Properties

Label 287.2.f.a.50.18
Level $287$
Weight $2$
Character 287.50
Analytic conductor $2.292$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [287,2,Mod(50,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.50");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 287.f (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 50.18
Character \(\chi\) \(=\) 287.50
Dual form 287.2.f.a.155.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.36496i q^{2} +(-0.345245 - 0.345245i) q^{3} -3.59302 q^{4} -3.38746i q^{5} +(0.816490 - 0.816490i) q^{6} +(-0.707107 - 0.707107i) q^{7} -3.76741i q^{8} -2.76161i q^{9} +O(q^{10})\) \(q+2.36496i q^{2} +(-0.345245 - 0.345245i) q^{3} -3.59302 q^{4} -3.38746i q^{5} +(0.816490 - 0.816490i) q^{6} +(-0.707107 - 0.707107i) q^{7} -3.76741i q^{8} -2.76161i q^{9} +8.01120 q^{10} +(-4.52500 - 4.52500i) q^{11} +(1.24047 + 1.24047i) q^{12} +(2.27384 + 2.27384i) q^{13} +(1.67228 - 1.67228i) q^{14} +(-1.16950 + 1.16950i) q^{15} +1.72373 q^{16} +(1.60375 - 1.60375i) q^{17} +6.53109 q^{18} +(-1.78722 + 1.78722i) q^{19} +12.1712i q^{20} +0.488250i q^{21} +(10.7014 - 10.7014i) q^{22} +2.09281 q^{23} +(-1.30068 + 1.30068i) q^{24} -6.47489 q^{25} +(-5.37752 + 5.37752i) q^{26} +(-1.98917 + 1.98917i) q^{27} +(2.54065 + 2.54065i) q^{28} +(5.04961 + 5.04961i) q^{29} +(-2.76583 - 2.76583i) q^{30} -7.03888 q^{31} -3.45827i q^{32} +3.12447i q^{33} +(3.79279 + 3.79279i) q^{34} +(-2.39530 + 2.39530i) q^{35} +9.92251i q^{36} -1.49096 q^{37} +(-4.22669 - 4.22669i) q^{38} -1.57006i q^{39} -12.7620 q^{40} +(6.37022 - 0.648351i) q^{41} -1.15469 q^{42} -8.39742i q^{43} +(16.2584 + 16.2584i) q^{44} -9.35485 q^{45} +4.94941i q^{46} +(3.22472 - 3.22472i) q^{47} +(-0.595110 - 0.595110i) q^{48} +1.00000i q^{49} -15.3128i q^{50} -1.10737 q^{51} +(-8.16993 - 8.16993i) q^{52} +(2.69379 + 2.69379i) q^{53} +(-4.70430 - 4.70430i) q^{54} +(-15.3283 + 15.3283i) q^{55} +(-2.66396 + 2.66396i) q^{56} +1.23406 q^{57} +(-11.9421 + 11.9421i) q^{58} +11.1417 q^{59} +(4.20205 - 4.20205i) q^{60} -3.84534i q^{61} -16.6466i q^{62} +(-1.95275 + 1.95275i) q^{63} +11.6261 q^{64} +(7.70253 - 7.70253i) q^{65} -7.38923 q^{66} +(8.06125 - 8.06125i) q^{67} +(-5.76229 + 5.76229i) q^{68} +(-0.722533 - 0.722533i) q^{69} +(-5.66477 - 5.66477i) q^{70} +(-6.19373 - 6.19373i) q^{71} -10.4041 q^{72} +0.337794i q^{73} -3.52607i q^{74} +(2.23542 + 2.23542i) q^{75} +(6.42150 - 6.42150i) q^{76} +6.39932i q^{77} +3.71313 q^{78} +(-6.02318 - 6.02318i) q^{79} -5.83907i q^{80} -6.91133 q^{81} +(1.53332 + 15.0653i) q^{82} +8.24654 q^{83} -1.75429i q^{84} +(-5.43263 - 5.43263i) q^{85} +19.8595 q^{86} -3.48671i q^{87} +(-17.0475 + 17.0475i) q^{88} +(7.27755 + 7.27755i) q^{89} -22.1238i q^{90} -3.21569i q^{91} -7.51951 q^{92} +(2.43014 + 2.43014i) q^{93} +(7.62632 + 7.62632i) q^{94} +(6.05413 + 6.05413i) q^{95} +(-1.19395 + 1.19395i) q^{96} +(-3.77195 + 3.77195i) q^{97} -2.36496 q^{98} +(-12.4963 + 12.4963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.36496i 1.67228i 0.548519 + 0.836138i \(0.315192\pi\)
−0.548519 + 0.836138i \(0.684808\pi\)
\(3\) −0.345245 0.345245i −0.199327 0.199327i 0.600384 0.799712i \(-0.295014\pi\)
−0.799712 + 0.600384i \(0.795014\pi\)
\(4\) −3.59302 −1.79651
\(5\) 3.38746i 1.51492i −0.652882 0.757459i \(-0.726440\pi\)
0.652882 0.757459i \(-0.273560\pi\)
\(6\) 0.816490 0.816490i 0.333330 0.333330i
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) 3.76741i 1.33198i
\(9\) 2.76161i 0.920537i
\(10\) 8.01120 2.53336
\(11\) −4.52500 4.52500i −1.36434 1.36434i −0.868300 0.496039i \(-0.834787\pi\)
−0.496039 0.868300i \(-0.665213\pi\)
\(12\) 1.24047 + 1.24047i 0.358093 + 0.358093i
\(13\) 2.27384 + 2.27384i 0.630648 + 0.630648i 0.948231 0.317582i \(-0.102871\pi\)
−0.317582 + 0.948231i \(0.602871\pi\)
\(14\) 1.67228 1.67228i 0.446935 0.446935i
\(15\) −1.16950 + 1.16950i −0.301965 + 0.301965i
\(16\) 1.72373 0.430933
\(17\) 1.60375 1.60375i 0.388966 0.388966i −0.485352 0.874319i \(-0.661309\pi\)
0.874319 + 0.485352i \(0.161309\pi\)
\(18\) 6.53109 1.53939
\(19\) −1.78722 + 1.78722i −0.410016 + 0.410016i −0.881744 0.471728i \(-0.843630\pi\)
0.471728 + 0.881744i \(0.343630\pi\)
\(20\) 12.1712i 2.72156i
\(21\) 0.488250i 0.106545i
\(22\) 10.7014 10.7014i 2.28155 2.28155i
\(23\) 2.09281 0.436382 0.218191 0.975906i \(-0.429984\pi\)
0.218191 + 0.975906i \(0.429984\pi\)
\(24\) −1.30068 + 1.30068i −0.265500 + 0.265500i
\(25\) −6.47489 −1.29498
\(26\) −5.37752 + 5.37752i −1.05462 + 1.05462i
\(27\) −1.98917 + 1.98917i −0.382816 + 0.382816i
\(28\) 2.54065 + 2.54065i 0.480137 + 0.480137i
\(29\) 5.04961 + 5.04961i 0.937690 + 0.937690i 0.998169 0.0604796i \(-0.0192630\pi\)
−0.0604796 + 0.998169i \(0.519263\pi\)
\(30\) −2.76583 2.76583i −0.504968 0.504968i
\(31\) −7.03888 −1.26422 −0.632110 0.774879i \(-0.717811\pi\)
−0.632110 + 0.774879i \(0.717811\pi\)
\(32\) 3.45827i 0.611342i
\(33\) 3.12447i 0.543900i
\(34\) 3.79279 + 3.79279i 0.650459 + 0.650459i
\(35\) −2.39530 + 2.39530i −0.404879 + 0.404879i
\(36\) 9.92251i 1.65375i
\(37\) −1.49096 −0.245113 −0.122557 0.992462i \(-0.539109\pi\)
−0.122557 + 0.992462i \(0.539109\pi\)
\(38\) −4.22669 4.22669i −0.685660 0.685660i
\(39\) 1.57006i 0.251411i
\(40\) −12.7620 −2.01784
\(41\) 6.37022 0.648351i 0.994860 0.101255i
\(42\) −1.15469 −0.178173
\(43\) 8.39742i 1.28059i −0.768127 0.640297i \(-0.778811\pi\)
0.768127 0.640297i \(-0.221189\pi\)
\(44\) 16.2584 + 16.2584i 2.45105 + 2.45105i
\(45\) −9.35485 −1.39454
\(46\) 4.94941i 0.729751i
\(47\) 3.22472 3.22472i 0.470373 0.470373i −0.431662 0.902035i \(-0.642073\pi\)
0.902035 + 0.431662i \(0.142073\pi\)
\(48\) −0.595110 0.595110i −0.0858967 0.0858967i
\(49\) 1.00000i 0.142857i
\(50\) 15.3128i 2.16556i
\(51\) −1.10737 −0.155063
\(52\) −8.16993 8.16993i −1.13296 1.13296i
\(53\) 2.69379 + 2.69379i 0.370021 + 0.370021i 0.867485 0.497464i \(-0.165735\pi\)
−0.497464 + 0.867485i \(0.665735\pi\)
\(54\) −4.70430 4.70430i −0.640174 0.640174i
\(55\) −15.3283 + 15.3283i −2.06686 + 2.06686i
\(56\) −2.66396 + 2.66396i −0.355987 + 0.355987i
\(57\) 1.23406 0.163455
\(58\) −11.9421 + 11.9421i −1.56808 + 1.56808i
\(59\) 11.1417 1.45052 0.725261 0.688474i \(-0.241719\pi\)
0.725261 + 0.688474i \(0.241719\pi\)
\(60\) 4.20205 4.20205i 0.542482 0.542482i
\(61\) 3.84534i 0.492346i −0.969226 0.246173i \(-0.920827\pi\)
0.969226 0.246173i \(-0.0791731\pi\)
\(62\) 16.6466i 2.11413i
\(63\) −1.95275 + 1.95275i −0.246024 + 0.246024i
\(64\) 11.6261 1.45327
\(65\) 7.70253 7.70253i 0.955381 0.955381i
\(66\) −7.38923 −0.909552
\(67\) 8.06125 8.06125i 0.984838 0.984838i −0.0150487 0.999887i \(-0.504790\pi\)
