Properties

Label 144.2.k.b.37.4
Level $144$
Weight $2$
Character 144.37
Analytic conductor $1.150$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.18939904.2
Defining polynomial: \(x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 43 x^{4} - 44 x^{3} + 30 x^{2} - 12 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.4
Root \(0.500000 - 2.10607i\) of defining polynomial
Character \(\chi\) \(=\) 144.37
Dual form 144.2.k.b.109.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.34277 - 0.443806i) q^{2} +(1.60607 - 1.19186i) q^{4} +(-1.27133 - 1.27133i) q^{5} -0.158942i q^{7} +(1.62764 - 2.31318i) q^{8} +O(q^{10})\) \(q+(1.34277 - 0.443806i) q^{2} +(1.60607 - 1.19186i) q^{4} +(-1.27133 - 1.27133i) q^{5} -0.158942i q^{7} +(1.62764 - 2.31318i) q^{8} +(-2.27133 - 1.14288i) q^{10} +(3.79793 + 3.79793i) q^{11} +(-4.21215 + 4.21215i) q^{13} +(-0.0705392 - 0.213422i) q^{14} +(1.15894 - 3.82843i) q^{16} -3.05320 q^{17} +(-2.15894 + 2.15894i) q^{19} +(-3.55710 - 0.526602i) q^{20} +(6.78530 + 3.41421i) q^{22} -2.82843i q^{23} -1.76744i q^{25} +(-3.78658 + 7.52533i) q^{26} +(-0.189436 - 0.255272i) q^{28} +(-2.09976 + 2.09976i) q^{29} +4.15894 q^{31} +(-0.142883 - 5.65505i) q^{32} +(-4.09976 + 1.35503i) q^{34} +(-0.202067 + 0.202067i) q^{35} +(-5.98737 - 5.98737i) q^{37} +(-1.94082 + 3.85712i) q^{38} +(-5.01008 + 0.871553i) q^{40} +2.60365i q^{41} +(5.75481 + 5.75481i) q^{43} +(10.6264 + 1.57316i) q^{44} +(-1.25527 - 3.79793i) q^{46} +2.82843 q^{47} +6.97474 q^{49} +(-0.784399 - 2.37327i) q^{50} +(-1.74473 + 11.7853i) q^{52} +(-3.55710 - 3.55710i) q^{53} -9.65685i q^{55} +(-0.367661 - 0.258699i) q^{56} +(-1.88761 + 3.75138i) q^{58} +(-4.00000 - 4.00000i) q^{59} +(3.66949 - 3.66949i) q^{61} +(5.58451 - 1.84576i) q^{62} +(-2.70160 - 7.53003i) q^{64} +10.7101 q^{65} +(0.767438 - 0.767438i) q^{67} +(-4.90367 + 3.63899i) q^{68} +(-0.181652 + 0.361009i) q^{70} -0.317883i q^{71} -1.33897i q^{73} +(-10.6969 - 5.38244i) q^{74} +(-0.894263 + 6.04057i) q^{76} +(0.603650 - 0.603650i) q^{77} -9.69382 q^{79} +(-6.34059 + 3.39380i) q^{80} +(1.15551 + 3.49611i) q^{82} +(-0.115816 + 0.115816i) q^{83} +(3.88163 + 3.88163i) q^{85} +(10.2814 + 5.17338i) q^{86} +(14.9670 - 2.60365i) q^{88} -14.3990i q^{89} +(0.669485 + 0.669485i) q^{91} +(-3.37109 - 4.54266i) q^{92} +(3.79793 - 1.25527i) q^{94} +5.48946 q^{95} -0.571533 q^{97} +(9.36548 - 3.09543i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{4} + 12q^{8} + O(q^{10}) \) \( 8q - 4q^{4} + 12q^{8} - 8q^{10} + 8q^{11} - 12q^{14} - 8q^{19} - 16q^{20} - 20q^{26} + 8q^{28} + 16q^{29} + 24q^{31} - 24q^{35} - 16q^{37} + 8q^{38} + 16q^{40} - 8q^{43} + 40q^{44} - 8q^{46} - 8q^{49} + 36q^{50} - 16q^{52} - 16q^{53} - 16q^{58} - 32q^{59} + 16q^{61} + 12q^{62} + 8q^{64} + 16q^{65} - 16q^{67} - 32q^{68} + 32q^{70} - 52q^{74} + 8q^{76} - 16q^{77} - 24q^{79} - 8q^{80} + 40q^{82} + 40q^{83} - 16q^{85} + 16q^{86} + 32q^{88} - 8q^{91} + 16q^{92} + 8q^{94} + 48q^{95} + 40q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.34277 0.443806i 0.949483 0.313818i
\(3\) 0 0
\(4\) 1.60607 1.19186i 0.803037 0.595930i
\(5\) −1.27133 1.27133i −0.568556 0.568556i 0.363168 0.931724i \(-0.381695\pi\)
−0.931724 + 0.363168i \(0.881695\pi\)
\(6\) 0 0
\(7\) 0.158942i 0.0600743i −0.999549 0.0300371i \(-0.990437\pi\)
0.999549 0.0300371i \(-0.00956256\pi\)
\(8\) 1.62764 2.31318i 0.575456 0.817833i
\(9\) 0 0
\(10\) −2.27133 1.14288i −0.718258 0.361411i
\(11\) 3.79793 + 3.79793i 1.14512 + 1.14512i 0.987500 + 0.157620i \(0.0503821\pi\)
0.157620 + 0.987500i \(0.449618\pi\)
\(12\) 0 0
\(13\) −4.21215 + 4.21215i −1.16824 + 1.16824i −0.185617 + 0.982622i \(0.559428\pi\)
−0.982622 + 0.185617i \(0.940572\pi\)
\(14\) −0.0705392 0.213422i −0.0188524 0.0570395i
\(15\) 0 0
\(16\) 1.15894 3.82843i 0.289735 0.957107i
\(17\) −3.05320 −0.740511 −0.370255 0.928930i \(-0.620730\pi\)
−0.370255 + 0.928930i \(0.620730\pi\)
\(18\) 0 0
\(19\) −2.15894 + 2.15894i −0.495295 + 0.495295i −0.909970 0.414675i \(-0.863895\pi\)
0.414675 + 0.909970i \(0.363895\pi\)
\(20\) −3.55710 0.526602i −0.795391 0.117752i
\(21\) 0 0
\(22\) 6.78530 + 3.41421i 1.44663 + 0.727913i
\(23\) 2.82843i 0.589768i −0.955533 0.294884i \(-0.904719\pi\)
0.955533 0.294884i \(-0.0952810\pi\)
\(24\) 0 0
\(25\) 1.76744i 0.353488i
\(26\) −3.78658 + 7.52533i −0.742609 + 1.47584i
\(27\) 0 0
\(28\) −0.189436 0.255272i −0.0358001 0.0482419i
\(29\) −2.09976 + 2.09976i −0.389915 + 0.389915i −0.874657 0.484742i \(-0.838913\pi\)
0.484742 + 0.874657i \(0.338913\pi\)
\(30\) 0 0
\(31\) 4.15894 0.746968 0.373484 0.927637i \(-0.378163\pi\)
0.373484 + 0.927637i \(0.378163\pi\)
\(32\) −0.142883 5.65505i −0.0252584 0.999681i
\(33\) 0 0
\(34\) −4.09976 + 1.35503i −0.703103 + 0.232386i
\(35\) −0.202067 + 0.202067i −0.0341556 + 0.0341556i
\(36\) 0 0
\(37\) −5.98737 5.98737i −0.984317 0.984317i 0.0155615 0.999879i \(-0.495046\pi\)
