Properties

Label 720.2.u.a.179.9
Level $720$
Weight $2$
Character 720.179
Analytic conductor $5.749$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 179.9
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22941 - 0.698958i) q^{2} +(1.02291 + 1.71862i) q^{4} +(-1.91479 + 1.15480i) q^{5} +3.02955i q^{7} +(-0.0563436 - 2.82787i) q^{8} +O(q^{10})\) \(q+(-1.22941 - 0.698958i) q^{2} +(1.02291 + 1.71862i) q^{4} +(-1.91479 + 1.15480i) q^{5} +3.02955i q^{7} +(-0.0563436 - 2.82787i) q^{8} +(3.16123 - 0.0813664i) q^{10} +(1.30581 - 1.30581i) q^{11} +(-1.56756 + 1.56756i) q^{13} +(2.11753 - 3.72457i) q^{14} +(-1.90729 + 3.51600i) q^{16} +2.98571 q^{17} +(1.25807 - 1.25807i) q^{19} +(-3.94333 - 2.10954i) q^{20} +(-2.51809 + 0.692674i) q^{22} -7.82148 q^{23} +(2.33287 - 4.42241i) q^{25} +(3.02283 - 0.831519i) q^{26} +(-5.20664 + 3.09897i) q^{28} +(-7.12073 + 7.12073i) q^{29} -0.0502896i q^{31} +(4.80238 - 2.98950i) q^{32} +(-3.67067 - 2.08689i) q^{34} +(-3.49853 - 5.80096i) q^{35} +(-6.22957 - 6.22957i) q^{37} +(-2.42603 + 0.667350i) q^{38} +(3.37351 + 5.34971i) q^{40} -4.05554 q^{41} +(-6.18655 + 6.18655i) q^{43} +(3.57992 + 0.908456i) q^{44} +(9.61583 + 5.46689i) q^{46} -5.87568i q^{47} -2.17818 q^{49} +(-5.95914 + 3.80639i) q^{50} +(-4.29751 - 1.09055i) q^{52} +(4.40639 - 4.40639i) q^{53} +(-0.992408 + 4.00831i) q^{55} +(8.56716 - 0.170696i) q^{56} +(13.7314 - 3.77723i) q^{58} +(-8.20735 + 8.20735i) q^{59} +(-4.93899 - 4.93899i) q^{61} +(-0.0351503 + 0.0618267i) q^{62} +(-7.99365 + 0.318664i) q^{64} +(1.19133 - 4.81176i) q^{65} +(-1.29973 - 1.29973i) q^{67} +(3.05413 + 5.13129i) q^{68} +(0.246504 + 9.57711i) q^{70} +13.9687i q^{71} +3.85841 q^{73} +(3.30451 + 12.0129i) q^{74} +(3.44904 + 0.875242i) q^{76} +(3.95602 + 3.95602i) q^{77} +1.07096i q^{79} +(-0.408208 - 8.93495i) q^{80} +(4.98593 + 2.83465i) q^{82} +(-7.16503 + 7.16503i) q^{83} +(-5.71702 + 3.44790i) q^{85} +(11.9300 - 3.28169i) q^{86} +(-3.76623 - 3.61909i) q^{88} +7.60356 q^{89} +(-4.74899 - 4.74899i) q^{91} +(-8.00071 - 13.4421i) q^{92} +(-4.10686 + 7.22364i) q^{94} +(-0.956125 + 3.86176i) q^{95} -9.70129i q^{97} +(2.67788 + 1.52245i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22941 0.698958i −0.869327 0.494238i
\(3\) 0 0
\(4\) 1.02291 + 1.71862i 0.511457 + 0.859309i
\(5\) −1.91479 + 1.15480i −0.856322 + 0.516443i
\(6\) 0 0
\(7\) 3.02955i 1.14506i 0.819883 + 0.572531i \(0.194038\pi\)
−0.819883 + 0.572531i \(0.805962\pi\)
\(8\) −0.0563436 2.82787i −0.0199205 0.999802i
\(9\) 0 0
\(10\) 3.16123 0.0813664i 0.999669 0.0257303i
\(11\) 1.30581 1.30581i 0.393717 0.393717i −0.482293 0.876010i \(-0.660196\pi\)
0.876010 + 0.482293i \(0.160196\pi\)
\(12\) 0 0
\(13\) −1.56756 + 1.56756i −0.434762 + 0.434762i −0.890245 0.455483i \(-0.849467\pi\)
0.455483 + 0.890245i \(0.349467\pi\)
\(14\) 2.11753 3.72457i 0.565933 0.995433i
\(15\) 0 0
\(16\) −1.90729 + 3.51600i −0.476823 + 0.879000i
\(17\) 2.98571 0.724141 0.362071 0.932151i \(-0.382070\pi\)
0.362071 + 0.932151i \(0.382070\pi\)
\(18\) 0 0
\(19\) 1.25807 1.25807i 0.288621 0.288621i −0.547914 0.836535i \(-0.684578\pi\)
0.836535 + 0.547914i \(0.184578\pi\)
\(20\) −3.94333 2.10954i −0.881756 0.471706i
\(21\) 0 0
\(22\) −2.51809 + 0.692674i −0.536858 + 0.147679i
\(23\) −7.82148 −1.63089 −0.815446 0.578834i \(-0.803508\pi\)
−0.815446 + 0.578834i \(0.803508\pi\)
\(24\) 0 0
\(25\) 2.33287 4.42241i 0.466574 0.884482i
\(26\) 3.02283 0.831519i 0.592826 0.163074i
\(27\) 0 0
\(28\) −5.20664 + 3.09897i −0.983962 + 0.585651i
\(29\) −7.12073 + 7.12073i −1.32229 + 1.32229i −0.410365 + 0.911921i \(0.634599\pi\)
−0.911921 + 0.410365i \(0.865401\pi\)
\(30\) 0 0
\(31\) 0.0502896i 0.00903227i −0.999990 0.00451614i \(-0.998562\pi\)
0.999990 0.00451614i \(-0.00143754\pi\)
\(32\) 4.80238 2.98950i 0.848950 0.528474i
\(33\) 0 0
\(34\) −3.67067 2.08689i −0.629515 0.357898i
\(35\) −3.49853 5.80096i −0.591359 0.980542i
\(36\) 0 0
\(37\) −6.22957 6.22957i −1.02413 1.02413i −0.999701 0.0244329i \(-0.992222\pi\)
−0.0244329 0.999701i \(-0.507778\pi\)
\(38\) −2.42603 + 0.667350i −0.393553 + 0.108258i
\(39\) 0 0
\(40\) 3.37351 + 5.34971i 0.533398 + 0.845864i
\(41\) −4.05554 −0.633368 −0.316684 0.948531i \(-0.602570\pi\)
−0.316684 + 0.948531i \(0.602570\pi\)
\(42\) 0 0
\(43\) −6.18655 + 6.18655i −0.943441 + 0.943441i −0.998484 0.0550434i \(-0.982470\pi\)
0.0550434 + 0.998484i \(0.482470\pi\)
\(44\) 3.57992 + 0.908456i 0.539694 + 0.136955i
\(45\) 0 0
\(46\) 9.61583 + 5.46689i 1.41778 + 0.806049i
\(47\) 5.87568i 0.857057i −0.903528 0.428528i \(-0.859032\pi\)
0.903528 0.428528i \(-0.140968\pi\)
\(48\) 0 0
\(49\) −2.17818 −0.311168
\(50\) −5.95914 + 3.80639i −0.842750 + 0.538305i
\(51\) 0 0
\(52\) −4.29751 1.09055i −0.595957 0.151232i
\(53\) 4.40639 4.40639i 0.605264 0.605264i −0.336440 0.941705i \(-0.609223\pi\)
