Properties

Label 1950.2.y.k.199.2
Level $1950$
Weight $2$
Character 1950.199
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.y (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
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 199.2
Root \(1.33404 + 1.33404i\) of defining polynomial
Character \(\chi\) \(=\) 1950.199
Dual form 1950.2.y.k.49.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(1.82233 + 3.15637i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(1.82233 + 3.15637i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.44460 - 0.834038i) q^{11} +1.00000i q^{12} +(-2.82233 - 2.24376i) q^{13} +3.64466 q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.46410 - 2.00000i) q^{17} +1.00000 q^{18} +(-5.46699 + 3.15637i) q^{19} -3.64466i q^{21} +(-1.44460 + 0.834038i) q^{22} +(1.07780 + 0.622266i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-3.35432 + 1.32233i) q^{26} -1.00000i q^{27} +(1.82233 - 3.15637i) q^{28} +(5.02239 - 8.69904i) q^{29} -4.21957i q^{31} +(0.500000 + 0.866025i) q^{32} +(0.834038 + 1.44460i) q^{33} -4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(4.93211 - 8.54267i) q^{37} +6.31274i q^{38} +(1.32233 + 3.35432i) q^{39} +(8.04479 + 4.64466i) q^{41} +(-3.15637 - 1.82233i) q^{42} +(6.55829 - 3.78643i) q^{43} +1.66808i q^{44} +(1.07780 - 0.622266i) q^{46} +6.82522 q^{47} +(0.866025 - 0.500000i) q^{48} +(-3.14177 + 5.44171i) q^{49} -4.00000 q^{51} +(-0.531987 + 3.56609i) q^{52} -0.848634i q^{53} +(-0.866025 - 0.500000i) q^{54} +(-1.82233 - 3.15637i) q^{56} +6.31274 q^{57} +(-5.02239 - 8.69904i) q^{58} +(-5.29034 + 3.05438i) q^{59} +(-3.73205 - 6.46410i) q^{61} +(-3.65425 - 2.10978i) q^{62} +(-1.82233 + 3.15637i) q^{63} +1.00000 q^{64} +1.66808 q^{66} +(7.37671 - 12.7768i) q^{67} +(-3.46410 - 2.00000i) q^{68} +(-0.622266 - 1.07780i) q^{69} +(-3.04056 + 1.75547i) q^{71} +(-0.500000 - 0.866025i) q^{72} +12.2175 q^{73} +(-4.93211 - 8.54267i) q^{74} +(5.46699 + 3.15637i) q^{76} -6.07957i q^{77} +(3.56609 + 0.531987i) q^{78} -9.93398 q^{79} +(-0.500000 + 0.866025i) q^{81} +(8.04479 - 4.64466i) q^{82} +7.95317 q^{83} +(-3.15637 + 1.82233i) q^{84} -7.57286i q^{86} +(-8.69904 + 5.02239i) q^{87} +(1.44460 + 0.834038i) q^{88} +(-5.15425 - 2.97581i) q^{89} +(1.93891 - 12.9972i) q^{91} -1.24453i q^{92} +(-2.10978 + 3.65425i) q^{93} +(3.41261 - 5.91081i) q^{94} -1.00000i q^{96} +(1.37671 + 2.38453i) q^{97} +(3.14177 + 5.44171i) q^{98} -1.66808i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{2} - 4q^{4} - 2q^{7} - 8q^{8} + 4q^{9} + O(q^{10}) \) \( 8q + 4q^{2} - 4q^{4} - 2q^{7} - 8q^{8} + 4q^{9} + 6q^{11} - 6q^{13} - 4q^{14} - 4q^{16} + 8q^{18} + 6q^{19} + 6q^{22} - 6q^{23} - 12q^{26} - 2q^{28} + 8q^{29} + 4q^{32} - 2q^{33} + 4q^{36} + 10q^{37} - 6q^{39} + 48q^{43} - 6q^{46} + 16q^{47} - 14q^{49} - 32q^{51} - 6q^{52} + 2q^{56} - 8q^{58} - 24q^{59} - 16q^{61} - 30q^{62} + 2q^{63} + 8q^{64} - 4q^{66} + 12q^{67} - 4q^{69} - 12q^{71} - 4q^{72} - 24q^{73} - 10q^{74} - 6q^{76} + 6q^{78} + 20q^{79} - 4q^{81} + 32q^{83} - 6q^{87} - 6q^{88} - 42q^{89} - 10q^{91} - 4q^{93} + 8q^{94} - 36q^{97} + 14q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −0.866025 + 0.500000i −0.353553 + 0.204124i
\(7\) 1.82233 + 3.15637i 0.688776 + 1.19299i 0.972234 + 0.234010i \(0.0751849\pi\)
−0.283458 + 0.958985i \(0.591482\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −1.44460 0.834038i −0.435562 0.251472i 0.266151 0.963931i \(-0.414248\pi\)
−0.701713 + 0.712459i \(0.747581\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −2.82233 2.24376i −0.782773 0.622307i
\(14\) 3.64466 0.974076
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.46410 2.00000i 0.840168 0.485071i −0.0171533 0.999853i \(-0.505460\pi\)
0.857321 + 0.514782i \(0.172127\pi\)
\(18\) 1.00000 0.235702
\(19\) −5.46699 + 3.15637i −1.25421 + 0.724120i −0.971943 0.235215i \(-0.924421\pi\)
−0.282270 + 0.959335i \(0.591087\pi\)
\(20\) 0 0
\(21\) 3.64466i 0.795330i
\(22\) −1.44460 + 0.834038i −0.307989 + 0.177817i
\(23\) 1.07780 + 0.622266i 0.224736 + 0.129752i 0.608141 0.793829i \(-0.291915\pi\)
−0.383405 + 0.923580i \(0.625249\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) −3.35432 + 1.32233i −0.657836 + 0.259330i
\(27\) 1.00000i 0.192450i
\(28\) 1.82233 3.15637i 0.344388 0.596497i
\(29\) 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 \(-0.123707\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0.834038 + 1.44460i 0.145187 + 0.251472i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 4.93211 8.54267i 0.810835 1.40441i −0.101446 0.994841i \(-0.532347\pi\)
0.912281 0.409566i \(-0.134320\pi\)
\(38\) 6.31274i 1.02406i
\(39\) 1.32233 + 3.35432i 0.211742 + 0.537121i
