Properties

Label 1950.2.z.j.1699.1
Level $1950$
Weight $2$
Character 1950.1699
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.z (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
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 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1699.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.1699
Dual form 1950.2.z.j.1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(4.33013 - 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(4.33013 - 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} -1.00000i q^{12} +(-2.59808 - 2.50000i) q^{13} -5.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(6.92820 - 4.00000i) q^{17} -1.00000i q^{18} +(-2.50000 - 4.33013i) q^{19} -5.00000 q^{21} +(-2.59808 + 1.50000i) q^{22} +(3.46410 + 2.00000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.00000 + 3.46410i) q^{26} -1.00000i q^{27} +(4.33013 + 2.50000i) q^{28} +(-2.00000 + 3.46410i) q^{29} -2.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.59808 + 1.50000i) q^{33} -8.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-6.06218 - 3.50000i) q^{37} +5.00000i q^{38} +(1.00000 + 3.46410i) q^{39} +(-3.00000 + 5.19615i) q^{41} +(4.33013 + 2.50000i) q^{42} +(5.19615 - 3.00000i) q^{43} +3.00000 q^{44} +(-2.00000 - 3.46410i) q^{46} +3.00000i q^{47} +(0.866025 - 0.500000i) q^{48} +(9.00000 - 15.5885i) q^{49} -8.00000 q^{51} +(0.866025 - 3.50000i) q^{52} +1.00000i q^{53} +(-0.500000 + 0.866025i) q^{54} +(-2.50000 - 4.33013i) q^{56} +5.00000i q^{57} +(3.46410 - 2.00000i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(1.73205 + 1.00000i) q^{62} +(4.33013 + 2.50000i) q^{63} -1.00000 q^{64} +3.00000 q^{66} +(6.92820 + 4.00000i) q^{67} +(6.92820 + 4.00000i) q^{68} +(-2.00000 - 3.46410i) q^{69} +(-1.00000 - 1.73205i) q^{71} +(0.866025 - 0.500000i) q^{72} +(3.50000 + 6.06218i) q^{74} +(2.50000 - 4.33013i) q^{76} -15.0000i q^{77} +(0.866025 - 3.50000i) q^{78} +2.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(5.19615 - 3.00000i) q^{82} +8.00000i q^{83} +(-2.50000 - 4.33013i) q^{84} -6.00000 q^{86} +(3.46410 - 2.00000i) q^{87} +(-2.59808 - 1.50000i) q^{88} +(-5.50000 + 9.52628i) q^{89} +(-17.5000 - 4.33013i) q^{91} +4.00000i q^{92} +(1.73205 + 1.00000i) q^{93} +(1.50000 - 2.59808i) q^{94} -1.00000 q^{96} +(-15.5885 + 9.00000i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + 2q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} + 2q^{6} + 2q^{9} + 6q^{11} - 20q^{14} - 2q^{16} - 10q^{19} - 20q^{21} - 2q^{24} + 4q^{26} - 8q^{29} - 8q^{31} - 32q^{34} - 2q^{36} + 4q^{39} - 12q^{41} + 12q^{44} - 8q^{46} + 36q^{49} - 32q^{51} - 2q^{54} - 10q^{56} + 24q^{59} - 4q^{61} - 4q^{64} + 12q^{66} - 8q^{69} - 4q^{71} + 14q^{74} + 10q^{76} + 8q^{79} - 2q^{81} - 10q^{84} - 24q^{86} - 22q^{89} - 70q^{91} + 6q^{94} - 4q^{96} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) 4.33013 2.50000i 1.63663 0.944911i 0.654654 0.755929i \(-0.272814\pi\)
0.981981 0.188982i \(-0.0605189\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −2.59808 2.50000i −0.720577 0.693375i
\(14\) −5.00000 −1.33631
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 6.92820 4.00000i 1.68034 0.970143i 0.718900 0.695113i \(-0.244646\pi\)
0.961436 0.275029i \(-0.0886875\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −2.50000 4.33013i −0.573539 0.993399i −0.996199 0.0871106i \(-0.972237\pi\)
0.422659 0.906289i \(-0.361097\pi\)
\(20\) 0 0
\(21\) −5.00000 −1.09109
\(22\) −2.59808 + 1.50000i −0.553912 + 0.319801i
\(23\) 3.46410 + 2.00000i 0.722315 + 0.417029i 0.815604 0.578610i \(-0.196405\pi\)
−0.0932891 + 0.995639i \(0.529738\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) 1.00000 + 3.46410i 0.196116 + 0.679366i
\(27\) 1.00000i 0.192450i
\(28\) 4.33013 + 2.50000i 0.818317 + 0.472456i
\(29\) −2.00000 + 3.46410i −0.371391 + 0.643268i −0.989780 0.142605i \(-0.954452\pi\)
0.618389 + 0.785872i \(0.287786\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) −2.59808 + 1.50000i −0.452267 + 0.261116i
\(34\) −8.00000 −1.37199
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −6.06218 3.50000i −0.996616 0.575396i −0.0893706 0.995998i \(-0.528486\pi\)
−0.907245 + 0.420602i \(0.861819\pi\)
\(38\) 5.00000i 0.811107i
\(39\) 1.00000 + 3.46410i 0.160128 + 0.554700i
\(40\) 0 0
\(41\) −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i \(-0.988546\pi\)
0.530831 + 0.847477i \(0.321880\pi\)
\(42\) 4.33013 + 2.50000i 0.668153 + 0.385758i
\(43\) 5.19615 3.00000i 0.792406 0.457496i −0.0484030 0.998828i \(-0.515413\pi\)
0.840809 + 0.541332i \(0.182080\pi\)
\(44\) 3.00000 0.452267
\(45\) 0 0
\(46\) −2.00000 3.46410i −0.294884 0.510754i
\(47\) 3.00000i 0.437595i 0.975770 + 0.218797i \(0.0702134\pi\)
−0.975770 + 0.218797i \(0.929787\pi\)
\(48\) 0.866025 0.500000i 0.125000 0.0721688i
