Properties

Label 403.2.h.b.118.11
Level 403
Weight 2
Character 403.118
Analytic conductor 3.218
Analytic rank 0
Dimension 34
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.h (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 118.11
Character \(\chi\) \(=\) 403.118
Dual form 403.2.h.b.222.11

$q$-expansion

\(f(q)\) \(=\) \(q+1.28826 q^{2} +(1.07551 + 1.86284i) q^{3} -0.340382 q^{4} +(-1.69851 + 2.94190i) q^{5} +(1.38554 + 2.39982i) q^{6} +(0.278041 + 0.481581i) q^{7} -3.01502 q^{8} +(-0.813438 + 1.40892i) q^{9} +O(q^{10})\) \(q+1.28826 q^{2} +(1.07551 + 1.86284i) q^{3} -0.340382 q^{4} +(-1.69851 + 2.94190i) q^{5} +(1.38554 + 2.39982i) q^{6} +(0.278041 + 0.481581i) q^{7} -3.01502 q^{8} +(-0.813438 + 1.40892i) q^{9} +(-2.18812 + 3.78994i) q^{10} +(2.38925 - 4.13830i) q^{11} +(-0.366083 - 0.634075i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(0.358189 + 0.620402i) q^{14} -7.30704 q^{15} -3.20338 q^{16} +(3.25861 + 5.64408i) q^{17} +(-1.04792 + 1.81505i) q^{18} +(1.33011 + 2.30381i) q^{19} +(0.578141 - 1.00137i) q^{20} +(-0.598070 + 1.03589i) q^{21} +(3.07798 - 5.33122i) q^{22} -7.99721 q^{23} +(-3.24268 - 5.61649i) q^{24} +(-3.26986 - 5.66356i) q^{25} +(-0.644131 + 1.11567i) q^{26} +2.95361 q^{27} +(-0.0946400 - 0.163921i) q^{28} +3.90984 q^{29} -9.41338 q^{30} +(4.90883 + 2.62744i) q^{31} +1.90326 q^{32} +10.2786 q^{33} +(4.19794 + 7.27105i) q^{34} -1.88902 q^{35} +(0.276879 - 0.479569i) q^{36} +(5.44537 + 9.43166i) q^{37} +(1.71352 + 2.96791i) q^{38} -2.15102 q^{39} +(5.12104 - 8.86990i) q^{40} +(6.00876 - 10.4075i) q^{41} +(-0.770471 + 1.33450i) q^{42} +(-4.19272 - 7.26200i) q^{43} +(-0.813257 + 1.40860i) q^{44} +(-2.76326 - 4.78611i) q^{45} -10.3025 q^{46} +4.74715 q^{47} +(-3.44526 - 5.96736i) q^{48} +(3.34539 - 5.79438i) q^{49} +(-4.21243 - 7.29615i) q^{50} +(-7.00933 + 12.1405i) q^{51} +(0.170191 - 0.294779i) q^{52} +(2.19963 - 3.80988i) q^{53} +3.80503 q^{54} +(8.11632 + 14.0579i) q^{55} +(-0.838300 - 1.45198i) q^{56} +(-2.86108 + 4.95554i) q^{57} +5.03690 q^{58} +(-3.33135 - 5.77007i) q^{59} +2.48718 q^{60} -8.01209 q^{61} +(6.32385 + 3.38483i) q^{62} -0.904675 q^{63} +8.85865 q^{64} +(-1.69851 - 2.94190i) q^{65} +13.2416 q^{66} +(-2.05361 + 3.55695i) q^{67} +(-1.10917 - 1.92114i) q^{68} +(-8.60107 - 14.8975i) q^{69} -2.43355 q^{70} +(-1.84977 + 3.20390i) q^{71} +(2.45253 - 4.24791i) q^{72} +(-5.46321 + 9.46256i) q^{73} +(7.01507 + 12.1505i) q^{74} +(7.03352 - 12.1824i) q^{75} +(-0.452744 - 0.784175i) q^{76} +2.65724 q^{77} -2.77107 q^{78} +(-1.00465 - 1.74011i) q^{79} +(5.44096 - 9.42402i) q^{80} +(5.61695 + 9.72885i) q^{81} +(7.74086 - 13.4076i) q^{82} +(4.62578 - 8.01208i) q^{83} +(0.203572 - 0.352597i) q^{84} -22.1391 q^{85} +(-5.40132 - 9.35536i) q^{86} +(4.20507 + 7.28339i) q^{87} +(-7.20365 + 12.4771i) q^{88} -5.05334 q^{89} +(-3.55980 - 6.16576i) q^{90} -0.556082 q^{91} +2.72210 q^{92} +(0.385000 + 11.9702i) q^{93} +6.11557 q^{94} -9.03678 q^{95} +(2.04697 + 3.54546i) q^{96} -3.19323 q^{97} +(4.30973 - 7.46468i) q^{98} +(3.88701 + 6.73250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} + O(q^{10}) \) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} - 7q^{10} - 5q^{11} - 28q^{12} - 17q^{13} - 7q^{14} + 8q^{15} + 18q^{16} - 8q^{17} + 6q^{18} + 3q^{19} - 8q^{20} + 13q^{21} + 12q^{22} - 14q^{23} - 6q^{24} - 26q^{25} - 3q^{26} + 28q^{27} - 7q^{28} - 18q^{29} - 60q^{30} - 9q^{31} + 58q^{32} - 14q^{33} - 15q^{34} + 50q^{35} - 49q^{36} - 6q^{37} + 2q^{38} + 4q^{39} - 29q^{40} - 5q^{41} + 8q^{42} - q^{43} - 22q^{44} + 13q^{45} + 34q^{46} + 16q^{47} - 49q^{48} + 3q^{49} - 35q^{51} - 17q^{52} + 30q^{53} - 2q^{54} + 21q^{55} - 7q^{56} + 34q^{58} - 9q^{59} - 38q^{60} - 28q^{61} - 62q^{62} + 88q^{63} + 56q^{64} - 5q^{65} + 140q^{66} - 31q^{67} - 39q^{68} + 5q^{69} + 56q^{70} + q^{71} - 32q^{72} - 10q^{73} - 39q^{74} - 2q^{75} - 16q^{76} + 76q^{77} - 23q^{79} - 22q^{80} - 29q^{81} - 10q^{82} + 3q^{83} + 52q^{84} - 32q^{85} + 4q^{86} + 18q^{87} - 10q^{88} + 26q^{89} + 35q^{90} + 4q^{91} - 94q^{92} - 41q^{93} + 70q^{94} + 28q^{95} - 23q^{96} + 32q^{97} - 38q^{98} - 70q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28826 0.910939 0.455469 0.890251i \(-0.349471\pi\)
0.455469 + 0.890251i \(0.349471\pi\)
\(3\) 1.07551 + 1.86284i 0.620945 + 1.07551i 0.989310 + 0.145827i \(0.0465844\pi\)
−0.368365 + 0.929681i \(0.620082\pi\)
\(4\) −0.340382 −0.170191
\(5\) −1.69851 + 2.94190i −0.759596 + 1.31566i 0.183461 + 0.983027i \(0.441270\pi\)
−0.943057 + 0.332631i \(0.892063\pi\)
\(6\) 1.38554 + 2.39982i 0.565643 + 0.979722i
\(7\) 0.278041 + 0.481581i 0.105090 + 0.182020i 0.913775 0.406221i \(-0.133154\pi\)
−0.808685 + 0.588242i \(0.799820\pi\)
\(8\) −3.01502 −1.06597
\(9\) −0.813438 + 1.40892i −0.271146 + 0.469639i
\(10\) −2.18812 + 3.78994i −0.691945 + 1.19848i
\(11\) 2.38925 4.13830i 0.720386 1.24775i −0.240459 0.970659i \(-0.577298\pi\)
0.960845 0.277086i \(-0.0893687\pi\)
\(12\) −0.366083 0.634075i −0.105679 0.183042i
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i
\(14\) 0.358189 + 0.620402i 0.0957301 + 0.165809i
\(15\) −7.30704 −1.88667
\(16\) −3.20338 −0.800844
\(17\) 3.25861 + 5.64408i 0.790329 + 1.36889i 0.925763 + 0.378104i \(0.123424\pi\)
−0.135434 + 0.990786i \(0.543243\pi\)
\(18\) −1.04792 + 1.81505i −0.246997 + 0.427812i
\(19\) 1.33011 + 2.30381i 0.305147 + 0.528531i 0.977294 0.211887i \(-0.0679610\pi\)
−0.672147 + 0.740418i \(0.734628\pi\)
\(20\) 0.578141 1.00137i 0.129276 0.223913i
\(21\) −0.598070 + 1.03589i −0.130510 + 0.226049i
\(22\) 3.07798 5.33122i 0.656227 1.13662i
\(23\) −7.99721 −1.66753 −0.833767 0.552117i \(-0.813820\pi\)
−0.833767 + 0.552117i \(0.813820\pi\)
