Properties

Label 336.4.bc.d.257.3
Level $336$
Weight $4$
Character 336.257
Analytic conductor $19.825$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.bc (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{3} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 257.3
Root \(-2.23014 + 2.00661i\) of defining polynomial
Character \(\chi\) \(=\) 336.257
Dual form 336.4.bc.d.17.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.60743 - 4.94127i) q^{3} +(-0.623706 + 1.08029i) q^{5} +(-10.0808 + 15.5363i) q^{7} +(-21.8323 + 15.8855i) q^{9} +O(q^{10})\) \(q+(-1.60743 - 4.94127i) q^{3} +(-0.623706 + 1.08029i) q^{5} +(-10.0808 + 15.5363i) q^{7} +(-21.8323 + 15.8855i) q^{9} +(35.2392 - 20.3453i) q^{11} -19.5973i q^{13} +(6.34057 + 1.34540i) q^{15} +(52.3592 + 90.6889i) q^{17} +(-35.0345 - 20.2272i) q^{19} +(92.9734 + 24.8386i) q^{21} +(69.6324 + 40.2023i) q^{23} +(61.7220 + 106.906i) q^{25} +(113.589 + 82.3444i) q^{27} -211.712i q^{29} +(86.6242 - 50.0125i) q^{31} +(-157.176 - 141.422i) q^{33} +(-10.4962 - 20.5803i) q^{35} +(94.9875 - 164.523i) q^{37} +(-96.8355 + 31.5014i) q^{39} +186.753 q^{41} -158.618 q^{43} +(-3.54405 - 33.4931i) q^{45} +(179.034 - 310.097i) q^{47} +(-139.753 - 313.238i) q^{49} +(363.954 - 404.498i) q^{51} +(366.460 - 211.576i) q^{53} +50.7580i q^{55} +(-43.6323 + 205.629i) q^{57} +(312.781 + 541.753i) q^{59} +(699.575 + 403.900i) q^{61} +(-26.7144 - 499.333i) q^{63} +(21.1708 + 12.2229i) q^{65} +(149.272 + 258.547i) q^{67} +(86.7208 - 408.695i) q^{69} -455.386i q^{71} +(-434.467 + 250.840i) q^{73} +(429.035 - 476.829i) q^{75} +(-39.1491 + 752.584i) q^{77} +(-30.9561 + 53.6176i) q^{79} +(224.299 - 693.636i) q^{81} -73.1180 q^{83} -130.627 q^{85} +(-1046.13 + 340.313i) q^{87} +(-57.3723 + 99.3717i) q^{89} +(304.469 + 197.557i) q^{91} +(-386.368 - 347.642i) q^{93} +(43.7025 - 25.2316i) q^{95} +1416.51i q^{97} +(-446.156 + 1003.98i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9} - 6 q^{15} - 300 q^{19} + 357 q^{21} - 42 q^{25} + 930 q^{31} - 855 q^{33} + 764 q^{37} + 426 q^{39} + 1012 q^{43} + 2367 q^{45} - 336 q^{49} + 1341 q^{51} + 270 q^{57} + 2358 q^{61} - 1071 q^{63} - 792 q^{67} - 2904 q^{73} + 2418 q^{75} - 1674 q^{79} + 837 q^{81} + 348 q^{85} - 1638 q^{87} + 1218 q^{91} - 1479 q^{93} + 3354 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.60743 4.94127i −0.309351 0.950948i
\(4\) 0 0
\(5\) −0.623706 + 1.08029i −0.0557859 + 0.0966240i −0.892570 0.450909i \(-0.851100\pi\)
0.836784 + 0.547533i \(0.184433\pi\)
\(6\) 0 0
\(7\) −10.0808 + 15.5363i −0.544314 + 0.838881i
\(8\) 0 0
\(9\) −21.8323 + 15.8855i −0.808604 + 0.588353i
\(10\) 0 0
\(11\) 35.2392 20.3453i 0.965910 0.557668i 0.0679230 0.997691i \(-0.478363\pi\)
0.897987 + 0.440022i \(0.145029\pi\)
\(12\) 0 0
\(13\) 19.5973i 0.418101i −0.977905 0.209050i \(-0.932963\pi\)
0.977905 0.209050i \(-0.0670373\pi\)
\(14\) 0 0
\(15\) 6.34057 + 1.34540i 0.109142 + 0.0231588i
\(16\) 0 0
\(17\) 52.3592 + 90.6889i 0.746999 + 1.29384i 0.949255 + 0.314507i \(0.101839\pi\)
−0.202256 + 0.979333i \(0.564827\pi\)
\(18\) 0 0
\(19\) −35.0345 20.2272i −0.423025 0.244234i 0.273346 0.961916i \(-0.411870\pi\)
−0.696371 + 0.717682i \(0.745203\pi\)
\(20\) 0 0
\(21\) 92.9734 + 24.8386i 0.966117 + 0.258106i
\(22\) 0 0
\(23\) 69.6324 + 40.2023i 0.631276 + 0.364467i 0.781246 0.624223i \(-0.214584\pi\)
−0.149970 + 0.988691i \(0.547918\pi\)
\(24\) 0 0
\(25\) 61.7220 + 106.906i 0.493776 + 0.855245i
\(26\) 0 0
\(27\) 113.589 + 82.3444i 0.809636 + 0.586933i
\(28\) 0 0
\(29\) 211.712i 1.35565i −0.735222 0.677827i \(-0.762922\pi\)
0.735222 0.677827i \(-0.237078\pi\)
\(30\) 0 0
\(31\) 86.6242 50.0125i 0.501876 0.289758i −0.227612 0.973752i \(-0.573092\pi\)
0.729488 + 0.683994i \(0.239758\pi\)
\(32\) 0 0
\(33\) −157.176 141.422i −0.829119 0.746015i
\(34\) 0 0
\(35\) −10.4962 20.5803i −0.0506910 0.0993916i
\(36\) 0 0
\(37\) 94.9875 164.523i 0.422050 0.731012i −0.574090 0.818792i \(-0.694644\pi\)
0.996140 + 0.0877801i \(0.0279773\pi\)
\(38\) 0 0
\(39\) −96.8355 + 31.5014i −0.397592 + 0.129340i
\(40\) 0 0
\(41\) 186.753 0.711362 0.355681 0.934607i \(-0.384249\pi\)
0.355681 + 0.934607i \(0.384249\pi\)
\(42\) 0 0
\(43\) −158.618 −0.562536 −0.281268 0.959629i \(-0.590755\pi\)
−0.281268 + 0.959629i \(0.590755\pi\)
\(44\) 0 0
