Properties

Label 387.2.h.d.307.1
Level 387
Weight 2
Character 387.307
Analytic conductor 3.090
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 387.h (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.09021055822\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 43)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 307.1
Root \(-0.309017 + 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 387.307
Dual form 387.2.h.d.208.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.381966 q^{2} -1.85410 q^{4} +(0.618034 - 1.07047i) q^{5} +(2.11803 + 3.66854i) q^{7} -1.47214 q^{8} +O(q^{10})\) \(q+0.381966 q^{2} -1.85410 q^{4} +(0.618034 - 1.07047i) q^{5} +(2.11803 + 3.66854i) q^{7} -1.47214 q^{8} +(0.236068 - 0.408882i) q^{10} +3.61803 q^{11} +(-0.690983 - 1.19682i) q^{13} +(0.809017 + 1.40126i) q^{14} +3.14590 q^{16} +(3.04508 + 5.27424i) q^{17} +(0.618034 - 1.07047i) q^{19} +(-1.14590 + 1.98475i) q^{20} +1.38197 q^{22} +(2.19098 - 3.79489i) q^{23} +(1.73607 + 3.00696i) q^{25} +(-0.263932 - 0.457144i) q^{26} +(-3.92705 - 6.80185i) q^{28} +(1.50000 + 2.59808i) q^{29} +4.14590 q^{32} +(1.16312 + 2.01458i) q^{34} +5.23607 q^{35} +(2.42705 - 4.20378i) q^{37} +(0.236068 - 0.408882i) q^{38} +(-0.909830 + 1.57587i) q^{40} -9.47214 q^{41} +(-6.50000 + 0.866025i) q^{43} -6.70820 q^{44} +(0.836881 - 1.44952i) q^{46} -1.14590 q^{47} +(-5.47214 + 9.47802i) q^{49} +(0.663119 + 1.14856i) q^{50} +(1.28115 + 2.21902i) q^{52} +(-0.690983 + 1.19682i) q^{53} +(2.23607 - 3.87298i) q^{55} +(-3.11803 - 5.40059i) q^{56} +(0.572949 + 0.992377i) q^{58} -5.09017 q^{59} +(-1.42705 - 2.47172i) q^{61} -4.70820 q^{64} -1.70820 q^{65} +(1.92705 - 3.33775i) q^{67} +(-5.64590 - 9.77898i) q^{68} +2.00000 q^{70} +(-5.39919 - 9.35167i) q^{71} +(-0.927051 - 1.60570i) q^{73} +(0.927051 - 1.60570i) q^{74} +(-1.14590 + 1.98475i) q^{76} +(7.66312 + 13.2729i) q^{77} +(0.690983 + 1.19682i) q^{79} +(1.94427 - 3.36758i) q^{80} -3.61803 q^{82} +(8.01722 - 13.8862i) q^{83} +7.52786 q^{85} +(-2.48278 + 0.330792i) q^{86} -5.32624 q^{88} +(-0.927051 + 1.60570i) q^{89} +(2.92705 - 5.06980i) q^{91} +(-4.06231 + 7.03612i) q^{92} -0.437694 q^{94} +(-0.763932 - 1.32317i) q^{95} -9.23607 q^{97} +(-2.09017 + 3.62028i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 6q^{2} + 6q^{4} - 2q^{5} + 4q^{7} + 12q^{8} + O(q^{10}) \) \( 4q + 6q^{2} + 6q^{4} - 2q^{5} + 4q^{7} + 12q^{8} - 8q^{10} + 10q^{11} - 5q^{13} + q^{14} + 26q^{16} + q^{17} - 2q^{19} - 18q^{20} + 10q^{22} + 11q^{23} - 2q^{25} - 10q^{26} - 9q^{28} + 6q^{29} + 30q^{32} - 11q^{34} + 12q^{35} + 3q^{37} - 8q^{38} - 26q^{40} - 20q^{41} - 26q^{43} + 19q^{46} - 18q^{47} - 4q^{49} - 13q^{50} - 15q^{52} - 5q^{53} - 8q^{56} + 9q^{58} + 2q^{59} + q^{61} + 8q^{64} + 20q^{65} + q^{67} - 36q^{68} + 8q^{70} + 3q^{71} + 3q^{73} - 3q^{74} - 18q^{76} + 15q^{77} + 5q^{79} - 28q^{80} - 10q^{82} + 3q^{83} + 48q^{85} - 39q^{86} + 10q^{88} + 3q^{89} + 5q^{91} + 24q^{92} - 42q^{94} - 12q^{95} - 28q^{97} + 14q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/387\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(173\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.381966 0.270091 0.135045 0.990839i \(-0.456882\pi\)
0.135045 + 0.990839i \(0.456882\pi\)
\(3\) 0 0
\(4\) −1.85410 −0.927051
\(5\) 0.618034 1.07047i 0.276393 0.478727i −0.694092 0.719886i \(-0.744194\pi\)
0.970486 + 0.241159i \(0.0775275\pi\)
\(6\) 0 0
\(7\) 2.11803 + 3.66854i 0.800542 + 1.38658i 0.919260 + 0.393651i \(0.128788\pi\)
−0.118718 + 0.992928i \(0.537879\pi\)
\(8\) −1.47214 −0.520479
\(9\) 0 0
\(10\) 0.236068 0.408882i 0.0746512 0.129300i
\(11\) 3.61803 1.09088 0.545439 0.838150i \(-0.316363\pi\)
0.545439 + 0.838150i \(0.316363\pi\)
\(12\) 0 0
\(13\) −0.690983 1.19682i −0.191644 0.331937i 0.754151 0.656701i \(-0.228049\pi\)
−0.945795 + 0.324763i \(0.894715\pi\)
\(14\) 0.809017 + 1.40126i 0.216219 + 0.374502i
\(15\) 0 0
\(16\) 3.14590 0.786475
\(17\) 3.04508 + 5.27424i 0.738542 + 1.27919i 0.953152 + 0.302492i \(0.0978185\pi\)
−0.214610 + 0.976700i \(0.568848\pi\)
\(18\) 0 0
\(19\) 0.618034 1.07047i 0.141787 0.245582i −0.786383 0.617740i \(-0.788049\pi\)
0.928170 + 0.372158i \(0.121382\pi\)
\(20\) −1.14590 + 1.98475i −0.256231 + 0.443804i
\(21\) 0 0
\(22\) 1.38197 0.294636
\(23\) 2.19098 3.79489i 0.456852 0.791290i −0.541941 0.840417i \(-0.682310\pi\)
0.998793 + 0.0491264i \(0.0156437\pi\)
\(24\) 0 0
\(25\) 1.73607 + 3.00696i 0.347214 + 0.601392i
\(26\) −0.263932 0.457144i −0.0517613 0.0896533i
\(27\) 0 0
\(28\) −3.92705 6.80185i −0.742143 1.28543i
\(29\) 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i \(-0.0768152\pi\)
−0.692480 + 0.721437i \(0.743482\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 4.14590 0.732898
