Properties

Label 342.4.g.h.163.2
Level $342$
Weight $4$
Character 342.163
Analytic conductor $20.179$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 342.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.1786532220\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.627014547.1
Defining polynomial: \(x^{6} + 26 x^{4} + 169 x^{2} + 147\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{3} \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 163.2
Root \(4.00355i\) of defining polynomial
Character \(\chi\) \(=\) 342.163
Dual form 342.4.g.h.235.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(2.09405 - 3.62701i) q^{5} +3.18810 q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(2.09405 - 3.62701i) q^{5} +3.18810 q^{7} -8.00000 q^{8} +(-4.18810 - 7.25401i) q^{10} -69.4003 q^{11} +(4.06431 + 7.03960i) q^{13} +(3.18810 - 5.52196i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-53.0418 + 91.8711i) q^{17} +(42.6656 - 70.9834i) q^{19} -16.7524 q^{20} +(-69.4003 + 120.205i) q^{22} +(-88.2468 - 152.848i) q^{23} +(53.7299 + 93.0629i) q^{25} +16.2573 q^{26} +(-6.37621 - 11.0439i) q^{28} +(-33.1109 - 57.3498i) q^{29} -140.915 q^{31} +(16.0000 + 27.7128i) q^{32} +(106.084 + 183.742i) q^{34} +(6.67606 - 11.5633i) q^{35} -156.003 q^{37} +(-80.2814 - 144.882i) q^{38} +(-16.7524 + 29.0160i) q^{40} +(-207.281 + 359.022i) q^{41} +(-57.9252 + 100.329i) q^{43} +(138.801 + 240.410i) q^{44} -352.987 q^{46} +(310.141 + 537.181i) q^{47} -332.836 q^{49} +214.920 q^{50} +(16.2573 - 28.1584i) q^{52} +(-185.993 - 322.149i) q^{53} +(-145.328 + 251.715i) q^{55} -25.5048 q^{56} -132.444 q^{58} +(45.8465 - 79.4084i) q^{59} +(-109.310 - 189.331i) q^{61} +(-140.915 + 244.072i) q^{62} +64.0000 q^{64} +34.0436 q^{65} +(72.6712 + 125.870i) q^{67} +424.334 q^{68} +(-13.3521 - 23.1265i) q^{70} +(443.915 - 768.883i) q^{71} +(-99.5081 + 172.353i) q^{73} +(-156.003 + 270.205i) q^{74} +(-331.225 - 5.83100i) q^{76} -221.255 q^{77} +(194.779 - 337.367i) q^{79} +(33.5048 + 58.0321i) q^{80} +(414.563 + 718.044i) q^{82} -380.039 q^{83} +(222.145 + 384.766i) q^{85} +(115.850 + 200.659i) q^{86} +555.202 q^{88} +(-212.899 - 368.753i) q^{89} +(12.9575 + 22.4430i) q^{91} +(-352.987 + 611.392i) q^{92} +1240.57 q^{94} +(-168.113 - 303.391i) q^{95} +(-209.923 + 363.597i) q^{97} +(-332.836 + 576.489i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} - 12 q^{4} + 10 q^{5} + 14 q^{7} - 48 q^{8} + O(q^{10}) \) \( 6 q + 6 q^{2} - 12 q^{4} + 10 q^{5} + 14 q^{7} - 48 q^{8} - 20 q^{10} + 88 q^{11} + 9 q^{13} + 14 q^{14} - 48 q^{16} - 84 q^{17} + 32 q^{19} - 80 q^{20} + 88 q^{22} - 2 q^{23} + 83 q^{25} + 36 q^{26} - 28 q^{28} + 92 q^{29} - 218 q^{31} + 96 q^{32} + 168 q^{34} + 282 q^{35} + 490 q^{37} + 74 q^{38} - 80 q^{40} - 688 q^{41} + 103 q^{43} - 176 q^{44} - 8 q^{46} + 322 q^{47} - 1508 q^{49} + 332 q^{50} + 36 q^{52} - 1322 q^{53} + 248 q^{55} - 112 q^{56} + 368 q^{58} + 252 q^{59} + 435 q^{61} - 218 q^{62} + 384 q^{64} + 3164 q^{65} + 719 q^{67} + 672 q^{68} - 564 q^{70} - 62 q^{71} + 581 q^{73} + 490 q^{74} + 20 q^{76} + 408 q^{77} + 489 q^{79} + 160 q^{80} + 1376 q^{82} - 4992 q^{83} - 1632 q^{85} - 206 q^{86} - 704 q^{88} + 1584 q^{89} + 1573 q^{91} - 8 q^{92} + 1288 q^{94} - 2362 q^{95} - 974 q^{97} - 1508 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(325\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) 2.09405 3.62701i 0.187298 0.324409i −0.757051 0.653356i \(-0.773360\pi\)
0.944348 + 0.328947i \(0.106694\pi\)
\(6\) 0 0
\(7\) 3.18810 0.172141 0.0860707 0.996289i \(-0.472569\pi\)
0.0860707 + 0.996289i \(0.472569\pi\)
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −4.18810 7.25401i −0.132440 0.229392i
\(11\) −69.4003 −1.90227 −0.951135 0.308774i \(-0.900081\pi\)
−0.951135 + 0.308774i \(0.900081\pi\)
\(12\) 0 0
\(13\) 4.06431 + 7.03960i 0.0867106 + 0.150187i 0.906119 0.423023i \(-0.139031\pi\)
−0.819408 + 0.573210i \(0.805698\pi\)
\(14\) 3.18810 5.52196i 0.0608612 0.105415i
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −53.0418 + 91.8711i −0.756737 + 1.31071i 0.187770 + 0.982213i \(0.439874\pi\)
−0.944506 + 0.328493i \(0.893459\pi\)
\(18\) 0 0
\(19\) 42.6656 70.9834i 0.515166 0.857090i
\(20\) −16.7524 −0.187298
\(21\) 0 0
\(22\) −69.4003 + 120.205i −0.672554 + 1.16490i
\(23\) −88.2468 152.848i −0.800031 1.38570i −0.919595 0.392869i \(-0.871483\pi\)
0.119563 0.992827i \(-0.461851\pi\)
\(24\) 0 0
\(25\) 53.7299 + 93.0629i 0.429839 + 0.744503i
\(26\) 16.2573 0.122627
\(27\) 0 0
\(28\) −6.37621 11.0439i −0.0430354 0.0745394i
\(29\) −33.1109 57.3498i −0.212019 0.367227i 0.740327 0.672247i \(-0.234670\pi\)
−0.952346 + 0.305019i \(0.901337\pi\)
\(30\) 0 0
\(31\) −140.915 −0.816421 −0.408210 0.912888i \(-0.633847\pi\)
