Properties

Label 693.2.m.i.190.3
Level 693
Weight 2
Character 693.190
Analytic conductor 5.534
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 693.m (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.53363286007\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 190.3
Root \(0.901622 - 0.655067i\)
Character \(\chi\) = 693.190
Dual form 693.2.m.i.631.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.901622 - 0.655067i) q^{2} +(-0.234224 + 0.720867i) q^{4} +(2.79603 + 2.03143i) q^{5} +(0.309017 - 0.951057i) q^{7} +(0.949813 + 2.92322i) q^{8} +O(q^{10})\) \(q+(0.901622 - 0.655067i) q^{2} +(-0.234224 + 0.720867i) q^{4} +(2.79603 + 2.03143i) q^{5} +(0.309017 - 0.951057i) q^{7} +(0.949813 + 2.92322i) q^{8} +3.85168 q^{10} +(-3.31530 - 0.0938970i) q^{11} +(1.66629 - 1.21063i) q^{13} +(-0.344389 - 1.05992i) q^{14} +(1.54487 + 1.12241i) q^{16} +(1.56442 + 1.13662i) q^{17} +(0.501522 + 1.54353i) q^{19} +(-2.11929 + 1.53975i) q^{20} +(-3.05065 + 2.08708i) q^{22} +0.807136 q^{23} +(2.14596 + 6.60459i) q^{25} +(0.709322 - 2.18307i) q^{26} +(0.613206 + 0.445520i) q^{28} +(-2.46400 + 7.58342i) q^{29} +(-0.637845 + 0.463421i) q^{31} -4.01918 q^{32} +2.15508 q^{34} +(2.79603 - 2.03143i) q^{35} +(3.10926 - 9.56931i) q^{37} +(1.46330 + 1.06315i) q^{38} +(-3.28263 + 10.1029i) q^{40} +(0.657011 + 2.02207i) q^{41} +3.08043 q^{43} +(0.844208 - 2.36789i) q^{44} +(0.727732 - 0.528728i) q^{46} +(-2.33812 - 7.19600i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(6.26129 + 4.54910i) q^{50} +(0.482420 + 1.48474i) q^{52} +(8.75554 - 6.36127i) q^{53} +(-9.07891 - 6.99733i) q^{55} +3.07366 q^{56} +(2.74605 + 8.45147i) q^{58} +(1.01872 - 3.13529i) q^{59} +(0.871010 + 0.632826i) q^{61} +(-0.271523 + 0.835662i) q^{62} +(-6.71351 + 4.87765i) q^{64} +7.11832 q^{65} +2.40314 q^{67} +(-1.18577 + 0.861515i) q^{68} +(1.19024 - 3.66317i) q^{70} +(-2.57963 - 1.87421i) q^{71} +(0.378940 - 1.16626i) q^{73} +(-3.46516 - 10.6647i) q^{74} -1.23015 q^{76} +(-1.11378 + 3.12402i) q^{77} +(7.67096 - 5.57328i) q^{79} +(2.03939 + 6.27659i) q^{80} +(1.91697 + 1.39276i) q^{82} +(-13.0004 - 9.44536i) q^{83} +(2.06520 + 6.35602i) q^{85} +(2.77738 - 2.01789i) q^{86} +(-2.87443 - 9.78053i) q^{88} +4.43830 q^{89} +(-0.636468 - 1.95885i) q^{91} +(-0.189050 + 0.581837i) q^{92} +(-6.82196 - 4.95645i) q^{94} +(-1.73330 + 5.33455i) q^{95} +(-5.23278 + 3.80184i) q^{97} -1.11447 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 3q^{2} - 11q^{4} + 5q^{5} - 4q^{7} + 5q^{8} + O(q^{10}) \) \( 16q + 3q^{2} - 11q^{4} + 5q^{5} - 4q^{7} + 5q^{8} + 12q^{10} + 3q^{11} - 7q^{13} - 2q^{14} + 17q^{16} + 5q^{17} + 19q^{19} - q^{20} - 33q^{22} - 32q^{23} + 7q^{25} + 27q^{26} + 4q^{28} - 3q^{29} - 7q^{31} - 32q^{32} - 24q^{34} + 5q^{35} + 4q^{37} + 5q^{38} - 10q^{40} + 10q^{41} - 8q^{43} + 38q^{44} - 42q^{46} + 23q^{47} - 4q^{49} - 52q^{50} + 33q^{52} - 4q^{53} - 12q^{55} + 20q^{58} - 17q^{59} - 7q^{61} - 79q^{62} + 7q^{64} + 8q^{65} - 38q^{67} + 2q^{68} - 18q^{70} + 14q^{71} - 35q^{73} + 29q^{74} + 52q^{76} + 3q^{77} + 15q^{79} + 87q^{80} + 19q^{82} - 5q^{83} + 6q^{85} + 52q^{86} + 55q^{88} - 74q^{89} + 13q^{91} + 55q^{92} - 24q^{94} - 32q^{95} + 20q^{97} - 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(442\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.901622 0.655067i 0.637543 0.463202i −0.221462 0.975169i \(-0.571083\pi\)
0.859005 + 0.511967i \(0.171083\pi\)
\(3\) 0 0
\(4\) −0.234224 + 0.720867i −0.117112 + 0.360433i
\(5\) 2.79603 + 2.03143i 1.25042 + 0.908484i 0.998246 0.0591979i \(-0.0188543\pi\)
0.252174 + 0.967682i \(0.418854\pi\)
\(6\) 0 0
\(7\) 0.309017 0.951057i 0.116797 0.359466i
\(8\) 0.949813 + 2.92322i 0.335810 + 1.03352i
\(9\) 0 0
\(10\) 3.85168 1.21801
\(11\) −3.31530 0.0938970i −0.999599 0.0283110i
\(12\) 0 0
\(13\) 1.66629 1.21063i 0.462147 0.335769i −0.332226 0.943200i \(-0.607800\pi\)
0.794373 + 0.607430i \(0.207800\pi\)
\(14\) −0.344389 1.05992i −0.0920419 0.283276i
\(15\) 0 0
\(16\) 1.54487 + 1.12241i 0.386217 + 0.280603i
\(17\) 1.56442 + 1.13662i 0.379427 + 0.275670i 0.761109 0.648624i \(-0.224655\pi\)
−0.381682 + 0.924294i \(0.624655\pi\)
\(18\) 0 0
\(19\) 0.501522 + 1.54353i 0.115057 + 0.354109i 0.991959 0.126560i \(-0.0403937\pi\)
−0.876902 + 0.480669i \(0.840394\pi\)
\(20\) −2.11929 + 1.53975i −0.473887 + 0.344299i
\(21\) 0 0
\(22\) −3.05065 + 2.08708i −0.650401 + 0.444967i
\(23\) 0.807136 0.168299 0.0841497 0.996453i \(-0.473183\pi\)
0.0841497 + 0.996453i \(0.473183\pi\)
\(24\) 0 0
\(25\) 2.14596 + 6.60459i 0.429192 + 1.32092i
\(26\) 0.709322 2.18307i 0.139109 0.428135i
\(27\) 0 0
\(28\) 0.613206 + 0.445520i 0.115885 + 0.0841954i
\(29\) −2.46400 + 7.58342i −0.457554 + 1.40821i 0.410557 + 0.911835i \(0.365334\pi\)
−0.868111 + 0.496371i \(0.834666\pi\)
\(30\) 0 0
\(31\) −0.637845 + 0.463421i −0.114560 + 0.0832330i −0.643590 0.765370i \(-0.722556\pi\)
0.529030 + 0.848603i \(0.322556\pi\)
