Properties

Label 630.2.u.c.289.2
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 289.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 630.289
Dual form 630.2.u.c.109.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.133975 - 2.23205i) q^{5} +(1.73205 - 2.00000i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.133975 - 2.23205i) q^{5} +(1.73205 - 2.00000i) q^{7} +1.00000i q^{8} +(1.23205 - 1.86603i) q^{10} +(-2.50000 - 4.33013i) q^{11} +1.00000i q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{17} +(3.50000 - 6.06218i) q^{19} +(2.00000 - 1.00000i) q^{20} -5.00000i q^{22} +(2.59808 + 1.50000i) q^{23} +(-4.96410 - 0.598076i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(2.59808 + 0.500000i) q^{28} +(3.00000 + 5.19615i) q^{31} +(-0.866025 + 0.500000i) q^{32} -2.00000 q^{34} +(-4.23205 - 4.13397i) q^{35} +(-4.33013 - 2.50000i) q^{37} +(6.06218 - 3.50000i) q^{38} +(2.23205 + 0.133975i) q^{40} +9.00000 q^{41} +10.0000i q^{43} +(2.50000 - 4.33013i) q^{44} +(1.50000 + 2.59808i) q^{46} +(11.2583 + 6.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-4.00000 - 3.00000i) q^{50} +(-0.866025 + 0.500000i) q^{52} +(0.866025 - 0.500000i) q^{53} +(-10.0000 + 5.00000i) q^{55} +(2.00000 + 1.73205i) q^{56} +(-2.00000 - 3.46410i) q^{59} +(1.00000 - 1.73205i) q^{61} +6.00000i q^{62} -1.00000 q^{64} +(2.23205 + 0.133975i) q^{65} +(-5.19615 + 3.00000i) q^{67} +(-1.73205 - 1.00000i) q^{68} +(-1.59808 - 5.69615i) q^{70} +2.00000 q^{71} +(3.46410 - 2.00000i) q^{73} +(-2.50000 - 4.33013i) q^{74} +7.00000 q^{76} +(-12.9904 - 2.50000i) q^{77} +(-7.00000 + 12.1244i) q^{79} +(1.86603 + 1.23205i) q^{80} +(7.79423 + 4.50000i) q^{82} +10.0000i q^{83} +(2.00000 + 4.00000i) q^{85} +(-5.00000 + 8.66025i) q^{86} +(4.33013 - 2.50000i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(2.00000 + 1.73205i) q^{91} +3.00000i q^{92} +(6.50000 + 11.2583i) q^{94} +(-13.0622 - 8.62436i) q^{95} -8.00000i q^{97} +(2.59808 - 6.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + 4q^{5} + O(q^{10}) \) \( 4q + 2q^{4} + 4q^{5} - 2q^{10} - 10q^{11} + 10q^{14} - 2q^{16} + 14q^{19} + 8q^{20} - 6q^{25} - 2q^{26} + 12q^{31} - 8q^{34} - 10q^{35} + 2q^{40} + 36q^{41} + 10q^{44} + 6q^{46} - 4q^{49} - 16q^{50} - 40q^{55} + 8q^{56} - 8q^{59} + 4q^{61} - 4q^{64} + 2q^{65} + 4q^{70} + 8q^{71} - 10q^{74} + 28q^{76} - 28q^{79} + 4q^{80} + 8q^{85} - 20q^{86} - 20q^{89} + 8q^{91} + 26q^{94} - 28q^{95} + O(q^{100}) \)

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
\(5\) 0.133975 2.23205i 0.0599153 0.998203i
\(6\) 0 0
\(7\) 1.73205 2.00000i 0.654654 0.755929i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.23205 1.86603i 0.389609 0.590089i
\(11\) −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 \(0.0442844\pi\)
−0.990338 + 0.138675i \(0.955716\pi\)
\(14\) 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 −0.695113 0.718900i \(-0.744646\pi\)
0.275029 + 0.961436i \(0.411312\pi\)
\(18\) 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 0.745782 0.666190i \(-0.232076\pi\)
−0.204046 + 0.978961i \(0.565409\pi\)
\(24\) 0 0
\(25\) −4.96410 0.598076i −0.992820 0.119615i
\(26\) −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
\(35\) −4.23205 4.13397i −0.715347 0.698769i
\(36\) 0 0
