Properties

Label 189.2.e.e.109.1
Level 189
Weight 2
Character 189.109
Analytic conductor 1.509
Analytic rank 0
Dimension 6
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 189.e (of order \(3\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(1.5091725982\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(0.500000 - 0.224437i\)
Character \(\chi\) = 189.109
Dual form 189.2.e.e.163.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(-1.34981 - 2.33795i) q^{2}\) \(+(-2.64400 + 4.57954i) q^{4}\) \(+(0.794182 + 1.37556i) q^{5}\) \(+(1.23855 + 2.33795i) q^{7}\) \(+8.87636 q^{8}\) \(+O(q^{10})\) \(q\)\(+(-1.34981 - 2.33795i) q^{2}\) \(+(-2.64400 + 4.57954i) q^{4}\) \(+(0.794182 + 1.37556i) q^{5}\) \(+(1.23855 + 2.33795i) q^{7}\) \(+8.87636 q^{8}\) \(+(2.14400 - 3.71351i) q^{10}\) \(+(-0.150186 + 0.260130i) q^{11}\) \(+2.81089 q^{13}\) \(+(3.79418 - 6.05146i) q^{14}\) \(+(-6.69344 - 11.5934i) q^{16}\) \(+(-2.93818 + 5.08907i) q^{17}\) \(+(1.14400 + 1.98146i) q^{19}\) \(-8.39926 q^{20}\) \(+0.810892 q^{22}\) \(+(-0.944368 - 1.63569i) q^{23}\) \(+(1.23855 - 2.14523i) q^{25}\) \(+(-3.79418 - 6.57172i) q^{26}\) \(+(-13.9814 - 0.509538i) q^{28}\) \(+2.52290 q^{29}\) \(+(2.40545 - 4.16635i) q^{31}\) \(+(-9.19344 + 15.9235i) q^{32}\) \(+15.8640 q^{34}\) \(+(-2.23236 + 3.56046i) q^{35}\) \(+(2.23855 + 3.87728i) q^{37}\) \(+(3.08836 - 5.34920i) q^{38}\) \(+(7.04944 + 12.2100i) q^{40}\) \(+8.90978 q^{41}\) \(-9.09888 q^{43}\) \(+(-0.794182 - 1.37556i) q^{44}\) \(+(-2.54944 + 4.41576i) q^{46}\) \(+(1.60507 + 2.78007i) q^{47}\) \(+(-3.93199 + 5.79133i) q^{49}\) \(-6.68725 q^{50}\) \(+(-7.43199 + 12.8726i) q^{52}\) \(+(-1.00619 + 1.74277i) q^{53}\) \(-0.477100 q^{55}\) \(+(10.9938 + 20.7524i) q^{56}\) \(+(-3.40545 - 5.89841i) q^{58}\) \(+(2.44437 - 4.23377i) q^{59}\) \(+(-3.78799 - 6.56099i) q^{61}\) \(-12.9876 q^{62}\) \(+22.8640 q^{64}\) \(+(2.23236 + 3.86656i) q^{65}\) \(+(-0.356004 + 0.616617i) q^{67}\) \(+(-15.5371 - 26.9110i) q^{68}\) \(+(11.3374 + 0.413181i) q^{70}\) \(-12.8640 q^{71}\) \(+(5.83743 - 10.1107i) q^{73}\) \(+(6.04325 - 10.4672i) q^{74}\) \(-12.0989 q^{76}\) \(+(-0.794182 - 0.0289431i) q^{77}\) \(+(-0.833104 - 1.44298i) q^{79}\) \(+(10.6316 - 18.4145i) q^{80}\) \(+(-12.0265 - 20.8306i) q^{82}\) \(-5.43268 q^{83}\) \(-9.33379 q^{85}\) \(+(12.2818 + 21.2727i) q^{86}\) \(+(-1.33310 + 2.30900i) q^{88}\) \(+(4.67673 + 8.10033i) q^{89}\) \(+(3.48143 + 6.57172i) q^{91}\) \(+9.98762 q^{92}\) \(+(4.33310 - 7.50516i) q^{94}\) \(+(-1.81708 + 3.14728i) q^{95}\) \(-12.5760 q^{97}\) \(+(18.8473 + 1.37556i) q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(6q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut +\mathstrut 4q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut -\mathstrut 10q^{16} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 26q^{20} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 17q^{26} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 24q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut +\mathstrut 24q^{40} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 18q^{43} \) \(\mathstrut +\mathstrut q^{44} \) \(\mathstrut +\mathstrut 3q^{46} \) \(\mathstrut -\mathstrut 9q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut +\mathstrut 8q^{50} \) \(\mathstrut -\mathstrut 9q^{52} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 48q^{56} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut q^{61} \) \(\mathstrut -\mathstrut 42q^{62} \) \(\mathstrut +\mathstrut 66q^{64} \) \(\mathstrut -\mathstrut 10q^{65} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut -\mathstrut 39q^{68} \) \(\mathstrut +\mathstrut 26q^{70} \) \(\mathstrut -\mathstrut 6q^{71} \) \(\mathstrut -\mathstrut 7q^{73} \) \(\mathstrut -\mathstrut 36q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{79} \) \(\mathstrut +\mathstrut 16q^{80} \) \(\mathstrut -\mathstrut 43q^{82} \) \(\mathstrut +\mathstrut 6q^{83} \) \(\mathstrut -\mathstrut 54q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 9q^{88} \) \(\mathstrut +\mathstrut 5q^{89} \) \(\mathstrut -\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut -\mathstrut 16q^{95} \) \(\mathstrut -\mathstrut 28q^{97} \) \(\mathstrut +\mathstrut 49q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34981 2.33795i −0.954463 1.65318i −0.735593 0.677424i \(-0.763096\pi\)
−0.218870 0.975754i \(-0.570237\pi\)
\(3\) 0 0
\(4\) −2.64400 + 4.57954i −1.32200 + 2.28977i
\(5\) 0.794182 + 1.37556i 0.355169 + 0.615171i 0.987147 0.159816i \(-0.0510900\pi\)
−0.631978 + 0.774986i \(0.717757\pi\)
\(6\) 0 0
\(7\) 1.23855 + 2.33795i 0.468128 + 0.883661i
\(8\) 8.87636 3.13827
\(9\) 0 0
\(10\) 2.14400 3.71351i 0.677991 1.17432i
\(11\) −0.150186 + 0.260130i −0.0452828 + 0.0784320i −0.887778 0.460271i \(-0.847752\pi\)
0.842496 + 0.538703i \(0.181086\pi\)
\(12\) 0 0
\(13\) 2.81089 0.779601 0.389801 0.920899i \(-0.372544\pi\)