\(49\) 9.00000 15.5885i 1.28571 2.22692i
\(50\) 0 0
\(51\) −8.00000 −1.12022
\(52\) 0.866025 3.50000i 0.120096 0.485363i
\(53\) 1.00000i 0.137361i 0.997639 + 0.0686803i \(0.0218788\pi\)
−0.997639 + 0.0686803i \(0.978121\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −2.50000 4.33013i −0.334077 0.578638i
\(57\) 5.00000i 0.662266i
\(58\) 3.46410 2.00000i 0.454859 0.262613i
\(59\) 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) 0 0
\(61\) −1.00000 1.73205i −0.128037 0.221766i 0.794879 0.606768i \(-0.207534\pi\)
−0.922916 + 0.385002i \(0.874201\pi\)
\(62\) 1.73205 + 1.00000i 0.219971 + 0.127000i
\(63\) 4.33013 + 2.50000i 0.545545 + 0.314970i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 3.00000 0.369274
\(67\) 6.92820 + 4.00000i 0.846415 + 0.488678i 0.859440 0.511237i \(-0.170813\pi\)
−0.0130248 + 0.999915i \(0.504146\pi\)
\(68\) 6.92820 + 4.00000i 0.840168 + 0.485071i
\(69\) −2.00000 3.46410i −0.240772 0.417029i
\(70\) 0 0
\(71\) −1.00000 1.73205i −0.118678 0.205557i 0.800566 0.599245i \(-0.204532\pi\)
−0.919244 + 0.393688i \(0.871199\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 3.50000 + 6.06218i 0.406867 + 0.704714i
\(75\) 0 0
\(76\) 2.50000 4.33013i 0.286770 0.496700i
\(77\) 15.0000i 1.70941i
\(78\) 0.866025 3.50000i 0.0980581 0.396297i
\(79\) 2.00000 0.225018 0.112509 0.993651i \(-0.464111\pi\)
0.112509 + 0.993651i \(0.464111\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 5.19615 3.00000i 0.573819 0.331295i
\(83\) 8.00000i 0.878114i 0.898459 + 0.439057i \(0.144687\pi\)
−0.898459 + 0.439057i \(0.855313\pi\)
\(84\) −2.50000 4.33013i −0.272772 0.472456i
\(85\) 0 0
\(86\) −6.00000 −0.646997
\(87\) 3.46410 2.00000i 0.371391 0.214423i
\(88\) −2.59808 1.50000i −0.276956 0.159901i
\(89\) −5.50000 + 9.52628i −0.582999 + 1.00978i 0.412123 + 0.911128i \(0.364787\pi\)
−0.995122 + 0.0986553i \(0.968546\pi\)
\(90\) 0 0
\(91\) −17.5000 4.33013i −1.83450 0.453921i
\(92\) 4.00000i 0.417029i
\(93\) 1.73205 + 1.00000i 0.179605 + 0.103695i
\(94\) 1.50000 2.59808i 0.154713 0.267971i
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(98\) −15.5885 + 9.00000i −1.57467 + 0.909137i
\(99\) 3.00000 0.301511
\(100\) 0 0
\(101\) 4.00000 6.92820i 0.398015 0.689382i −0.595466 0.803380i \(-0.703033\pi\)
0.993481 + 0.113998i \(0.0363659\pi\)
\(102\) 6.92820 + 4.00000i 0.685994 + 0.396059i
\(103\) 7.00000i 0.689730i −0.938652 0.344865i \(-0.887925\pi\)
0.938652 0.344865i \(-0.112075\pi\)
\(104\) −2.50000 + 2.59808i −0.245145 + 0.254762i
\(105\) 0 0
\(106\) 0.500000 0.866025i 0.0485643 0.0841158i
\(107\) −5.19615 3.00000i −0.502331 0.290021i 0.227345 0.973814i \(-0.426996\pi\)
−0.729676 + 0.683793i \(0.760329\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) −14.0000 −1.34096 −0.670478 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) 0 0
\(111\) 3.50000 + 6.06218i 0.332205 + 0.575396i
\(112\) 5.00000i 0.472456i
\(113\) 6.92820 4.00000i 0.651751 0.376288i −0.137376 0.990519i \(-0.543867\pi\)
0.789127 + 0.614231i \(0.210534\pi\)
\(114\) 2.50000 4.33013i 0.234146 0.405554i
\(115\) 0 0
\(116\) −4.00000 −0.371391
\(117\) 0.866025 3.50000i 0.0800641 0.323575i
\(118\) 12.0000i 1.10469i
\(119\) 20.0000 34.6410i 1.83340 3.17554i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 2.00000i 0.181071i
\(123\) 5.19615 3.00000i 0.468521 0.270501i
\(124\) −1.00000 1.73205i −0.0898027 0.155543i
\(125\) 0 0
\(126\) −2.50000 4.33013i −0.222718 0.385758i
\(127\) −18.1865 10.5000i −1.61379 0.931724i −0.988480 0.151351i \(-0.951638\pi\)
−0.625314 0.780373i \(-0.715029\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −6.00000 −0.528271
\(130\) 0 0
\(131\) −19.0000 −1.66004 −0.830019 0.557735i \(-0.811670\pi\)
−0.830019 + 0.557735i \(0.811670\pi\)
\(132\) −2.59808 1.50000i −0.226134 0.130558i
\(133\) −21.6506 12.5000i −1.87735 1.08389i
\(134\) −4.00000 6.92820i −0.345547 0.598506i
\(135\) 0 0
\(136\) −4.00000 6.92820i −0.342997 0.594089i
\(137\) 10.3923 6.00000i 0.887875 0.512615i 0.0146279 0.999893i \(-0.495344\pi\)
0.873247 + 0.487278i \(0.162010\pi\)
\(138\) 4.00000i 0.340503i
\(139\) 3.50000 + 6.06218i 0.296866 + 0.514187i 0.975417 0.220366i \(-0.0707252\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) 1.50000 2.59808i 0.126323 0.218797i
\(142\) 2.00000i 0.167836i
\(143\) −10.3923 + 3.00000i −0.869048 + 0.250873i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 0 0
\(147\) −15.5885 + 9.00000i −1.28571 + 0.742307i
\(148\) 7.00000i 0.575396i
\(149\) −1.00000 1.73205i −0.0819232 0.141895i 0.822153 0.569267i \(-0.192773\pi\)
−0.904076 + 0.427372i \(0.859440\pi\)
\(150\) 0 0
\(151\) 22.0000 1.79033 0.895167 0.445730i \(-0.147056\pi\)
0.895167 + 0.445730i \(0.147056\pi\)
\(152\) −4.33013 + 2.50000i −0.351220 + 0.202777i
\(153\) 6.92820 + 4.00000i 0.560112 + 0.323381i
\(154\) −7.50000 + 12.9904i −0.604367 + 1.04679i
