Properties

Label 600.2.k.f.301.11
Level 600
Weight 2
Character 600.301
Analytic conductor 4.791
Analytic rank 0
Dimension 12
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 600.k (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.79102412128\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: 12.0.180227832610816.1
Defining polynomial: \(x^{12} + x^{10} - 8 x^{6} + 16 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 301.11
Root \(1.37729 - 0.321037i\) of defining polynomial
Character \(\chi\) \(=\) 600.301
Dual form 600.2.k.f.301.12

$q$-expansion

\(f(q)\) \(=\) \(q+(1.37729 - 0.321037i) q^{2} -1.00000i q^{3} +(1.79387 - 0.884323i) q^{4} +(-0.321037 - 1.37729i) q^{6} +4.05705 q^{7} +(2.18678 - 1.79387i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(1.37729 - 0.321037i) q^{2} -1.00000i q^{3} +(1.79387 - 0.884323i) q^{4} +(-0.321037 - 1.37729i) q^{6} +4.05705 q^{7} +(2.18678 - 1.79387i) q^{8} -1.00000 q^{9} +0.985939i q^{11} +(-0.884323 - 1.79387i) q^{12} +4.94567i q^{13} +(5.58774 - 1.30246i) q^{14} +(2.43594 - 3.17272i) q^{16} -4.52323 q^{17} +(-1.37729 + 0.321037i) q^{18} -2.60492i q^{19} -4.05705i q^{21} +(0.316523 + 1.35793i) q^{22} -3.53729 q^{23} +(-1.79387 - 2.18678i) q^{24} +(1.58774 + 6.81163i) q^{26} +1.00000i q^{27} +(7.27782 - 3.58774i) q^{28} -7.59434i q^{29} -3.28415 q^{31} +(2.33645 - 5.15180i) q^{32} +0.985939 q^{33} +(-6.22982 + 1.45212i) q^{34} +(-1.79387 + 0.884323i) q^{36} +0.945668i q^{37} +(-0.836276 - 3.58774i) q^{38} +4.94567 q^{39} +0.568295 q^{41} +(-1.30246 - 5.58774i) q^{42} +8.45963i q^{43} +(0.871889 + 1.76865i) q^{44} +(-4.87189 + 1.13560i) q^{46} -2.60492 q^{47} +(-3.17272 - 2.43594i) q^{48} +9.45963 q^{49} +4.52323i q^{51} +(4.37357 + 8.87189i) q^{52} +0.229815i q^{53} +(0.321037 + 1.37729i) q^{54} +(8.87189 - 7.27782i) q^{56} -2.60492 q^{57} +(-2.43806 - 10.4596i) q^{58} +9.10003i q^{59} -11.0183i q^{61} +(-4.52323 + 1.05433i) q^{62} -4.05705 q^{63} +(1.56406 - 7.84562i) q^{64} +(1.35793 - 0.316523i) q^{66} +8.45963i q^{67} +(-8.11409 + 4.00000i) q^{68} +3.53729i q^{69} +1.43171 q^{71} +(-2.18678 + 1.79387i) q^{72} -11.9507 q^{73} +(0.303594 + 1.30246i) q^{74} +(-2.30359 - 4.67289i) q^{76} +4.00000i q^{77} +(6.81163 - 1.58774i) q^{78} -3.28415 q^{79} +1.00000 q^{81} +(0.782708 - 0.182443i) q^{82} +9.89134i q^{83} +(-3.58774 - 7.27782i) q^{84} +(2.71585 + 11.6514i) q^{86} -7.59434 q^{87} +(1.76865 + 2.15604i) q^{88} -12.3510 q^{89} +20.0648i q^{91} +(-6.34545 + 3.12811i) q^{92} +3.28415i q^{93} +(-3.58774 + 0.836276i) q^{94} +(-5.15180 - 2.33645i) q^{96} +3.23797 q^{97} +(13.0287 - 3.03689i) q^{98} -0.985939i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{4} - 2q^{6} - 12q^{9} + O(q^{10}) \) \( 12q - 2q^{4} - 2q^{6} - 12q^{9} + 20q^{14} + 2q^{16} + 2q^{24} - 28q^{26} - 32q^{31} - 24q^{34} + 2q^{36} + 16q^{39} - 8q^{41} - 44q^{44} - 4q^{46} + 12q^{49} + 2q^{54} + 52q^{56} + 46q^{64} + 20q^{66} + 32q^{71} - 36q^{74} + 12q^{76} - 32q^{79} + 12q^{81} + 4q^{84} + 40q^{86} + 40q^{89} + 4q^{94} - 42q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).

\(n\) \(151\) \(301\) \(401\) \(577\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.37729 0.321037i 0.973893 0.227007i
\(3\) 1.00000i 0.577350i
\(4\) 1.79387 0.884323i 0.896935 0.442162i
\(5\) 0 0
\(6\) −0.321037 1.37729i −0.131063 0.562277i
\(7\) 4.05705 1.53342 0.766710 0.641994i \(-0.221893\pi\)
0.766710 + 0.641994i \(0.221893\pi\)
\(8\) 2.18678 1.79387i 0.773145 0.634229i
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 0.985939i 0.297272i 0.988892 + 0.148636i \(0.0474882\pi\)
−0.988892 + 0.148636i \(0.952512\pi\)
\(12\) −0.884323 1.79387i −0.255282 0.517846i
\(13\) 4.94567i 1.37168i 0.727752 + 0.685841i \(0.240565\pi\)
−0.727752 + 0.685841i \(0.759435\pi\)
\(14\) 5.58774 1.30246i 1.49339 0.348097i
\(15\) 0 0
\(16\) 2.43594 3.17272i 0.608986 0.793181i
\(17\) −4.52323 −1.09704 −0.548522 0.836136i \(-0.684809\pi\)
−0.548522 + 0.836136i \(0.684809\pi\)
\(18\) −1.37729 + 0.321037i −0.324631 + 0.0756691i
\(19\) 2.60492i 0.597610i −0.954314 0.298805i \(-0.903412\pi\)
0.954314 0.298805i \(-0.0965881\pi\)
\(20\) 0 0
\(21\) 4.05705i 0.885320i
\(22\) 0.316523 + 1.35793i 0.0674829 + 0.289511i
\(23\) −3.53729 −0.737577 −0.368788 0.929513i \(-0.620227\pi\)
−0.368788 + 0.929513i \(0.620227\pi\)
\(24\) −1.79387 2.18678i −0.366172 0.446376i
\(25\) 0 0
\(26\) 1.58774 + 6.81163i 0.311382 + 1.33587i
\(27\) 1.00000i 0.192450i
\(28\) 7.27782 3.58774i 1.37538 0.678019i
\(29\) 7.59434i 1.41023i −0.709091 0.705117i \(-0.750895\pi\)
0.709091 0.705117i \(-0.249105\pi\)
\(30\) 0 0
\(31\) −3.28415 −0.589850 −0.294925 0.955520i \(-0.595295\pi\)
−0.294925 + 0.955520i \(0.595295\pi\)
\(32\) 2.33645 5.15180i 0.413029 0.910718i
\(33\) 0.985939 0.171630
\(34\) −6.22982 + 1.45212i −1.06840 + 0.249037i
