Properties

Label 378.2.g.d.163.1
Level $378$
Weight $2$
Character 378.163
Analytic conductor $3.018$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.01834519640\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 163.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 378.163
Dual form 378.2.g.d.109.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{10} +(2.50000 + 4.33013i) q^{11} +6.00000 q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(2.00000 - 3.46410i) q^{19} +2.00000 q^{20} +5.00000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} +(3.00000 - 5.19615i) q^{26} +(2.00000 - 1.73205i) q^{28} -7.00000 q^{29} +(-1.50000 - 2.59808i) q^{31} +(0.500000 + 0.866025i) q^{32} -4.00000 q^{34} +(-5.00000 - 1.73205i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(-2.00000 - 3.46410i) q^{38} +(1.00000 - 1.73205i) q^{40} +6.00000 q^{41} +8.00000 q^{43} +(2.50000 - 4.33013i) q^{44} +(2.00000 + 3.46410i) q^{46} +(3.00000 - 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +1.00000 q^{50} +(-3.00000 - 5.19615i) q^{52} +(-3.00000 - 5.19615i) q^{53} -10.0000 q^{55} +(-0.500000 - 2.59808i) q^{56} +(-3.50000 + 6.06218i) q^{58} +(3.50000 + 6.06218i) q^{59} -3.00000 q^{62} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(-5.00000 - 8.66025i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(-4.00000 + 3.46410i) q^{70} +4.00000 q^{71} +(-6.50000 - 11.2583i) q^{73} +(4.00000 + 6.92820i) q^{74} -4.00000 q^{76} +(-10.0000 + 8.66025i) q^{77} +(1.50000 - 2.59808i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(3.00000 - 5.19615i) q^{82} +7.00000 q^{83} +8.00000 q^{85} +(4.00000 - 6.92820i) q^{86} +(-2.50000 - 4.33013i) q^{88} +(3.00000 - 5.19615i) q^{89} +(3.00000 + 15.5885i) q^{91} +4.00000 q^{92} +(-3.00000 - 5.19615i) q^{94} +(4.00000 + 6.92820i) q^{95} -5.00000 q^{97} +(-1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} - 2 q^{5} + q^{7} - 2 q^{8} + O(q^{10}) \) \( 2 q + q^{2} - q^{4} - 2 q^{5} + q^{7} - 2 q^{8} + 2 q^{10} + 5 q^{11} + 12 q^{13} + 5 q^{14} - q^{16} - 4 q^{17} + 4 q^{19} + 4 q^{20} + 10 q^{22} - 4 q^{23} + q^{25} + 6 q^{26} + 4 q^{28} - 14 q^{29} - 3 q^{31} + q^{32} - 8 q^{34} - 10 q^{35} - 8 q^{37} - 4 q^{38} + 2 q^{40} + 12 q^{41} + 16 q^{43} + 5 q^{44} + 4 q^{46} + 6 q^{47} - 13 q^{49} + 2 q^{50} - 6 q^{52} - 6 q^{53} - 20 q^{55} - q^{56} - 7 q^{58} + 7 q^{59} - 6 q^{62} + 2 q^{64} - 12 q^{65} - 10 q^{67} - 4 q^{68} - 8 q^{70} + 8 q^{71} - 13 q^{73} + 8 q^{74} - 8 q^{76} - 20 q^{77} + 3 q^{79} - 2 q^{80} + 6 q^{82} + 14 q^{83} + 16 q^{85} + 8 q^{86} - 5 q^{88} + 6 q^{89} + 6 q^{91} + 8 q^{92} - 6 q^{94} + 8 q^{95} - 10 q^{97} - 2 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.00000 + 1.73205i −0.447214 + 0.774597i −0.998203 0.0599153i \(-0.980917\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(6\) 0 0
\(7\) 0.500000 + 2.59808i 0.188982 + 0.981981i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.00000 + 1.73205i 0.316228 + 0.547723i
\(11\) 2.50000 + 4.33013i 0.753778 + 1.30558i 0.945979 + 0.324227i \(0.105104\pi\)
−0.192201 + 0.981356i \(0.561563\pi\)
\(12\) 0 0
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 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 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 0 0
\(19\) 2.00000 3.46410i 0.458831 0.794719i −0.540068 0.841621i \(-0.681602\pi\)
0.998899 + 0.0469020i \(0.0149348\pi\)
\(20\) 2.00000 0.447214
\(21\) 0 0
\(22\) 5.00000 1.06600
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 3.00000 5.19615i 0.588348 1.01905i
\(27\) 0 0
\(28\) 2.00000 1.73205i 0.377964 0.327327i
\(29\) −7.00000 −1.29987 −0.649934 0.759991i \(-0.725203\pi\)
−0.649934 + 0.759991i \(0.725203\pi\)
\(30\) 0 0
\(31\) −1.50000 2.59808i −0.269408 0.466628i 0.699301 0.714827i \(-0.253495\pi\)
−0.968709 + 0.248199i \(0.920161\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −4.00000 −0.685994
\(35\) −5.00000 1.73205i −0.845154 0.292770i
\(36\) 0 0
\(37\) −4.00000 + 6.92820i −0.657596 + 1.13899i 0.323640 + 0.946180i \(0.395093\pi\)
−0.981236 + 0.192809i \(0.938240\pi\)
\(38\) −2.00000 3.46410i −0.324443 0.561951i
\(39\) 0 0
\(40\) 1.00000 1.73205i 0.158114 0.273861i
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 2.50000 4.33013i 0.376889 0.652791i
\(45\) 0 0
\(46\) 2.00000 + 3.46410i 0.294884 + 0.510754i
