Properties

Label 315.2.p.e.307.2
Level 315
Weight 2
Character 315.307
Analytic conductor 2.515
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.p (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.51528766367\)
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 307.2
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 \(\chi\) \(=\) 315.307
Dual form 315.2.p.e.118.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.48838 - 1.48838i) q^{2} +2.43055i q^{4} +(1.28999 + 1.82645i) q^{5} +(-1.97552 - 1.75993i) q^{7} +(0.640825 - 0.640825i) q^{8} +O(q^{10})\) \(q+(-1.48838 - 1.48838i) q^{2} +2.43055i q^{4} +(1.28999 + 1.82645i) q^{5} +(-1.97552 - 1.75993i) q^{7} +(0.640825 - 0.640825i) q^{8} +(0.798469 - 4.63845i) q^{10} +2.67187 q^{11} +(1.22714 + 1.22714i) q^{13} +(0.320879 + 5.55976i) q^{14} +2.95352 q^{16} +(4.74624 - 4.74624i) q^{17} +6.01729 q^{19} +(-4.43929 + 3.13538i) q^{20} +(-3.97676 - 3.97676i) q^{22} +(0.175684 - 0.175684i) q^{23} +(-1.67187 + 4.71220i) q^{25} -3.65291i q^{26} +(4.27759 - 4.80159i) q^{28} +0.304889i q^{29} -7.25379i q^{31} +(-5.67761 - 5.67761i) q^{32} -14.1284 q^{34} +(0.666037 - 5.87847i) q^{35} +(-0.735441 - 0.735441i) q^{37} +(-8.95602 - 8.95602i) q^{38} +(1.99709 + 0.343782i) q^{40} +7.05736i q^{41} +(0.304889 - 0.304889i) q^{43} +6.49412i q^{44} -0.522969 q^{46} +(-0.556866 + 0.556866i) q^{47} +(0.805321 + 6.95352i) q^{49} +(9.50193 - 4.52517i) q^{50} +(-2.98263 + 2.98263i) q^{52} +(4.99031 - 4.99031i) q^{53} +(3.44668 + 4.88005i) q^{55} +(-2.39376 + 0.138155i) q^{56} +(0.453791 - 0.453791i) q^{58} +7.98837 q^{59} +5.53409i q^{61} +(-10.7964 + 10.7964i) q^{62} +10.9939i q^{64} +(-0.658323 + 3.82432i) q^{65} +(-3.43055 - 3.43055i) q^{67} +(11.5360 + 11.5360i) q^{68} +(-9.74071 + 7.75808i) q^{70} -15.3087 q^{71} +(10.0208 + 10.0208i) q^{73} +2.18923i q^{74} +14.6253i q^{76} +(-5.27832 - 4.70230i) q^{77} -11.2973i q^{79} +(3.81000 + 5.39447i) q^{80} +(10.5040 - 10.5040i) q^{82} +(4.88941 + 4.88941i) q^{83} +(14.7914 + 2.54621i) q^{85} -0.907583 q^{86} +(1.71220 - 1.71220i) q^{88} -6.91251 q^{89} +(-0.264559 - 4.58392i) q^{91} +(0.427009 + 0.427009i) q^{92} +1.65766 q^{94} +(7.76222 + 10.9903i) q^{95} +(-8.84137 + 8.84137i) q^{97} +(9.15086 - 11.5481i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{7} - 24q^{8} + O(q^{10}) \) \( 16q - 8q^{7} - 24q^{8} + 16q^{11} - 48q^{16} - 16q^{22} + 40q^{23} + 24q^{28} - 48q^{32} + 8q^{35} + 32q^{37} - 16q^{43} + 64q^{46} + 72q^{50} - 24q^{53} - 24q^{56} + 32q^{58} - 40q^{65} - 32q^{67} - 40q^{70} - 64q^{71} + 24q^{77} + 48q^{85} - 64q^{86} - 64q^{88} - 48q^{91} + 40q^{92} + 72q^{95} + 96q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

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 \(-0.982836\pi\)
−0.0538973 0.998546i \(-0.517164\pi\)
\(3\) 0 0
\(4\) 2.43055i 1.21528i
\(5\) 1.28999 + 1.82645i 0.576899 + 0.816815i
\(6\) 0 0
\(7\) −1.97552 1.75993i −0.746675 0.665189i
\(8\) 0.640825 0.640825i 0.226566 0.226566i
\(9\) 0 0
\(10\) 0.798469 4.63845i 0.252498 1.46681i
\(11\) 2.67187 0.805600 0.402800 0.915288i \(-0.368037\pi\)
0.402800 + 0.915288i \(0.368037\pi\)
\(12\) 0 0
\(13\) 1.22714 + 1.22714i 0.340348 + 0.340348i 0.856498 0.516150i \(-0.172635\pi\)
−0.516150 + 0.856498i \(0.672635\pi\)
\(14\) 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 0.164807 0.986326i \(-0.447300\pi\)
0.986326 0.164807i \(-0.0527002\pi\)
\(18\) 0 0
\(19\) 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 0
\(22\) −3.97676 3.97676i −0.847848 0.847848i