0.999887 + 0.0150487i \(0.00479032\pi\)
\(68\) −5.76229 + 5.76229i −0.698781 + 0.698781i
\(69\) −0.722533 0.722533i −0.0869828 0.0869828i
\(70\) −5.66477 5.66477i −0.677070 0.677070i
\(71\) −6.19373 6.19373i −0.735060 0.735060i 0.236557 0.971618i \(-0.423981\pi\)
−0.971618 + 0.236557i \(0.923981\pi\)
\(72\) −10.4041 −1.22614
\(73\) 0.337794i 0.0395358i 0.999805 + 0.0197679i \(0.00629273\pi\)
−0.999805 + 0.0197679i \(0.993707\pi\)
\(74\) 3.52607i 0.409897i
\(75\) 2.23542 + 2.23542i 0.258125 + 0.258125i
\(76\) 6.42150 6.42150i 0.736596 0.736596i
\(77\) 6.39932i 0.729270i
\(78\) 3.71313 0.420429
\(79\) −6.02318 6.02318i −0.677661 0.677661i 0.281810 0.959470i \(-0.409065\pi\)
−0.959470 + 0.281810i \(0.909065\pi\)
\(80\) 5.83907i 0.652828i
\(81\) −6.91133 −0.767926
\(82\) 1.53332 + 15.0653i 0.169327 + 1.66368i
\(83\) 8.24654 0.905175 0.452588 0.891720i \(-0.350501\pi\)
0.452588 + 0.891720i \(0.350501\pi\)
\(84\) 1.75429i 0.191409i
\(85\) −5.43263 5.43263i −0.589252 0.589252i
\(86\) 19.8595 2.14151
\(87\) 3.48671i 0.373815i
\(88\) −17.0475 + 17.0475i −1.81727 + 1.81727i
\(89\) 7.27755 + 7.27755i 0.771419 + 0.771419i 0.978355 0.206936i \(-0.0663491\pi\)
−0.206936 + 0.978355i \(0.566349\pi\)
\(90\) 22.1238i 2.33205i
\(91\) 3.21569i 0.337096i
\(92\) −7.51951 −0.783963
\(93\) 2.43014 + 2.43014i 0.251994 + 0.251994i
\(94\) 7.62632 + 7.62632i 0.786594 + 0.786594i
\(95\) 6.05413 + 6.05413i 0.621140 + 0.621140i
\(96\) −1.19395 + 1.19395i −0.121857 + 0.121857i
\(97\) −3.77195 + 3.77195i −0.382983 + 0.382983i −0.872176 0.489193i \(-0.837292\pi\)
0.489193 + 0.872176i \(0.337292\pi\)
\(98\) −2.36496 −0.238897
\(99\) −12.4963 + 12.4963i −1.25593 + 1.25593i
\(100\) 23.2644 2.32644
\(101\) −5.69636 + 5.69636i −0.566809 + 0.566809i −0.931233 0.364424i \(-0.881266\pi\)
0.364424 + 0.931233i \(0.381266\pi\)
\(102\) 2.61889i 0.259308i
\(103\) 17.2056i 1.69532i 0.530543 + 0.847658i \(0.321988\pi\)
−0.530543 + 0.847658i \(0.678012\pi\)
\(104\) 8.56647 8.56647i 0.840012 0.840012i
\(105\) 1.65393 0.161407
\(106\) −6.37070 + 6.37070i −0.618777 + 0.618777i
\(107\) −13.1102 −1.26741 −0.633704 0.773575i \(-0.718466\pi\)
−0.633704 + 0.773575i \(0.718466\pi\)
\(108\) 7.14711 7.14711i 0.687731 0.687731i
\(109\) 7.54601 7.54601i 0.722776 0.722776i −0.246394 0.969170i \(-0.579246\pi\)
0.969170 + 0.246394i \(0.0792456\pi\)
\(110\) −36.2507 36.2507i −3.45637 3.45637i
\(111\) 0.514748 + 0.514748i 0.0488577 + 0.0488577i
\(112\) −1.21886 1.21886i −0.115172 0.115172i
\(113\) −11.7968 −1.10975 −0.554876 0.831933i \(-0.687234\pi\)
−0.554876 + 0.831933i \(0.687234\pi\)
\(114\) 2.91849i 0.273341i
\(115\) 7.08932i 0.661083i
\(116\) −18.1433 18.1433i −1.68457 1.68457i
\(117\) 6.27945 6.27945i 0.580535 0.580535i
\(118\) 26.3495i 2.42567i
\(119\) −2.26804 −0.207911
\(120\) 4.40601 + 4.40601i 0.402211 + 0.402211i
\(121\) 29.9513i 2.72284i
\(122\) 9.09407 0.823338
\(123\) −2.42313 1.97545i −0.218486 0.178120i
\(124\) 25.2908 2.27118
\(125\) 4.99614i 0.446868i
\(126\) −4.61818 4.61818i −0.411420 0.411420i
\(127\) 2.37889 0.211092 0.105546 0.994414i \(-0.466341\pi\)
0.105546 + 0.994414i \(0.466341\pi\)
\(128\) 20.5787i 1.81892i
\(129\) −2.89917 + 2.89917i −0.255257 + 0.255257i
\(130\) 18.2161 + 18.2161i 1.59766 + 1.59766i
\(131\) 3.83173i 0.334779i −0.985891 0.167390i \(-0.946466\pi\)
0.985891 0.167390i \(-0.0535338\pi\)
\(132\) 11.2263i 0.977121i
\(133\) 2.52751 0.219163
\(134\) 19.0645 + 19.0645i 1.64692 + 1.64692i
\(135\) 6.73823 + 6.73823i 0.579935 + 0.579935i
\(136\) −6.04198 6.04198i −0.518096 0.518096i
\(137\) 2.57611 2.57611i 0.220092 0.220092i −0.588445 0.808537i \(-0.700260\pi\)
0.808537 + 0.588445i \(0.200260\pi\)
\(138\) 1.70876 1.70876i 0.145459 0.145459i
\(139\) −9.28683 −0.787698 −0.393849 0.919175i \(-0.628857\pi\)
−0.393849 + 0.919175i \(0.628857\pi\)
\(140\) 8.60634 8.60634i 0.727368 0.727368i
\(141\) −2.22664 −0.187517
\(142\) 14.6479 14.6479i 1.22922 1.22922i
\(143\) 20.5782i 1.72084i
\(144\) 4.76028i 0.396690i
\(145\) 17.1054 17.1054i 1.42052 1.42052i
\(146\) −0.798868 −0.0661148
\(147\) 0.345245 0.345245i 0.0284753 0.0284753i
\(148\) 5.35706 0.440348
\(149\) 12.4251 12.4251i 1.01790 1.01790i 0.0180632 0.999837i \(-0.494250\pi\)
0.999837 0.0180632i \(-0.00575001\pi\)
\(150\) −5.28668 + 5.28668i −0.431656 + 0.431656i
\(151\) 13.4116 + 13.4116i 1.09142 + 1.09142i 0.995377 + 0.0960425i \(0.0306185\pi\)
0.0960425 + 0.995377i \(0.469382\pi\)
\(152\) 6.73318 + 6.73318i 0.546133 + 0.546133i
\(153\) −4.42893 4.42893i −0.358058 0.358058i
\(154\) −15.1341 −1.21954
\(155\) 23.8439i 1.91519i
\(156\) 5.64125i 0.451662i
\(157\) 10.4505 + 10.4505i 0.834044 + 0.834044i 0.988067 0.154023i \(-0.0492230\pi\)
−0.154023 + 0.988067i \(0.549223\pi\)
\(158\) 14.2446 14.2446i 1.13324 1.13324i
\(159\) 1.86004i 0.147511i
\(160\) −11.7148 −0.926134
\(161\) −1.47984 1.47984i −0.116628 0.116628i
\(162\) 16.3450i 1.28418i
\(163\) 2.73606 0.214305 0.107152 0.994243i \(-0.465827\pi\)
0.107152 + 0.994243i \(0.465827\pi\)
\(164\) −22.8883 + 2.32954i −1.78727 + 0.181906i
\(165\) 10.5840 0.823965
\(166\) 19.5027i 1.51370i
\(167\) 14.1570 + 14.1570i 1.09550 + 1.09550i 0.994930 + 0.100571i \(0.0320670\pi\)
0.100571 + 0.994930i \(0.467933\pi\)
\(168\) 1.83944 0.141916
\(169\) 2.65935i 0.204565i
\(170\) 12.8479 12.8479i 0.985392 0.985392i
\(171\) 4.93560 + 4.93560i 0.377435 + 0.377435i
\(172\) 30.1721i 2.30060i
\(173\) 22.2778i 1.69375i −0.531791 0.846875i \(-0.678481\pi\)
0.531791 0.846875i \(-0.321519\pi\)
\(174\) 8.24591 0.625121
\(175\) 4.57844 + 4.57844i 0.346098 + 0.346098i
\(176\) −7.79989 7.79989i −0.587939 0.587939i
\(177\) −3.84661 3.84661i −0.289129 0.289129i
\(178\) −17.2111 + 17.2111i −1.29003 + 1.29003i
\(179\) 0.620825 0.620825i 0.0464026 0.0464026i −0.683525 0.729927i \(-0.739554\pi\)
0.729927 + 0.683525i \(0.239554\pi\)
\(180\) 33.6121 2.50530
\(181\) 13.5643 13.5643i 1.00822 1.00822i 0.00825740 0.999966i \(-0.497372\pi\)
0.999966 0.00825740i \(-0.00262844\pi\)
\(182\) 7.60496 0.563717
\(183\) −1.32759 + 1.32759i −0.0981380 + 0.0981380i
\(184\) 7.88449i 0.581252i
\(185\) 5.05058i 0.371326i
\(186\) −5.74717 + 5.74717i −0.421403 + 0.421403i
\(187\) −14.5139 −1.06136
\(188\) −11.5865 + 11.5865i −0.845030 + 0.845030i
\(189\) 2.81311 0.204624
\(190\) −14.3177 + 14.3177i −1.03872 + 1.03872i
\(191\) 3.81740 3.81740i 0.276218 0.276218i −0.555379 0.831597i \(-0.687427\pi\)
0.831597 + 0.555379i \(0.187427\pi\)
\(192\) −4.01387 4.01387i −0.289676 0.289676i
\(193\) −11.6632 11.6632i −0.839535 0.839535i 0.149263 0.988798i \(-0.452310\pi\)
−0.988798 + 0.149263i \(0.952310\pi\)
