Properties

Label 630.2.k.h.361.1
Level $630$
Weight $2$
Character 630.361
Analytic conductor $5.031$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 630.361
Dual form 630.2.k.h.541.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} +7.00000 q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{19} -1.00000 q^{20} -1.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(3.50000 + 6.06218i) q^{26} +(0.500000 + 2.59808i) q^{28} +8.00000 q^{29} +(-3.00000 + 5.19615i) q^{31} +(0.500000 - 0.866025i) q^{32} -4.00000 q^{34} +(2.50000 + 0.866025i) q^{35} +(1.50000 + 2.59808i) q^{37} +(0.500000 - 0.866025i) q^{38} +(-0.500000 - 0.866025i) q^{40} -9.00000 q^{41} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-0.500000 + 0.866025i) q^{46} +(-1.50000 - 2.59808i) q^{47} +(1.00000 - 6.92820i) q^{49} -1.00000 q^{50} +(-3.50000 + 6.06218i) q^{52} +(-0.500000 + 0.866025i) q^{53} -1.00000 q^{55} +(-2.00000 + 1.73205i) q^{56} +(4.00000 + 6.92820i) q^{58} +(6.00000 - 10.3923i) q^{59} +(2.00000 + 3.46410i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(3.50000 + 6.06218i) q^{65} +(-6.00000 + 10.3923i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(0.500000 + 2.59808i) q^{70} +14.0000 q^{71} +(7.00000 - 12.1244i) q^{73} +(-1.50000 + 2.59808i) q^{74} +1.00000 q^{76} +(0.500000 + 2.59808i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{82} -12.0000 q^{83} -4.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(0.500000 - 0.866025i) q^{88} +(-1.00000 - 1.73205i) q^{89} +(14.0000 - 12.1244i) q^{91} -1.00000 q^{92} +(1.50000 - 2.59808i) q^{94} +(0.500000 - 0.866025i) q^{95} -16.0000 q^{97} +(6.50000 - 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} + q^{5} + 4q^{7} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{4} + q^{5} + 4q^{7} - 2q^{8} - q^{10} - q^{11} + 14q^{13} + 5q^{14} - q^{16} - 4q^{17} - q^{19} - 2q^{20} - 2q^{22} + q^{23} - q^{25} + 7q^{26} + q^{28} + 16q^{29} - 6q^{31} + q^{32} - 8q^{34} + 5q^{35} + 3q^{37} + q^{38} - q^{40} - 18q^{41} - 8q^{43} - q^{44} - q^{46} - 3q^{47} + 2q^{49} - 2q^{50} - 7q^{52} - q^{53} - 2q^{55} - 4q^{56} + 8q^{58} + 12q^{59} + 4q^{61} - 12q^{62} + 2q^{64} + 7q^{65} - 12q^{67} - 4q^{68} + q^{70} + 28q^{71} + 14q^{73} - 3q^{74} + 2q^{76} + q^{77} - 4q^{79} + q^{80} - 9q^{82} - 24q^{83} - 8q^{85} - 4q^{86} + q^{88} - 2q^{89} + 28q^{91} - 2q^{92} + 3q^{94} + q^{95} - 32q^{97} + 13q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 2.00000 1.73205i 0.755929 0.654654i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i −0.931505 0.363727i \(-0.881504\pi\)
0.780750 + 0.624844i \(0.214837\pi\)
\(12\) 0 0
\(13\) 7.00000 1.94145 0.970725 0.240192i \(-0.0772105\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) 2.50000 + 0.866025i 0.668153 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 0 0
\(19\) −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i \(-0.203260\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 0.500000 + 0.866025i 0.104257 + 0.180579i 0.913434 0.406986i \(-0.133420\pi\)
−0.809177 + 0.587565i \(0.800087\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 3.50000 + 6.06218i 0.686406 + 1.18889i
\(27\) 0 0
\(28\) 0.500000 + 2.59808i 0.0944911 + 0.490990i
\(29\) 8.00000 1.48556 0.742781 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) 0 0
\(31\) −3.00000 + 5.19615i −0.538816 + 0.933257i 0.460152 + 0.887840i \(0.347795\pi\)
−0.998968 + 0.0454165i \(0.985539\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −4.00000 −0.685994
\(35\) 2.50000 + 0.866025i 0.422577 + 0.146385i
\(36\) 0 0
\(37\) 1.50000 + 2.59808i 0.246598 + 0.427121i 0.962580 0.270998i \(-0.0873538\pi\)
−0.715981 + 0.698119i \(0.754020\pi\)
\(38\) 0.500000 0.866025i 0.0811107 0.140488i
\(39\) 0 0
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) −9.00000 −1.40556 −0.702782 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) 0 0
\(46\) −0.500000 + 0.866025i −0.0737210 + 0.127688i
\(47\) −1.50000 2.59808i −0.218797 0.378968i 0.735643 0.677369i \(-0.236880\pi\)
−0.954441 + 0.298401i \(0.903547\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) −3.50000 + 6.06218i −0.485363 + 0.840673i
\(53\) −0.500000 + 0.866025i −0.0686803 + 0.118958i −0.898321 0.439340i \(-0.855212\pi\)
0.829640 + 0.558298i \(0.188546\pi\)
\(54\) 0 0
\(55\) −1.00000 −0.134840
\(56\) −2.00000 + 1.73205i −0.267261 + 0.231455i
\(57\) 0 0