\(33\) 0 0
\(34\) 1.16312 + 2.01458i 0.199473 + 0.345498i
\(35\) 5.23607 0.885057
\(36\) 0 0
\(37\) 2.42705 4.20378i 0.399005 0.691096i −0.594599 0.804023i \(-0.702689\pi\)
0.993603 + 0.112926i \(0.0360224\pi\)
\(38\) 0.236068 0.408882i 0.0382953 0.0663294i
\(39\) 0 0
\(40\) −0.909830 + 1.57587i −0.143857 + 0.249167i
\(41\) −9.47214 −1.47930 −0.739650 0.672992i \(-0.765009\pi\)
−0.739650 + 0.672992i \(0.765009\pi\)
\(42\) 0 0
\(43\) −6.50000 + 0.866025i −0.991241 + 0.132068i
\(44\) −6.70820 −1.01130
\(45\) 0 0
\(46\) 0.836881 1.44952i 0.123391 0.213720i
\(47\) −1.14590 −0.167146 −0.0835732 0.996502i \(-0.526633\pi\)
−0.0835732 + 0.996502i \(0.526633\pi\)
\(48\) 0 0
\(49\) −5.47214 + 9.47802i −0.781734 + 1.35400i
\(50\) 0.663119 + 1.14856i 0.0937792 + 0.162430i
\(51\) 0 0
\(52\) 1.28115 + 2.21902i 0.177664 + 0.307723i
\(53\) −0.690983 + 1.19682i −0.0949138 + 0.164396i −0.909573 0.415545i \(-0.863591\pi\)
0.814659 + 0.579941i \(0.196924\pi\)
\(54\) 0 0
\(55\) 2.23607 3.87298i 0.301511 0.522233i
\(56\) −3.11803 5.40059i −0.416665 0.721685i
\(57\) 0 0
\(58\) 0.572949 + 0.992377i 0.0752319 + 0.130305i
\(59\) −5.09017 −0.662684 −0.331342 0.943511i \(-0.607501\pi\)
−0.331342 + 0.943511i \(0.607501\pi\)
\(60\) 0 0
\(61\) −1.42705 2.47172i −0.182715 0.316472i 0.760089 0.649819i \(-0.225155\pi\)
−0.942804 + 0.333347i \(0.891822\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −4.70820 −0.588525
\(65\) −1.70820 −0.211877
\(66\) 0 0
\(67\) 1.92705 3.33775i 0.235427 0.407771i −0.723970 0.689832i \(-0.757685\pi\)
0.959397 + 0.282061i \(0.0910179\pi\)
\(68\) −5.64590 9.77898i −0.684666 1.18588i
\(69\) 0 0
\(70\) 2.00000 0.239046
\(71\) −5.39919 9.35167i −0.640766 1.10984i −0.985262 0.171051i \(-0.945284\pi\)
0.344497 0.938788i \(-0.388050\pi\)
\(72\) 0 0
\(73\) −0.927051 1.60570i −0.108503 0.187933i 0.806661 0.591015i \(-0.201272\pi\)
−0.915164 + 0.403082i \(0.867939\pi\)
\(74\) 0.927051 1.60570i 0.107767 0.186659i
\(75\) 0 0
\(76\) −1.14590 + 1.98475i −0.131444 + 0.227667i
\(77\) 7.66312 + 13.2729i 0.873293 + 1.51259i
\(78\) 0 0
\(79\) 0.690983 + 1.19682i 0.0777417 + 0.134653i 0.902275 0.431161i \(-0.141896\pi\)
−0.824534 + 0.565813i \(0.808562\pi\)
\(80\) 1.94427 3.36758i 0.217376 0.376507i
\(81\) 0 0
\(82\) −3.61803 −0.399545
\(83\) 8.01722 13.8862i 0.880004 1.52421i 0.0286698 0.999589i \(-0.490873\pi\)
0.851335 0.524623i \(-0.175794\pi\)
\(84\) 0 0
\(85\) 7.52786 0.816511
\(86\) −2.48278 + 0.330792i −0.267725 + 0.0356702i
\(87\) 0 0
\(88\) −5.32624 −0.567779
\(89\) −0.927051 + 1.60570i −0.0982672 + 0.170204i −0.910968 0.412478i \(-0.864663\pi\)
0.812700 + 0.582682i \(0.197997\pi\)
\(90\) 0 0
\(91\) 2.92705 5.06980i 0.306838 0.531460i
\(92\) −4.06231 + 7.03612i −0.423525 + 0.733566i
\(93\) 0 0
\(94\) −0.437694 −0.0451447
\(95\) −0.763932 1.32317i −0.0783778 0.135754i
\(96\) 0 0
\(97\) −9.23607 −0.937781 −0.468890 0.883256i \(-0.655346\pi\)
−0.468890 + 0.883256i \(0.655346\pi\)
\(98\) −2.09017 + 3.62028i −0.211139 + 0.365704i
\(99\) 0 0
\(100\) −3.21885 5.57521i −0.321885 0.557521i
\(101\) 1.88197 + 3.25966i 0.187263 + 0.324348i 0.944337 0.328981i \(-0.106705\pi\)
−0.757074 + 0.653329i \(0.773372\pi\)
\(102\) 0 0
\(103\) 8.20820 + 14.2170i 0.808778 + 1.40085i 0.913710 + 0.406366i \(0.133204\pi\)
−0.104932 + 0.994479i \(0.533463\pi\)
\(104\) 1.01722 + 1.76188i 0.0997467 + 0.172766i
\(105\) 0 0
\(106\) −0.263932 + 0.457144i −0.0256353 + 0.0444017i
\(107\) −7.52786 −0.727746 −0.363873 0.931449i \(-0.618546\pi\)
−0.363873 + 0.931449i \(0.618546\pi\)
\(108\) 0 0
\(109\) 6.92705 11.9980i 0.663491 1.14920i −0.316201 0.948692i \(-0.602407\pi\)
0.979692 0.200508i \(-0.0642593\pi\)
\(110\) 0.854102 1.47935i 0.0814354 0.141050i
\(111\) 0 0
\(112\) 6.66312 + 11.5409i 0.629606 + 1.09051i
\(113\) 15.6180 1.46922 0.734611 0.678489i \(-0.237365\pi\)
0.734611 + 0.678489i \(0.237365\pi\)
\(114\) 0 0
\(115\) −2.70820 4.69075i −0.252541 0.437414i
\(116\) −2.78115 4.81710i −0.258224 0.447256i
\(117\) 0 0
\(118\) −1.94427 −0.178985
\(119\) −12.8992 + 22.3420i −1.18247 + 2.04809i
\(120\) 0 0
\(121\) 2.09017 0.190015
\(122\) −0.545085 0.944115i −0.0493497 0.0854761i
\(123\) 0 0
\(124\) 0 0
\(125\) 10.4721 0.936656
\(126\) 0 0
\(127\) −14.6525 −1.30020 −0.650098 0.759850i \(-0.725272\pi\)
−0.650098 + 0.759850i \(0.725272\pi\)
\(128\) −10.0902 −0.891853
\(129\) 0 0
\(130\) −0.652476 −0.0572259
\(131\) −9.94427 −0.868835 −0.434418 0.900712i \(-0.643046\pi\)
−0.434418 + 0.900712i \(0.643046\pi\)
\(132\) 0 0
\(133\) 5.23607 0.454025
\(134\) 0.736068 1.27491i 0.0635866 0.110135i
\(135\) 0 0
\(136\) −4.48278 7.76440i −0.384395 0.665792i
\(137\) −3.70820 −0.316813 −0.158407 0.987374i \(-0.550636\pi\)
−0.158407 + 0.987374i \(0.550636\pi\)
