Properties

Label 637.2.x.b.19.8
Level $637$
Weight $2$
Character 637.19
Analytic conductor $5.086$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.x (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 19.8
Character \(\chi\) \(=\) 637.19
Dual form 637.2.x.b.570.7

$q$-expansion

\(f(q)\) \(=\) \(q+(2.26733 + 0.607529i) q^{2} +2.76026i q^{3} +(3.03963 + 1.75493i) q^{4} +(-1.53921 + 0.412430i) q^{5} +(-1.67694 + 6.25841i) q^{6} +(2.50608 + 2.50608i) q^{8} -4.61904 q^{9} +O(q^{10})\) \(q+(2.26733 + 0.607529i) q^{2} +2.76026i q^{3} +(3.03963 + 1.75493i) q^{4} +(-1.53921 + 0.412430i) q^{5} +(-1.67694 + 6.25841i) q^{6} +(2.50608 + 2.50608i) q^{8} -4.61904 q^{9} -3.74046 q^{10} +(2.22138 + 2.22138i) q^{11} +(-4.84407 + 8.39018i) q^{12} +(-1.04831 - 3.44979i) q^{13} +(-1.13841 - 4.24862i) q^{15} +(0.649718 + 1.12534i) q^{16} +(0.320795 - 0.555633i) q^{17} +(-10.4729 - 2.80620i) q^{18} +(5.57436 + 5.57436i) q^{19} +(-5.40242 - 1.44757i) q^{20} +(3.68704 + 6.38614i) q^{22} +(0.126569 - 0.0730744i) q^{23} +(-6.91743 + 6.91743i) q^{24} +(-2.13106 + 1.23037i) q^{25} +(-0.281008 - 8.45868i) q^{26} -4.46896i q^{27} +(1.49412 - 2.58790i) q^{29} -10.3246i q^{30} +(1.73252 - 6.46586i) q^{31} +(-1.04513 - 3.90048i) q^{32} +(-6.13158 + 6.13158i) q^{33} +(1.06491 - 1.06491i) q^{34} +(-14.0402 - 8.10610i) q^{36} +(-1.00675 + 3.75725i) q^{37} +(9.25232 + 16.0255i) q^{38} +(9.52232 - 2.89360i) q^{39} +(-4.89096 - 2.82380i) q^{40} +(5.60356 - 1.50147i) q^{41} +(2.42713 - 1.40130i) q^{43} +(2.85380 + 10.6505i) q^{44} +(7.10966 - 1.90503i) q^{45} +(0.331367 - 0.0887896i) q^{46} +(-0.816005 - 3.04537i) q^{47} +(-3.10624 + 1.79339i) q^{48} +(-5.57930 + 1.49497i) q^{50} +(1.53369 + 0.885477i) q^{51} +(2.86768 - 12.3258i) q^{52} +(3.66059 + 6.34033i) q^{53} +(2.71502 - 10.1326i) q^{54} +(-4.33533 - 2.50300i) q^{55} +(-15.3867 + 15.3867i) q^{57} +(4.95989 - 4.95989i) q^{58} +(1.07349 + 4.00631i) q^{59} +(3.99568 - 14.9121i) q^{60} -4.50671i q^{61} +(7.85639 - 13.6077i) q^{62} -12.0775i q^{64} +(3.03636 + 4.87760i) q^{65} +(-17.6274 + 10.1772i) q^{66} +(-1.00126 + 1.00126i) q^{67} +(1.95020 - 1.12595i) q^{68} +(0.201704 + 0.349362i) q^{69} +(13.8300 + 3.70574i) q^{71} +(-11.5757 - 11.5757i) q^{72} +(-6.81760 - 1.82677i) q^{73} +(-4.56527 + 7.90729i) q^{74} +(-3.39614 - 5.88228i) q^{75} +(7.16138 + 26.7267i) q^{76} +(23.3482 - 0.775656i) q^{78} +(0.316458 - 0.548121i) q^{79} +(-1.46418 - 1.46418i) q^{80} -1.52162 q^{81} +13.6173 q^{82} +(1.07813 + 1.07813i) q^{83} +(-0.264611 + 0.987541i) q^{85} +(6.35443 - 1.70266i) q^{86} +(7.14327 + 4.12417i) q^{87} +11.1339i q^{88} +(-13.1203 - 3.51557i) q^{89} +17.2773 q^{90} +0.512963 q^{92} +(17.8475 + 4.78221i) q^{93} -7.40060i q^{94} +(-10.8791 - 6.28107i) q^{95} +(10.7663 - 2.88483i) q^{96} +(0.0487160 - 0.181811i) q^{97} +(-10.2606 - 10.2606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + O(q^{10}) \) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + 20q^{11} - 8q^{15} + 12q^{16} - 64q^{18} + 4q^{22} + 12q^{23} + 4q^{29} + 64q^{32} + 4q^{37} + 36q^{39} - 48q^{43} - 84q^{44} - 108q^{46} - 44q^{50} + 12q^{51} - 36q^{53} - 92q^{57} + 44q^{58} + 28q^{60} + 28q^{65} + 64q^{67} + 84q^{71} + 4q^{72} - 24q^{74} + 148q^{78} + 40q^{79} - 56q^{81} + 36q^{85} + 108q^{86} + 24q^{92} - 24q^{93} + 84q^{95} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.26733 + 0.607529i 1.60324 + 0.429588i 0.946020 0.324108i \(-0.105064\pi\)
0.657223 + 0.753696i \(0.271731\pi\)
\(3\) 2.76026i 1.59364i 0.604219 + 0.796818i \(0.293485\pi\)
−0.604219 + 0.796818i \(0.706515\pi\)
\(4\) 3.03963 + 1.75493i 1.51982 + 0.877467i
\(5\) −1.53921 + 0.412430i −0.688355 + 0.184444i −0.586009 0.810305i \(-0.699302\pi\)
−0.102346 + 0.994749i \(0.532635\pi\)
\(6\) −1.67694 + 6.25841i −0.684607 + 2.55499i
\(7\) 0 0
\(8\) 2.50608 + 2.50608i 0.886032 + 0.886032i
\(9\) −4.61904 −1.53968
\(10\) −3.74046 −1.18284
\(11\) 2.22138 + 2.22138i 0.669770 + 0.669770i 0.957663 0.287892i \(-0.0929546\pi\)
−0.287892 + 0.957663i \(0.592955\pi\)
\(12\) −4.84407 + 8.39018i −1.39836 + 2.42204i
\(13\) −1.04831 3.44979i −0.290748 0.956800i
\(14\) 0 0
\(15\) −1.13841 4.24862i −0.293937 1.09699i
\(16\) 0.649718 + 1.12534i 0.162430 + 0.281336i
\(17\) 0.320795 0.555633i 0.0778042 0.134761i −0.824498 0.565865i \(-0.808542\pi\)
0.902302 + 0.431104i \(0.141876\pi\)
\(18\) −10.4729 2.80620i −2.46848 0.661427i
\(19\) 5.57436 + 5.57436i 1.27885 + 1.27885i 0.941314 + 0.337532i \(0.109592\pi\)
0.337532 + 0.941314i \(0.390408\pi\)
\(20\) −5.40242 1.44757i −1.20802 0.323687i
\(21\) 0 0
\(22\) 3.68704 + 6.38614i 0.786080 + 1.36153i
\(23\) 0.126569 0.0730744i 0.0263914 0.0152371i −0.486746 0.873543i \(-0.661816\pi\)
0.513138 + 0.858306i \(0.328483\pi\)
\(24\) −6.91743 + 6.91743i −1.41201 + 1.41201i
\(25\) −2.13106 + 1.23037i −0.426212 + 0.246074i
\(26\) −0.281008 8.45868i −0.0551103 1.65888i
\(27\) 4.46896i 0.860051i
\(28\) 0 0
\(29\) 1.49412 2.58790i 0.277452 0.480561i −0.693299 0.720650i \(-0.743843\pi\)
0.970751 + 0.240089i \(0.0771768\pi\)
\(30\) 10.3246i 1.88501i
\(31\) 1.73252 6.46586i 0.311170 1.16130i −0.616333 0.787486i \(-0.711382\pi\)
0.927503 0.373817i \(-0.121951\pi\)
\(32\) −1.04513 3.90048i −0.184755 0.689514i
\(33\) −6.13158 + 6.13158i −1.06737 + 1.06737i
\(34\) 1.06491 1.06491i 0.182631 0.182631i
\(35\) 0 0
\(36\) −14.0402 8.10610i −2.34003 1.35102i
\(37\) −1.00675 + 3.75725i −0.165509 + 0.617688i 0.832466 + 0.554077i \(0.186929\pi\)
−0.997975 + 0.0636115i \(0.979738\pi\)
\(38\) 9.25232 + 16.0255i 1.50092 + 2.59968i
