Properties

Label 600.2.k.f.301.5
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
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 301.5
Root \(-0.450129 - 1.34067i\) of \(x^{12} + x^{10} - 8 x^{6} + 16 x^{2} + 64\)
Character \(\chi\) \(=\) 600.301
Dual form 600.2.k.f.301.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.450129 - 1.34067i) q^{2} -1.00000i q^{3} +(-1.59477 + 1.20695i) q^{4} +(-1.34067 + 0.450129i) q^{6} +2.64265 q^{7} +(2.33596 + 1.59477i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.450129 - 1.34067i) q^{2} -1.00000i q^{3} +(-1.59477 + 1.20695i) q^{4} +(-1.34067 + 0.450129i) q^{6} +2.64265 q^{7} +(2.33596 + 1.59477i) q^{8} -1.00000 q^{9} +1.51363i q^{11} +(1.20695 + 1.59477i) q^{12} -3.87086i q^{13} +(-1.18953 - 3.54291i) q^{14} +(1.08656 - 3.84959i) q^{16} +3.31415 q^{17} +(0.450129 + 1.34067i) q^{18} -7.08582i q^{19} -2.64265i q^{21} +(2.02927 - 0.681331i) q^{22} +4.82778 q^{23} +(1.59477 - 2.33596i) q^{24} +(-5.18953 + 1.74239i) q^{26} +1.00000i q^{27} +(-4.21441 + 3.18953i) q^{28} +2.18513i q^{29} -7.36266 q^{31} +(-5.65011 + 0.276098i) q^{32} +1.51363 q^{33} +(-1.49180 - 4.44317i) q^{34} +(1.59477 - 1.20695i) q^{36} -7.87086i q^{37} +(-9.49971 + 3.18953i) q^{38} -3.87086 q^{39} +8.72532 q^{41} +(-3.54291 + 1.18953i) q^{42} -1.01641i q^{43} +(-1.82687 - 2.41389i) q^{44} +(-2.17313 - 6.47244i) q^{46} -7.08582 q^{47} +(-3.84959 - 1.08656i) q^{48} -0.0164068 q^{49} -3.31415i q^{51} +(4.67192 + 6.17313i) q^{52} -4.50820i q^{53} +(1.34067 - 0.450129i) q^{54} +(6.17313 + 4.21441i) q^{56} -7.08582 q^{57} +(2.92953 - 0.983593i) q^{58} +6.79893i q^{59} +3.60104i q^{61} +(3.31415 + 9.87086i) q^{62} -2.64265 q^{63} +(2.91344 + 7.45063i) q^{64} +(-0.681331 - 2.02927i) q^{66} -1.01641i q^{67} +(-5.28530 + 4.00000i) q^{68} -4.82778i q^{69} -6.72532 q^{71} +(-2.33596 - 1.59477i) q^{72} +15.5146 q^{73} +(-10.5522 + 3.54291i) q^{74} +(8.55220 + 11.3002i) q^{76} +4.00000i q^{77} +(1.74239 + 5.18953i) q^{78} -7.36266 q^{79} +1.00000 q^{81} +(-3.92752 - 11.6977i) q^{82} -7.74173i q^{83} +(3.18953 + 4.21441i) q^{84} +(-1.36266 + 0.457515i) q^{86} +2.18513 q^{87} +(-2.41389 + 3.53579i) q^{88} +14.7581 q^{89} -10.2293i q^{91} +(-7.69919 + 5.82687i) q^{92} +7.36266i q^{93} +(3.18953 + 9.49971i) q^{94} +(0.276098 + 5.65011i) q^{96} +11.1444 q^{97} +(0.00738516 + 0.0219960i) q^{98} -1.51363i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{4} - 2q^{6} - 12q^{9} + O(q^{10}) \) \( 12q - 2q^{4} - 2q^{6} - 12q^{9} + 20q^{14} + 2q^{16} + 2q^{24} - 28q^{26} - 32q^{31} - 24q^{34} + 2q^{36} + 16q^{39} - 8q^{41} - 44q^{44} - 4q^{46} + 12q^{49} + 2q^{54} + 52q^{56} + 46q^{64} + 20q^{66} + 32q^{71} - 36q^{74} + 12q^{76} - 32q^{79} + 12q^{81} + 4q^{84} + 40q^{86} + 40q^{89} + 4q^{94} - 42q^{96} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.450129 1.34067i −0.318290 0.947994i
\(3\) 1.00000i 0.577350i
\(4\) −1.59477 + 1.20695i −0.797384 + 0.603473i
\(5\) 0 0
\(6\) −1.34067 + 0.450129i −0.547324 + 0.183765i
\(7\) 2.64265 0.998827 0.499414 0.866364i \(-0.333549\pi\)
0.499414 + 0.866364i \(0.333549\pi\)
\(8\) 2.33596 + 1.59477i 0.825887 + 0.563835i
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 1.51363i 0.456377i 0.973617 + 0.228189i \(0.0732803\pi\)
−0.973617 + 0.228189i \(0.926720\pi\)
\(12\) 1.20695 + 1.59477i 0.348415 + 0.460370i
\(13\) 3.87086i 1.07358i −0.843714 0.536792i \(-0.819636\pi\)
0.843714 0.536792i \(-0.180364\pi\)
\(14\) −1.18953 3.54291i −0.317916 0.946882i
\(15\) 0 0
\(16\) 1.08656 3.84959i 0.271641 0.962399i
\(17\) 3.31415 0.803800 0.401900 0.915684i \(-0.368350\pi\)
0.401900 + 0.915684i \(0.368350\pi\)
\(18\) 0.450129 + 1.34067i 0.106097 + 0.315998i
\(19\) 7.08582i 1.62560i −0.582545 0.812799i \(-0.697943\pi\)
0.582545 0.812799i \(-0.302057\pi\)
\(20\) 0 0
\(21\) 2.64265i 0.576673i
\(22\) 2.02927 0.681331i 0.432643 0.145260i
\(23\) 4.82778 1.00666 0.503331 0.864094i \(-0.332108\pi\)
0.503331 + 0.864094i \(0.332108\pi\)
\(24\) 1.59477 2.33596i 0.325530 0.476826i
\(25\) 0 0
\(26\) −5.18953 + 1.74239i −1.01775 + 0.341711i
\(27\) 1.00000i 0.192450i
\(28\) −4.21441 + 3.18953i −0.796448 + 0.602765i
\(29\) 2.18513i 0.405769i 0.979203 + 0.202885i \(0.0650316\pi\)
−0.979203 + 0.202885i \(0.934968\pi\)
\(30\) 0 0
\(31\) −7.36266 −1.32237 −0.661187 0.750222i \(-0.729947\pi\)
−0.661187 + 0.750222i \(0.729947\pi\)
\(32\) −5.65011 + 0.276098i −0.998808 + 0.0488076i
\(33\) 1.51363 0.263490
\(34\) −1.49180 4.44317i −0.255841 0.761997i
\(35\) 0 0
\(36\) 1.59477 1.20695i 0.265795 0.201158i
\(37\) 7.87086i 1.29396i −0.762506 0.646981i \(-0.776031\pi\)
0.762506 0.646981i \(-0.223969\pi\)
\(38\) −9.49971 + 3.18953i −1.54106 + 0.517411i
\(39\) −3.87086 −0.619834
\(40\) 0 0
\(41\) 8.72532 1.36267 0.681333 0.731973i \(-0.261400\pi\)
