Properties

Label 882.2.e.k.373.1
Level $882$
Weight $2$
Character 882.373
Analytic conductor $7.043$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
Defining polynomial: \(x^{4} - x^{3} - 2 x^{2} - 3 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.1
Root \(1.68614 + 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 882.373
Dual form 882.2.e.k.655.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-0.500000 - 1.65831i) q^{3} +1.00000 q^{4} +(2.18614 + 3.78651i) q^{5} +(0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(-2.50000 + 1.65831i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-0.500000 - 1.65831i) q^{3} +1.00000 q^{4} +(2.18614 + 3.78651i) q^{5} +(0.500000 + 1.65831i) q^{6} -1.00000 q^{8} +(-2.50000 + 1.65831i) q^{9} +(-2.18614 - 3.78651i) q^{10} +(0.686141 - 1.18843i) q^{11} +(-0.500000 - 1.65831i) q^{12} +(1.00000 - 1.73205i) q^{13} +(5.18614 - 5.51856i) q^{15} +1.00000 q^{16} +(0.686141 + 1.18843i) q^{17} +(2.50000 - 1.65831i) q^{18} +(2.50000 - 4.33013i) q^{19} +(2.18614 + 3.78651i) q^{20} +(-0.686141 + 1.18843i) q^{22} +(0.813859 + 1.40965i) q^{23} +(0.500000 + 1.65831i) q^{24} +(-7.05842 + 12.2255i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(4.00000 + 3.31662i) q^{27} +(4.37228 + 7.57301i) q^{29} +(-5.18614 + 5.51856i) q^{30} -2.00000 q^{31} -1.00000 q^{32} +(-2.31386 - 0.543620i) q^{33} +(-0.686141 - 1.18843i) q^{34} +(-2.50000 + 1.65831i) q^{36} +(-1.00000 + 1.73205i) q^{37} +(-2.50000 + 4.33013i) q^{38} +(-3.37228 - 0.792287i) q^{39} +(-2.18614 - 3.78651i) q^{40} +(2.31386 - 4.00772i) q^{41} +(4.05842 + 7.02939i) q^{43} +(0.686141 - 1.18843i) q^{44} +(-11.7446 - 5.84096i) q^{45} +(-0.813859 - 1.40965i) q^{46} +(-0.500000 - 1.65831i) q^{48} +(7.05842 - 12.2255i) q^{50} +(1.62772 - 1.73205i) q^{51} +(1.00000 - 1.73205i) q^{52} +(4.37228 + 7.57301i) q^{53} +(-4.00000 - 3.31662i) q^{54} +6.00000 q^{55} +(-8.43070 - 1.98072i) q^{57} +(-4.37228 - 7.57301i) q^{58} +10.1168 q^{59} +(5.18614 - 5.51856i) q^{60} -3.11684 q^{61} +2.00000 q^{62} +1.00000 q^{64} +8.74456 q^{65} +(2.31386 + 0.543620i) q^{66} -2.11684 q^{67} +(0.686141 + 1.18843i) q^{68} +(1.93070 - 2.05446i) q^{69} -7.11684 q^{71} +(2.50000 - 1.65831i) q^{72} +(6.05842 + 10.4935i) q^{73} +(1.00000 - 1.73205i) q^{74} +(23.8030 + 5.59230i) q^{75} +(2.50000 - 4.33013i) q^{76} +(3.37228 + 0.792287i) q^{78} -5.11684 q^{79} +(2.18614 + 3.78651i) q^{80} +(3.50000 - 8.29156i) q^{81} +(-2.31386 + 4.00772i) q^{82} +(8.74456 + 15.1460i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(-4.05842 - 7.02939i) q^{86} +(10.3723 - 11.0371i) q^{87} +(-0.686141 + 1.18843i) q^{88} +(7.37228 - 12.7692i) q^{89} +(11.7446 + 5.84096i) q^{90} +(0.813859 + 1.40965i) q^{92} +(1.00000 + 3.31662i) q^{93} +21.8614 q^{95} +(0.500000 + 1.65831i) q^{96} +(-4.05842 - 7.02939i) q^{97} +(0.255437 + 4.10891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} - 2q^{3} + 4q^{4} + 3q^{5} + 2q^{6} - 4q^{8} - 10q^{9} + O(q^{10}) \) \( 4q - 4q^{2} - 2q^{3} + 4q^{4} + 3q^{5} + 2q^{6} - 4q^{8} - 10q^{9} - 3q^{10} - 3q^{11} - 2q^{12} + 4q^{13} + 15q^{15} + 4q^{16} - 3q^{17} + 10q^{18} + 10q^{19} + 3q^{20} + 3q^{22} + 9q^{23} + 2q^{24} - 11q^{25} - 4q^{26} + 16q^{27} + 6q^{29} - 15q^{30} - 8q^{31} - 4q^{32} - 15q^{33} + 3q^{34} - 10q^{36} - 4q^{37} - 10q^{38} - 2q^{39} - 3q^{40} + 15q^{41} - q^{43} - 3q^{44} - 24q^{45} - 9q^{46} - 2q^{48} + 11q^{50} + 18q^{51} + 4q^{52} + 6q^{53} - 16q^{54} + 24q^{55} - 5q^{57} - 6q^{58} + 6q^{59} + 15q^{60} + 22q^{61} + 8q^{62} + 4q^{64} + 12q^{65} + 15q^{66} + 26q^{67} - 3q^{68} - 21q^{69} + 6q^{71} + 10q^{72} + 7q^{73} + 4q^{74} + 55q^{75} + 10q^{76} + 2q^{78} + 14q^{79} + 3q^{80} + 14q^{81} - 15q^{82} + 12q^{83} - 12q^{85} + q^{86} + 30q^{87} + 3q^{88} + 18q^{89} + 24q^{90} + 9q^{92} + 4q^{93} + 30q^{95} + 2q^{96} + q^{97} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.500000 1.65831i −0.288675 0.957427i
\(4\) 1.00000 0.500000
\(5\) 2.18614 + 3.78651i 0.977672 + 1.69338i 0.670820 + 0.741620i \(0.265942\pi\)
0.306851 + 0.951757i \(0.400725\pi\)
\(6\) 0.500000 + 1.65831i 0.204124 + 0.677003i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −2.50000 + 1.65831i −0.833333 + 0.552771i
\(10\) −2.18614 3.78651i −0.691318 1.19740i
\(11\) 0.686141 1.18843i 0.206879 0.358325i −0.743851 0.668346i \(-0.767003\pi\)
0.950730 + 0.310021i \(0.100336\pi\)
\(12\) −0.500000 1.65831i −0.144338 0.478714i
\(13\) 1.00000 1.73205i 0.277350 0.480384i −0.693375 0.720577i \(-0.743877\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) 0 0
\(15\) 5.18614 5.51856i 1.33906 1.42489i
\(16\) 1.00000 0.250000
\(17\) 0.686141 + 1.18843i 0.166414 + 0.288237i 0.937156 0.348910i \(-0.113448\pi\)
−0.770743 + 0.637146i \(0.780115\pi\)
\(18\) 2.50000 1.65831i 0.589256 0.390868i
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) 2.18614 + 3.78651i 0.488836 + 0.846689i
\(21\) 0 0
\(22\) −0.686141 + 1.18843i −0.146286 + 0.253374i
\(23\) 0.813859 + 1.40965i 0.169701 + 0.293931i 0.938315 0.345782i \(-0.112386\pi\)
−0.768613 + 0.639713i \(0.779053\pi\)
\(24\) 0.500000 + 1.65831i 0.102062 + 0.338502i
\(25\) −7.05842 + 12.2255i −1.41168 + 2.44511i
\(26\) −1.00000 + 1.73205i −0.196116 + 0.339683i
\(27\) 4.00000 + 3.31662i 0.769800 + 0.638285i
\(28\) 0 0
\(29\) 4.37228 + 7.57301i 0.811912 + 1.40627i 0.911524 + 0.411247i \(0.134907\pi\)
