Properties

Label 363.3.b.m.122.8
Level $363$
Weight $3$
Character 363.122
Analytic conductor $9.891$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 363.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.89103359628\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \( x^{8} + 29x^{6} + 282x^{4} + 1061x^{2} + 1331 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 122.8
Root \(3.58727i\) of defining polynomial
Character \(\chi\) \(=\) 363.122
Dual form 363.3.b.m.122.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.58727i q^{2} +(-2.74329 - 1.21424i) q^{3} -8.86854 q^{4} -2.08639i q^{5} +(4.35581 - 9.84093i) q^{6} +8.86303 q^{7} -17.4648i q^{8} +(6.05125 + 6.66201i) q^{9} +O(q^{10})\) \(q+3.58727i q^{2} +(-2.74329 - 1.21424i) q^{3} -8.86854 q^{4} -2.08639i q^{5} +(4.35581 - 9.84093i) q^{6} +8.86303 q^{7} -17.4648i q^{8} +(6.05125 + 6.66201i) q^{9} +7.48447 q^{10} +(24.3290 + 10.7685i) q^{12} -1.64480 q^{13} +31.7941i q^{14} +(-2.53338 + 5.72358i) q^{15} +27.1769 q^{16} +12.4235i q^{17} +(-23.8985 + 21.7075i) q^{18} +10.5657 q^{19} +18.5033i q^{20} +(-24.3138 - 10.7618i) q^{21} +20.3378i q^{23} +(-21.2064 + 47.9109i) q^{24} +20.6470 q^{25} -5.90037i q^{26} +(-8.51105 - 25.6235i) q^{27} -78.6021 q^{28} +11.6087i q^{29} +(-20.5320 - 9.08793i) q^{30} -23.3883 q^{31} +27.6317i q^{32} -44.5665 q^{34} -18.4918i q^{35} +(-53.6658 - 59.0823i) q^{36} +7.24593 q^{37} +37.9019i q^{38} +(4.51217 + 1.99719i) q^{39} -36.4384 q^{40} +38.8768i q^{41} +(38.6056 - 87.2204i) q^{42} -15.8444 q^{43} +(13.8996 - 12.6253i) q^{45} -72.9572 q^{46} +45.3086i q^{47} +(-74.5539 - 32.9992i) q^{48} +29.5532 q^{49} +74.0663i q^{50} +(15.0851 - 34.0812i) q^{51} +14.5870 q^{52} +40.3160i q^{53} +(91.9184 - 30.5315i) q^{54} -154.791i q^{56} +(-28.9847 - 12.8292i) q^{57} -41.6435 q^{58} +113.181i q^{59} +(22.4674 - 50.7598i) q^{60} +77.5161 q^{61} -83.9001i q^{62} +(53.6324 + 59.0456i) q^{63} +9.58504 q^{64} +3.43171i q^{65} +62.9082 q^{67} -110.178i q^{68} +(24.6949 - 55.7924i) q^{69} +66.3350 q^{70} -10.2125i q^{71} +(116.351 - 105.684i) q^{72} -74.6222 q^{73} +25.9931i q^{74} +(-56.6405 - 25.0703i) q^{75} -93.7020 q^{76} +(-7.16445 + 16.1864i) q^{78} +86.3123 q^{79} -56.7016i q^{80} +(-7.76472 + 80.6270i) q^{81} -139.462 q^{82} +11.8083i q^{83} +(215.628 + 95.4417i) q^{84} +25.9203 q^{85} -56.8381i q^{86} +(14.0957 - 31.8459i) q^{87} +74.5782i q^{89} +(45.2904 + 49.8616i) q^{90} -14.5779 q^{91} -180.366i q^{92} +(64.1607 + 28.3989i) q^{93} -162.534 q^{94} -22.0441i q^{95} +(33.5514 - 75.8016i) q^{96} -77.1678 q^{97} +106.016i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 5 q^{3} - 26 q^{4} + q^{6} + 28 q^{7} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 5 q^{3} - 26 q^{4} + q^{6} + 28 q^{7} + 11 q^{9} - 6 q^{10} + 53 q^{12} + 44 q^{13} - 54 q^{15} - 14 q^{16} + q^{18} + 68 q^{19} - 6 q^{21} + 33 q^{24} + 42 q^{25} - 25 q^{27} - 118 q^{28} + 10 q^{30} + 2 q^{31} - 66 q^{34} - 7 q^{36} + 140 q^{37} + 38 q^{39} + 58 q^{40} + 174 q^{42} - 78 q^{43} - 36 q^{45} - 286 q^{46} - 285 q^{48} - 140 q^{49} + 58 q^{51} - 102 q^{52} + 523 q^{54} - 22 q^{57} - 68 q^{58} + 262 q^{60} + 22 q^{61} + 246 q^{63} - 52 q^{64} + 184 q^{67} - 176 q^{69} + 374 q^{70} + 489 q^{72} - 378 q^{73} - 33 q^{75} - 450 q^{76} - 246 q^{78} - 252 q^{79} + 11 q^{81} - 200 q^{82} + 450 q^{84} - 156 q^{85} + 66 q^{87} + 598 q^{90} - 148 q^{91} + 380 q^{93} - 460 q^{94} + 399 q^{96} - 324 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.58727i 1.79364i 0.442398 + 0.896819i \(0.354128\pi\)
−0.442398 + 0.896819i \(0.645872\pi\)
\(3\) −2.74329 1.21424i −0.914429 0.404746i
\(4\) −8.86854 −2.21714
\(5\) 2.08639i 0.417279i −0.977993 0.208639i \(-0.933097\pi\)
0.977993 0.208639i \(-0.0669035\pi\)
\(6\) 4.35581 9.84093i 0.725968 1.64015i
\(7\) 8.86303 1.26615 0.633073 0.774092i \(-0.281793\pi\)
0.633073 + 0.774092i \(0.281793\pi\)
\(8\) 17.4648i 2.18310i
\(9\) 6.05125 + 6.66201i 0.672361 + 0.740223i
\(10\) 7.48447 0.748447
\(11\) 0 0
\(12\) 24.3290 + 10.7685i 2.02741 + 0.897377i
\(13\) −1.64480 −0.126523 −0.0632617 0.997997i \(-0.520150\pi\)
−0.0632617 + 0.997997i \(0.520150\pi\)
\(14\) 31.7941i 2.27101i
\(15\) −2.53338 + 5.72358i −0.168892 + 0.381572i
\(16\) 27.1769 1.69855
\(17\) 12.4235i 0.730794i 0.930852 + 0.365397i \(0.119067\pi\)
−0.930852 + 0.365397i \(0.880933\pi\)
\(18\) −23.8985 + 21.7075i −1.32769 + 1.20597i
\(19\) 10.5657 0.556088 0.278044 0.960568i \(-0.410314\pi\)
0.278044 + 0.960568i \(0.410314\pi\)
\(20\) 18.5033i 0.925163i
\(21\) −24.3138 10.7618i −1.15780 0.512468i
\(22\) 0 0
\(23\) 20.3378i 0.884251i 0.896953 + 0.442126i \(0.145775\pi\)
−0.896953 + 0.442126i \(0.854225\pi\)
\(24\) −21.2064 + 47.9109i −0.883601 + 1.99629i
\(25\) 20.6470 0.825878