\(194\) −8.92049 8.92049i −0.640454 0.640454i
\(195\) −5.31852 −0.380867
\(196\) 3.59302i 0.256644i
\(197\) 12.8279i 0.913953i −0.889479 0.456976i \(-0.848932\pi\)
0.889479 0.456976i \(-0.151068\pi\)
\(198\) −29.5532 29.5532i −2.10025 2.10025i
\(199\) −16.0847 + 16.0847i −1.14022 + 1.14022i −0.151807 + 0.988410i \(0.548509\pi\)
−0.988410 + 0.151807i \(0.951491\pi\)
\(200\) 24.3936i 1.72489i
\(201\) −5.56621 −0.392610
\(202\) −13.4716 13.4716i −0.947862 0.947862i
\(203\) 7.14123i 0.501216i
\(204\) 3.97881 0.278572
\(205\) −2.19626 21.5789i −0.153394 1.50713i
\(206\) −40.6904 −2.83504
\(207\) 5.77954i 0.401706i
\(208\) 3.91948 + 3.91948i 0.271767 + 0.271767i
\(209\) 16.1743 1.11880
\(210\) 3.91147i 0.269917i
\(211\) −6.58885 + 6.58885i −0.453595 + 0.453595i −0.896546 0.442951i \(-0.853932\pi\)
0.442951 + 0.896546i \(0.353932\pi\)
\(212\) −9.67884 9.67884i −0.664746 0.664746i
\(213\) 4.27671i 0.293035i
\(214\) 31.0050i 2.11946i
\(215\) −28.4459 −1.94000
\(216\) 7.49402 + 7.49402i 0.509903 + 0.509903i
\(217\) 4.97724 + 4.97724i 0.337877 + 0.337877i
\(218\) 17.8460 + 17.8460i 1.20868 + 1.20868i
\(219\) 0.116622 0.116622i 0.00788057 0.00788057i
\(220\) 55.0747 55.0747i 3.71314 3.71314i
\(221\) 7.29332 0.490602
\(222\) −1.21736 + 1.21736i −0.0817037 + 0.0817037i
\(223\) −11.6325 −0.778967 −0.389483 0.921033i \(-0.627346\pi\)
−0.389483 + 0.921033i \(0.627346\pi\)
\(224\) −2.44537 + 2.44537i −0.163388 + 0.163388i
\(225\) 17.8811i 1.19208i
\(226\) 27.8990i 1.85581i
\(227\) 1.05806 1.05806i 0.0702258 0.0702258i −0.671122 0.741347i \(-0.734187\pi\)
0.741347 + 0.671122i \(0.234187\pi\)
\(228\) −4.43398 −0.293648
\(229\) 14.7703 14.7703i 0.976047 0.976047i −0.0236727 0.999720i \(-0.507536\pi\)
0.999720 + 0.0236727i \(0.00753597\pi\)
\(230\) 16.7659 1.10551
\(231\) 2.20933 2.20933i 0.145363 0.145363i
\(232\) 19.0240 19.0240i 1.24899 1.24899i
\(233\) 3.21122 + 3.21122i 0.210374 + 0.210374i 0.804426 0.594052i \(-0.202473\pi\)
−0.594052 + 0.804426i \(0.702473\pi\)
\(234\) 14.8506 + 14.8506i 0.970815 + 0.970815i
\(235\) −10.9236 10.9236i −0.712577 0.712577i
\(236\) −40.0322 −2.60587
\(237\) 4.15895i 0.270153i
\(238\) 5.36382i 0.347685i
\(239\) 7.46058 + 7.46058i 0.482585 + 0.482585i 0.905956 0.423371i \(-0.139153\pi\)
−0.423371 + 0.905956i \(0.639153\pi\)
\(240\) −2.01591 + 2.01591i −0.130127 + 0.130127i
\(241\) 18.7378i 1.20701i 0.797361 + 0.603503i \(0.206229\pi\)
−0.797361 + 0.603503i \(0.793771\pi\)
\(242\) −70.8335 −4.55335
\(243\) 8.35361 + 8.35361i 0.535884 + 0.535884i
\(244\) 13.8164i 0.884503i
\(245\) 3.38746 0.216417
\(246\) 4.67184 5.73059i 0.297866 0.365369i
\(247\) −8.12767 −0.517151
\(248\) 26.5184i 1.68392i
\(249\) −2.84708 2.84708i −0.180426 0.180426i
\(250\) −11.8156 −0.747287
\(251\) 9.37994i 0.592057i −0.955179 0.296028i \(-0.904338\pi\)
0.955179 0.296028i \(-0.0956623\pi\)
\(252\) 7.01628 7.01628i 0.441984 0.441984i
\(253\) −9.46998 9.46998i −0.595373 0.595373i
\(254\) 5.62596i 0.353004i
\(255\) 3.75118i 0.234908i
\(256\) −25.4155 −1.58847
\(257\) −3.54473 3.54473i −0.221114 0.221114i 0.587853 0.808967i \(-0.299973\pi\)
−0.808967 + 0.587853i \(0.799973\pi\)
\(258\) −6.85640 6.85640i −0.426861 0.426861i
\(259\) 1.05427 + 1.05427i 0.0655092 + 0.0655092i
\(260\) −27.6753 + 27.6753i −1.71635 + 1.71635i
\(261\) 13.9451 13.9451i 0.863178 0.863178i
\(262\) 9.06186 0.559844
\(263\) −1.21091 + 1.21091i −0.0746679 + 0.0746679i −0.743454 0.668787i \(-0.766814\pi\)
0.668787 + 0.743454i \(0.266814\pi\)
\(264\) 11.7712 0.724465
\(265\) 9.12512 9.12512i 0.560552 0.560552i
\(266\) 5.97744i 0.366500i
\(267\) 5.02508i 0.307530i
\(268\) −28.9642 + 28.9642i −1.76927 + 1.76927i
\(269\) −13.9173 −0.848555 −0.424277 0.905532i \(-0.639472\pi\)
−0.424277 + 0.905532i \(0.639472\pi\)
\(270\) −15.9356 + 15.9356i −0.969811 + 0.969811i
\(271\) 26.4290 1.60545 0.802724 0.596351i \(-0.203383\pi\)
0.802724 + 0.596351i \(0.203383\pi\)
\(272\) 2.76443 2.76443i 0.167618 0.167618i
\(273\) −1.11020 + 1.11020i −0.0671924 + 0.0671924i
\(274\) 6.09238 + 6.09238i 0.368054 + 0.368054i
\(275\) 29.2989 + 29.2989i 1.76679 + 1.76679i
\(276\) 2.59607 + 2.59607i 0.156265 + 0.156265i
\(277\) −14.9441 −0.897903 −0.448952 0.893556i \(-0.648202\pi\)
−0.448952 + 0.893556i \(0.648202\pi\)
\(278\) 21.9629i 1.31725i
\(279\) 19.4387i 1.16376i
\(280\) 9.02407 + 9.02407i 0.539291 + 0.539291i
\(281\) −4.51235 + 4.51235i −0.269184 + 0.269184i −0.828772 0.559587i \(-0.810960\pi\)
0.559587 + 0.828772i \(0.310960\pi\)
\(282\) 5.26590i 0.313580i
\(283\) 1.27954 0.0760606 0.0380303 0.999277i \(-0.487892\pi\)
0.0380303 + 0.999277i \(0.487892\pi\)
\(284\) 22.2542 + 22.2542i 1.32054 + 1.32054i
\(285\) 4.18032i 0.247621i
\(286\) 48.6666 2.87771
\(287\) −4.96288 4.04597i −0.292949 0.238826i
\(288\) −9.55041 −0.562763
\(289\) 11.8560i 0.697411i
\(290\) 40.4534 + 40.4534i 2.37551 + 2.37551i
\(291\) 2.60449 0.152678
\(292\) 1.21370i 0.0710264i
\(293\) 9.79823 9.79823i 0.572419 0.572419i −0.360385 0.932804i \(-0.617355\pi\)
0.932804 + 0.360385i \(0.117355\pi\)
\(294\) 0.816490 + 0.816490i 0.0476186 + 0.0476186i
\(295\) 37.7420i 2.19742i
\(296\) 5.61708i 0.326486i
\(297\) 18.0020 1.04458
\(298\) 29.3847 + 29.3847i 1.70221 + 1.70221i
\(299\) 4.75871 + 4.75871i 0.275203 + 0.275203i
\(300\) −8.03192 8.03192i −0.463723 0.463723i
\(301\) −5.93787 + 5.93787i −0.342253 + 0.342253i
\(302\) −31.7178 + 31.7178i −1.82516 + 1.82516i
\(303\) 3.93328 0.225961
\(304\) −3.08068 + 3.08068i −0.176689 + 0.176689i
\(305\) −13.0259 −0.745864
\(306\) 10.4742 10.4742i 0.598771 0.598771i
\(307\) 15.9502i 0.910328i −0.890408 0.455164i \(-0.849581\pi\)
0.890408 0.455164i \(-0.150419\pi\)
\(308\) 22.9929i 1.31014i
\(309\) 5.94014 5.94014i 0.337923 0.337923i
\(310\) −56.3898 −3.20273
\(311\) 1.31932 1.31932i 0.0748115 0.0748115i −0.668711 0.743522i \(-0.733154\pi\)
0.743522 + 0.668711i \(0.233154\pi\)
\(312\) −5.91507 −0.334875
\(313\) −2.61177 + 2.61177i −0.147626 + 0.147626i −0.777057 0.629431i \(-0.783288\pi\)
0.629431 + 0.777057i \(0.283288\pi\)
\(314\) −24.7151 + 24.7151i −1.39475 + 1.39475i
\(315\) 6.61488 + 6.61488i 0.372706 + 0.372706i
\(316\) 21.6414 + 21.6414i 1.21742 + 1.21742i
\(317\) −8.17711 8.17711i −0.459272 0.459272i 0.439144 0.898416i \(-0.355282\pi\)
−0.898416 + 0.439144i \(0.855282\pi\)
\(318\) 4.39891 0.246679
\(319\) 45.6990i 2.55865i
\(320\) 39.3831i 2.20158i
\(321\) 4.52622 + 4.52622i 0.252629 + 0.252629i
\(322\) 3.49976 3.49976i 0.195034 0.195034i
\(323\) 5.73249i 0.318964i
\(324\) 24.8325 1.37959
\(325\) −14.7228 14.7228i −0.816676 0.816676i
\(326\) 6.47067i 0.358377i