\(23\) 0.175684 0.175684i 0.0366327 0.0366327i −0.688553 0.725186i \(-0.741754\pi\)
0.725186 + 0.688553i \(0.241754\pi\)
\(24\) 0 0
\(25\) −1.67187 + 4.71220i −0.334374 + 0.942440i
\(26\) 3.65291i 0.716394i
\(27\) 0 0
\(28\) 4.27759 4.80159i 0.808389 0.907416i
\(29\) 0.304889i 0.0566165i 0.999599 + 0.0283083i \(0.00901200\pi\)
−0.999599 + 0.0283083i \(0.990988\pi\)
\(30\) 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
\(33\) 0 0
\(34\) −14.1284 −2.42301
\(35\) 0.666037 5.87847i 0.112581 0.993643i
\(36\) 0 0
\(37\) −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
\(39\) 0 0
\(40\) 1.99709 + 0.343782i 0.315768 + 0.0543567i
\(41\) 7.05736i 1.10217i 0.834447 + 0.551087i \(0.185787\pi\)
−0.834447 + 0.551087i \(0.814213\pi\)
\(42\) 0 0
\(43\) 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
\(45\) 0 0
\(46\) −0.522969 −0.0771076
\(47\) −0.556866 + 0.556866i −0.0812273 + 0.0812273i −0.746553 0.665326i \(-0.768293\pi\)
0.665326 + 0.746553i \(0.268293\pi\)
\(48\) 0 0
\(49\) 0.805321 + 6.95352i 0.115046 + 0.993360i
\(50\) 9.50193 4.52517i 1.34378 0.639955i
\(51\) 0 0
\(52\) −2.98263 + 2.98263i −0.413617 + 0.413617i
\(53\) 4.99031 4.99031i 0.685472 0.685472i −0.275756 0.961228i \(-0.588928\pi\)
0.961228 + 0.275756i \(0.0889282\pi\)
\(54\) 0 0
\(55\) 3.44668 + 4.88005i 0.464750 + 0.658026i
\(56\) −2.39376 + 0.138155i −0.319880 + 0.0184617i
\(57\) 0 0
\(58\) 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
\(63\) 0 0
\(64\) 10.9939i 1.37423i
\(65\) −0.658323 + 3.82432i −0.0816549 + 0.474348i
\(66\) 0 0
\(67\) −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 0
\(70\) −9.74071 + 7.75808i −1.16424 + 0.927268i
\(71\) −15.3087 −1.81681 −0.908407 0.418087i \(-0.862701\pi\)
−0.908407 + 0.418087i \(0.862701\pi\)
\(72\) 0 0
\(73\) 10.0208 + 10.0208i 1.17285 + 1.17285i 0.981527 + 0.191323i \(0.0612778\pi\)
0.191323 + 0.981527i \(0.438722\pi\)
\(74\) 2.18923i 0.254493i
\(75\) 0 0
\(76\) 14.6253i 1.67764i
\(77\) −5.27832 4.70230i −0.601521 0.535876i
\(78\) 0 0
\(79\) 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
\(81\) 0 0
\(82\) 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 \(0.626099\pi\)
\(84\) 0 0
\(85\) 14.7914 + 2.54621i 1.60435 + 0.276175i
\(86\) −0.907583 −0.0978671
\(87\) 0 0
\(88\) 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
\(93\) 0 0
\(94\) 1.65766 0.170974
\(95\) 7.76222 + 10.9903i 0.796387 + 1.12758i
\(96\) 0 0
\(97\) −8.84137 + 8.84137i −0.897705 + 0.897705i −0.995233 0.0975276i \(-0.968907\pi\)
0.0975276 + 0.995233i \(0.468907\pi\)
\(98\) 9.15086 11.5481i 0.924376 1.16654i
\(99\) 0 0
\(100\) −11.4533 4.06357i −1.14533 0.406357i
\(101\) 7.22962i 0.719374i 0.933073 + 0.359687i \(0.117117\pi\)
−0.933073 + 0.359687i \(0.882883\pi\)
\(102\) 0 0
\(103\) −6.94538 6.94538i −0.684349 0.684349i 0.276628 0.960977i \(-0.410783\pi\)
−0.960977 + 0.276628i \(0.910783\pi\)
\(104\) 1.57277 0.154222
\(105\) 0 0
\(106\) −14.8550 −1.44284
\(107\) 7.47295 + 7.47295i 0.722437 + 0.722437i 0.969101 0.246664i \(-0.0793344\pi\)
−0.246664 + 0.969101i \(0.579334\pi\)
\(108\) 0 0
\(109\) 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
\(111\) 0 0
\(112\) −5.83473 5.19798i −0.551330 0.491163i
\(113\) −6.99031 + 6.99031i −0.657593 + 0.657593i −0.954810 0.297217i \(-0.903942\pi\)
0.297217 + 0.954810i \(0.403942\pi\)
\(114\) 0 0
\(115\) 0.547509 + 0.0942489i 0.0510555 + 0.00878876i
\(116\) −0.741049 −0.0688047
\(117\) 0 0
\(118\) −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
\(123\) 0 0
\(124\) 17.6307 1.58329