0.389801 + 0.920899i \(0.372544\pi\)
\(14\) 3.79418 6.05146i 1.01404 1.61732i
\(15\) 0 0
\(16\) −6.69344 11.5934i −1.67336 2.89834i
\(17\) −2.93818 + 5.08907i −0.712613 + 1.23428i 0.251260 + 0.967920i \(0.419155\pi\)
−0.963873 + 0.266362i \(0.914178\pi\)
\(18\) 0 0
\(19\) 1.14400 + 1.98146i 0.262451 + 0.454578i 0.966893 0.255184i \(-0.0821360\pi\)
−0.704442 + 0.709762i \(0.748803\pi\)
\(20\) −8.39926 −1.87813
\(21\) 0 0
\(22\) 0.810892 0.172883
\(23\) −0.944368 1.63569i −0.196914 0.341066i 0.750612 0.660743i \(-0.229759\pi\)
−0.947526 + 0.319678i \(0.896425\pi\)
\(24\) 0 0
\(25\) 1.23855 2.14523i 0.247710 0.429046i
\(26\) −3.79418 6.57172i −0.744100 1.28882i
\(27\) 0 0
\(28\) −13.9814 0.509538i −2.64224 0.0962937i
\(29\) 2.52290 0.468491 0.234245 0.972178i \(-0.424738\pi\)
0.234245 + 0.972178i \(0.424738\pi\)
\(30\) 0 0
\(31\) 2.40545 4.16635i 0.432031 0.748299i −0.565017 0.825079i \(-0.691130\pi\)
0.997048 + 0.0767797i \(0.0244638\pi\)
\(32\) −9.19344 + 15.9235i −1.62519 + 2.81490i
\(33\) 0 0
\(34\) 15.8640 2.72065
\(35\) −2.23236 + 3.56046i −0.377338 + 0.601827i
\(36\) 0 0
\(37\) 2.23855 + 3.87728i 0.368015 + 0.637421i 0.989255 0.146199i \(-0.0467041\pi\)
−0.621240 + 0.783620i \(0.713371\pi\)
\(38\) 3.08836 5.34920i 0.500999 0.867755i
\(39\) 0 0
\(40\) 7.04944 + 12.2100i 1.11461 + 1.93057i
\(41\) 8.90978 1.39147 0.695737 0.718297i \(-0.255078\pi\)
0.695737 + 0.718297i \(0.255078\pi\)
\(42\) 0 0
\(43\) −9.09888 −1.38757 −0.693783 0.720184i \(-0.744058\pi\)
−0.693783 + 0.720184i \(0.744058\pi\)
\(44\) −0.794182 1.37556i −0.119727 0.207374i
\(45\) 0 0
\(46\) −2.54944 + 4.41576i −0.375895 + 0.651069i
\(47\) 1.60507 + 2.78007i 0.234124 + 0.405515i 0.959018 0.283346i \(-0.0914444\pi\)
−0.724894 + 0.688861i \(0.758111\pi\)
\(48\) 0 0
\(49\) −3.93199 + 5.79133i −0.561713 + 0.827332i
\(50\) −6.68725 −0.945720
\(51\) 0 0
\(52\) −7.43199 + 12.8726i −1.03063 + 1.78511i
\(53\) −1.00619 + 1.74277i −0.138211 + 0.239388i −0.926819 0.375507i \(-0.877468\pi\)
0.788609 + 0.614895i \(0.210802\pi\)
\(54\) 0 0
\(55\) −0.477100 −0.0643321
\(56\) 10.9938 + 20.7524i 1.46911 + 2.77316i
\(57\) 0 0
\(58\) −3.40545 5.89841i −0.447157 0.774499i
\(59\) 2.44437 4.23377i 0.318230 0.551190i −0.661889 0.749602i \(-0.730245\pi\)
0.980119 + 0.198412i \(0.0635784\pi\)
\(60\) 0 0
\(61\) −3.78799 6.56099i −0.485003 0.840049i 0.514849 0.857281i \(-0.327848\pi\)
−0.999852 + 0.0172317i \(0.994515\pi\)
\(62\) −12.9876 −1.64943
\(63\) 0 0
\(64\) 22.8640 2.85800
\(65\) 2.23236 + 3.86656i 0.276890 + 0.479588i
\(66\) 0 0
\(67\) −0.356004 + 0.616617i −0.0434928 + 0.0753317i −0.886952 0.461861i \(-0.847182\pi\)
0.843460 + 0.537193i \(0.180515\pi\)
\(68\) −15.5371 26.9110i −1.88415 3.26344i
\(69\) 0 0
\(70\) 11.3374 + 0.413181i 1.35508 + 0.0493845i
\(71\) −12.8640 −1.52667 −0.763337 0.646001i \(-0.776440\pi\)
−0.763337 + 0.646001i \(0.776440\pi\)
\(72\) 0 0
\(73\) 5.83743 10.1107i 0.683220 1.18337i −0.290773 0.956792i \(-0.593912\pi\)
0.973993 0.226580i \(-0.0727543\pi\)
\(74\) 6.04325 10.4672i 0.702514 1.21679i
\(75\) 0 0
\(76\) −12.0989 −1.38784
\(77\) −0.794182 0.0289431i −0.0905054 0.00329837i
\(78\) 0 0
\(79\) −0.833104 1.44298i −0.0937315 0.162348i 0.815347 0.578973i \(-0.196546\pi\)
−0.909078 + 0.416625i \(0.863213\pi\)
\(80\) 10.6316 18.4145i 1.18865 2.05880i
\(81\) 0 0
\(82\) −12.0265 20.8306i −1.32811 2.30035i
\(83\) −5.43268 −0.596314 −0.298157 0.954517i \(-0.596372\pi\)
−0.298157 + 0.954517i \(0.596372\pi\)
\(84\) 0 0
\(85\) −9.33379 −1.01239
\(86\) 12.2818 + 21.2727i 1.32438 + 2.29389i
\(87\) 0 0
\(88\) −1.33310 + 2.30900i −0.142109 + 0.246141i
\(89\) 4.67673 + 8.10033i 0.495732 + 0.858633i 0.999988 0.00492107i \(-0.00156643\pi\)
−0.504256 + 0.863554i \(0.668233\pi\)
\(90\) 0 0
\(91\) 3.48143 + 6.57172i 0.364953 + 0.688903i
\(92\) 9.98762 1.04128
\(93\) 0 0
\(94\) 4.33310 7.50516i 0.446926 0.774098i
\(95\) −1.81708 + 3.14728i −0.186429 + 0.322904i
\(96\) 0 0
\(97\) −12.5760 −1.27690 −0.638449 0.769664i \(-0.720424\pi\)
−0.638449 + 0.769664i \(0.720424\pi\)
\(98\) 18.8473 + 1.37556i 1.90386 + 0.138953i
\(99\) 0 0
\(100\) 6.54944 + 11.3440i 0.654944 + 1.13440i
\(101\) 7.30470 12.6521i 0.726845 1.25893i −0.231365 0.972867i \(-0.574319\pi\)
0.958210 0.286066i \(-0.0923475\pi\)
\(102\) 0 0
\(103\) −4.59888 7.96550i −0.453142 0.784864i 0.545438 0.838151i \(-0.316363\pi\)
−0.998579 + 0.0532872i \(0.983030\pi\)
\(104\) 24.9505 2.44660
\(105\) 0 0
\(106\) 5.43268 0.527668
\(107\) −6.25526 10.8344i −0.604719 1.04740i −0.992096 0.125482i \(-0.959952\pi\)
0.387377 0.921921i \(-0.373381\pi\)
\(108\) 0 0
\(109\) 1.52290 2.63774i 0.145867 0.252650i −0.783829 0.620977i \(-0.786736\pi\)
0.929696 + 0.368327i \(0.120069\pi\)
\(110\) 0.643996 + 1.11543i 0.0614026 + 0.106352i
\(111\) 0 0
\(112\) 18.8145 30.0079i 1.77781 2.83548i
\(113\) 9.95420 0.936412 0.468206 0.883619i \(-0.344900\pi\)
0.468206 + 0.883619i \(0.344900\pi\)
