Properties

Label 349.2.e.a.123.4
Level 349
Weight 2
Character 349.123
Analytic conductor 2.787
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.78677903054\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 123.4
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.00748 + 1.15902i) q^{2} +(1.04619 - 1.81206i) q^{3} +(1.68665 - 2.92136i) q^{4} +(-0.198863 + 0.344441i) q^{5} +4.85022i q^{6} +(-2.47763 + 1.43046i) q^{7} +3.18335i q^{8} +(-0.689035 - 1.19344i) q^{9} +O(q^{10})\) \(q+(-2.00748 + 1.15902i) q^{2} +(1.04619 - 1.81206i) q^{3} +(1.68665 - 2.92136i) q^{4} +(-0.198863 + 0.344441i) q^{5} +4.85022i q^{6} +(-2.47763 + 1.43046i) q^{7} +3.18335i q^{8} +(-0.689035 - 1.19344i) q^{9} -0.921944i q^{10} +4.98737i q^{11} +(-3.52911 - 6.11260i) q^{12} +(-4.31756 + 2.49274i) q^{13} +(3.31586 - 5.74324i) q^{14} +(0.416098 + 0.720703i) q^{15} +(-0.316264 - 0.547785i) q^{16} +5.93523 q^{17} +(2.76644 + 1.59721i) q^{18} +(2.37072 - 4.10621i) q^{19} +(0.670824 + 1.16190i) q^{20} +5.98615i q^{21} +(-5.78045 - 10.0120i) q^{22} +(3.98625 + 6.90439i) q^{23} +(5.76841 + 3.33039i) q^{24} +(2.42091 + 4.19313i) q^{25} +(5.77827 - 10.0083i) q^{26} +3.39370 q^{27} +9.65074i q^{28} +(2.59263 - 4.49057i) q^{29} +(-1.67062 - 0.964530i) q^{30} +2.42891 q^{31} +(-4.24393 - 2.45024i) q^{32} +(9.03739 + 5.21774i) q^{33} +(-11.9148 + 6.87904i) q^{34} -1.13786i q^{35} -4.64863 q^{36} -9.42659 q^{37} +10.9908i q^{38} +10.4316i q^{39} +(-1.09648 - 0.633050i) q^{40} -0.791646 q^{41} +(-6.93806 - 12.0171i) q^{42} +(-6.54900 - 3.78107i) q^{43} +(14.5699 + 8.41193i) q^{44} +0.548094 q^{45} +(-16.0046 - 9.24028i) q^{46} +5.81645i q^{47} -1.32349 q^{48} +(0.592443 - 1.02614i) q^{49} +(-9.71984 - 5.61175i) q^{50} +(6.20939 - 10.7550i) q^{51} +16.8175i q^{52} +7.68414i q^{53} +(-6.81278 + 3.93336i) q^{54} +(-1.71785 - 0.991803i) q^{55} +(-4.55366 - 7.88717i) q^{56} +(-4.96046 - 8.59177i) q^{57} +12.0196i q^{58} +(-1.17170 - 0.676479i) q^{59} +2.80724 q^{60} +5.58802i q^{61} +(-4.87598 + 2.81515i) q^{62} +(3.41435 + 1.97128i) q^{63} +12.6245 q^{64} -1.98286i q^{65} -24.1898 q^{66} -3.17102 q^{67} +(10.0106 - 17.3389i) q^{68} +16.6815 q^{69} +(1.31881 + 2.28424i) q^{70} +(7.05659 - 4.07413i) q^{71} +(3.79914 - 2.19344i) q^{72} +(-5.71174 + 9.89302i) q^{73} +(18.9237 - 10.9256i) q^{74} +10.1309 q^{75} +(-7.99715 - 13.8515i) q^{76} +(-7.13424 - 12.3569i) q^{77} +(-12.0904 - 20.9411i) q^{78} -5.40938i q^{79} +0.251573 q^{80} +(5.61757 - 9.72991i) q^{81} +(1.58921 - 0.917532i) q^{82} +(-2.71361 - 4.70010i) q^{83} +(17.4877 + 10.0965i) q^{84} +(-1.18030 + 2.04434i) q^{85} +17.5293 q^{86} +(-5.42478 - 9.39599i) q^{87} -15.8765 q^{88} +(-1.00312 - 0.579154i) q^{89} +(-1.10029 + 0.635251i) q^{90} +(7.13155 - 12.3522i) q^{91} +26.8936 q^{92} +(2.54111 - 4.40132i) q^{93} +(-6.74138 - 11.6764i) q^{94} +(0.942899 + 1.63315i) q^{95} +(-8.87994 + 5.12684i) q^{96} +(11.1772 - 6.45318i) q^{97} +2.74661i q^{98} +(5.95214 - 3.43647i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} + O(q^{10}) \) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} - q^{12} - 3q^{13} - 10q^{14} + q^{15} - 29q^{16} - 10q^{17} + 15q^{18} - 9q^{19} - 3q^{22} - 17q^{23} - 48q^{24} - 29q^{25} - 4q^{26} + 18q^{27} - 2q^{29} + 9q^{30} + 32q^{31} + 9q^{32} - 12q^{33} - 63q^{34} + 24q^{36} - 16q^{37} + 54q^{40} - 10q^{41} - 15q^{42} - 45q^{43} + 18q^{44} - 2q^{45} + 27q^{46} + 6q^{48} + 35q^{49} + 6q^{50} - 14q^{51} + 27q^{54} + 24q^{55} + 11q^{56} - 29q^{57} - 18q^{59} + 116q^{60} - 9q^{62} - 21q^{63} - 132q^{64} + 130q^{66} + 58q^{67} + 42q^{69} + 40q^{70} - 24q^{71} + 72q^{72} - 6q^{73} + 30q^{74} - 58q^{75} + 37q^{76} - 4q^{77} - 33q^{78} - 40q^{80} - 81q^{81} + 21q^{82} + 12q^{83} + 18q^{84} - 11q^{85} - 126q^{86} - 42q^{87} - 50q^{88} + 3q^{89} - 12q^{90} - 28q^{91} - 120q^{92} + 31q^{93} + 29q^{94} + 60q^{95} - 120q^{96} - 15q^{97} + 39q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00748 + 1.15902i −1.41950 + 0.819550i −0.996255 0.0864646i \(-0.972443\pi\)
−0.423247 + 0.906014i \(0.639110\pi\)
\(3\) 1.04619 1.81206i 0.604019 1.04619i −0.388187 0.921581i \(-0.626898\pi\)
0.992206 0.124611i \(-0.0397683\pi\)
\(4\) 1.68665 2.92136i 0.843324 1.46068i
\(5\) −0.198863 + 0.344441i −0.0889343 + 0.154039i −0.907061 0.420999i \(-0.861679\pi\)
0.818127 + 0.575038i \(0.195013\pi\)
\(6\) 4.85022i 1.98009i
\(7\) −2.47763 + 1.43046i −0.936457 + 0.540664i −0.888848 0.458202i \(-0.848494\pi\)
−0.0476092 + 0.998866i \(0.515160\pi\)
\(8\) 3.18335i 1.12548i
\(9\) −0.689035 1.19344i −0.229678 0.397814i
\(10\) 0.921944i 0.291544i
\(11\) 4.98737i 1.50375i 0.659307 + 0.751874i \(0.270850\pi\)
−0.659307 + 0.751874i \(0.729150\pi\)
\(12\) −3.52911 6.11260i −1.01877 1.76456i
\(13\) −4.31756 + 2.49274i −1.19748 + 0.691363i −0.959992 0.280029i \(-0.909656\pi\)
−0.237484 + 0.971392i \(0.576323\pi\)
\(14\) 3.31586 5.74324i 0.886202 1.53495i
\(15\) 0.416098 + 0.720703i 0.107436 + 0.186085i
\(16\) −0.316264 0.547785i −0.0790659 0.136946i
\(17\) 5.93523 1.43950 0.719752 0.694231i \(-0.244255\pi\)
0.719752 + 0.694231i \(0.244255\pi\)
\(18\) 2.76644 + 1.59721i 0.652057 + 0.376465i
\(19\) 2.37072 4.10621i 0.543881 0.942030i −0.454795 0.890596i \(-0.650288\pi\)
0.998676 0.0514337i \(-0.0163791\pi\)
\(20\) 0.670824 + 1.16190i 0.150001 + 0.259809i
\(21\) 5.98615i 1.30629i
\(22\) −5.78045 10.0120i −1.23240 2.13457i
\(23\) 3.98625 + 6.90439i 0.831191 + 1.43967i 0.897094 + 0.441839i \(0.145674\pi\)
−0.0659030 + 0.997826i \(0.520993\pi\)
\(24\) 5.76841 + 3.33039i 1.17747 + 0.679813i
\(25\) 2.42091 + 4.19313i 0.484181 + 0.838627i
