Properties

Label 378.4.g.e.163.4
Level $378$
Weight $4$
Character 378.163
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: \( x^{8} - x^{7} + 66x^{6} + 59x^{5} + 3770x^{4} + 721x^{3} + 29779x^{2} + 1374x + 209764 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 163.4
Root \(4.05517 + 7.02376i\) of defining polynomial
Character \(\chi\) \(=\) 378.163
Dual form 378.4.g.e.109.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(8.00592 - 13.8667i) q^{5} +(1.70902 - 18.4412i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(8.00592 - 13.8667i) q^{5} +(1.70902 - 18.4412i) q^{7} -8.00000 q^{8} +(-16.0118 - 27.7333i) q^{10} +(-7.89520 - 13.6749i) q^{11} -50.4536 q^{13} +(-30.2321 - 21.4013i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(18.4772 + 32.0034i) q^{17} +(44.6871 - 77.4002i) q^{19} -64.0474 q^{20} -31.5808 q^{22} +(-30.6840 + 53.1462i) q^{23} +(-65.6896 - 113.778i) q^{25} +(-50.4536 + 87.3882i) q^{26} +(-67.3004 + 30.9623i) q^{28} +126.366 q^{29} +(129.992 + 225.153i) q^{31} +(16.0000 + 27.7128i) q^{32} +73.9087 q^{34} +(-242.036 - 171.338i) q^{35} +(123.048 - 213.126i) q^{37} +(-89.3741 - 154.800i) q^{38} +(-64.0474 + 110.933i) q^{40} -516.432 q^{41} -34.2518 q^{43} +(-31.5808 + 54.6996i) q^{44} +(61.3680 + 106.292i) q^{46} +(-182.851 + 316.707i) q^{47} +(-337.159 - 63.0328i) q^{49} -262.759 q^{50} +(100.907 + 174.776i) q^{52} +(23.5816 + 40.8445i) q^{53} -252.834 q^{55} +(-13.6721 + 147.530i) q^{56} +(126.366 - 218.872i) q^{58} +(-358.163 - 620.357i) q^{59} +(348.209 - 603.115i) q^{61} +519.968 q^{62} +64.0000 q^{64} +(-403.928 + 699.623i) q^{65} +(-55.3121 - 95.8034i) q^{67} +(73.9087 - 128.014i) q^{68} +(-538.802 + 247.882i) q^{70} -607.199 q^{71} +(140.081 + 242.627i) q^{73} +(-246.096 - 426.251i) q^{74} -357.496 q^{76} +(-265.675 + 122.227i) q^{77} +(441.645 - 764.951i) q^{79} +(128.095 + 221.867i) q^{80} +(-516.432 + 894.487i) q^{82} -63.1517 q^{83} +591.707 q^{85} +(-34.2518 + 59.3258i) q^{86} +(63.1616 + 109.399i) q^{88} +(337.796 - 585.080i) q^{89} +(-86.2261 + 930.426i) q^{91} +245.472 q^{92} +(365.701 + 633.413i) q^{94} +(-715.522 - 1239.32i) q^{95} +976.191 q^{97} +(-446.335 + 520.943i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} - 16 q^{4} - 4 q^{5} + 25 q^{7} - 64 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{2} - 16 q^{4} - 4 q^{5} + 25 q^{7} - 64 q^{8} + 8 q^{10} - 56 q^{11} - 18 q^{13} + 22 q^{14} - 64 q^{16} + 118 q^{17} + 37 q^{19} + 32 q^{20} - 224 q^{22} - 200 q^{23} - 104 q^{25} - 18 q^{26} - 56 q^{28} + 524 q^{29} + 276 q^{31} + 128 q^{32} + 472 q^{34} - 290 q^{35} - 185 q^{37} - 74 q^{38} + 32 q^{40} - 60 q^{41} - 1556 q^{43} - 224 q^{44} + 400 q^{46} - 30 q^{47} - 1159 q^{49} - 416 q^{50} + 36 q^{52} - 480 q^{53} + 1456 q^{55} - 200 q^{56} + 524 q^{58} + 296 q^{59} + 474 q^{61} + 1104 q^{62} + 512 q^{64} - 1542 q^{65} + 1319 q^{67} + 472 q^{68} - 32 q^{70} + 1852 q^{71} - 1423 q^{73} + 370 q^{74} - 296 q^{76} - 1228 q^{77} + 765 q^{79} - 64 q^{80} - 60 q^{82} + 1660 q^{83} - 584 q^{85} - 1556 q^{86} + 448 q^{88} + 864 q^{89} - 738 q^{91} + 1600 q^{92} + 60 q^{94} - 1766 q^{95} + 1088 q^{97} - 2704 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(5\) 8.00592 13.8667i 0.716072 1.24027i −0.246473 0.969150i \(-0.579272\pi\)
0.962545 0.271123i \(-0.0873949\pi\)
\(6\) 0 0
\(7\) 1.70902 18.4412i 0.0922783 0.995733i
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −16.0118 27.7333i −0.506339 0.877005i
\(11\) −7.89520 13.6749i −0.216409 0.374831i 0.737299 0.675567i \(-0.236101\pi\)
−0.953707 + 0.300736i \(0.902768\pi\)
\(12\) 0 0
\(13\) −50.4536 −1.07641 −0.538204 0.842815i \(-0.680897\pi\)
−0.538204 + 0.842815i \(0.680897\pi\)
\(14\) −30.2321 21.4013i −0.577134 0.408554i
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 18.4772 + 32.0034i 0.263610 + 0.456586i 0.967199 0.254022i \(-0.0817534\pi\)
−0.703588 + 0.710608i \(0.748420\pi\)
\(18\) 0 0
\(19\) 44.6871 77.4002i 0.539574 0.934570i −0.459352 0.888254i \(-0.651919\pi\)
0.998927 0.0463161i \(-0.0147482\pi\)
\(20\) −64.0474 −0.716072
\(21\) 0 0
\(22\) −31.5808 −0.306048
\(23\) −30.6840 + 53.1462i −0.278176 + 0.481816i −0.970932 0.239357i \(-0.923063\pi\)
0.692755 + 0.721173i \(0.256397\pi\)
\(24\) 0 0
\(25\) −65.6896 113.778i −0.525517 0.910222i
\(26\) −50.4536 + 87.3882i −0.380568 + 0.659163i
\(27\) 0 0
\(28\) −67.3004 + 30.9623i −0.454235 + 0.208976i
\(29\) 126.366 0.809156 0.404578 0.914504i \(-0.367418\pi\)
0.404578 + 0.914504i \(0.367418\pi\)
\(30\) 0 0
\(31\) 129.992 + 225.153i 0.753137 + 1.30447i 0.946295 + 0.323303i \(0.104793\pi\)
−0.193159 + 0.981167i \(0.561873\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 73.9087 0.372801
\(35\) −242.036 171.338i −1.16890 0.827467i
