Properties

Label 108.4.b.a.107.11
Level 108
Weight 4
Character 108.107
Analytic conductor 6.372
Analytic rank 0
Dimension 12
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{18}\cdot 3^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.11
Root \(1.61829 - 0.934317i\) of \(x^{12} - 12 x^{10} + 112 x^{8} - 368 x^{6} + 928 x^{4} - 256 x^{2} + 64\)
Character \(\chi\) \(=\) 108.107
Dual form 108.4.b.a.107.12

$q$-expansion

\(f(q)\) \(=\) \(q+(2.72087 - 0.772562i) q^{2} +(6.80630 - 4.20408i) q^{4} -3.33155i q^{5} -16.9016i q^{7} +(15.2712 - 16.6971i) q^{8} +O(q^{10})\) \(q+(2.72087 - 0.772562i) q^{2} +(6.80630 - 4.20408i) q^{4} -3.33155i q^{5} -16.9016i q^{7} +(15.2712 - 16.6971i) q^{8} +(-2.57383 - 9.06473i) q^{10} +16.8325 q^{11} +25.0775 q^{13} +(-13.0575 - 45.9871i) q^{14} +(28.6514 - 57.2285i) q^{16} +116.919i q^{17} -85.4801i q^{19} +(-14.0061 - 22.6755i) q^{20} +(45.7990 - 13.0041i) q^{22} -158.740 q^{23} +113.901 q^{25} +(68.2328 - 19.3739i) q^{26} +(-71.0557 - 115.037i) q^{28} +269.955i q^{29} +36.0884i q^{31} +(33.7442 - 177.846i) q^{32} +(90.3269 + 318.121i) q^{34} -56.3085 q^{35} -353.780 q^{37} +(-66.0386 - 232.580i) q^{38} +(-55.6272 - 50.8767i) q^{40} +144.415i q^{41} +368.186i q^{43} +(114.567 - 70.7651i) q^{44} +(-431.911 + 122.636i) q^{46} +397.333 q^{47} +57.3363 q^{49} +(309.909 - 87.9954i) q^{50} +(170.685 - 105.428i) q^{52} -96.0857i q^{53} -56.0783i q^{55} +(-282.207 - 258.107i) q^{56} +(208.557 + 734.514i) q^{58} -294.902 q^{59} +146.724 q^{61} +(27.8805 + 98.1920i) q^{62} +(-45.5837 - 509.967i) q^{64} -83.5471i q^{65} +301.433i q^{67} +(491.536 + 795.784i) q^{68} +(-153.208 + 43.5018i) q^{70} -687.794 q^{71} -312.138 q^{73} +(-962.590 + 273.317i) q^{74} +(-359.365 - 581.803i) q^{76} -284.496i q^{77} -602.063i q^{79} +(-190.660 - 95.4535i) q^{80} +(111.569 + 392.934i) q^{82} +1334.44 q^{83} +389.521 q^{85} +(284.446 + 1001.79i) q^{86} +(257.051 - 281.053i) q^{88} -856.292i q^{89} -423.850i q^{91} +(-1080.43 + 667.355i) q^{92} +(1081.09 - 306.964i) q^{94} -284.781 q^{95} +218.564 q^{97} +(156.005 - 44.2959i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 12q^{4} + O(q^{10}) \) \( 12q - 12q^{4} + 24q^{10} + 36q^{13} + 24q^{16} + 120q^{22} - 132q^{25} + 420q^{28} - 360q^{34} + 516q^{37} - 1152q^{40} - 696q^{46} - 720q^{49} + 204q^{52} + 2832q^{58} - 972q^{61} + 2496q^{64} - 1848q^{70} + 660q^{73} - 5004q^{76} - 3888q^{82} + 1056q^{85} + 3168q^{88} + 7608q^{94} + 2532q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.72087 0.772562i 0.961974 0.273142i
\(3\) 0 0
\(4\) 6.80630 4.20408i 0.850787 0.525510i
\(5\) 3.33155i 0.297983i −0.988838 0.148992i \(-0.952397\pi\)
0.988838 0.148992i \(-0.0476027\pi\)
\(6\) 0 0
\(7\) 16.9016i 0.912600i −0.889826 0.456300i \(-0.849174\pi\)
0.889826 0.456300i \(-0.150826\pi\)
\(8\) 15.2712 16.6971i 0.674896 0.737913i
\(9\) 0 0
\(10\) −2.57383 9.06473i −0.0813917 0.286652i
\(11\) 16.8325 0.461380 0.230690 0.973027i \(-0.425902\pi\)
0.230690 + 0.973027i \(0.425902\pi\)
\(12\) 0 0
\(13\) 25.0775 0.535020 0.267510 0.963555i \(-0.413799\pi\)
0.267510 + 0.963555i \(0.413799\pi\)
\(14\) −13.0575 45.9871i −0.249269 0.877897i
\(15\) 0 0
\(16\) 28.6514 57.2285i 0.447677 0.894195i
\(17\) 116.919i 1.66806i 0.551722 + 0.834028i \(0.313971\pi\)
−0.551722 + 0.834028i \(0.686029\pi\)
\(18\) 0 0
\(19\) 85.4801i 1.03213i −0.856549 0.516065i \(-0.827396\pi\)
0.856549 0.516065i \(-0.172604\pi\)
\(20\) −14.0061 22.6755i −0.156593 0.253520i
\(21\) 0 0
\(22\) 45.7990 13.0041i 0.443836 0.126022i
\(23\) −158.740 −1.43911 −0.719555 0.694436i \(-0.755654\pi\)
−0.719555 + 0.694436i \(0.755654\pi\)
\(24\) 0 0
\(25\) 113.901 0.911206
\(26\) 68.2328 19.3739i 0.514675 0.146136i
\(27\) 0 0
\(28\) −71.0557 115.037i −0.479581 0.776428i
\(29\) 269.955i 1.72860i 0.502976 + 0.864300i \(0.332238\pi\)
−0.502976 + 0.864300i \(0.667762\pi\)
\(30\) 0 0
\(31\) 36.0884i 0.209086i 0.994520 + 0.104543i \(0.0333380\pi\)
−0.994520 + 0.104543i \(0.966662\pi\)
\(32\) 33.7442 177.846i 0.186412 0.982472i
\(33\) 0 0
\(34\) 90.3269 + 318.121i 0.455616 + 1.60463i
\(35\) −56.3085 −0.271939
\(36\) 0 0
\(37\) −353.780 −1.57192 −0.785960 0.618277i \(-0.787831\pi\)
−0.785960 + 0.618277i \(0.787831\pi\)
\(38\) −66.0386 232.580i −0.281918 0.992882i
\(39\) 0 0
\(40\) −55.6272 50.8767i −0.219886 0.201108i
\(41\) 144.415i 0.550093i 0.961431 + 0.275046i \(0.0886932\pi\)