−0.408210 + 0.912888i \(0.633847\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 106.084 + 183.742i 0.535094 + 0.926809i
\(35\) 6.67606 11.5633i 0.0322417 0.0558443i
\(36\) 0 0
\(37\) −156.003 −0.693156 −0.346578 0.938021i \(-0.612656\pi\)
−0.346578 + 0.938021i \(0.612656\pi\)
\(38\) −80.2814 144.882i −0.342720 0.618501i
\(39\) 0 0
\(40\) −16.7524 + 29.0160i −0.0662198 + 0.114696i
\(41\) −207.281 + 359.022i −0.789559 + 1.36756i 0.136679 + 0.990615i \(0.456357\pi\)
−0.926238 + 0.376940i \(0.876976\pi\)
\(42\) 0 0
\(43\) −57.9252 + 100.329i −0.205430 + 0.355816i −0.950270 0.311428i \(-0.899193\pi\)
0.744839 + 0.667244i \(0.232526\pi\)
\(44\) 138.801 + 240.410i 0.475568 + 0.823707i
\(45\) 0 0
\(46\) −352.987 −1.13142
\(47\) 310.141 + 537.181i 0.962527 + 1.66715i 0.716117 + 0.697980i \(0.245918\pi\)
0.246410 + 0.969166i \(0.420749\pi\)
\(48\) 0 0
\(49\) −332.836 −0.970367
\(50\) 214.920 0.607884
\(51\) 0 0
\(52\) 16.2573 28.1584i 0.0433553 0.0750936i
\(53\) −185.993 322.149i −0.482039 0.834916i 0.517748 0.855533i \(-0.326770\pi\)
−0.999787 + 0.0206167i \(0.993437\pi\)
\(54\) 0 0
\(55\) −145.328 + 251.715i −0.356291 + 0.617114i
\(56\) −25.5048 −0.0608612
\(57\) 0 0
\(58\) −132.444 −0.299840
\(59\) 45.8465 79.4084i 0.101164 0.175222i −0.811000 0.585046i \(-0.801077\pi\)
0.912165 + 0.409824i \(0.134410\pi\)
\(60\) 0 0
\(61\) −109.310 189.331i −0.229438 0.397399i 0.728203 0.685361i \(-0.240356\pi\)
−0.957642 + 0.287962i \(0.907022\pi\)
\(62\) −140.915 + 244.072i −0.288648 + 0.499954i
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 34.0436 0.0649628
\(66\) 0 0
\(67\) 72.6712 + 125.870i 0.132510 + 0.229515i 0.924644 0.380833i \(-0.124363\pi\)
−0.792133 + 0.610348i \(0.791030\pi\)
\(68\) 424.334 0.756737
\(69\) 0 0
\(70\) −13.3521 23.1265i −0.0227983 0.0394879i
\(71\) 443.915 768.883i 0.742014 1.28521i −0.209563 0.977795i \(-0.567204\pi\)
0.951577 0.307410i \(-0.0994625\pi\)
\(72\) 0 0
\(73\) −99.5081 + 172.353i −0.159542 + 0.276334i −0.934703 0.355429i \(-0.884335\pi\)
0.775162 + 0.631763i \(0.217668\pi\)
\(74\) −156.003 + 270.205i −0.245067 + 0.424469i
\(75\) 0 0
\(76\) −331.225 5.83100i −0.499923 0.00880082i
\(77\) −221.255 −0.327460
\(78\) 0 0
\(79\) 194.779 337.367i 0.277397 0.480465i −0.693340 0.720610i \(-0.743862\pi\)
0.970737 + 0.240145i \(0.0771951\pi\)
\(80\) 33.5048 + 58.0321i 0.0468244 + 0.0811023i
\(81\) 0 0
\(82\) 414.563 + 718.044i 0.558302 + 0.967008i
\(83\) −380.039 −0.502586 −0.251293 0.967911i \(-0.580856\pi\)
−0.251293 + 0.967911i \(0.580856\pi\)
\(84\) 0 0
\(85\) 222.145 + 384.766i 0.283470 + 0.490985i
\(86\) 115.850 + 200.659i 0.145261 + 0.251600i
\(87\) 0 0
\(88\) 555.202 0.672554
\(89\) −212.899 368.753i −0.253565 0.439188i 0.710940 0.703253i \(-0.248270\pi\)
−0.964505 + 0.264065i \(0.914937\pi\)
\(90\) 0 0
\(91\) 12.9575 + 22.4430i 0.0149265 + 0.0258534i
\(92\) −352.987 + 611.392i −0.400016 + 0.692848i
\(93\) 0 0
\(94\) 1240.57 1.36122
\(95\) −168.113 303.391i −0.181559 0.327656i
\(96\) 0 0
\(97\) −209.923 + 363.597i −0.219736 + 0.380595i −0.954727 0.297482i \(-0.903853\pi\)
0.734991 + 0.678077i \(0.237186\pi\)
\(98\) −332.836 + 576.489i −0.343077 + 0.594226i
\(99\) 0 0
\(100\) 214.920 372.252i 0.214920 0.372252i
\(101\) −620.855 1075.35i −0.611657 1.05942i −0.990961 0.134150i \(-0.957170\pi\)
0.379304 0.925272i \(-0.376164\pi\)
\(102\) 0 0
\(103\) −593.606 −0.567862 −0.283931 0.958845i \(-0.591639\pi\)
−0.283931 + 0.958845i \(0.591639\pi\)
\(104\) −32.5145 56.3168i −0.0306568 0.0530992i
\(105\) 0 0
\(106\) −743.971 −0.681706
\(107\) 1778.56 1.60691 0.803457 0.595363i \(-0.202992\pi\)
0.803457 + 0.595363i \(0.202992\pi\)
\(108\) 0 0
\(109\) 534.995 926.639i 0.470121 0.814274i −0.529295 0.848438i \(-0.677543\pi\)
0.999416 + 0.0341638i \(0.0108768\pi\)
\(110\) 290.656 + 503.431i 0.251936 + 0.436366i
\(111\) 0 0
\(112\) −25.5048 + 44.1757i −0.0215177 + 0.0372697i
\(113\) −583.197 −0.485510 −0.242755 0.970088i \(-0.578051\pi\)
−0.242755 + 0.970088i \(0.578051\pi\)
\(114\) 0 0
\(115\) −739.173 −0.599376
\(116\) −132.444 + 229.399i −0.106009 + 0.183614i
\(117\) 0 0
\(118\) −91.6929 158.817i −0.0715341 0.123901i
\(119\) −169.103 + 292.895i −0.130266 + 0.225627i
\(120\) 0 0
\(121\) 3485.40 2.61863
\(122\) −437.241 −0.324475
\(123\) 0 0
\(124\) 281.830 + 488.143i 0.204105 + 0.353521i
\(125\) 973.566 0.696627
\(126\) 0 0
\(127\) −829.677 1437.04i −0.579700 1.00407i −0.995513 0.0946199i \(-0.969836\pi\)
0.415814 0.909450i \(-0.363497\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 34.0436 58.9652i 0.0229678 0.0397814i
\(131\) 298.773 517.490i 0.199267 0.345140i −0.749024 0.662543i \(-0.769477\pi\)
0.948291 + 0.317403i \(0.102811\pi\)
\(132\) 0 0
\(133\) 136.022 226.303i 0.0886814 0.147541i
