Properties

Label 105.2.m.a.97.7
Level 105
Weight 2
Character 105.97
Analytic conductor 0.838
Analytic rank 0
Dimension 16
CM no
Inner twists 4

Related objects

Downloads

Learn more about

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 97.7
Root \(-0.944649 + 1.05244i\) of \(x^{16} - 4 x^{14} + 6 x^{12} - 12 x^{10} + 33 x^{8} - 48 x^{6} + 96 x^{4} - 256 x^{2} + 256\)
Character \(\chi\) \(=\) 105.97
Dual form 105.2.m.a.13.7

$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

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

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 0.998546 + 0.0538973i \(0.0171644\pi\)
0.0538973 + 0.998546i \(0.482836\pi\)
\(3\) −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 0.516150 0.856498i \(-0.327365\pi\)
−0.856498 + 0.516150i \(0.827365\pi\)
\(14\) 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 0.164807 0.986326i \(-0.447300\pi\)
0.986326 0.164807i \(-0.0527002\pi\)
\(18\) −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 −0.725186 0.688553i \(-0.758246\pi\)
0.688553 + 0.725186i \(0.258246\pi\)
\(24\) 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 \(-0.990988\pi\)
0.999599 0.0283083i \(-0.00901200\pi\)
\(30\) 3.84448 2.71528i 0.701903 0.495739i
\(31\) 7.25379i 1.30282i 0.758726 + 0.651410i \(0.225822\pi\)
−0.758726 + 0.651410i \(0.774178\pi\)
\(32\) 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 0.644065 0.764971i \(-0.277247\pi\)
−0.764971 + 0.644065i \(0.777247\pi\)
\(38\) −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 \(0.185787\pi\)
−0.834447 + 0.551087i \(0.814213\pi\)
\(42\) −4.15824 + 3.70445i −0.641630 + 0.571608i
\(43\) 0.304889 0.304889i 0.0464952 0.0464952i −0.683477 0.729972i \(-0.739533\pi\)
0.729972 + 0.683477i \(0.239533\pi\)
\(44\) 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 −0.746553 0.665326i \(-0.768293\pi\)
0.665326 + 0.746553i \(0.268293\pi\)
\(48\) −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 −0.961228 0.275756i \(-0.911072\pi\)
0.275756 + 0.961228i \(0.411072\pi\)
\(54\) 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 \(-0.884725\pi\)
0.935138 0.354284i \(-0.115275\pi\)
\(62\) −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 0.465788 0.884896i \(-0.345771\pi\)
−0.884896 + 0.465788i \(0.845771\pi\)
\(68\) 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 −0.981527 0.191323i \(-0.938722\pi\)
−0.191323 0.981527i \(-0.561278\pi\)
\(74\) 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 \(-0.780785\pi\)
0.772084 0.635521i \(-0.219215\pi\)
\(80\) 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 0.922553 0.385871i \(-0.126099\pi\)
−0.385871 + 0.922553i \(0.626099\pi\)
\(84\) −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 −0.0975276 0.995233i \(-0.531093\pi\)
0.995233 + 0.0975276i \(0.0310934\pi\)
\(98\) −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 \(0.117117\pi\)
−0.933073 + 0.359687i \(0.882883\pi\)
\(102\) −9.99031 9.99031i −0.989188 0.989188i
\(103\) 6.94538 + 6.94538i 0.684349 + 0.684349i 0.960977 0.276628i \(-0.0892171\pi\)
−0.276628 + 0.960977i \(0.589217\pi\)
\(104\) 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 0.246664 0.969101i \(-0.420666\pi\)
−0.969101 + 0.246664i \(0.920666\pi\)
\(108\) 1.71866 + 1.71866i 0.165378 + 0.165378i
\(109\) 5.95352i 0.570244i −0.958491 0.285122i \(-0.907966\pi\)
0.958491 0.285122i \(-0.0920341\pi\)
\(110\) 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 −0.297217 0.954810i \(-0.596058\pi\)
0.954810 + 0.297217i \(0.0960585\pi\)
\(114\) 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 0.822560 0.568678i \(-0.192545\pi\)
−0.568678 + 0.822560i \(0.692545\pi\)
\(128\) −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 \(-0.866103\pi\)
0.912824 0.408353i \(-0.133897\pi\)
\(132\) −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 0.951152 0.308724i \(-0.0999019\pi\)
−0.308724 + 0.951152i \(0.599902\pi\)
\(138\) 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 \(0.198967\pi\)
−0.810920 + 0.585157i \(0.801033\pi\)
\(150\) 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 −0.788633 0.614864i \(-0.789211\pi\)
0.614864 + 0.788633i \(0.289211\pi\)
\(158\) 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 −0.0739001 + 0.997266i \(0.523545\pi\)
−0.997266 + 0.0739001i \(0.976455\pi\)
\(164\) −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 −0.423555 0.905870i \(-0.639218\pi\)
0.905870 + 0.423555i \(0.139218\pi\)
\(168\) −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 0.401288 0.915952i \(-0.368563\pi\)
−0.915952 + 0.401288i \(0.868563\pi\)
\(174\) −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 \(0.0154829\pi\)
