Properties

Label 189.2.e.e.163.1
Level 189
Weight 2
Character 189.163
Analytic conductor 1.509
Analytic rank 0
Dimension 6
CM No
Inner twists 2

Related objects

Downloads

Learn more about

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 163.1
Root \(0.500000 + 0.224437i\)
Character \(\chi\) = 189.163
Dual form 189.2.e.e.109.1

$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34981 + 2.33795i −0.954463 + 1.65318i −0.218870 + 0.975754i \(0.570237\pi\)
−0.735593 + 0.677424i \(0.763096\pi\)
\(3\) 0 0
\(4\) −2.64400 4.57954i −1.32200 2.28977i
\(5\) 0.794182 1.37556i 0.355169 0.615171i −0.631978 0.774986i \(-0.717757\pi\)
0.987147 + 0.159816i \(0.0510900\pi\)
\(6\) 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 0.842496 0.538703i \(-0.181086\pi\)
−0.887778 + 0.460271i \(0.847752\pi\)
\(12\) 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 −0.963873 0.266362i \(-0.914178\pi\)
0.251260 0.967920i \(-0.419155\pi\)
\(18\) 0 0
\(19\) 1.14400 1.98146i 0.262451 0.454578i −0.704442 0.709762i \(-0.748803\pi\)
0.966893 + 0.255184i \(0.0821360\pi\)
\(20\) −8.39926 −1.87813
\(21\) 0 0
\(22\) 0.810892 0.172883
\(23\) −0.944368 + 1.63569i −0.196914 + 0.341066i −0.947526 0.319678i \(-0.896425\pi\)
0.750612 + 0.660743i \(0.229759\pi\)
\(24\) 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 0.997048 0.0767797i \(-0.0244638\pi\)
−0.565017 + 0.825079i \(0.691130\pi\)
\(32\) −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 −0.621240 0.783620i \(-0.713371\pi\)
0.989255 + 0.146199i \(0.0467041\pi\)
\(38\) 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 −0.724894 0.688861i \(-0.758111\pi\)
0.959018 + 0.283346i \(0.0914444\pi\)
\(48\) 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 0.788609 0.614895i \(-0.210802\pi\)
−0.926819 + 0.375507i \(0.877468\pi\)
\(54\) 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 0.980119 0.198412i \(-0.0635784\pi\)
−0.661889 + 0.749602i \(0.730245\pi\)
\(60\) 0 0
\(61\) −3.78799 + 6.56099i −0.485003 + 0.840049i −0.999852 0.0172317i \(-0.994515\pi\)
0.514849 + 0.857281i \(0.327848\pi\)
\(62\) −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 0.843460 0.537193i \(-0.180515\pi\)
−0.886952 + 0.461861i \(0.847182\pi\)
\(68\) −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 0.973993 + 0.226580i \(0.0727543\pi\)
−0.290773 + 0.956792i \(0.593912\pi\)
\(74\) 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 −0.909078 0.416625i \(-0.863213\pi\)
0.815347 + 0.578973i \(0.196546\pi\)
\(80\) 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 −0.504256 0.863554i \(-0.668233\pi\)
0.999988 + 0.00492107i \(0.00156643\pi\)
\(90\) 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 0.958210 + 0.286066i \(0.0923475\pi\)
−0.231365 + 0.972867i \(0.574319\pi\)
\(102\) 0 0
\(103\) −4.59888 + 7.96550i −0.453142 + 0.784864i −0.998579 0.0532872i \(-0.983030\pi\)
0.545438 + 0.838151i \(0.316363\pi\)
\(104\) 24.9505 2.44660
\(105\) 0 0
\(106\) 5.43268 0.527668
\(107\) −6.25526 + 10.8344i −0.604719 + 1.04740i 0.387377 + 0.921921i \(0.373381\pi\)
−0.992096 + 0.125482i \(0.959952\pi\)
\(108\) 0 0
\(109\) 1.52290 + 2.63774i 0.145867 + 0.252650i 0.929696 0.368327i \(-0.120069\pi\)
−0.783829 + 0.620977i \(0.786736\pi\)
\(110\) 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 −0.999963 0.00854976i \(-0.997278\pi\)