\(24\) −3.24268 5.61649i −0.661910 1.14646i
\(25\) −3.26986 5.66356i −0.653971 1.13271i
\(26\) −0.644131 + 1.11567i −0.126324 + 0.218800i
\(27\) 2.95361 0.568423
\(28\) −0.0946400 0.163921i −0.0178853 0.0309782i
\(29\) 3.90984 0.726039 0.363019 0.931782i \(-0.381746\pi\)
0.363019 + 0.931782i \(0.381746\pi\)
\(30\) −9.41338 −1.71864
\(31\) 4.90883 + 2.62744i 0.881651 + 0.471902i
\(32\) 1.90326 0.336452
\(33\) 10.2786 1.78928
\(34\) 4.19794 + 7.27105i 0.719942 + 1.24698i
\(35\) −1.88902 −0.319302
\(36\) 0.276879 0.479569i 0.0461466 0.0799282i
\(37\) 5.44537 + 9.43166i 0.895214 + 1.55056i 0.833540 + 0.552460i \(0.186311\pi\)
0.0616742 + 0.998096i \(0.480356\pi\)
\(38\) 1.71352 + 2.96791i 0.277970 + 0.481459i
\(39\) −2.15102 −0.344438
\(40\) 5.12104 8.86990i 0.809708 1.40246i
\(41\) 6.00876 10.4075i 0.938411 1.62538i 0.169976 0.985448i \(-0.445631\pi\)
0.768435 0.639927i \(-0.221036\pi\)
\(42\) −0.770471 + 1.33450i −0.118886 + 0.205917i
\(43\) −4.19272 7.26200i −0.639383 1.10744i −0.985568 0.169278i \(-0.945856\pi\)
0.346185 0.938166i \(-0.387477\pi\)
\(44\) −0.813257 + 1.40860i −0.122603 + 0.212355i
\(45\) −2.76326 4.78611i −0.411923 0.713471i
\(46\) −10.3025 −1.51902
\(47\) 4.74715 0.692443 0.346221 0.938153i \(-0.387465\pi\)
0.346221 + 0.938153i \(0.387465\pi\)
\(48\) −3.44526 5.96736i −0.497280 0.861315i
\(49\) 3.34539 5.79438i 0.477912 0.827769i
\(50\) −4.21243 7.29615i −0.595728 1.03183i
\(51\) −7.00933 + 12.1405i −0.981503 + 1.70001i
\(52\) 0.170191 0.294779i 0.0236012 0.0408785i
\(53\) 2.19963 3.80988i 0.302143 0.523327i −0.674478 0.738295i \(-0.735631\pi\)
0.976621 + 0.214968i \(0.0689647\pi\)
\(54\) 3.80503 0.517799
\(55\) 8.11632 + 14.0579i 1.09440 + 1.89556i
\(56\) −0.838300 1.45198i −0.112022 0.194029i
\(57\) −2.86108 + 4.95554i −0.378959 + 0.656377i
\(58\) 5.03690 0.661377
\(59\) −3.33135 5.77007i −0.433705 0.751200i 0.563484 0.826127i \(-0.309461\pi\)
−0.997189 + 0.0749276i \(0.976127\pi\)
\(60\) 2.48718 0.321094
\(61\) −8.01209 −1.02584 −0.512921 0.858436i \(-0.671437\pi\)
−0.512921 + 0.858436i \(0.671437\pi\)
\(62\) 6.32385 + 3.38483i 0.803130 + 0.429874i
\(63\) −0.904675 −0.113978
\(64\) 8.85865 1.10733
\(65\) −1.69851 2.94190i −0.210674 0.364898i
\(66\) 13.2416 1.62993
\(67\) −2.05361 + 3.55695i −0.250888 + 0.434551i −0.963771 0.266733i \(-0.914056\pi\)
0.712882 + 0.701284i \(0.247389\pi\)
\(68\) −1.10917 1.92114i −0.134507 0.232973i
\(69\) −8.60107 14.8975i −1.03545 1.79345i
\(70\) −2.43355 −0.290865
\(71\) −1.84977 + 3.20390i −0.219528 + 0.380233i −0.954664 0.297686i \(-0.903785\pi\)
0.735136 + 0.677920i \(0.237118\pi\)
\(72\) 2.45253 4.24791i 0.289034 0.500622i
\(73\) −5.46321 + 9.46256i −0.639420 + 1.10751i 0.346140 + 0.938183i \(0.387492\pi\)
−0.985560 + 0.169325i \(0.945841\pi\)
\(74\) 7.01507 + 12.1505i 0.815485 + 1.41246i
\(75\) 7.03352 12.1824i 0.812161 1.40670i
\(76\) −0.452744 0.784175i −0.0519333 0.0899511i
\(77\) 2.65724 0.302820
\(78\) −2.77107 −0.313762
\(79\) −1.00465 1.74011i −0.113032 0.195777i 0.803959 0.594684i \(-0.202723\pi\)
−0.916991 + 0.398907i \(0.869390\pi\)
\(80\) 5.44096 9.42402i 0.608318 1.05364i
\(81\) 5.61695 + 9.72885i 0.624106 + 1.08098i
\(82\) 7.74086 13.4076i 0.854835 1.48062i
\(83\) 4.62578 8.01208i 0.507745 0.879440i −0.492215 0.870474i \(-0.663813\pi\)
0.999960 0.00896614i \(-0.00285405\pi\)
\(84\) 0.203572 0.352597i 0.0222116 0.0384715i
\(85\) −22.1391 −2.40132
\(86\) −5.40132 9.35536i −0.582439 1.00881i
\(87\) 4.20507 + 7.28339i 0.450830 + 0.780861i
\(88\) −7.20365 + 12.4771i −0.767911 + 1.33006i
\(89\) −5.05334 −0.535653 −0.267827 0.963467i \(-0.586305\pi\)
−0.267827 + 0.963467i \(0.586305\pi\)
\(90\) −3.55980 6.16576i −0.375236 0.649928i
\(91\) −0.556082 −0.0582932
\(92\) 2.72210 0.283799
\(93\) 0.385000 + 11.9702i 0.0399227 + 1.24125i
\(94\) 6.11557 0.630773
\(95\) −9.03678 −0.927154
\(96\) 2.04697 + 3.54546i 0.208918 + 0.361857i
\(97\) −3.19323 −0.324224 −0.162112 0.986772i \(-0.551831\pi\)
−0.162112 + 0.986772i \(0.551831\pi\)
\(98\) 4.30973 7.46468i 0.435349 0.754046i
\(99\) 3.88701 + 6.73250i 0.390659 + 0.676642i
\(100\) 1.11300 + 1.92777i 0.111300 + 0.192777i
\(101\) −0.564935 −0.0562132 −0.0281066 0.999605i \(-0.508948\pi\)
−0.0281066 + 0.999605i \(0.508948\pi\)
\(102\) −9.02985 + 15.6402i −0.894089 + 1.54861i
\(103\) −5.04132 + 8.73182i −0.496736 + 0.860372i −0.999993 0.00376467i \(-0.998802\pi\)
0.503257 + 0.864137i \(0.332135\pi\)
\(104\) 1.50751 2.61109i 0.147824 0.256038i
\(105\) −2.03165 3.51893i −0.198269 0.343412i
\(106\) 2.83370 4.90812i 0.275234 0.476719i
\(107\) −4.07492 7.05796i −0.393937 0.682319i 0.599028 0.800728i \(-0.295554\pi\)
−0.992965 + 0.118409i \(0.962220\pi\)
\(108\) −1.00536 −0.0967405
\(109\) 11.0090 1.05447 0.527236 0.849719i \(-0.323228\pi\)
0.527236 + 0.849719i \(0.323228\pi\)
\(110\) 10.4559 + 18.1102i 0.996935 + 1.72674i
\(111\) −11.7131 + 20.2877i −1.11176 + 1.92562i
\(112\) −0.890669 1.54268i −0.0841603 0.145770i
\(113\) 0.333706 0.577996i 0.0313924 0.0543733i −0.849902 0.526940i \(-0.823339\pi\)
0.881295 + 0.472567i \(0.156673\pi\)
\(114\) −3.68582 + 6.38403i −0.345209 + 0.597919i
\(115\) 13.5833 23.5270i 1.26665 2.19390i
\(116\) −1.33084 −0.123565
\(117\) −0.813438 1.40892i −0.0752024 0.130254i
\(118\) −4.29166 7.43336i −0.395079 0.684297i
\(119\) −1.81205 + 3.13857i −0.166111 + 0.287712i
\(120\) 22.0309 2.01114
\(121\) −5.91703 10.2486i −0.537912 0.931691i
\(122\) −10.3217 −0.934479
\(123\) 25.8499 2.33081
\(124\) −1.67087 0.894332i −0.150049 0.0803134i
\(125\) 5.23043 0.467824
\(126\) −1.16546 −0.103827
\(127\) −9.95414 17.2411i −0.883287 1.52990i −0.847665 0.530532i \(-0.821992\pi\)
−0.0356223 0.999365i \(-0.511341\pi\)
\(128\) 7.60574 0.672259
