Properties

Label 240.2.v.a.113.1
Level $240$
Weight $2$
Character 240.113
Analytic conductor $1.916$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.v (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.91640964851\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 113.1
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 240.113
Dual form 240.2.v.a.17.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.41421i) q^{3} +(1.00000 - 2.00000i) q^{5} +(-0.414214 + 0.414214i) q^{7} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.41421i) q^{3} +(1.00000 - 2.00000i) q^{5} +(-0.414214 + 0.414214i) q^{7} +(-1.00000 + 2.82843i) q^{9} -4.82843i q^{11} +(-1.82843 - 1.82843i) q^{13} +(-3.82843 + 0.585786i) q^{15} +(-3.82843 - 3.82843i) q^{17} +4.82843i q^{19} +(1.00000 + 0.171573i) q^{21} +(1.58579 - 1.58579i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(5.00000 - 1.41421i) q^{27} +7.65685 q^{29} +5.65685 q^{31} +(-6.82843 + 4.82843i) q^{33} +(0.414214 + 1.24264i) q^{35} +(-0.171573 + 0.171573i) q^{37} +(-0.757359 + 4.41421i) q^{39} +5.65685i q^{41} +(-2.41421 - 2.41421i) q^{43} +(4.65685 + 4.82843i) q^{45} +(6.41421 + 6.41421i) q^{47} +6.65685i q^{49} +(-1.58579 + 9.24264i) q^{51} +(3.00000 - 3.00000i) q^{53} +(-9.65685 - 4.82843i) q^{55} +(6.82843 - 4.82843i) q^{57} -4.00000 q^{59} +11.6569 q^{61} +(-0.757359 - 1.58579i) q^{63} +(-5.48528 + 1.82843i) q^{65} +(4.07107 - 4.07107i) q^{67} +(-3.82843 - 0.656854i) q^{69} -6.48528i q^{71} +(6.65685 + 6.65685i) q^{73} +(-2.65685 + 8.24264i) q^{75} +(2.00000 + 2.00000i) q^{77} -4.82843i q^{79} +(-7.00000 - 5.65685i) q^{81} +(-5.24264 + 5.24264i) q^{83} +(-11.4853 + 3.82843i) q^{85} +(-7.65685 - 10.8284i) q^{87} -4.34315 q^{89} +1.51472 q^{91} +(-5.65685 - 8.00000i) q^{93} +(9.65685 + 4.82843i) q^{95} +(1.00000 - 1.00000i) q^{97} +(13.6569 + 4.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} + 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{13} - 4 q^{15} - 4 q^{17} + 4 q^{21} + 12 q^{23} - 12 q^{25} + 20 q^{27} + 8 q^{29} - 16 q^{33} - 4 q^{35} - 12 q^{37} - 20 q^{39} - 4 q^{43} - 4 q^{45} + 20 q^{47} - 12 q^{51} + 12 q^{53} - 16 q^{55} + 16 q^{57} - 16 q^{59} + 24 q^{61} - 20 q^{63} + 12 q^{65} - 12 q^{67} - 4 q^{69} + 4 q^{73} + 12 q^{75} + 8 q^{77} - 28 q^{81} - 4 q^{83} - 12 q^{85} - 8 q^{87} - 40 q^{89} + 40 q^{91} + 16 q^{95} + 4 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 1.41421i −0.577350 0.816497i
\(4\) 0 0
\(5\) 1.00000 2.00000i 0.447214 0.894427i
\(6\) 0 0
\(7\) −0.414214 + 0.414214i −0.156558 + 0.156558i −0.781040 0.624482i \(-0.785310\pi\)
0.624482 + 0.781040i \(0.285310\pi\)
\(8\) 0 0
\(9\) −1.00000 + 2.82843i −0.333333 + 0.942809i
\(10\) 0 0
\(11\) 4.82843i 1.45583i −0.685670 0.727913i \(-0.740491\pi\)
0.685670 0.727913i \(-0.259509\pi\)
\(12\) 0 0
\(13\) −1.82843 1.82843i −0.507114 0.507114i 0.406525 0.913640i \(-0.366740\pi\)
−0.913640 + 0.406525i \(0.866740\pi\)
\(14\) 0 0
\(15\) −3.82843 + 0.585786i −0.988496 + 0.151249i
\(16\) 0 0
\(17\) −3.82843 3.82843i −0.928530 0.928530i 0.0690811 0.997611i \(-0.477993\pi\)
−0.997611 + 0.0690811i \(0.977993\pi\)
\(18\) 0 0
\(19\) 4.82843i 1.10772i 0.832611 + 0.553859i \(0.186845\pi\)
−0.832611 + 0.553859i \(0.813155\pi\)
\(20\) 0 0
\(21\) 1.00000 + 0.171573i 0.218218 + 0.0374403i
\(22\) 0 0
\(23\) 1.58579 1.58579i 0.330659 0.330659i −0.522178 0.852837i \(-0.674880\pi\)
0.852837 + 0.522178i \(0.174880\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 0 0
\(27\) 5.00000 1.41421i 0.962250 0.272166i
\(28\) 0 0
\(29\) 7.65685 1.42184 0.710921 0.703272i \(-0.248278\pi\)
0.710921 + 0.703272i \(0.248278\pi\)
\(30\) 0 0
\(31\) 5.65685 1.01600 0.508001 0.861357i \(-0.330385\pi\)
0.508001 + 0.861357i \(0.330385\pi\)
\(32\) 0 0
\(33\) −6.82843 + 4.82843i −1.18868 + 0.840521i
\(34\) 0 0
\(35\) 0.414214 + 1.24264i 0.0700149 + 0.210045i
\(36\) 0 0
\(37\) −0.171573 + 0.171573i −0.0282064 + 0.0282064i −0.721069 0.692863i \(-0.756349\pi\)
0.692863 + 0.721069i \(0.256349\pi\)
\(38\) 0 0
\(39\) −0.757359 + 4.41421i −0.121275 + 0.706840i
\(40\) 0 0
\(41\) 5.65685i 0.883452i 0.897150 + 0.441726i \(0.145634\pi\)
−0.897150 + 0.441726i \(0.854366\pi\)
\(42\) 0 0
