Properties

Label 105.2.m.a.13.7
Level 105
Weight 2
Character 105.13
Analytic conductor 0.838
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 13.7
Root \(-0.944649 - 1.05244i\)
Character \(\chi\) = 105.13
Dual form 105.2.m.a.97.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.48838 - 1.48838i) q^{2} +(-0.707107 + 0.707107i) q^{3} -2.43055i q^{4} +(1.28999 - 1.82645i) q^{5} +2.10489i q^{6} +(-1.75993 + 1.97552i) q^{7} +(-0.640825 - 0.640825i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(1.48838 - 1.48838i) q^{2} +(-0.707107 + 0.707107i) q^{3} -2.43055i q^{4} +(1.28999 - 1.82645i) q^{5} +2.10489i q^{6} +(-1.75993 + 1.97552i) q^{7} +(-0.640825 - 0.640825i) q^{8} -1.00000i q^{9} +(-0.798469 - 4.63845i) q^{10} -2.67187 q^{11} +(1.71866 + 1.71866i) q^{12} +(-1.22714 + 1.22714i) q^{13} +(0.320879 + 5.55976i) q^{14} +(0.379340 + 2.20366i) q^{15} +2.95352 q^{16} +(4.74624 + 4.74624i) q^{17} +(-1.48838 - 1.48838i) q^{18} -6.01729 q^{19} +(-4.43929 - 3.13538i) q^{20} +(-0.152445 - 2.64136i) q^{21} +(-3.97676 + 3.97676i) q^{22} +(-0.175684 - 0.175684i) q^{23} +0.906263 q^{24} +(-1.67187 - 4.71220i) q^{25} +3.65291i q^{26} +(0.707107 + 0.707107i) q^{27} +(4.80159 + 4.27759i) q^{28} +0.304889i q^{29} +(3.84448 + 2.71528i) q^{30} -7.25379i q^{31} +(5.67761 - 5.67761i) q^{32} +(1.88930 - 1.88930i) q^{33} +14.1284 q^{34} +(1.33791 + 5.76281i) q^{35} -2.43055 q^{36} +(-0.735441 + 0.735441i) q^{37} +(-8.95602 + 8.95602i) q^{38} -1.73544i q^{39} +(-1.99709 + 0.343782i) q^{40} -7.05736i q^{41} +(-4.15824 - 3.70445i) q^{42} +(0.304889 + 0.304889i) q^{43} +6.49412i q^{44} +(-1.82645 - 1.28999i) q^{45} -0.522969 q^{46} +(-0.556866 - 0.556866i) q^{47} +(-2.08845 + 2.08845i) q^{48} +(-0.805321 - 6.95352i) q^{49} +(-9.50193 - 4.52517i) q^{50} -6.71220 q^{51} +(2.98263 + 2.98263i) q^{52} +(-4.99031 - 4.99031i) q^{53} +2.10489 q^{54} +(-3.44668 + 4.88005i) q^{55} +(2.39376 - 0.138155i) q^{56} +(4.25487 - 4.25487i) q^{57} +(0.453791 + 0.453791i) q^{58} +7.98837 q^{59} +(5.35610 - 0.922006i) q^{60} +5.53409i q^{61} +(-10.7964 - 10.7964i) q^{62} +(1.97552 + 1.75993i) q^{63} -10.9939i q^{64} +(0.658323 + 3.82432i) q^{65} -5.62399i q^{66} +(-3.43055 + 3.43055i) q^{67} +(11.5360 - 11.5360i) q^{68} +0.248455 q^{69} +(10.5686 + 6.58594i) q^{70} +15.3087 q^{71} +(-0.640825 + 0.640825i) q^{72} +(-10.0208 + 10.0208i) q^{73} +2.18923i q^{74} +(4.51422 + 2.14984i) q^{75} +14.6253i q^{76} +(4.70230 - 5.27832i) q^{77} +(-2.58300 - 2.58300i) q^{78} +11.2973i q^{79} +(3.81000 - 5.39447i) q^{80} -1.00000 q^{81} +(-10.5040 - 10.5040i) q^{82} +(4.88941 - 4.88941i) q^{83} +(-6.41995 + 0.370525i) q^{84} +(14.7914 - 2.54621i) q^{85} +0.907583 q^{86} +(-0.215589 - 0.215589i) q^{87} +(1.71220 + 1.71220i) q^{88} -6.91251 q^{89} +(-4.63845 + 0.798469i) q^{90} +(-0.264559 - 4.58392i) q^{91} +(-0.427009 + 0.427009i) q^{92} +(5.12921 + 5.12921i) q^{93} -1.65766 q^{94} +(-7.76222 + 10.9903i) q^{95} +8.02936i q^{96} +(8.84137 + 8.84137i) q^{97} +(-11.5481 - 9.15086i) q^{98} +2.67187i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{7} + 24q^{8} + O(q^{10}) \) \( 16q - 8q^{7} + 24q^{8} - 16q^{11} + 8q^{15} - 48q^{16} + 8q^{21} - 16q^{22} - 40q^{23} + 24q^{28} - 8q^{30} + 48q^{32} - 8q^{35} - 16q^{36} + 32q^{37} - 16q^{42} - 16q^{43} + 64q^{46} - 72q^{50} - 16q^{51} + 24q^{53} + 24q^{56} + 8q^{57} + 32q^{58} + 40q^{60} + 8q^{63} + 40q^{65} - 32q^{67} - 40q^{70} + 64q^{71} + 24q^{72} - 24q^{77} - 8q^{78} - 16q^{81} + 48q^{85} + 64q^{86} - 64q^{88} - 48q^{91} - 40q^{92} + 24q^{93} - 72q^{95} - 96q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.48838 1.48838i 1.05244 1.05244i 0.0538973 0.998546i \(-0.482836\pi\)
0.998546 0.0538973i \(-0.0171644\pi\)
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 2.43055i 1.21528i
\(5\) 1.28999 1.82645i 0.576899 0.816815i
\(6\) 2.10489i 0.859317i
\(7\) −1.75993 + 1.97552i −0.665189 + 0.746675i
\(8\) −0.640825 0.640825i −0.226566 0.226566i
\(9\) 1.00000i 0.333333i
\(10\) −0.798469 4.63845i −0.252498 1.46681i
\(11\) −2.67187 −0.805600 −0.402800 0.915288i \(-0.631963\pi\)
−0.402800 + 0.915288i \(0.631963\pi\)
\(12\) 1.71866 + 1.71866i 0.496134 + 0.496134i
\(13\) −1.22714 + 1.22714i −0.340348 + 0.340348i −0.856498 0.516150i \(-0.827365\pi\)
0.516150 + 0.856498i \(0.327365\pi\)
\(14\) 0.320879 + 5.55976i 0.0857585 + 1.48591i
\(15\) 0.379340 + 2.20366i 0.0979452 + 0.568982i
\(16\) 2.95352 0.738380
\(17\) 4.74624 + 4.74624i 1.15113 + 1.15113i 0.986326 + 0.164807i \(0.0527002\pi\)
0.164807 + 0.986326i \(0.447300\pi\)
\(18\) −1.48838 1.48838i −0.350815 0.350815i
\(19\) −6.01729 −1.38046 −0.690231 0.723589i \(-0.742491\pi\)
−0.690231 + 0.723589i \(0.742491\pi\)
\(20\) −4.43929 3.13538i −0.992656 0.701092i
\(21\) −0.152445 2.64136i −0.0332662 0.576391i
\(22\) −3.97676 + 3.97676i −0.847848 + 0.847848i
\(23\) −0.175684 0.175684i −0.0366327 0.0366327i 0.688553 0.725186i \(-0.258246\pi\)
−0.725186 + 0.688553i \(0.758246\pi\)
\(24\) 0.906263 0.184990
\(25\) −1.67187 4.71220i −0.334374 0.942440i
\(26\) 3.65291i 0.716394i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 4.80159 + 4.27759i 0.907416 + 0.808389i
\(29\) 0.304889i 0.0566165i 0.999599 + 0.0283083i \(0.00901200\pi\)
−0.999599 + 0.0283083i \(0.990988\pi\)
\(30\) 3.84448 + 2.71528i 0.701903 + 0.495739i
\(31\) 7.25379i 1.30282i −0.758726 0.651410i \(-0.774178\pi\)
0.758726 0.651410i \(-0.225822\pi\)
\(32\) 5.67761 5.67761i 1.00367 1.00367i
\(33\) 1.88930 1.88930i 0.328885 0.328885i
\(34\) 14.1284 2.42301
\(35\) 1.33791 + 5.76281i 0.226148 + 0.974093i
\(36\) −2.43055 −0.405092