\(32\) −4.01918 −0.710497
\(33\) 0 0
\(34\) 2.15508 0.369592
\(35\) 2.79603 2.03143i 0.472615 0.343375i
\(36\) 0 0
\(37\) 3.10926 9.56931i 0.511159 1.57318i −0.279005 0.960290i \(-0.590005\pi\)
0.790164 0.612895i \(-0.209995\pi\)
\(38\) 1.46330 + 1.06315i 0.237378 + 0.172465i
\(39\) 0 0
\(40\) −3.28263 + 10.1029i −0.519029 + 1.59741i
\(41\) 0.657011 + 2.02207i 0.102608 + 0.315795i 0.989162 0.146831i \(-0.0469074\pi\)
−0.886554 + 0.462626i \(0.846907\pi\)
\(42\) 0 0
\(43\) 3.08043 0.469761 0.234880 0.972024i \(-0.424530\pi\)
0.234880 + 0.972024i \(0.424530\pi\)
\(44\) 0.844208 2.36789i 0.127269 0.356973i
\(45\) 0 0
\(46\) 0.727732 0.528728i 0.107298 0.0779567i
\(47\) −2.33812 7.19600i −0.341050 1.04964i −0.963665 0.267115i \(-0.913930\pi\)
0.622615 0.782529i \(-0.286070\pi\)
\(48\) 0 0
\(49\) −0.809017 0.587785i −0.115574 0.0839693i
\(50\) 6.26129 + 4.54910i 0.885481 + 0.643339i
\(51\) 0 0
\(52\) 0.482420 + 1.48474i 0.0668996 + 0.205896i
\(53\) 8.75554 6.36127i 1.20267 0.873788i 0.208122 0.978103i \(-0.433265\pi\)
0.994544 + 0.104315i \(0.0332649\pi\)
\(54\) 0 0
\(55\) −9.07891 6.99733i −1.22420 0.943520i
\(56\) 3.07366 0.410735
\(57\) 0 0
\(58\) 2.74605 + 8.45147i 0.360574 + 1.10973i
\(59\) 1.01872 3.13529i 0.132626 0.408180i −0.862587 0.505908i \(-0.831158\pi\)
0.995213 + 0.0977281i \(0.0311576\pi\)
\(60\) 0 0
\(61\) 0.871010 + 0.632826i 0.111521 + 0.0810250i 0.642148 0.766581i \(-0.278043\pi\)
−0.530627 + 0.847606i \(0.678043\pi\)
\(62\) −0.271523 + 0.835662i −0.0344835 + 0.106129i
\(63\) 0 0
\(64\) −6.71351 + 4.87765i −0.839189 + 0.609707i
\(65\) 7.11832 0.882919
\(66\) 0 0
\(67\) 2.40314 0.293590 0.146795 0.989167i \(-0.453104\pi\)
0.146795 + 0.989167i \(0.453104\pi\)
\(68\) −1.18577 + 0.861515i −0.143796 + 0.104474i
\(69\) 0 0
\(70\) 1.19024 3.66317i 0.142260 0.437832i
\(71\) −2.57963 1.87421i −0.306145 0.222428i 0.424095 0.905618i \(-0.360592\pi\)
−0.730241 + 0.683190i \(0.760592\pi\)
\(72\) 0 0
\(73\) 0.378940 1.16626i 0.0443516 0.136500i −0.926429 0.376470i \(-0.877138\pi\)
0.970780 + 0.239970i \(0.0771377\pi\)
\(74\) −3.46516 10.6647i −0.402817 1.23974i
\(75\) 0 0
\(76\) −1.23015 −0.141107
\(77\) −1.11378 + 3.12402i −0.126927 + 0.356015i
\(78\) 0 0
\(79\) 7.67096 5.57328i 0.863050 0.627043i −0.0656630 0.997842i \(-0.520916\pi\)
0.928713 + 0.370799i \(0.120916\pi\)
\(80\) 2.03939 + 6.27659i 0.228010 + 0.701744i
\(81\) 0 0
\(82\) 1.91697 + 1.39276i 0.211694 + 0.153805i
\(83\) −13.0004 9.44536i −1.42698 1.03676i −0.990569 0.137016i \(-0.956249\pi\)
−0.436412 0.899747i \(-0.643751\pi\)
\(84\) 0 0
\(85\) 2.06520 + 6.35602i 0.224002 + 0.689407i
\(86\) 2.77738 2.01789i 0.299493 0.217594i
\(87\) 0 0
\(88\) −2.87443 9.78053i −0.306415 1.04261i
\(89\) 4.43830 0.470459 0.235230 0.971940i \(-0.424416\pi\)
0.235230 + 0.971940i \(0.424416\pi\)
\(90\) 0 0
\(91\) −0.636468 1.95885i −0.0667199 0.205343i
\(92\) −0.189050 + 0.581837i −0.0197099 + 0.0606607i
\(93\) 0 0
\(94\) −6.82196 4.95645i −0.703632 0.511218i
\(95\) −1.73330 + 5.33455i −0.177833 + 0.547313i
\(96\) 0 0
\(97\) −5.23278 + 3.80184i −0.531308 + 0.386018i −0.820847 0.571148i \(-0.806498\pi\)
0.289539 + 0.957166i \(0.406498\pi\)
\(98\) −1.11447 −0.112578
\(99\) 0 0
\(100\) −5.26366 −0.526366
\(101\) −12.4952 + 9.07828i −1.24332 + 0.903323i −0.997815 0.0660728i \(-0.978953\pi\)
−0.245503 + 0.969396i \(0.578953\pi\)
\(102\) 0 0
\(103\) 2.75276 8.47213i 0.271238 0.834784i −0.718953 0.695059i \(-0.755378\pi\)
0.990190 0.139725i \(-0.0446218\pi\)
\(104\) 5.12162 + 3.72107i 0.502216 + 0.364881i
\(105\) 0 0
\(106\) 3.72713 11.4709i 0.362011 1.11416i
\(107\) −1.08533 3.34029i −0.104922 0.322918i 0.884790 0.465990i \(-0.154302\pi\)
−0.989712 + 0.143072i \(0.954302\pi\)
\(108\) 0 0
\(109\) 3.87655 0.371306 0.185653 0.982615i \(-0.440560\pi\)
0.185653 + 0.982615i \(0.440560\pi\)
\(110\) −12.7695 0.361662i −1.21752 0.0344831i
\(111\) 0 0
\(112\) 1.54487 1.12241i 0.145976 0.106058i
\(113\) −3.29224 10.1325i −0.309708 0.953183i −0.977878 0.209175i \(-0.932922\pi\)
0.668170 0.744008i \(-0.267078\pi\)
\(114\) 0 0
\(115\) 2.25677 + 1.63964i 0.210445 + 0.152897i
\(116\) −4.88951 3.55243i −0.453979 0.329835i
\(117\) 0 0
\(118\) −1.13533 3.49417i −0.104515 0.321665i
\(119\) 1.56442 1.13662i 0.143410 0.104194i
\(120\) 0 0
\(121\) 10.9824 + 0.622593i 0.998397 + 0.0565993i
\(122\) 1.19987 0.108631
\(123\) 0 0
\(124\) −0.184667 0.568346i −0.0165836 0.0510389i
\(125\) −2.07667 + 6.39134i −0.185743 + 0.571659i
\(126\) 0 0
\(127\) −15.7361 11.4330i −1.39635 1.01451i −0.995134 0.0985289i \(-0.968586\pi\)
−0.401220 0.915982i \(-0.631414\pi\)
\(128\) −0.373878 + 1.15068i −0.0330464 + 0.101706i
\(129\) 0 0
\(130\) 6.41804 4.66298i 0.562899 0.408970i
\(131\) −5.11284 −0.446711 −0.223355 0.974737i \(-0.571701\pi\)
−0.223355 + 0.974737i \(0.571701\pi\)
\(132\) 0 0
\(133\) 1.62296 0.140728
\(134\) 2.16672 1.57422i 0.187176 0.135992i
\(135\) 0 0
\(136\) −1.83668 + 5.65272i −0.157494 + 0.484717i