−0.999879 + 0.0155615i \(0.995046\pi\)
\(38\) −1.94082 + 3.85712i −0.314842 + 0.625707i
\(39\) 0 0
\(40\) −5.01008 + 0.871553i −0.792163 + 0.137805i
\(41\) 2.60365i 0.406622i 0.979114 + 0.203311i \(0.0651702\pi\)
−0.979114 + 0.203311i \(0.934830\pi\)
\(42\) 0 0
\(43\) 5.75481 + 5.75481i 0.877600 + 0.877600i 0.993286 0.115686i \(-0.0369066\pi\)
−0.115686 + 0.993286i \(0.536907\pi\)
\(44\) 10.6264 + 1.57316i 1.60198 + 0.237162i
\(45\) 0 0
\(46\) −1.25527 3.79793i −0.185080 0.559975i
\(47\) 2.82843 0.412568 0.206284 0.978492i \(-0.433863\pi\)
0.206284 + 0.978492i \(0.433863\pi\)
\(48\) 0 0
\(49\) 6.97474 0.996391
\(50\) −0.784399 2.37327i −0.110931 0.335631i
\(51\) 0 0
\(52\) −1.74473 + 11.7853i −0.241950 + 1.63433i
\(53\) −3.55710 3.55710i −0.488605 0.488605i 0.419261 0.907866i \(-0.362289\pi\)
−0.907866 + 0.419261i \(0.862289\pi\)
\(54\) 0 0
\(55\) 9.65685i 1.30213i
\(56\) −0.367661 0.258699i −0.0491307 0.0345701i
\(57\) 0 0
\(58\) −1.88761 + 3.75138i −0.247856 + 0.492580i
\(59\) −4.00000 4.00000i −0.520756 0.520756i 0.397044 0.917800i \(-0.370036\pi\)
−0.917800 + 0.397044i \(0.870036\pi\)
\(60\) 0 0
\(61\) 3.66949 3.66949i 0.469829 0.469829i −0.432030 0.901859i \(-0.642202\pi\)
0.901859 + 0.432030i \(0.142202\pi\)
\(62\) 5.58451 1.84576i 0.709234 0.234412i
\(63\) 0 0
\(64\) −2.70160 7.53003i −0.337700 0.941254i
\(65\) 10.7101 1.32842
\(66\) 0 0
\(67\) 0.767438 0.767438i 0.0937575 0.0937575i −0.658672 0.752430i \(-0.728882\pi\)
0.752430 + 0.658672i \(0.228882\pi\)
\(68\) −4.90367 + 3.63899i −0.594657 + 0.441292i
\(69\) 0 0
\(70\) −0.181652 + 0.361009i −0.0217115 + 0.0431488i
\(71\) 0.317883i 0.0377258i −0.999822 0.0188629i \(-0.993995\pi\)
0.999822 0.0188629i \(-0.00600460\pi\)
\(72\) 0 0
\(73\) 1.33897i 0.156715i −0.996925 0.0783573i \(-0.975032\pi\)
0.996925 0.0783573i \(-0.0249675\pi\)
\(74\) −10.6969 5.38244i −1.24349 0.625696i
\(75\) 0 0
\(76\) −0.894263 + 6.04057i −0.102579 + 0.692901i
\(77\) 0.603650 0.603650i 0.0687923 0.0687923i
\(78\) 0 0
\(79\) −9.69382 −1.09064 −0.545320 0.838228i \(-0.683592\pi\)
−0.545320 + 0.838228i \(0.683592\pi\)
\(80\) −6.34059 + 3.39380i −0.708900 + 0.379438i
\(81\) 0 0
\(82\) 1.15551 + 3.49611i 0.127605 + 0.386081i
\(83\) −0.115816 + 0.115816i −0.0127125 + 0.0127125i −0.713434 0.700722i \(-0.752861\pi\)
0.700722 + 0.713434i \(0.252861\pi\)
\(84\) 0 0
\(85\) 3.88163 + 3.88163i 0.421022 + 0.421022i
\(86\) 10.2814 + 5.17338i 1.10867 + 0.557860i
\(87\) 0 0
\(88\) 14.9670 2.60365i 1.59548 0.277550i
\(89\) 14.3990i 1.52629i −0.646225 0.763147i \(-0.723653\pi\)
0.646225 0.763147i \(-0.276347\pi\)
\(90\) 0 0
\(91\) 0.669485 + 0.669485i 0.0701811 + 0.0701811i
\(92\) −3.37109 4.54266i −0.351460 0.473605i
\(93\) 0 0
\(94\) 3.79793 1.25527i 0.391727 0.129471i
\(95\) 5.48946 0.563206
\(96\) 0 0
\(97\) −0.571533 −0.0580304 −0.0290152 0.999579i \(-0.509237\pi\)
−0.0290152 + 0.999579i \(0.509237\pi\)
\(98\) 9.36548 3.09543i 0.946057 0.312685i
\(99\) 0 0
\(100\) −2.10654 2.83863i −0.210654 0.283863i
\(101\) 7.15296 + 7.15296i 0.711746 + 0.711746i 0.966900 0.255154i \(-0.0821262\pi\)
−0.255154 + 0.966900i \(0.582126\pi\)
\(102\) 0 0
\(103\) 11.3507i 1.11841i −0.829028 0.559207i \(-0.811106\pi\)
0.829028 0.559207i \(-0.188894\pi\)
\(104\) 2.88761 + 16.5993i 0.283154 + 1.62769i
\(105\) 0 0
\(106\) −6.35503 3.19771i −0.617255 0.310589i
\(107\) 0.722018 + 0.722018i 0.0698001 + 0.0698001i 0.741145 0.671345i \(-0.234283\pi\)
−0.671345 + 0.741145i \(0.734283\pi\)
\(108\) 0 0
\(109\) −1.44471 + 1.44471i −0.138378 + 0.138378i −0.772903 0.634525i \(-0.781196\pi\)
0.634525 + 0.772903i \(0.281196\pi\)
\(110\) −4.28577 12.9670i −0.408632 1.23635i
\(111\) 0 0
\(112\) −0.608497 0.184204i −0.0574975 0.0174057i
\(113\) 3.53488 0.332533 0.166267 0.986081i \(-0.446829\pi\)
0.166267 + 0.986081i \(0.446829\pi\)
\(114\) 0 0
\(115\) −3.59587 + 3.59587i −0.335316 + 0.335316i
\(116\) −0.869748 + 5.87498i −0.0807541 + 0.545478i
\(117\) 0 0
\(118\) −7.14631 3.59587i −0.657871 0.331026i
\(119\) 0.485281i 0.0444857i
\(120\) 0 0
\(121\) 17.8486i 1.62260i
\(122\) 3.29874 6.55582i 0.298654 0.593536i
\(123\) 0 0
\(124\) 6.67956 4.95687i 0.599843 0.445140i
\(125\) −8.60365 + 8.60365i −0.769534 + 0.769534i
\(126\) 0 0
\(127\) −1.49791 −0.132918 −0.0664591 0.997789i \(-0.521170\pi\)
−0.0664591 + 0.997789i \(0.521170\pi\)
\(128\) −6.96951 8.91213i −0.616023 0.787728i
\(129\) 0 0
\(130\) 14.3812 4.75318i 1.26131 0.416882i
\(131\) −10.4243 + 10.4243i −0.910775 + 0.910775i −0.996333 0.0855585i \(-0.972733\pi\)
0.0855585 + 0.996333i \(0.472733\pi\)
\(132\) 0 0
\(133\) 0.343146 + 0.343146i 0.0297545 + 0.0297545i
\(134\) 0.689901 1.37109i 0.0595984 0.118444i
\(135\) 0 0
\(136\) −4.96951 + 7.06261i −0.426132 + 0.605614i
\(137\) 13.7954i 1.17862i 0.807907 + 0.589309i \(0.200600\pi\)
−0.807907 + 0.589309i \(0.799400\pi\)