\(134\) 290.685 0.187398
\(135\) 0 0
\(136\) 424.334 734.969i 0.267547 0.463405i
\(137\) −888.654 1539.19i −0.554182 0.959871i −0.997967 0.0637373i \(-0.979698\pi\)
0.443785 0.896133i \(-0.353635\pi\)
\(138\) 0 0
\(139\) −81.7836 141.653i −0.0499050 0.0864379i 0.839994 0.542596i \(-0.182559\pi\)
−0.889899 + 0.456158i \(0.849225\pi\)
\(140\) −53.4085 −0.0322417
\(141\) 0 0
\(142\) −887.829 1537.77i −0.524683 0.908778i
\(143\) −282.065 488.550i −0.164947 0.285697i
\(144\) 0 0
\(145\) −277.344 −0.158843
\(146\) 199.016 + 344.706i 0.112813 + 0.195398i
\(147\) 0 0
\(148\) 312.006 + 540.411i 0.173289 + 0.300145i
\(149\) −559.899 + 969.774i −0.307844 + 0.533201i −0.977890 0.209118i \(-0.932941\pi\)
0.670047 + 0.742319i \(0.266274\pi\)
\(150\) 0 0
\(151\) −2807.15 −1.51286 −0.756432 0.654073i \(-0.773059\pi\)
−0.756432 + 0.654073i \(0.773059\pi\)
\(152\) −341.325 + 567.868i −0.182139 + 0.303027i
\(153\) 0 0
\(154\) −221.255 + 383.226i −0.115774 + 0.200527i
\(155\) −295.083 + 511.099i −0.152914 + 0.264854i
\(156\) 0 0
\(157\) −501.971 + 869.439i −0.255170 + 0.441967i −0.964942 0.262465i \(-0.915465\pi\)
0.709772 + 0.704432i \(0.248798\pi\)
\(158\) −389.558 674.734i −0.196149 0.339740i
\(159\) 0 0
\(160\) 134.019 0.0662198
\(161\) −281.340 487.295i −0.137719 0.238536i
\(162\) 0 0
\(163\) 1271.99 0.611225 0.305612 0.952156i \(-0.401139\pi\)
0.305612 + 0.952156i \(0.401139\pi\)
\(164\) 1658.25 0.789559
\(165\) 0 0
\(166\) −380.039 + 658.246i −0.177691 + 0.307770i
\(167\) −1492.49 2585.07i −0.691572 1.19784i −0.971323 0.237765i \(-0.923585\pi\)
0.279751 0.960073i \(-0.409748\pi\)
\(168\) 0 0
\(169\) 1065.46 1845.44i 0.484963 0.839980i
\(170\) 888.578 0.400887
\(171\) 0 0
\(172\) 463.402 0.205430
\(173\) 28.3873 49.1683i 0.0124754 0.0216081i −0.859720 0.510765i \(-0.829362\pi\)
0.872196 + 0.489157i \(0.162696\pi\)
\(174\) 0 0
\(175\) 171.297 + 296.694i 0.0739931 + 0.128160i
\(176\) 555.202 961.639i 0.237784 0.411854i
\(177\) 0 0
\(178\) −851.598 −0.358595
\(179\) 4640.98 1.93790 0.968948 0.247266i \(-0.0795323\pi\)
0.968948 + 0.247266i \(0.0795323\pi\)
\(180\) 0 0
\(181\) −1887.70 3269.60i −0.775204 1.34269i −0.934680 0.355491i \(-0.884314\pi\)
0.159476 0.987202i \(-0.449020\pi\)
\(182\) 51.8298 0.0211093
\(183\) 0 0
\(184\) 705.974 + 1222.78i 0.282854 + 0.489917i
\(185\) −326.679 + 565.824i −0.129826 + 0.224866i
\(186\) 0 0
\(187\) 3681.12 6375.88i 1.43952 2.49332i
\(188\) 1240.57 2148.72i 0.481264 0.833573i
\(189\) 0 0
\(190\) −693.603 12.2104i −0.264838 0.00466230i
\(191\) 2762.53 1.04654 0.523271 0.852166i \(-0.324712\pi\)
0.523271 + 0.852166i \(0.324712\pi\)
\(192\) 0 0
\(193\) −1030.76 + 1785.32i −0.384433 + 0.665857i −0.991690 0.128648i \(-0.958936\pi\)
0.607258 + 0.794505i \(0.292270\pi\)
\(194\) 419.846 + 727.194i 0.155377 + 0.269121i
\(195\) 0 0
\(196\) 665.672 + 1152.98i 0.242592 + 0.420181i
\(197\) −2094.82 −0.757614 −0.378807 0.925476i \(-0.623666\pi\)
−0.378807 + 0.925476i \(0.623666\pi\)
\(198\) 0 0
\(199\) 858.681 + 1487.28i 0.305881 + 0.529801i 0.977457 0.211134i \(-0.0677158\pi\)
−0.671576 + 0.740935i \(0.734382\pi\)
\(200\) −429.839 744.503i −0.151971 0.263222i
\(201\) 0 0
\(202\) −2483.42 −0.865014
\(203\) −105.561 182.837i −0.0364972 0.0632151i
\(204\) 0 0
\(205\) 868.116 + 1503.62i 0.295765 + 0.512280i
\(206\) −593.606 + 1028.16i −0.200769 + 0.347743i
\(207\) 0 0
\(208\) −130.058 −0.0433553
\(209\) −2961.00 + 4926.27i −0.979985 + 1.63042i
\(210\) 0 0
\(211\) 1145.53 1984.11i 0.373750 0.647354i −0.616389 0.787442i \(-0.711405\pi\)
0.990139 + 0.140088i \(0.0447384\pi\)
\(212\) −743.971 + 1288.60i −0.241020 + 0.417458i
\(213\) 0 0
\(214\) 1778.56 3080.55i 0.568130 0.984030i
\(215\) 242.597 + 420.190i 0.0769533 + 0.133287i
\(216\) 0 0
\(217\) −449.251 −0.140540
\(218\) −1069.99 1853.28i −0.332426 0.575779i
\(219\) 0 0
\(220\) 1162.62 0.356291
\(221\) −862.314 −0.262468
\(222\) 0 0
\(223\) −1628.09 + 2819.94i −0.488902 + 0.846804i −0.999918 0.0127673i \(-0.995936\pi\)
0.511016 + 0.859571i \(0.329269\pi\)
\(224\) 51.0097 + 88.3514i 0.0152153 + 0.0263537i
\(225\) 0 0
\(226\) −583.197 + 1010.13i −0.171654 + 0.297313i
\(227\) 998.044 0.291817 0.145909 0.989298i \(-0.453389\pi\)
0.145909 + 0.989298i \(0.453389\pi\)
\(228\) 0 0
\(229\) −1028.59 −0.296816 −0.148408 0.988926i \(-0.547415\pi\)
−0.148408 + 0.988926i \(0.547415\pi\)
\(230\) −739.173 + 1280.29i −0.211912 + 0.367042i
\(231\) 0 0
\(232\) 264.887 + 458.799i 0.0749600 + 0.129835i
\(233\) −62.7431 + 108.674i −0.0176414 + 0.0305557i −0.874711 0.484644i \(-0.838949\pi\)
0.857070 + 0.515200i \(0.172282\pi\)
\(234\) 0 0
\(235\) 2597.81 0.721117
\(236\) −366.772 −0.101164
\(237\) 0 0
\(238\) 338.206 + 585.789i 0.0921118 + 0.159542i
