Properties

Label 15.4.b.a.4.3
Level $15$
Weight $4$
Character 15.4
Analytic conductor $0.885$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 15.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.885028650086\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{41})\)
Defining polynomial: \( x^{4} + 21x^{2} + 100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 4.3
Root \(2.70156i\) of defining polynomial
Character \(\chi\) \(=\) 15.4
Dual form 15.4.b.a.4.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.70156i q^{2} +3.00000i q^{3} +5.10469 q^{4} +(-8.10469 - 7.70156i) q^{5} -5.10469 q^{6} -22.2094i q^{7} +22.2984i q^{8} -9.00000 q^{9} +O(q^{10})\) \(q+1.70156i q^{2} +3.00000i q^{3} +5.10469 q^{4} +(-8.10469 - 7.70156i) q^{5} -5.10469 q^{6} -22.2094i q^{7} +22.2984i q^{8} -9.00000 q^{9} +(13.1047 - 13.7906i) q^{10} -1.79063 q^{11} +15.3141i q^{12} +58.2094i q^{13} +37.7906 q^{14} +(23.1047 - 24.3141i) q^{15} +2.89531 q^{16} -18.9844i q^{17} -15.3141i q^{18} -104.837 q^{19} +(-41.3719 - 39.3141i) q^{20} +66.6281 q^{21} -3.04686i q^{22} -49.6125i q^{23} -66.8953 q^{24} +(6.37188 + 124.837i) q^{25} -99.0469 q^{26} -27.0000i q^{27} -113.372i q^{28} +293.466 q^{29} +(41.3719 + 39.3141i) q^{30} +64.4187 q^{31} +183.314i q^{32} -5.37188i q^{33} +32.3031 q^{34} +(-171.047 + 180.000i) q^{35} -45.9422 q^{36} +19.8844i q^{37} -178.388i q^{38} -174.628 q^{39} +(171.733 - 180.722i) q^{40} -165.581 q^{41} +113.372i q^{42} -247.350i q^{43} -9.14059 q^{44} +(72.9422 + 69.3141i) q^{45} +84.4187 q^{46} -384.544i q^{47} +8.68594i q^{48} -150.256 q^{49} +(-212.419 + 10.8422i) q^{50} +56.9531 q^{51} +297.141i q^{52} +463.528i q^{53} +45.9422 q^{54} +(14.5125 + 13.7906i) q^{55} +495.234 q^{56} -314.512i q^{57} +499.350i q^{58} +73.7906 q^{59} +(117.942 - 124.116i) q^{60} -137.350 q^{61} +109.612i q^{62} +199.884i q^{63} -288.758 q^{64} +(448.303 - 471.769i) q^{65} +9.14059 q^{66} -173.906i q^{67} -96.9093i q^{68} +148.837 q^{69} +(-306.281 - 291.047i) q^{70} -594.281 q^{71} -200.686i q^{72} +320.231i q^{73} -33.8345 q^{74} +(-374.512 + 19.1156i) q^{75} -535.163 q^{76} +39.7687i q^{77} -297.141i q^{78} +770.469 q^{79} +(-23.4656 - 22.2984i) q^{80} +81.0000 q^{81} -281.747i q^{82} +173.925i q^{83} +340.116 q^{84} +(-146.209 + 153.862i) q^{85} +420.881 q^{86} +880.397i q^{87} -39.9282i q^{88} -1019.02 q^{89} +(-117.942 + 124.116i) q^{90} +1292.79 q^{91} -253.256i q^{92} +193.256i q^{93} +654.325 q^{94} +(849.675 + 807.412i) q^{95} -549.942 q^{96} -384.375i q^{97} -255.670i q^{98} +16.1156 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 18 q^{4} + 6 q^{5} + 18 q^{6} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 18 q^{4} + 6 q^{5} + 18 q^{6} - 36 q^{9} + 14 q^{10} - 84 q^{11} + 228 q^{14} + 54 q^{15} + 50 q^{16} - 112 q^{19} - 396 q^{20} + 36 q^{21} - 306 q^{24} + 256 q^{25} - 12 q^{26} + 636 q^{29} + 396 q^{30} + 104 q^{31} - 716 q^{34} - 300 q^{35} + 162 q^{36} - 468 q^{39} + 418 q^{40} - 816 q^{41} + 1116 q^{44} - 54 q^{45} + 184 q^{46} - 140 q^{49} - 696 q^{50} + 612 q^{51} - 162 q^{54} - 864 q^{55} + 60 q^{56} + 372 q^{59} + 126 q^{60} + 680 q^{61} + 958 q^{64} + 948 q^{65} - 1116 q^{66} + 288 q^{69} + 1080 q^{70} - 72 q^{71} - 3132 q^{74} - 576 q^{75} - 2448 q^{76} - 760 q^{79} + 444 q^{80} + 324 q^{81} + 2052 q^{84} - 508 q^{85} + 4296 q^{86} - 2232 q^{89} - 126 q^{90} + 1944 q^{91} + 3232 q^{94} + 2784 q^{95} - 1854 q^{96} + 756 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(-1\) \(1\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.70156i 0.601593i 0.953688 + 0.300797i \(0.0972525\pi\)
−0.953688 + 0.300797i \(0.902747\pi\)
\(3\) 3.00000i 0.577350i
\(4\) 5.10469 0.638086
\(5\) −8.10469 7.70156i −0.724905 0.688849i
\(6\) −5.10469 −0.347330
\(7\) 22.2094i 1.19919i −0.800302 0.599597i \(-0.795328\pi\)
0.800302 0.599597i \(-0.204672\pi\)
\(8\) 22.2984i 0.985461i
\(9\) −9.00000 −0.333333
\(10\) 13.1047 13.7906i 0.414407 0.436098i
\(11\) −1.79063 −0.0490813 −0.0245407 0.999699i \(-0.507812\pi\)
−0.0245407 + 0.999699i \(0.507812\pi\)
\(12\) 15.3141i 0.368399i
\(13\) 58.2094i 1.24188i 0.783860 + 0.620938i \(0.213248\pi\)
−0.783860 + 0.620938i \(0.786752\pi\)
\(14\) 37.7906 0.721426
\(15\) 23.1047 24.3141i 0.397707 0.418524i
\(16\) 2.89531 0.0452393
\(17\) 18.9844i 0.270846i −0.990788 0.135423i \(-0.956761\pi\)
0.990788 0.135423i \(-0.0432394\pi\)
\(18\) 15.3141i 0.200531i
\(19\) −104.837 −1.26586 −0.632931 0.774208i \(-0.718148\pi\)
−0.632931 + 0.774208i \(0.718148\pi\)
\(20\) −41.3719 39.3141i −0.462552 0.439545i
\(21\) 66.6281 0.692355
\(22\) 3.04686i 0.0295270i
\(23\) 49.6125i 0.449779i −0.974384 0.224890i \(-0.927798\pi\)
0.974384 0.224890i \(-0.0722021\pi\)
\(24\) −66.8953 −0.568956
