Properties

Label 690.3.k.b.277.18
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.18
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.18

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-2.00232 - 4.58156i) q^{5} -2.44949 q^{6} +(-5.25476 - 5.25476i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-2.00232 - 4.58156i) q^{5} -2.44949 q^{6} +(-5.25476 - 5.25476i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-2.57924 + 6.58388i) q^{10} +3.64219 q^{11} +(2.44949 + 2.44949i) q^{12} +(-7.35690 + 7.35690i) q^{13} +10.5095i q^{14} +(-8.06358 - 3.15892i) q^{15} -4.00000 q^{16} +(-14.6562 - 14.6562i) q^{17} +(-3.00000 + 3.00000i) q^{18} +3.37356i q^{19} +(9.16313 - 4.00464i) q^{20} -12.8715 q^{21} +(-3.64219 - 3.64219i) q^{22} +(-3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(-16.9814 + 18.3475i) q^{25} +14.7138 q^{26} +(-3.67423 - 3.67423i) q^{27} +(10.5095 - 10.5095i) q^{28} -1.23263i q^{29} +(4.90466 + 11.2225i) q^{30} +19.8064 q^{31} +(4.00000 + 4.00000i) q^{32} +(4.46076 - 4.46076i) q^{33} +29.3125i q^{34} +(-13.5533 + 34.5967i) q^{35} +6.00000 q^{36} +(-6.16415 - 6.16415i) q^{37} +(3.37356 - 3.37356i) q^{38} +18.0207i q^{39} +(-13.1678 - 5.15849i) q^{40} +47.2794 q^{41} +(12.8715 + 12.8715i) q^{42} +(-35.5800 + 35.5800i) q^{43} +7.28439i q^{44} +(-13.7447 + 6.00696i) q^{45} +6.78233 q^{46} +(33.2177 + 33.2177i) q^{47} +(-4.89898 + 4.89898i) q^{48} +6.22501i q^{49} +(35.3289 - 1.36607i) q^{50} -35.9003 q^{51} +(-14.7138 - 14.7138i) q^{52} +(-26.6463 + 26.6463i) q^{53} +7.34847i q^{54} +(-7.29284 - 16.6869i) q^{55} -21.0190 q^{56} +(4.13175 + 4.13175i) q^{57} +(-1.23263 + 1.23263i) q^{58} +44.0572i q^{59} +(6.31783 - 16.1272i) q^{60} -37.9182 q^{61} +(-19.8064 - 19.8064i) q^{62} +(-15.7643 + 15.7643i) q^{63} -8.00000i q^{64} +(48.4370 + 18.9752i) q^{65} -8.92152 q^{66} +(-87.7712 - 87.7712i) q^{67} +(29.3125 - 29.3125i) q^{68} +8.30662i q^{69} +(48.1500 - 21.0434i) q^{70} +7.77433 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-58.7976 + 58.7976i) q^{73} +12.3283i q^{74} +(1.67308 + 43.2689i) q^{75} -6.74712 q^{76} +(-19.1389 - 19.1389i) q^{77} +(18.0207 - 18.0207i) q^{78} -26.9312i q^{79} +(8.00928 + 18.3263i) q^{80} -9.00000 q^{81} +(-47.2794 - 47.2794i) q^{82} +(-1.79597 + 1.79597i) q^{83} -25.7430i q^{84} +(-37.8020 + 96.4949i) q^{85} +71.1600 q^{86} +(-1.50966 - 1.50966i) q^{87} +(7.28439 - 7.28439i) q^{88} +110.000i q^{89} +(19.7516 + 7.73773i) q^{90} +77.3175 q^{91} +(-6.78233 - 6.78233i) q^{92} +(24.2578 - 24.2578i) q^{93} -66.4354i q^{94} +(15.4562 - 6.75494i) q^{95} +9.79796 q^{96} +(1.22444 + 1.22444i) q^{97} +(6.22501 - 6.22501i) q^{98} -10.9266i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + O(q^{10}) \) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + 8q^{10} - 32q^{11} - 24q^{13} + 24q^{15} - 192q^{16} + 72q^{17} - 144q^{18} + 32q^{22} + 24q^{25} + 48q^{26} + 16q^{28} - 24q^{30} + 24q^{31} + 192q^{32} - 24q^{33} + 288q^{36} - 128q^{37} - 16q^{38} - 16q^{40} - 40q^{41} + 48q^{43} - 136q^{47} - 80q^{50} - 48q^{52} + 144q^{53} - 144q^{55} - 32q^{56} + 96q^{57} + 8q^{58} + 128q^{61} - 24q^{62} - 24q^{63} + 184q^{65} + 48q^{66} - 144q^{68} + 40q^{70} - 40q^{71} - 288q^{72} + 40q^{73} - 72q^{75} + 32q^{76} - 104q^{77} + 96q^{78} + 32q^{80} - 432q^{81} + 40q^{82} - 88q^{85} - 96q^{86} + 120q^{87} - 64q^{88} + 24q^{90} + 144q^{91} - 96q^{93} + 312q^{95} + 480q^{97} + 584q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 2.00000i 0.500000i
\(5\) −2.00232 4.58156i −0.400464 0.916313i
\(6\) −2.44949 −0.408248
\(7\) −5.25476 5.25476i −0.750680 0.750680i 0.223926 0.974606i \(-0.428113\pi\)
−0.974606 + 0.223926i \(0.928113\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −2.57924 + 6.58388i −0.257924 + 0.658388i
\(11\) 3.64219 0.331109 0.165554 0.986201i \(-0.447059\pi\)
0.165554 + 0.986201i \(0.447059\pi\)
\(12\) 2.44949 + 2.44949i 0.204124 + 0.204124i
\(13\) −7.35690 + 7.35690i −0.565916 + 0.565916i −0.930982 0.365066i \(-0.881046\pi\)
0.365066 + 0.930982i \(0.381046\pi\)
\(14\) 10.5095i 0.750680i
\(15\) −8.06358 3.15892i −0.537572 0.210594i
\(16\) −4.00000 −0.250000
\(17\) −14.6562 14.6562i −0.862132 0.862132i 0.129454 0.991585i \(-0.458678\pi\)
−0.991585 + 0.129454i \(0.958678\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 3.37356i 0.177556i 0.996051 + 0.0887779i \(0.0282961\pi\)
−0.996051 + 0.0887779i \(0.971704\pi\)
\(20\) 9.16313 4.00464i 0.458156 0.200232i
\(21\) −12.8715 −0.612928
\(22\) −3.64219 3.64219i −0.165554 0.165554i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) −16.9814 + 18.3475i −0.679257 + 0.733900i
\(26\) 14.7138 0.565916
\(27\) −3.67423 3.67423i −0.136083 0.136083i
\(28\) 10.5095 10.5095i 0.375340 0.375340i
\(29\) 1.23263i 0.0425045i −0.999774 0.0212523i \(-0.993235\pi\)
0.999774 0.0212523i \(-0.00676532\pi\)
\(30\) 4.90466 + 11.2225i 0.163489 + 0.374083i
\(31\) 19.8064 0.638917 0.319459 0.947600i \(-0.396499\pi\)
0.319459 + 0.947600i \(0.396499\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 4.46076 4.46076i 0.135175 0.135175i
\(34\) 29.3125i 0.862132i
\(35\) −13.5533 + 34.5967i −0.387237 + 0.988478i
\(36\) 6.00000 0.166667
\(37\) −6.16415 6.16415i −0.166599 0.166599i 0.618884 0.785482i \(-0.287585\pi\)
−0.785482 + 0.618884i \(0.787585\pi\)
\(38\) 3.37356 3.37356i 0.0887779 0.0887779i
\(39\) 18.0207i 0.462068i
\(40\) −13.1678 5.15849i −0.329194 0.128962i
\(41\) 47.2794 1.15316 0.576579 0.817042i \(-0.304387\pi\)
0.576579 + 0.817042i \(0.304387\pi\)