0.681333 + 0.731973i \(0.261400\pi\)
\(42\) −3.54291 + 1.18953i −0.546683 + 0.183549i
\(43\) 1.01641i 0.155001i −0.996992 0.0775003i \(-0.975306\pi\)
0.996992 0.0775003i \(-0.0246939\pi\)
\(44\) −1.82687 2.41389i −0.275411 0.363908i
\(45\) 0 0
\(46\) −2.17313 6.47244i −0.320410 0.954309i
\(47\) −7.08582 −1.03357 −0.516786 0.856114i \(-0.672872\pi\)
−0.516786 + 0.856114i \(0.672872\pi\)
\(48\) −3.84959 1.08656i −0.555641 0.156832i
\(49\) −0.0164068 −0.00234382
\(50\) 0 0
\(51\) 3.31415i 0.464074i
\(52\) 4.67192 + 6.17313i 0.647879 + 0.856059i
\(53\) 4.50820i 0.619249i −0.950859 0.309625i \(-0.899797\pi\)
0.950859 0.309625i \(-0.100203\pi\)
\(54\) 1.34067 0.450129i 0.182441 0.0612549i
\(55\) 0 0
\(56\) 6.17313 + 4.21441i 0.824919 + 0.563174i
\(57\) −7.08582 −0.938539
\(58\) 2.92953 0.983593i 0.384667 0.129152i
\(59\) 6.79893i 0.885145i 0.896733 + 0.442573i \(0.145934\pi\)
−0.896733 + 0.442573i \(0.854066\pi\)
\(60\) 0 0
\(61\) 3.60104i 0.461065i 0.973065 + 0.230533i \(0.0740469\pi\)
−0.973065 + 0.230533i \(0.925953\pi\)
\(62\) 3.31415 + 9.87086i 0.420898 + 1.25360i
\(63\) −2.64265 −0.332942
\(64\) 2.91344 + 7.45063i 0.364180 + 0.931329i
\(65\) 0 0
\(66\) −0.681331 2.02927i −0.0838660 0.249786i
\(67\) 1.01641i 0.124174i −0.998071 0.0620869i \(-0.980224\pi\)
0.998071 0.0620869i \(-0.0197756\pi\)
\(68\) −5.28530 + 4.00000i −0.640937 + 0.485071i
\(69\) 4.82778i 0.581197i
\(70\) 0 0
\(71\) −6.72532 −0.798149 −0.399074 0.916919i \(-0.630669\pi\)
−0.399074 + 0.916919i \(0.630669\pi\)
\(72\) −2.33596 1.59477i −0.275296 0.187945i
\(73\) 15.5146 1.81585 0.907925 0.419132i \(-0.137666\pi\)
0.907925 + 0.419132i \(0.137666\pi\)
\(74\) −10.5522 + 3.54291i −1.22667 + 0.411855i
\(75\) 0 0
\(76\) 8.55220 + 11.3002i 0.981004 + 1.29622i
\(77\) 4.00000i 0.455842i
\(78\) 1.74239 + 5.18953i 0.197287 + 0.587599i
\(79\) −7.36266 −0.828364 −0.414182 0.910194i \(-0.635932\pi\)
−0.414182 + 0.910194i \(0.635932\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −3.92752 11.6977i −0.433723 1.29180i
\(83\) 7.74173i 0.849765i −0.905248 0.424883i \(-0.860315\pi\)
0.905248 0.424883i \(-0.139685\pi\)
\(84\) 3.18953 + 4.21441i 0.348007 + 0.459830i
\(85\) 0 0
\(86\) −1.36266 + 0.457515i −0.146940 + 0.0493351i
\(87\) 2.18513 0.234271
\(88\) −2.41389 + 3.53579i −0.257322 + 0.376916i
\(89\) 14.7581 1.56436 0.782180 0.623053i \(-0.214108\pi\)
0.782180 + 0.623053i \(0.214108\pi\)
\(90\) 0 0
\(91\) 10.2293i 1.07233i
\(92\) −7.69919 + 5.82687i −0.802696 + 0.607493i
\(93\) 7.36266i 0.763472i
\(94\) 3.18953 + 9.49971i 0.328975 + 0.979820i
\(95\) 0 0
\(96\) 0.276098 + 5.65011i 0.0281791 + 0.576662i
\(97\) 11.1444 1.13154 0.565769 0.824563i \(-0.308579\pi\)
0.565769 + 0.824563i \(0.308579\pi\)
\(98\) 0.00738516 + 0.0219960i 0.000746014 + 0.00222193i
\(99\) 1.51363i 0.152126i
\(100\) 0 0
\(101\) 13.3295i 1.32633i 0.748471 + 0.663167i \(0.230788\pi\)
−0.748471 + 0.663167i \(0.769212\pi\)
\(102\) −4.44317 + 1.49180i −0.439939 + 0.147710i
\(103\) −0.958386 −0.0944326 −0.0472163 0.998885i \(-0.515035\pi\)
−0.0472163 + 0.998885i \(0.515035\pi\)
\(104\) 6.17313 9.04219i 0.605325 0.886660i
\(105\) 0 0
\(106\) −6.04399 + 2.02927i −0.587044 + 0.197101i
\(107\) 4.00000i 0.386695i −0.981130 0.193347i \(-0.938066\pi\)
0.981130 0.193347i \(-0.0619344\pi\)
\(108\) −1.20695 1.59477i −0.116138 0.153457i
\(109\) 0.769233i 0.0736792i −0.999321 0.0368396i \(-0.988271\pi\)
0.999321 0.0368396i \(-0.0117291\pi\)
\(110\) 0 0
\(111\) −7.87086 −0.747069
\(112\) 2.87141 10.1731i 0.271322 0.961270i
\(113\) −14.4585 −1.36014 −0.680071 0.733146i \(-0.738051\pi\)
−0.680071 + 0.733146i \(0.738051\pi\)
\(114\) 3.18953 + 9.49971i 0.298727 + 0.889729i
\(115\) 0 0
\(116\) −2.63734 3.48478i −0.244871 0.323554i
\(117\) 3.87086i 0.357862i
\(118\) 9.11509 3.06040i 0.839112 0.281733i
\(119\) 8.75814 0.802857
\(120\) 0 0
\(121\) 8.70892 0.791720
\(122\) 4.82778 1.62093i 0.437087 0.146752i
\(123\) 8.72532i 0.786736i
\(124\) 11.7417 8.88633i 1.05444 0.798016i
\(125\) 0 0
\(126\) 1.18953 + 3.54291i 0.105972 + 0.315627i
\(127\) 11.5290 1.02303 0.511516 0.859274i \(-0.329084\pi\)
0.511516 + 0.859274i \(0.329084\pi\)
\(128\) 8.67738 7.25969i 0.766979 0.641672i
\(129\) −1.01641 −0.0894896
\(130\) 0 0
\(131\) 7.37270i 0.644156i −0.946713 0.322078i \(-0.895619\pi\)
0.946713 0.322078i \(-0.104381\pi\)
\(132\) −2.41389 + 1.82687i −0.210102 + 0.159009i
\(133\) 18.7253i 1.62369i
\(134\) −1.36266 + 0.457515i −0.117716 + 0.0395232i
\(135\) 0 0
\(136\) 7.74173 + 5.28530i 0.663848 + 0.453211i
\(137\) −3.88792 −0.332167 −0.166084 0.986112i \(-0.553112\pi\)
−0.166084 + 0.986112i \(0.553112\pi\)
\(138\) −6.47244 + 2.17313i −0.550971 + 0.184989i
\(139\) 14.6291i 1.24083i 0.784275 + 0.620414i \(0.213035\pi\)
