Properties

Label 144.2.l.a.107.8
Level $144$
Weight $2$
Character 144.107
Analytic conductor $1.150$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{14} + 6 x^{12} - 12 x^{10} + 33 x^{8} - 48 x^{6} + 96 x^{4} - 256 x^{2} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 107.8
Root \(-0.944649 - 1.05244i\) of defining polynomial
Character \(\chi\) \(=\) 144.107
Dual form 144.2.l.a.35.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.32068 + 0.505776i) q^{2} +(1.48838 + 1.33594i) q^{4} +(2.10489 - 2.10489i) q^{5} -4.40731 q^{7} +(1.28999 + 2.51713i) q^{8} +O(q^{10})\) \(q+(1.32068 + 0.505776i) q^{2} +(1.48838 + 1.33594i) q^{4} +(2.10489 - 2.10489i) q^{5} -4.40731 q^{7} +(1.28999 + 2.51713i) q^{8} +(3.84448 - 1.71528i) q^{10} +(-0.215589 - 0.215589i) q^{11} +(-2.73544 + 2.73544i) q^{13} +(-5.82064 - 2.22912i) q^{14} +(0.430552 + 3.97676i) q^{16} -2.36438i q^{17} +(0.758681 + 0.758681i) q^{19} +(5.94487 - 0.320879i) q^{20} +(-0.175684 - 0.393764i) q^{22} +1.75549i q^{23} -3.86110i q^{25} +(-4.99616 + 2.22912i) q^{26} +(-6.55976 - 5.88789i) q^{28} +(-5.54221 - 5.54221i) q^{29} -9.01709i q^{31} +(-1.44273 + 5.46978i) q^{32} +(1.19585 - 3.12259i) q^{34} +(-9.27690 + 9.27690i) q^{35} +(3.10242 + 3.10242i) q^{37} +(0.618250 + 1.38570i) q^{38} +(8.01355 + 2.58300i) q^{40} +10.1014 q^{41} +(-3.54621 + 3.54621i) q^{43} +(-0.0328654 - 0.608892i) q^{44} +(-0.887886 + 2.31844i) q^{46} +3.90136 q^{47} +12.4244 q^{49} +(1.95286 - 5.09927i) q^{50} +(-7.72575 + 0.417003i) q^{52} +(-2.71378 + 2.71378i) q^{53} -0.907583 q^{55} +(-5.68537 - 11.0938i) q^{56} +(-4.51635 - 10.1226i) q^{58} +(3.40445 + 3.40445i) q^{59} +(-1.75868 + 1.75868i) q^{61} +(4.56063 - 11.9087i) q^{62} +(-4.67187 + 6.49412i) q^{64} +11.5156i q^{65} +(9.11951 + 9.11951i) q^{67} +(3.15866 - 3.51910i) q^{68} +(-16.9438 + 7.55976i) q^{70} -11.8897i q^{71} +0.482639i q^{73} +(2.52817 + 5.66643i) q^{74} +(0.115657 + 2.14275i) q^{76} +(0.950169 + 0.950169i) q^{77} +6.88995i q^{79} +(9.27690 + 7.46437i) q^{80} +(13.3407 + 5.10904i) q^{82} +(4.79951 - 4.79951i) q^{83} +(-4.97676 - 4.97676i) q^{85} +(-6.47699 + 2.88981i) q^{86} +(0.264559 - 0.820773i) q^{88} -7.00534 q^{89} +(12.0559 - 12.0559i) q^{91} +(-2.34522 + 2.61284i) q^{92} +(5.15244 + 1.97322i) q^{94} +3.19387 q^{95} -3.34374 q^{97} +(16.4086 + 6.28397i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 8q^{10} - 16q^{16} + 16q^{19} - 40q^{22} - 24q^{28} + 24q^{34} + 72q^{40} - 32q^{43} + 40q^{46} + 16q^{49} + 24q^{52} - 64q^{55} + 24q^{58} - 32q^{61} - 48q^{64} - 16q^{67} - 72q^{70} + 80q^{82} - 32q^{85} + 48q^{88} + 48q^{91} + 72q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.32068 + 0.505776i 0.933860 + 0.357638i
\(3\) 0 0
\(4\) 1.48838 + 1.33594i 0.744190 + 0.667968i
\(5\) 2.10489 2.10489i 0.941334 0.941334i −0.0570377 0.998372i \(-0.518166\pi\)
0.998372 + 0.0570377i \(0.0181655\pi\)
\(6\) 0 0
\(7\) −4.40731 −1.66581 −0.832904 0.553418i \(-0.813323\pi\)
−0.832904 + 0.553418i \(0.813323\pi\)
\(8\) 1.28999 + 2.51713i 0.456079 + 0.889939i
\(9\) 0 0
\(10\) 3.84448 1.71528i 1.21573 0.542418i
\(11\) −0.215589 0.215589i −0.0650026 0.0650026i 0.673858 0.738861i \(-0.264636\pi\)
−0.738861 + 0.673858i \(0.764636\pi\)
\(12\) 0 0
\(13\) −2.73544 + 2.73544i −0.758675 + 0.758675i −0.976081 0.217406i \(-0.930240\pi\)
0.217406 + 0.976081i \(0.430240\pi\)
\(14\) −5.82064 2.22912i −1.55563 0.595756i
\(15\) 0 0
\(16\) 0.430552 + 3.97676i 0.107638 + 0.994190i
\(17\) 2.36438i 0.573447i −0.958013 0.286724i \(-0.907434\pi\)
0.958013 0.286724i \(-0.0925661\pi\)
\(18\) 0 0
\(19\) 0.758681 + 0.758681i 0.174053 + 0.174053i 0.788758 0.614704i \(-0.210725\pi\)
−0.614704 + 0.788758i \(0.710725\pi\)
\(20\) 5.94487 0.320879i 1.32931 0.0717507i
\(21\) 0 0
\(22\) −0.175684 0.393764i −0.0374560 0.0839508i
\(23\) 1.75549i 0.366045i 0.983109 + 0.183023i \(0.0585881\pi\)
−0.983109 + 0.183023i \(0.941412\pi\)
\(24\) 0 0
\(25\) 3.86110i 0.772221i
\(26\) −4.99616 + 2.22912i −0.979827 + 0.437165i
\(27\) 0 0
\(28\) −6.55976 5.88789i −1.23968 1.11271i
\(29\) −5.54221 5.54221i −1.02916 1.02916i −0.999562 0.0296002i \(-0.990577\pi\)
−0.0296002 0.999562i \(1.49058\pi\)
\(30\) 0 0
\(31\) 9.01709i 1.61952i −0.586763 0.809759i \(-0.699598\pi\)
0.586763 0.809759i \(-0.300402\pi\)
\(32\) −1.44273 + 5.46978i −0.255041 + 0.966930i
\(33\) 0 0
\(34\) 1.19585 3.12259i 0.205086 0.535520i
\(35\) −9.27690 + 9.27690i −1.56808 + 1.56808i
\(36\) 0 0
\(37\) 3.10242 + 3.10242i 0.510035 + 0.510035i 0.914537 0.404502i \(-0.132555\pi\)
−0.404502 + 0.914537i \(0.632555\pi\)
\(38\) 0.618250 + 1.38570i 0.100293 + 0.224789i
\(39\) 0 0
\(40\) 8.01355 + 2.58300i 1.26705 + 0.408408i
\(41\) 10.1014 1.57757 0.788785 0.614669i \(-0.210710\pi\)
0.788785 + 0.614669i \(0.210710\pi\)
\(42\) 0 0
