Properties

Label 378.4.g.e.109.4
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: \( x^{8} - x^{7} + 66x^{6} + 59x^{5} + 3770x^{4} + 721x^{3} + 29779x^{2} + 1374x + 209764 \) 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 109.4
Root \(4.05517 - 7.02376i\) of defining polynomial
Character \(\chi\) \(=\) 378.109
Dual form 378.4.g.e.163.4

$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

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

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
\(5\) 8.00592 + 13.8667i 0.716072 + 1.24027i 0.962545 + 0.271123i \(0.0873949\pi\)
−0.246473 + 0.969150i \(0.579272\pi\)
\(6\) 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 −0.953707 0.300736i \(-0.902768\pi\)
0.737299 + 0.675567i \(0.236101\pi\)
\(12\) 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 −0.703588 0.710608i \(-0.748420\pi\)
0.967199 + 0.254022i \(0.0817534\pi\)
\(18\) 0 0
\(19\) 44.6871 + 77.4002i 0.539574 + 0.934570i 0.998927 + 0.0463161i \(0.0147482\pi\)
−0.459352 + 0.888254i \(0.651919\pi\)
\(20\) −64.0474 −0.716072
\(21\) 0 0
\(22\) −31.5808 −0.306048
\(23\) −30.6840 53.1462i −0.278176 0.481816i 0.692755 0.721173i \(-0.256397\pi\)
−0.970932 + 0.239357i \(0.923063\pi\)
\(24\) 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 −0.193159 0.981167i \(-0.561873\pi\)
0.946295 0.323303i \(-0.104793\pi\)
\(32\) 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 0.998496 + 0.0548266i \(0.0174606\pi\)
−0.451767 + 0.892136i \(0.649206\pi\)
\(38\) −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 −0.996814 0.0797571i \(-0.974586\pi\)
0.429335 0.903145i \(-0.358748\pi\)
\(48\) 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 −0.833848 0.551994i \(-0.813867\pi\)
0.894965 + 0.446137i \(0.147201\pi\)
\(54\) 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 0.135449 + 0.990784i \(0.456752\pi\)
−0.925769 + 0.378090i \(0.876581\pi\)
\(60\) 0 0
\(61\) 348.209 + 603.115i 0.730878 + 1.26592i 0.956508 + 0.291705i \(0.0942227\pi\)
−0.225630 + 0.974213i \(0.572444\pi\)
\(62\) 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 −0.912038 0.410105i \(-0.865492\pi\)
0.811181 + 0.584796i \(0.198825\pi\)
\(68\) 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 −0.731605 0.681729i \(-0.761228\pi\)
0.956197 + 0.292724i \(0.0945618\pi\)
\(74\) −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 0.987758 + 0.155994i \(0.0498580\pi\)
−0.358784 + 0.933420i \(0.616809\pi\)
\(80\) 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 0.994005 0.109332i \(-0.0348712\pi\)
−0.591687 + 0.806168i \(0.701538\pi\)
\(90\) 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 −0.387411 0.921907i \(-0.626631\pi\)
0.992100 0.125446i \(-0.0400361\pi\)
\(102\) 0 0
\(103\) 419.207 + 726.088i 0.401026 + 0.694598i 0.993850 0.110734i \(-0.0353203\pi\)
−0.592824 + 0.805332i \(0.701987\pi\)
\(104\) 403.629 0.380568
\(105\) 0 0
\(106\) 94.3264 0.0864320
\(107\) −215.777 373.737i −0.194953 0.337669i 0.751932 0.659241i \(-0.229122\pi\)
−0.946885 + 0.321572i \(0.895789\pi\)
\(108\) 0 0
\(109\) 653.539 1131.96i 0.574291 0.994701i −0.421827 0.906676i \(-0.638611\pi\)
0.996118 0.0880250i \(-0.0280555\pi\)
\(110\) −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 0.974088 + 0.226168i \(0.0726200\pi\)
−0.291176 + 0.956669i \(0.594047\pi\)
\(132\) 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 −0.151913 0.988394i \(-0.548543\pi\)
0.931931 0.362637i \(-0.118123\pi\)
\(138\) 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 0.735326 0.677713i \(-0.237029\pi\)
−0.954580 + 0.297955i \(0.903696\pi\)
\(150\) 0 0
\(151\) −1354.87 + 2346.70i −0.730181 + 1.26471i 0.226624 + 0.973982i \(0.427231\pi\)
−0.956806 + 0.290729i \(0.906102\pi\)
\(152\) −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 0.0292542 + 0.999572i \(0.490687\pi\)
−0.880282 + 0.474451i \(0.842647\pi\)
\(158\) −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 0.983284 + 0.182079i \(0.0582826\pi\)
−0.333957 + 0.942588i \(0.608384\pi\)
\(164\) 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 0.877847 + 0.478942i \(0.158979\pi\)
−0.0241476 + 0.999708i \(0.507687\pi\)
\(174\) 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 −0.459857 0.887993i \(-0.652099\pi\)
0.998953 0.0457482i \(-0.0145672\pi\)
\(180\) 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 −0.930887 0.365308i \(-0.880964\pi\)
