Properties

Label 720.2.u.a.179.4
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 179.4
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.39867 + 0.209116i) q^{2} +(1.91254 - 0.584968i) q^{4} +(1.73123 - 1.41522i) q^{5} +3.80565i q^{7} +(-2.55268 + 1.21812i) q^{8} +O(q^{10})\) \(q+(-1.39867 + 0.209116i) q^{2} +(1.91254 - 0.584968i) q^{4} +(1.73123 - 1.41522i) q^{5} +3.80565i q^{7} +(-2.55268 + 1.21812i) q^{8} +(-2.12547 + 2.34145i) q^{10} +(-0.761375 + 0.761375i) q^{11} +(-4.33164 + 4.33164i) q^{13} +(-0.795824 - 5.32284i) q^{14} +(3.31562 - 2.23755i) q^{16} -6.44408 q^{17} +(-2.98007 + 2.98007i) q^{19} +(2.48319 - 3.71937i) q^{20} +(0.905695 - 1.22413i) q^{22} -1.73120 q^{23} +(0.994326 - 4.90013i) q^{25} +(5.15271 - 6.96434i) q^{26} +(2.22619 + 7.27847i) q^{28} +(0.289500 - 0.289500i) q^{29} +3.89823i q^{31} +(-4.16955 + 3.82294i) q^{32} +(9.01313 - 1.34756i) q^{34} +(5.38582 + 6.58847i) q^{35} +(-1.64445 - 1.64445i) q^{37} +(3.54494 - 4.79130i) q^{38} +(-2.69538 + 5.72144i) q^{40} -2.59735 q^{41} +(7.61730 - 7.61730i) q^{43} +(-1.01078 + 1.90154i) q^{44} +(2.42137 - 0.362022i) q^{46} +5.14100i q^{47} -7.48300 q^{49} +(-0.366034 + 7.06159i) q^{50} +(-5.75057 + 10.8183i) q^{52} +(5.10351 - 5.10351i) q^{53} +(-0.240606 + 2.39563i) q^{55} +(-4.63574 - 9.71462i) q^{56} +(-0.344376 + 0.465454i) q^{58} +(-5.68382 + 5.68382i) q^{59} +(-0.647296 - 0.647296i) q^{61} +(-0.815183 - 5.45232i) q^{62} +(5.03237 - 6.21894i) q^{64} +(-1.36887 + 13.6293i) q^{65} +(9.09323 + 9.09323i) q^{67} +(-12.3246 + 3.76959i) q^{68} +(-8.91073 - 8.08881i) q^{70} +8.79742i q^{71} -12.1321 q^{73} +(2.64392 + 1.95616i) q^{74} +(-3.95625 + 7.44275i) q^{76} +(-2.89753 - 2.89753i) q^{77} -12.0907i q^{79} +(2.57349 - 8.56605i) q^{80} +(3.63283 - 0.543148i) q^{82} +(0.925156 - 0.925156i) q^{83} +(-11.1562 + 9.11977i) q^{85} +(-9.06116 + 12.2470i) q^{86} +(1.01610 - 2.87100i) q^{88} -13.2896 q^{89} +(-16.4847 - 16.4847i) q^{91} +(-3.31099 + 1.01270i) q^{92} +(-1.07507 - 7.19055i) q^{94} +(-0.941748 + 9.37663i) q^{95} +9.56150i q^{97} +(10.4662 - 1.56482i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39867 + 0.209116i −0.989007 + 0.147868i
\(3\) 0 0
\(4\) 1.91254 0.584968i 0.956270 0.292484i
\(5\) 1.73123 1.41522i 0.774230 0.632904i
\(6\) 0 0
\(7\) 3.80565i 1.43840i 0.694802 + 0.719201i \(0.255492\pi\)
−0.694802 + 0.719201i \(0.744508\pi\)
\(8\) −2.55268 + 1.21812i −0.902509 + 0.430670i
\(9\) 0 0
\(10\) −2.12547 + 2.34145i −0.672133 + 0.740430i
\(11\) −0.761375 + 0.761375i −0.229563 + 0.229563i −0.812510 0.582947i \(-0.801900\pi\)
0.582947 + 0.812510i \(0.301900\pi\)
\(12\) 0 0
\(13\) −4.33164 + 4.33164i −1.20138 + 1.20138i −0.227634 + 0.973747i \(0.573099\pi\)
−0.973747 + 0.227634i \(0.926901\pi\)
\(14\) −0.795824 5.32284i −0.212693 1.42259i
\(15\) 0 0
\(16\) 3.31562 2.23755i 0.828906 0.559388i
\(17\) −6.44408 −1.56292 −0.781460 0.623955i \(-0.785525\pi\)
−0.781460 + 0.623955i \(0.785525\pi\)
\(18\) 0 0
\(19\) −2.98007 + 2.98007i −0.683674 + 0.683674i −0.960826 0.277152i \(-0.910610\pi\)
0.277152 + 0.960826i \(0.410610\pi\)
\(20\) 2.48319 3.71937i 0.555259 0.831677i
\(21\) 0 0
\(22\) 0.905695 1.22413i 0.193095 0.260985i
\(23\) −1.73120 −0.360980 −0.180490 0.983577i \(-0.557768\pi\)
−0.180490 + 0.983577i \(0.557768\pi\)
\(24\) 0 0
\(25\) 0.994326 4.90013i 0.198865 0.980027i
\(26\) 5.15271 6.96434i 1.01053 1.36582i
\(27\) 0 0
\(28\) 2.22619 + 7.27847i 0.420710 + 1.37550i
\(29\) 0.289500 0.289500i 0.0537589 0.0537589i −0.679716 0.733475i \(-0.737897\pi\)
0.733475 + 0.679716i \(0.237897\pi\)
\(30\) 0 0
\(31\) 3.89823i 0.700142i 0.936723 + 0.350071i \(0.113843\pi\)
−0.936723 + 0.350071i \(0.886157\pi\)
\(32\) −4.16955 + 3.82294i −0.737079 + 0.675807i
\(33\) 0 0
\(34\) 9.01313 1.34756i 1.54574 0.231105i
\(35\) 5.38582 + 6.58847i 0.910370 + 1.11365i
\(36\) 0 0
\(37\) −1.64445 1.64445i −0.270346 0.270346i 0.558893 0.829239i \(-0.311226\pi\)
−0.829239 + 0.558893i \(0.811226\pi\)
\(38\) 3.54494 4.79130i 0.575066 0.777252i
\(39\) 0 0
\(40\) −2.69538 + 5.72144i −0.426177 + 0.904640i
\(41\) −2.59735 −0.405638 −0.202819 0.979216i \(-0.565010\pi\)
−0.202819 + 0.979216i \(0.565010\pi\)
\(42\) 0 0
\(43\) 7.61730 7.61730i 1.16163 1.16163i 0.177507 0.984119i \(-0.443197\pi\)
0.984119 0.177507i \(-0.0568034\pi\)
\(44\) −1.01078 + 1.90154i −0.152381 + 0.286668i
\(45\) 0 0
\(46\) 2.42137 0.362022i 0.357012 0.0533773i
\(47\) 5.14100i 0.749892i 0.927047 + 0.374946i \(0.122339\pi\)
−0.927047 + 0.374946i \(0.877661\pi\)
\(48\) 0 0
\(49\) −7.48300 −1.06900
\(50\) −0.366034 + 7.06159i −0.0517650 + 0.998659i
\(51\) 0 0
\(52\) −5.75057 + 10.8183i −0.797460 + 1.50023i
\(53\) 5.10351 5.10351i 0.701021 0.701021i −0.263609 0.964630i \(-0.584913\pi\)
0.964630 + 0.263609i \(0.0849128\pi\)
\(54\) 0 0
