Properties

Label 144.2.l.a.107.1
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 107.1
Root \(0.944649 + 1.05244i\) of defining polynomial
Character \(\chi\) \(=\) 144.107
Dual form 144.2.l.a.35.1

$q$-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 −0.998372 0.0570377i \(-0.981834\pi\)
0.0570377 + 0.998372i \(0.481834\pi\)
\(6\) 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 0.738861 0.673858i \(-0.235364\pi\)
−0.673858 + 0.738861i \(0.735364\pi\)
\(12\) 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 \(0.0925661\pi\)
−0.958013 + 0.286724i \(0.907434\pi\)
\(18\) 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 \(-0.941412\pi\)
0.983109 0.183023i \(-0.0585881\pi\)
\(24\) 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 \(0.00942341\pi\)
0.0296002 + 0.999562i \(0.490577\pi\)
\(30\) 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 \(-0.789290\pi\)
−0.788785 + 0.614669i \(0.789290\pi\)
\(42\) 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 \(-0.591840\pi\)
−0.284536 + 0.958665i \(0.591840\pi\)
\(48\) 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 −0.495717 0.868484i \(-0.665095\pi\)
0.868484 + 0.495717i \(0.165095\pi\)
\(54\) 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 0.449871 0.893093i \(-0.351470\pi\)
−0.893093 + 0.449871i \(0.851470\pi\)
\(60\) 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 \(0.249289\pi\)
−0.708684 + 0.705526i \(0.750711\pi\)
\(72\) 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 −0.919621 0.392807i \(-0.871504\pi\)
0.392807 + 0.919621i \(0.371504\pi\)
\(84\) 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 \(-0.378918\pi\)
0.371282 + 0.928520i \(0.378918\pi\)
\(90\) 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 −0.789385 0.613899i \(-0.789600\pi\)
0.613899 + 0.789385i \(0.289600\pi\)
\(102\) 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 0.810766 0.585370i \(-0.199051\pi\)
−0.585370 + 0.810766i \(0.699051\pi\)
\(108\) 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 \(-0.968556\pi\)
0.995125 0.0986237i \(-0.0314440\pi\)
\(114\) 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 −0.938950 0.344053i \(-0.888200\pi\)
0.344053 + 0.938950i \(0.388200\pi\)
\(132\) 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 \(-0.299454\pi\)
0.589172 + 0.808008i \(0.299454\pi\)
\(138\) 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 −0.313667 0.949533i \(-0.601557\pi\)
0.949533 + 0.313667i \(0.101557\pi\)
\(150\) 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 \(0.284875\pi\)
−0.625548 + 0.780186i \(0.715125\pi\)
\(168\) 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 0.539288 0.842121i \(-0.318693\pi\)
−0.842121 + 0.539288i \(0.818693\pi\)
\(174\) 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 \(0.533704\pi\)
−0.994399 + 0.105688i \(0.966296\pi\)
\(180\) 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 \(-0.410153\pi\)
0.278528 + 0.960428i \(0.410153\pi\)
\(192\) 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 −0.441135 0.897441i \(-0.645424\pi\)
0.897441 + 0.441135i \(0.145424\pi\)
\(198\) 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 \(-0.470343\pi\)
0.995663 0.0930369i \(-0.0296574\pi\)
\(228\) 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 \(-0.511042\pi\)
−0.0346817 + 0.999398i \(0.511042\pi\)
\(234\) 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 \(-0.503265\pi\)
−0.0102560 + 0.999947i \(0.503265\pi\)
\(240\) 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 0.449765 0.893147i \(-0.351508\pi\)
−0.893147 + 0.449765i \(0.851508\pi\)
\(252\) 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 \(0.263069\pi\)
−0.677487 + 0.735535i \(0.736931\pi\)
\(258\) 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 \(-0.786787\pi\)
0.783928 0.620851i \(-0.213213\pi\)
\(264\) 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 0.919285 0.393592i \(-0.128768\pi\)
−0.393592 + 0.919285i \(0.628768\pi\)
\(270\) 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 \(-0.354380\pi\)
0.441688 + 0.897169i \(0.354380\pi\)
\(282\) 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 −0.268265 0.963345i \(-0.586450\pi\)
0.963345 + 0.268265i \(0.0864503\pi\)
\(294\) 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 \(-0.799555\pi\)
0.808195 0.588915i \(-0.200445\pi\)
\(312\) 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 \(-0.902096\pi\)
−0.302749 0.953070i \(1.40210\pi\)