\(137\) 7.36247 + 5.34915i 0.629019 + 0.457009i 0.856060 0.516876i \(-0.172905\pi\)
−0.227042 + 0.973885i \(0.572905\pi\)
\(138\) 0 0
\(139\) −4.02234 + 12.3795i −0.341171 + 1.05002i 0.622431 + 0.782675i \(0.286145\pi\)
−0.963602 + 0.267341i \(0.913855\pi\)
\(140\) 0.809496 + 2.49137i 0.0684149 + 0.210559i
\(141\) 0 0
\(142\) −3.55358 −0.298210
\(143\) −5.63793 + 3.85715i −0.471468 + 0.322551i
\(144\) 0 0
\(145\) −22.2946 + 16.1980i −1.85147 + 1.34517i
\(146\) −0.422316 1.29975i −0.0349511 0.107568i
\(147\) 0 0
\(148\) 6.16994 + 4.48272i 0.507166 + 0.368477i
\(149\) −2.54557 1.84947i −0.208541 0.151514i 0.478612 0.878026i \(-0.341140\pi\)
−0.687153 + 0.726512i \(0.741140\pi\)
\(150\) 0 0
\(151\) 0.885940 + 2.72664i 0.0720968 + 0.221891i 0.980612 0.195962i \(-0.0627828\pi\)
−0.908515 + 0.417853i \(0.862783\pi\)
\(152\) −4.03572 + 2.93212i −0.327340 + 0.237827i
\(153\) 0 0
\(154\) 1.04223 + 3.54629i 0.0839851 + 0.285768i
\(155\) −2.72484 −0.218864
\(156\) 0 0
\(157\) −6.64062 20.4377i −0.529979 1.63111i −0.754254 0.656582i \(-0.772001\pi\)
0.224275 0.974526i \(-0.427999\pi\)
\(158\) 3.26544 10.0500i 0.259784 0.799534i
\(159\) 0 0
\(160\) −11.2377 8.16468i −0.888420 0.645475i
\(161\) 0.249419 0.767632i 0.0196569 0.0604978i
\(162\) 0 0
\(163\) 6.65210 4.83304i 0.521033 0.378553i −0.295960 0.955200i \(-0.595639\pi\)
0.816993 + 0.576648i \(0.195639\pi\)
\(164\) −1.61153 −0.125840
\(165\) 0 0
\(166\) −17.9088 −1.38999
\(167\) −17.5626 + 12.7600i −1.35904 + 0.987397i −0.360529 + 0.932748i \(0.617404\pi\)
−0.998506 + 0.0546489i \(0.982596\pi\)
\(168\) 0 0
\(169\) −2.70632 + 8.32919i −0.208178 + 0.640707i
\(170\) 6.02565 + 4.37789i 0.462146 + 0.335769i
\(171\) 0 0
\(172\) −0.721509 + 2.22058i −0.0550146 + 0.169317i
\(173\) 2.48624 + 7.65185i 0.189025 + 0.581760i 0.999994 0.00332915i \(-0.00105970\pi\)
−0.810969 + 0.585089i \(0.801060\pi\)
\(174\) 0 0
\(175\) 6.94447 0.524953
\(176\) −5.01630 3.86619i −0.378118 0.291425i
\(177\) 0 0
\(178\) 4.00167 2.90739i 0.299938 0.217918i
\(179\) 1.11892 + 3.44369i 0.0836322 + 0.257393i 0.984125 0.177478i \(-0.0567938\pi\)
−0.900493 + 0.434871i \(0.856794\pi\)
\(180\) 0 0
\(181\) −12.7970 9.29753i −0.951190 0.691080i −0.000102207 1.00000i \(-0.500033\pi\)
−0.951088 + 0.308920i \(0.900033\pi\)
\(182\) −1.85703 1.34921i −0.137652 0.100010i
\(183\) 0 0
\(184\) 0.766628 + 2.35944i 0.0565165 + 0.173940i
\(185\) 28.1330 20.4398i 2.06838 1.50276i
\(186\) 0 0
\(187\) −5.07979 3.91512i −0.371471 0.286302i
\(188\) 5.73500 0.418268
\(189\) 0 0
\(190\) 1.93170 + 5.94518i 0.140141 + 0.431308i
\(191\) −0.132593 + 0.408080i −0.00959411 + 0.0295276i −0.955739 0.294216i \(-0.904942\pi\)
0.946145 + 0.323744i \(0.104942\pi\)
\(192\) 0 0
\(193\) 12.2767 + 8.91954i 0.883696 + 0.642042i 0.934227 0.356680i \(-0.116091\pi\)
−0.0505310 + 0.998722i \(0.516091\pi\)
\(194\) −2.22753 + 6.85564i −0.159927 + 0.492206i
\(195\) 0 0
\(196\) 0.613206 0.445520i 0.0438004 0.0318229i
\(197\) 20.8082 1.48252 0.741262 0.671216i \(-0.234228\pi\)
0.741262 + 0.671216i \(0.234228\pi\)
\(198\) 0 0
\(199\) 8.44567 0.598698 0.299349 0.954144i \(-0.403231\pi\)
0.299349 + 0.954144i \(0.403231\pi\)
\(200\) −17.2684 + 12.5462i −1.22106 + 0.887153i
\(201\) 0 0
\(202\) −5.31906 + 16.3704i −0.374247 + 1.15182i
\(203\) 6.45084 + 4.68681i 0.452760 + 0.328950i
\(204\) 0 0
\(205\) −2.27068 + 6.98844i −0.158591 + 0.488094i
\(206\) −3.06786 9.44190i −0.213748 0.657849i
\(207\) 0 0
\(208\) 3.93303 0.272707
\(209\) −1.51776 5.16434i −0.104986 0.357225i
\(210\) 0 0
\(211\) 7.97632 5.79513i 0.549112 0.398953i −0.278346 0.960481i \(-0.589786\pi\)
0.827458 + 0.561528i \(0.189786\pi\)
\(212\) 2.53487 + 7.80154i 0.174096 + 0.535812i
\(213\) 0 0
\(214\) −3.16667 2.30072i −0.216469 0.157274i
\(215\) 8.61295 + 6.25768i 0.587399 + 0.426770i
\(216\) 0 0
\(217\) 0.243635 + 0.749832i 0.0165390 + 0.0509019i
\(218\) 3.49518 2.53940i 0.236724 0.171990i
\(219\) 0 0
\(220\) 7.17064 4.90574i 0.483445 0.330745i
\(221\) 3.98281 0.267913
\(222\) 0 0
\(223\) 5.37562 + 16.5445i 0.359978 + 1.10790i 0.953066 + 0.302762i \(0.0979087\pi\)
−0.593088 + 0.805138i \(0.702091\pi\)
\(224\) −1.24199 + 3.82246i −0.0829842 + 0.255399i
\(225\) 0 0
\(226\) −9.60581 6.97903i −0.638969 0.464238i
\(227\) 3.90334 12.0133i 0.259074 0.797348i −0.733926 0.679230i \(-0.762314\pi\)
0.993000 0.118118i \(-0.0376861\pi\)
\(228\) 0 0
\(229\) −3.69997 + 2.68819i −0.244501 + 0.177640i −0.703286 0.710907i \(-0.748285\pi\)
0.458785 + 0.888547i \(0.348285\pi\)
\(230\) 3.10883 0.204990
\(231\) 0 0
\(232\) −24.5084 −1.60905
\(233\) 19.3006 14.0227i 1.26443 0.918659i 0.265460 0.964122i \(-0.414476\pi\)
0.998966 + 0.0454624i \(0.0144761\pi\)
\(234\) 0 0
\(235\) 8.08073 24.8699i 0.527129 1.62234i
\(236\) 2.02152 + 1.46872i 0.131590 + 0.0956054i
\(237\) 0 0
\(238\) 0.665955 2.04960i 0.0431675 0.132856i
\(239\) −2.73114 8.40558i −0.176663 0.543711i 0.823043 0.567979i \(-0.192275\pi\)
