Properties

Label 105.2.j.a.8.6
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 8.6
Character \(\chi\) = 105.8
Dual form 105.2.j.a.92.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.260263 - 0.260263i) q^{2} +(-1.52191 + 0.826909i) q^{3} -1.86453i q^{4} +(0.895238 - 2.04904i) q^{5} +(0.611312 + 0.180884i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.00579 + 1.00579i) q^{8} +(1.63244 - 2.51697i) q^{9} +O(q^{10})\) \(q+(-0.260263 - 0.260263i) q^{2} +(-1.52191 + 0.826909i) 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} +(1.54179 + 2.83765i) q^{12} +(1.59420 + 1.59420i) q^{13} -0.368068 q^{14} +(0.331892 + 3.85874i) q^{15} -3.20551 q^{16} +(-0.140684 - 0.140684i) q^{17} +(-1.07994 + 0.230209i) 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} +(-0.403134 + 5.18049i) q^{27} +(-1.31842 - 1.31842i) q^{28} +9.49165 q^{29} +(0.917908 - 1.09067i) q^{30} +0.922582 q^{31} +(2.84586 + 2.84586i) q^{32} +(2.80115 + 5.15548i) 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} +(0.560167 - 0.304359i) q^{42} +(0.864526 + 0.864526i) q^{43} -6.31608 q^{44} +(-3.69593 - 5.59822i) q^{45} +1.15267 q^{46} +(-0.651346 - 0.651346i) q^{47} +(4.87851 - 2.65066i) 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} +(-6.07522 - 11.1814i) q^{57} +(-2.47033 - 2.47033i) q^{58} +6.25032 q^{59} +(7.19471 - 0.618821i) q^{60} +1.83261 q^{61} +(-0.240114 - 0.240114i) q^{62} +(-0.625454 - 2.93408i) 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} +(0.889650 + 4.17345i) q^{72} +(-4.80768 - 4.80768i) q^{73} -3.07921 q^{74} +(8.20381 + 2.77443i) q^{75} +13.6985 q^{76} +(-2.39532 - 2.39532i) q^{77} +(0.686187 + 1.26292i) 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} +(-14.4455 + 7.84873i) q^{87} +(3.40712 + 3.40712i) q^{88} -12.3767 q^{89} +(-0.495095 + 2.41893i) q^{90} +2.25454 q^{91} +(4.12888 + 4.12888i) q^{92} +(-1.40409 + 0.762891i) 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 0.609077 0.793111i \(-0.291540\pi\)
−0.793111 + 0.609077i \(0.791540\pi\)
\(3\) −1.52191 + 0.826909i −0.878677 + 0.477416i
\(4\) 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 \(-0.170608\pi\)
\(12\) 1.54179 + 2.83765i 0.445077 + 0.819158i
\(13\) 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
\(15\) 0.331892 + 3.85874i 0.0856941 + 0.996321i
\(16\) −3.20551 −0.801377
\(17\) −0.140684 0.140684i −0.0341210 0.0341210i 0.689840 0.723961i \(-0.257681\pi\)
−0.723961 + 0.689840i \(0.757681\pi\)
\(18\) −1.07994 + 0.230209i −0.254544 + 0.0542609i
\(19\) 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 −0.899226 0.437484i \(-0.855870\pi\)
0.437484 + 0.899226i \(0.355870\pi\)
\(24\) 0.699032 2.36243i 0.142689 0.482229i
\(25\) −3.39710 3.66875i −0.679420 0.733750i
\(26\) 0.829822i 0.162741i
\(27\) −0.403134 + 5.18049i −0.0775831 + 0.996986i
\(28\) −1.31842 1.31842i −0.249158 0.249158i
\(29\) 9.49165 1.76256 0.881278 0.472598i \(-0.156684\pi\)
0.881278 + 0.472598i \(0.156684\pi\)
\(30\) 0.917908 1.09067i 0.167586 0.199128i
\(31\) 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
\(33\) 2.80115 + 5.15548i 0.487618 + 0.897454i
\(34\) 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 \(0.0346818\pi\)
−0.994070 + 0.108741i \(0.965318\pi\)
\(42\) 0.560167 0.304359i 0.0864357 0.0469636i