−0.0996117 + 0.995026i \(0.531760\pi\)
\(30\) −5.18614 + 5.51856i −0.946855 + 1.00755i
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.31386 0.543620i −0.402791 0.0946322i
\(34\) −0.686141 1.18843i −0.117672 0.203814i
\(35\) 0 0
\(36\) −2.50000 + 1.65831i −0.416667 + 0.276385i
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) −2.50000 + 4.33013i −0.405554 + 0.702439i
\(39\) −3.37228 0.792287i −0.539997 0.126867i
\(40\) −2.18614 3.78651i −0.345659 0.598699i
\(41\) 2.31386 4.00772i 0.361364 0.625901i −0.626821 0.779163i \(-0.715644\pi\)
0.988186 + 0.153262i \(0.0489778\pi\)
\(42\) 0 0
\(43\) 4.05842 + 7.02939i 0.618904 + 1.07197i 0.989686 + 0.143253i \(0.0457562\pi\)
−0.370783 + 0.928720i \(0.620910\pi\)
\(44\) 0.686141 1.18843i 0.103440 0.179163i
\(45\) −11.7446 5.84096i −1.75078 0.870719i
\(46\) −0.813859 1.40965i −0.119997 0.207841i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) −0.500000 1.65831i −0.0721688 0.239357i
\(49\) 0 0
\(50\) 7.05842 12.2255i 0.998212 1.72895i
\(51\) 1.62772 1.73205i 0.227926 0.242536i
\(52\) 1.00000 1.73205i 0.138675 0.240192i
\(53\) 4.37228 + 7.57301i 0.600579 + 1.04023i 0.992733 + 0.120334i \(0.0383965\pi\)
−0.392154 + 0.919899i \(0.628270\pi\)
\(54\) −4.00000 3.31662i −0.544331 0.451335i
\(55\) 6.00000 0.809040
\(56\) 0 0
\(57\) −8.43070 1.98072i −1.11667 0.262352i
\(58\) −4.37228 7.57301i −0.574109 0.994385i
\(59\) 10.1168 1.31710 0.658550 0.752537i \(-0.271170\pi\)
0.658550 + 0.752537i \(0.271170\pi\)
\(60\) 5.18614 5.51856i 0.669528 0.712443i
\(61\) −3.11684 −0.399071 −0.199535 0.979891i \(-0.563943\pi\)
−0.199535 + 0.979891i \(0.563943\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 8.74456 1.08463
\(66\) 2.31386 + 0.543620i 0.284816 + 0.0669150i
\(67\) −2.11684 −0.258614 −0.129307 0.991605i \(-0.541275\pi\)
−0.129307 + 0.991605i \(0.541275\pi\)
\(68\) 0.686141 + 1.18843i 0.0832068 + 0.144118i
\(69\) 1.93070 2.05446i 0.232429 0.247327i
\(70\) 0 0
\(71\) −7.11684 −0.844614 −0.422307 0.906453i \(-0.638780\pi\)
−0.422307 + 0.906453i \(0.638780\pi\)
\(72\) 2.50000 1.65831i 0.294628 0.195434i
\(73\) 6.05842 + 10.4935i 0.709085 + 1.22817i 0.965197 + 0.261524i \(0.0842249\pi\)
−0.256112 + 0.966647i \(0.582442\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) 23.8030 + 5.59230i 2.74853 + 0.645743i
\(76\) 2.50000 4.33013i 0.286770 0.496700i
\(77\) 0 0
\(78\) 3.37228 + 0.792287i 0.381836 + 0.0897088i
\(79\) −5.11684 −0.575690 −0.287845 0.957677i \(-0.592939\pi\)
−0.287845 + 0.957677i \(0.592939\pi\)
\(80\) 2.18614 + 3.78651i 0.244418 + 0.423344i
\(81\) 3.50000 8.29156i 0.388889 0.921285i
\(82\) −2.31386 + 4.00772i −0.255523 + 0.442579i
\(83\) 8.74456 + 15.1460i 0.959840 + 1.66249i 0.722881 + 0.690973i \(0.242818\pi\)
0.236960 + 0.971519i \(0.423849\pi\)
\(84\) 0 0
\(85\) −3.00000 + 5.19615i −0.325396 + 0.563602i
\(86\) −4.05842 7.02939i −0.437631 0.757999i
\(87\) 10.3723 11.0371i 1.11203 1.18330i
\(88\) −0.686141 + 1.18843i −0.0731428 + 0.126687i
\(89\) 7.37228 12.7692i 0.781460 1.35353i −0.149631 0.988742i \(-0.547808\pi\)
0.931091 0.364787i \(-0.118858\pi\)
\(90\) 11.7446 + 5.84096i 1.23799 + 0.615692i
\(91\) 0 0
\(92\) 0.813859 + 1.40965i 0.0848507 + 0.146966i
\(93\) 1.00000 + 3.31662i 0.103695 + 0.343918i
\(94\) 0 0
\(95\) 21.8614 2.24293
\(96\) 0.500000 + 1.65831i 0.0510310 + 0.169251i
\(97\) −4.05842 7.02939i −0.412070 0.713727i 0.583046 0.812439i \(-0.301861\pi\)
−0.995116 + 0.0987127i \(0.968528\pi\)
\(98\) 0 0
\(99\) 0.255437 + 4.10891i 0.0256724 + 0.412961i
\(100\) −7.05842 + 12.2255i −0.705842 + 1.22255i
\(101\) 0.813859 1.40965i 0.0809820 0.140265i −0.822690 0.568490i \(-0.807528\pi\)
0.903672 + 0.428225i \(0.140861\pi\)
\(102\) −1.62772 + 1.73205i −0.161168 + 0.171499i
\(103\) −5.00000 8.66025i −0.492665 0.853320i 0.507300 0.861770i \(-0.330644\pi\)
−0.999964 + 0.00844953i \(0.997310\pi\)
\(104\) −1.00000 + 1.73205i −0.0980581 + 0.169842i
\(105\) 0 0
\(106\) −4.37228 7.57301i −0.424674 0.735556i
\(107\) 3.68614 6.38458i 0.356353 0.617221i −0.630996 0.775786i \(-0.717354\pi\)
0.987348 + 0.158565i \(0.0506868\pi\)
\(108\) 4.00000 + 3.31662i 0.384900 + 0.319142i
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) −6.00000 −0.572078
\(111\) 3.37228 + 0.792287i 0.320083 + 0.0752006i
\(112\) 0 0
\(113\) 2.18614 3.78651i 0.205655 0.356205i −0.744686 0.667415i \(-0.767401\pi\)
0.950341 + 0.311210i \(0.100734\pi\)
\(114\) 8.43070 + 1.98072i 0.789608 + 0.185511i
\(115\) −3.55842 + 6.16337i −0.331825 + 0.574737i
\(116\) 4.37228 + 7.57301i 0.405956 + 0.703137i
\(117\) 0.372281 + 5.98844i 0.0344174 + 0.553631i
\(118\) −10.1168 −0.931331
\(119\) 0 0
\(120\) −5.18614 + 5.51856i −0.473428 + 0.503773i
\(121\) 4.55842 + 7.89542i 0.414402 + 0.717765i
\(122\) 3.11684 0.282186
\(123\) −7.80298 1.83324i −0.703571 0.165298i
\(124\) −2.00000 −0.179605
\(125\) −39.8614 −3.56531
\(126\) 0 0
\(127\) 3.11684 0.276575 0.138288 0.990392i \(-0.455840\pi\)
0.138288 + 0.990392i \(0.455840\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 9.62772 10.2448i 0.847673 0.902007i
\(130\) −8.74456 −0.766949
\(131\) −0.813859 1.40965i −0.0711072 0.123161i 0.828280 0.560315i \(-0.189320\pi\)
−0.899387 + 0.437154i \(0.855987\pi\)
\(132\) −2.31386 0.543620i −0.201396 0.0473161i
\(133\) 0 0
\(134\) 2.11684 0.182867
\(135\) −3.81386 + 22.3966i −0.328245 + 1.92760i