\(125\) −10.7633 + 3.02508i −0.962700 + 0.270571i
\(126\) 0 0
\(127\) 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 0
\(130\) 6.67187 4.71220i 0.585162 0.413287i
\(131\) 9.34764i 0.816707i −0.912824 0.408353i \(-0.866103\pi\)
0.912824 0.408353i \(-0.133897\pi\)
\(132\) 0 0
\(133\) −11.8873 10.5900i −1.03076 0.918268i
\(134\) 10.2119i 0.882177i
\(135\) 0 0
\(136\) 6.08302i 0.521615i
\(137\) −7.51943 7.51943i −0.642428 0.642428i 0.308724 0.951152i \(-0.400098\pi\)
−0.951152 + 0.308724i \(0.900098\pi\)
\(138\) 0 0
\(139\) 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 0
\(142\) 22.7852 + 22.7852i 1.91209 + 1.91209i
\(143\) 3.27877 + 3.27877i 0.274184 + 0.274184i
\(144\) 0 0
\(145\) −0.556866 + 0.393303i −0.0462452 + 0.0326620i
\(146\) 29.8296i 2.46872i
\(147\) 0 0
\(148\) 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
\(153\) 0 0
\(154\) 0.857347 + 14.8550i 0.0690870 + 1.19705i
\(155\) 13.2487 9.35729i 1.06416 0.751596i
\(156\) 0 0
\(157\) 2.17731 2.17731i 0.173768 0.173768i −0.614864 0.788633i \(-0.710789\pi\)
0.788633 + 0.614864i \(0.210789\pi\)
\(158\) −16.8146 + 16.8146i −1.33770 + 1.33770i
\(159\) 0 0
\(160\) 3.04586 17.6939i 0.240796 1.39883i
\(161\) −0.656257 + 0.0378756i −0.0517203 + 0.00298502i
\(162\) 0 0
\(163\) −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
\(165\) 0 0
\(166\) 14.5546i 1.12966i
\(167\) 6.23288 6.23288i 0.482315 0.482315i −0.423555 0.905870i \(-0.639218\pi\)
0.905870 + 0.423555i \(0.139218\pi\)
\(168\) 0 0
\(169\) 9.98824i 0.768326i
\(170\) −18.2255 25.8049i −1.39783 1.97915i
\(171\) 0 0
\(172\) 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 0
\(175\) 11.5959 6.36666i 0.876570 0.481274i
\(176\) 7.89143 0.594839
\(177\) 0 0
\(178\) 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 \(0.897877\pi\)
\(182\) −6.42885 + 7.21638i −0.476538 + 0.534913i
\(183\) 0 0
\(184\) 0.225165i 0.0165994i
\(185\) 0.394541 2.29196i 0.0290072 0.168508i
\(186\) 0 0
\(187\) 12.6814 12.6814i 0.927352 0.927352i
\(188\) −1.35349 1.35349i −0.0987136 0.0987136i
\(189\) 0 0
\(190\) 4.80462 27.9109i 0.348564 2.02487i
\(191\) −1.93791 −0.140222 −0.0701110 0.997539i \(-0.522335\pi\)
−0.0701110 + 0.997539i \(0.522335\pi\)
\(192\) 0 0
\(193\) −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
\(195\) 0 0
\(196\) −16.9009 + 1.95738i −1.20721 + 0.139813i
\(197\) 8.50767 + 8.50767i 0.606146 + 0.606146i 0.941937 0.335790i \(-0.109003\pi\)
−0.335790 + 0.941937i \(0.609003\pi\)
\(198\) 0 0
\(199\) −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
\(201\) 0 0
\(202\) 10.7604 10.7604i 0.757101 0.757101i
\(203\) 0.536583 0.602314i 0.0376607 0.0422741i
\(204\) 0 0
\(205\) −12.8900 + 9.10390i −0.900273 + 0.635844i
\(206\) 20.6747i 1.44048i
\(207\) 0 0
\(208\) 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
\(213\) 0 0
\(214\) 22.2452i 1.52065i
\(215\) 0.950169 + 0.163563i 0.0648010 + 0.0111549i
\(216\) 0 0
\(217\) −12.7661 + 14.3300i −0.866622 + 0.972782i
\(218\) −8.86110 + 8.86110i −0.600150 + 0.600150i
\(219\) 0 0
\(220\) −11.8612 + 8.37733i −0.799683 + 0.564799i
\(221\) 11.6486 0.783572
\(222\) 0 0
\(223\) −4.58392 4.58392i −0.306962 0.306962i 0.536768 0.843730i \(-0.319645\pi\)
−0.843730 + 0.536768i \(0.819645\pi\)
\(224\) 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 \(-0.981408\pi\)
0.0583764 + 0.998295i \(0.481408\pi\)
\(228\) 0 0
\(229\) −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 0
\(232\) 0.195381 + 0.195381i 0.0128274 + 0.0128274i
