Properties

Label 210.3.k.a.167.13
Level $210$
Weight $3$
Character 210.167
Analytic conductor $5.722$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [210,3,Mod(83,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("210.83");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.k (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: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 167.13
Character \(\chi\) \(=\) 210.167
Dual form 210.3.k.a.83.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(2.28799 - 1.94039i) q^{3} -2.00000i q^{4} +(-4.58449 - 1.99562i) q^{5} +(-0.347606 + 4.22838i) q^{6} +(-4.23091 + 5.57668i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.46981 - 8.87917i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(2.28799 - 1.94039i) q^{3} -2.00000i q^{4} +(-4.58449 - 1.99562i) q^{5} +(-0.347606 + 4.22838i) q^{6} +(-4.23091 + 5.57668i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.46981 - 8.87917i) q^{9} +(6.58010 - 2.58887i) q^{10} -14.6047i q^{11} +(-3.88077 - 4.57598i) q^{12} +(3.48167 + 3.48167i) q^{13} +(-1.34578 - 9.80759i) q^{14} +(-14.3615 + 4.32971i) q^{15} -4.00000 q^{16} +(-20.1653 - 20.1653i) q^{17} +(7.40936 + 10.3490i) q^{18} -26.4132 q^{19} +(-3.99123 + 9.16897i) q^{20} +(1.14063 + 20.9690i) q^{21} +(14.6047 + 14.6047i) q^{22} +(-2.68095 - 2.68095i) q^{23} +(8.45675 + 0.695213i) q^{24} +(17.0350 + 18.2978i) q^{25} -6.96334 q^{26} +(-13.8661 - 23.1675i) q^{27} +(11.1534 + 8.46182i) q^{28} -28.5159 q^{29} +(10.0318 - 18.6912i) q^{30} -15.6511i q^{31} +(4.00000 - 4.00000i) q^{32} +(-28.3387 - 33.4154i) q^{33} +40.3306 q^{34} +(30.5255 - 17.1230i) q^{35} +(-17.7583 - 2.93962i) q^{36} +(7.69844 + 7.69844i) q^{37} +(26.4132 - 26.4132i) q^{38} +(14.7218 + 1.21025i) q^{39} +(-5.17774 - 13.1602i) q^{40} +37.9832 q^{41} +(-22.1096 - 19.8284i) q^{42} +(41.7817 - 41.7817i) q^{43} -29.2094 q^{44} +(-24.4578 + 37.7732i) q^{45} +5.36190 q^{46} +(21.0822 + 21.0822i) q^{47} +(-9.15197 + 7.76154i) q^{48} +(-13.1988 - 47.1889i) q^{49} +(-35.3328 - 1.26273i) q^{50} +(-85.2664 - 7.00958i) q^{51} +(6.96334 - 6.96334i) q^{52} +(47.4934 + 47.4934i) q^{53} +(37.0336 + 9.30137i) q^{54} +(-29.1453 + 66.9549i) q^{55} +(-19.6152 + 2.69155i) q^{56} +(-60.4332 + 51.2518i) q^{57} +(28.5159 - 28.5159i) q^{58} +61.6589i q^{59} +(8.65943 + 28.7231i) q^{60} -54.1777i q^{61} +(15.6511 + 15.6511i) q^{62} +(43.2977 + 45.7636i) q^{63} +8.00000i q^{64} +(-9.01359 - 22.9098i) q^{65} +(61.7541 + 5.07668i) q^{66} +(68.9882 + 68.9882i) q^{67} +(-40.3306 + 40.3306i) q^{68} +(-11.3361 - 0.931915i) q^{69} +(-13.4025 + 47.6484i) q^{70} -65.9594i q^{71} +(20.6980 - 14.8187i) q^{72} +(-6.51081 - 6.51081i) q^{73} -15.3969 q^{74} +(74.4807 + 8.81061i) q^{75} +52.8265i q^{76} +(81.4457 + 61.7911i) q^{77} +(-15.9321 + 13.5116i) q^{78} -42.7301i q^{79} +(18.3379 + 7.98247i) q^{80} +(-76.6793 - 26.1014i) q^{81} +(-37.9832 + 37.9832i) q^{82} +(9.52614 - 9.52614i) q^{83} +(41.9380 - 2.28126i) q^{84} +(52.2053 + 132.690i) q^{85} +83.5634i q^{86} +(-65.2441 + 55.3318i) q^{87} +(29.2094 - 29.2094i) q^{88} -19.3830i q^{89} +(-13.3155 - 62.2310i) q^{90} +(-34.1468 + 4.68555i) q^{91} +(-5.36190 + 5.36190i) q^{92} +(-30.3692 - 35.8096i) q^{93} -42.1644 q^{94} +(121.091 + 52.7107i) q^{95} +(1.39043 - 16.9135i) q^{96} +(84.6391 - 84.6391i) q^{97} +(60.3877 + 33.9901i) q^{98} +(-129.677 - 21.4661i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 32 q^{2} - 4 q^{7} + 64 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 32 q^{2} - 4 q^{7} + 64 q^{8} - 16 q^{9} + 8 q^{14} - 20 q^{15} - 128 q^{16} + 36 q^{18} + 12 q^{21} - 40 q^{22} + 24 q^{23} + 16 q^{25} - 8 q^{28} - 112 q^{29} + 68 q^{30} + 128 q^{32} - 48 q^{35} - 40 q^{36} + 32 q^{37} + 64 q^{39} - 44 q^{42} - 32 q^{43} + 80 q^{44} - 48 q^{46} - 8 q^{50} + 84 q^{51} - 136 q^{53} + 244 q^{57} + 112 q^{58} - 96 q^{60} + 72 q^{63} - 200 q^{65} + 32 q^{67} + 8 q^{72} - 64 q^{74} + 88 q^{77} - 124 q^{78} + 76 q^{81} + 64 q^{84} - 40 q^{85} - 80 q^{88} - 272 q^{91} + 48 q^{92} - 452 q^{93} + 544 q^{95} + 128 q^{98} + 160 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.00000i −0.500000 + 0.500000i
\(3\) 2.28799 1.94039i 0.762664 0.646795i
\(4\) 2.00000i 0.500000i
\(5\) −4.58449 1.99562i −0.916897 0.399123i
\(6\) −0.347606 + 4.22838i −0.0579344 + 0.704729i
\(7\) −4.23091 + 5.57668i −0.604416 + 0.796669i
\(8\) 2.00000 + 2.00000i 0.250000 + 0.250000i
\(9\) 1.46981 8.87917i 0.163312 0.986574i
\(10\) 6.58010 2.58887i 0.658010 0.258887i
\(11\) 14.6047i 1.32770i −0.747867 0.663849i \(-0.768922\pi\)
0.747867 0.663849i \(-0.231078\pi\)
\(12\) −3.88077 4.57598i −0.323398 0.381332i
\(13\) 3.48167 + 3.48167i 0.267821 + 0.267821i 0.828222 0.560401i \(-0.189353\pi\)
−0.560401 + 0.828222i \(0.689353\pi\)
\(14\) −1.34578 9.80759i −0.0961268 0.700542i
\(15\) −14.3615 + 4.32971i −0.957435 + 0.288648i
\(16\) −4.00000 −0.250000
\(17\) −20.1653 20.1653i −1.18619 1.18619i −0.978112 0.208081i \(-0.933278\pi\)
−0.208081 0.978112i \(-0.566722\pi\)
\(18\) 7.40936 + 10.3490i 0.411631 + 0.574943i
\(19\) −26.4132 −1.39017 −0.695085 0.718928i \(-0.744633\pi\)
−0.695085 + 0.718928i \(0.744633\pi\)
\(20\) −3.99123 + 9.16897i −0.199562 + 0.458449i
\(21\) 1.14063 + 20.9690i 0.0543157 + 0.998524i
\(22\) 14.6047 + 14.6047i 0.663849 + 0.663849i
\(23\) −2.68095 2.68095i −0.116563 0.116563i 0.646419 0.762982i \(-0.276266\pi\)
−0.762982 + 0.646419i \(0.776266\pi\)
\(24\) 8.45675 + 0.695213i 0.352365 + 0.0289672i
\(25\) 17.0350 + 18.2978i 0.681401 + 0.731910i
\(26\) −6.96334 −0.267821
\(27\) −13.8661 23.1675i −0.513559 0.858054i
\(28\) 11.1534 + 8.46182i 0.398335 + 0.302208i
\(29\) −28.5159 −0.983306 −0.491653 0.870791i \(-0.663607\pi\)
−0.491653 + 0.870791i \(0.663607\pi\)
\(30\) 10.0318 18.6912i 0.334394 0.623041i
\(31\) 15.6511i 0.504875i −0.967613 0.252438i \(-0.918768\pi\)
0.967613 0.252438i \(-0.0812322\pi\)
\(32\) 4.00000 4.00000i 0.125000 0.125000i
\(33\) −28.3387 33.4154i −0.858748 1.01259i
\(34\) 40.3306 1.18619
\(35\) 30.5255 17.1230i 0.872156 0.489227i
\(36\) −17.7583 2.93962i −0.493287 0.0816562i
\(37\) 7.69844 + 7.69844i 0.208066 + 0.208066i 0.803445 0.595379i \(-0.202998\pi\)
−0.595379 + 0.803445i \(0.702998\pi\)
\(38\) 26.4132 26.4132i 0.695085 0.695085i
\(39\) 14.7218 + 1.21025i 0.377483 + 0.0310321i
\(40\) −5.17774 13.1602i −0.129443 0.329005i
\(41\) 37.9832 0.926419 0.463209 0.886249i \(-0.346698\pi\)
0.463209 + 0.886249i \(0.346698\pi\)
\(42\) −22.1096 19.8284i −0.526420 0.472104i
\(43\) 41.7817 41.7817i 0.971667 0.971667i −0.0279426 0.999610i \(-0.508896\pi\)
0.999610 + 0.0279426i \(0.00889555\pi\)
\(44\) −29.2094 −0.663849
\(45\) −24.4578 + 37.7732i −0.543506 + 0.839406i
\(46\) 5.36190 0.116563
\(47\) 21.0822 + 21.0822i 0.448558 + 0.448558i 0.894875 0.446317i \(-0.147265\pi\)
−0.446317 + 0.894875i \(0.647265\pi\)
\(48\) −9.15197 + 7.76154i −0.190666 + 0.161699i
\(49\) −13.1988 47.1889i −0.269364 0.963039i
\(50\) −35.3328 1.26273i −0.706656 0.0252547i
\(51\) −85.2664 7.00958i −1.67189 0.137443i
\(52\) 6.96334 6.96334i 0.133910 0.133910i
\(53\) 47.4934 + 47.4934i 0.896102 + 0.896102i 0.995089 0.0989866i \(-0.0315601\pi\)
−0.0989866 + 0.995089i \(0.531560\pi\)
\(54\) 37.0336 + 9.30137i 0.685807 + 0.172248i
\(55\) −29.1453 + 66.9549i −0.529915 + 1.21736i
\(56\) −19.6152 + 2.69155i −0.350271 + 0.0480634i
\(57\) −60.4332 + 51.2518i −1.06023 + 0.899155i
\(58\) 28.5159 28.5159i 0.491653 0.491653i
\(59\) 61.6589i 1.04507i 0.852619 + 0.522533i \(0.175013\pi\)