\(26\) 5.90037i 0.226937i
\(27\) −8.51105 25.6235i −0.315224 0.949017i
\(28\) −78.6021 −2.80722
\(29\) 11.6087i 0.400299i 0.979765 + 0.200149i \(0.0641428\pi\)
−0.979765 + 0.200149i \(0.935857\pi\)
\(30\) −20.5320 9.08793i −0.684402 0.302931i
\(31\) −23.3883 −0.754460 −0.377230 0.926120i \(-0.623123\pi\)
−0.377230 + 0.926120i \(0.623123\pi\)
\(32\) 27.6317i 0.863489i
\(33\) 0 0
\(34\) −44.5665 −1.31078
\(35\) 18.4918i 0.528336i
\(36\) −53.6658 59.0823i −1.49072 1.64117i
\(37\) 7.24593 0.195836 0.0979179 0.995194i \(-0.468782\pi\)
0.0979179 + 0.995194i \(0.468782\pi\)
\(38\) 37.9019i 0.997420i
\(39\) 4.51217 + 1.99719i 0.115697 + 0.0512099i
\(40\) −36.4384 −0.910961
\(41\) 38.8768i 0.948215i 0.880467 + 0.474108i \(0.157229\pi\)
−0.880467 + 0.474108i \(0.842771\pi\)
\(42\) 38.6056 87.2204i 0.919181 2.07668i
\(43\) −15.8444 −0.368474 −0.184237 0.982882i \(-0.558981\pi\)
−0.184237 + 0.982882i \(0.558981\pi\)
\(44\) 0 0
\(45\) 13.8996 12.6253i 0.308879 0.280562i
\(46\) −72.9572 −1.58603
\(47\) 45.3086i 0.964013i 0.876168 + 0.482006i \(0.160092\pi\)
−0.876168 + 0.482006i \(0.839908\pi\)
\(48\) −74.5539 32.9992i −1.55321 0.687483i
\(49\) 29.5532 0.603127
\(50\) 74.0663i 1.48133i
\(51\) 15.0851 34.0812i 0.295786 0.668259i
\(52\) 14.5870 0.280520
\(53\) 40.3160i 0.760680i 0.924847 + 0.380340i \(0.124193\pi\)
−0.924847 + 0.380340i \(0.875807\pi\)
\(54\) 91.9184 30.5315i 1.70219 0.565398i
\(55\) 0 0
\(56\) 154.791i 2.76412i
\(57\) −28.9847 12.8292i −0.508503 0.225074i
\(58\) −41.6435 −0.717991
\(59\) 113.181i 1.91833i 0.282847 + 0.959165i \(0.408721\pi\)
−0.282847 + 0.959165i \(0.591279\pi\)
\(60\) 22.4674 50.7598i 0.374456 0.845996i
\(61\) 77.5161 1.27076 0.635378 0.772202i \(-0.280844\pi\)
0.635378 + 0.772202i \(0.280844\pi\)
\(62\) 83.9001i 1.35323i
\(63\) 53.6324 + 59.0456i 0.851308 + 0.937231i
\(64\) 9.58504 0.149766
\(65\) 3.43171i 0.0527956i
\(66\) 0 0
\(67\) 62.9082 0.938929 0.469464 0.882951i \(-0.344447\pi\)
0.469464 + 0.882951i \(0.344447\pi\)
\(68\) 110.178i 1.62027i
\(69\) 24.6949 55.7924i 0.357897 0.808585i
\(70\) 66.3350 0.947643
\(71\) 10.2125i 0.143839i −0.997410 0.0719193i \(-0.977088\pi\)
0.997410 0.0719193i \(-0.0229124\pi\)
\(72\) 116.351 105.684i 1.61598 1.46783i
\(73\) −74.6222 −1.02222 −0.511111 0.859515i \(-0.670766\pi\)
−0.511111 + 0.859515i \(0.670766\pi\)
\(74\) 25.9931i 0.351258i
\(75\) −56.6405 25.0703i −0.755207 0.334271i
\(76\) −93.7020 −1.23292
\(77\) 0 0
\(78\) −7.16445 + 16.1864i −0.0918519 + 0.207518i
\(79\) 86.3123 1.09256 0.546280 0.837602i \(-0.316043\pi\)
0.546280 + 0.837602i \(0.316043\pi\)
\(80\) 56.7016i 0.708770i
\(81\) −7.76472 + 80.6270i −0.0958608 + 0.995395i
\(82\) −139.462 −1.70075
\(83\) 11.8083i 0.142269i 0.997467 + 0.0711343i \(0.0226619\pi\)
−0.997467 + 0.0711343i \(0.977338\pi\)
\(84\) 215.628 + 95.4417i 2.56700 + 1.13621i
\(85\) 25.9203 0.304945
\(86\) 56.8381i 0.660908i
\(87\) 14.0957 31.8459i 0.162019 0.366045i
\(88\) 0 0
\(89\) 74.5782i 0.837957i 0.907996 + 0.418979i \(0.137612\pi\)
−0.907996 + 0.418979i \(0.862388\pi\)
\(90\) 45.2904 + 49.8616i 0.503227 + 0.554018i
\(91\) −14.5779 −0.160197
\(92\) 180.366i 1.96050i
\(93\) 64.1607 + 28.3989i 0.689900 + 0.305365i
\(94\) −162.534 −1.72909
\(95\) 22.0441i 0.232044i
\(96\) 33.5514 75.8016i 0.349494 0.789600i
\(97\) −77.1678 −0.795544 −0.397772 0.917484i \(-0.630217\pi\)
−0.397772 + 0.917484i \(0.630217\pi\)
\(98\) 106.016i 1.08179i
\(99\) 0 0
\(100\) −183.108 −1.83108
\(101\) 12.7954i 0.126687i 0.997992 + 0.0633436i \(0.0201764\pi\)
−0.997992 + 0.0633436i \(0.979824\pi\)
\(102\) 122.259 + 54.1143i 1.19861 + 0.530533i
\(103\) 70.5641 0.685088 0.342544 0.939502i \(-0.388711\pi\)
0.342544 + 0.939502i \(0.388711\pi\)
\(104\) 28.7262i 0.276213i
\(105\) −22.4534 + 50.7282i −0.213842 + 0.483126i
\(106\) −144.625 −1.36438
\(107\) 184.220i 1.72168i −0.508873 0.860842i \(-0.669938\pi\)
0.508873 0.860842i \(-0.330062\pi\)
\(108\) 75.4806 + 227.243i 0.698895 + 2.10410i
\(109\) −58.5394 −0.537058 −0.268529 0.963272i \(-0.586538\pi\)
−0.268529 + 0.963272i \(0.586538\pi\)
\(110\) 0 0
\(111\) −19.8777 8.79828i −0.179078 0.0792638i
\(112\) 240.869 2.15062
\(113\) 151.997i 1.34511i 0.740048 + 0.672555i \(0.234803\pi\)
−0.740048 + 0.672555i \(0.765197\pi\)
\(114\) 46.0220 103.976i 0.403702 0.912070i
\(115\) 42.4326 0.368979
\(116\) 102.952i 0.887517i
\(117\) −9.95313 10.9577i −0.0850695 0.0936556i
\(118\) −406.013 −3.44079
\(119\) 110.110i 0.925292i
\(120\) 99.9611 + 44.2449i 0.833009 + 0.368708i
\(121\) 0 0
\(122\) 278.071i 2.27927i
\(123\) 47.2057 106.650i 0.383786 0.867076i
\(124\) 207.420 1.67274
\(125\) 95.2375i 0.761900i
\(126\) −211.813 + 192.394i −1.68105 + 1.52694i
\(127\) −14.2743 −0.112396 −0.0561979 0.998420i \(-0.517898\pi\)
−0.0561979 + 0.998420i \(0.517898\pi\)
