Properties

Label 1183.2.e.j.508.1
Level $1183$
Weight $2$
Character 1183.508
Analytic conductor $9.446$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.1
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.j.170.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.29430 - 2.24179i) q^{2} +(-0.259233 + 0.449005i) q^{3} +(-2.35043 + 4.07106i) q^{4} +(-0.806027 - 1.39608i) q^{5} +1.34210 q^{6} +(2.13104 - 1.56802i) q^{7} +6.99143 q^{8} +(1.36560 + 2.36528i) q^{9} +O(q^{10})\) \(q+(-1.29430 - 2.24179i) q^{2} +(-0.259233 + 0.449005i) q^{3} +(-2.35043 + 4.07106i) q^{4} +(-0.806027 - 1.39608i) q^{5} +1.34210 q^{6} +(2.13104 - 1.56802i) q^{7} +6.99143 q^{8} +(1.36560 + 2.36528i) q^{9} +(-2.08648 + 3.61389i) q^{10} +(-1.35248 + 2.34256i) q^{11} +(-1.21862 - 2.11070i) q^{12} +(-6.27337 - 2.74787i) q^{14} +0.835795 q^{15} +(-4.34816 - 7.53123i) q^{16} +(-1.56330 + 2.70772i) q^{17} +(3.53498 - 6.12277i) q^{18} +(-1.84075 - 3.18828i) q^{19} +7.57803 q^{20} +(0.151611 + 1.36333i) q^{21} +7.00205 q^{22} +(-0.993019 - 1.71996i) q^{23} +(-1.81241 + 3.13918i) q^{24} +(1.20064 - 2.07957i) q^{25} -2.97143 q^{27} +(1.37463 + 12.3611i) q^{28} -5.37271 q^{29} +(-1.08177 - 1.87368i) q^{30} +(-5.23902 + 9.07425i) q^{31} +(-4.26421 + 7.38583i) q^{32} +(-0.701214 - 1.21454i) q^{33} +8.09354 q^{34} +(-3.90675 - 1.71124i) q^{35} -12.8389 q^{36} +(-2.97673 - 5.15585i) q^{37} +(-4.76497 + 8.25317i) q^{38} +(-5.63528 - 9.76059i) q^{40} -7.70150 q^{41} +(2.86007 - 2.10444i) q^{42} -3.35600 q^{43} +(-6.35780 - 11.0120i) q^{44} +(2.20141 - 3.81296i) q^{45} +(-2.57053 + 4.45229i) q^{46} +(-0.527542 - 0.913730i) q^{47} +4.50874 q^{48} +(2.08265 - 6.68300i) q^{49} -6.21596 q^{50} +(-0.810520 - 1.40386i) q^{51} +(-3.63284 + 6.29226i) q^{53} +(3.84592 + 6.66133i) q^{54} +4.36054 q^{55} +(14.8990 - 10.9627i) q^{56} +1.90873 q^{57} +(6.95390 + 12.0445i) q^{58} +(-5.71203 + 9.89352i) q^{59} +(-1.96447 + 3.40257i) q^{60} +(1.46254 + 2.53319i) q^{61} +27.1235 q^{62} +(6.61894 + 2.89923i) q^{63} +4.68406 q^{64} +(-1.81516 + 3.14395i) q^{66} +(6.79091 - 11.7622i) q^{67} +(-7.34886 - 12.7286i) q^{68} +1.02969 q^{69} +(1.22027 + 10.9730i) q^{70} -1.35111 q^{71} +(9.54747 + 16.5367i) q^{72} +(-4.55168 + 7.88374i) q^{73} +(-7.70557 + 13.3464i) q^{74} +(0.622492 + 1.07819i) q^{75} +17.3062 q^{76} +(0.790989 + 7.11280i) q^{77} +(3.10289 + 5.37436i) q^{79} +(-7.00946 + 12.1407i) q^{80} +(-3.32650 + 5.76166i) q^{81} +(9.96806 + 17.2652i) q^{82} -2.69672 q^{83} +(-5.90654 - 2.58718i) q^{84} +5.04026 q^{85} +(4.34367 + 7.52346i) q^{86} +(1.39278 - 2.41237i) q^{87} +(-9.45576 + 16.3779i) q^{88} +(-0.879938 - 1.52410i) q^{89} -11.3972 q^{90} +9.33607 q^{92} +(-2.71625 - 4.70469i) q^{93} +(-1.36560 + 2.36528i) q^{94} +(-2.96739 + 5.13967i) q^{95} +(-2.21085 - 3.82930i) q^{96} +15.4820 q^{97} +(-17.6775 + 3.98094i) q^{98} -7.38776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 6q^{3} - 8q^{4} - 2q^{9} + O(q^{10}) \) \( 24q - 6q^{3} - 8q^{4} - 2q^{9} - 24q^{10} + 2q^{12} + 8q^{14} - 16q^{16} - 34q^{17} + 60q^{22} - 6q^{23} + 10q^{25} + 24q^{27} + 4q^{29} - 22q^{30} - 24q^{35} - 52q^{36} - 38q^{38} - 2q^{40} + 32q^{42} + 44q^{43} - 76q^{48} + 12q^{49} - 8q^{51} - 16q^{53} + 60q^{55} + 54q^{56} + 10q^{61} + 164q^{62} - 4q^{64} - 68q^{66} - 22q^{68} + 28q^{69} - 66q^{74} - 2q^{75} + 38q^{77} - 70q^{79} + 28q^{81} - 10q^{82} + 20q^{87} + 28q^{88} - 132q^{92} + 2q^{94} - 4q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.29430 2.24179i −0.915209 1.58519i −0.806596 0.591104i \(-0.798692\pi\)
−0.108613 0.994084i \(-0.534641\pi\)
\(3\) −0.259233 + 0.449005i −0.149668 + 0.259233i −0.931105 0.364752i \(-0.881154\pi\)
0.781437 + 0.623985i \(0.214487\pi\)
\(4\) −2.35043 + 4.07106i −1.17521 + 2.03553i
\(5\) −0.806027 1.39608i −0.360466 0.624346i 0.627571 0.778559i \(-0.284049\pi\)
−0.988038 + 0.154213i \(0.950716\pi\)
\(6\) 1.34210 0.547910
\(7\) 2.13104 1.56802i 0.805457 0.592654i
\(8\) 6.99143 2.47184
\(9\) 1.36560 + 2.36528i 0.455199 + 0.788428i
\(10\) −2.08648 + 3.61389i −0.659803 + 1.14281i
\(11\) −1.35248 + 2.34256i −0.407788 + 0.706309i −0.994642 0.103384i \(-0.967033\pi\)
0.586854 + 0.809693i \(0.300366\pi\)
\(12\) −1.21862 2.11070i −0.351784 0.609308i
\(13\) 0 0
\(14\) −6.27337 2.74787i −1.67663 0.734398i
\(15\) 0.835795 0.215801
\(16\) −4.34816 7.53123i −1.08704 1.88281i
\(17\) −1.56330 + 2.70772i −0.379157 + 0.656719i −0.990940 0.134307i \(-0.957119\pi\)
0.611783 + 0.791026i \(0.290453\pi\)
\(18\) 3.53498 6.12277i 0.833204 1.44315i
\(19\) −1.84075 3.18828i −0.422297 0.731441i 0.573866 0.818949i \(-0.305443\pi\)
−0.996164 + 0.0875083i \(0.972110\pi\)
\(20\) 7.57803 1.69450
\(21\) 0.151611 + 1.36333i 0.0330842 + 0.297502i
\(22\) 7.00205 1.49284
\(23\) −0.993019 1.71996i −0.207059 0.358636i 0.743728 0.668482i \(-0.233056\pi\)
−0.950787 + 0.309846i \(0.899722\pi\)
\(24\) −1.81241 + 3.13918i −0.369956 + 0.640783i
\(25\) 1.20064 2.07957i 0.240128 0.415914i
\(26\) 0 0
\(27\) −2.97143 −0.571852
\(28\) 1.37463 + 12.3611i 0.259781 + 2.33603i
\(29\) −5.37271 −0.997687 −0.498844 0.866692i \(-0.666242\pi\)
−0.498844 + 0.866692i \(0.666242\pi\)
\(30\) −1.08177 1.87368i −0.197503 0.342086i
\(31\) −5.23902 + 9.07425i −0.940956 + 1.62978i −0.177303 + 0.984156i \(0.556737\pi\)
−0.763653 + 0.645627i \(0.776596\pi\)
\(32\) −4.26421 + 7.38583i −0.753813 + 1.30564i
\(33\) −0.701214 1.21454i −0.122066 0.211424i
\(34\) 8.09354 1.38803
\(35\) −3.90675 1.71124i −0.660361 0.289252i
\(36\) −12.8389 −2.13982
