Properties

Label 1170.2.bs.f.901.1
Level $1170$
Weight $2$
Character 1170.901
Analytic conductor $9.342$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bs (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.17284886784.1
Defining polynomial: \(x^{8} - 2 x^{7} + 2 x^{6} + 30 x^{5} + 185 x^{4} + 36 x^{3} + 8 x^{2} + 208 x + 2704\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 901.1
Root \(1.33404 + 1.33404i\) of defining polynomial
Character \(\chi\) \(=\) 1170.901
Dual form 1170.2.bs.f.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-3.15637 + 1.82233i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-3.15637 + 1.82233i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(1.44460 + 0.834038i) q^{11} +(-2.24376 + 2.82233i) q^{13} +3.64466 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(5.46699 - 3.15637i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-0.834038 - 1.44460i) q^{22} +(-0.622266 + 1.07780i) q^{23} -1.00000 q^{25} +(3.35432 - 1.32233i) q^{26} +(-3.15637 - 1.82233i) q^{28} +(5.02239 - 8.69904i) q^{29} -4.21957i q^{31} +(0.866025 - 0.500000i) q^{32} +4.00000i q^{34} +(1.82233 + 3.15637i) q^{35} +(8.54267 + 4.93211i) q^{37} -6.31274 q^{38} -1.00000 q^{40} +(-8.04479 - 4.64466i) q^{41} +(-3.78643 - 6.55829i) q^{43} +1.66808i q^{44} +(1.07780 - 0.622266i) q^{46} -6.82522i q^{47} +(3.14177 - 5.44171i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-3.56609 - 0.531987i) q^{52} +0.848634 q^{53} +(0.834038 - 1.44460i) q^{55} +(1.82233 + 3.15637i) q^{56} +(-8.69904 + 5.02239i) q^{58} +(-5.29034 + 3.05438i) q^{59} +(-3.73205 - 6.46410i) q^{61} +(-2.10978 + 3.65425i) q^{62} -1.00000 q^{64} +(2.82233 + 2.24376i) q^{65} +(12.7768 + 7.37671i) q^{67} +(2.00000 - 3.46410i) q^{68} -3.64466i q^{70} +(3.04056 - 1.75547i) q^{71} -12.2175i q^{73} +(-4.93211 - 8.54267i) q^{74} +(5.46699 + 3.15637i) q^{76} -6.07957 q^{77} +9.93398 q^{79} +(0.866025 + 0.500000i) q^{80} +(4.64466 + 8.04479i) q^{82} +7.95317i q^{83} +(-3.46410 + 2.00000i) q^{85} +7.57286i q^{86} +(0.834038 - 1.44460i) q^{88} +(-5.15425 - 2.97581i) q^{89} +(1.93891 - 12.9972i) q^{91} -1.24453 q^{92} +(-3.41261 + 5.91081i) q^{94} +(-3.15637 - 5.46699i) q^{95} +(-2.38453 + 1.37671i) q^{97} +(-5.44171 + 3.14177i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} + O(q^{10}) \) \( 8q + 4q^{4} - 4q^{10} - 6q^{11} - 12q^{13} - 4q^{14} - 4q^{16} - 16q^{17} - 6q^{19} + 2q^{22} - 4q^{23} - 8q^{25} + 12q^{26} + 8q^{29} - 2q^{35} + 30q^{37} - 8q^{40} + 14q^{43} - 6q^{46} + 14q^{49} - 6q^{52} - 16q^{53} - 2q^{55} - 2q^{56} - 6q^{58} - 24q^{59} - 16q^{61} - 4q^{62} - 8q^{64} + 6q^{65} + 24q^{67} + 16q^{68} + 12q^{71} - 10q^{74} - 6q^{76} - 16q^{77} - 20q^{79} + 4q^{82} - 2q^{88} - 42q^{89} - 10q^{91} - 8q^{92} - 8q^{94} - 24q^{97} - 48q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −3.15637 + 1.82233i −1.19299 + 0.688776i −0.958985 0.283458i \(-0.908518\pi\)
−0.234010 + 0.972234i \(0.575185\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) 1.44460 + 0.834038i 0.435562 + 0.251472i 0.701713 0.712459i \(-0.252419\pi\)
−0.266151 + 0.963931i \(0.585752\pi\)
\(12\) 0 0
\(13\) −2.24376 + 2.82233i −0.622307 + 0.782773i
\(14\) 3.64466 0.974076
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 0 0
\(19\) 5.46699 3.15637i 1.25421 0.724120i 0.282270 0.959335i \(-0.408913\pi\)
0.971943 + 0.235215i \(0.0755793\pi\)
\(20\) 0.866025 0.500000i 0.193649 0.111803i
\(21\) 0 0
\(22\) −0.834038 1.44460i −0.177817 0.307989i
\(23\) −0.622266 + 1.07780i −0.129752 + 0.224736i −0.923580 0.383405i \(-0.874751\pi\)
0.793829 + 0.608141i \(0.208085\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 3.35432 1.32233i 0.657836 0.259330i
\(27\) 0 0
\(28\) −3.15637 1.82233i −0.596497 0.344388i
\(29\) 5.02239 8.69904i 0.932635 1.61537i 0.153837 0.988096i \(-0.450837\pi\)
0.778798 0.627275i \(-0.215830\pi\)
\(30\) 0 0
\(31\) 4.21957i 0.757857i −0.925426 0.378928i \(-0.876293\pi\)
0.925426 0.378928i \(-0.123707\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 4.00000i 0.685994i
\(35\) 1.82233 + 3.15637i 0.308030 + 0.533524i
\(36\) 0 0
\(37\) 8.54267 + 4.93211i 1.40441 + 0.810835i 0.994841 0.101446i \(-0.0323469\pi\)
0.409566 + 0.912281i \(0.365680\pi\)
\(38\) −6.31274 −1.02406
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) −8.04479 4.64466i −1.25638 0.725374i −0.284015 0.958820i \(-0.591666\pi\)
−0.972370 + 0.233446i \(0.925000\pi\)
\(42\) 0 0
\(43\) −3.78643 6.55829i −0.577425 1.00013i −0.995773 0.0918433i \(-0.970724\pi\)
0.418348 0.908287i \(-0.362609\pi\)
\(44\) 1.66808i 0.251472i
\(45\) 0 0
\(46\) 1.07780 0.622266i 0.158912 0.0917482i
\(47\) 6.82522i 0.995560i −0.867303 0.497780i \(-0.834149\pi\)
