Properties

Label 847.2.f.x.323.3
Level 847
Weight 2
Character 847.323
Analytic conductor 6.763
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 847.f (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.76332905120\)
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 323.3
Root \(0.901622 + 0.655067i\)
Character \(\chi\) = 847.323
Dual form 847.2.f.x.729.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.901622 + 0.655067i) q^{2} +(-0.883423 + 2.71890i) q^{3} +(-0.234224 - 0.720867i) q^{4} +(-2.79603 + 2.03143i) q^{5} +(-2.57757 + 1.87272i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.949813 - 2.92322i) q^{8} +(-4.18492 - 3.04052i) q^{9} +O(q^{10})\) \(q+(0.901622 + 0.655067i) q^{2} +(-0.883423 + 2.71890i) q^{3} +(-0.234224 - 0.720867i) q^{4} +(-2.79603 + 2.03143i) q^{5} +(-2.57757 + 1.87272i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.949813 - 2.92322i) q^{8} +(-4.18492 - 3.04052i) q^{9} -3.85168 q^{10} +2.16688 q^{12} +(-1.66629 - 1.21063i) q^{13} +(0.344389 - 1.05992i) q^{14} +(-3.05318 - 9.39672i) q^{15} +(1.54487 - 1.12241i) q^{16} +(1.56442 - 1.13662i) q^{17} +(-1.78147 - 5.48280i) q^{18} +(-0.501522 + 1.54353i) q^{19} +(2.11929 + 1.53975i) q^{20} +2.85882 q^{21} -0.807136 q^{23} +(7.10886 + 5.16489i) q^{24} +(2.14596 - 6.60459i) q^{25} +(-0.709322 - 2.18307i) q^{26} +(5.02542 - 3.65118i) q^{27} +(-0.613206 + 0.445520i) q^{28} +(-2.46400 - 7.58342i) q^{29} +(3.40267 - 10.4723i) q^{30} +(-0.637845 - 0.463421i) q^{31} -4.01918 q^{32} +2.15508 q^{34} +(2.79603 + 2.03143i) q^{35} +(-1.21160 + 3.72893i) q^{36} +(3.10926 + 9.56931i) q^{37} +(-1.46330 + 1.06315i) q^{38} +(4.76363 - 3.46098i) q^{39} +(3.28263 + 10.1029i) q^{40} +(0.657011 - 2.02207i) q^{41} +(2.57757 + 1.87272i) q^{42} -3.08043 q^{43} +17.8777 q^{45} +(-0.727732 - 0.528728i) q^{46} +(2.33812 - 7.19600i) q^{47} +(1.68695 + 5.19190i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(6.26129 - 4.54910i) q^{50} +(1.70830 + 5.25761i) q^{51} +(-0.482420 + 1.48474i) q^{52} +(-8.75554 - 6.36127i) q^{53} +6.92280 q^{54} -3.07366 q^{56} +(-3.75363 - 2.72717i) q^{57} +(2.74605 - 8.45147i) q^{58} +(-1.01872 - 3.13529i) q^{59} +(-6.05866 + 4.40187i) q^{60} +(-0.871010 + 0.632826i) q^{61} +(-0.271523 - 0.835662i) q^{62} +(-1.59850 + 4.91966i) q^{63} +(-6.71351 - 4.87765i) q^{64} +7.11832 q^{65} +2.40314 q^{67} +(-1.18577 - 0.861515i) q^{68} +(0.713042 - 2.19452i) q^{69} +(1.19024 + 3.66317i) q^{70} +(2.57963 - 1.87421i) q^{71} +(-12.8630 + 9.34552i) q^{72} +(-0.378940 - 1.16626i) q^{73} +(-3.46516 + 10.6647i) q^{74} +(16.0614 + 11.6693i) q^{75} +1.23015 q^{76} +6.56217 q^{78} +(-7.67096 - 5.57328i) q^{79} +(-2.03939 + 6.27659i) q^{80} +(0.692124 + 2.13014i) q^{81} +(1.91697 - 1.39276i) q^{82} +(-13.0004 + 9.44536i) q^{83} +(-0.669603 - 2.06083i) q^{84} +(-2.06520 + 6.35602i) q^{85} +(-2.77738 - 2.01789i) q^{86} +22.7953 q^{87} -4.43830 q^{89} +(16.1190 + 11.7111i) q^{90} +(-0.636468 + 1.95885i) q^{91} +(0.189050 + 0.581837i) q^{92} +(1.82348 - 1.32484i) q^{93} +(6.82196 - 4.95645i) q^{94} +(-1.73330 - 5.33455i) q^{95} +(3.55063 - 10.9277i) q^{96} +(-5.23278 - 3.80184i) q^{97} -1.11447 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 3q^{2} - 2q^{3} - 11q^{4} - 5q^{5} - 3q^{6} + 4q^{7} + 5q^{8} - 12q^{9} + O(q^{10}) \) \( 16q + 3q^{2} - 2q^{3} - 11q^{4} - 5q^{5} - 3q^{6} + 4q^{7} + 5q^{8} - 12q^{9} - 12q^{10} + 18q^{12} + 7q^{13} + 2q^{14} - 18q^{15} + 17q^{16} + 5q^{17} - 11q^{18} - 19q^{19} + q^{20} - 8q^{21} + 32q^{23} + 35q^{24} + 7q^{25} - 27q^{26} + 10q^{27} - 4q^{28} - 3q^{29} + 2q^{30} - 7q^{31} - 32q^{32} - 24q^{34} + 5q^{35} + 52q^{36} + 4q^{37} - 5q^{38} - 11q^{39} + 10q^{40} + 10q^{41} + 3q^{42} + 8q^{43} + 70q^{45} + 42q^{46} - 23q^{47} - 36q^{48} - 4q^{49} - 52q^{50} + 29q^{51} - 33q^{52} + 4q^{53} - 60q^{54} + 11q^{57} + 20q^{58} + 17q^{59} - 30q^{60} + 7q^{61} - 79q^{62} + 2q^{63} + 7q^{64} + 8q^{65} - 38q^{67} + 2q^{68} + 10q^{69} - 18q^{70} - 14q^{71} + 35q^{73} + 29q^{74} + 9q^{75} - 52q^{76} - 58q^{78} - 15q^{79} - 87q^{80} - 14q^{81} + 19q^{82} - 5q^{83} - 8q^{84} - 6q^{85} - 52q^{86} + 72q^{87} + 74q^{89} + 14q^{90} + 13q^{91} - 55q^{92} + 32q^{93} + 24q^{94} - 32q^{95} + 42q^{96} + 20q^{97} - 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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 0.859005 0.511967i \(-0.171083\pi\)
−0.221462 + 0.975169i \(0.571083\pi\)
\(3\) −0.883423 + 2.71890i −0.510045 + 1.56976i 0.282076 + 0.959392i \(0.408977\pi\)
−0.792121 + 0.610364i \(0.791023\pi\)
\(4\) −0.234224 0.720867i −0.117112 0.360433i
\(5\) −2.79603 + 2.03143i −1.25042 + 0.908484i −0.998246 0.0591979i \(-0.981146\pi\)
−0.252174 + 0.967682i \(0.581146\pi\)
\(6\) −2.57757 + 1.87272i −1.05229 + 0.764534i
\(7\) −0.309017 0.951057i −0.116797 0.359466i
\(8\) 0.949813 2.92322i 0.335810 1.03352i
\(9\) −4.18492 3.04052i −1.39497 1.01351i
\(10\) −3.85168 −1.21801
\(11\) 0 0
\(12\) 2.16688 0.625525
\(13\) −1.66629 1.21063i −0.462147 0.335769i 0.332226 0.943200i \(-0.392200\pi\)
−0.794373 + 0.607430i \(0.792200\pi\)
\(14\) 0.344389 1.05992i 0.0920419 0.283276i
\(15\) −3.05318 9.39672i −0.788328 2.42622i
\(16\) 1.54487 1.12241i 0.386217 0.280603i
\(17\) 1.56442 1.13662i 0.379427 0.275670i −0.381682 0.924294i \(-0.624655\pi\)
0.761109 + 0.648624i \(0.224655\pi\)
\(18\) −1.78147 5.48280i −0.419897 1.29231i