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) −3.00000 5.19615i −0.416025 0.720577i
\(53\) −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) 0 0
\(55\) −10.0000 −1.34840
\(56\) −0.500000 2.59808i −0.0668153 0.347183i
\(57\) 0 0
\(58\) −3.50000 + 6.06218i −0.459573 + 0.796003i
\(59\) 3.50000 + 6.06218i 0.455661 + 0.789228i 0.998726 0.0504625i \(-0.0160695\pi\)
−0.543065 + 0.839691i \(0.682736\pi\)
\(60\) 0 0
\(61\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(62\) −3.00000 −0.381000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −6.00000 + 10.3923i −0.744208 + 1.28901i
\(66\) 0 0
\(67\) −5.00000 8.66025i −0.610847 1.05802i −0.991098 0.133135i \(-0.957496\pi\)
0.380251 0.924883i \(-0.375838\pi\)
\(68\) −2.00000 + 3.46410i −0.242536 + 0.420084i
\(69\) 0 0
\(70\) −4.00000 + 3.46410i −0.478091 + 0.414039i
\(71\) 4.00000 0.474713 0.237356 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(72\) 0 0
\(73\) −6.50000 11.2583i −0.760767 1.31769i −0.942455 0.334332i \(-0.891489\pi\)
0.181688 0.983356i \(-0.441844\pi\)
\(74\) 4.00000 + 6.92820i 0.464991 + 0.805387i
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) −10.0000 + 8.66025i −1.13961 + 0.986928i
\(78\) 0 0
\(79\) 1.50000 2.59808i 0.168763 0.292306i −0.769222 0.638982i \(-0.779356\pi\)
0.937985 + 0.346675i \(0.112689\pi\)
\(80\) −1.00000 1.73205i −0.111803 0.193649i
\(81\) 0 0
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) 7.00000 0.768350 0.384175 0.923260i \(-0.374486\pi\)
0.384175 + 0.923260i \(0.374486\pi\)
\(84\) 0 0
\(85\) 8.00000 0.867722
\(86\) 4.00000 6.92820i 0.431331 0.747087i
\(87\) 0 0
\(88\) −2.50000 4.33013i −0.266501 0.461593i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) 3.00000 + 15.5885i 0.314485 + 1.63411i
\(92\) 4.00000 0.417029
\(93\) 0 0
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) 4.00000 + 6.92820i 0.410391 + 0.710819i
\(96\) 0 0
\(97\) −5.00000 −0.507673 −0.253837 0.967247i \(-0.581693\pi\)
−0.253837 + 0.967247i \(0.581693\pi\)
\(98\) −1.00000 + 6.92820i −0.101015 + 0.699854i
\(99\) 0 0
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) −2.50000 4.33013i −0.248759 0.430864i 0.714423 0.699715i \(-0.246689\pi\)
−0.963182 + 0.268851i \(0.913356\pi\)
\(102\) 0 0
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 6.00000 10.3923i 0.580042 1.00466i −0.415432 0.909624i \(-0.636370\pi\)
0.995474 0.0950377i \(-0.0302972\pi\)
\(108\) 0 0
\(109\) −8.00000 13.8564i −0.766261 1.32720i −0.939577 0.342337i \(-0.888782\pi\)
0.173316 0.984866i \(-0.444552\pi\)
\(110\) −5.00000 + 8.66025i −0.476731 + 0.825723i
\(111\) 0 0
\(112\) −2.50000 0.866025i −0.236228 0.0818317i
\(113\) −4.00000 −0.376288 −0.188144 0.982141i \(-0.560247\pi\)
−0.188144 + 0.982141i \(0.560247\pi\)
\(114\) 0 0
\(115\) −4.00000 6.92820i −0.373002 0.646058i
\(116\) 3.50000 + 6.06218i 0.324967 + 0.562859i
\(117\) 0 0
\(118\) 7.00000 0.644402
\(119\) 8.00000 6.92820i 0.733359 0.635107i
\(120\) 0 0
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) 0 0
\(123\) 0 0
\(124\) −1.50000 + 2.59808i −0.134704 + 0.233314i
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 6.00000 + 10.3923i 0.526235 + 0.911465i
\(131\) 6.50000 11.2583i 0.567908 0.983645i −0.428865 0.903369i \(-0.641086\pi\)
0.996773 0.0802763i \(-0.0255803\pi\)
\(132\) 0 0
\(133\) 10.0000 + 3.46410i 0.867110 + 0.300376i
\(134\) −10.0000 −0.863868
\(135\) 0 0
\(136\) 2.00000 + 3.46410i 0.171499 + 0.297044i
\(137\) −4.00000 6.92820i −0.341743 0.591916i 0.643013 0.765855i \(-0.277684\pi\)
−0.984757 + 0.173939i \(0.944351\pi\)
\(138\) 0 0
\(139\) −8.00000 −0.678551 −0.339276 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) 1.00000 + 5.19615i 0.0845154 + 0.439155i
\(141\) 0 0
\(142\) 2.00000 3.46410i 0.167836 0.290701i
\(143\) 15.0000 + 25.9808i 1.25436 + 2.17262i
\(144\) 0 0
\(145\) 7.00000 12.1244i 0.581318 1.00687i
\(146\) −13.0000 −1.07589
\(147\) 0 0
\(148\) 8.00000 0.657596
\(149\) 4.50000 7.79423i 0.368654 0.638528i −0.620701 0.784047i \(-0.713152\pi\)
0.989355 + 0.145519i \(0.0464853\pi\)
\(150\) 0 0
\(151\) 8.50000 + 14.7224i 0.691720 + 1.19809i 0.971274 + 0.237964i \(0.0764802\pi\)
−0.279554 + 0.960130i \(0.590186\pi\)
\(152\) −2.00000 + 3.46410i −0.162221 + 0.280976i
\(153\) 0 0
\(154\) 2.50000 + 12.9904i 0.201456 + 1.04679i
\(155\) 6.00000 0.481932
\(156\) 0 0