\(36\) 0 0
\(37\) 123.048 213.126i 0.546729 0.946963i −0.451767 0.892136i \(-0.649206\pi\)
0.998496 0.0548266i \(-0.0174606\pi\)
\(38\) −89.3741 154.800i −0.381537 0.660841i
\(39\) 0 0
\(40\) −64.0474 + 110.933i −0.253170 + 0.438503i
\(41\) −516.432 −1.96715 −0.983575 0.180500i \(-0.942228\pi\)
−0.983575 + 0.180500i \(0.942228\pi\)
\(42\) 0 0
\(43\) −34.2518 −0.121473 −0.0607366 0.998154i \(-0.519345\pi\)
−0.0607366 + 0.998154i \(0.519345\pi\)
\(44\) −31.5808 + 54.6996i −0.108204 + 0.187415i
\(45\) 0 0
\(46\) 61.3680 + 106.292i 0.196700 + 0.340695i
\(47\) −182.851 + 316.707i −0.567479 + 0.982902i 0.429335 + 0.903145i \(0.358748\pi\)
−0.996814 + 0.0797571i \(0.974586\pi\)
\(48\) 0 0
\(49\) −337.159 63.0328i −0.982969 0.183769i
\(50\) −262.759 −0.743193
\(51\) 0 0
\(52\) 100.907 + 174.776i 0.269102 + 0.466098i
\(53\) 23.5816 + 40.8445i 0.0611166 + 0.105857i 0.894965 0.446137i \(-0.147201\pi\)
−0.833848 + 0.551994i \(0.813867\pi\)
\(54\) 0 0
\(55\) −252.834 −0.619856
\(56\) −13.6721 + 147.530i −0.0326253 + 0.352045i
\(57\) 0 0
\(58\) 126.366 218.872i 0.286080 0.495505i
\(59\) −358.163 620.357i −0.790320 1.36887i −0.925769 0.378090i \(-0.876581\pi\)
0.135449 0.990784i \(-0.456752\pi\)
\(60\) 0 0
\(61\) 348.209 603.115i 0.730878 1.26592i −0.225630 0.974213i \(-0.572444\pi\)
0.956508 0.291705i \(-0.0942227\pi\)
\(62\) 519.968 1.06510
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −403.928 + 699.623i −0.770785 + 1.33504i
\(66\) 0 0
\(67\) −55.3121 95.8034i −0.100857 0.174690i 0.811181 0.584796i \(-0.198825\pi\)
−0.912038 + 0.410105i \(0.865492\pi\)
\(68\) 73.9087 128.014i 0.131805 0.228293i
\(69\) 0 0
\(70\) −538.802 + 247.882i −0.919987 + 0.423250i
\(71\) −607.199 −1.01495 −0.507474 0.861667i \(-0.669421\pi\)
−0.507474 + 0.861667i \(0.669421\pi\)
\(72\) 0 0
\(73\) 140.081 + 242.627i 0.224592 + 0.389004i 0.956197 0.292724i \(-0.0945618\pi\)
−0.731605 + 0.681729i \(0.761228\pi\)
\(74\) −246.096 426.251i −0.386596 0.669604i
\(75\) 0 0
\(76\) −357.496 −0.539574
\(77\) −265.675 + 122.227i −0.393201 + 0.180896i
\(78\) 0 0
\(79\) 441.645 764.951i 0.628974 1.08941i −0.358784 0.933420i \(-0.616809\pi\)
0.987758 0.155994i \(-0.0498580\pi\)
\(80\) 128.095 + 221.867i 0.179018 + 0.310068i
\(81\) 0 0
\(82\) −516.432 + 894.487i −0.695492 + 1.20463i
\(83\) −63.1517 −0.0835157 −0.0417578 0.999128i \(-0.513296\pi\)
−0.0417578 + 0.999128i \(0.513296\pi\)
\(84\) 0 0
\(85\) 591.707 0.755055
\(86\) −34.2518 + 59.3258i −0.0429473 + 0.0743869i
\(87\) 0 0
\(88\) 63.1616 + 109.399i 0.0765120 + 0.132523i
\(89\) 337.796 585.080i 0.402318 0.696836i −0.591687 0.806168i \(-0.701538\pi\)
0.994005 + 0.109332i \(0.0348712\pi\)
\(90\) 0 0
\(91\) −86.2261 + 930.426i −0.0993291 + 1.07182i
\(92\) 245.472 0.278176
\(93\) 0 0
\(94\) 365.701 + 633.413i 0.401268 + 0.695017i
\(95\) −715.522 1239.32i −0.772748 1.33844i
\(96\) 0 0
\(97\) 976.191 1.02183 0.510913 0.859632i \(-0.329307\pi\)
0.510913 + 0.859632i \(0.329307\pi\)
\(98\) −446.335 + 520.943i −0.460067 + 0.536971i
\(99\) 0 0
\(100\) −262.759 + 455.111i −0.262759 + 0.455111i
\(101\) 613.782 + 1063.10i 0.604689 + 1.04735i 0.992100 + 0.125446i \(0.0400361\pi\)
−0.387411 + 0.921907i \(0.626631\pi\)
\(102\) 0 0
\(103\) 419.207 726.088i 0.401026 0.694598i −0.592824 0.805332i \(-0.701987\pi\)
0.993850 + 0.110734i \(0.0353203\pi\)
\(104\) 403.629 0.380568
\(105\) 0 0
\(106\) 94.3264 0.0864320
\(107\) −215.777 + 373.737i −0.194953 + 0.337669i −0.946885 0.321572i \(-0.895789\pi\)
0.751932 + 0.659241i \(0.229122\pi\)
\(108\) 0 0
\(109\) 653.539 + 1131.96i 0.574291 + 0.994701i 0.996118 + 0.0880250i \(0.0280555\pi\)
−0.421827 + 0.906676i \(0.638611\pi\)
\(110\) −252.834 + 437.921i −0.219152 + 0.379583i
\(111\) 0 0
\(112\) 241.857 + 171.211i 0.204048 + 0.144445i
\(113\) 1008.94 0.839943 0.419971 0.907537i \(-0.362040\pi\)
0.419971 + 0.907537i \(0.362040\pi\)
\(114\) 0 0
\(115\) 491.307 + 850.969i 0.398388 + 0.690029i
\(116\) −252.731 437.744i −0.202289 0.350375i
\(117\) 0 0
\(118\) −1432.65 −1.11768
\(119\) 621.760 286.047i 0.478963 0.220352i
\(120\) 0 0
\(121\) 540.831 936.748i 0.406335 0.703792i
\(122\) −696.418 1206.23i −0.516809 0.895140i
\(123\) 0 0
\(124\) 519.968 900.610i 0.376568 0.652235i
\(125\) −102.144 −0.0730883
\(126\) 0 0
\(127\) −882.265 −0.616444 −0.308222 0.951315i \(-0.599734\pi\)
−0.308222 + 0.951315i \(0.599734\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 807.855 + 1399.25i 0.545028 + 0.944015i
\(131\) 1023.93 1773.50i 0.682912 1.18284i −0.291176 0.956669i \(-0.594047\pi\)
0.974088 0.226168i \(-0.0726200\pi\)
\(132\) 0 0
\(133\) −1350.99 956.363i −0.880792 0.623513i
\(134\) −221.248 −0.142634
\(135\) 0 0
\(136\) −147.817 256.027i −0.0932002 0.161428i