\(318\) 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 \(0.0478471\pi\)
0.149751 + 0.988724i \(0.452153\pi\)
\(348\) 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 \(0.0902892\pi\)
−0.960040 + 0.279864i \(0.909711\pi\)
\(354\) 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 \(-0.899574\pi\)
0.950642 0.310289i \(-0.100426\pi\)
\(360\) 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 \(-0.216865\pi\)
0.776754 + 0.629805i \(0.216865\pi\)
\(384\) 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 −0.999910 0.0133943i \(-0.995736\pi\)
0.0133943 + 0.999910i \(0.495736\pi\)
\(390\) 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 \(0.190536\pi\)
−0.826133 + 0.563475i \(0.809464\pi\)
\(402\) 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 −0.449263 0.893400i \(-0.648313\pi\)
0.893400 + 0.449263i \(0.148313\pi\)
\(420\) 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 \(-0.765689\pi\)
−0.741085 + 0.671411i \(0.765689\pi\)
\(432\) 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 0.939980 0.341230i \(-0.110843\pi\)
−0.341230 + 0.939980i \(0.610843\pi\)
\(444\) 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 \(-0.924273\pi\)
0.971834 0.235665i \(-0.0757268\pi\)
\(450\) 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 0.957710 0.287734i \(-0.0929019\pi\)
−0.287734 + 0.957710i \(0.592902\pi\)
\(462\) 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 −0.809380 0.587285i \(-0.800197\pi\)
0.587285 + 0.809380i \(0.300197\pi\)
\(468\) 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 \(-0.678502\pi\)
−0.531847 + 0.846840i \(0.678502\pi\)
\(480\) 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 \(-0.935843\pi\)
−0.200194 0.979756i \(1.43584\pi\)
\(492\) 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 \(0.459488\pi\)
−0.126929 + 0.991912i \(0.540512\pi\)
\(504\) 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 0.918035 0.396499i \(-0.129775\pi\)
−0.396499 + 0.918035i \(0.629775\pi\)
\(510\) 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 \(-0.724759\pi\)
−0.648873 + 0.760897i \(0.724759\pi\)
\(522\) 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 \(-0.991016\pi\)
−0.0282205 0.999602i \(1.49102\pi\)
\(558\) 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 −0.335055 0.942198i \(-0.608755\pi\)
0.942198 + 0.335055i \(0.108755\pi\)
\(564\) 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 \(-0.251964\pi\)
0.702729 + 0.711457i \(0.251964\pi\)
\(570\) 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 0.968913 0.247401i \(-0.0795765\pi\)
−0.247401 + 0.968913i \(0.579576\pi\)
\(588\) 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 \(0.176657\pi\)
−0.849908 + 0.526930i \(0.823343\pi\)
\(594\) 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 \(-0.848225\pi\)
0.888461 0.458951i \(-0.151775\pi\)
\(600\) 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 \(-0.684118\pi\)
−0.546705 + 0.837325i \(0.684118\pi\)
\(618\) 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 \(-0.731772\pi\)
0.665477 0.746418i \(-0.268228\pi\)
\(642\) 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 \(0.000629993\pi\)
−0.999998 + 0.00197918i \(0.999370\pi\)
\(648\) 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 0.862446 0.506149i \(-0.168931\pi\)
−0.506149 + 0.862446i \(0.668931\pi\)
\(654\) 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 −0.931928 0.362643i \(-0.881874\pi\)
0.362643 + 0.931928i \(0.381874\pi\)
\(660\) 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 \(0.572889\pi\)
−0.973897 + 0.226992i \(0.927111\pi\)
\(678\) 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 0.358228 0.933634i \(-0.383381\pi\)
−0.933634 + 0.358228i \(0.883381\pi\)
\(684\) 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 0.107971 0.994154i \(-0.465565\pi\)
−0.994154 + 0.107971i \(0.965565\pi\)
\(702\) 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 \(-0.717153\pi\)
−0.630507 + 0.776184i \(0.717153\pi\)
\(720\) 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 \(0.210586\pi\)
−0.789025 + 0.614361i \(0.789414\pi\)
\(744\) 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 \(-0.493600\pi\)
0.0201037 + 0.999798i \(0.493600\pi\)
\(762\) 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 −0.985237 0.171196i \(-0.945237\pi\)
0.171196 + 0.985237i \(0.445237\pi\)
\(774\) 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
\(790\)