Properties

Label 300.3.c.d.151.2
Level $300$
Weight $3$
Character 300.151
Analytic conductor $8.174$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.17440793081\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.85100625.1
Defining polynomial: \(x^{8} - x^{7} - 2 x^{6} + x^{5} + 3 x^{4} + 2 x^{3} - 8 x^{2} - 8 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 151.2
Root \(1.04064 - 0.957636i\) of defining polynomial
Character \(\chi\) \(=\) 300.151
Dual form 300.3.c.d.151.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.87477 + 0.696577i) q^{2} +1.73205i q^{3} +(3.02956 - 2.61185i) q^{4} +(-1.20651 - 3.24721i) q^{6} -5.46770i q^{7} +(-3.86039 + 7.00695i) q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(-1.87477 + 0.696577i) q^{2} +1.73205i q^{3} +(3.02956 - 2.61185i) q^{4} +(-1.20651 - 3.24721i) q^{6} -5.46770i q^{7} +(-3.86039 + 7.00695i) q^{8} -3.00000 q^{9} +11.0403i q^{11} +(4.52386 + 5.24735i) q^{12} -10.1242 q^{13} +(3.80867 + 10.2507i) q^{14} +(2.35649 - 15.8255i) q^{16} +24.4146 q^{17} +(5.62432 - 2.08973i) q^{18} +23.7757i q^{19} +9.47033 q^{21} +(-7.69043 - 20.6981i) q^{22} +37.2526i q^{23} +(-12.1364 - 6.68640i) q^{24} +(18.9806 - 7.05227i) q^{26} -5.19615i q^{27} +(-14.2808 - 16.5647i) q^{28} -25.7726 q^{29} -4.83647i q^{31} +(6.60580 + 31.3108i) q^{32} -19.1224 q^{33} +(-45.7719 + 17.0066i) q^{34} +(-9.08868 + 7.83555i) q^{36} -35.6493 q^{37} +(-16.5616 - 44.5741i) q^{38} -17.5356i q^{39} -9.30410 q^{41} +(-17.7547 + 6.59682i) q^{42} +70.0287i q^{43} +(28.8356 + 33.4473i) q^{44} +(-25.9493 - 69.8401i) q^{46} +38.0223i q^{47} +(27.4106 + 4.08156i) q^{48} +19.1043 q^{49} +42.2873i q^{51} +(-30.6718 + 26.4428i) q^{52} -55.7762 q^{53} +(3.61952 + 9.74162i) q^{54} +(38.3119 + 21.1075i) q^{56} -41.1808 q^{57} +(48.3179 - 17.9526i) q^{58} +55.5411i q^{59} -82.2412 q^{61} +(3.36897 + 9.06729i) q^{62} +16.4031i q^{63} +(-34.1947 - 54.0992i) q^{64} +(35.8502 - 13.3202i) q^{66} -104.493i q^{67} +(73.9656 - 63.7673i) q^{68} -64.5233 q^{69} +76.7471i q^{71} +(11.5812 - 21.0209i) q^{72} +93.5215 q^{73} +(66.8344 - 24.8325i) q^{74} +(62.0986 + 72.0300i) q^{76} +60.3651 q^{77} +(12.2149 + 32.8753i) q^{78} -49.3762i q^{79} +9.00000 q^{81} +(17.4431 - 6.48102i) q^{82} -72.3768i q^{83} +(28.6910 - 24.7351i) q^{84} +(-48.7804 - 131.288i) q^{86} -44.6395i q^{87} +(-77.3589 - 42.6199i) q^{88} +115.691 q^{89} +55.3560i q^{91} +(97.2980 + 112.859i) q^{92} +8.37701 q^{93} +(-26.4854 - 71.2832i) q^{94} +(-54.2318 + 11.4416i) q^{96} +72.9589 q^{97} +(-35.8162 + 13.3076i) q^{98} -33.1209i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} + 10q^{4} - 6q^{6} + 20q^{8} - 24q^{9} + O(q^{10}) \) \( 8q - 4q^{2} + 10q^{4} - 6q^{6} + 20q^{8} - 24q^{9} - 16q^{13} - 20q^{14} + 34q^{16} + 12q^{18} - 48q^{21} - 68q^{22} + 18q^{24} - 36q^{26} - 28q^{28} + 64q^{29} + 76q^{32} - 92q^{34} - 30q^{36} + 112q^{37} + 40q^{38} - 16q^{41} - 108q^{42} + 172q^{44} + 152q^{46} - 48q^{48} - 56q^{49} + 128q^{52} - 352q^{53} + 18q^{54} + 116q^{56} - 144q^{57} + 204q^{58} - 176q^{61} + 56q^{62} - 110q^{64} + 108q^{66} + 184q^{68} - 96q^{69} - 60q^{72} + 240q^{73} + 132q^{74} - 24q^{76} + 288q^{77} + 240q^{78} + 72q^{81} - 40q^{82} - 36q^{84} - 200q^{86} - 140q^{88} + 80q^{89} - 144q^{92} - 144q^{93} - 96q^{94} - 174q^{96} - 432q^{97} - 660q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.87477 + 0.696577i −0.937387 + 0.348288i
\(3\) 1.73205i 0.577350i
\(4\) 3.02956 2.61185i 0.757390 0.652962i
\(5\) 0 0
\(6\) −1.20651 3.24721i −0.201084 0.541201i
\(7\) 5.46770i 0.781100i −0.920582 0.390550i \(-0.872285\pi\)
0.920582 0.390550i \(-0.127715\pi\)
\(8\) −3.86039 + 7.00695i −0.482549 + 0.875869i
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 11.0403i 1.00366i 0.864965 + 0.501832i \(0.167341\pi\)
−0.864965 + 0.501832i \(0.832659\pi\)
\(12\) 4.52386 + 5.24735i 0.376988 + 0.437280i
\(13\) −10.1242 −0.778784 −0.389392 0.921072i \(-0.627315\pi\)
−0.389392 + 0.921072i \(0.627315\pi\)
\(14\) 3.80867 + 10.2507i 0.272048 + 0.732193i
\(15\) 0 0
\(16\) 2.35649 15.8255i 0.147280 0.989095i
\(17\) 24.4146 1.43615 0.718077 0.695964i \(-0.245023\pi\)
0.718077 + 0.695964i \(0.245023\pi\)
\(18\) 5.62432 2.08973i 0.312462 0.116096i
\(19\) 23.7757i 1.25135i 0.780082 + 0.625677i \(0.215177\pi\)
−0.780082 + 0.625677i \(0.784823\pi\)
\(20\) 0 0
\(21\) 9.47033 0.450968
\(22\) −7.69043 20.6981i −0.349565 0.940823i
\(23\) 37.2526i 1.61968i 0.586653 + 0.809838i \(0.300445\pi\)
−0.586653 + 0.809838i \(0.699555\pi\)
\(24\) −12.1364 6.68640i −0.505683 0.278600i
\(25\) 0 0
\(26\) 18.9806 7.05227i 0.730022 0.271241i
\(27\) 5.19615i 0.192450i
\(28\) −14.2808 16.5647i −0.510029 0.591598i
\(29\) −25.7726 −0.888712 −0.444356 0.895850i \(-0.646567\pi\)
−0.444356 + 0.895850i \(0.646567\pi\)
\(30\) 0 0
\(31\) 4.83647i 0.156015i −0.996953 0.0780076i \(-0.975144\pi\)