\(37\) −0.735441 + 0.735441i −0.120906 + 0.120906i −0.764971 0.644065i \(-0.777247\pi\)
0.644065 + 0.764971i \(0.277247\pi\)
\(38\) −8.95602 + 8.95602i −1.45286 + 1.45286i
\(39\) 1.73544i 0.277893i
\(40\) −1.99709 + 0.343782i −0.315768 + 0.0543567i
\(41\) 7.05736i 1.10217i −0.834447 0.551087i \(-0.814213\pi\)
0.834447 0.551087i \(-0.185787\pi\)
\(42\) −4.15824 3.70445i −0.641630 0.571608i
\(43\) 0.304889 + 0.304889i 0.0464952 + 0.0464952i 0.729972 0.683477i \(-0.239533\pi\)
−0.683477 + 0.729972i \(0.739533\pi\)
\(44\) 6.49412i 0.979026i
\(45\) −1.82645 1.28999i −0.272272 0.192300i
\(46\) −0.522969 −0.0771076
\(47\) −0.556866 0.556866i −0.0812273 0.0812273i 0.665326 0.746553i \(-0.268293\pi\)
−0.746553 + 0.665326i \(0.768293\pi\)
\(48\) −2.08845 + 2.08845i −0.301442 + 0.301442i
\(49\) −0.805321 6.95352i −0.115046 0.993360i
\(50\) −9.50193 4.52517i −1.34378 0.639955i
\(51\) −6.71220 −0.939896
\(52\) 2.98263 + 2.98263i 0.413617 + 0.413617i
\(53\) −4.99031 4.99031i −0.685472 0.685472i 0.275756 0.961228i \(-0.411072\pi\)
−0.961228 + 0.275756i \(0.911072\pi\)
\(54\) 2.10489 0.286439
\(55\) −3.44668 + 4.88005i −0.464750 + 0.658026i
\(56\) 2.39376 0.138155i 0.319880 0.0184617i
\(57\) 4.25487 4.25487i 0.563571 0.563571i
\(58\) 0.453791 + 0.453791i 0.0595857 + 0.0595857i
\(59\) 7.98837 1.04000 0.519999 0.854167i \(-0.325932\pi\)
0.519999 + 0.854167i \(0.325932\pi\)
\(60\) 5.35610 0.922006i 0.691470 0.119031i
\(61\) 5.53409i 0.708567i 0.935138 + 0.354284i \(0.115275\pi\)
−0.935138 + 0.354284i \(0.884725\pi\)
\(62\) −10.7964 10.7964i −1.37114 1.37114i
\(63\) 1.97552 + 1.75993i 0.248892 + 0.221730i
\(64\) 10.9939i 1.37423i
\(65\) 0.658323 + 3.82432i 0.0816549 + 0.474348i
\(66\) 5.62399i 0.692265i
\(67\) −3.43055 + 3.43055i −0.419109 + 0.419109i −0.884896 0.465788i \(-0.845771\pi\)
0.465788 + 0.884896i \(0.345771\pi\)
\(68\) 11.5360 11.5360i 1.39894 1.39894i
\(69\) 0.248455 0.0299104
\(70\) 10.5686 + 6.58594i 1.26319 + 0.787170i
\(71\) 15.3087 1.81681 0.908407 0.418087i \(-0.137299\pi\)
0.908407 + 0.418087i \(0.137299\pi\)
\(72\) −0.640825 + 0.640825i −0.0755219 + 0.0755219i
\(73\) −10.0208 + 10.0208i −1.17285 + 1.17285i −0.191323 + 0.981527i \(0.561278\pi\)
−0.981527 + 0.191323i \(0.938722\pi\)
\(74\) 2.18923i 0.254493i
\(75\) 4.51422 + 2.14984i 0.521257 + 0.248242i
\(76\) 14.6253i 1.67764i
\(77\) 4.70230 5.27832i 0.535876 0.601521i
\(78\) −2.58300 2.58300i −0.292467 0.292467i
\(79\) 11.2973i 1.27104i 0.772084 + 0.635521i \(0.219215\pi\)
−0.772084 + 0.635521i \(0.780785\pi\)
\(80\) 3.81000 5.39447i 0.425971 0.603120i
\(81\) −1.00000 −0.111111
\(82\) −10.5040 10.5040i −1.15998 1.15998i
\(83\) 4.88941 4.88941i 0.536682 0.536682i −0.385871 0.922553i \(-0.626099\pi\)
0.922553 + 0.385871i \(0.126099\pi\)
\(84\) −6.41995 + 0.370525i −0.700474 + 0.0404276i
\(85\) 14.7914 2.54621i 1.60435 0.276175i
\(86\) 0.907583 0.0978671
\(87\) −0.215589 0.215589i −0.0231136 0.0231136i
\(88\) 1.71220 + 1.71220i 0.182521 + 0.182521i
\(89\) −6.91251 −0.732725 −0.366363 0.930472i \(-0.619397\pi\)
−0.366363 + 0.930472i \(0.619397\pi\)
\(90\) −4.63845 + 0.798469i −0.488935 + 0.0841660i
\(91\) −0.264559 4.58392i −0.0277333 0.480525i
\(92\) −0.427009 + 0.427009i −0.0445188 + 0.0445188i
\(93\) 5.12921 + 5.12921i 0.531874 + 0.531874i
\(94\) −1.65766 −0.170974
\(95\) −7.76222 + 10.9903i −0.796387 + 1.12758i
\(96\) 8.02936i 0.819493i
\(97\) 8.84137 + 8.84137i 0.897705 + 0.897705i 0.995233 0.0975276i \(-0.0310934\pi\)
−0.0975276 + 0.995233i \(0.531093\pi\)
\(98\) −11.5481 9.15086i −1.16654 0.924376i
\(99\) 2.67187i 0.268533i
\(100\) −11.4533 + 4.06357i −1.14533 + 0.406357i
\(101\) 7.22962i 0.719374i −0.933073 0.359687i \(-0.882883\pi\)
0.933073 0.359687i \(-0.117117\pi\)
\(102\) −9.99031 + 9.99031i −0.989188 + 0.989188i
\(103\) 6.94538 6.94538i 0.684349 0.684349i −0.276628 0.960977i \(-0.589217\pi\)
0.960977 + 0.276628i \(0.0892171\pi\)
\(104\) 1.57277 0.154222
\(105\) −5.02097 3.12888i −0.489996 0.305347i
\(106\) −14.8550 −1.44284
\(107\) −7.47295 + 7.47295i −0.722437 + 0.722437i −0.969101 0.246664i \(-0.920666\pi\)
0.246664 + 0.969101i \(0.420666\pi\)
\(108\) 1.71866 1.71866i 0.165378 0.165378i
\(109\) 5.95352i 0.570244i 0.958491 + 0.285122i \(0.0920341\pi\)
−0.958491 + 0.285122i \(0.907966\pi\)
\(110\) 2.13341 + 12.3933i 0.203412 + 1.18166i
\(111\) 1.04007i 0.0987192i
\(112\) −5.19798 + 5.83473i −0.491163 + 0.551330i
\(113\) 6.99031 + 6.99031i 0.657593 + 0.657593i 0.954810 0.297217i \(-0.0960585\pi\)
−0.297217 + 0.954810i \(0.596058\pi\)
\(114\) 12.6657i 1.18625i
\(115\) −0.547509 + 0.0942489i −0.0510555 + 0.00878876i
\(116\) 0.741049 0.0688047
\(117\) 1.22714 + 1.22714i 0.113449 + 0.113449i
\(118\) 11.8897 11.8897i 1.09454 1.09454i
\(119\) −17.7293 + 1.02324i −1.62524 + 0.0938002i
\(120\) 1.16907 1.65525i 0.106721 0.151103i
\(121\) −3.86110 −0.351009
\(122\) 8.23683 + 8.23683i 0.745727 + 0.745727i
\(123\) 4.99031 + 4.99031i 0.449961 + 0.449961i
\(124\) −17.6307 −1.58329
\(125\) −10.7633 3.02508i −0.962700 0.270571i
\(126\) 5.55976 0.320879i 0.495303 0.0285862i
\(127\) 2.86110 2.86110i 0.253882 0.253882i −0.568678 0.822560i \(-0.692545\pi\)
0.822560 + 0.568678i \(0.192545\pi\)
\(128\) −5.00781 5.00781i −0.442632 0.442632i
\(129\) −0.431179 −0.0379632
\(130\) 6.67187 + 4.71220i 0.585162 + 0.413287i
\(131\) 9.34764i 0.816707i 0.912824 + 0.408353i \(0.133897\pi\)
−0.912824 + 0.408353i \(0.866103\pi\)
\(132\) −4.59204 4.59204i −0.399686 0.399686i
\(133\) 10.5900 11.8873i 0.918268 1.03076i
\(134\) 10.2119i 0.882177i
\(135\) 2.20366 0.379340i 0.189661 0.0326484i
\(136\) 6.08302i 0.521615i