\(114\) 0 0
\(115\) 1.50000 2.59808i 0.139876 0.242272i
\(116\) −6.67054 + 11.5537i −0.619344 + 1.07274i
\(117\) 0 0
\(118\) −13.1978 −1.21495
\(119\) −15.5371 0.566231i −1.42428 0.0519064i
\(120\) 0 0
\(121\) 5.45489 + 9.44814i 0.495899 + 0.858922i
\(122\) −10.2262 + 17.7122i −0.925834 + 1.60359i
\(123\) 0 0
\(124\) 12.7200 + 22.0317i 1.14229 + 1.97850i
\(125\) 11.8764 1.06225
\(126\) 0 0
\(127\) −13.4400 −1.19260 −0.596302 0.802760i \(-0.703364\pi\)
−0.596302 + 0.802760i \(0.703364\pi\)
\(128\) −12.4752 21.6078i −1.10267 1.90987i
\(129\) 0 0
\(130\) 6.02654 10.4383i 0.528563 0.915497i
\(131\) −5.63781 9.76497i −0.492577 0.853169i 0.507386 0.861719i \(-0.330612\pi\)
−0.999963 + 0.00854976i \(0.997278\pi\)
\(132\) 0 0
\(133\) −3.21565 + 5.12874i −0.278832 + 0.444718i
\(134\) 1.92216 0.166049
\(135\) 0 0
\(136\) −26.0803 + 45.1724i −2.23637 + 3.87350i
\(137\) −1.88874 + 3.27139i −0.161366 + 0.279493i −0.935359 0.353701i \(-0.884923\pi\)
0.773993 + 0.633194i \(0.218256\pi\)
\(138\) 0 0
\(139\) 16.7193 1.41811 0.709056 0.705152i \(-0.249121\pi\)
0.709056 + 0.705152i \(0.249121\pi\)
\(140\) −10.4029 19.6370i −0.879205 1.65963i
\(141\) 0 0
\(142\) 17.3640 + 30.0753i 1.45715 + 2.52386i
\(143\) −0.422156 + 0.731196i −0.0353025 + 0.0611457i
\(144\) 0 0
\(145\) 2.00364 + 3.47041i 0.166393 + 0.288202i
\(146\) −31.5178 −2.60843
\(147\) 0 0
\(148\) −23.6749 −1.94606
\(149\) −5.44437 9.42992i −0.446020 0.772529i 0.552103 0.833776i \(-0.313826\pi\)
−0.998123 + 0.0612468i \(0.980492\pi\)
\(150\) 0 0
\(151\) 6.04944 10.4779i 0.492297 0.852683i −0.507664 0.861555i \(-0.669491\pi\)
0.999961 + 0.00887237i \(0.00282420\pi\)
\(152\) 10.1545 + 17.5881i 0.823640 + 1.42659i
\(153\) 0 0
\(154\) 1.00433 + 1.89582i 0.0809313 + 0.152770i
\(155\) 7.64145 0.613776
\(156\) 0 0
\(157\) 0.0945538 0.163772i 0.00754622 0.0130704i −0.862228 0.506521i \(-0.830931\pi\)
0.869774 + 0.493451i \(0.164265\pi\)
\(158\) −2.24907 + 3.89550i −0.178926 + 0.309910i
\(159\) 0 0
\(160\) −29.2051 −2.30886
\(161\) 2.65452 4.23377i 0.209205 0.333668i
\(162\) 0 0
\(163\) 4.47779 + 7.75576i 0.350727 + 0.607478i 0.986377 0.164500i \(-0.0526010\pi\)
−0.635650 + 0.771978i \(0.719268\pi\)
\(164\) −23.5574 + 40.8026i −1.83953 + 3.18615i
\(165\) 0 0
\(166\) 7.33310 + 12.7013i 0.569159 + 0.985813i
\(167\) −4.34108 −0.335923 −0.167961 0.985794i \(-0.553718\pi\)
−0.167961 + 0.985794i \(0.553718\pi\)
\(168\) 0 0
\(169\) −5.09888 −0.392222
\(170\) 12.5989 + 21.8219i 0.966290 + 1.67366i
\(171\) 0 0
\(172\) 24.0574 41.6687i 1.83436 3.17721i
\(173\) 3.15019 + 5.45628i 0.239504 + 0.414833i 0.960572 0.278031i \(-0.0896818\pi\)
−0.721068 + 0.692864i \(0.756348\pi\)
\(174\) 0 0
\(175\) 6.54944 + 0.238687i 0.495091 + 0.0180431i
\(176\) 4.02104 0.303097
\(177\) 0 0
\(178\) 12.6254 21.8679i 0.946316 1.63907i
\(179\) 6.97091 12.0740i 0.521030 0.902451i −0.478671 0.877995i \(-0.658881\pi\)
0.999701 0.0244564i \(-0.00778548\pi\)
\(180\) 0 0
\(181\) 18.3411 1.36328 0.681641 0.731687i \(-0.261267\pi\)
0.681641 + 0.731687i \(0.261267\pi\)
\(182\) 10.6650 17.0100i 0.790545 1.26086i
\(183\) 0 0
\(184\) −8.38255 14.5190i −0.617969 1.07035i
\(185\) −3.55563 + 6.15854i −0.261415 + 0.452785i
\(186\) 0 0
\(187\) −0.882546 1.52861i −0.0645382 0.111783i
\(188\) −16.9752 −1.23805
\(189\) 0 0
\(190\) 9.81089 0.711757
\(191\) −3.80401 6.58875i −0.275249 0.476745i 0.694949 0.719059i \(-0.255427\pi\)
−0.970198 + 0.242314i \(0.922094\pi\)
\(192\) 0 0
\(193\) −3.83310 + 6.63913i −0.275913 + 0.477895i −0.970365 0.241644i \(-0.922313\pi\)
0.694452 + 0.719539i \(0.255647\pi\)
\(194\) 16.9752 + 29.4020i 1.21875 + 2.11094i
\(195\) 0 0
\(196\) −16.1254 33.3189i −1.15182 2.37992i
\(197\) 18.3869 1.31001 0.655005 0.755624i \(-0.272666\pi\)
0.655005 + 0.755624i \(0.272666\pi\)
\(198\) 0 0
\(199\) −2.97710 + 5.15649i −0.211041 + 0.365534i −0.952041 0.305972i \(-0.901019\pi\)
0.741000 + 0.671505i \(0.234352\pi\)
\(200\) 10.9938 19.0418i 0.777380 1.34646i
\(201\) 0 0
\(202\) −39.4400 −2.77499
\(203\) 3.12474 + 5.89841i 0.219314 + 0.413987i
\(204\) 0 0
\(205\) 7.07598 + 12.2560i 0.494208 + 0.855994i
\(206\) −12.4153 + 21.5039i −0.865013 + 1.49825i
\(207\) 0 0
\(208\) −18.8145 32.5877i −1.30455 2.25955i
\(209\) −0.687248 −0.0475380
\(210\) 0 0
\(211\) 6.67487 0.459517 0.229758 0.973248i \(-0.426206\pi\)
0.229758 + 0.973248i \(0.426206\pi\)
\(212\) −5.32072 9.21576i −0.365429 0.632941i
\(213\) 0 0
\(214\) −16.8869 + 29.2489i −1.15436 + 1.99942i
\(215\) −7.22617 12.5161i −0.492821 0.853591i
\(216\) 0 0
\(217\) 12.7200 + 0.463566i 0.863489 + 0.0314689i
\(218\) −8.22253 −0.556900
\(219\) 0 0
\(220\) 1.26145 2.18490i 0.0850469 0.147306i
\(221\) −8.25890 + 14.3048i −0.555554 + 0.962248i
\(222\) 0 0
\(223\) 6.34108 0.424630 0.212315 0.977201i \(-0.431900\pi\)
0.212315 + 0.977201i \(0.431900\pi\)
\(224\) −48.6148 1.77172i −3.24821 0.118378i
\(225\) 0 0
\(226\) −13.4363 23.2724i −0.893771 1.54806i