\(137\) 1250.79 + 2166.44i 0.780018 + 1.35103i 0.931931 + 0.362637i \(0.118123\pi\)
−0.151913 + 0.988394i \(0.548543\pi\)
\(138\) 0 0
\(139\) −949.028 −0.579104 −0.289552 0.957162i \(-0.593506\pi\)
−0.289552 + 0.957162i \(0.593506\pi\)
\(140\) −109.458 + 1181.11i −0.0660779 + 0.713016i
\(141\) 0 0
\(142\) −607.199 + 1051.70i −0.358838 + 0.621526i
\(143\) 398.341 + 689.947i 0.232944 + 0.403471i
\(144\) 0 0
\(145\) 1011.67 1752.27i 0.579414 1.00357i
\(146\) 560.323 0.317621
\(147\) 0 0
\(148\) −984.385 −0.546729
\(149\) −398.773 + 690.696i −0.219254 + 0.379758i −0.954580 0.297955i \(-0.903696\pi\)
0.735326 + 0.677713i \(0.237029\pi\)
\(150\) 0 0
\(151\) −1354.87 2346.70i −0.730181 1.26471i −0.956806 0.290729i \(-0.906102\pi\)
0.226624 0.973982i \(-0.427231\pi\)
\(152\) −357.496 + 619.202i −0.190768 + 0.330420i
\(153\) 0 0
\(154\) −53.9722 + 582.389i −0.0282416 + 0.304742i
\(155\) 4162.82 2.15720
\(156\) 0 0
\(157\) −1674.15 2899.70i −0.851028 1.47402i −0.880282 0.474451i \(-0.842647\pi\)
0.0292542 0.999572i \(-0.490687\pi\)
\(158\) −883.290 1529.90i −0.444752 0.770332i
\(159\) 0 0
\(160\) 512.379 0.253170
\(161\) 927.643 + 656.679i 0.454090 + 0.321451i
\(162\) 0 0
\(163\) 1351.28 2340.48i 0.649327 1.12467i −0.333957 0.942588i \(-0.608384\pi\)
0.983284 0.182079i \(-0.0582826\pi\)
\(164\) 1032.86 + 1788.97i 0.491787 + 0.851801i
\(165\) 0 0
\(166\) −63.1517 + 109.382i −0.0295273 + 0.0511427i
\(167\) −737.971 −0.341951 −0.170976 0.985275i \(-0.554692\pi\)
−0.170976 + 0.985275i \(0.554692\pi\)
\(168\) 0 0
\(169\) 348.564 0.158654
\(170\) 591.707 1024.87i 0.266952 0.462375i
\(171\) 0 0
\(172\) 68.5036 + 118.652i 0.0303683 + 0.0525995i
\(173\) 1942.56 3364.61i 0.853699 1.47865i −0.0241476 0.999708i \(-0.507687\pi\)
0.877847 0.478942i \(-0.158979\pi\)
\(174\) 0 0
\(175\) −2210.47 + 1016.95i −0.954832 + 0.439281i
\(176\) 252.647 0.108204
\(177\) 0 0
\(178\) −675.593 1170.16i −0.284482 0.492737i
\(179\) 1291.06 + 2236.18i 0.539096 + 0.933741i 0.998953 + 0.0457482i \(0.0145672\pi\)
−0.459857 + 0.887993i \(0.652099\pi\)
\(180\) 0 0
\(181\) 2978.56 1.22317 0.611587 0.791177i \(-0.290531\pi\)
0.611587 + 0.791177i \(0.290531\pi\)
\(182\) 1525.32 + 1079.77i 0.621232 + 0.439770i
\(183\) 0 0
\(184\) 245.472 425.170i 0.0983502 0.170348i
\(185\) −1970.23 3412.53i −0.782994 1.35619i
\(186\) 0 0
\(187\) 291.762 505.347i 0.114095 0.197618i
\(188\) 1462.81 0.567479
\(189\) 0 0
\(190\) −2862.09 −1.09283
\(191\) −2063.72 + 3574.47i −0.781809 + 1.35413i 0.149077 + 0.988826i \(0.452370\pi\)
−0.930887 + 0.365308i \(0.880964\pi\)
\(192\) 0 0
\(193\) 1508.85 + 2613.41i 0.562743 + 0.974700i 0.997256 + 0.0740342i \(0.0235874\pi\)
−0.434512 + 0.900666i \(0.643079\pi\)
\(194\) 976.191 1690.81i 0.361270 0.625738i
\(195\) 0 0
\(196\) 455.965 + 1294.02i 0.166168 + 0.471581i
\(197\) 3959.32 1.43193 0.715964 0.698137i \(-0.245988\pi\)
0.715964 + 0.698137i \(0.245988\pi\)
\(198\) 0 0
\(199\) −2346.11 4063.57i −0.835734 1.44753i −0.893432 0.449199i \(-0.851709\pi\)
0.0576981 0.998334i \(-0.481624\pi\)
\(200\) 525.517 + 910.222i 0.185798 + 0.321812i
\(201\) 0 0
\(202\) 2455.13 0.855160
\(203\) 215.961 2330.34i 0.0746675 0.805703i
\(204\) 0 0
\(205\) −4134.52 + 7161.19i −1.40862 + 2.43980i
\(206\) −838.414 1452.18i −0.283568 0.491155i
\(207\) 0 0
\(208\) 403.629 699.105i 0.134551 0.233049i
\(209\) −1411.25 −0.467074
\(210\) 0 0
\(211\) −1542.58 −0.503297 −0.251648 0.967819i \(-0.580973\pi\)
−0.251648 + 0.967819i \(0.580973\pi\)
\(212\) 94.3264 163.378i 0.0305583 0.0529286i
\(213\) 0 0
\(214\) 431.555 + 747.475i 0.137853 + 0.238768i
\(215\) −274.217 + 474.958i −0.0869835 + 0.150660i
\(216\) 0 0
\(217\) 4374.25 2012.42i 1.36840 0.629549i
\(218\) 2614.16 0.812170
\(219\) 0 0
\(220\) 505.667 + 875.841i 0.154964 + 0.268406i
\(221\) −932.239 1614.69i −0.283752 0.491473i
\(222\) 0 0
\(223\) 5343.30 1.60455 0.802273 0.596958i \(-0.203624\pi\)
0.802273 + 0.596958i \(0.203624\pi\)
\(224\) 538.403 247.698i 0.160596 0.0738840i
\(225\) 0 0
\(226\) 1008.94 1747.54i 0.296965 0.514358i
\(227\) −1902.99 3296.08i −0.556415 0.963738i −0.997792 0.0664167i \(-0.978843\pi\)
0.441377 0.897322i \(-0.354490\pi\)
\(228\) 0 0
\(229\) −599.426 + 1038.24i −0.172975 + 0.299601i −0.939459 0.342663i \(-0.888671\pi\)
0.766484 + 0.642264i \(0.222005\pi\)
\(230\) 1965.23 0.563406
\(231\) 0 0
\(232\) −1010.93 −0.286080
\(233\) 1305.87 2261.84i 0.367170 0.635956i −0.621952 0.783055i \(-0.713660\pi\)
0.989122 + 0.147099i \(0.0469936\pi\)
\(234\) 0 0
\(235\) 2927.78 + 5071.06i 0.812711 + 1.40766i
\(236\) −1432.65 + 2481.43i −0.395160 + 0.684437i
\(237\) 0 0
\(238\) 126.311 1362.97i 0.0344014 0.371210i
\(239\) 3318.79 0.898220 0.449110 0.893477i \(-0.351741\pi\)
0.449110 + 0.893477i \(0.351741\pi\)