\(40\) 0 0
\(41\) 8.04479 + 4.64466i 1.25638 + 0.725374i 0.972370 0.233446i \(-0.0750002\pi\)
0.284015 + 0.958820i \(0.408334\pi\)
\(42\) −3.15637 1.82233i −0.487038 0.281192i
\(43\) 6.55829 3.78643i 1.00013 0.577425i 0.0918433 0.995773i \(-0.470724\pi\)
0.908287 + 0.418348i \(0.137391\pi\)
\(44\) 1.66808i 0.251472i
\(45\) 0 0
\(46\) 1.07780 0.622266i 0.158912 0.0917482i
\(47\) 6.82522 0.995560 0.497780 0.867303i \(-0.334149\pi\)
0.497780 + 0.867303i \(0.334149\pi\)
\(48\) 0.866025 0.500000i 0.125000 0.0721688i
\(49\) −3.14177 + 5.44171i −0.448825 + 0.777387i
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) −0.531987 + 3.56609i −0.0737734 + 0.494528i
\(53\) 0.848634i 0.116569i −0.998300 0.0582844i \(-0.981437\pi\)
0.998300 0.0582844i \(-0.0185630\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) 0 0
\(56\) −1.82233 3.15637i −0.243519 0.421787i
\(57\) 6.31274 0.836142
\(58\) −5.02239 8.69904i −0.659473 1.14224i
\(59\) −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 \(0.991914\pi\)
\(62\) −3.65425 2.10978i −0.464091 0.267943i
\(63\) −1.82233 + 3.15637i −0.229592 + 0.397665i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.66808 0.205326
\(67\) 7.37671 12.7768i 0.901209 1.56094i 0.0752814 0.997162i \(-0.476014\pi\)
0.825927 0.563777i \(-0.190652\pi\)
\(68\) −3.46410 2.00000i −0.420084 0.242536i
\(69\) −0.622266 1.07780i −0.0749121 0.129752i
\(70\) 0 0
\(71\) −3.04056 + 1.75547i −0.360848 + 0.208336i −0.669453 0.742855i \(-0.733471\pi\)
0.308605 + 0.951190i \(0.400138\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 12.2175 1.42995 0.714976 0.699149i \(-0.246437\pi\)
0.714976 + 0.699149i \(0.246437\pi\)
\(74\) −4.93211 8.54267i −0.573347 0.993065i
\(75\) 0 0
\(76\) 5.46699 + 3.15637i 0.627107 + 0.362060i
\(77\) 6.07957i 0.692831i
\(78\) 3.56609 + 0.531987i 0.403780 + 0.0602357i
\(79\) −9.93398 −1.11766 −0.558830 0.829282i \(-0.688750\pi\)
−0.558830 + 0.829282i \(0.688750\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 8.04479 4.64466i 0.888398 0.512917i
\(83\) 7.95317 0.872974 0.436487 0.899711i \(-0.356223\pi\)
0.436487 + 0.899711i \(0.356223\pi\)
\(84\) −3.15637 + 1.82233i −0.344388 + 0.198832i
\(85\) 0 0
\(86\) 7.57286i 0.816603i
\(87\) −8.69904 + 5.02239i −0.932635 + 0.538457i
\(88\) 1.44460 + 0.834038i 0.153994 + 0.0889087i
\(89\) −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
\(92\) 1.24453i 0.129752i
\(93\) −2.10978 + 3.65425i −0.218774 + 0.378928i
\(94\) 3.41261 5.91081i 0.351984 0.609654i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 1.37671 + 2.38453i 0.139784 + 0.242113i 0.927415 0.374035i \(-0.122026\pi\)
−0.787631 + 0.616147i \(0.788693\pi\)
\(98\) 3.14177 + 5.44171i 0.317367 + 0.549696i
\(99\) 1.66808i 0.167648i
\(100\) 0 0
\(101\) 2.66808 4.62124i 0.265483 0.459831i −0.702207 0.711973i \(-0.747802\pi\)
0.967690 + 0.252142i \(0.0811351\pi\)
\(102\) −2.00000 + 3.46410i −0.198030 + 0.342997i
\(103\) 7.51248i 0.740227i −0.928987 0.370113i \(-0.879319\pi\)
0.928987 0.370113i \(-0.120681\pi\)
\(104\) 2.82233 + 2.24376i 0.276752 + 0.220019i
\(105\) 0 0
\(106\) −0.734939 0.424317i −0.0713835 0.0412133i
\(107\) 14.6603 + 8.46410i 1.41726 + 0.818256i 0.996057 0.0887109i \(-0.0282747\pi\)
0.421203 + 0.906966i \(0.361608\pi\)
\(108\) −0.866025 + 0.500000i −0.0833333 + 0.0481125i
\(109\) 0.663848i 0.0635851i 0.999494 + 0.0317926i \(0.0101216\pi\)
−0.999494 + 0.0317926i \(0.989878\pi\)
\(110\) 0 0
\(111\) −8.54267 + 4.93211i −0.810835 + 0.468136i
\(112\) −3.64466 −0.344388
\(113\) −15.4759 + 8.93500i −1.45585 + 0.840534i −0.998803 0.0489094i \(-0.984425\pi\)
−0.457045 + 0.889444i \(0.651092\pi\)
\(114\) 3.15637 5.46699i 0.295621 0.512030i
\(115\) 0 0
\(116\) −10.0448 −0.932635
\(117\) 0.531987 3.56609i 0.0491823 0.329685i
\(118\) 6.10876i 0.562357i
\(119\) 12.6255 + 7.28932i 1.15738 + 0.668211i
\(120\) 0 0
\(121\) −4.10876 7.11658i −0.373524 0.646962i
\(122\) −7.46410 −0.675768
\(123\) −4.64466 8.04479i −0.418795 0.725374i
\(124\) −3.65425 + 2.10978i −0.328162 + 0.189464i
\(125\) 0 0
\(126\) 1.82233 + 3.15637i 0.162346 + 0.281192i
\(127\) −12.5060 7.22034i −1.10973 0.640702i −0.170969 0.985276i \(-0.554690\pi\)
−0.938759 + 0.344575i \(0.888023\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −7.57286 −0.666753
\(130\) 0 0
\(131\) −10.8892 −0.951393 −0.475697 0.879609i \(-0.657804\pi\)
−0.475697 + 0.879609i \(0.657804\pi\)
\(132\) 0.834038 1.44460i 0.0725937 0.125736i
\(133\) −19.9253 11.5039i −1.72774 0.997513i
\(134\) −7.37671 12.7768i −0.637251 1.10375i
\(135\) 0 0
\(136\) −3.46410 + 2.00000i −0.297044 + 0.171499i
\(137\) −3.51848 6.09419i −0.300604 0.520662i 0.675669 0.737205i \(-0.263855\pi\)
−0.976273 + 0.216544i \(0.930522\pi\)