0.507386 + 0.861719i \(0.330612\pi\)
\(132\) 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 0.773993 0.633194i \(-0.218256\pi\)
−0.935359 + 0.353701i \(0.884923\pi\)
\(138\) 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 −0.998123 0.0612468i \(-0.980492\pi\)
0.552103 + 0.833776i \(0.313826\pi\)
\(150\) 0 0
\(151\) 6.04944 + 10.4779i 0.492297 + 0.852683i 0.999961 0.00887237i \(-0.00282420\pi\)
−0.507664 + 0.861555i \(0.669491\pi\)
\(152\) 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 0.869774 0.493451i \(-0.164265\pi\)
−0.862228 + 0.506521i \(0.830931\pi\)
\(158\) −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 −0.635650 0.771978i \(-0.719268\pi\)
0.986377 + 0.164500i \(0.0526010\pi\)
\(164\) −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 −0.721068 0.692864i \(-0.756348\pi\)
0.960572 + 0.278031i \(0.0896818\pi\)
\(174\) 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 0.999701 + 0.0244564i \(0.00778548\pi\)
−0.478671 + 0.877995i \(0.658881\pi\)
\(180\) 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 −0.970198 0.242314i \(-0.922094\pi\)
0.694949 + 0.719059i \(0.255427\pi\)
\(192\) 0 0
\(193\) −3.83310 6.63913i −0.275913 0.477895i 0.694452 0.719539i \(-0.255647\pi\)
−0.970365 + 0.241644i \(0.922313\pi\)
\(194\) 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 0.741000 0.671505i \(-0.234352\pi\)
−0.952041 + 0.305972i \(0.901019\pi\)
\(200\) 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 0.828906 + 0.559388i \(0.188964\pi\)
0.0699913 + 0.997548i \(0.477703\pi\)
\(228\) 0 0
\(229\) −4.09820 + 7.09828i −0.270816 + 0.469068i −0.969071 0.246782i \(-0.920627\pi\)
0.698255 + 0.715849i \(0.253960\pi\)
\(230\) −8.09888 −0.534025
\(231\) 0 0
\(232\) 22.3942 1.47025
\(233\) −13.7101 + 23.7467i −0.898182 + 1.55570i −0.0683649 + 0.997660i \(0.521778\pi\)
−0.829817 + 0.558036i \(0.811555\pi\)
\(234\) 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 0.958707 + 0.284397i \(0.0917934\pi\)
−0.233058 + 0.972463i \(0.574873\pi\)
\(242\) 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 −0.661932 0.749564i \(-0.730263\pi\)
0.980107 + 0.198468i \(0.0635965\pi\)
\(258\) 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 −0.854086 0.520132i \(-0.825883\pi\)
−0.0234042 0.999726i \(-0.507450\pi\)
\(264\) 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 0.545088 0.838379i \(-0.316496\pi\)
−0.998601 + 0.0528702i \(0.983163\pi\)
\(270\) 0 0
\(271\) −0.0222115 + 0.0384714i −0.00134925 + 0.00233697i −0.866699 0.498831i \(-0.833763\pi\)
0.865350 + 0.501168i \(0.167096\pi\)
\(272\) 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 0.528540 0.848908i \(-0.322739\pi\)
−0.999446 + 0.0332754i \(0.989406\pi\)
\(278\) −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 0.762835 0.646593i \(-0.223807\pi\)
−0.941383 + 0.337339i \(0.890473\pi\)
\(284\) 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 0.730537 0.682873i \(-0.239270\pi\)
−0.956654 + 0.291227i \(0.905937\pi\)
\(312\) 0 0
\(313\) 11.2651 19.5117i 0.636741 1.10287i −0.349403 0.936973i \(-0.613616\pi\)
0.986143 0.165895i \(-0.0530511\pi\)
\(314\) −0.510520 −0.0288103
\(315\) 0 0
\(316\) 8.81089 0.495651
\(317\) 9.96905 17.2669i 0.559918 0.969806i −0.437585 0.899177i \(-0.644166\pi\)
0.997503 0.0706288i \(-0.0225006\pi\)
\(318\) 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 0.333837 + 0.942631i \(0.391656\pi\)
