Properties

Label 1183.2.e.j.170.12
Level $1183$
Weight $2$
Character 1183.170
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 170.12
Character \(\chi\) \(=\) 1183.170
Dual form 1183.2.e.j.508.12

$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

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

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 0.108613 0.994084i \(-0.465359\pi\)
0.806596 0.591104i \(-0.201308\pi\)
\(3\) −0.259233 0.449005i −0.149668 0.259233i 0.781437 0.623985i \(-0.214487\pi\)
−0.931105 + 0.364752i \(0.881154\pi\)
\(4\) −2.35043 4.07106i −1.17521 2.03553i
\(5\) 0.806027 1.39608i 0.360466 0.624346i −0.627571 0.778559i \(-0.715951\pi\)
0.988038 + 0.154213i \(0.0492843\pi\)
\(6\) −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 \(-0.0329670\pi\)
−0.586854 + 0.809693i \(0.699634\pi\)
\(12\) −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 0.611783 0.791026i \(-0.290453\pi\)
−0.990940 + 0.134307i \(0.957119\pi\)
\(18\) −3.53498 6.12277i −0.833204 1.44315i
\(19\) 1.84075 3.18828i 0.422297 0.731441i −0.573866 0.818949i \(-0.694557\pi\)
0.996164 + 0.0875083i \(0.0278904\pi\)
\(20\) −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 −0.950787 0.309846i \(-0.899722\pi\)
0.743728 + 0.668482i \(0.233056\pi\)
\(24\) 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 0.763653 + 0.645627i \(0.223404\pi\)
0.177303 + 0.984156i \(0.443263\pi\)
\(32\) 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 \(-0.670560\pi\)
0.999925 + 0.0122297i \(0.00389292\pi\)
\(38\) −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 \(-0.294615\pi\)
0.601386 + 0.798958i \(0.294615\pi\)
\(42\) 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 \(-0.808815\pi\)
0.901933 + 0.431877i \(0.142148\pi\)
\(48\) 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 0.500991 0.865453i \(-0.332969\pi\)
−0.999999 + 0.00114437i \(0.999636\pi\)
\(54\) −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 0.950826 + 0.309725i \(0.100237\pi\)
−0.207183 + 0.978302i \(0.566430\pi\)
\(60\) 1.96447 + 3.40257i 0.253613 + 0.439270i
\(61\) 1.46254 2.53319i 0.187259 0.324341i −0.757077 0.653326i \(-0.773373\pi\)
0.944335 + 0.328985i \(0.106706\pi\)
\(62\) 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 −0.898320 0.439343i \(-0.855211\pi\)
0.0686778 0.997639i \(-0.478122\pi\)
\(68\) −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 \(-0.474453\pi\)
0.0801736 + 0.996781i \(0.474453\pi\)
\(72\) −9.54747 + 16.5367i −1.12518 + 1.94887i
\(73\) 4.55168 + 7.88374i 0.532733 + 0.922721i 0.999269 + 0.0382192i \(0.0121685\pi\)
−0.466536 + 0.884502i \(0.654498\pi\)
\(74\) −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 −0.636988 0.770874i \(-0.719820\pi\)
0.986090 + 0.166211i \(0.0531532\pi\)
\(80\) 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 \(-0.452716\pi\)
0.148002 + 0.988987i \(0.452716\pi\)
\(84\) 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 \(-0.803600\pi\)
0.908887 + 0.417043i \(0.136934\pi\)
\(90\) −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 \(-0.787842\pi\)
−0.785981 + 0.618250i \(0.787842\pi\)
\(98\) 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 0.896093 0.443866i \(-0.146393\pi\)
−0.832446 + 0.554107i \(0.813060\pi\)
\(102\) 2.09811 + 3.63404i 0.207744 + 0.359823i
\(103\) 5.73367 9.93101i 0.564956 0.978532i −0.432098 0.901827i \(-0.642227\pi\)
0.997054 0.0767054i \(-0.0244401\pi\)
\(104\) 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 −0.714811 0.699318i \(-0.753487\pi\)
0.963033 + 0.269385i \(0.0868205\pi\)
\(108\) 6.98412 + 12.0969i 0.672048 + 1.16402i
\(109\) 0.863916 + 1.49635i 0.0827481 + 0.143324i 0.904429 0.426623i \(-0.140297\pi\)
−0.821681 + 0.569947i \(0.806964\pi\)
\(110\) 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 −0.998121 0.0612793i \(-0.980482\pi\)
0.552130 + 0.833758i \(0.313815\pi\)
\(132\) −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 \(-0.307048\pi\)
