Properties

Label 441.2.f.c.148.1
Level $441$
Weight $2$
Character 441.148
Analytic conductor $3.521$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 148.1
Root \(-0.766044 - 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.c.295.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.26604 - 2.19285i) q^{2} +(1.11334 + 1.32683i) q^{3} +(-2.20574 + 3.82045i) q^{4} +(-0.439693 + 0.761570i) q^{5} +(1.50000 - 4.12122i) q^{6} +6.10607 q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})\) \(q+(-1.26604 - 2.19285i) q^{2} +(1.11334 + 1.32683i) q^{3} +(-2.20574 + 3.82045i) q^{4} +(-0.439693 + 0.761570i) q^{5} +(1.50000 - 4.12122i) q^{6} +6.10607 q^{8} +(-0.520945 + 2.95442i) q^{9} +2.22668 q^{10} +(-1.93969 - 3.35965i) q^{11} +(-7.52481 + 1.32683i) q^{12} +(-2.72668 + 4.72275i) q^{13} +(-1.50000 + 0.264490i) q^{15} +(-3.31908 - 5.74881i) q^{16} -1.65270 q^{17} +(7.13816 - 2.59808i) q^{18} -2.41147 q^{19} +(-1.93969 - 3.35965i) q^{20} +(-4.91147 + 8.50692i) q^{22} +(-1.58125 + 2.73881i) q^{23} +(6.79813 + 8.10170i) q^{24} +(2.11334 + 3.66041i) q^{25} +13.8084 q^{26} +(-4.50000 + 2.59808i) q^{27} +(3.02481 + 5.23913i) q^{29} +(2.47906 + 2.95442i) q^{30} +(-2.27719 + 3.94421i) q^{31} +(-2.29813 + 3.98048i) q^{32} +(2.29813 - 6.31407i) q^{33} +(2.09240 + 3.62414i) q^{34} +(-10.1382 - 8.50692i) q^{36} -4.55438 q^{37} +(3.05303 + 5.28801i) q^{38} +(-9.30200 + 1.64019i) q^{39} +(-2.68479 + 4.65020i) q^{40} +(-0.592396 + 1.02606i) q^{41} +(-0.0923963 - 0.160035i) q^{43} +17.1138 q^{44} +(-2.02094 - 1.69577i) q^{45} +8.00774 q^{46} +(-0.511144 - 0.885328i) q^{47} +(3.93242 - 10.8042i) q^{48} +(5.35117 - 9.26849i) q^{50} +(-1.84002 - 2.19285i) q^{51} +(-12.0287 - 20.8343i) q^{52} +7.29086 q^{53} +(11.3944 + 6.57856i) q^{54} +3.41147 q^{55} +(-2.68479 - 3.19961i) q^{57} +(7.65910 - 13.2660i) q^{58} +(3.33022 - 5.76811i) q^{59} +(2.29813 - 6.31407i) q^{60} +(-1.29813 - 2.24843i) q^{61} +11.5321 q^{62} -1.63816 q^{64} +(-2.39780 - 4.15312i) q^{65} +(-16.7554 + 2.95442i) q^{66} +(1.47906 - 2.56180i) q^{67} +(3.64543 - 6.31407i) q^{68} +(-5.39440 + 0.951178i) q^{69} -3.68004 q^{71} +(-3.18092 + 18.0399i) q^{72} +12.7811 q^{73} +(5.76604 + 9.98708i) q^{74} +(-2.50387 + 6.87933i) q^{75} +(5.31908 - 9.21291i) q^{76} +(15.3735 + 18.3214i) q^{78} +(2.97906 + 5.15988i) q^{79} +5.83750 q^{80} +(-8.45723 - 3.07818i) q^{81} +3.00000 q^{82} +(-0.109470 - 0.189608i) q^{83} +(0.726682 - 1.25865i) q^{85} +(-0.233956 + 0.405223i) q^{86} +(-3.58378 + 9.84635i) q^{87} +(-11.8439 - 20.5142i) q^{88} -11.0273 q^{89} +(-1.15998 + 6.57856i) q^{90} +(-6.97565 - 12.0822i) q^{92} +(-7.76857 + 1.36981i) q^{93} +(-1.29426 + 2.24173i) q^{94} +(1.06031 - 1.83651i) q^{95} +(-7.84002 + 1.38241i) q^{96} +(6.25150 + 10.8279i) q^{97} +(10.9363 - 3.98048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{2} - 3q^{4} + 3q^{5} + 9q^{6} + 12q^{8} + O(q^{10}) \) \( 6q - 3q^{2} - 3q^{4} + 3q^{5} + 9q^{6} + 12q^{8} - 6q^{11} - 18q^{12} - 3q^{13} - 9q^{15} - 3q^{16} - 12q^{17} + 9q^{18} + 6q^{19} - 6q^{20} - 9q^{22} - 12q^{23} + 27q^{24} + 6q^{25} + 6q^{26} - 27q^{27} - 9q^{29} + 18q^{30} - 3q^{31} + 9q^{34} - 27q^{36} - 6q^{37} + 6q^{38} - 18q^{39} - 9q^{40} + 3q^{43} + 30q^{44} - 9q^{45} + 3q^{47} + 6q^{50} + 9q^{51} - 21q^{52} + 12q^{53} + 27q^{54} - 9q^{57} + 9q^{58} - 3q^{59} + 6q^{61} + 60q^{62} + 24q^{64} - 15q^{65} - 36q^{66} + 12q^{67} + 6q^{68} + 9q^{69} + 18q^{71} - 36q^{72} + 42q^{73} + 30q^{74} + 9q^{75} + 15q^{76} + 54q^{78} + 21q^{79} + 30q^{80} + 18q^{82} - 18q^{83} - 9q^{85} - 6q^{86} - 9q^{87} - 27q^{88} - 24q^{89} - 27q^{90} - 3q^{92} - 27q^{93} - 18q^{94} + 12q^{95} - 27q^{96} - 3q^{97} + 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.26604 2.19285i −0.895229 1.55058i −0.833521 0.552487i \(-0.813679\pi\)
−0.0617072 0.998094i \(-0.519654\pi\)
\(3\) 1.11334 + 1.32683i 0.642788 + 0.766044i
\(4\) −2.20574 + 3.82045i −1.10287 + 1.91022i
\(5\) −0.439693 + 0.761570i −0.196637 + 0.340584i −0.947436 0.319946i \(-0.896335\pi\)
0.750799 + 0.660530i \(0.229669\pi\)
\(6\) 1.50000 4.12122i 0.612372 1.68248i
\(7\) 0 0
\(8\) 6.10607 2.15882
\(9\) −0.520945 + 2.95442i −0.173648 + 0.984808i
\(10\) 2.22668 0.704139
\(11\) −1.93969 3.35965i −0.584839 1.01297i −0.994895 0.100911i \(-0.967824\pi\)
0.410056 0.912060i \(-0.365509\pi\)
\(12\) −7.52481 + 1.32683i −2.17223 + 0.383022i
\(13\) −2.72668 + 4.72275i −0.756245 + 1.30986i 0.188507 + 0.982072i \(0.439635\pi\)
−0.944753 + 0.327784i \(0.893698\pi\)
\(14\) 0 0
\(15\) −1.50000 + 0.264490i −0.387298 + 0.0682911i
\(16\) −3.31908 5.74881i −0.829769 1.43720i
\(17\) −1.65270 −0.400840 −0.200420 0.979710i \(-0.564231\pi\)
−0.200420 + 0.979710i \(0.564231\pi\)
\(18\) 7.13816 2.59808i 1.68248 0.612372i
\(19\) −2.41147 −0.553230 −0.276615 0.960981i \(-0.589213\pi\)
−0.276615 + 0.960981i \(0.589213\pi\)
\(20\) −1.93969 3.35965i −0.433728 0.751240i
\(21\) 0 0
\(22\) −4.91147 + 8.50692i −1.04713 + 1.81368i
\(23\) −1.58125 + 2.73881i −0.329714 + 0.571081i −0.982455 0.186500i \(-0.940286\pi\)
0.652741 + 0.757581i \(0.273619\pi\)
\(24\) 6.79813 + 8.10170i 1.38766 + 1.65375i
\(25\) 2.11334 + 3.66041i 0.422668 + 0.732083i
\(26\) 13.8084 2.70805
\(27\) −4.50000 + 2.59808i −0.866025 + 0.500000i
\(28\) 0 0
\(29\) 3.02481 + 5.23913i 0.561694 + 0.972883i 0.997349 + 0.0727688i \(0.0231835\pi\)
−0.435655 + 0.900114i \(0.643483\pi\)
\(30\) 2.47906 + 2.95442i 0.452612 + 0.539401i
