Properties

Label 144.2.l.a.35.8
Level $144$
Weight $2$
Character 144.35
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 35.8
Root \(-0.944649 + 1.05244i\) of defining polynomial
Character \(\chi\) \(=\) 144.35
Dual form 144.2.l.a.107.8

$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\)

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 \(-0.0181655\pi\)
−0.0570377 + 0.998372i \(0.518166\pi\)
\(6\) 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 \(-0.764636\pi\)
0.673858 + 0.738861i \(0.264636\pi\)
\(12\) 0 0
\(13\) −2.73544 2.73544i −0.758675 0.758675i 0.217406 0.976081i \(-0.430240\pi\)
−0.976081 + 0.217406i \(0.930240\pi\)
\(14\) −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 −0.614704 0.788758i \(-0.710725\pi\)
0.788758 + 0.614704i \(0.210725\pi\)
\(20\) 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 −0.0296002 + 0.999562i \(0.509423\pi\)
−0.999562 + 0.0296002i \(0.990577\pi\)
\(30\) 0 0
\(31\) 9.01709i 1.61952i 0.586763 + 0.809759i \(0.300402\pi\)
−0.586763 + 0.809759i \(0.699598\pi\)
\(32\) −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 −0.404502 0.914537i \(-0.632555\pi\)
0.914537 + 0.404502i \(0.132555\pi\)
\(38\) 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 0.382969 0.923761i \(-0.374901\pi\)
−0.923761 + 0.382969i \(0.874901\pi\)
\(44\) −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 0.495717 0.868484i \(-0.334905\pi\)
−0.868484 + 0.495717i \(0.834905\pi\)
\(54\) 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 \(-0.648530\pi\)
0.893093 + 0.449871i \(0.148530\pi\)
\(60\) 0 0
\(61\) −1.75868 1.75868i −0.225176 0.225176i 0.585498 0.810674i \(-0.300899\pi\)
−0.810674 + 0.585498i \(0.800899\pi\)
\(62\) 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 0.121539 0.992587i \(-0.461217\pi\)
0.992587 0.121539i \(-0.0387831\pi\)
\(68\) 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 \(-0.991008\pi\)
0.999601 0.0282443i \(-0.00899163\pi\)
\(74\) 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 \(-0.873308\pi\)
0.921832 0.387590i \(-0.126692\pi\)
\(80\) 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 \(-0.128496\pi\)
−0.392807 + 0.919621i \(0.628496\pi\)
\(84\) 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 0.789385 0.613899i \(-0.210400\pi\)
−0.613899 + 0.789385i \(0.710400\pi\)
\(102\) 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 \(-0.800949\pi\)
0.585370 + 0.810766i \(0.300949\pi\)
\(108\) 0 0
\(109\) −8.07918 8.07918i −0.773845 0.773845i 0.204931 0.978776i \(-0.434303\pi\)
−0.978776 + 0.204931i \(0.934303\pi\)
\(110\) −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 \(0.150757\pi\)
−0.889924 + 0.456109i \(0.849243\pi\)
\(128\) −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 \(-0.111800\pi\)
−0.344053 + 0.938950i \(0.611800\pi\)
\(132\) 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 −0.992773 0.120010i \(-0.961707\pi\)
−0.120010 0.992773i \(-0.538293\pi\)
\(140\) −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 \(-0.398443\pi\)
−0.949533 + 0.313667i \(0.898443\pi\)
\(150\) 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 0.841004 0.541029i \(-0.181965\pi\)
−0.541029 + 0.841004i \(0.681965\pi\)
\(158\) −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 −0.0400655 + 0.999197i \(0.512757\pi\)
−0.999197 + 0.0400655i \(0.987243\pi\)
\(164\) 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 \(-0.681307\pi\)
0.842121 + 0.539288i \(0.181307\pi\)
\(174\) 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 0.994399 + 0.105688i \(0.0337044\pi\)
0.105688 + 0.994399i \(0.466296\pi\)
\(180\) 0 0
\(181\) 3.26456 3.26456i 0.242653 0.242653i −0.575294 0.817947i \(-0.695112\pi\)
0.817947 + 0.575294i \(0.195112\pi\)
\(182\) 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 0.441135 0.897441i \(-0.354576\pi\)
