Properties

Label 378.4.g.c.109.3
Level $378$
Weight $4$
Character 378.109
Analytic conductor $22.303$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 378.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.3027219822\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - x^{7} + 18x^{6} + 9x^{5} + 283x^{4} - 48x^{3} + 186x^{2} + 40x + 100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.3
Root \(-1.84763 + 3.20018i\) of defining polynomial
Character \(\chi\) \(=\) 378.109
Dual form 378.4.g.c.163.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(5.04834 + 8.74398i) q^{5} +(-5.48778 + 17.6885i) q^{7} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(5.04834 + 8.74398i) q^{5} +(-5.48778 + 17.6885i) q^{7} +8.00000 q^{8} +(10.0967 - 17.4880i) q^{10} +(-18.0748 + 31.3065i) q^{11} -4.01927 q^{13} +(36.1252 - 8.18341i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-18.9802 + 32.8747i) q^{17} +(-28.5163 - 49.3917i) q^{19} -40.3867 q^{20} +72.2993 q^{22} +(-39.2198 - 67.9308i) q^{23} +(11.5285 - 19.9680i) q^{25} +(4.01927 + 6.96157i) q^{26} +(-50.2993 - 54.3873i) q^{28} -215.332 q^{29} +(91.1642 - 157.901i) q^{31} +(-16.0000 + 27.7128i) q^{32} +75.9208 q^{34} +(-182.372 + 41.3127i) q^{35} +(-156.279 - 270.683i) q^{37} +(-57.0327 + 98.7835i) q^{38} +(40.3867 + 69.9518i) q^{40} -186.557 q^{41} +262.266 q^{43} +(-72.2993 - 125.226i) q^{44} +(-78.4397 + 135.862i) q^{46} +(68.9606 + 119.443i) q^{47} +(-282.768 - 194.142i) q^{49} -46.1142 q^{50} +(8.03853 - 13.9231i) q^{52} +(-273.767 + 474.179i) q^{53} -364.991 q^{55} +(-43.9023 + 141.508i) q^{56} +(215.332 + 372.967i) q^{58} +(-1.86703 + 3.23378i) q^{59} +(57.5008 + 99.5943i) q^{61} -364.657 q^{62} +64.0000 q^{64} +(-20.2906 - 35.1444i) q^{65} +(-313.900 + 543.690i) q^{67} +(-75.9208 - 131.499i) q^{68} +(253.928 + 274.566i) q^{70} -533.107 q^{71} +(149.197 - 258.417i) q^{73} +(-312.557 + 541.365i) q^{74} +228.131 q^{76} +(-454.576 - 491.521i) q^{77} +(433.508 + 750.857i) q^{79} +(80.7734 - 139.904i) q^{80} +(186.557 + 323.126i) q^{82} +244.224 q^{83} -383.274 q^{85} +(-262.266 - 454.258i) q^{86} +(-144.599 + 250.452i) q^{88} +(223.508 + 387.128i) q^{89} +(22.0569 - 71.0949i) q^{91} +313.759 q^{92} +(137.921 - 238.887i) q^{94} +(287.920 - 498.692i) q^{95} -1803.99 q^{97} +(-53.4948 + 683.911i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{2} - 16 q^{4} + 2 q^{5} + 6 q^{7} + 64 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{2} - 16 q^{4} + 2 q^{5} + 6 q^{7} + 64 q^{8} + 4 q^{10} - 32 q^{11} - 4 q^{13} - 36 q^{14} - 64 q^{16} + 58 q^{17} + 70 q^{19} - 16 q^{20} + 128 q^{22} - 86 q^{23} - 156 q^{25} + 4 q^{26} + 48 q^{28} + 212 q^{29} - 64 q^{31} - 128 q^{32} - 232 q^{34} - 8 q^{35} - 146 q^{37} + 140 q^{38} + 16 q^{40} + 780 q^{41} + 880 q^{43} - 128 q^{44} - 172 q^{46} + 306 q^{47} + 50 q^{49} + 624 q^{50} + 8 q^{52} + 90 q^{53} - 64 q^{55} + 48 q^{56} - 212 q^{58} - 148 q^{59} - 364 q^{61} + 256 q^{62} + 512 q^{64} - 1296 q^{65} - 954 q^{67} + 232 q^{68} + 20 q^{70} + 1360 q^{71} - 54 q^{73} - 292 q^{74} - 560 q^{76} - 2224 q^{77} - 226 q^{79} + 32 q^{80} - 780 q^{82} + 3136 q^{83} + 3920 q^{85} - 880 q^{86} - 256 q^{88} + 1458 q^{89} + 3836 q^{91} + 688 q^{92} + 612 q^{94} - 1310 q^{95} - 4344 q^{97} - 776 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.353553 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 5.04834 + 8.74398i 0.451537 + 0.782085i 0.998482 0.0550835i \(-0.0175425\pi\)
−0.546945 + 0.837169i \(0.684209\pi\)
\(6\) 0 0
\(7\) −5.48778 + 17.6885i −0.296312 + 0.955091i
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) 10.0967 17.4880i 0.319285 0.553018i
\(11\) −18.0748 + 31.3065i −0.495433 + 0.858116i −0.999986 0.00526523i \(-0.998324\pi\)
0.504553 + 0.863381i \(0.331657\pi\)
\(12\) 0 0
\(13\) −4.01927 −0.0857495 −0.0428748 0.999080i \(-0.513652\pi\)
−0.0428748 + 0.999080i \(0.513652\pi\)
\(14\) 36.1252 8.18341i 0.689634 0.156222i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −18.9802 + 32.8747i −0.270787 + 0.469017i −0.969064 0.246811i \(-0.920617\pi\)
0.698277 + 0.715828i \(0.253951\pi\)
\(18\) 0 0
\(19\) −28.5163 49.3917i −0.344321 0.596381i 0.640909 0.767617i \(-0.278557\pi\)
−0.985230 + 0.171236i \(0.945224\pi\)
\(20\) −40.3867 −0.451537
\(21\) 0 0
\(22\) 72.2993 0.700648
\(23\) −39.2198 67.9308i −0.355561 0.615850i 0.631653 0.775251i \(-0.282377\pi\)
−0.987214 + 0.159402i \(0.949044\pi\)
\(24\) 0 0
\(25\) 11.5285 19.9680i 0.0922284 0.159744i
\(26\) 4.01927 + 6.96157i 0.0303170 + 0.0525107i
\(27\) 0 0
\(28\) −50.2993 54.3873i −0.339488 0.367080i
\(29\) −215.332 −1.37884 −0.689418 0.724364i \(-0.742134\pi\)
−0.689418 + 0.724364i \(0.742134\pi\)
\(30\) 0 0
\(31\) 91.1642 157.901i 0.528180 0.914834i −0.471281 0.881983i \(-0.656208\pi\)