−0.998817 + 0.0486218i \(0.984517\pi\)
\(180\) −3.13538 4.43929i −0.233697 0.330885i
\(181\) 8.48528i 0.630706i −0.948974 0.315353i \(-0.897877\pi\)
0.948974 0.315353i \(-0.102123\pi\)
\(182\) −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 −0.930289 0.366827i \(-0.880444\pi\)
0.366827 + 0.930289i \(0.380444\pi\)
\(194\) 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 0.335790 0.941937i \(-0.390997\pi\)
−0.941937 + 0.335790i \(0.890997\pi\)
\(198\) 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 0.843730 0.536768i \(-0.180355\pi\)
−0.536768 + 0.843730i \(0.680355\pi\)
\(224\) 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 −0.998295 0.0583764i \(-0.981408\pi\)
0.0583764 + 0.998295i \(0.481408\pi\)
\(228\) −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 −0.846266 0.532760i \(-0.821155\pi\)
0.532760 + 0.846266i \(0.321155\pi\)
\(234\) 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 \(0.175262\pi\)
−0.852210 + 0.523200i \(0.824738\pi\)
\(240\) 1.12039 6.50855i 0.0723208 0.420125i
\(241\) 11.3707i 0.732454i 0.930526 + 0.366227i \(0.119351\pi\)
−0.930526 + 0.366227i \(0.880649\pi\)
\(242\) −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 \(-0.929606\pi\)
0.975646 0.219352i \(-0.0703944\pi\)
\(252\) 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 −0.947899 0.318570i \(-0.896797\pi\)
0.318570 + 0.947899i \(0.396797\pi\)
\(258\) −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 0.130744 0.991416i \(-0.458263\pi\)
0.991416 0.130744i \(-0.0417367\pi\)
\(264\) −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 \(-0.867192\pi\)
0.914215 0.405229i \(-0.132808\pi\)
\(272\) 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 0.644282 0.764788i \(-0.277156\pi\)
−0.764788 + 0.644282i \(0.777156\pi\)
\(278\) −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 0.999429 0.0338017i \(-0.0107615\pi\)
−0.0338017 + 0.999429i \(0.510761\pi\)
\(284\) 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 0.774192 0.632951i \(-0.218157\pi\)
−0.632951 + 0.774192i \(0.718157\pi\)
\(294\) 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 −0.882319 0.470652i \(-0.844019\pi\)
0.470652 + 0.882319i \(0.344019\pi\)
\(308\) −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 \(-0.906102\pi\)
0.956805 0.290730i \(-0.0938981\pi\)
\(312\) −1.11211 1.11211i −0.0629611 0.0629611i
\(313\) −22.0904 22.0904i −1.24862 1.24862i −0.956329 0.292293i \(-0.905582\pi\)
−0.292293 0.956329i \(-0.594418\pi\)
\(314\) −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 0.273490 0.961875i \(-0.411822\pi\)
−0.961875 + 0.273490i \(0.911822\pi\)
\(318\) 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 0.397180 0.917741i \(-0.369989\pi\)
−0.917741 + 0.397180i \(0.869989\pi\)
\(338\) 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 0.860708 0.509099i \(-0.170021\pi\)
−0.509099 + 0.860708i \(0.670021\pi\)
\(348\) −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 0.732464 0.680806i \(-0.238370\pi\)
−0.680806 + 0.732464i \(0.738370\pi\)
\(354\) 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 \(-0.920831\pi\)
0.969229 0.246160i \(-0.0791688\pi\)
\(360\) 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 −0.959723 0.280948i \(-0.909351\pi\)
0.280948 + 0.959723i \(0.409351\pi\)
\(368\) −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 0.0732339 0.997315i \(-0.476668\pi\)
0.997315 0.0732339i \(-0.0233320\pi\)
\(374\) −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 \(0.191213\pi\)
−0.824933 + 0.565230i \(0.808787\pi\)
\(380\) 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 0.717010 0.697063i \(-0.245510\pi\)
−0.697063 + 0.717010i \(0.745510\pi\)
\(384\) 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 \(0.228323\pi\)
−0.753584 + 0.657352i \(0.771677\pi\)
\(390\) −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 −0.130109 0.991500i \(-0.541533\pi\)
0.991500 + 0.130109i \(0.0415327\pi\)
\(398\) 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 0.304935 0.952373i \(-0.401365\pi\)
−0.952373 + 0.304935i \(0.901365\pi\)
\(434\) 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 −0.973125 0.230279i \(-0.926036\pi\)
0.230279 + 0.973125i \(0.426036\pi\)
\(444\) −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 \(-0.947033\pi\)
0.986187 0.165635i \(-0.0529673\pi\)
\(450\) −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 0.918919 0.394447i \(-0.129064\pi\)
−0.394447 + 0.918919i \(0.629064\pi\)
\(458\) 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 \(0.246041\pi\)
−0.715846 + 0.698259i \(0.753959\pi\)
\(462\) 11.1103 9.89780i 0.516897 0.460488i
\(463\) 7.70220 7.70220i 0.357951 0.357951i −0.505106 0.863057i \(-0.668547\pi\)