\(327\) −5.21044 −0.288138
\(328\) −2.44261 23.9992i −0.134870 1.32514i
\(329\) −4.56044 −0.251425
\(330\) 25.0307i 1.37790i
\(331\) −5.68372 5.68372i −0.312405 0.312405i 0.533435 0.845841i \(-0.320901\pi\)
−0.845841 + 0.533435i \(0.820901\pi\)
\(332\) −29.6299 −1.62615
\(333\) 4.11747i 0.225636i
\(334\) −33.4807 + 33.4807i −1.83198 + 1.83198i
\(335\) −27.3072 27.3072i −1.49195 1.49195i
\(336\) 0.841613i 0.0459137i
\(337\) 26.9418i 1.46761i −0.679359 0.733806i \(-0.737742\pi\)
0.679359 0.733806i \(-0.262258\pi\)
\(338\) 6.28924 0.342090
\(339\) 4.07279 + 4.07279i 0.221204 + 0.221204i
\(340\) 19.5195 + 19.5195i 1.05860 + 1.05860i
\(341\) 31.8509 + 31.8509i 1.72483 + 1.72483i
\(342\) −11.6725 + 11.6725i −0.631175 + 0.631175i
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) −31.6365 −1.70573
\(345\) −2.44755 + 2.44755i −0.131772 + 0.131772i
\(346\) 52.6860 2.83242
\(347\) 21.5790 21.5790i 1.15842 1.15842i 0.173609 0.984815i \(-0.444457\pi\)
0.984815 0.173609i \(-0.0555430\pi\)
\(348\) 12.5278i 0.671561i
\(349\) 11.3453i 0.607298i 0.952784 + 0.303649i \(0.0982051\pi\)
−0.952784 + 0.303649i \(0.901795\pi\)
\(350\) −10.8278 + 10.8278i −0.578771 + 0.578771i
\(351\) −9.04608 −0.482844
\(352\) −15.6487 + 15.6487i −0.834079 + 0.834079i
\(353\) −11.8800 −0.632308 −0.316154 0.948708i \(-0.602392\pi\)
−0.316154 + 0.948708i \(0.602392\pi\)
\(354\) 9.09705 9.09705i 0.483503 0.483503i
\(355\) −20.9810 + 20.9810i −1.11356 + 1.11356i
\(356\) −26.1484 26.1484i −1.38586 1.38586i
\(357\) 0.783031 + 0.783031i 0.0414424 + 0.0414424i
\(358\) 1.46822 + 1.46822i 0.0775980 + 0.0775980i
\(359\) 11.8506 0.625452 0.312726 0.949843i \(-0.398758\pi\)
0.312726 + 0.949843i \(0.398758\pi\)
\(360\) 35.2436i 1.85750i
\(361\) 12.6117i 0.663774i
\(362\) 32.0789 + 32.0789i 1.68603 + 1.68603i
\(363\) 10.3405 10.3405i 0.542737 0.542737i
\(364\) 11.5540i 0.605595i
\(365\) 1.14426 0.0598935
\(366\) −3.13968 3.13968i −0.164114 0.164114i
\(367\) 0.112635i 0.00587948i −0.999996 0.00293974i \(-0.999064\pi\)
0.999996 0.00293974i \(-0.000935750\pi\)
\(368\) 3.60745 0.188051
\(369\) −1.79049 17.5921i −0.0932094 0.915806i
\(370\) −11.9444 −0.620960
\(371\) 3.80960i 0.197785i
\(372\) −8.73153 8.73153i −0.452709 0.452709i
\(373\) −7.31055 −0.378526 −0.189263 0.981926i \(-0.560610\pi\)
−0.189263 + 0.981926i \(0.560610\pi\)
\(374\) 34.3248i 1.77489i
\(375\) 1.72489 1.72489i 0.0890731 0.0890731i
\(376\) −12.1488 12.1488i −0.626529 0.626529i
\(377\) 22.9640i 1.18271i
\(378\) 6.65288i 0.342187i
\(379\) −12.5411 −0.644194 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(380\) −21.7526 21.7526i −1.11588 1.11588i
\(381\) −0.821299 0.821299i −0.0420764 0.0420764i
\(382\) 9.02799 + 9.02799i 0.461912 + 0.461912i
\(383\) 17.0533 17.0533i 0.871382 0.871382i −0.121241 0.992623i \(-0.538687\pi\)
0.992623 + 0.121241i \(0.0386873\pi\)
\(384\) 7.10471 7.10471i 0.362561 0.362561i
\(385\) 21.6774 1.10478
\(386\) 27.5829 27.5829i 1.40393 1.40393i
\(387\) −23.1904 −1.17883
\(388\) 13.5527 13.5527i 0.688033 0.688033i
\(389\) 9.88763i 0.501323i −0.968075 0.250661i \(-0.919352\pi\)
0.968075 0.250661i \(-0.0806481\pi\)
\(390\) 12.5781i 0.636915i
\(391\) 3.35634 3.35634i 0.169738 0.169738i
\(392\) 3.76741 0.190283
\(393\) −1.32288 + 1.32288i −0.0667307 + 0.0667307i
\(394\) 30.3375 1.52838
\(395\) −20.4033 + 20.4033i −1.02660 + 1.02660i
\(396\) 44.8994 44.8994i 2.25628 2.25628i
\(397\) 15.9964 + 15.9964i 0.802837 + 0.802837i 0.983538 0.180701i \(-0.0578367\pi\)
−0.180701 + 0.983538i \(0.557837\pi\)
\(398\) −38.0397 38.0397i −1.90676 1.90676i
\(399\) −0.872609 0.872609i −0.0436851 0.0436851i
\(400\) −11.1610 −0.558049
\(401\) 13.3023i 0.664286i 0.943229 + 0.332143i \(0.107772\pi\)
−0.943229 + 0.332143i \(0.892228\pi\)
\(402\) 13.1638i 0.656553i
\(403\) −16.0053 16.0053i −0.797278 0.797278i
\(404\) 20.4671 20.4671i 1.01828 1.01828i
\(405\) 23.4119i 1.16335i
\(406\) 16.8887 0.838172
\(407\) 6.74662 + 6.74662i 0.334417 + 0.334417i
\(408\) 4.17193i 0.206541i
\(409\) −10.0331 −0.496105 −0.248053 0.968747i \(-0.579791\pi\)
−0.248053 + 0.968747i \(0.579791\pi\)
\(410\) 51.0330 5.19407i 2.52034 0.256517i
\(411\) −1.77878 −0.0877406
\(412\) 61.8199i 3.04565i
\(413\) −7.87835 7.87835i −0.387668 0.387668i
\(414\) 13.6683 0.671763
\(415\) 27.9348i 1.37127i
\(416\) 7.86355 7.86355i 0.385542 0.385542i
\(417\) 3.20623 + 3.20623i 0.157010 + 0.157010i
\(418\) 38.2515i 1.87094i
\(419\) 38.0389i 1.85832i 0.369676 + 0.929161i \(0.379469\pi\)
−0.369676 + 0.929161i \(0.620531\pi\)
\(420\) −5.94259 −0.289969
\(421\) 6.25574 + 6.25574i 0.304886 + 0.304886i 0.842922 0.538036i \(-0.180833\pi\)
−0.538036 + 0.842922i \(0.680833\pi\)
\(422\) −15.5823 15.5823i −0.758536 0.758536i
\(423\) −8.90542 8.90542i −0.432996 0.432996i
\(424\) 10.1486 10.1486i 0.492861 0.492861i
\(425\) −10.3841 + 10.3841i −0.503703 + 0.503703i
\(426\) −10.1142 −0.490036
\(427\) −2.71907 + 2.71907i −0.131585 + 0.131585i
\(428\) 47.1051 2.27691
\(429\) −7.10453 + 7.10453i −0.343010 + 0.343010i
\(430\) 67.2734i 3.24421i
\(431\) 24.9643i 1.20249i 0.799066 + 0.601243i \(0.205328\pi\)
−0.799066 + 0.601243i \(0.794672\pi\)
\(432\) −3.42879 + 3.42879i −0.164968 + 0.164968i
\(433\) 31.2296 1.50080 0.750400 0.660984i \(-0.229861\pi\)
0.750400 + 0.660984i \(0.229861\pi\)
\(434\) −11.7710 + 11.7710i −0.565024 + 0.565024i
\(435\) −11.8111 −0.566299
\(436\) −27.1129 + 27.1129i −1.29847 + 1.29847i
\(437\) −3.74031 + 3.74031i −0.178923 + 0.178923i
\(438\) 0.275805 + 0.275805i 0.0131785 + 0.0131785i
\(439\) 1.37084 + 1.37084i 0.0654266 + 0.0654266i 0.739063 0.673636i \(-0.235269\pi\)
−0.673636 + 0.739063i \(0.735269\pi\)
\(440\) 57.7479 + 57.7479i 2.75302 + 2.75302i
\(441\) 2.76161 0.131505
\(442\) 17.2484i 0.820421i
\(443\) 14.0283i 0.666503i −0.942838 0.333251i \(-0.891854\pi\)
0.942838 0.333251i \(-0.108146\pi\)
\(444\) −1.84950 1.84950i −0.0877733 0.0877733i
\(445\) 24.6524 24.6524i 1.16864 1.16864i
\(446\) 27.5102i 1.30265i
\(447\) −8.57938 −0.405791
\(448\) −8.22092 8.22092i −0.388402 0.388402i
\(449\) 19.4083i 0.915937i −0.888969 0.457968i \(-0.848577\pi\)
0.888969 0.457968i \(-0.151423\pi\)
\(450\) −42.2881 −1.99348
\(451\) −31.7590 25.8914i −1.49547 1.21918i
\(452\) 42.3862 1.99368
\(453\) 9.26057i 0.435100i
\(454\) 2.50226 + 2.50226i 0.117437 + 0.117437i
\(455\) −10.8930 −0.510673
\(456\) 4.64920i 0.217719i
\(457\) −7.73063 + 7.73063i −0.361624 + 0.361624i −0.864410 0.502787i \(-0.832308\pi\)
0.502787 + 0.864410i \(0.332308\pi\)
\(458\) 34.9310 + 34.9310i 1.63222 + 1.63222i
\(459\) 6.38025i 0.297805i
\(460\) 25.4720i 1.18764i
