Properties

Label 630.2.u.c.289.1
Level $630$
Weight $2$
Character 630.289
Analytic conductor $5.031$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.u (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 289.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 630.289
Dual form 630.2.u.c.109.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.86603 - 1.23205i) q^{5} +(-1.73205 + 2.00000i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.86603 - 1.23205i) q^{5} +(-1.73205 + 2.00000i) q^{7} -1.00000i q^{8} +(-2.23205 + 0.133975i) q^{10} +(-2.50000 - 4.33013i) q^{11} -1.00000i q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.73205 - 1.00000i) q^{17} +(3.50000 - 6.06218i) q^{19} +(2.00000 + 1.00000i) q^{20} +5.00000i q^{22} +(-2.59808 - 1.50000i) q^{23} +(1.96410 - 4.59808i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(-2.59808 - 0.500000i) q^{28} +(3.00000 + 5.19615i) q^{31} +(0.866025 - 0.500000i) q^{32} -2.00000 q^{34} +(-0.767949 + 5.86603i) q^{35} +(4.33013 + 2.50000i) q^{37} +(-6.06218 + 3.50000i) q^{38} +(-1.23205 - 1.86603i) q^{40} +9.00000 q^{41} -10.0000i q^{43} +(2.50000 - 4.33013i) q^{44} +(1.50000 + 2.59808i) q^{46} +(-11.2583 - 6.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-4.00000 + 3.00000i) q^{50} +(0.866025 - 0.500000i) q^{52} +(-0.866025 + 0.500000i) q^{53} +(-10.0000 - 5.00000i) q^{55} +(2.00000 + 1.73205i) q^{56} +(-2.00000 - 3.46410i) q^{59} +(1.00000 - 1.73205i) q^{61} -6.00000i q^{62} -1.00000 q^{64} +(-1.23205 - 1.86603i) q^{65} +(5.19615 - 3.00000i) q^{67} +(1.73205 + 1.00000i) q^{68} +(3.59808 - 4.69615i) q^{70} +2.00000 q^{71} +(-3.46410 + 2.00000i) q^{73} +(-2.50000 - 4.33013i) q^{74} +7.00000 q^{76} +(12.9904 + 2.50000i) q^{77} +(-7.00000 + 12.1244i) q^{79} +(0.133975 + 2.23205i) q^{80} +(-7.79423 - 4.50000i) q^{82} -10.0000i q^{83} +(2.00000 - 4.00000i) q^{85} +(-5.00000 + 8.66025i) q^{86} +(-4.33013 + 2.50000i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(2.00000 + 1.73205i) q^{91} -3.00000i q^{92} +(6.50000 + 11.2583i) q^{94} +(-0.937822 - 15.6244i) q^{95} +8.00000i q^{97} +(-2.59808 + 6.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + 4q^{5} + O(q^{10}) \) \( 4q + 2q^{4} + 4q^{5} - 2q^{10} - 10q^{11} + 10q^{14} - 2q^{16} + 14q^{19} + 8q^{20} - 6q^{25} - 2q^{26} + 12q^{31} - 8q^{34} - 10q^{35} + 2q^{40} + 36q^{41} + 10q^{44} + 6q^{46} - 4q^{49} - 16q^{50} - 40q^{55} + 8q^{56} - 8q^{59} + 4q^{61} - 4q^{64} + 2q^{65} + 4q^{70} + 8q^{71} - 10q^{74} + 28q^{76} - 28q^{79} + 4q^{80} + 8q^{85} - 20q^{86} - 20q^{89} + 8q^{91} + 26q^{94} - 28q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.86603 1.23205i 0.834512 0.550990i
\(6\) 0 0
\(7\) −1.73205 + 2.00000i −0.654654 + 0.755929i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −2.23205 + 0.133975i −0.705836 + 0.0423665i
\(11\) −2.50000 4.33013i −0.753778 1.30558i −0.945979 0.324227i \(-0.894896\pi\)
0.192201 0.981356i \(-0.438437\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i −0.990338 0.138675i \(-0.955716\pi\)
0.990338 0.138675i \(-0.0442844\pi\)
\(14\) 2.50000 0.866025i 0.668153 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.73205 1.00000i 0.420084 0.242536i −0.275029 0.961436i \(-0.588688\pi\)
0.695113 + 0.718900i \(0.255354\pi\)
\(18\) 0 0
\(19\) 3.50000 6.06218i 0.802955 1.39076i −0.114708 0.993399i \(-0.536593\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) 2.00000 + 1.00000i 0.447214 + 0.223607i
\(21\) 0 0
\(22\) 5.00000i 1.06600i
\(23\) −2.59808 1.50000i −0.541736 0.312772i 0.204046 0.978961i \(-0.434591\pi\)
−0.745782 + 0.666190i \(0.767924\pi\)
\(24\) 0 0
\(25\) 1.96410 4.59808i 0.392820 0.919615i
\(26\) −0.500000 + 0.866025i −0.0980581 + 0.169842i
\(27\) 0 0
\(28\) −2.59808 0.500000i −0.490990 0.0944911i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 3.00000 + 5.19615i 0.538816 + 0.933257i 0.998968 + 0.0454165i \(0.0144615\pi\)
−0.460152 + 0.887840i \(0.652205\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) −0.767949 + 5.86603i −0.129807 + 0.991539i
\(36\) 0 0
\(37\) 4.33013 + 2.50000i 0.711868 + 0.410997i 0.811752 0.584002i \(-0.198514\pi\)
−0.0998840 + 0.994999i \(0.531847\pi\)
\(38\) −6.06218 + 3.50000i −0.983415 + 0.567775i
\(39\) 0 0
\(40\) −1.23205 1.86603i −0.194804 0.295045i
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 0 0
\(43\) 10.0000i 1.52499i −0.646997 0.762493i \(-0.723975\pi\)
0.646997 0.762493i \(-0.276025\pi\)
\(44\) 2.50000 4.33013i 0.376889 0.652791i
\(45\) 0 0
\(46\) 1.50000 + 2.59808i 0.221163 + 0.383065i