0.863057 + 0.505106i \(0.168547\pi\)
\(464\) 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 −0.747735 0.663997i \(-0.768859\pi\)
0.663997 + 0.747735i \(0.268859\pi\)
\(468\) 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 0.433969 0.900928i \(-0.357113\pi\)
−0.900928 + 0.433969i \(0.857113\pi\)
\(488\) 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 \(0.178462\pi\)
−0.846907 + 0.531741i \(0.821538\pi\)
\(500\) −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 0.983153 0.182786i \(-0.0585115\pi\)
−0.182786 + 0.983153i \(0.558511\pi\)
\(504\) −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 \(0.0552552\pi\)
−0.984971 + 0.172719i \(0.944745\pi\)
\(522\) 0.453791 + 0.453791i 0.0198619 + 0.0198619i
\(523\) 1.23149 + 1.23149i 0.0538493 + 0.0538493i 0.733519 0.679669i \(-0.237877\pi\)
−0.679669 + 0.733519i \(0.737877\pi\)
\(524\) 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 0.784333 0.620340i \(-0.213005\pi\)
−0.620340 + 0.784333i \(0.713005\pi\)
\(548\) −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 0.271238 0.962512i \(-0.412567\pi\)
−0.962512 + 0.271238i \(0.912567\pi\)
\(558\) −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 −0.999999 0.00103054i \(-0.999672\pi\)
−0.00103054 0.999999i \(-0.500328\pi\)
\(564\) 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 \(-0.998147\pi\)
0.999983 0.00582283i \(-0.00185348\pi\)
\(570\) −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 −0.268625 + 0.963245i \(0.586569\pi\)
−0.963245 + 0.268625i \(0.913431\pi\)
\(578\) 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 −0.105375 + 0.994433i \(0.533604\pi\)
−0.994433 + 0.105375i \(0.966396\pi\)
\(588\) 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 0.322751 0.946484i \(-0.395392\pi\)
−0.946484 + 0.322751i \(0.895392\pi\)
\(594\) −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 \(-0.849597\pi\)
0.890431 0.455119i \(-0.150403\pi\)
\(600\) −1.51516 + 4.27050i −0.0618560 + 0.174342i
\(601\) 22.3458i 0.911503i −0.890107 0.455752i \(-0.849371\pi\)
0.890107 0.455752i \(-0.150629\pi\)
\(602\) −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 −0.695320 0.718700i \(-0.744737\pi\)
0.718700 + 0.695320i \(0.244737\pi\)
\(608\) −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 −0.956613 0.291361i \(-0.905892\pi\)
0.291361 + 0.956613i \(0.405892\pi\)
\(614\) −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 0.628692 0.777654i \(-0.283590\pi\)
−0.777654 + 0.628692i \(0.783590\pi\)
\(618\) 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 −0.948063 0.318082i \(-0.896961\pi\)
−0.318082 0.948063i \(-0.603039\pi\)
\(644\) −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 −0.913986 0.405745i \(-0.867012\pi\)
0.405745 + 0.913986i \(0.367012\pi\)
\(648\) 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 −0.866684 0.498858i \(-0.833753\pi\)
0.498858 + 0.866684i \(0.333753\pi\)
\(654\) −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 \(-0.943042\pi\)
0.984033 0.177985i \(-0.0569577\pi\)
\(660\) −14.3108 2.46348i −0.557048 0.0958909i
\(661\) 28.4837i 1.10789i 0.832554 + 0.553943i \(0.186878\pi\)
−0.832554 + 0.553943i \(0.813122\pi\)
\(662\) 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 0.0368867 0.999319i \(-0.488256\pi\)
0.999319 0.0368867i \(-0.0117441\pi\)
\(674\) 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 −0.683731 0.729734i \(-0.739644\pi\)
0.729734 + 0.683731i \(0.239644\pi\)
\(678\) −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 −0.659381 0.751809i \(-0.729182\pi\)
0.751809 + 0.659381i \(0.229182\pi\)
\(684\) 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 \(-0.708724\pi\)
0.609735 0.792606i \(-0.291276\pi\)
\(692\) 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 \(0.153332\pi\)
−0.886205 + 0.463293i \(0.846668\pi\)
\(710\) −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 0.113491 0.993539i \(-0.463797\pi\)
0.993539 0.113491i \(-0.0362034\pi\)
\(728\) −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 0.774908 0.632074i \(-0.217796\pi\)
−0.632074 + 0.774908i \(0.717796\pi\)
\(734\) −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 \(-0.929320\pi\)
0.975449 0.220227i \(-0.0706797\pi\)
\(740\) 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 −0.892593 0.450864i \(-0.851116\pi\)
0.450864 + 0.892593i \(0.351116\pi\)
\(744\) 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 0.997768 + 0.0667825i \(0.0212733\pi\)
0.0667825 + 0.997768i \(0.478727\pi\)
\(758\) −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 \(0.199078\pi\)
−0.810716 + 0.585440i \(0.800922\pi\)
\(762\) 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