\(55\) −0.240606 + 2.39563i −0.0324434 + 0.323026i
\(56\) −4.63574 9.71462i −0.619477 1.29817i
\(57\) 0 0
\(58\) −0.344376 + 0.465454i −0.0452187 + 0.0611171i
\(59\) −5.68382 + 5.68382i −0.739971 + 0.739971i −0.972572 0.232601i \(-0.925276\pi\)
0.232601 + 0.972572i \(0.425276\pi\)
\(60\) 0 0
\(61\) −0.647296 0.647296i −0.0828778 0.0828778i 0.664453 0.747330i \(-0.268665\pi\)
−0.747330 + 0.664453i \(0.768665\pi\)
\(62\) −0.815183 5.45232i −0.103528 0.692446i
\(63\) 0 0
\(64\) 5.03237 6.21894i 0.629046 0.777368i
\(65\) −1.36887 + 13.6293i −0.169787 + 1.69050i
\(66\) 0 0
\(67\) 9.09323 + 9.09323i 1.11091 + 1.11091i 0.993027 + 0.117887i \(0.0376122\pi\)
0.117887 + 0.993027i \(0.462388\pi\)
\(68\) −12.3246 + 3.76959i −1.49457 + 0.457129i
\(69\) 0 0
\(70\) −8.91073 8.08881i −1.06504 0.966798i
\(71\) 8.79742i 1.04406i 0.852927 + 0.522031i \(0.174825\pi\)
−0.852927 + 0.522031i \(0.825175\pi\)
\(72\) 0 0
\(73\) −12.1321 −1.41995 −0.709976 0.704225i \(-0.751294\pi\)
−0.709976 + 0.704225i \(0.751294\pi\)
\(74\) 2.64392 + 1.95616i 0.307350 + 0.227399i
\(75\) 0 0
\(76\) −3.95625 + 7.44275i −0.453814 + 0.853741i
\(77\) −2.89753 2.89753i −0.330204 0.330204i
\(78\) 0 0
\(79\) 12.0907i 1.36031i −0.733068 0.680155i \(-0.761912\pi\)
0.733068 0.680155i \(-0.238088\pi\)
\(80\) 2.57349 8.56605i 0.287725 0.957713i
\(81\) 0 0
\(82\) 3.63283 0.543148i 0.401179 0.0599807i
\(83\) 0.925156 0.925156i 0.101549 0.101549i −0.654507 0.756056i \(-0.727124\pi\)
0.756056 + 0.654507i \(0.227124\pi\)
\(84\) 0 0
\(85\) −11.1562 + 9.11977i −1.21006 + 0.989178i
\(86\) −9.06116 + 12.2470i −0.977090 + 1.32062i
\(87\) 0 0
\(88\) 1.01610 2.87100i 0.108317 0.306049i
\(89\) −13.2896 −1.40870 −0.704349 0.709854i \(-0.748761\pi\)
−0.704349 + 0.709854i \(0.748761\pi\)
\(90\) 0 0
\(91\) −16.4847 16.4847i −1.72807 1.72807i
\(92\) −3.31099 + 1.01270i −0.345195 + 0.105581i
\(93\) 0 0
\(94\) −1.07507 7.19055i −0.110885 0.741649i
\(95\) −0.941748 + 9.37663i −0.0966213 + 0.962022i
\(96\) 0 0
\(97\) 9.56150i 0.970823i 0.874286 + 0.485411i \(0.161330\pi\)
−0.874286 + 0.485411i \(0.838670\pi\)
\(98\) 10.4662 1.56482i 1.05725 0.158070i
\(99\) 0 0
\(100\) −0.964734 9.95336i −0.0964734 0.995336i
\(101\) 11.7354 + 11.7354i 1.16771 + 1.16771i 0.982744 + 0.184969i \(0.0592184\pi\)
0.184969 + 0.982744i \(0.440782\pi\)
\(102\) 0 0
\(103\) 9.72480i 0.958213i −0.877757 0.479107i \(-0.840961\pi\)
0.877757 0.479107i \(-0.159039\pi\)
\(104\) 5.78084 16.3338i 0.566858 1.60166i
\(105\) 0 0
\(106\) −6.07088 + 8.20534i −0.589656 + 0.796973i
\(107\) 8.15735 + 8.15735i 0.788601 + 0.788601i 0.981265 0.192664i \(-0.0617127\pi\)
−0.192664 + 0.981265i \(0.561713\pi\)
\(108\) 0 0
\(109\) 8.72633 + 8.72633i 0.835831 + 0.835831i 0.988307 0.152477i \(-0.0487249\pi\)
−0.152477 + 0.988307i \(0.548725\pi\)
\(110\) −0.164437 3.40100i −0.0156784 0.324273i
\(111\) 0 0
\(112\) 8.51535 + 12.6181i 0.804625 + 1.19230i
\(113\) 16.2773 1.53124 0.765619 0.643295i \(-0.222433\pi\)
0.765619 + 0.643295i \(0.222433\pi\)
\(114\) 0 0
\(115\) −2.99711 + 2.45002i −0.279482 + 0.228466i
\(116\) 0.384333 0.723030i 0.0356844 0.0671316i
\(117\) 0 0
\(118\) 6.76120 9.13836i 0.622419 0.841254i
\(119\) 24.5240i 2.24811i
\(120\) 0 0
\(121\) 9.84061i 0.894601i
\(122\) 1.04071 + 0.769992i 0.0942217 + 0.0697118i
\(123\) 0 0
\(124\) 2.28034 + 7.45552i 0.204781 + 0.669525i
\(125\) −5.21334 9.89045i −0.466295 0.884629i
\(126\) 0 0
\(127\) 8.61277 0.764260 0.382130 0.924109i \(-0.375191\pi\)
0.382130 + 0.924109i \(0.375191\pi\)
\(128\) −5.73813 + 9.75058i −0.507184 + 0.861838i
\(129\) 0 0
\(130\) −0.935518 19.3491i −0.0820503 1.69703i
\(131\) 7.09695 + 7.09695i 0.620064 + 0.620064i 0.945548 0.325484i \(-0.105527\pi\)
−0.325484 + 0.945548i \(0.605527\pi\)
\(132\) 0 0
\(133\) −11.3411 11.3411i −0.983398 0.983398i
\(134\) −14.6199 10.8169i −1.26297 0.934434i
\(135\) 0 0
\(136\) 16.4497 7.84967i 1.41055 0.673103i
\(137\) 9.30582i 0.795050i −0.917591 0.397525i \(-0.869869\pi\)
0.917591 0.397525i \(-0.130131\pi\)
\(138\) 0 0
\(139\) 9.16328 + 9.16328i 0.777219 + 0.777219i 0.979357 0.202138i \(-0.0647889\pi\)
−0.202138 + 0.979357i \(0.564789\pi\)
\(140\) 14.1546 + 9.45018i 1.19629 + 0.798686i
\(141\) 0 0
\(142\) −1.83968 12.3047i −0.154383 1.03258i
\(143\) 6.59601i 0.551586i
\(144\) 0 0
\(145\) 0.0914866 0.910898i 0.00759755 0.0756460i
\(146\) 16.9687 2.53702i 1.40434 0.209965i
\(147\) 0 0
\(148\) −4.10703 2.18313i −0.337596 0.179452i
\(149\) 0.389077 + 0.389077i 0.0318744 + 0.0318744i 0.722864 0.690990i \(-0.242825\pi\)
−0.690990 + 0.722864i \(0.742825\pi\)
\(150\) 0 0
\(151\) 12.5843 1.02409 0.512047 0.858958i \(-0.328887\pi\)
0.512047 + 0.858958i \(0.328887\pi\)
\(152\) 3.97709 11.2372i 0.322584 0.911461i
\(153\) 0 0
\(154\) 4.65860 + 3.44676i 0.375401 + 0.277748i