\(227\) 13.5433 23.4576i 0.898897 1.55694i 0.0699913 0.997548i \(-0.477703\pi\)
0.828906 0.559388i \(-0.188964\pi\)
\(228\) 0 0
\(229\) −4.09820 7.09828i −0.270816 0.469068i 0.698255 0.715849i \(-0.253960\pi\)
−0.969071 + 0.246782i \(0.920627\pi\)
\(230\) −8.09888 −0.534025
\(231\) 0 0
\(232\) 22.3942 1.47025
\(233\) −13.7101 23.7467i −0.898182 1.55570i −0.829817 0.558036i \(-0.811555\pi\)
−0.0683649 0.997660i \(-0.521778\pi\)
\(234\) 0 0
\(235\) −2.54944 + 4.41576i −0.166307 + 0.288053i
\(236\) 12.9258 + 22.3881i 0.841398 + 1.45734i
\(237\) 0 0
\(238\) 19.6483 + 37.0891i 1.27361 + 2.40413i
\(239\) −27.8640 −1.80237 −0.901185 0.433434i \(-0.857302\pi\)
−0.901185 + 0.433434i \(0.857302\pi\)
\(240\) 0 0
\(241\) 11.2651 19.5117i 0.725648 1.25686i −0.233058 0.972463i \(-0.574873\pi\)
0.958707 0.284397i \(-0.0917934\pi\)
\(242\) 14.7262 25.5065i 0.946634 1.63962i
\(243\) 0 0
\(244\) 40.0617 2.56469
\(245\) −11.0891 0.809332i −0.708454 0.0517063i
\(246\) 0 0
\(247\) 3.21565 + 5.56967i 0.204607 + 0.354390i
\(248\) 21.3516 36.9821i 1.35583 2.34836i
\(249\) 0 0
\(250\) −16.0309 27.7663i −1.01388 1.75609i
\(251\) 31.2509 1.97254 0.986268 0.165152i \(-0.0528114\pi\)
0.986268 + 0.165152i \(0.0528114\pi\)
\(252\) 0 0
\(253\) 0.567323 0.0356673
\(254\) 18.1414 + 31.4219i 1.13830 + 1.97159i
\(255\) 0 0
\(256\) −10.8145 + 18.7313i −0.675908 + 1.17071i
\(257\) 5.10074 + 8.83475i 0.318176 + 0.551096i 0.980107 0.198468i \(-0.0635965\pi\)
−0.661932 + 0.749564i \(0.730263\pi\)
\(258\) 0 0
\(259\) −6.29232 + 10.0358i −0.390986 + 0.623595i
\(260\) −23.6094 −1.46419
\(261\) 0 0
\(262\) −15.2200 + 26.3618i −0.940294 + 1.62864i
\(263\) −14.2305 + 24.6480i −0.877490 + 1.51986i −0.0234042 + 0.999726i \(0.507450\pi\)
−0.854086 + 0.520132i \(0.825883\pi\)
\(264\) 0 0
\(265\) −3.19639 −0.196353
\(266\) 16.3312 + 0.595175i 1.00133 + 0.0364925i
\(267\) 0 0
\(268\) −1.88255 3.26067i −0.114995 0.199177i
\(269\) −7.43818 + 12.8833i −0.453514 + 0.785509i −0.998601 0.0528702i \(-0.983163\pi\)
0.545088 + 0.838379i \(0.316496\pi\)
\(270\) 0 0
\(271\) −0.0222115 0.0384714i −0.00134925 0.00233697i 0.865350 0.501168i \(-0.167096\pi\)
−0.866699 + 0.498831i \(0.833763\pi\)
\(272\) 78.6661 4.76983
\(273\) 0 0
\(274\) 10.1978 0.616070
\(275\) 0.372026 + 0.644367i 0.0224340 + 0.0388568i
\(276\) 0 0
\(277\) −7.83743 + 13.5748i −0.470906 + 0.815633i −0.999446 0.0332754i \(-0.989406\pi\)
0.528540 + 0.848908i \(0.322739\pi\)
\(278\) −22.5679 39.0888i −1.35353 2.34439i
\(279\) 0 0
\(280\) −19.8152 + 31.6039i −1.18419 + 1.88869i
\(281\) 11.9098 0.710478 0.355239 0.934776i \(-0.384400\pi\)
0.355239 + 0.934776i \(0.384400\pi\)
\(282\) 0 0
\(283\) −3.00364 + 5.20246i −0.178548 + 0.309254i −0.941383 0.337339i \(-0.890473\pi\)
0.762835 + 0.646593i \(0.223807\pi\)
\(284\) 34.0123 58.9110i 2.01826 3.49573i
\(285\) 0 0
\(286\) 2.27933 0.134780
\(287\) 11.0352 + 20.8306i 0.651387 + 1.22959i
\(288\) 0 0
\(289\) −8.76578 15.1828i −0.515634 0.893105i
\(290\) 5.40909 9.36882i 0.317633 0.550156i
\(291\) 0 0
\(292\) 30.8683 + 53.4655i 1.80643 + 3.12883i
\(293\) −4.95558 −0.289508 −0.144754 0.989468i \(-0.546239\pi\)
−0.144754 + 0.989468i \(0.546239\pi\)
\(294\) 0 0
\(295\) 7.76509 0.452101
\(296\) 19.8702 + 34.4161i 1.15493 + 2.00040i
\(297\) 0 0
\(298\) −14.6978 + 25.4573i −0.851419 + 1.47470i
\(299\) −2.65452 4.59776i −0.153515 0.265895i
\(300\) 0 0
\(301\) −11.2694 21.2727i −0.649559 1.22614i
\(302\) −32.6625 −1.87952
\(303\) 0 0
\(304\) 15.3145 26.5256i 0.878349 1.52134i
\(305\) 6.01671 10.4212i 0.344516 0.596719i
\(306\) 0 0
\(307\) −22.0531 −1.25864 −0.629318 0.777148i \(-0.716666\pi\)
−0.629318 + 0.777148i \(0.716666\pi\)
\(308\) 2.23236 3.56046i 0.127201 0.202876i
\(309\) 0 0
\(310\) −10.3145 17.8653i −0.585826 1.01468i
\(311\) −3.98762 + 6.90676i −0.226117 + 0.391646i −0.956654 0.291227i \(-0.905937\pi\)
0.730537 + 0.682873i \(0.239270\pi\)
\(312\) 0 0
\(313\) 11.2651 + 19.5117i 0.636741 + 1.10287i 0.986143 + 0.165895i \(0.0530511\pi\)
−0.349403 + 0.936973i \(0.613616\pi\)
\(314\) −0.510520 −0.0288103
\(315\) 0 0
\(316\) 8.81089 0.495651
\(317\) 9.96905 + 17.2669i 0.559918 + 0.969806i 0.997503 + 0.0706288i \(0.0225006\pi\)
−0.437585 + 0.899177i \(0.644166\pi\)
\(318\) 0 0
\(319\) −0.378904 + 0.656281i −0.0212146 + 0.0367447i
\(320\) 18.1582 + 31.4509i 1.01507 + 1.75816i
\(321\) 0 0
\(322\) −13.4814 0.491316i −0.751291 0.0273800i
\(323\) −13.4451 −0.748103
\(324\) 0 0
\(325\) 3.48143 6.03001i 0.193115 0.334485i
\(326\) 12.0884 20.9377i 0.669513 1.15963i
\(327\) 0 0
\(328\) 79.0864 4.36681
\(329\) −4.51169 + 7.19583i −0.248738 + 0.396719i
\(330\) 0 0
\(331\) −11.8152 20.4646i −0.649423 1.12483i −0.983261 0.182204i \(-0.941677\pi\)
0.333837 0.942631i \(-0.391656\pi\)
\(332\) 14.3640 24.8791i 0.788326 1.36542i
\(333\) 0 0
\(334\) 5.85965 + 10.1492i 0.320626 + 0.555340i
\(335\) −1.13093 −0.0617892
\(336\) 0 0