−0.784275 + 0.620414i \(0.786965\pi\)
\(140\) 0 0
\(141\) 7.08582i 0.596733i
\(142\) 3.02727 + 9.01641i 0.254042 + 0.756640i
\(143\) 5.85907 0.489960
\(144\) −1.08656 + 3.84959i −0.0905470 + 0.320800i
\(145\) 0 0
\(146\) −6.98359 20.7999i −0.577966 1.72141i
\(147\) 0.0164068i 0.00135321i
\(148\) 9.49971 + 12.5522i 0.780871 + 1.03178i
\(149\) 11.0715i 0.907010i 0.891254 + 0.453505i \(0.149827\pi\)
−0.891254 + 0.453505i \(0.850173\pi\)
\(150\) 0 0
\(151\) 0.637339 0.0518659 0.0259329 0.999664i \(-0.491744\pi\)
0.0259329 + 0.999664i \(0.491744\pi\)
\(152\) 11.3002 16.5522i 0.916569 1.34256i
\(153\) −3.31415 −0.267933
\(154\) 5.36266 1.80052i 0.432136 0.145090i
\(155\) 0 0
\(156\) 6.17313 4.67192i 0.494246 0.374053i
\(157\) 0.129135i 0.0103061i 0.999987 + 0.00515306i \(0.00164028\pi\)
−0.999987 + 0.00515306i \(0.998360\pi\)
\(158\) 3.31415 + 9.87086i 0.263660 + 0.785284i
\(159\) −4.50820 −0.357524
\(160\) 0 0
\(161\) 12.7581 1.00548
\(162\) −0.450129 1.34067i −0.0353655 0.105333i
\(163\) 19.4835i 1.52606i 0.646362 + 0.763031i \(0.276290\pi\)
−0.646362 + 0.763031i \(0.723710\pi\)
\(164\) −13.9149 + 10.5310i −1.08657 + 0.822332i
\(165\) 0 0
\(166\) −10.3791 + 3.48478i −0.805572 + 0.270471i
\(167\) 1.80052 0.139328 0.0696641 0.997571i \(-0.477807\pi\)
0.0696641 + 0.997571i \(0.477807\pi\)
\(168\) 4.21441 6.17313i 0.325149 0.476267i
\(169\) −1.98359 −0.152584
\(170\) 0 0
\(171\) 7.08582i 0.541866i
\(172\) 1.22675 + 1.62093i 0.0935386 + 0.123595i
\(173\) 23.2335i 1.76641i 0.468985 + 0.883206i \(0.344620\pi\)
−0.468985 + 0.883206i \(0.655380\pi\)
\(174\) −0.983593 2.92953i −0.0745660 0.222087i
\(175\) 0 0
\(176\) 5.82687 + 1.64466i 0.439217 + 0.123971i
\(177\) 6.79893 0.511039
\(178\) −6.64307 19.7857i −0.497919 1.48300i
\(179\) 2.85664i 0.213515i 0.994285 + 0.106757i \(0.0340468\pi\)
−0.994285 + 0.106757i \(0.965953\pi\)
\(180\) 0 0
\(181\) 5.28530i 0.392853i −0.980519 0.196427i \(-0.937066\pi\)
0.980519 0.196427i \(-0.0629337\pi\)
\(182\) −13.7141 + 4.60453i −1.01656 + 0.341310i
\(183\) 3.60104 0.266196
\(184\) 11.2775 + 7.69919i 0.831390 + 0.567592i
\(185\) 0 0
\(186\) 9.87086 3.31415i 0.723767 0.243005i
\(187\) 5.01641i 0.366836i
\(188\) 11.3002 8.55220i 0.824154 0.623733i
\(189\) 2.64265i 0.192224i
\(190\) 0 0
\(191\) −5.96719 −0.431770 −0.215885 0.976419i \(-0.569264\pi\)
−0.215885 + 0.976419i \(0.569264\pi\)
\(192\) 7.45063 2.91344i 0.537703 0.210259i
\(193\) −14.9409 −1.07547 −0.537733 0.843115i \(-0.680719\pi\)
−0.537733 + 0.843115i \(0.680719\pi\)
\(194\) −5.01641 14.9409i −0.360157 1.07269i
\(195\) 0 0
\(196\) 0.0261649 0.0198021i 0.00186892 0.00141443i
\(197\) 3.23353i 0.230379i 0.993344 + 0.115190i \(0.0367476\pi\)
−0.993344 + 0.115190i \(0.963252\pi\)
\(198\) −2.02927 + 0.681331i −0.144214 + 0.0484201i
\(199\) −8.12080 −0.575668 −0.287834 0.957680i \(-0.592935\pi\)
−0.287834 + 0.957680i \(0.592935\pi\)
\(200\) 0 0
\(201\) −1.01641 −0.0716918
\(202\) 17.8704 6.00000i 1.25736 0.422159i
\(203\) 5.77454i 0.405293i
\(204\) 4.00000 + 5.28530i 0.280056 + 0.370045i
\(205\) 0 0
\(206\) 0.431398 + 1.28488i 0.0300569 + 0.0895215i
\(207\) −4.82778 −0.335554
\(208\) −14.9013 4.20594i −1.03322 0.291630i
\(209\) 10.7253 0.741886
\(210\) 0 0
\(211\) 13.7141i 0.944119i 0.881567 + 0.472059i \(0.156489\pi\)
−0.881567 + 0.472059i \(0.843511\pi\)
\(212\) 5.44116 + 7.18953i 0.373700 + 0.493779i
\(213\) 6.72532i 0.460812i
\(214\) −5.36266 + 1.80052i −0.366584 + 0.123081i
\(215\) 0 0
\(216\) −1.59477 + 2.33596i −0.108510 + 0.158942i
\(217\) −19.4569 −1.32082
\(218\) −1.03128 + 0.346255i −0.0698474 + 0.0234513i
\(219\) 15.5146i 1.04838i
\(220\) 0 0
\(221\) 12.8286i 0.862947i
\(222\) 3.54291 + 10.5522i 0.237784 + 0.708217i
\(223\) −9.84472 −0.659251 −0.329626 0.944112i \(-0.606923\pi\)
−0.329626 + 0.944112i \(0.606923\pi\)
\(224\) −14.9313 + 0.729629i −0.997637 + 0.0487504i
\(225\) 0 0
\(226\) 6.50820 + 19.3840i 0.432919 + 1.28941i
\(227\) 5.70892i 0.378914i −0.981889 0.189457i \(-0.939327\pi\)
0.981889 0.189457i \(-0.0606728\pi\)
\(228\) 11.3002 8.55220i 0.748376 0.566383i
\(229\) 0.769233i 0.0508324i 0.999677 + 0.0254162i \(0.00809109\pi\)
−0.999677 + 0.0254162i \(0.991909\pi\)
\(230\) 0 0
\(231\) 4.00000 0.263181
\(232\) −3.48478 + 5.10439i −0.228787 + 0.335120i
\(233\) 18.4008 1.20548 0.602739 0.797939i \(-0.294076\pi\)
0.602739 + 0.797939i \(0.294076\pi\)
\(234\) 5.18953 1.74239i 0.339250 0.113904i
\(235\) 0 0
\(236\) −8.20594 10.8427i −0.534161 0.705800i
\(237\) 7.36266i 0.478256i
\(238\) −3.94229 11.7417i −0.255541 0.761103i
\(239\) 10.0328 0.648969 0.324484 0.945891i \(-0.394809\pi\)
0.324484 + 0.945891i \(0.394809\pi\)
\(240\) 0 0
\(241\) 10.7581 0.692992 0.346496 0.938051i \(-0.387371\pi\)
0.346496 + 0.938051i \(0.387371\pi\)
\(242\) −3.92014 11.6757i −0.251996 0.750545i