\(239\) −3591.03 −0.971901 −0.485950 0.873986i \(-0.661526\pi\)
−0.485950 + 0.873986i \(0.661526\pi\)
\(240\) 0 0
\(241\) 1845.92 + 3197.23i 0.493386 + 0.854570i 0.999971 0.00762002i \(-0.00242555\pi\)
−0.506585 + 0.862190i \(0.669092\pi\)
\(242\) 3485.40 6036.89i 0.925827 1.60358i
\(243\) 0 0
\(244\) −437.241 + 757.324i −0.114719 + 0.198700i
\(245\) −696.976 + 1207.20i −0.181748 + 0.314796i
\(246\) 0 0
\(247\) 673.101 + 11.8495i 0.173394 + 0.00305250i
\(248\) 1127.32 0.288648
\(249\) 0 0
\(250\) 973.566 1686.27i 0.246295 0.426595i
\(251\) 3647.44 + 6317.55i 0.917228 + 1.58869i 0.803606 + 0.595162i \(0.202912\pi\)
0.113622 + 0.993524i \(0.463755\pi\)
\(252\) 0 0
\(253\) 6124.35 + 10607.7i 1.52188 + 2.63597i
\(254\) −3318.71 −0.819820
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 1151.60 + 1994.63i 0.279513 + 0.484131i 0.971264 0.238006i \(-0.0764937\pi\)
−0.691751 + 0.722136i \(0.743160\pi\)
\(258\) 0 0
\(259\) −497.354 −0.119321
\(260\) −68.0871 117.930i −0.0162407 0.0281297i
\(261\) 0 0
\(262\) −597.546 1034.98i −0.140903 0.244051i
\(263\) 3569.19 6182.01i 0.836827 1.44943i −0.0557070 0.998447i \(-0.517741\pi\)
0.892534 0.450980i \(-0.148925\pi\)
\(264\) 0 0
\(265\) −1557.91 −0.361139
\(266\) −255.945 461.900i −0.0589963 0.106470i
\(267\) 0 0
\(268\) 290.685 503.481i 0.0662552 0.114757i
\(269\) −2723.33 + 4716.95i −0.617265 + 1.06913i 0.372717 + 0.927945i \(0.378426\pi\)
−0.989983 + 0.141190i \(0.954907\pi\)
\(270\) 0 0
\(271\) 1701.84 2947.67i 0.381474 0.660732i −0.609799 0.792556i \(-0.708750\pi\)
0.991273 + 0.131824i \(0.0420834\pi\)
\(272\) −848.669 1469.94i −0.189184 0.327677i
\(273\) 0 0
\(274\) −3554.62 −0.783731
\(275\) −3728.87 6458.59i −0.817670 1.41625i
\(276\) 0 0
\(277\) −5131.93 −1.11317 −0.556584 0.830791i \(-0.687888\pi\)
−0.556584 + 0.830791i \(0.687888\pi\)
\(278\) −327.134 −0.0705763
\(279\) 0 0
\(280\) −53.4085 + 92.5062i −0.0113992 + 0.0197439i
\(281\) 1683.34 + 2915.63i 0.357365 + 0.618975i 0.987520 0.157495i \(-0.0503417\pi\)
−0.630154 + 0.776470i \(0.717008\pi\)
\(282\) 0 0
\(283\) −3342.88 + 5790.04i −0.702168 + 1.21619i 0.265535 + 0.964101i \(0.414451\pi\)
−0.967704 + 0.252090i \(0.918882\pi\)
\(284\) −3551.32 −0.742014
\(285\) 0 0
\(286\) −1128.26 −0.233270
\(287\) −660.835 + 1144.60i −0.135916 + 0.235413i
\(288\) 0 0
\(289\) −3170.36 5491.23i −0.645301 1.11769i
\(290\) −277.344 + 480.374i −0.0561593 + 0.0972708i
\(291\) 0 0
\(292\) 796.065 0.159542
\(293\) 5625.93 1.12174 0.560871 0.827903i \(-0.310466\pi\)
0.560871 + 0.827903i \(0.310466\pi\)
\(294\) 0 0
\(295\) −192.010 332.571i −0.0378957 0.0656374i
\(296\) 1248.02 0.245067
\(297\) 0 0
\(298\) 1119.80 + 1939.55i 0.217678 + 0.377030i
\(299\) 717.325 1242.44i 0.138742 0.240309i
\(300\) 0 0
\(301\) −184.672 + 319.861i −0.0353631 + 0.0612507i
\(302\) −2807.15 + 4862.12i −0.534878 + 0.926436i
\(303\) 0 0
\(304\) 642.251 + 1159.06i 0.121170 + 0.218673i
\(305\) −915.606 −0.171893
\(306\) 0 0
\(307\) −2801.77 + 4852.81i −0.520865 + 0.902164i 0.478841 + 0.877902i \(0.341057\pi\)
−0.999706 + 0.0242627i \(0.992276\pi\)
\(308\) 442.511 + 766.451i 0.0818649 + 0.141794i
\(309\) 0 0
\(310\) 590.166 + 1022.20i 0.108126 + 0.187280i
\(311\) −6668.20 −1.21582 −0.607908 0.794008i \(-0.707991\pi\)
−0.607908 + 0.794008i \(0.707991\pi\)
\(312\) 0 0
\(313\) −2245.70 3889.67i −0.405541 0.702418i 0.588843 0.808247i \(-0.299584\pi\)
−0.994384 + 0.105829i \(0.966250\pi\)
\(314\) 1003.94 + 1738.88i 0.180432 + 0.312518i
\(315\) 0 0
\(316\) −1558.23 −0.277397
\(317\) −633.023 1096.43i −0.112158 0.194264i 0.804482 0.593977i \(-0.202443\pi\)
−0.916640 + 0.399713i \(0.869110\pi\)
\(318\) 0 0
\(319\) 2297.91 + 3980.10i 0.403317 + 0.698566i
\(320\) 134.019 232.128i 0.0234122 0.0405512i
\(321\) 0 0
\(322\) −1125.36 −0.194764
\(323\) 4258.27 + 7684.82i 0.733549 + 1.32382i
\(324\) 0 0
\(325\) −436.750 + 756.474i −0.0745432 + 0.129113i
\(326\) 1271.99 2203.14i 0.216101 0.374297i
\(327\) 0 0
\(328\) 1658.25 2872.17i 0.279151 0.483504i
\(329\) 988.763 + 1712.59i 0.165691 + 0.286985i
\(330\) 0 0
\(331\) −5068.09 −0.841594 −0.420797 0.907155i \(-0.638249\pi\)
−0.420797 + 0.907155i \(0.638249\pi\)
\(332\) 760.077 + 1316.49i 0.125647 + 0.217626i
\(333\) 0 0
\(334\) −5969.97 −0.978031
\(335\) 608.709 0.0992757
\(336\) 0 0
\(337\) −5372.06 + 9304.68i −0.868352 + 1.50403i −0.00467268 + 0.999989i \(0.501487\pi\)
−0.863680 + 0.504041i \(0.831846\pi\)
\(338\) −2130.93 3690.87i −0.342920 0.593955i
\(339\) 0 0
\(340\) 888.578 1539.06i 0.141735 0.245492i
\(341\) 9779.53 1.55305
\(342\) 0 0
\(343\) −2154.64 −0.339182
\(344\) 463.402 802.635i 0.0726306 0.125800i
\(345\) 0 0
\(346\) −56.7747 98.3367i −0.00882146 0.0152792i
\(347\) −2425.67 + 4201.38i −0.375264 + 0.649977i −0.990367 0.138471i \(-0.955781\pi\)