\(43\) −2.41421 2.41421i −0.368164 0.368164i 0.498643 0.866807i \(-0.333832\pi\)
−0.866807 + 0.498643i \(0.833832\pi\)
\(44\) 0 0
\(45\) 4.65685 + 4.82843i 0.694203 + 0.719779i
\(46\) 0 0
\(47\) 6.41421 + 6.41421i 0.935609 + 0.935609i 0.998049 0.0624395i \(-0.0198881\pi\)
−0.0624395 + 0.998049i \(0.519888\pi\)
\(48\) 0 0
\(49\) 6.65685i 0.950979i
\(50\) 0 0
\(51\) −1.58579 + 9.24264i −0.222055 + 1.29423i
\(52\) 0 0
\(53\) 3.00000 3.00000i 0.412082 0.412082i −0.470381 0.882463i \(-0.655884\pi\)
0.882463 + 0.470381i \(0.155884\pi\)
\(54\) 0 0
\(55\) −9.65685 4.82843i −1.30213 0.651065i
\(56\) 0 0
\(57\) 6.82843 4.82843i 0.904447 0.639541i
\(58\) 0 0
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) 11.6569 1.49251 0.746254 0.665662i \(-0.231851\pi\)
0.746254 + 0.665662i \(0.231851\pi\)
\(62\) 0 0
\(63\) −0.757359 1.58579i −0.0954183 0.199790i
\(64\) 0 0
\(65\) −5.48528 + 1.82843i −0.680365 + 0.226788i
\(66\) 0 0
\(67\) 4.07107 4.07107i 0.497360 0.497360i −0.413255 0.910615i \(-0.635608\pi\)
0.910615 + 0.413255i \(0.135608\pi\)
\(68\) 0 0
\(69\) −3.82843 0.656854i −0.460888 0.0790760i
\(70\) 0 0
\(71\) 6.48528i 0.769661i −0.922987 0.384831i \(-0.874260\pi\)
0.922987 0.384831i \(-0.125740\pi\)
\(72\) 0 0
\(73\) 6.65685 + 6.65685i 0.779126 + 0.779126i 0.979682 0.200556i \(-0.0642750\pi\)
−0.200556 + 0.979682i \(0.564275\pi\)
\(74\) 0 0
\(75\) −2.65685 + 8.24264i −0.306787 + 0.951778i
\(76\) 0 0
\(77\) 2.00000 + 2.00000i 0.227921 + 0.227921i
\(78\) 0 0
\(79\) 4.82843i 0.543240i −0.962405 0.271620i \(-0.912441\pi\)
0.962405 0.271620i \(-0.0875595\pi\)
\(80\) 0 0
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) 0 0
\(83\) −5.24264 + 5.24264i −0.575455 + 0.575455i −0.933648 0.358193i \(-0.883393\pi\)
0.358193 + 0.933648i \(0.383393\pi\)
\(84\) 0 0
\(85\) −11.4853 + 3.82843i −1.24575 + 0.415251i
\(86\) 0 0
\(87\) −7.65685 10.8284i −0.820901 1.16093i
\(88\) 0 0
\(89\) −4.34315 −0.460373 −0.230186 0.973147i \(-0.573934\pi\)
−0.230186 + 0.973147i \(0.573934\pi\)
\(90\) 0 0
\(91\) 1.51472 0.158786
\(92\) 0 0
\(93\) −5.65685 8.00000i −0.586588 0.829561i
\(94\) 0 0
\(95\) 9.65685 + 4.82843i 0.990772 + 0.495386i
\(96\) 0 0
\(97\) 1.00000 1.00000i 0.101535 0.101535i −0.654515 0.756049i \(-0.727127\pi\)
0.756049 + 0.654515i \(0.227127\pi\)
\(98\) 0 0
\(99\) 13.6569 + 4.82843i 1.37257 + 0.485275i
\(100\) 0 0
\(101\) 1.65685i 0.164863i −0.996597 0.0824316i \(-0.973731\pi\)
0.996597 0.0824316i \(-0.0262686\pi\)
\(102\) 0 0
\(103\) 8.41421 + 8.41421i 0.829077 + 0.829077i 0.987389 0.158312i \(-0.0506052\pi\)
−0.158312 + 0.987389i \(0.550605\pi\)
\(104\) 0 0
\(105\) 1.34315 1.82843i 0.131078 0.178436i
\(106\) 0 0
\(107\) −12.4142 12.4142i −1.20013 1.20013i −0.974127 0.226000i \(-0.927435\pi\)
−0.226000 0.974127i \(-0.572565\pi\)
\(108\) 0 0
\(109\) 4.00000i 0.383131i −0.981480 0.191565i \(-0.938644\pi\)
0.981480 0.191565i \(-0.0613564\pi\)
\(110\) 0 0
\(111\) 0.414214 + 0.0710678i 0.0393154 + 0.00674546i
\(112\) 0 0
\(113\) 7.48528 7.48528i 0.704156 0.704156i −0.261144 0.965300i \(-0.584100\pi\)
0.965300 + 0.261144i \(0.0840997\pi\)
\(114\) 0 0
\(115\) −1.58579 4.75736i −0.147875 0.443626i
\(116\) 0 0
\(117\) 7.00000 3.34315i 0.647150 0.309074i
\(118\) 0 0
\(119\) 3.17157 0.290738
\(120\) 0 0
\(121\) −12.3137 −1.11943
\(122\) 0 0
\(123\) 8.00000 5.65685i 0.721336 0.510061i
\(124\) 0 0
\(125\) −11.0000 + 2.00000i −0.983870 + 0.178885i
\(126\) 0 0
\(127\) −8.41421 + 8.41421i −0.746641 + 0.746641i −0.973847 0.227206i \(-0.927041\pi\)
0.227206 + 0.973847i \(0.427041\pi\)
\(128\) 0 0
\(129\) −1.00000 + 5.82843i −0.0880451 + 0.513164i
\(130\) 0 0
\(131\) 3.17157i 0.277102i 0.990355 + 0.138551i \(0.0442444\pi\)
−0.990355 + 0.138551i \(0.955756\pi\)
\(132\) 0 0
\(133\) −2.00000 2.00000i −0.173422 0.173422i
\(134\) 0 0
\(135\) 2.17157 11.4142i 0.186899 0.982379i
\(136\) 0 0
\(137\) 4.17157 + 4.17157i 0.356402 + 0.356402i 0.862485 0.506083i \(-0.168907\pi\)
−0.506083 + 0.862485i \(0.668907\pi\)
\(138\) 0 0
\(139\) 3.17157i 0.269009i −0.990913 0.134505i \(-0.957056\pi\)
0.990913 0.134505i \(-0.0429443\pi\)
\(140\) 0 0
\(141\) 2.65685 15.4853i 0.223747 1.30410i
\(142\) 0 0
\(143\) −8.82843 + 8.82843i −0.738270 + 0.738270i