0.867303 0.497780i \(-0.165851\pi\)
\(48\) 0 0
\(49\) 3.14177 5.44171i 0.448825 0.777387i
\(50\) 0.866025 + 0.500000i 0.122474 + 0.0707107i
\(51\) 0 0
\(52\) −3.56609 0.531987i −0.494528 0.0737734i
\(53\) 0.848634 0.116569 0.0582844 0.998300i \(-0.481437\pi\)
0.0582844 + 0.998300i \(0.481437\pi\)
\(54\) 0 0
\(55\) 0.834038 1.44460i 0.112462 0.194789i
\(56\) 1.82233 + 3.15637i 0.243519 + 0.421787i
\(57\) 0 0
\(58\) −8.69904 + 5.02239i −1.14224 + 0.659473i
\(59\) −5.29034 + 3.05438i −0.688744 + 0.397646i −0.803141 0.595789i \(-0.796840\pi\)
0.114397 + 0.993435i \(0.463506\pi\)
\(60\) 0 0
\(61\) −3.73205 6.46410i −0.477840 0.827643i 0.521837 0.853045i \(-0.325247\pi\)
−0.999677 + 0.0254017i \(0.991914\pi\)
\(62\) −2.10978 + 3.65425i −0.267943 + 0.464091i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 2.82233 + 2.24376i 0.350067 + 0.278304i
\(66\) 0 0
\(67\) 12.7768 + 7.37671i 1.56094 + 0.901209i 0.997162 + 0.0752814i \(0.0239855\pi\)
0.563777 + 0.825927i \(0.309348\pi\)
\(68\) 2.00000 3.46410i 0.242536 0.420084i
\(69\) 0 0
\(70\) 3.64466i 0.435620i
\(71\) 3.04056 1.75547i 0.360848 0.208336i −0.308605 0.951190i \(-0.599862\pi\)
0.669453 + 0.742855i \(0.266529\pi\)
\(72\) 0 0
\(73\) 12.2175i 1.42995i −0.699149 0.714976i \(-0.746437\pi\)
0.699149 0.714976i \(-0.253563\pi\)
\(74\) −4.93211 8.54267i −0.573347 0.993065i
\(75\) 0 0
\(76\) 5.46699 + 3.15637i 0.627107 + 0.362060i
\(77\) −6.07957 −0.692831
\(78\) 0 0
\(79\) 9.93398 1.11766 0.558830 0.829282i \(-0.311250\pi\)
0.558830 + 0.829282i \(0.311250\pi\)
\(80\) 0.866025 + 0.500000i 0.0968246 + 0.0559017i
\(81\) 0 0
\(82\) 4.64466 + 8.04479i 0.512917 + 0.888398i
\(83\) 7.95317i 0.872974i 0.899711 + 0.436487i \(0.143777\pi\)
−0.899711 + 0.436487i \(0.856223\pi\)
\(84\) 0 0
\(85\) −3.46410 + 2.00000i −0.375735 + 0.216930i
\(86\) 7.57286i 0.816603i
\(87\) 0 0
\(88\) 0.834038 1.44460i 0.0889087 0.153994i
\(89\) −5.15425 2.97581i −0.546350 0.315435i 0.201299 0.979530i \(-0.435484\pi\)
−0.747648 + 0.664095i \(0.768817\pi\)
\(90\) 0 0
\(91\) 1.93891 12.9972i 0.203253 1.36247i
\(92\) −1.24453 −0.129752
\(93\) 0 0
\(94\) −3.41261 + 5.91081i −0.351984 + 0.609654i
\(95\) −3.15637 5.46699i −0.323837 0.560901i
\(96\) 0 0
\(97\) −2.38453 + 1.37671i −0.242113 + 0.139784i −0.616147 0.787631i \(-0.711307\pi\)
0.374035 + 0.927415i \(0.377974\pi\)
\(98\) −5.44171 + 3.14177i −0.549696 + 0.317367i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −2.66808 + 4.62124i −0.265483 + 0.459831i −0.967690 0.252142i \(-0.918865\pi\)
0.702207 + 0.711973i \(0.252198\pi\)
\(102\) 0 0
\(103\) −7.51248 −0.740227 −0.370113 0.928987i \(-0.620681\pi\)
−0.370113 + 0.928987i \(0.620681\pi\)
\(104\) 2.82233 + 2.24376i 0.276752 + 0.220019i
\(105\) 0 0
\(106\) −0.734939 0.424317i −0.0713835 0.0412133i
\(107\) 8.46410 14.6603i 0.818256 1.41726i −0.0887109 0.996057i \(-0.528275\pi\)
0.906966 0.421203i \(-0.138392\pi\)
\(108\) 0 0
\(109\) 0.663848i 0.0635851i −0.999494 0.0317926i \(-0.989878\pi\)
0.999494 0.0317926i \(-0.0101216\pi\)
\(110\) −1.44460 + 0.834038i −0.137737 + 0.0795224i
\(111\) 0 0
\(112\) 3.64466i 0.344388i
\(113\) −8.93500 15.4759i −0.840534 1.45585i −0.889444 0.457045i \(-0.848908\pi\)
0.0489094 0.998803i \(-0.484425\pi\)
\(114\) 0 0
\(115\) 1.07780 + 0.622266i 0.100505 + 0.0580266i
\(116\) 10.0448 0.932635
\(117\) 0 0
\(118\) 6.10876 0.562357
\(119\) 12.6255 + 7.28932i 1.15738 + 0.668211i
\(120\) 0 0
\(121\) −4.10876 7.11658i −0.373524 0.646962i
\(122\) 7.46410i 0.675768i
\(123\) 0 0
\(124\) 3.65425 2.10978i 0.328162 0.189464i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 7.22034 12.5060i 0.640702 1.10973i −0.344575 0.938759i \(-0.611977\pi\)
0.985276 0.170969i \(-0.0546898\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −1.32233 3.35432i −0.115976 0.294193i
\(131\) 10.8892 0.951393 0.475697 0.879609i \(-0.342196\pi\)
0.475697 + 0.879609i \(0.342196\pi\)
\(132\) 0 0
\(133\) −11.5039 + 19.9253i −0.997513 + 1.72774i
\(134\) −7.37671 12.7768i −0.637251 1.10375i
\(135\) 0 0
\(136\) −3.46410 + 2.00000i −0.297044 + 0.171499i
\(137\) −6.09419 + 3.51848i −0.520662 + 0.300604i −0.737205 0.675669i \(-0.763855\pi\)
0.216544 + 0.976273i \(0.430522\pi\)
\(138\) 0 0
\(139\) −5.82233 10.0846i −0.493844 0.855362i 0.506131 0.862456i \(-0.331075\pi\)
−0.999975 + 0.00709431i \(0.997742\pi\)
\(140\) −1.82233 + 3.15637i −0.154015 + 0.266762i
\(141\) 0 0
\(142\) −3.51093 −0.294631
\(143\) −5.59526 + 2.20575i −0.467899 + 0.184454i
\(144\) 0 0
\(145\) −8.69904 5.02239i −0.722416 0.417087i
\(146\) −6.10876 + 10.5807i −0.505565 + 0.875664i
\(147\) 0 0
\(148\) 9.86423i 0.810835i