\(137\) 7.51943 7.51943i 0.642428 0.642428i −0.308724 0.951152i \(-0.599902\pi\)
0.951152 + 0.308724i \(0.0999019\pi\)
\(138\) 0.369795 0.369795i 0.0314791 0.0314791i
\(139\) −7.78902 −0.660656 −0.330328 0.943866i \(-0.607159\pi\)
−0.330328 + 0.943866i \(0.607159\pi\)
\(140\) 14.0068 3.25186i 1.18379 0.274832i
\(141\) 0.787528 0.0663218
\(142\) 22.7852 22.7852i 1.91209 1.91209i
\(143\) 3.27877 3.27877i 0.274184 0.274184i
\(144\) 2.95352i 0.246127i
\(145\) 0.556866 + 0.393303i 0.0462452 + 0.0326620i
\(146\) 29.8296i 2.46872i
\(147\) 5.48633 + 4.34743i 0.452505 + 0.358570i
\(148\) 1.78753 + 1.78753i 0.146934 + 0.146934i
\(149\) 14.2855i 1.17031i −0.810920 0.585157i \(-0.801033\pi\)
0.810920 0.585157i \(-0.198967\pi\)
\(150\) 9.91866 3.51910i 0.809855 0.287333i
\(151\) 9.77990 0.795877 0.397939 0.917412i \(-0.369726\pi\)
0.397939 + 0.917412i \(0.369726\pi\)
\(152\) 3.85603 + 3.85603i 0.312765 + 0.312765i
\(153\) 4.74624 4.74624i 0.383711 0.383711i
\(154\) −0.857347 14.8550i −0.0690870 1.19705i
\(155\) −13.2487 9.35729i −1.06416 0.751596i
\(156\) −4.21808 −0.337717
\(157\) −2.17731 2.17731i −0.173768 0.173768i 0.614864 0.788633i \(-0.289211\pi\)
−0.788633 + 0.614864i \(0.789211\pi\)
\(158\) 16.8146 + 16.8146i 1.33770 + 1.33770i
\(159\) 7.05736 0.559685
\(160\) −3.04586 17.6939i −0.240796 1.39883i
\(161\) 0.656257 0.0378756i 0.0517203 0.00298502i
\(162\) −1.48838 + 1.48838i −0.116938 + 0.116938i
\(163\) −13.6757 13.6757i −1.07117 1.07117i −0.997266 0.0739001i \(-0.976455\pi\)
−0.0739001 0.997266i \(-0.523545\pi\)
\(164\) −17.1533 −1.33945
\(165\) −1.01355 5.88789i −0.0789046 0.458371i
\(166\) 14.5546i 1.12966i
\(167\) 6.23288 + 6.23288i 0.482315 + 0.482315i 0.905870 0.423555i \(-0.139218\pi\)
−0.423555 + 0.905870i \(0.639218\pi\)
\(168\) −1.59496 + 1.79034i −0.123054 + 0.138128i
\(169\) 9.98824i 0.768326i
\(170\) 18.2255 25.8049i 1.39783 1.97915i
\(171\) 6.01729i 0.460154i
\(172\) 0.741049 0.741049i 0.0565045 0.0565045i
\(173\) −6.76935 + 6.76935i −0.514664 + 0.514664i −0.915952 0.401288i \(-0.868563\pi\)
0.401288 + 0.915952i \(0.368563\pi\)
\(174\) −0.641758 −0.0486515
\(175\) 12.2514 + 4.99032i 0.926119 + 0.377233i
\(176\) −7.89143 −0.594839
\(177\) −5.64863 + 5.64863i −0.424577 + 0.424577i
\(178\) −10.2885 + 10.2885i −0.771152 + 0.771152i
\(179\) 1.30103i 0.0972437i −0.998817 0.0486218i \(-0.984517\pi\)
0.998817 0.0486218i \(-0.0154829\pi\)
\(180\) −3.13538 + 4.43929i −0.233697 + 0.330885i
\(181\) 8.48528i 0.630706i 0.948974 + 0.315353i \(0.102123\pi\)
−0.948974 + 0.315353i \(0.897877\pi\)
\(182\) −7.21638 6.42885i −0.534913 0.476538i
\(183\) −3.91319 3.91319i −0.289271 0.289271i
\(184\) 0.225165i 0.0165994i
\(185\) 0.394541 + 2.29196i 0.0290072 + 0.168508i
\(186\) 15.2684 1.11953
\(187\) −12.6814 12.6814i −0.927352 0.927352i
\(188\) −1.35349 + 1.35349i −0.0987136 + 0.0987136i
\(189\) −2.64136 + 0.152445i −0.192130 + 0.0110887i
\(190\) 4.80462 + 27.9109i 0.348564 + 2.02487i
\(191\) 1.93791 0.140222 0.0701110 0.997539i \(-0.477665\pi\)
0.0701110 + 0.997539i \(0.477665\pi\)
\(192\) 7.77383 + 7.77383i 0.561028 + 0.561028i
\(193\) −7.82786 7.82786i −0.563462 0.563462i 0.366827 0.930289i \(-0.380444\pi\)
−0.930289 + 0.366827i \(0.880444\pi\)
\(194\) 26.3186 1.88957
\(195\) −3.16970 2.23870i −0.226987 0.160316i
\(196\) −16.9009 + 1.95738i −1.20721 + 0.139813i
\(197\) −8.50767 + 8.50767i −0.606146 + 0.606146i −0.941937 0.335790i \(-0.890997\pi\)
0.335790 + 0.941937i \(0.390997\pi\)
\(198\) 3.97676 + 3.97676i 0.282616 + 0.282616i
\(199\) 3.25460 0.230712 0.115356 0.993324i \(-0.463199\pi\)
0.115356 + 0.993324i \(0.463199\pi\)
\(200\) −1.94832 + 4.09107i −0.137767 + 0.289283i
\(201\) 4.85153i 0.342201i
\(202\) −10.7604 10.7604i −0.757101 0.757101i
\(203\) −0.602314 0.536583i −0.0422741 0.0376607i
\(204\) 16.3144i 1.14223i
\(205\) −12.8900 9.10390i −0.900273 0.635844i
\(206\) 20.6747i 1.44048i
\(207\) −0.175684 + 0.175684i −0.0122109 + 0.0122109i
\(208\) −3.62439 + 3.62439i −0.251306 + 0.251306i
\(209\) 16.0774 1.11210
\(210\) −12.1301 + 2.81615i −0.837054 + 0.194333i
\(211\) −17.2508 −1.18759 −0.593797 0.804615i \(-0.702372\pi\)
−0.593797 + 0.804615i \(0.702372\pi\)
\(212\) −12.1292 + 12.1292i −0.833037 + 0.833037i
\(213\) −10.8249 + 10.8249i −0.741711 + 0.741711i
\(214\) 22.2452i 1.52065i
\(215\) 0.950169 0.163563i 0.0648010 0.0111549i
\(216\) 0.906263i 0.0616634i
\(217\) 14.3300 + 12.7661i 0.972782 + 0.866622i
\(218\) 8.86110 + 8.86110i 0.600150 + 0.600150i
\(219\) 14.1716i 0.957628i
\(220\) 11.8612 + 8.37733i 0.799683 + 0.564799i
\(221\) −11.6486 −0.783572
\(222\) −1.54802 1.54802i −0.103896 0.103896i
\(223\) 4.58392 4.58392i 0.306962 0.306962i −0.536768 0.843730i \(-0.680355\pi\)
0.843730 + 0.536768i \(0.180355\pi\)
\(224\) 1.22403 + 21.2084i 0.0817841 + 1.41705i
\(225\) −4.71220 + 1.67187i −0.314147 + 0.111458i
\(226\) 20.8085 1.38416
\(227\) −14.1613 14.1613i −0.939918 0.939918i 0.0583764 0.998295i \(-0.481408\pi\)
−0.998295 + 0.0583764i \(0.981408\pi\)
\(228\) −10.3417 10.3417i −0.684894 0.684894i
\(229\) 28.9307 1.91180 0.955898 0.293699i \(-0.0948864\pi\)
0.955898 + 0.293699i \(0.0948864\pi\)
\(230\) −0.674623 + 0.955180i −0.0444833 + 0.0629827i
\(231\) 0.407313 + 7.05736i 0.0267992 + 0.464340i
\(232\) 0.195381 0.195381i 0.0128274 0.0128274i
\(233\) −4.78546 4.78546i −0.313506 0.313506i 0.532760 0.846266i \(-0.321155\pi\)
−0.846266 + 0.532760i \(0.821155\pi\)
\(234\) 3.65291 0.238798
\(235\) −1.73544 + 0.298741i −0.113208 + 0.0194877i
\(236\) 19.4162i 1.26388i
\(237\) −7.98837 7.98837i −0.518901 0.518901i
\(238\) −24.8650 + 27.9109i −1.61176 + 1.80920i
\(239\) 16.1769i 1.04640i −0.852210 0.523200i \(-0.824738\pi\)
