Properties

Label 605.2.g.e.366.2
Level $605$
Weight $2$
Character 605.366
Analytic conductor $4.831$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
Defining polynomial: \(x^{8} - 3 x^{7} + 5 x^{6} - 3 x^{5} + 4 x^{4} + 3 x^{3} + 5 x^{2} + 3 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 366.2
Root \(-0.386111 - 0.280526i\) of defining polynomial
Character \(\chi\) \(=\) 605.366
Dual form 605.2.g.e.81.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.386111 - 0.280526i) q^{2} +(0.0998345 + 0.307259i) q^{3} +(-0.547647 + 1.68548i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.124741 + 0.0906300i) q^{6} +(-0.829779 + 2.55380i) q^{7} +(0.556333 + 1.71222i) q^{8} +(2.34261 - 1.70201i) q^{9} +O(q^{10})\) \(q+(0.386111 - 0.280526i) q^{2} +(0.0998345 + 0.307259i) q^{3} +(-0.547647 + 1.68548i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.124741 + 0.0906300i) q^{6} +(-0.829779 + 2.55380i) q^{7} +(0.556333 + 1.71222i) q^{8} +(2.34261 - 1.70201i) q^{9} +0.477260 q^{10} -0.572554 q^{12} +(-3.77637 + 2.74369i) q^{13} +(0.396020 + 1.21882i) q^{14} +(-0.0998345 + 0.307259i) q^{15} +(-2.17239 - 1.57833i) q^{16} +(-3.74278 - 2.71929i) q^{17} +(0.427051 - 1.31433i) q^{18} +(1.34127 + 4.12801i) q^{19} +(-1.43376 + 1.04169i) q^{20} -0.867517 q^{21} +2.77222 q^{23} +(-0.470553 + 0.341876i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.688421 + 2.11874i) q^{26} +(1.54094 + 1.11956i) q^{27} +(-3.84996 - 2.79716i) q^{28} +(0.931196 - 2.86593i) q^{29} +(0.0476470 + 0.146642i) q^{30} +(-1.93056 + 1.40263i) q^{31} -4.88221 q^{32} -2.20796 q^{34} +(-2.17239 + 1.57833i) q^{35} +(1.58578 + 4.88053i) q^{36} +(-3.28884 + 10.1220i) q^{37} +(1.67589 + 1.21761i) q^{38} +(-1.22004 - 0.886408i) q^{39} +(-0.556333 + 1.71222i) q^{40} +(0.683053 + 2.10222i) q^{41} +(-0.334958 + 0.243361i) q^{42} +7.06719 q^{43} +2.89563 q^{45} +(1.07039 - 0.777682i) q^{46} +(1.34798 + 4.14865i) q^{47} +(0.268077 - 0.825058i) q^{48} +(-0.170221 - 0.123673i) q^{49} +(0.386111 + 0.280526i) q^{50} +(0.461867 - 1.42148i) q^{51} +(-2.55633 - 7.86758i) q^{52} +(5.12435 - 3.72306i) q^{53} +0.909040 q^{54} -4.83428 q^{56} +(-1.13446 + 0.824235i) q^{57} +(-0.444423 - 1.36779i) q^{58} +(3.63011 - 11.1723i) q^{59} +(-0.463206 - 0.336539i) q^{60} +(-3.22201 - 2.34093i) q^{61} +(-0.351935 + 1.08314i) q^{62} +(2.40273 + 7.39484i) q^{63} +(2.45970 - 1.78708i) q^{64} -4.66785 q^{65} +7.31984 q^{67} +(6.63303 - 4.81918i) q^{68} +(0.276763 + 0.851790i) q^{69} +(-0.396020 + 1.21882i) q^{70} +(-0.967351 - 0.702822i) q^{71} +(4.21747 + 3.06417i) q^{72} +(-0.315724 + 0.971700i) q^{73} +(1.56963 + 4.83083i) q^{74} +(-0.261370 + 0.189896i) q^{75} -7.69223 q^{76} -0.719730 q^{78} +(2.83328 - 2.05850i) q^{79} +(-0.829779 - 2.55380i) q^{80} +(2.49424 - 7.67647i) q^{81} +(0.853463 + 0.620077i) q^{82} +(8.99290 + 6.53372i) q^{83} +(0.475093 - 1.46219i) q^{84} +(-1.42961 - 4.39990i) q^{85} +(2.72872 - 1.98253i) q^{86} +0.973547 q^{87} +2.76978 q^{89} +(1.11803 - 0.812299i) q^{90} +(-3.87328 - 11.9207i) q^{91} +(-1.51820 + 4.67254i) q^{92} +(-0.623707 - 0.453150i) q^{93} +(1.68428 + 1.22370i) q^{94} +(-1.34127 + 4.12801i) q^{95} +(-0.487413 - 1.50010i) q^{96} +(-14.9945 + 10.8941i) q^{97} -0.100418 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 3q^{2} + 5q^{3} + 3q^{4} + 2q^{5} - 8q^{6} - 4q^{7} + q^{8} + 5q^{9} + O(q^{10}) \) \( 8q - 3q^{2} + 5q^{3} + 3q^{4} + 2q^{5} - 8q^{6} - 4q^{7} + q^{8} + 5q^{9} - 2q^{10} + 16q^{12} - 3q^{13} + 14q^{14} - 5q^{15} - q^{16} - 12q^{17} - 10q^{18} - 5q^{19} + 2q^{20} + 20q^{21} + 10q^{23} + 2q^{24} - 2q^{25} + 5q^{26} + 5q^{27} - 19q^{28} - 21q^{29} - 7q^{30} + 15q^{31} - 16q^{32} + 4q^{34} - q^{35} + 15q^{36} - 31q^{37} - 20q^{38} + 14q^{39} - q^{40} - 3q^{41} - 21q^{42} + 38q^{43} + 7q^{46} - 5q^{47} + 5q^{48} - 4q^{49} - 3q^{50} - 6q^{51} - 17q^{52} - 2q^{53} - 16q^{54} + 22q^{56} - 40q^{57} + 2q^{58} + 18q^{59} + 4q^{60} - 6q^{61} + 5q^{62} + 30q^{63} + 29q^{64} - 2q^{65} - 38q^{67} + 14q^{68} + 9q^{69} - 14q^{70} + 15q^{71} - 5q^{72} + 2q^{73} + 20q^{74} - 5q^{75} - 16q^{78} + 3q^{79} - 4q^{80} - 12q^{81} - 22q^{82} + 38q^{83} + 17q^{84} - 13q^{85} + 2q^{86} - 38q^{87} - 16q^{89} - 36q^{91} + q^{92} + 40q^{93} + 18q^{94} + 5q^{95} + 17q^{96} - 56q^{97} - 16q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.386111 0.280526i 0.273022 0.198362i −0.442846 0.896598i \(-0.646031\pi\)
0.715868 + 0.698236i \(0.246031\pi\)
\(3\) 0.0998345 + 0.307259i 0.0576395 + 0.177396i 0.975731 0.218972i \(-0.0702704\pi\)
−0.918092 + 0.396368i \(0.870270\pi\)
\(4\) −0.547647 + 1.68548i −0.273823 + 0.842742i
\(5\) 0.809017 + 0.587785i 0.361803 + 0.262866i
\(6\) 0.124741 + 0.0906300i 0.0509255 + 0.0369995i
\(7\) −0.829779 + 2.55380i −0.313627 + 0.965244i 0.662689 + 0.748895i \(0.269415\pi\)
−0.976316 + 0.216350i \(0.930585\pi\)
\(8\) 0.556333 + 1.71222i 0.196693 + 0.605360i
\(9\) 2.34261 1.70201i 0.780870 0.567335i
\(10\) 0.477260 0.150923
\(11\) 0 0
\(12\) −0.572554 −0.165282
\(13\) −3.77637 + 2.74369i −1.04738 + 0.760963i −0.971712 0.236170i \(-0.924108\pi\)
−0.0756644 + 0.997133i \(0.524108\pi\)
\(14\) 0.396020 + 1.21882i 0.105841 + 0.325745i
\(15\) −0.0998345 + 0.307259i −0.0257771 + 0.0793339i
\(16\) −2.17239 1.57833i −0.543097 0.394583i
\(17\) −3.74278 2.71929i −0.907756 0.659524i 0.0326901 0.999466i \(-0.489593\pi\)
−0.940446 + 0.339942i \(0.889593\pi\)
\(18\) 0.427051 1.31433i 0.100657 0.309790i
\(19\) 1.34127 + 4.12801i 0.307709 + 0.947030i 0.978653 + 0.205522i \(0.0658891\pi\)
−0.670944 + 0.741508i \(0.734111\pi\)
\(20\) −1.43376 + 1.04169i −0.320598 + 0.232928i
\(21\) −0.867517 −0.189308
\(22\) 0 0
\(23\) 2.77222 0.578048 0.289024 0.957322i \(-0.406669\pi\)
0.289024 + 0.957322i \(0.406669\pi\)
\(24\) −0.470553 + 0.341876i −0.0960511 + 0.0697852i