\(144\) 0 0
\(145\) 7.65685 15.3137i 0.635867 1.27173i
\(146\) 0 0
\(147\) 9.41421 6.65685i 0.776471 0.549048i
\(148\) 0 0
\(149\) −9.31371 −0.763009 −0.381504 0.924367i \(-0.624594\pi\)
−0.381504 + 0.924367i \(0.624594\pi\)
\(150\) 0 0
\(151\) 2.34315 0.190682 0.0953412 0.995445i \(-0.469606\pi\)
0.0953412 + 0.995445i \(0.469606\pi\)
\(152\) 0 0
\(153\) 14.6569 7.00000i 1.18494 0.565916i
\(154\) 0 0
\(155\) 5.65685 11.3137i 0.454369 0.908739i
\(156\) 0 0
\(157\) −11.4853 + 11.4853i −0.916625 + 0.916625i −0.996782 0.0801570i \(-0.974458\pi\)
0.0801570 + 0.996782i \(0.474458\pi\)
\(158\) 0 0
\(159\) −7.24264 1.24264i −0.574379 0.0985478i
\(160\) 0 0
\(161\) 1.31371i 0.103535i
\(162\) 0 0
\(163\) −2.41421 2.41421i −0.189096 0.189096i 0.606209 0.795305i \(-0.292689\pi\)
−0.795305 + 0.606209i \(0.792689\pi\)
\(164\) 0 0
\(165\) 2.82843 + 18.4853i 0.220193 + 1.43908i
\(166\) 0 0
\(167\) 0.757359 + 0.757359i 0.0586062 + 0.0586062i 0.735802 0.677196i \(-0.236805\pi\)
−0.677196 + 0.735802i \(0.736805\pi\)
\(168\) 0 0
\(169\) 6.31371i 0.485670i
\(170\) 0 0
\(171\) −13.6569 4.82843i −1.04437 0.369239i
\(172\) 0 0
\(173\) −10.6569 + 10.6569i −0.810226 + 0.810226i −0.984667 0.174442i \(-0.944188\pi\)
0.174442 + 0.984667i \(0.444188\pi\)
\(174\) 0 0
\(175\) 2.89949 + 0.414214i 0.219181 + 0.0313116i
\(176\) 0 0
\(177\) 4.00000 + 5.65685i 0.300658 + 0.425195i
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 17.3137 1.28692 0.643459 0.765481i \(-0.277499\pi\)
0.643459 + 0.765481i \(0.277499\pi\)
\(182\) 0 0
\(183\) −11.6569 16.4853i −0.861699 1.21863i
\(184\) 0 0
\(185\) 0.171573 + 0.514719i 0.0126143 + 0.0378429i
\(186\) 0 0
\(187\) −18.4853 + 18.4853i −1.35178 + 1.35178i
\(188\) 0 0
\(189\) −1.48528 + 2.65685i −0.108038 + 0.193258i
\(190\) 0 0
\(191\) 24.1421i 1.74686i 0.486946 + 0.873432i \(0.338111\pi\)
−0.486946 + 0.873432i \(0.661889\pi\)
\(192\) 0 0
\(193\) 3.34315 + 3.34315i 0.240645 + 0.240645i 0.817117 0.576472i \(-0.195571\pi\)
−0.576472 + 0.817117i \(0.695571\pi\)
\(194\) 0 0
\(195\) 8.07107 + 5.92893i 0.577981 + 0.424580i
\(196\) 0 0
\(197\) −3.34315 3.34315i −0.238189 0.238189i 0.577911 0.816100i \(-0.303868\pi\)
−0.816100 + 0.577911i \(0.803868\pi\)
\(198\) 0 0
\(199\) 1.51472i 0.107376i −0.998558 0.0536878i \(-0.982902\pi\)
0.998558 0.0536878i \(-0.0170976\pi\)
\(200\) 0 0
\(201\) −9.82843 1.68629i −0.693244 0.118942i
\(202\) 0 0
\(203\) −3.17157 + 3.17157i −0.222601 + 0.222601i
\(204\) 0 0
\(205\) 11.3137 + 5.65685i 0.790184 + 0.395092i
\(206\) 0 0
\(207\) 2.89949 + 6.07107i 0.201529 + 0.421968i
\(208\) 0 0
\(209\) 23.3137 1.61264
\(210\) 0 0
\(211\) 12.9706 0.892930 0.446465 0.894801i \(-0.352683\pi\)
0.446465 + 0.894801i \(0.352683\pi\)
\(212\) 0 0
\(213\) −9.17157 + 6.48528i −0.628426 + 0.444364i
\(214\) 0 0
\(215\) −7.24264 + 2.41421i −0.493944 + 0.164648i
\(216\) 0 0
\(217\) −2.34315 + 2.34315i −0.159063 + 0.159063i
\(218\) 0 0
\(219\) 2.75736 16.0711i 0.186325 1.08598i
\(220\) 0 0
\(221\) 14.0000i 0.941742i
\(222\) 0 0
\(223\) 8.41421 + 8.41421i 0.563457 + 0.563457i 0.930288 0.366830i \(-0.119557\pi\)
−0.366830 + 0.930288i \(0.619557\pi\)
\(224\) 0 0
\(225\) 14.3137 4.48528i 0.954247 0.299019i
\(226\) 0 0
\(227\) 14.8995 + 14.8995i 0.988914 + 0.988914i 0.999939 0.0110250i \(-0.00350944\pi\)
−0.0110250 + 0.999939i \(0.503509\pi\)
\(228\) 0 0
\(229\) 25.6569i 1.69545i −0.530434 0.847726i \(-0.677971\pi\)
0.530434 0.847726i \(-0.322029\pi\)
\(230\) 0 0
\(231\) 0.828427 4.82843i 0.0545065 0.317687i
\(232\) 0 0
\(233\) −6.17157 + 6.17157i −0.404313 + 0.404313i −0.879750 0.475437i \(-0.842290\pi\)
0.475437 + 0.879750i \(0.342290\pi\)
\(234\) 0 0
\(235\) 19.2426 6.41421i 1.25525 0.418417i
\(236\) 0 0
\(237\) −6.82843 + 4.82843i −0.443554 + 0.313640i
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) −11.6569 −0.750884 −0.375442 0.926846i \(-0.622509\pi\)
−0.375442 + 0.926846i \(0.622509\pi\)
\(242\) 0 0
\(243\) −1.00000 + 15.5563i −0.0641500 + 0.997940i
\(244\) 0 0
\(245\) 13.3137 + 6.65685i 0.850582 + 0.425291i
\(246\) 0 0
\(247\) 8.82843 8.82843i 0.561739 0.561739i
\(248\) 0 0
\(249\) 12.6569 + 2.17157i 0.802096 + 0.137618i
\(250\) 0 0