\(43\) 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
\(45\) −3.69593 5.59822i −0.550957 0.834533i
\(46\) 1.15267 0.169952
\(47\) −0.651346 0.651346i −0.0950085 0.0950085i 0.658005 0.753014i \(-0.271401\pi\)
−0.753014 + 0.658005i \(0.771401\pi\)
\(48\) 4.87851 2.65066i 0.704152 0.382591i
\(49\) 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 \(-0.969134\pi\)
0.0968158 + 0.995302i \(0.469134\pi\)
\(54\) 1.45321 1.24337i 0.197757 0.169201i
\(55\) −6.94110 3.03262i −0.935938 0.408918i
\(56\) 1.42241i 0.190077i
\(57\) −6.07522 11.1814i −0.804683 1.48101i
\(58\) −2.47033 2.47033i −0.324370 0.324370i
\(59\) 6.25032 0.813722 0.406861 0.913490i \(-0.366623\pi\)
0.406861 + 0.913490i \(0.366623\pi\)
\(60\) 7.19471 0.618821i 0.928834 0.0798894i
\(61\) 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
\(63\) −0.625454 2.93408i −0.0787998 0.369659i
\(64\) 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 \(0.196998\pi\)
−0.814524 + 0.580129i \(0.803002\pi\)
\(72\) 0.889650 + 4.17345i 0.104846 + 0.491846i
\(73\) −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
\(75\) 8.20381 + 2.77443i 0.947295 + 0.320363i
\(76\) 13.6985 1.57133
\(77\) −2.39532 2.39532i −0.272972 0.272972i
\(78\) 0.686187 + 1.26292i 0.0776954 + 0.142997i
\(79\) 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 −0.273693 0.961817i \(-0.588245\pi\)
0.961817 + 0.273693i \(0.0882453\pi\)
\(84\) 3.09673 + 0.916307i 0.337881 + 0.0999773i
\(85\) −0.414214 + 0.162321i −0.0449278 + 0.0176062i
\(86\) 0.450009i 0.0485257i
\(87\) −14.4455 + 7.84873i −1.54872 + 0.841473i
\(88\) 3.40712 + 3.40712i 0.363201 + 0.363201i
\(89\) −12.3767 −1.31192 −0.655962 0.754794i \(-0.727737\pi\)
−0.655962 + 0.754794i \(0.727737\pi\)
\(90\) −0.495095 + 2.41893i −0.0521876 + 0.254977i
\(91\) 2.25454 0.236340
\(92\) 4.12888 + 4.12888i 0.430465 + 0.430465i
\(93\) −1.40409 + 0.762891i −0.145597 + 0.0791082i
\(94\) 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 \(0.212675\pi\)
−0.784976 + 0.619526i \(0.787325\pi\)
\(102\) −0.0605545 0.111450i −0.00599579 0.0110352i
\(103\) −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
\(105\) 2.96322 + 2.49386i 0.289181 + 0.243375i
\(106\) 3.40481 0.330704
\(107\) −5.21866 5.21866i −0.504507 0.504507i 0.408328 0.912835i \(-0.366112\pi\)
−0.912835 + 0.408328i \(0.866112\pi\)
\(108\) 9.65916 + 0.751653i 0.929453 + 0.0723279i
\(109\) 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 −0.204276 0.978913i \(-0.565484\pi\)
0.978913 + 0.204276i \(0.0654841\pi\)
\(114\) −1.32894 + 4.49125i −0.124467 + 0.420644i
\(115\) 2.55501 + 6.51991i 0.238256 + 0.607985i
\(116\) 17.6974i 1.64317i
\(117\) 6.61498 1.41011i 0.611555 0.130365i
\(118\) −1.62673 1.62673i −0.149752 0.149752i
\(119\) −0.198958 −0.0182384
\(120\) −4.21491 3.54728i −0.384767 0.323821i
\(121\) −0.475134 −0.0431940
\(122\) −0.476962 0.476962i −0.0431821 0.0431821i
\(123\) −1.15152 2.11936i −0.103829 0.191096i
\(124\) 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 \(-0.871821\pi\)
0.920012 0.391891i \(-0.128179\pi\)
\(132\) 9.61252 5.22282i 0.836663 0.454588i
\(133\) 5.19505 + 5.19505i 0.450468 + 0.450468i
\(134\) 0.424489 0.0366703
\(135\) 10.2541 + 5.46381i 0.882533 + 0.470250i
\(136\) 0.282999 0.0242670