0.999460 0.0328507i \(-0.0104586\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 75.9208 0.382950
\(35\) −182.372 + 41.3127i −0.880759 + 0.199518i
\(36\) 0 0
\(37\) −156.279 270.683i −0.694380 1.20270i −0.970389 0.241546i \(-0.922346\pi\)
0.276010 0.961155i \(-0.410988\pi\)
\(38\) −57.0327 + 98.7835i −0.243472 + 0.421705i
\(39\) 0 0
\(40\) 40.3867 + 69.9518i 0.159642 + 0.276509i
\(41\) −186.557 −0.710617 −0.355308 0.934749i \(-0.615624\pi\)
−0.355308 + 0.934749i \(0.615624\pi\)
\(42\) 0 0
\(43\) 262.266 0.930121 0.465061 0.885279i \(-0.346033\pi\)
0.465061 + 0.885279i \(0.346033\pi\)
\(44\) −72.2993 125.226i −0.247717 0.429058i
\(45\) 0 0
\(46\) −78.4397 + 135.862i −0.251420 + 0.435472i
\(47\) 68.9606 + 119.443i 0.214020 + 0.370693i 0.952969 0.303068i \(-0.0980109\pi\)
−0.738949 + 0.673761i \(0.764678\pi\)
\(48\) 0 0
\(49\) −282.768 194.142i −0.824398 0.566011i
\(50\) −46.1142 −0.130431
\(51\) 0 0
\(52\) 8.03853 13.9231i 0.0214374 0.0371306i
\(53\) −273.767 + 474.179i −0.709526 + 1.22893i 0.255508 + 0.966807i \(0.417757\pi\)
−0.965033 + 0.262127i \(0.915576\pi\)
\(54\) 0 0
\(55\) −364.991 −0.894826
\(56\) −43.9023 + 141.508i −0.104762 + 0.337676i
\(57\) 0 0
\(58\) 215.332 + 372.967i 0.487492 + 0.844361i
\(59\) −1.86703 + 3.23378i −0.00411976 + 0.00713564i −0.868078 0.496428i \(-0.834645\pi\)
0.863958 + 0.503564i \(0.167978\pi\)
\(60\) 0 0
\(61\) 57.5008 + 99.5943i 0.120692 + 0.209045i 0.920041 0.391822i \(-0.128155\pi\)
−0.799349 + 0.600868i \(0.794822\pi\)
\(62\) −364.657 −0.746959
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −20.2906 35.1444i −0.0387191 0.0670635i
\(66\) 0 0
\(67\) −313.900 + 543.690i −0.572373 + 0.991378i 0.423949 + 0.905686i \(0.360644\pi\)
−0.996322 + 0.0856924i \(0.972690\pi\)
\(68\) −75.9208 131.499i −0.135393 0.234508i
\(69\) 0 0
\(70\) 253.928 + 274.566i 0.433574 + 0.468812i
\(71\) −533.107 −0.891100 −0.445550 0.895257i \(-0.646992\pi\)
−0.445550 + 0.895257i \(0.646992\pi\)
\(72\) 0 0
\(73\) 149.197 258.417i 0.239208 0.414320i −0.721279 0.692644i \(-0.756446\pi\)
0.960487 + 0.278324i \(0.0897789\pi\)
\(74\) −312.557 + 541.365i −0.491001 + 0.850438i
\(75\) 0 0
\(76\) 228.131 0.344321
\(77\) −454.576 491.521i −0.672775 0.727454i
\(78\) 0 0
\(79\) 433.508 + 750.857i 0.617385 + 1.06934i 0.989961 + 0.141340i \(0.0451412\pi\)
−0.372576 + 0.928002i \(0.621525\pi\)
\(80\) 80.7734 139.904i 0.112884 0.195521i
\(81\) 0 0
\(82\) 186.557 + 323.126i 0.251241 + 0.435162i
\(83\) 244.224 0.322977 0.161489 0.986875i \(-0.448370\pi\)
0.161489 + 0.986875i \(0.448370\pi\)
\(84\) 0 0
\(85\) −383.274 −0.489081
\(86\) −262.266 454.258i −0.328847 0.569580i
\(87\) 0 0
\(88\) −144.599 + 250.452i −0.175162 + 0.303390i
\(89\) 223.508 + 387.128i 0.266200 + 0.461073i 0.967877 0.251423i \(-0.0808984\pi\)
−0.701677 + 0.712495i \(0.747565\pi\)
\(90\) 0 0
\(91\) 22.0569 71.0949i 0.0254087 0.0818986i
\(92\) 313.759 0.355561
\(93\) 0 0
\(94\) 137.921 238.887i 0.151335 0.262120i
\(95\) 287.920 498.692i 0.310947 0.538576i
\(96\) 0 0
\(97\) −1803.99 −1.88832 −0.944162 0.329481i \(-0.893126\pi\)
−0.944162 + 0.329481i \(0.893126\pi\)
\(98\) −53.4948 + 683.911i −0.0551407 + 0.704954i
\(99\) 0 0
\(100\) 46.1142 + 79.8721i 0.0461142 + 0.0798721i
\(101\) −842.134 + 1458.62i −0.829658 + 1.43701i 0.0686484 + 0.997641i \(0.478131\pi\)
−0.898307 + 0.439369i \(0.855202\pi\)
\(102\) 0 0
\(103\) −820.532 1421.20i −0.784946 1.35957i −0.929031 0.370001i \(-0.879357\pi\)
0.144085 0.989565i \(-0.453976\pi\)
\(104\) −32.1541 −0.0303170
\(105\) 0 0
\(106\) 1095.07 1.00342
\(107\) −160.547 278.076i −0.145053 0.251239i 0.784340 0.620332i \(-0.213002\pi\)
−0.929393 + 0.369092i \(0.879669\pi\)
\(108\) 0 0
\(109\) −280.005 + 484.982i −0.246051 + 0.426173i −0.962427 0.271542i \(-0.912466\pi\)
0.716376 + 0.697715i \(0.245800\pi\)
\(110\) 364.991 + 632.184i 0.316369 + 0.547967i
\(111\) 0 0
\(112\) 289.002 65.4673i 0.243822 0.0552329i
\(113\) 1870.65 1.55731 0.778655 0.627452i \(-0.215902\pi\)
0.778655 + 0.627452i \(0.215902\pi\)
\(114\) 0 0
\(115\) 395.990 685.875i 0.321098 0.556158i
\(116\) 430.665 745.934i 0.344709 0.597053i
\(117\) 0 0
\(118\) 7.46811 0.00582623
\(119\) −477.346 516.141i −0.367716 0.397602i
\(120\) 0 0
\(121\) 12.1012 + 20.9598i 0.00909179 + 0.0157474i
\(122\) 115.002 199.189i 0.0853423 0.147817i
\(123\) 0 0
\(124\) 364.657 + 631.604i 0.264090 + 0.457417i
\(125\) 1494.88 1.06965
\(126\) 0 0
\(127\) 790.048 0.552011 0.276006 0.961156i \(-0.410989\pi\)
0.276006 + 0.961156i \(0.410989\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −40.5812 + 70.2888i −0.0273785 + 0.0474210i
\(131\) −819.041 1418.62i −0.546259 0.946148i −0.998527 0.0542661i \(-0.982718\pi\)
0.452267 0.891882i \(-0.350615\pi\)
\(132\) 0 0
\(133\) 1030.16 233.361i 0.671625 0.152143i
