Properties

Label 189.2.s.b.17.4
Level $189$
Weight $2$
Character 189.17
Analytic conductor $1.509$
Analytic rank $0$
Dimension $10$
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] = [189,2,Mod(17,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.s (of order \(6\), degree \(2\), not 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: \(1.50917259820\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: 10.0.288778218147.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.4
Root \(0.187540 - 0.324828i\) of defining polynomial
Character \(\chi\) \(=\) 189.17
Dual form 189.2.s.b.89.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.621951 + 0.359083i) q^{2} +(-0.742118 - 1.28539i) q^{4} +1.44755 q^{5} +(2.19442 + 1.47801i) q^{7} -2.50226i q^{8} +O(q^{10})\) \(q+(0.621951 + 0.359083i) q^{2} +(-0.742118 - 1.28539i) q^{4} +1.44755 q^{5} +(2.19442 + 1.47801i) q^{7} -2.50226i q^{8} +(0.900304 + 0.519791i) q^{10} -1.80056i q^{11} +(1.88867 + 1.09042i) q^{13} +(0.834091 + 1.70723i) q^{14} +(-0.585716 + 1.01449i) q^{16} +(1.95230 - 3.38149i) q^{17} +(-3.47456 + 2.00604i) q^{19} +(-1.07425 - 1.86066i) q^{20} +(0.646552 - 1.11986i) q^{22} +5.67561i q^{23} -2.90460 q^{25} +(0.783106 + 1.35638i) q^{26} +(0.271298 - 3.91754i) q^{28} +(-8.49418 + 4.90412i) q^{29} +(-2.45129 + 1.41525i) q^{31} +(-5.06262 + 2.92290i) q^{32} +(2.42847 - 1.40208i) q^{34} +(3.17653 + 2.13949i) q^{35} +(-0.411767 - 0.713202i) q^{37} -2.88134 q^{38} -3.62215i q^{40} +(5.90617 - 10.2298i) q^{41} +(-3.76766 - 6.52578i) q^{43} +(-2.31442 + 1.33623i) q^{44} +(-2.03802 + 3.52995i) q^{46} +(-1.16920 + 2.02511i) q^{47} +(2.63096 + 6.48676i) q^{49} +(-1.80652 - 1.04299i) q^{50} -3.23689i q^{52} +(0.996713 + 0.575453i) q^{53} -2.60640i q^{55} +(3.69838 - 5.49102i) q^{56} -7.04395 q^{58} +(4.89555 + 8.47934i) q^{59} +(2.03980 + 1.17768i) q^{61} -2.03277 q^{62} -1.85540 q^{64} +(2.73394 + 1.57844i) q^{65} +(0.156402 + 0.270897i) q^{67} -5.79536 q^{68} +(1.20739 + 2.47130i) q^{70} -1.94933i q^{71} +(2.42847 + 1.40208i) q^{73} -0.591435i q^{74} +(5.15706 + 2.97743i) q^{76} +(2.66125 - 3.95119i) q^{77} +(-6.21583 + 10.7661i) q^{79} +(-0.847852 + 1.46852i) q^{80} +(7.34669 - 4.24162i) q^{82} +(3.60916 + 6.25124i) q^{83} +(2.82605 - 4.89486i) q^{85} -5.41161i q^{86} -4.50548 q^{88} +(-5.28999 - 9.16253i) q^{89} +(2.53287 + 5.18433i) q^{91} +(7.29536 - 4.21198i) q^{92} +(-1.45436 + 0.839677i) q^{94} +(-5.02959 + 2.90383i) q^{95} +(13.4322 - 7.75510i) q^{97} +(-0.692961 + 4.97918i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 4 q^{4} + 3 