\(233\) 4.78546 4.78546i 0.313506 0.313506i −0.532760 0.846266i \(-0.678845\pi\)
0.846266 + 0.532760i \(0.178845\pi\)
\(234\) 0 0
\(235\) −1.73544 0.298741i −0.113208 0.0194877i
\(236\) 19.4162i 1.26388i
\(237\) 0 0
\(238\) 27.9109 + 24.8650i 1.80920 + 1.61176i
\(239\) 16.1769i 1.04640i −0.852210 0.523200i \(-0.824738\pi\)
0.852210 0.523200i \(-0.175262\pi\)
\(240\) 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 0
\(244\) −13.4509 −0.861105
\(245\) −11.6614 + 10.4408i −0.745022 + 0.667040i
\(246\) 0 0
\(247\) 7.38407 + 7.38407i 0.469837 + 0.469837i
\(248\) −4.64841 4.64841i −0.295174 0.295174i
\(249\) 0 0
\(250\) 20.5224 + 11.5174i 1.29795 + 0.728427i
\(251\) 6.95039i 0.438705i −0.975646 0.219352i \(-0.929606\pi\)
0.975646 0.219352i \(-0.0703944\pi\)
\(252\) 0 0
\(253\) 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 \(-0.896797\pi\)
0.318570 + 0.947899i \(0.396797\pi\)
\(258\) 0 0
\(259\) 0.158553 + 2.74720i 0.00985202 + 0.170703i
\(260\) −9.29520 1.60009i −0.576464 0.0992332i
\(261\) 0 0
\(262\) −13.9128 + 13.9128i −0.859538 + 0.859538i
\(263\) −18.1984 + 18.1984i −1.12216 + 1.12216i −0.130744 + 0.991416i \(0.541737\pi\)
−0.991416 + 0.130744i \(0.958263\pi\)
\(264\) 0 0
\(265\) 15.5520 + 2.67714i 0.955352 + 0.164456i
\(266\) 1.93082 + 33.4547i 0.118386 + 2.05124i
\(267\) 0 0
\(268\) 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
\(273\) 0 0
\(274\) 22.3835i 1.35224i
\(275\) −4.46702 + 12.5904i −0.269372 + 0.759229i
\(276\) 0 0
\(277\) −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
\(279\) 0 0
\(280\) −3.34026 4.19388i −0.199619 0.250632i
\(281\) −13.5557 −0.808664 −0.404332 0.914612i \(-0.632496\pi\)
−0.404332 + 0.914612i \(0.632496\pi\)
\(282\) 0 0
\(283\) −16.2444 16.2444i −0.965627 0.965627i 0.0338017 0.999429i \(-0.489239\pi\)
−0.999429 + 0.0338017i \(0.989239\pi\)
\(284\) 37.2087i 2.20793i
\(285\) 0 0
\(286\) 9.76010i 0.577127i
\(287\) 12.4204 13.9419i 0.733155 0.822966i
\(288\) 0 0
\(289\) 28.0537i 1.65021i
\(290\) 1.41421 + 0.243445i 0.0830455 + 0.0142956i
\(291\) 0 0
\(292\) −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 \(0.718157\pi\)
\(294\) 0 0
\(295\) 10.3049 + 14.5904i 0.599974 + 0.849486i
\(296\) −0.942578 −0.0547862
\(297\) 0 0
\(298\) −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
\(303\) 0 0
\(304\) 17.7722 1.01931
\(305\) −10.1078 + 7.13890i −0.578769 + 0.408772i
\(306\) 0 0
\(307\) 7.21300 7.21300i 0.411667 0.411667i −0.470652 0.882319i \(-0.655981\pi\)
0.882319 + 0.470652i \(0.155981\pi\)
\(308\) 11.4292 12.8292i 0.651238 0.731014i
\(309\) 0 0
\(310\) −33.6463 5.79193i −1.91098 0.328959i
\(311\) 10.2542i 0.581460i −0.956805 0.290730i \(-0.906102\pi\)
0.956805 0.290730i \(-0.0938981\pi\)
\(312\) 0 0
\(313\) 22.0904 + 22.0904i 1.24862 + 1.24862i 0.956329 + 0.292293i \(0.0944182\pi\)
0.292293 + 0.956329i \(0.405582\pi\)
\(314\) −6.48134 −0.365763
\(315\) 0 0
\(316\) 27.4586 1.54467
\(317\) 12.2563 + 12.2563i 0.688385 + 0.688385i 0.961875 0.273490i \(-0.0881780\pi\)
−0.273490 + 0.961875i \(0.588178\pi\)
\(318\) 0 0
\(319\) 0.814625i 0.0456102i
\(320\) −20.0798 + 14.1819i −1.12249 + 0.792793i
\(321\) 0 0
\(322\) 1.03313 + 0.920387i 0.0575743 + 0.0512912i
\(323\) 28.5595 28.5595i 1.58909 1.58909i
\(324\) 0 0
\(325\) −7.83417 + 3.73092i −0.434561 + 0.206954i
\(326\) 40.7094 2.25468
\(327\) 0 0
\(328\) 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 0
\(334\) −18.5538 −1.01522
\(335\) 1.84038 10.6911i 0.100551 0.584118i
\(336\) 0 0
\(337\) −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