−0.852619 + 0.522533i \(0.824987\pi\)
\(60\) 8.65943 + 28.7231i 0.144324 + 0.478718i
\(61\) 54.1777i 0.888159i −0.895987 0.444080i \(-0.853531\pi\)
0.895987 0.444080i \(-0.146469\pi\)
\(62\) 15.6511 + 15.6511i 0.252438 + 0.252438i
\(63\) 43.2977 + 45.7636i 0.687265 + 0.726407i
\(64\) 8.00000i 0.125000i
\(65\) −9.01359 22.9098i −0.138671 0.352458i
\(66\) 61.7541 + 5.07668i 0.935668 + 0.0769194i
\(67\) 68.9882 + 68.9882i 1.02967 + 1.02967i 0.999546 + 0.0301280i \(0.00959148\pi\)
0.0301280 + 0.999546i \(0.490409\pi\)
\(68\) −40.3306 + 40.3306i −0.593096 + 0.593096i
\(69\) −11.3361 0.931915i −0.164291 0.0135060i
\(70\) −13.4025 + 47.6484i −0.191465 + 0.680692i
\(71\) 65.9594i 0.929006i −0.885572 0.464503i \(-0.846233\pi\)
0.885572 0.464503i \(-0.153767\pi\)
\(72\) 20.6980 14.8187i 0.287472 0.205816i
\(73\) −6.51081 6.51081i −0.0891892 0.0891892i 0.661105 0.750294i \(-0.270088\pi\)
−0.750294 + 0.661105i \(0.770088\pi\)
\(74\) −15.3969 −0.208066
\(75\) 74.4807 + 8.81061i 0.993076 + 0.117475i
\(76\) 52.8265i 0.695085i
\(77\) 81.4457 + 61.7911i 1.05774 + 0.802481i
\(78\) −15.9321 + 13.5116i −0.204257 + 0.173225i
\(79\) 42.7301i 0.540887i −0.962736 0.270443i \(-0.912830\pi\)
0.962736 0.270443i \(-0.0871703\pi\)
\(80\) 18.3379 + 7.98247i 0.229224 + 0.0997809i
\(81\) −76.6793 26.1014i −0.946658 0.322240i
\(82\) −37.9832 + 37.9832i −0.463209 + 0.463209i
\(83\) 9.52614 9.52614i 0.114773 0.114773i −0.647388 0.762161i \(-0.724139\pi\)
0.762161 + 0.647388i \(0.224139\pi\)
\(84\) 41.9380 2.28126i 0.499262 0.0271579i
\(85\) 52.2053 + 132.690i 0.614180 + 1.56105i
\(86\) 83.5634i 0.971667i
\(87\) −65.2441 + 55.3318i −0.749932 + 0.635998i
\(88\) 29.2094 29.2094i 0.331924 0.331924i
\(89\) 19.3830i 0.217786i −0.994053 0.108893i \(-0.965269\pi\)
0.994053 0.108893i \(-0.0347306\pi\)
\(90\) −13.3155 62.2310i −0.147950 0.691456i
\(91\) −34.1468 + 4.68555i −0.375240 + 0.0514895i
\(92\) −5.36190 + 5.36190i −0.0582815 + 0.0582815i
\(93\) −30.3692 35.8096i −0.326551 0.385050i
\(94\) −42.1644 −0.448558
\(95\) 121.091 + 52.7107i 1.27464 + 0.554849i
\(96\) 1.39043 16.9135i 0.0144836 0.176182i
\(97\) 84.6391 84.6391i 0.872568 0.872568i −0.120184 0.992752i \(-0.538348\pi\)
0.992752 + 0.120184i \(0.0383484\pi\)
\(98\) 60.3877 + 33.9901i 0.616201 + 0.346837i
\(99\) −129.677 21.4661i −1.30987 0.216829i
\(100\) 36.5955 34.0700i 0.365955 0.340700i
\(101\) −112.859 −1.11741 −0.558707 0.829365i \(-0.688702\pi\)
−0.558707 + 0.829365i \(0.688702\pi\)
\(102\) 92.2760 78.2568i 0.904666 0.767224i
\(103\) 82.5883 + 82.5883i 0.801828 + 0.801828i 0.983381 0.181553i \(-0.0581123\pi\)
−0.181553 + 0.983381i \(0.558112\pi\)
\(104\) 13.9267i 0.133910i
\(105\) 36.6169 98.4083i 0.348732 0.937222i
\(106\) −94.9868 −0.896102
\(107\) −125.554 + 125.554i −1.17340 + 1.17340i −0.192011 + 0.981393i \(0.561501\pi\)
−0.981393 + 0.192011i \(0.938499\pi\)
\(108\) −46.3349 + 27.7322i −0.429027 + 0.256780i
\(109\) 1.60754i 0.0147481i 0.999973 + 0.00737405i \(0.00234725\pi\)
−0.999973 + 0.00737405i \(0.997653\pi\)
\(110\) −37.8096 96.1003i −0.343724 0.873639i
\(111\) 32.5519 + 2.67603i 0.293261 + 0.0241084i
\(112\) 16.9236 22.3067i 0.151104 0.199167i
\(113\) −141.505 141.505i −1.25226 1.25226i −0.954704 0.297556i \(-0.903828\pi\)
−0.297556 0.954704i \(-0.596172\pi\)
\(114\) 9.18141 111.685i 0.0805387 0.979694i
\(115\) 6.94062 + 17.6409i 0.0603532 + 0.153399i
\(116\) 57.0318i 0.491653i
\(117\) 36.0318 25.7970i 0.307964 0.220487i
\(118\) −61.6589 61.6589i −0.522533 0.522533i
\(119\) 197.773 27.1379i 1.66196 0.228050i
\(120\) −37.3825 20.0636i −0.311521 0.167197i
\(121\) −92.2966 −0.762782
\(122\) 54.1777 + 54.1777i 0.444080 + 0.444080i
\(123\) 86.9052 73.7020i 0.706546 0.599203i
\(124\) −31.3023 −0.252438
\(125\) −41.5815 117.881i −0.332652 0.943050i
\(126\) −89.0613 2.46594i −0.706836 0.0195710i
\(127\) −39.5166 39.5166i −0.311154 0.311154i 0.534202 0.845357i \(-0.320612\pi\)
−0.845357 + 0.534202i \(0.820612\pi\)
\(128\) −8.00000 8.00000i −0.0625000 0.0625000i
\(129\) 14.5236 176.669i 0.112586 1.36952i
\(130\) 31.9234 + 13.8962i 0.245564 + 0.106894i
\(131\) −122.046 −0.931652 −0.465826 0.884876i \(-0.654243\pi\)
−0.465826 + 0.884876i \(0.654243\pi\)
\(132\) −66.8308 + 56.6774i −0.506294 + 0.429374i
\(133\) 111.752 147.298i 0.840240 1.10751i
\(134\) −137.976 −1.02967
\(135\) 17.3355 + 133.882i 0.128411 + 0.991721i
\(136\) 80.6611i 0.593096i
\(137\) 141.949 141.949i 1.03612 1.03612i 0.0368001 0.999323i \(-0.488284\pi\)
0.999323 0.0368001i \(-0.0117165\pi\)
\(138\) 12.2680 10.4041i 0.0888984 0.0753924i
\(139\) −41.4554 −0.298240 −0.149120 0.988819i \(-0.547644\pi\)
−0.149120 + 0.988819i \(0.547644\pi\)
\(140\) −34.2459 61.0509i −0.244614 0.436078i
\(141\) 89.1435 + 7.32831i 0.632224 + 0.0519739i
\(142\) 65.9594 + 65.9594i 0.464503 + 0.464503i
\(143\) 50.8487 50.8487i 0.355585 0.355585i
\(144\) −5.87924 + 35.5167i −0.0408281 + 0.246644i
\(145\) 130.731 + 56.9068i 0.901591 + 0.392461i
\(146\) 13.0216 0.0891892
\(147\) −121.763 82.3570i −0.828322 0.560252i
\(148\) 15.3969 15.3969i 0.104033 0.104033i
\(149\) 189.375 1.27097 0.635485 0.772113i \(-0.280800\pi\)
0.635485 + 0.772113i \(0.280800\pi\)
\(150\) −83.2913 + 65.6701i −0.555275 + 0.437801i
\(151\) −117.328 −0.777007 −0.388503 0.921447i \(-0.627008\pi\)
−0.388503 + 0.921447i \(0.627008\pi\)
\(152\) −52.8265 52.8265i −0.347542 0.347542i
\(153\) −208.690 + 149.412i −1.36399 + 0.976548i
\(154\) −143.237 + 19.6546i −0.930109 + 0.127627i
\(155\) −31.2337 + 71.7524i −0.201507 + 0.462919i
\(156\) 2.42050 29.4436i 0.0155160 0.188741i
\(157\) 123.504 123.504i 0.786651 0.786651i −0.194293 0.980944i \(-0.562241\pi\)
0.980944 + 0.194293i \(0.0622411\pi\)
\(158\) 42.7301 + 42.7301i 0.270443 + 0.270443i
\(159\) 200.820 + 16.5090i 1.26302 + 0.103830i
\(160\) −26.3204 + 10.3555i −0.164503 + 0.0647217i
\(161\) 26.2937 3.60795i 0.163315 0.0224096i
\(162\) 102.781 50.5779i 0.634449 0.312209i
\(163\) −173.541 + 173.541i −1.06467 + 1.06467i −0.0669121 + 0.997759i \(0.521315\pi\)
−0.997759 + 0.0669121i \(0.978685\pi\)
\(164\) 75.9663i 0.463209i
\(165\) 63.2341 + 209.746i 0.383237 + 1.27119i
\(166\) 19.0523i 0.114773i
\(167\) −32.6021 32.6021i −0.195222 0.195222i 0.602726 0.797948i \(-0.294081\pi\)
−0.797948 + 0.602726i \(0.794081\pi\)
\(168\) −39.6567 + 44.2193i −0.236052 + 0.263210i
\(169\) 144.756i 0.856544i
\(170\) −184.895 80.4844i −1.08762 0.473437i
\(171\) −38.8225 + 234.528i −0.227032 + 1.37151i
\(172\) −83.5634 83.5634i −0.485833 0.485833i
\(173\) 122.097 122.097i 0.705761 0.705761i −0.259880 0.965641i \(-0.583683\pi\)
0.965641 + 0.259880i \(0.0836830\pi\)
\(174\) 9.91231 120.576i 0.0569673 0.692965i
\(175\) −174.114 + 17.5828i −0.994940 + 0.100473i
\(176\) 58.4187i 0.331924i
\(177\) 119.642 + 141.075i 0.675943 + 0.797034i
\(178\) 19.3830 + 19.3830i 0.108893 + 0.108893i
\(179\) −48.8414 −0.272857 −0.136429 0.990650i \(-0.543562\pi\)
−0.136429 + 0.990650i \(0.543562\pi\)
\(180\) 75.5465 + 48.9155i 0.419703 + 0.271753i
\(181\) 74.5578i 0.411921i −0.978560 0.205961i \(-0.933968\pi\)
0.978560 0.205961i \(-0.0660319\pi\)
\(182\) 29.4613 38.8324i 0.161875 0.213365i
\(183\) −105.126 123.958i −0.574457 0.677367i
\(184\) 10.7238i 0.0582815i
\(185\) −19.9303 50.6565i −0.107731 0.273819i
\(186\) 66.1789 + 5.44043i 0.355800 + 0.0292496i
\(187\) −294.507 + 294.507i −1.57491 + 1.57491i
\(188\) 42.1644 42.1644i 0.224279 0.224279i
\(189\) 187.864 + 20.6926i 0.993988 + 0.109485i
\(190\) −173.802 + 68.3804i −0.914746 + 0.359897i