\(138\) 0 0
\(139\) 2.64590 4.58283i 0.224422 0.388711i −0.731724 0.681601i \(-0.761284\pi\)
0.956146 + 0.292891i \(0.0946172\pi\)
\(140\) −9.70820 −0.820493
\(141\) 0 0
\(142\) −2.06231 3.57202i −0.173065 0.299757i
\(143\) −2.50000 4.33013i −0.209061 0.362103i
\(144\) 0 0
\(145\) 3.70820 0.307950
\(146\) −0.354102 0.613323i −0.0293057 0.0507589i
\(147\) 0 0
\(148\) −4.50000 + 7.79423i −0.369898 + 0.640682i
\(149\) 4.50000 7.79423i 0.368654 0.638528i −0.620701 0.784047i \(-0.713152\pi\)
0.989355 + 0.145519i \(0.0464853\pi\)
\(150\) 0 0
\(151\) −8.85410 −0.720537 −0.360268 0.932849i \(-0.617315\pi\)
−0.360268 + 0.932849i \(0.617315\pi\)
\(152\) −0.909830 + 1.57587i −0.0737970 + 0.127820i
\(153\) 0 0
\(154\) 2.92705 + 5.06980i 0.235868 + 0.408536i
\(155\) 0 0
\(156\) 0 0
\(157\) 2.57295 + 4.45648i 0.205344 + 0.355666i 0.950242 0.311512i \(-0.100835\pi\)
−0.744898 + 0.667178i \(0.767502\pi\)
\(158\) 0.263932 + 0.457144i 0.0209973 + 0.0363684i
\(159\) 0 0
\(160\) 2.56231 4.43804i 0.202568 0.350858i
\(161\) 18.5623 1.46291
\(162\) 0 0
\(163\) −7.00000 12.1244i −0.548282 0.949653i −0.998392 0.0566798i \(-0.981949\pi\)
0.450110 0.892973i \(-0.351385\pi\)
\(164\) 17.5623 1.37139
\(165\) 0 0
\(166\) 3.06231 5.30407i 0.237681 0.411676i
\(167\) 7.11803 12.3288i 0.550810 0.954031i −0.447406 0.894331i \(-0.647652\pi\)
0.998216 0.0597001i \(-0.0190144\pi\)
\(168\) 0 0
\(169\) 5.54508 9.60437i 0.426545 0.738798i
\(170\) 2.87539 0.220532
\(171\) 0 0
\(172\) 12.0517 1.60570i 0.918931 0.122433i
\(173\) 3.76393 0.286166 0.143083 0.989711i \(-0.454298\pi\)
0.143083 + 0.989711i \(0.454298\pi\)
\(174\) 0 0
\(175\) −7.35410 + 12.7377i −0.555918 + 0.962878i
\(176\) 11.3820 0.857948
\(177\) 0 0
\(178\) −0.354102 + 0.613323i −0.0265411 + 0.0459705i
\(179\) 4.82624 + 8.35929i 0.360730 + 0.624803i 0.988081 0.153934i \(-0.0491943\pi\)
−0.627351 + 0.778736i \(0.715861\pi\)
\(180\) 0 0
\(181\) 9.69098 + 16.7853i 0.720325 + 1.24764i 0.960869 + 0.277002i \(0.0893407\pi\)
−0.240544 + 0.970638i \(0.577326\pi\)
\(182\) 1.11803 1.93649i 0.0828742 0.143542i
\(183\) 0 0
\(184\) −3.22542 + 5.58660i −0.237781 + 0.411850i
\(185\) −3.00000 5.19615i −0.220564 0.382029i
\(186\) 0 0
\(187\) 11.0172 + 19.0824i 0.805659 + 1.39544i
\(188\) 2.12461 0.154953
\(189\) 0 0
\(190\) −0.291796 0.505406i −0.0211691 0.0366660i
\(191\) −7.26393 + 12.5815i −0.525600 + 0.910365i 0.473956 + 0.880549i \(0.342826\pi\)
−0.999555 + 0.0298167i \(0.990508\pi\)
\(192\) 0 0
\(193\) 2.70820 0.194941 0.0974704 0.995238i \(-0.468925\pi\)
0.0974704 + 0.995238i \(0.468925\pi\)
\(194\) −3.52786 −0.253286
\(195\) 0 0
\(196\) 10.1459 17.5732i 0.724707 1.25523i
\(197\) −1.47214 2.54981i −0.104885 0.181667i 0.808806 0.588076i \(-0.200114\pi\)
−0.913691 + 0.406409i \(0.866781\pi\)
\(198\) 0 0
\(199\) 1.94427 0.137826 0.0689129 0.997623i \(-0.478047\pi\)
0.0689129 + 0.997623i \(0.478047\pi\)
\(200\) −2.55573 4.42665i −0.180717 0.313011i
\(201\) 0 0
\(202\) 0.718847 + 1.24508i 0.0505779 + 0.0876035i
\(203\) −6.35410 + 11.0056i −0.445971 + 0.772444i
\(204\) 0 0
\(205\) −5.85410 + 10.1396i −0.408868 + 0.708181i
\(206\) 3.13525 + 5.43042i 0.218444 + 0.378355i
\(207\) 0 0
\(208\) −2.17376 3.76507i −0.150723 0.261060i
\(209\) 2.23607 3.87298i 0.154672 0.267900i
\(210\) 0 0
\(211\) −9.23607 −0.635837 −0.317919 0.948118i \(-0.602984\pi\)
−0.317919 + 0.948118i \(0.602984\pi\)
\(212\) 1.28115 2.21902i 0.0879899 0.152403i
\(213\) 0 0
\(214\) −2.87539 −0.196557
\(215\) −3.09017 + 7.49326i −0.210748 + 0.511036i
\(216\) 0 0
\(217\) 0 0
\(218\) 2.64590 4.58283i 0.179203 0.310388i
\(219\) 0 0
\(220\) −4.14590 + 7.18091i −0.279516 + 0.484137i
\(221\) 4.20820 7.28882i 0.283074 0.490299i
\(222\) 0 0
\(223\) 2.76393 0.185087 0.0925433 0.995709i \(-0.470500\pi\)
0.0925433 + 0.995709i \(0.470500\pi\)
\(224\) 8.78115 + 15.2094i 0.586715 + 1.01622i
\(225\) 0 0
\(226\) 5.96556 0.396823
\(227\) −0.736068 + 1.27491i −0.0488545 + 0.0846186i −0.889419 0.457094i \(-0.848890\pi\)
0.840564 + 0.541712i \(0.182224\pi\)
\(228\) 0 0
\(229\) 1.14590 + 1.98475i 0.0757231 + 0.131156i 0.901400 0.432986i \(-0.142540\pi\)
−0.825677 + 0.564143i \(0.809207\pi\)
\(230\) −1.03444 1.79171i −0.0682091 0.118142i
\(231\) 0 0
\(232\) −2.20820 3.82472i −0.144976 0.251105i
\(233\) 9.01722 + 15.6183i 0.590738 + 1.02319i 0.994133 + 0.108162i \(0.0344966\pi\)
−0.403395 + 0.915026i \(0.632170\pi\)
\(234\) 0 0
\(235\) −0.708204 + 1.22665i −0.0461981 + 0.0800175i
\(236\) 9.43769 0.614342
\(237\) 0 0
\(238\) −4.92705 + 8.53390i −0.319373 + 0.553171i
\(239\) −4.14590 + 7.18091i −0.268176 + 0.464494i −0.968391 0.249438i \(-0.919754\pi\)
0.700215 + 0.713932i \(0.253087\pi\)
\(240\) 0 0
