Properties

Label 315.3.ca.b.37.5
Level 315
Weight 3
Character 315.37
Analytic conductor 8.583
Analytic rank 0
Dimension 64
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 315.ca (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.58312832735\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.5
Character \(\chi\) \(=\) 315.37
Dual form 315.3.ca.b.298.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.13226 + 0.571337i) q^{2} +(0.756006 - 0.436480i) q^{4} +(-2.78563 - 4.15214i) q^{5} +(2.73668 - 6.44287i) q^{7} +(4.88107 - 4.88107i) q^{8} +O(q^{10})\) \(q+(-2.13226 + 0.571337i) q^{2} +(0.756006 - 0.436480i) q^{4} +(-2.78563 - 4.15214i) q^{5} +(2.73668 - 6.44287i) q^{7} +(4.88107 - 4.88107i) q^{8} +(8.31195 + 7.26192i) q^{10} +(4.69282 + 8.12820i) q^{11} +(-0.405222 + 0.405222i) q^{13} +(-2.15427 + 15.3014i) q^{14} +(-9.36489 + 16.2205i) q^{16} +(-2.82961 + 10.5602i) q^{17} +(-23.8500 - 13.7698i) q^{19} +(-3.91828 - 1.92317i) q^{20} +(-14.6503 - 14.6503i) q^{22} +(-1.02354 - 3.81990i) q^{23} +(-9.48058 + 23.1326i) q^{25} +(0.632520 - 1.09556i) q^{26} +(-0.743235 - 6.06535i) q^{28} -34.6601i q^{29} +(-11.8284 - 20.4874i) q^{31} +(3.55465 - 13.2661i) q^{32} -24.1338i q^{34} +(-34.3751 + 6.58431i) q^{35} +(25.6130 - 6.86297i) q^{37} +(58.7215 + 15.7344i) q^{38} +(-33.8637 - 6.67007i) q^{40} -54.6731 q^{41} +(-47.3942 + 47.3942i) q^{43} +(7.09560 + 4.09664i) q^{44} +(4.36491 + 7.56024i) q^{46} +(16.9830 - 4.55058i) q^{47} +(-34.0211 - 35.2642i) q^{49} +(6.99854 - 54.7414i) q^{50} +(-0.129479 + 0.483221i) q^{52} +(-14.7503 - 3.95234i) q^{53} +(20.6770 - 42.1274i) q^{55} +(-18.0901 - 44.8060i) q^{56} +(19.8026 + 73.9044i) q^{58} +(-90.3630 + 52.1711i) q^{59} +(-12.5803 + 21.7897i) q^{61} +(36.9264 + 36.9264i) q^{62} -44.6014i q^{64} +(2.81133 + 0.553743i) q^{65} +(0.364564 - 1.36057i) q^{67} +(2.47014 + 9.21867i) q^{68} +(69.5348 - 33.6792i) q^{70} -86.5935 q^{71} +(-84.9471 - 22.7615i) q^{73} +(-50.6924 + 29.2673i) q^{74} -24.0409 q^{76} +(65.2117 - 7.99089i) q^{77} +(128.353 + 74.1049i) q^{79} +(93.4368 - 6.29977i) q^{80} +(116.577 - 31.2368i) q^{82} +(-35.5711 + 35.5711i) q^{83} +(51.7299 - 17.6679i) q^{85} +(73.9787 - 128.135i) q^{86} +(62.5803 + 16.7683i) q^{88} +(-130.143 - 75.1382i) q^{89} +(1.50183 + 3.71975i) q^{91} +(-2.44111 - 2.44111i) q^{92} +(-33.6122 + 19.4060i) q^{94} +(9.26295 + 137.386i) q^{95} +(74.8462 + 74.8462i) q^{97} +(92.6896 + 55.7549i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} + O(q^{10}) \) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} - 16q^{10} - 16q^{11} + 80q^{16} - 56q^{17} - 96q^{22} - 72q^{23} - 4q^{25} + 288q^{26} - 380q^{28} - 136q^{31} + 48q^{32} - 76q^{35} - 28q^{37} + 68q^{38} + 164q^{40} - 128q^{41} + 344q^{43} + 240q^{46} - 412q^{47} + 72q^{50} + 388q^{52} + 40q^{53} - 8q^{55} + 864q^{56} + 56q^{58} - 216q^{61} + 912q^{62} - 20q^{65} - 368q^{67} + 492q^{68} + 416q^{70} - 784q^{71} - 316q^{73} - 32q^{76} - 844q^{77} - 908q^{80} + 556q^{82} - 1408q^{83} - 536q^{85} - 1024q^{86} + 372q^{88} - 1064q^{91} + 1704q^{92} - 260q^{95} + 352q^{97} - 272q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.13226 + 0.571337i −1.06613 + 0.285669i −0.748902 0.662681i \(-0.769419\pi\)
−0.317228 + 0.948349i \(0.602752\pi\)
\(3\) 0 0
\(4\) 0.756006 0.436480i 0.189001 0.109120i
\(5\) −2.78563 4.15214i −0.557125 0.830429i
\(6\) 0 0
\(7\) 2.73668 6.44287i 0.390955 0.920410i
\(8\) 4.88107 4.88107i 0.610133 0.610133i
\(9\) 0 0
\(10\) 8.31195 + 7.26192i 0.831195 + 0.726192i
\(11\) 4.69282 + 8.12820i 0.426620 + 0.738927i 0.996570 0.0827519i \(-0.0263709\pi\)
−0.569950 + 0.821679i \(0.693038\pi\)
\(12\) 0 0
\(13\) −0.405222 + 0.405222i −0.0311709 + 0.0311709i −0.722520 0.691350i \(-0.757016\pi\)
0.691350 + 0.722520i \(0.257016\pi\)
\(14\) −2.15427 + 15.3014i −0.153877 + 1.09296i
\(15\) 0 0
\(16\) −9.36489 + 16.2205i −0.585306 + 1.01378i
\(17\) −2.82961 + 10.5602i −0.166448 + 0.621191i 0.831404 + 0.555669i \(0.187538\pi\)
−0.997851 + 0.0655217i \(0.979129\pi\)
\(18\) 0 0
\(19\) −23.8500 13.7698i −1.25526 0.724725i −0.283111 0.959087i \(-0.591367\pi\)
−0.972149 + 0.234362i \(0.924700\pi\)
\(20\) −3.91828 1.92317i −0.195914 0.0961587i
\(21\) 0 0
\(22\) −14.6503 14.6503i −0.665921 0.665921i
\(23\) −1.02354 3.81990i −0.0445017 0.166083i 0.940099 0.340902i \(-0.110732\pi\)
−0.984601 + 0.174819i \(0.944066\pi\)
\(24\) 0 0
\(25\) −9.48058 + 23.1326i −0.379223 + 0.925305i
\(26\) 0.632520 1.09556i 0.0243277 0.0421368i
\(27\) 0 0
\(28\) −0.743235 6.06535i −0.0265441 0.216620i
\(29\) 34.6601i 1.19518i −0.801803 0.597588i \(-0.796126\pi\)
0.801803 0.597588i \(-0.203874\pi\)
\(30\) 0 0
\(31\) −11.8284 20.4874i −0.381561 0.660883i 0.609724 0.792613i \(-0.291280\pi\)
−0.991286 + 0.131730i \(0.957947\pi\)
\(32\) 3.55465 13.2661i 0.111083 0.414566i
\(33\) 0 0
\(34\) 24.1338i 0.709819i
\(35\) −34.3751 + 6.58431i −0.982145 + 0.188123i
\(36\) 0 0
\(37\) 25.6130 6.86297i 0.692242 0.185486i 0.104489 0.994526i \(-0.466679\pi\)