\(25\) 6.37188 + 124.837i 0.0509751 + 0.998700i
\(26\) −99.0469 −0.747103
\(27\) 27.0000i 0.192450i
\(28\) 113.372i 0.765188i
\(29\) 293.466 1.87914 0.939572 0.342350i \(-0.111223\pi\)
0.939572 + 0.342350i \(0.111223\pi\)
\(30\) 41.3719 + 39.3141i 0.251781 + 0.239258i
\(31\) 64.4187 0.373224 0.186612 0.982434i \(-0.440249\pi\)
0.186612 + 0.982434i \(0.440249\pi\)
\(32\) 183.314i 1.01268i
\(33\) 5.37188i 0.0283371i
\(34\) 32.3031 0.162939
\(35\) −171.047 + 180.000i −0.826063 + 0.869302i
\(36\) −45.9422 −0.212695
\(37\) 19.8844i 0.0883505i 0.999024 + 0.0441752i \(0.0140660\pi\)
−0.999024 + 0.0441752i \(0.985934\pi\)
\(38\) 178.388i 0.761534i
\(39\) −174.628 −0.716997
\(40\) 171.733 180.722i 0.678834 0.714366i
\(41\) −165.581 −0.630718 −0.315359 0.948972i \(-0.602125\pi\)
−0.315359 + 0.948972i \(0.602125\pi\)
\(42\) 113.372i 0.416516i
\(43\) 247.350i 0.877221i −0.898677 0.438611i \(-0.855471\pi\)
0.898677 0.438611i \(-0.144529\pi\)
\(44\) −9.14059 −0.0313181
\(45\) 72.9422 + 69.3141i 0.241635 + 0.229616i
\(46\) 84.4187 0.270584
\(47\) 384.544i 1.19344i −0.802451 0.596718i \(-0.796471\pi\)
0.802451 0.596718i \(-0.203529\pi\)
\(48\) 8.68594i 0.0261189i
\(49\) −150.256 −0.438065
\(50\) −212.419 + 10.8422i −0.600811 + 0.0306662i
\(51\) 56.9531 0.156373
\(52\) 297.141i 0.792423i
\(53\) 463.528i 1.20133i 0.799501 + 0.600665i \(0.205097\pi\)
−0.799501 + 0.600665i \(0.794903\pi\)
\(54\) 45.9422 0.115777
\(55\) 14.5125 + 13.7906i 0.0355793 + 0.0338096i
\(56\) 495.234 1.18176
\(57\) 314.512i 0.730846i
\(58\) 499.350i 1.13048i
\(59\) 73.7906 0.162826 0.0814129 0.996680i \(-0.474057\pi\)
0.0814129 + 0.996680i \(0.474057\pi\)
\(60\) 117.942 124.116i 0.253771 0.267054i
\(61\) −137.350 −0.288293 −0.144146 0.989556i \(-0.546044\pi\)
−0.144146 + 0.989556i \(0.546044\pi\)
\(62\) 109.612i 0.224529i
\(63\) 199.884i 0.399731i
\(64\) −288.758 −0.563980
\(65\) 448.303 471.769i 0.855464 0.900242i
\(66\) 9.14059 0.0170474
\(67\) 173.906i 0.317105i −0.987351 0.158552i \(-0.949317\pi\)
0.987351 0.158552i \(-0.0506827\pi\)
\(68\) 96.9093i 0.172823i
\(69\) 148.837 0.259680
\(70\) −306.281 291.047i −0.522966 0.496954i
\(71\) −594.281 −0.993355 −0.496677 0.867935i \(-0.665447\pi\)
−0.496677 + 0.867935i \(0.665447\pi\)
\(72\) 200.686i 0.328487i
\(73\) 320.231i 0.513428i 0.966487 + 0.256714i \(0.0826398\pi\)
−0.966487 + 0.256714i \(0.917360\pi\)
\(74\) −33.8345 −0.0531510
\(75\) −374.512 + 19.1156i −0.576600 + 0.0294305i
\(76\) −535.163 −0.807728
\(77\) 39.7687i 0.0588580i
\(78\) 297.141i 0.431340i
\(79\) 770.469 1.09727 0.548636 0.836061i \(-0.315147\pi\)
0.548636 + 0.836061i \(0.315147\pi\)
\(80\) −23.4656 22.2984i −0.0327942 0.0311630i
\(81\) 81.0000 0.111111
\(82\) 281.747i 0.379436i
\(83\) 173.925i 0.230009i 0.993365 + 0.115004i \(0.0366882\pi\)
−0.993365 + 0.115004i \(0.963312\pi\)
\(84\) 340.116 0.441782
\(85\) −146.209 + 153.862i −0.186572 + 0.196338i
\(86\) 420.881 0.527730
\(87\) 880.397i 1.08492i
\(88\) 39.9282i 0.0483677i
\(89\) −1019.02 −1.21367 −0.606834 0.794829i \(-0.707561\pi\)
−0.606834 + 0.794829i \(0.707561\pi\)
\(90\) −117.942 + 124.116i −0.138136 + 0.145366i
\(91\) 1292.79 1.48925
\(92\) 253.256i 0.286998i
\(93\) 193.256i 0.215481i
\(94\) 654.325 0.717962
\(95\) 849.675 + 807.412i 0.917630 + 0.871987i
\(96\) −549.942 −0.584669
\(97\) 384.375i 0.402344i −0.979556 0.201172i \(-0.935525\pi\)
0.979556 0.201172i \(-0.0644750\pi\)
\(98\) 255.670i 0.263537i
\(99\) 16.1156 0.0163604
\(100\) 32.5265 + 637.256i 0.0325265 + 0.637256i
\(101\) 34.4906 0.0339796 0.0169898 0.999856i \(-0.494592\pi\)
0.0169898 + 0.999856i \(0.494592\pi\)
\(102\) 96.9093i 0.0940730i
\(103\) 1756.30i 1.68013i −0.542484 0.840066i \(-0.682516\pi\)
0.542484 0.840066i \(-0.317484\pi\)
\(104\) −1297.98 −1.22382
\(105\) −540.000 513.141i −0.501891 0.476928i
\(106\) −788.722 −0.722712
\(107\) 1361.74i 1.23032i 0.788403 + 0.615159i \(0.210908\pi\)
−0.788403 + 0.615159i \(0.789092\pi\)
\(108\) 137.827i 0.122800i
\(109\) −321.119 −0.282180 −0.141090 0.989997i \(-0.545061\pi\)
−0.141090 + 0.989997i \(0.545061\pi\)
\(110\) −23.4656 + 24.6939i −0.0203396 + 0.0214043i
\(111\) −59.6531 −0.0510092
\(112\) 64.3031i 0.0542506i
\(113\) 1582.25i 1.31721i −0.752487 0.658607i \(-0.771146\pi\)
0.752487 0.658607i \(-0.228854\pi\)
\(114\) 535.163 0.439672
\(115\) −382.094 + 402.094i −0.309830 + 0.326047i
\(116\) 1498.05 1.19906
\(117\) 523.884i 0.413958i
\(118\) 125.559i 0.0979549i
\(119\) −421.631 −0.324797
\(120\) 542.166 + 515.198i 0.412439 + 0.391925i
\(121\) −1327.79 −0.997591
\(122\) 233.709i 0.173435i
\(123\) 496.744i 0.364145i
\(124\) 328.837 0.238149
\(125\) 909.802 1060.84i 0.651001 0.759077i
\(126\) −340.116 −0.240475
\(127\) 1197.14i 0.836449i 0.908344 + 0.418225i \(0.137348\pi\)