\(129\) 9.01861 15.6207i 0.794044 1.37532i
\(130\) −2.18812 3.78994i −0.191911 0.332400i
\(131\) −4.12049 7.13691i −0.360009 0.623554i 0.627953 0.778252i \(-0.283893\pi\)
−0.987962 + 0.154697i \(0.950560\pi\)
\(132\) −3.49866 −0.304519
\(133\) −0.739647 + 1.28111i −0.0641356 + 0.111086i
\(134\) −2.64558 + 4.58229i −0.228544 + 0.395849i
\(135\) −5.01674 + 8.68924i −0.431772 + 0.747851i
\(136\) −9.82479 17.0170i −0.842469 1.45920i
\(137\) −0.407109 + 0.705134i −0.0347817 + 0.0602436i −0.882892 0.469576i \(-0.844407\pi\)
0.848111 + 0.529819i \(0.177740\pi\)
\(138\) −11.0804 19.1919i −0.943228 1.63372i
\(139\) 4.25650 0.361031 0.180516 0.983572i \(-0.442223\pi\)
0.180516 + 0.983572i \(0.442223\pi\)
\(140\) 0.642987 0.0543423
\(141\) 5.10560 + 8.84316i 0.429969 + 0.744728i
\(142\) −2.38299 + 4.12747i −0.199976 + 0.346369i
\(143\) 2.38925 + 4.13830i 0.199799 + 0.346062i
\(144\) 2.60575 4.51329i 0.217146 0.376107i
\(145\) −6.64089 + 11.5024i −0.551496 + 0.955219i
\(146\) −7.03804 + 12.1902i −0.582473 + 1.00887i
\(147\) 14.3920 1.18703
\(148\) −1.85351 3.21037i −0.152357 0.263890i
\(149\) −7.21838 12.5026i −0.591353 1.02425i −0.994050 0.108920i \(-0.965261\pi\)
0.402697 0.915333i \(-0.368073\pi\)
\(150\) 9.06101 15.6941i 0.739829 1.28142i
\(151\) 23.9202 1.94659 0.973297 0.229549i \(-0.0737251\pi\)
0.973297 + 0.229549i \(0.0737251\pi\)
\(152\) −4.01030 6.94605i −0.325278 0.563399i
\(153\) −10.6027 −0.857178
\(154\) 3.42321 0.275851
\(155\) −16.0673 + 9.97856i −1.29056 + 0.801497i
\(156\) 0.732167 0.0586203
\(157\) −8.67546 −0.692377 −0.346189 0.938165i \(-0.612524\pi\)
−0.346189 + 0.938165i \(0.612524\pi\)
\(158\) −1.29425 2.24171i −0.102965 0.178341i
\(159\) 9.46290 0.750457
\(160\) −3.23270 + 5.59921i −0.255568 + 0.442656i
\(161\) −2.22355 3.85130i −0.175240 0.303525i
\(162\) 7.23610 + 12.5333i 0.568522 + 0.984709i
\(163\) −14.6951 −1.15101 −0.575505 0.817798i \(-0.695195\pi\)
−0.575505 + 0.817798i \(0.695195\pi\)
\(164\) −2.04527 + 3.54252i −0.159709 + 0.276624i
\(165\) −17.4583 + 30.2387i −1.35913 + 2.35408i
\(166\) 5.95921 10.3217i 0.462524 0.801116i
\(167\) 9.69086 + 16.7851i 0.749901 + 1.29887i 0.947870 + 0.318658i \(0.103232\pi\)
−0.197969 + 0.980208i \(0.563434\pi\)
\(168\) 1.80320 3.12323i 0.139120 0.240962i
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) −28.5210 −2.18746
\(171\) −4.32783 −0.330958
\(172\) 1.42712 + 2.47185i 0.108817 + 0.188477i
\(173\) −0.664824 + 1.15151i −0.0505456 + 0.0875476i −0.890191 0.455587i \(-0.849429\pi\)
0.839646 + 0.543135i \(0.182763\pi\)
\(174\) 5.41723 + 9.38291i 0.410679 + 0.711317i
\(175\) 1.81831 3.14940i 0.137451 0.238072i
\(176\) −7.65367 + 13.2565i −0.576917 + 0.999249i
\(177\) 7.16580 12.4115i 0.538614 0.932908i
\(178\) −6.51003 −0.487947
\(179\) −8.98982 15.5708i −0.671931 1.16382i −0.977356 0.211602i \(-0.932132\pi\)
0.305425 0.952216i \(-0.401201\pi\)
\(180\) 0.940563 + 1.62910i 0.0701055 + 0.121426i
\(181\) 2.59517 4.49497i 0.192897 0.334108i −0.753312 0.657664i \(-0.771545\pi\)
0.946209 + 0.323555i \(0.104878\pi\)
\(182\) −0.716379 −0.0531015
\(183\) −8.61707 14.9252i −0.636992 1.10330i
\(184\) 24.1118 1.77754
\(185\) −36.9960 −2.72000
\(186\) 0.495981 + 15.4207i 0.0363671 + 1.13070i
\(187\) 31.1426 2.27737
\(188\) −1.61584 −0.117847
\(189\) 0.821225 + 1.42240i 0.0597353 + 0.103465i
\(190\) −11.6417 −0.844581
\(191\) 2.84969 4.93580i 0.206196 0.357142i −0.744317 0.667826i \(-0.767225\pi\)
0.950513 + 0.310684i \(0.100558\pi\)
\(192\) 9.52756 + 16.5022i 0.687592 + 1.19094i
\(193\) 6.47978 + 11.2233i 0.466425 + 0.807871i 0.999265 0.0383450i \(-0.0122086\pi\)
−0.532840 + 0.846216i \(0.678875\pi\)
\(194\) −4.11372 −0.295348
\(195\) 3.65352 6.32808i 0.261634 0.453163i
\(196\) −1.13871 + 1.97230i −0.0813363 + 0.140879i
\(197\) 1.51535 2.62466i 0.107964 0.186999i −0.806981 0.590577i \(-0.798900\pi\)
0.914945 + 0.403578i \(0.132234\pi\)
\(198\) 5.00749 + 8.67323i 0.355867 + 0.616379i
\(199\) 5.59389 9.68891i 0.396541 0.686828i −0.596756 0.802423i \(-0.703544\pi\)
0.993297 + 0.115594i \(0.0368773\pi\)
\(200\) 9.85870 + 17.0758i 0.697115 + 1.20744i
\(201\) −8.83469 −0.623151
\(202\) −0.727784 −0.0512067
\(203\) 1.08709 + 1.88290i 0.0762991 + 0.132154i
\(204\) 2.38585 4.13241i 0.167043 0.289327i
\(205\) 20.4119 + 35.3544i 1.42563 + 2.46926i
\(206\) −6.49454 + 11.2489i −0.452496 + 0.783746i
\(207\) 6.50523 11.2674i 0.452145 0.783138i
\(208\) 1.60169 2.77421i 0.111057 0.192357i
\(209\) 12.7118 0.879295
\(210\) −2.61730 4.53330i −0.180611 0.312828i
\(211\) 12.9316 + 22.3983i 0.890251 + 1.54196i 0.839574 + 0.543245i \(0.182804\pi\)
0.0506765 + 0.998715i \(0.483862\pi\)
\(212\) −0.748715 + 1.29681i −0.0514220 + 0.0890655i
\(213\) −7.95780 −0.545259
\(214\) −5.24956 9.09250i −0.358852 0.621550i
\(215\) 28.4855 1.94269
\(216\) −8.90522 −0.605923
\(217\) 0.0995304 + 3.09453i 0.00675656 + 0.210070i
\(218\) 14.1825 0.960560
\(219\) −23.5029 −1.58818
\(220\) −2.76265 4.78504i −0.186258 0.322608i
\(221\) −6.51722 −0.438396
\(222\) −15.0895 + 26.1358i −1.01274 + 1.75412i
\(223\) −6.75524 11.7004i −0.452365 0.783519i 0.546168 0.837676i \(-0.316086\pi\)
−0.998532 + 0.0541573i \(0.982753\pi\)
\(224\) 0.529184 + 0.916574i 0.0353576 + 0.0612411i
\(225\) 10.6393 0.709287
\(226\) 0.429901 0.744610i 0.0285966 0.0495307i
\(227\) −2.75995 + 4.78038i −0.183184 + 0.317285i −0.942963 0.332897i \(-0.891974\pi\)
0.759779 + 0.650182i \(0.225307\pi\)
\(228\) 0.973860 1.68677i 0.0644954 0.111709i
\(229\) 1.56376 + 2.70850i 0.103336 + 0.178983i 0.913057 0.407832i \(-0.133715\pi\)
−0.809721 + 0.586815i \(0.800382\pi\)
\(230\) 17.4989 30.3089i 1.15384 1.99851i
\(231\) 2.85788 + 4.94999i 0.188035 + 0.325686i
\(232\) −11.7883 −0.773937