0.996953 0.0780076i \(-0.0248558\pi\)
\(32\) 6.60580 + 31.3108i 0.206431 + 0.978461i
\(33\) −19.1224 −0.579466
\(34\) −45.7719 + 17.0066i −1.34623 + 0.500196i
\(35\) 0 0
\(36\) −9.08868 + 7.83555i −0.252463 + 0.217654i
\(37\) −35.6493 −0.963495 −0.481747 0.876310i \(-0.659998\pi\)
−0.481747 + 0.876310i \(0.659998\pi\)
\(38\) −16.5616 44.5741i −0.435832 1.17300i
\(39\) 17.5356i 0.449631i
\(40\) 0 0
\(41\) −9.30410 −0.226929 −0.113465 0.993542i \(-0.536195\pi\)
−0.113465 + 0.993542i \(0.536195\pi\)
\(42\) −17.7547 + 6.59682i −0.422732 + 0.157067i
\(43\) 70.0287i 1.62857i 0.580462 + 0.814287i \(0.302872\pi\)
−0.580462 + 0.814287i \(0.697128\pi\)
\(44\) 28.8356 + 33.4473i 0.655355 + 0.760166i
\(45\) 0 0
\(46\) −25.9493 69.8401i −0.564114 1.51826i
\(47\) 38.0223i 0.808984i 0.914542 + 0.404492i \(0.132552\pi\)
−0.914542 + 0.404492i \(0.867448\pi\)
\(48\) 27.4106 + 4.08156i 0.571054 + 0.0850324i
\(49\) 19.1043 0.389883
\(50\) 0 0
\(51\) 42.2873i 0.829164i
\(52\) −30.6718 + 26.4428i −0.589843 + 0.508516i
\(53\) −55.7762 −1.05238 −0.526191 0.850366i \(-0.676380\pi\)
−0.526191 + 0.850366i \(0.676380\pi\)
\(54\) 3.61952 + 9.74162i 0.0670281 + 0.180400i
\(55\) 0 0
\(56\) 38.3119 + 21.1075i 0.684141 + 0.376919i
\(57\) −41.1808 −0.722470
\(58\) 48.3179 17.9526i 0.833067 0.309528i
\(59\) 55.5411i 0.941374i 0.882300 + 0.470687i \(0.155994\pi\)
−0.882300 + 0.470687i \(0.844006\pi\)
\(60\) 0 0
\(61\) −82.2412 −1.34822 −0.674108 0.738633i \(-0.735472\pi\)
−0.674108 + 0.738633i \(0.735472\pi\)
\(62\) 3.36897 + 9.06729i 0.0543383 + 0.146247i
\(63\) 16.4031i 0.260367i
\(64\) −34.1947 54.0992i −0.534293 0.845299i
\(65\) 0 0
\(66\) 35.8502 13.3202i 0.543184 0.201821i
\(67\) 104.493i 1.55960i −0.626026 0.779802i \(-0.715320\pi\)
0.626026 0.779802i \(-0.284680\pi\)
\(68\) 73.9656 63.7673i 1.08773 0.937754i
\(69\) −64.5233 −0.935120
\(70\) 0 0
\(71\) 76.7471i 1.08094i 0.841362 + 0.540472i \(0.181754\pi\)
−0.841362 + 0.540472i \(0.818246\pi\)
\(72\) 11.5812 21.0209i 0.160850 0.291956i
\(73\) 93.5215 1.28112 0.640558 0.767910i \(-0.278703\pi\)
0.640558 + 0.767910i \(0.278703\pi\)
\(74\) 66.8344 24.8325i 0.903168 0.335574i
\(75\) 0 0
\(76\) 62.0986 + 72.0300i 0.817087 + 0.947764i
\(77\) 60.3651 0.783963
\(78\) 12.2149 + 32.8753i 0.156601 + 0.421478i
\(79\) 49.3762i 0.625016i −0.949915 0.312508i \(-0.898831\pi\)
0.949915 0.312508i \(-0.101169\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 17.4431 6.48102i 0.212721 0.0790368i
\(83\) 72.3768i 0.872010i −0.899944 0.436005i \(-0.856393\pi\)
0.899944 0.436005i \(-0.143607\pi\)
\(84\) 28.6910 24.7351i 0.341559 0.294465i
\(85\) 0 0
\(86\) −48.7804 131.288i −0.567214 1.52661i
\(87\) 44.6395i 0.513098i
\(88\) −77.3589 42.6199i −0.879079 0.484318i
\(89\) 115.691 1.29990 0.649950 0.759977i \(-0.274790\pi\)
0.649950 + 0.759977i \(0.274790\pi\)
\(90\) 0 0
\(91\) 55.3560i 0.608308i
\(92\) 97.2980 + 112.859i 1.05759 + 1.22673i
\(93\) 8.37701 0.0900754
\(94\) −26.4854 71.2832i −0.281760 0.758332i
\(95\) 0 0
\(96\) −54.2318 + 11.4416i −0.564915 + 0.119183i
\(97\) 72.9589 0.752154 0.376077 0.926588i \(-0.377273\pi\)
0.376077 + 0.926588i \(0.377273\pi\)
\(98\) −35.8162 + 13.3076i −0.365471 + 0.135792i
\(99\) 33.1209i 0.334555i
\(100\) 0 0
\(101\) 29.4092 0.291180 0.145590 0.989345i \(-0.453492\pi\)
0.145590 + 0.989345i \(0.453492\pi\)
\(102\) −29.4564 79.2792i −0.288788 0.777247i
\(103\) 28.1884i 0.273673i 0.990594 + 0.136837i \(0.0436935\pi\)
−0.990594 + 0.136837i \(0.956306\pi\)
\(104\) 39.0833 70.9397i 0.375801 0.682112i
\(105\) 0 0
\(106\) 104.568 38.8524i 0.986490 0.366532i
\(107\) 4.50700i 0.0421215i 0.999778 + 0.0210607i \(0.00670434\pi\)
−0.999778 + 0.0210607i \(0.993296\pi\)
\(108\) −13.5716 15.7421i −0.125663 0.145760i
\(109\) 193.315 1.77353 0.886767 0.462217i \(-0.152946\pi\)
0.886767 + 0.462217i \(0.152946\pi\)
\(110\) 0 0
\(111\) 61.7464i 0.556274i
\(112\) −86.5292 12.8846i −0.772582 0.115041i
\(113\) −75.5727 −0.668785 −0.334392 0.942434i \(-0.608531\pi\)
−0.334392 + 0.942434i \(0.608531\pi\)
\(114\) 77.2047 28.6856i 0.677234 0.251628i
\(115\) 0 0
\(116\) −78.0798 + 67.3142i −0.673102 + 0.580295i
\(117\) 30.3726 0.259595
\(118\) −38.6886 104.127i −0.327870 0.882432i
\(119\) 133.492i 1.12178i
\(120\) 0 0
\(121\) −0.888544 −0.00734334
\(122\) 154.184 57.2873i 1.26380 0.469568i
\(123\) 16.1152i 0.131018i
\(124\) −12.6321 14.6524i −0.101872 0.118164i
\(125\) 0 0
\(126\) −11.4260 30.7521i −0.0906827 0.244064i
\(127\) 131.306i 1.03390i 0.856015 + 0.516951i \(0.172933\pi\)
−0.856015 + 0.516951i \(0.827067\pi\)
\(128\) 101.792 + 77.6045i 0.795247 + 0.606285i
\(129\) −121.293 −0.940258
\(130\) 0 0
\(131\) 75.7533i 0.578270i −0.957288 0.289135i \(-0.906632\pi\)
0.957288 0.289135i \(-0.0933676\pi\)
\(132\) −57.9324 + 49.9448i −0.438882 + 0.378370i
