Properties

Label 105.2.m.a.13.8
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 13.8
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 \(\chi\) \(=\) 105.13
Dual form 105.2.m.a.97.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.48838 - 1.48838i) q^{2} +(0.707107 - 0.707107i) q^{3} -2.43055i q^{4} +(-1.28999 + 1.82645i) q^{5} -2.10489i q^{6} +(-1.97552 + 1.75993i) q^{7} +(-0.640825 - 0.640825i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(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} +(-1.97552 + 1.75993i) 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} +(4.27759 + 4.80159i) 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} +(-0.666037 - 5.87847i) 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} +(3.70445 + 4.15824i) 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} +(1.75993 + 1.97552i) 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} +(-9.74071 - 7.75808i) 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} +(5.27832 - 4.70230i) 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} +(-9.15086 - 11.5481i) 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
\(7\) −1.97552 + 1.75993i −0.746675 + 0.665189i
\(8\) −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 \(-0.672635\pi\)
0.856498 + 0.516150i \(0.172635\pi\)
\(14\) −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 \(-0.947300\pi\)
−0.164807 0.986326i \(-0.552700\pi\)
\(18\) −1.48838 1.48838i −0.350815 0.350815i
\(19\) 6.01729 1.38046 0.690231 0.723589i \(-0.257509\pi\)
0.690231 + 0.723589i \(0.257509\pi\)
\(20\) 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
\(28\) 4.27759 + 4.80159i 0.808389 + 0.907416i
\(29\) 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 \(0.225822\pi\)
−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
\(35\) −0.666037 5.87847i −0.112581 0.993643i
\(36\) −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 \(0.185787\pi\)
−0.834447 + 0.551087i \(0.814213\pi\)
\(42\) 3.70445 + 4.15824i 0.571608 + 0.641630i
\(43\) 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 0.746553 0.665326i \(-0.231707\pi\)
−0.665326 + 0.746553i \(0.731707\pi\)
\(48\) 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 \(-0.674068\pi\)
−0.519999 + 0.854167i \(0.674068\pi\)
\(60\) 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
\(63\) 1.75993 + 1.97552i 0.221730 + 0.248892i
\(64\) 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
\(70\) −9.74071 7.75808i −1.16424 0.927268i
\(71\) 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 \(-0.438722\pi\)
0.981527 0.191323i \(-0.0612778\pi\)
\(74\) 2.18923i 0.254493i
\(75\) −4.51422 2.14984i −0.521257 0.248242i
\(76\) 14.6253i 1.67764i
\(77\) 5.27832 4.70230i 0.601521 0.535876i
\(78\) −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 −0.922553 0.385871i \(-0.873901\pi\)
0.385871 + 0.922553i \(0.373901\pi\)
\(84\) 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 \(-0.380603\pi\)
0.366363 + 0.930472i \(0.380603\pi\)
\(90\) 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 \(-0.468907\pi\)
−0.995233 + 0.0975276i \(0.968907\pi\)
\(98\) −9.15086 11.5481i −0.924376 1.16654i
\(99\) 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 \(-0.910783\pi\)
0.276628 + 0.960977i \(0.410783\pi\)
\(104\) −1.57277 −0.154222
\(105\) −4.62766 3.68575i −0.451614 0.359692i
\(106\) −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
\(112\) −5.83473 + 5.19798i −0.551330 + 0.491163i
\(113\) 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 \(-0.866103\pi\)
0.912824 0.408353i \(-0.133897\pi\)
\(132\) 4.59204 + 4.59204i 0.399686 + 0.399686i
\(133\) −11.8873 + 10.5900i −1.03076 + 0.918268i
\(134\) 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 \(-0.392841\pi\)