\(39\) 9.52232 2.89360i 1.52479 0.463347i
\(40\) −4.89096 2.82380i −0.773328 0.446481i
\(41\) 5.60356 1.50147i 0.875129 0.234490i 0.206825 0.978378i \(-0.433687\pi\)
0.668305 + 0.743888i \(0.267020\pi\)
\(42\) 0 0
\(43\) 2.42713 1.40130i 0.370133 0.213697i −0.303383 0.952869i \(-0.598116\pi\)
0.673517 + 0.739172i \(0.264783\pi\)
\(44\) 2.85380 + 10.6505i 0.430227 + 1.60563i
\(45\) 7.10966 1.90503i 1.05985 0.283985i
\(46\) 0.331367 0.0887896i 0.0488574 0.0130913i
\(47\) −0.816005 3.04537i −0.119027 0.444213i 0.880530 0.473990i \(-0.157187\pi\)
−0.999557 + 0.0297773i \(0.990520\pi\)
\(48\) −3.10624 + 1.79339i −0.448348 + 0.258854i
\(49\) 0 0
\(50\) −5.57930 + 1.49497i −0.789032 + 0.211420i
\(51\) 1.53369 + 0.885477i 0.214760 + 0.123992i
\(52\) 2.86768 12.3258i 0.397676 1.70928i
\(53\) 3.66059 + 6.34033i 0.502821 + 0.870912i 0.999995 + 0.00326078i \(0.00103794\pi\)
−0.497173 + 0.867651i \(0.665629\pi\)
\(54\) 2.71502 10.1326i 0.369467 1.37887i
\(55\) −4.33533 2.50300i −0.584575 0.337505i
\(56\) 0 0
\(57\) −15.3867 + 15.3867i −2.03802 + 2.03802i
\(58\) 4.95989 4.95989i 0.651266 0.651266i
\(59\) 1.07349 + 4.00631i 0.139756 + 0.521578i 0.999933 + 0.0115814i \(0.00368656\pi\)
−0.860177 + 0.509996i \(0.829647\pi\)
\(60\) 3.99568 14.9121i 0.515840 1.92514i
\(61\) 4.50671i 0.577025i −0.957476 0.288512i \(-0.906839\pi\)
0.957476 0.288512i \(-0.0931607\pi\)
\(62\) 7.85639 13.6077i 0.997763 1.72818i
\(63\) 0 0
\(64\) 12.0775i 1.50969i
\(65\) 3.03636 + 4.87760i 0.376614 + 0.604991i
\(66\) −17.6274 + 10.1772i −2.16978 + 1.25273i
\(67\) −1.00126 + 1.00126i −0.122323 + 0.122323i −0.765618 0.643295i \(-0.777567\pi\)
0.643295 + 0.765618i \(0.277567\pi\)
\(68\) 1.95020 1.12595i 0.236496 0.136541i
\(69\) 0.201704 + 0.349362i 0.0242823 + 0.0420582i
\(70\) 0 0
\(71\) 13.8300 + 3.70574i 1.64132 + 0.439791i 0.957165 0.289544i \(-0.0935038\pi\)
0.684157 + 0.729335i \(0.260170\pi\)
\(72\) −11.5757 11.5757i −1.36420 1.36420i
\(73\) −6.81760 1.82677i −0.797940 0.213807i −0.163261 0.986583i \(-0.552201\pi\)
−0.634679 + 0.772776i \(0.718868\pi\)
\(74\) −4.56527 + 7.90729i −0.530702 + 0.919203i
\(75\) −3.39614 5.88228i −0.392152 0.679227i
\(76\) 7.16138 + 26.7267i 0.821467 + 3.06576i
\(77\) 0 0
\(78\) 23.3482 0.775656i 2.64366 0.0878258i
\(79\) 0.316458 0.548121i 0.0356043 0.0616685i −0.847674 0.530517i \(-0.821998\pi\)
0.883278 + 0.468849i \(0.155331\pi\)
\(80\) −1.46418 1.46418i −0.163700 0.163700i
\(81\) −1.52162 −0.169069
\(82\) 13.6173 1.50378
\(83\) 1.07813 + 1.07813i 0.118340 + 0.118340i 0.763797 0.645457i \(-0.223333\pi\)
−0.645457 + 0.763797i \(0.723333\pi\)
\(84\) 0 0
\(85\) −0.264611 + 0.987541i −0.0287011 + 0.107114i
\(86\) 6.35443 1.70266i 0.685215 0.183603i
\(87\) 7.14327 + 4.12417i 0.765839 + 0.442158i
\(88\) 11.1339i 1.18688i
\(89\) −13.1203 3.51557i −1.39075 0.372649i −0.515734 0.856749i \(-0.672481\pi\)
−0.875013 + 0.484099i \(0.839147\pi\)
\(90\) 17.2773 1.82119
\(91\) 0 0
\(92\) 0.512963 0.0534801
\(93\) 17.8475 + 4.78221i 1.85069 + 0.495892i
\(94\) 7.40060i 0.763314i
\(95\) −10.8791 6.28107i −1.11618 0.644425i
\(96\) 10.7663 2.88483i 1.09884 0.294432i
\(97\) 0.0487160 0.181811i 0.00494637 0.0184601i −0.963409 0.268037i \(-0.913625\pi\)
0.968355 + 0.249577i \(0.0802916\pi\)
\(98\) 0 0
\(99\) −10.2606 10.2606i −1.03123 1.03123i
\(100\) −8.63686 −0.863686
\(101\) 1.19381 0.118788 0.0593942 0.998235i \(-0.481083\pi\)
0.0593942 + 0.998235i \(0.481083\pi\)
\(102\) 2.93943 + 2.93943i 0.291047 + 0.291047i
\(103\) −2.39792 + 4.15331i −0.236274 + 0.409238i −0.959642 0.281224i \(-0.909260\pi\)
0.723368 + 0.690462i \(0.242593\pi\)
\(104\) 6.01830 11.2726i 0.590143 1.10537i
\(105\) 0 0
\(106\) 4.44783 + 16.5995i 0.432012 + 1.61229i
\(107\) −7.64819 13.2471i −0.739378 1.28064i −0.952776 0.303675i \(-0.901786\pi\)
0.213397 0.976966i \(-0.431547\pi\)
\(108\) 7.84273 13.5840i 0.754667 1.30712i
\(109\) −12.4638 3.33967i −1.19382 0.319883i −0.393424 0.919357i \(-0.628710\pi\)
−0.800394 + 0.599475i \(0.795376\pi\)
\(110\) −8.30896 8.30896i −0.792228 0.792228i
\(111\) −10.3710 2.77890i −0.984370 0.263761i
\(112\) 0 0
\(113\) −0.770731 1.33494i −0.0725042 0.125581i 0.827494 0.561475i \(-0.189766\pi\)
−0.899998 + 0.435894i \(0.856432\pi\)
\(114\) −44.2345 + 25.5388i −4.14294 + 2.39193i
\(115\) −0.164677 + 0.164677i −0.0153562 + 0.0153562i
\(116\) 9.08318 5.24418i 0.843352 0.486910i
\(117\) 4.84217 + 15.9347i 0.447658 + 1.47316i
\(118\) 9.73580i 0.896253i
\(119\) 0 0
\(120\) 7.79441 13.5003i 0.711529 1.23240i
\(121\) 1.13097i 0.102815i
\(122\) 2.73796 10.2182i 0.247883 0.925111i
\(123\) 4.14445 + 15.4673i 0.373692 + 1.39464i
\(124\) 16.6134 16.6134i 1.49193 1.49193i
\(125\) 8.40660 8.40660i 0.751910 0.751910i
\(126\) 0 0
\(127\) 2.81842 + 1.62722i 0.250095 + 0.144392i 0.619808 0.784754i \(-0.287211\pi\)
−0.369713 + 0.929146i \(0.620544\pi\)
\(128\) 5.24716 19.5827i 0.463788 1.73088i
\(129\) 3.86796 + 6.69950i 0.340555 + 0.589858i
\(130\) 3.92114 + 12.9038i 0.343907 + 1.13174i
\(131\) 14.2615 + 8.23390i 1.24604 + 0.719400i 0.970317 0.241838i \(-0.0777504\pi\)
0.275720 + 0.961238i \(0.411084\pi\)
\(132\) −29.3983 + 7.87724i −2.55879 + 0.685626i
\(133\) 0 0
\(134\) −2.87848 + 1.66189i −0.248663 + 0.143565i
\(135\) 1.84313 + 6.87866i 0.158632 + 0.592021i
\(136\) 2.19640 0.588523i 0.188339 0.0504654i
\(137\) 0.365056 0.0978163i 0.0311888 0.00835701i −0.243191 0.969978i \(-0.578194\pi\)
0.274380 + 0.961621i \(0.411527\pi\)
\(138\) 0.245082 + 0.914659i 0.0208628 + 0.0778610i
\(139\) −8.52132 + 4.91978i −0.722769 + 0.417291i −0.815771 0.578375i \(-0.803687\pi\)