\(47\) −11.2583 6.50000i −1.64220 0.948122i −0.980051 0.198747i \(-0.936313\pi\)
−0.662145 0.749375i \(-0.730354\pi\)
\(48\) 0 0
\(49\) −1.00000 6.92820i −0.142857 0.989743i
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) 0 0
\(52\) 0.866025 0.500000i 0.120096 0.0693375i
\(53\) −0.866025 + 0.500000i −0.118958 + 0.0686803i −0.558298 0.829640i \(-0.688546\pi\)
0.439340 + 0.898321i \(0.355212\pi\)
\(54\) 0 0
\(55\) −10.0000 5.00000i −1.34840 0.674200i
\(56\) 2.00000 + 1.73205i 0.267261 + 0.231455i
\(57\) 0 0
\(58\) 0 0
\(59\) −2.00000 3.46410i −0.260378 0.450988i 0.705965 0.708247i \(-0.250514\pi\)
−0.966342 + 0.257260i \(0.917180\pi\)
\(60\) 0 0
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 6.00000i 0.762001i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −1.23205 1.86603i −0.152817 0.231452i
\(66\) 0 0
\(67\) 5.19615 3.00000i 0.634811 0.366508i −0.147802 0.989017i \(-0.547220\pi\)
0.782613 + 0.622509i \(0.213886\pi\)
\(68\) 1.73205 + 1.00000i 0.210042 + 0.121268i
\(69\) 0 0
\(70\) 3.59808 4.69615i 0.430052 0.561298i
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 0 0
\(73\) −3.46410 + 2.00000i −0.405442 + 0.234082i −0.688830 0.724923i \(-0.741875\pi\)
0.283387 + 0.959006i \(0.408542\pi\)
\(74\) −2.50000 4.33013i −0.290619 0.503367i
\(75\) 0 0
\(76\) 7.00000 0.802955
\(77\) 12.9904 + 2.50000i 1.48039 + 0.284901i
\(78\) 0 0
\(79\) −7.00000 + 12.1244i −0.787562 + 1.36410i 0.139895 + 0.990166i \(0.455323\pi\)
−0.927457 + 0.373930i \(0.878010\pi\)
\(80\) 0.133975 + 2.23205i 0.0149788 + 0.249551i
\(81\) 0 0
\(82\) −7.79423 4.50000i −0.860729 0.496942i
\(83\) 10.0000i 1.09764i −0.835940 0.548821i \(-0.815077\pi\)
0.835940 0.548821i \(-0.184923\pi\)
\(84\) 0 0
\(85\) 2.00000 4.00000i 0.216930 0.433861i
\(86\) −5.00000 + 8.66025i −0.539164 + 0.933859i
\(87\) 0 0
\(88\) −4.33013 + 2.50000i −0.461593 + 0.266501i
\(89\) −5.00000 + 8.66025i −0.529999 + 0.917985i 0.469389 + 0.882992i \(0.344474\pi\)
−0.999388 + 0.0349934i \(0.988859\pi\)
\(90\) 0 0
\(91\) 2.00000 + 1.73205i 0.209657 + 0.181568i
\(92\) 3.00000i 0.312772i
\(93\) 0 0
\(94\) 6.50000 + 11.2583i 0.670424 + 1.16121i
\(95\) −0.937822 15.6244i −0.0962185 1.60303i
\(96\) 0 0
\(97\) 8.00000i 0.812277i 0.913812 + 0.406138i \(0.133125\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) −2.59808 + 6.50000i −0.262445 + 0.656599i
\(99\) 0 0
\(100\) 4.96410 0.598076i 0.496410 0.0598076i
\(101\) 4.00000 + 6.92820i 0.398015 + 0.689382i 0.993481 0.113998i \(-0.0363659\pi\)
−0.595466 + 0.803380i \(0.703033\pi\)
\(102\) 0 0
\(103\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 1.00000 0.0971286
\(107\) 10.3923 + 6.00000i 1.00466 + 0.580042i 0.909624 0.415432i \(-0.136370\pi\)
0.0950377 + 0.995474i \(0.469703\pi\)
\(108\) 0 0
\(109\) −9.00000 15.5885i −0.862044 1.49310i −0.869953 0.493135i \(-0.835851\pi\)
0.00790932 0.999969i \(-0.497482\pi\)
\(110\) 6.16025 + 9.33013i 0.587357 + 0.889593i
\(111\) 0 0
\(112\) −0.866025 2.50000i −0.0818317 0.236228i
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) 0 0
\(115\) −6.69615 + 0.401924i −0.624419 + 0.0374796i
\(116\) 0 0
\(117\) 0 0
\(118\) 4.00000i 0.368230i
\(119\) −1.00000 + 5.19615i −0.0916698 + 0.476331i
\(120\) 0 0
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) −1.73205 + 1.00000i −0.156813 + 0.0905357i
\(123\) 0 0
\(124\) −3.00000 + 5.19615i −0.269408 + 0.466628i
\(125\) −2.00000 11.0000i −0.178885 0.983870i
\(126\) 0 0
\(127\) 9.00000i 0.798621i 0.916816 + 0.399310i \(0.130750\pi\)
−0.916816 + 0.399310i \(0.869250\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 0.133975 + 2.23205i 0.0117503 + 0.195764i
\(131\) −8.50000 + 14.7224i −0.742648 + 1.28630i 0.208637 + 0.977993i \(0.433097\pi\)
−0.951285 + 0.308312i \(0.900236\pi\)
\(132\) 0 0
\(133\) 6.06218 + 17.5000i 0.525657 + 1.51744i
\(134\) −6.00000 −0.518321
\(135\) 0 0
\(136\) −1.00000 1.73205i −0.0857493 0.148522i
\(137\) 3.46410 2.00000i 0.295958 0.170872i −0.344668 0.938725i \(-0.612008\pi\)
0.640626 + 0.767853i \(0.278675\pi\)
\(138\) 0 0
\(139\) 8.00000 0.678551 0.339276 0.940687i \(-0.389818\pi\)
0.339276 + 0.940687i \(0.389818\pi\)
\(140\) −5.46410 + 2.26795i −0.461801 + 0.191677i
\(141\) 0 0
\(142\) −1.73205 1.00000i −0.145350 0.0839181i
\(143\) −4.33013 + 2.50000i −0.362103 + 0.209061i
\(144\) 0 0
\(145\) 0 0
\(146\) 4.00000 0.331042
\(147\) 0 0
\(148\) 5.00000i 0.410997i
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) 11.0000 + 19.0526i 0.895167 + 1.55048i 0.833597 + 0.552372i \(0.186277\pi\)
0.0615699 + 0.998103i \(0.480389\pi\)