\(233\) 1.16805 0.0765212 0.0382606 0.999268i \(-0.487818\pi\)
0.0382606 + 0.999268i \(0.487818\pi\)
\(234\) −1.04792 1.81505i −0.0685047 0.118654i
\(235\) −8.06307 + 13.9656i −0.525976 + 0.911018i
\(236\) 1.13393 + 1.96403i 0.0738127 + 0.127847i
\(237\) 2.16102 3.74300i 0.140373 0.243134i
\(238\) −2.33440 + 4.04330i −0.151317 + 0.262088i
\(239\) 8.67505 15.0256i 0.561143 0.971927i −0.436255 0.899823i \(-0.643695\pi\)
0.997397 0.0721041i \(-0.0229714\pi\)
\(240\) 23.4072 1.51093
\(241\) 4.95865 + 8.58864i 0.319415 + 0.553243i 0.980366 0.197186i \(-0.0631803\pi\)
−0.660951 + 0.750429i \(0.729847\pi\)
\(242\) −7.62268 13.2029i −0.490005 0.848713i
\(243\) −7.65174 + 13.2532i −0.490859 + 0.850193i
\(244\) 2.72717 0.174589
\(245\) 11.3643 + 19.6836i 0.726040 + 1.25754i
\(246\) 33.3014 2.12322
\(247\) −2.66021 −0.169265
\(248\) −14.8002 7.92179i −0.939815 0.503034i
\(249\) 19.9002 1.26113
\(250\) 6.73817 0.426159
\(251\) −7.13022 12.3499i −0.450055 0.779519i 0.548334 0.836260i \(-0.315262\pi\)
−0.998389 + 0.0567411i \(0.981929\pi\)
\(252\) 0.307935 0.0193981
\(253\) −19.1073 + 33.0949i −1.20127 + 2.08066i
\(254\) −12.8235 22.2110i −0.804620 1.39364i
\(255\) −23.8108 41.2415i −1.49109 2.58264i
\(256\) −7.91912 −0.494945
\(257\) −8.39783 + 14.5455i −0.523842 + 0.907322i 0.475772 + 0.879568i \(0.342169\pi\)
−0.999615 + 0.0277531i \(0.991165\pi\)
\(258\) 11.6183 20.1235i 0.723325 1.25284i
\(259\) −3.02807 + 5.24477i −0.188155 + 0.325894i
\(260\) 0.578141 + 1.00137i 0.0358548 + 0.0621023i
\(261\) −3.18041 + 5.50863i −0.196862 + 0.340976i
\(262\) −5.30828 9.19420i −0.327946 0.568020i
\(263\) −7.89727 −0.486966 −0.243483 0.969905i \(-0.578290\pi\)
−0.243483 + 0.969905i \(0.578290\pi\)
\(264\) −30.9903 −1.90732
\(265\) 7.47219 + 12.9422i 0.459013 + 0.795034i
\(266\) −0.952859 + 1.65040i −0.0584236 + 0.101193i
\(267\) −5.43491 9.41354i −0.332611 0.576100i
\(268\) 0.699011 1.21072i 0.0426989 0.0739566i
\(269\) 0.139069 0.240875i 0.00847919 0.0146864i −0.861755 0.507325i \(-0.830634\pi\)
0.870234 + 0.492639i \(0.163968\pi\)
\(270\) −6.46287 + 11.1940i −0.393318 + 0.681246i
\(271\) 14.7643 0.896865 0.448432 0.893817i \(-0.351983\pi\)
0.448432 + 0.893817i \(0.351983\pi\)
\(272\) −10.4386 18.0801i −0.632931 1.09627i
\(273\) −0.598070 1.03589i −0.0361969 0.0626948i
\(274\) −0.524463 + 0.908397i −0.0316840 + 0.0548783i
\(275\) −31.2500 −1.88445
\(276\) 2.92765 + 5.07083i 0.176224 + 0.305228i
\(277\) −27.7571 −1.66776 −0.833882 0.551943i \(-0.813887\pi\)
−0.833882 + 0.551943i \(0.813887\pi\)
\(278\) 5.48348 0.328877
\(279\) −7.69486 + 4.77886i −0.460679 + 0.286103i
\(280\) 5.69543 0.340367
\(281\) 5.14865 0.307143 0.153571 0.988138i \(-0.450923\pi\)
0.153571 + 0.988138i \(0.450923\pi\)
\(282\) 6.57735 + 11.3923i 0.391675 + 0.678401i
\(283\) 11.9313 0.709244 0.354622 0.935010i \(-0.384610\pi\)
0.354622 + 0.935010i \(0.384610\pi\)
\(284\) 0.629630 1.09055i 0.0373616 0.0647123i
\(285\) −9.71914 16.8340i −0.575712 0.997162i
\(286\) 3.07798 + 5.33122i 0.182005 + 0.315241i
\(287\) 6.68272 0.394469
\(288\) −1.54818 + 2.68153i −0.0912276 + 0.158011i
\(289\) −12.7371 + 22.0613i −0.749241 + 1.29772i
\(290\) −8.55521 + 14.8181i −0.502379 + 0.870146i
\(291\) −3.43435 5.94847i −0.201325 0.348705i
\(292\) 1.85958 3.22088i 0.108823 0.188488i
\(293\) −3.13875 5.43647i −0.183367 0.317602i 0.759658 0.650323i \(-0.225366\pi\)
−0.943025 + 0.332721i \(0.892033\pi\)
\(294\) 18.5406 1.08131
\(295\) 22.6333 1.31776
\(296\) −16.4179 28.4367i −0.954273 1.65285i
\(297\) 7.05692 12.2229i 0.409484 0.709247i
\(298\) −9.29917 16.1066i −0.538686 0.933032i
\(299\) 3.99860 6.92579i 0.231245 0.400528i
\(300\) −2.39408 + 4.14667i −0.138222 + 0.239408i
\(301\) 2.33149 4.03826i 0.134385 0.232762i
\(302\) 30.8154 1.77323
\(303\) −0.607593 1.05238i −0.0349053 0.0604577i
\(304\) −4.26083 7.37998i −0.244375 0.423271i
\(305\) 13.6086 23.5708i 0.779226 1.34966i
\(306\) −13.6591 −0.780837
\(307\) 11.7575 + 20.3647i 0.671038 + 1.16227i 0.977610 + 0.210425i \(0.0674848\pi\)
−0.306572 + 0.951848i \(0.599182\pi\)
\(308\) −0.904474 −0.0515372
\(309\) −21.6879 −1.23378
\(310\) −20.6989 + 12.8550i −1.17562 + 0.730115i
\(311\) 5.95141 0.337473 0.168737 0.985661i \(-0.446031\pi\)
0.168737 + 0.985661i \(0.446031\pi\)
\(312\) 6.48537 0.367162
\(313\) 12.5991 + 21.8223i 0.712145 + 1.23347i 0.964051 + 0.265719i \(0.0856093\pi\)
−0.251906 + 0.967752i \(0.581057\pi\)
\(314\) −11.1763 −0.630713
\(315\) 1.53660 2.66147i 0.0865775 0.149957i
\(316\) 0.341965 + 0.592300i 0.0192370 + 0.0333195i
\(317\) 2.57366 + 4.45770i 0.144551 + 0.250369i 0.929205 0.369564i \(-0.120493\pi\)
−0.784654 + 0.619933i \(0.787160\pi\)
\(318\) 12.1907 0.683620
\(319\) 9.34158 16.1801i 0.523028 0.905912i
\(320\) −15.0465 + 26.0613i −0.841124 + 1.45687i
\(321\) 8.76521 15.1818i 0.489226 0.847365i
\(322\) −2.86451 4.96148i −0.159633 0.276493i
\(323\) −8.66860 + 15.0145i −0.482334 + 0.835426i
\(324\) −1.91191 3.31152i −0.106217 0.183973i
\(325\) 6.53971 0.362758
\(326\) −18.9312 −1.04850
\(327\) 11.8403 + 20.5080i 0.654770 + 1.13409i
\(328\) −18.1166 + 31.3788i −1.00032 + 1.73260i
\(329\) 1.31990 + 2.28613i 0.0727685 + 0.126039i
\(330\) −22.4909 + 38.9554i −1.23808 + 2.14442i
\(331\) 7.84954 13.5958i 0.431449 0.747292i −0.565549 0.824715i \(-0.691336\pi\)
0.996998 + 0.0774223i \(0.0246690\pi\)
\(332\) −1.57453 + 2.72716i −0.0864135 + 0.149673i
\(333\) −17.7179 −0.970934
\(334\) 12.4844 + 21.6235i 0.683114 + 1.18319i
\(335\) −6.97614 12.0830i −0.381147 0.660166i
\(336\) 1.91585 3.31834i 0.104518 0.181030i
\(337\) −7.20525 −0.392495 −0.196247 0.980554i \(-0.562876\pi\)
−0.196247 + 0.980554i \(0.562876\pi\)
\(338\) −0.644131 1.11567i −0.0350361 0.0606843i
