Properties

Label 105.2.j.a.8.7
Level 105
Weight 2
Character 105.8
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 8.7
Character \(\chi\) = 105.8
Dual form 105.2.j.a.92.7

$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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 0.793111 0.609077i \(-0.208460\pi\)
−0.609077 + 0.793111i \(0.708460\pi\)
\(3\) 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 \(0.170608\pi\)
−0.859768 + 0.510684i \(0.829392\pi\)
\(12\) −2.83765 1.54179i −0.819158 0.445077i
\(13\) 1.59420 + 1.59420i 0.442151 + 0.442151i 0.892734 0.450583i \(-0.148784\pi\)
−0.450583 + 0.892734i \(0.648784\pi\)
\(14\) 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 0.723961 0.689840i \(-0.242319\pi\)
−0.689840 + 0.723961i \(0.742319\pi\)
\(18\) 0.230209 1.07994i 0.0542609 0.254544i
\(19\) 7.34691i 1.68550i 0.538308 + 0.842748i \(0.319064\pi\)
−0.538308 + 0.842748i \(0.680936\pi\)
\(20\) 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 −0.437484 0.899226i \(-0.644130\pi\)
0.899226 + 0.437484i \(0.144130\pi\)
\(24\) −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 −0.0271173 0.999632i \(-0.508633\pi\)
0.999632 + 0.0271173i \(0.00863275\pi\)
\(38\) −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 \(-0.965318\pi\)
0.994070 0.108741i \(-0.0346818\pi\)
\(42\) 0.304359 0.560167i 0.0469636 0.0864357i
\(43\) 0.864526 + 0.864526i 0.131839 + 0.131839i 0.769947 0.638108i \(-0.220283\pi\)
−0.638108 + 0.769947i \(0.720283\pi\)
\(44\) 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 0.753014 0.658005i \(-0.228599\pi\)
−0.658005 + 0.753014i \(0.728599\pi\)
\(48\) −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 −0.0968158 0.995302i \(-0.530866\pi\)
0.995302 + 0.0968158i \(0.0308658\pi\)
\(54\) −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 −0.755165 0.655535i \(-0.772443\pi\)
0.655535 + 0.755165i \(0.272443\pi\)
\(68\) 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 \(-0.803002\pi\)
0.814524 0.580129i \(-0.196998\pi\)
\(72\) −4.17345 0.889650i −0.491846 0.104846i
\(73\) −4.80768 4.80768i −0.562697 0.562697i 0.367376 0.930073i \(-0.380256\pi\)
−0.930073 + 0.367376i \(0.880256\pi\)
\(74\) 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 \(0.0615712\pi\)
−0.981350 + 0.192228i \(0.938429\pi\)
\(80\) 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 −0.961817 0.273693i \(-0.911755\pi\)
0.273693 + 0.961817i \(0.411755\pi\)
\(84\) −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 −0.960367 0.278739i \(-0.910084\pi\)
0.278739 + 0.960367i \(0.410084\pi\)
\(98\) 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 \(-0.787325\pi\)
0.784976 0.619526i \(-0.212675\pi\)
\(102\) 0.111450 + 0.0605545i 0.0110352 + 0.00599579i
\(103\) −9.78924 9.78924i −0.964563 0.964563i 0.0348303 0.999393i \(-0.488911\pi\)
−0.999393 + 0.0348303i \(0.988911\pi\)
\(104\) 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 0.912835 0.408328i \(-0.133888\pi\)
−0.408328 + 0.912835i \(0.633888\pi\)
\(108\) 0.751653 + 9.65916i 0.0723279 + 0.929453i
\(109\) 6.67661i 0.639504i 0.947501 + 0.319752i \(0.103600\pi\)
−0.947501 + 0.319752i \(0.896400\pi\)
\(110\) −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 −0.978913 0.204276i \(-0.934516\pi\)
0.204276 + 0.978913i \(0.434516\pi\)
\(114\) 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 −0.618669 0.785652i \(-0.712328\pi\)
0.785652 + 0.618669i \(0.212328\pi\)