\(43\) −3.54621 + 3.54621i −0.540792 + 0.540792i −0.923761 0.382969i \(-0.874901\pi\)
0.382969 + 0.923761i \(0.374901\pi\)
\(44\) −0.0328654 0.608892i −0.00495465 0.0917940i
\(45\) 0 0
\(46\) −0.887886 + 2.31844i −0.130912 + 0.341835i
\(47\) 3.90136 0.569072 0.284536 0.958665i \(-0.408160\pi\)
0.284536 + 0.958665i \(0.408160\pi\)
\(48\) 0 0
\(49\) 12.4244 1.77491
\(50\) 1.95286 5.09927i 0.276175 0.721146i
\(51\) 0 0
\(52\) −7.72575 + 0.417003i −1.07137 + 0.0578280i
\(53\) −2.71378 + 2.71378i −0.372766 + 0.372766i −0.868484 0.495717i \(-0.834905\pi\)
0.495717 + 0.868484i \(0.334905\pi\)
\(54\) 0 0
\(55\) −0.907583 −0.122378
\(56\) −5.68537 11.0938i −0.759740 1.48247i
\(57\) 0 0
\(58\) −4.51635 10.1226i −0.593026 1.32916i
\(59\) 3.40445 + 3.40445i 0.443222 + 0.443222i 0.893093 0.449871i \(-0.148530\pi\)
−0.449871 + 0.893093i \(0.648530\pi\)
\(60\) 0 0
\(61\) −1.75868 + 1.75868i −0.225176 + 0.225176i −0.810674 0.585498i \(-0.800899\pi\)
0.585498 + 0.810674i \(0.300899\pi\)
\(62\) 4.56063 11.9087i 0.579201 1.51240i
\(63\) 0 0
\(64\) −4.67187 + 6.49412i −0.583984 + 0.811765i
\(65\) 11.5156i 1.42833i
\(66\) 0 0
\(67\) 9.11951 + 9.11951i 1.11413 + 1.11413i 0.992587 + 0.121539i \(0.0387831\pi\)
0.121539 + 0.992587i \(0.461217\pi\)
\(68\) 3.15866 3.51910i 0.383044 0.426754i
\(69\) 0 0
\(70\) −16.9438 + 7.55976i −2.02518 + 0.903564i
\(71\) 11.8897i 1.41105i −0.708684 0.705526i \(-0.750711\pi\)
0.708684 0.705526i \(-0.249289\pi\)
\(72\) 0 0
\(73\) 0.482639i 0.0564886i 0.999601 + 0.0282443i \(0.00899163\pi\)
−0.999601 + 0.0282443i \(0.991008\pi\)
\(74\) 2.52817 + 5.66643i 0.293894 + 0.658710i
\(75\) 0 0
\(76\) 0.115657 + 2.14275i 0.0132667 + 0.245791i
\(77\) 0.950169 + 0.950169i 0.108282 + 0.108282i
\(78\) 0 0
\(79\) 6.88995i 0.775180i 0.921832 + 0.387590i \(0.126692\pi\)
−0.921832 + 0.387590i \(0.873308\pi\)
\(80\) 9.27690 + 7.46437i 1.03719 + 0.834542i
\(81\) 0 0
\(82\) 13.3407 + 5.10904i 1.47323 + 0.564199i
\(83\) 4.79951 4.79951i 0.526814 0.526814i −0.392807 0.919621i \(-0.628496\pi\)
0.919621 + 0.392807i \(0.128496\pi\)
\(84\) 0 0
\(85\) −4.97676 4.97676i −0.539805 0.539805i
\(86\) −6.47699 + 2.88981i −0.698432 + 0.311616i
\(87\) 0 0
\(88\) 0.264559 0.820773i 0.0282021 0.0874947i
\(89\) −7.00534 −0.742564 −0.371282 0.928520i \(-0.621082\pi\)
−0.371282 + 0.928520i \(0.621082\pi\)
\(90\) 0 0
\(91\) 12.0559 12.0559i 1.26381 1.26381i
\(92\) −2.34522 + 2.61284i −0.244506 + 0.272407i
\(93\) 0 0
\(94\) 5.15244 + 1.97322i 0.531434 + 0.203522i
\(95\) 3.19387 0.327685
\(96\) 0 0
\(97\) −3.34374 −0.339506 −0.169753 0.985487i \(-0.554297\pi\)
−0.169753 + 0.985487i \(0.554297\pi\)
\(98\) 16.4086 + 6.28397i 1.65752 + 0.634777i
\(99\) 0 0
\(100\) 5.15819 5.74679i 0.515819 0.574679i
\(101\) 1.76361 1.76361i 0.175486 0.175486i −0.613899 0.789385i \(-0.710400\pi\)
0.789385 + 0.613899i \(0.210400\pi\)
\(102\) 0 0
\(103\) −1.01709 −0.100217 −0.0501085 0.998744i \(-0.515957\pi\)
−0.0501085 + 0.998744i \(0.515957\pi\)
\(104\) −10.4141 3.35678i −1.02119 0.329159i
\(105\) 0 0
\(106\) −4.95660 + 2.21146i −0.481427 + 0.214796i
\(107\) −2.33152 2.33152i −0.225396 0.225396i 0.585370 0.810766i \(-0.300949\pi\)
−0.810766 + 0.585370i \(0.800949\pi\)
\(108\) 0 0
\(109\) −8.07918 + 8.07918i −0.773845 + 0.773845i −0.978776 0.204931i \(-0.934303\pi\)
0.204931 + 0.978776i \(0.434303\pi\)
\(110\) −1.19862 0.459034i −0.114284 0.0437672i
\(111\) 0 0
\(112\) −1.89758 17.5268i −0.179304 1.65613i
\(113\) 2.09677i 0.197247i 0.995125 + 0.0986237i \(0.0314440\pi\)
−0.995125 + 0.0986237i \(0.968556\pi\)
\(114\) 0 0
\(115\) 3.69511 + 3.69511i 0.344571 + 0.344571i
\(116\) −0.844880 15.6529i −0.0784451 1.45334i
\(117\) 0 0
\(118\) 2.77429 + 6.21808i 0.255395 + 0.572421i
\(119\) 10.4206i 0.955253i
\(120\) 0 0
\(121\) 10.9070i 0.991549i
\(122\) −3.21215 + 1.43315i −0.290814 + 0.129751i
\(123\) 0 0
\(124\) 12.0463 13.4209i 1.08179 1.20523i
\(125\) 2.39725 + 2.39725i 0.214416 + 0.214416i
\(126\) 0 0
\(127\) 10.2802i 0.912218i −0.889924 0.456109i \(-0.849243\pi\)
0.889924 0.456109i \(-0.150757\pi\)
\(128\) −9.45461 + 6.21372i −0.835677 + 0.549221i
\(129\) 0 0
\(130\) −5.82432 + 15.2084i −0.510826 + 1.33386i
\(131\) 6.80891 6.80891i 0.594897 0.594897i −0.344053 0.938950i \(-0.611800\pi\)
0.938950 + 0.344053i \(0.111800\pi\)
\(132\) 0 0
\(133\) −3.34374 3.34374i −0.289939 0.289939i
\(134\) 7.43151 + 16.6564i 0.641984 + 1.43889i
\(135\) 0 0
\(136\) 5.95146 3.05002i 0.510333 0.261537i
\(137\) −13.7922 −1.17834 −0.589172 0.808008i \(-0.700546\pi\)
−0.589172 + 0.808008i \(0.700546\pi\)
\(138\) 0 0
\(139\) −13.1195 + 13.1195i −1.11278 + 1.11278i −0.120010 + 0.992773i \(0.538293\pi\)
−0.992773 + 0.120010i \(0.961707\pi\)
\(140\) −26.2009 + 1.41421i −2.21438 + 0.119523i
\(141\) 0 0
\(142\) 6.01355 15.7025i 0.504646 1.31773i