\(243\) 1.00000i 0.0641500i
\(244\) −4.34625 5.74281i −0.278240 0.367646i
\(245\) 0 0
\(246\) −11.6977 + 3.92752i −0.745820 + 0.250410i
\(247\) −27.4282 −1.74522
\(248\) −17.1989 11.7417i −1.09213 0.745601i
\(249\) −7.74173 −0.490612
\(250\) 0 0
\(251\) 12.6580i 0.798966i 0.916741 + 0.399483i \(0.130810\pi\)
−0.916741 + 0.399483i \(0.869190\pi\)
\(252\) 4.21441 3.18953i 0.265483 0.200922i
\(253\) 7.30749i 0.459418i
\(254\) −5.18953 15.4565i −0.325620 0.969827i
\(255\) 0 0
\(256\) −13.6388 8.36566i −0.852422 0.522854i
\(257\) −13.3110 −0.830316 −0.415158 0.909749i \(-0.636274\pi\)
−0.415158 + 0.909749i \(0.636274\pi\)
\(258\) 0.457515 + 1.36266i 0.0284836 + 0.0848356i
\(259\) 20.7999i 1.29244i
\(260\) 0 0
\(261\) 2.18513i 0.135256i
\(262\) −9.88432 + 3.31867i −0.610656 + 0.205028i
\(263\) −18.4256 −1.13617 −0.568087 0.822969i \(-0.692316\pi\)
−0.568087 + 0.822969i \(0.692316\pi\)
\(264\) 3.53579 + 2.41389i 0.217613 + 0.148565i
\(265\) 0 0
\(266\) −25.1044 + 8.42882i −1.53925 + 0.516804i
\(267\) 14.7581i 0.903183i
\(268\) 1.22675 + 1.62093i 0.0749356 + 0.0990142i
\(269\) 3.86940i 0.235921i 0.993018 + 0.117961i \(0.0376357\pi\)
−0.993018 + 0.117961i \(0.962364\pi\)
\(270\) 0 0
\(271\) −17.3955 −1.05670 −0.528350 0.849027i \(-0.677189\pi\)
−0.528350 + 0.849027i \(0.677189\pi\)
\(272\) 3.60104 12.7581i 0.218345 0.773576i
\(273\) −10.2293 −0.619108
\(274\) 1.75007 + 5.21240i 0.105725 + 0.314893i
\(275\) 0 0
\(276\) 5.82687 + 7.69919i 0.350737 + 0.463437i
\(277\) 0.887271i 0.0533110i 0.999645 + 0.0266555i \(0.00848571\pi\)
−0.999645 + 0.0266555i \(0.991514\pi\)
\(278\) 19.6128 6.58501i 1.17630 0.394943i
\(279\) 7.36266 0.440791
\(280\) 0 0
\(281\) −13.4835 −0.804356 −0.402178 0.915562i \(-0.631747\pi\)
−0.402178 + 0.915562i \(0.631747\pi\)
\(282\) 9.49971 3.18953i 0.565699 0.189934i
\(283\) 28.4342i 1.69024i 0.534577 + 0.845120i \(0.320471\pi\)
−0.534577 + 0.845120i \(0.679529\pi\)
\(284\) 10.7253 8.11710i 0.636431 0.481661i
\(285\) 0 0
\(286\) −2.63734 7.85505i −0.155949 0.464479i
\(287\) 23.0580 1.36107
\(288\) 5.65011 0.276098i 0.332936 0.0162692i
\(289\) −6.01641 −0.353906
\(290\) 0 0
\(291\) 11.1444i 0.653294i
\(292\) −24.7422 + 18.7253i −1.44793 + 1.09582i
\(293\) 7.99166i 0.466878i 0.972371 + 0.233439i \(0.0749979\pi\)
−0.972371 + 0.233439i \(0.925002\pi\)
\(294\) 0.0219960 0.00738516i 0.00128283 0.000430711i
\(295\) 0 0
\(296\) 12.5522 18.3860i 0.729582 1.06867i
\(297\) −1.51363 −0.0878299
\(298\) 14.8431 4.98359i 0.859840 0.288692i
\(299\) 18.6877i 1.08074i
\(300\) 0 0
\(301\) 2.68601i 0.154819i
\(302\) −0.286885 0.854458i −0.0165084 0.0491685i
\(303\) 13.3295 0.765760
\(304\) −27.2775 7.69919i −1.56447 0.441579i
\(305\) 0 0
\(306\) 1.49180 + 4.44317i 0.0852803 + 0.253999i
\(307\) 17.4506i 0.995961i 0.867188 + 0.497980i \(0.165925\pi\)
−0.867188 + 0.497980i \(0.834075\pi\)
\(308\) −4.82778 6.37907i −0.275088 0.363481i
\(309\) 0.958386i 0.0545207i
\(310\) 0 0
\(311\) 21.4506 1.21635 0.608177 0.793801i \(-0.291901\pi\)
0.608177 + 0.793801i \(0.291901\pi\)
\(312\) −9.04219 6.17313i −0.511913 0.349485i
\(313\) −7.73879 −0.437422 −0.218711 0.975790i \(-0.570185\pi\)
−0.218711 + 0.975790i \(0.570185\pi\)
\(314\) 0.173127 0.0581276i 0.00977014 0.00328033i
\(315\) 0 0
\(316\) 11.7417 8.88633i 0.660524 0.499895i
\(317\) 11.2335i 0.630938i 0.948936 + 0.315469i \(0.102162\pi\)
−0.948936 + 0.315469i \(0.897838\pi\)
\(318\) 2.02927 + 6.04399i 0.113796 + 0.338930i
\(319\) −3.30749 −0.185184
\(320\) 0 0
\(321\) −4.00000 −0.223258
\(322\) −5.74281 17.1044i −0.320034 0.953190i
\(323\) 23.4835i 1.30665i
\(324\) −1.59477 + 1.20695i −0.0885982 + 0.0670525i
\(325\) 0 0
\(326\) 26.1208 8.77008i 1.44670 0.485730i
\(327\) −0.769233 −0.0425387
\(328\) 20.3820 + 13.9149i 1.12541 + 0.768319i
\(329\) −18.7253 −1.03236
\(330\) 0 0
\(331\) 8.00084i 0.439766i −0.975526 0.219883i \(-0.929432\pi\)
0.975526 0.219883i \(-0.0705676\pi\)
\(332\) 9.34385 + 12.3463i 0.512810 + 0.677589i
\(333\) 7.87086i 0.431321i
\(334\) −0.810466 2.41389i −0.0443467 0.132082i
\(335\) 0 0
\(336\) −10.1731 2.87141i −0.554990 0.156648i
\(337\) 21.5692 1.17495 0.587474 0.809243i \(-0.300123\pi\)
0.587474 + 0.809243i \(0.300123\pi\)
\(338\) 0.892874 + 2.65933i 0.0485659 + 0.144649i
\(339\) 14.4585i 0.785279i
\(340\) 0 0
\(341\) 11.1444i 0.603501i
\(342\) 9.49971 3.18953i 0.513685 0.172470i
\(343\) −18.5419 −1.00117
\(344\) 1.62093 2.37429i 0.0873948 0.128013i
\(345\) 0 0
\(346\) 31.1484 10.4581i 1.67455 0.562231i
\(347\) 21.7089i 1.16540i 0.812689 + 0.582698i \(0.198003\pi\)
−0.812689 + 0.582698i \(0.801997\pi\)
\(348\) −3.48478 + 2.63734i −0.186804 + 0.141376i
\(349\) 24.7422i 1.32442i −0.749318 0.662211i \(-0.769618\pi\)
0.749318 0.662211i \(-0.230382\pi\)
\(350\) 0 0