0.0930022 + 0.995666i \(0.470354\pi\)
\(140\) 0 0
\(141\) 8.40602 2.25239i 0.707914 0.189685i
\(142\) 29.1058 + 16.8043i 2.44251 + 1.41018i
\(143\) 5.33460 9.99197i 0.446102 0.835570i
\(144\) −3.00107 5.19801i −0.250089 0.433167i
\(145\) −1.23244 + 4.59954i −0.102349 + 0.381971i
\(146\) −14.3479 8.28378i −1.18744 0.685570i
\(147\) 0 0
\(148\) −9.65388 + 9.65388i −0.793544 + 0.793544i
\(149\) 3.92698 3.92698i 0.321711 0.321711i −0.527712 0.849423i \(-0.676950\pi\)
0.849423 + 0.527712i \(0.176950\pi\)
\(150\) −4.12650 15.4003i −0.336927 1.25743i
\(151\) 1.22809 4.58330i 0.0999406 0.372983i −0.897782 0.440441i \(-0.854822\pi\)
0.997722 + 0.0674576i \(0.0214887\pi\)
\(152\) 27.9396i 2.26620i
\(153\) −1.48176 + 2.56649i −0.119793 + 0.207488i
\(154\) 0 0
\(155\) 10.6669i 0.856782i
\(156\) 34.0224 + 7.91556i 2.72398 + 0.633752i
\(157\) 10.9293 6.31006i 0.872257 0.503598i 0.00415919 0.999991i \(-0.498676\pi\)
0.868098 + 0.496394i \(0.165343\pi\)
\(158\) 1.05051 1.05051i 0.0835744 0.0835744i
\(159\) −17.5010 + 10.1042i −1.38792 + 0.801314i
\(160\) 3.21735 + 5.57262i 0.254354 + 0.440554i
\(161\) 0 0
\(162\) −3.45001 0.924428i −0.271058 0.0726299i
\(163\) −9.23004 9.23004i −0.722952 0.722952i 0.246253 0.969206i \(-0.420801\pi\)
−0.969206 + 0.246253i \(0.920801\pi\)
\(164\) 19.6678 + 5.26996i 1.53579 + 0.411515i
\(165\) 6.90893 11.9666i 0.537860 0.931601i
\(166\) 1.78948 + 3.09948i 0.138891 + 0.240566i
\(167\) −4.79697 17.9025i −0.371201 1.38534i −0.858817 0.512282i \(-0.828800\pi\)
0.487616 0.873058i \(-0.337867\pi\)
\(168\) 0 0
\(169\) −10.8021 + 7.23288i −0.830931 + 0.556375i
\(170\) −1.19992 + 2.07832i −0.0920296 + 0.159400i
\(171\) −25.7482 25.7482i −1.96901 1.96901i
\(172\) 9.83677 0.750047
\(173\) 5.59369 0.425280 0.212640 0.977131i \(-0.431794\pi\)
0.212640 + 0.977131i \(0.431794\pi\)
\(174\) 13.6906 + 13.6906i 1.03788 + 1.03788i
\(175\) 0 0
\(176\) −1.05655 + 3.94308i −0.0796402 + 0.297221i
\(177\) −11.0585 + 2.96311i −0.831205 + 0.222721i
\(178\) −27.6122 15.9419i −2.06962 1.19490i
\(179\) 9.49080i 0.709376i −0.934985 0.354688i \(-0.884587\pi\)
0.934985 0.354688i \(-0.115413\pi\)
\(180\) 24.9540 + 6.68640i 1.85996 + 0.498375i
\(181\) 6.91516 0.514000 0.257000 0.966411i \(-0.417266\pi\)
0.257000 + 0.966411i \(0.417266\pi\)
\(182\) 0 0
\(183\) 12.4397 0.919568
\(184\) 0.500321 + 0.134060i 0.0368841 + 0.00988307i
\(185\) 6.19841i 0.455716i
\(186\) 37.5607 + 21.6857i 2.75408 + 1.59007i
\(187\) 1.94688 0.521664i 0.142370 0.0381479i
\(188\) 2.86407 10.6889i 0.208884 0.779565i
\(189\) 0 0
\(190\) −20.8506 20.8506i −1.51266 1.51266i
\(191\) −2.50503 −0.181257 −0.0906287 0.995885i \(-0.528888\pi\)
−0.0906287 + 0.995885i \(0.528888\pi\)
\(192\) 33.3370 2.40589
\(193\) −15.9501 15.9501i −1.14811 1.14811i −0.986924 0.161187i \(-0.948468\pi\)
−0.161187 0.986924i \(-0.551532\pi\)
\(194\) 0.220911 0.382628i 0.0158605 0.0274711i
\(195\) −13.4634 + 8.38114i −0.964136 + 0.600186i
\(196\) 0 0
\(197\) −4.63560 17.3003i −0.330273 1.23259i −0.908904 0.417005i \(-0.863080\pi\)
0.578631 0.815589i \(-0.303587\pi\)
\(198\) −17.0306 29.4978i −1.21031 2.09632i
\(199\) −8.20617 + 14.2135i −0.581720 + 1.00757i 0.413556 + 0.910479i \(0.364287\pi\)
−0.995276 + 0.0970896i \(0.969047\pi\)
\(200\) −8.42400 2.25720i −0.595667 0.159608i
\(201\) −2.76374 2.76374i −0.194939 0.194939i
\(202\) 2.70675 + 0.725273i 0.190447 + 0.0510300i
\(203\) 0 0
\(204\) 3.10791 + 5.38306i 0.217597 + 0.376889i
\(205\) −8.00580 + 4.62215i −0.559150 + 0.322825i
\(206\) −7.96012 + 7.96012i −0.554608 + 0.554608i
\(207\) −0.584624 + 0.337533i −0.0406342 + 0.0234602i
\(208\) 3.20110 3.42110i 0.221956 0.237210i
\(209\) 24.7655i 1.71307i
\(210\) 0 0
\(211\) 4.93176 8.54207i 0.339517 0.588060i −0.644825 0.764330i \(-0.723070\pi\)
0.984342 + 0.176270i \(0.0564032\pi\)
\(212\) 25.6964i 1.76484i
\(213\) −10.2288 + 38.1744i −0.700867 + 2.61567i
\(214\) −9.29299 34.6819i −0.635256 2.37081i
\(215\) −3.15792 + 3.15792i −0.215368 + 0.215368i
\(216\) 11.1996 11.1996i 0.762033 0.762033i
\(217\) 0 0
\(218\) −26.2306 15.1443i −1.77656 1.02570i
\(219\) 5.04236 18.8184i 0.340731 1.27163i
\(220\) −8.78520 15.2164i −0.592298 1.02589i
\(221\) −2.25311 0.524201i −0.151561 0.0352616i
\(222\) −21.8262 12.6013i −1.46488 0.845747i
\(223\) −8.41926 + 2.25594i −0.563796 + 0.151069i −0.529450 0.848341i \(-0.677602\pi\)
−0.0343461 + 0.999410i \(0.510935\pi\)
\(224\) 0 0
\(225\) 9.84344 5.68312i 0.656230 0.378874i
\(226\) −0.936482 3.49500i −0.0622939 0.232484i
\(227\) −16.3175 + 4.37226i −1.08303 + 0.290197i −0.755837 0.654760i \(-0.772770\pi\)
−0.327194 + 0.944957i \(0.606103\pi\)
\(228\) −73.7725 + 19.7673i −4.88570 + 1.30912i
\(229\) 0.632892 + 2.36198i 0.0418227 + 0.156084i 0.983679 0.179931i \(-0.0575874\pi\)
−0.941857 + 0.336015i \(0.890921\pi\)
\(230\) −0.473424 + 0.273331i −0.0312166 + 0.0180229i
\(231\) 0 0
\(232\) 10.2299 2.74108i 0.671624 0.179961i
\(233\) −4.65474 2.68741i −0.304942 0.176058i 0.339719 0.940527i \(-0.389668\pi\)
−0.644661 + 0.764469i \(0.723001\pi\)
\(234\) 1.29799 + 39.0710i 0.0848521 + 2.55415i
\(235\) 2.51200 + 4.35092i 0.163865 + 0.283823i
\(236\) −3.76780 + 14.0616i −0.245263 + 0.915334i
\(237\) 1.51296 + 0.873507i 0.0982772 + 0.0567404i
\(238\) 0 0
\(239\) −11.9572 + 11.9572i −0.773448 + 0.773448i −0.978708 0.205260i \(-0.934196\pi\)
0.205260 + 0.978708i \(0.434196\pi\)
\(240\) 4.04151 4.04151i 0.260878 0.260878i
\(241\) −3.48047 12.9893i −0.224197 0.836713i −0.982725 0.185073i \(-0.940748\pi\)