\(191\) 22.0006i 0.115187i −0.998340 0.0575933i \(-0.981657\pi\)
0.998340 0.0575933i \(-0.0183427\pi\)
\(192\) 15.5231 + 18.3039i 0.0808494 + 0.0953330i
\(193\) −73.7660 + 73.7660i −0.382207 + 0.382207i −0.871897 0.489690i \(-0.837110\pi\)
0.489690 + 0.871897i \(0.337110\pi\)
\(194\) 169.278i 0.872568i
\(195\) −65.0768 34.9275i −0.333727 0.179115i
\(196\) −94.3778 + 26.3976i −0.481519 + 0.134682i
\(197\) −124.480 + 124.480i −0.631878 + 0.631878i −0.948539 0.316661i \(-0.897438\pi\)
0.316661 + 0.948539i \(0.397438\pi\)
\(198\) 151.144 108.211i 0.763351 0.546522i
\(199\) 324.188 1.62908 0.814542 0.580104i \(-0.196988\pi\)
0.814542 + 0.580104i \(0.196988\pi\)
\(200\) −2.52547 + 70.6656i −0.0126273 + 0.353328i
\(201\) 291.708 + 23.9807i 1.45128 + 0.119307i
\(202\) 112.859 112.859i 0.558707 0.558707i
\(203\) 120.648 159.024i 0.594326 0.783370i
\(204\) −14.0192 + 170.533i −0.0687214 + 0.835945i
\(205\) −174.133 75.7999i −0.849431 0.369755i
\(206\) −165.177 −0.801828
\(207\) −27.7451 + 19.8641i −0.134034 + 0.0959619i
\(208\) −13.9267 13.9267i −0.0669552 0.0669552i
\(209\) 385.757i 1.84573i
\(210\) 61.7915 + 135.025i 0.294245 + 0.642977i
\(211\) 29.3640 0.139166 0.0695828 0.997576i \(-0.477833\pi\)
0.0695828 + 0.997576i \(0.477833\pi\)
\(212\) 94.9868 94.9868i 0.448051 0.448051i
\(213\) −127.987 150.915i −0.600876 0.708519i
\(214\) 251.108i 1.17340i
\(215\) −274.928 + 108.167i −1.27873 + 0.503104i
\(216\) 18.6027 74.0671i 0.0861238 0.342903i
\(217\) 87.2814 + 66.2185i 0.402218 + 0.305154i
\(218\) −1.60754 1.60754i −0.00737405 0.00737405i
\(219\) −27.5302 2.26320i −0.125709 0.0103342i
\(220\) 133.910 + 58.2907i 0.608681 + 0.264958i
\(221\) 140.418i 0.635375i
\(222\) −35.2279 + 29.8759i −0.158684 + 0.134576i
\(223\) 203.552 + 203.552i 0.912788 + 0.912788i 0.996491 0.0837032i \(-0.0266748\pi\)
−0.0837032 + 0.996491i \(0.526675\pi\)
\(224\) 5.38310 + 39.2304i 0.0240317 + 0.175136i
\(225\) 187.507 124.363i 0.833365 0.552723i
\(226\) 283.011 1.25226
\(227\) 152.211 + 152.211i 0.670535 + 0.670535i 0.957839 0.287305i \(-0.0927592\pi\)
−0.287305 + 0.957839i \(0.592759\pi\)
\(228\) 102.504 + 120.866i 0.449577 + 0.530116i
\(229\) −219.445 −0.958275 −0.479138 0.877740i \(-0.659051\pi\)
−0.479138 + 0.877740i \(0.659051\pi\)
\(230\) −24.5815 10.7003i −0.106876 0.0465230i
\(231\) 306.245 16.6585i 1.32574 0.0721149i
\(232\) −57.0318 57.0318i −0.245827 0.245827i
\(233\) −216.913 216.913i −0.930957 0.930957i 0.0668091 0.997766i \(-0.478718\pi\)
−0.997766 + 0.0668091i \(0.978718\pi\)
\(234\) −10.2348 + 61.8287i −0.0437385 + 0.264225i
\(235\) −54.5791 138.723i −0.232251 0.590311i
\(236\) 123.318 0.522533
\(237\) −82.9128 97.7660i −0.349843 0.412515i
\(238\) −170.635 + 224.911i −0.716953 + 0.945003i
\(239\) −261.894 −1.09579 −0.547896 0.836547i \(-0.684571\pi\)
−0.547896 + 0.836547i \(0.684571\pi\)
\(240\) 57.4461 17.3189i 0.239359 0.0721619i
\(241\) 187.969i 0.779955i −0.920824 0.389978i \(-0.872483\pi\)
0.920824 0.389978i \(-0.127517\pi\)
\(242\) 92.2966 92.2966i 0.381391 0.381391i
\(243\) −226.088 + 89.0676i −0.930405 + 0.366533i
\(244\) −108.355 −0.444080
\(245\) −33.6612 + 242.677i −0.137393 + 0.990517i
\(246\) −13.2032 + 160.607i −0.0536715 + 0.652875i
\(247\) −91.9622 91.9622i −0.372317 0.372317i
\(248\) 31.3023 31.3023i 0.126219 0.126219i
\(249\) 3.31135 40.2801i 0.0132986 0.161768i
\(250\) 159.463 + 76.2997i 0.637851 + 0.305199i
\(251\) 406.255 1.61855 0.809273 0.587433i \(-0.199861\pi\)
0.809273 + 0.587433i \(0.199861\pi\)
\(252\) 91.5273 86.5954i 0.363203 0.343632i
\(253\) −39.1544 + 39.1544i −0.154760 + 0.154760i
\(254\) 79.0332 0.311154
\(255\) 376.914 + 202.294i 1.47809 + 0.793311i
\(256\) 16.0000 0.0625000
\(257\) −55.7465 55.7465i −0.216912 0.216912i 0.590284 0.807196i \(-0.299016\pi\)
−0.807196 + 0.590284i \(0.799016\pi\)
\(258\) 162.145 + 191.192i 0.628469 + 0.741055i
\(259\) −75.5032 + 10.3604i −0.291518 + 0.0400014i
\(260\) −45.8195 + 18.0272i −0.176229 + 0.0693353i
\(261\) −41.9130 + 253.197i −0.160586 + 0.970105i
\(262\) 122.046 122.046i 0.465826 0.465826i
\(263\) 96.5716 + 96.5716i 0.367192 + 0.367192i 0.866452 0.499260i \(-0.166395\pi\)
−0.499260 + 0.866452i \(0.666395\pi\)
\(264\) 10.1534 123.508i 0.0384597 0.467834i
\(265\) −122.954 312.512i −0.463978 1.17929i
\(266\) 35.5463 + 259.050i 0.133633 + 0.973873i
\(267\) −37.6105 44.3481i −0.140863 0.166098i
\(268\) 137.976 137.976i 0.514837 0.514837i
\(269\) 100.672i 0.374246i 0.982336 + 0.187123i \(0.0599163\pi\)
−0.982336 + 0.187123i \(0.940084\pi\)
\(270\) −151.218 116.547i −0.560066 0.431655i
\(271\) 299.070i 1.10358i −0.833983 0.551790i \(-0.813945\pi\)
0.833983 0.551790i \(-0.186055\pi\)
\(272\) 80.6611 + 80.6611i 0.296548 + 0.296548i
\(273\) −69.0359 + 76.9785i −0.252879 + 0.281972i
\(274\) 283.898i 1.03612i
\(275\) 267.233 248.791i 0.971756 0.904695i
\(276\) −1.86383 + 22.6721i −0.00675301 + 0.0821454i
\(277\) −310.502 310.502i −1.12095 1.12095i −0.991599 0.129348i \(-0.958712\pi\)
−0.129348 0.991599i \(-0.541288\pi\)
\(278\) 41.4554 41.4554i 0.149120 0.149120i
\(279\) −138.969 23.0042i −0.498097 0.0824523i
\(280\) 95.2969 + 26.8050i 0.340346 + 0.0957323i
\(281\) 229.692i 0.817409i −0.912667 0.408704i \(-0.865981\pi\)
0.912667 0.408704i \(-0.134019\pi\)
\(282\) −96.4718 + 81.8152i −0.342099 + 0.290125i
\(283\) −170.587 170.587i −0.602781 0.602781i 0.338269 0.941049i \(-0.390159\pi\)
−0.941049 + 0.338269i \(0.890159\pi\)
\(284\) −131.919 −0.464503
\(285\) 379.334 114.362i 1.33100 0.401269i
\(286\) 101.697i 0.355585i
\(287\) −160.703 + 211.820i −0.559942 + 0.738049i
\(288\) −29.6374 41.3959i −0.102908 0.143736i
\(289\) 524.277i 1.81411i
\(290\) −187.637 + 73.8239i −0.647026 + 0.254565i
\(291\) 29.4211 357.886i 0.101103 1.22985i
\(292\) −13.0216 + 13.0216i −0.0445946 + 0.0445946i
\(293\) 186.419 186.419i 0.636243 0.636243i −0.313384 0.949627i \(-0.601463\pi\)
0.949627 + 0.313384i \(0.101463\pi\)
\(294\) 204.120 39.4064i 0.694287 0.134035i
\(295\) 123.047 282.674i 0.417110 0.958218i
\(296\) 30.7938i 0.104033i
\(297\) −338.353 + 202.510i −1.13924 + 0.681851i
\(298\) −189.375 + 189.375i −0.635485 + 0.635485i
\(299\) 18.6684i 0.0624360i
\(300\) 17.6212 148.961i 0.0587374 0.496538i
\(301\) 56.2287 + 409.778i 0.186806 + 1.36139i
\(302\) 117.328 117.328i 0.388503 0.388503i
\(303\) −258.220 + 218.990i −0.852211 + 0.722738i
\(304\) 105.653 0.347542
\(305\) −108.118 + 248.377i −0.354485 + 0.814351i
\(306\) 59.2783 358.102i 0.193720 1.17027i
\(307\) 9.77168 9.77168i 0.0318296 0.0318296i −0.691013 0.722842i \(-0.742835\pi\)
0.722842 + 0.691013i \(0.242835\pi\)
\(308\) 123.582 162.891i 0.401241 0.528868i
\(309\) 349.215 + 28.7082i 1.13014 + 0.0929069i
\(310\) −40.5187 102.986i −0.130706 0.332213i
\(311\) −145.632 −0.468271 −0.234136 0.972204i \(-0.575226\pi\)
−0.234136 + 0.972204i \(0.575226\pi\)
\(312\) 27.0231 + 31.8641i 0.0866126 + 0.102129i
\(313\) −354.096 354.096i −1.13130 1.13130i −0.989962 0.141335i \(-0.954861\pi\)
−0.141335 0.989962i \(-0.545139\pi\)
\(314\) 247.008i 0.786651i
\(315\) −107.171 296.208i −0.340225 0.940344i
\(316\) −85.4601 −0.270443
\(317\) −136.486 + 136.486i −0.430556 + 0.430556i −0.888817 0.458262i \(-0.848472\pi\)
0.458262 + 0.888817i \(0.348472\pi\)
\(318\) −217.329 + 184.311i −0.683425 + 0.579594i
\(319\) 416.465i 1.30553i
\(320\) 15.9649 36.6759i 0.0498904 0.114612i
\(321\) −43.6435 + 530.891i −0.135961 + 1.65386i
\(322\) −22.6857 + 29.9016i −0.0704525 + 0.0928621i