0.615102 + 0.788447i \(0.289115\pi\)
\(348\) 0 0
\(349\) −7611.35 −1.16741 −0.583705 0.811966i \(-0.698398\pi\)
−0.583705 + 0.811966i \(0.698398\pi\)
\(350\) 685.186 0.104642
\(351\) 0 0
\(352\) −1110.40 1923.28i −0.168139 0.291225i
\(353\) −5567.64 −0.839477 −0.419739 0.907645i \(-0.637878\pi\)
−0.419739 + 0.907645i \(0.637878\pi\)
\(354\) 0 0
\(355\) −1859.16 3220.16i −0.277955 0.481432i
\(356\) −851.598 + 1475.01i −0.126783 + 0.219594i
\(357\) 0 0
\(358\) 4640.98 8038.42i 0.685149 1.18671i
\(359\) 2170.66 3759.69i 0.319116 0.552726i −0.661187 0.750221i \(-0.729947\pi\)
0.980304 + 0.197495i \(0.0632805\pi\)
\(360\) 0 0
\(361\) −3218.30 6057.10i −0.469208 0.883088i
\(362\) −7550.82 −1.09630
\(363\) 0 0
\(364\) 51.8298 89.7719i 0.00746325 0.0129267i
\(365\) 416.750 + 721.833i 0.0597636 + 0.103514i
\(366\) 0 0
\(367\) 4482.24 + 7763.47i 0.637524 + 1.10422i 0.985974 + 0.166896i \(0.0533745\pi\)
−0.348451 + 0.937327i \(0.613292\pi\)
\(368\) 2823.90 0.400016
\(369\) 0 0
\(370\) 653.357 + 1131.65i 0.0918012 + 0.159004i
\(371\) −592.965 1027.04i −0.0829789 0.143724i
\(372\) 0 0
\(373\) 5048.11 0.700755 0.350377 0.936609i \(-0.386053\pi\)
0.350377 + 0.936609i \(0.386053\pi\)
\(374\) −7362.23 12751.8i −1.01789 1.76304i
\(375\) 0 0
\(376\) −2481.13 4297.45i −0.340305 0.589425i
\(377\) 269.147 466.175i 0.0367686 0.0636850i
\(378\) 0 0
\(379\) −9290.41 −1.25915 −0.629573 0.776941i \(-0.716770\pi\)
−0.629573 + 0.776941i \(0.716770\pi\)
\(380\) −714.752 + 1189.14i −0.0964894 + 0.160531i
\(381\) 0 0
\(382\) 2762.53 4784.84i 0.370009 0.640874i
\(383\) 2081.13 3604.62i 0.277652 0.480907i −0.693149 0.720794i \(-0.743777\pi\)
0.970801 + 0.239887i \(0.0771105\pi\)
\(384\) 0 0
\(385\) −463.320 + 802.495i −0.0613325 + 0.106231i
\(386\) 2061.51 + 3570.65i 0.271835 + 0.470832i
\(387\) 0 0
\(388\) 1679.38 0.219736
\(389\) 2092.61 + 3624.51i 0.272750 + 0.472417i 0.969565 0.244834i \(-0.0787335\pi\)
−0.696815 + 0.717251i \(0.745400\pi\)
\(390\) 0 0
\(391\) 18723.1 2.42165
\(392\) 2662.69 0.343077
\(393\) 0 0
\(394\) −2094.82 + 3628.34i −0.267857 + 0.463942i
\(395\) −815.754 1412.93i −0.103912 0.179980i
\(396\) 0 0
\(397\) 2264.88 3922.89i 0.286325 0.495930i −0.686605 0.727031i \(-0.740900\pi\)
0.972930 + 0.231101i \(0.0742329\pi\)
\(398\) 3434.72 0.432581
\(399\) 0 0
\(400\) −1719.36 −0.214920
\(401\) −4748.53 + 8224.69i −0.591347 + 1.02424i 0.402704 + 0.915330i \(0.368070\pi\)
−0.994051 + 0.108913i \(0.965263\pi\)
\(402\) 0 0
\(403\) −572.722 991.984i −0.0707924 0.122616i
\(404\) −2483.42 + 4301.41i −0.305829 + 0.529711i
\(405\) 0 0
\(406\) −422.245 −0.0516149
\(407\) 10826.7 1.31857
\(408\) 0 0
\(409\) 2677.22 + 4637.08i 0.323667 + 0.560608i 0.981242 0.192781i \(-0.0617508\pi\)
−0.657574 + 0.753390i \(0.728417\pi\)
\(410\) 3472.46 0.418275
\(411\) 0 0
\(412\) 1187.21 + 2056.31i 0.141965 + 0.245891i
\(413\) 146.163 253.162i 0.0174146 0.0301630i
\(414\) 0 0
\(415\) −795.821 + 1378.40i −0.0941333 + 0.163044i
\(416\) −130.058 + 225.267i −0.0153284 + 0.0265496i
\(417\) 0 0
\(418\) 5571.55 + 10054.9i 0.651946 + 1.17656i
\(419\) −14506.1 −1.69134 −0.845668 0.533709i \(-0.820798\pi\)
−0.845668 + 0.533709i \(0.820798\pi\)
\(420\) 0 0
\(421\) 631.724 1094.18i 0.0731315 0.126667i −0.827141 0.561995i \(-0.810034\pi\)
0.900272 + 0.435327i \(0.143367\pi\)
\(422\) −2291.05 3968.22i −0.264281 0.457749i
\(423\) 0 0
\(424\) 1487.94 + 2577.19i 0.170427 + 0.295187i
\(425\) −11399.7 −1.30110
\(426\) 0 0
\(427\) −348.493 603.607i −0.0394959 0.0684089i
\(428\) −3557.12 6161.11i −0.401729 0.695814i
\(429\) 0 0
\(430\) 970.387 0.108828
\(431\) −4093.81 7090.69i −0.457522 0.792451i 0.541308 0.840825i \(-0.317929\pi\)
−0.998829 + 0.0483738i \(0.984596\pi\)
\(432\) 0 0
\(433\) 4621.47 + 8004.63i 0.512919 + 0.888401i 0.999888 + 0.0149820i \(0.00476910\pi\)
−0.486969 + 0.873419i \(0.661898\pi\)
\(434\) −449.251 + 778.126i −0.0496884 + 0.0860628i
\(435\) 0 0
\(436\) −4279.96 −0.470121
\(437\) −14614.8 257.284i −1.59982 0.0281637i
\(438\) 0 0
\(439\) 1021.52 1769.33i 0.111059 0.192359i −0.805139 0.593086i \(-0.797909\pi\)
0.916197 + 0.400727i \(0.131243\pi\)
\(440\) 1162.62 2013.72i 0.125968 0.218183i
\(441\) 0 0
\(442\) −862.314 + 1493.57i −0.0927966 + 0.160728i
\(443\) −4834.57 8373.71i −0.518504 0.898075i −0.999769 0.0214998i \(-0.993156\pi\)
0.481265 0.876575i \(-0.340177\pi\)
\(444\) 0 0
\(445\) −1783.29 −0.189969
\(446\) 3256.19 + 5639.88i 0.345706 + 0.598781i
\(447\) 0 0
\(448\) 204.039 0.0215177
\(449\) 13227.2 1.39027 0.695134 0.718881i \(-0.255345\pi\)
0.695134 + 0.718881i \(0.255345\pi\)
\(450\) 0 0
\(451\) 14385.4 24916.2i 1.50195 2.60146i
\(452\) 1166.39 + 2020.26i 0.121377 + 0.210232i
\(453\) 0 0
\(454\) 998.044 1728.66i 0.103173 0.178701i