\(337\) −12.3855 −0.674681 −0.337341 0.941383i \(-0.609527\pi\)
−0.337341 + 0.941383i \(0.609527\pi\)
\(338\) 6.88255 + 11.9209i 0.374361 + 0.648413i
\(339\) 0 0
\(340\) 24.6785 42.7444i 1.33838 2.31814i
\(341\) 0.722528 + 1.25146i 0.0391271 + 0.0677701i
\(342\) 0 0
\(343\) −18.4098 2.01993i −0.994035 0.109066i
\(344\) −80.7649 −4.35455
\(345\) 0 0
\(346\) 8.50433 14.7299i 0.457196 0.791886i
\(347\) 1.92216 3.32927i 0.103187 0.178725i −0.809809 0.586693i \(-0.800429\pi\)
0.912996 + 0.407969i \(0.133763\pi\)
\(348\) 0 0
\(349\) −12.1891 −0.652468 −0.326234 0.945289i \(-0.605780\pi\)
−0.326234 + 0.945289i \(0.605780\pi\)
\(350\) −8.28249 15.6344i −0.442718 0.835695i
\(351\) 0 0
\(352\) −2.76145 4.78297i −0.147186 0.254933i
\(353\) 1.78180 3.08617i 0.0948358 0.164260i −0.814704 0.579877i \(-0.803101\pi\)
0.909540 + 0.415616i \(0.136434\pi\)
\(354\) 0 0
\(355\) −10.2163 17.6952i −0.542227 0.939165i
\(356\) −49.4610 −2.62143
\(357\) 0 0
\(358\) −37.6377 −1.98922
\(359\) 0.483978 + 0.838275i 0.0255434 + 0.0442425i 0.878515 0.477716i \(-0.158535\pi\)
−0.852971 + 0.521958i \(0.825202\pi\)
\(360\) 0 0
\(361\) 6.88255 11.9209i 0.362239 0.627417i
\(362\) −24.7570 42.8805i −1.30120 2.25375i
\(363\) 0 0
\(364\) −39.3003 1.43226i −2.05990 0.0750707i
\(365\) 18.5439 0.970634
\(366\) 0 0
\(367\) −10.4771 + 18.1469i −0.546900 + 0.947259i 0.451585 + 0.892228i \(0.350859\pi\)
−0.998485 + 0.0550305i \(0.982474\pi\)
\(368\) −12.6421 + 21.8968i −0.659017 + 1.14145i
\(369\) 0 0
\(370\) 19.1978 0.998044
\(371\) −5.32072 0.193908i −0.276238 0.0100672i
\(372\) 0 0
\(373\) −1.00000 1.73205i −0.0517780 0.0896822i 0.838975 0.544170i \(-0.183156\pi\)
−0.890753 + 0.454488i \(0.849822\pi\)
\(374\) −2.38255 + 4.12669i −0.123199 + 0.213386i
\(375\) 0 0
\(376\) 14.2472 + 24.6769i 0.734744 + 1.27261i
\(377\) 7.09160 0.365236
\(378\) 0 0
\(379\) −7.14331 −0.366927 −0.183464 0.983027i \(-0.558731\pi\)
−0.183464 + 0.983027i \(0.558731\pi\)
\(380\) −9.60872 16.6428i −0.492917 0.853757i
\(381\) 0 0
\(382\) −10.2694 + 17.7872i −0.525429 + 0.910070i
\(383\) 5.98831 + 10.3721i 0.305988 + 0.529987i 0.977481 0.211024i \(-0.0676798\pi\)
−0.671493 + 0.741011i \(0.734346\pi\)
\(384\) 0 0
\(385\) −0.590912 1.11543i −0.0301157 0.0568478i
\(386\) 20.6959 1.05339
\(387\) 0 0
\(388\) 33.2509 57.5922i 1.68806 2.92380i
\(389\) −6.88942 + 11.9328i −0.349308 + 0.605019i −0.986127 0.165995i \(-0.946917\pi\)
0.636819 + 0.771013i \(0.280250\pi\)
\(390\) 0 0
\(391\) 11.0989 0.561295
\(392\) −34.9017 + 51.4059i −1.76280 + 2.59639i
\(393\) 0 0
\(394\) −24.8189 42.9875i −1.25036 2.16568i
\(395\) 1.32327 2.29197i 0.0665810 0.115322i
\(396\) 0 0
\(397\) −4.19344 7.26325i −0.210463 0.364532i 0.741397 0.671067i \(-0.234164\pi\)
−0.951859 + 0.306535i \(0.900830\pi\)
\(398\) 16.0741 0.805723
\(399\) 0 0
\(400\) −33.1606 −1.65803
\(401\) −13.8083 23.9168i −0.689556 1.19435i −0.971982 0.235057i \(-0.924472\pi\)
0.282426 0.959289i \(-0.408861\pi\)
\(402\) 0 0
\(403\) 6.76145 11.7112i 0.336812 0.583375i
\(404\) 38.6272 + 66.9043i 1.92178 + 3.32861i
\(405\) 0 0
\(406\) 9.57234 15.2672i 0.475067 0.757699i
\(407\) −1.34479 −0.0666590
\(408\) 0 0
\(409\) −15.2658 + 26.4411i −0.754844 + 1.30743i 0.190607 + 0.981666i \(0.438954\pi\)
−0.945452 + 0.325762i \(0.894379\pi\)
\(410\) 19.1025 33.0865i 0.943407 1.63403i
\(411\) 0 0
\(412\) 48.6377 2.39621
\(413\) 12.9258 + 0.471067i 0.636037 + 0.0231797i
\(414\) 0 0
\(415\) −4.31453 7.47299i −0.211792 0.366835i
\(416\) −25.8418 + 44.7592i −1.26700 + 2.19450i
\(417\) 0 0
\(418\) 0.927658 + 1.60675i 0.0453732 + 0.0785887i
\(419\) 21.0000 1.02592 0.512959 0.858413i \(-0.328549\pi\)
0.512959 + 0.858413i \(0.328549\pi\)
\(420\) 0 0
\(421\) 34.7293 1.69260 0.846302 0.532703i \(-0.178824\pi\)
0.846302 + 0.532703i \(0.178824\pi\)
\(422\) −9.00983 15.6055i −0.438592 0.759663i
\(423\) 0 0
\(424\) −8.93130 + 15.4695i −0.433742 + 0.751264i
\(425\) 7.27816 + 12.6061i 0.353043 + 0.611488i
\(426\) 0 0
\(427\) 10.6476 16.9822i 0.515275 0.821828i
\(428\) 66.1555 3.19775
\(429\) 0 0
\(430\) −19.5080 + 33.7888i −0.940758 + 1.62944i
\(431\) −15.8022 + 27.3701i −0.761163 + 1.31837i 0.181088 + 0.983467i \(0.442038\pi\)
−0.942251 + 0.334906i \(0.891295\pi\)
\(432\) 0 0
\(433\) −6.48576 −0.311686 −0.155843 0.987782i \(-0.549809\pi\)
−0.155843 + 0.987782i \(0.549809\pi\)
\(434\) −16.0858 30.3644i −0.772144 1.45754i
\(435\) 0 0
\(436\) 8.05308 + 13.9484i 0.385673 + 0.668005i
\(437\) 2.16071 3.74245i 0.103361 0.179026i
\(438\) 0 0
\(439\) 7.78799 + 13.4892i 0.371701 + 0.643804i 0.989827 0.142274i \(-0.0454415\pi\)
−0.618127 + 0.786078i \(0.712108\pi\)
\(440\) −4.23491 −0.201891
\(441\) 0 0
\(442\) 44.5919 2.12102
\(443\) 12.5371 + 21.7148i 0.595654 + 1.03170i 0.993454 + 0.114231i \(0.0364403\pi\)
−0.397800 + 0.917472i \(0.630226\pi\)
\(444\) 0 0
\(445\) −7.42835 + 12.8663i −0.352137 + 0.609920i
\(446\) −8.55927 14.8251i −0.405293 0.701989i
\(447\) 0 0