\(26\) 5.77827 10.0083i 1.13321 1.96278i
\(27\) 3.39370 0.653118
\(28\) 9.65074i 1.82382i
\(29\) 2.59263 4.49057i 0.481439 0.833877i −0.518334 0.855178i \(-0.673447\pi\)
0.999773 + 0.0213010i \(0.00678082\pi\)
\(30\) −1.67062 0.964530i −0.305011 0.176098i
\(31\) 2.42891 0.436245 0.218123 0.975921i \(-0.430007\pi\)
0.218123 + 0.975921i \(0.430007\pi\)
\(32\) −4.24393 2.45024i −0.750229 0.433145i
\(33\) 9.03739 + 5.21774i 1.57321 + 0.908292i
\(34\) −11.9148 + 6.87904i −2.04338 + 1.17975i
\(35\) 1.13786i 0.192334i
\(36\) −4.64863 −0.774772
\(37\) −9.42659 −1.54972 −0.774861 0.632132i \(-0.782180\pi\)
−0.774861 + 0.632132i \(0.782180\pi\)
\(38\) 10.9908i 1.78295i
\(39\) 10.4316i 1.67038i
\(40\) −1.09648 0.633050i −0.173368 0.100094i
\(41\) −0.791646 −0.123634 −0.0618172 0.998087i \(-0.519690\pi\)
−0.0618172 + 0.998087i \(0.519690\pi\)
\(42\) −6.93806 12.0171i −1.07057 1.85427i
\(43\) −6.54900 3.78107i −0.998713 0.576607i −0.0908457 0.995865i \(-0.528957\pi\)
−0.907867 + 0.419258i \(0.862290\pi\)
\(44\) 14.5699 + 8.41193i 2.19649 + 1.26815i
\(45\) 0.548094 0.0817051
\(46\) −16.0046 9.24028i −2.35975 1.36241i
\(47\) 5.81645i 0.848417i 0.905565 + 0.424208i \(0.139448\pi\)
−0.905565 + 0.424208i \(0.860552\pi\)
\(48\) −1.32349 −0.191029
\(49\) 0.592443 1.02614i 0.0846348 0.146592i
\(50\) −9.71984 5.61175i −1.37459 0.793621i
\(51\) 6.20939 10.7550i 0.869488 1.50600i
\(52\) 16.8175i 2.33217i
\(53\) 7.68414i 1.05550i 0.849400 + 0.527749i \(0.176964\pi\)
−0.849400 + 0.527749i \(0.823036\pi\)
\(54\) −6.81278 + 3.93336i −0.927102 + 0.535263i
\(55\) −1.71785 0.991803i −0.231635 0.133735i
\(56\) −4.55366 7.88717i −0.608508 1.05397i
\(57\) −4.96046 8.59177i −0.657029 1.13801i
\(58\) 12.0196i 1.57825i
\(59\) −1.17170 0.676479i −0.152542 0.0880700i 0.421786 0.906695i \(-0.361403\pi\)
−0.574328 + 0.818625i \(0.694737\pi\)
\(60\) 2.80724 0.362413
\(61\) 5.58802i 0.715473i 0.933823 + 0.357736i \(0.116451\pi\)
−0.933823 + 0.357736i \(0.883549\pi\)
\(62\) −4.87598 + 2.81515i −0.619251 + 0.357525i
\(63\) 3.41435 + 1.97128i 0.430168 + 0.248357i
\(64\) 12.6245 1.57807
\(65\) 1.98286i 0.245943i
\(66\) −24.1898 −2.97756
\(67\) −3.17102 −0.387401 −0.193701 0.981061i \(-0.562049\pi\)
−0.193701 + 0.981061i \(0.562049\pi\)
\(68\) 10.0106 17.3389i 1.21397 2.10266i
\(69\) 16.6815 2.00822
\(70\) 1.31881 + 2.28424i 0.157627 + 0.273019i
\(71\) 7.05659 4.07413i 0.837464 0.483510i −0.0189377 0.999821i \(-0.506028\pi\)
0.856401 + 0.516311i \(0.172695\pi\)
\(72\) 3.79914 2.19344i 0.447733 0.258499i
\(73\) −5.71174 + 9.89302i −0.668509 + 1.15789i 0.309813 + 0.950798i \(0.399734\pi\)
−0.978321 + 0.207093i \(0.933600\pi\)
\(74\) 18.9237 10.9256i 2.19983 1.27007i
\(75\) 10.1309 1.16982
\(76\) −7.99715 13.8515i −0.917336 1.58887i
\(77\) −7.13424 12.3569i −0.813022 1.40820i
\(78\) −12.0904 20.9411i −1.36896 2.37111i
\(79\) 5.40938i 0.608603i −0.952576 0.304301i \(-0.901577\pi\)
0.952576 0.304301i \(-0.0984230\pi\)
\(80\) 0.251573 0.0281267
\(81\) 5.61757 9.72991i 0.624174 1.08110i
\(82\) 1.58921 0.917532i 0.175499 0.101325i
\(83\) −2.71361 4.70010i −0.297857 0.515903i 0.677789 0.735257i \(-0.262938\pi\)
−0.975645 + 0.219354i \(0.929605\pi\)
\(84\) 17.4877 + 10.0965i 1.90806 + 1.10162i
\(85\) −1.18030 + 2.04434i −0.128021 + 0.221739i
\(86\) 17.5293 1.89023
\(87\) −5.42478 9.39599i −0.581597 1.00736i
\(88\) −15.8765 −1.69244
\(89\) −1.00312 0.579154i −0.106331 0.0613902i 0.445891 0.895087i \(-0.352887\pi\)
−0.552222 + 0.833697i \(0.686220\pi\)
\(90\) −1.10029 + 0.635251i −0.115981 + 0.0669614i
\(91\) 7.13155 12.3522i 0.747590 1.29486i
\(92\) 26.8936 2.80385
\(93\) 2.54111 4.40132i 0.263500 0.456396i
\(94\) −6.74138 11.6764i −0.695320 1.20433i
\(95\) 0.942899 + 1.63315i 0.0967394 + 0.167558i
\(96\) −8.87994 + 5.12684i −0.906305 + 0.523255i
\(97\) 11.1772 6.45318i 1.13488 0.655221i 0.189719 0.981838i \(-0.439242\pi\)
0.945157 + 0.326618i \(0.105909\pi\)
\(98\) 2.74661i 0.277450i
\(99\) 5.95214 3.43647i 0.598212 0.345378i
\(100\) 16.3329 1.63329
\(101\) 19.1662i 1.90711i 0.301222 + 0.953554i \(0.402605\pi\)
−0.301222 + 0.953554i \(0.597395\pi\)
\(102\) 28.7872i 2.85036i
\(103\) 9.30686i 0.917032i −0.888686 0.458516i \(-0.848381\pi\)
0.888686 0.458516i \(-0.151619\pi\)
\(104\) −7.93527 13.7443i −0.778117 1.34774i
\(105\) −2.06188 1.19042i −0.201219 0.116174i
\(106\) −8.90606 15.4257i −0.865033 1.49828i
\(107\) −5.21561 + 3.01123i −0.504212 + 0.291107i −0.730451 0.682965i \(-0.760690\pi\)
0.226239 + 0.974072i \(0.427357\pi\)
\(108\) 5.72398 9.91422i 0.550790 0.953996i
\(109\) −4.68912 + 8.12179i −0.449136 + 0.777926i −0.998330 0.0577687i \(-0.981601\pi\)
0.549194 + 0.835695i \(0.314935\pi\)
\(110\) 4.59807 0.438409
\(111\) −9.86202 + 17.0815i −0.936062 + 1.62131i
\(112\) 1.56717 + 0.904806i 0.148084 + 0.0854962i
\(113\) −1.66450 + 0.960999i −0.156583 + 0.0904032i −0.576244 0.817278i \(-0.695482\pi\)
0.419661 + 0.907681i \(0.362149\pi\)
\(114\) 19.9160 + 11.4985i 1.86531 + 1.07694i
\(115\) −3.17088 −0.295686
\(116\) −8.74571 15.1480i −0.812018 1.40646i
\(117\) 5.94989 + 3.43517i 0.550068 + 0.317582i
\(118\) 3.13621 0.288711
\(119\) −14.7053 + 8.49012i −1.34803 + 0.778288i
\(120\) −2.29425 + 1.32458i −0.209435 + 0.120917i
\(121\) −13.8738 −1.26126
\(122\) −6.47662 11.2178i −0.586365 1.01561i
\(123\) −0.828214 + 1.43451i −0.0746775 + 0.129345i
\(124\) 4.09671 7.09572i 0.367896 0.637214i
\(125\) −3.91435 −0.350110
\(126\) −9.13898 −0.814165
\(127\) 16.0745i 1.42638i −0.700971 0.713190i \(-0.747250\pi\)
0.700971 0.713190i \(-0.252750\pi\)
\(128\) −16.8556 + 9.73159i −1.48984 + 0.860159i