\(157\) −7.00000 12.1244i −0.558661 0.967629i −0.997609 0.0691164i \(-0.977982\pi\)
0.438948 0.898513i \(-0.355351\pi\)
\(158\) −1.50000 2.59808i −0.119334 0.206692i
\(159\) 0 0
\(160\) −2.00000 −0.158114
\(161\) −10.0000 3.46410i −0.788110 0.273009i
\(162\) 0 0
\(163\) −1.00000 + 1.73205i −0.0783260 + 0.135665i −0.902528 0.430632i \(-0.858291\pi\)
0.824202 + 0.566296i \(0.191624\pi\)
\(164\) −3.00000 5.19615i −0.234261 0.405751i
\(165\) 0 0
\(166\) 3.50000 6.06218i 0.271653 0.470516i
\(167\) 14.0000 1.08335 0.541676 0.840587i \(-0.317790\pi\)
0.541676 + 0.840587i \(0.317790\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 4.00000 6.92820i 0.306786 0.531369i
\(171\) 0 0
\(172\) −4.00000 6.92820i −0.304997 0.528271i
\(173\) 0.500000 0.866025i 0.0380143 0.0658427i −0.846392 0.532560i \(-0.821230\pi\)
0.884407 + 0.466717i \(0.154563\pi\)
\(174\) 0 0
\(175\) −2.00000 + 1.73205i −0.151186 + 0.130931i
\(176\) −5.00000 −0.376889
\(177\) 0 0
\(178\) −3.00000 5.19615i −0.224860 0.389468i
\(179\) −7.50000 12.9904i −0.560576 0.970947i −0.997446 0.0714220i \(-0.977246\pi\)
0.436870 0.899525i \(-0.356087\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 15.0000 + 5.19615i 1.11187 + 0.385164i
\(183\) 0 0
\(184\) 2.00000 3.46410i 0.147442 0.255377i
\(185\) −8.00000 13.8564i −0.588172 1.01874i
\(186\) 0 0
\(187\) 10.0000 17.3205i 0.731272 1.26660i
\(188\) −6.00000 −0.437595
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) −9.00000 + 15.5885i −0.651217 + 1.12794i 0.331611 + 0.943416i \(0.392408\pi\)
−0.982828 + 0.184525i \(0.940925\pi\)
\(192\) 0 0
\(193\) 9.50000 + 16.4545i 0.683825 + 1.18442i 0.973805 + 0.227387i \(0.0730182\pi\)
−0.289980 + 0.957033i \(0.593649\pi\)
\(194\) −2.50000 + 4.33013i −0.179490 + 0.310885i
\(195\) 0 0
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) 25.0000 1.78118 0.890588 0.454811i \(-0.150293\pi\)
0.890588 + 0.454811i \(0.150293\pi\)
\(198\) 0 0
\(199\) 9.50000 + 16.4545i 0.673437 + 1.16643i 0.976923 + 0.213591i \(0.0685161\pi\)
−0.303486 + 0.952836i \(0.598151\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 0 0
\(202\) −5.00000 −0.351799
\(203\) −3.50000 18.1865i −0.245652 1.27644i
\(204\) 0 0
\(205\) −6.00000 + 10.3923i −0.419058 + 0.725830i
\(206\) 4.00000 + 6.92820i 0.278693 + 0.482711i
\(207\) 0 0
\(208\) −3.00000 + 5.19615i −0.208013 + 0.360288i
\(209\) 20.0000 1.38343
\(210\) 0 0
\(211\) 26.0000 1.78991 0.894957 0.446153i \(-0.147206\pi\)
0.894957 + 0.446153i \(0.147206\pi\)
\(212\) −3.00000 + 5.19615i −0.206041 + 0.356873i
\(213\) 0 0
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) −8.00000 + 13.8564i −0.545595 + 0.944999i
\(216\) 0 0
\(217\) 6.00000 5.19615i 0.407307 0.352738i
\(218\) −16.0000 −1.08366
\(219\) 0 0
\(220\) 5.00000 + 8.66025i 0.337100 + 0.583874i
\(221\) −12.0000 20.7846i −0.807207 1.39812i
\(222\) 0 0
\(223\) −1.00000 −0.0669650 −0.0334825 0.999439i \(-0.510660\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) −2.00000 + 1.73205i −0.133631 + 0.115728i
\(225\) 0 0
\(226\) −2.00000 + 3.46410i −0.133038 + 0.230429i
\(227\) −13.5000 23.3827i −0.896026 1.55196i −0.832529 0.553981i \(-0.813108\pi\)
−0.0634974 0.997982i \(-0.520225\pi\)
\(228\) 0 0
\(229\) −2.00000 + 3.46410i −0.132164 + 0.228914i −0.924510 0.381157i \(-0.875526\pi\)
0.792347 + 0.610071i \(0.208859\pi\)
\(230\) −8.00000 −0.527504
\(231\) 0 0
\(232\) 7.00000 0.459573
\(233\) −11.0000 + 19.0526i −0.720634 + 1.24817i 0.240112 + 0.970745i \(0.422816\pi\)
−0.960746 + 0.277429i \(0.910518\pi\)
\(234\) 0 0
\(235\) 6.00000 + 10.3923i 0.391397 + 0.677919i
\(236\) 3.50000 6.06218i 0.227831 0.394614i
\(237\) 0 0
\(238\) −2.00000 10.3923i −0.129641 0.673633i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) 7.00000 + 12.1244i 0.449977 + 0.779383i
\(243\) 0 0
\(244\) 0 0
\(245\) 2.00000 13.8564i 0.127775 0.885253i
\(246\) 0 0
\(247\) 12.0000 20.7846i 0.763542 1.32249i
\(248\) 1.50000 + 2.59808i 0.0952501 + 0.164978i
\(249\) 0 0
\(250\) −6.00000 + 10.3923i −0.379473 + 0.657267i
\(251\) 21.0000 1.32551 0.662754 0.748837i \(-0.269387\pi\)
0.662754 + 0.748837i \(0.269387\pi\)
\(252\) 0 0
\(253\) −20.0000 −1.25739
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) 0 0
\(259\) −20.0000 6.92820i −1.24274 0.430498i
\(260\) 12.0000 0.744208
\(261\) 0 0
\(262\) −6.50000 11.2583i −0.401571 0.695542i