\(25\) 0.309017 + 0.951057i 0.0618034 + 0.190211i
\(26\) −0.688421 + 2.11874i −0.135010 + 0.415519i
\(27\) 1.54094 + 1.11956i 0.296554 + 0.215459i
\(28\) −3.84996 2.79716i −0.727573 0.528613i
\(29\) 0.931196 2.86593i 0.172919 0.532189i −0.826613 0.562770i \(-0.809736\pi\)
0.999532 + 0.0305806i \(0.00973564\pi\)
\(30\) 0.0476470 + 0.146642i 0.00869911 + 0.0267731i
\(31\) −1.93056 + 1.40263i −0.346738 + 0.251920i −0.747499 0.664262i \(-0.768746\pi\)
0.400761 + 0.916183i \(0.368746\pi\)
\(32\) −4.88221 −0.863061
\(33\) 0 0
\(34\) −2.20796 −0.378662
\(35\) −2.17239 + 1.57833i −0.367201 + 0.266787i
\(36\) 1.58578 + 4.88053i 0.264297 + 0.813422i
\(37\) −3.28884 + 10.1220i −0.540682 + 1.66405i 0.190360 + 0.981714i \(0.439035\pi\)
−0.731041 + 0.682333i \(0.760965\pi\)
\(38\) 1.67589 + 1.21761i 0.271866 + 0.197522i
\(39\) −1.22004 0.886408i −0.195362 0.141939i
\(40\) −0.556333 + 1.71222i −0.0879640 + 0.270725i
\(41\) 0.683053 + 2.10222i 0.106675 + 0.328312i 0.990120 0.140223i \(-0.0447820\pi\)
−0.883445 + 0.468535i \(0.844782\pi\)
\(42\) −0.334958 + 0.243361i −0.0516852 + 0.0375515i
\(43\) 7.06719 1.07774 0.538868 0.842390i \(-0.318852\pi\)
0.538868 + 0.842390i \(0.318852\pi\)
\(44\) 0 0
\(45\) 2.89563 0.431654
\(46\) 1.07039 0.777682i 0.157820 0.114663i
\(47\) 1.34798 + 4.14865i 0.196623 + 0.605143i 0.999954 + 0.00961001i \(0.00305901\pi\)
−0.803331 + 0.595533i \(0.796941\pi\)
\(48\) 0.268077 0.825058i 0.0386936 0.119087i
\(49\) −0.170221 0.123673i −0.0243174 0.0176676i
\(50\) 0.386111 + 0.280526i 0.0546044 + 0.0396724i
\(51\) 0.461867 1.42148i 0.0646743 0.199047i
\(52\) −2.55633 7.86758i −0.354500 1.09104i
\(53\) 5.12435 3.72306i 0.703883 0.511401i −0.177311 0.984155i \(-0.556740\pi\)
0.881195 + 0.472754i \(0.156740\pi\)
\(54\) 0.909040 0.123705
\(55\) 0 0
\(56\) −4.83428 −0.646008
\(57\) −1.13446 + 0.824235i −0.150263 + 0.109173i
\(58\) −0.444423 1.36779i −0.0583556 0.179600i
\(59\) 3.63011 11.1723i 0.472600 1.45451i −0.376567 0.926389i \(-0.622896\pi\)
0.849167 0.528124i \(-0.177104\pi\)
\(60\) −0.463206 0.336539i −0.0597996 0.0434470i
\(61\) −3.22201 2.34093i −0.412537 0.299725i 0.362091 0.932143i \(-0.382063\pi\)
−0.774628 + 0.632417i \(0.782063\pi\)
\(62\) −0.351935 + 1.08314i −0.0446958 + 0.137559i
\(63\) 2.40273 + 7.39484i 0.302715 + 0.931662i
\(64\) 2.45970 1.78708i 0.307462 0.223385i
\(65\) −4.66785 −0.578975
\(66\) 0 0
\(67\) 7.31984 0.894260 0.447130 0.894469i \(-0.352446\pi\)
0.447130 + 0.894469i \(0.352446\pi\)
\(68\) 6.63303 4.81918i 0.804373 0.584411i
\(69\) 0.276763 + 0.851790i 0.0333184 + 0.102543i
\(70\) −0.396020 + 1.21882i −0.0473335 + 0.145677i
\(71\) −0.967351 0.702822i −0.114803 0.0834096i 0.528902 0.848683i \(-0.322604\pi\)
−0.643706 + 0.765273i \(0.722604\pi\)
\(72\) 4.21747 + 3.06417i 0.497034 + 0.361116i
\(73\) −0.315724 + 0.971700i −0.0369528 + 0.113729i −0.967831 0.251600i \(-0.919043\pi\)
0.930879 + 0.365329i \(0.119043\pi\)
\(74\) 1.56963 + 4.83083i 0.182466 + 0.561572i
\(75\) −0.261370 + 0.189896i −0.0301804 + 0.0219274i
\(76\) −7.69223 −0.882360
\(77\) 0 0
\(78\) −0.719730 −0.0814934
\(79\) 2.83328 2.05850i 0.318769 0.231600i −0.416881 0.908961i \(-0.636877\pi\)
0.735650 + 0.677362i \(0.236877\pi\)
\(80\) −0.829779 2.55380i −0.0927721 0.285523i
\(81\) 2.49424 7.67647i 0.277137 0.852941i
\(82\) 0.853463 + 0.620077i 0.0942492 + 0.0684761i
\(83\) 8.99290 + 6.53372i 0.987099 + 0.717169i 0.959284 0.282444i \(-0.0911451\pi\)
0.0278149 + 0.999613i \(0.491145\pi\)
\(84\) 0.475093 1.46219i 0.0518369 0.159538i
\(85\) −1.42961 4.39990i −0.155063 0.477236i
\(86\) 2.72872 1.98253i 0.294246 0.213782i
\(87\) 0.973547 0.104375
\(88\) 0 0
\(89\) 2.76978 0.293596 0.146798 0.989167i \(-0.453103\pi\)
0.146798 + 0.989167i \(0.453103\pi\)
\(90\) 1.11803 0.812299i 0.117851 0.0856239i
\(91\) −3.87328 11.9207i −0.406030 1.24963i
\(92\) −1.51820 + 4.67254i −0.158283 + 0.487146i
\(93\) −0.623707 0.453150i −0.0646754 0.0469894i
\(94\) 1.68428 + 1.22370i 0.173720 + 0.126215i
\(95\) −1.34127 + 4.12801i −0.137611 + 0.423525i
\(96\) −0.487413 1.50010i −0.0497464 0.153104i
\(97\) −14.9945 + 10.8941i −1.52246 + 1.10613i −0.562207 + 0.826997i \(0.690048\pi\)
−0.960252 + 0.279134i \(0.909952\pi\)
\(98\) −0.100418 −0.0101438
\(99\) 0 0
\(100\) −1.77222 −0.177222
\(101\) −5.75580 + 4.18183i −0.572723 + 0.416108i −0.836093 0.548587i \(-0.815166\pi\)
0.263370 + 0.964695i \(0.415166\pi\)
\(102\) −0.220430 0.678415i −0.0218259 0.0671731i
\(103\) 2.32639 7.15989i 0.229226 0.705485i −0.768609 0.639719i \(-0.779051\pi\)
0.997835 0.0657661i \(-0.0209491\pi\)
\(104\) −6.79871 4.93955i −0.666669 0.484363i
\(105\) −0.701836 0.509914i −0.0684922 0.0497625i
\(106\) 0.934153 2.87503i 0.0907330 0.279247i
\(107\) −5.57133 17.1468i −0.538601 1.65764i −0.735737 0.677267i \(-0.763164\pi\)
0.197136 0.980376i \(-0.436836\pi\)
\(108\) −2.73089 + 1.98411i −0.262780 + 0.190921i
\(109\) 16.3653 1.56751 0.783756 0.621068i \(-0.213301\pi\)
0.783756 + 0.621068i \(0.213301\pi\)
\(110\) 0 0
\(111\) −3.43842 −0.326360
\(112\) 5.83334 4.23817i 0.551199 0.400469i
\(113\) −0.634650 1.95325i −0.0597029 0.183747i 0.916757 0.399445i \(-0.130797\pi\)
−0.976460 + 0.215699i \(0.930797\pi\)
\(114\) −0.206809 + 0.636493i −0.0193694 + 0.0596130i
\(115\) 2.24278 + 1.62947i 0.209140 + 0.151949i
\(116\) 4.32051 + 3.13903i 0.401149 + 0.291452i
\(117\) −4.17678 + 12.8548i −0.386143 + 1.18843i
\(118\) −1.73251 5.33211i −0.159490 0.490860i
\(119\) 10.0502 7.30188i 0.921298 0.669362i
\(120\) −0.581635 −0.0530958
\(121\) 0 0
\(122\) −1.90075 −0.172086
\(123\) −0.577734 + 0.419748i −0.0520925 + 0.0378474i
\(124\) −1.30685 4.02207i −0.117359 0.361193i
\(125\) −0.309017 + 0.951057i −0.0276393 + 0.0850651i
\(126\) 3.00217 + 2.18120i 0.267454 + 0.194317i
\(127\) −0.0617011 0.0448285i −0.00547509 0.00397788i 0.585044 0.811001i \(-0.301077\pi\)