0.941705 + 0.336440i \(0.109223\pi\)
\(54\) 0 0
\(55\) −0.992408 + 4.00831i −0.133816 + 0.540481i
\(56\) 8.56716 0.170696i 1.14484 0.0228102i
\(57\) 0 0
\(58\) 13.7314 3.77723i 1.80302 0.495974i
\(59\) −8.20735 + 8.20735i −1.06851 + 1.06851i −0.0710318 + 0.997474i \(0.522629\pi\)
−0.997474 + 0.0710318i \(0.977371\pi\)
\(60\) 0 0
\(61\) −4.93899 4.93899i −0.632373 0.632373i 0.316290 0.948663i \(-0.397563\pi\)
−0.948663 + 0.316290i \(0.897563\pi\)
\(62\) −0.0351503 + 0.0618267i −0.00446409 + 0.00785199i
\(63\) 0 0
\(64\) −7.99365 + 0.318664i −0.999206 + 0.0398330i
\(65\) 1.19133 4.81176i 0.147767 0.596826i
\(66\) 0 0
\(67\) −1.29973 1.29973i −0.158787 0.158787i 0.623242 0.782029i \(-0.285815\pi\)
−0.782029 + 0.623242i \(0.785815\pi\)
\(68\) 3.05413 + 5.13129i 0.370367 + 0.622261i
\(69\) 0 0
\(70\) 0.246504 + 9.57711i 0.0294628 + 1.14468i
\(71\) 13.9687i 1.65778i 0.559414 + 0.828888i \(0.311026\pi\)
−0.559414 + 0.828888i \(0.688974\pi\)
\(72\) 0 0
\(73\) 3.85841 0.451593 0.225796 0.974175i \(-0.427502\pi\)
0.225796 + 0.974175i \(0.427502\pi\)
\(74\) 3.30451 + 12.0129i 0.384141 + 1.39647i
\(75\) 0 0
\(76\) 3.44904 + 0.875242i 0.395632 + 0.100397i
\(77\) 3.95602 + 3.95602i 0.450830 + 0.450830i
\(78\) 0 0
\(79\) 1.07096i 0.120492i 0.998184 + 0.0602461i \(0.0191885\pi\)
−0.998184 + 0.0602461i \(0.980811\pi\)
\(80\) −0.408208 8.93495i −0.0456391 0.998958i
\(81\) 0 0
\(82\) 4.98593 + 2.83465i 0.550604 + 0.313035i
\(83\) −7.16503 + 7.16503i −0.786464 + 0.786464i −0.980913 0.194448i \(-0.937708\pi\)
0.194448 + 0.980913i \(0.437708\pi\)
\(84\) 0 0
\(85\) −5.71702 + 3.44790i −0.620098 + 0.373977i
\(86\) 11.9300 3.28169i 1.28644 0.353874i
\(87\) 0 0
\(88\) −3.76623 3.61909i −0.401482 0.385796i
\(89\) 7.60356 0.805975 0.402988 0.915205i \(-0.367972\pi\)
0.402988 + 0.915205i \(0.367972\pi\)
\(90\) 0 0
\(91\) −4.74899 4.74899i −0.497830 0.497830i
\(92\) −8.00071 13.4421i −0.834131 1.40144i
\(93\) 0 0
\(94\) −4.10686 + 7.22364i −0.423590 + 0.745062i
\(95\) −0.956125 + 3.86176i −0.0980963 + 0.396209i
\(96\) 0 0
\(97\) 9.70129i 0.985017i −0.870308 0.492508i \(-0.836080\pi\)
0.870308 0.492508i \(-0.163920\pi\)
\(98\) 2.67788 + 1.52245i 0.270507 + 0.153791i
\(99\) 0 0
\(100\) 9.98676 0.514436i 0.998676 0.0514436i
\(101\) −6.49754 6.49754i −0.646530 0.646530i 0.305623 0.952153i \(-0.401135\pi\)
−0.952153 + 0.305623i \(0.901135\pi\)
\(102\) 0 0
\(103\) 13.3352i 1.31396i 0.753908 + 0.656980i \(0.228167\pi\)
−0.753908 + 0.656980i \(0.771833\pi\)
\(104\) 4.52116 + 4.34452i 0.443336 + 0.426015i
\(105\) 0 0
\(106\) −8.49716 + 2.33739i −0.825317 + 0.227028i
\(107\) 2.06506 + 2.06506i 0.199637 + 0.199637i 0.799844 0.600208i \(-0.204915\pi\)
−0.600208 + 0.799844i \(0.704915\pi\)
\(108\) 0 0
\(109\) −9.84623 9.84623i −0.943098 0.943098i 0.0553682 0.998466i \(-0.482367\pi\)
−0.998466 + 0.0553682i \(0.982367\pi\)
\(110\) 4.02172 4.23422i 0.383456 0.403717i
\(111\) 0 0
\(112\) −10.6519 5.77823i −1.00651 0.545992i
\(113\) 2.82213 0.265484 0.132742 0.991151i \(-0.457622\pi\)
0.132742 + 0.991151i \(0.457622\pi\)
\(114\) 0 0
\(115\) 14.9765 9.03225i 1.39657 0.842262i
\(116\) −19.5217 4.95391i −1.81255 0.459959i
\(117\) 0 0
\(118\) 15.8268 4.35363i 1.45698 0.400784i
\(119\) 9.04536i 0.829187i
\(120\) 0 0
\(121\) 7.58971i 0.689974i
\(122\) 2.61991 + 9.52420i 0.237196 + 0.862281i
\(123\) 0 0
\(124\) 0.0864285 0.0514419i 0.00776151 0.00461962i
\(125\) 0.640034 + 11.1620i 0.0572464 + 0.998360i
\(126\) 0 0
\(127\) −4.95854 −0.439999 −0.219999 0.975500i \(-0.570606\pi\)
−0.219999 + 0.975500i \(0.570606\pi\)
\(128\) 10.0502 + 5.19546i 0.888324 + 0.459218i
\(129\) 0 0
\(130\) −4.82786 + 5.08295i −0.423431 + 0.445805i
\(131\) −9.28233 9.28233i −0.811001 0.811001i 0.173783 0.984784i \(-0.444401\pi\)
−0.984784 + 0.173783i \(0.944401\pi\)
\(132\) 0 0
\(133\) 3.81139 + 3.81139i 0.330489 + 0.330489i
\(134\) 0.689448 + 2.50636i 0.0595592 + 0.216517i
\(135\) 0 0
\(136\) −0.168226 8.44319i −0.0144252 0.723997i
\(137\) 6.60046i 0.563916i 0.959427 + 0.281958i \(0.0909838\pi\)
−0.959427 + 0.281958i \(0.909016\pi\)
\(138\) 0 0
\(139\) −0.376168 0.376168i −0.0319062 0.0319062i 0.690974 0.722880i \(-0.257182\pi\)
−0.722880 + 0.690974i \(0.757182\pi\)
\(140\) 6.39094 11.9465i 0.540133 1.00967i
\(141\) 0 0
\(142\) 9.76352 17.1733i 0.819336 1.44115i
\(143\) 4.09387i 0.342346i
\(144\) 0 0
\(145\) 5.41171 21.8578i 0.449418 1.81519i
\(146\) −4.74358 2.69687i −0.392582 0.223194i
\(147\) 0 0
\(148\) 4.33392 17.0786i 0.356246 1.40385i
\(149\) 8.71533 + 8.71533i 0.713988 + 0.713988i 0.967367 0.253379i \(-0.0815420\pi\)
−0.253379 + 0.967367i \(0.581542\pi\)
\(150\) 0 0
\(151\) 7.25811 0.590657 0.295328 0.955396i \(-0.404571\pi\)
0.295328 + 0.955396i \(0.404571\pi\)
\(152\) −3.62854 3.48677i −0.294313 0.282814i
\(153\) 0 0