\(263\) 6.00000 + 10.3923i 0.369976 + 0.640817i 0.989561 0.144112i \(-0.0460326\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(264\) 0 0
\(265\) 12.0000 0.737154
\(266\) 8.00000 6.92820i 0.490511 0.424795i
\(267\) 0 0
\(268\) −5.00000 + 8.66025i −0.305424 + 0.529009i
\(269\) 15.5000 + 26.8468i 0.945052 + 1.63688i 0.755648 + 0.654978i \(0.227322\pi\)
0.189404 + 0.981899i \(0.439344\pi\)
\(270\) 0 0
\(271\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) −8.00000 −0.483298
\(275\) −2.50000 + 4.33013i −0.150756 + 0.261116i
\(276\) 0 0
\(277\) −1.00000 1.73205i −0.0600842 0.104069i 0.834419 0.551131i \(-0.185804\pi\)
−0.894503 + 0.447062i \(0.852470\pi\)
\(278\) −4.00000 + 6.92820i −0.239904 + 0.415526i
\(279\) 0 0
\(280\) 5.00000 + 1.73205i 0.298807 + 0.103510i
\(281\) −2.00000 −0.119310 −0.0596550 0.998219i \(-0.519000\pi\)
−0.0596550 + 0.998219i \(0.519000\pi\)
\(282\) 0 0
\(283\) −8.00000 13.8564i −0.475551 0.823678i 0.524057 0.851683i \(-0.324418\pi\)
−0.999608 + 0.0280052i \(0.991084\pi\)
\(284\) −2.00000 3.46410i −0.118678 0.205557i
\(285\) 0 0
\(286\) 30.0000 1.77394
\(287\) 3.00000 + 15.5885i 0.177084 + 0.920158i
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) −7.00000 12.1244i −0.411054 0.711967i
\(291\) 0 0
\(292\) −6.50000 + 11.2583i −0.380384 + 0.658844i
\(293\) −27.0000 −1.57736 −0.788678 0.614806i \(-0.789234\pi\)
−0.788678 + 0.614806i \(0.789234\pi\)
\(294\) 0 0
\(295\) −14.0000 −0.815112
\(296\) 4.00000 6.92820i 0.232495 0.402694i
\(297\) 0 0
\(298\) −4.50000 7.79423i −0.260678 0.451508i
\(299\) −12.0000 + 20.7846i −0.693978 + 1.20201i
\(300\) 0 0
\(301\) 4.00000 + 20.7846i 0.230556 + 1.19800i
\(302\) 17.0000 0.978240
\(303\) 0 0
\(304\) 2.00000 + 3.46410i 0.114708 + 0.198680i
\(305\) 0 0
\(306\) 0 0
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) 12.5000 + 4.33013i 0.712254 + 0.246732i
\(309\) 0 0
\(310\) 3.00000 5.19615i 0.170389 0.295122i
\(311\) 11.0000 + 19.0526i 0.623753 + 1.08037i 0.988781 + 0.149375i \(0.0477261\pi\)
−0.365028 + 0.930997i \(0.618941\pi\)
\(312\) 0 0
\(313\) −5.00000 + 8.66025i −0.282617 + 0.489506i −0.972028 0.234863i \(-0.924536\pi\)
0.689412 + 0.724370i \(0.257869\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) −3.00000 −0.168763
\(317\) −16.5000 + 28.5788i −0.926732 + 1.60515i −0.137981 + 0.990435i \(0.544061\pi\)
−0.788751 + 0.614713i \(0.789272\pi\)
\(318\) 0 0
\(319\) −17.5000 30.3109i −0.979812 1.69708i
\(320\) −1.00000 + 1.73205i −0.0559017 + 0.0968246i
\(321\) 0 0
\(322\) −8.00000 + 6.92820i −0.445823 + 0.386094i
\(323\) −16.0000 −0.890264
\(324\) 0 0
\(325\) 3.00000 + 5.19615i 0.166410 + 0.288231i
\(326\) 1.00000 + 1.73205i 0.0553849 + 0.0959294i
\(327\) 0 0
\(328\) −6.00000 −0.331295
\(329\) 15.0000 + 5.19615i 0.826977 + 0.286473i
\(330\) 0 0
\(331\) −16.0000 + 27.7128i −0.879440 + 1.52323i −0.0274825 + 0.999622i \(0.508749\pi\)
−0.851957 + 0.523612i \(0.824584\pi\)
\(332\) −3.50000 6.06218i −0.192087 0.332705i
\(333\) 0 0
\(334\) 7.00000 12.1244i 0.383023 0.663415i
\(335\) 20.0000 1.09272
\(336\) 0 0
\(337\) −27.0000 −1.47078 −0.735392 0.677642i \(-0.763002\pi\)
−0.735392 + 0.677642i \(0.763002\pi\)
\(338\) 11.5000 19.9186i 0.625518 1.08343i
\(339\) 0 0
\(340\) −4.00000 6.92820i −0.216930 0.375735i
\(341\) 7.50000 12.9904i 0.406148 0.703469i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) −0.500000 0.866025i −0.0268802 0.0465578i
\(347\) −13.5000 23.3827i −0.724718 1.25525i −0.959090 0.283101i \(-0.908637\pi\)
0.234372 0.972147i \(-0.424697\pi\)
\(348\) 0 0
\(349\) −20.0000 −1.07058 −0.535288 0.844670i \(-0.679797\pi\)
−0.535288 + 0.844670i \(0.679797\pi\)
\(350\) 0.500000 + 2.59808i 0.0267261 + 0.138873i
\(351\) 0 0
\(352\) −2.50000 + 4.33013i −0.133250 + 0.230797i
\(353\) −15.0000 25.9808i −0.798369 1.38282i −0.920677 0.390324i \(-0.872363\pi\)
0.122308 0.992492i \(-0.460970\pi\)
\(354\) 0 0
\(355\) −4.00000 + 6.92820i −0.212298 + 0.367711i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −15.0000 −0.792775
\(359\) 8.00000 13.8564i 0.422224 0.731313i −0.573933 0.818902i \(-0.694583\pi\)
0.996157 + 0.0875892i \(0.0279163\pi\)
\(360\) 0 0
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) 0 0
\(363\) 0 0
\(364\) 12.0000 10.3923i 0.628971 0.544705i
\(365\) 26.0000 1.36090
\(366\) 0 0