\(19\) −0.501522 + 1.54353i −0.115057 + 0.354109i −0.991959 0.126560i \(-0.959606\pi\)
0.876902 + 0.480669i \(0.159606\pi\)
\(20\) 2.11929 + 1.53975i 0.473887 + 0.344299i
\(21\) 2.85882 0.623845
\(22\) 0 0
\(23\) −0.807136 −0.168299 −0.0841497 0.996453i \(-0.526817\pi\)
−0.0841497 + 0.996453i \(0.526817\pi\)
\(24\) 7.10886 + 5.16489i 1.45109 + 1.05428i
\(25\) 2.14596 6.60459i 0.429192 1.32092i
\(26\) −0.709322 2.18307i −0.139109 0.428135i
\(27\) 5.02542 3.65118i 0.967142 0.702670i
\(28\) −0.613206 + 0.445520i −0.115885 + 0.0841954i
\(29\) −2.46400 7.58342i −0.457554 1.40821i −0.868111 0.496371i \(-0.834666\pi\)
0.410557 0.911835i \(-0.365334\pi\)
\(30\) 3.40267 10.4723i 0.621239 1.91198i
\(31\) −0.637845 0.463421i −0.114560 0.0832330i 0.529030 0.848603i \(-0.322556\pi\)
−0.643590 + 0.765370i \(0.722556\pi\)
\(32\) −4.01918 −0.710497
\(33\) 0 0
\(34\) 2.15508 0.369592
\(35\) 2.79603 + 2.03143i 0.472615 + 0.343375i
\(36\) −1.21160 + 3.72893i −0.201934 + 0.621488i
\(37\) 3.10926 + 9.56931i 0.511159 + 1.57318i 0.790164 + 0.612895i \(0.209995\pi\)
−0.279005 + 0.960290i \(0.590005\pi\)
\(38\) −1.46330 + 1.06315i −0.237378 + 0.172465i
\(39\) 4.76363 3.46098i 0.762792 0.554200i
\(40\) 3.28263 + 10.1029i 0.519029 + 1.59741i
\(41\) 0.657011 2.02207i 0.102608 0.315795i −0.886554 0.462626i \(-0.846907\pi\)
0.989162 + 0.146831i \(0.0469074\pi\)
\(42\) 2.57757 + 1.87272i 0.397728 + 0.288967i
\(43\) −3.08043 −0.469761 −0.234880 0.972024i \(-0.575470\pi\)
−0.234880 + 0.972024i \(0.575470\pi\)
\(44\) 0 0
\(45\) 17.8777 2.66506
\(46\) −0.727732 0.528728i −0.107298 0.0779567i
\(47\) 2.33812 7.19600i 0.341050 1.04964i −0.622615 0.782529i \(-0.713930\pi\)
0.963665 0.267115i \(-0.0860705\pi\)
\(48\) 1.68695 + 5.19190i 0.243490 + 0.749387i
\(49\) −0.809017 + 0.587785i −0.115574 + 0.0839693i
\(50\) 6.26129 4.54910i 0.885481 0.643339i
\(51\) 1.70830 + 5.25761i 0.239210 + 0.736213i
\(52\) −0.482420 + 1.48474i −0.0668996 + 0.205896i
\(53\) −8.75554 6.36127i −1.20267 0.873788i −0.208122 0.978103i \(-0.566735\pi\)
−0.994544 + 0.104315i \(0.966735\pi\)
\(54\) 6.92280 0.942073
\(55\) 0 0
\(56\) −3.07366 −0.410735
\(57\) −3.75363 2.72717i −0.497181 0.361223i
\(58\) 2.74605 8.45147i 0.360574 1.10973i
\(59\) −1.01872 3.13529i −0.132626 0.408180i 0.862587 0.505908i \(-0.168842\pi\)
−0.995213 + 0.0977281i \(0.968842\pi\)
\(60\) −6.05866 + 4.40187i −0.782169 + 0.568279i
\(61\) −0.871010 + 0.632826i −0.111521 + 0.0810250i −0.642148 0.766581i \(-0.721957\pi\)
0.530627 + 0.847606i \(0.321957\pi\)
\(62\) −0.271523 0.835662i −0.0344835 0.106129i
\(63\) −1.59850 + 4.91966i −0.201392 + 0.619819i
\(64\) −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
\(69\) 0.713042 2.19452i 0.0858402 0.264189i
\(70\) 1.19024 + 3.66317i 0.142260 + 0.437832i
\(71\) 2.57963 1.87421i 0.306145 0.222428i −0.424095 0.905618i \(-0.639408\pi\)
0.730241 + 0.683190i \(0.239408\pi\)
\(72\) −12.8630 + 9.34552i −1.51592 + 1.10138i
\(73\) −0.378940 1.16626i −0.0443516 0.136500i 0.926429 0.376470i \(-0.122862\pi\)
−0.970780 + 0.239970i \(0.922862\pi\)
\(74\) −3.46516 + 10.6647i −0.402817 + 1.23974i
\(75\) 16.0614 + 11.6693i 1.85461 + 1.34745i
\(76\) 1.23015 0.141107
\(77\) 0 0
\(78\) 6.56217 0.743020
\(79\) −7.67096 5.57328i −0.863050 0.627043i 0.0656630 0.997842i \(-0.479084\pi\)
−0.928713 + 0.370799i \(0.879084\pi\)
\(80\) −2.03939 + 6.27659i −0.228010 + 0.701744i
\(81\) 0.692124 + 2.13014i 0.0769027 + 0.236682i
\(82\) 1.91697 1.39276i 0.211694 0.153805i
\(83\) −13.0004 + 9.44536i −1.42698 + 1.03676i −0.436412 + 0.899747i \(0.643751\pi\)
−0.990569 + 0.137016i \(0.956249\pi\)
\(84\) −0.669603 2.06083i −0.0730597 0.224855i
\(85\) −2.06520 + 6.35602i −0.224002 + 0.689407i
\(86\) −2.77738 2.01789i −0.299493 0.217594i
\(87\) 22.7953 2.44391
\(88\) 0 0
\(89\) −4.43830 −0.470459 −0.235230 0.971940i \(-0.575584\pi\)
−0.235230 + 0.971940i \(0.575584\pi\)
\(90\) 16.1190 + 11.7111i 1.69909 + 1.23446i
\(91\) −0.636468 + 1.95885i −0.0667199 + 0.205343i
\(92\) 0.189050 + 0.581837i 0.0197099 + 0.0606607i
\(93\) 1.82348 1.32484i 0.189086 0.137379i
\(94\) 6.82196 4.95645i 0.703632 0.511218i
\(95\) −1.73330 5.33455i −0.177833 0.547313i
\(96\) 3.55063 10.9277i 0.362385 1.11531i
\(97\) −5.23278 3.80184i −0.531308 0.386018i 0.289539 0.957166i \(-0.406498\pi\)
−0.820847 + 0.571148i \(0.806498\pi\)
\(98\) −1.11447 −0.112578
\(99\) 0 0
\(100\) −5.26366 −0.526366
\(101\) −12.4952 9.07828i −1.24332 0.903323i −0.245503 0.969396i \(-0.578953\pi\)
−0.997815 + 0.0660728i \(0.978953\pi\)
\(102\) −1.90384 + 5.85943i −0.188509 + 0.580170i
\(103\) 2.75276 + 8.47213i 0.271238 + 0.834784i 0.990190 + 0.139725i \(0.0446218\pi\)
−0.718953 + 0.695059i \(0.755378\pi\)
\(104\) −5.12162 + 3.72107i −0.502216 + 0.364881i
\(105\) −7.99333 + 5.80749i −0.780069 + 0.566753i
\(106\) −3.72713 11.4709i −0.362011 1.11416i
\(107\) −1.08533 + 3.34029i −0.104922 + 0.322918i −0.989712 0.143072i \(-0.954302\pi\)
0.884790 + 0.465990i \(0.154302\pi\)
\(108\) −3.80909 2.76746i −0.366530 0.266299i
\(109\) −3.87655 −0.371306 −0.185653 0.982615i \(-0.559440\pi\)
−0.185653 + 0.982615i \(0.559440\pi\)
\(110\) 0 0
\(111\) −28.7648 −2.73023
\(112\) −1.54487 1.12241i −0.145976 0.106058i
\(113\) 3.29224 10.1325i 0.309708 0.953183i −0.668170 0.744008i \(-0.732922\pi\)
0.977878 0.209175i \(-0.0670777\pi\)
\(114\) −1.59788 4.91776i −0.149655 0.460591i
\(115\) 2.25677 1.63964i 0.210445 0.152897i