\(154\) −2.09849 7.62868i −0.169101 0.614736i
\(155\) 0.0580744 + 0.0962941i 0.00466465 + 0.00773453i
\(156\) 0 0
\(157\) 16.0087 16.0087i 1.27764 1.27764i 0.335647 0.941988i \(-0.391045\pi\)
0.941988 0.335647i \(-0.108955\pi\)
\(158\) 0.748555 1.31665i 0.0595518 0.104747i
\(159\) 0 0
\(160\) −5.74330 + 11.2701i −0.454048 + 0.890977i
\(161\) 23.6956i 1.86747i
\(162\) 0 0
\(163\) 3.07484 + 3.07484i 0.240840 + 0.240840i 0.817198 0.576357i \(-0.195526\pi\)
−0.576357 + 0.817198i \(0.695526\pi\)
\(164\) −4.14847 6.96991i −0.323941 0.544259i
\(165\) 0 0
\(166\) 13.8168 3.80073i 1.07240 0.294994i
\(167\) 6.32858 0.489720 0.244860 0.969558i \(-0.421258\pi\)
0.244860 + 0.969558i \(0.421258\pi\)
\(168\) 0 0
\(169\) 8.08553i 0.621964i
\(170\) 9.43852 0.242937i 0.723901 0.0186324i
\(171\) 0 0
\(172\) −16.9606 4.30400i −1.29324 0.328177i
\(173\) 3.51897 + 3.51897i 0.267542 + 0.267542i 0.828109 0.560567i \(-0.189417\pi\)
−0.560567 + 0.828109i \(0.689417\pi\)
\(174\) 0 0
\(175\) 13.3979 + 7.06755i 1.01279 + 0.534257i
\(176\) 2.10067 + 7.08179i 0.158344 + 0.533810i
\(177\) 0 0
\(178\) −9.34791 5.31457i −0.700656 0.398344i
\(179\) −6.22219 6.22219i −0.465068 0.465068i 0.435244 0.900312i \(-0.356662\pi\)
−0.900312 + 0.435244i \(0.856662\pi\)
\(180\) 0 0
\(181\) 14.9790 14.9790i 1.11338 1.11338i 0.120689 0.992690i \(-0.461490\pi\)
0.992690 0.120689i \(-0.0385103\pi\)
\(182\) 2.51913 + 9.15782i 0.186730 + 0.678823i
\(183\) 0 0
\(184\) 0.440690 + 22.1181i 0.0324881 + 1.63057i
\(185\) 19.1222 + 4.73443i 1.40590 + 0.348082i
\(186\) 0 0
\(187\) 3.89877 3.89877i 0.285107 0.285107i
\(188\) 10.0981 6.01032i 0.736476 0.438348i
\(189\) 0 0
\(190\) 3.87468 4.07941i 0.281099 0.295952i
\(191\) 20.4321 1.47842 0.739208 0.673477i \(-0.235200\pi\)
0.739208 + 0.673477i \(0.235200\pi\)
\(192\) 0 0
\(193\) 0.107996i 0.00777370i −0.999992 0.00388685i \(-0.998763\pi\)
0.999992 0.00388685i \(-0.00123723\pi\)
\(194\) −6.78080 + 11.9269i −0.486833 + 0.856301i
\(195\) 0 0
\(196\) −2.22809 3.74345i −0.159149 0.267389i
\(197\) 13.3111 13.3111i 0.948378 0.948378i −0.0503537 0.998731i \(-0.516035\pi\)
0.998731 + 0.0503537i \(0.0160349\pi\)
\(198\) 0 0
\(199\) −27.0544 −1.91784 −0.958918 0.283684i \(-0.908443\pi\)
−0.958918 + 0.283684i \(0.908443\pi\)
\(200\) −12.6374 6.34787i −0.893601 0.448862i
\(201\) 0 0
\(202\) 3.44666 + 12.5297i 0.242506 + 0.881585i
\(203\) −21.5726 21.5726i −1.51410 1.51410i
\(204\) 0 0
\(205\) 7.76552 4.68334i 0.542367 0.327098i
\(206\) 9.32078 16.3945i 0.649409 1.14226i
\(207\) 0 0
\(208\) −2.52174 8.50131i −0.174851 0.589460i
\(209\) 3.28560i 0.227270i
\(210\) 0 0
\(211\) −5.20964 + 5.20964i −0.358646 + 0.358646i −0.863314 0.504667i \(-0.831615\pi\)
0.504667 + 0.863314i \(0.331615\pi\)
\(212\) 12.0803 + 3.06554i 0.829676 + 0.210542i
\(213\) 0 0
\(214\) −1.09542 3.98220i −0.0748814 0.272217i
\(215\) 4.70174 18.9902i 0.320656 1.29512i
\(216\) 0 0
\(217\) 0.152355 0.0103425
\(218\) 5.22298 + 18.9872i 0.353745 + 1.28597i
\(219\) 0 0
\(220\) −7.90390 + 2.39459i −0.532881 + 0.161443i
\(221\) −4.68027 + 4.68027i −0.314829 + 0.314829i
\(222\) 0 0
\(223\) −8.50474 −0.569519 −0.284760 0.958599i \(-0.591914\pi\)
−0.284760 + 0.958599i \(0.591914\pi\)
\(224\) 9.05684 + 14.5491i 0.605135 + 0.972100i
\(225\) 0 0
\(226\) −3.46956 1.97255i −0.230792 0.131212i
\(227\) −14.4132 + 14.4132i −0.956639 + 0.956639i −0.999098 0.0424594i \(-0.986481\pi\)
0.0424594 + 0.999098i \(0.486481\pi\)
\(228\) 0 0
\(229\) −15.5816 + 15.5816i −1.02966 + 1.02966i −0.0301163 + 0.999546i \(0.509588\pi\)
−0.999546 + 0.0301163i \(0.990412\pi\)
\(230\) −24.7255 + 0.636406i −1.63035 + 0.0419634i
\(231\) 0 0
\(232\) 20.5377 + 19.7353i 1.34836 + 1.29568i
\(233\) 17.5226i 1.14794i −0.818875 0.573972i \(-0.805402\pi\)
0.818875 0.573972i \(-0.194598\pi\)
\(234\) 0 0
\(235\) 6.78524 + 11.2507i 0.442620 + 0.733916i
\(236\) −22.5007 5.70987i −1.46467 0.371681i
\(237\) 0 0
\(238\) 6.32233 11.1205i 0.409816 0.720834i
\(239\) 23.9921 1.55192 0.775960 0.630782i \(-0.217266\pi\)
0.775960 + 0.630782i \(0.217266\pi\)
\(240\) 0 0
\(241\) 28.5345 1.83807 0.919033 0.394181i \(-0.128972\pi\)
0.919033 + 0.394181i \(0.128972\pi\)
\(242\) 5.30489 9.33090i 0.341011 0.599813i
\(243\) 0 0
\(244\) 3.43607 13.5404i 0.219972 0.866835i
\(245\) 4.17076 2.51536i 0.266460 0.160700i
\(246\) 0 0
\(247\) 3.94419i 0.250963i
\(248\) −0.142212 + 0.00283350i −0.00903048 + 0.000179927i
\(249\) 0 0
\(250\) 7.01491 14.1701i 0.443662 0.896194i
\(251\) −0.638332 + 0.638332i −0.0402912 + 0.0402912i −0.726965 0.686674i \(-0.759070\pi\)
0.686674 + 0.726965i \(0.259070\pi\)
\(252\) 0 0
\(253\) −10.2134 + 10.2134i −0.642110 + 0.642110i
\(254\) 6.09609 + 3.46581i 0.382503 + 0.217464i
\(255\) 0 0
\(256\) −8.72449 13.4121i −0.545280 0.838254i
\(257\) −6.32219 −0.394367 −0.197184 0.980367i \(-0.563180\pi\)