\(128\) −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 \(0.128179\pi\)
−0.920012 + 0.391891i \(0.871821\pi\)
\(132\) 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 0.372924 0.927862i \(-0.378355\pi\)
−0.927862 + 0.372924i \(0.878355\pi\)
\(138\) 0.953156 1.75427i 0.0811380 0.149333i
\(139\) 1.83916i 0.155995i −0.996954 0.0779976i \(-0.975147\pi\)
0.996954 0.0779976i \(-0.0248526\pi\)
\(140\) 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 −0.465179 0.885217i \(-0.654010\pi\)
0.885217 + 0.465179i \(0.154010\pi\)
\(158\) −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 0.993361 + 0.115041i \(0.0367000\pi\)
0.115041 + 0.993361i \(0.463300\pi\)
\(164\) −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 0.882018 + 0.471215i \(0.156184\pi\)
0.471215 + 0.882018i \(0.343816\pi\)
\(168\) −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 −0.160150 0.987093i \(-0.551198\pi\)
0.987093 + 0.160150i \(0.0511979\pi\)
\(174\) −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 \(0.222491\pi\)
−0.765501 + 0.643435i \(0.777509\pi\)
\(192\) 7.50253 + 4.07639i 0.541449 + 0.294188i
\(193\) 14.3394 + 14.3394i 1.03217 + 1.03217i 0.999465 + 0.0327052i \(0.0104123\pi\)
0.0327052 + 0.999465i \(0.489588\pi\)
\(194\) −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 0.545509 0.838105i \(-0.316336\pi\)
−0.838105 + 0.545509i \(0.816336\pi\)
\(198\) 3.65829 + 0.779834i 0.259983 + 0.0554204i
\(199\) 13.4148i 0.950949i 0.879730 + 0.475474i \(0.157724\pi\)
−0.879730 + 0.475474i \(0.842276\pi\)
\(200\) −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 0.205643 0.978627i \(-0.434072\pi\)
−0.978627 + 0.205643i \(0.934072\pi\)
\(224\) −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 0.433506 0.901151i \(-0.357276\pi\)
−0.901151 + 0.433506i \(0.857276\pi\)
\(228\) 11.3274 20.8479i 0.750176 1.38069i
\(229\) 4.80117i 0.317270i 0.987337 + 0.158635i \(0.0507093\pi\)
−0.987337 + 0.158635i \(0.949291\pi\)
\(230\) −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 −0.0625851 0.998040i \(-0.519934\pi\)
0.998040 + 0.0625851i \(0.0199345\pi\)
\(234\) 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 \(-0.918457\pi\)
0.967367 0.253381i \(-0.0815426\pi\)
\(252\) −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 −0.999321 0.0368323i \(-0.988273\pi\)
−0.0368323 0.999321i \(-0.511727\pi\)
\(258\) 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 −0.137350 0.990523i \(-0.543858\pi\)
0.990523 + 0.137350i \(0.0438584\pi\)
\(264\) 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 −0.212293 0.977206i \(-0.568093\pi\)
0.977206 + 0.212293i \(0.0680930\pi\)
\(278\) 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 \(0.0420160\pi\)
−0.991301 + 0.131614i \(0.957984\pi\)
\(282\) 0.515994 + 0.280357i 0.0307270 + 0.0166950i
\(283\) 2.07246 + 2.07246i 0.123195 + 0.123195i 0.766016 0.642821i \(-0.222236\pi\)
−0.642821 + 0.766016i \(0.722236\pi\)
\(284\) −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 −0.458029 0.888937i \(-0.651445\pi\)
0.888937 + 0.458029i \(0.151445\pi\)
\(294\) −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 −0.304209 0.952605i \(-0.598392\pi\)
0.952605 + 0.304209i \(0.0983922\pi\)
\(308\) 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 \(0.0815992\pi\)
−0.967322 + 0.253553i \(0.918401\pi\)
\(312\) 2.65179 4.88058i 0.150128 0.276308i
\(313\) 4.52473 + 4.52473i 0.255753 + 0.255753i 0.823324 0.567571i \(-0.192117\pi\)
−0.567571 + 0.823324i \(0.692117\pi\)
