Properties

Label 105.2.j.a.92.7
Level 105
Weight 2
Character 105.92
Analytic conductor 0.838
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 92.7
Character \(\chi\) = 105.92
Dual form 105.2.j.a.8.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.260263 - 0.260263i) q^{2} +(0.826909 + 1.52191i) q^{3} +1.86453i q^{4} +(-0.895238 - 2.04904i) q^{5} +(0.611312 + 0.180884i) q^{6} +(0.707107 + 0.707107i) q^{7} +(1.00579 + 1.00579i) q^{8} +(-1.63244 + 2.51697i) q^{9} +O(q^{10})\) \(q+(0.260263 - 0.260263i) q^{2} +(0.826909 + 1.52191i) q^{3} +1.86453i q^{4} +(-0.895238 - 2.04904i) q^{5} +(0.611312 + 0.180884i) q^{6} +(0.707107 + 0.707107i) q^{7} +(1.00579 + 1.00579i) q^{8} +(-1.63244 + 2.51697i) q^{9} +(-0.766286 - 0.300291i) q^{10} -3.38750i q^{11} +(-2.83765 + 1.54179i) q^{12} +(1.59420 - 1.59420i) q^{13} +0.368068 q^{14} +(2.37818 - 3.05684i) q^{15} -3.20551 q^{16} +(0.140684 - 0.140684i) q^{17} +(0.230209 + 1.07994i) q^{18} -7.34691i q^{19} +(3.82048 - 1.66919i) q^{20} +(-0.491443 + 1.66087i) q^{21} +(-0.881641 - 0.881641i) q^{22} +(2.21444 + 2.21444i) q^{23} +(-0.699032 + 2.36243i) q^{24} +(-3.39710 + 3.66875i) q^{25} -0.829822i q^{26} +(-5.18049 - 0.403134i) q^{27} +(-1.31842 + 1.31842i) q^{28} -9.49165 q^{29} +(-0.176632 - 1.41454i) q^{30} +0.922582 q^{31} +(-2.84586 + 2.84586i) q^{32} +(5.15548 - 2.80115i) q^{33} -0.0732300i q^{34} +(0.815859 - 2.08192i) q^{35} +(-4.69295 - 3.04373i) q^{36} +(5.91558 + 5.91558i) q^{37} +(-1.91213 - 1.91213i) q^{38} +(3.74449 + 1.10797i) q^{39} +(1.16048 - 2.96133i) q^{40} +1.39256i q^{41} +(0.304359 + 0.560167i) q^{42} +(0.864526 - 0.864526i) q^{43} +6.31608 q^{44} +(6.61878 + 1.09165i) q^{45} +1.15267 q^{46} +(0.651346 - 0.651346i) q^{47} +(-2.65066 - 4.87851i) q^{48} +1.00000i q^{49} +(0.0707006 + 1.83898i) q^{50} +(0.330443 + 0.0977764i) q^{51} +(2.97242 + 2.97242i) q^{52} +(6.54108 + 6.54108i) q^{53} +(-1.45321 + 1.24337i) q^{54} +(-6.94110 + 3.03262i) q^{55} +1.42241i q^{56} +(11.1814 - 6.07522i) q^{57} +(-2.47033 + 2.47033i) q^{58} -6.25032 q^{59} +(5.69956 + 4.43417i) q^{60} +1.83261 q^{61} +(0.240114 - 0.240114i) q^{62} +(-2.93408 + 0.625454i) q^{63} -4.92967i q^{64} +(-4.69375 - 1.83938i) q^{65} +(0.612745 - 2.07082i) q^{66} +(-0.815500 - 0.815500i) q^{67} +(0.262310 + 0.262310i) q^{68} +(-1.53904 + 5.20132i) q^{69} +(-0.329508 - 0.754184i) q^{70} +9.77651i q^{71} +(-4.17345 + 0.889650i) q^{72} +(-4.80768 + 4.80768i) q^{73} +3.07921 q^{74} +(-8.39261 - 2.13637i) q^{75} +13.6985 q^{76} +(2.39532 - 2.39532i) q^{77} +(1.26292 - 0.686187i) q^{78} -3.41711i q^{79} +(2.86969 + 6.56821i) q^{80} +(-3.67026 - 8.21761i) q^{81} +(0.362432 + 0.362432i) q^{82} +(-6.26911 - 6.26911i) q^{83} +(-3.09673 - 0.916307i) q^{84} +(-0.414214 - 0.162321i) q^{85} -0.450009i q^{86} +(-7.84873 - 14.4455i) q^{87} +(3.40712 - 3.40712i) q^{88} +12.3767 q^{89} +(2.00674 - 1.43851i) q^{90} +2.25454 q^{91} +(-4.12888 + 4.12888i) q^{92} +(0.762891 + 1.40409i) q^{93} -0.339043i q^{94} +(-15.0541 + 6.57723i) q^{95} +(-6.68443 - 1.97789i) q^{96} +(-6.71326 - 6.71326i) q^{97} +(0.260263 + 0.260263i) q^{98} +(8.52622 + 5.52990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 4q^{3} + O(q^{10}) \) \( 24q - 4q^{3} - 16q^{10} + 16q^{12} - 8q^{13} - 16q^{15} - 16q^{16} - 20q^{18} + 4q^{21} + 8q^{22} - 16q^{25} - 16q^{27} + 20q^{30} + 28q^{33} + 16q^{36} - 16q^{37} + 64q^{40} - 20q^{42} - 40q^{43} + 20q^{45} - 64q^{46} + 16q^{48} - 20q^{51} + 40q^{55} + 4q^{57} + 40q^{58} + 32q^{60} + 32q^{61} - 8q^{63} - 16q^{66} + 24q^{67} - 8q^{70} - 8q^{72} + 32q^{73} - 60q^{75} + 32q^{76} + 60q^{78} + 52q^{81} - 80q^{82} + 24q^{85} + 4q^{87} + 96q^{88} - 24q^{90} - 24q^{91} - 76q^{93} - 96q^{96} + 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.260263 0.260263i 0.184034 0.184034i −0.609077 0.793111i \(-0.708460\pi\)
0.793111 + 0.609077i \(0.208460\pi\)
\(3\) 0.826909 + 1.52191i 0.477416 + 0.878677i
\(4\) 1.86453i 0.932263i
\(5\) −0.895238 2.04904i −0.400362 0.916357i
\(6\) 0.611312 + 0.180884i 0.249567 + 0.0738457i
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) 1.00579 + 1.00579i 0.355602 + 0.355602i
\(9\) −1.63244 + 2.51697i −0.544148 + 0.838989i
\(10\) −0.766286 0.300291i −0.242321 0.0949605i
\(11\) 3.38750i 1.02137i −0.859768 0.510684i \(-0.829392\pi\)
0.859768 0.510684i \(-0.170608\pi\)
\(12\) −2.83765 + 1.54179i −0.819158 + 0.445077i
\(13\) 1.59420 1.59420i 0.442151 0.442151i −0.450583 0.892734i \(-0.648784\pi\)
0.892734 + 0.450583i \(0.148784\pi\)
\(14\) 0.368068 0.0983703
\(15\) 2.37818 3.05684i 0.614042 0.789273i
\(16\) −3.20551 −0.801377
\(17\) 0.140684 0.140684i 0.0341210 0.0341210i −0.689840 0.723961i \(-0.742319\pi\)
0.723961 + 0.689840i \(0.242319\pi\)
\(18\) 0.230209 + 1.07994i 0.0542609 + 0.254544i
\(19\) 7.34691i 1.68550i −0.538308 0.842748i \(-0.680936\pi\)
0.538308 0.842748i \(-0.319064\pi\)
\(20\) 3.82048 1.66919i 0.854286 0.373243i
\(21\) −0.491443 + 1.66087i −0.107242 + 0.362431i
\(22\) −0.881641 0.881641i −0.187966 0.187966i
\(23\) 2.21444 + 2.21444i 0.461742 + 0.461742i 0.899226 0.437484i \(-0.144130\pi\)
−0.437484 + 0.899226i \(0.644130\pi\)
\(24\) −0.699032 + 2.36243i −0.142689 + 0.482229i
\(25\) −3.39710 + 3.66875i −0.679420 + 0.733750i
\(26\) 0.829822i 0.162741i
\(27\) −5.18049 0.403134i −0.996986 0.0775831i
\(28\) −1.31842 + 1.31842i −0.249158 + 0.249158i
\(29\) −9.49165 −1.76256 −0.881278 0.472598i \(-0.843316\pi\)
−0.881278 + 0.472598i \(0.843316\pi\)
\(30\) −0.176632 1.41454i −0.0322484 0.258258i
\(31\) 0.922582 0.165701 0.0828503 0.996562i \(-0.473598\pi\)
0.0828503 + 0.996562i \(0.473598\pi\)
\(32\) −2.84586 + 2.84586i −0.503083 + 0.503083i
\(33\) 5.15548 2.80115i 0.897454 0.487618i
\(34\) 0.0732300i 0.0125588i
\(35\) 0.815859 2.08192i 0.137905 0.351908i