\(155\) 5.51683 + 6.74873i 0.443123 + 0.542071i
\(156\) 0 0
\(157\) −0.397418 + 0.397418i −0.0317174 + 0.0317174i −0.722788 0.691070i \(-0.757140\pi\)
0.691070 + 0.722788i \(0.257140\pi\)
\(158\) 2.52836 + 16.9109i 0.201146 + 1.34536i
\(159\) 0 0
\(160\) −1.80816 + 12.5192i −0.142948 + 0.989730i
\(161\) 6.58835i 0.519235i
\(162\) 0 0
\(163\) −7.61573 7.61573i −0.596510 0.596510i 0.342872 0.939382i \(-0.388600\pi\)
−0.939382 + 0.342872i \(0.888600\pi\)
\(164\) −4.96754 + 1.51937i −0.387899 + 0.118643i
\(165\) 0 0
\(166\) −1.10052 + 1.48745i −0.0854169 + 0.115449i
\(167\) −2.33425 −0.180629 −0.0903147 0.995913i \(-0.528787\pi\)
−0.0903147 + 0.995913i \(0.528787\pi\)
\(168\) 0 0
\(169\) 24.5262i 1.88663i
\(170\) 13.6967 15.0885i 1.05049 1.15723i
\(171\) 0 0
\(172\) 10.1125 19.0243i 0.771072 1.45059i
\(173\) −0.625160 0.625160i −0.0475300 0.0475300i 0.682942 0.730472i \(-0.260700\pi\)
−0.730472 + 0.682942i \(0.760700\pi\)
\(174\) 0 0
\(175\) 18.6482 + 3.78406i 1.40967 + 0.286048i
\(176\) −0.820818 + 4.22805i −0.0618715 + 0.318701i
\(177\) 0 0
\(178\) 18.5878 2.77908i 1.39321 0.208301i
\(179\) 4.33232 + 4.33232i 0.323813 + 0.323813i 0.850228 0.526415i \(-0.176464\pi\)
−0.526415 + 0.850228i \(0.676464\pi\)
\(180\) 0 0
\(181\) 0.834317 0.834317i 0.0620143 0.0620143i −0.675419 0.737434i \(-0.736037\pi\)
0.737434 + 0.675419i \(0.236037\pi\)
\(182\) 26.5039 + 19.6094i 1.96460 + 1.45355i
\(183\) 0 0
\(184\) 4.41920 2.10881i 0.325788 0.155464i
\(185\) −5.17418 0.519672i −0.380413 0.0382071i
\(186\) 0 0
\(187\) 4.90637 4.90637i 0.358789 0.358789i
\(188\) 3.00732 + 9.83238i 0.219332 + 0.717100i
\(189\) 0 0
\(190\) −0.643614 13.3117i −0.0466927 0.965733i
\(191\) −18.1527 −1.31349 −0.656743 0.754114i \(-0.728066\pi\)
−0.656743 + 0.754114i \(0.728066\pi\)
\(192\) 0 0
\(193\) 15.2659i 1.09886i −0.835538 0.549432i \(-0.814844\pi\)
0.835538 0.549432i \(-0.185156\pi\)
\(194\) −1.99947 13.3734i −0.143553 0.960151i
\(195\) 0 0
\(196\) −14.3115 + 4.37732i −1.02225 + 0.312665i
\(197\) −0.287217 + 0.287217i −0.0204633 + 0.0204633i −0.717264 0.696801i \(-0.754606\pi\)
0.696801 + 0.717264i \(0.254606\pi\)
\(198\) 0 0
\(199\) 15.9569 1.13115 0.565576 0.824696i \(-0.308654\pi\)
0.565576 + 0.824696i \(0.308654\pi\)
\(200\) 3.43075 + 13.7197i 0.242591 + 0.970129i
\(201\) 0 0
\(202\) −18.8679 13.9598i −1.32754 0.982210i
\(203\) 1.10174 + 1.10174i 0.0773269 + 0.0773269i
\(204\) 0 0
\(205\) −4.49661 + 3.67581i −0.314057 + 0.256730i
\(206\) 2.03361 + 13.6018i 0.141689 + 0.947680i
\(207\) 0 0
\(208\) −4.66982 + 24.0544i −0.323794 + 1.66787i
\(209\) 4.53790i 0.313893i
\(210\) 0 0
\(211\) −15.7303 + 15.7303i −1.08292 + 1.08292i −0.0866837 + 0.996236i \(0.527627\pi\)
−0.996236 + 0.0866837i \(0.972373\pi\)
\(212\) 6.77528 12.7461i 0.465328 0.875403i
\(213\) 0 0
\(214\) −13.1153 9.70358i −0.896540 0.663323i
\(215\) 2.40718 23.9674i 0.164169 1.63457i
\(216\) 0 0
\(217\) −14.8353 −1.00709
\(218\) −14.0300 10.3804i −0.950235 0.703050i
\(219\) 0 0
\(220\) 0.941197 + 4.72248i 0.0634555 + 0.318390i
\(221\) 27.9135 27.9135i 1.87766 1.87766i
\(222\) 0 0
\(223\) 12.4886 0.836301 0.418150 0.908378i \(-0.362678\pi\)
0.418150 + 0.908378i \(0.362678\pi\)
\(224\) −14.5488 15.8678i −0.972082 1.06022i
\(225\) 0 0
\(226\) −22.7665 + 3.40384i −1.51440 + 0.226420i
\(227\) −20.1265 + 20.1265i −1.33584 + 1.33584i −0.435800 + 0.900043i \(0.643535\pi\)
−0.900043 + 0.435800i \(0.856465\pi\)
\(228\) 0 0
\(229\) 5.05312 5.05312i 0.333920 0.333920i −0.520153 0.854073i \(-0.674125\pi\)
0.854073 + 0.520153i \(0.174125\pi\)
\(230\) 3.67962 4.05351i 0.242627 0.267281i
\(231\) 0 0
\(232\) −0.386356 + 1.09165i −0.0253655 + 0.0716702i
\(233\) 12.6841i 0.830960i −0.909602 0.415480i \(-0.863614\pi\)
0.909602 0.415480i \(-0.136386\pi\)
\(234\) 0 0
\(235\) 7.27563 + 8.90027i 0.474610 + 0.580589i
\(236\) −7.54569 + 14.1954i −0.491182 + 0.924042i
\(237\) 0 0
\(238\) 5.12836 + 34.3009i 0.332422 + 2.22339i
\(239\) 5.00305 0.323621 0.161810 0.986822i \(-0.448267\pi\)
0.161810 + 0.986822i \(0.448267\pi\)
\(240\) 0 0
\(241\) −9.34398 −0.601898 −0.300949 0.953640i \(-0.597303\pi\)
−0.300949 + 0.953640i \(0.597303\pi\)
\(242\) −2.05783 13.7637i −0.132283 0.884767i
\(243\) 0 0
\(244\) −1.61663 0.859333i −0.103494 0.0550132i
\(245\) −12.9548 + 10.5901i −0.827652 + 0.676574i
\(246\) 0 0
\(247\) 25.8172i 1.64271i
\(248\) −4.74851 9.95093i −0.301531 0.631885i
\(249\) 0 0
\(250\) 9.35998 + 12.7433i 0.591977 + 0.805955i
\(251\) −11.8770 + 11.8770i −0.749672 + 0.749672i −0.974418 0.224745i \(-0.927845\pi\)
0.224745 + 0.974418i \(0.427845\pi\)
\(252\) 0 0
\(253\) 1.31809 1.31809i 0.0828678 0.0828678i
\(254\) −12.0464 + 1.80107i −0.755859 + 0.113009i
\(255\) 0 0
\(256\) 5.98673 14.8378i 0.374170 0.927360i
\(257\) 4.63622 0.289199 0.144600 0.989490i \(-0.453811\pi\)