\(149\) 0.669099 0.386305i 0.0548147 0.0316473i −0.472342 0.881415i \(-0.656591\pi\)
0.527157 + 0.849768i \(0.323258\pi\)
\(150\) 0 0
\(151\) 9.77838i 0.795754i 0.917439 + 0.397877i \(0.130253\pi\)
−0.917439 + 0.397877i \(0.869747\pi\)
\(152\) −3.15637 5.46699i −0.256015 0.443431i
\(153\) 0 0
\(154\) 5.26506 + 3.03978i 0.424271 + 0.244953i
\(155\) −4.21957 −0.338924
\(156\) 0 0
\(157\) −12.0135 −0.958786 −0.479393 0.877600i \(-0.659143\pi\)
−0.479393 + 0.877600i \(0.659143\pi\)
\(158\) −8.60308 4.96699i −0.684424 0.395152i
\(159\) 0 0
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) 4.53590i 0.357479i
\(162\) 0 0
\(163\) −8.73960 + 5.04581i −0.684538 + 0.395218i −0.801563 0.597911i \(-0.795998\pi\)
0.117025 + 0.993129i \(0.462664\pi\)
\(164\) 9.28932i 0.725374i
\(165\) 0 0
\(166\) 3.97658 6.88764i 0.308643 0.534585i
\(167\) 6.83902 + 3.94851i 0.529219 + 0.305545i 0.740698 0.671838i \(-0.234495\pi\)
−0.211479 + 0.977382i \(0.567828\pi\)
\(168\) 0 0
\(169\) −2.93109 12.6653i −0.225469 0.974250i
\(170\) 4.00000 0.306786
\(171\) 0 0
\(172\) 3.78643 6.55829i 0.288713 0.500065i
\(173\) 0.220343 + 0.381645i 0.0167523 + 0.0290159i 0.874280 0.485422i \(-0.161334\pi\)
−0.857528 + 0.514438i \(0.828001\pi\)
\(174\) 0 0
\(175\) 3.15637 1.82233i 0.238599 0.137755i
\(176\) −1.44460 + 0.834038i −0.108891 + 0.0628680i
\(177\) 0 0
\(178\) 2.97581 + 5.15425i 0.223046 + 0.386328i
\(179\) 9.81842 17.0060i 0.733863 1.27109i −0.221357 0.975193i \(-0.571049\pi\)
0.955220 0.295895i \(-0.0956180\pi\)
\(180\) 0 0
\(181\) 6.21752 0.462145 0.231072 0.972937i \(-0.425777\pi\)
0.231072 + 0.972937i \(0.425777\pi\)
\(182\) −8.17774 + 10.2864i −0.606174 + 0.762481i
\(183\) 0 0
\(184\) 1.07780 + 0.622266i 0.0794562 + 0.0458741i
\(185\) 4.93211 8.54267i 0.362616 0.628070i
\(186\) 0 0
\(187\) 6.67230i 0.487927i
\(188\) 5.91081 3.41261i 0.431090 0.248890i
\(189\) 0 0
\(190\) 6.31274i 0.457974i
\(191\) 7.84081 + 13.5807i 0.567341 + 0.982664i 0.996828 + 0.0795905i \(0.0253613\pi\)
−0.429486 + 0.903073i \(0.641305\pi\)
\(192\) 0 0
\(193\) 7.03901 + 4.06397i 0.506679 + 0.292531i 0.731468 0.681876i \(-0.238836\pi\)
−0.224788 + 0.974408i \(0.572169\pi\)
\(194\) 2.75342 0.197684
\(195\) 0 0
\(196\) 6.28354 0.448825
\(197\) −0.771835 0.445619i −0.0549910 0.0317491i 0.472252 0.881463i \(-0.343441\pi\)
−0.527243 + 0.849714i \(0.676774\pi\)
\(198\) 0 0
\(199\) 0.180558 + 0.312736i 0.0127994 + 0.0221692i 0.872354 0.488874i \(-0.162592\pi\)
−0.859555 + 0.511044i \(0.829259\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 0 0
\(202\) 4.62124 2.66808i 0.325150 0.187725i
\(203\) 36.6098i 2.56951i
\(204\) 0 0
\(205\) −4.64466 + 8.04479i −0.324397 + 0.561872i
\(206\) 6.50600 + 3.75624i 0.453295 + 0.261710i
\(207\) 0 0
\(208\) −1.32233 3.35432i −0.0916871 0.232580i
\(209\) 10.5301 0.728384
\(210\) 0 0
\(211\) −1.11370 + 1.92898i −0.0766700 + 0.132796i −0.901811 0.432130i \(-0.857762\pi\)
0.825141 + 0.564926i \(0.191095\pi\)
\(212\) 0.424317 + 0.734939i 0.0291422 + 0.0504758i
\(213\) 0 0
\(214\) −14.6603 + 8.46410i −1.00215 + 0.578594i
\(215\) −6.55829 + 3.78643i −0.447272 + 0.258232i
\(216\) 0 0
\(217\) 7.68945 + 13.3185i 0.521994 + 0.904119i
\(218\) −0.331924 + 0.574909i −0.0224807 + 0.0389378i
\(219\) 0 0
\(220\) 1.66808 0.112462
\(221\) 14.2644 + 2.12795i 0.959524 + 0.143141i
\(222\) 0 0
\(223\) 5.26872 + 3.04190i 0.352820 + 0.203701i 0.665927 0.746017i \(-0.268036\pi\)
−0.313107 + 0.949718i \(0.601370\pi\)
\(224\) −1.82233 + 3.15637i −0.121760 + 0.210894i
\(225\) 0 0
\(226\) 17.8700i 1.18869i
\(227\) 13.2679 7.66025i 0.880625 0.508429i 0.00976038 0.999952i \(-0.496893\pi\)
0.870864 + 0.491523i \(0.163560\pi\)
\(228\) 0 0
\(229\) 22.2644i 1.47127i 0.677378 + 0.735635i \(0.263116\pi\)
−0.677378 + 0.735635i \(0.736884\pi\)
\(230\) −0.622266 1.07780i −0.0410310 0.0710678i
\(231\) 0 0
\(232\) −8.69904 5.02239i −0.571120 0.329736i
\(233\) −10.8366 −0.709928 −0.354964 0.934880i \(-0.615507\pi\)
−0.354964 + 0.934880i \(0.615507\pi\)
\(234\) 0 0
\(235\) −6.82522 −0.445228
\(236\) −5.29034 3.05438i −0.344372 0.198823i
\(237\) 0 0
\(238\) −7.28932 12.6255i −0.472496 0.818388i
\(239\) 16.4975i 1.06714i 0.845757 + 0.533568i \(0.179149\pi\)
−0.845757 + 0.533568i \(0.820851\pi\)
\(240\) 0 0
\(241\) 3.81428 2.20218i 0.245700 0.141855i −0.372094 0.928195i \(-0.621360\pi\)
0.617794 + 0.786340i \(0.288027\pi\)
\(242\) 8.21752i 0.528242i
\(243\) 0 0
\(244\) 3.73205 6.46410i 0.238920 0.413822i
\(245\) −5.44171 3.14177i −0.347658 0.200720i
\(246\) 0 0
\(247\) −3.35830 + 22.5118i −0.213683 + 1.43239i
\(248\) −4.21957 −0.267943
\(249\) 0 0
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) −5.97267 10.3450i −0.376992 0.652969i 0.613631 0.789593i \(-0.289708\pi\)