\(136\) −0.686141 1.18843i −0.0588361 0.101907i
\(137\) −5.31386 + 9.20387i −0.453994 + 0.786340i −0.998630 0.0523324i \(-0.983334\pi\)
0.544636 + 0.838672i \(0.316668\pi\)
\(138\) −1.93070 + 2.05446i −0.164352 + 0.174887i
\(139\) 6.61684 11.4607i 0.561233 0.972085i −0.436156 0.899871i \(-0.643660\pi\)
0.997389 0.0722136i \(-0.0230063\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 7.11684 0.597232
\(143\) −1.37228 2.37686i −0.114756 0.198763i
\(144\) −2.50000 + 1.65831i −0.208333 + 0.138193i
\(145\) −19.1168 + 33.1113i −1.58757 + 2.74975i
\(146\) −6.05842 10.4935i −0.501399 0.868448i
\(147\) 0 0
\(148\) −1.00000 + 1.73205i −0.0821995 + 0.142374i
\(149\) −1.62772 2.81929i −0.133348 0.230965i 0.791617 0.611017i \(-0.209239\pi\)
−0.924965 + 0.380052i \(0.875906\pi\)
\(150\) −23.8030 5.59230i −1.94351 0.456609i
\(151\) −4.55842 + 7.89542i −0.370959 + 0.642520i −0.989713 0.143065i \(-0.954304\pi\)
0.618754 + 0.785585i \(0.287638\pi\)
\(152\) −2.50000 + 4.33013i −0.202777 + 0.351220i
\(153\) −3.68614 1.83324i −0.298007 0.148209i
\(154\) 0 0
\(155\) −4.37228 7.57301i −0.351190 0.608279i
\(156\) −3.37228 0.792287i −0.269999 0.0634337i
\(157\) −9.11684 −0.727603 −0.363802 0.931476i \(-0.618521\pi\)
−0.363802 + 0.931476i \(0.618521\pi\)
\(158\) 5.11684 0.407074
\(159\) 10.3723 11.0371i 0.822575 0.875300i
\(160\) −2.18614 3.78651i −0.172830 0.299350i
\(161\) 0 0
\(162\) −3.50000 + 8.29156i −0.274986 + 0.651447i
\(163\) 9.11684 15.7908i 0.714086 1.23683i −0.249225 0.968446i \(-0.580176\pi\)
0.963311 0.268388i \(-0.0864909\pi\)
\(164\) 2.31386 4.00772i 0.180682 0.312951i
\(165\) −3.00000 9.94987i −0.233550 0.774597i
\(166\) −8.74456 15.1460i −0.678710 1.17556i
\(167\) −2.74456 + 4.75372i −0.212381 + 0.367854i −0.952459 0.304666i \(-0.901455\pi\)
0.740078 + 0.672521i \(0.234788\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 3.00000 5.19615i 0.230089 0.398527i
\(171\) 0.930703 + 14.9711i 0.0711727 + 1.14487i
\(172\) 4.05842 + 7.02939i 0.309452 + 0.535986i
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −10.3723 + 11.0371i −0.786321 + 0.836722i
\(175\) 0 0
\(176\) 0.686141 1.18843i 0.0517198 0.0895813i
\(177\) −5.05842 16.7769i −0.380214 1.26103i
\(178\) −7.37228 + 12.7692i −0.552576 + 0.957089i
\(179\) −1.62772 2.81929i −0.121661 0.210724i 0.798762 0.601648i \(-0.205489\pi\)
−0.920423 + 0.390924i \(0.872156\pi\)
\(180\) −11.7446 5.84096i −0.875388 0.435360i
\(181\) −0.883156 −0.0656445 −0.0328222 0.999461i \(-0.510450\pi\)
−0.0328222 + 0.999461i \(0.510450\pi\)
\(182\) 0 0
\(183\) 1.55842 + 5.16870i 0.115202 + 0.382081i
\(184\) −0.813859 1.40965i −0.0599985 0.103920i
\(185\) −8.74456 −0.642913
\(186\) −1.00000 3.31662i −0.0733236 0.243187i
\(187\) 1.88316 0.137710
\(188\) 0 0
\(189\) 0 0
\(190\) −21.8614 −1.58599
\(191\) −19.1168 −1.38325 −0.691623 0.722259i \(-0.743104\pi\)
−0.691623 + 0.722259i \(0.743104\pi\)
\(192\) −0.500000 1.65831i −0.0360844 0.119678i
\(193\) −7.00000 −0.503871 −0.251936 0.967744i \(-0.581067\pi\)
−0.251936 + 0.967744i \(0.581067\pi\)
\(194\) 4.05842 + 7.02939i 0.291378 + 0.504681i
\(195\) −4.37228 14.5012i −0.313106 1.03845i
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) −0.255437 4.10891i −0.0181531 0.292008i
\(199\) −5.00000 8.66025i −0.354441 0.613909i 0.632581 0.774494i \(-0.281995\pi\)
−0.987022 + 0.160585i \(0.948662\pi\)
\(200\) 7.05842 12.2255i 0.499106 0.864477i
\(201\) 1.05842 + 3.51039i 0.0746553 + 0.247604i
\(202\) −0.813859 + 1.40965i −0.0572629 + 0.0991823i
\(203\) 0 0
\(204\) 1.62772 1.73205i 0.113963 0.121268i
\(205\) 20.2337 1.41318
\(206\) 5.00000 + 8.66025i 0.348367 + 0.603388i
\(207\) −4.37228 2.17448i −0.303895 0.151137i
\(208\) 1.00000 1.73205i 0.0693375 0.120096i
\(209\) −3.43070 5.94215i −0.237307 0.411027i
\(210\) 0 0
\(211\) 8.00000 13.8564i 0.550743 0.953914i −0.447478 0.894295i \(-0.647678\pi\)
0.998221 0.0596196i \(-0.0189888\pi\)
\(212\) 4.37228 + 7.57301i 0.300290 + 0.520117i
\(213\) 3.55842 + 11.8020i 0.243819 + 0.808656i
\(214\) −3.68614 + 6.38458i −0.251979 + 0.436441i
\(215\) −17.7446 + 30.7345i −1.21017 + 2.09607i
\(216\) −4.00000 3.31662i −0.272166 0.225668i
\(217\) 0 0
\(218\) 7.00000 + 12.1244i 0.474100 + 0.821165i
\(219\) 14.3723 15.2935i 0.971189 1.03344i
\(220\) 6.00000 0.404520
\(221\) 2.74456 0.184619
\(222\) −3.37228 0.792287i −0.226333 0.0531748i
\(223\) −2.00000 3.46410i −0.133930 0.231973i 0.791258 0.611482i \(-0.209426\pi\)
−0.925188 + 0.379509i \(0.876093\pi\)
\(224\) 0 0
\(225\) −2.62772 42.2689i −0.175181 2.81793i
\(226\) −2.18614 + 3.78651i −0.145420 + 0.251875i
\(227\) −6.12772 + 10.6135i −0.406711 + 0.704444i −0.994519 0.104556i \(-0.966658\pi\)
0.587808 + 0.809000i \(0.299991\pi\)
\(228\) −8.43070 1.98072i −0.558337 0.131176i
\(229\) −1.44158 2.49689i −0.0952622 0.164999i 0.814456 0.580226i \(-0.197036\pi\)
−0.909718 + 0.415227i \(0.863702\pi\)
\(230\) 3.55842 6.16337i 0.234635 0.406400i
\(231\) 0 0
\(232\) −4.37228 7.57301i −0.287054 0.497193i
\(233\) 0.127719 0.221215i 0.00836713 0.0144923i −0.861812 0.507229i \(-0.830670\pi\)
0.870179 + 0.492736i \(0.164003\pi\)
\(234\) −0.372281 5.98844i −0.0243368 0.391477i
\(235\) 0 0
\(236\) 10.1168 0.658550
\(237\) 2.55842 + 8.48533i 0.166187 + 0.551181i
\(238\) 0 0
\(239\) −4.93070 + 8.54023i −0.318941 + 0.552421i −0.980267 0.197677i \(-0.936660\pi\)
0.661327 + 0.750098i \(0.269994\pi\)