\(133\) 129.999 0.977433
\(134\) 72.7877 + 195.902i 0.543192 + 1.46195i
\(135\) 0 0
\(136\) −94.2500 + 171.072i −0.693014 + 1.25788i
\(137\) −66.7927 −0.487538 −0.243769 0.969833i \(-0.578384\pi\)
−0.243769 + 0.969833i \(0.578384\pi\)
\(138\) 120.967 44.9454i 0.876570 0.325692i
\(139\) 38.1214i 0.274255i 0.990553 + 0.137127i \(0.0437869\pi\)
−0.990553 + 0.137127i \(0.956213\pi\)
\(140\) 0 0
\(141\) −65.8565 −0.467067
\(142\) −53.4602 143.884i −0.376481 1.01326i
\(143\) 111.774i 0.781638i
\(144\) −7.06946 + 47.4765i −0.0490935 + 0.329698i
\(145\) 0 0
\(146\) −175.332 + 65.1449i −1.20090 + 0.446198i
\(147\) 33.0895i 0.225099i
\(148\) −108.002 + 93.1106i −0.729742 + 0.629126i
\(149\) −126.717 −0.850449 −0.425225 0.905088i \(-0.639805\pi\)
−0.425225 + 0.905088i \(0.639805\pi\)
\(150\) 0 0
\(151\) 68.4403i 0.453247i −0.973982 0.226623i \(-0.927231\pi\)
0.973982 0.226623i \(-0.0727687\pi\)
\(152\) −166.595 91.7836i −1.09602 0.603840i
\(153\) −73.2438 −0.478718
\(154\) −113.171 + 42.0489i −0.734877 + 0.273045i
\(155\) 0 0
\(156\) −45.8004 53.1252i −0.293592 0.340546i
\(157\) −25.5777 −0.162915 −0.0814577 0.996677i \(-0.525958\pi\)
−0.0814577 + 0.996677i \(0.525958\pi\)
\(158\) 34.3943 + 92.5693i 0.217686 + 0.585882i
\(159\) 96.6073i 0.607593i
\(160\) 0 0
\(161\) 203.686 1.26513
\(162\) −16.8730 + 6.26919i −0.104154 + 0.0386987i
\(163\) 63.4771i 0.389430i −0.980860 0.194715i \(-0.937622\pi\)
0.980860 0.194715i \(-0.0623782\pi\)
\(164\) −28.1873 + 24.3009i −0.171874 + 0.148176i
\(165\) 0 0
\(166\) 50.4160 + 135.690i 0.303711 + 0.817411i
\(167\) 12.3771i 0.0741144i −0.999313 0.0370572i \(-0.988202\pi\)
0.999313 0.0370572i \(-0.0117984\pi\)
\(168\) −36.5592 + 66.3582i −0.217614 + 0.394989i
\(169\) −66.5008 −0.393496
\(170\) 0 0
\(171\) 71.3272i 0.417118i
\(172\) 182.904 + 212.156i 1.06340 + 1.23347i
\(173\) −59.3729 −0.343196 −0.171598 0.985167i \(-0.554893\pi\)
−0.171598 + 0.985167i \(0.554893\pi\)
\(174\) 31.0948 + 83.6890i 0.178706 + 0.480971i
\(175\) 0 0
\(176\) 174.719 + 26.0164i 0.992720 + 0.147820i
\(177\) −96.2000 −0.543503
\(178\) −216.895 + 80.5877i −1.21851 + 0.452740i
\(179\) 252.782i 1.41219i 0.708118 + 0.706094i \(0.249545\pi\)
−0.708118 + 0.706094i \(0.750455\pi\)
\(180\) 0 0
\(181\) 125.373 0.692670 0.346335 0.938111i \(-0.387426\pi\)
0.346335 + 0.938111i \(0.387426\pi\)
\(182\) −38.5597 103.780i −0.211867 0.570220i
\(183\) 142.446i 0.778393i
\(184\) −261.027 143.809i −1.41862 0.781573i
\(185\) 0 0
\(186\) −15.7050 + 5.83523i −0.0844355 + 0.0313722i
\(187\) 269.545i 1.44142i
\(188\) 99.3084 + 115.191i 0.528236 + 0.612717i
\(189\) −28.4110 −0.150323
\(190\) 0 0
\(191\) 97.4640i 0.510283i −0.966904 0.255141i \(-0.917878\pi\)
0.966904 0.255141i \(-0.0821220\pi\)
\(192\) 93.7025 59.2270i 0.488034 0.308474i
\(193\) 342.376 1.77397 0.886985 0.461798i \(-0.152796\pi\)
0.886985 + 0.461798i \(0.152796\pi\)
\(194\) −136.782 + 50.8215i −0.705060 + 0.261966i
\(195\) 0 0
\(196\) 57.8775 49.8974i 0.295293 0.254579i
\(197\) −74.4829 −0.378086 −0.189043 0.981969i \(-0.560539\pi\)
−0.189043 + 0.981969i \(0.560539\pi\)
\(198\) 23.0713 + 62.0943i 0.116522 + 0.313608i
\(199\) 178.027i 0.894606i 0.894382 + 0.447303i \(0.147615\pi\)
−0.894382 + 0.447303i \(0.852385\pi\)
\(200\) 0 0
\(201\) 180.988 0.900438
\(202\) −55.1356 + 20.4858i −0.272949 + 0.101415i
\(203\) 140.917i 0.694173i
\(204\) 110.448 + 128.112i 0.541413 + 0.628000i
\(205\) 0 0
\(206\) −19.6354 52.8468i −0.0953172 0.256538i
\(207\) 111.758i 0.539892i
\(208\) −23.8575 + 160.220i −0.114700 + 0.770291i
\(209\) −262.491 −1.25594
\(210\) 0 0
\(211\) 185.893i 0.881008i −0.897751 0.440504i \(-0.854800\pi\)
0.897751 0.440504i \(-0.145200\pi\)
\(212\) −168.978 + 145.679i −0.797064 + 0.687166i
\(213\) −132.930 −0.624084
\(214\) −3.13947 8.44961i −0.0146704 0.0394842i
\(215\) 0 0
\(216\) 36.4092 + 20.0592i 0.168561 + 0.0928666i
\(217\) −26.4444 −0.121863
\(218\) −362.422 + 134.659i −1.66249 + 0.617701i
\(219\) 161.984i 0.739653i
\(220\) 0 0
\(221\) −247.178 −1.11845
\(222\) 43.0111 + 115.761i 0.193744 + 0.521444i
\(223\) 202.724i 0.909074i −0.890728 0.454537i \(-0.849805\pi\)
0.890728 0.454537i \(-0.150195\pi\)
\(224\) 171.198 36.1186i 0.764276 0.161244i
\(225\) 0 0
\(226\) 141.682 52.6422i 0.626910 0.232930i
\(227\) 51.2708i 0.225863i −0.993603 0.112931i \(-0.963976\pi\)
0.993603 0.112931i \(-0.0360240\pi\)
\(228\) −124.760 + 107.558i −0.547192 + 0.471745i
\(229\) 337.056 1.47186 0.735930 0.677058i \(-0.236745\pi\)
0.735930 + 0.677058i \(0.236745\pi\)
\(230\) 0 0
\(231\) 104.555i 0.452621i
\(232\) 99.4925 180.588i 0.428847 0.778395i
\(233\) 80.2851 0.344571 0.172286 0.985047i \(-0.444885\pi\)
0.172286 + 0.985047i \(0.444885\pi\)
\(234\) −56.9417 + 21.1568i −0.243341 + 0.0904138i
\(235\) 0 0
\(236\) 145.065 + 168.265i 0.614682 + 0.712988i