\(35\) 0 0
\(36\) −1.79387 + 0.884323i −0.298978 + 0.147387i
\(37\) 0.945668i 0.155467i 0.996974 + 0.0777334i \(0.0247683\pi\)
−0.996974 + 0.0777334i \(0.975232\pi\)
\(38\) −0.836276 3.58774i −0.135662 0.582009i
\(39\) 4.94567 0.791941
\(40\) 0 0
\(41\) 0.568295 0.0887527 0.0443763 0.999015i \(-0.485870\pi\)
0.0443763 + 0.999015i \(0.485870\pi\)
\(42\) −1.30246 5.58774i −0.200974 0.862207i
\(43\) 8.45963i 1.29008i 0.764148 + 0.645041i \(0.223160\pi\)
−0.764148 + 0.645041i \(0.776840\pi\)
\(44\) 0.871889 + 1.76865i 0.131442 + 0.266634i
\(45\) 0 0
\(46\) −4.87189 + 1.13560i −0.718321 + 0.167435i
\(47\) −2.60492 −0.379967 −0.189984 0.981787i \(-0.560843\pi\)
−0.189984 + 0.981787i \(0.560843\pi\)
\(48\) −3.17272 2.43594i −0.457943 0.351598i
\(49\) 9.45963 1.35138
\(50\) 0 0
\(51\) 4.52323i 0.633379i
\(52\) 4.37357 + 8.87189i 0.606505 + 1.23031i
\(53\) 0.229815i 0.0315675i 0.999875 + 0.0157838i \(0.00502434\pi\)
−0.999875 + 0.0157838i \(0.994976\pi\)
\(54\) 0.321037 + 1.37729i 0.0436876 + 0.187426i
\(55\) 0 0
\(56\) 8.87189 7.27782i 1.18556 0.972539i
\(57\) −2.60492 −0.345030
\(58\) −2.43806 10.4596i −0.320133 1.37342i
\(59\) 9.10003i 1.18472i 0.805672 + 0.592362i \(0.201804\pi\)
−0.805672 + 0.592362i \(0.798196\pi\)
\(60\) 0 0
\(61\) 11.0183i 1.41075i −0.708832 0.705377i \(-0.750778\pi\)
0.708832 0.705377i \(-0.249222\pi\)
\(62\) −4.52323 + 1.05433i −0.574451 + 0.133900i
\(63\) −4.05705 −0.511140
\(64\) 1.56406 7.84562i 0.195507 0.980702i
\(65\) 0 0
\(66\) 1.35793 0.316523i 0.167149 0.0389612i
\(67\) 8.45963i 1.03351i 0.856134 + 0.516754i \(0.172860\pi\)
−0.856134 + 0.516754i \(0.827140\pi\)
\(68\) −8.11409 + 4.00000i −0.983978 + 0.485071i
\(69\) 3.53729i 0.425840i
\(70\) 0 0
\(71\) 1.43171 0.169912 0.0849561 0.996385i \(-0.472925\pi\)
0.0849561 + 0.996385i \(0.472925\pi\)
\(72\) −2.18678 + 1.79387i −0.257715 + 0.211410i
\(73\) −11.9507 −1.39873 −0.699363 0.714767i \(-0.746533\pi\)
−0.699363 + 0.714767i \(0.746533\pi\)
\(74\) 0.303594 + 1.30246i 0.0352921 + 0.151408i
\(75\) 0 0
\(76\) −2.30359 4.67289i −0.264240 0.536018i
\(77\) 4.00000i 0.455842i
\(78\) 6.81163 1.58774i 0.771266 0.179776i
\(79\) −3.28415 −0.369495 −0.184748 0.982786i \(-0.559147\pi\)
−0.184748 + 0.982786i \(0.559147\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0.782708 0.182443i 0.0864356 0.0201475i
\(83\) 9.89134i 1.08572i 0.839825 + 0.542858i \(0.182658\pi\)
−0.839825 + 0.542858i \(0.817342\pi\)
\(84\) −3.58774 7.27782i −0.391455 0.794075i
\(85\) 0 0
\(86\) 2.71585 + 11.6514i 0.292858 + 1.25640i
\(87\) −7.59434 −0.814199
\(88\) 1.76865 + 2.15604i 0.188538 + 0.229834i
\(89\) −12.3510 −1.30920 −0.654600 0.755976i \(-0.727163\pi\)
−0.654600 + 0.755976i \(0.727163\pi\)
\(90\) 0 0
\(91\) 20.0648i 2.10336i
\(92\) −6.34545 + 3.12811i −0.661559 + 0.326128i
\(93\) 3.28415i 0.340550i
\(94\) −3.58774 + 0.836276i −0.370047 + 0.0862553i
\(95\) 0 0
\(96\) −5.15180 2.33645i −0.525803 0.238463i
\(97\) 3.23797 0.328766 0.164383 0.986397i \(-0.447437\pi\)
0.164383 + 0.986397i \(0.447437\pi\)
\(98\) 13.0287 3.03689i 1.31610 0.306772i
\(99\) 0.985939i 0.0990906i
\(100\) 0 0
\(101\) 4.35637i 0.433475i −0.976230 0.216738i \(-0.930458\pi\)
0.976230 0.216738i \(-0.0695416\pi\)
\(102\) 1.45212 + 6.22982i 0.143782 + 0.616844i
\(103\) 15.0754 1.48542 0.742711 0.669612i \(-0.233540\pi\)
0.742711 + 0.669612i \(0.233540\pi\)
\(104\) 8.87189 + 10.8151i 0.869960 + 1.06051i
\(105\) 0 0
\(106\) 0.0737791 + 0.316523i 0.00716606 + 0.0307434i
\(107\) 4.00000i 0.386695i −0.981130 0.193347i \(-0.938066\pi\)
0.981130 0.193347i \(-0.0619344\pi\)
\(108\) 0.884323 + 1.79387i 0.0850941 + 0.172615i
\(109\) 4.17034i 0.399446i 0.979852 + 0.199723i \(0.0640042\pi\)
−0.979852 + 0.199723i \(0.935996\pi\)
\(110\) 0 0
\(111\) 0.945668 0.0897588
\(112\) 9.88274 12.8719i 0.933831 1.21628i
\(113\) 1.28526 0.120907 0.0604537 0.998171i \(-0.480745\pi\)
0.0604537 + 0.998171i \(0.480745\pi\)
\(114\) −3.58774 + 0.836276i −0.336023 + 0.0783244i
\(115\) 0 0
\(116\) −6.71585 13.6233i −0.623551 1.26489i
\(117\) 4.94567i 0.457227i
\(118\) 2.92145 + 12.5334i 0.268941 + 1.15379i
\(119\) −18.3510 −1.68223
\(120\) 0 0
\(121\) 10.0279 0.911630
\(122\) −3.53729 15.1755i −0.320252 1.37392i
\(123\) 0.568295i 0.0512414i
\(124\) −5.89134 + 2.90425i −0.529058 + 0.260809i
\(125\) 0 0
\(126\) −5.58774 + 1.30246i −0.497796 + 0.116032i
\(127\) 1.15280 0.102294 0.0511472 0.998691i \(-0.483712\pi\)
0.0511472 + 0.998691i \(0.483712\pi\)
\(128\) −0.364570 11.3078i −0.0322237 0.999481i
\(129\) 8.45963 0.744829
\(130\) 0 0
\(131\) 3.89019i 0.339887i 0.985454 + 0.169944i \(0.0543586\pi\)
−0.985454 + 0.169944i \(0.945641\pi\)
\(132\) 1.76865 0.871889i 0.153941 0.0758882i
\(133\) 10.5683i 0.916387i
\(134\) 2.71585 + 11.6514i 0.234614 + 1.00653i
\(135\) 0 0
