Properties

Label 1170.2.bs.f.361.1
Level $1170$
Weight $2$
Character 1170.361
Analytic conductor $9.342$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 361.1
Root \(1.33404 - 1.33404i\) of defining polynomial
Character \(\chi\) \(=\) 1170.361
Dual form 1170.2.bs.f.901.1

$q$-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 \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 −0.234010 0.972234i \(-0.575185\pi\)
−0.958985 + 0.283458i \(0.908518\pi\)
\(8\) 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 −0.266151 0.963931i \(-0.585752\pi\)
0.701713 + 0.712459i \(0.252419\pi\)
\(12\) 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 −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 0 0
\(19\) 5.46699 + 3.15637i 1.25421 + 0.724120i 0.971943 0.235215i \(-0.0755793\pi\)
0.282270 + 0.959335i \(0.408913\pi\)
\(20\) 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 0.793829 0.608141i \(-0.208085\pi\)
−0.923580 + 0.383405i \(0.874751\pi\)
\(24\) 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 0.778798 + 0.627275i \(0.215830\pi\)
0.153837 + 0.988096i \(0.450837\pi\)
\(30\) 0 0
\(31\) 4.21957i 0.757857i 0.925426 + 0.378928i \(0.123707\pi\)
−0.925426 + 0.378928i \(0.876293\pi\)
\(32\) 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 0.409566 0.912281i \(-0.365680\pi\)
0.994841 + 0.101446i \(0.0323469\pi\)
\(38\) −6.31274 −1.02406
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) −8.04479 + 4.64466i −1.25638 + 0.725374i −0.972370 0.233446i \(-0.925000\pi\)
−0.284015 + 0.958820i \(0.591666\pi\)
\(42\) 0 0
\(43\) −3.78643 + 6.55829i −0.577425 + 1.00013i 0.418348 + 0.908287i \(0.362609\pi\)
−0.995773 + 0.0918433i \(0.970724\pi\)
\(44\) 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 \(0.165851\pi\)
−0.867303 + 0.497780i \(0.834149\pi\)
\(48\) 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 0.114397 0.993435i \(-0.463506\pi\)
−0.803141 + 0.595789i \(0.796840\pi\)
\(60\) 0 0
\(61\) −3.73205 + 6.46410i −0.477840 + 0.827643i −0.999677 0.0254017i \(-0.991914\pi\)
0.521837 + 0.853045i \(0.325247\pi\)
\(62\) −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 0.563777 0.825927i \(-0.309348\pi\)
0.997162 0.0752814i \(-0.0239855\pi\)
\(68\) 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 0.669453 0.742855i \(-0.266529\pi\)
−0.308605 + 0.951190i \(0.599862\pi\)
\(72\) 0 0
\(73\) 12.2175i 1.42995i 0.699149 + 0.714976i \(0.253563\pi\)
−0.699149 + 0.714976i \(0.746437\pi\)
\(74\) −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 \(-0.856223\pi\)
0.899711 0.436487i \(-0.143777\pi\)
\(84\) 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 −0.747648 0.664095i \(-0.768817\pi\)
0.201299 + 0.979530i \(0.435484\pi\)
\(90\) 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 0.374035 0.927415i \(-0.377974\pi\)
−0.616147 + 0.787631i \(0.711307\pi\)
\(98\) −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 0.702207 0.711973i \(-0.252198\pi\)
−0.967690 + 0.252142i \(0.918865\pi\)
\(102\) 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 0.906966 + 0.421203i \(0.138392\pi\)
−0.0887109 + 0.996057i \(0.528275\pi\)
\(108\) 0 0
\(109\) 0.663848i 0.0635851i 0.999494 + 0.0317926i \(0.0101216\pi\)
−0.999494 + 0.0317926i \(0.989878\pi\)
\(110\) −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 0.0489094 + 0.998803i \(0.484425\pi\)
−0.889444 + 0.457045i \(0.848908\pi\)
\(114\) 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 0.985276 + 0.170969i \(0.0546898\pi\)
−0.344575 + 0.938759i \(0.611977\pi\)
\(128\) 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 0.216544 0.976273i \(-0.430522\pi\)
−0.737205 + 0.675669i \(0.763855\pi\)
\(138\) 0 0
\(139\) −5.82233 + 10.0846i −0.493844 + 0.855362i −0.999975 0.00709431i \(-0.997742\pi\)
0.506131 + 0.862456i \(0.331075\pi\)
\(140\) −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 0.527157 0.849768i \(-0.323258\pi\)
−0.472342 + 0.881415i \(0.656591\pi\)
