Properties

Label 3150.2.m.e.2843.2
Level 3150
Weight 2
Character 3150.2843
Analytic conductor 25.153
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 2843.2
Root \(0.707107 - 0.707107i\)
Character \(\chi\) = 3150.2843
Dual form 3150.2.m.e.1457.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -4.82843i q^{11} +(3.41421 + 3.41421i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(1.58579 + 1.58579i) q^{17} +7.07107i q^{19} +(3.41421 - 3.41421i) q^{22} +(4.82843 - 4.82843i) q^{23} +4.82843i q^{26} +(-0.707107 - 0.707107i) q^{28} +3.17157 q^{29} -8.82843 q^{31} +(-0.707107 - 0.707107i) q^{32} +2.24264i q^{34} +(6.07107 - 6.07107i) q^{37} +(-5.00000 + 5.00000i) q^{38} +4.82843i q^{41} +(-6.41421 - 6.41421i) q^{43} +4.82843 q^{44} +6.82843 q^{46} +(6.41421 + 6.41421i) q^{47} -1.00000i q^{49} +(-3.41421 + 3.41421i) q^{52} +(-4.82843 + 4.82843i) q^{53} -1.00000i q^{56} +(2.24264 + 2.24264i) q^{58} +8.00000 q^{59} +6.58579 q^{61} +(-6.24264 - 6.24264i) q^{62} -1.00000i q^{64} +(-0.414214 + 0.414214i) q^{67} +(-1.58579 + 1.58579i) q^{68} +12.2426i q^{71} +(6.00000 + 6.00000i) q^{73} +8.58579 q^{74} -7.07107 q^{76} +(3.41421 + 3.41421i) q^{77} +13.3137i q^{79} +(-3.41421 + 3.41421i) q^{82} +(-9.65685 + 9.65685i) q^{83} -9.07107i q^{86} +(3.41421 + 3.41421i) q^{88} +13.3137 q^{89} -4.82843 q^{91} +(4.82843 + 4.82843i) q^{92} +9.07107i q^{94} +(8.24264 - 8.24264i) q^{97} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + O(q^{10}) \) \( 4q + 8q^{13} - 4q^{14} - 4q^{16} + 12q^{17} + 8q^{22} + 8q^{23} + 24q^{29} - 24q^{31} - 4q^{37} - 20q^{38} - 20q^{43} + 8q^{44} + 16q^{46} + 20q^{47} - 8q^{52} - 8q^{53} - 8q^{58} + 32q^{59} + 32q^{61} - 8q^{62} + 4q^{67} - 12q^{68} + 24q^{73} + 40q^{74} + 8q^{77} - 8q^{82} - 16q^{83} + 8q^{88} + 8q^{89} - 8q^{91} + 8q^{92} + 16q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) 0 0
\(7\) −0.707107 + 0.707107i −0.267261 + 0.267261i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 0 0
\(10\) 0 0
\(11\) 4.82843i 1.45583i −0.685670 0.727913i \(-0.740491\pi\)
0.685670 0.727913i \(-0.259509\pi\)
\(12\) 0 0
\(13\) 3.41421 + 3.41421i 0.946932 + 0.946932i 0.998661 0.0517287i \(-0.0164731\pi\)
−0.0517287 + 0.998661i \(0.516473\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 1.58579 + 1.58579i 0.384610 + 0.384610i 0.872760 0.488150i \(-0.162328\pi\)
−0.488150 + 0.872760i \(0.662328\pi\)
\(18\) 0 0
\(19\) 7.07107i 1.62221i 0.584898 + 0.811107i \(0.301135\pi\)
−0.584898 + 0.811107i \(0.698865\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 3.41421 3.41421i 0.727913 0.727913i
\(23\) 4.82843 4.82843i 1.00680 1.00680i 0.00681991 0.999977i \(-0.497829\pi\)
0.999977 0.00681991i \(-0.00217086\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 4.82843i 0.946932i
\(27\) 0 0
\(28\) −0.707107 0.707107i −0.133631 0.133631i
\(29\) 3.17157 0.588946 0.294473 0.955660i \(-0.404856\pi\)
0.294473 + 0.955660i \(0.404856\pi\)
\(30\) 0 0
\(31\) −8.82843 −1.58563 −0.792816 0.609461i \(-0.791386\pi\)
−0.792816 + 0.609461i \(0.791386\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 0 0
\(34\) 2.24264i 0.384610i
\(35\) 0 0
\(36\) 0 0
\(37\) 6.07107 6.07107i 0.998077 0.998077i −0.00192076 0.999998i \(-0.500611\pi\)
0.999998 + 0.00192076i \(0.000611396\pi\)
\(38\) −5.00000 + 5.00000i −0.811107 + 0.811107i
\(39\) 0 0
\(40\) 0 0
\(41\) 4.82843i 0.754074i 0.926198 + 0.377037i \(0.123057\pi\)
−0.926198 + 0.377037i \(0.876943\pi\)
\(42\) 0 0
\(43\) −6.41421 6.41421i −0.978158 0.978158i 0.0216081 0.999767i \(-0.493121\pi\)
−0.999767 + 0.0216081i \(0.993121\pi\)
\(44\) 4.82843 0.727913
\(45\) 0 0
\(46\) 6.82843 1.00680
\(47\) 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
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) −3.41421 + 3.41421i −0.473466 + 0.473466i
\(53\) −4.82843 + 4.82843i −0.663235 + 0.663235i −0.956141 0.292906i \(-0.905378\pi\)
0.292906 + 0.956141i \(0.405378\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 0.133631i
\(57\) 0 0
\(58\) 2.24264 + 2.24264i 0.294473 + 0.294473i
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 0 0