\(137\) 6.49538 + 6.49538i 0.554938 + 0.554938i 0.927862 0.372924i \(-0.121645\pi\)
−0.372924 + 0.927862i \(0.621645\pi\)
\(138\) −1.75427 + 0.953156i −0.149333 + 0.0811380i
\(139\) 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
\(147\) 0.826909 + 1.52191i 0.0682023 + 0.125525i
\(148\) −11.0297 11.0297i −0.906640 0.906640i
\(149\) 0.987227 0.0808768 0.0404384 0.999182i \(-0.487125\pi\)
0.0404384 + 0.999182i \(0.487125\pi\)
\(150\) −1.41307 2.85723i −0.115377 0.233292i
\(151\) −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
\(153\) −0.583758 + 0.124439i −0.0471940 + 0.0100603i
\(154\) 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
\(162\) −1.18351 + 3.09398i −0.0929853 + 0.243086i
\(163\) 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
\(165\) 13.0715 1.12428i 1.01761 0.0875253i
\(166\) −3.26324 −0.253276
\(167\) −17.4876 17.4876i −1.35323 1.35323i −0.882018 0.471215i \(-0.843816\pi\)
−0.471215 0.882018i \(-0.656184\pi\)
\(168\) −1.17620 2.16478i −0.0907459 0.167017i
\(169\) 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 \(-0.948802\pi\)
0.160150 + 0.987093i \(0.448802\pi\)
\(174\) 5.80236 + 1.71689i 0.439876 + 0.130157i
\(175\) −4.99631 0.192086i −0.377685 0.0145203i
\(176\) 10.8587i 0.818502i
\(177\) −9.51244 + 5.16844i −0.714999 + 0.388484i
\(178\) 3.22119 + 3.22119i 0.241439 + 0.241439i
\(179\) −17.6524 −1.31941 −0.659703 0.751527i \(-0.729318\pi\)
−0.659703 + 0.751527i \(0.729318\pi\)
\(180\) −10.4380 + 6.89117i −0.778005 + 0.513637i
\(181\) −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
\(183\) −2.78908 + 1.51541i −0.206175 + 0.112022i
\(184\) 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 \(-0.222491\pi\)
\(192\) −4.07639 7.50253i −0.294188 0.541449i
\(193\) 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
\(195\) −5.62249 + 6.68069i −0.402635 + 0.478414i
\(196\) −1.86453 −0.133180
\(197\) 4.10678 + 4.10678i 0.292596 + 0.292596i 0.838105 0.545509i \(-0.183664\pi\)
−0.545509 + 0.838105i \(0.683664\pi\)
\(198\) 0.779834 + 3.65829i 0.0554204 + 0.259983i
\(199\) 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
\(207\) 1.95873 + 9.18861i 0.136141 + 0.638653i
\(208\) −5.11022 5.11022i −0.354330 0.354330i
\(209\) 24.8876 1.72151
\(210\) −0.122159 1.42028i −0.00842975 0.0980084i
\(211\) 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
\(213\) −8.08429 14.8790i −0.553926 1.01949i
\(214\) 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
\(222\) 4.68630 2.54623i 0.314524 0.170892i
\(223\) −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
\(225\) −14.7797 + 2.56137i −0.985313 + 0.170758i
\(226\) −4.28628 −0.285119
\(227\) 7.04578 + 7.04578i 0.467645 + 0.467645i 0.901151 0.433506i \(-0.142724\pi\)
−0.433506 + 0.901151i \(0.642724\pi\)
\(228\) −20.8479 + 11.3274i −1.38069 + 0.750176i
\(229\) 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 −0.998040 0.0625851i \(-0.980066\pi\)
0.0625851 + 0.998040i \(0.480066\pi\)
\(234\) −2.08864 1.35464i −0.136538 0.0885554i
\(235\) −1.91774 + 0.751522i −0.125100 + 0.0490239i
\(236\) 11.6539i 0.758603i
\(237\) −2.82564 5.20055i −0.183545 0.337812i
\(238\) 0.0517814 + 0.0517814i 0.00335649 + 0.00335649i
\(239\) −12.8618 −0.831961 −0.415981 0.909373i \(-0.636562\pi\)
−0.415981 + 0.909373i \(0.636562\pi\)