\(339\) 1.43562 0.0779719
\(340\) 7.53575 0.408683
\(341\) 22.6015 14.0366i 1.22394 0.760125i
\(342\) −5.57538 −0.301482
\(343\) 7.61319 0.411073
\(344\) 12.6411 + 21.8951i 0.681565 + 1.18050i
\(345\) 58.4359 3.14608
\(346\) −0.856467 + 1.48344i −0.0460439 + 0.0797505i
\(347\) −9.57121 16.5778i −0.513810 0.889944i −0.999872 0.0160200i \(-0.994900\pi\)
0.486062 0.873924i \(-0.338433\pi\)
\(348\) −1.43133 2.47913i −0.0767272 0.132895i
\(349\) −13.3373 −0.713927 −0.356963 0.934118i \(-0.616188\pi\)
−0.356963 + 0.934118i \(0.616188\pi\)
\(350\) 2.34246 4.05725i 0.125210 0.216869i
\(351\) −1.47681 + 2.55791i −0.0788261 + 0.136531i
\(352\) 4.54737 7.87627i 0.242375 0.419806i
\(353\) −14.7712 25.5845i −0.786191 1.36172i −0.928285 0.371870i \(-0.878717\pi\)
0.142094 0.989853i \(-0.454617\pi\)
\(354\) 9.23142 15.9893i 0.490645 0.849822i
\(355\) −6.28371 10.8837i −0.333505 0.577647i
\(356\) 1.72006 0.0911633
\(357\) −7.79552 −0.412583
\(358\) −11.5812 20.0593i −0.612088 1.06017i
\(359\) 4.08018 7.06708i 0.215344 0.372986i −0.738035 0.674762i \(-0.764246\pi\)
0.953379 + 0.301776i \(0.0975795\pi\)
\(360\) 8.33130 + 14.4302i 0.439098 + 0.760540i
\(361\) 5.96164 10.3259i 0.313770 0.543466i
\(362\) 3.34326 5.79069i 0.175718 0.304352i
\(363\) 12.7276 22.0449i 0.668028 1.15706i
\(364\) 0.189280 0.00992097
\(365\) −18.5586 32.1444i −0.971402 1.68252i
\(366\) −11.1010 19.2276i −0.580261 1.00504i
\(367\) −2.38972 + 4.13911i −0.124742 + 0.216060i −0.921632 0.388065i \(-0.873144\pi\)
0.796890 + 0.604125i \(0.206477\pi\)
\(368\) 25.6181 1.33543
\(369\) 9.77551 + 16.9317i 0.508893 + 0.881428i
\(370\) −47.6606 −2.47776
\(371\) 2.44635 0.127008
\(372\) −0.131047 4.07443i −0.00679447 0.211249i
\(373\) −2.23562 −0.115756 −0.0578781 0.998324i \(-0.518433\pi\)
−0.0578781 + 0.998324i \(0.518433\pi\)
\(374\) 40.1198 2.07454
\(375\) 5.62538 + 9.74344i 0.290493 + 0.503149i
\(376\) −14.3128 −0.738124
\(377\) −1.95492 + 3.38602i −0.100683 + 0.174389i
\(378\) 1.05795 + 1.83243i 0.0544152 + 0.0942499i
\(379\) −1.86488 3.23007i −0.0957925 0.165917i 0.814147 0.580659i \(-0.197205\pi\)
−0.909939 + 0.414742i \(0.863872\pi\)
\(380\) 3.07596 0.157793
\(381\) 21.4115 37.0858i 1.09695 1.89997i
\(382\) 3.67114 6.35860i 0.187832 0.325334i
\(383\) −10.1268 + 17.5401i −0.517454 + 0.896257i 0.482340 + 0.875984i \(0.339787\pi\)
−0.999794 + 0.0202728i \(0.993547\pi\)
\(384\) 8.18004 + 14.1682i 0.417436 + 0.723020i
\(385\) −4.51334 + 7.81733i −0.230021 + 0.398408i
\(386\) 8.34765 + 14.4586i 0.424884 + 0.735921i
\(387\) 13.6421 0.693465
\(388\) 1.08692 0.0551799
\(389\) −6.68884 11.5854i −0.339137 0.587403i 0.645133 0.764070i \(-0.276802\pi\)
−0.984271 + 0.176667i \(0.943468\pi\)
\(390\) 4.70669 8.15223i 0.238332 0.412804i
\(391\) −26.0598 45.1369i −1.31790 2.28267i
\(392\) −10.0864 + 17.4702i −0.509441 + 0.882378i
\(393\) 8.86326 15.3516i 0.447092 0.774386i
\(394\) 1.95216 3.38125i 0.0983486 0.170345i
\(395\) 6.82563 0.343435
\(396\) −1.32307 2.29162i −0.0664867 0.115158i
\(397\) 4.46105 + 7.72677i 0.223894 + 0.387795i 0.955987 0.293409i \(-0.0947898\pi\)
−0.732093 + 0.681205i \(0.761456\pi\)
\(398\) 7.20640 12.4818i 0.361224 0.625659i
\(399\) −3.18199 −0.159299
\(400\) 10.4746 + 18.1425i 0.523729 + 0.907126i
\(401\) −5.56728 −0.278017 −0.139008 0.990291i \(-0.544391\pi\)
−0.139008 + 0.990291i \(0.544391\pi\)
\(402\) −11.3814 −0.567653
\(403\) −4.72984 + 2.93745i −0.235610 + 0.146325i
\(404\) 0.192294 0.00956697
\(405\) −38.1617 −1.89627
\(406\) 1.40046 + 2.42567i 0.0695038 + 0.120384i
\(407\) 52.0414 2.57960
\(408\) 21.1333 36.6040i 1.04625 1.81217i
\(409\) 10.6233 + 18.4000i 0.525287 + 0.909824i 0.999566 + 0.0294492i \(0.00937534\pi\)
−0.474279 + 0.880374i \(0.657291\pi\)
\(410\) 26.2958 + 45.5457i 1.29866 + 2.24934i
\(411\) −1.75140 −0.0863901
\(412\) 1.71597 2.97215i 0.0845399 0.146427i
\(413\) 1.85250 3.20863i 0.0911558 0.157886i
\(414\) 8.38044 14.5153i 0.411876 0.713390i
\(415\) 15.7138 + 27.2172i 0.771362 + 1.33604i
\(416\) −0.951630 + 1.64827i −0.0466575 + 0.0808132i
\(417\) 4.57790 + 7.92916i 0.224181 + 0.388292i
\(418\) 16.3762 0.800984
\(419\) 9.77903 0.477737 0.238869 0.971052i \(-0.423224\pi\)
0.238869 + 0.971052i \(0.423224\pi\)
\(420\) 0.691538 + 1.19778i 0.0337436 + 0.0584456i
\(421\) −9.29415 + 16.0979i −0.452969 + 0.784565i −0.998569 0.0534804i \(-0.982969\pi\)
0.545600 + 0.838046i \(0.316302\pi\)
\(422\) 16.6593 + 28.8548i 0.810964 + 1.40463i
\(423\) −3.86151 + 6.68833i −0.187753 + 0.325198i
\(424\) −6.63195 + 11.4869i −0.322076 + 0.557852i
\(425\) 21.3104 36.9107i 1.03371 1.79043i
\(426\) −10.2517 −0.496698
\(427\) −2.22769 3.85847i −0.107805 0.186724i
\(428\) 1.38703 + 2.40240i 0.0670445 + 0.116124i
\(429\) −5.13932 + 8.90156i −0.248129 + 0.429771i
\(430\) 36.6967 1.76967
\(431\) −1.49908 2.59648i −0.0722081 0.125068i 0.827661 0.561229i \(-0.189671\pi\)
−0.899869 + 0.436161i \(0.856338\pi\)
\(432\) −9.46154 −0.455219
\(433\) 25.0436 1.20352 0.601759 0.798677i \(-0.294467\pi\)
0.601759 + 0.798677i \(0.294467\pi\)
\(434\) 0.128221 + 3.98657i 0.00615481 + 0.191361i
\(435\) −28.5693 −1.36980
\(436\) −3.74727 −0.179462
\(437\) −10.6371 18.4241i −0.508843 0.881342i
\(438\) −30.2779 −1.44673
\(439\) 3.15891 5.47140i 0.150767 0.261136i −0.780743 0.624853i \(-0.785159\pi\)
0.931510 + 0.363717i \(0.118492\pi\)
\(440\) −24.4709 42.3848i −1.16660 2.02062i
\(441\) 5.44253 + 9.42673i 0.259168 + 0.448892i
\(442\) −8.39589 −0.399352
\(443\) −0.761832 + 1.31953i −0.0361957 + 0.0626928i −0.883556 0.468326i \(-0.844857\pi\)
0.847360 + 0.531019i \(0.178191\pi\)
\(444\) 3.98692 6.90555i 0.189211 0.327723i
\(445\) 8.58314 14.8664i 0.406880 0.704737i