\(128\) 144.911i 1.13212i
\(129\) 43.4657 + 19.2388i 0.336943 + 0.149138i
\(130\) −12.3105 −0.0946961
\(131\) 153.686i 1.17318i −0.809885 0.586589i \(-0.800471\pi\)
0.809885 0.586589i \(-0.199529\pi\)
\(132\) 0 0
\(133\) 93.6438 0.704088
\(134\) 225.669i 1.68410i
\(135\) −53.4606 + 17.7574i −0.396005 + 0.131536i
\(136\) 216.974 1.59540
\(137\) 80.6411i 0.588621i −0.955710 0.294311i \(-0.904910\pi\)
0.955710 0.294311i \(-0.0950900\pi\)
\(138\) 200.143 + 88.5874i 1.45031 + 0.641938i
\(139\) 211.941 1.52476 0.762379 0.647130i \(-0.224031\pi\)
0.762379 + 0.647130i \(0.224031\pi\)
\(140\) 163.995i 1.17139i
\(141\) 55.0154 124.295i 0.390180 0.881521i
\(142\) 36.6352 0.257994
\(143\) 0 0
\(144\) 164.454 + 181.052i 1.14204 + 1.25731i
\(145\) 24.2202 0.167036
\(146\) 267.690i 1.83350i
\(147\) −81.0730 35.8847i −0.551517 0.244113i
\(148\) −64.2608 −0.434194
\(149\) 226.330i 1.51899i −0.650513 0.759495i \(-0.725446\pi\)
0.650513 0.759495i \(-0.274554\pi\)
\(150\) 89.9342 203.185i 0.599561 1.35457i
\(151\) 272.729 1.80615 0.903076 0.429481i \(-0.141304\pi\)
0.903076 + 0.429481i \(0.141304\pi\)
\(152\) 184.527i 1.21399i
\(153\) −82.7654 + 75.1777i −0.540951 + 0.491357i
\(154\) 0 0
\(155\) 48.7971i 0.314820i
\(156\) −40.0164 17.7121i −0.256515 0.113539i
\(157\) 6.05930 0.0385943 0.0192971 0.999814i \(-0.493857\pi\)
0.0192971 + 0.999814i \(0.493857\pi\)
\(158\) 309.626i 1.95966i
\(159\) 48.9533 110.598i 0.307882 0.695588i
\(160\) 57.6505 0.360316
\(161\) 180.254i 1.11959i
\(162\) −289.231 27.8542i −1.78538 0.171939i
\(163\) 161.927 0.993416 0.496708 0.867918i \(-0.334542\pi\)
0.496708 + 0.867918i \(0.334542\pi\)
\(164\) 344.781i 2.10232i
\(165\) 0 0
\(166\) −42.3596 −0.255178
\(167\) 159.209i 0.953347i 0.879081 + 0.476673i \(0.158158\pi\)
−0.879081 + 0.476673i \(0.841842\pi\)
\(168\) −187.953 + 424.636i −1.11877 + 2.52759i
\(169\) −166.295 −0.983992
\(170\) 92.9832i 0.546960i
\(171\) 63.9355 + 70.3886i 0.373892 + 0.411629i
\(172\) 140.516 0.816956
\(173\) 38.4198i 0.222080i −0.993816 0.111040i \(-0.964582\pi\)
0.993816 0.111040i \(-0.0354181\pi\)
\(174\) 114.240 + 50.5651i 0.656552 + 0.290604i
\(175\) 182.995 1.04568
\(176\) 0 0
\(177\) 137.429 310.489i 0.776437 1.75418i
\(178\) −267.532 −1.50299
\(179\) 136.154i 0.760635i −0.924856 0.380317i \(-0.875815\pi\)
0.924856 0.380317i \(-0.124185\pi\)
\(180\) −123.269 + 111.968i −0.684827 + 0.622044i
\(181\) −130.340 −0.720110 −0.360055 0.932931i \(-0.617242\pi\)
−0.360055 + 0.932931i \(0.617242\pi\)
\(182\) 52.2951i 0.287336i
\(183\) −212.649 94.1230i −1.16202 0.514333i
\(184\) 355.195 1.93041
\(185\) 15.1179i 0.0817181i
\(186\) −101.875 + 230.162i −0.547713 + 1.23743i
\(187\) 0 0
\(188\) 401.821i 2.13735i
\(189\) −75.4337 227.101i −0.399120 1.20159i
\(190\) 79.0784 0.416202
\(191\) 315.580i 1.65225i −0.563486 0.826125i \(-0.690540\pi\)
0.563486 0.826125i \(-0.309460\pi\)
\(192\) −26.2945 11.6385i −0.136951 0.0606173i
\(193\) 146.410 0.758601 0.379300 0.925274i \(-0.376165\pi\)
0.379300 + 0.925274i \(0.376165\pi\)
\(194\) 276.822i 1.42692i
\(195\) 4.16691 9.41417i 0.0213688 0.0482778i
\(196\) −262.094 −1.33721
\(197\) 229.459i 1.16476i 0.812915 + 0.582382i \(0.197879\pi\)
−0.812915 + 0.582382i \(0.802121\pi\)
\(198\) 0 0
\(199\) −389.358 −1.95657 −0.978287 0.207253i \(-0.933548\pi\)
−0.978287 + 0.207253i \(0.933548\pi\)
\(200\) 360.595i 1.80297i
\(201\) −172.575 76.3856i −0.858584 0.380028i
\(202\) −45.9006 −0.227231
\(203\) 102.888i 0.506837i
\(204\) −133.783 + 302.251i −0.655797 + 1.48162i
\(205\) 81.1124 0.395670
\(206\) 253.133i 1.22880i
\(207\) −135.490 + 123.069i −0.654543 + 0.594536i
\(208\) −44.7006 −0.214907
\(209\) 0 0
\(210\) −181.976 80.5465i −0.866553 0.383555i
\(211\) 203.989 0.966774 0.483387 0.875407i \(-0.339406\pi\)
0.483387 + 0.875407i \(0.339406\pi\)
\(212\) 357.544i 1.68653i
\(213\) −12.4005 + 28.0159i −0.0582181 + 0.131530i
\(214\) 660.848 3.08808
\(215\) 33.0576i 0.153756i
\(216\) −447.509 + 148.644i −2.07180 + 0.688166i
\(217\) −207.291 −0.955257
\(218\) 209.997i 0.963288i
\(219\) 204.710 + 90.6091i 0.934750 + 0.413740i
\(220\) 0 0
\(221\) 20.4342i 0.0924626i
\(222\) 31.5618 71.3066i 0.142170 0.321201i
\(223\) −16.5198 −0.0740799 −0.0370399 0.999314i \(-0.511793\pi\)
−0.0370399 + 0.999314i \(0.511793\pi\)
\(224\) 244.900i 1.09330i
\(225\) 124.940 + 137.550i 0.555289 + 0.611334i
\(226\) −545.256 −2.41264
\(227\) 112.858i 0.497173i 0.968610 + 0.248587i \(0.0799661\pi\)
−0.968610 + 0.248587i \(0.920034\pi\)
\(228\) 257.052 + 113.777i 1.12742 + 0.499020i
\(229\) −368.618 −1.60969 −0.804843 0.593487i \(-0.797751\pi\)
−0.804843 + 0.593487i \(0.797751\pi\)
\(230\) 152.217i 0.661815i
\(231\) 0 0
\(232\) 202.743 0.873892
\(233\) 174.540i 0.749100i 0.927207 + 0.374550i \(0.122203\pi\)