\(134\) 1255.60 0.809457
\(135\) 0 0
\(136\) −151.842 + 262.997i −0.0957376 + 0.165822i
\(137\) −994.660 + 1722.80i −0.620289 + 1.07437i 0.369143 + 0.929373i \(0.379651\pi\)
−0.989432 + 0.144999i \(0.953682\pi\)
\(138\) 0 0
\(139\) −655.628 −0.400069 −0.200035 0.979789i \(-0.564105\pi\)
−0.200035 + 0.979789i \(0.564105\pi\)
\(140\) 221.634 714.382i 0.133796 0.431259i
\(141\) 0 0
\(142\) 533.107 + 923.368i 0.315052 + 0.545685i
\(143\) 72.6475 125.829i 0.0424832 0.0735830i
\(144\) 0 0
\(145\) −1087.07 1882.86i −0.622596 1.07837i
\(146\) −596.788 −0.338291
\(147\) 0 0
\(148\) 1250.23 0.694380
\(149\) −1494.77 2589.01i −0.821853 1.42349i −0.904301 0.426895i \(-0.859607\pi\)
0.0824482 0.996595i \(-0.473726\pi\)
\(150\) 0 0
\(151\) 547.979 949.128i 0.295324 0.511516i −0.679736 0.733457i \(-0.737906\pi\)
0.975060 + 0.221940i \(0.0712391\pi\)
\(152\) −228.131 395.134i −0.121736 0.210853i
\(153\) 0 0
\(154\) −396.763 + 1278.87i −0.207611 + 0.669183i
\(155\) 1840.91 0.953971
\(156\) 0 0
\(157\) −250.513 + 433.901i −0.127345 + 0.220567i −0.922647 0.385646i \(-0.873979\pi\)
0.795302 + 0.606213i \(0.207312\pi\)
\(158\) 867.015 1501.71i 0.436557 0.756139i
\(159\) 0 0
\(160\) −323.094 −0.159642
\(161\) 1416.83 320.952i 0.693550 0.157109i
\(162\) 0 0
\(163\) −1134.21 1964.50i −0.545018 0.943998i −0.998606 0.0527870i \(-0.983190\pi\)
0.453588 0.891211i \(-0.350144\pi\)
\(164\) 373.114 646.252i 0.177654 0.307706i
\(165\) 0 0
\(166\) −244.224 423.009i −0.114190 0.197782i
\(167\) 1369.97 0.634799 0.317400 0.948292i \(-0.397190\pi\)
0.317400 + 0.948292i \(0.397190\pi\)
\(168\) 0 0
\(169\) −2180.85 −0.992647
\(170\) 383.274 + 663.850i 0.172916 + 0.299500i
\(171\) 0 0
\(172\) −524.532 + 908.516i −0.232530 + 0.402754i
\(173\) 921.885 + 1596.75i 0.405142 + 0.701727i 0.994338 0.106264i \(-0.0338887\pi\)
−0.589196 + 0.807990i \(0.700555\pi\)
\(174\) 0 0
\(175\) 289.939 + 313.503i 0.125242 + 0.135421i
\(176\) 578.395 0.247717
\(177\) 0 0
\(178\) 447.017 774.255i 0.188232 0.326028i
\(179\) 530.785 919.346i 0.221635 0.383884i −0.733669 0.679507i \(-0.762194\pi\)
0.955305 + 0.295623i \(0.0955272\pi\)
\(180\) 0 0
\(181\) 2441.54 1.00264 0.501320 0.865262i \(-0.332848\pi\)
0.501320 + 0.865262i \(0.332848\pi\)
\(182\) −145.197 + 32.8913i −0.0591358 + 0.0133960i
\(183\) 0 0
\(184\) −313.759 543.446i −0.125710 0.217736i
\(185\) 1577.90 2732.99i 0.627077 1.08613i
\(186\) 0 0
\(187\) −686.128 1188.41i −0.268314 0.464733i
\(188\) −551.685 −0.214020
\(189\) 0 0
\(190\) −1151.68 −0.439746
\(191\) 1846.08 + 3197.50i 0.699359 + 1.21132i 0.968689 + 0.248277i \(0.0798642\pi\)
−0.269331 + 0.963048i \(0.586802\pi\)
\(192\) 0 0
\(193\) −1571.16 + 2721.33i −0.585982 + 1.01495i 0.408770 + 0.912637i \(0.365958\pi\)
−0.994752 + 0.102313i \(0.967376\pi\)
\(194\) 1803.99 + 3124.60i 0.667623 + 1.15636i
\(195\) 0 0
\(196\) 1238.06 591.255i 0.451189 0.215472i
\(197\) 2273.51 0.822236 0.411118 0.911582i \(-0.365138\pi\)
0.411118 + 0.911582i \(0.365138\pi\)
\(198\) 0 0
\(199\) 1368.26 2369.89i 0.487403 0.844206i −0.512492 0.858692i \(-0.671278\pi\)
0.999895 + 0.0144854i \(0.00461100\pi\)
\(200\) 92.2284 159.744i 0.0326076 0.0564781i
\(201\) 0 0
\(202\) 3368.54 1.17331
\(203\) 1181.70 3808.92i 0.408566 1.31691i
\(204\) 0 0
\(205\) −941.803 1631.25i −0.320870 0.555763i
\(206\) −1641.06 + 2842.41i −0.555041 + 0.961359i
\(207\) 0 0
\(208\) 32.1541 + 55.6926i 0.0107187 + 0.0185653i
\(209\) 2061.71 0.682352
\(210\) 0 0
\(211\) 2915.84 0.951349 0.475675 0.879621i \(-0.342204\pi\)
0.475675 + 0.879621i \(0.342204\pi\)
\(212\) −1095.07 1896.72i −0.354763 0.614467i
\(213\) 0 0
\(214\) −321.094 + 556.151i −0.102568 + 0.177653i
\(215\) 1324.01 + 2293.25i 0.419984 + 0.727434i
\(216\) 0 0
\(217\) 2292.75 + 2479.09i 0.717244 + 0.775536i
\(218\) 1120.02 0.347969
\(219\) 0 0
\(220\) 729.983 1264.37i 0.223707 0.387471i
\(221\) 76.2865 132.132i 0.0232198 0.0402179i
\(222\) 0 0
\(223\) −1875.11 −0.563078 −0.281539 0.959550i \(-0.590845\pi\)
−0.281539 + 0.959550i \(0.590845\pi\)
\(224\) −402.395 435.098i −0.120027 0.129782i
\(225\) 0 0
\(226\) −1870.65 3240.06i −0.550592 0.953654i
\(227\) −2019.15 + 3497.27i −0.590377 + 1.02256i 0.403805 + 0.914845i \(0.367688\pi\)
−0.994182 + 0.107717i \(0.965646\pi\)
\(228\) 0 0
\(229\) −686.456 1188.98i −0.198089 0.343099i 0.749820 0.661642i \(-0.230140\pi\)
−0.947909 + 0.318542i \(0.896807\pi\)
\(230\) −1583.96 −0.454101
\(231\) 0 0
\(232\) −1722.66 −0.487492
\(233\) −2087.15 3615.06i −0.586841 1.01644i −0.994643 0.103368i \(-0.967038\pi\)
0.407802 0.913070i \(-0.366295\pi\)
\(234\) 0 0
\(235\) −696.273 + 1205.98i −0.193276 + 0.334764i
\(236\) −7.46811 12.9351i −0.00205988 0.00356782i
\(237\) 0 0
\(238\) −416.637 + 1342.93i −0.113473 + 0.365753i