\(31\) −2.27719 + 3.94421i −0.408995 + 0.708400i −0.994777 0.102068i \(-0.967454\pi\)
0.585782 + 0.810468i \(0.300787\pi\)
\(32\) −2.29813 + 3.98048i −0.406256 + 0.703657i
\(33\) 2.29813 6.31407i 0.400054 1.09914i
\(34\) 2.09240 + 3.62414i 0.358843 + 0.621534i
\(35\) 0 0
\(36\) −10.1382 8.50692i −1.68969 1.41782i
\(37\) −4.55438 −0.748735 −0.374368 0.927280i \(-0.622140\pi\)
−0.374368 + 0.927280i \(0.622140\pi\)
\(38\) 3.05303 + 5.28801i 0.495267 + 0.857828i
\(39\) −9.30200 + 1.64019i −1.48951 + 0.262641i
\(40\) −2.68479 + 4.65020i −0.424503 + 0.735261i
\(41\) −0.592396 + 1.02606i −0.0925168 + 0.160244i −0.908570 0.417734i \(-0.862825\pi\)
0.816053 + 0.577977i \(0.196158\pi\)
\(42\) 0 0
\(43\) −0.0923963 0.160035i −0.0140903 0.0244051i 0.858894 0.512153i \(-0.171152\pi\)
−0.872985 + 0.487748i \(0.837819\pi\)
\(44\) 17.1138 2.58000
\(45\) −2.02094 1.69577i −0.301265 0.252791i
\(46\) 8.00774 1.18068
\(47\) −0.511144 0.885328i −0.0745581 0.129138i 0.826336 0.563178i \(-0.190421\pi\)
−0.900894 + 0.434039i \(0.857088\pi\)
\(48\) 3.93242 10.8042i 0.567596 1.55946i
\(49\) 0 0
\(50\) 5.35117 9.26849i 0.756769 1.31076i
\(51\) −1.84002 2.19285i −0.257655 0.307061i
\(52\) −12.0287 20.8343i −1.66808 2.88920i
\(53\) 7.29086 1.00148 0.500738 0.865599i \(-0.333062\pi\)
0.500738 + 0.865599i \(0.333062\pi\)
\(54\) 11.3944 + 6.57856i 1.55058 + 0.895229i
\(55\) 3.41147 0.460003
\(56\) 0 0
\(57\) −2.68479 3.19961i −0.355609 0.423799i
\(58\) 7.65910 13.2660i 1.00569 1.74190i
\(59\) 3.33022 5.76811i 0.433558 0.750944i −0.563619 0.826035i \(-0.690591\pi\)
0.997177 + 0.0750906i \(0.0239246\pi\)
\(60\) 2.29813 6.31407i 0.296688 0.815143i
\(61\) −1.29813 2.24843i −0.166209 0.287882i 0.770875 0.636986i \(-0.219819\pi\)
−0.937084 + 0.349104i \(0.886486\pi\)
\(62\) 11.5321 1.46458
\(63\) 0 0
\(64\) −1.63816 −0.204769
\(65\) −2.39780 4.15312i −0.297411 0.515131i
\(66\) −16.7554 + 2.95442i −2.06244 + 0.363664i
\(67\) 1.47906 2.56180i 0.180695 0.312974i −0.761422 0.648256i \(-0.775499\pi\)
0.942118 + 0.335283i \(0.108832\pi\)
\(68\) 3.64543 6.31407i 0.442073 0.765693i
\(69\) −5.39440 + 0.951178i −0.649409 + 0.114508i
\(70\) 0 0
\(71\) −3.68004 −0.436741 −0.218370 0.975866i \(-0.570074\pi\)
−0.218370 + 0.975866i \(0.570074\pi\)
\(72\) −3.18092 + 18.0399i −0.374875 + 2.12602i
\(73\) 12.7811 1.49591 0.747955 0.663750i \(-0.231036\pi\)
0.747955 + 0.663750i \(0.231036\pi\)
\(74\) 5.76604 + 9.98708i 0.670289 + 1.16097i
\(75\) −2.50387 + 6.87933i −0.289122 + 0.794356i
\(76\) 5.31908 9.21291i 0.610140 1.05679i
\(77\) 0 0
\(78\) 15.3735 + 18.3214i 1.74070 + 2.07449i
\(79\) 2.97906 + 5.15988i 0.335170 + 0.580531i 0.983517 0.180813i \(-0.0578729\pi\)
−0.648348 + 0.761345i \(0.724540\pi\)
\(80\) 5.83750 0.652652
\(81\) −8.45723 3.07818i −0.939693 0.342020i
\(82\) 3.00000 0.331295
\(83\) −0.109470 0.189608i −0.0120159 0.0208122i 0.859955 0.510370i \(-0.170492\pi\)
−0.871971 + 0.489558i \(0.837158\pi\)
\(84\) 0 0
\(85\) 0.726682 1.25865i 0.0788197 0.136520i
\(86\) −0.233956 + 0.405223i −0.0252281 + 0.0436963i
\(87\) −3.58378 + 9.84635i −0.384221 + 1.05564i
\(88\) −11.8439 20.5142i −1.26256 2.18682i
\(89\) −11.0273 −1.16890 −0.584448 0.811431i \(-0.698689\pi\)
−0.584448 + 0.811431i \(0.698689\pi\)
\(90\) −1.15998 + 6.57856i −0.122272 + 0.693441i
\(91\) 0 0
\(92\) −6.97565 12.0822i −0.727262 1.25965i
\(93\) −7.76857 + 1.36981i −0.805563 + 0.142043i
\(94\) −1.29426 + 2.24173i −0.133493 + 0.231217i
\(95\) 1.06031 1.83651i 0.108785 0.188422i
\(96\) −7.84002 + 1.38241i −0.800169 + 0.141091i
\(97\) 6.25150 + 10.8279i 0.634743 + 1.09941i 0.986569 + 0.163342i \(0.0522275\pi\)
−0.351826 + 0.936065i \(0.614439\pi\)
\(98\) 0 0
\(99\) 10.9363 3.98048i 1.09914 0.400054i
\(100\) −18.6459 −1.86459
\(101\) −4.85844 8.41507i −0.483433 0.837330i 0.516386 0.856356i \(-0.327277\pi\)
−0.999819 + 0.0190255i \(0.993944\pi\)
\(102\) −2.47906 + 6.81115i −0.245463 + 0.674404i
\(103\) 3.29813 5.71253i 0.324975 0.562873i −0.656533 0.754298i \(-0.727978\pi\)
0.981507 + 0.191425i \(0.0613109\pi\)
\(104\) −16.6493 + 28.8374i −1.63260 + 2.82774i
\(105\) 0 0
\(106\) −9.23055 15.9878i −0.896550 1.55287i
\(107\) 2.38919 0.230971 0.115486 0.993309i \(-0.463158\pi\)
0.115486 + 0.993309i \(0.463158\pi\)
\(108\) 22.9227i 2.20574i
\(109\) 3.95811 0.379118 0.189559 0.981869i \(-0.439294\pi\)
0.189559 + 0.981869i \(0.439294\pi\)
\(110\) −4.31908 7.48086i −0.411808 0.713272i
\(111\) −5.07057 6.04288i −0.481278 0.573564i
\(112\) 0 0
\(113\) −8.22668 + 14.2490i −0.773901 + 1.34044i 0.161509 + 0.986871i \(0.448364\pi\)
−0.935410 + 0.353565i \(0.884969\pi\)
\(114\) −3.61721 + 9.93821i −0.338783 + 0.930798i
\(115\) −1.39053 2.40847i −0.129668 0.224591i
\(116\) −26.6878 −2.47790
\(117\) −12.5326 10.5161i −1.15864 0.972210i
\(118\) −16.8648 −1.55253
\(119\) 0 0
\(120\) −9.15910 + 1.61500i −0.836108 + 0.147428i
\(121\) −2.02481 + 3.50708i −0.184074 + 0.318826i
\(122\) −3.28699 + 5.69323i −0.297590 + 0.515441i
\(123\) −2.02094 + 0.356347i −0.182222 + 0.0321307i
\(124\) −10.0458 17.3998i −0.902136 1.56255i
\(125\) −8.11381 −0.725721
\(126\) 0 0
\(127\) 17.6536 1.56651 0.783253 0.621702i \(-0.213559\pi\)
0.783253 + 0.621702i \(0.213559\pi\)
\(128\) 6.67024 + 11.5532i 0.589572 + 1.02117i
\(129\) 0.109470 0.300767i 0.00963833 0.0264811i
\(130\) −6.07145 + 10.5161i −0.532502 + 0.922320i
\(131\) −9.59879 + 16.6256i −0.838650 + 1.45259i 0.0523729 + 0.998628i \(0.483322\pi\)
−0.891023 + 0.453958i \(0.850012\pi\)