\(240\) 0 0
\(241\) 1388.03 + 2404.14i 0.370999 + 0.642590i 0.989720 0.143022i \(-0.0456819\pi\)
−0.618720 + 0.785611i \(0.712349\pi\)
\(242\) −1081.66 1873.50i −0.287322 0.497656i
\(243\) 0 0
\(244\) −2785.67 −0.730878
\(245\) −3573.32 + 4170.63i −0.931800 + 1.08756i
\(246\) 0 0
\(247\) −2254.62 + 3905.12i −0.580802 + 1.00598i
\(248\) −1039.94 1801.22i −0.266274 0.461200i
\(249\) 0 0
\(250\) −102.144 + 176.919i −0.0258406 + 0.0447573i
\(251\) −1339.17 −0.336764 −0.168382 0.985722i \(-0.553854\pi\)
−0.168382 + 0.985722i \(0.553854\pi\)
\(252\) 0 0
\(253\) 969.026 0.240799
\(254\) −882.265 + 1528.13i −0.217946 + 0.377493i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) −1513.62 + 2621.66i −0.367381 + 0.636322i −0.989155 0.146874i \(-0.953079\pi\)
0.621774 + 0.783196i \(0.286412\pi\)
\(258\) 0 0
\(259\) −3720.01 2633.39i −0.892471 0.631781i
\(260\) 3231.42 0.770785
\(261\) 0 0
\(262\) −2047.87 3547.01i −0.482892 0.836393i
\(263\) 3106.65 + 5380.87i 0.728381 + 1.26159i 0.957567 + 0.288210i \(0.0930602\pi\)
−0.229186 + 0.973383i \(0.573606\pi\)
\(264\) 0 0
\(265\) 755.170 0.175056
\(266\) −3007.45 + 1383.61i −0.693229 + 0.318927i
\(267\) 0 0
\(268\) −221.248 + 383.214i −0.0504287 + 0.0873451i
\(269\) −309.272 535.674i −0.0700990 0.121415i 0.828846 0.559478i \(-0.188998\pi\)
−0.898945 + 0.438063i \(0.855665\pi\)
\(270\) 0 0
\(271\) −1368.21 + 2369.81i −0.306690 + 0.531202i −0.977636 0.210304i \(-0.932555\pi\)
0.670946 + 0.741506i \(0.265888\pi\)
\(272\) −591.269 −0.131805
\(273\) 0 0
\(274\) 5003.17 1.10311
\(275\) −1037.27 + 1796.60i −0.227453 + 0.393960i
\(276\) 0 0
\(277\) 2065.70 + 3577.91i 0.448073 + 0.776085i 0.998261 0.0589561i \(-0.0187772\pi\)
−0.550188 + 0.835041i \(0.685444\pi\)
\(278\) −949.028 + 1643.76i −0.204744 + 0.354628i
\(279\) 0 0
\(280\) 1936.29 + 1370.70i 0.413269 + 0.292554i
\(281\) −1741.24 −0.369658 −0.184829 0.982771i \(-0.559173\pi\)
−0.184829 + 0.982771i \(0.559173\pi\)
\(282\) 0 0
\(283\) −1707.54 2957.54i −0.358666 0.621227i 0.629072 0.777347i \(-0.283435\pi\)
−0.987738 + 0.156119i \(0.950102\pi\)
\(284\) 1214.40 + 2103.40i 0.253737 + 0.439485i
\(285\) 0 0
\(286\) 1593.37 0.329432
\(287\) −882.592 + 9523.65i −0.181525 + 1.95876i
\(288\) 0 0
\(289\) 1773.69 3072.12i 0.361019 0.625304i
\(290\) −2023.35 3504.54i −0.409707 0.709634i
\(291\) 0 0
\(292\) 560.323 970.507i 0.112296 0.194502i
\(293\) −8652.18 −1.72514 −0.862569 0.505939i \(-0.831146\pi\)
−0.862569 + 0.505939i \(0.831146\pi\)
\(294\) 0 0
\(295\) −11469.7 −2.26370
\(296\) −984.385 + 1705.00i −0.193298 + 0.334802i
\(297\) 0 0
\(298\) 797.547 + 1381.39i 0.155036 + 0.268530i
\(299\) 1548.12 2681.42i 0.299431 0.518630i
\(300\) 0 0
\(301\) −58.5369 + 631.645i −0.0112093 + 0.120955i
\(302\) −5419.46 −1.03263
\(303\) 0 0
\(304\) 714.993 + 1238.40i 0.134894 + 0.233643i
\(305\) −5575.47 9656.99i −1.04672 1.81298i
\(306\) 0 0
\(307\) −695.737 −0.129341 −0.0646707 0.997907i \(-0.520600\pi\)
−0.0646707 + 0.997907i \(0.520600\pi\)
\(308\) 954.756 + 675.872i 0.176631 + 0.125037i
\(309\) 0 0
\(310\) 4162.82 7210.22i 0.762685 1.32101i
\(311\) −3347.24 5797.60i −0.610305 1.05708i −0.991189 0.132456i \(-0.957714\pi\)
0.380884 0.924623i \(-0.375620\pi\)
\(312\) 0 0
\(313\) 5092.10 8819.78i 0.919561 1.59273i 0.119478 0.992837i \(-0.461878\pi\)
0.800083 0.599890i \(-0.204789\pi\)
\(314\) −6696.58 −1.20353
\(315\) 0 0
\(316\) −3533.16 −0.628974
\(317\) 1765.83 3058.50i 0.312867 0.541901i −0.666115 0.745849i \(-0.732044\pi\)
0.978982 + 0.203948i \(0.0653773\pi\)
\(318\) 0 0
\(319\) −997.683 1728.04i −0.175108 0.303296i
\(320\) 512.379 887.467i 0.0895090 0.155034i
\(321\) 0 0
\(322\) 2065.04 950.046i 0.357393 0.164422i
\(323\) 3302.76 0.568949
\(324\) 0 0
\(325\) 3314.28 + 5740.50i 0.565671 + 0.979771i
\(326\) −2702.56 4680.96i −0.459143 0.795260i
\(327\) 0 0
\(328\) 4131.46 0.695492
\(329\) 5527.97 + 3913.25i 0.926342 + 0.655758i
\(330\) 0 0
\(331\) −5436.54 + 9416.37i −0.902778 + 1.56366i −0.0789050 + 0.996882i \(0.525142\pi\)
−0.823873 + 0.566775i \(0.808191\pi\)
\(332\) 126.303 + 218.764i 0.0208789 + 0.0361634i
\(333\) 0 0
\(334\) −737.971 + 1278.20i −0.120898 + 0.209402i
\(335\) −1771.30 −0.288885
\(336\) 0 0
\(337\) −978.004 −0.158087 −0.0790434 0.996871i \(-0.525187\pi\)
−0.0790434 + 0.996871i \(0.525187\pi\)
\(338\) 348.564 603.730i 0.0560928 0.0971556i
\(339\) 0 0
\(340\) −1183.41 2049.73i −0.188764 0.326948i
\(341\) 2052.63 3555.25i 0.325970 0.564597i
\(342\) 0 0
\(343\) −1738.61 + 6109.90i −0.273692 + 0.961817i
\(344\) 274.014 0.0429473
\(345\) 0 0
\(346\) −3885.12 6729.22i −0.603656 1.04556i
\(347\) −2759.56 4779.70i −0.426919 0.739446i 0.569678 0.821868i \(-0.307068\pi\)
−0.996598 + 0.0824220i \(0.973734\pi\)
\(348\) 0 0