−0.996592 + 0.0824839i \(0.973715\pi\)
\(138\) 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 −0.101234 0.994863i \(-0.532279\pi\)
0.912193 0.409760i \(-0.134387\pi\)
\(150\) −1.61138 2.79100i −0.131569 0.227884i
\(151\) 3.76746 + 6.52544i 0.306592 + 0.531033i 0.977614 0.210404i \(-0.0674780\pi\)
−0.671023 + 0.741437i \(0.734145\pi\)
\(152\) −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 −0.997594 0.0693309i \(-0.977914\pi\)
0.438755 0.898607i \(-0.355420\pi\)
\(158\) −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 \(-0.923932\pi\)
0.690784 + 0.723061i \(0.257265\pi\)
\(164\) −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 \(-0.255099\pi\)
0.695688 + 0.718344i \(0.255099\pi\)
\(168\) 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 −0.512865 0.858469i \(-0.671416\pi\)
0.999889 + 0.0149198i \(0.00474930\pi\)
\(174\) 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 0.829589 0.558375i \(-0.188575\pi\)
−0.898361 + 0.439258i \(0.855242\pi\)
\(180\) −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 −0.940898 0.338689i \(-0.890017\pi\)
0.763762 + 0.645498i \(0.223350\pi\)
\(192\) −1.21426 2.10316i −0.0876318 0.151783i
\(193\) 1.50955 + 2.61462i 0.108660 + 0.188204i 0.915228 0.402937i \(-0.132011\pi\)
−0.806568 + 0.591142i \(0.798677\pi\)
\(194\) −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 \(-0.552971\pi\)
−0.165646 + 0.986185i \(0.552971\pi\)
\(198\) 9.56198 16.5618i 0.679540 1.17700i
\(199\) −0.205360 0.355694i −0.0145576 0.0252145i 0.858655 0.512554i \(-0.171301\pi\)
−0.873212 + 0.487340i \(0.837967\pi\)
\(200\) −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 \(-0.227143\pi\)
0.756016 + 0.654553i \(0.227143\pi\)
\(224\) 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 \(-0.0167661\pi\)
−0.544901 + 0.838500i \(0.683433\pi\)
\(228\) 4.48634 + 7.77057i 0.297115 + 0.514618i
\(229\) 3.96543 6.86832i 0.262043 0.453872i −0.704742 0.709464i \(-0.748937\pi\)
0.966785 + 0.255592i \(0.0822705\pi\)
\(230\) 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 −0.738091 0.674702i \(-0.764272\pi\)
0.953354 + 0.301854i \(0.0976056\pi\)
\(234\) 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 \(-0.401749\pi\)
0.303786 + 0.952740i \(0.401749\pi\)
\(240\) 3.63417 6.29456i 0.234584 0.406312i
\(241\) −5.04292 8.73460i −0.324843 0.562645i 0.656637 0.754206i \(-0.271978\pi\)
−0.981481 + 0.191562i \(0.938645\pi\)
\(242\) −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 −0.963275 0.268517i \(-0.913466\pi\)
0.714180 + 0.699962i \(0.246800\pi\)
\(258\) 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 0.777431 0.628968i \(-0.216522\pi\)
−0.933418 + 0.358792i \(0.883189\pi\)
\(264\) −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 0.572823 0.819679i \(-0.305848\pi\)
−0.996274 + 0.0862400i \(0.972515\pi\)
\(270\) 6.19983 + 10.7384i 0.377310 + 0.653519i
\(271\) −4.16361 + 7.21158i −0.252921 + 0.438072i −0.964329 0.264707i \(-0.914725\pi\)
0.711408 + 0.702780i \(0.248058\pi\)
\(272\) 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 0.969391 + 0.245523i \(0.0789598\pi\)
−0.272066 + 0.962279i \(0.587707\pi\)
\(278\) −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 \(-0.800587\pi\)
−0.810100 + 0.586292i \(0.800587\pi\)
\(282\) −0.708015 + 1.22632i −0.0421617 + 0.0730262i
\(283\) 8.07563 + 13.9874i 0.480046 + 0.831464i 0.999738 0.0228894i \(-0.00728654\pi\)
−0.519692 + 0.854354i \(0.673953\pi\)
\(284\) −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 \(-0.359292\pi\)
0.427791 + 0.903878i \(0.359292\pi\)
\(294\) −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 \(-0.417525\pi\)
0.256213 + 0.966620i \(0.417525\pi\)
\(308\) −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 0.640045 0.768338i \(-0.278916\pi\)
−0.985422 + 0.170126i \(0.945583\pi\)
\(312\) 0 0
\(313\) −6.56198 + 11.3657i −0.370905 + 0.642427i −0.989705 0.143122i \(-0.954286\pi\)
0.618800 + 0.785549i \(0.287619\pi\)