−0.961431 + 0.275046i \(0.911307\pi\)
\(42\) 0 0
\(43\) 368.186i 1.30576i 0.757460 + 0.652881i \(0.226440\pi\)
−0.757460 + 0.652881i \(0.773560\pi\)
\(44\) 114.567 70.7651i 0.392536 0.242460i
\(45\) 0 0
\(46\) −431.911 + 122.636i −1.38439 + 0.393081i
\(47\) 397.333 1.23313 0.616563 0.787305i \(-0.288524\pi\)
0.616563 + 0.787305i \(0.288524\pi\)
\(48\) 0 0
\(49\) 57.3363 0.167161
\(50\) 309.909 87.9954i 0.876556 0.248888i
\(51\) 0 0
\(52\) 170.685 105.428i 0.455188 0.281158i
\(53\) 96.0857i 0.249026i −0.992218 0.124513i \(-0.960263\pi\)
0.992218 0.124513i \(-0.0397369\pi\)
\(54\) 0 0
\(55\) 56.0783i 0.137484i
\(56\) −282.207 258.107i −0.673419 0.615910i
\(57\) 0 0
\(58\) 208.557 + 734.514i 0.472153 + 1.66287i
\(59\) −294.902 −0.650727 −0.325364 0.945589i \(-0.605487\pi\)
−0.325364 + 0.945589i \(0.605487\pi\)
\(60\) 0 0
\(61\) 146.724 0.307969 0.153984 0.988073i \(-0.450789\pi\)
0.153984 + 0.988073i \(0.450789\pi\)
\(62\) 27.8805 + 98.1920i 0.0571102 + 0.201135i
\(63\) 0 0
\(64\) −45.5837 509.967i −0.0890307 0.996029i
\(65\) 83.5471i 0.159427i
\(66\) 0 0
\(67\) 301.433i 0.549641i 0.961496 + 0.274820i \(0.0886184\pi\)
−0.961496 + 0.274820i \(0.911382\pi\)
\(68\) 491.536 + 795.784i 0.876581 + 1.41916i
\(69\) 0 0
\(70\) −153.208 + 43.5018i −0.261599 + 0.0742780i
\(71\) −687.794 −1.14966 −0.574832 0.818272i \(-0.694933\pi\)
−0.574832 + 0.818272i \(0.694933\pi\)
\(72\) 0 0
\(73\) −312.138 −0.500452 −0.250226 0.968187i \(-0.580505\pi\)
−0.250226 + 0.968187i \(0.580505\pi\)
\(74\) −962.590 + 273.317i −1.51215 + 0.429357i
\(75\) 0 0
\(76\) −359.365 581.803i −0.542395 0.878123i
\(77\) 284.496i 0.421056i
\(78\) 0 0
\(79\) 602.063i 0.857436i −0.903438 0.428718i \(-0.858965\pi\)
0.903438 0.428718i \(-0.141035\pi\)
\(80\) −190.660 95.4535i −0.266455 0.133400i
\(81\) 0 0
\(82\) 111.569 + 392.934i 0.150253 + 0.529175i
\(83\) 1334.44 1.76475 0.882373 0.470551i \(-0.155945\pi\)
0.882373 + 0.470551i \(0.155945\pi\)
\(84\) 0 0
\(85\) 389.521 0.497053
\(86\) 284.446 + 1001.79i 0.356658 + 1.25611i
\(87\) 0 0
\(88\) 257.051 281.053i 0.311384 0.340458i
\(89\) 856.292i 1.01985i −0.860218 0.509926i \(-0.829673\pi\)
0.860218 0.509926i \(-0.170327\pi\)
\(90\) 0 0
\(91\) 423.850i 0.488259i
\(92\) −1080.43 + 667.355i −1.22438 + 0.756267i
\(93\) 0 0
\(94\) 1081.09 306.964i 1.18624 0.336818i
\(95\) −284.781 −0.307557
\(96\) 0 0
\(97\) 218.564 0.228782 0.114391 0.993436i \(-0.463508\pi\)
0.114391 + 0.993436i \(0.463508\pi\)
\(98\) 156.005 44.2959i 0.160805 0.0456587i
\(99\) 0 0
\(100\) 775.242 478.848i 0.775242 0.478848i
\(101\) 793.625i 0.781868i −0.920419 0.390934i \(-0.872152\pi\)
0.920419 0.390934i \(-0.127848\pi\)
\(102\) 0 0
\(103\) 1245.59i 1.19157i −0.803145 0.595784i \(-0.796841\pi\)
0.803145 0.595784i \(-0.203159\pi\)
\(104\) 382.963 418.721i 0.361083 0.394798i
\(105\) 0 0
\(106\) −74.2321 261.437i −0.0680194 0.239557i
\(107\) 95.7189 0.0864813 0.0432406 0.999065i \(-0.486232\pi\)
0.0432406 + 0.999065i \(0.486232\pi\)
\(108\) 0 0
\(109\) 1349.09 1.18550 0.592749 0.805387i \(-0.298043\pi\)
0.592749 + 0.805387i \(0.298043\pi\)
\(110\) −43.3239 152.582i −0.0375525 0.132256i
\(111\) 0 0
\(112\) −967.252 484.253i −0.816042 0.408550i
\(113\) 1885.41i 1.56960i −0.619750 0.784799i \(-0.712766\pi\)
0.619750 0.784799i \(-0.287234\pi\)
\(114\) 0 0
\(115\) 528.850i 0.428831i
\(116\) 1134.91 + 1837.40i 0.908398 + 1.47067i
\(117\) 0 0
\(118\) −802.390 + 227.830i −0.625983 + 0.177741i
\(119\) 1976.11 1.52227
\(120\) 0 0
\(121\) −1047.67 −0.787128
\(122\) 399.217 113.353i 0.296258 0.0841191i
\(123\) 0 0
\(124\) 151.719 + 245.629i 0.109877 + 0.177888i
\(125\) 795.911i 0.569507i
\(126\) 0 0
\(127\) 714.330i 0.499106i 0.968361 + 0.249553i \(0.0802838\pi\)
−0.968361 + 0.249553i \(0.919716\pi\)
\(128\) −518.008 1352.34i −0.357702 0.933836i
\(129\) 0 0
\(130\) −64.5453 227.321i −0.0435461 0.153364i
\(131\) −2153.89 −1.43654 −0.718268 0.695766i \(-0.755065\pi\)
−0.718268 + 0.695766i \(0.755065\pi\)
\(132\) 0 0
\(133\) −1444.75 −0.941922
\(134\) 232.876 + 820.161i 0.150130 + 0.528740i
\(135\) 0 0
\(136\) 1952.20 + 1785.48i 1.23088 + 1.12576i
\(137\) 2053.68i 1.28071i 0.768079 + 0.640356i \(0.221213\pi\)
−0.768079 + 0.640356i \(0.778787\pi\)
\(138\) 0 0
\(139\) 2000.40i 1.22066i 0.792148 + 0.610329i \(0.208963\pi\)
−0.792148 + 0.610329i \(0.791037\pi\)
\(140\) −383.253 + 236.726i −0.231363 + 0.142907i
\(141\) 0 0
\(142\) −1871.40 + 531.363i −1.10595 + 0.314021i