\(138\) 0 0
\(139\) −2.42429 2.42429i −0.205626 0.205626i 0.596779 0.802405i \(-0.296447\pi\)
−0.802405 + 0.596779i \(0.796447\pi\)
\(140\) −0.0836990 + 0.565371i −0.00707386 + 0.0477826i
\(141\) 0 0
\(142\) −0.141078 0.426845i −0.0118390 0.0358200i
\(143\) −31.9949 −2.67555
\(144\) 0 0
\(145\) 5.33897 0.443377
\(146\) −0.594243 1.79793i −0.0491799 0.148798i
\(147\) 0 0
\(148\) −16.7523 2.48005i −1.37703 0.203859i
\(149\) −2.92818 2.92818i −0.239886 0.239886i 0.576917 0.816803i \(-0.304256\pi\)
−0.816803 + 0.576917i \(0.804256\pi\)
\(150\) 0 0
\(151\) 22.6644i 1.84440i 0.386712 + 0.922201i \(0.373611\pi\)
−0.386712 + 0.922201i \(0.626389\pi\)
\(152\) 1.48005 + 8.50799i 0.120048 + 0.690089i
\(153\) 0 0
\(154\) 0.542661 1.07847i 0.0437288 0.0869053i
\(155\) −5.28739 5.28739i −0.424693 0.424693i
\(156\) 0 0
\(157\) −2.78007 + 2.78007i −0.221874 + 0.221874i −0.809287 0.587413i \(-0.800146\pi\)
0.587413 + 0.809287i \(0.300146\pi\)
\(158\) −13.0166 + 4.30217i −1.03554 + 0.342262i
\(159\) 0 0
\(160\) −7.00778 + 7.37109i −0.554014 + 0.582736i
\(161\) −0.449555 −0.0354299
\(162\) 0 0
\(163\) −5.43692 + 5.43692i −0.425853 + 0.425853i −0.887213 0.461360i \(-0.847362\pi\)
0.461360 + 0.887213i \(0.347362\pi\)
\(164\) 3.10318 + 4.18165i 0.242318 + 0.326532i
\(165\) 0 0
\(166\) −0.104115 + 0.206914i −0.00808086 + 0.0160597i
\(167\) 3.95458i 0.306015i 0.988225 + 0.153007i \(0.0488958\pi\)
−0.988225 + 0.153007i \(0.951104\pi\)
\(168\) 0 0
\(169\) 22.4844i 1.72957i
\(170\) 6.93484 + 3.48946i 0.531878 + 0.267629i
\(171\) 0 0
\(172\) 16.1016 + 2.38372i 1.22773 + 0.181757i
\(173\) 15.9814 15.9814i 1.21504 1.21504i 0.245695 0.969347i \(-0.420984\pi\)
0.969347 0.245695i \(-0.0790163\pi\)
\(174\) 0 0
\(175\) −0.280920 −0.0212355
\(176\) 18.9417 10.1385i 1.42778 0.764220i
\(177\) 0 0
\(178\) −6.39037 19.3346i −0.478979 1.44919i
\(179\) 12.2316 12.2316i 0.914235 0.914235i −0.0823670 0.996602i \(-0.526248\pi\)
0.996602 + 0.0823670i \(0.0262480\pi\)
\(180\) 0 0
\(181\) 5.76259 + 5.76259i 0.428330 + 0.428330i 0.888059 0.459729i \(-0.152054\pi\)
−0.459729 + 0.888059i \(0.652054\pi\)
\(182\) 1.19609 + 0.601845i 0.0886599 + 0.0446117i
\(183\) 0 0
\(184\) −6.54266 4.60365i −0.482331 0.339386i
\(185\) 15.2238i 1.11928i
\(186\) 0 0
\(187\) −11.5959 11.5959i −0.847974 0.847974i
\(188\) 4.54266 3.37109i 0.331308 0.245862i
\(189\) 0 0
\(190\) 7.37109 2.43625i 0.534755 0.176744i
\(191\) 16.1674 1.16983 0.584916 0.811094i \(-0.301127\pi\)
0.584916 + 0.811094i \(0.301127\pi\)
\(192\) 0 0
\(193\) −22.1454 −1.59406 −0.797030 0.603940i \(-0.793597\pi\)
−0.797030 + 0.603940i \(0.793597\pi\)
\(194\) −0.767438 + 0.253649i −0.0550989 + 0.0182110i
\(195\) 0 0
\(196\) 11.2019 8.31291i 0.800138 0.593779i
\(197\) 14.2993 + 14.2993i 1.01878 + 1.01878i 0.999820 + 0.0189608i \(0.00603576\pi\)
0.0189608 + 0.999820i \(0.493964\pi\)
\(198\) 0 0
\(199\) 25.0075i 1.77274i 0.462981 + 0.886368i \(0.346780\pi\)
−0.462981 + 0.886368i \(0.653220\pi\)
\(200\) −4.08840 2.87675i −0.289094 0.203417i
\(201\) 0 0
\(202\) 12.7793 + 6.43027i 0.899150 + 0.452432i
\(203\) 0.333739 + 0.333739i 0.0234239 + 0.0234239i
\(204\) 0 0
\(205\) 3.31010 3.31010i 0.231187 0.231187i
\(206\) −5.03749 15.2414i −0.350979 1.06192i
\(207\) 0 0
\(208\) 11.2443 + 21.0075i 0.779649 + 1.45661i
\(209\) −16.3990 −1.13434
\(210\) 0 0
\(211\) 18.4243 18.4243i 1.26838 1.26838i 0.321456 0.946924i \(-0.395828\pi\)
0.946924 0.321456i \(-0.104172\pi\)
\(212\) −9.95252 1.47340i −0.683542 0.101193i
\(213\) 0 0
\(214\) 1.28994 + 0.649070i 0.0881786 + 0.0443695i
\(215\) 14.6325i 0.997930i
\(216\) 0 0
\(217\) 0.661029i 0.0448736i
\(218\) −1.29874 + 2.58108i −0.0879620 + 0.174813i
\(219\) 0 0
\(220\) −11.5096 15.5096i −0.775978 1.04566i
\(221\) 12.8605 12.8605i 0.865094 0.865094i
\(222\) 0 0
\(223\) 18.3465 1.22857 0.614286 0.789083i \(-0.289444\pi\)
0.614286 + 0.789083i \(0.289444\pi\)
\(224\) −0.898823 + 0.0227101i −0.0600551 + 0.00151738i
\(225\) 0 0
\(226\) 4.74653 1.56880i 0.315735 0.104355i
\(227\) 0.115816 0.115816i 0.00768697 0.00768697i −0.703253 0.710940i \(-0.748270\pi\)
0.710940 + 0.703253i \(0.248270\pi\)
\(228\) 0 0
\(229\) 2.84791 + 2.84791i 0.188195 + 0.188195i 0.794916 0.606720i \(-0.207515\pi\)
−0.606720 + 0.794916i \(0.707515\pi\)
\(230\) −3.23256 + 6.42429i −0.213149 + 0.423605i
\(231\) 0 0
\(232\) 1.43948 + 8.27476i 0.0945062 + 0.543264i
\(233\) 11.7211i 0.767874i −0.923359 0.383937i \(-0.874568\pi\)
0.923359 0.383937i \(-0.125432\pi\)
\(234\) 0 0
\(235\) −3.59587 3.59587i −0.234568 0.234568i
\(236\) −11.1917 1.65685i −0.728520 0.107852i
\(237\) 0 0
\(238\) 0.215371 + 0.651622i 0.0139604 + 0.0422384i
\(239\) 13.6517 0.883058 0.441529 0.897247i \(-0.354436\pi\)
0.441529 + 0.897247i \(0.354436\pi\)
\(240\) 0 0
\(241\) 2.13167 0.137313 0.0686565 0.997640i \(-0.478129\pi\)