\(351\) 3.87086 0.206611
\(352\) −0.417910 8.55220i −0.0222747 0.455834i
\(353\) −3.31415 −0.176394 −0.0881972 0.996103i \(-0.528111\pi\)
−0.0881972 + 0.996103i \(0.528111\pi\)
\(354\) −3.06040 9.11509i −0.162658 0.484462i
\(355\) 0 0
\(356\) −23.5358 + 17.8123i −1.24739 + 0.944048i
\(357\) 8.75814i 0.463530i
\(358\) 3.82979 1.28586i 0.202411 0.0679596i
\(359\) −16.7581 −0.884461 −0.442230 0.896902i \(-0.645813\pi\)
−0.442230 + 0.896902i \(0.645813\pi\)
\(360\) 0 0
\(361\) −31.2088 −1.64257
\(362\) −7.08582 + 2.37907i −0.372422 + 0.125041i
\(363\) 8.70892i 0.457100i
\(364\) 12.3463 + 16.3134i 0.647120 + 0.855055i
\(365\) 0 0
\(366\) −1.62093 4.82778i −0.0847275 0.252352i
\(367\) −28.5324 −1.48938 −0.744690 0.667411i \(-0.767403\pi\)
−0.744690 + 0.667411i \(0.767403\pi\)
\(368\) 5.24569 18.5850i 0.273451 0.968811i
\(369\) −8.72532 −0.454222
\(370\) 0 0
\(371\) 11.9136i 0.618523i
\(372\) −8.88633 11.7417i −0.460735 0.608780i
\(373\) 37.5798i 1.94581i −0.231211 0.972904i \(-0.574269\pi\)
0.231211 0.972904i \(-0.425731\pi\)
\(374\) 6.72532 2.25803i 0.347758 0.116760i
\(375\) 0 0
\(376\) −16.5522 11.3002i −0.853614 0.582765i
\(377\) 8.45836 0.435628
\(378\) 3.54291 1.18953i 0.182228 0.0611830i
\(379\) 6.74456i 0.346445i 0.984883 + 0.173222i \(0.0554179\pi\)
−0.984883 + 0.173222i \(0.944582\pi\)
\(380\) 0 0
\(381\) 11.5290i 0.590648i
\(382\) 2.68601 + 8.00000i 0.137428 + 0.409316i
\(383\) −21.8312 −1.11552 −0.557762 0.830001i \(-0.688340\pi\)
−0.557762 + 0.830001i \(0.688340\pi\)
\(384\) −7.25969 8.67738i −0.370470 0.442816i
\(385\) 0 0
\(386\) 6.72532 + 20.0307i 0.342310 + 1.01954i
\(387\) 1.01641i 0.0516669i
\(388\) −17.7727 + 13.4506i −0.902270 + 0.682853i
\(389\) 8.81344i 0.446859i −0.974720 0.223429i \(-0.928275\pi\)
0.974720 0.223429i \(-0.0717252\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) −0.0383256 0.0261649i −0.00193573 0.00132153i
\(393\) −7.37270 −0.371904
\(394\) 4.33508 1.45551i 0.218398 0.0733273i
\(395\) 0 0
\(396\) 1.82687 + 2.41389i 0.0918038 + 0.121303i
\(397\) 0.821644i 0.0412372i −0.999787 0.0206186i \(-0.993436\pi\)
0.999787 0.0206186i \(-0.00656356\pi\)
\(398\) 3.65541 + 10.8873i 0.183229 + 0.545730i
\(399\) −18.7253 −0.937439
\(400\) 0 0
\(401\) −12.7253 −0.635472 −0.317736 0.948179i \(-0.602923\pi\)
−0.317736 + 0.948179i \(0.602923\pi\)
\(402\) 0.457515 + 1.36266i 0.0228188 + 0.0679634i
\(403\) 28.4999i 1.41968i
\(404\) −16.0880 21.2574i −0.800407 1.05760i
\(405\) 0 0
\(406\) 7.74173 2.59929i 0.384216 0.129001i
\(407\) 11.9136 0.590535
\(408\) 5.28530 7.74173i 0.261661 0.383273i
\(409\) 2.25827 0.111664 0.0558321 0.998440i \(-0.482219\pi\)
0.0558321 + 0.998440i \(0.482219\pi\)
\(410\) 0 0
\(411\) 3.88792i 0.191777i
\(412\) 1.52840 1.15672i 0.0752990 0.0569875i
\(413\) 17.9672i 0.884107i
\(414\) 2.17313 + 6.47244i 0.106803 + 0.318103i
\(415\) 0 0
\(416\) 1.06874 + 21.8708i 0.0523991 + 1.07231i
\(417\) 14.6291 0.716392
\(418\) −4.82778 14.3791i −0.236135 0.703303i
\(419\) 33.4579i 1.63453i 0.576264 + 0.817263i \(0.304510\pi\)
−0.576264 + 0.817263i \(0.695490\pi\)
\(420\) 0 0
\(421\) 11.3398i 0.552669i 0.961061 + 0.276335i \(0.0891198\pi\)
−0.961061 + 0.276335i \(0.910880\pi\)
\(422\) 18.3860 6.17313i 0.895018 0.300503i
\(423\) 7.08582 0.344524
\(424\) 7.18953 10.5310i 0.349155 0.511430i
\(425\) 0 0
\(426\) 9.01641 3.02727i 0.436846 0.146671i
\(427\) 9.51627i 0.460525i
\(428\) 4.82778 + 6.37907i 0.233360 + 0.308344i
\(429\) 5.85907i 0.282878i
\(430\) 0 0
\(431\) 10.6597 0.513459 0.256730 0.966483i \(-0.417355\pi\)
0.256730 + 0.966483i \(0.417355\pi\)
\(432\) 3.84959 + 1.08656i 0.185214 + 0.0522773i
\(433\) 26.5132 1.27414 0.637072 0.770805i \(-0.280146\pi\)
0.637072 + 0.770805i \(0.280146\pi\)
\(434\) 8.75814 + 26.0852i 0.420404 + 1.25213i
\(435\) 0 0
\(436\) 0.928423 + 1.22675i 0.0444634 + 0.0587506i
\(437\) 34.2088i 1.63643i
\(438\) −20.7999 + 6.98359i −0.993859 + 0.333689i
\(439\) 32.8789 1.56923 0.784613 0.619986i \(-0.212862\pi\)
0.784613 + 0.619986i \(0.212862\pi\)
\(440\) 0 0
\(441\) 0.0164068 0.000781274
\(442\) −17.1989 + 5.77454i −0.818068 + 0.274667i
\(443\) 5.70892i 0.271239i −0.990761 0.135619i \(-0.956698\pi\)
0.990761 0.135619i \(-0.0433024\pi\)
\(444\) 12.5522 9.49971i 0.595701 0.450836i
\(445\) 0 0
\(446\) 4.43140 + 13.1985i 0.209833 + 0.624966i
\(447\) 11.0715 0.523662
\(448\) 7.69919 + 19.6894i 0.363753 + 0.930237i
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 0 0
\(451\) 13.2069i 0.621890i
\(452\) 23.0580 17.4506i 1.08456 0.820809i
\(453\) 0.637339i 0.0299448i
\(454\) −7.65375 + 2.56975i −0.359208 + 0.120604i
\(455\) 0 0
\(456\) −16.5522 11.3002i −0.775128 0.529182i
\(457\) −3.94229 −0.184413 −0.0922064 0.995740i \(-0.529392\pi\)
−0.0922064 + 0.995740i \(0.529392\pi\)