−0.897441 + 0.441135i \(0.854576\pi\)
\(198\) 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 −0.897637 0.440736i \(-0.854718\pi\)
0.440736 + 0.897637i \(0.354718\pi\)
\(212\) −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 \(-0.854020\pi\)
0.896668 0.442703i \(-0.145980\pi\)
\(224\) 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 −0.995663 0.0930369i \(-0.970343\pi\)
−0.0930369 0.995663i \(1.47034\pi\)
\(228\) 0 0
\(229\) −4.98677 + 4.98677i −0.329535 + 0.329535i −0.852410 0.522875i \(-0.824860\pi\)
0.522875 + 0.852410i \(0.324860\pi\)
\(230\) 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 −0.449765 0.893147i \(-0.648492\pi\)
0.893147 + 0.449765i \(0.148492\pi\)
\(252\) 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 \(-0.871232\pi\)
0.393592 + 0.919285i \(0.371232\pi\)
\(270\) 0 0
\(271\) 2.18722i 0.132864i 0.997791 + 0.0664319i \(0.0211615\pi\)
−0.997791 + 0.0664319i \(0.978838\pi\)
\(272\) 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 −0.398076 0.917352i \(-0.630322\pi\)
0.917352 + 0.398076i \(0.130322\pi\)
\(278\) −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 0.865364 0.501144i \(-0.167087\pi\)
−0.501144 + 0.865364i \(0.667087\pi\)
\(284\) 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 \(-0.413550\pi\)
−0.963345 + 0.268265i \(0.913550\pi\)
\(294\) 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 −0.552811 0.833306i \(-0.686445\pi\)
0.833306 + 0.552811i \(0.186445\pi\)
\(308\) 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 \(0.153299\pi\)
−0.886254 + 0.463200i \(0.846701\pi\)
\(314\) 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 0.302749 0.953070i \(-0.402096\pi\)
0.953070 0.302749i \(-0.0979044\pi\)
\(318\) 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 0.485044 0.874490i \(-0.338803\pi\)
−0.874490 + 0.485044i \(0.838803\pi\)
\(332\) 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 −0.149751 + 0.988724i \(0.547847\pi\)
−0.988724 + 0.149751i \(0.952153\pi\)
\(348\) 0 0
\(349\) 5.38022 + 5.38022i 0.287996 + 0.287996i 0.836288 0.548291i \(-0.184721\pi\)
−0.548291 + 0.836288i \(0.684721\pi\)
\(350\) −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 \(0.0291157\pi\)
−0.995820 + 0.0913422i \(0.970884\pi\)
\(368\) −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 −0.00671500 0.999977i \(-0.502137\pi\)
0.999977 + 0.00671500i \(0.00213747\pi\)
\(374\) −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 0.207792 0.978173i \(-0.433372\pi\)
−0.978173 + 0.207792i \(0.933372\pi\)
\(380\) 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 0.999910 0.0133943i \(-0.00426365\pi\)
−0.0133943 + 0.999910i \(0.504264\pi\)
\(390\) 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 −0.999665 0.0258815i \(-0.991761\pi\)
−0.0258815 0.999665i \(-0.508239\pi\)
\(398\) 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 \(-0.922241\pi\)
0.970310 0.241866i \(-0.0777593\pi\)
\(410\) 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 \(-0.351687\pi\)
−0.893400 + 0.449263i \(0.851687\pi\)
\(420\) 0 0
\(421\) −17.9862 + 17.9862i −0.876595 + 0.876595i −0.993181 0.116586i \(-0.962805\pi\)
0.116586 + 0.993181i \(0.462805\pi\)
\(422\) −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 −0.939980 0.341230i \(-0.889157\pi\)
0.341230 + 0.939980i \(0.389157\pi\)
\(444\) 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 \(-0.883902\pi\)
0.934219 0.356701i \(-0.116098\pi\)
\(458\) −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 \(-0.907098\pi\)
0.287734 + 0.957710i \(0.407098\pi\)
\(462\) 0 0
\(463\) 22.1295i 1.02845i −0.857657 0.514223i \(-0.828080\pi\)
0.857657 0.514223i \(-0.171920\pi\)
\(464\) 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 \(-0.199803\pi\)
−0.587285 + 0.809380i \(0.699803\pi\)
