 0.142697
\(330\) −1.44228 3.36064i −0.0793949 0.184997i
\(331\) 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
\(333\) −13.0593 + 1.49432i −0.715643 + 0.0818885i
\(334\) 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
\(342\) 2.98055 0.341054i 0.161170 0.0184421i
\(343\) 4.23562 4.23562i 0.228702 0.228702i
\(344\) 4.52043 0.243725
\(345\) −10.8053 25.1774i −0.581740 1.35550i
\(346\) −13.5954 −0.730896
\(347\) −5.68399 + 5.68399i −0.305133 + 0.305133i −0.843018 0.537885i \(-0.819223\pi\)
0.537885 + 0.843018i \(0.319223\pi\)
\(348\) 1.33896 + 2.77424i 0.0717759 + 0.148715i
\(349\) 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 0.902506 0.430677i \(-0.141725\pi\)
−0.430677 + 0.902506i \(0.641725\pi\)
\(354\) 4.29635 12.3124i 0.228348 0.654398i
\(355\) −21.4170 + 19.6000i −1.13669 + 1.04026i
\(356\) 8.88554i 0.470933i
\(357\) 2.08846 1.00798i 0.110533 0.0533478i
\(358\) −16.0287 + 16.0287i −0.847143 + 0.847143i
\(359\) 10.7838 0.569150 0.284575 0.958654i \(-0.408148\pi\)
0.284575 + 0.958654i \(0.408148\pi\)
\(360\) 5.06208 + 4.40174i 0.266795 + 0.231992i
\(361\) −1.00000 −0.0526316
\(362\) 2.79442 2.79442i 0.146871 0.146871i
\(363\) −15.7678 + 7.61020i −0.827596 + 0.399432i
\(364\) 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
\(372\) −8.24852 17.0904i −0.427666 0.886094i
\(373\) −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
\(375\) −8.74487 + 17.2779i −0.451583 + 0.892229i
\(376\) −5.96810 −0.307781
\(377\) −8.64454 + 8.64454i −0.445216 + 0.445216i
\(378\) −0.495747 + 2.19831i −0.0254985 + 0.113069i
\(379\) 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 \(-0.995843\pi\)
−0.0130600 0.999915i \(-0.504157\pi\)
\(384\) −1.63535 0.570645i −0.0834535 0.0291206i
\(385\) −0.914795 0.0405230i −0.0466222 0.00206524i
\(386\) 12.6772i 0.645253i
\(387\) 1.54171 + 13.4734i 0.0783696 + 0.684891i
\(388\) −0.722973 + 0.722973i −0.0367034 + 0.0367034i
\(389\) −18.0320 −0.914258 −0.457129 0.889400i \(-0.651122\pi\)
−0.457129 + 0.889400i \(0.651122\pi\)
\(390\) −9.87485 + 24.7233i −0.500033 + 1.25191i
\(391\) 21.8390 1.10445
\(392\) −4.81675 + 4.81675i −0.243283 + 0.243283i
\(393\) 13.9638 + 28.9320i 0.704379 + 1.45943i
\(394\) 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 \(0.0814034\pi\)
−0.967477 + 0.252958i \(0.918597\pi\)
\(402\) −16.8773 + 8.14570i −0.841765 + 0.406270i
\(403\) 53.2536 53.2536i 2.65275 2.65275i
\(404\) 1.65814 0.0824956
\(405\) −11.3932 + 16.5890i −0.566131 + 0.824315i
\(406\) 0.771317 0.0382798
\(407\) −2.92545 + 2.92545i −0.145009 + 0.145009i
\(408\) −4.81557 + 2.32419i −0.238406 + 0.115065i
\(409\) 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
\(417\) −14.2764 29.5797i −0.699118 1.44853i
\(418\) 0.667684 0.667684i 0.0326575 0.0326575i
\(419\) −20.6060 −1.00667 −0.503333 0.864092i \(-0.667893\pi\)
−0.503333 + 0.864092i \(0.667893\pi\)
\(420\) 1.54353 0.662433i 0.0753164 0.0323234i
\(421\) 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
\(423\) −2.03544 17.7882i −0.0989666 0.864892i
\(424\) 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 \(0.0569936\pi\)
−0.984013 + 0.178095i \(0.943006\pi\)
\(432\) 1.14309 5.06886i 0.0549971 0.243876i
\(433\) −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
\(435\) 6.39674 + 2.55495i 0.306700 + 0.122501i
\(436\) 7.49186 0.358795
\(437\) 5.00219 5.00219i 0.239287 0.239287i
\(438\) 2.70184 + 5.59802i 0.129099 + 0.267484i
\(439\) 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 0.562366 0.826888i \(-0.309891\pi\)