\(132\) 19.0535 + 22.7071i 1.65839 + 1.97640i
\(133\) 0 0
\(134\) −7.49020 −0.647055
\(135\) 4.56942i 0.393273i
\(136\) −10.0915 −0.865341
\(137\) −9.07785 15.7233i −0.775573 1.34333i −0.934472 0.356037i \(-0.884128\pi\)
0.158899 0.987295i \(-0.449206\pi\)
\(138\) 8.91534 + 10.6249i 0.758925 + 0.904451i
\(139\) 11.0287 19.1022i 0.935441 1.62023i 0.161595 0.986857i \(-0.448336\pi\)
0.773846 0.633374i \(-0.218330\pi\)
\(140\) 0 0
\(141\) 0.605600 1.66387i 0.0510007 0.140123i
\(142\) 4.65910 + 8.06980i 0.390983 + 0.677202i
\(143\) 21.1557 1.76913
\(144\) 18.7135 6.81115i 1.55946 0.567596i
\(145\) −5.31996 −0.441798
\(146\) −16.1814 28.0270i −1.33918 2.31953i
\(147\) 0 0
\(148\) 10.0458 17.3998i 0.825756 1.43025i
\(149\) 7.57785 13.1252i 0.620802 1.07526i −0.368535 0.929614i \(-0.620141\pi\)
0.989337 0.145646i \(-0.0465261\pi\)
\(150\) 18.2554 3.21891i 1.49054 0.262823i
\(151\) 9.47818 + 16.4167i 0.771323 + 1.33597i 0.936838 + 0.349764i \(0.113738\pi\)
−0.165515 + 0.986207i \(0.552929\pi\)
\(152\) −14.7246 −1.19432
\(153\) 0.860967 4.88279i 0.0696051 0.394750i
\(154\) 0 0
\(155\) −2.00253 3.46848i −0.160847 0.278595i
\(156\) 14.2515 39.1557i 1.14103 3.13496i
\(157\) −9.02869 + 15.6381i −0.720568 + 1.24806i 0.240205 + 0.970722i \(0.422785\pi\)
−0.960773 + 0.277337i \(0.910548\pi\)
\(158\) 7.54323 13.0653i 0.600107 1.03942i
\(159\) 8.11721 + 9.67372i 0.643737 + 0.767176i
\(160\) −2.02094 3.50038i −0.159770 0.276729i
\(161\) 0 0
\(162\) 3.95723 + 22.4426i 0.310910 + 1.76326i
\(163\) 0.958111 0.0750450 0.0375225 0.999296i \(-0.488053\pi\)
0.0375225 + 0.999296i \(0.488053\pi\)
\(164\) −2.61334 4.52644i −0.204068 0.353456i
\(165\) 3.79813 + 4.52644i 0.295684 + 0.352383i
\(166\) −0.277189 + 0.480105i −0.0215140 + 0.0372634i
\(167\) 9.91921 17.1806i 0.767572 1.32947i −0.171304 0.985218i \(-0.554798\pi\)
0.938876 0.344255i \(-0.111869\pi\)
\(168\) 0 0
\(169\) −8.36959 14.4965i −0.643814 1.11512i
\(170\) −3.68004 −0.282247
\(171\) 1.25624 7.12452i 0.0960674 0.544825i
\(172\) 0.815207 0.0621590
\(173\) 11.3414 + 19.6438i 0.862268 + 1.49349i 0.869734 + 0.493520i \(0.164290\pi\)
−0.00746626 + 0.999972i \(0.502377\pi\)
\(174\) 26.1288 4.60722i 1.98082 0.349272i
\(175\) 0 0
\(176\) −12.8760 + 22.3019i −0.970564 + 1.68107i
\(177\) 11.3610 2.00324i 0.853943 0.150573i
\(178\) 13.9611 + 24.1813i 1.04643 + 1.81247i
\(179\) −7.34730 −0.549163 −0.274581 0.961564i \(-0.588539\pi\)
−0.274581 + 0.961564i \(0.588539\pi\)
\(180\) 10.9363 3.98048i 0.815143 0.296688i
\(181\) 3.44562 0.256111 0.128056 0.991767i \(-0.459126\pi\)
0.128056 + 0.991767i \(0.459126\pi\)
\(182\) 0 0
\(183\) 1.53802 4.22567i 0.113694 0.312371i
\(184\) −9.65523 + 16.7233i −0.711793 + 1.23286i
\(185\) 2.00253 3.46848i 0.147229 0.255008i
\(186\) 12.8391 + 15.3011i 0.941412 + 1.12193i
\(187\) 3.20574 + 5.55250i 0.234427 + 0.406039i
\(188\) 4.50980 0.328911
\(189\) 0 0
\(190\) −5.36959 −0.389551
\(191\) −2.82888 4.89976i −0.204690 0.354534i 0.745344 0.666680i \(-0.232285\pi\)
−0.950034 + 0.312146i \(0.898952\pi\)
\(192\) −1.82383 2.17355i −0.131623 0.156863i
\(193\) −4.79813 + 8.31061i −0.345377 + 0.598211i −0.985422 0.170127i \(-0.945582\pi\)
0.640045 + 0.768337i \(0.278916\pi\)
\(194\) 15.8293 27.4172i 1.13648 1.96844i
\(195\) 2.84090 7.80531i 0.203441 0.558950i
\(196\) 0 0
\(197\) 8.31996 0.592772 0.296386 0.955068i \(-0.404218\pi\)
0.296386 + 0.955068i \(0.404218\pi\)
\(198\) −22.5744 18.9422i −1.60430 1.34616i
\(199\) −6.59627 −0.467597 −0.233798 0.972285i \(-0.575116\pi\)
−0.233798 + 0.972285i \(0.575116\pi\)
\(200\) 12.9042 + 22.3507i 0.912465 + 1.58044i
\(201\) 5.04576 0.889704i 0.355900 0.0627548i
\(202\) −12.3020 + 21.3077i −0.865566 + 1.49920i
\(203\) 0 0
\(204\) 12.4363 2.19285i 0.870714 0.153530i
\(205\) −0.520945 0.902302i −0.0363843 0.0630195i
\(206\) −16.7023 −1.16371
\(207\) −7.26786 6.09845i −0.505151 0.423872i
\(208\) 36.2003 2.51004
\(209\) 4.67752 + 8.10170i 0.323551 + 0.560406i
\(210\) 0 0
\(211\) 1.68479 2.91815i 0.115986 0.200893i −0.802188 0.597072i \(-0.796331\pi\)
0.918173 + 0.396179i \(0.129664\pi\)
\(212\) −16.0817 + 27.8544i −1.10450 + 1.91304i
\(213\) −4.09714 4.88279i −0.280732 0.334563i
\(214\) −3.02481 5.23913i −0.206772 0.358140i
\(215\) 0.162504 0.0110827
\(216\) −27.4773 + 15.8640i −1.86959 + 1.07941i
\(217\) 0 0
\(218\) −5.01114 8.67956i −0.339398 0.587854i
\(219\) 14.2297 + 16.9583i 0.961552 + 1.14593i
\(220\) −7.52481 + 13.0334i −0.507323 + 0.878709i
\(221\) 4.50640 7.80531i 0.303133 0.525042i
\(222\) −6.83157 + 18.7696i −0.458505 + 1.25973i
\(223\) −3.13816 5.43545i −0.210146 0.363984i 0.741614 0.670827i \(-0.234061\pi\)
−0.951760 + 0.306843i \(0.900727\pi\)
\(224\) 0 0
\(225\) −11.9153 + 4.33683i −0.794356 + 0.289122i
\(226\) 41.6614 2.77127
\(227\) −3.08125 5.33688i −0.204510 0.354221i 0.745467 0.666543i \(-0.232227\pi\)
−0.949976 + 0.312322i \(0.898893\pi\)
\(228\) 18.1459 3.19961i 1.20174 0.211899i
\(229\) 11.6925 20.2521i 0.772664 1.33829i −0.163434 0.986554i \(-0.552257\pi\)
0.936098 0.351740i \(-0.114410\pi\)
\(230\) −3.52094 + 6.09845i −0.232164 + 0.402120i
\(231\) 0 0
\(232\) 18.4697 + 31.9905i 1.21260 + 2.10028i
\(233\) −8.52528 −0.558510 −0.279255 0.960217i \(-0.590087\pi\)
−0.279255 + 0.960217i \(0.590087\pi\)
\(234\) −7.19341 + 40.7959i −0.470248 + 2.66691i
\(235\) 0.898986 0.0586434
\(236\) 14.6912 + 25.4459i 0.956315 + 1.65639i
\(237\) −3.52956 + 9.69739i −0.229270 + 0.629913i
