Properties

Label 225.4.p.b.32.12
Level $225$
Weight $4$
Character 225.32
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.p (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 32.12
Character \(\chi\) \(=\) 225.32
Dual form 225.4.p.b.218.12

$q$-expansion

\(f(q)\) \(=\) \(q+(2.79258 + 0.748271i) q^{2} +(-5.18419 - 0.352314i) q^{3} +(0.310415 + 0.179218i) q^{4} +(-14.2137 - 4.86305i) q^{6} +(-5.03374 + 18.7862i) q^{7} +(-15.6218 - 15.6218i) q^{8} +(26.7517 + 3.65293i) q^{9} +O(q^{10})\) \(q+(2.79258 + 0.748271i) q^{2} +(-5.18419 - 0.352314i) q^{3} +(0.310415 + 0.179218i) q^{4} +(-14.2137 - 4.86305i) q^{6} +(-5.03374 + 18.7862i) q^{7} +(-15.6218 - 15.6218i) q^{8} +(26.7517 + 3.65293i) q^{9} +(49.0377 - 28.3119i) q^{11} +(-1.54611 - 1.03846i) q^{12} +(0.616650 + 2.30137i) q^{13} +(-28.1143 + 48.6954i) q^{14} +(-33.3695 - 57.7977i) q^{16} +(92.5976 - 92.5976i) q^{17} +(71.9731 + 30.2187i) q^{18} -21.7774i q^{19} +(32.7146 - 95.6178i) q^{21} +(158.127 - 42.3700i) q^{22} +(98.8952 - 26.4989i) q^{23} +(75.4824 + 86.4900i) q^{24} +6.88818i q^{26} +(-137.399 - 28.3625i) q^{27} +(-4.92937 + 4.92937i) q^{28} +(-40.6009 - 70.3228i) q^{29} +(4.26447 - 7.38628i) q^{31} +(-4.19518 - 15.6566i) q^{32} +(-264.196 + 129.498i) q^{33} +(327.875 - 189.298i) q^{34} +(7.64946 + 5.92832i) q^{36} +(-8.92697 - 8.92697i) q^{37} +(16.2954 - 60.8153i) q^{38} +(-2.38603 - 12.1480i) q^{39} +(-28.1572 - 16.2566i) q^{41} +(162.906 - 242.541i) q^{42} +(428.714 + 114.874i) q^{43} +20.2960 q^{44} +296.002 q^{46} +(140.159 + 37.5556i) q^{47} +(152.631 + 311.391i) q^{48} +(-30.5356 - 17.6297i) q^{49} +(-512.667 + 447.420i) q^{51} +(-0.221029 + 0.824893i) q^{52} +(-82.9808 - 82.9808i) q^{53} +(-362.476 - 182.017i) q^{54} +(372.109 - 214.837i) q^{56} +(-7.67250 + 112.898i) q^{57} +(-60.7609 - 226.763i) q^{58} +(-129.436 + 224.189i) q^{59} +(-282.613 - 489.500i) q^{61} +(17.4358 - 17.4358i) q^{62} +(-203.286 + 484.175i) q^{63} +487.051i q^{64} +(-834.688 + 163.944i) q^{66} +(-434.879 + 116.526i) q^{67} +(45.3388 - 12.1485i) q^{68} +(-522.028 + 102.533i) q^{69} +16.2978i q^{71} +(-360.844 - 474.974i) q^{72} +(-59.2407 + 59.2407i) q^{73} +(-18.2495 - 31.6091i) q^{74} +(3.90290 - 6.76003i) q^{76} +(285.030 + 1063.75i) q^{77} +(2.42681 - 35.7097i) q^{78} +(472.049 - 272.538i) q^{79} +(702.312 + 195.445i) q^{81} +(-66.4671 - 66.4671i) q^{82} +(260.644 - 972.735i) q^{83} +(27.2915 - 23.8181i) q^{84} +(1111.26 + 641.588i) q^{86} +(185.707 + 378.871i) q^{87} +(-1208.34 - 323.773i) q^{88} -844.831 q^{89} -46.3380 q^{91} +(35.4476 + 9.49816i) q^{92} +(-24.7101 + 36.7895i) q^{93} +(363.305 + 209.754i) q^{94} +(16.2326 + 82.6450i) q^{96} +(105.374 - 393.261i) q^{97} +(-72.0814 - 72.0814i) q^{98} +(1415.27 - 578.262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.79258 + 0.748271i 0.987328 + 0.264554i 0.716128 0.697969i \(-0.245913\pi\)
0.271200 + 0.962523i \(0.412580\pi\)
\(3\) −5.18419 0.352314i −0.997699 0.0678029i
\(4\) 0.310415 + 0.179218i 0.0388018 + 0.0224022i
\(5\) 0 0
\(6\) −14.2137 4.86305i −0.967118 0.330889i
\(7\) −5.03374 + 18.7862i −0.271797 + 1.01436i 0.686161 + 0.727450i \(0.259294\pi\)
−0.957958 + 0.286909i \(0.907372\pi\)
\(8\) −15.6218 15.6218i −0.690390 0.690390i
\(9\) 26.7517 + 3.65293i 0.990806 + 0.135294i
\(10\) 0 0
\(11\) 49.0377 28.3119i 1.34413 0.776033i 0.356718 0.934212i \(-0.383896\pi\)
0.987410 + 0.158179i \(0.0505623\pi\)
\(12\) −1.54611 1.03846i −0.0371936 0.0249816i
\(13\) 0.616650 + 2.30137i 0.0131560 + 0.0490988i 0.972192 0.234186i \(-0.0752425\pi\)
−0.959036 + 0.283285i \(0.908576\pi\)
\(14\) −28.1143 + 48.6954i −0.536705 + 0.929600i
\(15\) 0 0
\(16\) −33.3695 57.7977i −0.521399 0.903089i
\(17\) 92.5976 92.5976i 1.32107 1.32107i 0.408161 0.912910i \(-0.366170\pi\)
0.912910 0.408161i \(-0.133830\pi\)
\(18\) 71.9731 + 30.2187i 0.942457 + 0.395700i
\(19\) 21.7774i 0.262952i −0.991319 0.131476i \(-0.958028\pi\)
0.991319 0.131476i \(-0.0419716\pi\)
\(20\) 0 0
\(21\) 32.7146 95.6178i 0.339948 0.993596i
\(22\) 158.127 42.3700i 1.53240 0.410605i
\(23\) 98.8952 26.4989i 0.896569 0.240235i 0.219027 0.975719i \(-0.429712\pi\)
0.677542 + 0.735484i \(0.263045\pi\)
\(24\) 75.4824 + 86.4900i 0.641991 + 0.735612i
\(25\) 0 0
\(26\) 6.88818i 0.0519571i
\(27\) −137.399 28.3625i −0.979352 0.202162i
\(28\) −4.92937 + 4.92937i −0.0332701 + 0.0332701i
\(29\) −40.6009 70.3228i −0.259979 0.450297i 0.706257 0.707956i \(-0.250382\pi\)
−0.966236 + 0.257659i \(0.917049\pi\)
\(30\) 0 0
\(31\) 4.26447 7.38628i 0.0247071 0.0427940i −0.853407 0.521244i \(-0.825468\pi\)
0.878115 + 0.478450i \(0.158801\pi\)
\(32\) −4.19518 15.6566i −0.0231753 0.0864914i
\(33\) −264.196 + 129.498i −1.39365 + 0.683111i
\(34\) 327.875 189.298i 1.65382 0.954836i
\(35\) 0 0
\(36\) 7.64946 + 5.92832i 0.0354142 + 0.0274459i
\(37\) −8.92697 8.92697i −0.0396645 0.0396645i 0.686996 0.726661i \(-0.258929\pi\)
−0.726661 + 0.686996i \(0.758929\pi\)
\(38\) 16.2954 60.8153i 0.0695648 0.259619i
\(39\) −2.38603 12.1480i −0.00979667 0.0498778i
\(40\) 0 0
\(41\) −28.1572 16.2566i −0.107254 0.0619232i 0.445413 0.895325i \(-0.353057\pi\)
−0.552668 + 0.833402i \(0.686390\pi\)
\(42\) 162.906 242.541i 0.598499 0.891070i
\(43\) 428.714 + 114.874i 1.52042 + 0.407396i 0.919882 0.392196i \(-0.128285\pi\)
0.600543 + 0.799593i \(0.294951\pi\)
\(44\) 20.2960 0.0695395
\(45\) 0 0
\(46\) 296.002 0.948762