\(129\) −13.7030 + 7.91144i −1.20648 + 0.696563i
\(130\) 2.29817 + 3.98055i 0.201563 + 0.349117i
\(131\) 0.743618i 0.0649702i −0.999472 0.0324851i \(-0.989658\pi\)
0.999472 0.0324851i \(-0.0103421\pi\)
\(132\) 30.4858 17.6010i 2.65345 1.53197i
\(133\) 13.5649i 1.17623i
\(134\) 6.36575 3.67526i 0.549917 0.317495i
\(135\) −0.674882 + 1.16893i −0.0580846 + 0.100605i
\(136\) 18.8939i 1.62014i
\(137\) 9.95475 + 5.74738i 0.850492 + 0.491032i 0.860817 0.508915i \(-0.169953\pi\)
−0.0103251 + 0.999947i \(0.503287\pi\)
\(138\) −33.4878 + 19.3342i −2.85067 + 1.64584i
\(139\) 1.46808 0.124521 0.0622605 0.998060i \(-0.480169\pi\)
0.0622605 + 0.998060i \(0.480169\pi\)
\(140\) −3.32411 1.91918i −0.280939 0.162200i
\(141\) 10.5397 + 6.08513i 0.887607 + 0.512460i
\(142\) −9.44397 + 16.3574i −0.792521 + 1.37269i
\(143\) −12.4322 21.5332i −1.03963 1.80070i
\(144\) −0.435833 + 0.754885i −0.0363194 + 0.0629071i
\(145\) 1.03116 + 1.78602i 0.0856329 + 0.148321i
\(146\) 26.4800i 2.19150i
\(147\) −1.23962 2.14708i −0.102242 0.177088i
\(148\) −15.8993 + 27.5385i −1.30692 + 2.26365i
\(149\) 7.74922 4.47402i 0.634841 0.366526i −0.147783 0.989020i \(-0.547214\pi\)
0.782624 + 0.622494i \(0.213881\pi\)
\(150\) −20.3376 + 11.7419i −1.66056 + 0.958725i
\(151\) −4.76085 + 8.24604i −0.387433 + 0.671053i −0.992103 0.125423i \(-0.959971\pi\)
0.604671 + 0.796475i \(0.293305\pi\)
\(152\) 13.0715 + 7.54683i 1.06024 + 0.612129i
\(153\) −4.08958 7.08336i −0.330623 0.572656i
\(154\) 28.6437 + 16.5374i 2.30817 + 1.33262i
\(155\) −0.483021 + 0.836616i −0.0387972 + 0.0671986i
\(156\) 30.4743 + 17.5943i 2.43990 + 1.40868i
\(157\) 0.464102 0.803848i 0.0370394 0.0641540i −0.846911 0.531734i \(-0.821541\pi\)
0.883951 + 0.467580i \(0.154874\pi\)
\(158\) 6.26957 + 10.8592i 0.498780 + 0.863913i
\(159\) 13.9241 + 8.03908i 1.10425 + 0.637541i
\(160\) 1.68792 0.974524i 0.133442 0.0770428i
\(161\) −19.7529 11.4044i −1.55675 0.898790i
\(162\) 26.0435i 2.04617i
\(163\) 22.4570i 1.75897i −0.475930 0.879483i \(-0.657888\pi\)
0.475930 0.879483i \(-0.342112\pi\)
\(164\) −1.33523 + 2.31268i −0.104264 + 0.180590i
\(165\) −3.59441 + 2.07523i −0.279824 + 0.161557i
\(166\) 10.8950 + 6.29024i 0.845617 + 0.488217i
\(167\) 9.38473i 0.726212i −0.931748 0.363106i \(-0.881716\pi\)
0.931748 0.363106i \(-0.118284\pi\)
\(168\) −19.0560 −1.47020
\(169\) 5.92754 10.2668i 0.455964 0.789754i
\(170\) 5.47195i 0.419680i
\(171\) −6.53404 −0.499671
\(172\) −22.0917 + 12.7546i −1.68448 + 0.972533i
\(173\) −2.49363 + 1.43970i −0.189588 + 0.109458i −0.591789 0.806093i \(-0.701578\pi\)
0.402202 + 0.915551i \(0.368245\pi\)
\(174\) 21.7803 + 12.5748i 1.65116 + 0.953296i
\(175\) −11.9962 6.92603i −0.906830 0.523559i
\(176\) 2.73200 1.57732i 0.205933 0.118895i
\(177\) −2.45164 + 1.41545i −0.184276 + 0.106392i
\(178\) 2.68500 0.201249
\(179\) 23.4052i 1.74938i −0.484680 0.874692i \(-0.661064\pi\)
0.484680 0.874692i \(-0.338936\pi\)
\(180\) 0.924442 1.60118i 0.0689038 0.119345i
\(181\) 12.9310 0.961156 0.480578 0.876952i \(-0.340427\pi\)
0.480578 + 0.876952i \(0.340427\pi\)
\(182\) 33.0624i 2.45075i
\(183\) 10.1258 + 5.84614i 0.748522 + 0.432159i
\(184\) −21.9791 + 12.6896i −1.62032 + 0.935492i
\(185\) 1.87460 3.24690i 0.137823 0.238717i
\(186\) 11.7808i 0.863807i
\(187\) 29.6012i 2.16465i
\(188\) 16.9919 + 9.81031i 1.23927 + 0.715490i
\(189\) −8.40835 + 4.85456i −0.611617 + 0.353117i
\(190\) −3.78570 2.18567i −0.274643 0.158565i
\(191\) −2.87935 4.98717i −0.208342 0.360859i 0.742850 0.669458i \(-0.233473\pi\)
−0.951192 + 0.308598i \(0.900140\pi\)
\(192\) 13.2077 22.8764i 0.953182 1.65096i
\(193\) 18.5079 + 10.6855i 1.33223 + 0.769161i 0.985641 0.168857i \(-0.0540076\pi\)
0.346586 + 0.938018i \(0.387341\pi\)
\(194\) −14.9587 + 25.9092i −1.07397 + 1.86017i
\(195\) −3.59305 2.07445i −0.257304 0.148555i
\(196\) −1.99849 3.46148i −0.142749 0.247249i
\(197\) −12.9195 7.45908i −0.920477 0.531438i −0.0366899 0.999327i \(-0.511681\pi\)
−0.883787 + 0.467889i \(0.845015\pi\)
\(198\) −7.96586 + 13.7973i −0.566109 + 0.980530i
\(199\) 15.7187 9.07521i 1.11427 0.643325i 0.174339 0.984686i \(-0.444221\pi\)
0.939932 + 0.341361i \(0.110888\pi\)
\(200\) −13.3482 + 7.70659i −0.943860 + 0.544938i
\(201\) −3.31749 + 5.74606i −0.233998 + 0.405296i
\(202\) −22.2140 38.4757i −1.56297 2.70714i
\(203\) 14.8346i 1.04119i
\(204\) −20.9461 36.2797i −1.46652 2.54009i
\(205\) 0.157429 0.272675i 0.0109953 0.0190445i
\(206\) 10.7868 + 18.6833i 0.751553 + 1.30173i
\(207\) 5.49333 9.51473i 0.381813 0.661320i
\(208\) 2.73097 + 1.57673i 0.189359 + 0.109326i
\(209\) 20.4792 + 11.8237i 1.41657 + 0.817860i
\(210\) 5.51890 0.380840
\(211\) 18.3501 10.5944i 1.26327 0.729349i 0.289564 0.957159i \(-0.406490\pi\)
0.973706 + 0.227809i \(0.0731562\pi\)
\(212\) 22.4481 + 12.9604i 1.54174 + 0.890126i
\(213\) 17.0493i 1.16820i
\(214\) 6.98015 12.0900i 0.477153 0.826454i
\(215\) 2.60471 1.50383i 0.177640 0.102560i
\(216\) 10.8033i 0.735074i
\(217\) −6.01795 + 3.47446i −0.408525 + 0.235862i
\(218\) 21.7391i 1.47236i
\(219\) 11.9512 + 20.7000i 0.807584 + 1.39878i
\(220\) −5.79483 + 3.34565i −0.390687 + 0.225563i
\(221\) −25.6257 + 14.7950i −1.72377 + 0.995220i
\(222\) 45.7211i 3.06860i
\(223\) −8.91308 −0.596864 −0.298432 0.954431i \(-0.596464\pi\)
−0.298432 + 0.954431i \(0.596464\pi\)
\(224\) 14.0199 0.936743
\(225\) 3.33618 5.77843i 0.222412 0.385229i
\(226\) 2.22763 3.85837i 0.148180 0.256655i
\(227\) 12.1577 + 21.0578i 0.806937 + 1.39766i 0.914976 + 0.403509i \(0.132210\pi\)
−0.108039 + 0.994147i \(0.534457\pi\)
\(228\) −33.4662 −2.21635