\(152\) −6.06218 3.50000i −0.491708 0.283887i
\(153\) 0 0
\(154\) −10.0000 8.66025i −0.805823 0.697863i
\(155\) 12.0000 + 6.00000i 0.963863 + 0.481932i
\(156\) 0 0
\(157\) 11.2583 6.50000i 0.898513 0.518756i 0.0217953 0.999762i \(-0.493062\pi\)
0.876717 + 0.481006i \(0.159728\pi\)
\(158\) 12.1244 7.00000i 0.964562 0.556890i
\(159\) 0 0
\(160\) 1.00000 2.00000i 0.0790569 0.158114i
\(161\) 7.50000 2.59808i 0.591083 0.204757i
\(162\) 0 0
\(163\) −10.3923 6.00000i −0.813988 0.469956i 0.0343508 0.999410i \(-0.489064\pi\)
−0.848339 + 0.529454i \(0.822397\pi\)
\(164\) 4.50000 + 7.79423i 0.351391 + 0.608627i
\(165\) 0 0
\(166\) −5.00000 + 8.66025i −0.388075 + 0.672166i
\(167\) 19.0000i 1.47026i 0.677924 + 0.735132i \(0.262880\pi\)
−0.677924 + 0.735132i \(0.737120\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) −3.73205 + 2.46410i −0.286235 + 0.188988i
\(171\) 0 0
\(172\) 8.66025 5.00000i 0.660338 0.381246i
\(173\) −6.06218 3.50000i −0.460899 0.266100i 0.251523 0.967851i \(-0.419068\pi\)
−0.712422 + 0.701751i \(0.752402\pi\)
\(174\) 0 0
\(175\) 5.79423 + 11.8923i 0.438003 + 0.898974i
\(176\) 5.00000 0.376889
\(177\) 0 0
\(178\) 8.66025 5.00000i 0.649113 0.374766i
\(179\) 5.50000 + 9.52628i 0.411089 + 0.712028i 0.995009 0.0997838i \(-0.0318151\pi\)
−0.583920 + 0.811811i \(0.698482\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) −0.866025 2.50000i −0.0641941 0.185312i
\(183\) 0 0
\(184\) −1.50000 + 2.59808i −0.110581 + 0.191533i
\(185\) 11.1603 0.669873i 0.820518 0.0492500i
\(186\) 0 0
\(187\) −8.66025 5.00000i −0.633300 0.365636i
\(188\) 13.0000i 0.948122i
\(189\) 0 0
\(190\) −7.00000 + 14.0000i −0.507833 + 1.01567i
\(191\) −8.00000 + 13.8564i −0.578860 + 1.00261i 0.416751 + 0.909021i \(0.363169\pi\)
−0.995610 + 0.0935936i \(0.970165\pi\)
\(192\) 0 0
\(193\) 15.5885 9.00000i 1.12208 0.647834i 0.180150 0.983639i \(-0.442342\pi\)
0.941932 + 0.335805i \(0.109008\pi\)
\(194\) 4.00000 6.92820i 0.287183 0.497416i
\(195\) 0 0
\(196\) 5.50000 4.33013i 0.392857 0.309295i
\(197\) 27.0000i 1.92367i 0.273629 + 0.961835i \(0.411776\pi\)
−0.273629 + 0.961835i \(0.588224\pi\)
\(198\) 0 0
\(199\) −7.00000 12.1244i −0.496217 0.859473i 0.503774 0.863836i \(-0.331945\pi\)
−0.999990 + 0.00436292i \(0.998611\pi\)
\(200\) −4.59808 1.96410i −0.325133 0.138883i
\(201\) 0 0
\(202\) 8.00000i 0.562878i
\(203\) 0 0
\(204\) 0 0
\(205\) 16.7942 11.0885i 1.17296 0.774451i
\(206\) 0 0
\(207\) 0 0
\(208\) 0.866025 + 0.500000i 0.0600481 + 0.0346688i
\(209\) −35.0000 −2.42100
\(210\) 0 0
\(211\) 19.0000 1.30801 0.654007 0.756489i \(-0.273087\pi\)
0.654007 + 0.756489i \(0.273087\pi\)
\(212\) −0.866025 0.500000i −0.0594789 0.0343401i
\(213\) 0 0
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) −12.3205 18.6603i −0.840252 1.27262i
\(216\) 0 0
\(217\) −15.5885 3.00000i −1.05821 0.203653i
\(218\) 18.0000i 1.21911i
\(219\) 0 0
\(220\) −0.669873 11.1603i −0.0451628 0.752424i
\(221\) −1.00000 1.73205i −0.0672673 0.116510i
\(222\) 0 0
\(223\) 16.0000i 1.07144i −0.844396 0.535720i \(-0.820040\pi\)
0.844396 0.535720i \(-0.179960\pi\)
\(224\) −0.500000 + 2.59808i −0.0334077 + 0.173591i
\(225\) 0 0
\(226\) 3.00000 5.19615i 0.199557 0.345643i
\(227\) −12.1244 + 7.00000i −0.804722 + 0.464606i −0.845120 0.534577i \(-0.820471\pi\)
0.0403978 + 0.999184i \(0.487137\pi\)
\(228\) 0 0
\(229\) −2.00000 + 3.46410i −0.132164 + 0.228914i −0.924510 0.381157i \(-0.875526\pi\)
0.792347 + 0.610071i \(0.208859\pi\)
\(230\) 6.00000 + 3.00000i 0.395628 + 0.197814i
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(234\) 0 0
\(235\) −29.0167 + 1.74167i −1.89284 + 0.113614i
\(236\) 2.00000 3.46410i 0.130189 0.225494i
\(237\) 0 0
\(238\) 3.46410 4.00000i 0.224544 0.259281i
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) 12.1244 7.00000i 0.779383 0.449977i
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) −10.4019 11.6962i −0.664555 0.747240i
\(246\) 0 0
\(247\) −6.06218 3.50000i −0.385727 0.222700i
\(248\) 5.19615 3.00000i 0.329956 0.190500i
\(249\) 0 0
\(250\) −3.76795 + 10.5263i −0.238306 + 0.665740i
\(251\) 3.00000 0.189358 0.0946792 0.995508i \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) 0 0
\(253\) 15.0000i 0.943042i
\(254\) 4.50000 7.79423i 0.282355 0.489053i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −8.66025 5.00000i −0.540212 0.311891i 0.204953 0.978772i \(-0.434296\pi\)
−0.745165 + 0.666880i \(0.767629\pi\)
\(258\) 0 0
\(259\) −12.5000 + 4.33013i −0.776712 + 0.269061i
\(260\) 1.00000 2.00000i 0.0620174 0.124035i
\(261\) 0 0