\(58\) 4.00000 + 6.92820i 0.525226 + 0.909718i
\(59\) 6.00000 10.3923i 0.781133 1.35296i −0.150148 0.988663i \(-0.547975\pi\)
0.931282 0.364299i \(-0.118692\pi\)
\(60\) 0 0
\(61\) 2.00000 + 3.46410i 0.256074 + 0.443533i 0.965187 0.261562i \(-0.0842377\pi\)
−0.709113 + 0.705095i \(0.750904\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 3.50000 + 6.06218i 0.434122 + 0.751921i
\(66\) 0 0
\(67\) −6.00000 + 10.3923i −0.733017 + 1.26962i 0.222571 + 0.974916i \(0.428555\pi\)
−0.955588 + 0.294706i \(0.904778\pi\)
\(68\) −2.00000 3.46410i −0.242536 0.420084i
\(69\) 0 0
\(70\) 0.500000 + 2.59808i 0.0597614 + 0.310530i
\(71\) 14.0000 1.66149 0.830747 0.556650i \(-0.187914\pi\)
0.830747 + 0.556650i \(0.187914\pi\)
\(72\) 0 0
\(73\) 7.00000 12.1244i 0.819288 1.41905i −0.0869195 0.996215i \(-0.527702\pi\)
0.906208 0.422833i \(-0.138964\pi\)
\(74\) −1.50000 + 2.59808i −0.174371 + 0.302020i
\(75\) 0 0
\(76\) 1.00000 0.114708
\(77\) 0.500000 + 2.59808i 0.0569803 + 0.296078i
\(78\) 0 0
\(79\) −2.00000 3.46410i −0.225018 0.389742i 0.731307 0.682048i \(-0.238911\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) 0 0
\(82\) −4.50000 7.79423i −0.496942 0.860729i
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) −2.00000 3.46410i −0.215666 0.373544i
\(87\) 0 0
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) −1.00000 1.73205i −0.106000 0.183597i 0.808146 0.588982i \(-0.200471\pi\)
−0.914146 + 0.405385i \(0.867138\pi\)
\(90\) 0 0
\(91\) 14.0000 12.1244i 1.46760 1.27098i
\(92\) −1.00000 −0.104257
\(93\) 0 0
\(94\) 1.50000 2.59808i 0.154713 0.267971i
\(95\) 0.500000 0.866025i 0.0512989 0.0888523i
\(96\) 0 0
\(97\) −16.0000 −1.62455 −0.812277 0.583272i \(-0.801772\pi\)
−0.812277 + 0.583272i \(0.801772\pi\)
\(98\) 6.50000 2.59808i 0.656599 0.262445i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) −8.00000 13.8564i −0.788263 1.36531i −0.927030 0.374987i \(-0.877647\pi\)
0.138767 0.990325i \(-0.455686\pi\)
\(104\) −7.00000 −0.686406
\(105\) 0 0
\(106\) −1.00000 −0.0971286
\(107\) −9.00000 15.5885i −0.870063 1.50699i −0.861931 0.507026i \(-0.830745\pi\)
−0.00813215 0.999967i \(-0.502589\pi\)
\(108\) 0 0
\(109\) 5.00000 8.66025i 0.478913 0.829502i −0.520794 0.853682i \(-0.674364\pi\)
0.999708 + 0.0241802i \(0.00769755\pi\)
\(110\) −0.500000 0.866025i −0.0476731 0.0825723i
\(111\) 0 0
\(112\) −2.50000 0.866025i −0.236228 0.0818317i
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) −0.500000 + 0.866025i −0.0466252 + 0.0807573i
\(116\) −4.00000 + 6.92820i −0.371391 + 0.643268i
\(117\) 0 0
\(118\) 12.0000 1.10469
\(119\) 2.00000 + 10.3923i 0.183340 + 0.952661i
\(120\) 0 0
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) −2.00000 + 3.46410i −0.181071 + 0.313625i
\(123\) 0 0
\(124\) −3.00000 5.19615i −0.269408 0.466628i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −3.50000 + 6.06218i −0.306970 + 0.531688i
\(131\) −6.50000 11.2583i −0.567908 0.983645i −0.996773 0.0802763i \(-0.974420\pi\)
0.428865 0.903369i \(-0.358914\pi\)
\(132\) 0 0
\(133\) −2.50000 0.866025i −0.216777 0.0750939i
\(134\) −12.0000 −1.03664
\(135\) 0 0
\(136\) 2.00000 3.46410i 0.171499 0.297044i
\(137\) −1.00000 + 1.73205i −0.0854358 + 0.147979i −0.905577 0.424182i \(-0.860562\pi\)
0.820141 + 0.572161i \(0.193895\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −2.00000 + 1.73205i −0.169031 + 0.146385i
\(141\) 0 0
\(142\) 7.00000 + 12.1244i 0.587427 + 1.01745i
\(143\) −3.50000 + 6.06218i −0.292685 + 0.506945i
\(144\) 0 0
\(145\) 4.00000 + 6.92820i 0.332182 + 0.575356i
\(146\) 14.0000 1.15865
\(147\) 0 0
\(148\) −3.00000 −0.246598
\(149\) −2.00000 3.46410i −0.163846 0.283790i 0.772399 0.635138i \(-0.219057\pi\)
−0.936245 + 0.351348i \(0.885723\pi\)
\(150\) 0 0
\(151\) 1.00000 1.73205i 0.0813788 0.140952i −0.822464 0.568818i \(-0.807401\pi\)
0.903842 + 0.427865i \(0.140734\pi\)
\(152\) 0.500000 + 0.866025i 0.0405554 + 0.0702439i
\(153\) 0 0
\(154\) −2.00000 + 1.73205i −0.161165 + 0.139573i
\(155\) −6.00000 −0.481932
\(156\) 0 0
\(157\) −7.50000 + 12.9904i −0.598565 + 1.03675i 0.394468 + 0.918910i \(0.370929\pi\)
−0.993033 + 0.117836i \(0.962404\pi\)
\(158\) 2.00000 3.46410i 0.159111 0.275589i
\(159\) 0 0
\(160\) 1.00000 0.0790569
\(161\) 2.50000 + 0.866025i 0.197028 + 0.0682524i
\(162\) 0 0
\(163\) −4.00000 6.92820i −0.313304 0.542659i 0.665771 0.746156i \(-0.268103\pi\)
−0.979076 + 0.203497i \(0.934769\pi\)