\(239\) 5544.70 1.50066 0.750329 0.661065i \(-0.229895\pi\)
0.750329 + 0.661065i \(0.229895\pi\)
\(240\) 0 0
\(241\) −2445.07 + 4234.98i −0.653530 + 1.13195i 0.328730 + 0.944424i \(0.393379\pi\)
−0.982260 + 0.187524i \(0.939954\pi\)
\(242\) 24.2023 41.9197i 0.00642887 0.0111351i
\(243\) 0 0
\(244\) −460.007 −0.120692
\(245\) 270.060 3452.61i 0.0704224 0.900324i
\(246\) 0 0
\(247\) 114.615 + 198.519i 0.0295253 + 0.0511394i
\(248\) 729.313 1263.21i 0.186740 0.323443i
\(249\) 0 0
\(250\) −1494.88 2589.22i −0.378179 0.655026i
\(251\) −7560.15 −1.90117 −0.950583 0.310470i \(-0.899513\pi\)
−0.950583 + 0.310470i \(0.899513\pi\)
\(252\) 0 0
\(253\) 2835.57 0.704627
\(254\) −790.048 1368.40i −0.195165 0.338037i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −1616.43 2799.74i −0.392335 0.679545i 0.600422 0.799683i \(-0.294999\pi\)
−0.992757 + 0.120139i \(0.961666\pi\)
\(258\) 0 0
\(259\) 5645.60 1278.89i 1.35444 0.306821i
\(260\) 162.325 0.0387191
\(261\) 0 0
\(262\) −1638.08 + 2837.24i −0.386263 + 0.669028i
\(263\) −2142.26 + 3710.51i −0.502272 + 0.869961i 0.497724 + 0.867335i \(0.334169\pi\)
−0.999997 + 0.00262575i \(0.999164\pi\)
\(264\) 0 0
\(265\) −5528.28 −1.28151
\(266\) −1434.35 1550.93i −0.330623 0.357494i
\(267\) 0 0
\(268\) −1255.60 2174.76i −0.286186 0.495689i
\(269\) −3348.26 + 5799.36i −0.758912 + 1.31447i 0.184495 + 0.982834i \(0.440935\pi\)
−0.943406 + 0.331640i \(0.892398\pi\)
\(270\) 0 0
\(271\) 3157.89 + 5469.63i 0.707854 + 1.22604i 0.965652 + 0.259840i \(0.0836698\pi\)
−0.257798 + 0.966199i \(0.582997\pi\)
\(272\) 607.367 0.135393
\(273\) 0 0
\(274\) 3978.64 0.877221
\(275\) 416.753 + 721.837i 0.0913860 + 0.158285i
\(276\) 0 0
\(277\) −1377.62 + 2386.12i −0.298821 + 0.517573i −0.975866 0.218368i \(-0.929927\pi\)
0.677045 + 0.735941i \(0.263260\pi\)
\(278\) 655.628 + 1135.58i 0.141446 + 0.244991i
\(279\) 0 0
\(280\) −1458.98 + 330.501i −0.311395 + 0.0705401i
\(281\) −1453.00 −0.308464 −0.154232 0.988035i \(-0.549290\pi\)
−0.154232 + 0.988035i \(0.549290\pi\)
\(282\) 0 0
\(283\) −2715.92 + 4704.11i −0.570476 + 0.988093i 0.426042 + 0.904704i \(0.359908\pi\)
−0.996517 + 0.0833890i \(0.973426\pi\)
\(284\) 1066.21 1846.74i 0.222775 0.385858i
\(285\) 0 0
\(286\) −290.590 −0.0600803
\(287\) 1023.78 3299.92i 0.210565 0.678704i
\(288\) 0 0
\(289\) 1736.00 + 3006.85i 0.353349 + 0.612018i
\(290\) −2174.14 + 3765.73i −0.440242 + 0.762521i
\(291\) 0 0
\(292\) 596.788 + 1033.67i 0.119604 + 0.207160i
\(293\) −6227.21 −1.24163 −0.620815 0.783957i \(-0.713198\pi\)
−0.620815 + 0.783957i \(0.713198\pi\)
\(294\) 0 0
\(295\) −37.7015 −0.00744091
\(296\) −1250.23 2165.46i −0.245500 0.425219i
\(297\) 0 0
\(298\) −2989.53 + 5178.02i −0.581138 + 1.00656i
\(299\) 157.635 + 273.032i 0.0304892 + 0.0528088i
\(300\) 0 0
\(301\) −1439.26 + 4639.10i −0.275606 + 0.888350i
\(302\) −2191.92 −0.417651
\(303\) 0 0
\(304\) −456.261 + 790.268i −0.0860802 + 0.149095i
\(305\) −580.567 + 1005.57i −0.108994 + 0.188783i
\(306\) 0 0
\(307\) 8621.61 1.60281 0.801403 0.598125i \(-0.204088\pi\)
0.801403 + 0.598125i \(0.204088\pi\)
\(308\) 2611.83 591.655i 0.483191 0.109457i
\(309\) 0 0
\(310\) −1840.91 3188.55i −0.337280 0.584186i
\(311\) −3712.11 + 6429.56i −0.676831 + 1.17230i 0.299100 + 0.954222i \(0.403314\pi\)
−0.975930 + 0.218083i \(0.930020\pi\)
\(312\) 0 0
\(313\) −1633.30 2828.96i −0.294951 0.510870i 0.680022 0.733191i \(-0.261970\pi\)
−0.974974 + 0.222321i \(0.928637\pi\)
\(314\) 1002.05 0.180092
\(315\) 0 0
\(316\) −3468.06 −0.617385
\(317\) −2440.25 4226.63i −0.432359 0.748868i 0.564717 0.825285i \(-0.308985\pi\)
−0.997076 + 0.0764167i \(0.975652\pi\)
\(318\) 0 0
\(319\) 3892.10 6741.31i 0.683121 1.18320i
\(320\) 323.094 + 559.615i 0.0564421 + 0.0977607i
\(321\) 0 0
\(322\) −1972.73 2133.06i −0.341416 0.369164i
\(323\) 2164.98 0.372950
\(324\) 0 0
\(325\) −46.3363 + 80.2568i −0.00790854 + 0.0136980i
\(326\) −2268.41 + 3929.01i −0.385386 + 0.667508i
\(327\) 0 0
\(328\) −1492.46 −0.251241
\(329\) −2491.22 + 564.333i −0.417463 + 0.0945675i
\(330\) 0 0
\(331\) 4799.58 + 8313.11i 0.797005 + 1.38045i 0.921558 + 0.388240i \(0.126917\pi\)
−0.124554 + 0.992213i \(0.539750\pi\)
\(332\) −488.449 + 846.018i −0.0807443 + 0.139853i
\(333\) 0 0
\(334\) −1369.97 2372.86i −0.224436 0.388734i
\(335\) −6338.69 −1.03379
\(336\) 0 0
\(337\) −2895.79 −0.468082 −0.234041 0.972227i \(-0.575195\pi\)
−0.234041 + 0.972227i \(0.575195\pi\)
\(338\) 2180.85 + 3777.34i 0.350954 + 0.607870i
\(339\) 0 0
\(340\) 766.548 1327.70i 0.122270 0.211778i
\(341\) 3295.55 + 5708.07i 0.523356 + 0.906478i
\(342\) 0 0
\(343\) 4985.85 3936.35i 0.784871 0.619659i
\(344\) 2098.13 0.328847
\(345\) 0 0
\(346\) 1843.77 3193.50i 0.286479 0.496196i
\(347\) −2678.81 + 4639.83i −0.414426 + 0.717807i −0.995368 0.0961381i \(-0.969351\pi\)