\(143\) 422.117 0.246847
\(144\) 0 0
\(145\) 899.370 0.515094
\(146\) −849.287 + 241.146i −0.481421 + 0.136694i
\(147\) 0 0
\(148\) −2407.93 + 1487.32i −1.33737 + 0.826060i
\(149\) 988.026i 0.543236i 0.962405 + 0.271618i \(0.0875588\pi\)
−0.962405 + 0.271618i \(0.912441\pi\)
\(150\) 0 0
\(151\) 1630.56i 0.878764i −0.898300 0.439382i \(-0.855197\pi\)
0.898300 0.439382i \(-0.144803\pi\)
\(152\) −1427.27 1305.38i −0.761622 0.696580i
\(153\) 0 0
\(154\) −219.790 774.076i −0.115008 0.405044i
\(155\) 120.231 0.0623042
\(156\) 0 0
\(157\) −690.002 −0.350752 −0.175376 0.984501i \(-0.556114\pi\)
−0.175376 + 0.984501i \(0.556114\pi\)
\(158\) −465.131 1638.14i −0.234202 0.824831i
\(159\) 0 0
\(160\) −592.505 112.420i −0.292760 0.0555476i
\(161\) 2682.95i 1.31333i
\(162\) 0 0
\(163\) 3414.58i 1.64080i 0.571790 + 0.820400i \(0.306249\pi\)
−0.571790 + 0.820400i \(0.693751\pi\)
\(164\) 607.132 + 982.930i 0.289080 + 0.468012i
\(165\) 0 0
\(166\) 3630.84 1030.94i 1.69764 0.482026i
\(167\) −1372.95 −0.636180 −0.318090 0.948061i \(-0.603041\pi\)
−0.318090 + 0.948061i \(0.603041\pi\)
\(168\) 0 0
\(169\) −1568.12 −0.713754
\(170\) 1059.84 300.929i 0.478152 0.135766i
\(171\) 0 0
\(172\) 1547.88 + 2505.98i 0.686192 + 1.11093i
\(173\) 1118.25i 0.491441i 0.969341 + 0.245721i \(0.0790246\pi\)
−0.969341 + 0.245721i \(0.920975\pi\)
\(174\) 0 0
\(175\) 1925.10i 0.831567i
\(176\) 482.273 963.297i 0.206549 0.412564i
\(177\) 0 0
\(178\) −661.539 2329.86i −0.278564 0.981071i
\(179\) −1755.59 −0.733067 −0.366534 0.930405i \(-0.619456\pi\)
−0.366534 + 0.930405i \(0.619456\pi\)
\(180\) 0 0
\(181\) 312.973 0.128525 0.0642626 0.997933i \(-0.479530\pi\)
0.0642626 + 0.997933i \(0.479530\pi\)
\(182\) −327.450 1153.24i −0.133364 0.469692i
\(183\) 0 0
\(184\) −2424.14 + 2650.49i −0.971249 + 1.06194i
\(185\) 1178.64i 0.468406i
\(186\) 0 0
\(187\) 1968.03i 0.769608i
\(188\) 2704.36 1670.42i 1.04913 0.648021i
\(189\) 0 0
\(190\) −774.854 + 220.011i −0.295862 + 0.0840068i
\(191\) −2024.40 −0.766915 −0.383457 0.923559i \(-0.625267\pi\)
−0.383457 + 0.923559i \(0.625267\pi\)
\(192\) 0 0
\(193\) 1138.00 0.424431 0.212216 0.977223i \(-0.431932\pi\)
0.212216 + 0.977223i \(0.431932\pi\)
\(194\) 594.686 168.854i 0.220082 0.0624899i
\(195\) 0 0
\(196\) 390.248 241.047i 0.142219 0.0878450i
\(197\) 2345.77i 0.848370i 0.905576 + 0.424185i \(0.139439\pi\)
−0.905576 + 0.424185i \(0.860561\pi\)
\(198\) 0 0
\(199\) 2839.16i 1.01137i −0.862718 0.505686i \(-0.831240\pi\)
0.862718 0.505686i \(-0.168760\pi\)
\(200\) 1739.40 1901.81i 0.614969 0.672391i
\(201\) 0 0
\(202\) −613.124 2159.35i −0.213561 0.752136i
\(203\) 4562.67 1.57752
\(204\) 0 0
\(205\) 481.126 0.163918
\(206\) −962.294 3389.09i −0.325467 1.14626i
\(207\) 0 0
\(208\) 718.505 1435.15i 0.239516 0.478412i
\(209\) 1438.84i 0.476204i
\(210\) 0 0
\(211\) 256.564i 0.0837091i 0.999124 + 0.0418545i \(0.0133266\pi\)
−0.999124 + 0.0418545i \(0.986673\pi\)
\(212\) −403.952 653.988i −0.130866 0.211868i
\(213\) 0 0
\(214\) 260.439 73.9488i 0.0831927 0.0236217i
\(215\) 1226.63 0.389095
\(216\) 0 0
\(217\) 609.952 0.190812
\(218\) 3670.70 1042.25i 1.14042 0.323809i
\(219\) 0 0
\(220\) −235.758 381.685i −0.0722490 0.116969i
\(221\) 2932.03i 0.892443i
\(222\) 0 0
\(223\) 4020.58i 1.20734i −0.797233 0.603672i \(-0.793704\pi\)
0.797233 0.603672i \(-0.206296\pi\)
\(224\) −3005.89 570.330i −0.896604 0.170120i
\(225\) 0 0
\(226\) −1456.60 5129.97i −0.428723 1.50991i
\(227\) −2958.44 −0.865016 −0.432508 0.901630i \(-0.642371\pi\)
−0.432508 + 0.901630i \(0.642371\pi\)
\(228\) 0 0
\(229\) 226.069 0.0652360 0.0326180 0.999468i \(-0.489616\pi\)
0.0326180 + 0.999468i \(0.489616\pi\)
\(230\) 408.569 + 1438.93i 0.117132 + 0.412524i
\(231\) 0 0
\(232\) 4507.46 + 4122.53i 1.27556 + 1.16663i
\(233\) 2356.56i 0.662591i −0.943527 0.331295i \(-0.892514\pi\)
0.943527 0.331295i \(-0.107486\pi\)
\(234\) 0 0
\(235\) 1323.74i 0.367451i
\(236\) −2007.19 + 1239.79i −0.553630 + 0.341964i
\(237\) 0 0
\(238\) 5376.75 1526.67i 1.46438 0.415795i
\(239\) 2191.70 0.593176 0.296588 0.955006i \(-0.404151\pi\)
0.296588 + 0.955006i \(0.404151\pi\)
\(240\) 0 0
\(241\) 6532.08 1.74593 0.872963 0.487787i \(-0.162196\pi\)
0.872963 + 0.487787i \(0.162196\pi\)
\(242\) −2850.57 + 809.388i −0.757197 + 0.214998i
\(243\) 0 0
\(244\) 998.647 616.840i 0.262016 0.161841i
\(245\) 191.019i 0.0498113i
\(246\) 0 0