0.852210 0.523200i \(-0.175262\pi\)
\(240\) 1.12039 + 6.50855i 0.0723208 + 0.420125i
\(241\) 11.3707i 0.732454i −0.930526 0.366227i \(-0.880649\pi\)
0.930526 0.366227i \(-0.119351\pi\)
\(242\) −5.74679 + 5.74679i −0.369418 + 0.369418i
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) 13.4509 0.861105
\(245\) −13.7391 7.49906i −0.877762 0.479098i
\(246\) 14.8550 0.947117
\(247\) 7.38407 7.38407i 0.469837 0.469837i
\(248\) −4.64841 + 4.64841i −0.295174 + 0.295174i
\(249\) 6.91467i 0.438199i
\(250\) −20.5224 + 11.5174i −1.29795 + 0.728427i
\(251\) 6.95039i 0.438705i 0.975646 + 0.219352i \(0.0703944\pi\)
−0.975646 + 0.219352i \(0.929606\pi\)
\(252\) 4.27759 4.80159i 0.269463 0.302472i
\(253\) 0.469405 + 0.469405i 0.0295112 + 0.0295112i
\(254\) 8.51682i 0.534393i
\(255\) −8.65865 + 12.2595i −0.542226 + 0.767722i
\(256\) 7.08066 0.442541
\(257\) −10.0889 10.0889i −0.629329 0.629329i 0.318570 0.947899i \(-0.396797\pi\)
−0.947899 + 0.318570i \(0.896797\pi\)
\(258\) −0.641758 + 0.641758i −0.0399541 + 0.0399541i
\(259\) −0.158553 2.74720i −0.00985202 0.170703i
\(260\) 9.29520 1.60009i 0.576464 0.0992332i
\(261\) 0.304889 0.0188722
\(262\) 13.9128 + 13.9128i 0.859538 + 0.859538i
\(263\) 18.1984 + 18.1984i 1.12216 + 1.12216i 0.991416 + 0.130744i \(0.0417367\pi\)
0.130744 + 0.991416i \(0.458263\pi\)
\(264\) −2.42142 −0.149028
\(265\) −15.5520 + 2.67714i −0.955352 + 0.164456i
\(266\) −1.93082 33.4547i −0.118386 2.05124i
\(267\) 4.88789 4.88789i 0.299134 0.299134i
\(268\) 8.33813 + 8.33813i 0.509333 + 0.509333i
\(269\) 15.5119 0.945775 0.472888 0.881123i \(-0.343212\pi\)
0.472888 + 0.881123i \(0.343212\pi\)
\(270\) 2.71528 3.84448i 0.165246 0.233968i
\(271\) 13.3418i 0.810458i 0.914215 + 0.405229i \(0.132808\pi\)
−0.914215 + 0.405229i \(0.867192\pi\)
\(272\) 14.0181 + 14.0181i 0.849974 + 0.849974i
\(273\) 3.42839 + 3.05425i 0.207496 + 0.184852i
\(274\) 22.3835i 1.35224i
\(275\) 4.46702 + 12.5904i 0.269372 + 0.759229i
\(276\) 0.603882i 0.0363494i
\(277\) −2.00561 + 2.00561i −0.120505 + 0.120505i −0.764788 0.644282i \(-0.777156\pi\)
0.644282 + 0.764788i \(0.277156\pi\)
\(278\) −11.5930 + 11.5930i −0.695304 + 0.695304i
\(279\) −7.25379 −0.434273
\(280\) 2.83559 4.55032i 0.169459 0.271934i
\(281\) 13.5557 0.808664 0.404332 0.914612i \(-0.367504\pi\)
0.404332 + 0.914612i \(0.367504\pi\)
\(282\) 1.17214 1.17214i 0.0698000 0.0698000i
\(283\) 16.2444 16.2444i 0.965627 0.965627i −0.0338017 0.999429i \(-0.510761\pi\)
0.999429 + 0.0338017i \(0.0107615\pi\)
\(284\) 37.2087i 2.20793i
\(285\) −2.28260 13.2600i −0.135210 0.785457i
\(286\) 9.76010i 0.577127i
\(287\) 13.9419 + 12.4204i 0.822966 + 0.733155i
\(288\) −5.67761 5.67761i −0.334557 0.334557i
\(289\) 28.0537i 1.65021i
\(290\) 1.41421 0.243445i 0.0830455 0.0142956i
\(291\) −12.5036 −0.732973
\(292\) 24.3562 + 24.3562i 1.42534 + 1.42534i
\(293\) 2.41765 2.41765i 0.141240 0.141240i −0.632951 0.774192i \(-0.718157\pi\)
0.774192 + 0.632951i \(0.218157\pi\)
\(294\) 14.6364 1.69511i 0.853611 0.0988609i
\(295\) 10.3049 14.5904i 0.599974 0.849486i
\(296\) 0.942578 0.0547862
\(297\) −1.88930 1.88930i −0.109628 0.109628i
\(298\) −21.2623 21.2623i −1.23169 1.23169i
\(299\) 0.431179 0.0249357
\(300\) 5.22529 10.9720i 0.301682 0.633472i
\(301\) −1.13890 + 0.0657309i −0.0656449 + 0.00378867i
\(302\) 14.5562 14.5562i 0.837616 0.837616i
\(303\) 5.11211 + 5.11211i 0.293683 + 0.293683i
\(304\) −17.7722 −1.01931
\(305\) 10.1078 + 7.13890i 0.578769 + 0.408772i
\(306\) 14.1284i 0.807669i
\(307\) −7.21300 7.21300i −0.411667 0.411667i 0.470652 0.882319i \(-0.344019\pi\)
−0.882319 + 0.470652i \(0.844019\pi\)
\(308\) −12.8292 11.4292i −0.731014 0.651238i
\(309\) 9.82225i 0.558768i
\(310\) −33.6463 + 5.79193i −1.91098 + 0.328959i
\(311\) 10.2542i 0.581460i 0.956805 + 0.290730i \(0.0938981\pi\)
−0.956805 + 0.290730i \(0.906102\pi\)
\(312\) −1.11211 + 1.11211i −0.0629611 + 0.0629611i
\(313\) −22.0904 + 22.0904i −1.24862 + 1.24862i −0.292293 + 0.956329i \(0.594418\pi\)
−0.956329 + 0.292293i \(0.905582\pi\)
\(314\) −6.48134 −0.365763
\(315\) 5.76281 1.33791i 0.324698 0.0753826i
\(316\) 27.4586 1.54467
\(317\) −12.2563 + 12.2563i −0.688385 + 0.688385i −0.961875 0.273490i \(-0.911822\pi\)
0.273490 + 0.961875i \(0.411822\pi\)
\(318\) 10.5040 10.5040i 0.589037 0.589037i
\(319\) 0.814625i 0.0456102i
\(320\) −20.0798 14.1819i −1.12249 0.792793i
\(321\) 10.5683i 0.589867i
\(322\) 0.920387 1.03313i 0.0512912 0.0575743i
\(323\) −28.5595 28.5595i −1.58909 1.58909i
\(324\) 2.43055i 0.135031i
\(325\) 7.83417 + 3.73092i 0.434561 + 0.206954i
\(326\) −40.7094 −2.25468
\(327\) −4.20978 4.20978i −0.232801 0.232801i
\(328\) −4.52253 + 4.52253i −0.249715 + 0.249715i
\(329\) 2.08014 0.120054i 0.114682 0.00661882i
\(330\) −10.2720 7.25487i −0.565453 0.399367i
\(331\) 1.26308 0.0694252 0.0347126 0.999397i \(-0.488948\pi\)
0.0347126 + 0.999397i \(0.488948\pi\)
\(332\) −11.8840 11.8840i −0.652217 0.652217i
\(333\) 0.735441 + 0.735441i 0.0403019 + 0.0403019i
\(334\) 18.5538 1.01522
\(335\) 1.84038 + 10.6911i 0.100551 + 0.584118i
\(336\) −0.450249 7.80130i −0.0245631 0.425596i
\(337\) −9.55621 + 9.55621i −0.520560 + 0.520560i −0.917741 0.397180i \(-0.869989\pi\)
0.397180 + 0.917741i \(0.369989\pi\)
\(338\) 14.8663 + 14.8663i 0.808620 + 0.808620i
\(339\) −9.88579 −0.536922
\(340\) −6.18869 35.9512i −0.335629 1.94973i
\(341\) 19.3812i 1.04955i
\(342\) 8.95602 + 8.95602i 0.484286 + 0.484286i
\(343\) 15.1541 + 10.6468i 0.818244 + 0.574871i
\(344\) 0.390761i 0.0210684i
\(345\) 0.320503 0.453791i 0.0172553 0.0244313i
\(346\) 20.1507i 1.08331i