\(61\) 6.58579 0.843224 0.421612 0.906776i \(-0.361465\pi\)
0.421612 + 0.906776i \(0.361465\pi\)
\(62\) −6.24264 6.24264i −0.792816 0.792816i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.414214 + 0.414214i −0.0506042 + 0.0506042i −0.731956 0.681352i \(-0.761392\pi\)
0.681352 + 0.731956i \(0.261392\pi\)
\(68\) −1.58579 + 1.58579i −0.192305 + 0.192305i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.2426i 1.45293i 0.687201 + 0.726467i \(0.258839\pi\)
−0.687201 + 0.726467i \(0.741161\pi\)
\(72\) 0 0
\(73\) 6.00000 + 6.00000i 0.702247 + 0.702247i 0.964892 0.262646i \(-0.0845950\pi\)
−0.262646 + 0.964892i \(0.584595\pi\)
\(74\) 8.58579 0.998077
\(75\) 0 0
\(76\) −7.07107 −0.811107
\(77\) 3.41421 + 3.41421i 0.389086 + 0.389086i
\(78\) 0 0
\(79\) 13.3137i 1.49791i 0.662621 + 0.748955i \(0.269444\pi\)
−0.662621 + 0.748955i \(0.730556\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −3.41421 + 3.41421i −0.377037 + 0.377037i
\(83\) −9.65685 + 9.65685i −1.05998 + 1.05998i −0.0618948 + 0.998083i \(0.519714\pi\)
−0.998083 + 0.0618948i \(0.980286\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 9.07107i 0.978158i
\(87\) 0 0
\(88\) 3.41421 + 3.41421i 0.363956 + 0.363956i
\(89\) 13.3137 1.41125 0.705625 0.708585i \(-0.250666\pi\)
0.705625 + 0.708585i \(0.250666\pi\)
\(90\) 0 0
\(91\) −4.82843 −0.506157
\(92\) 4.82843 + 4.82843i 0.503398 + 0.503398i
\(93\) 0 0
\(94\) 9.07107i 0.935609i
\(95\) 0 0
\(96\) 0 0
\(97\) 8.24264 8.24264i 0.836913 0.836913i −0.151538 0.988451i \(-0.548423\pi\)
0.988451 + 0.151538i \(0.0484226\pi\)
\(98\) 0.707107 0.707107i 0.0714286 0.0714286i
\(99\) 0 0
\(100\) 0 0
\(101\) 4.34315i 0.432159i 0.976376 + 0.216080i \(0.0693271\pi\)
−0.976376 + 0.216080i \(0.930673\pi\)
\(102\) 0 0
\(103\) −3.41421 3.41421i −0.336412 0.336412i 0.518603 0.855015i \(-0.326452\pi\)
−0.855015 + 0.518603i \(0.826452\pi\)
\(104\) −4.82843 −0.473466
\(105\) 0 0
\(106\) −6.82843 −0.663235
\(107\) 9.07107 + 9.07107i 0.876933 + 0.876933i 0.993216 0.116283i \(-0.0370979\pi\)
−0.116283 + 0.993216i \(0.537098\pi\)
\(108\) 0 0
\(109\) 20.1421i 1.92927i 0.263595 + 0.964633i \(0.415092\pi\)
−0.263595 + 0.964633i \(0.584908\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.707107 0.707107i 0.0668153 0.0668153i
\(113\) 5.41421 5.41421i 0.509326 0.509326i −0.404993 0.914320i \(-0.632726\pi\)
0.914320 + 0.404993i \(0.132726\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 3.17157i 0.294473i
\(117\) 0 0
\(118\) 5.65685 + 5.65685i 0.520756 + 0.520756i
\(119\) −2.24264 −0.205583
\(120\) 0 0
\(121\) −12.3137 −1.11943
\(122\) 4.65685 + 4.65685i 0.421612 + 0.421612i
\(123\) 0 0
\(124\) 8.82843i 0.792816i
\(125\) 0 0
\(126\) 0 0
\(127\) −1.17157 + 1.17157i −0.103960 + 0.103960i −0.757174 0.653213i \(-0.773420\pi\)
0.653213 + 0.757174i \(0.273420\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 0 0
\(130\) 0 0
\(131\) 6.00000i 0.524222i −0.965038 0.262111i \(-0.915581\pi\)
0.965038 0.262111i \(-0.0844187\pi\)
\(132\) 0 0
\(133\) −5.00000 5.00000i −0.433555 0.433555i
\(134\) −0.585786 −0.0506042
\(135\) 0 0
\(136\) −2.24264 −0.192305
\(137\) −1.07107 1.07107i −0.0915075 0.0915075i 0.659871 0.751379i \(-0.270611\pi\)
−0.751379 + 0.659871i \(0.770611\pi\)
\(138\) 0 0
\(139\) 0.242641i 0.0205805i 0.999947 + 0.0102903i \(0.00327555\pi\)
−0.999947 + 0.0102903i \(0.996724\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −8.65685 + 8.65685i −0.726467 + 0.726467i
\(143\) 16.4853 16.4853i 1.37857 1.37857i
\(144\) 0 0
\(145\) 0 0
\(146\) 8.48528i 0.702247i
\(147\) 0 0
\(148\) 6.07107 + 6.07107i 0.499039 + 0.499039i
\(149\) −5.31371 −0.435316 −0.217658 0.976025i \(-0.569842\pi\)
−0.217658 + 0.976025i \(0.569842\pi\)
\(150\) 0 0
\(151\) −13.3137 −1.08345 −0.541727 0.840554i \(-0.682229\pi\)
−0.541727 + 0.840554i \(0.682229\pi\)
\(152\) −5.00000 5.00000i −0.405554 0.405554i
\(153\) 0 0
\(154\) 4.82843i 0.389086i
\(155\) 0 0
\(156\) 0 0
\(157\) −2.58579 + 2.58579i −0.206368 + 0.206368i −0.802722 0.596354i \(-0.796616\pi\)
0.596354 + 0.802722i \(0.296616\pi\)