\(155\) 0 0
\(156\) −2.50000 + 2.59808i −0.200160 + 0.208013i
\(157\) 15.0000i 1.19713i −0.801074 0.598565i \(-0.795738\pi\)
0.801074 0.598565i \(-0.204262\pi\)
\(158\) −1.73205 1.00000i −0.137795 0.0795557i
\(159\) 0.500000 0.866025i 0.0396526 0.0686803i
\(160\) 0 0
\(161\) 20.0000 1.57622
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) −17.3205 + 10.0000i −1.35665 + 0.783260i −0.989170 0.146772i \(-0.953112\pi\)
−0.367477 + 0.930033i \(0.619778\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) 4.00000 6.92820i 0.310460 0.537733i
\(167\) −19.9186 11.5000i −1.54135 0.889897i −0.998754 0.0499004i \(-0.984110\pi\)
−0.542592 0.839996i \(-0.682557\pi\)
\(168\) 5.00000i 0.385758i
\(169\) 0.500000 + 12.9904i 0.0384615 + 0.999260i
\(170\) 0 0
\(171\) 2.50000 4.33013i 0.191180 0.331133i
\(172\) 5.19615 + 3.00000i 0.396203 + 0.228748i
\(173\) 4.33013 2.50000i 0.329213 0.190071i −0.326278 0.945274i \(-0.605795\pi\)
0.655492 + 0.755202i \(0.272461\pi\)
\(174\) −4.00000 −0.303239
\(175\) 0 0
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) 12.0000i 0.901975i
\(178\) 9.52628 5.50000i 0.714025 0.412242i
\(179\) 2.00000 3.46410i 0.149487 0.258919i −0.781551 0.623841i \(-0.785571\pi\)
0.931038 + 0.364922i \(0.118904\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 12.9904 + 12.5000i 0.962911 + 0.926562i
\(183\) 2.00000i 0.147844i
\(184\) 2.00000 3.46410i 0.147442 0.255377i
\(185\) 0 0
\(186\) −1.00000 1.73205i −0.0733236 0.127000i
\(187\) 24.0000i 1.75505i
\(188\) −2.59808 + 1.50000i −0.189484 + 0.109399i
\(189\) −2.50000 4.33013i −0.181848 0.314970i
\(190\) 0 0
\(191\) −1.00000 1.73205i −0.0723575 0.125327i 0.827577 0.561353i \(-0.189719\pi\)
−0.899934 + 0.436026i \(0.856386\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) −20.7846 12.0000i −1.49611 0.863779i −0.496119 0.868255i \(-0.665242\pi\)
−0.999990 + 0.00447566i \(0.998575\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 18.0000 1.28571
\(197\) 2.59808 + 1.50000i 0.185105 + 0.106871i 0.589689 0.807630i \(-0.299250\pi\)
−0.404584 + 0.914501i \(0.632584\pi\)
\(198\) −2.59808 1.50000i −0.184637 0.106600i
\(199\) 11.0000 + 19.0526i 0.779769 + 1.35060i 0.932075 + 0.362267i \(0.117997\pi\)
−0.152305 + 0.988334i \(0.548670\pi\)
\(200\) 0 0
\(201\) −4.00000 6.92820i −0.282138 0.488678i
\(202\) −6.92820 + 4.00000i −0.487467 + 0.281439i
\(203\) 20.0000i 1.40372i
\(204\) −4.00000 6.92820i −0.280056 0.485071i
\(205\) 0 0
\(206\) −3.50000 + 6.06218i −0.243857 + 0.422372i
\(207\) 4.00000i 0.278019i
\(208\) 3.46410 1.00000i 0.240192 0.0693375i
\(209\) −15.0000 −1.03757
\(210\) 0 0
\(211\) 7.50000 12.9904i 0.516321 0.894295i −0.483499 0.875345i \(-0.660634\pi\)
0.999820 0.0189499i \(-0.00603229\pi\)
\(212\) −0.866025 + 0.500000i −0.0594789 + 0.0343401i
\(213\) 2.00000i 0.137038i
\(214\) 3.00000 + 5.19615i 0.205076 + 0.355202i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −8.66025 + 5.00000i −0.587896 + 0.339422i
\(218\) 12.1244 + 7.00000i 0.821165 + 0.474100i
\(219\) 0 0
\(220\) 0 0
\(221\) −28.0000 6.92820i −1.88348 0.466041i
\(222\) 7.00000i 0.469809i
\(223\) 2.59808 + 1.50000i 0.173980 + 0.100447i 0.584461 0.811422i \(-0.301306\pi\)
−0.410481 + 0.911869i \(0.634639\pi\)
\(224\) 2.50000 4.33013i 0.167038 0.289319i
\(225\) 0 0
\(226\) −8.00000 −0.532152
\(227\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(228\) −4.33013 + 2.50000i −0.286770 + 0.165567i
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) −7.50000 + 12.9904i −0.493464 + 0.854704i
\(232\) 3.46410 + 2.00000i 0.227429 + 0.131306i
\(233\) 14.0000i 0.917170i −0.888650 0.458585i \(-0.848356\pi\)
0.888650 0.458585i \(-0.151644\pi\)
\(234\) −2.50000 + 2.59808i −0.163430 + 0.169842i
\(235\) 0 0
\(236\) −6.00000 + 10.3923i −0.390567 + 0.676481i
\(237\) −1.73205 1.00000i −0.112509 0.0649570i
\(238\) −34.6410 + 20.0000i −2.24544 + 1.29641i
\(239\) 18.0000 1.16432 0.582162 0.813073i \(-0.302207\pi\)
0.582162 + 0.813073i \(0.302207\pi\)
\(240\) 0 0
\(241\) 12.5000 + 21.6506i 0.805196 + 1.39464i 0.916159 + 0.400815i \(0.131273\pi\)
−0.110963 + 0.993825i \(0.535394\pi\)
\(242\) 2.00000i 0.128565i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) 1.00000 1.73205i 0.0640184 0.110883i
\(245\) 0 0
\(246\) −6.00000 −0.382546
\(247\) −4.33013 + 17.5000i −0.275519 + 1.11350i
\(248\) 2.00000i 0.127000i
\(249\) 4.00000 6.92820i 0.253490 0.439057i
\(250\) 0 0
\(251\) −7.50000 12.9904i −0.473396 0.819946i 0.526140 0.850398i \(-0.323639\pi\)
−0.999536 + 0.0304521i \(0.990305\pi\)
\(252\) 5.00000i 0.314970i
\(253\) 10.3923 6.00000i 0.653359 0.377217i
\(254\) 10.5000 + 18.1865i 0.658829 + 1.14112i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 24.2487 + 14.0000i 1.51259 + 0.873296i 0.999892 + 0.0147291i \(0.00468859\pi\)
0.512702 + 0.858567i \(0.328645\pi\)