0.580942 + 0.813945i \(0.302684\pi\)
\(348\) 0 0
\(349\) −6049.21 −0.927813 −0.463906 0.885884i \(-0.653553\pi\)
−0.463906 + 0.885884i \(0.653553\pi\)
\(350\) 253.065 815.692i 0.0386482 0.124573i
\(351\) 0 0
\(352\) −578.395 1001.81i −0.0875811 0.151695i
\(353\) −3440.28 + 5958.74i −0.518718 + 0.898446i 0.481045 + 0.876696i \(0.340257\pi\)
−0.999763 + 0.0217505i \(0.993076\pi\)
\(354\) 0 0
\(355\) −2691.30 4661.47i −0.402365 0.696916i
\(356\) −1788.07 −0.266200
\(357\) 0 0
\(358\) −2123.14 −0.313440
\(359\) −2995.95 5189.15i −0.440447 0.762876i 0.557276 0.830328i \(-0.311847\pi\)
−0.997723 + 0.0674511i \(0.978513\pi\)
\(360\) 0 0
\(361\) 1803.14 3123.13i 0.262886 0.455333i
\(362\) −2441.54 4228.86i −0.354487 0.613989i
\(363\) 0 0
\(364\) 202.166 + 218.597i 0.0291110 + 0.0314769i
\(365\) 3012.79 0.432045
\(366\) 0 0
\(367\) 3285.52 5690.70i 0.467311 0.809406i −0.531992 0.846749i \(-0.678556\pi\)
0.999302 + 0.0373437i \(0.0118896\pi\)
\(368\) −627.518 + 1086.89i −0.0888903 + 0.153962i
\(369\) 0 0
\(370\) −6311.58 −0.886820
\(371\) −6885.16 7444.74i −0.963503 1.04181i
\(372\) 0 0
\(373\) 1866.81 + 3233.41i 0.259141 + 0.448846i 0.966012 0.258497i \(-0.0832272\pi\)
−0.706871 + 0.707343i \(0.749894\pi\)
\(374\) −1372.26 + 2376.82i −0.189726 + 0.328616i
\(375\) 0 0
\(376\) 551.685 + 955.546i 0.0756675 + 0.131060i
\(377\) 865.479 0.118235
\(378\) 0 0
\(379\) 8419.14 1.14106 0.570531 0.821276i \(-0.306738\pi\)
0.570531 + 0.821276i \(0.306738\pi\)
\(380\) 1151.68 + 1994.77i 0.155474 + 0.269288i
\(381\) 0 0
\(382\) 3692.15 6395.00i 0.494521 0.856536i
\(383\) 2665.21 + 4616.28i 0.355577 + 0.615877i 0.987217 0.159385i \(-0.0509511\pi\)
−0.631640 + 0.775262i \(0.717618\pi\)
\(384\) 0 0
\(385\) 2002.99 6456.16i 0.265148 0.854640i
\(386\) 6284.64 0.828704
\(387\) 0 0
\(388\) 3607.98 6249.21i 0.472081 0.817668i
\(389\) 3905.58 6764.67i 0.509051 0.881703i −0.490894 0.871219i \(-0.663330\pi\)
0.999945 0.0104832i \(-0.00333696\pi\)
\(390\) 0 0
\(391\) 2977.60 0.385125
\(392\) −2262.15 1553.13i −0.291469 0.200115i
\(393\) 0 0
\(394\) −2273.51 3937.83i −0.290704 0.503515i
\(395\) −4376.99 + 7581.16i −0.557544 + 0.965695i
\(396\) 0 0
\(397\) −455.847 789.550i −0.0576279 0.0998145i 0.835772 0.549076i \(-0.185020\pi\)
−0.893400 + 0.449262i \(0.851687\pi\)
\(398\) −5473.03 −0.689292
\(399\) 0 0
\(400\) −368.913 −0.0461142
\(401\) 834.008 + 1444.54i 0.103861 + 0.179893i 0.913272 0.407349i \(-0.133547\pi\)
−0.809411 + 0.587242i \(0.800214\pi\)
\(402\) 0 0
\(403\) −366.413 + 634.646i −0.0452912 + 0.0784466i
\(404\) −3368.54 5834.48i −0.414829 0.718505i
\(405\) 0 0
\(406\) −7778.93 + 1762.15i −0.950892 + 0.215405i
\(407\) 11298.8 1.37608
\(408\) 0 0
\(409\) −4555.24 + 7889.90i −0.550714 + 0.953864i 0.447509 + 0.894279i \(0.352311\pi\)
−0.998223 + 0.0595852i \(0.981022\pi\)
\(410\) −1883.61 + 3262.50i −0.226889 + 0.392984i
\(411\) 0 0
\(412\) 6564.26 0.784946
\(413\) −46.9551 50.7713i −0.00559445 0.00604913i
\(414\) 0 0
\(415\) 1232.93 + 2135.49i 0.145836 + 0.252596i
\(416\) 64.3083 111.385i 0.00757926 0.0131277i
\(417\) 0 0
\(418\) −2061.71 3570.99i −0.241248 0.417853i
\(419\) −12626.4 −1.47217 −0.736085 0.676889i \(-0.763328\pi\)
−0.736085 + 0.676889i \(0.763328\pi\)
\(420\) 0 0
\(421\) −4805.61 −0.556320 −0.278160 0.960535i \(-0.589725\pi\)
−0.278160 + 0.960535i \(0.589725\pi\)
\(422\) −2915.84 5050.38i −0.336353 0.582580i
\(423\) 0 0
\(424\) −2190.14 + 3793.43i −0.250855 + 0.434494i
\(425\) 437.628 + 757.994i 0.0499484 + 0.0865132i
\(426\) 0 0
\(427\) −2077.23 + 470.553i −0.235420 + 0.0533294i
\(428\) 1284.38 0.145053
\(429\) 0 0
\(430\) 2648.02 4586.50i 0.296974 0.514374i
\(431\) 3341.06 5786.89i 0.373395 0.646739i −0.616690 0.787206i \(-0.711527\pi\)
0.990085 + 0.140467i \(0.0448603\pi\)
\(432\) 0 0
\(433\) −8502.27 −0.943632 −0.471816 0.881697i \(-0.656401\pi\)
−0.471816 + 0.881697i \(0.656401\pi\)
\(434\) 2001.16 6450.24i 0.221333 0.713414i
\(435\) 0 0
\(436\) −1120.02 1939.93i −0.123026 0.213087i
\(437\) −2236.81 + 3874.27i −0.244854 + 0.424100i
\(438\) 0 0
\(439\) 6814.77 + 11803.5i 0.740891 + 1.28326i 0.952090 + 0.305818i \(0.0989299\pi\)
−0.211199 + 0.977443i \(0.567737\pi\)
\(440\) −2919.93 −0.316369
\(441\) 0 0
\(442\) −305.146 −0.0328378
\(443\) −3427.16 5936.02i −0.367561 0.636634i 0.621623 0.783317i \(-0.286474\pi\)
−0.989184 + 0.146683i \(0.953140\pi\)
\(444\) 0 0
\(445\) −2256.69 + 3908.70i −0.240399 + 0.416383i
\(446\) 1875.11 + 3247.78i 0.199078 + 0.344813i
\(447\) 0 0
\(448\) −351.218 + 1132.07i −0.0370391 + 0.119386i
\(449\) 10372.3 1.09019 0.545097 0.838373i \(-0.316493\pi\)
0.545097 + 0.838373i \(0.316493\pi\)
\(450\) 0 0
\(451\) 3371.98 5840.45i 0.352063 0.609791i
\(452\) −3741.30 + 6480.13i −0.389328 + 0.674335i