\(150\) 0 0
\(151\) 9.77838i 0.795754i −0.917439 0.397877i \(-0.869747\pi\)
0.917439 0.397877i \(-0.130253\pi\)
\(152\) −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 0.117025 0.993129i \(-0.462664\pi\)
−0.801563 + 0.597911i \(0.795998\pi\)
\(164\) 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 −0.211479 0.977382i \(-0.567828\pi\)
0.740698 + 0.671838i \(0.234495\pi\)
\(168\) 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 −0.857528 0.514438i \(-0.828001\pi\)
0.874280 + 0.485422i \(0.161334\pi\)
\(174\) 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 0.955220 + 0.295895i \(0.0956180\pi\)
−0.221357 + 0.975193i \(0.571049\pi\)
\(180\) 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 −0.429486 0.903073i \(-0.641305\pi\)
0.996828 0.0795905i \(-0.0253613\pi\)
\(192\) 0 0
\(193\) 7.03901 4.06397i 0.506679 0.292531i −0.224788 0.974408i \(-0.572169\pi\)
0.731468 + 0.681876i \(0.238836\pi\)
\(194\) 2.75342 0.197684
\(195\) 0 0
\(196\) 6.28354 0.448825
\(197\) −0.771835 + 0.445619i −0.0549910 + 0.0317491i −0.527243 0.849714i \(-0.676774\pi\)
0.472252 + 0.881463i \(0.343441\pi\)
\(198\) 0 0
\(199\) 0.180558 0.312736i 0.0127994 0.0221692i −0.859555 0.511044i \(-0.829259\pi\)
0.872354 + 0.488874i \(0.162592\pi\)
\(200\) 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 0.825141 0.564926i \(-0.191095\pi\)
−0.901811 + 0.432130i \(0.857762\pi\)
\(212\) 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 −0.313107 0.949718i \(-0.601370\pi\)
0.665927 + 0.746017i \(0.268036\pi\)
\(224\) −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 0.870864 0.491523i \(-0.163560\pi\)
0.00976038 + 0.999952i \(0.496893\pi\)
\(228\) 0 0
\(229\) 22.2644i 1.47127i −0.677378 0.735635i \(-0.736884\pi\)
0.677378 0.735635i \(-0.263116\pi\)
\(230\) −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 \(-0.820851\pi\)
0.845757 0.533568i \(-0.179149\pi\)
\(240\) 0 0
\(241\) 3.81428 + 2.20218i 0.245700 + 0.141855i 0.617794 0.786340i \(-0.288027\pi\)
−0.372094 + 0.928195i \(0.621360\pi\)
\(242\) 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 −0.990623 0.136624i \(-0.956375\pi\)
0.613631 + 0.789593i \(0.289708\pi\)
\(252\) 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 −0.991731 0.128333i \(-0.959038\pi\)
0.384726 0.923031i \(-0.374296\pi\)
\(258\) 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 0.895687 0.444685i \(-0.146684\pi\)
−0.832952 + 0.553345i \(0.813351\pi\)
\(264\) 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 −0.362551 0.931964i \(-0.618094\pi\)
0.988380 0.152003i \(-0.0485725\pi\)
\(270\) 0 0
\(271\) 22.1184 12.7700i 1.34359 0.775725i 0.356261 0.934386i \(-0.384051\pi\)
0.987333 + 0.158662i \(0.0507179\pi\)
\(272\) 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 −0.456184 0.889886i \(-0.650784\pi\)
0.998755 0.0498760i \(-0.0158826\pi\)
\(278\) 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 \(-0.793957\pi\)
0.797712 0.603038i \(-0.206043\pi\)
\(282\) 0 0
\(283\) 4.34575 + 7.52705i 0.258328 + 0.447437i 0.965794 0.259310i \(-0.0834952\pi\)
−0.707466 + 0.706747i \(0.750162\pi\)
\(284\) 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 0.296758 0.954953i \(-0.404095\pi\)
−0.678634 + 0.734476i \(0.737428\pi\)
\(294\) 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 \(0.266678\pi\)
−0.669104 + 0.743169i \(0.733322\pi\)
\(308\) −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 \(0.244111\pi\)
−0.720066 + 0.693905i \(0.755889\pi\)
\(318\) 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 0.360667 0.932695i \(-0.382549\pi\)
−0.627404 + 0.778694i \(0.715883\pi\)
\(332\) −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 −0.706338 0.707875i \(-0.749654\pi\)
0.966206 + 0.257769i \(0.0829875\pi\)
\(348\) 0 0
\(349\) 16.7321 9.66025i 0.895646 0.517102i 0.0198610 0.999803i \(-0.493678\pi\)
0.875785 + 0.482701i \(0.160344\pi\)
\(350\) −3.64466 −0.194815
\(351\) 0 0