\(461\) −6.71449 −0.312725 −0.156362 0.987700i \(-0.549977\pi\)
−0.156362 + 0.987700i \(0.549977\pi\)
\(462\) 5.22498 + 5.22498i 0.243088 + 0.243088i
\(463\) −1.67116 1.67116i −0.0776654 0.0776654i 0.667207 0.744872i \(-0.267490\pi\)
−0.744872 + 0.667207i \(0.767490\pi\)
\(464\) 8.70418 + 8.70418i 0.404081 + 0.404081i
\(465\) 8.23200 8.23200i 0.381750 0.381750i
\(466\) −7.59440 + 7.59440i −0.351804 + 0.351804i
\(467\) 16.5906 0.767720 0.383860 0.923391i \(-0.374594\pi\)
0.383860 + 0.923391i \(0.374594\pi\)
\(468\) −22.5622 + 22.5622i −1.04294 + 1.04294i
\(469\) −11.4003 −0.526418
\(470\) 25.8338 25.8338i 1.19163 1.19163i
\(471\) 7.21600i 0.332496i
\(472\) 41.9753i 1.93207i
\(473\) −37.9983 + 37.9983i −1.74716 + 1.74716i
\(474\) −9.83573 −0.451770
\(475\) 11.5720 11.5720i 0.530961 0.530961i
\(476\) 8.14911 0.373514
\(477\) 7.43921 7.43921i 0.340618 0.340618i
\(478\) −17.6439 + 17.6439i −0.807015 + 0.807015i
\(479\) −12.8402 12.8402i −0.586683 0.586683i 0.350048 0.936732i \(-0.386165\pi\)
−0.936732 + 0.350048i \(0.886165\pi\)
\(480\) 4.04447 + 4.04447i 0.184604 + 0.184604i
\(481\) −3.39021 3.39021i −0.154580 0.154580i
\(482\) −44.3140 −2.01845
\(483\) 1.02182i 0.0464943i
\(484\) 107.615i 4.89161i
\(485\) 12.7773 + 12.7773i 0.580189 + 0.580189i
\(486\) −19.7559 + 19.7559i −0.896147 + 0.896147i
\(487\) 31.7450i 1.43850i 0.694750 + 0.719251i \(0.255515\pi\)
−0.694750 + 0.719251i \(0.744485\pi\)
\(488\) −14.4870 −0.655795
\(489\) −0.944612 0.944612i −0.0427168 0.0427168i
\(490\) 8.01120i 0.361909i
\(491\) −22.1790 −1.00092 −0.500461 0.865759i \(-0.666836\pi\)
−0.500461 + 0.865759i \(0.666836\pi\)
\(492\) 8.70633 + 7.09781i 0.392512 + 0.319994i
\(493\) 16.1966 0.729459
\(494\) 19.2216i 0.864820i
\(495\) 42.3307 + 42.3307i 1.90262 + 1.90262i
\(496\) −12.1331 −0.544794
\(497\) 8.75925i 0.392906i
\(498\) 6.73321 6.73321i 0.301722 0.301722i
\(499\) 15.4353 + 15.4353i 0.690977 + 0.690977i 0.962447 0.271470i \(-0.0875097\pi\)
−0.271470 + 0.962447i \(0.587510\pi\)
\(500\) 17.9512i 0.802802i
\(501\) 9.77527i 0.436727i
\(502\) 22.1831 0.990082
\(503\) 20.2826 + 20.2826i 0.904356 + 0.904356i 0.995809 0.0914529i \(-0.0291511\pi\)
−0.0914529 + 0.995809i \(0.529151\pi\)
\(504\) 7.35683 + 7.35683i 0.327699 + 0.327699i
\(505\) 19.2962 + 19.2962i 0.858670 + 0.858670i
\(506\) 22.3961 22.3961i 0.995628 0.995628i
\(507\) −0.918127 + 0.918127i −0.0407754 + 0.0407754i
\(508\) −8.54738 −0.379229
\(509\) −5.12520 + 5.12520i −0.227171 + 0.227171i −0.811510 0.584339i \(-0.801354\pi\)
0.584339 + 0.811510i \(0.301354\pi\)
\(510\) −8.87138 −0.392831
\(511\) 0.238857 0.238857i 0.0105664 0.0105664i
\(512\) 18.9492i 0.837442i
\(513\) 7.11015i 0.313921i
\(514\) 8.38313 8.38313i 0.369764 0.369764i
\(515\) 58.2832 2.56827
\(516\) 10.4168 10.4168i 0.458572 0.458572i
\(517\) −29.1837 −1.28350
\(518\) −2.49330 + 2.49330i −0.109550 + 0.109550i
\(519\) −7.69131 + 7.69131i −0.337611 + 0.337611i
\(520\) −29.0186 29.0186i −1.27255 1.27255i
\(521\) −12.4076 12.4076i −0.543586 0.543586i 0.380992 0.924578i \(-0.375583\pi\)
−0.924578 + 0.380992i \(0.875583\pi\)
\(522\) 32.9795 + 32.9795i 1.44347 + 1.44347i
\(523\) −7.87303 −0.344264 −0.172132 0.985074i \(-0.555065\pi\)
−0.172132 + 0.985074i \(0.555065\pi\)
\(524\) 13.7675i 0.601434i
\(525\) 3.16137i 0.137973i
\(526\) −2.86375 2.86375i −0.124865 0.124865i
\(527\) −11.2886 + 11.2886i −0.491739 + 0.491739i
\(528\) 5.38575i 0.234385i
\(529\) −18.6201 −0.809571
\(530\) 21.5805 + 21.5805i 0.937397 + 0.937397i
\(531\) 30.7690i 1.33526i
\(532\) −9.08137 −0.393727
\(533\) 15.9591 + 13.0106i 0.691264 + 0.563551i
\(534\) 11.8841 0.514275
\(535\) 44.4102i 1.92002i
\(536\) −30.3700 30.3700i −1.31179 1.31179i
\(537\) −0.428674 −0.0184986
\(538\) 32.9139i 1.41902i
\(539\) 4.52500 4.52500i 0.194906 0.194906i
\(540\) −24.2106 24.2106i −1.04186 1.04186i
\(541\) 20.9792i 0.901967i 0.892532 + 0.450983i \(0.148927\pi\)
−0.892532 + 0.450983i \(0.851073\pi\)
\(542\) 62.5034i 2.68475i
\(543\) −9.36599 −0.401933
\(544\) −5.54620 5.54620i −0.237791 0.237791i
\(545\) −25.5618 25.5618i −1.09495 1.09495i
\(546\) −2.62558 2.62558i −0.112364 0.112364i
\(547\) 2.82793 2.82793i 0.120914 0.120914i −0.644061 0.764974i \(-0.722752\pi\)
0.764974 + 0.644061i \(0.222752\pi\)
\(548\) −9.25599 + 9.25599i −0.395396 + 0.395396i
\(549\) −10.6193 −0.453223
\(550\) −69.2906 + 69.2906i −2.95456 + 2.95456i
\(551\) −18.0495 −0.768935
\(552\) −2.72208 + 2.72208i −0.115859 + 0.115859i
\(553\) 8.51806i 0.362225i
\(554\) 35.3421i 1.50154i
\(555\) 1.74369 1.74369i 0.0740155 0.0740155i
\(556\) 33.3677 1.41511
\(557\) 4.53365 4.53365i 0.192097 0.192097i −0.604505 0.796602i \(-0.706629\pi\)
0.796602 + 0.604505i \(0.206629\pi\)
\(558\) −45.9716 −1.94613
\(559\) 19.0943 19.0943i 0.807605 0.807605i
\(560\) −4.12885 + 4.12885i −0.174476 + 0.174476i
\(561\) 5.01086 + 5.01086i 0.211559 + 0.211559i
\(562\) −10.6715 10.6715i −0.450151 0.450151i
\(563\) −7.17733 7.17733i −0.302488 0.302488i 0.539498 0.841987i \(-0.318614\pi\)
−0.841987 + 0.539498i \(0.818614\pi\)
\(564\) 8.00034 0.336875
\(565\) 39.9613i 1.68118i
\(566\) 3.02605i 0.127194i
\(567\) 4.88705 + 4.88705i 0.205237 + 0.205237i
\(568\) −23.3343 + 23.3343i −0.979087 + 0.979087i
\(569\) 7.20779i 0.302166i −0.988521 0.151083i \(-0.951724\pi\)
0.988521 0.151083i \(-0.0482761\pi\)
\(570\) 9.88626 0.414090
\(571\) 23.6673 + 23.6673i 0.990447 + 0.990447i 0.999955 0.00950800i \(-0.00302654\pi\)
−0.00950800 + 0.999955i \(0.503027\pi\)
\(572\) 73.9379i 3.09150i
\(573\) −2.63588 −0.110116
\(574\) 9.56854 11.7370i 0.399383 0.489892i
\(575\) −13.5507 −0.565105
\(576\) 32.1069i 1.33779i
\(577\) 24.2356 + 24.2356i 1.00894 + 1.00894i 0.999960 + 0.00898091i \(0.00285875\pi\)
0.00898091 + 0.999960i \(0.497141\pi\)
\(578\) −28.0389 −1.16626
\(579\) 8.05332i 0.334685i
\(580\) −61.4599 + 61.4599i −2.55198 + 2.55198i
\(581\) −5.83118 5.83118i −0.241918 0.241918i
\(582\) 6.15951i 0.255320i
\(583\) 24.3788i 1.00967i
\(584\) 1.27261 0.0526610
\(585\) −21.2714 21.2714i −0.879464 0.879464i
\(586\) 23.1724 + 23.1724i 0.957242 + 0.957242i
\(587\) 13.7688 + 13.7688i 0.568301 + 0.568301i 0.931652 0.363351i \(-0.118368\pi\)
−0.363351 + 0.931652i \(0.618368\pi\)
\(588\) −1.24047 + 1.24047i −0.0511562 + 0.0511562i
\(589\) 12.5800 12.5800i 0.518350 0.518350i
\(590\) 89.2581 3.67470
\(591\) −4.42878 + 4.42878i −0.182176 + 0.182176i
\(592\) −2.57002 −0.105627
\(593\) −28.3190 + 28.3190i −1.16292 + 1.16292i −0.179091 + 0.983833i \(0.557316\pi\)
−0.983833 + 0.179091i \(0.942684\pi\)
\(594\) 42.5739i 1.74683i
\(595\) 7.68291i 0.314968i
\(596\) −44.6434 + 44.6434i −1.82867 + 1.82867i