\(47\) 140.159 + 37.5556i 0.434986 + 0.116554i 0.469666 0.882844i \(-0.344374\pi\)
−0.0346799 + 0.999398i \(0.511041\pi\)
\(48\) 152.631 + 311.391i 0.458967 + 0.936363i
\(49\) −30.5356 17.6297i −0.0890251 0.0513987i
\(50\) 0 0
\(51\) −512.667 + 447.420i −1.40760 + 1.22846i
\(52\) −0.221029 + 0.824893i −0.000589447 + 0.00219985i
\(53\) −82.9808 82.9808i −0.215062 0.215062i 0.591352 0.806414i \(-0.298595\pi\)
−0.806414 + 0.591352i \(0.798595\pi\)
\(54\) −362.476 182.017i −0.913459 0.458691i
\(55\) 0 0
\(56\) 372.109 214.837i 0.887950 0.512658i
\(57\) −7.67250 + 112.898i −0.0178289 + 0.262347i
\(58\) −60.7609 226.763i −0.137557 0.513369i
\(59\) −129.436 + 224.189i −0.285612 + 0.494695i −0.972757 0.231825i \(-0.925530\pi\)
0.687145 + 0.726520i \(0.258864\pi\)
\(60\) 0 0
\(61\) −282.613 489.500i −0.593195 1.02744i −0.993799 0.111192i \(-0.964533\pi\)
0.400604 0.916251i \(-0.368800\pi\)
\(62\) 17.4358 17.4358i 0.0357153 0.0357153i
\(63\) −203.286 + 484.175i −0.406534 + 0.968260i
\(64\) 487.051i 0.951271i
\(65\) 0 0
\(66\) −834.688 + 163.944i −1.55671 + 0.305759i
\(67\) −434.879 + 116.526i −0.792970 + 0.212476i −0.632495 0.774564i \(-0.717969\pi\)
−0.160475 + 0.987040i \(0.551302\pi\)
\(68\) 45.3388 12.1485i 0.0808549 0.0216650i
\(69\) −522.028 + 102.533i −0.910794 + 0.178892i
\(70\) 0 0
\(71\) 16.2978i 0.0272422i 0.999907 + 0.0136211i \(0.00433587\pi\)
−0.999907 + 0.0136211i \(0.995664\pi\)
\(72\) −360.844 474.974i −0.590637 0.777448i
\(73\) −59.2407 + 59.2407i −0.0949809 + 0.0949809i −0.753001 0.658020i \(-0.771394\pi\)
0.658020 + 0.753001i \(0.271394\pi\)
\(74\) −18.2495 31.6091i −0.0286684 0.0496552i
\(75\) 0 0
\(76\) 3.90290 6.76003i 0.00589071 0.0102030i
\(77\) 285.030 + 1063.75i 0.421846 + 1.57435i
\(78\) 2.42681 35.7097i 0.00352284 0.0518375i
\(79\) 472.049 272.538i 0.672274 0.388138i −0.124663 0.992199i \(-0.539785\pi\)
0.796938 + 0.604061i \(0.206452\pi\)
\(80\) 0 0
\(81\) 702.312 + 195.445i 0.963391 + 0.268100i
\(82\) −66.4671 66.4671i −0.0895129 0.0895129i
\(83\) 260.644 972.735i 0.344691 1.28640i −0.548282 0.836294i \(-0.684718\pi\)
0.892973 0.450110i \(-0.148615\pi\)
\(84\) 27.2915 23.8181i 0.0354494 0.0309377i
\(85\) 0 0
\(86\) 1111.26 + 641.588i 1.39338 + 0.804467i
\(87\) 185.707 + 378.871i 0.228849 + 0.466888i
\(88\) −1208.34 323.773i −1.46374 0.392208i
\(89\) −844.831 −1.00620 −0.503101 0.864228i \(-0.667808\pi\)
−0.503101 + 0.864228i \(0.667808\pi\)
\(90\) 0 0
\(91\) −46.3380 −0.0533796
\(92\) 35.4476 + 9.49816i 0.0401703 + 0.0107636i
\(93\) −24.7101 + 36.7895i −0.0275518 + 0.0410203i
\(94\) 363.305 + 209.754i 0.398639 + 0.230154i
\(95\) 0 0
\(96\) 16.2326 + 82.6450i 0.0172576 + 0.0878637i
\(97\) 105.374 393.261i 0.110300 0.411645i −0.888592 0.458698i \(-0.848316\pi\)
0.998892 + 0.0470524i \(0.0149828\pi\)
\(98\) −72.0814 72.0814i −0.0742992 0.0742992i
\(99\) 1415.27 578.262i 1.43676 0.587046i
\(100\) 0 0
\(101\) −398.138 + 229.865i −0.392240 + 0.226460i −0.683130 0.730297i \(-0.739382\pi\)
0.290890 + 0.956756i \(0.406049\pi\)
\(102\) −1766.46 + 865.845i −1.71476 + 0.840504i
\(103\) −360.103 1343.92i −0.344485 1.28564i −0.893212 0.449635i \(-0.851554\pi\)
0.548727 0.836001i \(-0.315113\pi\)
\(104\) 26.3182 45.5845i 0.0248146 0.0429801i
\(105\) 0 0
\(106\) −169.639 293.823i −0.155441 0.269232i
\(107\) −319.287 + 319.287i −0.288473 + 0.288473i −0.836476 0.548003i \(-0.815388\pi\)
0.548003 + 0.836476i \(0.315388\pi\)
\(108\) −37.5677 33.4286i −0.0334718 0.0297839i
\(109\) 1126.24i 0.989672i −0.868986 0.494836i \(-0.835228\pi\)
0.868986 0.494836i \(-0.164772\pi\)
\(110\) 0 0
\(111\) 43.1341 + 49.4243i 0.0368838 + 0.0422625i
\(112\) 1253.77 335.947i 1.05777 0.283429i
\(113\) 1458.69 390.853i 1.21435 0.325384i 0.405883 0.913925i \(-0.366964\pi\)
0.808467 + 0.588541i \(0.200297\pi\)
\(114\) −105.905 + 309.537i −0.0870077 + 0.254305i
\(115\) 0 0
\(116\) 29.1056i 0.0232965i
\(117\) 8.08972 + 63.8182i 0.00639226 + 0.0504273i
\(118\) −529.215 + 529.215i −0.412866 + 0.412866i
\(119\) 1273.44 + 2205.67i 0.980977 + 1.69910i
\(120\) 0 0
\(121\) 937.629 1624.02i 0.704455 1.22015i
\(122\) −422.942 1578.44i −0.313864 1.17136i
\(123\) 140.245 + 94.1974i 0.102809 + 0.0690528i
\(124\) 2.64751 1.52854i 0.00191736 0.00110699i
\(125\) 0 0
\(126\) −929.988 + 1199.99i −0.657539 + 0.848440i
\(127\) 638.135 + 638.135i 0.445869 + 0.445869i 0.893979 0.448110i \(-0.147903\pi\)
−0.448110 + 0.893979i \(0.647903\pi\)
\(128\) −398.007 + 1485.38i −0.274837 + 1.02571i
\(129\) −2182.06 746.569i −1.48930 0.509548i
\(130\) 0 0
\(131\) 2261.94 + 1305.93i 1.50860 + 0.870992i 0.999950 + 0.0100207i \(0.00318975\pi\)
0.508653 + 0.860972i \(0.330144\pi\)
\(132\) −105.218 7.15058i −0.0693795 0.00471498i
\(133\) 409.115 + 109.622i 0.266727 + 0.0714694i
\(134\) −1301.63 −0.839132
\(135\) 0 0
\(136\) −2893.07 −1.82411
\(137\) −942.088 252.432i −0.587504 0.157421i −0.0471916 0.998886i \(-0.515027\pi\)
−0.540312 + 0.841465i \(0.681694\pi\)
\(138\) −1534.53 104.286i −0.946579 0.0643288i
\(139\) −1106.34 638.748i −0.675099 0.389769i 0.122907 0.992418i \(-0.460778\pi\)
−0.798006 + 0.602649i \(0.794112\pi\)
\(140\) 0 0
\(141\) −713.382 244.075i −0.426082 0.145779i
\(142\) −12.1952 + 45.5131i −0.00720703 + 0.0268970i
\(143\) 95.3952 + 95.3952i 0.0557856 + 0.0557856i
\(144\) −681.562 1668.09i −0.394422 0.965327i
\(145\) 0 0
\(146\) −209.763 + 121.107i −0.118905 + 0.0686497i
\(147\) 152.091 + 102.154i 0.0853352 + 0.0573165i