\(42\) 12.8715 + 12.8715i 0.306464 + 0.306464i
\(43\) −35.5800 + 35.5800i −0.827442 + 0.827442i −0.987162 0.159721i \(-0.948941\pi\)
0.159721 + 0.987162i \(0.448941\pi\)
\(44\) 7.28439i 0.165554i
\(45\) −13.7447 + 6.00696i −0.305438 + 0.133488i
\(46\) 6.78233 0.147442
\(47\) 33.2177 + 33.2177i 0.706760 + 0.706760i 0.965852 0.259093i \(-0.0834236\pi\)
−0.259093 + 0.965852i \(0.583424\pi\)
\(48\) −4.89898 + 4.89898i −0.102062 + 0.102062i
\(49\) 6.22501i 0.127041i
\(50\) 35.3289 1.36607i 0.706579 0.0273213i
\(51\) −35.9003 −0.703927
\(52\) −14.7138 14.7138i −0.282958 0.282958i
\(53\) −26.6463 + 26.6463i −0.502760 + 0.502760i −0.912294 0.409535i \(-0.865691\pi\)
0.409535 + 0.912294i \(0.365691\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −7.29284 16.6869i −0.132597 0.303399i
\(56\) −21.0190 −0.375340
\(57\) 4.13175 + 4.13175i 0.0724868 + 0.0724868i
\(58\) −1.23263 + 1.23263i −0.0212523 + 0.0212523i
\(59\) 44.0572i 0.746732i 0.927684 + 0.373366i \(0.121796\pi\)
−0.927684 + 0.373366i \(0.878204\pi\)
\(60\) 6.31783 16.1272i 0.105297 0.268786i
\(61\) −37.9182 −0.621609 −0.310805 0.950474i \(-0.600599\pi\)
−0.310805 + 0.950474i \(0.600599\pi\)
\(62\) −19.8064 19.8064i −0.319459 0.319459i
\(63\) −15.7643 + 15.7643i −0.250227 + 0.250227i
\(64\) 8.00000i 0.125000i
\(65\) 48.4370 + 18.9752i 0.745184 + 0.291927i
\(66\) −8.92152 −0.135175
\(67\) −87.7712 87.7712i −1.31002 1.31002i −0.921398 0.388620i \(-0.872952\pi\)
−0.388620 0.921398i \(-0.627048\pi\)
\(68\) 29.3125 29.3125i 0.431066 0.431066i
\(69\) 8.30662i 0.120386i
\(70\) 48.1500 21.0434i 0.687858 0.300620i
\(71\) 7.77433 0.109498 0.0547488 0.998500i \(-0.482564\pi\)
0.0547488 + 0.998500i \(0.482564\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) −58.7976 + 58.7976i −0.805446 + 0.805446i −0.983941 0.178494i \(-0.942877\pi\)
0.178494 + 0.983941i \(0.442877\pi\)
\(74\) 12.3283i 0.166599i
\(75\) 1.67308 + 43.2689i 0.0223078 + 0.576919i
\(76\) −6.74712 −0.0887779
\(77\) −19.1389 19.1389i −0.248557 0.248557i
\(78\) 18.0207 18.0207i 0.231034 0.231034i
\(79\) 26.9312i 0.340901i −0.985366 0.170450i \(-0.945478\pi\)
0.985366 0.170450i \(-0.0545222\pi\)
\(80\) 8.00928 + 18.3263i 0.100116 + 0.229078i
\(81\) −9.00000 −0.111111
\(82\) −47.2794 47.2794i −0.576579 0.576579i
\(83\) −1.79597 + 1.79597i −0.0216382 + 0.0216382i −0.717843 0.696205i \(-0.754871\pi\)
0.696205 + 0.717843i \(0.254871\pi\)
\(84\) 25.7430i 0.306464i
\(85\) −37.8020 + 96.4949i −0.444729 + 1.13523i
\(86\) 71.1600 0.827442
\(87\) −1.50966 1.50966i −0.0173524 0.0173524i
\(88\) 7.28439 7.28439i 0.0827771 0.0827771i
\(89\) 110.000i 1.23595i 0.786197 + 0.617976i \(0.212047\pi\)
−0.786197 + 0.617976i \(0.787953\pi\)
\(90\) 19.7516 + 7.73773i 0.219463 + 0.0859748i
\(91\) 77.3175 0.849643
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) 24.2578 24.2578i 0.260837 0.260837i
\(94\) 66.4354i 0.706760i
\(95\) 15.4562 6.75494i 0.162697 0.0711047i
\(96\) 9.79796 0.102062
\(97\) 1.22444 + 1.22444i 0.0126231 + 0.0126231i 0.713390 0.700767i \(-0.247159\pi\)
−0.700767 + 0.713390i \(0.747159\pi\)
\(98\) 6.22501 6.22501i 0.0635205 0.0635205i
\(99\) 10.9266i 0.110370i
\(100\) −36.6950 33.9629i −0.366950 0.339629i
\(101\) 134.532 1.33200 0.665999 0.745953i \(-0.268006\pi\)
0.665999 + 0.745953i \(0.268006\pi\)
\(102\) 35.9003 + 35.9003i 0.351964 + 0.351964i
\(103\) −60.5363 + 60.5363i −0.587731 + 0.587731i −0.937016 0.349286i \(-0.886424\pi\)
0.349286 + 0.937016i \(0.386424\pi\)
\(104\) 29.4276i 0.282958i
\(105\) 25.7728 + 58.9715i 0.245455 + 0.561633i
\(106\) 53.2925 0.502760
\(107\) 43.6880 + 43.6880i 0.408299 + 0.408299i 0.881145 0.472846i \(-0.156773\pi\)
−0.472846 + 0.881145i \(0.656773\pi\)
\(108\) 7.34847 7.34847i 0.0680414 0.0680414i
\(109\) 4.39089i 0.0402834i 0.999797 + 0.0201417i \(0.00641173\pi\)
−0.999797 + 0.0201417i \(0.993588\pi\)
\(110\) −9.39411 + 23.9798i −0.0854010 + 0.217998i
\(111\) −15.0990 −0.136027
\(112\) 21.0190 + 21.0190i 0.187670 + 0.187670i
\(113\) −68.8182 + 68.8182i −0.609011 + 0.609011i −0.942688 0.333677i \(-0.891711\pi\)
0.333677 + 0.942688i \(0.391711\pi\)
\(114\) 8.26350i 0.0724868i
\(115\) 22.3270 + 8.74664i 0.194148 + 0.0760577i
\(116\) 2.46526 0.0212523
\(117\) 22.0707 + 22.0707i 0.188639 + 0.188639i
\(118\) 44.0572 44.0572i 0.373366 0.373366i
\(119\) 154.030i 1.29437i
\(120\) −22.4450 + 9.80932i −0.187042 + 0.0817443i
\(121\) −107.734 −0.890367
\(122\) 37.9182 + 37.9182i 0.310805 + 0.310805i
\(123\) 57.9053 57.9053i 0.470774 0.470774i
\(124\) 39.6129i 0.319459i
\(125\) 118.062 + 41.0640i 0.944500 + 0.328512i
\(126\) 31.5286 0.250227
\(127\) −13.4330 13.4330i −0.105771 0.105771i 0.652241 0.758012i \(-0.273829\pi\)
−0.758012 + 0.652241i \(0.773829\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 87.1528i 0.675603i
\(130\) −29.4617 67.4122i −0.226629 0.518556i
\(131\) −121.821 −0.929935 −0.464967 0.885328i \(-0.653934\pi\)
−0.464967 + 0.885328i \(0.653934\pi\)
\(132\) 8.92152 + 8.92152i 0.0675873 + 0.0675873i
\(133\) 17.7272 17.7272i 0.133288 0.133288i
\(134\) 175.542i 1.31002i
\(135\) −9.47675 + 24.1907i −0.0701981 + 0.179191i
\(136\) −58.6249 −0.431066
\(137\) −122.729 122.729i −0.895829 0.895829i 0.0992347 0.995064i \(-0.468361\pi\)
−0.995064 + 0.0992347i \(0.968361\pi\)
\(138\) 8.30662 8.30662i 0.0601929 0.0601929i
\(139\) 7.58478i 0.0545668i −0.999628 0.0272834i \(-0.991314\pi\)
0.999628 0.0272834i \(-0.00868565\pi\)
\(140\) −69.1934 27.1066i −0.494239 0.193619i
\(141\) 81.3664 0.577067