\(143\) 1.17946 0.0986317
\(144\) 0 0
\(145\) −23.3314 −1.93757
\(146\) −0.244107 + 0.637410i −0.0202025 + 0.0527525i
\(147\) 0 0
\(148\) 0.472948 + 8.76222i 0.0388761 + 0.720250i
\(149\) −7.76174 + 7.76174i −0.635867 + 0.635867i −0.949533 0.313667i \(-0.898443\pi\)
0.313667 + 0.949533i \(0.398443\pi\)
\(150\) 0 0
\(151\) −0.202466 −0.0164765 −0.00823823 0.999966i \(-0.502622\pi\)
−0.00823823 + 0.999966i \(0.502622\pi\)
\(152\) −0.931009 + 2.88838i −0.0755148 + 0.234279i
\(153\) 0 0
\(154\) 0.774294 + 1.73544i 0.0623944 + 0.139846i
\(155\) −18.9800 18.9800i −1.52451 1.52451i
\(156\) 0 0
\(157\) 3.75868 3.75868i 0.299975 0.299975i −0.541029 0.841004i \(-0.681965\pi\)
0.841004 + 0.541029i \(0.181965\pi\)
\(158\) −3.48478 + 9.09941i −0.277234 + 0.723910i
\(159\) 0 0
\(160\) 8.47649 + 14.5501i 0.670125 + 1.15028i
\(161\) 7.73700i 0.609761i
\(162\) 0 0
\(163\) −13.2684 13.2684i −1.03926 1.03926i −0.999197 0.0400655i \(-0.987243\pi\)
−0.0400655 0.999197i \(-0.512757\pi\)
\(164\) 15.0347 + 13.4948i 1.17401 + 1.05377i
\(165\) 0 0
\(166\) 8.76608 3.91113i 0.680380 0.303562i
\(167\) 20.1644i 1.56037i −0.625548 0.780186i \(-0.715125\pi\)
0.625548 0.780186i \(-0.284875\pi\)
\(168\) 0 0
\(169\) 1.96528i 0.151175i
\(170\) −4.05557 9.08983i −0.311048 0.697158i
\(171\) 0 0
\(172\) −10.0156 + 0.540601i −0.763683 + 0.0412204i
\(173\) 3.98315 + 3.98315i 0.302833 + 0.302833i 0.842121 0.539288i \(-0.181307\pi\)
−0.539288 + 0.842121i \(0.681307\pi\)
\(174\) 0 0
\(175\) 17.0171i 1.28637i
\(176\) 0.764525 0.950169i 0.0576282 0.0716217i
\(177\) 0 0
\(178\) −9.25179 3.54313i −0.693451 0.265569i
\(179\) 14.7182 14.7182i 1.10009 1.10009i 0.105688 0.994399i \(-0.466296\pi\)
0.994399 0.105688i \(-0.0337044\pi\)
\(180\) 0 0
\(181\) 3.26456 + 3.26456i 0.242653 + 0.242653i 0.817947 0.575294i \(-0.195112\pi\)
−0.575294 + 0.817947i \(0.695112\pi\)
\(182\) 22.0196 9.82441i 1.63220 0.728233i
\(183\) 0 0
\(184\) −4.41880 + 2.26456i −0.325758 + 0.166945i
\(185\) 13.0605 0.960227
\(186\) 0 0
\(187\) −0.509736 + 0.509736i −0.0372756 + 0.0372756i
\(188\) 5.80671 + 5.21197i 0.423498 + 0.380122i
\(189\) 0 0
\(190\) 4.21808 + 1.61539i 0.306012 + 0.117192i
\(191\) −7.69868 −0.557057 −0.278528 0.960428i \(-0.589847\pi\)
−0.278528 + 0.960428i \(0.589847\pi\)
\(192\) 0 0
\(193\) −3.51736 −0.253185 −0.126593 0.991955i \(-0.540404\pi\)
−0.126593 + 0.991955i \(0.540404\pi\)
\(194\) −4.41601 1.69119i −0.317051 0.121420i
\(195\) 0 0
\(196\) 18.4922 + 16.5982i 1.32087 + 1.18559i
\(197\) −6.40456 + 6.40456i −0.456306 + 0.456306i −0.897441 0.441135i \(-0.854576\pi\)
0.441135 + 0.897441i \(0.354576\pi\)
\(198\) 0 0
\(199\) 23.3491 1.65517 0.827586 0.561339i \(-0.189714\pi\)
0.827586 + 0.561339i \(0.189714\pi\)
\(200\) 9.71889 4.98077i 0.687230 0.352194i
\(201\) 0 0
\(202\) 3.22115 1.43717i 0.226640 0.101119i
\(203\) 24.4262 + 24.4262i 1.71439 + 1.71439i
\(204\) 0 0
\(205\) 21.2623 21.2623i 1.48502 1.48502i
\(206\) −1.34325 0.514421i −0.0935887 0.0358414i
\(207\) 0 0
\(208\) −12.0559 9.70045i −0.835929 0.672605i
\(209\) 0.327127i 0.0226278i
\(210\) 0 0
\(211\) −6.63688 6.63688i −0.456901 0.456901i 0.440736 0.897637i \(-0.354718\pi\)
−0.897637 + 0.440736i \(0.854718\pi\)
\(212\) −7.66457 + 0.413701i −0.526405 + 0.0284131i
\(213\) 0 0
\(214\) −1.89996 4.25841i −0.129878 0.291099i
\(215\) 14.9287i 1.01813i
\(216\) 0 0
\(217\) 39.7411i 2.69780i
\(218\) −14.7563 + 6.58374i −0.999420 + 0.445907i
\(219\) 0 0
\(220\) −1.35083 1.21247i −0.0910728 0.0817448i
\(221\) 6.46763 + 6.46763i 0.435060 + 0.435060i
\(222\) 0 0
\(223\) 13.2219i 0.885406i 0.896668 + 0.442703i \(0.145980\pi\)
−0.896668 + 0.442703i \(0.854020\pi\)
\(224\) 6.35857 24.1070i 0.424850 1.61072i
\(225\) 0 0
\(226\) −1.06050 + 2.76916i −0.0705431 + 0.184201i
\(227\) −16.4029 + 16.4029i −1.08870 + 1.08870i −0.0930369 + 0.995663i \(0.529657\pi\)
−0.995663 + 0.0930369i \(0.970343\pi\)
\(228\) 0 0
\(229\) −4.98677 4.98677i −0.329535 0.329535i 0.522875 0.852410i \(-0.324860\pi\)
−0.852410 + 0.522875i \(0.824860\pi\)
\(230\) 3.01115 + 6.74895i 0.198549 + 0.445013i
\(231\) 0 0
\(232\) 6.80108 21.0998i 0.446513 1.38527i
\(233\) 1.05879 0.0693634 0.0346817 0.999398i \(-0.488958\pi\)
0.0346817 + 0.999398i \(0.488958\pi\)
\(234\) 0 0
\(235\) 8.21193 8.21193i 0.535687 0.535687i
\(236\) 0.518991 + 9.61525i 0.0337834 + 0.625900i
\(237\) 0 0
\(238\) −5.27048 + 13.7622i −0.341635 + 0.892072i
\(239\) 0.317107 0.0205119 0.0102560 0.999947i \(-0.496735\pi\)
0.0102560 + 0.999947i \(0.496735\pi\)
\(240\) 0 0
\(241\) 11.7334 0.755816 0.377908 0.925843i \(-0.376644\pi\)
0.377908 + 0.925843i \(0.376644\pi\)
\(242\) 5.51653 14.4047i 0.354616 0.925969i
\(243\) 0 0
\(244\) −4.96707 + 0.268101i −0.317984 + 0.0171634i
\(245\) 26.1520 26.1520i 1.67079 1.67079i
\(246\) 0 0
\(247\) −4.15065 −0.264100