\(241\) −2.13525 3.69837i −0.137544 0.238233i 0.789022 0.614364i \(-0.210587\pi\)
−0.926566 + 0.376131i \(0.877254\pi\)
\(242\) 0.798374 0.0513214
\(243\) 0 0
\(244\) 2.64590 + 4.58283i 0.169386 + 0.293386i
\(245\) 6.76393 + 11.7155i 0.432132 + 0.748474i
\(246\) 0 0
\(247\) −1.70820 −0.108690
\(248\) 0 0
\(249\) 0 0
\(250\) 4.00000 0.252982
\(251\) −14.5902 25.2709i −0.920923 1.59509i −0.797990 0.602671i \(-0.794103\pi\)
−0.122934 0.992415i \(-0.539230\pi\)
\(252\) 0 0
\(253\) 7.92705 13.7301i 0.498369 0.863201i
\(254\) −5.59675 −0.351171
\(255\) 0 0
\(256\) 5.56231 0.347644
\(257\) −3.43769 −0.214437 −0.107219 0.994235i \(-0.534195\pi\)
−0.107219 + 0.994235i \(0.534195\pi\)
\(258\) 0 0
\(259\) 20.5623 1.27768
\(260\) 3.16718 0.196420
\(261\) 0 0
\(262\) −3.79837 −0.234664
\(263\) 13.7533 23.8214i 0.848064 1.46889i −0.0348693 0.999392i \(-0.511101\pi\)
0.882933 0.469498i \(-0.155565\pi\)
\(264\) 0 0
\(265\) 0.854102 + 1.47935i 0.0524671 + 0.0908756i
\(266\) 2.00000 0.122628
\(267\) 0 0
\(268\) −3.57295 + 6.18853i −0.218253 + 0.378025i
\(269\) −11.5623 −0.704966 −0.352483 0.935818i \(-0.614663\pi\)
−0.352483 + 0.935818i \(0.614663\pi\)
\(270\) 0 0
\(271\) −6.92705 11.9980i −0.420788 0.728827i 0.575228 0.817993i \(-0.304913\pi\)
−0.996017 + 0.0891660i \(0.971580\pi\)
\(272\) 9.57953 + 16.5922i 0.580844 + 1.00605i
\(273\) 0 0
\(274\) −1.41641 −0.0855683
\(275\) 6.28115 + 10.8793i 0.378768 + 0.656045i
\(276\) 0 0
\(277\) 6.23607 10.8012i 0.374689 0.648980i −0.615591 0.788065i \(-0.711083\pi\)
0.990280 + 0.139085i \(0.0444161\pi\)
\(278\) 1.01064 1.75049i 0.0606143 0.104987i
\(279\) 0 0
\(280\) −7.70820 −0.460653
\(281\) 3.73607 6.47106i 0.222875 0.386031i −0.732805 0.680439i \(-0.761789\pi\)
0.955680 + 0.294408i \(0.0951224\pi\)
\(282\) 0 0
\(283\) −5.38197 9.32184i −0.319925 0.554126i 0.660547 0.750784i \(-0.270324\pi\)
−0.980472 + 0.196659i \(0.936991\pi\)
\(284\) 10.0106 + 17.3389i 0.594022 + 1.02888i
\(285\) 0 0
\(286\) −0.954915 1.65396i −0.0564653 0.0978008i
\(287\) −20.0623 34.7489i −1.18424 2.05116i
\(288\) 0 0
\(289\) −10.0451 + 17.3986i −0.590887 + 1.02345i
\(290\) 1.41641 0.0831743
\(291\) 0 0
\(292\) 1.71885 + 2.97713i 0.100588 + 0.174223i
\(293\) 12.0902 0.706315 0.353158 0.935564i \(-0.385108\pi\)
0.353158 + 0.935564i \(0.385108\pi\)
\(294\) 0 0
\(295\) −3.14590 + 5.44886i −0.183161 + 0.317245i
\(296\) −3.57295 + 6.18853i −0.207673 + 0.359701i
\(297\) 0 0
\(298\) 1.71885 2.97713i 0.0995701 0.172461i
\(299\) −6.05573 −0.350212
\(300\) 0 0
\(301\) −16.9443 22.0113i −0.976652 1.26871i
\(302\) −3.38197 −0.194610
\(303\) 0 0
\(304\) 1.94427 3.36758i 0.111512 0.193144i
\(305\) −3.52786 −0.202005
\(306\) 0 0
\(307\) 11.6074 20.1046i 0.662469 1.14743i −0.317496 0.948260i \(-0.602842\pi\)
0.979965 0.199170i \(-0.0638246\pi\)
\(308\) −14.2082 24.6093i −0.809588 1.40225i
\(309\) 0 0
\(310\) 0 0
\(311\) −14.9164 + 25.8360i −0.845832 + 1.46502i 0.0390649 + 0.999237i \(0.487562\pi\)
−0.884897 + 0.465787i \(0.845771\pi\)
\(312\) 0 0
\(313\) −6.56231 + 11.3662i −0.370923 + 0.642458i −0.989708 0.143103i \(-0.954292\pi\)
0.618784 + 0.785561i \(0.287625\pi\)
\(314\) 0.982779 + 1.70222i 0.0554614 + 0.0960620i
\(315\) 0 0
\(316\) −1.28115 2.21902i −0.0720705 0.124830i
\(317\) −33.3050 −1.87059 −0.935296 0.353866i \(-0.884867\pi\)
−0.935296 + 0.353866i \(0.884867\pi\)
\(318\) 0 0
\(319\) 5.42705 + 9.39993i 0.303857 + 0.526295i
\(320\) −2.90983 + 5.03997i −0.162664 + 0.281743i
\(321\) 0 0
\(322\) 7.09017 0.395120
\(323\) 7.52786 0.418862
\(324\) 0 0
\(325\) 2.39919 4.15551i 0.133083 0.230506i
\(326\) −2.67376 4.63109i −0.148086 0.256492i
\(327\) 0 0
\(328\) 13.9443 0.769944
\(329\) −2.42705 4.20378i −0.133808 0.231762i
\(330\) 0 0
\(331\) 2.73607 + 4.73901i 0.150388 + 0.260479i 0.931370 0.364074i \(-0.118614\pi\)
−0.780982 + 0.624553i \(0.785281\pi\)
\(332\) −14.8647 + 25.7465i −0.815809 + 1.41302i
\(333\) 0 0
\(334\) 2.71885 4.70918i 0.148769 0.257675i
\(335\) −2.38197 4.12569i −0.130141 0.225410i
\(336\) 0 0
\(337\) −14.0000 24.2487i −0.762629 1.32091i −0.941491 0.337037i \(-0.890575\pi\)
0.178863 0.983874i \(-0.442758\pi\)
\(338\) 2.11803 3.66854i 0.115206 0.199542i
\(339\) 0 0
\(340\) −13.9574 −0.756948
\(341\) 0 0
\(342\) 0 0
\(343\) −16.7082 −0.902158
\(344\) 9.56888 1.27491i 0.515920 0.0687384i
\(345\) 0 0
\(346\) 1.43769 0.0772909
\(347\) 5.04508 8.73834i 0.270834 0.469099i −0.698241 0.715862i \(-0.746034\pi\)
0.969076 + 0.246764i \(0.0793671\pi\)
\(348\) 0 0
\(349\) −10.3541 + 17.9338i −0.554242 + 0.959976i 0.443720 + 0.896166i \(0.353659\pi\)
−0.997962 + 0.0638103i \(0.979675\pi\)
\(350\) −2.80902 + 4.86536i −0.150148 + 0.260064i
\(351\) 0 0
\(352\) 15.0000 0.799503
\(353\) −8.61803 14.9269i −0.458692 0.794477i 0.540200 0.841536i \(-0.318348\pi\)