\(247\) 2143.63i 0.552210i
\(248\) 602.571 + 551.112i 0.154287 + 0.141111i
\(249\) 0 0
\(250\) −614.890 2165.57i −0.155556 0.547851i
\(251\) 34.6697 0.00871844 0.00435922 0.999990i \(-0.498612\pi\)
0.00435922 + 0.999990i \(0.498612\pi\)
\(252\) 0 0
\(253\) −2671.98 −0.663977
\(254\) 551.864 + 1943.60i 0.136327 + 0.480127i
\(255\) 0 0
\(256\) −2454.20 3279.35i −0.599170 0.800622i
\(257\) 3945.92i 0.957742i 0.877885 + 0.478871i \(0.158954\pi\)
−0.877885 + 0.478871i \(0.841046\pi\)
\(258\) 0 0
\(259\) 5979.44i 1.43453i
\(260\) −351.239 568.647i −0.0837805 0.135638i
\(261\) 0 0
\(262\) −5860.46 + 1664.01i −1.38191 + 0.392378i
\(263\) −6558.79 −1.53777 −0.768883 0.639390i \(-0.779187\pi\)
−0.768883 + 0.639390i \(0.779187\pi\)
\(264\) 0 0
\(265\) −320.115 −0.0742056
\(266\) −3930.98 + 1116.16i −0.906104 + 0.257278i
\(267\) 0 0
\(268\) 1267.25 + 2051.64i 0.288842 + 0.467627i
\(269\) 3741.27i 0.847991i −0.905664 0.423995i \(-0.860627\pi\)
0.905664 0.423995i \(-0.139373\pi\)
\(270\) 0 0
\(271\) 6011.98i 1.34761i −0.738910 0.673804i \(-0.764659\pi\)
0.738910 0.673804i \(-0.235341\pi\)
\(272\) 6691.08 + 3349.88i 1.49157 + 0.746751i
\(273\) 0 0
\(274\) 1586.59 + 5587.79i 0.349816 + 1.23201i
\(275\) 1917.23 0.420412
\(276\) 0 0
\(277\) −4524.48 −0.981407 −0.490704 0.871327i \(-0.663260\pi\)
−0.490704 + 0.871327i \(0.663260\pi\)
\(278\) 1545.43 + 5442.83i 0.333413 + 1.17424i
\(279\) 0 0
\(280\) −859.896 + 940.187i −0.183531 + 0.200668i
\(281\) 4251.22i 0.902514i −0.892394 0.451257i \(-0.850976\pi\)
0.892394 0.451257i \(-0.149024\pi\)
\(282\) 0 0
\(283\) 4433.04i 0.931154i 0.885007 + 0.465577i \(0.154153\pi\)
−0.885007 + 0.465577i \(0.845847\pi\)
\(284\) −4681.33 + 2891.54i −0.978119 + 0.604160i
\(285\) 0 0
\(286\) 1148.53 326.111i 0.237461 0.0674243i
\(287\) 2440.84 0.502015
\(288\) 0 0
\(289\) −8756.99 −1.78241
\(290\) 2447.07 694.819i 0.495507 0.140694i
\(291\) 0 0
\(292\) −2124.50 + 1312.25i −0.425778 + 0.262993i
\(293\) 7734.73i 1.54221i −0.636708 0.771105i \(-0.719704\pi\)
0.636708 0.771105i \(-0.280296\pi\)
\(294\) 0 0
\(295\) 982.480i 0.193906i
\(296\) −5402.63 + 5907.08i −1.06088 + 1.15994i
\(297\) 0 0
\(298\) 763.311 + 2688.29i 0.148381 + 0.522579i
\(299\) −3980.80 −0.769952
\(300\) 0 0
\(301\) 6222.92 1.19164
\(302\) −1259.71 4436.56i −0.240027 0.845348i
\(303\) 0 0
\(304\) −4891.89 2449.12i −0.922926 0.462061i
\(305\) 488.819i 0.0917694i
\(306\) 0 0
\(307\) 8510.18i 1.58209i 0.611759 + 0.791045i \(0.290462\pi\)
−0.611759 + 0.791045i \(0.709538\pi\)
\(308\) −1196.04 1936.36i −0.221269 0.358229i
\(309\) 0 0
\(310\) 327.132 92.8855i 0.0599350 0.0170179i
\(311\) 8133.65 1.48301 0.741507 0.670945i \(-0.234112\pi\)
0.741507 + 0.670945i \(0.234112\pi\)
\(312\) 0 0
\(313\) 5066.73 0.914979 0.457489 0.889215i \(-0.348749\pi\)
0.457489 + 0.889215i \(0.348749\pi\)
\(314\) −1877.41 + 533.069i −0.337415 + 0.0958052i
\(315\) 0 0
\(316\) −2531.13 4097.82i −0.450591 0.729495i
\(317\) 4122.54i 0.730425i −0.930924 0.365212i \(-0.880996\pi\)
0.930924 0.365212i \(-0.119004\pi\)
\(318\) 0 0
\(319\) 4544.01i 0.797542i
\(320\) −1698.98 + 151.865i −0.296800 + 0.0265296i
\(321\) 0 0
\(322\) 2072.75 + 7299.98i 0.358726 + 1.26339i
\(323\) 9994.22 1.72165
\(324\) 0 0
\(325\) 2856.35 0.487513
\(326\) 2637.97 + 9290.63i 0.448171 + 1.57841i
\(327\) 0 0
\(328\) 2411.30 + 2205.38i 0.405921 + 0.371256i
\(329\) 6715.55i 1.12535i
\(330\) 0 0
\(331\) 3819.96i 0.634332i −0.948370 0.317166i \(-0.897269\pi\)
0.948370 0.317166i \(-0.102731\pi\)
\(332\) 9082.60 5610.10i 1.50142 0.927392i
\(333\) 0 0
\(334\) −3735.62 + 1060.69i −0.611988 + 0.173767i
\(335\) 1004.24 0.163784
\(336\) 0 0
\(337\) −9712.35 −1.56993 −0.784963 0.619542i \(-0.787318\pi\)
−0.784963 + 0.619542i \(0.787318\pi\)
\(338\) −4266.65 + 1211.47i −0.686613 + 0.194956i
\(339\) 0 0
\(340\) 2651.20 1637.58i 0.422886 0.261206i
\(341\) 607.457i 0.0964682i
\(342\) 0 0
\(343\) 6766.32i 1.06515i
\(344\) 6147.62 + 5622.62i 0.963539 + 0.881254i
\(345\) 0 0
\(346\) 863.921 + 3042.63i 0.134233 + 0.472754i
\(347\) −3315.20 −0.512880 −0.256440 0.966560i \(-0.582550\pi\)
−0.256440 + 0.966560i \(0.582550\pi\)
\(348\) 0 0
\(349\) −2864.88 −0.439408 −0.219704 0.975567i \(-0.570509\pi\)
−0.219704 + 0.975567i \(0.570509\pi\)
\(350\) −1487.26 5237.96i −0.227136 0.799945i
\(351\) 0 0
\(352\) 567.998 2993.59i 0.0860068 0.453293i
\(353\) 4904.72i 0.739523i −0.929127 0.369762i \(-0.879439\pi\)