\(138\) −1.24453 −0.105942
\(139\) 5.82233 + 10.0846i 0.493844 + 0.855362i 0.999975 0.00709431i \(-0.00225821\pi\)
−0.506131 + 0.862456i \(0.668925\pi\)
\(140\) 0 0
\(141\) −5.91081 3.41261i −0.497780 0.287394i
\(142\) 3.51093i 0.294631i
\(143\) 2.20575 + 5.59526i 0.184454 + 0.467899i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 6.10876 10.5807i 0.505565 0.875664i
\(147\) 5.44171 3.14177i 0.448825 0.259129i
\(148\) −9.86423 −0.810835
\(149\) 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 \(0.869747\pi\)
\(152\) 5.46699 3.15637i 0.443431 0.256015i
\(153\) 3.46410 + 2.00000i 0.280056 + 0.161690i
\(154\) −5.26506 3.03978i −0.424271 0.244953i
\(155\) 0 0
\(156\) 2.24376 2.82233i 0.179644 0.225967i
\(157\) 12.0135i 0.958786i 0.877600 + 0.479393i \(0.159143\pi\)
−0.877600 + 0.479393i \(0.840857\pi\)
\(158\) −4.96699 + 8.60308i −0.395152 + 0.684424i
\(159\) −0.424317 + 0.734939i −0.0336505 + 0.0582844i
\(160\) 0 0
\(161\) 4.53590i 0.357479i
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) −5.04581 8.73960i −0.395218 0.684538i 0.597911 0.801563i \(-0.295998\pi\)
−0.993129 + 0.117025i \(0.962664\pi\)
\(164\) 9.28932i 0.725374i
\(165\) 0 0
\(166\) 3.97658 6.88764i 0.308643 0.534585i
\(167\) −3.94851 + 6.83902i −0.305545 + 0.529219i −0.977382 0.211479i \(-0.932172\pi\)
0.671838 + 0.740698i \(0.265505\pi\)
\(168\) 3.64466i 0.281192i
\(169\) 2.93109 + 12.6653i 0.225469 + 0.974250i
\(170\) 0 0
\(171\) −5.46699 3.15637i −0.418071 0.241373i
\(172\) −6.55829 3.78643i −0.500065 0.288713i
\(173\) 0.381645 0.220343i 0.0290159 0.0167523i −0.485422 0.874280i \(-0.661334\pi\)
0.514438 + 0.857528i \(0.328001\pi\)
\(174\) 10.0448i 0.761493i
\(175\) 0 0
\(176\) 1.44460 0.834038i 0.108891 0.0628680i
\(177\) 6.10876 0.459163
\(178\) −5.15425 + 2.97581i −0.386328 + 0.223046i
\(179\) 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 \(0.425777\pi\)
\(182\) −10.2864 8.17774i −0.762481 0.606174i
\(183\) 7.46410i 0.551762i
\(184\) −1.07780 0.622266i −0.0794562 0.0458741i
\(185\) 0 0
\(186\) 2.10978 + 3.65425i 0.154697 + 0.267943i
\(187\) −6.67230 −0.487927
\(188\) −3.41261 5.91081i −0.248890 0.431090i
\(189\) 3.15637 1.82233i 0.229592 0.132555i
\(190\) 0 0
\(191\) −7.84081 13.5807i −0.567341 0.982664i −0.996828 0.0795905i \(-0.974639\pi\)
0.429486 0.903073i \(-0.358695\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) −4.06397 + 7.03901i −0.292531 + 0.506679i −0.974408 0.224788i \(-0.927831\pi\)
0.681876 + 0.731468i \(0.261164\pi\)
\(194\) 2.75342 0.197684
\(195\) 0 0
\(196\) 6.28354 0.448825
\(197\) 0.445619 0.771835i 0.0317491 0.0549910i −0.849714 0.527243i \(-0.823226\pi\)
0.881463 + 0.472252i \(0.156559\pi\)
\(198\) −1.44460 0.834038i −0.102663 0.0592725i
\(199\) −0.180558 0.312736i −0.0127994 0.0221692i 0.859555 0.511044i \(-0.170741\pi\)
−0.872354 + 0.488874i \(0.837408\pi\)
\(200\) 0 0
\(201\) −12.7768 + 7.37671i −0.901209 + 0.520313i
\(202\) −2.66808 4.62124i −0.187725 0.325150i
\(203\) 36.6098 2.56951
\(204\) 2.00000 + 3.46410i 0.140028 + 0.242536i
\(205\) 0 0
\(206\) −6.50600 3.75624i −0.453295 0.261710i
\(207\) 1.24453i 0.0865010i
\(208\) 3.35432 1.32233i 0.232580 0.0916871i
\(209\) 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 \(0.191095\pi\)
\(212\) −0.734939 + 0.424317i −0.0504758 + 0.0291422i
\(213\) 3.51093 0.240565
\(214\) 14.6603 8.46410i 1.00215 0.578594i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 13.3185 7.68945i 0.904119 0.521994i
\(218\) 0.574909 + 0.331924i 0.0389378 + 0.0224807i
\(219\) −10.5807 6.10876i −0.714976 0.412792i
\(220\) 0 0
\(221\) −14.2644 2.12795i −0.959524 0.143141i
\(222\) 9.86423i 0.662044i
\(223\) −3.04190 + 5.26872i −0.203701 + 0.352820i −0.949718 0.313107i \(-0.898630\pi\)
0.746017 + 0.665927i \(0.231964\pi\)
\(224\) −1.82233 + 3.15637i −0.121760 + 0.210894i
\(225\) 0 0
\(226\) 17.8700i 1.18869i
\(227\) 7.66025 + 13.2679i 0.508429 + 0.880625i 0.999952 + 0.00976038i \(0.00310687\pi\)
−0.491523 + 0.870864i \(0.663560\pi\)
\(228\) −3.15637 5.46699i −0.209036 0.362060i
\(229\) 22.2644i 1.47127i −0.677378 0.735635i \(-0.736884\pi\)
0.677378 0.735635i \(-0.263116\pi\)
\(230\) 0 0
\(231\) −3.03978 + 5.26506i −0.200003 + 0.346416i
\(232\) −5.02239 + 8.69904i −0.329736 + 0.571120i
\(233\) 10.8366i 0.709928i 0.934880 + 0.354964i \(0.115507\pi\)
−0.934880 + 0.354964i \(0.884493\pi\)
\(234\) −2.82233 2.24376i −0.184501 0.146679i
\(235\) 0 0
\(236\) 5.29034 + 3.05438i 0.344372 + 0.198823i
\(237\) 8.60308 + 4.96699i 0.558830 + 0.322641i
\(238\) 12.6255 7.28932i 0.818388 0.472496i
\(239\) 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 \(0.288027\pi\)
\(242\) −8.21752 −0.528242
