Properties

Label 525.2.m.b.118.2
Level 525
Weight 2
Character 525.118
Analytic conductor 4.192
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.19214610612\)
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: \( 2^{8} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 118.2
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 \(\chi\) \(=\) 525.118
Dual form 525.2.m.b.307.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.48838 + 1.48838i) q^{2} +(0.707107 - 0.707107i) q^{3} -2.43055i q^{4} +2.10489i q^{6} +(1.75993 - 1.97552i) q^{7} +(0.640825 + 0.640825i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-1.48838 + 1.48838i) q^{2} +(0.707107 - 0.707107i) q^{3} -2.43055i q^{4} +2.10489i q^{6} +(1.75993 - 1.97552i) q^{7} +(0.640825 + 0.640825i) q^{8} -1.00000i q^{9} -2.67187 q^{11} +(-1.71866 - 1.71866i) q^{12} +(1.22714 - 1.22714i) q^{13} +(0.320879 + 5.55976i) q^{14} +2.95352 q^{16} +(-4.74624 - 4.74624i) q^{17} +(1.48838 + 1.48838i) q^{18} -6.01729 q^{19} +(-0.152445 - 2.64136i) q^{21} +(3.97676 - 3.97676i) q^{22} +(0.175684 + 0.175684i) q^{23} +0.906263 q^{24} +3.65291i q^{26} +(-0.707107 - 0.707107i) q^{27} +(-4.80159 - 4.27759i) q^{28} +0.304889i q^{29} -7.25379i q^{31} +(-5.67761 + 5.67761i) q^{32} +(-1.88930 + 1.88930i) q^{33} +14.1284 q^{34} -2.43055 q^{36} +(0.735441 - 0.735441i) q^{37} +(8.95602 - 8.95602i) q^{38} -1.73544i q^{39} -7.05736i q^{41} +(4.15824 + 3.70445i) q^{42} +(-0.304889 - 0.304889i) q^{43} +6.49412i q^{44} -0.522969 q^{46} +(0.556866 + 0.556866i) q^{47} +(2.08845 - 2.08845i) q^{48} +(-0.805321 - 6.95352i) q^{49} -6.71220 q^{51} +(-2.98263 - 2.98263i) q^{52} +(4.99031 + 4.99031i) q^{53} +2.10489 q^{54} +(2.39376 - 0.138155i) q^{56} +(-4.25487 + 4.25487i) q^{57} +(-0.453791 - 0.453791i) q^{58} +7.98837 q^{59} +5.53409i q^{61} +(10.7964 + 10.7964i) q^{62} +(-1.97552 - 1.75993i) q^{63} -10.9939i q^{64} -5.62399i q^{66} +(3.43055 - 3.43055i) q^{67} +(-11.5360 + 11.5360i) q^{68} +0.248455 q^{69} +15.3087 q^{71} +(0.640825 - 0.640825i) q^{72} +(10.0208 - 10.0208i) q^{73} +2.18923i q^{74} +14.6253i q^{76} +(-4.70230 + 5.27832i) q^{77} +(2.58300 + 2.58300i) q^{78} +11.2973i q^{79} -1.00000 q^{81} +(10.5040 + 10.5040i) q^{82} +(-4.88941 + 4.88941i) q^{83} +(-6.41995 + 0.370525i) q^{84} +0.907583 q^{86} +(0.215589 + 0.215589i) q^{87} +(-1.71220 - 1.71220i) q^{88} -6.91251 q^{89} +(-0.264559 - 4.58392i) q^{91} +(0.427009 - 0.427009i) q^{92} +(-5.12921 - 5.12921i) q^{93} -1.65766 q^{94} +8.02936i q^{96} +(-8.84137 - 8.84137i) q^{97} +(11.5481 + 9.15086i) q^{98} +2.67187i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{7} - 24q^{8} + O(q^{10}) \) \( 16q + 8q^{7} - 24q^{8} - 16q^{11} - 48q^{16} + 8q^{21} + 16q^{22} + 40q^{23} - 24q^{28} - 48q^{32} - 16q^{36} - 32q^{37} + 16q^{42} + 16q^{43} + 64q^{46} - 16q^{51} - 24q^{53} + 24q^{56} - 8q^{57} - 32q^{58} - 8q^{63} + 32q^{67} + 64q^{71} - 24q^{72} + 24q^{77} + 8q^{78} - 16q^{81} + 64q^{86} + 64q^{88} - 48q^{91} + 40q^{92} - 24q^{93} + 96q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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 \(0.517164\pi\)
−0.998546 + 0.0538973i \(0.982836\pi\)
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 2.43055i 1.21528i
\(5\) 0 0
\(6\) 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 0
\(11\) −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 0
\(16\) 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 \(-0.742491\pi\)
−0.690231 + 0.723589i \(0.742491\pi\)