\(455\) 108.534 0.0111828
\(456\) 0 0
\(457\) −5380.98 −0.550791 −0.275396 0.961331i \(-0.588809\pi\)
−0.275396 + 0.961331i \(0.588809\pi\)
\(458\) −1028.59 + 1781.56i −0.104940 + 0.181762i
\(459\) 0 0
\(460\) 1478.35 + 2560.57i 0.149844 + 0.259538i
\(461\) −1422.33 + 2463.55i −0.143698 + 0.248892i −0.928886 0.370365i \(-0.879233\pi\)
0.785189 + 0.619257i \(0.212566\pi\)
\(462\) 0 0
\(463\) 6625.39 0.665028 0.332514 0.943098i \(-0.392103\pi\)
0.332514 + 0.943098i \(0.392103\pi\)
\(464\) 1059.55 0.106009
\(465\) 0 0
\(466\) 125.486 + 217.348i 0.0124743 + 0.0216062i
\(467\) 18635.1 1.84653 0.923264 0.384167i \(-0.125511\pi\)
0.923264 + 0.384167i \(0.125511\pi\)
\(468\) 0 0
\(469\) 231.683 + 401.288i 0.0228106 + 0.0395090i
\(470\) 2597.81 4499.54i 0.254953 0.441592i
\(471\) 0 0
\(472\) −366.772 + 635.267i −0.0357670 + 0.0619503i
\(473\) 4020.03 6962.89i 0.390784 0.676858i
\(474\) 0 0
\(475\) 8898.34 + 156.650i 0.859545 + 0.0151317i
\(476\) 1352.82 0.130266
\(477\) 0 0
\(478\) −3591.03 + 6219.84i −0.343619 + 0.595165i
\(479\) 778.310 + 1348.07i 0.0742420 + 0.128591i 0.900756 0.434325i \(-0.143013\pi\)
−0.826514 + 0.562916i \(0.809680\pi\)
\(480\) 0 0
\(481\) −634.046 1098.20i −0.0601039 0.104103i
\(482\) 7383.68 0.697754
\(483\) 0 0
\(484\) −6970.80 12073.8i −0.654659 1.13390i
\(485\) 879.179 + 1522.78i 0.0823123 + 0.142569i
\(486\) 0 0
\(487\) 19339.5 1.79950 0.899751 0.436405i \(-0.143748\pi\)
0.899751 + 0.436405i \(0.143748\pi\)
\(488\) 874.482 + 1514.65i 0.0811188 + 0.140502i
\(489\) 0 0
\(490\) 1393.95 + 2414.40i 0.128515 + 0.222594i
\(491\) −3419.12 + 5922.10i −0.314262 + 0.544319i −0.979280 0.202509i \(-0.935091\pi\)
0.665018 + 0.746827i \(0.268424\pi\)
\(492\) 0 0
\(493\) 7025.05 0.641770
\(494\) 693.625 1154.00i 0.0631734 0.105103i
\(495\) 0 0
\(496\) 1127.32 1952.57i 0.102053 0.176760i
\(497\) 1415.25 2451.28i 0.127731 0.221237i
\(498\) 0 0
\(499\) 9057.49 15688.0i 0.812563 1.40740i −0.0985021 0.995137i \(-0.531405\pi\)
0.911065 0.412263i \(-0.135262\pi\)
\(500\) −1947.13 3372.53i −0.174157 0.301648i
\(501\) 0 0
\(502\) 14589.8 1.29716
\(503\) −2915.92 5050.53i −0.258478 0.447698i 0.707356 0.706857i \(-0.249888\pi\)
−0.965834 + 0.259160i \(0.916554\pi\)
\(504\) 0 0
\(505\) −5200.41 −0.458248
\(506\) 24497.4 2.15226
\(507\) 0 0
\(508\) −3318.71 + 5748.17i −0.289850 + 0.502035i
\(509\) 4957.32 + 8586.34i 0.431689 + 0.747707i 0.997019 0.0771579i \(-0.0245846\pi\)
−0.565330 + 0.824865i \(0.691251\pi\)
\(510\) 0 0
\(511\) −317.242 + 549.480i −0.0274637 + 0.0475686i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 4606.40 0.395291
\(515\) −1243.04 + 2153.01i −0.106359 + 0.184220i
\(516\) 0 0
\(517\) −21523.9 37280.5i −1.83099 3.17136i
\(518\) −497.354 + 861.443i −0.0421863 + 0.0730688i
\(519\) 0 0
\(520\) −272.348 −0.0229678
\(521\) 5851.91 0.492086 0.246043 0.969259i \(-0.420869\pi\)
0.246043 + 0.969259i \(0.420869\pi\)
\(522\) 0 0
\(523\) −3447.05 5970.46i −0.288200 0.499178i 0.685180 0.728374i \(-0.259724\pi\)
−0.973380 + 0.229196i \(0.926390\pi\)
\(524\) −2390.19 −0.199267
\(525\) 0 0
\(526\) −7138.38 12364.0i −0.591726 1.02490i
\(527\) 7474.37 12946.0i 0.617816 1.07009i
\(528\) 0 0
\(529\) −9491.49 + 16439.7i −0.780101 + 1.35117i
\(530\) −1557.91 + 2698.39i −0.127682 + 0.221152i
\(531\) 0 0
\(532\) −1055.98 18.5899i −0.0860574 0.00151499i
\(533\) −3369.83 −0.273853
\(534\) 0 0
\(535\) 3724.40 6450.84i 0.300971 0.521298i
\(536\) −581.370 1006.96i −0.0468495 0.0811458i
\(537\) 0 0
\(538\) 5446.66 + 9433.89i 0.436472 + 0.755992i
\(539\) 23098.9 1.84590
\(540\) 0 0
\(541\) 2812.50 + 4871.39i 0.223509 + 0.387130i 0.955871 0.293786i \(-0.0949153\pi\)
−0.732362 + 0.680916i \(0.761582\pi\)
\(542\) −3403.68 5895.34i −0.269743 0.467208i
\(543\) 0 0
\(544\) −3394.67 −0.267547
\(545\) −2240.62 3880.86i −0.176105 0.305023i
\(546\) 0 0
\(547\) −1798.07 3114.35i −0.140548 0.243437i 0.787155 0.616755i \(-0.211553\pi\)
−0.927703 + 0.373319i \(0.878220\pi\)
\(548\) −3554.62 + 6156.78i −0.277091 + 0.479935i
\(549\) 0 0
\(550\) −14915.5 −1.15636
\(551\) −5483.59 96.5350i −0.423972 0.00746376i
\(552\) 0 0
\(553\) 620.975 1075.56i 0.0477515 0.0827080i
\(554\) −5131.93 + 8888.76i −0.393564 + 0.681674i
\(555\) 0 0
\(556\) −327.134 + 566.613i −0.0249525 + 0.0432190i
\(557\) 9190.73 + 15918.8i 0.699145 + 1.21095i 0.968763 + 0.247987i \(0.0797692\pi\)
−0.269618 + 0.962967i \(0.586897\pi\)
\(558\) 0 0
\(559\) −941.705 −0.0712520
\(560\) 106.817 + 185.012i 0.00806043 + 0.0139611i
\(561\) 0 0
\(562\) 6733.36 0.505391
\(563\) −5578.33 −0.417582 −0.208791 0.977960i \(-0.566953\pi\)
−0.208791 + 0.977960i \(0.566953\pi\)
\(564\) 0 0
\(565\) −1221.25 + 2115.26i −0.0909349 + 0.157504i
\(566\) 6685.76 + 11580.1i 0.496508 + 0.859977i
\(567\) 0 0