\(262\) 14.7224 8.50000i 0.909555 0.525132i
\(263\) 20.7846 12.0000i 1.28163 0.739952i 0.304487 0.952517i \(-0.401515\pi\)
0.977147 + 0.212565i \(0.0681817\pi\)
\(264\) 0 0
\(265\) −1.00000 + 2.00000i −0.0614295 + 0.122859i
\(266\) 3.50000 18.1865i 0.214599 1.11509i
\(267\) 0 0
\(268\) 5.19615 + 3.00000i 0.317406 + 0.183254i
\(269\) −7.00000 12.1244i −0.426798 0.739235i 0.569789 0.821791i \(-0.307025\pi\)
−0.996586 + 0.0825561i \(0.973692\pi\)
\(270\) 0 0
\(271\) −4.00000 + 6.92820i −0.242983 + 0.420858i −0.961563 0.274586i \(-0.911459\pi\)
0.718580 + 0.695444i \(0.244792\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) −4.00000 −0.241649
\(275\) −24.8205 + 2.99038i −1.49673 + 0.180327i
\(276\) 0 0
\(277\) 1.73205 1.00000i 0.104069 0.0600842i −0.447062 0.894503i \(-0.647530\pi\)
0.551131 + 0.834419i \(0.314196\pi\)
\(278\) −6.92820 4.00000i −0.415526 0.239904i
\(279\) 0 0
\(280\) 5.86603 + 0.767949i 0.350562 + 0.0458937i
\(281\) 11.0000 0.656205 0.328102 0.944642i \(-0.393591\pi\)
0.328102 + 0.944642i \(0.393591\pi\)
\(282\) 0 0
\(283\) −22.5167 + 13.0000i −1.33848 + 0.772770i −0.986581 0.163270i \(-0.947796\pi\)
−0.351895 + 0.936039i \(0.614463\pi\)
\(284\) 1.00000 + 1.73205i 0.0593391 + 0.102778i
\(285\) 0 0
\(286\) 5.00000 0.295656
\(287\) −15.5885 + 18.0000i −0.920158 + 1.06251i
\(288\) 0 0
\(289\) −6.50000 + 11.2583i −0.382353 + 0.662255i
\(290\) 0 0
\(291\) 0 0
\(292\) −3.46410 2.00000i −0.202721 0.117041i
\(293\) 1.00000i 0.0584206i 0.999573 + 0.0292103i \(0.00929925\pi\)
−0.999573 + 0.0292103i \(0.990701\pi\)
\(294\) 0 0
\(295\) −8.00000 4.00000i −0.465778 0.232889i
\(296\) 2.50000 4.33013i 0.145310 0.251684i
\(297\) 0 0
\(298\) −5.19615 + 3.00000i −0.301005 + 0.173785i
\(299\) −1.50000 + 2.59808i −0.0867472 + 0.150251i
\(300\) 0 0
\(301\) 20.0000 + 17.3205i 1.15278 + 0.998337i
\(302\) 22.0000i 1.26596i
\(303\) 0 0
\(304\) 3.50000 + 6.06218i 0.200739 + 0.347690i
\(305\) −0.267949 4.46410i −0.0153427 0.255614i
\(306\) 0 0
\(307\) 2.00000i 0.114146i 0.998370 + 0.0570730i \(0.0181768\pi\)
−0.998370 + 0.0570730i \(0.981823\pi\)
\(308\) 4.33013 + 12.5000i 0.246732 + 0.712254i
\(309\) 0 0
\(310\) −7.39230 11.1962i −0.419855 0.635899i
\(311\) −13.0000 22.5167i −0.737162 1.27680i −0.953768 0.300544i \(-0.902832\pi\)
0.216606 0.976259i \(-0.430501\pi\)
\(312\) 0 0
\(313\) −8.66025 5.00000i −0.489506 0.282617i 0.234863 0.972028i \(-0.424536\pi\)
−0.724370 + 0.689412i \(0.757869\pi\)
\(314\) −13.0000 −0.733632
\(315\) 0 0
\(316\) −14.0000 −0.787562
\(317\) 1.73205 + 1.00000i 0.0972817 + 0.0561656i 0.547852 0.836576i \(-0.315446\pi\)
−0.450570 + 0.892741i \(0.648779\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.86603 + 1.23205i −0.104314 + 0.0688737i
\(321\) 0 0
\(322\) −7.79423 1.50000i −0.434355 0.0835917i
\(323\) 14.0000i 0.778981i
\(324\) 0 0
\(325\) −4.59808 1.96410i −0.255055 0.108949i
\(326\) 6.00000 + 10.3923i 0.332309 + 0.575577i
\(327\) 0 0
\(328\) 9.00000i 0.496942i
\(329\) 32.5000 11.2583i 1.79178 0.620692i
\(330\) 0 0
\(331\) 7.50000 12.9904i 0.412237 0.714016i −0.582897 0.812546i \(-0.698081\pi\)
0.995134 + 0.0985303i \(0.0314141\pi\)
\(332\) 8.66025 5.00000i 0.475293 0.274411i
\(333\) 0 0
\(334\) 9.50000 16.4545i 0.519817 0.900349i
\(335\) 6.00000 12.0000i 0.327815 0.655630i
\(336\) 0 0
\(337\) 14.0000i 0.762629i −0.924445 0.381314i \(-0.875472\pi\)
0.924445 0.381314i \(-0.124528\pi\)
\(338\) −10.3923 6.00000i −0.565267 0.326357i
\(339\) 0 0
\(340\) 4.46410 0.267949i 0.242100 0.0145316i
\(341\) 15.0000 25.9808i 0.812296 1.40694i
\(342\) 0 0
\(343\) 15.5885 + 10.0000i 0.841698 + 0.539949i
\(344\) −10.0000 −0.539164
\(345\) 0 0
\(346\) 3.50000 + 6.06218i 0.188161 + 0.325905i
\(347\) 13.8564 8.00000i 0.743851 0.429463i −0.0796169 0.996826i \(-0.525370\pi\)
0.823468 + 0.567363i \(0.192036\pi\)
\(348\) 0 0
\(349\) 24.0000 1.28469 0.642345 0.766415i \(-0.277962\pi\)
0.642345 + 0.766415i \(0.277962\pi\)
\(350\) 0.928203 13.1962i 0.0496145 0.705364i
\(351\) 0 0
\(352\) −4.33013 2.50000i −0.230797 0.133250i
\(353\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(354\) 0 0
\(355\) 3.73205 2.46410i 0.198077 0.130781i
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) 11.0000i 0.581368i
\(359\) 14.0000 24.2487i 0.738892 1.27980i −0.214103 0.976811i \(-0.568683\pi\)
0.952995 0.302987i \(-0.0979839\pi\)
\(360\) 0 0
\(361\) −15.0000 25.9808i −0.789474 1.36741i
\(362\) 1.73205 + 1.00000i 0.0910346 + 0.0525588i
\(363\) 0 0
\(364\) −0.500000 + 2.59808i −0.0262071 + 0.136176i
\(365\) −4.00000 + 8.00000i −0.209370 + 0.418739i