−0.990623 + 0.136624i \(0.956375\pi\)
\(252\) 0 0
\(253\) −1.79785 + 1.03799i −0.113030 + 0.0652577i
\(254\) −12.5060 + 7.22034i −0.784696 + 0.453045i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −9.73103 + 16.8546i −0.607005 + 1.05136i 0.384726 + 0.923031i \(0.374296\pi\)
−0.991731 + 0.128333i \(0.959038\pi\)
\(258\) 0 0
\(259\) −35.9518 −2.23393
\(260\) −0.531987 + 3.56609i −0.0329925 + 0.221159i
\(261\) 0 0
\(262\) −9.43032 5.44460i −0.582607 0.336368i
\(263\) 1.01739 1.76217i 0.0627350 0.108660i −0.832952 0.553345i \(-0.813351\pi\)
0.895687 + 0.444685i \(0.146684\pi\)
\(264\) 0 0
\(265\) 0.848634i 0.0521312i
\(266\) 19.9253 11.5039i 1.22170 0.705349i
\(267\) 0 0
\(268\) 14.7534i 0.901209i
\(269\) 10.2644 + 17.7784i 0.625829 + 1.08397i 0.988380 + 0.152003i \(0.0485725\pi\)
−0.362551 + 0.931964i \(0.618094\pi\)
\(270\) 0 0
\(271\) 22.1184 + 12.7700i 1.34359 + 0.775725i 0.987333 0.158662i \(-0.0507179\pi\)
0.356261 + 0.934386i \(0.384051\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) 7.03696 0.425119
\(275\) −1.44460 0.834038i −0.0871124 0.0502944i
\(276\) 0 0
\(277\) 9.03019 + 15.6407i 0.542572 + 0.939762i 0.998755 + 0.0498760i \(0.0158826\pi\)
−0.456184 + 0.889886i \(0.650784\pi\)
\(278\) 11.6447i 0.698400i
\(279\) 0 0
\(280\) 3.15637 1.82233i 0.188629 0.108905i
\(281\) 20.2175i 1.20608i 0.797712 + 0.603038i \(0.206043\pi\)
−0.797712 + 0.603038i \(0.793957\pi\)
\(282\) 0 0
\(283\) 4.34575 7.52705i 0.258328 0.447437i −0.707466 0.706747i \(-0.750162\pi\)
0.965794 + 0.259310i \(0.0834952\pi\)
\(284\) 3.04056 + 1.75547i 0.180424 + 0.104168i
\(285\) 0 0
\(286\) 5.94851 + 0.887395i 0.351743 + 0.0524728i
\(287\) 33.8564 1.99848
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 5.02239 + 8.69904i 0.294925 + 0.510825i
\(291\) 0 0
\(292\) 10.5807 6.10876i 0.619188 0.357488i
\(293\) −6.53667 + 3.77395i −0.381876 + 0.220476i −0.678634 0.734476i \(-0.737428\pi\)
0.296758 + 0.954953i \(0.404095\pi\)
\(294\) 0 0
\(295\) 3.05438 + 5.29034i 0.177833 + 0.308016i
\(296\) 4.93211 8.54267i 0.286673 0.496533i
\(297\) 0 0
\(298\) −0.772609 −0.0447560
\(299\) −1.64568 4.17456i −0.0951723 0.241421i
\(300\) 0 0
\(301\) 23.9027 + 13.8003i 1.37773 + 0.795433i
\(302\) 4.88919 8.46833i 0.281341 0.487298i
\(303\) 0 0
\(304\) 6.31274i 0.362060i
\(305\) −6.46410 + 3.73205i −0.370133 + 0.213697i
\(306\) 0 0
\(307\) 26.0427i 1.48634i −0.669104 0.743169i \(-0.733322\pi\)
0.669104 0.743169i \(-0.266678\pi\)
\(308\) −3.03978 5.26506i −0.173208 0.300005i
\(309\) 0 0
\(310\) 3.65425 + 2.10978i 0.207548 + 0.119828i
\(311\) −25.3789 −1.43910 −0.719552 0.694438i \(-0.755653\pi\)
−0.719552 + 0.694438i \(0.755653\pi\)
\(312\) 0 0
\(313\) −31.4600 −1.77822 −0.889112 0.457689i \(-0.848677\pi\)
−0.889112 + 0.457689i \(0.848677\pi\)
\(314\) 10.4040 + 6.00677i 0.587134 + 0.338982i
\(315\) 0 0
\(316\) 4.96699 + 8.60308i 0.279415 + 0.483961i
\(317\) 24.7093i 1.38781i −0.720066 0.693905i \(-0.755889\pi\)
0.720066 0.693905i \(-0.244111\pi\)
\(318\) 0 0
\(319\) 14.5107 8.37773i 0.812441 0.469063i
\(320\) 1.00000i 0.0559017i
\(321\) 0 0
\(322\) −2.26795 + 3.92820i −0.126388 + 0.218910i
\(323\) −21.8680 12.6255i −1.21677 0.702500i
\(324\) 0 0
\(325\) 2.24376 2.82233i 0.124461 0.156555i
\(326\) 10.0916 0.558923
\(327\) 0 0
\(328\) −4.64466 + 8.04479i −0.256458 + 0.444199i
\(329\) 12.4378 + 21.5429i 0.685718 + 1.18770i
\(330\) 0 0
\(331\) −4.85286 + 2.80180i −0.266737 + 0.154001i −0.627404 0.778694i \(-0.715883\pi\)
0.360667 + 0.932695i \(0.382549\pi\)
\(332\) −6.88764 + 3.97658i −0.378009 + 0.218243i
\(333\) 0 0
\(334\) −3.94851 6.83902i −0.216053 0.374214i
\(335\) 7.37671 12.7768i 0.403033 0.698073i
\(336\) 0 0
\(337\) 21.7868 1.18680 0.593402 0.804906i \(-0.297784\pi\)
0.593402 + 0.804906i \(0.297784\pi\)
\(338\) −3.79423 + 12.4340i −0.206379 + 0.676319i
\(339\) 0 0
\(340\) −3.46410 2.00000i −0.187867 0.108465i
\(341\) 3.51928 6.09557i 0.190580 0.330094i
\(342\) 0 0
\(343\) 2.61124i 0.140994i
\(344\) −6.55829 + 3.78643i −0.353599 + 0.204151i
\(345\) 0 0
\(346\) 0.440685i 0.0236914i
\(347\) 4.84081 + 8.38453i 0.259868 + 0.450105i 0.966206 0.257769i \(-0.0829875\pi\)
−0.706338 + 0.707875i \(0.749654\pi\)
\(348\) 0 0
\(349\) 16.7321 + 9.66025i 0.895646 + 0.517102i 0.875785 0.482701i \(-0.160344\pi\)
0.0198610 + 0.999803i \(0.493678\pi\)
\(350\) −3.64466 −0.194815
\(351\) 0 0
\(352\) 1.66808 0.0889087
\(353\) 19.8970 + 11.4875i 1.05901 + 0.611419i 0.925158 0.379583i \(-0.123932\pi\)
0.133851 + 0.991002i \(0.457266\pi\)
\(354\) 0 0
\(355\) −1.75547 3.04056i −0.0931705 0.161376i
\(356\) 5.95162i 0.315435i
\(357\) 0 0