−0.826888 + 0.562366i \(0.809891\pi\)
\(444\) 2.50027 7.16526i 0.118658 0.340048i
\(445\) −13.4138 14.6572i −0.635874 0.694820i
\(446\) 6.10946i 0.289291i
\(447\) 20.2136 9.75590i 0.956068 0.461438i
\(448\) −0.306664 + 0.306664i −0.0144885 + 0.0144885i
\(449\) −22.1426 −1.04497 −0.522487 0.852647i \(-0.674996\pi\)
−0.522487 + 0.852647i \(0.674996\pi\)
\(450\) 14.9952 0.380871i 0.706879 0.0179544i
\(451\) 5.74605 0.270571
\(452\) −11.8230 + 11.8230i −0.556109 + 0.556109i
\(453\) −6.78804 + 3.27619i −0.318930 + 0.153929i
\(454\) 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 \(0.259754\pi\)
−0.685111 + 0.728439i \(0.740246\pi\)
\(462\) 0.308303 + 0.638783i 0.0143436 + 0.0297189i
\(463\) 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
\(465\) −39.4064 15.7395i −1.82743 0.729902i
\(466\) 14.9831 0.694079
\(467\) 3.08706 3.08706i 0.142852 0.142852i −0.632064 0.774916i \(-0.717792\pi\)
0.774916 + 0.632064i \(0.217792\pi\)
\(468\) 20.4880 2.34436i 0.947056 0.108368i
\(469\) 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
\(477\) 21.4227 2.45132i 0.980876 0.112238i
\(478\) −8.20758 + 8.20758i −0.375406 + 0.375406i
\(479\) 3.14915 0.143888 0.0719441 0.997409i \(-0.477080\pi\)
0.0719441 + 0.997409i \(0.477080\pi\)
\(480\) −3.55906 + 1.52744i −0.162448 + 0.0697177i
\(481\) 30.1178 1.37326
\(482\) 14.6298 14.6298i 0.666369 0.666369i
\(483\) 2.30976 + 4.78567i 0.105098 + 0.217755i
\(484\) 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 \(-0.974386\pi\)
0.996764 0.0803823i \(-0.0256141\pi\)
\(492\) −9.49233 + 4.58139i −0.427947 + 0.206545i
\(493\) −3.88238 + 3.88238i −0.174854 + 0.174854i
\(494\) −6.87388 −0.309271
\(495\) 0.440900 + 6.31884i 0.0198170 + 0.284011i
\(496\) 10.9563 0.491951
\(497\) 3.98156 3.98156i 0.178597 0.178597i
\(498\) 17.3128 8.35586i 0.775804 0.374435i
\(499\) 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 0.640208 0.768201i \(-0.278848\pi\)
−0.768201 + 0.640208i \(0.778848\pi\)
\(504\) −1.01862 0.809440i −0.0453728 0.0360553i
\(505\) 2.73521 2.50316i 0.121715 0.111389i
\(506\) 6.67976i 0.296951i
\(507\) 25.7856 + 53.4260i 1.14518 + 2.37273i
\(508\) 1.42736 1.42736i 0.0633291 0.0633291i
\(509\) 12.2215 0.541709 0.270854 0.962620i \(-0.412694\pi\)
0.270854 + 0.962620i \(0.412694\pi\)
\(510\) −4.43493 + 11.1036i −0.196382 + 0.491674i
\(511\) 1.55641 0.0688515
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −5.06886 1.14309i −0.223796 0.0504688i
\(514\) 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 \(-0.638194\pi\)
0.420639 0.907228i \(-0.361806\pi\)
\(522\) −0.606566 5.30092i −0.0265487 0.232015i
\(523\) −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
\(525\) 1.54612 3.42286i 0.0674782 0.149386i
\(526\) −12.1014 −0.527648
\(527\) 23.9169 23.9169i 1.04184 1.04184i
\(528\) −0.710886 1.47291i −0.0309373 0.0641000i
\(529\) 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
\(537\) 35.3592 17.0658i 1.52586 0.736444i
\(538\) −7.80290 + 7.80290i −0.336407 + 0.336407i
\(539\) −6.43213 −0.277052
\(540\) −5.76644 10.0870i −0.248148 0.434077i
\(541\) −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
\(543\) −6.16447 + 2.97523i −0.264543 + 0.127679i
\(544\) 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
\(552\) −5.32585 11.0348i −0.226683 0.469672i
\(553\) 2.91422 2.91422i 0.123925 0.123925i
\(554\) 6.80049 0.288925
\(555\) −6.69245 15.5940i −0.284079 0.661928i
\(556\) 18.9629 0.804206
\(557\) 18.8971 18.8971i 0.800694 0.800694i −0.182510 0.983204i \(-0.558422\pi\)