\(164\) 4.50000 7.79423i 0.351391 0.608627i
\(165\) 0 0
\(166\) −6.00000 10.3923i −0.465690 0.806599i
\(167\) 5.00000 0.386912 0.193456 0.981109i \(-0.438030\pi\)
0.193456 + 0.981109i \(0.438030\pi\)
\(168\) 0 0
\(169\) 36.0000 2.76923
\(170\) −2.00000 3.46410i −0.153393 0.265684i
\(171\) 0 0
\(172\) 2.00000 3.46410i 0.152499 0.264135i
\(173\) −10.5000 18.1865i −0.798300 1.38270i −0.920722 0.390218i \(-0.872399\pi\)
0.122422 0.992478i \(-0.460934\pi\)
\(174\) 0 0
\(175\) 0.500000 + 2.59808i 0.0377964 + 0.196396i
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) 1.00000 1.73205i 0.0749532 0.129823i
\(179\) 6.50000 11.2583i 0.485833 0.841487i −0.514035 0.857769i \(-0.671850\pi\)
0.999867 + 0.0162823i \(0.00518305\pi\)
\(180\) 0 0
\(181\) −12.0000 −0.891953 −0.445976 0.895045i \(-0.647144\pi\)
−0.445976 + 0.895045i \(0.647144\pi\)
\(182\) 17.5000 + 6.06218i 1.29719 + 0.449359i
\(183\) 0 0
\(184\) −0.500000 0.866025i −0.0368605 0.0638442i
\(185\) −1.50000 + 2.59808i −0.110282 + 0.191014i
\(186\) 0 0
\(187\) −2.00000 3.46410i −0.146254 0.253320i
\(188\) 3.00000 0.218797
\(189\) 0 0
\(190\) 1.00000 0.0725476
\(191\) −5.00000 8.66025i −0.361787 0.626634i 0.626468 0.779447i \(-0.284500\pi\)
−0.988255 + 0.152813i \(0.951167\pi\)
\(192\) 0 0
\(193\) −13.0000 + 22.5167i −0.935760 + 1.62078i −0.162488 + 0.986710i \(0.551952\pi\)
−0.773272 + 0.634074i \(0.781381\pi\)
\(194\) −8.00000 13.8564i −0.574367 0.994832i
\(195\) 0 0
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) 3.00000 0.213741 0.106871 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) 0 0
\(199\) 6.00000 10.3923i 0.425329 0.736691i −0.571122 0.820865i \(-0.693492\pi\)
0.996451 + 0.0841740i \(0.0268252\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) 0 0
\(202\) 0 0
\(203\) 16.0000 13.8564i 1.12298 0.972529i
\(204\) 0 0
\(205\) −4.50000 7.79423i −0.314294 0.544373i
\(206\) 8.00000 13.8564i 0.557386 0.965422i
\(207\) 0 0
\(208\) −3.50000 6.06218i −0.242681 0.420336i
\(209\) 1.00000 0.0691714
\(210\) 0 0
\(211\) −15.0000 −1.03264 −0.516321 0.856395i \(-0.672699\pi\)
−0.516321 + 0.856395i \(0.672699\pi\)
\(212\) −0.500000 0.866025i −0.0343401 0.0594789i
\(213\) 0 0
\(214\) 9.00000 15.5885i 0.615227 1.06561i
\(215\) −2.00000 3.46410i −0.136399 0.236250i
\(216\) 0 0
\(217\) 3.00000 + 15.5885i 0.203653 + 1.05821i
\(218\) 10.0000 0.677285
\(219\) 0 0
\(220\) 0.500000 0.866025i 0.0337100 0.0583874i
\(221\) −14.0000 + 24.2487i −0.941742 + 1.63114i
\(222\) 0 0
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) −0.500000 2.59808i −0.0334077 0.173591i
\(225\) 0 0
\(226\) 3.00000 + 5.19615i 0.199557 + 0.345643i
\(227\) −10.0000 + 17.3205i −0.663723 + 1.14960i 0.315906 + 0.948790i \(0.397691\pi\)
−0.979630 + 0.200812i \(0.935642\pi\)
\(228\) 0 0
\(229\) 11.0000 + 19.0526i 0.726900 + 1.25903i 0.958187 + 0.286143i \(0.0923732\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) −1.00000 −0.0659380
\(231\) 0 0
\(232\) −8.00000 −0.525226
\(233\) 13.0000 + 22.5167i 0.851658 + 1.47512i 0.879711 + 0.475509i \(0.157736\pi\)
−0.0280525 + 0.999606i \(0.508931\pi\)
\(234\) 0 0
\(235\) 1.50000 2.59808i 0.0978492 0.169480i
\(236\) 6.00000 + 10.3923i 0.390567 + 0.676481i
\(237\) 0 0
\(238\) −8.00000 + 6.92820i −0.518563 + 0.449089i
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) −3.50000 + 6.06218i −0.225455 + 0.390499i −0.956456 0.291877i \(-0.905720\pi\)
0.731001 + 0.682376i \(0.239053\pi\)
\(242\) −5.00000 + 8.66025i −0.321412 + 0.556702i
\(243\) 0 0
\(244\) −4.00000 −0.256074
\(245\) 6.50000 2.59808i 0.415270 0.165985i
\(246\) 0 0
\(247\) −3.50000 6.06218i −0.222700 0.385727i
\(248\) 3.00000 5.19615i 0.190500 0.329956i
\(249\) 0 0
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) 3.00000 0.189358 0.0946792 0.995508i \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) 0 0
\(253\) −1.00000 −0.0628695
\(254\) 2.50000 + 4.33013i 0.156864 + 0.271696i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −4.00000 6.92820i −0.249513 0.432169i 0.713878 0.700270i \(-0.246937\pi\)
−0.963391 + 0.268101i \(0.913604\pi\)
\(258\) 0 0
\(259\) 7.50000 + 2.59808i 0.466027 + 0.161437i
\(260\) −7.00000 −0.434122
\(261\) 0 0
\(262\) 6.50000 11.2583i 0.401571 0.695542i
\(263\) −8.00000 + 13.8564i −0.493301 + 0.854423i −0.999970 0.00771799i \(-0.997543\pi\)
0.506669 + 0.862141i \(0.330877\pi\)
\(264\) 0 0
\(265\) −1.00000 −0.0614295