\(238\) 0 0
\(239\) −7.28106 + 12.6112i −0.470973 + 0.815748i −0.999449 0.0331997i \(-0.989430\pi\)
0.528476 + 0.848948i \(0.322764\pi\)
\(240\) 6.49912 + 7.74535i 0.419517 + 0.499960i
\(241\) −2.70187 4.67977i −0.174043 0.301451i 0.765787 0.643094i \(-0.222350\pi\)
−0.939830 + 0.341644i \(0.889016\pi\)
\(242\) 10.2540 0.659154
\(243\) −5.33157 14.6484i −0.342020 0.939693i
\(244\) 11.4534 0.733226
\(245\) 0 0
\(246\) 3.34002 + 3.98048i 0.212952 + 0.253786i
\(247\) 6.57532 11.3888i 0.418378 0.724651i
\(248\) −13.9047 + 24.0836i −0.882947 + 1.52931i
\(249\) 0.129700 0.356347i 0.00821939 0.0225826i
\(250\) 10.2724 + 17.7924i 0.649686 + 1.12529i
\(251\) 12.0669 0.761654 0.380827 0.924646i \(-0.375639\pi\)
0.380827 + 0.924646i \(0.375639\pi\)
\(252\) 0 0
\(253\) 12.2686 0.771318
\(254\) −22.3503 38.7118i −1.40238 2.42900i
\(255\) 2.47906 0.437124i 0.155244 0.0273738i
\(256\) 15.2515 26.4164i 0.953219 1.65102i
\(257\) 5.28312 9.15063i 0.329552 0.570801i −0.652871 0.757469i \(-0.726436\pi\)
0.982423 + 0.186668i \(0.0597690\pi\)
\(258\) −0.798133 + 0.140732i −0.0496896 + 0.00876162i
\(259\) 0 0
\(260\) 21.1557 1.31202
\(261\) −17.0544 + 6.20729i −1.05564 + 0.384221i
\(262\) 48.6100 3.00314
\(263\) 14.1766 + 24.5547i 0.874169 + 1.51411i 0.857645 + 0.514242i \(0.171927\pi\)
0.0165240 + 0.999863i \(0.494740\pi\)
\(264\) 14.0326 38.5541i 0.863644 2.37284i
\(265\) −3.20574 + 5.55250i −0.196927 + 0.341087i
\(266\) 0 0
\(267\) −12.2772 14.6314i −0.751352 0.895426i
\(268\) 6.52481 + 11.3013i 0.398567 + 0.690337i
\(269\) −7.48339 −0.456271 −0.228135 0.973629i \(-0.573263\pi\)
−0.228135 + 0.973629i \(0.573263\pi\)
\(270\) −10.0201 + 5.78509i −0.609802 + 0.352069i
\(271\) −13.6382 −0.828459 −0.414229 0.910172i \(-0.635949\pi\)
−0.414229 + 0.910172i \(0.635949\pi\)
\(272\) 5.48545 + 9.50108i 0.332604 + 0.576088i
\(273\) 0 0
\(274\) −22.9859 + 39.8128i −1.38863 + 2.40518i
\(275\) 8.19846 14.2002i 0.494386 0.856302i
\(276\) 8.26470 22.7071i 0.497476 1.36681i
\(277\) 3.07532 + 5.32661i 0.184778 + 0.320045i 0.943502 0.331368i \(-0.107510\pi\)
−0.758724 + 0.651413i \(0.774177\pi\)
\(278\) −55.8512 −3.34973
\(279\) −10.4666 8.78249i −0.626617 0.525794i
\(280\) 0 0
\(281\) −1.65611 2.86846i −0.0987951 0.171118i 0.812391 0.583113i \(-0.198165\pi\)
−0.911186 + 0.411995i \(0.864832\pi\)
\(282\) −4.41534 + 0.778544i −0.262930 + 0.0463616i
\(283\) 14.5116 25.1348i 0.862626 1.49411i −0.00675974 0.999977i \(-0.502152\pi\)
0.869385 0.494134i \(-0.164515\pi\)
\(284\) 8.11721 14.0594i 0.481668 0.834273i
\(285\) 3.61721 0.637812i 0.214265 0.0377807i
\(286\) −26.7841 46.3913i −1.58377 2.74318i
\(287\) 0 0
\(288\) −10.5628 8.86327i −0.622421 0.522273i
\(289\) −14.2686 −0.839328
\(290\) 6.73530 + 11.6659i 0.395510 + 0.685044i
\(291\) −7.40673 + 20.3498i −0.434190 + 1.19293i
\(292\) −28.1917 + 48.8294i −1.64979 + 2.85752i
\(293\) −4.20961 + 7.29125i −0.245928 + 0.425960i −0.962392 0.271664i \(-0.912426\pi\)
0.716464 + 0.697624i \(0.245759\pi\)
\(294\) 0 0
\(295\) 2.92855 + 5.07239i 0.170507 + 0.295326i
\(296\) −27.8093 −1.61638
\(297\) 17.4572 + 10.0789i 1.01297 + 0.584839i
\(298\) −38.3756 −2.22304
\(299\) −8.62314 14.9357i −0.498689 0.863755i
\(300\) −20.7592 24.7399i −1.19854 1.42836i
\(301\) 0 0
\(302\) 23.9996 41.5685i 1.38102 2.39200i
\(303\) 5.75624 15.8152i 0.330688 0.908557i
\(304\) 8.00387 + 13.8631i 0.459053 + 0.795104i
\(305\) 2.28312 0.130731
\(306\) −11.7973 + 4.29385i −0.674404 + 0.245463i
\(307\) 12.6878 0.724130 0.362065 0.932153i \(-0.382072\pi\)
0.362065 + 0.932153i \(0.382072\pi\)
\(308\) 0 0
\(309\) 11.2515 1.98394i 0.640075 0.112863i
\(310\) −5.07057 + 8.78249i −0.287989 + 0.498812i
\(311\) −8.24510 + 14.2809i −0.467537 + 0.809797i −0.999312 0.0370881i \(-0.988192\pi\)
0.531775 + 0.846886i \(0.321525\pi\)
\(312\) −56.7987 + 10.0151i −3.21559 + 0.566995i
\(313\) 14.2592 + 24.6977i 0.805980 + 1.39600i 0.915628 + 0.402027i \(0.131694\pi\)
−0.109648 + 0.993970i \(0.534972\pi\)
\(314\) 45.7229 2.58029
\(315\) 0 0
\(316\) −26.2841 −1.47859
\(317\) 12.9474 + 22.4256i 0.727200 + 1.25955i 0.958062 + 0.286561i \(0.0925122\pi\)
−0.230862 + 0.972987i \(0.574154\pi\)
\(318\) 10.9363 30.0472i 0.613277 1.68496i
\(319\) 11.7344 20.3246i 0.657002 1.13796i
\(320\) 0.720285 1.24757i 0.0402652 0.0697413i
\(321\) 2.65998 + 3.17004i 0.148465 + 0.176934i
\(322\) 0 0
\(323\) 3.98545 0.221756
\(324\) 30.4145 25.5208i 1.68969 1.41782i
\(325\) −23.0496 −1.27856
\(326\) −1.21301 2.10100i −0.0671825 0.116363i
\(327\) 4.40673 + 5.25173i 0.243693 + 0.290421i
\(328\) −3.61721 + 6.26519i −0.199727 + 0.345937i
\(329\) 0 0
\(330\) 5.11721 14.0594i 0.281693 0.773946i
\(331\) −4.10947 7.11781i −0.225877 0.391230i 0.730705 0.682693i \(-0.239191\pi\)
−0.956582 + 0.291463i \(0.905858\pi\)
\(332\) 0.965852 0.0530080
\(333\) 2.37258 13.4556i 0.130016 0.737360i
\(334\) −50.2327 −2.74861
\(335\) 1.30066 + 2.25281i 0.0710626 + 0.123084i
\(336\) 0 0
\(337\) −2.28564 + 3.95885i −0.124507 + 0.215652i −0.921540 0.388283i \(-0.873068\pi\)
0.797033 + 0.603936i \(0.206402\pi\)
\(338\) −21.1925 + 36.7065i −1.15272 + 1.99657i
\(339\) −28.0651 + 4.94864i −1.52429 + 0.268773i
\(340\) 3.20574 + 5.55250i 0.173856 + 0.301127i
\(341\) 17.6682 0.956786
\(342\) −17.2135 + 6.26519i −0.930798 + 0.338783i
\(343\) 0 0
\(344\) −0.564178 0.977185i −0.0304184 0.0526863i
\(345\) 1.64749 4.52644i 0.0886978 0.243695i
\(346\) 28.7173 49.7399i 1.54385 2.67403i