\(45\) −3.54405 33.4931i −0.0117404 0.110952i
\(46\) 0 0
\(47\) 179.034 310.097i 0.555635 0.962388i −0.442219 0.896907i \(-0.645809\pi\)
0.997854 0.0654808i \(-0.0208581\pi\)
\(48\) 0 0
\(49\) −139.753 313.238i −0.407444 0.913230i
\(50\) 0 0
\(51\) 363.954 404.498i 0.999290 1.11061i
\(52\) 0 0
\(53\) 366.460 211.576i 0.949758 0.548343i 0.0567521 0.998388i \(-0.481926\pi\)
0.893006 + 0.450045i \(0.148592\pi\)
\(54\) 0 0
\(55\) 50.7580i 0.124440i
\(56\) 0 0
\(57\) −43.6323 + 205.629i −0.101390 + 0.477829i
\(58\) 0 0
\(59\) 312.781 + 541.753i 0.690180 + 1.19543i 0.971779 + 0.235895i \(0.0758020\pi\)
−0.281599 + 0.959532i \(0.590865\pi\)
\(60\) 0 0
\(61\) 699.575 + 403.900i 1.46838 + 0.847772i 0.999372 0.0354209i \(-0.0112772\pi\)
0.469011 + 0.883192i \(0.344611\pi\)
\(62\) 0 0
\(63\) −26.7144 499.333i −0.0534239 0.998572i
\(64\) 0 0
\(65\) 21.1708 + 12.2229i 0.0403986 + 0.0233241i
\(66\) 0 0
\(67\) 149.272 + 258.547i 0.272187 + 0.471441i 0.969421 0.245402i \(-0.0789199\pi\)
−0.697235 + 0.716843i \(0.745587\pi\)
\(68\) 0 0
\(69\) 86.7208 408.695i 0.151304 0.713059i
\(70\) 0 0
\(71\) 455.386i 0.761189i −0.924742 0.380594i \(-0.875719\pi\)
0.924742 0.380594i \(-0.124281\pi\)
\(72\) 0 0
\(73\) −434.467 + 250.840i −0.696582 + 0.402172i −0.806073 0.591816i \(-0.798411\pi\)
0.109491 + 0.993988i \(0.465078\pi\)
\(74\) 0 0
\(75\) 429.035 476.829i 0.660543 0.734126i
\(76\) 0 0
\(77\) −39.1491 + 752.584i −0.0579410 + 1.11383i
\(78\) 0 0
\(79\) −30.9561 + 53.6176i −0.0440865 + 0.0763601i −0.887227 0.461334i \(-0.847371\pi\)
0.843140 + 0.537694i \(0.180704\pi\)
\(80\) 0 0
\(81\) 224.299 693.636i 0.307681 0.951490i
\(82\) 0 0
\(83\) −73.1180 −0.0966957 −0.0483478 0.998831i \(-0.515396\pi\)
−0.0483478 + 0.998831i \(0.515396\pi\)
\(84\) 0 0
\(85\) −130.627 −0.166688
\(86\) 0 0
\(87\) −1046.13 + 340.313i −1.28916 + 0.419373i
\(88\) 0 0
\(89\) −57.3723 + 99.3717i −0.0683309 + 0.118353i −0.898167 0.439655i \(-0.855101\pi\)
0.829836 + 0.558008i \(0.188434\pi\)
\(90\) 0 0
\(91\) 304.469 + 197.557i 0.350737 + 0.227578i
\(92\) 0 0
\(93\) −386.368 347.642i −0.430801 0.387621i
\(94\) 0 0
\(95\) 43.7025 25.2316i 0.0471977 0.0272496i
\(96\) 0 0
\(97\) 1416.51i 1.48273i 0.671101 + 0.741366i \(0.265822\pi\)
−0.671101 + 0.741366i \(0.734178\pi\)
\(98\) 0 0
\(99\) −446.156 + 1003.98i −0.452933 + 1.01923i
\(100\) 0 0
\(101\) −120.406 208.549i −0.118622 0.205459i 0.800600 0.599199i \(-0.204514\pi\)
−0.919222 + 0.393740i \(0.871181\pi\)
\(102\) 0 0
\(103\) 960.453 + 554.518i 0.918799 + 0.530469i 0.883252 0.468899i \(-0.155349\pi\)
0.0355471 + 0.999368i \(0.488683\pi\)
\(104\) 0 0
\(105\) −84.8209 + 84.9462i −0.0788349 + 0.0789514i
\(106\) 0 0
\(107\) 924.644 + 533.843i 0.835408 + 0.482323i 0.855701 0.517471i \(-0.173126\pi\)
−0.0202926 + 0.999794i \(0.506460\pi\)
\(108\) 0 0
\(109\) −5.04376 8.73604i −0.00443215 0.00767671i 0.863801 0.503833i \(-0.168077\pi\)
−0.868233 + 0.496157i \(0.834744\pi\)
\(110\) 0 0
\(111\) −965.640 204.899i −0.825716 0.175208i
\(112\) 0 0
\(113\) 884.294i 0.736171i −0.929792 0.368086i \(-0.880013\pi\)
0.929792 0.368086i \(-0.119987\pi\)
\(114\) 0 0
\(115\) −86.8602 + 50.1487i −0.0704326 + 0.0406643i
\(116\) 0 0
\(117\) 311.314 + 427.854i 0.245991 + 0.338078i
\(118\) 0 0
\(119\) −1936.79 100.751i −1.49198 0.0776122i
\(120\) 0 0
\(121\) 162.366 281.226i 0.121988 0.211289i
\(122\) 0 0
\(123\) −300.192 922.795i −0.220061 0.676468i
\(124\) 0 0
\(125\) −309.912 −0.221755
\(126\) 0 0
\(127\) 840.132 0.587005 0.293503 0.955958i \(-0.405179\pi\)
0.293503 + 0.955958i \(0.405179\pi\)
\(128\) 0 0
\(129\) 254.968 + 783.776i 0.174021 + 0.534943i
\(130\) 0 0
\(131\) −258.951 + 448.517i −0.172707 + 0.299138i −0.939366 0.342918i \(-0.888585\pi\)
0.766658 + 0.642056i \(0.221918\pi\)
\(132\) 0 0
\(133\) 667.434 340.400i 0.435142 0.221928i
\(134\) 0 0
\(135\) −159.802 + 71.3501i −0.101878 + 0.0454877i
\(136\) 0 0
\(137\) −950.957 + 549.035i −0.593034 + 0.342389i −0.766296 0.642487i \(-0.777903\pi\)
0.173262 + 0.984876i \(0.444569\pi\)
\(138\) 0 0
\(139\) 828.268i 0.505416i 0.967543 + 0.252708i \(0.0813212\pi\)
−0.967543 + 0.252708i \(0.918679\pi\)
\(140\) 0 0
\(141\) −1820.06 386.197i −1.08707 0.230664i
\(142\) 0 0
\(143\) −398.714 690.592i −0.233162 0.403848i
\(144\) 0 0
\(145\) 228.710 + 132.046i 0.130989 + 0.0756264i