\(366\) 0 0
\(367\) −32.0429 + 18.5000i −1.67263 + 0.965692i −0.706469 + 0.707744i \(0.749713\pi\)
−0.966159 + 0.257948i \(0.916954\pi\)
\(368\) 2.59808 1.50000i 0.135434 0.0781929i
\(369\) 0 0
\(370\) −10.0000 5.00000i −0.519875 0.259938i
\(371\) 0.500000 2.59808i 0.0259587 0.134885i
\(372\) 0 0
\(373\) 5.19615 + 3.00000i 0.269047 + 0.155334i 0.628454 0.777847i \(-0.283688\pi\)
−0.359408 + 0.933181i \(0.617021\pi\)
\(374\) 5.00000 + 8.66025i 0.258544 + 0.447811i
\(375\) 0 0
\(376\) −6.50000 + 11.2583i −0.335212 + 0.580604i
\(377\) 0 0
\(378\) 0 0
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) 13.0622 8.62436i 0.670076 0.442420i
\(381\) 0 0
\(382\) 13.8564 8.00000i 0.708955 0.409316i
\(383\) 7.79423 + 4.50000i 0.398266 + 0.229939i 0.685736 0.727851i \(-0.259481\pi\)
−0.287469 + 0.957790i \(0.592814\pi\)
\(384\) 0 0
\(385\) 27.3205 11.3397i 1.39238 0.577927i
\(386\) −18.0000 −0.916176
\(387\) 0 0
\(388\) −6.92820 + 4.00000i −0.351726 + 0.203069i
\(389\) −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) 0 0
\(391\) −6.00000 −0.303433
\(392\) −6.92820 + 1.00000i −0.349927 + 0.0505076i
\(393\) 0 0
\(394\) 13.5000 23.3827i 0.680120 1.17800i
\(395\) 1.87564 + 31.2487i 0.0943739 + 1.57229i
\(396\) 0 0
\(397\) 1.73205 + 1.00000i 0.0869291 + 0.0501886i 0.542834 0.839840i \(-0.317351\pi\)
−0.455905 + 0.890028i \(0.650684\pi\)
\(398\) 14.0000i 0.701757i
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) −13.5000 + 23.3827i −0.674158 + 1.16768i 0.302556 + 0.953131i \(0.402160\pi\)
−0.976714 + 0.214544i \(0.931173\pi\)
\(402\) 0 0
\(403\) 5.19615 3.00000i 0.258839 0.149441i
\(404\) −4.00000 + 6.92820i −0.199007 + 0.344691i
\(405\) 0 0
\(406\) 0 0
\(407\) 25.0000i 1.23920i
\(408\) 0 0
\(409\) 5.00000 + 8.66025i 0.247234 + 0.428222i 0.962757 0.270367i \(-0.0871450\pi\)
−0.715523 + 0.698589i \(0.753812\pi\)
\(410\) −20.0885 + 1.20577i −0.992098 + 0.0595488i
\(411\) 0 0
\(412\) 0 0
\(413\) 10.3923 + 2.00000i 0.511372 + 0.0984136i
\(414\) 0 0
\(415\) −12.3205 18.6603i −0.604790 0.915996i
\(416\) −0.500000 0.866025i −0.0245145 0.0424604i
\(417\) 0 0
\(418\) 30.3109 + 17.5000i 1.48255 + 0.855953i
\(419\) 3.00000 0.146560 0.0732798 0.997311i \(-0.476653\pi\)
0.0732798 + 0.997311i \(0.476653\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) −16.4545 9.50000i −0.800992 0.462453i
\(423\) 0 0
\(424\) 0.500000 + 0.866025i 0.0242821 + 0.0420579i
\(425\) −1.19615 9.92820i −0.0580219 0.481589i
\(426\) 0 0
\(427\) 1.73205 + 5.00000i 0.0838198 + 0.241967i
\(428\) 12.0000i 0.580042i
\(429\) 0 0
\(430\) 1.33975 + 22.3205i 0.0646083 + 1.07639i
\(431\) 9.00000 + 15.5885i 0.433515 + 0.750870i 0.997173 0.0751385i \(-0.0239399\pi\)
−0.563658 + 0.826008i \(0.690607\pi\)
\(432\) 0 0
\(433\) 4.00000i 0.192228i −0.995370 0.0961139i \(-0.969359\pi\)
0.995370 0.0961139i \(-0.0306413\pi\)
\(434\) 12.0000 + 10.3923i 0.576018 + 0.498847i
\(435\) 0 0
\(436\) 9.00000 15.5885i 0.431022 0.746552i
\(437\) −18.1865 + 10.5000i −0.869980 + 0.502283i
\(438\) 0 0
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) −5.00000 + 10.0000i −0.238366 + 0.476731i
\(441\) 0 0
\(442\) 2.00000i 0.0951303i
\(443\) 5.19615 + 3.00000i 0.246877 + 0.142534i 0.618333 0.785916i \(-0.287808\pi\)
−0.371457 + 0.928450i \(0.621142\pi\)
\(444\) 0 0
\(445\) 1.33975 + 22.3205i 0.0635100 + 1.05809i
\(446\) −8.00000 + 13.8564i −0.378811 + 0.656120i
\(447\) 0 0
\(448\) 1.73205 2.00000i 0.0818317 0.0944911i
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) 0 0
\(451\) −22.5000 38.9711i −1.05948 1.83508i
\(452\) −5.19615 + 3.00000i −0.244406 + 0.141108i
\(453\) 0 0
\(454\) 14.0000 0.657053
\(455\) 5.86603 + 0.767949i 0.275004 + 0.0360020i
\(456\) 0 0
\(457\) 32.9090 + 19.0000i 1.53942 + 0.888783i 0.998873 + 0.0474665i \(0.0151147\pi\)
0.540544 + 0.841316i \(0.318219\pi\)
\(458\) 3.46410 2.00000i 0.161867 0.0934539i
\(459\) 0 0
\(460\) −3.69615 5.59808i −0.172334 0.261012i
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) 15.0000i 0.697109i 0.937288 + 0.348555i \(0.113327\pi\)
−0.937288 + 0.348555i \(0.886673\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.73205 + 1.00000i 0.0801498 + 0.0462745i 0.539539 0.841960i \(-0.318598\pi\)
−0.459390 + 0.888235i \(0.651932\pi\)
\(468\) 0 0
\(469\) −3.00000 + 15.5885i −0.138527 + 0.719808i
\(470\) 26.0000 + 13.0000i 1.19929 + 0.599645i
\(471\) 0 0
\(472\) −3.46410 + 2.00000i −0.159448 + 0.0920575i
\(473\) −43.3013 + 25.0000i −1.99099 + 1.14950i
\(474\) 0 0
\(475\) −21.0000 28.0000i −0.963546 1.28473i
\(476\) −5.00000 + 1.73205i −0.229175 + 0.0793884i