0.983204 + 0.182510i \(0.0584222\pi\)
\(558\) 3.73668 + 32.6557i 0.158186 + 1.38243i
\(559\) 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 0.729092 0.684416i \(-0.239943\pi\)
−0.684416 + 0.729092i \(0.739943\pi\)
\(564\) 9.75992 + 3.40566i 0.410967 + 0.143404i
\(565\) −1.65455 + 37.3511i −0.0696076 + 1.57137i
\(566\) 12.2396i 0.514467i
\(567\) 2.06517 3.31210i 0.0867291 0.139095i
\(568\) −9.18067 + 9.18067i −0.385212 + 0.385212i
\(569\) 5.21442 0.218600 0.109300 0.994009i \(-0.465139\pi\)
0.109300 + 0.994009i \(0.465139\pi\)
\(570\) 1.52744 + 3.55906i 0.0639773 + 0.149073i
\(571\) 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
\(573\) 2.42404 + 5.02244i 0.101266 + 0.209816i
\(574\) 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
\(582\) 1.59487 0.769752i 0.0661096 0.0319072i
\(583\) 4.79897 4.79897i 0.198753 0.198753i
\(584\) −3.58877 −0.148504
\(585\) 30.2570 34.7962i 1.25097 1.43864i
\(586\) 10.1766 0.420392
\(587\) −4.54157 + 4.54157i −0.187450 + 0.187450i −0.794593 0.607142i \(-0.792316\pi\)
0.607142 + 0.794593i \(0.292316\pi\)
\(588\) 10.6257 5.12841i 0.438197 0.211492i
\(589\) 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 0.555835 0.831293i \(-0.312399\pi\)
−0.831293 + 0.555835i \(0.812399\pi\)
\(594\) 4.14762 2.62117i 0.170179 0.107548i
\(595\) 2.02117 + 2.20854i 0.0828601 + 0.0905413i
\(596\) 12.9585i 0.530799i
\(597\) 16.2054 + 33.5765i 0.663243 + 1.37419i
\(598\) 34.3844 34.3844i 1.40608 1.40608i
\(599\) 25.3428 1.03548 0.517740 0.855538i \(-0.326774\pi\)
0.517740 + 0.855538i \(0.326774\pi\)
\(600\) −3.56505 + 7.89243i −0.145542 + 0.322207i
\(601\) 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
\(603\) 32.2486 3.69010i 1.31327 0.150272i
\(604\) 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
\(612\) 9.20142 1.05289i 0.371945 0.0425604i
\(613\) 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
\(615\) −8.74203 + 21.8871i −0.352513 + 0.882572i
\(616\) −0.409510 −0.0164996
\(617\) 6.58274 6.58274i 0.265011 0.265011i −0.562075 0.827086i \(-0.689997\pi\)
0.827086 + 0.562075i \(0.189997\pi\)
\(618\) −1.80219 3.73402i −0.0724948 0.150204i
\(619\) 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
\(627\) −1.47291 + 0.710886i −0.0588222 + 0.0283900i
\(628\) −5.26086 + 5.26086i −0.209931 + 0.209931i
\(629\) 13.5263 0.539330
\(630\) −2.90222 + 0.202504i −0.115627 + 0.00806794i
\(631\) −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
\(633\) 1.61300 0.778502i 0.0641111 0.0309427i
\(634\) 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 \(0.439196\pi\)
−0.189862 + 0.981811i \(0.560804\pi\)
\(642\) −7.90835 16.3856i −0.312118 0.646686i
\(643\) −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
\(645\) −16.0885 + 6.90468i −0.633485 + 0.271872i
\(646\) −3.08715 −0.121462
\(647\) 5.87644 5.87644i 0.231027 0.231027i −0.582094 0.813121i \(-0.697767\pi\)
0.813121 + 0.582094i \(0.197767\pi\)
\(648\) −4.76187 + 7.63705i −0.187064 + 0.300012i
\(649\) 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 0.824296 0.566159i \(-0.191571\pi\)
−0.566159 + 0.824296i \(0.691571\pi\)
\(654\) −12.2518 4.27519i −0.479084 0.167173i
\(655\) −30.5955 + 27.9999i −1.19547 + 1.09405i
\(656\) 6.08532i 0.237592i
\(657\) −1.22396 10.6965i −0.0477514 0.417311i
\(658\) 1.83020 1.83020i 0.0713487 0.0713487i
\(659\) −26.7046 −1.04026 −0.520132 0.854086i \(-0.674117\pi\)
−0.520132 + 0.854086i \(0.674117\pi\)
\(660\) −3.39618 1.35648i −0.132196 0.0528010i