−0.999705 + 0.0242677i \(0.992275\pi\)
\(240\) 0 0
\(241\) 18.9464 1.22045 0.610224 0.792229i \(-0.291079\pi\)
0.610224 + 0.792229i \(0.291079\pi\)
\(242\) 10.3098 6.63284i 0.662738 0.426375i
\(243\) 0 0
\(244\) −0.660194 + 0.479659i −0.0422646 + 0.0307070i
\(245\) −1.06799 3.28693i −0.0682312 0.209994i
\(246\) 0 0
\(247\) 2.70433 + 1.96481i 0.172072 + 0.125018i
\(248\) −1.96052 1.42440i −0.124493 0.0904495i
\(249\) 0 0
\(250\) 2.31438 + 7.12294i 0.146374 + 0.450494i
\(251\) −2.31938 + 1.68513i −0.146398 + 0.106364i −0.658573 0.752516i \(-0.728840\pi\)
0.512175 + 0.858881i \(0.328840\pi\)
\(252\) 0 0
\(253\) −2.67589 0.0757876i −0.168232 0.00476473i
\(254\) −21.6774 −1.36016
\(255\) 0 0
\(256\) −4.71199 14.5020i −0.294500 0.906377i
\(257\) −6.92689 + 21.3188i −0.432087 + 1.32983i 0.463955 + 0.885859i \(0.346430\pi\)
−0.896042 + 0.443969i \(0.853570\pi\)
\(258\) 0 0
\(259\) −8.14014 5.91416i −0.505804 0.367488i
\(260\) −1.66728 + 5.13136i −0.103400 + 0.318234i
\(261\) 0 0
\(262\) −4.60985 + 3.34925i −0.284797 + 0.206917i
\(263\) −0.990706 −0.0610895 −0.0305448 0.999533i \(-0.509724\pi\)
−0.0305448 + 0.999533i \(0.509724\pi\)
\(264\) 0 0
\(265\) 37.4032 2.29766
\(266\) 1.46330 1.06315i 0.0897205 0.0651858i
\(267\) 0 0
\(268\) −0.562873 + 1.73234i −0.0343829 + 0.105820i
\(269\) −5.81713 4.22639i −0.354677 0.257688i 0.396152 0.918185i \(-0.370345\pi\)
−0.750828 + 0.660497i \(0.770345\pi\)
\(270\) 0 0
\(271\) −8.39423 + 25.8348i −0.509913 + 1.56935i 0.282438 + 0.959285i \(0.408857\pi\)
−0.792351 + 0.610065i \(0.791143\pi\)
\(272\) 1.14107 + 3.51185i 0.0691874 + 0.212937i
\(273\) 0 0
\(274\) 10.1422 0.612714
\(275\) −6.49434 22.0977i −0.391624 1.33254i
\(276\) 0 0
\(277\) −16.9777 + 12.3350i −1.02009 + 0.741140i −0.966302 0.257412i \(-0.917130\pi\)
−0.0537900 + 0.998552i \(0.517130\pi\)
\(278\) 4.48277 + 13.7965i 0.268859 + 0.827462i
\(279\) 0 0
\(280\) 8.59403 + 6.24393i 0.513592 + 0.373146i
\(281\) −22.7803 16.5509i −1.35896 0.987341i −0.998510 0.0545621i \(-0.982624\pi\)
−0.360448 0.932779i \(-0.617376\pi\)
\(282\) 0 0
\(283\) −8.09369 24.9098i −0.481120 1.48074i −0.837523 0.546403i \(-0.815997\pi\)
0.356403 0.934332i \(-0.384003\pi\)
\(284\) 1.95527 1.42058i 0.116024 0.0842961i
\(285\) 0 0
\(286\) −2.55660 + 7.17091i −0.151175 + 0.424025i
\(287\) 2.12613 0.125502
\(288\) 0 0
\(289\) −4.09778 12.6117i −0.241046 0.741863i
\(290\) −9.49056 + 29.2089i −0.557305 + 1.71521i
\(291\) 0 0
\(292\) 0.751959 + 0.546331i 0.0440051 + 0.0319716i
\(293\) 1.37941 4.24538i 0.0805858 0.248017i −0.902644 0.430388i \(-0.858377\pi\)
0.983230 + 0.182370i \(0.0583769\pi\)
\(294\) 0 0
\(295\) 9.21748 6.69689i 0.536663 0.389908i
\(296\) 30.9264 1.79756
\(297\) 0 0
\(298\) −3.50667 −0.203136
\(299\) 1.34493 0.977145i 0.0777790 0.0565098i
\(300\) 0 0
\(301\) 0.951904 2.92966i 0.0548669 0.168863i
\(302\) 2.58492 + 1.87805i 0.148745 + 0.108070i
\(303\) 0 0
\(304\) −0.957688 + 2.94746i −0.0549271 + 0.169048i
\(305\) 1.14982 + 3.53879i 0.0658387 + 0.202631i
\(306\) 0 0
\(307\) 12.8841 0.735334 0.367667 0.929957i \(-0.380157\pi\)
0.367667 + 0.929957i \(0.380157\pi\)
\(308\) −1.99113 1.53461i −0.113455 0.0874425i
\(309\) 0 0
\(310\) −2.45678 + 1.78495i −0.139536 + 0.101379i
\(311\) −8.28779 25.5072i −0.469957 1.44638i −0.852639 0.522500i \(-0.824999\pi\)
0.382682 0.923880i \(-0.375001\pi\)
\(312\) 0 0
\(313\) −2.90331 2.10938i −0.164105 0.119229i 0.502702 0.864460i \(-0.332339\pi\)
−0.666807 + 0.745231i \(0.732339\pi\)
\(314\) −19.3754 14.0771i −1.09342 0.794415i
\(315\) 0 0
\(316\) 2.22087 + 6.83513i 0.124934 + 0.384506i
\(317\) −13.6870 + 9.94418i −0.768738 + 0.558521i −0.901578 0.432617i \(-0.857590\pi\)
0.132840 + 0.991138i \(0.457590\pi\)
\(318\) 0 0
\(319\) 8.88095 24.9099i 0.497238 1.39469i
\(320\) −28.6798 −1.60325
\(321\) 0 0
\(322\) −0.277969 0.855500i −0.0154906 0.0476751i
\(323\) −0.969808 + 2.98476i −0.0539616 + 0.166077i
\(324\) 0 0
\(325\) 11.5715 + 8.40721i 0.641873 + 0.466348i
\(326\) 2.83172 8.71515i 0.156835 0.482687i
\(327\) 0 0
\(328\) −5.28693 + 3.84118i −0.291922 + 0.212094i
\(329\) −7.56632 −0.417145
\(330\) 0 0
\(331\) −1.23826 −0.0680610 −0.0340305 0.999421i \(-0.510834\pi\)
−0.0340305 + 0.999421i \(0.510834\pi\)
\(332\) 9.85385 7.15924i 0.540800 0.392914i
\(333\) 0 0
\(334\) −7.47620 + 23.0094i −0.409079 + 1.25902i
\(335\) 6.71924 + 4.88181i 0.367111 + 0.266722i
\(336\) 0 0
\(337\) −6.32885 + 19.4782i −0.344754 + 1.06104i 0.616961 + 0.786994i \(0.288364\pi\)
−0.961715 + 0.274051i \(0.911636\pi\)
\(338\) 3.01610 + 9.28261i 0.164054 + 0.504907i
\(339\) 0 0
\(340\) −5.06556 −0.274719
\(341\) 2.15816 1.47649i 0.116871 0.0799563i
\(342\) 0 0
\(343\) −0.809017 + 0.587785i −0.0436828 + 0.0317374i
\(344\) 2.92583 + 9.00478i 0.157750 + 0.485505i
\(345\) 0 0
\(346\) 7.25412 + 5.27043i 0.389984 + 0.283340i
\(347\) 22.0618 + 16.0288i 1.18434 + 0.860472i 0.992654 0.120985i \(-0.0386052\pi\)