0.929127 0.369762i \(-0.120561\pi\)
\(354\) 0 0
\(355\) 2291.42i 0.342580i
\(356\) −3599.92 5828.18i −0.535943 0.867677i
\(357\) 0 0
\(358\) −4776.74 + 1356.30i −0.705191 + 0.200231i
\(359\) −4185.24 −0.615288 −0.307644 0.951501i \(-0.599541\pi\)
−0.307644 + 0.951501i \(0.599541\pi\)
\(360\) 0 0
\(361\) −447.841 −0.0652924
\(362\) 851.559 241.791i 0.123638 0.0351056i
\(363\) 0 0
\(364\) −1781.90 2884.85i −0.256585 0.415404i
\(365\) 1039.90i 0.149126i
\(366\) 0 0
\(367\) 4979.97i 0.708317i 0.935185 + 0.354158i \(0.115233\pi\)
−0.935185 + 0.354158i \(0.884767\pi\)
\(368\) −4548.11 + 9084.44i −0.644257 + 1.28684i
\(369\) 0 0
\(370\) 910.569 + 3206.92i 0.127941 + 0.450594i
\(371\) −1624.00 −0.227261
\(372\) 0 0
\(373\) 6411.84 0.890060 0.445030 0.895516i \(-0.353193\pi\)
0.445030 + 0.895516i \(0.353193\pi\)
\(374\) 1520.43 + 5354.76i 0.210212 + 0.740343i
\(375\) 0 0
\(376\) 6067.73 6634.29i 0.832232 0.909940i
\(377\) 6769.81i 0.924835i
\(378\) 0 0
\(379\) 5294.51i 0.717574i 0.933419 + 0.358787i \(0.116810\pi\)
−0.933419 + 0.358787i \(0.883190\pi\)
\(380\) −1938.31 + 1197.24i −0.261666 + 0.161625i
\(381\) 0 0
\(382\) −5508.14 + 1563.98i −0.737752 + 0.209476i
\(383\) −5923.23 −0.790242 −0.395121 0.918629i \(-0.629297\pi\)
−0.395121 + 0.918629i \(0.629297\pi\)
\(384\) 0 0
\(385\) −947.812 −0.125467
\(386\) 3096.36 879.177i 0.408292 0.115930i
\(387\) 0 0
\(388\) 1487.61 918.863i 0.194645 0.120227i
\(389\) 4084.92i 0.532426i 0.963914 + 0.266213i \(0.0857724\pi\)
−0.963914 + 0.266213i \(0.914228\pi\)
\(390\) 0 0
\(391\) 18559.6i 2.40052i
\(392\) 875.592 957.348i 0.112817 0.123350i
\(393\) 0 0
\(394\) 1812.25 + 6382.53i 0.231725 + 0.816110i
\(395\) −2005.81 −0.255501
\(396\) 0 0
\(397\) 2821.56 0.356700 0.178350 0.983967i \(-0.442924\pi\)
0.178350 + 0.983967i \(0.442924\pi\)
\(398\) −2193.43 7725.00i −0.276248 0.972912i
\(399\) 0 0
\(400\) 3263.41 6518.37i 0.407926 0.814796i
\(401\) 4215.14i 0.524923i 0.964942 + 0.262461i \(0.0845343\pi\)
−0.964942 + 0.262461i \(0.915466\pi\)
\(402\) 0 0
\(403\) 905.009i 0.111865i
\(404\) −3336.47 5401.65i −0.410880 0.665203i
\(405\) 0 0
\(406\) 12414.4 3524.94i 1.51753 0.430887i
\(407\) −5954.99 −0.725253
\(408\) 0 0
\(409\) 605.285 0.0731771 0.0365885 0.999330i \(-0.488351\pi\)
0.0365885 + 0.999330i \(0.488351\pi\)
\(410\) 1309.08 371.699i 0.157685 0.0447730i
\(411\) 0 0
\(412\) −5236.56 8477.85i −0.626181 1.01377i
\(413\) 4984.30i 0.593854i
\(414\) 0 0
\(415\) 4445.76i 0.525865i
\(416\) 846.220 4459.95i 0.0997340 0.525642i
\(417\) 0 0
\(418\) −1111.59 3914.90i −0.130071 0.458096i
\(419\) 6479.90 0.755523 0.377761 0.925903i \(-0.376694\pi\)
0.377761 + 0.925903i \(0.376694\pi\)
\(420\) 0 0
\(421\) −363.812 −0.0421166 −0.0210583 0.999778i \(-0.506704\pi\)
−0.0210583 + 0.999778i \(0.506704\pi\)
\(422\) 198.212 + 698.079i 0.0228645 + 0.0805260i
\(423\) 0 0
\(424\) −1604.35 1467.34i −0.183760 0.168067i
\(425\) 13317.1i 1.51994i
\(426\) 0 0
\(427\) 2479.87i 0.281052i
\(428\) 651.491 402.410i 0.0735772 0.0454468i
\(429\) 0 0
\(430\) 3337.50 947.647i 0.374299 0.106278i
\(431\) 1486.97 0.166182 0.0830912 0.996542i \(-0.473521\pi\)
0.0830912 + 0.996542i \(0.473521\pi\)
\(432\) 0 0
\(433\) 12322.8 1.36765 0.683827 0.729644i \(-0.260314\pi\)
0.683827 + 0.729644i \(0.260314\pi\)
\(434\) 1659.60 471.225i 0.183556 0.0521188i
\(435\) 0 0
\(436\) 9182.30 5671.69i 1.00861 0.622992i
\(437\) 13569.1i 1.48535i
\(438\) 0 0
\(439\) 10918.0i 1.18698i −0.804840 0.593492i \(-0.797749\pi\)
0.804840 0.593492i \(-0.202251\pi\)
\(440\) −936.343 856.380i −0.101451 0.0927871i
\(441\) 0 0
\(442\) 2265.18 + 7977.69i 0.243763 + 0.858507i
\(443\) 3934.04 0.421923 0.210961 0.977494i \(-0.432341\pi\)
0.210961 + 0.977494i \(0.432341\pi\)
\(444\) 0 0
\(445\) −2852.78 −0.303899
\(446\) −3106.14 10939.5i −0.329776 1.16143i
\(447\) 0 0
\(448\) −8619.25 + 770.437i −0.908976 + 0.0812494i
\(449\) 9560.84i 1.00491i −0.864604 0.502454i \(-0.832430\pi\)
0.864604 0.502454i \(-0.167570\pi\)
\(450\) 0 0
\(451\) 2430.86i 0.253802i
\(452\) −7926.43 12832.7i −0.824840 1.33539i
\(453\) 0 0
\(454\) −8049.54 + 2285.58i −0.832123 + 0.236272i
\(455\) −1412.08 −0.145493
\(456\) 0 0
\(457\) 6479.90 0.663276 0.331638 0.943407i \(-0.392399\pi\)
0.331638 + 0.943407i \(0.392399\pi\)
\(458\) 615.105 174.652i 0.0627553 0.0178187i
\(459\) 0 0
\(460\) 2223.33 + 3599.51i 0.225355 + 0.364843i