\(142\) −7.77433 7.77433i −0.0547488 0.0547488i
\(143\) −26.7953 + 26.7953i −0.187379 + 0.187379i
\(144\) 12.0000i 0.0833333i
\(145\) −5.64738 + 2.46812i −0.0389474 + 0.0170215i
\(146\) 117.595 0.805446
\(147\) 7.62405 + 7.62405i 0.0518643 + 0.0518643i
\(148\) 12.3283 12.3283i 0.0832993 0.0832993i
\(149\) 221.285i 1.48514i −0.669770 0.742568i \(-0.733607\pi\)
0.669770 0.742568i \(-0.266393\pi\)
\(150\) 41.5959 44.9420i 0.277306 0.299613i
\(151\) 4.57858 0.0303217 0.0151608 0.999885i \(-0.495174\pi\)
0.0151608 + 0.999885i \(0.495174\pi\)
\(152\) 6.74712 + 6.74712i 0.0443889 + 0.0443889i
\(153\) −43.9687 + 43.9687i −0.287377 + 0.287377i
\(154\) 38.2777i 0.248557i
\(155\) −39.6588 90.7444i −0.255863 0.585448i
\(156\) −36.0413 −0.231034
\(157\) −19.5364 19.5364i −0.124436 0.124436i 0.642146 0.766582i \(-0.278044\pi\)
−0.766582 + 0.642146i \(0.778044\pi\)
\(158\) −26.9312 + 26.9312i −0.170450 + 0.170450i
\(159\) 65.2697i 0.410502i
\(160\) 10.3170 26.3355i 0.0644811 0.164597i
\(161\) 35.6395 0.221363
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) 96.3330 96.3330i 0.591000 0.591000i −0.346902 0.937902i \(-0.612766\pi\)
0.937902 + 0.346902i \(0.112766\pi\)
\(164\) 94.5589i 0.576579i
\(165\) −29.3691 11.5054i −0.177995 0.0697296i
\(166\) 3.59195 0.0216382
\(167\) −161.676 161.676i −0.968120 0.968120i 0.0313878 0.999507i \(-0.490007\pi\)
−0.999507 + 0.0313878i \(0.990007\pi\)
\(168\) −25.7430 + 25.7430i −0.153232 + 0.153232i
\(169\) 60.7520i 0.359479i
\(170\) 134.297 58.6929i 0.789982 0.345252i
\(171\) 10.1207 0.0591853
\(172\) −71.1600 71.1600i −0.413721 0.413721i
\(173\) 171.585 171.585i 0.991820 0.991820i −0.00814708 0.999967i \(-0.502593\pi\)
0.999967 + 0.00814708i \(0.00259333\pi\)
\(174\) 3.01932i 0.0173524i
\(175\) 185.645 7.17835i 1.06083 0.0410191i
\(176\) −14.5688 −0.0827771
\(177\) 53.9588 + 53.9588i 0.304852 + 0.304852i
\(178\) 110.000 110.000i 0.617976 0.617976i
\(179\) 178.228i 0.995688i 0.867267 + 0.497844i \(0.165875\pi\)
−0.867267 + 0.497844i \(0.834125\pi\)
\(180\) −12.0139 27.4894i −0.0667440 0.152719i
\(181\) −107.395 −0.593342 −0.296671 0.954980i \(-0.595876\pi\)
−0.296671 + 0.954980i \(0.595876\pi\)
\(182\) −77.3175 77.3175i −0.424821 0.424821i
\(183\) −46.4401 + 46.4401i −0.253771 + 0.253771i
\(184\) 13.5647i 0.0737210i
\(185\) −15.8988 + 40.5840i −0.0859397 + 0.219373i
\(186\) −48.5157 −0.260837
\(187\) −53.3809 53.3809i −0.285459 0.285459i
\(188\) −66.4354 + 66.4354i −0.353380 + 0.353380i
\(189\) 38.6144i 0.204309i
\(190\) −22.2111 8.70123i −0.116901 0.0457960i
\(191\) −120.021 −0.628383 −0.314191 0.949360i \(-0.601733\pi\)
−0.314191 + 0.949360i \(0.601733\pi\)
\(192\) −9.79796 9.79796i −0.0510310 0.0510310i
\(193\) 51.5373 51.5373i 0.267033 0.267033i −0.560871 0.827903i \(-0.689534\pi\)
0.827903 + 0.560871i \(0.189534\pi\)
\(194\) 2.44889i 0.0126231i
\(195\) 82.5628 36.0831i 0.423399 0.185042i
\(196\) −12.4500 −0.0635205
\(197\) −20.5257 20.5257i −0.104192 0.104192i 0.653089 0.757281i \(-0.273473\pi\)
−0.757281 + 0.653089i \(0.773473\pi\)
\(198\) −10.9266 + 10.9266i −0.0551848 + 0.0551848i
\(199\) 261.408i 1.31361i −0.754061 0.656805i \(-0.771908\pi\)
0.754061 0.656805i \(-0.228092\pi\)
\(200\) 2.73213 + 70.6579i 0.0136607 + 0.353289i
\(201\) −214.995 −1.06963
\(202\) −134.532 134.532i −0.665999 0.665999i
\(203\) −6.47718 + 6.47718i −0.0319073 + 0.0319073i
\(204\) 71.8006i 0.351964i
\(205\) −94.6685 216.614i −0.461798 1.05665i
\(206\) 121.073 0.587731
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) 29.4276 29.4276i 0.141479 0.141479i
\(209\) 12.2872i 0.0587902i
\(210\) 33.1987 84.7443i 0.158089 0.403544i
\(211\) −215.468 −1.02118 −0.510588 0.859825i \(-0.670572\pi\)
−0.510588 + 0.859825i \(0.670572\pi\)
\(212\) −53.2925 53.2925i −0.251380 0.251380i
\(213\) 9.52156 9.52156i 0.0447022 0.0447022i
\(214\) 87.3760i 0.408299i
\(215\) 234.254 + 91.7695i 1.08956 + 0.426835i
\(216\) −14.6969 −0.0680414
\(217\) −104.078 104.078i −0.479622 0.479622i
\(218\) 4.39089 4.39089i 0.0201417 0.0201417i
\(219\) 144.024i 0.657644i
\(220\) 33.3739 14.5857i 0.151699 0.0662985i
\(221\) 215.649 0.975787
\(222\) 15.0990 + 15.0990i 0.0680136 + 0.0680136i
\(223\) 165.267 165.267i 0.741110 0.741110i −0.231682 0.972792i \(-0.574423\pi\)
0.972792 + 0.231682i \(0.0744229\pi\)
\(224\) 42.0381i 0.187670i
\(225\) 55.0425 + 50.9443i 0.244633 + 0.226419i
\(226\) 137.636 0.609011
\(227\) −178.325 178.325i −0.785574 0.785574i 0.195191 0.980765i \(-0.437467\pi\)
−0.980765 + 0.195191i \(0.937467\pi\)
\(228\) −8.26350 + 8.26350i −0.0362434 + 0.0362434i
\(229\) 50.6019i 0.220969i −0.993878 0.110484i \(-0.964760\pi\)
0.993878 0.110484i \(-0.0352403\pi\)
\(230\) −13.5804 31.0737i −0.0590452 0.135103i
\(231\) −46.8804 −0.202946
\(232\) −2.46526 2.46526i −0.0106261 0.0106261i
\(233\) 13.2676 13.2676i 0.0569423 0.0569423i −0.678062 0.735005i \(-0.737180\pi\)
0.735005 + 0.678062i \(0.237180\pi\)
\(234\) 44.1414i 0.188639i
\(235\) 85.6765 218.701i 0.364581 0.930644i
\(236\) −88.1143 −0.373366
\(237\) −32.9838 32.9838i −0.139172 0.139172i
\(238\) 154.030 154.030i 0.647185 0.647185i
\(239\) 336.857i 1.40944i −0.709484 0.704721i \(-0.751072\pi\)
0.709484 0.704721i \(-0.248928\pi\)
\(240\) 32.2543 + 12.6357i 0.134393 + 0.0526486i
\(241\) −349.220 −1.44905 −0.724524 0.689250i \(-0.757940\pi\)
−0.724524 + 0.689250i \(0.757940\pi\)
\(242\) 107.734 + 107.734i 0.445184 + 0.445184i
\(243\) −11.0227 + 11.0227i −0.0453609 + 0.0453609i
\(244\) 75.8363i 0.310805i