\(229\) 14.1713 8.18178i 0.936463 0.540667i 0.0476135 0.998866i \(-0.484838\pi\)
0.888850 + 0.458198i \(0.151505\pi\)
\(230\) 6.36546 3.67510i 0.419726 0.242329i
\(231\) −29.8551 −1.96432
\(232\) 14.2950 + 8.25324i 0.938515 + 0.541852i
\(233\) −6.63900 11.4991i −0.434935 0.753330i 0.562355 0.826896i \(-0.309895\pi\)
−0.997290 + 0.0735659i \(0.976562\pi\)
\(234\) −15.9257 −1.04110
\(235\) −2.00343 1.15668i −0.130689 0.0754534i
\(236\) −3.95247 + 2.28196i −0.257284 + 0.148543i
\(237\) −9.80211 5.65925i −0.636715 0.367608i
\(238\) 19.6804 34.0875i 1.27569 2.20956i
\(239\) 1.29712 0.0839035 0.0419517 0.999120i \(-0.486642\pi\)
0.0419517 + 0.999120i \(0.486642\pi\)
\(240\) 0.263193 0.455864i 0.0169891 0.0294259i
\(241\) 3.07384 5.32404i 0.198003 0.342952i −0.749878 0.661576i \(-0.769888\pi\)
0.947881 + 0.318625i \(0.103221\pi\)
\(242\) 27.8514 16.0800i 1.79036 1.03366i
\(243\) −6.66355 11.5416i −0.427467 0.740395i
\(244\) 16.3246 + 9.42502i 1.04508 + 0.603375i
\(245\) 0.235630 + 0.408124i 0.0150539 + 0.0260741i
\(246\) 3.83966i 0.244808i
\(247\) 23.6384i 1.50408i
\(248\) 7.73206i 0.490987i
\(249\) −11.3558 −0.719645
\(250\) 7.85797 4.53680i 0.496982 0.286933i
\(251\) 17.4969i 1.10440i 0.833713 + 0.552199i \(0.186211\pi\)
−0.833713 + 0.552199i \(0.813789\pi\)
\(252\) 11.5176 6.64969i 0.725541 0.418891i
\(253\) −34.4347 + 19.8809i −2.16489 + 1.24990i
\(254\) 18.6306 + 32.2692i 1.16899 + 2.02475i
\(255\) 2.46964 + 4.27754i 0.154655 + 0.267870i
\(256\) 9.93366 17.2056i 0.620853 1.07535i
\(257\) −6.05169 −0.377494 −0.188747 0.982026i \(-0.560443\pi\)
−0.188747 + 0.982026i \(0.560443\pi\)
\(258\) 18.3390 31.7641i 1.14174 1.97755i
\(259\) 23.3556 13.4844i 1.45125 0.837879i
\(260\) −5.79264 3.34438i −0.359244 0.207410i
\(261\) −7.14565 −0.442305
\(262\) 0.861867 + 1.49280i 0.0532463 + 0.0922253i
\(263\) 25.9903 1.60263 0.801314 0.598244i \(-0.204135\pi\)
0.801314 + 0.598244i \(0.204135\pi\)
\(264\) −16.6099 + 28.7692i −1.02227 + 1.77062i
\(265\) −2.64673 1.52809i −0.162588 0.0938699i
\(266\) −15.7220 27.2313i −0.963977 1.66966i
\(267\) −2.09892 + 1.21181i −0.128452 + 0.0741618i
\(268\) −5.34838 + 9.26367i −0.326705 + 0.565869i
\(269\) 3.36461 0.205144 0.102572 0.994726i \(-0.467293\pi\)
0.102572 + 0.994726i \(0.467293\pi\)
\(270\) 3.12880i 0.190413i
\(271\) −5.09181 8.81927i −0.309305 0.535732i 0.668905 0.743348i \(-0.266763\pi\)
−0.978211 + 0.207615i \(0.933430\pi\)
\(272\) −1.87710 3.25123i −0.113816 0.197135i
\(273\) −14.9219 25.8456i −0.903117 1.56424i
\(274\) −26.6453 −1.60970
\(275\) −20.9127 + 12.0740i −1.26108 + 0.728087i
\(276\) 28.1359 48.7328i 1.69358 2.93337i
\(277\) −23.0308 + 13.2968i −1.38379 + 0.798930i −0.992606 0.121384i \(-0.961267\pi\)
−0.391181 + 0.920314i \(0.627933\pi\)
\(278\) −2.94714 + 1.70153i −0.176758 + 0.102051i
\(279\) −1.67360 2.89877i −0.100196 0.173545i
\(280\) 3.62222 0.216469
\(281\) 10.5331 18.2439i 0.628352 1.08834i −0.359530 0.933134i \(-0.617063\pi\)
0.987882 0.155205i \(-0.0496037\pi\)
\(282\) −28.2111 −1.67995
\(283\) 7.83319 0.465635 0.232817 0.972520i \(-0.425206\pi\)
0.232817 + 0.972520i \(0.425206\pi\)
\(284\) 27.4865i 1.63102i
\(285\) 3.94581 0.233730
\(286\) 49.9149 + 28.8184i 2.95153 + 1.70407i
\(287\) 1.96141 1.13242i 0.115778 0.0668446i
\(288\) 6.75319i 0.397936i
\(289\) 18.2270 1.07217
\(290\) −4.14005 2.39026i −0.243112 0.140361i
\(291\) 27.0050i 1.58306i
\(292\) 19.2674 + 33.3721i 1.12754 + 1.95295i
\(293\) −0.475816 0.824137i −0.0277974 0.0481466i 0.851792 0.523880i \(-0.175516\pi\)
−0.879589 + 0.475733i \(0.842183\pi\)
\(294\) 4.97702 + 2.87348i 0.290265 + 0.167585i
\(295\) 0.466014 0.269053i 0.0271324 0.0156649i
\(296\) 30.0081i 1.74419i
\(297\) 16.9256i 0.982125i
\(298\) −10.3709 + 17.9630i −0.600772 + 1.04057i
\(299\) −34.4218 19.8734i −1.99066 1.14931i
\(300\) 17.0873 29.5961i 0.986536 1.70873i
\(301\) 21.6347 1.24700
\(302\) 22.0717i 1.27008i
\(303\) 34.7302 + 20.0515i 1.99520 + 1.15193i
\(304\) −2.99909 −0.172010
\(305\) −1.92474 1.11125i −0.110210 0.0636301i
\(306\) 16.4195 + 9.47980i 0.938640 + 0.541924i
\(307\) 3.05365 + 5.28908i 0.174281 + 0.301864i 0.939912 0.341416i \(-0.110906\pi\)
−0.765631 + 0.643280i \(0.777573\pi\)
\(308\) −48.1318 −2.74256
\(309\) −16.8646 9.73676i −0.959391 0.553905i
\(310\) 2.23932i 0.127185i
\(311\) 2.13204i 0.120897i −0.998171 0.0604484i \(-0.980747\pi\)
0.998171 0.0604484i \(-0.0192530\pi\)
\(312\) −33.2073 −1.87999
\(313\) 16.0453 0.906932 0.453466 0.891274i \(-0.350187\pi\)
0.453466 + 0.891274i \(0.350187\pi\)
\(314\) 2.15161i 0.121422i
\(315\) −1.35798 + 0.784028i −0.0765133 + 0.0441750i
\(316\) −15.8027 9.12371i −0.888973 0.513249i
\(317\) 1.66090 + 0.958920i 0.0932854 + 0.0538583i 0.545917 0.837839i \(-0.316181\pi\)
−0.452632 + 0.891698i \(0.649515\pi\)
\(318\) −37.2698 −2.08999
\(319\) 22.3961 + 12.9304i 1.25394 + 0.723963i
\(320\) −2.51055 + 4.34841i −0.140344 + 0.243083i
\(321\) 12.6013i 0.703337i
\(322\) 52.8715 2.94641
\(323\) 14.0708 24.3713i 0.782920 1.35606i
\(324\) −18.9497 32.8219i −1.05276 1.82344i
\(325\) −20.9048 12.0694i −1.15959 0.669490i
\(326\) 26.0281 + 45.0819i 1.44156 + 2.49686i
\(327\) 9.81143 + 16.9939i 0.542573 + 0.939764i
\(328\) 2.52008i 0.139148i
\(329\) −8.32022 14.4110i −0.458708 0.794506i
\(330\) 4.81047 8.33197i 0.264807 0.458660i
\(331\) 10.5231 + 6.07552i 0.578402 + 0.333941i 0.760498 0.649340i \(-0.224955\pi\)
−0.182096 + 0.983281i \(0.558288\pi\)
\(332\) −18.3076 −1.00476
\(333\) 6.49525 + 11.2501i 0.355937 + 0.616502i
\(334\) 10.8771 + 18.8396i 0.595167 + 1.03086i
\(335\) 0.630598 1.09223i 0.0344533 0.0596748i