\(237\) 85.5221 0.360853
\(238\) 92.9873 + 250.267i 0.390703 + 1.05154i
\(239\) 330.808i 1.38413i −0.721834 0.692066i \(-0.756701\pi\)
0.721834 0.692066i \(-0.243299\pi\)
\(240\) 0 0
\(241\) −359.914 −1.49342 −0.746710 0.665150i \(-0.768368\pi\)
−0.746710 + 0.665150i \(0.768368\pi\)
\(242\) 1.66582 0.618939i 0.00688355 0.00255760i
\(243\) 15.5885i 0.0641500i
\(244\) −249.155 + 214.802i −1.02113 + 0.880334i
\(245\) 0 0
\(246\) 11.2255 + 30.2123i 0.0456319 + 0.122814i
\(247\) 240.710i 0.974534i
\(248\) 33.8889 + 18.6707i 0.136649 + 0.0752850i
\(249\) 125.360 0.503455
\(250\) 0 0
\(251\) 312.213i 1.24388i −0.783067 0.621938i \(-0.786346\pi\)
0.783067 0.621938i \(-0.213654\pi\)
\(252\) 42.8424 + 49.6942i 0.170010 + 0.197199i
\(253\) −411.280 −1.62561
\(254\) −91.4645 246.169i −0.360096 0.969167i
\(255\) 0 0
\(256\) −244.894 74.5853i −0.956617 0.291349i
\(257\) −80.2592 −0.312293 −0.156146 0.987734i \(-0.549907\pi\)
−0.156146 + 0.987734i \(0.549907\pi\)
\(258\) 227.398 84.4901i 0.881386 0.327481i
\(259\) 194.920i 0.752586i
\(260\) 0 0
\(261\) 77.3179 0.296237
\(262\) 52.7680 + 142.020i 0.201405 + 0.542063i
\(263\) 487.967i 1.85539i −0.373342 0.927694i \(-0.621788\pi\)
0.373342 0.927694i \(-0.378212\pi\)
\(264\) 73.8199 133.990i 0.279621 0.507536i
\(265\) 0 0
\(266\) −243.718 + 90.5540i −0.916233 + 0.340428i
\(267\) 200.383i 0.750498i
\(268\) −272.921 316.569i −1.01836 1.18123i
\(269\) −309.553 −1.15076 −0.575378 0.817888i \(-0.695145\pi\)
−0.575378 + 0.817888i \(0.695145\pi\)
\(270\) 0 0
\(271\) 48.9693i 0.180698i −0.995910 0.0903492i \(-0.971202\pi\)
0.995910 0.0903492i \(-0.0287983\pi\)
\(272\) 57.5327 386.374i 0.211517 1.42049i
\(273\) −95.8794 −0.351207
\(274\) 125.221 46.5262i 0.457012 0.169804i
\(275\) 0 0
\(276\) −195.477 + 168.525i −0.708251 + 0.610598i
\(277\) 199.644 0.720736 0.360368 0.932810i \(-0.382651\pi\)
0.360368 + 0.932810i \(0.382651\pi\)
\(278\) −26.5545 71.4690i −0.0955197 0.257083i
\(279\) 14.5094i 0.0520051i
\(280\) 0 0
\(281\) 61.1598 0.217650 0.108825 0.994061i \(-0.465291\pi\)
0.108825 + 0.994061i \(0.465291\pi\)
\(282\) 123.466 45.8741i 0.437823 0.162674i
\(283\) 432.506i 1.52829i 0.645044 + 0.764145i \(0.276839\pi\)
−0.645044 + 0.764145i \(0.723161\pi\)
\(284\) 200.452 + 232.510i 0.705816 + 0.818697i
\(285\) 0 0
\(286\) 77.8593 + 209.551i 0.272235 + 0.732697i
\(287\) 50.8720i 0.177254i
\(288\) −19.8174 93.9323i −0.0688105 0.326154i
\(289\) 307.073 1.06254
\(290\) 0 0
\(291\) 126.369i 0.434256i
\(292\) 283.329 244.264i 0.970305 0.836521i
\(293\) 283.234 0.966668 0.483334 0.875436i \(-0.339426\pi\)
0.483334 + 0.875436i \(0.339426\pi\)
\(294\) −23.0494 62.0354i −0.0783993 0.211005i
\(295\) 0 0
\(296\) 137.620 249.793i 0.464933 0.843895i
\(297\) 57.3672 0.193155
\(298\) 237.566 88.2681i 0.797200 0.296202i
\(299\) 377.152i 1.26138i
\(300\) 0 0
\(301\) 382.896 1.27208
\(302\) 47.6739 + 128.310i 0.157861 + 0.424868i
\(303\) 50.9382i 0.168113i
\(304\) 376.263 + 56.0272i 1.23771 + 0.184300i
\(305\) 0 0
\(306\) 137.316 51.0199i 0.448744 0.166732i
\(307\) 100.077i 0.325983i −0.986627 0.162992i \(-0.947886\pi\)
0.986627 0.162992i \(-0.0521144\pi\)
\(308\) 182.880 157.665i 0.593766 0.511898i
\(309\) −48.8237 −0.158005
\(310\) 0 0
\(311\) 404.185i 1.29963i 0.760092 + 0.649815i \(0.225154\pi\)
−0.760092 + 0.649815i \(0.774846\pi\)
\(312\) 122.871 + 67.6943i 0.393818 + 0.216969i
\(313\) 128.579 0.410795 0.205398 0.978679i \(-0.434151\pi\)
0.205398 + 0.978679i \(0.434151\pi\)
\(314\) 47.9525 17.8168i 0.152715 0.0567415i
\(315\) 0 0
\(316\) −128.963 149.588i −0.408112 0.473381i
\(317\) −85.9315 −0.271077 −0.135539 0.990772i \(-0.543276\pi\)
−0.135539 + 0.990772i \(0.543276\pi\)
\(318\) 67.2944 + 181.117i 0.211618 + 0.569550i
\(319\) 284.538i 0.891969i
\(320\) 0 0
\(321\) −7.80635 −0.0243189
\(322\) −381.865 + 141.883i −1.18592 + 0.440630i
\(323\) 580.475i 1.79714i
\(324\) 27.2661 23.5066i 0.0841545 0.0725514i
\(325\) 0 0
\(326\) 44.2167 + 119.005i 0.135634 + 0.365047i
\(327\) 334.832i 1.02395i
\(328\) 35.9175 65.1934i 0.109505 0.198760i
\(329\) 207.894 0.631898
\(330\) 0 0
\(331\) 183.391i 0.554052i −0.960862 0.277026i \(-0.910651\pi\)
0.960862 0.277026i \(-0.0893488\pi\)
\(332\) −189.037 219.270i −0.569390 0.660452i
\(333\) 106.948 0.321165
\(334\) 8.62160 + 23.2043i 0.0258132 + 0.0694739i
\(335\) 0 0
\(336\) 22.3167 149.873i 0.0664188 0.446050i
\(337\) −168.130 −0.498901 −0.249451 0.968388i \(-0.580250\pi\)
−0.249451 + 0.968388i \(0.580250\pi\)
\(338\) 124.674 46.3229i 0.368858 0.137050i
\(339\) 130.896i 0.386123i
\(340\) 0 0
\(341\) 53.3962 0.156587
\(342\) 49.6849 + 133.722i 0.145277 + 0.391001i
\(343\) 372.374i 1.08564i
\(344\) −490.688 270.338i −1.42642 0.785867i
\(345\) 0 0
\(346\) 111.311 41.3578i 0.321708 0.119531i
\(347\) 137.414i 0.396006i −0.980201 0.198003i \(-0.936554\pi\)