−0.983261 + 0.182204i \(0.941677\pi\)
\(332\) 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 0.912996 0.407969i \(-0.133763\pi\)
−0.809809 + 0.586693i \(0.800429\pi\)
\(348\) 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 0.909540 0.415616i \(-0.136434\pi\)
−0.814704 + 0.579877i \(0.803101\pi\)
\(354\) 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 −0.852971 0.521958i \(-0.825202\pi\)
0.878515 + 0.477716i \(0.158535\pi\)
\(360\) 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 −0.998485 0.0550305i \(-0.982474\pi\)
0.451585 0.892228i \(-0.350859\pi\)
\(368\) −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 −0.890753 0.454488i \(-0.849822\pi\)
0.838975 + 0.544170i \(0.183156\pi\)
\(374\) −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 −0.671493 0.741011i \(-0.734346\pi\)
0.977481 + 0.211024i \(0.0676798\pi\)
\(384\) 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 0.636819 0.771013i \(-0.280250\pi\)
−0.986127 + 0.165995i \(0.946917\pi\)
\(390\) 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 −0.951859 0.306535i \(-0.900830\pi\)
0.741397 + 0.671067i \(0.234164\pi\)
\(398\) 16.0741 0.805723
\(399\) 0 0
\(400\) −33.1606 −1.65803
\(401\) −13.8083 + 23.9168i −0.689556 + 1.19435i 0.282426 + 0.959289i \(0.408861\pi\)
−0.971982 + 0.235057i \(0.924472\pi\)
\(402\) 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 −0.945452 0.325762i \(-0.894379\pi\)
0.190607 0.981666i \(-0.438954\pi\)
\(410\) 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 −0.942251 0.334906i \(-0.891295\pi\)
0.181088 0.983467i \(-0.442038\pi\)
\(432\) 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 −0.618127 0.786078i \(-0.712108\pi\)
0.989827 + 0.142274i \(0.0454415\pi\)
\(440\) −4.23491 −0.201891
\(441\) 0 0
\(442\) 44.5919 2.12102
\(443\) 12.5371 21.7148i 0.595654 1.03170i −0.397800 0.917472i \(-0.630226\pi\)
0.993454 0.114231i \(-0.0364403\pi\)
\(444\) 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 −0.999684 0.0251395i \(-0.991997\pi\)
0.521613 + 0.853182i \(0.325330\pi\)
\(458\) −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 −0.584506 0.811389i \(-0.698712\pi\)
0.994937 + 0.100503i \(0.0320451\pi\)
\(468\) 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 0.998938 + 0.0460744i \(0.0146711\pi\)
−0.459567 + 0.888143i \(0.651996\pi\)
\(480\) 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 −0.925895 0.377780i \(-0.876687\pi\)
0.135780 0.990739i \(-0.456646\pi\)
\(488\) −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 −0.800255 0.599660i \(-0.795303\pi\)
0.919448 + 0.393212i \(0.128636\pi\)
\(500\) −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 −0.882188 0.470898i \(-0.843930\pi\)
0.848903 + 0.528548i \(0.177263\pi\)
\(510\) 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 −0.900577 0.434697i \(-0.856855\pi\)
0.0738295 0.997271i \(-0.476478\pi\)
\(522\) 0 0
\(523\) 8.97779 15.5500i 0.392571 0.679953i −0.600217 0.799837i \(-0.704919\pi\)
0.992788 + 0.119884i \(0.0382523\pi\)
\(524\) 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 −0.941862 0.335999i \(-0.890926\pi\)
0.761915 + 0.647677i \(0.224259\pi\)
\(542\) −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 0.635993 0.771695i \(-0.280591\pi\)
−0.986304 + 0.164938i \(0.947257\pi\)