\(367\) 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i \(-0.133375\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) −2.00000 3.46410i −0.104257 0.180579i
\(369\) 0 0
\(370\) −16.0000 −0.831800
\(371\) 12.0000 10.3923i 0.623009 0.539542i
\(372\) 0 0
\(373\) 10.0000 17.3205i 0.517780 0.896822i −0.482006 0.876168i \(-0.660092\pi\)
0.999787 0.0206542i \(-0.00657489\pi\)
\(374\) −10.0000 17.3205i −0.517088 0.895622i
\(375\) 0 0
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) −42.0000 −2.16311
\(378\) 0 0
\(379\) 10.0000 0.513665 0.256833 0.966456i \(-0.417321\pi\)
0.256833 + 0.966456i \(0.417321\pi\)
\(380\) 4.00000 6.92820i 0.205196 0.355409i
\(381\) 0 0
\(382\) 9.00000 + 15.5885i 0.460480 + 0.797575i
\(383\) −2.00000 + 3.46410i −0.102195 + 0.177007i −0.912589 0.408879i \(-0.865920\pi\)
0.810394 + 0.585886i \(0.199253\pi\)
\(384\) 0 0
\(385\) −5.00000 25.9808i −0.254824 1.32410i
\(386\) 19.0000 0.967075
\(387\) 0 0
\(388\) 2.50000 + 4.33013i 0.126918 + 0.219829i
\(389\) 0.500000 + 0.866025i 0.0253510 + 0.0439092i 0.878423 0.477885i \(-0.158596\pi\)
−0.853072 + 0.521794i \(0.825263\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 6.50000 2.59808i 0.328300 0.131223i
\(393\) 0 0
\(394\) 12.5000 21.6506i 0.629741 1.09074i
\(395\) 3.00000 + 5.19615i 0.150946 + 0.261447i
\(396\) 0 0
\(397\) 9.00000 15.5885i 0.451697 0.782362i −0.546795 0.837267i \(-0.684152\pi\)
0.998492 + 0.0549046i \(0.0174855\pi\)
\(398\) 19.0000 0.952384
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) 0 0
\(403\) −9.00000 15.5885i −0.448322 0.776516i
\(404\) −2.50000 + 4.33013i −0.124380 + 0.215432i
\(405\) 0 0
\(406\) −17.5000 6.06218i −0.868510 0.300861i
\(407\) −40.0000 −1.98273
\(408\) 0 0
\(409\) 5.00000 + 8.66025i 0.247234 + 0.428222i 0.962757 0.270367i \(-0.0871450\pi\)
−0.715523 + 0.698589i \(0.753812\pi\)
\(410\) 6.00000 + 10.3923i 0.296319 + 0.513239i
\(411\) 0 0
\(412\) 8.00000 0.394132
\(413\) −14.0000 + 12.1244i −0.688895 + 0.596601i
\(414\) 0 0
\(415\) −7.00000 + 12.1244i −0.343616 + 0.595161i
\(416\) 3.00000 + 5.19615i 0.147087 + 0.254762i
\(417\) 0 0
\(418\) 10.0000 17.3205i 0.489116 0.847174i
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −18.0000 −0.877266 −0.438633 0.898666i \(-0.644537\pi\)
−0.438633 + 0.898666i \(0.644537\pi\)
\(422\) 13.0000 22.5167i 0.632830 1.09609i
\(423\) 0 0
\(424\) 3.00000 + 5.19615i 0.145693 + 0.252347i
\(425\) 2.00000 3.46410i 0.0970143 0.168034i
\(426\) 0 0
\(427\) 0 0
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) 8.00000 + 13.8564i 0.385794 + 0.668215i
\(431\) −9.00000 15.5885i −0.433515 0.750870i 0.563658 0.826008i \(-0.309393\pi\)
−0.997173 + 0.0751385i \(0.976060\pi\)
\(432\) 0 0
\(433\) −7.00000 −0.336399 −0.168199 0.985753i \(-0.553795\pi\)
−0.168199 + 0.985753i \(0.553795\pi\)
\(434\) −1.50000 7.79423i −0.0720023 0.374135i
\(435\) 0 0
\(436\) −8.00000 + 13.8564i −0.383131 + 0.663602i
\(437\) 8.00000 + 13.8564i 0.382692 + 0.662842i
\(438\) 0 0
\(439\) −1.50000 + 2.59808i −0.0715911 + 0.123999i −0.899599 0.436717i \(-0.856141\pi\)
0.828008 + 0.560717i \(0.189474\pi\)
\(440\) 10.0000 0.476731
\(441\) 0 0
\(442\) −24.0000 −1.14156
\(443\) 5.50000 9.52628i 0.261313 0.452607i −0.705278 0.708931i \(-0.749178\pi\)
0.966591 + 0.256323i \(0.0825112\pi\)
\(444\) 0 0
\(445\) 6.00000 + 10.3923i 0.284427 + 0.492642i
\(446\) −0.500000 + 0.866025i −0.0236757 + 0.0410075i
\(447\) 0 0
\(448\) 0.500000 + 2.59808i 0.0236228 + 0.122748i
\(449\) 14.0000 0.660701 0.330350 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) 0 0
\(451\) 15.0000 + 25.9808i 0.706322 + 1.22339i
\(452\) 2.00000 + 3.46410i 0.0940721 + 0.162938i
\(453\) 0 0
\(454\) −27.0000 −1.26717
\(455\) −30.0000 10.3923i −1.40642 0.487199i
\(456\) 0 0
\(457\) 13.0000 22.5167i 0.608114 1.05328i −0.383437 0.923567i \(-0.625260\pi\)
0.991551 0.129718i \(-0.0414071\pi\)
\(458\) 2.00000 + 3.46410i 0.0934539 + 0.161867i
\(459\) 0 0
\(460\) −4.00000 + 6.92820i −0.186501 + 0.323029i
\(461\) 23.0000 1.07122 0.535608 0.844466i \(-0.320082\pi\)
0.535608 + 0.844466i \(0.320082\pi\)
\(462\) 0 0
\(463\) −29.0000 −1.34774 −0.673872 0.738848i \(-0.735370\pi\)
−0.673872 + 0.738848i \(0.735370\pi\)
\(464\) 3.50000 6.06218i 0.162483 0.281430i
\(465\) 0 0
\(466\) 11.0000 + 19.0526i 0.509565 + 0.882593i
\(467\) 3.50000 6.06218i 0.161961 0.280524i −0.773611 0.633661i \(-0.781552\pi\)