\(347\) 6.54975 6.54975i 0.351609 0.351609i −0.509099 0.860708i \(-0.670021\pi\)
0.860708 + 0.509099i \(0.170021\pi\)
\(348\) −0.524001 + 0.524001i −0.0280894 + 0.0280894i
\(349\) 2.77139 0.148349 0.0741746 0.997245i \(-0.476368\pi\)
0.0741746 + 0.997245i \(0.476368\pi\)
\(350\) 25.6622 10.8072i 1.37170 0.577672i
\(351\) −1.73544 −0.0926310
\(352\) −15.1699 + 15.1699i −0.808556 + 0.808556i
\(353\) 0.970568 0.970568i 0.0516581 0.0516581i −0.680806 0.732464i \(-0.738370\pi\)
0.732464 + 0.680806i \(0.238370\pi\)
\(354\) 16.8146i 0.893687i
\(355\) 19.7481 27.9607i 1.04812 1.48400i
\(356\) 16.8012i 0.890463i
\(357\) 11.8130 13.2601i 0.625209 0.701797i
\(358\) −1.93643 1.93643i −0.102344 0.102344i
\(359\) 9.32813i 0.492320i 0.969229 + 0.246160i \(0.0791688\pi\)
−0.969229 + 0.246160i \(0.920831\pi\)
\(360\) 0.343782 + 1.99709i 0.0181189 + 0.105256i
\(361\) 17.2078 0.905674
\(362\) 12.6293 + 12.6293i 0.663783 + 0.663783i
\(363\) 2.73021 2.73021i 0.143299 0.143299i
\(364\) −11.1415 + 0.643024i −0.583971 + 0.0337036i
\(365\) 5.37586 + 31.2293i 0.281385 + 1.63462i
\(366\) −11.6486 −0.608884
\(367\) −13.0035 13.0035i −0.678776 0.678776i 0.280948 0.959723i \(-0.409351\pi\)
−0.959723 + 0.280948i \(0.909351\pi\)
\(368\) −0.518887 0.518887i −0.0270488 0.0270488i
\(369\) −7.05736 −0.367392
\(370\) 3.99853 + 2.82408i 0.207874 + 0.146817i
\(371\) 18.6410 1.07586i 0.967793 0.0558557i
\(372\) 12.4668 12.4668i 0.646373 0.646373i
\(373\) 20.6757 + 20.6757i 1.07055 + 1.07055i 0.997315 + 0.0732339i \(0.0233320\pi\)
0.0732339 + 0.997315i \(0.476668\pi\)
\(374\) −37.7493 −1.95197
\(375\) 9.74986 5.47176i 0.503481 0.282560i
\(376\) 0.713708i 0.0368067i
\(377\) −0.374143 0.374143i −0.0192693 0.0192693i
\(378\) −3.70445 + 4.15824i −0.190536 + 0.213877i
\(379\) 22.0077i 1.13046i −0.824933 0.565230i \(-0.808787\pi\)
0.824933 0.565230i \(-0.191213\pi\)
\(380\) 26.7125 + 18.8665i 1.37032 + 0.967830i
\(381\) 4.04621i 0.207294i
\(382\) 2.88434 2.88434i 0.147576 0.147576i
\(383\) 0.390382 0.390382i 0.0199476 0.0199476i −0.697063 0.717010i \(-0.745510\pi\)
0.717010 + 0.697063i \(0.245510\pi\)
\(384\) 7.08211 0.361407
\(385\) −3.57472 15.3975i −0.182185 0.784729i
\(386\) −23.3017 −1.18602
\(387\) 0.304889 0.304889i 0.0154984 0.0154984i
\(388\) 21.4894 21.4894i 1.09096 1.09096i
\(389\) 25.9300i 1.31470i −0.753584 0.657352i \(-0.771677\pi\)
0.753584 0.657352i \(-0.228323\pi\)
\(390\) −8.04976 + 1.38570i −0.407615 + 0.0701674i
\(391\) 1.66768i 0.0843381i
\(392\) −3.93992 + 4.97206i −0.198996 + 0.251127i
\(393\) −6.60978 6.60978i −0.333419 0.333419i
\(394\) 25.3253i 1.27587i
\(395\) 20.6339 + 14.5733i 1.03821 + 0.733263i
\(396\) 6.49412 0.326342
\(397\) 17.1631 + 17.1631i 0.861391 + 0.861391i 0.991500 0.130109i \(-0.0415327\pi\)
−0.130109 + 0.991500i \(0.541533\pi\)
\(398\) 4.84408 4.84408i 0.242812 0.242812i
\(399\) 0.917304 + 15.8938i 0.0459226 + 0.795686i
\(400\) −4.93791 13.9176i −0.246895 0.695879i
\(401\) −12.9418 −0.646281 −0.323140 0.946351i \(-0.604739\pi\)
−0.323140 + 0.946351i \(0.604739\pi\)
\(402\) −7.22093 7.22093i −0.360147 0.360147i
\(403\) 8.90143 + 8.90143i 0.443412 + 0.443412i
\(404\) −17.5720 −0.874238
\(405\) −1.28999 + 1.82645i −0.0640999 + 0.0907572i
\(406\) −1.69511 + 0.0978326i −0.0841269 + 0.00485535i
\(407\) 1.96500 1.96500i 0.0974016 0.0974016i
\(408\) 4.30135 + 4.30135i 0.212948 + 0.212948i
\(409\) 2.64278 0.130677 0.0653386 0.997863i \(-0.479187\pi\)
0.0653386 + 0.997863i \(0.479187\pi\)
\(410\) −32.7352 + 5.63508i −1.61668 + 0.278297i
\(411\) 10.6341i 0.524540i
\(412\) −16.8811 16.8811i −0.831672 0.831672i
\(413\) −14.0589 + 15.7812i −0.691795 + 0.776540i
\(414\) 0.522969i 0.0257025i
\(415\) −2.62301 15.2376i −0.128759 0.747982i
\(416\) 13.9345i 0.683194i
\(417\) 5.50767 5.50767i 0.269712 0.269712i
\(418\) 23.9293 23.9293i 1.17042 1.17042i
\(419\) −10.0302 −0.490007 −0.245003 0.969522i \(-0.578789\pi\)
−0.245003 + 0.969522i \(0.578789\pi\)
\(420\) −7.60490 + 12.2037i −0.371081 + 0.595481i
\(421\) −26.6440 −1.29855 −0.649274 0.760555i \(-0.724927\pi\)
−0.649274 + 0.760555i \(0.724927\pi\)
\(422\) −25.6757 + 25.6757i −1.24987 + 1.24987i
\(423\) −0.556866 + 0.556866i −0.0270758 + 0.0270758i
\(424\) 6.39583i 0.310609i
\(425\) 14.4301 30.3004i 0.699965 1.46978i
\(426\) 32.2232i 1.56122i
\(427\) −10.9327 9.73958i −0.529069 0.471332i
\(428\) 18.1634 + 18.1634i 0.877960 + 0.877960i
\(429\) 4.63688i 0.223870i
\(430\) 1.17077 1.65766i 0.0564595 0.0799394i
\(431\) 22.3747 1.07775 0.538876 0.842385i \(-0.318849\pi\)
0.538876 + 0.842385i \(0.318849\pi\)
\(432\) 2.08845 + 2.08845i 0.100481 + 0.100481i
\(433\) −13.4723 + 13.4723i −0.647438 + 0.647438i −0.952373 0.304935i \(-0.901365\pi\)
0.304935 + 0.952373i \(0.401365\pi\)
\(434\) 40.3293 2.32759i 1.93587 0.111728i
\(435\) −0.671871 + 0.115657i −0.0322138 + 0.00554532i
\(436\) 14.4703 0.693004
\(437\) 1.05714 + 1.05714i 0.0505700 + 0.0505700i
\(438\) −21.0927 21.0927i −1.00785 1.00785i
\(439\) −25.6790 −1.22559 −0.612795 0.790242i \(-0.709955\pi\)
−0.612795 + 0.790242i \(0.709955\pi\)
\(440\) 5.33598 0.918542i 0.254383 0.0437898i
\(441\) −6.95352 + 0.805321i −0.331120 + 0.0383486i
\(442\) −17.3376 + 17.3376i −0.824665 + 0.824665i
\(443\) −15.6351 15.6351i −0.742845 0.742845i 0.230279 0.973125i \(-0.426036\pi\)
−0.973125 + 0.230279i \(0.926036\pi\)
\(444\) −2.52795 −0.119971
\(445\) −8.91705 + 12.6254i −0.422709 + 0.598501i
\(446\) 13.6452i 0.646120i
\(447\) 10.1014 + 10.1014i 0.477779 + 0.477779i
\(448\) 21.7185 + 19.3484i 1.02610 + 0.914124i
\(449\) 7.01947i 0.331269i 0.986187 + 0.165635i \(0.0529673\pi\)
−0.986187 + 0.165635i \(0.947033\pi\)