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 4 q^{4} + 3 q^{7} - 15 q^{10} + 6 q^{13} + 6 q^{14} - 6 q^{16} + 12 q^{17} + 3 q^{19} + 3 q^{20} + 5 q^{22} - 14 q^{25} - 3 q^{26} + 2 q^{28} + 15 q^{29} - 9 q^{31} - 48 q^{32} + 3 q^{34} + 15 q^{35} + 6 q^{37} - 36 q^{38} + 9 q^{41} + 3 q^{43} - 24 q^{44} - 13 q^{46} - 15 q^{47} - 23 q^{49} - 3 q^{50} + 9 q^{53} + 51 q^{56} - 16 q^{58} + 18 q^{59} + 12 q^{61} - 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} + 54 q^{68} + 9 q^{70} + 3 q^{73} + 9 q^{76} - 45 q^{77} + 20 q^{79} + 30 q^{80} + 9 q^{82} + 15 q^{83} + 18 q^{85} + 16 q^{88} - 24 q^{89} - 24 q^{91} - 39 q^{92} - 3 q^{94} + 6 q^{97} - 45 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.621951 + 0.359083i 0.439785 + 0.253910i 0.703507 0.710689i \(-0.251617\pi\)
−0.263721 + 0.964599i \(0.584950\pi\)
\(3\) 0 0
\(4\) −0.742118 1.28539i −0.371059 0.642693i
\(5\) 1.44755 0.647363 0.323682 0.946166i \(-0.395079\pi\)
0.323682 + 0.946166i \(0.395079\pi\)
\(6\) 0 0
\(7\) 2.19442 + 1.47801i 0.829413 + 0.558636i
\(8\) 2.50226i 0.884683i
\(9\) 0 0
\(10\) 0.900304 + 0.519791i 0.284701 + 0.164372i
\(11\) 1.80056i 0.542890i −0.962454 0.271445i \(-0.912499\pi\)
0.962454 0.271445i \(-0.0875015\pi\)
\(12\) 0 0
\(13\) 1.88867 + 1.09042i 0.523823 + 0.302429i 0.738497 0.674256i \(-0.235536\pi\)
−0.214675 + 0.976686i \(0.568869\pi\)
\(14\) 0.834091 + 1.70723i 0.222920 + 0.456277i
\(15\) 0 0
\(16\) −0.585716 + 1.01449i −0.146429 + 0.253622i
\(17\) 1.95230 3.38149i 0.473503 0.820131i −0.526037 0.850462i \(-0.676323\pi\)
0.999540 + 0.0303308i \(0.00965608\pi\)
\(18\) 0 0
\(19\) −3.47456 + 2.00604i −0.797118 + 0.460216i −0.842462 0.538755i \(-0.818895\pi\)
0.0453446 + 0.998971i \(0.485561\pi\)
\(20\) −1.07425 1.86066i −0.240210 0.416056i
\(21\) 0 0
\(22\) 0.646552 1.11986i 0.137845 0.238755i
\(23\) 5.67561i 1.18345i 0.806141 + 0.591723i \(0.201552\pi\)
−0.806141 + 0.591723i \(0.798448\pi\)
\(24\) 0 0
\(25\) −2.90460 −0.580921
\(26\) 0.783106 + 1.35638i 0.153580 + 0.266008i
\(27\) 0 0
\(28\) 0.271298 3.91754i 0.0512705 0.740345i
\(29\) −8.49418 + 4.90412i −1.57733 + 0.910672i −0.582100 + 0.813117i \(0.697769\pi\)
−0.995230 + 0.0975551i \(0.968898\pi\)
\(30\) 0 0
\(31\) −2.45129 + 1.41525i −0.440264 + 0.254187i −0.703710 0.710488i \(-0.748474\pi\)
0.263445 + 0.964674i \(0.415141\pi\)
\(32\) −5.06262 + 2.92290i −0.894953 + 0.516701i
\(33\) 0 0
\(34\) 2.42847 1.40208i 0.416479 0.240454i
\(35\) 3.17653 + 2.13949i 0.536931 + 0.361641i
\(36\) 0 0
\(37\) −0.411767 0.713202i −0.0676941 0.117250i 0.830192 0.557478i \(-0.188231\pi\)