0.144600 + 0.989490i \(0.453811\pi\)
\(258\) 0 0
\(259\) 6.25821 6.25821i 0.388866 0.388866i
\(260\) 5.35469 + 26.8673i 0.332084 + 1.66624i
\(261\) 0 0
\(262\) −11.4104 8.44219i −0.704935 0.521560i
\(263\) 11.6055 0.715624 0.357812 0.933794i \(-0.383523\pi\)
0.357812 + 0.933794i \(0.383523\pi\)
\(264\) 0 0
\(265\) 1.61279 16.0579i 0.0990728 0.986430i
\(266\) 18.2340 + 13.4908i 1.11800 + 0.827175i
\(267\) 0 0
\(268\) 22.7104 + 12.0719i 1.38726 + 0.737410i
\(269\) 9.90154 9.90154i 0.603708 0.603708i −0.337587 0.941294i \(-0.609611\pi\)
0.941294 + 0.337587i \(0.109611\pi\)
\(270\) 0 0
\(271\) 3.50755i 0.213068i −0.994309 0.106534i \(-0.966025\pi\)
0.994309 0.106534i \(-0.0339753\pi\)
\(272\) −21.3662 + 14.4190i −1.29551 + 0.874279i
\(273\) 0 0
\(274\) 1.94600 + 13.0158i 0.117562 + 0.786310i
\(275\) 2.97379 + 4.48790i 0.179326 + 0.270630i
\(276\) 0 0
\(277\) 5.62344 + 5.62344i 0.337880 + 0.337880i 0.855569 0.517689i \(-0.173208\pi\)
−0.517689 + 0.855569i \(0.673208\pi\)
\(278\) −14.7326 10.9002i −0.883601 0.653750i
\(279\) 0 0
\(280\) −21.7738 10.2577i −1.30124 0.613014i
\(281\) −24.9686 −1.48950 −0.744752 0.667341i \(-0.767432\pi\)
−0.744752 + 0.667341i \(0.767432\pi\)
\(282\) 0 0
\(283\) −18.5071 + 18.5071i −1.10014 + 1.10014i −0.105742 + 0.994394i \(0.533722\pi\)
−0.994394 + 0.105742i \(0.966278\pi\)
\(284\) 5.14621 + 16.8254i 0.305371 + 0.998405i
\(285\) 0 0
\(286\) 1.37933 + 9.22562i 0.0815617 + 0.545523i
\(287\) 9.88461i 0.583470i
\(288\) 0 0
\(289\) 24.5262 1.44272
\(290\) 0.0625243 + 1.29317i 0.00367155 + 0.0759378i
\(291\) 0 0
\(292\) −23.2031 + 7.09688i −1.35786 + 0.415314i
\(293\) 3.44258 3.44258i 0.201118 0.201118i −0.599361 0.800479i \(-0.704579\pi\)
0.800479 + 0.599361i \(0.204579\pi\)
\(294\) 0 0
\(295\) −1.79618 + 17.8839i −0.104577 + 1.04124i
\(296\) 6.20090 + 2.19462i 0.360420 + 0.127560i
\(297\) 0 0
\(298\) −0.625552 0.462827i −0.0362372 0.0268108i
\(299\) 7.49894 7.49894i 0.433675 0.433675i
\(300\) 0 0
\(301\) 28.9888 + 28.9888i 1.67089 + 1.67089i
\(302\) −17.6012 + 2.63158i −1.01284 + 0.151430i
\(303\) 0 0
\(304\) −3.21273 + 16.5488i −0.184263 + 0.949141i
\(305\) −2.03668 0.204556i −0.116620 0.0117128i
\(306\) 0 0
\(307\) 13.4561 + 13.4561i 0.767977 + 0.767977i 0.977750 0.209773i \(-0.0672724\pi\)
−0.209773 + 0.977750i \(0.567272\pi\)
\(308\) −7.23661 3.84668i −0.412344 0.219185i
\(309\) 0 0
\(310\) −9.12749 8.28557i −0.518406 0.470589i
\(311\) 10.6693i 0.604999i −0.953150 0.302500i \(-0.902179\pi\)
0.953150 0.302500i \(-0.0978211\pi\)
\(312\) 0 0
\(313\) −10.3187 −0.583250 −0.291625 0.956533i \(-0.594196\pi\)
−0.291625 + 0.956533i \(0.594196\pi\)
\(314\) 0.472749 0.638963i 0.0266788 0.0360587i
\(315\) 0 0
\(316\) −7.07268 23.1240i −0.397869 1.30082i
\(317\) 15.8698 + 15.8698i 0.891336 + 0.891336i 0.994649 0.103313i \(-0.0329444\pi\)
−0.103313 + 0.994649i \(0.532944\pi\)
\(318\) 0 0
\(319\) 0.440837i 0.0246821i
\(320\) −0.0889531 17.8883i −0.00497263 0.999988i
\(321\) 0 0
\(322\) 1.37773 + 9.21491i 0.0767780 + 0.513527i
\(323\) 19.2038 19.2038i 1.06853 1.06853i
\(324\) 0 0
\(325\) 16.9186 + 25.5327i 0.938473 + 1.41630i
\(326\) 12.2444 + 9.05929i 0.678157 + 0.501748i
\(327\) 0 0
\(328\) 6.63021 3.16388i 0.366092 0.174696i
\(329\) −19.5649 −1.07865
\(330\) 0 0
\(331\) −9.80202 9.80202i −0.538768 0.538768i 0.384399 0.923167i \(-0.374409\pi\)
−0.923167 + 0.384399i \(0.874409\pi\)
\(332\) 1.22821 2.31058i 0.0674068 0.126810i
\(333\) 0 0
\(334\) 3.26484 0.488129i 0.178644 0.0267092i
\(335\) 28.6114 + 2.87360i 1.56321 + 0.157002i
\(336\) 0 0
\(337\) 13.6823i 0.745323i 0.927967 + 0.372662i \(0.121555\pi\)
−0.927967 + 0.372662i \(0.878445\pi\)
\(338\) 5.12884 + 34.3040i 0.278972 + 1.86589i
\(339\) 0 0
\(340\) −16.0019 + 23.9680i −0.867826 + 1.29985i
\(341\) −2.96801 2.96801i −0.160727 0.160727i
\(342\) 0 0
\(343\) 1.83811i 0.0992487i
\(344\) −10.1658 + 28.7233i −0.548101 + 1.54866i
\(345\) 0 0
\(346\) 1.00512 + 0.743660i 0.0540357 + 0.0399794i
\(347\) −15.5812 15.5812i −0.836445 0.836445i 0.151944 0.988389i \(-0.451447\pi\)
−0.988389 + 0.151944i \(0.951447\pi\)
\(348\) 0 0
\(349\) −4.64370 4.64370i −0.248572 0.248572i 0.571813 0.820384i \(-0.306240\pi\)
−0.820384 + 0.571813i \(0.806240\pi\)
\(350\) −26.8740 1.39300i −1.43647 0.0744589i
\(351\) 0 0
\(352\) 0.263896 6.08528i 0.0140657 0.324347i
\(353\) −19.8254 −1.05520 −0.527601 0.849492i \(-0.676908\pi\)
−0.527601 + 0.849492i \(0.676908\pi\)
\(354\) 0 0
\(355\) 12.4502 + 15.2304i 0.660790 + 0.808344i
\(356\) −25.4169 + 7.77401i −1.34710 + 0.412022i
\(357\) 0 0
\(358\) −6.96543 5.15352i −0.368135 0.272372i
\(359\) 20.1443i 1.06318i −0.847003 0.531589i \(-0.821595\pi\)
0.847003 0.531589i \(-0.178405\pi\)
\(360\) 0 0
\(361\) 1.23840i 0.0651788i
\(362\) −0.992463 + 1.34140i −0.0521627 + 0.0705025i