\(314\) −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 \(-0.988870\pi\)
0.529971 + 0.848016i \(0.322203\pi\)
\(318\) 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 \(-0.868102\pi\)
0.806357 + 0.591428i \(0.201436\pi\)
\(332\) −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 0.965393 + 0.260800i \(0.0839863\pi\)
−0.256837 + 0.966455i \(0.582680\pi\)
\(348\) 6.54727 11.3402i 0.350971 0.607899i
\(349\) −4.89024 −0.261769 −0.130884 0.991398i \(-0.541782\pi\)
−0.130884 + 0.991398i \(0.541782\pi\)
\(350\) −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 \(-0.0491696\pi\)
−0.627291 + 0.778785i \(0.715836\pi\)
\(354\) −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 \(-0.760583\pi\)
0.956789 + 0.290785i \(0.0939163\pi\)
\(360\) 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 0.886914 0.461935i \(-0.152845\pi\)
−0.843504 + 0.537123i \(0.819511\pi\)
\(368\) −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 −0.988208 0.153117i \(-0.951069\pi\)
0.626707 + 0.779255i \(0.284402\pi\)
\(374\) −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 \(-0.198941\pi\)
0.810969 + 0.585089i \(0.198941\pi\)
\(380\) −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 0.0939554 + 0.995576i \(0.470049\pi\)
−0.909172 + 0.416420i \(0.863284\pi\)
\(384\) 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 0.984464 + 0.175589i \(0.0561829\pi\)
−0.340168 + 0.940365i \(0.610484\pi\)
\(390\) 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 \(-0.800052\pi\)
0.913479 + 0.406885i \(0.133385\pi\)
\(398\) −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 \(-0.996126\pi\)
0.510504 + 0.859875i \(0.329459\pi\)
\(402\) 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 \(-0.310260\pi\)
−0.997374 + 0.0724249i \(0.976926\pi\)
\(410\) −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 \(-0.398598\pi\)
0.313203 + 0.949686i \(0.398598\pi\)
\(422\) −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 \(-0.235984\pi\)
−0.953597 + 0.301087i \(0.902650\pi\)
\(432\) 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 0.118304 0.992977i \(-0.462254\pi\)
0.800792 0.598943i \(-0.204412\pi\)
\(440\) −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 −0.630222 0.776415i \(-0.717036\pi\)
0.987506 + 0.157580i \(0.0503693\pi\)
\(444\) 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 \(-0.870564\pi\)
−0.918456 + 0.395522i \(0.870564\pi\)
\(450\) 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 \(-0.727621\pi\)
0.981721 + 0.190325i \(0.0609541\pi\)
\(458\) −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 \(-0.162547\pi\)
0.872424 + 0.488749i \(0.162547\pi\)
\(462\) −1.06159 + 9.54609i −0.0493895 + 0.444124i
\(463\) 6.75275 0.313827 0.156913 0.987612i \(-0.449846\pi\)
0.156913 + 0.987612i \(0.449846\pi\)
\(464\) 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 −0.918518 0.395379i \(-0.870613\pi\)
0.801667 + 0.597770i \(0.203947\pi\)
\(468\) 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 \(-0.0973774\pi\)
−0.737607 + 0.675231i \(0.764044\pi\)
\(480\) −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 0.819194 + 0.573517i \(0.194421\pi\)
0.0870831 + 0.996201i \(0.472245\pi\)
\(488\) −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 \(-0.751516\pi\)
0.964682 + 0.263416i \(0.0848491\pi\)
\(500\) −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 \(-0.978050\pi\)
0.558483 + 0.829516i \(0.311384\pi\)
\(510\) 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 0.974630 + 0.223823i \(0.0718537\pi\)
−0.293479 + 0.955966i \(0.594813\pi\)
\(522\) 18.9924 + 32.8959i 0.831277 + 1.43981i
\(523\) −11.3601 + 19.6763i −0.496742 + 0.860383i −0.999993 0.00375758i \(-0.998804\pi\)
0.503251 + 0.864140i \(0.332137\pi\)
\(524\) 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 \(-0.818968\pi\)
0.887701 + 0.460420i \(0.152301\pi\)
\(542\) 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 −0.770164 0.637846i \(-0.779826\pi\)
−0.167309 0.985904i \(-0.553508\pi\)