−0.197184 + 0.980367i \(0.563180\pi\)
\(258\) 0 0
\(259\) 18.8728 18.8728i 1.17270 1.17270i
\(260\) 9.48821 2.87458i 0.588434 0.178274i
\(261\) 0 0
\(262\) 4.92386 + 17.8998i 0.304197 + 1.10585i
\(263\) 0.335400 0.0206817 0.0103408 0.999947i \(-0.496708\pi\)
0.0103408 + 0.999947i \(0.496708\pi\)
\(264\) 0 0
\(265\) −3.34883 + 13.5258i −0.205717 + 0.830885i
\(266\) −2.02177 7.34977i −0.123963 0.450643i
\(267\) 0 0
\(268\) 0.904224 3.56325i 0.0552343 0.217660i
\(269\) −8.03777 + 8.03777i −0.490071 + 0.490071i −0.908329 0.418257i \(-0.862641\pi\)
0.418257 + 0.908329i \(0.362641\pi\)
\(270\) 0 0
\(271\) 28.1406i 1.70942i 0.519105 + 0.854711i \(0.326265\pi\)
−0.519105 + 0.854711i \(0.673735\pi\)
\(272\) −5.69462 + 10.4978i −0.345287 + 0.636520i
\(273\) 0 0
\(274\) 4.61345 8.11470i 0.278709 0.490227i
\(275\) −2.72854 8.82112i −0.164537 0.531934i
\(276\) 0 0
\(277\) −4.06316 4.06316i −0.244132 0.244132i 0.574425 0.818557i \(-0.305226\pi\)
−0.818557 + 0.574425i \(0.805226\pi\)
\(278\) 0.199541 + 0.725393i 0.0119676 + 0.0435062i
\(279\) 0 0
\(280\) −16.2072 + 10.2202i −0.968567 + 0.610774i
\(281\) −0.511034 −0.0304858 −0.0152429 0.999884i \(-0.504852\pi\)
−0.0152429 + 0.999884i \(0.504852\pi\)
\(282\) 0 0
\(283\) −13.0685 + 13.0685i −0.776839 + 0.776839i −0.979292 0.202453i \(-0.935109\pi\)
0.202453 + 0.979292i \(0.435109\pi\)
\(284\) −24.0068 + 14.2888i −1.42454 + 0.847882i
\(285\) 0 0
\(286\) 2.86144 5.03305i 0.169201 0.297611i
\(287\) 12.2865i 0.725246i
\(288\) 0 0
\(289\) −8.08553 −0.475620
\(290\) −21.9309 + 23.0897i −1.28783 + 1.35587i
\(291\) 0 0
\(292\) 3.94683 + 6.63113i 0.230970 + 0.388058i
\(293\) −19.3164 + 19.3164i −1.12848 + 1.12848i −0.138054 + 0.990425i \(0.544085\pi\)
−0.990425 + 0.138054i \(0.955915\pi\)
\(294\) 0 0
\(295\) 6.23753 25.1932i 0.363163 1.46681i
\(296\) −17.2654 + 17.9674i −1.00353 + 1.04433i
\(297\) 0 0
\(298\) −4.62309 16.8064i −0.267809 0.973569i
\(299\) 12.2606 12.2606i 0.709050 0.709050i
\(300\) 0 0
\(301\) −18.7425 18.7425i −1.08030 1.08030i
\(302\) −8.92322 5.07312i −0.513474 0.291925i
\(303\) 0 0
\(304\) 2.02387 + 6.82288i 0.116077 + 0.391319i
\(305\) 15.1607 + 3.75360i 0.868098 + 0.214930i
\(306\) 0 0
\(307\) 17.1442 + 17.1442i 0.978471 + 0.978471i 0.999773 0.0213024i \(-0.00678126\pi\)
−0.0213024 + 0.999773i \(0.506781\pi\)
\(308\) −2.75221 + 10.8456i −0.156822 + 0.617983i
\(309\) 0 0
\(310\) −0.00409188 0.158977i −0.000232403 0.00902928i
\(311\) 21.2420i 1.20452i 0.798299 + 0.602261i \(0.205733\pi\)
−0.798299 + 0.602261i \(0.794267\pi\)
\(312\) 0 0
\(313\) −19.9351 −1.12680 −0.563400 0.826184i \(-0.690507\pi\)
−0.563400 + 0.826184i \(0.690507\pi\)
\(314\) −30.8708 + 8.49191i −1.74214 + 0.479226i
\(315\) 0 0
\(316\) −1.84057 + 1.09550i −0.103540 + 0.0616266i
\(317\) 14.9282 + 14.9282i 0.838450 + 0.838450i 0.988655 0.150205i \(-0.0479934\pi\)
−0.150205 + 0.988655i \(0.547993\pi\)
\(318\) 0 0
\(319\) 18.5967i 1.04121i
\(320\) 14.9382 9.84125i 0.835071 0.550143i
\(321\) 0 0
\(322\) −16.5622 + 29.1317i −0.922976 + 1.62344i
\(323\) 3.75623 3.75623i 0.209002 0.209002i
\(324\) 0 0
\(325\) 3.27547 + 10.5893i 0.181690 + 0.587388i
\(326\) −1.63107 5.92944i −0.0903365 0.328401i
\(327\) 0 0
\(328\) 0.228504 + 11.4685i 0.0126170 + 0.633243i
\(329\) 17.8007 0.981383
\(330\) 0 0
\(331\) 5.72462 + 5.72462i 0.314653 + 0.314653i 0.846709 0.532056i \(-0.178580\pi\)
−0.532056 + 0.846709i \(0.678580\pi\)
\(332\) −19.6432 4.98473i −1.07806 0.273573i
\(333\) 0 0
\(334\) −7.78044 4.42341i −0.425727 0.242038i
\(335\) 3.98964 + 0.987785i 0.217977 + 0.0539685i
\(336\) 0 0
\(337\) 28.0570i 1.52836i 0.645003 + 0.764180i \(0.276856\pi\)
−0.645003 + 0.764180i \(0.723144\pi\)
\(338\) 5.65145 9.94046i 0.307398 0.540690i
\(339\) 0 0
\(340\) −11.7736 6.29846i −0.638516 0.341582i
\(341\) −0.0656687 0.0656687i −0.00355616 0.00355616i
\(342\) 0 0
\(343\) 14.6080i 0.788756i
\(344\) 17.8433 + 17.1462i 0.962047 + 0.924460i
\(345\) 0 0
\(346\) −1.86666 6.78588i −0.100352 0.364811i
\(347\) 8.55200 + 8.55200i 0.459095 + 0.459095i 0.898358 0.439263i \(-0.144760\pi\)
−0.439263 + 0.898358i \(0.644760\pi\)
\(348\) 0 0
\(349\) 5.51139 + 5.51139i 0.295018 + 0.295018i 0.839059 0.544041i \(-0.183106\pi\)
−0.544041 + 0.839059i \(0.683106\pi\)
\(350\) −11.5317 18.0535i −0.616393 0.965001i
\(351\) 0 0
\(352\) 2.36729 10.1747i 0.126177 0.542315i
\(353\) −22.2023 −1.18171 −0.590853 0.806779i \(-0.701209\pi\)
−0.590853 + 0.806779i \(0.701209\pi\)
\(354\) 0 0
\(355\) −16.1310 26.7471i −0.856146 1.41959i
\(356\) 7.77779 + 13.0676i 0.412222 + 0.692582i
\(357\) 0 0
\(358\) 3.30059 + 11.9987i 0.174442 + 0.634150i
\(359\) 6.73781i 0.355608i 0.984066 + 0.177804i \(0.0568993\pi\)
−0.984066 + 0.177804i \(0.943101\pi\)
\(360\) 0 0
\(361\) 15.8345i 0.833396i
\(362\) −28.8851 + 7.94568i −1.51816 + 0.417616i