\(358\) −17.0060 + 9.81842i −0.898795 + 0.518920i
\(359\) 2.21752i 0.117036i −0.998286 0.0585182i \(-0.981362\pi\)
0.998286 0.0585182i \(-0.0186376\pi\)
\(360\) 0 0
\(361\) 10.4253 18.0572i 0.548701 0.950378i
\(362\) −5.38453 3.10876i −0.283005 0.163393i
\(363\) 0 0
\(364\) 12.2253 4.81944i 0.640782 0.252607i
\(365\) −12.2175 −0.639494
\(366\) 0 0
\(367\) 3.04056 5.26640i 0.158716 0.274904i −0.775690 0.631114i \(-0.782598\pi\)
0.934406 + 0.356210i \(0.115931\pi\)
\(368\) −0.622266 1.07780i −0.0324379 0.0561841i
\(369\) 0 0
\(370\) −8.54267 + 4.93211i −0.444112 + 0.256408i
\(371\) −2.67860 + 1.54649i −0.139066 + 0.0802898i
\(372\) 0 0
\(373\) −7.83904 13.5776i −0.405890 0.703022i 0.588535 0.808472i \(-0.299705\pi\)
−0.994425 + 0.105450i \(0.966372\pi\)
\(374\) −3.33615 + 5.77838i −0.172508 + 0.298793i
\(375\) 0 0
\(376\) −6.82522 −0.351984
\(377\) 13.2825 + 33.6934i 0.684085 + 1.73530i
\(378\) 0 0
\(379\) 26.6013 + 15.3583i 1.36642 + 0.788903i 0.990469 0.137737i \(-0.0439829\pi\)
0.375951 + 0.926640i \(0.377316\pi\)
\(380\) 3.15637 5.46699i 0.161918 0.280451i
\(381\) 0 0
\(382\) 15.6816i 0.802342i
\(383\) −17.3741 + 10.0310i −0.887777 + 0.512558i −0.873215 0.487336i \(-0.837969\pi\)
−0.0145623 + 0.999894i \(0.504635\pi\)
\(384\) 0 0
\(385\) 6.07957i 0.309844i
\(386\) −4.06397 7.03901i −0.206851 0.358276i
\(387\) 0 0
\(388\) −2.38453 1.37671i −0.121056 0.0698919i
\(389\) −27.0314 −1.37055 −0.685273 0.728287i \(-0.740317\pi\)
−0.685273 + 0.728287i \(0.740317\pi\)
\(390\) 0 0
\(391\) 4.97813 0.251755
\(392\) −5.44171 3.14177i −0.274848 0.158683i
\(393\) 0 0
\(394\) 0.445619 + 0.771835i 0.0224500 + 0.0388845i
\(395\) 9.93398i 0.499833i
\(396\) 0 0
\(397\) −3.23571 + 1.86814i −0.162396 + 0.0937592i −0.578995 0.815331i \(-0.696555\pi\)
0.416600 + 0.909090i \(0.363222\pi\)
\(398\) 0.361116i 0.0181011i
\(399\) 0 0
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) −24.3276 14.0456i −1.21486 0.701402i −0.251049 0.967974i \(-0.580775\pi\)
−0.963815 + 0.266573i \(0.914109\pi\)
\(402\) 0 0
\(403\) 11.9090 + 9.46770i 0.593230 + 0.471620i
\(404\) −5.33615 −0.265483
\(405\) 0 0
\(406\) 18.3049 31.7050i 0.908458 1.57349i
\(407\) 8.22714 + 14.2498i 0.407804 + 0.706338i
\(408\) 0 0
\(409\) 23.7122 13.6902i 1.17249 0.676938i 0.218225 0.975898i \(-0.429973\pi\)
0.954265 + 0.298961i \(0.0966399\pi\)
\(410\) 8.04479 4.64466i 0.397304 0.229383i
\(411\) 0 0
\(412\) −3.75624 6.50600i −0.185057 0.320528i
\(413\) 11.1322 19.2815i 0.547779 0.948780i
\(414\) 0 0
\(415\) 7.95317 0.390406
\(416\) −0.531987 + 3.56609i −0.0260828 + 0.174842i
\(417\) 0 0
\(418\) −9.11935 5.26506i −0.446042 0.257523i
\(419\) −6.58068 + 11.3981i −0.321487 + 0.556833i −0.980795 0.195041i \(-0.937516\pi\)
0.659308 + 0.751873i \(0.270849\pi\)
\(420\) 0 0
\(421\) 1.29341i 0.0630370i 0.999503 + 0.0315185i \(0.0100343\pi\)
−0.999503 + 0.0315185i \(0.989966\pi\)
\(422\) 1.92898 1.11370i 0.0939011 0.0542138i
\(423\) 0 0
\(424\) 0.848634i 0.0412133i
\(425\) 2.00000 + 3.46410i 0.0970143 + 0.168034i
\(426\) 0 0
\(427\) 23.5595 + 13.6021i 1.14012 + 0.658250i
\(428\) 16.9282 0.818256
\(429\) 0 0
\(430\) 7.57286 0.365196
\(431\) −10.5031 6.06397i −0.505917 0.292091i 0.225237 0.974304i \(-0.427684\pi\)
−0.731154 + 0.682213i \(0.761018\pi\)
\(432\) 0 0
\(433\) −1.03901 1.79962i −0.0499317 0.0864842i 0.839979 0.542618i \(-0.182567\pi\)
−0.889911 + 0.456134i \(0.849234\pi\)
\(434\) 15.3789i 0.738210i
\(435\) 0 0
\(436\) 0.574909 0.331924i 0.0275332 0.0158963i
\(437\) 7.85641i 0.375823i
\(438\) 0 0
\(439\) −1.19820 + 2.07534i −0.0571869 + 0.0990506i −0.893202 0.449656i \(-0.851546\pi\)
0.836015 + 0.548707i \(0.184880\pi\)
\(440\) −1.44460 0.834038i −0.0688684 0.0397612i
\(441\) 0 0
\(442\) −11.2893 8.97504i −0.536978 0.426899i
\(443\) −21.9959 −1.04506 −0.522529 0.852622i \(-0.675011\pi\)
−0.522529 + 0.852622i \(0.675011\pi\)
\(444\) 0 0
\(445\) −2.97581 + 5.15425i −0.141067 + 0.244335i
\(446\) −3.04190 5.26872i −0.144038 0.249481i
\(447\) 0 0
\(448\) 3.15637 1.82233i 0.149124 0.0860970i
\(449\) −25.3098 + 14.6126i −1.19445 + 0.689613i −0.959312 0.282350i \(-0.908886\pi\)
−0.235134 + 0.971963i \(0.575553\pi\)
\(450\) 0 0
\(451\) −7.74765 13.4193i −0.364822 0.631891i
\(452\) 8.93500 15.4759i 0.420267 0.727924i
\(453\) 0 0
\(454\) −15.3205 −0.719027
\(455\) −12.9972 1.93891i −0.609317 0.0908976i
\(456\) 0 0
\(457\) −34.3321 19.8216i −1.60599 0.927216i −0.990256 0.139259i \(-0.955528\pi\)
−0.615730 0.787957i \(-0.711139\pi\)
\(458\) 11.1322 19.2815i 0.520172 0.900965i
\(459\) 0 0
\(460\) 1.24453i 0.0580266i
\(461\) −14.4417 + 8.33792i −0.672617 + 0.388336i −0.797068 0.603890i \(-0.793617\pi\)
0.124450 + 0.992226i \(0.460283\pi\)