0.0686565 + 0.997640i \(0.478129\pi\)
\(242\) 7.92130 + 23.9666i 0.509201 + 1.54063i
\(243\) 0 0
\(244\) 1.51995 10.2670i 0.0973049 0.657276i
\(245\) −8.86720 8.86720i −0.566504 0.566504i
\(246\) 0 0
\(247\) 18.1876i 1.15725i
\(248\) 6.76924 9.62038i 0.429847 0.610895i
\(249\) 0 0
\(250\) −7.73439 + 15.3711i −0.489166 + 0.972153i
\(251\) 4.43370 + 4.43370i 0.279853 + 0.279853i 0.833050 0.553198i \(-0.186593\pi\)
−0.553198 + 0.833050i \(0.686593\pi\)
\(252\) 0 0
\(253\) 10.7422 10.7422i 0.675355 0.675355i
\(254\) −2.01136 + 0.664782i −0.126204 + 0.0417121i
\(255\) 0 0
\(256\) −13.3137 8.87385i −0.832107 0.554615i
\(257\) −15.0853 −0.940997 −0.470498 0.882401i \(-0.655926\pi\)
−0.470498 + 0.882401i \(0.655926\pi\)
\(258\) 0 0
\(259\) −0.951642 + 0.951642i −0.0591322 + 0.0591322i
\(260\) 17.2011 12.7649i 1.06677 0.791645i
\(261\) 0 0
\(262\) −9.37109 + 18.6238i −0.578948 + 1.15058i
\(263\) 26.1706i 1.61375i 0.590722 + 0.806875i \(0.298843\pi\)
−0.590722 + 0.806875i \(0.701157\pi\)
\(264\) 0 0
\(265\) 9.04449i 0.555599i
\(266\) 0.613057 + 0.308476i 0.0375889 + 0.0189139i
\(267\) 0 0
\(268\) 0.317883 2.14724i 0.0194178 0.131164i
\(269\) −8.59700 + 8.59700i −0.524168 + 0.524168i −0.918828 0.394659i \(-0.870863\pi\)
0.394659 + 0.918828i \(0.370863\pi\)
\(270\) 0 0
\(271\) 10.6644 0.647815 0.323907 0.946089i \(-0.395003\pi\)
0.323907 + 0.946089i \(0.395003\pi\)
\(272\) −3.53849 + 11.6890i −0.214552 + 0.708748i
\(273\) 0 0
\(274\) 6.12247 + 18.5240i 0.369872 + 1.11908i
\(275\) 6.71261 6.71261i 0.404786 0.404786i
\(276\) 0 0
\(277\) −2.66170 2.66170i −0.159926 0.159926i 0.622608 0.782534i \(-0.286073\pi\)
−0.782534 + 0.622608i \(0.786073\pi\)
\(278\) −4.33119 2.17936i −0.259767 0.130709i
\(279\) 0 0
\(280\) 0.138526 + 0.796310i 0.00827851 + 0.0475886i
\(281\) 10.4496i 0.623368i −0.950186 0.311684i \(-0.899107\pi\)
0.950186 0.311684i \(-0.100893\pi\)
\(282\) 0 0
\(283\) −12.4853 12.4853i −0.742173 0.742173i 0.230823 0.972996i \(-0.425858\pi\)
−0.972996 + 0.230823i \(0.925858\pi\)
\(284\) −0.378872 0.510544i −0.0224819 0.0302952i
\(285\) 0 0
\(286\) −42.9618 + 14.1995i −2.54039 + 0.839635i
\(287\) 0.413828 0.0244275
\(288\) 0 0
\(289\) −7.67794 −0.451644
\(290\) 7.16902 2.36947i 0.420979 0.139140i
\(291\) 0 0
\(292\) −1.59587 2.15049i −0.0933910 0.125848i
\(293\) −21.7410 21.7410i −1.27013 1.27013i −0.946022 0.324104i \(-0.894937\pi\)
−0.324104 0.946022i \(-0.605063\pi\)
\(294\) 0 0
\(295\) 10.1706i 0.592158i
\(296\) −23.5951 + 4.10460i −1.37144 + 0.238575i
\(297\) 0 0
\(298\) −5.23143 2.63234i −0.303049 0.152487i
\(299\) 11.9137 + 11.9137i 0.688990 + 0.688990i
\(300\) 0 0
\(301\) 0.914679 0.914679i 0.0527212 0.0527212i
\(302\) 10.0586 + 30.4331i 0.578806 + 1.75123i
\(303\) 0 0
\(304\) 5.76326 + 10.7674i 0.330546 + 0.617555i
\(305\) −9.33026 −0.534249
\(306\) 0 0
\(307\) 15.0601 15.0601i 0.859523 0.859523i −0.131759 0.991282i \(-0.542062\pi\)
0.991282 + 0.131759i \(0.0420624\pi\)
\(308\) 0.250040 1.68897i 0.0142473 0.0962381i
\(309\) 0 0
\(310\) −9.44633 4.75318i −0.536516 0.269963i
\(311\) 1.77883i 0.100868i 0.998727 + 0.0504342i \(0.0160605\pi\)
−0.998727 + 0.0504342i \(0.983939\pi\)
\(312\) 0 0
\(313\) 2.70320i 0.152794i −0.997077 0.0763971i \(-0.975658\pi\)
0.997077 0.0763971i \(-0.0243417\pi\)
\(314\) −2.49919 + 4.96681i −0.141037 + 0.280293i
\(315\) 0 0
\(316\) −15.5690 + 11.5537i −0.875824 + 0.649945i
\(317\) −15.6025 + 15.6025i −0.876325 + 0.876325i −0.993152 0.116828i \(-0.962728\pi\)
0.116828 + 0.993152i \(0.462728\pi\)
\(318\) 0 0
\(319\) −15.9495 −0.892999
\(320\) −6.13853 + 13.0078i −0.343154 + 0.727157i
\(321\) 0 0
\(322\) −0.603650 + 0.199515i −0.0336401 + 0.0111185i
\(323\) 6.59169 6.59169i 0.366771 0.366771i
\(324\) 0 0
\(325\) 7.44471 + 7.44471i 0.412958 + 0.412958i
\(326\) −4.88761 + 9.71349i −0.270700 + 0.537980i
\(327\) 0 0
\(328\) 6.02271 + 4.23779i 0.332549 + 0.233993i
\(329\) 0.449555i 0.0247848i
\(330\) 0 0
\(331\) 15.4454 + 15.4454i 0.848955 + 0.848955i 0.990003 0.141048i \(-0.0450472\pi\)
−0.141048 + 0.990003i \(0.545047\pi\)
\(332\) −0.0479725 + 0.324045i −0.00263284 + 0.0177843i
\(333\) 0 0
\(334\) 1.75506 + 5.31010i 0.0960329 + 0.290556i
\(335\) −1.95133 −0.106613
\(336\) 0 0
\(337\) −18.8738 −1.02812 −0.514062 0.857753i \(-0.671860\pi\)
−0.514062 + 0.857753i \(0.671860\pi\)
\(338\) −9.97868 30.1914i −0.542769 1.64219i
\(339\) 0 0
\(340\) 10.8605 + 1.60782i 0.588996 + 0.0871965i
\(341\) 15.7954 + 15.7954i 0.855368 + 0.855368i
\(342\) 0 0
\(343\) 2.22117i 0.119932i
\(344\) 22.6786 3.94517i 1.22275 0.212709i
\(345\) 0 0
\(346\) 14.3667 28.5520i 0.772360 1.53496i
\(347\) −19.8337 19.8337i −1.06473 1.06473i −0.997755 0.0669717i \(-0.978666\pi\)
−0.0669717 0.997755i \(-0.521334\pi\)
\(348\) 0 0
\(349\) 11.9718 11.9718i 0.640836 0.640836i −0.309925 0.950761i \(-0.600304\pi\)
0.950761 + 0.309925i \(0.100304\pi\)