\(136\) −9.89134 + 8.11409i −0.848175 + 0.695778i
\(137\) 17.5135 1.49628 0.748138 0.663544i \(-0.230948\pi\)
0.748138 + 0.663544i \(0.230948\pi\)
\(138\) 1.13560 + 4.87189i 0.0966688 + 0.414723i
\(139\) 16.8612i 1.43015i 0.699047 + 0.715076i \(0.253608\pi\)
−0.699047 + 0.715076i \(0.746392\pi\)
\(140\) 0 0
\(141\) 2.60492i 0.219374i
\(142\) 1.97188 0.459630i 0.165476 0.0385713i
\(143\) −4.87613 −0.407762
\(144\) −2.43594 + 3.17272i −0.202995 + 0.264394i
\(145\) 0 0
\(146\) −16.4596 + 3.83662i −1.36221 + 0.317521i
\(147\) 9.45963i 0.780217i
\(148\) 0.836276 + 1.69641i 0.0687415 + 0.139444i
\(149\) 10.4986i 0.860078i −0.902810 0.430039i \(-0.858500\pi\)
0.902810 0.430039i \(-0.141500\pi\)
\(150\) 0 0
\(151\) 4.71585 0.383771 0.191885 0.981417i \(-0.438540\pi\)
0.191885 + 0.981417i \(0.438540\pi\)
\(152\) −4.67289 5.69641i −0.379022 0.462040i
\(153\) 4.52323 0.365682
\(154\) 1.28415 + 5.50917i 0.103480 + 0.443942i
\(155\) 0 0
\(156\) 8.87189 4.37357i 0.710320 0.350166i
\(157\) 8.94567i 0.713942i 0.934115 + 0.356971i \(0.116191\pi\)
−0.934115 + 0.356971i \(0.883809\pi\)
\(158\) −4.52323 + 1.05433i −0.359849 + 0.0838782i
\(159\) 0.229815 0.0182255
\(160\) 0 0
\(161\) −14.3510 −1.13101
\(162\) 1.37729 0.321037i 0.108210 0.0252230i
\(163\) 15.7827i 1.23619i −0.786102 0.618097i \(-0.787904\pi\)
0.786102 0.618097i \(-0.212096\pi\)
\(164\) 1.01945 0.502556i 0.0796054 0.0392430i
\(165\) 0 0
\(166\) 3.17548 + 13.6233i 0.246465 + 1.05737i
\(167\) −5.50917 −0.426312 −0.213156 0.977018i \(-0.568374\pi\)
−0.213156 + 0.977018i \(0.568374\pi\)
\(168\) −7.27782 8.87189i −0.561496 0.684481i
\(169\) −11.4596 −0.881510
\(170\) 0 0
\(171\) 2.60492i 0.199203i
\(172\) 7.48105 + 15.1755i 0.570425 + 1.15712i
\(173\) 10.3385i 0.786020i 0.919534 + 0.393010i \(0.128566\pi\)
−0.919534 + 0.393010i \(0.871434\pi\)
\(174\) −10.4596 + 2.43806i −0.792943 + 0.184829i
\(175\) 0 0
\(176\) 3.12811 + 2.40169i 0.235790 + 0.181034i
\(177\) 9.10003 0.684000
\(178\) −17.0109 + 3.96511i −1.27502 + 0.297198i
\(179\) 16.1746i 1.20895i −0.796625 0.604474i \(-0.793383\pi\)
0.796625 0.604474i \(-0.206617\pi\)
\(180\) 0 0
\(181\) 8.11409i 0.603116i −0.953448 0.301558i \(-0.902493\pi\)
0.953448 0.301558i \(-0.0975067\pi\)
\(182\) 6.44154 + 27.6351i 0.477479 + 2.04845i
\(183\) −11.0183 −0.814499
\(184\) −7.73530 + 6.34545i −0.570254 + 0.467793i
\(185\) 0 0
\(186\) 1.05433 + 4.52323i 0.0773074 + 0.331659i
\(187\) 4.45963i 0.326120i
\(188\) −4.67289 + 2.30359i −0.340806 + 0.168007i
\(189\) 4.05705i 0.295107i
\(190\) 0 0
\(191\) −24.9193 −1.80309 −0.901547 0.432681i \(-0.857568\pi\)
−0.901547 + 0.432681i \(0.857568\pi\)
\(192\) −7.84562 1.56406i −0.566209 0.112876i
\(193\) −1.03951 −0.0748254 −0.0374127 0.999300i \(-0.511912\pi\)
−0.0374127 + 0.999300i \(0.511912\pi\)
\(194\) 4.45963 1.03951i 0.320183 0.0746323i
\(195\) 0 0
\(196\) 16.9694 8.36537i 1.21210 0.597527i
\(197\) 9.66152i 0.688355i −0.938905 0.344177i \(-0.888158\pi\)
0.938905 0.344177i \(-0.111842\pi\)
\(198\) −0.316523 1.35793i −0.0224943 0.0965036i
\(199\) 23.0668 1.63516 0.817582 0.575813i \(-0.195314\pi\)
0.817582 + 0.575813i \(0.195314\pi\)
\(200\) 0 0
\(201\) 8.45963 0.596696
\(202\) −1.39856 6.00000i −0.0984020 0.422159i
\(203\) 30.8106i 2.16248i
\(204\) 4.00000 + 8.11409i 0.280056 + 0.568100i
\(205\) 0 0
\(206\) 20.7632 4.83975i 1.44664 0.337202i
\(207\) 3.53729 0.245859
\(208\) 15.6912 + 12.0474i 1.08799 + 0.835335i
\(209\) 2.56829 0.177653
\(210\) 0 0
\(211\) 6.44154i 0.443454i −0.975109 0.221727i \(-0.928831\pi\)
0.975109 0.221727i \(-0.0711694\pi\)
\(212\) 0.203231 + 0.412259i 0.0139580 + 0.0283140i
\(213\) 1.43171i 0.0980988i
\(214\) −1.28415 5.50917i −0.0877825 0.376599i
\(215\) 0 0
\(216\) 1.79387 + 2.18678i 0.122057 + 0.148792i
\(217\) −13.3239 −0.904488
\(218\) 1.33883 + 5.74378i 0.0906772 + 0.389018i
\(219\) 11.9507i 0.807554i
\(220\) 0 0
\(221\) 22.3704i 1.50480i
\(222\) 1.30246 0.303594i 0.0874155 0.0203759i
\(223\) 17.9796 1.20401 0.602003 0.798494i \(-0.294370\pi\)
0.602003 + 0.798494i \(0.294370\pi\)
\(224\) 9.47908 20.9011i 0.633347 1.39651i
\(225\) 0 0
\(226\) 1.77018 0.412617i 0.117751 0.0274469i
\(227\) 7.02792i 0.466460i −0.972422 0.233230i \(-0.925071\pi\)
0.972422 0.233230i \(-0.0749295\pi\)
\(228\) −4.67289 + 2.30359i −0.309470 + 0.152559i
\(229\) 4.17034i 0.275584i −0.990461 0.137792i \(-0.955999\pi\)
0.990461 0.137792i \(-0.0440005\pi\)
\(230\) 0 0
\(231\) 4.00000 0.263181
\(232\) −13.6233 16.6072i −0.894411 1.09032i
\(233\) 23.9894 1.57160 0.785799 0.618483i \(-0.212252\pi\)
0.785799 + 0.618483i \(0.212252\pi\)
\(234\) −1.58774 6.81163i −0.103794 0.445290i
\(235\) 0 0
\(236\) 8.04737 + 16.3243i 0.523839 + 1.06262i
\(237\) 3.28415i 0.213328i
\(238\) −25.2747 + 5.89134i −1.63831 + 0.381879i
\(239\) −8.91926 −0.576939 −0.288469 0.957489i \(-0.593146\pi\)