\(363\) 0 0
\(364\) 3.30388 13.0195i 0.173171 0.682408i
\(365\) −7.38806 + 4.45569i −0.386709 + 0.233222i
\(366\) 0 0
\(367\) −7.64267 −0.398944 −0.199472 0.979904i \(-0.563923\pi\)
−0.199472 + 0.979904i \(0.563923\pi\)
\(368\) 14.9178 27.5003i 0.777646 1.43355i
\(369\) 0 0
\(370\) −20.2000 19.1862i −1.05015 0.997444i
\(371\) 13.3494 + 13.3494i 0.693065 + 0.693065i
\(372\) 0 0
\(373\) 5.20096 + 5.20096i 0.269296 + 0.269296i 0.828816 0.559521i \(-0.189015\pi\)
−0.559521 + 0.828816i \(0.689015\pi\)
\(374\) −7.51829 + 2.06813i −0.388761 + 0.106940i
\(375\) 0 0
\(376\) −16.6156 + 0.331057i −0.856886 + 0.0170730i
\(377\) 22.3243i 1.14976i
\(378\) 0 0
\(379\) 7.64201 + 7.64201i 0.392544 + 0.392544i 0.875593 0.483049i \(-0.160471\pi\)
−0.483049 + 0.875593i \(0.660471\pi\)
\(380\) −7.61493 + 2.30704i −0.390638 + 0.118349i
\(381\) 0 0
\(382\) −25.1195 14.2812i −1.28523 0.730690i
\(383\) 28.1288i 1.43732i −0.695363 0.718658i \(-0.744757\pi\)
0.695363 0.718658i \(-0.255243\pi\)
\(384\) 0 0
\(385\) −12.1434 3.00655i −0.618884 0.153228i
\(386\) −0.0754844 + 0.132771i −0.00384206 + 0.00675788i
\(387\) 0 0
\(388\) 16.6728 9.92359i 0.846433 0.503794i
\(389\) 8.26812 + 8.26812i 0.419210 + 0.419210i 0.884931 0.465721i \(-0.154205\pi\)
−0.465721 + 0.884931i \(0.654205\pi\)
\(390\) 0 0
\(391\) −23.3527 −1.18100
\(392\) 0.122726 + 6.15959i 0.00619861 + 0.311106i
\(393\) 0 0
\(394\) −25.6688 + 7.06095i −1.29317 + 0.355726i
\(395\) −1.23674 2.05066i −0.0622273 0.103180i
\(396\) 0 0
\(397\) −6.70437 + 6.70437i −0.336482 + 0.336482i −0.855042 0.518559i \(-0.826469\pi\)
0.518559 + 0.855042i \(0.326469\pi\)
\(398\) 33.2610 + 18.9099i 1.66723 + 0.947868i
\(399\) 0 0
\(400\) 11.0997 + 16.6372i 0.554986 + 0.831860i
\(401\) 33.5732i 1.67657i −0.545235 0.838283i \(-0.683560\pi\)
0.545235 0.838283i \(-0.316440\pi\)
\(402\) 0 0
\(403\) 0.0788317 + 0.0788317i 0.00392689 + 0.00392689i
\(404\) 4.52036 17.8132i 0.224896 0.886241i
\(405\) 0 0
\(406\) 11.4433 + 41.6000i 0.567922 + 2.06457i
\(407\) −16.2693 −0.806438
\(408\) 0 0
\(409\) 3.99913i 0.197744i −0.995100 0.0988720i \(-0.968477\pi\)
0.995100 0.0988720i \(-0.0315234\pi\)
\(410\) −12.8205 + 0.329984i −0.633159 + 0.0162968i
\(411\) 0 0
\(412\) −22.9182 + 13.6408i −1.12910 + 0.672035i
\(413\) −24.8646 24.8646i −1.22351 1.22351i
\(414\) 0 0
\(415\) 5.44538 21.9937i 0.267303 1.07963i
\(416\) −2.84180 + 12.2142i −0.139331 + 0.598851i
\(417\) 0 0
\(418\) −2.29650 + 4.03937i −0.112325 + 0.197572i
\(419\) −18.7540 18.7540i −0.916195 0.916195i 0.0805555 0.996750i \(-0.474331\pi\)
−0.996750 + 0.0805555i \(0.974331\pi\)
\(420\) 0 0
\(421\) 1.12082 1.12082i 0.0546255 0.0546255i −0.679266 0.733892i \(-0.737702\pi\)
0.733892 + 0.679266i \(0.237702\pi\)
\(422\) 10.0461 2.76348i 0.489038 0.134524i
\(423\) 0 0
\(424\) −12.7090 12.2124i −0.617201 0.593087i
\(425\) 6.96528 13.2040i 0.337866 0.640490i
\(426\) 0 0
\(427\) 14.9629 14.9629i 0.724106 0.724106i
\(428\) −1.43667 + 5.66142i −0.0694438 + 0.273655i
\(429\) 0 0
\(430\) −19.0537 + 20.0605i −0.918853 + 0.967403i
\(431\) 37.3679 1.79995 0.899975 0.435941i \(-0.143584\pi\)
0.899975 + 0.435941i \(0.143584\pi\)
\(432\) 0 0
\(433\) 4.89665i 0.235318i 0.993054 + 0.117659i \(0.0375389\pi\)
−0.993054 + 0.117659i \(0.962461\pi\)
\(434\) −0.187307 0.106490i −0.00899102 0.00511166i
\(435\) 0 0
\(436\) 6.85005 26.9938i 0.328058 1.29277i
\(437\) −9.83997 + 9.83997i −0.470710 + 0.470710i
\(438\) 0 0
\(439\) 30.8742 1.47354 0.736772 0.676141i \(-0.236349\pi\)
0.736772 + 0.676141i \(0.236349\pi\)
\(440\) 11.3909 + 2.58055i 0.543039 + 0.123023i
\(441\) 0 0
\(442\) 9.02530 2.48267i 0.429290 0.118089i
\(443\) 21.6532 + 21.6532i 1.02878 + 1.02878i 0.999574 + 0.0292029i \(0.00929690\pi\)
0.0292029 + 0.999574i \(0.490703\pi\)
\(444\) 0 0
\(445\) −14.5592 + 8.78059i −0.690174 + 0.416240i
\(446\) 10.4558 + 5.94446i 0.495098 + 0.281478i
\(447\) 0 0
\(448\) −0.965410 24.2172i −0.0456113 1.14415i
\(449\) 0.573598i 0.0270698i 0.999908 + 0.0135349i \(0.00430842\pi\)
−0.999908 + 0.0135349i \(0.995692\pi\)
\(450\) 0 0
\(451\) −5.29577 + 5.29577i −0.249368 + 0.249368i
\(452\) 2.88680 + 4.85016i 0.135784 + 0.228132i
\(453\) 0 0
\(454\) 27.7940 7.64557i 1.30444 0.358824i
\(455\) 14.5775 + 3.60920i 0.683403 + 0.169202i
\(456\) 0 0
\(457\) 30.6962 1.43591 0.717953 0.696092i \(-0.245079\pi\)
0.717953 + 0.696092i \(0.245079\pi\)
\(458\) 30.0472 8.26535i 1.40401 0.386215i
\(459\) 0 0
\(460\) 30.8427 + 16.4997i 1.43805 + 0.769302i
\(461\) 3.93792 3.93792i 0.183407 0.183407i −0.609431 0.792839i \(-0.708602\pi\)
0.792839 + 0.609431i \(0.208602\pi\)
\(462\) 0 0
\(463\) 34.4600 1.60149 0.800746 0.599004i \(-0.204437\pi\)
0.800746 + 0.599004i \(0.204437\pi\)
\(464\) −11.4552 38.6178i −0.531793 1.79279i
\(465\) 0 0
\(466\) −12.2476 + 21.5425i −0.567358 + 0.997938i