\(258\) 5.19615 + 3.00000i 0.323498 + 0.186772i
\(259\) −35.0000 −2.17479
\(260\) 0 0
\(261\) −4.00000 −0.247594
\(262\) 16.4545 + 9.50000i 1.01656 + 0.586912i
\(263\) 12.9904 + 7.50000i 0.801021 + 0.462470i 0.843828 0.536614i \(-0.180297\pi\)
−0.0428069 + 0.999083i \(0.513630\pi\)
\(264\) 1.50000 + 2.59808i 0.0923186 + 0.159901i
\(265\) 0 0
\(266\) 12.5000 + 21.6506i 0.766424 + 1.32749i
\(267\) 9.52628 5.50000i 0.582999 0.336595i
\(268\) 8.00000i 0.488678i
\(269\) 2.00000 + 3.46410i 0.121942 + 0.211210i 0.920534 0.390664i \(-0.127754\pi\)
−0.798591 + 0.601874i \(0.794421\pi\)
\(270\) 0 0
\(271\) −2.00000 + 3.46410i −0.121491 + 0.210429i −0.920356 0.391082i \(-0.872101\pi\)
0.798865 + 0.601511i \(0.205434\pi\)
\(272\) 8.00000i 0.485071i
\(273\) 12.9904 + 12.5000i 0.786214 + 0.756534i
\(274\) −12.0000 −0.724947
\(275\) 0 0
\(276\) 2.00000 3.46410i 0.120386 0.208514i
\(277\) 12.9904 7.50000i 0.780516 0.450631i −0.0560969 0.998425i \(-0.517866\pi\)
0.836613 + 0.547794i \(0.184532\pi\)
\(278\) 7.00000i 0.419832i
\(279\) −1.00000 1.73205i −0.0598684 0.103695i
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) −2.59808 + 1.50000i −0.154713 + 0.0893237i
\(283\) 8.66025 + 5.00000i 0.514799 + 0.297219i 0.734804 0.678280i \(-0.237274\pi\)
−0.220005 + 0.975499i \(0.570607\pi\)
\(284\) 1.00000 1.73205i 0.0593391 0.102778i
\(285\) 0 0
\(286\) 10.5000 + 2.59808i 0.620878 + 0.153627i
\(287\) 30.0000i 1.77084i
\(288\) 0.866025 + 0.500000i 0.0510310 + 0.0294628i
\(289\) 23.5000 40.7032i 1.38235 2.39431i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7.79423 + 4.50000i −0.455344 + 0.262893i −0.710084 0.704117i \(-0.751343\pi\)
0.254741 + 0.967009i \(0.418010\pi\)
\(294\) 18.0000 1.04978
\(295\) 0 0
\(296\) −3.50000 + 6.06218i −0.203433 + 0.352357i
\(297\) −2.59808 1.50000i −0.150756 0.0870388i
\(298\) 2.00000i 0.115857i
\(299\) −4.00000 13.8564i −0.231326 0.801337i
\(300\) 0 0
\(301\) 15.0000 25.9808i 0.864586 1.49751i
\(302\) −19.0526 11.0000i −1.09635 0.632979i
\(303\) −6.92820 + 4.00000i −0.398015 + 0.229794i
\(304\) 5.00000 0.286770
\(305\) 0 0
\(306\) −4.00000 6.92820i −0.228665 0.396059i
\(307\) 6.00000i 0.342438i 0.985233 + 0.171219i \(0.0547706\pi\)
−0.985233 + 0.171219i \(0.945229\pi\)
\(308\) 12.9904 7.50000i 0.740196 0.427352i
\(309\) −3.50000 + 6.06218i −0.199108 + 0.344865i
\(310\) 0 0
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 3.46410 1.00000i 0.196116 0.0566139i
\(313\) 6.00000i 0.339140i −0.985518 0.169570i \(-0.945762\pi\)
0.985518 0.169570i \(-0.0542379\pi\)
\(314\) −7.50000 + 12.9904i −0.423249 + 0.733090i
\(315\) 0 0
\(316\) 1.00000 + 1.73205i 0.0562544 + 0.0974355i
\(317\) 23.0000i 1.29181i 0.763418 + 0.645904i \(0.223520\pi\)
−0.763418 + 0.645904i \(0.776480\pi\)
\(318\) −0.866025 + 0.500000i −0.0485643 + 0.0280386i
\(319\) 6.00000 + 10.3923i 0.335936 + 0.581857i
\(320\) 0 0
\(321\) 3.00000 + 5.19615i 0.167444 + 0.290021i
\(322\) −17.3205 10.0000i −0.965234 0.557278i
\(323\) −34.6410 20.0000i −1.92748 1.11283i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) 20.0000 1.10770
\(327\) 12.1244 + 7.00000i 0.670478 + 0.387101i
\(328\) 5.19615 + 3.00000i 0.286910 + 0.165647i
\(329\) 7.50000 + 12.9904i 0.413488 + 0.716183i
\(330\) 0 0
\(331\) −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i \(-0.201729\pi\)
−0.915742 + 0.401768i \(0.868396\pi\)
\(332\) −6.92820 + 4.00000i −0.380235 + 0.219529i
\(333\) 7.00000i 0.383598i
\(334\) 11.5000 + 19.9186i 0.629252 + 1.08990i
\(335\) 0 0
\(336\) 2.50000 4.33013i 0.136386 0.236228i
\(337\) 14.0000i 0.762629i −0.924445 0.381314i \(-0.875472\pi\)
0.924445 0.381314i \(-0.124528\pi\)
\(338\) 6.06218 11.5000i 0.329739 0.625518i
\(339\) −8.00000 −0.434500
\(340\) 0 0
\(341\) −3.00000 + 5.19615i −0.162459 + 0.281387i
\(342\) −4.33013 + 2.50000i −0.234146 + 0.135185i
\(343\) 55.0000i 2.96972i
\(344\) −3.00000 5.19615i −0.161749 0.280158i
\(345\) 0 0
\(346\) −5.00000 −0.268802
\(347\) 13.8564 8.00000i 0.743851 0.429463i −0.0796169 0.996826i \(-0.525370\pi\)
0.823468 + 0.567363i \(0.192036\pi\)
\(348\) 3.46410 + 2.00000i 0.185695 + 0.107211i
\(349\) 4.00000 6.92820i 0.214115 0.370858i −0.738883 0.673833i \(-0.764647\pi\)
0.952998 + 0.302975i \(0.0979799\pi\)
\(350\) 0 0
\(351\) −2.50000 + 2.59808i −0.133440 + 0.138675i
\(352\) 3.00000i 0.159901i
\(353\) −13.8564 8.00000i −0.737502 0.425797i 0.0836583 0.996495i \(-0.473340\pi\)
−0.821160 + 0.570697i \(0.806673\pi\)
\(354\) −6.00000 + 10.3923i −0.318896 + 0.552345i
\(355\) 0 0
\(356\) −11.0000 −0.582999
\(357\) −34.6410 + 20.0000i −1.83340 + 1.05851i
\(358\) −3.46410 + 2.00000i −0.183083 + 0.105703i
\(359\) 18.0000 0.950004 0.475002 0.879985i \(-0.342447\pi\)
0.475002 + 0.879985i \(0.342447\pi\)
\(360\) 0 0
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) 1.73205 + 1.00000i 0.0910346 + 0.0525588i
\(363\) 2.00000i 0.104973i