0.980201 0.198003i \(-0.0634455\pi\)
\(348\) −116.592 135.238i −0.335034 0.388615i
\(349\) −13.4893 −0.0386513 −0.0193256 0.999813i \(-0.506152\pi\)
−0.0193256 + 0.999813i \(0.506152\pi\)
\(350\) 0 0
\(351\) 52.6068i 0.149877i
\(352\) −345.681 + 72.9301i −0.982047 + 0.207188i
\(353\) −243.547 −0.689935 −0.344968 0.938615i \(-0.612110\pi\)
−0.344968 + 0.938615i \(0.612110\pi\)
\(354\) 180.353 67.0107i 0.509473 0.189296i
\(355\) 0 0
\(356\) 350.493 302.168i 0.984532 0.848786i
\(357\) 231.215 0.647660
\(358\) −176.082 473.909i −0.491849 1.32377i
\(359\) 17.9166i 0.0499068i −0.999689 0.0249534i \(-0.992056\pi\)
0.999689 0.0249534i \(-0.00794374\pi\)
\(360\) 0 0
\(361\) −204.285 −0.565887
\(362\) −235.047 + 87.3321i −0.649300 + 0.241249i
\(363\) 1.53900i 0.00423968i
\(364\) 144.582 + 167.704i 0.397202 + 0.460727i
\(365\) 0 0
\(366\) 99.2245 + 267.054i 0.271105 + 0.729656i
\(367\) 238.417i 0.649637i −0.945776 0.324818i \(-0.894697\pi\)
0.945776 0.324818i \(-0.105303\pi\)
\(368\) 589.541 + 87.7852i 1.60201 + 0.238547i
\(369\) 27.9123 0.0756431
\(370\) 0 0
\(371\) 304.968i 0.822016i
\(372\) 25.3787 21.8795i 0.0682222 0.0588158i
\(373\) 181.271 0.485981 0.242990 0.970029i \(-0.421872\pi\)
0.242990 + 0.970029i \(0.421872\pi\)
\(374\) −187.759 505.336i −0.502029 1.35117i
\(375\) 0 0
\(376\) −266.420 146.781i −0.708564 0.390375i
\(377\) 260.927 0.692114
\(378\) 53.2642 19.7904i 0.140911 0.0523557i
\(379\) 306.206i 0.807931i 0.914774 + 0.403965i \(0.132368\pi\)
−0.914774 + 0.403965i \(0.867632\pi\)
\(380\) 0 0
\(381\) −227.428 −0.596924
\(382\) 67.8912 + 182.723i 0.177726 + 0.478333i
\(383\) 144.027i 0.376050i 0.982164 + 0.188025i \(0.0602086\pi\)
−0.982164 + 0.188025i \(0.939791\pi\)
\(384\) −134.415 + 176.308i −0.350039 + 0.459136i
\(385\) 0 0
\(386\) −641.878 + 238.491i −1.66290 + 0.617853i
\(387\) 210.086i 0.542858i
\(388\) 221.034 190.558i 0.569674 0.491128i
\(389\) 14.0099 0.0360152 0.0180076 0.999838i \(-0.494268\pi\)
0.0180076 + 0.999838i \(0.494268\pi\)
\(390\) 0 0
\(391\) 909.506i 2.32610i
\(392\) −73.7499 + 133.863i −0.188138 + 0.341486i
\(393\) 131.209 0.333864
\(394\) 139.639 51.8831i 0.354413 0.131683i
\(395\) 0 0
\(396\) −86.5069 100.342i −0.218452 0.253389i
\(397\) −39.1084 −0.0985098 −0.0492549 0.998786i \(-0.515685\pi\)
−0.0492549 + 0.998786i \(0.515685\pi\)
\(398\) −124.009 333.760i −0.311581 0.838592i
\(399\) 225.164i 0.564321i
\(400\) 0 0
\(401\) −121.067 −0.301913 −0.150957 0.988540i \(-0.548235\pi\)
−0.150957 + 0.988540i \(0.548235\pi\)
\(402\) −339.312 + 126.072i −0.844059 + 0.313612i
\(403\) 48.9653i 0.121502i
\(404\) 89.0970 76.8124i 0.220537 0.190130i
\(405\) 0 0
\(406\) −98.1595 264.188i −0.241772 0.650709i
\(407\) 393.579i 0.967026i
\(408\) −296.305 163.246i −0.726239 0.400112i
\(409\) −541.795 −1.32468 −0.662342 0.749202i \(-0.730437\pi\)
−0.662342 + 0.749202i \(0.730437\pi\)
\(410\) 0 0
\(411\) 115.688i 0.281480i
\(412\) 73.6237 + 85.3983i 0.178698 + 0.207278i
\(413\) 303.682 0.735307
\(414\) 77.8478 + 209.520i 0.188038 + 0.506088i
\(415\) 0 0
\(416\) −66.8784 316.996i −0.160765 0.762009i
\(417\) −66.0282 −0.158341
\(418\) 492.112 182.845i 1.17730 0.437429i
\(419\) 687.825i 1.64159i 0.571224 + 0.820794i \(0.306469\pi\)
−0.571224 + 0.820794i \(0.693531\pi\)
\(420\) 0 0
\(421\) −454.396 −1.07932 −0.539662 0.841882i \(-0.681448\pi\)
−0.539662 + 0.841882i \(0.681448\pi\)
\(422\) 129.489 + 348.507i 0.306845 + 0.825846i
\(423\) 114.067i 0.269661i
\(424\) 215.318 390.821i 0.507826 0.921749i
\(425\) 0 0
\(426\) 249.214 92.5959i 0.585008 0.217361i
\(427\) 449.670i 1.05309i
\(428\) 11.7716 + 13.6542i 0.0275037 + 0.0319024i
\(429\) 193.599 0.451279
\(430\) 0 0
\(431\) 466.145i 1.08154i 0.841169 + 0.540772i \(0.181868\pi\)
−0.841169 + 0.540772i \(0.818132\pi\)
\(432\) −82.2318 12.2447i −0.190351 0.0283441i
\(433\) −457.094 −1.05565 −0.527823 0.849355i \(-0.676991\pi\)
−0.527823 + 0.849355i \(0.676991\pi\)
\(434\) 49.5772 18.4205i 0.114233 0.0424436i
\(435\) 0 0
\(436\) 585.660 504.910i 1.34326 1.15805i
\(437\) −885.706 −2.02679
\(438\) −112.834 303.684i −0.257613 0.693341i
\(439\) 777.467i 1.77100i −0.464644 0.885498i \(-0.653818\pi\)
0.464644 0.885498i \(-0.346182\pi\)
\(440\) 0 0
\(441\) −57.3128 −0.129961
\(442\) 463.403 172.178i 1.04842 0.389544i
\(443\) 247.484i 0.558654i 0.960196 + 0.279327i \(0.0901114\pi\)
−0.960196 + 0.279327i \(0.909889\pi\)
\(444\) −161.272 187.065i −0.363226 0.421316i
\(445\) 0 0
\(446\) 141.213 + 380.061i 0.316620 + 0.852155i
\(447\) 219.480i 0.491007i
\(448\) −295.798 + 186.967i −0.660263 + 0.417336i
\(449\) 412.508 0.918726 0.459363 0.888249i \(-0.348078\pi\)
0.459363 + 0.888249i \(0.348078\pi\)
\(450\) 0 0
\(451\) 102.720i 0.227761i
\(452\) −228.952 + 197.384i −0.506531 + 0.436691i
\(453\) 118.542 0.261682
\(454\) 35.7141 + 96.1213i 0.0786654 + 0.211721i