\(248\) 22.6972 11.6319i 1.44127 0.738628i
\(249\) 0 0
\(250\) 1.95352 + 4.37847i 0.123552 + 0.276918i
\(251\) 7.02450 + 7.02450i 0.443382 + 0.443382i 0.893147 0.449765i \(-0.148492\pi\)
−0.449765 + 0.893147i \(0.648492\pi\)
\(252\) 0 0
\(253\) 0.378465 0.378465i 0.0237939 0.0237939i
\(254\) 5.19947 13.5768i 0.326244 0.851884i
\(255\) 0 0
\(256\) −15.6293 + 3.42440i −0.976828 + 0.214025i
\(257\) 23.5830i 1.47107i −0.677487 0.735535i \(-0.736931\pi\)
0.677487 0.735535i \(-0.263069\pi\)
\(258\) 0 0
\(259\) −13.6733 13.6733i −0.849621 0.849621i
\(260\) −15.3841 + 17.1396i −0.954081 + 1.06295i
\(261\) 0 0
\(262\) 12.4362 5.54859i 0.768309 0.342793i
\(263\) 20.1370i 1.24170i 0.783928 + 0.620851i \(0.213213\pi\)
−0.783928 + 0.620851i \(0.786787\pi\)
\(264\) 0 0
\(265\) 11.4244i 0.701796i
\(266\) −2.72482 6.10719i −0.167069 0.374456i
\(267\) 0 0
\(268\) 1.39022 + 25.7564i 0.0849213 + 1.57332i
\(269\) −8.62201 8.62201i −0.525693 0.525693i 0.393592 0.919285i \(-0.371232\pi\)
−0.919285 + 0.393592i \(0.871232\pi\)
\(270\) 0 0
\(271\) 2.18722i 0.132864i −0.997791 0.0664319i \(-0.978838\pi\)
0.997791 0.0664319i \(-0.0211615\pi\)
\(272\) 9.40259 1.01799i 0.570115 0.0617247i
\(273\) 0 0
\(274\) −18.2150 6.97575i −1.10041 0.421421i
\(275\) −0.832413 + 0.832413i −0.0501964 + 0.0501964i
\(276\) 0 0
\(277\) 8.64248 + 8.64248i 0.519277 + 0.519277i 0.917352 0.398076i \(-0.130322\pi\)
−0.398076 + 0.917352i \(0.630322\pi\)
\(278\) −23.9622 + 10.6911i −1.43716 + 0.641210i
\(279\) 0 0
\(280\) −35.3182 11.3841i −2.11067 0.680328i
\(281\) −14.8081 −0.883375 −0.441688 0.897169i \(-0.645620\pi\)
−0.441688 + 0.897169i \(0.645620\pi\)
\(282\) 0 0
\(283\) 6.12714 6.12714i 0.364221 0.364221i −0.501144 0.865364i \(-0.667087\pi\)
0.865364 + 0.501144i \(0.167087\pi\)
\(284\) 15.8839 17.6964i 0.942537 1.05009i
\(285\) 0 0
\(286\) 1.55769 + 0.596545i 0.0921082 + 0.0352744i
\(287\) −44.5199 −2.62793
\(288\) 0 0
\(289\) 11.4097 0.671158
\(290\) −30.8133 11.8005i −1.80942 0.692949i
\(291\) 0 0
\(292\) −0.644774 + 0.718350i −0.0377326 + 0.0420383i
\(293\) −11.8979 + 11.8979i −0.695080 + 0.695080i −0.963345 0.268265i \(-0.913550\pi\)
0.268265 + 0.963345i \(0.413550\pi\)
\(294\) 0 0
\(295\) 14.3320 0.834441
\(296\) −3.80711 + 11.8113i −0.221284 + 0.686517i
\(297\) 0 0
\(298\) −14.1765 + 6.32505i −0.821221 + 0.366401i
\(299\) −4.80204 4.80204i −0.277709 0.277709i
\(300\) 0 0
\(301\) 15.6293 15.6293i 0.900855 0.900855i
\(302\) −0.267393 0.102403i −0.0153867 0.00589261i
\(303\) 0 0
\(304\) −2.69044 + 3.34374i −0.154307 + 0.191777i
\(305\) 7.40365i 0.423932i
\(306\) 0 0
\(307\) 4.91467 + 4.91467i 0.280495 + 0.280495i 0.833306 0.552811i \(-0.186445\pi\)
−0.552811 + 0.833306i \(0.686445\pi\)
\(308\) 0.144848 + 2.68358i 0.00825350 + 0.152911i
\(309\) 0 0
\(310\) −15.4668 34.6660i −0.878455 1.96890i
\(311\) 20.7712i 1.17783i 0.808195 + 0.588915i \(0.200445\pi\)
−0.808195 + 0.588915i \(0.799555\pi\)
\(312\) 0 0
\(313\) 16.3897i 0.926400i −0.886254 0.463200i \(-0.846701\pi\)
0.886254 0.463200i \(-0.153299\pi\)
\(314\) 6.86506 3.06295i 0.387418 0.172853i
\(315\) 0 0
\(316\) −9.20453 + 10.2549i −0.517795 + 0.576881i
\(317\) 22.3592 + 22.3592i 1.25582 + 1.25582i 0.953070 + 0.302749i \(0.0979044\pi\)
0.302749 + 0.953070i \(0.402096\pi\)
\(318\) 0 0
\(319\) 2.38968i 0.133796i
\(320\) 3.83563 + 23.5032i 0.214418 + 1.31387i
\(321\) 0 0
\(322\) 3.91319 10.2181i 0.218074 0.569431i
\(323\) 1.79381 1.79381i 0.0998103 0.0998103i
\(324\) 0 0
\(325\) 10.5618 + 10.5618i 0.585865 + 0.585865i
\(326\) −10.8125 24.2342i −0.598846 1.34221i
\(327\) 0 0
\(328\) 13.0306 + 25.4265i 0.719497 + 1.40394i
\(329\) −17.1945 −0.947965
\(330\) 0 0
\(331\) −7.08533 + 7.08533i −0.389445 + 0.389445i −0.874490 0.485044i \(-0.838803\pi\)
0.485044 + 0.874490i \(0.338803\pi\)
\(332\) 13.5553 0.731659i 0.743945 0.0401550i
\(333\) 0 0
\(334\) 10.1987 26.6307i 0.558048 1.45717i
\(335\) 38.3911 2.09753
\(336\) 0 0
\(337\) −23.3314 −1.27094 −0.635472 0.772124i \(-0.719195\pi\)
−0.635472 + 0.772124i \(0.719195\pi\)
\(338\) 0.993991 2.59550i 0.0540660 0.141177i
\(339\) 0 0
\(340\) −0.758681 14.0559i −0.0411452 0.762291i
\(341\) −1.94399 + 1.94399i −0.105273 + 0.105273i
\(342\) 0 0
\(343\) −23.9070 −1.29086
\(344\) −13.5008 4.35170i −0.727916 0.234628i
\(345\) 0 0
\(346\) 3.24587 + 7.27503i 0.174499 + 0.391108i
\(347\) −21.2074 21.2074i −1.13847 1.13847i −0.988724 0.149751i \(-0.952153\pi\)
−0.149751 0.988724i \(1.45215\pi\)
\(348\) 0 0
\(349\) 5.38022 5.38022i 0.287996 0.287996i −0.548291 0.836288i \(-0.684721\pi\)
0.836288 + 0.548291i \(0.184721\pi\)
\(350\) −8.60684 + 22.4741i −0.460055 + 1.20129i
\(351\) 0 0
\(352\) 1.49026 0.868189i 0.0794314 0.0462746i
\(353\) 10.5163i 0.559727i −0.960040 0.279864i \(-0.909711\pi\)
0.960040 0.279864i \(-0.0902892\pi\)