\(158\) −9.41421 + 9.41421i −0.748955 + 0.748955i
\(159\) 0 0
\(160\) 0 0
\(161\) 6.82843i 0.538155i
\(162\) 0 0
\(163\) −4.89949 4.89949i −0.383758 0.383758i 0.488696 0.872454i \(-0.337473\pi\)
−0.872454 + 0.488696i \(0.837473\pi\)
\(164\) −4.82843 −0.377037
\(165\) 0 0
\(166\) −13.6569 −1.05998
\(167\) −6.89949 6.89949i −0.533899 0.533899i 0.387831 0.921730i \(-0.373224\pi\)
−0.921730 + 0.387831i \(0.873224\pi\)
\(168\) 0 0
\(169\) 10.3137i 0.793362i
\(170\) 0 0
\(171\) 0 0
\(172\) 6.41421 6.41421i 0.489079 0.489079i
\(173\) 8.00000 8.00000i 0.608229 0.608229i −0.334254 0.942483i \(-0.608484\pi\)
0.942483 + 0.334254i \(0.108484\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 4.82843i 0.363956i
\(177\) 0 0
\(178\) 9.41421 + 9.41421i 0.705625 + 0.705625i
\(179\) −13.3137 −0.995113 −0.497557 0.867431i \(-0.665769\pi\)
−0.497557 + 0.867431i \(0.665769\pi\)
\(180\) 0 0
\(181\) −11.0711 −0.822906 −0.411453 0.911431i \(-0.634979\pi\)
−0.411453 + 0.911431i \(0.634979\pi\)
\(182\) −3.41421 3.41421i −0.253078 0.253078i
\(183\) 0 0
\(184\) 6.82843i 0.503398i
\(185\) 0 0
\(186\) 0 0
\(187\) 7.65685 7.65685i 0.559925 0.559925i
\(188\) −6.41421 + 6.41421i −0.467805 + 0.467805i
\(189\) 0 0
\(190\) 0 0
\(191\) 13.4142i 0.970618i 0.874343 + 0.485309i \(0.161293\pi\)
−0.874343 + 0.485309i \(0.838707\pi\)
\(192\) 0 0
\(193\) −6.00000 6.00000i −0.431889 0.431889i 0.457381 0.889271i \(-0.348787\pi\)
−0.889271 + 0.457381i \(0.848787\pi\)
\(194\) 11.6569 0.836913
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 3.17157 + 3.17157i 0.225965 + 0.225965i 0.811005 0.585040i \(-0.198921\pi\)
−0.585040 + 0.811005i \(0.698921\pi\)
\(198\) 0 0
\(199\) 0.343146i 0.0243250i −0.999926 0.0121625i \(-0.996128\pi\)
0.999926 0.0121625i \(-0.00387153\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −3.07107 + 3.07107i −0.216080 + 0.216080i
\(203\) −2.24264 + 2.24264i −0.157403 + 0.157403i
\(204\) 0 0
\(205\) 0 0
\(206\) 4.82843i 0.336412i
\(207\) 0 0
\(208\) −3.41421 3.41421i −0.236733 0.236733i
\(209\) 34.1421 2.36166
\(210\) 0 0
\(211\) 3.51472 0.241963 0.120982 0.992655i \(-0.461396\pi\)
0.120982 + 0.992655i \(0.461396\pi\)
\(212\) −4.82843 4.82843i −0.331618 0.331618i
\(213\) 0 0
\(214\) 12.8284i 0.876933i
\(215\) 0 0
\(216\) 0 0
\(217\) 6.24264 6.24264i 0.423778 0.423778i
\(218\) −14.2426 + 14.2426i −0.964633 + 0.964633i
\(219\) 0 0
\(220\) 0 0
\(221\) 10.8284i 0.728399i
\(222\) 0 0
\(223\) −7.89949 7.89949i −0.528989 0.528989i 0.391282 0.920271i \(-0.372032\pi\)
−0.920271 + 0.391282i \(0.872032\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 7.65685 0.509326
\(227\) −4.34315 4.34315i −0.288265 0.288265i 0.548129 0.836394i \(-0.315340\pi\)
−0.836394 + 0.548129i \(0.815340\pi\)
\(228\) 0 0
\(229\) 4.92893i 0.325713i −0.986650 0.162857i \(-0.947929\pi\)
0.986650 0.162857i \(-0.0520708\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −2.24264 + 2.24264i −0.147237 + 0.147237i
\(233\) −5.41421 + 5.41421i −0.354697 + 0.354697i −0.861854 0.507157i \(-0.830696\pi\)
0.507157 + 0.861854i \(0.330696\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 8.00000i 0.520756i
\(237\) 0 0
\(238\) −1.58579 1.58579i −0.102791 0.102791i
\(239\) 25.2132 1.63091 0.815453 0.578823i \(-0.196488\pi\)
0.815453 + 0.578823i \(0.196488\pi\)
\(240\) 0 0
\(241\) −7.65685 −0.493221 −0.246611 0.969115i \(-0.579317\pi\)
−0.246611 + 0.969115i \(0.579317\pi\)
\(242\) −8.70711 8.70711i −0.559714 0.559714i
\(243\) 0 0
\(244\) 6.58579i 0.421612i
\(245\) 0 0
\(246\) 0 0
\(247\) −24.1421 + 24.1421i −1.53613 + 1.53613i
\(248\) 6.24264 6.24264i 0.396408 0.396408i
\(249\) 0 0
\(250\) 0 0
\(251\) 6.97056i 0.439978i −0.975502 0.219989i \(-0.929398\pi\)
0.975502 0.219989i \(-0.0706022\pi\)
\(252\) 0 0
\(253\) −23.3137 23.3137i −1.46572 1.46572i
\(254\) −1.65685 −0.103960
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.89949 + 6.89949i 0.430379 + 0.430379i 0.888757 0.458378i \(-0.151570\pi\)
−0.458378 + 0.888757i \(0.651570\pi\)
\(258\) 0 0
\(259\) 8.58579i 0.533495i
\(260\) 0 0
\(261\) 0 0
\(262\) 4.24264 4.24264i 0.262111 0.262111i