\(364\) −5.00000 17.3205i −0.262071 0.907841i
\(365\) 0 0
\(366\) 1.00000 1.73205i 0.0522708 0.0905357i
\(367\) −6.92820 4.00000i −0.361649 0.208798i 0.308155 0.951336i \(-0.400289\pi\)
−0.669804 + 0.742538i \(0.733622\pi\)
\(368\) −3.46410 + 2.00000i −0.180579 + 0.104257i
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) 2.50000 + 4.33013i 0.129794 + 0.224809i
\(372\) 2.00000i 0.103695i
\(373\) 32.9090 19.0000i 1.70396 0.983783i 0.762299 0.647225i \(-0.224071\pi\)
0.941663 0.336557i \(-0.109263\pi\)
\(374\) −12.0000 + 20.7846i −0.620505 + 1.07475i
\(375\) 0 0
\(376\) 3.00000 0.154713
\(377\) 13.8564 4.00000i 0.713641 0.206010i
\(378\) 5.00000i 0.257172i
\(379\) −12.5000 + 21.6506i −0.642082 + 1.11212i 0.342885 + 0.939377i \(0.388596\pi\)
−0.984967 + 0.172741i \(0.944738\pi\)
\(380\) 0 0
\(381\) 10.5000 + 18.1865i 0.537931 + 0.931724i
\(382\) 2.00000i 0.102329i
\(383\) −24.2487 + 14.0000i −1.23905 + 0.715367i −0.968900 0.247451i \(-0.920407\pi\)
−0.270151 + 0.962818i \(0.587074\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 0 0
\(386\) 12.0000 + 20.7846i 0.610784 + 1.05791i
\(387\) 5.19615 + 3.00000i 0.264135 + 0.152499i
\(388\) 0 0
\(389\) 32.0000 1.62246 0.811232 0.584724i \(-0.198797\pi\)
0.811232 + 0.584724i \(0.198797\pi\)
\(390\) 0 0
\(391\) 32.0000 1.61831
\(392\) −15.5885 9.00000i −0.787336 0.454569i
\(393\) 16.4545 + 9.50000i 0.830019 + 0.479212i
\(394\) −1.50000 2.59808i −0.0755689 0.130889i
\(395\) 0 0
\(396\) 1.50000 + 2.59808i 0.0753778 + 0.130558i
\(397\) −21.6506 + 12.5000i −1.08661 + 0.627357i −0.932673 0.360723i \(-0.882530\pi\)
−0.153941 + 0.988080i \(0.549197\pi\)
\(398\) 22.0000i 1.10276i
\(399\) 12.5000 + 21.6506i 0.625783 + 1.08389i
\(400\) 0 0
\(401\) 9.50000 16.4545i 0.474407 0.821698i −0.525163 0.851002i \(-0.675996\pi\)
0.999571 + 0.0293039i \(0.00932905\pi\)
\(402\) 8.00000i 0.399004i
\(403\) 5.19615 + 5.00000i 0.258839 + 0.249068i
\(404\) 8.00000 0.398015
\(405\) 0 0
\(406\) 10.0000 17.3205i 0.496292 0.859602i
\(407\) −18.1865 + 10.5000i −0.901473 + 0.520466i
\(408\) 8.00000i 0.396059i
\(409\) 12.5000 + 21.6506i 0.618085 + 1.07056i 0.989835 + 0.142222i \(0.0454247\pi\)
−0.371750 + 0.928333i \(0.621242\pi\)
\(410\) 0 0
\(411\) −12.0000 −0.591916
\(412\) 6.06218 3.50000i 0.298662 0.172433i
\(413\) 51.9615 + 30.0000i 2.55686 + 1.47620i
\(414\) 2.00000 3.46410i 0.0982946 0.170251i
\(415\) 0 0
\(416\) −3.50000 0.866025i −0.171602 0.0424604i
\(417\) 7.00000i 0.342791i
\(418\) 12.9904 + 7.50000i 0.635380 + 0.366837i
\(419\) −6.00000 + 10.3923i −0.293119 + 0.507697i −0.974546 0.224189i \(-0.928027\pi\)
0.681426 + 0.731887i \(0.261360\pi\)
\(420\) 0 0
\(421\) 12.0000 0.584844 0.292422 0.956289i \(-0.405539\pi\)
0.292422 + 0.956289i \(0.405539\pi\)
\(422\) −12.9904 + 7.50000i −0.632362 + 0.365094i
\(423\) −2.59808 + 1.50000i −0.126323 + 0.0729325i
\(424\) 1.00000 0.0485643
\(425\) 0 0
\(426\) 1.00000 1.73205i 0.0484502 0.0839181i
\(427\) −8.66025 5.00000i −0.419099 0.241967i
\(428\) 6.00000i 0.290021i
\(429\) 10.5000 + 2.59808i 0.506945 + 0.125436i
\(430\) 0 0
\(431\) −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i \(-0.926659\pi\)
0.684564 + 0.728953i \(0.259993\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) 13.8564 8.00000i 0.665896 0.384455i −0.128624 0.991693i \(-0.541056\pi\)
0.794520 + 0.607238i \(0.207723\pi\)
\(434\) 10.0000 0.480015
\(435\) 0 0
\(436\) −7.00000 12.1244i −0.335239 0.580651i
\(437\) 20.0000i 0.956730i
\(438\) 0 0
\(439\) 5.00000 8.66025i 0.238637 0.413331i −0.721686 0.692220i \(-0.756633\pi\)
0.960323 + 0.278889i \(0.0899661\pi\)
\(440\) 0 0
\(441\) 18.0000 0.857143
\(442\) 20.7846 + 20.0000i 0.988623 + 0.951303i
\(443\) 6.00000i 0.285069i 0.989790 + 0.142534i \(0.0455251\pi\)
−0.989790 + 0.142534i \(0.954475\pi\)
\(444\) −3.50000 + 6.06218i −0.166103 + 0.287698i
\(445\) 0 0
\(446\) −1.50000 2.59808i −0.0710271 0.123022i
\(447\) 2.00000i 0.0945968i
\(448\) −4.33013 + 2.50000i −0.204579 + 0.118114i
\(449\) −13.5000 23.3827i −0.637104 1.10350i −0.986065 0.166360i \(-0.946799\pi\)
0.348961 0.937137i \(-0.386535\pi\)
\(450\) 0 0
\(451\) 9.00000 + 15.5885i 0.423793 + 0.734032i
\(452\) 6.92820 + 4.00000i 0.325875 + 0.188144i
\(453\) −19.0526 11.0000i −0.895167 0.516825i
\(454\) 0 0
\(455\) 0 0
\(456\) 5.00000 0.234146
\(457\) 25.9808 + 15.0000i 1.21533 + 0.701670i 0.963915 0.266209i \(-0.0857713\pi\)
0.251414 + 0.967880i \(0.419105\pi\)
\(458\) 12.1244 + 7.00000i 0.566534 + 0.327089i
\(459\) −4.00000 6.92820i −0.186704 0.323381i
\(460\) 0 0
\(461\) −4.00000 6.92820i −0.186299 0.322679i 0.757715 0.652586i \(-0.226316\pi\)
−0.944013 + 0.329907i \(0.892983\pi\)
\(462\) 12.9904 7.50000i 0.604367 0.348932i
\(463\) 8.00000i 0.371792i 0.982569 + 0.185896i \(0.0595187\pi\)
−0.982569 + 0.185896i \(0.940481\pi\)
\(464\) −2.00000 3.46410i −0.0928477 0.160817i
