Properties

Label 315.2.p.e.118.1
Level 315
Weight 2
Character 315.118
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 118.1
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 \(\chi\) \(=\) 315.118
Dual form 315.2.p.e.307.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.48838 + 1.48838i) q^{2} -2.43055i q^{4} +(-1.28999 + 1.82645i) q^{5} +(-1.75993 + 1.97552i) q^{7} +(0.640825 + 0.640825i) q^{8} +O(q^{10})\) \(q+(-1.48838 + 1.48838i) q^{2} -2.43055i q^{4} +(-1.28999 + 1.82645i) q^{5} +(-1.75993 + 1.97552i) q^{7} +(0.640825 + 0.640825i) q^{8} +(-0.798469 - 4.63845i) q^{10} +2.67187 q^{11} +(-1.22714 + 1.22714i) q^{13} +(-0.320879 - 5.55976i) q^{14} +2.95352 q^{16} +(-4.74624 - 4.74624i) q^{17} -6.01729 q^{19} +(4.43929 + 3.13538i) q^{20} +(-3.97676 + 3.97676i) q^{22} +(0.175684 + 0.175684i) q^{23} +(-1.67187 - 4.71220i) q^{25} -3.65291i q^{26} +(4.80159 + 4.27759i) q^{28} -0.304889i q^{29} -7.25379i q^{31} +(-5.67761 + 5.67761i) q^{32} +14.1284 q^{34} +(-1.33791 - 5.76281i) q^{35} +(-0.735441 + 0.735441i) q^{37} +(8.95602 - 8.95602i) q^{38} +(-1.99709 + 0.343782i) q^{40} +7.05736i q^{41} +(0.304889 + 0.304889i) q^{43} -6.49412i q^{44} -0.522969 q^{46} +(0.556866 + 0.556866i) q^{47} +(-0.805321 - 6.95352i) q^{49} +(9.50193 + 4.52517i) q^{50} +(2.98263 + 2.98263i) q^{52} +(4.99031 + 4.99031i) q^{53} +(-3.44668 + 4.88005i) q^{55} +(-2.39376 + 0.138155i) q^{56} +(0.453791 + 0.453791i) q^{58} -7.98837 q^{59} +5.53409i q^{61} +(10.7964 + 10.7964i) q^{62} -10.9939i q^{64} +(-0.658323 - 3.82432i) q^{65} +(-3.43055 + 3.43055i) q^{67} +(-11.5360 + 11.5360i) q^{68} +(10.5686 + 6.58594i) q^{70} -15.3087 q^{71} +(-10.0208 + 10.0208i) q^{73} -2.18923i q^{74} +14.6253i q^{76} +(-4.70230 + 5.27832i) q^{77} +11.2973i q^{79} +(-3.81000 + 5.39447i) q^{80} +(-10.5040 - 10.5040i) q^{82} +(-4.88941 + 4.88941i) q^{83} +(14.7914 - 2.54621i) q^{85} -0.907583 q^{86} +(1.71220 + 1.71220i) q^{88} +6.91251 q^{89} +(-0.264559 - 4.58392i) q^{91} +(0.427009 - 0.427009i) q^{92} -1.65766 q^{94} +(7.76222 - 10.9903i) q^{95} +(8.84137 + 8.84137i) q^{97} +(11.5481 + 9.15086i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{7} - 24q^{8} + O(q^{10}) \) \( 16q - 8q^{7} - 24q^{8} + 16q^{11} - 48q^{16} - 16q^{22} + 40q^{23} + 24q^{28} - 48q^{32} + 8q^{35} + 32q^{37} - 16q^{43} + 64q^{46} + 72q^{50} - 24q^{53} - 24q^{56} + 32q^{58} - 40q^{65} - 32q^{67} - 40q^{70} - 64q^{71} + 24q^{77} + 48q^{85} - 64q^{86} - 64q^{88} - 48q^{91} + 40q^{92} + 72q^{95} + 96q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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 0
\(4\) 2.43055i 1.21528i
\(5\) −1.28999 + 1.82645i −0.576899 + 0.816815i
\(6\) 0 0
\(7\) −1.75993 + 1.97552i −0.665189 + 0.746675i
\(8\) 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 \(-0.827365\pi\)
0.516150 + 0.856498i \(0.327365\pi\)
\(14\) −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 \(-0.552700\pi\)
\(18\) 0 0
\(19\) −6.01729 −1.38046 −0.690231 0.723589i \(-0.742491\pi\)
−0.690231 + 0.723589i \(0.742491\pi\)
\(20\) 4.43929 + 3.13538i 0.992656 + 0.701092i
\(21\) 0 0
\(22\) −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 0
\(25\) −1.67187 4.71220i −0.334374 0.942440i
\(26\) 3.65291i 0.716394i
\(27\) 0 0
\(28\) 4.80159 + 4.27759i 0.907416 + 0.808389i
\(29\) 0.304889i 0.0566165i −0.999599 0.0283083i \(-0.990988\pi\)
0.999599 0.0283083i \(-0.00901200\pi\)
\(30\) 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
\(35\) −1.33791 5.76281i −0.226148 0.974093i
\(36\) 0 0
\(37\) −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
\(39\) 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 0.729972 0.683477i \(-0.239533\pi\)
−0.683477 + 0.729972i \(0.739533\pi\)