\(263\) 22.0000 22.0000i 1.35658 1.35658i 0.478479 0.878099i \(-0.341188\pi\)
0.878099 0.478479i \(-0.158812\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 7.07107i 0.433555i
\(267\) 0 0
\(268\) −0.414214 0.414214i −0.0253021 0.0253021i
\(269\) −21.3137 −1.29952 −0.649760 0.760140i \(-0.725131\pi\)
−0.649760 + 0.760140i \(0.725131\pi\)
\(270\) 0 0
\(271\) 7.17157 0.435642 0.217821 0.975989i \(-0.430105\pi\)
0.217821 + 0.975989i \(0.430105\pi\)
\(272\) −1.58579 1.58579i −0.0961524 0.0961524i
\(273\) 0 0
\(274\) 1.51472i 0.0915075i
\(275\) 0 0
\(276\) 0 0
\(277\) 18.0711 18.0711i 1.08579 1.08579i 0.0898279 0.995957i \(-0.471368\pi\)
0.995957 0.0898279i \(-0.0286317\pi\)
\(278\) −0.171573 + 0.171573i −0.0102903 + 0.0102903i
\(279\) 0 0
\(280\) 0 0
\(281\) 12.9289i 0.771275i −0.922650 0.385638i \(-0.873981\pi\)
0.922650 0.385638i \(-0.126019\pi\)
\(282\) 0 0
\(283\) 18.0000 + 18.0000i 1.06999 + 1.06999i 0.997359 + 0.0726300i \(0.0231392\pi\)
0.0726300 + 0.997359i \(0.476861\pi\)
\(284\) −12.2426 −0.726467
\(285\) 0 0
\(286\) 23.3137 1.37857
\(287\) −3.41421 3.41421i −0.201535 0.201535i
\(288\) 0 0
\(289\) 11.9706i 0.704151i
\(290\) 0 0
\(291\) 0 0
\(292\) −6.00000 + 6.00000i −0.351123 + 0.351123i
\(293\) 22.4853 22.4853i 1.31360 1.31360i 0.394865 0.918739i \(-0.370791\pi\)
0.918739 0.394865i \(-0.129209\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 8.58579i 0.499039i
\(297\) 0 0
\(298\) −3.75736 3.75736i −0.217658 0.217658i
\(299\) 32.9706 1.90674
\(300\) 0 0
\(301\) 9.07107 0.522848
\(302\) −9.41421 9.41421i −0.541727 0.541727i
\(303\) 0 0
\(304\) 7.07107i 0.405554i
\(305\) 0 0
\(306\) 0 0
\(307\) 7.51472 7.51472i 0.428888 0.428888i −0.459362 0.888249i \(-0.651922\pi\)
0.888249 + 0.459362i \(0.151922\pi\)
\(308\) −3.41421 + 3.41421i −0.194543 + 0.194543i
\(309\) 0 0
\(310\) 0 0
\(311\) 16.0000i 0.907277i −0.891186 0.453638i \(-0.850126\pi\)
0.891186 0.453638i \(-0.149874\pi\)
\(312\) 0 0
\(313\) 19.6569 + 19.6569i 1.11107 + 1.11107i 0.993006 + 0.118065i \(0.0376692\pi\)
0.118065 + 0.993006i \(0.462331\pi\)
\(314\) −3.65685 −0.206368
\(315\) 0 0
\(316\) −13.3137 −0.748955
\(317\) 12.2426 + 12.2426i 0.687615 + 0.687615i 0.961704 0.274089i \(-0.0883763\pi\)
−0.274089 + 0.961704i \(0.588376\pi\)
\(318\) 0 0
\(319\) 15.3137i 0.857403i
\(320\) 0 0
\(321\) 0 0
\(322\) −4.82843 + 4.82843i −0.269078 + 0.269078i
\(323\) −11.2132 + 11.2132i −0.623919 + 0.623919i
\(324\) 0 0
\(325\) 0 0
\(326\) 6.92893i 0.383758i
\(327\) 0 0
\(328\) −3.41421 3.41421i −0.188518 0.188518i
\(329\) −9.07107 −0.500104
\(330\) 0 0
\(331\) −1.85786 −0.102117 −0.0510587 0.998696i \(-0.516260\pi\)
−0.0510587 + 0.998696i \(0.516260\pi\)
\(332\) −9.65685 9.65685i −0.529989 0.529989i
\(333\) 0 0
\(334\) 9.75736i 0.533899i
\(335\) 0 0
\(336\) 0 0
\(337\) 1.51472 1.51472i 0.0825120 0.0825120i −0.664646 0.747158i \(-0.731418\pi\)
0.747158 + 0.664646i \(0.231418\pi\)
\(338\) −7.29289 + 7.29289i −0.396681 + 0.396681i
\(339\) 0 0
\(340\) 0 0
\(341\) 42.6274i 2.30840i
\(342\) 0 0
\(343\) 0.707107 + 0.707107i 0.0381802 + 0.0381802i
\(344\) 9.07107 0.489079
\(345\) 0 0
\(346\) 11.3137 0.608229
\(347\) −14.8284 14.8284i −0.796032 0.796032i 0.186436 0.982467i \(-0.440306\pi\)
−0.982467 + 0.186436i \(0.940306\pi\)
\(348\) 0 0
\(349\) 8.72792i 0.467195i 0.972333 + 0.233597i \(0.0750498\pi\)
−0.972333 + 0.233597i \(0.924950\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3.41421 + 3.41421i −0.181978 + 0.181978i
\(353\) 15.3848 15.3848i 0.818849 0.818849i −0.167092 0.985941i \(-0.553438\pi\)
0.985941 + 0.167092i \(0.0534378\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 13.3137i 0.705625i
\(357\) 0 0
\(358\) −9.41421 9.41421i −0.497557 0.497557i
\(359\) −20.7279 −1.09398 −0.546989 0.837140i \(-0.684226\pi\)
−0.546989 + 0.837140i \(0.684226\pi\)
\(360\) 0 0
\(361\) −31.0000 −1.63158
\(362\) −7.82843 7.82843i −0.411453 0.411453i
\(363\) 0 0
\(364\) 4.82843i 0.253078i
\(365\) 0 0
\(366\) 0 0
\(367\) −20.0000 + 20.0000i −1.04399 + 1.04399i −0.0450047 + 0.998987i \(0.514330\pi\)