\(477\) 0 0
\(478\) −17.3205 10.0000i −0.792222 0.457389i
\(479\) −4.00000 6.92820i −0.182765 0.316558i 0.760056 0.649857i \(-0.225171\pi\)
−0.942821 + 0.333300i \(0.891838\pi\)
\(480\) 0 0
\(481\) 2.50000 4.33013i 0.113990 0.197437i
\(482\) 1.00000i 0.0455488i
\(483\) 0 0
\(484\) −14.0000 −0.636364
\(485\) 9.85641 + 14.9282i 0.447556 + 0.677855i
\(486\) 0 0
\(487\) 20.7846 12.0000i 0.941841 0.543772i 0.0513038 0.998683i \(-0.483662\pi\)
0.890537 + 0.454911i \(0.150329\pi\)
\(488\) −1.73205 1.00000i −0.0784063 0.0452679i
\(489\) 0 0
\(490\) 3.16025 + 15.3301i 0.142766 + 0.692545i
\(491\) −24.0000 −1.08310 −0.541552 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 3.50000 + 6.06218i 0.157472 + 0.272750i
\(495\) 0 0
\(496\) −6.00000 −0.269408
\(497\) −3.46410 + 4.00000i −0.155386 + 0.179425i
\(498\) 0 0
\(499\) −14.0000 + 24.2487i −0.626726 + 1.08552i 0.361478 + 0.932381i \(0.382272\pi\)
−0.988204 + 0.153141i \(0.951061\pi\)
\(500\) 8.52628 7.23205i 0.381307 0.323427i
\(501\) 0 0
\(502\) −2.59808 1.50000i −0.115958 0.0669483i
\(503\) 24.0000i 1.07011i 0.844818 + 0.535054i \(0.179709\pi\)
−0.844818 + 0.535054i \(0.820291\pi\)
\(504\) 0 0
\(505\) 16.0000 + 8.00000i 0.711991 + 0.355995i
\(506\) 7.50000 12.9904i 0.333416 0.577493i
\(507\) 0 0
\(508\) −7.79423 + 4.50000i −0.345813 + 0.199655i
\(509\) −7.00000 + 12.1244i −0.310270 + 0.537403i −0.978421 0.206623i \(-0.933753\pi\)
0.668151 + 0.744026i \(0.267086\pi\)
\(510\) 0 0
\(511\) 2.00000 10.3923i 0.0884748 0.459728i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 5.00000 + 8.66025i 0.220541 + 0.381987i
\(515\) 0 0
\(516\) 0 0
\(517\) 65.0000i 2.85870i
\(518\) 12.9904 + 2.50000i 0.570765 + 0.109844i
\(519\) 0 0
\(520\) −1.86603 + 1.23205i −0.0818306 + 0.0540290i
\(521\) −7.50000 12.9904i −0.328581 0.569119i 0.653650 0.756797i \(-0.273237\pi\)
−0.982231 + 0.187678i \(0.939904\pi\)
\(522\) 0 0
\(523\) 10.3923 + 6.00000i 0.454424 + 0.262362i 0.709697 0.704507i \(-0.248832\pi\)
−0.255273 + 0.966869i \(0.582165\pi\)
\(524\) −17.0000 −0.742648
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) 10.3923 + 6.00000i 0.452696 + 0.261364i
\(528\) 0 0
\(529\) −7.00000 12.1244i −0.304348 0.527146i
\(530\) 1.86603 1.23205i 0.0810550 0.0535169i
\(531\) 0 0
\(532\) −12.1244 + 14.0000i −0.525657 + 0.606977i
\(533\) 9.00000i 0.389833i
\(534\) 0 0
\(535\) 26.7846 1.60770i 1.15800 0.0695067i
\(536\) −3.00000 5.19615i −0.129580 0.224440i
\(537\) 0 0
\(538\) 14.0000i 0.603583i
\(539\) −27.5000 + 21.6506i −1.18451 + 0.932559i
\(540\) 0 0
\(541\) −2.00000 + 3.46410i −0.0859867 + 0.148933i −0.905811 0.423681i \(-0.860738\pi\)
0.819825 + 0.572615i \(0.194071\pi\)
\(542\) 6.92820 4.00000i 0.297592 0.171815i
\(543\) 0 0
\(544\) 1.00000 1.73205i 0.0428746 0.0742611i
\(545\) −36.0000 18.0000i −1.54207 0.771035i
\(546\) 0 0
\(547\) 14.0000i 0.598597i −0.954160 0.299298i \(-0.903247\pi\)
0.954160 0.299298i \(-0.0967526\pi\)
\(548\) 3.46410 + 2.00000i 0.147979 + 0.0854358i
\(549\) 0 0
\(550\) 22.9904 + 9.82051i 0.980313 + 0.418748i
\(551\) 0 0
\(552\) 0 0
\(553\) −12.1244 35.0000i −0.515580 1.48835i
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) 4.00000 + 6.92820i 0.169638 + 0.293821i
\(557\) 33.7750 19.5000i 1.43109 0.826242i 0.433888 0.900967i \(-0.357141\pi\)
0.997204 + 0.0747252i \(0.0238080\pi\)
\(558\) 0 0
\(559\) −10.0000 −0.422955
\(560\) −4.69615 3.59808i −0.198449 0.152046i
\(561\) 0 0
\(562\) −9.52628 5.50000i −0.401842 0.232003i
\(563\) 25.9808 15.0000i 1.09496 0.632175i 0.160066 0.987106i \(-0.448829\pi\)
0.934892 + 0.354932i \(0.115496\pi\)
\(564\) 0 0
\(565\) 7.39230 + 11.1962i 0.310997 + 0.471026i
\(566\) 26.0000 1.09286
\(567\) 0 0
\(568\) 2.00000i 0.0839181i
\(569\) 1.50000 2.59808i 0.0628833 0.108917i −0.832870 0.553469i \(-0.813304\pi\)
0.895753 + 0.444552i \(0.146637\pi\)
\(570\) 0 0
\(571\) 4.00000 + 6.92820i 0.167395 + 0.289936i 0.937503 0.347977i \(-0.113131\pi\)
−0.770108 + 0.637913i \(0.779798\pi\)
\(572\) −4.33013 2.50000i −0.181052 0.104530i
\(573\) 0 0
\(574\) 22.5000 7.79423i 0.939132 0.325325i
\(575\) −12.0000 + 9.00000i −0.500435 + 0.375326i
\(576\) 0 0
\(577\) 20.7846 12.0000i 0.865275 0.499567i −0.000500448 1.00000i \(-0.500159\pi\)
0.865775 + 0.500433i \(0.166826\pi\)
\(578\) 11.2583 6.50000i 0.468285 0.270364i
\(579\) 0 0
\(580\) 0 0
\(581\) 20.0000 + 17.3205i 0.829740 + 0.718576i
\(582\) 0 0
\(583\) 4.33013 + 2.50000i 0.179336 + 0.103539i
\(584\) 2.00000 + 3.46410i 0.0827606 + 0.143346i
\(585\) 0 0
\(586\) 0.500000 0.866025i 0.0206548 0.0357752i