\(20\) 0 0
\(21\) −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 \(-0.241754\pi\)
−0.688553 + 0.725186i \(0.741754\pi\)
\(24\) 0.906263 0.184990
\(25\) 0 0
\(26\) 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 \(0.990988\pi\)
\(30\) 0 0
\(31\) 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
\(35\) 0 0
\(36\) −2.43055 −0.405092
\(37\) 0.735441 0.735441i 0.120906 0.120906i −0.644065 0.764971i \(-0.722753\pi\)
0.764971 + 0.644065i \(0.222753\pi\)
\(38\) 8.95602 8.95602i 1.45286 1.45286i
\(39\) 1.73544i 0.277893i
\(40\) 0 0
\(41\) 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 0.683477 0.729972i \(-0.260467\pi\)
−0.729972 + 0.683477i \(0.760467\pi\)
\(44\) 6.49412i 0.979026i
\(45\) 0 0
\(46\) −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
\(50\) 0 0
\(51\) −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 \(-0.0889282\pi\)
−0.275756 + 0.961228i \(0.588928\pi\)
\(54\) 2.10489 0.286439
\(55\) 0 0
\(56\) 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 \(0.325932\pi\)
\(60\) 0 0
\(61\) 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 0
\(66\) 5.62399i 0.692265i
\(67\) 3.43055 3.43055i 0.419109 0.419109i −0.465788 0.884896i \(-0.654229\pi\)
0.884896 + 0.465788i \(0.154229\pi\)
\(68\) −11.5360 + 11.5360i −1.39894 + 1.39894i
\(69\) 0.248455 0.0299104
\(70\) 0 0
\(71\) 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
\(75\) 0 0
\(76\) 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 \(0.780785\pi\)
\(80\) 0 0
\(81\) −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
\(85\) 0 0
\(86\) 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 \(0.619397\pi\)
\(90\) 0 0
\(91\) −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
\(95\) 0 0
\(96\) 8.02936i 0.819493i
\(97\) −8.84137 8.84137i −0.897705 0.897705i 0.0975276 0.995233i \(-0.468907\pi\)
−0.995233 + 0.0975276i \(0.968907\pi\)
\(98\) 11.5481 + 9.15086i 1.16654 + 0.924376i
\(99\) 2.67187i 0.268533i
\(100\) 0 0
\(101\) 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 −0.960977 0.276628i \(-0.910783\pi\)
0.276628 + 0.960977i \(0.410783\pi\)
\(104\) 1.57277 0.154222
\(105\) 0 0
\(106\) −14.8550 −1.44284
\(107\) 7.47295 7.47295i 0.722437 0.722437i −0.246664 0.969101i \(-0.579334\pi\)
0.969101 + 0.246664i \(0.0793344\pi\)
\(108\) −1.71866 + 1.71866i −0.165378 + 0.165378i
\(109\) 5.95352i 0.570244i 0.958491 + 0.285122i \(0.0920341\pi\)
−0.958491 + 0.285122i \(0.907966\pi\)
\(110\) 0 0
\(111\) 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 \(-0.403942\pi\)
−0.954810 + 0.297217i \(0.903942\pi\)
\(114\) 12.6657i 1.18625i
\(115\) 0 0
\(116\) 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
\(120\) 0 0
\(121\) −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
\(125\) 0 0
\(126\) 5.55976 0.320879i 0.495303 0.0285862i
\(127\) −2.86110 + 2.86110i −0.253882 + 0.253882i −0.822560 0.568678i \(-0.807455\pi\)
0.568678 + 0.822560i \(0.307455\pi\)
\(128\) 5.00781 + 5.00781i 0.442632 + 0.442632i
\(129\) −0.431179 −0.0379632
\(130\) 0 0
\(131\) 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
\(135\) 0 0
\(136\) 6.08302i 0.521615i
\(137\) −7.51943 + 7.51943i −0.642428 + 0.642428i −0.951152 0.308724i \(-0.900098\pi\)
0.308724 + 0.951152i \(0.400098\pi\)
\(138\) −0.369795 + 0.369795i −0.0314791 + 0.0314791i
\(139\) −7.78902 −0.660656 −0.330328 0.943866i \(-0.607159\pi\)
−0.330328 + 0.943866i \(0.607159\pi\)
\(140\) 0 0
\(141\) 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 0