\(354\) 0 0
\(355\) −25.0266 25.0266i −1.32827 1.32827i
\(356\) −10.4266 9.35868i −0.552609 0.496009i
\(357\) 0 0
\(358\) 26.8821 11.9939i 1.42076 0.633895i
\(359\) 11.7583i 0.620578i 0.950642 + 0.310289i \(0.100426\pi\)
−0.950642 + 0.310289i \(0.899574\pi\)
\(360\) 0 0
\(361\) 17.8488i 0.939411i
\(362\) 2.66029 + 5.96257i 0.139822 + 0.313386i
\(363\) 0 0
\(364\) 34.0498 1.83786i 1.78469 0.0963303i
\(365\) 1.01590 + 1.01590i 0.0531747 + 0.0531747i
\(366\) 0 0
\(367\) 3.49973i 0.182684i −0.995820 0.0913422i \(-0.970884\pi\)
0.995820 0.0913422i \(-0.0291157\pi\)
\(368\) −6.98117 + 0.755830i −0.363918 + 0.0394004i
\(369\) 0 0
\(370\) 17.2487 + 6.60570i 0.896718 + 0.343414i
\(371\) 11.9605 11.9605i 0.620957 0.620957i
\(372\) 0 0
\(373\) 19.1831 + 19.1831i 0.993262 + 0.993262i 0.999977 0.00671500i \(-0.00213747\pi\)
−0.00671500 + 0.999977i \(0.502137\pi\)
\(374\) −0.931009 + 0.415384i −0.0481413 + 0.0214790i
\(375\) 0 0
\(376\) 5.03271 + 9.82023i 0.259542 + 0.506440i
\(377\) 30.3208 1.56160
\(378\) 0 0
\(379\) −14.9977 + 14.9977i −0.770381 + 0.770381i −0.978173 0.207792i \(-0.933372\pi\)
0.207792 + 0.978173i \(0.433372\pi\)
\(380\) 4.75370 + 4.26681i 0.243860 + 0.218883i
\(381\) 0 0
\(382\) −10.1675 3.89381i −0.520213 0.199225i
\(383\) −30.4027 −1.55351 −0.776754 0.629805i \(-0.783135\pi\)
−0.776754 + 0.629805i \(0.783135\pi\)
\(384\) 0 0
\(385\) 4.00000 0.203859
\(386\) −4.64530 1.77900i −0.236440 0.0905486i
\(387\) 0 0
\(388\) −4.97676 4.46702i −0.252657 0.226779i
\(389\) 19.4571 19.4571i 0.986516 0.986516i −0.0133943 0.999910i \(-0.504264\pi\)
0.999910 + 0.0133943i \(0.00426365\pi\)
\(390\) 0 0
\(391\) 4.15065 0.209908
\(392\) 16.0273 + 31.2738i 0.809501 + 1.57957i
\(393\) 0 0
\(394\) −11.6976 + 5.21909i −0.589319 + 0.262934i
\(395\) 14.5026 + 14.5026i 0.729704 + 0.729704i
\(396\) 0 0
\(397\) −20.4339 + 20.4339i −1.02555 + 1.02555i −0.0258815 + 0.999665i \(0.508239\pi\)
−0.999665 + 0.0258815i \(0.991761\pi\)
\(398\) 30.8366 + 11.8094i 1.54570 + 0.591952i
\(399\) 0 0
\(400\) 15.3547 1.66241i 0.767734 0.0831203i
\(401\) 22.5671i 1.12695i −0.826133 0.563475i \(-0.809464\pi\)
0.826133 0.563475i \(-0.190536\pi\)
\(402\) 0 0
\(403\) 24.6657 + 24.6657i 1.22869 + 1.22869i
\(404\) 4.98099 0.268853i 0.247814 0.0133759i
\(405\) 0 0
\(406\) 19.9050 + 44.6134i 0.987867 + 2.21413i
\(407\) 1.33770i 0.0663073i
\(408\) 0 0
\(409\) 9.78286i 0.483731i 0.970310 + 0.241866i \(0.0777593\pi\)
−0.970310 + 0.241866i \(0.922241\pi\)
\(410\) 38.8346 17.3267i 1.91790 0.855702i
\(411\) 0 0
\(412\) −1.51382 1.35877i −0.0745805 0.0669417i
\(413\) −15.0045 15.0045i −0.738323 0.738323i
\(414\) 0 0
\(415\) 20.2048i 0.991817i
\(416\) −11.0158 18.9088i −0.540092 0.927079i
\(417\) 0 0
\(418\) 0.165453 0.432029i 0.00809257 0.0211312i
\(419\) −9.09125 + 9.09125i −0.444137 + 0.444137i −0.893400 0.449263i \(-0.851687\pi\)
0.449263 + 0.893400i \(0.351687\pi\)
\(420\) 0 0
\(421\) −17.9862 17.9862i −0.876595 0.876595i 0.116586 0.993181i \(-0.462805\pi\)
−0.993181 + 0.116586i \(0.962805\pi\)
\(422\) −5.40840 12.1220i −0.263277 0.590087i
\(423\) 0 0
\(424\) −10.3317 3.33019i −0.501750 0.161729i
\(425\) −9.12913 −0.442828
\(426\) 0 0
\(427\) 7.75106 7.75106i 0.375100 0.375100i
\(428\) −0.355427 6.58494i −0.0171802 0.318295i
\(429\) 0 0
\(430\) −7.55061 + 19.7161i −0.364123 + 0.950793i
\(431\) 30.7707 1.48217 0.741085 0.671411i \(-0.234311\pi\)
0.741085 + 0.671411i \(0.234311\pi\)
\(432\) 0 0
\(433\) 3.49735 0.168072 0.0840360 0.996463i \(-0.473219\pi\)
0.0840360 + 0.996463i \(0.473219\pi\)
\(434\) −20.1001 + 52.4852i −0.964837 + 2.51937i
\(435\) 0 0
\(436\) −22.8182 + 1.23163i −1.09279 + 0.0589843i
\(437\) −1.33186 + 1.33186i −0.0637113 + 0.0637113i
\(438\) 0 0
\(439\) −21.1290 −1.00843 −0.504216 0.863578i \(-0.668218\pi\)
−0.504216 + 0.863578i \(0.668218\pi\)
\(440\) −1.17077 2.28450i −0.0558142 0.108909i
\(441\) 0 0
\(442\) 5.27048 + 11.8128i 0.250691 + 0.561879i
\(443\) −12.6022 12.6022i −0.598750 0.598750i 0.341230 0.939980i \(-0.389157\pi\)
−0.939980 + 0.341230i \(0.889157\pi\)
\(444\) 0 0
\(445\) −14.7454 + 14.7454i −0.699001 + 0.699001i
\(446\) −6.68735 + 17.4619i −0.316655 + 0.826846i
\(447\) 0 0
\(448\) 20.5904 28.6216i 0.972805 1.35224i
\(449\) 9.98731i 0.471330i 0.971834 + 0.235665i \(0.0757268\pi\)
−0.971834 + 0.235665i \(0.924273\pi\)
\(450\) 0 0
\(451\) −2.17775 2.17775i −0.102546 0.102546i
\(452\) −2.80115 + 3.12079i −0.131755 + 0.146790i
\(453\) 0 0
\(454\) −29.9592 + 13.3668i −1.40605 + 0.627333i
\(455\) 50.7528i 2.37933i
\(456\) 0 0
\(457\) 15.2508i 0.713402i 0.934219 + 0.356701i \(0.116098\pi\)
−0.934219 + 0.356701i \(0.883902\pi\)
\(458\) −4.06372 9.10810i −0.189885 0.425594i
\(459\) 0 0
\(460\) 0.563300 + 10.4362i 0.0262640 + 0.486588i