\(597\) 11.1064 0.454553
\(598\) −11.2541 + 11.2541i −0.460216 + 0.460216i
\(599\) 15.7542 0.643699 0.321850 0.946791i \(-0.395695\pi\)
0.321850 + 0.946791i \(0.395695\pi\)
\(600\) 8.42177 8.42177i 0.343817 0.343817i
\(601\) −27.4544 + 27.4544i −1.11989 + 1.11989i −0.128131 + 0.991757i \(0.540898\pi\)
−0.991757 + 0.128131i \(0.959102\pi\)
\(602\) −14.0428 14.0428i −0.572342 0.572342i
\(603\) −22.2620 22.2620i −0.906580 0.906580i
\(604\) −48.1881 48.1881i −1.96074 1.96074i
\(605\) 101.459 4.12489
\(606\) 9.30204i 0.377870i
\(607\) 2.17266i 0.0881857i 0.999027 + 0.0440928i \(0.0140397\pi\)
−0.999027 + 0.0440928i \(0.985960\pi\)
\(608\) 6.18069 + 6.18069i 0.250660 + 0.250660i
\(609\) −2.46548 + 2.46548i −0.0999061 + 0.0999061i
\(610\) 30.8058i 1.24729i
\(611\) 14.6650 0.593281
\(612\) 15.9132 + 15.9132i 0.643254 + 0.643254i
\(613\) 2.17153i 0.0877073i 0.999038 + 0.0438536i \(0.0139635\pi\)
−0.999038 + 0.0438536i \(0.986036\pi\)
\(614\) 37.7216 1.52232
\(615\) −6.69175 + 8.20824i −0.269837 + 0.330988i
\(616\) 24.1089 0.971374
\(617\) 35.5485i 1.43113i −0.698548 0.715564i \(-0.746170\pi\)
0.698548 0.715564i \(-0.253830\pi\)
\(618\) 14.0482 + 14.0482i 0.565101 + 0.565101i
\(619\) −0.332688 −0.0133719 −0.00668593 0.999978i \(-0.502128\pi\)
−0.00668593 + 0.999978i \(0.502128\pi\)
\(620\) 85.6716i 3.44066i
\(621\) −4.16296 + 4.16296i −0.167054 + 0.167054i
\(622\) 3.12012 + 3.12012i 0.125106 + 0.125106i
\(623\) 10.2920i 0.412341i
\(624\) 2.70636i 0.108341i
\(625\) −15.4502 −0.618009
\(626\) −6.17672 6.17672i −0.246871 0.246871i
\(627\) −5.58411 5.58411i −0.223008 0.223008i
\(628\) −37.5490 37.5490i −1.49837 1.49837i
\(629\) −2.39113 + 2.39113i −0.0953407 + 0.0953407i
\(630\) −15.6439 + 15.6439i −0.623268 + 0.623268i
\(631\) −10.0432 −0.399814 −0.199907 0.979815i \(-0.564064\pi\)
−0.199907 + 0.979815i \(0.564064\pi\)
\(632\) −22.6918 + 22.6918i −0.902631 + 0.902631i
\(633\) 4.54953 0.180828
\(634\) 19.3385 19.3385i 0.768030 0.768030i
\(635\) 8.05839i 0.319787i
\(636\) 6.68315i 0.265004i
\(637\) −2.27384 + 2.27384i −0.0900926 + 0.0900926i
\(638\) 108.076 4.27878
\(639\) −17.1047 + 17.1047i −0.676650 + 0.676650i
\(640\) 69.7097 2.75552
\(641\) −32.6859 + 32.6859i −1.29101 + 1.29101i −0.356854 + 0.934160i \(0.616151\pi\)
−0.934160 + 0.356854i \(0.883849\pi\)
\(642\) −10.7043 + 10.7043i −0.422466 + 0.422466i
\(643\) 5.54903 + 5.54903i 0.218833 + 0.218833i 0.808006 0.589174i \(-0.200547\pi\)
−0.589174 + 0.808006i \(0.700547\pi\)
\(644\) 5.31710 + 5.31710i 0.209523 + 0.209523i
\(645\) 9.82082 + 9.82082i 0.386694 + 0.386694i
\(646\) −13.5571 −0.533397
\(647\) 40.0890i 1.57606i −0.615637 0.788030i \(-0.711101\pi\)
0.615637 0.788030i \(-0.288899\pi\)
\(648\) 26.0378i 1.02286i
\(649\) −50.4161 50.4161i −1.97900 1.97900i
\(650\) 34.8189 34.8189i 1.36571 1.36571i
\(651\) 3.43674i 0.134696i
\(652\) −9.83072 −0.385001
\(653\) −0.757485 0.757485i −0.0296427 0.0296427i 0.692130 0.721773i \(-0.256672\pi\)
−0.721773 + 0.692130i \(0.756672\pi\)
\(654\) 12.3225i 0.481847i
\(655\) −12.9798 −0.507164
\(656\) 10.9805 1.11758i 0.428718 0.0436343i
\(657\) 0.932856 0.0363942
\(658\) 10.7852i 0.420452i
\(659\) 11.5728 + 11.5728i 0.450812 + 0.450812i 0.895624 0.444812i \(-0.146730\pi\)
−0.444812 + 0.895624i \(0.646730\pi\)
\(660\) −38.0286 −1.48026
\(661\) 0.349292i 0.0135859i −0.999977 0.00679294i \(-0.997838\pi\)
0.999977 0.00679294i \(-0.00216228\pi\)
\(662\) 13.4417 13.4417i 0.522428 0.522428i
\(663\) −2.51798 2.51798i −0.0977903 0.0977903i
\(664\) 31.0681i 1.20568i
\(665\) 8.56183i 0.332014i
\(666\) −9.73762 −0.377325
\(667\) 10.5679 + 10.5679i 0.409191 + 0.409191i
\(668\) −50.8663 50.8663i −1.96808 1.96808i
\(669\) 4.01605 + 4.01605i 0.155269 + 0.155269i
\(670\) 64.5802 64.5802i 2.49495 2.49495i
\(671\) −17.4002 + 17.4002i −0.671727 + 0.671727i
\(672\) 1.68850 0.0651355
\(673\) 5.03945 5.03945i 0.194257 0.194257i −0.603276 0.797533i \(-0.706138\pi\)
0.797533 + 0.603276i \(0.206138\pi\)
\(674\) 63.7161 2.45425
\(675\) 12.8797 12.8797i 0.495738 0.495738i
\(676\) 9.55508i 0.367503i
\(677\) 50.4366i 1.93844i −0.246201 0.969219i \(-0.579182\pi\)
0.246201 0.969219i \(-0.420818\pi\)
\(678\) −9.63198 + 9.63198i −0.369914 + 0.369914i
\(679\) 5.33434 0.204713
\(680\) −20.4670 + 20.4670i −0.784873 + 0.784873i
\(681\) −0.730579 −0.0279958
\(682\) −75.3261 + 75.3261i −2.88438 + 2.88438i
\(683\) −2.68737 + 2.68737i −0.102829 + 0.102829i −0.756650 0.653820i \(-0.773165\pi\)
0.653820 + 0.756650i \(0.273165\pi\)
\(684\) −17.7337 17.7337i −0.678064 0.678064i
\(685\) −8.72646 8.72646i −0.333421 0.333421i
\(686\) 1.67228 + 1.67228i 0.0638478 + 0.0638478i
\(687\) −10.1987 −0.389106
\(688\) 14.4749i 0.551850i
\(689\) 12.2505i 0.466706i
\(690\) −5.78836 5.78836i −0.220359 0.220359i
\(691\) −19.6831 + 19.6831i −0.748780 + 0.748780i −0.974250 0.225470i \(-0.927608\pi\)
0.225470 + 0.974250i \(0.427608\pi\)
\(692\) 80.0445i 3.04284i
\(693\) 17.6724 0.671320
\(694\) 51.0335 + 51.0335i 1.93720 + 1.93720i
\(695\) 31.4588i 1.19330i
\(696\) −13.1359 −0.497914
\(697\) 9.17643 11.2560i 0.347582 0.426352i
\(698\) −26.8311 −1.01557
\(699\) 2.21732i 0.0838667i
\(700\) −16.4504 16.4504i −0.621767 0.621767i
\(701\) −23.2918 −0.879720 −0.439860 0.898066i \(-0.644972\pi\)
−0.439860 + 0.898066i \(0.644972\pi\)
\(702\) 21.3936i 0.807449i
\(703\) 2.66468 2.66468i 0.100500 0.100500i
\(704\) −52.6083 52.6083i −1.98275 1.98275i
\(705\) 7.54264i 0.284072i
\(706\) 28.0956i 1.05739i
\(707\) 8.05587 0.302972
\(708\) 13.8209 + 13.8209i 0.519422 + 0.519422i
\(709\) 29.6639 + 29.6639i 1.11405 + 1.11405i 0.992597 + 0.121453i \(0.0387553\pi\)
0.121453 + 0.992597i \(0.461245\pi\)
\(710\) −49.6192 49.6192i −1.86217 1.86217i
\(711\) −16.6337 + 16.6337i −0.623812 + 0.623812i
\(712\) 27.4175 27.4175i 1.02752 1.02752i
\(713\) −14.7311 −0.551682
\(714\) −1.85183 + 1.85183i −0.0693031 + 0.0693031i
\(715\) −69.7079 −2.60693
\(716\) −2.23063 + 2.23063i −0.0833627 + 0.0833627i
\(717\) 5.15146i 0.192385i
\(718\) 28.0262i 1.04593i
\(719\) 11.2635 11.2635i 0.420056 0.420056i −0.465167 0.885223i \(-0.654006\pi\)
0.885223 + 0.465167i \(0.154006\pi\)
\(720\) −16.1253 −0.600953
\(721\) 12.1662 12.1662i 0.453092 0.453092i
\(722\) −29.8261 −1.11001
\(723\) 6.46913 6.46913i 0.240589 0.240589i
\(724\) −48.7366 + 48.7366i −1.81128 + 1.81128i
\(725\) −32.6957 32.6957i −1.21429 1.21429i
\(726\) 24.4549 + 24.4549i 0.907607 + 0.907607i
\(727\) 20.7669 + 20.7669i 0.770203 + 0.770203i 0.978142 0.207939i \(-0.0666756\pi\)
−0.207939 + 0.978142i \(0.566676\pi\)
\(728\) −12.1148 −0.449005
\(729\) 14.9659i 0.554293i