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −3.73205 + 6.46410i −0.238920 + 0.413822i
\(245\) 0 0
\(246\) −9.28932 −0.592265
\(247\) 22.5118 + 3.35830i 1.43239 + 0.213683i
\(248\) 4.21957i 0.267943i
\(249\) −6.88764 3.97658i −0.436487 0.252006i
\(250\) 0 0
\(251\) 5.97267 + 10.3450i 0.376992 + 0.652969i 0.990623 0.136624i \(-0.0436252\pi\)
−0.613631 + 0.789593i \(0.710292\pi\)
\(252\) 3.64466 0.229592
\(253\) −1.03799 1.79785i −0.0652577 0.113030i
\(254\) −12.5060 + 7.22034i −0.784696 + 0.453045i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −16.8546 9.73103i −1.05136 0.607005i −0.128333 0.991731i \(-0.540962\pi\)
−0.923031 + 0.384726i \(0.874296\pi\)
\(258\) −3.78643 + 6.55829i −0.235733 + 0.408301i
\(259\) 35.9518 2.23393
\(260\) 0 0
\(261\) 10.0448 0.621757
\(262\) −5.44460 + 9.43032i −0.336368 + 0.582607i
\(263\) −1.76217 1.01739i −0.108660 0.0627350i 0.444685 0.895687i \(-0.353316\pi\)
−0.553345 + 0.832952i \(0.686649\pi\)
\(264\) −0.834038 1.44460i −0.0513315 0.0889087i
\(265\) 0 0
\(266\) −19.9253 + 11.5039i −1.22170 + 0.705349i
\(267\) 2.97581 + 5.15425i 0.182117 + 0.315435i
\(268\) −14.7534 −0.901209
\(269\) 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 \(0.384051\pi\)
\(272\) 4.00000i 0.242536i
\(273\) −8.17774 + 10.2864i −0.494939 + 0.622563i
\(274\) −7.03696 −0.425119
\(275\) 0 0
\(276\) −0.622266 + 1.07780i −0.0374560 + 0.0648758i
\(277\) 15.6407 9.03019i 0.939762 0.542572i 0.0498760 0.998755i \(-0.484117\pi\)
0.889886 + 0.456184i \(0.150784\pi\)
\(278\) 11.6447 0.698400
\(279\) 3.65425 2.10978i 0.218774 0.126309i
\(280\) 0 0
\(281\) 20.2175i 1.20608i −0.797712 0.603038i \(-0.793957\pi\)
0.797712 0.603038i \(-0.206043\pi\)
\(282\) −5.91081 + 3.41261i −0.351984 + 0.203218i
\(283\) 7.52705 + 4.34575i 0.447437 + 0.258328i 0.706747 0.707466i \(-0.250162\pi\)
−0.259310 + 0.965794i \(0.583495\pi\)
\(284\) 3.04056 + 1.75547i 0.180424 + 0.104168i
\(285\) 0 0
\(286\) 5.94851 + 0.887395i 0.351743 + 0.0524728i
\(287\) 33.8564i 1.99848i
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 2.75342i 0.161408i
\(292\) −6.10876 10.5807i −0.357488 0.619188i
\(293\) 3.77395 + 6.53667i 0.220476 + 0.381876i 0.954953 0.296758i \(-0.0959054\pi\)
−0.734476 + 0.678634i \(0.762572\pi\)
\(294\) 6.28354i 0.366464i
\(295\) 0 0
\(296\) −4.93211 + 8.54267i −0.286673 + 0.496533i
\(297\) −0.834038 + 1.44460i −0.0483958 + 0.0838240i
\(298\) 0.772609i 0.0447560i
\(299\) −1.64568 4.17456i −0.0951723 0.241421i
\(300\) 0 0
\(301\) 23.9027 + 13.8003i 1.37773 + 0.795433i
\(302\) 8.46833 + 4.88919i 0.487298 + 0.281341i
\(303\) −4.62124 + 2.66808i −0.265483 + 0.153277i
\(304\) 6.31274i 0.362060i
\(305\) 0 0
\(306\) 3.46410 2.00000i 0.198030 0.114332i
\(307\) −26.0427 −1.48634 −0.743169 0.669104i \(-0.766678\pi\)
−0.743169 + 0.669104i \(0.766678\pi\)
\(308\) −5.26506 + 3.03978i −0.300005 + 0.173208i
\(309\) −3.75624 + 6.50600i −0.213685 + 0.370113i
\(310\) 0 0
\(311\) 25.3789 1.43910 0.719552 0.694438i \(-0.244347\pi\)
0.719552 + 0.694438i \(0.244347\pi\)
\(312\) −1.32233 3.35432i −0.0748622 0.189901i
\(313\) 31.4600i 1.77822i −0.457689 0.889112i \(-0.651323\pi\)
0.457689 0.889112i \(-0.348677\pi\)
\(314\) 10.4040 + 6.00677i 0.587134 + 0.338982i
\(315\) 0 0
\(316\) 4.96699 + 8.60308i 0.279415 + 0.483961i
\(317\) 24.7093 1.38781 0.693905 0.720066i \(-0.255889\pi\)
0.693905 + 0.720066i \(0.255889\pi\)
\(318\) 0.424317 + 0.734939i 0.0237945 + 0.0412133i
\(319\) −14.5107 + 8.37773i −0.812441 + 0.469063i
\(320\) 0 0
\(321\) −8.46410 14.6603i −0.472420 0.818256i
\(322\) 3.92820 + 2.26795i 0.218910 + 0.126388i
\(323\) −12.6255 + 21.8680i −0.702500 + 1.21677i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −10.0916 −0.558923
\(327\) 0.331924 0.574909i 0.0183554 0.0317926i
\(328\) −8.04479 4.64466i −0.444199 0.256458i
\(329\) 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 \(0.382549\pi\)
\(332\) −3.97658 6.88764i −0.218243 0.378009i
\(333\) 9.86423 0.540556
\(334\) 3.94851 + 6.83902i 0.216053 + 0.374214i
\(335\) 0 0
\(336\) 3.15637 + 1.82233i 0.172194 + 0.0994162i
\(337\) 21.7868i 1.18680i −0.804906 0.593402i \(-0.797784\pi\)
0.804906 0.593402i \(-0.202216\pi\)
\(338\) 12.4340 + 3.79423i 0.676319 + 0.206379i
\(339\) 17.8700 0.970565
\(340\) 0 0
\(341\) −3.51928 + 6.09557i −0.190580 + 0.330094i
\(342\) −5.46699 + 3.15637i −0.295621 + 0.170677i
\(343\) 2.61124 0.140994
\(344\) −6.55829 + 3.78643i −0.353599 + 0.204151i
\(345\) 0 0
\(346\) 0.440685i 0.0236914i
\(347\) −8.38453 + 4.84081i −0.450105 + 0.259868i −0.707875 0.706338i \(-0.750346\pi\)
0.257769 + 0.966206i \(0.417013\pi\)
\(348\) 8.69904 + 5.02239i 0.466318 + 0.269229i
\(349\) −16.7321 9.66025i −0.895646 0.517102i −0.0198610 0.999803i \(-0.506322\pi\)