\(37\) −2.97673 5.15585i −0.489371 0.847616i 0.510554 0.859846i \(-0.329440\pi\)
−0.999925 + 0.0122297i \(0.996107\pi\)
\(38\) −4.76497 + 8.25317i −0.772981 + 1.33884i
\(39\) 0 0
\(40\) −5.63528 9.76059i −0.891016 1.54329i
\(41\) −7.70150 −1.20277 −0.601386 0.798958i \(-0.705385\pi\)
−0.601386 + 0.798958i \(0.705385\pi\)
\(42\) 2.86007 2.10444i 0.441318 0.324721i
\(43\) −3.35600 −0.511785 −0.255892 0.966705i \(-0.582369\pi\)
−0.255892 + 0.966705i \(0.582369\pi\)
\(44\) −6.35780 11.0120i −0.958475 1.66013i
\(45\) 2.20141 3.81296i 0.328168 0.568403i
\(46\) −2.57053 + 4.45229i −0.379004 + 0.656454i
\(47\) −0.527542 0.913730i −0.0769500 0.133281i 0.824983 0.565158i \(-0.191185\pi\)
−0.901933 + 0.431877i \(0.857852\pi\)
\(48\) 4.50874 0.650781
\(49\) 2.08265 6.68300i 0.297522 0.954715i
\(50\) −6.21596 −0.879070
\(51\) −0.810520 1.40386i −0.113495 0.196580i
\(52\) 0 0
\(53\) −3.63284 + 6.29226i −0.499009 + 0.864308i −0.999999 0.00114437i \(-0.999636\pi\)
0.500991 + 0.865453i \(0.332969\pi\)
\(54\) 3.84592 + 6.66133i 0.523363 + 0.906492i
\(55\) 4.36054 0.587975
\(56\) 14.8990 10.9627i 1.99096 1.46495i
\(57\) 1.90873 0.252818
\(58\) 6.95390 + 12.0445i 0.913092 + 1.58152i
\(59\) −5.71203 + 9.89352i −0.743643 + 1.28803i 0.207183 + 0.978302i \(0.433570\pi\)
−0.950826 + 0.309725i \(0.899763\pi\)
\(60\) −1.96447 + 3.40257i −0.253613 + 0.439270i
\(61\) 1.46254 + 2.53319i 0.187259 + 0.324341i 0.944335 0.328985i \(-0.106706\pi\)
−0.757077 + 0.653326i \(0.773373\pi\)
\(62\) 27.1235 3.44468
\(63\) 6.61894 + 2.89923i 0.833908 + 0.365269i
\(64\) 4.68406 0.585507
\(65\) 0 0
\(66\) −1.81516 + 3.14395i −0.223431 + 0.386994i
\(67\) 6.79091 11.7622i 0.829642 1.43698i −0.0686778 0.997639i \(-0.521878\pi\)
0.898320 0.439343i \(-0.144789\pi\)
\(68\) −7.34886 12.7286i −0.891180 1.54357i
\(69\) 1.02969 0.123960
\(70\) 1.22027 + 10.9730i 0.145850 + 1.31152i
\(71\) −1.35111 −0.160347 −0.0801736 0.996781i \(-0.525547\pi\)
−0.0801736 + 0.996781i \(0.525547\pi\)
\(72\) 9.54747 + 16.5367i 1.12518 + 1.94887i
\(73\) −4.55168 + 7.88374i −0.532733 + 0.922721i 0.466536 + 0.884502i \(0.345502\pi\)
−0.999269 + 0.0382192i \(0.987831\pi\)
\(74\) −7.70557 + 13.3464i −0.895754 + 1.55149i
\(75\) 0.622492 + 1.07819i 0.0718791 + 0.124498i
\(76\) 17.3062 1.98516
\(77\) 0.790989 + 7.11280i 0.0901416 + 0.810578i
\(78\) 0 0
\(79\) 3.10289 + 5.37436i 0.349102 + 0.604663i 0.986090 0.166211i \(-0.0531532\pi\)
−0.636988 + 0.770874i \(0.719820\pi\)
\(80\) −7.00946 + 12.1407i −0.783682 + 1.35738i
\(81\) −3.32650 + 5.76166i −0.369611 + 0.640185i
\(82\) 9.96806 + 17.2652i 1.10079 + 1.90662i
\(83\) −2.69672 −0.296003 −0.148002 0.988987i \(-0.547284\pi\)
−0.148002 + 0.988987i \(0.547284\pi\)
\(84\) −5.90654 2.58718i −0.644456 0.282285i
\(85\) 5.04026 0.546693
\(86\) 4.34367 + 7.52346i 0.468390 + 0.811275i
\(87\) 1.39278 2.41237i 0.149322 0.258633i
\(88\) −9.45576 + 16.3779i −1.00799 + 1.74589i
\(89\) −0.879938 1.52410i −0.0932732 0.161554i 0.815613 0.578597i \(-0.196400\pi\)
−0.908887 + 0.417043i \(0.863066\pi\)
\(90\) −11.3972 −1.20137
\(91\) 0 0
\(92\) 9.33607 0.973353
\(93\) −2.71625 4.70469i −0.281662 0.487853i
\(94\) −1.36560 + 2.36528i −0.140851 + 0.243960i
\(95\) −2.96739 + 5.13967i −0.304448 + 0.527319i
\(96\) −2.21085 3.82930i −0.225644 0.390827i
\(97\) 15.4820 1.57196 0.785981 0.618250i \(-0.212158\pi\)
0.785981 + 0.618250i \(0.212158\pi\)
\(98\) −17.6775 + 3.98094i −1.78570 + 0.402135i
\(99\) −7.38776 −0.742498
\(100\) 5.64404 + 9.77576i 0.564404 + 0.977576i
\(101\) 0.639651 1.10791i 0.0636477 0.110241i −0.832446 0.554107i \(-0.813060\pi\)
0.896093 + 0.443866i \(0.146393\pi\)
\(102\) −2.09811 + 3.63404i −0.207744 + 0.359823i
\(103\) 5.73367 + 9.93101i 0.564956 + 0.978532i 0.997054 + 0.0767054i \(0.0244401\pi\)
−0.432098 + 0.901827i \(0.642227\pi\)
\(104\) 0 0
\(105\) 1.78111 1.31054i 0.173819 0.127896i
\(106\) 18.8079 1.82679
\(107\) 2.56763 + 4.44726i 0.248222 + 0.429933i 0.963033 0.269385i \(-0.0868205\pi\)
−0.714811 + 0.699318i \(0.753487\pi\)
\(108\) 6.98412 12.0969i 0.672048 1.16402i
\(109\) −0.863916 + 1.49635i −0.0827481 + 0.143324i −0.904429 0.426623i \(-0.859703\pi\)
0.821681 + 0.569947i \(0.193036\pi\)
\(110\) −5.64384 9.77542i −0.538119 0.932050i
\(111\) 3.08667 0.292973
\(112\) −21.0752 9.23136i −1.99142 0.872282i
\(113\) −8.59113 −0.808185 −0.404093 0.914718i \(-0.632413\pi\)
−0.404093 + 0.914718i \(0.632413\pi\)
\(114\) −2.47048 4.27899i −0.231381 0.400764i
\(115\) −1.60080 + 2.77267i −0.149275 + 0.258552i
\(116\) 12.6282 21.8726i 1.17250 2.03082i
\(117\) 0 0
\(118\) 29.5723 2.72235
\(119\) 0.914289 + 8.22154i 0.0838127 + 0.753668i
\(120\) 5.84340 0.533427
\(121\) 1.84160 + 3.18975i 0.167419 + 0.289977i
\(122\) 3.78592 6.55741i 0.342761 0.593680i
\(123\) 1.99648 3.45801i 0.180017 0.311798i
\(124\) −24.6279 42.6567i −2.21165 3.83069i
\(125\) −11.9313 −1.06716
\(126\) −2.06741 18.5908i −0.184180 1.65620i
\(127\) −3.12412 −0.277221 −0.138610 0.990347i \(-0.544264\pi\)
−0.138610 + 0.990347i \(0.544264\pi\)
\(128\) 2.46585 + 4.27097i 0.217952 + 0.377504i
\(129\) 0.869985 1.50686i 0.0765979 0.132671i
\(130\) 0 0
\(131\) −5.10460 8.84142i −0.445991 0.772479i 0.552130 0.833758i \(-0.313815\pi\)
−0.998121 + 0.0612793i \(0.980482\pi\)
\(132\) 6.59261 0.573813
\(133\) −8.92198 3.90801i −0.773634 0.338868i
\(134\) −35.1579 −3.03718
\(135\) 2.39505 + 4.14835i 0.206133 + 0.357033i
\(136\) −10.9297 + 18.9308i −0.937216 + 1.62331i
\(137\) 4.99630 8.65385i 0.426863 0.739348i −0.569729 0.821832i \(-0.692952\pi\)