\(448\) 28.3182 + 53.4548i 1.33791 + 2.52550i
\(449\) −15.2967 −0.721894 −0.360947 0.932586i \(-0.617546\pi\)
−0.360947 + 0.932586i \(0.617546\pi\)
\(450\) 0 0
\(451\) −1.33812 + 2.31770i −0.0630098 + 0.109136i
\(452\) −26.3189 + 45.5856i −1.23794 + 2.14417i
\(453\) 0 0
\(454\) −73.1235 −3.43186
\(455\) −6.27492 + 10.0081i −0.294173 + 0.469185i
\(456\) 0 0
\(457\) −10.2200 17.7015i −0.478071 0.828042i 0.521613 0.853182i \(-0.325330\pi\)
−0.999684 + 0.0251395i \(0.991997\pi\)
\(458\) −11.0636 + 19.1627i −0.516968 + 0.895415i
\(459\) 0 0
\(460\) 7.93199 + 13.7386i 0.369831 + 0.640566i
\(461\) −40.8182 −1.90109 −0.950546 0.310584i \(-0.899475\pi\)
−0.950546 + 0.310584i \(0.899475\pi\)
\(462\) 0 0
\(463\) 9.90840 0.460482 0.230241 0.973134i \(-0.426048\pi\)
0.230241 + 0.973134i \(0.426048\pi\)
\(464\) −16.8869 29.2489i −0.783954 1.35785i
\(465\) 0 0
\(466\) −37.0123 + 64.1072i −1.71456 + 2.96971i
\(467\) 8.86948 + 15.3624i 0.410430 + 0.710886i 0.994937 0.100503i \(-0.0320451\pi\)
−0.584506 + 0.811389i \(0.698712\pi\)
\(468\) 0 0
\(469\) −1.88255 0.0686074i −0.0869279 0.00316799i
\(470\) 13.7651 0.634936
\(471\) 0 0
\(472\) 21.6971 37.5804i 0.998689 1.72978i
\(473\) 1.36652 2.36689i 0.0628329 0.108830i
\(474\) 0 0
\(475\) 5.66758 0.260047
\(476\) 43.6730 69.6554i 2.00175 3.19265i
\(477\) 0 0
\(478\) 37.6112 + 65.1445i 1.72030 + 2.97964i
\(479\) 11.8047 20.4463i 0.539371 0.934217i −0.459567 0.888143i \(-0.651996\pi\)
0.998938 0.0460744i \(-0.0146711\pi\)
\(480\) 0 0
\(481\) 6.29232 + 10.8986i 0.286905 + 0.496934i
\(482\) −60.8231 −2.77042
\(483\) 0 0
\(484\) −57.6908 −2.62231
\(485\) −9.98762 17.2991i −0.453514 0.785510i
\(486\) 0 0
\(487\) −17.4363 + 30.2006i −0.790115 + 1.36852i 0.135780 + 0.990739i \(0.456646\pi\)
−0.925895 + 0.377780i \(0.876687\pi\)
\(488\) −33.6236 58.2377i −1.52207 2.63630i
\(489\) 0 0
\(490\) 13.0760 + 27.0181i 0.590713 + 1.22055i
\(491\) 23.2051 1.04723 0.523615 0.851955i \(-0.324583\pi\)
0.523615 + 0.851955i \(0.324583\pi\)
\(492\) 0 0
\(493\) −7.41273 + 12.8392i −0.333853 + 0.578250i
\(494\) 8.68106 15.0360i 0.390579 0.676503i
\(495\) 0 0
\(496\) −64.4028 −2.89177
\(497\) −15.9327 30.0753i −0.714678 1.34906i
\(498\) 0 0
\(499\) 2.66257 + 4.61170i 0.119193 + 0.206448i 0.919448 0.393212i \(-0.128636\pi\)
−0.800255 + 0.599660i \(0.795303\pi\)
\(500\) −31.4010 + 54.3882i −1.40430 + 2.43231i
\(501\) 0 0
\(502\) −42.1828 73.0628i −1.88271 3.26095i
\(503\) −10.4313 −0.465109 −0.232554 0.972583i \(-0.574708\pi\)
−0.232554 + 0.972583i \(0.574708\pi\)
\(504\) 0 0
\(505\) 23.2051 1.03261
\(506\) −0.765781 1.32637i −0.0340431 0.0589644i
\(507\) 0 0
\(508\) 35.5352 61.5488i 1.57662 2.73079i
\(509\) −0.750930 1.30065i −0.0332844 0.0576502i 0.848903 0.528548i \(-0.177263\pi\)
−0.882188 + 0.470898i \(0.843930\pi\)
\(510\) 0 0
\(511\) 30.8683 + 1.12496i 1.36553 + 0.0497654i
\(512\) 8.48948 0.375186
\(513\) 0 0
\(514\) 13.7701 23.8505i 0.607374 1.05200i
\(515\) 7.30470 12.6521i 0.321884 0.557519i
\(516\) 0 0
\(517\) −0.964238 −0.0424072
\(518\) 31.9567 + 1.16463i 1.40410 + 0.0511707i
\(519\) 0 0
\(520\) 19.8152 + 34.3210i 0.868955 + 1.50507i
\(521\) −18.8709 + 32.6853i −0.826747 + 1.43197i 0.0738295 + 0.997271i \(0.476478\pi\)
−0.900577 + 0.434697i \(0.856855\pi\)
\(522\) 0 0
\(523\) 8.97779 + 15.5500i 0.392571 + 0.679953i 0.992788 0.119884i \(-0.0382523\pi\)
−0.600217 + 0.799837i \(0.704919\pi\)
\(524\) 59.6253 2.60475
\(525\) 0 0
\(526\) 76.8341 3.35013
\(527\) 14.1353 + 24.4830i 0.615742 + 1.06650i
\(528\) 0 0
\(529\) 9.71634 16.8292i 0.422449 0.731704i
\(530\) 4.31453 + 7.47299i 0.187411 + 0.324606i
\(531\) 0 0
\(532\) −14.9851 28.2865i −0.649685 1.22638i
\(533\) 25.0444 1.08479
\(534\) 0 0
\(535\) 9.93563 17.2090i 0.429555 0.744011i
\(536\) −3.16002 + 5.47331i −0.136492 + 0.236411i
\(537\) 0 0
\(538\) 40.1606 1.73145
\(539\) −0.915967 1.89260i −0.0394535 0.0815202i
\(540\) 0 0
\(541\) −4.18547 7.24944i −0.179947 0.311678i 0.761915 0.647677i \(-0.224259\pi\)
−0.941862 + 0.335999i \(0.890926\pi\)
\(542\) −0.0599627 + 0.103858i −0.00257562 + 0.00446110i
\(543\) 0 0
\(544\) −54.0239 93.5722i −2.31626 4.01187i
\(545\) 4.83784 0.207230
\(546\) 0 0
\(547\) 30.1075 1.28731 0.643653 0.765318i \(-0.277418\pi\)
0.643653 + 0.765318i \(0.277418\pi\)
\(548\) −9.98762 17.2991i −0.426650 0.738979i
\(549\) 0 0
\(550\) 1.00433 1.73955i 0.0428248 0.0741747i
\(551\) 2.88619 + 4.99902i 0.122956 + 0.212966i
\(552\) 0 0
\(553\) 2.34176 3.73495i 0.0995820 0.158826i
\(554\) 42.3163 1.79785
\(555\) 0 0
\(556\) −44.2057 + 76.5666i −1.87474 + 3.24715i
\(557\) −8.26764 + 14.3200i −0.350311 + 0.606757i −0.986304 0.164938i \(-0.947257\pi\)
0.635993 + 0.771695i \(0.280591\pi\)
\(558\) 0 0
\(559\) −25.5760 −1.08175
\(560\) 56.2199 + 2.04887i 2.37572 + 0.0865807i
\(561\) 0 0
\(562\) −16.0760 27.8444i −0.678124 1.17455i
\(563\) 11.1156 19.2528i 0.468466 0.811408i −0.530884 0.847444i \(-0.678140\pi\)