\(323\) 532.630 + 532.630i 1.64901 + 1.64901i
\(324\) −52.2028 + 153.359i −0.161120 + 0.473329i
\(325\) −4.39643 + 123.017i −0.0135275 + 0.378514i
\(326\) 347.083i 1.06467i
\(327\) 3.11925 + 3.67804i 0.00953899 + 0.0112478i
\(328\) 75.9663 + 75.9663i 0.231605 + 0.231605i
\(329\) −206.766 + 28.3719i −0.628467 + 0.0862368i
\(330\) −272.980 146.511i −0.827211 0.443974i
\(331\) 317.945 0.960559 0.480279 0.877116i \(-0.340535\pi\)
0.480279 + 0.877116i \(0.340535\pi\)
\(332\) −19.0523 19.0523i −0.0573864 0.0573864i
\(333\) 79.6710 57.0405i 0.239252 0.171293i
\(334\) 65.2042 0.195222
\(335\) −178.601 453.949i −0.533138 1.35507i
\(336\) −4.56252 83.8760i −0.0135789 0.249631i
\(337\) 95.8647 + 95.8647i 0.284465 + 0.284465i 0.834887 0.550422i \(-0.185533\pi\)
−0.550422 + 0.834887i \(0.685533\pi\)
\(338\) 144.756 + 144.756i 0.428272 + 0.428272i
\(339\) −598.338 49.1882i −1.76501 0.145098i
\(340\) 265.379 104.411i 0.780527 0.307090i
\(341\) −228.580 −0.670322
\(342\) −195.705 273.350i −0.572237 0.799269i
\(343\) 319.001 + 126.046i 0.930031 + 0.367482i
\(344\) 167.127 0.485833
\(345\) 50.1103 + 26.8948i 0.145247 + 0.0779559i
\(346\) 244.193i 0.705761i
\(347\) −76.3053 + 76.3053i −0.219900 + 0.219900i −0.808456 0.588556i \(-0.799697\pi\)
0.588556 + 0.808456i \(0.299697\pi\)
\(348\) 110.664 + 130.488i 0.317999 + 0.374966i
\(349\) 27.7850 0.0796133 0.0398067 0.999207i \(-0.487326\pi\)
0.0398067 + 0.999207i \(0.487326\pi\)
\(350\) 156.532 191.697i 0.447233 0.547706i
\(351\) 32.3843 128.939i 0.0922630 0.367347i
\(352\) −58.4187 58.4187i −0.165962 0.165962i
\(353\) 188.774 188.774i 0.534769 0.534769i −0.387218 0.921988i \(-0.626564\pi\)
0.921988 + 0.387218i \(0.126564\pi\)
\(354\) −260.717 21.4330i −0.736488 0.0605452i
\(355\) −131.630 + 302.390i −0.370788 + 0.851803i
\(356\) −38.7660 −0.108893
\(357\) 399.845 445.847i 1.12001 1.24887i
\(358\) 48.8414 48.8414i 0.136429 0.136429i
\(359\) 171.974 0.479037 0.239519 0.970892i \(-0.423010\pi\)
0.239519 + 0.970892i \(0.423010\pi\)
\(360\) −124.462 + 26.6310i −0.345728 + 0.0739750i
\(361\) 336.659 0.932572
\(362\) 74.5578 + 74.5578i 0.205961 + 0.205961i
\(363\) −211.174 + 179.091i −0.581746 + 0.493364i
\(364\) 9.37109 + 68.2936i 0.0257448 + 0.187620i
\(365\) 16.8556 + 42.8418i 0.0461798 + 0.117375i
\(366\) 229.084 + 18.8325i 0.625912 + 0.0514550i
\(367\) 181.555 181.555i 0.494700 0.494700i −0.415083 0.909784i \(-0.636247\pi\)
0.909784 + 0.415083i \(0.136247\pi\)
\(368\) 10.7238 + 10.7238i 0.0291407 + 0.0291407i
\(369\) 55.8281 337.259i 0.151296 0.913981i
\(370\) 70.5868 + 30.7263i 0.190775 + 0.0830440i
\(371\) −465.796 + 63.9154i −1.25552 + 0.172279i
\(372\) −71.6193 + 60.7384i −0.192525 + 0.163275i
\(373\) −104.153 + 104.153i −0.279231 + 0.279231i −0.832802 0.553571i \(-0.813265\pi\)
0.553571 + 0.832802i \(0.313265\pi\)
\(374\) 589.015i 1.57491i
\(375\) −323.873 189.027i −0.863662 0.504072i
\(376\) 84.3288i 0.224279i
\(377\) −99.2830 99.2830i −0.263350 0.263350i
\(378\) −208.556 + 167.171i −0.551737 + 0.442252i
\(379\) 339.431i 0.895596i −0.894135 0.447798i \(-0.852208\pi\)
0.894135 0.447798i \(-0.147792\pi\)
\(380\) 105.421 242.182i 0.277425 0.637321i
\(381\) −167.091 13.7362i −0.438559 0.0360531i
\(382\) 22.0006 + 22.0006i 0.0575933 + 0.0575933i
\(383\) −187.161 + 187.161i −0.488670 + 0.488670i −0.907886 0.419217i \(-0.862305\pi\)
0.419217 + 0.907886i \(0.362305\pi\)
\(384\) −33.8270 2.78085i −0.0880912 0.00724180i
\(385\) −250.075 445.815i −0.649546 1.15796i
\(386\) 147.532i 0.382207i
\(387\) −309.575 432.398i −0.799937 1.11731i
\(388\) −169.278 169.278i −0.436284 0.436284i
\(389\) −511.312 −1.31443 −0.657214 0.753704i \(-0.728265\pi\)
−0.657214 + 0.753704i \(0.728265\pi\)
\(390\) 100.004 30.1493i 0.256421 0.0773059i
\(391\) 108.124i 0.276532i
\(392\) 67.9801 120.775i 0.173419 0.308101i
\(393\) −279.241 + 236.817i −0.710537 + 0.602588i
\(394\) 248.960i 0.631878i
\(395\) −85.2729 + 195.895i −0.215881 + 0.495938i
\(396\) −42.9322 + 259.355i −0.108415 + 0.654936i
\(397\) −448.583 + 448.583i −1.12993 + 1.12993i −0.139744 + 0.990188i \(0.544628\pi\)
−0.990188 + 0.139744i \(0.955372\pi\)
\(398\) −324.188 + 324.188i −0.814542 + 0.814542i
\(399\) −30.1277 553.859i −0.0755081 1.38812i
\(400\) −68.1401 73.1910i −0.170350 0.182978i
\(401\) 44.3430i 0.110581i 0.998470 + 0.0552905i \(0.0176085\pi\)
−0.998470 + 0.0552905i \(0.982391\pi\)
\(402\) −315.689 + 267.727i −0.785295 + 0.665988i
\(403\) 54.4921 54.4921i 0.135216 0.135216i
\(404\) 225.718i 0.558707i
\(405\) 299.447 + 272.684i 0.739375 + 0.673294i
\(406\) 38.3760 + 279.672i 0.0945221 + 0.688848i
\(407\) 112.433 112.433i 0.276249 0.276249i
\(408\) −156.514 184.552i −0.383612 0.452333i
\(409\) 392.358 0.959311 0.479656 0.877457i \(-0.340762\pi\)
0.479656 + 0.877457i \(0.340762\pi\)
\(410\) 249.933 98.3335i 0.609593 0.239838i
\(411\) 49.3423 600.213i 0.120054 1.46037i
\(412\) 165.177 165.177i 0.400914 0.400914i
\(413\) −343.852 260.873i −0.832571 0.631654i
\(414\) 7.88097 47.6092i 0.0190362 0.114998i
\(415\) −62.6830 + 24.6619i −0.151043 + 0.0594263i
\(416\) 27.8534 0.0669552
\(417\) −94.8495 + 80.4394i −0.227457 + 0.192900i
\(418\) −385.757 385.757i −0.922863 0.922863i
\(419\) 383.324i 0.914855i −0.889247 0.457427i \(-0.848771\pi\)
0.889247 0.457427i \(-0.151229\pi\)
\(420\) −196.817 73.2338i −0.468611 0.174366i
\(421\) 809.373 1.92250 0.961250 0.275678i \(-0.0889023\pi\)
0.961250 + 0.275678i \(0.0889023\pi\)
\(422\) −29.3640 + 29.3640i −0.0695828 + 0.0695828i
\(423\) 218.179 156.206i 0.515791 0.369281i
\(424\) 189.974i 0.448051i
\(425\) 25.4634 712.495i 0.0599139 1.67646i
\(426\) 278.901 + 22.9279i 0.654698 + 0.0538214i
\(427\) 302.132 + 229.221i 0.707569 + 0.536817i
\(428\) 251.108 + 251.108i 0.586702 + 0.586702i
\(429\) 17.6753 215.007i 0.0412012 0.501183i
\(430\) 166.760 383.095i 0.387815 0.890919i
\(431\) 432.674i 1.00388i 0.864902 + 0.501942i \(0.167381\pi\)
−0.864902 + 0.501942i \(0.832619\pi\)
\(432\) 55.4644 + 92.6699i 0.128390 + 0.214514i
\(433\) 288.449 + 288.449i 0.666163 + 0.666163i 0.956826 0.290662i \(-0.0938756\pi\)
−0.290662 + 0.956826i \(0.593876\pi\)
\(434\) −153.500 + 21.0629i −0.353686 + 0.0485320i
\(435\) 409.532 123.466i 0.941452 0.283829i
\(436\) 3.21508 0.00737405
\(437\) 70.8125 + 70.8125i 0.162042 + 0.162042i
\(438\) 29.7934 25.2670i 0.0680214 0.0576871i
\(439\) 652.665 1.48671 0.743354 0.668898i \(-0.233234\pi\)
0.743354 + 0.668898i \(0.233234\pi\)
\(440\) −192.201 + 75.6192i −0.436819 + 0.171862i
\(441\) −438.398 + 47.8358i −0.994100 + 0.108471i
\(442\) 140.418 + 140.418i 0.317687 + 0.317687i
\(443\) 429.708 + 429.708i 0.969996 + 0.969996i 0.999563 0.0295673i \(-0.00941292\pi\)
−0.0295673 + 0.999563i \(0.509413\pi\)
\(444\) 5.35206 65.1038i 0.0120542 0.146630i
\(445\) −38.6810 + 88.8610i −0.0869236 + 0.199688i
\(446\) −407.103 −0.912788
\(447\) 433.287 367.460i 0.969323 0.822057i
\(448\) −44.6135 33.8473i −0.0995836 0.0755519i
\(449\) 544.342 1.21234 0.606171 0.795334i \(-0.292705\pi\)
0.606171 + 0.795334i \(0.292705\pi\)
\(450\) −63.1445 + 311.870i −0.140321 + 0.693044i
\(451\) 554.732i 1.23000i
\(452\) −283.011 + 283.011i −0.626130 + 0.626130i
\(453\) −268.446 + 227.662i −0.592595 + 0.502564i
\(454\) −304.423 −0.670535
\(455\) 165.896 + 46.6632i 0.364607 + 0.102556i
\(456\) −223.370 18.3628i −0.489847 0.0402693i
\(457\) −100.300 100.300i −0.219475 0.219475i 0.588802 0.808277i \(-0.299600\pi\)
−0.808277 + 0.588802i \(0.799600\pi\)
\(458\) 219.445 219.445i 0.479138 0.479138i