\(146\) 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 \(-0.198967\pi\)
\(150\) 0 0
\(151\) 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
\(155\) 0 0
\(156\) −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
\(160\) 0 0
\(161\) 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 \(0.0235446\pi\)
0.0739001 + 0.997266i \(0.476455\pi\)
\(164\) −17.1533 −1.33945
\(165\) 0 0
\(166\) 14.5546i 1.12966i
\(167\) −6.23288 6.23288i −0.482315 0.482315i 0.423555 0.905870i \(-0.360782\pi\)
−0.905870 + 0.423555i \(0.860782\pi\)
\(168\) 1.59496 1.79034i 0.123054 0.138128i
\(169\) 9.98824i 0.768326i
\(170\) 0 0
\(171\) 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
\(175\) 0 0
\(176\) −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 \(-0.0154829\pi\)
\(180\) 0 0
\(181\) 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 0
\(186\) 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
\(190\) 0 0
\(191\) 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 \(-0.119556\pi\)
−0.366827 + 0.930289i \(0.619556\pi\)
\(194\) 26.3186 1.88957
\(195\) 0 0
\(196\) −16.9009 + 1.95738i −1.20721 + 0.139813i
\(197\) 8.50767 8.50767i 0.606146 0.606146i −0.335790 0.941937i \(-0.609003\pi\)
0.941937 + 0.335790i \(0.109003\pi\)
\(198\) −3.97676 3.97676i −0.282616 0.282616i
\(199\) 3.25460 0.230712 0.115356 0.993324i \(-0.463199\pi\)
0.115356 + 0.993324i \(0.463199\pi\)
\(200\) 0 0
\(201\) 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
\(205\) 0 0
\(206\) 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
\(210\) 0 0
\(211\) −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 0
\(216\) 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
\(220\) 0 0
\(221\) −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
\(225\) 0 0
\(226\) 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 \(-0.0948864\pi\)
0.955898 + 0.293699i \(0.0948864\pi\)
\(230\) 0 0
\(231\) 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 \(-0.178845\pi\)
−0.532760 + 0.846266i \(0.678845\pi\)
\(234\) 3.65291 0.238798
\(235\) 0 0
\(236\) 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 \(-0.175262\pi\)
\(240\) 0 0
\(241\) 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
\(245\) 0 0
\(246\) 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
\(250\) 0 0
\(251\) 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
\(255\) 0 0
\(256\) 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
\(260\) 0 0
\(261\) 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 \(-0.958263\pi\)
−0.130744 0.991416i \(-0.541737\pi\)
\(264\) −2.42142 −0.149028
\(265\) 0 0
\(266\) −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 \(0.343212\pi\)
\(270\) 0 0
\(271\) 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
\(275\) 0 0
\(276\) 0.603882i 0.0363494i
\(277\) 2.00561 2.00561i 0.120505 0.120505i −0.644282 0.764788i \(-0.722844\pi\)
0.764788 + 0.644282i \(0.222844\pi\)
\(278\) 11.5930 11.5930i 0.695304 0.695304i
\(279\) −7.25379 −0.434273
\(280\) 0 0
\(281\) 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
\(285\) 0 0
\(286\) 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
\(290\) 0 0
\(291\) −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
\(295\) 0 0
\(296\) 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
\(300\) 0 0
\(301\) −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
\(305\) 0 0
\(306\) 14.1284i 0.807669i
\(307\) 7.21300 + 7.21300i 0.411667 + 0.411667i 0.882319 0.470652i \(-0.155981\pi\)