\(465\) 0 0
\(466\) −7.00000 + 12.1244i −0.324269 + 0.561650i
\(467\) 24.0000i 1.11059i 0.831654 + 0.555294i \(0.187394\pi\)
−0.831654 + 0.555294i \(0.812606\pi\)
\(468\) 3.46410 1.00000i 0.160128 0.0462250i
\(469\) 40.0000 1.84703
\(470\) 0 0
\(471\) −7.50000 + 12.9904i −0.345582 + 0.598565i
\(472\) 10.3923 6.00000i 0.478345 0.276172i
\(473\) 18.0000i 0.827641i
\(474\) 1.00000 + 1.73205i 0.0459315 + 0.0795557i
\(475\) 0 0
\(476\) 40.0000 1.83340
\(477\) −0.866025 + 0.500000i −0.0396526 + 0.0228934i
\(478\) −15.5885 9.00000i −0.712999 0.411650i
\(479\) −14.0000 + 24.2487i −0.639676 + 1.10795i 0.345827 + 0.938298i \(0.387598\pi\)
−0.985504 + 0.169654i \(0.945735\pi\)
\(480\) 0 0
\(481\) 7.00000 + 24.2487i 0.319173 + 1.10565i
\(482\) 25.0000i 1.13872i
\(483\) −17.3205 10.0000i −0.788110 0.455016i
\(484\) −1.00000 + 1.73205i −0.0454545 + 0.0787296i
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) −32.0429 + 18.5000i −1.45200 + 0.838315i −0.998595 0.0529875i \(-0.983126\pi\)
−0.453409 + 0.891303i \(0.649792\pi\)
\(488\) −1.73205 + 1.00000i −0.0784063 + 0.0452679i
\(489\) 20.0000 0.904431
\(490\) 0 0
\(491\) −10.5000 + 18.1865i −0.473858 + 0.820747i −0.999552 0.0299272i \(-0.990472\pi\)
0.525694 + 0.850674i \(0.323806\pi\)
\(492\) 5.19615 + 3.00000i 0.234261 + 0.135250i
\(493\) 32.0000i 1.44121i
\(494\) 12.5000 12.9904i 0.562402 0.584465i
\(495\) 0 0
\(496\) 1.00000 1.73205i 0.0449013 0.0777714i
\(497\) −8.66025 5.00000i −0.388465 0.224281i
\(498\) −6.92820 + 4.00000i −0.310460 + 0.179244i
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) 11.5000 + 19.9186i 0.513782 + 0.889897i
\(502\) 15.0000i 0.669483i
\(503\) −9.52628 + 5.50000i −0.424756 + 0.245233i −0.697110 0.716964i \(-0.745531\pi\)
0.272354 + 0.962197i \(0.412198\pi\)
\(504\) 2.50000 4.33013i 0.111359 0.192879i
\(505\) 0 0
\(506\) −12.0000 −0.533465
\(507\) 6.06218 11.5000i 0.269231 0.510733i
\(508\) 21.0000i 0.931724i
\(509\) 5.00000 8.66025i 0.221621 0.383859i −0.733679 0.679496i \(-0.762199\pi\)
0.955300 + 0.295637i \(0.0955319\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) −4.33013 + 2.50000i −0.191180 + 0.110378i
\(514\) −14.0000 24.2487i −0.617514 1.06956i
\(515\) 0 0
\(516\) −3.00000 5.19615i −0.132068 0.228748i
\(517\) 7.79423 + 4.50000i 0.342790 + 0.197910i
\(518\) 30.3109 + 17.5000i 1.33178 + 0.768906i
\(519\) −5.00000 −0.219476
\(520\) 0 0
\(521\) 5.00000 0.219054 0.109527 0.993984i \(-0.465066\pi\)
0.109527 + 0.993984i \(0.465066\pi\)
\(522\) 3.46410 + 2.00000i 0.151620 + 0.0875376i
\(523\) 8.66025 + 5.00000i 0.378686 + 0.218635i 0.677247 0.735756i \(-0.263173\pi\)
−0.298560 + 0.954391i \(0.596506\pi\)
\(524\) −9.50000 16.4545i −0.415009 0.718817i
\(525\) 0 0
\(526\) −7.50000 12.9904i −0.327016 0.566408i
\(527\) −13.8564 + 8.00000i −0.603595 + 0.348485i
\(528\) 3.00000i 0.130558i
\(529\) −3.50000 6.06218i −0.152174 0.263573i
\(530\) 0 0
\(531\) −6.00000 + 10.3923i −0.260378 + 0.450988i
\(532\) 25.0000i 1.08389i
\(533\) 20.7846 6.00000i 0.900281 0.259889i
\(534\) −11.0000 −0.476017
\(535\) 0 0
\(536\) 4.00000 6.92820i 0.172774 0.299253i
\(537\) −3.46410 + 2.00000i −0.149487 + 0.0863064i
\(538\) 4.00000i 0.172452i
\(539\) −27.0000 46.7654i −1.16297 2.01433i
\(540\) 0 0
\(541\) 34.0000 1.46177 0.730887 0.682498i \(-0.239107\pi\)
0.730887 + 0.682498i \(0.239107\pi\)
\(542\) 3.46410 2.00000i 0.148796 0.0859074i
\(543\) 1.73205 + 1.00000i 0.0743294 + 0.0429141i
\(544\) 4.00000 6.92820i 0.171499 0.297044i
\(545\) 0 0
\(546\) −5.00000 17.3205i −0.213980 0.741249i
\(547\) 6.00000i 0.256541i −0.991739 0.128271i \(-0.959057\pi\)
0.991739 0.128271i \(-0.0409426\pi\)
\(548\) 10.3923 + 6.00000i 0.443937 + 0.256307i
\(549\) 1.00000 1.73205i 0.0426790 0.0739221i
\(550\) 0 0
\(551\) 20.0000 0.852029
\(552\) −3.46410 + 2.00000i −0.147442 + 0.0851257i
\(553\) 8.66025 5.00000i 0.368271 0.212622i
\(554\) −15.0000 −0.637289
\(555\) 0 0
\(556\) −3.50000 + 6.06218i −0.148433 + 0.257094i
\(557\) 12.9904 + 7.50000i 0.550420 + 0.317785i 0.749291 0.662240i \(-0.230394\pi\)
−0.198871 + 0.980026i \(0.563728\pi\)
\(558\) 2.00000i 0.0846668i
\(559\) −21.0000 5.19615i −0.888205 0.219774i
\(560\) 0 0
\(561\) −12.0000 + 20.7846i −0.506640 + 0.877527i
\(562\) −15.5885 9.00000i −0.657559 0.379642i
\(563\) 31.1769 18.0000i 1.31395 0.758610i 0.331202 0.943560i \(-0.392546\pi\)
0.982748 + 0.184950i \(0.0592124\pi\)
\(564\) 3.00000 0.126323
\(565\) 0 0
\(566\) −5.00000 8.66025i −0.210166 0.364018i
\(567\) 5.00000i 0.209980i
\(568\) −1.73205 + 1.00000i −0.0726752 + 0.0419591i
\(569\) −7.50000 + 12.9904i −0.314416 + 0.544585i −0.979313 0.202350i \(-0.935142\pi\)
0.664897 + 0.746935i \(0.268475\pi\)
\(570\) 0 0
\(571\) −33.0000 −1.38101 −0.690504 0.723329i \(-0.742611\pi\)
−0.690504 + 0.723329i \(0.742611\pi\)
\(572\) −7.79423 7.50000i −0.325893 0.313591i