\(453\) 0 0
\(454\) 8076.59 0.834919
\(455\) 733.003 166.047i 0.0755247 0.0171085i
\(456\) 0 0
\(457\) 3950.40 + 6842.30i 0.404359 + 0.700370i 0.994247 0.107115i \(-0.0341613\pi\)
−0.589888 + 0.807485i \(0.700828\pi\)
\(458\) −1372.91 + 2377.95i −0.140070 + 0.242608i
\(459\) 0 0
\(460\) 1583.96 + 2743.50i 0.160549 + 0.278079i
\(461\) 11359.7 1.14767 0.573834 0.818972i \(-0.305456\pi\)
0.573834 + 0.818972i \(0.305456\pi\)
\(462\) 0 0
\(463\) 7346.85 0.737445 0.368723 0.929539i \(-0.379795\pi\)
0.368723 + 0.929539i \(0.379795\pi\)
\(464\) 1722.66 + 2983.73i 0.172354 + 0.298527i
\(465\) 0 0
\(466\) −4174.31 + 7230.11i −0.414959 + 0.718731i
\(467\) 473.289 + 819.760i 0.0468976 + 0.0812291i 0.888521 0.458835i \(-0.151733\pi\)
−0.841624 + 0.540064i \(0.818400\pi\)
\(468\) 0 0
\(469\) −7894.47 8536.08i −0.777256 0.840426i
\(470\) 2785.09 0.273333
\(471\) 0 0
\(472\) −14.9362 + 25.8703i −0.00145656 + 0.00252283i
\(473\) −4740.41 + 8210.64i −0.460813 + 0.798151i
\(474\) 0 0
\(475\) −1315.01 −0.127025
\(476\) 2742.66 621.292i 0.264096 0.0598253i
\(477\) 0 0
\(478\) −5544.70 9603.71i −0.530562 0.918961i
\(479\) 7657.75 13263.6i 0.730462 1.26520i −0.226224 0.974075i \(-0.572638\pi\)
0.956686 0.291122i \(-0.0940287\pi\)
\(480\) 0 0
\(481\) 628.125 + 1087.95i 0.0595427 + 0.103131i
\(482\) 9780.28 0.924231
\(483\) 0 0
\(484\) −96.8094 −0.00909179
\(485\) −9107.15 15774.1i −0.852649 1.47683i
\(486\) 0 0
\(487\) 4320.19 7482.78i 0.401984 0.696257i −0.591981 0.805952i \(-0.701654\pi\)
0.993965 + 0.109695i \(0.0349873\pi\)
\(488\) 460.007 + 796.755i 0.0426711 + 0.0739086i
\(489\) 0 0
\(490\) −6250.16 + 2984.86i −0.576232 + 0.275188i
\(491\) 13425.6 1.23399 0.616996 0.786966i \(-0.288349\pi\)
0.616996 + 0.786966i \(0.288349\pi\)
\(492\) 0 0
\(493\) 4087.05 7078.99i 0.373371 0.646697i
\(494\) 229.229 397.037i 0.0208776 0.0361610i
\(495\) 0 0
\(496\) −2917.25 −0.264090
\(497\) 2925.57 9429.88i 0.264044 0.851082i
\(498\) 0 0
\(499\) 5489.01 + 9507.24i 0.492429 + 0.852911i 0.999962 0.00872085i \(-0.00277597\pi\)
−0.507533 + 0.861632i \(0.669443\pi\)
\(500\) −2989.77 + 5178.43i −0.267413 + 0.463173i
\(501\) 0 0
\(502\) 7560.15 + 13094.6i 0.672164 + 1.16422i
\(503\) 7829.41 0.694028 0.347014 0.937860i \(-0.387196\pi\)
0.347014 + 0.937860i \(0.387196\pi\)
\(504\) 0 0
\(505\) −17005.5 −1.49849
\(506\) −2835.57 4911.35i −0.249123 0.431494i
\(507\) 0 0
\(508\) −1580.10 + 2736.81i −0.138003 + 0.239028i
\(509\) 9091.90 + 15747.6i 0.791732 + 1.37132i 0.924894 + 0.380225i \(0.124153\pi\)
−0.133162 + 0.991094i \(0.542513\pi\)
\(510\) 0 0
\(511\) 3752.25 + 4057.21i 0.324833 + 0.351234i
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) −3232.86 + 5599.48i −0.277423 + 0.480511i
\(515\) 8284.65 14349.4i 0.708865 1.22779i
\(516\) 0 0
\(517\) −4985.80 −0.424130
\(518\) −7860.71 8499.57i −0.666756 0.720946i
\(519\) 0 0
\(520\) −162.325 281.155i −0.0136893 0.0237105i
\(521\) −11202.3 + 19402.9i −0.941997 + 1.63159i −0.180341 + 0.983604i \(0.557720\pi\)
−0.761656 + 0.647982i \(0.775613\pi\)
\(522\) 0 0
\(523\) −2843.67 4925.38i −0.237753 0.411801i 0.722316 0.691563i \(-0.243078\pi\)
−0.960069 + 0.279763i \(0.909744\pi\)
\(524\) 6552.33 0.546259
\(525\) 0 0
\(526\) 8569.05 0.710320
\(527\) 3460.63 + 5993.99i 0.286048 + 0.495450i
\(528\) 0 0
\(529\) 3007.11 5208.46i 0.247153 0.428081i
\(530\) 5528.28 + 9575.27i 0.453082 + 0.784761i
\(531\) 0 0
\(532\) −1251.93 + 4035.30i −0.102027 + 0.328858i
\(533\) 749.822 0.0609351
\(534\) 0 0
\(535\) 1620.99 2807.64i 0.130994 0.226888i
\(536\) −2511.20 + 4349.52i −0.202364 + 0.350505i
\(537\) 0 0
\(538\) 13393.1 1.07326
\(539\) 11188.9 5343.42i 0.894137 0.427008i
\(540\) 0 0
\(541\) 6508.78 + 11273.5i 0.517254 + 0.895910i 0.999799 + 0.0200392i \(0.00637910\pi\)
−0.482545 + 0.875871i \(0.660288\pi\)
\(542\) 6315.79 10939.3i 0.500528 0.866940i
\(543\) 0 0
\(544\) −607.367 1051.99i −0.0478688 0.0829112i
\(545\) −5654.23 −0.444405
\(546\) 0 0
\(547\) −6353.31 −0.496614 −0.248307 0.968681i \(-0.579874\pi\)
−0.248307 + 0.968681i \(0.579874\pi\)
\(548\) −3978.64 6891.21i −0.310144 0.537186i
\(549\) 0 0
\(550\) 833.506 1443.67i 0.0646197 0.111925i
\(551\) 6140.49 + 10635.6i 0.474762 + 0.822311i
\(552\) 0 0
\(553\) −15660.6 + 3547.57i −1.20426 + 0.272799i
\(554\) 5510.50 0.422597
\(555\) 0 0
\(556\) 1311.26 2271.16i 0.100017 0.173235i
\(557\) 7759.69 13440.2i 0.590285 1.02240i −0.403909 0.914799i \(-0.632349\pi\)
0.994194 0.107604i \(-0.0343179\pi\)
\(558\) 0 0
\(559\) −1054.12 −0.0797574
\(560\) 2031.42 + 2196.52i 0.153292 + 0.165750i
\(561\) 0 0
\(562\) 1453.00 + 2516.66i 0.109059 + 0.188895i
\(563\) 9095.49 15753.9i 0.680869 1.17930i −0.293847 0.955853i \(-0.594936\pi\)
0.974716 0.223448i \(-0.0717311\pi\)
\(564\) 0 0
\(565\) 9443.68 + 16356.9i 0.703184 + 1.21795i