0.996592 + 0.0824839i \(0.0262853\pi\)
\(138\) −1.33273 2.30836i −0.113450 0.196501i
\(139\) −1.66420 −0.141156 −0.0705778 0.997506i \(-0.522484\pi\)
−0.0705778 + 0.997506i \(0.522484\pi\)
\(140\) 16.1491 11.8825i 1.36485 1.00425i
\(141\) 0.547025 0.0460679
\(142\) 1.74874 + 3.02891i 0.146751 + 0.254180i
\(143\) 0 0
\(144\) 11.8757 20.5692i 0.989638 1.71410i
\(145\) 4.33055 + 7.50073i 0.359633 + 0.622902i
\(146\) 23.5649 1.95025
\(147\) 2.46081 + 2.66758i 0.202964 + 0.220018i
\(148\) 27.9863 2.30046
\(149\) −9.89902 17.1456i −0.810959 1.40462i −0.912193 0.409760i \(-0.865613\pi\)
0.101234 0.994863i \(-0.467721\pi\)
\(150\) 1.61138 2.79100i 0.131569 0.227884i
\(151\) −3.76746 + 6.52544i −0.306592 + 0.531033i −0.977614 0.210404i \(-0.932522\pi\)
0.671023 + 0.741437i \(0.265855\pi\)
\(152\) −12.8695 22.2906i −1.04385 1.80801i
\(153\) −8.53937 −0.690367
\(154\) 14.9216 10.9793i 1.20242 0.884740i
\(155\) 16.8912 1.35673
\(156\) 0 0
\(157\) −7.00223 + 12.1282i −0.558839 + 0.967938i 0.438755 + 0.898607i \(0.355420\pi\)
−0.997594 + 0.0693309i \(0.977914\pi\)
\(158\) 8.03214 13.9121i 0.639003 1.10679i
\(159\) −1.88350 3.26232i −0.149371 0.258719i
\(160\) 13.7483 1.08690
\(161\) −4.81308 2.10823i −0.379324 0.166152i
\(162\) 17.2219 1.35308
\(163\) 3.58498 + 6.20936i 0.280797 + 0.486355i 0.971581 0.236706i \(-0.0760679\pi\)
−0.690784 + 0.723061i \(0.742735\pi\)
\(164\) 18.1018 31.3533i 1.41351 2.44828i
\(165\) −1.13039 + 1.95790i −0.0880011 + 0.152422i
\(166\) 3.49036 + 6.04548i 0.270904 + 0.469220i
\(167\) −17.9805 −1.39138 −0.695688 0.718344i \(-0.744901\pi\)
−0.695688 + 0.718344i \(0.744901\pi\)
\(168\) 1.05998 + 9.53161i 0.0817790 + 0.735380i
\(169\) 0 0
\(170\) −6.52361 11.2992i −0.500338 0.866611i
\(171\) 5.02745 8.70780i 0.384459 0.665902i
\(172\) 7.88803 13.6625i 0.601456 1.04175i
\(173\) 6.40579 + 11.0952i 0.487023 + 0.843549i 0.999889 0.0149198i \(-0.00474930\pi\)
−0.512865 + 0.858469i \(0.671416\pi\)
\(174\) −7.21072 −0.546643
\(175\) −0.702188 6.31427i −0.0530804 0.477314i
\(176\) 23.5232 1.77312
\(177\) −2.96149 5.12945i −0.222599 0.385553i
\(178\) −2.27781 + 3.94528i −0.170729 + 0.295711i
\(179\) −0.920110 + 1.59368i −0.0687723 + 0.119117i −0.898361 0.439258i \(-0.855242\pi\)
0.829589 + 0.558375i \(0.188575\pi\)
\(180\) 10.3485 + 17.9242i 0.771334 + 1.33599i
\(181\) 3.29928 0.245234 0.122617 0.992454i \(-0.460871\pi\)
0.122617 + 0.992454i \(0.460871\pi\)
\(182\) 0 0
\(183\) −1.51655 −0.112107
\(184\) −6.94262 12.0250i −0.511817 0.886493i
\(185\) −4.79865 + 8.31150i −0.352804 + 0.611074i
\(186\) −7.03129 + 12.1786i −0.515560 + 0.892975i
\(187\) −4.22867 7.32427i −0.309231 0.535604i
\(188\) 4.95980 0.361731
\(189\) −6.33223 + 4.65925i −0.460602 + 0.338910i
\(190\) 15.3628 1.11453
\(191\) −2.44807 4.24018i −0.177136 0.306809i 0.763762 0.645498i \(-0.223350\pi\)
−0.940898 + 0.338689i \(0.890017\pi\)
\(192\) −1.21426 + 2.10316i −0.0876318 + 0.151783i
\(193\) −1.50955 + 2.61462i −0.108660 + 0.188204i −0.915228 0.402937i \(-0.867989\pi\)
0.806568 + 0.591142i \(0.201323\pi\)
\(194\) −20.0384 34.7075i −1.43867 2.49186i
\(195\) 0 0
\(196\) 22.3118 + 24.1865i 1.59370 + 1.72761i
\(197\) 4.64991 0.331292 0.165646 0.986185i \(-0.447029\pi\)
0.165646 + 0.986185i \(0.447029\pi\)
\(198\) 9.56198 + 16.5618i 0.679540 + 1.17700i
\(199\) −0.205360 + 0.355694i −0.0145576 + 0.0252145i −0.873212 0.487340i \(-0.837967\pi\)
0.858655 + 0.512554i \(0.171301\pi\)
\(200\) 8.39420 14.5392i 0.593560 1.02808i
\(201\) 3.52085 + 6.09830i 0.248342 + 0.430141i
\(202\) −3.31160 −0.233004
\(203\) −11.4495 + 8.42450i −0.803594 + 0.591284i
\(204\) 7.62027 0.533525
\(205\) 6.20762 + 10.7519i 0.433559 + 0.750946i
\(206\) 14.8422 25.7074i 1.03410 1.79112i
\(207\) 2.71213 4.69754i 0.188506 0.326502i
\(208\) 0 0
\(209\) 9.95831 0.688831
\(210\) −5.24325 2.29665i −0.361819 0.158484i
\(211\) −7.51600 −0.517423 −0.258711 0.965955i \(-0.583298\pi\)
−0.258711 + 0.965955i \(0.583298\pi\)
\(212\) −17.0774 29.5790i −1.17288 2.03149i
\(213\) 0.350252 0.606654i 0.0239989 0.0415672i
\(214\) 6.64656 11.5122i 0.454349 0.786956i
\(215\) 2.70502 + 4.68524i 0.184481 + 0.319531i
\(216\) −20.7745 −1.41353
\(217\) 3.06401 + 27.5524i 0.207999 + 1.87038i
\(218\) 4.47267 0.302927
\(219\) −2.35989 4.08745i −0.159467 0.276204i
\(220\) −10.2491 + 17.7520i −0.690996 + 1.19684i
\(221\) 0 0
\(222\) −3.99507 6.91967i −0.268132 0.464418i
\(223\) −22.5794 −1.51203 −0.756016 0.654553i \(-0.772857\pi\)
−0.756016 + 0.654553i \(0.772857\pi\)
\(224\) 2.49390 + 22.4259i 0.166631 + 1.49839i
\(225\) 6.55837 0.437225
\(226\) 11.1195 + 19.2595i 0.739658 + 1.28113i
\(227\) −6.83586 + 11.8401i −0.453712 + 0.785853i −0.998613 0.0526478i \(-0.983234\pi\)
0.544901 + 0.838500i \(0.316567\pi\)
\(228\) −4.48634 + 7.77057i −0.297115 + 0.514618i
\(229\) −3.96543 6.86832i −0.262043 0.453872i 0.704742 0.709464i \(-0.251063\pi\)
−0.966785 + 0.255592i \(0.917730\pi\)
\(230\) 8.28766 0.546472
\(231\) −3.39873 1.48871i −0.223620 0.0979502i
\(232\) −37.5629 −2.46613
\(233\) 3.28585 + 5.69127i 0.215263 + 0.372847i 0.953354 0.301854i \(-0.0976056\pi\)
−0.738091 + 0.674702i \(0.764272\pi\)
\(234\) 0 0
\(235\) −0.850427 + 1.47298i −0.0554757 + 0.0960868i
\(236\) −26.8514 46.5080i −1.74788 3.02741i
\(237\) −3.21749 −0.208998
\(238\) 17.2476 12.6908i 1.11800 0.822622i
\(239\) −9.39284 −0.607572 −0.303786 0.952740i \(-0.598251\pi\)
−0.303786 + 0.952740i \(0.598251\pi\)
\(240\) −3.63417 6.29456i −0.234584 0.406312i
