Properties

Label 637.2.x.b.19.7
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 19.7
Character \(\chi\) \(=\) 637.19
Dual form 637.2.x.b.570.8

$q$-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 \(-0.706515\pi\)
0.604219 0.796818i \(-0.293485\pi\)
\(4\) 3.03963 + 1.75493i 1.51982 + 0.877467i
\(5\) 1.53921 0.412430i 0.688355 0.184444i 0.102346 0.994749i \(-0.467365\pi\)
0.586009 + 0.810305i \(0.300698\pi\)
\(6\) 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 −0.902302 0.431104i \(-0.858124\pi\)
0.824498 + 0.565865i \(0.191458\pi\)
\(18\) −10.4729 2.80620i −2.46848 0.661427i
\(19\) −5.57436 5.57436i −1.27885 1.27885i −0.941314 0.337532i \(-0.890408\pi\)
−0.337532 0.941314i \(-0.609592\pi\)
\(20\) 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 \(0.288618\pi\)
−0.927503 + 0.373817i \(0.878049\pi\)
\(32\) −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 −0.668305 0.743888i \(-0.732980\pi\)
−0.206825 + 0.978378i \(0.566313\pi\)
\(42\) 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 0.999557 0.0297773i \(-0.00947981\pi\)
−0.880530 + 0.473990i \(0.842813\pi\)
\(48\) 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 \(-0.996313\pi\)
0.860177 0.509996i \(-0.170353\pi\)
\(60\) 3.99568 14.9121i 0.515840 1.92514i
\(61\) 4.50671i 0.577025i 0.957476 + 0.288512i \(0.0931607\pi\)
−0.957476 + 0.288512i \(0.906839\pi\)
\(62\) −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 0.634679 0.772776i \(-0.281132\pi\)
0.163261 + 0.986583i \(0.447799\pi\)
\(74\) −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 0.645457 0.763797i \(-0.276667\pi\)
−0.763797 + 0.645457i \(0.776667\pi\)
\(84\) 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 0.875013 0.484099i \(-0.160853\pi\)
0.515734 + 0.856749i \(0.327519\pi\)
\(90\) −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 −0.968355 0.249577i \(-0.919708\pi\)
0.963409 + 0.268037i \(0.0863750\pi\)
\(98\) 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 \(-0.518917\pi\)
−0.0593942 + 0.998235i \(0.518917\pi\)
\(102\) 2.93943 + 2.93943i 0.291047 + 0.291047i
\(103\) 2.39792 4.15331i 0.236274 0.409238i −0.723368 0.690462i \(-0.757407\pi\)
0.959642 + 0.281224i \(0.0907404\pi\)
\(104\) −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 −0.275720 0.961238i \(-0.588916\pi\)
−0.970317 + 0.241838i \(0.922250\pi\)
\(132\) 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 −0.0930022 0.995666i \(-0.529646\pi\)
0.815771 + 0.578375i \(0.196313\pi\)
\(140\) 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 −0.868098 0.496394i \(-0.834657\pi\)
−0.00415919 + 0.999991i \(0.501324\pi\)
\(158\) 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 \(0.171200\pi\)
−0.487616 + 0.873058i \(0.662133\pi\)
\(168\) 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 \(-0.568206\pi\)
−0.212640 + 0.977131i \(0.568206\pi\)
\(174\) −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 \(-0.582734\pi\)
−0.257000 + 0.966411i \(0.582734\pi\)
\(182\) 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 \(-0.635713\pi\)
0.995276 0.0970896i \(-0.0309533\pi\)
\(200\) −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 0.0343461 0.999410i \(-0.489065\pi\)
0.529450 + 0.848341i \(0.322398\pi\)
\(224\) 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 0.327194 0.944957i \(-0.393897\pi\)
0.755837 + 0.654760i \(0.227230\pi\)
\(228\) −73.7725 + 19.7673i −4.88570 + 1.30912i
\(229\) −0.632892 2.36198i −0.0418227 0.156084i 0.941857 0.336015i \(-0.109079\pi\)
−0.983679 + 0.179931i \(0.942413\pi\)
\(230\) 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 \(0.0592521\pi\)
−0.758528 + 0.651640i \(0.774081\pi\)
\(242\) 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 0.590098 0.807332i \(-0.299089\pi\)
−0.994219 + 0.107374i \(0.965756\pi\)
\(252\) 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 0.657496 0.753458i \(-0.271616\pi\)
−0.981262 + 0.192679i \(0.938282\pi\)
\(258\) −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 0.158713 0.987325i \(-0.449266\pi\)
−0.775692 + 0.631112i \(0.782599\pi\)
\(270\) 16.7159i 1.01730i
\(271\) 29.6470 + 7.94389i 1.80093 + 0.482557i 0.994122 0.108262i \(-0.0345287\pi\)
0.806804 + 0.590819i \(0.201195\pi\)
\(272\) −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 \(-0.419315\pi\)
0.250772 + 0.968046i \(0.419315\pi\)
\(284\) 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 0.484998 0.874516i \(-0.338820\pi\)
−0.0172376 + 0.999851i \(0.505487\pi\)
\(294\) 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 −0.0100865 0.999949i \(-0.503211\pi\)
0.999949 + 0.0100865i \(0.00321069\pi\)
\(308\) 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 \(0.0680243\pi\)