−0.998987 + 0.0450047i \(0.985670\pi\)
\(368\) −4.82843 + 4.82843i −0.251699 + 0.251699i
\(369\) 0 0
\(370\) 0 0
\(371\) 6.82843i 0.354514i
\(372\) 0 0
\(373\) 11.2426 + 11.2426i 0.582122 + 0.582122i 0.935486 0.353364i \(-0.114962\pi\)
−0.353364 + 0.935486i \(0.614962\pi\)
\(374\) 10.8284 0.559925
\(375\) 0 0
\(376\) −9.07107 −0.467805
\(377\) 10.8284 + 10.8284i 0.557692 + 0.557692i
\(378\) 0 0
\(379\) 5.65685i 0.290573i 0.989390 + 0.145287i \(0.0464104\pi\)
−0.989390 + 0.145287i \(0.953590\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −9.48528 + 9.48528i −0.485309 + 0.485309i
\(383\) 5.24264 5.24264i 0.267886 0.267886i −0.560362 0.828248i \(-0.689338\pi\)
0.828248 + 0.560362i \(0.189338\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 8.48528i 0.431889i
\(387\) 0 0
\(388\) 8.24264 + 8.24264i 0.418457 + 0.418457i
\(389\) −5.31371 −0.269416 −0.134708 0.990885i \(-0.543010\pi\)
−0.134708 + 0.990885i \(0.543010\pi\)
\(390\) 0 0
\(391\) 15.3137 0.774448
\(392\) 0.707107 + 0.707107i 0.0357143 + 0.0357143i
\(393\) 0 0
\(394\) 4.48528i 0.225965i
\(395\) 0 0
\(396\) 0 0
\(397\) −25.4142 + 25.4142i −1.27550 + 1.27550i −0.332345 + 0.943158i \(0.607840\pi\)
−0.943158 + 0.332345i \(0.892160\pi\)
\(398\) 0.242641 0.242641i 0.0121625 0.0121625i
\(399\) 0 0
\(400\) 0 0
\(401\) 31.0711i 1.55162i −0.630970 0.775808i \(-0.717343\pi\)
0.630970 0.775808i \(-0.282657\pi\)
\(402\) 0 0
\(403\) −30.1421 30.1421i −1.50149 1.50149i
\(404\) −4.34315 −0.216080
\(405\) 0 0
\(406\) −3.17157 −0.157403
\(407\) −29.3137 29.3137i −1.45303 1.45303i
\(408\) 0 0
\(409\) 37.3137i 1.84504i 0.385944 + 0.922522i \(0.373876\pi\)
−0.385944 + 0.922522i \(0.626124\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 3.41421 3.41421i 0.168206 0.168206i
\(413\) −5.65685 + 5.65685i −0.278356 + 0.278356i
\(414\) 0 0
\(415\) 0 0
\(416\) 4.82843i 0.236733i
\(417\) 0 0
\(418\) 24.1421 + 24.1421i 1.18083 + 1.18083i
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) 0 0
\(421\) 28.1421 1.37156 0.685782 0.727807i \(-0.259460\pi\)
0.685782 + 0.727807i \(0.259460\pi\)
\(422\) 2.48528 + 2.48528i 0.120982 + 0.120982i
\(423\) 0 0
\(424\) 6.82843i 0.331618i
\(425\) 0 0
\(426\) 0 0
\(427\) −4.65685 + 4.65685i −0.225361 + 0.225361i
\(428\) −9.07107 + 9.07107i −0.438467 + 0.438467i
\(429\) 0 0
\(430\) 0 0
\(431\) 13.2132i 0.636458i −0.948014 0.318229i \(-0.896912\pi\)
0.948014 0.318229i \(-0.103088\pi\)
\(432\) 0 0
\(433\) −24.2426 24.2426i −1.16503 1.16503i −0.983360 0.181667i \(-0.941851\pi\)
−0.181667 0.983360i \(-0.558149\pi\)
\(434\) 8.82843 0.423778
\(435\) 0 0
\(436\) −20.1421 −0.964633
\(437\) 34.1421 + 34.1421i 1.63324 + 1.63324i
\(438\) 0 0
\(439\) 25.7990i 1.23132i −0.788012 0.615659i \(-0.788890\pi\)
0.788012 0.615659i \(-0.211110\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −7.65685 + 7.65685i −0.364199 + 0.364199i
\(443\) 24.4853 24.4853i 1.16333 1.16333i 0.179589 0.983742i \(-0.442523\pi\)
0.983742 0.179589i \(-0.0574768\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 11.1716i 0.528989i
\(447\) 0 0
\(448\) 0.707107 + 0.707107i 0.0334077 + 0.0334077i
\(449\) −32.2426 −1.52162 −0.760812 0.648972i \(-0.775199\pi\)
−0.760812 + 0.648972i \(0.775199\pi\)
\(450\) 0 0
\(451\) 23.3137 1.09780
\(452\) 5.41421 + 5.41421i 0.254663 + 0.254663i
\(453\) 0 0
\(454\) 6.14214i 0.288265i
\(455\) 0 0
\(456\) 0 0
\(457\) −7.51472 + 7.51472i −0.351524 + 0.351524i −0.860676 0.509153i \(-0.829959\pi\)
0.509153 + 0.860676i \(0.329959\pi\)
\(458\) 3.48528 3.48528i 0.162857 0.162857i
\(459\) 0 0
\(460\) 0 0
\(461\) 37.3137i 1.73787i −0.494924 0.868936i \(-0.664804\pi\)
0.494924 0.868936i \(-0.335196\pi\)
\(462\) 0 0
\(463\) −5.51472 5.51472i −0.256291 0.256291i 0.567253 0.823544i \(-0.308006\pi\)
−0.823544 + 0.567253i \(0.808006\pi\)
\(464\) −3.17157 −0.147237
\(465\) 0 0
\(466\) −7.65685 −0.354697
\(467\) −9.65685 9.65685i −0.446866 0.446866i 0.447445 0.894311i \(-0.352334\pi\)
−0.894311 + 0.447445i \(0.852334\pi\)
\(468\) 0 0
\(469\) 0.585786i 0.0270491i
\(470\) 0 0
\(471\) 0 0
\(472\) −5.65685 + 5.65685i −0.260378 + 0.260378i