\(266\) −0.500000 2.59808i −0.0306570 0.159298i
\(267\) 0 0
\(268\) −6.00000 10.3923i −0.366508 0.634811i
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 0 0
\(271\) −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i \(-0.328199\pi\)
−0.999870 + 0.0161307i \(0.994865\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) −0.500000 0.866025i −0.0301511 0.0522233i
\(276\) 0 0
\(277\) 1.00000 1.73205i 0.0600842 0.104069i −0.834419 0.551131i \(-0.814196\pi\)
0.894503 + 0.447062i \(0.147530\pi\)
\(278\) −2.00000 3.46410i −0.119952 0.207763i
\(279\) 0 0
\(280\) −2.50000 0.866025i −0.149404 0.0517549i
\(281\) −3.00000 −0.178965 −0.0894825 0.995988i \(-0.528521\pi\)
−0.0894825 + 0.995988i \(0.528521\pi\)
\(282\) 0 0
\(283\) 1.00000 1.73205i 0.0594438 0.102960i −0.834772 0.550596i \(-0.814401\pi\)
0.894216 + 0.447636i \(0.147734\pi\)
\(284\) −7.00000 + 12.1244i −0.415374 + 0.719448i
\(285\) 0 0
\(286\) −7.00000 −0.413919
\(287\) −18.0000 + 15.5885i −1.06251 + 0.920158i
\(288\) 0 0
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) −4.00000 + 6.92820i −0.234888 + 0.406838i
\(291\) 0 0
\(292\) 7.00000 + 12.1244i 0.409644 + 0.709524i
\(293\) −9.00000 −0.525786 −0.262893 0.964825i \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(294\) 0 0
\(295\) 12.0000 0.698667
\(296\) −1.50000 2.59808i −0.0871857 0.151010i
\(297\) 0 0
\(298\) 2.00000 3.46410i 0.115857 0.200670i
\(299\) 3.50000 + 6.06218i 0.202410 + 0.350585i
\(300\) 0 0
\(301\) −8.00000 + 6.92820i −0.461112 + 0.399335i
\(302\) 2.00000 0.115087
\(303\) 0 0
\(304\) −0.500000 + 0.866025i −0.0286770 + 0.0496700i
\(305\) −2.00000 + 3.46410i −0.114520 + 0.198354i
\(306\) 0 0
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) −2.50000 0.866025i −0.142451 0.0493464i
\(309\) 0 0
\(310\) −3.00000 5.19615i −0.170389 0.295122i
\(311\) 8.00000 13.8564i 0.453638 0.785725i −0.544970 0.838455i \(-0.683459\pi\)
0.998609 + 0.0527306i \(0.0167924\pi\)
\(312\) 0 0
\(313\) 12.0000 + 20.7846i 0.678280 + 1.17482i 0.975499 + 0.220006i \(0.0706077\pi\)
−0.297218 + 0.954810i \(0.596059\pi\)
\(314\) −15.0000 −0.846499
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) 5.00000 + 8.66025i 0.280828 + 0.486408i 0.971589 0.236675i \(-0.0760576\pi\)
−0.690761 + 0.723083i \(0.742724\pi\)
\(318\) 0 0
\(319\) −4.00000 + 6.92820i −0.223957 + 0.387905i
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) 0 0
\(322\) 0.500000 + 2.59808i 0.0278639 + 0.144785i
\(323\) 4.00000 0.222566
\(324\) 0 0
\(325\) −3.50000 + 6.06218i −0.194145 + 0.336269i
\(326\) 4.00000 6.92820i 0.221540 0.383718i
\(327\) 0 0
\(328\) 9.00000 0.496942
\(329\) −7.50000 2.59808i −0.413488 0.143237i
\(330\) 0 0
\(331\) 4.50000 + 7.79423i 0.247342 + 0.428410i 0.962788 0.270259i \(-0.0871094\pi\)
−0.715445 + 0.698669i \(0.753776\pi\)
\(332\) 6.00000 10.3923i 0.329293 0.570352i
\(333\) 0 0
\(334\) 2.50000 + 4.33013i 0.136794 + 0.236934i
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 18.0000 + 31.1769i 0.979071 + 1.69580i
\(339\) 0 0
\(340\) 2.00000 3.46410i 0.108465 0.187867i
\(341\) −3.00000 5.19615i −0.162459 0.281387i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 10.5000 18.1865i 0.564483 0.977714i
\(347\) −17.0000 + 29.4449i −0.912608 + 1.58068i −0.102241 + 0.994760i \(0.532601\pi\)
−0.810366 + 0.585923i \(0.800732\pi\)
\(348\) 0 0
\(349\) −28.0000 −1.49881 −0.749403 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) −2.00000 + 1.73205i −0.106904 + 0.0925820i
\(351\) 0 0
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) −4.00000 + 6.92820i −0.212899 + 0.368751i −0.952620 0.304162i \(-0.901624\pi\)
0.739722 + 0.672913i \(0.234957\pi\)
\(354\) 0 0
\(355\) 7.00000 + 12.1244i 0.371521 + 0.643494i
\(356\) 2.00000 0.106000
\(357\) 0 0
\(358\) 13.0000 0.687071
\(359\) 18.0000 + 31.1769i 0.950004 + 1.64545i 0.745409 + 0.666608i \(0.232254\pi\)
0.204595 + 0.978847i \(0.434412\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) −6.00000 10.3923i −0.315353 0.546207i
\(363\) 0 0
\(364\) 3.50000 + 18.1865i 0.183450 + 0.953233i
\(365\) 14.0000 0.732793
\(366\) 0 0
\(367\) −9.50000 + 16.4545i −0.495896 + 0.858917i −0.999989 0.00473247i \(-0.998494\pi\)
0.504093 + 0.863649i \(0.331827\pi\)
\(368\) 0.500000 0.866025i 0.0260643 0.0451447i
\(369\) 0 0
\(370\) −3.00000 −0.155963
\(371\) 0.500000 + 2.59808i 0.0259587 + 0.134885i
\(372\) 0 0