\(240\) −1.06388 12.3692i −0.0686733 0.798430i
\(241\) −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
\(243\) 12.3810 + 9.47153i 0.794244 + 0.607599i
\(244\) 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 \(0.918457\pi\)
\(252\) −5.47066 + 1.16618i −0.344619 + 0.0734621i
\(253\) 7.50140 + 7.50140i 0.471609 + 0.471609i
\(254\) −0.979525 −0.0614609
\(255\) 0.496172 0.589556i 0.0310715 0.0369194i
\(256\) 6.22880 0.389300
\(257\) 16.6108 + 16.6108i 1.03615 + 1.03615i 0.999321 + 0.0368323i \(0.0117267\pi\)
0.0368323 + 0.999321i \(0.488273\pi\)
\(258\) 0.372116 + 0.684874i 0.0231669 + 0.0426384i
\(259\) 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 \(-0.956142\pi\)
0.137350 + 0.990523i \(0.456142\pi\)
\(264\) −8.00273 2.36797i −0.492534 0.145738i
\(265\) 7.54709 + 19.2587i 0.463614 + 1.18305i
\(266\) 2.70416i 0.165803i
\(267\) 18.8362 10.2344i 1.15276 0.626334i
\(268\) 1.52052 + 1.52052i 0.0928806 + 0.0928806i
\(269\) 11.4632 0.698925 0.349463 0.936950i \(-0.386364\pi\)
0.349463 + 0.936950i \(0.386364\pi\)
\(270\) −1.24674 4.09080i −0.0758742 0.248958i
\(271\) 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
\(273\) −3.43121 + 1.86430i −0.207666 + 0.112832i
\(274\) 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 \(-0.957984\pi\)
0.991301 0.131614i \(-0.0420160\pi\)
\(282\) −0.280357 0.515994i −0.0166950 0.0307270i
\(283\) 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
\(285\) −28.3498 + 2.43838i −1.67930 + 0.144437i
\(286\) −2.81102 −0.166219
\(287\) 0.984688 + 0.984688i 0.0581243 + 0.0581243i
\(288\) 11.8087 2.51724i 0.695832 0.148330i
\(289\) 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 \(-0.848555\pi\)
0.458029 + 0.888937i \(0.348555\pi\)
\(294\) 0.180884 0.611312i 0.0105494 0.0356525i
\(295\) 5.59552 12.8071i 0.325784 0.745660i
\(296\) 11.8997i 0.691656i
\(297\) 17.5489 + 1.36561i 1.01829 + 0.0792410i
\(298\) −0.256939 0.256939i −0.0148841 0.0148841i
\(299\) −7.06050 −0.408319
\(300\) 5.17299 15.2962i 0.298663 0.883128i
\(301\) 1.22262 0.0704709
\(302\) 2.26711 + 2.26711i 0.130458 + 0.130458i
\(303\) −10.2969 18.9513i −0.591543 1.08873i
\(304\) 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 \(-0.918401\pi\)
0.967322 0.253553i \(-0.0815992\pi\)
\(312\) 4.88058 2.65179i 0.276308 0.150128i
\(313\) 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
\(315\) −6.57196 1.34512i −0.370288 0.0757889i
\(316\) 6.37130 0.358414
\(317\) 1.78453 + 1.78453i 0.100229 + 0.100229i 0.755443 0.655214i \(-0.227422\pi\)
−0.655214 + 0.755443i \(0.727422\pi\)
\(318\) −5.18182 + 2.81546i −0.290582 + 0.157883i
\(319\) 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
\(327\) −5.52095 10.1612i −0.305309 0.561917i
\(328\) −1.40063 1.40063i −0.0773368 0.0773368i
\(329\) −0.921142 −0.0507842
\(330\) −3.69463 3.10941i −0.203383 0.171167i
\(331\) −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
\(333\) −5.23248 24.5462i −0.286738 1.34512i
\(334\) 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
\(342\) −1.69133 7.93421i −0.0914565 0.429033i
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) −1.73907 −0.0937644
\(345\) −9.27989 7.80998i −0.499612 0.420475i
\(346\) 5.66162 0.304371
\(347\) −5.48573 5.48573i −0.294489 0.294489i 0.544361 0.838851i \(-0.316772\pi\)