\(363\) 0 0
\(364\) −41.1707 21.8847i −2.15793 1.14707i
\(365\) −21.0034 + 17.1695i −1.09937 + 0.898694i
\(366\) 0 0
\(367\) −36.1117 −1.88502 −0.942508 0.334183i \(-0.891540\pi\)
−0.942508 + 0.334183i \(0.891540\pi\)
\(368\) −5.74001 + 3.87365i −0.299219 + 0.201928i
\(369\) 0 0
\(370\) 7.34563 0.355157i 0.381881 0.0184637i
\(371\) 19.4222 + 19.4222i 1.00835 + 1.00835i
\(372\) 0 0
\(373\) −1.62188 1.62188i −0.0839777 0.0839777i 0.663870 0.747848i \(-0.268913\pi\)
−0.747848 + 0.663870i \(0.768913\pi\)
\(374\) −5.83637 + 7.88838i −0.301792 + 0.407898i
\(375\) 0 0
\(376\) −6.26236 13.1233i −0.322956 0.676785i
\(377\) 2.50802i 0.129170i
\(378\) 0 0
\(379\) −10.9432 10.9432i −0.562115 0.562115i 0.367793 0.929908i \(-0.380114\pi\)
−0.929908 + 0.367793i \(0.880114\pi\)
\(380\) 3.68390 + 18.4841i 0.188980 + 0.948213i
\(381\) 0 0
\(382\) 25.3896 3.79603i 1.29905 0.194222i
\(383\) 31.2822i 1.59845i 0.601035 + 0.799223i \(0.294755\pi\)
−0.601035 + 0.799223i \(0.705245\pi\)
\(384\) 0 0
\(385\) −9.11693 0.915665i −0.464642 0.0466666i
\(386\) 3.19235 + 21.3519i 0.162486 + 1.08678i
\(387\) 0 0
\(388\) 5.59317 + 18.2868i 0.283950 + 0.928369i
\(389\) −4.10132 4.10132i −0.207945 0.207945i 0.595448 0.803394i \(-0.296974\pi\)
−0.803394 + 0.595448i \(0.796974\pi\)
\(390\) 0 0
\(391\) 11.1560 0.564183
\(392\) 19.1017 9.11518i 0.964782 0.460386i
\(393\) 0 0
\(394\) 0.341659 0.461782i 0.0172125 0.0232643i
\(395\) −17.1110 20.9318i −0.860946 1.05319i
\(396\) 0 0
\(397\) 22.7531 22.7531i 1.14194 1.14194i 0.153849 0.988094i \(-0.450833\pi\)
0.988094 0.153849i \(-0.0491670\pi\)
\(398\) −22.3183 + 3.33684i −1.11872 + 0.167261i
\(399\) 0 0
\(400\) −7.66749 18.4719i −0.383375 0.923593i
\(401\) 21.2428i 1.06082i −0.847743 0.530408i \(-0.822039\pi\)
0.847743 0.530408i \(-0.177961\pi\)
\(402\) 0 0
\(403\) −16.8857 16.8857i −0.841138 0.841138i
\(404\) 29.3092 + 15.5796i 1.45819 + 0.775112i
\(405\) 0 0
\(406\) −1.77136 1.31057i −0.0879110 0.0650427i
\(407\) 2.50409 0.124123
\(408\) 0 0
\(409\) 3.41459i 0.168841i 0.996430 + 0.0844204i \(0.0269039\pi\)
−0.996430 + 0.0844204i \(0.973096\pi\)
\(410\) 5.52060 6.08155i 0.272643 0.300346i
\(411\) 0 0
\(412\) −5.68870 18.5991i −0.280262 0.916311i
\(413\) −21.6307 21.6307i −1.06438 1.06438i
\(414\) 0 0
\(415\) 0.292364 2.91095i 0.0143516 0.142893i
\(416\) 1.50137 34.6206i 0.0736106 1.69741i
\(417\) 0 0
\(418\) 0.948949 + 6.34701i 0.0464146 + 0.310443i
\(419\) −2.45392 2.45392i −0.119882 0.119882i 0.644621 0.764503i \(-0.277015\pi\)
−0.764503 + 0.644621i \(0.777015\pi\)
\(420\) 0 0
\(421\) 16.7130 16.7130i 0.814540 0.814540i −0.170770 0.985311i \(-0.554626\pi\)
0.985311 + 0.170770i \(0.0546257\pi\)
\(422\) 18.7120 25.2909i 0.910887 1.23114i
\(423\) 0 0
\(424\) −6.81095 + 19.2443i −0.330769 + 0.934587i
\(425\) −6.40752 + 31.5769i −0.310811 + 1.53170i
\(426\) 0 0
\(427\) 2.46339 2.46339i 0.119212 0.119212i
\(428\) 20.3731 + 10.8295i 0.984769 + 0.523462i
\(429\) 0 0
\(430\) 1.64513 + 34.0258i 0.0793352 + 1.64087i
\(431\) −20.7930 −1.00156 −0.500782 0.865573i \(-0.666954\pi\)
−0.500782 + 0.865573i \(0.666954\pi\)
\(432\) 0 0
\(433\) 8.98760i 0.431916i −0.976403 0.215958i \(-0.930712\pi\)
0.976403 0.215958i \(-0.0692875\pi\)
\(434\) 20.7497 3.10230i 0.996015 0.148915i
\(435\) 0 0
\(436\) 21.7941 + 11.5848i 1.04375 + 0.554813i
\(437\) 5.15910 5.15910i 0.246793 0.246793i
\(438\) 0 0
\(439\) 18.6849 0.891780 0.445890 0.895088i \(-0.352887\pi\)
0.445890 + 0.895088i \(0.352887\pi\)
\(440\) −2.30397 6.40836i −0.109837 0.305507i
\(441\) 0 0
\(442\) −33.2045 + 44.8788i −1.57938 + 2.13467i
\(443\) −1.69635 1.69635i −0.0805958 0.0805958i 0.665660 0.746255i \(-0.268150\pi\)
−0.746255 + 0.665660i \(0.768150\pi\)
\(444\) 0 0
\(445\) −23.0074 + 18.8077i −1.09066 + 0.891570i
\(446\) −17.4674 + 2.61158i −0.827108 + 0.123662i
\(447\) 0 0
\(448\) 23.6671 + 19.1515i 1.11817 + 0.904821i
\(449\) 20.9833i 0.990264i 0.868818 + 0.495132i \(0.164880\pi\)
−0.868818 + 0.495132i \(0.835120\pi\)
\(450\) 0 0
\(451\) 1.97756 1.97756i 0.0931196 0.0931196i
\(452\) 31.1309 9.52169i 1.46428 0.447863i
\(453\) 0 0
\(454\) 23.9415 32.3591i 1.12363 1.51869i
\(455\) −51.8683 5.20943i −2.43162 0.244222i
\(456\) 0 0
\(457\) −0.679238 −0.0317734 −0.0158867 0.999874i \(-0.505057\pi\)
−0.0158867 + 0.999874i \(0.505057\pi\)
\(458\) −6.01094 + 8.12432i −0.280873 + 0.379625i
\(459\) 0 0
\(460\) −4.29891 + 6.43898i −0.200438 + 0.300219i
\(461\) 30.3013 30.3013i 1.41127 1.41127i 0.660048 0.751223i \(-0.270536\pi\)
0.751223 0.660048i \(-0.229464\pi\)
\(462\) 0 0
\(463\) −40.6442 −1.88889 −0.944447 0.328664i \(-0.893402\pi\)
−0.944447 + 0.328664i \(0.893402\pi\)
\(464\) 0.312102 1.60765i 0.0144890 0.0746331i
\(465\) 0 0
\(466\) 2.65244 + 17.7408i 0.122872 + 0.821825i