\(251\) 9.51472i 0.600564i −0.953851 0.300282i \(-0.902919\pi\)
0.953851 0.300282i \(-0.0970807\pi\)
\(252\) 0 0
\(253\) −7.65685 7.65685i −0.481382 0.481382i
\(254\) 0 0
\(255\) 16.8995 + 12.4142i 1.05829 + 0.777408i
\(256\) 0 0
\(257\) 7.48528 + 7.48528i 0.466919 + 0.466919i 0.900915 0.433996i \(-0.142897\pi\)
−0.433996 + 0.900915i \(0.642897\pi\)
\(258\) 0 0
\(259\) 0.142136i 0.00883188i
\(260\) 0 0
\(261\) −7.65685 + 21.6569i −0.473947 + 1.34053i
\(262\) 0 0
\(263\) 12.8995 12.8995i 0.795417 0.795417i −0.186952 0.982369i \(-0.559861\pi\)
0.982369 + 0.186952i \(0.0598609\pi\)
\(264\) 0 0
\(265\) −3.00000 9.00000i −0.184289 0.552866i
\(266\) 0 0
\(267\) 4.34315 + 6.14214i 0.265796 + 0.375893i
\(268\) 0 0
\(269\) −28.6274 −1.74544 −0.872722 0.488217i \(-0.837647\pi\)
−0.872722 + 0.488217i \(0.837647\pi\)
\(270\) 0 0
\(271\) −21.6569 −1.31556 −0.657780 0.753210i \(-0.728504\pi\)
−0.657780 + 0.753210i \(0.728504\pi\)
\(272\) 0 0
\(273\) −1.51472 2.14214i −0.0916749 0.129648i
\(274\) 0 0
\(275\) −19.3137 + 14.4853i −1.16466 + 0.873495i
\(276\) 0 0
\(277\) −13.8284 + 13.8284i −0.830870 + 0.830870i −0.987636 0.156766i \(-0.949893\pi\)
0.156766 + 0.987636i \(0.449893\pi\)
\(278\) 0 0
\(279\) −5.65685 + 16.0000i −0.338667 + 0.957895i
\(280\) 0 0
\(281\) 5.65685i 0.337460i −0.985662 0.168730i \(-0.946033\pi\)
0.985662 0.168730i \(-0.0539665\pi\)
\(282\) 0 0
\(283\) 3.24264 + 3.24264i 0.192755 + 0.192755i 0.796885 0.604130i \(-0.206479\pi\)
−0.604130 + 0.796885i \(0.706479\pi\)
\(284\) 0 0
\(285\) −2.82843 18.4853i −0.167542 1.09497i
\(286\) 0 0
\(287\) −2.34315 2.34315i −0.138312 0.138312i
\(288\) 0 0
\(289\) 12.3137i 0.724336i
\(290\) 0 0
\(291\) −2.41421 0.414214i −0.141524 0.0242816i
\(292\) 0 0
\(293\) 5.34315 5.34315i 0.312150 0.312150i −0.533592 0.845742i \(-0.679158\pi\)
0.845742 + 0.533592i \(0.179158\pi\)
\(294\) 0 0
\(295\) −4.00000 + 8.00000i −0.232889 + 0.465778i
\(296\) 0 0
\(297\) −6.82843 24.1421i −0.396226 1.40087i
\(298\) 0 0
\(299\) −5.79899 −0.335364
\(300\) 0 0
\(301\) 2.00000 0.115278
\(302\) 0 0
\(303\) −2.34315 + 1.65685i −0.134610 + 0.0951838i
\(304\) 0 0
\(305\) 11.6569 23.3137i 0.667470 1.33494i
\(306\) 0 0
\(307\) −12.8995 + 12.8995i −0.736213 + 0.736213i −0.971843 0.235630i \(-0.924285\pi\)
0.235630 + 0.971843i \(0.424285\pi\)
\(308\) 0 0
\(309\) 3.48528 20.3137i 0.198271 1.15561i
\(310\) 0 0
\(311\) 22.4853i 1.27502i −0.770441 0.637512i \(-0.779964\pi\)
0.770441 0.637512i \(-0.220036\pi\)
\(312\) 0 0
\(313\) 20.3137 + 20.3137i 1.14820 + 1.14820i 0.986907 + 0.161292i \(0.0515661\pi\)
0.161292 + 0.986907i \(0.448434\pi\)
\(314\) 0 0
\(315\) −3.92893 0.0710678i −0.221370 0.00400422i
\(316\) 0 0
\(317\) −6.65685 6.65685i −0.373886 0.373886i 0.495004 0.868891i \(-0.335166\pi\)
−0.868891 + 0.495004i \(0.835166\pi\)
\(318\) 0 0
\(319\) 36.9706i 2.06995i
\(320\) 0 0
\(321\) −5.14214 + 29.9706i −0.287006 + 1.67279i
\(322\) 0 0
\(323\) 18.4853 18.4853i 1.02855 1.02855i
\(324\) 0 0
\(325\) −1.82843 + 12.7990i −0.101423 + 0.709960i
\(326\) 0 0
\(327\) −5.65685 + 4.00000i −0.312825 + 0.221201i
\(328\) 0 0
\(329\) −5.31371 −0.292954
\(330\) 0 0
\(331\) −1.65685 −0.0910689 −0.0455345 0.998963i \(-0.514499\pi\)
−0.0455345 + 0.998963i \(0.514499\pi\)
\(332\) 0 0
\(333\) −0.313708 0.656854i −0.0171911 0.0359954i
\(334\) 0 0
\(335\) −4.07107 12.2132i −0.222426 0.667279i
\(336\) 0 0
\(337\) 1.00000 1.00000i 0.0544735 0.0544735i −0.679345 0.733819i \(-0.737736\pi\)
0.733819 + 0.679345i \(0.237736\pi\)
\(338\) 0 0
\(339\) −18.0711 3.10051i −0.981486 0.168396i
\(340\) 0 0
\(341\) 27.3137i 1.47912i
\(342\) 0 0
\(343\) −5.65685 5.65685i −0.305441 0.305441i
\(344\) 0 0
\(345\) −5.14214 + 7.00000i −0.276843 + 0.376867i
\(346\) 0 0
\(347\) −2.07107 2.07107i −0.111181 0.111181i 0.649328 0.760509i \(-0.275050\pi\)
−0.760509 + 0.649328i \(0.775050\pi\)
\(348\) 0 0
\(349\) 1.65685i 0.0886894i −0.999016 0.0443447i \(-0.985880\pi\)
0.999016 0.0443447i \(-0.0141200\pi\)
\(350\) 0 0
\(351\) −11.7279 6.55635i −0.625990 0.349952i
\(352\) 0 0
\(353\) −1.48528 + 1.48528i −0.0790536 + 0.0790536i −0.745528 0.666474i \(-0.767803\pi\)
0.666474 + 0.745528i \(0.267803\pi\)
\(354\) 0 0
\(355\) −12.9706 6.48528i −0.688406 0.344203i