\(373\) −13.0000 22.5167i −0.673114 1.16587i −0.977016 0.213165i \(-0.931623\pi\)
0.303902 0.952703i \(-0.401711\pi\)
\(374\) 2.00000 3.46410i 0.103418 0.179124i
\(375\) 0 0
\(376\) 1.50000 + 2.59808i 0.0773566 + 0.133986i
\(377\) 56.0000 2.88415
\(378\) 0 0
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) 0.500000 + 0.866025i 0.0256495 + 0.0444262i
\(381\) 0 0
\(382\) 5.00000 8.66025i 0.255822 0.443097i
\(383\) 6.50000 + 11.2583i 0.332134 + 0.575274i 0.982930 0.183979i \(-0.0588979\pi\)
−0.650796 + 0.759253i \(0.725565\pi\)
\(384\) 0 0
\(385\) −2.00000 + 1.73205i −0.101929 + 0.0882735i
\(386\) −26.0000 −1.32337
\(387\) 0 0
\(388\) 8.00000 13.8564i 0.406138 0.703452i
\(389\) −7.00000 + 12.1244i −0.354914 + 0.614729i −0.987103 0.160085i \(-0.948823\pi\)
0.632189 + 0.774814i \(0.282157\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) −1.00000 + 6.92820i −0.0505076 + 0.349927i
\(393\) 0 0
\(394\) 1.50000 + 2.59808i 0.0755689 + 0.130889i
\(395\) 2.00000 3.46410i 0.100631 0.174298i
\(396\) 0 0
\(397\) −9.00000 15.5885i −0.451697 0.782362i 0.546795 0.837267i \(-0.315848\pi\)
−0.998492 + 0.0549046i \(0.982515\pi\)
\(398\) 12.0000 0.601506
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −8.50000 14.7224i −0.424470 0.735203i 0.571901 0.820323i \(-0.306206\pi\)
−0.996371 + 0.0851195i \(0.972873\pi\)
\(402\) 0 0
\(403\) −21.0000 + 36.3731i −1.04608 + 1.81187i
\(404\) 0 0
\(405\) 0 0
\(406\) 20.0000 + 6.92820i 0.992583 + 0.343841i
\(407\) −3.00000 −0.148704
\(408\) 0 0
\(409\) −5.00000 + 8.66025i −0.247234 + 0.428222i −0.962757 0.270367i \(-0.912855\pi\)
0.715523 + 0.698589i \(0.246188\pi\)
\(410\) 4.50000 7.79423i 0.222239 0.384930i
\(411\) 0 0
\(412\) 16.0000 0.788263
\(413\) −6.00000 31.1769i −0.295241 1.53412i
\(414\) 0 0
\(415\) −6.00000 10.3923i −0.294528 0.510138i
\(416\) 3.50000 6.06218i 0.171602 0.297223i
\(417\) 0 0
\(418\) 0.500000 + 0.866025i 0.0244558 + 0.0423587i
\(419\) −11.0000 −0.537385 −0.268693 0.963226i \(-0.586592\pi\)
−0.268693 + 0.963226i \(0.586592\pi\)
\(420\) 0 0
\(421\) −14.0000 −0.682318 −0.341159 0.940006i \(-0.610819\pi\)
−0.341159 + 0.940006i \(0.610819\pi\)
\(422\) −7.50000 12.9904i −0.365094 0.632362i
\(423\) 0 0
\(424\) 0.500000 0.866025i 0.0242821 0.0420579i
\(425\) −2.00000 3.46410i −0.0970143 0.168034i
\(426\) 0 0
\(427\) 10.0000 + 3.46410i 0.483934 + 0.167640i
\(428\) 18.0000 0.870063
\(429\) 0 0
\(430\) 2.00000 3.46410i 0.0964486 0.167054i
\(431\) −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i \(-0.926659\pi\)
0.684564 + 0.728953i \(0.259993\pi\)
\(432\) 0 0
\(433\) 40.0000 1.92228 0.961139 0.276066i \(-0.0890309\pi\)
0.961139 + 0.276066i \(0.0890309\pi\)
\(434\) −12.0000 + 10.3923i −0.576018 + 0.498847i
\(435\) 0 0
\(436\) 5.00000 + 8.66025i 0.239457 + 0.414751i
\(437\) 0.500000 0.866025i 0.0239182 0.0414276i
\(438\) 0 0
\(439\) −8.00000 13.8564i −0.381819 0.661330i 0.609503 0.792784i \(-0.291369\pi\)
−0.991322 + 0.131453i \(0.958036\pi\)
\(440\) 1.00000 0.0476731
\(441\) 0 0
\(442\) −28.0000 −1.33182
\(443\) −18.0000 31.1769i −0.855206 1.48126i −0.876454 0.481486i \(-0.840097\pi\)
0.0212481 0.999774i \(-0.493236\pi\)
\(444\) 0 0
\(445\) 1.00000 1.73205i 0.0474045 0.0821071i
\(446\) −2.00000 3.46410i −0.0947027 0.164030i
\(447\) 0 0
\(448\) 2.00000 1.73205i 0.0944911 0.0818317i
\(449\) 25.0000 1.17982 0.589911 0.807468i \(-0.299163\pi\)
0.589911 + 0.807468i \(0.299163\pi\)
\(450\) 0 0
\(451\) 4.50000 7.79423i 0.211897 0.367016i
\(452\) −3.00000 + 5.19615i −0.141108 + 0.244406i
\(453\) 0 0
\(454\) −20.0000 −0.938647
\(455\) 17.5000 + 6.06218i 0.820413 + 0.284199i
\(456\) 0 0
\(457\) −5.00000 8.66025i −0.233890 0.405110i 0.725059 0.688686i \(-0.241812\pi\)
−0.958950 + 0.283577i \(0.908479\pi\)
\(458\) −11.0000 + 19.0526i −0.513996 + 0.890268i
\(459\) 0 0
\(460\) −0.500000 0.866025i −0.0233126 0.0403786i
\(461\) 28.0000 1.30409 0.652045 0.758180i \(-0.273911\pi\)
0.652045 + 0.758180i \(0.273911\pi\)
\(462\) 0 0
\(463\) 33.0000 1.53364 0.766820 0.641862i \(-0.221838\pi\)
0.766820 + 0.641862i \(0.221838\pi\)
\(464\) −4.00000 6.92820i −0.185695 0.321634i
\(465\) 0 0
\(466\) −13.0000 + 22.5167i −0.602213 + 1.04306i
\(467\) 6.00000 + 10.3923i 0.277647 + 0.480899i 0.970799 0.239892i \(-0.0771121\pi\)
−0.693153 + 0.720791i \(0.743779\pi\)
\(468\) 0 0
\(469\) 6.00000 + 31.1769i 0.277054 + 1.43962i
\(470\) 3.00000 0.138380
\(471\) 0 0