\(146\) 0 0
\(147\) −1323.15 + 1194.07i −0.742391 + 0.669967i
\(148\) 0 0
\(149\) −773.007 446.296i −0.425015 0.245382i 0.272206 0.962239i \(-0.412247\pi\)
−0.697221 + 0.716857i \(0.745580\pi\)
\(150\) 0 0
\(151\) 712.518 + 1234.12i 0.383999 + 0.665106i 0.991630 0.129113i \(-0.0412131\pi\)
−0.607630 + 0.794220i \(0.707880\pi\)
\(152\) 0 0
\(153\) −2583.76 1148.19i −1.36526 0.606705i
\(154\) 0 0
\(155\) 124.772i 0.0646577i
\(156\) 0 0
\(157\) −244.872 + 141.377i −0.124477 + 0.0718670i −0.560946 0.827853i \(-0.689562\pi\)
0.436468 + 0.899720i \(0.356229\pi\)
\(158\) 0 0
\(159\) −1634.51 1470.68i −0.815254 0.733540i
\(160\) 0 0
\(161\) −1326.55 + 676.557i −0.649358 + 0.331181i
\(162\) 0 0
\(163\) 1158.07 2005.83i 0.556484 0.963858i −0.441303 0.897358i \(-0.645484\pi\)
0.997786 0.0664997i \(-0.0211832\pi\)
\(164\) 0 0
\(165\) 250.809 81.5902i 0.118336 0.0384957i
\(166\) 0 0
\(167\) −2344.70 −1.08646 −0.543229 0.839585i \(-0.682798\pi\)
−0.543229 + 0.839585i \(0.682798\pi\)
\(168\) 0 0
\(169\) 1812.95 0.825192
\(170\) 0 0
\(171\) 1086.21 114.936i 0.485755 0.0513999i
\(172\) 0 0
\(173\) −516.901 + 895.298i −0.227163 + 0.393458i −0.956966 0.290199i \(-0.906278\pi\)
0.729803 + 0.683657i \(0.239612\pi\)
\(174\) 0 0
\(175\) −2283.13 118.767i −0.986218 0.0513026i
\(176\) 0 0
\(177\) 2174.17 2416.37i 0.923281 1.02613i
\(178\) 0 0
\(179\) −125.472 + 72.4412i −0.0523922 + 0.0302486i −0.525967 0.850505i \(-0.676297\pi\)
0.473575 + 0.880753i \(0.342963\pi\)
\(180\) 0 0
\(181\) 2057.17i 0.844797i 0.906410 + 0.422398i \(0.138812\pi\)
−0.906410 + 0.422398i \(0.861188\pi\)
\(182\) 0 0
\(183\) 871.257 4106.03i 0.351941 1.65862i
\(184\) 0 0
\(185\) 118.489 + 205.228i 0.0470889 + 0.0815604i
\(186\) 0 0
\(187\) 3690.19 + 2130.53i 1.44307 + 0.833155i
\(188\) 0 0
\(189\) −2424.40 + 934.648i −0.933063 + 0.359712i
\(190\) 0 0
\(191\) −2553.66 1474.36i −0.967417 0.558538i −0.0689690 0.997619i \(-0.521971\pi\)
−0.898448 + 0.439080i \(0.855304\pi\)
\(192\) 0 0
\(193\) 1135.40 + 1966.57i 0.423460 + 0.733455i 0.996275 0.0862300i \(-0.0274820\pi\)
−0.572815 + 0.819685i \(0.694149\pi\)
\(194\) 0 0
\(195\) 26.3662 124.258i 0.00968270 0.0456323i
\(196\) 0 0
\(197\) 495.849i 0.179329i −0.995972 0.0896645i \(-0.971421\pi\)
0.995972 0.0896645i \(-0.0285795\pi\)
\(198\) 0 0
\(199\) −727.207 + 419.853i −0.259047 + 0.149561i −0.623900 0.781504i \(-0.714453\pi\)
0.364853 + 0.931065i \(0.381119\pi\)
\(200\) 0 0
\(201\) 1037.61 1153.19i 0.364115 0.404676i
\(202\) 0 0
\(203\) 3289.22 + 2134.24i 1.13723 + 0.737902i
\(204\) 0 0
\(205\) −116.479 + 201.747i −0.0396840 + 0.0687347i
\(206\) 0 0
\(207\) −2158.87 + 228.439i −0.724888 + 0.0767035i
\(208\) 0 0
\(209\) −1646.12 −0.544805
\(210\) 0 0
\(211\) −4001.71 −1.30564 −0.652818 0.757514i \(-0.726414\pi\)
−0.652818 + 0.757514i \(0.726414\pi\)
\(212\) 0 0
\(213\) −2250.19 + 732.004i −0.723851 + 0.235474i
\(214\) 0 0
\(215\) 98.9311 171.354i 0.0313816 0.0543545i
\(216\) 0 0
\(217\) −96.2355 + 1849.99i −0.0301055 + 0.578734i
\(218\) 0 0
\(219\) 1937.84 + 1743.61i 0.597933 + 0.538001i
\(220\) 0 0
\(221\) 1777.26 1026.10i 0.540955 0.312321i
\(222\) 0 0
\(223\) 3040.54i 0.913047i 0.889711 + 0.456523i \(0.150905\pi\)
−0.889711 + 0.456523i \(0.849095\pi\)
\(224\) 0 0
\(225\) −3045.79 1353.51i −0.902455 0.401040i
\(226\) 0 0
\(227\) 2198.24 + 3807.46i 0.642741 + 1.11326i 0.984818 + 0.173588i \(0.0555360\pi\)
−0.342078 + 0.939672i \(0.611131\pi\)
\(228\) 0 0
\(229\) −1717.81 991.778i −0.495703 0.286194i 0.231234 0.972898i \(-0.425724\pi\)
−0.726937 + 0.686704i \(0.759057\pi\)
\(230\) 0 0
\(231\) 3781.65 1016.28i 1.07712 0.289466i
\(232\) 0 0
\(233\) 3787.78 + 2186.87i 1.06500 + 0.614879i 0.926812 0.375526i \(-0.122538\pi\)
0.138191 + 0.990406i \(0.455871\pi\)
\(234\) 0 0
\(235\) 223.329 + 386.818i 0.0619932 + 0.107375i
\(236\) 0 0
\(237\) 314.699 + 66.7758i 0.0862527 + 0.0183019i
\(238\) 0 0
\(239\) 3826.41i 1.03561i −0.855500 0.517803i \(-0.826750\pi\)
0.855500 0.517803i \(-0.173250\pi\)
\(240\) 0 0
\(241\) 2979.03 1719.94i 0.796250 0.459715i −0.0459083 0.998946i \(-0.514618\pi\)
0.842158 + 0.539231i \(0.181285\pi\)
\(242\) 0 0
\(243\) −3787.99 + 6.65062i −0.999998 + 0.00175571i
\(244\) 0 0
\(245\) 425.553 + 44.3943i 0.110970 + 0.0115765i
\(246\) 0 0
\(247\) −396.398 + 686.582i −0.102114 + 0.176867i