\(314\) 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 0.655214 0.755443i \(-0.272578\pi\)
−0.755443 + 0.655214i \(0.772578\pi\)
\(318\) 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 −0.997779 0.0666042i \(-0.978784\pi\)
0.0666042 + 0.997779i \(0.478784\pi\)
\(338\) 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 0.838851 0.544361i \(-0.183228\pi\)
−0.544361 + 0.838851i \(0.683228\pi\)
\(348\) 26.9340 + 14.6342i 1.44381 + 0.784474i
\(349\) 14.8272i 0.793681i 0.917888 + 0.396841i \(0.129893\pi\)
−0.917888 + 0.396841i \(0.870107\pi\)
\(350\) −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 −0.476841 0.878990i \(-0.658218\pi\)
0.878990 + 0.476841i \(0.158218\pi\)
\(354\) −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 −0.609019 0.793155i \(-0.708437\pi\)
0.793155 + 0.609019i \(0.208437\pi\)
\(368\) −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 0.499942 0.866059i \(-0.333355\pi\)
−0.866059 + 0.499942i \(0.833355\pi\)
\(374\) −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 \(0.185929\pi\)
−0.834202 + 0.551459i \(0.814071\pi\)
\(380\) −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 −0.974269 0.225388i \(-0.927635\pi\)
0.225388 + 0.974269i \(0.427635\pi\)
\(384\) 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 −0.269907 + 0.962886i \(0.586993\pi\)
−0.962886 + 0.269907i \(0.913007\pi\)
\(398\) −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 \(-0.873496\pi\)
0.922061 0.387044i \(-0.126504\pi\)
\(402\) −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 \(-0.708950\pi\)
0.610298 0.792172i \(-0.291050\pi\)
\(410\) 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 \(-0.912473\pi\)
0.962432 0.271523i \(-0.0875271\pi\)
\(432\) 16.6061 1.29225i 0.798962 0.0621733i
\(433\) 9.75098 + 9.75098i 0.468602 + 0.468602i 0.901462 0.432859i \(-0.142495\pi\)
−0.432859 + 0.901462i \(0.642495\pi\)
\(434\) 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 \(0.237424\pi\)
−0.734485 + 0.678625i \(0.762576\pi\)
\(440\) −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 −0.996491 0.0836955i \(-0.973328\pi\)
0.0836955 + 0.996491i \(0.473328\pi\)
\(444\) −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 −0.546617 0.837383i \(-0.684084\pi\)
0.837383 + 0.546617i \(0.184084\pi\)
\(458\) −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 \(0.308769\pi\)
−0.565278 + 0.824900i \(0.691231\pi\)
\(462\) 1.89757 + 1.03101i 0.0882827 + 0.0479671i
\(463\) −20.0869 20.0869i −0.933519 0.933519i 0.0644045 0.997924i \(-0.479485\pi\)
−0.997924 + 0.0644045i \(0.979485\pi\)
\(464\) 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 0.559903 0.828558i \(-0.310838\pi\)
−0.828558 + 0.559903i \(0.810838\pi\)
\(468\) −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 −0.0980363 0.995183i \(-0.531256\pi\)
0.995183 + 0.0980363i \(0.0312561\pi\)
\(488\) 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 \(0.310494\pi\)
−0.560798 + 0.827952i \(0.689506\pi\)
\(492\) −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 \(-0.945403\pi\)
0.985326 0.170682i \(-0.0545970\pi\)
\(500\) −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 −0.964926 0.262521i \(-0.915446\pi\)
0.262521 + 0.964926i \(0.415446\pi\)
\(504\) −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 \(0.187691\pi\)
−0.831136 + 0.556069i \(0.812309\pi\)
\(522\) −2.18507 + 10.2504i −0.0956378 + 0.448648i
\(523\) −16.0464 16.0464i −0.701661 0.701661i 0.263106 0.964767i \(-0.415253\pi\)