\(336\) 3.27912 1.89320i 0.178891 0.103283i
\(337\) −10.8552 18.8018i −0.591323 1.02420i −0.994055 0.108883i \(-0.965273\pi\)
0.402732 0.915318i \(-0.368061\pi\)
\(338\) 27.4805i 1.49474i
\(339\) 4.02156i 0.218421i
\(340\) 3.98149 + 6.89615i 0.215927 + 0.373996i
\(341\) 12.1139i 0.656002i
\(342\) 13.1169 7.57307i 0.709283 0.409505i
\(343\) 16.6366i 0.898292i
\(344\) 12.0364 20.8477i 0.648962 1.12403i
\(345\) −3.31734 + 5.74581i −0.178600 + 0.309344i
\(346\) 3.33728 5.78034i 0.179413 0.310753i
\(347\) 1.14719 0.662333i 0.0615846 0.0355559i −0.468892 0.883256i \(-0.655346\pi\)
0.530476 + 0.847700i \(0.322013\pi\)
\(348\) −36.5987 −1.96190
\(349\) −16.2365 9.23986i −0.869122 0.494599i
\(350\) 32.1096 1.71633
\(351\) −14.6525 + 8.45963i −0.782093 + 0.451541i
\(352\) 12.2202 21.1661i 0.651340 1.12815i
\(353\) 1.35544 2.34769i 0.0721429 0.124955i −0.827697 0.561175i \(-0.810350\pi\)
0.899840 + 0.436220i \(0.143683\pi\)
\(354\) 3.28107 5.68298i 0.174387 0.302047i
\(355\) 3.24077i 0.172002i
\(356\) −3.38384 + 1.95366i −0.179343 + 0.103544i
\(357\) 35.5292i 1.88040i
\(358\) 27.1270 + 46.9854i 1.43371 + 2.48325i
\(359\) 30.1789i 1.59278i 0.604783 + 0.796390i \(0.293260\pi\)
−0.604783 + 0.796390i \(0.706740\pi\)
\(360\) 1.74477i 0.0919577i
\(361\) −1.74065 3.01490i −0.0916134 0.158679i
\(362\) −25.9588 + 14.9873i −1.36436 + 0.787715i
\(363\) −14.5147 + 25.1402i −0.761823 + 1.31952i
\(364\) −24.0568 41.6676i −1.26092 2.18398i
\(365\) −2.27171 3.93472i −0.118907 0.205952i
\(366\) −27.1031 −1.41670
\(367\) 5.02994 + 2.90404i 0.262561 + 0.151590i 0.625502 0.780222i \(-0.284894\pi\)
−0.362941 + 0.931812i \(0.618227\pi\)
\(368\) 2.52141 4.36722i 0.131438 0.227657i
\(369\) 0.545472 + 0.944785i 0.0283961 + 0.0491835i
\(370\) 8.69079i 0.451813i
\(371\) −10.9919 19.0385i −0.570669 0.988428i
\(372\) −8.57190 14.8470i −0.444432 0.769779i
\(373\) −32.7174 18.8894i −1.69404 0.978056i −0.951192 0.308600i \(-0.900140\pi\)
−0.742851 0.669456i \(-0.766527\pi\)
\(374\) −34.3083 59.4237i −1.77404 3.07273i
\(375\) −4.09516 + 7.09302i −0.211473 + 0.366282i
\(376\) −18.5158 −0.954879
\(377\) 25.8510i 1.33140i
\(378\) 11.2531 19.4909i 0.578794 1.00250i
\(379\) −7.80625 4.50694i −0.400980 0.231506i 0.285927 0.958251i \(-0.407699\pi\)
−0.686907 + 0.726746i \(0.741032\pi\)
\(380\) 6.36135 0.326330
\(381\) −29.1279 16.8170i −1.49227 0.861561i
\(382\) 11.5604 + 6.67443i 0.591484 + 0.341493i
\(383\) 7.59605 4.38558i 0.388140 0.224093i −0.293214 0.956047i \(-0.594725\pi\)
0.681354 + 0.731954i \(0.261391\pi\)
\(384\) 40.7244i 2.07821i
\(385\) 5.67495 0.289222
\(386\) −49.5389 −2.52146
\(387\) 10.4211i 0.529736i
\(388\) 43.5369i 2.21025i
\(389\) −4.48239 2.58791i −0.227266 0.131212i 0.382044 0.924144i \(-0.375220\pi\)
−0.609310 + 0.792932i \(0.708554\pi\)
\(390\) 9.61731 0.486991
\(391\) 23.6593 + 40.9792i 1.19650 + 2.07241i
\(392\) 3.26657 + 1.88595i 0.164987 + 0.0952550i
\(393\) −1.34748 0.777967i −0.0679713 0.0392432i
\(394\) 34.5809 1.74216
\(395\) 1.86321 + 1.07573i 0.0937484 + 0.0541257i
\(396\) 23.1844i 1.16506i
\(397\) 15.5125 0.778550 0.389275 0.921121i \(-0.372726\pi\)
0.389275 + 0.921121i \(0.372726\pi\)
\(398\) −21.0367 + 36.4366i −1.05447 + 1.82640i
\(399\) 24.5804 + 14.1915i 1.23056 + 0.710464i
\(400\) 1.53129 2.65227i 0.0765645 0.132614i
\(401\) 32.4489i 1.62042i 0.586140 + 0.810210i \(0.300647\pi\)
−0.586140 + 0.810210i \(0.699353\pi\)
\(402\) 15.3801i 0.767091i
\(403\) −10.4870 + 6.05465i −0.522393 + 0.301604i
\(404\) 55.9913 + 32.3266i 2.78567 + 1.60831i
\(405\) 2.23425 + 3.86984i 0.111021 + 0.192294i
\(406\) −17.1936 29.7802i −0.853305 1.47797i
\(407\) 47.0139i 2.33039i
\(408\) 34.2368 + 19.7666i 1.69498 + 0.978595i
\(409\) −4.73154 −0.233960 −0.116980 0.993134i \(-0.537321\pi\)
−0.116980 + 0.993134i \(0.537321\pi\)
\(410\) 0.729853i 0.0360449i
\(411\) 20.8292 12.0257i 1.02743 0.593185i
\(412\) −27.1887 15.6974i −1.33949 0.773355i
\(413\) 3.87071 0.190465
\(414\) 25.4675i 1.25166i
\(415\) 2.15854 0.105959
\(416\) 24.4312 1.19784
\(417\) 1.53590 2.66025i 0.0752131 0.130273i
\(418\) −54.8154 −2.68111
\(419\) −11.6265 20.1377i −0.567991 0.983790i −0.996764 0.0803777i \(-0.974387\pi\)
0.428773 0.903412i \(-0.358946\pi\)
\(420\) −6.95532 + 4.01565i −0.339385 + 0.195944i
\(421\) −26.6962 + 15.4131i −1.30109 + 0.751186i −0.980591 0.196062i \(-0.937185\pi\)
−0.320501 + 0.947248i \(0.603851\pi\)
\(422\) −24.5582 + 42.5361i −1.19548 + 2.07063i
\(423\) 6.94161 4.00774i 0.337512 0.194863i
\(424\) −24.4613 −1.18794
\(425\) 14.3686 + 24.8872i 0.696981 + 1.20721i
\(426\) 19.7604 + 34.2260i 0.957395 + 1.65826i
\(427\) −7.99345 13.8451i −0.386830 0.670009i
\(428\) 20.3156i 0.981990i
\(429\) −52.0260 −2.51184
\(430\) −3.48593 + 6.03781i −0.168107 + 0.291169i
\(431\) 22.7086 13.1108i 1.09383 0.631526i 0.159240 0.987240i \(-0.449096\pi\)
0.934595 + 0.355714i \(0.115762\pi\)
\(432\) −1.07330 1.85902i −0.0516394 0.0894420i
\(433\) 2.61641 + 1.51059i 0.125737 + 0.0725942i 0.561549 0.827443i \(-0.310206\pi\)
−0.435812 + 0.900038i \(0.643539\pi\)
\(434\) 8.05393 13.9498i 0.386601 0.669613i
\(435\) 4.31515 0.206896
\(436\) 15.8178 + 27.3972i 0.757534 + 1.31209i
\(437\) 37.8012 1.80828
\(438\) −47.9834 27.7032i −2.29273 1.32371i
\(439\) 4.32255 2.49562i 0.206304 0.119110i −0.393289 0.919415i \(-0.628663\pi\)
0.599592 + 0.800305i \(0.295329\pi\)
\(440\) 3.15725 5.46853i 0.150516 0.260702i
\(441\) −1.63286 −0.0777550
\(442\) 34.2954 59.4013i 1.63126 2.82543i
\(443\) 10.8276 + 18.7540i 0.514436 + 0.891029i 0.999860 + 0.0167498i \(0.00533188\pi\)