\(459\) −187.565 + 746.792i −0.408638 + 1.62700i
\(460\) 35.2818 13.8812i 0.0766996 0.0301766i
\(461\) −16.3102 −0.0353801 −0.0176900 0.999844i \(-0.505631\pi\)
−0.0176900 + 0.999844i \(0.505631\pi\)
\(462\) −289.587 + 322.904i −0.626812 + 0.698926i
\(463\) −401.469 + 401.469i −0.867104 + 0.867104i −0.992151 0.125047i \(-0.960092\pi\)
0.125047 + 0.992151i \(0.460092\pi\)
\(464\) 114.064 0.245827
\(465\) 67.7649 + 224.774i 0.145731 + 0.483385i
\(466\) 433.826 0.930957
\(467\) 371.481 + 371.481i 0.795462 + 0.795462i 0.982376 0.186914i \(-0.0598486\pi\)
−0.186914 + 0.982376i \(0.559849\pi\)
\(468\) −51.5939 72.0635i −0.110243 0.153982i
\(469\) −676.608 + 92.8425i −1.44266 + 0.197959i
\(470\) 193.302 + 84.1441i 0.411281 + 0.179030i
\(471\) 42.9309 522.222i 0.0911483 1.10875i
\(472\) −123.318 + 123.318i −0.261266 + 0.261266i
\(473\) −610.208 610.208i −1.29008 1.29008i
\(474\) 180.679 + 14.8532i 0.381179 + 0.0313360i
\(475\) −449.950 483.303i −0.947263 1.01748i
\(476\) −54.2759 395.546i −0.114025 0.830978i
\(477\) 491.508 351.896i 1.03042 0.737727i
\(478\) 261.894 261.894i 0.547896 0.547896i
\(479\) 615.307i 1.28457i 0.766467 + 0.642283i \(0.222013\pi\)
−0.766467 + 0.642283i \(0.777987\pi\)
\(480\) −40.1273 + 74.7650i −0.0835985 + 0.155760i
\(481\) 53.6069i 0.111449i
\(482\) 187.969 + 187.969i 0.389978 + 0.389978i
\(483\) 53.1588 59.2748i 0.110060 0.122722i
\(484\) 184.593i 0.381391i
\(485\) −556.934 + 219.119i −1.14832 + 0.451793i
\(486\) 137.021 315.156i 0.281936 0.648469i
\(487\) 597.102 + 597.102i 1.22608 + 1.22608i 0.965434 + 0.260649i \(0.0839364\pi\)
0.260649 + 0.965434i \(0.416064\pi\)
\(488\) 108.355 108.355i 0.222040 0.222040i
\(489\) −60.3241 + 733.798i −0.123362 + 1.50061i
\(490\) −209.015 276.338i −0.426562 0.563955i
\(491\) 11.7151i 0.0238597i 0.999929 + 0.0119298i \(0.00379747\pi\)
−0.999929 + 0.0119298i \(0.996203\pi\)
\(492\) −147.404 173.810i −0.299602 0.353273i
\(493\) 575.031 + 575.031i 1.16639 + 1.16639i
\(494\) 183.924 0.372317
\(495\) 551.666 + 357.198i 1.11448 + 0.721611i
\(496\) 62.6045i 0.126219i
\(497\) 367.835 + 279.068i 0.740110 + 0.561506i
\(498\) 36.9688 + 43.5915i 0.0742345 + 0.0875330i
\(499\) 11.1783i 0.0224014i −0.999937 0.0112007i \(-0.996435\pi\)
0.999937 0.0112007i \(-0.00356537\pi\)
\(500\) −235.762 + 83.1630i −0.471525 + 0.166326i
\(501\) −137.854 11.3327i −0.275157 0.0226201i
\(502\) −406.255 + 406.255i −0.809273 + 0.809273i
\(503\) 15.0212 15.0212i 0.0298632 0.0298632i −0.692017 0.721881i \(-0.743278\pi\)
0.721881 + 0.692017i \(0.243278\pi\)
\(504\) −4.93189 + 178.123i −0.00978549 + 0.353418i
\(505\) 517.400 + 225.223i 1.02455 + 0.445986i
\(506\) 78.3088i 0.154760i
\(507\) −280.882 331.200i −0.554008 0.653255i
\(508\) −79.0332 + 79.0332i −0.155577 + 0.155577i
\(509\) 62.6374i 0.123060i 0.998105 + 0.0615298i \(0.0195979\pi\)
−0.998105 + 0.0615298i \(0.980402\pi\)
\(510\) −579.209 + 174.620i −1.13570 + 0.342392i
\(511\) 63.8554 8.76209i 0.124962 0.0171469i
\(512\) −16.0000 + 16.0000i −0.0312500 + 0.0312500i
\(513\) 366.248 + 611.928i 0.713934 + 1.19284i
\(514\) 111.493 0.216912
\(515\) −213.810 543.440i −0.415166 1.05522i
\(516\) −353.337 29.0472i −0.684762 0.0562930i
\(517\) 307.899 307.899i 0.595549 0.595549i
\(518\) 65.1428 85.8636i 0.125758 0.165760i
\(519\) 42.4416 516.271i 0.0817757 0.994741i
\(520\) 27.7923 63.8467i 0.0534468 0.122782i
\(521\) 2.86685 0.00550258 0.00275129 0.999996i \(-0.499124\pi\)
0.00275129 + 0.999996i \(0.499124\pi\)
\(522\) −211.284 295.110i −0.404759 0.565345i
\(523\) −216.205 216.205i −0.413394 0.413394i 0.469525 0.882919i \(-0.344425\pi\)
−0.882919 + 0.469525i \(0.844425\pi\)
\(524\) 244.093i 0.465826i
\(525\) −364.255 + 378.078i −0.693819 + 0.720149i
\(526\) −193.143 −0.367192
\(527\) −315.609 + 315.609i −0.598879 + 0.598879i
\(528\) 113.355 + 133.662i 0.214687 + 0.253147i
\(529\) 514.625i 0.972826i
\(530\) 435.466 + 189.557i 0.821634 + 0.357655i
\(531\) 547.479 + 90.6269i 1.03103 + 0.170672i
\(532\) −294.596 223.504i −0.553753 0.420120i
\(533\) 132.245 + 132.245i 0.248114 + 0.248114i
\(534\) 81.9586 + 6.73765i 0.153480 + 0.0126173i
\(535\) 826.160 325.043i 1.54422 0.607558i
\(536\) 275.953i 0.514837i
\(537\) −111.749 + 94.7712i −0.208098 + 0.176483i
\(538\) −100.672 100.672i −0.187123 0.187123i
\(539\) −689.179 + 192.764i −1.27862 + 0.357633i
\(540\) 267.765 34.6710i 0.495861 0.0642056i
\(541\) −544.738 −1.00691 −0.503454 0.864022i \(-0.667938\pi\)
−0.503454 + 0.864022i \(0.667938\pi\)
\(542\) 299.070 + 299.070i 0.551790 + 0.551790i
\(543\) −144.671 170.588i −0.266429 0.314158i
\(544\) −161.322 −0.296548
\(545\) 3.20804 7.36976i 0.00588631 0.0135225i
\(546\) −7.94260 146.014i −0.0145469 0.267426i
\(547\) −644.286 644.286i −1.17785 1.17785i −0.980290 0.197564i \(-0.936697\pi\)
−0.197564 0.980290i \(-0.563303\pi\)
\(548\) −283.898 283.898i −0.518061 0.518061i
\(549\) −481.053 79.6310i −0.876235 0.145047i
\(550\) −18.4418 + 516.024i −0.0335306 + 0.938225i
\(551\) 753.197 1.36696
\(552\) −20.8083 24.5359i −0.0376962 0.0444492i
\(553\) 238.292 + 180.787i 0.430908 + 0.326921i
\(554\) 621.005 1.12095
\(555\) −143.893 77.2294i −0.259268 0.139152i
\(556\) 82.9107i 0.149120i
\(557\) 180.720 180.720i 0.324452 0.324452i −0.526020 0.850472i \(-0.676316\pi\)
0.850472 + 0.526020i \(0.176316\pi\)
\(558\) 161.973 115.965i 0.290275 0.207822i
\(559\) 290.940 0.520465
\(560\) −122.102 + 68.4918i −0.218039 + 0.122307i
\(561\) −102.373 + 1245.29i −0.182482 + 2.21977i
\(562\) 229.692 + 229.692i 0.408704 + 0.408704i
\(563\) −16.4783 + 16.4783i −0.0292687 + 0.0292687i −0.721590 0.692321i \(-0.756588\pi\)
0.692321 + 0.721590i \(0.256588\pi\)
\(564\) 14.6566 178.287i 0.0259869 0.316112i
\(565\) 366.339 + 931.120i 0.648388 + 1.64800i
\(566\) 341.174 0.602781
\(567\) 469.982 317.184i 0.828893 0.559407i
\(568\) 131.919 131.919i 0.232251 0.232251i
\(569\) 354.571 0.623147 0.311574 0.950222i \(-0.399144\pi\)
0.311574 + 0.950222i \(0.399144\pi\)
\(570\) −264.973 + 493.696i −0.464864 + 0.866133i
\(571\) −110.075 −0.192777 −0.0963883 0.995344i \(-0.530729\pi\)
−0.0963883 + 0.995344i \(0.530729\pi\)
\(572\) −101.697 101.697i −0.177793 0.177793i
\(573\) −42.6897 50.3372i −0.0745021 0.0878486i
\(574\) −51.1168 372.524i −0.0890537 0.648996i
\(575\) 3.38533 94.7254i 0.00588752 0.164740i
\(576\) 71.0334 + 11.7585i 0.123322 + 0.0204140i
\(577\) −212.392 + 212.392i −0.368097 + 0.368097i −0.866783 0.498686i \(-0.833816\pi\)
0.498686 + 0.866783i \(0.333816\pi\)
\(578\) −524.277 524.277i −0.907054 0.907054i
\(579\) −25.6415 + 311.910i −0.0442859 + 0.538705i
\(580\) 113.814 261.461i 0.196230 0.450795i
\(581\) 12.8200 + 93.4285i 0.0220655 + 0.160806i
\(582\) 328.465 + 387.307i 0.564372 + 0.665476i
\(583\) 693.626 693.626i 1.18975 1.18975i
\(584\) 26.0432i 0.0445946i
\(585\) −216.668 + 46.3602i −0.370373 + 0.0792482i
\(586\) 372.838i 0.636243i
\(587\) −277.047 277.047i −0.471972 0.471972i 0.430580 0.902552i \(-0.358309\pi\)
−0.902552 + 0.430580i \(0.858309\pi\)
\(588\) −164.714 + 243.527i −0.280126 + 0.414161i
\(589\) 413.397i 0.701862i
\(590\) 159.627 + 405.722i 0.270554 + 0.687664i
\(591\) −43.2700 + 526.348i −0.0732150 + 0.890606i
\(592\) −30.7938 30.7938i −0.0520165 0.0520165i
\(593\) 118.407 118.407i 0.199674 0.199674i −0.600186 0.799860i \(-0.704907\pi\)
0.799860 + 0.600186i \(0.204907\pi\)
\(594\) 135.844 540.863i 0.228693 0.910544i
\(595\) −960.844 270.265i −1.61486 0.454228i
\(596\) 378.749i 0.635485i
\(597\) 741.739 629.049i 1.24244 1.05368i