0.330328 + 0.943866i \(0.392841\pi\)
\(140\) −14.2879 + 1.61884i −1.20755 + 0.136817i
\(141\) 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
\(147\) −4.34743 5.48633i −0.358570 0.452505i
\(148\) 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 0.788633 0.614864i \(-0.210789\pi\)
−0.614864 + 0.788633i \(0.710789\pi\)
\(158\) 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 0.423555 0.905870i \(-0.360782\pi\)
−0.905870 + 0.423555i \(0.860782\pi\)
\(168\) 1.79034 1.59496i 0.138128 0.123054i
\(169\) 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 \(-0.631437\pi\)
0.915952 + 0.401288i \(0.131437\pi\)
\(174\) 0.641758 0.0486515
\(175\) 11.5959 + 6.36666i 0.876570 + 0.481274i
\(176\) −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 \(-0.897877\pi\)
0.948974 0.315353i \(-0.102123\pi\)
\(182\) 6.42885 + 7.21638i 0.476538 + 0.534913i
\(183\) −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 \(-0.536801\pi\)
−0.115356 + 0.993324i \(0.536801\pi\)
\(200\) −1.94832 + 4.09107i −0.137767 + 0.289283i
\(201\) 4.85153i 0.342201i
\(202\) 10.7604 + 10.7604i 0.757101 + 0.757101i
\(203\) −0.536583 0.602314i −0.0376607 0.0422741i
\(204\) 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
\(210\) −12.3735 + 1.40193i −0.853854 + 0.0967426i
\(211\) −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
\(217\) −12.7661 14.3300i −0.866622 0.972782i
\(218\) 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 \(-0.819645\pi\)
0.536768 + 0.843730i \(0.319645\pi\)
\(224\) −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 \(-0.0185924\pi\)
−0.0583764 + 0.998295i \(0.518592\pi\)
\(228\) −10.3417 10.3417i −0.684894 0.684894i
\(229\) −28.9307 −1.91180 −0.955898 0.293699i \(-0.905114\pi\)
−0.955898 + 0.293699i \(0.905114\pi\)
\(230\) 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
\(238\) 27.9109 24.8650i 1.80920 1.61176i
\(239\) 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 \(0.119351\pi\)
−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
\(245\) 11.6614 + 10.4408i 0.745022 + 0.667040i
\(246\) 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 \(-0.0703944\pi\)
\(252\) 4.80159 4.27759i 0.302472 0.269463i
\(253\) 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 \(-0.103203\pi\)
−0.318570 + 0.947899i \(0.603203\pi\)
\(258\) 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 \(-0.656788\pi\)
−0.472888 + 0.881123i \(0.656788\pi\)
\(270\) 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
\(273\) 3.05425 + 3.42839i 0.184852 + 0.207496i
\(274\) 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
\(280\) −3.34026 + 4.19388i −0.199619 + 0.250632i
\(281\) 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 \(-0.989239\pi\)
0.0338017 + 0.999429i \(0.489239\pi\)
\(284\) 37.2087i 2.20793i
\(285\) 2.28260 + 13.2600i 0.135210 + 0.785457i
\(286\) 9.76010i 0.577127i
\(287\) −12.4204 13.9419i −0.733155 0.822966i
\(288\) −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 \(-0.781843\pi\)
0.632951 + 0.774192i \(0.281843\pi\)
\(294\) −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 \(-0.155981\pi\)
−0.470652 + 0.882319i \(0.655981\pi\)
\(308\) −11.4292 12.8292i −0.651238 0.731014i
\(309\) 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 0.292293 0.956329i \(-0.405582\pi\)
0.956329 0.292293i \(-0.0944182\pi\)
\(314\) 6.48134 0.365763
\(315\) −5.87847 + 0.666037i −0.331214 + 0.0375269i
\(316\) 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
\(322\) 1.03313 0.920387i 0.0575743 0.0512912i
\(323\) −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
\(343\) 10.6468 + 15.1541i 0.574871 + 0.818244i
\(344\) 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 \(-0.523632\pi\)
−0.0741746 + 0.997245i \(0.523632\pi\)