−0.908344 + 0.418225i \(0.862652\pi\)
\(128\) 975.173i 0.673390i
\(129\) 742.050 0.506464
\(130\) 802.744 + 762.816i 0.541579 + 0.514641i
\(131\) −321.647 −0.214522 −0.107261 0.994231i \(-0.534208\pi\)
−0.107261 + 0.994231i \(0.534208\pi\)
\(132\) 27.4218i 0.0180815i
\(133\) 2328.37i 1.51801i
\(134\) 295.912 0.190768
\(135\) −207.942 + 218.827i −0.132569 + 0.139508i
\(136\) 423.322 0.266909
\(137\) 354.291i 0.220942i −0.993879 0.110471i \(-0.964764\pi\)
0.993879 0.110471i \(-0.0352360\pi\)
\(138\) 253.256i 0.156222i
\(139\) −77.2562 −0.0471424 −0.0235712 0.999722i \(-0.507504\pi\)
−0.0235712 + 0.999722i \(0.507504\pi\)
\(140\) −873.141 + 918.844i −0.527099 + 0.554689i
\(141\) 1153.63 0.689030
\(142\) 1011.21i 0.597595i
\(143\) 104.231i 0.0609529i
\(144\) −26.0578 −0.0150798
\(145\) −2378.45 2260.14i −1.36220 1.29445i
\(146\) −544.893 −0.308875
\(147\) 450.769i 0.252917i
\(148\) 101.503i 0.0563752i
\(149\) 1705.38 0.937651 0.468826 0.883291i \(-0.344677\pi\)
0.468826 + 0.883291i \(0.344677\pi\)
\(150\) −32.5265 637.256i −0.0177052 0.346878i
\(151\) 758.281 0.408663 0.204331 0.978902i \(-0.434498\pi\)
0.204331 + 0.978902i \(0.434498\pi\)
\(152\) 2337.71i 1.24746i
\(153\) 170.859i 0.0902821i
\(154\) −67.6689 −0.0354086
\(155\) −522.094 496.125i −0.270552 0.257095i
\(156\) −891.422 −0.457506
\(157\) 1769.05i 0.899273i 0.893212 + 0.449636i \(0.148446\pi\)
−0.893212 + 0.449636i \(0.851554\pi\)
\(158\) 1311.00i 0.660111i
\(159\) −1390.58 −0.693588
\(160\) 1411.80 1485.70i 0.697581 0.734095i
\(161\) −1101.86 −0.539372
\(162\) 137.827i 0.0668437i
\(163\) 881.719i 0.423690i −0.977303 0.211845i \(-0.932053\pi\)
0.977303 0.211845i \(-0.0679473\pi\)
\(164\) −845.240 −0.402452
\(165\) −41.3719 + 43.5374i −0.0195200 + 0.0205417i
\(166\) −295.944 −0.138372
\(167\) 216.900i 0.100504i 0.998737 + 0.0502522i \(0.0160025\pi\)
−0.998737 + 0.0502522i \(0.983997\pi\)
\(168\) 1485.70i 0.682289i
\(169\) −1191.33 −0.542254
\(170\) −261.806 248.784i −0.118116 0.112241i
\(171\) 943.537 0.421954
\(172\) 1262.64i 0.559742i
\(173\) 4125.91i 1.81322i 0.421970 + 0.906610i \(0.361339\pi\)
−0.421970 + 0.906610i \(0.638661\pi\)
\(174\) −1498.05 −0.652683
\(175\) 2772.56 141.515i 1.19763 0.0611289i
\(176\) −5.18443 −0.00222040
\(177\) 221.372i 0.0940075i
\(178\) 1733.93i 0.730134i
\(179\) 3213.14 1.34168 0.670842 0.741600i \(-0.265933\pi\)
0.670842 + 0.741600i \(0.265933\pi\)
\(180\) 372.347 + 353.827i 0.154184 + 0.146515i
\(181\) 3394.42 1.39395 0.696976 0.717095i \(-0.254529\pi\)
0.696976 + 0.717095i \(0.254529\pi\)
\(182\) 2199.77i 0.895921i
\(183\) 412.050i 0.166446i
\(184\) 1106.28 0.443240
\(185\) 153.141 161.156i 0.0608601 0.0640457i
\(186\) −328.837 −0.129632
\(187\) 33.9939i 0.0132935i
\(188\) 1962.98i 0.761514i
\(189\) −599.653 −0.230785
\(190\) −1373.86 + 1445.77i −0.524581 + 0.552040i
\(191\) −3467.49 −1.31361 −0.656804 0.754062i \(-0.728092\pi\)
−0.656804 + 0.754062i \(0.728092\pi\)
\(192\) 866.273i 0.325614i
\(193\) 1792.14i 0.668401i 0.942502 + 0.334200i \(0.108466\pi\)
−0.942502 + 0.334200i \(0.891534\pi\)
\(194\) 654.038 0.242047
\(195\) 1415.31 + 1344.91i 0.519755 + 0.493902i
\(196\) −767.011 −0.279523
\(197\) 1678.19i 0.606935i −0.952842 0.303467i \(-0.901856\pi\)
0.952842 0.303467i \(-0.0981443\pi\)
\(198\) 27.4218i 0.00984233i
\(199\) −3108.23 −1.10722 −0.553610 0.832776i \(-0.686750\pi\)
−0.553610 + 0.832776i \(0.686750\pi\)
\(200\) −2783.68 + 142.083i −0.984180 + 0.0502339i
\(201\) 521.719 0.183081
\(202\) 58.6878i 0.0204419i
\(203\) 6517.69i 2.25346i
\(204\) 290.728 0.0997795
\(205\) 1341.98 + 1275.23i 0.457211 + 0.434469i
\(206\) 2988.46 1.01076
\(207\) 446.512i 0.149926i
\(208\) 168.534i 0.0561815i
\(209\) 187.725 0.0621301
\(210\) 873.141 918.844i 0.286916 0.301934i
\(211\) −4473.27 −1.45949 −0.729745 0.683719i \(-0.760361\pi\)
−0.729745 + 0.683719i \(0.760361\pi\)
\(212\) 2366.17i 0.766551i
\(213\) 1782.84i 0.573514i
\(214\) −2317.08 −0.740151
\(215\) −1904.98 + 2004.69i −0.604273 + 0.635902i
\(216\) 602.058 0.189652
\(217\) 1430.70i 0.447568i
\(218\) 546.403i 0.169757i
\(219\) −960.694 −0.296428
\(220\) 74.0816 + 70.3968i 0.0227026 + 0.0215734i
\(221\) 1105.07 0.336357
\(222\) 101.503i 0.0306868i
\(223\) 1753.42i 0.526535i −0.964723 0.263268i \(-0.915200\pi\)
0.964723 0.263268i \(-0.0848003\pi\)
\(224\) 4071.29 1.21440
\(225\) −57.3469 1123.54i −0.0169917 0.332900i
\(226\) 2692.29 0.792427
\(227\) 936.900i 0.273939i 0.990575 + 0.136970i \(0.0437363\pi\)
−0.990575 + 0.136970i \(0.956264\pi\)
\(228\) 1605.49i 0.466342i
\(229\) 2582.06 0.745096 0.372548 0.928013i \(-0.378484\pi\)
0.372548 + 0.928013i \(0.378484\pi\)
\(230\) −684.187 650.156i −0.196148 0.186391i
\(231\) −119.306 −0.0339817