0.758528 0.651640i \(-0.225919\pi\)
\(242\) 0.687097 2.56428i 0.0441682 0.164838i
\(243\) 17.6069i 1.12949i
\(244\) 7.90898 13.6987i 0.506320 0.876972i
\(245\) 0 0
\(246\) 37.5873i 2.39648i
\(247\) 13.3867 25.0740i 0.851778 1.59542i
\(248\) 20.5458 11.8621i 1.30466 0.753245i
\(249\) −2.97593 + 2.97593i −0.188592 + 0.188592i
\(250\) 24.1678 13.9533i 1.52850 0.882483i
\(251\) 6.40248 + 11.0894i 0.404121 + 0.699958i 0.994219 0.107374i \(-0.0342441\pi\)
−0.590098 + 0.807332i \(0.700911\pi\)
\(252\) 0 0
\(253\) 0.443482 + 0.118831i 0.0278815 + 0.00747082i
\(254\) 5.40171 + 5.40171i 0.338933 + 0.338933i
\(255\) −2.72587 0.730395i −0.170701 0.0457391i
\(256\) 11.7166 20.2937i 0.732286 1.26836i
\(257\) 5.19036 + 8.98997i 0.323766 + 0.560779i 0.981262 0.192679i \(-0.0617176\pi\)
−0.657496 + 0.753458i \(0.728384\pi\)
\(258\) 4.69979 + 17.5399i 0.292596 + 1.09198i
\(259\) 0 0
\(260\) 0.669566 + 20.1547i 0.0415247 + 1.24994i
\(261\) −6.90141 + 11.9536i −0.427187 + 0.739909i
\(262\) 27.3333 + 27.3333i 1.68865 + 1.68865i
\(263\) −4.37954 −0.270054 −0.135027 0.990842i \(-0.543112\pi\)
−0.135027 + 0.990842i \(0.543112\pi\)
\(264\) −30.7324 −1.89145
\(265\) −8.24936 8.24936i −0.506754 0.506754i
\(266\) 0 0
\(267\) 9.70388 36.2154i 0.593868 2.21635i
\(268\) −4.80061 + 1.28632i −0.293244 + 0.0785744i
\(269\) 10.1192 + 5.84233i 0.616980 + 0.356213i 0.775692 0.631112i \(-0.217401\pi\)
−0.158713 + 0.987325i \(0.550734\pi\)
\(270\) 16.7159i 1.01730i
\(271\) −29.6470 7.94389i −1.80093 0.482557i −0.806804 0.590819i \(-0.798805\pi\)
−0.994122 + 0.108262i \(0.965471\pi\)
\(272\) 0.833705 0.0505508
\(273\) 0 0
\(274\) 0.887127 0.0535933
\(275\) −7.46700 2.00078i −0.450277 0.120651i
\(276\) 1.41591i 0.0852278i
\(277\) 16.5109 + 9.53260i 0.992047 + 0.572758i 0.905885 0.423523i \(-0.139207\pi\)
0.0861613 + 0.996281i \(0.472540\pi\)
\(278\) −22.3095 + 5.97782i −1.33804 + 0.358526i
\(279\) −8.00258 + 29.8660i −0.479102 + 1.78803i
\(280\) 0 0
\(281\) 11.8671 + 11.8671i 0.707931 + 0.707931i 0.966100 0.258169i \(-0.0831190\pi\)
−0.258169 + 0.966100i \(0.583119\pi\)
\(282\) 20.4276 1.21645
\(283\) −8.43728 −0.501544 −0.250772 0.968046i \(-0.580685\pi\)
−0.250772 + 0.968046i \(0.580685\pi\)
\(284\) 35.5349 + 35.5349i 2.10861 + 2.10861i
\(285\) 17.3374 30.0292i 1.02698 1.77878i
\(286\) 18.1657 19.4141i 1.07416 1.14798i
\(287\) 0 0
\(288\) 4.82750 + 18.0165i 0.284463 + 1.06163i
\(289\) 8.29418 + 14.3659i 0.487893 + 0.845055i
\(290\) −5.58870 + 9.67992i −0.328180 + 0.568424i
\(291\) 0.501845 + 0.134469i 0.0294187 + 0.00788271i
\(292\) −17.5172 17.5172i −1.02511 1.02511i
\(293\) −8.00676 2.14541i −0.467760 0.125336i 0.0172376 0.999851i \(-0.494513\pi\)
−0.484998 + 0.874516i \(0.661180\pi\)
\(294\) 0 0
\(295\) −3.30465 5.72382i −0.192404 0.333253i
\(296\) −11.9390 + 6.89296i −0.693938 + 0.400645i
\(297\) 9.92724 9.92724i 0.576037 0.576037i
\(298\) 11.2895 6.51800i 0.653984 0.377578i
\(299\) −0.384774 0.360031i −0.0222520 0.0208211i
\(300\) 23.8400i 1.37640i
\(301\) 0 0
\(302\) 5.56897 9.64574i 0.320458 0.555050i
\(303\) 3.29522i 0.189306i
\(304\) −2.65131 + 9.89484i −0.152063 + 0.567508i
\(305\) 1.85870 + 6.93677i 0.106429 + 0.397198i
\(306\) −4.91886 + 4.91886i −0.281192 + 0.281192i
\(307\) −17.3438 + 17.3438i −0.989863 + 0.989863i −0.999949 0.0100865i \(-0.996789\pi\)
0.0100865 + 0.999949i \(0.496789\pi\)
\(308\) 0 0
\(309\) −11.4642 6.61887i −0.652177 0.376535i
\(310\) −6.48042 + 24.1853i −0.368063 + 1.37363i
\(311\) −11.8560 20.5353i −0.672294 1.16445i −0.977252 0.212082i \(-0.931976\pi\)
0.304958 0.952366i \(-0.401358\pi\)
\(312\) 31.1153 + 16.6121i 1.76155 + 0.940474i
\(313\) 12.1862 + 7.03573i 0.688808 + 0.397683i 0.803165 0.595756i \(-0.203148\pi\)
−0.114358 + 0.993440i \(0.536481\pi\)
\(314\) 28.6140 7.66709i 1.61478 0.432679i
\(315\) 0 0
\(316\) 1.92383 1.11073i 0.108224 0.0624832i
\(317\) 4.33262 + 16.1695i 0.243344 + 0.908172i 0.974209 + 0.225649i \(0.0724504\pi\)
−0.730865 + 0.682522i \(0.760883\pi\)
\(318\) −45.8190 + 12.2772i −2.56940 + 0.688470i
\(319\) 9.06771 2.42969i 0.507694 0.136036i
\(320\) 4.98112 + 18.5898i 0.278453 + 1.03920i
\(321\) 36.5653 21.1110i 2.04088 1.17830i
\(322\) 0 0
\(323\) 4.88553 1.30907i 0.271838 0.0728388i
\(324\) −4.62517 2.67034i −0.256954 0.148352i
\(325\) 6.47852 + 6.06191i 0.359364 + 0.336254i
\(326\) −15.3200 26.5350i −0.848497 1.46964i
\(327\) 9.21836 34.4034i 0.509777 1.90251i
\(328\) 17.8058 + 10.2802i 0.983159 + 0.567627i
\(329\) 0 0
\(330\) 22.9349 22.9349i 1.26252 1.26252i
\(331\) −6.84348 + 6.84348i −0.376152 + 0.376152i −0.869712 0.493560i \(-0.835695\pi\)
0.493560 + 0.869712i \(0.335695\pi\)
\(332\) 1.38508 + 5.16918i 0.0760160 + 0.283696i
\(333\) 4.65022 17.3549i 0.254831 0.951041i
\(334\) 43.5052i 2.38050i
\(335\) 1.12820 1.95410i 0.0616401 0.106764i
\(336\) 0 0
\(337\) 20.0838i 1.09403i 0.837122 + 0.547016i \(0.184236\pi\)
−0.837122 + 0.547016i \(0.815764\pi\)
\(338\) −28.8861 + 9.83671i −1.57120 + 0.535047i
\(339\) 3.68479 2.12742i 0.200131 0.115545i
\(340\) −2.53739 + 2.53739i −0.137609 + 0.137609i
\(341\) 18.2117 10.5145i 0.986218 0.569393i
\(342\) −42.7368 74.0223i −2.31094 4.00267i
\(343\) 0 0
\(344\) 9.59434 + 2.57080i 0.517292 + 0.138608i
\(345\) −0.454552 0.454552i −0.0244723 0.0244723i
\(346\) 12.6827 + 3.39833i 0.681827 + 0.182695i
\(347\) 11.1008 19.2271i 0.595920 1.03216i −0.397496 0.917604i \(-0.630121\pi\)
0.993416 0.114560i \(-0.0365458\pi\)
\(348\) 14.4753 + 25.0719i 0.775957 + 1.34400i
\(349\) −1.38593 5.17235i −0.0741869 0.276869i 0.918861 0.394582i \(-0.129111\pi\)