−0.875785 + 0.482701i \(0.839656\pi\)
\(350\) 0 0
\(351\) −2.24376 + 2.82233i −0.119763 + 0.150645i
\(352\) 1.66808i 0.0889087i
\(353\) 11.4875 19.8970i 0.611419 1.05901i −0.379583 0.925158i \(-0.623932\pi\)
0.991002 0.133851i \(-0.0427343\pi\)
\(354\) 3.05438 5.29034i 0.162338 0.281179i
\(355\) 0 0
\(356\) 5.95162i 0.315435i
\(357\) −7.28932 12.6255i −0.385792 0.668211i
\(358\) −9.81842 17.0060i −0.518920 0.898795i
\(359\) 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
\(362\) 3.10876 5.38453i 0.163393 0.283005i
\(363\) 8.21752i 0.431308i
\(364\) −12.2253 + 4.81944i −0.640782 + 0.252607i
\(365\) 0 0
\(366\) 6.46410 + 3.73205i 0.337884 + 0.195077i
\(367\) −5.26640 3.04056i −0.274904 0.158716i 0.356210 0.934406i \(-0.384069\pi\)
−0.631114 + 0.775690i \(0.717402\pi\)
\(368\) −1.07780 + 0.622266i −0.0561841 + 0.0324379i
\(369\) 9.28932i 0.483583i
\(370\) 0 0
\(371\) 2.67860 1.54649i 0.139066 0.0802898i
\(372\) 4.21957 0.218774
\(373\) 13.5776 7.83904i 0.703022 0.405890i −0.105450 0.994425i \(-0.533628\pi\)
0.808472 + 0.588535i \(0.200295\pi\)
\(374\) −3.33615 + 5.77838i −0.172508 + 0.298793i
\(375\) 0 0
\(376\) −6.82522 −0.351984
\(377\) −33.6934 + 13.2825i −1.73530 + 0.684085i
\(378\) 3.64466i 0.187461i
\(379\) −26.6013 15.3583i −1.36642 0.788903i −0.375951 0.926640i \(-0.622684\pi\)
−0.990469 + 0.137737i \(0.956017\pi\)
\(380\) 0 0
\(381\) 7.22034 + 12.5060i 0.369909 + 0.640702i
\(382\) −15.6816 −0.802342
\(383\) 10.0310 + 17.3741i 0.512558 + 0.887777i 0.999894 + 0.0145623i \(0.00463550\pi\)
−0.487336 + 0.873215i \(0.662031\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) 4.06397 + 7.03901i 0.206851 + 0.358276i
\(387\) 6.55829 + 3.78643i 0.333377 + 0.192475i
\(388\) 1.37671 2.38453i 0.0698919 0.121056i
\(389\) −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
\(392\) 3.14177 5.44171i 0.158683 0.274848i
\(393\) 9.43032 + 5.44460i 0.475697 + 0.274644i
\(394\) −0.445619 0.771835i −0.0224500 0.0388845i
\(395\) 0 0
\(396\) −1.44460 + 0.834038i −0.0725937 + 0.0419120i
\(397\) 1.86814 + 3.23571i 0.0937592 + 0.162396i 0.909090 0.416600i \(-0.136778\pi\)
−0.815331 + 0.578995i \(0.803445\pi\)
\(398\) −0.361116 −0.0181011
\(399\) 11.5039 + 19.9253i 0.575915 + 0.997513i
\(400\) 0 0
\(401\) 24.3276 + 14.0456i 1.21486 + 0.701402i 0.963815 0.266573i \(-0.0858912\pi\)
0.251049 + 0.967974i \(0.419225\pi\)
\(402\) 14.7534i 0.735834i
\(403\) −9.46770 + 11.9090i −0.471620 + 0.593230i
\(404\) −5.33615 −0.265483
\(405\) 0 0
\(406\) 18.3049 31.7050i 0.908458 1.57349i
\(407\) −14.2498 + 8.22714i −0.706338 + 0.407804i
\(408\) 4.00000 0.198030
\(409\) −23.7122 + 13.6902i −1.17249 + 0.676938i −0.954265 0.298961i \(-0.903360\pi\)
−0.218225 + 0.975898i \(0.570027\pi\)
\(410\) 0 0
\(411\) 7.03696i 0.347108i
\(412\) −6.50600 + 3.75624i −0.320528 + 0.185057i
\(413\) −19.2815 11.1322i −0.948780 0.547779i
\(414\) 1.07780 + 0.622266i 0.0529708 + 0.0305827i
\(415\) 0 0
\(416\) 0.531987 3.56609i 0.0260828 0.174842i
\(417\) 11.6447i 0.570241i
\(418\) 5.26506 9.11935i 0.257523 0.446042i
\(419\) −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 \(0.989966\pi\)
\(422\) 1.11370 + 1.92898i 0.0542138 + 0.0939011i
\(423\) 3.41261 + 5.91081i 0.165927 + 0.287394i
\(424\) 0.848634i 0.0412133i
\(425\) 0 0
\(426\) 1.75547 3.04056i 0.0850527 0.147316i
\(427\) 13.6021 23.5595i 0.658250 1.14012i
\(428\) 16.9282i 0.818256i
\(429\) 0.887395 5.94851i 0.0428439 0.287197i
\(430\) 0 0
\(431\) 10.5031 + 6.06397i 0.505917 + 0.292091i 0.731154 0.682213i \(-0.238982\pi\)
−0.225237 + 0.974304i \(0.572316\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) 1.79962 1.03901i 0.0864842 0.0499317i −0.456134 0.889911i \(-0.650766\pi\)
0.542618 + 0.839979i \(0.317433\pi\)
\(434\) 15.3789i 0.738210i
\(435\) 0 0
\(436\) 0.574909 0.331924i 0.0275332 0.0158963i
\(437\) −7.85641 −0.375823
\(438\) −10.5807 + 6.10876i −0.505565 + 0.291888i
\(439\) 1.19820 2.07534i 0.0571869 0.0990506i −0.836015 0.548707i \(-0.815120\pi\)
0.893202 + 0.449656i \(0.148454\pi\)
\(440\) 0 0
\(441\) −6.28354 −0.299216
\(442\) −8.97504 + 11.2893i −0.426899 + 0.536978i
\(443\) 21.9959i 1.04506i 0.852622 + 0.522529i \(0.175011\pi\)
−0.852622 + 0.522529i \(0.824989\pi\)
\(444\) 8.54267 + 4.93211i 0.405417 + 0.234068i
\(445\) 0 0
\(446\) 3.04190 + 5.26872i 0.144038 + 0.249481i
\(447\) −0.772609 −0.0365432
\(448\) 1.82233 + 3.15637i 0.0860970 + 0.149124i
\(449\) −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
\(452\) 15.4759 + 8.93500i 0.727924 + 0.420267i
\(453\) 4.88919 8.46833i 0.229714 0.397877i
\(454\) 15.3205 0.719027
\(455\) 0 0
\(456\) −6.31274 −0.295621
\(457\) −19.8216 + 34.3321i −0.927216 + 1.60599i −0.139259 + 0.990256i \(0.544472\pi\)