−0.838851 + 0.544361i \(0.816772\pi\)
\(348\) 14.6342 + 26.9340i 0.784474 + 1.44381i
\(349\) 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 −0.878990 0.476841i \(-0.841782\pi\)
0.476841 + 0.878990i \(0.341782\pi\)
\(354\) 3.82089 + 1.13058i 0.203078 + 0.0600898i
\(355\) 20.0324 + 8.75231i 1.06321 + 0.464524i
\(356\) 23.0766i 1.22306i
\(357\) 0.302797 0.164520i 0.0160257 0.00870732i
\(358\) 4.59428 + 4.59428i 0.242815 + 0.242815i
\(359\) 6.09504 0.321684 0.160842 0.986980i \(-0.448579\pi\)
0.160842 + 0.986980i \(0.448579\pi\)
\(360\) 9.34801 + 1.91331i 0.492683 + 0.100840i
\(361\) −34.9770 −1.84090
\(362\) 3.10330 + 3.10330i 0.163106 + 0.163106i
\(363\) 0.723114 0.392893i 0.0379536 0.0206215i
\(364\) 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
\(372\) 1.42243 + 2.61796i 0.0737496 + 0.135735i
\(373\) −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
\(375\) 13.0293 14.3261i 0.672828 0.739799i
\(376\) 1.31024 0.0675704
\(377\) 15.1316 + 15.1316i 0.779315 + 0.779315i
\(378\) 0.148381 1.90677i 0.00763187 0.0980738i
\(379\) 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 −0.225388 0.974269i \(-0.572365\pi\)
0.974269 + 0.225388i \(0.0723648\pi\)
\(384\) −4.84748 + 16.3824i −0.247372 + 0.836012i
\(385\) −7.05248 + 2.76372i −0.359428 + 0.140852i
\(386\) 7.46402i 0.379909i
\(387\) 3.58727 0.764695i 0.182351 0.0388716i
\(388\) 12.5170 + 12.5170i 0.635457 + 0.635457i
\(389\) −13.6323 −0.691185 −0.345592 0.938385i \(-0.612322\pi\)
−0.345592 + 0.938385i \(0.612322\pi\)
\(390\) 3.20206 0.275411i 0.162143 0.0139460i
\(391\) 0.623074 0.0315102
\(392\) 1.00579 + 1.00579i 0.0508003 + 0.0508003i
\(393\) 7.41804 + 13.6528i 0.374190 + 0.688692i
\(394\) 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 \(0.126504\pi\)
−0.922061 + 0.387044i \(0.873496\pi\)
\(402\) −0.646036 + 0.351014i −0.0322214 + 0.0175070i
\(403\) 1.47078 + 1.47078i 0.0732647 + 0.0732647i
\(404\) 23.2177 1.15512
\(405\) −20.1239 + 0.163776i −0.999967 + 0.00813810i
\(406\) −3.49357 −0.173383
\(407\) −20.0390 20.0390i −0.993296 0.993296i
\(408\) −0.430700 + 0.234015i −0.0213228 + 0.0115854i
\(409\) 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
\(417\) 1.52081 + 2.79904i 0.0744746 + 0.137069i
\(418\) −6.47733 6.47733i −0.316817 0.316817i
\(419\) 5.95062 0.290707 0.145353 0.989380i \(-0.453568\pi\)
0.145353 + 0.989380i \(0.453568\pi\)
\(420\) 4.64986 5.52500i 0.226890 0.269593i
\(421\) −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
\(423\) −2.70270 + 0.576132i −0.131410 + 0.0280125i
\(424\) 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 \(0.912473\pi\)
\(432\) 1.29225 16.6061i 0.0621733 0.798962i
\(433\) 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
\(435\) 3.15020 + 36.6258i 0.151041 + 1.75607i
\(436\) 12.4487 0.596185
\(437\) −16.2693 16.2693i −0.778265 0.778265i
\(438\) −2.06936 3.80863i −0.0988779 0.181983i
\(439\) 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 −0.0836955 0.996491i \(-0.526672\pi\)
0.996491 + 0.0836955i \(0.0266723\pi\)
\(444\) 25.9069 + 7.66573i 1.22949 + 0.363799i
\(445\) −11.0801 + 25.3602i −0.525245 + 1.20219i
\(446\) 6.00850i 0.284511i
\(447\) −1.50247 + 0.816347i −0.0710646 + 0.0386119i
\(448\) 3.48580 + 3.48580i 0.164689 + 0.164689i