\(573\) 2.00000i 0.0835512i
\(574\) 15.0000 25.9808i 0.626088 1.08442i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 2.00000i 0.0832611i −0.999133 0.0416305i \(-0.986745\pi\)
0.999133 0.0416305i \(-0.0132552\pi\)
\(578\) −40.7032 + 23.5000i −1.69303 + 0.977471i
\(579\) 12.0000 + 20.7846i 0.498703 + 0.863779i
\(580\) 0 0
\(581\) 20.0000 + 34.6410i 0.829740 + 1.43715i
\(582\) 0 0
\(583\) 2.59808 + 1.50000i 0.107601 + 0.0621237i
\(584\) 0 0
\(585\) 0 0
\(586\) 9.00000 0.371787
\(587\) 15.5885 + 9.00000i 0.643404 + 0.371470i 0.785925 0.618322i \(-0.212187\pi\)
−0.142520 + 0.989792i \(0.545521\pi\)
\(588\) −15.5885 9.00000i −0.642857 0.371154i
\(589\) 5.00000 + 8.66025i 0.206021 + 0.356840i
\(590\) 0 0
\(591\) −1.50000 2.59808i −0.0617018 0.106871i
\(592\) 6.06218 3.50000i 0.249154 0.143849i
\(593\) 20.0000i 0.821302i 0.911793 + 0.410651i \(0.134698\pi\)
−0.911793 + 0.410651i \(0.865302\pi\)
\(594\) 1.50000 + 2.59808i 0.0615457 + 0.106600i
\(595\) 0 0
\(596\) 1.00000 1.73205i 0.0409616 0.0709476i
\(597\) 22.0000i 0.900400i
\(598\) −3.46410 + 14.0000i −0.141658 + 0.572503i
\(599\) −34.0000 −1.38920 −0.694601 0.719395i \(-0.744419\pi\)
−0.694601 + 0.719395i \(0.744419\pi\)
\(600\) 0 0
\(601\) −18.5000 + 32.0429i −0.754631 + 1.30706i 0.190927 + 0.981604i \(0.438851\pi\)
−0.945558 + 0.325455i \(0.894483\pi\)
\(602\) −25.9808 + 15.0000i −1.05890 + 0.611354i
\(603\) 8.00000i 0.325785i
\(604\) 11.0000 + 19.0526i 0.447584 + 0.775238i
\(605\) 0 0
\(606\) 8.00000 0.324978
\(607\) 25.1147 14.5000i 1.01938 0.588537i 0.105453 0.994424i \(-0.466371\pi\)
0.913923 + 0.405887i \(0.133038\pi\)
\(608\) −4.33013 2.50000i −0.175610 0.101388i
\(609\) 10.0000 17.3205i 0.405220 0.701862i
\(610\) 0 0
\(611\) 7.50000 7.79423i 0.303418 0.315321i
\(612\) 8.00000i 0.323381i
\(613\) −21.6506 12.5000i −0.874461 0.504870i −0.00563283 0.999984i \(-0.501793\pi\)
−0.868828 + 0.495114i \(0.835126\pi\)
\(614\) 3.00000 5.19615i 0.121070 0.209700i
\(615\) 0 0
\(616\) −15.0000 −0.604367
\(617\) 12.1244 7.00000i 0.488108 0.281809i −0.235681 0.971830i \(-0.575732\pi\)
0.723789 + 0.690021i \(0.242399\pi\)
\(618\) 6.06218 3.50000i 0.243857 0.140791i
\(619\) −17.0000 −0.683288 −0.341644 0.939829i \(-0.610984\pi\)
−0.341644 + 0.939829i \(0.610984\pi\)
\(620\) 0 0
\(621\) 2.00000 3.46410i 0.0802572 0.139010i
\(622\) 10.3923 + 6.00000i 0.416693 + 0.240578i
\(623\) 55.0000i 2.20353i
\(624\) −3.50000 0.866025i −0.140112 0.0346688i
\(625\) 0 0
\(626\) −3.00000 + 5.19615i −0.119904 + 0.207680i
\(627\) 12.9904 + 7.50000i 0.518786 + 0.299521i
\(628\) 12.9904 7.50000i 0.518373 0.299283i
\(629\) −56.0000 −2.23287
\(630\) 0 0
\(631\) −6.00000 10.3923i −0.238856 0.413711i 0.721530 0.692383i \(-0.243439\pi\)
−0.960386 + 0.278672i \(0.910106\pi\)
\(632\) 2.00000i 0.0795557i
\(633\) −12.9904 + 7.50000i −0.516321 + 0.298098i
\(634\) 11.5000 19.9186i 0.456723 0.791068i
\(635\) 0 0
\(636\) 1.00000 0.0396526
\(637\) −62.3538 + 18.0000i −2.47055 + 0.713186i
\(638\) 12.0000i 0.475085i
\(639\) 1.00000 1.73205i 0.0395594 0.0685189i
\(640\) 0 0
\(641\) −13.5000 23.3827i −0.533218 0.923561i −0.999247 0.0387913i \(-0.987649\pi\)
0.466029 0.884769i \(-0.345684\pi\)
\(642\) 6.00000i 0.236801i
\(643\) −38.1051 + 22.0000i −1.50272 + 0.867595i −0.502724 + 0.864447i \(0.667669\pi\)
−0.999995 + 0.00314839i \(0.998998\pi\)
\(644\) 10.0000 + 17.3205i 0.394055 + 0.682524i
\(645\) 0 0
\(646\) 20.0000 + 34.6410i 0.786889 + 1.36293i
\(647\) 2.59808 + 1.50000i 0.102141 + 0.0589711i 0.550200 0.835033i \(-0.314551\pi\)
−0.448059 + 0.894004i \(0.647885\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) 36.0000 1.41312
\(650\) 0 0
\(651\) 10.0000 0.391931
\(652\) −17.3205 10.0000i −0.678323 0.391630i
\(653\) −23.3827 13.5000i −0.915035 0.528296i −0.0329874 0.999456i \(-0.510502\pi\)
−0.882048 + 0.471160i \(0.843835\pi\)
\(654\) −7.00000 12.1244i −0.273722 0.474100i
\(655\) 0 0
\(656\) −3.00000 5.19615i −0.117130 0.202876i
\(657\) 0 0
\(658\) 15.0000i 0.584761i
\(659\) 18.0000 + 31.1769i 0.701180 + 1.21448i 0.968052 + 0.250748i \(0.0806766\pi\)
−0.266872 + 0.963732i \(0.585990\pi\)
\(660\) 0 0
\(661\) 5.00000 8.66025i 0.194477 0.336845i −0.752252 0.658876i \(-0.771032\pi\)
0.946729 + 0.322031i \(0.104366\pi\)
\(662\) 4.00000i 0.155464i
\(663\) 20.7846 + 20.0000i 0.807207 + 0.776736i
\(664\) 8.00000 0.310460
\(665\) 0 0
\(666\) −3.50000 + 6.06218i −0.135622 + 0.234905i
\(667\) −13.8564 + 8.00000i −0.536522 + 0.309761i
\(668\) 23.0000i 0.889897i
\(669\) −1.50000 2.59808i −0.0579934 0.100447i
\(670\) 0 0
\(671\) −6.00000 −0.231627
\(672\) −4.33013 + 2.50000i −0.167038 + 0.0964396i
\(673\) 27.7128 + 16.0000i 1.06825 + 0.616755i 0.927703 0.373319i \(-0.121780\pi\)
0.140548 + 0.990074i \(0.455114\pi\)
\(674\) −7.00000 + 12.1244i −0.269630 + 0.467013i
\(675\) 0 0
\(676\) −11.0000 + 6.92820i −0.423077 + 0.266469i