\(116\) −4.88951 + 3.55243i −0.453979 + 0.329835i
\(117\) 3.29235 + 10.1328i 0.304378 + 0.936778i
\(118\) 1.13533 3.49417i 0.104515 0.321665i
\(119\) −1.56442 1.13662i −0.143410 0.104194i
\(120\) −30.3687 −2.77227
\(121\) 0 0
\(122\) −1.19987 −0.108631
\(123\) 4.91739 + 3.57269i 0.443386 + 0.322139i
\(124\) −0.184667 + 0.568346i −0.0165836 + 0.0510389i
\(125\) 2.07667 + 6.39134i 0.185743 + 0.571659i
\(126\) −4.66395 + 3.38856i −0.415498 + 0.301877i
\(127\) 15.7361 11.4330i 1.39635 1.01451i 0.401220 0.915982i \(-0.368586\pi\)
0.995134 0.0985289i \(-0.0314137\pi\)
\(128\) −0.373878 1.15068i −0.0330464 0.101706i
\(129\) 2.72132 8.37537i 0.239599 0.737410i
\(130\) 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
\(135\) −6.63407 + 20.4176i −0.570970 + 1.75727i
\(136\) −1.83668 5.65272i −0.157494 0.484717i
\(137\) −7.36247 + 5.34915i −0.629019 + 0.457009i −0.856060 0.516876i \(-0.827095\pi\)
0.227042 + 0.973885i \(0.427095\pi\)
\(138\) 2.08045 1.51154i 0.177100 0.128671i
\(139\) 4.02234 + 12.3795i 0.341171 + 1.05002i 0.963602 + 0.267341i \(0.0861450\pi\)
−0.622431 + 0.782675i \(0.713855\pi\)
\(140\) 0.809496 2.49137i 0.0684149 0.210559i
\(141\) 17.4996 + 12.7142i 1.47373 + 1.07073i
\(142\) 3.55358 0.298210
\(143\) 0 0
\(144\) −9.87786 −0.823155
\(145\) 22.2946 + 16.1980i 1.85147 + 1.34517i
\(146\) 0.422316 1.29975i 0.0349511 0.107568i
\(147\) −0.883423 2.71890i −0.0728635 0.224251i
\(148\) 6.16994 4.48272i 0.507166 0.368477i
\(149\) −2.54557 + 1.84947i −0.208541 + 0.151514i −0.687153 0.726512i \(-0.741140\pi\)
0.478612 + 0.878026i \(0.341140\pi\)
\(150\) 6.83715 + 21.0426i 0.558251 + 1.71812i
\(151\) −0.885940 + 2.72664i −0.0720968 + 0.221891i −0.980612 0.195962i \(-0.937217\pi\)
0.908515 + 0.417853i \(0.137217\pi\)
\(152\) 4.03572 + 2.93212i 0.327340 + 0.237827i
\(153\) −10.0029 −0.808684
\(154\) 0 0
\(155\) 2.72484 0.218864
\(156\) −3.61066 2.62330i −0.289084 0.210032i
\(157\) −6.64062 + 20.4377i −0.529979 + 1.63111i 0.224275 + 0.974526i \(0.427999\pi\)
−0.754254 + 0.656582i \(0.772001\pi\)
\(158\) −3.26544 10.0500i −0.259784 0.799534i
\(159\) 25.0305 18.1857i 1.98505 1.44222i
\(160\) 11.2377 8.16468i 0.888420 0.645475i
\(161\) 0.249419 + 0.767632i 0.0196569 + 0.0604978i
\(162\) −0.771349 + 2.37397i −0.0606029 + 0.186517i
\(163\) 6.65210 + 4.83304i 0.521033 + 0.378553i 0.816993 0.576648i \(-0.195639\pi\)
−0.295960 + 0.955200i \(0.595639\pi\)
\(164\) −1.61153 −0.125840
\(165\) 0 0
\(166\) −17.9088 −1.38999
\(167\) −17.5626 12.7600i −1.35904 0.987397i −0.998506 0.0546489i \(-0.982596\pi\)
−0.360529 0.932748i \(-0.617404\pi\)
\(168\) 2.71534 8.35696i 0.209493 0.644754i
\(169\) −2.70632 8.32919i −0.208178 0.640707i
\(170\) −6.02565 + 4.37789i −0.462146 + 0.335769i
\(171\) 6.79195 4.93464i 0.519393 0.377361i
\(172\) 0.721509 + 2.22058i 0.0550146 + 0.169317i
\(173\) 2.48624 7.65185i 0.189025 0.581760i −0.810969 0.585089i \(-0.801060\pi\)
0.999994 + 0.00332915i \(0.00105970\pi\)
\(174\) 20.5527 + 14.9324i 1.55810 + 1.13203i
\(175\) −6.94447 −0.524953
\(176\) 0 0
\(177\) 9.42449 0.708388
\(178\) −4.00167 2.90739i −0.299938 0.217918i
\(179\) −1.11892 + 3.44369i −0.0836322 + 0.257393i −0.984125 0.177478i \(-0.943206\pi\)
0.900493 + 0.434871i \(0.143206\pi\)
\(180\) −4.18739 12.8875i −0.312110 0.960575i
\(181\) −12.7970 + 9.29753i −0.951190 + 0.691080i −0.951088 0.308920i \(-0.900033\pi\)
−0.000102207 1.00000i \(0.500033\pi\)
\(182\) −1.85703 + 1.34921i −0.137652 + 0.100010i
\(183\) −0.951118 2.92724i −0.0703087 0.216388i
\(184\) −0.766628 + 2.35944i −0.0565165 + 0.173940i
\(185\) −28.1330 20.4398i −2.06838 1.50276i
\(186\) 2.51195 0.184185
\(187\) 0 0
\(188\) −5.73500 −0.418268
\(189\) −5.02542 3.65118i −0.365545 0.265584i
\(190\) 1.93170 5.94518i 0.140141 0.431308i
\(191\) 0.132593 + 0.408080i 0.00959411 + 0.0295276i 0.955739 0.294216i \(-0.0950585\pi\)
−0.946145 + 0.323744i \(0.895058\pi\)
\(192\) 19.1927 13.9443i 1.38511 1.00634i
\(193\) −12.2767 + 8.91954i −0.883696 + 0.642042i −0.934227 0.356680i \(-0.883909\pi\)
0.0505310 + 0.998722i \(0.483909\pi\)
\(194\) −2.22753 6.85564i −0.159927 0.492206i
\(195\) −6.28849 + 19.3540i −0.450328 + 1.38597i
\(196\) 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
\(201\) −2.12299 + 6.53389i −0.149744 + 0.460865i
\(202\) −5.31906 16.3704i −0.374247 1.15182i
\(203\) −6.45084 + 4.68681i −0.452760 + 0.328950i
\(204\) 3.38991 2.46292i 0.237341 0.172439i
\(205\) 2.27068 + 6.98844i 0.158591 + 0.488094i
\(206\) −3.06786 + 9.44190i −0.213748 + 0.657849i
\(207\) 3.37779 + 2.45411i 0.234773 + 0.170573i
\(208\) −3.93303 −0.272707
\(209\) 0 0
\(210\) −11.0113 −0.759849
\(211\) −7.97632 5.79513i −0.549112 0.398953i 0.278346 0.960481i \(-0.410214\pi\)
−0.827458 + 0.561528i \(0.810214\pi\)
\(212\) −2.53487 + 7.80154i −0.174096 + 0.535812i
\(213\) 2.81688 + 8.66946i 0.193009 + 0.594022i
\(214\) −3.16667 + 2.30072i −0.216469 + 0.157274i
\(215\) 8.61295 6.25768i 0.587399 0.426770i
\(216\) −5.90001 18.1584i −0.401445 1.23552i
\(217\) −0.243635 + 0.749832i −0.0165390 + 0.0509019i
\(218\) −3.49518 2.53940i −0.236724 0.171990i
\(219\) 3.50570 0.236893
\(220\) 0 0
\(221\) −3.98281 −0.267913
\(222\) −25.9350 18.8429i −1.74064 1.26465i
\(223\) 5.37562 16.5445i 0.359978 1.10790i −0.593088 0.805138i \(-0.702091\pi\)
0.953066 0.302762i \(-0.0979087\pi\)
\(224\) 1.24199 + 3.82246i 0.0829842 + 0.255399i