\(37\) −4.33013 2.50000i −0.711868 0.410997i 0.0998840 0.994999i \(-0.468153\pi\)
−0.811752 + 0.584002i \(0.801486\pi\)
\(38\) 6.06218 3.50000i 0.983415 0.567775i
\(39\) 0 0
\(40\) 2.23205 + 0.133975i 0.352918 + 0.0211832i
\(41\) 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 \(0.276025\pi\)
−0.646997 + 0.762493i \(0.723975\pi\)
\(44\) 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 \(0.0636872\pi\)
0.662145 + 0.749375i \(0.269646\pi\)
\(48\) 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 −0.439340 0.898321i \(-0.644788\pi\)
0.558298 + 0.829640i \(0.311454\pi\)
\(54\) 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
\(65\) 2.23205 + 0.133975i 0.276852 + 0.0166175i
\(66\) 0 0
\(67\) −5.19615 + 3.00000i −0.634811 + 0.366508i −0.782613 0.622509i \(-0.786114\pi\)
0.147802 + 0.989017i \(0.452780\pi\)
\(68\) −1.73205 1.00000i −0.210042 0.121268i
\(69\) 0 0
\(70\) −1.59808 5.69615i −0.191007 0.680820i
\(71\) 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 −0.283387 0.959006i \(-0.591458\pi\)
0.688830 + 0.724923i \(0.258125\pi\)
\(74\) −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 \(0.878010\pi\)
\(80\) 1.86603 + 1.23205i 0.208628 + 0.137747i
\(81\) 0 0
\(82\) 7.79423 + 4.50000i 0.860729 + 0.496942i
\(83\) 10.0000i 1.09764i 0.835940 + 0.548821i \(0.184923\pi\)
−0.835940 + 0.548821i \(0.815077\pi\)
\(84\) 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
\(95\) −13.0622 8.62436i −1.34015 0.884840i
\(96\) 0 0
\(97\) 8.00000i 0.812277i −0.913812 0.406138i \(-0.866875\pi\)
0.913812 0.406138i \(-0.133125\pi\)
\(98\) 2.59808 6.50000i 0.262445 0.656599i
\(99\) 0 0
\(100\) −1.96410 4.59808i −0.196410 0.459808i
\(101\) 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 −0.0950377 0.995474i \(-0.530297\pi\)
−0.909624 + 0.415432i \(0.863630\pi\)
\(108\) 0 0
\(109\) −9.00000 15.5885i −0.862044 1.49310i −0.869953 0.493135i \(-0.835851\pi\)
0.00790932 0.999969i \(-0.497482\pi\)
\(110\) −11.1603 0.669873i −1.06409 0.0638699i
\(111\) 0 0
\(112\) 0.866025 + 2.50000i 0.0818317 + 0.236228i
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 0 0
\(115\) 3.69615 5.59808i 0.344668 0.522023i
\(116\) 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 \(-0.869250\pi\)
0.916816 0.399310i \(-0.130750\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) 1.86603 + 1.23205i 0.163661 + 0.108058i
\(131\) −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 −0.640626 0.767853i \(-0.721325\pi\)
0.344668 + 0.938725i \(0.387992\pi\)
\(138\) 0 0
\(139\) 8.00000 0.678551 0.339276 0.940687i \(-0.389818\pi\)
0.339276 + 0.940687i \(0.389818\pi\)
\(140\) 1.46410 5.73205i 0.123739 0.484447i
\(141\) 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 −0.876717 0.481006i \(-0.840272\pi\)
−0.0217953 + 0.999762i \(0.506938\pi\)
\(158\) −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 0.848339 0.529454i \(-0.177603\pi\)
−0.0343508 + 0.999410i \(0.510936\pi\)
\(164\) 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 \(-0.737120\pi\)
0.677924 0.735132i \(-0.262880\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) −0.267949 + 4.46410i −0.0205508 + 0.342381i
\(171\) 0 0
\(172\) −8.66025 + 5.00000i −0.660338 + 0.381246i
\(173\) 6.06218 + 3.50000i 0.460899 + 0.266100i 0.712422 0.701751i \(-0.247598\pi\)