0.587753 + 0.809040i \(0.300013\pi\)
\(38\) 58.7215 + 15.7344i 1.54530 + 0.414063i
\(39\) 0 0
\(40\) −33.8637 6.67007i −0.846593 0.166752i
\(41\) −54.6731 −1.33349 −0.666745 0.745286i \(-0.732313\pi\)
−0.666745 + 0.745286i \(0.732313\pi\)
\(42\) 0 0
\(43\) −47.3942 + 47.3942i −1.10219 + 1.10219i −0.108044 + 0.994146i \(0.534459\pi\)
−0.994146 + 0.108044i \(0.965541\pi\)
\(44\) 7.09560 + 4.09664i 0.161264 + 0.0931055i
\(45\) 0 0
\(46\) 4.36491 + 7.56024i 0.0948893 + 0.164353i
\(47\) 16.9830 4.55058i 0.361340 0.0968208i −0.0735811 0.997289i \(-0.523443\pi\)
0.434921 + 0.900468i \(0.356776\pi\)
\(48\) 0 0
\(49\) −34.0211 35.2642i −0.694308 0.719678i
\(50\) 6.99854 54.7414i 0.139971 1.09483i
\(51\) 0 0
\(52\) −0.129479 + 0.483221i −0.00248997 + 0.00929271i
\(53\) −14.7503 3.95234i −0.278308 0.0745725i 0.116965 0.993136i \(-0.462683\pi\)
−0.395273 + 0.918564i \(0.629350\pi\)
\(54\) 0 0
\(55\) 20.6770 42.1274i 0.375946 0.765952i
\(56\) −18.0901 44.8060i −0.323038 0.800108i
\(57\) 0 0
\(58\) 19.8026 + 73.9044i 0.341424 + 1.27421i
\(59\) −90.3630 + 52.1711i −1.53158 + 0.884256i −0.532288 + 0.846564i \(0.678667\pi\)
−0.999289 + 0.0376927i \(0.987999\pi\)
\(60\) 0 0
\(61\) −12.5803 + 21.7897i −0.206235 + 0.357209i −0.950525 0.310647i \(-0.899454\pi\)
0.744291 + 0.667856i \(0.232788\pi\)
\(62\) 36.9264 + 36.9264i 0.595587 + 0.595587i
\(63\) 0 0
\(64\) 44.6014i 0.696897i
\(65\) 2.81133 + 0.553743i 0.0432513 + 0.00851912i
\(66\) 0 0
\(67\) 0.364564 1.36057i 0.00544126 0.0203071i −0.963152 0.268958i \(-0.913321\pi\)
0.968593 + 0.248651i \(0.0799873\pi\)
\(68\) 2.47014 + 9.21867i 0.0363255 + 0.135569i
\(69\) 0 0
\(70\) 69.5348 33.6792i 0.993354 0.481132i
\(71\) −86.5935 −1.21963 −0.609813 0.792545i \(-0.708756\pi\)
−0.609813 + 0.792545i \(0.708756\pi\)
\(72\) 0 0
\(73\) −84.9471 22.7615i −1.16366 0.311802i −0.375233 0.926931i \(-0.622437\pi\)
−0.788427 + 0.615129i \(0.789104\pi\)
\(74\) −50.6924 + 29.2673i −0.685033 + 0.395504i
\(75\) 0 0
\(76\) −24.0409 −0.316328
\(77\) 65.2117 7.99089i 0.846905 0.103778i
\(78\) 0 0
\(79\) 128.353 + 74.1049i 1.62473 + 0.938036i 0.985632 + 0.168909i \(0.0540243\pi\)
0.639095 + 0.769128i \(0.279309\pi\)
\(80\) 93.4368 6.29977i 1.16796 0.0787472i
\(81\) 0 0
\(82\) 116.577 31.2368i 1.42167 0.380936i
\(83\) −35.5711 + 35.5711i −0.428567 + 0.428567i −0.888140 0.459573i \(-0.848002\pi\)
0.459573 + 0.888140i \(0.348002\pi\)
\(84\) 0 0
\(85\) 51.7299 17.6679i 0.608587 0.207858i
\(86\) 73.9787 128.135i 0.860217 1.48994i
\(87\) 0 0
\(88\) 62.5803 + 16.7683i 0.711139 + 0.190549i
\(89\) −130.143 75.1382i −1.46228 0.844250i −0.463166 0.886271i \(-0.653287\pi\)
−0.999117 + 0.0420218i \(0.986620\pi\)
\(90\) 0 0
\(91\) 1.50183 + 3.71975i 0.0165036 + 0.0408764i
\(92\) −2.44111 2.44111i −0.0265338 0.0265338i
\(93\) 0 0
\(94\) −33.6122 + 19.4060i −0.357577 + 0.206447i
\(95\) 9.26295 + 137.386i 0.0975047 + 1.44617i
\(96\) 0 0
\(97\) 74.8462 + 74.8462i 0.771610 + 0.771610i 0.978388 0.206778i \(-0.0662977\pi\)
−0.206778 + 0.978388i \(0.566298\pi\)
\(98\) 92.6896 + 55.7549i 0.945812 + 0.568928i
\(99\) 0 0
\(100\) 2.92956 + 21.6265i 0.0292956 + 0.216265i
\(101\) 65.3840 + 113.248i 0.647366 + 1.12127i 0.983750 + 0.179546i \(0.0574628\pi\)
−0.336384 + 0.941725i \(0.609204\pi\)
\(102\) 0 0
\(103\) 9.95292 + 37.1448i 0.0966303 + 0.360629i 0.997262 0.0739549i \(-0.0235621\pi\)
−0.900631 + 0.434584i \(0.856895\pi\)
\(104\) 3.95583i 0.0380368i
\(105\) 0 0
\(106\) 33.7097 0.318016
\(107\) 193.691 51.8993i 1.81019 0.485040i 0.814701 0.579881i \(-0.196901\pi\)
0.995492 + 0.0948408i \(0.0302342\pi\)
\(108\) 0 0
\(109\) −126.264 + 72.8985i −1.15838 + 0.668793i −0.950916 0.309449i \(-0.899856\pi\)
−0.207468 + 0.978242i \(0.566522\pi\)
\(110\) −20.0198 + 101.640i −0.181998 + 0.924001i
\(111\) 0 0
\(112\) 78.8776 + 104.727i 0.704264 + 0.935063i
\(113\) 50.0612 50.0612i 0.443020 0.443020i −0.450006 0.893026i \(-0.648578\pi\)
0.893026 + 0.450006i \(0.148578\pi\)
\(114\) 0 0
\(115\) −13.0096 + 14.8907i −0.113127 + 0.129484i
\(116\) −15.1284 26.2032i −0.130418 0.225890i
\(117\) 0 0
\(118\) 162.870 162.870i 1.38026 1.38026i
\(119\) 60.2945 + 47.1308i 0.506677 + 0.396058i
\(120\) 0 0
\(121\) 16.4549 28.5007i 0.135991 0.235543i
\(122\) 14.3752 53.6490i 0.117830 0.439746i
\(123\) 0 0
\(124\) −17.8847 10.3257i −0.144231 0.0832719i
\(125\) 122.459 25.0741i 0.979675 0.200593i
\(126\) 0 0
\(127\) −120.362 120.362i −0.947736 0.947736i 0.0509644 0.998700i \(-0.483771\pi\)
−0.998700 + 0.0509644i \(0.983771\pi\)
\(128\) 39.7010 + 148.166i 0.310164 + 1.15755i
\(129\) 0 0
\(130\) −6.31087 + 0.425497i −0.0485451 + 0.00327305i
\(131\) 61.7290 106.918i 0.471214 0.816166i −0.528244 0.849093i \(-0.677149\pi\)
0.999458 + 0.0329263i \(0.0104827\pi\)
\(132\) 0 0
\(133\) −153.987 + 115.979i −1.15779 + 0.872019i
\(134\) 3.10939i 0.0232044i
\(135\) 0 0
\(136\) 37.7337 + 65.3568i 0.277454 + 0.480564i