−0.998892 + 0.0470591i \(0.985015\pi\)
\(354\) 0 0
\(355\) −13.3475 −0.708413
\(356\) 1.71885 2.97713i 0.0910987 0.157788i
\(357\) 0 0
\(358\) 1.84346 + 3.19296i 0.0974298 + 0.168753i
\(359\) −2.67376 4.63109i −0.141116 0.244420i 0.786801 0.617206i \(-0.211736\pi\)
−0.927917 + 0.372787i \(0.878402\pi\)
\(360\) 0 0
\(361\) 8.73607 + 15.1313i 0.459793 + 0.796385i
\(362\) 3.70163 + 6.41140i 0.194553 + 0.336976i
\(363\) 0 0
\(364\) −5.42705 + 9.39993i −0.284455 + 0.492690i
\(365\) −2.29180 −0.119958
\(366\) 0 0
\(367\) −9.59017 + 16.6107i −0.500603 + 0.867069i 0.499397 + 0.866373i \(0.333555\pi\)
−1.00000 0.000696189i \(0.999778\pi\)
\(368\) 6.89261 11.9383i 0.359302 0.622329i
\(369\) 0 0
\(370\) −1.14590 1.98475i −0.0595724 0.103182i
\(371\) −5.85410 −0.303930
\(372\) 0 0
\(373\) −3.00000 5.19615i −0.155334 0.269047i 0.777847 0.628454i \(-0.216312\pi\)
−0.933181 + 0.359408i \(0.882979\pi\)
\(374\) 4.20820 + 7.28882i 0.217601 + 0.376896i
\(375\) 0 0
\(376\) 1.68692 0.0869961
\(377\) 2.07295 3.59045i 0.106762 0.184918i
\(378\) 0 0
\(379\) −27.3607 −1.40542 −0.702712 0.711475i \(-0.748028\pi\)
−0.702712 + 0.711475i \(0.748028\pi\)
\(380\) 1.41641 + 2.45329i 0.0726602 + 0.125851i
\(381\) 0 0
\(382\) −2.77458 + 4.80571i −0.141960 + 0.245881i
\(383\) −38.1246 −1.94808 −0.974038 0.226383i \(-0.927310\pi\)
−0.974038 + 0.226383i \(0.927310\pi\)
\(384\) 0 0
\(385\) 18.9443 0.965489
\(386\) 1.03444 0.0526517
\(387\) 0 0
\(388\) 17.1246 0.869370
\(389\) 35.0689 1.77806 0.889031 0.457846i \(-0.151379\pi\)
0.889031 + 0.457846i \(0.151379\pi\)
\(390\) 0 0
\(391\) 26.6869 1.34962
\(392\) 8.05573 13.9529i 0.406876 0.704729i
\(393\) 0 0
\(394\) −0.562306 0.973942i −0.0283286 0.0490665i
\(395\) 1.70820 0.0859491
\(396\) 0 0
\(397\) −16.2082 + 28.0734i −0.813466 + 1.40897i 0.0969574 + 0.995289i \(0.469089\pi\)
−0.910424 + 0.413677i \(0.864244\pi\)
\(398\) 0.742646 0.0372255
\(399\) 0 0
\(400\) 5.46149 + 9.45958i 0.273075 + 0.472979i
\(401\) −12.7082 22.0113i −0.634617 1.09919i −0.986596 0.163182i \(-0.947824\pi\)
0.351979 0.936008i \(-0.385509\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −3.48936 6.04374i −0.173602 0.300687i
\(405\) 0 0
\(406\) −2.42705 + 4.20378i −0.120453 + 0.208630i
\(407\) 8.78115 15.2094i 0.435266 0.753902i
\(408\) 0 0
\(409\) 8.90983 0.440563 0.220281 0.975436i \(-0.429302\pi\)
0.220281 + 0.975436i \(0.429302\pi\)
\(410\) −2.23607 + 3.87298i −0.110432 + 0.191273i
\(411\) 0 0
\(412\) −15.2188 26.3598i −0.749779 1.29865i
\(413\) −10.7812 18.6735i −0.530506 0.918863i
\(414\) 0 0
\(415\) −9.90983 17.1643i −0.486454 0.842564i
\(416\) −2.86475 4.96188i −0.140456 0.243276i
\(417\) 0 0
\(418\) 0.854102 1.47935i 0.0417755 0.0723573i
\(419\) 10.2361 0.500065 0.250032 0.968237i \(-0.419559\pi\)
0.250032 + 0.968237i \(0.419559\pi\)
\(420\) 0 0
\(421\) 3.82624 + 6.62724i 0.186479 + 0.322992i 0.944074 0.329734i \(-0.106959\pi\)
−0.757595 + 0.652725i \(0.773626\pi\)
\(422\) −3.52786 −0.171734
\(423\) 0 0
\(424\) 1.01722 1.76188i 0.0494006 0.0855644i
\(425\) −10.5729 + 18.3129i −0.512863 + 0.888305i
\(426\) 0 0
\(427\) 6.04508 10.4704i 0.292542 0.506698i
\(428\) 13.9574 0.674658
\(429\) 0 0
\(430\) −1.18034 + 2.86217i −0.0569210 + 0.138026i
\(431\) 24.7984 1.19450 0.597248 0.802057i \(-0.296261\pi\)
0.597248 + 0.802057i \(0.296261\pi\)
\(432\) 0 0
\(433\) 17.3541 30.0582i 0.833985 1.44450i −0.0608693 0.998146i \(-0.519387\pi\)
0.894854 0.446359i \(-0.147279\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −12.8435 + 22.2455i −0.615090 + 1.06537i
\(437\) −2.70820 4.69075i −0.129551 0.224389i
\(438\) 0 0
\(439\) −0.572949 0.992377i −0.0273454 0.0473636i 0.852029 0.523495i \(-0.175372\pi\)
−0.879374 + 0.476131i \(0.842039\pi\)
\(440\) −3.29180 + 5.70156i −0.156930 + 0.271811i
\(441\) 0 0
\(442\) 1.60739 2.78408i 0.0764558 0.132425i
\(443\) 1.23607 + 2.14093i 0.0587274 + 0.101719i 0.893894 0.448278i \(-0.147962\pi\)
−0.835167 + 0.549996i \(0.814629\pi\)
\(444\) 0 0
\(445\) 1.14590 + 1.98475i 0.0543208 + 0.0940863i
\(446\) 1.05573 0.0499902
\(447\) 0 0
\(448\) −9.97214 17.2722i −0.471139 0.816037i
\(449\) −16.4164 + 28.4341i −0.774738 + 1.34189i 0.160203 + 0.987084i \(0.448785\pi\)
−0.934942 + 0.354802i \(0.884548\pi\)
\(450\) 0 0
\(451\) −34.2705 −1.61374
\(452\) −28.9574 −1.36204
\(453\) 0 0
\(454\) −0.281153 + 0.486971i −0.0131952 + 0.0228547i
\(455\) −3.61803 6.26662i −0.169616 0.293784i
\(456\) 0 0
\(457\) −15.7082 −0.734799 −0.367399 0.930063i \(-0.619752\pi\)
−0.367399 + 0.930063i \(0.619752\pi\)
\(458\) 0.437694 + 0.758108i 0.0204521 + 0.0354241i
\(459\) 0 0
\(460\) 5.02129 + 8.69712i 0.234119 + 0.405505i
\(461\) −15.7984 + 27.3636i −0.735804 + 1.27445i 0.218566 + 0.975822i \(0.429862\pi\)