−0.251523 + 0.967851i \(0.580932\pi\)
\(174\) 0 0
\(175\) −9.79423 + 8.89230i −0.740374 + 0.672195i
\(176\) 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
\(185\) −6.16025 + 9.33013i −0.452911 + 0.685965i
\(186\) 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 −0.941932 0.335805i \(-0.890992\pi\)
−0.180150 + 0.983639i \(0.557658\pi\)
\(194\) 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 \(-0.588224\pi\)
0.273629 0.961835i \(-0.411776\pi\)
\(198\) 0 0
\(199\) −7.00000 12.1244i −0.496217 0.859473i 0.503774 0.863836i \(-0.331945\pi\)
−0.999990 + 0.00436292i \(0.998611\pi\)
\(200\) 0.598076 4.96410i 0.0422904 0.351015i
\(201\) 0 0
\(202\) 8.00000i 0.562878i
\(203\) 0 0
\(204\) 0 0
\(205\) 1.20577 20.0885i 0.0842147 1.40304i
\(206\) 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
\(215\) 22.3205 + 1.33975i 1.52225 + 0.0913699i
\(216\) 0 0
\(217\) 15.5885 + 3.00000i 1.05821 + 0.203653i
\(218\) 18.0000i 1.21911i
\(219\) 0 0
\(220\) −9.33013 6.16025i −0.629037 0.415324i
\(221\) −1.00000 1.73205i −0.0672673 0.116510i
\(222\) 0 0
\(223\) 16.0000i 1.07144i 0.844396 + 0.535720i \(0.179960\pi\)
−0.844396 + 0.535720i \(0.820040\pi\)
\(224\) −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 −0.0403978 0.999184i \(-0.512863\pi\)
0.845120 + 0.534577i \(0.179529\pi\)
\(228\) 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
\(235\) 16.0167 24.2583i 1.04481 1.58244i
\(236\) 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
\(245\) −15.5981 + 1.30385i −0.996525 + 0.0832998i
\(246\) 0 0
\(247\) 6.06218 + 3.50000i 0.385727 + 0.222700i
\(248\) −5.19615 + 3.00000i −0.329956 + 0.190500i
\(249\) 0 0
\(250\) −7.23205 + 8.52628i −0.457395 + 0.539249i
\(251\) 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 0.745165 0.666880i \(-0.232371\pi\)
−0.204953 + 0.978772i \(0.565704\pi\)
\(258\) 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 −0.977147 0.212565i \(-0.931818\pi\)
−0.304487 + 0.952517i \(0.598485\pi\)
\(264\) 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
\(275\) 9.82051 + 22.9904i 0.592199 + 1.38637i
\(276\) 0 0
\(277\) −1.73205 + 1.00000i −0.104069 + 0.0600842i −0.551131 0.834419i \(-0.685804\pi\)
0.447062 + 0.894503i \(0.352470\pi\)
\(278\) 6.92820 + 4.00000i 0.415526 + 0.239904i
\(279\) 0 0
\(280\) 4.13397 4.23205i 0.247052 0.252913i
\(281\) 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 0.351895 0.936039i \(-0.385537\pi\)
0.986581 + 0.163270i \(0.0522041\pi\)
\(284\) 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 \(-0.990701\pi\)
0.999573 0.0292103i \(-0.00929925\pi\)
\(294\) 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
\(305\) −3.73205 2.46410i −0.213697 0.141094i
\(306\) 0 0
\(307\) 2.00000i 0.114146i −0.998370 0.0570730i \(-0.981823\pi\)
0.998370 0.0570730i \(-0.0181768\pi\)
\(308\) −4.33013 12.5000i −0.246732 0.712254i
\(309\) 0 0
\(310\) 13.3923 + 0.803848i 0.760632 + 0.0456555i
\(311\) −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 0.724370 0.689412i \(-0.242131\pi\)
−0.234863 + 0.972028i \(0.575464\pi\)
\(314\) −13.0000 −0.733632
\(315\) 0 0
\(316\) −14.0000 −0.787562
\(317\) −1.73205 1.00000i −0.0972817 0.0561656i 0.450570 0.892741i \(-0.351221\pi\)