\(248\) 0 0
\(249\) 117.532 + 361.296i 0.0299129 + 0.0919525i
\(250\) 0 0
\(251\) −2046.61 −0.514664 −0.257332 0.966323i \(-0.582843\pi\)
−0.257332 + 0.966323i \(0.582843\pi\)
\(252\) 0 0
\(253\) 3271.72 0.813008
\(254\) 0 0
\(255\) 209.974 + 645.463i 0.0515651 + 0.158512i
\(256\) 0 0
\(257\) 3025.57 5240.44i 0.734357 1.27194i −0.220648 0.975354i \(-0.570817\pi\)
0.955005 0.296590i \(-0.0958496\pi\)
\(258\) 0 0
\(259\) 1598.53 + 3134.29i 0.383505 + 0.751950i
\(260\) 0 0
\(261\) 3363.16 + 4622.16i 0.797603 + 1.09619i
\(262\) 0 0
\(263\) 5433.69 3137.14i 1.27398 0.735530i 0.298242 0.954490i \(-0.403600\pi\)
0.975734 + 0.218960i \(0.0702665\pi\)
\(264\) 0 0
\(265\) 527.844i 0.122359i
\(266\) 0 0
\(267\) 583.245 + 123.758i 0.133685 + 0.0283666i
\(268\) 0 0
\(269\) 1668.18 + 2889.37i 0.378106 + 0.654899i 0.990787 0.135432i \(-0.0432421\pi\)
−0.612681 + 0.790331i \(0.709909\pi\)
\(270\) 0 0
\(271\) −2462.26 1421.59i −0.551925 0.318654i 0.197973 0.980207i \(-0.436564\pi\)
−0.749898 + 0.661553i \(0.769897\pi\)
\(272\) 0 0
\(273\) 486.769 1822.03i 0.107914 0.403934i
\(274\) 0 0
\(275\) 4350.06 + 2511.51i 0.953886 + 0.550726i
\(276\) 0 0
\(277\) −3174.17 5497.82i −0.688510 1.19253i −0.972320 0.233654i \(-0.924932\pi\)
0.283809 0.958881i \(-0.408402\pi\)
\(278\) 0 0
\(279\) −1096.73 + 2467.96i −0.235339 + 0.529580i
\(280\) 0 0
\(281\) 3735.88i 0.793110i −0.918011 0.396555i \(-0.870206\pi\)
0.918011 0.396555i \(-0.129794\pi\)
\(282\) 0 0
\(283\) 4777.96 2758.56i 1.00361 0.579432i 0.0942927 0.995545i \(-0.469941\pi\)
0.909313 + 0.416112i \(0.136608\pi\)
\(284\) 0 0
\(285\) −194.925 175.388i −0.0405136 0.0364529i
\(286\) 0 0
\(287\) −1882.62 + 2901.44i −0.387205 + 0.596748i
\(288\) 0 0
\(289\) −3026.48 + 5242.01i −0.616014 + 1.06697i
\(290\) 0 0
\(291\) 6999.37 2276.95i 1.41000 0.458685i
\(292\) 0 0
\(293\) −7574.50 −1.51026 −0.755131 0.655574i \(-0.772427\pi\)
−0.755131 + 0.655574i \(0.772427\pi\)
\(294\) 0 0
\(295\) −780.333 −0.154009
\(296\) 0 0
\(297\) 5678.10 + 590.745i 1.10935 + 0.115416i
\(298\) 0 0
\(299\) 787.855 1364.61i 0.152384 0.263937i
\(300\) 0 0
\(301\) 1599.01 2464.34i 0.306196 0.471901i
\(302\) 0 0
\(303\) −836.951 + 930.184i −0.158685 + 0.176362i
\(304\) 0 0
\(305\) −872.657 + 503.829i −0.163830 + 0.0945874i
\(306\) 0 0
\(307\) 10635.6i 1.97723i −0.150480 0.988613i \(-0.548082\pi\)
0.150480 0.988613i \(-0.451918\pi\)
\(308\) 0 0
\(309\) 1196.16 5637.21i 0.220217 1.03783i
\(310\) 0 0
\(311\) −2885.59 4997.99i −0.526132 0.911287i −0.999537 0.0304419i \(-0.990309\pi\)
0.473405 0.880845i \(-0.343025\pi\)
\(312\) 0 0
\(313\) −2030.41 1172.26i −0.366664 0.211694i 0.305336 0.952245i \(-0.401231\pi\)
−0.672000 + 0.740551i \(0.734565\pi\)
\(314\) 0 0
\(315\) 556.086 + 282.577i 0.0994664 + 0.0505442i
\(316\) 0 0
\(317\) 6852.10 + 3956.06i 1.21405 + 0.700929i 0.963638 0.267211i \(-0.0861021\pi\)
0.250407 + 0.968141i \(0.419435\pi\)
\(318\) 0 0
\(319\) −4307.36 7460.56i −0.756005 1.30944i
\(320\) 0 0
\(321\) 1151.56 5427.03i 0.200230 0.943637i
\(322\) 0 0
\(323\) 4236.32i 0.729769i
\(324\) 0 0
\(325\) 2095.06 1209.58i 0.357579 0.206448i
\(326\) 0 0
\(327\) −35.0596 + 38.9652i −0.00592906 + 0.00658954i
\(328\) 0 0
\(329\) 3012.94 + 5907.57i 0.504889 + 0.989953i
\(330\) 0 0
\(331\) −2440.02 + 4226.23i −0.405182 + 0.701797i −0.994343 0.106220i \(-0.966125\pi\)
0.589160 + 0.808016i \(0.299459\pi\)
\(332\) 0 0
\(333\) 539.743 + 5100.85i 0.0888220 + 0.839414i
\(334\) 0 0
\(335\) −372.407 −0.0607367
\(336\) 0 0
\(337\) −4136.39 −0.668616 −0.334308 0.942464i \(-0.608503\pi\)
−0.334308 + 0.942464i \(0.608503\pi\)
\(338\) 0 0
\(339\) −4369.53 + 1421.44i −0.700061 + 0.227735i
\(340\) 0 0
\(341\) 2035.04 3524.80i 0.323178 0.559761i
\(342\) 0 0
\(343\) 6275.39 + 986.454i 0.987869 + 0.155287i
\(344\) 0 0
\(345\) 387.421 + 348.589i 0.0604580 + 0.0543982i
\(346\) 0 0
\(347\) 2009.83 1160.38i 0.310933 0.179517i −0.336411 0.941715i \(-0.609213\pi\)
0.647344 + 0.762198i \(0.275880\pi\)
\(348\) 0 0
\(349\) 226.795i 0.0347853i 0.999849 + 0.0173926i \(0.00553653\pi\)
−0.999849 + 0.0173926i \(0.994463\pi\)
\(350\) 0 0
\(351\) 1613.73 2226.03i 0.245397 0.338509i
\(352\) 0 0
\(353\) −742.854 1286.66i −0.112006 0.194000i 0.804573 0.593854i \(-0.202394\pi\)
−0.916579 + 0.399854i \(0.869061\pi\)