\(661\) −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
\(663\) 15.9762 + 33.1016i 0.620465 + 1.28556i
\(664\) 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
\(672\) 0.676500 0.326507i 0.0260965 0.0125953i
\(673\) 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
\(675\) −24.7397 7.93405i −0.952230 0.305382i
\(676\) −34.2502 −1.31732
\(677\) −35.0885 + 35.0885i −1.34856 + 1.34856i −0.461331 + 0.887228i \(0.652628\pi\)
−0.887228 + 0.461331i \(0.847372\pi\)
\(678\) 26.0815 12.5880i 1.00165 0.483440i
\(679\) 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 0.951201 0.308572i \(-0.0998512\pi\)
−0.308572 + 0.951201i \(0.599851\pi\)
\(684\) 1.86641 2.34873i 0.0713638 0.0898059i
\(685\) 7.02125 + 0.311023i 0.268268 + 0.0118836i
\(686\) 5.99007i 0.228702i
\(687\) −16.3124 33.7983i −0.622358 1.28948i
\(688\) 3.19643 3.19643i 0.121863 0.121863i
\(689\) −49.4059 −1.88221
\(690\) −25.4436 10.1626i −0.968622 0.386882i
\(691\) −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
\(693\) −0.139665 1.22056i −0.00530543 0.0463654i
\(694\) 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 \(0.268876\pi\)
−0.663957 + 0.747771i \(0.731124\pi\)
\(702\) −34.8427 7.85749i −1.31505 0.296562i
\(703\) 3.09818 3.09818i 0.116850 0.116850i
\(704\) 0.944248 0.0355877
\(705\) 21.2408 9.11590i 0.799976 0.343325i
\(706\) 12.5368 0.471829
\(707\) −0.508493 + 0.508493i −0.0191238 + 0.0191238i
\(708\) −5.66823 11.7442i −0.213025 0.441373i
\(709\) 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
\(717\) 18.1059 8.73865i 0.676176 0.326351i
\(718\) 7.62533 7.62533i 0.284575 0.284575i
\(719\) 34.6703 1.29298 0.646491 0.762921i \(-0.276236\pi\)
0.646491 + 0.762921i \(0.276236\pi\)
\(720\) 6.69193 0.466933i 0.249394 0.0174016i
\(721\) −1.03816 −0.0386632
\(722\) −0.707107 + 0.707107i −0.0263158 + 0.0263158i
\(723\) −32.2732 + 15.5764i −1.20025 + 0.579293i
\(724\) 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
\(732\) 3.41413 + 7.07384i 0.126190 + 0.261457i
\(733\) −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
\(735\) 9.78583 24.5004i 0.360956 0.903711i
\(736\) 7.07416 0.260757
\(737\) 7.22413 7.22413i 0.266104 0.266104i
\(738\) 18.1376 2.07542i 0.667655 0.0763974i
\(739\) 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 0.746915 0.664920i \(-0.231534\pi\)
−0.664920 + 0.746915i \(0.731534\pi\)
\(744\) −17.9173 6.25213i −0.656880 0.229214i
\(745\) 19.5623 + 21.3758i 0.716708 + 0.783148i
\(746\) 6.60357i 0.241774i
\(747\) −33.0806 + 3.78530i −1.21036 + 0.138497i
\(748\) 2.06124 2.06124i 0.0753665 0.0753665i
\(749\) −4.55565 −0.166460
\(750\) 6.03379 + 18.4009i 0.220323 + 0.671906i
\(751\) −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
\(753\) −11.7144 24.2714i −0.426895 0.884498i
\(754\) 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 \(0.116259\pi\)
−0.934039 + 0.357171i \(0.883741\pi\)
\(762\) −3.14876 + 1.51972i −0.114067 + 0.0550537i
\(763\) −2.29749 + 2.29749i −0.0831746 + 0.0831746i
\(764\) −3.21978 −0.116487
\(765\) 13.5889 15.6274i 0.491306 0.565011i
\(766\) −28.0358 −1.01297
\(767\) 36.5949 36.5949i 1.32136 1.32136i
\(768\) −1.55987 + 0.752859i −0.0562871 + 0.0271665i
\(769\) 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 0.504197 0.863589i \(-0.331789\pi\)
−0.863589 + 0.504197i \(0.831789\pi\)
\(774\) 10.6173 + 8.43697i 0.381630 + 0.303260i
\(775\) 4.84383 54.5667i 0.173995 1.96009i
\(776\) 1.02244i 0.0367034i
\(777\) 1.43059 + 2.96408i 0.0513220 + 0.106336i