−0.590519 + 0.807023i \(0.701077\pi\)
\(128\) 3.46577 10.6665i 0.306333 0.942798i
\(129\) 0.705549 + 2.17146i 0.0621201 + 0.191186i
\(130\) −1.80231 + 1.30945i −0.158073 + 0.114847i
\(131\) 11.4831 1.00328 0.501642 0.865075i \(-0.332730\pi\)
0.501642 + 0.865075i \(0.332730\pi\)
\(132\) 0 0
\(133\) −11.6550 −1.01062
\(134\) 2.82627 2.05341i 0.244153 0.177387i
\(135\) 0.588587 + 1.81148i 0.0506575 + 0.155908i
\(136\) 2.57378 7.92127i 0.220700 0.679243i
\(137\) 14.8287 + 10.7737i 1.26690 + 0.920458i 0.999075 0.0430086i \(-0.0136943\pi\)
0.267827 + 0.963467i \(0.413694\pi\)
\(138\) 0.345811 + 0.251246i 0.0294374 + 0.0213875i
\(139\) 7.16529 22.0525i 0.607752 1.87047i 0.131114 0.991367i \(-0.458145\pi\)
0.476638 0.879100i \(-0.341855\pi\)
\(140\) −1.47055 4.52590i −0.124284 0.382508i
\(141\) −1.14013 + 0.828356i −0.0960167 + 0.0697602i
\(142\) −0.570666 −0.0478892
\(143\) 0 0
\(144\) −7.77539 −0.647949
\(145\) 2.43790 1.77124i 0.202457 0.147094i
\(146\) 0.150683 + 0.463754i 0.0124706 + 0.0383805i
\(147\) 0.0210057 0.0646489i 0.00173252 0.00533215i
\(148\) −15.2594 11.0866i −1.25431 0.911311i
\(149\) 11.8639 + 8.61964i 0.971930 + 0.706149i 0.955891 0.293723i \(-0.0948942\pi\)
0.0160396 + 0.999871i \(0.494894\pi\)
\(150\) −0.0476470 + 0.146642i −0.00389036 + 0.0119733i
\(151\) 2.32350 + 7.15101i 0.189084 + 0.581941i 0.999995 0.00322899i \(-0.00102782\pi\)
−0.810911 + 0.585170i \(0.801028\pi\)
\(152\) −6.32185 + 4.59309i −0.512770 + 0.372549i
\(153\) −13.3961 −1.08301
\(154\) 0 0
\(155\) −2.38630 −0.191672
\(156\) 2.16217 1.57091i 0.173113 0.125774i
\(157\) −4.13523 12.7269i −0.330028 1.01572i −0.969120 0.246590i \(-0.920690\pi\)
0.639092 0.769130i \(-0.279310\pi\)
\(158\) 0.516500 1.58962i 0.0410905 0.126464i
\(159\) 1.65553 + 1.20281i 0.131292 + 0.0953892i
\(160\) −3.94979 2.86969i −0.312258 0.226869i
\(161\) −2.30033 + 7.07969i −0.181291 + 0.557958i
\(162\) −1.19040 3.66367i −0.0935266 0.287845i
\(163\) 0.624553 0.453764i 0.0489188 0.0355416i −0.563057 0.826418i \(-0.690375\pi\)
0.611976 + 0.790876i \(0.290375\pi\)
\(164\) −3.91733 −0.305892
\(165\) 0 0
\(166\) 5.30514 0.411759
\(167\) −6.86234 + 4.98578i −0.531024 + 0.385811i −0.820741 0.571301i \(-0.806439\pi\)
0.289717 + 0.957112i \(0.406439\pi\)
\(168\) −0.482628 1.48538i −0.0372356 0.114599i
\(169\) 2.71589 8.35865i 0.208915 0.642973i
\(170\) −1.78628 1.29781i −0.137001 0.0995372i
\(171\) 10.1680 + 7.38746i 0.777564 + 0.564933i
\(172\) −3.87032 + 11.9116i −0.295109 + 0.908253i
\(173\) −1.56941 4.83014i −0.119320 0.367229i 0.873504 0.486818i \(-0.161842\pi\)
−0.992824 + 0.119589i \(0.961842\pi\)
\(174\) 0.375898 0.273106i 0.0284967 0.0207041i
\(175\) −2.68522 −0.202984
\(176\) 0 0
\(177\) 3.79521 0.285265
\(178\) 1.06944 0.776996i 0.0801581 0.0582383i
\(179\) −3.49716 10.7632i −0.261390 0.804476i −0.992503 0.122219i \(-0.960999\pi\)
0.731113 0.682256i \(-0.239001\pi\)
\(180\) −1.58578 + 4.88053i −0.118197 + 0.363773i
\(181\) −5.98677 4.34965i −0.444993 0.323307i 0.342623 0.939473i \(-0.388685\pi\)
−0.787616 + 0.616167i \(0.788685\pi\)
\(182\) −4.83960 3.51617i −0.358735 0.260636i
\(183\) 0.397604 1.22370i 0.0293917 0.0904583i
\(184\) 1.54228 + 4.74665i 0.113698 + 0.349927i
\(185\) −8.61029 + 6.25574i −0.633041 + 0.459931i
\(186\) −0.367941 −0.0269787
\(187\) 0 0
\(188\) −7.73070 −0.563819
\(189\) −4.13776 + 3.00626i −0.300978 + 0.218673i
\(190\) 0.640135 + 1.97013i 0.0464403 + 0.142928i
\(191\) −1.59332 + 4.90372i −0.115288 + 0.354821i −0.992007 0.126183i \(-0.959728\pi\)
0.876719 + 0.481003i \(0.159728\pi\)
\(192\) 0.794658 + 0.577353i 0.0573495 + 0.0416668i
\(193\) −3.26220 2.37013i −0.234818 0.170605i 0.464153 0.885755i \(-0.346359\pi\)
−0.698972 + 0.715149i \(0.746359\pi\)
\(194\) −2.73345 + 8.41270i −0.196250 + 0.603996i
\(195\) −0.466012 1.43424i −0.0333718 0.102708i
\(196\) 0.301670 0.219176i 0.0215479 0.0156555i
\(197\) −11.4176 −0.813469 −0.406734 0.913547i \(-0.633333\pi\)
−0.406734 + 0.913547i \(0.633333\pi\)
\(198\) 0 0
\(199\) −7.16644 −0.508015 −0.254008 0.967202i \(-0.581749\pi\)
−0.254008 + 0.967202i \(0.581749\pi\)
\(200\) −1.45650 + 1.05821i −0.102990 + 0.0748266i
\(201\) 0.730772 + 2.24908i 0.0515447 + 0.158638i
\(202\) −1.04926 + 3.22930i −0.0738260 + 0.227213i
\(203\) 6.54631 + 4.75617i 0.459461 + 0.333818i
\(204\) 2.14294 + 1.55694i 0.150036 + 0.109007i
\(205\) −0.683053 + 2.10222i −0.0477065 + 0.146825i
\(206\) −1.11029 3.41713i −0.0773577 0.238083i
\(207\) 6.49424 4.71834i 0.451381 0.327947i
\(208\) 12.5342 0.869090
\(209\) 0 0
\(210\) −0.414031 −0.0285709
\(211\) 2.81829 2.04760i 0.194019 0.140963i −0.486535 0.873661i \(-0.661739\pi\)
0.680554 + 0.732698i \(0.261739\pi\)
\(212\) 3.46882 + 10.6759i 0.238239 + 0.733226i
\(213\) 0.119373 0.367393i 0.00817932 0.0251734i
\(214\) −6.96128 5.05767i −0.475864 0.345735i
\(215\) 5.71747 + 4.15399i 0.389928 + 0.283300i
\(216\) −1.05965 + 3.26127i −0.0721001 + 0.221901i
\(217\) −1.98010 6.09412i −0.134418 0.413696i
\(218\) 6.31884 4.59090i 0.427966 0.310935i
\(219\) −0.330084 −0.0223050
\(220\) 0 0
\(221\) 21.5950 1.45264
\(222\) −1.32761 + 0.964566i −0.0891035 + 0.0647374i
\(223\) 3.25856 + 10.0288i 0.218210 + 0.671580i 0.998910 + 0.0466747i \(0.0148624\pi\)
−0.780701 + 0.624905i \(0.785138\pi\)
\(224\) 4.05115 12.4682i 0.270679 0.833064i
\(225\) 2.34261 + 1.70201i 0.156174 + 0.113467i
\(226\) −0.792984 0.576137i −0.0527485 0.0383241i
\(227\) −0.0667531 + 0.205445i −0.00443056 + 0.0136359i −0.953247 0.302191i \(-0.902282\pi\)
0.948817 + 0.315827i \(0.102282\pi\)
\(228\) −0.767950 2.36351i −0.0508587 0.156527i
\(229\) 0.0612504 0.0445011i 0.00404754 0.00294071i −0.585760 0.810485i \(-0.699204\pi\)
0.589807 + 0.807544i \(0.299204\pi\)
\(230\) 1.32307 0.0872407
\(231\) 0 0
\(232\) 5.42514 0.356178