\(356\) 0 0
\(357\) −3.17157 4.48528i −0.167857 0.237386i
\(358\) 0 0
\(359\) −12.6863 −0.669557 −0.334778 0.942297i \(-0.608661\pi\)
−0.334778 + 0.942297i \(0.608661\pi\)
\(360\) 0 0
\(361\) −4.31371 −0.227037
\(362\) 0 0
\(363\) 12.3137 + 17.4142i 0.646302 + 0.914009i
\(364\) 0 0
\(365\) 19.9706 6.65685i 1.04531 0.348436i
\(366\) 0 0
\(367\) 13.2426 13.2426i 0.691260 0.691260i −0.271249 0.962509i \(-0.587437\pi\)
0.962509 + 0.271249i \(0.0874367\pi\)
\(368\) 0 0
\(369\) −16.0000 5.65685i −0.832927 0.294484i
\(370\) 0 0
\(371\) 2.48528i 0.129029i
\(372\) 0 0
\(373\) 17.4853 + 17.4853i 0.905354 + 0.905354i 0.995893 0.0905393i \(-0.0288591\pi\)
−0.0905393 + 0.995893i \(0.528859\pi\)
\(374\) 0 0
\(375\) 13.8284 + 13.5563i 0.714097 + 0.700047i
\(376\) 0 0
\(377\) −14.0000 14.0000i −0.721037 0.721037i
\(378\) 0 0
\(379\) 9.79899i 0.503340i −0.967813 0.251670i \(-0.919020\pi\)
0.967813 0.251670i \(-0.0809798\pi\)
\(380\) 0 0
\(381\) 20.3137 + 3.48528i 1.04070 + 0.178556i
\(382\) 0 0
\(383\) 9.58579 9.58579i 0.489811 0.489811i −0.418436 0.908246i \(-0.637421\pi\)
0.908246 + 0.418436i \(0.137421\pi\)
\(384\) 0 0
\(385\) 6.00000 2.00000i 0.305788 0.101929i
\(386\) 0 0
\(387\) 9.24264 4.41421i 0.469830 0.224387i
\(388\) 0 0
\(389\) 29.3137 1.48626 0.743132 0.669145i \(-0.233339\pi\)
0.743132 + 0.669145i \(0.233339\pi\)
\(390\) 0 0
\(391\) −12.1421 −0.614054
\(392\) 0 0
\(393\) 4.48528 3.17157i 0.226253 0.159985i
\(394\) 0 0
\(395\) −9.65685 4.82843i −0.485889 0.242945i
\(396\) 0 0
\(397\) 2.17157 2.17157i 0.108988 0.108988i −0.650510 0.759498i \(-0.725445\pi\)
0.759498 + 0.650510i \(0.225445\pi\)
\(398\) 0 0
\(399\) −0.828427 + 4.82843i −0.0414732 + 0.241724i
\(400\) 0 0
\(401\) 16.0000i 0.799002i −0.916733 0.399501i \(-0.869183\pi\)
0.916733 0.399501i \(-0.130817\pi\)
\(402\) 0 0
\(403\) −10.3431 10.3431i −0.515229 0.515229i
\(404\) 0 0
\(405\) −18.3137 + 8.34315i −0.910015 + 0.414574i
\(406\) 0 0
\(407\) 0.828427 + 0.828427i 0.0410636 + 0.0410636i
\(408\) 0 0
\(409\) 10.3431i 0.511436i −0.966751 0.255718i \(-0.917688\pi\)
0.966751 0.255718i \(-0.0823118\pi\)
\(410\) 0 0
\(411\) 1.72792 10.0711i 0.0852321 0.496769i
\(412\) 0 0
\(413\) 1.65685 1.65685i 0.0815285 0.0815285i
\(414\) 0 0
\(415\) 5.24264 + 15.7279i 0.257351 + 0.772053i
\(416\) 0 0
\(417\) −4.48528 + 3.17157i −0.219645 + 0.155313i
\(418\) 0 0
\(419\) 37.9411 1.85355 0.926773 0.375623i \(-0.122571\pi\)
0.926773 + 0.375623i \(0.122571\pi\)
\(420\) 0 0
\(421\) −2.97056 −0.144776 −0.0723882 0.997377i \(-0.523062\pi\)
−0.0723882 + 0.997377i \(0.523062\pi\)
\(422\) 0 0
\(423\) −24.5563 + 11.7279i −1.19397 + 0.570231i
\(424\) 0 0
\(425\) −3.82843 + 26.7990i −0.185706 + 1.29994i
\(426\) 0 0
\(427\) −4.82843 + 4.82843i −0.233664 + 0.233664i
\(428\) 0 0
\(429\) 21.3137 + 3.65685i 1.02904 + 0.176555i
\(430\) 0 0
\(431\) 8.14214i 0.392193i 0.980585 + 0.196096i \(0.0628266\pi\)
−0.980585 + 0.196096i \(0.937173\pi\)
\(432\) 0 0
\(433\) −15.0000 15.0000i −0.720854 0.720854i 0.247925 0.968779i \(-0.420251\pi\)
−0.968779 + 0.247925i \(0.920251\pi\)
\(434\) 0 0
\(435\) −29.3137 + 4.48528i −1.40548 + 0.215053i
\(436\) 0 0
\(437\) 7.65685 + 7.65685i 0.366277 + 0.366277i
\(438\) 0 0
\(439\) 25.7990i 1.23132i 0.788012 + 0.615659i \(0.211110\pi\)
−0.788012 + 0.615659i \(0.788890\pi\)
\(440\) 0 0
\(441\) −18.8284 6.65685i −0.896592 0.316993i
\(442\) 0 0
\(443\) 14.0711 14.0711i 0.668537 0.668537i −0.288841 0.957377i \(-0.593270\pi\)
0.957377 + 0.288841i \(0.0932698\pi\)
\(444\) 0 0
\(445\) −4.34315 + 8.68629i −0.205885 + 0.411770i
\(446\) 0 0
\(447\) 9.31371 + 13.1716i 0.440523 + 0.622994i
\(448\) 0 0
\(449\) −21.3137 −1.00586 −0.502928 0.864328i \(-0.667744\pi\)
−0.502928 + 0.864328i \(0.667744\pi\)
\(450\) 0 0
\(451\) 27.3137 1.28615
\(452\) 0 0
\(453\) −2.34315 3.31371i −0.110091 0.155692i
\(454\) 0 0
\(455\) 1.51472 3.02944i 0.0710111 0.142022i
\(456\) 0 0
\(457\) 1.00000 1.00000i 0.0467780 0.0467780i −0.683331 0.730109i \(-0.739469\pi\)
0.730109 + 0.683331i \(0.239469\pi\)
\(458\) 0 0
\(459\) −24.5563 13.7279i −1.14619 0.640765i
\(460\) 0 0
\(461\) 4.97056i 0.231502i −0.993278 0.115751i \(-0.963073\pi\)
0.993278 0.115751i \(-0.0369275\pi\)