0.935572 + 0.353137i \(0.114885\pi\)
\(468\) 0 0
\(469\) 20.0000 17.3205i 0.923514 0.799787i
\(470\) 12.0000 0.553519
\(471\) 0 0
\(472\) −3.50000 6.06218i −0.161101 0.279034i
\(473\) 20.0000 + 34.6410i 0.919601 + 1.59280i
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) −10.0000 3.46410i −0.458349 0.158777i
\(477\) 0 0
\(478\) 0 0
\(479\) 13.0000 + 22.5167i 0.593985 + 1.02881i 0.993689 + 0.112168i \(0.0357796\pi\)
−0.399704 + 0.916644i \(0.630887\pi\)
\(480\) 0 0
\(481\) −24.0000 + 41.5692i −1.09431 + 1.89539i
\(482\) 1.00000 0.0455488
\(483\) 0 0
\(484\) 14.0000 0.636364
\(485\) 5.00000 8.66025i 0.227038 0.393242i
\(486\) 0 0
\(487\) 6.50000 + 11.2583i 0.294543 + 0.510164i 0.974879 0.222737i \(-0.0714992\pi\)
−0.680335 + 0.732901i \(0.738166\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −11.0000 8.66025i −0.496929 0.391230i
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 0 0
\(493\) 14.0000 + 24.2487i 0.630528 + 1.09211i
\(494\) −12.0000 20.7846i −0.539906 0.935144i
\(495\) 0 0
\(496\) 3.00000 0.134704
\(497\) 2.00000 + 10.3923i 0.0897123 + 0.466159i
\(498\) 0 0
\(499\) 4.00000 6.92820i 0.179065 0.310149i −0.762496 0.646993i \(-0.776026\pi\)
0.941560 + 0.336844i \(0.109360\pi\)
\(500\) 6.00000 + 10.3923i 0.268328 + 0.464758i
\(501\) 0 0
\(502\) 10.5000 18.1865i 0.468638 0.811705i
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) −10.0000 + 17.3205i −0.444554 + 0.769991i
\(507\) 0 0
\(508\) 0 0
\(509\) 1.50000 2.59808i 0.0664863 0.115158i −0.830866 0.556473i \(-0.812154\pi\)
0.897352 + 0.441315i \(0.145488\pi\)
\(510\) 0 0
\(511\) 26.0000 22.5167i 1.15017 0.996078i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 0 0
\(515\) −8.00000 13.8564i −0.352522 0.610586i
\(516\) 0 0
\(517\) 30.0000 1.31940
\(518\) −16.0000 + 13.8564i −0.703000 + 0.608816i
\(519\) 0 0
\(520\) 6.00000 10.3923i 0.263117 0.455733i
\(521\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(522\) 0 0
\(523\) −13.0000 + 22.5167i −0.568450 + 0.984585i 0.428269 + 0.903651i \(0.359124\pi\)
−0.996719 + 0.0809336i \(0.974210\pi\)
\(524\) −13.0000 −0.567908
\(525\) 0 0
\(526\) 12.0000 0.523225
\(527\) −6.00000 + 10.3923i −0.261364 + 0.452696i
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 6.00000 10.3923i 0.260623 0.451413i
\(531\) 0 0
\(532\) −2.00000 10.3923i −0.0867110 0.450564i
\(533\) 36.0000 1.55933
\(534\) 0 0
\(535\) 12.0000 + 20.7846i 0.518805 + 0.898597i
\(536\) 5.00000 + 8.66025i 0.215967 + 0.374066i
\(537\) 0 0
\(538\) 31.0000 1.33650
\(539\) −27.5000 21.6506i −1.18451 0.932559i
\(540\) 0 0
\(541\) 15.0000 25.9808i 0.644900 1.11700i −0.339424 0.940633i \(-0.610232\pi\)
0.984325 0.176367i \(-0.0564345\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 2.00000 3.46410i 0.0857493 0.148522i
\(545\) 32.0000 1.37073
\(546\) 0 0
\(547\) −18.0000 −0.769624 −0.384812 0.922995i \(-0.625734\pi\)
−0.384812 + 0.922995i \(0.625734\pi\)
\(548\) −4.00000 + 6.92820i −0.170872 + 0.295958i
\(549\) 0 0
\(550\) 2.50000 + 4.33013i 0.106600 + 0.184637i
\(551\) −14.0000 + 24.2487i −0.596420 + 1.03303i
\(552\) 0 0
\(553\) 7.50000 + 2.59808i 0.318932 + 0.110481i
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) 4.00000 + 6.92820i 0.169638 + 0.293821i
\(557\) −5.50000 9.52628i −0.233042 0.403641i 0.725660 0.688054i \(-0.241535\pi\)
−0.958702 + 0.284413i \(0.908201\pi\)
\(558\) 0 0
\(559\) 48.0000 2.03018
\(560\) 4.00000 3.46410i 0.169031 0.146385i
\(561\) 0 0
\(562\) −1.00000 + 1.73205i −0.0421825 + 0.0730622i
\(563\) 10.0000 + 17.3205i 0.421450 + 0.729972i 0.996082 0.0884397i \(-0.0281881\pi\)
−0.574632 + 0.818412i \(0.694855\pi\)
\(564\) 0 0
\(565\) 4.00000 6.92820i 0.168281 0.291472i
\(566\) −16.0000 −0.672530
\(567\) 0 0
\(568\) −4.00000 −0.167836
\(569\) −6.00000 + 10.3923i −0.251533 + 0.435668i −0.963948 0.266090i \(-0.914268\pi\)
0.712415 + 0.701758i \(0.247601\pi\)
\(570\) 0 0
\(571\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(572\) 15.0000 25.9808i 0.627182 1.08631i
\(573\) 0 0
\(574\) 15.0000 + 5.19615i 0.626088 + 0.216883i
\(575\) −4.00000 −0.166812
\(576\) 0 0
\(577\) −21.5000 37.2391i −0.895057 1.55028i −0.833734 0.552166i \(-0.813802\pi\)
−0.0613223 0.998118i \(-0.519532\pi\)
\(578\) −0.500000 0.866025i −0.0207973 0.0360219i
\(579\) 0 0
\(580\) −14.0000 −0.581318
\(581\) 3.50000 + 18.1865i 0.145204 + 0.754505i