\(461\) 3560.77i 0.359743i −0.983690 0.179872i \(-0.942432\pi\)
0.983690 0.179872i \(-0.0575682\pi\)
\(462\) 0 0
\(463\) 15775.3i 1.58346i 0.610874 + 0.791728i \(0.290818\pi\)
−0.610874 + 0.791728i \(0.709182\pi\)
\(464\) 15449.1 + 7734.58i 1.54571 + 0.773856i
\(465\) 0 0
\(466\) −1820.59 6411.91i −0.180981 0.637395i
\(467\) −14291.6 −1.41614 −0.708071 0.706141i \(-0.750434\pi\)
−0.708071 + 0.706141i \(0.750434\pi\)
\(468\) 0 0
\(469\) 5094.70 0.501602
\(470\) −1022.67 3601.72i −0.100366 0.353478i
\(471\) 0 0
\(472\) −4503.49 + 4923.99i −0.439173 + 0.480180i
\(473\) 6197.48i 0.602453i
\(474\) 0 0
\(475\) 9736.24i 0.940483i
\(476\) 13450.0 8307.74i 1.29513 0.799968i
\(477\) 0 0
\(478\) 5963.32 1693.22i 0.570619 0.162021i
\(479\) 14630.0 1.39553 0.697766 0.716326i \(-0.254178\pi\)
0.697766 + 0.716326i \(0.254178\pi\)
\(480\) 0 0
\(481\) −8871.92 −0.841008
\(482\) 17772.9 5046.43i 1.67953 0.476885i
\(483\) 0 0
\(484\) −7130.74 + 4404.48i −0.669679 + 0.413644i
\(485\) 728.159i 0.0681732i
\(486\) 0 0
\(487\) 16742.7i 1.55787i 0.627102 + 0.778937i \(0.284241\pi\)
−0.627102 + 0.778937i \(0.715759\pi\)
\(488\) 2240.64 2449.86i 0.207847 0.227254i
\(489\) 0 0
\(490\) −147.574 519.739i −0.0136055 0.0479171i
\(491\) −7342.23 −0.674847 −0.337424 0.941353i \(-0.609555\pi\)
−0.337424 + 0.941353i \(0.609555\pi\)
\(492\) 0 0
\(493\) −31562.8 −2.88340
\(494\) −1656.09 5832.54i −0.150832 0.531211i
\(495\) 0 0
\(496\) 2065.29 + 1033.98i 0.186964 + 0.0936032i
\(497\) 11624.8i 1.04918i
\(498\) 0 0
\(499\) 1565.06i 0.140404i 0.997533 + 0.0702020i \(0.0223644\pi\)
−0.997533 + 0.0702020i \(0.977636\pi\)
\(500\) −3346.07 5417.20i −0.299282 0.484529i
\(501\) 0 0
\(502\) 94.3317 26.7844i 0.00838691 0.00238137i
\(503\) 1257.87 0.111503 0.0557513 0.998445i \(-0.482245\pi\)
0.0557513 + 0.998445i \(0.482245\pi\)
\(504\) 0 0
\(505\) −2644.00 −0.232983
\(506\) −7270.12 + 2064.27i −0.638728 + 0.181360i
\(507\) 0 0
\(508\) 3003.10 + 4861.94i 0.262286 + 0.424633i
\(509\) 3160.96i 0.275260i −0.990484 0.137630i \(-0.956052\pi\)
0.990484 0.137630i \(-0.0439484\pi\)
\(510\) 0 0
\(511\) 5275.63i 0.456712i
\(512\) −9211.06 7026.67i −0.795069 0.606519i
\(513\) 0 0
\(514\) 3048.47 + 10736.3i 0.261599 + 0.921323i
\(515\) −4149.75 −0.355067
\(516\) 0 0
\(517\) 6688.09 0.568940
\(518\) 4619.49 + 16269.3i 0.391831 + 1.37998i
\(519\) 0 0
\(520\) −1394.99 1275.86i −0.117643 0.107597i
\(521\) 2973.62i 0.250051i −0.992154 0.125026i \(-0.960099\pi\)
0.992154 0.125026i \(-0.0399013\pi\)
\(522\) 0 0
\(523\) 8019.43i 0.670488i −0.942131 0.335244i \(-0.891181\pi\)
0.942131 0.335244i \(-0.108819\pi\)
\(524\) −14660.0 + 9055.14i −1.22219 + 0.754915i
\(525\) 0 0
\(526\) −17845.6 + 5067.07i −1.47929 + 0.420028i
\(527\) −4219.41 −0.348768
\(528\) 0 0
\(529\) 13031.3 1.07104
\(530\) −870.991 + 247.308i −0.0713838 + 0.0202687i
\(531\) 0 0
\(532\) −9833.39 + 6073.84i −0.801375 + 0.494990i
\(533\) 3621.57i 0.294311i
\(534\) 0 0
\(535\) 318.893i 0.0257700i
\(536\) 5033.05 + 4603.23i 0.405587 + 0.370950i
\(537\) 0 0
\(538\) −2890.36 10179.5i −0.231622 0.815745i
\(539\) 965.112 0.0771249
\(540\) 0 0
\(541\) 11815.3 0.938961 0.469480 0.882943i \(-0.344441\pi\)
0.469480 + 0.882943i \(0.344441\pi\)
\(542\) −4644.63 16357.8i −0.368088 1.29636i
\(543\) 0 0
\(544\) 20793.6 + 3945.32i 1.63882 + 0.310946i
\(545\) 4494.56i 0.353259i
\(546\) 0 0
\(547\) 15596.6i 1.21913i 0.792737 + 0.609564i \(0.208655\pi\)
−0.792737 + 0.609564i \(0.791345\pi\)
\(548\) 8633.83 + 13977.9i 0.673027 + 1.08961i
\(549\) 0 0
\(550\) 5216.54 1481.18i 0.404426 0.114832i
\(551\) 23075.8 1.78414
\(552\) 0 0
\(553\) −10175.8 −0.782496
\(554\) −12310.5 + 3495.44i −0.944088 + 0.268063i
\(555\) 0 0
\(556\) 8409.84 + 13615.3i 0.641469 + 1.03852i
\(557\) 19104.3i 1.45327i 0.687022 + 0.726637i \(0.258918\pi\)
−0.687022 + 0.726637i \(0.741082\pi\)
\(558\) 0 0
\(559\) 9233.19i 0.698608i
\(560\) −1613.32 + 3222.45i −0.121741 + 0.243167i
\(561\) 0 0
\(562\) −3284.33 11567.0i −0.246514 0.868195i
\(563\) −13747.5 −1.02911 −0.514555 0.857458i \(-0.672043\pi\)
−0.514555 + 0.857458i \(0.672043\pi\)
\(564\) 0 0
\(565\) −6281.35 −0.467714
\(566\) 3424.79 + 12061.7i 0.254337 + 0.895746i
\(567\) 0 0
\(568\) −10503.4 + 11484.1i −0.775903 + 0.848352i
\(569\) 18303.4i 1.34854i −0.738486 0.674269i \(-0.764459\pi\)
0.738486 0.674269i \(-0.235541\pi\)
\(570\) 0 0
\(571\) 8345.58i 0.611649i −0.952088 0.305824i \(-0.901068\pi\)