\(461\) −14.3850 14.3850i −0.669976 0.669976i 0.287734 0.957710i \(-0.407098\pi\)
−0.957710 + 0.287734i \(0.907098\pi\)
\(462\) 0 0
\(463\) 22.1295i 1.02845i 0.857657 + 0.514223i \(0.171920\pi\)
−0.857657 + 0.514223i \(0.828080\pi\)
\(464\) 19.6538 24.4262i 0.912406 1.13396i
\(465\) 0 0
\(466\) 1.39832 + 0.535509i 0.0647757 + 0.0248070i
\(467\) 4.79951 4.79951i 0.222095 0.222095i −0.587285 0.809380i \(-0.699803\pi\)
0.809380 + 0.587285i \(0.199803\pi\)
\(468\) 0 0
\(469\) −40.1926 40.1926i −1.85592 1.85592i
\(470\) 14.9987 6.69192i 0.691839 0.308675i
\(471\) 0 0
\(472\) −4.17775 + 12.9611i −0.192297 + 0.596585i
\(473\) 1.52905 0.0703058
\(474\) 0 0
\(475\) 2.92934 2.92934i 0.134408 0.134408i
\(476\) −13.9212 + 15.5098i −0.638078 + 0.710890i
\(477\) 0 0
\(478\) 0.418796 + 0.160385i 0.0191553 + 0.00733584i
\(479\) 23.2801 1.06369 0.531847 0.846840i \(-0.321498\pi\)
0.531847 + 0.846840i \(0.321498\pi\)
\(480\) 0 0
\(481\) −16.9730 −0.773902
\(482\) 15.4961 + 5.93449i 0.705827 + 0.270309i
\(483\) 0 0
\(484\) 14.5711 16.2338i 0.662323 0.737901i
\(485\) −7.03820 + 7.03820i −0.319588 + 0.319588i
\(486\) 0 0
\(487\) 21.0748 0.954990 0.477495 0.878635i \(-0.341545\pi\)
0.477495 + 0.878635i \(0.341545\pi\)
\(488\) −6.69550 2.15815i −0.303091 0.0976949i
\(489\) 0 0
\(490\) 47.7654 21.3113i 2.15782 0.962746i
\(491\) 26.1459 + 26.1459i 1.17995 + 1.17995i 0.979756 + 0.200194i \(0.0641571\pi\)
0.200194 + 0.979756i \(0.435843\pi\)
\(492\) 0 0
\(493\) −13.1039 + 13.1039i −0.590170 + 0.590170i
\(494\) −5.48168 2.09930i −0.246632 0.0944521i
\(495\) 0 0
\(496\) 35.8588 3.88233i 1.61011 0.174322i
\(497\) 52.4018i 2.35054i
\(498\) 0 0
\(499\) 21.0195 + 21.0195i 0.940961 + 0.940961i 0.998352 0.0573910i \(-0.0182782\pi\)
−0.0573910 + 0.998352i \(0.518278\pi\)
\(500\) 0.365448 + 6.77059i 0.0163433 + 0.302790i
\(501\) 0 0
\(502\) 5.72427 + 12.8299i 0.255487 + 0.572628i
\(503\) 44.4925i 1.98382i −0.126929 0.991912i \(-0.540512\pi\)
0.126929 0.991912i \(-0.459488\pi\)
\(504\) 0 0
\(505\) 7.42440i 0.330382i
\(506\) 0.691249 0.308412i 0.0307298 0.0137106i
\(507\) 0 0
\(508\) 13.7336 15.3008i 0.609332 0.678864i
\(509\) −11.7664 11.7664i −0.521536 0.521536i 0.396499 0.918035i \(-0.370225\pi\)
−0.918035 + 0.396499i \(0.870225\pi\)
\(510\) 0 0
\(511\) 2.12714i 0.0940991i
\(512\) −22.3732 3.38237i −0.988765 0.149481i
\(513\) 0 0
\(514\) 11.9277 31.1456i 0.526110 1.37377i
\(515\) −2.14086 + 2.14086i −0.0943377 + 0.0943377i
\(516\) 0 0
\(517\) −0.841092 0.841092i −0.0369912 0.0369912i
\(518\) −11.1424 24.9737i −0.489570 1.09728i
\(519\) 0 0
\(520\) −28.9862 + 14.8550i −1.27113 + 0.651433i
\(521\) 29.6216 1.29775 0.648873 0.760897i \(-0.275241\pi\)
0.648873 + 0.760897i \(0.275241\pi\)
\(522\) 0 0
\(523\) 4.96353 4.96353i 0.217040 0.217040i −0.590210 0.807250i \(-0.700955\pi\)
0.807250 + 0.590210i \(0.200955\pi\)
\(524\) 19.2305 1.03798i 0.840089 0.0453444i
\(525\) 0 0
\(526\) −10.1848 + 26.5945i −0.444080 + 1.15958i
\(527\) −21.3199 −0.928708
\(528\) 0 0
\(529\) 19.9183 0.866011
\(530\) −5.77819 + 15.0880i −0.250989 + 0.655379i
\(531\) 0 0
\(532\) −0.509736 9.44379i −0.0220998 0.409440i
\(533\) −27.6317 + 27.6317i −1.19686 + 1.19686i
\(534\) 0 0
\(535\) −9.81517 −0.424347
\(536\) −11.1909 + 34.7190i −0.483375 + 1.49963i
\(537\) 0 0
\(538\) −7.02609 15.7477i −0.302916 0.678932i
\(539\) −2.67857 2.67857i −0.115374 0.115374i
\(540\) 0 0
\(541\) 10.0792 10.0792i 0.433338 0.433338i −0.456424 0.889762i \(-0.650870\pi\)
0.889762 + 0.456424i \(0.150870\pi\)
\(542\) 1.10624 2.88861i 0.0475172 0.124076i
\(543\) 0 0
\(544\) 12.9327 + 3.41117i 0.554483 + 0.146253i
\(545\) 34.0115i 1.45689i
\(546\) 0 0
\(547\) 2.48797 + 2.48797i 0.106378 + 0.106378i 0.758293 0.651914i \(-0.226034\pi\)
−0.651914 + 0.758293i \(0.726034\pi\)
\(548\) −20.5280 18.4254i −0.876912 0.787096i
\(549\) 0 0
\(550\) −1.52036 + 0.678334i −0.0648285 + 0.0289243i
\(551\) 8.40953i 0.358258i
\(552\) 0 0
\(553\) 30.3662i 1.29130i
\(554\) 7.04277 + 15.7851i 0.299219 + 0.670645i
\(555\) 0 0
\(556\) −37.0537 + 2.00000i −1.57142 + 0.0848189i
\(557\) 24.2575 + 24.2575i 1.02782 + 1.02782i 0.999602 + 0.0282205i \(0.00898407\pi\)
0.0282205 + 0.999602i \(0.491016\pi\)
\(558\) 0 0
\(559\) 19.4009i 0.820570i
\(560\) −40.8862 32.8978i −1.72776 1.39019i
\(561\) 0 0
\(562\) −19.5567 7.48957i −0.824949 0.315928i
\(563\) −14.4061 + 14.4061i −0.607143 + 0.607143i −0.942198 0.335055i \(-0.891245\pi\)
0.335055 + 0.942198i \(0.391245\pi\)
\(564\) 0 0
\(565\) 4.41346 + 4.41346i 0.185676 + 0.185676i
\(566\) 11.1909 4.99302i 0.470390 0.209872i
\(567\) 0 0
\(568\) 29.9280 15.3376i 1.25575 0.643551i
\(569\) −33.5254 −1.40546 −0.702729 0.711457i \(-0.748036\pi\)
−0.702729 + 0.711457i \(0.748036\pi\)
\(570\) 0 0
\(571\) 14.5368 14.5368i 0.608348 0.608348i −0.334167 0.942514i \(-0.608455\pi\)