\(148\) −1.17119 4.37094i −0.000650480 0.00242763i
\(149\) 69.6092 120.567i 0.0382725 0.0662900i −0.846255 0.532779i \(-0.821148\pi\)
0.884527 + 0.466489i \(0.154481\pi\)
\(150\) 0 0
\(151\) 706.994 + 1224.55i 0.381022 + 0.659950i 0.991209 0.132308i \(-0.0422388\pi\)
−0.610186 + 0.792258i \(0.708905\pi\)
\(152\) −340.201 + 340.201i −0.181539 + 0.181539i
\(153\) 2815.40 2138.89i 1.48766 1.13019i
\(154\) 3183.88i 1.66600i
\(155\) 0 0
\(156\) 1.43648 4.19853i 0.000737247 0.00215482i
\(157\) −2293.99 + 614.674i −1.16612 + 0.312461i −0.789407 0.613870i \(-0.789612\pi\)
−0.376712 + 0.926330i \(0.622945\pi\)
\(158\) 1522.17 407.864i 0.766438 0.205367i
\(159\) 400.953 + 459.424i 0.199985 + 0.229149i
\(160\) 0 0
\(161\) 1991.25i 0.974738i
\(162\) 1815.02 + 1071.32i 0.880256 + 0.519571i
\(163\) −940.543 + 940.543i −0.451957 + 0.451957i −0.896004 0.444046i \(-0.853543\pi\)
0.444046 + 0.896004i \(0.353543\pi\)
\(164\) −5.82694 10.0926i −0.00277444 0.00480547i
\(165\) 0 0
\(166\) 1455.74 2521.41i 0.680646 1.17891i
\(167\) 973.893 + 3634.62i 0.451270 + 1.68416i 0.698828 + 0.715290i \(0.253705\pi\)
−0.247558 + 0.968873i \(0.579628\pi\)
\(168\) −2004.78 + 982.659i −0.920666 + 0.451273i
\(169\) 1897.74 1095.66i 0.863788 0.498708i
\(170\) 0 0
\(171\) 79.5514 582.584i 0.0355757 0.260534i
\(172\) 112.492 + 112.492i 0.0498686 + 0.0498686i
\(173\) −1129.62 + 4215.81i −0.496437 + 1.85273i 0.0253882 + 0.999678i \(0.491918\pi\)
−0.521826 + 0.853052i \(0.674749\pi\)
\(174\) 235.105 + 1196.99i 0.102432 + 0.521515i
\(175\) 0 0
\(176\) −3272.73 1889.51i −1.40165 0.809245i
\(177\) 750.006 1116.64i 0.318497 0.474191i
\(178\) −2359.26 632.163i −0.993451 0.266194i
\(179\) 2857.68 1.19326 0.596628 0.802518i \(-0.296507\pi\)
0.596628 + 0.802518i \(0.296507\pi\)
\(180\) 0 0
\(181\) −1459.11 −0.599199 −0.299599 0.954065i \(-0.596853\pi\)
−0.299599 + 0.954065i \(0.596853\pi\)
\(182\) −129.403 34.6734i −0.0527031 0.0141218i
\(183\) 1292.66 + 2637.23i 0.522166 + 1.06530i
\(184\) −1958.88 1130.96i −0.784838 0.453127i
\(185\) 0 0
\(186\) −96.5336 + 84.2478i −0.0380548 + 0.0332116i
\(187\) 1919.15 7162.38i 0.750495 2.80088i
\(188\) 36.7768 + 36.7768i 0.0142672 + 0.0142672i
\(189\) 1224.46 2438.44i 0.471249 0.938468i
\(190\) 0 0
\(191\) 610.123 352.255i 0.231136 0.133446i −0.379960 0.925003i \(-0.624062\pi\)
0.611096 + 0.791557i \(0.290729\pi\)
\(192\) 171.595 2524.96i 0.0644989 0.949081i
\(193\) −396.828 1480.98i −0.148001 0.552349i −0.999603 0.0281599i \(-0.991035\pi\)
0.851602 0.524189i \(-0.175631\pi\)
\(194\) 588.531 1019.37i 0.217804 0.377248i
\(195\) 0 0
\(196\) −6.31913 10.9451i −0.00230289 0.00398872i
\(197\) 989.475 989.475i 0.357854 0.357854i −0.505168 0.863021i \(-0.668569\pi\)
0.863021 + 0.505168i \(0.168569\pi\)
\(198\) 4384.94 555.844i 1.57386 0.199506i
\(199\) 2035.66i 0.725146i 0.931955 + 0.362573i \(0.118102\pi\)
−0.931955 + 0.362573i \(0.881898\pi\)
\(200\) 0 0
\(201\) 2295.55 450.877i 0.805551 0.158221i
\(202\) −1283.84 + 344.003i −0.447180 + 0.119822i
\(203\) 1525.47 408.749i 0.527424 0.141323i
\(204\) −239.325 + 47.0066i −0.0821378 + 0.0161330i
\(205\) 0 0
\(206\) 4022.47i 1.36048i
\(207\) 2742.42 347.634i 0.920828 0.116726i
\(208\) 112.436 112.436i 0.0374811 0.0374811i
\(209\) −616.560 1067.91i −0.204059 0.353441i
\(210\) 0 0
\(211\) −688.380 + 1192.31i −0.224597 + 0.389014i −0.956199 0.292719i \(-0.905440\pi\)
0.731601 + 0.681733i \(0.238773\pi\)
\(212\) −10.8868 40.6301i −0.00352693 0.0131627i
\(213\) 5.74196 84.4912i 0.00184710 0.0271795i
\(214\) −1130.55 + 652.723i −0.361134 + 0.208501i
\(215\) 0 0
\(216\) 1703.35 + 2589.49i 0.536565 + 0.815706i
\(217\) 117.294 + 117.294i 0.0366932 + 0.0366932i
\(218\) 842.733 3145.12i 0.261821 0.977131i
\(219\) 327.987 286.244i 0.101202 0.0883223i
\(220\) 0 0
\(221\) 270.201 + 156.001i 0.0822430 + 0.0474830i
\(222\) 83.4728 + 170.297i 0.0252357 + 0.0514847i
\(223\) 3795.71 + 1017.06i 1.13982 + 0.305413i 0.778878 0.627176i \(-0.215789\pi\)
0.360940 + 0.932589i \(0.382456\pi\)
\(224\) 315.246 0.0940323
\(225\) 0 0
\(226\) 4365.96 1.28504
\(227\) 872.812 + 233.869i 0.255201 + 0.0683809i 0.384151 0.923270i \(-0.374494\pi\)
−0.128950 + 0.991651i \(0.541161\pi\)
\(228\) −22.6151 + 33.6703i −0.00656895 + 0.00978012i
\(229\) 3128.15 + 1806.04i 0.902682 + 0.521164i 0.878069 0.478533i \(-0.158831\pi\)
0.0246126 + 0.999697i \(0.492165\pi\)
\(230\) 0 0
\(231\) −1102.88 5615.09i −0.314130 1.59933i
\(232\) −464.308 + 1732.82i −0.131394 + 0.490368i
\(233\) −2992.27 2992.27i −0.841332 0.841332i 0.147700 0.989032i \(-0.452813\pi\)
−0.989032 + 0.147700i \(0.952813\pi\)
\(234\) −25.1621 + 184.271i −0.00702947 + 0.0514794i
\(235\) 0 0
\(236\) −80.3575 + 46.3945i −0.0221645 + 0.0127967i
\(237\) −2543.21 + 1246.58i −0.697044 + 0.341662i
\(238\) 1905.76 + 7112.39i 0.519042 + 1.93709i
\(239\) 1931.06 3344.69i 0.522635 0.905230i −0.477018 0.878893i \(-0.658282\pi\)
0.999653 0.0263367i \(-0.00838419\pi\)
\(240\) 0 0
\(241\) 858.250 + 1486.53i 0.229397 + 0.397328i 0.957630 0.288003i \(-0.0929912\pi\)
−0.728232 + 0.685330i \(0.759658\pi\)
\(242\) 3833.62 3833.62i 1.01832 1.01832i
\(243\) −3572.07 1260.66i −0.942996 0.332803i
\(244\) 202.597i 0.0531556i
\(245\) 0 0
\(246\) 321.161 + 367.996i 0.0832377 + 0.0953762i
\(247\) 50.1178 13.4290i 0.0129106 0.00345939i
\(248\) −182.005 + 48.7681i −0.0466021 + 0.0124870i