0.952088 0.305824i \(-0.0989320\pi\)
\(572\) 2873.05 1774.61i 0.210015 0.129721i
\(573\) 0 0
\(574\) 6641.22 1885.70i 0.482925 0.137121i
\(575\) −18080.6 −1.31133
\(576\) 0 0
\(577\) −21336.5 −1.53943 −0.769713 0.638390i \(-0.779601\pi\)
−0.769713 + 0.638390i \(0.779601\pi\)
\(578\) −23826.6 + 6765.31i −1.71463 + 0.486851i
\(579\) 0 0
\(580\) 6121.38 3781.03i 0.438235 0.270687i
\(581\) 22554.2i 1.61051i
\(582\) 0 0
\(583\) 1617.36i 0.114896i
\(584\) −4766.71 + 5211.78i −0.337753 + 0.369290i
\(585\) 0 0
\(586\) −5975.55 21045.2i −0.421242 1.48357i
\(587\) 26431.2 1.85849 0.929244 0.369467i \(-0.120460\pi\)
0.929244 + 0.369467i \(0.120460\pi\)
\(588\) 0 0
\(589\) 3084.84 0.215804
\(590\) 759.027 + 2673.20i 0.0529638 + 0.186532i
\(591\) 0 0
\(592\) −10136.3 + 20246.3i −0.703713 + 1.40560i
\(593\) 248.904i 0.0172366i 0.999963 + 0.00861828i \(0.00274332\pi\)
−0.999963 + 0.00861828i \(0.997257\pi\)
\(594\) 0 0
\(595\) 6583.52i 0.453610i
\(596\) 4153.74 + 6724.80i 0.285476 + 0.462179i
\(597\) 0 0
\(598\) −10831.3 + 3075.41i −0.740674 + 0.210306i
\(599\) −14995.9 −1.02290 −0.511449 0.859313i \(-0.670891\pi\)
−0.511449 + 0.859313i \(0.670891\pi\)
\(600\) 0 0
\(601\) 23747.1 1.61175 0.805876 0.592085i \(-0.201695\pi\)
0.805876 + 0.592085i \(0.201695\pi\)
\(602\) 16931.8 4807.59i 1.14633 0.325486i
\(603\) 0 0
\(604\) −6855.03 11098.1i −0.461800 0.747641i
\(605\) 3490.36i 0.234551i
\(606\) 0 0
\(607\) 6539.02i 0.437250i 0.975809 + 0.218625i \(0.0701571\pi\)
−0.975809 + 0.218625i \(0.929843\pi\)
\(608\) −15202.3 2884.45i −1.01404 0.192401i
\(609\) 0 0
\(610\) −377.643 1330.01i −0.0250661 0.0882798i
\(611\) 9964.12 0.659747
\(612\) 0 0
\(613\) −5985.95 −0.394405 −0.197202 0.980363i \(-0.563186\pi\)
−0.197202 + 0.980363i \(0.563186\pi\)
\(614\) 6574.64 + 23155.1i 0.432135 + 1.52193i
\(615\) 0 0
\(616\) −4750.24 4344.57i −0.310702 0.284169i
\(617\) 6168.16i 0.402465i −0.979544 0.201232i \(-0.935505\pi\)
0.979544 0.201232i \(-0.0644947\pi\)
\(618\) 0 0
\(619\) 6667.31i 0.432927i −0.976291 0.216464i \(-0.930548\pi\)
0.976291 0.216464i \(-0.0694523\pi\)
\(620\) 818.325 505.459i 0.0530076 0.0327415i
\(621\) 0 0
\(622\) 22130.6 6283.75i 1.42662 0.405073i
\(623\) −14472.7 −0.930717
\(624\) 0 0
\(625\) 11586.0 0.741502
\(626\) 13785.9 3914.36i 0.880186 0.249919i
\(627\) 0 0
\(628\) −4696.36 + 2900.83i −0.298416 + 0.184324i
\(629\) 41363.5i 2.62205i
\(630\) 0 0
\(631\) 8168.49i 0.515344i −0.966232 0.257672i \(-0.917045\pi\)
0.966232 0.257672i \(-0.0829554\pi\)
\(632\) −10052.7 9194.20i −0.632713 0.578680i
\(633\) 0 0
\(634\) −3184.91 11216.9i −0.199510 0.702649i
\(635\) 2379.83 0.148725
\(636\) 0 0
\(637\) 1437.85 0.0894346
\(638\) 3510.53 + 12363.7i 0.217842 + 0.767215i
\(639\) 0 0
\(640\) −4505.39 + 1725.77i −0.278267 + 0.106589i
\(641\) 6332.36i 0.390192i −0.980784 0.195096i \(-0.937498\pi\)
0.980784 0.195096i \(-0.0625018\pi\)
\(642\) 0 0
\(643\) 9433.98i 0.578600i −0.957239 0.289300i \(-0.906578\pi\)
0.957239 0.289300i \(-0.0934225\pi\)
\(644\) 11279.4 + 18261.0i 0.690169 + 1.11737i
\(645\) 0 0
\(646\) 27193.0 7721.15i 1.65618 0.470255i
\(647\) 20479.8 1.24442 0.622212 0.782848i \(-0.286234\pi\)
0.622212 + 0.782848i \(0.286234\pi\)
\(648\) 0 0
\(649\) −4963.92 −0.300233
\(650\) 7771.76 2206.71i 0.468975 0.133160i
\(651\) 0 0
\(652\) 14355.2 + 23240.6i 0.862258 + 1.39597i
\(653\) 24435.7i 1.46438i −0.681099 0.732192i \(-0.738498\pi\)
0.681099 0.732192i \(-0.261502\pi\)
\(654\) 0 0
\(655\) 7175.80i 0.428064i
\(656\) 8264.64 + 4137.68i 0.491890 + 0.246264i
\(657\) 0 0
\(658\) −5188.18 18272.2i −0.307380 1.08256i
\(659\) 32183.0 1.90238 0.951192 0.308601i \(-0.0998607\pi\)
0.951192 + 0.308601i \(0.0998607\pi\)
\(660\) 0 0
\(661\) 13990.4 0.823245 0.411622 0.911355i \(-0.364962\pi\)
0.411622 + 0.911355i \(0.364962\pi\)
\(662\) −2951.15 10393.6i −0.173263 0.610211i
\(663\) 0 0
\(664\) 20378.5 22281.2i 1.19102 1.30223i
\(665\) 4813.26i 0.280677i
\(666\) 0 0
\(667\) 42852.6i 2.48765i
\(668\) −9344.71 + 5772.00i −0.541254 + 0.334319i
\(669\) 0 0
\(670\) 2732.41 775.838i 0.157556 0.0447362i
\(671\) 2469.73 0.142091
\(672\) 0 0
\(673\) 12289.9 0.703923 0.351961 0.936014i \(-0.385515\pi\)
0.351961 + 0.936014i \(0.385515\pi\)
\(674\) −26426.1 + 7503.39i −1.51023 + 0.428813i
\(675\) 0 0
\(676\) −10673.1 + 6592.50i −0.607253 + 0.375085i
\(677\) 16303.5i 0.925548i 0.886476 + 0.462774i \(0.153146\pi\)
−0.886476 + 0.462774i \(0.846854\pi\)