\(225\) −29.0620 + 21.1148i −1.93747 + 1.40765i
\(226\) 9.60581 6.97903i 0.638969 0.464238i
\(227\) 3.90334 + 12.0133i 0.259074 + 0.797348i 0.993000 + 0.118118i \(0.0376861\pi\)
−0.733926 + 0.679230i \(0.762314\pi\)
\(228\) −1.08674 + 3.34464i −0.0719711 + 0.221504i
\(229\) −3.69997 2.68819i −0.244501 0.177640i 0.458785 0.888547i \(-0.348285\pi\)
−0.703286 + 0.710907i \(0.748285\pi\)
\(230\) 3.10883 0.204990
\(231\) 0 0
\(232\) −24.5084 −1.60905
\(233\) 19.3006 + 14.0227i 1.26443 + 0.918659i 0.998966 0.0454624i \(-0.0144761\pi\)
0.265460 + 0.964122i \(0.414476\pi\)
\(234\) −3.66921 + 11.2927i −0.239864 + 0.738225i
\(235\) 8.08073 + 24.8699i 0.527129 + 1.62234i
\(236\) −2.02152 + 1.46872i −0.131590 + 0.0956054i
\(237\) 21.9299 15.9330i 1.42450 1.03496i
\(238\) −0.665955 2.04960i −0.0431675 0.132856i
\(239\) −2.73114 + 8.40558i −0.176663 + 0.543711i −0.999705 0.0242677i \(-0.992275\pi\)
0.823043 + 0.567979i \(0.192275\pi\)
\(240\) −15.2638 11.0898i −0.985271 0.715841i
\(241\) −18.9464 −1.22045 −0.610224 0.792229i \(-0.708921\pi\)
−0.610224 + 0.792229i \(0.708921\pi\)
\(242\) 0 0
\(243\) 12.2322 0.784696
\(244\) 0.660194 + 0.479659i 0.0422646 + 0.0307070i
\(245\) 1.06799 3.28693i 0.0682312 0.209994i
\(246\) 2.09328 + 6.44244i 0.133462 + 0.410755i
\(247\) 2.70433 1.96481i 0.172072 0.125018i
\(248\) −1.96052 + 1.42440i −0.124493 + 0.0904495i
\(249\) −14.1961 43.6911i −0.899640 2.76881i
\(250\) −2.31438 + 7.12294i −0.146374 + 0.450494i
\(251\) 2.31938 + 1.68513i 0.146398 + 0.106364i 0.658573 0.752516i \(-0.271160\pi\)
−0.512175 + 0.858881i \(0.671160\pi\)
\(252\) 3.92083 0.246989
\(253\) 0 0
\(254\) 21.6774 1.36016
\(255\) −15.4569 11.2301i −0.967950 0.703257i
\(256\) −4.71199 + 14.5020i −0.294500 + 0.906377i
\(257\) 6.92689 + 21.3188i 0.432087 + 1.32983i 0.896042 + 0.443969i \(0.146430\pi\)
−0.463955 + 0.885859i \(0.653570\pi\)
\(258\) 7.94003 5.76877i 0.494325 0.359148i
\(259\) 8.14014 5.91416i 0.505804 0.367488i
\(260\) −1.66728 5.13136i −0.103400 0.318234i
\(261\) −12.7459 + 39.2278i −0.788951 + 2.42814i
\(262\) −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
\(267\) 3.92090 12.0673i 0.239955 0.738506i
\(268\) −0.562873 1.73234i −0.0343829 0.105820i
\(269\) 5.81713 4.22639i 0.354677 0.257688i −0.396152 0.918185i \(-0.629655\pi\)
0.750828 + 0.660497i \(0.229655\pi\)
\(270\) −19.3563 + 14.0632i −1.17799 + 0.855858i
\(271\) 8.39423 + 25.8348i 0.509913 + 1.56935i 0.792351 + 0.610065i \(0.208857\pi\)
−0.282438 + 0.959285i \(0.591143\pi\)
\(272\) 1.14107 3.51185i 0.0691874 0.212937i
\(273\) −4.76363 3.46098i −0.288308 0.209468i
\(274\) −10.1422 −0.612714
\(275\) 0 0
\(276\) −1.74897 −0.105275
\(277\) 16.9777 + 12.3350i 1.02009 + 0.741140i 0.966302 0.257412i \(-0.0828698\pi\)
0.0537900 + 0.998552i \(0.482870\pi\)
\(278\) −4.48277 + 13.7965i −0.268859 + 0.827462i
\(279\) 1.26029 + 3.87876i 0.0754513 + 0.232215i
\(280\) 8.59403 6.24393i 0.513592 0.373146i
\(281\) −22.7803 + 16.5509i −1.35896 + 0.987341i −0.360448 + 0.932779i \(0.617376\pi\)
−0.998510 + 0.0545621i \(0.982624\pi\)
\(282\) 7.44939 + 22.9269i 0.443605 + 1.36527i
\(283\) 8.09369 24.9098i 0.481120 1.48074i −0.356403 0.934332i \(-0.615997\pi\)
0.837523 0.546403i \(-0.184003\pi\)
\(284\) −1.95527 1.42058i −0.116024 0.0842961i
\(285\) 16.0353 0.949851
\(286\) 0 0
\(287\) −2.12613 −0.125502
\(288\) 16.8199 + 12.2204i 0.991123 + 0.720093i
\(289\) −4.09778 + 12.6117i −0.241046 + 0.741863i
\(290\) 9.49056 + 29.2089i 0.557305 + 1.71521i
\(291\) 14.9596 10.8688i 0.876945 0.637138i
\(292\) −0.751959 + 0.546331i −0.0440051 + 0.0319716i
\(293\) 1.37941 + 4.24538i 0.0805858 + 0.248017i 0.983230 0.182370i \(-0.0583769\pi\)
−0.902644 + 0.430388i \(0.858377\pi\)
\(294\) 0.984546 3.03012i 0.0574199 0.176720i
\(295\) 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
\(300\) 4.65004 14.3114i 0.268470 0.826267i
\(301\) 0.951904 + 2.92966i 0.0548669 + 0.168863i
\(302\) −2.58492 + 1.87805i −0.148745 + 0.108070i
\(303\) 35.7215 25.9532i 2.05214 1.49097i
\(304\) 0.957688 + 2.94746i 0.0549271 + 0.169048i
\(305\) 1.14982 3.53879i 0.0658387 0.202631i
\(306\) −9.01881 6.55255i −0.515571 0.374584i
\(307\) −12.8841 −0.735334 −0.367667 0.929957i \(-0.619843\pi\)
−0.367667 + 0.929957i \(0.619843\pi\)
\(308\) 0 0
\(309\) −25.4667 −1.44875
\(310\) 2.45678 + 1.78495i 0.139536 + 0.101379i
\(311\) 8.28779 25.5072i 0.469957 1.44638i −0.382682 0.923880i \(-0.624999\pi\)
0.852639 0.522500i \(-0.175001\pi\)
\(312\) −5.59266 17.2124i −0.316622 0.974463i
\(313\) −2.90331 + 2.10938i −0.164105 + 0.119229i −0.666807 0.745231i \(-0.732339\pi\)
0.502702 + 0.864460i \(0.332339\pi\)
\(314\) −19.3754 + 14.0771i −1.09342 + 0.794415i
\(315\) −5.52453 17.0027i −0.311272 0.957996i
\(316\) −2.22087 + 6.83513i −0.124934 + 0.384506i
\(317\) 13.6870 + 9.94418i 0.768738 + 0.558521i 0.901578 0.432617i \(-0.142410\pi\)
−0.132840 + 0.991138i \(0.542410\pi\)
\(318\) 34.4809 1.93359
\(319\) 0 0
\(320\) 28.6798 1.60325
\(321\) −8.12311 5.90178i −0.453388 0.329405i
\(322\) −0.277969 + 0.855500i −0.0154906 + 0.0476751i
\(323\) 0.969808 + 2.98476i 0.0539616 + 0.166077i
\(324\) 1.37343 0.997859i 0.0763019 0.0554366i
\(325\) −11.5715 + 8.40721i −0.641873 + 0.466348i
\(326\) 2.83172 + 8.71515i 0.156835 + 0.482687i
\(327\) 3.42463 10.5399i 0.189383 0.582860i
\(328\) −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
\(333\) 16.0837 49.5005i 0.881381 2.71261i