\(339\) 0 0
\(340\) −6.18869 + 35.9512i −0.335629 + 1.94973i
\(341\) 19.3812i 1.04955i
\(342\) 0 0
\(343\) 10.6468 15.1541i 0.574871 0.818244i
\(344\) 0.390761i 0.0210684i
\(345\) 0 0
\(346\) 20.1507i 1.08331i
\(347\) −6.54975 6.54975i −0.351609 0.351609i 0.509099 0.860708i \(-0.329979\pi\)
−0.860708 + 0.509099i \(0.829979\pi\)
\(348\) 0 0
\(349\) −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
\(351\) 0 0
\(352\) −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 \(0.738370\pi\)
\(354\) 0 0
\(355\) −19.7481 27.9607i −1.04812 1.48400i
\(356\) 16.8012i 0.890463i
\(357\) 0 0
\(358\) −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
\(363\) 0 0
\(364\) 11.1415 0.643024i 0.583971 0.0337036i
\(365\) −5.37586 + 31.2293i −0.281385 + 1.63462i
\(366\) 0 0
\(367\) 13.0035 13.0035i 0.678776 0.678776i −0.280948 0.959723i \(-0.590649\pi\)
0.959723 + 0.280948i \(0.0906487\pi\)
\(368\) 0.518887 0.518887i 0.0270488 0.0270488i
\(369\) 0 0
\(370\) −3.99853 + 2.82408i −0.207874 + 0.146817i
\(371\) −18.6410 + 1.07586i −0.967793 + 0.0558557i
\(372\) 0 0
\(373\) 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
\(375\) 0 0
\(376\) 0.713708i 0.0368067i
\(377\) −0.374143 + 0.374143i −0.0192693 + 0.0192693i
\(378\) 0 0
\(379\) 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
\(381\) 0 0
\(382\) 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 \(0.745510\pi\)
\(384\) 0 0
\(385\) 1.77957 15.7065i 0.0906950 0.800478i
\(386\) 23.3017 1.18602
\(387\) 0 0
\(388\) −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
\(392\) 4.97206 + 3.93992i 0.251127 + 0.198996i
\(393\) 0 0
\(394\) 25.3253i 1.27587i
\(395\) 20.6339 14.5733i 1.03821 0.733263i
\(396\) 0 0
\(397\) −17.1631 + 17.1631i −0.861391 + 0.861391i −0.991500 0.130109i \(-0.958467\pi\)
0.130109 + 0.991500i \(0.458467\pi\)
\(398\) 4.84408 + 4.84408i 0.242812 + 0.242812i
\(399\) 0 0
\(400\) −4.93791 + 13.9176i −0.246895 + 0.695879i
\(401\) 12.9418 0.646281 0.323140 0.946351i \(-0.395261\pi\)
0.323140 + 0.946351i \(0.395261\pi\)
\(402\) 0 0
\(403\) 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
\(408\) 0 0
\(409\) −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
\(411\) 0 0
\(412\) 16.8811 16.8811i 0.831672 0.831672i
\(413\) −15.7812 14.0589i −0.776540 0.691795i
\(414\) 0 0
\(415\) −2.62301 + 15.2376i −0.128759 + 0.747982i
\(416\) 13.9345i 0.683194i
\(417\) 0 0
\(418\) −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 0
\(424\) 6.39583i 0.310609i
\(425\) 14.4301 + 30.3004i 0.699965 + 1.46978i
\(426\) 0 0
\(427\) 9.73958 10.9327i 0.471332 0.529069i
\(428\) −18.1634 + 18.1634i −0.877960 + 0.877960i
\(429\) 0 0
\(430\) −1.17077 1.65766i −0.0564595 0.0799394i
\(431\) −22.3747 −1.07775 −0.538876 0.842385i \(-0.681151\pi\)
−0.538876 + 0.842385i \(0.681151\pi\)
\(432\) 0 0
\(433\) 13.4723 + 13.4723i 0.647438 + 0.647438i 0.952373 0.304935i \(-0.0986349\pi\)
−0.304935 + 0.952373i \(0.598635\pi\)
\(434\) 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
\(438\) 0 0
\(439\) 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
\(441\) 0 0
\(442\) −17.3376 17.3376i −0.824665 0.824665i
\(443\) 15.6351 15.6351i 0.742845 0.742845i −0.230279 0.973125i \(-0.573964\pi\)
0.973125 + 0.230279i \(0.0739640\pi\)
\(444\) 0 0
\(445\) −8.91705 12.6254i −0.422709 0.598501i
\(446\) 13.6452i 0.646120i
\(447\) 0 0
\(448\) 19.3484 21.7185i 0.914124 1.02610i
\(449\) 7.01947i 0.331269i 0.986187 + 0.165635i \(0.0529673\pi\)
−0.986187 + 0.165635i \(0.947033\pi\)
\(450\) 0 0
\(451\) 18.8564i 0.887912i