\(677\) 22.0000i 0.845529i 0.906240 + 0.422764i \(0.138940\pi\)
−0.906240 + 0.422764i \(0.861060\pi\)
\(678\) 6.92820 + 4.00000i 0.266076 + 0.153619i
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 5.19615 3.00000i 0.198971 0.114876i
\(683\) 25.9808 15.0000i 0.994126 0.573959i 0.0876211 0.996154i \(-0.472074\pi\)
0.906505 + 0.422195i \(0.138740\pi\)
\(684\) 5.00000 0.191180
\(685\) 0 0
\(686\) −27.5000 + 47.6314i −1.04995 + 1.81858i
\(687\) 12.1244 + 7.00000i 0.462573 + 0.267067i
\(688\) 6.00000i 0.228748i
\(689\) 2.50000 2.59808i 0.0952424 0.0989788i
\(690\) 0 0
\(691\) −8.50000 + 14.7224i −0.323355 + 0.560068i −0.981178 0.193105i \(-0.938144\pi\)
0.657823 + 0.753173i \(0.271478\pi\)
\(692\) 4.33013 + 2.50000i 0.164607 + 0.0950357i
\(693\) 12.9904 7.50000i 0.493464 0.284901i
\(694\) −16.0000 −0.607352
\(695\) 0 0
\(696\) −2.00000 3.46410i −0.0758098 0.131306i
\(697\) 48.0000i 1.81813i
\(698\) −6.92820 + 4.00000i −0.262236 + 0.151402i
\(699\) −7.00000 + 12.1244i −0.264764 + 0.458585i
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 3.46410 1.00000i 0.130744 0.0377426i
\(703\) 35.0000i 1.32005i
\(704\) −1.50000 + 2.59808i −0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) 8.00000 + 13.8564i 0.301084 + 0.521493i
\(707\) 40.0000i 1.50435i
\(708\) 10.3923 6.00000i 0.390567 0.225494i
\(709\) 16.0000 + 27.7128i 0.600893 + 1.04078i 0.992686 + 0.120723i \(0.0385214\pi\)
−0.391794 + 0.920053i \(0.628145\pi\)
\(710\) 0 0
\(711\) 1.00000 + 1.73205i 0.0375029 + 0.0649570i
\(712\) 9.52628 + 5.50000i 0.357012 + 0.206121i
\(713\) −6.92820 4.00000i −0.259463 0.149801i
\(714\) 40.0000 1.49696
\(715\) 0 0
\(716\) 4.00000 0.149487
\(717\) −15.5885 9.00000i −0.582162 0.336111i
\(718\) −15.5885 9.00000i −0.581756 0.335877i
\(719\) −10.0000 17.3205i −0.372937 0.645946i 0.617079 0.786901i \(-0.288316\pi\)
−0.990016 + 0.140955i \(0.954983\pi\)
\(720\) 0 0
\(721\) −17.5000 30.3109i −0.651734 1.12884i
\(722\) 5.19615 3.00000i 0.193381 0.111648i
\(723\) 25.0000i 0.929760i
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) 0 0
\(726\) −1.00000 + 1.73205i −0.0371135 + 0.0642824i
\(727\) 11.0000i 0.407967i 0.978974 + 0.203984i \(0.0653890\pi\)
−0.978974 + 0.203984i \(0.934611\pi\)
\(728\) −4.33013 + 17.5000i −0.160485 + 0.648593i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 24.0000 41.5692i 0.887672 1.53749i
\(732\) −1.73205 + 1.00000i −0.0640184 + 0.0369611i
\(733\) 43.0000i 1.58824i −0.607760 0.794121i \(-0.707932\pi\)
0.607760 0.794121i \(-0.292068\pi\)
\(734\) 4.00000 + 6.92820i 0.147643 + 0.255725i
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) 20.7846 12.0000i 0.765611 0.442026i
\(738\) 5.19615 + 3.00000i 0.191273 + 0.110432i
\(739\) 9.50000 16.4545i 0.349463 0.605288i −0.636691 0.771119i \(-0.719697\pi\)
0.986154 + 0.165831i \(0.0530307\pi\)
\(740\) 0 0
\(741\) 12.5000 12.9904i 0.459199 0.477214i
\(742\) 5.00000i 0.183556i
\(743\) 13.8564 + 8.00000i 0.508342 + 0.293492i 0.732152 0.681141i \(-0.238516\pi\)
−0.223810 + 0.974633i \(0.571849\pi\)
\(744\) 1.00000 1.73205i 0.0366618 0.0635001i
\(745\) 0 0
\(746\) −38.0000 −1.39128
\(747\) −6.92820 + 4.00000i −0.253490 + 0.146352i
\(748\) 20.7846 12.0000i 0.759961 0.438763i
\(749\) −30.0000 −1.09618
\(750\) 0 0
\(751\) 4.00000 6.92820i 0.145962 0.252814i −0.783769 0.621052i \(-0.786706\pi\)
0.929731 + 0.368238i \(0.120039\pi\)
\(752\) −2.59808 1.50000i −0.0947421 0.0546994i
\(753\) 15.0000i 0.546630i
\(754\) −14.0000 3.46410i −0.509850 0.126155i
\(755\) 0 0
\(756\) 2.50000 4.33013i 0.0909241 0.157485i
\(757\) 14.7224 + 8.50000i 0.535096 + 0.308938i 0.743089 0.669193i \(-0.233360\pi\)
−0.207993 + 0.978130i \(0.566693\pi\)
\(758\) 21.6506 12.5000i 0.786386 0.454020i
\(759\) −12.0000 −0.435572
\(760\) 0 0
\(761\) −4.50000 7.79423i −0.163125 0.282541i 0.772863 0.634573i \(-0.218824\pi\)
−0.935988 + 0.352032i \(0.885491\pi\)
\(762\) 21.0000i 0.760750i
\(763\) −60.6218 + 35.0000i −2.19466 + 1.26709i
\(764\) 1.00000 1.73205i 0.0361787 0.0626634i
\(765\) 0 0
\(766\) 28.0000 1.01168
\(767\) 10.3923 42.0000i 0.375244 1.51653i
\(768\) 1.00000i 0.0360844i
\(769\) −17.0000 + 29.4449i −0.613036 + 1.06181i 0.377690 + 0.925932i \(0.376718\pi\)
−0.990726 + 0.135877i \(0.956615\pi\)
\(770\) 0 0
\(771\) −14.0000 24.2487i −0.504198 0.873296i
\(772\) 24.0000i 0.863779i
\(773\) 0.866025 0.500000i 0.0311488 0.0179838i −0.484345 0.874877i \(-0.660942\pi\)
0.515494 + 0.856893i \(0.327609\pi\)
\(774\) −3.00000 5.19615i −0.107833 0.186772i
\(775\) 0 0
\(776\) 0 0
\(777\) 30.3109 + 17.5000i 1.08740 + 0.627809i
\(778\) −27.7128 16.0000i −0.993552 0.573628i
\(779\) 30.0000 1.07486
\(780\) 0 0
\(781\) −6.00000 −0.214697
\(782\) −27.7128 16.0000i −0.991008 0.572159i
\(783\) 3.46410 + 2.00000i 0.123797 + 0.0714742i
\(784\) 9.00000 + 15.5885i 0.321429 + 0.556731i
\(785\)