\(566\) 10863.7 0.806774
\(567\) 0 0
\(568\) −4264.85 −0.315052
\(569\) −6159.38 10668.4i −0.453804 0.786012i 0.544814 0.838557i \(-0.316600\pi\)
−0.998619 + 0.0525449i \(0.983267\pi\)
\(570\) 0 0
\(571\) 8694.98 15060.2i 0.637257 1.10376i −0.348775 0.937206i \(-0.613402\pi\)
0.986032 0.166555i \(-0.0532644\pi\)
\(572\) 290.590 + 503.317i 0.0212416 + 0.0367915i
\(573\) 0 0
\(574\) −6739.41 + 1526.67i −0.490065 + 0.111014i
\(575\) −1808.59 −0.131171
\(576\) 0 0
\(577\) −1625.45 + 2815.37i −0.117276 + 0.203129i −0.918687 0.394985i \(-0.870750\pi\)
0.801411 + 0.598114i \(0.204083\pi\)
\(578\) 3472.01 6013.69i 0.249855 0.432762i
\(579\) 0 0
\(580\) 8696.57 0.622596
\(581\) −1340.25 + 4319.97i −0.0957022 + 0.308473i
\(582\) 0 0
\(583\) −9896.60 17141.4i −0.703045 1.21771i
\(584\) 1193.58 2067.33i 0.0845728 0.146484i
\(585\) 0 0
\(586\) 6227.21 + 10785.8i 0.438982 + 0.760339i
\(587\) −6993.54 −0.491745 −0.245872 0.969302i \(-0.579074\pi\)
−0.245872 + 0.969302i \(0.579074\pi\)
\(588\) 0 0
\(589\) −10398.7 −0.727453
\(590\) 37.7015 + 65.3010i 0.00263076 + 0.00455661i
\(591\) 0 0
\(592\) −2500.46 + 4330.92i −0.173595 + 0.300675i
\(593\) −5001.10 8662.15i −0.346324 0.599851i 0.639269 0.768983i \(-0.279237\pi\)
−0.985593 + 0.169132i \(0.945904\pi\)
\(594\) 0 0
\(595\) 2103.32 6779.56i 0.144921 0.467117i
\(596\) 11958.1 0.821853
\(597\) 0 0
\(598\) 315.270 546.064i 0.0215591 0.0373415i
\(599\) −12362.1 + 21411.8i −0.843241 + 1.46054i 0.0438997 + 0.999036i \(0.486022\pi\)
−0.887140 + 0.461500i \(0.847312\pi\)
\(600\) 0 0
\(601\) −4825.50 −0.327515 −0.163757 0.986501i \(-0.552361\pi\)
−0.163757 + 0.986501i \(0.552361\pi\)
\(602\) 9474.42 2146.23i 0.641443 0.145305i
\(603\) 0 0
\(604\) 2191.92 + 3796.51i 0.147662 + 0.255758i
\(605\) −122.182 + 211.625i −0.00821056 + 0.0142211i
\(606\) 0 0
\(607\) −12365.1 21417.0i −0.826826 1.43210i −0.900516 0.434824i \(-0.856811\pi\)
0.0736896 0.997281i \(-0.476523\pi\)
\(608\) 1825.04 0.121736
\(609\) 0 0
\(610\) 2322.27 0.154141
\(611\) −277.171 480.074i −0.0183521 0.0317868i
\(612\) 0 0
\(613\) 3804.29 6589.22i 0.250659 0.434154i −0.713049 0.701115i \(-0.752686\pi\)
0.963707 + 0.266961i \(0.0860195\pi\)
\(614\) −8621.61 14933.1i −0.566677 0.981514i
\(615\) 0 0
\(616\) −3636.61 3932.16i −0.237862 0.257194i
\(617\) 25089.8 1.63708 0.818538 0.574452i \(-0.194785\pi\)
0.818538 + 0.574452i \(0.194785\pi\)
\(618\) 0 0
\(619\) −11452.5 + 19836.3i −0.743642 + 1.28803i 0.207185 + 0.978302i \(0.433570\pi\)
−0.950827 + 0.309724i \(0.899763\pi\)
\(620\) −3681.82 + 6377.10i −0.238493 + 0.413082i
\(621\) 0 0
\(622\) 14848.4 0.957183
\(623\) −8074.29 + 1829.06i −0.519245 + 0.117624i
\(624\) 0 0
\(625\) 6105.62 + 10575.2i 0.390760 + 0.676815i
\(626\) −3266.61 + 5657.93i −0.208562 + 0.361240i
\(627\) 0 0
\(628\) −1002.05 1735.60i −0.0636723 0.110284i
\(629\) 11864.8 0.752116
\(630\) 0 0
\(631\) 2253.93 0.142199 0.0710996 0.997469i \(-0.477349\pi\)
0.0710996 + 0.997469i \(0.477349\pi\)
\(632\) 3468.06 + 6006.86i 0.218279 + 0.378070i
\(633\) 0 0
\(634\) −4880.49 + 8453.26i −0.305724 + 0.529530i
\(635\) 3988.43 + 6908.17i 0.249254 + 0.431720i
\(636\) 0 0
\(637\) 1136.52 + 780.307i 0.0706917 + 0.0485352i
\(638\) −15568.4 −0.966079
\(639\) 0 0
\(640\) 646.187 1119.23i 0.0399106 0.0691272i
\(641\) −6014.77 + 10417.9i −0.370623 + 0.641938i −0.989661 0.143423i \(-0.954189\pi\)
0.619039 + 0.785361i \(0.287522\pi\)
\(642\) 0 0
\(643\) −4738.59 −0.290625 −0.145312 0.989386i \(-0.546419\pi\)
−0.145312 + 0.989386i \(0.546419\pi\)
\(644\) −1721.84 + 5549.93i −0.105357 + 0.339593i
\(645\) 0 0
\(646\) −2164.98 3749.86i −0.131858 0.228384i
\(647\) 2869.84 4970.71i 0.174382 0.302038i −0.765565 0.643358i \(-0.777541\pi\)
0.939947 + 0.341320i \(0.110874\pi\)
\(648\) 0 0
\(649\) −67.4924 116.900i −0.00408214 0.00707047i
\(650\) 185.345 0.0111844
\(651\) 0 0
\(652\) 9073.65 0.545018
\(653\) 863.084 + 1494.91i 0.0517230 + 0.0895868i 0.890728 0.454537i \(-0.150195\pi\)
−0.839005 + 0.544124i \(0.816862\pi\)
\(654\) 0 0
\(655\) 8269.59 14323.4i 0.493313 0.854442i
\(656\) 1492.46 + 2585.01i 0.0888271 + 0.153853i
\(657\) 0 0
\(658\) 3468.67 + 3750.58i 0.205506 + 0.222208i
\(659\) 10987.7 0.649501 0.324751 0.945800i \(-0.394720\pi\)
0.324751 + 0.945800i \(0.394720\pi\)
\(660\) 0 0
\(661\) −16020.4 + 27748.1i −0.942695 + 1.63280i −0.182393 + 0.983226i \(0.558384\pi\)
−0.760302 + 0.649570i \(0.774949\pi\)
\(662\) 9599.15 16626.2i 0.563567 0.976127i
\(663\) 0 0
\(664\) 1953.80 0.114190
\(665\) 7241.09 + 7829.60i 0.422252 + 0.456570i
\(666\) 0 0
\(667\) 8445.31 + 14627.7i 0.490260 + 0.849156i
\(668\) −2739.94 + 4745.72i −0.158700 + 0.274876i
\(669\) 0 0
\(670\) 6338.69 + 10978.9i 0.365500 + 0.633065i
\(671\) −4157.27 −0.239180
\(672\) 0 0