\(240\) 5.18614 5.51856i 0.334764 0.356221i
\(241\) 9.05842 15.6896i 0.583504 1.01066i −0.411556 0.911385i \(-0.635014\pi\)
0.995060 0.0992745i \(-0.0316522\pi\)
\(242\) −4.55842 7.89542i −0.293026 0.507537i
\(243\) −15.5000 1.65831i −0.994325 0.106381i
\(244\) −3.11684 −0.199535
\(245\) 0 0
\(246\) 7.80298 + 1.83324i 0.497500 + 0.116883i
\(247\) −5.00000 8.66025i −0.318142 0.551039i
\(248\) 2.00000 0.127000
\(249\) 20.7446 22.0742i 1.31463 1.39890i
\(250\) 39.8614 2.52106
\(251\) 9.00000 0.568075 0.284037 0.958813i \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) 0 0
\(253\) 2.23369 0.140431
\(254\) −3.11684 −0.195568
\(255\) 10.1168 + 2.37686i 0.633541 + 0.148845i
\(256\) 1.00000 0.0625000
\(257\) −3.43070 5.94215i −0.214001 0.370661i 0.738962 0.673747i \(-0.235316\pi\)
−0.952963 + 0.303086i \(0.901983\pi\)
\(258\) −9.62772 + 10.2448i −0.599396 + 0.637815i
\(259\) 0 0
\(260\) 8.74456 0.542315
\(261\) −23.4891 11.6819i −1.45394 0.723093i
\(262\) 0.813859 + 1.40965i 0.0502804 + 0.0870882i
\(263\) −3.81386 + 6.60580i −0.235173 + 0.407331i −0.959323 0.282311i \(-0.908899\pi\)
0.724150 + 0.689642i \(0.242232\pi\)
\(264\) 2.31386 + 0.543620i 0.142408 + 0.0334575i
\(265\) −19.1168 + 33.1113i −1.17434 + 2.03401i
\(266\) 0 0
\(267\) −24.8614 5.84096i −1.52149 0.357461i
\(268\) −2.11684 −0.129307
\(269\) −0.813859 1.40965i −0.0496219 0.0859476i 0.840148 0.542358i \(-0.182468\pi\)
−0.889769 + 0.456410i \(0.849135\pi\)
\(270\) 3.81386 22.3966i 0.232104 1.36302i
\(271\) 8.11684 14.0588i 0.493063 0.854010i −0.506905 0.862002i \(-0.669210\pi\)
0.999968 + 0.00799154i \(0.00254381\pi\)
\(272\) 0.686141 + 1.18843i 0.0416034 + 0.0720592i
\(273\) 0 0
\(274\) 5.31386 9.20387i 0.321022 0.556026i
\(275\) 9.68614 + 16.7769i 0.584096 + 1.01168i
\(276\) 1.93070 2.05446i 0.116215 0.123664i
\(277\) 6.11684 10.5947i 0.367526 0.636573i −0.621652 0.783293i \(-0.713538\pi\)
0.989178 + 0.146720i \(0.0468717\pi\)
\(278\) −6.61684 + 11.4607i −0.396852 + 0.687368i
\(279\) 5.00000 3.31662i 0.299342 0.198561i
\(280\) 0 0
\(281\) −8.18614 14.1788i −0.488344 0.845837i 0.511566 0.859244i \(-0.329066\pi\)
−0.999910 + 0.0134071i \(0.995732\pi\)
\(282\) 0 0
\(283\) −27.1168 −1.61193 −0.805965 0.591964i \(-0.798353\pi\)
−0.805965 + 0.591964i \(0.798353\pi\)
\(284\) −7.11684 −0.422307
\(285\) −10.9307 36.2530i −0.647479 2.14744i
\(286\) 1.37228 + 2.37686i 0.0811447 + 0.140547i
\(287\) 0 0
\(288\) 2.50000 1.65831i 0.147314 0.0977170i
\(289\) 7.55842 13.0916i 0.444613 0.770092i
\(290\) 19.1168 33.1113i 1.12258 1.94437i
\(291\) −9.62772 + 10.2448i −0.564387 + 0.600562i
\(292\) 6.05842 + 10.4935i 0.354542 + 0.614085i
\(293\) −5.18614 + 8.98266i −0.302978 + 0.524773i −0.976809 0.214113i \(-0.931314\pi\)
0.673831 + 0.738885i \(0.264647\pi\)
\(294\) 0 0
\(295\) 22.1168 + 38.3075i 1.28769 + 2.23035i
\(296\) 1.00000 1.73205i 0.0581238 0.100673i
\(297\) 6.68614 2.47805i 0.387969 0.143791i
\(298\) 1.62772 + 2.81929i 0.0942912 + 0.163317i
\(299\) 3.25544 0.188267
\(300\) 23.8030 + 5.59230i 1.37427 + 0.322871i
\(301\) 0 0
\(302\) 4.55842 7.89542i 0.262308 0.454330i
\(303\) −2.74456 0.644810i −0.157671 0.0370434i
\(304\) 2.50000 4.33013i 0.143385 0.248350i
\(305\) −6.81386 11.8020i −0.390160 0.675778i
\(306\) 3.68614 + 1.83324i 0.210723 + 0.104799i
\(307\) 13.0000 0.741949 0.370975 0.928643i \(-0.379024\pi\)
0.370975 + 0.928643i \(0.379024\pi\)
\(308\) 0 0
\(309\) −11.8614 + 12.6217i −0.674772 + 0.718023i
\(310\) 4.37228 + 7.57301i 0.248329 + 0.430118i
\(311\) −8.23369 −0.466890 −0.233445 0.972370i \(-0.575000\pi\)
−0.233445 + 0.972370i \(0.575000\pi\)
\(312\) 3.37228 + 0.792287i 0.190918 + 0.0448544i
\(313\) 20.1168 1.13707 0.568536 0.822659i \(-0.307510\pi\)
0.568536 + 0.822659i \(0.307510\pi\)
\(314\) 9.11684 0.514493
\(315\) 0 0
\(316\) −5.11684 −0.287845
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) −10.3723 + 11.0371i −0.581649 + 0.618931i
\(319\) 12.0000 0.671871
\(320\) 2.18614 + 3.78651i 0.122209 + 0.211672i
\(321\) −12.4307 2.92048i −0.693814 0.163005i
\(322\) 0 0
\(323\) 6.86141 0.381779
\(324\) 3.50000 8.29156i 0.194444 0.460642i
\(325\) 14.1168 + 24.4511i 0.783062 + 1.35630i
\(326\) −9.11684 + 15.7908i −0.504935 + 0.874574i
\(327\) −16.6060 + 17.6704i −0.918312 + 0.977173i
\(328\) −2.31386 + 4.00772i −0.127762 + 0.221289i
\(329\) 0 0
\(330\) 3.00000 + 9.94987i 0.165145 + 0.547723i
\(331\) 22.2337 1.22207 0.611037 0.791602i \(-0.290753\pi\)
0.611037 + 0.791602i \(0.290753\pi\)
\(332\) 8.74456 + 15.1460i 0.479920 + 0.831246i
\(333\) −0.372281 5.98844i −0.0204009 0.328164i
\(334\) 2.74456 4.75372i 0.150176 0.260112i
\(335\) −4.62772 8.01544i −0.252839 0.437930i
\(336\) 0 0
\(337\) 4.05842 7.02939i 0.221076 0.382915i −0.734059 0.679086i \(-0.762376\pi\)
0.955135 + 0.296171i \(0.0957097\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) −7.37228 1.73205i −0.400407 0.0940721i
\(340\) −3.00000 + 5.19615i −0.162698 + 0.281801i
\(341\) −1.37228 + 2.37686i −0.0743132 + 0.128714i
\(342\) −0.930703 14.9711i −0.0503267 0.809544i
\(343\) 0 0
\(344\) −4.05842 7.02939i −0.218815 0.378999i
\(345\) 12.0000 + 2.81929i 0.646058 + 0.151786i
\(346\) −6.00000 −0.322562
\(347\) −10.1168 −0.543101 −0.271550 0.962424i \(-0.587536\pi\)
−0.271550 + 0.962424i \(0.587536\pi\)
\(348\) 10.3723 11.0371i 0.556013 0.591651i
\(349\) −11.0000 19.0526i −0.588817 1.01986i −0.994388 0.105797i \(-0.966261\pi\)