\(245\) 28.5203 12.4645i 0.116409 0.0508753i
\(246\) −115.811 −0.470774
\(247\) −24.8189 24.8189i −0.100482 0.100482i
\(248\) 39.6129 39.6129i 0.159729 0.159729i
\(249\) 4.39922i 0.0176676i
\(250\) −76.9985 159.126i −0.307994 0.636506i
\(251\) −410.838 −1.63680 −0.818402 0.574645i \(-0.805140\pi\)
−0.818402 + 0.574645i \(0.805140\pi\)
\(252\) −31.5286 31.5286i −0.125113 0.125113i
\(253\) −12.3513 + 12.3513i −0.0488193 + 0.0488193i
\(254\) 26.8659i 0.105771i
\(255\) 71.8839 + 164.479i 0.281897 + 0.645018i
\(256\) 16.0000 0.0625000
\(257\) −113.403 113.403i −0.441255 0.441255i 0.451179 0.892434i \(-0.351004\pi\)
−0.892434 + 0.451179i \(0.851004\pi\)
\(258\) 87.1528 87.1528i 0.337802 0.337802i
\(259\) 64.7822i 0.250124i
\(260\) −37.9505 + 96.8739i −0.145963 + 0.372592i
\(261\) −3.69789 −0.0141682
\(262\) 121.821 + 121.821i 0.464967 + 0.464967i
\(263\) 290.995 290.995i 1.10644 1.10644i 0.112829 0.993614i \(-0.464009\pi\)
0.993614 0.112829i \(-0.0359911\pi\)
\(264\) 17.8430i 0.0675873i
\(265\) 175.436 + 68.7272i 0.662022 + 0.259348i
\(266\) −35.4545 −0.133288
\(267\) 134.722 + 134.722i 0.504575 + 0.504575i
\(268\) 175.542 175.542i 0.655009 0.655009i
\(269\) 82.3667i 0.306196i 0.988211 + 0.153098i \(0.0489250\pi\)
−0.988211 + 0.153098i \(0.951075\pi\)
\(270\) 33.6675 14.7140i 0.124694 0.0544962i
\(271\) −397.792 −1.46787 −0.733933 0.679222i \(-0.762317\pi\)
−0.733933 + 0.679222i \(0.762317\pi\)
\(272\) 58.6249 + 58.6249i 0.215533 + 0.215533i
\(273\) 94.6942 94.6942i 0.346865 0.346865i
\(274\) 245.457i 0.895829i
\(275\) −61.8497 + 66.8252i −0.224908 + 0.243001i
\(276\) −16.6132 −0.0601929
\(277\) −103.267 103.267i −0.372804 0.372804i 0.495693 0.868498i \(-0.334914\pi\)
−0.868498 + 0.495693i \(0.834914\pi\)
\(278\) −7.58478 + 7.58478i −0.0272834 + 0.0272834i
\(279\) 59.4193i 0.212972i
\(280\) 42.0868 + 96.3001i 0.150310 + 0.343929i
\(281\) 355.895 1.26653 0.633264 0.773936i \(-0.281715\pi\)
0.633264 + 0.773936i \(0.281715\pi\)
\(282\) −81.3664 81.3664i −0.288533 0.288533i
\(283\) 81.4946 81.4946i 0.287967 0.287967i −0.548309 0.836276i \(-0.684728\pi\)
0.836276 + 0.548309i \(0.184728\pi\)
\(284\) 15.5487i 0.0547488i
\(285\) 10.6568 27.2030i 0.0373922 0.0954490i
\(286\) 53.5905 0.187379
\(287\) −248.442 248.442i −0.865652 0.865652i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 140.610i 0.486541i
\(290\) 8.11550 + 3.17926i 0.0279845 + 0.0109630i
\(291\) 2.99926 0.0103067
\(292\) −117.595 117.595i −0.402723 0.402723i
\(293\) −51.2472 + 51.2472i −0.174905 + 0.174905i −0.789131 0.614226i \(-0.789469\pi\)
0.614226 + 0.789131i \(0.289469\pi\)
\(294\) 15.2481i 0.0518643i
\(295\) 201.851 88.2165i 0.684240 0.299039i
\(296\) −24.6566 −0.0832993
\(297\) −13.3823 13.3823i −0.0450582 0.0450582i
\(298\) −221.285 + 221.285i −0.742568 + 0.742568i
\(299\) 49.8969i 0.166879i
\(300\) −86.5379 + 3.34617i −0.288460 + 0.0111539i
\(301\) 373.929 1.24229
\(302\) −4.57858 4.57858i −0.0151608 0.0151608i
\(303\) 164.767 164.767i 0.543786 0.543786i
\(304\) 13.4942i 0.0443889i
\(305\) 75.9243 + 173.724i 0.248932 + 0.569588i
\(306\) 87.9374 0.287377
\(307\) −134.262 134.262i −0.437336 0.437336i 0.453778 0.891115i \(-0.350076\pi\)
−0.891115 + 0.453778i \(0.850076\pi\)
\(308\) 38.2777 38.2777i 0.124278 0.124278i
\(309\) 148.283i 0.479880i
\(310\) −51.0856 + 130.403i −0.164792 + 0.420656i
\(311\) 287.922 0.925795 0.462897 0.886412i \(-0.346810\pi\)
0.462897 + 0.886412i \(0.346810\pi\)
\(312\) 36.0413 + 36.0413i 0.115517 + 0.115517i
\(313\) −115.283 + 115.283i −0.368316 + 0.368316i −0.866863 0.498547i \(-0.833867\pi\)
0.498547 + 0.866863i \(0.333867\pi\)
\(314\) 39.0728i 0.124436i
\(315\) 103.790 + 40.6599i 0.329493 + 0.129079i
\(316\) 53.8623 0.170450
\(317\) 90.5079 + 90.5079i 0.285514 + 0.285514i 0.835303 0.549789i \(-0.185292\pi\)
−0.549789 + 0.835303i \(0.685292\pi\)
\(318\) 65.2697 65.2697i 0.205251 0.205251i
\(319\) 4.48948i 0.0140736i
\(320\) −36.6525 + 16.0186i −0.114539 + 0.0500580i
\(321\) 107.013 0.333375
\(322\) −35.6395 35.6395i −0.110682 0.110682i
\(323\) 49.4437 49.4437i 0.153076 0.153076i
\(324\) 18.0000i 0.0555556i
\(325\) −10.0500 259.912i −0.0309231 0.799728i
\(326\) −192.666 −0.591000
\(327\) 5.37772 + 5.37772i 0.0164456 + 0.0164456i
\(328\) 94.5589 94.5589i 0.288289 0.288289i
\(329\) 349.102i 1.06110i
\(330\) 17.8637 + 40.8745i 0.0541325 + 0.123862i
\(331\) −225.894 −0.682458 −0.341229 0.939980i \(-0.610843\pi\)
−0.341229 + 0.939980i \(0.610843\pi\)
\(332\) −3.59195 3.59195i −0.0108191 0.0108191i
\(333\) −18.4924 + 18.4924i −0.0555329 + 0.0555329i
\(334\) 323.352i 0.968120i
\(335\) −226.383 + 577.875i −0.675771 + 1.72500i
\(336\) 51.4859 0.153232
\(337\) 82.0993 + 82.0993i 0.243618 + 0.243618i 0.818345 0.574727i \(-0.194892\pi\)
−0.574727 + 0.818345i \(0.694892\pi\)
\(338\) 60.7520 60.7520i 0.179740 0.179740i
\(339\) 168.570i 0.497255i
\(340\) −192.990 75.6040i −0.567617 0.222365i
\(341\) 72.1389 0.211551
\(342\) −10.1207 10.1207i −0.0295926 0.0295926i
\(343\) −224.772 + 224.772i −0.655313 + 0.655313i
\(344\) 142.320i 0.413721i
\(345\) 38.0573 16.6325i 0.110311 0.0482102i
\(346\) −343.170 −0.991820
\(347\) −164.374 164.374i −0.473701 0.473701i 0.429409 0.903110i \(-0.358722\pi\)
−0.903110 + 0.429409i \(0.858722\pi\)
\(348\) 3.01932 3.01932i 0.00867620 0.00867620i
\(349\) 130.319i 0.373408i −0.982416 0.186704i \(-0.940220\pi\)
0.982416 0.186704i \(-0.0597805\pi\)
\(350\) −192.823 178.467i −0.550924 0.509905i
\(351\) 54.0620 0.154023