−0.964767 + 0.263106i \(0.915253\pi\)
\(524\) 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 −0.210929 0.977501i \(-0.567649\pi\)
0.977501 + 0.210929i \(0.0676489\pi\)
\(548\) −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 0.589301 0.807914i \(-0.299403\pi\)
−0.807914 + 0.589301i \(0.799403\pi\)
\(558\) 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 −0.999805 0.0197332i \(-0.993718\pi\)
0.0197332 + 0.999805i \(0.493718\pi\)
\(564\) −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 −0.822957 0.568104i \(-0.807677\pi\)
0.568104 + 0.822957i \(0.307677\pi\)
\(578\) 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 0.624992 0.780632i \(-0.285102\pi\)
−0.780632 + 0.624992i \(0.785102\pi\)
\(588\) −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 −0.857918 0.513786i \(-0.828242\pi\)
0.513786 + 0.857918i \(0.328242\pi\)
\(594\) 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 −0.649641 0.760241i \(-0.725081\pi\)
0.760241 + 0.649641i \(0.225081\pi\)
\(608\) 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 0.948323 0.317306i \(-0.102778\pi\)
−0.317306 + 0.948323i \(0.602778\pi\)
\(614\) 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 0.808590 0.588373i \(-0.200231\pi\)
−0.588373 + 0.808590i \(0.700231\pi\)
\(618\) −7.75500 4.21357i −0.311952 0.169494i
\(619\) 42.9951i 1.72812i 0.503389 + 0.864060i \(0.332086\pi\)
−0.503389 + 0.864060i \(0.667914\pi\)
\(620\) 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 \(-0.791859\pi\)
0.793721 0.608282i \(-0.208141\pi\)
\(642\) 4.13420 + 2.24626i 0.163164 + 0.0886527i
\(643\) −6.17366 6.17366i −0.243465 0.243465i 0.574817 0.818282i \(-0.305073\pi\)
−0.818282 + 0.574817i \(0.805073\pi\)
\(644\) −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 0.0759964 0.997108i \(-0.475786\pi\)
−0.997108 + 0.0759964i \(0.975786\pi\)
\(648\) 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 −0.285557 0.958362i \(-0.592179\pi\)
0.958362 + 0.285557i \(0.0921786\pi\)
\(654\) 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 0.618651 0.785666i \(-0.287680\pi\)
−0.785666 + 0.618651i \(0.787680\pi\)
\(674\) −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 0.773697 0.633556i \(-0.218405\pi\)
−0.633556 + 0.773697i \(0.718405\pi\)
\(678\) −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 −0.357718 + 0.933830i \(0.616445\pi\)
−0.933830 + 0.357718i \(0.883555\pi\)
\(684\) −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 \(-0.865001\pi\)
0.911404 0.411512i \(-0.134999\pi\)
\(702\) −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 \(-0.914319\pi\)
0.963990 0.265937i \(-0.0856814\pi\)
\(710\) 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 −0.496585 0.867988i \(-0.665413\pi\)
0.867988 + 0.496585i \(0.165413\pi\)
\(728\) 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 −0.990297 0.138967i \(-0.955622\pi\)
−0.138967 0.990297i \(-0.544378\pi\)
\(734\) 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 \(0.0957525\pi\)
−0.955095 + 0.296299i \(0.904247\pi\)
\(740\) 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 −0.140180 0.990126i \(-0.544768\pi\)
0.990126 + 0.140180i \(0.0447681\pi\)
\(744\) −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 −0.730166 0.683270i \(-0.760557\pi\)
0.683270 + 0.730166i \(0.260557\pi\)
\(758\) −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 \(0.211326\pi\)
−0.787596 + 0.616193i \(0.788674\pi\)
\(762\) 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