\(44\) 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 \(0.731707\pi\)
\(48\) 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 0.961228 0.275756i \(-0.0889282\pi\)
−0.275756 + 0.961228i \(0.588928\pi\)
\(54\) 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 \(-0.674068\pi\)
−0.519999 + 0.854167i \(0.674068\pi\)
\(60\) 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 −0.884896 0.465788i \(-0.845771\pi\)
0.465788 + 0.884896i \(0.345771\pi\)
\(68\) −11.5360 + 11.5360i −1.39894 + 1.39894i
\(69\) 0 0
\(70\) 10.5686 + 6.58594i 1.26319 + 0.787170i
\(71\) −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 −0.191323 + 0.981527i \(0.561278\pi\)
−0.981527 + 0.191323i \(0.938722\pi\)
\(74\) 2.18923i 0.254493i
\(75\) 0 0
\(76\) 14.6253i 1.67764i
\(77\) −4.70230 + 5.27832i −0.535876 + 0.601521i
\(78\) 0 0
\(79\) 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
\(81\) 0 0
\(82\) −10.5040 10.5040i −1.15998 1.15998i
\(83\) −4.88941 + 4.88941i −0.536682 + 0.536682i −0.922553 0.385871i \(-0.873901\pi\)
0.385871 + 0.922553i \(0.373901\pi\)
\(84\) 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 \(-0.380603\pi\)
0.366363 + 0.930472i \(0.380603\pi\)
\(90\) 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 \(-0.0310934\pi\)
−0.0975276 + 0.995233i \(0.531093\pi\)
\(98\) 11.5481 + 9.15086i 1.16654 + 0.924376i
\(99\) 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 \(-0.589217\pi\)
0.960977 + 0.276628i \(0.0892171\pi\)
\(104\) −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 \(0.0793344\pi\)
\(108\) 0 0
\(109\) 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
\(111\) 0 0
\(112\) −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 \(0.903942\pi\)
\(114\) 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 −0.568678 0.822560i \(-0.692545\pi\)
0.822560 + 0.568678i \(0.192545\pi\)
\(128\) 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
\(133\) 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 0
\(139\) −7.78902 −0.660656 −0.330328 0.943866i \(-0.607159\pi\)
−0.330328 + 0.943866i \(0.607159\pi\)
\(140\) −14.0068 + 3.25186i −1.18379 + 0.274832i
\(141\) 0 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 \(0.198967\pi\)
−0.810920 + 0.585157i \(0.801033\pi\)
\(150\) 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 \(-0.289211\pi\)
−0.788633 + 0.614864i \(0.789211\pi\)
\(158\) −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 −0.997266 0.0739001i \(-0.976455\pi\)
−0.0739001 0.997266i \(-0.523545\pi\)
\(164\) 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 \(0.860782\pi\)
\(168\) 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 \(-0.631437\pi\)
0.915952 + 0.401288i \(0.131437\pi\)
\(174\) 0 0
\(175\) 12.2514 + 4.99032i 0.926119 + 0.377233i
\(176\) 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 \(0.0154829\pi\)
−0.998817 + 0.0486218i \(0.984517\pi\)
\(180\) 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
\(183\) 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 0.366827 0.930289i \(-0.380444\pi\)
−0.930289 + 0.366827i \(0.880444\pi\)
\(194\) −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 \(0.109003\pi\)
\(198\) 0 0
\(199\) 3.25460 0.230712 0.115356 0.993324i \(-0.463199\pi\)
0.115356 + 0.993324i \(0.463199\pi\)
\(200\) 1.94832 4.09107i 0.137767 0.289283i
\(201\) 0 0
\(202\) −10.7604 10.7604i −0.757101 0.757101i
\(203\) 0.602314 + 0.536583i 0.0422741 + 0.0376607i
\(204\) 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
\(217\) 14.3300 + 12.7661i 0.972782 + 0.866622i
\(218\) −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 \(-0.680355\pi\)
0.843730 + 0.536768i \(0.180355\pi\)