\(347\) −11.2331 + 19.4563i −0.603023 + 1.04447i 0.389337 + 0.921095i \(0.372704\pi\)
−0.992361 + 0.123372i \(0.960629\pi\)
\(348\) −29.7126 35.4101i −1.59276 1.89818i
\(349\) 13.0496 + 22.6026i 0.698531 + 1.20989i 0.968976 + 0.247155i \(0.0794958\pi\)
−0.270445 + 0.962735i \(0.587171\pi\)
\(350\) 0 0
\(351\) 28.3365i 1.51249i
\(352\) 17.8307 0.950379
\(353\) −0.177519 0.307471i −0.00944836 0.0163650i 0.861263 0.508160i \(-0.169674\pi\)
−0.870711 + 0.491795i \(0.836341\pi\)
\(354\) −18.7763 22.3767i −0.997950 1.18931i
\(355\) 1.61809 2.80261i 0.0858792 0.148747i
\(356\) 24.3234 42.1294i 1.28914 2.23285i
\(357\) 0 0
\(358\) 9.30200 + 16.1115i 0.491626 + 0.851522i
\(359\) 5.45605 0.287959 0.143980 0.989581i \(-0.454010\pi\)
0.143980 + 0.989581i \(0.454010\pi\)
\(360\) −12.3400 10.3545i −0.650376 0.545731i
\(361\) −13.1848 −0.693936
\(362\) −4.36231 7.55574i −0.229278 0.397121i
\(363\) −6.90760 + 1.21800i −0.362555 + 0.0639283i
\(364\) 0 0
\(365\) −5.61974 + 9.73367i −0.294150 + 0.509484i
\(366\) −11.2135 + 1.97724i −0.586138 + 0.103352i
\(367\) 5.46198 + 9.46043i 0.285113 + 0.493830i 0.972637 0.232332i \(-0.0746355\pi\)
−0.687523 + 0.726162i \(0.741302\pi\)
\(368\) 20.9932 1.09435
\(369\) −2.72281 2.28471i −0.141744 0.118937i
\(370\) −10.1411 −0.527213
\(371\) 0 0
\(372\) 11.9021 32.7009i 0.617097 1.69546i
\(373\) −0.865715 + 1.49946i −0.0448250 + 0.0776392i −0.887567 0.460678i \(-0.847606\pi\)
0.842742 + 0.538317i \(0.180940\pi\)
\(374\) 8.11721 14.0594i 0.419731 0.726995i
\(375\) −9.03343 10.7656i −0.466484 0.555935i
\(376\) −3.12108 5.40587i −0.160957 0.278787i
\(377\) −32.9908 −1.69911
\(378\) 0 0
\(379\) −12.1334 −0.623251 −0.311626 0.950205i \(-0.600873\pi\)
−0.311626 + 0.950205i \(0.600873\pi\)
\(380\) 4.67752 + 8.10170i 0.239952 + 0.415608i
\(381\) 19.6545 + 23.4233i 1.00693 + 1.20001i
\(382\) −7.16297 + 12.4066i −0.366489 + 0.634778i
\(383\) −4.35591 + 7.54467i −0.222577 + 0.385514i −0.955590 0.294700i \(-0.904780\pi\)
0.733013 + 0.680215i \(0.238113\pi\)
\(384\) −7.90286 + 21.7129i −0.403291 + 1.10803i
\(385\) 0 0
\(386\) 24.2986 1.23677
\(387\) 0.520945 0.189608i 0.0264811 0.00963833i
\(388\) −55.1566 −2.80015
\(389\) −1.82160 3.15511i −0.0923590 0.159970i 0.816144 0.577848i \(-0.196107\pi\)
−0.908503 + 0.417878i \(0.862774\pi\)
\(390\) −20.7126 + 3.65219i −1.04882 + 0.184936i
\(391\) 2.61334 4.52644i 0.132162 0.228912i
\(392\) 0 0
\(393\) −32.7460 + 5.77401i −1.65182 + 0.291260i
\(394\) −10.5334 18.2444i −0.530667 0.919142i
\(395\) −5.23947 −0.263627
\(396\) −8.91534 + 50.5614i −0.448013 + 2.54081i
\(397\) 15.4456 0.775194 0.387597 0.921829i \(-0.373305\pi\)
0.387597 + 0.921829i \(0.373305\pi\)
\(398\) 8.35117 + 14.4646i 0.418606 + 0.725047i
\(399\) 0 0
\(400\) 14.0287 24.2984i 0.701434 1.21492i
\(401\) −9.21095 + 15.9538i −0.459973 + 0.796697i −0.998959 0.0456182i \(-0.985474\pi\)
0.538986 + 0.842315i \(0.318808\pi\)
\(402\) −8.33915 9.93821i −0.415919 0.495673i
\(403\) −12.4183 21.5092i −0.618601 1.07145i
\(404\) 42.8658 2.13265
\(405\) 6.06283 5.08732i 0.301265 0.252791i
\(406\) 0 0
\(407\) 8.83409 + 15.3011i 0.437890 + 0.758447i
\(408\) −11.2353 13.3897i −0.556230 0.662889i
\(409\) −14.3182 + 24.7999i −0.707989 + 1.22627i 0.257612 + 0.966248i \(0.417064\pi\)
−0.965602 + 0.260025i \(0.916269\pi\)
\(410\) −1.31908 + 2.28471i −0.0651446 + 0.112834i
\(411\) 10.7554 29.5501i 0.530523 1.45760i
\(412\) 14.5496 + 25.2007i 0.716809 + 1.24155i
\(413\) 0 0
\(414\) −4.17159 + 23.6583i −0.205022 + 1.16274i
\(415\) 0.192533 0.00945109
\(416\) −12.5326 21.7070i −0.614459 1.06427i
\(417\) 37.6241 6.63414i 1.84246 0.324875i
\(418\) 11.8439 20.5142i 0.579304 1.00338i
\(419\) −17.3478 + 30.0472i −0.847494 + 1.46790i 0.0359442 + 0.999354i \(0.488556\pi\)
−0.883438 + 0.468548i \(0.844777\pi\)
\(420\) 0 0
\(421\) 13.7010 + 23.7308i 0.667745 + 1.15657i 0.978533 + 0.206090i \(0.0660738\pi\)
−0.310788 + 0.950479i \(0.600593\pi\)
\(422\) −8.53209 −0.415336
\(423\) 2.88191 1.04893i 0.140123 0.0510007i
\(424\) 44.5185 2.16201
\(425\) −3.49273 6.04958i −0.169422 0.293448i
\(426\) −5.52007 + 15.1663i −0.267448 + 0.734808i
\(427\) 0 0
\(428\) −5.26991 + 9.12776i −0.254731 + 0.441207i
\(429\) 23.5535 + 28.0700i 1.13717 + 1.35523i
\(430\) −0.205737 0.356347i −0.00992152 0.0171846i
\(431\) 26.5921 1.28090 0.640449 0.768000i \(-0.278748\pi\)
0.640449 + 0.768000i \(0.278748\pi\)
\(432\) 29.8717 + 17.2464i 1.43720 + 0.829769i
\(433\) −37.1830 −1.78690 −0.893451 0.449160i \(-0.851723\pi\)
−0.893451 + 0.449160i \(0.851723\pi\)
\(434\) 0 0
\(435\) −5.92292 7.05866i −0.283982 0.338437i
\(436\) −8.73055 + 15.1218i −0.418118 + 0.724201i
\(437\) 3.81315 6.60457i 0.182408 0.315939i
\(438\) 19.1716 52.6735i 0.916054 2.51684i
\(439\) 12.5373 + 21.7152i 0.598373 + 1.03641i 0.993061 + 0.117597i \(0.0375192\pi\)
−0.394689 + 0.918815i \(0.629147\pi\)
\(440\) 20.8307 0.993064
\(441\) 0 0
\(442\) −22.8212 −1.08549
\(443\) −1.02229 1.77066i −0.0485704 0.0841264i 0.840718 0.541473i \(-0.182133\pi\)
−0.889288 + 0.457347i \(0.848800\pi\)
\(444\) 34.2708 6.04288i 1.62642 0.286782i
\(445\) 4.84864 8.39809i 0.229848 0.398108i
\(446\) −7.94609 + 13.7630i −0.376258 + 0.651698i
\(447\) 25.8516 4.55834i 1.22274 0.215602i
\(448\) 0 0
\(449\) −10.2344 −0.482992 −0.241496 0.970402i \(-0.577638\pi\)
−0.241496 + 0.970402i \(0.577638\pi\)
\(450\) 24.5954 + 20.6380i 1.15944 + 0.972884i
\(451\) 4.59627 0.216430
\(452\) −36.2918 62.8592i −1.70702 2.95665i