\(350\) 26.7352 7.78315i 1.42905 0.416027i
\(351\) −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 \(-0.761630\pi\)
0.680806 + 0.732464i \(0.261630\pi\)
\(354\) 16.8146i 0.893687i
\(355\) −19.7481 + 27.9607i −1.04812 + 1.48400i
\(356\) 16.8012i 0.890463i
\(357\) 13.2601 11.8130i 0.701797 0.625209i
\(358\) −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 0.959723 0.280948i \(-0.0906487\pi\)
−0.280948 + 0.959723i \(0.590649\pi\)
\(368\) −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
\(378\) 4.15824 3.70445i 0.213877 0.190536i
\(379\) 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 −0.717010 0.697063i \(-0.754490\pi\)
0.697063 + 0.717010i \(0.254490\pi\)
\(384\) −7.08211 −0.361407
\(385\) 1.77957 + 15.7065i 0.0906950 + 0.800478i
\(386\) −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
\(392\) −4.97206 + 3.93992i −0.251127 + 0.198996i
\(393\) −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 \(-0.458467\pi\)
−0.991500 + 0.130109i \(0.958467\pi\)
\(398\) −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 \(-0.520813\pi\)
−0.0653386 + 0.997863i \(0.520813\pi\)
\(410\) −32.7352 + 5.63508i −1.61668 + 0.278297i
\(411\) 10.6341i 0.524540i
\(412\) 16.8811 + 16.8811i 0.831672 + 0.831672i
\(413\) 15.7812 14.0589i 0.776540 0.691795i
\(414\) 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 \(-0.421211\pi\)
0.245003 + 0.969522i \(0.421211\pi\)
\(420\) −8.95840 + 11.2478i −0.437125 + 0.548835i
\(421\) −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
\(427\) 9.73958 + 10.9327i 0.471332 + 0.529069i
\(428\) 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 \(-0.598635\pi\)
0.952373 + 0.304935i \(0.0986349\pi\)
\(434\) −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 \(-0.290045\pi\)
0.612795 + 0.790242i \(0.290045\pi\)
\(440\) −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
\(448\) 19.3484 + 21.7185i 0.914124 + 1.02610i
\(449\) 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
\(455\) −8.03104 6.39640i −0.376501 0.299868i
\(456\) −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 \(0.246041\pi\)
−0.715846 + 0.698259i \(0.753959\pi\)
\(462\) −9.89780 11.1103i −0.460488 0.516897i
\(463\) 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 0.747735 0.663997i \(-0.231141\pi\)
−0.663997 + 0.747735i \(0.731141\pi\)
\(468\) −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 \(-0.470181\pi\)
0.0935425 + 0.995615i \(0.470181\pi\)
\(480\) 14.6653 + 10.3578i 0.669374 + 0.472765i
\(481\) 1.80498i 0.0823001i
\(482\) 16.9240 + 16.9240i 0.770867 + 0.770867i
\(483\) 0.490826 0.437262i 0.0223334 0.0198961i
\(484\) 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
\(490\) 32.8966 1.81673i 1.48612 0.0820714i
\(491\) −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
\(497\) −30.2427 + 26.9423i −1.35657 + 1.20853i
\(498\) 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 −0.983153 0.182786i \(-0.941489\pi\)
0.182786 + 0.983153i \(0.441489\pi\)
\(504\) 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 \(-0.377818\pi\)
0.374489 + 0.927231i \(0.377818\pi\)
\(510\) −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
\(518\) −3.85289 4.32486i −0.169286 0.190024i
\(519\) 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 \(-0.762123\pi\)
0.679669 + 0.733519i \(0.262123\pi\)
\(524\) −22.7199 −0.992524
\(525\) 12.7015 3.69766i 0.554338 0.161379i
\(526\) 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
\(532\) 25.7395 + 28.8926i 1.11595 + 1.25265i
\(533\) 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
\(553\) −19.8823 22.3179i −0.845483 0.949054i
\(554\) 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
\(560\) −1.96715 17.3622i −0.0831275 0.733686i