\(352\) 14.5688 + 14.5688i 0.0413886 + 0.0413886i
\(353\) 184.926 184.926i 0.523869 0.523869i −0.394868 0.918738i \(-0.629210\pi\)
0.918738 + 0.394868i \(0.129210\pi\)
\(354\) 107.918i 0.304852i
\(355\) −15.5667 35.6186i −0.0438498 0.100334i
\(356\) −219.999 −0.617976
\(357\) 188.647 + 188.647i 0.528424 + 0.528424i
\(358\) 178.228 178.228i 0.497844 0.497844i
\(359\) 211.235i 0.588398i 0.955744 + 0.294199i \(0.0950528\pi\)
−0.955744 + 0.294199i \(0.904947\pi\)
\(360\) −15.4755 + 39.5033i −0.0429874 + 0.109731i
\(361\) 349.619 0.968474
\(362\) 107.395 + 107.395i 0.296671 + 0.296671i
\(363\) −131.947 + 131.947i −0.363491 + 0.363491i
\(364\) 154.635i 0.424821i
\(365\) 387.116 + 151.653i 1.06059 + 0.415489i
\(366\) 92.8802 0.253771
\(367\) −384.033 384.033i −1.04641 1.04641i −0.998869 0.0475425i \(-0.984861\pi\)
−0.0475425 0.998869i \(-0.515139\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 141.838i 0.384386i
\(370\) 56.4829 24.6852i 0.152656 0.0667167i
\(371\) 280.039 0.754823
\(372\) 48.5157 + 48.5157i 0.130418 + 0.130418i
\(373\) −208.764 + 208.764i −0.559689 + 0.559689i −0.929219 0.369530i \(-0.879519\pi\)
0.369530 + 0.929219i \(0.379519\pi\)
\(374\) 106.762i 0.285459i
\(375\) 194.889 94.3036i 0.519705 0.251476i
\(376\) 132.871 0.353380
\(377\) 9.06835 + 9.06835i 0.0240540 + 0.0240540i
\(378\) 38.6144 38.6144i 0.102155 0.102155i
\(379\) 706.994i 1.86542i 0.360629 + 0.932709i \(0.382562\pi\)
−0.360629 + 0.932709i \(0.617438\pi\)
\(380\) 13.5099 + 30.9124i 0.0355523 + 0.0813483i
\(381\) −32.9039 −0.0863620
\(382\) 120.021 + 120.021i 0.314191 + 0.314191i
\(383\) 399.956 399.956i 1.04427 1.04427i 0.0452983 0.998974i \(-0.485576\pi\)
0.998974 0.0452983i \(-0.0144238\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −49.3638 + 126.008i −0.128218 + 0.327293i
\(386\) −103.075 −0.267033
\(387\) 106.740 + 106.740i 0.275814 + 0.275814i
\(388\) −2.44889 + 2.44889i −0.00631156 + 0.00631156i
\(389\) 174.609i 0.448867i −0.974489 0.224434i \(-0.927947\pi\)
0.974489 0.224434i \(-0.0720532\pi\)
\(390\) −118.646 46.4797i −0.304220 0.119179i
\(391\) 99.4034 0.254229
\(392\) 12.4500 + 12.4500i 0.0317602 + 0.0317602i
\(393\) −149.200 + 149.200i −0.379644 + 0.379644i
\(394\) 41.0515i 0.104192i
\(395\) −123.387 + 53.9248i −0.312372 + 0.136518i
\(396\) 21.8532 0.0551848
\(397\) 180.755 + 180.755i 0.455302 + 0.455302i 0.897110 0.441808i \(-0.145663\pi\)
−0.441808 + 0.897110i \(0.645663\pi\)
\(398\) −261.408 + 261.408i −0.656805 + 0.656805i
\(399\) 43.4227i 0.108829i
\(400\) 67.9257 73.3900i 0.169814 0.183475i
\(401\) 48.1197 0.119999 0.0599997 0.998198i \(-0.480890\pi\)
0.0599997 + 0.998198i \(0.480890\pi\)
\(402\) 214.995 + 214.995i 0.534813 + 0.534813i
\(403\) −145.714 + 145.714i −0.361573 + 0.361573i
\(404\) 269.063i 0.665999i
\(405\) 18.0209 + 41.2341i 0.0444960 + 0.101813i
\(406\) 12.9544 0.0319073
\(407\) −22.4510 22.4510i −0.0551622 0.0551622i
\(408\) −71.8006 + 71.8006i −0.175982 + 0.175982i
\(409\) 690.337i 1.68787i 0.536448 + 0.843933i \(0.319766\pi\)
−0.536448 + 0.843933i \(0.680234\pi\)
\(410\) −121.945 + 311.282i −0.297427 + 0.759225i
\(411\) −300.623 −0.731442
\(412\) −121.073 121.073i −0.293865 0.293865i
\(413\) 231.510 231.510i 0.560557 0.560557i
\(414\) 20.3470i 0.0491473i
\(415\) 11.8245 + 4.63226i 0.0284927 + 0.0111621i
\(416\) −58.8552 −0.141479
\(417\) −9.28942 9.28942i −0.0222768 0.0222768i
\(418\) 12.2872 12.2872i 0.0293951 0.0293951i
\(419\) 377.004i 0.899770i 0.893087 + 0.449885i \(0.148535\pi\)
−0.893087 + 0.449885i \(0.851465\pi\)
\(420\) −117.943 + 51.5456i −0.280817 + 0.122728i
\(421\) 87.0930 0.206872 0.103436 0.994636i \(-0.467016\pi\)
0.103436 + 0.994636i \(0.467016\pi\)
\(422\) 215.468 + 215.468i 0.510588 + 0.510588i
\(423\) 99.6531 99.6531i 0.235587 0.235587i
\(424\) 106.585i 0.251380i
\(425\) 517.789 20.0214i 1.21833 0.0471092i
\(426\) −19.0431 −0.0447022
\(427\) 199.251 + 199.251i 0.466630 + 0.466630i
\(428\) −87.3760 + 87.3760i −0.204150 + 0.204150i
\(429\) 65.6347i 0.152995i
\(430\) −142.485 326.024i −0.331360 0.758195i
\(431\) −669.508 −1.55338 −0.776691 0.629881i \(-0.783103\pi\)
−0.776691 + 0.629881i \(0.783103\pi\)
\(432\) 14.6969 + 14.6969i 0.0340207 + 0.0340207i
\(433\) −526.019 + 526.019i −1.21483 + 1.21483i −0.245404 + 0.969421i \(0.578921\pi\)
−0.969421 + 0.245404i \(0.921079\pi\)
\(434\) 208.156i 0.479622i
\(435\) −3.89378 + 9.93942i −0.00895121 + 0.0228492i
\(436\) −8.78178 −0.0201417
\(437\) −11.4403 11.4403i −0.0261792 0.0261792i
\(438\) 144.024 144.024i 0.328822 0.328822i
\(439\) 776.442i 1.76866i −0.466862 0.884330i \(-0.654616\pi\)
0.466862 0.884330i \(-0.345384\pi\)
\(440\) −47.9596 18.7882i −0.108999 0.0427005i
\(441\) 18.6750 0.0423470
\(442\) −215.649 215.649i −0.487894 0.487894i
\(443\) 71.2577 71.2577i 0.160853 0.160853i −0.622092 0.782944i \(-0.713717\pi\)
0.782944 + 0.622092i \(0.213717\pi\)
\(444\) 30.1980i 0.0680136i
\(445\) 503.971 220.255i 1.13252 0.494954i
\(446\) −330.535 −0.741110
\(447\) −271.018 271.018i −0.606305 0.606305i
\(448\) −42.0381 + 42.0381i −0.0938350 + 0.0938350i
\(449\) 597.802i 1.33141i 0.746217 + 0.665703i \(0.231868\pi\)
−0.746217 + 0.665703i \(0.768132\pi\)
\(450\) −4.09820 105.987i −0.00910711 0.235526i
\(451\) 172.201 0.381820
\(452\) −137.636 137.636i −0.304505 0.304505i
\(453\) 5.60759 5.60759i 0.0123788 0.0123788i
\(454\) 356.651i 0.785574i
\(455\) −154.814 354.235i −0.340251 0.778539i
\(456\) 16.5270 0.0362434
\(457\) 548.139 + 548.139i 1.19943 + 1.19943i 0.974338 + 0.225090i \(0.0722677\pi\)