\(249\) −1693.94 + 4951.02i −0.431120 + 1.26007i
\(250\) 0 0
\(251\) 2285.88i 0.574836i −0.957805 0.287418i \(-0.907203\pi\)
0.957805 0.287418i \(-0.0927968\pi\)
\(252\) −149.876 + 113.863i −0.0374655 + 0.0284630i
\(253\) 4099.36 4099.36i 1.01867 1.01867i
\(254\) 1304.55 + 2259.54i 0.322262 + 0.558175i
\(255\) 0 0
\(256\) −274.734 + 475.854i −0.0670738 + 0.116175i
\(257\) −988.996 3690.98i −0.240046 0.895865i −0.975809 0.218625i \(-0.929843\pi\)
0.735763 0.677239i \(-0.236824\pi\)
\(258\) −5534.96 3717.63i −1.33563 0.897091i
\(259\) 212.640 122.768i 0.0510147 0.0294533i
\(260\) 0 0
\(261\) −829.260 2029.57i −0.196666 0.481330i
\(262\) 5339.48 + 5339.48i 1.25906 + 1.25906i
\(263\) −1276.64 + 4764.50i −0.299320 + 1.11708i 0.638405 + 0.769701i \(0.279595\pi\)
−0.937725 + 0.347378i \(0.887072\pi\)
\(264\) 6150.18 + 2104.21i 1.43378 + 0.490551i
\(265\) 0 0
\(266\) 1060.46 + 612.257i 0.244440 + 0.141127i
\(267\) 4379.77 + 297.646i 1.00389 + 0.0682234i
\(268\) −155.876 41.7669i −0.0355286 0.00951986i
\(269\) −6569.52 −1.48904 −0.744518 0.667602i \(-0.767321\pi\)
−0.744518 + 0.667602i \(0.767321\pi\)
\(270\) 0 0
\(271\) −1603.65 −0.359465 −0.179733 0.983715i \(-0.557523\pi\)
−0.179733 + 0.983715i \(0.557523\pi\)
\(272\) −8441.86 2261.99i −1.88185 0.504240i
\(273\) 240.225 + 16.3255i 0.0532567 + 0.00361929i
\(274\) −2441.97 1409.87i −0.538412 0.310852i
\(275\) 0 0
\(276\) −180.421 61.7290i −0.0393481 0.0134625i
\(277\) −2276.92 + 8497.59i −0.493888 + 1.84322i 0.0422830 + 0.999106i \(0.486537\pi\)
−0.536171 + 0.844109i \(0.680130\pi\)
\(278\) −2611.60 2611.60i −0.563430 0.563430i
\(279\) 141.064 182.018i 0.0302697 0.0390578i
\(280\) 0 0
\(281\) −5805.61 + 3351.87i −1.23250 + 0.711586i −0.967551 0.252675i \(-0.918690\pi\)
−0.264953 + 0.964261i \(0.585356\pi\)
\(282\) −1809.54 1215.40i −0.382116 0.256653i
\(283\) −295.723 1103.65i −0.0621163 0.231821i 0.927888 0.372859i \(-0.121623\pi\)
−0.990004 + 0.141038i \(0.954956\pi\)
\(284\) −2.92087 + 5.05909i −0.000610287 + 0.00105705i
\(285\) 0 0
\(286\) 195.018 + 337.781i 0.0403204 + 0.0698370i
\(287\) 447.135 447.135i 0.0919636 0.0919636i
\(288\) −55.0358 434.167i −0.0112605 0.0888316i
\(289\) 12235.6i 2.49046i
\(290\) 0 0
\(291\) −684.830 + 2001.62i −0.137957 + 0.403219i
\(292\) −29.0062 + 7.77218i −0.00581322 + 0.00155765i
\(293\) −6076.51 + 1628.20i −1.21158 + 0.324642i −0.807382 0.590029i \(-0.799116\pi\)
−0.404199 + 0.914671i \(0.632450\pi\)
\(294\) 348.289 + 399.080i 0.0690905 + 0.0791660i
\(295\) 0 0
\(296\) 278.910i 0.0547679i
\(297\) −7540.74 + 2499.20i −1.47326 + 0.488278i
\(298\) 284.606 284.606i 0.0553248 0.0553248i
\(299\) 121.967 + 211.254i 0.0235905 + 0.0408599i
\(300\) 0 0
\(301\) −4316.07 + 7475.65i −0.826492 + 1.43153i
\(302\) 1058.05 + 3948.68i 0.201602 + 0.752388i
\(303\) 2145.01 1051.40i 0.406692 0.199344i
\(304\) −1258.68 + 726.702i −0.237469 + 0.137103i
\(305\) 0 0
\(306\) 9462.71 3866.36i 1.76780 0.722304i
\(307\) −4998.67 4998.67i −0.929281 0.929281i 0.0683782 0.997659i \(-0.478218\pi\)
−0.997659 + 0.0683782i \(0.978218\pi\)
\(308\) −102.165 + 381.285i −0.0189006 + 0.0705380i
\(309\) 1393.36 + 7094.02i 0.256523 + 1.30603i
\(310\) 0 0
\(311\) −2626.45 1516.38i −0.478882 0.276483i 0.241068 0.970508i \(-0.422502\pi\)
−0.719950 + 0.694025i \(0.755835\pi\)
\(312\) −152.499 + 227.047i −0.0276717 + 0.0411987i
\(313\) 4163.08 + 1115.49i 0.751793 + 0.201442i 0.614313 0.789062i \(-0.289433\pi\)
0.137480 + 0.990505i \(0.456100\pi\)
\(314\) −6866.12 −1.23400
\(315\) 0 0
\(316\) 195.375 0.0347806
\(317\) 4660.18 + 1248.69i 0.825684 + 0.221241i 0.646830 0.762634i \(-0.276094\pi\)
0.178854 + 0.983876i \(0.442761\pi\)
\(318\) 775.922 + 1583.00i 0.136829 + 0.279152i
\(319\) −3981.95 2298.98i −0.698891 0.403505i
\(320\) 0 0
\(321\) 1767.74 1542.76i 0.307369 0.268250i
\(322\) −1490.00 + 5560.74i −0.257870 + 0.962385i
\(323\) −2016.54 2016.54i −0.347378 0.347378i
\(324\) 182.981 + 186.536i 0.0313753 + 0.0319849i
\(325\) 0 0
\(326\) −3330.33 + 1922.77i −0.565797 + 0.326663i
\(327\) −396.791 + 5838.65i −0.0671027 + 0.987395i
\(328\) 185.909 + 693.821i 0.0312960 + 0.116798i
\(329\) −1411.05 + 2444.01i −0.236455 + 0.409553i
\(330\) 0 0
\(331\) 5632.10 + 9755.08i 0.935251 + 1.61990i 0.774186 + 0.632958i \(0.218160\pi\)
0.161065 + 0.986944i \(0.448507\pi\)
\(332\) 255.239 255.239i 0.0421930 0.0421930i
\(333\) −206.202 271.422i −0.0339334 0.0446661i
\(334\) 10878.7i 1.78221i
\(335\) 0 0
\(336\) −6618.16 + 1299.89i −1.07455 + 0.211057i
\(337\) −2284.24 + 612.060i −0.369230 + 0.0989348i −0.438663 0.898652i \(-0.644548\pi\)
0.0694329 + 0.997587i \(0.477881\pi\)
\(338\) 6119.46 1639.70i 0.984777 0.263870i
\(339\) −7699.81 + 1512.34i −1.23362 + 0.242299i
\(340\) 0 0
\(341\) 482.941i 0.0766942i
\(342\) 658.085 1567.39i 0.104050 0.247821i
\(343\) −4232.18 + 4232.18i −0.666229 + 0.666229i
\(344\) −4902.73 8491.79i −0.768424 1.33095i
\(345\) 0 0
\(346\) −6309.14 + 10927.7i −0.980293 + 1.69792i
\(347\) 266.565 + 994.834i 0.0412391 + 0.153906i 0.983475 0.181043i \(-0.0579474\pi\)
−0.942236 + 0.334950i \(0.891281\pi\)
\(348\) −10.2543 + 150.889i −0.00157957 + 0.0232429i
\(349\) −4729.47 + 2730.56i −0.725394 + 0.418807i −0.816735 0.577013i \(-0.804218\pi\)
0.0913406 + 0.995820i \(0.470885\pi\)
\(350\) 0 0
\(351\) −19.4546 333.696i −0.00295843 0.0507447i
\(352\) −648.991 648.991i −0.0982708 0.0982708i
\(353\) 172.316 643.090i 0.0259814 0.0969638i −0.951718 0.306975i \(-0.900683\pi\)