\(472\) −6.00000 + 10.3923i −0.276172 + 0.478345i
\(473\) 2.00000 3.46410i 0.0919601 0.159280i
\(474\) 0 0
\(475\) 1.00000 0.0458831
\(476\) −10.0000 3.46410i −0.458349 0.158777i
\(477\) 0 0
\(478\) 3.00000 + 5.19615i 0.137217 + 0.237666i
\(479\) 13.0000 22.5167i 0.593985 1.02881i −0.399704 0.916644i \(-0.630887\pi\)
0.993689 0.112168i \(-0.0357796\pi\)
\(480\) 0 0
\(481\) 10.5000 + 18.1865i 0.478759 + 0.829235i
\(482\) −7.00000 −0.318841
\(483\) 0 0
\(484\) −10.0000 −0.454545
\(485\) −8.00000 13.8564i −0.363261 0.629187i
\(486\) 0 0
\(487\) 4.00000 6.92820i 0.181257 0.313947i −0.761052 0.648691i \(-0.775317\pi\)
0.942309 + 0.334744i \(0.108650\pi\)
\(488\) −2.00000 3.46410i −0.0905357 0.156813i
\(489\) 0 0
\(490\) 5.50000 + 4.33013i 0.248465 + 0.195615i
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) −16.0000 + 27.7128i −0.720604 + 1.24812i
\(494\) 3.50000 6.06218i 0.157472 0.272750i
\(495\) 0 0
\(496\) 6.00000 0.269408
\(497\) 28.0000 24.2487i 1.25597 1.08770i
\(498\) 0 0
\(499\) −12.0000 20.7846i −0.537194 0.930447i −0.999054 0.0434940i \(-0.986151\pi\)
0.461860 0.886953i \(-0.347182\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) 0 0
\(502\) 1.50000 + 2.59808i 0.0669483 + 0.115958i
\(503\) −28.0000 −1.24846 −0.624229 0.781241i \(-0.714587\pi\)
−0.624229 + 0.781241i \(0.714587\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −0.500000 0.866025i −0.0222277 0.0384995i
\(507\) 0 0
\(508\) −2.50000 + 4.33013i −0.110920 + 0.192118i
\(509\) 15.0000 + 25.9808i 0.664863 + 1.15158i 0.979322 + 0.202306i \(0.0648436\pi\)
−0.314459 + 0.949271i \(0.601823\pi\)
\(510\) 0 0
\(511\) −7.00000 36.3731i −0.309662 1.60905i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 4.00000 6.92820i 0.176432 0.305590i
\(515\) 8.00000 13.8564i 0.352522 0.610586i
\(516\) 0 0
\(517\) 3.00000 0.131940
\(518\) 1.50000 + 7.79423i 0.0659062 + 0.342459i
\(519\) 0 0
\(520\) −3.50000 6.06218i −0.153485 0.265844i
\(521\) −10.5000 + 18.1865i −0.460013 + 0.796766i −0.998961 0.0455727i \(-0.985489\pi\)
0.538948 + 0.842339i \(0.318822\pi\)
\(522\) 0 0
\(523\) 7.00000 + 12.1244i 0.306089 + 0.530161i 0.977503 0.210921i \(-0.0676463\pi\)
−0.671414 + 0.741082i \(0.734313\pi\)
\(524\) 13.0000 0.567908
\(525\) 0 0
\(526\) −16.0000 −0.697633
\(527\) −12.0000 20.7846i −0.522728 0.905392i
\(528\) 0 0
\(529\) 11.0000 19.0526i 0.478261 0.828372i
\(530\) −0.500000 0.866025i −0.0217186 0.0376177i
\(531\) 0 0
\(532\) 2.00000 1.73205i 0.0867110 0.0750939i
\(533\) −63.0000 −2.72883
\(534\) 0 0
\(535\) 9.00000 15.5885i 0.389104 0.673948i
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) 0 0
\(538\) 0 0
\(539\) 5.50000 + 4.33013i 0.236902 + 0.186512i
\(540\) 0 0
\(541\) −1.00000 1.73205i −0.0429934 0.0744667i 0.843728 0.536771i \(-0.180356\pi\)
−0.886721 + 0.462304i \(0.847023\pi\)
\(542\) 8.00000 13.8564i 0.343629 0.595184i
\(543\) 0 0
\(544\) 2.00000 + 3.46410i 0.0857493 + 0.148522i
\(545\) 10.0000 0.428353
\(546\) 0 0
\(547\) 36.0000 1.53925 0.769624 0.638497i \(-0.220443\pi\)
0.769624 + 0.638497i \(0.220443\pi\)
\(548\) −1.00000 1.73205i −0.0427179 0.0739895i
\(549\) 0 0
\(550\) 0.500000 0.866025i 0.0213201 0.0369274i
\(551\) −4.00000 6.92820i −0.170406 0.295151i
\(552\) 0 0
\(553\) −10.0000 3.46410i −0.425243 0.147309i
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) 22.5000 38.9711i 0.953356 1.65126i 0.215268 0.976555i \(-0.430937\pi\)
0.738087 0.674705i \(-0.235729\pi\)
\(558\) 0 0
\(559\) −28.0000 −1.18427
\(560\) −0.500000 2.59808i −0.0211289 0.109789i
\(561\) 0 0
\(562\) −1.50000 2.59808i −0.0632737 0.109593i
\(563\) 7.00000 12.1244i 0.295015 0.510981i −0.679974 0.733237i \(-0.738009\pi\)
0.974988 + 0.222256i \(0.0713421\pi\)
\(564\) 0 0
\(565\) 3.00000 + 5.19615i 0.126211 + 0.218604i
\(566\) 2.00000 0.0840663
\(567\) 0 0
\(568\) −14.0000 −0.587427
\(569\) −18.5000 32.0429i −0.775560 1.34331i −0.934479 0.356018i \(-0.884134\pi\)
0.158919 0.987292i \(-0.449199\pi\)
\(570\) 0 0
\(571\) 4.00000 6.92820i 0.167395 0.289936i −0.770108 0.637913i \(-0.779798\pi\)
0.937503 + 0.347977i \(0.113131\pi\)
\(572\) −3.50000 6.06218i −0.146342 0.253472i
\(573\) 0 0
\(574\) −22.5000 7.79423i −0.939132 0.325325i
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) 7.00000 12.1244i 0.291414 0.504744i −0.682730 0.730670i \(-0.739208\pi\)
0.974144 + 0.225927i \(0.0725410\pi\)
\(578\) −0.500000 + 0.866025i −0.0207973 + 0.0360219i