\(473\) −30.9706 + 30.9706i −1.42403 + 1.42403i
\(474\) 0 0
\(475\) 0 0
\(476\) 2.24264i 0.102791i
\(477\) 0 0
\(478\) 17.8284 + 17.8284i 0.815453 + 0.815453i
\(479\) 9.65685 0.441233 0.220616 0.975361i \(-0.429193\pi\)
0.220616 + 0.975361i \(0.429193\pi\)
\(480\) 0 0
\(481\) 41.4558 1.89022
\(482\) −5.41421 5.41421i −0.246611 0.246611i
\(483\) 0 0
\(484\) 12.3137i 0.559714i
\(485\) 0 0
\(486\) 0 0
\(487\) 20.0000 20.0000i 0.906287 0.906287i −0.0896838 0.995970i \(-0.528586\pi\)
0.995970 + 0.0896838i \(0.0285856\pi\)
\(488\) −4.65685 + 4.65685i −0.210806 + 0.210806i
\(489\) 0 0
\(490\) 0 0
\(491\) 22.9706i 1.03665i 0.855185 + 0.518323i \(0.173444\pi\)
−0.855185 + 0.518323i \(0.826556\pi\)
\(492\) 0 0
\(493\) 5.02944 + 5.02944i 0.226514 + 0.226514i
\(494\) −34.1421 −1.53613
\(495\) 0 0
\(496\) 8.82843 0.396408
\(497\) −8.65685 8.65685i −0.388313 0.388313i
\(498\) 0 0
\(499\) 24.0000i 1.07439i 0.843459 + 0.537194i \(0.180516\pi\)
−0.843459 + 0.537194i \(0.819484\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 4.92893 4.92893i 0.219989 0.219989i
\(503\) 20.4142 20.4142i 0.910225 0.910225i −0.0860648 0.996290i \(-0.527429\pi\)
0.996290 + 0.0860648i \(0.0274292\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 32.9706i 1.46572i
\(507\) 0 0
\(508\) −1.17157 1.17157i −0.0519801 0.0519801i
\(509\) −18.3431 −0.813046 −0.406523 0.913641i \(-0.633259\pi\)
−0.406523 + 0.913641i \(0.633259\pi\)
\(510\) 0 0
\(511\) −8.48528 −0.375367
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 9.75736i 0.430379i
\(515\) 0 0
\(516\) 0 0
\(517\) 30.9706 30.9706i 1.36208 1.36208i
\(518\) −6.07107 + 6.07107i −0.266747 + 0.266747i
\(519\) 0 0
\(520\) 0 0
\(521\) 6.97056i 0.305386i −0.988274 0.152693i \(-0.951205\pi\)
0.988274 0.152693i \(-0.0487946\pi\)
\(522\) 0 0
\(523\) −30.2843 30.2843i −1.32424 1.32424i −0.910309 0.413930i \(-0.864156\pi\)
−0.413930 0.910309i \(-0.635844\pi\)
\(524\) 6.00000 0.262111
\(525\) 0 0
\(526\) 31.1127 1.35658
\(527\) −14.0000 14.0000i −0.609850 0.609850i
\(528\) 0 0
\(529\) 23.6274i 1.02728i
\(530\) 0 0
\(531\) 0 0
\(532\) 5.00000 5.00000i 0.216777 0.216777i
\(533\) −16.4853 + 16.4853i −0.714057 + 0.714057i
\(534\) 0 0
\(535\) 0 0
\(536\) 0.585786i 0.0253021i
\(537\) 0 0
\(538\) −15.0711 15.0711i −0.649760 0.649760i
\(539\) −4.82843 −0.207975
\(540\) 0 0
\(541\) 9.51472 0.409070 0.204535 0.978859i \(-0.434432\pi\)
0.204535 + 0.978859i \(0.434432\pi\)
\(542\) 5.07107 + 5.07107i 0.217821 + 0.217821i
\(543\) 0 0
\(544\) 2.24264i 0.0961524i
\(545\) 0 0
\(546\) 0 0
\(547\) 23.7279 23.7279i 1.01453 1.01453i 0.0146399 0.999893i \(-0.495340\pi\)
0.999893 0.0146399i \(-0.00466018\pi\)
\(548\) 1.07107 1.07107i 0.0457537 0.0457537i
\(549\) 0 0
\(550\) 0 0
\(551\) 22.4264i 0.955397i
\(552\) 0 0
\(553\) −9.41421 9.41421i −0.400333 0.400333i
\(554\) 25.5563 1.08579
\(555\) 0 0
\(556\) −0.242641 −0.0102903
\(557\) 2.10051 + 2.10051i 0.0890013 + 0.0890013i 0.750206 0.661204i \(-0.229954\pi\)
−0.661204 + 0.750206i \(0.729954\pi\)
\(558\) 0 0
\(559\) 43.7990i 1.85250i
\(560\) 0 0
\(561\) 0 0
\(562\) 9.14214 9.14214i 0.385638 0.385638i
\(563\) 20.1421 20.1421i 0.848890 0.848890i −0.141105 0.989995i \(-0.545065\pi\)
0.989995 + 0.141105i \(0.0450655\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 25.4558i 1.06999i
\(567\) 0 0
\(568\) −8.65685 8.65685i −0.363234 0.363234i
\(569\) −10.3848 −0.435352 −0.217676 0.976021i \(-0.569848\pi\)
−0.217676 + 0.976021i \(0.569848\pi\)
\(570\) 0 0
\(571\) 8.97056 0.375406 0.187703 0.982226i \(-0.439896\pi\)
0.187703 + 0.982226i \(0.439896\pi\)
\(572\) 16.4853 + 16.4853i 0.689284 + 0.689284i
\(573\) 0 0
\(574\) 4.82843i 0.201535i
\(575\) 0 0
\(576\) 0 0
\(577\) −11.1716 + 11.1716i −0.465079 + 0.465079i −0.900316 0.435237i \(-0.856665\pi\)
0.435237 + 0.900316i \(0.356665\pi\)
\(578\) 8.46447 8.46447i 0.352075 0.352075i
\(579\) 0 0
\(580\) 0 0
\(581\) 13.6569i 0.566582i
\(582\) 0 0
\(583\) 23.3137 + 23.3137i 0.965555 + 0.965555i
\(584\) −8.48528 −0.351123
\(585\) 0 0
\(586\) 31.7990 1.31360