−0.787957 + 0.615730i \(0.788861\pi\)
\(458\) −19.2815 11.1322i −0.900965 0.520172i
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) 0 0
\(461\) 14.4417 8.33792i 0.672617 0.388336i −0.124450 0.992226i \(-0.539717\pi\)
0.797068 + 0.603890i \(0.206383\pi\)
\(462\) 3.03978 + 5.26506i 0.141424 + 0.244953i
\(463\) 32.2175 1.49728 0.748638 0.662979i \(-0.230708\pi\)
0.748638 + 0.662979i \(0.230708\pi\)
\(464\) 5.02239 + 8.69904i 0.233159 + 0.403843i
\(465\) 0 0
\(466\) 9.38476 + 5.41829i 0.434740 + 0.250998i
\(467\) 6.88137i 0.318432i 0.987244 + 0.159216i \(0.0508966\pi\)
−0.987244 + 0.159216i \(0.949103\pi\)
\(468\) −3.35432 + 1.32233i −0.155053 + 0.0611247i
\(469\) 53.7712 2.48292
\(470\) 0 0
\(471\) 6.00677 10.4040i 0.276778 0.479393i
\(472\) 5.29034 3.05438i 0.243508 0.140589i
\(473\) −12.6321 −0.580825
\(474\) 8.60308 4.96699i 0.395152 0.228141i
\(475\) 0 0
\(476\) 14.5786i 0.668211i
\(477\) 0.734939 0.424317i 0.0336505 0.0194281i
\(478\) 14.2873 + 8.24876i 0.653485 + 0.377290i
\(479\) 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
\(482\) 4.40435i 0.200613i
\(483\) 2.26795 3.92820i 0.103195 0.178739i
\(484\) −4.10876 + 7.11658i −0.186762 + 0.323481i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −0.958101 1.65948i −0.0434157 0.0751982i 0.843501 0.537128i \(-0.180491\pi\)
−0.886917 + 0.461929i \(0.847157\pi\)
\(488\) 3.73205 + 6.46410i 0.168942 + 0.292616i
\(489\) 10.0916i 0.456359i
\(490\) 0 0
\(491\) −16.8187 + 29.1309i −0.759019 + 1.31466i 0.184332 + 0.982864i \(0.440988\pi\)
−0.943351 + 0.331795i \(0.892346\pi\)
\(492\) −4.64466 + 8.04479i −0.209397 + 0.362687i
\(493\) 40.1791i 1.80958i
\(494\) 14.1643 17.8166i 0.637280 0.801608i
\(495\) 0 0
\(496\) 3.65425 + 2.10978i 0.164081 + 0.0947321i
\(497\) −11.0818 6.39808i −0.497087 0.286993i
\(498\) −6.88764 + 3.97658i −0.308643 + 0.178195i
\(499\) 1.82522i 0.0817080i −0.999165 0.0408540i \(-0.986992\pi\)
0.999165 0.0408540i \(-0.0130078\pi\)
\(500\) 0 0
\(501\) 6.83902 3.94851i 0.305545 0.176406i
\(502\) 11.9453 0.533147
\(503\) −17.3192 + 9.99923i −0.772224 + 0.445843i −0.833667 0.552267i \(-0.813763\pi\)
0.0614437 + 0.998111i \(0.480430\pi\)
\(504\) 1.82233 3.15637i 0.0811730 0.140596i
\(505\) 0 0
\(506\) −2.07598 −0.0922884
\(507\) 3.79423 12.4340i 0.168508 0.552212i
\(508\) 14.4407i 0.640702i
\(509\) −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
\(512\) −1.00000 −0.0441942
\(513\) 3.15637 + 5.46699i 0.139357 + 0.241373i
\(514\) −16.8546 + 9.73103i −0.743426 + 0.429217i
\(515\) 0 0
\(516\) 3.78643 + 6.55829i 0.166688 + 0.288713i
\(517\) −9.85968 5.69249i −0.433628 0.250355i
\(518\) 17.9759 31.1351i 0.789815 1.36800i
\(519\) −0.440685 −0.0193439
\(520\) 0 0
\(521\) 32.0370 1.40356 0.701782 0.712391i \(-0.252388\pi\)
0.701782 + 0.712391i \(0.252388\pi\)
\(522\) 5.02239 8.69904i 0.219824 0.380747i
\(523\) −33.5313 19.3593i −1.46622 0.846523i −0.466934 0.884292i \(-0.654641\pi\)
−0.999286 + 0.0377693i \(0.987975\pi\)
\(524\) 5.44460 + 9.43032i 0.237848 + 0.411965i
\(525\) 0 0
\(526\) −1.76217 + 1.01739i −0.0768344 + 0.0443604i
\(527\) −8.43914 14.6170i −0.367615 0.636727i
\(528\) −1.66808 −0.0725937
\(529\) −10.7256 18.5772i −0.466329 0.807706i
\(530\) 0 0
\(531\) −5.29034 3.05438i −0.229581 0.132549i
\(532\) 23.0078i 0.997513i
\(533\) −12.2835 31.1593i −0.532059 1.34966i
\(534\) 5.95162 0.257552
\(535\) 0 0
\(536\) −7.37671 + 12.7768i −0.318625 + 0.551875i
\(537\) −17.0060 + 9.81842i −0.733863 + 0.423696i
\(538\) 20.5287 0.885056
\(539\) 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 \(0.811535\pi\)
\(542\) 22.1184 12.7700i 0.950065 0.548520i
\(543\) −5.38453 3.10876i −0.231072 0.133410i
\(544\) 3.46410 + 2.00000i 0.148522 + 0.0857493i
\(545\) 0 0
\(546\) 4.81944 + 12.2253i 0.206253 + 0.523196i
\(547\) 17.7596i 0.759348i 0.925120 + 0.379674i \(0.123964\pi\)
−0.925120 + 0.379674i \(0.876036\pi\)
\(548\) −3.51848 + 6.09419i −0.150302 + 0.260331i
\(549\) 3.73205 6.46410i 0.159280 0.275881i
\(550\) 0 0
\(551\) 63.4101i 2.70136i
\(552\) 0.622266 + 1.07780i 0.0264854 + 0.0458741i
\(553\) −18.1030 31.3553i −0.769817 1.33336i
\(554\) 18.0604i 0.767312i
\(555\) 0 0
\(556\) 5.82233 10.0846i 0.246922 0.427681i
\(557\) −13.1101 + 22.7074i −0.555493 + 0.962142i 0.442372 + 0.896832i \(0.354137\pi\)
−0.997865 + 0.0653102i \(0.979196\pi\)
\(558\) 4.21957i 0.178629i
\(559\) −27.0055 4.02867i −1.14221 0.170394i
\(560\) 0 0
\(561\) 5.77838 + 3.33615i 0.243964 + 0.140852i
\(562\) −17.5089 10.1088i −0.738568 0.426412i
\(563\) 22.5104 12.9964i 0.948702 0.547733i 0.0560243 0.998429i \(-0.482158\pi\)
0.892677 + 0.450696i \(0.148824\pi\)
\(564\) 6.82522i 0.287394i
\(565\) 0 0