\(224\) −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 \(0.518592\pi\)
\(228\) 0 0
\(229\) 28.9307 1.91180 0.955898 0.293699i \(-0.0948864\pi\)
0.955898 + 0.293699i \(0.0948864\pi\)
\(230\) 0.674623 0.955180i 0.0444833 0.0629827i
\(231\) 0 0
\(232\) 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 \(0.678845\pi\)
\(234\) 0 0
\(235\) −1.73544 + 0.298741i −0.113208 + 0.0194877i
\(236\) 19.4162i 1.26388i
\(237\) 0 0
\(238\) −24.8650 + 27.9109i −1.61176 + 1.80920i
\(239\) 16.1769i 1.04640i 0.852210 + 0.523200i \(0.175262\pi\)
−0.852210 + 0.523200i \(0.824738\pi\)
\(240\) 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
\(245\) 13.7391 + 7.49906i 0.877762 + 0.479098i
\(246\) 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 \(-0.103203\pi\)
−0.318570 + 0.947899i \(0.603203\pi\)
\(258\) 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 −0.991416 0.130744i \(-0.958263\pi\)
−0.130744 0.991416i \(-0.541737\pi\)
\(264\) 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 \(-0.656788\pi\)
−0.472888 + 0.881123i \(0.656788\pi\)
\(270\) 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 −0.764788 0.644282i \(-0.777156\pi\)
0.644282 + 0.764788i \(0.277156\pi\)
\(278\) 11.5930 11.5930i 0.695304 0.695304i
\(279\) 0 0
\(280\) 2.83559 4.55032i 0.169459 0.271934i
\(281\) −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 \(-0.510761\pi\)
0.999429 + 0.0338017i \(0.0107615\pi\)
\(284\) 37.2087i 2.20793i
\(285\) 0 0
\(286\) 9.76010i 0.577127i
\(287\) −13.9419 12.4204i −0.822966 0.733155i
\(288\) 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 \(-0.781843\pi\)
0.632951 + 0.774192i \(0.281843\pi\)
\(294\) 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 \(-0.344019\pi\)
−0.882319 + 0.470652i \(0.844019\pi\)
\(308\) 12.8292 + 11.4292i 0.731014 + 0.651238i
\(309\) 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 −0.292293 + 0.956329i \(0.594418\pi\)
−0.956329 + 0.292293i \(0.905582\pi\)
\(314\) 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 \(0.0881780\pi\)
\(318\) 0 0
\(319\) 0.814625i 0.0456102i
\(320\) 20.0798 + 14.1819i 1.12249 + 0.792793i
\(321\) 0 0
\(322\) 0.920387 1.03313i 0.0512912 0.0575743i
\(323\) 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 −0.917741 0.397180i \(-0.869989\pi\)
0.397180 + 0.917741i \(0.369989\pi\)
\(338\) −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
\(343\) 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 0
\(349\) 2.77139 0.148349 0.0741746 0.997245i \(-0.476368\pi\)
0.0741746 + 0.997245i \(0.476368\pi\)
\(350\) −25.6622 + 10.8072i −1.37170 + 0.577672i
\(351\) 0 0
\(352\) −15.1699 + 15.1699i −0.808556 + 0.808556i
\(353\) −0.970568 + 0.970568i −0.0516581 + 0.0516581i −0.732464 0.680806i \(-0.761630\pi\)
0.680806 + 0.732464i \(0.261630\pi\)
\(354\) 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 \(-0.920831\pi\)
0.969229 0.246160i \(-0.0791688\pi\)
\(360\) 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 \(-0.409351\pi\)
−0.959723 + 0.280948i \(0.909351\pi\)
\(368\) 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 0.997315 + 0.0732339i \(0.0233320\pi\)
0.0732339 + 0.997315i \(0.476668\pi\)
\(374\) 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 \(-0.808787\pi\)
0.824933 0.565230i \(-0.191213\pi\)
\(380\) −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 \(-0.754490\pi\)
0.697063 + 0.717010i \(0.254490\pi\)
\(384\) 0 0
\(385\) −3.57472 15.3975i −0.182185 0.784729i
\(386\) 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 \(0.228323\pi\)
−0.753584 + 0.657352i \(0.771677\pi\)
\(390\) 0 0
\(391\) 1.66768i 0.0843381i
\(392\) 3.93992 4.97206i 0.198996 0.251127i
\(393\) 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 \(-0.0415327\pi\)