\(350\) −0.377211 + 0.124674i −0.0201628 + 0.00666409i
\(351\) 0 0
\(352\) 20.9348 22.0202i 1.11583 1.17368i
\(353\) 12.6202 0.671705 0.335853 0.941915i \(-0.390976\pi\)
0.335853 + 0.941915i \(0.390976\pi\)
\(354\) 0 0
\(355\) −0.404135 + 0.404135i −0.0214492 + 0.0214492i
\(356\) −17.1616 23.1259i −0.909564 1.22567i
\(357\) 0 0
\(358\) 10.9958 21.8528i 0.581147 1.15495i
\(359\) 27.0867i 1.42958i 0.699339 + 0.714790i \(0.253478\pi\)
−0.699339 + 0.714790i \(0.746522\pi\)
\(360\) 0 0
\(361\) 9.67794i 0.509365i
\(362\) 10.2953 + 5.18038i 0.541110 + 0.272274i
\(363\) 0 0
\(364\) 1.87318 + 0.277310i 0.0981811 + 0.0145350i
\(365\) −1.70227 + 1.70227i −0.0891011 + 0.0891011i
\(366\) 0 0
\(367\) −20.4937 −1.06976 −0.534882 0.844927i \(-0.679644\pi\)
−0.534882 + 0.844927i \(0.679644\pi\)
\(368\) −10.8284 3.27798i −0.564471 0.170877i
\(369\) 0 0
\(370\) 6.75643 + 20.4422i 0.351250 + 1.06274i
\(371\) −0.565371 + 0.565371i −0.0293526 + 0.0293526i
\(372\) 0 0
\(373\) 1.03372 + 1.03372i 0.0535239 + 0.0535239i 0.733362 0.679838i \(-0.237950\pi\)
−0.679838 + 0.733362i \(0.737950\pi\)
\(374\) −20.7169 10.4243i −1.07125 0.539027i
\(375\) 0 0
\(376\) 4.60365 6.54266i 0.237415 0.337412i
\(377\) 17.6890i 0.911028i
\(378\) 0 0
\(379\) 17.6686 + 17.6686i 0.907573 + 0.907573i 0.996076 0.0885032i \(-0.0282083\pi\)
−0.0885032 + 0.996076i \(0.528208\pi\)
\(380\) 8.81647 6.54266i 0.452275 0.335631i
\(381\) 0 0
\(382\) 21.7091 7.17518i 1.11074 0.367114i
\(383\) 31.0958 1.58892 0.794460 0.607316i \(-0.207754\pi\)
0.794460 + 0.607316i \(0.207754\pi\)
\(384\) 0 0
\(385\) −1.53488 −0.0782245
\(386\) −29.7362 + 9.82824i −1.51353 + 0.500244i
\(387\) 0 0
\(388\) −0.917923 + 0.681187i −0.0466005 + 0.0345820i
\(389\) 2.56127 + 2.56127i 0.129862 + 0.129862i 0.769050 0.639188i \(-0.220730\pi\)
−0.639188 + 0.769050i \(0.720730\pi\)
\(390\) 0 0
\(391\) 8.63577i 0.436729i
\(392\) 11.3523 16.1338i 0.573379 0.814881i
\(393\) 0 0
\(394\) 25.5468 + 12.8546i 1.28703 + 0.647604i
\(395\) 12.3240 + 12.3240i 0.620090 + 0.620090i
\(396\) 0 0
\(397\) −5.09795 + 5.09795i −0.255859 + 0.255859i −0.823367 0.567509i \(-0.807907\pi\)
0.567509 + 0.823367i \(0.307907\pi\)
\(398\) 11.0985 + 33.5794i 0.556317 + 1.68318i
\(399\) 0 0
\(400\) −6.76651 2.04836i −0.338325 0.102418i
\(401\) 15.2660 0.762349 0.381174 0.924503i \(-0.375520\pi\)
0.381174 + 0.924503i \(0.375520\pi\)
\(402\) 0 0
\(403\) −17.5181 + 17.5181i −0.872637 + 0.872637i
\(404\) 20.0135 + 2.96285i 0.995709 + 0.147407i
\(405\) 0 0
\(406\) 0.596250 + 0.300020i 0.0295914 + 0.0148897i
\(407\) 45.4792i 2.25432i
\(408\) 0 0
\(409\) 11.3779i 0.562603i −0.959619 0.281302i \(-0.909234\pi\)
0.959619 0.281302i \(-0.0907661\pi\)
\(410\) 2.97567 5.91375i 0.146958 0.292059i
\(411\) 0 0
\(412\) −13.5284 18.2300i −0.666497 0.898128i
\(413\) −0.635767 + 0.635767i −0.0312840 + 0.0312840i
\(414\) 0 0
\(415\) 0.294481 0.0144555
\(416\) 24.4217 + 23.2181i 1.19737 + 1.13836i
\(417\) 0 0
\(418\) −22.0202 + 7.27798i −1.07704 + 0.355978i
\(419\) −23.3075 + 23.3075i −1.13865 + 1.13865i −0.149955 + 0.988693i \(0.547913\pi\)
−0.988693 + 0.149955i \(0.952087\pi\)
\(420\) 0 0
\(421\) −17.6154 17.6154i −0.858520 0.858520i 0.132644 0.991164i \(-0.457653\pi\)
−0.991164 + 0.132644i \(0.957653\pi\)
\(422\) 16.5628 32.9164i 0.806265 1.60235i
\(423\) 0 0
\(424\) −14.0179 + 2.43855i −0.680768 + 0.118426i
\(425\) 5.39635i 0.261761i
\(426\) 0 0
\(427\) −0.583234 0.583234i −0.0282247 0.0282247i
\(428\) 2.02016 + 0.299070i 0.0976480 + 0.0144561i
\(429\) 0 0
\(430\) −6.49400 19.6481i −0.313168 0.947517i
\(431\) −10.3211 −0.497151 −0.248576 0.968612i \(-0.579962\pi\)
−0.248576 + 0.968612i \(0.579962\pi\)
\(432\) 0 0
\(433\) −15.3137 −0.735930 −0.367965 0.929840i \(-0.619945\pi\)
−0.367965 + 0.929840i \(0.619945\pi\)
\(434\) −0.293368 0.887611i −0.0140821 0.0426067i
\(435\) 0 0
\(436\) −0.598418 + 4.04220i −0.0286590 + 0.193586i
\(437\) 6.10641 + 6.10641i 0.292109 + 0.292109i
\(438\) 0 0
\(439\) 22.5735i 1.07738i −0.842505 0.538688i \(-0.818920\pi\)
0.842505 0.538688i \(-0.181080\pi\)
\(440\) −22.3380 15.7178i −1.06492 0.749319i
\(441\) 0 0
\(442\) 11.5612 22.9764i 0.549910 1.09287i
\(443\) −23.7117 23.7117i −1.12658 1.12658i −0.990730 0.135846i \(-0.956625\pi\)
−0.135846 0.990730i \(-0.543375\pi\)
\(444\) 0 0
\(445\) −18.3059 + 18.3059i −0.867784 + 0.867784i
\(446\) 24.6352 8.14228i 1.16651 0.385548i
\(447\) 0 0
\(448\) −1.19684 + 0.429397i −0.0565452 + 0.0202871i
\(449\) 1.75506 0.0828266 0.0414133 0.999142i \(-0.486814\pi\)
0.0414133 + 0.999142i \(0.486814\pi\)
\(450\) 0 0
\(451\) −9.88849 + 9.88849i −0.465631 + 0.465631i
\(452\) 5.67727 4.21308i 0.267036 0.198166i
\(453\) 0 0
\(454\) 0.104115 0.206914i 0.00488634 0.00971096i
\(455\) 1.70227i 0.0798039i
\(456\) 0 0
\(457\) 26.7422i 1.25095i 0.780246 + 0.625473i \(0.215094\pi\)
−0.780246 + 0.625473i \(0.784906\pi\)