\(36\) −4.69295 3.04373i −0.782159 0.507289i
\(37\) 5.91558 + 5.91558i 0.972515 + 0.972515i 0.999632 0.0271173i \(-0.00863275\pi\)
−0.0271173 + 0.999632i \(0.508633\pi\)
\(38\) −1.91213 1.91213i −0.310188 0.310188i
\(39\) 3.74449 + 1.10797i 0.599598 + 0.177418i
\(40\) 1.16048 2.96133i 0.183489 0.468228i
\(41\) 1.39256i 0.217481i 0.994070 + 0.108741i \(0.0346818\pi\)
−0.994070 + 0.108741i \(0.965318\pi\)
\(42\) 0.304359 + 0.560167i 0.0469636 + 0.0864357i
\(43\) 0.864526 0.864526i 0.131839 0.131839i −0.638108 0.769947i \(-0.720283\pi\)
0.769947 + 0.638108i \(0.220283\pi\)
\(44\) 6.31608 0.952184
\(45\) 6.61878 + 1.09165i 0.986670 + 0.162734i
\(46\) 1.15267 0.169952
\(47\) 0.651346 0.651346i 0.0950085 0.0950085i −0.658005 0.753014i \(-0.728599\pi\)
0.753014 + 0.658005i \(0.228599\pi\)
\(48\) −2.65066 4.87851i −0.382591 0.704152i
\(49\) 1.00000i 0.142857i
\(50\) 0.0707006 + 1.83898i 0.00999858 + 0.260071i
\(51\) 0.330443 + 0.0977764i 0.0462713 + 0.0136914i
\(52\) 2.97242 + 2.97242i 0.412201 + 0.412201i
\(53\) 6.54108 + 6.54108i 0.898486 + 0.898486i 0.995302 0.0968158i \(-0.0308658\pi\)
−0.0968158 + 0.995302i \(0.530866\pi\)
\(54\) −1.45321 + 1.24337i −0.197757 + 0.169201i
\(55\) −6.94110 + 3.03262i −0.935938 + 0.408918i
\(56\) 1.42241i 0.190077i
\(57\) 11.1814 6.07522i 1.48101 0.804683i
\(58\) −2.47033 + 2.47033i −0.324370 + 0.324370i
\(59\) −6.25032 −0.813722 −0.406861 0.913490i \(-0.633377\pi\)
−0.406861 + 0.913490i \(0.633377\pi\)
\(60\) 5.69956 + 4.43417i 0.735810 + 0.572449i
\(61\) 1.83261 0.234642 0.117321 0.993094i \(-0.462569\pi\)
0.117321 + 0.993094i \(0.462569\pi\)
\(62\) 0.240114 0.240114i 0.0304945 0.0304945i
\(63\) −2.93408 + 0.625454i −0.369659 + 0.0787998i
\(64\) 4.92967i 0.616209i
\(65\) −4.69375 1.83938i −0.582189 0.228147i
\(66\) 0.612745 2.07082i 0.0754237 0.254900i
\(67\) −0.815500 0.815500i −0.0996292 0.0996292i 0.655535 0.755165i \(-0.272443\pi\)
−0.755165 + 0.655535i \(0.772443\pi\)
\(68\) 0.262310 + 0.262310i 0.0318097 + 0.0318097i
\(69\) −1.53904 + 5.20132i −0.185279 + 0.626166i
\(70\) −0.329508 0.754184i −0.0393838 0.0901423i
\(71\) 9.77651i 1.16026i 0.814524 + 0.580129i \(0.196998\pi\)
−0.814524 + 0.580129i \(0.803002\pi\)
\(72\) −4.17345 + 0.889650i −0.491846 + 0.104846i
\(73\) −4.80768 + 4.80768i −0.562697 + 0.562697i −0.930073 0.367376i \(-0.880256\pi\)
0.367376 + 0.930073i \(0.380256\pi\)
\(74\) 3.07921 0.357951
\(75\) −8.39261 2.13637i −0.969095 0.246687i
\(76\) 13.6985 1.57133
\(77\) 2.39532 2.39532i 0.272972 0.272972i
\(78\) 1.26292 0.686187i 0.142997 0.0776954i
\(79\) 3.41711i 0.384455i −0.981350 0.192228i \(-0.938429\pi\)
0.981350 0.192228i \(-0.0615712\pi\)
\(80\) 2.86969 + 6.56821i 0.320841 + 0.734348i
\(81\) −3.67026 8.21761i −0.407807 0.913068i
\(82\) 0.362432 + 0.362432i 0.0400239 + 0.0400239i
\(83\) −6.26911 6.26911i −0.688124 0.688124i 0.273693 0.961817i \(-0.411755\pi\)
−0.961817 + 0.273693i \(0.911755\pi\)
\(84\) −3.09673 0.916307i −0.337881 0.0999773i
\(85\) −0.414214 0.162321i −0.0449278 0.0176062i
\(86\) 0.450009i 0.0485257i
\(87\) −7.84873 14.4455i −0.841473 1.54872i
\(88\) 3.40712 3.40712i 0.363201 0.363201i
\(89\) 12.3767 1.31192 0.655962 0.754794i \(-0.272263\pi\)
0.655962 + 0.754794i \(0.272263\pi\)
\(90\) 2.00674 1.43851i 0.211529 0.151632i
\(91\) 2.25454 0.236340
\(92\) −4.12888 + 4.12888i −0.430465 + 0.430465i
\(93\) 0.762891 + 1.40409i 0.0791082 + 0.145597i
\(94\) 0.339043i 0.0349696i
\(95\) −15.0541 + 6.57723i −1.54452 + 0.674809i
\(96\) −6.68443 1.97789i −0.682227 0.201867i
\(97\) −6.71326 6.71326i −0.681628 0.681628i 0.278739 0.960367i \(-0.410084\pi\)
−0.960367 + 0.278739i \(0.910084\pi\)
\(98\) 0.260263 + 0.260263i 0.0262906 + 0.0262906i
\(99\) 8.52622 + 5.52990i 0.856918 + 0.555775i
\(100\) −6.84048 6.33398i −0.684048 0.633398i
\(101\) 12.4523i 1.23905i 0.784976 + 0.619526i \(0.212675\pi\)
−0.784976 + 0.619526i \(0.787325\pi\)
\(102\) 0.111450 0.0605545i 0.0110352 0.00599579i
\(103\) −9.78924 + 9.78924i −0.964563 + 0.964563i −0.999393 0.0348303i \(-0.988911\pi\)
0.0348303 + 0.999393i \(0.488911\pi\)
\(104\) 3.20687 0.314459
\(105\) 3.84314 0.479889i 0.375052 0.0468323i
\(106\) 3.40481 0.330704
\(107\) 5.21866 5.21866i 0.504507 0.504507i −0.408328 0.912835i \(-0.633888\pi\)
0.912835 + 0.408328i \(0.133888\pi\)
\(108\) 0.751653 9.65916i 0.0723279 0.929453i
\(109\) 6.67661i 0.639504i −0.947501 0.319752i \(-0.896400\pi\)
0.947501 0.319752i \(-0.103600\pi\)
\(110\) −1.01724 + 2.59579i −0.0969896 + 0.247499i
\(111\) −4.11135 + 13.8946i −0.390233 + 1.31882i
\(112\) −2.26664 2.26664i −0.214177 0.214177i
\(113\) −8.23451 8.23451i −0.774637 0.774637i 0.204276 0.978913i \(-0.434516\pi\)
−0.978913 + 0.204276i \(0.934516\pi\)
\(114\) 1.32894 4.49125i 0.124467 0.420644i
\(115\) 2.55501 6.51991i 0.238256 0.607985i
\(116\) 17.6974i 1.64317i
\(117\) 1.41011 + 6.61498i 0.130365 + 0.611555i
\(118\) −1.62673 + 1.62673i −0.149752 + 0.149752i
\(119\) 0.198958 0.0182384
\(120\) 5.46651 0.682597i 0.499022 0.0623123i
\(121\) −0.475134 −0.0431940
\(122\) 0.476962 0.476962i 0.0431821 0.0431821i
\(123\) −2.11936 + 1.15152i −0.191096 + 0.103829i
\(124\) 1.72018i 0.154477i
\(125\) 10.5586 + 3.67638i 0.944391 + 0.328825i
\(126\) −0.600850 + 0.926415i −0.0535279 + 0.0825316i
\(127\) 1.88180 + 1.88180i 0.166983 + 0.166983i 0.785652 0.618669i \(-0.212328\pi\)
−0.618669 + 0.785652i \(0.712328\pi\)
\(128\) −6.97474 6.97474i −0.616486 0.616486i
\(129\) 2.03062 + 0.600850i 0.178786 + 0.0529019i
\(130\) −1.70034 + 0.742888i −0.149129 + 0.0651556i
\(131\) 8.97080i 0.783783i −0.920012 0.391891i \(-0.871821\pi\)
0.920012 0.391891i \(-0.128179\pi\)
\(132\) 5.22282 + 9.61252i 0.454588 + 0.836663i
\(133\) 5.19505 5.19505i 0.450468 0.450468i
\(134\) −0.424489 −0.0366703
\(135\) 3.81174 + 10.9759i 0.328062 + 0.944656i