0.977699 + 0.210011i \(0.0673500\pi\)
\(354\) 2930.00 2557.10i 0.439909 0.383922i
\(355\) 0 0
\(356\) −262.248 151.409i −0.0390425 0.0225412i
\(357\) −5824.69 11883.3i −0.863516 1.76171i
\(358\) 7980.30 + 2138.31i 1.17813 + 0.315680i
\(359\) 6703.88 0.985563 0.492781 0.870153i \(-0.335980\pi\)
0.492781 + 0.870153i \(0.335980\pi\)
\(360\) 0 0
\(361\) 6384.74 0.930856
\(362\) −4074.69 1091.81i −0.591605 0.158520i
\(363\) −5433.02 + 8088.90i −0.785563 + 1.16958i
\(364\) −14.3840 8.30460i −0.00207122 0.00119582i
\(365\) 0 0
\(366\) 1636.51 + 8331.95i 0.233720 + 1.18994i
\(367\) −845.191 + 3154.29i −0.120214 + 0.448645i −0.999624 0.0274202i \(-0.991271\pi\)
0.879410 + 0.476065i \(0.157937\pi\)
\(368\) −4831.66 4831.66i −0.684423 0.684423i
\(369\) −693.871 537.748i −0.0978901 0.0758646i
\(370\) 0 0
\(371\) 1976.60 1141.19i 0.276603 0.159697i
\(372\) −14.2637 + 6.99149i −0.00198801 + 0.000974440i
\(373\) −1093.97 4082.74i −0.151859 0.566747i −0.999354 0.0359425i \(-0.988557\pi\)
0.847495 0.530804i \(-0.178110\pi\)
\(374\) 10718.8 18565.5i 1.48197 2.56684i
\(375\) 0 0
\(376\) −1602.85 2776.22i −0.219842 0.380778i
\(377\) 136.802 136.802i 0.0186888 0.0186888i
\(378\) 5244.01 5893.32i 0.713553 0.801904i
\(379\) 2005.61i 0.271824i −0.990721 0.135912i \(-0.956604\pi\)
0.990721 0.135912i \(-0.0433965\pi\)
\(380\) 0 0
\(381\) −3083.39 3533.04i −0.414612 0.475074i
\(382\) 1967.40 527.164i 0.263511 0.0706074i
\(383\) −1133.16 + 303.630i −0.151180 + 0.0405085i −0.333615 0.942709i \(-0.608269\pi\)
0.182435 + 0.983218i \(0.441602\pi\)
\(384\) 2586.67 7560.29i 0.343751 1.00471i
\(385\) 0 0
\(386\) 4432.70i 0.584504i
\(387\) 11049.2 + 4639.13i 1.45133 + 0.609355i
\(388\) 103.189 103.189i 0.0135016 0.0135016i
\(389\) 5874.10 + 10174.2i 0.765627 + 1.32610i 0.939915 + 0.341410i \(0.110904\pi\)
−0.174288 + 0.984695i \(0.555762\pi\)
\(390\) 0 0
\(391\) 6703.72 11611.2i 0.867064 1.50180i
\(392\) 201.612 + 752.427i 0.0259769 + 0.0969472i
\(393\) −11266.3 7567.13i −1.44608 0.971276i
\(394\) 3503.59 2022.80i 0.447990 0.258647i
\(395\) 0 0
\(396\) 542.954 + 74.1400i 0.0689001 + 0.00940826i
\(397\) −10419.9 10419.9i −1.31728 1.31728i −0.915919 0.401363i \(-0.868537\pi\)
−0.401363 0.915919i \(-0.631463\pi\)
\(398\) −1523.22 + 5684.75i −0.191840 + 0.715957i
\(399\) −2082.31 712.439i −0.261268 0.0893898i
\(400\) 0 0
\(401\) −4827.90 2787.39i −0.601231 0.347121i 0.168295 0.985737i \(-0.446174\pi\)
−0.769526 + 0.638616i \(0.779507\pi\)
\(402\) 6747.90 + 458.583i 0.837201 + 0.0568956i
\(403\) 19.6282 + 5.25937i 0.00242618 + 0.000650093i
\(404\) −164.784 −0.0202928
\(405\) 0 0
\(406\) 4565.86 0.558128
\(407\) −690.498 185.018i −0.0840951 0.0225332i
\(408\) 14998.2 + 1019.27i 1.81991 + 0.123680i
\(409\) 8856.21 + 5113.13i 1.07069 + 0.618162i 0.928369 0.371659i \(-0.121211\pi\)
0.142318 + 0.989821i \(0.454544\pi\)
\(410\) 0 0
\(411\) 4795.03 + 1640.57i 0.575478 + 0.196893i
\(412\) 129.074 481.710i 0.0154345 0.0576023i
\(413\) −3560.12 3560.12i −0.424169 0.424169i
\(414\) 7918.56 + 1081.27i 0.940039 + 0.128362i
\(415\) 0 0
\(416\) 33.4447 19.3093i 0.00394173 0.00227576i
\(417\) 5510.46 + 3701.17i 0.647118 + 0.434646i
\(418\) −922.708 3443.59i −0.107969 0.402947i
\(419\) −4387.14 + 7598.75i −0.511517 + 0.885974i 0.488394 + 0.872623i \(0.337583\pi\)
−0.999911 + 0.0133505i \(0.995750\pi\)
\(420\) 0 0
\(421\) −6005.42 10401.7i −0.695217 1.20415i −0.970108 0.242675i \(-0.921975\pi\)
0.274891 0.961475i \(-0.411358\pi\)
\(422\) −2814.53 + 2814.53i −0.324666 + 0.324666i
\(423\) 3612.32 + 1516.67i 0.415217 + 0.174333i
\(424\) 2592.61i 0.296954i
\(425\) 0 0
\(426\) 79.2572 231.652i 0.00901414 0.0263464i
\(427\) 10618.4 2845.20i 1.20342 0.322457i
\(428\) −156.333 + 41.8894i −0.0176557 + 0.00473084i
\(429\) −460.938 528.156i −0.0518748 0.0594397i
\(430\) 0 0
\(431\) 4099.38i 0.458145i −0.973409 0.229072i \(-0.926431\pi\)
0.973409 0.229072i \(-0.0735692\pi\)
\(432\) 2945.66 + 8887.80i 0.328063 + 0.989849i
\(433\) −4324.33 + 4324.33i −0.479940 + 0.479940i −0.905112 0.425172i \(-0.860213\pi\)
0.425172 + 0.905112i \(0.360213\pi\)
\(434\) 239.785 + 415.320i 0.0265209 + 0.0459355i
\(435\) 0 0
\(436\) 201.843 349.602i 0.0221709 0.0384011i
\(437\) −577.078 2153.68i −0.0631702 0.235754i
\(438\) 1130.12 553.938i 0.123286 0.0604296i
\(439\) −10469.7 + 6044.67i −1.13825 + 0.657167i −0.945996 0.324179i \(-0.894912\pi\)
−0.192251 + 0.981346i \(0.561579\pi\)
\(440\) 0 0
\(441\) −752.481 583.171i −0.0812526 0.0629706i
\(442\) 637.829 + 637.829i 0.0686390 + 0.0686390i
\(443\) −2391.39 + 8924.79i −0.256475 + 0.957177i 0.710789 + 0.703405i \(0.248338\pi\)
−0.967264 + 0.253772i \(0.918329\pi\)
\(444\) 4.53173 + 23.0724i 0.000484383 + 0.00246614i
\(445\) 0 0
\(446\) 9838.80 + 5680.43i 1.04458 + 0.603086i
\(447\) −403.345 + 600.517i −0.0426791 + 0.0635424i
\(448\) −9149.82 2451.69i −0.964930 0.258552i
\(449\) −702.553 −0.0738431 −0.0369215 0.999318i \(-0.511755\pi\)
−0.0369215 + 0.999318i \(0.511755\pi\)
\(450\) 0 0
\(451\) −1841.02 −0.192218
\(452\) 522.845 + 140.096i 0.0544083 + 0.0145787i
\(453\) −3233.77 6597.39i −0.335399 0.684266i
\(454\) 2262.40 + 1306.20i 0.233876 + 0.135029i
\(455\) 0 0
\(456\) 1883.53 1643.81i 0.193430 0.168813i
\(457\) 1175.37 4386.55i 0.120310 0.449002i −0.879319 0.476232i \(-0.842002\pi\)
0.999629 + 0.0272303i \(0.00866873\pi\)