\(354\) 0 0
\(355\) 491.949 + 284.027i 0.0735491 + 0.0424636i
\(356\) 0 0
\(357\) 2615.43 + 9732.18i 0.387740 + 1.44280i
\(358\) 0 0
\(359\) 9419.94 + 5438.60i 1.38486 + 0.799550i 0.992730 0.120359i \(-0.0384045\pi\)
0.392131 + 0.919909i \(0.371738\pi\)
\(360\) 0 0
\(361\) −2611.22 4522.77i −0.380700 0.659392i
\(362\) 0 0
\(363\) −1650.61 350.241i −0.238662 0.0506416i
\(364\) 0 0
\(365\) 625.800i 0.0897421i
\(366\) 0 0
\(367\) 3299.69 1905.08i 0.469325 0.270965i −0.246632 0.969109i \(-0.579324\pi\)
0.715957 + 0.698144i \(0.245991\pi\)
\(368\) 0 0
\(369\) −4077.24 + 2966.66i −0.575210 + 0.418532i
\(370\) 0 0
\(371\) −407.121 + 7826.30i −0.0569721 + 1.09521i
\(372\) 0 0
\(373\) 4869.55 8434.30i 0.675967 1.17081i −0.300219 0.953870i \(-0.597060\pi\)
0.976185 0.216938i \(-0.0696070\pi\)
\(374\) 0 0
\(375\) 498.163 + 1531.36i 0.0686001 + 0.210877i
\(376\) 0 0
\(377\) −4148.98 −0.566800
\(378\) 0 0
\(379\) −320.171 −0.0433933 −0.0216967 0.999765i \(-0.506907\pi\)
−0.0216967 + 0.999765i \(0.506907\pi\)
\(380\) 0 0
\(381\) −1350.46 4151.32i −0.181591 0.558211i
\(382\) 0 0
\(383\) −2185.13 + 3784.75i −0.291527 + 0.504939i −0.974171 0.225812i \(-0.927497\pi\)
0.682644 + 0.730751i \(0.260830\pi\)
\(384\) 0 0
\(385\) −788.592 511.683i −0.104391 0.0677346i
\(386\) 0 0
\(387\) 3463.00 2519.74i 0.454869 0.330970i
\(388\) 0 0
\(389\) 11877.4 6857.42i 1.54809 0.893791i 0.549805 0.835293i \(-0.314702\pi\)
0.998288 0.0584981i \(-0.0186311\pi\)
\(390\) 0 0
\(391\) 8419.84i 1.08903i
\(392\) 0 0
\(393\) 2632.49 + 558.587i 0.337892 + 0.0716971i
\(394\) 0 0
\(395\) −38.6150 66.8832i −0.00491882 0.00851964i
\(396\) 0 0
\(397\) −2181.61 1259.55i −0.275798 0.159232i 0.355722 0.934592i \(-0.384235\pi\)
−0.631520 + 0.775360i \(0.717568\pi\)
\(398\) 0 0
\(399\) −2754.86 2750.80i −0.345653 0.345143i
\(400\) 0 0
\(401\) 2268.96 + 1309.98i 0.282560 + 0.163136i 0.634582 0.772856i \(-0.281172\pi\)
−0.352022 + 0.935992i \(0.614506\pi\)
\(402\) 0 0
\(403\) −980.109 1697.60i −0.121148 0.209835i
\(404\) 0 0
\(405\) 609.431 + 674.933i 0.0747725 + 0.0828091i
\(406\) 0 0
\(407\) 7730.22i 0.941456i
\(408\) 0 0
\(409\) −12058.7 + 6962.09i −1.45786 + 0.841694i −0.998906 0.0467669i \(-0.985108\pi\)
−0.458952 + 0.888461i \(0.651775\pi\)
\(410\) 0 0
\(411\) 4241.53 + 3816.40i 0.509049 + 0.458027i
\(412\) 0 0
\(413\) −11569.9 601.863i −1.37850 0.0717088i
\(414\) 0 0
\(415\) 45.6041 78.9886i 0.00539426 0.00934313i
\(416\) 0 0
\(417\) 4092.70 1331.39i 0.480624 0.156351i
\(418\) 0 0
\(419\) −15171.1 −1.76887 −0.884433 0.466666i \(-0.845455\pi\)
−0.884433 + 0.466666i \(0.845455\pi\)
\(420\) 0 0
\(421\) −1052.53 −0.121846 −0.0609228 0.998142i \(-0.519404\pi\)
−0.0609228 + 0.998142i \(0.519404\pi\)
\(422\) 0 0
\(423\) 1017.32 + 9614.18i 0.116935 + 1.10510i
\(424\) 0 0
\(425\) −6463.43 + 11195.0i −0.737700 + 1.27773i
\(426\) 0 0
\(427\) −13327.4 + 6797.16i −1.51044 + 0.770345i
\(428\) 0 0
\(429\) −2771.50 + 3080.23i −0.311909 + 0.346655i
\(430\) 0 0
\(431\) −6923.58 + 3997.33i −0.773776 + 0.446740i −0.834220 0.551432i \(-0.814082\pi\)
0.0604442 + 0.998172i \(0.480748\pi\)
\(432\) 0 0
\(433\) 12889.4i 1.43055i 0.698845 + 0.715273i \(0.253697\pi\)
−0.698845 + 0.715273i \(0.746303\pi\)
\(434\) 0 0
\(435\) 284.838 1342.38i 0.0313953 0.147959i
\(436\) 0 0
\(437\) −1626.36 2816.94i −0.178030 0.308358i
\(438\) 0 0
\(439\) −12456.7 7191.89i −1.35427 0.781891i −0.365430 0.930839i \(-0.619078\pi\)
−0.988845 + 0.148948i \(0.952411\pi\)
\(440\) 0 0
\(441\) 8027.09 + 4618.65i 0.866763 + 0.498721i
\(442\) 0 0
\(443\) −3432.16 1981.56i −0.368097 0.212521i 0.304530 0.952503i \(-0.401501\pi\)
−0.672627 + 0.739982i \(0.734834\pi\)
\(444\) 0 0
\(445\) −71.5668 123.957i −0.00762380 0.0132048i
\(446\) 0 0
\(447\) −962.710 + 4537.03i −0.101867 + 0.480076i
\(448\) 0 0
\(449\) 13479.1i 1.41675i −0.705838 0.708373i \(-0.749430\pi\)
0.705838 0.708373i \(-0.250570\pi\)
\(450\) 0 0
\(451\) 6581.00 3799.54i 0.687112 0.396704i
\(452\) 0 0
\(453\) 4952.78 5504.51i 0.513691 0.570915i
\(454\) 0 0
\(455\) −403.318 + 205.698i −0.0415557 + 0.0211940i
\(456\) 0 0
\(457\) −1989.79 + 3446.42i −0.203673 + 0.352772i −0.949709 0.313134i \(-0.898621\pi\)
0.746036 + 0.665905i \(0.231955\pi\)
\(458\) 0 0
\(459\) −1520.30 + 14612.7i −0.154600 + 1.48598i
\(460\) 0 0