\(136\) 0.282999 0.0242670
\(137\) −6.49538 + 6.49538i −0.554938 + 0.554938i −0.927862 0.372924i \(-0.878355\pi\)
0.372924 + 0.927862i \(0.378355\pi\)
\(138\) 0.953156 + 1.75427i 0.0811380 + 0.149333i
\(139\) 1.83916i 0.155995i 0.996954 + 0.0779976i \(0.0248526\pi\)
−0.996954 + 0.0779976i \(0.975147\pi\)
\(140\) 3.88179 + 1.52119i 0.328071 + 0.128564i
\(141\) 1.52990 + 0.452688i 0.128840 + 0.0381232i
\(142\) 2.54447 + 2.54447i 0.213527 + 0.213527i
\(143\) −5.40034 5.40034i −0.451599 0.451599i
\(144\) 5.23281 8.06817i 0.436068 0.672347i
\(145\) 8.49729 + 19.4487i 0.705661 + 1.61513i
\(146\) 2.50253i 0.207110i
\(147\) −1.52191 + 0.826909i −0.125525 + 0.0682023i
\(148\) −11.0297 + 11.0297i −0.906640 + 0.906640i
\(149\) −0.987227 −0.0808768 −0.0404384 0.999182i \(-0.512875\pi\)
−0.0404384 + 0.999182i \(0.512875\pi\)
\(150\) −2.74031 + 1.62827i −0.223745 + 0.132948i
\(151\) −8.71084 −0.708878 −0.354439 0.935079i \(-0.615328\pi\)
−0.354439 + 0.935079i \(0.615328\pi\)
\(152\) 7.38948 7.38948i 0.599366 0.599366i
\(153\) 0.124439 + 0.583758i 0.0100603 + 0.0471940i
\(154\) 1.24683i 0.100472i
\(155\) −0.825930 1.89040i −0.0663403 0.151841i
\(156\) −2.06585 + 6.98169i −0.165400 + 0.558983i
\(157\) 5.26306 + 5.26306i 0.420038 + 0.420038i 0.885217 0.465179i \(-0.154010\pi\)
−0.465179 + 0.885217i \(0.654010\pi\)
\(158\) −0.889349 0.889349i −0.0707528 0.0707528i
\(159\) −4.54608 + 15.3638i −0.360528 + 1.21843i
\(160\) 8.37901 + 3.28355i 0.662419 + 0.259588i
\(161\) 3.13169i 0.246812i
\(162\) −3.09398 1.18351i −0.243086 0.0929853i
\(163\) 14.1511 14.1511i 1.10840 1.10840i 0.115041 0.993361i \(-0.463300\pi\)
0.993361 0.115041i \(-0.0367000\pi\)
\(164\) −2.59646 −0.202750
\(165\) −10.3550 8.05606i −0.806139 0.627164i
\(166\) −3.26324 −0.253276
\(167\) 17.4876 17.4876i 1.35323 1.35323i 0.471215 0.882018i \(-0.343816\pi\)
0.882018 0.471215i \(-0.156184\pi\)
\(168\) −2.16478 + 1.17620i −0.167017 + 0.0907459i
\(169\) 7.91707i 0.609005i
\(170\) −0.150051 + 0.0655582i −0.0115084 + 0.00502809i
\(171\) 18.4919 + 11.9934i 1.41411 + 0.917159i
\(172\) 1.61193 + 1.61193i 0.122909 + 0.122909i
\(173\) 10.8767 + 10.8767i 0.826942 + 0.826942i 0.987093 0.160150i \(-0.0511979\pi\)
−0.160150 + 0.987093i \(0.551198\pi\)
\(174\) −5.80236 1.71689i −0.439876 0.130157i
\(175\) −4.99631 + 0.192086i −0.377685 + 0.0145203i
\(176\) 10.8587i 0.818502i
\(177\) −5.16844 9.51244i −0.388484 0.714999i
\(178\) 3.22119 3.22119i 0.241439 0.241439i
\(179\) 17.6524 1.31941 0.659703 0.751527i \(-0.270682\pi\)
0.659703 + 0.751527i \(0.270682\pi\)
\(180\) −2.03541 + 12.3409i −0.151710 + 0.919836i
\(181\) −11.9237 −0.886282 −0.443141 0.896452i \(-0.646136\pi\)
−0.443141 + 0.896452i \(0.646136\pi\)
\(182\) 0.586773 0.586773i 0.0434945 0.0434945i
\(183\) 1.51541 + 2.78908i 0.112022 + 0.206175i
\(184\) 4.45454i 0.328393i
\(185\) 6.82538 17.4171i 0.501812 1.28053i
\(186\) 0.563986 + 0.166881i 0.0413534 + 0.0122363i
\(187\) −0.476568 0.476568i −0.0348501 0.0348501i
\(188\) 1.21445 + 1.21445i 0.0885729 + 0.0885729i
\(189\) −3.37810 3.94822i −0.245721 0.287191i
\(190\) −2.20621 + 5.62983i −0.160055 + 0.408431i
\(191\) 17.7849i 1.28687i −0.765501 0.643435i \(-0.777509\pi\)
0.765501 0.643435i \(-0.222491\pi\)
\(192\) 7.50253 4.07639i 0.541449 0.294188i
\(193\) 14.3394 14.3394i 1.03217 1.03217i 0.0327052 0.999465i \(-0.489588\pi\)
0.999465 0.0327052i \(-0.0104123\pi\)
\(194\) −3.49443 −0.250885
\(195\) −1.08193 8.66449i −0.0774783 0.620477i
\(196\) −1.86453 −0.133180
\(197\) −4.10678 + 4.10678i −0.292596 + 0.292596i −0.838105 0.545509i \(-0.816336\pi\)
0.545509 + 0.838105i \(0.316336\pi\)
\(198\) 3.65829 0.779834i 0.259983 0.0554204i
\(199\) 13.4148i 0.950949i −0.879730 0.475474i \(-0.842276\pi\)
0.879730 0.475474i \(-0.157724\pi\)
\(200\) −7.10679 + 0.273224i −0.502526 + 0.0193199i
\(201\) 0.566776 1.91547i 0.0399773 0.135107i
\(202\) 3.24088 + 3.24088i 0.228027 + 0.228027i
\(203\) −6.71161 6.71161i −0.471063 0.471063i
\(204\) −0.182307 + 0.616119i −0.0127640 + 0.0431370i
\(205\) 2.85341 1.24667i 0.199290 0.0870714i
\(206\) 5.09556i 0.355025i
\(207\) −9.18861 + 1.95873i −0.638653 + 0.136141i
\(208\) −5.11022 + 5.11022i −0.354330 + 0.354330i
\(209\) −24.8876 −1.72151
\(210\) 0.875330 1.12512i 0.0604035 0.0776410i
\(211\) 8.11525 0.558677 0.279338 0.960193i \(-0.409885\pi\)
0.279338 + 0.960193i \(0.409885\pi\)
\(212\) −12.1960 + 12.1960i −0.837626 + 0.837626i
\(213\) −14.8790 + 8.08429i −1.01949 + 0.553926i
\(214\) 2.71645i 0.185693i
\(215\) −2.54540 0.997489i −0.173595 0.0680282i
\(216\) −4.80504 5.61598i −0.326941 0.382119i
\(217\) 0.652364 + 0.652364i 0.0442854 + 0.0442854i
\(218\) −1.73768 1.73768i −0.117690 0.117690i
\(219\) −11.2924 3.34136i −0.763069 0.225788i
\(220\) −5.65439 12.9419i −0.381219 0.872541i
\(221\) 0.448558i 0.0301732i
\(222\) 2.54623 + 4.68630i 0.170892 + 0.314524i
\(223\) −11.5431 + 11.5431i −0.772984 + 0.772984i −0.978627 0.205643i \(-0.934072\pi\)
0.205643 + 0.978627i \(0.434072\pi\)
\(224\) −4.02466 −0.268909
\(225\) −3.68856 14.5394i −0.245904 0.969294i
\(226\) −4.28628 −0.285119
\(227\) −7.04578 + 7.04578i −0.467645 + 0.467645i −0.901151 0.433506i \(-0.857276\pi\)
0.433506 + 0.901151i \(0.357276\pi\)
\(228\) 11.3274 + 20.8479i 0.750176 + 1.38069i
\(229\) 4.80117i 0.317270i −0.987337 0.158635i \(-0.949291\pi\)
0.987337 0.158635i \(-0.0507093\pi\)
\(230\) −1.03192 2.36187i −0.0680426 0.155737i
\(231\) 5.62619 + 1.66476i 0.370176 + 0.109533i
\(232\) −9.54665 9.54665i −0.626768 0.626768i
\(233\) 14.2791 + 14.2791i 0.935455 + 0.935455i 0.998040 0.0625851i \(-0.0199345\pi\)
−0.0625851 + 0.998040i \(0.519934\pi\)
\(234\) 2.08864 + 1.35464i 0.136538 + 0.0885554i
\(235\) −1.91774 0.751522i −0.125100 0.0490239i
\(236\) 11.6539i 0.758603i
\(237\) 5.20055 2.82564i 0.337812 0.183545i