\(137\) 38.7216 144.511i 0.282639 1.05482i −0.667908 0.744244i \(-0.732810\pi\)
0.950547 0.310581i \(-0.100523\pi\)
\(138\) 0 0
\(139\) 86.7413i 0.624038i −0.950076 0.312019i \(-0.898995\pi\)
0.950076 0.312019i \(-0.101005\pi\)
\(140\) −23.1138 + 19.9818i −0.165099 + 0.142727i
\(141\) 0 0
\(142\) 184.640 49.4741i 1.30028 0.348409i
\(143\) −5.19535 1.39209i −0.0363311 0.00973490i
\(144\) 0 0
\(145\) −143.914 + 96.5501i −0.992508 + 0.665863i
\(146\) 194.134 1.32968
\(147\) 0 0
\(148\) 16.3680 16.3680i 0.110595 0.110595i
\(149\) 21.7762 + 12.5725i 0.146149 + 0.0843791i 0.571291 0.820747i \(-0.306443\pi\)
−0.425142 + 0.905126i \(0.639776\pi\)
\(150\) 0 0
\(151\) −100.832 174.647i −0.667765 1.15660i −0.978528 0.206115i \(-0.933918\pi\)
0.310763 0.950487i \(-0.399415\pi\)
\(152\) −183.624 + 49.2020i −1.20806 + 0.323697i
\(153\) 0 0
\(154\) −134.483 + 54.2965i −0.873265 + 0.352575i
\(155\) −52.1171 + 106.183i −0.336239 + 0.685054i
\(156\) 0 0
\(157\) 7.52733 28.0924i 0.0479448 0.178932i −0.937801 0.347173i \(-0.887142\pi\)
0.985746 + 0.168240i \(0.0538084\pi\)
\(158\) −316.022 84.6778i −2.00014 0.535935i
\(159\) 0 0
\(160\) −64.9847 + 22.1950i −0.406155 + 0.138719i
\(161\) −27.4122 3.85934i −0.170262 0.0239710i
\(162\) 0 0
\(163\) −21.9253 81.8264i −0.134511 0.502003i −0.999999 0.00107335i \(-0.999658\pi\)
0.865488 0.500929i \(-0.167008\pi\)
\(164\) −41.3332 + 23.8637i −0.252032 + 0.145510i
\(165\) 0 0
\(166\) 55.5237 96.1699i 0.334480 0.579336i
\(167\) −147.643 147.643i −0.884091 0.884091i 0.109856 0.993947i \(-0.464961\pi\)
−0.993947 + 0.109856i \(0.964961\pi\)
\(168\) 0 0
\(169\) 168.672i 0.998057i
\(170\) −100.207 + 67.2279i −0.589454 + 0.395458i
\(171\) 0 0
\(172\) −15.1437 + 56.5169i −0.0880445 + 0.328587i
\(173\) 18.0662 + 67.4239i 0.104429 + 0.389733i 0.998280 0.0586307i \(-0.0186734\pi\)
−0.893851 + 0.448364i \(0.852007\pi\)
\(174\) 0 0
\(175\) 123.095 + 124.389i 0.703401 + 0.710794i
\(176\) −175.791 −0.998812
\(177\) 0 0
\(178\) 320.428 + 85.8585i 1.80016 + 0.482351i
\(179\) 10.7449 6.20357i 0.0600273 0.0346568i −0.469686 0.882834i \(-0.655633\pi\)
0.529713 + 0.848177i \(0.322300\pi\)
\(180\) 0 0
\(181\) −163.979 −0.905964 −0.452982 0.891520i \(-0.649640\pi\)
−0.452982 + 0.891520i \(0.649640\pi\)
\(182\) −5.32752 7.07343i −0.0292721 0.0388650i
\(183\) 0 0
\(184\) −23.6412 13.6492i −0.128485 0.0741806i
\(185\) −99.8441 87.2310i −0.539698 0.471519i
\(186\) 0 0
\(187\) −99.1146 + 26.5577i −0.530025 + 0.142020i
\(188\) 10.8530 10.8530i 0.0577287 0.0577287i
\(189\) 0 0
\(190\) −98.2447 287.650i −0.517077 1.51395i
\(191\) −63.0093 + 109.135i −0.329892 + 0.571389i −0.982490 0.186315i \(-0.940346\pi\)
0.652598 + 0.757704i \(0.273679\pi\)
\(192\) 0 0
\(193\) 53.1737 + 14.2479i 0.275512 + 0.0738231i 0.393929 0.919141i \(-0.371115\pi\)
−0.118418 + 0.992964i \(0.537782\pi\)
\(194\) −202.354 116.829i −1.04306 0.602212i
\(195\) 0 0
\(196\) −41.1123 11.8104i −0.209757 0.0602571i
\(197\) −62.0394 62.0394i −0.314921 0.314921i 0.531892 0.846812i \(-0.321481\pi\)
−0.846812 + 0.531892i \(0.821481\pi\)
\(198\) 0 0
\(199\) 242.793 140.177i 1.22007 0.704405i 0.255134 0.966906i \(-0.417880\pi\)
0.964932 + 0.262501i \(0.0845472\pi\)
\(200\) 66.6366 + 159.187i 0.333183 + 0.795937i
\(201\) 0 0
\(202\) −204.119 204.119i −1.01049 1.01049i
\(203\) −223.311 94.8538i −1.10005 0.467260i
\(204\) 0 0
\(205\) 152.299 + 227.011i 0.742921 + 1.10737i
\(206\) −42.4444 73.5159i −0.206041 0.356873i
\(207\) 0 0
\(208\) −2.77803 10.3677i −0.0133559 0.0498449i
\(209\) 258.476i 1.23673i
\(210\) 0 0
\(211\) 215.254 1.02016 0.510081 0.860126i \(-0.329615\pi\)
0.510081 + 0.860126i \(0.329615\pi\)
\(212\) −12.8765 + 3.45024i −0.0607380 + 0.0162747i
\(213\) 0 0
\(214\) −383.347 + 221.326i −1.79134 + 1.03423i
\(215\) 328.810 + 64.7650i 1.52935 + 0.301233i
\(216\) 0 0
\(217\) −164.368 + 20.1413i −0.757457 + 0.0928170i
\(218\) 227.578 227.578i 1.04393 1.04393i
\(219\) 0 0
\(220\) −2.75582 40.8736i −0.0125264 0.185789i
\(221\) −3.13262 5.42586i −0.0141747 0.0245514i
\(222\) 0 0
\(223\) 129.293 129.293i 0.579788 0.579788i −0.355057 0.934845i \(-0.615538\pi\)
0.934845 + 0.355057i \(0.115538\pi\)
\(224\) −75.7439 59.2073i −0.338142 0.264318i
\(225\) 0 0
\(226\) −78.1417 + 135.345i −0.345760 + 0.598874i
\(227\) 12.3978 46.2690i 0.0546156 0.203828i −0.933227 0.359289i \(-0.883019\pi\)
0.987842 + 0.155460i \(0.0496860\pi\)
\(228\) 0 0
\(229\) −275.307 158.949i −1.20221 0.694099i −0.241168 0.970483i \(-0.577530\pi\)
−0.961047 + 0.276384i \(0.910864\pi\)
\(230\) 19.2322 39.1837i 0.0836183 0.170364i
\(231\) 0 0
\(232\) −169.178 169.178i −0.729217 0.729217i
\(233\) 70.2155 + 262.048i 0.301354 + 1.12467i 0.936039 + 0.351897i \(0.114463\pi\)
−0.634685 + 0.772771i \(0.718870\pi\)
\(234\) 0 0
\(235\) −66.2029 57.8396i −0.281715 0.246126i
\(236\) −45.5433 + 78.8833i −0.192980 + 0.334251i
\(237\) 0 0
\(238\) −155.491 66.0467i −0.653324 0.277507i
\(239\) 18.7596i 0.0784918i 0.999230 + 0.0392459i \(0.0124956\pi\)