\(450\) −4.52517 + 9.50193i −0.213318 + 0.447925i
\(451\) 18.8564i 0.887912i
\(452\) 16.9903 16.9903i 0.799157 0.799157i
\(453\) −6.91544 + 6.91544i −0.324916 + 0.324916i
\(454\) −42.1548 −1.97842
\(455\) −8.71359 5.42999i −0.408500 0.254562i
\(456\) −5.45325 −0.255372
\(457\) 11.2119 11.2119i 0.524472 0.524472i −0.394447 0.918919i \(-0.629064\pi\)
0.918919 + 0.394447i \(0.129064\pi\)
\(458\) 43.0599 43.0599i 2.01206 2.01206i
\(459\) 6.71220i 0.313299i
\(460\) 0.229077 + 1.33075i 0.0106808 + 0.0620465i
\(461\) 29.9845i 1.39652i −0.715846 0.698259i \(-0.753959\pi\)
0.715846 0.698259i \(-0.246041\pi\)
\(462\) 11.1103 + 9.89780i 0.516897 + 0.460488i
\(463\) 7.70220 + 7.70220i 0.357951 + 0.357951i 0.863057 0.505106i \(-0.168547\pi\)
−0.505106 + 0.863057i \(0.668547\pi\)
\(464\) 0.900497i 0.0418045i
\(465\) 15.9849 2.75166i 0.741280 0.127605i
\(466\) −14.2452 −0.659895
\(467\) −1.80961 1.80961i −0.0837386 0.0837386i 0.663997 0.747735i \(-0.268859\pi\)
−0.747735 + 0.663997i \(0.768859\pi\)
\(468\) 2.98263 2.98263i 0.137872 0.137872i
\(469\) −0.739590 12.8146i −0.0341511 0.591724i
\(470\) −2.13836 + 3.02764i −0.0986350 + 0.139654i
\(471\) 3.07918 0.141881
\(472\) −5.11915 5.11915i −0.235628 0.235628i
\(473\) −0.814625 0.814625i −0.0374565 0.0374565i
\(474\) −23.7795 −1.09223
\(475\) 10.0601 + 28.3547i 0.461591 + 1.30100i
\(476\) 2.48704 + 43.0920i 0.113993 + 1.97512i
\(477\) −4.99031 + 4.99031i −0.228491 + 0.228491i
\(478\) −24.0774 24.0774i −1.10128 1.10128i
\(479\) −4.09455 −0.187085 −0.0935425 0.995615i \(-0.529819\pi\)
−0.0935425 + 0.995615i \(0.529819\pi\)
\(480\) 14.6653 + 10.3578i 0.669374 + 0.472765i
\(481\) 1.80498i 0.0823001i
\(482\) −16.9240 16.9240i −0.770867 0.770867i
\(483\) −0.437262 + 0.490826i −0.0198961 + 0.0223334i
\(484\) 9.38461i 0.426573i
\(485\) 27.5536 4.74311i 1.25114 0.215374i
\(486\) 2.10489i 0.0954796i
\(487\) −10.3049 + 10.3049i −0.466959 + 0.466959i −0.900928 0.433969i \(-0.857113\pi\)
0.433969 + 0.900928i \(0.357113\pi\)
\(488\) 3.54638 3.54638i 0.160537 0.160537i
\(489\) 19.3404 0.874603
\(490\) −31.6105 + 9.28761i −1.42802 + 0.419571i
\(491\) −8.55953 −0.386286 −0.193143 0.981171i \(-0.561868\pi\)
−0.193143 + 0.981171i \(0.561868\pi\)
\(492\) 12.1292 12.1292i 0.546827 0.546827i
\(493\) −1.44708 + 1.44708i −0.0651732 + 0.0651732i
\(494\) 21.9806i 0.988955i
\(495\) 4.88005 + 3.44668i 0.219342 + 0.154917i
\(496\) 21.4242i 0.961976i
\(497\) −26.9423 + 30.2427i −1.20853 + 1.35657i
\(498\) 10.2917 + 10.2917i 0.461180 + 0.461180i
\(499\) 23.7564i 1.06348i −0.846907 0.531741i \(-0.821538\pi\)
0.846907 0.531741i \(-0.178462\pi\)
\(500\) −7.35261 + 26.1608i −0.328819 + 1.16995i
\(501\) −8.81463 −0.393808
\(502\) 10.3448 + 10.3448i 0.461712 + 0.461712i
\(503\) 17.9504 17.9504i 0.800367 0.800367i −0.182786 0.983153i \(-0.558511\pi\)
0.983153 + 0.182786i \(0.0585115\pi\)
\(504\) −0.138155 2.39376i −0.00615391 0.106627i
\(505\) −13.2046 9.32611i −0.587596 0.415007i
\(506\) 1.39731 0.0621179
\(507\) −7.06275 7.06275i −0.313668 0.313668i
\(508\) −6.95406 6.95406i −0.308537 0.308537i
\(509\) −16.8977 −0.748979 −0.374489 0.927231i \(-0.622182\pi\)
−0.374489 + 0.927231i \(0.622182\pi\)
\(510\) 5.35948 + 31.1342i 0.237322 + 1.37865i
\(511\) −2.16039 37.4322i −0.0955698 1.65590i
\(512\) 20.5543 20.5543i 0.908382 0.908382i
\(513\) −4.25487 4.25487i −0.187857 0.187857i
\(514\) −30.0323 −1.32467
\(515\) −3.72598 21.6449i −0.164186 0.953787i
\(516\) 1.04800i 0.0461357i
\(517\) 1.48788 + 1.48788i 0.0654367 + 0.0654367i
\(518\) −4.32486 3.85289i −0.190024 0.169286i
\(519\) 9.57331i 0.420221i
\(520\) 2.02885 2.87259i 0.0889708 0.125971i
\(521\) 7.88477i 0.345438i −0.984971 0.172719i \(-0.944745\pi\)
0.984971 0.172719i \(-0.0552552\pi\)
\(522\) 0.453791 0.453791i 0.0198619 0.0198619i
\(523\) 1.23149 1.23149i 0.0538493 0.0538493i −0.679669 0.733519i \(-0.737877\pi\)
0.733519 + 0.679669i \(0.237877\pi\)
\(524\) 22.7199 0.992524
\(525\) −12.1917 + 5.13436i −0.532091 + 0.224082i
\(526\) 54.1722 2.36202
\(527\) 34.4283 34.4283i 1.49972 1.49972i
\(528\) 5.58008 5.58008i 0.242842 0.242842i
\(529\) 22.9383i 0.997316i
\(530\) −19.1627 + 27.1319i −0.832374 + 1.17853i
\(531\) 7.98837i 0.346666i
\(532\) −28.8926 25.7395i −1.25265 1.11595i
\(533\) 8.66039 + 8.66039i 0.375123 + 0.375123i
\(534\) 14.5501i 0.629643i
\(535\) 4.00900 + 23.2890i 0.173324 + 1.00687i
\(536\) 4.39677 0.189911
\(537\) 0.919968 + 0.919968i 0.0396996 + 0.0396996i
\(538\) 23.0876 23.0876i 0.995375 0.995375i
\(539\) 2.15171 + 18.5789i 0.0926809 + 0.800250i
\(540\) −0.922006 5.35610i −0.0396768 0.230490i
\(541\) 34.9495 1.50260 0.751298 0.659963i \(-0.229428\pi\)
0.751298 + 0.659963i \(0.229428\pi\)
\(542\) 19.8577 + 19.8577i 0.852962 + 0.852962i
\(543\) −6.00000 6.00000i −0.257485 0.257485i
\(544\) 53.8947 2.31071
\(545\) 10.8738 + 7.67996i 0.465784 + 0.328973i
\(546\) 9.64863 0.556866i 0.412923 0.0238317i
\(547\) 3.83548 3.83548i 0.163993 0.163993i −0.620340 0.784333i \(-0.713005\pi\)
0.784333 + 0.620340i \(0.213005\pi\)
\(548\) −18.2764 18.2764i −0.780727 0.780727i
\(549\) 5.53409 0.236189
\(550\) 25.3879 + 12.0907i 1.08255 + 0.515548i
\(551\) 1.83461i 0.0781569i
\(552\) −0.159216 0.159216i −0.00677668 0.00677668i
\(553\) −22.3179 19.8823i −0.949054 0.845483i
\(554\) 5.97022i 0.253650i
\(555\) −1.89964 1.34168i −0.0806353 0.0569510i
\(556\) 18.9316i 0.802880i
\(557\) −16.3147 + 16.3147i −0.691275 + 0.691275i −0.962512 0.271238i \(-0.912567\pi\)
0.271238 + 0.962512i \(0.412567\pi\)
\(558\) −10.7964 + 10.7964i −0.457048 + 0.457048i
\(559\) −0.748285 −0.0316491