\(458\) 1.03128 0.346255i 0.0481888 0.0161794i
\(459\) 3.31415i 0.154691i
\(460\) 0 0
\(461\) 33.8969i 1.57874i 0.613920 + 0.789369i \(0.289592\pi\)
−0.613920 + 0.789369i \(0.710408\pi\)
\(462\) −1.80052 5.36266i −0.0837677 0.249494i
\(463\) 22.8688 1.06280 0.531402 0.847120i \(-0.321665\pi\)
0.531402 + 0.847120i \(0.321665\pi\)
\(464\) 8.41188 + 2.37429i 0.390512 + 0.110224i
\(465\) 0 0
\(466\) −8.28275 24.6693i −0.383691 1.14278i
\(467\) 15.7417i 0.728440i −0.931313 0.364220i \(-0.881336\pi\)
0.931313 0.364220i \(-0.118664\pi\)
\(468\) −4.67192 6.17313i −0.215960 0.285353i
\(469\) 2.68601i 0.124028i
\(470\) 0 0
\(471\) 0.129135 0.00595024
\(472\) −10.8427 + 15.8820i −0.499076 + 0.731030i
\(473\) 1.53847 0.0707388
\(474\) 9.87086 3.31415i 0.453384 0.152224i
\(475\) 0 0
\(476\) −13.9672 + 10.5706i −0.640185 + 0.484502i
\(477\) 4.50820i 0.206416i
\(478\) −4.51606 13.4506i −0.206560 0.615218i
\(479\) 20.6925 0.945465 0.472732 0.881206i \(-0.343268\pi\)
0.472732 + 0.881206i \(0.343268\pi\)
\(480\) 0 0
\(481\) −30.4671 −1.38918
\(482\) −4.84255 14.4231i −0.220572 0.656952i
\(483\) 12.7581i 0.580515i
\(484\) −13.8887 + 10.5112i −0.631304 + 0.477781i
\(485\) 0 0
\(486\) −1.34067 + 0.450129i −0.0608138 + 0.0204183i
\(487\) 30.8401 1.39750 0.698750 0.715366i \(-0.253740\pi\)
0.698750 + 0.715366i \(0.253740\pi\)
\(488\) −5.74281 + 8.41188i −0.259965 + 0.380788i
\(489\) 19.4835 0.881072
\(490\) 0 0
\(491\) 10.9737i 0.495238i 0.968858 + 0.247619i \(0.0796481\pi\)
−0.968858 + 0.247619i \(0.920352\pi\)
\(492\) 10.5310 + 13.9149i 0.474774 + 0.627330i
\(493\) 7.24186i 0.326157i
\(494\) 12.3463 + 36.7721i 0.555484 + 1.65445i
\(495\) 0 0
\(496\) −8.00000 + 28.3433i −0.359211 + 1.27265i
\(497\) −17.7727 −0.797213
\(498\) 3.48478 + 10.3791i 0.156157 + 0.465097i
\(499\) 3.71729i 0.166409i −0.996533 0.0832044i \(-0.973485\pi\)
0.996533 0.0832044i \(-0.0265154\pi\)
\(500\) 0 0
\(501\) 1.80052i 0.0804412i
\(502\) 16.9701 5.69774i 0.757414 0.254302i
\(503\) 39.9451 1.78107 0.890533 0.454919i \(-0.150332\pi\)
0.890533 + 0.454919i \(0.150332\pi\)
\(504\) −6.17313 4.21441i −0.274973 0.187725i
\(505\) 0 0
\(506\) 9.79690 3.28932i 0.435525 0.146228i
\(507\) 1.98359i 0.0880945i
\(508\) −18.3860 + 13.9149i −0.815749 + 0.617372i
\(509\) 0.0728979i 0.00323114i 0.999999 + 0.00161557i \(0.000514253\pi\)
−0.999999 + 0.00161557i \(0.999486\pi\)
\(510\) 0 0
\(511\) 40.9997 1.81372
\(512\) −5.07634 + 22.0506i −0.224345 + 0.974510i
\(513\) 7.08582 0.312846
\(514\) 5.99166 + 17.8456i 0.264281 + 0.787134i
\(515\) 0 0
\(516\) 1.62093 1.22675i 0.0713576 0.0540046i
\(517\) 10.7253i 0.471699i
\(518\) −27.8857 + 9.36266i −1.22523 + 0.411372i
\(519\) 23.2335 1.01984
\(520\) 0 0
\(521\) −11.9672 −0.524292 −0.262146 0.965028i \(-0.584430\pi\)
−0.262146 + 0.965028i \(0.584430\pi\)
\(522\) −2.92953 + 0.983593i −0.128222 + 0.0430507i
\(523\) 16.0656i 0.702501i −0.936282 0.351250i \(-0.885757\pi\)
0.936282 0.351250i \(-0.114243\pi\)
\(524\) 8.89845 + 11.7577i 0.388731 + 0.513639i
\(525\) 0 0
\(526\) 8.29392 + 24.7026i 0.361632 + 1.07709i
\(527\) −24.4010 −1.06292
\(528\) 1.64466 5.82687i 0.0715746 0.253582i
\(529\) 0.307491 0.0133692
\(530\) 0 0
\(531\) 6.79893i 0.295048i
\(532\) 22.6004 + 29.8625i 0.979854 + 1.29470i
\(533\) 33.7745i 1.46294i
\(534\) −19.7857 + 6.64307i −0.856212 + 0.287474i
\(535\) 0 0
\(536\) 1.62093 2.37429i 0.0700136 0.102554i
\(537\) 2.85664 0.123273
\(538\) 5.18757 1.74173i 0.223652 0.0750913i
\(539\) 0.0248338i 0.00106967i
\(540\) 0 0
\(541\) 15.8559i 0.681698i −0.940118 0.340849i \(-0.889285\pi\)
0.940118 0.340849i \(-0.110715\pi\)
\(542\) 7.83021 + 23.3215i 0.336337 + 1.00174i
\(543\) −5.28530 −0.226814
\(544\) −18.7253 + 0.915029i −0.802842 + 0.0392316i
\(545\) 0 0
\(546\) 4.60453 + 13.7141i 0.197055 + 0.586910i
\(547\) 4.95078i 0.211680i 0.994383 + 0.105840i \(0.0337531\pi\)
−0.994383 + 0.105840i \(0.966247\pi\)
\(548\) 6.20033 4.69251i 0.264865 0.200454i
\(549\) 3.60104i 0.153688i
\(550\) 0 0
\(551\) 15.4835 0.659618
\(552\) 7.69919 11.2775i 0.327699 0.480003i
\(553\) −19.4569 −0.827393
\(554\) 1.18953 0.399387i 0.0505385 0.0169683i
\(555\) 0 0
\(556\) −17.6566 23.3301i −0.748806 0.989416i
\(557\) 1.26634i 0.0536565i −0.999640 0.0268283i \(-0.991459\pi\)
0.999640 0.0268283i \(-0.00854073\pi\)
\(558\) −3.31415 9.87086i −0.140299 0.417867i
\(559\) −3.93437 −0.166406
\(560\) 0 0
\(561\) 5.01641 0.211793
\(562\) 6.06930 + 18.0768i 0.256018 + 0.762524i
\(563\) 5.70892i 0.240602i 0.992737 + 0.120301i \(0.0383860\pi\)
−0.992737 + 0.120301i \(0.961614\pi\)
\(564\) −8.55220 11.3002i −0.360112 0.475825i
\(565\) 0 0
\(566\) 38.1208 12.7991i 1.60234 0.537986i
\(567\) 2.64265 0.110981
\(568\) −15.7101 10.7253i −0.659181 0.450025i
\(569\) −2.75814 −0.115627 −0.0578135 0.998327i \(-0.518413\pi\)