−0.288469 + 0.957489i \(0.593146\pi\)
\(240\) 0 0
\(241\) −16.3510 −1.05326 −0.526629 0.850095i \(-0.676544\pi\)
−0.526629 + 0.850095i \(0.676544\pi\)
\(242\) 13.8114 3.21933i 0.887830 0.206947i
\(243\) 1.00000i 0.0641500i
\(244\) −9.74378 19.7655i −0.623781 1.26536i
\(245\) 0 0
\(246\) −0.182443 0.782708i −0.0116322 0.0499036i
\(247\) 12.8831 0.819731
\(248\) −7.18172 + 5.89134i −0.456040 + 0.374100i
\(249\) 9.89134 0.626838
\(250\) 0 0
\(251\) 4.22391i 0.266611i 0.991075 + 0.133305i \(0.0425591\pi\)
−0.991075 + 0.133305i \(0.957441\pi\)
\(252\) −7.27782 + 3.58774i −0.458459 + 0.226006i
\(253\) 3.48755i 0.219261i
\(254\) 1.58774 0.370091i 0.0996238 0.0232216i
\(255\) 0 0
\(256\) −4.13235 15.4572i −0.258272 0.966072i
\(257\) −24.6952 −1.54044 −0.770221 0.637777i \(-0.779854\pi\)
−0.770221 + 0.637777i \(0.779854\pi\)
\(258\) 11.6514 2.71585i 0.725384 0.169082i
\(259\) 3.83662i 0.238396i
\(260\) 0 0
\(261\) 7.59434i 0.470078i
\(262\) 1.24889 + 5.35793i 0.0771569 + 0.331014i
\(263\) −14.6628 −0.904145 −0.452073 0.891981i \(-0.649315\pi\)
−0.452073 + 0.891981i \(0.649315\pi\)
\(264\) 2.15604 1.76865i 0.132695 0.108853i
\(265\) 0 0
\(266\) −3.39281 14.5556i −0.208027 0.892463i
\(267\) 12.3510i 0.755867i
\(268\) 7.48105 + 15.1755i 0.456978 + 0.926990i
\(269\) 11.5381i 0.703490i 0.936096 + 0.351745i \(0.114412\pi\)
−0.936096 + 0.351745i \(0.885588\pi\)
\(270\) 0 0
\(271\) 5.63511 0.342309 0.171154 0.985244i \(-0.445250\pi\)
0.171154 + 0.985244i \(0.445250\pi\)
\(272\) −11.0183 + 14.3510i −0.668085 + 0.870155i
\(273\) 20.0648 1.21438
\(274\) 24.1212 5.62246i 1.45721 0.339665i
\(275\) 0 0
\(276\) 3.12811 + 6.34545i 0.188290 + 0.381951i
\(277\) 17.4053i 1.04578i −0.852399 0.522892i \(-0.824853\pi\)
0.852399 0.522892i \(-0.175147\pi\)
\(278\) 5.41308 + 23.2229i 0.324655 + 1.39281i
\(279\) 3.28415 0.196617
\(280\) 0 0
\(281\) 21.7827 1.29945 0.649723 0.760171i \(-0.274885\pi\)
0.649723 + 0.760171i \(0.274885\pi\)
\(282\) 0.836276 + 3.58774i 0.0497995 + 0.213647i
\(283\) 21.5962i 1.28376i 0.766804 + 0.641881i \(0.221846\pi\)
−0.766804 + 0.641881i \(0.778154\pi\)
\(284\) 2.56829 1.26609i 0.152400 0.0751287i
\(285\) 0 0
\(286\) −6.71585 + 1.56542i −0.397117 + 0.0925650i
\(287\) 2.30560 0.136095
\(288\) −2.33645 + 5.15180i −0.137676 + 0.303573i
\(289\) 3.45963 0.203508
\(290\) 0 0
\(291\) 3.23797i 0.189813i
\(292\) −21.4380 + 10.5683i −1.25457 + 0.618463i
\(293\) 32.0125i 1.87019i −0.354398 0.935095i \(-0.615314\pi\)
0.354398 0.935095i \(-0.384686\pi\)
\(294\) −3.03689 13.0287i −0.177115 0.759848i
\(295\) 0 0
\(296\) 1.69641 + 2.06797i 0.0986016 + 0.120198i
\(297\) −0.985939 −0.0572100
\(298\) −3.37043 14.4596i −0.195244 0.837624i
\(299\) 17.4943i 1.01172i
\(300\) 0 0
\(301\) 34.3211i 1.97824i
\(302\) 6.49511 1.51396i 0.373752 0.0871187i
\(303\) −4.35637 −0.250267
\(304\) −8.26470 6.34545i −0.474013 0.363936i
\(305\) 0 0
\(306\) 6.22982 1.45212i 0.356135 0.0830124i
\(307\) 1.13659i 0.0648686i 0.999474 + 0.0324343i \(0.0103260\pi\)
−0.999474 + 0.0324343i \(0.989674\pi\)
\(308\) 3.53729 + 7.17548i 0.201556 + 0.408861i
\(309\) 15.0754i 0.857609i
\(310\) 0 0
\(311\) 5.13659 0.291269 0.145635 0.989338i \(-0.453478\pi\)
0.145635 + 0.989338i \(0.453478\pi\)
\(312\) 10.8151 8.87189i 0.612285 0.502272i
\(313\) −23.0762 −1.30434 −0.652172 0.758071i \(-0.726142\pi\)
−0.652172 + 0.758071i \(0.726142\pi\)
\(314\) 2.87189 + 12.3208i 0.162070 + 0.695303i
\(315\) 0 0
\(316\) −5.89134 + 2.90425i −0.331414 + 0.163377i
\(317\) 1.66152i 0.0933203i −0.998911 0.0466601i \(-0.985142\pi\)
0.998911 0.0466601i \(-0.0148578\pi\)
\(318\) 0.316523 0.0737791i 0.0177497 0.00413733i
\(319\) 7.48755 0.419223
\(320\) 0 0
\(321\) −4.00000 −0.223258
\(322\) −19.7655 + 4.60719i −1.10149 + 0.256749i
\(323\) 11.7827i 0.655605i
\(324\) 1.79387 0.884323i 0.0996595 0.0491291i
\(325\) 0 0
\(326\) −5.06682 21.7374i −0.280625 1.20392i
\(327\) 4.17034 0.230620
\(328\) 1.24274 1.01945i 0.0686187 0.0562895i
\(329\) −10.5683 −0.582649
\(330\) 0 0
\(331\) 25.9077i 1.42402i −0.702171 0.712008i \(-0.747786\pi\)
0.702171 0.712008i \(-0.252214\pi\)
\(332\) 8.74714 + 17.7438i 0.480062 + 0.973816i
\(333\) 0.945668i 0.0518223i
\(334\) −7.58774 + 1.76865i −0.415183 + 0.0967760i
\(335\) 0 0
\(336\) −12.8719 9.88274i −0.702219 0.539148i
\(337\) −8.00696 −0.436167 −0.218083 0.975930i \(-0.569980\pi\)
−0.218083 + 0.975930i \(0.569980\pi\)
\(338\) −15.7833 + 3.67896i −0.858496 + 0.200109i
\(339\) 1.28526i 0.0698060i
\(340\) 0 0
\(341\) 3.23797i 0.175346i
\(342\) 0.836276 + 3.58774i 0.0452206 + 0.194003i
\(343\) 9.97884 0.538806
\(344\) 15.1755 + 18.4994i 0.818207 + 0.997420i
\(345\) 0 0
\(346\) 3.31903 + 14.2391i 0.178432 + 0.765499i
\(347\) 23.0279i 1.23620i 0.786098 + 0.618102i \(0.212098\pi\)
−0.786098 + 0.618102i \(0.787902\pi\)