\(558\) 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 0.906034 + 0.423205i \(0.139095\pi\)
−0.0865108 + 0.996251i \(0.527572\pi\)
\(564\) 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 −0.264832 + 0.964294i \(0.585317\pi\)
−0.702687 + 0.711499i \(0.748017\pi\)
\(570\) 3.98254 + 6.89796i 0.166810 + 0.288924i
\(571\) −10.5684 18.3050i −0.442274 0.766041i 0.555584 0.831461i \(-0.312495\pi\)
−0.997858 + 0.0654194i \(0.979161\pi\)
\(572\) 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 0.999495 + 0.0317671i \(0.0101135\pi\)
−0.472237 + 0.881472i \(0.656553\pi\)
\(578\) −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 \(-0.523426\pi\)
−0.0735278 + 0.997293i \(0.523426\pi\)
\(588\) −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 −0.479141 0.877738i \(-0.659052\pi\)
0.999714 0.0239212i \(-0.00761509\pi\)
\(594\) −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 0.732633 0.680624i \(-0.238291\pi\)
−0.955754 + 0.294166i \(0.904958\pi\)
\(600\) −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 −0.748535 0.663096i \(-0.769242\pi\)
0.948525 + 0.316702i \(0.102576\pi\)
\(608\) 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 \(-0.143009\pi\)
−0.826508 + 0.562926i \(0.809676\pi\)
\(614\) 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 \(-0.376832\pi\)
0.377359 + 0.926067i \(0.376832\pi\)
\(618\) −7.69517 + 13.3284i −0.309545 + 0.536148i
\(619\) −7.94725 13.7650i −0.319427 0.553264i 0.660942 0.750437i \(-0.270157\pi\)
−0.980369 + 0.197174i \(0.936824\pi\)
\(620\) −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 \(-0.371430\pi\)
0.393020 + 0.919530i \(0.371430\pi\)
\(632\) −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 0.994482 + 0.104905i \(0.0334539\pi\)
−0.406390 + 0.913699i \(0.633213\pi\)
\(642\) −3.44601 + 5.96867i −0.136003 + 0.235565i
\(643\) 11.5725 0.456373 0.228187 0.973617i \(-0.426720\pi\)
0.228187 + 0.973617i \(0.426720\pi\)
\(644\) −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 −0.999999 0.00159698i \(-0.999492\pi\)
0.498616 0.866823i \(-0.333842\pi\)
\(648\) 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 0.0227004 0.999742i \(-0.492774\pi\)
0.854452 0.519530i \(-0.173893\pi\)
\(654\) −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 \(-0.306669\pi\)
−0.996493 + 0.0836719i \(0.973335\pi\)
\(662\) 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 −0.889533 0.456871i \(-0.848970\pi\)
0.840428 + 0.541923i \(0.182303\pi\)
\(678\) 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 0.973820 + 0.227320i \(0.0729962\pi\)
−0.290045 + 0.957013i \(0.593670\pi\)
\(684\) −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 \(-0.998201\pi\)
0.504885 + 0.863186i \(0.331535\pi\)
\(692\) −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 \(-0.797091\pi\)
0.917224 + 0.398372i \(0.130425\pi\)
\(710\) −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 −0.0257170 + 0.999669i \(0.508187\pi\)
−0.852880 + 0.522106i \(0.825146\pi\)
\(720\) 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 −0.0571848 0.998364i \(-0.518212\pi\)
0.893201 0.449658i \(-0.148454\pi\)
\(734\) 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 \(-0.0513962\pi\)
−0.632723 + 0.774378i \(0.718063\pi\)
\(740\) −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 \(-0.721028\pi\)
−0.639908 + 0.768452i \(0.721028\pi\)
\(744\) −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 −0.543193 0.839608i \(-0.682785\pi\)
0.998718 + 0.0506146i \(0.0161180\pi\)
\(752\) 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 0.402442 + 0.915446i \(0.368162\pi\)
−0.994020 + 0.109198i \(0.965172\pi\)
\(762\) 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 \(-0.110129\pi\)
0.940744 + 0.339119i \(0.110129\pi\)
\(770\) −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 −0.984958 0.172794i \(-0.944721\pi\)
0.342835 0.939396i \(-0.388613\pi\)
\(774\) 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