−0.470652 + 0.882319i \(0.655981\pi\)
\(308\) 12.8292 + 11.4292i 0.731014 + 0.651238i
\(309\) 9.82225i 0.558768i
\(310\) 0 0
\(311\) 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 \(-0.405582\pi\)
0.956329 0.292293i \(-0.0944182\pi\)
\(314\) −6.48134 −0.365763
\(315\) 0 0
\(316\) 27.4586 1.54467
\(317\) 12.2563 12.2563i 0.688385 0.688385i −0.273490 0.961875i \(-0.588178\pi\)
0.961875 + 0.273490i \(0.0881780\pi\)
\(318\) −10.5040 + 10.5040i −0.589037 + 0.589037i
\(319\) 0.814625i 0.0456102i
\(320\) 0 0
\(321\) 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
\(325\) 0 0
\(326\) −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
\(330\) 0 0
\(331\) 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
\(335\) 0 0
\(336\) −0.450249 7.80130i −0.0245631 0.425596i
\(337\) 9.55621 9.55621i 0.520560 0.520560i −0.397180 0.917741i \(-0.630011\pi\)
0.917741 + 0.397180i \(0.130011\pi\)
\(338\) −14.8663 14.8663i −0.808620 0.808620i
\(339\) −9.88579 −0.536922
\(340\) 0 0
\(341\) 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 0
\(346\) 20.1507i 1.08331i
\(347\) −6.54975 + 6.54975i −0.351609 + 0.351609i −0.860708 0.509099i \(-0.829979\pi\)
0.509099 + 0.860708i \(0.329979\pi\)
\(348\) 0.524001 0.524001i 0.0280894 0.0280894i
\(349\) 2.77139 0.148349 0.0741746 0.997245i \(-0.476368\pi\)
0.0741746 + 0.997245i \(0.476368\pi\)
\(350\) 0 0
\(351\) −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
\(355\) 0 0
\(356\) 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 0
\(361\) 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
\(365\) 0 0
\(366\) −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
\(370\) 0 0
\(371\) 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 \(-0.976668\pi\)
−0.0732339 0.997315i \(-0.523332\pi\)
\(374\) −37.7493 −1.95197
\(375\) 0 0
\(376\) 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 \(-0.191213\pi\)
\(380\) 0 0
\(381\) 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
\(385\) 0 0
\(386\) −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 \(-0.228323\pi\)
\(390\) 0 0
\(391\) 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
\(395\) 0 0
\(396\) 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
\(400\) 0 0
\(401\) −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
\(405\) 0 0
\(406\) −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 \(0.479187\pi\)
\(410\) 0 0
\(411\) 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
\(415\) 0 0
\(416\) 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 \(0.578789\pi\)
\(420\) 0 0
\(421\) −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
\(425\) 0 0
\(426\) 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
\(430\) 0 0
\(431\) 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 0
\(436\) 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 \(0.709955\pi\)
\(440\) 0 0
\(441\) −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 \(-0.0739640\pi\)
−0.230279 + 0.973125i \(0.573964\pi\)
\(444\) −2.52795 −0.119971
\(445\) 0 0
\(446\) 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 \(0.947033\pi\)
\(450\) 0 0
\(451\) 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
\(455\) 0 0
\(456\) −5.45325 −0.255372
\(457\) −11.2119 + 11.2119i −0.524472 + 0.524472i −0.918919 0.394447i \(-0.870936\pi\)
0.394447 + 0.918919i \(0.370936\pi\)
\(458\) −43.0599 + 43.0599i −2.01206 + 2.01206i
\(459\) 6.71220i 0.313299i
\(460\) 0 0
\(461\) 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 0.505106 0.863057i \(-0.331453\pi\)