−0.993048 + 0.117713i \(0.962444\pi\)
\(350\) 0 0
\(351\) −15.4170 + 4.68484i −0.822897 + 0.250058i
\(352\) 6.34281 10.9861i 0.338073 0.585560i
\(353\) 18.4554 + 18.4554i 0.982281 + 0.982281i 0.999846 0.0175643i \(-0.00559119\pi\)
−0.0175643 + 0.999846i \(0.505591\pi\)
\(354\) −26.8733 −1.42830
\(355\) −22.8157 −1.21093
\(356\) −33.7113 33.7113i −1.78669 1.78669i
\(357\) 0 0
\(358\) 5.76594 21.5188i 0.304739 1.13730i
\(359\) 21.8723 5.86066i 1.15437 0.309314i 0.369658 0.929168i \(-0.379475\pi\)
0.784717 + 0.619854i \(0.212808\pi\)
\(360\) 22.5915 + 13.0432i 1.19068 + 0.687438i
\(361\) 43.1470i 2.27089i
\(362\) 15.6789 + 4.20116i 0.824066 + 0.220808i
\(363\) 3.12177 0.163850
\(364\) 0 0
\(365\) 11.2471 0.588702
\(366\) 28.2049 + 7.55747i 1.47429 + 0.395035i
\(367\) 14.1961i 0.741032i −0.928826 0.370516i \(-0.879181\pi\)
0.928826 0.370516i \(-0.120819\pi\)
\(368\) 0.164468 + 0.0949555i 0.00857347 + 0.00494990i
\(369\) −25.8831 + 6.93534i −1.34742 + 0.361040i
\(370\) 3.76571 14.0538i 0.195770 0.730624i
\(371\) 0 0
\(372\) 45.8573 + 45.8573i 2.37759 + 2.37759i
\(373\) 3.50642 0.181556 0.0907778 0.995871i \(-0.471065\pi\)
0.0907778 + 0.995871i \(0.471065\pi\)
\(374\) 4.73114 0.244641
\(375\) 23.2044 + 23.2044i 1.19827 + 1.19827i
\(376\) 5.58697 9.67691i 0.288126 0.499048i
\(377\) −10.4940 2.44150i −0.540469 0.125744i
\(378\) 0 0
\(379\) 6.94797 + 25.9302i 0.356893 + 1.33194i 0.878085 + 0.478504i \(0.158821\pi\)
−0.521192 + 0.853439i \(0.674513\pi\)
\(380\) −22.0457 38.1843i −1.13092 1.95882i
\(381\) −4.49154 + 7.77958i −0.230109 + 0.398560i
\(382\) −5.67972 1.52188i −0.290600 0.0778660i
\(383\) 24.1497 + 24.1497i 1.23399 + 1.23399i 0.962417 + 0.271576i \(0.0875448\pi\)
0.271576 + 0.962417i \(0.412455\pi\)
\(384\) 54.0533 + 14.4835i 2.75839 + 0.739110i
\(385\) 0 0
\(386\) −26.4739 45.8542i −1.34749 2.33392i
\(387\) −11.2110 + 6.47267i −0.569887 + 0.329024i
\(388\) 0.467145 0.467145i 0.0237157 0.0237157i
\(389\) −23.7849 + 13.7322i −1.20594 + 0.696251i −0.961870 0.273506i \(-0.911817\pi\)
−0.244072 + 0.969757i \(0.578483\pi\)
\(390\) −35.6178 + 10.8234i −1.80358 + 0.548063i
\(391\) 0.0937676i 0.00474203i
\(392\) 0 0
\(393\) −22.7277 + 39.3656i −1.14646 + 1.98573i
\(394\) 42.0417i 2.11803i
\(395\) −0.261034 + 0.974190i −0.0131340 + 0.0490168i
\(396\) −13.1818 49.1952i −0.662412 2.47215i
\(397\) −26.2097 + 26.2097i −1.31543 + 1.31543i −0.398076 + 0.917352i \(0.630322\pi\)
−0.917352 + 0.398076i \(0.869678\pi\)
\(398\) −27.2412 + 27.2412i −1.36548 + 1.36548i
\(399\) 0 0
\(400\) −2.76918 1.59879i −0.138459 0.0799393i
\(401\) 4.49729 16.7841i 0.224584 0.838158i −0.757987 0.652269i \(-0.773817\pi\)
0.982571 0.185888i \(-0.0595163\pi\)
\(402\) −4.58725 7.94535i −0.228791 0.396278i
\(403\) −24.1221 + 0.801366i −1.20161 + 0.0399189i
\(404\) 3.62874 + 2.09505i 0.180537 + 0.104233i
\(405\) 2.34209 0.627561i 0.116379 0.0311838i
\(406\) 0 0
\(407\) −10.5826 + 6.10989i −0.524562 + 0.302856i
\(408\) 1.62448 + 6.06263i 0.0804235 + 0.300145i
\(409\) −10.8988 + 2.92033i −0.538913 + 0.144401i −0.518001 0.855380i \(-0.673324\pi\)
−0.0209119 + 0.999781i \(0.506657\pi\)
\(410\) −20.9599 + 5.61618i −1.03513 + 0.277363i
\(411\) 0.269999 + 1.00765i 0.0133180 + 0.0497036i
\(412\) −14.5776 + 8.41637i −0.718186 + 0.414645i
\(413\) 0 0
\(414\) −1.53060 + 0.410122i −0.0752247 + 0.0201564i
\(415\) −2.10413 1.21482i −0.103287 0.0596330i
\(416\) −12.3602 + 7.69439i −0.606010 + 0.377248i
\(417\) −13.5799 23.5211i −0.665010 1.15183i
\(418\) −15.0458 + 56.1515i −0.735912 + 2.74646i
\(419\) 16.1248 + 9.30964i 0.787747 + 0.454806i 0.839169 0.543871i \(-0.183042\pi\)
−0.0514220 + 0.998677i \(0.516375\pi\)
\(420\) 0 0
\(421\) 18.9024 18.9024i 0.921247 0.921247i −0.0758709 0.997118i \(-0.524174\pi\)
0.997118 + 0.0758709i \(0.0241737\pi\)
\(422\) 16.3715 16.3715i 0.796951 0.796951i
\(423\) 3.76916 + 14.0667i 0.183263 + 0.683945i
\(424\) −6.71564 + 25.0631i −0.326140 + 1.21717i
\(425\) 1.57878i 0.0765823i
\(426\) −46.3841 + 80.3397i −2.24732 + 3.89247i
\(427\) 0 0
\(428\) 53.6883i 2.59512i
\(429\) 27.5804 + 14.7249i 1.33160 + 0.710924i
\(430\) −9.07856 + 5.24151i −0.437807 + 0.252768i
\(431\) −20.8750 + 20.8750i −1.00552 + 1.00552i −0.00553055 + 0.999985i \(0.501760\pi\)
−0.999985 + 0.00553055i \(0.998240\pi\)
\(432\) 5.02912 2.90356i 0.241964 0.139698i
\(433\) 17.9660 + 31.1180i 0.863390 + 1.49543i 0.868637 + 0.495449i \(0.164996\pi\)
−0.00524758 + 0.999986i \(0.501670\pi\)
\(434\) 0 0
\(435\) −12.6959 3.40186i −0.608723 0.163107i
\(436\) −32.0246 32.0246i −1.53370 1.53370i
\(437\) 1.11288 + 0.298196i 0.0532363 + 0.0142646i
\(438\) 22.8654 39.6040i 1.09255 1.89235i
\(439\) −4.87991 8.45226i −0.232906 0.403404i 0.725756 0.687952i \(-0.241490\pi\)
−0.958662 + 0.284548i \(0.908157\pi\)
\(440\) −4.59195 17.1374i −0.218912 0.816992i
\(441\) 0 0
\(442\) −4.79007 2.55737i −0.227840 0.121641i
\(443\) −19.3899 + 33.5843i −0.921241 + 1.59564i −0.123744 + 0.992314i \(0.539490\pi\)
−0.797497 + 0.603323i \(0.793843\pi\)
\(444\) −26.6472 26.6472i −1.26462 1.26462i
\(445\) 21.6448 1.02606
\(446\) −20.4598 −0.968799
\(447\) 10.8395 + 10.8395i 0.512690 + 0.512690i
\(448\) 0 0
\(449\) −2.42216 + 9.03963i −0.114309 + 0.426606i −0.999234 0.0391263i \(-0.987543\pi\)
0.884925 + 0.465733i \(0.154209\pi\)
\(450\) 25.7710 6.90531i 1.21486 0.325520i
\(451\) 15.7830 + 9.11229i 0.743190 + 0.429081i
\(452\) 5.41033i 0.254480i
\(453\) 12.6511 + 3.38985i 0.594400 + 0.159269i
\(454\) −39.6534 −1.86103
\(455\) 0 0
\(456\) −77.1204 −3.61150