\(461\) −9053.72 −0.914694 −0.457347 0.889288i \(-0.651200\pi\)
−0.457347 + 0.889288i \(0.651200\pi\)
\(462\) 0 0
\(463\) 5736.10 0.575764 0.287882 0.957666i \(-0.407049\pi\)
0.287882 + 0.957666i \(0.407049\pi\)
\(464\) 0 0
\(465\) 616.534 200.563i 0.0614862 0.0200019i
\(466\) 0 0
\(467\) 6196.30 10732.3i 0.613984 1.06345i −0.376578 0.926385i \(-0.622899\pi\)
0.990562 0.137067i \(-0.0437675\pi\)
\(468\) 0 0
\(469\) −5521.65 287.234i −0.543638 0.0282798i
\(470\) 0 0
\(471\) 1092.20 + 982.726i 0.106849 + 0.0961393i
\(472\) 0 0
\(473\) −5589.57 + 3227.14i −0.543359 + 0.313709i
\(474\) 0 0
\(475\) 4993.85i 0.482387i
\(476\) 0 0
\(477\) −4639.67 + 10440.6i −0.445359 + 1.00219i
\(478\) 0 0
\(479\) 4133.87 + 7160.07i 0.394324 + 0.682989i 0.993015 0.117991i \(-0.0376455\pi\)
−0.598691 + 0.800980i \(0.704312\pi\)
\(480\) 0 0
\(481\) −3224.21 1861.50i −0.305637 0.176460i
\(482\) 0 0
\(483\) 5475.39 + 5467.31i 0.515815 + 0.515054i
\(484\) 0 0
\(485\) −1530.24 883.487i −0.143268 0.0827156i
\(486\) 0 0
\(487\) 470.075 + 814.194i 0.0437395 + 0.0757590i 0.887066 0.461642i \(-0.152740\pi\)
−0.843327 + 0.537401i \(0.819406\pi\)
\(488\) 0 0
\(489\) −11772.9 2498.08i −1.08873 0.231017i
\(490\) 0 0
\(491\) 1057.30i 0.0971801i −0.998819 0.0485900i \(-0.984527\pi\)
0.998819 0.0485900i \(-0.0154728\pi\)
\(492\) 0 0
\(493\) 19199.9 11085.1i 1.75400 1.01267i
\(494\) 0 0
\(495\) −806.318 1108.16i −0.0732148 0.100623i
\(496\) 0 0
\(497\) 7075.02 + 4590.68i 0.638547 + 0.414326i
\(498\) 0 0
\(499\) −3086.65 + 5346.23i −0.276909 + 0.479620i −0.970615 0.240638i \(-0.922643\pi\)
0.693706 + 0.720258i \(0.255977\pi\)
\(500\) 0 0
\(501\) 3768.95 + 11585.8i 0.336097 + 1.03316i
\(502\) 0 0
\(503\) −4284.28 −0.379775 −0.189887 0.981806i \(-0.560812\pi\)
−0.189887 + 0.981806i \(0.560812\pi\)
\(504\) 0 0
\(505\) 300.390 0.0264697
\(506\) 0 0
\(507\) −2914.19 8958.26i −0.255274 0.784714i
\(508\) 0 0
\(509\) −7550.52 + 13077.9i −0.657507 + 1.13884i 0.323752 + 0.946142i \(0.395056\pi\)
−0.981259 + 0.192693i \(0.938278\pi\)
\(510\) 0 0
\(511\) 482.673 9278.68i 0.0417851 0.803258i
\(512\) 0 0
\(513\) −2313.93 5182.48i −0.199148 0.446028i
\(514\) 0 0
\(515\) −1198.08 + 691.712i −0.102512 + 0.0591854i
\(516\) 0 0
\(517\) 14570.1i 1.23944i
\(518\) 0 0
\(519\) 5254.79 + 1115.01i 0.444431 + 0.0943037i
\(520\) 0 0
\(521\) 6894.00 + 11940.8i 0.579715 + 1.00410i 0.995512 + 0.0946385i \(0.0301695\pi\)
−0.415796 + 0.909458i \(0.636497\pi\)
\(522\) 0 0
\(523\) 832.513 + 480.652i 0.0696047 + 0.0401863i 0.534398 0.845233i \(-0.320538\pi\)
−0.464794 + 0.885419i \(0.653872\pi\)
\(524\) 0 0
\(525\) 3083.12 + 11472.5i 0.256301 + 0.953713i
\(526\) 0 0
\(527\) 9071.15 + 5237.23i 0.749802 + 0.432898i
\(528\) 0 0
\(529\) −2851.06 4938.17i −0.234327 0.405866i
\(530\) 0 0
\(531\) −15434.8 6859.02i −1.26142 0.560557i
\(532\) 0 0
\(533\) 3659.84i 0.297421i
\(534\) 0 0
\(535\) −1153.41 + 665.922i −0.0932080 + 0.0538137i
\(536\) 0 0
\(537\) 559.639 + 503.545i 0.0449724 + 0.0404648i
\(538\) 0 0
\(539\) −11297.7 8194.92i −0.902834 0.654880i
\(540\) 0 0
\(541\) 597.846 1035.50i 0.0475109 0.0822913i −0.841292 0.540581i \(-0.818204\pi\)
0.888803 + 0.458290i \(0.151538\pi\)
\(542\) 0 0
\(543\) 10165.0 3306.77i 0.803358 0.261339i
\(544\) 0 0
\(545\) 12.5833 0.000989006
\(546\) 0 0
\(547\) −18601.8 −1.45403 −0.727014 0.686622i \(-0.759093\pi\)
−0.727014 + 0.686622i \(0.759093\pi\)
\(548\) 0 0
\(549\) −21689.5 + 2295.06i −1.68613 + 0.178417i
\(550\) 0 0
\(551\) −4282.34 + 7417.24i −0.331096 + 0.573475i
\(552\) 0 0
\(553\) −520.955 1021.45i −0.0400601 0.0785473i
\(554\) 0 0
\(555\) 823.625 915.375i 0.0629927 0.0700099i
\(556\) 0 0
\(557\) −5908.09 + 3411.04i −0.449432 + 0.259480i −0.707590 0.706623i \(-0.750218\pi\)
0.258158 + 0.966103i \(0.416884\pi\)
\(558\) 0 0
\(559\) 3108.49i 0.235197i
\(560\) 0 0
\(561\) 4595.80 21658.9i 0.345873 1.63002i
\(562\) 0 0
\(563\) −5679.80 9837.71i −0.425178 0.736430i 0.571259 0.820770i \(-0.306455\pi\)
−0.996437 + 0.0843399i \(0.973122\pi\)
\(564\) 0 0
\(565\) 955.293 + 551.539i 0.0711318 + 0.0410680i
\(566\) 0 0
\(567\) 8515.41 + 10477.2i 0.630712 + 0.776017i
\(568\) 0 0
\(569\) −18467.2 10662.1i −1.36061 0.785549i −0.370905 0.928671i \(-0.620953\pi\)
−0.989705 + 0.143122i \(0.954286\pi\)
\(570\) 0 0