−0.130109 + 0.991500i \(0.541533\pi\)
\(398\) −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 \(-0.479187\pi\)
0.0653386 + 0.997863i \(0.479187\pi\)
\(410\) 32.7352 5.63508i 1.61668 0.278297i
\(411\) 0 0
\(412\) −16.8811 16.8811i −0.831672 0.831672i
\(413\) 14.0589 15.7812i 0.691795 0.776540i
\(414\) 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 \(-0.421211\pi\)
0.245003 + 0.969522i \(0.421211\pi\)
\(420\) 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
\(427\) −10.9327 9.73958i −0.529069 0.471332i
\(428\) −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 \(-0.901365\pi\)
0.304935 + 0.952373i \(0.401365\pi\)
\(434\) −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 \(-0.709955\pi\)
−0.612795 + 0.790242i \(0.709955\pi\)
\(440\) −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 0.973125 0.230279i \(-0.0739640\pi\)
−0.230279 + 0.973125i \(0.573964\pi\)
\(444\) 0 0
\(445\) −8.91705 + 12.6254i −0.422709 + 0.598501i
\(446\) 13.6452i 0.646120i
\(447\) 0 0
\(448\) 21.7185 + 19.3484i 1.02610 + 0.914124i
\(449\) 7.01947i 0.331269i −0.986187 0.165635i \(-0.947033\pi\)
0.986187 0.165635i \(-0.0529673\pi\)
\(450\) 0 0
\(451\) 18.8564i 0.887912i
\(452\) −16.9903 + 16.9903i −0.799157 + 0.799157i
\(453\) 0 0
\(454\) −42.1548 −1.97842
\(455\) 8.71359 + 5.42999i 0.408500 + 0.254562i
\(456\) 0 0
\(457\) 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
\(459\) 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 0.863057 0.505106i \(-0.168547\pi\)
−0.505106 + 0.863057i \(0.668547\pi\)
\(464\) 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 \(0.731141\pi\)
\(468\) 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 \(-0.470181\pi\)
0.0935425 + 0.995615i \(0.470181\pi\)
\(480\) 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 −0.900928 0.433969i \(-0.857113\pi\)
0.433969 + 0.900928i \(0.357113\pi\)
\(488\) −3.54638 + 3.54638i −0.160537 + 0.160537i
\(489\) 0 0
\(490\) −31.6105 + 9.28761i −1.42802 + 0.419571i
\(491\) 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
\(497\) 26.9423 30.2427i 1.20853 1.35657i
\(498\) 0 0
\(499\) 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
\(501\) 0 0
\(502\) 10.3448 + 10.3448i 0.461712 + 0.461712i
\(503\) −17.9504 + 17.9504i −0.800367 + 0.800367i −0.983153 0.182786i \(-0.941489\pi\)
0.182786 + 0.983153i \(0.441489\pi\)
\(504\) 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 \(-0.377818\pi\)
0.374489 + 0.927231i \(0.377818\pi\)
\(510\) 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
\(518\) 4.32486 + 3.85289i 0.190024 + 0.169286i
\(519\) 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 \(-0.737877\pi\)
0.733519 + 0.679669i \(0.237877\pi\)
\(524\) −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
\(532\) −28.8926 25.7395i −1.25265 1.11595i
\(533\) −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 −0.620340 0.784333i \(-0.713005\pi\)
0.784333 + 0.620340i \(0.213005\pi\)
\(548\) 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
\(553\) −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 \(0.0874329\pi\)
\(558\) 0 0
\(559\) −0.748285 −0.0316491
\(560\) −3.95154 17.0206i −0.166983 0.719251i
\(561\) 0 0
\(562\) 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 \(-0.000328032\pi\)
\(564\) 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 \(-0.998147\pi\)
0.999983 0.00582283i \(-0.00185348\pi\)
\(570\) 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 −0.963245 0.268625i \(-0.913431\pi\)
−0.268625 0.963245i \(-0.586569\pi\)
\(578\) −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 0.994433 + 0.105375i \(0.0336041\pi\)
0.105375 + 0.994433i \(0.466396\pi\)
\(588\) 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 \(-0.604608\pi\)