\(348\) −13.6233 + 6.71585i −0.730284 + 0.360007i
\(349\) 21.4380i 1.14755i −0.819012 0.573776i \(-0.805478\pi\)
0.819012 0.573776i \(-0.194522\pi\)
\(350\) 0 0
\(351\) −4.94567 −0.263980
\(352\) 5.07936 + 2.30359i 0.270731 + 0.122782i
\(353\) 4.52323 0.240747 0.120374 0.992729i \(-0.461591\pi\)
0.120374 + 0.992729i \(0.461591\pi\)
\(354\) 12.5334 2.92145i 0.666143 0.155273i
\(355\) 0 0
\(356\) −22.1560 + 10.9222i −1.17427 + 0.578878i
\(357\) 18.3510i 0.971236i
\(358\) −5.19265 22.2772i −0.274440 1.17739i
\(359\) 10.3510 0.546303 0.273152 0.961971i \(-0.411934\pi\)
0.273152 + 0.961971i \(0.411934\pi\)
\(360\) 0 0
\(361\) 12.2144 0.642862
\(362\) −2.60492 11.1755i −0.136912 0.587370i
\(363\) 10.0279i 0.526330i
\(364\) 17.7438 + 35.9937i 0.930027 + 1.88658i
\(365\) 0 0
\(366\) −15.1755 + 3.53729i −0.793235 + 0.184897i
\(367\) 0.485359 0.0253355 0.0126678 0.999920i \(-0.495968\pi\)
0.0126678 + 0.999920i \(0.495968\pi\)
\(368\) −8.61665 + 11.2229i −0.449174 + 0.585032i
\(369\) −0.568295 −0.0295842
\(370\) 0 0
\(371\) 0.932371i 0.0484063i
\(372\) 2.90425 + 5.89134i 0.150578 + 0.305452i
\(373\) 30.0823i 1.55760i −0.627272 0.778800i \(-0.715829\pi\)
0.627272 0.778800i \(-0.284171\pi\)
\(374\) −1.43171 6.14222i −0.0740317 0.317606i
\(375\) 0 0
\(376\) −5.69641 + 4.67289i −0.293770 + 0.240986i
\(377\) 37.5591 1.93439
\(378\) 1.30246 + 5.58774i 0.0669914 + 0.287402i
\(379\) 33.6881i 1.73044i −0.501392 0.865220i \(-0.667179\pi\)
0.501392 0.865220i \(-0.332821\pi\)
\(380\) 0 0
\(381\) 1.15280i 0.0590597i
\(382\) −34.3211 + 8.00000i −1.75602 + 0.409316i
\(383\) 5.17545 0.264453 0.132227 0.991220i \(-0.457787\pi\)
0.132227 + 0.991220i \(0.457787\pi\)
\(384\) −11.3078 + 0.364570i −0.577050 + 0.0186044i
\(385\) 0 0
\(386\) −1.43171 + 0.333720i −0.0728719 + 0.0169859i
\(387\) 8.45963i 0.430027i
\(388\) 5.80850 2.86341i 0.294882 0.145368i
\(389\) 16.6408i 0.843722i 0.906660 + 0.421861i \(0.138623\pi\)
−0.906660 + 0.421861i \(0.861377\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 20.6862 16.9694i 1.04481 0.857082i
\(393\) 3.89019 0.196234
\(394\) −3.10170 13.3067i −0.156262 0.670384i
\(395\) 0 0
\(396\) −0.871889 1.76865i −0.0438141 0.0888778i
\(397\) 20.4332i 1.02551i −0.858534 0.512757i \(-0.828624\pi\)
0.858534 0.512757i \(-0.171376\pi\)
\(398\) 31.7698 7.40530i 1.59247 0.371194i
\(399\) −10.5683 −0.529076
\(400\) 0 0
\(401\) −4.56829 −0.228130 −0.114065 0.993473i \(-0.536387\pi\)
−0.114065 + 0.993473i \(0.536387\pi\)
\(402\) 11.6514 2.71585i 0.581118 0.135454i
\(403\) 16.2423i 0.809087i
\(404\) −3.85244 7.81477i −0.191666 0.388799i
\(405\) 0 0
\(406\) −9.89134 42.4352i −0.490899 2.10602i
\(407\) −0.932371 −0.0462159
\(408\) 8.11409 + 9.89134i 0.401708 + 0.489694i
\(409\) 19.8913 0.983563 0.491782 0.870719i \(-0.336346\pi\)
0.491782 + 0.870719i \(0.336346\pi\)
\(410\) 0 0
\(411\) 17.5135i 0.863875i
\(412\) 27.0433 13.3315i 1.33233 0.656797i
\(413\) 36.9193i 1.81668i
\(414\) 4.87189 1.13560i 0.239440 0.0558118i
\(415\) 0 0
\(416\) 25.4791 + 11.5553i 1.24921 + 0.566545i
\(417\) 16.8612 0.825698
\(418\) 3.53729 0.824517i 0.173015 0.0403284i
\(419\) 0.387288i 0.0189203i 0.999955 + 0.00946013i \(0.00301130\pi\)
−0.999955 + 0.00946013i \(0.996989\pi\)
\(420\) 0 0
\(421\) 12.0578i 0.587664i 0.955857 + 0.293832i \(0.0949306\pi\)
−0.955857 + 0.293832i \(0.905069\pi\)
\(422\) −2.06797 8.87189i −0.100667 0.431877i
\(423\) 2.60492 0.126656
\(424\) 0.412259 + 0.502556i 0.0200210 + 0.0244063i
\(425\) 0 0
\(426\) −0.459630 1.97188i −0.0222692 0.0955378i
\(427\) 44.7019i 2.16328i
\(428\) −3.53729 7.17548i −0.170982 0.346840i
\(429\) 4.87613i 0.235422i
\(430\) 0 0
\(431\) 40.4068 1.94633 0.973164 0.230113i \(-0.0739096\pi\)
0.973164 + 0.230113i \(0.0739096\pi\)
\(432\) 3.17272 + 2.43594i 0.152648 + 0.117199i
\(433\) −36.1859 −1.73898 −0.869491 0.493949i \(-0.835553\pi\)
−0.869491 + 0.493949i \(0.835553\pi\)
\(434\) −18.3510 + 4.27748i −0.880875 + 0.205325i
\(435\) 0 0
\(436\) 3.68793 + 7.48105i 0.176620 + 0.358277i
\(437\) 9.21438i 0.440783i
\(438\) 3.83662 + 16.4596i 0.183321 + 0.786472i
\(439\) −25.4178 −1.21312 −0.606562 0.795036i \(-0.707452\pi\)
−0.606562 + 0.795036i \(0.707452\pi\)
\(440\) 0 0
\(441\) −9.45963 −0.450459
\(442\) −7.18172 30.8106i −0.341600 1.46551i
\(443\) 7.02792i 0.333907i −0.985965 0.166953i \(-0.946607\pi\)
0.985965 0.166953i \(-0.0533929\pi\)
\(444\) 1.69641 0.836276i 0.0805079 0.0396879i
\(445\) 0 0
\(446\) 24.7632 5.77213i 1.17257 0.273318i
\(447\) −10.4986 −0.496566
\(448\) 6.34545 31.8300i 0.299794 1.50383i
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 0 0
\(451\) 0.560304i 0.0263837i
\(452\) 2.30560 1.13659i 0.108446 0.0534607i
\(453\) 4.71585i 0.221570i
\(454\) −2.25622 9.67951i −0.105890 0.454282i
\(455\) 0 0
\(456\) −5.69641 + 4.67289i −0.266759 + 0.218828i