\(673\) −13026.7 −0.746124 −0.373062 0.927806i \(-0.621692\pi\)
−0.373062 + 0.927806i \(0.621692\pi\)
\(674\) 2895.79 + 5015.65i 0.165492 + 0.286641i
\(675\) 0 0
\(676\) 4361.69 7554.67i 0.248162 0.429829i
\(677\) −2360.39 4088.32i −0.133999 0.232093i 0.791216 0.611537i \(-0.209449\pi\)
−0.925215 + 0.379444i \(0.876115\pi\)
\(678\) 0 0
\(679\) 9899.91 31909.9i 0.559534 1.80352i
\(680\) −3066.19 −0.172916
\(681\) 0 0
\(682\) 6591.11 11416.1i 0.370068 0.640977i
\(683\) −5585.00 + 9673.51i −0.312890 + 0.541942i −0.978987 0.203924i \(-0.934631\pi\)
0.666096 + 0.745866i \(0.267964\pi\)
\(684\) 0 0
\(685\) −20085.5 −1.12033
\(686\) −11803.8 4699.40i −0.656956 0.261551i
\(687\) 0 0
\(688\) −2098.13 3634.07i −0.116265 0.201377i
\(689\) 1100.34 1905.85i 0.0608415 0.105381i
\(690\) 0 0
\(691\) 6986.42 + 12100.8i 0.384625 + 0.666190i 0.991717 0.128441i \(-0.0409974\pi\)
−0.607092 + 0.794632i \(0.707664\pi\)
\(692\) −7375.08 −0.405142
\(693\) 0 0
\(694\) 10715.2 0.586087
\(695\) −3309.83 5732.79i −0.180646 0.312888i
\(696\) 0 0
\(697\) 3540.89 6133.00i 0.192426 0.333291i
\(698\) 6049.21 + 10477.5i 0.328031 + 0.568167i
\(699\) 0 0
\(700\) −1665.88 + 377.371i −0.0899493 + 0.0203761i
\(701\) −9694.83 −0.522352 −0.261176 0.965291i \(-0.584110\pi\)
−0.261176 + 0.965291i \(0.584110\pi\)
\(702\) 0 0
\(703\) −8912.99 + 15437.7i −0.478179 + 0.828230i
\(704\) −1156.79 + 2003.62i −0.0619292 + 0.107264i
\(705\) 0 0
\(706\) 13761.1 0.733578
\(707\) −21179.4 22900.7i −1.12664 1.21820i
\(708\) 0 0
\(709\) −12712.8 22019.3i −0.673399 1.16636i −0.976934 0.213541i \(-0.931500\pi\)
0.303535 0.952820i \(-0.401833\pi\)
\(710\) −5382.61 + 9322.95i −0.284515 + 0.492794i
\(711\) 0 0
\(712\) 1788.07 + 3097.02i 0.0941160 + 0.163014i
\(713\) −14301.8 −0.751200
\(714\) 0 0
\(715\) 1467.00 0.0767309
\(716\) 2123.14 + 3677.39i 0.110818 + 0.191942i
\(717\) 0 0
\(718\) −5991.91 + 10378.3i −0.311443 + 0.539435i
\(719\) −8796.40 15235.8i −0.456259 0.790264i 0.542500 0.840056i \(-0.317478\pi\)
−0.998760 + 0.0497912i \(0.984144\pi\)
\(720\) 0 0
\(721\) 29641.9 6714.76i 1.53110 0.346839i
\(722\) −7212.55 −0.371778
\(723\) 0 0
\(724\) −4883.07 + 8457.73i −0.250660 + 0.434156i
\(725\) −2482.47 + 4299.76i −0.127168 + 0.220261i
\(726\) 0 0
\(727\) −10087.1 −0.514596 −0.257298 0.966332i \(-0.582832\pi\)
−0.257298 + 0.966332i \(0.582832\pi\)
\(728\) 176.455 568.759i 0.00898332 0.0289555i
\(729\) 0 0
\(730\) −3012.79 5218.30i −0.152751 0.264572i
\(731\) −4977.86 + 8621.91i −0.251865 + 0.436242i
\(732\) 0 0
\(733\) −15904.3 27547.1i −0.801417 1.38810i −0.918683 0.394995i \(-0.870746\pi\)
0.117266 0.993101i \(-0.462587\pi\)
\(734\) −13142.1 −0.660877
\(735\) 0 0
\(736\) 2510.07 0.125710
\(737\) −11347.4 19654.2i −0.567145 0.982324i
\(738\) 0 0
\(739\) 8287.63 14354.6i 0.412538 0.714536i −0.582629 0.812738i \(-0.697976\pi\)
0.995166 + 0.0982021i \(0.0313092\pi\)
\(740\) 6311.58 + 10932.0i 0.313538 + 0.543064i
\(741\) 0 0
\(742\) −6009.51 + 19370.2i −0.297326 + 0.958358i
\(743\) −11053.4 −0.545773 −0.272886 0.962046i \(-0.587978\pi\)
−0.272886 + 0.962046i \(0.587978\pi\)
\(744\) 0 0
\(745\) 15092.2 26140.4i 0.742194 1.28552i
\(746\) 3733.61 6466.81i 0.183240 0.317382i
\(747\) 0 0
\(748\) 5489.02 0.268314
\(749\) 5799.80 1313.82i 0.282937 0.0640935i
\(750\) 0 0
\(751\) −1589.84 2753.68i −0.0772490 0.133799i 0.824813 0.565405i \(-0.191280\pi\)
−0.902062 + 0.431606i \(0.857947\pi\)
\(752\) 1103.37 1911.09i 0.0535050 0.0926733i
\(753\) 0 0
\(754\) −865.479 1499.05i −0.0418022 0.0724036i
\(755\) 11065.5 0.533399
\(756\) 0 0
\(757\) −31130.8 −1.49467 −0.747336 0.664446i \(-0.768667\pi\)
−0.747336 + 0.664446i \(0.768667\pi\)
\(758\) −8419.14 14582.4i −0.403426 0.698755i
\(759\) 0 0
\(760\) 2303.36 3989.54i 0.109936 0.190416i
\(761\) −3915.15 6781.24i −0.186497 0.323022i 0.757583 0.652739i \(-0.226380\pi\)
−0.944080 + 0.329717i \(0.893047\pi\)
\(762\) 0 0
\(763\) −7042.02 7614.35i −0.334126 0.361282i
\(764\) −14768.6 −0.699359
\(765\) 0 0
\(766\) 5330.42 9232.56i 0.251431 0.435491i
\(767\) 7.50408 12.9974i 0.000353268 0.000611878i
\(768\) 0 0
\(769\) 9389.21 0.440291 0.220145 0.975467i \(-0.429347\pi\)
0.220145 + 0.975467i \(0.429347\pi\)
\(770\) −13185.4 + 2986.88i −0.617102 + 0.139792i
\(771\) 0 0
\(772\) −6284.64 10885.3i −0.292991 0.507475i
\(773\) −13896.1 + 24068.8i −0.646584 + 1.11992i 0.337349 + 0.941380i \(0.390470\pi\)
−0.983933 + 0.178537i \(0.942864\pi\)
\(774\) 0 0
\(775\) −2101.98 3640.74i −0.0974263 0.168747i
\(776\) −14431.9 −0.667623
\(777\) 0 0
\(778\) −15622.3 −0.719907
\(779\) 5319.92 + 9214.37i 0.244680 + 0.423798i
\(780\) 0 0
\(781\) 9635.81 16689.7i 0.441481 0.764667i
\(782\) −2977.60 5157.36i −0.136162 0.235840i
\(783\) 0 0
\(784\) −427.958 + 5471.29i −0.0194952 + 0.249239i