\(453\) −11.2297 + 30.8533i −0.527616 + 1.44961i
\(454\) −7.80200 + 13.5135i −0.366166 + 0.634218i
\(455\) 0 0
\(456\) −16.3935 19.5370i −0.767697 0.914906i
\(457\) 21.2973 + 36.8879i 0.996244 + 1.72554i 0.573115 + 0.819475i \(0.305735\pi\)
0.423129 + 0.906070i \(0.360932\pi\)
\(458\) −59.2131 −2.76684
\(459\) 7.43717 4.29385i 0.347137 0.200420i
\(460\) 12.2686 0.572025
\(461\) 0.252374 + 0.437124i 0.0117542 + 0.0203589i 0.871843 0.489786i \(-0.162925\pi\)
−0.860088 + 0.510145i \(0.829592\pi\)
\(462\) 0 0
\(463\) −1.34002 + 2.32099i −0.0622761 + 0.107865i −0.895482 0.445097i \(-0.853169\pi\)
0.833206 + 0.552962i \(0.186503\pi\)
\(464\) 20.0792 34.7782i 0.932153 1.61454i
\(465\) 2.37258 6.51860i 0.110026 0.302293i
\(466\) 10.7934 + 18.6947i 0.499994 + 0.866015i
\(467\) 31.4165 1.45378 0.726892 0.686752i \(-0.240964\pi\)
0.726892 + 0.686752i \(0.240964\pi\)
\(468\) 67.8196 24.6843i 3.13496 1.14103i
\(469\) 0 0
\(470\) −1.13816 1.97134i −0.0524992 0.0909313i
\(471\) −30.8011 + 5.43107i −1.41924 + 0.250250i
\(472\) 20.3346 35.2205i 0.935974 1.62115i
\(473\) −0.358441 + 0.620838i −0.0164811 + 0.0285461i
\(474\) 25.7335 4.53752i 1.18198 0.208415i
\(475\) −5.09627 8.82699i −0.233833 0.405010i
\(476\) 0 0
\(477\) −3.79813 + 21.5403i −0.173905 + 0.986262i
\(478\) 36.8726 1.68651
\(479\) −8.22028 14.2380i −0.375594 0.650549i 0.614821 0.788666i \(-0.289228\pi\)
−0.990416 + 0.138118i \(0.955895\pi\)
\(480\) 2.39440 6.57856i 0.109289 0.300269i
\(481\) 12.4183 21.5092i 0.566227 0.980735i
\(482\) −6.84137 + 11.8496i −0.311616 + 0.539734i
\(483\) 0 0
\(484\) −8.93242 15.4714i −0.406019 0.703246i
\(485\) −10.9949 −0.499255
\(486\) −25.3717 + 30.2368i −1.15088 + 1.37157i
\(487\) −2.97535 −0.134826 −0.0674129 0.997725i \(-0.521474\pi\)
−0.0674129 + 0.997725i \(0.521474\pi\)
\(488\) −7.92649 13.7291i −0.358815 0.621486i
\(489\) 1.06670 + 1.27125i 0.0482380 + 0.0574878i
\(490\) 0 0
\(491\) 13.2430 22.9376i 0.597650 1.03516i −0.395517 0.918459i \(-0.629435\pi\)
0.993167 0.116702i \(-0.0372321\pi\)
\(492\) 3.09627 8.50692i 0.139590 0.383522i
\(493\) −4.99912 8.65873i −0.225149 0.389970i
\(494\) −33.2986 −1.49817
\(495\) −1.77719 + 10.0789i −0.0798787 + 0.453015i
\(496\) 30.2327 1.35749
\(497\) 0 0
\(498\) −0.945622 + 0.166739i −0.0423744 + 0.00747174i
\(499\) 6.72193 11.6427i 0.300915 0.521200i −0.675428 0.737426i \(-0.736041\pi\)
0.976343 + 0.216225i \(0.0693746\pi\)
\(500\) 17.8969 30.9984i 0.800375 1.38629i
\(501\) 33.8391 5.96675i 1.51182 0.266575i
\(502\) −15.2772 26.4609i −0.681854 1.18101i
\(503\) 22.6631 1.01050 0.505250 0.862973i \(-0.331400\pi\)
0.505250 + 0.862973i \(0.331400\pi\)
\(504\) 0 0
\(505\) 8.54488 0.380242
\(506\) −15.5326 26.9032i −0.690506 1.19599i
\(507\) 9.91622 27.2446i 0.440395 1.20997i
\(508\) −38.9393 + 67.4448i −1.72765 + 2.99238i
\(509\) 4.77379 8.26844i 0.211594 0.366492i −0.740619 0.671925i \(-0.765468\pi\)
0.952214 + 0.305433i \(0.0988011\pi\)
\(510\) −4.09714 4.88279i −0.181425 0.216213i
\(511\) 0 0
\(512\) −50.5553 −2.23425
\(513\) 10.8516 6.26519i 0.479111 0.276615i
\(514\) −26.7547 −1.18010
\(515\) 2.90033 + 5.02352i 0.127804 + 0.221363i
\(516\) 0.907604 + 1.08164i 0.0399550 + 0.0476165i
\(517\) −1.98293 + 3.43453i −0.0872090 + 0.151050i
\(518\) 0 0
\(519\) −13.4372 + 36.9183i −0.589826 + 1.62053i
\(520\) −14.6411 25.3592i −0.642057 1.11208i
\(521\) 3.11287 0.136377 0.0681887 0.997672i \(-0.478278\pi\)
0.0681887 + 0.997672i \(0.478278\pi\)
\(522\) 35.2033 + 29.5390i 1.54081 + 1.29289i
\(523\) 16.1489 0.706142 0.353071 0.935597i \(-0.385137\pi\)
0.353071 + 0.935597i \(0.385137\pi\)
\(524\) −42.3448 73.3434i −1.84984 3.20402i
\(525\) 0 0
\(526\) 35.8965 62.1746i 1.56516 2.71094i
\(527\) 3.76352 6.51860i 0.163941 0.283955i
\(528\) −43.9261 + 7.74535i −1.91164 + 0.337073i
\(529\) 6.49928 + 11.2571i 0.282578 + 0.489439i
\(530\) 16.2344 0.705178
\(531\) 15.3066 + 12.8438i 0.664249 + 0.557371i
\(532\) 0 0
\(533\) −3.23055 5.59548i −0.139931 0.242367i
\(534\) −16.5410 + 45.4461i −0.715800 + 1.96664i
\(535\) −1.05051 + 1.81953i −0.0454174 + 0.0786652i
\(536\) 9.03121 15.6425i 0.390089 0.675654i
\(537\) −8.18004 9.74860i −0.352995 0.420683i
\(538\) 9.47431 + 16.4100i 0.408466 + 0.707485i
\(539\) 0 0
\(540\) 17.4572 + 10.0789i 0.751240 + 0.433728i
\(541\) −5.01548 −0.215632 −0.107816 0.994171i \(-0.534386\pi\)
−0.107816 + 0.994171i \(0.534386\pi\)
\(542\) 17.2665 + 29.9065i 0.741660 + 1.28459i
\(543\) 3.83615 + 4.57175i 0.164625 + 0.196192i
\(544\) 3.79813 6.57856i 0.162844 0.282053i
\(545\) −1.74035 + 3.01438i −0.0745485 + 0.129122i
\(546\) 0 0
\(547\) −8.23901 14.2704i −0.352275 0.610157i 0.634373 0.773027i \(-0.281258\pi\)
−0.986648 + 0.162870i \(0.947925\pi\)
\(548\) 80.0934 3.42142
\(549\) 7.31908 2.66393i 0.312371 0.113694i
\(550\) −41.5185 −1.77035
\(551\) −7.29426 12.6340i −0.310746 0.538228i
\(552\) −32.9386 + 5.80796i −1.40196 + 0.247203i
\(553\) 0 0
\(554\) 7.78699 13.4875i 0.330837 0.573027i
\(555\) 6.83157 1.20459i 0.289984 0.0511320i
\(556\) 48.6528 + 84.2691i 2.06334 + 3.57380i
\(557\) −34.5631 −1.46448 −0.732242 0.681045i \(-0.761526\pi\)
−0.732242 + 0.681045i \(0.761526\pi\)
\(558\) −6.00758 + 34.0707i −0.254321 + 1.44233i
\(559\) 1.00774 0.0426229
\(560\) 0 0
\(561\) −3.79813 + 10.4353i −0.160357 + 0.440578i
\(562\) −4.19341 + 7.26320i −0.176888 + 0.306380i
\(563\) −18.6052 + 32.2251i −0.784115 + 1.35813i 0.145411 + 0.989371i \(0.453550\pi\)