\(238\) 0.0517814 0.0517814i 0.00335649 0.00335649i
\(239\) 12.8618 0.831961 0.415981 0.909373i \(-0.363438\pi\)
0.415981 + 0.909373i \(0.363438\pi\)
\(240\) −7.62327 + 9.79873i −0.492080 + 0.632506i
\(241\) −16.1856 −1.04261 −0.521304 0.853371i \(-0.674554\pi\)
−0.521304 + 0.853371i \(0.674554\pi\)
\(242\) −0.123660 + 0.123660i −0.00794917 + 0.00794917i
\(243\) 9.47153 12.3810i 0.607599 0.794244i
\(244\) 3.41696i 0.218748i
\(245\) 2.04904 0.895238i 0.130908 0.0571946i
\(246\) −0.251892 + 0.851289i −0.0160601 + 0.0542762i
\(247\) −11.7124 11.7124i −0.745243 0.745243i
\(248\) 0.927928 + 0.927928i 0.0589235 + 0.0589235i
\(249\) 4.35706 14.7250i 0.276117 0.933160i
\(250\) 3.70484 1.79119i 0.234315 0.113285i
\(251\) 8.02862i 0.506762i 0.967367 + 0.253381i \(0.0815426\pi\)
−0.967367 + 0.253381i \(0.918457\pi\)
\(252\) −1.16618 5.47066i −0.0734621 0.344619i
\(253\) 7.50140 7.50140i 0.471609 0.471609i
\(254\) 0.979525 0.0614609
\(255\) −0.0954776 0.764622i −0.00597904 0.0478825i
\(256\) 6.22880 0.389300
\(257\) −16.6108 + 16.6108i −1.03615 + 1.03615i −0.0368323 + 0.999321i \(0.511727\pi\)
−0.999321 + 0.0368323i \(0.988273\pi\)
\(258\) 0.684874 0.372116i 0.0426384 0.0231669i
\(259\) 8.36589i 0.519831i
\(260\) 3.42958 8.75163i 0.212693 0.542753i
\(261\) 15.4946 23.8902i 0.959091 1.47877i
\(262\) −2.33477 2.33477i −0.144243 0.144243i
\(263\) 13.8361 + 13.8361i 0.853173 + 0.853173i 0.990523 0.137350i \(-0.0438584\pi\)
−0.137350 + 0.990523i \(0.543858\pi\)
\(264\) 8.00273 + 2.36797i 0.492534 + 0.145738i
\(265\) 7.54709 19.2587i 0.463614 1.18305i
\(266\) 2.70416i 0.165803i
\(267\) 10.2344 + 18.8362i 0.626334 + 1.15276i
\(268\) 1.52052 1.52052i 0.0928806 0.0928806i
\(269\) −11.4632 −0.698925 −0.349463 0.936950i \(-0.613636\pi\)
−0.349463 + 0.936950i \(0.613636\pi\)
\(270\) 3.84868 + 1.86457i 0.234223 + 0.113474i
\(271\) 8.42276 0.511646 0.255823 0.966724i \(-0.417654\pi\)
0.255823 + 0.966724i \(0.417654\pi\)
\(272\) −0.450965 + 0.450965i −0.0273438 + 0.0273438i
\(273\) 1.86430 + 3.43121i 0.112832 + 0.207666i
\(274\) 3.38102i 0.204255i
\(275\) 12.4279 + 11.5077i 0.749429 + 0.693938i
\(276\) −9.69800 2.86959i −0.583751 0.172729i
\(277\) 12.7307 + 12.7307i 0.764914 + 0.764914i 0.977206 0.212293i \(-0.0680930\pi\)
−0.212293 + 0.977206i \(0.568093\pi\)
\(278\) 0.478665 + 0.478665i 0.0287084 + 0.0287084i
\(279\) −1.50606 + 2.32211i −0.0901656 + 0.139021i
\(280\) 2.91456 1.27339i 0.174179 0.0760998i
\(281\) 4.41251i 0.263228i −0.991301 0.131614i \(-0.957984\pi\)
0.991301 0.131614i \(-0.0420160\pi\)
\(282\) 0.515994 0.280357i 0.0307270 0.0166950i
\(283\) 2.07246 2.07246i 0.123195 0.123195i −0.642821 0.766016i \(-0.722236\pi\)
0.766016 + 0.642821i \(0.222236\pi\)
\(284\) −18.2286 −1.08167
\(285\) −22.4583 17.4722i −1.33032 1.03497i
\(286\) −2.81102 −0.166219
\(287\) −0.984688 + 0.984688i −0.0581243 + 0.0581243i
\(288\) −2.51724 11.8087i −0.148330 0.695832i
\(289\) 16.9604i 0.997672i
\(290\) 7.27332 + 2.85026i 0.427104 + 0.167373i
\(291\) 4.66575 15.7683i 0.273511 0.924352i
\(292\) −8.96405 8.96405i −0.524581 0.524581i
\(293\) 7.37595 + 7.37595i 0.430908 + 0.430908i 0.888937 0.458029i \(-0.151445\pi\)
−0.458029 + 0.888937i \(0.651445\pi\)
\(294\) −0.180884 + 0.611312i −0.0105494 + 0.0356525i
\(295\) 5.59552 + 12.8071i 0.325784 + 0.745660i
\(296\) 11.8997i 0.691656i
\(297\) −1.36561 + 17.5489i −0.0792410 + 1.01829i
\(298\) −0.256939 + 0.256939i −0.0148841 + 0.0148841i
\(299\) 7.06050 0.408319
\(300\) 3.98332 15.6482i 0.229977 0.903452i
\(301\) 1.22262 0.0704709
\(302\) −2.26711 + 2.26711i −0.130458 + 0.130458i
\(303\) −18.9513 + 10.2969i −1.08873 + 0.591543i
\(304\) 23.5506i 1.35072i
\(305\) −1.64063 3.75509i −0.0939420 0.215016i
\(306\) 0.184318 + 0.119544i 0.0105367 + 0.00683386i
\(307\) 11.3608 + 11.3608i 0.648396 + 0.648396i 0.952605 0.304209i \(-0.0983922\pi\)
−0.304209 + 0.952605i \(0.598392\pi\)
\(308\) 4.46614 + 4.46614i 0.254482 + 0.254482i
\(309\) −22.9932 6.80357i −1.30804 0.387042i
\(310\) −0.706962 0.277043i −0.0401527 0.0157350i
\(311\) 8.94291i 0.507106i −0.967322 0.253553i \(-0.918401\pi\)
0.967322 0.253553i \(-0.0815992\pi\)
\(312\) 2.65179 + 4.88058i 0.150128 + 0.276308i
\(313\) 4.52473 4.52473i 0.255753 0.255753i −0.567571 0.823324i \(-0.692117\pi\)
0.823324 + 0.567571i \(0.192117\pi\)
\(314\) 2.73956 0.154602
\(315\) 3.90827 + 5.45210i 0.220206 + 0.307191i
\(316\) 6.37130 0.358414
\(317\) −1.78453 + 1.78453i −0.100229 + 0.100229i −0.755443 0.655214i \(-0.772578\pi\)
0.655214 + 0.755443i \(0.272578\pi\)
\(318\) 2.81546 + 5.18182i 0.157883 + 0.290582i
\(319\) 32.1529i 1.80022i
\(320\) −10.1011 + 4.41323i −0.564667 + 0.246707i
\(321\) 12.2577 + 3.62699i 0.684158 + 0.202439i
\(322\) 0.815063 + 0.815063i 0.0454217 + 0.0454217i
\(323\) −1.03360 1.03360i −0.0575108 0.0575108i
\(324\) 15.3220 6.84330i 0.851220 0.380183i
\(325\) 0.433064 + 11.2644i 0.0240221 + 0.624834i
\(326\) 7.36604i 0.407967i
\(327\) 10.1612 5.52095i 0.561917 0.305309i
\(328\) −1.40063 + 1.40063i −0.0773368 + 0.0773368i
\(329\) 0.921142 0.0507842
\(330\) −4.79173 + 0.598339i −0.263776 + 0.0329375i
\(331\) −3.61857 −0.198895 −0.0994474 0.995043i \(-0.531707\pi\)
−0.0994474 + 0.995043i \(0.531707\pi\)
\(332\) 11.6889 11.6889i 0.641512 0.641512i
\(333\) −24.5462 + 5.23248i −1.34512 + 0.286738i
\(334\) 9.10277i 0.498082i
\(335\) −0.940923 + 2.40106i −0.0514081 + 0.131184i
\(336\) 1.57532 5.32393i 0.0859410 0.290444i
\(337\) −17.0941 17.0941i −0.931175 0.931175i 0.0666042 0.997779i \(-0.478784\pi\)
−0.997779 + 0.0666042i \(0.978784\pi\)
\(338\) 2.06052 + 2.06052i 0.112078 + 0.112078i
\(339\) 5.72302 19.3414i 0.310832 1.05048i
\(340\) 0.302653 0.772312i 0.0164136 0.0418845i
\(341\) 3.12524i 0.169241i
\(342\) 7.93421 1.69133i 0.429033 0.0914565i