\(349\) −234.793 −0.0360120 −0.0180060 0.999838i \(-0.505732\pi\)
−0.0180060 + 0.999838i \(0.505732\pi\)
\(350\) −449.059 + 4845.59i −0.0685806 + 0.740022i
\(351\) 0 0
\(352\) 252.647 437.597i 0.0382560 0.0662613i
\(353\) −1597.40 2766.78i −0.240853 0.417170i 0.720104 0.693866i \(-0.244094\pi\)
−0.960958 + 0.276696i \(0.910761\pi\)
\(354\) 0 0
\(355\) −4861.19 + 8419.83i −0.726775 + 1.25881i
\(356\) −2702.37 −0.402318
\(357\) 0 0
\(358\) 5164.23 0.762396
\(359\) −5938.35 + 10285.5i −0.873020 + 1.51211i −0.0141629 + 0.999900i \(0.504508\pi\)
−0.858857 + 0.512215i \(0.828825\pi\)
\(360\) 0 0
\(361\) −564.365 977.509i −0.0822810 0.142515i
\(362\) 2978.56 5159.01i 0.432457 0.749038i
\(363\) 0 0
\(364\) 3395.54 1562.16i 0.488942 0.224943i
\(365\) 4485.90 0.643295
\(366\) 0 0
\(367\) 2974.87 + 5152.62i 0.423125 + 0.732874i 0.996243 0.0865989i \(-0.0275998\pi\)
−0.573118 + 0.819473i \(0.694267\pi\)
\(368\) −490.944 850.340i −0.0695441 0.120454i
\(369\) 0 0
\(370\) −7880.91 −1.10732
\(371\) 793.525 365.070i 0.111045 0.0510875i
\(372\) 0 0
\(373\) 1311.66 2271.86i 0.182078 0.315368i −0.760510 0.649326i \(-0.775051\pi\)
0.942588 + 0.333958i \(0.108384\pi\)
\(374\) −583.524 1010.69i −0.0806773 0.139737i
\(375\) 0 0
\(376\) 1462.81 2533.65i 0.200634 0.347508i
\(377\) −6375.60 −0.870982
\(378\) 0 0
\(379\) 3206.76 0.434618 0.217309 0.976103i \(-0.430272\pi\)
0.217309 + 0.976103i \(0.430272\pi\)
\(380\) −2862.09 + 4957.28i −0.386374 + 0.669219i
\(381\) 0 0
\(382\) 4127.44 + 7148.94i 0.552823 + 0.957517i
\(383\) −3223.28 + 5582.89i −0.430031 + 0.744836i −0.996875 0.0789891i \(-0.974831\pi\)
0.566844 + 0.823825i \(0.308164\pi\)
\(384\) 0 0
\(385\) −432.097 + 4662.57i −0.0571993 + 0.617211i
\(386\) 6035.40 0.795839
\(387\) 0 0
\(388\) −1952.38 3381.62i −0.255457 0.442464i
\(389\) 1476.74 + 2557.79i 0.192478 + 0.333381i 0.946071 0.323960i \(-0.105014\pi\)
−0.753593 + 0.657341i \(0.771681\pi\)
\(390\) 0 0
\(391\) −2267.81 −0.293320
\(392\) 2697.27 + 504.263i 0.347532 + 0.0649722i
\(393\) 0 0
\(394\) 3959.32 6857.74i 0.506263 0.876873i
\(395\) −7071.55 12248.3i −0.900780 1.56020i
\(396\) 0 0
\(397\) 2303.53 3989.83i 0.291211 0.504393i −0.682885 0.730526i \(-0.739275\pi\)
0.974096 + 0.226133i \(0.0726084\pi\)
\(398\) −9384.42 −1.18191
\(399\) 0 0
\(400\) 2102.07 0.262759
\(401\) −5282.15 + 9148.95i −0.657800 + 1.13934i 0.323384 + 0.946268i \(0.395180\pi\)
−0.981184 + 0.193076i \(0.938154\pi\)
\(402\) 0 0
\(403\) −6558.56 11359.8i −0.810682 1.40414i
\(404\) 2455.13 4252.41i 0.302345 0.523676i
\(405\) 0 0
\(406\) −3820.31 2704.40i −0.466992 0.330583i
\(407\) −3885.96 −0.473267
\(408\) 0 0
\(409\) 1360.31 + 2356.12i 0.164457 + 0.284848i 0.936462 0.350768i \(-0.114080\pi\)
−0.772005 + 0.635616i \(0.780746\pi\)
\(410\) 8269.03 + 14322.4i 0.996045 + 1.72520i
\(411\) 0 0
\(412\) −3353.66 −0.401026
\(413\) −12052.3 + 5544.77i −1.43596 + 0.660630i
\(414\) 0 0
\(415\) −505.588 + 875.704i −0.0598032 + 0.103582i
\(416\) −807.257 1398.21i −0.0951419 0.164791i
\(417\) 0 0
\(418\) −1411.25 + 2444.36i −0.165136 + 0.286023i
\(419\) 13647.0 1.59116 0.795582 0.605846i \(-0.207165\pi\)
0.795582 + 0.605846i \(0.207165\pi\)
\(420\) 0 0
\(421\) 9396.95 1.08784 0.543918 0.839138i \(-0.316940\pi\)
0.543918 + 0.839138i \(0.316940\pi\)
\(422\) −1542.58 + 2671.83i −0.177942 + 0.308205i
\(423\) 0 0
\(424\) −188.653 326.756i −0.0216080 0.0374261i
\(425\) 2427.52 4204.58i 0.277063 0.479888i
\(426\) 0 0
\(427\) −10527.1 7452.14i −1.19307 0.844577i
\(428\) 1726.22 0.194953
\(429\) 0 0
\(430\) 548.435 + 949.916i 0.0615067 + 0.106533i
\(431\) −3631.56 6290.04i −0.405861 0.702971i 0.588561 0.808453i \(-0.299695\pi\)
−0.994421 + 0.105482i \(0.966362\pi\)
\(432\) 0 0
\(433\) 3288.50 0.364977 0.182489 0.983208i \(-0.441585\pi\)
0.182489 + 0.983208i \(0.441585\pi\)
\(434\) 888.634 9588.85i 0.0982853 1.06055i
\(435\) 0 0
\(436\) 2614.16 4527.85i 0.287146 0.497351i
\(437\) 2742.35 + 4749.90i 0.300194 + 0.519951i
\(438\) 0 0
\(439\) −443.607 + 768.350i −0.0482283 + 0.0835339i −0.889132 0.457651i \(-0.848691\pi\)
0.840903 + 0.541185i \(0.182024\pi\)
\(440\) 2022.67 0.219152
\(441\) 0 0
\(442\) −3728.96 −0.401286
\(443\) −3940.57 + 6825.27i −0.422624 + 0.732006i −0.996195 0.0871497i \(-0.972224\pi\)
0.573571 + 0.819156i \(0.305557\pi\)
\(444\) 0 0
\(445\) −5408.74 9368.22i −0.576177 0.997969i
\(446\) 5343.30 9254.86i 0.567292 0.982579i
\(447\) 0 0
\(448\) 109.377 1180.24i 0.0115348 0.124467i
\(449\) 13593.0 1.42872 0.714359 0.699780i \(-0.246719\pi\)
0.714359 + 0.699780i \(0.246719\pi\)
\(450\) 0 0
\(451\) 4077.34 + 7062.16i 0.425708 + 0.737348i
\(452\) −2017.89 3495.09i −0.209986 0.363706i
\(453\) 0 0
\(454\) −7611.97 −0.786889
\(455\) 12211.6 + 8644.59i 1.25822 + 0.890692i