\(233\) 12.2324 8.88735i 0.801370 0.582229i −0.109946 0.993938i \(-0.535068\pi\)
0.911316 + 0.411708i \(0.135068\pi\)
\(234\) 1.99341 + 6.13508i 0.130313 + 0.401063i
\(235\) −1.34798 + 4.14865i −0.0879324 + 0.270628i
\(236\) 16.8428 + 12.2370i 1.09637 + 0.796560i
\(237\) 0.915352 + 0.665042i 0.0594585 + 0.0431991i
\(238\) 1.83212 5.63868i 0.118759 0.365501i
\(239\) 7.15826 + 22.0309i 0.463029 + 1.42506i 0.861444 + 0.507853i \(0.169561\pi\)
−0.398414 + 0.917206i \(0.630439\pi\)
\(240\) 0.701836 0.509914i 0.0453033 0.0329148i
\(241\) 21.3349 1.37430 0.687151 0.726515i \(-0.258861\pi\)
0.687151 + 0.726515i \(0.258861\pi\)
\(242\) 0 0
\(243\) 8.32179 0.533843
\(244\) 5.71013 4.14865i 0.365553 0.265590i
\(245\) −0.0650188 0.200107i −0.00415390 0.0127844i
\(246\) −0.105319 + 0.324139i −0.00671490 + 0.0206664i
\(247\) −16.3911 11.9088i −1.04294 0.757741i
\(248\) −3.47564 2.52520i −0.220704 0.160350i
\(249\) −1.10974 + 3.41544i −0.0703271 + 0.216445i
\(250\) 0.147481 + 0.453901i 0.00932755 + 0.0287072i
\(251\) 5.03359 3.65712i 0.317718 0.230835i −0.417483 0.908685i \(-0.637088\pi\)
0.735201 + 0.677849i \(0.237088\pi\)
\(252\) −13.7797 −0.868041
\(253\) 0 0
\(254\) −0.0363991 −0.00228388
\(255\) 1.20918 0.878523i 0.0757219 0.0550152i
\(256\) 0.224971 + 0.692389i 0.0140607 + 0.0432743i
\(257\) −4.41595 + 13.5909i −0.275460 + 0.847778i 0.713638 + 0.700515i \(0.247046\pi\)
−0.989097 + 0.147263i \(0.952954\pi\)
\(258\) 0.881571 + 0.640499i 0.0548842 + 0.0398757i
\(259\) −23.1205 16.7980i −1.43664 1.04378i
\(260\) 2.55633 7.86758i 0.158537 0.487927i
\(261\) −2.69640 8.29865i −0.166903 0.513674i
\(262\) 4.43376 3.22131i 0.273919 0.199013i
\(263\) −4.13132 −0.254748 −0.127374 0.991855i \(-0.540655\pi\)
−0.127374 + 0.991855i \(0.540655\pi\)
\(264\) 0 0
\(265\) 6.33404 0.389097
\(266\) −4.50015 + 3.26955i −0.275922 + 0.200469i
\(267\) 0.276519 + 0.851039i 0.0169227 + 0.0520827i
\(268\) −4.00869 + 12.3375i −0.244869 + 0.753631i
\(269\) 1.36234 + 0.989796i 0.0830632 + 0.0603489i 0.628542 0.777776i \(-0.283652\pi\)
−0.545479 + 0.838125i \(0.683652\pi\)
\(270\) 0.735429 + 0.534320i 0.0447568 + 0.0325177i
\(271\) 5.69549 17.5289i 0.345976 1.06481i −0.615083 0.788463i \(-0.710877\pi\)
0.961059 0.276343i \(-0.0891226\pi\)
\(272\) 3.83883 + 11.8147i 0.232763 + 0.716371i
\(273\) 3.27606 2.38020i 0.198276 0.144056i
\(274\) 8.74784 0.528476
\(275\) 0 0
\(276\) −1.58725 −0.0955411
\(277\) −2.77286 + 2.01460i −0.166605 + 0.121046i −0.667964 0.744194i \(-0.732834\pi\)
0.501358 + 0.865240i \(0.332834\pi\)
\(278\) −3.41970 10.5248i −0.205100 0.631234i
\(279\) −2.13525 + 6.57164i −0.127834 + 0.393434i
\(280\) −3.91102 2.84152i −0.233728 0.169813i
\(281\) −18.4632 13.4143i −1.10142 0.800229i −0.120129 0.992758i \(-0.538331\pi\)
−0.981291 + 0.192529i \(0.938331\pi\)
\(282\) −0.207843 + 0.639676i −0.0123769 + 0.0380921i
\(283\) 8.99211 + 27.6749i 0.534525 + 1.64510i 0.744673 + 0.667430i \(0.232606\pi\)
−0.210147 + 0.977670i \(0.567394\pi\)
\(284\) 1.71436 1.24556i 0.101729 0.0739102i
\(285\) −1.40227 −0.0830634
\(286\) 0 0
\(287\) −5.93542 −0.350357
\(288\) −11.4371 + 8.30955i −0.673938 + 0.489645i
\(289\) 1.36057 + 4.18739i 0.0800333 + 0.246317i
\(290\) 0.444423 1.36779i 0.0260974 0.0803196i
\(291\) −4.84428 3.51958i −0.283977 0.206321i
\(292\) −1.46488 1.06430i −0.0857256 0.0622833i
\(293\) −6.55535 + 20.1753i −0.382968 + 1.17865i 0.554976 + 0.831866i \(0.312727\pi\)
−0.937944 + 0.346787i \(0.887273\pi\)
\(294\) −0.0100252 0.0308543i −0.000584680 0.00179946i
\(295\) 9.50375 6.90488i 0.553330 0.402018i
\(296\) −19.1608 −1.11370
\(297\) 0 0
\(298\) 6.99883 0.405432
\(299\) −10.4689 + 7.60613i −0.605434 + 0.439874i
\(300\) −0.176929 0.544531i −0.0102150 0.0314385i
\(301\) −5.86420 + 18.0481i −0.338007 + 1.04028i
\(302\) 2.90318 + 2.10928i 0.167059 + 0.121376i
\(303\) −1.85953 1.35103i −0.106827 0.0776146i
\(304\) 3.60161 11.0846i 0.206566 0.635746i
\(305\) −1.23070 3.78770i −0.0704697 0.216883i
\(306\) −5.17239 + 3.75796i −0.295686 + 0.214828i
\(307\) 6.87520 0.392388 0.196194 0.980565i \(-0.437142\pi\)
0.196194 + 0.980565i \(0.437142\pi\)
\(308\) 0 0
\(309\) 2.43219 0.138363
\(310\) −0.921378 + 0.669420i −0.0523307 + 0.0380205i
\(311\) 7.77415 + 23.9264i 0.440831 + 1.35674i 0.886991 + 0.461786i \(0.152791\pi\)
−0.446160 + 0.894953i \(0.647209\pi\)
\(312\) 0.838976 2.58210i 0.0474977 0.146183i
\(313\) 9.36788 + 6.80616i 0.529504 + 0.384707i 0.820172 0.572117i \(-0.193878\pi\)
−0.290668 + 0.956824i \(0.593878\pi\)
\(314\) −5.16690 3.75398i −0.291585 0.211849i
\(315\) −2.40273 + 7.39484i −0.135378 + 0.416652i
\(316\) 1.91793 + 5.90279i 0.107892 + 0.332058i
\(317\) −16.7800 + 12.1914i −0.942460 + 0.684737i −0.949012 0.315241i \(-0.897915\pi\)
0.00655133 + 0.999979i \(0.497915\pi\)
\(318\) 0.976639 0.0547672
\(319\) 0 0
\(320\) 3.04036 0.169961
\(321\) 4.71229 3.42368i 0.263015 0.191091i
\(322\) 1.09786 + 3.37885i 0.0611811 + 0.188296i
\(323\) 6.20515 19.0975i 0.345264 1.06261i
\(324\) 11.5726 + 8.40799i 0.642923 + 0.467111i
\(325\) −3.77637 2.74369i −0.209475 0.152193i
\(326\) 0.113854 0.350407i 0.00630580 0.0194073i
\(327\) 1.63382 + 5.02839i 0.0903506 + 0.278071i
\(328\) −3.21945 + 2.33907i −0.177764 + 0.129153i
\(329\) −11.7133 −0.645777
\(330\) 0 0
\(331\) −32.1415 −1.76665 −0.883327 0.468757i \(-0.844702\pi\)
−0.883327 + 0.468757i \(0.844702\pi\)
\(332\) −15.9374 + 11.5792i −0.874679 + 0.635492i
\(333\) 9.52324 + 29.3095i 0.521871 + 1.60615i
\(334\) −1.25098 + 3.85013i −0.0684508 + 0.210670i
\(335\) 5.92187 + 4.30249i 0.323546 + 0.235070i
\(336\) 1.88458 + 1.36923i 0.102812 + 0.0746976i
\(337\) 5.56119 17.1156i 0.302937 0.932345i −0.677502 0.735521i \(-0.736937\pi\)
0.980439 0.196824i \(-0.0630627\pi\)
\(338\) −1.29619 3.98925i −0.0705032 0.216987i
\(339\) 0.536794 0.390004i 0.0291547 0.0211821i
\(340\) 8.19888 0.444647