−0.927207 + 0.374550i \(0.877797\pi\)
\(234\) 39.3083 35.7046i 0.167984 0.152584i
\(235\) 94.5316 0.402262
\(236\) 1003.75i 4.25320i
\(237\) −236.779 104.804i −0.999069 0.442210i
\(238\) −394.994 −1.65964
\(239\) 345.353i 1.44499i −0.691375 0.722496i \(-0.742995\pi\)
0.691375 0.722496i \(-0.257005\pi\)
\(240\) −68.8493 + 155.549i −0.286872 + 0.648120i
\(241\) −261.447 −1.08484 −0.542421 0.840107i \(-0.682492\pi\)
−0.542421 + 0.840107i \(0.682492\pi\)
\(242\) 0 0
\(243\) 119.201 211.755i 0.490540 0.871419i
\(244\) −687.454 −2.81744
\(245\) 61.6597i 0.251672i
\(246\) 382.584 + 169.340i 1.55522 + 0.688374i
\(247\) −17.3785 −0.0703581
\(248\) 408.471i 1.64706i
\(249\) 14.3381 32.3935i 0.0575826 0.130095i
\(250\) 341.643 1.36657
\(251\) 198.345i 0.790220i −0.918634 0.395110i \(-0.870706\pi\)
0.918634 0.395110i \(-0.129294\pi\)
\(252\) −475.641 523.648i −1.88746 2.07797i
\(253\) 0 0
\(254\) 51.2057i 0.201597i
\(255\) −71.1068 31.4734i −0.278850 0.123425i
\(256\) −481.495 −1.88084
\(257\) 1.86519i 0.00725755i −0.999993 0.00362878i \(-0.998845\pi\)
0.999993 0.00362878i \(-0.00115508\pi\)
\(258\) −69.0150 + 155.923i −0.267500 + 0.604354i
\(259\) 64.2208 0.247957
\(260\) 30.4343i 0.117055i
\(261\) −77.3370 + 70.2469i −0.296310 + 0.269145i
\(262\) 551.315 2.10425
\(263\) 27.0901i 0.103004i −0.998673 0.0515020i \(-0.983599\pi\)
0.998673 0.0515020i \(-0.0164009\pi\)
\(264\) 0 0
\(265\) 84.1151 0.317416
\(266\) 335.926i 1.26288i
\(267\) 90.5557 204.589i 0.339160 0.766252i
\(268\) −557.904 −2.08173
\(269\) 142.848i 0.531033i 0.964106 + 0.265516i \(0.0855425\pi\)
−0.964106 + 0.265516i \(0.914458\pi\)
\(270\) −63.7007 191.778i −0.235929 0.710289i
\(271\) −105.327 −0.388661 −0.194331 0.980936i \(-0.562254\pi\)
−0.194331 + 0.980936i \(0.562254\pi\)
\(272\) 337.631i 1.24129i
\(273\) 39.9915 + 17.7011i 0.146489 + 0.0648392i
\(274\) 289.282 1.05577
\(275\) 0 0
\(276\) −219.008 + 494.797i −0.793507 + 1.79274i
\(277\) 244.920 0.884186 0.442093 0.896969i \(-0.354236\pi\)
0.442093 + 0.896969i \(0.354236\pi\)
\(278\) 760.292i 2.73486i
\(279\) −141.528 155.813i −0.507270 0.558469i
\(280\) −322.955 −1.15341
\(281\) 65.1115i 0.231713i −0.993266 0.115857i \(-0.963039\pi\)
0.993266 0.115857i \(-0.0369613\pi\)
\(282\) 445.879 + 197.356i 1.58113 + 0.699842i
\(283\) −157.576 −0.556805 −0.278403 0.960464i \(-0.589805\pi\)
−0.278403 + 0.960464i \(0.589805\pi\)
\(284\) 90.5703i 0.318910i
\(285\) −26.7668 + 60.4734i −0.0939187 + 0.212187i
\(286\) 0 0
\(287\) 344.566i 1.20058i
\(288\) −184.082 + 167.206i −0.639175 + 0.580577i
\(289\) 134.657 0.465940
\(290\) 86.8847i 0.299602i
\(291\) 211.693 + 93.7001i 0.727469 + 0.321993i
\(292\) 661.790 2.26640
\(293\) 184.009i 0.628018i −0.949420 0.314009i \(-0.898328\pi\)
0.949420 0.314009i \(-0.101672\pi\)
\(294\) 128.728 290.831i 0.437851 0.989221i
\(295\) 236.141 0.800478
\(296\) 126.549i 0.427529i
\(297\) 0 0
\(298\) 811.906 2.72452
\(299\) 33.4517i 0.111879i
\(300\) 502.319 + 222.337i 1.67440 + 0.741124i
\(301\) −140.429 −0.466542
\(302\) 978.353i 3.23958i
\(303\) 15.5367 35.1015i 0.0512761 0.115846i
\(304\) 287.142 0.944544
\(305\) 161.729i 0.530259i
\(306\) −269.683 296.902i −0.881317 0.970269i
\(307\) 386.672 1.25952 0.629759 0.776790i \(-0.283154\pi\)
0.629759 + 0.776790i \(0.283154\pi\)
\(308\) 0 0
\(309\) −193.578 85.6816i −0.626465 0.277287i
\(310\) −175.049 −0.564673
\(311\) 92.2420i 0.296598i 0.988943 + 0.148299i \(0.0473798\pi\)
−0.988943 + 0.148299i \(0.952620\pi\)
\(312\) 34.8804 78.8042i 0.111796 0.252577i
\(313\) −74.3978 −0.237693 −0.118846 0.992913i \(-0.537920\pi\)
−0.118846 + 0.992913i \(0.537920\pi\)
\(314\) 21.7364i 0.0692242i
\(315\) 123.192 111.898i 0.391087 0.355233i
\(316\) −765.464 −2.42236
\(317\) 523.779i 1.65230i 0.563450 + 0.826150i \(0.309474\pi\)
−0.563450 + 0.826150i \(0.690526\pi\)
\(318\) 396.747 + 175.609i 1.24763 + 0.552229i
\(319\) 0 0
\(320\) 19.9982i 0.0624943i
\(321\) −223.687 + 505.369i −0.696845 + 1.57436i
\(322\) −646.622 −2.00814
\(323\) 131.262i 0.406385i
\(324\) 68.8617 715.044i 0.212536 2.20692i
\(325\) −33.9602 −0.104493
\(326\) 580.876i 1.78183i
\(327\) 160.590 + 71.0807i 0.491102 + 0.217372i
\(328\) 678.976 2.07005
\(329\) 401.571i 1.22058i
\(330\) 0 0
\(331\) 251.706 0.760441 0.380221 0.924896i \(-0.375848\pi\)
0.380221 + 0.924896i \(0.375848\pi\)
\(332\) 104.722i 0.315429i
\(333\) 43.8469 + 48.2724i 0.131672 + 0.144962i
\(334\) −571.126 −1.70996
\(335\) 131.251i 0.391795i
\(336\) −660.773 292.473i −1.96659 0.870454i
\(337\) −49.6503 −0.147330 −0.0736651 0.997283i \(-0.523470\pi\)
−0.0736651 + 0.997283i \(0.523470\pi\)
\(338\) 596.544i 1.76492i
\(339\) 184.561 416.972i 0.544428 1.23001i
\(340\) −229.875 −0.676104
\(341\) 0 0
\(342\) −252.503 + 229.354i −0.738313 + 0.670626i