\(582\) 0 0
\(583\) 15.0000 25.9808i 0.621237 1.07601i
\(584\) 6.50000 + 11.2583i 0.268972 + 0.465873i
\(585\) 0 0
\(586\) −13.5000 + 23.3827i −0.557680 + 0.965930i
\(587\) −20.0000 −0.825488 −0.412744 0.910847i \(-0.635430\pi\)
−0.412744 + 0.910847i \(0.635430\pi\)
\(588\) 0 0
\(589\) −12.0000 −0.494451
\(590\) −7.00000 + 12.1244i −0.288185 + 0.499152i
\(591\) 0 0
\(592\) −4.00000 6.92820i −0.164399 0.284747i
\(593\) 18.0000 31.1769i 0.739171 1.28028i −0.213697 0.976900i \(-0.568551\pi\)
0.952869 0.303383i \(-0.0981160\pi\)
\(594\) 0 0
\(595\) 4.00000 + 20.7846i 0.163984 + 0.852086i
\(596\) −9.00000 −0.368654
\(597\) 0 0
\(598\) 12.0000 + 20.7846i 0.490716 + 0.849946i
\(599\) 15.0000 + 25.9808i 0.612883 + 1.06155i 0.990752 + 0.135686i \(0.0433238\pi\)
−0.377869 + 0.925859i \(0.623343\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 20.0000 + 6.92820i 0.815139 + 0.282372i
\(603\) 0 0
\(604\) 8.50000 14.7224i 0.345860 0.599047i
\(605\) −14.0000 24.2487i −0.569181 0.985850i
\(606\) 0 0
\(607\) 4.50000 7.79423i 0.182649 0.316358i −0.760133 0.649768i \(-0.774866\pi\)
0.942782 + 0.333410i \(0.108199\pi\)
\(608\) 4.00000 0.162221
\(609\) 0 0
\(610\) 0 0
\(611\) 18.0000 31.1769i 0.728202 1.26128i
\(612\) 0 0
\(613\) 3.00000 + 5.19615i 0.121169 + 0.209871i 0.920229 0.391381i \(-0.128002\pi\)
−0.799060 + 0.601251i \(0.794669\pi\)
\(614\) −1.00000 + 1.73205i −0.0403567 + 0.0698999i
\(615\) 0 0
\(616\) 10.0000 8.66025i 0.402911 0.348932i
\(617\) −2.00000 −0.0805170 −0.0402585 0.999189i \(-0.512818\pi\)
−0.0402585 + 0.999189i \(0.512818\pi\)
\(618\) 0 0
\(619\) −2.00000 3.46410i −0.0803868 0.139234i 0.823029 0.567999i \(-0.192282\pi\)
−0.903416 + 0.428765i \(0.858949\pi\)
\(620\) −3.00000 5.19615i −0.120483 0.208683i
\(621\) 0 0
\(622\) 22.0000 0.882120
\(623\) 15.0000 + 5.19615i 0.600962 + 0.208179i
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 5.00000 + 8.66025i 0.199840 + 0.346133i
\(627\) 0 0
\(628\) −7.00000 + 12.1244i −0.279330 + 0.483814i
\(629\) 32.0000 1.27592
\(630\) 0 0
\(631\) 5.00000 0.199047 0.0995234 0.995035i \(-0.468268\pi\)
0.0995234 + 0.995035i \(0.468268\pi\)
\(632\) −1.50000 + 2.59808i −0.0596668 + 0.103346i
\(633\) 0 0
\(634\) 16.5000 + 28.5788i 0.655299 + 1.13501i
\(635\) 0 0
\(636\) 0 0
\(637\) −39.0000 + 15.5885i −1.54524 + 0.617637i
\(638\) −35.0000 −1.38566
\(639\) 0 0
\(640\) 1.00000 + 1.73205i 0.0395285 + 0.0684653i
\(641\) 7.00000 + 12.1244i 0.276483 + 0.478883i 0.970508 0.241068i \(-0.0774976\pi\)
−0.694025 + 0.719951i \(0.744164\pi\)
\(642\) 0 0
\(643\) 14.0000 0.552106 0.276053 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) 2.00000 + 10.3923i 0.0788110 + 0.409514i
\(645\) 0 0
\(646\) −8.00000 + 13.8564i −0.314756 + 0.545173i
\(647\) −9.00000 15.5885i −0.353827 0.612845i 0.633090 0.774078i \(-0.281786\pi\)
−0.986916 + 0.161233i \(0.948453\pi\)
\(648\) 0 0
\(649\) −17.5000 + 30.3109i −0.686935 + 1.18981i
\(650\) 6.00000 0.235339
\(651\) 0 0
\(652\) 2.00000 0.0783260
\(653\) 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i \(-0.718768\pi\)
0.986634 + 0.162951i \(0.0521013\pi\)
\(654\) 0 0
\(655\) 13.0000 + 22.5167i 0.507952 + 0.879799i
\(656\) −3.00000 + 5.19615i −0.117130 + 0.202876i
\(657\) 0 0
\(658\) 12.0000 10.3923i 0.467809 0.405134i
\(659\) −41.0000 −1.59713 −0.798567 0.601906i \(-0.794408\pi\)
−0.798567 + 0.601906i \(0.794408\pi\)
\(660\) 0 0
\(661\) 19.0000 + 32.9090i 0.739014 + 1.28001i 0.952940 + 0.303160i \(0.0980418\pi\)
−0.213925 + 0.976850i \(0.568625\pi\)
\(662\) 16.0000 + 27.7128i 0.621858 + 1.07709i
\(663\) 0 0
\(664\) −7.00000 −0.271653
\(665\) −16.0000 + 13.8564i −0.620453 + 0.537328i
\(666\) 0 0
\(667\) 14.0000 24.2487i 0.542082 0.938914i
\(668\) −7.00000 12.1244i −0.270838 0.469105i
\(669\) 0 0
\(670\) 10.0000 17.3205i 0.386334 0.669150i
\(671\) 0 0
\(672\) 0 0
\(673\) 2.00000 0.0770943 0.0385472 0.999257i \(-0.487727\pi\)
0.0385472 + 0.999257i \(0.487727\pi\)
\(674\) −13.5000 + 23.3827i −0.520001 + 0.900667i
\(675\) 0 0
\(676\) −11.5000 19.9186i −0.442308 0.766099i
\(677\) 4.50000 7.79423i 0.172949 0.299557i −0.766501 0.642244i \(-0.778004\pi\)
0.939450 + 0.342687i \(0.111337\pi\)
\(678\) 0 0
\(679\) −2.50000 12.9904i −0.0959412 0.498525i
\(680\) −8.00000 −0.306786
\(681\) 0 0
\(682\) −7.50000 12.9904i −0.287190 0.497427i