\(467\) −1.24171 + 1.24171i −0.0574594 + 0.0574594i −0.735253 0.677793i \(-0.762936\pi\)
0.677793 + 0.735253i \(0.262936\pi\)
\(468\) 0 0
\(469\) 3.93759 3.93759i 0.181821 0.181821i
\(470\) −0.478083 18.5744i −0.0220523 0.856773i
\(471\) 0 0
\(472\) 23.6717 + 22.7469i 1.08958 + 1.04701i
\(473\) 16.1569i 0.742897i
\(474\) 0 0
\(475\) −2.62879 8.49862i −0.120617 0.389943i
\(476\) −15.5455 + 9.25263i −0.712527 + 0.424094i
\(477\) 0 0
\(478\) −29.4962 16.7695i −1.34913 0.767018i
\(479\) −29.6130 −1.35305 −0.676527 0.736418i \(-0.736516\pi\)
−0.676527 + 0.736418i \(0.736516\pi\)
\(480\) 0 0
\(481\) 19.5304 0.890509
\(482\) −35.0806 19.9444i −1.59788 0.908442i
\(483\) 0 0
\(484\) −13.0438 + 7.76363i −0.592901 + 0.352892i
\(485\) 11.2031 + 18.5760i 0.508705 + 0.843491i
\(486\) 0 0
\(487\) 20.4343i 0.925966i −0.886367 0.462983i \(-0.846779\pi\)
0.886367 0.462983i \(-0.153221\pi\)
\(488\) −13.6885 + 14.2451i −0.619650 + 0.644844i
\(489\) 0 0
\(490\) −6.88571 + 0.177230i −0.311065 + 0.00800645i
\(491\) −1.49438 + 1.49438i −0.0674405 + 0.0674405i −0.740023 0.672582i \(-0.765185\pi\)
0.672582 + 0.740023i \(0.265185\pi\)
\(492\) 0 0
\(493\) −21.2604 + 21.2604i −0.957522 + 0.957522i
\(494\) 2.75683 4.84904i 0.124035 0.218169i
\(495\) 0 0
\(496\) 0.176818 + 0.0959168i 0.00793936 + 0.00430679i
\(497\) −42.3188 −1.89826
\(498\) 0 0
\(499\) −7.82960 + 7.82960i −0.350501 + 0.350501i −0.860296 0.509795i \(-0.829721\pi\)
0.509795 + 0.860296i \(0.329721\pi\)
\(500\) −18.5285 + 12.5178i −0.828620 + 0.559811i
\(501\) 0 0
\(502\) 1.23094 0.338606i 0.0549396 0.0151127i
\(503\) −6.45561 −0.287841 −0.143921 0.989589i \(-0.545971\pi\)
−0.143921 + 0.989589i \(0.545971\pi\)
\(504\) 0 0
\(505\) 19.9448 + 4.93809i 0.887533 + 0.219742i
\(506\) 19.6952 5.41774i 0.875558 0.240848i
\(507\) 0 0
\(508\) −5.07216 8.52182i −0.225041 0.378095i
\(509\) −3.08846 + 3.08846i −0.136894 + 0.136894i −0.772233 0.635339i \(-0.780860\pi\)
0.635339 + 0.772233i \(0.280860\pi\)
\(510\) 0 0
\(511\) 11.6892i 0.517102i
\(512\) 1.35153 + 22.5870i 0.0597298 + 0.998215i
\(513\) 0 0
\(514\) 7.77258 + 4.41894i 0.342834 + 0.194911i
\(515\) −15.3995 25.5342i −0.678585 1.12517i
\(516\) 0 0
\(517\) −7.67253 7.67253i −0.337438 0.337438i
\(518\) −36.3937 + 10.0112i −1.59905 + 0.439865i
\(519\) 0 0
\(520\) −13.6741 3.09782i −0.599651 0.135848i
\(521\) −6.66855 −0.292155 −0.146077 0.989273i \(-0.546665\pi\)
−0.146077 + 0.989273i \(0.546665\pi\)
\(522\) 0 0
\(523\) −13.2266 + 13.2266i −0.578361 + 0.578361i −0.934451 0.356091i \(-0.884109\pi\)
0.356091 + 0.934451i \(0.384109\pi\)
\(524\) 6.45774 25.4478i 0.282108 1.11169i
\(525\) 0 0
\(526\) −0.412346 0.234431i −0.0179791 0.0102217i
\(527\) 0.150150i 0.00654064i
\(528\) 0 0
\(529\) 38.1756 1.65981
\(530\) 13.5711 14.2881i 0.589490 0.620637i
\(531\) 0 0
\(532\) −2.65159 + 10.4490i −0.114961 + 0.453023i
\(533\) 6.35728 6.35728i 0.275364 0.275364i
\(534\) 0 0
\(535\) −6.33889 1.56943i −0.274054 0.0678524i
\(536\) −3.60223 + 3.74869i −0.155593 + 0.161919i
\(537\) 0 0
\(538\) 15.4998 4.26368i 0.668244 0.183820i
\(539\) −2.84429 + 2.84429i −0.122512 + 0.122512i
\(540\) 0 0
\(541\) 21.3672 + 21.3672i 0.918646 + 0.918646i 0.996931 0.0782848i \(-0.0249444\pi\)
−0.0782848 + 0.996931i \(0.524944\pi\)
\(542\) 19.6691 34.5965i 0.844861 1.48605i
\(543\) 0 0
\(544\) 14.3385 8.92578i 0.614759 0.382690i
\(545\) 30.2239 + 7.48307i 1.29465 + 0.320539i
\(546\) 0 0
\(547\) −14.3033 14.3033i −0.611566 0.611566i 0.331788 0.943354i \(-0.392348\pi\)
−0.943354 + 0.331788i \(0.892348\pi\)
\(548\) −11.3437 + 6.75171i −0.484578 + 0.288419i
\(549\) 0 0
\(550\) −2.81109 + 12.7519i −0.119865 + 0.543745i
\(551\) 17.9168i 0.763279i
\(552\) 0 0
\(553\) −3.24452 −0.137971
\(554\) 2.15533 + 7.83529i 0.0915711 + 0.332890i
\(555\) 0 0
\(556\) 0.261701 1.03128i 0.0110986 0.0437359i
\(557\) −5.11093 5.11093i −0.216557 0.216557i 0.590489 0.807046i \(-0.298935\pi\)
−0.807046 + 0.590489i \(0.798935\pi\)
\(558\) 0 0
\(559\) 19.3955i 0.820344i
\(560\) 27.0689 1.23669i 1.14387 0.0522596i
\(561\) 0 0
\(562\) 0.628273 + 0.357192i 0.0265021 + 0.0150672i
\(563\) 14.2208 14.2208i 0.599336 0.599336i −0.340800 0.940136i \(-0.610698\pi\)
0.940136 + 0.340800i \(0.110698\pi\)
\(564\) 0 0
\(565\) −5.40379 + 3.25900i −0.227339 + 0.137107i
\(566\) 25.2008 6.93223i 1.05927 0.291383i
\(567\) 0 0
\(568\) 39.5015 0.787045i 1.65745 0.0330237i
\(569\) 9.55464 0.400551 0.200276 0.979740i \(-0.435816\pi\)
0.200276 + 0.979740i \(0.435816\pi\)
\(570\) 0 0
\(571\) −23.2036 23.2036i −0.971041 0.971041i 0.0285510 0.999592i \(-0.490911\pi\)
−0.999592 + 0.0285510i \(0.990911\pi\)
\(572\) −7.03579 + 4.18768i −0.294181 + 0.175096i
\(573\) 0 0
\(574\) −8.58772 + 15.1051i −0.358444 + 0.630476i
\(575\) −18.2465 + 34.5898i −0.760932 + 1.44249i
\(576\) 0 0