\(343\) −172.357 −0.502499
\(344\) 276.719i 0.804415i
\(345\) −116.405 51.5233i −0.337405 0.149343i
\(346\) 137.822 0.398330
\(347\) 459.779i 1.32501i −0.749057 0.662505i \(-0.769493\pi\)
0.749057 0.662505i \(-0.230507\pi\)
\(348\) −125.008 + 282.427i −0.359219 + 0.811571i
\(349\) −393.749 −1.12822 −0.564111 0.825699i \(-0.690781\pi\)
−0.564111 + 0.825699i \(0.690781\pi\)
\(350\) 656.452i 1.87558i
\(351\) 13.9990 + 42.1456i 0.0398833 + 0.120073i
\(352\) 0 0
\(353\) 16.9433i 0.0479980i −0.999712 0.0239990i \(-0.992360\pi\)
0.999712 0.0239990i \(-0.00763985\pi\)
\(354\) 1113.81 + 492.997i 3.14636 + 1.39265i
\(355\) −21.3074 −0.0600208
\(356\) 661.400i 1.85786i
\(357\) 133.699 302.063i 0.374508 0.846114i
\(358\) 488.421 1.36430
\(359\) 75.8881i 0.211387i −0.994399 0.105694i \(-0.966294\pi\)
0.994399 0.105694i \(-0.0337063\pi\)
\(360\) −220.498 242.753i −0.612495 0.674314i
\(361\) −249.367 −0.690767
\(362\) 467.565i 1.29162i
\(363\) 0 0
\(364\) 129.285 0.355179
\(365\) 155.691i 0.426552i
\(366\) 337.645 762.830i 0.922527 2.08423i
\(367\) 619.307 1.68749 0.843743 0.536748i \(-0.180347\pi\)
0.843743 + 0.536748i \(0.180347\pi\)
\(368\) 552.717i 1.50195i
\(369\) −258.998 + 235.253i −0.701891 + 0.637543i
\(370\) 54.2319 0.146573
\(371\) 357.322i 0.963132i
\(372\) −569.012 251.857i −1.52960 0.677035i
\(373\) −365.674 −0.980359 −0.490179 0.871622i \(-0.663069\pi\)
−0.490179 + 0.871622i \(0.663069\pi\)
\(374\) 0 0
\(375\) −115.641 + 261.264i −0.308376 + 0.696704i
\(376\) 791.305 2.10454
\(377\) 19.0940i 0.0506472i
\(378\) 814.675 270.601i 2.15523 0.715877i
\(379\) −409.884 −1.08149 −0.540744 0.841187i \(-0.681857\pi\)
−0.540744 + 0.841187i \(0.681857\pi\)
\(380\) 195.499i 0.514472i
\(381\) 39.1584 + 17.3324i 0.102778 + 0.0454918i
\(382\) 1132.07 2.96354
\(383\) 52.9616i 0.138281i 0.997607 + 0.0691404i \(0.0220257\pi\)
−0.997607 + 0.0691404i \(0.977974\pi\)
\(384\) 175.956 397.532i 0.458219 1.03524i
\(385\) 0 0
\(386\) 525.213i 1.36065i
\(387\) −95.8783 105.555i −0.247748 0.272753i
\(388\) 684.366 1.76383
\(389\) 90.6661i 0.233075i 0.993186 + 0.116537i \(0.0371795\pi\)
−0.993186 + 0.116537i \(0.962821\pi\)
\(390\) 33.7712 + 14.9479i 0.0865929 + 0.0383279i
\(391\) −252.666 −0.646205
\(392\) 516.141i 1.31669i
\(393\) −186.612 + 421.606i −0.474839 + 1.07279i
\(394\) −823.131 −2.08916
\(395\) 180.081i 0.455902i
\(396\) 0 0
\(397\) −335.768 −0.845763 −0.422882 0.906185i \(-0.638981\pi\)
−0.422882 + 0.906185i \(0.638981\pi\)
\(398\) 1396.74i 3.50939i
\(399\) −256.892 113.706i −0.643839 0.284977i
\(400\) 561.119 1.40280
\(401\) 18.9212i 0.0471849i −0.999722 0.0235925i \(-0.992490\pi\)
0.999722 0.0235925i \(-0.00751041\pi\)
\(402\) 274.016 619.075i 0.681632 1.53999i
\(403\) 38.4691 0.0954569
\(404\) 113.477i 0.280883i
\(405\) 168.220 + 16.2003i 0.415357 + 0.0400007i
\(406\) −369.087 −0.909082
\(407\) 0 0
\(408\) −595.221 263.458i −1.45888 0.645730i
\(409\) −119.263 −0.291596 −0.145798 0.989314i \(-0.546575\pi\)
−0.145798 + 0.989314i \(0.546575\pi\)
\(410\) 290.972i 0.709689i
\(411\) −97.9175 + 221.222i −0.238242 + 0.538252i
\(412\) −625.800 −1.51893
\(413\) 1003.13i 2.42889i
\(414\) −441.482 486.042i −1.06638 1.17401i
\(415\) 24.6367 0.0593657
\(416\) 45.4487i 0.109252i
\(417\) −581.416 257.347i −1.39428 0.617140i
\(418\) 0 0
\(419\) 412.874i 0.985381i −0.870205 0.492690i \(-0.836014\pi\)
0.870205 0.492690i \(-0.163986\pi\)
\(420\) 199.129 449.885i 0.474117 1.07116i
\(421\) 604.942 1.43692 0.718458 0.695570i \(-0.244848\pi\)
0.718458 + 0.695570i \(0.244848\pi\)
\(422\) 731.766i 1.73404i
\(423\) −301.846 + 274.174i −0.713585 + 0.648165i
\(424\) 704.111 1.66064
\(425\) 256.507i 0.603547i
\(426\) −100.501 44.4839i −0.235918 0.104422i
\(427\) 687.027 1.60896
\(428\) 1633.76i 3.81721i
\(429\) 0 0
\(430\) −118.587 −0.275783
\(431\) 443.420i 1.02882i −0.857545 0.514409i \(-0.828011\pi\)
0.857545 0.514409i \(-0.171989\pi\)
\(432\) −231.304 696.365i −0.535425 1.61196i
\(433\) 218.980 0.505727 0.252864 0.967502i \(-0.418628\pi\)
0.252864 + 0.967502i \(0.418628\pi\)
\(434\) 743.609i 1.71338i
\(435\) −66.4431 29.4092i −0.152743 0.0676072i
\(436\) 519.159 1.19073
\(437\) 214.882i 0.491721i
\(438\) −325.040 + 734.352i −0.742100 + 1.67660i
\(439\) 171.641 0.390982 0.195491 0.980705i \(-0.437370\pi\)
0.195491 + 0.980705i \(0.437370\pi\)
\(440\) 0 0
\(441\) 178.834 + 196.884i 0.405519 + 0.446449i
\(442\) 73.3032 0.165844
\(443\) 592.539i 1.33756i 0.743461 + 0.668780i \(0.233183\pi\)
−0.743461 + 0.668780i \(0.766817\pi\)
\(444\) 176.286 + 78.0279i 0.397040 + 0.175739i
\(445\) 155.599 0.349662
\(446\) 59.2611i 0.132872i
\(447\) −274.818 + 620.887i −0.614805 + 1.38901i
\(448\) 84.9525 0.189626
\(449\) 436.128i 0.971331i −0.874145 0.485665i \(-0.838577\pi\)