0.191684 + 0.981457i \(0.438605\pi\)
\(348\) 0 0
\(349\) 2.46730 + 7.59356i 0.132071 + 0.406474i 0.995123 0.0986418i \(-0.0314498\pi\)
−0.863052 + 0.505116i \(0.831450\pi\)
\(350\) 6.26129 4.54910i 0.334680 0.243159i
\(351\) 0 0
\(352\) 13.3248 + 0.377388i 0.710212 + 0.0201149i
\(353\) −5.93472 −0.315873 −0.157937 0.987449i \(-0.550484\pi\)
−0.157937 + 0.987449i \(0.550484\pi\)
\(354\) 0 0
\(355\) −3.40538 10.4807i −0.180739 0.556256i
\(356\) −1.03956 + 3.19942i −0.0550964 + 0.169569i
\(357\) 0 0
\(358\) 3.26469 + 2.37194i 0.172544 + 0.125361i
\(359\) −8.78235 + 27.0293i −0.463515 + 1.42655i 0.397326 + 0.917677i \(0.369938\pi\)
−0.860841 + 0.508874i \(0.830062\pi\)
\(360\) 0 0
\(361\) 13.2404 9.61969i 0.696862 0.506300i
\(362\) −17.6285 −0.926535
\(363\) 0 0
\(364\) 1.56114 0.0818261
\(365\) 3.42870 2.49109i 0.179466 0.130390i
\(366\) 0 0
\(367\) −9.39456 + 28.9135i −0.490392 + 1.50927i 0.333625 + 0.942706i \(0.391728\pi\)
−0.824017 + 0.566565i \(0.808272\pi\)
\(368\) 1.24692 + 0.905939i 0.0650001 + 0.0472253i
\(369\) 0 0
\(370\) 11.9759 36.8580i 0.622596 1.91615i
\(371\) −3.34432 10.2928i −0.173628 0.534373i
\(372\) 0 0
\(373\) 14.4226 0.746772 0.373386 0.927676i \(-0.378197\pi\)
0.373386 + 0.927676i \(0.378197\pi\)
\(374\) −7.14471 0.202355i −0.369444 0.0104635i
\(375\) 0 0
\(376\) 18.8147 13.6697i 0.970296 0.704961i
\(377\) 5.07499 + 15.6192i 0.261375 + 0.804430i
\(378\) 0 0
\(379\) 18.1278 + 13.1706i 0.931163 + 0.676529i 0.946277 0.323356i \(-0.104811\pi\)
−0.0151144 + 0.999886i \(0.504811\pi\)
\(380\) −3.43952 2.49896i −0.176444 0.128194i
\(381\) 0 0
\(382\) 0.147771 + 0.454792i 0.00756061 + 0.0232692i
\(383\) 27.2465 19.7957i 1.39223 1.01152i 0.396615 0.917985i \(-0.370185\pi\)
0.995616 0.0935305i \(-0.0298153\pi\)
\(384\) 0 0
\(385\) −9.46040 + 6.47226i −0.482146 + 0.329857i
\(386\) 16.9118 0.860790
\(387\) 0 0
\(388\) −1.51498 4.66262i −0.0769112 0.236708i
\(389\) −0.750241 + 2.30900i −0.0380387 + 0.117071i −0.968273 0.249896i \(-0.919604\pi\)
0.930234 + 0.366967i \(0.119604\pi\)
\(390\) 0 0
\(391\) 1.26270 + 0.917404i 0.0638574 + 0.0463951i
\(392\) 0.949813 2.92322i 0.0479728 0.147645i
\(393\) 0 0
\(394\) 18.7611 13.6308i 0.945173 0.686708i
\(395\) 32.7699 1.64883
\(396\) 0 0
\(397\) −5.89696 −0.295960 −0.147980 0.988990i \(-0.547277\pi\)
−0.147980 + 0.988990i \(0.547277\pi\)
\(398\) 7.61481 5.53248i 0.381696 0.277318i
\(399\) 0 0
\(400\) −4.09784 + 12.6119i −0.204892 + 0.630593i
\(401\) 9.09302 + 6.60646i 0.454084 + 0.329911i 0.791206 0.611550i \(-0.209454\pi\)
−0.337122 + 0.941461i \(0.609454\pi\)
\(402\) 0 0
\(403\) −0.501804 + 1.54439i −0.0249966 + 0.0769317i
\(404\) −3.61756 11.1337i −0.179981 0.553923i
\(405\) 0 0
\(406\) 8.88640 0.441025
\(407\) −11.2066 + 31.4331i −0.555492 + 1.55808i
\(408\) 0 0
\(409\) −23.7320 + 17.2423i −1.17347 + 0.852578i −0.991421 0.130711i \(-0.958274\pi\)
−0.182052 + 0.983289i \(0.558274\pi\)
\(410\) 2.53060 + 7.78839i 0.124977 + 0.384641i
\(411\) 0 0
\(412\) 5.46251 + 3.96875i 0.269119 + 0.195526i
\(413\) −2.66704 1.93771i −0.131236 0.0953487i
\(414\) 0 0
\(415\) −17.1619 52.8189i −0.842445 2.59278i
\(416\) −6.69713 + 4.86575i −0.328354 + 0.238563i
\(417\) 0 0
\(418\) −4.75144 3.66205i −0.232400 0.179117i
\(419\) 20.2858 0.991027 0.495514 0.868600i \(-0.334980\pi\)
0.495514 + 0.868600i \(0.334980\pi\)
\(420\) 0 0
\(421\) −0.945600 2.91026i −0.0460857 0.141837i 0.925366 0.379075i \(-0.123758\pi\)
−0.971452 + 0.237238i \(0.923758\pi\)
\(422\) 3.39542 10.4500i 0.165287 0.508700i
\(423\) 0 0
\(424\) 26.9116 + 19.5524i 1.30694 + 0.949548i
\(425\) −4.14971 + 12.7715i −0.201290 + 0.619508i
\(426\) 0 0
\(427\) 0.871010 0.632826i 0.0421511 0.0306246i
\(428\) 2.66211 0.128678
\(429\) 0 0
\(430\) 11.8648 0.572173
\(431\) 6.10158 4.43306i 0.293903 0.213533i −0.431056 0.902325i \(-0.641859\pi\)
0.724959 + 0.688792i \(0.241859\pi\)
\(432\) 0 0
\(433\) −9.93848 + 30.5875i −0.477613 + 1.46994i 0.364788 + 0.931091i \(0.381141\pi\)
−0.842401 + 0.538851i \(0.818859\pi\)
\(434\) 0.710857 + 0.516468i 0.0341222 + 0.0247912i
\(435\) 0 0
\(436\) −0.907980 + 2.79447i −0.0434844 + 0.133831i
\(437\) 0.404796 + 1.24584i 0.0193640 + 0.0595964i
\(438\) 0 0
\(439\) −4.66725 −0.222756 −0.111378 0.993778i \(-0.535526\pi\)
−0.111378 + 0.993778i \(0.535526\pi\)
\(440\) 11.8315 33.1858i 0.564045 1.58207i
\(441\) 0 0
\(442\) 3.59099 2.60901i 0.170806 0.124098i
\(443\) −5.33893 16.4315i −0.253660 0.780686i −0.994091 0.108553i \(-0.965378\pi\)
0.740430 0.672133i \(-0.234622\pi\)
\(444\) 0 0
\(445\) 12.4096 + 9.01611i 0.588272 + 0.427404i
\(446\) 15.6845 + 11.3955i 0.742684 + 0.539591i
\(447\) 0 0
\(448\) 2.56433 + 7.89221i 0.121153 + 0.372872i
\(449\) −13.5430 + 9.83957i −0.639134 + 0.464358i −0.859553 0.511047i \(-0.829258\pi\)
0.220418 + 0.975405i \(0.429258\pi\)
\(450\) 0 0
\(451\) −1.98832 6.76546i −0.0936264 0.318573i
\(452\) 8.07529 0.379829
\(453\) 0 0