\(455\) 0 0
\(456\) 158.974 288.552i 0.348627 0.632789i
\(457\) 745.400 1.63107 0.815537 0.578706i \(-0.196442\pi\)
0.815537 + 0.578706i \(0.196442\pi\)
\(458\) −631.904 + 234.785i −1.37970 + 0.512631i
\(459\) 126.862i 0.276388i
\(460\) 0 0
\(461\) 81.6151 0.177039 0.0885196 0.996074i \(-0.471786\pi\)
0.0885196 + 0.996074i \(0.471786\pi\)
\(462\) −72.8309 196.018i −0.157643 0.424281i
\(463\) 292.248i 0.631205i 0.948891 + 0.315603i \(0.102207\pi\)
−0.948891 + 0.315603i \(0.897793\pi\)
\(464\) −60.7329 + 407.865i −0.130890 + 0.879020i
\(465\) 0 0
\(466\) −150.517 + 55.9248i −0.322997 + 0.120010i
\(467\) 51.4163i 0.110099i −0.998484 0.0550495i \(-0.982468\pi\)
0.998484 0.0550495i \(-0.0175317\pi\)
\(468\) 92.0155 79.3285i 0.196614 0.169505i
\(469\) −571.339 −1.21821
\(470\) 0 0
\(471\) 44.3019i 0.0940592i
\(472\) −389.174 214.410i −0.824520 0.454259i
\(473\) −773.139 −1.63454
\(474\) −160.335 + 59.5727i −0.338259 + 0.125681i
\(475\) 0 0
\(476\) −348.660 404.422i −0.732480 0.849625i
\(477\) 167.329 0.350794
\(478\) 230.433 + 620.190i 0.482077 + 1.29747i
\(479\) 122.593i 0.255935i −0.991778 0.127967i \(-0.959155\pi\)
0.991778 0.127967i \(-0.0408453\pi\)
\(480\) 0 0
\(481\) 360.920 0.750354
\(482\) 674.758 250.708i 1.39991 0.520141i
\(483\) 352.794i 0.730423i
\(484\) −2.69190 + 2.32074i −0.00556177 + 0.00479492i
\(485\) 0 0
\(486\) −10.8586 29.2248i −0.0223427 0.0601334i
\(487\) 65.9859i 0.135495i 0.997703 + 0.0677474i \(0.0215812\pi\)
−0.997703 + 0.0677474i \(0.978419\pi\)
\(488\) 317.483 576.260i 0.650580 1.18086i
\(489\) 109.946 0.224837
\(490\) 0 0
\(491\) 361.163i 0.735567i −0.929911 0.367783i \(-0.880117\pi\)
0.929911 0.367783i \(-0.119883\pi\)
\(492\) −42.0904 48.8219i −0.0855496 0.0992315i
\(493\) −629.229 −1.27633
\(494\) 167.673 + 451.277i 0.339419 + 0.913516i
\(495\) 0 0
\(496\) −76.5396 11.3971i −0.154314 0.0229780i
\(497\) 419.630 0.844326
\(498\) −235.022 + 87.3231i −0.471933 + 0.175348i
\(499\) 711.138i 1.42513i 0.701608 + 0.712564i \(0.252466\pi\)
−0.701608 + 0.712564i \(0.747534\pi\)
\(500\) 0 0
\(501\) 21.4378 0.0427900
\(502\) 217.480 + 585.328i 0.433227 + 1.16599i
\(503\) 353.756i 0.703292i 0.936133 + 0.351646i \(0.114378\pi\)
−0.936133 + 0.351646i \(0.885622\pi\)
\(504\) −114.936 63.3224i −0.228047 0.125640i
\(505\) 0 0
\(506\) 771.057 286.488i 1.52383 0.566182i
\(507\) 115.183i 0.227185i
\(508\) 342.951 + 397.799i 0.675100 + 0.783068i
\(509\) 478.049 0.939192 0.469596 0.882881i \(-0.344400\pi\)
0.469596 + 0.882881i \(0.344400\pi\)
\(510\) 0 0
\(511\) 511.348i 1.00068i
\(512\) 511.075 30.7568i 0.998194 0.0600720i
\(513\) 123.542 0.240823
\(514\) 150.468 55.9067i 0.292739 0.108768i
\(515\) 0 0
\(516\) −367.466 + 316.800i −0.712142 + 0.613953i
\(517\) −419.778 −0.811949
\(518\) −135.777 365.431i −0.262117 0.705464i
\(519\) 102.837i 0.198144i
\(520\) 0 0
\(521\) −35.7365 −0.0685921 −0.0342960 0.999412i \(-0.510919\pi\)
−0.0342960 + 0.999412i \(0.510919\pi\)
\(522\) −144.954 + 53.8579i −0.277689 + 0.103176i
\(523\) 733.562i 1.40260i 0.712864 + 0.701302i \(0.247398\pi\)
−0.712864 + 0.701302i \(0.752602\pi\)
\(524\) −197.856 229.499i −0.377588 0.437976i
\(525\) 0 0
\(526\) 339.906 + 914.828i 0.646210 + 1.73922i
\(527\) 118.081i 0.224062i
\(528\) −45.0617 + 302.622i −0.0853441 + 0.573147i
\(529\) −858.753 −1.62335
\(530\) 0 0
\(531\) 166.623i 0.313791i
\(532\) 393.839 339.537i 0.740298 0.638227i
\(533\) 94.1965 0.176729
\(534\) −139.582 375.673i −0.261390 0.703507i
\(535\) 0 0
\(536\) 732.181 + 403.386i 1.36601 + 0.752585i
\(537\) −437.831 −0.815327
\(538\) 580.342 215.628i 1.07870 0.400795i
\(539\) 210.917i 0.391312i
\(540\) 0 0
\(541\) 608.939 1.12558 0.562790 0.826600i \(-0.309728\pi\)
0.562790 + 0.826600i \(0.309728\pi\)
\(542\) 34.1109 + 91.8064i 0.0629352 + 0.169384i
\(543\) 217.153i 0.399913i
\(544\) 161.278 + 764.440i 0.296467 + 1.40522i
\(545\) 0 0
\(546\) 179.752 66.7874i 0.329217 0.122321i
\(547\) 78.5868i 0.143669i −0.997417 0.0718344i \(-0.977115\pi\)
0.997417 0.0718344i \(-0.0228853\pi\)
\(548\) −202.353 + 174.452i −0.369257 + 0.318344i
\(549\) 246.724 0.449405
\(550\) 0 0
\(551\) 612.763i 1.11209i
\(552\) 249.085 452.112i 0.451242 0.819043i
\(553\) −269.974 −0.488200
\(554\) −374.287 + 139.067i −0.675609 + 0.251024i
\(555\) 0 0
\(556\) 99.5673 + 115.491i 0.179078 + 0.207718i
\(557\) 928.488 1.66694 0.833472 0.552561i \(-0.186349\pi\)
0.833472 + 0.552561i \(0.186349\pi\)
\(558\) −10.1069 27.2019i −0.0181128 0.0487489i
\(559\) 708.984i 1.26831i
\(560\) 0 0
\(561\) −466.866 −0.832202
\(562\) −114.661 + 42.6025i −0.204023 + 0.0758051i
\(563\) 447.978i 0.795697i −0.917451 0.397849i \(-0.869757\pi\)
0.917451 0.397849i \(-0.130243\pi\)
\(564\) −199.516 + 172.007i −0.353752 + 0.304977i
\(565\) 0 0
\(566\) −301.274 810.852i −0.532286 1.43260i
\(567\) 49.2093i 0.0867889i