\(683\) 10.5000 + 18.1865i 0.401771 + 0.695888i 0.993940 0.109926i \(-0.0350613\pi\)
−0.592168 + 0.805814i \(0.701728\pi\)
\(684\) 0 0
\(685\) 16.0000 0.611329
\(686\) −18.5000 + 0.866025i −0.706333 + 0.0330650i
\(687\) 0 0
\(688\) −4.00000 + 6.92820i −0.152499 + 0.264135i
\(689\) −18.0000 31.1769i −0.685745 1.18775i
\(690\) 0 0
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) −1.00000 −0.0380143
\(693\) 0 0
\(694\) −27.0000 −1.02491
\(695\) 8.00000 13.8564i 0.303457 0.525603i
\(696\) 0 0
\(697\) −12.0000 20.7846i −0.454532 0.787273i
\(698\) −10.0000 + 17.3205i −0.378506 + 0.655591i
\(699\) 0 0
\(700\) 2.50000 + 0.866025i 0.0944911 + 0.0327327i
\(701\) 14.0000 0.528773 0.264386 0.964417i \(-0.414831\pi\)
0.264386 + 0.964417i \(0.414831\pi\)
\(702\) 0 0
\(703\) 16.0000 + 27.7128i 0.603451 + 1.04521i
\(704\) 2.50000 + 4.33013i 0.0942223 + 0.163198i
\(705\) 0 0
\(706\) −30.0000 −1.12906
\(707\) 10.0000 8.66025i 0.376089 0.325702i
\(708\) 0 0
\(709\) −4.00000 + 6.92820i −0.150223 + 0.260194i −0.931309 0.364229i \(-0.881333\pi\)
0.781086 + 0.624423i \(0.214666\pi\)
\(710\) 4.00000 + 6.92820i 0.150117 + 0.260011i
\(711\) 0 0
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) 12.0000 0.449404
\(714\) 0 0
\(715\) −60.0000 −2.24387
\(716\) −7.50000 + 12.9904i −0.280288 + 0.485473i
\(717\) 0 0
\(718\) −8.00000 13.8564i −0.298557 0.517116i
\(719\) 3.00000 5.19615i 0.111881 0.193784i −0.804648 0.593753i \(-0.797646\pi\)
0.916529 + 0.399969i \(0.130979\pi\)
\(720\) 0 0
\(721\) −20.0000 6.92820i −0.744839 0.258020i
\(722\) 3.00000 0.111648
\(723\) 0 0
\(724\) 0 0
\(725\) −3.50000 6.06218i −0.129987 0.225144i
\(726\) 0 0
\(727\) −32.0000 −1.18681 −0.593407 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) −3.00000 15.5885i −0.111187 0.577747i
\(729\) 0 0
\(730\) 13.0000 22.5167i 0.481152 0.833379i
\(731\) −16.0000 27.7128i −0.591781 1.02500i
\(732\) 0 0
\(733\) 18.0000 31.1769i 0.664845 1.15155i −0.314482 0.949263i \(-0.601831\pi\)
0.979327 0.202282i \(-0.0648358\pi\)
\(734\) 4.00000 0.147643
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) 25.0000 43.3013i 0.920887 1.59502i
\(738\) 0 0
\(739\) 3.00000 + 5.19615i 0.110357 + 0.191144i 0.915914 0.401374i \(-0.131467\pi\)
−0.805557 + 0.592518i \(0.798134\pi\)
\(740\) −8.00000 + 13.8564i −0.294086 + 0.509372i
\(741\) 0 0
\(742\) −3.00000 15.5885i −0.110133 0.572270i
\(743\) 6.00000 0.220119 0.110059 0.993925i \(-0.464896\pi\)
0.110059 + 0.993925i \(0.464896\pi\)
\(744\) 0 0
\(745\) 9.00000 + 15.5885i 0.329734 + 0.571117i
\(746\) −10.0000 17.3205i −0.366126 0.634149i
\(747\) 0 0
\(748\) −20.0000 −0.731272
\(749\) 30.0000 + 10.3923i 1.09618 + 0.379727i
\(750\) 0 0
\(751\) −6.00000 + 10.3923i −0.218943 + 0.379221i −0.954485 0.298259i \(-0.903594\pi\)
0.735542 + 0.677479i \(0.236928\pi\)
\(752\) 3.00000 + 5.19615i 0.109399 + 0.189484i
\(753\) 0 0
\(754\) −21.0000 + 36.3731i −0.764775 + 1.32463i
\(755\) −34.0000 −1.23739
\(756\) 0 0
\(757\) −18.0000 −0.654221 −0.327111 0.944986i \(-0.606075\pi\)
−0.327111 + 0.944986i \(0.606075\pi\)
\(758\) 5.00000 8.66025i 0.181608 0.314555i
\(759\) 0 0
\(760\) −4.00000 6.92820i −0.145095 0.251312i
\(761\) 4.00000 6.92820i 0.145000 0.251147i −0.784373 0.620289i \(-0.787015\pi\)
0.929373 + 0.369142i \(0.120348\pi\)
\(762\) 0 0
\(763\) 32.0000 27.7128i 1.15848 1.00327i
\(764\) 18.0000 0.651217
\(765\) 0 0
\(766\) 2.00000 + 3.46410i 0.0722629 + 0.125163i
\(767\) 21.0000 + 36.3731i 0.758266 + 1.31336i
\(768\) 0 0
\(769\) 1.00000 0.0360609 0.0180305 0.999837i \(-0.494260\pi\)
0.0180305 + 0.999837i \(0.494260\pi\)
\(770\) −25.0000 8.66025i −0.900937 0.312094i
\(771\) 0 0
\(772\) 9.50000 16.4545i 0.341912 0.592210i
\(773\) −19.0000 32.9090i −0.683383 1.18365i −0.973942 0.226796i \(-0.927175\pi\)
0.290560 0.956857i \(-0.406159\pi\)
\(774\) 0 0
\(775\) 1.50000 2.59808i 0.0538816 0.0933257i
\(776\) 5.00000 0.179490
\(777\) 0 0
\(778\) 1.00000 0.0358517
\(779\) 12.0000 20.7846i 0.429945 0.744686i
\(780\) 0 0
\(781\) 10.0000 + 17.3205i 0.357828 + 0.619777i
\(782\) 8.00000 13.8564i 0.286079 0.495504i
\(783\) 0 0
\(784\) 1.00000 6.92820i 0.0357143 0.247436i
\(785\) 28.0000 0.999363
\(786\) 0 0
\(787\) −9.00000 15.5885i −0.320815 0.555668i 0.659841 0.751405i \(-0.270624\pi\)
−0.980656 + 0.195737i \(0.937290\pi\)
\(788\) −12.5000 21.6506i −0.445294 0.771272i
\(789\) 0 0
\(790\) 6.00000