\(449\) 2.40628 0.113559 0.0567796 0.998387i \(-0.481917\pi\)
0.0567796 + 0.998387i \(0.481917\pi\)
\(450\) 4.51324 + 3.17998i 0.212756 + 0.149906i
\(451\) 4.71729 0.222129
\(452\) −15.3534 15.3534i −0.722166 0.722166i
\(453\) 13.2572 7.20307i 0.622875 0.338430i
\(454\) 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 \(-0.691231\pi\)
0.565278 0.824900i \(-0.308769\pi\)
\(462\) −1.03101 1.89757i −0.0479671 0.0882827i
\(463\) −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
\(465\) 0.306197 + 3.56000i 0.0141996 + 0.165091i
\(466\) 7.43265 0.344311
\(467\) 5.80567 + 5.80567i 0.268654 + 0.268654i 0.828558 0.559903i \(-0.189162\pi\)
−0.559903 + 0.828558i \(0.689162\pi\)
\(468\) −2.62918 12.3338i −0.121534 0.570130i
\(469\) 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
\(477\) 5.78575 + 27.1416i 0.264911 + 1.24273i
\(478\) 3.34746 + 3.34746i 0.153109 + 0.153109i
\(479\) −40.3829 −1.84514 −0.922571 0.385828i \(-0.873916\pi\)
−0.922571 + 0.385828i \(0.873916\pi\)
\(480\) −10.0369 + 11.9260i −0.458121 + 0.544343i
\(481\) 18.8612 0.859997
\(482\) 4.21252 + 4.21252i 0.191875 + 0.191875i
\(483\) −2.58962 4.76616i −0.117832 0.216868i
\(484\) 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 \(-0.689506\pi\)
0.560798 0.827952i \(-0.310494\pi\)
\(492\) −3.95159 + 2.14704i −0.178152 + 0.0967960i
\(493\) −1.33533 1.33533i −0.0601402 0.0601402i
\(494\) 6.09662 0.274300
\(495\) −18.9640 + 12.5200i −0.852366 + 0.562731i
\(496\) −2.95735 −0.132789
\(497\) 6.91304 + 6.91304i 0.310092 + 0.310092i
\(498\) 4.96636 2.69840i 0.222548 0.120918i
\(499\) 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 −0.262521 0.964926i \(-0.584554\pi\)
0.964926 + 0.262521i \(0.0845538\pi\)
\(504\) 3.58016 + 2.32200i 0.159473 + 0.103430i
\(505\) 25.5152 + 11.1478i 1.13541 + 0.496070i
\(506\) 3.90468i 0.173584i
\(507\) 6.54670 + 12.0491i 0.290749 + 0.535119i
\(508\) −3.50866 3.50866i −0.155672 0.155672i
\(509\) −14.4091 −0.638673 −0.319336 0.947641i \(-0.603460\pi\)
−0.319336 + 0.947641i \(0.603460\pi\)
\(510\) −0.282575 + 0.0243044i −0.0125126 + 0.00107622i
\(511\) −6.79909 −0.300774
\(512\) −15.5706 15.5706i −0.688130 0.688130i
\(513\) −38.0606 2.96178i −1.68042 0.130766i
\(514\) 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 \(-0.187691\pi\)
\(522\) −10.2504 + 2.18507i −0.448648 + 0.0956378i
\(523\) −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
\(525\) 7.76279 3.83915i 0.338796 0.167554i
\(526\) 7.20208 0.314026
\(527\) −0.129793 0.129793i −0.00565387 0.00565387i
\(528\) −8.97912 16.5259i −0.390766 0.719199i
\(529\) 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
\(537\) 26.8655 14.5970i 1.15933 0.629905i
\(538\) −2.98346 2.98346i −0.128626 0.128626i
\(539\) −3.38750 −0.145910
\(540\) 10.1874 19.1191i 0.438396 0.822753i
\(541\) −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
\(543\) 18.1468 9.85981i 0.778756 0.423125i
\(544\) 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
\(552\) 3.68350 + 6.77942i 0.156780 + 0.288551i
\(553\) 2.41627 + 2.41627i 0.102750 + 0.102750i
\(554\) −6.62667 −0.281540
\(555\) 24.7900 + 20.8633i 1.05228 + 0.885599i
\(556\) −3.42915 −0.145428
\(557\) 5.15944 + 5.15944i 0.218613 + 0.218613i 0.807914 0.589301i \(-0.200597\pi\)
−0.589301 + 0.807914i \(0.700597\pi\)