0.225090 + 0.974338i \(0.427732\pi\)
\(458\) −50.6019 + 50.6019i −0.110484 + 0.110484i
\(459\) 107.701i 0.234642i
\(460\) −17.4933 + 44.6541i −0.0380289 + 0.0970740i
\(461\) −647.631 −1.40484 −0.702420 0.711763i \(-0.747897\pi\)
−0.702420 + 0.711763i \(0.747897\pi\)
\(462\) 46.8804 + 46.8804i 0.101473 + 0.101473i
\(463\) −26.9735 + 26.9735i −0.0582581 + 0.0582581i −0.735636 0.677377i \(-0.763116\pi\)
0.677377 + 0.735636i \(0.263116\pi\)
\(464\) 4.93053i 0.0106261i
\(465\) −159.711 62.5669i −0.343464 0.134552i
\(466\) −26.5351 −0.0569423
\(467\) −620.663 620.663i −1.32904 1.32904i −0.906205 0.422838i \(-0.861034\pi\)
−0.422838 0.906205i \(-0.638966\pi\)
\(468\) −44.1414 + 44.1414i −0.0943193 + 0.0943193i
\(469\) 922.433i 1.96681i
\(470\) −304.378 + 133.025i −0.647613 + 0.283032i
\(471\) −47.8543 −0.101601
\(472\) 88.1143 + 88.1143i 0.186683 + 0.186683i
\(473\) −129.589 + 129.589i −0.273973 + 0.273973i
\(474\) 65.9676i 0.139172i
\(475\) −61.8964 57.2879i −0.130308 0.120606i
\(476\) −308.060 −0.647185
\(477\) 79.9388 + 79.9388i 0.167587 + 0.167587i
\(478\) −336.857 + 336.857i −0.704721 + 0.704721i
\(479\) 270.238i 0.564171i −0.959389 0.282085i \(-0.908974\pi\)
0.959389 0.282085i \(-0.0910262\pi\)
\(480\) −19.6186 44.8900i −0.0408722 0.0935208i
\(481\) 90.6981 0.188561
\(482\) 349.220 + 349.220i 0.724524 + 0.724524i
\(483\) 43.6493 43.6493i 0.0903713 0.0903713i
\(484\) 215.469i 0.445184i
\(485\) 3.15814 8.06159i 0.00651162 0.0166218i
\(486\) 22.0454 0.0453609
\(487\) 124.905 + 124.905i 0.256479 + 0.256479i 0.823621 0.567141i \(-0.191951\pi\)
−0.567141 + 0.823621i \(0.691951\pi\)
\(488\) −75.8363 + 75.8363i −0.155402 + 0.155402i
\(489\) 235.967i 0.482549i
\(490\) −40.9847 16.0558i −0.0836423 0.0327670i
\(491\) −598.054 −1.21803 −0.609016 0.793158i \(-0.708436\pi\)
−0.609016 + 0.793158i \(0.708436\pi\)
\(492\) 115.811 + 115.811i 0.235387 + 0.235387i
\(493\) −18.0657 + 18.0657i −0.0366445 + 0.0366445i
\(494\) 49.6379i 0.100482i
\(495\) −50.0608 + 21.8785i −0.101133 + 0.0441990i
\(496\) −79.2257 −0.159729
\(497\) −40.8522 40.8522i −0.0821976 0.0821976i
\(498\) 4.39922 4.39922i 0.00883378 0.00883378i
\(499\) 160.709i 0.322062i 0.986949 + 0.161031i \(0.0514820\pi\)
−0.986949 + 0.161031i \(0.948518\pi\)
\(500\) −82.1279 + 236.125i −0.164256 + 0.472250i
\(501\) −396.024 −0.790466
\(502\) 410.838 + 410.838i 0.818402 + 0.818402i
\(503\) −369.487 + 369.487i −0.734566 + 0.734566i −0.971521 0.236955i \(-0.923851\pi\)
0.236955 + 0.971521i \(0.423851\pi\)
\(504\) 63.0571i 0.125113i
\(505\) −269.375 616.365i −0.533417 1.22053i
\(506\) 24.7026 0.0488193
\(507\) 74.4057 + 74.4057i 0.146757 + 0.146757i
\(508\) 26.8659 26.8659i 0.0528857 0.0528857i
\(509\) 760.982i 1.49505i 0.664232 + 0.747526i \(0.268759\pi\)
−0.664232 + 0.747526i \(0.731241\pi\)
\(510\) 92.5956 236.363i 0.181560 0.463458i
\(511\) 617.934 1.20927
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) 12.3952 12.3952i 0.0241623 0.0241623i
\(514\) 226.805i 0.441255i
\(515\) 398.564 + 156.138i 0.773910 + 0.303180i
\(516\) −174.306 −0.337802
\(517\) 120.985 + 120.985i 0.234014 + 0.234014i
\(518\) 64.7822 64.7822i 0.125062 0.125062i
\(519\) 420.295i 0.809817i
\(520\) 134.824 58.9235i 0.259278 0.113314i
\(521\) 254.214 0.487934 0.243967 0.969784i \(-0.421551\pi\)
0.243967 + 0.969784i \(0.421551\pi\)
\(522\) 3.69789 + 3.69789i 0.00708409 + 0.00708409i
\(523\) 4.21088 4.21088i 0.00805140 0.00805140i −0.703070 0.711121i \(-0.748188\pi\)
0.711121 + 0.703070i \(0.248188\pi\)
\(524\) 243.643i 0.464967i
\(525\) 218.576 236.160i 0.416336 0.449828i
\(526\) −581.989 −1.10644
\(527\) −290.288 290.288i −0.550831 0.550831i
\(528\) −17.8430 + 17.8430i −0.0337936 + 0.0337936i
\(529\) 23.0000i 0.0434783i
\(530\) −106.709 244.163i −0.201337 0.460685i
\(531\) 132.172 0.248911
\(532\) 35.4545 + 35.4545i 0.0666438 + 0.0666438i
\(533\) −347.830 + 347.830i −0.652589 + 0.652589i
\(534\) 269.443i 0.504575i
\(535\) 112.682 287.637i 0.210621 0.537639i
\(536\) −351.085 −0.655009
\(537\) 218.284 + 218.284i 0.406488 + 0.406488i
\(538\) 82.3667 82.3667i 0.153098 0.153098i
\(539\) 22.6727i 0.0420644i
\(540\) −48.3815 18.9535i −0.0895953 0.0350991i
\(541\) 828.433 1.53130 0.765650 0.643258i \(-0.222418\pi\)
0.765650 + 0.643258i \(0.222418\pi\)
\(542\) 397.792 + 397.792i 0.733933 + 0.733933i
\(543\) −131.531 + 131.531i −0.242231 + 0.242231i
\(544\) 117.250i 0.215533i
\(545\) 20.1171 8.79196i 0.0369122 0.0161320i
\(546\) −189.388 −0.346865
\(547\) 427.144 + 427.144i 0.780885 + 0.780885i 0.979980 0.199095i \(-0.0638003\pi\)
−0.199095 + 0.979980i \(0.563800\pi\)
\(548\) 245.457 245.457i 0.447915 0.447915i
\(549\) 113.755i 0.207203i
\(550\) 128.675 4.97548i 0.233954 0.00904633i
\(551\) 4.15836 0.00754692
\(552\) 16.6132 + 16.6132i 0.0300965 + 0.0300965i
\(553\) −141.517 + 141.517i −0.255907 + 0.255907i
\(554\) 206.534i 0.372804i
\(555\) 30.2330 + 69.1771i 0.0544740 + 0.124643i
\(556\) 15.1696 0.0272834
\(557\) 49.8244 + 49.8244i 0.0894514 + 0.0894514i 0.750417 0.660965i \(-0.229853\pi\)
−0.660965 + 0.750417i \(0.729853\pi\)
\(558\) −59.4193 + 59.4193i −0.106486 + 0.106486i
\(559\) 523.517i 0.936524i
\(560\) 54.2132 138.387i 0.0968093 0.247119i
\(561\) −130.756 −0.233076
\(562\) −355.895 355.895i −0.633264 0.633264i
\(563\) 669.424 669.424i 1.18903 1.18903i 0.211695 0.977336i \(-0.432102\pi\)
0.977336 0.211695i \(-0.0678983\pi\)
\(564\) 162.733i 0.288533i
\(565\) 453.091 + 177.499i 0.801931 + 0.314157i