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) 1.73907 0.0937644
\(345\) 12.0355 1.50286i 0.647970 0.0809113i
\(346\) 5.66162 0.304371
\(347\) 5.48573 5.48573i 0.294489 0.294489i −0.544361 0.838851i \(-0.683228\pi\)
0.838851 + 0.544361i \(0.183228\pi\)
\(348\) 26.9340 14.6342i 1.44381 0.784474i
\(349\) 14.8272i 0.793681i −0.917888 0.396841i \(-0.870107\pi\)
0.917888 0.396841i \(-0.129893\pi\)
\(350\) −1.25036 + 1.35035i −0.0668347 + 0.0721792i
\(351\) −8.90140 + 7.61605i −0.475122 + 0.406515i
\(352\) 9.64036 + 9.64036i 0.513833 + 0.513833i
\(353\) 7.55570 + 7.55570i 0.402149 + 0.402149i 0.878990 0.476841i \(-0.158218\pi\)
−0.476841 + 0.878990i \(0.658218\pi\)
\(354\) −3.82089 1.13058i −0.203078 0.0600898i
\(355\) 20.0324 8.75231i 1.06321 0.464524i
\(356\) 23.0766i 1.22306i
\(357\) 0.164520 + 0.302797i 0.00870732 + 0.0160257i
\(358\) 4.59428 4.59428i 0.242815 0.242815i
\(359\) −6.09504 −0.321684 −0.160842 0.986980i \(-0.551421\pi\)
−0.160842 + 0.986980i \(0.551421\pi\)
\(360\) 5.55916 + 7.75511i 0.292993 + 0.408730i
\(361\) −34.9770 −1.84090
\(362\) −3.10330 + 3.10330i −0.163106 + 0.163106i
\(363\) −0.392893 0.723114i −0.0206215 0.0379536i
\(364\) 4.20364i 0.220331i
\(365\) 14.1551 + 5.54710i 0.740913 + 0.290348i
\(366\) 1.12030 + 0.331491i 0.0585590 + 0.0173273i
\(367\) 3.52753 + 3.52753i 0.184136 + 0.184136i 0.793155 0.609019i \(-0.208437\pi\)
−0.609019 + 0.793155i \(0.708437\pi\)
\(368\) −7.09840 7.09840i −0.370030 0.370030i
\(369\) −3.50503 2.27327i −0.182465 0.118342i
\(370\) −2.75663 6.30942i −0.143310 0.328011i
\(371\) 9.25048i 0.480261i
\(372\) −2.61796 + 1.42243i −0.135735 + 0.0737496i
\(373\) −7.07089 + 7.07089i −0.366117 + 0.366117i −0.866059 0.499942i \(-0.833355\pi\)
0.499942 + 0.866059i \(0.333355\pi\)
\(374\) −0.248066 −0.0128272
\(375\) 3.13588 + 19.1093i 0.161936 + 0.986801i
\(376\) 1.31024 0.0675704
\(377\) −15.1316 + 15.1316i −0.779315 + 0.779315i
\(378\) −1.90677 0.148381i −0.0980738 0.00763187i
\(379\) 21.4715i 1.10292i −0.834202 0.551459i \(-0.814071\pi\)
0.834202 0.551459i \(-0.185929\pi\)
\(380\) −12.2634 28.0687i −0.629100 1.43989i
\(381\) −1.30786 + 4.42001i −0.0670036 + 0.226444i
\(382\) −4.62875 4.62875i −0.236828 0.236828i
\(383\) −14.6559 14.6559i −0.748882 0.748882i 0.225388 0.974269i \(-0.427635\pi\)
−0.974269 + 0.225388i \(0.927635\pi\)
\(384\) 4.84748 16.3824i 0.247372 0.836012i
\(385\) −7.05248 2.76372i −0.359428 0.140852i
\(386\) 7.46402i 0.379909i
\(387\) 0.764695 + 3.58727i 0.0388716 + 0.182351i
\(388\) 12.5170 12.5170i 0.635457 0.635457i
\(389\) 13.6323 0.691185 0.345592 0.938385i \(-0.387678\pi\)
0.345592 + 0.938385i \(0.387678\pi\)
\(390\) −2.53663 1.97346i −0.128447 0.0999302i
\(391\) 0.623074 0.0315102
\(392\) −1.00579 + 1.00579i −0.0508003 + 0.0508003i
\(393\) 13.6528 7.41804i 0.688692 0.374190i
\(394\) 2.13769i 0.107695i
\(395\) −7.00179 + 3.05913i −0.352298 + 0.153922i
\(396\) −10.3106 + 15.8974i −0.518129 + 0.798873i
\(397\) −24.5632 24.5632i −1.23279 1.23279i −0.962886 0.269907i \(-0.913007\pi\)
−0.269907 0.962886i \(-0.586993\pi\)
\(398\) −3.49137 3.49137i −0.175007 0.175007i
\(399\) 12.2022 + 3.61058i 0.610876 + 0.180755i
\(400\) 10.8894 11.7602i 0.544472 0.588011i
\(401\) 15.5011i 0.774088i 0.922061 + 0.387044i \(0.126504\pi\)
−0.922061 + 0.387044i \(0.873496\pi\)
\(402\) −0.351014 0.646036i −0.0175070 0.0322214i
\(403\) 1.47078 1.47078i 0.0732647 0.0732647i
\(404\) −23.2177 −1.15512
\(405\) −13.5524 + 14.8772i −0.673426 + 0.739255i
\(406\) −3.49357 −0.173383
\(407\) 20.0390 20.0390i 0.993296 0.993296i
\(408\) 0.234015 + 0.430700i 0.0115854 + 0.0213228i
\(409\) 32.0414i 1.58434i 0.610298 + 0.792172i \(0.291050\pi\)
−0.610298 + 0.792172i \(0.708950\pi\)
\(410\) 0.418174 1.06710i 0.0206521 0.0527003i
\(411\) −15.2565 4.51432i −0.752547 0.222675i
\(412\) −18.2523 18.2523i −0.899226 0.899226i
\(413\) −4.41964 4.41964i −0.217476 0.217476i
\(414\) −1.88167 + 2.90124i −0.0924792 + 0.142588i
\(415\) −7.23329 + 18.4580i −0.355068 + 0.906066i
\(416\) 9.07374i 0.444877i
\(417\) −2.79904 + 1.52081i −0.137069 + 0.0744746i
\(418\) −6.47733 + 6.47733i −0.316817 + 0.316817i
\(419\) −5.95062 −0.290707 −0.145353 0.989380i \(-0.546432\pi\)
−0.145353 + 0.989380i \(0.546432\pi\)
\(420\) 0.894765 + 7.16563i 0.0436600 + 0.349647i
\(421\) −10.6388 −0.518504 −0.259252 0.965810i \(-0.583476\pi\)
−0.259252 + 0.965810i \(0.583476\pi\)
\(422\) 2.11210 2.11210i 0.102816 0.102816i
\(423\) 0.576132 + 2.70270i 0.0280125 + 0.131410i
\(424\) 13.1580i 0.639007i
\(425\) 0.0382170 + 0.994055i 0.00185380 + 0.0482187i
\(426\) −1.76842 + 5.97650i −0.0856801 + 0.289563i
\(427\) 1.29585 + 1.29585i 0.0627108 + 0.0627108i
\(428\) 9.73032 + 9.73032i 0.470333 + 0.470333i
\(429\) 3.75326 12.6844i 0.181209 0.612410i
\(430\) −0.922084 + 0.402865i −0.0444668 + 0.0194279i
\(431\) 11.2739i 0.543045i 0.962432 + 0.271523i \(0.0875271\pi\)
−0.962432 + 0.271523i \(0.912473\pi\)
\(432\) 16.6061 + 1.29225i 0.798962 + 0.0621733i
\(433\) 9.75098 9.75098i 0.468602 0.468602i −0.432859 0.901462i \(-0.642495\pi\)
0.901462 + 0.432859i \(0.142495\pi\)
\(434\) 0.339573 0.0163000
\(435\) −22.5728 + 29.0145i −1.08228 + 1.39114i
\(436\) 12.4487 0.596185
\(437\) 16.2693 16.2693i 0.778265 0.778265i
\(438\) −3.80863 + 2.06936i −0.181983 + 0.0988779i
\(439\) 28.4375i 1.35725i −0.734485 0.678625i \(-0.762576\pi\)
0.734485 0.678625i \(-0.237424\pi\)
\(440\) −10.0315 3.93113i −0.478233 0.187409i
\(441\) −2.51697 1.63244i −0.119856 0.0777354i
\(442\) −0.116743 0.116743i −0.00555290 0.00555290i
\(443\) −19.2121 19.2121i −0.912796 0.912796i 0.0836955 0.996491i \(-0.473328\pi\)
−0.996491 + 0.0836955i \(0.973328\pi\)
\(444\) −25.9069 7.66573i −1.22949 0.363799i
\(445\) −11.0801 25.3602i −0.525245 1.20219i
\(446\) 6.00850i 0.284511i
\(447\) −0.816347 1.50247i −0.0386119 0.0710646i