\(457\) −25.2747 −1.18230 −0.591149 0.806562i \(-0.701326\pi\)
−0.591149 + 0.806562i \(0.701326\pi\)
\(458\) −1.33883 5.74378i −0.0625595 0.268389i
\(459\) 4.52323i 0.211126i
\(460\) 0 0
\(461\) 41.0902i 1.91376i 0.290479 + 0.956881i \(0.406185\pi\)
−0.290479 + 0.956881i \(0.593815\pi\)
\(462\) 5.50917 1.28415i 0.256310 0.0597439i
\(463\) 13.2106 0.613951 0.306975 0.951717i \(-0.400683\pi\)
0.306975 + 0.951717i \(0.400683\pi\)
\(464\) −24.0947 18.4994i −1.11857 0.858813i
\(465\) 0 0
\(466\) 33.0404 7.70148i 1.53057 0.356764i
\(467\) 1.89134i 0.0875206i 0.999042 + 0.0437603i \(0.0139338\pi\)
−0.999042 + 0.0437603i \(0.986066\pi\)
\(468\) −4.37357 8.87189i −0.202168 0.410103i
\(469\) 34.3211i 1.58480i
\(470\) 0 0
\(471\) 8.94567 0.412195
\(472\) 16.3243 + 19.8998i 0.751386 + 0.915963i
\(473\) −8.34068 −0.383505
\(474\) 1.05433 + 4.52323i 0.0484271 + 0.207759i
\(475\) 0 0
\(476\) −32.9193 + 16.2282i −1.50885 + 0.743818i
\(477\) 0.229815i 0.0105225i
\(478\) −12.2844 + 2.86341i −0.561877 + 0.130969i
\(479\) 31.4876 1.43870 0.719352 0.694646i \(-0.244439\pi\)
0.719352 + 0.694646i \(0.244439\pi\)
\(480\) 0 0
\(481\) −4.67696 −0.213251
\(482\) −22.5201 + 5.24926i −1.02576 + 0.239097i
\(483\) 14.3510i 0.652992i
\(484\) 17.9888 8.86793i 0.817673 0.403088i
\(485\) 0 0
\(486\) −0.321037 1.37729i −0.0145625 0.0624753i
\(487\) −12.9964 −0.588922 −0.294461 0.955664i \(-0.595140\pi\)
−0.294461 + 0.955664i \(0.595140\pi\)
\(488\) −19.7655 24.0947i −0.894741 1.09072i
\(489\) −15.7827 −0.713717
\(490\) 0 0
\(491\) 14.9085i 0.672812i −0.941717 0.336406i \(-0.890788\pi\)
0.941717 0.336406i \(-0.109212\pi\)
\(492\) −0.502556 1.01945i −0.0226570 0.0459602i
\(493\) 34.3510i 1.54709i
\(494\) 17.7438 4.13594i 0.798330 0.186085i
\(495\) 0 0
\(496\) −8.00000 + 10.4197i −0.359211 + 0.467858i
\(497\) 5.80850 0.260547
\(498\) 13.6233 3.17548i 0.610473 0.142297i
\(499\) 35.6599i 1.59636i 0.602420 + 0.798179i \(0.294203\pi\)
−0.602420 + 0.798179i \(0.705797\pi\)
\(500\) 0 0
\(501\) 5.50917i 0.246132i
\(502\) 1.35603 + 5.81756i 0.0605226 + 0.259650i
\(503\) 25.3090 1.12847 0.564237 0.825613i \(-0.309170\pi\)
0.564237 + 0.825613i \(0.309170\pi\)
\(504\) −8.87189 + 7.27782i −0.395185 + 0.324180i
\(505\) 0 0
\(506\) −1.11963 4.80338i −0.0497738 0.213536i
\(507\) 11.4596i 0.508940i
\(508\) 2.06797 1.01945i 0.0917514 0.0452306i
\(509\) 13.7366i 0.608862i 0.952534 + 0.304431i \(0.0984663\pi\)
−0.952534 + 0.304431i \(0.901534\pi\)
\(510\) 0 0
\(511\) −48.4846 −2.14483
\(512\) −10.6538 19.9624i −0.470835 0.882221i
\(513\) 2.60492 0.115010
\(514\) −34.0125 + 7.92806i −1.50023 + 0.349692i
\(515\) 0 0
\(516\) 15.1755 7.48105i 0.668063 0.329335i
\(517\) 2.56829i 0.112953i
\(518\) 1.23170 + 5.28415i 0.0541176 + 0.232172i
\(519\) 10.3385 0.453809
\(520\) 0 0
\(521\) −30.9193 −1.35460 −0.677299 0.735708i \(-0.736850\pi\)
−0.677299 + 0.735708i \(0.736850\pi\)
\(522\) 2.43806 + 10.4596i 0.106711 + 0.457806i
\(523\) 21.8385i 0.954932i 0.878650 + 0.477466i \(0.158445\pi\)
−0.878650 + 0.477466i \(0.841555\pi\)
\(524\) 3.44018 + 6.97849i 0.150285 + 0.304857i
\(525\) 0 0
\(526\) −20.1949 + 4.70729i −0.880541 + 0.205248i
\(527\) 14.8550 0.647092
\(528\) 2.40169 3.12811i 0.104520 0.136134i
\(529\) −10.4876 −0.455981
\(530\) 0 0
\(531\) 9.10003i 0.394908i
\(532\) −9.34579 18.9582i −0.405191 0.821940i
\(533\) 2.81060i 0.121740i
\(534\) 3.96511 + 17.0109i 0.171587 + 0.736133i
\(535\) 0 0
\(536\) 15.1755 + 18.4994i 0.655481 + 0.799052i
\(537\) −16.1746 −0.697986
\(538\) 3.70415 + 15.8913i 0.159697 + 0.685124i
\(539\) 9.32662i 0.401726i
\(540\) 0 0
\(541\) 24.3423i 1.04656i −0.852162 0.523278i \(-0.824709\pi\)
0.852162 0.523278i \(-0.175291\pi\)
\(542\) 7.76120 1.80908i 0.333372 0.0777066i
\(543\) −8.11409 −0.348209
\(544\) −10.5683 + 23.3028i −0.453112 + 0.999098i
\(545\) 0 0
\(546\) 27.6351 6.44154i 1.18267 0.275673i
\(547\) 33.3789i 1.42718i 0.700564 + 0.713589i \(0.252932\pi\)
−0.700564 + 0.713589i \(0.747068\pi\)
\(548\) 31.4169 15.4876i 1.34206 0.661596i
\(549\) 11.0183i 0.470251i
\(550\) 0 0
\(551\) −19.7827 −0.842770
\(552\) 6.34545 + 7.73530i 0.270080 + 0.329236i
\(553\) −13.3239 −0.566592
\(554\) −5.58774 23.9722i −0.237400 1.01848i
\(555\) 0 0
\(556\) 14.9108 + 30.2469i 0.632358 + 1.28275i
\(557\) 30.5808i 1.29575i 0.761747 + 0.647875i \(0.224342\pi\)
−0.761747 + 0.647875i \(0.775658\pi\)
\(558\) 4.52323 1.05433i 0.191484 0.0446334i
\(559\) −41.8385 −1.76958
\(560\) 0 0
\(561\) −4.45963 −0.188286
\(562\) 30.0011 6.99304i 1.26552 0.294984i
\(563\) 7.02792i 0.296192i 0.988973 + 0.148096i \(0.0473144\pi\)
−0.988973 + 0.148096i \(0.952686\pi\)
\(564\) 2.30359 + 4.67289i 0.0969988 + 0.196764i
\(565\) 0 0
\(566\) 6.93318 + 29.7443i 0.291423 + 1.25025i
\(567\) 4.05705 0.170380
\(568\) 3.13083 2.56829i 0.131367 0.107763i