\(467\) 20.4572 20.4572i 0.946646 0.946646i −0.0520011 0.998647i \(-0.516560\pi\)
0.998647 + 0.0520011i \(0.0165599\pi\)
\(468\) 0 0
\(469\) −34.6057 + 34.6057i −1.59794 + 1.59794i
\(470\) −12.0374 10.9271i −0.555243 0.504028i
\(471\) 0 0
\(472\) 7.58542 21.4326i 0.349147 0.986514i
\(473\) 11.5992i 0.533334i
\(474\) 0 0
\(475\) 11.6396 + 17.5659i 0.534060 + 0.805978i
\(476\) −14.3457 46.9031i −0.657536 2.14980i
\(477\) 0 0
\(478\) −6.99760 + 1.04622i −0.320063 + 0.0478530i
\(479\) −20.9399 −0.956768 −0.478384 0.878151i \(-0.658777\pi\)
−0.478384 + 0.878151i \(0.658777\pi\)
\(480\) 0 0
\(481\) 14.2463 0.649577
\(482\) 13.0691 1.95398i 0.595282 0.0890013i
\(483\) 0 0
\(484\) 5.75645 + 18.8206i 0.261657 + 0.855481i
\(485\) 13.5316 + 16.5532i 0.614438 + 0.751641i
\(486\) 0 0
\(487\) 27.6996i 1.25519i 0.778540 + 0.627595i \(0.215961\pi\)
−0.778540 + 0.627595i \(0.784039\pi\)
\(488\) 2.44083 + 0.863857i 0.110491 + 0.0391050i
\(489\) 0 0
\(490\) 15.9049 17.5210i 0.718510 0.791519i
\(491\) −12.9711 + 12.9711i −0.585377 + 0.585377i −0.936376 0.350999i \(-0.885842\pi\)
0.350999 + 0.936376i \(0.385842\pi\)
\(492\) 0 0
\(493\) −1.86557 + 1.86557i −0.0840208 + 0.0840208i
\(494\) 5.39879 + 36.1096i 0.242903 + 1.62465i
\(495\) 0 0
\(496\) 8.72248 + 12.9251i 0.391651 + 0.580352i
\(497\) −33.4799 −1.50178
\(498\) 0 0
\(499\) −8.96696 + 8.96696i −0.401416 + 0.401416i −0.878732 0.477316i \(-0.841610\pi\)
0.477316 + 0.878732i \(0.341610\pi\)
\(500\) −15.7563 15.8663i −0.704644 0.709561i
\(501\) 0 0
\(502\) 14.1283 19.0957i 0.630579 0.852283i
\(503\) 9.23509 0.411772 0.205886 0.978576i \(-0.433992\pi\)
0.205886 + 0.978576i \(0.433992\pi\)
\(504\) 0 0
\(505\) 36.9247 + 3.70856i 1.64313 + 0.165029i
\(506\) −1.56794 + 2.11921i −0.0697034 + 0.0942104i
\(507\) 0 0
\(508\) 16.4723 5.03820i 0.730839 0.223534i
\(509\) −0.418802 + 0.418802i −0.0185631 + 0.0185631i −0.716327 0.697764i \(-0.754178\pi\)
0.697764 + 0.716327i \(0.254178\pi\)
\(510\) 0 0
\(511\) 46.1705i 2.04246i
\(512\) −5.27062 + 22.0050i −0.232931 + 0.972493i
\(513\) 0 0
\(514\) −6.48452 + 0.969508i −0.286020 + 0.0427632i
\(515\) −13.7627 16.8359i −0.606457 0.741878i
\(516\) 0 0
\(517\) −3.91423 3.91423i −0.172148 0.172148i
\(518\) −7.44446 + 10.0618i −0.327091 + 0.442092i
\(519\) 0 0
\(520\) −13.1078 36.4587i −0.574816 1.59882i
\(521\) 31.0344 1.35964 0.679821 0.733378i \(-0.262057\pi\)
0.679821 + 0.733378i \(0.262057\pi\)
\(522\) 0 0
\(523\) 12.5701 12.5701i 0.549653 0.549653i −0.376687 0.926340i \(-0.622937\pi\)
0.926340 + 0.376687i \(0.122937\pi\)
\(524\) 17.7247 + 9.42172i 0.774307 + 0.411590i
\(525\) 0 0
\(526\) −16.2322 + 2.42689i −0.707757 + 0.105818i
\(527\) 25.1205i 1.09427i
\(528\) 0 0
\(529\) −20.0029 −0.869693
\(530\) 1.10222 + 22.7970i 0.0478774 + 0.990236i
\(531\) 0 0
\(532\) −28.3245 15.0561i −1.22802 0.652766i
\(533\) 11.2508 11.2508i 0.487326 0.487326i
\(534\) 0 0
\(535\) 25.6667 + 2.57785i 1.10967 + 0.111450i
\(536\) −34.2887 12.1355i −1.48105 0.524173i
\(537\) 0 0
\(538\) −11.7784 + 15.9195i −0.507802 + 0.686340i
\(539\) 5.69737 5.69737i 0.245403 0.245403i
\(540\) 0 0
\(541\) 7.64792 + 7.64792i 0.328810 + 0.328810i 0.852134 0.523324i \(-0.175308\pi\)
−0.523324 + 0.852134i \(0.675308\pi\)
\(542\) 0.733485 + 4.90589i 0.0315059 + 0.210726i
\(543\) 0 0
\(544\) 26.8689 24.6354i 1.15200 1.05623i
\(545\) 27.4569 + 2.75766i 1.17613 + 0.118125i
\(546\) 0 0
\(547\) 5.50694 + 5.50694i 0.235460 + 0.235460i 0.814967 0.579507i \(-0.196755\pi\)
−0.579507 + 0.814967i \(0.696755\pi\)
\(548\) −5.44361 17.7978i −0.232540 0.760283i
\(549\) 0 0
\(550\) −5.09783 5.65521i −0.217372 0.241139i
\(551\) 1.72546i 0.0735071i
\(552\) 0 0
\(553\) 46.0130 1.95667
\(554\) −9.04128 6.68937i −0.384127 0.284204i
\(555\) 0 0
\(556\) 22.8854 + 12.1649i 0.970556 + 0.515907i
\(557\) 13.9022 + 13.9022i 0.589056 + 0.589056i 0.937376 0.348320i \(-0.113248\pi\)
−0.348320 + 0.937376i \(0.613248\pi\)
\(558\) 0 0
\(559\) 65.9908i 2.79111i
\(560\) 32.5994 + 9.79383i 1.37758 + 0.413865i
\(561\) 0 0
\(562\) 34.9228 5.22135i 1.47313 0.220249i
\(563\) 4.81937 4.81937i 0.203112 0.203112i −0.598220 0.801332i \(-0.704125\pi\)
0.801332 + 0.598220i \(0.204125\pi\)
\(564\) 0 0
\(565\) 28.1797 23.0359i 1.18553 0.969126i
\(566\) 22.0152 29.7555i 0.925367 1.25072i
\(567\) 0 0
\(568\) −10.7163 22.4570i −0.449646 0.942275i
\(569\) 17.9682 0.753268 0.376634 0.926362i \(-0.377081\pi\)
0.376634 + 0.926362i \(0.377081\pi\)
\(570\) 0 0
\(571\) 3.94277 + 3.94277i 0.165000 + 0.165000i 0.784777 0.619778i \(-0.212777\pi\)
−0.619778 + 0.784777i \(0.712777\pi\)
\(572\) −3.85846 12.6151i −0.161330 0.527465i
\(573\) 0 0
\(574\) 2.06703 + 13.8253i 0.0862763 + 0.577056i
\(575\) −1.72138 + 8.48312i −0.0717865 + 0.353770i
\(576\) 0 0
\(577\) 16.1502i 0.672343i 0.941801 + 0.336172i \(0.109132\pi\)