\(566\) 7.52705 4.34575i 0.316386 0.182665i
\(567\) −3.64466 −0.153061
\(568\) 3.04056 1.75547i 0.127579 0.0736578i
\(569\) 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 \(0.556544\pi\)
\(572\) 3.74276 4.70786i 0.156493 0.196846i
\(573\) 15.6816i 0.655109i
\(574\) 29.3205 + 16.9282i 1.22381 + 0.706570i
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) −35.4216 −1.47462 −0.737311 0.675554i \(-0.763905\pi\)
−0.737311 + 0.675554i \(0.763905\pi\)
\(578\) 0.500000 + 0.866025i 0.0207973 + 0.0360219i
\(579\) 7.03901 4.06397i 0.292531 0.168893i
\(580\) 0 0
\(581\) 14.4933 + 25.1031i 0.601283 + 1.04145i
\(582\) −2.38453 1.37671i −0.0988420 0.0570665i
\(583\) −0.707793 + 1.22593i −0.0293138 + 0.0507730i
\(584\) −12.2175 −0.505565
\(585\) 0 0
\(586\) 7.54790 0.311801
\(587\) 13.6894 23.7108i 0.565024 0.978650i −0.432024 0.901862i \(-0.642200\pi\)
0.997047 0.0767878i \(-0.0244664\pi\)
\(588\) −5.44171 3.14177i −0.224412 0.129564i
\(589\) 13.3185 + 23.0683i 0.548780 + 0.950514i
\(590\) 0 0
\(591\) −0.771835 + 0.445619i −0.0317491 + 0.0183303i
\(592\) 4.93211 + 8.54267i 0.202709 + 0.351102i
\(593\) −12.0619 −0.495324 −0.247662 0.968846i \(-0.579662\pi\)
−0.247662 + 0.968846i \(0.579662\pi\)
\(594\) 0.834038 + 1.44460i 0.0342210 + 0.0592725i
\(595\) 0 0
\(596\) −0.669099 0.386305i −0.0274074 0.0158237i
\(597\) 0.361116i 0.0147795i
\(598\) −4.43811 0.662076i −0.181488 0.0270743i
\(599\) 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 \(0.0388197\pi\)
\(602\) 23.9027 13.8003i 0.974203 0.562456i
\(603\) 14.7534 0.600806
\(604\) 8.46833 4.88919i 0.344571 0.198938i
\(605\) 0 0
\(606\) 5.33615i 0.216766i
\(607\) −16.4010 + 9.46910i −0.665695 + 0.384339i −0.794443 0.607338i \(-0.792237\pi\)
0.128749 + 0.991677i \(0.458904\pi\)
\(608\) −5.46699 3.15637i −0.221716 0.128008i
\(609\) −31.7050 18.3049i −1.28475 0.741753i
\(610\) 0 0
\(611\) −19.2630 15.3141i −0.779298 0.619544i
\(612\) 4.00000i 0.161690i
\(613\) 8.98472 15.5620i 0.362890 0.628543i −0.625546 0.780188i \(-0.715124\pi\)
0.988435 + 0.151645i \(0.0484569\pi\)
\(614\) −13.0214 + 22.5537i −0.525500 + 0.910192i
\(615\) 0 0
\(616\) 6.07957i 0.244953i
\(617\) 9.00755 + 15.6015i 0.362630 + 0.628094i 0.988393 0.151920i \(-0.0485455\pi\)
−0.625763 + 0.780014i \(0.715212\pi\)
\(618\) 3.75624 + 6.50600i 0.151098 + 0.261710i
\(619\) 25.0505i 1.00687i −0.864035 0.503433i \(-0.832070\pi\)
0.864035 0.503433i \(-0.167930\pi\)
\(620\) 0 0
\(621\) 0.622266 1.07780i 0.0249707 0.0432505i
\(622\) 12.6894 21.9788i 0.508800 0.881268i
\(623\) 21.6916i 0.869057i
\(624\) −3.56609 0.531987i −0.142758 0.0212965i
\(625\) 0 0
\(626\) −27.2452 15.7300i −1.08894 0.628697i
\(627\) −9.11935 5.26506i −0.364192 0.210266i
\(628\) 10.4040 6.00677i 0.415166 0.239696i
\(629\) 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 \(0.342314\pi\)
\(632\) 9.93398 0.395152
\(633\) 1.92898 1.11370i 0.0766700 0.0442654i
\(634\) 12.3546 21.3989i 0.490665 0.849857i
\(635\) 0 0
\(636\) 0.848634 0.0336505
\(637\) 21.0770 8.30892i 0.835101 0.329211i
\(638\) 16.7555i 0.663355i
\(639\) −3.04056 1.75547i −0.120283 0.0694452i
\(640\) 0 0
\(641\) 2.30985 + 4.00077i 0.0912335 + 0.158021i 0.908030 0.418904i \(-0.137586\pi\)
−0.816797 + 0.576925i \(0.804252\pi\)
\(642\) −16.9282 −0.668103
\(643\) 24.0448 + 41.6468i 0.948234 + 1.64239i 0.749143 + 0.662408i \(0.230465\pi\)
0.199091 + 0.979981i \(0.436201\pi\)
\(644\) 3.92820 2.26795i 0.154793 0.0893697i
\(645\) 0 0
\(646\) 12.6255 + 21.8680i 0.496743 + 0.860383i
\(647\) −3.24383 1.87282i −0.127528 0.0736283i 0.434879 0.900489i \(-0.356791\pi\)
−0.562407 + 0.826861i \(0.690125\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 10.1899 0.399988
\(650\) 0 0
\(651\) −15.3789 −0.602746
\(652\) −5.04581 + 8.73960i −0.197609 + 0.342269i
\(653\) −36.6241 21.1450i −1.43321 0.827466i −0.435849 0.900020i \(-0.643552\pi\)
−0.997364 + 0.0725541i \(0.976885\pi\)
\(654\) −0.331924 0.574909i −0.0129793 0.0224807i
\(655\) 0 0
\(656\) −8.04479 + 4.64466i −0.314096 + 0.181343i
\(657\) 6.10876 + 10.5807i 0.238325 + 0.412792i
\(658\) 24.8756 0.969752
\(659\) −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 \(0.999201\pi\)
\(662\) 5.60360i 0.217790i
\(663\) 11.2893 + 8.97504i 0.438441 + 0.348562i
\(664\) −7.95317 −0.308643
\(665\) 0 0
\(666\) 4.93211 8.54267i 0.191116 0.331022i
\(667\) 10.8262 6.25053i 0.419194 0.242022i
\(668\) 7.89701 0.305545
\(669\) 5.26872 3.04190i 0.203701 0.117607i
\(670\) 0 0
\(671\) 12.4507i 0.480654i
\(672\) 3.15637 1.82233i 0.121760 0.0702979i
\(673\) 6.84709 + 3.95317i 0.263936 + 0.152383i 0.626129 0.779720i \(-0.284638\pi\)
−0.362193 + 0.932103i \(0.617972\pi\)
\(674\) −18.8680 10.8934i −0.726767 0.419599i
\(675\) 0 0