−0.954370 + 0.298627i \(0.903471\pi\)
\(462\) 0 0
\(463\) 14.9164 25.8360i 0.693224 1.20070i −0.277551 0.960711i \(-0.589523\pi\)
0.970776 0.239989i \(-0.0771438\pi\)
\(464\) 4.71885 + 8.17328i 0.219067 + 0.379435i
\(465\) 0 0
\(466\) 3.44427 + 5.96565i 0.159553 + 0.276354i
\(467\) −7.52786 + 13.0386i −0.348348 + 0.603356i −0.985956 0.167004i \(-0.946591\pi\)
0.637608 + 0.770361i \(0.279924\pi\)
\(468\) 0 0
\(469\) 16.3262 0.753876
\(470\) −0.270510 + 0.468537i −0.0124777 + 0.0216120i
\(471\) 0 0
\(472\) 7.49342 0.344913
\(473\) −23.5172 + 3.13331i −1.08132 + 0.144070i
\(474\) 0 0
\(475\) 4.29180 0.196921
\(476\) 23.9164 41.4244i 1.09621 1.89869i
\(477\) 0 0
\(478\) −1.58359 + 2.74286i −0.0724318 + 0.125456i
\(479\) −6.90983 + 11.9682i −0.315718 + 0.546840i −0.979590 0.201007i \(-0.935579\pi\)
0.663872 + 0.747846i \(0.268912\pi\)
\(480\) 0 0
\(481\) −6.70820 −0.305868
\(482\) −0.815595 1.41265i −0.0371493 0.0643445i
\(483\) 0 0
\(484\) −3.87539 −0.176154
\(485\) −5.70820 + 9.88690i −0.259196 + 0.448941i
\(486\) 0 0
\(487\) −0.663119 1.14856i −0.0300488 0.0520460i 0.850610 0.525797i \(-0.176233\pi\)
−0.880659 + 0.473751i \(0.842900\pi\)
\(488\) 2.10081 + 3.63871i 0.0950993 + 0.164717i
\(489\) 0 0
\(490\) 2.58359 + 4.47491i 0.116715 + 0.202156i
\(491\) 10.8262 + 18.7516i 0.488581 + 0.846248i 0.999914 0.0131354i \(-0.00418125\pi\)
−0.511332 + 0.859383i \(0.670848\pi\)
\(492\) 0 0
\(493\) −9.13525 + 15.8227i −0.411431 + 0.712620i
\(494\) −0.652476 −0.0293563
\(495\) 0 0
\(496\) 0 0
\(497\) 22.8713 39.6143i 1.02592 1.77694i
\(498\) 0 0
\(499\) −6.92705 11.9980i −0.310097 0.537104i 0.668286 0.743905i \(-0.267028\pi\)
−0.978383 + 0.206800i \(0.933695\pi\)
\(500\) −19.4164 −0.868328
\(501\) 0 0
\(502\) −5.57295 9.65263i −0.248733 0.430818i
\(503\) −6.73607 11.6672i −0.300346 0.520215i 0.675868 0.737023i \(-0.263769\pi\)
−0.976214 + 0.216807i \(0.930436\pi\)
\(504\) 0 0
\(505\) 4.65248 0.207032
\(506\) 3.02786 5.24441i 0.134605 0.233143i
\(507\) 0 0
\(508\) 27.1672 1.20535
\(509\) 9.35410 + 16.2018i 0.414613 + 0.718131i 0.995388 0.0959332i \(-0.0305835\pi\)
−0.580774 + 0.814064i \(0.697250\pi\)
\(510\) 0 0
\(511\) 3.92705 6.80185i 0.173723 0.300896i
\(512\) 22.3050 0.985749
\(513\) 0 0
\(514\) −1.31308 −0.0579176
\(515\) 20.2918 0.894163
\(516\) 0 0
\(517\) −4.14590 −0.182336
\(518\) 7.85410 0.345089
\(519\) 0 0
\(520\) 2.51471 0.110277
\(521\) −11.0172 + 19.0824i −0.482673 + 0.836015i −0.999802 0.0198930i \(-0.993667\pi\)
0.517129 + 0.855908i \(0.327001\pi\)
\(522\) 0 0
\(523\) −17.9164 31.0321i −0.783430 1.35694i −0.929933 0.367730i \(-0.880135\pi\)
0.146503 0.989210i \(-0.453198\pi\)
\(524\) 18.4377 0.805454
\(525\) 0 0
\(526\) 5.25329 9.09896i 0.229054 0.396734i
\(527\) 0 0
\(528\) 0 0
\(529\) 1.89919 + 3.28949i 0.0825733 + 0.143021i
\(530\) 0.326238 + 0.565061i 0.0141709 + 0.0245447i
\(531\) 0 0
\(532\) −9.70820 −0.420904
\(533\) 6.54508 + 11.3364i 0.283499 + 0.491035i
\(534\) 0 0
\(535\) −4.65248 + 8.05832i −0.201144 + 0.348392i
\(536\) −2.83688 + 4.91362i −0.122535 + 0.212236i
\(537\) 0 0
\(538\) −4.41641 −0.190405
\(539\) −19.7984 + 34.2918i −0.852776 + 1.47705i
\(540\) 0 0
\(541\) 18.9721 + 32.8607i 0.815676 + 1.41279i 0.908842 + 0.417141i \(0.136968\pi\)
−0.0931658 + 0.995651i \(0.529699\pi\)
\(542\) −2.64590 4.58283i −0.113651 0.196849i
\(543\) 0 0
\(544\) 12.6246 + 21.8665i 0.541276 + 0.937517i
\(545\) −8.56231 14.8303i −0.366769 0.635262i
\(546\) 0 0
\(547\) −10.5000 + 18.1865i −0.448948 + 0.777600i −0.998318 0.0579790i \(-0.981534\pi\)
0.549370 + 0.835579i \(0.314868\pi\)
\(548\) 6.87539 0.293702
\(549\) 0 0
\(550\) 2.39919 + 4.15551i 0.102302 + 0.177192i
\(551\) 3.70820 0.157975
\(552\) 0 0
\(553\) −2.92705 + 5.06980i −0.124471 + 0.215590i
\(554\) 2.38197 4.12569i 0.101200 0.175284i
\(555\) 0 0
\(556\) −4.90576 + 8.49703i −0.208051 + 0.360354i
\(557\) 38.5623 1.63394 0.816969 0.576682i \(-0.195653\pi\)
0.816969 + 0.576682i \(0.195653\pi\)
\(558\) 0 0
\(559\) 5.52786 + 7.18091i 0.233804 + 0.303720i
\(560\) 16.4721 0.696075
\(561\) 0 0
\(562\) 1.42705 2.47172i 0.0601965 0.104263i
\(563\) 1.32624 0.0558943 0.0279471 0.999609i \(-0.491103\pi\)
0.0279471 + 0.999609i \(0.491103\pi\)
\(564\) 0 0
\(565\) 9.65248 16.7186i 0.406083 0.703356i
\(566\) −2.05573 3.56063i −0.0864087 0.149664i
\(567\) 0 0
\(568\) 7.94834 + 13.7669i 0.333505 + 0.577647i
\(569\) −12.9721 + 22.4684i −0.543820 + 0.941924i 0.454860 + 0.890563i \(0.349689\pi\)
−0.998680 + 0.0513613i \(0.983644\pi\)
\(570\) 0 0
\(571\) 21.5902 37.3953i 0.903520 1.56494i 0.0806295 0.996744i \(-0.474307\pi\)
0.822891 0.568199i \(-0.192360\pi\)
\(572\) 4.63525 + 8.02850i 0.193810 + 0.335688i
\(573\) 0 0
\(574\) −7.66312 13.2729i −0.319852 0.554001i