\(577\) 40.8559i 1.70085i 0.526095 + 0.850426i \(0.323656\pi\)
−0.526095 + 0.850426i \(0.676344\pi\)
\(578\) 9.94046 + 5.65145i 0.413469 + 0.235069i
\(579\) 0 0
\(580\) 43.1008 13.0580i 1.78966 0.542203i
\(581\) −21.7068 21.7068i −0.900551 0.900551i
\(582\) 0 0
\(583\) 11.5078i 0.476606i
\(584\) −0.217397 10.9111i −0.00899594 0.451503i
\(585\) 0 0
\(586\) 37.2493 10.2465i 1.53875 0.423279i
\(587\) 20.0208 + 20.0208i 0.826345 + 0.826345i 0.987009 0.160664i \(-0.0513635\pi\)
−0.160664 + 0.987009i \(0.551364\pi\)
\(588\) 0 0
\(589\) −0.0632678 0.0632678i −0.00260690 0.00260690i
\(590\) −25.2775 + 26.6131i −1.04066 + 1.09565i
\(591\) 0 0
\(592\) 33.7847 10.0216i 1.38854 0.411883i
\(593\) 0.595901 0.0244707 0.0122354 0.999925i \(-0.496105\pi\)
0.0122354 + 0.999925i \(0.496105\pi\)
\(594\) 0 0
\(595\) −10.4456 17.3200i −0.428227 0.710051i
\(596\) −6.06328 + 23.8934i −0.248362 + 0.978710i
\(597\) 0 0
\(598\) −23.6430 + 6.50371i −0.966835 + 0.265956i
\(599\) 26.0628i 1.06490i −0.846462 0.532449i \(-0.821272\pi\)
0.846462 0.532449i \(-0.178728\pi\)
\(600\) 0 0
\(601\) 38.7272i 1.57971i −0.613291 0.789857i \(-0.710155\pi\)
0.613291 0.789857i \(-0.289845\pi\)
\(602\) 9.94204 + 36.1425i 0.405207 + 1.47306i
\(603\) 0 0
\(604\) 7.42443 + 12.4739i 0.302096 + 0.507556i
\(605\) −8.76461 14.5327i −0.356332 0.590840i
\(606\) 0 0
\(607\) −40.5499 −1.64587 −0.822934 0.568136i \(-0.807665\pi\)
−0.822934 + 0.568136i \(0.807665\pi\)
\(608\) 2.28074 9.80273i 0.0924961 0.397553i
\(609\) 0 0
\(610\) −16.0151 15.2114i −0.648434 0.615892i
\(611\) 9.21047 + 9.21047i 0.372616 + 0.372616i
\(612\) 0 0
\(613\) 5.91500 + 5.91500i 0.238905 + 0.238905i 0.816396 0.577492i \(-0.195968\pi\)
−0.577492 + 0.816396i \(0.695968\pi\)
\(614\) −9.09423 33.0604i −0.367013 1.33421i
\(615\) 0 0
\(616\) 10.9642 11.4100i 0.441760 0.459722i
\(617\) 37.5004i 1.50971i 0.655893 + 0.754854i \(0.272292\pi\)
−0.655893 + 0.754854i \(0.727708\pi\)
\(618\) 0 0
\(619\) −19.2329 19.2329i −0.773034 0.773034i 0.205602 0.978636i \(-0.434085\pi\)
−0.978636 + 0.205602i \(0.934085\pi\)
\(620\) −0.106088 + 0.198308i −0.00426058 + 0.00796426i
\(621\) 0 0
\(622\) 14.8473 26.1152i 0.595321 1.04712i
\(623\) 23.0354i 0.922892i
\(624\) 0 0
\(625\) −14.1154 20.6338i −0.564617 0.825353i
\(626\) 24.5085 + 13.9338i 0.979557 + 0.556907i
\(627\) 0 0
\(628\) 43.8884 + 11.1373i 1.75134 + 0.444427i
\(629\) −18.5997 18.5997i −0.741618 0.741618i
\(630\) 0 0
\(631\) −46.9373 −1.86855 −0.934273 0.356559i \(-0.883950\pi\)
−0.934273 + 0.356559i \(0.883950\pi\)
\(632\) 3.02852 0.0603416i 0.120468 0.00240026i
\(633\) 0 0
\(634\) −7.91873 28.7871i −0.314493 1.14328i
\(635\) 9.49457 5.72612i 0.376781 0.227234i
\(636\) 0 0
\(637\) 3.41441 3.41441i 0.135284 0.135284i
\(638\) 12.9983 22.8630i 0.514607 0.905154i
\(639\) 0 0
\(640\) −25.2438 + 1.65779i −0.997851 + 0.0655298i
\(641\) 8.84689i 0.349431i 0.984619 + 0.174716i \(0.0559006\pi\)
−0.984619 + 0.174716i \(0.944099\pi\)
\(642\) 0 0
\(643\) −18.7263 18.7263i −0.738491 0.738491i 0.233795 0.972286i \(-0.424886\pi\)
−0.972286 + 0.233795i \(0.924886\pi\)
\(644\) 40.7236 24.2385i 1.60474 0.955133i
\(645\) 0 0
\(646\) −7.24341 + 1.99251i −0.284988 + 0.0783944i
\(647\) 32.7789 1.28867 0.644335 0.764744i \(-0.277134\pi\)
0.644335 + 0.764744i \(0.277134\pi\)
\(648\) 0 0
\(649\) 21.4345i 0.841378i
\(650\) 3.37456 15.3080i 0.132361 0.600430i
\(651\) 0 0
\(652\) −2.13918 + 8.42979i −0.0837766 + 0.330136i
\(653\) −1.54050 1.54050i −0.0602843 0.0602843i 0.676322 0.736606i \(-0.263573\pi\)
−0.736606 + 0.676322i \(0.763573\pi\)
\(654\) 0 0
\(655\) 28.4930 + 7.05451i 1.11331 + 0.275643i
\(656\) 7.73509 14.2593i 0.302004 0.556731i
\(657\) 0 0
\(658\) −21.8844 12.4419i −0.853143 0.485037i
\(659\) −6.00170 6.00170i −0.233793 0.233793i 0.580481 0.814274i \(-0.302865\pi\)
−0.814274 + 0.580481i \(0.802865\pi\)
\(660\) 0 0
\(661\) 5.39733 5.39733i 0.209932 0.209932i −0.594307 0.804239i \(-0.702573\pi\)
0.804239 + 0.594307i \(0.202573\pi\)
\(662\) −3.03665 11.0392i −0.118023 0.429050i
\(663\) 0 0
\(664\) 20.6655 + 19.8580i 0.801975 + 0.770642i
\(665\) −11.6994 2.89663i −0.453684 0.112326i
\(666\) 0 0
\(667\) 55.6947 55.6947i 2.15651 2.15651i
\(668\) 6.47360 + 10.8764i 0.250471 + 0.420821i
\(669\) 0 0
\(670\) −4.21450 4.00299i −0.162820 0.154649i
\(671\) −12.8988 −0.497952
\(672\) 0 0
\(673\) 0.683677i 0.0263538i −0.999913 0.0131769i \(-0.995806\pi\)
0.999913 0.0131769i \(-0.00419446\pi\)
\(674\) 19.6106 34.4936i 0.755374 1.32864i
\(675\) 0 0
\(676\) −13.8959 + 8.27081i −0.534459 + 0.318108i
\(677\) 20.9613 20.9613i 0.805610 0.805610i −0.178356 0.983966i \(-0.557078\pi\)
0.983966 + 0.178356i \(0.0570779\pi\)
\(678\) 0 0
\(679\) 29.3905 1.12791
\(680\) 10.0723 + 15.9727i 0.386256 + 0.612525i
\(681\) 0 0
\(682\) 0.0348343 + 0.126634i 0.00133387 + 0.00484905i