\(579\) 0 0
\(580\) −8.00000 −0.332182
\(581\) −24.0000 + 20.7846i −0.995688 + 0.862291i
\(582\) 0 0
\(583\) −0.500000 0.866025i −0.0207079 0.0358671i
\(584\) −7.00000 + 12.1244i −0.289662 + 0.501709i
\(585\) 0 0
\(586\) −4.50000 7.79423i −0.185893 0.321977i
\(587\) −42.0000 −1.73353 −0.866763 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) 0 0
\(589\) 6.00000 0.247226
\(590\) 6.00000 + 10.3923i 0.247016 + 0.427844i
\(591\) 0 0
\(592\) 1.50000 2.59808i 0.0616496 0.106780i
\(593\) 6.00000 + 10.3923i 0.246390 + 0.426761i 0.962522 0.271205i \(-0.0874221\pi\)
−0.716131 + 0.697966i \(0.754089\pi\)
\(594\) 0 0
\(595\) −8.00000 + 6.92820i −0.327968 + 0.284029i
\(596\) 4.00000 0.163846
\(597\) 0 0
\(598\) −3.50000 + 6.06218i −0.143126 + 0.247901i
\(599\) 3.00000 5.19615i 0.122577 0.212309i −0.798206 0.602384i \(-0.794218\pi\)
0.920783 + 0.390075i \(0.127551\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) −10.0000 3.46410i −0.407570 0.141186i
\(603\) 0 0
\(604\) 1.00000 + 1.73205i 0.0406894 + 0.0704761i
\(605\) −5.00000 + 8.66025i −0.203279 + 0.352089i
\(606\) 0 0
\(607\) −12.5000 21.6506i −0.507359 0.878772i −0.999964 0.00851879i \(-0.997288\pi\)
0.492604 0.870253i \(-0.336045\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 0 0
\(610\) −4.00000 −0.161955
\(611\) −10.5000 18.1865i −0.424785 0.735748i
\(612\) 0 0
\(613\) 7.50000 12.9904i 0.302922 0.524677i −0.673874 0.738846i \(-0.735371\pi\)
0.976797 + 0.214169i \(0.0687045\pi\)
\(614\) 4.00000 + 6.92820i 0.161427 + 0.279600i
\(615\) 0 0
\(616\) −0.500000 2.59808i −0.0201456 0.104679i
\(617\) −8.00000 −0.322068 −0.161034 0.986949i \(-0.551483\pi\)
−0.161034 + 0.986949i \(0.551483\pi\)
\(618\) 0 0
\(619\) 3.50000 6.06218i 0.140677 0.243659i −0.787075 0.616858i \(-0.788405\pi\)
0.927752 + 0.373198i \(0.121739\pi\)
\(620\) 3.00000 5.19615i 0.120483 0.208683i
\(621\) 0 0
\(622\) 16.0000 0.641542
\(623\) −5.00000 1.73205i −0.200321 0.0693932i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −12.0000 + 20.7846i −0.479616 + 0.830720i
\(627\) 0 0
\(628\) −7.50000 12.9904i −0.299283 0.518373i
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) 14.0000 0.557331 0.278666 0.960388i \(-0.410108\pi\)
0.278666 + 0.960388i \(0.410108\pi\)
\(632\) 2.00000 + 3.46410i 0.0795557 + 0.137795i
\(633\) 0 0
\(634\) −5.00000 + 8.66025i −0.198575 + 0.343943i
\(635\) 2.50000 + 4.33013i 0.0992095 + 0.171836i
\(636\) 0 0
\(637\) 7.00000 48.4974i 0.277350 1.92154i
\(638\) −8.00000 −0.316723
\(639\) 0 0
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) −11.5000 + 19.9186i −0.454223 + 0.786737i −0.998643 0.0520757i \(-0.983416\pi\)
0.544420 + 0.838812i \(0.316750\pi\)
\(642\) 0 0
\(643\) 26.0000 1.02534 0.512670 0.858586i \(-0.328656\pi\)
0.512670 + 0.858586i \(0.328656\pi\)
\(644\) −2.00000 + 1.73205i −0.0788110 + 0.0682524i
\(645\) 0 0
\(646\) 2.00000 + 3.46410i 0.0786889 + 0.136293i
\(647\) −7.50000 + 12.9904i −0.294855 + 0.510705i −0.974951 0.222419i \(-0.928605\pi\)
0.680096 + 0.733123i \(0.261938\pi\)
\(648\) 0 0
\(649\) 6.00000 + 10.3923i 0.235521 + 0.407934i
\(650\) −7.00000 −0.274563
\(651\) 0 0
\(652\) 8.00000 0.313304
\(653\) 14.5000 + 25.1147i 0.567429 + 0.982816i 0.996819 + 0.0796966i \(0.0253951\pi\)
−0.429390 + 0.903119i \(0.641272\pi\)
\(654\) 0 0
\(655\) 6.50000 11.2583i 0.253976 0.439899i
\(656\) 4.50000 + 7.79423i 0.175695 + 0.304314i
\(657\) 0 0
\(658\) −1.50000 7.79423i −0.0584761 0.303851i
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) −4.00000 + 6.92820i −0.155582 + 0.269476i −0.933271 0.359174i \(-0.883059\pi\)
0.777689 + 0.628649i \(0.216392\pi\)
\(662\) −4.50000 + 7.79423i −0.174897 + 0.302931i
\(663\) 0 0
\(664\) 12.0000 0.465690
\(665\) −0.500000 2.59808i −0.0193892 0.100749i
\(666\) 0 0
\(667\) 4.00000 + 6.92820i 0.154881 + 0.268261i
\(668\) −2.50000 + 4.33013i −0.0967279 + 0.167538i
\(669\) 0 0
\(670\) −6.00000 10.3923i −0.231800 0.401490i
\(671\) −4.00000 −0.154418
\(672\) 0 0
\(673\) −12.0000 −0.462566 −0.231283 0.972887i \(-0.574292\pi\)
−0.231283 + 0.972887i \(0.574292\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −18.0000 + 31.1769i −0.692308 + 1.19911i
\(677\) 0.500000 + 0.866025i 0.0192166 + 0.0332841i 0.875474 0.483266i \(-0.160549\pi\)
−0.856257 + 0.516550i \(0.827216\pi\)
\(678\) 0 0
\(679\) −32.0000 + 27.7128i −1.22805 + 1.06352i
\(680\) 4.00000 0.153393
\(681\) 0 0