\(598\) 18.6684 + 18.6684i 0.0312180 + 0.0312180i
\(599\) −254.409 −0.424722 −0.212361 0.977191i \(-0.568115\pi\)
−0.212361 + 0.977191i \(0.568115\pi\)
\(600\) 131.340 + 166.583i 0.218900 + 0.277638i
\(601\) 335.032i 0.557458i 0.960370 + 0.278729i \(0.0899131\pi\)
−0.960370 + 0.278729i \(0.910087\pi\)
\(602\) −466.006 353.549i −0.774097 0.587291i
\(603\) 713.957 511.158i 1.18401 0.847692i
\(604\) 234.656i 0.388503i
\(605\) 423.132 + 184.189i 0.699393 + 0.304444i
\(606\) 39.2304 477.210i 0.0647367 0.787474i
\(607\) −537.196 + 537.196i −0.885002 + 0.885002i −0.994038 0.109036i \(-0.965224\pi\)
0.109036 + 0.994038i \(0.465224\pi\)
\(608\) −105.653 + 105.653i −0.173771 + 0.173771i
\(609\) −32.5261 597.950i −0.0534090 0.981855i
\(610\) −140.259 356.495i −0.229933 0.584418i
\(611\) 146.803i 0.240266i
\(612\) 298.824 + 417.380i 0.488274 + 0.681994i
\(613\) −155.599 + 155.599i −0.253832 + 0.253832i −0.822540 0.568708i \(-0.807444\pi\)
0.568708 + 0.822540i \(0.307444\pi\)
\(614\) 19.5434i 0.0318296i
\(615\) −545.497 + 164.456i −0.886986 + 0.267409i
\(616\) 39.3092 + 286.473i 0.0638137 + 0.465054i
\(617\) 533.777 533.777i 0.865116 0.865116i −0.126811 0.991927i \(-0.540474\pi\)
0.991927 + 0.126811i \(0.0404741\pi\)
\(618\) −377.923 + 320.506i −0.611526 + 0.518619i
\(619\) 96.5213 0.155931 0.0779655 0.996956i \(-0.475158\pi\)
0.0779655 + 0.996956i \(0.475158\pi\)
\(620\) 143.505 + 62.4673i 0.231459 + 0.100754i
\(621\) −24.9365 + 99.2851i −0.0401554 + 0.159879i
\(622\) 145.632 145.632i 0.234136 0.234136i
\(623\) 108.093 + 82.0076i 0.173504 + 0.131633i
\(624\) −58.8873 4.84101i −0.0943706 0.00775802i
\(625\) −44.6159 + 623.406i −0.0713855 + 0.997449i
\(626\) 708.192 1.13130
\(627\) 748.516 + 882.608i 1.19381 + 1.40767i
\(628\) −247.008 247.008i −0.393326 0.393326i
\(629\) 310.482i 0.493613i
\(630\) 403.379 + 189.037i 0.640285 + 0.300059i
\(631\) −797.287 −1.26353 −0.631765 0.775160i \(-0.717669\pi\)
−0.631765 + 0.775160i \(0.717669\pi\)
\(632\) 85.4601 85.4601i 0.135222 0.135222i
\(633\) 67.1845 56.9774i 0.106137 0.0900117i
\(634\) 272.972i 0.430556i
\(635\) 102.303 + 260.023i 0.161108 + 0.409485i
\(636\) 33.0180 401.640i 0.0519151 0.631510i
\(637\) 118.342 210.250i 0.185781 0.330063i
\(638\) −416.465 416.465i −0.652767 0.652767i
\(639\) −585.665 96.9479i −0.916533 0.151718i
\(640\) 20.7110 + 52.6408i 0.0323609 + 0.0822513i
\(641\) 816.250i 1.27340i 0.771111 + 0.636701i \(0.219701\pi\)
−0.771111 + 0.636701i \(0.780299\pi\)
\(642\) −487.247 574.534i −0.758952 0.894913i
\(643\) −397.740 397.740i −0.618569 0.618569i 0.326595 0.945164i \(-0.394099\pi\)
−0.945164 + 0.326595i \(0.894099\pi\)
\(644\) −7.21591 52.5873i −0.0112048 0.0816573i
\(645\) −419.146 + 780.952i −0.649839 + 1.21078i
\(646\) −1065.26 −1.64901
\(647\) −593.146 593.146i −0.916763 0.916763i 0.0800295 0.996792i \(-0.474499\pi\)
−0.996792 + 0.0800295i \(0.974499\pi\)
\(648\) −101.156 205.561i −0.156105 0.317224i
\(649\) 900.508 1.38753
\(650\) −118.621 127.414i −0.182493 0.196021i
\(651\) 328.189 17.8522i 0.504130 0.0274227i
\(652\) 347.083 + 347.083i 0.532335 + 0.532335i
\(653\) −525.550 525.550i −0.804824 0.804824i 0.179021 0.983845i \(-0.442707\pi\)
−0.983845 + 0.179021i \(0.942707\pi\)
\(654\) −6.79729 0.558792i −0.0103934 0.000854422i
\(655\) 559.520 + 243.558i 0.854229 + 0.371844i
\(656\) −151.933 −0.231605
\(657\) −67.3803 + 48.2409i −0.102557 + 0.0734261i
\(658\) 178.394 235.138i 0.271115 0.357352i
\(659\) 415.401 0.630350 0.315175 0.949034i \(-0.397937\pi\)
0.315175 + 0.949034i \(0.397937\pi\)
\(660\) 419.491 126.468i 0.635593 0.191618i
\(661\) 723.547i 1.09462i −0.836929 0.547312i \(-0.815651\pi\)
0.836929 0.547312i \(-0.184349\pi\)
\(662\) −317.945 + 317.945i −0.480279 + 0.480279i
\(663\) −272.465 321.275i −0.410957 0.484577i
\(664\) 38.1046 0.0573864
\(665\) −806.276 + 452.273i −1.21245 + 0.680109i
\(666\) −22.6305 + 136.712i −0.0339797 + 0.205273i
\(667\) 76.4496 + 76.4496i 0.114617 + 0.114617i
\(668\) −65.2042 + 65.2042i −0.0976110 + 0.0976110i
\(669\) 860.693 + 70.7559i 1.28654 + 0.105764i
\(670\) 632.550 + 275.348i 0.944105 + 0.410967i
\(671\) −791.248 −1.17921
\(672\) 88.4385 + 79.3135i 0.131605 + 0.118026i
\(673\) 95.8909 95.8909i 0.142483 0.142483i −0.632267 0.774750i \(-0.717876\pi\)
0.774750 + 0.632267i \(0.217876\pi\)
\(674\) −191.729 −0.284465
\(675\) 187.703 648.377i 0.278079 0.960558i
\(676\) −289.512 −0.428272
\(677\) −90.8203 90.8203i −0.134151 0.134151i 0.636843 0.770994i \(-0.280240\pi\)
−0.770994 + 0.636843i \(0.780240\pi\)
\(678\) 647.526 549.150i 0.955054 0.809956i
\(679\) 113.905 + 830.106i 0.167754 + 1.22254i
\(680\) −160.969 + 369.790i −0.236719 + 0.543808i
\(681\) 643.607 + 52.9096i 0.945091 + 0.0776940i
\(682\) 228.580 228.580i 0.335161 0.335161i
\(683\) 572.076 + 572.076i 0.837593 + 0.837593i 0.988542 0.150948i \(-0.0482327\pi\)
−0.150948 + 0.988542i \(0.548233\pi\)
\(684\) 469.055 + 77.6449i 0.685753 + 0.113516i
\(685\) −934.038 + 367.487i −1.36356 + 0.536477i
\(686\) −445.047 + 192.954i −0.648756 + 0.281274i
\(687\) −502.088 + 425.808i −0.730842 + 0.619808i
\(688\) −167.127 + 167.127i −0.242917 + 0.242917i
\(689\) 330.713i 0.479990i
\(690\) −77.0050 + 23.2155i −0.111602 + 0.0336456i
\(691\) 941.057i 1.36188i −0.732340 0.680939i \(-0.761572\pi\)
0.732340 0.680939i \(-0.238428\pi\)
\(692\) −244.193 244.193i −0.352880 0.352880i
\(693\) 668.363 632.349i 0.964449 0.912480i
\(694\) 152.611i 0.219900i
\(695\) 190.052 + 82.7290i 0.273455 + 0.119035i
\(696\) −241.152 19.8246i −0.346482 0.0284836i
\(697\) −765.941 765.941i −1.09891 1.09891i
\(698\) −27.7850 + 27.7850i −0.0398067 + 0.0398067i
\(699\) −917.189 75.4003i −1.31215 0.107869i
\(700\) 35.1656 + 348.229i 0.0502366 + 0.497470i
\(701\) 305.599i 0.435947i −0.975955 0.217973i \(-0.930055\pi\)
0.975955 0.217973i \(-0.0699446\pi\)
\(702\) 96.5544 + 161.323i 0.137542 + 0.229805i
\(703\) −203.341 203.341i −0.289247 0.289247i
\(704\) 116.837 0.165962
\(705\) −394.053 211.493i −0.558940 0.299990i
\(706\) 377.547i 0.534769i
\(707\) 477.495 629.378i 0.675382 0.890209i
\(708\) 282.150 239.284i 0.398517 0.337972i
\(709\) 976.020i 1.37661i −0.725419 0.688307i \(-0.758354\pi\)
0.725419 0.688307i \(-0.241646\pi\)
\(710\) −170.760 434.020i −0.240507 0.611295i
\(711\) −379.408 62.8051i −0.533625 0.0883335i
\(712\) 38.7660 38.7660i 0.0544466 0.0544466i
\(713\) −41.9599 + 41.9599i −0.0588497 + 0.0588497i
\(714\) 46.0023 + 845.691i 0.0644289 + 1.18444i
\(715\) −334.590 + 131.641i −0.467958 + 0.184113i
\(716\) 97.6829i 0.136429i
\(717\) −599.212 + 508.176i −0.835721 + 0.708753i
\(718\) −171.974 + 171.974i −0.239519 + 0.239519i
\(719\) 792.968i 1.10288i −0.834216 0.551438i \(-0.814079\pi\)
0.834216 0.551438i \(-0.185921\pi\)
\(720\) 97.8310 151.093i 0.135876 0.209851i
\(721\) −809.993 + 111.145i −1.12343 + 0.154154i
\(722\) −336.659 + 336.659i −0.466286 + 0.466286i
\(723\) −364.733 430.072i −0.504471 0.594844i
\(724\) −149.116 −0.205961
\(725\) −485.769 521.777i −0.670026 0.719692i
\(726\) 32.0829 390.265i 0.0441913 0.537555i
\(727\) 666.489 666.489i 0.916767 0.916767i −0.0800261 0.996793i \(-0.525500\pi\)
0.996793 + 0.0800261i \(0.0255004\pi\)
\(728\) −77.6647 58.9226i −0.106682 0.0809376i
\(729\) −344.463 + 642.484i −0.472514 + 0.881323i
\(730\) −59.6975 25.9862i −0.0817773 0.0355975i
\(731\) −1685.08 −2.30517
\(732\) −247.916 + 210.251i −0.338683 + 0.287228i
\(733\) −338.466 338.466i −0.461754 0.461754i 0.437476 0.899230i \(-0.355873\pi\)
−0.899230 + 0.437476i \(0.855873\pi\)