\(575\) 15.2148 0.634500
\(576\) 0 0
\(577\) 14.1074 + 24.4347i 0.587298 + 1.01723i 0.994585 + 0.103930i \(0.0331418\pi\)
−0.407286 + 0.913301i \(0.633525\pi\)
\(578\) −3.83688 + 6.64567i −0.159593 + 0.276424i
\(579\) 0 0
\(580\) −6.87539 −0.285485
\(581\) 67.9230 2.81792
\(582\) 0 0
\(583\) −2.50000 + 4.33013i −0.103539 + 0.179336i
\(584\) 1.36475 + 2.36381i 0.0564736 + 0.0978151i
\(585\) 0 0
\(586\) 4.61803 0.190769
\(587\) 7.87132 + 13.6335i 0.324884 + 0.562716i 0.981489 0.191519i \(-0.0613413\pi\)
−0.656605 + 0.754235i \(0.728008\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −1.20163 + 2.08128i −0.0494702 + 0.0856848i
\(591\) 0 0
\(592\) 7.63525 13.2246i 0.313807 0.543530i
\(593\) −15.2361 26.3896i −0.625670 1.08369i −0.988411 0.151803i \(-0.951492\pi\)
0.362741 0.931890i \(-0.381841\pi\)
\(594\) 0 0
\(595\) 15.9443 + 27.6163i 0.653651 + 1.13216i
\(596\) −8.34346 + 14.4513i −0.341761 + 0.591948i
\(597\) 0 0
\(598\) −2.31308 −0.0945890
\(599\) 18.1180 31.3814i 0.740283 1.28221i −0.212084 0.977252i \(-0.568025\pi\)
0.952366 0.304956i \(-0.0986417\pi\)
\(600\) 0 0
\(601\) 29.4164 1.19992 0.599960 0.800030i \(-0.295183\pi\)
0.599960 + 0.800030i \(0.295183\pi\)
\(602\) −6.47214 8.40755i −0.263785 0.342666i
\(603\) 0 0
\(604\) 16.4164 0.667974
\(605\) 1.29180 2.23746i 0.0525190 0.0909655i
\(606\) 0 0
\(607\) 11.9271 20.6583i 0.484104 0.838493i −0.515729 0.856752i \(-0.672479\pi\)
0.999833 + 0.0182588i \(0.00581228\pi\)
\(608\) 2.56231 4.43804i 0.103915 0.179986i
\(609\) 0 0
\(610\) −1.34752 −0.0545597
\(611\) 0.791796 + 1.37143i 0.0320326 + 0.0554822i
\(612\) 0 0
\(613\) 5.20163 0.210092 0.105046 0.994467i \(-0.466501\pi\)
0.105046 + 0.994467i \(0.466501\pi\)
\(614\) 4.43363 7.67927i 0.178927 0.309910i
\(615\) 0 0
\(616\) −11.2812 19.5395i −0.454531 0.787270i
\(617\) 4.85410 + 8.40755i 0.195419 + 0.338475i 0.947038 0.321122i \(-0.104060\pi\)
−0.751619 + 0.659598i \(0.770727\pi\)
\(618\) 0 0
\(619\) 15.1353 + 26.2150i 0.608337 + 1.05367i 0.991514 + 0.129996i \(0.0414965\pi\)
−0.383177 + 0.923675i \(0.625170\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −5.69756 + 9.86846i −0.228451 + 0.395689i
\(623\) −7.85410 −0.314668
\(624\) 0 0
\(625\) −2.20820 + 3.82472i −0.0883282 + 0.152989i
\(626\) −2.50658 + 4.34152i −0.100183 + 0.173522i
\(627\) 0 0
\(628\) −4.77051 8.26277i −0.190364 0.329720i
\(629\) 29.5623 1.17873
\(630\) 0 0
\(631\) 13.5451 + 23.4608i 0.539221 + 0.933959i 0.998946 + 0.0458973i \(0.0146147\pi\)
−0.459725 + 0.888061i \(0.652052\pi\)
\(632\) −1.01722 1.76188i −0.0404629 0.0700838i
\(633\) 0 0
\(634\) −12.7214 −0.505230
\(635\) −9.05573 + 15.6850i −0.359366 + 0.622439i
\(636\) 0 0
\(637\) 15.1246 0.599259
\(638\) 2.07295 + 3.59045i 0.0820688 + 0.142147i
\(639\) 0 0
\(640\) −6.23607 + 10.8012i −0.246502 + 0.426954i
\(641\) −10.8197 −0.427351 −0.213675 0.976905i \(-0.568543\pi\)
−0.213675 + 0.976905i \(0.568543\pi\)
\(642\) 0 0
\(643\) 9.43769 0.372186 0.186093 0.982532i \(-0.440417\pi\)
0.186093 + 0.982532i \(0.440417\pi\)
\(644\) −34.4164 −1.35620
\(645\) 0 0
\(646\) 2.87539 0.113131
\(647\) 21.6738 0.852084 0.426042 0.904703i \(-0.359908\pi\)
0.426042 + 0.904703i \(0.359908\pi\)
\(648\) 0 0
\(649\) −18.4164 −0.722907
\(650\) 0.916408 1.58726i 0.0359445 0.0622577i
\(651\) 0 0
\(652\) 12.9787 + 22.4798i 0.508286 + 0.880377i
\(653\) 32.8885 1.28703 0.643514 0.765434i \(-0.277476\pi\)
0.643514 + 0.765434i \(0.277476\pi\)
\(654\) 0 0
\(655\) −6.14590 + 10.6450i −0.240140 + 0.415935i
\(656\) −29.7984 −1.16343
\(657\) 0 0
\(658\) −0.927051 1.60570i −0.0361402 0.0625967i
\(659\) −14.6803 25.4271i −0.571865 0.990499i −0.996375 0.0850756i \(-0.972887\pi\)
0.424510 0.905423i \(-0.360447\pi\)
\(660\) 0 0
\(661\) −43.3951 −1.68787 −0.843937 0.536442i \(-0.819768\pi\)
−0.843937 + 0.536442i \(0.819768\pi\)
\(662\) 1.04508 + 1.81014i 0.0406184 + 0.0703531i
\(663\) 0 0
\(664\) −11.8024 + 20.4424i −0.458023 + 0.793320i
\(665\) 3.23607 5.60503i 0.125489 0.217354i
\(666\) 0 0
\(667\) 13.1459 0.509011
\(668\) −13.1976 + 22.8588i −0.510629 + 0.884435i
\(669\) 0 0
\(670\) −0.909830 1.57587i −0.0351498 0.0608812i
\(671\) −5.16312 8.94278i −0.199320 0.345232i
\(672\) 0 0
\(673\) −6.91641 11.9796i −0.266608 0.461778i 0.701376 0.712792i \(-0.252570\pi\)
−0.967984 + 0.251013i \(0.919236\pi\)
\(674\) −5.34752 9.26218i −0.205979 0.356766i
\(675\) 0 0
\(676\) −10.2812 + 17.8075i −0.395429 + 0.684903i
\(677\) 31.7639 1.22079 0.610394 0.792098i \(-0.291011\pi\)
0.610394 + 0.792098i \(0.291011\pi\)
\(678\) 0 0
\(679\) −19.5623 33.8829i −0.750732 1.30031i
\(680\) −11.0820 −0.424977
\(681\) 0 0
\(682\) 0 0
\(683\) −5.56231 + 9.63420i −0.212836 + 0.368642i −0.952601 0.304223i \(-0.901603\pi\)