\(568\) −537.763 296.274i −0.946766 0.521609i
\(569\) 571.441 1.00429 0.502145 0.864783i \(-0.332544\pi\)
0.502145 + 0.864783i \(0.332544\pi\)
\(570\) 0 0
\(571\) 990.801i 1.73520i 0.497260 + 0.867602i \(0.334340\pi\)
−0.497260 + 0.867602i \(0.665660\pi\)
\(572\) −291.937 338.627i −0.510380 0.592005i
\(573\) 168.813 0.294612
\(574\) −35.4363 95.3736i −0.0617357 0.166156i
\(575\) 0 0
\(576\) 102.584 + 162.298i 0.178098 + 0.281766i
\(577\) −826.638 −1.43265 −0.716324 0.697768i \(-0.754177\pi\)
−0.716324 + 0.697768i \(0.754177\pi\)
\(578\) −575.693 + 213.900i −0.996008 + 0.370069i
\(579\) 593.013i 1.02420i
\(580\) 0 0
\(581\) −395.735 −0.681127
\(582\) −88.0254 236.913i −0.151246 0.407066i
\(583\) 615.787i 1.05624i
\(584\) −361.030 + 655.301i −0.618202 + 1.12209i
\(585\) 0 0
\(586\) −530.999 + 197.294i −0.906142 + 0.336679i
\(587\) 900.009i 1.53323i 0.642104 + 0.766617i \(0.278062\pi\)
−0.642104 + 0.766617i \(0.721938\pi\)
\(588\) 86.4249 + 100.247i 0.146981 + 0.170488i
\(589\) 114.991 0.195230
\(590\) 0 0
\(591\) 129.008i 0.218288i
\(592\) −84.0071 + 564.169i −0.141904 + 0.952987i
\(593\) 704.088 1.18733 0.593666 0.804711i \(-0.297680\pi\)
0.593666 + 0.804711i \(0.297680\pi\)
\(594\) −107.551 + 39.9606i −0.181061 + 0.0672738i
\(595\) 0 0
\(596\) −383.897 + 330.965i −0.644122 + 0.555311i
\(597\) −308.351 −0.516501
\(598\) 262.715 + 707.075i 0.439323 + 1.18240i
\(599\) 376.098i 0.627876i 0.949444 + 0.313938i \(0.101648\pi\)
−0.949444 + 0.313938i \(0.898352\pi\)
\(600\) 0 0
\(601\) 430.191 0.715791 0.357896 0.933762i \(-0.383494\pi\)
0.357896 + 0.933762i \(0.383494\pi\)
\(602\) −717.844 + 266.716i −1.19243 + 0.443051i
\(603\) 313.480i 0.519868i
\(604\) −178.756 207.344i −0.295953 0.343285i
\(605\) 0 0
\(606\) −35.4824 95.4977i −0.0585518 0.157587i
\(607\) 93.4019i 0.153875i −0.997036 0.0769373i \(-0.975486\pi\)
0.997036 0.0769373i \(-0.0245141\pi\)
\(608\) −744.436 + 157.058i −1.22440 + 0.258319i
\(609\) −244.075 −0.400781
\(610\) 0 0
\(611\) 384.944i 0.630024i
\(612\) −221.897 + 191.302i −0.362576 + 0.312585i
\(613\) 156.506 0.255312 0.127656 0.991818i \(-0.459255\pi\)
0.127656 + 0.991818i \(0.459255\pi\)
\(614\) 69.7113 + 187.622i 0.113536 + 0.305573i
\(615\) 0 0
\(616\) −233.033 + 422.976i −0.378301 + 0.686649i
\(617\) 553.493 0.897072 0.448536 0.893765i \(-0.351946\pi\)
0.448536 + 0.893765i \(0.351946\pi\)
\(618\) 91.5334 34.0094i 0.148112 0.0550314i
\(619\) 14.4398i 0.0233276i 0.999932 + 0.0116638i \(0.00371278\pi\)
−0.999932 + 0.0116638i \(0.996287\pi\)
\(620\) 0 0
\(621\) 193.570 0.311707
\(622\) −281.546 757.756i −0.452646 1.21826i
\(623\) 632.564i 1.01535i
\(624\) −277.510 41.3224i −0.444728 0.0662219i
\(625\) 0 0
\(626\) −241.056 + 89.5651i −0.385074 + 0.143075i
\(627\) 454.649i 0.725117i
\(628\) −77.4893 + 66.8051i −0.123391 + 0.106378i
\(629\) −870.364 −1.38373
\(630\) 0 0
\(631\) 352.389i 0.558460i 0.960224 + 0.279230i \(0.0900793\pi\)
−0.960224 + 0.279230i \(0.909921\pi\)
\(632\) 345.977 + 190.612i 0.547432 + 0.301601i
\(633\) 321.976 0.508650
\(634\) 161.102 59.8579i 0.254104 0.0944130i
\(635\) 0 0
\(636\) −252.324 292.678i −0.396735 0.460185i
\(637\) −193.415 −0.303634
\(638\) 198.203 + 533.445i 0.310662 + 0.836120i
\(639\) 230.241i 0.360315i
\(640\) 0 0
\(641\) −545.742 −0.851391 −0.425696 0.904866i \(-0.639971\pi\)
−0.425696 + 0.904866i \(0.639971\pi\)
\(642\) 14.6352 5.43772i 0.0227962 0.00846997i
\(643\) 757.447i 1.17799i −0.808137 0.588995i \(-0.799524\pi\)
0.808137 0.588995i \(-0.200476\pi\)
\(644\) 617.079 531.997i 0.958197 0.826082i
\(645\) 0 0
\(646\) −404.345 1088.26i −0.625922 1.68461i
\(647\) 1161.36i 1.79500i 0.441016 + 0.897499i \(0.354618\pi\)
−0.441016 + 0.897499i \(0.645382\pi\)
\(648\) −34.7435 + 63.0626i −0.0536166 + 0.0973188i
\(649\) −613.191 −0.944824
\(650\) 0 0
\(651\) 45.8030i 0.0703579i
\(652\) −165.793 192.308i −0.254283 0.294950i
\(653\) 621.231 0.951348 0.475674 0.879622i \(-0.342204\pi\)
0.475674 + 0.879622i \(0.342204\pi\)
\(654\) −233.236 627.734i −0.356630 0.959838i
\(655\) 0 0
\(656\) −21.9250 + 147.242i −0.0334223 + 0.224455i
\(657\) −280.565 −0.427039
\(658\) −389.755 + 144.814i −0.592333 + 0.220083i
\(659\) 736.047i 1.11692i 0.829533 + 0.558458i \(0.188607\pi\)
−0.829533 + 0.558458i \(0.811393\pi\)
\(660\) 0 0
\(661\) 383.845 0.580704 0.290352 0.956920i \(-0.406228\pi\)
0.290352 + 0.956920i \(0.406228\pi\)
\(662\) 127.746 + 343.817i 0.192970 + 0.519362i
\(663\) 428.125i 0.645739i
\(664\) 507.141 + 279.403i 0.763766 + 0.420788i
\(665\) 0 0
\(666\) −200.503 + 74.4974i −0.301056 + 0.111858i
\(667\) 960.096i 1.43942i
\(668\) −32.3271 37.4972i −0.0483939 0.0561335i
\(669\) 351.128 0.524854
\(670\) 0 0
\(671\) 907.968i 1.35316i
\(672\) 62.5592 + 296.523i 0.0930940 + 0.441255i
\(673\) −984.464 −1.46280 −0.731400 0.681949i \(-0.761133\pi\)