\(566\) −162.989 −0.287967
\(567\) 47.2928 + 47.2928i 0.0834089 + 0.0834089i
\(568\) 15.5487 15.5487i 0.0273744 0.0273744i
\(569\) 1024.87i 1.80118i −0.434671 0.900589i \(-0.643135\pi\)
0.434671 0.900589i \(-0.356865\pi\)
\(570\) −37.8597 + 16.5462i −0.0664206 + 0.0290284i
\(571\) 900.323 1.57675 0.788374 0.615197i \(-0.210923\pi\)
0.788374 + 0.615197i \(0.210923\pi\)
\(572\) −53.5905 53.5905i −0.0936897 0.0936897i
\(573\) −146.995 + 146.995i −0.256536 + 0.256536i
\(574\) 496.884i 0.865652i
\(575\) −4.63256 119.806i −0.00805662 0.208359i
\(576\) −24.0000 −0.0416667
\(577\) 509.691 + 509.691i 0.883346 + 0.883346i 0.993873 0.110527i \(-0.0352539\pi\)
−0.110527 + 0.993873i \(0.535254\pi\)
\(578\) 140.610 140.610i 0.243271 0.243271i
\(579\) 126.240i 0.218031i
\(580\) −4.93624 11.2948i −0.00851076 0.0194737i
\(581\) 18.8748 0.0324868
\(582\) −2.99926 2.99926i −0.00515337 0.00515337i
\(583\) −97.0509 + 97.0509i −0.166468 + 0.166468i
\(584\) 235.190i 0.402723i
\(585\) 56.9257 145.311i 0.0973089 0.248395i
\(586\) 102.494 0.174905
\(587\) −240.945 240.945i −0.410468 0.410468i 0.471433 0.881902i \(-0.343737\pi\)
−0.881902 + 0.471433i \(0.843737\pi\)
\(588\) −15.2481 + 15.2481i −0.0259321 + 0.0259321i
\(589\) 66.8182i 0.113443i
\(590\) −290.067 113.634i −0.491639 0.192600i
\(591\) −50.2776 −0.0850721
\(592\) 24.6566 + 24.6566i 0.0416496 + 0.0416496i
\(593\) −205.486 + 205.486i −0.346519 + 0.346519i −0.858811 0.512292i \(-0.828797\pi\)
0.512292 + 0.858811i \(0.328797\pi\)
\(594\) 26.7646i 0.0450582i
\(595\) 705.698 308.417i 1.18605 0.518348i
\(596\) 442.571 0.742568
\(597\) −320.158 320.158i −0.536279 0.536279i
\(598\) −49.8969 + 49.8969i −0.0834397 + 0.0834397i
\(599\) 902.715i 1.50704i −0.657426 0.753519i \(-0.728355\pi\)
0.657426 0.753519i \(-0.271645\pi\)
\(600\) 89.8840 + 83.1917i 0.149807 + 0.138653i
\(601\) −267.744 −0.445497 −0.222749 0.974876i \(-0.571503\pi\)
−0.222749 + 0.974876i \(0.571503\pi\)
\(602\) −373.929 373.929i −0.621144 0.621144i
\(603\) −263.314 + 263.314i −0.436673 + 0.436673i
\(604\) 9.15715i 0.0151608i
\(605\) 215.719 + 493.592i 0.356560 + 0.815855i
\(606\) −329.534 −0.543786
\(607\) 438.783 + 438.783i 0.722871 + 0.722871i 0.969189 0.246318i \(-0.0792207\pi\)
−0.246318 + 0.969189i \(0.579221\pi\)
\(608\) −13.4942 + 13.4942i −0.0221945 + 0.0221945i
\(609\) 15.8658i 0.0260522i
\(610\) 97.8002 249.649i 0.160328 0.409260i
\(611\) −488.759 −0.799932
\(612\) −87.9374 87.9374i −0.143689 0.143689i
\(613\) 152.241 152.241i 0.248354 0.248354i −0.571941 0.820295i \(-0.693809\pi\)
0.820295 + 0.571941i \(0.193809\pi\)
\(614\) 268.524i 0.437336i
\(615\) −381.241 149.352i −0.619905 0.242848i
\(616\) −76.5554 −0.124278
\(617\) 451.575 + 451.575i 0.731888 + 0.731888i 0.970994 0.239105i \(-0.0768541\pi\)
−0.239105 + 0.970994i \(0.576854\pi\)
\(618\) 148.283 148.283i 0.239940 0.239940i
\(619\) 579.724i 0.936550i −0.883583 0.468275i \(-0.844876\pi\)
0.883583 0.468275i \(-0.155124\pi\)
\(620\) 181.489 79.3176i 0.292724 0.127932i
\(621\) 24.9199 0.0401286
\(622\) −287.922 287.922i −0.462897 0.462897i
\(623\) 578.022 578.022i 0.927805 0.927805i
\(624\) 72.0826i 0.115517i
\(625\) −48.2617 623.134i −0.0772187 0.997014i
\(626\) 230.566 0.368316
\(627\) 15.0486 + 15.0486i 0.0240010 + 0.0240010i
\(628\) 39.0728 39.0728i 0.0622179 0.0622179i
\(629\) 180.686i 0.287260i
\(630\) −63.1302 144.450i −0.100207 0.229286i
\(631\) −708.881 −1.12342 −0.561712 0.827333i \(-0.689857\pi\)
−0.561712 + 0.827333i \(0.689857\pi\)
\(632\) −53.8623 53.8623i −0.0852252 0.0852252i
\(633\) −263.894 + 263.894i −0.416894 + 0.416894i
\(634\) 181.016i 0.285514i
\(635\) −34.6469 + 88.4411i −0.0545621 + 0.139277i
\(636\) −130.539 −0.205251
\(637\) −45.7968 45.7968i −0.0718945 0.0718945i
\(638\) −4.48948 + 4.48948i −0.00703681 + 0.00703681i
\(639\) 23.3230i 0.0364992i
\(640\) 52.6711 + 20.6339i 0.0822985 + 0.0322405i
\(641\) 1062.59 1.65770 0.828852 0.559468i \(-0.188995\pi\)
0.828852 + 0.559468i \(0.188995\pi\)
\(642\) −107.013 107.013i −0.166687 0.166687i
\(643\) −686.400 + 686.400i −1.06750 + 1.06750i −0.0699458 + 0.997551i \(0.522283\pi\)
−0.997551 + 0.0699458i \(0.977717\pi\)
\(644\) 71.2790i 0.110682i
\(645\) 399.296 174.508i 0.619064 0.270555i
\(646\) −98.8874 −0.153076
\(647\) −229.470 229.470i −0.354668 0.354668i 0.507175 0.861843i \(-0.330690\pi\)
−0.861843 + 0.507175i \(0.830690\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 160.465i 0.247249i
\(650\) −249.862 + 269.962i −0.384402 + 0.415325i
\(651\) −254.938 −0.391610
\(652\) 192.666 + 192.666i 0.295500 + 0.295500i
\(653\) 372.281 372.281i 0.570109 0.570109i −0.362050 0.932159i \(-0.617923\pi\)
0.932159 + 0.362050i \(0.117923\pi\)
\(654\) 10.7554i 0.0164456i
\(655\) 243.925 + 558.133i 0.372405 + 0.852111i
\(656\) −189.118 −0.288289
\(657\) 176.393 + 176.393i 0.268482 + 0.268482i
\(658\) −349.102 + 349.102i −0.530550 + 0.530550i
\(659\) 78.1061i 0.118522i 0.998243 + 0.0592611i \(0.0188744\pi\)
−0.998243 + 0.0592611i \(0.981126\pi\)
\(660\) 23.0108 58.7382i 0.0348648 0.0889973i
\(661\) −79.4275 −0.120163 −0.0600813 0.998193i \(-0.519136\pi\)
−0.0600813 + 0.998193i \(0.519136\pi\)
\(662\) 225.894 + 225.894i 0.341229 + 0.341229i
\(663\) 264.115 264.115i 0.398363 0.398363i
\(664\) 7.18390i 0.0108191i
\(665\) −116.714 45.7229i −0.175510 0.0687562i
\(666\) 36.9849 0.0555329
\(667\) 4.18006 + 4.18006i 0.00626695 + 0.00626695i
\(668\) 323.352 323.352i 0.484060 0.484060i
\(669\) 404.821i 0.605113i
\(670\) 804.259 351.492i 1.20039 0.524615i