\(352\) 1.66808 0.0889087
\(353\) 19.8970 11.4875i 1.05901 0.611419i 0.133851 0.991002i \(-0.457266\pi\)
0.925158 + 0.379583i \(0.123932\pi\)
\(354\) 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 \(0.0186376\pi\)
−0.998286 + 0.0585182i \(0.981362\pi\)
\(360\) 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 0.934406 0.356210i \(-0.115931\pi\)
−0.775690 + 0.631114i \(0.782598\pi\)
\(368\) −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 −0.994425 0.105450i \(-0.966372\pi\)
0.588535 + 0.808472i \(0.299705\pi\)
\(374\) −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 0.375951 0.926640i \(-0.377316\pi\)
0.990469 + 0.137737i \(0.0439829\pi\)
\(380\) 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 −0.0145623 0.999894i \(-0.504635\pi\)
−0.873215 + 0.487336i \(0.837969\pi\)
\(384\) 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 0.416600 0.909090i \(-0.363222\pi\)
−0.578995 + 0.815331i \(0.696555\pi\)
\(398\) 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 −0.963815 0.266573i \(-0.914109\pi\)
−0.251049 + 0.967974i \(0.580775\pi\)
\(402\) 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 0.954265 0.298961i \(-0.0966399\pi\)
0.218225 + 0.975898i \(0.429973\pi\)
\(410\) 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 0.659308 0.751873i \(-0.270849\pi\)
−0.980795 + 0.195041i \(0.937516\pi\)
\(420\) 0 0
\(421\) 1.29341i 0.0630370i −0.999503 0.0315185i \(-0.989966\pi\)
0.999503 0.0315185i \(-0.0100343\pi\)
\(422\) 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 −0.731154 0.682213i \(-0.761018\pi\)
0.225237 + 0.974304i \(0.427684\pi\)
\(432\) 0 0
\(433\) −1.03901 + 1.79962i −0.0499317 + 0.0864842i −0.889911 0.456134i \(-0.849234\pi\)
0.839979 + 0.542618i \(0.182567\pi\)
\(434\) 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 0.836015 0.548707i \(-0.184880\pi\)
−0.893202 + 0.449656i \(0.851546\pi\)
\(440\) −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 −0.235134 0.971963i \(-0.575553\pi\)
−0.959312 + 0.282350i \(0.908886\pi\)
\(450\) 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 −0.615730 + 0.787957i \(0.711139\pi\)
−0.990256 + 0.139259i \(0.955528\pi\)
\(458\) 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 0.124450 0.992226i \(-0.460283\pi\)
−0.797068 + 0.603890i \(0.793617\pi\)
\(462\) 0 0
\(463\) 32.2175i 1.49728i 0.662979 + 0.748638i \(0.269292\pi\)
−0.662979 + 0.748638i \(0.730708\pi\)
\(464\) 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 −0.0752629 0.997164i \(-0.523980\pi\)
0.825938 + 0.563761i \(0.190646\pi\)
\(480\) 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 0.537128 0.843501i \(-0.319509\pi\)
−0.461929 + 0.886917i \(0.652843\pi\)
\(488\) −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 0.943351 + 0.331795i \(0.107654\pi\)
−0.184332 + 0.982864i \(0.559012\pi\)
\(492\) 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 \(-0.986992\pi\)
0.999165 0.0408540i \(-0.0130078\pi\)
\(500\) −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 −0.998111 0.0614437i \(-0.980430\pi\)
0.552267 + 0.833667i \(0.313763\pi\)
\(504\) 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 −0.608790 0.793331i \(-0.708345\pi\)
0.382650 + 0.923893i \(0.375012\pi\)
\(510\) 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 −0.884292 0.466934i \(-0.845359\pi\)
0.0377693 0.999286i \(-0.487975\pi\)
\(524\) 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 \(-0.811535\pi\)
0.829781 0.558089i \(-0.188465\pi\)
\(542\) −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 0.0653102 0.997865i \(-0.479196\pi\)
0.896832 + 0.442372i \(0.145863\pi\)
\(558\) 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 −0.450696 0.892677i \(-0.648824\pi\)
0.998429 0.0560243i \(-0.0178424\pi\)
\(564\) 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 0.999217 + 0.0395693i \(0.0125986\pi\)
−0.465340 + 0.885132i \(0.654068\pi\)
\(570\) 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 \(0.263905\pi\)