\(454\) −4.35015 13.3884i −0.204162 0.628347i
\(455\) 2.19968 6.76992i 0.103123 0.317379i
\(456\) 0 0
\(457\) 17.5536 + 12.7534i 0.821121 + 0.596580i 0.917033 0.398810i \(-0.130577\pi\)
−0.0959121 + 0.995390i \(0.530577\pi\)
\(458\) −1.57503 + 4.84746i −0.0735965 + 0.226507i
\(459\) 0 0
\(460\) −1.71055 + 1.24279i −0.0797549 + 0.0579453i
\(461\) 6.07778 0.283070 0.141535 0.989933i \(-0.454796\pi\)
0.141535 + 0.989933i \(0.454796\pi\)
\(462\) 0 0
\(463\) −5.14719 −0.239210 −0.119605 0.992822i \(-0.538163\pi\)
−0.119605 + 0.992822i \(0.538163\pi\)
\(464\) −12.3183 + 8.94975i −0.571862 + 0.415482i
\(465\) 0 0
\(466\) 8.21605 25.2864i 0.380601 1.17137i
\(467\) −3.17076 2.30369i −0.146725 0.106602i 0.512001 0.858985i \(-0.328904\pi\)
−0.658726 + 0.752383i \(0.728904\pi\)
\(468\) 0 0
\(469\) 0.742611 2.28552i 0.0342906 0.105536i
\(470\) −9.00570 27.7167i −0.415402 1.27848i
\(471\) 0 0
\(472\) 10.1327 0.466397
\(473\) −10.2125 0.289243i −0.469572 0.0132994i
\(474\) 0 0
\(475\) −9.11811 + 6.62469i −0.418368 + 0.303962i
\(476\) 0.452925 + 1.39396i 0.0207598 + 0.0638921i
\(477\) 0 0
\(478\) −7.96867 5.78958i −0.364478 0.264809i
\(479\) −12.2266 8.88315i −0.558648 0.405882i 0.272316 0.962208i \(-0.412210\pi\)
−0.830964 + 0.556326i \(0.812210\pi\)
\(480\) 0 0
\(481\) −6.40399 19.7095i −0.291997 0.898674i
\(482\) 17.0825 12.4112i 0.778088 0.565314i
\(483\) 0 0
\(484\) −3.02114 + 7.77100i −0.137324 + 0.353227i
\(485\) −22.3541 −1.01505
\(486\) 0 0
\(487\) 7.74916 + 23.8495i 0.351148 + 1.08072i 0.958210 + 0.286067i \(0.0923480\pi\)
−0.607062 + 0.794655i \(0.707652\pi\)
\(488\) −1.02259 + 3.14722i −0.0462907 + 0.142468i
\(489\) 0 0
\(490\) −3.11608 2.26396i −0.140770 0.102275i
\(491\) −11.5019 + 35.3991i −0.519071 + 1.59754i 0.256679 + 0.966497i \(0.417372\pi\)
−0.775750 + 0.631040i \(0.782628\pi\)
\(492\) 0 0
\(493\) −12.4742 + 9.06302i −0.561809 + 0.408178i
\(494\) 3.72536 0.167612
\(495\) 0 0
\(496\) −1.50554 −0.0676006
\(497\) −2.57963 + 1.87421i −0.115712 + 0.0840698i
\(498\) 0 0
\(499\) −9.83087 + 30.2563i −0.440090 + 1.35446i 0.447689 + 0.894189i \(0.352247\pi\)
−0.887780 + 0.460269i \(0.847753\pi\)
\(500\) −4.12090 2.99401i −0.184292 0.133896i
\(501\) 0 0
\(502\) −0.987334 + 3.03870i −0.0440669 + 0.135624i
\(503\) 5.93493 + 18.2658i 0.264626 + 0.814434i 0.991779 + 0.127959i \(0.0408426\pi\)
−0.727154 + 0.686474i \(0.759157\pi\)
\(504\) 0 0
\(505\) −53.3788 −2.37532
\(506\) −2.46229 + 1.68456i −0.109462 + 0.0748877i
\(507\) 0 0
\(508\) 11.9274 8.66577i 0.529193 0.384481i
\(509\) −0.777328 2.39237i −0.0344545 0.106040i 0.932350 0.361556i \(-0.117754\pi\)
−0.966805 + 0.255516i \(0.917754\pi\)
\(510\) 0 0
\(511\) −0.992078 0.720787i −0.0438869 0.0318857i
\(512\) −15.7059 11.4110i −0.694109 0.504300i
\(513\) 0 0
\(514\) 7.71978 + 23.7590i 0.340505 + 1.04797i
\(515\) 24.9073 18.0962i 1.09755 0.797416i
\(516\) 0 0
\(517\) 7.07588 + 24.0764i 0.311197 + 1.05888i
\(518\) −11.2135 −0.492693
\(519\) 0 0
\(520\) 6.76107 + 20.8084i 0.296493 + 0.912510i
\(521\) −4.60335 + 14.1677i −0.201677 + 0.620697i 0.798157 + 0.602450i \(0.205809\pi\)
−0.999834 + 0.0182471i \(0.994191\pi\)
\(522\) 0 0
\(523\) 8.01333 + 5.82203i 0.350399 + 0.254579i 0.749036 0.662529i \(-0.230517\pi\)
−0.398638 + 0.917109i \(0.630517\pi\)
\(524\) 1.19755 3.68567i 0.0523151 0.161009i
\(525\) 0 0
\(526\) −0.893242 + 0.648979i −0.0389472 + 0.0282968i
\(527\) −1.52459 −0.0664122
\(528\) 0 0
\(529\) −22.3485 −0.971675
\(530\) 33.7236 24.5016i 1.46486 1.06428i
\(531\) 0 0
\(532\) −0.380136 + 1.16994i −0.0164810 + 0.0507232i
\(533\) 3.54276 + 2.57397i 0.153454 + 0.111491i
\(534\) 0 0
\(535\) 3.75097 11.5443i 0.162169 0.499104i
\(536\) 2.28253 + 7.02491i 0.0985904 + 0.303430i
\(537\) 0 0
\(538\) −8.01342 −0.345483
\(539\) 2.62694 + 2.02465i 0.113150 + 0.0872077i
\(540\) 0 0
\(541\) 17.8052 12.9362i 0.765503 0.556171i −0.135090 0.990833i \(-0.543132\pi\)
0.900593 + 0.434663i \(0.143132\pi\)
\(542\) 9.35508 + 28.7920i 0.401835 + 1.23672i
\(543\) 0 0
\(544\) −6.28768 4.56826i −0.269582 0.195863i
\(545\) 10.8389 + 7.87494i 0.464289 + 0.337325i
\(546\) 0 0
\(547\) −3.35724 10.3325i −0.143545 0.441787i 0.853276 0.521460i \(-0.174612\pi\)
−0.996821 + 0.0796728i \(0.974612\pi\)
\(548\) −5.58049 + 4.05446i −0.238387 + 0.173198i
\(549\) 0 0
\(550\) −20.3309 15.6695i −0.866912 0.668150i
\(551\) −12.9410 −0.551303
\(552\) 0 0
\(553\) −2.93004 9.01775i −0.124598 0.383474i
\(554\) −7.22721 + 22.2431i −0.307055 + 0.945018i
\(555\) 0 0
\(556\) −7.98184 5.79915i −0.338506 0.245939i
\(557\) −10.3869 + 31.9675i −0.440105 + 1.35451i 0.447658 + 0.894205i \(0.352258\pi\)
−0.887763 + 0.460300i \(0.847742\pi\)
\(558\) 0 0
\(559\) 5.13290 3.72927i 0.217098 0.157731i
\(560\) 6.59959 0.278884
\(561\) 0 0
\(562\) −31.3811 −1.32373
\(563\) −1.66130 + 1.20701i −0.0700155 + 0.0508693i −0.622242 0.782825i \(-0.713778\pi\)
0.552227 + 0.833694i \(0.313778\pi\)
\(564\) 0 0