−0.863057 + 0.505106i \(0.831453\pi\)
\(464\) 0.900497i 0.0418045i
\(465\) 0 0
\(466\) −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
\(470\) 0 0
\(471\) 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
\(475\) 0 0
\(476\) 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 \(0.529819\pi\)
\(480\) 0 0
\(481\) 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
\(485\) 0 0
\(486\) 2.10489i 0.0954796i
\(487\) 10.3049 10.3049i 0.466959 0.466959i −0.433969 0.900928i \(-0.642887\pi\)
0.900928 + 0.433969i \(0.142887\pi\)
\(488\) −3.54638 + 3.54638i −0.160537 + 0.160537i
\(489\) 19.3404 0.874603
\(490\) 0 0
\(491\) −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
\(495\) 0 0
\(496\) 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 \(-0.178462\pi\)
\(500\) 0 0
\(501\) −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
\(505\) 0 0
\(506\) 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 \(0.622182\pi\)
\(510\) 0 0
\(511\) −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
\(515\) 0 0
\(516\) 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
\(520\) 0 0
\(521\) 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 −0.733519 0.679669i \(-0.762123\pi\)
0.679669 + 0.733519i \(0.262123\pi\)
\(524\) 22.7199 0.992524
\(525\) 0 0
\(526\) 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
\(530\) 0 0
\(531\) 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
\(535\) 0 0
\(536\) 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 0
\(541\) 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
\(545\) 0 0
\(546\) 9.64863 0.556866i 0.412923 0.0238317i
\(547\) −3.83548 + 3.83548i −0.163993 + 0.163993i −0.784333 0.620340i \(-0.786995\pi\)
0.620340 + 0.784333i \(0.286995\pi\)
\(548\) 18.2764 + 18.2764i 0.780727 + 0.780727i
\(549\) 5.53409 0.236189
\(550\) 0 0
\(551\) 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
\(555\) 0 0
\(556\) 18.9316i 0.802880i
\(557\) 16.3147 16.3147i 0.691275 0.691275i −0.271238 0.962512i \(-0.587433\pi\)
0.962512 + 0.271238i \(0.0874329\pi\)
\(558\) 10.7964 10.7964i 0.457048 0.457048i
\(559\) −0.748285 −0.0316491
\(560\) 0 0
\(561\) 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
\(565\) 0 0
\(566\) 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 \(0.998147\pi\)
\(570\) 0 0
\(571\) −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 0
\(576\) −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 0
\(581\) 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
\(585\) 0 0
\(586\) 7.19676i 0.297295i
\(587\) 26.6462 + 26.6462i 1.09981 + 1.09981i 0.994433 + 0.105375i \(0.0336041\pi\)
0.105375 + 0.994433i \(0.466396\pi\)
\(588\) −10.5667 + 13.3348i −0.435762 + 0.549918i
\(589\) 43.6482i 1.79849i
\(590\) 0 0
\(591\) 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
\(595\) 0 0
\(596\) −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 \(0.849597\pi\)
\(600\) 0 0
\(601\) 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
\(605\) 0 0
\(606\) 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
\(610\) 0 0
\(611\) 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 \(-0.0941080\pi\)
−0.291361 + 0.956613i \(0.594108\pi\)
\(614\) −21.4714 −0.866514
\(615\) 0 0
\(616\) −6.39583 + 0.369132i −0.257695 + 0.0148728i
\(617\) 3.70013 3.70013i 0.148962 0.148962i −0.628692 0.777654i \(-0.716410\pi\)
0.777654 + 0.628692i \(0.216410\pi\)
\(618\) −14.6192 14.6192i −0.588072 0.588072i