\(558\) −0.996333 + 0.212387i −0.0421781 + 0.00899106i
\(559\) 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 \(-0.506282\pi\)
0.999805 + 0.0197332i \(0.00628169\pi\)
\(564\) 0.844049 2.85253i 0.0355409 0.120113i
\(565\) −9.50096 24.2446i −0.399708 1.01998i
\(566\) 1.07877i 0.0453442i
\(567\) −8.40600 3.21547i −0.353019 0.135037i
\(568\) −9.83316 9.83316i −0.412590 0.412590i
\(569\) 45.1914 1.89452 0.947260 0.320466i \(-0.103839\pi\)
0.947260 + 0.320466i \(0.103839\pi\)
\(570\) 8.01302 + 6.74378i 0.335629 + 0.282466i
\(571\) 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
\(573\) 14.7065 + 27.0671i 0.614372 + 1.13074i
\(574\) 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
\(582\) −5.31822 + 2.88958i −0.220447 + 0.119777i
\(583\) 22.1579 + 22.1579i 0.917686 + 0.917686i
\(584\) 9.67107 0.400192
\(585\) 3.03262 14.8167i 0.125383 0.612596i
\(586\) 3.83938 0.158603
\(587\) 3.77086 + 3.77086i 0.155640 + 0.155640i 0.780632 0.624992i \(-0.214898\pi\)
−0.624992 + 0.780632i \(0.714898\pi\)
\(588\) 2.83765 1.54179i 0.117023 0.0635825i
\(589\) 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 \(-0.671758\pi\)
0.857918 + 0.513786i \(0.171758\pi\)
\(594\) −4.21191 4.92275i −0.172817 0.201983i
\(595\) −0.178115 + 0.407672i −0.00730199 + 0.0167129i
\(596\) 1.84071i 0.0753985i
\(597\) −11.0928 20.4161i −0.453998 0.835577i
\(598\) 1.83759 + 1.83759i 0.0751446 + 0.0751446i
\(599\) 6.75588 0.276038 0.138019 0.990430i \(-0.455927\pi\)
0.138019 + 0.990430i \(0.455927\pi\)
\(600\) −11.0419 + 5.46084i −0.450782 + 0.222938i
\(601\) 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
\(603\) 0.721331 + 3.38385i 0.0293749 + 0.137801i
\(604\) 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
\(612\) 0.232020 + 1.08843i 0.00937884 + 0.0439972i
\(613\) 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
\(615\) −5.37352 + 0.462179i −0.216681 + 0.0186369i
\(616\) 4.81840 0.194139
\(617\) −5.47009 5.47009i −0.220218 0.220218i 0.588373 0.808590i \(-0.299769\pi\)
−0.808590 + 0.588373i \(0.799769\pi\)
\(618\) −4.21357 7.75500i −0.169494 0.311952i
\(619\) 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
\(627\) −37.8768 + 20.5798i −1.51265 + 0.821878i
\(628\) −9.81311 9.81311i −0.391586 0.391586i
\(629\) −1.66446 −0.0663664
\(630\) 1.36035 + 2.06052i 0.0541978 + 0.0820933i
\(631\) −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
\(633\) −12.3507 + 6.71057i −0.490897 + 0.266721i
\(634\) 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 \(0.791859\pi\)
\(642\) −2.24626 4.13420i −0.0886527 0.163164i
\(643\) −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
\(645\) −3.04905 + 3.62291i −0.120056 + 0.142652i
\(646\) −0.538014 −0.0211679
\(647\) 23.4296 + 23.4296i 0.921112 + 0.921112i 0.997108 0.0759964i \(-0.0242137\pi\)
−0.0759964 + 0.997108i \(0.524214\pi\)
\(648\) 11.9568 + 4.57370i 0.469706 + 0.179672i
\(649\) 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 \(-0.907821\pi\)
0.285557 + 0.958362i \(0.407821\pi\)
\(654\) −1.20769 + 4.08150i −0.0472246 + 0.159599i
\(655\) −18.3815 8.03100i −0.718225 0.313797i
\(656\) 4.46386i 0.174285i
\(657\) −19.9490 + 4.25252i −0.778286 + 0.165906i
\(658\) 0.239739 + 0.239739i 0.00934601 + 0.00934601i
\(659\) −0.0375362 −0.00146220 −0.000731101 1.00000i \(-0.500233\pi\)