\(683\) −9.01650 9.01650i −0.345007 0.345007i 0.513239 0.858246i \(-0.328445\pi\)
−0.858246 + 0.513239i \(0.828445\pi\)
\(684\) 0 0
\(685\) −7.62222 12.6385i −0.291230 0.482893i
\(686\) 10.2104 17.9592i 0.389833 0.685686i
\(687\) 0 0
\(688\) −9.95236 33.5515i −0.379430 1.27914i
\(689\) 13.8145i 0.526292i
\(690\) 0 0
\(691\) −11.0043 + 11.0043i −0.418623 + 0.418623i −0.884729 0.466106i \(-0.845657\pi\)
0.466106 + 0.884729i \(0.345657\pi\)
\(692\) −2.44815 + 9.64737i −0.0930649 + 0.366738i
\(693\) 0 0
\(694\) −4.53645 16.4914i −0.172201 0.626006i
\(695\) 1.15468 + 0.285886i 0.0437997 + 0.0108443i
\(696\) 0 0
\(697\) −12.1087 −0.458648
\(698\) −2.92355 10.6280i −0.110658 0.402276i
\(699\) 0 0
\(700\) 1.55851 + 30.2554i 0.0589061 + 1.14355i
\(701\) −24.8888 + 24.8888i −0.940038 + 0.940038i −0.998301 0.0582634i \(-0.981444\pi\)
0.0582634 + 0.998301i \(0.481444\pi\)
\(702\) 0 0
\(703\) −15.6745 −0.591173
\(704\) −10.0221 + 10.8543i −0.377722 + 0.409087i
\(705\) 0 0
\(706\) 27.2957 + 15.5184i 1.02729 + 0.584044i
\(707\) 19.6846 19.6846i 0.740317 0.740317i
\(708\) 0 0
\(709\) 12.7063 12.7063i 0.477196 0.477196i −0.427038 0.904234i \(-0.640443\pi\)
0.904234 + 0.427038i \(0.140443\pi\)
\(710\) 1.13658 + 44.1582i 0.0426551 + 1.65723i
\(711\) 0 0
\(712\) −0.428412 21.5018i −0.0160554 0.805815i
\(713\) 0.393339i 0.0147307i
\(714\) 0 0
\(715\) −4.72760 7.83891i −0.176802 0.293159i
\(716\) 4.32879 17.0583i 0.161774 0.637499i
\(717\) 0 0
\(718\) 4.70945 8.28355i 0.175755 0.309139i
\(719\) −1.74421 −0.0650482 −0.0325241 0.999471i \(-0.510355\pi\)
−0.0325241 + 0.999471i \(0.510355\pi\)
\(720\) 0 0
\(721\) −40.3998 −1.50457
\(722\) 11.0677 19.4672i 0.411896 0.724493i
\(723\) 0 0
\(724\) 41.0654 + 10.4209i 1.52618 + 0.387290i
\(725\) 14.8790 + 48.1025i 0.552594 + 1.78648i
\(726\) 0 0
\(727\) 2.82244i 0.104679i 0.998629 + 0.0523393i \(0.0166677\pi\)
−0.998629 + 0.0523393i \(0.983332\pi\)
\(728\) −13.1619 + 13.6971i −0.487814 + 0.507648i
\(729\) 0 0
\(730\) 12.1973 0.313945i 0.451443 0.0116196i
\(731\) −18.4713 + 18.4713i −0.683184 + 0.683184i
\(732\) 0 0
\(733\) −7.06892 + 7.06892i −0.261097 + 0.261097i −0.825500 0.564403i \(-0.809106\pi\)
0.564403 + 0.825500i \(0.309106\pi\)
\(734\) 9.39600 + 5.34190i 0.346813 + 0.197173i
\(735\) 0 0
\(736\) −37.5618 + 23.3823i −1.38454 + 0.861883i
\(737\) −3.39440 −0.125034
\(738\) 0 0
\(739\) 0.328385 0.328385i 0.0120798 0.0120798i −0.701041 0.713121i \(-0.747281\pi\)
0.713121 + 0.701041i \(0.247281\pi\)
\(740\) 11.4238 + 37.7067i 0.419946 + 1.38613i
\(741\) 0 0
\(742\) −7.08125 25.7426i −0.259961 0.945039i
\(743\) 35.2559 1.29341 0.646707 0.762739i \(-0.276146\pi\)
0.646707 + 0.762739i \(0.276146\pi\)
\(744\) 0 0
\(745\) −26.7525 6.62359i −0.980137 0.242670i
\(746\) −2.75888 10.0294i −0.101010 0.367202i
\(747\) 0 0
\(748\) 10.6886 + 2.71239i 0.390814 + 0.0991747i
\(749\) −6.25619 + 6.25619i −0.228596 + 0.228596i
\(750\) 0 0
\(751\) 36.1388i 1.31872i −0.751826 0.659362i \(-0.770827\pi\)
0.751826 0.659362i \(-0.229173\pi\)
\(752\) 20.6589 + 11.2066i 0.753352 + 0.408664i
\(753\) 0 0
\(754\) −15.6037 + 27.4458i −0.568255 + 0.999517i
\(755\) −13.8978 + 8.38167i −0.505792 + 0.305040i
\(756\) 0 0
\(757\) −15.0827 15.0827i −0.548188 0.548188i 0.377728 0.925917i \(-0.376705\pi\)
−0.925917 + 0.377728i \(0.876705\pi\)
\(758\) −4.05374 14.7366i −0.147239 0.535259i
\(759\) 0 0
\(760\) 10.9744 + 2.48621i 0.398084 + 0.0901842i
\(761\) −27.3466 −0.991312 −0.495656 0.868519i \(-0.665072\pi\)
−0.495656 + 0.868519i \(0.665072\pi\)
\(762\) 0 0
\(763\) 29.8296 29.8296i 1.07991 1.07991i
\(764\) 20.9003 + 35.1150i 0.756147 + 1.27042i
\(765\) 0 0
\(766\) −19.6609 + 34.5820i −0.710377 + 1.24950i
\(767\) 25.7310i 0.929091i
\(768\) 0 0
\(769\) −15.0021 −0.540989 −0.270494 0.962722i \(-0.587187\pi\)
−0.270494 + 0.962722i \(0.587187\pi\)
\(770\) 12.8278 + 12.1840i 0.462281 + 0.439081i
\(771\) 0 0
\(772\) 0.185603 0.110470i 0.00668000 0.00397591i
\(773\) −13.7968 + 13.7968i −0.496236 + 0.496236i −0.910264 0.414028i \(-0.864121\pi\)
0.414028 + 0.910264i \(0.364121\pi\)
\(774\) 0 0
\(775\) −0.222401 0.117319i −0.00798888 0.00421423i
\(776\) −27.4339 + 0.546606i −0.984821 + 0.0196220i
\(777\) 0 0
\(778\) −4.38587 15.9440i −0.157241 0.571620i
\(779\) −5.10215 + 5.10215i −0.182803 + 0.182803i
\(780\) 0 0
\(781\) 18.2404 + 18.2404i 0.652695 + 0.652695i
\(782\) 28.7101 + 16.3225i 1.02667 + 0.583693i
\(783\) 0 0
\(784\) 4.15441 7.65846i 0.148372 0.273516i
\(785\) −12.1665 + 49.1403i −0.434242 + 1.75389i
\(786\) 0 0
\(787\) 29.8134 + 29.8134i 1.06273 + 1.06273i 0.997896 + 0.0648379i \(0.0206530\pi\)
0.0648379 + 0.997896i \(0.479347\pi\)
\(788\) 36.4929 + 9.26058i 1.30000 + 0.329894i
\(789\) 0 0
\(790\) 0.0871400 + 3.38554i 0.00310030 + 0.120452i
\(791\) 8.54978i 0.303995i