\(341\) 0 0
\(342\) 5.99834 0.324353
\(343\) −14.7496 + 10.7162i −0.796406 + 0.578622i
\(344\) 3.93171 + 12.1006i 0.211983 + 0.652418i
\(345\) −0.276763 + 0.851790i −0.0149004 + 0.0458588i
\(346\) −1.96095 1.42471i −0.105421 0.0765930i
\(347\) −6.51244 4.73156i −0.349606 0.254004i 0.399098 0.916908i \(-0.369323\pi\)
−0.748704 + 0.662905i \(0.769323\pi\)
\(348\) −0.533160 + 1.64090i −0.0285804 + 0.0879614i
\(349\) −5.94220 18.2882i −0.318079 0.978946i −0.974469 0.224524i \(-0.927917\pi\)
0.656390 0.754422i \(-0.272083\pi\)
\(350\) −1.03679 + 0.753275i −0.0554190 + 0.0402642i
\(351\) −8.89088 −0.474560
\(352\) 0 0
\(353\) 14.8497 0.790371 0.395186 0.918601i \(-0.370680\pi\)
0.395186 + 0.918601i \(0.370680\pi\)
\(354\) 1.46537 1.06466i 0.0778837 0.0565858i
\(355\) −0.369495 1.13719i −0.0196108 0.0603558i
\(356\) −1.51686 + 4.66842i −0.0803934 + 0.247426i
\(357\) 3.24692 + 2.35903i 0.171845 + 0.124853i
\(358\) −4.36964 3.17473i −0.230943 0.167790i
\(359\) −3.15916 + 9.72290i −0.166734 + 0.513155i −0.999160 0.0409816i \(-0.986952\pi\)
0.832426 + 0.554137i \(0.186952\pi\)
\(360\) 1.61093 + 4.95794i 0.0849035 + 0.261306i
\(361\) 0.129892 0.0943721i 0.00683642 0.00496695i
\(362\) −3.53175 −0.185625
\(363\) 0 0
\(364\) 22.2134 1.16430
\(365\) −0.826577 + 0.600544i −0.0432650 + 0.0314339i
\(366\) −0.189760 0.584022i −0.00991893 0.0305273i
\(367\) 4.37055 13.4512i 0.228141 0.702145i −0.769817 0.638265i \(-0.779653\pi\)
0.997958 0.0638800i \(-0.0203475\pi\)
\(368\) −6.02234 4.37549i −0.313936 0.228088i
\(369\) 5.17812 + 3.76212i 0.269562 + 0.195848i
\(370\) −1.56963 + 4.83083i −0.0816012 + 0.251143i
\(371\) 5.25585 + 16.1758i 0.272870 + 0.839808i
\(372\) 1.10535 0.803083i 0.0573096 0.0416379i
\(373\) −12.4600 −0.645154 −0.322577 0.946543i \(-0.604549\pi\)
−0.322577 + 0.946543i \(0.604549\pi\)
\(374\) 0 0
\(375\) −0.323071 −0.0166833
\(376\) −6.35346 + 4.61606i −0.327655 + 0.238055i
\(377\) 4.34668 + 13.3777i 0.223866 + 0.688987i
\(378\) −0.754302 + 2.32150i −0.0387971 + 0.119405i
\(379\) −13.2169 9.60263i −0.678906 0.493254i 0.194089 0.980984i \(-0.437825\pi\)
−0.872995 + 0.487730i \(0.837825\pi\)
\(380\) −6.22315 4.52138i −0.319241 0.231942i
\(381\) 0.00761405 0.0234336i 0.000390080 0.00120054i
\(382\) 0.760426 + 2.34035i 0.0389068 + 0.119743i
\(383\) 0.657446 0.477662i 0.0335939 0.0244074i −0.570862 0.821046i \(-0.693391\pi\)
0.604456 + 0.796639i \(0.293391\pi\)
\(384\) 3.62339 0.184905
\(385\) 0 0
\(386\) −1.92445 −0.0979522
\(387\) 16.5557 12.0284i 0.841571 0.611437i
\(388\) −10.1502 31.2391i −0.515298 1.58592i
\(389\) −9.39230 + 28.9065i −0.476208 + 1.46562i 0.368113 + 0.929781i \(0.380004\pi\)
−0.844321 + 0.535837i \(0.819996\pi\)
\(390\) −0.582274 0.423047i −0.0294846 0.0214218i
\(391\) −10.3758 7.53847i −0.524727 0.381237i
\(392\) 0.117055 0.360259i 0.00591219 0.0181958i
\(393\) 1.14641 + 3.52829i 0.0578287 + 0.177978i
\(394\) −4.40846 + 3.20293i −0.222095 + 0.161361i
\(395\) 3.50213 0.176211
\(396\) 0 0
\(397\) −14.8996 −0.747789 −0.373894 0.927471i \(-0.621978\pi\)
−0.373894 + 0.927471i \(0.621978\pi\)
\(398\) −2.76704 + 2.01037i −0.138699 + 0.100771i
\(399\) −1.16357 3.58112i −0.0582516 0.179280i
\(400\) 0.829779 2.55380i 0.0414889 0.127690i
\(401\) −9.84508 7.15287i −0.491640 0.357197i 0.314175 0.949365i \(-0.398272\pi\)
−0.805815 + 0.592168i \(0.798272\pi\)
\(402\) 0.913087 + 0.663396i 0.0455406 + 0.0330872i
\(403\) 3.44210 10.5937i 0.171463 0.527710i
\(404\) −3.89626 11.9915i −0.193846 0.596598i
\(405\) 6.53000 4.74432i 0.324478 0.235747i
\(406\) 3.86184 0.191660
\(407\) 0 0
\(408\) 2.69083 0.133216
\(409\) −0.212050 + 0.154063i −0.0104852 + 0.00761793i −0.593016 0.805191i \(-0.702063\pi\)
0.582530 + 0.812809i \(0.302063\pi\)
\(410\) 0.325994 + 1.00331i 0.0160997 + 0.0495497i
\(411\) −1.82990 + 5.63184i −0.0902621 + 0.277798i
\(412\) 10.7938 + 7.84218i 0.531774 + 0.386357i
\(413\) 25.5197 + 18.5411i 1.25574 + 0.912349i
\(414\) 1.18388 3.64361i 0.0581846 0.179074i
\(415\) 3.43498 + 10.5718i 0.168617 + 0.518949i
\(416\) 18.4370 13.3953i 0.903949 0.656758i
\(417\) 7.49116 0.366844
\(418\) 0 0
\(419\) −1.26916 −0.0620023 −0.0310012 0.999519i \(-0.509870\pi\)
−0.0310012 + 0.999519i \(0.509870\pi\)
\(420\) 1.24381 0.903681i 0.0606917 0.0440951i
\(421\) −9.16714 28.2135i −0.446779 1.37504i −0.880521 0.474007i \(-0.842807\pi\)
0.433742 0.901037i \(-0.357193\pi\)
\(422\) 0.513765 1.58121i 0.0250097 0.0769720i
\(423\) 10.2188 + 7.42440i 0.496856 + 0.360987i
\(424\) 9.22552 + 6.70273i 0.448031 + 0.325513i
\(425\) 1.42961 4.39990i 0.0693464 0.213426i
\(426\) −0.0569721 0.175342i −0.00276031 0.00849535i
\(427\) 8.65182 6.28591i 0.418691 0.304197i
\(428\) 31.9518 1.54445
\(429\) 0 0
\(430\) 3.37289 0.162655
\(431\) 25.3666 18.4299i 1.22187 0.887739i 0.225614 0.974217i \(-0.427561\pi\)
0.996254 + 0.0864778i \(0.0275611\pi\)
\(432\) −1.58048 4.86423i −0.0760411 0.234030i
\(433\) −8.04449 + 24.7584i −0.386594 + 1.18981i 0.548724 + 0.836003i \(0.315114\pi\)
−0.935318 + 0.353809i \(0.884886\pi\)
\(434\) −2.47410 1.79754i −0.118761 0.0862847i
\(435\) 0.787616 + 0.572237i 0.0377633 + 0.0274367i
\(436\) −8.96242 + 27.5835i −0.429222 + 1.32101i
\(437\) 3.71830 + 11.4438i 0.177870 + 0.547429i
\(438\) −0.127449 + 0.0925972i −0.00608975 + 0.00442446i
\(439\) −14.4191 −0.688185 −0.344093 0.938936i \(-0.611813\pi\)
−0.344093 + 0.938936i \(0.611813\pi\)
\(440\) 0 0
\(441\) −0.609255 −0.0290121
\(442\) 8.33807 6.05796i 0.396602 0.288148i
\(443\) −0.102163 0.314427i −0.00485393 0.0149389i 0.948600 0.316477i \(-0.102500\pi\)
−0.953454 + 0.301538i \(0.902500\pi\)
\(444\) 1.88304 5.79539i 0.0893650 0.275037i
\(445\) 2.24080 + 1.62803i 0.106224 + 0.0771762i
\(446\) 4.07152 + 2.95813i 0.192792 + 0.140072i
\(447\) −1.46403 + 4.50583i −0.0692464 + 0.213119i