0.874145 0.485665i \(-0.161423\pi\)
\(450\) −493.430 + 448.194i −1.09651 + 0.995986i
\(451\) 0 0
\(452\) 1347.99i 2.98229i
\(453\) −748.174 331.158i −1.65160 0.731033i
\(454\) −404.854 −0.891749
\(455\) 30.4153i 0.0668469i
\(456\) −224.060 + 506.211i −0.491360 + 1.11011i
\(457\) 238.541 0.521973 0.260986 0.965343i \(-0.415952\pi\)
0.260986 + 0.965343i \(0.415952\pi\)
\(458\) 1322.34i 2.88719i
\(459\) 318.333 105.737i 0.693536 0.230364i
\(460\) −376.315 −0.818077
\(461\) 711.175i 1.54268i −0.636424 0.771339i \(-0.719587\pi\)
0.636424 0.771339i \(-0.280413\pi\)
\(462\) 0 0
\(463\) −461.487 −0.996732 −0.498366 0.866967i \(-0.666066\pi\)
−0.498366 + 0.866967i \(0.666066\pi\)
\(464\) 315.487i 0.679929i
\(465\) 59.2513 133.865i 0.127422 0.287881i
\(466\) −626.124 −1.34361
\(467\) 48.3844i 0.103607i −0.998657 0.0518035i \(-0.983503\pi\)
0.998657 0.0518035i \(-0.0164969\pi\)
\(468\) 88.2697 + 97.1789i 0.188611 + 0.207647i
\(469\) 557.557 1.18882
\(470\) 339.111i 0.721512i
\(471\) −16.6224 7.35744i −0.0352917 0.0156209i
\(472\) 1976.69 4.18790
\(473\) 0 0
\(474\) 375.960 849.393i 0.793164 1.79197i
\(475\) 218.149 0.459261
\(476\) 976.513i 2.05150i
\(477\) −268.586 + 243.962i −0.563073 + 0.511452i
\(478\) 1238.88 2.59179
\(479\) 171.425i 0.357880i 0.983860 + 0.178940i \(0.0572668\pi\)
−0.983860 + 0.178940i \(0.942733\pi\)
\(480\) −158.152 70.0015i −0.329483 0.145836i
\(481\) −11.9181 −0.0247778
\(482\) 937.883i 1.94581i
\(483\) 218.872 494.489i 0.453150 1.02379i
\(484\) 0 0
\(485\) 161.002i 0.331964i
\(486\) 759.622 + 427.608i 1.56301 + 0.879851i
\(487\) −495.498 −1.01745 −0.508725 0.860929i \(-0.669883\pi\)
−0.508725 + 0.860929i \(0.669883\pi\)
\(488\) 1353.80i 2.77418i
\(489\) −444.212 196.618i −0.908409 0.402081i
\(490\) 221.190 0.451408
\(491\) 330.249i 0.672604i −0.941754 0.336302i \(-0.890824\pi\)
0.941754 0.336302i \(-0.109176\pi\)
\(492\) −418.646 + 945.833i −0.850906 + 1.92242i
\(493\) −144.220 −0.292536
\(494\) 62.3413i 0.126197i
\(495\) 0 0
\(496\) −635.619 −1.28149
\(497\) 90.5140i 0.182121i
\(498\) 116.205 + 51.4346i 0.233342 + 0.103282i
\(499\) 109.801 0.220042 0.110021 0.993929i \(-0.464908\pi\)
0.110021 + 0.993929i \(0.464908\pi\)
\(500\) 844.618i 1.68924i
\(501\) 193.318 436.756i 0.385863 0.871768i
\(502\) 711.519 1.41737
\(503\) 571.702i 1.13658i 0.822827 + 0.568292i \(0.192396\pi\)
−0.822827 + 0.568292i \(0.807604\pi\)
\(504\) 1031.22 936.679i 2.04607 1.85849i
\(505\) 26.6963 0.0528639
\(506\) 0 0
\(507\) 456.194 + 201.921i 0.899791 + 0.398267i
\(508\) 126.592 0.249197
\(509\) 540.924i 1.06272i −0.847146 0.531360i \(-0.821681\pi\)
0.847146 0.531360i \(-0.178319\pi\)
\(510\) 112.904 255.080i 0.221380 0.500156i
\(511\) −661.379 −1.29428
\(512\) 1147.61i 2.24143i
\(513\) −89.9250 270.729i −0.175292 0.527737i
\(514\) 6.69095 0.0130174
\(515\) 147.224i 0.285873i
\(516\) −385.477 170.620i −0.747049 0.330660i
\(517\) 0 0
\(518\) 230.378i 0.444745i
\(519\) −46.6507 + 105.396i −0.0898858 + 0.203076i
\(520\) 59.9341 0.115258
\(521\) 337.888i 0.648537i 0.945965 + 0.324269i \(0.105118\pi\)
−0.945965 + 0.324269i \(0.894882\pi\)
\(522\) −251.995 277.429i −0.482749 0.531474i
\(523\) 307.433 0.587827 0.293913 0.955832i \(-0.405042\pi\)
0.293913 + 0.955832i \(0.405042\pi\)
\(524\) 1362.97i 2.60109i
\(525\) −502.007 222.199i −0.956203 0.423236i
\(526\) 97.1795 0.184752
\(527\) 290.564i 0.551355i
\(528\) 0 0
\(529\) 115.375 0.218100
\(530\) 301.744i 0.569329i
\(531\) −754.016 + 684.889i −1.41999 + 1.28981i
\(532\) −830.484 −1.56106
\(533\) 63.9448i 0.119971i
\(534\) 733.918 + 324.848i 1.37438 + 0.608330i
\(535\) −384.356 −0.718422
\(536\) 1098.68i 2.04978i
\(537\) −165.323 + 373.509i −0.307864 + 0.695547i
\(538\) −512.434 −0.952480
\(539\) 0 0
\(540\) 474.118 157.482i 0.877996 0.291634i
\(541\) −82.7018 −0.152868 −0.0764342 0.997075i \(-0.524354\pi\)
−0.0764342 + 0.997075i \(0.524354\pi\)
\(542\) 377.838i 0.697118i
\(543\) 357.560 + 158.264i 0.658490 + 0.291462i
\(544\) −343.282 −0.631033
\(545\) 122.136i 0.224103i
\(546\) −63.4987 + 143.461i −0.116298 + 0.262748i
\(547\) −396.695 −0.725220 −0.362610 0.931941i \(-0.618114\pi\)
−0.362610 + 0.931941i \(0.618114\pi\)
\(548\) 715.169i 1.30505i
\(549\) 469.069 + 516.413i 0.854407 + 0.940642i
\(550\) 0 0
\(551\) 122.653i 0.222601i
\(552\) −974.402 431.291i −1.76522 0.781325i
\(553\) 764.988 1.38334
\(554\) 878.594i 1.58591i
\(555\) −18.3567 + 41.4726i −0.0330751 + 0.0747254i
\(556\) −1879.61 −3.38060
\(557\) 383.089i 0.687771i −0.939012 0.343886i \(-0.888257\pi\)
0.939012 0.343886i \(-0.111743\pi\)
\(558\) 558.943 507.701i 1.00169 0.909858i
\(559\) 26.0609 0.0466206
\(560\) 502.548i 0.897407i
\(561\) 0 0
\(562\) 233.573 0.415610
\(563\) 144.837i 0.257259i 0.991693 + 0.128629i \(0.0410577\pi\)