\(452\) −16.9903 16.9903i −0.799157 0.799157i
\(453\) 0 0
\(454\) 42.1548 1.97842
\(455\) 8.03104 6.39640i 0.376501 0.299868i
\(456\) 0 0
\(457\) 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
\(459\) 0 0
\(460\) −0.229077 + 1.33075i −0.0106808 + 0.0620465i
\(461\) 29.9845i 1.39652i 0.715846 + 0.698259i \(0.246041\pi\)
−0.715846 + 0.698259i \(0.753959\pi\)
\(462\) 0 0
\(463\) 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
\(465\) 0 0
\(466\) −14.2452 −0.659895
\(467\) −1.80961 + 1.80961i −0.0837386 + 0.0837386i −0.747735 0.663997i \(-0.768859\pi\)
0.663997 + 0.747735i \(0.268859\pi\)
\(468\) 0 0
\(469\) 0.739590 + 12.8146i 0.0341511 + 0.591724i
\(470\) 2.13836 + 3.02764i 0.0986350 + 0.139654i
\(471\) 0 0
\(472\) 5.11915 5.11915i 0.235628 0.235628i
\(473\) 0.814625 0.814625i 0.0374565 0.0374565i
\(474\) 0 0
\(475\) −10.0601 + 28.3547i −0.461591 + 1.30100i
\(476\) −2.48704 43.0920i −0.113993 1.97512i
\(477\) 0 0
\(478\) −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 0
\(484\) 9.38461i 0.426573i
\(485\) −27.5536 4.74311i −1.25114 0.215374i
\(486\) 0 0
\(487\) −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
\(489\) 0 0
\(490\) 32.8966 + 1.81673i 1.48612 + 0.0820714i
\(491\) 8.55953 0.386286 0.193143 0.981171i \(-0.438132\pi\)
0.193143 + 0.981171i \(0.438132\pi\)
\(492\) 0 0
\(493\) 1.44708 + 1.44708i 0.0651732 + 0.0651732i
\(494\) 21.9806i 0.988955i
\(495\) 0 0
\(496\) 21.4242i 0.961976i
\(497\) 30.2427 + 26.9423i 1.35657 + 1.20853i
\(498\) 0 0
\(499\) 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
\(501\) 0 0
\(502\) −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 0
\(505\) −13.2046 + 9.32611i −0.587596 + 0.415007i
\(506\) −1.39731 −0.0621179
\(507\) 0 0
\(508\) −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
\(513\) 0 0
\(514\) 30.0323 1.32467
\(515\) 3.72598 21.6449i 0.164186 0.953787i
\(516\) 0 0
\(517\) −1.48788 + 1.48788i −0.0654367 + 0.0654367i
\(518\) 3.85289 4.32486i 0.169286 0.190024i
\(519\) 0 0
\(520\) 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 0
\(523\) −1.23149 1.23149i −0.0538493 0.0538493i 0.679669 0.733519i \(-0.262123\pi\)
−0.733519 + 0.679669i \(0.762123\pi\)
\(524\) 22.7199 0.992524
\(525\) 0 0
\(526\) 54.1722 2.36202
\(527\) −34.4283 34.4283i −1.49972 1.49972i
\(528\) 0 0
\(529\) 22.9383i 0.997316i
\(530\) −19.1627 27.1319i −0.832374 1.17853i
\(531\) 0 0
\(532\) 25.7395 28.8926i 1.11595 1.25265i
\(533\) −8.66039 + 8.66039i −0.375123 + 0.375123i
\(534\) 0 0
\(535\) −4.00900 + 23.2890i −0.173324 + 1.00687i
\(536\) −4.39677 −0.189911
\(537\) 0 0
\(538\) −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
\(543\) 0 0
\(544\) −53.8947 −2.31071
\(545\) 10.8738 7.67996i 0.465784 0.328973i
\(546\) 0 0
\(547\) 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
\(549\) 0 0
\(550\) 25.3879 12.0907i 1.08255 0.515548i
\(551\) 1.83461i 0.0781569i
\(552\) 0 0
\(553\) −19.8823 + 22.3179i −0.845483 + 0.949054i
\(554\) 5.97022i 0.253650i
\(555\) 0 0
\(556\) 18.9316i 0.802880i
\(557\) 16.3147 + 16.3147i 0.691275 + 0.691275i 0.962512 0.271238i \(-0.0874329\pi\)
−0.271238 + 0.962512i \(0.587433\pi\)
\(558\) 0 0
\(559\) 0.748285 0.0316491
\(560\) 1.96715 17.3622i 0.0831275 0.733686i
\(561\) 0 0
\(562\) 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 \(-0.500328\pi\)
\(564\) 0 0
\(565\) −21.7849 3.75008i −0.916497 0.157767i
\(566\) 48.3556i 2.03254i
\(567\) 0 0
\(568\) −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
\(573\) 0 0