−0.547852 + 0.836576i \(0.684554\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.133975 + 2.23205i −0.00748941 + 0.124775i
\(321\) 0 0
\(322\) 7.79423 + 1.50000i 0.434355 + 0.0835917i
\(323\) 14.0000i 0.778981i
\(324\) 0 0
\(325\) 0.598076 4.96410i 0.0331753 0.275359i
\(326\) 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 \(0.124528\pi\)
−0.924445 + 0.381314i \(0.875472\pi\)
\(338\) 10.3923 + 6.00000i 0.565267 + 0.326357i
\(339\) 0 0
\(340\) −2.46410 + 3.73205i −0.133635 + 0.202399i
\(341\) 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 −0.823468 0.567363i \(-0.807964\pi\)
0.0796169 + 0.996826i \(0.474630\pi\)
\(348\) 0 0
\(349\) 24.0000 1.28469 0.642345 0.766415i \(-0.277962\pi\)
0.642345 + 0.766415i \(0.277962\pi\)
\(350\) −12.9282 + 2.80385i −0.691042 + 0.149872i
\(351\) 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
\(355\) 0.267949 4.46410i 0.0142213 0.236930i
\(356\) −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 \(-0.250287\pi\)
0.966159 0.257948i \(-0.0830464\pi\)
\(368\) −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 0.359408 0.933181i \(-0.382979\pi\)
−0.628454 + 0.777847i \(0.716312\pi\)
\(374\) 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 \(0.491824\pi\)
\(380\) 0.937822 15.6244i 0.0481093 0.801513i
\(381\) 0 0
\(382\) −13.8564 + 8.00000i −0.708955 + 0.409316i
\(383\) −7.79423 4.50000i −0.398266 0.229939i 0.287469 0.957790i \(-0.407186\pi\)
−0.685736 + 0.727851i \(0.740519\pi\)
\(384\) 0 0
\(385\) −7.32051 + 28.6603i −0.373088 + 1.46066i
\(386\) −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
\(395\) 26.1244 + 17.2487i 1.31446 + 0.867877i
\(396\) 0 0
\(397\) −1.73205 1.00000i −0.0869291 0.0501886i 0.455905 0.890028i \(-0.349316\pi\)
−0.542834 + 0.839840i \(0.682649\pi\)
\(398\) 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 \(0.753812\pi\)
\(410\) 11.0885 16.7942i 0.547620 0.829408i
\(411\) 0 0
\(412\) 0 0
\(413\) −10.3923 2.00000i −0.511372 0.0984136i
\(414\) 0 0
\(415\) 22.3205 + 1.33975i 1.09567 + 0.0657655i
\(416\) −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
\(425\) 9.19615 3.92820i 0.446079 0.190546i
\(426\) 0 0
\(427\) −1.73205 5.00000i −0.0838198 0.241967i
\(428\) 12.0000i 0.580042i
\(429\) 0 0
\(430\) 18.6603 + 12.3205i 0.899877 + 0.594148i
\(431\) 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 \(0.0306413\pi\)
−0.995370 + 0.0961139i \(0.969359\pi\)
\(434\) 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 0.371457 0.928450i \(-0.378858\pi\)
−0.618333 + 0.785916i \(0.712192\pi\)
\(444\) 0 0
\(445\) 18.6603 + 12.3205i 0.884581 + 0.584048i
\(446\) −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
\(455\) 4.13397 4.23205i 0.193804 0.198402i
\(456\) 0 0
\(457\) −32.9090 19.0000i −1.53942 0.888783i −0.998873 0.0474665i \(-0.984885\pi\)
−0.540544 0.841316i \(-0.681781\pi\)
\(458\) −3.46410 + 2.00000i −0.161867 + 0.0934539i
\(459\) 0 0
\(460\) 6.69615 + 0.401924i 0.312210 + 0.0187398i
\(461\) 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 \(-0.886673\pi\)
0.937288 0.348555i \(-0.113327\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.73205 1.00000i −0.0801498 0.0462745i 0.459390 0.888235i \(-0.348068\pi\)
−0.539539 + 0.841960i \(0.681402\pi\)
\(468\) 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