\(571\) −7384.00 12789.5i −0.541175 0.937343i −0.998837 0.0482163i \(-0.984646\pi\)
0.457662 0.889126i \(-0.348687\pi\)
\(572\) 0 0
\(573\) −3180.36 + 14988.3i −0.231870 + 1.09275i
\(574\) 0 0
\(575\) 9925.45i 0.719861i
\(576\) 0 0
\(577\) 16718.5 9652.44i 1.20624 0.696424i 0.244305 0.969698i \(-0.421440\pi\)
0.961936 + 0.273275i \(0.0881068\pi\)
\(578\) 0 0
\(579\) 7892.27 8771.45i 0.566479 0.629584i
\(580\) 0 0
\(581\) 737.091 1135.98i 0.0526328 0.0811162i
\(582\) 0 0
\(583\) 8609.17 14911.5i 0.611587 1.05930i
\(584\) 0 0
\(585\) −656.374 + 69.4538i −0.0463893 + 0.00490865i
\(586\) 0 0
\(587\) 4397.46 0.309204 0.154602 0.987977i \(-0.450590\pi\)
0.154602 + 0.987977i \(0.450590\pi\)
\(588\) 0 0
\(589\) −4046.45 −0.283075
\(590\) 0 0
\(591\) −2450.13 + 797.045i −0.170532 + 0.0554756i
\(592\) 0 0
\(593\) 10970.1 19000.8i 0.759677 1.31580i −0.183339 0.983050i \(-0.558691\pi\)
0.943015 0.332749i \(-0.107976\pi\)
\(594\) 0 0
\(595\) 1316.83 2029.46i 0.0907307 0.139832i
\(596\) 0 0
\(597\) 3243.54 + 2918.44i 0.222361 + 0.200073i
\(598\) 0 0
\(599\) −4765.07 + 2751.12i −0.325034 + 0.187659i −0.653634 0.756810i \(-0.726757\pi\)
0.328600 + 0.944469i \(0.393423\pi\)
\(600\) 0 0
\(601\) 5814.58i 0.394645i 0.980339 + 0.197322i \(0.0632246\pi\)
−0.980339 + 0.197322i \(0.936775\pi\)
\(602\) 0 0
\(603\) −7366.11 3273.41i −0.497465 0.221067i
\(604\) 0 0
\(605\) 202.537 + 350.804i 0.0136104 + 0.0235739i
\(606\) 0 0
\(607\) 11510.7 + 6645.69i 0.769693 + 0.444382i 0.832765 0.553627i \(-0.186756\pi\)
−0.0630721 + 0.998009i \(0.520090\pi\)
\(608\) 0 0
\(609\) 5258.63 19683.6i 0.349902 1.30972i
\(610\) 0 0
\(611\) −6077.05 3508.59i −0.402375 0.232311i
\(612\) 0 0
\(613\) −9797.17 16969.2i −0.645520 1.11807i −0.984181 0.177166i \(-0.943307\pi\)
0.338661 0.940909i \(-0.390026\pi\)
\(614\) 0 0
\(615\) 1184.12 + 251.257i 0.0776394 + 0.0164743i
\(616\) 0 0
\(617\) 348.388i 0.0227319i 0.999935 + 0.0113660i \(0.00361797\pi\)
−0.999935 + 0.0113660i \(0.996382\pi\)
\(618\) 0 0
\(619\) −5867.68 + 3387.71i −0.381005 + 0.219973i −0.678255 0.734826i \(-0.737264\pi\)
0.297251 + 0.954799i \(0.403930\pi\)
\(620\) 0 0
\(621\) 4599.02 + 10300.4i 0.297186 + 0.665602i
\(622\) 0 0
\(623\) −965.508 1893.10i −0.0620903 0.121742i
\(624\) 0 0
\(625\) −7521.95 + 13028.4i −0.481405 + 0.833818i
\(626\) 0 0
\(627\) 2646.03 + 8133.91i 0.168536 + 0.518082i
\(628\) 0 0
\(629\) 19893.9 1.26108
\(630\) 0 0
\(631\) 7326.82 0.462244 0.231122 0.972925i \(-0.425760\pi\)
0.231122 + 0.972925i \(0.425760\pi\)
\(632\) 0 0
\(633\) 6432.49 + 19773.6i 0.403900 + 1.24159i
\(634\) 0 0
\(635\) −523.995 + 907.586i −0.0327466 + 0.0567188i
\(636\) 0 0
\(637\) −6138.62 + 2738.79i −0.381822 + 0.170353i
\(638\) 0 0
\(639\) 7234.06 + 9942.13i 0.447848 + 0.615500i
\(640\) 0 0
\(641\) 2433.38 1404.91i 0.149942 0.0865689i −0.423152 0.906059i \(-0.639076\pi\)
0.573094 + 0.819490i \(0.305743\pi\)
\(642\) 0 0
\(643\) 27485.5i 1.68573i 0.538128 + 0.842863i \(0.319132\pi\)
−0.538128 + 0.842863i \(0.680868\pi\)
\(644\) 0 0
\(645\) −1005.73 213.405i −0.0613962 0.0130276i
\(646\) 0 0
\(647\) 14659.9 + 25391.7i 0.890790 + 1.54289i 0.838930 + 0.544239i \(0.183181\pi\)
0.0518595 + 0.998654i \(0.483485\pi\)
\(648\) 0 0
\(649\) 22044.3 + 12727.3i 1.33330 + 0.769783i
\(650\) 0 0
\(651\) 9295.98 2498.21i 0.559659 0.150403i
\(652\) 0 0
\(653\) 14500.6 + 8371.91i 0.868992 + 0.501713i 0.867013 0.498285i \(-0.166037\pi\)
0.00197863 + 0.999998i \(0.499370\pi\)
\(654\) 0 0
\(655\) −323.019 559.485i −0.0192693 0.0333754i
\(656\) 0 0
\(657\) 5500.69 12378.1i 0.326640 0.735034i
\(658\) 0 0
\(659\) 9520.47i 0.562769i −0.959595 0.281385i \(-0.909206\pi\)
0.959595 0.281385i \(-0.0907937\pi\)
\(660\) 0 0
\(661\) −20217.5 + 11672.6i −1.18966 + 0.686853i −0.958230 0.285998i \(-0.907675\pi\)
−0.231434 + 0.972851i \(0.574342\pi\)
\(662\) 0 0
\(663\) −7927.06 7132.51i −0.464346 0.417804i
\(664\) 0 0
\(665\) −48.5515 + 933.331i −0.00283120 + 0.0544256i
\(666\) 0 0
\(667\) 8511.31 14742.0i 0.494092 0.855792i
\(668\) 0 0
\(669\) 15024.1 4887.46i 0.868260 0.282452i
\(670\) 0 0
\(671\) 32869.9 1.89110
\(672\) 0 0
\(673\) −12283.5 −0.703559 −0.351780 0.936083i \(-0.614423\pi\)
−0.351780 + 0.936083i \(0.614423\pi\)
\(674\) 0 0
\(675\) −1792.15 + 17225.7i −0.102193 + 0.982250i
\(676\) 0 0
\(677\) 6495.88 11251.2i 0.368769 0.638727i −0.620604 0.784124i \(-0.713113\pi\)