0.999350 + 0.0360368i \(0.0114733\pi\)
\(564\) 0 0
\(565\) 7.90545 + 13.6926i 0.332585 + 0.576053i
\(566\) 16.2174 0.681670
\(567\) 0 0
\(568\) −114.185 −4.79111
\(569\) −1.15638 2.00290i −0.0484778 0.0839660i 0.840768 0.541395i \(-0.182104\pi\)
−0.889246 + 0.457429i \(0.848770\pi\)
\(570\) 0 0
\(571\) 3.04944 5.28179i 0.127615 0.221036i −0.795137 0.606430i \(-0.792601\pi\)
0.922752 + 0.385394i \(0.125934\pi\)
\(572\) −2.23236 3.86656i −0.0933397 0.161669i
\(573\) 0 0
\(574\) 33.8053 53.9171i 1.41101 2.25046i
\(575\) −4.67859 −0.195111
\(576\) 0 0
\(577\) −10.1032 + 17.4993i −0.420602 + 0.728505i −0.995998 0.0893702i \(-0.971515\pi\)
0.575396 + 0.817875i \(0.304848\pi\)
\(578\) −23.6643 + 40.9879i −0.984307 + 1.70487i
\(579\) 0 0
\(580\) −21.1905 −0.879887
\(581\) −6.72864 12.7013i −0.279151 0.526939i
\(582\) 0 0
\(583\) −0.302231 0.523480i −0.0125171 0.0216803i
\(584\) 51.8151 89.7465i 2.14413 3.71374i
\(585\) 0 0
\(586\) 6.68911 + 11.5859i 0.276324 + 0.478608i
\(587\) 38.6822 1.59658 0.798292 0.602271i \(-0.205737\pi\)
0.798292 + 0.602271i \(0.205737\pi\)
\(588\) 0 0
\(589\) 11.0073 0.453547
\(590\) −10.4814 18.1544i −0.431514 0.747404i
\(591\) 0 0
\(592\) 29.9672 51.9047i 1.23164 2.13327i
\(593\) −11.8578 20.5383i −0.486941 0.843406i 0.512946 0.858421i \(-0.328554\pi\)
−0.999887 + 0.0150142i \(0.995221\pi\)
\(594\) 0 0
\(595\) −11.5604 21.8219i −0.473929 0.894611i
\(596\) 57.5795 2.35855
\(597\) 0 0
\(598\) −7.16621 + 12.4122i −0.293048 + 0.507574i
\(599\) 17.2403 29.8611i 0.704421 1.22009i −0.262479 0.964938i \(-0.584540\pi\)
0.966900 0.255155i \(-0.0821265\pi\)
\(600\) 0 0
\(601\) −7.28071 −0.296986 −0.148493 0.988913i \(-0.547442\pi\)
−0.148493 + 0.988913i \(0.547442\pi\)
\(602\) −34.5228 + 55.0615i −1.40705 + 2.24414i
\(603\) 0 0
\(604\) 31.9894 + 55.4073i 1.30163 + 2.25449i
\(605\) −8.66435 + 15.0071i −0.352256 + 0.610125i
\(606\) 0 0
\(607\) 12.5796 + 21.7886i 0.510591 + 0.884370i 0.999925 + 0.0122732i \(0.00390679\pi\)
−0.489333 + 0.872097i \(0.662760\pi\)
\(608\) −42.0690 −1.70612
\(609\) 0 0
\(610\) −32.4858 −1.31531
\(611\) 4.51169 + 7.81448i 0.182523 + 0.316140i
\(612\) 0 0
\(613\) 18.7731 32.5159i 0.758237 1.31330i −0.185512 0.982642i \(-0.559394\pi\)
0.943749 0.330663i \(-0.107272\pi\)
\(614\) 29.7676 + 51.5589i 1.20132 + 2.08075i
\(615\) 0 0
\(616\) −7.04944 0.256909i −0.284030 0.0103512i
\(617\) −13.7280 −0.552667 −0.276333 0.961062i \(-0.589119\pi\)
−0.276333 + 0.961062i \(0.589119\pi\)
\(618\) 0 0
\(619\) −5.90545 + 10.2285i −0.237360 + 0.411119i −0.959956 0.280151i \(-0.909615\pi\)
0.722596 + 0.691271i \(0.242949\pi\)
\(620\) −20.2040 + 34.9943i −0.811411 + 1.40540i
\(621\) 0 0
\(622\) 21.5302 0.863282
\(623\) −13.1458 + 20.9666i −0.526675 + 0.840009i
\(624\) 0 0
\(625\) 3.23924 + 5.61053i 0.129570 + 0.224421i
\(626\) 30.4116 52.6744i 1.21549 2.10529i
\(627\) 0 0
\(628\) 0.500000 + 0.866025i 0.0199522 + 0.0345582i
\(629\) −26.3090 −1.04901
\(630\) 0 0
\(631\) 29.6304 1.17957 0.589785 0.807561i \(-0.299213\pi\)
0.589785 + 0.807561i \(0.299213\pi\)
\(632\) −7.39493 12.8084i −0.294154 0.509490i
\(633\) 0 0
\(634\) 26.9127 46.6142i 1.06884 1.85129i
\(635\) −10.6738 18.4875i −0.423576 0.733655i
\(636\) 0 0
\(637\) −11.0524 + 16.2788i −0.437912 + 0.644989i
\(638\) 2.04580 0.0809940
\(639\) 0 0
\(640\) 19.8152 34.3210i 0.783265 1.35666i
\(641\) 7.32623 12.6894i 0.289368 0.501201i −0.684291 0.729209i \(-0.739888\pi\)
0.973659 + 0.228008i \(0.0732214\pi\)
\(642\) 0 0
\(643\) 2.03714 0.0803369 0.0401685 0.999193i \(-0.487211\pi\)
0.0401685 + 0.999193i \(0.487211\pi\)
\(644\) 12.3702 + 23.3505i 0.487453 + 0.920139i
\(645\) 0 0
\(646\) 18.1483 + 31.4338i 0.714036 + 1.23675i
\(647\) −5.89307 + 10.2071i −0.231680 + 0.401282i −0.958303 0.285755i \(-0.907756\pi\)
0.726622 + 0.687037i \(0.241089\pi\)
\(648\) 0 0
\(649\) 0.734219 + 1.27171i 0.0288206 + 0.0499188i
\(650\) −18.7971 −0.737284
\(651\) 0 0
\(652\) −47.3570 −1.85464
\(653\) −17.0920 29.6042i −0.668862 1.15850i −0.978223 0.207558i \(-0.933448\pi\)
0.309361 0.950945i \(-0.399885\pi\)
\(654\) 0 0
\(655\) 8.95489 15.5103i 0.349896 0.606038i
\(656\) −59.6370 103.294i −2.32844 4.03297i
\(657\) 0 0
\(658\) 22.9134 + 0.835055i 0.893258 + 0.0325538i
\(659\) −24.8640 −0.968563 −0.484282 0.874912i \(-0.660919\pi\)
−0.484282 + 0.874912i \(0.660919\pi\)
\(660\) 0 0
\(661\) −12.7694 + 22.1173i −0.496673 + 0.860263i −0.999993 0.00383747i \(-0.998778\pi\)
0.503320 + 0.864100i \(0.332112\pi\)
\(662\) −31.8967 + 55.2467i −1.23970 + 2.14722i
\(663\) 0 0
\(664\) −48.2224 −1.87139
\(665\) −9.60872 0.350179i −0.372610 0.0135794i
\(666\) 0 0
\(667\) −2.38255 4.12669i −0.0922525 0.159786i
\(668\) 11.4778 19.8801i 0.444089 0.769185i
\(669\) 0 0
\(670\) 1.52654 + 2.64405i 0.0589755 + 0.102149i
\(671\) 2.27561 0.0878490
\(672\) 0 0
\(673\) −3.81955 −0.147233 −0.0736165 0.997287i \(-0.523454\pi\)
−0.0736165 + 0.997287i \(0.523454\pi\)