\(456\) 0 0
\(457\) 4175.62 7232.39i 0.427412 0.740300i −0.569230 0.822178i \(-0.692759\pi\)
0.996642 + 0.0818784i \(0.0260919\pi\)
\(458\) 1198.85 + 2076.47i 0.122312 + 0.211850i
\(459\) 0 0
\(460\) 1965.23 3403.88i 0.199194 0.345014i
\(461\) −9295.22 −0.939093 −0.469546 0.882908i \(-0.655583\pi\)
−0.469546 + 0.882908i \(0.655583\pi\)
\(462\) 0 0
\(463\) 272.006 0.0273028 0.0136514 0.999907i \(-0.495654\pi\)
0.0136514 + 0.999907i \(0.495654\pi\)
\(464\) −1010.93 + 1750.97i −0.101144 + 0.175187i
\(465\) 0 0
\(466\) −2611.74 4523.67i −0.259628 0.449689i
\(467\) 4440.72 7691.56i 0.440026 0.762147i −0.557665 0.830066i \(-0.688303\pi\)
0.997691 + 0.0679189i \(0.0216359\pi\)
\(468\) 0 0
\(469\) −1861.26 + 856.294i −0.183252 + 0.0843070i
\(470\) 11711.1 1.14935
\(471\) 0 0
\(472\) 2865.31 + 4962.85i 0.279420 + 0.483970i
\(473\) 270.425 + 468.390i 0.0262878 + 0.0455319i
\(474\) 0 0
\(475\) −11741.9 −1.13422
\(476\) −2234.42 1581.74i −0.215156 0.152309i
\(477\) 0 0
\(478\) 3318.79 5748.31i 0.317569 0.550045i
\(479\) −9482.73 16424.6i −0.904545 1.56672i −0.821527 0.570169i \(-0.806878\pi\)
−0.0830174 0.996548i \(-0.526456\pi\)
\(480\) 0 0
\(481\) −6208.22 + 10752.9i −0.588504 + 1.01932i
\(482\) 5552.12 0.524672
\(483\) 0 0
\(484\) −4326.65 −0.406335
\(485\) 7815.31 13536.5i 0.731701 1.26734i
\(486\) 0 0
\(487\) −8984.26 15561.2i −0.835966 1.44794i −0.893241 0.449578i \(-0.851574\pi\)
0.0572748 0.998358i \(-0.481759\pi\)
\(488\) −2785.67 + 4824.92i −0.258405 + 0.447570i
\(489\) 0 0
\(490\) 3650.42 + 10359.8i 0.336549 + 0.955119i
\(491\) 5379.38 0.494435 0.247218 0.968960i \(-0.420484\pi\)
0.247218 + 0.968960i \(0.420484\pi\)
\(492\) 0 0
\(493\) 2334.88 + 4044.13i 0.213302 + 0.369449i
\(494\) 4509.24 + 7810.24i 0.410689 + 0.711335i
\(495\) 0 0
\(496\) −4159.74 −0.376568
\(497\) −1037.71 + 11197.5i −0.0936577 + 1.01062i
\(498\) 0 0
\(499\) −5839.80 + 10114.8i −0.523899 + 0.907419i 0.475714 + 0.879600i \(0.342190\pi\)
−0.999613 + 0.0278191i \(0.991144\pi\)
\(500\) 204.288 + 353.837i 0.0182721 + 0.0316482i
\(501\) 0 0
\(502\) −1339.17 + 2319.52i −0.119064 + 0.206225i
\(503\) 1522.74 0.134981 0.0674906 0.997720i \(-0.478501\pi\)
0.0674906 + 0.997720i \(0.478501\pi\)
\(504\) 0 0
\(505\) 19655.6 1.73200
\(506\) 969.026 1678.40i 0.0851353 0.147459i
\(507\) 0 0
\(508\) 1764.53 + 3056.25i 0.154111 + 0.266928i
\(509\) −2821.79 + 4887.49i −0.245725 + 0.425607i −0.962335 0.271866i \(-0.912359\pi\)
0.716611 + 0.697474i \(0.245693\pi\)
\(510\) 0 0
\(511\) 4713.74 2168.61i 0.408070 0.187737i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 3027.23 + 5243.32i 0.259777 + 0.449948i
\(515\) −6712.28 11626.0i −0.574327 0.994764i
\(516\) 0 0
\(517\) 5774.57 0.491229
\(518\) −8281.18 + 3809.85i −0.702421 + 0.323156i
\(519\) 0 0
\(520\) 3231.42 5596.98i 0.272514 0.472008i
\(521\) 8363.93 + 14486.8i 0.703322 + 1.21819i 0.967294 + 0.253659i \(0.0816340\pi\)
−0.263972 + 0.964530i \(0.585033\pi\)
\(522\) 0 0
\(523\) 2319.53 4017.55i 0.193931 0.335899i −0.752618 0.658457i \(-0.771209\pi\)
0.946550 + 0.322558i \(0.104543\pi\)
\(524\) −8191.46 −0.682912
\(525\) 0 0
\(526\) 12426.6 1.03009
\(527\) −4803.76 + 8320.36i −0.397069 + 0.687743i
\(528\) 0 0
\(529\) 4200.48 + 7275.45i 0.345236 + 0.597966i
\(530\) 755.170 1307.99i 0.0618915 0.107199i
\(531\) 0 0
\(532\) −610.968 + 6592.68i −0.0497910 + 0.537272i
\(533\) 26055.8 2.11746
\(534\) 0 0
\(535\) 3455.00 + 5984.23i 0.279201 + 0.483590i
\(536\) 442.497 + 766.427i 0.0356585 + 0.0617623i
\(537\) 0 0
\(538\) −1237.09 −0.0991349
\(539\) 1799.97 + 5108.26i 0.143841 + 0.408216i
\(540\) 0 0
\(541\) −8647.63 + 14978.1i −0.687229 + 1.19032i 0.285502 + 0.958378i \(0.407840\pi\)
−0.972731 + 0.231937i \(0.925494\pi\)
\(542\) 2736.42 + 4739.62i 0.216862 + 0.375617i
\(543\) 0 0
\(544\) −591.269 + 1024.11i −0.0466001 + 0.0807138i
\(545\) 20928.7 1.64493
\(546\) 0 0
\(547\) 2832.09 0.221373 0.110687 0.993855i \(-0.464695\pi\)
0.110687 + 0.993855i \(0.464695\pi\)
\(548\) 5003.17 8665.75i 0.390009 0.675515i
\(549\) 0 0
\(550\) 2074.53 + 3593.20i 0.160833 + 0.278572i
\(551\) 5646.91 9780.73i 0.436600 0.756213i
\(552\) 0 0
\(553\) −13351.9 9451.79i −1.02673 0.726819i
\(554\) 8262.82 0.633671
\(555\) 0 0
\(556\) 1898.06 + 3287.53i 0.144776 + 0.250760i
\(557\) 4779.35 + 8278.07i 0.363568 + 0.629718i 0.988545 0.150925i \(-0.0482251\pi\)
−0.624977 + 0.780643i \(0.714892\pi\)
\(558\) 0 0
\(559\) 1728.13 0.130755
\(560\) 4310.41 1983.05i 0.325265 0.149642i
\(561\) 0 0
\(562\) −1741.24 + 3015.92i −0.130694 + 0.226368i
\(563\) −2642.28 4576.56i −0.197795 0.342591i 0.750018 0.661417i \(-0.230045\pi\)
−0.947813 + 0.318826i \(0.896711\pi\)
\(564\) 0 0
\(565\) 8077.53 13990.7i 0.601459 1.04176i
\(566\) −6830.14 −0.507230