\(448\) 3.48580 3.48580i 0.164689 0.164689i
\(449\) −2.40628 −0.113559 −0.0567796 0.998387i \(-0.518083\pi\)
−0.0567796 + 0.998387i \(0.518083\pi\)
\(450\) −4.74407 2.82408i −0.223638 0.133128i
\(451\) 4.71729 0.222129
\(452\) 15.3534 15.3534i 0.722166 0.722166i
\(453\) −7.20307 13.2572i −0.338430 0.622875i
\(454\) 3.66752i 0.172125i
\(455\) −2.01835 4.61963i −0.0946215 0.216571i
\(456\) 17.3566 + 5.13572i 0.812796 + 0.240502i
\(457\) 6.21588 + 6.21588i 0.290767 + 0.290767i 0.837383 0.546617i \(-0.184084\pi\)
−0.546617 + 0.837383i \(0.684084\pi\)
\(458\) −1.24957 1.24957i −0.0583884 0.0583884i
\(459\) −0.785529 + 0.672100i −0.0366654 + 0.0313709i
\(460\) 12.1565 + 4.76389i 0.566802 + 0.222118i
\(461\) 35.4227i 1.64980i −0.565278 0.824900i \(-0.691231\pi\)
0.565278 0.824900i \(-0.308769\pi\)
\(462\) 1.89757 1.03101i 0.0882827 0.0479671i
\(463\) −20.0869 + 20.0869i −0.933519 + 0.933519i −0.997924 0.0644045i \(-0.979485\pi\)
0.0644045 + 0.997924i \(0.479485\pi\)
\(464\) 30.4256 1.41247
\(465\) 2.19406 2.82019i 0.101747 0.130783i
\(466\) 7.43265 0.344311
\(467\) −5.80567 + 5.80567i −0.268654 + 0.268654i −0.828558 0.559903i \(-0.810838\pi\)
0.559903 + 0.828558i \(0.310838\pi\)
\(468\) −12.3338 + 2.62918i −0.570130 + 0.121534i
\(469\) 1.15329i 0.0532540i
\(470\) −0.694711 + 0.303524i −0.0320446 + 0.0140005i
\(471\) −3.65785 + 12.3620i −0.168545 + 0.569610i
\(472\) −6.28653 6.28653i −0.289361 0.289361i
\(473\) −2.92858 2.92858i −0.134656 0.134656i
\(474\) 0.618102 2.08892i 0.0283904 0.0959475i
\(475\) 26.9540 + 24.9582i 1.23673 + 1.14516i
\(476\) 0.370962i 0.0170030i
\(477\) −27.1416 + 5.78575i −1.24273 + 0.264911i
\(478\) 3.34746 3.34746i 0.153109 0.153109i
\(479\) 40.3829 1.84514 0.922571 0.385828i \(-0.126084\pi\)
0.922571 + 0.385828i \(0.126084\pi\)
\(480\) 1.93139 + 15.4673i 0.0881554 + 0.705984i
\(481\) 18.8612 0.859997
\(482\) −4.21252 + 4.21252i −0.191875 + 0.191875i
\(483\) −4.76616 + 2.58962i −0.216868 + 0.117832i
\(484\) 0.885900i 0.0402682i
\(485\) −7.74575 + 19.7657i −0.351716 + 0.897513i
\(486\) −0.757238 5.68742i −0.0343490 0.257987i
\(487\) 19.7983 + 19.7983i 0.897147 + 0.897147i 0.995183 0.0980363i \(-0.0312561\pi\)
−0.0980363 + 0.995183i \(0.531256\pi\)
\(488\) 1.84323 + 1.84323i 0.0834393 + 0.0834393i
\(489\) 33.2385 + 9.83510i 1.50310 + 0.444759i
\(490\) 0.300291 0.766286i 0.0135658 0.0346173i
\(491\) 36.6924i 1.65590i −0.560798 0.827952i \(-0.689506\pi\)
0.560798 0.827952i \(-0.310494\pi\)
\(492\) −2.14704 3.95159i −0.0967960 0.178152i
\(493\) −1.33533 + 1.33533i −0.0601402 + 0.0601402i
\(494\) −6.09662 −0.274300
\(495\) 3.69796 22.4211i 0.166211 1.00775i
\(496\) −2.95735 −0.132789
\(497\) −6.91304 + 6.91304i −0.310092 + 0.310092i
\(498\) −2.69840 4.96636i −0.120918 0.222548i
\(499\) 7.62548i 0.341363i 0.985326 + 0.170682i \(0.0545970\pi\)
−0.985326 + 0.170682i \(0.945403\pi\)
\(500\) −6.85470 + 19.6868i −0.306551 + 0.880421i
\(501\) 41.0753 + 12.1540i 1.83511 + 0.543000i
\(502\) 2.08955 + 2.08955i 0.0932614 + 0.0932614i
\(503\) −15.7533 15.7533i −0.702406 0.702406i 0.262521 0.964926i \(-0.415446\pi\)
−0.964926 + 0.262521i \(0.915446\pi\)
\(504\) −3.58016 2.32200i −0.159473 0.103430i
\(505\) 25.5152 11.1478i 1.13541 0.496070i
\(506\) 3.90468i 0.173584i
\(507\) −12.0491 + 6.54670i −0.535119 + 0.290749i
\(508\) −3.50866 + 3.50866i −0.155672 + 0.155672i
\(509\) 14.4091 0.638673 0.319336 0.947641i \(-0.396540\pi\)
0.319336 + 0.947641i \(0.396540\pi\)
\(510\) −0.223852 0.174154i −0.00991235 0.00771166i
\(511\) −6.79909 −0.300774
\(512\) 15.5706 15.5706i 0.688130 0.688130i
\(513\) −2.96178 + 38.0606i −0.130766 + 1.68042i
\(514\) 8.64637i 0.381375i
\(515\) 28.8222 + 11.2948i 1.27006 + 0.497709i
\(516\) −1.12030 + 3.78614i −0.0493185 + 0.166676i
\(517\) −2.20643 2.20643i −0.0970387 0.0970387i
\(518\) 2.17733 + 2.17733i 0.0956666 + 0.0956666i
\(519\) −7.55938 + 25.5475i −0.331820 + 1.12141i
\(520\) −2.87091 6.57099i −0.125898 0.288157i
\(521\) 25.3850i 1.11214i −0.831136 0.556069i \(-0.812309\pi\)
0.831136 0.556069i \(-0.187691\pi\)
\(522\) −2.18507 10.2504i −0.0956378 0.448648i
\(523\) −16.0464 + 16.0464i −0.701661 + 0.701661i −0.964767 0.263106i \(-0.915253\pi\)
0.263106 + 0.964767i \(0.415253\pi\)
\(524\) 16.7263 0.730692
\(525\) −4.42383 7.44511i −0.193072 0.324931i
\(526\) 7.20208 0.314026
\(527\) 0.129793 0.129793i 0.00565387 0.00565387i
\(528\) −16.5259 + 8.97912i −0.719199 + 0.390766i
\(529\) 13.1925i 0.573588i
\(530\) −3.04811 6.97657i −0.132401 0.303043i
\(531\) 10.2033 15.7318i 0.442785 0.682704i
\(532\) 9.68630 + 9.68630i 0.419954 + 0.419954i
\(533\) 2.22002 + 2.22002i 0.0961595 + 0.0961595i
\(534\) 7.56601 + 2.23874i 0.327413 + 0.0968799i
\(535\) −15.3652 6.02128i −0.664294 0.260323i
\(536\) 1.64045i 0.0708567i
\(537\) 14.5970 + 26.8655i 0.629905 + 1.15933i
\(538\) −2.98346 + 2.98346i −0.128626 + 0.128626i
\(539\) 3.38750 0.145910
\(540\) −20.4649 + 7.10708i −0.880668 + 0.305840i
\(541\) −26.9427 −1.15836 −0.579178 0.815201i \(-0.696626\pi\)
−0.579178 + 0.815201i \(0.696626\pi\)
\(542\) 2.19213 2.19213i 0.0941602 0.0941602i
\(543\) −9.85981 18.1468i −0.423125 0.778756i
\(544\) 0.800738i 0.0343313i
\(545\) −13.6806 + 5.97716i −0.586013 + 0.256033i
\(546\) 1.37823 + 0.407810i 0.0589826 + 0.0174527i
\(547\) 17.9286 + 17.9286i 0.766572 + 0.766572i 0.977501 0.210929i \(-0.0676489\pi\)
−0.210929 + 0.977501i \(0.567649\pi\)
\(548\) −12.1108 12.1108i −0.517348 0.517348i
\(549\) −2.99164 + 4.61263i −0.127680 + 0.196862i
\(550\) 6.22954 0.239498i 0.265629 0.0102122i
\(551\) 69.7343i 2.97078i
\(552\) −6.77942 + 3.68350i −0.288551 + 0.156780i
\(553\) 2.41627 2.41627i 0.102750 0.102750i
\(554\) 6.62667 0.281540
\(555\) 32.1513 4.01470i 1.36475 0.170414i
\(556\) −3.42915 −0.145428