\(587\) −14.0000 14.0000i −0.577842 0.577842i 0.356466 0.934308i \(-0.383981\pi\)
−0.934308 + 0.356466i \(0.883981\pi\)
\(588\) 0 0
\(589\) 62.4264i 2.57224i
\(590\) 0 0
\(591\) 0 0
\(592\) −6.07107 + 6.07107i −0.249519 + 0.249519i
\(593\) −14.4142 + 14.4142i −0.591921 + 0.591921i −0.938150 0.346229i \(-0.887462\pi\)
0.346229 + 0.938150i \(0.387462\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 5.31371i 0.217658i
\(597\) 0 0
\(598\) 23.3137 + 23.3137i 0.953368 + 0.953368i
\(599\) 4.92893 0.201391 0.100695 0.994917i \(-0.467893\pi\)
0.100695 + 0.994917i \(0.467893\pi\)
\(600\) 0 0
\(601\) −18.0000 −0.734235 −0.367118 0.930175i \(-0.619655\pi\)
−0.367118 + 0.930175i \(0.619655\pi\)
\(602\) 6.41421 + 6.41421i 0.261424 + 0.261424i
\(603\) 0 0
\(604\) 13.3137i 0.541727i
\(605\) 0 0
\(606\) 0 0
\(607\) −12.3848 + 12.3848i −0.502683 + 0.502683i −0.912271 0.409588i \(-0.865672\pi\)
0.409588 + 0.912271i \(0.365672\pi\)
\(608\) 5.00000 5.00000i 0.202777 0.202777i
\(609\) 0 0
\(610\) 0 0
\(611\) 43.7990i 1.77192i
\(612\) 0 0
\(613\) −3.58579 3.58579i −0.144829 0.144829i 0.630975 0.775803i \(-0.282655\pi\)
−0.775803 + 0.630975i \(0.782655\pi\)
\(614\) 10.6274 0.428888
\(615\) 0 0
\(616\) −4.82843 −0.194543
\(617\) 24.5858 + 24.5858i 0.989786 + 0.989786i 0.999948 0.0101619i \(-0.00323468\pi\)
−0.0101619 + 0.999948i \(0.503235\pi\)
\(618\) 0 0
\(619\) 34.8701i 1.40155i −0.713384 0.700773i \(-0.752839\pi\)
0.713384 0.700773i \(-0.247161\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 11.3137 11.3137i 0.453638 0.453638i
\(623\) −9.41421 + 9.41421i −0.377173 + 0.377173i
\(624\) 0 0
\(625\) 0 0
\(626\) 27.7990i 1.11107i
\(627\) 0 0
\(628\) −2.58579 2.58579i −0.103184 0.103184i
\(629\) 19.2548 0.767741
\(630\) 0 0
\(631\) 4.97056 0.197875 0.0989375 0.995094i \(-0.468456\pi\)
0.0989375 + 0.995094i \(0.468456\pi\)
\(632\) −9.41421 9.41421i −0.374477 0.374477i
\(633\) 0 0
\(634\) 17.3137i 0.687615i
\(635\) 0 0
\(636\) 0 0
\(637\) 3.41421 3.41421i 0.135276 0.135276i
\(638\) 10.8284 10.8284i 0.428702 0.428702i
\(639\) 0 0
\(640\) 0 0
\(641\) 40.5269i 1.60072i −0.599522 0.800358i \(-0.704643\pi\)
0.599522 0.800358i \(-0.295357\pi\)
\(642\) 0 0
\(643\) 0.142136 + 0.142136i 0.00560528 + 0.00560528i 0.709904 0.704299i \(-0.248738\pi\)
−0.704299 + 0.709904i \(0.748738\pi\)
\(644\) −6.82843 −0.269078
\(645\) 0 0
\(646\) −15.8579 −0.623919
\(647\) 18.2132 + 18.2132i 0.716035 + 0.716035i 0.967791 0.251756i \(-0.0810080\pi\)
−0.251756 + 0.967791i \(0.581008\pi\)
\(648\) 0 0
\(649\) 38.6274i 1.51626i
\(650\) 0 0
\(651\) 0 0
\(652\) 4.89949 4.89949i 0.191879 0.191879i
\(653\) 2.58579 2.58579i 0.101190 0.101190i −0.654700 0.755889i \(-0.727205\pi\)
0.755889 + 0.654700i \(0.227205\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 4.82843i 0.188518i
\(657\) 0 0
\(658\) −6.41421 6.41421i −0.250052 0.250052i
\(659\) −17.7990 −0.693350 −0.346675 0.937985i \(-0.612689\pi\)
−0.346675 + 0.937985i \(0.612689\pi\)
\(660\) 0 0
\(661\) −27.7574 −1.07964 −0.539818 0.841782i \(-0.681507\pi\)
−0.539818 + 0.841782i \(0.681507\pi\)
\(662\) −1.31371 1.31371i −0.0510587 0.0510587i
\(663\) 0 0
\(664\) 13.6569i 0.529989i
\(665\) 0 0
\(666\) 0 0
\(667\) 15.3137 15.3137i 0.592949 0.592949i
\(668\) 6.89949 6.89949i 0.266949 0.266949i
\(669\) 0 0
\(670\) 0 0
\(671\) 31.7990i 1.22759i
\(672\) 0 0
\(673\) 13.7990 + 13.7990i 0.531912 + 0.531912i 0.921141 0.389229i \(-0.127259\pi\)
−0.389229 + 0.921141i \(0.627259\pi\)
\(674\) 2.14214 0.0825120
\(675\) 0 0
\(676\) −10.3137 −0.396681
\(677\) 7.51472 + 7.51472i 0.288814 + 0.288814i 0.836611 0.547797i \(-0.184533\pi\)
−0.547797 + 0.836611i \(0.684533\pi\)
\(678\) 0 0
\(679\) 11.6569i 0.447349i
\(680\) 0 0
\(681\) 0 0
\(682\) −30.1421 + 30.1421i −1.15420 + 1.15420i
\(683\) 3.89949 3.89949i 0.149210 0.149210i −0.628555 0.777765i \(-0.716353\pi\)
0.777765 + 0.628555i \(0.216353\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000i 0.0381802i
\(687\) 0 0
\(688\) 6.41421 + 6.41421i 0.244540 + 0.244540i
\(689\) −32.9706 −1.25608
\(690\) 0 0
\(691\) −17.2132 −0.654821 −0.327411 0.944882i \(-0.606176\pi\)