\(734\) 363.110i 0.494700i
\(735\) 393.870 + 620.558i 0.535877 + 0.844296i
\(736\) −21.4476 −0.0291407
\(737\) 1007.55 1007.55i 1.36710 1.36710i
\(738\) 281.431 + 393.087i 0.381343 + 0.532638i
\(739\) 1021.49i 1.38226i −0.722730 0.691130i \(-0.757113\pi\)
0.722730 0.691130i \(-0.242887\pi\)
\(740\) −101.313 + 39.8605i −0.136910 + 0.0538656i
\(741\) −388.851 31.9667i −0.524765 0.0431399i
\(742\) 401.881 529.712i 0.541618 0.713897i
\(743\) 262.382 + 262.382i 0.353138 + 0.353138i 0.861276 0.508138i \(-0.169666\pi\)
−0.508138 + 0.861276i \(0.669666\pi\)
\(744\) 10.8809 132.358i 0.0146248 0.177900i
\(745\) −868.185 377.919i −1.16535 0.507274i
\(746\) 208.307i 0.279231i
\(747\) −70.5826 98.5858i −0.0944881 0.131976i
\(748\) 589.015 + 589.015i 0.787453 + 0.787453i
\(749\) −168.968 1231.38i −0.225591 1.64404i
\(750\) 512.900 134.846i 0.683867 0.179795i
\(751\) −429.513 −0.571922 −0.285961 0.958241i \(-0.592313\pi\)
−0.285961 + 0.958241i \(0.592313\pi\)
\(752\) −84.3288 84.3288i −0.112139 0.112139i
\(753\) 929.508 788.291i 1.23441 1.04687i
\(754\) 198.566 0.263350
\(755\) 537.889 + 234.142i 0.712436 + 0.310122i
\(756\) 41.3852 375.728i 0.0547424 0.496994i
\(757\) 439.564 + 439.564i 0.580666 + 0.580666i 0.935086 0.354420i \(-0.115322\pi\)
−0.354420 + 0.935086i \(0.615322\pi\)
\(758\) 339.431 + 339.431i 0.447798 + 0.447798i
\(759\) −13.6103 + 165.559i −0.0179319 + 0.218128i
\(760\) 136.761 + 347.604i 0.179948 + 0.457373i
\(761\) 1005.16 1.32084 0.660420 0.750897i \(-0.270378\pi\)
0.660420 + 0.750897i \(0.270378\pi\)
\(762\) 180.827 153.355i 0.237306 0.201253i
\(763\) −8.96476 6.80137i −0.0117494 0.00891398i
\(764\) −44.0013 −0.0575933
\(765\) 1254.91 268.511i 1.64040 0.350994i
\(766\) 374.321i 0.488670i
\(767\) −214.676 + 214.676i −0.279890 + 0.279890i
\(768\) 36.6079 31.0462i 0.0476665 0.0404247i
\(769\) −156.235 −0.203167 −0.101583 0.994827i \(-0.532391\pi\)
−0.101583 + 0.994827i \(0.532391\pi\)
\(770\) 695.890 + 195.739i 0.903753 + 0.254207i
\(771\) −235.717 19.3778i −0.305729 0.0251334i
\(772\) 147.532 + 147.532i 0.191104 + 0.191104i
\(773\) −95.1552 + 95.1552i −0.123099 + 0.123099i −0.765972 0.642874i \(-0.777742\pi\)
0.642874 + 0.765972i \(0.277742\pi\)
\(774\) 741.973 + 122.822i 0.958622 + 0.158685i
\(775\) 286.381 266.617i 0.369523 0.344022i
\(776\) 338.556 0.436284
\(777\) −152.648 + 170.210i −0.196458 + 0.219060i
\(778\) 511.312 511.312i 0.657214 0.657214i
\(779\) −1003.26 −1.28788
\(780\) −69.8550 + 130.154i −0.0895577 + 0.166864i
\(781\) −963.316 −1.23344
\(782\) −108.124 108.124i −0.138266 0.138266i
\(783\) 395.404 + 660.641i 0.504986 + 0.843730i
\(784\) 52.7953 + 188.756i 0.0673409 + 0.240760i
\(785\) −812.671 + 319.736i −1.03525 + 0.407307i
\(786\) 42.4241 516.058i 0.0539747 0.656563i
\(787\) −909.207 + 909.207i −1.15528 + 1.15528i −0.169804 + 0.985478i \(0.554313\pi\)
−0.985478 + 0.169804i \(0.945687\pi\)
\(788\) 248.960 + 248.960i 0.315939 + 0.315939i
\(789\) 408.341 + 33.5689i 0.517543 + 0.0425462i
\(790\) −110.623 281.168i −0.140029 0.355909i
\(791\) 1387.83 190.434i 1.75452 0.240752i
\(792\) −216.423 302.287i −0.273261 0.381676i
\(793\) 188.629 188.629i 0.237868 0.237868i
\(794\) 897.166i 1.12993i
\(795\) −887.711 476.445i −1.11662 0.599302i
\(796\) 648.376i 0.814542i
\(797\) −8.09283 8.09283i −0.0101541 0.0101541i 0.702011 0.712166i \(-0.252285\pi\)
−0.712166 + 0.702011i \(0.752285\pi\)
\(798\) 583.987 + 523.731i 0.731813 + 0.656305i
\(799\) 850.257i 1.06415i
\(800\) 141.331 + 5.05094i 0.176664 + 0.00631367i
\(801\) −172.105 28.4893i −0.214862 0.0355672i
\(802\) −44.3430 44.3430i −0.0552905 0.0552905i
\(803\) −95.0883 + 95.0883i −0.118416 + 0.118416i
\(804\) 47.9615 583.416i 0.0596536 0.725642i
\(805\) −127.743 35.9314i −0.158687 0.0446353i
\(806\) 108.984i 0.135216i
\(807\) 195.343 + 230.337i 0.242061 + 0.285424i
\(808\) −225.718 225.718i −0.279353 0.279353i
\(809\) 1556.68 1.92421 0.962103 0.272686i \(-0.0879120\pi\)
0.962103 + 0.272686i \(0.0879120\pi\)
\(810\) −572.131 + 26.7627i −0.706334 + 0.0330404i
\(811\) 849.941i 1.04802i 0.851713 + 0.524008i \(0.175564\pi\)
−0.851713 + 0.524008i \(0.824436\pi\)
\(812\) −318.048 241.296i −0.391685 0.297163i
\(813\) −580.312 684.270i −0.713790 0.841661i
\(814\) 224.867i 0.276249i
\(815\) 1141.92 449.276i 1.40113 0.551259i
\(816\) 341.066 + 28.0383i 0.417973 + 0.0343607i
\(817\) −1103.59 + 1103.59i −1.35078 + 1.35078i
\(818\) −392.358 + 392.358i −0.479656 + 0.479656i
\(819\) −8.58561 + 310.082i −0.0104830 + 0.378611i
\(820\) −151.600 + 348.267i −0.184878 + 0.424715i
\(821\) 164.509i 0.200376i 0.994969 + 0.100188i \(0.0319445\pi\)
−0.994969 + 0.100188i \(0.968056\pi\)
\(822\) 550.871 + 649.555i 0.670159 + 0.790213i
\(823\) −90.7701 + 90.7701i −0.110292 + 0.110292i −0.760099 0.649807i \(-0.774850\pi\)
0.649807 + 0.760099i \(0.274850\pi\)
\(824\) 330.353i 0.400914i
\(825\) 128.676 1087.77i 0.155971 1.31850i
\(826\) 604.725 82.9790i 0.732113 0.100459i
\(827\) −369.738 + 369.738i −0.447083 + 0.447083i −0.894384 0.447300i \(-0.852385\pi\)
0.447300 + 0.894384i \(0.352385\pi\)
\(828\) 39.7282 + 55.4902i 0.0479809 + 0.0670171i
\(829\) 61.7867 0.0745316 0.0372658 0.999305i \(-0.488135\pi\)
0.0372658 + 0.999305i \(0.488135\pi\)
\(830\) 38.0211 87.3449i 0.0458085 0.105235i
\(831\) −1312.92 107.933i −1.57993 0.129883i
\(832\) −27.8534 + 27.8534i −0.0334776 + 0.0334776i
\(833\) −685.419 + 1217.73i −0.822832 + 1.46187i
\(834\) 14.4102 175.289i 0.0172784 0.210179i
\(835\) 84.4025 + 214.525i 0.101081 + 0.256916i
\(836\) 771.513 0.922863
\(837\) −362.597 + 217.020i −0.433210 + 0.259283i
\(838\) 383.324 + 383.324i 0.457427 + 0.457427i
\(839\) 77.9554i 0.0929146i −0.998920 0.0464573i \(-0.985207\pi\)
0.998920 0.0464573i \(-0.0147931\pi\)
\(840\) 270.050 123.583i 0.321489 0.147123i
\(841\) −27.8443 −0.0331086
\(842\) −809.373 + 809.373i −0.961250 + 0.961250i
\(843\) −445.691 525.533i −0.528696 0.623408i
\(844\) 58.7279i 0.0695828i
\(845\) −288.877 + 663.631i −0.341867 + 0.785363i
\(846\) −61.9737 + 374.385i −0.0732550 + 0.442536i
\(847\) 390.499 514.709i 0.461037 0.607685i
\(848\) −189.974 189.974i −0.224026 0.224026i
\(849\) −721.306 59.2971i −0.849594 0.0698435i
\(850\) 687.032 + 737.959i 0.808273 + 0.868187i
\(851\) 41.2783i 0.0485056i
\(852\) −301.829 + 255.973i −0.354260 + 0.300438i
\(853\) 1148.30 + 1148.30i 1.34620 + 1.34620i 0.889753 + 0.456443i \(0.150877\pi\)
0.456443 + 0.889753i \(0.349123\pi\)
\(854\) −531.353 + 72.9110i −0.622193 + 0.0853759i
\(855\) 646.008 997.713i 0.755565 1.16692i
\(856\) −502.217 −0.586702
\(857\) 663.238 + 663.238i 0.773906 + 0.773906i 0.978787 0.204881i \(-0.0656806\pi\)
−0.204881 + 0.978787i \(0.565681\pi\)
\(858\) 197.332 + 232.683i 0.229991 + 0.271192i
\(859\) −726.339 −0.845564 −0.422782 0.906231i \(-0.638946\pi\)
−0.422782 + 0.906231i \(0.638946\pi\)
\(860\) 216.335 + 549.856i 0.251552 + 0.639367i
\(861\) 43.3248 + 796.469i 0.0503191 + 0.925051i
\(862\) −432.674 432.674i −0.501942 0.501942i
\(863\) 881.430 + 881.430i 1.02136 + 1.02136i 0.999767 + 0.0215890i \(0.00687252\pi\)
0.0215890 + 0.999767i \(0.493127\pi\)
\(864\) −148.134 37.2055i −0.171452 0.0430619i
\(865\) −803.408 + 316.092i −0.928796 + 0.365424i
\(866\) −576.898 −0.666163
\(867\) 1017.30 + 1199.54i 1.17336 + 1.38355i
\(868\) 132.437 174.563i 0.152577 0.201109i
\(869\) −624.059 −0.718134
\(870\) −286.066 + 532.997i −0.328812 + 0.612641i
\(871\) 480.388i 0.551536i
\(872\) −3.21508 + 3.21508i −0.00368702 + 0.00368702i