\(674\) 16.7181 + 28.9566i 0.643958 + 1.11537i
\(675\) 0 0
\(676\) 13.4814 23.3505i 0.518517 0.898097i
\(677\) −8.61126 14.9151i −0.330958 0.573236i 0.651742 0.758441i \(-0.274038\pi\)
−0.982700 + 0.185205i \(0.940705\pi\)
\(678\) 0 0
\(679\) −15.5760 29.4020i −0.597751 1.12834i
\(680\) −82.8501 −3.17715
\(681\) 0 0
\(682\) 1.95056 3.37847i 0.0746907 0.129368i
\(683\) 16.8585 29.1997i 0.645072 1.11730i −0.339213 0.940709i \(-0.610161\pi\)
0.984285 0.176587i \(-0.0565058\pi\)
\(684\) 0 0
\(685\) −6.00000 −0.229248
\(686\) 20.1273 + 45.7676i 0.768463 + 1.74742i
\(687\) 0 0
\(688\) 60.9028 + 105.487i 2.32190 + 4.02165i
\(689\) −2.82829 + 4.89874i −0.107749 + 0.186627i
\(690\) 0 0
\(691\) 12.7465 + 22.0776i 0.484901 + 0.839872i 0.999850 0.0173484i \(-0.00552246\pi\)
−0.514949 + 0.857221i \(0.672189\pi\)
\(692\) −33.3163 −1.26650
\(693\) 0 0
\(694\) −10.3782 −0.393952
\(695\) 13.2782 + 22.9984i 0.503669 + 0.872381i
\(696\) 0 0
\(697\) −26.1785 + 45.3425i −0.991582 + 1.71747i
\(698\) 16.4530 + 28.4975i 0.622756 + 1.07865i
\(699\) 0 0
\(700\) −18.4098 + 29.3623i −0.695824 + 1.10979i
\(701\) −10.1606 −0.383762 −0.191881 0.981418i \(-0.561459\pi\)
−0.191881 + 0.981418i \(0.561459\pi\)
\(702\) 0 0
\(703\) −5.12178 + 8.87119i −0.193172 + 0.334583i
\(704\) −3.43385 + 5.94760i −0.129418 + 0.224159i
\(705\) 0 0
\(706\) −9.62041 −0.362069
\(707\) 38.6272 + 1.40773i 1.45273 + 0.0529430i
\(708\) 0 0
\(709\) 7.97346 + 13.8104i 0.299449 + 0.518662i 0.976010 0.217725i \(-0.0698637\pi\)
−0.676561 + 0.736387i \(0.736530\pi\)
\(710\) −27.5803 + 47.7705i −1.03507 + 1.79280i
\(711\) 0 0
\(712\) 41.5123 + 71.9014i 1.55574 + 2.69462i
\(713\) −9.08650 −0.340292
\(714\) 0 0
\(715\) −1.34108 −0.0501534
\(716\) 36.8621 + 63.8471i 1.37760 + 2.38608i
\(717\) 0 0
\(718\) 1.30656 2.26303i 0.0487604 0.0844556i
\(719\) −8.20877 14.2180i −0.306136 0.530242i 0.671378 0.741115i \(-0.265703\pi\)
−0.977513 + 0.210873i \(0.932369\pi\)
\(720\) 0 0
\(721\) 12.9270 20.6176i 0.481425 0.767840i
\(722\) −37.1606 −1.38298
\(723\) 0 0
\(724\) −48.4937 + 83.9936i −1.80226 + 3.12160i
\(725\) 3.12474 5.41220i 0.116050 0.201004i
\(726\) 0 0
\(727\) −35.8282 −1.32879 −0.664397 0.747379i \(-0.731312\pi\)
−0.664397 + 0.747379i \(0.731312\pi\)
\(728\) 30.9024 + 58.3329i 1.14532 + 2.16196i
\(729\) 0 0
\(730\) −25.0309 43.3547i −0.926434 1.60463i
\(731\) 26.7341 46.3049i 0.988798 1.71265i
\(732\) 0 0
\(733\) −19.6440 34.0244i −0.725568 1.25672i −0.958740 0.284284i \(-0.908244\pi\)
0.233172 0.972435i \(-0.425089\pi\)
\(734\) 56.5685 2.08798
\(735\) 0 0
\(736\) 34.7280 1.28009
\(737\) −0.106934 0.185214i −0.00393895 0.00682246i
\(738\) 0 0
\(739\) −1.04511 + 1.81019i −0.0384451 + 0.0665888i −0.884608 0.466336i \(-0.845574\pi\)
0.846163 + 0.532925i \(0.178907\pi\)
\(740\) −18.8022 32.5663i −0.691181 1.19716i
\(741\) 0 0
\(742\) 6.72864 + 12.7013i 0.247016 + 0.466280i
\(743\) −30.7266 −1.12725 −0.563624 0.826031i \(-0.690593\pi\)
−0.563624 + 0.826031i \(0.690593\pi\)
\(744\) 0 0
\(745\) 8.64764 14.9781i 0.316825 0.548757i
\(746\) −2.69963 + 4.67589i −0.0988404 + 0.171197i
\(747\) 0 0
\(748\) 9.33379 0.341277
\(749\) 17.5829 28.0434i 0.642464 1.02469i
\(750\) 0 0
\(751\) −10.3869 17.9906i −0.379023 0.656486i 0.611898 0.790937i \(-0.290406\pi\)
−0.990920 + 0.134451i \(0.957073\pi\)
\(752\) 21.4869 37.2165i 0.783548 1.35714i
\(753\) 0 0
\(754\) −9.57234 16.5798i −0.348604 0.603800i
\(755\) 19.2174 0.699394
\(756\) 0 0
\(757\) 16.9257 0.615176 0.307588 0.951520i \(-0.400478\pi\)
0.307588 + 0.951520i \(0.400478\pi\)
\(758\) 9.64214 + 16.7007i 0.350218 + 0.606596i
\(759\) 0 0
\(760\) −16.1291 + 27.9364i −0.585063 + 1.01336i
\(761\) 16.4196 + 28.4396i 0.595210 + 1.03093i 0.993517 + 0.113682i \(0.0362646\pi\)
−0.398307 + 0.917252i \(0.630402\pi\)
\(762\) 0 0
\(763\) 8.05308 + 0.293486i 0.291541 + 0.0106249i
\(764\) 40.2312 1.45551
\(765\) 0 0
\(766\) 16.1662 28.0007i 0.584109 1.01171i
\(767\) 6.87085 11.9007i 0.248092 0.429708i
\(768\) 0 0
\(769\) 31.7293 1.14419 0.572094 0.820188i \(-0.306131\pi\)
0.572094 + 0.820188i \(0.306131\pi\)
\(770\) −1.81020 + 2.88715i −0.0652352 + 0.104046i
\(771\) 0 0
\(772\) −20.2694 35.1077i −0.729512 1.26355i
\(773\) 3.18656 5.51928i 0.114613 0.198515i −0.803012 0.595963i \(-0.796771\pi\)
0.917625 + 0.397448i \(0.130104\pi\)
\(774\) 0 0
\(775\) −5.95853 10.3205i −0.214037 0.370722i
\(776\) −111.629 −4.00724
\(777\) 0 0
\(778\) 37.1978 1.33360
\(779\) 10.1927 + 17.6544i 0.365193 + 0.632533i
\(780\) 0 0
\(781\) 1.93199 3.34630i 0.0691320 0.119740i
\(782\) −14.9814 25.9486i −0.535735 0.927920i
\(783\) 0 0
\(784\) 93.4595 + 6.82112i 3.33784 + 0.243612i
\(785\) 0.300372 0.0107207
\(786\) 0 0
\(787\) 9.93996 17.2165i 0.354321 0.613703i −0.632680 0.774413i \(-0.718045\pi\)
0.987002 + 0.160711i \(0.0513786\pi\)
\(788\) −48.6148 + 84.2034i −1.73183 + 2.99962i
\(789\) 0 0
\(790\) −7.14468 −0.254196
\(791\) 12.3288 + 23.2724i 0.438361 + 0.827471i