\(567\) 0 0
\(568\) 4857.59 0.358838
\(569\) 2532.77 4386.89i 0.186607 0.323213i −0.757510 0.652824i \(-0.773584\pi\)
0.944117 + 0.329611i \(0.106918\pi\)
\(570\) 0 0
\(571\) 6695.36 + 11596.7i 0.490704 + 0.849925i 0.999943 0.0107008i \(-0.00340623\pi\)
−0.509239 + 0.860625i \(0.670073\pi\)
\(572\) 1593.37 2759.79i 0.116472 0.201735i
\(573\) 0 0
\(574\) 15612.8 + 11052.3i 1.13531 + 0.803686i
\(575\) 8062.48 0.584746
\(576\) 0 0
\(577\) 12027.8 + 20832.7i 0.867804 + 1.50308i 0.864236 + 0.503087i \(0.167803\pi\)
0.00356838 + 0.999994i \(0.498864\pi\)
\(578\) −3547.38 6144.24i −0.255279 0.442157i
\(579\) 0 0
\(580\) −8093.39 −0.579414
\(581\) −107.927 + 1164.60i −0.00770669 + 0.0831593i
\(582\) 0 0
\(583\) 372.363 644.952i 0.0264523 0.0458168i
\(584\) −1120.65 1941.01i −0.0794052 0.137534i
\(585\) 0 0
\(586\) −8652.18 + 14986.0i −0.609929 + 1.05643i
\(587\) 27108.0 1.90608 0.953039 0.302849i \(-0.0979378\pi\)
0.953039 + 0.302849i \(0.0979378\pi\)
\(588\) 0 0
\(589\) 23235.8 1.62549
\(590\) −11469.7 + 19866.1i −0.800340 + 1.38623i
\(591\) 0 0
\(592\) 1968.77 + 3410.01i 0.136682 + 0.236741i
\(593\) −1276.43 + 2210.85i −0.0883927 + 0.153101i −0.906832 0.421492i \(-0.861506\pi\)
0.818439 + 0.574593i \(0.194840\pi\)
\(594\) 0 0
\(595\) 1011.24 10911.8i 0.0696752 0.751833i
\(596\) 3190.19 0.219254
\(597\) 0 0
\(598\) −3096.23 5362.84i −0.211730 0.366727i
\(599\) 4297.99 + 7444.33i 0.293173 + 0.507791i 0.974558 0.224134i \(-0.0719553\pi\)
−0.681385 + 0.731925i \(0.738622\pi\)
\(600\) 0 0
\(601\) 6026.80 0.409049 0.204524 0.978861i \(-0.434435\pi\)
0.204524 + 0.978861i \(0.434435\pi\)
\(602\) 1035.51 + 733.034i 0.0701064 + 0.0496283i
\(603\) 0 0
\(604\) −5419.46 + 9386.78i −0.365091 + 0.632355i
\(605\) −8659.71 14999.1i −0.581929 1.00793i
\(606\) 0 0
\(607\) −652.013 + 1129.32i −0.0435986 + 0.0755151i −0.887001 0.461767i \(-0.847216\pi\)
0.843403 + 0.537282i \(0.180549\pi\)
\(608\) 2859.97 0.190768
\(609\) 0 0
\(610\) −22301.9 −1.48029
\(611\) 9225.47 15979.0i 0.610839 1.05800i
\(612\) 0 0
\(613\) −8953.92 15508.6i −0.589960 1.02184i −0.994237 0.107204i \(-0.965810\pi\)
0.404277 0.914637i \(-0.367523\pi\)
\(614\) −695.737 + 1205.05i −0.0457291 + 0.0792051i
\(615\) 0 0
\(616\) 2125.40 977.814i 0.139018 0.0639565i
\(617\) 26896.2 1.75494 0.877472 0.479628i \(-0.159228\pi\)
0.877472 + 0.479628i \(0.159228\pi\)
\(618\) 0 0
\(619\) −5252.53 9097.65i −0.341061 0.590735i 0.643569 0.765388i \(-0.277453\pi\)
−0.984630 + 0.174653i \(0.944120\pi\)
\(620\) −8325.64 14420.4i −0.539300 0.934094i
\(621\) 0 0
\(622\) −13389.0 −0.863101
\(623\) −10212.3 7229.29i −0.656737 0.464905i
\(624\) 0 0
\(625\) 7393.45 12805.8i 0.473181 0.819573i
\(626\) −10184.2 17639.6i −0.650228 1.12623i
\(627\) 0 0
\(628\) −6696.58 + 11598.8i −0.425514 + 0.737012i
\(629\) 9094.32 0.576493
\(630\) 0 0
\(631\) −23670.2 −1.49334 −0.746668 0.665197i \(-0.768348\pi\)
−0.746668 + 0.665197i \(0.768348\pi\)
\(632\) −3533.16 + 6119.61i −0.222376 + 0.385166i
\(633\) 0 0
\(634\) −3531.66 6117.01i −0.221230 0.383182i
\(635\) −7063.35 + 12234.1i −0.441418 + 0.764558i
\(636\) 0 0
\(637\) 17010.9 + 3180.23i 1.05808 + 0.197811i
\(638\) −3990.73 −0.247640
\(639\) 0 0
\(640\) −1024.76 1774.93i −0.0632924 0.109626i
\(641\) −11664.4 20203.4i −0.718747 1.24491i −0.961496 0.274817i \(-0.911383\pi\)
0.242749 0.970089i \(-0.421951\pi\)
\(642\) 0 0
\(643\) 13384.9 0.820914 0.410457 0.911880i \(-0.365369\pi\)
0.410457 + 0.911880i \(0.365369\pi\)
\(644\) 419.516 4526.81i 0.0256696 0.276989i
\(645\) 0 0
\(646\) 3302.76 5720.55i 0.201154 0.348409i
\(647\) 4779.80 + 8278.86i 0.290438 + 0.503053i 0.973913 0.226920i \(-0.0728657\pi\)
−0.683475 + 0.729974i \(0.739532\pi\)
\(648\) 0 0
\(649\) −5655.54 + 9795.69i −0.342064 + 0.592472i
\(650\) 13257.1 0.799979
\(651\) 0 0
\(652\) −10810.2 −0.649327
\(653\) −10103.9 + 17500.5i −0.605507 + 1.04877i 0.386464 + 0.922304i \(0.373696\pi\)
−0.991971 + 0.126464i \(0.959637\pi\)
\(654\) 0 0
\(655\) −16395.1 28397.1i −0.978027 1.69399i
\(656\) 4131.46 7155.89i 0.245894 0.425900i
\(657\) 0 0
\(658\) 12305.9 5661.47i 0.729080 0.335421i
\(659\) −22497.2 −1.32984 −0.664920 0.746914i \(-0.731534\pi\)
−0.664920 + 0.746914i \(0.731534\pi\)
\(660\) 0 0
\(661\) −12408.4 21492.0i −0.730152 1.26466i −0.956818 0.290687i \(-0.906116\pi\)
0.226667 0.973972i \(-0.427217\pi\)
\(662\) 10873.1 + 18832.7i 0.638360 + 1.10567i
\(663\) 0 0
\(664\) 505.214 0.0295273
\(665\) −24077.5 + 11077.1i −1.40404 + 0.645942i
\(666\) 0 0
\(667\) −3877.40 + 6715.86i −0.225088 + 0.389864i
\(668\) 1475.94 + 2556.41i 0.0854879 + 0.148069i
\(669\) 0 0
\(670\) −1771.30 + 3067.98i −0.102136 + 0.176905i
\(671\) −10996.7 −0.632673
\(672\) 0 0
\(673\) 2331.38 0.133534 0.0667669 0.997769i \(-0.478732\pi\)