\(587\) 2.00000i 0.0825488i −0.999148 0.0412744i \(-0.986858\pi\)
0.999148 0.0412744i \(-0.0131418\pi\)
\(588\) 0 0
\(589\) 42.0000 1.73058
\(590\) 4.92820 + 7.46410i 0.202891 + 0.307292i
\(591\) 0 0
\(592\) −4.33013 + 2.50000i −0.177967 + 0.102749i
\(593\) 29.4449 + 17.0000i 1.20916 + 0.698106i 0.962575 0.271016i \(-0.0873596\pi\)
0.246581 + 0.969122i \(0.420693\pi\)
\(594\) 0 0
\(595\) 4.53590 + 10.9282i 0.185954 + 0.448013i
\(596\) 6.00000 0.245770
\(597\) 0 0
\(598\) 2.59808 1.50000i 0.106243 0.0613396i
\(599\) 14.0000 + 24.2487i 0.572024 + 0.990775i 0.996358 + 0.0852695i \(0.0271751\pi\)
−0.424333 + 0.905506i \(0.639492\pi\)
\(600\) 0 0
\(601\) −30.0000 −1.22373 −0.611863 0.790964i \(-0.709580\pi\)
−0.611863 + 0.790964i \(0.709580\pi\)
\(602\) −8.66025 25.0000i −0.352966 1.01892i
\(603\) 0 0
\(604\) −11.0000 + 19.0526i −0.447584 + 0.775238i
\(605\) 1.87564 + 31.2487i 0.0762558 + 1.27044i
\(606\) 0 0
\(607\) −11.2583 6.50000i −0.456962 0.263827i 0.253804 0.967256i \(-0.418318\pi\)
−0.710766 + 0.703429i \(0.751651\pi\)
\(608\) 7.00000i 0.283887i
\(609\) 0 0
\(610\) −2.00000 + 4.00000i −0.0809776 + 0.161955i
\(611\) −6.50000 + 11.2583i −0.262962 + 0.455463i
\(612\) 0 0
\(613\) −16.4545 + 9.50000i −0.664590 + 0.383701i −0.794024 0.607887i \(-0.792017\pi\)
0.129433 + 0.991588i \(0.458684\pi\)
\(614\) 1.00000 1.73205i 0.0403567 0.0698999i
\(615\) 0 0
\(616\) 2.50000 12.9904i 0.100728 0.523397i
\(617\) 30.0000i 1.20775i −0.797077 0.603877i \(-0.793622\pi\)
0.797077 0.603877i \(-0.206378\pi\)
\(618\) 0 0
\(619\) 7.50000 + 12.9904i 0.301450 + 0.522127i 0.976465 0.215677i \(-0.0691959\pi\)
−0.675014 + 0.737805i \(0.735863\pi\)
\(620\) 0.803848 + 13.3923i 0.0322833 + 0.537848i
\(621\) 0 0
\(622\) 26.0000i 1.04251i
\(623\) −8.66025 25.0000i −0.346966 1.00160i
\(624\) 0 0
\(625\) −17.2846 18.0622i −0.691384 0.722487i
\(626\) 5.00000 + 8.66025i 0.199840 + 0.346133i
\(627\) 0 0
\(628\) 11.2583 + 6.50000i 0.449256 + 0.259378i
\(629\) 10.0000 0.398726
\(630\) 0 0
\(631\) 18.0000 0.716569 0.358284 0.933613i \(-0.383362\pi\)
0.358284 + 0.933613i \(0.383362\pi\)
\(632\) 12.1244 + 7.00000i 0.482281 + 0.278445i
\(633\) 0 0
\(634\) −1.00000 1.73205i −0.0397151 0.0687885i
\(635\) 11.0885 + 16.7942i 0.440032 + 0.666459i
\(636\) 0 0
\(637\) −6.92820 + 1.00000i −0.274505 + 0.0396214i
\(638\) 0 0
\(639\) 0 0
\(640\) 2.23205 0.133975i 0.0882296 0.00529581i
\(641\) −16.5000 28.5788i −0.651711 1.12880i −0.982708 0.185164i \(-0.940718\pi\)
0.330997 0.943632i \(-0.392615\pi\)
\(642\) 0 0
\(643\) 38.0000i 1.49857i −0.662246 0.749287i \(-0.730396\pi\)
0.662246 0.749287i \(-0.269604\pi\)
\(644\) 6.00000 + 5.19615i 0.236433 + 0.204757i
\(645\) 0 0
\(646\) −7.00000 + 12.1244i −0.275411 + 0.477026i
\(647\) 0.866025 0.500000i 0.0340470 0.0196570i −0.482880 0.875687i \(-0.660409\pi\)
0.516927 + 0.856030i \(0.327076\pi\)
\(648\) 0 0
\(649\) −10.0000 + 17.3205i −0.392534 + 0.679889i
\(650\) 3.00000 + 4.00000i 0.117670 + 0.156893i
\(651\) 0 0
\(652\) 12.0000i 0.469956i
\(653\) −4.33013 2.50000i −0.169451 0.0978326i 0.412876 0.910787i \(-0.364524\pi\)
−0.582327 + 0.812955i \(0.697858\pi\)
\(654\) 0 0
\(655\) 2.27757 + 37.9449i 0.0889920 + 1.48263i
\(656\) −4.50000 + 7.79423i −0.175695 + 0.304314i
\(657\) 0 0
\(658\) −33.7750 6.50000i −1.31669 0.253396i
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) −20.0000 34.6410i −0.777910 1.34738i −0.933144 0.359502i \(-0.882947\pi\)
0.155235 0.987878i \(-0.450387\pi\)
\(662\) −12.9904 + 7.50000i −0.504885 + 0.291496i
\(663\) 0 0
\(664\) −10.0000 −0.388075
\(665\) 32.8731 + 25.1865i 1.27476 + 0.976692i
\(666\) 0 0
\(667\) 0 0
\(668\) −16.4545 + 9.50000i −0.636643 + 0.367566i
\(669\) 0 0
\(670\) −11.1962 + 7.39230i −0.432545 + 0.285590i
\(671\) −10.0000 −0.386046
\(672\) 0 0
\(673\) 36.0000i 1.38770i −0.720121 0.693849i \(-0.755914\pi\)
0.720121 0.693849i \(-0.244086\pi\)
\(674\) −7.00000 + 12.1244i −0.269630 + 0.467013i
\(675\) 0 0
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) 28.5788 + 16.5000i 1.09837 + 0.634147i 0.935793 0.352549i \(-0.114685\pi\)
0.162581 + 0.986695i \(0.448018\pi\)
\(678\) 0 0
\(679\) −16.0000 13.8564i −0.614024 0.531760i
\(680\) −4.00000 2.00000i −0.153393 0.0766965i
\(681\) 0 0
\(682\) −25.9808 + 15.0000i −0.994855 + 0.574380i
\(683\) −3.46410 + 2.00000i −0.132550 + 0.0765279i −0.564809 0.825222i \(-0.691050\pi\)
0.432259 + 0.901750i \(0.357717\pi\)
\(684\) 0 0
\(685\) 4.00000 8.00000i 0.152832 0.305664i
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) 0 0