−0.304958 + 0.952366i \(0.598642\pi\)
\(312\) 31.1153 + 16.6121i 1.76155 + 0.940474i
\(313\) −12.1862 7.03573i −0.688808 0.397683i 0.114358 0.993440i \(-0.463519\pi\)
−0.803165 + 0.595756i \(0.796852\pi\)
\(314\) −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 0.993048 0.117713i \(-0.0375561\pi\)
−0.918861 + 0.394582i \(0.870889\pi\)
\(350\) 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 0.0175643 0.999846i \(-0.494409\pi\)
−0.999846 + 0.0175643i \(0.994409\pi\)
\(354\) −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 \(0.120819\pi\)
−0.928826 + 0.370516i \(0.879181\pi\)
\(368\) 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 \(-0.912455\pi\)
−0.271576 0.962417i \(-0.587545\pi\)
\(384\) −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 \(-0.369678\pi\)
0.917352 0.398076i \(-0.130322\pi\)
\(398\) 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 0.0209119 0.999781i \(-0.493343\pi\)
0.518001 + 0.855380i \(0.326676\pi\)
\(410\) −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 0.0514220 0.998677i \(-0.483625\pi\)
−0.839169 + 0.543871i \(0.816958\pi\)
\(420\) 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 \(-0.835004\pi\)
0.00524758 0.999986i \(-0.498330\pi\)
\(434\) 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 0.958662 0.284548i \(-0.0918434\pi\)
−0.725756 + 0.687952i \(0.758510\pi\)
\(440\) 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 \(0.185449\pi\)
−0.998260 + 0.0589733i \(0.981217\pi\)
\(462\) 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 \(0.420985\pi\)
−0.962326 + 0.271899i \(0.912348\pi\)
\(468\) 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 −0.578426 0.815735i \(-0.696333\pi\)
0.815735 + 0.578426i \(0.196333\pi\)
\(480\) −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 0.0666068 0.997779i \(-0.478783\pi\)
0.897406 + 0.441206i \(0.145449\pi\)
\(504\) 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 −0.949260 0.314491i \(-0.898166\pi\)
0.979329 + 0.202273i \(0.0648328\pi\)
\(510\) 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 −0.944672 0.328016i \(-0.893620\pi\)
−0.188266 + 0.982118i \(0.560287\pi\)
\(522\) −22.9099 + 22.9099i −1.00274 + 1.00274i
\(523\) 13.9268 8.04062i 0.608975 0.351592i −0.163589 0.986529i \(-0.552307\pi\)
0.772564 + 0.634937i \(0.218974\pi\)
\(524\) −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 −0.996544 0.0830642i \(-0.973529\pi\)
0.570208 + 0.821500i \(0.306863\pi\)
\(564\) 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 \(-0.776184\pi\)
0.983926 0.178575i \(-0.0571488\pi\)
\(578\) 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 −0.643715 0.765265i \(-0.722608\pi\)
−0.174842 + 0.984597i \(0.555941\pi\)
\(588\) 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 \(0.242549\pi\)
−0.281357 + 0.959603i \(0.590784\pi\)
\(594\) −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 0.612117 0.790767i \(-0.290318\pi\)
−0.378766 + 0.925492i \(0.623652\pi\)
\(602\) 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 \(-0.615854\pi\)
0.355985 0.934492i \(-0.384146\pi\)
\(608\) −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 0.957376 0.288843i \(-0.0932706\pi\)
0.684691 + 0.728834i \(0.259937\pi\)
\(620\) −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 \(0.206158\pi\)
−0.992314 + 0.123746i \(0.960509\pi\)
\(644\) 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 \(-0.723895\pi\)
−0.646804 + 0.762656i \(0.723895\pi\)
\(648\) −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 −0.294790 0.955562i \(-0.595250\pi\)
0.955562 + 0.294790i \(0.0952498\pi\)
\(662\) −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 0.999309 0.0371822i \(-0.0118382\pi\)
0.467454 + 0.884018i \(0.345172\pi\)
\(678\) −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 −0.979337 0.202234i \(-0.935180\pi\)
0.949248 + 0.314528i \(0.101846\pi\)
\(692\) −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 \(-0.787467\pi\)
−0.785252 + 0.619176i \(0.787467\pi\)
\(720\) −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 \(-0.440087\pi\)
0.187111 + 0.982339i \(0.440087\pi\)
\(728\) 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 0.248540 0.968622i \(-0.420049\pi\)
0.699553 + 0.714581i \(0.253382\pi\)
\(734\) −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 −0.820312 0.571916i \(-0.806200\pi\)
0.571916 + 0.820312i \(0.306200\pi\)
\(762\) 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 −0.512269 0.858825i \(-0.671195\pi\)
−0.0142256 + 0.999899i \(0.504528\pi\)
\(770\) 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 −0.863364 0.504582i \(-0.831647\pi\)
−0.495404 + 0.868663i \(0.664980\pi\)
\(774\) −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