−0.485424 + 0.874279i \(0.661335\pi\)
\(444\) 33.2675 + 57.6210i 1.57881 + 2.73457i
\(445\) 0.398969 0.230345i 0.0189130 0.0109194i
\(446\) 17.8928 10.3304i 0.847250 0.489160i
\(447\) 18.7227i 0.885554i
\(448\) −31.2790 + 18.0589i −1.47779 + 0.853203i
\(449\) −24.1837 −1.14130 −0.570649 0.821194i \(-0.693308\pi\)
−0.570649 + 0.821194i \(0.693308\pi\)
\(450\) 15.4668i 0.729110i
\(451\) 3.94823i 0.185915i
\(452\) 6.48347i 0.304957i
\(453\) 9.96153 + 17.2539i 0.468033 + 0.810658i
\(454\) −48.8128 28.1821i −2.29090 1.32265i
\(455\) 2.83640 + 4.91280i 0.132973 + 0.230315i
\(456\) 27.3506 15.7909i 1.28081 0.739475i
\(457\) 5.81820 10.0774i 0.272164 0.471401i −0.697252 0.716826i \(-0.745594\pi\)
0.969416 + 0.245425i \(0.0789274\pi\)
\(458\) −18.9657 + 32.8495i −0.886208 + 1.53496i
\(459\) 20.1424 0.940167
\(460\) −5.34815 + 9.26326i −0.249359 + 0.431902i
\(461\) 35.1603 + 20.2998i 1.63758 + 0.945455i 0.981664 + 0.190617i \(0.0610490\pi\)
0.655912 + 0.754838i \(0.272284\pi\)
\(462\) 59.9335 34.6026i 2.78836 1.60986i
\(463\) 13.9011 + 8.02579i 0.646038 + 0.372990i 0.786936 0.617034i \(-0.211666\pi\)
−0.140899 + 0.990024i \(0.544999\pi\)
\(464\) −3.27982 −0.152262
\(465\) 1.01066 + 1.75052i 0.0468684 + 0.0811785i
\(466\) 26.6553 + 15.3894i 1.23478 + 0.712902i
\(467\) −3.18262 −0.147274 −0.0736369 0.997285i \(-0.523461\pi\)
−0.0736369 + 0.997285i \(0.523461\pi\)
\(468\) 20.0707 11.5879i 0.927771 0.535649i
\(469\) 7.85661 4.53602i 0.362785 0.209454i
\(470\) 5.36245 0.247351
\(471\) −0.971079 1.68196i −0.0447450 0.0775005i
\(472\) 2.15347 3.72991i 0.0991214 0.171683i
\(473\) 18.8576 32.6623i 0.867072 1.50181i
\(474\) 26.2367 1.20509
\(475\) 22.9572 1.05335
\(476\) 57.2794i 2.62540i
\(477\) 9.17058 5.29464i 0.419892 0.242425i
\(478\) −2.60393 + 1.50338i −0.119101 + 0.0687631i
\(479\) −11.7583 20.3660i −0.537252 0.930548i −0.999051 0.0435633i \(-0.986129\pi\)
0.461798 0.886985i \(-0.347204\pi\)
\(480\) 4.07815i 0.186141i
\(481\) 40.6998 23.4981i 1.85575 1.07142i
\(482\) 14.2505i 0.649094i
\(483\) −41.3307 + 23.8623i −1.88061 + 1.08577i
\(484\) −23.4003 + 40.5304i −1.06365 + 1.84229i
\(485\) 5.13320i 0.233086i
\(486\) 26.7539 + 15.4464i 1.21358 + 0.700661i
\(487\) 1.38709 0.800836i 0.0628550 0.0362894i −0.468243 0.883600i \(-0.655113\pi\)
0.531098 + 0.847310i \(0.321780\pi\)
\(488\) −17.7886 −0.805252
\(489\) −40.6933 23.4943i −1.84022 1.06245i
\(490\) −0.946046 0.546200i −0.0427380 0.0246748i
\(491\) 14.9833 25.9519i 0.676189 1.17119i −0.299931 0.953961i \(-0.596964\pi\)
0.976120 0.217233i \(-0.0697031\pi\)
\(492\) 2.79381 + 4.83902i 0.125955 + 0.218160i
\(493\) 15.3879 26.6526i 0.693034 1.20037i
\(494\) −27.3974 47.4536i −1.23267 2.13504i
\(495\) 2.73355i 0.122864i
\(496\) −0.768176 1.33052i −0.0344921 0.0597421i
\(497\) −11.6558 + 20.1884i −0.522833 + 0.905573i
\(498\) 22.7965 13.1616i 1.02154 0.589785i
\(499\) 14.7199 8.49856i 0.658955 0.380448i −0.132924 0.991126i \(-0.542436\pi\)
0.791879 + 0.610678i \(0.209103\pi\)
\(500\) −6.60212 + 11.4352i −0.295256 + 0.511398i
\(501\) −17.0057 9.81823i −0.759757 0.438646i
\(502\) −20.2793 35.1247i −0.905109 1.56769i
\(503\) −14.2162 8.20774i −0.633870 0.365965i 0.148379 0.988931i \(-0.452594\pi\)
−0.782249 + 0.622965i \(0.785928\pi\)
\(504\) −6.27526 + 10.8691i −0.279522 + 0.484147i
\(505\) −6.60163 3.81145i −0.293768 0.169607i
\(506\) 46.0847 79.8210i 2.04871 3.54848i
\(507\) −12.4027 21.4821i −0.550823 0.954053i
\(508\) −46.9593 27.1120i −2.08348 1.20290i
\(509\) −20.1416 + 11.6287i −0.892760 + 0.515435i −0.874844 0.484404i \(-0.839036\pi\)
−0.0179156 + 0.999840i \(0.505703\pi\)
\(510\) −9.91549 5.72471i −0.439065 0.253494i
\(511\) 32.6817i 1.44575i
\(512\) 7.12679i 0.314963i
\(513\) 8.04553 13.9353i 0.355219 0.615257i
\(514\) 12.1486 7.01402i 0.535853 0.309375i
\(515\) 3.20566 + 1.85079i 0.141258 + 0.0815556i
\(516\) 53.3752i 2.34971i
\(517\) −29.0088 −1.27580
\(518\) −31.2573 + 54.1392i −1.37337 + 2.37874i
\(519\) 6.02481i 0.264460i
\(520\) 6.31213 0.276805
\(521\) −13.3935 + 7.73274i −0.586780 + 0.338778i −0.763823 0.645425i \(-0.776680\pi\)
0.177043 + 0.984203i \(0.443347\pi\)
\(522\) 14.3447 8.28194i 0.627852 0.362491i
\(523\) −30.2761 17.4799i −1.32388 0.764344i −0.339537 0.940593i \(-0.610270\pi\)
−0.984346 + 0.176249i \(0.943604\pi\)
\(524\) −2.17237 1.25422i −0.0949006 0.0547909i
\(525\) −25.1007 + 14.4919i −1.09549 + 0.632479i
\(526\) −52.1749 + 30.1232i −2.27493 + 1.31343i
\(527\) 14.4161 0.627977
\(528\) 6.60073i 0.287260i
\(529\) −20.2804 + 35.1267i −0.881758 + 1.52725i
\(530\) 7.08435 0.307724
\(531\) 1.86447i 0.0809111i
\(532\) 39.6280 + 22.8792i 1.71809 + 0.991940i
\(533\) 3.41798 1.97337i 0.148049 0.0854762i
\(534\) 2.80903 4.86538i 0.121559 0.210546i
\(535\) 2.39529i 0.103558i
\(536\) 10.0944i 0.436014i
\(537\) −42.4115 24.4863i −1.83019 1.05666i
\(538\) −6.75438 + 3.89964i −0.291202 + 0.168125i
\(539\) 5.11775 + 2.95473i 0.220437 + 0.127269i
\(540\) 2.27658 + 3.94315i 0.0979682 + 0.169686i
\(541\) 11.4665 19.8605i 0.492982 0.853869i −0.506986 0.861954i \(-0.669240\pi\)
0.999967 + 0.00808526i \(0.00257365\pi\)
\(542\) 20.4434 + 11.8030i 0.878119 + 0.506982i
\(543\) 13.5283 23.4318i 0.580557 1.00555i
\(544\) −25.1887 14.5427i −1.07996 0.623514i
\(545\) −1.86498 3.23025i −0.0798872 0.138369i
\(546\) 59.9109 + 34.5896i 2.56395 + 1.48030i
\(547\) −12.9726 + 22.4692i −0.554667 + 0.960712i 0.443262 + 0.896392i \(0.353821\pi\)
−0.997929 + 0.0643201i \(0.979512\pi\)
\(548\) 33.5803 19.3876i 1.43448 0.828197i
\(549\) 6.66898 3.85034i 0.284625 0.164328i
\(550\) 27.9879 48.4764i 1.19341 2.06704i