\(232\) 6543.82i 1.85182i
\(233\) 2295.01i 0.645284i 0.946521 + 0.322642i \(0.104571\pi\)
−0.946521 + 0.322642i \(0.895429\pi\)
\(234\) 891.422 0.249034
\(235\) −2961.59 + 3116.61i −0.822096 + 0.865128i
\(236\) 376.678 0.103897
\(237\) 2311.41i 0.633510i
\(238\) 717.432i 0.195396i
\(239\) 2294.01 0.620866 0.310433 0.950595i \(-0.399526\pi\)
0.310433 + 0.950595i \(0.399526\pi\)
\(240\) 66.8953 70.3968i 0.0179920 0.0189337i
\(241\) 382.287 0.102180 0.0510898 0.998694i \(-0.483731\pi\)
0.0510898 + 0.998694i \(0.483731\pi\)
\(242\) 2259.32i 0.600144i
\(243\) 243.000i 0.0641500i
\(244\) −701.128 −0.183956
\(245\) 1217.78 + 1157.21i 0.317555 + 0.301760i
\(246\) 845.240 0.219067
\(247\) 6102.52i 1.57204i
\(248\) 1436.44i 0.367798i
\(249\) −521.775 −0.132796
\(250\) 1805.09 + 1548.08i 0.456655 + 0.391638i
\(251\) −2259.98 −0.568322 −0.284161 0.958777i \(-0.591715\pi\)
−0.284161 + 0.958777i \(0.591715\pi\)
\(252\) 1020.35i 0.255063i
\(253\) 88.8375i 0.0220758i
\(254\) −2037.01 −0.503202
\(255\) −461.587 438.628i −0.113356 0.107717i
\(256\) −3969.38 −0.969087
\(257\) 92.7843i 0.0225203i 0.999937 + 0.0112602i \(0.00358430\pi\)
−0.999937 + 0.0112602i \(0.996416\pi\)
\(258\) 1262.64i 0.304685i
\(259\) 441.619 0.105949
\(260\) 2288.45 2408.23i 0.545859 0.574431i
\(261\) −2641.19 −0.626382
\(262\) 547.302i 0.129055i
\(263\) 568.312i 0.133246i −0.997778 0.0666229i \(-0.978778\pi\)
0.997778 0.0666229i \(-0.0212224\pi\)
\(264\) 119.785 0.0279251
\(265\) 3569.89 3756.75i 0.827534 0.870850i
\(266\) −3961.87 −0.913226
\(267\) 3057.07i 0.700711i
\(268\) 887.737i 0.202340i
\(269\) −7582.41 −1.71862 −0.859309 0.511458i \(-0.829106\pi\)
−0.859309 + 0.511458i \(0.829106\pi\)
\(270\) −372.347 353.827i −0.0839271 0.0797526i
\(271\) 7943.69 1.78061 0.890304 0.455366i \(-0.150492\pi\)
0.890304 + 0.455366i \(0.150492\pi\)
\(272\) 54.9657i 0.0122529i
\(273\) 3878.38i 0.859818i
\(274\) 602.847 0.132917
\(275\) −11.4097 223.537i −0.00250192 0.0490175i
\(276\) 759.769 0.165698
\(277\) 6823.00i 1.47998i −0.672618 0.739990i \(-0.734830\pi\)
0.672618 0.739990i \(-0.265170\pi\)
\(278\) 131.456i 0.0283605i
\(279\) −579.769 −0.124408
\(280\) −4013.72 3814.08i −0.856663 0.814053i
\(281\) 3315.86 0.703942 0.351971 0.936011i \(-0.385512\pi\)
0.351971 + 0.936011i \(0.385512\pi\)
\(282\) 1962.98i 0.414516i
\(283\) 6602.76i 1.38690i 0.720504 + 0.693451i \(0.243910\pi\)
−0.720504 + 0.693451i \(0.756090\pi\)
\(284\) −3033.62 −0.633846
\(285\) −2422.24 + 2549.02i −0.503442 + 0.529794i
\(286\) 177.356 0.0366688
\(287\) 3677.46i 0.756353i
\(288\) 1649.83i 0.337559i
\(289\) 4552.59 0.926642
\(290\) 3845.77 4047.07i 0.778730 0.819491i
\(291\) 1153.12 0.232293
\(292\) 1634.68i 0.327611i
\(293\) 5814.14i 1.15927i 0.814877 + 0.579634i \(0.196805\pi\)
−0.814877 + 0.579634i \(0.803195\pi\)
\(294\) 767.011 0.152153
\(295\) −598.050 568.303i −0.118033 0.112162i
\(296\) −443.390 −0.0870660
\(297\) 48.3469i 0.00944570i
\(298\) 2901.81i 0.564084i
\(299\) 2887.91 0.558570
\(300\) −1911.77 + 97.5794i −0.367920 + 0.0187792i
\(301\) −5493.49 −1.05196
\(302\) 1290.26i 0.245849i
\(303\) 103.472i 0.0196181i
\(304\) −303.537 −0.0572667
\(305\) 1113.18 + 1057.81i 0.208985 + 0.198590i
\(306\) −290.728 −0.0543131
\(307\) 8124.86i 1.51046i 0.655462 + 0.755229i \(0.272474\pi\)
−0.655462 + 0.755229i \(0.727526\pi\)
\(308\) 203.007i 0.0375564i
\(309\) 5268.91 0.970025
\(310\) 844.187 888.375i 0.154667 0.162762i
\(311\) 7336.26 1.33762 0.668812 0.743432i \(-0.266803\pi\)
0.668812 + 0.743432i \(0.266803\pi\)
\(312\) 3893.93i 0.706572i
\(313\) 2202.66i 0.397768i −0.980023 0.198884i \(-0.936268\pi\)
0.980023 0.198884i \(-0.0637318\pi\)
\(314\) −3010.15 −0.540996
\(315\) 1539.42 1620.00i 0.275354 0.289767i
\(316\) 3933.00 0.700154
\(317\) 10008.9i 1.77336i −0.462386 0.886679i \(-0.653007\pi\)
0.462386 0.886679i \(-0.346993\pi\)
\(318\) 2366.17i 0.417258i
\(319\) −525.488 −0.0922309
\(320\) 2340.29 + 2223.89i 0.408832 + 0.388497i
\(321\) −4085.21 −0.710325
\(322\) 1874.89i 0.324483i
\(323\) 1990.27i 0.342854i
\(324\) 413.480 0.0708984
\(325\) −7266.71 + 370.903i −1.24026 + 0.0633046i
\(326\) 1500.30 0.254889
\(327\) 963.356i 0.162917i
\(328\) 3692.20i 0.621548i
\(329\) −8540.47 −1.43116
\(330\) −74.0816 70.3968i −0.0123578 0.0117431i
\(331\) −8695.94 −1.44402 −0.722012 0.691881i \(-0.756782\pi\)
−0.722012 + 0.691881i \(0.756782\pi\)
\(332\) 887.832i 0.146765i
\(333\) 178.959i 0.0294502i
\(334\) −369.069 −0.0604627
\(335\) −1339.35 + 1409.46i −0.218437 + 0.229871i
\(336\) 192.909 0.0313216
\(337\) 7400.61i 1.19625i 0.801402 + 0.598126i \(0.204088\pi\)
−0.801402 + 0.598126i \(0.795912\pi\)
\(338\) 2027.12i 0.326216i
\(339\) 4746.74 0.760494
\(340\) −746.353 + 785.419i −0.119049 + 0.125280i