0.149077 0.988826i \(-0.452370\pi\)
\(192\) 0 0
\(193\) 1508.85 2613.41i 0.562743 0.974700i −0.434512 0.900666i \(-0.643079\pi\)
0.997256 0.0740342i \(-0.0235874\pi\)
\(194\) 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 0.0576981 + 0.998334i \(0.481624\pi\)
−0.893432 + 0.449199i \(0.851709\pi\)
\(200\) 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 0.441377 + 0.897322i \(0.354490\pi\)
−0.997792 + 0.0664167i \(0.978843\pi\)
\(228\) 0 0
\(229\) −599.426 1038.24i −0.172975 0.299601i 0.766484 0.642264i \(-0.222005\pi\)
−0.939459 + 0.342663i \(0.888671\pi\)
\(230\) 1965.23 0.563406
\(231\) 0 0
\(232\) −1010.93 −0.286080
\(233\) 1305.87 + 2261.84i 0.367170 + 0.635956i 0.989122 0.147099i \(-0.0469936\pi\)
−0.621952 + 0.783055i \(0.713660\pi\)
\(234\) 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 −0.618720 0.785611i \(-0.712349\pi\)
0.989720 + 0.143022i \(0.0456819\pi\)
\(242\) −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 0.621774 0.783196i \(-0.286412\pi\)
−0.989155 + 0.146874i \(0.953079\pi\)
\(258\) 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 −0.229186 0.973383i \(-0.573606\pi\)
0.957567 0.288210i \(-0.0930602\pi\)
\(264\) 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 −0.898945 0.438063i \(-0.855665\pi\)
0.828846 + 0.559478i \(0.188998\pi\)
\(270\) 0 0
\(271\) −1368.21 2369.81i −0.306690 0.531202i 0.670946 0.741506i \(-0.265888\pi\)
−0.977636 + 0.210304i \(0.932555\pi\)
\(272\) −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 −0.550188 0.835041i \(-0.685444\pi\)
0.998261 + 0.0589561i \(0.0187772\pi\)
\(278\) −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 −0.987738 0.156119i \(-0.950102\pi\)
0.629072 + 0.777347i \(0.283435\pi\)
\(284\) 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 0.380884 + 0.924623i \(0.375620\pi\)
−0.991189 + 0.132456i \(0.957714\pi\)
\(312\) 0 0
\(313\) 5092.10 + 8819.78i 0.919561 + 1.59273i 0.800083 + 0.599890i \(0.204789\pi\)
0.119478 + 0.992837i \(0.461878\pi\)
\(314\) −6696.58 −1.20353
\(315\) 0 0
\(316\) −3533.16 −0.628974
\(317\) 1765.83 + 3058.50i 0.312867 + 0.541901i 0.978982 0.203948i \(-0.0653773\pi\)
−0.666115 + 0.745849i \(0.732044\pi\)
\(318\) 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 −0.823873 0.566775i \(-0.808191\pi\)
−0.0789050 0.996882i \(-0.525142\pi\)
\(332\) 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 −0.996598 0.0824220i \(-0.973734\pi\)
0.569678 + 0.821868i \(0.307068\pi\)
\(348\) 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 −0.960958 0.276696i \(-0.910761\pi\)
0.720104 + 0.693866i \(0.244094\pi\)
\(354\) 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 −0.858857 0.512215i \(-0.828825\pi\)
−0.0141629 0.999900i \(-0.504508\pi\)
\(360\) 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 −0.573118 0.819473i \(-0.694267\pi\)
0.996243 + 0.0865989i \(0.0275998\pi\)
\(368\) −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 0.942588 0.333958i \(-0.108384\pi\)
−0.760510 + 0.649326i \(0.775051\pi\)
\(374\) −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 0.566844 0.823825i \(-0.308164\pi\)
−0.996875 + 0.0789891i \(0.974831\pi\)
\(384\) 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 −0.753593 0.657341i \(-0.771681\pi\)
0.946071 + 0.323960i \(0.105014\pi\)
\(390\) 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 0.974096 0.226133i \(-0.0726084\pi\)
−0.682885 + 0.730526i \(0.739275\pi\)
\(398\) −9384.42 −1.18191
\(399\) 0 0
\(400\) 2102.07 0.262759
\(401\) −5282.15 9148.95i −0.657800 1.13934i −0.981184 0.193076i \(-0.938154\pi\)
0.323384 0.946268i \(-0.395180\pi\)
\(402\) 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 −0.772005 0.635616i \(-0.780746\pi\)
0.936462 + 0.350768i \(0.114080\pi\)
\(410\) 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 −0.994421 0.105482i \(-0.966362\pi\)
0.588561 + 0.808453i \(0.299695\pi\)
\(432\) 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 0.840903 0.541185i \(-0.182024\pi\)
−0.889132 + 0.457651i \(0.848691\pi\)
\(440\) 2022.67 0.219152
\(441\) 0 0
\(442\) −3728.96 −0.401286
\(443\) −3940.57 6825.27i −0.422624 0.732006i 0.573571 0.819156i \(-0.305557\pi\)
−0.996195 + 0.0871497i \(0.972224\pi\)
\(444\) 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 0.996642 0.0818784i \(-0.0260919\pi\)
−0.569230 + 0.822178i \(0.692759\pi\)
\(458\) 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 0.997691 0.0679189i \(-0.0216359\pi\)