0.405571 0.914063i \(-0.367073\pi\)
\(350\) 0 0
\(351\) 9.74456 3.61158i 0.520126 0.192772i
\(352\) −0.686141 + 1.18843i −0.0365714 + 0.0633436i
\(353\) −6.68614 + 11.5807i −0.355867 + 0.616380i −0.987266 0.159078i \(-0.949148\pi\)
0.631399 + 0.775458i \(0.282481\pi\)
\(354\) 5.05842 + 16.7769i 0.268852 + 0.891682i
\(355\) −15.5584 26.9480i −0.825755 1.43025i
\(356\) 7.37228 12.7692i 0.390730 0.676764i
\(357\) 0 0
\(358\) 1.62772 + 2.81929i 0.0860276 + 0.149004i
\(359\) −10.9307 + 18.9325i −0.576900 + 0.999221i 0.418932 + 0.908018i \(0.362405\pi\)
−0.995832 + 0.0912032i \(0.970929\pi\)
\(360\) 11.7446 + 5.84096i 0.618993 + 0.307846i
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 0.883156 0.0464177
\(363\) 10.8139 11.5070i 0.567580 0.603961i
\(364\) 0 0
\(365\) −26.4891 + 45.8805i −1.38650 + 2.40150i
\(366\) −1.55842 5.16870i −0.0814600 0.270172i
\(367\) −6.11684 + 10.5947i −0.319297 + 0.553038i −0.980341 0.197308i \(-0.936780\pi\)
0.661045 + 0.750346i \(0.270113\pi\)
\(368\) 0.813859 + 1.40965i 0.0424254 + 0.0734829i
\(369\) 0.861407 + 13.8564i 0.0448430 + 0.721336i
\(370\) 8.74456 0.454608
\(371\) 0 0
\(372\) 1.00000 + 3.31662i 0.0518476 + 0.171959i
\(373\) 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i \(-0.0833099\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(374\) −1.88316 −0.0973757
\(375\) 19.9307 + 66.1027i 1.02922 + 3.41353i
\(376\) 0 0
\(377\) 17.4891 0.900736
\(378\) 0 0
\(379\) −8.11684 −0.416934 −0.208467 0.978029i \(-0.566847\pi\)
−0.208467 + 0.978029i \(0.566847\pi\)
\(380\) 21.8614 1.12147
\(381\) −1.55842 5.16870i −0.0798404 0.264801i
\(382\) 19.1168 0.978103
\(383\) −16.3723 28.3576i −0.836584 1.44901i −0.892734 0.450584i \(-0.851216\pi\)
0.0561493 0.998422i \(-0.482118\pi\)
\(384\) 0.500000 + 1.65831i 0.0255155 + 0.0846254i
\(385\) 0 0
\(386\) 7.00000 0.356291
\(387\) −21.8030 10.8434i −1.10831 0.551199i
\(388\) −4.05842 7.02939i −0.206035 0.356863i
\(389\) −5.48913 + 9.50744i −0.278310 + 0.482047i −0.970965 0.239222i \(-0.923107\pi\)
0.692655 + 0.721269i \(0.256441\pi\)
\(390\) 4.37228 + 14.5012i 0.221399 + 0.734298i
\(391\) −1.11684 + 1.93443i −0.0564812 + 0.0978284i
\(392\) 0 0
\(393\) −1.93070 + 2.05446i −0.0973911 + 0.103634i
\(394\) 6.00000 0.302276
\(395\) −11.1861 19.3750i −0.562836 0.974860i
\(396\) 0.255437 + 4.10891i 0.0128362 + 0.206481i
\(397\) −11.0000 + 19.0526i −0.552074 + 0.956221i 0.446051 + 0.895008i \(0.352830\pi\)
−0.998125 + 0.0612128i \(0.980503\pi\)
\(398\) 5.00000 + 8.66025i 0.250627 + 0.434099i
\(399\) 0 0
\(400\) −7.05842 + 12.2255i −0.352921 + 0.611277i
\(401\) 5.87228 + 10.1711i 0.293248 + 0.507920i 0.974576 0.224058i \(-0.0719306\pi\)
−0.681328 + 0.731978i \(0.738597\pi\)
\(402\) −1.05842 3.51039i −0.0527893 0.175082i
\(403\) −2.00000 + 3.46410i −0.0996271 + 0.172559i
\(404\) 0.813859 1.40965i 0.0404910 0.0701325i
\(405\) 39.0475 4.87375i 1.94029 0.242178i
\(406\) 0 0
\(407\) 1.37228 + 2.37686i 0.0680215 + 0.117817i
\(408\) −1.62772 + 1.73205i −0.0805841 + 0.0857493i
\(409\) 22.3505 1.10516 0.552581 0.833459i \(-0.313643\pi\)
0.552581 + 0.833459i \(0.313643\pi\)
\(410\) −20.2337 −0.999271
\(411\) 17.9198 + 4.21010i 0.883920 + 0.207669i
\(412\) −5.00000 8.66025i −0.246332 0.426660i
\(413\) 0 0
\(414\) 4.37228 + 2.17448i 0.214886 + 0.106870i
\(415\) −38.2337 + 66.2227i −1.87682 + 3.25074i
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) −22.3139 5.24244i −1.09271 0.256723i
\(418\) 3.43070 + 5.94215i 0.167801 + 0.290640i
\(419\) −6.30298 + 10.9171i −0.307921 + 0.533335i −0.977907 0.209039i \(-0.932967\pi\)
0.669986 + 0.742373i \(0.266300\pi\)
\(420\) 0 0
\(421\) −17.1168 29.6472i −0.834224 1.44492i −0.894661 0.446746i \(-0.852583\pi\)
0.0604368 0.998172i \(-0.480751\pi\)
\(422\) −8.00000 + 13.8564i −0.389434 + 0.674519i
\(423\) 0 0
\(424\) −4.37228 7.57301i −0.212337 0.367778i
\(425\) −19.3723 −0.939694
\(426\) −3.55842 11.8020i −0.172406 0.571806i
\(427\) 0 0
\(428\) 3.68614 6.38458i 0.178176 0.308610i
\(429\) −3.25544 + 3.46410i −0.157174 + 0.167248i
\(430\) 17.7446 30.7345i 0.855719 1.48215i
\(431\) 3.25544 + 5.63858i 0.156809 + 0.271601i 0.933716 0.358014i \(-0.116546\pi\)
−0.776907 + 0.629615i \(0.783213\pi\)
\(432\) 4.00000 + 3.31662i 0.192450 + 0.159571i
\(433\) 20.1168 0.966754 0.483377 0.875412i \(-0.339410\pi\)
0.483377 + 0.875412i \(0.339410\pi\)
\(434\) 0 0
\(435\) 64.4674 + 15.1460i 3.09097 + 0.726196i
\(436\) −7.00000 12.1244i −0.335239 0.580651i
\(437\) 8.13859 0.389322
\(438\) −14.3723 + 15.2935i −0.686734 + 0.730752i
\(439\) −8.00000 −0.381819 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) −6.00000 −0.286039
\(441\) 0 0
\(442\) −2.74456 −0.130546
\(443\) −40.1168 −1.90601 −0.953004 0.302956i \(-0.902026\pi\)
−0.953004 + 0.302956i \(0.902026\pi\)
\(444\) 3.37228 + 0.792287i 0.160041 + 0.0376003i
\(445\) 64.4674 3.05605
\(446\) 2.00000 + 3.46410i 0.0947027 + 0.164030i
\(447\) −3.86141 + 4.10891i −0.182638 + 0.194345i
\(448\) 0 0
\(449\) 33.0000 1.55737 0.778683 0.627417i \(-0.215888\pi\)
0.778683 + 0.627417i \(0.215888\pi\)
\(450\) 2.62772 + 42.2689i 0.123872 + 1.99258i
\(451\) −3.17527 5.49972i −0.149517 0.258972i
\(452\) 2.18614 3.78651i 0.102827 0.178102i
\(453\) 15.3723 + 3.61158i 0.722253 + 0.169687i
\(454\) 6.12772 10.6135i 0.287588 0.498117i
\(455\) 0 0