\(341\) −115.350 −0.0183183
\(342\) 1605.49i 0.253845i
\(343\) 4280.72i 0.673869i
\(344\) 5515.52 0.864467
\(345\) −1206.28 1146.28i −0.188243 0.178880i
\(346\) −7020.49 −1.09082
\(347\) 7841.44i 1.21311i −0.795040 0.606557i \(-0.792550\pi\)
0.795040 0.606557i \(-0.207450\pi\)
\(348\) 4494.15i 0.692275i
\(349\) 4961.26 0.760946 0.380473 0.924792i \(-0.375761\pi\)
0.380473 + 0.924792i \(0.375761\pi\)
\(350\) 240.797 + 4717.69i 0.0367748 + 0.720489i
\(351\) 1571.65 0.238999
\(352\) 328.247i 0.0497035i
\(353\) 12163.0i 1.83392i −0.398981 0.916959i \(-0.630636\pi\)
0.398981 0.916959i \(-0.369364\pi\)
\(354\) −376.678 −0.0565543
\(355\) 4816.46 + 4576.89i 0.720088 + 0.684271i
\(356\) −5201.80 −0.774424
\(357\) 1264.89i 0.187522i
\(358\) 5467.36i 0.807148i
\(359\) −5193.79 −0.763559 −0.381779 0.924253i \(-0.624689\pi\)
−0.381779 + 0.924253i \(0.624689\pi\)
\(360\) −1545.60 + 1626.50i −0.226278 + 0.238122i
\(361\) 4131.90 0.602406
\(362\) 5775.81i 0.838591i
\(363\) 3983.38i 0.575959i
\(364\) 6599.31 0.950268
\(365\) 2466.28 2595.37i 0.353674 0.372187i
\(366\) 701.128 0.100133
\(367\) 6086.09i 0.865644i 0.901479 + 0.432822i \(0.142482\pi\)
−0.901479 + 0.432822i \(0.857518\pi\)
\(368\) 143.644i 0.0203477i
\(369\) 1490.23 0.210239
\(370\) 274.218 + 260.578i 0.0385295 + 0.0366130i
\(371\) 10294.7 1.44063
\(372\) 986.512i 0.137495i
\(373\) 10581.9i 1.46893i −0.678646 0.734466i \(-0.737433\pi\)
0.678646 0.734466i \(-0.262567\pi\)
\(374\) −57.8428 −0.00799727
\(375\) 3182.53 + 2729.40i 0.438253 + 0.375856i
\(376\) 8574.72 1.17608
\(377\) 17082.4i 2.33366i
\(378\) 1020.35i 0.138839i
\(379\) −11655.2 −1.57964 −0.789822 0.613336i \(-0.789827\pi\)
−0.789822 + 0.613336i \(0.789827\pi\)
\(380\) 4337.32 + 4121.59i 0.585526 + 0.556403i
\(381\) −3591.42 −0.482924
\(382\) 5900.16i 0.790257i
\(383\) 6364.97i 0.849177i 0.905387 + 0.424588i \(0.139581\pi\)
−0.905387 + 0.424588i \(0.860419\pi\)
\(384\) −2925.52 −0.388782
\(385\) 306.281 322.313i 0.0405442 0.0426665i
\(386\) −3049.44 −0.402105
\(387\) 2226.15i 0.292407i
\(388\) 1962.11i 0.256730i
\(389\) −6134.33 −0.799545 −0.399773 0.916614i \(-0.630911\pi\)
−0.399773 + 0.916614i \(0.630911\pi\)
\(390\) −2288.45 + 2408.23i −0.297128 + 0.312681i
\(391\) −941.862 −0.121821
\(392\) 3350.48i 0.431696i
\(393\) 964.941i 0.123855i
\(394\) 2855.55 0.365128
\(395\) −6244.41 5933.81i −0.795418 0.755854i
\(396\) 82.2653 0.0104394
\(397\) 9746.46i 1.23214i −0.787690 0.616072i \(-0.788723\pi\)
0.787690 0.616072i \(-0.211277\pi\)
\(398\) 5288.85i 0.666096i
\(399\) −6985.12 −0.876425
\(400\) 18.4486 + 361.444i 0.00230607 + 0.0451805i
\(401\) −1306.44 −0.162695 −0.0813474 0.996686i \(-0.525922\pi\)
−0.0813474 + 0.996686i \(0.525922\pi\)
\(402\) 887.737i 0.110140i
\(403\) 3749.77i 0.463498i
\(404\) 176.063 0.0216819
\(405\) −656.480 623.827i −0.0805450 0.0765387i
\(406\) 11090.2 1.35566
\(407\) 35.6055i 0.00433636i
\(408\) 1269.97i 0.154100i
\(409\) 3876.93 0.468709 0.234354 0.972151i \(-0.424702\pi\)
0.234354 + 0.972151i \(0.424702\pi\)
\(410\) −2169.89 + 2283.47i −0.261374 + 0.275055i
\(411\) 1062.87 0.127561
\(412\) 8965.38i 1.07207i
\(413\) 1638.84i 0.195260i
\(414\) −759.769 −0.0901947
\(415\) 1339.49 1409.61i 0.158441 0.166735i
\(416\) −10670.6 −1.25762
\(417\) 231.769i 0.0272177i
\(418\) 319.426i 0.0373771i
\(419\) 16022.5 1.86814 0.934071 0.357088i \(-0.116230\pi\)
0.934071 + 0.357088i \(0.116230\pi\)
\(420\) −2756.53 2619.42i −0.320250 0.304321i
\(421\) −8119.73 −0.939980 −0.469990 0.882672i \(-0.655742\pi\)
−0.469990 + 0.882672i \(0.655742\pi\)
\(422\) 7611.54i 0.878019i
\(423\) 3460.89i 0.397812i
\(424\) −10336.0 −1.18386
\(425\) 2369.96 120.966i 0.270494 0.0138064i
\(426\) 3033.62 0.345022
\(427\) 3050.46i 0.345719i
\(428\) 6951.24i 0.785049i
\(429\) 312.694 0.0351911
\(430\) −3411.11 3241.44i −0.382554 0.363526i
\(431\) −5713.99 −0.638592 −0.319296 0.947655i \(-0.603446\pi\)
−0.319296 + 0.947655i \(0.603446\pi\)
\(432\) 78.1735i 0.00870630i
\(433\) 6251.34i 0.693811i 0.937900 + 0.346906i \(0.112768\pi\)
−0.937900 + 0.346906i \(0.887232\pi\)
\(434\) 2434.42 0.269254
\(435\) 6780.43 7135.34i 0.747349 0.786468i
\(436\) −1639.21 −0.180055
\(437\) 5201.25i 0.569358i
\(438\) 1634.68i 0.178329i
\(439\) 4230.97 0.459984 0.229992 0.973192i \(-0.426130\pi\)
0.229992 + 0.973192i \(0.426130\pi\)
\(440\) −307.509 + 323.605i −0.0333180 + 0.0350620i
\(441\) 1352.31 0.146022
\(442\) 1880.34i 0.202350i
\(443\) 6314.29i 0.677203i 0.940930 + 0.338601i \(0.109954\pi\)
−0.940930 + 0.338601i \(0.890046\pi\)
\(444\) −304.510 −0.0325482
\(445\) 8258.88 + 7848.08i 0.879794 + 0.836033i
\(446\) 2983.55 0.316760
\(447\) 5116.13i 0.541353i
\(448\) 6413.13i 0.676321i