\(676\) 9.50289 8.87103i 0.365496 0.341193i
\(677\) 7.05615i 0.271190i 0.990764 + 0.135595i \(0.0432946\pi\)
−0.990764 + 0.135595i \(0.956705\pi\)
\(678\) 8.93500 15.4759i 0.343147 0.594347i
\(679\) −5.01764 + 8.69081i −0.192559 + 0.333523i
\(680\) 0 0
\(681\) 15.3205i 0.587083i
\(682\) 3.51928 + 6.09557i 0.134760 + 0.233412i
\(683\) −2.97658 5.15559i −0.113896 0.197273i 0.803442 0.595383i \(-0.203000\pi\)
−0.917338 + 0.398110i \(0.869666\pi\)
\(684\) 6.31274i 0.241373i
\(685\) 0 0
\(686\) 1.30562 2.26140i 0.0498488 0.0863406i
\(687\) −11.1322 + 19.2815i −0.424719 + 0.735635i
\(688\) 7.57286i 0.288713i
\(689\) −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 \(0.550530\pi\)
\(692\) −0.381645 0.220343i −0.0145080 0.00837617i
\(693\) 5.26506 3.03978i 0.200003 0.115472i
\(694\) 9.68162i 0.367509i
\(695\) 0 0
\(696\) 8.69904 5.02239i 0.329736 0.190373i
\(697\) 37.1573 1.40743
\(698\) −16.7321 + 9.66025i −0.633317 + 0.365646i
\(699\) 5.41829 9.38476i 0.204939 0.354964i
\(700\) 0 0
\(701\) −28.5298 −1.07755 −0.538777 0.842448i \(-0.681113\pi\)
−0.538777 + 0.842448i \(0.681113\pi\)
\(702\) 1.32233 + 3.35432i 0.0499081 + 0.126601i
\(703\) 62.2703i 2.34857i
\(704\) −1.44460 0.834038i −0.0544453 0.0314340i
\(705\) 0 0
\(706\) −11.4875 19.8970i −0.432338 0.748832i
\(707\) 19.4485 0.731435
\(708\) −3.05438 5.29034i −0.114791 0.198823i
\(709\) 20.0853 11.5963i 0.754321 0.435507i −0.0729321 0.997337i \(-0.523236\pi\)
0.827253 + 0.561830i \(0.189902\pi\)
\(710\) 0 0
\(711\) −4.96699 8.60308i −0.186277 0.322641i
\(712\) 5.15425 + 2.97581i 0.193164 + 0.111523i
\(713\) 2.62570 4.54784i 0.0983331 0.170318i
\(714\) −14.5786 −0.545592
\(715\) 0 0
\(716\) −19.6368 −0.733863
\(717\) 8.24876 14.2873i 0.308056 0.533568i
\(718\) −1.92043 1.10876i −0.0716698 0.0413786i
\(719\) −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
\(722\) −10.4253 18.0572i −0.387990 0.672019i
\(723\) −4.40435 −0.163800
\(724\) −3.10876 5.38453i −0.115536 0.200115i
\(725\) 0 0
\(726\) 7.11658 + 4.10876i 0.264121 + 0.152490i
\(727\) 3.82677i 0.141927i −0.997479 0.0709634i \(-0.977393\pi\)
0.997479 0.0709634i \(-0.0226074\pi\)
\(728\) −1.93891 + 12.9972i −0.0718609 + 0.481708i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 15.1457 26.2332i 0.560185 0.970269i
\(732\) 6.46410 3.73205i 0.238920 0.137941i
\(733\) −12.9340 −0.477727 −0.238864 0.971053i \(-0.576775\pi\)
−0.238864 + 0.971053i \(0.576775\pi\)
\(734\) −5.26640 + 3.04056i −0.194386 + 0.112229i
\(735\) 0 0
\(736\) 1.24453i 0.0458741i
\(737\) −21.3127 + 12.3049i −0.785065 + 0.453257i
\(738\) 8.04479 + 4.64466i 0.296133 + 0.170972i
\(739\) 30.6107 + 17.6731i 1.12603 + 0.650115i 0.942934 0.332980i \(-0.108054\pi\)
0.183098 + 0.983095i \(0.441388\pi\)
\(740\) 0 0
\(741\) −17.8166 14.1643i −0.654510 0.520337i
\(742\) 3.09298i 0.113547i
\(743\) 18.5477 32.1255i 0.680448 1.17857i −0.294396 0.955684i \(-0.595118\pi\)
0.974844 0.222887i \(-0.0715482\pi\)
\(744\) 2.10978 3.65425i 0.0773484 0.133971i
\(745\) 0 0
\(746\) 15.6781i 0.574015i
\(747\) 3.97658 + 6.88764i 0.145496 + 0.252006i
\(748\) 3.33615 + 5.77838i 0.121982 + 0.211279i
\(749\) 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 \(0.223052\pi\)
\(752\) −3.41261 + 5.91081i −0.124445 + 0.215545i
\(753\) 11.9453i 0.435313i
\(754\) −5.34370 + 35.8206i −0.194606 + 1.30451i
\(755\) 0 0
\(756\) −3.15637 1.82233i −0.114796 0.0662775i
\(757\) −37.8354 21.8443i −1.37515 0.793943i −0.383579 0.923508i \(-0.625309\pi\)
−0.991571 + 0.129565i \(0.958642\pi\)
\(758\) −26.6013 + 15.3583i −0.966204 + 0.557838i
\(759\) 2.07598i 0.0753531i
\(760\) 0 0
\(761\) 34.5550 19.9503i 1.25262 0.723200i 0.280990 0.959711i \(-0.409337\pi\)
0.971629 + 0.236511i \(0.0760040\pi\)
\(762\) 14.4407 0.523131
\(763\) −2.09535 + 1.20975i −0.0758567 + 0.0437959i
\(764\) −7.84081 + 13.5807i −0.283671 + 0.491332i
\(765\) 0 0
\(766\) 20.0619 0.724867
\(767\) 21.7844 + 3.24978i 0.786589 + 0.117343i
\(768\) 1.00000i 0.0360844i
\(769\) 15.2064 + 8.77941i 0.548356 + 0.316594i 0.748459 0.663181i \(-0.230794\pi\)
−0.200103 + 0.979775i \(0.564128\pi\)
\(770\) 0 0
\(771\) 9.73103 + 16.8546i 0.350454 + 0.607005i
\(772\) 8.12795 0.292531
\(773\) 6.41861 + 11.1174i 0.230861 + 0.399864i 0.958062 0.286562i \(-0.0925123\pi\)
−0.727201 + 0.686425i \(0.759179\pi\)
\(774\) 6.55829 3.78643i 0.235733 0.136100i
\(775\) 0 0
\(776\) −1.37671 2.38453i −0.0494210 0.0855997i
\(777\) −31.1351 17.9759i −1.11697 0.644881i
\(778\) −13.5157 + 23.4099i −0.484561 + 0.839284i
\(779\) −58.6410 −2.10103
\(780\) 0 0
\(781\) 5.85651 0.209562
\(782\) 2.48907 4.31119i 0.0890088 0.154168i
\(783\) −8.69904 5.02239i −0.310878 0.179486i
\(784\) −3.14177 5.44171i −0.112206 0.194347i