−0.731400 + 0.681949i \(0.761133\pi\)
\(674\) 315.205 117.115i 0.467664 0.173761i
\(675\) 0 0
\(676\) −201.468 + 173.690i −0.298030 + 0.256938i
\(677\) −673.154 −0.994319 −0.497160 0.867659i \(-0.665624\pi\)
−0.497160 + 0.867659i \(0.665624\pi\)
\(678\) 91.1789 + 245.400i 0.134482 + 0.361947i
\(679\) 398.918i 0.587507i
\(680\) 0 0
\(681\) 88.8037 0.130402
\(682\) −100.106 + 37.1945i −0.146783 + 0.0545374i
\(683\) 291.192i 0.426343i −0.977015 0.213171i \(-0.931621\pi\)
0.977015 0.213171i \(-0.0683793\pi\)
\(684\) −186.296 216.090i −0.272362 0.315921i
\(685\) 0 0
\(686\) 259.387 + 698.117i 0.378115 + 1.01766i
\(687\) 583.798i 0.849778i
\(688\) 1108.24 + 165.022i 1.61081 + 0.239857i
\(689\) 564.689 0.819578
\(690\) 0 0
\(691\) 943.693i 1.36569i −0.730563 0.682846i \(-0.760742\pi\)
0.730563 0.682846i \(-0.239258\pi\)
\(692\) −179.874 + 155.073i −0.259933 + 0.224094i
\(693\) −181.095 −0.261321
\(694\) 95.7193 + 257.620i 0.137924 + 0.371211i
\(695\) 0 0
\(696\) 312.787 + 172.326i 0.449406 + 0.247595i
\(697\) −227.156 −0.325905
\(698\) 25.2894 9.39633i 0.0362312 0.0134618i
\(699\) 139.058i 0.198938i
\(700\) 0 0
\(701\) 885.681 1.26345 0.631727 0.775191i \(-0.282346\pi\)
0.631727 + 0.775191i \(0.282346\pi\)
\(702\) −36.6447 98.6259i −0.0522004 0.140493i
\(703\) 847.588i 1.20567i
\(704\) 597.272 377.521i 0.848397 0.536251i
\(705\) 0 0
\(706\) 456.596 169.649i 0.646737 0.240296i
\(707\) 160.801i 0.227441i
\(708\) −291.444 + 251.260i −0.411644 + 0.354887i
\(709\) −286.183 −0.403644 −0.201822 0.979422i \(-0.564686\pi\)
−0.201822 + 0.979422i \(0.564686\pi\)
\(710\) 0 0
\(711\) 148.129i 0.208339i
\(712\) −446.613 + 810.642i −0.627266 + 1.13854i
\(713\) 180.171 0.252694
\(714\) −433.475 + 161.059i −0.607108 + 0.225572i
\(715\) 0 0
\(716\) 660.228 + 765.818i 0.922106 + 1.06958i
\(717\) 572.976 0.799129
\(718\) 12.4803 + 33.5895i 0.0173820 + 0.0467820i
\(719\) 666.163i 0.926513i −0.886224 0.463257i \(-0.846681\pi\)
0.886224 0.463257i \(-0.153319\pi\)
\(720\) 0 0
\(721\) 154.125 0.213766
\(722\) 382.989 142.300i 0.530455 0.197092i
\(723\) 623.389i 0.862226i
\(724\) 379.826 327.456i 0.524622 0.452287i
\(725\) 0 0
\(726\) 1.07203 + 2.88528i 0.00147663 + 0.00397422i
\(727\) 856.270i 1.17781i 0.808201 + 0.588907i \(0.200441\pi\)
−0.808201 + 0.588907i \(0.799559\pi\)
\(728\) −387.877 213.696i −0.532798 0.293538i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 1709.72i 2.33888i
\(732\) −372.047 431.549i −0.508261 0.589547i
\(733\) 769.487 1.04978 0.524889 0.851171i \(-0.324107\pi\)
0.524889 + 0.851171i \(0.324107\pi\)
\(734\) 166.076 + 446.978i 0.226261 + 0.608961i
\(735\) 0 0
\(736\) −1166.41 + 246.083i −1.58479 + 0.334352i
\(737\) 1153.64 1.56532
\(738\) −52.3293 + 19.4431i −0.0709069 + 0.0263456i
\(739\) 1156.70i 1.56522i −0.622511 0.782611i \(-0.713887\pi\)
0.622511 0.782611i \(-0.286113\pi\)
\(740\) 0 0
\(741\) 416.922 0.562647
\(742\) −212.433 571.746i −0.286298 0.770547i
\(743\) 426.794i 0.574421i −0.957868 0.287210i \(-0.907272\pi\)
0.957868 0.287210i \(-0.0927278\pi\)
\(744\) −32.3386 + 58.6973i −0.0434658 + 0.0788942i
\(745\) 0 0
\(746\) −339.842 + 126.269i −0.455552 + 0.169261i
\(747\) 217.130i 0.290670i
\(748\) 704.011 + 816.603i 0.941191 + 1.09172i
\(749\) 24.6429 0.0329011
\(750\) 0 0
\(751\) 1222.03i 1.62721i −0.581420 0.813604i \(-0.697503\pi\)
0.581420 0.813604i \(-0.302497\pi\)
\(752\) 601.722 + 89.5990i 0.800162 + 0.119148i
\(753\) 540.768 0.718152
\(754\) −489.179 + 181.756i −0.648779 + 0.241055i
\(755\) 0 0
\(756\) −86.0729 + 74.2053i −0.113853 + 0.0981551i
\(757\) 1312.95 1.73442 0.867209 0.497945i \(-0.165912\pi\)
0.867209 + 0.497945i \(0.165912\pi\)
\(758\) −213.296 574.067i −0.281393 0.757344i
\(759\) 712.358i 0.938548i
\(760\) 0 0
\(761\) −189.584 −0.249124 −0.124562 0.992212i \(-0.539753\pi\)
−0.124562 + 0.992212i \(0.539753\pi\)
\(762\) 426.376 158.421i 0.559549 0.207902i
\(763\) 1056.99i 1.38531i
\(764\) −254.561 295.273i −0.333195 0.386483i
\(765\) 0 0
\(766\) −100.326 270.019i −0.130974 0.352505i
\(767\) 562.308i 0.733127i
\(768\) 129.185 424.169i 0.168210 0.552303i
\(769\) 254.995 0.331594 0.165797 0.986160i \(-0.446980\pi\)
0.165797 + 0.986160i \(0.446980\pi\)
\(770\) 0 0
\(771\) 139.013i 0.180302i
\(772\) 1037.25 894.235i 1.34359 1.15834i
\(773\) −23.2536 −0.0300823 −0.0150411 0.999887i \(-0.504788\pi\)
−0.0150411 + 0.999887i \(0.504788\pi\)
\(774\) 146.341 + 393.864i 0.189071 + 0.508869i
\(775\) 0 0
\(776\) −281.650 + 511.220i −0.362951 + 0.658788i
\(777\) −337.611 −0.434506
\(778\) −26.2654 + 9.75897i −0.0337602 + 0.0125437i
\(779\) 221.212i 0.283969i
\(780\) 0 0
\(781\) −847.312 −1.08491
\(782\) −633.541 1705.12i −0.810155 2.18046i
\(783\) 133.919i 0.171033i
\(784\) 45.0189 302.335i 0.0574221 0.385631i
\(785\) 0 0
\(786\) −245.987 + 91.3969i −0.312960 + 0.116281i
\(787\)