\(485\) −17.8564 1.07180i −0.810818 0.0486678i
\(486\) 0 0
\(487\) −20.7846 + 12.0000i −0.941841 + 0.543772i −0.890537 0.454911i \(-0.849671\pi\)
−0.0513038 + 0.998683i \(0.516338\pi\)
\(488\) 1.73205 + 1.00000i 0.0784063 + 0.0452679i
\(489\) 0 0
\(490\) −14.1603 6.66987i −0.639695 0.301314i
\(491\) −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 \(0.951061\pi\)
\(500\) −10.5263 + 3.76795i −0.470750 + 0.168508i
\(501\) 0 0
\(502\) 2.59808 + 1.50000i 0.115958 + 0.0669483i
\(503\) 24.0000i 1.07011i −0.844818 0.535054i \(-0.820291\pi\)
0.844818 0.535054i \(-0.179709\pi\)
\(504\) 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
\(520\) −0.133975 + 2.23205i −0.00587517 + 0.0978819i
\(521\) −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 0.255273 0.966869i \(-0.417835\pi\)
−0.709697 + 0.704507i \(0.751168\pi\)
\(524\) −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
\(530\) 0.133975 2.23205i 0.00581948 0.0969541i
\(531\) 0 0
\(532\) 12.1244 14.0000i 0.525657 0.606977i
\(533\) 9.00000i 0.389833i
\(534\) 0 0
\(535\) −14.7846 + 22.3923i −0.639194 + 0.968104i
\(536\) −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 \(0.0967526\pi\)
−0.954160 + 0.299298i \(0.903247\pi\)
\(548\) −3.46410 2.00000i −0.147979 0.0854358i
\(549\) 0 0
\(550\) −2.99038 + 24.8205i −0.127510 + 1.05835i
\(551\) 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 −0.997204 0.0747252i \(-0.976192\pi\)
−0.433888 + 0.900967i \(0.642859\pi\)
\(558\) 0 0
\(559\) −10.0000 −0.422955
\(560\) 5.69615 1.59808i 0.240706 0.0675310i
\(561\) 0 0
\(562\) 9.52628 + 5.50000i 0.401842 + 0.232003i
\(563\) −25.9808 + 15.0000i −1.09496 + 0.632175i −0.934892 0.354932i \(-0.884504\pi\)
−0.160066 + 0.987106i \(0.551171\pi\)
\(564\) 0 0
\(565\) −13.3923 0.803848i −0.563418 0.0338181i
\(566\) 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 −0.865775 0.500433i \(-0.833174\pi\)
0.000500448 1.00000i \(0.499841\pi\)
\(578\) −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 \(0.0131418\pi\)
−0.999148 + 0.0412744i \(0.986858\pi\)
\(588\) 0 0
\(589\) 42.0000 1.73058
\(590\) −8.92820 0.535898i −0.367568 0.0220626i
\(591\) 0 0
\(592\) 4.33013 2.50000i 0.177967 0.102749i
\(593\) −29.4449 17.0000i −1.20916 0.698106i −0.246581 0.969122i \(-0.579307\pi\)
−0.962575 + 0.271016i \(0.912640\pi\)
\(594\) 0 0
\(595\) 11.4641 + 2.92820i 0.469982 + 0.120045i
\(596\) 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
\(605\) 26.1244 + 17.2487i 1.06211 + 0.701260i
\(606\) 0 0
\(607\) 11.2583 + 6.50000i 0.456962 + 0.263827i 0.710766 0.703429i \(-0.248349\pi\)
−0.253804 + 0.967256i \(0.581682\pi\)
\(608\) 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 −0.129433 0.991588i \(-0.541316\pi\)
0.794024 + 0.607887i \(0.207983\pi\)
\(614\) 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 \(0.206378\pi\)
−0.797077 + 0.603877i \(0.793622\pi\)
\(618\) 0 0
\(619\) 7.50000 + 12.9904i 0.301450 + 0.522127i 0.976465 0.215677i \(-0.0691959\pi\)
−0.675014 + 0.737805i \(0.735863\pi\)
\(620\) 11.1962 + 7.39230i 0.449648 + 0.296882i
\(621\) 0 0
\(622\) 26.0000i 1.04251i
\(623\) 8.66025 + 25.0000i 0.346966 + 1.00160i
\(624\) 0 0
\(625\) 24.2846 + 5.93782i 0.971384 + 0.237513i
\(626\) 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
\(635\) −20.0885 1.20577i −0.797186 0.0478496i