−0.0578135 + 0.998327i \(0.518413\pi\)
\(570\) 0 0
\(571\) 25.7735i 1.07859i −0.842118 0.539294i \(-0.818691\pi\)
0.842118 0.539294i \(-0.181309\pi\)
\(572\) −9.34385 + 7.07158i −0.390686 + 0.295677i
\(573\) 5.96719i 0.249283i
\(574\) −10.3791 30.9130i −0.433214 1.29028i
\(575\) 0 0
\(576\) −2.91344 7.45063i −0.121393 0.310443i
\(577\) −32.7135 −1.36188 −0.680941 0.732338i \(-0.738429\pi\)
−0.680941 + 0.732338i \(0.738429\pi\)
\(578\) 2.70816 + 8.06599i 0.112645 + 0.335501i
\(579\) 14.9409i 0.620921i
\(580\) 0 0
\(581\) 20.4587i 0.848769i
\(582\) −14.9409 + 5.01641i −0.619319 + 0.207937i
\(583\) 6.82376 0.282611
\(584\) 36.2416 + 24.7422i 1.49969 + 1.02384i
\(585\) 0 0
\(586\) 10.7141 3.59728i 0.442597 0.148602i
\(587\) 43.4835i 1.79475i −0.441264 0.897377i \(-0.645470\pi\)
0.441264 0.897377i \(-0.354530\pi\)
\(588\) −0.0198021 0.0261649i −0.000816623 0.00107902i
\(589\) 52.1705i 2.14965i
\(590\) 0 0
\(591\) 3.23353 0.133009
\(592\) −30.2996 8.55220i −1.24531 0.351493i
\(593\) 7.83021 0.321548 0.160774 0.986991i \(-0.448601\pi\)
0.160774 + 0.986991i \(0.448601\pi\)
\(594\) 0.681331 + 2.02927i 0.0279553 + 0.0832622i
\(595\) 0 0
\(596\) −13.3627 17.6564i −0.547356 0.723235i
\(597\) 8.12080i 0.332362i
\(598\) −25.0539 + 8.41188i −1.02453 + 0.343987i
\(599\) −32.7581 −1.33846 −0.669231 0.743055i \(-0.733376\pi\)
−0.669231 + 0.743055i \(0.733376\pi\)
\(600\) 0 0
\(601\) 17.8074 0.726377 0.363189 0.931716i \(-0.381688\pi\)
0.363189 + 0.931716i \(0.381688\pi\)
\(602\) −3.60104 + 1.20905i −0.146767 + 0.0492772i
\(603\) 1.01641i 0.0413913i
\(604\) −1.01641 + 0.769233i −0.0413570 + 0.0312997i
\(605\) 0 0
\(606\) −6.00000 17.8704i −0.243733 0.725935i
\(607\) −3.41188 −0.138484 −0.0692420 0.997600i \(-0.522058\pi\)
−0.0692420 + 0.997600i \(0.522058\pi\)
\(608\) 1.95638 + 40.0357i 0.0793416 + 1.62366i
\(609\) 5.77454 0.233996
\(610\) 0 0
\(611\) 27.4282i 1.10963i
\(612\) 5.28530 4.00000i 0.213646 0.161690i
\(613\) 36.6290i 1.47943i −0.672920 0.739716i \(-0.734960\pi\)
0.672920 0.739716i \(-0.265040\pi\)
\(614\) 23.3955 7.85505i 0.944165 0.317004i
\(615\) 0 0
\(616\) −6.37907 + 9.34385i −0.257020 + 0.376474i
\(617\) 40.3979 1.62636 0.813180 0.582012i \(-0.197734\pi\)
0.813180 + 0.582012i \(0.197734\pi\)
\(618\) 1.28488 0.431398i 0.0516853 0.0173534i
\(619\) 24.5172i 0.985430i 0.870191 + 0.492715i \(0.163996\pi\)
−0.870191 + 0.492715i \(0.836004\pi\)
\(620\) 0 0
\(621\) 4.82778i 0.193732i
\(622\) −9.65557 28.7581i −0.387153 1.15310i
\(623\) 39.0006 1.56252
\(624\) −4.20594 + 14.9013i −0.168372 + 0.596528i
\(625\) 0 0
\(626\) 3.48346 + 10.3751i 0.139227 + 0.414674i
\(627\) 10.7253i 0.428328i
\(628\) −0.155859 0.205941i −0.00621947 0.00821793i
\(629\) 26.0852i 1.04009i
\(630\) 0 0
\(631\) 18.7805 0.747640 0.373820 0.927501i \(-0.378048\pi\)
0.373820 + 0.927501i \(0.378048\pi\)
\(632\) −17.1989 11.7417i −0.684135 0.467061i
\(633\) 13.7141 0.545087
\(634\) 15.0604 5.05654i 0.598125 0.200821i
\(635\) 0 0
\(636\) 7.18953 5.44116i 0.285084 0.215756i
\(637\) 0.0635083i 0.00251629i
\(638\) 1.48880 + 4.43424i 0.0589421 + 0.175553i
\(639\) 6.72532 0.266050
\(640\) 0 0
\(641\) −15.5163 −0.612856 −0.306428 0.951894i \(-0.599134\pi\)
−0.306428 + 0.951894i \(0.599134\pi\)
\(642\) 1.80052 + 5.36266i 0.0710608 + 0.211647i
\(643\) 17.4506i 0.688186i −0.938936 0.344093i \(-0.888186\pi\)
0.938936 0.344093i \(-0.111814\pi\)
\(644\) −20.3463 + 15.3984i −0.801755 + 0.606781i
\(645\) 0 0
\(646\) −31.4835 + 10.5706i −1.23870 + 0.415895i
\(647\) −13.1403 −0.516600 −0.258300 0.966065i \(-0.583162\pi\)
−0.258300 + 0.966065i \(0.583162\pi\)
\(648\) 2.33596 + 1.59477i 0.0917653 + 0.0626484i
\(649\) −10.2911 −0.403960
\(650\) 0 0
\(651\) 19.4569i 0.762577i
\(652\) −23.5155 31.0716i −0.920937 1.21686i
\(653\) 14.7993i 0.579141i 0.957157 + 0.289570i \(0.0935124\pi\)
−0.957157 + 0.289570i \(0.906488\pi\)
\(654\) 0.346255 + 1.03128i 0.0135396 + 0.0403264i
\(655\) 0 0
\(656\) 9.48062 33.5890i 0.370156 1.31143i
\(657\) −15.5146 −0.605284
\(658\) 8.42882 + 25.1044i 0.328590 + 0.978671i
\(659\) 7.99614i 0.311485i −0.987798 0.155743i \(-0.950223\pi\)
0.987798 0.155743i \(-0.0497771\pi\)
\(660\) 0 0
\(661\) 0.915029i 0.0355905i 0.999842 + 0.0177953i \(0.00566470\pi\)
−0.999842 + 0.0177953i \(0.994335\pi\)
\(662\) −10.7265 + 3.60142i −0.416896 + 0.139973i
\(663\) −12.8286 −0.498223
\(664\) 12.3463 18.0844i 0.479128 0.701810i
\(665\) 0 0
\(666\) 10.5522 3.54291i 0.408889 0.137285i
\(667\) 10.5494i 0.408473i
\(668\) −2.87141 + 2.17313i −0.111098 + 0.0840808i
\(669\) 9.84472i 0.380619i
\(670\) 0 0
\(671\) −5.45065 −0.210420
\(672\) 0.729629 + 14.9313i 0.0281461 + 0.575986i
\(673\) 34.3978 1.32594 0.662969 0.748647i \(-0.269296\pi\)
0.662969 + 0.748647i \(0.269296\pi\)