\(456\) 8.43070 + 1.98072i 0.394804 + 0.0927556i
\(457\) −35.4674 −1.65909 −0.829547 0.558437i \(-0.811401\pi\)
−0.829547 + 0.558437i \(0.811401\pi\)
\(458\) 1.44158 + 2.49689i 0.0673605 + 0.116672i
\(459\) −1.19702 + 7.02939i −0.0558719 + 0.328104i
\(460\) −3.55842 + 6.16337i −0.165912 + 0.287368i
\(461\) 1.06930 + 1.85208i 0.0498021 + 0.0862598i 0.889852 0.456250i \(-0.150808\pi\)
−0.840050 + 0.542509i \(0.817474\pi\)
\(462\) 0 0
\(463\) 11.5584 20.0198i 0.537165 0.930398i −0.461890 0.886937i \(-0.652828\pi\)
0.999055 0.0434604i \(-0.0138382\pi\)
\(464\) 4.37228 + 7.57301i 0.202978 + 0.351568i
\(465\) −10.3723 + 11.0371i −0.481003 + 0.511834i
\(466\) −0.127719 + 0.221215i −0.00591645 + 0.0102476i
\(467\) 16.5475 28.6612i 0.765729 1.32628i −0.174131 0.984722i \(-0.555712\pi\)
0.939860 0.341559i \(-0.110955\pi\)
\(468\) 0.372281 + 5.98844i 0.0172087 + 0.276816i
\(469\) 0 0
\(470\) 0 0
\(471\) 4.55842 + 15.1186i 0.210041 + 0.696627i
\(472\) −10.1168 −0.465665
\(473\) 11.1386 0.512153
\(474\) −2.55842 8.48533i −0.117512 0.389744i
\(475\) 35.2921 + 61.1277i 1.61931 + 2.80473i
\(476\) 0 0
\(477\) −23.4891 11.6819i −1.07549 0.534879i
\(478\) 4.93070 8.54023i 0.225525 0.390621i
\(479\) 16.3723 28.3576i 0.748069 1.29569i −0.200679 0.979657i \(-0.564315\pi\)
0.948747 0.316036i \(-0.102352\pi\)
\(480\) −5.18614 + 5.51856i −0.236714 + 0.251887i
\(481\) 2.00000 + 3.46410i 0.0911922 + 0.157949i
\(482\) −9.05842 + 15.6896i −0.412600 + 0.714644i
\(483\) 0 0
\(484\) 4.55842 + 7.89542i 0.207201 + 0.358883i
\(485\) 17.7446 30.7345i 0.805739 1.39558i
\(486\) 15.5000 + 1.65831i 0.703094 + 0.0752226i
\(487\) −17.6753 30.6145i −0.800943 1.38727i −0.918996 0.394266i \(-0.870999\pi\)
0.118053 0.993007i \(-0.462335\pi\)
\(488\) 3.11684 0.141093
\(489\) −30.7446 7.22316i −1.39032 0.326642i
\(490\) 0 0
\(491\) 12.6861 21.9730i 0.572518 0.991629i −0.423789 0.905761i \(-0.639300\pi\)
0.996306 0.0858685i \(-0.0273665\pi\)
\(492\) −7.80298 1.83324i −0.351786 0.0826489i
\(493\) −6.00000 + 10.3923i −0.270226 + 0.468046i
\(494\) 5.00000 + 8.66025i 0.224961 + 0.389643i
\(495\) −15.0000 + 9.94987i −0.674200 + 0.447214i
\(496\) −2.00000 −0.0898027
\(497\) 0 0
\(498\) −20.7446 + 22.0742i −0.929586 + 0.989170i
\(499\) −9.05842 15.6896i −0.405511 0.702365i 0.588870 0.808228i \(-0.299573\pi\)
−0.994381 + 0.105863i \(0.966240\pi\)
\(500\) −39.8614 −1.78266
\(501\) 9.25544 + 2.17448i 0.413502 + 0.0971487i
\(502\) −9.00000 −0.401690
\(503\) 32.2337 1.43723 0.718615 0.695409i \(-0.244777\pi\)
0.718615 + 0.695409i \(0.244777\pi\)
\(504\) 0 0
\(505\) 7.11684 0.316695
\(506\) −2.23369 −0.0992995
\(507\) 10.6753 11.3595i 0.474105 0.504494i
\(508\) 3.11684 0.138288
\(509\) −14.4891 25.0959i −0.642219 1.11236i −0.984936 0.172918i \(-0.944681\pi\)
0.342717 0.939439i \(-0.388653\pi\)
\(510\) −10.1168 2.37686i −0.447981 0.105249i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 24.3614 9.02895i 1.07558 0.398638i
\(514\) 3.43070 + 5.94215i 0.151322 + 0.262097i
\(515\) 21.8614 37.8651i 0.963329 1.66853i
\(516\) 9.62772 10.2448i 0.423837 0.451003i
\(517\) 0 0
\(518\) 0 0
\(519\) −3.00000 9.94987i −0.131685 0.436751i
\(520\) −8.74456 −0.383474
\(521\) −12.4307 21.5306i −0.544599 0.943273i −0.998632 0.0522883i \(-0.983349\pi\)
0.454033 0.890985i \(-0.349985\pi\)
\(522\) 23.4891 + 11.6819i 1.02809 + 0.511304i
\(523\) −17.5584 + 30.4121i −0.767776 + 1.32983i 0.170990 + 0.985273i \(0.445303\pi\)
−0.938766 + 0.344555i \(0.888030\pi\)
\(524\) −0.813859 1.40965i −0.0355536 0.0615807i
\(525\) 0 0
\(526\) 3.81386 6.60580i 0.166292 0.288026i
\(527\) −1.37228 2.37686i −0.0597775 0.103538i
\(528\) −2.31386 0.543620i −0.100698 0.0236580i
\(529\) 10.1753 17.6241i 0.442403 0.766264i
\(530\) 19.1168 33.1113i 0.830383 1.43826i
\(531\) −25.2921 + 16.7769i −1.09758 + 0.728055i
\(532\) 0 0
\(533\) −4.62772 8.01544i −0.200449 0.347187i
\(534\) 24.8614 + 5.84096i 1.07586 + 0.252763i
\(535\) 32.2337 1.39358
\(536\) 2.11684 0.0914337
\(537\) −3.86141 + 4.10891i −0.166632 + 0.177313i
\(538\) 0.813859 + 1.40965i 0.0350880 + 0.0607741i
\(539\) 0 0
\(540\) −3.81386 + 22.3966i −0.164122 + 0.963798i
\(541\) 3.11684 5.39853i 0.134004 0.232101i −0.791213 0.611541i \(-0.790550\pi\)
0.925216 + 0.379440i \(0.123883\pi\)
\(542\) −8.11684 + 14.0588i −0.348648 + 0.603877i
\(543\) 0.441578 + 1.46455i 0.0189499 + 0.0628498i
\(544\) −0.686141 1.18843i −0.0294180 0.0509535i
\(545\) 30.6060 53.0111i 1.31102 2.27075i
\(546\) 0 0
\(547\) −9.05842 15.6896i −0.387310 0.670841i 0.604777 0.796395i \(-0.293262\pi\)
−0.992087 + 0.125554i \(0.959929\pi\)
\(548\) −5.31386 + 9.20387i −0.226997 + 0.393170i
\(549\) 7.79211 5.16870i 0.332559 0.220595i
\(550\) −9.68614 16.7769i −0.413018 0.715369i
\(551\) 43.7228 1.86265
\(552\) −1.93070 + 2.05446i −0.0821762 + 0.0874434i
\(553\) 0 0
\(554\) −6.11684 + 10.5947i −0.259880 + 0.450125i
\(555\) 4.37228 + 14.5012i 0.185593 + 0.615542i
\(556\) 6.61684 11.4607i 0.280617 0.486042i
\(557\) −14.7446 25.5383i −0.624747 1.08209i −0.988590 0.150633i \(-0.951869\pi\)
0.363843 0.931460i \(-0.381465\pi\)
\(558\) −5.00000 + 3.31662i −0.211667 + 0.140404i
\(559\) 16.2337 0.686612
\(560\) 0 0
\(561\) −0.941578 3.12286i −0.0397535 0.131847i
\(562\) 8.18614 + 14.1788i 0.345312 + 0.598097i
\(563\) −3.00000 −0.126435 −0.0632175 0.998000i \(-0.520136\pi\)
−0.0632175 + 0.998000i \(0.520136\pi\)