0.0667669 + 0.997769i \(0.478732\pi\)
\(674\) −978.004 + 1693.95i −0.0558922 + 0.0968080i
\(675\) 0 0
\(676\) −697.128 1207.46i −0.0396636 0.0686994i
\(677\) −837.086 + 1449.88i −0.0475212 + 0.0823090i −0.888808 0.458281i \(-0.848465\pi\)
0.841286 + 0.540590i \(0.181799\pi\)
\(678\) 0 0
\(679\) 1668.33 18002.2i 0.0942924 1.01747i
\(680\) −4733.66 −0.266952
\(681\) 0 0
\(682\) −4105.25 7110.50i −0.230496 0.399231i
\(683\) 1402.89 + 2429.87i 0.0785944 + 0.136129i 0.902644 0.430389i \(-0.141623\pi\)
−0.824049 + 0.566518i \(0.808290\pi\)
\(684\) 0 0
\(685\) 40055.0 2.23419
\(686\) 8844.04 + 9121.26i 0.492226 + 0.507655i
\(687\) 0 0
\(688\) 274.014 474.607i 0.0151842 0.0262997i
\(689\) −1189.78 2060.75i −0.0657864 0.113945i
\(690\) 0 0
\(691\) −2493.67 + 4319.16i −0.137284 + 0.237784i −0.926468 0.376374i \(-0.877171\pi\)
0.789183 + 0.614158i \(0.210504\pi\)
\(692\) −15540.5 −0.853699
\(693\) 0 0
\(694\) −11038.2 −0.603755
\(695\) −7597.85 + 13159.9i −0.414680 + 0.718247i
\(696\) 0 0
\(697\) −9542.20 16527.6i −0.518561 0.898173i
\(698\) −234.793 + 406.674i −0.0127322 + 0.0220528i
\(699\) 0 0
\(700\) 7943.75 + 5623.39i 0.428922 + 0.303634i
\(701\) −15941.5 −0.858921 −0.429460 0.903086i \(-0.641296\pi\)
−0.429460 + 0.903086i \(0.641296\pi\)
\(702\) 0 0
\(703\) −10997.3 19047.9i −0.590002 1.02191i
\(704\) −505.293 875.193i −0.0270511 0.0468538i
\(705\) 0 0
\(706\) −6389.61 −0.340618
\(707\) 20653.9 9502.04i 1.09868 0.505461i
\(708\) 0 0
\(709\) −3071.65 + 5320.25i −0.162706 + 0.281814i −0.935838 0.352430i \(-0.885355\pi\)
0.773133 + 0.634244i \(0.218689\pi\)
\(710\) 9722.38 + 16839.7i 0.513908 + 0.890114i
\(711\) 0 0
\(712\) −2702.37 + 4680.64i −0.142241 + 0.246369i
\(713\) −15954.7 −0.838019
\(714\) 0 0
\(715\) 12756.4 0.667218
\(716\) 5164.23 8944.70i 0.269548 0.466870i
\(717\) 0 0
\(718\) 11876.7 + 20571.1i 0.617318 + 1.06923i
\(719\) 2001.23 3466.24i 0.103802 0.179790i −0.809446 0.587194i \(-0.800233\pi\)
0.913248 + 0.407404i \(0.133566\pi\)
\(720\) 0 0
\(721\) −12673.5 8971.60i −0.654628 0.463412i
\(722\) −2257.46 −0.116363
\(723\) 0 0
\(724\) −5957.12 10318.0i −0.305794 0.529650i
\(725\) −8300.92 14377.6i −0.425225 0.736512i
\(726\) 0 0
\(727\) −37145.8 −1.89500 −0.947498 0.319763i \(-0.896397\pi\)
−0.947498 + 0.319763i \(0.896397\pi\)
\(728\) 689.809 7443.41i 0.0351181 0.378944i
\(729\) 0 0
\(730\) 4485.90 7769.81i 0.227439 0.393936i
\(731\) −632.876 1096.17i −0.0320216 0.0554630i
\(732\) 0 0
\(733\) 97.6418 169.121i 0.00492017 0.00852198i −0.863555 0.504255i \(-0.831767\pi\)
0.868475 + 0.495733i \(0.165101\pi\)
\(734\) 11899.5 0.598389
\(735\) 0 0
\(736\) −1963.78 −0.0983502
\(737\) −873.401 + 1512.78i −0.0436528 + 0.0756089i
\(738\) 0 0
\(739\) 2574.43 + 4459.05i 0.128149 + 0.221960i 0.922959 0.384897i \(-0.125763\pi\)
−0.794811 + 0.606858i \(0.792430\pi\)
\(740\) −7880.91 + 13650.1i −0.391497 + 0.678093i
\(741\) 0 0
\(742\) 161.206 1739.50i 0.00797580 0.0860632i
\(743\) −21310.2 −1.05221 −0.526106 0.850419i \(-0.676349\pi\)
−0.526106 + 0.850419i \(0.676349\pi\)
\(744\) 0 0
\(745\) 6385.10 + 11059.3i 0.314003 + 0.543869i
\(746\) −2623.31 4543.71i −0.128748 0.222999i
\(747\) 0 0
\(748\) −2334.10 −0.114095
\(749\) 6523.41 + 4617.93i 0.318238 + 0.225281i
\(750\) 0 0
\(751\) −7507.47 + 13003.3i −0.364782 + 0.631822i −0.988741 0.149635i \(-0.952190\pi\)
0.623959 + 0.781457i \(0.285523\pi\)
\(752\) −2925.61 5067.31i −0.141870 0.245726i
\(753\) 0 0
\(754\) −6375.60 + 11042.9i −0.307939 + 0.533365i
\(755\) −43387.8 −2.09145
\(756\) 0 0
\(757\) 3951.68 0.189731 0.0948654 0.995490i \(-0.469758\pi\)
0.0948654 + 0.995490i \(0.469758\pi\)
\(758\) 3206.76 5554.27i 0.153661 0.266148i
\(759\) 0 0
\(760\) 5724.18 + 9914.57i 0.273208 + 0.473209i
\(761\) 16117.9 27917.1i 0.767773 1.32982i −0.170996 0.985272i \(-0.554698\pi\)
0.938768 0.344549i \(-0.111968\pi\)
\(762\) 0 0
\(763\) 21991.7 10117.5i 1.04345 0.480051i
\(764\) 16509.8 0.781809
\(765\) 0 0
\(766\) 6446.56 + 11165.8i 0.304078 + 0.526678i
\(767\) 18070.6 + 31299.2i 0.850707 + 1.47347i
\(768\) 0 0
\(769\) 9297.59 0.435994 0.217997 0.975949i \(-0.430048\pi\)
0.217997 + 0.975949i \(0.430048\pi\)
\(770\) 7643.70 + 5410.98i 0.357740 + 0.253244i
\(771\) 0 0
\(772\) 6035.40 10453.6i 0.281372 0.487350i
\(773\) 17411.2 + 30157.0i 0.810138 + 1.40320i 0.912767 + 0.408480i \(0.133941\pi\)
−0.102630 + 0.994720i \(0.532726\pi\)
\(774\) 0 0
\(775\) 17078.2 29580.4i 0.791572 1.37104i
\(776\) −7809.53 −0.361270
\(777\) 0 0
\(778\) 5906.97 0.272205
\(779\) −23077.8 + 39972.0i −1.06142 + 1.83844i
\(780\) 0 0
\(781\) 4793.96 + 8303.39i 0.219643 + 0.380433i
\(782\) −2267.81 + 3927.97i −0.103704 + 0.179621i
\(783\) 0 0
\(784\) 3570.68 4167.54i 0.162658 0.189848i