\(448\) 2.52282 + 7.76445i 0.119192 + 0.366836i
\(449\) −6.88334 + 5.00104i −0.324845 + 0.236014i −0.738240 0.674538i \(-0.764343\pi\)
0.413395 + 0.910552i \(0.364343\pi\)
\(450\) 1.38197 0.0651465
\(451\) 0 0
\(452\) 3.63974 0.171199
\(453\) −1.96525 + 1.42783i −0.0923353 + 0.0670855i
\(454\) 0.0318586 + 0.0980507i 0.00149520 + 0.00460175i
\(455\) 3.87328 11.9207i 0.181582 0.558852i
\(456\) −2.04241 1.48390i −0.0956444 0.0694898i
\(457\) 0.921044 + 0.669177i 0.0430846 + 0.0313028i 0.609119 0.793079i \(-0.291523\pi\)
−0.566035 + 0.824382i \(0.691523\pi\)
\(458\) 0.0111658 0.0343647i 0.000521743 0.00160576i
\(459\) −2.72299 8.38051i −0.127098 0.391169i
\(460\) −3.97470 + 2.88779i −0.185321 + 0.134644i
\(461\) −14.5073 −0.675670 −0.337835 0.941205i \(-0.609695\pi\)
−0.337835 + 0.941205i \(0.609695\pi\)
\(462\) 0 0
\(463\) −4.89739 −0.227601 −0.113801 0.993504i \(-0.536302\pi\)
−0.113801 + 0.993504i \(0.536302\pi\)
\(464\) −6.54631 + 4.75617i −0.303905 + 0.220800i
\(465\) −0.238235 0.733212i −0.0110479 0.0340019i
\(466\) 2.22993 6.86301i 0.103299 0.317923i
\(467\) −26.2308 19.0578i −1.21382 0.881889i −0.218245 0.975894i \(-0.570033\pi\)
−0.995572 + 0.0940049i \(0.970033\pi\)
\(468\) −19.3792 14.0798i −0.895802 0.650838i
\(469\) −6.07384 + 18.6934i −0.280464 + 0.863179i
\(470\) 0.643336 + 1.97998i 0.0296749 + 0.0913299i
\(471\) 3.49763 2.54117i 0.161162 0.117091i
\(472\) 21.1490 0.973461
\(473\) 0 0
\(474\) 0.539990 0.0248026
\(475\) −3.51149 + 2.55125i −0.161118 + 0.117059i
\(476\) 6.80325 + 20.9383i 0.311827 + 0.959704i
\(477\) 5.66768 17.4433i 0.259505 0.798675i
\(478\) 8.94413 + 6.49829i 0.409095 + 0.297225i
\(479\) 14.3482 + 10.4246i 0.655588 + 0.476313i 0.865170 0.501478i \(-0.167210\pi\)
−0.209582 + 0.977791i \(0.567210\pi\)
\(480\) 0.487413 1.50010i 0.0222472 0.0684700i
\(481\) −15.3518 47.2480i −0.699982 2.15432i
\(482\) 8.23765 5.98500i 0.375215 0.272609i
\(483\) −2.40495 −0.109429
\(484\) 0 0
\(485\) −18.5342 −0.841595
\(486\) 3.21314 2.33448i 0.145751 0.105894i
\(487\) −5.70454 17.5568i −0.258497 0.795573i −0.993120 0.117097i \(-0.962641\pi\)
0.734623 0.678475i \(-0.237359\pi\)
\(488\) 2.21567 6.81912i 0.100299 0.308687i
\(489\) 0.201775 + 0.146598i 0.00912458 + 0.00662940i
\(490\) −0.0812399 0.0590242i −0.00367004 0.00266644i
\(491\) 3.53325 10.8742i 0.159453 0.490747i −0.839131 0.543929i \(-0.816936\pi\)
0.998585 + 0.0531814i \(0.0169362\pi\)
\(492\) −0.391085 1.20363i −0.0176315 0.0542640i
\(493\) −11.2785 + 8.19434i −0.507960 + 0.369054i
\(494\) −9.66954 −0.435053
\(495\) 0 0
\(496\) 6.40774 0.287716
\(497\) 2.59755 1.88723i 0.116516 0.0846539i
\(498\) 0.529636 + 1.63005i 0.0237336 + 0.0730444i
\(499\) 3.36258 10.3490i 0.150530 0.463283i −0.847151 0.531353i \(-0.821684\pi\)
0.997681 + 0.0680695i \(0.0216839\pi\)
\(500\) −1.43376 1.04169i −0.0641196 0.0465856i
\(501\) −2.21702 1.61076i −0.0990493 0.0719635i
\(502\) 0.917609 2.82411i 0.0409549 0.126046i
\(503\) −13.8207 42.5357i −0.616234 1.89657i −0.380652 0.924718i \(-0.624301\pi\)
−0.235582 0.971855i \(-0.575699\pi\)
\(504\) −11.3248 + 8.22798i −0.504449 + 0.366503i
\(505\) −7.11455 −0.316594
\(506\) 0 0
\(507\) 2.83941 0.126103
\(508\) 0.109348 0.0794460i 0.00485154 0.00352485i
\(509\) −4.26732 13.1335i −0.189146 0.582131i 0.810849 0.585255i \(-0.199006\pi\)
−0.999995 + 0.00312421i \(0.999006\pi\)
\(510\) 0.220430 0.678415i 0.00976083 0.0300407i
\(511\) −2.21954 1.61259i −0.0981868 0.0713368i
\(512\) 18.4281 + 13.3888i 0.814414 + 0.591707i
\(513\) −2.55473 + 7.86264i −0.112794 + 0.347144i
\(514\) 2.10756 + 6.48640i 0.0929604 + 0.286103i
\(515\) 6.09056 4.42505i 0.268382 0.194991i
\(516\) −4.04635 −0.178130
\(517\) 0 0
\(518\) −13.6394 −0.599281
\(519\) 1.32742 0.964429i 0.0582674 0.0423337i
\(520\) −2.59688 7.99237i −0.113881 0.350488i
\(521\) −1.12783 + 3.47109i −0.0494110 + 0.152071i −0.972718 0.231992i \(-0.925476\pi\)
0.923307 + 0.384063i \(0.125476\pi\)
\(522\) −3.36910 2.44779i −0.147462 0.107137i
\(523\) −4.03463 2.93133i −0.176422 0.128178i 0.496070 0.868283i \(-0.334776\pi\)
−0.672492 + 0.740105i \(0.734776\pi\)
\(524\) −6.28869 + 19.3546i −0.274723 + 0.845509i
\(525\) −0.268077 0.825058i −0.0116999 0.0360085i
\(526\) −1.59515 + 1.15894i −0.0695518 + 0.0505323i
\(527\) 11.0398 0.480901
\(528\) 0 0
\(529\) −15.3148 −0.665860
\(530\) 2.44565 1.77687i 0.106232 0.0771821i
\(531\) −10.5114 32.3509i −0.456157 1.40391i
\(532\) 6.38285 19.6444i 0.276732 0.851692i
\(533\) −8.34730 6.06467i −0.361562 0.262690i
\(534\) 0.345506 + 0.251025i 0.0149515 + 0.0108629i
\(535\) 5.57133 17.1468i 0.240870 0.741321i
\(536\) 4.07227 + 12.5331i 0.175895 + 0.541349i
\(537\) 2.95794 2.14907i 0.127644 0.0927391i
\(538\) 0.803678 0.0346490
\(539\) 0 0
\(540\) −3.37556 −0.145261
\(541\) 0.200308 0.145532i 0.00861192 0.00625692i −0.583471 0.812134i \(-0.698306\pi\)
0.592083 + 0.805877i \(0.298306\pi\)
\(542\) −2.71823 8.36585i −0.116758 0.359344i
\(543\) 0.738781 2.27373i 0.0317041 0.0975753i
\(544\) 18.2730 + 13.2761i 0.783449 + 0.569209i
\(545\) 13.2398 + 9.61929i 0.567132 + 0.412045i
\(546\) 0.597217 1.83804i 0.0255585 0.0786610i
\(547\) 7.82185 + 24.0732i 0.334438 + 1.02929i 0.966998 + 0.254783i \(0.0820041\pi\)
−0.632560 + 0.774511i \(0.717996\pi\)
\(548\) −26.2798 + 19.0934i −1.12262 + 0.815629i
\(549\) −11.5322 −0.492182
\(550\) 0 0
\(551\) 13.0796 0.557208
\(552\) −1.30448 + 0.947758i −0.0555222 + 0.0403392i
\(553\) 2.90599 + 8.94373i 0.123575 + 0.380326i
\(554\) −0.505485 + 1.55572i −0.0214760 + 0.0660963i
\(555\) −2.78174 2.02105i −0.118078 0.0857888i
\(556\) 33.2451 + 24.1540i 1.40990 + 1.02436i
\(557\) 11.9488 36.7746i 0.506287 1.55819i −0.292309 0.956324i \(-0.594424\pi\)
0.798596 0.601867i \(-0.205576\pi\)
\(558\) 1.01907 + 3.13638i 0.0431407 + 0.132774i
\(559\) −26.6883 + 19.3902i −1.12879 + 0.820117i