−0.999230 + 0.0392459i \(0.987504\pi\)
\(240\) 0 0
\(241\) −39.4000 68.2427i −0.163485 0.283165i 0.772631 0.634855i \(-0.218940\pi\)
−0.936116 + 0.351690i \(0.885607\pi\)
\(242\) −18.8026 + 70.1723i −0.0776968 + 0.289968i
\(243\) 0 0
\(244\) 21.9642i 0.0900173i
\(245\) −51.6519 + 239.493i −0.210824 + 0.977524i
\(246\) 0 0
\(247\) 15.2443 4.08470i 0.0617179 0.0165373i
\(248\) −157.735 42.2651i −0.636030 0.170424i
\(249\) 0 0
\(250\) −246.789 + 123.430i −0.987158 + 0.493720i
\(251\) 86.2825 0.343755 0.171877 0.985118i \(-0.445017\pi\)
0.171877 + 0.985118i \(0.445017\pi\)
\(252\) 0 0
\(253\) 26.2456 26.2456i 0.103738 0.103738i
\(254\) 325.412 + 187.877i 1.28115 + 0.739671i
\(255\) 0 0
\(256\) −80.1031 138.743i −0.312903 0.541963i
\(257\) 241.586 64.7328i 0.940024 0.251879i 0.243900 0.969800i \(-0.421573\pi\)
0.696124 + 0.717922i \(0.254906\pi\)
\(258\) 0 0
\(259\) 25.8774 183.803i 0.0999126 0.709663i
\(260\) 2.36708 0.808459i 0.00910416 0.00310946i
\(261\) 0 0
\(262\) −70.5362 + 263.245i −0.269222 + 1.00475i
\(263\) 350.527 + 93.9235i 1.33280 + 0.357123i 0.853759 0.520668i \(-0.174317\pi\)
0.479043 + 0.877791i \(0.340984\pi\)
\(264\) 0 0
\(265\) 24.6782 + 72.2553i 0.0931254 + 0.272661i
\(266\) 262.077 335.275i 0.985251 1.26043i
\(267\) 0 0
\(268\) −0.318250 1.18773i −0.00118750 0.00443181i
\(269\) −255.637 + 147.592i −0.950323 + 0.548669i −0.893181 0.449697i \(-0.851532\pi\)
−0.0571419 + 0.998366i \(0.518199\pi\)
\(270\) 0 0
\(271\) 208.489 361.113i 0.769332 1.33252i −0.168594 0.985686i \(-0.553923\pi\)
0.937926 0.346836i \(-0.112744\pi\)
\(272\) −144.793 144.793i −0.532328 0.532328i
\(273\) 0 0
\(274\) 330.258i 1.20532i
\(275\) −232.517 + 31.4971i −0.845517 + 0.114535i
\(276\) 0 0
\(277\) −65.5326 + 244.571i −0.236580 + 0.882927i 0.740851 + 0.671670i \(0.234423\pi\)
−0.977430 + 0.211258i \(0.932244\pi\)
\(278\) 49.5586 + 184.955i 0.178268 + 0.665306i
\(279\) 0 0
\(280\) −135.649 + 199.926i −0.484460 + 0.714020i
\(281\) −235.018 −0.836363 −0.418181 0.908363i \(-0.637332\pi\)
−0.418181 + 0.908363i \(0.637332\pi\)
\(282\) 0 0
\(283\) 45.4761 + 12.1853i 0.160693 + 0.0430576i 0.338269 0.941050i \(-0.390159\pi\)
−0.177576 + 0.984107i \(0.556825\pi\)
\(284\) −65.4652 + 37.7963i −0.230511 + 0.133086i
\(285\) 0 0
\(286\) 11.8732 0.0415147
\(287\) −149.623 + 352.252i −0.521335 + 1.22736i
\(288\) 0 0
\(289\) 146.769 + 84.7373i 0.507852 + 0.293209i
\(290\) 251.699 288.093i 0.867927 0.993425i
\(291\) 0 0
\(292\) −74.1555 + 19.8699i −0.253957 + 0.0680476i
\(293\) 12.1766 12.1766i 0.0415584 0.0415584i −0.686022 0.727581i \(-0.740645\pi\)
0.727581 + 0.686022i \(0.240645\pi\)
\(294\) 0 0
\(295\) 468.340 + 229.871i 1.58759 + 0.779224i
\(296\) 91.5200 158.517i 0.309189 0.535531i
\(297\) 0 0
\(298\) −53.6156 14.3663i −0.179918 0.0482089i
\(299\) 1.96267 + 1.13315i 0.00656410 + 0.00378979i
\(300\) 0 0
\(301\) 175.652 + 435.058i 0.583560 + 1.44537i
\(302\) 314.783 + 314.783i 1.04233 + 1.04233i
\(303\) 0 0
\(304\) 446.704 257.905i 1.46942 0.848371i
\(305\) 125.518 8.46279i 0.411535 0.0277468i
\(306\) 0 0
\(307\) −104.260 104.260i −0.339609 0.339609i 0.516611 0.856220i \(-0.327193\pi\)
−0.856220 + 0.516611i \(0.827193\pi\)
\(308\) 45.8125 34.5048i 0.148742 0.112028i
\(309\) 0 0
\(310\) 50.4606 256.187i 0.162776 0.826410i
\(311\) 16.5632 + 28.6884i 0.0532580 + 0.0922455i 0.891425 0.453168i \(-0.149706\pi\)
−0.838167 + 0.545413i \(0.816373\pi\)
\(312\) 0 0
\(313\) −112.285 419.052i −0.358737 1.33882i −0.875716 0.482826i \(-0.839610\pi\)
0.516980 0.855998i \(-0.327056\pi\)
\(314\) 64.2009i 0.204462i
\(315\) 0 0
\(316\) 129.381 0.409434
\(317\) −270.012 + 72.3496i −0.851774 + 0.228232i −0.658190 0.752852i \(-0.728678\pi\)
−0.193584 + 0.981084i \(0.562011\pi\)
\(318\) 0 0
\(319\) 281.724 162.654i 0.883148 0.509886i
\(320\) −185.191 + 124.243i −0.578723 + 0.388259i
\(321\) 0 0
\(322\) 60.6550 7.43252i 0.188370 0.0230824i
\(323\) 212.898 212.898i 0.659128 0.659128i
\(324\) 0 0
\(325\) −5.53210 13.2156i −0.0170219 0.0406633i
\(326\) 93.5010 + 161.948i 0.286813 + 0.496774i
\(327\) 0 0
\(328\) −266.863 + 266.863i −0.813607 + 0.813607i
\(329\) 17.1583 121.873i 0.0521529 0.370434i
\(330\) 0 0
\(331\) −125.181 + 216.820i −0.378191 + 0.655047i −0.990799 0.135340i \(-0.956787\pi\)
0.612608 + 0.790387i \(0.290121\pi\)
\(332\) −11.3659 + 42.4180i −0.0342345 + 0.127765i
\(333\) 0 0
\(334\) 399.168 + 230.460i 1.19511 + 0.689999i
\(335\) −6.66483 + 2.27632i −0.0198950 + 0.00679499i
\(336\) 0 0
\(337\) −7.57759 7.57759i −0.0224854 0.0224854i 0.695775 0.718260i \(-0.255061\pi\)
−0.718260 + 0.695775i \(0.755061\pi\)
\(338\) −96.3684 359.652i −0.285114 1.06406i
\(339\) 0 0
\(340\) 31.3964 35.9361i 0.0923423 0.105694i
\(341\) 111.017 192.287i 0.325563 0.563892i
\(342\) 0 0
\(343\) −320.308 + 122.687i −0.933842 + 0.357687i
\(344\) 462.669i 1.34497i
\(345\) 0 0
\(346\) −77.0436 133.443i −0.222669 0.385675i
\(347\) 80.6472 300.979i 0.232413 0.867376i −0.746885 0.664953i \(-0.768452\pi\)