\(457\) −18.5661 4.97477i −0.868485 0.232710i −0.203053 0.979168i \(-0.565086\pi\)
−0.665433 + 0.746458i \(0.731753\pi\)
\(458\) 5.73989i 0.268208i
\(459\) −2.48310 1.43362i −0.115901 0.0669156i
\(460\) −0.789557 + 0.211561i −0.0368133 + 0.00986409i
\(461\) 3.50466 13.0796i 0.163228 0.609175i −0.835031 0.550202i \(-0.814551\pi\)
0.998260 0.0589733i \(-0.0187827\pi\)
\(462\) 0 0
\(463\) −14.6336 14.6336i −0.680081 0.680081i 0.279937 0.960018i \(-0.409686\pi\)
−0.960018 + 0.279937i \(0.909686\pi\)
\(464\) 3.88304 0.180266
\(465\) −29.4433 −1.36540
\(466\) −8.92114 8.92114i −0.413264 0.413264i
\(467\) 15.4866 26.8236i 0.716634 1.24125i −0.245692 0.969348i \(-0.579015\pi\)
0.962326 0.271899i \(-0.0876515\pi\)
\(468\) −13.2459 + 56.9334i −0.612294 + 2.63175i
\(469\) 0 0
\(470\) 3.05223 + 11.3911i 0.140789 + 0.525431i
\(471\) 17.4174 + 30.1678i 0.802552 + 1.39006i
\(472\) −7.34989 + 12.7304i −0.338306 + 0.585963i
\(473\) 8.50439 + 2.27874i 0.391032 + 0.104777i
\(474\) 2.89969 + 2.89969i 0.133187 + 0.133187i
\(475\) −18.7378 5.02078i −0.859750 0.230369i
\(476\) 0 0
\(477\) −16.9084 29.2862i −0.774183 1.34092i
\(478\) −34.3753 + 19.8466i −1.57229 + 0.907761i
\(479\) −5.19377 + 5.19377i −0.237310 + 0.237310i −0.815735 0.578426i \(-0.803667\pi\)
0.578426 + 0.815735i \(0.303667\pi\)
\(480\) −15.3819 + 8.88072i −0.702083 + 0.405348i
\(481\) 14.0171 0.465666i 0.639125 0.0212326i
\(482\) 31.5654i 1.43777i
\(483\) 0 0
\(484\) 1.98478 3.43773i 0.0902171 0.156261i
\(485\) 0.299937i 0.0136194i
\(486\) 10.6967 39.9207i 0.485213 1.81084i
\(487\) −2.55251 9.52611i −0.115665 0.431669i 0.883670 0.468110i \(-0.155065\pi\)
−0.999336 + 0.0364405i \(0.988398\pi\)
\(488\) 11.2942 11.2942i 0.511263 0.511263i
\(489\) 25.4773 25.4773i 1.15212 1.15212i
\(490\) 0 0
\(491\) 33.1372 + 19.1318i 1.49546 + 0.863404i 0.999986 0.00521946i \(-0.00166141\pi\)
0.495473 + 0.868623i \(0.334995\pi\)
\(492\) −14.5465 + 54.2881i −0.655805 + 2.44750i
\(493\) −0.958615 1.66037i −0.0431738 0.0747793i
\(494\) 45.5853 48.7182i 2.05098 2.19193i
\(495\) 20.0250 + 11.5615i 0.900058 + 0.519649i
\(496\) 8.40197 2.25130i 0.377260 0.101086i
\(497\) 0 0
\(498\) −8.55536 + 4.93944i −0.383375 + 0.221342i
\(499\) 0.000375951 0.00140307i 1.68299e−5 6.28100e-5i 0.965934 0.258788i \(-0.0833230\pi\)
−0.965917 + 0.258850i \(0.916656\pi\)
\(500\) 40.3060 10.8000i 1.80254 0.482989i
\(501\) 49.4157 13.2409i 2.20773 0.591559i
\(502\) 7.77938 + 29.0331i 0.347211 + 1.29581i
\(503\) −21.6205 + 12.4826i −0.964012 + 0.556573i −0.897406 0.441206i \(-0.854551\pi\)
−0.0666068 + 0.997779i \(0.521217\pi\)
\(504\) 0 0
\(505\) −1.83752 + 0.492362i −0.0817686 + 0.0219098i
\(506\) 0.933326 + 0.538856i 0.0414914 + 0.0239551i
\(507\) −19.9646 29.8166i −0.886660 1.32420i
\(508\) 5.71132 + 9.89229i 0.253399 + 0.438900i
\(509\) −0.678383 + 2.53176i −0.0300688 + 0.112218i −0.979329 0.202273i \(-0.935167\pi\)
0.949260 + 0.314491i \(0.101834\pi\)
\(510\) −5.73671 3.31209i −0.254026 0.146662i
\(511\) 0 0
\(512\) 10.2233 10.2233i 0.451811 0.451811i
\(513\) 24.9116 24.9116i 1.09987 1.09987i
\(514\) 6.30659 + 23.5365i 0.278172 + 1.03815i
\(515\) 1.97795 7.38179i 0.0871587 0.325281i
\(516\) 27.1521i 1.19530i
\(517\) 4.95226 8.57757i 0.217800 0.377241i
\(518\) 0 0
\(519\) 15.4400i 0.677742i
\(520\) −4.61428 + 19.8330i −0.202350 + 0.869734i
\(521\) 25.8598 14.9302i 1.13294 0.654102i 0.188266 0.982118i \(-0.439713\pi\)
0.944672 + 0.328016i \(0.106380\pi\)
\(522\) −22.9099 + 22.9099i −1.00274 + 1.00274i
\(523\) −13.9268 + 8.04062i −0.608975 + 0.351592i −0.772564 0.634937i \(-0.781026\pi\)
0.163589 + 0.986529i \(0.447693\pi\)
\(524\) 28.8999 + 50.0561i 1.26250 + 2.18671i
\(525\) 0 0
\(526\) −9.92985 2.66069i −0.432962 0.116012i
\(527\) −3.03686 3.03686i −0.132288 0.132288i
\(528\) −10.8839 2.91634i −0.473663 0.126918i
\(529\) −11.4893 + 19.9001i −0.499536 + 0.865221i
\(530\) −13.6923 23.7157i −0.594755 1.03015i
\(531\) −4.95848 18.5053i −0.215180 0.803062i
\(532\) 0 0
\(533\) −11.0540 17.7571i −0.478802 0.769146i
\(534\) 44.0038 76.2168i 1.90423 3.29822i
\(535\) 17.2356 + 17.2356i 0.745162 + 0.745162i
\(536\) −5.01847 −0.216765
\(537\) 26.1971 1.13049
\(538\) 19.3942 + 19.3942i 0.836143 + 0.836143i
\(539\) 0 0
\(540\) −6.46915 + 24.1432i −0.278388 + 1.03896i
\(541\) −17.0022 + 4.55572i −0.730980 + 0.195866i −0.605066 0.796176i \(-0.706853\pi\)
−0.125915 + 0.992041i \(0.540187\pi\)
\(542\) −62.3933 36.0228i −2.68002 1.54731i
\(543\) 19.0876i 0.819129i
\(544\) −2.50251 0.670546i −0.107294 0.0287494i
\(545\) 20.5618 0.880771
\(546\) 0 0
\(547\) −15.8734 −0.678698 −0.339349 0.940661i \(-0.610207\pi\)
−0.339349 + 0.940661i \(0.610207\pi\)
\(548\) 1.28130 + 0.343322i 0.0547343 + 0.0146660i
\(549\) 20.8166i 0.888433i
\(550\) −15.7146 9.07284i −0.670073 0.386867i
\(551\) 22.7547 6.09709i 0.969381 0.259745i
\(552\) −0.370042 + 1.38101i −0.0157500 + 0.0587799i
\(553\) 0 0
\(554\) 31.6444 + 31.6444i 1.34444 + 1.34444i
\(555\) 17.1092 0.726246
\(556\) −34.5356 −1.46464
\(557\) 1.79108 + 1.79108i 0.0758906 + 0.0758906i 0.744033 0.668143i \(-0.232910\pi\)
−0.668143 + 0.744033i \(0.732910\pi\)
\(558\) −36.2889 + 62.8543i −1.53623 + 2.66083i
\(559\) −7.37857 6.90409i −0.312080 0.292012i
\(560\) 0 0
\(561\) 1.43993 + 5.37389i 0.0607938 + 0.226886i
\(562\) 19.6970 + 34.1162i 0.830867 + 1.43910i
\(563\) 10.1159 17.5213i 0.426336 0.738436i −0.570208 0.821500i \(-0.693137\pi\)
0.996544 + 0.0830642i \(0.0264707\pi\)
\(564\) 29.5040 + 7.90558i 1.24234 + 0.332885i
\(565\) 1.73689 + 1.73689i 0.0730714 + 0.0730714i