\(458\) 5.08802 + 2.56018i 0.237747 + 0.119629i
\(459\) 0 0
\(460\) −1.48946 + 10.0610i −0.0694463 + 0.469096i
\(461\) −9.23921 + 9.23921i −0.430313 + 0.430313i −0.888735 0.458422i \(-0.848415\pi\)
0.458422 + 0.888735i \(0.348415\pi\)
\(462\) 0 0
\(463\) 29.4474 1.36854 0.684268 0.729231i \(-0.260122\pi\)
0.684268 + 0.729231i \(0.260122\pi\)
\(464\) 5.60527 + 10.4723i 0.260218 + 0.486163i
\(465\) 0 0
\(466\) −5.20189 15.7387i −0.240973 0.729083i
\(467\) 19.5897 19.5897i 0.906503 0.906503i −0.0894848 0.995988i \(-0.528522\pi\)
0.995988 + 0.0894848i \(0.0285221\pi\)
\(468\) 0 0
\(469\) −0.121978 0.121978i −0.00563242 0.00563242i
\(470\) −6.42429 3.23256i −0.296331 0.149107i
\(471\) 0 0
\(472\) −15.7633 + 2.74218i −0.725563 + 0.126219i
\(473\) 43.7127i 2.00991i
\(474\) 0 0
\(475\) 3.81580 + 3.81580i 0.175081 + 0.175081i
\(476\) 0.578387 + 0.779397i 0.0265103 + 0.0357236i
\(477\) 0 0
\(478\) 18.3312 6.05872i 0.838449 0.277120i
\(479\) −35.5499 −1.62432 −0.812159 0.583436i \(-0.801708\pi\)
−0.812159 + 0.583436i \(0.801708\pi\)
\(480\) 0 0
\(481\) 50.4393 2.29984
\(482\) 2.86235 0.946048i 0.130376 0.0430913i
\(483\) 0 0
\(484\) 21.2730 + 28.6661i 0.966955 + 1.30301i
\(485\) 0.726607 + 0.726607i 0.0329935 + 0.0329935i
\(486\) 0 0
\(487\) 9.86632i 0.447086i 0.974694 + 0.223543i \(0.0717623\pi\)
−0.974694 + 0.223543i \(0.928238\pi\)
\(488\) −2.51559 14.4608i −0.113876 0.654608i
\(489\) 0 0
\(490\) −15.8419 7.97131i −0.715666 0.360107i
\(491\) 0.449555 + 0.449555i 0.0202881 + 0.0202881i 0.717178 0.696890i \(-0.245433\pi\)
−0.696890 + 0.717178i \(0.745433\pi\)
\(492\) 0 0
\(493\) 6.41099 6.41099i 0.288736 0.288736i
\(494\) −8.07174 24.4217i −0.363165 1.09879i
\(495\) 0 0
\(496\) 4.81997 15.9222i 0.216423 0.714928i
\(497\) −0.0505249 −0.00226635
\(498\) 0 0
\(499\) 2.70645 2.70645i 0.121157 0.121157i −0.643928 0.765086i \(-0.722697\pi\)
0.765086 + 0.643928i \(0.222697\pi\)
\(500\) −3.56375 + 24.0724i −0.159376 + 1.07655i
\(501\) 0 0
\(502\) 7.92115 + 3.98575i 0.353538 + 0.177893i
\(503\) 23.6719i 1.05548i 0.849407 + 0.527739i \(0.176960\pi\)
−0.849407 + 0.527739i \(0.823040\pi\)
\(504\) 0 0
\(505\) 18.1876i 0.809336i
\(506\) 9.65685 19.1917i 0.429300 0.853176i
\(507\) 0 0
\(508\) −2.40576 + 1.78530i −0.106738 + 0.0792099i
\(509\) 24.6052 24.6052i 1.09061 1.09061i 0.0951425 0.995464i \(-0.469669\pi\)
0.995464 0.0951425i \(-0.0303307\pi\)
\(510\) 0 0
\(511\) −0.212818 −0.00941453
\(512\) −21.8155 6.00685i −0.964120 0.265468i
\(513\) 0 0
\(514\) −20.2561 + 6.69495i −0.893460 + 0.295302i
\(515\) −14.4305 + 14.4305i −0.635882 + 0.635882i
\(516\) 0 0
\(517\) 10.7422 + 10.7422i 0.472440 + 0.472440i
\(518\) −0.855494 + 1.70018i −0.0375883 + 0.0747017i
\(519\) 0 0
\(520\) 17.4321 24.7743i 0.764447 1.08642i
\(521\) 14.4889i 0.634770i −0.948297 0.317385i \(-0.897195\pi\)
0.948297 0.317385i \(-0.102805\pi\)
\(522\) 0 0
\(523\) −19.4979 19.4979i −0.852584 0.852584i 0.137867 0.990451i \(-0.455975\pi\)
−0.990451 + 0.137867i \(0.955975\pi\)
\(524\) −4.31788 + 29.1665i −0.188628 + 1.27414i
\(525\) 0 0
\(526\) 11.6147 + 35.1412i 0.506424 + 1.53223i
\(527\) −12.6981 −0.553138
\(528\) 0 0
\(529\) 15.0000 0.652174
\(530\) 4.01400 + 12.1447i 0.174357 + 0.527532i
\(531\) 0 0
\(532\) 0.960099 + 0.142136i 0.0416256 + 0.00616236i
\(533\) −10.9670 10.9670i −0.475031 0.475031i
\(534\) 0 0
\(535\) 1.83585i 0.0793706i
\(536\) −0.526113 3.02433i −0.0227246 0.130631i
\(537\) 0 0
\(538\) −7.72841 + 15.3592i −0.333195 + 0.662182i
\(539\) 26.4896 + 26.4896i 1.14099 + 1.14099i
\(540\) 0 0
\(541\) −10.0396 + 10.0396i −0.431638 + 0.431638i −0.889185 0.457547i \(-0.848728\pi\)
0.457547 + 0.889185i \(0.348728\pi\)
\(542\) 14.3198 4.73291i 0.615089 0.203296i
\(543\) 0 0
\(544\) 0.436252 + 17.2660i 0.0187041 + 0.740275i
\(545\) 3.67340 0.157351
\(546\) 0 0
\(547\) −7.19884 + 7.19884i −0.307800 + 0.307800i −0.844056 0.536255i \(-0.819838\pi\)
0.536255 + 0.844056i \(0.319838\pi\)
\(548\) 16.4422 + 22.1564i 0.702374 + 0.946474i
\(549\) 0 0
\(550\) 6.03441 11.9926i 0.257308 0.511366i
\(551\) 9.06651i 0.386246i
\(552\) 0 0
\(553\) 1.54075i 0.0655194i
\(554\) −4.75534 2.39278i −0.202035 0.101659i
\(555\) 0 0
\(556\) −6.78301 1.00417i −0.287664 0.0425865i
\(557\) −1.02129 + 1.02129i −0.0432735 + 0.0432735i −0.728412 0.685139i \(-0.759741\pi\)
0.685139 + 0.728412i \(0.259741\pi\)
\(558\) 0 0
\(559\) −48.4802 −2.05049
\(560\) 0.539416 + 1.00778i 0.0227945 + 0.0425867i
\(561\) 0 0
\(562\) −4.63757 14.0314i −0.195624 0.591878i
\(563\) −6.70751 + 6.70751i −0.282688 + 0.282688i −0.834180 0.551492i \(-0.814059\pi\)
0.551492 + 0.834180i \(0.314059\pi\)
\(564\) 0 0
\(565\) −4.49400 4.49400i −0.189064 0.189064i
\(566\) −22.3059 11.2238i −0.937588 0.471774i
\(567\) 0 0
\(568\) −0.735321 0.517398i −0.0308534 0.0217096i
\(569\) 8.98711i 0.376759i −0.982096 0.188380i \(-0.939676\pi\)