0.979298 0.202423i \(-0.0648817\pi\)
\(348\) 0 0
\(349\) 396.973i 1.13746i −0.822525 0.568729i \(-0.807435\pi\)
0.822525 0.568729i \(-0.192565\pi\)
\(350\) −333.539 194.901i −0.952968 0.556859i
\(351\) 0 0
\(352\) 124.511 33.3626i 0.353724 0.0947802i
\(353\) 127.946 + 34.2831i 0.362454 + 0.0971193i 0.435450 0.900213i \(-0.356589\pi\)
−0.0729959 + 0.997332i \(0.523256\pi\)
\(354\) 0 0
\(355\) 241.217 + 359.548i 0.679484 + 1.01281i
\(356\) −131.185 −0.368498
\(357\) 0 0
\(358\) −19.3666 + 19.3666i −0.0540966 + 0.0540966i
\(359\) 66.6339 + 38.4711i 0.185610 + 0.107162i 0.589926 0.807458i \(-0.299157\pi\)
−0.404316 + 0.914619i \(0.632490\pi\)
\(360\) 0 0
\(361\) 198.713 + 344.182i 0.550453 + 0.953412i
\(362\) 349.647 93.6876i 0.965875 0.258805i
\(363\) 0 0
\(364\) 2.75899 + 2.15664i 0.00757963 + 0.00592483i
\(365\) 142.122 + 416.118i 0.389375 + 1.14005i
\(366\) 0 0
\(367\) 60.6221 226.245i 0.165183 0.616471i −0.832834 0.553523i \(-0.813283\pi\)
0.998017 0.0629479i \(-0.0200502\pi\)
\(368\) 71.5459 + 19.1707i 0.194418 + 0.0520942i
\(369\) 0 0
\(370\) 262.732 + 128.955i 0.710087 + 0.348526i
\(371\) −65.8315 + 84.2182i −0.177443 + 0.227003i
\(372\) 0 0
\(373\) −98.3605 367.087i −0.263701 0.984146i −0.963041 0.269356i \(-0.913189\pi\)
0.699339 0.714790i \(-0.253478\pi\)
\(374\) 196.165 113.256i 0.524505 0.302823i
\(375\) 0 0
\(376\) 60.6835 105.107i 0.161392 0.279539i
\(377\) 14.0450 + 14.0450i 0.0372547 + 0.0372547i
\(378\) 0 0
\(379\) 369.290i 0.974379i 0.873296 + 0.487190i \(0.161978\pi\)
−0.873296 + 0.487190i \(0.838022\pi\)
\(380\) 66.9690 + 99.8214i 0.176234 + 0.262688i
\(381\) 0 0
\(382\) 71.9991 268.704i 0.188479 0.703415i
\(383\) −187.821 700.956i −0.490393 1.83017i −0.554439 0.832224i \(-0.687067\pi\)
0.0640459 0.997947i \(-0.479600\pi\)
\(384\) 0 0
\(385\) −214.835 248.509i −0.558012 0.645477i
\(386\) −121.521 −0.314820
\(387\) 0 0
\(388\) 89.2530 + 23.9153i 0.230034 + 0.0616373i
\(389\) −135.464 + 78.2101i −0.348236 + 0.201054i −0.663908 0.747814i \(-0.731103\pi\)
0.315672 + 0.948868i \(0.397770\pi\)
\(390\) 0 0
\(391\) 43.2353 0.110576
\(392\) −338.186 6.06760i −0.862720 0.0154786i
\(393\) 0 0
\(394\) 167.730 + 96.8387i 0.425710 + 0.245784i
\(395\) −49.8504 739.370i −0.126204 1.87182i
\(396\) 0 0
\(397\) 608.327 163.001i 1.53231 0.410581i 0.608538 0.793525i \(-0.291756\pi\)
0.923772 + 0.382944i \(0.125090\pi\)
\(398\) −437.610 + 437.610i −1.09952 + 1.09952i
\(399\) 0 0
\(400\) −286.437 370.414i −0.716093 0.926035i
\(401\) −175.823 + 304.535i −0.438463 + 0.759439i −0.997571 0.0696551i \(-0.977810\pi\)
0.559109 + 0.829094i \(0.311143\pi\)
\(402\) 0 0
\(403\) 13.0950 + 3.50881i 0.0324939 + 0.00870672i
\(404\) 98.8613 + 57.0776i 0.244706 + 0.141281i
\(405\) 0 0
\(406\) 530.350 + 74.6673i 1.30628 + 0.183910i
\(407\) 175.981 + 175.981i 0.432385 + 0.432385i
\(408\) 0 0
\(409\) 63.4064 36.6077i 0.155028 0.0895055i −0.420479 0.907302i \(-0.638138\pi\)
0.575507 + 0.817797i \(0.304805\pi\)
\(410\) −454.440 397.032i −1.10839 0.968370i
\(411\) 0 0
\(412\) 23.7374 + 23.7374i 0.0576151 + 0.0576151i
\(413\) 88.8365 + 724.973i 0.215101 + 1.75538i
\(414\) 0 0
\(415\) 246.784 + 48.6085i 0.594660 + 0.117129i
\(416\) 3.93530 + 6.81614i 0.00945985 + 0.0163849i
\(417\) 0 0
\(418\) 147.677 + 551.139i 0.353295 + 1.31851i
\(419\) 19.8543i 0.0473849i −0.999719 0.0236925i \(-0.992458\pi\)
0.999719 0.0236925i \(-0.00754225\pi\)
\(420\) 0 0
\(421\) −19.3162 −0.0458817 −0.0229408 0.999737i \(-0.507303\pi\)
−0.0229408 + 0.999737i \(0.507303\pi\)
\(422\) −458.978 + 122.983i −1.08763 + 0.291429i
\(423\) 0 0
\(424\) −91.2891 + 52.7058i −0.215304 + 0.124306i
\(425\) −217.460 165.574i −0.511670 0.389585i
\(426\) 0 0
\(427\) 105.960 + 140.685i 0.248150 + 0.329473i
\(428\) 123.778 123.778i 0.289202 0.289202i
\(429\) 0 0
\(430\) −738.111 + 49.7655i −1.71654 + 0.115734i
\(431\) 129.158 + 223.709i 0.299671 + 0.519046i 0.976061 0.217498i \(-0.0697897\pi\)
−0.676389 + 0.736544i \(0.736456\pi\)
\(432\) 0 0
\(433\) −307.927 + 307.927i −0.711147 + 0.711147i −0.966775 0.255628i \(-0.917718\pi\)
0.255628 + 0.966775i \(0.417718\pi\)
\(434\) 338.968 136.856i 0.781032 0.315337i
\(435\) 0 0
\(436\) −63.6375 + 110.223i −0.145957 + 0.252806i
\(437\) −28.1878 + 105.198i −0.0645030 + 0.240729i
\(438\) 0 0
\(439\) −544.482 314.357i −1.24028 0.716074i −0.271127 0.962544i \(-0.587396\pi\)
−0.969151 + 0.246469i \(0.920730\pi\)
\(440\) −104.701 306.552i −0.237956 0.696710i
\(441\) 0 0
\(442\) 9.77955 + 9.77955i 0.0221257 + 0.0221257i
\(443\) −173.821 648.708i −0.392372 1.46435i −0.826211 0.563361i \(-0.809508\pi\)
0.433839 0.900990i \(-0.357159\pi\)
\(444\) 0 0
\(445\) 50.5456 + 749.680i 0.113586 + 1.68467i
\(446\) −201.816 + 349.556i −0.452502 + 0.783757i
\(447\) 0 0
\(448\) −287.361 122.060i −0.641431 0.272455i
\(449\) 36.1975i 0.0806181i 0.999187 + 0.0403091i \(0.0128342\pi\)
−0.999187 + 0.0403091i \(0.987166\pi\)
\(450\) 0 0