\(574\) −39.2372 + 2.26456i −1.63773 + 0.0945209i
\(575\) 0.534138 + 1.12158i 0.0222751 + 0.0467731i
\(576\) 0 0
\(577\) 29.5905 29.5905i 1.23187 1.23187i 0.268625 0.963245i \(-0.413431\pi\)
0.963245 0.268625i \(-0.0865693\pi\)
\(578\) −41.7545 + 41.7545i −1.73676 + 1.73676i
\(579\) 0 0
\(580\) −0.955943 1.35349i −0.0396934 0.0562007i
\(581\) −1.05410 18.2641i −0.0437316 0.757722i
\(582\) 0 0
\(583\) 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 −0.105375 + 0.994433i \(0.533604\pi\)
−0.994433 + 0.105375i \(0.966396\pi\)
\(588\) 0 0
\(589\) 43.6482i 1.79849i
\(590\) 6.37847 37.0537i 0.262597 1.52547i
\(591\) 0 0
\(592\) −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 \(0.895392\pi\)
\(594\) 0 0
\(595\) −24.7395 31.0618i −1.01422 1.27341i
\(596\) 34.7217 1.42225
\(597\) 0 0
\(598\) −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 \(0.849371\pi\)
\(602\) 1.79294 + 1.59728i 0.0730749 + 0.0651002i
\(603\) 0 0
\(604\) 23.7706i 0.967210i
\(605\) −4.98077 7.05213i −0.202497 0.286710i
\(606\) 0 0
\(607\) −0.576027 + 0.576027i −0.0233802 + 0.0233802i −0.718700 0.695320i \(-0.755263\pi\)
0.695320 + 0.718700i \(0.255263\pi\)
\(608\) −34.1639 34.1639i −1.38553 1.38553i
\(609\) 0 0
\(610\) 25.6696 + 4.41880i 1.03933 + 0.178912i
\(611\) −1.36671 −0.0552911
\(612\) 0 0
\(613\) −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
\(615\) 0 0
\(616\) −6.39583 + 0.369132i −0.257695 + 0.0148728i
\(617\) 3.70013 + 3.70013i 0.148962 + 0.148962i 0.777654 0.628692i \(-0.216410\pi\)
−0.628692 + 0.777654i \(0.716410\pi\)
\(618\) 0 0
\(619\) −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 0
\(622\) −15.2621 + 15.2621i −0.611954 + 0.611954i
\(623\) 13.6558 + 12.1655i 0.547107 + 0.487401i
\(624\) 0 0
\(625\) −19.4097 15.7564i −0.776388 0.630256i
\(626\) 65.7578i 2.62821i
\(627\) 0 0
\(628\) 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
\(633\) 0 0
\(634\) 36.4842i 1.44897i
\(635\) −1.53489 + 8.91646i −0.0609103 + 0.353839i
\(636\) 0 0
\(637\) −7.54472 + 9.52120i −0.298933 + 0.377244i
\(638\) 1.21247 1.21247i 0.0480022 0.0480022i
\(639\) 0 0
\(640\) 15.6065 + 2.68653i 0.616902 + 0.106194i
\(641\) 18.1113 0.715352 0.357676 0.933846i \(-0.383569\pi\)
0.357676 + 0.933846i \(0.383569\pi\)
\(642\) 0 0
\(643\) 32.1062 + 32.1062i 1.26614 + 1.26614i 0.948063 + 0.318082i \(0.103039\pi\)
0.318082 + 0.948063i \(0.396961\pi\)
\(644\) −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 \(-0.867012\pi\)
0.405745 + 0.913986i \(0.367012\pi\)
\(648\) 0 0
\(649\) 21.3439 0.837821
\(650\) 17.2132 + 6.10719i 0.675159 + 0.239544i
\(651\) 0 0
\(652\) −33.2396 33.2396i −1.30176 1.30176i
\(653\) 9.39937 9.39937i 0.367826 0.367826i −0.498858 0.866684i \(-0.666247\pi\)
0.866684 + 0.498858i \(0.166247\pi\)
\(654\) 0 0
\(655\) 17.0730 12.0583i 0.667099 0.471158i
\(656\) 20.8441i 0.813824i
\(657\) 0 0
\(658\) −3.27473 2.91736i −0.127662 0.113730i
\(659\) 9.13808i 0.355969i 0.984033 + 0.177985i \(0.0569577\pi\)
−0.984033 + 0.177985i \(0.943042\pi\)
\(660\) 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
\(663\) 0 0
\(664\) 6.26651 0.243188
\(665\) 4.00774 35.3725i 0.155413 1.37169i
\(666\) 0 0
\(667\) 0.0535642 + 0.0535642i 0.00207401 + 0.00207401i
\(668\) 15.1493 + 15.1493i 0.586146 + 0.586146i
\(669\) 0 0
\(670\) −18.6516 + 13.1733i −0.720575 + 0.508927i
\(671\) 14.7864i 0.570821i
\(672\) 0 0
\(673\) 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
\(675\) 0 0
\(676\) 24.2769 0.933729
\(677\) 1.19694 1.19694i 0.0460022 0.0460022i −0.683731 0.729734i \(-0.739644\pi\)