−0.557665 + 0.830066i \(0.688303\pi\)
\(468\) 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 −0.0830174 + 0.996548i \(0.526456\pi\)
−0.821527 + 0.570169i \(0.806878\pi\)
\(480\) 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 0.0572748 + 0.998358i \(0.481759\pi\)
−0.893241 + 0.449578i \(0.851574\pi\)
\(488\) −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 −0.999613 0.0278191i \(-0.991144\pi\)
0.475714 0.879600i \(-0.342190\pi\)
\(500\) 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 0.716611 0.697474i \(-0.245693\pi\)
−0.962335 + 0.271866i \(0.912359\pi\)
\(510\) 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 −0.263972 0.964530i \(-0.585033\pi\)
0.967294 0.253659i \(-0.0816340\pi\)
\(522\) 0 0
\(523\) 2319.53 + 4017.55i 0.193931 + 0.335899i 0.946550 0.322558i \(-0.104543\pi\)
−0.752618 + 0.658457i \(0.771209\pi\)
\(524\) −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 −0.972731 0.231937i \(-0.925494\pi\)
0.285502 0.958378i \(-0.407840\pi\)
\(542\) 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 −0.624977 0.780643i \(-0.714892\pi\)
0.988545 + 0.150925i \(0.0482251\pi\)
\(558\) 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 −0.947813 0.318826i \(-0.896711\pi\)
0.750018 + 0.661417i \(0.230045\pi\)
\(564\) 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 0.944117 0.329611i \(-0.106918\pi\)
−0.757510 + 0.652824i \(0.773584\pi\)
\(570\) 0 0
\(571\) 6695.36 11596.7i 0.490704 0.849925i −0.509239 0.860625i \(-0.670073\pi\)
0.999943 + 0.0107008i \(0.00340623\pi\)
\(572\) 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 0.00356838 0.999994i \(-0.498864\pi\)
0.864236 0.503087i \(-0.167803\pi\)
\(578\) −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 0.818439 0.574593i \(-0.194840\pi\)
−0.906832 + 0.421492i \(0.861506\pi\)
\(594\) 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 −0.681385 0.731925i \(-0.738622\pi\)
0.974558 + 0.224134i \(0.0719553\pi\)
\(600\) 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 0.843403 0.537282i \(-0.180549\pi\)
−0.887001 + 0.461767i \(0.847216\pi\)
\(608\) 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 0.404277 + 0.914637i \(0.367523\pi\)
−0.994237 + 0.107204i \(0.965810\pi\)
\(614\) −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 −0.984630 0.174653i \(-0.944120\pi\)
0.643569 + 0.765388i \(0.277453\pi\)
\(620\) −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 0.242749 + 0.970089i \(0.421951\pi\)
−0.961496 + 0.274817i \(0.911383\pi\)
\(642\) 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 −0.683475 0.729974i \(-0.739532\pi\)
0.973913 + 0.226920i \(0.0728657\pi\)
\(648\) 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 −0.991971 0.126464i \(-0.959637\pi\)
0.386464 0.922304i \(-0.373696\pi\)
\(654\) 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 0.226667 + 0.973972i \(0.427217\pi\)
−0.956818 + 0.290687i \(0.906116\pi\)
\(662\) 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 0.841286 0.540590i \(-0.181799\pi\)
−0.888808 + 0.458281i \(0.848465\pi\)
\(678\) 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 −0.824049 0.566518i \(-0.808290\pi\)
0.902644 + 0.430389i \(0.141623\pi\)
\(684\) 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 0.789183 0.614158i \(-0.210504\pi\)
−0.926468 + 0.376374i \(0.877171\pi\)
\(692\) −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 0.773133 0.634244i \(-0.218689\pi\)
−0.935838 + 0.352430i \(0.885355\pi\)
\(710\) 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 0.913248 0.407404i \(-0.133566\pi\)
−0.809446 + 0.587194i \(0.800233\pi\)
\(720\) 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 0.868475 0.495733i \(-0.165101\pi\)
−0.863555 + 0.504255i \(0.831767\pi\)
\(734\) 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 −0.794811 0.606858i \(-0.792430\pi\)
0.922959 + 0.384897i \(0.125763\pi\)
\(740\) −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 0.623959 0.781457i \(-0.285523\pi\)
−0.988741 + 0.149635i \(0.952190\pi\)
\(752\) −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 0.938768 + 0.344549i \(0.111968\pi\)
−0.170996 + 0.985272i \(0.554698\pi\)
\(762\) 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 −0.102630 0.994720i \(-0.532726\pi\)
0.912767 0.408480i \(-0.133941\pi\)
\(774\) 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