\(682\) 3.00000 5.19615i 0.114876 0.198971i
\(683\) 6.00000 10.3923i 0.229584 0.397650i −0.728101 0.685470i \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) 0 0
\(685\) −2.00000 −0.0764161
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) 0 0
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) −3.50000 + 6.06218i −0.133339 + 0.230951i
\(690\) 0 0
\(691\) −6.00000 10.3923i −0.228251 0.395342i 0.729039 0.684472i \(-0.239967\pi\)
−0.957290 + 0.289130i \(0.906634\pi\)
\(692\) 21.0000 0.798300
\(693\) 0 0
\(694\) −34.0000 −1.29062
\(695\) −2.00000 3.46410i −0.0758643 0.131401i
\(696\) 0 0
\(697\) 18.0000 31.1769i 0.681799 1.18091i
\(698\) −14.0000 24.2487i −0.529908 0.917827i
\(699\) 0 0
\(700\) −2.50000 0.866025i −0.0944911 0.0327327i
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 0 0
\(703\) 1.50000 2.59808i 0.0565736 0.0979883i
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) −8.00000 −0.301084
\(707\) 0 0
\(708\) 0 0
\(709\) −2.00000 3.46410i −0.0751116 0.130097i 0.826023 0.563636i \(-0.190598\pi\)
−0.901135 + 0.433539i \(0.857265\pi\)
\(710\) −7.00000 + 12.1244i −0.262705 + 0.455019i
\(711\) 0 0
\(712\) 1.00000 + 1.73205i 0.0374766 + 0.0649113i
\(713\) −6.00000 −0.224702
\(714\) 0 0
\(715\) −7.00000 −0.261785
\(716\) 6.50000 + 11.2583i 0.242916 + 0.420744i
\(717\) 0 0
\(718\) −18.0000 + 31.1769i −0.671754 + 1.16351i
\(719\) 13.0000 + 22.5167i 0.484818 + 0.839730i 0.999848 0.0174426i \(-0.00555244\pi\)
−0.515030 + 0.857172i \(0.672219\pi\)
\(720\) 0 0
\(721\) −40.0000 13.8564i −1.48968 0.516040i
\(722\) 18.0000 0.669891
\(723\) 0 0
\(724\) 6.00000 10.3923i 0.222988 0.386227i
\(725\) −4.00000 + 6.92820i −0.148556 + 0.257307i
\(726\) 0 0
\(727\) 17.0000 0.630495 0.315248 0.949009i \(-0.397912\pi\)
0.315248 + 0.949009i \(0.397912\pi\)
\(728\) −14.0000 + 12.1244i −0.518875 + 0.449359i
\(729\) 0 0
\(730\) 7.00000 + 12.1244i 0.259082 + 0.448743i
\(731\) 8.00000 13.8564i 0.295891 0.512498i
\(732\) 0 0
\(733\) −18.5000 32.0429i −0.683313 1.18353i −0.973964 0.226704i \(-0.927205\pi\)
0.290651 0.956829i \(-0.406128\pi\)
\(734\) −19.0000 −0.701303
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) −6.00000 10.3923i −0.221013 0.382805i
\(738\) 0 0
\(739\) −20.5000 + 35.5070i −0.754105 + 1.30615i 0.191714 + 0.981451i \(0.438596\pi\)
−0.945818 + 0.324697i \(0.894738\pi\)
\(740\) −1.50000 2.59808i −0.0551411 0.0955072i
\(741\) 0 0
\(742\) −2.00000 + 1.73205i −0.0734223 + 0.0635856i
\(743\) 9.00000 0.330178 0.165089 0.986279i \(-0.447209\pi\)
0.165089 + 0.986279i \(0.447209\pi\)
\(744\) 0 0
\(745\) 2.00000 3.46410i 0.0732743 0.126915i
\(746\) 13.0000 22.5167i 0.475964 0.824394i
\(747\) 0 0
\(748\) 4.00000 0.146254
\(749\) −45.0000 15.5885i −1.64426 0.569590i
\(750\) 0 0
\(751\) 13.0000 + 22.5167i 0.474377 + 0.821645i 0.999570 0.0293387i \(-0.00934013\pi\)
−0.525193 + 0.850983i \(0.676007\pi\)
\(752\) −1.50000 + 2.59808i −0.0546994 + 0.0947421i
\(753\) 0 0
\(754\) 28.0000 + 48.4974i 1.01970 + 1.76617i
\(755\) 2.00000 0.0727875
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) 0.500000 + 0.866025i 0.0181608 + 0.0314555i
\(759\) 0 0
\(760\) −0.500000 + 0.866025i −0.0181369 + 0.0314140i
\(761\) −8.50000 14.7224i −0.308125 0.533688i 0.669827 0.742517i \(-0.266368\pi\)
−0.977952 + 0.208829i \(0.933035\pi\)
\(762\) 0 0
\(763\) −5.00000 25.9808i −0.181012 0.940567i
\(764\) 10.0000 0.361787
\(765\) 0 0
\(766\) −6.50000 + 11.2583i −0.234855 + 0.406780i
\(767\) 42.0000 72.7461i 1.51653 2.62671i
\(768\) 0 0
\(769\) −29.0000 −1.04577 −0.522883 0.852404i \(-0.675144\pi\)
−0.522883 + 0.852404i \(0.675144\pi\)
\(770\) −2.50000 0.866025i −0.0900937 0.0312094i
\(771\) 0 0
\(772\) −13.0000 22.5167i −0.467880 0.810392i
\(773\) 21.5000 37.2391i 0.773301 1.33940i −0.162443 0.986718i \(-0.551937\pi\)
0.935744 0.352679i \(-0.114729\pi\)
\(774\) 0 0
\(775\) −3.00000 5.19615i −0.107763 0.186651i
\(776\) 16.0000 0.574367
\(777\) 0 0
\(778\) −14.0000 −0.501924
\(779\) 4.50000 + 7.79423i 0.161229 + 0.279257i
\(780\) 0 0
\(781\) −7.00000 + 12.1244i −0.250480 + 0.433844i
\(782\) −2.00000 3.46410i −0.0715199 0.123876i
\(783\) 0 0
\(784\) −6.50000 + 2.59808i −0.232143 + 0.0927884i
\(785\) −15.0000 −0.535373
\(786\) 0 0
\(787\) 11.0000 19.0526i 0.392108 0.679150i −0.600620 0.799535i \(-0.705079\pi\)
0.992727 + 0.120384i \(0.0384127\pi\)
\(788\) −1.50000 + 2.59808i −0.0534353 + 0.0925526i
\(789\) 0 0