\(462\) 0 0
\(463\) 24.4142 + 24.4142i 1.13462 + 1.13462i 0.989398 + 0.145226i \(0.0463910\pi\)
0.145226 + 0.989398i \(0.453609\pi\)
\(464\) 0 0
\(465\) −21.6569 + 3.31371i −1.00431 + 0.153670i
\(466\) 0 0
\(467\) −13.3848 13.3848i −0.619374 0.619374i 0.325997 0.945371i \(-0.394300\pi\)
−0.945371 + 0.325997i \(0.894300\pi\)
\(468\) 0 0
\(469\) 3.37258i 0.155731i
\(470\) 0 0
\(471\) 27.7279 + 4.75736i 1.27764 + 0.219208i
\(472\) 0 0
\(473\) −11.6569 + 11.6569i −0.535983 + 0.535983i
\(474\) 0 0
\(475\) 19.3137 14.4853i 0.886174 0.664630i
\(476\) 0 0
\(477\) 5.48528 + 11.4853i 0.251154 + 0.525875i
\(478\) 0 0
\(479\) −22.6274 −1.03387 −0.516937 0.856024i \(-0.672928\pi\)
−0.516937 + 0.856024i \(0.672928\pi\)
\(480\) 0 0
\(481\) 0.627417 0.0286078
\(482\) 0 0
\(483\) 1.85786 1.31371i 0.0845358 0.0597758i
\(484\) 0 0
\(485\) −1.00000 3.00000i −0.0454077 0.136223i
\(486\) 0 0
\(487\) 16.5563 16.5563i 0.750240 0.750240i −0.224284 0.974524i \(-0.572004\pi\)
0.974524 + 0.224284i \(0.0720043\pi\)
\(488\) 0 0
\(489\) −1.00000 + 5.82843i −0.0452216 + 0.263571i
\(490\) 0 0
\(491\) 38.4853i 1.73682i 0.495850 + 0.868408i \(0.334857\pi\)
−0.495850 + 0.868408i \(0.665143\pi\)
\(492\) 0 0
\(493\) −29.3137 29.3137i −1.32022 1.32022i
\(494\) 0 0
\(495\) 23.3137 22.4853i 1.04787 1.01064i
\(496\) 0 0
\(497\) 2.68629 + 2.68629i 0.120497 + 0.120497i
\(498\) 0 0
\(499\) 38.7696i 1.73556i 0.496945 + 0.867782i \(0.334455\pi\)
−0.496945 + 0.867782i \(0.665545\pi\)
\(500\) 0 0
\(501\) 0.313708 1.82843i 0.0140155 0.0816881i
\(502\) 0 0
\(503\) −20.0711 + 20.0711i −0.894925 + 0.894925i −0.994982 0.100057i \(-0.968097\pi\)
0.100057 + 0.994982i \(0.468097\pi\)
\(504\) 0 0
\(505\) −3.31371 1.65685i −0.147458 0.0737290i
\(506\) 0 0
\(507\) −8.92893 + 6.31371i −0.396548 + 0.280402i
\(508\) 0 0
\(509\) 7.65685 0.339384 0.169692 0.985497i \(-0.445723\pi\)
0.169692 + 0.985497i \(0.445723\pi\)
\(510\) 0 0
\(511\) −5.51472 −0.243957
\(512\) 0 0
\(513\) 6.82843 + 24.1421i 0.301482 + 1.06590i
\(514\) 0 0
\(515\) 25.2426 8.41421i 1.11232 0.370775i
\(516\) 0 0
\(517\) 30.9706 30.9706i 1.36208 1.36208i
\(518\) 0 0
\(519\) 25.7279 + 4.41421i 1.12933 + 0.193762i
\(520\) 0 0
\(521\) 24.0000i 1.05146i 0.850652 + 0.525730i \(0.176208\pi\)
−0.850652 + 0.525730i \(0.823792\pi\)
\(522\) 0 0
\(523\) −7.10051 7.10051i −0.310483 0.310483i 0.534613 0.845097i \(-0.320457\pi\)
−0.845097 + 0.534613i \(0.820457\pi\)
\(524\) 0 0
\(525\) −2.31371 4.51472i −0.100979 0.197038i
\(526\) 0 0
\(527\) −21.6569 21.6569i −0.943387 0.943387i
\(528\) 0 0
\(529\) 17.9706i 0.781329i
\(530\) 0 0
\(531\) 4.00000 11.3137i 0.173585 0.490973i
\(532\) 0 0
\(533\) 10.3431 10.3431i 0.448011 0.448011i
\(534\) 0 0
\(535\) −37.2426 + 12.4142i −1.61014 + 0.536713i
\(536\) 0 0
\(537\) 12.0000 + 16.9706i 0.517838 + 0.732334i
\(538\) 0 0
\(539\) 32.1421 1.38446
\(540\) 0 0
\(541\) −6.68629 −0.287466 −0.143733 0.989616i \(-0.545911\pi\)
−0.143733 + 0.989616i \(0.545911\pi\)
\(542\) 0 0
\(543\) −17.3137 24.4853i −0.743002 1.05076i
\(544\) 0 0
\(545\) −8.00000 4.00000i −0.342682 0.171341i
\(546\) 0 0
\(547\) 9.72792 9.72792i 0.415936 0.415936i −0.467864 0.883800i \(-0.654976\pi\)
0.883800 + 0.467864i \(0.154976\pi\)
\(548\) 0 0
\(549\) −11.6569 + 32.9706i −0.497502 + 1.40715i
\(550\) 0 0
\(551\) 36.9706i 1.57500i
\(552\) 0 0
\(553\) 2.00000 + 2.00000i 0.0850487 + 0.0850487i
\(554\) 0 0
\(555\) 0.556349 0.757359i 0.0236157 0.0321481i
\(556\) 0 0
\(557\) 29.6274 + 29.6274i 1.25535 + 1.25535i 0.953287 + 0.302067i \(0.0976768\pi\)
0.302067 + 0.953287i \(0.402323\pi\)
\(558\) 0 0
\(559\) 8.82843i 0.373403i
\(560\) 0 0
\(561\) 44.6274 + 7.65685i 1.88417 + 0.323273i
\(562\) 0 0
\(563\) −32.5563 + 32.5563i −1.37209 + 1.37209i −0.514740 + 0.857346i \(0.672112\pi\)
−0.857346 + 0.514740i \(0.827888\pi\)
\(564\) 0 0
\(565\) −7.48528 22.4558i −0.314908 0.944724i
\(566\) 0 0
\(567\) 5.24264 0.556349i 0.220170 0.0233645i
\(568\) 0 0
\(569\) −22.6863 −0.951059 −0.475529 0.879700i \(-0.657743\pi\)
−0.475529 + 0.879700i \(0.657743\pi\)
\(570\) 0 0
\(571\) −28.9706 −1.21238 −0.606190 0.795320i \(-0.707303\pi\)
−0.606190 + 0.795320i \(0.707303\pi\)
\(572\) 0 0