0.739765 + 0.672865i \(0.234937\pi\)
\(684\) 0 0
\(685\) −2.29180 + 3.96951i −0.0875650 + 0.151667i
\(686\) −6.38197 −0.243665
\(687\) 0 0
\(688\) −20.4483 + 2.72443i −0.779586 + 0.103868i
\(689\) 1.90983 0.0727587
\(690\) 0 0
\(691\) −7.86475 + 13.6221i −0.299189 + 0.518211i −0.975951 0.217992i \(-0.930049\pi\)
0.676762 + 0.736202i \(0.263383\pi\)
\(692\) −6.97871 −0.265291
\(693\) 0 0
\(694\) 1.92705 3.33775i 0.0731499 0.126699i
\(695\) −3.27051 5.66469i −0.124058 0.214874i
\(696\) 0 0
\(697\) −28.8435 49.9583i −1.09252 1.89231i
\(698\) −3.95492 + 6.85011i −0.149696 + 0.259281i
\(699\) 0 0
\(700\) 13.6353 23.6170i 0.515364 0.892637i
\(701\) −7.25329 12.5631i −0.273953 0.474500i 0.695917 0.718122i \(-0.254998\pi\)
−0.969870 + 0.243621i \(0.921665\pi\)
\(702\) 0 0
\(703\) −3.00000 5.19615i −0.113147 0.195977i
\(704\) −17.0344 −0.642010
\(705\) 0 0
\(706\) −3.29180 5.70156i −0.123888 0.214581i
\(707\) −7.97214 + 13.8081i −0.299823 + 0.519309i
\(708\) 0 0
\(709\) 28.8885 1.08493 0.542466 0.840078i \(-0.317491\pi\)
0.542466 + 0.840078i \(0.317491\pi\)
\(710\) −5.09830 −0.191336
\(711\) 0 0
\(712\) 1.36475 2.36381i 0.0511460 0.0885874i
\(713\) 0 0
\(714\) 0 0
\(715\) −6.18034 −0.231132
\(716\) −8.94834 15.4990i −0.334415 0.579224i
\(717\) 0 0
\(718\) −1.02129 1.76892i −0.0381141 0.0660155i
\(719\) −5.39919 + 9.35167i −0.201356 + 0.348758i −0.948965 0.315380i \(-0.897868\pi\)
0.747610 + 0.664138i \(0.231201\pi\)
\(720\) 0 0
\(721\) −34.7705 + 60.2243i −1.29492 + 2.24287i
\(722\) 3.33688 + 5.77965i 0.124186 + 0.215096i
\(723\) 0 0
\(724\) −17.9681 31.1216i −0.667778 1.15663i
\(725\) −5.20820 + 9.02087i −0.193428 + 0.335027i
\(726\) 0 0
\(727\) −17.9787 −0.666794 −0.333397 0.942787i \(-0.608195\pi\)
−0.333397 + 0.942787i \(0.608195\pi\)
\(728\) −4.30902 + 7.46344i −0.159703 + 0.276613i
\(729\) 0 0
\(730\) −0.875388 −0.0323996
\(731\) −24.3607 31.6455i −0.901012 1.17045i
\(732\) 0 0
\(733\) 24.5410 0.906443 0.453222 0.891398i \(-0.350275\pi\)
0.453222 + 0.891398i \(0.350275\pi\)
\(734\) −3.66312 + 6.34471i −0.135208 + 0.234187i
\(735\) 0 0
\(736\) 9.08359 15.7332i 0.334826 0.579935i
\(737\) 6.97214 12.0761i 0.256822 0.444829i
\(738\) 0 0
\(739\) 49.5410 1.82240 0.911198 0.411969i \(-0.135159\pi\)
0.911198 + 0.411969i \(0.135159\pi\)
\(740\) 5.56231 + 9.63420i 0.204474 + 0.354160i
\(741\) 0 0
\(742\) −2.23607 −0.0820886
\(743\) 16.6803 28.8912i 0.611942 1.05992i −0.378970 0.925409i \(-0.623722\pi\)
0.990913 0.134506i \(-0.0429449\pi\)
\(744\) 0 0
\(745\) −5.56231 9.63420i −0.203787 0.352970i
\(746\) −1.14590 1.98475i −0.0419543 0.0726670i
\(747\) 0 0
\(748\) −20.4271 35.3807i −0.746887 1.29365i
\(749\) −15.9443 27.6163i −0.582591 1.00908i
\(750\) 0 0
\(751\) 18.9894 32.8905i 0.692931 1.20019i −0.277942 0.960598i \(-0.589652\pi\)
0.970873 0.239595i \(-0.0770145\pi\)
\(752\) −3.60488 −0.131456
\(753\) 0 0
\(754\) 0.791796 1.37143i 0.0288355 0.0499446i
\(755\) −5.47214 + 9.47802i −0.199151 + 0.344940i
\(756\) 0 0
\(757\) 15.4894 + 26.8284i 0.562970 + 0.975093i 0.997235 + 0.0743080i \(0.0236748\pi\)
−0.434265 + 0.900785i \(0.642992\pi\)
\(758\) −10.4508 −0.379592
\(759\) 0 0
\(760\) 1.12461 + 1.94788i 0.0407940 + 0.0706572i
\(761\) 0.545085 + 0.944115i 0.0197593 + 0.0342241i 0.875736 0.482790i \(-0.160377\pi\)
−0.855977 + 0.517014i \(0.827043\pi\)
\(762\) 0 0
\(763\) 58.6869 2.12461
\(764\) 13.4681 23.3274i 0.487258 0.843955i
\(765\) 0 0
\(766\) −14.5623 −0.526157
\(767\) 3.51722 + 6.09201i 0.126999 + 0.219970i
\(768\) 0 0
\(769\) −9.94427 + 17.2240i −0.358600 + 0.621113i −0.987727 0.156189i \(-0.950079\pi\)
0.629128 + 0.777302i \(0.283412\pi\)
\(770\) 7.23607 0.260770
\(771\) 0 0
\(772\) −5.02129 −0.180720
\(773\) −15.5967 −0.560976 −0.280488 0.959858i \(-0.590496\pi\)
−0.280488 + 0.959858i \(0.590496\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 13.5967 0.488095
\(777\) 0 0
\(778\) 13.3951 0.480238
\(779\) −5.85410 + 10.1396i −0.209745 + 0.363289i
\(780\) 0 0
\(781\) −19.5344 33.8346i −0.698997 1.21070i
\(782\) 10.1935 0.364519
\(783\) 0 0
\(784\) −17.2148 + 29.8169i −0.614814 + 1.06489i
\(785\) 6.36068 0.227022
\(786\) 0 0
\(787\) −5.22542 9.05070i −0.186266 0.322623i 0.757736 0.652561i \(-0.226305\pi\)
−0.944002 + 0.329938i \(0.892972\pi\)
\(788\) 2.72949 + 4.72762i 0.0972341 + 0.168414i
\(789\) 0 0
\(790\) 0.652476 0.0232140
\(791\) 33.0795 + 57.2954i 1.17617 + 2.03719i
\(792\) 0 0
\(793\) −1.97214 + 3.41584i −0.0700326 + 0.121300i
\(794\) −6.19098 + 10.7231i −0.219710 + 0.380548i
\(795\) 0 0
\(796\) −3.60488 −0.127772
\(797\) −4.11803 + 7.13264i −0.145868 + 0.252651i −0.929697 0.368326i \(-0.879931\pi\)
0.783828 + 0.620978i \(0.213264\pi\)
\(798\) 0 0
\(799\) −3.48936 6.04374i −0.123445 0.213812i