\(565\) 11.3782 35.0186i 0.478686 1.47324i
\(566\) −23.6151 17.1573i −0.992615 0.721177i
\(567\) 0 0
\(568\) 3.02857 9.32098i 0.127076 0.391099i
\(569\) −1.01177 3.11391i −0.0424156 0.130542i 0.927606 0.373559i \(-0.121863\pi\)
−0.970022 + 0.243017i \(0.921863\pi\)
\(570\) 0 0
\(571\) −43.8897 −1.83673 −0.918363 0.395738i \(-0.870489\pi\)
−0.918363 + 0.395738i \(0.870489\pi\)
\(572\) −1.45995 4.96763i −0.0610437 0.207707i
\(573\) 0 0
\(574\) 1.91697 1.39276i 0.0800128 0.0581327i
\(575\) 1.73208 + 5.33080i 0.0722328 + 0.222310i
\(576\) 0 0
\(577\) 35.5081 + 25.7981i 1.47822 + 1.07399i 0.978125 + 0.208020i \(0.0667019\pi\)
0.500096 + 0.865970i \(0.333298\pi\)
\(578\) −11.9561 8.68664i −0.497310 0.361317i
\(579\) 0 0
\(580\) −6.45466 19.8654i −0.268015 0.824866i
\(581\) −13.0004 + 9.44536i −0.539348 + 0.391859i
\(582\) 0 0
\(583\) −29.6245 + 20.2674i −1.22692 + 0.839389i
\(584\) 3.76915 0.155969
\(585\) 0 0
\(586\) −1.53730 4.73133i −0.0635054 0.195449i
\(587\) −0.862670 + 2.65503i −0.0356062 + 0.109585i −0.967280 0.253711i \(-0.918349\pi\)
0.931674 + 0.363296i \(0.118349\pi\)
\(588\) 0 0
\(589\) −1.03520 0.752114i −0.0426545 0.0309903i
\(590\) 3.92378 12.0761i 0.161539 0.497167i
\(591\) 0 0
\(592\) 15.5441 11.2935i 0.638859 0.464158i
\(593\) −23.2526 −0.954871 −0.477435 0.878667i \(-0.658434\pi\)
−0.477435 + 0.878667i \(0.658434\pi\)
\(594\) 0 0
\(595\) 6.68312 0.273981
\(596\) 1.92945 1.40183i 0.0790334 0.0574211i
\(597\) 0 0
\(598\) 0.572519 1.76203i 0.0234120 0.0720549i
\(599\) 8.46187 + 6.14791i 0.345743 + 0.251197i 0.747081 0.664733i \(-0.231455\pi\)
−0.401338 + 0.915930i \(0.631455\pi\)
\(600\) 0 0
\(601\) 6.89406 21.2177i 0.281215 0.865489i −0.706293 0.707919i \(-0.749634\pi\)
0.987508 0.157570i \(-0.0503660\pi\)
\(602\) −1.06087 3.26501i −0.0432376 0.133072i
\(603\) 0 0
\(604\) −2.17306 −0.0884204
\(605\) 29.4422 + 24.0507i 1.19700 + 0.977800i
\(606\) 0 0
\(607\) −15.3619 + 11.1611i −0.623522 + 0.453015i −0.854150 0.520027i \(-0.825922\pi\)
0.230628 + 0.973042i \(0.425922\pi\)
\(608\) −2.01571 6.20370i −0.0817477 0.251593i
\(609\) 0 0
\(610\) 3.35485 + 2.43744i 0.135834 + 0.0986892i
\(611\) −12.6077 9.16004i −0.510053 0.370576i
\(612\) 0 0
\(613\) 6.23030 + 19.1749i 0.251639 + 0.774467i 0.994473 + 0.104991i \(0.0334813\pi\)
−0.742834 + 0.669476i \(0.766519\pi\)
\(614\) 11.6166 8.43995i 0.468807 0.340608i
\(615\) 0 0
\(616\) −10.1901 0.288607i −0.410570 0.0116283i
\(617\) −7.03919 −0.283387 −0.141694 0.989911i \(-0.545255\pi\)
−0.141694 + 0.989911i \(0.545255\pi\)
\(618\) 0 0
\(619\) −9.60520 29.5618i −0.386066 1.18819i −0.935704 0.352785i \(-0.885235\pi\)
0.549639 0.835402i \(-0.314765\pi\)
\(620\) 0.638222 1.96425i 0.0256316 0.0788860i
\(621\) 0 0
\(622\) −24.1814 17.5688i −0.969585 0.704445i
\(623\) 1.37151 4.22108i 0.0549484 0.169114i
\(624\) 0 0
\(625\) 9.30098 6.75756i 0.372039 0.270302i
\(626\) −3.99947 −0.159851
\(627\) 0 0
\(628\) 16.2883 0.649973
\(629\) 15.7408 11.4364i 0.627628 0.455998i
\(630\) 0 0
\(631\) 6.78971 20.8966i 0.270294 0.831880i −0.720132 0.693837i \(-0.755919\pi\)
0.990426 0.138043i \(-0.0440812\pi\)
\(632\) 23.5779 + 17.1303i 0.937879 + 0.681409i
\(633\) 0 0
\(634\) −5.82639 + 17.9318i −0.231396 + 0.712163i
\(635\) −20.7733 63.9337i −0.824364 2.53713i
\(636\) 0 0
\(637\) −2.05965 −0.0816064
\(638\) −8.31039 28.2770i −0.329012 1.11950i
\(639\) 0 0
\(640\) −3.38290 + 2.45782i −0.133721 + 0.0971538i
\(641\) 4.10713 + 12.6404i 0.162222 + 0.499267i 0.998821 0.0485485i \(-0.0154595\pi\)
−0.836599 + 0.547816i \(0.815460\pi\)
\(642\) 0 0
\(643\) −11.8848 8.63480i −0.468690 0.340523i 0.328241 0.944594i \(-0.393544\pi\)
−0.796930 + 0.604071i \(0.793544\pi\)
\(644\) 0.494940 + 0.359595i 0.0195034 + 0.0141700i
\(645\) 0 0
\(646\) 1.08082 + 3.32642i 0.0425242 + 0.130876i
\(647\) −4.97160 + 3.61208i −0.195454 + 0.142005i −0.681208 0.732090i \(-0.738545\pi\)
0.485754 + 0.874095i \(0.338545\pi\)
\(648\) 0 0
\(649\) −3.67174 + 10.2988i −0.144128 + 0.404261i
\(650\) 15.9404 0.625236
\(651\) 0 0
\(652\) 1.92589 + 5.92729i 0.0754238 + 0.232131i
\(653\) 12.5674 38.6786i 0.491802 1.51361i −0.330079 0.943953i \(-0.607076\pi\)
0.821882 0.569658i \(-0.192924\pi\)
\(654\) 0 0
\(655\) −14.2956 10.3864i −0.558576 0.405829i
\(656\) −1.25460 + 3.86127i −0.0489841 + 0.150757i
\(657\) 0 0
\(658\) −6.82196 + 4.95645i −0.265948 + 0.193222i
\(659\) −18.0090 −0.701531 −0.350765 0.936463i \(-0.614079\pi\)
−0.350765 + 0.936463i \(0.614079\pi\)
\(660\) 0 0
\(661\) −17.1420 −0.666745 −0.333373 0.942795i \(-0.608187\pi\)
−0.333373 + 0.942795i \(0.608187\pi\)
\(662\) −1.11644 + 0.811145i −0.0433919 + 0.0315260i
\(663\) 0 0
\(664\) 15.2629 46.9744i 0.592316 1.82296i
\(665\) 4.53784 + 3.29693i 0.175970 + 0.127850i
\(666\) 0 0
\(667\) −1.98878 + 6.12085i −0.0770060 + 0.237000i
\(668\) −5.08466 15.6490i −0.196732 0.605478i
\(669\) 0 0
\(670\) 9.25613 0.357596
\(671\) −2.82823 2.17979i −0.109183 0.0841498i
\(672\) 0 0