\(446\) −8.70252 15.0732i −0.412076 0.713737i
\(447\) 15.5269 26.8933i 0.734396 1.27201i
\(448\) 2.46307 + 4.26616i 0.116369 + 0.201557i
\(449\) 25.8776 1.22124 0.610621 0.791923i \(-0.290920\pi\)
0.610621 + 0.791923i \(0.290920\pi\)
\(450\) 13.7062 0.646117
\(451\) −28.7129 49.7322i −1.35204 2.34180i
\(452\) −0.113587 + 0.196739i −0.00534271 + 0.00925384i
\(453\) 25.7263 + 44.5593i 1.20873 + 2.09358i
\(454\) −3.55554 + 6.15838i −0.166870 + 0.289027i
\(455\) 0.944509 1.63594i 0.0442793 0.0766939i
\(456\) 8.62623 14.9411i 0.403960 0.699680i
\(457\) 3.70424 0.173277 0.0866386 0.996240i \(-0.472387\pi\)
0.0866386 + 0.996240i \(0.472387\pi\)
\(458\) 2.01453 + 3.48926i 0.0941327 + 0.163043i
\(459\) 9.62468 + 16.6704i 0.449242 + 0.778109i
\(460\) −4.62351 + 8.00816i −0.215572 + 0.373382i
\(461\) −4.70201 −0.218994 −0.109497 0.993987i \(-0.534924\pi\)
−0.109497 + 0.993987i \(0.534924\pi\)
\(462\) 3.68170 + 6.37689i 0.171288 + 0.296680i
\(463\) −2.93054 −0.136194 −0.0680968 0.997679i \(-0.521693\pi\)
−0.0680968 + 0.997679i \(0.521693\pi\)
\(464\) −12.5247 −0.581444
\(465\) −35.8690 19.1988i −1.66338 0.890323i
\(466\) 1.50475 0.0697061
\(467\) −10.4504 −0.483586 −0.241793 0.970328i \(-0.577735\pi\)
−0.241793 + 0.970328i \(0.577735\pi\)
\(468\) 0.276879 + 0.479569i 0.0127988 + 0.0221681i
\(469\) −2.28395 −0.105463
\(470\) −10.3873 + 17.9914i −0.479132 + 0.829881i
\(471\) −9.33053 16.1610i −0.429928 0.744658i
\(472\) 10.0441 + 17.3969i 0.462318 + 0.800758i
\(473\) −40.0698 −1.84241
\(474\) 2.78396 4.82196i 0.127872 0.221480i
\(475\) 8.69851 15.0663i 0.399115 0.691288i
\(476\) 0.616790 1.06831i 0.0282705 0.0489660i
\(477\) 3.57853 + 6.19820i 0.163850 + 0.283796i
\(478\) 11.1757 19.3569i 0.511166 0.885366i
\(479\) −1.32556 2.29594i −0.0605665 0.104904i 0.834152 0.551534i \(-0.185957\pi\)
−0.894719 + 0.446630i \(0.852624\pi\)
\(480\) −13.9072 −0.634774
\(481\) −10.8907 −0.496575
\(482\) 6.38804 + 11.0644i 0.290967 + 0.503970i
\(483\) 4.78289 8.28422i 0.217629 0.376945i
\(484\) 2.01405 + 3.48844i 0.0915477 + 0.158565i
\(485\) 5.42373 9.39418i 0.246279 0.426568i
\(486\) −9.85744 + 17.0736i −0.447143 + 0.774474i
\(487\) 18.0760 31.3085i 0.819101 1.41872i −0.0872448 0.996187i \(-0.527806\pi\)
0.906346 0.422537i \(-0.138860\pi\)
\(488\) 24.1566 1.09352
\(489\) −15.8047 27.3746i −0.714715 1.23792i
\(490\) 14.6402 + 25.3576i 0.661378 + 1.14554i
\(491\) −5.35437 + 9.27404i −0.241639 + 0.418532i −0.961181 0.275917i \(-0.911018\pi\)
0.719542 + 0.694449i \(0.244352\pi\)
\(492\) −8.79883 −0.396682
\(493\) 12.7406 + 22.0674i 0.573810 + 0.993868i
\(494\) −3.42705 −0.154190
\(495\) −26.4085 −1.18697
\(496\) −15.7248 8.41667i −0.706065 0.377920i
\(497\) −2.05725 −0.0922803
\(498\) 25.6367 1.14881
\(499\) 4.74370 + 8.21632i 0.212357 + 0.367813i 0.952452 0.304689i \(-0.0985527\pi\)
−0.740095 + 0.672503i \(0.765219\pi\)
\(500\) −1.78034 −0.0796194
\(501\) −20.8452 + 36.1049i −0.931295 + 1.61305i
\(502\) −9.18558 15.9099i −0.409973 0.710094i
\(503\) −10.0778 17.4552i −0.449346 0.778290i 0.548997 0.835824i \(-0.315010\pi\)
−0.998344 + 0.0575337i \(0.981676\pi\)
\(504\) 2.72762 0.121498
\(505\) 0.959547 1.66198i 0.0426993 0.0739573i
\(506\) −24.6152 + 42.6348i −1.09428 + 1.89535i
\(507\) 1.07551 1.86284i 0.0477650 0.0827314i
\(508\) 3.38821 + 5.86855i 0.150327 + 0.260375i
\(509\) −19.5271 + 33.8218i −0.865521 + 1.49913i 0.00100720 + 0.999999i \(0.499679\pi\)
−0.866529 + 0.499127i \(0.833654\pi\)
\(510\) −30.6745 53.1299i −1.35829 2.35263i
\(511\) −6.07598 −0.268785
\(512\) −25.4134 −1.12312
\(513\) 3.92862 + 6.80457i 0.173453 + 0.300429i
\(514\) −10.8186 + 18.7384i −0.477188 + 0.826514i
\(515\) −17.1254 29.6621i −0.754637 1.30707i
\(516\) −3.06977 + 5.31700i −0.135139 + 0.234068i
\(517\) 11.3421 19.6451i 0.498826 0.863992i
\(518\) −3.90095 + 6.75664i −0.171398 + 0.296870i
\(519\) −2.86009 −0.125544
\(520\) 5.12104 + 8.86990i 0.224573 + 0.388971i
\(521\) −9.22697 15.9816i −0.404241 0.700166i 0.589992 0.807409i \(-0.299131\pi\)
−0.994233 + 0.107243i \(0.965798\pi\)
\(522\) −4.09720 + 7.09656i −0.179330 + 0.310608i
\(523\) −8.69059 −0.380013 −0.190006 0.981783i \(-0.560851\pi\)
−0.190006 + 0.981783i \(0.560851\pi\)
\(524\) 1.40254 + 2.42927i 0.0612703 + 0.106123i
\(525\) 7.82242 0.341398
\(526\) −10.1737 −0.443597
\(527\) 1.16649 + 36.2676i 0.0508130 + 1.57984i
\(528\) −32.9263 −1.43294
\(529\) 40.9553 1.78067
\(530\) 9.62614 + 16.6730i 0.418133 + 0.724227i
\(531\) 10.8394 0.470390
\(532\) 0.251762 0.436065i 0.0109153 0.0189058i
\(533\) 6.00876 + 10.4075i 0.260268 + 0.450798i
\(534\) −7.00159 12.1271i −0.302988 0.524791i
\(535\) 27.6851 1.19693
\(536\) 6.19168 10.7243i 0.267440 0.463219i
\(537\) 19.3373 33.4931i 0.834464 1.44533i
\(538\) 0.179157 0.310310i 0.00772402 0.0133784i
\(539\) −15.9859 27.6884i −0.688563 1.19263i
\(540\) 1.70761 2.95766i 0.0734836 0.127277i
\(541\) 7.83771 + 13.5753i 0.336969 + 0.583648i 0.983861 0.178934i \(-0.0572648\pi\)
−0.646892 + 0.762582i \(0.723931\pi\)
\(542\) 19.0202 0.816989
\(543\) 11.1645 0.479115
\(544\) 6.20199 + 10.7422i 0.265908 + 0.460566i
\(545\) −18.6989 + 32.3875i −0.800973 + 1.38733i
\(546\) −0.770471 1.33450i −0.0329731 0.0571111i
\(547\) −3.74731 + 6.49053i −0.160223 + 0.277515i −0.934949 0.354783i \(-0.884555\pi\)
0.774725 + 0.632298i \(0.217888\pi\)
\(548\) 0.138573 0.240015i 0.00591952 0.0102529i
\(549\) 6.51733 11.2884i 0.278153 0.481775i
\(550\) −40.2582 −1.71662
\(551\) 5.20050 + 9.00753i 0.221549 + 0.383734i
\(552\) 25.9324 + 44.9163i 1.10376 + 1.91176i
\(553\) 0.558668 0.967641i 0.0237570 0.0411483i
\(554\) −35.7584 −1.51923
\(555\) −39.7896 68.9175i −1.68897 2.92539i
\(556\) −1.44883 −0.0614442
\(557\) 5.52145 0.233951 0.116976 0.993135i \(-0.462680\pi\)