\(462\) 0 0
\(463\) 32.2175i 1.49728i −0.662979 0.748638i \(-0.730708\pi\)
0.662979 0.748638i \(-0.269292\pi\)
\(464\) 5.02239 + 8.69904i 0.233159 + 0.403843i
\(465\) 0 0
\(466\) 9.38476 + 5.41829i 0.434740 + 0.250998i
\(467\) 6.88137 0.318432 0.159216 0.987244i \(-0.449103\pi\)
0.159216 + 0.987244i \(0.449103\pi\)
\(468\) 0 0
\(469\) −53.7712 −2.48292
\(470\) 5.91081 + 3.41261i 0.272645 + 0.157412i
\(471\) 0 0
\(472\) 3.05438 + 5.29034i 0.140589 + 0.243508i
\(473\) 12.6321i 0.580825i
\(474\) 0 0
\(475\) −5.46699 + 3.15637i −0.250843 + 0.144824i
\(476\) 14.5786i 0.668211i
\(477\) 0 0
\(478\) 8.24876 14.2873i 0.377290 0.653485i
\(479\) 16.4293 + 9.48547i 0.750675 + 0.433402i 0.825938 0.563761i \(-0.190646\pi\)
−0.0752629 + 0.997164i \(0.523980\pi\)
\(480\) 0 0
\(481\) −33.0878 + 13.0438i −1.50867 + 0.594744i
\(482\) −4.40435 −0.200613
\(483\) 0 0
\(484\) 4.10876 7.11658i 0.186762 0.323481i
\(485\) 1.37671 + 2.38453i 0.0625132 + 0.108276i
\(486\) 0 0
\(487\) 1.65948 0.958101i 0.0751982 0.0434157i −0.461929 0.886917i \(-0.652843\pi\)
0.537128 + 0.843501i \(0.319509\pi\)
\(488\) −6.46410 + 3.73205i −0.292616 + 0.168942i
\(489\) 0 0
\(490\) 3.14177 + 5.44171i 0.141931 + 0.245831i
\(491\) 16.8187 29.1309i 0.759019 1.31466i −0.184332 0.982864i \(-0.559012\pi\)
0.943351 0.331795i \(-0.107654\pi\)
\(492\) 0 0
\(493\) −40.1791 −1.80958
\(494\) 14.1643 17.8166i 0.637280 0.801608i
\(495\) 0 0
\(496\) 3.65425 + 2.10978i 0.164081 + 0.0947321i
\(497\) −6.39808 + 11.0818i −0.286993 + 0.497087i
\(498\) 0 0
\(499\) 1.82522i 0.0817080i 0.999165 + 0.0408540i \(0.0130078\pi\)
−0.999165 + 0.0408540i \(0.986992\pi\)
\(500\) −0.866025 + 0.500000i −0.0387298 + 0.0223607i
\(501\) 0 0
\(502\) 11.9453i 0.533147i
\(503\) −9.99923 17.3192i −0.445843 0.772224i 0.552267 0.833667i \(-0.313763\pi\)
−0.998111 + 0.0614437i \(0.980430\pi\)
\(504\) 0 0
\(505\) 4.62124 + 2.66808i 0.205643 + 0.118728i
\(506\) 2.07598 0.0922884
\(507\) 0 0
\(508\) 14.4407 0.640702
\(509\) −5.10196 2.94562i −0.226141 0.130562i 0.382650 0.923893i \(-0.375012\pi\)
−0.608790 + 0.793331i \(0.708345\pi\)
\(510\) 0 0
\(511\) 22.2644 + 38.5630i 0.984917 + 1.70593i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 16.8546 9.73103i 0.743426 0.429217i
\(515\) 7.51248i 0.331040i
\(516\) 0 0
\(517\) 5.69249 9.85968i 0.250355 0.433628i
\(518\) 31.1351 + 17.9759i 1.36800 + 0.789815i
\(519\) 0 0
\(520\) 2.24376 2.82233i 0.0983953 0.123767i
\(521\) −32.0370 −1.40356 −0.701782 0.712391i \(-0.747612\pi\)
−0.701782 + 0.712391i \(0.747612\pi\)
\(522\) 0 0
\(523\) −19.3593 + 33.5313i −0.846523 + 1.46622i 0.0377693 + 0.999286i \(0.487975\pi\)
−0.884292 + 0.466934i \(0.845359\pi\)
\(524\) 5.44460 + 9.43032i 0.237848 + 0.411965i
\(525\) 0 0
\(526\) −1.76217 + 1.01739i −0.0768344 + 0.0443604i
\(527\) −14.6170 + 8.43914i −0.636727 + 0.367615i
\(528\) 0 0
\(529\) 10.7256 + 18.5772i 0.466329 + 0.807706i
\(530\) −0.424317 + 0.734939i −0.0184312 + 0.0319237i
\(531\) 0 0
\(532\) −23.0078 −0.997513
\(533\) 31.1593 12.2835i 1.34966 0.532059i
\(534\) 0 0
\(535\) −14.6603 8.46410i −0.633818 0.365935i
\(536\) 7.37671 12.7768i 0.318625 0.551875i
\(537\) 0 0
\(538\) 20.5287i 0.885056i
\(539\) 9.07718 5.24071i 0.390982 0.225734i
\(540\) 0 0
\(541\) 25.9616i 1.11618i 0.829781 + 0.558089i \(0.188465\pi\)
−0.829781 + 0.558089i \(0.811535\pi\)
\(542\) −12.7700 22.1184i −0.548520 0.950065i
\(543\) 0 0
\(544\) −3.46410 2.00000i −0.148522 0.0857493i
\(545\) −0.663848 −0.0284361
\(546\) 0 0
\(547\) −17.7596 −0.759348 −0.379674 0.925120i \(-0.623964\pi\)
−0.379674 + 0.925120i \(0.623964\pi\)
\(548\) −6.09419 3.51848i −0.260331 0.150302i
\(549\) 0 0
\(550\) 0.834038 + 1.44460i 0.0355635 + 0.0615978i
\(551\) 63.4101i 2.70136i
\(552\) 0 0
\(553\) −31.3553 + 18.1030i −1.33336 + 0.769817i
\(554\) 18.0604i 0.767312i
\(555\) 0 0
\(556\) 5.82233 10.0846i 0.246922 0.427681i
\(557\) 22.7074 + 13.1101i 0.962142 + 0.555493i 0.896832 0.442372i \(-0.145863\pi\)
0.0653102 + 0.997865i \(0.479196\pi\)
\(558\) 0 0
\(559\) 27.0055 + 4.02867i 1.14221 + 0.170394i
\(560\) −3.64466 −0.154015
\(561\) 0 0
\(562\) 10.1088 17.5089i 0.426412 0.738568i
\(563\) 12.9964 + 22.5104i 0.547733 + 0.948702i 0.998429 + 0.0560243i \(0.0178424\pi\)
−0.450696 + 0.892677i \(0.648824\pi\)
\(564\) 0 0
\(565\) −15.4759 + 8.93500i −0.651075 + 0.375898i
\(566\) −7.52705 + 4.34575i −0.316386 + 0.182665i
\(567\) 0 0
\(568\) −1.75547 3.04056i −0.0736578 0.127579i
\(569\) 12.7349 22.0576i 0.533876 0.924701i −0.465340 0.885132i \(-0.654068\pi\)
0.999217 0.0395693i \(-0.0125986\pi\)
\(570\) 0 0
\(571\) −8.44491 −0.353409 −0.176704 0.984264i \(-0.556544\pi\)
−0.176704 + 0.984264i \(0.556544\pi\)