0.982096 0.188380i \(-0.0603235\pi\)
\(570\) 0 0
\(571\) −9.17157 9.17157i −0.383818 0.383818i 0.488657 0.872476i \(-0.337487\pi\)
−0.872476 + 0.488657i \(0.837487\pi\)
\(572\) −51.3861 + 38.1334i −2.14856 + 1.59444i
\(573\) 0 0
\(574\) 0.555677 0.183659i 0.0231935 0.00766579i
\(575\) −4.99907 −0.208476
\(576\) 0 0
\(577\) 29.5013 1.22815 0.614077 0.789246i \(-0.289528\pi\)
0.614077 + 0.789246i \(0.289528\pi\)
\(578\) −10.3097 + 3.40751i −0.428828 + 0.141734i
\(579\) 0 0
\(580\) 8.57478 6.36330i 0.356048 0.264222i
\(581\) 0.0184080 + 0.0184080i 0.000763692 + 0.000763692i
\(582\) 0 0
\(583\) 27.0192i 1.11902i
\(584\) −3.09728 2.17936i −0.128166 0.0901824i
\(585\) 0 0
\(586\) −38.8421 19.5445i −1.60455 0.807374i
\(587\) −1.82425 1.82425i −0.0752950 0.0752950i 0.668456 0.743751i \(-0.266955\pi\)
−0.743751 + 0.668456i \(0.766955\pi\)
\(588\) 0 0
\(589\) −8.97891 + 8.97891i −0.369970 + 0.369970i
\(590\) 4.51379 + 13.6569i 0.185830 + 0.562244i
\(591\) 0 0
\(592\) −29.8612 + 15.9832i −1.22729 + 0.656905i
\(593\) 35.4338 1.45509 0.727546 0.686058i \(-0.240661\pi\)
0.727546 + 0.686058i \(0.240661\pi\)
\(594\) 0 0
\(595\) 0.616953 0.616953i 0.0252926 0.0252926i
\(596\) −8.19286 1.21289i −0.335593 0.0496821i
\(597\) 0 0
\(598\) 21.2848 + 10.7101i 0.870402 + 0.437967i
\(599\) 27.1632i 1.10986i −0.831897 0.554930i \(-0.812745\pi\)
0.831897 0.554930i \(-0.187255\pi\)
\(600\) 0 0
\(601\) 5.33897i 0.217781i −0.994054 0.108891i \(-0.965270\pi\)
0.994054 0.108891i \(-0.0347298\pi\)
\(602\) 0.822265 1.63414i 0.0335130 0.0666027i
\(603\) 0 0
\(604\) 27.0128 + 36.4007i 1.09913 + 1.48112i
\(605\) 22.6914 22.6914i 0.922539 0.922539i
\(606\) 0 0
\(607\) 16.1084 0.653820 0.326910 0.945055i \(-0.393993\pi\)
0.326910 + 0.945055i \(0.393993\pi\)
\(608\) 12.5174 + 11.9004i 0.507648 + 0.482627i
\(609\) 0 0
\(610\) −12.5284 + 4.14082i −0.507260 + 0.167657i
\(611\) −11.9137 + 11.9137i −0.481979 + 0.481979i
\(612\) 0 0
\(613\) 0.436924 + 0.436924i 0.0176472 + 0.0176472i 0.715875 0.698228i \(-0.246028\pi\)
−0.698228 + 0.715875i \(0.746028\pi\)
\(614\) 13.5385 26.9060i 0.546369 1.08584i
\(615\) 0 0
\(616\) −0.413828 2.37887i −0.0166736 0.0958475i
\(617\) 8.80641i 0.354533i 0.984163 + 0.177266i \(0.0567254\pi\)
−0.984163 + 0.177266i \(0.943275\pi\)
\(618\) 0 0
\(619\) 1.92932 + 1.92932i 0.0775458 + 0.0775458i 0.744816 0.667270i \(-0.232537\pi\)
−0.667270 + 0.744816i \(0.732537\pi\)
\(620\) −14.7938 2.19011i −0.594132 0.0879569i
\(621\) 0 0
\(622\) 0.789456 + 2.38857i 0.0316543 + 0.0957728i
\(623\) −2.28861 −0.0916910
\(624\) 0 0
\(625\) 13.0390 0.521559
\(626\) −1.19970 3.62979i −0.0479495 0.145075i
\(627\) 0 0
\(628\) −1.15154 + 7.77845i −0.0459515 + 0.310394i
\(629\) 18.2807 + 18.2807i 0.728898 + 0.728898i
\(630\) 0 0
\(631\) 38.7864i 1.54406i −0.635586 0.772030i \(-0.719241\pi\)
0.635586 0.772030i \(-0.280759\pi\)
\(632\) −15.7780 + 22.4235i −0.627615 + 0.891961i
\(633\) 0 0
\(634\) −14.0261 + 27.8751i −0.557049 + 1.10706i
\(635\) 1.90434 + 1.90434i 0.0755715 + 0.0755715i
\(636\) 0 0
\(637\) −29.3786 + 29.3786i −1.16402 + 1.16402i
\(638\) −21.4165 + 7.07847i −0.847888 + 0.280239i
\(639\) 0 0
\(640\) −2.46971 + 20.1908i −0.0976240 + 0.798111i
\(641\) −33.1091 −1.30773 −0.653865 0.756611i \(-0.726854\pi\)
−0.653865 + 0.756611i \(0.726854\pi\)
\(642\) 0 0
\(643\) −19.2897 + 19.2897i −0.760711 + 0.760711i −0.976451 0.215740i \(-0.930784\pi\)
0.215740 + 0.976451i \(0.430784\pi\)
\(644\) −0.722018 + 0.535806i −0.0284515 + 0.0211137i
\(645\) 0 0
\(646\) 5.92571 11.7766i 0.233144 0.463343i
\(647\) 41.8477i 1.64520i −0.568620 0.822601i \(-0.692522\pi\)
0.568620 0.822601i \(-0.307478\pi\)
\(648\) 0 0
\(649\) 30.3835i 1.19266i
\(650\) 13.3005 + 6.69254i 0.521690 + 0.262503i
\(651\) 0 0
\(652\) −2.25205 + 15.2121i −0.0881970 + 0.595754i
\(653\) −14.7741 + 14.7741i −0.578155 + 0.578155i −0.934395 0.356240i \(-0.884059\pi\)
0.356240 + 0.934395i \(0.384059\pi\)
\(654\) 0 0
\(655\) 26.5054 1.03565
\(656\) 9.96788 + 3.01748i 0.389180 + 0.117813i
\(657\) 0 0
\(658\) −0.199515 0.603650i −0.00777790 0.0235327i
\(659\) 2.22839 2.22839i 0.0868056 0.0868056i −0.662371 0.749176i \(-0.730450\pi\)
0.749176 + 0.662371i \(0.230450\pi\)
\(660\) 0 0
\(661\) −18.0685 18.0685i −0.702784 0.702784i 0.262223 0.965007i \(-0.415544\pi\)
−0.965007 + 0.262223i \(0.915544\pi\)
\(662\) 27.5944 + 13.8849i 1.07249 + 0.539651i
\(663\) 0 0
\(664\) 0.0793969 + 0.456409i 0.00308120 + 0.0177121i
\(665\) 0.872503i 0.0338342i
\(666\) 0 0
\(667\) 5.93901 + 5.93901i 0.229959 + 0.229959i
\(668\) 4.71330 + 6.35134i 0.182363 + 0.245741i
\(669\) 0 0
\(670\) −2.62020 + 0.866013i −0.101227 + 0.0334570i
\(671\) 27.8729 1.07602
\(672\) 0 0
\(673\) 20.7981 0.801706 0.400853 0.916142i \(-0.368714\pi\)
0.400853 + 0.916142i \(0.368714\pi\)
\(674\) −25.3433 + 8.37632i −0.976186 + 0.322644i
\(675\) 0 0