\(569\) 24.3510 1.02085 0.510423 0.859924i \(-0.329489\pi\)
0.510423 + 0.859924i \(0.329489\pi\)
\(570\) 0 0
\(571\) 20.0992i 0.841125i −0.907263 0.420563i \(-0.861833\pi\)
0.907263 0.420563i \(-0.138167\pi\)
\(572\) −8.74714 + 4.31207i −0.365736 + 0.180297i
\(573\) 24.9193i 1.04102i
\(574\) 3.17548 0.740182i 0.132542 0.0308946i
\(575\) 0 0
\(576\) −1.56406 + 7.84562i −0.0651690 + 0.326901i
\(577\) 4.76899 0.198536 0.0992678 0.995061i \(-0.468350\pi\)
0.0992678 + 0.995061i \(0.468350\pi\)
\(578\) 4.76492 1.11067i 0.198195 0.0461977i
\(579\) 1.03951i 0.0432004i
\(580\) 0 0
\(581\) 40.1296i 1.66486i
\(582\) −1.03951 4.45963i −0.0430890 0.184858i
\(583\) −0.226584 −0.00938413
\(584\) −26.1336 + 21.4380i −1.08142 + 0.887112i
\(585\) 0 0
\(586\) −10.2772 44.0906i −0.424547 1.82136i
\(587\) 8.21733i 0.339165i −0.985516 0.169583i \(-0.945758\pi\)
0.985516 0.169583i \(-0.0542420\pi\)
\(588\) −8.36537 16.9694i −0.344982 0.699804i
\(589\) 8.55495i 0.352501i
\(590\) 0 0
\(591\) −9.66152 −0.397422
\(592\) 3.00034 + 2.30359i 0.123313 + 0.0946771i
\(593\) 7.76120 0.318714 0.159357 0.987221i \(-0.449058\pi\)
0.159357 + 0.987221i \(0.449058\pi\)
\(594\) −1.35793 + 0.316523i −0.0557164 + 0.0129871i
\(595\) 0 0
\(596\) −9.28415 18.8331i −0.380293 0.771434i
\(597\) 23.0668i 0.944062i
\(598\) −5.61631 24.0947i −0.229668 0.985307i
\(599\) −5.64903 −0.230813 −0.115407 0.993318i \(-0.536817\pi\)
−0.115407 + 0.993318i \(0.536817\pi\)
\(600\) 0 0
\(601\) −37.7299 −1.53903 −0.769516 0.638627i \(-0.779503\pi\)
−0.769516 + 0.638627i \(0.779503\pi\)
\(602\) 11.0183 + 47.2702i 0.449074 + 1.92659i
\(603\) 8.45963i 0.344503i
\(604\) 8.45963 4.17034i 0.344217 0.169689i
\(605\) 0 0
\(606\) −6.00000 + 1.39856i −0.243733 + 0.0568124i
\(607\) 0.113292 0.00459837 0.00229919 0.999997i \(-0.499268\pi\)
0.00229919 + 0.999997i \(0.499268\pi\)
\(608\) −13.4200 6.08627i −0.544254 0.246831i
\(609\) −30.8106 −1.24851
\(610\) 0 0
\(611\) 12.8831i 0.521194i
\(612\) 8.11409 4.00000i 0.327993 0.161690i
\(613\) 0.703366i 0.0284087i −0.999899 0.0142044i \(-0.995478\pi\)
0.999899 0.0142044i \(-0.00452154\pi\)
\(614\) 0.364887 + 1.56542i 0.0147256 + 0.0631750i
\(615\) 0 0
\(616\) 7.17548 + 8.74714i 0.289108 + 0.352432i
\(617\) −24.4809 −0.985564 −0.492782 0.870153i \(-0.664020\pi\)
−0.492782 + 0.870153i \(0.664020\pi\)
\(618\) −4.83975 20.7632i −0.194683 0.835219i
\(619\) 39.4966i 1.58750i −0.608243 0.793751i \(-0.708126\pi\)
0.608243 0.793751i \(-0.291874\pi\)
\(620\) 0 0
\(621\) 3.53729i 0.141947i
\(622\) 7.07459 1.64903i 0.283665 0.0661202i
\(623\) −50.1084 −2.00755
\(624\) 12.0474 15.6912i 0.482281 0.628152i
\(625\) 0 0
\(626\) −31.7827 + 7.40831i −1.27029 + 0.296095i
\(627\) 2.56829i 0.102568i
\(628\) 7.91086 + 16.0474i 0.315678 + 0.640360i
\(629\) 4.27748i 0.170554i
\(630\) 0 0
\(631\) 17.3400 0.690294 0.345147 0.938549i \(-0.387829\pi\)
0.345147 + 0.938549i \(0.387829\pi\)
\(632\) −7.18172 + 5.89134i −0.285674 + 0.234345i
\(633\) −6.44154 −0.256028
\(634\) −0.533409 2.28840i −0.0211844 0.0908840i
\(635\) 0 0
\(636\) 0.412259 0.203231i 0.0163471 0.00805863i
\(637\) 46.7842i 1.85366i
\(638\) 10.3126 2.40378i 0.408278 0.0951666i
\(639\) −1.43171 −0.0566374
\(640\) 0 0
\(641\) 38.7019 1.52863 0.764317 0.644840i \(-0.223076\pi\)
0.764317 + 0.644840i \(0.223076\pi\)
\(642\) −5.50917 + 1.28415i −0.217430 + 0.0506812i
\(643\) 1.13659i 0.0448227i −0.999749 0.0224113i \(-0.992866\pi\)
0.999749 0.0224113i \(-0.00713435\pi\)
\(644\) −25.7438 + 12.6909i −1.01445 + 0.500091i
\(645\) 0 0
\(646\) 3.78267 + 16.2282i 0.148827 + 0.638490i
\(647\) −6.54868 −0.257455 −0.128728 0.991680i \(-0.541089\pi\)
−0.128728 + 0.991680i \(0.541089\pi\)
\(648\) 2.18678 1.79387i 0.0859050 0.0704699i
\(649\) −8.97208 −0.352185
\(650\) 0 0
\(651\) 13.3239i 0.522206i
\(652\) −13.9570 28.3121i −0.546598 1.10879i
\(653\) 8.74226i 0.342111i 0.985261 + 0.171056i \(0.0547178\pi\)
−0.985261 + 0.171056i \(0.945282\pi\)
\(654\) 5.74378 1.33883i 0.224599 0.0523525i
\(655\) 0 0
\(656\) 1.38433 1.80304i 0.0540492 0.0703969i
\(657\) 11.9507 0.466242
\(658\) −14.5556 + 3.39281i −0.567438 + 0.132266i
\(659\) 35.5336i 1.38419i 0.721804 + 0.692097i \(0.243313\pi\)
−0.721804 + 0.692097i \(0.756687\pi\)
\(660\) 0 0
\(661\) 23.3028i 0.906373i 0.891416 + 0.453186i \(0.149713\pi\)
−0.891416 + 0.453186i \(0.850287\pi\)
\(662\) −8.31732 35.6825i −0.323262 1.38684i
\(663\) −22.3704 −0.868795
\(664\) 17.7438 + 21.6302i 0.688592 + 0.839415i
\(665\) 0 0
\(666\) −0.303594 1.30246i −0.0117640 0.0504694i
\(667\) 26.8634i 1.04016i
\(668\) −9.88274 + 4.87189i −0.382375 + 0.188499i
\(669\) 17.9796i 0.695133i
\(670\) 0 0
\(671\) 10.8634 0.419377
\(672\) −20.9011 9.47908i −0.806277 0.365663i
\(673\) 14.3634 0.553670 0.276835 0.960917i \(-0.410714\pi\)
0.276835 + 0.960917i \(0.410714\pi\)