\(551\) −12.2928 21.2918i −0.523692 0.907060i
\(552\) 53.1031i 2.26022i
\(553\) 7.73791 + 13.4025i 0.329049 + 0.569930i
\(554\) 30.8226 53.3862i 1.30953 2.26816i
\(555\) −3.92238 6.79377i −0.166496 0.288379i
\(556\) 2.47614 4.28879i 0.105012 0.181885i
\(557\) 14.0736 + 8.12542i 0.596319 + 0.344285i 0.767592 0.640939i \(-0.221455\pi\)
−0.171273 + 0.985224i \(0.554788\pi\)
\(558\) 6.71945 + 3.87947i 0.284457 + 0.164231i
\(559\) 37.7009 1.59458
\(560\) −0.623305 + 0.359865i −0.0263394 + 0.0152071i
\(561\) 53.6390 + 30.9685i 2.26464 + 1.30749i
\(562\) 48.8323i 2.05986i
\(563\) 1.34417 2.32817i 0.0566499 0.0981205i −0.836310 0.548257i \(-0.815291\pi\)
0.892960 + 0.450137i \(0.148625\pi\)
\(564\) 35.5537 20.5269i 1.49708 0.864339i
\(565\) 0.764429i 0.0321598i
\(566\) −15.7250 + 9.07881i −0.660970 + 0.381611i
\(567\) 32.1429i 1.34987i
\(568\) 12.9694 + 22.4636i 0.544182 + 0.942551i
\(569\) 6.59339 3.80670i 0.276409 0.159585i −0.355387 0.934719i \(-0.615651\pi\)
0.631797 + 0.775134i \(0.282318\pi\)
\(570\) −7.92113 + 4.57327i −0.331780 + 0.191553i
\(571\) 6.34067i 0.265349i −0.991160 0.132674i \(-0.957644\pi\)
0.991160 0.132674i \(-0.0423564\pi\)
\(572\) −83.8751 −3.50699
\(573\) −12.0494 −0.503370
\(574\) −2.62499 + 4.54662i −0.109565 + 0.189772i
\(575\) −19.3007 + 33.4298i −0.804895 + 1.39412i
\(576\) −8.69874 15.0667i −0.362448 0.627778i
\(577\) 40.4615 1.68443 0.842216 0.539140i \(-0.181250\pi\)
0.842216 + 0.539140i \(0.181250\pi\)
\(578\) −36.5902 + 21.1254i −1.52195 + 0.878700i
\(579\) 38.7256 22.3582i 1.60938 0.929176i
\(580\) 6.95679 0.288865
\(581\) 13.4466 + 7.76342i 0.557860 + 0.322081i
\(582\) 31.2993 + 54.2120i 1.29740 + 2.24716i
\(583\) −38.3236 −1.58720
\(584\) −31.4929 18.1825i −1.30319 0.752395i
\(585\) −2.36643 + 1.36626i −0.0978398 + 0.0564878i
\(586\) 1.91038 + 1.10296i 0.0789170 + 0.0455628i
\(587\) 11.5811 20.0591i 0.478005 0.827928i −0.521678 0.853143i \(-0.674694\pi\)
0.999682 + 0.0252146i \(0.00802692\pi\)
\(588\) −8.36320 −0.344892
\(589\) 5.75827 9.97362i 0.237265 0.410956i
\(590\) −0.623676 + 1.08024i −0.0256763 + 0.0444727i
\(591\) −27.0326 + 15.6073i −1.11197 + 0.641997i
\(592\) 2.98129 + 5.16374i 0.122530 + 0.212228i
\(593\) 35.6960 + 20.6091i 1.46586 + 0.846313i 0.999272 0.0381621i \(-0.0121503\pi\)
0.466586 + 0.884476i \(0.345484\pi\)
\(594\) −19.6171 33.9778i −0.804900 1.39413i
\(595\) 6.75349i 0.276866i
\(596\) 30.1843i 1.23640i
\(597\) 37.9777i 1.55432i
\(598\) 92.1346 3.76766
\(599\) 16.1762 9.33935i 0.660943 0.381596i −0.131693 0.991291i \(-0.542041\pi\)
0.792636 + 0.609695i \(0.208708\pi\)
\(600\) 32.2503i 1.31661i
\(601\) −21.4621 + 12.3911i −0.875457 + 0.505445i −0.869158 0.494535i \(-0.835338\pi\)
−0.00629885 + 0.999980i \(0.502005\pi\)
\(602\) −43.4312 + 25.0750i −1.77012 + 1.02198i
\(603\) 2.18494 + 3.78443i 0.0889776 + 0.154114i
\(604\) 16.0598 + 27.8163i 0.653462 + 1.13183i
\(605\) 2.75899 4.77872i 0.112169 0.194282i
\(606\) −92.9603 −3.77625
\(607\) −9.79430 + 16.9642i −0.397539 + 0.688557i −0.993422 0.114514i \(-0.963469\pi\)
0.595883 + 0.803071i \(0.296802\pi\)
\(608\) −20.1224 + 11.6177i −0.816070 + 0.471158i
\(609\) 26.8812 + 15.5199i 1.08928 + 0.628897i
\(610\) 5.15184 0.208592
\(611\) −14.4989 25.1129i −0.586564 1.01596i
\(612\) −27.5907 −1.11529
\(613\) 4.87372 8.44153i 0.196848 0.340950i −0.750657 0.660692i \(-0.770263\pi\)
0.947505 + 0.319742i \(0.103596\pi\)
\(614\) −12.2603 7.07848i −0.494785 0.285664i
\(615\) −0.329402 0.570542i −0.0132828 0.0230065i
\(616\) 39.3362 22.7108i 1.58490 0.915043i
\(617\) 8.52293 14.7622i 0.343120 0.594302i −0.641890 0.766797i \(-0.721849\pi\)
0.985010 + 0.172495i \(0.0551828\pi\)
\(618\) 45.1403 1.81581
\(619\) 37.8201i 1.52012i 0.649854 + 0.760059i \(0.274830\pi\)
−0.649854 + 0.760059i \(0.725170\pi\)
\(620\) 1.62937 + 2.82215i 0.0654371 + 0.113340i
\(621\) 13.5282 + 23.4314i 0.542866 + 0.940271i
\(622\) 2.47107 + 4.28002i 0.0990809 + 0.171613i
\(623\) 3.31383 0.132766
\(624\) 5.71424 3.29912i 0.228753 0.132071i
\(625\) −11.3261 + 19.6174i −0.453045 + 0.784696i
\(626\) −32.2105 + 18.5968i −1.28739 + 0.743276i
\(627\) 42.8503 24.7396i 1.71128 0.988006i
\(628\) −1.56555 2.71162i −0.0624723 0.108205i
\(629\) −55.9490 −2.23083
\(630\) 1.81741 3.14784i 0.0724072 0.125413i
\(631\) −44.3622 −1.76603 −0.883016 0.469343i \(-0.844491\pi\)
−0.883016 + 0.469343i \(0.844491\pi\)
\(632\) 17.2199 0.684972
\(633\) 44.3351i 1.76216i
\(634\) −4.44563 −0.176558
\(635\) 5.53671 + 3.19662i 0.219718 + 0.126854i
\(636\) 46.9701 27.1182i 1.86249 1.07531i
\(637\) 5.90724i 0.234053i
\(638\) −59.9463 −2.37330
\(639\) −9.72447 5.61443i −0.384694 0.222103i
\(640\) 7.74102i 0.305991i
\(641\) −8.25957 14.3060i −0.326234 0.565053i 0.655528 0.755171i \(-0.272446\pi\)
−0.981761 + 0.190118i \(0.939113\pi\)
\(642\) −14.6052 25.2969i −0.576419 0.998388i
\(643\) 24.7008 + 14.2610i 0.974103 + 0.562399i 0.900485 0.434888i \(-0.143212\pi\)
0.0736187 + 0.997286i \(0.476545\pi\)
\(644\) −66.6325 + 38.4703i −2.62569 + 1.51594i
\(645\) 6.29318i 0.247794i
\(646\) 65.2332i 2.56657i
\(647\) −19.5152 + 33.8013i −0.767220 + 1.32886i 0.171844 + 0.985124i \(0.445027\pi\)
−0.939065 + 0.343740i \(0.888306\pi\)
\(648\) 30.9737 + 17.8827i 1.21676 + 0.702497i
\(649\) 3.37385 5.84368i 0.132435 0.229384i
\(650\) 55.9546 2.19472
\(651\) 14.5398i 0.569860i
\(652\) −65.6049 37.8770i −2.56929 1.48338i
\(653\) −2.47715 −0.0969383 −0.0484691 0.998825i \(-0.515434\pi\)
−0.0484691 + 0.998825i \(0.515434\pi\)
\(654\) −39.3925 22.7433i −1.54037 0.889332i
\(655\) 0.256133 + 0.147878i 0.0100079 + 0.00577808i