\(560\) 3.95154 + 17.0206i 0.166983 + 0.719251i
\(561\) 17.9341 0.757180
\(562\) 20.1760 20.1760i 0.851073 0.851073i
\(563\) −23.7521 + 23.7521i −1.00103 + 1.00103i −0.00103054 + 0.999999i \(0.500328\pi\)
−0.999999 + 0.00103054i \(0.999672\pi\)
\(564\) 1.91413i 0.0805993i
\(565\) 21.7849 3.75008i 0.916497 0.157767i
\(566\) 48.3556i 2.03254i
\(567\) 1.75993 1.97552i 0.0739099 0.0829638i
\(568\) −9.81023 9.81023i −0.411628 0.411628i
\(569\) 0.277792i 0.0116457i 0.999983 + 0.00582283i \(0.00185348\pi\)
−0.999983 + 0.00582283i \(0.998147\pi\)
\(570\) −23.1334 16.3386i −0.968950 0.684349i
\(571\) −3.11538 −0.130375 −0.0651874 0.997873i \(-0.520765\pi\)
−0.0651874 + 0.997873i \(0.520765\pi\)
\(572\) −7.96921 7.96921i −0.333209 0.333209i
\(573\) −1.37031 + 1.37031i −0.0572454 + 0.0572454i
\(574\) 39.2372 2.26456i 1.63773 0.0945209i
\(575\) −0.534138 + 1.12158i −0.0222751 + 0.0467731i
\(576\) −10.9939 −0.458077
\(577\) −29.5905 29.5905i −1.23187 1.23187i −0.963245 0.268625i \(-0.913431\pi\)
−0.268625 0.963245i \(-0.586569\pi\)
\(578\) 41.7545 + 41.7545i 1.73676 + 1.73676i
\(579\) 11.0703 0.460064
\(580\) 0.955943 1.35349i 0.0396934 0.0562007i
\(581\) 1.05410 + 18.2641i 0.0437316 + 0.757722i
\(582\) −18.6101 + 18.6101i −0.771413 + 0.771413i
\(583\) 13.3335 + 13.3335i 0.552216 + 0.552216i
\(584\) 12.8432 0.531456
\(585\) 3.82432 0.658323i 0.158116 0.0272183i
\(586\) 7.19676i 0.297295i
\(587\) −26.6462 26.6462i −1.09981 1.09981i −0.994433 0.105375i \(-0.966396\pi\)
−0.105375 0.994433i \(-0.533604\pi\)
\(588\) 10.5667 13.3348i 0.435762 0.549918i
\(589\) 43.6482i 1.79849i
\(590\) −6.37847 37.0537i −0.262597 1.52547i
\(591\) 12.0317i 0.494916i
\(592\) −2.17214 + 2.17214i −0.0892745 + 0.0892745i
\(593\) −15.1889 + 15.1889i −0.623733 + 0.623733i −0.946484 0.322751i \(-0.895392\pi\)
0.322751 + 0.946484i \(0.395392\pi\)
\(594\) −5.62399 −0.230755
\(595\) −21.0017 + 33.7017i −0.860985 + 1.38164i
\(596\) −34.7217 −1.42225
\(597\) −2.30135 + 2.30135i −0.0941878 + 0.0941878i
\(598\) 0.641758 0.641758i 0.0262434 0.0262434i
\(599\) 22.2776i 0.910238i 0.890431 + 0.455119i \(0.150403\pi\)
−0.890431 + 0.455119i \(0.849597\pi\)
\(600\) −1.51516 4.27050i −0.0618560 0.174342i
\(601\) 22.3458i 0.911503i 0.890107 + 0.455752i \(0.150629\pi\)
−0.890107 + 0.455752i \(0.849371\pi\)
\(602\) −1.59728 + 1.79294i −0.0651002 + 0.0730749i
\(603\) 3.43055 + 3.43055i 0.139703 + 0.139703i
\(604\) 23.7706i 0.967210i
\(605\) −4.98077 + 7.05213i −0.202497 + 0.286710i
\(606\) 15.2175 0.618170
\(607\) 0.576027 + 0.576027i 0.0233802 + 0.0233802i 0.718700 0.695320i \(-0.244737\pi\)
−0.695320 + 0.718700i \(0.744737\pi\)
\(608\) −34.1639 + 34.1639i −1.38553 + 1.38553i
\(609\) 0.805321 0.0464788i 0.0326333 0.00188341i
\(610\) 25.6696 4.41880i 1.03933 0.178912i
\(611\) 1.36671 0.0552911
\(612\) −11.5360 11.5360i −0.466315 0.466315i
\(613\) −16.4709 16.4709i −0.665253 0.665253i 0.291361 0.956613i \(-0.405892\pi\)
−0.956613 + 0.291361i \(0.905892\pi\)
\(614\) −21.4714 −0.866514
\(615\) 15.5520 2.67714i 0.627117 0.107953i
\(616\) −6.39583 + 0.369132i −0.257695 + 0.0148728i
\(617\) −3.70013 + 3.70013i −0.148962 + 0.148962i −0.777654 0.628692i \(-0.783590\pi\)
0.628692 + 0.777654i \(0.283590\pi\)
\(618\) 14.6192 + 14.6192i 0.588072 + 0.588072i
\(619\) 39.8840 1.60307 0.801536 0.597946i \(-0.204016\pi\)
0.801536 + 0.597946i \(0.204016\pi\)
\(620\) −22.7434 + 32.2017i −0.913396 + 1.29325i
\(621\) 0.248455i 0.00997015i
\(622\) 15.2621 + 15.2621i 0.611954 + 0.611954i
\(623\) 12.1655 13.6558i 0.487401 0.547107i
\(624\) 5.12566i 0.205191i
\(625\) −19.4097 + 15.7564i −0.776388 + 0.630256i
\(626\) 65.7578i 2.62821i
\(627\) −11.3685 + 11.3685i −0.454013 + 0.454013i
\(628\) −5.29207 + 5.29207i −0.211177 + 0.211177i
\(629\) −6.98117 −0.278357
\(630\) 6.58594 10.5686i 0.262390 0.421062i
\(631\) −33.9725 −1.35242 −0.676211 0.736708i \(-0.736379\pi\)
−0.676211 + 0.736708i \(0.736379\pi\)
\(632\) 7.23957 7.23957i 0.287975 0.287975i
\(633\) 12.1981 12.1981i 0.484833 0.484833i
\(634\) 36.4842i 1.44897i
\(635\) −1.53489 8.91646i −0.0609103 0.353839i
\(636\) 17.1533i 0.680172i
\(637\) 9.52120 + 7.54472i 0.377244 + 0.298933i
\(638\) −1.21247 1.21247i −0.0480022 0.0480022i
\(639\) 15.3087i 0.605605i
\(640\) −15.6065 + 2.68653i −0.616902 + 0.106194i
\(641\) −18.1113 −0.715352 −0.357676 0.933846i \(-0.616431\pi\)
−0.357676 + 0.933846i \(0.616431\pi\)
\(642\) −15.7297 15.7297i −0.620802 0.620802i
\(643\) −32.1062 + 32.1062i −1.26614 + 1.26614i −0.318082 + 0.948063i \(0.603039\pi\)
−0.948063 + 0.318082i \(0.896961\pi\)
\(644\) −0.0920586 1.59507i −0.00362762 0.0628545i
\(645\) −0.556214 + 0.787528i −0.0219009 + 0.0310089i
\(646\) −85.0149 −3.34487
\(647\) −12.9277 12.9277i −0.508241 0.508241i 0.405745 0.913986i \(-0.367012\pi\)
−0.913986 + 0.405745i \(0.867012\pi\)
\(648\) 0.640825 + 0.640825i 0.0251740 + 0.0251740i
\(649\) −21.3439 −0.837821
\(650\) 17.2132 6.10719i 0.675159 0.239544i
\(651\) −19.1598 + 1.10580i −0.750934 + 0.0433398i
\(652\) −33.2396 + 33.2396i −1.30176 + 1.30176i
\(653\) −9.39937 9.39937i −0.367826 0.367826i 0.498858 0.866684i \(-0.333753\pi\)
−0.866684 + 0.498858i \(0.833753\pi\)
\(654\) −12.5315 −0.490020
\(655\) 17.0730 + 12.0583i 0.667099 + 0.471158i
\(656\) 20.8441i 0.813824i
\(657\) 10.0208 + 10.0208i 0.390950 + 0.390950i
\(658\) 2.91736 3.27473i 0.113730 0.127662i
\(659\) 9.13808i 0.355969i 0.984033 + 0.177985i \(0.0569577\pi\)
−0.984033 + 0.177985i \(0.943042\pi\)
\(660\) −14.3108 + 2.46348i −0.557048 + 0.0958909i
\(661\) 28.4837i 1.10789i −0.832554 0.553943i \(-0.813122\pi\)
0.832554 0.553943i \(-0.186878\pi\)