\(449\) 9349.71 0.982717 0.491358 0.870957i \(-0.336501\pi\)
0.491358 + 0.870957i \(0.336501\pi\)
\(450\) 1911.77 97.5794i 0.200270 0.0102221i
\(451\) 296.494 0.0309565
\(452\) 8076.87i 0.840496i
\(453\) 2274.84i 0.235941i
\(454\) −1594.19 −0.164800
\(455\) −10477.7 9956.53i −1.07956 1.02587i
\(456\) 7013.14 0.720220
\(457\) 9547.46i 0.977268i 0.872489 + 0.488634i \(0.162505\pi\)
−0.872489 + 0.488634i \(0.837495\pi\)
\(458\) 4393.53i 0.448245i
\(459\) −512.578 −0.0521244
\(460\) −1950.47 + 2052.56i −0.197698 + 0.208046i
\(461\) 6237.23 0.630145 0.315073 0.949068i \(-0.397971\pi\)
0.315073 + 0.949068i \(0.397971\pi\)
\(462\) 203.007i 0.0204431i
\(463\) 6469.98i 0.649428i 0.945812 + 0.324714i \(0.105268\pi\)
−0.945812 + 0.324714i \(0.894732\pi\)
\(464\) 849.675 0.0850111
\(465\) 1488.37 1566.28i 0.148434 0.156203i
\(466\) −3905.10 −0.388198
\(467\) 7206.64i 0.714097i −0.934086 0.357049i \(-0.883783\pi\)
0.934086 0.357049i \(-0.116217\pi\)
\(468\) 2674.27i 0.264141i
\(469\) −3862.35 −0.380270
\(470\) −5303.10 5039.32i −0.520455 0.494567i
\(471\) −5307.16 −0.519195
\(472\) 1645.42i 0.160458i
\(473\) 442.912i 0.0430552i
\(474\) −3933.00 −0.381115
\(475\) −668.012 13087.6i −0.0645274 1.26422i
\(476\) −2152.29 −0.207248
\(477\) 4171.75i 0.400443i
\(478\) 3903.39i 0.373509i
\(479\) 10851.8 1.03514 0.517571 0.855640i \(-0.326836\pi\)
0.517571 + 0.855640i \(0.326836\pi\)
\(480\) 4457.11 + 4235.41i 0.423830 + 0.402749i
\(481\) −1157.46 −0.109720
\(482\) 650.485i 0.0614705i
\(483\) 3305.59i 0.311407i
\(484\) −6777.97 −0.636549
\(485\) −2960.29 + 3115.24i −0.277154 + 0.291661i
\(486\) −413.480 −0.0385922
\(487\) 12757.1i 1.18702i −0.804827 0.593510i \(-0.797742\pi\)
0.804827 0.593510i \(-0.202258\pi\)
\(488\) 3062.69i 0.284101i
\(489\) 2645.16 0.244618
\(490\) −1969.06 + 2072.13i −0.181537 + 0.191039i
\(491\) −7016.52 −0.644911 −0.322455 0.946585i \(-0.604508\pi\)
−0.322455 + 0.946585i \(0.604508\pi\)
\(492\) 2535.72i 0.232356i
\(493\) 5571.26i 0.508960i
\(494\) 10383.8 0.945729
\(495\) −130.612 124.116i −0.0118598 0.0112699i
\(496\) 186.512 0.0168844
\(497\) 13198.6i 1.19122i
\(498\) 887.832i 0.0798890i
\(499\) −11372.3 −1.02023 −0.510113 0.860107i \(-0.670396\pi\)
−0.510113 + 0.860107i \(0.670396\pi\)
\(500\) 4644.25 5415.27i 0.415395 0.484356i
\(501\) −650.700 −0.0580262
\(502\) 3845.50i 0.341899i
\(503\) 5587.37i 0.495285i −0.968851 0.247643i \(-0.920344\pi\)
0.968851 0.247643i \(-0.0796559\pi\)
\(504\) −4457.11 −0.393919
\(505\) −279.535 265.631i −0.0246320 0.0234068i
\(506\) −151.163 −0.0132806
\(507\) 3573.99i 0.313070i
\(508\) 6111.03i 0.533726i
\(509\) −16256.7 −1.41565 −0.707825 0.706388i \(-0.750324\pi\)
−0.707825 + 0.706388i \(0.750324\pi\)
\(510\) 746.353 785.419i 0.0648021 0.0681940i
\(511\) 7112.14 0.615699
\(512\) 1047.24i 0.0903943i
\(513\) 2830.61i 0.243615i
\(514\) −157.878 −0.0135481
\(515\) −13526.3 + 14234.3i −1.15736 + 1.21794i
\(516\) 3787.93 0.323167
\(517\) 688.574i 0.0585754i
\(518\) 751.442i 0.0637384i
\(519\) −12377.7 −1.04686
\(520\) 10519.7 + 9996.46i 0.887153 + 0.843026i
\(521\) 19748.4 1.66064 0.830320 0.557286i \(-0.188157\pi\)
0.830320 + 0.557286i \(0.188157\pi\)
\(522\) 4494.15i 0.376827i
\(523\) 7843.44i 0.655774i −0.944717 0.327887i \(-0.893663\pi\)
0.944717 0.327887i \(-0.106337\pi\)
\(524\) −1641.91 −0.136884
\(525\) 424.546 + 8317.69i 0.0352928 + 0.691455i
\(526\) 967.019 0.0801597
\(527\) 1222.95i 0.101086i
\(528\) 15.5533i 0.00128195i
\(529\) 9705.60 0.797699
\(530\) 6392.34 + 6074.39i 0.523897 + 0.497839i
\(531\) −664.116 −0.0542753
\(532\) 11885.6i 0.968622i
\(533\) 9638.38i 0.783273i
\(534\) 5201.80 0.421543
\(535\) 10487.5 11036.5i 0.847504 0.891865i
\(536\) 3877.84 0.312495
\(537\) 9639.42i 0.774622i
\(538\) 12902.0i 1.03391i
\(539\) 269.053 0.0215008
\(540\) −1061.48 + 1117.04i −0.0845904 + 0.0890181i
\(541\) 7383.29 0.586751 0.293376 0.955997i \(-0.405221\pi\)
0.293376 + 0.955997i \(0.405221\pi\)
\(542\) 13516.7i 1.07120i
\(543\) 10183.3i 0.804798i
\(544\) 3480.10 0.274280
\(545\) 2602.57 + 2473.12i 0.204554 + 0.194379i
\(546\) −6599.31 −0.517260
\(547\) 3354.90i 0.262240i 0.991367 + 0.131120i \(0.0418573\pi\)
−0.991367 + 0.131120i \(0.958143\pi\)
\(548\) 1808.54i 0.140980i
\(549\) 1236.15 0.0960976
\(550\) 380.363 19.4143i 0.0294886 0.00150514i
\(551\) −30766.2 −2.37874
\(552\) 3318.84i 0.255905i
\(553\) 17111.6i 1.31584i
\(554\) 11609.8 0.890346
\(555\) 483.469 + 459.422i 0.0369768 + 0.0351376i
\(556\) −394.369 −0.0300809
\(557\) 20771.8i 1.58012i −0.613028 0.790061i \(-0.710049\pi\)
0.613028 0.790061i \(-0.289951\pi\)
\(558\) 986.512i 0.0748430i
\(559\) 14398.1 1.08940
\(560\) −495.234 + 521.156i −0.0373705 + 0.0393266i
\(561\) −101.982 −0.00767500
\(562\) 5642.15i 0.423487i