\(671\) −138.105 −0.205820
\(672\) −51.4859 51.4859i −0.0766160 0.0766160i
\(673\) −726.361 + 726.361i −1.07929 + 1.07929i −0.0827151 + 0.996573i \(0.526359\pi\)
−0.996573 + 0.0827151i \(0.973641\pi\)
\(674\) 164.199i 0.243618i
\(675\) 129.807 5.01925i 0.192306 0.00743592i
\(676\) −121.504 −0.179740
\(677\) 335.914 + 335.914i 0.496180 + 0.496180i 0.910247 0.414067i \(-0.135892\pi\)
−0.414067 + 0.910247i \(0.635892\pi\)
\(678\) 168.570 168.570i 0.248628 0.248628i
\(679\) 12.8683i 0.0189519i
\(680\) 117.386 + 268.594i 0.172626 + 0.394991i
\(681\) −436.806 −0.641419
\(682\) −72.1389 72.1389i −0.105775 0.105775i
\(683\) −188.131 + 188.131i −0.275448 + 0.275448i −0.831289 0.555841i \(-0.812396\pi\)
0.555841 + 0.831289i \(0.312396\pi\)
\(684\) 20.2414i 0.0295926i
\(685\) −316.547 + 808.031i −0.462112 + 1.17961i
\(686\) 449.545 0.655313
\(687\) −61.9744 61.9744i −0.0902102 0.0902102i
\(688\) 142.320 142.320i 0.206860 0.206860i
\(689\) 392.068i 0.569039i
\(690\) −54.6898 21.4248i −0.0792606 0.0310504i
\(691\) −729.123 −1.05517 −0.527585 0.849502i \(-0.676902\pi\)
−0.527585 + 0.849502i \(0.676902\pi\)
\(692\) 343.170 + 343.170i 0.495910 + 0.495910i
\(693\) −57.4166 + 57.4166i −0.0828522 + 0.0828522i
\(694\) 328.748i 0.473701i
\(695\) −34.7502 + 15.1872i −0.0500002 + 0.0218520i
\(696\) −6.03864 −0.00867620
\(697\) −692.939 692.939i −0.994173 0.994173i
\(698\) −130.319 + 130.319i −0.186704 + 0.186704i
\(699\) 32.4987i 0.0464932i
\(700\) 14.3567 + 371.290i 0.0205096 + 0.530415i
\(701\) 616.629 0.879642 0.439821 0.898085i \(-0.355042\pi\)
0.439821 + 0.898085i \(0.355042\pi\)
\(702\) −54.0620 54.0620i −0.0770113 0.0770113i
\(703\) 20.7951 20.7951i 0.0295805 0.0295805i
\(704\) 29.1376i 0.0413886i
\(705\) −162.922 372.785i −0.231094 0.528774i
\(706\) −369.852 −0.523869
\(707\) −706.932 706.932i −0.999904 0.999904i
\(708\) −107.918 + 107.918i −0.152426 + 0.152426i
\(709\) 446.810i 0.630197i 0.949059 + 0.315099i \(0.102038\pi\)
−0.949059 + 0.315099i \(0.897962\pi\)
\(710\) −20.0519 + 51.1852i −0.0282421 + 0.0720919i
\(711\) −80.7935 −0.113634
\(712\) 219.999 + 219.999i 0.308988 + 0.308988i
\(713\) −67.1669 + 67.1669i −0.0942032 + 0.0942032i
\(714\) 377.295i 0.528424i
\(715\) 176.417 + 69.1115i 0.246737 + 0.0966595i
\(716\) −356.456 −0.497844
\(717\) −412.564 412.564i −0.575403 0.575403i
\(718\) 211.235 211.235i 0.294199 0.294199i
\(719\) 359.922i 0.500587i −0.968170 0.250294i \(-0.919473\pi\)
0.968170 0.250294i \(-0.0805272\pi\)
\(720\) 54.9788 24.0278i 0.0763594 0.0333720i
\(721\) 636.207 0.882395
\(722\) −349.619 349.619i −0.484237 0.484237i
\(723\) −427.706 + 427.706i −0.591571 + 0.591571i
\(724\) 214.790i 0.296671i
\(725\) 22.6157 + 20.9319i 0.0311941 + 0.0288715i
\(726\) 263.894 0.363491
\(727\) −541.443 541.443i −0.744764 0.744764i 0.228727 0.973491i \(-0.426544\pi\)
−0.973491 + 0.228727i \(0.926544\pi\)
\(728\) 154.635 154.635i 0.212411 0.212411i
\(729\) 27.0000i 0.0370370i
\(730\) −235.463 538.770i −0.322552 0.738041i
\(731\) 1042.94 1.42673
\(732\) −92.8802 92.8802i −0.126885 0.126885i
\(733\) 283.315 283.315i 0.386515 0.386515i −0.486928 0.873442i \(-0.661882\pi\)
0.873442 + 0.486928i \(0.161882\pi\)
\(734\) 768.066i 1.04641i
\(735\) 19.6643 50.1958i 0.0267541 0.0682936i
\(736\) −27.1293 −0.0368605
\(737\) −319.680 319.680i −0.433758 0.433758i
\(738\) −141.838 + 141.838i −0.192193 + 0.192193i
\(739\) 514.041i 0.695591i −0.937571 0.347795i \(-0.886930\pi\)
0.937571 0.347795i \(-0.113070\pi\)
\(740\) −81.1680 31.7977i −0.109687 0.0429698i
\(741\) −60.7938 −0.0820429
\(742\) −280.039 280.039i −0.377412 0.377412i
\(743\) 229.186 229.186i 0.308460 0.308460i −0.535852 0.844312i \(-0.680009\pi\)
0.844312 + 0.535852i \(0.180009\pi\)
\(744\) 97.0313i 0.130418i
\(745\) −1013.83 + 443.084i −1.36085 + 0.594744i
\(746\) 417.528 0.559689
\(747\) 5.38792 + 5.38792i 0.00721275 + 0.00721275i
\(748\) 106.762 106.762i 0.142730 0.142730i
\(749\) 459.140i 0.613004i
\(750\) −289.193 100.586i −0.385590 0.134114i
\(751\) 208.038 0.277014 0.138507 0.990361i \(-0.455770\pi\)
0.138507 + 0.990361i \(0.455770\pi\)
\(752\) −132.871 132.871i −0.176690 0.176690i
\(753\) −503.172 + 503.172i −0.668223 + 0.668223i
\(754\) 18.1367i 0.0240540i
\(755\) −9.16777 20.9770i −0.0121427 0.0277841i
\(756\) −77.2289 −0.102155
\(757\) 630.839 + 630.839i 0.833340 + 0.833340i 0.987972 0.154632i \(-0.0494191\pi\)
−0.154632 + 0.987972i \(0.549419\pi\)
\(758\) 706.994 706.994i 0.932709 0.932709i
\(759\) 30.2543i 0.0398608i
\(760\) 17.4025 44.4222i 0.0228980 0.0584503i
\(761\) −76.3458 −0.100323 −0.0501615 0.998741i \(-0.515974\pi\)
−0.0501615 + 0.998741i \(0.515974\pi\)
\(762\) 32.9039 + 32.9039i 0.0431810 + 0.0431810i
\(763\) 23.0731 23.0731i 0.0302399 0.0302399i
\(764\) 240.042i 0.314191i
\(765\) 289.485 + 113.406i 0.378411 + 0.148243i
\(766\) −799.912 −1.04427
\(767\) −324.124 324.124i −0.422587 0.422587i
\(768\) 19.5959 19.5959i 0.0255155 0.0255155i
\(769\) 975.201i 1.26814i −0.773275 0.634071i \(-0.781383\pi\)
0.773275 0.634071i \(-0.218617\pi\)
\(770\) 175.372 76.6442i 0.227756 0.0995379i
\(771\) −277.778 −0.360283
\(772\) 103.075 + 103.075i 0.133516 + 0.133516i
\(773\) −660.918 + 660.918i −0.855004 + 0.855004i −0.990744 0.135740i \(-0.956659\pi\)
0.135740 + 0.990744i \(0.456659\pi\)
\(774\) 213.480i 0.275814i
\(775\) −336.342 + 363.399i −0.433989 + 0.468901i
\(776\) 4.89777 0.00631156
\(777\) 79.3417 + 79.3417i 0.102113 + 0.102113i
\(778\) −174.609 + 174.609i −0.224434 + 0.224434i