\(458\) 7384.22 + 7384.22i 0.753367 + 0.753367i
\(459\) −15349.1 + 10096.5i −1.56086 + 1.02672i
\(460\) 0 0
\(461\) −7776.73 + 4489.90i −0.785680 + 0.453613i −0.838440 0.544995i \(-0.816532\pi\)
0.0527593 + 0.998607i \(0.483198\pi\)
\(462\) 1121.73 16505.9i 0.112960 1.66217i
\(463\) 1770.40 + 6607.21i 0.177705 + 0.663204i 0.996075 + 0.0885123i \(0.0282112\pi\)
−0.818370 + 0.574691i \(0.805122\pi\)
\(464\) −2709.66 + 4693.27i −0.271106 + 0.469569i
\(465\) 0 0
\(466\) −6117.14 10595.2i −0.608093 1.05325i
\(467\) 1646.02 1646.02i 0.163102 0.163102i −0.620837 0.783939i \(-0.713207\pi\)
0.783939 + 0.620837i \(0.213207\pi\)
\(468\) −8.92620 + 21.2599i −0.000881653 + 0.00209987i
\(469\) 8756.28i 0.862106i
\(470\) 0 0
\(471\) 12109.1 2378.38i 1.18462 0.232675i
\(472\) 5524.25 1480.22i 0.538716 0.144349i
\(473\) 24275.4 6504.58i 2.35980 0.632306i
\(474\) −8034.92 + 1578.16i −0.778599 + 0.152927i
\(475\) 0 0
\(476\) 912.895i 0.0879044i
\(477\) −1916.76 2523.00i −0.183988 0.242181i
\(478\) 7895.37 7895.37i 0.755494 0.755494i
\(479\) 7066.68 + 12239.8i 0.674081 + 1.16754i 0.976737 + 0.214442i \(0.0687933\pi\)
−0.302656 + 0.953100i \(0.597873\pi\)
\(480\) 0 0
\(481\) 15.0394 26.0491i 0.00142565 0.00246930i
\(482\) 1284.41 + 4793.47i 0.121376 + 0.452980i
\(483\) 701.547 10323.0i 0.0660901 0.972494i
\(484\) 582.107 336.080i 0.0546682 0.0315627i
\(485\) 0 0
\(486\) −9031.98 6193.36i −0.843002 0.578059i
\(487\) 6660.19 + 6660.19i 0.619717 + 0.619717i 0.945459 0.325742i \(-0.105614\pi\)
−0.325742 + 0.945459i \(0.605614\pi\)
\(488\) −3231.94 + 12061.8i −0.299801 + 1.11887i
\(489\) 5207.33 4544.59i 0.481561 0.420273i
\(490\) 0 0
\(491\) −4778.58 2758.92i −0.439215 0.253581i 0.264050 0.964509i \(-0.414942\pi\)
−0.703264 + 0.710928i \(0.748275\pi\)
\(492\) 26.6522 + 54.3747i 0.00244223 + 0.00498252i
\(493\) −10271.3 2752.18i −0.938325 0.251424i
\(494\) 150.007 0.0136622
\(495\) 0 0
\(496\) −569.213 −0.0515291
\(497\) −306.174 82.0392i −0.0276334 0.00740435i
\(498\) −8435.16 + 12558.6i −0.759013 + 1.13005i
\(499\) 4628.28 + 2672.14i 0.415211 + 0.239722i 0.693026 0.720913i \(-0.256277\pi\)
−0.277816 + 0.960634i \(0.589610\pi\)
\(500\) 0 0
\(501\) −3768.32 19185.7i −0.336040 1.71088i
\(502\) 1710.46 6383.52i 0.152075 0.567551i
\(503\) 3380.78 + 3380.78i 0.299685 + 0.299685i 0.840890 0.541205i \(-0.182032\pi\)
−0.541205 + 0.840890i \(0.682032\pi\)
\(504\) 10739.4 4387.98i 0.949145 0.387810i
\(505\) 0 0
\(506\) 14515.2 8380.37i 1.27526 0.736271i
\(507\) −10224.3 + 5011.52i −0.895614 + 0.438993i
\(508\) 83.7212 + 312.452i 0.00731206 + 0.0272890i
\(509\) 6234.51 10798.5i 0.542908 0.940344i −0.455828 0.890068i \(-0.650657\pi\)
0.998735 0.0502756i \(-0.0160100\pi\)
\(510\) 0 0
\(511\) −814.705 1411.11i −0.0705292 0.122160i
\(512\) 7575.72 7575.72i 0.653911 0.653911i
\(513\) −617.663 + 2992.20i −0.0531588 + 0.257522i
\(514\) 11047.4i 0.948017i
\(515\) 0 0
\(516\) −543.546 622.811i −0.0463726 0.0531351i
\(517\) 7936.35 2126.54i 0.675127 0.180900i
\(518\) 685.678 183.727i 0.0581602 0.0155840i
\(519\) 7341.48 21457.6i 0.620916 1.81481i
\(520\) 0 0
\(521\) 16543.1i 1.39111i 0.718473 + 0.695555i \(0.244841\pi\)
−0.718473 + 0.695555i \(0.755159\pi\)
\(522\) −797.112 6288.26i −0.0668365 0.527260i
\(523\) 937.744 937.744i 0.0784029 0.0784029i −0.666818 0.745221i \(-0.732344\pi\)
0.745221 + 0.666818i \(0.232344\pi\)
\(524\) 468.094 + 810.762i 0.0390244 + 0.0675922i
\(525\) 0 0
\(526\) −7130.27 + 12350.0i −0.591054 + 1.02374i
\(527\) −289.072 1078.83i −0.0238940 0.0891738i
\(528\) 16300.7 + 10948.6i 1.34356 + 0.902419i
\(529\) −1458.85 + 842.270i −0.119903 + 0.0692258i
\(530\) 0 0
\(531\) −4281.58 + 5524.64i −0.349915 + 0.451505i
\(532\) 107.349 + 107.349i 0.00874843 + 0.00874843i
\(533\) 20.0492 74.8247i 0.00162932 0.00608071i
\(534\) 12008.2 + 4108.46i 0.973116 + 0.332941i
\(535\) 0 0
\(536\) 8613.91 + 4973.24i 0.694150 + 0.400768i
\(537\) −14814.7 1006.80i −1.19051 0.0809062i
\(538\) −18345.9 4915.78i −1.47017 0.393930i
\(539\) −1996.53 −0.159548
\(540\) 0 0
\(541\) −946.946 −0.0752540 −0.0376270 0.999292i \(-0.511980\pi\)
−0.0376270 + 0.999292i \(0.511980\pi\)
\(542\) −4478.34 1199.97i −0.354910 0.0950979i
\(543\) 7564.32 + 514.066i 0.597820 + 0.0406274i
\(544\) −1838.23 1061.30i −0.144878 0.0836451i
\(545\) 0 0
\(546\) 658.633 + 225.344i 0.0516243 + 0.0176627i
\(547\) 3015.33 11253.3i 0.235697 0.879631i −0.742137 0.670248i \(-0.766188\pi\)
0.977834 0.209383i \(-0.0671456\pi\)
\(548\) −247.198 247.198i −0.0192696 0.0192696i
\(549\) −5772.28 14127.3i −0.448734 1.09825i
\(550\) 0 0
\(551\) −1531.45 + 884.183i −0.118406 + 0.0683620i
\(552\) 9756.74 + 6553.25i 0.752309 + 0.505298i
\(553\) 2743.77 + 10239.9i 0.210989 + 0.787422i
\(554\) −12717.0 + 22026.5i −0.975259 + 1.68920i
\(555\) 0 0
\(556\) −228.950 396.553i −0.0174634 0.0302475i
\(557\) 1609.11 1609.11i 0.122406 0.122406i −0.643250 0.765656i \(-0.722414\pi\)
0.765656 + 0.643250i \(0.222414\pi\)
\(558\) 530.131 402.747i 0.0402190 0.0305549i
\(559\) 1057.46i 0.0800107i
\(560\) 0 0
\(561\) −12472.7 + 36455.0i −0.938676 + 2.74355i
\(562\) −18720.8 + 5016.21i −1.40514 + 0.376506i
\(563\) −17547.6 + 4701.86i −1.31357 + 0.351971i −0.846567 0.532282i \(-0.821335\pi\)
−0.467008 + 0.884253i \(0.654668\pi\)
\(564\) −177.701 203.615i −0.0132670 0.0152017i
\(565\) 0 0
\(566\) 3303.33i 0.245317i
\(567\) −7206.92 + 12210.0i −0.533796 + 0.904356i