\(566\) −19.1301 5.12589i −0.804098 0.215457i
\(567\) 0 0
\(568\) 25.3722 + 43.9460i 1.06459 + 1.84393i
\(569\) 12.8801 7.43632i 0.539961 0.311747i −0.205102 0.978741i \(-0.565753\pi\)
0.745063 + 0.666994i \(0.232419\pi\)
\(570\) 57.5532 57.5532i 2.41064 2.41064i
\(571\) 31.9767 18.4617i 1.33818 0.772600i 0.351645 0.936133i \(-0.385622\pi\)
0.986538 + 0.163533i \(0.0522891\pi\)
\(572\) 33.7505 21.0101i 1.41118 0.878475i
\(573\) 6.91453i 0.288859i
\(574\) 0 0
\(575\) −0.179817 + 0.311452i −0.00749888 + 0.0129884i
\(576\) 55.7864i 2.32443i
\(577\) −5.31122 + 19.8217i −0.221109 + 0.825189i 0.762817 + 0.646614i \(0.223816\pi\)
−0.983926 + 0.178575i \(0.942851\pi\)
\(578\) 10.0779 + 37.6113i 0.419186 + 1.56442i
\(579\) 44.0263 44.0263i 1.82967 1.82967i
\(580\) −11.8181 + 11.8181i −0.490718 + 0.490718i
\(581\) 0 0
\(582\) 1.05615 + 0.609771i 0.0437790 + 0.0252758i
\(583\) −5.95271 + 22.2158i −0.246536 + 0.920086i
\(584\) −12.5074 21.6635i −0.517560 0.896441i
\(585\) −14.0251 22.5298i −0.579865 0.931492i
\(586\) −16.8506 9.72867i −0.696090 0.401888i
\(587\) 19.8321 5.31399i 0.818557 0.219332i 0.174842 0.984597i \(-0.444059\pi\)
0.643715 + 0.765265i \(0.277392\pi\)
\(588\) 0 0
\(589\) 45.7007 26.3853i 1.88307 1.08719i
\(590\) −4.01534 14.9854i −0.165309 0.616941i
\(591\) 47.7533 12.7955i 1.96431 0.526335i
\(592\) −4.88231 + 1.30821i −0.200662 + 0.0537671i
\(593\) −10.7660 40.1793i −0.442107 1.64997i −0.723464 0.690362i \(-0.757451\pi\)
0.281357 0.959603i \(-0.409216\pi\)
\(594\) 28.5394 16.4772i 1.17099 0.676069i
\(595\) 0 0
\(596\) 18.8282 5.04500i 0.771233 0.206651i
\(597\) −39.2330 22.6512i −1.60570 0.927050i
\(598\) −0.653680 1.05007i −0.0267310 0.0429405i
\(599\) 2.16999 + 3.75853i 0.0886634 + 0.153569i 0.906946 0.421246i \(-0.138407\pi\)
−0.818283 + 0.574816i \(0.805074\pi\)
\(600\) 6.23047 23.2524i 0.254358 0.949277i
\(601\) −5.72067 3.30283i −0.233351 0.134725i 0.378766 0.925492i \(-0.376348\pi\)
−0.612117 + 0.790767i \(0.709682\pi\)
\(602\) 0 0
\(603\) 4.62485 4.62485i 0.188339 0.188339i
\(604\) 11.7763 11.7763i 0.479172 0.479172i
\(605\) 0.466446 + 1.74080i 0.0189637 + 0.0707735i
\(606\) −2.00194 + 7.47135i −0.0813233 + 0.303503i
\(607\) 46.0468i 1.86898i 0.355985 + 0.934492i \(0.384146\pi\)
−0.355985 + 0.934492i \(0.615854\pi\)
\(608\) 15.9168 27.5686i 0.645510 1.11806i
\(609\) 0 0
\(610\) 16.8571i 0.682526i
\(611\) −9.65047 + 6.00753i −0.390416 + 0.243039i
\(612\) −9.00804 + 5.20079i −0.364128 + 0.210230i
\(613\) 20.2929 20.2929i 0.819624 0.819624i −0.166429 0.986053i \(-0.553224\pi\)
0.986053 + 0.166429i \(0.0532237\pi\)
\(614\) −49.8609 + 28.7872i −2.01222 + 1.16176i
\(615\) −12.7583 22.0981i −0.514466 0.891081i
\(616\) 0 0
\(617\) 0.0947548 + 0.0253895i 0.00381469 + 0.00102214i 0.260726 0.965413i \(-0.416038\pi\)
−0.256911 + 0.966435i \(0.582705\pi\)
\(618\) −21.9720 21.9720i −0.883844 0.883844i
\(619\) −40.8542 10.9468i −1.64207 0.439991i −0.684691 0.728834i \(-0.740063\pi\)
−0.957376 + 0.288843i \(0.906729\pi\)
\(620\) −18.7196 + 32.4233i −0.751798 + 1.30215i
\(621\) −0.326566 0.565629i −0.0131047 0.0226979i
\(622\) −14.4058 53.7630i −0.577619 2.15570i
\(623\) 0 0
\(624\) 9.44312 + 8.83587i 0.378027 + 0.353718i
\(625\) −3.32054 + 5.75135i −0.132822 + 0.230054i
\(626\) 23.3558 + 23.3558i 0.933486 + 0.933486i
\(627\) −68.3592 −2.73001
\(628\) 44.2950 1.76756
\(629\) 1.76469 + 1.76469i 0.0703629 + 0.0703629i
\(630\) 0 0
\(631\) 2.02584 7.56053i 0.0806473 0.300980i −0.913807 0.406148i \(-0.866872\pi\)
0.994454 + 0.105169i \(0.0335383\pi\)
\(632\) 2.16670 0.580566i 0.0861868 0.0230937i
\(633\) 23.5783 + 13.6130i 0.937154 + 0.541066i
\(634\) 39.2938i 1.56056i
\(635\) −5.00926 1.34223i −0.198786 0.0532646i
\(636\) −70.9288 −2.81251
\(637\) 0 0
\(638\) 22.0356 0.872397
\(639\) −63.8813 17.1170i −2.52711 0.677136i
\(640\) 32.3059i 1.27700i
\(641\) 28.9275 + 16.7013i 1.14257 + 0.659661i 0.947065 0.321042i \(-0.104033\pi\)
0.195502 + 0.980703i \(0.437366\pi\)
\(642\) 95.7311 25.6511i 3.77820 1.01237i
\(643\) 4.94009 18.4367i 0.194818 0.727071i −0.797496 0.603324i \(-0.793842\pi\)
0.992314 0.123746i \(-0.0394909\pi\)
\(644\) 0 0
\(645\) −8.71667 8.71667i −0.343219 0.343219i
\(646\) 11.8724 0.467113
\(647\) 32.9045 1.29361 0.646804 0.762656i \(-0.276105\pi\)
0.646804 + 0.762656i \(0.276105\pi\)
\(648\) −3.81330 3.81330i −0.149800 0.149800i
\(649\) −6.51491 + 11.2842i −0.255733 + 0.442942i
\(650\) 11.0061 + 17.6802i 0.431696 + 0.693475i
\(651\) 0 0
\(652\) −11.8578 44.2541i −0.464389 1.73312i
\(653\) −13.9982 24.2457i −0.547793 0.948806i −0.998425 0.0560961i \(-0.982135\pi\)
0.450632 0.892710i \(-0.351199\pi\)
\(654\) 41.8021 72.4034i 1.63459 2.83120i
\(655\) −25.3474 6.79182i −0.990405 0.265378i
\(656\) 5.33041 + 5.33041i 0.208117 + 0.208117i
\(657\) 31.4907 + 8.43792i 1.22857 + 0.329195i
\(658\) 0 0
\(659\) −5.35203 9.27000i −0.208486 0.361108i 0.742752 0.669567i \(-0.233520\pi\)
−0.951238 + 0.308459i \(0.900187\pi\)
\(660\) 42.0013 24.2494i 1.63490 0.943908i
\(661\) −16.9884 + 16.9884i −0.660772 + 0.660772i −0.955562 0.294790i \(-0.904750\pi\)
0.294790 + 0.955562i \(0.404750\pi\)
\(662\) −19.6740 + 11.3588i −0.764653 + 0.441473i
\(663\) 1.44693 6.21917i 0.0561942 0.241532i
\(664\) 5.40377i 0.209707i
\(665\) 0 0
\(666\) 21.0872 36.5240i 0.817111 1.41528i
\(667\) 0.436729i 0.0169102i
\(668\) 16.8367 62.8356i 0.651433 2.43118i
\(669\) −6.22697 23.2394i −0.240748 0.898486i
\(670\) 3.74517 3.74517i 0.144688 0.144688i
\(671\) 10.0111 10.0111i 0.386474 0.386474i
\(672\) 0 0