\(688\) 8.66025 + 5.00000i 0.330169 + 0.190623i
\(689\) 0.500000 + 0.866025i 0.0190485 + 0.0329929i
\(690\) 0 0
\(691\) 10.0000 17.3205i 0.380418 0.658903i −0.610704 0.791859i \(-0.709113\pi\)
0.991122 + 0.132956i \(0.0424468\pi\)
\(692\) 7.00000i 0.266100i
\(693\) 0 0
\(694\) −16.0000 −0.607352
\(695\) 14.9282 9.85641i 0.566259 0.373875i
\(696\) 0 0
\(697\) 15.5885 9.00000i 0.590455 0.340899i
\(698\) −20.7846 12.0000i −0.786709 0.454207i
\(699\) 0 0
\(700\) −7.40192 + 10.9641i −0.279766 + 0.414404i
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) 30.3109 17.5000i 1.14320 0.660025i
\(704\) 2.50000 + 4.33013i 0.0942223 + 0.163198i
\(705\) 0 0
\(706\) 0 0
\(707\) −20.7846 4.00000i −0.781686 0.150435i
\(708\) 0 0
\(709\) 8.00000 13.8564i 0.300446 0.520388i −0.675791 0.737093i \(-0.736198\pi\)
0.976237 + 0.216705i \(0.0695310\pi\)
\(710\) −4.46410 + 0.267949i −0.167535 + 0.0100560i
\(711\) 0 0
\(712\) 8.66025 + 5.00000i 0.324557 + 0.187383i
\(713\) 18.0000i 0.674105i
\(714\) 0 0
\(715\) −5.00000 + 10.0000i −0.186989 + 0.373979i
\(716\) −5.50000 + 9.52628i −0.205545 + 0.356014i
\(717\) 0 0
\(718\) −24.2487 + 14.0000i −0.904954 + 0.522475i
\(719\) 1.00000 1.73205i 0.0372937 0.0645946i −0.846776 0.531949i \(-0.821460\pi\)
0.884070 + 0.467355i \(0.154793\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 30.0000i 1.11648i
\(723\) 0 0
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) 0 0
\(726\) 0 0
\(727\) 53.0000i 1.96566i 0.184510 + 0.982831i \(0.440930\pi\)
−0.184510 + 0.982831i \(0.559070\pi\)
\(728\) 1.73205 2.00000i 0.0641941 0.0741249i
\(729\) 0 0
\(730\) 7.46410 4.92820i 0.276259 0.182401i
\(731\) −10.0000 17.3205i −0.369863 0.640622i
\(732\) 0 0
\(733\) −18.1865 10.5000i −0.671735 0.387826i 0.124999 0.992157i \(-0.460107\pi\)
−0.796734 + 0.604331i \(0.793441\pi\)
\(734\) 37.0000 1.36569
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) −25.9808 15.0000i −0.957014 0.552532i
\(738\) 0 0
\(739\) 23.5000 + 40.7032i 0.864461 + 1.49729i 0.867581 + 0.497296i \(0.165674\pi\)
−0.00311943 + 0.999995i \(0.500993\pi\)
\(740\) 6.16025 + 9.33013i 0.226455 + 0.342982i
\(741\) 0 0
\(742\) −1.73205 + 2.00000i −0.0635856 + 0.0734223i
\(743\) 31.0000i 1.13728i −0.822587 0.568640i \(-0.807470\pi\)
0.822587 0.568640i \(-0.192530\pi\)
\(744\) 0 0
\(745\) −0.803848 13.3923i −0.0294507 0.490656i
\(746\) −3.00000 5.19615i −0.109838 0.190245i
\(747\) 0 0
\(748\) 10.0000i 0.365636i
\(749\) −30.0000 + 10.3923i −1.09618 + 0.379727i
\(750\) 0 0
\(751\) −2.00000 + 3.46410i −0.0729810 + 0.126407i −0.900207 0.435463i \(-0.856585\pi\)
0.827225 + 0.561870i \(0.189918\pi\)
\(752\) 11.2583 6.50000i 0.410549 0.237031i
\(753\) 0 0
\(754\) 0 0
\(755\) 44.0000 + 22.0000i 1.60132 + 0.800662i
\(756\) 0 0
\(757\) 26.0000i 0.944986i −0.881334 0.472493i \(-0.843354\pi\)
0.881334 0.472493i \(-0.156646\pi\)
\(758\) −0.866025 0.500000i −0.0314555 0.0181608i
\(759\) 0 0
\(760\) −15.6244 + 0.937822i −0.566755 + 0.0340184i
\(761\) −1.50000 + 2.59808i −0.0543750 + 0.0941802i −0.891932 0.452170i \(-0.850650\pi\)
0.837557 + 0.546350i \(0.183983\pi\)
\(762\) 0 0
\(763\) 46.7654 + 9.00000i 1.69302 + 0.325822i
\(764\) −16.0000 −0.578860
\(765\) 0 0
\(766\) −4.50000 7.79423i −0.162592 0.281617i
\(767\) −3.46410 + 2.00000i −0.125081 + 0.0722158i
\(768\) 0 0
\(769\) −51.0000 −1.83911 −0.919554 0.392965i \(-0.871449\pi\)
−0.919554 + 0.392965i \(0.871449\pi\)
\(770\) −29.3301 3.83975i −1.05698 0.138375i
\(771\) 0 0
\(772\) 15.5885 + 9.00000i 0.561041 + 0.323917i
\(773\) −32.0429 + 18.5000i −1.15250 + 0.665399i −0.949496 0.313778i \(-0.898405\pi\)
−0.203008 + 0.979177i \(0.565072\pi\)
\(774\) 0 0
\(775\) 29.7846 3.58846i 1.06989 0.128901i
\(776\) 8.00000 0.287183
\(777\) 0 0
\(778\) 6.00000i 0.215110i
\(779\) 31.5000 54.5596i 1.12860 1.95480i
\(780\) 0 0
\(781\) −5.00000 8.66025i −0.178914 0.309888i
\(782\) 5.19615 + 3.00000i 0.185814 + 0.107280i
\(783\) 0 0
\(784\) 6.50000 + 2.59808i 0.232143 + 0.0927884i
\(785\) 13.0000 26.0000i 0.463990 0.927980i
\(786\) 0 0
\(787\) 32.9090 19.0000i 1.17308 0.677277i 0.218675 0.975798i \(-0.429827\pi\)
0.954403 + 0.298521i \(0.0964933\pi\)
\(788\) −23.3827 + 13.5000i −0.832974 + 0.480918i
\(789\) 0 0
\(790\) 14.0000 28.0000i 0.498098 0.996195i
\(791\) −12.0000 10.3923i −0.426671 0.369508i
\(792\) 0 0
\(793\) −1.73205 1.00000i −0.0615069 0.0355110i
\(794\) −1.00000 1.73205i −0.0354887 0.0614682i
\(795\) 0 0
\(796\) 7.00000 12.1244i 0.248108 0.429736i
\(797\) 30.0000i 1.06265i 0.847167 + 0.531327i \(0.178307\pi\)
−0.847167 + 0.531327i