−0.929526 + 0.368756i \(0.879784\pi\)
\(564\) 5.02094 + 5.98373i 0.211420 + 0.251960i
\(565\) −7.23442 12.5304i −0.304354 0.527157i
\(566\) −73.4894 −3.08899
\(567\) 0 0
\(568\) −22.4706 −0.942845
\(569\) −0.202333 0.350452i −0.00848226 0.0146917i 0.861753 0.507328i \(-0.169367\pi\)
−0.870235 + 0.492636i \(0.836033\pi\)
\(570\) −5.97818 7.12452i −0.250398 0.298413i
\(571\) 18.8897 32.7178i 0.790507 1.36920i −0.135146 0.990826i \(-0.543150\pi\)
0.925653 0.378373i \(-0.123516\pi\)
\(572\) −46.6639 + 80.8243i −1.95112 + 3.37943i
\(573\) 3.35163 9.20854i 0.140017 0.384692i
\(574\) 0 0
\(575\) −13.3669 −0.557438
\(576\) 0.853388 4.83981i 0.0355578 0.201659i
\(577\) 2.21120 0.0920535 0.0460267 0.998940i \(-0.485344\pi\)
0.0460267 + 0.998940i \(0.485344\pi\)
\(578\) 18.0646 + 31.2889i 0.751390 + 1.30145i
\(579\) −16.3687 + 2.88624i −0.680260 + 0.119948i
\(580\) 11.7344 20.3246i 0.487245 0.843934i
\(581\) 0 0
\(582\) 54.0014 9.52190i 2.23843 0.394696i
\(583\) −14.1420 24.4947i −0.585703 1.01447i
\(584\) 78.0420 3.22940
\(585\) 13.5192 4.92058i 0.558950 0.203441i
\(586\) 21.3182 0.880647
\(587\) 12.1049 + 20.9663i 0.499622 + 0.865371i 1.00000 0.000436347i \(-0.000138894\pi\)
−0.500378 + 0.865807i \(0.666806\pi\)
\(588\) 0 0
\(589\) 5.49138 9.51135i 0.226268 0.391908i
\(590\) 7.41534 12.8438i 0.305285 0.528769i
\(591\) 9.26295 + 11.0391i 0.381027 + 0.454090i
\(592\) 15.1163 + 26.1823i 0.621277 + 1.07608i
\(593\) −12.2385 −0.502577 −0.251288 0.967912i \(-0.580854\pi\)
−0.251288 + 0.967912i \(0.580854\pi\)
\(594\) 51.0415i 2.09426i
\(595\) 0 0
\(596\) 33.4295 + 57.9016i 1.36932 + 2.37174i
\(597\) −7.34389 8.75211i −0.300566 0.358200i
\(598\) −21.8346 + 37.8186i −0.892882 + 1.54652i
\(599\) −19.8084 + 34.3092i −0.809349 + 1.40183i 0.103966 + 0.994581i \(0.466847\pi\)
−0.913315 + 0.407253i \(0.866487\pi\)
\(600\) −15.2888 + 42.0056i −0.624163 + 1.71487i
\(601\) −15.0039 25.9875i −0.612021 1.06005i −0.990899 0.134605i \(-0.957024\pi\)
0.378879 0.925446i \(-0.376310\pi\)
\(602\) 0 0
\(603\) 6.79813 + 5.70431i 0.276841 + 0.232298i
\(604\) −83.6255 −3.40267
\(605\) −1.78059 3.08408i −0.0723914 0.125386i
\(606\) −41.9680 + 7.40008i −1.70483 + 0.300608i
\(607\) −9.74216 + 16.8739i −0.395422 + 0.684891i −0.993155 0.116804i \(-0.962735\pi\)
0.597733 + 0.801695i \(0.296068\pi\)
\(608\) 5.54189 9.59883i 0.224753 0.389284i
\(609\) 0 0
\(610\) −2.89053 5.00654i −0.117034 0.202709i
\(611\) 5.57491 0.225537
\(612\) 16.7554 + 14.0594i 0.677296 + 0.568318i
\(613\) −18.5276 −0.748325 −0.374162 0.927363i \(-0.622070\pi\)
−0.374162 + 0.927363i \(0.622070\pi\)
\(614\) −16.0633 27.8225i −0.648262 1.12282i
\(615\) 0.617211 1.69577i 0.0248884 0.0683802i
\(616\) 0 0
\(617\) −13.9201 + 24.1103i −0.560402 + 0.970644i 0.437059 + 0.899433i \(0.356020\pi\)
−0.997461 + 0.0712118i \(0.977313\pi\)
\(618\) −18.5954 22.1611i −0.748016 0.891451i
\(619\) −22.4907 38.9550i −0.903976 1.56573i −0.822286 0.569075i \(-0.807301\pi\)
−0.0816906 0.996658i \(-0.526032\pi\)
\(620\) 17.6682 0.709571
\(621\) 16.4329i 0.659428i
\(622\) 41.7547 1.67421
\(623\) 0 0
\(624\) 40.3032 + 48.0315i 1.61342 + 1.92280i
\(625\) −6.99912 + 12.1228i −0.279965 + 0.484913i
\(626\) 36.1057 62.5368i 1.44307 2.49947i
\(627\) −5.54189 + 15.2262i −0.221322 + 0.608076i
\(628\) −39.8298 68.9873i −1.58938 2.75289i
\(629\) 7.52704 0.300123
\(630\) 0 0
\(631\) 9.43613 0.375646 0.187823 0.982203i \(-0.439857\pi\)
0.187823 + 0.982203i \(0.439857\pi\)
\(632\) 18.1903 + 31.5065i 0.723572 + 1.25326i
\(633\) 5.74763 1.01346i 0.228448 0.0402815i
\(634\) 32.7841 56.7836i 1.30202 2.25517i
\(635\) −7.76217 + 13.4445i −0.308032 + 0.533528i
\(636\) −54.8624 + 9.67372i −2.17543 + 0.383588i
\(637\) 0 0
\(638\) −59.4252 −2.35267
\(639\) 1.91710 10.8724i 0.0758393 0.430106i
\(640\) −11.7314 −0.463725
\(641\) −18.6951 32.3808i −0.738410 1.27896i −0.953211 0.302306i \(-0.902243\pi\)
0.214800 0.976658i \(-0.431090\pi\)
\(642\) 3.58378 9.84635i 0.141440 0.388604i
\(643\) 0.805874 1.39581i 0.0317806 0.0550456i −0.849698 0.527270i \(-0.823216\pi\)
0.881478 + 0.472225i \(0.156549\pi\)
\(644\) 0 0
\(645\) 0.180922 + 0.215615i 0.00712380 + 0.00848982i
\(646\) −5.04576 8.73951i −0.198523 0.343851i
\(647\) 41.1762 1.61880 0.809402 0.587255i \(-0.199791\pi\)
0.809402 + 0.587255i \(0.199791\pi\)
\(648\) −51.6404 18.7956i −2.02863 0.738360i
\(649\) −25.8384 −1.01425
\(650\) 29.1819 + 50.5445i 1.14461 + 1.98252i
\(651\) 0 0
\(652\) −2.11334 + 3.66041i −0.0827648 + 0.143353i
\(653\) −1.52600 + 2.64310i −0.0597169 + 0.103433i −0.894338 0.447391i \(-0.852353\pi\)
0.834621 + 0.550824i \(0.185686\pi\)
\(654\) 5.93717 16.3122i 0.232162 0.637859i
\(655\) −8.44104 14.6203i −0.329819 0.571263i
\(656\) 7.86484 0.307070
\(657\) −6.65822 + 37.7607i −0.259762 + 1.47318i
\(658\) 0 0
\(659\) −20.8175 36.0569i −0.810934 1.40458i −0.912211 0.409721i \(-0.865626\pi\)
0.101277 0.994858i \(-0.467707\pi\)
\(660\) −25.6707 + 4.52644i −0.999231 + 0.176191i
\(661\) 10.1505 17.5812i 0.394808 0.683828i −0.598269 0.801296i \(-0.704144\pi\)
0.993077 + 0.117468i \(0.0374778\pi\)
\(662\) −10.4055 + 18.0229i −0.404423 + 0.700481i
\(663\) 15.3735 2.71075i 0.597056 0.105277i
\(664\) −0.668434 1.15776i −0.0259403 0.0449298i
\(665\) 0 0
\(666\) −32.5099 + 11.8326i −1.25973 + 0.458505i
\(667\) −19.1320 −0.740793
\(668\) 43.7584 + 75.7917i 1.69306 + 2.93247i
\(669\) 3.71806 10.2153i 0.143749 0.394946i
\(670\) 3.29339 5.70431i 0.127235 0.220377i