\(241\) 5.04292 8.73460i 0.324843 0.562645i −0.656637 0.754206i \(-0.728022\pi\)
0.981481 + 0.191562i \(0.0613552\pi\)
\(242\) 4.76718 8.25699i 0.306446 0.530780i
\(243\) −6.18182 10.7072i −0.396564 0.686869i
\(244\) −13.7503 −0.880275
\(245\) −11.0087 + 2.47913i −0.703319 + 0.158386i
\(246\) −10.3362 −0.659012
\(247\) 0 0
\(248\) −36.6282 + 63.4420i −2.32590 + 4.02857i
\(249\) 0.699078 1.21084i 0.0443022 0.0767337i
\(250\) 15.4426 + 26.7474i 0.976678 + 1.69166i
\(251\) −10.3485 −0.653194 −0.326597 0.945164i \(-0.605902\pi\)
−0.326597 + 0.945164i \(0.605902\pi\)
\(252\) −27.3603 + 20.1317i −1.72354 + 1.26818i
\(253\) 5.37215 0.337744
\(254\) 4.04355 + 7.00363i 0.253715 + 0.439447i
\(255\) −1.30660 + 2.26310i −0.0818225 + 0.141721i
\(256\) 11.0672 19.1689i 0.691697 1.19805i
\(257\) −3.99329 6.91658i −0.249095 0.431445i 0.714180 0.699962i \(-0.246800\pi\)
−0.963275 + 0.268517i \(0.913466\pi\)
\(258\) −4.50409 −0.280412
\(259\) −14.4280 6.31975i −0.896511 0.392690i
\(260\) 0 0
\(261\) −7.33696 12.7080i −0.454146 0.786604i
\(262\) −13.2138 + 22.8869i −0.816349 + 1.41396i
\(263\) −2.52967 + 4.38152i −0.155986 + 0.270176i −0.933418 0.358792i \(-0.883189\pi\)
0.777431 + 0.628968i \(0.216522\pi\)
\(264\) −4.90249 8.49136i −0.301727 0.522607i
\(265\) 11.7127 0.719503
\(266\) 2.78677 + 25.0594i 0.170868 + 1.53649i
\(267\) 0.912435 0.0558401
\(268\) 31.9231 + 55.2924i 1.95001 + 3.37752i
\(269\) −6.94512 + 12.0293i −0.423451 + 0.733439i −0.996274 0.0862400i \(-0.972515\pi\)
0.572823 + 0.819679i \(0.305848\pi\)
\(270\) 6.19983 10.7384i 0.377310 0.653519i
\(271\) 4.16361 + 7.21158i 0.252921 + 0.438072i 0.964329 0.264707i \(-0.0852754\pi\)
−0.711408 + 0.702780i \(0.751942\pi\)
\(272\) 27.1900 1.64863
\(273\) 0 0
\(274\) −25.8669 −1.56267
\(275\) 3.24768 + 5.62515i 0.195843 + 0.339210i
\(276\) −2.42022 + 4.19194i −0.145680 + 0.252325i
\(277\) 11.6058 20.1018i 0.697325 1.20780i −0.272066 0.962279i \(-0.587707\pi\)
0.969391 0.245523i \(-0.0789598\pi\)
\(278\) 2.15398 + 3.73080i 0.129187 + 0.223758i
\(279\) −28.6176 −1.71329
\(280\) −27.3138 11.9640i −1.63231 0.714985i
\(281\) 27.1595 1.62020 0.810100 0.586292i \(-0.199413\pi\)
0.810100 + 0.586292i \(0.199413\pi\)
\(282\) −0.708015 1.22632i −0.0421617 0.0730262i
\(283\) 8.07563 13.9874i 0.480046 0.831464i −0.519692 0.854354i \(-0.673953\pi\)
0.999738 + 0.0228894i \(0.00728654\pi\)
\(284\) 3.17568 5.50044i 0.188442 0.326391i
\(285\) −1.53849 2.66474i −0.0911323 0.157846i
\(286\) 0 0
\(287\) −16.4122 + 12.0761i −0.968782 + 0.712828i
\(288\) −23.2928 −1.37254
\(289\) 3.61216 + 6.25645i 0.212480 + 0.368027i
\(290\) 11.2101 19.4164i 0.658278 1.14017i
\(291\) −4.01345 + 6.95151i −0.235273 + 0.407504i
\(292\) −21.3968 37.0603i −1.25215 2.16879i
\(293\) −14.6452 −0.855582 −0.427791 0.903878i \(-0.640708\pi\)
−0.427791 + 0.903878i \(0.640708\pi\)
\(294\) 2.79513 8.96927i 0.163015 0.523098i
\(295\) 18.4162 1.07223
\(296\) −20.8116 36.0468i −1.20965 2.09517i
\(297\) 4.01879 6.96075i 0.233194 0.403904i
\(298\) −25.6246 + 44.3831i −1.48439 + 2.57104i
\(299\) 0 0
\(300\) −5.85248 −0.337893
\(301\) −7.15176 + 5.26226i −0.412221 + 0.303311i
\(302\) 19.5049 1.12238
\(303\) 0.331637 + 0.574412i 0.0190521 + 0.0329991i
\(304\) −16.0078 + 27.7263i −0.918108 + 1.59021i
\(305\) 2.35769 4.08363i 0.135001 0.233828i
\(306\) 11.0525 + 19.1435i 0.631830 + 1.09436i
\(307\) −8.97844 −0.512427 −0.256213 0.966620i \(-0.582475\pi\)
−0.256213 + 0.966620i \(0.582475\pi\)
\(308\) −30.8158 13.4979i −1.75589 0.769117i
\(309\) −5.94543 −0.338224
\(310\) −21.8622 37.8665i −1.24169 2.15067i
\(311\) −6.09080 + 10.5496i −0.345378 + 0.598212i −0.985422 0.170126i \(-0.945583\pi\)
0.640045 + 0.768338i \(0.278916\pi\)
\(312\) 0 0
\(313\) −6.56198 11.3657i −0.370905 0.642427i 0.618800 0.785549i \(-0.287619\pi\)
−0.989705 + 0.143122i \(0.954286\pi\)
\(314\) 36.2520 2.04582
\(315\) −1.28748 11.5774i −0.0725415 0.652314i
\(316\) −29.1725 −1.64108
\(317\) 8.35775 + 14.4761i 0.469418 + 0.813056i 0.999389 0.0349599i \(-0.0111304\pi\)
−0.529971 + 0.848016i \(0.677797\pi\)
\(318\) −4.87563 + 8.44485i −0.273412 + 0.473564i
\(319\) 7.26648 12.5859i 0.406845 0.704675i
\(320\) −3.77548 6.53932i −0.211056 0.365559i
\(321\) −2.66245 −0.148604
\(322\) 1.50336 + 13.5186i 0.0837789 + 0.753364i
\(323\) 11.5106 0.640468
\(324\) −15.6374 27.0847i −0.868743 1.50471i
\(325\) 0 0
\(326\) 9.28007 16.0736i 0.513976 0.890232i
\(327\) −0.447911 0.775804i −0.0247695 0.0429021i
\(328\) −53.8445 −2.97307
\(329\) −2.55696 1.12000i −0.140970 0.0617476i
\(330\) 5.85228 0.322157
\(331\) 1.98332 + 3.43522i 0.109013 + 0.188817i 0.915371 0.402612i \(-0.131898\pi\)
−0.806357 + 0.591428i \(0.798564\pi\)
\(332\) 6.33843 10.9785i 0.347867 0.602523i
\(333\) 8.13002 14.0816i 0.445523 0.771668i
\(334\) 23.2722 + 40.3087i 1.27340 + 2.20559i
\(335\) −21.8946 −1.19623
\(336\) 9.60831 7.06978i 0.524176 0.385688i
\(337\) 13.7032 0.746461 0.373230 0.927739i \(-0.378250\pi\)
0.373230 + 0.927739i \(0.378250\pi\)
\(338\) 0 0
\(339\) 2.22710 3.85746i 0.120960 0.209508i
\(340\) −11.8468 + 20.5192i −0.642481 + 1.11281i
\(341\) −14.1713 24.5455i −0.767420 1.32921i
\(342\) −26.0281 −1.40744
\(343\) −6.04084 17.5074i −0.326175 0.945309i
\(344\) −23.4632 −1.26505
\(345\) −0.829960 1.43753i −0.0446835 0.0773942i
\(346\) 16.5820 28.7209i 0.891456 1.54405i
\(347\) 13.1989 22.8612i 0.708556 1.22725i −0.256837 0.966455i \(-0.582680\pi\)
0.965393 0.260800i \(-0.0839863\pi\)
\(348\) 6.54727 + 11.3402i 0.350971 + 0.607899i
\(349\) 4.89024 0.261769 0.130884 0.991398i \(-0.458218\pi\)