\(560\) 7.21041 0.304695
\(561\) 0 0
\(562\) −10.8919 −0.459447
\(563\) 11.2746 8.19150i 0.475169 0.345231i −0.324283 0.945960i \(-0.605123\pi\)
0.799452 + 0.600729i \(0.205123\pi\)
\(564\) −0.771790 2.37533i −0.0324982 0.100019i
\(565\) 0.634650 1.95325i 0.0266999 0.0821739i
\(566\) 11.2355 + 8.16306i 0.472263 + 0.343119i
\(567\) 17.5345 + 12.7395i 0.736379 + 0.535011i
\(568\) 0.665214 2.04732i 0.0279118 0.0859036i
\(569\) −8.62543 26.5463i −0.361597 1.11288i −0.952085 0.305834i \(-0.901065\pi\)
0.590488 0.807046i \(-0.298935\pi\)
\(570\) −0.541433 + 0.393374i −0.0226781 + 0.0164766i
\(571\) 31.4113 1.31452 0.657261 0.753663i \(-0.271715\pi\)
0.657261 + 0.753663i \(0.271715\pi\)
\(572\) 0 0
\(573\) −1.66578 −0.0695889
\(574\) −2.29174 + 1.66504i −0.0956552 + 0.0694976i
\(575\) 0.856664 + 2.63654i 0.0357254 + 0.109951i
\(576\) 2.72050 8.37285i 0.113354 0.348869i
\(577\) −16.7749 12.1877i −0.698348 0.507380i 0.181045 0.983475i \(-0.442052\pi\)
−0.879394 + 0.476095i \(0.842052\pi\)
\(578\) 1.70000 + 1.23512i 0.0707108 + 0.0513744i
\(579\) 0.402562 1.23896i 0.0167299 0.0514894i
\(580\) 1.65029 + 5.07906i 0.0685245 + 0.210897i
\(581\) −24.1479 + 17.5445i −1.00182 + 0.727868i
\(582\) −2.85777 −0.118458
\(583\) 0 0
\(584\) −1.83941 −0.0761153
\(585\) −10.9349 + 7.94470i −0.452104 + 0.328473i
\(586\) 3.12861 + 9.62887i 0.129242 + 0.397765i
\(587\) 4.70840 14.4910i 0.194336 0.598106i −0.805647 0.592396i \(-0.798182\pi\)
0.999984 0.00571050i \(-0.00181772\pi\)
\(588\) 0.0974610 + 0.0708095i 0.00401922 + 0.00292014i
\(589\) −8.37947 6.08804i −0.345270 0.250853i
\(590\) 1.73251 5.33211i 0.0713261 0.219519i
\(591\) −1.13987 3.50815i −0.0468879 0.144306i
\(592\) 23.1205 16.7980i 0.950248 0.690395i
\(593\) −27.5413 −1.13098 −0.565492 0.824754i \(-0.691314\pi\)
−0.565492 + 0.824754i \(0.691314\pi\)
\(594\) 0 0
\(595\) 12.4227 0.509281
\(596\) −21.0255 + 15.2759i −0.861239 + 0.625726i
\(597\) −0.715457 2.20195i −0.0292817 0.0901199i
\(598\) −1.90846 + 5.87362i −0.0780426 + 0.240190i
\(599\) 21.6275 + 15.7133i 0.883676 + 0.642028i 0.934222 0.356693i \(-0.116096\pi\)
−0.0505453 + 0.998722i \(0.516096\pi\)
\(600\) −0.470553 0.341876i −0.0192102 0.0139570i
\(601\) −0.743741 + 2.28900i −0.0303378 + 0.0933702i −0.965079 0.261959i \(-0.915631\pi\)
0.934741 + 0.355330i \(0.115631\pi\)
\(602\) 2.79875 + 8.61366i 0.114068 + 0.351067i
\(603\) 17.1475 12.4584i 0.698301 0.507345i
\(604\) −13.3254 −0.542202
\(605\) 0 0
\(606\) −1.09699 −0.0445620
\(607\) 8.32710 6.04999i 0.337987 0.245562i −0.405825 0.913951i \(-0.633016\pi\)
0.743812 + 0.668389i \(0.233016\pi\)
\(608\) −6.54837 20.1538i −0.265571 0.817344i
\(609\) −0.807829 + 2.48624i −0.0327349 + 0.100748i
\(610\) −1.53774 1.11723i −0.0622612 0.0452354i
\(611\) −16.4731 11.9684i −0.666429 0.484189i
\(612\) 7.33634 22.5789i 0.296554 0.912699i
\(613\) −8.61404 26.5113i −0.347918 1.07078i −0.960003 0.279989i \(-0.909669\pi\)
0.612085 0.790792i \(-0.290331\pi\)
\(614\) 2.65459 1.92867i 0.107131 0.0778350i
\(615\) −0.714118 −0.0287960
\(616\) 0 0
\(617\) −28.7216 −1.15629 −0.578143 0.815935i \(-0.696222\pi\)
−0.578143 + 0.815935i \(0.696222\pi\)
\(618\) 0.939098 0.682294i 0.0377760 0.0274459i
\(619\) 7.01370 + 21.5859i 0.281904 + 0.867612i 0.987310 + 0.158808i \(0.0507650\pi\)
−0.705405 + 0.708804i \(0.749235\pi\)
\(620\) 1.30685 4.02207i 0.0524844 0.161530i
\(621\) 4.27183 + 3.10366i 0.171423 + 0.124546i
\(622\) 9.71366 + 7.05739i 0.389482 + 0.282976i
\(623\) −2.29830 + 7.07345i −0.0920795 + 0.283392i
\(624\) 1.25134 + 3.85124i 0.0500939 + 0.154173i
\(625\) −0.809017 + 0.587785i −0.0323607 + 0.0235114i
\(626\) 5.52635 0.220877
\(627\) 0 0
\(628\) 23.7157 0.946360
\(629\) 39.8340 28.9411i 1.58829 1.15396i
\(630\) 1.14673 + 3.52926i 0.0456866 + 0.140609i
\(631\) 8.81823 27.1397i 0.351048 1.08042i −0.607217 0.794536i \(-0.707714\pi\)
0.958266 0.285880i \(-0.0922857\pi\)
\(632\) 5.10085 + 3.70598i 0.202901 + 0.147416i
\(633\) 0.910507 + 0.661522i 0.0361894 + 0.0262931i
\(634\) −3.05895 + 9.41448i −0.121486 + 0.373897i
\(635\) −0.0235677 0.0725340i −0.000935256 0.00287842i
\(636\) −2.93396 + 2.13165i −0.116339 + 0.0845254i
\(637\) 0.982140 0.0389138
\(638\) 0 0
\(639\) −3.46233 −0.136968
\(640\) 9.07350 6.59228i 0.358662 0.260583i
\(641\) 0.733529 + 2.25757i 0.0289727 + 0.0891687i 0.964497 0.264093i \(-0.0850726\pi\)
−0.935525 + 0.353262i \(0.885073\pi\)
\(642\) 0.859037 2.64385i 0.0339035 0.104344i
\(643\) −9.19069 6.67742i −0.362445 0.263332i 0.391626 0.920124i \(-0.371913\pi\)
−0.754071 + 0.656793i \(0.771913\pi\)
\(644\) −10.6729 7.75434i −0.420573 0.305564i
\(645\) −0.705549 + 2.17146i −0.0277810 + 0.0855010i
\(646\) −2.96147 9.11447i −0.116518 0.358604i
\(647\) 39.1742 28.4617i 1.54010 1.11895i 0.589821 0.807534i \(-0.299198\pi\)
0.950275 0.311411i \(-0.100802\pi\)
\(648\) 14.5314 0.570848
\(649\) 0 0
\(650\) −2.22778 −0.0873806
\(651\) 1.67479 1.21681i 0.0656402 0.0476904i
\(652\) 0.422778 + 1.30118i 0.0165573 + 0.0509580i
\(653\) 9.19474 28.2985i 0.359818 1.10741i −0.593345 0.804949i \(-0.702193\pi\)
0.953163 0.302458i \(-0.0978071\pi\)
\(654\) 2.04143 + 1.48319i 0.0798264 + 0.0579972i
\(655\) 9.29003 + 6.74960i 0.362991 + 0.263729i
\(656\) 1.83415 5.64492i 0.0716114 0.220397i
\(657\) 0.914220 + 2.81368i 0.0356671 + 0.109772i
\(658\) −4.52265 + 3.28590i −0.176311 + 0.128098i
\(659\) 28.4931 1.10993 0.554966 0.831873i \(-0.312731\pi\)
0.554966 + 0.831873i \(0.312731\pi\)
\(660\) 0 0
\(661\) −1.02875 −0.0400139 −0.0200070 0.999800i \(-0.506369\pi\)
−0.0200070 + 0.999800i \(0.506369\pi\)
\(662\) −12.4102 + 9.01653i −0.482336 + 0.350437i
\(663\) 2.15592 + 6.63525i 0.0837291 + 0.257692i
\(664\) −6.18410 + 19.0327i −0.239990 + 0.738613i
\(665\) −9.42913 6.85066i −0.365646 0.265657i
\(666\) 11.8991 + 8.64522i 0.461082 + 0.334996i