\(563\) 7194.86i 0.538592i 0.963057 + 0.269296i \(0.0867910\pi\)
−0.963057 + 0.269296i \(0.913209\pi\)
\(564\) 5888.93 0.439660
\(565\) −12185.8 + 12823.6i −0.907361 + 0.954856i
\(566\) −11235.0 −0.834350
\(567\) 1798.96i 0.133244i
\(568\) 13251.5i 0.978913i
\(569\) −11549.5 −0.850931 −0.425466 0.904975i \(-0.639890\pi\)
−0.425466 + 0.904975i \(0.639890\pi\)
\(570\) −4337.32 4121.59i −0.318720 0.302867i
\(571\) 1482.54 0.108655 0.0543277 0.998523i \(-0.482698\pi\)
0.0543277 + 0.998523i \(0.482698\pi\)
\(572\) 532.068i 0.0388932i
\(573\) 10402.5i 0.758412i
\(574\) −6257.42 −0.455017
\(575\) 6193.50 316.125i 0.449194 0.0229275i
\(576\) 2598.82 0.187993
\(577\) 15264.0i 1.10130i 0.834737 + 0.550649i \(0.185620\pi\)
−0.834737 + 0.550649i \(0.814380\pi\)
\(578\) 7746.52i 0.557462i
\(579\) −5376.43 −0.385901
\(580\) −12141.2 11537.3i −0.869202 0.825968i
\(581\) 3862.76 0.275825
\(582\) 1962.11i 0.139746i
\(583\) 830.006i 0.0589628i
\(584\) −7140.66 −0.505963
\(585\) −4034.73 + 4245.92i −0.285155 + 0.300081i
\(586\) −9893.12 −0.697408
\(587\) 1736.89i 0.122128i −0.998134 0.0610639i \(-0.980551\pi\)
0.998134 0.0610639i \(-0.0194493\pi\)
\(588\) 2301.03i 0.161383i
\(589\) −6753.50 −0.472450
\(590\) 967.003 1017.62i 0.0674761 0.0710080i
\(591\) 5034.57 0.350414
\(592\) 57.5714i 0.00399691i
\(593\) 11764.8i 0.814707i −0.913271 0.407353i \(-0.866452\pi\)
0.913271 0.407353i \(-0.133548\pi\)
\(594\) −82.2653 −0.00568247
\(595\) 3417.19 + 3247.22i 0.235447 + 0.223736i
\(596\) 8705.42 0.598302
\(597\) 9324.69i 0.639253i
\(598\) 4913.96i 0.336032i
\(599\) 9451.99 0.644737 0.322369 0.946614i \(-0.395521\pi\)
0.322369 + 0.946614i \(0.395521\pi\)
\(600\) −426.249 8351.04i −0.0290026 0.568217i
\(601\) −3131.93 −0.212569 −0.106285 0.994336i \(-0.533895\pi\)
−0.106285 + 0.994336i \(0.533895\pi\)
\(602\) 9347.51i 0.632851i
\(603\) 1565.16i 0.105702i
\(604\) 3870.79 0.260762
\(605\) 10761.4 + 10226.1i 0.723159 + 0.687189i
\(606\) −176.063 −0.0118021
\(607\) 22700.8i 1.51795i −0.651120 0.758975i \(-0.725700\pi\)
0.651120 0.758975i \(-0.274300\pi\)
\(608\) 19218.2i 1.28191i
\(609\) 19553.1 1.30103
\(610\) −1799.93 + 1894.14i −0.119470 + 0.125724i
\(611\) 22384.0 1.48210
\(612\) 872.184i 0.0576077i
\(613\) 28911.6i 1.90494i 0.304629 + 0.952471i \(0.401468\pi\)
−0.304629 + 0.952471i \(0.598532\pi\)
\(614\) −13825.0 −0.908681
\(615\) −3825.70 + 4025.95i −0.250841 + 0.263971i
\(616\) −886.780 −0.0580023
\(617\) 5566.87i 0.363231i 0.983370 + 0.181616i \(0.0581326\pi\)
−0.983370 + 0.181616i \(0.941867\pi\)
\(618\) 8965.38i 0.583560i
\(619\) −4150.32 −0.269492 −0.134746 0.990880i \(-0.543022\pi\)
−0.134746 + 0.990880i \(0.543022\pi\)
\(620\) −2665.12 2532.56i −0.172635 0.164049i
\(621\) −1339.54 −0.0865600
\(622\) 12483.1i 0.804705i
\(623\) 22631.9i 1.45542i
\(624\) −505.603 −0.0324364
\(625\) −15543.8 + 1590.90i −0.994803 + 0.101818i
\(626\) 3747.96 0.239295
\(627\) 563.175i 0.0358709i
\(628\) 9030.46i 0.573813i
\(629\) 377.492 0.0239294
\(630\) 2756.53 + 2619.42i 0.174322 + 0.165651i
\(631\) −4090.09 −0.258041 −0.129021 0.991642i \(-0.541183\pi\)
−0.129021 + 0.991642i \(0.541183\pi\)
\(632\) 17180.2i 1.08132i
\(633\) 13419.8i 0.842637i
\(634\) 17030.7 1.06684
\(635\) 9219.85 9702.45i 0.576187 0.606346i
\(636\) −7098.50 −0.442569
\(637\) 8746.32i 0.544022i
\(638\) 894.150i 0.0554855i
\(639\) 5348.53 0.331118
\(640\) 7510.36 7903.47i 0.463864 0.488144i
\(641\) 3909.35 0.240890 0.120445 0.992720i \(-0.461568\pi\)
0.120445 + 0.992720i \(0.461568\pi\)
\(642\) 6951.24i 0.427327i
\(643\) 30539.5i 1.87303i 0.350624 + 0.936516i \(0.385969\pi\)
−0.350624 + 0.936516i \(0.614031\pi\)
\(644\) −5624.66 −0.344166
\(645\) −6014.08 5714.94i −0.367138 0.348877i
\(646\) −3386.58 −0.206259
\(647\) 12707.7i 0.772167i 0.922464 + 0.386083i \(0.126172\pi\)
−0.922464 + 0.386083i \(0.873828\pi\)
\(648\) 1806.17i 0.109496i
\(649\) −132.132 −0.00799170
\(650\) −631.115 12364.8i −0.0380836 0.746132i
\(651\) 4292.10 0.258403
\(652\) 4500.90i 0.270351i
\(653\) 12777.6i 0.765737i 0.923803 + 0.382869i \(0.125064\pi\)
−0.923803 + 0.382869i \(0.874936\pi\)
\(654\) 1639.21 0.0980095
\(655\) 2606.85 + 2477.18i 0.155508 + 0.147773i
\(656\) −479.410 −0.0285332
\(657\) 2882.08i 0.171143i
\(658\) 14532.1i 0.860976i
\(659\) −23563.5 −1.39287 −0.696435 0.717620i \(-0.745232\pi\)
−0.696435 + 0.717620i \(0.745232\pi\)
\(660\) −211.190 + 222.245i −0.0124554 + 0.0131074i
\(661\) −4361.31 −0.256634 −0.128317 0.991733i \(-0.540958\pi\)
−0.128317 + 0.991733i \(0.540958\pi\)
\(662\) 14796.7i 0.868715i
\(663\) 3315.21i 0.194196i
\(664\) −3878.25 −0.226665
\(665\) 17932.1 18870.7i 1.04568 1.10042i
\(666\) 304.510 0.0177170
\(667\) 14559.6i 0.845200i
\(668\) 1107.21i 0.0641304i