\(656\) 0.250369 + 0.433652i 0.00977526 + 0.0169313i
\(657\) 15.7423 0.614167
\(658\) 33.4053 + 19.2866i 1.30227 + 0.751869i
\(659\) 15.4194i 0.600653i 0.953836 + 0.300326i \(0.0970956\pi\)
−0.953836 + 0.300326i \(0.902904\pi\)
\(660\) 14.0007i 0.544978i
\(661\) −37.1346 −1.44437 −0.722184 0.691701i \(-0.756862\pi\)
−0.722184 + 0.691701i \(0.756862\pi\)
\(662\) −28.1666 −1.09472
\(663\) 61.9137i 2.40453i
\(664\) 14.9621 8.63835i 0.580640 0.335233i
\(665\) −4.67231 2.69756i −0.181185 0.104607i
\(666\) −26.0781 15.0562i −1.01051 0.583417i
\(667\) 41.3395 1.60067
\(668\) −27.4162 15.8287i −1.06076 0.612432i
\(669\) −9.32479 + 16.1510i −0.360517 + 0.624434i
\(670\) 2.92350i 0.112945i
\(671\) −27.8695 −1.07589
\(672\) 14.6675 25.4048i 0.565811 0.980013i
\(673\) −8.23652 14.2661i −0.317495 0.549917i 0.662470 0.749088i \(-0.269508\pi\)
−0.979965 + 0.199172i \(0.936175\pi\)
\(674\) 43.5834 + 25.1629i 1.67877 + 0.969237i
\(675\) 8.21583 + 14.2302i 0.316228 + 0.547722i
\(676\) −19.9953 34.6329i −0.769051 1.33204i
\(677\) 15.7105i 0.603805i 0.953339 + 0.301903i \(0.0976218\pi\)
−0.953339 + 0.301903i \(0.902378\pi\)
\(678\) −4.66106 8.07319i −0.179007 0.310049i
\(679\) −18.4620 + 31.9772i −0.708508 + 1.22717i
\(680\) −6.50784 3.75730i −0.249564 0.144086i
\(681\) 50.8773 1.94962
\(682\) −14.0402 24.3183i −0.537627 0.931197i
\(683\) 11.9902 + 20.7676i 0.458792 + 0.794652i 0.998897 0.0469460i \(-0.0149489\pi\)
−0.540105 + 0.841598i \(0.681616\pi\)
\(684\) −11.0206 + 19.0883i −0.421384 + 0.729859i
\(685\) −3.95927 + 2.28588i −0.151276 + 0.0873391i
\(686\) 19.2821 + 33.3976i 0.736195 + 1.27513i
\(687\) 34.2389i 1.30629i
\(688\) 4.78326i 0.182360i
\(689\) −19.1546 33.1767i −0.729732 1.26393i
\(690\) 15.3794i 0.585486i
\(691\) 4.84757 2.79875i 0.184410 0.106469i −0.404953 0.914338i \(-0.632712\pi\)
0.589363 + 0.807868i \(0.299379\pi\)
\(692\) 9.71307i 0.369235i
\(693\) −9.83148 + 17.0286i −0.373467 + 0.646864i
\(694\) −1.53531 + 2.65924i −0.0582796 + 0.100943i
\(695\) −0.291947 + 0.505668i −0.0110742 + 0.0191811i
\(696\) 29.9107 17.2690i 1.13376 0.654578i
\(697\) −4.69860 −0.177972
\(698\) 43.3037 0.269607i 1.63907 0.0102048i
\(699\) −27.7827 −1.05084
\(700\) −40.4668 + 23.3635i −1.52950 + 0.883059i
\(701\) −10.0652 + 17.4335i −0.380159 + 0.658455i −0.991085 0.133233i \(-0.957464\pi\)
0.610926 + 0.791688i \(0.290797\pi\)
\(702\) 19.6097 33.9650i 0.740121 1.28193i
\(703\) −22.3478 + 38.7076i −0.842864 + 1.45988i
\(704\) 62.9632i 2.37301i
\(705\) −4.19193 + 2.42021i −0.157877 + 0.0911506i
\(706\) 6.28393i 0.236499i
\(707\) −27.4165 47.4868i −1.03110 1.78592i
\(708\) 9.54948i 0.358892i
\(709\) 43.9863i 1.65194i −0.563715 0.825969i \(-0.690628\pi\)
0.563715 0.825969i \(-0.309372\pi\)
\(710\) −3.75612 6.50579i −0.140965 0.244158i
\(711\) −6.45579 + 3.72725i −0.242111 + 0.139783i
\(712\) 1.84365 3.19330i 0.0690937 0.119674i
\(713\) 9.68225 + 16.7701i 0.362603 + 0.628047i
\(714\) −41.1790 71.3241i −1.54108 2.66924i
\(715\) 9.88924 0.369837
\(716\) −68.3749 39.4762i −2.55529 1.47530i
\(717\) 1.35703 2.35045i 0.0506793 0.0877791i
\(718\) −34.9779 60.5835i −1.30536 2.26095i
\(719\) 4.12650i 0.153893i −0.997035 0.0769463i \(-0.975483\pi\)
0.997035 0.0769463i \(-0.0245170\pi\)
\(720\) −0.173342 0.300238i −0.00646009 0.0111892i
\(721\) 13.3131 + 23.0590i 0.495806 + 0.858761i
\(722\) 6.98865 + 4.03490i 0.260091 + 0.150163i
\(723\) −6.43164 11.1399i −0.239195 0.414299i
\(724\) 21.8101 37.7762i 0.810566 1.40394i
\(725\) 25.1061 0.932416
\(726\) 67.2911i 2.49741i
\(727\) −18.4204 + 31.9050i −0.683174 + 1.18329i 0.290833 + 0.956774i \(0.406068\pi\)
−0.974007 + 0.226518i \(0.927266\pi\)
\(728\) 39.3214 + 22.7022i 1.45735 + 0.841399i
\(729\) 5.81998 0.215555
\(730\) 9.12082 + 5.26591i 0.337577 + 0.194900i
\(731\) −38.8698 22.4415i −1.43765 0.830029i
\(732\) 34.1573 19.7208i 1.26249 0.728900i
\(733\) 40.4803i 1.49517i −0.664164 0.747587i \(-0.731212\pi\)
0.664164 0.747587i \(-0.268788\pi\)
\(734\) −13.4633 −0.496941
\(735\) 0.986058 0.0363713
\(736\) 39.0691i 1.44010i
\(737\) 15.8150i 0.582554i
\(738\) −2.19005 1.26442i −0.0806167 0.0465441i
\(739\) −21.8264 −0.802896 −0.401448 0.915882i \(-0.631493\pi\)
−0.401448 + 0.915882i \(0.631493\pi\)
\(740\) −6.32358 10.9528i −0.232460 0.402632i
\(741\) 42.8342 + 24.7303i 1.57355 + 0.908491i
\(742\) 44.1319 + 25.4796i 1.62013 + 0.935384i
\(743\) 6.79409 0.249251 0.124626 0.992204i \(-0.460227\pi\)
0.124626 + 0.992204i \(0.460227\pi\)
\(744\) 14.0109 + 8.08922i 0.513666 + 0.296565i
\(745\) 3.55887i 0.130387i
\(746\) 87.5727 3.20626
\(747\) −3.73954 + 6.47707i −0.136822 + 0.236983i
\(748\) 86.4756 + 49.9267i 3.16186 + 1.82550i
\(749\) 8.61491 14.9215i 0.314782 0.545218i
\(750\) 18.9855i 0.693251i
\(751\) 27.5941i 1.00692i −0.864017 0.503462i \(-0.832059\pi\)
0.864017 0.503462i \(-0.167941\pi\)
\(752\) 3.18616 1.83953i 0.116187 0.0670809i
\(753\) 31.7055 + 18.3052i 1.15541 + 0.667077i
\(754\) −29.9618 51.8954i −1.09115 1.88992i
\(755\) −1.89352 3.27967i −0.0689121 0.119359i
\(756\) 32.7517i 1.19117i
\(757\) 24.6936 + 14.2568i 0.897503 + 0.518174i 0.876389 0.481604i \(-0.159945\pi\)
0.0211137 + 0.999777i \(0.493279\pi\)
\(758\) 20.8945 0.758922
\(759\) 83.1970i 3.01986i
\(760\) −5.19888 + 3.00157i −0.188583 + 0.108879i
\(761\) 26.6548 + 15.3891i 0.966234 + 0.557856i 0.898086 0.439820i \(-0.144958\pi\)
0.0681482 + 0.997675i \(0.478291\pi\)
\(762\) 77.9648 2.82437
\(763\) 26.8304i 0.971326i
\(764\) −19.4258 −0.702799
\(765\) 3.25307 0.117615
\(766\) −10.1659 + 17.6079i −0.367310 + 0.636200i
\(767\) 6.74515