0.130884 + 0.991398i \(0.458218\pi\)
\(350\) −13.2465 + 9.74673i −0.708053 + 0.520984i
\(351\) 0 0
\(352\) −11.5345 19.9784i −0.614792 1.06485i
\(353\) −6.77886 + 11.7413i −0.360802 + 0.624928i −0.988093 0.153857i \(-0.950830\pi\)
0.627291 + 0.778785i \(0.284164\pi\)
\(354\) −7.66612 + 13.2781i −0.407450 + 0.705724i
\(355\) 1.08903 + 1.88626i 0.0577997 + 0.100112i
\(356\) 8.27291 0.438464
\(357\) −3.92852 1.72077i −0.207920 0.0910731i
\(358\) 4.76360 0.251764
\(359\) −4.29284 7.43541i −0.226567 0.392426i 0.730221 0.683211i \(-0.239417\pi\)
−0.956789 + 0.290785i \(0.906084\pi\)
\(360\) 15.3910 26.6581i 0.811179 1.40500i
\(361\) 2.72326 4.71683i 0.143330 0.248254i
\(362\) −4.27026 7.39632i −0.224440 0.388742i
\(363\) −1.90962 −0.100229
\(364\) 0 0
\(365\) 14.6751 0.768130
\(366\) 1.96287 + 3.39979i 0.102601 + 0.177710i
\(367\) 0.831612 1.44039i 0.0434098 0.0751880i −0.843504 0.537123i \(-0.819511\pi\)
0.886914 + 0.461935i \(0.152845\pi\)
\(368\) −8.63560 + 14.9573i −0.450162 + 0.779703i
\(369\) −10.5171 18.2162i −0.547501 0.948299i
\(370\) 24.8436 1.29156
\(371\) 2.12464 + 19.1054i 0.110306 + 0.991903i
\(372\) 25.5374 1.32405
\(373\) −6.98174 12.0927i −0.361501 0.626138i 0.626707 0.779255i \(-0.284402\pi\)
−0.988208 + 0.153117i \(0.951069\pi\)
\(374\) −10.9463 + 18.9596i −0.566022 + 0.980378i
\(375\) 3.09298 5.35719i 0.159721 0.276644i
\(376\) −3.68828 6.38828i −0.190208 0.329450i
\(377\) 0 0
\(378\) 18.6409 + 8.16509i 0.958783 + 0.419967i
\(379\) −31.5758 −1.62194 −0.810969 0.585089i \(-0.801059\pi\)
−0.810969 + 0.585089i \(0.801059\pi\)
\(380\) −13.9493 24.1608i −0.715582 1.23943i
\(381\) 0.809874 1.40274i 0.0414911 0.0718647i
\(382\) −6.33707 + 10.9761i −0.324233 + 0.561588i
\(383\) 15.9541 + 27.6333i 0.815217 + 1.41200i 0.909172 + 0.416420i \(0.136716\pi\)
−0.0939554 + 0.995576i \(0.529951\pi\)
\(384\) −2.55692 −0.130482
\(385\) 9.29247 6.83739i 0.473588 0.348466i
\(386\) 7.81525 0.397786
\(387\) −4.58294 7.93788i −0.232964 0.403505i
\(388\) −36.3894 + 63.0283i −1.84739 + 3.19978i
\(389\) 12.7075 22.0100i 0.644296 1.11595i −0.340168 0.940365i \(-0.610484\pi\)
0.984464 0.175589i \(-0.0561829\pi\)
\(390\) 0 0
\(391\) 6.20956 0.314031
\(392\) 14.5607 46.7238i 0.735428 2.35991i
\(393\) 5.29312 0.267003
\(394\) −6.01838 10.4241i −0.303202 0.525161i
\(395\) 5.00203 8.66376i 0.251679 0.435921i
\(396\) 17.3644 30.0760i 0.872593 1.51138i
\(397\) −2.07949 3.60178i −0.104366 0.180768i 0.809113 0.587653i \(-0.199948\pi\)
−0.913479 + 0.406885i \(0.866615\pi\)
\(398\) 1.06319 0.0532930
\(399\) 4.06759 2.99293i 0.203634 0.149834i
\(400\) −20.8823 −1.04412
\(401\) 9.80067 + 16.9753i 0.489422 + 0.847704i 0.999926 0.0121716i \(-0.00387443\pi\)
−0.510504 + 0.859875i \(0.670541\pi\)
\(402\) 9.11409 15.7861i 0.454569 0.787337i
\(403\) 0 0
\(404\) 3.00691 + 5.20811i 0.149599 + 0.259113i
\(405\) 10.7250 0.532929
\(406\) 33.7050 + 14.7635i 1.67275 + 0.732700i
\(407\) 16.1039 0.798238
\(408\) −5.66669 9.81500i −0.280543 0.485915i
\(409\) 8.81685 15.2712i 0.435965 0.755114i −0.561409 0.827539i \(-0.689740\pi\)
0.997374 + 0.0724249i \(0.0230738\pi\)
\(410\) 16.0690 27.8324i 0.793594 1.37454i
\(411\) 2.59041 + 4.48673i 0.127776 + 0.221314i
\(412\) −53.9063 −2.65577
\(413\) 3.34065 + 30.0400i 0.164382 + 1.47817i
\(414\) −14.0412 −0.690088
\(415\) 2.17363 + 3.76483i 0.106699 + 0.184808i
\(416\) 0 0
\(417\) 0.431416 0.747234i 0.0211265 0.0365922i
\(418\) −12.8890 22.3245i −0.630424 1.09193i
\(419\) 29.8911 1.46027 0.730137 0.683301i \(-0.239456\pi\)
0.730137 + 0.683301i \(0.239456\pi\)
\(420\) 1.14891 + 10.3313i 0.0560611 + 0.504117i
\(421\) −12.8528 −0.626407 −0.313203 0.949686i \(-0.601402\pi\)
−0.313203 + 0.949686i \(0.601402\pi\)
\(422\) 9.72796 + 16.8493i 0.473550 + 0.820212i
\(423\) 1.44082 2.49557i 0.0700551 0.121339i
\(424\) −25.3987 + 43.9919i −1.23347 + 2.13644i
\(425\) 3.75393 + 6.50200i 0.182093 + 0.315394i
\(426\) −1.81332 −0.0878559
\(427\) 7.08880 + 3.10504i 0.343051 + 0.150263i
\(428\) −24.1401 −1.16685
\(429\) 0 0
\(430\) 7.00223 12.1282i 0.337677 0.584874i
\(431\) 4.48530 7.76876i 0.216049 0.374208i −0.737547 0.675295i \(-0.764016\pi\)
0.953597 + 0.301087i \(0.0973495\pi\)
\(432\) 12.9202 + 22.3785i 0.621625 + 1.07669i
\(433\) −3.45062 −0.165826 −0.0829132 0.996557i \(-0.526422\pi\)
−0.0829132 + 0.996557i \(0.526422\pi\)
\(434\) 57.8012 42.5300i 2.77454 2.04151i
\(435\) −4.49048 −0.215302
\(436\) −4.06114 7.03410i −0.194493 0.336872i
\(437\) −3.65580 + 6.33204i −0.174881 + 0.302902i
\(438\) −6.10881 + 10.5808i −0.291890 + 0.505569i
\(439\) 19.2572 + 33.3544i 0.919096 + 1.59192i 0.800792 + 0.598943i \(0.204412\pi\)
0.118304 + 0.992977i \(0.462254\pi\)
\(440\) 30.4864 1.45338
\(441\) 18.6513 4.20023i 0.888155 0.200011i
\(442\) 0 0
\(443\) 7.51997 + 13.0250i 0.357284 + 0.618835i 0.987506 0.157580i \(-0.0503693\pi\)
−0.630222 + 0.776415i \(0.717036\pi\)
\(444\) −7.25498 + 12.5660i −0.344306 + 0.596356i
\(445\) −1.41851 + 2.45693i −0.0672437 + 0.116469i
\(446\) 29.2246 + 50.6185i 1.38382 + 2.39685i
\(447\) 10.2646 0.485499
\(448\) 9.98191 7.34468i 0.471601 0.347003i
\(449\) 38.9235 1.83691 0.918456 0.395522i \(-0.129436\pi\)
0.918456 + 0.395522i \(0.129436\pi\)
\(450\) −8.48850 14.7025i −0.400152 0.693083i
\(451\) 10.4161 18.0412i 0.490476 0.849529i
\(452\) 20.1928 34.9750i 0.949790 1.64509i
\(453\) −1.95330 3.38322i −0.0917741 0.158957i
\(454\) 35.3906 1.66097
\(455\) 0 0
\(456\) 13.3448 0.624927