\(636\) 0 0
\(637\) 6.92820 1.00000i 0.274505 0.0396214i
\(638\) 0 0
\(639\) 0 0
\(640\) −1.23205 + 1.86603i −0.0487011 + 0.0737611i
\(641\) −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 \(0.269604\pi\)
−0.662246 + 0.749287i \(0.730396\pi\)
\(644\) 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 −0.516927 0.856030i \(-0.672924\pi\)
0.482880 + 0.875687i \(0.339591\pi\)
\(648\) 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 0.582327 0.812955i \(-0.302142\pi\)
−0.412876 + 0.910787i \(0.635476\pi\)
\(654\) 0 0
\(655\) 31.7224 + 20.9449i 1.23950 + 0.818384i
\(656\) −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
\(665\) −39.8731 + 11.1865i −1.54621 + 0.433795i
\(666\) 0 0
\(667\) 0 0
\(668\) 16.4545 9.50000i 0.636643 0.367566i
\(669\) 0 0
\(670\) −0.803848 + 13.3923i −0.0310553 + 0.517390i
\(671\) −10.0000 −0.386046
\(672\) 0 0
\(673\) 36.0000i 1.38770i 0.720121 + 0.693849i \(0.244086\pi\)
−0.720121 + 0.693849i \(0.755914\pi\)
\(674\) −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 −0.162581 0.986695i \(-0.551982\pi\)
−0.935793 + 0.352549i \(0.885315\pi\)
\(678\) 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 −0.432259 0.901750i \(-0.642283\pi\)
0.564809 + 0.825222i \(0.308950\pi\)
\(684\) 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
\(695\) 1.07180 17.8564i 0.0406556 0.677332i
\(696\) 0 0
\(697\) −15.5885 + 9.00000i −0.590455 + 0.340899i
\(698\) 20.7846 + 12.0000i 0.786709 + 0.454207i
\(699\) 0 0
\(700\) −12.5981 4.03590i −0.476163 0.152543i
\(701\) −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 \(0.0695310\pi\)
\(710\) 2.46410 3.73205i 0.0924761 0.140061i
\(711\) 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 \(-0.559070\pi\)
0.184510 0.982831i \(-0.440930\pi\)
\(728\) −1.73205 + 2.00000i −0.0641941 + 0.0741249i
\(729\) 0 0
\(730\) 0.535898 8.92820i 0.0198345 0.330448i
\(731\) −10.0000 17.3205i −0.369863 0.640622i
\(732\) 0 0
\(733\) 18.1865 + 10.5000i 0.671735 + 0.387826i 0.796734 0.604331i \(-0.206559\pi\)
−0.124999 + 0.992157i \(0.539893\pi\)
\(734\) 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 \(0.500993\pi\)
\(740\) −11.1603 0.669873i −0.410259 0.0246250i
\(741\) 0 0
\(742\) 1.73205 2.00000i 0.0635856 0.0734223i
\(743\) 31.0000i 1.13728i 0.822587 + 0.568640i \(0.192530\pi\)
−0.822587 + 0.568640i \(0.807470\pi\)
\(744\) 0 0
\(745\) −11.1962 7.39230i −0.410195 0.270833i
\(746\) −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 \(0.156646\pi\)
−0.881334 + 0.472493i \(0.843354\pi\)
\(758\) 0.866025 + 0.500000i 0.0314555 + 0.0181608i
\(759\) 0 0
\(760\) 8.62436 13.0622i 0.312838 0.473815i
\(761\) −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 \(0.871449\pi\)
\(770\) −20.6699 + 21.1603i −0.744891 + 0.762563i
\(771\) 0 0
\(772\) −15.5885 9.00000i −0.561041 0.323917i
\(773\) 32.0429 18.5000i 1.15250 0.665399i 0.203008 0.979177i \(-0.434928\pi\)
0.949496 + 0.313778i \(0.101595\pi\)
\(774\) 0 0
\(775\) −11.7846 27.5885i −0.423316 0.991007i
\(776\) 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 −0.954403 0.298521i \(-0.903507\pi\)
−0.218675 + 0.975798i \(0.570173\pi\)
\(788\) 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 \(-0.821693\pi\)
0.847167 0.531327i \(-0.178307\pi\)