−0.991693 + 0.128629i \(0.958942\pi\)
\(564\) −487.907 + 1102.31i −0.865083 + 1.95445i
\(565\) 317.126 0.561285
\(566\) 565.268i 0.998707i
\(567\) −68.8189 + 714.599i −0.121374 + 1.26032i
\(568\) −178.360 −0.314014
\(569\) 923.151i 1.62241i 0.584763 + 0.811204i \(0.301188\pi\)
−0.584763 + 0.811204i \(0.698812\pi\)
\(570\) −216.935 96.0200i −0.380587 0.168456i
\(571\) 421.725 0.738573 0.369287 0.929316i \(-0.379602\pi\)
0.369287 + 0.929316i \(0.379602\pi\)
\(572\) 0 0
\(573\) −383.189 + 865.726i −0.668742 + 1.51087i
\(574\) −1236.05 −2.15340
\(575\) 419.913i 0.730284i
\(576\) 58.0015 + 63.8556i 0.100697 + 0.110860i
\(577\) 460.408 0.797934 0.398967 0.916965i \(-0.369369\pi\)
0.398967 + 0.916965i \(0.369369\pi\)
\(578\) 483.051i 0.835728i
\(579\) −401.644 177.776i −0.693686 0.307041i
\(580\) −214.798 −0.370342
\(581\) 104.657i 0.180133i
\(582\) −336.128 + 759.403i −0.577539 + 1.30482i
\(583\) 0 0
\(584\) 1303.26i 2.23161i
\(585\) −22.8621 + 20.7661i −0.0390805 + 0.0354977i
\(586\) 660.091 1.12644
\(587\) 42.4644i 0.0723413i 0.999346 + 0.0361707i \(0.0115160\pi\)
−0.999346 + 0.0361707i \(0.988484\pi\)
\(588\) 718.999 + 318.245i 1.22279 + 0.541232i
\(589\) −247.112 −0.419546
\(590\) 847.103i 1.43577i
\(591\) 278.617 629.471i 0.471434 1.06509i
\(592\) 196.921 0.332638
\(593\) 106.267i 0.179203i 0.995978 + 0.0896015i \(0.0285593\pi\)
−0.995978 + 0.0896015i \(0.971441\pi\)
\(594\) 0 0
\(595\) 229.732 0.386105
\(596\) 2007.21i 3.36781i
\(597\) 1068.12 + 472.774i 1.78915 + 0.791916i
\(598\) 120.000 0.200670
\(599\) 728.012i 1.21538i 0.794174 + 0.607690i \(0.207904\pi\)
−0.794174 + 0.607690i \(0.792096\pi\)
\(600\) −437.848 + 989.215i −0.729747 + 1.64869i
\(601\) −118.594 −0.197327 −0.0986635 0.995121i \(-0.531457\pi\)
−0.0986635 + 0.995121i \(0.531457\pi\)
\(602\) 503.758i 0.836807i
\(603\) 380.674 + 419.095i 0.631299 + 0.695017i
\(604\) −2418.71 −4.00448
\(605\) 0 0
\(606\) 125.919 + 55.7343i 0.207787 + 0.0919708i
\(607\) 713.203 1.17496 0.587482 0.809237i \(-0.300119\pi\)
0.587482 + 0.809237i \(0.300119\pi\)
\(608\) 291.947i 0.480176i
\(609\) 124.930 282.251i 0.205140 0.463466i
\(610\) 580.167 0.951093
\(611\) 74.5238i 0.121970i
\(612\) 734.009 666.716i 1.19936 1.08941i
\(613\) 687.465 1.12148 0.560739 0.827993i \(-0.310517\pi\)
0.560739 + 0.827993i \(0.310517\pi\)
\(614\) 1387.10i 2.25912i
\(615\) −222.515 98.4898i −0.361812 0.160146i
\(616\) 0 0
\(617\) 762.156i 1.23526i 0.786468 + 0.617631i \(0.211907\pi\)
−0.786468 + 0.617631i \(0.788093\pi\)
\(618\) 307.363 694.416i 0.497352 1.12365i
\(619\) −530.698 −0.857348 −0.428674 0.903459i \(-0.641019\pi\)
−0.428674 + 0.903459i \(0.641019\pi\)
\(620\) 432.759i 0.697999i
\(621\) 521.124 173.096i 0.839170 0.278737i
\(622\) −330.897 −0.531989
\(623\) 660.988i 1.06098i
\(624\) 122.627 + 54.2772i 0.196517 + 0.0869827i
\(625\) 317.471 0.507954
\(626\) 266.885i 0.426334i
\(627\) 0 0
\(628\) −53.7372 −0.0855688
\(629\) 90.0197i 0.143116i
\(630\) 401.410 + 441.925i 0.637159 + 0.701468i
\(631\) 676.449 1.07203 0.536013 0.844210i \(-0.319930\pi\)
0.536013 + 0.844210i \(0.319930\pi\)
\(632\) 1507.43i 2.38517i
\(633\) −559.602 247.692i −0.884047 0.391298i
\(634\) −1878.94 −2.96363
\(635\) 29.7817i 0.0469004i
\(636\) −434.144 + 980.847i −0.682617 + 1.54221i
\(637\) −48.6093 −0.0763097
\(638\) 0 0
\(639\) 68.0360 61.7987i 0.106473 0.0967115i
\(640\) 302.341 0.472408
\(641\) 785.884i 1.22603i −0.790072 0.613014i \(-0.789957\pi\)
0.790072 0.613014i \(-0.210043\pi\)
\(642\) −1812.90 802.427i −2.82383 1.24989i
\(643\) −849.706 −1.32147 −0.660736 0.750619i \(-0.729756\pi\)
−0.660736 + 0.750619i \(0.729756\pi\)
\(644\) 1598.59i 2.48229i
\(645\) 40.1398 90.6865i 0.0622323 0.140599i
\(646\) −470.875 −0.728908
\(647\) 1169.38i 1.80738i −0.428184 0.903692i \(-0.640846\pi\)
0.428184 0.903692i \(-0.359154\pi\)
\(648\) 1408.13 + 135.609i 2.17305 + 0.209274i
\(649\) 0 0
\(650\) 121.825i 0.187423i
\(651\) 568.658 + 251.700i 0.873515 + 0.386636i
\(652\) −1436.05 −2.20254
\(653\) 535.533i 0.820111i 0.912060 + 0.410056i \(0.134491\pi\)
−0.912060 + 0.410056i \(0.865509\pi\)
\(654\) −254.986 + 576.082i −0.389887 + 0.880859i
\(655\) −320.650 −0.489542
\(656\) 1056.55i 1.61059i
\(657\) −451.558 497.134i −0.687303 0.756673i
\(658\) −1440.55 −2.18928
\(659\) 138.756i 0.210555i −0.994443 0.105278i \(-0.966427\pi\)
0.994443 0.105278i \(-0.0335731\pi\)
\(660\) 0 0
\(661\) 27.1690 0.0411029 0.0205515 0.999789i \(-0.493458\pi\)
0.0205515 + 0.999789i \(0.493458\pi\)
\(662\) 902.939i 1.36396i
\(663\) −24.8120 + 56.0570i −0.0374239 + 0.0845505i
\(664\) 206.229 0.310586
\(665\) 195.378i 0.293801i
\(666\) −173.166 + 157.291i −0.260010 + 0.236173i
\(667\) −236.094 −0.353965
\(668\) 1411.95i 2.11370i
\(669\) 45.3186 + 20.0590i 0.0677408 + 0.0299835i