\(674\) −9.70892 28.9170i −0.373973 1.11384i
\(675\) 0 0
\(676\) 3.16337 2.39409i 0.121668 0.0920804i
\(677\) 40.1676i 1.54377i 0.635764 + 0.771884i \(0.280685\pi\)
−0.635764 + 0.771884i \(0.719315\pi\)
\(678\) 19.3840 6.50820i 0.744439 0.249946i
\(679\) 29.4506 1.13021
\(680\) 0 0
\(681\) −5.70892 −0.218766
\(682\) −14.9409 + 5.01641i −0.572115 + 0.192088i
\(683\) 33.2580i 1.27258i −0.771449 0.636291i \(-0.780468\pi\)
0.771449 0.636291i \(-0.219532\pi\)
\(684\) −8.55220 11.3002i −0.327001 0.432075i
\(685\) 0 0
\(686\) 8.34625 + 24.8585i 0.318661 + 0.949101i
\(687\) 0.769233 0.0293481
\(688\) −3.91275 1.10439i −0.149172 0.0421045i
\(689\) −17.4506 −0.664817
\(690\) 0 0
\(691\) 50.2241i 1.91062i 0.295611 + 0.955308i \(0.404477\pi\)
−0.295611 + 0.955308i \(0.595523\pi\)
\(692\) −28.0416 37.0521i −1.06598 1.40851i
\(693\) 4.00000i 0.151947i
\(694\) 29.1044 9.77182i 1.10479 0.370933i
\(695\) 0 0
\(696\) 5.10439 + 3.48478i 0.193481 + 0.132090i
\(697\) 28.9170 1.09531
\(698\) −33.1710 + 11.1372i −1.25554 + 0.421549i
\(699\) 18.4008i 0.695983i
\(700\) 0 0
\(701\) 23.7543i 0.897188i −0.893736 0.448594i \(-0.851925\pi\)
0.893736 0.448594i \(-0.148075\pi\)
\(702\) −1.74239 5.18953i −0.0657623 0.195866i
\(703\) −55.7715 −2.10346
\(704\) −11.2775 + 4.40987i −0.425037 + 0.166203i
\(705\) 0 0
\(706\) 1.49180 + 4.44317i 0.0561445 + 0.167221i
\(707\) 35.2252i 1.32478i
\(708\) −10.8427 + 8.20594i −0.407494 + 0.308398i
\(709\) 36.3146i 1.36382i 0.731435 + 0.681911i \(0.238851\pi\)
−0.731435 + 0.681911i \(0.761149\pi\)
\(710\) 0 0
\(711\) 7.36266 0.276121
\(712\) 34.4744 + 23.5358i 1.29198 + 0.882041i
\(713\) −35.5453 −1.33118
\(714\) −11.7417 + 3.94229i −0.439423 + 0.147537i
\(715\) 0 0
\(716\) −3.44780 4.55567i −0.128851 0.170253i
\(717\) 10.0328i 0.374682i
\(718\) 7.54333 + 22.4671i 0.281515 + 0.838463i
\(719\) 30.7253 1.14586 0.572931 0.819604i \(-0.305806\pi\)
0.572931 + 0.819604i \(0.305806\pi\)
\(720\) 0 0
\(721\) −2.53268 −0.0943219
\(722\) 14.0480 + 41.8405i 0.522812 + 1.55714i
\(723\) 10.7581i 0.400099i
\(724\) 6.37907 + 8.42882i 0.237076 + 0.313255i
\(725\) 0 0
\(726\) −11.6757 + 3.92014i −0.433327 + 0.145490i
\(727\) 5.47445 0.203036 0.101518 0.994834i \(-0.467630\pi\)
0.101518 + 0.994834i \(0.467630\pi\)
\(728\) 16.3134 23.8953i 0.604615 0.885620i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 3.36852i 0.124589i
\(732\) −5.74281 + 4.34625i −0.212260 + 0.160642i
\(733\) 17.1455i 0.633285i 0.948545 + 0.316643i \(0.102556\pi\)
−0.948545 + 0.316643i \(0.897444\pi\)
\(734\) 12.8433 + 38.2524i 0.474054 + 1.41192i
\(735\) 0 0
\(736\) −27.2775 + 1.33294i −1.00546 + 0.0491328i
\(737\) 1.53847 0.0566701
\(738\) 3.92752 + 11.6977i 0.144574 + 0.430600i
\(739\) 11.6019i 0.426782i −0.976967 0.213391i \(-0.931549\pi\)
0.976967 0.213391i \(-0.0684508\pi\)
\(740\) 0 0
\(741\) 27.4282i 1.00760i
\(742\) −15.9721 + 5.36266i −0.586356 + 0.196869i
\(743\) −23.6613 −0.868048 −0.434024 0.900901i \(-0.642907\pi\)
−0.434024 + 0.900901i \(0.642907\pi\)
\(744\) −11.7417 + 17.1989i −0.430473 + 0.630542i
\(745\) 0 0
\(746\) −50.3819 + 16.9158i −1.84461 + 0.619330i
\(747\) 7.74173i 0.283255i
\(748\) −6.05453 8.00000i −0.221376 0.292509i
\(749\) 10.5706i 0.386241i
\(750\) 0 0
\(751\) −11.4283 −0.417024 −0.208512 0.978020i \(-0.566862\pi\)
−0.208512 + 0.978020i \(0.566862\pi\)
\(752\) −7.69919 + 27.2775i −0.280761 + 0.994709i
\(753\) 12.6580 0.461283
\(754\) −3.80736 11.3398i −0.138656 0.412972i
\(755\) 0 0
\(756\) −3.18953 4.21441i −0.116002 0.153277i
\(757\) 19.1784i 0.697049i −0.937300 0.348525i \(-0.886683\pi\)
0.937300 0.348525i \(-0.113317\pi\)
\(758\) 9.04219 3.03592i 0.328427 0.110270i
\(759\) 7.30749 0.265245
\(760\) 0 0
\(761\) 4.03281 0.146189 0.0730947 0.997325i \(-0.476712\pi\)
0.0730947 + 0.997325i \(0.476712\pi\)
\(762\) −15.4565 + 5.18953i −0.559930 + 0.187997i
\(763\) 2.03281i 0.0735928i
\(764\) 9.51627 7.20207i 0.344287 0.260562i
\(765\) 0 0
\(766\) 9.82687 + 29.2684i 0.355059 + 1.05751i
\(767\) 26.3177 0.950279
\(768\) −8.36566 + 13.6388i −0.301870 + 0.492146i
\(769\) −2.95078 −0.106408 −0.0532039 0.998584i \(-0.516943\pi\)
−0.0532039 + 0.998584i \(0.516943\pi\)
\(770\) 0 0
\(771\) 13.3110i 0.479383i
\(772\) 23.8272 18.0328i 0.857560 0.649015i
\(773\) 45.2663i 1.62812i −0.580783 0.814059i \(-0.697253\pi\)
0.580783 0.814059i \(-0.302747\pi\)
\(774\) 1.36266 0.457515i 0.0489798 0.0164450i
\(775\) 0 0
\(776\) 26.0328 + 17.7727i 0.934524 + 0.638002i
\(777\) −20.7999 −0.746193
\(778\) −11.8159 + 3.96719i −0.423619 + 0.142231i
\(779\) 61.8260i 2.21515i
\(780\) 0 0
\(781\) 10.1797i 0.364257i
\(782\) −7.20207 21.4506i −0.257546 0.767074i
\(783\) −2.18513 −0.0780903
\(784\) −0.0178270 + 0.0631594i −0.000636678 + 0.00225569i
\(785\) 0 0
\(786\) 3.31867 + 9.88432i 0.118373 +