\(561\) 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 \(-0.499672\pi\)
0.999999 0.00103054i \(-0.000328032\pi\)
\(564\) 1.91413i 0.0805993i
\(565\) −21.7849 + 3.75008i −0.916497 + 0.157767i
\(566\) 48.3556i 2.03254i
\(567\) 1.97552 1.75993i 0.0829638 0.0739099i
\(568\) −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 \(0.0865693\pi\)
0.268625 + 0.963245i \(0.413431\pi\)
\(578\) 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 \(0.0336041\pi\)
0.105375 + 0.994433i \(0.466396\pi\)
\(588\) −13.3348 + 10.5667i −0.549918 + 0.435762i
\(589\) 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 \(-0.604608\pi\)
0.946484 + 0.322751i \(0.104608\pi\)
\(594\) 5.62399 0.230755
\(595\) −24.7395 + 31.0618i −1.01422 + 1.27341i
\(596\) −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 \(-0.849371\pi\)
0.890107 0.455752i \(-0.150629\pi\)
\(602\) −1.79294 + 1.59728i −0.0730749 + 0.0651002i
\(603\) 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 \(-0.255263\pi\)
−0.718700 + 0.695320i \(0.755263\pi\)
\(608\) 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 \(-0.795984\pi\)
−0.801536 + 0.597946i \(0.795984\pi\)
\(620\) −22.7434 + 32.2017i −0.913396 + 1.29325i
\(621\) 0.248455i 0.00997015i
\(622\) −15.2621 15.2621i −0.611954 0.611954i
\(623\) −13.6558 + 12.1655i −0.547107 + 0.487401i
\(624\) 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
\(630\) −7.75808 + 9.74071i −0.309089 + 0.388079i
\(631\) −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
\(637\) −7.54472 9.52120i −0.298933 0.377244i
\(638\) −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 \(-0.396961\pi\)
0.948063 0.318082i \(-0.103039\pi\)
\(644\) 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 \(-0.132988\pi\)
−0.405745 + 0.913986i \(0.632988\pi\)
\(648\) 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
\(658\) −3.27473 + 2.91736i −0.127662 + 0.113730i
\(659\) 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 \(0.186878\pi\)
−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
\(665\) −4.00774 35.3725i −0.155413 1.37169i
\(666\) 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
\(672\) 14.1311 + 15.8621i 0.545118 + 0.611894i
\(673\) 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 0.683731 0.729734i \(-0.260356\pi\)
−0.729734 + 0.683731i \(0.760356\pi\)
\(678\) 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 \(-0.708724\pi\)
0.609735 0.792606i \(-0.291276\pi\)
\(692\) −16.4533 16.4533i −0.625459 0.625459i
\(693\) −4.70230 5.27832i −0.178625 0.200507i
\(694\) 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
\(700\) 15.4745 28.1845i 0.584881 1.06527i
\(701\) 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
\(707\) −12.7236 14.2822i −0.478520 0.537138i
\(708\) 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 \(-0.688338\pi\)
−0.557758 + 0.830003i \(0.688338\pi\)
\(720\) 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 \(-0.963797\pi\)
−0.113491 0.993539i \(-0.536203\pi\)
\(728\) 3.10702 2.76795i 0.115154 0.102587i
\(729\) 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 \(-0.782204\pi\)
0.632074 + 0.774908i \(0.282204\pi\)
\(734\) 38.7082 1.42875
\(735\) 15.6287 0.863100i 0.576472 0.0318359i
\(736\) −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
\(742\) 29.3462 26.1436i 1.07733 0.959763i
\(743\) −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 \(0.199078\pi\)
−0.810716 + 0.585440i \(0.800922\pi\)
\(762\) −6.02230 6.02230i −0.218165 0.218165i
\(763\) −10.4778 11.7613i −0.379320 0.425787i
\(764\) 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 \(-0.392169\pi\)
0.332320 + 0.943167i \(0.392169\pi\)
\(770\) 26.0259 + 20.7286i 0.937910 + 0.747007i
\(771\) 14.2679 0.513845
\(772\) −19.0260 + 19.0260i −0.684761 + 0.684761i
\(773\) 17.7963