\(557\) −5.15944 + 5.15944i −0.218613 + 0.218613i −0.807914 0.589301i \(-0.799403\pi\)
0.589301 + 0.807914i \(0.299403\pi\)
\(558\) 0.212387 + 0.996333i 0.00899106 + 0.0421781i
\(559\) 2.75645i 0.116585i
\(560\) −2.61524 + 6.67360i −0.110514 + 0.282011i
\(561\) 0.331217 1.11937i 0.0139840 0.0472600i
\(562\) −1.14841 1.14841i −0.0484429 0.0484429i
\(563\) −23.2548 23.2548i −0.980072 0.980072i 0.0197332 0.999805i \(-0.493718\pi\)
−0.999805 + 0.0197332i \(0.993718\pi\)
\(564\) −0.844049 + 2.85253i −0.0355409 + 0.120113i
\(565\) −9.50096 + 24.2446i −0.399708 + 1.01998i
\(566\) 1.07877i 0.0453442i
\(567\) 3.21547 8.40600i 0.135037 0.353019i
\(568\) −9.83316 + 9.83316i −0.412590 + 0.412590i
\(569\) −45.1914 −1.89452 −0.947260 0.320466i \(-0.896161\pi\)
−0.947260 + 0.320466i \(0.896161\pi\)
\(570\) −10.3925 + 1.29770i −0.435292 + 0.0543545i
\(571\) 15.2468 0.638059 0.319029 0.947745i \(-0.396643\pi\)
0.319029 + 0.947745i \(0.396643\pi\)
\(572\) 10.0691 10.0691i 0.421009 0.421009i
\(573\) 27.0671 14.7065i 1.13074 0.614372i
\(574\) 0.512556i 0.0213937i
\(575\) −15.6469 + 0.601553i −0.652520 + 0.0250865i
\(576\) 12.4078 + 8.04741i 0.516993 + 0.335309i
\(577\) −6.12177 6.12177i −0.254853 0.254853i 0.568104 0.822957i \(-0.307677\pi\)
−0.822957 + 0.568104i \(0.807677\pi\)
\(578\) 4.41417 + 4.41417i 0.183605 + 0.183605i
\(579\) 33.6806 + 9.96593i 1.39972 + 0.414170i
\(580\) −36.2627 + 15.8434i −1.50573 + 0.657862i
\(581\) 8.86586i 0.367818i
\(582\) −2.88958 5.31822i −0.119777 0.220447i
\(583\) 22.1579 22.1579i 0.917686 0.917686i
\(584\) −9.67107 −0.400192
\(585\) 12.2920 8.81134i 0.508210 0.364304i
\(586\) 3.83938 0.158603
\(587\) −3.77086 + 3.77086i −0.155640 + 0.155640i −0.780632 0.624992i \(-0.785102\pi\)
0.624992 + 0.780632i \(0.285102\pi\)
\(588\) −1.54179 2.83765i −0.0635825 0.117023i
\(589\) 6.77812i 0.279288i
\(590\) 4.78953 + 1.87692i 0.197182 + 0.0772714i
\(591\) −9.64610 2.85423i −0.396787 0.117407i
\(592\) −18.9624 18.9624i −0.779352 0.779352i
\(593\) −8.38017 8.38017i −0.344132 0.344132i 0.513786 0.857918i \(-0.328242\pi\)
−0.857918 + 0.513786i \(0.828242\pi\)
\(594\) 4.21191 + 4.92275i 0.172817 + 0.201983i
\(595\) −0.178115 0.407672i −0.00730199 0.0167129i
\(596\) 1.84071i 0.0753985i
\(597\) 20.4161 11.0928i 0.835577 0.453998i
\(598\) 1.83759 1.83759i 0.0751446 0.0751446i
\(599\) −6.75588 −0.276038 −0.138019 0.990430i \(-0.544073\pi\)
−0.138019 + 0.990430i \(0.544073\pi\)
\(600\) −6.29249 10.5900i −0.256890 0.432334i
\(601\) 21.2564 0.867068 0.433534 0.901137i \(-0.357266\pi\)
0.433534 + 0.901137i \(0.357266\pi\)
\(602\) 0.318204 0.318204i 0.0129690 0.0129690i
\(603\) 3.38385 0.721331i 0.137801 0.0293749i
\(604\) 16.2416i 0.660861i
\(605\) 0.425358 + 0.973568i 0.0172933 + 0.0395812i
\(606\) −2.25243 + 7.61225i −0.0914986 + 0.309227i
\(607\) 2.72491 + 2.72491i 0.110601 + 0.110601i 0.760241 0.649641i \(-0.225081\pi\)
−0.649641 + 0.760241i \(0.725081\pi\)
\(608\) 20.9083 + 20.9083i 0.847944 + 0.847944i
\(609\) 4.66460 15.7644i 0.189019 0.638805i
\(610\) −1.40431 0.550318i −0.0568588 0.0222817i
\(611\) 2.07675i 0.0840162i
\(612\) −1.08843 + 0.232020i −0.0439972 + 0.00937884i
\(613\) 15.6232 15.6232i 0.631017 0.631017i −0.317306 0.948323i \(-0.602778\pi\)
0.948323 + 0.317306i \(0.102778\pi\)
\(614\) 5.91361 0.238654
\(615\) 4.25683 + 3.31175i 0.171652 + 0.133543i
\(616\) 4.81840 0.194139
\(617\) 5.47009 5.47009i 0.220218 0.220218i −0.588373 0.808590i \(-0.700231\pi\)
0.808590 + 0.588373i \(0.200231\pi\)
\(618\) −7.75500 + 4.21357i −0.311952 + 0.169494i
\(619\) 42.9951i 1.72812i −0.503389 0.864060i \(-0.667914\pi\)
0.503389 0.864060i \(-0.332086\pi\)
\(620\) 3.52471 1.53997i 0.141556 0.0618466i
\(621\) −10.5792 12.3646i −0.424527 0.496174i
\(622\) −2.32751 2.32751i −0.0933247 0.0933247i
\(623\) 8.75163 + 8.75163i 0.350627 + 0.350627i
\(624\) −12.0030 3.55162i −0.480504 0.142179i
\(625\) −1.91944 24.9262i −0.0767776 0.997048i
\(626\) 2.35524i 0.0941344i
\(627\) −20.5798 37.8768i −0.821878 1.51265i
\(628\) −9.81311 + 9.81311i −0.391586 + 0.391586i
\(629\) 1.66446 0.0663664
\(630\) 2.43616 + 0.401801i 0.0970590 + 0.0160081i
\(631\) −38.0091 −1.51312 −0.756560 0.653925i \(-0.773121\pi\)
−0.756560 + 0.653925i \(0.773121\pi\)
\(632\) 3.43691 3.43691i 0.136713 0.136713i
\(633\) 6.71057 + 12.3507i 0.266721 + 0.490897i
\(634\) 0.928896i 0.0368912i
\(635\) 2.17121 5.54053i 0.0861620 0.219869i
\(636\) −28.6463 8.47629i −1.13590 0.336107i
\(637\) 1.59420 + 1.59420i 0.0631644 + 0.0631644i
\(638\) 8.36823 + 8.36823i 0.331301 + 0.331301i
\(639\) −24.6072 15.9596i −0.973445 0.631352i
\(640\) −8.04745 + 20.5355i −0.318103 + 0.811739i
\(641\) 30.8009i 1.21656i 0.793721 + 0.608282i \(0.208141\pi\)
−0.793721 + 0.608282i \(0.791859\pi\)
\(642\) 4.13420 2.24626i 0.163164 0.0886527i
\(643\) −6.17366 + 6.17366i −0.243465 + 0.243465i −0.818282 0.574817i \(-0.805073\pi\)
0.574817 + 0.818282i \(0.305073\pi\)
\(644\) −5.83911 −0.230093
\(645\) −0.586724 4.69871i −0.0231022 0.185012i
\(646\) −0.538014 −0.0211679
\(647\) −23.4296 + 23.4296i −0.921112 + 0.921112i −0.997108 0.0759964i \(-0.975786\pi\)
0.0759964 + 0.997108i \(0.475786\pi\)
\(648\) 4.57370 11.9568i 0.179672 0.469706i
\(649\) 21.1729i 0.831110i
\(650\) 3.04441 + 2.81899i 0.119412 + 0.110570i
\(651\) −0.453396 + 1.53229i −0.0177700 + 0.0600551i
\(652\) 26.3851 + 26.3851i 1.03332 + 1.03332i
\(653\) 17.1928 + 17.1928i 0.672805 + 0.672805i 0.958362 0.285557i \(-0.0921786\pi\)
−0.285557 + 0.958362i \(0.592179\pi\)
\(654\) 1.20769 4.08150i 0.0472246 0.159599i
\(655\) −18.3815 + 8.03100i −0.718225 + 0.313797i
\(656\) 4.46386i 0.174285i
\(657\) −4.25252 19.9490i −0.165906 0.778286i
\(658\) 0.239739 0.239739i 0.00934601 0.00934601i
\(659\) 0.0375362 0.00146220 0.000731101 1.00000i \(-0.499767\pi\)
0.000731101 1.00000i \(0.499767\pi\)