−0.941801 + 0.336172i \(0.890868\pi\)
\(578\) −34.3040 + 5.12884i −1.42686 + 0.213331i
\(579\) 0 0
\(580\) −0.357875 1.79565i −0.0148599 0.0745602i
\(581\) 3.52082 + 3.52082i 0.146068 + 0.146068i
\(582\) 0 0
\(583\) 7.77137i 0.321857i
\(584\) 30.9693 14.7783i 1.28152 0.611532i
\(585\) 0 0
\(586\) −4.09512 + 5.53492i −0.169168 + 0.228645i
\(587\) 17.3882 + 17.3882i 0.717687 + 0.717687i 0.968131 0.250444i \(-0.0805767\pi\)
−0.250444 + 0.968131i \(0.580577\pi\)
\(588\) 0 0
\(589\) −11.6170 11.6170i −0.478669 0.478669i
\(590\) −1.22755 25.3892i −0.0505375 1.04526i
\(591\) 0 0
\(592\) −9.13193 1.77284i −0.375320 0.0728632i
\(593\) 18.7727 0.770904 0.385452 0.922728i \(-0.374045\pi\)
0.385452 + 0.922728i \(0.374045\pi\)
\(594\) 0 0
\(595\) −34.7067 42.4566i −1.42284 1.74055i
\(596\) 0.971723 + 0.516528i 0.0398033 + 0.0211578i
\(597\) 0 0
\(598\) −8.92037 + 12.0567i −0.364781 + 0.493034i
\(599\) 15.7898i 0.645154i 0.946543 + 0.322577i \(0.104549\pi\)
−0.946543 + 0.322577i \(0.895451\pi\)
\(600\) 0 0
\(601\) 19.1187i 0.779868i −0.920843 0.389934i \(-0.872498\pi\)
0.920843 0.389934i \(-0.127502\pi\)
\(602\) −46.6077 34.4836i −1.89959 1.40545i
\(603\) 0 0
\(604\) 24.0679 7.36140i 0.979310 0.299531i
\(605\) 13.9266 + 17.0364i 0.566197 + 0.692628i
\(606\) 0 0
\(607\) −20.4524 −0.830139 −0.415069 0.909790i \(-0.636243\pi\)
−0.415069 + 0.909790i \(0.636243\pi\)
\(608\) 1.03291 23.8182i 0.0418899 0.965954i
\(609\) 0 0
\(610\) 2.89142 0.139799i 0.117070 0.00566028i
\(611\) −22.2690 22.2690i −0.900907 0.900907i
\(612\) 0 0
\(613\) −0.158629 0.158629i −0.00640697 0.00640697i 0.703896 0.710303i \(-0.251442\pi\)
−0.710303 + 0.703896i \(0.751442\pi\)
\(614\) −21.6344 16.0067i −0.873094 0.645976i
\(615\) 0 0
\(616\) 10.9260 + 3.86693i 0.440222 + 0.155803i
\(617\) 28.8981i 1.16340i 0.813405 + 0.581698i \(0.197611\pi\)
−0.813405 + 0.581698i \(0.802389\pi\)
\(618\) 0 0
\(619\) −13.3003 13.3003i −0.534582 0.534582i 0.387350 0.921933i \(-0.373390\pi\)
−0.921933 + 0.387350i \(0.873390\pi\)
\(620\) 14.4990 + 9.68006i 0.582293 + 0.388760i
\(621\) 0 0
\(622\) 2.23112 + 14.9228i 0.0894597 + 0.598348i
\(623\) 50.5757i 2.02627i
\(624\) 0 0
\(625\) −23.0226 9.74467i −0.920905 0.389787i
\(626\) 14.4325 2.15782i 0.576838 0.0862437i
\(627\) 0 0
\(628\) −0.527602 + 0.992556i −0.0210536 + 0.0396073i
\(629\) 10.5970 + 10.5970i 0.422529 + 0.422529i
\(630\) 0 0
\(631\) −40.6293 −1.61743 −0.808713 0.588203i \(-0.799836\pi\)
−0.808713 + 0.588203i \(0.799836\pi\)
\(632\) 14.7279 + 30.8637i 0.585845 + 1.22769i
\(633\) 0 0
\(634\) −25.5152 18.8779i −1.01334 0.749738i
\(635\) 14.9107 12.1889i 0.591713 0.483703i
\(636\) 0 0
\(637\) 32.4136 32.4136i 1.28428 1.28428i
\(638\) −0.0921862 0.616584i −0.00364969 0.0244108i
\(639\) 0 0
\(640\) 3.86516 + 25.0012i 0.152784 + 0.988260i
\(641\) 2.75673i 0.108884i −0.998517 0.0544422i \(-0.982662\pi\)
0.998517 0.0544422i \(-0.0173380\pi\)
\(642\) 0 0
\(643\) −14.9757 14.9757i −0.590582 0.590582i 0.347206 0.937789i \(-0.387130\pi\)
−0.937789 + 0.347206i \(0.887130\pi\)
\(644\) −3.85398 12.6005i −0.151868 0.496529i
\(645\) 0 0
\(646\) −22.8439 + 30.8756i −0.898782 + 1.21478i
\(647\) 35.4556 1.39390 0.696952 0.717117i \(-0.254539\pi\)
0.696952 + 0.717117i \(0.254539\pi\)
\(648\) 0 0
\(649\) 8.65505i 0.339740i
\(650\) −29.0027 32.1738i −1.13758 1.26196i
\(651\) 0 0
\(652\) −19.0203 10.1104i −0.744894 0.395955i
\(653\) 24.6436 + 24.6436i 0.964380 + 0.964380i 0.999387 0.0350074i \(-0.0111455\pi\)
−0.0350074 + 0.999387i \(0.511145\pi\)
\(654\) 0 0
\(655\) 22.3302 + 2.24275i 0.872513 + 0.0876314i
\(656\) −8.61184 + 5.81170i −0.336236 + 0.226909i
\(657\) 0 0
\(658\) 27.3648 4.09133i 1.06679 0.159497i
\(659\) 27.1141 + 27.1141i 1.05621 + 1.05621i 0.998323 + 0.0578905i \(0.0184374\pi\)
0.0578905 + 0.998323i \(0.481563\pi\)
\(660\) 0 0
\(661\) −20.5120 + 20.5120i −0.797822 + 0.797822i −0.982752 0.184929i \(-0.940794\pi\)
0.184929 + 0.982752i \(0.440794\pi\)
\(662\) 15.7595 + 11.6600i 0.612512 + 0.453179i
\(663\) 0 0
\(664\) −1.23468 + 3.48858i −0.0479148 + 0.135383i
\(665\) −35.6842 3.58396i −1.38377 0.138980i
\(666\) 0 0
\(667\) −0.501183 + 0.501183i −0.0194059 + 0.0194059i
\(668\) −4.46434 + 1.36546i −0.172731 + 0.0528313i
\(669\) 0 0
\(670\) −40.6187 + 1.96389i −1.56924 + 0.0758717i
\(671\) 0.985671 0.0380514
\(672\) 0 0
\(673\) 27.8896i 1.07506i −0.843243 0.537532i \(-0.819357\pi\)
0.843243 0.537532i \(-0.180643\pi\)
\(674\) −2.86120 19.1370i −0.110209 0.737130i
\(675\) 0 0
\(676\) −14.3471 46.9074i −0.551810 1.80413i
\(677\) −1.09939 + 1.09939i −0.0422530 + 0.0422530i −0.727918 0.685665i \(-0.759512\pi\)
0.685665 + 0.727918i \(0.259512\pi\)
\(678\) 0 0
\(679\) −36.3877 −1.39643
\(680\) 17.3693 36.8695i 0.666081 1.41388i
\(681\) 0 0