\(670\) 470.835 0.702738
\(671\) 0 0
\(672\) 297.367 671.831i 0.442511 0.999749i
\(673\) −657.485 −0.976946 −0.488473 0.872579i \(-0.662446\pi\)
−0.488473 + 0.872579i \(0.662446\pi\)
\(674\) 178.109i 0.264257i
\(675\) −175.727 529.047i −0.260337 0.783773i
\(676\) 1474.79 2.18164
\(677\) 611.265i 0.902902i −0.892296 0.451451i \(-0.850907\pi\)
0.892296 0.451451i \(-0.149093\pi\)
\(678\) 1495.79 + 662.071i 2.20619 + 0.976506i
\(679\) −683.940 −1.00728
\(680\) 452.693i 0.665725i
\(681\) 137.037 309.603i 0.201229 0.454630i
\(682\) 0 0
\(683\) 990.520i 1.45025i −0.688618 0.725124i \(-0.741782\pi\)
0.688618 0.725124i \(-0.258218\pi\)
\(684\) −567.015 624.244i −0.828969 0.912637i
\(685\) −168.249 −0.245619
\(686\) 618.293i 0.901302i
\(687\) 1011.23 + 447.590i 1.47194 + 0.651514i
\(688\) −430.600 −0.625872
\(689\) 66.3120i 0.0962439i
\(690\) 184.828 417.576i 0.267867 0.605183i
\(691\) 573.077 0.829345 0.414672 0.909971i \(-0.363896\pi\)
0.414672 + 0.909971i \(0.363896\pi\)
\(692\) 340.727i 0.492380i
\(693\) 0 0
\(694\) 1649.35 2.37659
\(695\) 442.193i 0.636249i
\(696\) −556.182 246.178i −0.799112 0.353704i
\(697\) −482.986 −0.692950
\(698\) 1412.49i 2.02362i
\(699\) 211.933 478.814i 0.303195 0.684999i
\(700\) −1622.89 −2.31842
\(701\) 819.026i 1.16837i −0.811621 0.584184i \(-0.801415\pi\)
0.811621 0.584184i \(-0.198585\pi\)
\(702\) −151.188 + 50.2183i −0.215367 + 0.0715361i
\(703\) 76.5580 0.108902
\(704\) 0 0
\(705\) −259.327 114.784i −0.367840 0.162814i
\(706\) 60.7802 0.0860910
\(707\) 113.406i 0.160405i
\(708\) −1218.80 + 2753.59i −1.72146 + 3.88925i
\(709\) 179.842 0.253656 0.126828 0.991925i \(-0.459520\pi\)
0.126828 + 0.991925i \(0.459520\pi\)
\(710\) 76.4354i 0.107656i
\(711\) 522.297 + 575.013i 0.734596 + 0.808739i
\(712\) 1302.49 1.82934
\(713\) 475.665i 0.667132i
\(714\) 1083.58 + 479.617i 1.51762 + 0.671732i
\(715\) 0 0
\(716\) 1207.48i 1.68643i
\(717\) −419.341 + 947.403i −0.584855 + 1.32134i
\(718\) 272.231 0.379152
\(719\) 666.337i 0.926755i −0.886161 0.463378i \(-0.846637\pi\)
0.886161 0.463378i \(-0.153363\pi\)
\(720\) 377.747 343.116i 0.524648 0.476550i
\(721\) 625.411 0.867422
\(722\) 894.547i 1.23898i
\(723\) 717.225 + 317.459i 0.992012 + 0.439086i
\(724\) 1155.92 1.59658
\(725\) 239.684i 0.330598i
\(726\) 0 0
\(727\) 162.429 0.223424 0.111712 0.993741i \(-0.464367\pi\)
0.111712 + 0.993741i \(0.464367\pi\)
\(728\) 254.601i 0.349726i
\(729\) −584.124 + 436.165i −0.801267 + 0.598306i
\(730\) −558.508 −0.765079
\(731\) 196.842i 0.269278i
\(732\) 1885.88 + 834.733i 2.57635 + 1.14035i
\(733\) 1169.88 1.59602 0.798008 0.602646i \(-0.205887\pi\)
0.798008 + 0.602646i \(0.205887\pi\)
\(734\) 2221.62i 3.02674i
\(735\) −74.8695 + 169.150i −0.101863 + 0.230136i
\(736\) −561.967 −0.763542
\(737\) 0 0
\(738\) −843.919 929.096i −1.14352 1.25894i
\(739\) −242.377 −0.327979 −0.163990 0.986462i \(-0.552436\pi\)
−0.163990 + 0.986462i \(0.552436\pi\)
\(740\) 134.073i 0.181180i
\(741\) 47.6741 + 21.1016i 0.0643375 + 0.0284772i
\(742\) −1281.81 −1.72751
\(743\) 823.655i 1.10855i 0.832333 + 0.554277i \(0.187005\pi\)
−0.832333 + 0.554277i \(0.812995\pi\)
\(744\) 495.981 1120.55i 0.666641 1.50612i
\(745\) −472.213 −0.633842
\(746\) 1311.77i 1.75841i
\(747\) −78.6669 + 71.4549i −0.105310 + 0.0956559i
\(748\) 0 0
\(749\) 1632.75i 2.17990i
\(750\) −937.226 414.836i −1.24963 0.553115i
\(751\) −6.13817 −0.00817333 −0.00408666 0.999992i \(-0.501301\pi\)
−0.00408666 + 0.999992i \(0.501301\pi\)
\(752\) 1231.35i 1.63743i
\(753\) −240.838 + 544.118i −0.319839 + 0.722600i
\(754\) 68.4954 0.0908427
\(755\) 569.020i 0.753669i
\(756\) 668.987 + 2014.06i 0.884903 + 2.66410i
\(757\) −1102.27 −1.45610 −0.728052 0.685522i \(-0.759574\pi\)
−0.728052 + 0.685522i \(0.759574\pi\)
\(758\) 1470.37i 1.93980i
\(759\) 0 0
\(760\) −384.996 −0.506574
\(761\) 1200.28i 1.57724i −0.614882 0.788619i \(-0.710796\pi\)
0.614882 0.788619i \(-0.289204\pi\)
\(762\) −62.1759 + 140.472i −0.0815957 + 0.184346i
\(763\) −518.836 −0.679995
\(764\) 2798.73i 3.66326i
\(765\) 156.850 + 172.681i 0.205033 + 0.225727i
\(766\) −189.988 −0.248026
\(767\) 186.161i 0.242714i
\(768\) 1320.88 + 584.649i 1.71989 + 0.761262i
\(769\) −1038.16 −1.35001 −0.675007 0.737811i \(-0.735859\pi\)
−0.675007 + 0.737811i \(0.735859\pi\)
\(770\) 0 0
\(771\) −2.26479 + 5.11676i −0.00293747 + 0.00663652i
\(772\) −1298.44 −1.68192
\(773\) 586.211i 0.758359i −0.925323 0.379179i \(-0.876206\pi\)
0.925323 0.379179i \(-0.123794\pi\)
\(774\) 378.656 343.942i 0.489220 0.444369i
\(775\) −482.896 −0.623092
\(776\) 1347.72i 1.73675i
\(777\) −176.176 77.9794i −0.226739 0.100360i
\(778\) −325.244 −0.418052
\(779\) 410.760i 0.527291i
\(780\) −36.9545 + 83.4899i −0.0473775 + 0.107038i
\(781\) 0 0
\(782\) 906.383i 1.15906i
\(783\) 297.454