\(673\) 4.79792 + 2.77008i 0.184946 + 0.106779i 0.589615 0.807685i \(-0.299280\pi\)
−0.404668 + 0.914464i \(0.632613\pi\)
\(674\) −12.2015 + 45.5365i −0.469983 + 1.75400i
\(675\) 5.49846 + 9.52362i 0.211636 + 0.366564i
\(676\) −45.5277 + 3.02832i −1.75106 + 0.116474i
\(677\) −38.1640 22.0340i −1.46676 0.846835i −0.467454 0.884018i \(-0.654828\pi\)
−0.999309 + 0.0371822i \(0.988162\pi\)
\(678\) 9.64710 2.58493i 0.370495 0.0992738i
\(679\) 0 0
\(680\) −3.13799 + 1.81172i −0.120336 + 0.0694763i
\(681\) −12.0686 45.0406i −0.462469 1.72596i
\(682\) 47.6798 12.7758i 1.82575 0.489209i
\(683\) −4.97587 + 1.33328i −0.190396 + 0.0510166i −0.352757 0.935715i \(-0.614756\pi\)
0.162361 + 0.986731i \(0.448089\pi\)
\(684\) −33.0787 123.451i −1.26480 4.72028i
\(685\) −0.521554 + 0.301120i −0.0199276 + 0.0115052i
\(686\) 0 0
\(687\) −6.51969 + 1.74695i −0.248742 + 0.0666501i
\(688\) 3.15390 + 1.82090i 0.120241 + 0.0694213i
\(689\) 18.0354 19.2749i 0.687094 0.734315i
\(690\) −0.754466 1.30677i −0.0287220 0.0497480i
\(691\) 0.790947 2.95186i 0.0300891 0.112294i −0.949248 0.314528i \(-0.898154\pi\)
0.979337 + 0.202234i \(0.0648203\pi\)
\(692\) 17.0028 + 9.81655i 0.646348 + 0.373169i
\(693\) 0 0
\(694\) 36.8501 36.8501i 1.39881 1.39881i
\(695\) 11.0870 11.0870i 0.420555 0.420555i
\(696\) 7.56611 + 28.2371i 0.286793 + 1.07032i
\(697\) 0.963328 3.59519i 0.0364886 0.136177i
\(698\) 12.5694i 0.475759i
\(699\) 7.41796 12.8483i 0.280573 0.485967i
\(700\) 0 0
\(701\) 11.0158i 0.416061i −0.978122 0.208031i \(-0.933295\pi\)
0.978122 0.208031i \(-0.0667054\pi\)
\(702\) −37.8015 + 1.25581i −1.42673 + 0.0473977i
\(703\) −26.5563 + 15.3323i −1.00159 + 0.578267i
\(704\) 26.8287 26.8287i 1.01114 1.01114i
\(705\) −12.0097 + 6.93378i −0.452310 + 0.261141i
\(706\) 30.6322 + 53.0566i 1.15286 + 1.99681i
\(707\) 0 0
\(708\) −38.8138 10.4001i −1.45871 0.390860i
\(709\) 19.9197 + 19.9197i 0.748101 + 0.748101i 0.974122 0.226021i \(-0.0725719\pi\)
−0.226021 + 0.974122i \(0.572572\pi\)
\(710\) −51.7306 13.8612i −1.94141 0.520200i
\(711\) −1.46173 + 2.53179i −0.0548192 + 0.0949496i
\(712\) −24.0702 41.6907i −0.902067 1.56243i
\(713\) −0.253206 0.944977i −0.00948263 0.0353897i
\(714\) 0 0
\(715\) −4.09008 + 17.5799i −0.152960 + 0.657450i
\(716\) 16.6557 28.8486i 0.622454 1.07812i
\(717\) −33.0050 33.0050i −1.23260 1.23260i
\(718\) 53.1522 1.98362
\(719\) 42.1118 1.57050 0.785252 0.619176i \(-0.212533\pi\)
0.785252 + 0.619176i \(0.212533\pi\)
\(720\) 6.76309 + 6.76309i 0.252045 + 0.252045i
\(721\) 0 0
\(722\) −26.2130 + 97.8284i −0.975548 + 3.64079i
\(723\) 35.8538 9.60699i 1.33342 0.357288i
\(724\) 21.0195 + 12.1356i 0.781185 + 0.451018i
\(725\) 7.35329i 0.273094i
\(726\) 7.07808 + 1.89657i 0.262692 + 0.0703881i
\(727\) −10.0901 −0.374223 −0.187111 0.982339i \(-0.559913\pi\)
−0.187111 + 0.982339i \(0.559913\pi\)
\(728\) 0 0
\(729\) 44.0349 1.63092
\(730\) 25.5009 + 6.83295i 0.943832 + 0.252899i
\(731\) 1.79812i 0.0665060i
\(732\) 37.8121 + 21.8308i 1.39758 + 0.806891i
\(733\) −25.6687 + 6.87790i −0.948093 + 0.254041i −0.699553 0.714581i \(-0.746618\pi\)
−0.248540 + 0.968622i \(0.579951\pi\)
\(734\) 8.62455 32.1873i 0.318338 1.18805i
\(735\) 0 0
\(736\) −0.417306 0.417306i −0.0153821 0.0153821i
\(737\) −4.44835 −0.163857
\(738\) −62.8988 −2.31534
\(739\) 17.7896 + 17.7896i 0.654402 + 0.654402i 0.954050 0.299648i \(-0.0968692\pi\)
−0.299648 + 0.954050i \(0.596869\pi\)
\(740\) 10.8778 18.8409i 0.399876 0.692605i
\(741\) 69.2108 + 36.9509i 2.54252 + 1.35742i
\(742\) 0 0
\(743\) −2.81817 10.5175i −0.103388 0.385851i 0.894769 0.446530i \(-0.147340\pi\)
−0.998157 + 0.0606785i \(0.980674\pi\)
\(744\) 32.7425 + 56.7117i 1.20040 + 2.07915i
\(745\) −4.42484 + 7.66405i −0.162114 + 0.280789i
\(746\) 7.95021 + 2.13025i 0.291078 + 0.0779941i
\(747\) −4.97993 4.97993i −0.182206 0.182206i
\(748\) 6.83328 + 1.83097i 0.249850 + 0.0669470i
\(749\) 0 0
\(750\) 38.5147 + 66.7094i 1.40636 + 2.43588i
\(751\) 27.9154 16.1170i 1.01865 0.588117i 0.104936 0.994479i \(-0.466536\pi\)
0.913712 + 0.406362i \(0.133203\pi\)
\(752\) 2.89692 2.89692i 0.105640 0.105640i
\(753\) −30.6097 + 17.6725i −1.11548 + 0.644022i
\(754\) −22.3101 11.9111i −0.812485 0.433777i
\(755\) 7.56115i 0.275179i
\(756\) 0 0
\(757\) −16.9609 + 29.3771i −0.616453 + 1.06773i 0.373675 + 0.927560i \(0.378098\pi\)
−0.990128 + 0.140168i \(0.955236\pi\)
\(758\) 63.0133i 2.28875i
\(759\) −0.328004 + 1.22413i −0.0119058 + 0.0444330i
\(760\) −11.5231 43.0048i −0.417987 1.55995i
\(761\) 6.85232 6.85232i 0.248397 0.248397i −0.571916 0.820312i \(-0.693800\pi\)
0.820312 + 0.571916i \(0.193800\pi\)
\(762\) −14.9101 + 14.9101i −0.540137 + 0.540137i
\(763\) 0 0
\(764\) −7.61437 4.39616i −0.275478 0.159047i
\(765\) 1.22225 4.56149i 0.0441904 0.164921i
\(766\) 40.0837 + 69.4270i 1.44828 + 2.50850i
\(767\) 12.6956 7.90316i 0.458411 0.285366i
\(768\) 56.0159 + 32.3408i 2.02130 + 1.16700i
\(769\) 14.6001 3.91210i 0.526495 0.141074i 0.0142256 0.999899i \(-0.495472\pi\)
0.512269 + 0.858825i \(0.328805\pi\)
\(770\) 0 0
\(771\) −24.8147 + 14.3268i −0.893678 + 0.515965i
\(772\) −20.4911 76.4737i −0.737490 2.75235i
\(773\) 37.7776 10.1225i 1.35877 0.364081i 0.495404 0.868663i \(-0.335020\pi\)
0.863364 + 0.504582i \(0.168353\pi\)
\(774\) −29.3513 + 7.86466i −1.05501 + 0.282689i
\(775\) 4.26328 + 15.9108i 0.153142 + 0.571532i
\(776\) 0.577718 0.333546i 0.0207389 0.0119736i
\(777\) 0 0
\(778\) −62.2709 + 16.6854i −2.23252 + 0.598202i
\(779\) 39.6060 + 22.8665i 1.41903 + 0.819279i
\(780\) −55.6323 + 1.84818i −1.99195 + 0.0661753i
\(781\) 22.4898 + 38.9535i