\(451\) −256.571 444.394i −0.568893 0.985352i
\(452\) 15.9958 59.6973i 0.0353890 0.132074i
\(453\) 0 0
\(454\) 105.741i 0.232910i
\(455\) 11.2614 16.5976i 0.0247504 0.0364783i
\(456\) 0 0
\(457\) −628.547 + 168.419i −1.37538 + 0.368531i −0.869440 0.494039i \(-0.835520\pi\)
−0.505937 + 0.862570i \(0.668853\pi\)
\(458\) 677.840 + 181.627i 1.48000 + 0.396565i
\(459\) 0 0
\(460\) −3.33582 + 16.9359i −0.00725179 + 0.0368171i
\(461\) 224.604 0.487210 0.243605 0.969875i \(-0.421670\pi\)
0.243605 + 0.969875i \(0.421670\pi\)
\(462\) 0 0
\(463\) 36.7738 36.7738i 0.0794250 0.0794250i −0.666278 0.745703i \(-0.732114\pi\)
0.745703 + 0.666278i \(0.232114\pi\)
\(464\) 562.203 + 324.588i 1.21164 + 0.699543i
\(465\) 0 0
\(466\) −299.435 518.637i −0.642565 1.11296i
\(467\) 249.401 66.8267i 0.534049 0.143098i 0.0182915 0.999833i \(-0.494177\pi\)
0.515757 + 0.856735i \(0.327511\pi\)
\(468\) 0 0
\(469\) −7.76830 6.07230i −0.0165635 0.0129473i
\(470\) 174.208 + 85.5049i 0.370655 + 0.181925i
\(471\) 0 0
\(472\) −186.417 + 695.719i −0.394952 + 1.47398i
\(473\) −607.642 162.817i −1.28465 0.344222i
\(474\) 0 0
\(475\) 544.643 421.167i 1.14662 0.886666i
\(476\) 66.1547 + 9.31384i 0.138980 + 0.0195669i
\(477\) 0 0
\(478\) −10.7180 40.0002i −0.0224227 0.0836825i
\(479\) 633.380 365.682i 1.32230 0.763429i 0.338202 0.941073i \(-0.390181\pi\)
0.984095 + 0.177645i \(0.0568478\pi\)
\(480\) 0 0
\(481\) −7.59790 + 13.1599i −0.0157960 + 0.0273596i
\(482\) 123.001 + 123.001i 0.255188 + 0.255188i
\(483\) 0 0
\(484\) 28.7290i 0.0593574i
\(485\) 102.279 519.266i 0.210884 1.07065i
\(486\) 0 0
\(487\) 194.148 724.570i 0.398661 1.48782i −0.416792 0.909002i \(-0.636846\pi\)
0.815454 0.578823i \(-0.196488\pi\)
\(488\) 44.9518 + 167.762i 0.0921144 + 0.343776i
\(489\) 0 0
\(490\) −26.6961 540.173i −0.0544819 1.10239i
\(491\) 114.225 0.232638 0.116319 0.993212i \(-0.462891\pi\)
0.116319 + 0.993212i \(0.462891\pi\)
\(492\) 0 0
\(493\) 366.019 + 98.0745i 0.742432 + 0.198934i
\(494\) −30.1711 + 17.4193i −0.0610751 + 0.0352618i
\(495\) 0 0
\(496\) 443.087 0.893320
\(497\) −236.979 + 557.910i −0.476819 + 1.12256i
\(498\) 0 0
\(499\) −326.723 188.633i −0.654755 0.378023i 0.135521 0.990775i \(-0.456729\pi\)
−0.790275 + 0.612752i \(0.790063\pi\)
\(500\) 81.6356 72.4072i 0.163271 0.144814i
\(501\) 0 0
\(502\) −183.977 + 49.2964i −0.366487 + 0.0982000i
\(503\) 29.7057 29.7057i 0.0590572 0.0590572i −0.676961 0.736019i \(-0.736704\pi\)
0.736019 + 0.676961i \(0.236704\pi\)
\(504\) 0 0
\(505\) 288.088 586.951i 0.570472 1.16228i
\(506\) −40.9674 + 70.9576i −0.0809633 + 0.140233i
\(507\) 0 0
\(508\) −143.531 38.4589i −0.282540 0.0757065i
\(509\) 147.952 + 85.4202i 0.290672 + 0.167820i 0.638245 0.769833i \(-0.279661\pi\)
−0.347573 + 0.937653i \(0.612994\pi\)
\(510\) 0 0
\(511\) −379.123 + 485.012i −0.741924 + 0.949143i
\(512\) −183.792 183.792i −0.358968 0.358968i
\(513\) 0 0
\(514\) −478.141 + 276.055i −0.930234 + 0.537071i
\(515\) 126.505 144.797i 0.245642 0.281160i
\(516\) 0 0
\(517\) 116.686 + 116.686i 0.225699 + 0.225699i
\(518\) 49.8361 + 406.700i 0.0962087 + 0.785135i
\(519\) 0 0
\(520\) 16.4252 11.0195i 0.0315869 0.0211913i
\(521\) 75.4299 + 130.648i 0.144779 + 0.250765i 0.929291 0.369350i \(-0.120420\pi\)
−0.784511 + 0.620114i \(0.787086\pi\)
\(522\) 0 0
\(523\) 210.608 + 786.001i 0.402693 + 1.50287i 0.808271 + 0.588810i \(0.200403\pi\)
−0.405579 + 0.914060i \(0.632930\pi\)
\(524\) 107.774i 0.205676i
\(525\) 0 0
\(526\) −801.077 −1.52296
\(527\) 249.821 66.9395i 0.474044 0.127020i
\(528\) 0 0
\(529\) 444.583 256.680i 0.840422 0.485218i
\(530\) −93.9026 139.967i −0.177175 0.264090i
\(531\) 0 0
\(532\) −65.7925 + 154.893i −0.123670 + 0.291151i
\(533\) 22.1547 22.1547i 0.0415661 0.0415661i
\(534\) 0 0
\(535\) −755.043 659.660i −1.41130 1.23301i
\(536\) −4.86159 8.42051i −0.00907012 0.0157099i
\(537\) 0 0
\(538\) 460.760 460.760i 0.856431 0.856431i
\(539\) 126.980 442.019i 0.235584 0.820072i
\(540\) 0 0
\(541\) −525.462 + 910.127i −0.971280 + 1.68231i −0.279577 + 0.960123i \(0.590194\pi\)
−0.691702 + 0.722183i \(0.743139\pi\)
\(542\) −238.235 + 889.105i −0.439548 + 1.64042i
\(543\) 0 0
\(544\) 130.035 + 75.0758i 0.239035 + 0.138007i
\(545\) 654.409 + 321.198i 1.20075 + 0.589354i
\(546\) 0 0
\(547\) 332.845 + 332.845i 0.608492 + 0.608492i 0.942552 0.334060i \(-0.108419\pi\)
−0.334060 + 0.942552i \(0.608419\pi\)
\(548\) −33.8024 126.152i −0.0616833 0.230205i
\(549\) 0 0
\(550\) 477.792 200.006i 0.868712 0.363647i
\(551\) −477.262 + 826.642i −0.866174 + 1.50026i
\(552\) 0 0
\(553\) 828.711 624.163i 1.49857 1.12868i
\(554\) 558.930i 1.00890i
\(555\) 0 0
\(556\) −37.8609 65.5769i −0.0680951 0.117944i
\(557\) −177.542 + 662.596i −0.318747 + 1.18958i 0.601703 + 0.798720i \(0.294489\pi\)
−0.920450 + 0.390860i \(0.872177\pi\)
\(558\) 0 0
\(559\) 38.4103i 0.0687125i
\(560\) 215.118 619.241i 0.384140 1.10579i
\(561\) 0 0
\(562\) 501.120 134.275i 0.891672 0.238923i