\(730\) 2.70613i 0.100159i
\(731\) −13.4673 13.4673i −0.498108 0.498108i
\(732\) 4.77004 4.77004i 0.176306 0.176306i
\(733\) 23.5888i 0.871271i −0.900123 0.435636i \(-0.856524\pi\)
0.900123 0.435636i \(-0.143476\pi\)
\(734\) 0.266376 0.00983212
\(735\) −1.16950 1.16950i −0.0431378 0.0431378i
\(736\) 7.23752i 0.266779i
\(737\) −72.9543 −2.68731
\(738\) 41.6044 4.23444i 1.53148 0.155872i
\(739\) −3.86485 −0.142171 −0.0710854 0.997470i \(-0.522646\pi\)
−0.0710854 + 0.997470i \(0.522646\pi\)
\(740\) 18.1468i 0.667091i
\(741\) 2.80604 + 2.80604i 0.103082 + 0.103082i
\(742\) 9.00953 0.330750
\(743\) 53.8393i 1.97517i −0.157074 0.987587i \(-0.550206\pi\)
0.157074 0.987587i \(-0.449794\pi\)
\(744\) 9.15534 9.15534i 0.335651 0.335651i
\(745\) −42.0894 42.0894i −1.54204 1.54204i
\(746\) 17.2891i 0.633000i
\(747\) 22.7737i 0.833248i
\(748\) 52.1488 1.90675
\(749\) 9.27029 + 9.27029i 0.338729 + 0.338729i
\(750\) 4.07929 + 4.07929i 0.148955 + 0.148955i
\(751\) −25.5321 25.5321i −0.931679 0.931679i 0.0661315 0.997811i \(-0.478934\pi\)
−0.997811 + 0.0661315i \(0.978934\pi\)
\(752\) 5.55855 5.55855i 0.202699 0.202699i
\(753\) −3.23838 + 3.23838i −0.118013 + 0.118013i
\(754\) −54.3088 −1.97781
\(755\) 45.4312 45.4312i 1.65341 1.65341i
\(756\) −10.1075 −0.367608
\(757\) −24.4734 + 24.4734i −0.889499 + 0.889499i −0.994475 0.104975i \(-0.966524\pi\)
0.104975 + 0.994475i \(0.466524\pi\)
\(758\) 29.6592i 1.07727i
\(759\) 6.53893i 0.237348i
\(760\) 22.8084 22.8084i 0.827347 0.827347i
\(761\) −49.6878 −1.80118 −0.900591 0.434668i \(-0.856866\pi\)
−0.900591 + 0.434668i \(0.856866\pi\)
\(762\) 1.94234 1.94234i 0.0703634 0.0703634i
\(763\) −10.6717 −0.386340
\(764\) −13.7160 + 13.7160i −0.496227 + 0.496227i
\(765\) −15.0028 + 15.0028i −0.542428 + 0.542428i
\(766\) 40.3303 + 40.3303i 1.45719 + 1.45719i
\(767\) 25.3343 + 25.3343i 0.914769 + 0.914769i
\(768\) 8.77459 + 8.77459i 0.316626 + 0.316626i
\(769\) 41.4266 1.49388 0.746941 0.664890i \(-0.231522\pi\)
0.746941 + 0.664890i \(0.231522\pi\)
\(770\) 51.2662i 1.84751i
\(771\) 2.44760i 0.0881482i
\(772\) 41.9060 + 41.9060i 1.50823 + 1.50823i
\(773\) 8.72433 8.72433i 0.313792 0.313792i −0.532584 0.846377i \(-0.678779\pi\)
0.846377 + 0.532584i \(0.178779\pi\)
\(774\) 54.8443i 1.97134i
\(775\) 45.5760 1.63714
\(776\) 14.2105 + 14.2105i 0.510127 + 0.510127i
\(777\) 0.727964i 0.0261156i
\(778\) 23.3838 0.838351
\(779\) −10.2262 + 12.5437i −0.366392 + 0.449425i
\(780\) 19.1095 0.684231
\(781\) 56.0533i 2.00574i
\(782\) 7.93761 + 7.93761i 0.283848 + 0.283848i
\(783\) −20.0891 −0.717925
\(784\) 1.72373i 0.0615619i
\(785\) 35.4008 35.4008i 1.26351 1.26351i
\(786\) −3.12856 3.12856i −0.111592 0.111592i
\(787\) 29.1445i 1.03889i 0.854504 + 0.519445i \(0.173861\pi\)
−0.854504 + 0.519445i \(0.826139\pi\)
\(788\) 46.0910i 1.64192i
\(789\) 0.836121 0.0297667
\(790\) −48.2529 48.2529i −1.71676 1.71676i
\(791\) 8.34161 + 8.34161i 0.296594 + 0.296594i
\(792\) 47.0787 + 47.0787i 1.67287 + 1.67287i
\(793\) 8.74368 8.74368i 0.310497 0.310497i
\(794\) −37.8308 + 37.8308i −1.34257 + 1.34257i
\(795\) −6.30081 −0.223467
\(796\) 57.7927 57.7927i 2.04841 2.04841i
\(797\) 30.3753 1.07595 0.537974 0.842961i \(-0.319190\pi\)
0.537974 + 0.842961i \(0.319190\pi\)
\(798\) 2.06368 2.06368i 0.0730536 0.0730536i
\(799\) 10.3433i 0.365919i
\(800\) 22.3920i 0.791675i
\(801\) 20.0978 20.0978i 0.710120 0.710120i
\(802\) −31.4594 −1.11087
\(803\) 1.52852 1.52852i 0.0539403 0.0539403i
\(804\) 19.9995 0.705328
\(805\) −5.01291 + 5.01291i −0.176682 + 0.176682i
\(806\) 37.8517 37.8517i 1.33327 1.33327i
\(807\) 4.80489 + 4.80489i 0.169140 + 0.169140i
\(808\) 21.4606 + 21.4606i 0.754980 + 0.754980i
\(809\) 19.6017 + 19.6017i 0.689161 + 0.689161i 0.962046 0.272886i \(-0.0879781\pi\)
−0.272886 + 0.962046i \(0.587978\pi\)
\(810\) −55.3680 −1.94543
\(811\) 48.0748i 1.68813i −0.536238 0.844067i \(-0.680155\pi\)
0.536238 0.844067i \(-0.319845\pi\)
\(812\) 25.6586i 0.900439i
\(813\) −9.12449 9.12449i −0.320010 0.320010i
\(814\) −15.9555 + 15.9555i −0.559238 + 0.559238i
\(815\) 9.26830i 0.324655i
\(816\) −1.90881 −0.0668218
\(817\) 15.0080 + 15.0080i 0.525064 + 0.525064i
\(818\) 23.7279i 0.829625i
\(819\) −8.88048 −0.310309
\(820\) 7.89121 + 77.5332i 0.275573 + 2.70758i
\(821\) −22.6320 −0.789863 −0.394931 0.918711i \(-0.629232\pi\)
−0.394931 + 0.918711i \(0.629232\pi\)
\(822\) 4.20673i 0.146727i
\(823\) 6.69343 + 6.69343i 0.233318 + 0.233318i 0.814076 0.580758i \(-0.197244\pi\)
−0.580758 + 0.814076i \(0.697244\pi\)
\(824\) 64.8205 2.25813
\(825\) 20.2306i 0.704339i
\(826\) 18.6319 18.6319i 0.648288 0.648288i
\(827\) 30.5431 + 30.5431i 1.06209 + 1.06209i 0.997940 + 0.0641464i \(0.0204325\pi\)
0.0641464 + 0.997940i \(0.479568\pi\)
\(828\) 20.7660i 0.721667i
\(829\) 45.0033i 1.56303i −0.623887 0.781515i \(-0.714447\pi\)
0.623887 0.781515i \(-0.285553\pi\)
\(830\) 66.0646 2.29314
\(831\) 5.15938 + 5.15938i 0.178977 + 0.178977i
\(832\) 26.4359 + 26.4359i 0.916500 + 0.916500i
\(833\) 1.60375 + 1.60375i 0.0555666 + 0.0555666i
\(834\) −7.58260 + 7.58260i −0.262564 + 0.262564i
\(835\) 47.9563 47.9563i 1.65960 1.65960i
\(836\) −58.1146 −2.00994
\(837\) 14.0015 14.0015i 0.483963 0.483963i
\(838\) −89.9603 −3.10763
\(839\) −26.5463 + 26.5463i −0.916480 + 0.916480i −0.996771 0.0802918i \(-0.974415\pi\)
0.0802918 + 0.996771i \(0.474415\pi\)
\(840\) 6.23103i 0.214991i
\(841\) 21.9972i 0.758524i
\(842\) −14.7946 + 14.7946i −0.509854 + 0.509854i
\(843\) 3.11574 0.107312
\(844\) 23.6738 23.6738i 0.814887 0.814887i
\(845\) −9.00844 −0.309900
\(846\) 21.0609 21.0609i 0.724089 0.724089i
\(847\) 21.1788 21.1788i 0.727711 0.727711i
\(848\) 4.64338 + 4.64338i 0.159454 + 0.159454i
\(849\) −0.441754 0.441754i −0.0151610 0.0151610i
\(850\) −24.5579 24.5579i −0.842330 0.842330i
\(851\) −3.12031 −0.106963
\(852\) 15.3663i 0.526440i
\(853\) 7.89965i 0.270479i 0.990813 + 0.135239i \(0.0431804\pi\)
−0.990813 + 0.135239i \(0.956820\pi\)
\(854\) −6.43048 6.43048i −0.220046 0.220046i
\(855\) 16.7191 16.7191i 0.571783 0.571783i
\(856\) 49.3914i 1.68816i
\(857\) 54.5233 1.86248 0.931240 0.364406i \(-0.118728\pi\)
0.931240 + 0.364406i \(0.118728\pi\)
\(858\) −16.8019 16.8019i −0.573607 0.573607i
\(859\) 11.2917i 0.385267i 0.981271 + 0.192633i \(0.0617028\pi\)
−0.981271 + 0.192633i \(0.938297\pi\)
\(860\) 102.207 3.48522
\(861\) 0.316558 + 3.11026i 0.0107883 + 0.105997i
\(862\) −59.0394 −2.01089
\(863\) 0.277647i 0.00945121i −0.999989 0.00472560i \(-0.998496\pi\)
0.999989 0.00472560i \(-0.00150421\pi\)
\(864\) 6.87909 + 6.87909i 0.234031 + 0.234031i
\(865\) −75.4652 −2.56589
\(866\) 73.8567i 2.50975i