\(678\) 0 0
\(679\) 3694.09i 0.208786i
\(680\) 5948.43 6503.86i 0.335459 0.366782i
\(681\) 0 0
\(682\) 469.298 + 1652.81i 0.0263495 + 0.0927999i
\(683\) −9720.93 −0.544599 −0.272299 0.962213i \(-0.587784\pi\)
−0.272299 + 0.962213i \(0.587784\pi\)
\(684\) 0 0
\(685\) 6841.93 0.381630
\(686\) −5227.40 18410.3i −0.290937 1.02465i
\(687\) 0 0
\(688\) 21070.7 + 10549.0i 1.16761 + 0.584560i
\(689\) 2409.59i 0.133234i
\(690\) 0 0
\(691\) 80.4083i 0.00442674i −0.999998 0.00221337i \(-0.999295\pi\)
0.999998 0.00221337i \(-0.000704538\pi\)
\(692\) 4701.24 + 7611.17i 0.258257 + 0.418112i
\(693\) 0 0
\(694\) −9020.24 + 2561.20i −0.493377 + 0.140089i
\(695\) 6664.43 0.363736
\(696\) 0 0
\(697\) −16884.8 −0.917586
\(698\) −7794.97 + 2213.29i −0.422699 + 0.120021i
\(699\) 0 0
\(700\) −8093.30 13102.8i −0.436997 0.707486i
\(701\) 4285.46i 0.230898i −0.993313 0.115449i \(-0.963169\pi\)
0.993313 0.115449i \(-0.0368307\pi\)
\(702\) 0 0
\(703\) 30241.1i 1.62243i
\(704\) −767.287 8584.00i −0.0410770 0.459548i
\(705\) 0 0
\(706\) −3789.19 13345.1i −0.201995 0.711402i
\(707\) −13413.5 −0.713532
\(708\) 0 0
\(709\) −8587.44 −0.454878 −0.227439 0.973792i \(-0.573035\pi\)
−0.227439 + 0.973792i \(0.573035\pi\)
\(710\) 1770.26 + 6234.67i 0.0935730 + 0.329553i
\(711\) 0 0
\(712\) −14297.6 13076.6i −0.752562 0.688294i
\(713\) 5728.67i 0.300898i
\(714\) 0 0
\(715\) 1406.30i 0.0735564i
\(716\) −11949.1 + 7380.65i −0.623684 + 0.385234i
\(717\) 0 0
\(718\) −11387.5 + 3233.36i −0.591891 + 0.168061i
\(719\) 665.197 0.0345030 0.0172515 0.999851i \(-0.494508\pi\)
0.0172515 + 0.999851i \(0.494508\pi\)
\(720\) 0 0
\(721\) −21052.4 −1.08742
\(722\) −1218.52 + 345.984i −0.0628096 + 0.0178341i
\(723\) 0 0
\(724\) 2130.18 1315.76i 0.109348 0.0675414i
\(725\) 30748.1i 1.57511i
\(726\) 0 0
\(727\) 1269.94i 0.0647860i −0.999475 0.0323930i \(-0.989687\pi\)
0.999475 0.0323930i \(-0.0103128\pi\)
\(728\) −7077.05 6472.68i −0.360292 0.329524i
\(729\) 0 0
\(730\) 803.390 + 2829.45i 0.0407326 + 0.143455i
\(731\) −43047.8 −2.17809
\(732\) 0 0
\(733\) 26425.0 1.33155 0.665777 0.746151i \(-0.268100\pi\)
0.665777 + 0.746151i \(0.268100\pi\)
\(734\) 3847.33 + 13549.9i 0.193471 + 0.681382i
\(735\) 0 0
\(736\) −5356.54 + 28231.3i −0.268267 + 1.41388i
\(737\) 5073.87i 0.253593i
\(738\) 0 0
\(739\) 4732.65i 0.235579i 0.993039 + 0.117790i \(0.0375809\pi\)
−0.993039 + 0.117790i \(0.962419\pi\)
\(740\) 4955.09 + 8022.15i 0.246152 + 0.398514i
\(741\) 0 0
\(742\) −4418.70 + 1254.64i −0.218619 + 0.0620745i
\(743\) 14771.2 0.729346 0.364673 0.931136i \(-0.381181\pi\)
0.364673 + 0.931136i \(0.381181\pi\)
\(744\) 0 0
\(745\) 3291.66 0.161875
\(746\) 17445.8 4953.54i 0.856214 0.243113i
\(747\) 0 0
\(748\) 8273.77 + 13395.0i 0.404437 + 0.654773i
\(749\) 1617.80i 0.0789228i
\(750\) 0 0
\(751\) 27071.9i 1.31540i 0.753280 + 0.657700i \(0.228471\pi\)
−0.753280 + 0.657700i \(0.771529\pi\)
\(752\) 11384.1 22738.8i 0.552043 1.10266i
\(753\) 0 0
\(754\) 5230.09 + 18419.8i 0.252611 + 0.889667i
\(755\) −5432.31 −0.261857
\(756\) 0 0
\(757\) −12404.5 −0.595576 −0.297788 0.954632i \(-0.596249\pi\)
−0.297788 + 0.954632i \(0.596249\pi\)
\(758\) 4090.33 + 14405.7i 0.196000 + 0.690288i
\(759\) 0 0
\(760\) −4348.94 + 4755.01i −0.207569 + 0.226951i
\(761\) 8564.67i 0.407975i 0.978973 + 0.203988i \(0.0653902\pi\)
−0.978973 + 0.203988i \(0.934610\pi\)
\(762\) 0 0
\(763\) 22801.8i 1.08189i
\(764\) −13778.7 + 8510.76i −0.652481 + 0.403022i
\(765\) 0 0
\(766\) −16116.4 + 4576.06i −0.760193 + 0.215848i
\(767\) −7395.40 −0.348152
\(768\) 0 0
\(769\) −19117.5 −0.896483 −0.448241 0.893913i \(-0.647949\pi\)
−0.448241 + 0.893913i \(0.647949\pi\)
\(770\) −2578.88 + 732.243i −0.120696 + 0.0342704i
\(771\) 0 0
\(772\) 7745.58 4784.26i 0.361101 0.223043i
\(773\) 28145.2i 1.30959i 0.755807 + 0.654794i \(0.227245\pi\)
−0.755807 + 0.654794i \(0.772755\pi\)
\(774\) 0 0
\(775\) 4110.50i 0.190521i
\(776\) 3337.73 3649.38i 0.154404 0.168821i
\(777\) 0 0
\(778\) 3155.85 + 11114.5i 0.145428 + 0.512180i
\(779\) 12344.6 0.567767
\(780\) 0 0
\(781\) −11577.3 −0.530432
\(782\) −14338.5 50498.4i −0.655681 2.30923i
\(783\) 0 0
\(784\) 1642.76 3281.27i 0.0748344 0.149475i
\(785\) 2298.78i 0.104518i
\(786\) 0 0
\(787\) 15895.3i 0.719959i 0.932960 + 0.359979i \(0.117216\pi\)
−0.932960 + 0.359979i \(0.882784\pi\)
\(788\) 9861.80 + 15966.0i 0.445827 + 0.721782i
\(789\) 0 0
\(790\) −5457.54 +