\(573\) 34.1421 24.1421i 1.42631 1.00855i
\(574\) 0 0
\(575\) −11.1005 1.58579i −0.462923 0.0661319i
\(576\) 0 0
\(577\) 3.34315 3.34315i 0.139177 0.139177i −0.634086 0.773263i \(-0.718623\pi\)
0.773263 + 0.634086i \(0.218623\pi\)
\(578\) 0 0
\(579\) 1.38478 8.07107i 0.0575493 0.335422i
\(580\) 0 0
\(581\) 4.34315i 0.180184i
\(582\) 0 0
\(583\) −14.4853 14.4853i −0.599919 0.599919i
\(584\) 0 0
\(585\) 0.313708 17.3431i 0.0129703 0.717051i
\(586\) 0 0
\(587\) 20.5563 + 20.5563i 0.848451 + 0.848451i 0.989940 0.141489i \(-0.0451888\pi\)
−0.141489 + 0.989940i \(0.545189\pi\)
\(588\) 0 0
\(589\) 27.3137i 1.12544i
\(590\) 0 0
\(591\) −1.38478 + 8.07107i −0.0569621 + 0.331999i
\(592\) 0 0
\(593\) −1.48528 + 1.48528i −0.0609932 + 0.0609932i −0.736945 0.675952i \(-0.763733\pi\)
0.675952 + 0.736945i \(0.263733\pi\)
\(594\) 0 0
\(595\) 3.17157 6.34315i 0.130022 0.260044i
\(596\) 0 0
\(597\) −2.14214 + 1.51472i −0.0876718 + 0.0619933i
\(598\) 0 0
\(599\) 25.9411 1.05993 0.529963 0.848021i \(-0.322206\pi\)
0.529963 + 0.848021i \(0.322206\pi\)
\(600\) 0 0
\(601\) 18.9706 0.773825 0.386913 0.922116i \(-0.373541\pi\)
0.386913 + 0.922116i \(0.373541\pi\)
\(602\) 0 0
\(603\) 7.44365 + 15.5858i 0.303129 + 0.634702i
\(604\) 0 0
\(605\) −12.3137 + 24.6274i −0.500623 + 1.00125i
\(606\) 0 0
\(607\) −15.0416 + 15.0416i −0.610521 + 0.610521i −0.943082 0.332561i \(-0.892087\pi\)
0.332561 + 0.943082i \(0.392087\pi\)
\(608\) 0 0
\(609\) 7.65685 + 1.31371i 0.310271 + 0.0532342i
\(610\) 0 0
\(611\) 23.4558i 0.948922i
\(612\) 0 0
\(613\) −7.48528 7.48528i −0.302328 0.302328i 0.539596 0.841924i \(-0.318577\pi\)
−0.841924 + 0.539596i \(0.818577\pi\)
\(614\) 0 0
\(615\) −3.31371 21.6569i −0.133622 0.873289i
\(616\) 0 0
\(617\) 17.8284 + 17.8284i 0.717745 + 0.717745i 0.968143 0.250398i \(-0.0805614\pi\)
−0.250398 + 0.968143i \(0.580561\pi\)
\(618\) 0 0
\(619\) 8.14214i 0.327260i 0.986522 + 0.163630i \(0.0523203\pi\)
−0.986522 + 0.163630i \(0.947680\pi\)
\(620\) 0 0
\(621\) 5.68629 10.1716i 0.228183 0.408171i
\(622\) 0 0
\(623\) 1.79899 1.79899i 0.0720750 0.0720750i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 0 0
\(627\) −23.3137 32.9706i −0.931060 1.31672i
\(628\) 0 0
\(629\) 1.31371 0.0523810
\(630\) 0 0
\(631\) 47.5980 1.89485 0.947423 0.319984i \(-0.103678\pi\)
0.947423 + 0.319984i \(0.103678\pi\)
\(632\) 0 0
\(633\) −12.9706 18.3431i −0.515534 0.729075i
\(634\) 0 0
\(635\) 8.41421 + 25.2426i 0.333908 + 1.00172i
\(636\) 0 0
\(637\) 12.1716 12.1716i 0.482255 0.482255i
\(638\) 0 0
\(639\) 18.3431 + 6.48528i 0.725644 + 0.256554i
\(640\) 0 0
\(641\) 36.2843i 1.43314i −0.697514 0.716571i \(-0.745710\pi\)
0.697514 0.716571i \(-0.254290\pi\)
\(642\) 0 0
\(643\) −30.6985 30.6985i −1.21063 1.21063i −0.970820 0.239810i \(-0.922915\pi\)
−0.239810 0.970820i \(-0.577085\pi\)
\(644\) 0 0
\(645\) 10.6569 + 7.82843i 0.419613 + 0.308244i
\(646\) 0 0
\(647\) −16.2132 16.2132i −0.637407 0.637407i 0.312508 0.949915i \(-0.398831\pi\)
−0.949915 + 0.312508i \(0.898831\pi\)
\(648\) 0 0
\(649\) 19.3137i 0.758129i
\(650\) 0 0
\(651\) 5.65685 + 0.970563i 0.221710 + 0.0380394i
\(652\) 0 0
\(653\) −15.3431 + 15.3431i −0.600424 + 0.600424i −0.940425 0.340001i \(-0.889572\pi\)
0.340001 + 0.940425i \(0.389572\pi\)
\(654\) 0 0
\(655\) 6.34315 + 3.17157i 0.247847 + 0.123924i
\(656\) 0 0
\(657\) −25.4853 + 12.1716i −0.994276 + 0.474858i
\(658\) 0 0
\(659\) −34.6274 −1.34889 −0.674446 0.738324i \(-0.735618\pi\)
−0.674446 + 0.738324i \(0.735618\pi\)
\(660\) 0 0
\(661\) 3.65685 0.142235 0.0711176 0.997468i \(-0.477343\pi\)
0.0711176 + 0.997468i \(0.477343\pi\)
\(662\) 0 0
\(663\) 19.7990 14.0000i 0.768929 0.543715i
\(664\) 0 0
\(665\) −6.00000 + 2.00000i −0.232670 + 0.0775567i
\(666\) 0 0
\(667\) 12.1421 12.1421i 0.470145 0.470145i
\(668\) 0 0
\(669\) 3.48528 20.3137i 0.134749 0.785373i
\(670\) 0 0
\(671\) 56.2843i 2.17283i
\(672\) 0 0
\(673\) −26.3137 26.3137i −1.01432 1.01432i −0.999896 0.0144229i \(-0.995409\pi\)
−0.0144229 0.999896i \(-0.504591\pi\)
\(674\) 0 0
\(675\) −20.6569 15.7574i −0.795083 0.606501i
\(676\) 0 0
\(677\) −21.2843 21.2843i −0.818021 0.818021i 0.167800 0.985821i \(-0.446334\pi\)
−0.985821 + 0.167800i \(0.946334\pi\)
\(678\) 0 0