\(457\) −6.96982 12.0721i −0.326034 0.564708i 0.655687 0.755033i \(-0.272379\pi\)
−0.981721 + 0.190325i \(0.939046\pi\)
\(458\) −10.2649 + 17.7793i −0.479648 + 0.830774i
\(459\) 4.64524 8.04580i 0.216821 0.375546i
\(460\) −7.52512 13.0339i −0.350861 0.607709i
\(461\) −37.4635 −1.74485 −0.872424 0.488749i \(-0.837453\pi\)
−0.872424 + 0.488749i \(0.837453\pi\)
\(462\) 1.06159 + 9.54609i 0.0493895 + 0.444124i
\(463\) −6.75275 −0.313827 −0.156913 0.987612i \(-0.550154\pi\)
−0.156913 + 0.987612i \(0.550154\pi\)
\(464\) 23.3614 + 40.4631i 1.08453 + 1.87845i
\(465\) −4.37875 + 7.58421i −0.203059 + 0.351709i
\(466\) 8.50576 14.7324i 0.394022 0.682466i
\(467\) −2.52516 4.37371i −0.116851 0.202391i 0.801667 0.597770i \(-0.203947\pi\)
−0.918518 + 0.395379i \(0.870613\pi\)
\(468\) 0 0
\(469\) −3.97162 35.7140i −0.183393 1.64912i
\(470\) 4.40283 0.203087
\(471\) −3.63042 6.28807i −0.167281 0.289739i
\(472\) −39.9353 + 69.1699i −1.83817 + 3.18380i
\(473\) 4.53892 7.86163i 0.208700 0.361478i
\(474\) 4.16439 + 7.21294i 0.191277 + 0.331301i
\(475\) −8.84033 −0.405622
\(476\) −35.6194 15.6020i −1.63261 0.715117i
\(477\) −19.8440 −0.908593
\(478\) 12.1572 + 21.0568i 0.556055 + 0.963116i
\(479\) −4.72659 + 8.18670i −0.215964 + 0.374060i −0.953570 0.301171i \(-0.902623\pi\)
0.737607 + 0.675231i \(0.235956\pi\)
\(480\) −3.56401 + 6.17304i −0.162674 + 0.281759i
\(481\) 0 0
\(482\) −26.1082 −1.18920
\(483\) 2.19432 1.61457i 0.0998448 0.0734657i
\(484\) −17.3142 −0.787010
\(485\) −12.4789 21.6142i −0.566639 0.981448i
\(486\) −16.0023 + 27.7167i −0.725877 + 1.25726i
\(487\) −19.9998 + 34.6407i −0.906277 + 1.56972i −0.0870831 + 0.996201i \(0.527755\pi\)
−0.819194 + 0.573517i \(0.805579\pi\)
\(488\) 10.2252 + 17.7106i 0.462874 + 0.801721i
\(489\) −3.71737 −0.168105
\(490\) 19.8062 + 21.4705i 0.894755 + 0.969936i
\(491\) −6.76097 −0.305118 −0.152559 0.988294i \(-0.548751\pi\)
−0.152559 + 0.988294i \(0.548751\pi\)
\(492\) 9.38518 + 16.2556i 0.423116 + 0.732859i
\(493\) 8.39918 14.5478i 0.378280 0.655200i
\(494\) 0 0
\(495\) 5.95473 + 10.3139i 0.267645 + 0.463575i
\(496\) 91.1203 4.09142
\(497\) −2.87927 + 2.11856i −0.129153 + 0.0950304i
\(498\) −3.61927 −0.162183
\(499\) −5.67877 9.83591i −0.254217 0.440316i 0.710466 0.703732i \(-0.248484\pi\)
−0.964682 + 0.263416i \(0.915151\pi\)
\(500\) 28.0436 48.5729i 1.25415 2.17225i
\(501\) 4.66115 8.07335i 0.208245 0.360691i
\(502\) 13.3941 + 23.1993i 0.597808 + 1.03543i
\(503\) −13.9285 −0.621040 −0.310520 0.950567i \(-0.600503\pi\)
−0.310520 + 0.950567i \(0.600503\pi\)
\(504\) 46.2759 + 20.2698i 2.06129 + 0.902888i
\(505\) −2.06230 −0.0917713
\(506\) −6.95317 12.0432i −0.309106 0.535388i
\(507\) 0 0
\(508\) 7.34301 12.7185i 0.325793 0.564290i
\(509\) 9.90746 + 17.1602i 0.439141 + 0.760614i 0.997623 0.0689022i \(-0.0219497\pi\)
−0.558483 + 0.829516i \(0.688616\pi\)
\(510\) 6.76454 0.299539
\(511\) 2.66202 + 23.9376i 0.117761 + 1.05894i
\(512\) −47.4335 −2.09628
\(513\) 5.46966 + 9.47373i 0.241491 + 0.418276i
\(514\) −10.3370 + 17.9043i −0.455947 + 0.789724i
\(515\) 9.24299 16.0093i 0.407295 0.705455i
\(516\) 4.08967 + 7.08352i 0.180038 + 0.311835i
\(517\) 2.85396 0.125517
\(518\) 4.50655 + 40.5242i 0.198007 + 1.78053i
\(519\) −6.64237 −0.291568
\(520\) 0 0
\(521\) 15.5476 26.9292i 0.681151 1.17979i −0.293479 0.955966i \(-0.594813\pi\)
0.974630 0.223823i \(-0.0718537\pi\)
\(522\) −18.9924 + 32.8959i −0.831277 + 1.43981i
\(523\) −11.3601 19.6763i −0.496742 0.860383i 0.503251 0.864140i \(-0.332137\pi\)
−0.999993 + 0.00375758i \(0.998804\pi\)
\(524\) 47.9919 2.09654
\(525\) 3.01717 + 1.32158i 0.131680 + 0.0576786i
\(526\) 13.0966 0.571040
\(527\) −16.3804 28.3716i −0.713540 1.23589i
\(528\) −6.09798 + 10.5620i −0.265380 + 0.459652i
\(529\) 9.52783 16.5027i 0.414253 0.717508i
\(530\) −15.1597 26.2574i −0.658495 1.14055i
\(531\) −31.2013 −1.35402
\(532\) 36.8802 27.1364i 1.59896 1.17651i
\(533\) 0 0
\(534\) −1.18097 2.04549i −0.0511054 0.0885171i
\(535\) 4.13915 7.16922i 0.178951 0.309952i
\(536\) 47.4782 82.2346i 2.05074 3.55199i
\(537\) −0.477046 0.826267i −0.0205860 0.0356561i
\(538\) 35.9563 1.55018
\(539\) 12.8386 + 13.9174i 0.552998 + 0.599463i
\(540\) −22.5176 −0.969002
\(541\) −1.04936 1.81754i −0.0451155 0.0781423i 0.842586 0.538562i \(-0.181032\pi\)
−0.887701 + 0.460420i \(0.847699\pi\)
\(542\) 10.7779 18.6679i 0.462951 0.801855i
\(543\) −0.855283 + 1.48139i −0.0367037 + 0.0635727i
\(544\) −13.3325 23.0926i −0.571627 0.990087i
\(545\) 2.78536 0.119312
\(546\) 0 0
\(547\) 25.3770 1.08504 0.542521 0.840042i \(-0.317470\pi\)
0.542521 + 0.840042i \(0.317470\pi\)
\(548\) 23.4869 + 40.6805i 1.00331 + 1.73778i
\(549\) −3.99447 + 6.91862i −0.170480 + 0.295280i
\(550\) 8.40696 14.5613i 0.358474 0.620895i
\(551\) 9.88983 + 17.1297i 0.421321 + 0.729749i
\(552\) 7.19902 0.306411
\(553\) 15.0395 + 6.58760i 0.639543 + 0.280133i
\(554\) −60.0855 −2.55279
\(555\) −2.48794 4.30923i −0.105607 0.182917i
\(556\) 3.91158 6.77506i 0.165888 0.287327i
\(557\) 22.1252 38.3219i 0.937473 1.62375i 0.167309 0.985904i \(-0.446492\pi\)
0.770164 0.637846i \(-0.220174\pi\)
\(558\) 37.0397 + 64.1547i 1.56802 + 2.71588i
\(559\) 0 0
\(560\) 4.09944 + 36.8634i 0.173233 + 1.55776i
\(561\) 4.38484 0.185128
\(562\) −35.1526 60.8860i −1.48282 2.56832i
\(563\) 19.4453 33.6803i 0.819523 1.41946i −0.0865108 0.996251i \(-0.527572\pi\)
0.906034 0.423205i \(-0.139095\pi\)
\(564\) −1.28574 + 2.22697i −0.0541396 + 0.0937725i
\(565\) 6.92468 + 11.9939i 0.291324 + 0.504587i
\(566\) −41.8092 −1.75737