\(619\) 39.8840 1.60307 0.801536 0.597946i \(-0.204016\pi\)
0.801536 + 0.597946i \(0.204016\pi\)
\(620\) 0 0
\(621\) 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
\(625\) 0 0
\(626\) 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
\(630\) 0 0
\(631\) −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
\(635\) 0 0
\(636\) 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
\(640\) 0 0
\(641\) −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 0
\(646\) −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
\(650\) 0 0
\(651\) −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 \(-0.166247\pi\)
−0.498858 + 0.866684i \(0.666247\pi\)
\(654\) −12.5315 −0.490020
\(655\) 0 0
\(656\) 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 \(0.943042\pi\)
\(660\) 0 0
\(661\) 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
\(665\) 0 0
\(666\) 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
\(670\) 0 0
\(671\) 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 \(-0.988256\pi\)
−0.0368867 0.999319i \(-0.511744\pi\)
\(674\) 28.4466i 1.09572i
\(675\) 0 0
\(676\) 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
\(680\) 0 0
\(681\) 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 \(-0.270818\pi\)
−0.751809 + 0.659381i \(0.770818\pi\)
\(684\) 14.6253 0.559214
\(685\) 0 0
\(686\) 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 0
\(691\) 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
\(695\) 0 0
\(696\) 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
\(700\) 0 0
\(701\) 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
\(705\) 0 0
\(706\) 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 \(-0.153332\pi\)
\(710\) 0 0
\(711\) 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
\(715\) 0 0
\(716\) −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 \(0.311662\pi\)
\(720\) 0 0
\(721\) 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
\(725\) 0 0
\(726\) 8.12719i 0.301628i
\(727\) −29.8488 29.8488i −1.10703 1.10703i −0.993539 0.113491i \(-0.963797\pi\)
−0.113491 0.993539i \(-0.536203\pi\)
\(728\) 2.76795 3.10702i 0.102587 0.115154i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 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
\(735\) 0 0
\(736\) −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 \(0.929320\pi\)
\(740\) 0 0
\(741\) 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 \(-0.148884\pi\)
−0.450864 + 0.892593i \(0.648884\pi\)
\(744\) 6.57385i 0.241009i
\(745\) 0 0
\(746\) 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
\(750\) 0 0
\(751\) −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
\(755\) 0 0
\(756\) 0.370525 + 6.41995i 0.0134759 + 0.233491i
\(757\) −29.2896 + 29.2896i −1.06455 + 1.06455i −0.0667825 + 0.997768i \(0.521273\pi\)
−0.997768 + 0.0667825i \(0.978727\pi\)
\(758\) 32.7558 + 32.7558i 1.18975 + 1.18975i
\(759\) −0.663839 −0.0240958
\(760\) 0 0
\(761\) 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
\(765\) 0 0
\(766\) 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 \(0.607831\pi\)
\(770\) 0 0
\(771\) 14.2679 0.513845
\(772\) 19.0260 19.0260i 0.684761 0.684761i
\(773\) 17.7963 17.7963i 0.640088 0.640088i −0.310489 0.950577i \(-0.600493\pi\)
0.950577 + 0.310489i \(0.100493\pi\)
\(774\) 0.907583i 0.0326224i
\(775\) 0 0
\(776\) 11.3315i 0.406779i
\(777\) −2.05468 1.83045i −0.0737111 0.0656670i
\(778\) 38.5937 + 38.5937i 1.38365 + 1.38365i
\(779\) 42.4662i 1.52151i
\(780\) 0 0
\(781\) −40.9030 −1.46362