0.946484 + 0.322751i \(0.104608\pi\)
\(594\) 0 0
\(595\) −21.0017 + 33.7017i −0.860985 + 1.38164i
\(596\) 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 \(-0.849597\pi\)
0.890431 0.455119i \(-0.150403\pi\)
\(600\) 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
\(603\) 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 \(-0.244737\pi\)
−0.695320 + 0.718700i \(0.744737\pi\)
\(608\) 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 0.291361 0.956613i \(-0.405892\pi\)
−0.956613 + 0.291361i \(0.905892\pi\)
\(614\) 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 \(0.216410\pi\)
\(618\) 0 0
\(619\) 39.8840 1.60307 0.801536 0.597946i \(-0.204016\pi\)
0.801536 + 0.597946i \(0.204016\pi\)
\(620\) 22.7434 32.2017i 0.913396 1.29325i
\(621\) 0 0
\(622\) 15.2621 + 15.2621i 0.611954 + 0.611954i
\(623\) −12.1655 + 13.6558i −0.487401 + 0.547107i
\(624\) 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
\(637\) 9.52120 + 7.54472i 0.377244 + 0.298933i
\(638\) 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 −0.318082 + 0.948063i \(0.603039\pi\)
−0.948063 + 0.318082i \(0.896961\pi\)
\(644\) 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 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 0.866684 0.498858i \(-0.166247\pi\)
−0.498858 + 0.866684i \(0.666247\pi\)
\(654\) 0 0
\(655\) 17.0730 + 12.0583i 0.667099 + 0.471158i
\(656\) 20.8441i 0.813824i
\(657\) 0 0
\(658\) 2.91736 3.27473i 0.113730 0.127662i
\(659\) 9.13808i 0.355969i −0.984033 0.177985i \(-0.943042\pi\)
0.984033 0.177985i \(-0.0569577\pi\)
\(660\) 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
\(665\) 8.05059 + 34.6765i 0.312188 + 1.34470i
\(666\) 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 0.999319 + 0.0368867i \(0.0117441\pi\)
0.0368867 + 0.999319i \(0.488256\pi\)
\(674\) 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 \(0.760356\pi\)
\(678\) 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 0.659381 0.751809i \(-0.270818\pi\)
−0.751809 + 0.659381i \(0.770818\pi\)
\(684\) 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
\(700\) 12.1292 29.7777i 0.458442 1.12549i
\(701\) −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
\(707\) −14.2822 12.7236i −0.537138 0.478520i
\(708\) 0 0
\(709\) 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
\(711\) 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 \(-0.688338\pi\)
−0.557758 + 0.830003i \(0.688338\pi\)
\(720\) 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 0.993539 + 0.113491i \(0.0362034\pi\)
0.113491 + 0.993539i \(0.463797\pi\)
\(728\) 2.76795 3.10702i 0.102587 0.115154i
\(729\) 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 \(-0.717796\pi\)
0.774908 + 0.632074i \(0.217796\pi\)
\(734\) 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 \(0.0706797\pi\)
−0.975449 + 0.220227i \(0.929320\pi\)
\(740\) −5.57073 + 0.958952i −0.204784 + 0.0352518i
\(741\) 0 0
\(742\) 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 \(0.648884\pi\)
\(744\) 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 0.0667825 0.997768i \(-0.478727\pi\)
0.997768 0.0667825i \(-0.0212733\pi\)
\(758\) 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
\(763\) −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
\(768\) 0 0
\(769\) −18.4310 −0.664640 −0.332320 0.943167i \(-0.607831\pi\)
−0.332320 + 0.943167i \(0.607831\pi\)
\(770\) 28.2379 + 17.5968i 1.01762 + 0.634144i
\(771\) 0 0
\(772\) −19.0260 + 19.0260i −0.684761 + 0.684761i
\(773\) 17.7963 17.7963i 0.640088 0.640088i −0.310489 0.950577i \(-0.600493\pi\)
0.950577 + 0.310489i \(0.100493\pi\)
\(774\) 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 <