\(568\) 254.601 254.601i 0.0188078 0.0188078i
\(569\) −149.738 259.354i −0.0110322 0.0191084i 0.860457 0.509524i \(-0.170178\pi\)
−0.871489 + 0.490415i \(0.836845\pi\)
\(570\) 0 0
\(571\) 10802.7 18710.8i 0.791732 1.37132i −0.133162 0.991094i \(-0.542513\pi\)
0.924894 0.380226i \(-0.124154\pi\)
\(572\) 12.5155 + 46.7086i 0.000914861 + 0.00341431i
\(573\) −3287.10 + 1611.20i −0.239652 + 0.117468i
\(574\) 1583.24 914.085i 0.115128 0.0664689i
\(575\) 0 0
\(576\) −1779.16 + 13029.5i −0.128701 + 0.942524i
\(577\) 6073.88 + 6073.88i 0.438231 + 0.438231i 0.891416 0.453186i \(-0.149712\pi\)
−0.453186 + 0.891416i \(0.649712\pi\)
\(578\) 9155.55 34169.0i 0.658859 2.45890i
\(579\) 1535.46 + 7817.50i 0.110210 + 0.561113i
\(580\) 0 0
\(581\) 16962.0 + 9793.00i 1.21119 + 0.699281i
\(582\) −3410.20 + 5077.24i −0.242882 + 0.361613i
\(583\) −6418.53 1719.84i −0.455966 0.122176i
\(584\) 1850.89 0.131148
\(585\) 0 0
\(586\) −18187.5 −1.28211
\(587\) 10872.4 + 2913.25i 0.764484 + 0.204843i 0.619933 0.784654i \(-0.287160\pi\)
0.144551 + 0.989497i \(0.453826\pi\)
\(588\) 28.9035 + 58.9676i 0.00202714 + 0.00413569i
\(589\) −160.854 92.8691i −0.0112528 0.00649678i
\(590\) 0 0
\(591\) −5478.24 + 4781.02i −0.381294 + 0.332767i
\(592\) −218.070 + 813.847i −0.0151395 + 0.0565015i
\(593\) 19651.0 + 19651.0i 1.36082 + 1.36082i 0.872870 + 0.487953i \(0.162256\pi\)
0.487953 + 0.872870i \(0.337744\pi\)
\(594\) −22928.2 + 1336.72i −1.58377 + 0.0923341i
\(595\) 0 0
\(596\) 43.2154 24.9504i 0.00297009 0.00171478i
\(597\) 717.192 10553.3i 0.0491670 0.723478i
\(598\) 182.529 + 681.209i 0.0124819 + 0.0465831i
\(599\) −1419.69 + 2458.97i −0.0968396 + 0.167731i −0.910375 0.413784i \(-0.864207\pi\)
0.813535 + 0.581516i \(0.197540\pi\)
\(600\) 0 0
\(601\) −254.777 441.286i −0.0172921 0.0299508i 0.857250 0.514901i \(-0.172171\pi\)
−0.874542 + 0.484950i \(0.838838\pi\)
\(602\) −17646.8 + 17646.8i −1.19473 + 1.19473i
\(603\) −12059.4 + 1528.68i −0.814425 + 0.103238i
\(604\) 506.824i 0.0341430i
\(605\) 0 0
\(606\) 6776.85 1331.06i 0.454275 0.0892257i
\(607\) −3306.40 + 885.947i −0.221092 + 0.0592413i −0.367664 0.929959i \(-0.619842\pi\)
0.146573 + 0.989200i \(0.453176\pi\)
\(608\) −340.961 + 91.3602i −0.0227431 + 0.00609399i
\(609\) −8052.35 + 1581.59i −0.535793 + 0.105237i
\(610\) 0 0
\(611\) 345.717i 0.0228907i
\(612\) 1257.27 159.374i 0.0830426 0.0105266i
\(613\) 6435.77 6435.77i 0.424043 0.424043i −0.462550 0.886593i \(-0.653066\pi\)
0.886593 + 0.462550i \(0.153066\pi\)
\(614\) −10218.9 17699.6i −0.671660 1.16335i
\(615\) 0 0
\(616\) 12164.9 21070.2i 0.795679 1.37816i
\(617\) −556.352 2076.34i −0.0363013 0.135478i 0.945397 0.325921i \(-0.105674\pi\)
−0.981698 + 0.190443i \(0.939008\pi\)
\(618\) −1417.17 + 20853.3i −0.0922444 + 1.35735i
\(619\) 16359.4 9445.11i 1.06226 0.613297i 0.136205 0.990681i \(-0.456509\pi\)
0.926057 + 0.377383i \(0.123176\pi\)
\(620\) 0 0
\(621\) −14339.7 + 836.011i −0.926623 + 0.0540225i
\(622\) −6199.92 6199.92i −0.399669 0.399669i
\(623\) 4252.66 15871.2i 0.273482 1.02065i
\(624\) −622.505 + 543.279i −0.0399361 + 0.0348535i
\(625\) 0 0
\(626\) 10791.1 + 6230.22i 0.688974 + 0.397779i
\(627\) 2820.13 + 5753.50i 0.179625 + 0.366463i
\(628\) −822.250 220.321i −0.0522474 0.0139996i
\(629\) −1653.23 −0.104799
\(630\) 0 0
\(631\) 865.068 0.0545766 0.0272883 0.999628i \(-0.491313\pi\)
0.0272883 + 0.999628i \(0.491313\pi\)
\(632\) −11631.8 3116.72i −0.732099 0.196165i
\(633\) 3988.77 5938.64i 0.250457 0.372891i
\(634\) 12079.6 + 6974.16i 0.756691 + 0.436876i
\(635\) 0 0
\(636\) 42.1247 + 214.470i 0.00262634 + 0.0133715i
\(637\) 21.7427 81.1450i 0.00135240 0.00504723i
\(638\) −9399.66 9399.66i −0.583286 0.583286i
\(639\) −59.5349 + 435.996i −0.00368570 + 0.0269917i
\(640\) 0 0
\(641\) 6830.18 3943.41i 0.420867 0.242988i −0.274581 0.961564i \(-0.588539\pi\)
0.695448 + 0.718576i \(0.255206\pi\)
\(642\) 6090.95 2985.53i 0.374440 0.183535i
\(643\) −1839.94 6866.75i −0.112846 0.421148i 0.886270 0.463168i \(-0.153287\pi\)
−0.999117 + 0.0420200i \(0.986621\pi\)
\(644\) −356.868 + 618.114i −0.0218363 + 0.0378216i
\(645\) 0 0
\(646\) −4122.43 7140.26i −0.251076 0.434876i
\(647\) 1933.74 1933.74i 0.117501 0.117501i −0.645911 0.763412i \(-0.723522\pi\)
0.763412 + 0.645911i \(0.223522\pi\)
\(648\) −7918.16 14024.5i −0.480023 0.850210i
\(649\) 14658.3i 0.886578i
\(650\) 0 0
\(651\) −566.749 649.398i −0.0341208 0.0390966i
\(652\) −460.521 + 123.396i −0.0276616 + 0.00741191i
\(653\) 6232.28 1669.93i 0.373488 0.100076i −0.0671918 0.997740i \(-0.521404\pi\)
0.440680 + 0.897664i \(0.354737\pi\)
\(654\) −5476.96 + 16008.0i −0.327471 + 0.957130i
\(655\) 0 0
\(656\) 2169.90i 0.129147i
\(657\) −1801.20 + 1368.39i −0.106958 + 0.0812572i
\(658\) −5769.26 + 5769.26i −0.341807 + 0.341807i
\(659\) −3849.42 6667.40i −0.227545 0.394120i 0.729535 0.683944i \(-0.239737\pi\)
−0.957080 + 0.289824i \(0.906403\pi\)
\(660\) 0 0
\(661\) −1130.78 + 1958.57i −0.0665392 + 0.115249i −0.897376 0.441267i \(-0.854529\pi\)
0.830837 + 0.556517i \(0.187862\pi\)
\(662\) 8428.67 + 31456.2i 0.494848 + 1.84680i
\(663\) −1345.81 903.934i −0.0788343 0.0529501i
\(664\) −19267.5 + 11124.1i −1.12609 + 0.650150i
\(665\) 0 0
\(666\) −372.741 912.263i −0.0216868 0.0530773i
\(667\) −5878.71 5878.71i −0.341266 0.341266i
\(668\) −349.078 + 1302.78i −0.0202189 + 0.0754581i
\(669\) −19319.4 6609.90i −1.11649 0.381993i
\(670\) 0 0