\(673\) 18.7632 13.6322i 0.723268 0.525485i −0.164159 0.986434i \(-0.552491\pi\)
0.887426 + 0.460949i \(0.152491\pi\)
\(674\) 7.05329 + 21.7078i 0.271683 + 0.836153i
\(675\) 0 0
\(676\) −5.37035 3.90179i −0.206552 0.150069i
\(677\) −22.3050 16.2056i −0.857252 0.622830i 0.0698841 0.997555i \(-0.477737\pi\)
−0.927136 + 0.374725i \(0.877737\pi\)
\(678\) 0 0
\(679\) 1.99874 + 6.15150i 0.0767047 + 0.236073i
\(680\) −16.6185 + 12.0741i −0.637291 + 0.463019i
\(681\) 0 0
\(682\) 0.978646 2.74497i 0.0374743 0.105110i
\(683\) −21.9351 −0.839322 −0.419661 0.907681i \(-0.637851\pi\)
−0.419661 + 0.907681i \(0.637851\pi\)
\(684\) 0 0
\(685\) 9.71923 + 29.9127i 0.371353 + 1.14291i
\(686\) −0.344389 + 1.05992i −0.0131488 + 0.0404680i
\(687\) 0 0
\(688\) 4.75885 + 3.45751i 0.181430 + 0.131816i
\(689\) 6.88814 21.1995i 0.262417 0.807637i
\(690\) 0 0
\(691\) 20.7647 15.0865i 0.789928 0.573916i −0.118014 0.993012i \(-0.537653\pi\)
0.907942 + 0.419096i \(0.137653\pi\)
\(692\) −6.09830 −0.231823
\(693\) 0 0
\(694\) 30.3913 1.15364
\(695\) −36.3947 + 26.4423i −1.38053 + 1.00301i
\(696\) 0 0
\(697\) −1.27048 + 3.91014i −0.0481229 + 0.148107i
\(698\) 7.19886 + 5.23028i 0.272481 + 0.197969i
\(699\) 0 0
\(700\) −1.62656 + 5.00604i −0.0614782 + 0.189211i
\(701\) 5.69007 + 17.5122i 0.214911 + 0.661428i 0.999160 + 0.0409817i \(0.0130485\pi\)
−0.784249 + 0.620446i \(0.786951\pi\)
\(702\) 0 0
\(703\) 16.3298 0.615892
\(704\) 22.7153 15.5405i 0.856114 0.585704i
\(705\) 0 0
\(706\) −5.35087 + 3.88764i −0.201383 + 0.146313i
\(707\) 4.77274 + 14.6890i 0.179497 + 0.552436i
\(708\) 0 0
\(709\) −19.1430 13.9082i −0.718930 0.522334i 0.167112 0.985938i \(-0.446556\pi\)
−0.886042 + 0.463604i \(0.846556\pi\)
\(710\) −9.93591 7.21886i −0.372888 0.270919i
\(711\) 0 0
\(712\) 4.21556 + 12.9741i 0.157985 + 0.486227i
\(713\) −0.514827 + 0.374044i −0.0192804 + 0.0140081i
\(714\) 0 0
\(715\) −23.5993 0.668389i −0.882565 0.0249963i
\(716\) −2.74452 −0.102568
\(717\) 0 0
\(718\) 9.78763 + 30.1232i 0.365271 + 1.12419i
\(719\) −3.43696 + 10.5779i −0.128177 + 0.394488i −0.994467 0.105054i \(-0.966498\pi\)
0.866289 + 0.499542i \(0.166498\pi\)
\(720\) 0 0
\(721\) −7.20682 5.23606i −0.268396 0.195001i
\(722\) 5.63627 17.3467i 0.209760 0.645576i
\(723\) 0 0
\(724\) 9.69964 7.04720i 0.360484 0.261907i
\(725\) −55.3730 −2.05650
\(726\) 0 0
\(727\) 42.4803 1.57551 0.787753 0.615991i \(-0.211244\pi\)
0.787753 + 0.615991i \(0.211244\pi\)
\(728\) 5.12162 3.72107i 0.189820 0.137912i
\(729\) 0 0
\(730\) 1.45956 4.49205i 0.0540206 0.166258i
\(731\) 4.81908 + 3.50127i 0.178240 + 0.129499i
\(732\) 0 0
\(733\) 6.85660 21.1025i 0.253254 0.779437i −0.740914 0.671600i \(-0.765607\pi\)
0.994169 0.107837i \(-0.0343925\pi\)
\(734\) 10.4699 + 32.2231i 0.386452 + 1.18938i
\(735\) 0 0
\(736\) −3.24402 −0.119576
\(737\) −7.96712 0.225648i −0.293473 0.00831184i
\(738\) 0 0
\(739\) −23.8240 + 17.3092i −0.876381 + 0.636728i −0.932292 0.361708i \(-0.882194\pi\)
0.0559106 + 0.998436i \(0.482194\pi\)
\(740\) 8.14496 + 25.0676i 0.299415 + 0.921504i
\(741\) 0 0
\(742\) −9.75776 7.08943i −0.358219 0.260261i
\(743\) 13.6772 + 9.93704i 0.501766 + 0.364555i 0.809691 0.586856i \(-0.199635\pi\)
−0.307925 + 0.951411i \(0.599635\pi\)
\(744\) 0 0
\(745\) −3.36042 10.3423i −0.123116 0.378913i
\(746\) 13.0037 9.44774i 0.476099 0.345906i
\(747\) 0 0
\(748\) 4.01208 2.74484i 0.146696 0.100361i
\(749\) −3.51219 −0.128333
\(750\) 0 0
\(751\) −0.479429 1.47553i −0.0174946 0.0538429i 0.941928 0.335815i \(-0.109012\pi\)
−0.959423 + 0.281972i \(0.909012\pi\)
\(752\) 4.46479 13.7412i 0.162814 0.501090i
\(753\) 0 0
\(754\) 14.8074 + 10.7582i 0.539252 + 0.391789i
\(755\) −3.06188 + 9.42349i −0.111433 + 0.342956i
\(756\) 0 0
\(757\) −10.1505 + 7.37474i −0.368925 + 0.268040i −0.756765 0.653687i \(-0.773221\pi\)
0.387840 + 0.921727i \(0.373221\pi\)
\(758\) 24.9721 0.907027
\(759\) 0 0
\(760\) −17.2404 −0.625375
\(761\) −7.30895 + 5.31026i −0.264949 + 0.192497i −0.712326 0.701849i \(-0.752358\pi\)
0.447377 + 0.894346i \(0.352358\pi\)
\(762\) 0 0
\(763\) 1.19792 3.68682i 0.0433676 0.133472i
\(764\) −0.263115 0.191164i −0.00951916 0.00691608i
\(765\) 0 0
\(766\) 11.5985 35.6966i 0.419072 1.28977i
\(767\) −2.09820 6.45761i −0.0757617 0.233171i
\(768\) 0 0
\(769\) −16.1383 −0.581963 −0.290981 0.956729i \(-0.593982\pi\)
−0.290981 + 0.956729i \(0.593982\pi\)
\(770\) −4.28994 + 12.0327i −0.154599 + 0.433629i
\(771\) 0 0
\(772\) −9.30529 + 6.76069i −0.334905 + 0.243323i
\(773\) 5.69007 + 17.5122i 0.204657 + 0.629871i 0.999727 + 0.0233530i \(0.00743416\pi\)
−0.795070 + 0.606518i \(0.792566\pi\)
\(774\) 0 0
\(775\) −4.42950 3.21822i −0.159112 0.115602i
\(776\) −16.0838 11.6855i −0.577374 0.419487i
\(777\) 0 0
\(778\) 0.836118 + 2.57331i 0.0299763 + 0.0922575i
\(779\) −2.79162 + 2.02823i −0.100020 + 0.0726689i
\(780\) 0 0
\(781\) 8.37624 + 6.45578i 0.299726 + 0.231006i
\(782\) 1.73944 0.0622022
\(783\) 0 0