\(334\) −7.47620 23.0094i −0.409079 1.25902i
\(335\) −6.71924 + 4.88181i −0.367111 + 0.266722i
\(336\) 4.41650 3.20877i 0.240940 0.175053i
\(337\) 6.32885 + 19.4782i 0.344754 + 1.06104i 0.961715 + 0.274051i \(0.0883637\pi\)
−0.616961 + 0.786994i \(0.711636\pi\)
\(338\) 3.01610 9.28261i 0.164054 0.504907i
\(339\) 24.6407 + 17.9025i 1.33830 + 0.972332i
\(340\) 5.06556 0.274719
\(341\) 0 0
\(342\) 9.35630 0.505931
\(343\) 0.809017 + 0.587785i 0.0436828 + 0.0317374i
\(344\) −2.92583 + 9.00478i −0.157750 + 0.485505i
\(345\) 2.46433 + 7.58443i 0.132675 + 0.408332i
\(346\) 7.25412 5.27043i 0.389984 0.283340i
\(347\) 22.0618 16.0288i 1.18434 0.860472i 0.191684 0.981457i \(-0.438605\pi\)
0.992654 + 0.120985i \(0.0386052\pi\)
\(348\) −5.33920 16.4324i −0.286211 0.880868i
\(349\) −2.46730 + 7.59356i −0.132071 + 0.406474i −0.995123 0.0986418i \(-0.968550\pi\)
0.863052 + 0.505116i \(0.168550\pi\)
\(350\) −6.26129 4.54910i −0.334680 0.243159i
\(351\) −12.7941 −0.682897
\(352\) 0 0
\(353\) 5.93472 0.315873 0.157937 0.987449i \(-0.449516\pi\)
0.157937 + 0.987449i \(0.449516\pi\)
\(354\) 8.49733 + 6.17367i 0.451628 + 0.328127i
\(355\) −3.40538 + 10.4807i −0.180739 + 0.556256i
\(356\) 1.03956 + 3.19942i 0.0550964 + 0.169569i
\(357\) 4.47239 3.24938i 0.236704 0.171976i
\(358\) −3.26469 + 2.37194i −0.172544 + 0.125361i
\(359\) −8.78235 27.0293i −0.463515 1.42655i −0.860841 0.508874i \(-0.830062\pi\)
0.397326 0.917677i \(-0.369938\pi\)
\(360\) 16.9805 52.2606i 0.894951 2.75438i
\(361\) 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
\(366\) 1.05999 3.26231i 0.0554065 0.170524i
\(367\) −9.39456 28.9135i −0.490392 1.50927i −0.824017 0.566565i \(-0.808272\pi\)
0.333625 0.942706i \(-0.391728\pi\)
\(368\) −1.24692 + 0.905939i −0.0650001 + 0.0472253i
\(369\) −8.89769 + 6.46455i −0.463195 + 0.336531i
\(370\) −11.9759 36.8580i −0.622596 1.91615i
\(371\) −3.34432 + 10.2928i −0.173628 + 0.534373i
\(372\) −1.38213 1.00418i −0.0716603 0.0520643i
\(373\) −14.4226 −0.746772 −0.373386 0.927676i \(-0.621803\pi\)
−0.373386 + 0.927676i \(0.621803\pi\)
\(374\) 0 0
\(375\) −19.2120 −0.992103
\(376\) −18.8147 13.6697i −0.970296 0.704961i
\(377\) −5.07499 + 15.6192i −0.261375 + 0.804430i
\(378\) −2.13926 6.58397i −0.110032 0.338643i
\(379\) 18.1278 13.1706i 0.931163 0.676529i −0.0151144 0.999886i \(-0.504811\pi\)
0.946277 + 0.323356i \(0.104811\pi\)
\(380\) −3.43952 + 2.49896i −0.176444 + 0.128194i
\(381\) 17.1834 + 52.8850i 0.880331 + 2.70938i
\(382\) −0.147771 + 0.454792i −0.00756061 + 0.0232692i
\(383\) −27.2465 19.7957i −1.39223 1.01152i −0.995616 0.0935305i \(-0.970185\pi\)
−0.396615 0.917985i \(-0.629815\pi\)
\(384\) 3.45887 0.176510
\(385\) 0 0
\(386\) −16.9118 −0.860790
\(387\) 12.8913 + 9.36610i 0.655303 + 0.476106i
\(388\) −1.51498 + 4.66262i −0.0769112 + 0.236708i
\(389\) 0.750241 + 2.30900i 0.0380387 + 0.117071i 0.968273 0.249896i \(-0.0803963\pi\)
−0.930234 + 0.366967i \(0.880396\pi\)
\(390\) −18.3480 + 13.3306i −0.929087 + 0.675021i
\(391\) −1.26270 + 0.917404i −0.0638574 + 0.0463951i
\(392\) 0.949813 + 2.92322i 0.0479728 + 0.147645i
\(393\) 4.51680 13.9013i 0.227842 0.701227i
\(394\) 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
\(399\) −1.43376 + 4.41266i −0.0717778 + 0.220909i
\(400\) −4.09784 12.6119i −0.204892 0.630593i
\(401\) −9.09302 + 6.60646i −0.454084 + 0.329911i −0.791206 0.611550i \(-0.790546\pi\)
0.337122 + 0.941461i \(0.390546\pi\)
\(402\) −6.19427 + 4.50040i −0.308942 + 0.224460i
\(403\) 0.501804 + 1.54439i 0.0249966 + 0.0769317i
\(404\) −3.61756 + 11.1337i −0.179981 + 0.553923i
\(405\) −6.26243 4.54992i −0.311183 0.226087i
\(406\) −8.88640 −0.441025
\(407\) 0 0
\(408\) 16.9917 0.841216
\(409\) 23.7320 + 17.2423i 1.17347 + 0.852578i 0.991421 0.130711i \(-0.0417260\pi\)
0.182052 + 0.983289i \(0.441726\pi\)
\(410\) −2.53060 + 7.78839i −0.124977 + 0.384641i
\(411\) −8.03961 24.7434i −0.396565 1.22050i
\(412\) 5.46251 3.96875i 0.269119 0.195526i
\(413\) −2.66704 + 1.93771i −0.131236 + 0.0953487i
\(414\) 1.43789 + 4.42536i 0.0706683 + 0.217495i
\(415\) 17.1619 52.8189i 0.842445 2.59278i
\(416\) 6.69713 + 4.86575i 0.328354 + 0.238563i
\(417\) −37.2120 −1.82228
\(418\) 0 0
\(419\) −20.2858 −0.991027 −0.495514 0.868600i \(-0.665020\pi\)
−0.495514 + 0.868600i \(0.665020\pi\)
\(420\) 6.05866 + 4.40187i 0.295632 + 0.214789i
\(421\) −0.945600 + 2.91026i −0.0460857 + 0.141837i −0.971452 0.237238i \(-0.923758\pi\)
0.925366 + 0.379075i \(0.123758\pi\)
\(422\) −3.39542 10.4500i −0.165287 0.508700i
\(423\) −31.6644 + 23.0055i −1.53958 + 1.11857i
\(424\) −26.9116 + 19.5524i −1.30694 + 0.949548i
\(425\) −4.14971 12.7715i −0.201290 0.619508i
\(426\) −3.13932 + 9.66183i −0.152100 + 0.468117i
\(427\) 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 0.724959 0.688792i \(-0.241859\pi\)
−0.431056 + 0.902325i \(0.641859\pi\)
\(432\) 3.66548 11.2812i 0.176355 0.542766i
\(433\) −9.93848 30.5875i −0.477613 1.46994i −0.842401 0.538851i \(-0.818859\pi\)
0.364788 0.931091i \(-0.381141\pi\)
\(434\) −0.710857 + 0.516468i −0.0341222 + 0.0247912i
\(435\) −63.7362 + 46.3071i −3.05592 + 2.22025i
\(436\) 0.907980 + 2.79447i 0.0434844 + 0.133831i
\(437\) 0.404796 1.24584i 0.0193640 0.0595964i
\(438\) 3.16082 + 2.29647i 0.151030 + 0.109729i
\(439\) 4.66725 0.222756 0.111378 0.993778i \(-0.464474\pi\)
0.111378 + 0.993778i \(0.464474\pi\)
\(440\) 0 0