\(660\) 15.0207 19.3072i 0.584682 0.751533i
\(661\) 19.6937 0.765995 0.382998 0.923749i \(-0.374892\pi\)
0.382998 + 0.923749i \(0.374892\pi\)
\(662\) −0.941782 + 0.941782i −0.0366034 + 0.0366034i
\(663\) 0.682666 0.370916i 0.0265125 0.0144052i
\(664\) 12.6109i 0.489396i
\(665\) −15.2956 5.99404i −0.593140 0.232439i
\(666\) −5.02664 + 7.75029i −0.194778 + 0.300318i
\(667\) −21.0187 21.0187i −0.813846 0.813846i
\(668\) 32.6061 + 32.6061i 1.26157 + 1.26157i
\(669\) −27.1127 8.02252i −1.04824 0.310169i
\(670\) 0.380019 + 0.869794i 0.0146814 + 0.0336031i
\(671\) 6.20798i 0.239656i
\(672\) −3.32803 6.12519i −0.128381 0.236284i
\(673\) −4.33276 + 4.33276i −0.167016 + 0.167016i −0.785666 0.618651i \(-0.787680\pi\)
0.618651 + 0.785666i \(0.287680\pi\)
\(674\) −8.89793 −0.342736
\(675\) 19.0776 17.6364i 0.734298 0.678827i
\(676\) −14.7616 −0.567753
\(677\) 3.64637 3.64637i 0.140142 0.140142i −0.633556 0.773697i \(-0.718405\pi\)
0.773697 + 0.633556i \(0.218405\pi\)
\(678\) −3.54436 6.52335i −0.136120 0.250528i
\(679\) 9.49398i 0.364346i
\(680\) −0.253352 0.579876i −0.00971559 0.0222372i
\(681\) −16.5493 4.89685i −0.634170 0.187648i
\(682\) −0.813386 0.813386i −0.0311462 0.0311462i
\(683\) −33.7536 33.7536i −1.29155 1.29155i −0.933830 0.357718i \(-0.883555\pi\)
−0.357718 0.933830i \(-0.616445\pi\)
\(684\) −22.3620 + 34.4787i −0.855033 + 1.31833i
\(685\) 19.1242 + 7.49436i 0.730697 + 0.286345i
\(686\) 0.368068i 0.0140529i
\(687\) 7.30696 3.97013i 0.278778 0.151470i
\(688\) −2.77125 + 2.77125i −0.105653 + 0.105653i
\(689\) 20.8555 0.794533
\(690\) 2.74126 3.52354i 0.104358 0.134139i
\(691\) −12.2184 −0.464812 −0.232406 0.972619i \(-0.574660\pi\)
−0.232406 + 0.972619i \(0.574660\pi\)
\(692\) −20.2799 + 20.2799i −0.770928 + 0.770928i
\(693\) 2.11872 + 9.93918i 0.0804836 + 0.377558i
\(694\) 2.85547i 0.108392i
\(695\) 3.76850 1.64648i 0.142947 0.0624546i
\(696\) 6.63497 22.4234i 0.251498 0.849956i
\(697\) 0.195912 + 0.195912i 0.00742068 + 0.00742068i
\(698\) −3.85897 3.85897i −0.146064 0.146064i
\(699\) −9.92404 + 33.5391i −0.375362 + 1.26856i
\(700\) −0.358149 9.31575i −0.0135368 0.352102i
\(701\) 21.7907i 0.823024i 0.911404 + 0.411512i \(0.134999\pi\)
−0.911404 + 0.411512i \(0.865001\pi\)
\(702\) −0.334529 + 4.29889i −0.0126260 + 0.162251i
\(703\) 43.4612 43.4612i 1.63917 1.63917i
\(704\) −16.6992 −0.629377
\(705\) −0.442045 3.54007i −0.0166484 0.133327i
\(706\) 3.93294 0.148018
\(707\) −8.80511 + 8.80511i −0.331150 + 0.331150i
\(708\) 17.7362 9.63670i 0.666567 0.362169i
\(709\) 14.1622i 0.531874i 0.963990 + 0.265937i \(0.0856814\pi\)
−0.963990 + 0.265937i \(0.914319\pi\)
\(710\) 2.93580 7.49161i 0.110179 0.281155i
\(711\) 8.60077 + 5.57825i 0.322554 + 0.209201i
\(712\) 12.4484 + 12.4484i 0.466523 + 0.466523i
\(713\) 2.04300 + 2.04300i 0.0765110 + 0.0765110i
\(714\) 0.121625 + 0.0359883i 0.00455172 + 0.00134683i
\(715\) −6.23090 + 15.9001i −0.233023 + 0.594629i
\(716\) 32.9134i 1.23003i
\(717\) 10.6355 + 19.5746i 0.397192 + 0.731026i
\(718\) −1.58632 + 1.58632i −0.0592008 + 0.0592008i
\(719\) −39.3153 −1.46621 −0.733106 0.680114i \(-0.761930\pi\)
−0.733106 + 0.680114i \(0.761930\pi\)
\(720\) −21.2166 3.49929i −0.790695 0.130411i
\(721\) −13.8441 −0.515581
\(722\) −9.10324 + 9.10324i −0.338787 + 0.338787i
\(723\) −13.3840 24.6331i −0.497757 0.916115i
\(724\) 22.2320i 0.826248i
\(725\) 32.2441 34.8225i 1.19752 1.29328i
\(726\) −0.290455 0.0859443i −0.0107798 0.00318969i
\(727\) 10.0141 + 10.0141i 0.371403 + 0.371403i 0.867988 0.496585i \(-0.165413\pi\)
−0.496585 + 0.867988i \(0.665413\pi\)
\(728\) 2.26760 + 2.26760i 0.0840428 + 0.0840428i
\(729\) 26.6750 + 4.17686i 0.987962 + 0.154699i
\(730\) 5.12777 2.24036i 0.189787 0.0829193i
\(731\) 0.243251i 0.00899695i
\(732\) −5.20032 + 2.82551i −0.192209 + 0.104434i
\(733\) −30.5737 + 30.5737i −1.12926 + 1.12926i −0.138967 + 0.990297i \(0.544378\pi\)
−0.990297 + 0.138967i \(0.955622\pi\)
\(734\) 1.83618 0.0677745
\(735\) 3.05684 + 2.37818i 0.112753 + 0.0877204i
\(736\) −12.6040 −0.464589
\(737\) −2.76250 + 2.76250i −0.101758 + 0.101758i
\(738\) −1.50388 + 0.320580i −0.0553586 + 0.0118007i
\(739\) 16.1095i 0.592598i −0.955095 0.296299i \(-0.904247\pi\)
0.955095 0.296299i \(-0.0957525\pi\)
\(740\) 32.4746 + 12.7261i 1.19379 + 0.467821i
\(741\) 8.14019 27.5104i 0.299037 1.01062i
\(742\) 2.40756 + 2.40756i 0.0883844 + 0.0883844i
\(743\) 23.1679 + 23.1679i 0.849946 + 0.849946i 0.990126 0.140180i \(-0.0447681\pi\)
−0.140180 + 0.990126i \(0.544768\pi\)
\(744\) −0.644914 + 2.17954i −0.0236437 + 0.0799057i
\(745\) 0.883803 + 2.02286i 0.0323800 + 0.0741120i
\(746\) 3.68059i 0.134756i
\(747\) 26.0131 5.54518i 0.951770 0.202888i
\(748\) 0.888574 0.888574i 0.0324895 0.0324895i
\(749\) 7.38030 0.269670
\(750\) 5.78961 + 4.15730i 0.211407 + 0.151803i
\(751\) 28.7540 1.04925 0.524625 0.851334i \(-0.324206\pi\)
0.524625 + 0.851334i \(0.324206\pi\)
\(752\) −2.08789 + 2.08789i −0.0761377 + 0.0761377i
\(753\) −12.2189 + 6.63894i −0.445280 + 0.241936i
\(754\) 7.87638i 0.286841i
\(755\) 7.79827 + 17.8488i 0.283808 + 0.649585i
\(756\) 7.36156 6.29856i 0.267737 0.229076i
\(757\) −1.29026 1.29026i −0.0468952 0.0468952i 0.683270 0.730166i \(-0.260557\pi\)
−0.730166 + 0.683270i \(0.760557\pi\)
\(758\) −5.58825 5.58825i −0.202974 0.202974i
\(759\) 17.6195 + 5.21351i 0.639546 + 0.189238i
\(760\) −21.7566 8.52596i −0.789196 0.309269i
\(761\) 33.9969i 1.23239i −0.787596 0.616193i \(-0.788674\pi\)
0.787596 0.616193i \(-0.211326\pi\)
\(762\) 0.809978 + 1.49075i 0.0293424 + 0.0540043i
\(763\) 4.72108 4.72108i 0.170915 0.170915i
\(764\) 33.1604 1.19970
\(765\) 1.08474 0.777582i 0.0392188 0.0281135i
\(766\) −7.62879 −0.275639
\(767\) −9.96424 + 9.96424i −0.359788 + 0.359788i
\(768\) 5.15065 + 9.47970i 0.185858 + 0.342069i
\(769\) 21.4206i