\(867\) 4.09322 4.09322i 0.139013 0.139013i
\(868\) −17.8833 17.8833i −0.606999 0.606999i
\(869\) 54.5098i 1.84912i
\(870\) 27.9327i 0.947008i
\(871\) 36.6599 1.24217
\(872\) −28.4289 28.4289i −0.962725 0.962725i
\(873\) 10.4167 + 10.4167i 0.352550 + 0.352550i
\(874\) −8.84567 8.84567i −0.299209 0.299209i
\(875\) 3.53280 3.53280i 0.119431 0.119431i
\(876\) −0.419024 + 0.419024i −0.0141575 + 0.0141575i
\(877\) 46.4874 1.56977 0.784884 0.619642i \(-0.212722\pi\)
0.784884 + 0.619642i \(0.212722\pi\)
\(878\) −3.24197 + 3.24197i −0.109411 + 0.109411i
\(879\) −6.76558 −0.228197
\(880\) −26.4218 + 26.4218i −0.890679 + 0.890679i
\(881\) 11.4935i 0.387225i 0.981078 + 0.193613i \(0.0620205\pi\)
−0.981078 + 0.193613i \(0.937980\pi\)
\(882\) 6.53109i 0.219913i
\(883\) −9.33299 + 9.33299i −0.314080 + 0.314080i −0.846488 0.532408i \(-0.821287\pi\)
0.532408 + 0.846488i \(0.321287\pi\)
\(884\) −26.2050 −0.881370
\(885\) −13.0302 + 13.0302i −0.438006 + 0.438006i
\(886\) 33.1762 1.11458
\(887\) −20.2074 + 20.2074i −0.678499 + 0.678499i −0.959660 0.281162i \(-0.909280\pi\)
0.281162 + 0.959660i \(0.409280\pi\)
\(888\) 1.93927 1.93927i 0.0650776 0.0650776i
\(889\) −1.68213 1.68213i −0.0564167 0.0564167i
\(890\) 58.3019 + 58.3019i 1.95428 + 1.95428i
\(891\) 31.2738 + 31.2738i 1.04771 + 1.04771i
\(892\) 41.7956 1.39942
\(893\) 11.5265i 0.385721i
\(894\) 20.2899i 0.678594i
\(895\) −2.10302 2.10302i −0.0702962 0.0702962i
\(896\) 14.5514 14.5514i 0.486127 0.486127i
\(897\) 3.28584i 0.109711i
\(898\) 45.8999 1.53170
\(899\) −35.5436 35.5436i −1.18545 1.18545i
\(900\) 64.2472i 2.14157i
\(901\) 8.64033 0.287851
\(902\) 61.2321 75.1087i 2.03881 2.50085i
\(903\) 4.10004 0.136441
\(904\) 44.4435i 1.47817i
\(905\) −45.9484 45.9484i −1.52738 1.52738i
\(906\) 21.9008 0.727607
\(907\) 17.6975i 0.587637i 0.955861 + 0.293818i \(0.0949261\pi\)
−0.955861 + 0.293818i \(0.905074\pi\)
\(908\) −3.80162 + 3.80162i −0.126161 + 0.126161i
\(909\) 15.7311 + 15.7311i 0.521769 + 0.521769i
\(910\) 25.7615i 0.853986i
\(911\) 13.1925i 0.437087i 0.975827 + 0.218544i \(0.0701306\pi\)
−0.975827 + 0.218544i \(0.929869\pi\)
\(912\) 2.12718 0.0704380
\(913\) −37.3156 37.3156i −1.23497 1.23497i
\(914\) −18.2826 18.2826i −0.604735 0.604735i
\(915\) 4.49715 + 4.49715i 0.148671 + 0.148671i
\(916\) −53.0698 + 53.0698i −1.75348 + 1.75348i
\(917\) −2.70944 + 2.70944i −0.0894736 + 0.0894736i
\(918\) −15.0890 −0.498012
\(919\) 30.6508 30.6508i 1.01108 1.01108i 0.0111379 0.999938i \(-0.496455\pi\)
0.999938 0.0111379i \(-0.00354538\pi\)
\(920\) −26.7084 −0.880550
\(921\) −5.50674 + 5.50674i −0.181453 + 0.181453i
\(922\) 15.8795i 0.522963i
\(923\) 28.1670i 0.927129i
\(924\) −7.93817 + 7.93817i −0.261147 + 0.261147i
\(925\) 9.65383 0.317416
\(926\) 3.95222 3.95222i 0.129878 0.129878i
\(927\) 47.5151 1.56060
\(928\) 17.4630 17.4630i 0.573250 0.573250i
\(929\) 12.3559 12.3559i 0.405383 0.405383i −0.474742 0.880125i \(-0.657459\pi\)
0.880125 + 0.474742i \(0.157459\pi\)
\(930\) 19.4683 + 19.4683i 0.638391 + 0.638391i
\(931\) −1.78722 1.78722i −0.0585737 0.0585737i
\(932\) −11.5380 11.5380i −0.377939 0.377939i
\(933\) −0.910975 −0.0298240
\(934\) 39.2360i 1.28384i
\(935\) 49.1654i 1.60788i
\(936\) −23.6573 23.6573i −0.773262 0.773262i
\(937\) 15.8474 15.8474i 0.517712 0.517712i −0.399167 0.916878i \(-0.630701\pi\)
0.916878 + 0.399167i \(0.130701\pi\)
\(938\) 26.9613i 0.880317i
\(939\) 1.80340 0.0588518
\(940\) 39.2487 + 39.2487i 1.28015 + 1.28015i
\(941\) 43.2082i 1.40855i 0.709929 + 0.704274i \(0.248727\pi\)
−0.709929 + 0.704274i \(0.751273\pi\)
\(942\) 17.0655 0.556025
\(943\) 13.3317 1.35688i 0.434139 0.0441860i
\(944\) 19.2052 0.625078
\(945\) 9.52930i 0.309988i
\(946\) −89.8644 89.8644i −2.92174 2.92174i
\(947\) 6.19364 0.201266 0.100633 0.994924i \(-0.467913\pi\)
0.100633 + 0.994924i \(0.467913\pi\)
\(948\) 14.9432i 0.485331i
\(949\) −0.768088 + 0.768088i −0.0249332 + 0.0249332i
\(950\) 27.3674 + 27.3674i 0.887914 + 0.887914i
\(951\) 5.64621i 0.183091i
\(952\) 8.54465i 0.276934i
\(953\) −10.6028 −0.343457 −0.171729 0.985144i \(-0.554935\pi\)
−0.171729 + 0.985144i \(0.554935\pi\)
\(954\) 17.5934 + 17.5934i 0.569608 + 0.569608i
\(955\) −12.9313 12.9313i −0.418447 0.418447i
\(956\) −26.8060 26.8060i −0.866967 0.866967i
\(957\) −15.7774 + 15.7774i −0.510010 + 0.510010i
\(958\) 30.3665 30.3665i 0.981097 0.981097i
\(959\) −3.64317 −0.117644
\(960\) −13.5968 + 13.5968i −0.438835 + 0.438835i
\(961\) 18.5458 0.598252
\(962\) 8.01769 8.01769i 0.258501 0.258501i
\(963\) 36.2052i 1.16670i
\(964\) 67.3251i 2.16840i
\(965\) −39.5086 + 39.5086i −1.27183 + 1.27183i
\(966\) −2.41655 −0.0777513
\(967\) 16.4960 16.4960i 0.530476 0.530476i −0.390238 0.920714i \(-0.627607\pi\)
0.920714 + 0.390238i \(0.127607\pi\)
\(968\) 112.839 3.62678
\(969\) 1.97911 1.97911i 0.0635783 0.0635783i
\(970\) −30.2178 + 30.2178i −0.970236 + 0.970236i
\(971\) −2.19274 2.19274i −0.0703684 0.0703684i 0.671047 0.741415i \(-0.265845\pi\)
−0.741415 + 0.671047i \(0.765845\pi\)
\(972\) −30.0147 30.0147i −0.962720 0.962720i
\(973\) 6.56678 + 6.56678i 0.210521 + 0.210521i
\(974\) −75.0755 −2.40557
\(975\) 10.1660i 0.325572i
\(976\) 6.62834i 0.212168i
\(977\) −13.4743 13.4743i −0.431082 0.431082i 0.457914 0.888996i \(-0.348597\pi\)
−0.888996 + 0.457914i \(0.848597\pi\)
\(978\) 2.23397 2.23397i 0.0714344 0.0714344i
\(979\) 65.8618i 2.10495i
\(980\) −12.1712 −0.388795
\(981\) −20.8391 20.8391i −0.665342 0.665342i
\(982\) 52.4523i 1.67382i
\(983\) −3.89718 −0.124301 −0.0621504 0.998067i \(-0.519796\pi\)
−0.0621504 + 0.998067i \(0.519796\pi\)
\(984\) −7.44232 + 9.12891i −0.237252 + 0.291019i
\(985\) −43.4541 −1.38456
\(986\) 38.3043i 1.21986i
\(987\) 1.57447 + 1.57447i 0.0501159 + 0.0501159i
\(988\) 29.2029 0.929067
\(989\) 17.5742i 0.558828i
\(990\) −100.110 + 100.110i −3.18171 + 3.18171i
\(991\) −1.83130 1.83130i −0.0581732 0.0581732i 0.677422 0.735595i \(-0.263097\pi\)
−0.735595 + 0.677422i \(0.763097\pi\)
\(992\) 24.3424i 0.772871i
\(993\) 3.92455i 0.124542i
\(994\) −20.7152 −0.657048
\(995\) 54.4864 + 54.4864i 1.72734 + 1.72734i
\(996\) 10.2296 + 10.2296i 0.324137 + 0.324137i
\(997\) 19.4793 + 19.4793i 0.616915 + 0.616915i 0.944739 0.327824i \(-0.106315\pi\)
−0.327824 + 0.944739i \(0.606315\pi\)
\(998\) −36.5037 + 36.5037i −1.15550 + 1.15550i
\(999\) 2.96578 2.96578i 0.0938331 0.0938331i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 287.2.f.a.50.18 40
41.32 even 4 inner 287.2.f.a.155.3 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.2.f.a.50.18 40 1.1 even 1 trivial
287.2.f.a.155.3 yes 40 41.32 even 4 inner