0.116976 + 0.993135i \(0.462680\pi\)
\(558\) −9.91300 + 6.15643i −0.419651 + 0.260622i
\(559\) 8.38543 0.354666
\(560\) 6.05124 0.255711
\(561\) 33.4941 + 58.0135i 1.41412 + 2.44933i
\(562\) 6.63281 0.279788
\(563\) 1.13056 1.95818i 0.0476472 0.0825274i −0.841218 0.540696i \(-0.818161\pi\)
0.888865 + 0.458168i \(0.151494\pi\)
\(564\) −1.73785 3.01005i −0.0731768 0.126746i
\(565\) 1.13361 + 1.96346i 0.0476911 + 0.0826035i
\(566\) 15.3707 0.646078
\(567\) −3.12348 + 5.41003i −0.131174 + 0.227200i
\(568\) 5.57712 9.65985i 0.234011 0.405318i
\(569\) −11.6134 + 20.1149i −0.486858 + 0.843262i −0.999886 0.0151096i \(-0.995190\pi\)
0.513028 + 0.858372i \(0.328524\pi\)
\(570\) −12.5208 21.6866i −0.524438 0.908354i
\(571\) −3.97157 + 6.87896i −0.166205 + 0.287876i −0.937083 0.349108i \(-0.886485\pi\)
0.770877 + 0.636983i \(0.219818\pi\)
\(572\) −0.813257 1.40860i −0.0340040 0.0588966i
\(573\) 12.2594 0.512146
\(574\) 8.60910 0.359337
\(575\) 26.1497 + 45.2927i 1.09052 + 1.88883i
\(576\) −7.20596 + 12.4811i −0.300248 + 0.520046i
\(577\) −5.34226 9.25307i −0.222401 0.385211i 0.733135 0.680083i \(-0.238056\pi\)
−0.955537 + 0.294872i \(0.904723\pi\)
\(578\) −16.4087 + 28.4207i −0.682513 + 1.18215i
\(579\) −13.9381 + 24.1415i −0.579248 + 1.00329i
\(580\) 2.26044 3.91519i 0.0938596 0.162570i
\(581\) 5.14462 0.213435
\(582\) −4.42434 7.66319i −0.183395 0.317649i
\(583\) −10.5110 18.2055i −0.435319 0.753995i
\(584\) 16.4717 28.5298i 0.681604 1.18057i
\(585\) 5.52652 0.228494
\(586\) −4.04353 7.00359i −0.167037 0.289316i
\(587\) 22.4935 0.928405 0.464202 0.885729i \(-0.346341\pi\)
0.464202 + 0.885729i \(0.346341\pi\)
\(588\) −4.89876 −0.202022
\(589\) 0.476139 + 14.8038i 0.0196190 + 0.609979i
\(590\) 29.1576 1.20040
\(591\) 6.51907 0.268159
\(592\) −17.4436 30.2132i −0.716927 1.24175i
\(593\) 0.141633 0.00581615 0.00290808 0.999996i \(-0.499074\pi\)
0.00290808 + 0.999996i \(0.499074\pi\)
\(594\) 9.09116 15.7464i 0.373015 0.646081i
\(595\) −6.15557 10.6618i −0.252354 0.437090i
\(596\) 2.45701 + 4.25566i 0.100643 + 0.174319i
\(597\) 24.0651 0.984920
\(598\) 5.15125 8.92222i 0.210650 0.364857i
\(599\) −4.99372 + 8.64938i −0.204038 + 0.353404i −0.949826 0.312779i \(-0.898740\pi\)
0.745788 + 0.666183i \(0.232073\pi\)
\(600\) −21.2062 + 36.7303i −0.865741 + 1.49951i
\(601\) −10.0860 17.4695i −0.411418 0.712597i 0.583627 0.812022i \(-0.301633\pi\)
−0.995045 + 0.0994246i \(0.968300\pi\)
\(602\) 3.00357 5.20234i 0.122416 0.212032i
\(603\) −3.34097 5.78672i −0.136055 0.235654i
\(604\) −8.14198 −0.331293
\(605\) 40.2005 1.63438
\(606\) −0.782738 1.35574i −0.0317966 0.0550733i
\(607\) −0.334064 + 0.578615i −0.0135592 + 0.0234853i −0.872725 0.488211i \(-0.837650\pi\)
0.859166 + 0.511697i \(0.170983\pi\)
\(608\) 2.53154 + 4.38475i 0.102667 + 0.177825i
\(609\) −2.33836 + 4.05016i −0.0947551 + 0.164121i
\(610\) 17.5314 30.3653i 0.709827 1.22946i
\(611\) −2.37357 + 4.11115i −0.0960245 + 0.166319i
\(612\) 3.60897 0.145884
\(613\) −6.57392 11.3864i −0.265518 0.459891i 0.702181 0.711998i \(-0.252210\pi\)
−0.967699 + 0.252107i \(0.918876\pi\)
\(614\) 15.1468 + 26.2350i 0.611275 + 1.05876i
\(615\) −43.9063 + 76.0479i −1.77047 + 3.06655i
\(616\) −8.01163 −0.322798
\(617\) −13.8967 24.0699i −0.559462 0.969017i −0.997541 0.0700803i \(-0.977674\pi\)
0.438079 0.898936i \(-0.355659\pi\)
\(618\) −27.9397 −1.12390
\(619\) −35.9015 −1.44300 −0.721501 0.692413i \(-0.756548\pi\)
−0.721501 + 0.692413i \(0.756548\pi\)
\(620\) 5.46903 3.39652i 0.219641 0.136407i
\(621\) −23.6207 −0.947865
\(622\) 7.66697 0.307418
\(623\) −1.40503 2.43359i −0.0562915 0.0974998i
\(624\) 6.89052 0.275842
\(625\) 7.46536 12.9304i 0.298614 0.517215i
\(626\) 16.2310 + 28.1129i 0.648720 + 1.12362i
\(627\) 13.6717 + 23.6800i 0.545994 + 0.945690i
\(628\) 2.95297 0.117836
\(629\) −35.4887 + 61.4683i −1.41503 + 2.45090i
\(630\) 1.97954 3.42867i 0.0788668 0.136601i
\(631\) 2.24715 3.89218i 0.0894577 0.154945i −0.817824 0.575468i \(-0.804820\pi\)
0.907282 + 0.420523i \(0.138153\pi\)
\(632\) 3.02905 + 5.24646i 0.120489 + 0.208693i
\(633\) −27.8162 + 48.1790i −1.10559 + 1.91495i
\(634\) 3.31554 + 5.74269i 0.131677 + 0.228071i
\(635\) 67.6287 2.68376
\(636\) −3.22100 −0.127721
\(637\) 3.34539 + 5.79438i 0.132549 + 0.229582i
\(638\) 12.0344 20.8442i 0.476447 0.825230i
\(639\) −3.00935 5.21235i −0.119048 0.206198i
\(640\) −12.9184 + 22.3753i −0.510645 + 0.884463i
\(641\) −19.3448 + 33.5063i −0.764076 + 1.32342i 0.176658 + 0.984272i \(0.443471\pi\)
−0.940734 + 0.339145i \(0.889862\pi\)
\(642\) 11.2919 19.5581i 0.445655 0.771898i
\(643\) 21.3222 0.840867 0.420433 0.907323i \(-0.361878\pi\)
0.420433 + 0.907323i \(0.361878\pi\)
\(644\) 0.756856 + 1.31091i 0.0298243 + 0.0516572i
\(645\) 30.6364 + 53.0637i 1.20631 + 2.08938i
\(646\) −11.1674 + 19.3425i −0.439376 + 0.761022i
\(647\) −16.4679 −0.647422 −0.323711 0.946156i \(-0.604930\pi\)
−0.323711 + 0.946156i \(0.604930\pi\)
\(648\) −16.9352 29.3327i −0.665279 1.15230i
\(649\) −31.8377 −1.24974
\(650\) 8.42486 0.330450
\(651\) −5.65756 + 3.51360i −0.221737 + 0.137709i
\(652\) 5.00195 0.195892
\(653\) −33.6345 −1.31622 −0.658110 0.752922i \(-0.728644\pi\)
−0.658110 + 0.752922i \(0.728644\pi\)
\(654\) 15.2534 + 26.4197i 0.596455 + 1.03309i
\(655\) 27.9948 1.09385
\(656\) −19.2483 + 33.3391i −0.751521 + 1.30167i
\(657\) −8.88796 15.3944i −0.346752 0.600593i
\(658\) 1.70038 + 2.94514i 0.0662876 + 0.114814i
\(659\) −8.87797 −0.345837 −0.172918 0.984936i \(-0.555320\pi\)
−0.172918 + 0.984936i \(0.555320\pi\)
\(660\) 5.94250 10.2927i 0.231312 0.400643i
\(661\) −15.8836 + 27.5112i −0.617801 + 1.07006i 0.372085 + 0.928199i \(0.378643\pi\)
−0.989886 + 0.141864i \(0.954690\pi\)