\(679\) 0.828427i 0.0317921i
\(680\) 0 0
\(681\) 6.17157 35.9706i 0.236495 1.37839i
\(682\) 0 0
\(683\) −8.55635 + 8.55635i −0.327400 + 0.327400i −0.851597 0.524197i \(-0.824365\pi\)
0.524197 + 0.851597i \(0.324365\pi\)
\(684\) 0 0
\(685\) 12.5147 4.17157i 0.478163 0.159388i
\(686\) 0 0
\(687\) −36.2843 + 25.6569i −1.38433 + 0.978870i
\(688\) 0 0
\(689\) −10.9706 −0.417945
\(690\) 0 0
\(691\) 22.3431 0.849973 0.424987 0.905200i \(-0.360279\pi\)
0.424987 + 0.905200i \(0.360279\pi\)
\(692\) 0 0
\(693\) −7.65685 + 3.65685i −0.290860 + 0.138912i
\(694\) 0 0
\(695\) −6.34315 3.17157i −0.240609 0.120305i
\(696\) 0 0
\(697\) 21.6569 21.6569i 0.820312 0.820312i
\(698\) 0 0
\(699\) 14.8995 + 2.55635i 0.563551 + 0.0966900i
\(700\) 0 0
\(701\) 4.00000i 0.151078i 0.997143 + 0.0755390i \(0.0240677\pi\)
−0.997143 + 0.0755390i \(0.975932\pi\)
\(702\) 0 0
\(703\) −0.828427 0.828427i −0.0312447 0.0312447i
\(704\) 0 0
\(705\) −28.3137 20.7990i −1.06636 0.783335i
\(706\) 0 0
\(707\) 0.686292 + 0.686292i 0.0258106 + 0.0258106i
\(708\) 0 0
\(709\) 24.2843i 0.912015i 0.889976 + 0.456007i \(0.150721\pi\)
−0.889976 + 0.456007i \(0.849279\pi\)
\(710\) 0 0
\(711\) 13.6569 + 4.82843i 0.512172 + 0.181080i
\(712\) 0 0
\(713\) 8.97056 8.97056i 0.335950 0.335950i
\(714\) 0 0
\(715\) 8.82843 + 26.4853i 0.330164 + 0.990493i
\(716\) 0 0
\(717\) −16.0000 22.6274i −0.597531 0.845036i
\(718\) 0 0
\(719\) −16.0000 −0.596699 −0.298350 0.954457i \(-0.596436\pi\)
−0.298350 + 0.954457i \(0.596436\pi\)
\(720\) 0 0
\(721\) −6.97056 −0.259597
\(722\) 0 0
\(723\) 11.6569 + 16.4853i 0.433523 + 0.613094i
\(724\) 0 0
\(725\) −22.9706 30.6274i −0.853105 1.13747i
\(726\) 0 0
\(727\) 21.2426 21.2426i 0.787846 0.787846i −0.193295 0.981141i \(-0.561917\pi\)
0.981141 + 0.193295i \(0.0619174\pi\)
\(728\) 0 0
\(729\) 23.0000 14.1421i 0.851852 0.523783i
\(730\) 0 0
\(731\) 18.4853i 0.683703i
\(732\) 0 0
\(733\) 23.1421 + 23.1421i 0.854774 + 0.854774i 0.990717 0.135942i \(-0.0434062\pi\)
−0.135942 + 0.990717i \(0.543406\pi\)
\(734\) 0 0
\(735\) −3.89949 25.4853i −0.143835 0.940039i
\(736\) 0 0
\(737\) −19.6569 19.6569i −0.724070 0.724070i
\(738\) 0 0
\(739\) 52.8284i 1.94333i 0.236372 + 0.971663i \(0.424041\pi\)
−0.236372 + 0.971663i \(0.575959\pi\)
\(740\) 0 0
\(741\) −21.3137 3.65685i −0.782979 0.134338i
\(742\) 0 0
\(743\) 0.615224 0.615224i 0.0225704 0.0225704i −0.695732 0.718302i \(-0.744920\pi\)
0.718302 + 0.695732i \(0.244920\pi\)
\(744\) 0 0
\(745\) −9.31371 + 18.6274i −0.341228 + 0.682456i
\(746\) 0 0
\(747\) −9.58579 20.0711i −0.350726 0.734362i
\(748\) 0 0
\(749\) 10.2843 0.375779
\(750\) 0 0
\(751\) −44.2843 −1.61596 −0.807978 0.589213i \(-0.799438\pi\)
−0.807978 + 0.589213i \(0.799438\pi\)
\(752\) 0 0
\(753\) −13.4558 + 9.51472i −0.490358 + 0.346736i
\(754\) 0 0
\(755\) 2.34315 4.68629i 0.0852758 0.170552i
\(756\) 0 0
\(757\) −36.4558 + 36.4558i −1.32501 + 1.32501i −0.415347 + 0.909663i \(0.636340\pi\)
−0.909663 + 0.415347i \(0.863660\pi\)
\(758\) 0 0
\(759\) −3.17157 + 18.4853i −0.115121 + 0.670973i
\(760\) 0 0
\(761\) 35.3137i 1.28012i 0.768325 + 0.640060i \(0.221091\pi\)
−0.768325 + 0.640060i \(0.778909\pi\)
\(762\) 0 0
\(763\) 1.65685 + 1.65685i 0.0599822 + 0.0599822i
\(764\) 0 0
\(765\) 0.656854 36.3137i 0.0237486 1.31292i
\(766\) 0 0
\(767\) 7.31371 + 7.31371i 0.264083 + 0.264083i
\(768\) 0 0
\(769\) 17.9411i 0.646974i −0.946233 0.323487i \(-0.895145\pi\)
0.946233 0.323487i \(-0.104855\pi\)
\(770\) 0 0
\(771\) 3.10051 18.0711i 0.111662 0.650814i
\(772\) 0 0
\(773\) 0.656854 0.656854i 0.0236254 0.0236254i −0.695195 0.718821i \(-0.744682\pi\)
0.718821 + 0.695195i \(0.244682\pi\)
\(774\) 0 0
\(775\) −16.9706 22.6274i −0.609601 0.812801i
\(776\) 0 0
\(777\) −0.201010 + 0.142136i −0.00721120 + 0.00509909i
\(778\) 0 0
\(779\) −27.3137 −0.978615
\(780\) 0 0
\(781\) −31.3137 −1.12049
\(782\) 0 0
\(783\) 38.2843 10.8284i 1.36817 0.386976i
\(784\) 0 0
\(785\) 11.4853 + 34.4558i 0.409927 + 1.22978i
\(786\) 0 0
\(787\) 30.4142 30.4142i 1.08415 1.08415i 0.0880320 0.996118i \(-0.471942\pi\)
0.996118 0.0880320i \(-0.0280578\pi\)
\(788\) 0 0
\(789\) −31.1421 5.34315i −1.10869 0.190221i
\(790\) 0 0
\(791\) 6.20101i 0.220483i
\(792\) 0 0