\(567\) 1.94548 + 17.4943i 0.0817026 + 0.734693i
\(568\) −9.44618 −0.396353
\(569\) −23.0789 39.9739i −0.967520 1.67579i −0.702687 0.711499i \(-0.748017\pi\)
−0.264832 0.964294i \(-0.585317\pi\)
\(570\) −3.98254 + 6.89796i −0.166810 + 0.288924i
\(571\) −10.5684 + 18.3050i −0.442274 + 0.766041i −0.997858 0.0654194i \(-0.979161\pi\)
0.555584 + 0.831461i \(0.312495\pi\)
\(572\) 0 0
\(573\) 2.53848 0.106047
\(574\) 48.3144 + 21.1627i 2.01660 + 0.883314i
\(575\) −4.76904 −0.198883
\(576\) 6.39653 + 11.0791i 0.266522 + 0.461630i
\(577\) −12.6652 + 21.9368i −0.527259 + 0.913239i 0.472237 + 0.881472i \(0.343447\pi\)
−0.999495 + 0.0317671i \(0.989887\pi\)
\(578\) 9.35045 16.1955i 0.388927 0.673642i
\(579\) −0.782650 1.35559i −0.0325258 0.0563364i
\(580\) −40.7146 −1.69058
\(581\) −5.74681 + 4.22849i −0.238418 + 0.175427i
\(582\) 20.7785 0.861295
\(583\) −9.82667 17.0203i −0.406979 0.704908i
\(584\) −31.8227 + 55.1186i −1.31683 + 2.28082i
\(585\) 0 0
\(586\) 18.9553 + 32.8315i 0.783036 + 1.35626i
\(587\) 3.56287 0.147056 0.0735278 0.997293i \(-0.476574\pi\)
0.0735278 + 0.997293i \(0.476574\pi\)
\(588\) −16.6438 + 3.74815i −0.686379 + 0.154571i
\(589\) 38.5749 1.58945
\(590\) −23.8361 41.2853i −0.981316 1.69969i
\(591\) −1.20541 + 2.08783i −0.0495839 + 0.0858819i
\(592\) −25.8866 + 44.8369i −1.06393 + 1.84278i
\(593\) −12.6768 21.9568i −0.520573 0.901659i −0.999714 0.0239212i \(-0.992385\pi\)
0.479141 0.877738i \(-0.340948\pi\)
\(594\) −20.8061 −0.853685
\(595\) 10.7410 7.90320i 0.440338 0.324000i
\(596\) 93.0677 3.81220
\(597\) −0.106472 0.184415i −0.00435762 0.00754762i
\(598\) 0 0
\(599\) −5.46078 + 9.45835i −0.223122 + 0.386458i −0.955754 0.294166i \(-0.904958\pi\)
0.732633 + 0.680624i \(0.238291\pi\)
\(600\) 4.35211 + 7.53807i 0.177674 + 0.307740i
\(601\) 24.2564 0.989439 0.494720 0.869053i \(-0.335271\pi\)
0.494720 + 0.869053i \(0.335271\pi\)
\(602\) 21.0534 + 9.22183i 0.858074 + 0.375854i
\(603\) 37.0946 1.51061
\(604\) −17.7103 30.6751i −0.720621 1.24815i
\(605\) 2.96876 5.14205i 0.120697 0.209054i
\(606\) 0.858476 1.48692i 0.0348732 0.0604022i
\(607\) 4.92724 + 8.53422i 0.199990 + 0.346393i 0.948525 0.316702i \(-0.102576\pi\)
−0.748535 + 0.663096i \(0.769242\pi\)
\(608\) 31.3974 1.27333
\(609\) −0.814561 7.32476i −0.0330077 0.296814i
\(610\) −12.2062 −0.494215
\(611\) 0 0
\(612\) 20.0712 34.7643i 0.811328 1.40526i
\(613\) −1.83844 + 3.18428i −0.0742540 + 0.128612i −0.900762 0.434314i \(-0.856991\pi\)
0.826508 + 0.562926i \(0.190324\pi\)
\(614\) 11.6208 + 20.1278i 0.468977 + 0.812293i
\(615\) −6.43688 −0.259560
\(616\) 5.53015 + 49.7286i 0.222816 + 2.00362i
\(617\) −18.7468 −0.754718 −0.377359 0.926067i \(-0.623168\pi\)
−0.377359 + 0.926067i \(0.623168\pi\)
\(618\) 7.69517 + 13.3284i 0.309545 + 0.536148i
\(619\) 7.94725 13.7650i 0.319427 0.553264i −0.660942 0.750437i \(-0.729843\pi\)
0.980369 + 0.197174i \(0.0631763\pi\)
\(620\) −39.7014 + 68.7649i −1.59445 + 2.76167i
\(621\) 2.95068 + 5.11073i 0.118407 + 0.205087i
\(622\) 31.5333 1.26437
\(623\) −4.26499 1.86815i −0.170873 0.0748460i
\(624\) 0 0
\(625\) 3.61371 + 6.25913i 0.144549 + 0.250365i
\(626\) −16.9864 + 29.4212i −0.678911 + 1.17591i
\(627\) −2.58152 + 4.47133i −0.103096 + 0.178568i
\(628\) −32.9165 57.0130i −1.31351 2.27507i
\(629\) 18.6141 0.742194
\(630\) −24.2878 + 17.8709i −0.967649 + 0.711995i
\(631\) −19.7451 −0.786040 −0.393020 0.919530i \(-0.628570\pi\)
−0.393020 + 0.919530i \(0.628570\pi\)
\(632\) 21.6936 + 37.5745i 0.862927 + 1.49463i
\(633\) 1.94839 3.37472i 0.0774417 0.134133i
\(634\) 21.6349 37.4727i 0.859231 1.48823i
\(635\) 2.51812 + 4.36151i 0.0999286 + 0.173081i
\(636\) 17.7081 0.702173
\(637\) 0 0
\(638\) −37.6200 −1.48939
\(639\) −1.84507 3.19575i −0.0729898 0.126422i
\(640\) 3.97508 6.88504i 0.157129 0.272155i
\(641\) 14.8893 25.7890i 0.588092 1.01860i −0.406390 0.913699i \(-0.633213\pi\)
0.994482 0.104905i \(-0.0334539\pi\)
\(642\) 3.44601 + 5.96867i 0.136003 + 0.235565i
\(643\) −11.5725 −0.456373 −0.228187 0.973617i \(-0.573280\pi\)
−0.228187 + 0.973617i \(0.573280\pi\)
\(644\) 19.8955 14.6391i 0.783994 0.576862i
\(645\) −2.80493 −0.110444
\(646\) −14.8982 25.8044i −0.586162 1.01526i
\(647\) −12.7533 + 22.0893i −0.501382 + 0.868420i 0.498616 + 0.866823i \(0.333842\pi\)
−0.999999 + 0.00159698i \(0.999492\pi\)
\(648\) −23.2570 + 40.2823i −0.913620 + 1.58244i
\(649\) −15.4508 26.7616i −0.606497 1.05048i
\(650\) 0 0
\(651\) −13.1655 5.76675i −0.515995 0.226017i
\(652\) −33.7049 −1.31999
\(653\) 22.4146 + 38.8233i 0.877152 + 1.51927i 0.854452 + 0.519530i \(0.173893\pi\)
0.0227004 + 0.999742i \(0.492774\pi\)
\(654\) −1.15946 + 2.00825i −0.0453386 + 0.0785287i
\(655\) −8.22889 + 14.2529i −0.321529 + 0.556905i
\(656\) 33.4874 + 58.0018i 1.30746 + 2.26459i
\(657\) −24.8630 −0.969999
\(658\) 0.798661 + 7.18179i 0.0311350 + 0.279975i
\(659\) 41.1734 1.60389 0.801944 0.597399i \(-0.203799\pi\)
0.801944 + 0.597399i \(0.203799\pi\)
\(660\) −5.31382 9.20380i −0.206840 0.358258i
\(661\) 10.9469 18.9606i 0.425785 0.737481i −0.570709 0.821153i \(-0.693331\pi\)
0.996493 + 0.0836719i \(0.0266648\pi\)
\(662\) 5.13404 8.89241i 0.199540 0.345613i
\(663\) 0 0
\(664\) −18.8539 −0.731673
\(665\) 1.73546 + 15.6058i 0.0672983 + 0.605165i
\(666\) −42.0908 −1.63098
\(667\) 5.33520 + 9.24084i 0.206580 + 0.357807i
\(668\) 42.2620 73.1999i 1.63516 2.83219i
\(669\) 5.85334 10.1383i 0.226303 0.391968i
\(670\) 28.3382 + 49.0832i 1.09480 + 1.89625i
\(671\) −7.91219 −0.305447
\(672\) −10.7158 4.69375i −0.413371 0.181065i