\(468\) 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 0.200194 0.979756i \(-0.435843\pi\)
0.979756 0.200194i \(-0.0641571\pi\)
\(492\) 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 −0.0573910 0.998352i \(-0.518278\pi\)
0.998352 + 0.0573910i \(0.0182782\pi\)
\(500\) 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 \(-0.870225\pi\)
0.396499 + 0.918035i \(0.370225\pi\)
\(510\) 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 0.807250 0.590210i \(-0.200955\pi\)
−0.590210 + 0.807250i \(0.700955\pi\)
\(524\) 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 0.889762 0.456424i \(-0.150870\pi\)
−0.456424 + 0.889762i \(0.650870\pi\)
\(542\) 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 −0.651914 0.758293i \(-0.726034\pi\)
0.758293 + 0.651914i \(0.226034\pi\)
\(548\) −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 0.0282205 0.999602i \(-0.491016\pi\)
0.999602 0.0282205i \(-0.00898407\pi\)
\(558\) 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 \(-0.391245\pi\)
−0.942198 + 0.335055i \(0.891245\pi\)
\(564\) 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 0.942514 0.334167i \(-0.108455\pi\)
−0.334167 + 0.942514i \(0.608455\pi\)
\(572\) 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 \(-0.920424\pi\)
0.247401 + 0.968913i \(0.420424\pi\)
\(588\) 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 \(0.224725\pi\)
−0.760967 + 0.648790i \(0.775275\pi\)
\(602\) 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 \(0.0983453\pi\)
−0.952650 + 0.304069i \(0.901655\pi\)
\(608\) −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 0.0376494 0.999291i \(-0.488013\pi\)
0.999291 0.0376494i \(-0.0119870\pi\)
\(614\) 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 −0.979051 0.203616i \(-0.934731\pi\)
−0.203616 0.979051i \(-0.565269\pi\)
\(620\) −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 0.0799071 0.996802i \(-0.474538\pi\)
0.996802 0.0799071i \(-0.0254624\pi\)
\(644\) 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 \(-0.831069\pi\)
0.506149 + 0.862446i \(0.331069\pi\)
\(654\) 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 \(-0.118126\pi\)
−0.362643 + 0.931928i \(0.618126\pi\)
\(660\) 0 0
\(661\) 5.87057 5.87057i 0.228339 0.228339i −0.583660 0.811998i \(-0.698380\pi\)
0.811998 + 0.583660i \(0.198380\pi\)
\(662\) −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 0.973897 + 0.226992i \(0.0728891\pi\)
0.226992 + 0.973897i \(0.427111\pi\)
\(678\) 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 \(-0.616619\pi\)
0.933634 + 0.358228i \(0.116619\pi\)
\(684\) 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 −0.621654 0.783292i \(-0.713539\pi\)
0.783292 + 0.621654i \(0.213539\pi\)
\(692\) 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 \(-0.534435\pi\)
0.994154 + 0.107971i \(0.0344354\pi\)
\(702\) 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 −0.652710 0.757608i \(-0.726368\pi\)
0.757608 + 0.652710i \(0.226368\pi\)
\(710\) −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 0.946227 0.323503i \(-0.104860\pi\)
−0.323503 + 0.946227i \(0.604860\pi\)
\(734\) 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 −0.0696780 0.997570i \(-0.522197\pi\)
0.997570 + 0.0696780i \(0.0221972\pi\)
\(740\) 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 \(-0.893949\pi\)
0.945010 0.327040i \(-0.106051\pi\)
\(752\) 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 −0.648402 0.761298i \(-0.724562\pi\)
0.761298 + 0.648402i \(0.224562\pi\)
\(758\) −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 0.985237 0.171196i \(-0.0547631\pi\)
−0.171196 + 0.985237i \(0.554763\pi\)
\(774\) 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 −0.529315 + 0.848425i \(0.677551\pi\)
−0.848425 + 0.529315i \(0.822449\pi\)
\(788\) −18.0885 0.976342i −0.644377 0.0347807i
\(789\) 0 0
\(790\)