\(676\) −26.7982 36.1115i −1.03070 1.38890i
\(677\) −29.0213 29.0213i −1.11538 1.11538i −0.992411 0.122968i \(-0.960759\pi\)
−0.122968 0.992411i \(-0.539241\pi\)
\(678\) 0 0
\(679\) 0.0908404i 0.00348613i
\(680\) 15.2968 2.66103i 0.586605 0.102046i
\(681\) 0 0
\(682\) 28.2197 + 14.1995i 1.08059 + 0.543728i
\(683\) 18.7938 + 18.7938i 0.719123 + 0.719123i 0.968426 0.249303i \(-0.0802013\pi\)
−0.249303 + 0.968426i \(0.580201\pi\)
\(684\) 0 0
\(685\) 17.5385 17.5385i 0.670111 0.670111i
\(686\) −0.985767 2.98252i −0.0376368 0.113873i
\(687\) 0 0
\(688\) 28.7013 15.3624i 1.09423 0.585685i
\(689\) 29.9660 1.14161
\(690\) 0 0
\(691\) 10.4580 10.4580i 0.397841 0.397841i −0.479630 0.877471i \(-0.659229\pi\)
0.877471 + 0.479630i \(0.159229\pi\)
\(692\) 6.61971 44.7149i 0.251644 1.69980i
\(693\) 0 0
\(694\) −35.4344 17.8298i −1.34507 0.676810i
\(695\) 6.16415i 0.233820i
\(696\) 0 0
\(697\) 7.94948i 0.301108i
\(698\) 10.7622 21.3885i 0.407357 0.809569i
\(699\) 0 0
\(700\) −0.451177 + 0.334817i −0.0170529 + 0.0126549i
\(701\) −18.3314 + 18.3314i −0.692367 + 0.692367i −0.962752 0.270385i \(-0.912849\pi\)
0.270385 + 0.962752i \(0.412849\pi\)
\(702\) 0 0
\(703\) 25.8528 0.975055
\(704\) 18.3380 38.8590i 0.691141 1.46456i
\(705\) 0 0
\(706\) 16.9460 5.60091i 0.637773 0.210793i
\(707\) 1.13690 1.13690i 0.0427577 0.0427577i
\(708\) 0 0
\(709\) 14.5722 + 14.5722i 0.547271 + 0.547271i 0.925650 0.378380i \(-0.123519\pi\)
−0.378380 + 0.925650i \(0.623519\pi\)
\(710\) −0.363303 + 0.722018i −0.0136345 + 0.0270969i
\(711\) 0 0
\(712\) −33.3075 23.4364i −1.24825 0.878315i
\(713\) 11.7633i 0.440538i
\(714\) 0 0
\(715\) 40.6761 + 40.6761i 1.52120 + 1.52120i
\(716\) 5.06651 34.2233i 0.189344 1.27898i
\(717\) 0 0
\(718\) 12.0212 + 36.3712i 0.448628 + 1.35736i
\(719\) −44.0949 −1.64446 −0.822230 0.569155i \(-0.807270\pi\)
−0.822230 + 0.569155i \(0.807270\pi\)
\(720\) 0 0
\(721\) −1.80409 −0.0671880
\(722\) 4.29513 + 12.9953i 0.159848 + 0.483634i
\(723\) 0 0
\(724\) 16.1233 + 2.38694i 0.599219 + 0.0887101i
\(725\) 3.71119 + 3.71119i 0.137830 + 0.137830i
\(726\) 0 0
\(727\) 9.23457i 0.342491i 0.985228 + 0.171246i \(0.0547792\pi\)
−0.985228 + 0.171246i \(0.945221\pi\)
\(728\) 2.63832 0.458962i 0.0977826 0.0170103i
\(729\) 0 0
\(730\) −1.53029 + 3.04125i −0.0566385 + 0.112562i
\(731\) −17.5706 17.5706i −0.649872 0.649872i
\(732\) 0 0
\(733\) 18.2764 18.2764i 0.675053 0.675053i −0.283823 0.958877i \(-0.591603\pi\)
0.958877 + 0.283823i \(0.0916029\pi\)
\(734\) −27.5184 + 9.09524i −1.01572 + 0.335711i
\(735\) 0 0
\(736\) −15.9949 + 0.404135i −0.589580 + 0.0148966i
\(737\) 5.82936 0.214727
\(738\) 0 0
\(739\) 16.9991 16.9991i 0.625321 0.625321i −0.321566 0.946887i \(-0.604209\pi\)
0.946887 + 0.321566i \(0.104209\pi\)
\(740\) 18.1447 + 24.4506i 0.667012 + 0.898822i
\(741\) 0 0
\(742\) −0.508249 + 1.01008i −0.0186584 + 0.0370812i
\(743\) 17.8748i 0.655762i 0.944719 + 0.327881i \(0.106335\pi\)
−0.944719 + 0.327881i \(0.893665\pi\)
\(744\) 0 0
\(745\) 7.44538i 0.272778i
\(746\) 1.84682 + 0.929278i 0.0676168 + 0.0340233i
\(747\) 0 0
\(748\) −32.4445 4.80316i −1.18629 0.175621i
\(749\) 0.114759 0.114759i 0.00419319 0.00419319i
\(750\) 0 0
\(751\) −35.0731 −1.27984 −0.639918 0.768443i \(-0.721032\pi\)
−0.639918 + 0.768443i \(0.721032\pi\)
\(752\) 3.27798 10.8284i 0.119536 0.394872i
\(753\) 0 0
\(754\) −7.85047 23.7523i −0.285897 0.865006i
\(755\) 28.8139 28.8139i 1.04865 1.04865i
\(756\) 0 0
\(757\) −32.8071 32.8071i −1.19239 1.19239i −0.976393 0.216000i \(-0.930699\pi\)
−0.216000 0.976393i \(-0.569301\pi\)
\(758\) 31.5662 + 15.8834i 1.14654 + 0.576912i
\(759\) 0 0
\(760\) 8.93484 12.6981i 0.324101 0.460608i
\(761\) 10.5531i 0.382550i 0.981536 + 0.191275i \(0.0612623\pi\)
−0.981536 + 0.191275i \(0.938738\pi\)
\(762\) 0 0
\(763\) 0.229624 + 0.229624i 0.00831296 + 0.00831296i
\(764\) 25.9660 19.2693i 0.939418 0.697138i
\(765\) 0 0
\(766\) 41.7545 13.8005i 1.50865 0.498632i
\(767\) 33.6972 1.21673
\(768\) 0 0
\(769\) −35.2068 −1.26959 −0.634795 0.772681i \(-0.718915\pi\)
−0.634795 + 0.772681i \(0.718915\pi\)
\(770\) −2.06099 + 0.681187i −0.0742729 + 0.0245483i
\(771\) 0 0
\(772\) −35.5671 + 26.3942i −1.28009 + 0.949947i
\(773\) 19.3897 + 19.3897i 0.697399 + 0.697399i 0.963849 0.266450i \(-0.0858507\pi\)
−0.266450 + 0.963849i \(0.585851\pi\)
\(774\) 0 0
\(775\) 7.35067i 0.264044i
\(776\) −0.930247 + 1.32206i −0.0333939 + 0.0474591i
\(777\) 0 0
\(778\) 4.57591 + 2.30250i 0.164054 + 0.0825485i
\(779\) −5.62113 5.62113i −0.201398 0.201398i
\(780\) 0 0
\(781\) 1.20730 1.20730i 0.0432006 0.0432006i
\(782\) 3.83260 + 11.5959i 0.137054 + 0.414667i
\(783\) 0 0
\(784\) 8.08331 26.7023i 0.288690 0.953653i
\(785\) 7.06877 0.252295
\(786\) 0 0
\(787\) −6.68964 + 6.68964i −0.238460 + 0.238460i −0.816212 0.577752i \(-0.803930\pi\)
0.577752 + 0.816212i \(0.303930\pi\)
\(788\)