−0.675554 + 0.737311i \(0.736095\pi\)
\(578\) −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 −0.901862 0.432024i \(-0.857800\pi\)
−0.0767878 + 0.997047i \(0.524466\pi\)
\(588\) 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 \(0.0796623\pi\)
−0.968846 + 0.247662i \(0.920338\pi\)
\(594\) 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 0.992573 0.121654i \(-0.0388197\pi\)
−0.601641 + 0.798766i \(0.705486\pi\)
\(602\) −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 −0.991677 0.128749i \(-0.958904\pi\)
0.607338 + 0.794443i \(0.292237\pi\)
\(608\) 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 −0.780188 0.625546i \(-0.784876\pi\)
0.151645 + 0.988435i \(0.451543\pi\)
\(614\) −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 0.780014 0.625763i \(-0.215212\pi\)
−0.151920 + 0.988393i \(0.548545\pi\)
\(618\) 0 0
\(619\) 25.0505i 1.00687i −0.864035 0.503433i \(-0.832070\pi\)
0.864035 0.503433i \(-0.167930\pi\)
\(620\) −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 0.475370 0.879786i \(-0.342314\pi\)
−0.524232 + 0.851576i \(0.675647\pi\)
\(632\) 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 −0.908030 0.418904i \(-0.862414\pi\)
0.816797 + 0.576925i \(0.195748\pi\)
\(642\) 0 0
\(643\) 41.6468 + 24.0448i 1.64239 + 0.948234i 0.979981 + 0.199091i \(0.0637988\pi\)
0.662408 + 0.749143i \(0.269535\pi\)
\(644\) 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 0.826861 0.562407i \(-0.190125\pi\)
−0.900489 + 0.434879i \(0.856791\pi\)
\(648\) 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 0.900020 + 0.435849i \(0.143552\pi\)
−0.0725541 + 0.997364i \(0.523115\pi\)
\(654\) 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 0.428492 + 0.903546i \(0.359045\pi\)
−0.996739 + 0.0806881i \(0.974288\pi\)
\(660\) 0 0
\(661\) −38.5089 + 22.2331i −1.49782 + 0.864768i −0.999997 0.00250931i \(-0.999201\pi\)
−0.497825 + 0.867277i \(0.665868\pi\)
\(662\) 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 0.932103 0.362193i \(-0.117972\pi\)
−0.779720 + 0.626129i \(0.784638\pi\)
\(674\) −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 0.595383 0.803442i \(-0.297000\pi\)
−0.398110 + 0.917338i \(0.630334\pi\)
\(684\) 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 −0.158078 0.987427i \(-0.550530\pi\)
0.776098 + 0.630613i \(0.217196\pi\)
\(692\) −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 0.0729321 0.997337i \(-0.476764\pi\)
−0.827253 + 0.561830i \(0.810098\pi\)
\(710\) 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 −0.954321 0.298783i \(-0.903419\pi\)
0.735914 + 0.677075i \(0.236753\pi\)
\(720\) 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 \(-0.923225\pi\)
0.971053 0.238864i \(-0.0767749\pi\)
\(734\) −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 −0.942934 0.332980i \(-0.891946\pi\)
−0.183098 + 0.983095i \(0.558612\pi\)
\(740\) 9.86423 0.362616
\(741\) 0 0
\(742\) 3.09298 0.113547
\(743\) 32.1255 18.5477i 1.17857 0.680448i 0.222887 0.974844i \(-0.428452\pi\)
0.955684 + 0.294396i \(0.0951185\pi\)
\(744\) 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 0.764367 0.644782i \(-0.223052\pi\)
−0.940581 + 0.339570i \(0.889718\pi\)
\(752\) 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 0.923508 + 0.383579i \(0.125309\pi\)
−0.129565 + 0.991571i \(0.541358\pi\)
\(758\) −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 −0.280990 0.959711i \(-0.590663\pi\)
−0.971629 + 0.236511i \(0.923996\pi\)
\(762\) 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 −0.748459 0.663181i \(-0.769206\pi\)
0.200103 + 0.979775i \(0.435872\pi\)
\(770\) 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 0.286562 0.958062i \(-0.407488\pi\)
−0.686425 + 0.727201i \(0.740821\pi\)
\(774\) 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 0.388753 0.921342i \(-0.372906\pi\)
−0.603529 + 0.797341i \(0.706239\pi\)
\(788\) 0.891239i 0.0317491i
\(789\) 0 0
\(790\)