−0.327411 + 0.944882i \(0.606176\pi\)
\(692\) 8.00000 + 8.00000i 0.304114 + 0.304114i
\(693\) 0 0
\(694\) 20.9706i 0.796032i
\(695\) 0 0
\(696\) 0 0
\(697\) −7.65685 + 7.65685i −0.290024 + 0.290024i
\(698\) −6.17157 + 6.17157i −0.233597 + 0.233597i
\(699\) 0 0
\(700\) 0 0
\(701\) 26.4853i 1.00034i 0.865929 + 0.500168i \(0.166728\pi\)
−0.865929 + 0.500168i \(0.833272\pi\)
\(702\) 0 0
\(703\) 42.9289 + 42.9289i 1.61910 + 1.61910i
\(704\) −4.82843 −0.181978
\(705\) 0 0
\(706\) 21.7574 0.818849
\(707\) −3.07107 3.07107i −0.115499 0.115499i
\(708\) 0 0
\(709\) 5.31371i 0.199561i −0.995009 0.0997803i \(-0.968186\pi\)
0.995009 0.0997803i \(-0.0318140\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −9.41421 + 9.41421i −0.352813 + 0.352813i
\(713\) −42.6274 + 42.6274i −1.59641 + 1.59641i
\(714\) 0 0
\(715\) 0 0
\(716\) 13.3137i 0.497557i
\(717\) 0 0
\(718\) −14.6569 14.6569i −0.546989 0.546989i
\(719\) 5.45584 0.203469 0.101734 0.994812i \(-0.467561\pi\)
0.101734 + 0.994812i \(0.467561\pi\)
\(720\) 0 0
\(721\) 4.82843 0.179820
\(722\) −21.9203 21.9203i −0.815789 0.815789i
\(723\) 0 0
\(724\) 11.0711i 0.411453i
\(725\) 0 0
\(726\) 0 0
\(727\) −10.2426 + 10.2426i −0.379879 + 0.379879i −0.871058 0.491180i \(-0.836566\pi\)
0.491180 + 0.871058i \(0.336566\pi\)
\(728\) 3.41421 3.41421i 0.126539 0.126539i
\(729\) 0 0
\(730\) 0 0
\(731\) 20.3431i 0.752418i
\(732\) 0 0
\(733\) 20.7279 + 20.7279i 0.765603 + 0.765603i 0.977329 0.211726i \(-0.0679084\pi\)
−0.211726 + 0.977329i \(0.567908\pi\)
\(734\) −28.2843 −1.04399
\(735\) 0 0
\(736\) −6.82843 −0.251699
\(737\) 2.00000 + 2.00000i 0.0736709 + 0.0736709i
\(738\) 0 0
\(739\) 2.62742i 0.0966511i −0.998832 0.0483255i \(-0.984612\pi\)
0.998832 0.0483255i \(-0.0153885\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 4.82843 4.82843i 0.177257 0.177257i
\(743\) −18.1421 + 18.1421i −0.665570 + 0.665570i −0.956687 0.291117i \(-0.905973\pi\)
0.291117 + 0.956687i \(0.405973\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 15.8995i 0.582122i
\(747\) 0 0
\(748\) 7.65685 + 7.65685i 0.279962 + 0.279962i
\(749\) −12.8284 −0.468741
\(750\) 0 0
\(751\) 44.9706 1.64100 0.820500 0.571647i \(-0.193695\pi\)
0.820500 + 0.571647i \(0.193695\pi\)
\(752\) −6.41421 6.41421i −0.233902 0.233902i
\(753\) 0 0
\(754\) 15.3137i 0.557692i
\(755\) 0 0
\(756\) 0 0
\(757\) 24.0711 24.0711i 0.874878 0.874878i −0.118121 0.992999i \(-0.537687\pi\)
0.992999 + 0.118121i \(0.0376872\pi\)
\(758\) −4.00000 + 4.00000i −0.145287 + 0.145287i
\(759\) 0 0
\(760\) 0 0
\(761\) 15.6569i 0.567561i −0.958889 0.283780i \(-0.908411\pi\)
0.958889 0.283780i \(-0.0915886\pi\)
\(762\) 0 0
\(763\) −14.2426 14.2426i −0.515618 0.515618i
\(764\) −13.4142 −0.485309
\(765\) 0 0
\(766\) 7.41421 0.267886
\(767\) 27.3137 + 27.3137i 0.986241 + 0.986241i
\(768\) 0 0
\(769\) 12.1421i 0.437857i −0.975741 0.218928i \(-0.929744\pi\)
0.975741 0.218928i \(-0.0702561\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.00000 6.00000i 0.215945 0.215945i
\(773\) 31.9411 31.9411i 1.14884 1.14884i 0.162062 0.986781i \(-0.448186\pi\)
0.986781 0.162062i \(-0.0518144\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 11.6569i 0.418457i
\(777\) 0 0
\(778\) −3.75736 3.75736i −0.134708 0.134708i
\(779\) −34.1421 −1.22327
\(780\) 0 0
\(781\) 59.1127 2.11522
\(782\) 10.8284 + 10.8284i 0.387224 + 0.387224i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) 0 0
\(786\) 0 0
\(787\) −35.3137 + 35.3137i −1.25880 + 1.25880i −0.307130 + 0.951667i \(0.599369\pi\)
−0.951667 + 0.307130i \(0.900631\pi\)
\(788\) −3.17157 + 3.17157i −0.112983 + 0.112983i
\(789\) 0 0
\(790\) 0 0
\(791\) 7.65685i 0.272246i
\(792\) 0 0
\(793\) 22.4853 + 22.4853i 0.798476 + 0.798476i
\(794\) −35.9411 −1.27550
\(795\) 0 0
\(796\) 0.343146 0.0121625
\(797\) −3.79899 3.79899i −0.134567 0.134567i 0.636615 0.771182i \(-0.280334\pi\)
−0.771182 + 0.636615i \(0.780334\pi\)
\(798\) 0 0
\(799\) 20.3431i 0.719689i
\(800\) 0 0
\(801\) 0 0
\(802\) 21.9706 21.9706i 0.775808 0.775808i
\(803\) 28.9706 28.9706i 1.02235 1.02235i
\(804\) 0 0
\(805\)