\(662\) 10.1123 17.5149i 0.393024 0.680738i
\(663\) −7.00933 12.1405i −0.272220 0.471499i
\(664\) −13.9468 + 24.1566i −0.541242 + 0.937458i
\(665\) −2.51259 4.35194i −0.0974342 0.168761i
\(666\) −22.8253 −0.884462
\(667\) −31.2678 −1.21069
\(668\) −3.29859 5.71333i −0.127626 0.221055i
\(669\) 14.5306 25.1678i 0.561787 0.973044i
\(670\) −8.98709 15.5661i −0.347202 0.601371i
\(671\) −19.1429 + 33.1564i −0.739002 + 1.27999i
\(672\) −1.13828 + 1.97157i −0.0439103 + 0.0760548i
\(673\) −12.5128 + 21.6728i −0.482334 + 0.835426i −0.999794 0.0202805i \(-0.993544\pi\)
0.517461 + 0.855707i \(0.326877\pi\)
\(674\) −9.28224 −0.357539
\(675\) −9.65790 16.7280i −0.371733 0.643860i
\(676\) 0.170191 + 0.294779i 0.00654580 + 0.0113377i
\(677\) 16.8637 29.2088i 0.648124 1.12258i −0.335446 0.942059i \(-0.608887\pi\)
0.983570 0.180524i \(-0.0577795\pi\)
\(678\) 1.84945 0.0710277
\(679\) −0.887849 1.53780i −0.0340725 0.0590153i
\(680\) 66.7499 2.55974
\(681\) −11.8734 −0.454990
\(682\) 29.1167 18.0828i 1.11494 0.692427i
\(683\) 11.2620 0.430927 0.215464 0.976512i \(-0.430874\pi\)
0.215464 + 0.976512i \(0.430874\pi\)
\(684\) 1.47312 0.0563260
\(685\) −1.38296 2.39535i −0.0528400 0.0915216i
\(686\) 9.80778 0.374463
\(687\) −3.36367 + 5.82604i −0.128332 + 0.222277i
\(688\) 13.4309 + 23.2629i 0.512047 + 0.886891i
\(689\) 2.19963 + 3.80988i 0.0837994 + 0.145145i
\(690\) 75.2807 2.86589
\(691\) −0.00437220 + 0.00757288i −0.000166326 + 0.000288086i −0.866109 0.499856i \(-0.833386\pi\)
0.865942 + 0.500144i \(0.166720\pi\)
\(692\) 0.226294 0.391952i 0.00860240 0.0148998i
\(693\) −2.16150 + 3.74382i −0.0821084 + 0.142216i
\(694\) −12.3302 21.3566i −0.468049 0.810685i
\(695\) −7.22969 + 12.5222i −0.274238 + 0.474994i
\(696\) −12.6784 21.9596i −0.480573 0.832376i
\(697\) 78.3209 2.96662
\(698\) −17.1819 −0.650343
\(699\) 1.25624 + 2.17588i 0.0475155 + 0.0822992i
\(700\) −0.618918 + 1.07200i −0.0233929 + 0.0405177i
\(701\) 12.3747 + 21.4336i 0.467386 + 0.809536i 0.999306 0.0372584i \(-0.0118625\pi\)
−0.531920 + 0.846795i \(0.678529\pi\)
\(702\) −1.90251 + 3.29525i −0.0718058 + 0.124371i
\(703\) −14.4858 + 25.0902i −0.546344 + 0.946296i
\(704\) 21.1655 36.6598i 0.797706 1.38167i
\(705\) −34.6876 −1.30641
\(706\) −19.0292 32.9595i −0.716172 1.24045i
\(707\) −0.157075 0.272062i −0.00590741 0.0102319i
\(708\) −2.43911 + 4.22466i −0.0916673 + 0.158772i
\(709\) −43.2844 −1.62558 −0.812790 0.582557i \(-0.802052\pi\)
−0.812790 + 0.582557i \(0.802052\pi\)
\(710\) −8.09507 14.0211i −0.303802 0.526201i
\(711\) 3.26888 0.122593
\(712\) 15.2359 0.570991
\(713\) −39.2569 21.0122i −1.47018 0.786912i
\(714\) −10.0427 −0.375837
\(715\) −16.2326 −0.607066
\(716\) 3.05997 + 5.30002i 0.114356 + 0.198071i
\(717\) 37.3204 1.39376
\(718\) 5.25634 9.10425i 0.196165 0.339768i
\(719\) 0.693219 + 1.20069i 0.0258527 + 0.0447782i 0.878662 0.477444i \(-0.158437\pi\)
−0.852810 + 0.522222i \(0.825103\pi\)
\(720\) 8.85177 + 15.3317i 0.329886 + 0.571379i
\(721\) −5.60677 −0.208807
\(722\) 7.68015 13.3024i 0.285825 0.495064i
\(723\) −10.6662 + 18.4743i −0.396678 + 0.687067i
\(724\) −0.883348 + 1.53000i −0.0328294 + 0.0568621i
\(725\) −12.7846 22.1436i −0.474809 0.822393i
\(726\) 16.3965 28.3996i 0.608532 1.05401i
\(727\) 11.5948 + 20.0828i 0.430027 + 0.744829i 0.996875 0.0789932i \(-0.0251705\pi\)
−0.566848 + 0.823823i \(0.691837\pi\)
\(728\) 1.67660 0.0621389
\(729\) 0.783665 0.0290246
\(730\) −23.9083 41.4105i −0.884887 1.53267i
\(731\) 27.3249 47.3281i 1.01065 1.75049i
\(732\) 2.93309 + 5.08026i 0.108410 + 0.187772i
\(733\) 0.552407 0.956796i 0.0204036 0.0353401i −0.855643 0.517566i \(-0.826838\pi\)
0.876047 + 0.482226i \(0.160172\pi\)
\(734\) −3.07858 + 5.33226i −0.113633 + 0.196817i
\(735\) −24.4449 + 42.3398i −0.901663 + 1.56173i
\(736\) −15.2208 −0.561045
\(737\) 9.81317 + 16.9969i 0.361473 + 0.626089i
\(738\) 12.5934 + 21.8124i 0.463570 + 0.802927i
\(739\) 13.0859 22.6655i 0.481373 0.833763i −0.518398 0.855139i \(-0.673472\pi\)
0.999771 + 0.0213765i \(0.00680488\pi\)
\(740\) 12.5928 0.462920
\(741\) −2.86108 4.95554i −0.105104 0.182046i
\(742\) 3.15154 0.115697
\(743\) 52.7509 1.93524 0.967621 0.252409i \(-0.0812228\pi\)
0.967621 + 0.252409i \(0.0812228\pi\)
\(744\) −1.16079 36.0903i −0.0425565 1.32314i
\(745\) 49.0419 1.79676
\(746\) −2.88007 −0.105447
\(747\) 7.52556 + 13.0347i 0.275346 + 0.476913i
\(748\) −10.6004 −0.387587
\(749\) 2.26599 3.92480i 0.0827973 0.143409i
\(750\) 7.24696 + 12.5521i 0.264621 + 0.458338i
\(751\) 1.62856 + 2.82074i 0.0594269 + 0.102930i 0.894208 0.447651i \(-0.147739\pi\)
−0.834781 + 0.550582i \(0.814406\pi\)
\(752\) −15.2069 −0.554539
\(753\) 15.3372 26.5648i 0.558919 0.968077i
\(754\) −2.51845 + 4.36208i −0.0917165 + 0.158858i
\(755\) −40.6286 + 70.3707i −1.47862 + 2.56105i
\(756\) −0.279530 0.484160i −0.0101664 0.0176087i
\(757\) 11.7390 20.3325i 0.426660 0.738997i −0.569914 0.821705i \(-0.693023\pi\)
0.996574 + 0.0827074i \(0.0263567\pi\)
\(758\) −2.40246 4.16117i −0.0872611 0.151141i
\(759\) −82.2004 −2.98369
\(760\) 27.2461 0.988320
\(761\) −26.8997 46.5917i −0.975114 1.68895i −0.679558 0.733621i \(-0.737829\pi\)
−0.295556 0.955326i \(-0.595505\pi\)
\(762\) 27.5836 47.7763i 0.999250 1.73075i
\(763\) 3.06096 + 5.30173i 0.110814 + 0.191936i
\(764\) −0.969981 + 1.68006i −0.0350927 + 0.0607823i
\(765\) 18.0088 31.1921i 0.651109 1.12775i
\(766\) −13.0459 + 22.5962i −0.471369 + 0.816435i
\(767\) 6.66271 0.240576
\(768\) −8.51708 14.7520i −0.307334 0.532318i
\(769\) 21.5619 + 37.3463i 0.777542 + 1.34674i 0.933355 + 0.358955i \(0.116867\pi\)
−0.155813 + 0.987787i \(0.549800\pi\)
\(770\) −5.81436 + 10.0708i −0.209535 + 0.362925i
\(771\) −36.1278 −1.30111