\(671\) −27717.4 16002.6i −1.59466 0.920678i
\(672\) −1634.29 111.066i −0.0938159 0.00637566i
\(673\) 8335.28 + 2233.43i 0.477417 + 0.127923i 0.489499 0.872004i \(-0.337180\pi\)
−0.0120828 + 0.999927i \(0.503846\pi\)
\(674\) −6836.92 −0.390724
\(675\) 0 0
\(676\) 785.449 0.0446887
\(677\) 12923.2 + 3462.76i 0.733646 + 0.196580i 0.606252 0.795272i \(-0.292672\pi\)
0.127394 + 0.991852i \(0.459339\pi\)
\(678\) −22634.0 1538.19i −1.28209 0.0871297i
\(679\) 6857.45 + 3959.15i 0.387577 + 0.223768i
\(680\) 0 0
\(681\) −4442.43 1519.93i −0.249977 0.0855269i
\(682\) 361.371 1348.65i 0.0202897 0.0757223i
\(683\) −14959.7 14959.7i −0.838091 0.838091i 0.150516 0.988608i \(-0.451906\pi\)
−0.988608 + 0.150516i \(0.951906\pi\)
\(684\) 129.103 166.586i 0.00721695 0.00931222i
\(685\) 0 0
\(686\) −14985.6 + 8651.91i −0.834039 + 0.481533i
\(687\) −15580.7 10465.0i −0.865268 0.581169i
\(688\) −7666.54 28611.9i −0.424832 1.58549i
\(689\) 139.799 242.139i 0.00772994 0.0133886i
\(690\) 0 0
\(691\) 14446.2 + 25021.6i 0.795311 + 1.37752i 0.922642 + 0.385658i \(0.126026\pi\)
−0.127331 + 0.991860i \(0.540641\pi\)
\(692\) −1106.20 + 1106.20i −0.0607680 + 0.0607680i
\(693\) 3739.26 + 29498.3i 0.204968 + 1.61695i
\(694\) 2977.62i 0.162866i
\(695\) 0 0
\(696\) 3017.56 8819.71i 0.164340 0.480331i
\(697\) −4112.61 + 1101.97i −0.223495 + 0.0598854i
\(698\) −15250.6 + 4086.39i −0.826999 + 0.221594i
\(699\) 14458.3 + 16566.7i 0.782351 + 0.896440i
\(700\) 0 0
\(701\) 4479.63i 0.241360i 0.992691 + 0.120680i \(0.0385075\pi\)
−0.992691 + 0.120680i \(0.961493\pi\)
\(702\) 195.366 946.432i 0.0105037 0.0508843i
\(703\) −194.406 + 194.406i −0.0104298 + 0.0104298i
\(704\) 13789.3 + 23883.8i 0.738217 + 1.27863i
\(705\) 0 0
\(706\) 962.411 1666.94i 0.0513043 0.0888616i
\(707\) −2314.17 8636.58i −0.123102 0.459423i
\(708\) 432.935 212.207i 0.0229812 0.0112644i
\(709\) 25712.6 14845.2i 1.36200 0.786351i 0.372110 0.928188i \(-0.378634\pi\)
0.989890 + 0.141837i \(0.0453009\pi\)
\(710\) 0 0
\(711\) 13623.7 5566.50i 0.718606 0.293615i
\(712\) 13197.7 + 13197.7i 0.694672 + 0.694672i
\(713\) 226.007 843.471i 0.0118710 0.0443033i
\(714\) −7374.03 37543.5i −0.386507 1.96783i
\(715\) 0 0
\(716\) 887.064 + 512.147i 0.0463005 + 0.0267316i
\(717\) −11189.4 + 16659.2i −0.582809 + 0.867711i
\(718\) 18721.1 + 5016.31i 0.973073 + 0.260734i
\(719\) 17740.3 0.920171 0.460085 0.887875i \(-0.347819\pi\)
0.460085 + 0.887875i \(0.347819\pi\)
\(720\) 0 0
\(721\) 27059.8 1.39773
\(722\) 17829.9 + 4777.52i 0.919060 + 0.246261i
\(723\) −3925.61 8008.85i −0.201929 0.411967i
\(724\) −452.930 261.499i −0.0232500 0.0134234i
\(725\) 0 0
\(726\) −21224.8 + 18523.6i −1.08502 + 0.946934i
\(727\) −7841.69 + 29265.6i −0.400044 + 1.49299i 0.412972 + 0.910744i \(0.364491\pi\)
−0.813016 + 0.582242i \(0.802176\pi\)
\(728\) 723.881 + 723.881i 0.0368527 + 0.0368527i
\(729\) 18074.1 + 7793.98i 0.918261 + 0.395975i
\(730\) 0 0
\(731\) 50334.8 29060.8i 2.54679 1.47039i
\(732\) −71.3779 + 1050.30i −0.00360410 + 0.0530333i
\(733\) −6548.68 24440.0i −0.329988 1.23153i −0.909202 0.416355i \(-0.863307\pi\)
0.579214 0.815175i \(-0.303359\pi\)
\(734\) −4720.53 + 8176.20i −0.237381 + 0.411157i
\(735\) 0 0
\(736\) −829.766 1437.20i −0.0415565 0.0719780i
\(737\) −18026.4 + 18026.4i −0.900965 + 0.900965i
\(738\) −1535.31 2020.91i −0.0765794 0.100800i
\(739\) 27310.7i 1.35946i −0.733463 0.679730i \(-0.762097\pi\)
0.733463 0.679730i \(-0.237903\pi\)
\(740\) 0 0
\(741\) −264.552 + 51.9615i −0.0131155 + 0.00257605i
\(742\) 6373.73 1707.84i 0.315346 0.0844968i
\(743\) 9929.86 2660.70i 0.490298 0.131375i −0.00519568 0.999987i \(-0.501654\pi\)
0.495494 + 0.868612i \(0.334987\pi\)
\(744\) 960.731 188.700i 0.0473416 0.00929851i
\(745\) 0 0
\(746\) 12220.0i 0.599739i
\(747\) 10526.0 25070.2i 0.515564 1.22794i
\(748\) 1879.36 1879.36i 0.0918666 0.0918666i
\(749\) −4390.98 7605.39i −0.214209 0.371021i
\(750\) 0 0
\(751\) −12313.5 + 21327.6i −0.598302 + 1.03629i 0.394770 + 0.918780i \(0.370824\pi\)
−0.993072 + 0.117509i \(0.962509\pi\)
\(752\) −2506.42 9354.09i −0.121542 0.453602i
\(753\) −805.350 + 11850.5i −0.0389755 + 0.573513i
\(754\) 484.396 279.666i 0.0233961 0.0135078i
\(755\) 0 0
\(756\) 817.101 537.483i 0.0393091 0.0258572i
\(757\) −3491.44 3491.44i −0.167633 0.167633i 0.618305 0.785938i \(-0.287820\pi\)
−0.785938 + 0.618305i \(0.787820\pi\)
\(758\) 1500.74 5600.84i 0.0719121 0.268380i
\(759\) −22696.1 + 19807.6i −1.08540 + 0.947260i
\(760\) 0 0
\(761\) 1927.71 + 1112.96i 0.0918256 + 0.0530155i 0.545210 0.838300i \(-0.316450\pi\)
−0.453384 + 0.891315i \(0.649783\pi\)
\(762\) −5966.96 12173.5i −0.283675 0.578741i
\(763\) 21157.8 + 5669.21i 1.00388 + 0.268990i
\(764\) 252.521 0.0119580
\(765\) 0 0
\(766\) −3391.65 −0.159981
\(767\) −595.759 159.633i −0.0280464 0.00751502i
\(768\) 1591.93 2370.13i 0.0747965 0.111360i
\(769\) −28584.4 16503.2i −1.34042 0.773890i −0.353548 0.935416i \(-0.615025\pi\)
−0.986868 + 0.161526i \(0.948358\pi\)
\(770\) 0 0
\(771\) 3826.76 + 19483.2i 0.178752 + 0.910079i
\(772\) 142.237 530.837i 0.00663113 0.0247477i
\(773\) −9771.76 9771.76i −0.454677 0.454677i 0.442226 0.896904i \(-0.354189\pi\)
−0.896904 + 0.442226i \(0.854189\pi\)
\(774\) 27384.5 + 21223.0i 1.27173 + 0.985586i
\(775\) 0 0
\(776\) −7789.55 + 4497.30i −0.360346 + 0.208046i
\(777\) −1145.62 + 561.535i −0.0528943 + 0.0259266i
\(778\) 8790.84 + 32807.8i 0.405099 + 1.51185i