\(441\) 5.17284 0.246326
\(442\) −3.59099 2.60901i −0.170806 0.124098i
\(443\) 5.33893 16.4315i 0.253660 0.780686i −0.740430 0.672133i \(-0.765378\pi\)
0.994091 0.108553i \(-0.0346218\pi\)
\(444\) 6.73739 + 20.7356i 0.319743 + 0.984066i
\(445\) 12.4096 9.01611i 0.588272 0.427404i
\(446\) 15.6845 11.3955i 0.742684 0.539591i
\(447\) −2.77969 8.55501i −0.131475 0.404638i
\(448\) −2.56433 + 7.89221i −0.121153 + 0.372872i
\(449\) 13.5430 + 9.83957i 0.639134 + 0.464358i 0.859553 0.511047i \(-0.170742\pi\)
−0.220418 + 0.975405i \(0.570742\pi\)
\(450\) −40.0346 −1.88725
\(451\) 0 0
\(452\) −8.07529 −0.379829
\(453\) −6.63080 4.81756i −0.311542 0.226349i
\(454\) −4.35015 + 13.3884i −0.204162 + 0.628347i
\(455\) −2.19968 6.76992i −0.103123 0.317379i
\(456\) −11.5374 + 8.38241i −0.540288 + 0.392542i
\(457\) −17.5536 + 12.7534i −0.821121 + 0.596580i −0.917033 0.398810i \(-0.869423\pi\)
0.0959121 + 0.995390i \(0.469423\pi\)
\(458\) −1.57503 4.84746i −0.0735965 0.226507i
\(459\) 3.71187 11.4240i 0.173255 0.533224i
\(460\) −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
\(465\) −2.40719 + 7.40856i −0.111631 + 0.343564i
\(466\) 8.21605 + 25.2864i 0.380601 + 1.17137i
\(467\) 3.17076 2.30369i 0.146725 0.106602i −0.512001 0.858985i \(-0.671096\pi\)
0.658726 + 0.752383i \(0.271096\pi\)
\(468\) 6.53325 4.74669i 0.302000 0.219416i
\(469\) −0.742611 2.28552i −0.0342906 0.105536i
\(470\) −9.00570 + 27.7167i −0.415402 + 1.27848i
\(471\) −49.7016 36.1103i −2.29013 1.66388i
\(472\) −10.1327 −0.466397
\(473\) 0 0
\(474\) 30.2096 1.38757
\(475\) 9.11811 + 6.62469i 0.418368 + 0.303962i
\(476\) −0.452925 + 1.39396i −0.0207598 + 0.0638921i
\(477\) 17.2996 + 53.2428i 0.792096 + 2.43782i
\(478\) −7.96867 + 5.78958i −0.364478 + 0.264809i
\(479\) −12.2266 + 8.88315i −0.558648 + 0.405882i −0.830964 0.556326i \(-0.812210\pi\)
0.272316 + 0.962208i \(0.412210\pi\)
\(480\) 12.2713 + 37.7671i 0.560104 + 1.72382i
\(481\) 6.40399 19.7095i 0.291997 0.898674i
\(482\) −17.0825 12.4112i −0.778088 0.565314i
\(483\) −2.30745 −0.104993
\(484\) 0 0
\(485\) 22.3541 1.01505
\(486\) 11.0288 + 8.01291i 0.500278 + 0.363473i
\(487\) 7.74916 23.8495i 0.351148 1.08072i −0.607062 0.794655i \(-0.707652\pi\)
0.958210 0.286067i \(-0.0923480\pi\)
\(488\) 1.02259 + 3.14722i 0.0462907 + 0.142468i
\(489\) −19.0172 + 13.8168i −0.859985 + 0.624816i
\(490\) 3.11608 2.26396i 0.140770 0.102275i
\(491\) −11.5019 35.3991i −0.519071 1.59754i −0.775750 0.631040i \(-0.782628\pi\)
0.256679 0.966497i \(-0.417372\pi\)
\(492\) 1.42367 4.38159i 0.0641838 0.197538i
\(493\) −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
\(498\) 15.8211 48.6922i 0.708959 2.18195i
\(499\) −9.83087 30.2563i −0.440090 1.35446i −0.887780 0.460269i \(-0.847753\pi\)
0.447689 0.894189i \(-0.352247\pi\)
\(500\) 4.12090 2.99401i 0.184292 0.133896i
\(501\) 50.2083 36.4785i 2.24314 1.62974i
\(502\) 0.987334 + 3.03870i 0.0440669 + 0.135624i
\(503\) 5.93493 18.2658i 0.264626 0.814434i −0.727154 0.686474i \(-0.759157\pi\)
0.991779 0.127959i \(-0.0408426\pi\)
\(504\) 12.8630 + 9.34552i 0.572964 + 0.416283i
\(505\) 53.3788 2.37532
\(506\) 0 0
\(507\) 25.0370 1.11193
\(508\) −11.9274 8.66577i −0.529193 0.384481i
\(509\) 0.777328 2.39237i 0.0344545 0.106040i −0.932350 0.361556i \(-0.882246\pi\)
0.966805 + 0.255516i \(0.0822455\pi\)
\(510\) −6.57984 20.2506i −0.291360 0.896714i
\(511\) −0.992078 + 0.720787i −0.0438869 + 0.0318857i
\(512\) −15.7059 + 11.4110i −0.694109 + 0.504300i
\(513\) 3.11533 + 9.58801i 0.137545 + 0.423321i
\(514\) −7.71978 + 23.7590i −0.340505 + 1.04797i
\(515\) −24.9073 18.0962i −1.09755 0.797416i
\(516\) −6.67492 −0.293847
\(517\) 0 0
\(518\) 11.2135 0.492693
\(519\) 18.6082 + 13.5196i 0.816809 + 0.593447i
\(520\) 6.76107 20.8084i 0.296493 0.912510i
\(521\) 4.60335 + 14.1677i 0.201677 + 0.620697i 0.999834 + 0.0182471i \(0.00580856\pi\)
−0.798157 + 0.602450i \(0.794191\pi\)
\(522\) −37.1888 + 27.0193i −1.62771 + 1.18260i
\(523\) −8.01333 + 5.82203i −0.350399 + 0.254579i −0.749036 0.662529i \(-0.769483\pi\)
0.398638 + 0.917109i \(0.369483\pi\)
\(524\) 1.19755 + 3.68567i 0.0523151 + 0.161009i
\(525\) 6.13491 18.8813i 0.267749 0.824048i
\(526\) −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
\(531\) −5.26966 + 16.2183i −0.228684 + 0.703816i
\(532\) −0.380136 1.16994i −0.0164810 0.0507232i
\(533\) −3.54276 + 2.57397i −0.153454 + 0.111491i
\(534\) 11.4401 8.31169i 0.495060 0.359682i
\(535\) −3.75097 11.5443i −0.162169 0.499104i
\(536\) 2.28253 7.02491i 0.0985904 0.303430i
\(537\) −8.37456 6.08447i −0.361389 0.262564i
\(538\) 8.01342 0.345483
\(539\) 0 0
\(540\) 16.2722 0.700245
\(541\) −17.8052 12.9362i −0.765503 0.556171i 0.135090 0.990833i \(-0.456868\pi\)
−0.900593 + 0.434663i \(0.856868\pi\)
\(542\) −9.35508 + 28.7920i −0.401835 + 1.23672i
\(543\) −13.9739 43.0073i −0.599678 1.84562i
\(544\) −6.28768 + 4.56826i −0.269582 + 0.195863i
\(545\) 10.8389 7.87494i 0.464289 0.337325i
\(546\) −2.02782 6.24100i −0.0867828 0.267090i
\(547\) 3.35724 10.3325i 0.143545 0.441787i −0.853276 0.521460i \(-0.825388\pi\)
0.996821 + 0.0796728i \(0.0253875\pi\)
\(548\) 5.58049 + 4.05446i 0.238387 + 0.173198i
\(549\) 5.56922 0.237689
\(550\) 0 0
\(551\) 12.9410 0.551303
\(552\) −5.73781 4.16876i −0.244218 0.177434i
\(553\) −2.93004 + 9.01775i −0.124598 + 0.383474i
\(554\) 7.22721 + 22.2431i 0.307055 + 0.945018i