\(563\) −451.611 121.009i −0.802152 0.214936i −0.165623 0.986189i \(-0.552964\pi\)
−0.636528 + 0.771253i \(0.719630\pi\)
\(564\) 0 0
\(565\) −347.313 68.4096i −0.614714 0.121079i
\(566\) −103.929 −0.183620
\(567\) 0 0
\(568\) −422.669 + 422.669i −0.744135 + 0.744135i
\(569\) −492.294 284.226i −0.865192 0.499519i 0.000555696 1.00000i \(-0.499823\pi\)
−0.865747 + 0.500481i \(0.833156\pi\)
\(570\) 0 0
\(571\) 377.172 + 653.280i 0.660546 + 1.14410i 0.980472 + 0.196657i \(0.0630084\pi\)
−0.319927 + 0.947442i \(0.603658\pi\)
\(572\) −4.53534 + 1.21524i −0.00792891 + 0.00212455i
\(573\) 0 0
\(574\) 117.781 836.577i 0.205193 1.45745i
\(575\) 98.0681 + 12.5377i 0.170553 + 0.0218048i
\(576\) 0 0
\(577\) −146.947 + 548.414i −0.254675 + 0.950458i 0.713597 + 0.700557i \(0.247065\pi\)
−0.968271 + 0.249902i \(0.919602\pi\)
\(578\) −361.364 96.8272i −0.625197 0.167521i
\(579\) 0 0
\(580\) −66.6574 + 135.808i −0.114927 + 0.234152i
\(581\) 131.833 + 326.527i 0.226907 + 0.562008i
\(582\) 0 0
\(583\) −37.0953 138.441i −0.0636282 0.237464i
\(584\) −525.733 + 303.532i −0.900228 + 0.519747i
\(585\) 0 0
\(586\) −19.0067 + 32.9206i −0.0324347 + 0.0561786i
\(587\) −191.752 191.752i −0.326665 0.326665i 0.524652 0.851317i \(-0.324195\pi\)
−0.851317 + 0.524652i \(0.824195\pi\)
\(588\) 0 0
\(589\) 651.497i 1.10611i
\(590\) −1129.96 222.565i −1.91518 0.377229i
\(591\) 0 0
\(592\) −128.542 + 479.725i −0.217132 + 0.810346i
\(593\) −158.838 592.793i −0.267856 0.999651i −0.960479 0.278352i \(-0.910212\pi\)
0.692623 0.721299i \(-0.256455\pi\)
\(594\) 0 0
\(595\) 27.7361 381.640i 0.0466154 0.641412i
\(596\) 21.9506 0.0368298
\(597\) 0 0
\(598\) −4.83233 1.29482i −0.00808081 0.00216525i
\(599\) 649.805 375.165i 1.08482 0.626319i 0.152625 0.988284i \(-0.451227\pi\)
0.932192 + 0.361965i \(0.117894\pi\)
\(600\) 0 0
\(601\) −592.685 −0.986165 −0.493083 0.869982i \(-0.664130\pi\)
−0.493083 + 0.869982i \(0.664130\pi\)
\(602\) −623.100 827.300i −1.03505 1.37425i
\(603\) 0 0
\(604\) −152.460 88.0227i −0.252417 0.145733i
\(605\) −164.176 + 11.0692i −0.271366 + 0.0182963i
\(606\) 0 0
\(607\) 387.642 103.868i 0.638619 0.171117i 0.0750410 0.997180i \(-0.476091\pi\)
0.563578 + 0.826063i \(0.309425\pi\)
\(608\) −267.450 + 267.450i −0.439884 + 0.439884i
\(609\) 0 0
\(610\) −262.802 + 89.7581i −0.430823 + 0.147144i
\(611\) −5.03788 + 8.72587i −0.00824531 + 0.0142813i
\(612\) 0 0
\(613\) −212.730 57.0009i −0.347031 0.0929868i 0.0810932 0.996707i \(-0.474159\pi\)
−0.428125 + 0.903720i \(0.640826\pi\)
\(614\) 281.877 + 162.742i 0.459084 + 0.265052i
\(615\) 0 0
\(616\) 279.299 357.307i 0.453407 0.580043i
\(617\) −338.020 338.020i −0.547844 0.547844i 0.377973 0.925817i \(-0.376621\pi\)
−0.925817 + 0.377973i \(0.876621\pi\)
\(618\) 0 0
\(619\) 266.400 153.806i 0.430371 0.248475i −0.269134 0.963103i \(-0.586737\pi\)
0.699505 + 0.714628i \(0.253404\pi\)
\(620\) 6.94612 + 103.023i 0.0112034 + 0.166167i
\(621\) 0 0
\(622\) −51.7078 51.7078i −0.0831316 0.0831316i
\(623\) −840.266 + 632.866i −1.34874 + 1.01584i
\(624\) 0 0
\(625\) −445.237 438.622i −0.712379 0.701795i
\(626\) 478.840 + 829.375i 0.764920 + 1.32488i
\(627\) 0 0
\(628\) −6.57106 24.5235i −0.0104635 0.0390502i
\(629\) 289.899i 0.460888i
\(630\) 0 0
\(631\) −219.545 −0.347931 −0.173966 0.984752i \(-0.555658\pi\)
−0.173966 + 0.984752i \(0.555658\pi\)
\(632\) 988.213 264.791i 1.56363 0.418973i
\(633\) 0 0
\(634\) 534.401 308.536i 0.842903 0.486650i
\(635\) −164.477 + 835.047i −0.259020 + 1.31503i
\(636\) 0 0
\(637\) 28.0759 + 0.503726i 0.0440752 + 0.000790779i
\(638\) −507.779 + 507.779i −0.795892 + 0.795892i
\(639\) 0 0
\(640\) 504.615 577.580i 0.788462 0.902469i
\(641\) −417.537 723.194i −0.651383 1.12823i −0.982787 0.184740i \(-0.940856\pi\)
0.331404 0.943489i \(-0.392478\pi\)
\(642\) 0 0
\(643\) −649.916 + 649.916i −1.01076 + 1.01076i −0.0108149 + 0.999942i \(0.503443\pi\)
−0.999942 + 0.0108149i \(0.996557\pi\)
\(644\) −22.4083 + 9.04721i −0.0347955 + 0.0140485i
\(645\) 0 0
\(646\) −332.318 + 575.591i −0.514424 + 0.891008i
\(647\) −95.3328 + 355.787i −0.147346 + 0.549902i 0.852294 + 0.523063i \(0.175211\pi\)
−0.999640 + 0.0268391i \(0.991456\pi\)
\(648\) 0 0
\(649\) −848.115 489.659i −1.30680 0.754483i
\(650\) 19.3464 + 25.0184i 0.0297637 + 0.0384898i
\(651\) 0 0
\(652\) −52.2913 52.2913i −0.0802014 0.0802014i
\(653\) −117.038 436.792i −0.179232 0.668901i −0.995792 0.0916414i \(-0.970789\pi\)
0.816561 0.577260i \(-0.195878\pi\)
\(654\) 0 0
\(655\) −615.892 + 41.5252i −0.940293 + 0.0633972i
\(656\) 512.008 886.823i 0.780499 1.35186i
\(657\) 0 0
\(658\) 33.0444 + 269.668i 0.0502195 + 0.409829i
\(659\) 395.881i 0.600730i −0.953824 0.300365i \(-0.902892\pi\)
0.953824 0.300365i \(-0.0971085\pi\)
\(660\) 0 0
\(661\) −41.2693 71.4804i −0.0624346 0.108140i 0.833119 0.553094i \(-0.186553\pi\)
−0.895553 + 0.444955i \(0.853220\pi\)
\(662\) 143.042 533.838i 0.216075 0.806403i
\(663\) 0 0
\(664\) 347.250i 0.522966i
\(665\) 910.509 + 316.302i 1.36919 + 0.475642i