\(873\) −627.121 875.928i −0.718352 1.00335i
\(874\) −141.625 −0.162042
\(875\) 833.314 + 266.858i 0.952359 + 0.304980i
\(876\) −4.52640 + 55.0603i −0.00516712 + 0.0628543i
\(877\) 1201.58 + 1201.58i 1.37010 + 1.37010i 0.860280 + 0.509822i \(0.170289\pi\)
0.509822 + 0.860280i \(0.329711\pi\)
\(878\) −652.665 + 652.665i −0.743354 + 0.743354i
\(879\) 64.8005 788.251i 0.0737207 0.896759i
\(880\) 116.581 267.820i 0.132479 0.304341i
\(881\) −403.967 −0.458533 −0.229266 0.973364i \(-0.573633\pi\)
−0.229266 + 0.973364i \(0.573633\pi\)
\(882\) 390.562 486.234i 0.442814 0.551285i
\(883\) −740.709 + 740.709i −0.838855 + 0.838855i −0.988708 0.149853i \(-0.952120\pi\)
0.149853 + 0.988708i \(0.452120\pi\)
\(884\) −280.836 −0.317687
\(885\) −266.965 885.516i −0.301656 1.00058i
\(886\) −859.416 −0.969996
\(887\) 703.405 + 703.405i 0.793016 + 0.793016i 0.981983 0.188968i \(-0.0605142\pi\)
−0.188968 + 0.981983i \(0.560514\pi\)
\(888\) 59.7518 + 70.4559i 0.0672880 + 0.0793422i
\(889\) 387.563 53.1804i 0.435954 0.0598205i
\(890\) −50.1800 127.542i −0.0563820 0.143306i
\(891\) −381.203 + 1119.88i −0.427837 + 1.25688i
\(892\) 407.103 407.103i 0.456394 0.456394i
\(893\) −556.849 556.849i −0.623571 0.623571i
\(894\) −65.8278 + 800.747i −0.0736329 + 0.895690i
\(895\) 223.913 + 97.4688i 0.250182 + 0.108904i
\(896\) 78.4607 10.7662i 0.0875678 0.0120158i
\(897\) −36.2238 42.7131i −0.0403833 0.0476177i
\(898\) −544.342 + 544.342i −0.606171 + 0.606171i
\(899\) 446.306i 0.496447i
\(900\) −248.725 375.014i −0.276361 0.416683i
\(901\) 1915.44i 2.12590i
\(902\) 554.732 + 554.732i 0.615002 + 0.615002i
\(903\) 923.778 + 828.463i 1.02301 + 0.917456i
\(904\) 566.022i 0.626130i
\(905\) −148.789 + 341.809i −0.164407 + 0.377690i
\(906\) 40.7840 496.107i 0.0450154 0.547580i
\(907\) −141.537 141.537i −0.156050 0.156050i 0.624764 0.780814i \(-0.285195\pi\)
−0.780814 + 0.624764i \(0.785195\pi\)
\(908\) 304.423 304.423i 0.335267 0.335267i
\(909\) −165.881 + 1002.09i −0.182487 + 1.10241i
\(910\) −212.559 + 119.233i −0.233582 + 0.131025i
\(911\) 379.247i 0.416298i −0.978097 0.208149i \(-0.933256\pi\)
0.978097 0.208149i \(-0.0667439\pi\)
\(912\) 241.733 205.007i 0.265058 0.224789i
\(913\) −139.126 139.126i −0.152384 0.152384i
\(914\) 200.600 0.219475
\(915\) 234.574 + 778.075i 0.256365 + 0.850355i
\(916\) 438.890i 0.479138i
\(917\) 516.367 680.614i 0.563105 0.742219i
\(918\) −559.227 934.357i −0.609180 1.01782i
\(919\) 589.717i 0.641695i 0.947131 + 0.320847i \(0.103968\pi\)
−0.947131 + 0.320847i \(0.896032\pi\)
\(920\) −21.4006 + 49.1631i −0.0232615 + 0.0534381i
\(921\) 3.39670 41.3184i 0.00368806 0.0448625i
\(922\) 16.3102 16.3102i 0.0176900 0.0176900i
\(923\) 229.649 229.649i 0.248807 0.248807i
\(924\) −33.3171 612.491i −0.0360574 0.662869i
\(925\) −9.72109 + 272.007i −0.0105093 + 0.294062i
\(926\) 802.938i 0.867104i
\(927\) 854.705 611.927i 0.922012 0.660115i
\(928\) −114.064 + 114.064i −0.122913 + 0.122913i
\(929\) 409.557i 0.440858i −0.975403 0.220429i \(-0.929254\pi\)
0.975403 0.220429i \(-0.0707457\pi\)
\(930\) −292.539 157.009i −0.314558 0.168827i
\(931\) 348.623 + 1246.41i 0.374461 + 1.33879i
\(932\) −433.826 + 433.826i −0.465478 + 0.465478i
\(933\) −333.206 + 282.583i −0.357134 + 0.302875i
\(934\) −742.962 −0.795462
\(935\) 1937.89 762.441i 2.07261 0.815445i
\(936\) 123.657 + 20.4696i 0.132113 + 0.0218692i
\(937\) 275.806 275.806i 0.294350 0.294350i −0.544446 0.838796i \(-0.683260\pi\)
0.838796 + 0.544446i \(0.183260\pi\)
\(938\) 583.765 769.450i 0.622351 0.820310i
\(939\) −1497.25 123.086i −1.59452 0.131082i
\(940\) −277.446 + 109.158i −0.295156 + 0.116126i
\(941\) 769.189 0.817416 0.408708 0.912665i \(-0.365979\pi\)
0.408708 + 0.912665i \(0.365979\pi\)
\(942\) 479.291 + 565.153i 0.508802 + 0.599950i
\(943\) −101.831 101.831i −0.107986 0.107986i
\(944\) 246.635i 0.261266i
\(945\) −819.965 469.769i −0.867687 0.497110i
\(946\) 1220.42 1.29008
\(947\) 148.857 148.857i 0.157188 0.157188i −0.624132 0.781319i \(-0.714547\pi\)
0.781319 + 0.624132i \(0.214547\pi\)
\(948\) −195.532 + 165.826i −0.206257 + 0.174921i
\(949\) 45.3370i 0.0477735i
\(950\) 933.253 + 33.3529i 0.982371 + 0.0351083i
\(951\) −47.4435 + 577.115i −0.0498880 + 0.606851i
\(952\) 449.822 + 341.270i 0.472502 + 0.358477i
\(953\) −99.9670 99.9670i −0.104897 0.104897i 0.652710 0.757608i \(-0.273632\pi\)
−0.757608 + 0.652710i \(0.773632\pi\)
\(954\) −139.613 + 843.404i −0.146345 + 0.884071i
\(955\) −43.9048 + 100.862i −0.0459736 + 0.105614i
\(956\) 523.788i 0.547896i
\(957\) 808.103 + 952.869i 0.844413 + 0.995683i
\(958\) −615.307 615.307i −0.642283 0.642283i
\(959\) 191.031 + 1392.18i 0.199198 + 1.45170i
\(960\) −34.6377 114.892i −0.0360809 0.119679i
\(961\) 716.042 0.745101
\(962\) −53.6069 53.6069i −0.0557244 0.0557244i
\(963\) 930.276 + 1299.36i 0.966019 + 1.34928i
\(964\) −375.938 −0.389978
\(965\) 485.388 190.970i 0.502992 0.197897i
\(966\) 6.11594 + 112.434i 0.00633120 + 0.116391i
\(967\) −452.536 452.536i −0.467979 0.467979i 0.433280 0.901259i \(-0.357356\pi\)
−0.901259 + 0.433280i \(0.857356\pi\)
\(968\) −184.593 184.593i −0.190695 0.190695i
\(969\) 2252.16 + 185.146i 2.32421 + 0.191069i
\(970\) 337.814 776.053i 0.348262 0.800055i
\(971\) 625.077 0.643746 0.321873 0.946783i \(-0.395688\pi\)
0.321873 + 0.946783i \(0.395688\pi\)
\(972\) 178.135 + 452.177i 0.183267 + 0.465202i
\(973\) 175.394 231.183i 0.180261 0.237599i
\(974\) −1194.20 −1.22608
\(975\) 228.642 + 289.993i 0.234504 + 0.297429i
\(976\) 216.711i 0.222040i
\(977\) 172.179 172.179i 0.176232 0.176232i −0.613479 0.789711i \(-0.710230\pi\)
0.789711 + 0.613479i \(0.210230\pi\)
\(978\) −673.474 794.122i −0.688624 0.811986i
\(979\) −283.082 −0.289154
\(980\) 485.353 + 67.3224i 0.495258 + 0.0686963i
\(981\) 14.2736 + 2.36278i 0.0145501 + 0.00240855i
\(982\) −11.7151 11.7151i −0.0119298 0.0119298i
\(983\) −612.197 + 612.197i −0.622785 + 0.622785i −0.946243 0.323458i \(-0.895155\pi\)
0.323458 + 0.946243i \(0.395155\pi\)
\(984\) 321.214 + 26.4064i 0.326437 + 0.0268358i
\(985\) 819.091 322.262i 0.831565 0.327170i
\(986\) −1150.06 −1.16639
\(987\) −418.026 + 466.120i −0.423532 + 0.472259i
\(988\) −183.924 + 183.924i −0.186158 + 0.186158i
\(989\) −224.029 −0.226521
\(990\) −908.864 + 194.469i −0.918044 + 0.196433i
\(991\) 1736.43 1.75220 0.876102 0.482125i \(-0.160135\pi\)
0.876102 + 0.482125i \(0.160135\pi\)
\(992\) −62.6045 62.6045i −0.0631094 0.0631094i
\(993\) 727.455 616.936i 0.732583 0.621285i
\(994\) −646.903 + 88.7665i −0.650808 + 0.0893024i
\(995\) −1486.23 646.955i −1.49370 0.650206i
\(996\) −80.5602 6.62270i −0.0808838 0.00664929i
\(997\) 817.471 817.471i 0.819930 0.819930i −0.166167 0.986098i \(-0.553139\pi\)
0.986098 + 0.166167i \(0.0531392\pi\)
\(998\) 11.1783 + 11.1783i 0.0112007 + 0.0112007i
\(999\) 71.6061 285.101i 0.0716778 0.285386i
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 210.3.k.a.167.13 yes 32
3.2 odd 2 210.3.k.b.167.5 yes 32
5.3 odd 4 210.3.k.b.83.12 yes 32
7.6 odd 2 inner 210.3.k.a.167.4 yes 32
15.8 even 4 inner 210.3.k.a.83.4 32
21.20 even 2 210.3.k.b.167.12 yes 32
35.13 even 4 210.3.k.b.83.5 yes 32
105.83 odd 4 inner 210.3.k.a.83.13 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.3.k.a.83.4 32 15.8 even 4 inner
210.3.k.a.83.13 yes 32 105.83 odd 4 inner
210.3.k.a.167.4 yes 32 7.6 odd 2 inner
210.3.k.a.167.13 yes 32 1.1 even 1 trivial
210.3.k.b.83.5 yes 32 35.13 even 4
210.3.k.b.83.12 yes 32 5.3 odd 4
210.3.k.b.167.5 yes 32 3.2 odd 2
210.3.k.b.167.12 yes 32 21.20 even 2