\(558\) 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 0.999350 0.0360368i \(-0.0114733\pi\)
−0.530884 + 0.847444i \(0.678140\pi\)
\(564\) 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 −0.889246 0.457429i \(-0.848770\pi\)
0.840768 + 0.541395i \(0.182104\pi\)
\(570\) 0 0
\(571\) 3.04944 + 5.28179i 0.127615 + 0.221036i 0.922752 0.385394i \(-0.125934\pi\)
−0.795137 + 0.606430i \(0.792601\pi\)
\(572\) −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 0.575396 0.817875i \(-0.304848\pi\)
−0.995998 + 0.0893702i \(0.971515\pi\)
\(578\) −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 −0.999887 0.0150142i \(-0.995221\pi\)
0.512946 + 0.858421i \(0.328554\pi\)
\(594\) 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 0.966900 + 0.255155i \(0.0821265\pi\)
−0.262479 + 0.964938i \(0.584540\pi\)
\(600\) 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 −0.489333 0.872097i \(-0.662760\pi\)
0.999925 0.0122732i \(-0.00390679\pi\)
\(608\) −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 0.943749 + 0.330663i \(0.107272\pi\)
−0.185512 + 0.982642i \(0.559394\pi\)
\(614\) 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 0.722596 0.691271i \(-0.242949\pi\)
−0.959956 + 0.280151i \(0.909615\pi\)
\(620\) −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 0.973659 0.228008i \(-0.0732214\pi\)
−0.684291 + 0.729209i \(0.739888\pi\)
\(642\) 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 0.726622 0.687037i \(-0.241089\pi\)
−0.958303 + 0.285755i \(0.907756\pi\)
\(648\) 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 0.309361 + 0.950945i \(0.399885\pi\)
−0.978223 + 0.207558i \(0.933448\pi\)
\(654\) 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 0.503320 0.864100i \(-0.332112\pi\)
−0.999993 + 0.00383747i \(0.998778\pi\)
\(662\) −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 −0.982700 0.185205i \(-0.940705\pi\)
0.651742 + 0.758441i \(0.274038\pi\)
\(678\) 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 0.984285 + 0.176587i \(0.0565058\pi\)
−0.339213 + 0.940709i \(0.610161\pi\)
\(684\) 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 −0.514949 0.857221i \(-0.672189\pi\)
0.999850 + 0.0173484i \(0.00552246\pi\)
\(692\) −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 −0.676561 0.736387i \(-0.736530\pi\)
0.976010 + 0.217725i \(0.0698637\pi\)
\(710\) −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 −0.977513 0.210873i \(-0.932369\pi\)
0.671378 + 0.741115i \(0.265703\pi\)
\(720\) 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 0.233172 + 0.972435i \(0.425089\pi\)
−0.958740 + 0.284284i \(0.908244\pi\)
\(734\) 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 0.846163 0.532925i \(-0.178907\pi\)
−0.884608 + 0.466336i \(0.845574\pi\)
\(740\) −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 −0.990920 0.134451i \(-0.957073\pi\)
0.611898 + 0.790937i \(0.290406\pi\)
\(752\) 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 −0.398307 0.917252i \(-0.630402\pi\)
0.993517 0.113682i \(-0.0362646\pi\)
\(762\) 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 0.917625 0.397448i \(-0.130104\pi\)
−0.803012 + 0.595963i \(0.796771\pi\)
\(774\) 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 0.987002 0.160711i \(-0.0513786\pi\)
−0.632680 + 0.774413i \(0.718045\pi\)
\(788\) −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