\(555\) 80.4270 58.4337i 3.41394 2.48037i
\(556\) 7.98184 5.79915i 0.338506 0.245939i
\(557\) −10.3869 31.9675i −0.440105 1.35451i −0.887763 0.460300i \(-0.847742\pi\)
0.447658 0.894205i \(-0.352258\pi\)
\(558\) −1.40455 + 4.32275i −0.0594592 + 0.182997i
\(559\) 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 0.552227 0.833694i \(-0.313778\pi\)
−0.622242 + 0.782825i \(0.713778\pi\)
\(564\) 5.06643 15.5929i 0.213335 0.656578i
\(565\) 11.3782 + 35.0186i 0.478686 + 1.47324i
\(566\) 23.6151 17.1573i 0.992615 0.721177i
\(567\) 1.81200 1.31650i 0.0760971 0.0552877i
\(568\) −3.02857 9.32098i −0.127076 0.391099i
\(569\) −1.01177 + 3.11391i −0.0424156 + 0.130542i −0.970022 0.243017i \(-0.921863\pi\)
0.927606 + 0.373559i \(0.121863\pi\)
\(570\) 14.4578 + 10.5042i 0.605571 + 0.439973i
\(571\) 43.8897 1.83673 0.918363 0.395738i \(-0.129511\pi\)
0.918363 + 0.395738i \(0.129511\pi\)
\(572\) 0 0
\(573\) −1.22666 −0.0512446
\(574\) −1.91697 1.39276i −0.0800128 0.0581327i
\(575\) −1.73208 + 5.33080i −0.0722328 + 0.222310i
\(576\) 13.2649 + 40.8251i 0.552704 + 1.70105i
\(577\) 35.5081 25.7981i 1.47822 1.07399i 0.500096 0.865970i \(-0.333298\pi\)
0.978125 0.208020i \(-0.0667019\pi\)
\(578\) −11.9561 + 8.68664i −0.497310 + 0.361317i
\(579\) −13.4058 41.2588i −0.557126 1.71466i
\(580\) 6.45466 19.8654i 0.268015 0.824866i
\(581\) 13.0004 + 9.44536i 0.539348 + 0.391859i
\(582\) 20.6076 0.854214
\(583\) 0 0
\(584\) −3.76915 −0.155969
\(585\) −29.7896 21.6434i −1.23165 0.894844i
\(586\) −1.53730 + 4.73133i −0.0635054 + 0.195449i
\(587\) 0.862670 + 2.65503i 0.0356062 + 0.109585i 0.967280 0.253711i \(-0.0816513\pi\)
−0.931674 + 0.363296i \(0.881651\pi\)
\(588\) −1.75304 + 1.27366i −0.0722943 + 0.0525249i
\(589\) 1.03520 0.752114i 0.0426545 0.0309903i
\(590\) 3.92378 + 12.0761i 0.161539 + 0.497167i
\(591\) −18.3825 + 56.5754i −0.756153 + 2.32720i
\(592\) 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
\(597\) −7.46111 + 22.9629i −0.305363 + 0.939810i
\(598\) 0.572519 + 1.76203i 0.0234120 + 0.0720549i
\(599\) −8.46187 + 6.14791i −0.345743 + 0.251197i −0.747081 0.664733i \(-0.768545\pi\)
0.401338 + 0.915930i \(0.368545\pi\)
\(600\) 49.3673 35.8674i 2.01541 1.46428i
\(601\) −6.89406 21.2177i −0.281215 0.865489i −0.987508 0.157570i \(-0.949634\pi\)
0.706293 0.707919i \(-0.250366\pi\)
\(602\) −1.06087 + 3.26501i −0.0432376 + 0.133072i
\(603\) −10.0569 7.30679i −0.409550 0.297556i
\(604\) 2.17306 0.0884204
\(605\) 0 0
\(606\) 49.2083 1.99895
\(607\) 15.3619 + 11.1611i 0.623522 + 0.453015i 0.854150 0.520027i \(-0.174078\pi\)
−0.230628 + 0.973042i \(0.574078\pi\)
\(608\) 2.01571 6.20370i 0.0817477 0.251593i
\(609\) −7.04413 21.6796i −0.285443 0.878502i
\(610\) 3.35485 2.43744i 0.135834 0.0986892i
\(611\) −12.6077 + 9.16004i −0.510053 + 0.370576i
\(612\) 2.34291 + 7.21074i 0.0947066 + 0.291477i
\(613\) −6.23030 + 19.1749i −0.251639 + 0.774467i 0.742834 + 0.669476i \(0.233481\pi\)
−0.994473 + 0.104991i \(0.966519\pi\)
\(614\) −11.6166 8.43995i −0.468807 0.340608i
\(615\) −21.0068 −0.847077
\(616\) 0 0
\(617\) 7.03919 0.283387 0.141694 0.989911i \(-0.454745\pi\)
0.141694 + 0.989911i \(0.454745\pi\)
\(618\) −22.9614 16.6824i −0.923641 0.671064i
\(619\) −9.60520 + 29.5618i −0.386066 + 1.18819i 0.549639 + 0.835402i \(0.314765\pi\)
−0.935704 + 0.352785i \(0.885235\pi\)
\(620\) −0.638222 1.96425i −0.0256316 0.0788860i
\(621\) −4.05619 + 2.94700i −0.162769 + 0.118259i
\(622\) 24.1814 17.5688i 0.969585 0.704445i
\(623\) 1.37151 + 4.22108i 0.0549484 + 0.169114i
\(624\) 3.47453 10.6935i 0.139093 0.428083i
\(625\) 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
\(630\) 6.15690 18.9490i 0.245297 0.754946i
\(631\) 6.78971 + 20.8966i 0.270294 + 0.831880i 0.990426 + 0.138043i \(0.0440812\pi\)
−0.720132 + 0.693837i \(0.755919\pi\)
\(632\) −23.5779 + 17.1303i −0.937879 + 0.681409i
\(633\) 22.8028 16.5672i 0.906331 0.658488i
\(634\) 5.82639 + 17.9318i 0.231396 + 0.712163i
\(635\) −20.7733 + 63.9337i −0.824364 + 2.53713i
\(636\) −18.9722 13.7841i −0.752298 0.546576i
\(637\) 2.05965 0.0816064
\(638\) 0 0
\(639\) −16.4941 −0.652496
\(640\) 3.38290 + 2.45782i 0.133721 + 0.0971538i
\(641\) −4.10713 + 12.6404i −0.162222 + 0.499267i −0.998821 0.0485485i \(-0.984540\pi\)
0.836599 + 0.547816i \(0.184540\pi\)
\(642\) −3.45791 10.6424i −0.136473 0.420020i
\(643\) −11.8848 + 8.63480i −0.468690 + 0.340523i −0.796930 0.604071i \(-0.793544\pi\)
0.328241 + 0.944594i \(0.393544\pi\)
\(644\) 0.494940 0.359595i 0.0195034 0.0141700i
\(645\) 9.40510 + 28.9459i 0.370325 + 1.13974i
\(646\) −1.08082 + 3.32642i −0.0425242 + 0.130876i
\(647\) 4.97160 + 3.61208i 0.195454 + 0.142005i 0.681208 0.732090i \(-0.261455\pi\)
−0.485754 + 0.874095i \(0.661455\pi\)
\(648\) 6.88426 0.270439
\(649\) 0 0
\(650\) −15.9404 −0.625236
\(651\) −1.82348 1.32484i −0.0714679 0.0519245i
\(652\) 1.92589 5.92729i 0.0754238 0.232131i
\(653\) −12.5674 38.6786i −0.491802 1.51361i −0.821882 0.569658i \(-0.807076\pi\)
0.330079 0.943953i \(-0.392924\pi\)
\(654\) 9.99209 7.25968i 0.390722 0.283876i
\(655\) 14.2956 10.3864i 0.558576 0.405829i
\(656\) −1.25460 3.86127i −0.0489841 0.150757i
\(657\) −1.96020 + 6.03286i −0.0764745 + 0.235364i
\(658\) −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
\(663\) 3.51851 10.8289i 0.136647 0.420558i
\(664\) 15.2629 + 46.9744i 0.592316 + 1.82296i
\(665\) −4.53784 + 3.29693i −0.175970 + 0.127850i