\(572\) −4.70786 3.74276i −0.196846 0.156493i
\(573\) 0 0
\(574\) −29.3205 16.9282i −1.22381 0.706570i
\(575\) 0.622266 1.07780i 0.0259503 0.0449472i
\(576\) 0 0
\(577\) 35.4216i 1.47462i −0.675554 0.737311i \(-0.736095\pi\)
0.675554 0.737311i \(-0.263905\pi\)
\(578\) −0.866025 + 0.500000i −0.0360219 + 0.0207973i
\(579\) 0 0
\(580\) 10.0448i 0.417087i
\(581\) −14.4933 25.1031i −0.601283 1.04145i
\(582\) 0 0
\(583\) 1.22593 + 0.707793i 0.0507730 + 0.0293138i
\(584\) −12.2175 −0.505565
\(585\) 0 0
\(586\) 7.54790 0.311801
\(587\) −23.7108 13.6894i −0.978650 0.565024i −0.0767878 0.997047i \(-0.524466\pi\)
−0.901862 + 0.432024i \(0.857800\pi\)
\(588\) 0 0
\(589\) −13.3185 23.0683i −0.548780 0.950514i
\(590\) 6.10876i 0.251494i
\(591\) 0 0
\(592\) −8.54267 + 4.93211i −0.351102 + 0.202709i
\(593\) 12.0619i 0.495324i −0.968846 0.247662i \(-0.920338\pi\)
0.968846 0.247662i \(-0.0796623\pi\)
\(594\) 0 0
\(595\) 7.28932 12.6255i 0.298833 0.517594i
\(596\) 0.669099 + 0.386305i 0.0274074 + 0.0158237i
\(597\) 0 0
\(598\) −0.662076 + 4.43811i −0.0270743 + 0.181488i
\(599\) 28.6129 1.16909 0.584546 0.811360i \(-0.301273\pi\)
0.584546 + 0.811360i \(0.301273\pi\)
\(600\) 0 0
\(601\) 9.58380 16.5996i 0.390931 0.677113i −0.601641 0.798766i \(-0.705486\pi\)
0.992573 + 0.121654i \(0.0388197\pi\)
\(602\) −13.8003 23.9027i −0.562456 0.974203i
\(603\) 0 0
\(604\) −8.46833 + 4.88919i −0.344571 + 0.198938i
\(605\) −7.11658 + 4.10876i −0.289330 + 0.167045i
\(606\) 0 0
\(607\) −9.46910 16.4010i −0.384339 0.665695i 0.607338 0.794443i \(-0.292237\pi\)
−0.991677 + 0.128749i \(0.958904\pi\)
\(608\) 3.15637 5.46699i 0.128008 0.221716i
\(609\) 0 0
\(610\) 7.46410 0.302213
\(611\) 19.2630 + 15.3141i 0.779298 + 0.619544i
\(612\) 0 0
\(613\) −15.5620 8.98472i −0.628543 0.362890i 0.151645 0.988435i \(-0.451543\pi\)
−0.780188 + 0.625546i \(0.784876\pi\)
\(614\) −13.0214 + 22.5537i −0.525500 + 0.910192i
\(615\) 0 0
\(616\) 6.07957i 0.244953i
\(617\) 15.6015 9.00755i 0.628094 0.362630i −0.151920 0.988393i \(-0.548545\pi\)
0.780014 + 0.625763i \(0.215212\pi\)
\(618\) 0 0
\(619\) 25.0505i 1.00687i 0.864035 + 0.503433i \(0.167930\pi\)
−0.864035 + 0.503433i \(0.832070\pi\)
\(620\) −2.10978 3.65425i −0.0847310 0.146758i
\(621\) 0 0
\(622\) 21.9788 + 12.6894i 0.881268 + 0.508800i
\(623\) 21.6916 0.869057
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 27.2452 + 15.7300i 1.08894 + 0.628697i
\(627\) 0 0
\(628\) −6.00677 10.4040i −0.239696 0.415166i
\(629\) 39.4569i 1.57325i
\(630\) 0 0
\(631\) −1.22739 + 0.708634i −0.0488617 + 0.0282103i −0.524232 0.851576i \(-0.675647\pi\)
0.475370 + 0.879786i \(0.342314\pi\)
\(632\) 9.93398i 0.395152i
\(633\) 0 0
\(634\) −12.3546 + 21.3989i −0.490665 + 0.849857i
\(635\) −12.5060 7.22034i −0.496285 0.286531i
\(636\) 0 0
\(637\) 8.30892 + 21.0770i 0.329211 + 0.835101i
\(638\) −16.7555 −0.663355
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −2.30985 4.00077i −0.0912335 0.158021i 0.816797 0.576925i \(-0.195748\pi\)
−0.908030 + 0.418904i \(0.862414\pi\)
\(642\) 0 0
\(643\) 41.6468 24.0448i 1.64239 0.948234i 0.662408 0.749143i \(-0.269535\pi\)
0.979981 0.199091i \(-0.0637988\pi\)
\(644\) 3.92820 2.26795i 0.154793 0.0893697i
\(645\) 0 0
\(646\) 12.6255 + 21.8680i 0.496743 + 0.860383i
\(647\) −1.87282 + 3.24383i −0.0736283 + 0.127528i −0.900489 0.434879i \(-0.856791\pi\)
0.826861 + 0.562407i \(0.190125\pi\)
\(648\) 0 0
\(649\) −10.1899 −0.399988
\(650\) −3.35432 + 1.32233i −0.131567 + 0.0518660i
\(651\) 0 0
\(652\) −8.73960 5.04581i −0.342269 0.197609i
\(653\) 21.1450 36.6241i 0.827466 1.43321i −0.0725541 0.997364i \(-0.523115\pi\)
0.900020 0.435849i \(-0.143552\pi\)
\(654\) 0 0
\(655\) 10.8892i 0.425476i
\(656\) 8.04479 4.64466i 0.314096 0.181343i
\(657\) 0 0
\(658\) 24.8756i 0.969752i
\(659\) −14.5875 25.2663i −0.568248 0.984234i −0.996739 0.0806881i \(-0.974288\pi\)
0.428492 0.903546i \(-0.359045\pi\)
\(660\) 0 0
\(661\) −38.5089 22.2331i −1.49782 0.864768i −0.497825 0.867277i \(-0.665868\pi\)
−0.999997 + 0.00250931i \(0.999201\pi\)
\(662\) 5.60360 0.217790
\(663\) 0 0
\(664\) 7.95317 0.308643
\(665\) 19.9253 + 11.5039i 0.772671 + 0.446102i
\(666\) 0 0
\(667\) 6.25053 + 10.8262i 0.242022 + 0.419194i
\(668\) 7.89701i 0.305545i
\(669\) 0 0
\(670\) −12.7768 + 7.37671i −0.493612 + 0.284987i
\(671\) 12.4507i 0.480654i
\(672\) 0 0
\(673\) 3.95317 6.84709i 0.152383 0.263936i −0.779720 0.626129i \(-0.784638\pi\)
0.932103 + 0.362193i \(0.117972\pi\)
\(674\) −18.8680 10.8934i −0.726767 0.419599i
\(675\) 0 0
\(676\) 9.50289 8.87103i 0.365496 0.341193i
\(677\) 7.05615 0.271190 0.135595 0.990764i \(-0.456705\pi\)
0.135595 + 0.990764i \(0.456705\pi\)