\(568\) −3551.32 + 6151.06i −0.262341 + 0.454389i
\(569\) −16981.3 −1.25113 −0.625564 0.780173i \(-0.715131\pi\)
−0.625564 + 0.780173i \(0.715131\pi\)
\(570\) 0 0
\(571\) −19520.5 −1.43066 −0.715332 0.698785i \(-0.753724\pi\)
−0.715332 + 0.698785i \(0.753724\pi\)
\(572\) −1128.26 + 1954.20i −0.0824735 + 0.142848i
\(573\) 0 0
\(574\) 1321.67 + 2289.20i 0.0961070 + 0.166462i
\(575\) 9482.98 16425.0i 0.687770 1.19125i
\(576\) 0 0
\(577\) 6371.35 0.459693 0.229846 0.973227i \(-0.426178\pi\)
0.229846 + 0.973227i \(0.426178\pi\)
\(578\) −12681.4 −0.912593
\(579\) 0 0
\(580\) 554.688 + 960.748i 0.0397107 + 0.0687809i
\(581\) −1211.60 −0.0865159
\(582\) 0 0
\(583\) 12908.0 + 22357.2i 0.916969 + 1.58824i
\(584\) 796.065 1378.82i 0.0564065 0.0976989i
\(585\) 0 0
\(586\) 5625.93 9744.39i 0.396596 0.686924i
\(587\) 5379.52 9317.61i 0.378257 0.655160i −0.612552 0.790430i \(-0.709857\pi\)
0.990809 + 0.135271i \(0.0431904\pi\)
\(588\) 0 0
\(589\) −6012.21 + 10002.6i −0.420592 + 0.699747i
\(590\) −768.039 −0.0535927
\(591\) 0 0
\(592\) 1248.02 2161.64i 0.0866444 0.150073i
\(593\) 1805.88 + 3127.87i 0.125057 + 0.216604i 0.921755 0.387773i \(-0.126755\pi\)
−0.796698 + 0.604377i \(0.793422\pi\)
\(594\) 0 0
\(595\) 708.220 + 1226.67i 0.0487970 + 0.0845188i
\(596\) 4479.19 0.307844
\(597\) 0 0
\(598\) −1434.65 2484.89i −0.0981057 0.169924i
\(599\) −4590.12 7950.31i −0.313100 0.542306i 0.665932 0.746013i \(-0.268034\pi\)
−0.979032 + 0.203707i \(0.934701\pi\)
\(600\) 0 0
\(601\) 12700.4 0.862000 0.431000 0.902352i \(-0.358161\pi\)
0.431000 + 0.902352i \(0.358161\pi\)
\(602\) 369.343 + 639.721i 0.0250055 + 0.0433108i
\(603\) 0 0
\(604\) 5614.29 + 9724.24i 0.378216 + 0.655089i
\(605\) 7298.61 12641.6i 0.490464 0.849509i
\(606\) 0 0
\(607\) −24227.5 −1.62004 −0.810019 0.586404i \(-0.800543\pi\)
−0.810019 + 0.586404i \(0.800543\pi\)
\(608\) 2649.80 + 46.6480i 0.176749 + 0.00311156i
\(609\) 0 0
\(610\) −915.606 + 1585.88i −0.0607734 + 0.105263i
\(611\) −2521.02 + 4366.54i −0.166923 + 0.289119i
\(612\) 0 0
\(613\) 8106.74 14041.3i 0.534141 0.925159i −0.465064 0.885277i \(-0.653969\pi\)
0.999204 0.0398814i \(-0.0126980\pi\)
\(614\) 5603.54 + 9705.62i 0.368307 + 0.637927i
\(615\) 0 0
\(616\) 1770.04 0.115774
\(617\) −10757.7 18632.8i −0.701924 1.21577i −0.967790 0.251758i \(-0.918991\pi\)
0.265866 0.964010i \(-0.414342\pi\)
\(618\) 0 0
\(619\) −15878.5 −1.03103 −0.515516 0.856880i \(-0.672400\pi\)
−0.515516 + 0.856880i \(0.672400\pi\)
\(620\) 2360.66 0.152914
\(621\) 0 0
\(622\) −6668.20 + 11549.7i −0.429856 + 0.744532i
\(623\) −678.746 1175.62i −0.0436491 0.0756024i
\(624\) 0 0
\(625\) −4677.54 + 8101.73i −0.299362 + 0.518511i
\(626\) −8982.80 −0.573522
\(627\) 0 0
\(628\) 4015.77 0.255170
\(629\) 8274.68 14332.2i 0.524536 0.908523i
\(630\) 0 0
\(631\) −2779.87 4814.88i −0.175380 0.303768i 0.764912 0.644134i \(-0.222782\pi\)
−0.940293 + 0.340366i \(0.889449\pi\)
\(632\) −1558.23 + 2698.94i −0.0980745 + 0.169870i
\(633\) 0 0
\(634\) −2532.09 −0.158616
\(635\) −6949.55 −0.434306
\(636\) 0 0
\(637\) −1352.75 2343.03i −0.0841412 0.145737i
\(638\) 9191.64 0.570377
\(639\) 0 0
\(640\) −268.039 464.257i −0.0165549 0.0286740i
\(641\) −10243.5 + 17742.2i −0.631190 + 1.09325i 0.356119 + 0.934441i \(0.384100\pi\)
−0.987309 + 0.158812i \(0.949234\pi\)
\(642\) 0 0
\(643\) 2051.15 3552.69i 0.125800 0.217892i −0.796245 0.604974i \(-0.793184\pi\)
0.922045 + 0.387082i \(0.126517\pi\)
\(644\) −1125.36 + 1949.18i −0.0688593 + 0.119268i
\(645\) 0 0
\(646\) 17568.8 + 309.287i 1.07002 + 0.0188370i
\(647\) −22860.4 −1.38908 −0.694539 0.719455i \(-0.744392\pi\)
−0.694539 + 0.719455i \(0.744392\pi\)
\(648\) 0 0
\(649\) −3181.76 + 5510.97i −0.192442 + 0.333320i
\(650\) 873.501 + 1512.95i 0.0527100 + 0.0912964i
\(651\) 0 0
\(652\) −2543.97 4406.29i −0.152806 0.264668i
\(653\) −26388.5 −1.58141 −0.790706 0.612197i \(-0.790286\pi\)
−0.790706 + 0.612197i \(0.790286\pi\)
\(654\) 0 0
\(655\) −1251.29 2167.30i −0.0746444 0.129288i
\(656\) −3316.50 5744.35i −0.197390 0.341889i
\(657\) 0 0
\(658\) 3955.05 0.234322
\(659\) 1611.65 + 2791.45i 0.0952668 + 0.165007i 0.909720 0.415222i \(-0.136296\pi\)
−0.814453 + 0.580229i \(0.802963\pi\)
\(660\) 0 0
\(661\) 13740.1 + 23798.5i 0.808513 + 1.40039i 0.913894 + 0.405953i \(0.133060\pi\)
−0.105381 + 0.994432i \(0.533606\pi\)
\(662\) −5068.09 + 8778.19i −0.297548 + 0.515369i
\(663\) 0 0
\(664\) 3040.31 0.177691
\(665\) −535.963 967.243i −0.0312538 0.0564031i
\(666\) 0 0
\(667\) −5843.87 + 10121.9i −0.339244 + 0.587587i
\(668\) −5969.97 + 10340.3i −0.345786 + 0.598919i
\(669\) 0 0
\(670\) 608.709 1054.32i 0.0350992 0.0607937i
\(671\) 7586.17 + 13139.6i 0.436454 + 0.755961i
\(672\) 0 0
\(673\) −2165.00 −0.124004 −0.0620020 0.998076i \(-0.519749\pi\)