\(564\) 0 0
\(565\) 19.1168 0.804252
\(566\) 27.1168 1.13981
\(567\) 0 0
\(568\) 7.11684 0.298616
\(569\) 16.1168 0.675653 0.337827 0.941208i \(-0.390308\pi\)
0.337827 + 0.941208i \(0.390308\pi\)
\(570\) 10.9307 + 36.2530i 0.457837 + 1.51847i
\(571\) −22.3505 −0.935341 −0.467670 0.883903i \(-0.654907\pi\)
−0.467670 + 0.883903i \(0.654907\pi\)
\(572\) −1.37228 2.37686i −0.0573780 0.0993815i
\(573\) 9.55842 + 31.7017i 0.399309 + 1.32436i
\(574\) 0 0
\(575\) −22.9783 −0.958259
\(576\) −2.50000 + 1.65831i −0.104167 + 0.0690963i
\(577\) 4.94158 + 8.55906i 0.205721 + 0.356319i 0.950362 0.311146i \(-0.100713\pi\)
−0.744641 + 0.667465i \(0.767380\pi\)
\(578\) −7.55842 + 13.0916i −0.314389 + 0.544538i
\(579\) 3.50000 + 11.6082i 0.145455 + 0.482420i
\(580\) −19.1168 + 33.1113i −0.793784 + 1.37487i
\(581\) 0 0
\(582\) 9.62772 10.2448i 0.399082 0.424662i
\(583\) 12.0000 0.496989
\(584\) −6.05842 10.4935i −0.250699 0.434224i
\(585\) −21.8614 + 14.5012i −0.903858 + 0.599552i
\(586\) 5.18614 8.98266i 0.214237 0.371070i
\(587\) 7.24456 + 12.5480i 0.299015 + 0.517909i 0.975911 0.218170i \(-0.0700086\pi\)
−0.676896 + 0.736079i \(0.736675\pi\)
\(588\) 0 0
\(589\) −5.00000 + 8.66025i −0.206021 + 0.356840i
\(590\) −22.1168 38.3075i −0.910536 1.57709i
\(591\) 3.00000 + 9.94987i 0.123404 + 0.409283i
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) 7.37228 12.7692i 0.302743 0.524367i −0.674013 0.738719i \(-0.735431\pi\)
0.976756 + 0.214353i \(0.0687642\pi\)
\(594\) −6.68614 + 2.47805i −0.274336 + 0.101676i
\(595\) 0 0
\(596\) −1.62772 2.81929i −0.0666740 0.115483i
\(597\) −11.8614 + 12.6217i −0.485455 + 0.516571i
\(598\) −3.25544 −0.133125
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) −23.8030 5.59230i −0.971753 0.228305i
\(601\) 12.0584 + 20.8858i 0.491873 + 0.851950i 0.999956 0.00935863i \(-0.00297899\pi\)
−0.508083 + 0.861308i \(0.669646\pi\)
\(602\) 0 0
\(603\) 5.29211 3.51039i 0.215511 0.142954i
\(604\) −4.55842 + 7.89542i −0.185480 + 0.321260i
\(605\) −19.9307 + 34.5210i −0.810298 + 1.40348i
\(606\) 2.74456 + 0.644810i 0.111490 + 0.0261936i
\(607\) 11.1168 + 19.2549i 0.451219 + 0.781534i 0.998462 0.0554398i \(-0.0176561\pi\)
−0.547243 + 0.836974i \(0.684323\pi\)
\(608\) −2.50000 + 4.33013i −0.101388 + 0.175610i
\(609\) 0 0
\(610\) 6.81386 + 11.8020i 0.275885 + 0.477847i
\(611\) 0 0
\(612\) −3.68614 1.83324i −0.149003 0.0741044i
\(613\) 18.1168 + 31.3793i 0.731732 + 1.26740i 0.956142 + 0.292903i \(0.0946213\pi\)
−0.224410 + 0.974495i \(0.572045\pi\)
\(614\) −13.0000 −0.524637
\(615\) −10.1168 33.5538i −0.407951 1.35302i
\(616\) 0 0
\(617\) −9.43070 + 16.3345i −0.379666 + 0.657600i −0.991014 0.133762i \(-0.957294\pi\)
0.611348 + 0.791362i \(0.290628\pi\)
\(618\) 11.8614 12.6217i 0.477136 0.507719i
\(619\) 22.7337 39.3759i 0.913744 1.58265i 0.105014 0.994471i \(-0.466511\pi\)
0.808730 0.588180i \(-0.200156\pi\)
\(620\) −4.37228 7.57301i −0.175595 0.304140i
\(621\) −1.41983 + 8.33785i −0.0569758 + 0.334586i
\(622\) 8.23369 0.330141
\(623\) 0 0
\(624\) −3.37228 0.792287i −0.134999 0.0317169i
\(625\) −51.8505 89.8078i −2.07402 3.59231i
\(626\) −20.1168 −0.804031
\(627\) −8.13859 + 8.66025i −0.325024 + 0.345857i
\(628\) −9.11684 −0.363802
\(629\) −2.74456 −0.109433
\(630\) 0 0
\(631\) −37.3505 −1.48690 −0.743451 0.668791i \(-0.766812\pi\)
−0.743451 + 0.668791i \(0.766812\pi\)
\(632\) 5.11684 0.203537
\(633\) −26.9783 6.33830i −1.07229 0.251925i
\(634\) 6.00000 0.238290
\(635\) 6.81386 + 11.8020i 0.270400 + 0.468346i
\(636\) 10.3723 11.0371i 0.411288 0.437650i
\(637\) 0 0
\(638\) −12.0000 −0.475085
\(639\) 17.7921 11.8020i 0.703845 0.466878i
\(640\) −2.18614 3.78651i −0.0864148 0.149675i
\(641\) −17.1060 + 29.6284i −0.675645 + 1.17025i 0.300635 + 0.953739i \(0.402802\pi\)
−0.976280 + 0.216512i \(0.930532\pi\)
\(642\) 12.4307 + 2.92048i 0.490601 + 0.115262i
\(643\) 13.1753 22.8202i 0.519582 0.899942i −0.480159 0.877181i \(-0.659421\pi\)
0.999741 0.0227606i \(-0.00724556\pi\)
\(644\) 0 0
\(645\) 59.8397 + 14.0588i 2.35618 + 0.553564i
\(646\) −6.86141 −0.269958
\(647\) 2.74456 + 4.75372i 0.107900 + 0.186888i 0.914919 0.403637i \(-0.132254\pi\)
−0.807019 + 0.590525i \(0.798921\pi\)
\(648\) −3.50000 + 8.29156i −0.137493 + 0.325723i
\(649\) 6.94158 12.0232i 0.272481 0.471951i
\(650\) −14.1168 24.4511i −0.553708 0.959051i
\(651\) 0 0
\(652\) 9.11684 15.7908i 0.357043 0.618417i
\(653\) 13.3723 + 23.1615i 0.523298 + 0.906378i 0.999632 + 0.0271143i \(0.00863179\pi\)
−0.476335 + 0.879264i \(0.658035\pi\)
\(654\) 16.6060 17.6704i 0.649345 0.690966i
\(655\) 3.55842 6.16337i 0.139039 0.240823i
\(656\) 2.31386 4.00772i 0.0903410 0.156475i
\(657\) −32.5475 16.1870i −1.26980 0.631514i
\(658\) 0 0
\(659\) 10.3723 + 17.9653i 0.404047 + 0.699829i 0.994210 0.107454i \(-0.0342700\pi\)
−0.590163 + 0.807284i \(0.700937\pi\)
\(660\) −3.00000 9.94987i −0.116775 0.387298i
\(661\) −27.1168 −1.05472 −0.527361 0.849641i \(-0.676819\pi\)
−0.527361 + 0.849641i \(0.676819\pi\)
\(662\) −22.2337 −0.864137
\(663\) −1.37228 4.55134i −0.0532950 0.176759i
\(664\) −8.74456 15.1460i −0.339355 0.587780i
\(665\) 0 0
\(666\) 0.372281 + 5.98844i 0.0144256 + 0.232047i
\(667\) −7.11684 + 12.3267i −0.275565 + 0.477293i
\(668\) −2.74456 + 4.75372i −0.106190 + 0.183927i
\(669\) −4.74456 + 5.04868i −0.183435 + 0.195193i
\(670\) 4.62772 + 8.01544i 0.178784 + 0.309664i