0.942514 + 0.334167i \(0.108455\pi\)
\(572\) 1.75549 + 1.57569i 0.0734008 + 0.0658828i
\(573\) 0 0
\(574\) −58.7965 22.5171i −2.45412 0.939847i
\(575\) 6.77813 0.282668
\(576\) 0 0
\(577\) 20.3662 0.847855 0.423927 0.905696i \(-0.360651\pi\)
0.423927 + 0.905696i \(0.360651\pi\)
\(578\) 15.0685 + 5.77075i 0.626768 + 0.240032i
\(579\) 0 0
\(580\) −34.7261 31.1693i −1.44192 1.29424i
\(581\) −21.1529 + 21.1529i −0.877571 + 0.877571i
\(582\) 0 0
\(583\) 1.17012 0.0484616
\(584\) −1.21486 + 0.622597i −0.0502714 + 0.0257633i
\(585\) 0 0
\(586\) −21.7309 + 9.69558i −0.897695 + 0.400521i
\(587\) −17.4809 17.4809i −0.721512 0.721512i 0.247401 0.968913i \(-0.420424\pi\)
−0.968913 + 0.247401i \(0.920424\pi\)
\(588\) 0 0
\(589\) 6.84109 6.84109i 0.281882 0.281882i
\(590\) 18.9279 + 7.24878i 0.779251 + 0.298428i
\(591\) 0 0
\(592\) −11.0018 + 13.6733i −0.452173 + 0.561971i
\(593\) 25.6632i 1.05386i −0.849908 0.526930i \(-0.823343\pi\)
0.849908 0.526930i \(-0.176657\pi\)
\(594\) 0 0
\(595\) 21.9341 + 21.9341i 0.899212 + 0.899212i
\(596\) −21.9216 + 1.18324i −0.897944 + 0.0484672i
\(597\) 0 0
\(598\) −3.91319 8.77071i −0.160022 0.358661i
\(599\) 22.4652i 0.917902i 0.888461 + 0.458951i \(0.151775\pi\)
−0.888461 + 0.458951i \(0.848225\pi\)
\(600\) 0 0
\(601\) 31.8106i 1.29758i −0.760967 0.648790i \(-0.775275\pi\)
0.760967 0.648790i \(-0.224725\pi\)
\(602\) 28.5461 12.7363i 1.16345 0.519093i
\(603\) 0 0
\(604\) −0.301347 0.270482i −0.0122616 0.0110057i
\(605\) −22.9581 22.9581i −0.933379 0.933379i
\(606\) 0 0
\(607\) 14.9829i 0.608138i −0.952650 0.304069i \(-0.901655\pi\)
0.952650 0.304069i \(-0.0983453\pi\)
\(608\) −5.24439 + 3.05525i −0.212688 + 0.123907i
\(609\) 0 0
\(610\) −3.74459 + 9.77784i −0.151614 + 0.395893i
\(611\) −10.6720 + 10.6720i −0.431741 + 0.431741i
\(612\) 0 0
\(613\) 25.6734 + 25.6734i 1.03694 + 1.03694i 0.999291 + 0.0376494i \(0.0119870\pi\)
0.0376494 + 0.999291i \(0.488013\pi\)
\(614\) 4.00497 + 8.97642i 0.161627 + 0.362259i
\(615\) 0 0
\(616\) −1.16599 + 3.61740i −0.0469792 + 0.145749i
\(617\) 27.1598 1.09341 0.546705 0.837325i \(-0.315882\pi\)
0.546705 + 0.837325i \(0.315882\pi\)
\(618\) 0 0
\(619\) −29.4244 + 29.4244i −1.18267 + 1.18267i −0.203616 + 0.979051i \(0.565269\pi\)
−0.979051 + 0.203616i \(0.934731\pi\)
\(620\) −2.89339 53.6054i −0.116202 2.15285i
\(621\) 0 0
\(622\) −10.5056 + 27.4321i −0.421236 + 1.09993i
\(623\) 30.8747 1.23697
\(624\) 0 0
\(625\) 29.3974 1.17590
\(626\) 8.28952 21.6455i 0.331316 0.865128i
\(627\) 0 0
\(628\) 10.6157 0.572991i 0.423613 0.0228648i
\(629\) 7.33532 7.33532i 0.292478 0.292478i
\(630\) 0 0
\(631\) −7.84697 −0.312383 −0.156191 0.987727i \(-0.549922\pi\)
−0.156191 + 0.987727i \(0.549922\pi\)
\(632\) −17.3429 + 8.88794i −0.689863 + 0.353543i
\(633\) 0 0
\(634\) 18.2206 + 40.8381i 0.723631 + 1.62189i
\(635\) −21.6386 21.6386i −0.858702 0.858702i
\(636\) 0 0
\(637\) −33.9862 + 33.9862i −1.34658 + 1.34658i
\(638\) −1.20864 + 3.15600i −0.0478507 + 0.124947i
\(639\) 0 0
\(640\) −6.82171 + 32.9801i −0.269652 + 1.30365i
\(641\) 37.7956i 1.49284i 0.665477 + 0.746418i \(0.268228\pi\)
−0.665477 + 0.746418i \(0.731772\pi\)
\(642\) 0 0
\(643\) 27.3026 + 27.3026i 1.07671 + 1.07671i 0.996802 + 0.0799071i \(0.0254624\pi\)
0.0799071 + 0.996802i \(0.474538\pi\)
\(644\) 10.3361 11.5156i 0.407301 0.453778i
\(645\) 0 0
\(646\) 3.27632 1.46178i 0.128905 0.0575130i
\(647\) 0.100686i 0.00395836i −0.999998 0.00197918i \(-0.999370\pi\)
0.999998 0.00197918i \(-0.000629993\pi\)
\(648\) 0 0
\(649\) 1.46793i 0.0576212i
\(650\) 8.60684 + 19.2907i 0.337588 + 0.756643i
\(651\) 0 0
\(652\) −2.02270 37.4742i −0.0792150 1.46760i
\(653\) −9.10477 9.10477i −0.356297 0.356297i 0.506149 0.862446i \(-0.331069\pi\)
−0.862446 + 0.506149i \(0.831069\pi\)
\(654\) 0 0
\(655\) 28.6640i 1.11999i
\(656\) 4.34917 + 40.1708i 0.169806 + 1.56840i
\(657\) 0 0
\(658\) −22.7084 8.69659i −0.885267 0.339028i
\(659\) 14.6141 14.6141i 0.569285 0.569285i −0.362643 0.931928i \(-0.618126\pi\)
0.931928 + 0.362643i \(0.118126\pi\)
\(660\) 0 0
\(661\) 5.87057 + 5.87057i 0.228339 + 0.228339i 0.811998 0.583660i \(-0.198380\pi\)
−0.583660 + 0.811998i \(0.698380\pi\)
\(662\) −12.9410 + 5.77385i −0.502968 + 0.224407i
\(663\) 0 0
\(664\) 18.2723 + 5.88968i 0.709102 + 0.228564i
\(665\) −14.0764 −0.545860
\(666\) 0 0
\(667\) 9.72929 9.72929i 0.376720 0.376720i
\(668\) 26.9384 30.0124i 1.04228 1.16121i
\(669\) 0 0
\(670\) 50.7023 + 19.4173i 1.95880 + 0.750156i
\(671\) 0.758305 0.0292741
\(672\) 0 0
\(673\) −27.3515 −1.05432 −0.527161 0.849766i \(-0.676743\pi\)
−0.527161 + 0.849766i \(0.676743\pi\)
\(674\) −30.8133 11.8005i −1.18688 0.454538i
\(675\) 0 0
\(676\) 2.62548 2.92508i 0.100980 0.112503i
\(677\) 31.2462 31.2462i 1.20089 1.20089i 0.226992 0.973897i \(-0.427111\pi\)