−0.000731101 1.00000i \(0.500233\pi\)
\(660\) −2.09625 24.3721i −0.0815966 0.948682i
\(661\) 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
\(663\) 0.370916 + 0.682666i 0.0144052 + 0.0265125i
\(664\) 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
\(672\) −6.12519 + 3.32803i −0.236284 + 0.128381i
\(673\) −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
\(675\) 20.3754 16.1196i 0.784250 0.620445i
\(676\) −14.7616 −0.567753
\(677\) −3.64637 3.64637i −0.140142 0.140142i 0.633556 0.773697i \(-0.281595\pi\)
−0.773697 + 0.633556i \(0.781595\pi\)
\(678\) 6.52335 3.54436i 0.250528 0.136120i
\(679\) 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 \(-0.383555\pi\)
0.933830 0.357718i \(-0.116445\pi\)
\(684\) 22.3620 34.4787i 0.855033 1.31833i
\(685\) 19.1242 7.49436i 0.730697 0.286345i
\(686\) 0.368068i 0.0140529i
\(687\) −3.97013 7.30696i −0.151470 0.278778i
\(688\) −2.77125 2.77125i −0.105653 0.105653i
\(689\) −20.8555 −0.794533
\(690\) 0.382563 + 4.44786i 0.0145639 + 0.169327i
\(691\) −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
\(693\) −9.93918 + 2.11872i −0.377558 + 0.0804836i
\(694\) 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 \(0.865001\pi\)
\(702\) 4.29889 + 0.334529i 0.162251 + 0.0126260i
\(703\) 43.4612 + 43.4612i 1.63917 + 1.63917i
\(704\) 16.6992 0.629377
\(705\) 2.29719 2.72955i 0.0865174 0.102801i
\(706\) 3.93294 0.148018
\(707\) 8.80511 + 8.80511i 0.331150 + 0.331150i
\(708\) 9.63670 + 17.7362i 0.362169 + 0.666567i
\(709\) 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
\(717\) 19.5746 10.6355i 0.731026 0.397192i
\(718\) −1.58632 1.58632i −0.0592008 0.0592008i
\(719\) 39.3153 1.46621 0.733106 0.680114i \(-0.238070\pi\)
0.733106 + 0.680114i \(0.238070\pi\)
\(720\) 11.8474 + 17.9451i 0.441525 + 0.668776i
\(721\) −13.8441 −0.515581
\(722\) 9.10324 + 9.10324i 0.338787 + 0.338787i
\(723\) 24.6331 13.3840i 0.916115 0.497757i
\(724\) 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
\(732\) 2.82551 + 5.20032i 0.104434 + 0.192209i
\(733\) −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
\(735\) 3.85874 0.331892i 0.142332 0.0122420i
\(736\) −12.6040 −0.464589
\(737\) 2.76250 + 2.76250i 0.101758 + 0.101758i
\(738\) −0.320580 1.50388i −0.0118007 0.0553586i
\(739\) 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 −0.990126 0.140180i \(-0.955232\pi\)
0.140180 + 0.990126i \(0.455232\pi\)
\(744\) 0.644914 2.17954i 0.0236437 0.0799057i
\(745\) 0.883803 2.02286i 0.0323800 0.0741120i
\(746\) 3.68059i 0.134756i
\(747\) −5.54518 26.0131i −0.202888 0.951770i
\(748\) 0.888574 + 0.888574i 0.0324895 + 0.0324895i
\(749\) −7.38030 −0.269670
\(750\) −7.11961 + 0.337528i −0.259971 + 0.0123248i
\(751\) 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
\(753\) −6.63894 12.2189i −0.241936 0.445280i
\(754\) 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 \(-0.788674\pi\)
0.787596 0.616193i \(-0.211326\pi\)
\(762\) 1.49075 0.809978i 0.0540043 0.0293424i
\(763\) 4.72108 + 4.72108i 0.170915 + 0.170915i
\(764\) −33.1604 −1.19970
\(765\) −0.267622 + 1.30754i −0.00967589 + 0.0472743i
\(766\) −7.62879 −0.275639
\(767\) 9.96424 + 9.96424i 0.359788 + 0.359788i
\(768\) −9.47970 + 5.15065i −0.342069 + 0.185858i
\(769\) 21.4206i 0.772448i