−0.0620020 + 0.998076i \(0.519749\pi\)
\(674\) 10744.1 + 18609.4i 0.614018 + 1.06351i
\(675\) 0 0
\(676\) −8523.70 −0.484963
\(677\) −11999.0 −0.681179 −0.340589 0.940212i \(-0.610627\pi\)
−0.340589 + 0.940212i \(0.610627\pi\)
\(678\) 0 0
\(679\) −669.256 + 1159.19i −0.0378258 + 0.0655161i
\(680\) −1777.16 3078.13i −0.100222 0.173589i
\(681\) 0 0
\(682\) 9779.53 16938.6i 0.549087 0.951047i
\(683\) −5234.35 −0.293246 −0.146623 0.989192i \(-0.546840\pi\)
−0.146623 + 0.989192i \(0.546840\pi\)
\(684\) 0 0
\(685\) −7443.56 −0.415188
\(686\) −2154.64 + 3731.94i −0.119919 + 0.207706i
\(687\) 0 0
\(688\) −926.803 1605.27i −0.0513576 0.0889540i
\(689\) 1511.87 2618.63i 0.0835958 0.144792i
\(690\) 0 0
\(691\) −5160.63 −0.284109 −0.142055 0.989859i \(-0.545371\pi\)
−0.142055 + 0.989859i \(0.545371\pi\)
\(692\) −227.099 −0.0124754
\(693\) 0 0
\(694\) 4851.34 + 8402.76i 0.265352 + 0.459603i
\(695\) −685.036 −0.0373884
\(696\) 0 0
\(697\) −21989.1 38086.3i −1.19498 2.06976i
\(698\) −7611.35 + 13183.2i −0.412742 + 0.714890i
\(699\) 0 0
\(700\) 685.186 1186.78i 0.0369966 0.0640799i
\(701\) −1657.51 + 2870.90i −0.0893059 + 0.154682i −0.907218 0.420661i \(-0.861798\pi\)
0.817912 + 0.575343i \(0.195132\pi\)
\(702\) 0 0
\(703\) −6655.96 + 11073.6i −0.357090 + 0.594097i
\(704\) −4441.62 −0.237784
\(705\) 0 0
\(706\) −5567.64 + 9643.43i −0.296800 + 0.514073i
\(707\) −1979.35 3428.34i −0.105292 0.182370i
\(708\) 0 0
\(709\) 9166.60 + 15877.0i 0.485555 + 0.841007i 0.999862 0.0165995i \(-0.00528404\pi\)
−0.514307 + 0.857606i \(0.671951\pi\)
\(710\) −7436.64 −0.393088
\(711\) 0 0
\(712\) 1703.20 + 2950.02i 0.0896488 + 0.155276i
\(713\) 12435.3 + 21538.5i 0.653162 + 1.13131i
\(714\) 0 0
\(715\) −2362.63 −0.123577
\(716\) −9281.96 16076.8i −0.484474 0.839133i
\(717\) 0 0
\(718\) −4341.31 7519.37i −0.225649 0.390836i
\(719\) 4873.50 8441.15i 0.252783 0.437833i −0.711508 0.702678i \(-0.751987\pi\)
0.964291 + 0.264845i \(0.0853208\pi\)
\(720\) 0 0
\(721\) −1892.48 −0.0977526
\(722\) −13709.5 482.844i −0.706669 0.0248886i
\(723\) 0 0
\(724\) −7550.82 + 13078.4i −0.387602 + 0.671346i
\(725\) 3558.09 6162.80i 0.182268 0.315697i
\(726\) 0 0
\(727\) −16361.8 + 28339.4i −0.834697 + 1.44574i 0.0595791 + 0.998224i \(0.481024\pi\)
−0.894277 + 0.447515i \(0.852309\pi\)
\(728\) −103.660 179.544i −0.00527731 0.00914057i
\(729\) 0 0
\(730\) 1667.00 0.0845185
\(731\) −6144.91 10643.3i −0.310914 0.538518i
\(732\) 0 0
\(733\) 36938.2 1.86131 0.930657 0.365894i \(-0.119237\pi\)
0.930657 + 0.365894i \(0.119237\pi\)
\(734\) 17929.0 0.901594
\(735\) 0 0
\(736\) 2823.90 4891.13i 0.141427 0.244959i
\(737\) −5043.40 8735.43i −0.252071 0.436599i
\(738\) 0 0
\(739\) 4993.60 8649.16i 0.248569 0.430534i −0.714560 0.699574i \(-0.753373\pi\)
0.963129 + 0.269040i \(0.0867064\pi\)
\(740\) 2613.43 0.129826
\(741\) 0 0
\(742\) −2371.86 −0.117350
\(743\) 10869.9 18827.2i 0.536713 0.929615i −0.462365 0.886690i \(-0.652999\pi\)
0.999078 0.0429249i \(-0.0136676\pi\)
\(744\) 0 0
\(745\) 2344.92 + 4061.51i 0.115317 + 0.199735i
\(746\) 5048.11 8743.59i 0.247754 0.429123i
\(747\) 0 0
\(748\) −29448.9 −1.43952
\(749\) 5670.23 0.276617
\(750\) 0 0
\(751\) 19033.7 + 32967.3i 0.924833 + 1.60186i 0.791830 + 0.610742i \(0.209129\pi\)
0.133003 + 0.991116i \(0.457538\pi\)
\(752\) −9924.53 −0.481264
\(753\) 0 0
\(754\) −538.293 932.351i −0.0259993 0.0450321i
\(755\) −5878.31 + 10181.5i −0.283356 + 0.490787i
\(756\) 0 0
\(757\) 5682.61 9842.58i 0.272838 0.472569i −0.696750 0.717314i \(-0.745371\pi\)
0.969587 + 0.244746i \(0.0787045\pi\)
\(758\) −9290.41 + 16091.5i −0.445176 + 0.771067i
\(759\) 0 0
\(760\) 1344.91 + 2427.13i 0.0641907 + 0.115844i
\(761\) −24549.3 −1.16940 −0.584699 0.811250i \(-0.698787\pi\)
−0.584699 + 0.811250i \(0.698787\pi\)
\(762\) 0 0
\(763\) 1705.62 2954.22i 0.0809274 0.140170i
\(764\) −5525.06 9569.68i −0.261636 0.453166i
\(765\) 0 0
\(766\) −4162.26 7209.24i −0.196330 0.340053i
\(767\) 745.338 0.0350881
\(768\) 0 0
\(769\) −7111.27 12317.1i −0.333471 0.577588i 0.649719 0.760174i \(-0.274886\pi\)
−0.983190 + 0.182586i \(0.941553\pi\)
\(770\) 926.641 + 1604.99i 0.0433686 + 0.0751166i
\(771\) 0 0
\(772\) 8246.06 0.384433
\(773\) 8041.29 + 13927.9i 0.374159 + 0.648063i 0.990201 0.139651i \(-0.0445980\pi\)
−0.616041 + 0.787714i \(0.711265\pi\)
\(774\) 0 0
\(775\) −7571.34 13113.9i −0.350930 0.607828i
\(776\) 1679.38 2908.78i 0.0776886 0.134561i
\(777\) 0 0
\(778\) 8370.46 0.385727
\(779\) 16640.8 + 30031.4i 0.765365 + 1.38124i
\(780\) 0 0
\(781\) −30807.8 + 53360.7i −1.41151 + 2.44481i
\(782\) 18723.1 32429.3i 0.856183 1.48295i
\(783\) 0 0
\(784\) 2662.69 4611.91i 0.121296 0.210091i
\(785\) 2102.31 + 3641.30i 0.0955854 + 0.165559i
\(786\) 0 0
\(787\) 30058.0 1.36144