0.973897 0.226992i \(-0.0728891\pi\)
\(678\) 0 0
\(679\) 14.7369 0.565551
\(680\) 6.10719 18.9471i 0.234200 0.726588i
\(681\) 0 0
\(682\) −3.55061 + 1.58416i −0.135960 + 0.0606606i
\(683\) 15.0378 + 15.0378i 0.575406 + 0.575406i 0.933634 0.358228i \(-0.116619\pi\)
−0.358228 + 0.933634i \(0.616619\pi\)
\(684\) 0 0
\(685\) −29.0310 + 29.0310i −1.10922 + 1.10922i
\(686\) −31.5735 12.0916i −1.20548 0.461660i
\(687\) 0 0
\(688\) −15.6293 12.5756i −0.595860 0.479440i
\(689\) 14.8468i 0.565617i
\(690\) 0 0
\(691\) 4.24894 + 4.24894i 0.161637 + 0.161637i 0.783292 0.621654i \(-0.213539\pi\)
−0.621654 + 0.783292i \(0.713539\pi\)
\(692\) 0.607209 + 11.2497i 0.0230826 + 0.427648i
\(693\) 0 0
\(694\) −17.2820 38.7344i −0.656014 1.47034i
\(695\) 55.2302i 2.09500i
\(696\) 0 0
\(697\) 23.8835i 0.904653i
\(698\) 9.82672 4.38435i 0.371947 0.165950i
\(699\) 0 0
\(700\) −22.7337 + 25.3279i −0.859255 + 0.957305i
\(701\) 23.4629 + 23.4629i 0.886183 + 0.886183i 0.994154 0.107971i \(-0.0344354\pi\)
−0.107971 + 0.994154i \(0.534435\pi\)
\(702\) 0 0
\(703\) 4.70750i 0.177547i
\(704\) 2.40727 0.392858i 0.0907274 0.0148064i
\(705\) 0 0
\(706\) 5.31891 13.8887i 0.200180 0.522707i
\(707\) −7.77278 + 7.77278i −0.292326 + 0.292326i
\(708\) 0 0
\(709\) 2.79314 + 2.79314i 0.104898 + 0.104898i 0.757608 0.652710i \(-0.226368\pi\)
−0.652710 + 0.757608i \(0.726368\pi\)
\(710\) −20.3942 45.7099i −0.765380 1.71546i
\(711\) 0 0
\(712\) −9.03679 17.6333i −0.338668 0.660837i
\(713\) 15.8294 0.592816
\(714\) 0 0
\(715\) 2.48264 2.48264i 0.0928454 0.0928454i
\(716\) 41.5687 2.24371i 1.55350 0.0838512i
\(717\) 0 0
\(718\) −5.94706 + 15.5289i −0.221942 + 0.579533i
\(719\) 33.8130 1.26101 0.630507 0.776184i \(-0.282847\pi\)
0.630507 + 0.776184i \(0.282847\pi\)
\(720\) 0 0
\(721\) 4.48264 0.166942
\(722\) 9.02751 23.5725i 0.335969 0.877279i
\(723\) 0 0
\(724\) 0.497665 + 9.22015i 0.0184956 + 0.342664i
\(725\) −21.3990 + 21.3990i −0.794740 + 0.794740i
\(726\) 0 0
\(727\) −2.42732 −0.0900245 −0.0450122 0.998986i \(-0.514333\pi\)
−0.0450122 + 0.998986i \(0.514333\pi\)
\(728\) 45.8984 + 14.7944i 1.70111 + 0.548315i
\(729\) 0 0
\(730\) 0.827859 + 1.85550i 0.0306404 + 0.0686750i
\(731\) 8.38460 + 8.38460i 0.310115 + 0.310115i
\(732\) 0 0
\(733\) 16.8596 16.8596i 0.622725 0.622725i −0.323503 0.946227i \(-0.604860\pi\)
0.946227 + 0.323503i \(0.104860\pi\)
\(734\) 1.77008 4.62202i 0.0653349 0.170602i
\(735\) 0 0
\(736\) −9.60215 2.53270i −0.353940 0.0933566i
\(737\) 3.93214i 0.144842i
\(738\) 0 0
\(739\) 25.2243 + 25.2243i 0.927892 + 0.927892i 0.997570 0.0696780i \(-0.0221972\pi\)
−0.0696780 + 0.997570i \(0.522197\pi\)
\(740\) 19.4390 + 17.4480i 0.714592 + 0.641401i
\(741\) 0 0
\(742\) 21.8453 9.74661i 0.801965 0.357809i
\(743\) 33.4926i 1.22872i −0.789025 0.614361i \(-0.789414\pi\)
0.789025 0.614361i \(-0.210586\pi\)
\(744\) 0 0
\(745\) 32.6752i 1.19713i
\(746\) 15.6323 + 35.0370i 0.572340 + 1.28280i
\(747\) 0 0
\(748\) −1.43965 + 0.0777065i −0.0526390 + 0.00284123i
\(749\) 10.2757 + 10.2757i 0.375467 + 0.375467i
\(750\) 0 0
\(751\) 17.9247i 0.654081i 0.945010 + 0.327040i \(0.106051\pi\)
−0.945010 + 0.327040i \(0.893949\pi\)
\(752\) 1.67974 + 15.5148i 0.0612538 + 0.565766i
\(753\) 0 0
\(754\) 40.0440 + 15.3355i 1.45832 + 0.558487i
\(755\) −0.426168 + 0.426168i −0.0155099 + 0.0155099i
\(756\) 0 0
\(757\) 3.10619 + 3.10619i 0.112896 + 0.112896i 0.761298 0.648402i \(-0.224562\pi\)
−0.648402 + 0.761298i \(0.724562\pi\)
\(758\) −27.3926 + 12.2217i −0.994945 + 0.443910i
\(759\) 0 0
\(760\) 4.12005 + 8.03939i 0.149450 + 0.291619i
\(761\) −1.10917 −0.0402073 −0.0201037 0.999798i \(-0.506400\pi\)
−0.0201037 + 0.999798i \(0.506400\pi\)
\(762\) 0 0
\(763\) 35.6075 35.6075i 1.28908 1.28908i
\(764\) −11.4586 10.2849i −0.414556 0.372096i
\(765\) 0 0
\(766\) −40.1522 15.3770i −1.45076 0.555593i
\(767\) −18.6254 −0.672523
\(768\) 0 0
\(769\) 22.4591 0.809897 0.404948 0.914340i \(-0.367289\pi\)
0.404948 + 0.914340i \(0.367289\pi\)
\(770\) 5.28271 + 2.02311i 0.190376 + 0.0729077i
\(771\) 0 0
\(772\) −5.23517 4.69897i −0.188418 0.169120i
\(773\) 22.6327 22.6327i 0.814041 0.814041i −0.171196 0.985237i \(-0.554763\pi\)
0.985237 + 0.171196i \(0.0547631\pi\)
\(774\) 0 0
\(775\) −34.8159 −1.25062
\(776\) −4.31338 8.41663i −0.154841 0.302139i
\(777\) 0 0
\(778\) 35.5376 15.8556i 1.27408 0.568453i
\(779\) 7.66372 + 7.66372i 0.274581 + 0.274581i
\(780\) 0 0
\(781\) −2.56330 + 2.56330i −0.0917221 + 0.0917221i
\(782\) 5.48168 + 2.09930i 0.196024 + 0.0750709i
\(783\) 0 0
\(784\) 5.34935 + 49.4089i 0.191048 + 1.76460i
\(785\) 15.8232i 0.564754i
\(786\) 0 0
\(787\) −38.6505 38.6505i −1.37774 1.37774i −0.848425 0.529315i \(-0.822449\pi\)
−0.529315 0.848425i \(-0.677551\pi\)
\(788\) −18.0885 + 0.976342i −0.644377 + 0.0347807i
\(789\) 0 0
\(790\) 11.8182