\(678\) 0 0
\(679\) 5.01764 8.69081i 0.192559 0.333523i
\(680\) 2.00000 + 3.46410i 0.0766965 + 0.132842i
\(681\) 0 0
\(682\) −6.09557 + 3.51928i −0.233412 + 0.134760i
\(683\) 5.15559 2.97658i 0.197273 0.113896i −0.398110 0.917338i \(-0.630334\pi\)
0.595383 + 0.803442i \(0.297000\pi\)
\(684\) 0 0
\(685\) 3.51848 + 6.09419i 0.134434 + 0.232847i
\(686\) −1.30562 + 2.26140i −0.0498488 + 0.0863406i
\(687\) 0 0
\(688\) 7.57286 0.288713
\(689\) −1.90413 + 2.39513i −0.0725416 + 0.0912470i
\(690\) 0 0
\(691\) 16.2458 + 9.37953i 0.618020 + 0.356814i 0.776098 0.630613i \(-0.217196\pi\)
−0.158078 + 0.987427i \(0.550530\pi\)
\(692\) −0.220343 + 0.381645i −0.00837617 + 0.0145080i
\(693\) 0 0
\(694\) 9.68162i 0.367509i
\(695\) −10.0846 + 5.82233i −0.382530 + 0.220854i
\(696\) 0 0
\(697\) 37.1573i 1.40743i
\(698\) −9.66025 16.7321i −0.365646 0.633317i
\(699\) 0 0
\(700\) 3.15637 + 1.82233i 0.119299 + 0.0688776i
\(701\) 28.5298 1.07755 0.538777 0.842448i \(-0.318887\pi\)
0.538777 + 0.842448i \(0.318887\pi\)
\(702\) 0 0
\(703\) 62.2703 2.34857
\(704\) −1.44460 0.834038i −0.0544453 0.0314340i
\(705\) 0 0
\(706\) −11.4875 19.8970i −0.432338 0.748832i
\(707\) 19.4485i 0.731435i
\(708\) 0 0
\(709\) −20.0853 + 11.5963i −0.754321 + 0.435507i −0.827253 0.561830i \(-0.810098\pi\)
0.0729321 + 0.997337i \(0.476764\pi\)
\(710\) 3.51093i 0.131763i
\(711\) 0 0
\(712\) −2.97581 + 5.15425i −0.111523 + 0.193164i
\(713\) 4.54784 + 2.62570i 0.170318 + 0.0983331i
\(714\) 0 0
\(715\) 2.20575 + 5.59526i 0.0824902 + 0.209251i
\(716\) 19.6368 0.733863
\(717\) 0 0
\(718\) −1.10876 + 1.92043i −0.0413786 + 0.0716698i
\(719\) −5.85641 10.1436i −0.218407 0.378292i 0.735914 0.677075i \(-0.236753\pi\)
−0.954321 + 0.298783i \(0.903419\pi\)
\(720\) 0 0
\(721\) 23.7122 13.6902i 0.883087 0.509850i
\(722\) −18.0572 + 10.4253i −0.672019 + 0.387990i
\(723\) 0 0
\(724\) 3.10876 + 5.38453i 0.115536 + 0.200115i
\(725\) −5.02239 + 8.69904i −0.186527 + 0.323074i
\(726\) 0 0
\(727\) 3.82677 0.141927 0.0709634 0.997479i \(-0.477393\pi\)
0.0709634 + 0.997479i \(0.477393\pi\)
\(728\) −12.9972 1.93891i −0.481708 0.0718609i
\(729\) 0 0
\(730\) 10.5807 + 6.10876i 0.391609 + 0.226095i
\(731\) −15.1457 + 26.2332i −0.560185 + 0.970269i
\(732\) 0 0
\(733\) 12.9340i 0.477727i 0.971053 + 0.238864i \(0.0767749\pi\)
−0.971053 + 0.238864i \(0.923225\pi\)
\(734\) −5.26640 + 3.04056i −0.194386 + 0.112229i
\(735\) 0 0
\(736\) 1.24453i 0.0458741i
\(737\) 12.3049 + 21.3127i 0.453257 + 0.785065i
\(738\) 0 0
\(739\) −30.6107 17.6731i −1.12603 0.650115i −0.183098 0.983095i \(-0.558612\pi\)
−0.942934 + 0.332980i \(0.891946\pi\)
\(740\) 9.86423 0.362616
\(741\) 0 0
\(742\) 3.09298 0.113547
\(743\) 32.1255 + 18.5477i 1.17857 + 0.680448i 0.955684 0.294396i \(-0.0951185\pi\)
0.222887 + 0.974844i \(0.428452\pi\)
\(744\) 0 0
\(745\) −0.386305 0.669099i −0.0141531 0.0245139i
\(746\) 15.6781i 0.574015i
\(747\) 0 0
\(748\) 5.77838 3.33615i 0.211279 0.121982i
\(749\) 61.6975i 2.25438i
\(750\) 0 0
\(751\) −4.82904 + 8.36414i −0.176214 + 0.305212i −0.940581 0.339570i \(-0.889718\pi\)
0.764367 + 0.644782i \(0.223052\pi\)
\(752\) 5.91081 + 3.41261i 0.215545 + 0.124445i
\(753\) 0 0
\(754\) 5.34370 35.8206i 0.194606 1.30451i
\(755\) 9.77838 0.355872
\(756\) 0 0
\(757\) 21.8443 37.8354i 0.793943 1.37515i −0.129565 0.991571i \(-0.541358\pi\)
0.923508 0.383579i \(-0.125309\pi\)
\(758\) −15.3583 26.6013i −0.557838 0.966204i
\(759\) 0 0
\(760\) −5.46699 + 3.15637i −0.198309 + 0.114493i
\(761\) −34.5550 + 19.9503i −1.25262 + 0.723200i −0.971629 0.236511i \(-0.923996\pi\)
−0.280990 + 0.959711i \(0.590663\pi\)
\(762\) 0 0
\(763\) 1.20975 + 2.09535i 0.0437959 + 0.0758567i
\(764\) −7.84081 + 13.5807i −0.283671 + 0.491332i
\(765\) 0 0
\(766\) 20.0619 0.724867
\(767\) 3.24978 21.7844i 0.117343 0.786589i
\(768\) 0 0
\(769\) −15.2064 8.77941i −0.548356 0.316594i 0.200103 0.979775i \(-0.435872\pi\)
−0.748459 + 0.663181i \(0.769206\pi\)
\(770\) 3.03978 5.26506i 0.109546 0.189740i
\(771\) 0 0
\(772\) 8.12795i 0.292531i
\(773\) −11.1174 + 6.41861i −0.399864 + 0.230861i −0.686425 0.727201i \(-0.740821\pi\)
0.286562 + 0.958062i \(0.407488\pi\)
\(774\) 0 0
\(775\) 4.21957i 0.151571i
\(776\) 1.37671 + 2.38453i 0.0494210 + 0.0855997i
\(777\) 0 0
\(778\) 23.4099 + 13.5157i 0.839284 + 0.484561i
\(779\) −58.6410 −2.10103
\(780\) 0 0
\(781\) 5.85651 0.209562
\(782\) −4.31119 2.48907i −0.154168 0.0890088i
\(783\) 0 0
\(784\) 3.14177 + 5.44171i 0.112206 + 0.194347i
\(785\) 12.0135i 0.428782i
\(786\) 0 0
\(787\) −6.02524 + 3.47867i −0.214777 + 0.124001i −0.603529 0.797341i \(-0.706239\pi\)
0.388753 + 0.921342i \(0.372906\pi\)
\(788\) 0.891239i 0.0317491i
\(789\) 0 0
\(790\)