0.989373 + 0.145397i \(0.0464459\pi\)
\(678\) 0 0
\(679\) −22007.4 14279.6i −1.24384 0.807072i
\(680\) 0 0
\(681\) 15280.2 16982.3i 0.859819 0.955601i
\(682\) 0 0
\(683\) 7366.62 4253.12i 0.412703 0.238274i −0.279248 0.960219i \(-0.590085\pi\)
0.691950 + 0.721945i \(0.256752\pi\)
\(684\) 0 0
\(685\) 1369.74i 0.0764018i
\(686\) 0 0
\(687\) −2139.38 + 10082.4i −0.118810 + 0.559923i
\(688\) 0 0
\(689\) −4146.31 7181.62i −0.229263 0.397095i
\(690\) 0 0
\(691\) 22372.0 + 12916.5i 1.23165 + 0.711093i 0.967374 0.253354i \(-0.0815336\pi\)
0.264276 + 0.964447i \(0.414867\pi\)
\(692\) 0 0
\(693\) −11100.5 17052.6i −0.608475 0.934738i
\(694\) 0 0
\(695\) −894.770 516.595i −0.0488353 0.0281951i
\(696\) 0 0
\(697\) 9778.22 + 16936.4i 0.531387 + 0.920389i
\(698\) 0 0
\(699\) 4717.33 22231.7i 0.255259 1.20298i
\(700\) 0 0
\(701\) 22607.8i 1.21810i 0.793134 + 0.609048i \(0.208448\pi\)
−0.793134 + 0.609048i \(0.791552\pi\)
\(702\) 0 0
\(703\) −6655.69 + 3842.67i −0.357076 + 0.206158i
\(704\) 0 0
\(705\) 1552.38 1725.32i 0.0829308 0.0921690i
\(706\) 0 0
\(707\) 4453.86 + 231.688i 0.236923 + 0.0123246i
\(708\) 0 0
\(709\) 5472.41 9478.50i 0.289874 0.502077i −0.683905 0.729571i \(-0.739720\pi\)
0.973779 + 0.227494i \(0.0730532\pi\)
\(710\) 0 0
\(711\) −175.900 1662.35i −0.00927818 0.0876835i
\(712\) 0 0
\(713\) 8042.46 0.422430
\(714\) 0 0
\(715\) 994.720 0.0520285
\(716\) 0 0
\(717\) −18907.3 + 6150.70i −0.984808 + 0.320366i
\(718\) 0 0
\(719\) 12885.3 22317.9i 0.668344 1.15761i −0.310023 0.950729i \(-0.600337\pi\)
0.978367 0.206877i \(-0.0663299\pi\)
\(720\) 0 0
\(721\) −18297.3 + 9331.88i −0.945116 + 0.482021i
\(722\) 0 0
\(723\) −13287.3 11955.5i −0.683486 0.614979i
\(724\) 0 0
\(725\) 22633.2 13067.3i 1.15942 0.669389i
\(726\) 0 0
\(727\) 15593.1i 0.795485i 0.917497 + 0.397742i \(0.130206\pi\)
−0.917497 + 0.397742i \(0.869794\pi\)
\(728\) 0 0
\(729\) 6121.81 + 18706.8i 0.311020 + 0.950403i
\(730\) 0 0
\(731\) −8305.13 14384.9i −0.420214 0.727832i
\(732\) 0 0
\(733\) 692.858 + 400.022i 0.0349131 + 0.0201571i 0.517355 0.855771i \(-0.326917\pi\)
−0.482442 + 0.875928i \(0.660250\pi\)
\(734\) 0 0
\(735\) −464.684 2174.13i −0.0233199 0.109108i
\(736\) 0 0
\(737\) 10520.5 + 6073.99i 0.525815 + 0.303580i
\(738\) 0 0
\(739\) −454.445 787.122i −0.0226211 0.0391810i 0.854493 0.519463i \(-0.173868\pi\)
−0.877114 + 0.480282i \(0.840534\pi\)
\(740\) 0 0
\(741\) 4029.77 + 855.076i 0.199781 + 0.0423914i
\(742\) 0 0
\(743\) 8109.00i 0.400391i −0.979756 0.200195i \(-0.935842\pi\)
0.979756 0.200195i \(-0.0641577\pi\)
\(744\) 0 0
\(745\) 964.258 556.715i 0.0474197 0.0273778i
\(746\) 0 0
\(747\) 1596.33 1161.52i 0.0781885 0.0568912i
\(748\) 0 0
\(749\) −17615.1 + 8983.95i −0.859337 + 0.438273i
\(750\) 0 0
\(751\) −10382.2 + 17982.5i −0.504463 + 0.873756i 0.495524 + 0.868594i \(0.334976\pi\)
−0.999987 + 0.00516122i \(0.998357\pi\)
\(752\) 0 0
\(753\) 3289.79 + 10112.8i 0.159212 + 0.489419i
\(754\) 0 0
\(755\) −1777.61 −0.0856870
\(756\) 0 0
\(757\) 23295.6 1.11848 0.559242 0.829005i \(-0.311092\pi\)
0.559242 + 0.829005i \(0.311092\pi\)
\(758\) 0 0
\(759\) −5259.07 16166.4i −0.251505 0.773128i
\(760\) 0 0
\(761\) −5014.38 + 8685.16i −0.238858 + 0.413715i −0.960387 0.278670i \(-0.910106\pi\)
0.721529 + 0.692385i \(0.243440\pi\)
\(762\) 0 0
\(763\) 186.571 + 9.70535i 0.00885233 + 0.000460494i
\(764\) 0 0
\(765\) 2851.89 2075.08i 0.134785 0.0980715i
\(766\) 0 0
\(767\) 10616.9 6129.66i 0.499809 0.288565i
\(768\) 0 0
\(769\) 13500.3i 0.633074i 0.948580 + 0.316537i \(0.102520\pi\)
−0.948580 + 0.316537i \(0.897480\pi\)
\(770\) 0 0
\(771\) −30757.8 6526.49i −1.43673 0.304858i
\(772\) 0 0
\(773\) −11644.9 20169.5i −0.541833 0.938482i −0.998799 0.0489979i \(-0.984397\pi\)
0.456966 0.889484i \(-0.348936\pi\)
\(774\) 0 0
\(775\) 10693.2 + 6173.74i 0.495629 + 0.286151i
\(776\) 0 0
\(777\) 12917.8 12936.9i 0.596428 0.597310i
\(778\) 0 0
\(779\) −6542.79 3777.48i −0.300924 0.173739i
\(780\) 0 0
\(781\) −9264.99 16047.4i −0.424491 0.735240i
\(782\) 0 0
\(783\) 17433.3 24048.1i 0.795677 1.09759i
\(784\) 0 0
\(785\) 352.711i 0.0160367i
\(786\) 0 0
\(787\) 20635.4 11913.8i 0.934653 0.539622i 0.0463726 0.998924i \(-0.485234\pi\)
0.888280 + 0.459302i \(0.151901\pi\)
\(788\) 0 0
\(789\) −24235.8 21806.6i