\(674\) −11.0279 + 2.57053i −0.424780 + 0.0990130i
\(675\) 0 0
\(676\) −20.5571 + 10.1340i −0.790658 + 0.389770i
\(677\) 24.3076i 0.934217i −0.884200 0.467109i \(-0.845296\pi\)
0.884200 0.467109i \(-0.154704\pi\)
\(678\) −0.412617 1.77018i −0.0158465 0.0679835i
\(679\) 13.1366 0.504136
\(680\) 0 0
\(681\) −7.02792 −0.269311
\(682\) −1.03951 4.45963i −0.0398048 0.170768i
\(683\) 38.5933i 1.47673i 0.674401 + 0.738365i \(0.264402\pi\)
−0.674401 + 0.738365i \(0.735598\pi\)
\(684\) 2.30359 + 4.67289i 0.0880801 + 0.178673i
\(685\) 0 0
\(686\) 13.7438 3.20357i 0.524740 0.122313i
\(687\) −4.17034 −0.159108
\(688\) 26.8401 + 20.6072i 1.02327 + 0.785642i
\(689\) −1.13659 −0.0433006
\(690\) 0 0
\(691\) 13.4090i 0.510102i −0.966928 0.255051i \(-0.917908\pi\)
0.966928 0.255051i \(-0.0820923\pi\)
\(692\) 9.14256 + 18.5459i 0.347548 + 0.705009i
\(693\) 4.00000i 0.151947i
\(694\) 7.39281 + 31.7162i 0.280627 + 1.20393i
\(695\) 0 0
\(696\) −16.6072 + 13.6233i −0.629494 + 0.516389i
\(697\) −2.57053 −0.0973657
\(698\) −6.88240 29.5264i −0.260503 1.11759i
\(699\) 23.9894i 0.907362i
\(700\) 0 0
\(701\) 15.6013i 0.589253i 0.955613 + 0.294626i \(0.0951952\pi\)
−0.955613 + 0.294626i \(0.904805\pi\)
\(702\) −6.81163 + 1.58774i −0.257089 + 0.0599254i
\(703\) 2.46339 0.0929086
\(704\) 7.73530 + 1.54206i 0.291535 + 0.0581187i
\(705\) 0 0
\(706\) 6.22982 1.45212i 0.234462 0.0546514i
\(707\) 17.6740i 0.664699i
\(708\) 16.3243 8.04737i 0.613504 0.302439i
\(709\) 15.7873i 0.592906i −0.955047 0.296453i \(-0.904196\pi\)
0.955047 0.296453i \(-0.0958038\pi\)
\(710\) 0 0
\(711\) 3.28415 0.123165
\(712\) −27.0089 + 22.1560i −1.01220 + 0.830333i
\(713\) 11.6170 0.435060
\(714\) 5.89134 + 25.2747i 0.220478 + 0.945880i
\(715\) 0 0
\(716\) −14.3036 29.0152i −0.534550 1.08435i
\(717\) 8.91926i 0.333096i
\(718\) 14.2563 3.32304i 0.532041 0.124015i
\(719\) 22.5683 0.841655 0.420828 0.907141i \(-0.361740\pi\)
0.420828 + 0.907141i \(0.361740\pi\)
\(720\) 0 0
\(721\) 61.1616 2.27778
\(722\) 16.8228 3.92126i 0.626079 0.145934i
\(723\) 16.3510i 0.608099i
\(724\) −7.17548 14.5556i −0.266675 0.540956i
\(725\) 0 0
\(726\) −3.21933 13.8114i −0.119481 0.512589i
\(727\) −2.79096 −0.103511 −0.0517554 0.998660i \(-0.516482\pi\)
−0.0517554 + 0.998660i \(0.516482\pi\)
\(728\) 35.9937 + 43.8774i 1.33401 + 1.62621i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 38.2649i 1.41528i
\(732\) −19.7655 + 9.74378i −0.730553 + 0.360140i
\(733\) 16.4860i 0.608926i 0.952524 + 0.304463i \(0.0984769\pi\)
−0.952524 + 0.304463i \(0.901523\pi\)
\(734\) 0.668481 0.155818i 0.0246741 0.00575135i
\(735\) 0 0
\(736\) −8.26470 + 18.2234i −0.304641 + 0.671724i
\(737\) −8.34068 −0.307233
\(738\) −0.782708 + 0.182443i −0.0288119 + 0.00671584i
\(739\) 14.8894i 0.547714i −0.961770 0.273857i \(-0.911701\pi\)
0.961770 0.273857i \(-0.0882995\pi\)
\(740\) 0 0
\(741\) 12.8831i 0.473272i
\(742\) 0.299325 + 1.28415i 0.0109886 + 0.0471425i
\(743\) −41.4301 −1.51992 −0.759961 0.649968i \(-0.774782\pi\)
−0.759961 + 0.649968i \(0.774782\pi\)
\(744\) 5.89134 + 7.18172i 0.215987 + 0.263295i
\(745\) 0 0
\(746\) −9.65751 41.4321i −0.353587 1.51694i
\(747\) 9.89134i 0.361905i
\(748\) −3.94376 8.00000i −0.144198 0.292509i
\(749\) 16.2282i 0.592965i
\(750\) 0 0
\(751\) 30.5544 1.11494 0.557472 0.830195i \(-0.311771\pi\)
0.557472 + 0.830195i \(0.311771\pi\)
\(752\) −6.34545 + 8.26470i −0.231395 + 0.301383i
\(753\) 4.22391 0.153928
\(754\) 51.7299 12.0578i 1.88389 0.439121i
\(755\) 0 0
\(756\) 3.58774 + 7.27782i 0.130485 + 0.264692i
\(757\) 0.433223i 0.0157457i 0.999969 + 0.00787287i \(0.00250604\pi\)
−0.999969 + 0.00787287i \(0.997494\pi\)
\(758\) −10.8151 46.3983i −0.392823 1.68526i
\(759\) −3.48755 −0.126590
\(760\) 0 0
\(761\) −14.9193 −0.540823 −0.270411 0.962745i \(-0.587160\pi\)
−0.270411 + 0.962745i \(0.587160\pi\)
\(762\) −0.370091 1.58774i −0.0134070 0.0575178i
\(763\) 16.9193i 0.612518i
\(764\) −44.7019 + 22.0367i −1.61726 + 0.797259i
\(765\) 0 0
\(766\) 7.12811 1.66151i 0.257549 0.0600328i
\(767\) −45.0057 −1.62506
\(768\) −15.4572 + 4.13235i −0.557762 + 0.149113i
\(769\) −31.3789 −1.13155 −0.565776 0.824559i \(-0.691423\pi\)
−0.565776 + 0.824559i \(0.691423\pi\)
\(770\) 0 0
\(771\) 24.6952i 0.889375i
\(772\) −1.86474 + 0.919260i −0.0671135 + 0.0330849i
\(773\) 13.4192i 0.482656i −0.970444 0.241328i \(-0.922417\pi\)
0.970444 0.241328i \(-0.0775829\pi\)
\(774\) −2.71585 11.6514i −0.0976193 0.418800i
\(775\) 0 0
\(776\) 7.08074 5.80850i 0.254184 0.208513i
\(777\) 3.83662 0.137638
\(778\) 5.34231 + 22.9193i 0.191531 + 0.821695i
\(779\) 1.48036i 0.0530395i
\(780\) 0 0
\(781\) 1.41157i 0.0505101i
\(782\) 22.0367 5.13659i 0.788030 0.183684i
\(783\) 7.59434 0.271400
\(784\) 23.0431 30.0128i 0.822969 1.07189i
\(785\) 0 0
\(786\) 5.35793 1.24889i 0.191111 0.0445465i
\(787\) 36.4846i 1.30054i