\(666\) 46.9276 34.0949i 1.81841 1.32115i
\(667\) 1.98878 + 6.12085i 0.0770060 + 0.237000i
\(668\) −5.08466 + 15.6490i −0.196732 + 0.605478i
\(669\) 40.2338 + 29.2315i 1.55553 + 1.13016i
\(670\) −9.25613 −0.357596
\(671\) 0 0
\(672\) −11.4901 −0.443240
\(673\) −18.7632 13.6322i −0.723268 0.525485i 0.164159 0.986434i \(-0.447509\pi\)
−0.887426 + 0.460949i \(0.847509\pi\)
\(674\) −7.05329 + 21.7078i −0.271683 + 0.836153i
\(675\) −13.3302 41.0261i −0.513079 1.57910i
\(676\) −5.37035 + 3.90179i −0.206552 + 0.150069i
\(677\) −22.3050 + 16.2056i −0.857252 + 0.622830i −0.927136 0.374725i \(-0.877737\pi\)
0.0698841 + 0.997555i \(0.477737\pi\)
\(678\) 10.4893 + 32.2826i 0.402838 + 1.23981i
\(679\) −1.99874 + 6.15150i −0.0767047 + 0.236073i
\(680\) 16.6185 + 12.0741i 0.637291 + 0.463019i
\(681\) −36.1111 −1.38378
\(682\) 0 0
\(683\) 21.9351 0.839322 0.419661 0.907681i \(-0.362149\pi\)
0.419661 + 0.907681i \(0.362149\pi\)
\(684\) −5.14806 3.74028i −0.196841 0.143013i
\(685\) 9.71923 29.9127i 0.371353 1.14291i
\(686\) 0.344389 + 1.05992i 0.0131488 + 0.0404680i
\(687\) 10.5775 7.68503i 0.403558 0.293202i
\(688\) −4.75885 + 3.45751i −0.181430 + 0.131816i
\(689\) 6.88814 + 21.1995i 0.262417 + 0.807637i
\(690\) −2.74641 + 8.45259i −0.104554 + 0.321785i
\(691\) 20.7647 + 15.0865i 0.789928 + 0.573916i 0.907942 0.419096i \(-0.137653\pi\)
−0.118014 + 0.993012i \(0.537653\pi\)
\(692\) −6.09830 −0.231823
\(693\) 0 0
\(694\) 30.3913 1.15364
\(695\) −36.3947 26.4423i −1.38053 1.00301i
\(696\) 21.6513 66.6357i 0.820689 2.52582i
\(697\) −1.27048 3.91014i −0.0481229 0.148107i
\(698\) −7.19886 + 5.23028i −0.272481 + 0.197969i
\(699\) −55.1770 + 40.0884i −2.08699 + 1.51628i
\(700\) 1.62656 + 5.00604i 0.0614782 + 0.189211i
\(701\) 5.69007 17.5122i 0.214911 0.661428i −0.784249 0.620446i \(-0.786951\pi\)
0.999160 0.0409817i \(-0.0130485\pi\)
\(702\) −11.5354 8.38097i −0.435376 0.316319i
\(703\) −16.3298 −0.615892
\(704\) 0 0
\(705\) −74.7575 −2.81553
\(706\) 5.35087 + 3.88764i 0.201383 + 0.146313i
\(707\) −4.77274 + 14.6890i −0.179497 + 0.552436i
\(708\) −2.20744 6.79380i −0.0829607 0.255327i
\(709\) −19.1430 + 13.9082i −0.718930 + 0.522334i −0.886042 0.463604i \(-0.846556\pi\)
0.167112 + 0.985938i \(0.446556\pi\)
\(710\) −9.93591 + 7.21886i −0.372888 + 0.270919i
\(711\) 15.1567 + 46.6474i 0.568419 + 1.74941i
\(712\) −4.21556 + 12.9741i −0.157985 + 0.486227i
\(713\) 0.514827 + 0.374044i 0.0192804 + 0.0140081i
\(714\) 6.16097 0.230569
\(715\) 0 0
\(716\) 2.74452 0.102568
\(717\) −20.4411 14.8514i −0.763389 0.554634i
\(718\) 9.78763 30.1232i 0.365271 1.12419i
\(719\) 3.43696 + 10.5779i 0.128177 + 0.394488i 0.994467 0.105054i \(-0.0335015\pi\)
−0.866289 + 0.499542i \(0.833502\pi\)
\(720\) 27.6187 20.0662i 1.02929 0.747823i
\(721\) 7.20682 5.23606i 0.268396 0.195001i
\(722\) 5.63627 + 17.3467i 0.209760 + 0.645576i
\(723\) 16.7377 51.5135i 0.622483 1.91581i
\(724\) 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
\(729\) −12.8826 + 39.6485i −0.477133 + 1.46846i
\(730\) 1.45956 + 4.49205i 0.0540206 + 0.166258i
\(731\) −4.81908 + 3.50127i −0.178240 + 0.129499i
\(732\) −1.88738 + 1.37126i −0.0697594 + 0.0506832i
\(733\) −6.85660 21.1025i −0.253254 0.779437i −0.994169 0.107837i \(-0.965607\pi\)
0.740914 0.671600i \(-0.234393\pi\)
\(734\) 10.4699 32.2231i 0.386452 1.18938i
\(735\) 7.99333 + 5.80749i 0.294838 + 0.214213i
\(736\) 3.24402 0.119576
\(737\) 0 0
\(738\) −12.2571 −0.451189
\(739\) 23.8240 + 17.3092i 0.876381 + 0.636728i 0.932292 0.361708i \(-0.117806\pi\)
−0.0559106 + 0.998436i \(0.517806\pi\)
\(740\) −8.14496 + 25.0676i −0.299415 + 0.921504i
\(741\) 2.95305 + 9.08855i 0.108483 + 0.333876i
\(742\) −9.75776 + 7.08943i −0.358219 + 0.260261i
\(743\) 13.6772 9.93704i 0.501766 0.364555i −0.307925 0.951411i \(-0.599635\pi\)
0.809691 + 0.586856i \(0.199635\pi\)
\(744\) −2.14083 6.58879i −0.0784866 0.241557i
\(745\) 3.36042 10.3423i 0.123116 0.378913i
\(746\) −13.0037 9.44774i −0.476099 0.345906i
\(747\) 83.1244 3.04136
\(748\) 0 0
\(749\) 3.51219 0.128333
\(750\) −17.3220 12.5851i −0.632508 0.459544i
\(751\) −0.479429 + 1.47553i −0.0174946 + 0.0538429i −0.959423 0.281972i \(-0.909012\pi\)
0.941928 + 0.335815i \(0.109012\pi\)
\(752\) −4.46479 13.7412i −0.162814 0.501090i
\(753\) −6.63069 + 4.81748i −0.241636 + 0.175559i
\(754\) −14.8074 + 10.7582i −0.539252 + 0.391789i
\(755\) −3.06188 9.42349i −0.111433 0.342956i
\(756\) −1.45494 + 4.47785i −0.0529157 + 0.162858i
\(757\) −10.1505 7.37474i −0.368925 0.268040i 0.387840 0.921727i \(-0.373221\pi\)
−0.756765 + 0.653687i \(0.773221\pi\)
\(758\) 24.9721 0.907027
\(759\) 0 0
\(760\) −17.2404 −0.625375
\(761\) −7.30895 5.31026i −0.264949 0.192497i 0.447377 0.894346i \(-0.352358\pi\)
−0.712326 + 0.701849i \(0.752358\pi\)
\(762\) −19.1503 + 58.9386i −0.693742 + 2.13512i
\(763\) 1.19792 + 3.68682i 0.0433676 + 0.133472i
\(764\) 0.263115 0.191164i 0.00951916 0.00691608i
\(765\) 27.9683 20.3201i 1.01120 0.734677i
\(766\) −11.5985 35.6966i −0.419072 1.28977i
\(767\) −2.09820 + 6.45761i −0.0757617 + 0.233171i
\(768\) −35.2668 25.6229i −1.27258 0.924585i
\(769\) 16.1383 0.581963 0.290981 0.956729i \(-0.406018\pi\)
0.290981 + 0.956729i \(0.406018\pi\)
\(770\) 0 0
\(771\) −64.0829 −2.30789
\(772\) 9.30529 + 6.76069i 0.334905 + 0.243323i
\(773\) −5.69007 + 17.5122i −0.204657 + 0.629871i 0.795070 + 0.606518i \(0.207434\pi\)