\(662\) 1.87995 1.87995i 0.0730662 0.0730662i
\(663\) 8.23683 8.23683i 0.319892 0.319892i
\(664\) −6.26651 −0.243188
\(665\) −8.05059 34.6765i −0.312188 1.34470i
\(666\) 2.18923 0.0848310
\(667\) 0.0535642 0.0535642i 0.00207401 0.00207401i
\(668\) 15.1493 15.1493i 0.586146 0.586146i
\(669\) 6.48264i 0.250633i
\(670\) 18.6516 + 13.1733i 0.720575 + 0.508927i
\(671\) 14.7864i 0.570821i
\(672\) −15.8621 14.1311i −0.611894 0.545118i
\(673\) 26.8815 + 26.8815i 1.03621 + 1.03621i 0.999319 + 0.0368867i \(0.0117441\pi\)
0.0368867 + 0.999319i \(0.488256\pi\)
\(674\) 28.4466i 1.09572i
\(675\) 2.14984 4.51422i 0.0827473 0.173752i
\(676\) 24.2769 0.933729
\(677\) 1.19694 + 1.19694i 0.0460022 + 0.0460022i 0.729734 0.683731i \(-0.239644\pi\)
−0.683731 + 0.729734i \(0.739644\pi\)
\(678\) −14.7138 + 14.7138i −0.565081 + 0.565081i
\(679\) −33.0264 + 1.90611i −1.26744 + 0.0731496i
\(680\) −11.1104 7.84702i −0.426063 0.300919i
\(681\) 20.0271 0.767440
\(682\) 28.8466 + 28.8466i 1.10459 + 1.10459i
\(683\) 2.41553 + 2.41553i 0.0924275 + 0.0924275i 0.751809 0.659381i \(-0.229182\pi\)
−0.659381 + 0.751809i \(0.729182\pi\)
\(684\) 14.6253 0.559214
\(685\) −4.03393 23.4338i −0.154129 0.895361i
\(686\) 38.4015 6.70863i 1.46618 0.256137i
\(687\) −20.4571 + 20.4571i −0.780487 + 0.780487i
\(688\) 0.900497 + 0.900497i 0.0343311 + 0.0343311i
\(689\) 12.2476 0.466598
\(690\) −0.198383 1.15244i −0.00755233 0.0438728i
\(691\) 41.6703i 1.58521i 0.609735 + 0.792606i \(0.291276\pi\)
−0.609735 + 0.792606i \(0.708724\pi\)
\(692\) 16.4533 + 16.4533i 0.625459 + 0.625459i
\(693\) −5.27832 4.70230i −0.200507 0.178625i
\(694\) 19.4970i 0.740098i
\(695\) −10.0477 + 14.2263i −0.381132 + 0.539634i
\(696\) 0.276310i 0.0104735i
\(697\) 33.4960 33.4960i 1.26875 1.26875i
\(698\) 4.12488 4.12488i 0.156129 0.156129i
\(699\) 6.76767 0.255977
\(700\) 12.1292 29.7777i 0.458442 1.12549i
\(701\) 13.7870 0.520727 0.260364 0.965511i \(-0.416158\pi\)
0.260364 + 0.965511i \(0.416158\pi\)
\(702\) −2.58300 + 2.58300i −0.0974889 + 0.0974889i
\(703\) 4.42536 4.42536i 0.166906 0.166906i
\(704\) 29.3742i 1.10708i
\(705\) 1.01590 1.43838i 0.0382610 0.0541727i
\(706\) 2.88915i 0.108735i
\(707\) 14.2822 + 12.7236i 0.537138 + 0.478520i
\(708\) 13.7293 + 13.7293i 0.515978 + 0.515978i
\(709\) 24.6722i 0.926585i −0.886205 0.463293i \(-0.846668\pi\)
0.886205 0.463293i \(-0.153332\pi\)
\(710\) −12.2236 71.0088i −0.458742 2.66491i
\(711\) 11.2973 0.423680
\(712\) 4.42971 + 4.42971i 0.166010 + 0.166010i
\(713\) −1.27438 + 1.27438i −0.0477257 + 0.0477257i
\(714\) −2.15380 37.3182i −0.0806041 1.39660i
\(715\) −1.75895 10.2181i −0.0657811 0.382135i
\(716\) −3.16223 −0.118178
\(717\) 11.4388 + 11.4388i 0.427191 + 0.427191i
\(718\) 13.8838 + 13.8838i 0.518139 + 0.518139i
\(719\) 29.9117 1.11552 0.557758 0.830003i \(-0.311662\pi\)
0.557758 + 0.830003i \(0.311662\pi\)
\(720\) −5.39447 3.81000i −0.201040 0.141990i
\(721\) 1.49735 + 25.9441i 0.0557642 + 0.966207i
\(722\) 25.6118 25.6118i 0.953171 0.953171i
\(723\) 8.04033 + 8.04033i 0.299023 + 0.299023i
\(724\) 20.6239 0.766482
\(725\) 1.43670 0.509736i 0.0533577 0.0189311i
\(726\) 8.12719i 0.301628i
\(727\) 29.8488 + 29.8488i 1.10703 + 1.10703i 0.993539 + 0.113491i \(0.0362034\pi\)
0.113491 + 0.993539i \(0.463797\pi\)
\(728\) −2.76795 + 3.10702i −0.102587 + 0.115154i
\(729\) 1.00000i 0.0370370i
\(730\) 54.4825 + 38.4798i 2.01649 + 1.42420i
\(731\) 2.89416i 0.107044i
\(732\) −9.51121 + 9.51121i −0.351545 + 0.351545i
\(733\) 3.86707 3.86707i 0.142834 0.142834i −0.632074 0.774908i \(-0.717796\pi\)
0.774908 + 0.632074i \(0.217796\pi\)
\(734\) −38.7082 −1.42875
\(735\) 15.0177 4.41240i 0.553935 0.162754i
\(736\) −1.99493 −0.0735342
\(737\) 9.16599 9.16599i 0.337634 0.337634i
\(738\) −10.5040 + 10.5040i −0.386659 + 0.386659i
\(739\) 11.9735i 0.440454i 0.975449 + 0.220227i \(0.0706797\pi\)
−0.975449 + 0.220227i \(0.929320\pi\)
\(740\) 5.57073 0.958952i 0.204784 0.0352518i
\(741\) 10.4427i 0.383621i
\(742\) 26.1436 29.3462i 0.959763 1.07733i
\(743\) −12.0406 12.0406i −0.441728 0.441728i 0.450864 0.892593i \(-0.351116\pi\)
−0.892593 + 0.450864i \(0.851116\pi\)
\(744\) 6.57385i 0.241009i
\(745\) −26.0918 18.4281i −0.955931 0.675154i
\(746\) 61.5467 2.25338
\(747\) −4.88941 4.88941i −0.178894 0.178894i
\(748\) −30.8227 + 30.8227i −1.12699 + 1.12699i
\(749\) −1.61109 27.9148i −0.0588679 1.01998i
\(750\) 6.36745 22.6556i 0.232506 0.827264i
\(751\) −24.1119 −0.879855 −0.439928 0.898033i \(-0.644996\pi\)
−0.439928 + 0.898033i \(0.644996\pi\)
\(752\) −1.64472 1.64472i −0.0599767 0.0599767i
\(753\) −4.91467 4.91467i −0.179100 0.179100i
\(754\) −1.11373 −0.0405598
\(755\) 12.6159 17.8625i 0.459141 0.650085i
\(756\) 0.370525 + 6.41995i 0.0134759 + 0.233491i
\(757\) 29.2896 29.2896i 1.06455 1.06455i 0.0667825 0.997768i \(-0.478727\pi\)
0.997768 0.0667825i \(-0.0212733\pi\)
\(758\) −32.7558 32.7558i −1.18975 1.18975i
\(759\) −0.663839 −0.0240958
\(760\) 12.0171 2.06864i 0.435906 0.0750374i
\(761\) 32.3002i 1.17088i −0.810716 0.585440i \(-0.800922\pi\)
0.810716 0.585440i \(-0.199078\pi\)
\(762\) 6.02230 + 6.02230i 0.218165 + 0.218165i
\(763\) −11.7613 10.4778i −0.425787 0.379320i
\(764\) 4.71018i 0.170408i
\(765\) −2.54621 14.7914i −0.0920584 0.534784i
\(766\) 1.16207i 0.0419874i
\(767\) −9.80287 + 9.80287i −0.353961 + 0.353961i
\(768\) −5.00678 + 5.00678i −0.180667 + 0.180667i
\(769\) −18.4310 −0.664640 −0.332320 0.943167i \(-0.607831\pi\)
−0.332320 + 0.943167i \(0.607831\pi\)
\(770\) −28.2379 17.5968i −1.01762 0.634144i
\(771\) 14.2679 0.513845
\(772\) −19.0260 + 19.0260i −0.684761 + 0.684761i
\(773\) −17.7963 + 17.7963i