\(667\) 2.58148 7.94499i 0.0999555 0.307631i
\(668\) −4.64531 14.2968i −0.179733 0.553160i
\(669\) −2.75613 + 2.00245i −0.106558 + 0.0774190i
\(670\) 3.49346 0.134964
\(671\) 0 0
\(672\) 4.23540 0.163384
\(673\) 10.5471 7.66291i 0.406560 0.295383i −0.365647 0.930753i \(-0.619152\pi\)
0.772208 + 0.635370i \(0.219152\pi\)
\(674\) −2.65413 8.16858i −0.102233 0.314642i
\(675\) −0.588587 + 1.81148i −0.0226547 + 0.0697240i
\(676\) 12.6010 + 9.15518i 0.484655 + 0.352122i
\(677\) −30.0197 21.8106i −1.15375 0.838250i −0.164777 0.986331i \(-0.552690\pi\)
−0.988975 + 0.148081i \(0.952690\pi\)
\(678\) 0.0978560 0.301170i 0.00375814 0.0115664i
\(679\) −15.3793 47.3326i −0.590203 1.81646i
\(680\) 6.73823 4.89561i 0.258400 0.187738i
\(681\) −0.0697890 −0.00267432
\(682\) 0 0
\(683\) −32.8992 −1.25885 −0.629426 0.777061i \(-0.716710\pi\)
−0.629426 + 0.777061i \(0.716710\pi\)
\(684\) −18.0199 + 13.0922i −0.689008 + 0.500594i
\(685\) 5.66406 + 17.4322i 0.216413 + 0.666050i
\(686\) −2.68882 + 8.27532i −0.102659 + 0.315953i
\(687\) 0.0197882 + 0.0143770i 0.000754969 + 0.000548517i
\(688\) −15.3527 11.1544i −0.585315 0.425256i
\(689\) −9.13650 + 28.1193i −0.348073 + 1.07126i
\(690\) 0.132088 + 0.406525i 0.00502851 + 0.0154762i
\(691\) −29.6908 + 21.5716i −1.12949 + 0.820623i −0.985621 0.168973i \(-0.945955\pi\)
−0.143871 + 0.989597i \(0.545955\pi\)
\(692\) 9.00061 0.342152
\(693\) 0 0
\(694\) −3.84185 −0.145835
\(695\) 18.7590 13.6292i 0.711568 0.516984i
\(696\) 0.541616 + 1.66692i 0.0205299 + 0.0631846i
\(697\) 3.16002 9.72555i 0.119694 0.368382i
\(698\) −7.42468 5.39434i −0.281028 0.204179i
\(699\) 3.95193 + 2.87124i 0.149476 + 0.108600i
\(700\) 1.47055 4.52590i 0.0555817 0.171063i
\(701\) 11.2018 + 34.4755i 0.423085 + 1.30212i 0.904816 + 0.425802i \(0.140008\pi\)
−0.481731 + 0.876319i \(0.659992\pi\)
\(702\) −3.43287 + 2.49413i −0.129565 + 0.0941347i
\(703\) −46.1949 −1.74227
\(704\) 0 0
\(705\) −1.40928 −0.0530767
\(706\) 5.73365 4.16574i 0.215789 0.156780i
\(707\) −5.90350 18.1691i −0.222024 0.683320i
\(708\) −2.07843 + 6.39676i −0.0781123 + 0.240405i
\(709\) 15.0487 + 10.9336i 0.565167 + 0.410618i 0.833347 0.552751i \(-0.186422\pi\)
−0.268179 + 0.963369i \(0.586422\pi\)
\(710\) −0.461678 0.335429i −0.0173265 0.0125884i
\(711\) 3.13370 9.64453i 0.117523 0.361698i
\(712\) 1.54092 + 4.74246i 0.0577484 + 0.177731i
\(713\) −5.35193 + 3.88841i −0.200432 + 0.145622i
\(714\) 1.91544 0.0716836
\(715\) 0 0
\(716\) 20.0563 0.749540
\(717\) −6.05454 + 4.39888i −0.226111 + 0.164279i
\(718\) 1.50774 + 4.64035i 0.0562684 + 0.173176i
\(719\) −11.5659 + 35.5961i −0.431335 + 1.32751i 0.465462 + 0.885068i \(0.345888\pi\)
−0.896796 + 0.442444i \(0.854112\pi\)
\(720\) −6.29042 4.57026i −0.234430 0.170324i
\(721\) 16.3545 + 11.8822i 0.609074 + 0.442518i
\(722\) 0.0236789 0.0728763i 0.000881239 0.00271217i
\(723\) 2.12996 + 6.55534i 0.0792140 + 0.243796i
\(724\) 10.6099 7.70854i 0.394314 0.286486i
\(725\) 3.01341 0.111915
\(726\) 0 0
\(727\) 14.6011 0.541526 0.270763 0.962646i \(-0.412724\pi\)
0.270763 + 0.962646i \(0.412724\pi\)
\(728\) 18.2560 13.2638i 0.676614 0.491589i
\(729\) −6.65191 20.4725i −0.246367 0.758240i
\(730\) −0.150683 + 0.463754i −0.00557702 + 0.0171643i
\(731\) −26.4509 19.2177i −0.978321 0.710792i
\(732\) 1.84478 + 1.34031i 0.0681849 + 0.0495392i
\(733\) −12.9283 + 39.7893i −0.477518 + 1.46965i 0.365013 + 0.931002i \(0.381064\pi\)
−0.842531 + 0.538647i \(0.818936\pi\)
\(734\) −2.08589 6.41970i −0.0769915 0.236955i
\(735\) 0.0549936 0.0399552i 0.00202847 0.00147377i
\(736\) −13.5346 −0.498891
\(737\) 0 0
\(738\) 3.05470 0.112445
\(739\) −9.65149 + 7.01222i −0.355036 + 0.257949i −0.750979 0.660327i \(-0.770418\pi\)
0.395943 + 0.918275i \(0.370418\pi\)
\(740\) −5.82856 17.9385i −0.214262 0.659431i
\(741\) 2.02270 6.22523i 0.0743057 0.228689i
\(742\) 6.56710 + 4.77127i 0.241086 + 0.175159i
\(743\) 37.7651 + 27.4380i 1.38547 + 1.00660i 0.996345 + 0.0854162i \(0.0272220\pi\)
0.389123 + 0.921186i \(0.372778\pi\)
\(744\) 0.428902 1.32002i 0.0157243 0.0483944i
\(745\) 4.53161 + 13.9469i 0.166026 + 0.510974i
\(746\) −4.81095 + 3.49536i −0.176141 + 0.127974i
\(747\) 32.1873 1.17767
\(748\) 0 0
\(749\) 48.4124 1.76895
\(750\) −0.124741 + 0.0906300i −0.00455491 + 0.00330934i
\(751\) 4.45106 + 13.6989i 0.162421 + 0.499882i 0.998837 0.0482140i \(-0.0153529\pi\)
−0.836416 + 0.548096i \(0.815353\pi\)
\(752\) 3.61962 11.1400i 0.131994 0.406235i
\(753\) 1.62621 + 1.18151i 0.0592623 + 0.0430566i
\(754\) 5.43111 + 3.94593i 0.197789 + 0.143702i
\(755\) −2.32350 + 7.15101i −0.0845610 + 0.260252i
\(756\) −2.80097 8.62050i −0.101870 0.313525i
\(757\) 12.9941 9.44076i 0.472278 0.343130i −0.326050 0.945352i \(-0.605718\pi\)
0.798328 + 0.602222i \(0.205718\pi\)
\(758\) −7.79698 −0.283199
\(759\) 0 0
\(760\) −7.81423 −0.283452
\(761\) −31.4578 + 22.8555i −1.14035 + 0.828510i −0.987167 0.159689i \(-0.948951\pi\)
−0.153178 + 0.988199i \(0.548951\pi\)
\(762\) −0.00363388 0.0111839i −0.000131642 0.000405151i
\(763\) −13.5796 + 41.7937i −0.491614 + 1.51303i
\(764\) −7.39257 5.37102i −0.267454 0.194317i
\(765\) −10.8377 7.87403i −0.391837 0.284686i
\(766\) 0.119850 0.368862i 0.00433037 0.0133275i
\(767\) 16.9448 + 52.1507i 0.611841 + 1.88305i
\(768\) −0.190283 + 0.138249i −0.00686624 + 0.00498862i
\(769\) −43.0017 −1.55068 −0.775341 0.631543i \(-0.782422\pi\)
−0.775341 + 0.631543i \(0.782422\pi\)
\(770\) 0 0
\(771\) −4.61679 −0.166270
\(772\) 5.78134 4.20039i 0.208075 0.151175i
\(773\) −2.42721 7.47019i −0.0873007 0.268684i 0.897870 0.440261i \(-0.145114\pi\)
−0.985171 + 0.171576i \(0.945114\pi\)
\(774\) 3.01805 9.28860i 0.108482 0.333872i
\(775\) −1.93056 1.40263i −0.0693477 0.0503840i
\(776\) −26.9950 19.6130i −0.969065 0.704067i
\(777\) 2.85312 8.78101i 0.102355 0.315017i
\(778\) 4.48257 + 13.7959i 0.160708 +