\(666\) 0 0
\(667\) −132.398 + 35.4760i −0.198498 + 0.0531874i
\(668\) −176.062 47.1758i −0.263567 0.0706225i
\(669\) 0 0
\(670\) 12.9106 8.66158i 0.0192696 0.0129277i
\(671\) −236.148 −0.351935
\(672\) 0 0
\(673\) 923.540 923.540i 1.37227 1.37227i 0.515207 0.857066i \(-0.327715\pi\)
0.857066 0.515207i \(-0.172285\pi\)
\(674\) 20.4868 + 11.8280i 0.0303958 + 0.0175490i
\(675\) 0 0
\(676\) 73.6218 + 127.517i 0.108908 + 0.188634i
\(677\) 242.099 64.8703i 0.357606 0.0958203i −0.0755429 0.997143i \(-0.524069\pi\)
0.433149 + 0.901322i \(0.357402\pi\)
\(678\) 0 0
\(679\) 687.055 277.394i 1.01186 0.408533i
\(680\) 166.259 338.735i 0.244498 0.498140i
\(681\) 0 0
\(682\) −126.856 + 473.434i −0.186006 + 0.694185i
\(683\) 1283.82 + 344.000i 1.87968 + 0.503660i 0.999583 + 0.0288723i \(0.00919162\pi\)
0.880101 + 0.474787i \(0.157475\pi\)
\(684\) 0 0
\(685\) −707.894 + 241.776i −1.03342 + 0.352957i
\(686\) 612.884 444.603i 0.893417 0.648110i
\(687\) 0 0
\(688\) −324.914 1212.60i −0.472259 1.76250i
\(689\) 7.57873 4.37558i 0.0109996 0.00635063i
\(690\) 0 0
\(691\) 161.274 279.335i 0.233392 0.404247i −0.725412 0.688315i \(-0.758351\pi\)
0.958804 + 0.284068i \(0.0916840\pi\)
\(692\) 43.0873 + 43.0873i 0.0622649 + 0.0622649i
\(693\) 0 0
\(694\) 687.843i 0.991129i
\(695\) −360.162 + 241.629i −0.518219 + 0.347667i
\(696\) 0 0
\(697\) 154.703 577.361i 0.221956 0.828352i
\(698\) 226.805 + 846.449i 0.324936 + 1.21268i
\(699\) 0 0
\(700\) 147.354 + 40.3101i 0.210506 + 0.0575859i
\(701\) −993.695 −1.41754 −0.708769 0.705440i \(-0.750749\pi\)
−0.708769 + 0.705440i \(0.750749\pi\)
\(702\) 0 0
\(703\) −705.369 189.003i −1.00337 0.268852i
\(704\) 362.529 209.306i 0.514956 0.297310i
\(705\) 0 0
\(706\) −292.402 −0.414167
\(707\) 908.580 111.335i 1.28512 0.157476i
\(708\) 0 0
\(709\) 594.099 + 343.003i 0.837940 + 0.483785i 0.856563 0.516042i \(-0.172595\pi\)
−0.0186238 + 0.999827i \(0.505928\pi\)
\(710\) −719.761 628.835i −1.01375 0.885683i
\(711\) 0 0
\(712\) −1001.99 + 268.483i −1.40729 + 0.377083i
\(713\) −66.1530 + 66.1530i −0.0927811 + 0.0927811i
\(714\) 0 0
\(715\) 8.69215 + 25.4497i 0.0121568 + 0.0355940i
\(716\) 5.41547 9.37986i 0.00756350 0.0131004i
\(717\) 0 0
\(718\) −164.061 43.9599i −0.228497 0.0612255i
\(719\) −258.622 149.315i −0.359696 0.207671i 0.309251 0.950980i \(-0.399922\pi\)
−0.668948 + 0.743310i \(0.733255\pi\)
\(720\) 0 0
\(721\) 266.557 + 37.5282i 0.369705 + 0.0520503i
\(722\) −620.353 620.353i −0.859214 0.859214i
\(723\) 0 0
\(724\) −123.969 + 71.5738i −0.171228 + 0.0988588i
\(725\) 801.779 + 328.598i 1.10590 + 0.453239i
\(726\) 0 0
\(727\) 427.959 + 427.959i 0.588665 + 0.588665i 0.937270 0.348605i \(-0.113344\pi\)
−0.348605 + 0.937270i \(0.613344\pi\)
\(728\) 25.4869 + 10.8259i 0.0350094 + 0.0148707i
\(729\) 0 0
\(730\) −540.784 806.072i −0.740800 1.10421i
\(731\) −366.387 634.601i −0.501214 0.868127i
\(732\) 0 0
\(733\) 112.025 + 418.082i 0.152830 + 0.570370i 0.999281 + 0.0379039i \(0.0120681\pi\)
−0.846451 + 0.532466i \(0.821265\pi\)
\(734\) 517.048i 0.704426i
\(735\) 0 0
\(736\) −54.3136 −0.0737956
\(737\) 12.7698 3.42167i 0.0173268 0.00464270i
\(738\) 0 0
\(739\) −160.126 + 92.4489i −0.216680 + 0.125100i −0.604412 0.796672i \(-0.706592\pi\)
0.387732 + 0.921772i \(0.373259\pi\)
\(740\) −113.557 22.3672i −0.153456 0.0302259i
\(741\) 0 0
\(742\) 92.2528 217.187i 0.124330 0.292705i
\(743\) 576.263 576.263i 0.775589 0.775589i −0.203488 0.979077i \(-0.565228\pi\)
0.979077 + 0.203488i \(0.0652278\pi\)
\(744\) 0 0
\(745\) −8.45753 125.440i −0.0113524 0.168376i
\(746\) 419.461 + 726.527i 0.562280 + 0.973897i
\(747\) 0 0
\(748\) −63.3393 + 63.3393i −0.0846782 + 0.0846782i
\(749\) 195.690 1389.96i 0.261269 1.85575i
\(750\) 0 0
\(751\) 710.061 1229.86i 0.945487 1.63763i 0.190715 0.981645i \(-0.438919\pi\)
0.754772 0.655987i \(-0.227747\pi\)
\(752\) −85.2314 + 318.088i −0.113340 + 0.422989i
\(753\) 0 0
\(754\) −37.9721 21.9232i −0.0503609 0.0290759i
\(755\) −444.278 + 905.172i −0.588447 + 1.19890i
\(756\) 0 0
\(757\) −316.057 316.057i −0.417512 0.417512i 0.466833 0.884345i \(-0.345395\pi\)
−0.884345 + 0.466833i \(0.845395\pi\)
\(758\) −210.989 787.422i −0.278350 1.03882i
\(759\) 0 0
\(760\) 715.803 + 625.377i 0.941846 + 0.822864i
\(761\) −393.410 + 681.407i −0.516965 + 0.895409i 0.482841 + 0.875708i \(0.339605\pi\)
−0.999806 + 0.0197013i \(0.993728\pi\)
\(762\) 0 0
\(763\) 124.131 + 1013.00i 0.162688 + 1.32766i
\(764\) 110.009i 0.143991i
\(765\) 0 0
\(766\) 800.964 + 1387.31i 1.04565 + 1.81111i
\(767\) 15.4762 57.7579i 0.0201776 0.0753037i
\(768\) 0 0
\(769\) 1512.03i 1.96622i 0.183008 + 0.983111i \(0.441417\pi\)
−0.183008 + 0.983111i \(0.558583\pi\)
\(770\) 600.066 + 407.142i 0.779306 + 0.528756i
\(771\) 0 0
\(772\) 46.4186 12.4378i 0.0601277 0.0161112i
\(773\) 228.469 + 61.2182i 0.295562 + 0.0791956i 0.403553 0.914956i \(-0.367775\pi\)
−0.107991 + 0.994152i \(0.534442\pi\)
\(774\) 0 0
\(775\) 586.067 79.3895i