\(669\) 5260.25 0.303995
\(670\) −2398.28 2278.99i −0.138289 0.131410i
\(671\) 245.943 0.0141498
\(672\) 12213.9i 0.701131i
\(673\) 8203.52i 0.469870i −0.972011 0.234935i \(-0.924512\pi\)
0.972011 0.234935i \(-0.0754877\pi\)
\(674\) −12592.6 −0.719657
\(675\) 3370.61 172.041i 0.192200 0.00981015i
\(676\) −6081.37 −0.346004
\(677\) 28057.1i 1.59279i −0.604774 0.796397i \(-0.706737\pi\)
0.604774 0.796397i \(-0.293263\pi\)
\(678\) 8076.87i 0.457508i
\(679\) −8536.73 −0.482488
\(680\) −3430.89 3260.24i −0.193483 0.183860i
\(681\) −2810.70 −0.158159
\(682\) 196.275i 0.0110202i
\(683\) 3344.62i 0.187377i −0.995602 0.0936885i \(-0.970134\pi\)
0.995602 0.0936885i \(-0.0298658\pi\)
\(684\) 4816.46 0.269243
\(685\) −2728.59 + 2871.41i −0.152196 + 0.160162i
\(686\) 7283.91 0.405395
\(687\) 7746.17i 0.430182i
\(688\) 716.156i 0.0396849i
\(689\) −26981.7 −1.49190
\(690\) 1950.47 2052.56i 0.107613 0.113246i
\(691\) 12964.8 0.713757 0.356879 0.934151i \(-0.383841\pi\)
0.356879 + 0.934151i \(0.383841\pi\)
\(692\) 21061.5i 1.15699i
\(693\) 357.918i 0.0196193i
\(694\) 13342.7 0.729801
\(695\) 626.138 + 594.994i 0.0341737 + 0.0324740i
\(696\) −19631.5 −1.06915
\(697\) 3143.46i 0.170828i
\(698\) 8441.90i 0.457780i
\(699\) −6885.03 −0.372555
\(700\) 14153.1 722.392i 0.764193 0.0390055i
\(701\) −16162.1 −0.870806 −0.435403 0.900236i \(-0.643394\pi\)
−0.435403 + 0.900236i \(0.643394\pi\)
\(702\) 2674.27i 0.143780i
\(703\) 2084.63i 0.111839i
\(704\) 517.058 0.0276809
\(705\) −9349.82 8884.76i −0.499482 0.474638i
\(706\) 20696.2 1.10327
\(707\) 766.014i 0.0407481i
\(708\) 1130.03i 0.0599849i
\(709\) 14244.4 0.754529 0.377265 0.926105i \(-0.376865\pi\)
0.377265 + 0.926105i \(0.376865\pi\)
\(710\) −7787.87 + 8195.51i −0.411653 + 0.433200i
\(711\) −6934.22 −0.365757
\(712\) 22722.7i 1.19602i
\(713\) 3195.97i 0.167868i
\(714\) 2152.29 0.112812
\(715\) −802.744 + 844.762i −0.0419873 + 0.0441850i
\(716\) 16402.1 0.856109
\(717\) 6882.02i 0.358457i
\(718\) 8837.55i 0.459352i
\(719\) 27638.5 1.43358 0.716790 0.697289i \(-0.245611\pi\)
0.716790 + 0.697289i \(0.245611\pi\)
\(720\) 211.190 + 200.686i 0.0109314 + 0.0103877i
\(721\) −39006.4 −2.01480
\(722\) 7030.68i 0.362403i
\(723\) 1146.86i 0.0589934i
\(724\) 17327.4 0.889460
\(725\) 1869.93 + 36635.5i 0.0957895 + 1.87670i
\(726\) 6777.97 0.346493
\(727\) 2525.52i 0.128840i 0.997923 + 0.0644199i \(0.0205197\pi\)
−0.997923 + 0.0644199i \(0.979480\pi\)
\(728\) 28827.3i 1.46760i
\(729\) −729.000 −0.0370370
\(730\) 4416.19 + 4196.53i 0.223905 + 0.212768i
\(731\) −4695.79 −0.237592
\(732\) 2103.39i 0.106207i
\(733\) 8400.27i 0.423289i −0.977347 0.211645i \(-0.932118\pi\)
0.977347 0.211645i \(-0.0678820\pi\)
\(734\) −10355.9 −0.520765
\(735\) −3471.62 + 3653.34i −0.174221 + 0.183341i
\(736\) 9094.67 0.455481
\(737\) 311.401i 0.0155639i
\(738\) 2535.72i 0.126479i
\(739\) 19689.1 0.980074 0.490037 0.871702i \(-0.336983\pi\)
0.490037 + 0.871702i \(0.336983\pi\)
\(740\) 781.735 822.653i 0.0388340 0.0408667i
\(741\) 18307.6 0.907619
\(742\) 17517.0i 0.866671i
\(743\) 22526.6i 1.11227i −0.831091 0.556137i \(-0.812283\pi\)
0.831091 0.556137i \(-0.187717\pi\)
\(744\) −4309.31 −0.212348
\(745\) −13821.6 13134.1i −0.679708 0.645900i
\(746\) 18005.8 0.883699
\(747\) 1565.32i 0.0766696i
\(748\) 173.528i 0.00848239i
\(749\) 30243.3 1.47539
\(750\) −4644.25 + 5415.27i −0.226112 + 0.263650i
\(751\) 34691.1 1.68562 0.842808 0.538215i \(-0.180901\pi\)
0.842808 + 0.538215i \(0.180901\pi\)
\(752\) 1113.37i 0.0539902i
\(753\) 6779.95i 0.328121i
\(754\) −29066.8 −1.40392
\(755\) −6145.63 5839.95i −0.296242 0.281507i
\(756\) −3061.04 −0.147261
\(757\) 6619.98i 0.317843i −0.987291 0.158922i \(-0.949198\pi\)
0.987291 0.158922i \(-0.0508017\pi\)
\(758\) 19832.0i 0.950303i
\(759\) −266.512 −0.0127454
\(760\) −18004.0 + 18946.4i −0.859309 + 0.904288i
\(761\) −29368.7 −1.39897 −0.699483 0.714649i \(-0.746586\pi\)
−0.699483 + 0.714649i \(0.746586\pi\)
\(762\) 6111.03i 0.290524i
\(763\) 7131.84i 0.338388i
\(764\) −17700.5 −0.838194
\(765\) 1315.88 1384.76i 0.0621907 0.0654460i
\(766\) −10830.4 −0.510859
\(767\) 4295.31i 0.202209i
\(768\) 11908.1i 0.559503i
\(769\) −32677.4 −1.53235 −0.766174 0.642633i \(-0.777842\pi\)
−0.766174 + 0.642633i \(0.777842\pi\)
\(770\) 548.435 + 521.156i 0.0256678 + 0.0243911i
\(771\) −278.353 −0.0130021
\(772\) 9148.33i 0.426497i
\(773\) 28047.5i 1.30504i −0.757770 0.652522i \(-0.773711\pi\)
0.757770 0.652522i \(-0.226289\pi\)
\(774\) −3787.93 −0.175910
\(775\) 410.469 + 8041.87i 0.0190251 + 0.372739i
\(776\) 8570.96 0.396494
\(777\) 1324.86i 0.0611699i
\(778\) 10438.0i 0.481001i
\(779\) 17359.1 0.798402
\(780\) 7224.69 + 6865.34i 0.331648 + 0.315152i
\(781\) 1064.14 0.0487552
\(782\) 1602.64i