\(671\) −2.13859 + 3.70415i −0.0825595 + 0.142997i
\(672\) 0 0
\(673\) 1.44158 + 2.49689i 0.0555687 + 0.0962479i 0.892472 0.451103i \(-0.148969\pi\)
−0.836903 + 0.547351i \(0.815636\pi\)
\(674\) −4.05842 + 7.02939i −0.156325 + 0.270762i
\(675\) −68.7812 + 25.4920i −2.64739 + 0.981189i
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) −34.4674 −1.32469 −0.662344 0.749199i \(-0.730438\pi\)
−0.662344 + 0.749199i \(0.730438\pi\)
\(678\) 7.37228 + 1.73205i 0.283131 + 0.0665190i
\(679\) 0 0
\(680\) 3.00000 5.19615i 0.115045 0.199263i
\(681\) 20.6644 + 4.85491i 0.791861 + 0.186041i
\(682\) 1.37228 2.37686i 0.0525474 0.0910147i
\(683\) −14.9198 25.8419i −0.570891 0.988813i −0.996475 0.0838936i \(-0.973264\pi\)
0.425583 0.904919i \(-0.360069\pi\)
\(684\) 0.930703 + 14.9711i 0.0355863 + 0.572434i
\(685\) −46.4674 −1.77543
\(686\) 0 0
\(687\) −3.41983 + 3.63903i −0.130475 + 0.138838i
\(688\) 4.05842 + 7.02939i 0.154726 + 0.267993i
\(689\) 17.4891 0.666283
\(690\) −12.0000 2.81929i −0.456832 0.107329i
\(691\) 23.1168 0.879406 0.439703 0.898143i \(-0.355084\pi\)
0.439703 + 0.898143i \(0.355084\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 10.1168 0.384030
\(695\) 57.8614 2.19481
\(696\) −10.3723 + 11.0371i −0.393160 + 0.418361i
\(697\) 6.35053 0.240544
\(698\) 11.0000 + 19.0526i 0.416356 + 0.721150i
\(699\) −0.430703 0.101190i −0.0162907 0.00382735i
\(700\) 0 0
\(701\) −38.2337 −1.44407 −0.722033 0.691858i \(-0.756792\pi\)
−0.722033 + 0.691858i \(0.756792\pi\)
\(702\) −9.74456 + 3.61158i −0.367785 + 0.136310i
\(703\) 5.00000 + 8.66025i 0.188579 + 0.326628i
\(704\) 0.686141 1.18843i 0.0258599 0.0447907i
\(705\) 0 0
\(706\) 6.68614 11.5807i 0.251636 0.435847i
\(707\) 0 0
\(708\) −5.05842 16.7769i −0.190107 0.630514i
\(709\) 44.0000 1.65245 0.826227 0.563337i \(-0.190483\pi\)
0.826227 + 0.563337i \(0.190483\pi\)
\(710\) 15.5584 + 26.9480i 0.583897 + 1.01134i
\(711\) 12.7921 8.48533i 0.479742 0.318225i
\(712\) −7.37228 + 12.7692i −0.276288 + 0.478545i
\(713\) −1.62772 2.81929i −0.0609585 0.105583i
\(714\) 0 0
\(715\) 6.00000 10.3923i 0.224387 0.388650i
\(716\) −1.62772 2.81929i −0.0608307 0.105362i
\(717\) 16.6277 + 3.90653i 0.620974 + 0.145892i
\(718\) 10.9307 18.9325i 0.407930 0.706556i
\(719\) 1.37228 2.37686i 0.0511775 0.0886420i −0.839302 0.543666i \(-0.817036\pi\)
0.890479 + 0.455024i \(0.150369\pi\)
\(720\) −11.7446 5.84096i −0.437694 0.217680i
\(721\) 0 0
\(722\) 3.00000 + 5.19615i 0.111648 + 0.193381i
\(723\) −30.5475 7.17687i −1.13608 0.266911i
\(724\) −0.883156 −0.0328222
\(725\) −123.446 −4.58466
\(726\) −10.8139 + 11.5070i −0.401340 + 0.427065i
\(727\) −18.1168 31.3793i −0.671917 1.16379i −0.977360 0.211583i \(-0.932138\pi\)
0.305443 0.952210i \(-0.401195\pi\)
\(728\) 0 0
\(729\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(730\) 26.4891 45.8805i 0.980407 1.69811i
\(731\) −5.56930 + 9.64630i −0.205988 + 0.356781i
\(732\) 1.55842 + 5.16870i 0.0576009 + 0.191041i
\(733\) −20.5584 35.6082i −0.759343 1.31522i −0.943186 0.332265i \(-0.892187\pi\)
0.183844 0.982956i \(-0.441146\pi\)
\(734\) 6.11684 10.5947i 0.225777 0.391057i
\(735\) 0 0
\(736\) −0.813859 1.40965i −0.0299993 0.0519602i
\(737\) −1.45245 + 2.51572i −0.0535018 + 0.0926678i
\(738\) −0.861407 13.8564i −0.0317088 0.510061i
\(739\) 4.05842 + 7.02939i 0.149291 + 0.258580i 0.930966 0.365106i \(-0.118967\pi\)
−0.781674 + 0.623687i \(0.785634\pi\)
\(740\) −8.74456 −0.321457
\(741\) −11.8614 + 12.6217i −0.435740 + 0.463669i
\(742\) 0 0
\(743\) 6.86141 11.8843i 0.251721 0.435993i −0.712279 0.701896i \(-0.752337\pi\)
0.964000 + 0.265904i \(0.0856703\pi\)
\(744\) −1.00000 3.31662i −0.0366618 0.121593i
\(745\) 7.11684 12.3267i 0.260741 0.451617i
\(746\) −5.00000 8.66025i −0.183063 0.317074i
\(747\) −46.9783 23.3639i −1.71884 0.854839i
\(748\) 1.88316 0.0688550
\(749\) 0 0
\(750\) −19.9307 66.1027i −0.727766 2.41373i
\(751\) 8.55842 + 14.8236i 0.312301 + 0.540922i 0.978860 0.204531i \(-0.0655668\pi\)
−0.666559 + 0.745452i \(0.732234\pi\)
\(752\) 0 0
\(753\) −4.50000 14.9248i −0.163989 0.543890i
\(754\) −17.4891 −0.636916
\(755\) −39.8614 −1.45071
\(756\) 0 0
\(757\) 46.2337 1.68039 0.840196 0.542283i \(-0.182440\pi\)
0.840196 + 0.542283i \(0.182440\pi\)
\(758\) 8.11684 0.294817
\(759\) −1.11684 3.70415i −0.0405389 0.134452i
\(760\) −21.8614 −0.792997
\(761\) 17.7446 + 30.7345i 0.643240 + 1.11412i 0.984705 + 0.174230i \(0.0557435\pi\)
−0.341465 + 0.939894i \(0.610923\pi\)
\(762\) 1.55842 + 5.16870i 0.0564557 + 0.187242i
\(763\) 0 0
\(764\) −19.1168 −0.691623
\(765\) −1.11684 17.9653i −0.0403796 0.649537i
\(766\) 16.3723 + 28.3576i 0.591555 + 1.02460i
\(767\) 10.1168 17.5229i 0.365298 0.632715i
\(768\) −0.500000 1.65831i −0.0180422 0.0598392i
\(769\) −5.00000 + 8.66025i −0.180305 + 0.312297i −0.941984 0.335657i \(-0.891042\pi\)
0.761680 + 0.647954i \(0.224375\pi\)
\(770\) 0 0
\(771\) −8.13859 + 8.66025i −0.293104 + 0.311891i
\(772\) −7.00000 −0.251936
\(773\) −19.9307 34.5210i −0.716858 1.24163i −0.962239 0.272207i \(-0.912246\pi\)
0.245381 0.969427i \(-0.421087\pi\)
\(774\) 21.8030 + 10.8434i 0.783692 + 0.389756i
\(775\) 14.1168 24.4511i 0.507092 0.878309i
\(776\) 4.05842 + 7.02939i 0.145689 + 0.252341i
\(777\) 0 0
\(778\) 5.48913 9.50744i 0.196795 0.340858i
\(779\) −11.5693 20.0386i −0.414513 0.717958i
\(780\) −4.37228 14.5012i −0.156553 0.519227i