0.729734 + 0.683731i \(0.239644\pi\)
\(678\) 0 0
\(679\) 33.0264 1.90611i 1.26744 0.0731496i
\(680\) 11.1104 7.84702i 0.426063 0.300919i
\(681\) 0 0
\(682\) −28.8466 + 28.8466i −1.10459 + 1.10459i
\(683\) −2.41553 + 2.41553i −0.0924275 + 0.0924275i −0.751809 0.659381i \(-0.770818\pi\)
0.659381 + 0.751809i \(0.270818\pi\)
\(684\) 0 0
\(685\) 4.03393 23.4338i 0.154129 0.895361i
\(686\) −38.4015 + 6.70863i −1.46618 + 0.256137i
\(687\) 0 0
\(688\) 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
\(693\) 0 0
\(694\) 19.4970i 0.740098i
\(695\) 10.0477 + 14.2263i 0.381132 + 0.539634i
\(696\) 0 0
\(697\) 33.4960 + 33.4960i 1.26875 + 1.26875i
\(698\) 4.12488 + 4.12488i 0.156129 + 0.156129i
\(699\) 0 0
\(700\) 15.4745 + 28.1845i 0.584881 + 1.06527i
\(701\) −13.7870 −0.520727 −0.260364 0.965511i \(-0.583842\pi\)
−0.260364 + 0.965511i \(0.583842\pi\)
\(702\) 0 0
\(703\) −4.42536 4.42536i −0.166906 0.166906i
\(704\) 29.3742i 1.10708i
\(705\) 0 0
\(706\) 2.88915i 0.108735i
\(707\) 12.7236 14.2822i 0.478520 0.537138i
\(708\) 0 0
\(709\) 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
\(711\) 0 0
\(712\) −4.42971 + 4.42971i −0.166010 + 0.166010i
\(713\) −1.27438 1.27438i −0.0477257 0.0477257i
\(714\) 0 0
\(715\) −1.75895 + 10.2181i −0.0657811 + 0.382135i
\(716\) 3.16223 0.118178
\(717\) 0 0
\(718\) 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
\(723\) 0 0
\(724\) −20.6239 −0.766482
\(725\) −1.43670 0.509736i −0.0533577 0.0189311i
\(726\) 0 0
\(727\) −29.8488 + 29.8488i −1.10703 + 1.10703i −0.113491 + 0.993539i \(0.536203\pi\)
−0.993539 + 0.113491i \(0.963797\pi\)
\(728\) −3.10702 2.76795i −0.115154 0.102587i
\(729\) 0 0
\(730\) 54.4825 38.4798i 2.01649 1.42420i
\(731\) 2.89416i 0.107044i
\(732\) 0 0
\(733\) −3.86707 3.86707i −0.142834 0.142834i 0.632074 0.774908i \(-0.282204\pi\)
−0.774908 + 0.632074i \(0.782204\pi\)
\(734\) −38.7082 −1.42875
\(735\) 0 0
\(736\) −1.99493 −0.0735342
\(737\) −9.16599 9.16599i −0.337634 0.337634i
\(738\) 0 0
\(739\) 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
\(741\) 0 0
\(742\) 29.3462 + 26.1436i 1.07733 + 0.959763i
\(743\) 12.0406 12.0406i 0.441728 0.441728i −0.450864 0.892593i \(-0.648884\pi\)
0.892593 + 0.450864i \(0.148884\pi\)
\(744\) 0 0
\(745\) 26.0918 18.4281i 0.955931 0.675154i
\(746\) −61.5467 −2.25338
\(747\) 0 0
\(748\) 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
\(753\) 0 0
\(754\) 1.11373 0.0405598
\(755\) 12.6159 + 17.8625i 0.459141 + 0.650085i
\(756\) 0 0
\(757\) 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 0
\(760\) 12.0171 + 2.06864i 0.435906 + 0.0750374i
\(761\) 32.3002i 1.17088i 0.810716 + 0.585440i \(0.199078\pi\)
−0.810716 + 0.585440i \(0.800922\pi\)
\(762\) 0 0
\(763\) −10.4778 + 11.7613i −0.379320 + 0.425787i
\(764\) 4.71018i 0.170408i
\(765\) 0 0
\(766\) 1.16207i 0.0419874i
\(767\) 9.80287 + 9.80287i 0.353961 + 0.353961i
\(768\) 0 0
\(769\) 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
\(771\) 0 0
\(772\) −19.0260 19.0260i −0.684761 0.684761i
\(773\) −17.7963 17.7963i −0.640088 0.640088i 0.310489 0.950577i \(-0.399507\pi\)
−0.950577 + 0.310489i \(0.899507\pi\)
\(774\) 0 0
\(775\) 34.1813 + 12.1274i 1.22783 + 0.435629i
\(776\) 11.3315i 0.406779i
\(777\) 0 0
\(778\) −38.5937 + 38.5937i −1.38365 + 1.38365i
\(779\) 42.4662i 1.52151i
\(780\) 0 0
\(781\) −40.9030 −1.46362
\(782\) −2.48214 + 2.48214i −0.0887611 + 0.0887611i
\(783\) 0 0
\(784\) 2.37853 + 20.5374i 0.0849476 + 0.733478i
\(785\) 6.78546 + 1.16806i 0.242184 + 0.0416898i