\(671\) −5.03596 + 8.72254i −0.194411 + 0.336730i
\(672\) 0 0
\(673\) 0.415345 + 0.719398i 0.0160104 + 0.0277307i 0.873920 0.486071i \(-0.161570\pi\)
−0.857909 + 0.513801i \(0.828237\pi\)
\(674\) 11.5749 0.445849
\(675\) −19.0201 10.9812i −0.732083 0.422668i
\(676\) 73.8444 2.84017
\(677\) 5.43360 + 9.41127i 0.208830 + 0.361705i 0.951346 0.308124i \(-0.0997011\pi\)
−0.742516 + 0.669828i \(0.766368\pi\)
\(678\) 46.3833 + 55.2775i 1.78134 + 2.12292i
\(679\) 0 0
\(680\) 4.43717 7.68540i 0.170158 0.294722i
\(681\) 3.65064 10.0301i 0.139893 0.384353i
\(682\) −22.3687 38.7437i −0.856542 1.48357i
\(683\) 32.6946 1.25102 0.625512 0.780215i \(-0.284890\pi\)
0.625512 + 0.780215i \(0.284890\pi\)
\(684\) 24.4479 + 20.5142i 0.934789 + 0.784381i
\(685\) 15.9659 0.610024
\(686\) 0 0
\(687\) 39.8888 7.03347i 1.52185 0.268344i
\(688\) −0.613341 + 1.06234i −0.0233834 + 0.0405012i
\(689\) −19.8799 + 34.4329i −0.757362 + 1.31179i
\(690\) −12.0116 + 2.11797i −0.457274 + 0.0806298i
\(691\) 7.49912 + 12.9889i 0.285280 + 0.494120i 0.972677 0.232162i \(-0.0745801\pi\)
−0.687397 + 0.726282i \(0.741247\pi\)
\(692\) −100.064 −3.80387
\(693\) 0 0
\(694\) 56.8863 2.15937
\(695\) 9.69846 + 16.7982i 0.367884 + 0.637193i
\(696\) −21.8828 + 60.1225i −0.829465 + 2.27894i
\(697\) 0.979055 1.69577i 0.0370844 0.0642320i
\(698\) 33.0428 57.2318i 1.25069 2.16626i
\(699\) −9.49154 11.3116i −0.359003 0.427843i
\(700\) 0 0
\(701\) 26.4688 0.999714 0.499857 0.866108i \(-0.333386\pi\)
0.499857 + 0.866108i \(0.333386\pi\)
\(702\) −62.1378 + 35.8753i −2.34524 + 1.35403i
\(703\) 10.9828 0.414223
\(704\) 3.17752 + 5.50362i 0.119757 + 0.207426i
\(705\) 1.00088 + 1.19280i 0.0376952 + 0.0449234i
\(706\) −0.449493 + 0.778544i −0.0169169 + 0.0293009i
\(707\) 0 0
\(708\) −17.4060 + 47.8226i −0.654158 + 1.79728i
\(709\) −7.68004 13.3022i −0.288430 0.499576i 0.685005 0.728538i \(-0.259800\pi\)
−0.973435 + 0.228963i \(0.926467\pi\)
\(710\) −8.19429 −0.307526
\(711\) −16.7964 + 6.11338i −0.629913 + 0.229270i
\(712\) −67.3337 −2.52344
\(713\) −7.20162 12.4736i −0.269703 0.467139i
\(714\) 0 0
\(715\) −9.30200 + 16.1115i −0.347875 + 0.602538i
\(716\) 16.2062 28.0700i 0.605654 1.04902i
\(717\) −24.8391 + 4.37981i −0.927635 + 0.163567i
\(718\) −6.90760 11.9643i −0.257789 0.446504i
\(719\) −26.7306 −0.996883 −0.498442 0.866923i \(-0.666094\pi\)
−0.498442 + 0.866923i \(0.666094\pi\)
\(720\) −3.04101 + 17.2464i −0.113332 + 0.642737i
\(721\) 0 0
\(722\) 16.6925 + 28.9123i 0.621232 + 1.07600i
\(723\) 3.20115 8.79509i 0.119052 0.327093i
\(724\) −7.60014 + 13.1638i −0.282457 + 0.489230i
\(725\) −12.7849 + 22.1441i −0.474820 + 0.822413i
\(726\) 11.4162 + 13.6053i 0.423696 + 0.504941i
\(727\) −22.8221 39.5290i −0.846424 1.46605i −0.884379 0.466770i \(-0.845418\pi\)
0.0379552 0.999279i \(-0.487916\pi\)
\(728\) 0 0
\(729\) 13.5000 23.3827i 0.500000 0.866025i
\(730\) 28.4593 1.05333
\(731\) 0.152704 + 0.264490i 0.00564795 + 0.00978253i
\(732\) 12.7515 + 15.1966i 0.471309 + 0.561684i
\(733\) 2.98751 5.17452i 0.110346 0.191125i −0.805564 0.592509i \(-0.798137\pi\)
0.915910 + 0.401384i \(0.131471\pi\)
\(734\) 13.8302 23.9546i 0.510483 0.884182i
\(735\) 0 0
\(736\) −7.26786 12.5883i −0.267897 0.464011i
\(737\) −11.4757 −0.422711
\(738\) −1.56283 + 8.86327i −0.0575287 + 0.326261i
\(739\) −35.5963 −1.30943 −0.654715 0.755876i \(-0.727211\pi\)
−0.654715 + 0.755876i \(0.727211\pi\)
\(740\) 8.83409 + 15.3011i 0.324748 + 0.562480i
\(741\) 22.4315 3.95529i 0.824043 0.145301i
\(742\) 0 0
\(743\) 14.6544 25.3821i 0.537616 0.931178i −0.461416 0.887184i \(-0.652658\pi\)
0.999032 0.0439943i \(-0.0140083\pi\)
\(744\) −47.4354 + 8.36414i −1.73907 + 0.306644i
\(745\) 6.66385 + 11.5421i 0.244145 + 0.422871i
\(746\) 4.38413 0.160515
\(747\) 0.617211 0.224647i 0.0225826 0.00821939i
\(748\) −28.2841 −1.03417
\(749\) 0 0
\(750\) −12.1707 + 33.4388i −0.444412 + 1.22101i
\(751\) 8.66684 15.0114i 0.316258 0.547774i −0.663446 0.748224i \(-0.730907\pi\)
0.979704 + 0.200450i \(0.0642403\pi\)
\(752\) −3.39306 + 5.87695i −0.123732 + 0.214310i
\(753\) 13.4345 + 16.0107i 0.489582 + 0.583461i
\(754\) 41.7679 + 72.3440i 1.52110 + 2.63461i
\(755\) −16.6699 −0.606681
\(756\) 0 0
\(757\) −2.77156 −0.100734 −0.0503671 0.998731i \(-0.516039\pi\)
−0.0503671 + 0.998731i \(0.516039\pi\)
\(758\) 15.3614 + 26.6068i 0.557952 + 0.966402i
\(759\) 13.6591 + 16.2783i 0.495794 + 0.590864i
\(760\) 6.47431 11.2138i 0.234848 0.406768i
\(761\) 3.75372 6.50163i 0.136072 0.235684i −0.789934 0.613191i \(-0.789885\pi\)
0.926007 + 0.377508i \(0.123219\pi\)
\(762\) 26.4805 72.7545i 0.959286 2.63562i
\(763\) 0 0
\(764\) 24.9590 0.902987
\(765\) 3.34002 + 2.80261i 0.120759 + 0.101329i
\(766\) 22.0591 0.797029
\(767\) 18.1609 + 31.4556i 0.655752 + 1.13580i
\(768\) 52.0301 9.17431i 1.87747 0.331049i
\(769\) 1.02182 1.76985i 0.0368478 0.0638223i −0.847013 0.531572i \(-0.821602\pi\)
0.883861 + 0.467749i \(0.154935\pi\)
\(770\) 0 0
\(771\) 18.0232 3.17798i 0.649090 0.114452i
\(772\) −21.1668 36.6620i −0.761811 1.31950i
\(773\) 24.9418 0.897094 0.448547 0.893759i \(-0.351942\pi\)
0.448547 + 0.893759i \(0.351942\pi\)
\(774\) −1.07532 0.902302i −0.0386517 0.0324326i
\(775\) −19.2499 −0.691477
\(776\) 38.1721 + 66.1159i 1.37030 + 2.37342i
\(777\) 0 0
\(778\) −4.61246 + 7.98902i −0.165365 + 0.286420i
\(779\) 1.42855 2.47432i 0.0511831 0.0886516i
\(780\) 23.5535 + 28.0700i 0.843351 + 1.00507i
\(781\) 7.13816 +