\(673\) 35.6688 1.37493 0.687466 0.726217i \(-0.258723\pi\)
0.687466 + 0.726217i \(0.258723\pi\)
\(674\) −17.7361 30.7197i −0.683167 1.18328i
\(675\) −3.56762 + 6.17930i −0.137318 + 0.237841i
\(676\) 0 0
\(677\) −1.27766 2.21297i −0.0491044 0.0850514i 0.840428 0.541923i \(-0.182303\pi\)
−0.889533 + 0.456871i \(0.848970\pi\)
\(678\) −11.5302 −0.442813
\(679\) 32.9928 24.2761i 1.26615 0.931630i
\(680\) 35.2386 1.35134
\(681\) −3.54416 6.13867i −0.135813 0.235234i
\(682\) −36.6839 + 63.5384i −1.40470 + 2.43301i
\(683\) −17.8700 + 30.9517i −0.683775 + 1.18433i 0.290045 + 0.957013i \(0.406330\pi\)
−0.973820 + 0.227320i \(0.927004\pi\)
\(684\) 23.6333 + 40.9341i 0.903642 + 1.56515i
\(685\) −16.1086 −0.615479
\(686\) −31.4293 + 36.2021i −1.19997 + 1.38220i
\(687\) 4.11188 0.156878
\(688\) 14.5924 + 25.2748i 0.556330 + 0.963592i
\(689\) 0 0
\(690\) −2.14843 + 3.72120i −0.0817895 + 0.141664i
\(691\) 13.0146 + 22.5419i 0.495099 + 0.857536i 0.999984 0.00565028i \(-0.00179855\pi\)
−0.504885 + 0.863186i \(0.668465\pi\)
\(692\) −60.2254 −2.28943
\(693\) −15.7436 + 11.5841i −0.598050 + 0.440045i
\(694\) −68.3335 −2.59391
\(695\) 1.34139 + 2.32336i 0.0508818 + 0.0881299i
\(696\) 9.73755 16.8659i 0.369101 0.639301i
\(697\) 12.0398 20.8535i 0.456040 0.789884i
\(698\) −6.32944 10.9629i −0.239573 0.414952i
\(699\) −3.40721 −0.128872
\(700\) 27.3562 + 11.9826i 1.03397 + 0.452899i
\(701\) 1.12731 0.0425779 0.0212890 0.999773i \(-0.493223\pi\)
0.0212890 + 0.999773i \(0.493223\pi\)
\(702\) 0 0
\(703\) −10.9588 + 18.9813i −0.413321 + 0.715892i
\(704\) −6.33509 + 10.9727i −0.238763 + 0.413549i
\(705\) −0.440917 0.763691i −0.0166059 0.0287623i
\(706\) 35.0955 1.32084
\(707\) −0.374096 3.36398i −0.0140693 0.126515i
\(708\) 27.8431 1.04641
\(709\) −3.02515 5.23972i −0.113612 0.196782i 0.803612 0.595153i \(-0.202909\pi\)
−0.917224 + 0.398372i \(0.869575\pi\)
\(710\) 2.81906 4.88276i 0.105798 0.183247i
\(711\) −8.47459 + 14.6784i −0.317822 + 0.550484i
\(712\) −6.15202 10.6556i −0.230557 0.399336i
\(713\) 20.8098 0.779332
\(714\) 1.22707 + 11.0341i 0.0459219 + 0.412942i
\(715\) 0 0
\(716\) −4.32530 7.49164i −0.161644 0.279976i
\(717\) 2.43493 4.21743i 0.0909342 0.157503i
\(718\) −11.1124 + 19.2473i −0.414713 + 0.718304i
\(719\) −23.5589 40.8052i −0.878597 1.52178i −0.852880 0.522106i \(-0.825146\pi\)
−0.0257170 0.999669i \(-0.508187\pi\)
\(720\) −38.2884 −1.42692
\(721\) 27.7907 + 12.1729i 1.03498 + 0.453342i
\(722\) −14.0989 −0.524706
\(723\) 2.61458 + 4.52859i 0.0972374 + 0.168420i
\(724\) −7.75473 + 13.4316i −0.288202 + 0.499181i
\(725\) −6.45070 + 11.1729i −0.239573 + 0.414953i
\(726\) 2.47162 + 4.28097i 0.0917303 + 0.158882i
\(727\) −17.9215 −0.664671 −0.332335 0.943161i \(-0.607837\pi\)
−0.332335 + 0.943161i \(0.607837\pi\)
\(728\) 0 0
\(729\) −13.5489 −0.501810
\(730\) −18.9940 32.8985i −0.702999 1.21763i
\(731\) 5.24644 9.08711i 0.194047 0.336099i
\(732\) 3.56454 6.17396i 0.131749 0.228196i
\(733\) −22.6343 39.2037i −0.836016 1.44802i −0.893201 0.449658i \(-0.851546\pi\)
0.0571848 0.998364i \(-0.481788\pi\)
\(734\) −4.30542 −0.158916
\(735\) 1.74067 5.58562i 0.0642056 0.206029i
\(736\) 16.9378 0.624335
\(737\) 18.3691 + 31.8163i 0.676635 + 1.17197i
\(738\) −27.2247 + 47.1546i −1.00215 + 1.73578i
\(739\) −9.63066 + 16.6808i −0.354270 + 0.613613i −0.986993 0.160765i \(-0.948604\pi\)
0.632723 + 0.774378i \(0.281937\pi\)
\(740\) −22.5577 39.0712i −0.829239 1.43628i
\(741\) 0 0
\(742\) 40.0804 29.4911i 1.47140 1.08265i
\(743\) 34.8853 1.27982 0.639908 0.768452i \(-0.278972\pi\)
0.639908 + 0.768452i \(0.278972\pi\)
\(744\) −18.9905 32.8925i −0.696225 1.20590i
\(745\) −15.9577 + 27.6396i −0.584647 + 1.01264i
\(746\) −18.0729 + 31.3032i −0.661697 + 1.14609i
\(747\) −3.68263 6.37850i −0.134740 0.233377i
\(748\) 39.7567 1.45365
\(749\) 12.4451 + 5.45120i 0.454733 + 0.199183i
\(750\) −16.0130 −0.584711
\(751\) 12.4834 + 21.6219i 0.455526 + 0.788993i 0.998718 0.0506146i \(-0.0161180\pi\)
−0.543193 + 0.839608i \(0.682785\pi\)
\(752\) −4.58767 + 7.94609i −0.167295 + 0.289764i
\(753\) 2.68268 4.64654i 0.0977623 0.169329i
\(754\) 0 0
\(755\) 12.1467 0.442064
\(756\) −4.08462 36.7301i −0.148556 1.33586i
\(757\) −10.6049 −0.385440 −0.192720 0.981254i \(-0.561731\pi\)
−0.192720 + 0.981254i \(0.561731\pi\)
\(758\) 40.8685 + 70.7863i 1.48441 + 2.57108i
\(759\) −1.39264 + 2.41212i −0.0505495 + 0.0875543i
\(760\) −20.7463 + 35.9337i −0.752548 + 1.30345i
\(761\) 16.3194 + 28.2660i 0.591578 + 1.02464i 0.994020 + 0.109198i \(0.0348282\pi\)
−0.402442 + 0.915446i \(0.631838\pi\)
\(762\) −4.19288 −0.151892
\(763\) 0.505256 + 4.54340i 0.0182915 + 0.164482i
\(764\) 23.0160 0.832691
\(765\) 6.88296 + 11.9216i 0.248854 + 0.431028i
\(766\) 41.2988 71.5316i 1.49219 2.58454i
\(767\) 0 0
\(768\) 5.73794 + 9.93841i 0.207050 + 0.358621i
\(769\) −52.1752 −1.88149 −0.940744 0.339119i \(-0.889871\pi\)
−0.940744 + 0.339119i \(0.889871\pi\)
\(770\) −27.3553 11.9822i −0.985815 0.431807i
\(771\) 4.14077 0.149126
\(772\) −7.09618 12.2909i −0.255397 0.442360i
\(773\) 17.8529 30.9221i 0.642123 1.11219i −0.342835 0.939396i \(-0.611387\pi\)
0.984958 0.172794i \(-0.0552794\pi\)
\(774\) −11.8634 + 20.5480i −0.426421 + 0.738583i
\(775\) 12.5804 + 21.7898i 0.451900 + 0.782714i
\(776\) 108.242 3.88565
\(777\) 6.57780 4.83994i 0.235977 0.173632i
\(778\) −65.7893 −2.35866
\(779\) 14.1766 + 24.5545i 0.507928 + 0.879757i
\(780\) 0 0
\(781\) 1.82735 3.16506i 0.0653876 0.113255i
\(782\) −8.03703 13.9206i −0.287404 0.497798i</