\(682\) 4.77193 + 3.53060i 0.182726 + 0.135194i
\(683\) 16.3630 + 16.3630i 0.626115 + 0.626115i 0.947088 0.320974i \(-0.104010\pi\)
−0.320974 + 0.947088i \(0.604010\pi\)
\(684\) 0 0
\(685\) −13.1698 16.1105i −0.503190 0.615552i
\(686\) 0.384379 + 2.57091i 0.0146757 + 0.0981577i
\(687\) 0 0
\(688\) 8.21200 42.3002i 0.313079 1.61268i
\(689\) 44.2131i 1.68439i
\(690\) 0 0
\(691\) −1.38110 + 1.38110i −0.0525396 + 0.0525396i −0.732888 0.680349i \(-0.761828\pi\)
0.680349 + 0.732888i \(0.261828\pi\)
\(692\) −1.56134 0.829945i −0.0593534 0.0315498i
\(693\) 0 0
\(694\) 25.0513 + 18.5347i 0.950934 + 0.703567i
\(695\) 28.8318 + 2.89574i 1.09365 + 0.109842i
\(696\) 0 0
\(697\) 16.7375 0.633980
\(698\) 7.46607 + 5.52392i 0.282595 + 0.209084i
\(699\) 0 0
\(700\) 37.8790 3.67144i 1.43169 0.138767i
\(701\) −21.1577 + 21.1577i −0.799115 + 0.799115i −0.982956 0.183841i \(-0.941147\pi\)
0.183841 + 0.982956i \(0.441147\pi\)
\(702\) 0 0
\(703\) 9.80115 0.369657
\(704\) 0.903429 + 8.56647i 0.0340493 + 0.322861i
\(705\) 0 0
\(706\) 27.7292 4.14582i 1.04360 0.156030i
\(707\) −44.6608 + 44.6608i −1.67964 + 1.67964i
\(708\) 0 0
\(709\) 3.59943 3.59943i 0.135180 0.135180i −0.636279 0.771459i \(-0.719527\pi\)
0.771459 + 0.636279i \(0.219527\pi\)
\(710\) −20.5987 18.6987i −0.773054 0.701748i
\(711\) 0 0
\(712\) 33.9242 16.1884i 1.27136 0.606684i
\(713\) 6.74861i 0.252738i
\(714\) 0 0
\(715\) −9.33478 11.4192i −0.349101 0.427055i
\(716\) 10.8200 + 5.75147i 0.404363 + 0.214942i
\(717\) 0 0
\(718\) 4.21251 + 28.1752i 0.157209 + 1.05149i
\(719\) 24.6502 0.919298 0.459649 0.888101i \(-0.347975\pi\)
0.459649 + 0.888101i \(0.347975\pi\)
\(720\) 0 0
\(721\) 37.0092 1.37830
\(722\) −0.258969 1.73211i −0.00963784 0.0644623i
\(723\) 0 0
\(724\) 1.10762 2.08371i 0.0411642 0.0774406i
\(725\) −1.13073 1.70645i −0.0419944 0.0633759i
\(726\) 0 0
\(727\) 47.1505i 1.74872i −0.485281 0.874358i \(-0.661283\pi\)
0.485281 0.874358i \(-0.338717\pi\)
\(728\) 62.1606 + 21.9999i 2.30383 + 0.815370i
\(729\) 0 0
\(730\) 25.7864 28.4066i 0.954398 1.05138i
\(731\) −49.0865 + 49.0865i −1.81553 + 1.81553i
\(732\) 0 0
\(733\) 12.4236 12.4236i 0.458875 0.458875i −0.439411 0.898286i \(-0.644813\pi\)
0.898286 + 0.439411i \(0.144813\pi\)
\(734\) 50.5083 7.55155i 1.86429 0.278733i
\(735\) 0 0
\(736\) 7.21832 6.61828i 0.266071 0.243953i
\(737\) −13.8467 −0.510050
\(738\) 0 0
\(739\) −10.3865 + 10.3865i −0.382075 + 0.382075i −0.871849 0.489774i \(-0.837079\pi\)
0.489774 + 0.871849i \(0.337079\pi\)
\(740\) −10.1998 + 2.03284i −0.374953 + 0.0747286i
\(741\) 0 0
\(742\) −31.2267 23.1037i −1.14637 0.848163i
\(743\) −34.4041 −1.26216 −0.631082 0.775716i \(-0.717389\pi\)
−0.631082 + 0.775716i \(0.717389\pi\)
\(744\) 0 0
\(745\) 1.22421 + 0.122954i 0.0448516 + 0.00450470i
\(746\) 2.60763 + 1.92931i 0.0954721 + 0.0706370i
\(747\) 0 0
\(748\) 6.51356 12.2537i 0.238159 0.448040i
\(749\) −31.0440 + 31.0440i −1.13432 + 1.13432i
\(750\) 0 0
\(751\) 6.29639i 0.229759i 0.993379 + 0.114879i \(0.0366481\pi\)
−0.993379 + 0.114879i \(0.963352\pi\)
\(752\) 11.5033 + 17.0456i 0.419481 + 0.621590i
\(753\) 0 0
\(754\) −0.524469 3.50789i −0.0191000 0.127750i
\(755\) 21.7863 17.8095i 0.792884 0.648153i
\(756\) 0 0
\(757\) −13.9886 13.9886i −0.508425 0.508425i 0.405618 0.914043i \(-0.367056\pi\)
−0.914043 + 0.405618i \(0.867056\pi\)
\(758\) 17.5943 + 13.0175i 0.639054 + 0.472817i
\(759\) 0 0
\(760\) −9.01787 25.0827i −0.327113 0.909845i
\(761\) 45.7177 1.65726 0.828632 0.559793i \(-0.189119\pi\)
0.828632 + 0.559793i \(0.189119\pi\)
\(762\) 0 0
\(763\) −33.2094 + 33.2094i −1.20226 + 1.20226i
\(764\) −34.7179 + 10.6188i −1.25605 + 0.384174i
\(765\) 0 0
\(766\) −6.54162 43.7534i −0.236358 1.58087i
\(767\) 49.2406i 1.77797i
\(768\) 0 0
\(769\) −34.9628 −1.26079 −0.630395 0.776274i \(-0.717107\pi\)
−0.630395 + 0.776274i \(0.717107\pi\)
\(770\) 12.9430 0.625788i 0.466434 0.0225518i
\(771\) 0 0
\(772\) −8.93007 29.1967i −0.321400 1.05081i
\(773\) −30.9289 + 30.9289i −1.11243 + 1.11243i −0.119614 + 0.992820i \(0.538166\pi\)
−0.992820 + 0.119614i \(0.961834\pi\)
\(774\) 0 0
\(775\) 19.1018 + 3.87611i 0.686158 + 0.139234i
\(776\) −11.6470 24.4075i −0.418105 0.876177i
\(777\) 0 0
\(778\) 6.59404 + 4.87873i 0.236408 + 0.174911i
\(779\) 7.74028 7.74028i 0.277324 0.277324i
\(780\) 0 0
\(781\) −6.69814 6.69814i −0.239678 0.239678i
\(782\) −15.6035 + 2.33290i −0.557981 + 0.0834244i
\(783\) 0 0
\(784\) −24.8108 + 16.7436i −0.886100 + 0.597985i
\(785\) −0.125590 + 1.25046i −0.00448251 + 0.0446307i
\(786\) 0 0
\(787\) 12.2948 + 12.2948i 0.438261 + 0.438261i 0.891427 0.453165i \(-0.149705\pi\)
−0.453165 + 0.891427i \(0.649705\pi\)
\(788\) −0.381301 + 0.717326i −0.0135833 + 0.0255537i
\(789\) 0 0
\(790\) 28.3097 + 25.6985i 1.00721 + 0.914310i
\(791\) 61.9457i 2.20253i