−0.897886 + 0.440228i \(0.854898\pi\)
\(38\) −2.88134 −0.467414
\(39\) 0 0
\(40\) 3.62215i 0.572712i
\(41\) 5.90617 10.2298i 0.922389 1.59762i 0.126681 0.991943i \(-0.459567\pi\)
0.795708 0.605681i \(-0.207099\pi\)
\(42\) 0 0
\(43\) −3.76766 6.52578i −0.574563 0.995172i −0.996089 0.0883555i \(-0.971839\pi\)
0.421526 0.906816i \(-0.361494\pi\)
\(44\) −2.31442 + 1.33623i −0.348912 + 0.201444i
\(45\) 0 0
\(46\) −2.03802 + 3.52995i −0.300489 + 0.520463i
\(47\) −1.16920 + 2.02511i −0.170545 + 0.295392i −0.938610 0.344979i \(-0.887886\pi\)
0.768066 + 0.640371i \(0.221219\pi\)
\(48\) 0 0
\(49\) 2.63096 + 6.48676i 0.375851 + 0.926680i
\(50\) −1.80652 1.04299i −0.255480 0.147502i
\(51\) 0 0
\(52\) 3.23689i 0.448877i
\(53\) 0.996713 + 0.575453i 0.136909 + 0.0790445i 0.566890 0.823793i \(-0.308146\pi\)
−0.429981 + 0.902838i \(0.641480\pi\)
\(54\) 0 0
\(55\) 2.60640i 0.351447i
\(56\) 3.69838 5.49102i 0.494216 0.733768i
\(57\) 0 0
\(58\) −7.04395 −0.924916
\(59\) 4.89555 + 8.47934i 0.637346 + 1.10392i 0.986013 + 0.166669i \(0.0533013\pi\)
−0.348666 + 0.937247i \(0.613365\pi\)
\(60\) 0 0
\(61\) 2.03980 + 1.17768i 0.261170 + 0.150786i 0.624868 0.780730i \(-0.285153\pi\)
−0.363698 + 0.931517i \(0.618486\pi\)
\(62\) −2.03277 −0.258163
\(63\) 0 0
\(64\) −1.85540 −0.231925
\(65\) 2.73394 + 1.57844i 0.339104 + 0.195782i
\(66\) 0 0
\(67\) 0.156402 + 0.270897i 0.0191076 + 0.0330953i 0.875421 0.483361i \(-0.160584\pi\)
−0.856313 + 0.516456i \(0.827251\pi\)
\(68\) −5.79536 −0.702790
\(69\) 0 0
\(70\) 1.20739 + 2.47130i 0.144310 + 0.295377i
\(71\) 1.94933i 0.231343i −0.993288 0.115671i \(-0.963098\pi\)
0.993288 0.115671i \(-0.0369019\pi\)
\(72\) 0 0
\(73\) 2.42847 + 1.40208i 0.284231 + 0.164101i 0.635337 0.772235i \(-0.280861\pi\)
−0.351106 + 0.936336i \(0.614194\pi\)
\(74\) 0.591435i 0.0687529i
\(75\) 0 0
\(76\) 5.15706 + 2.97743i 0.591556 + 0.341535i
\(77\) 2.66125 3.95119i 0.303278 0.450280i
\(78\) 0 0
\(79\) −6.21583 + 10.7661i −0.699336 + 1.21128i 0.269361 + 0.963039i \(0.413187\pi\)
−0.968697 + 0.248246i \(0.920146\pi\)
\(80\) −0.847852 + 1.46852i −0.0947927 + 0.164186i
\(81\) 0 0
\(82\) 7.34669 4.24162i 0.811306 0.468408i
\(83\) 3.60916 + 6.25124i 0.396157 + 0.686163i 0.993248 0.116010i \(-0.0370104\pi\)
−0.597092 + 0.802173i \(0.703677\pi\)
\(84\) 0 0
\(85\) 2.82605 4.89486i 0.306528 0.530923i
\(86\) 5.41161i 0.583549i
\(87\) 0 0
\(88\) −4.50548 −0.480286
\(89\) −5.28999 9.16253i −0.560737 0.971226i −0.997432 0.0716161i \(-0.977184\pi\)
0.436695 0.899610i \(-0.356149\pi\)
\(90\) 0 0
\(91\) 2.53287 + 5.18433i 0.265517 + 0.543465i
\(92\) 7.29536 4.21198i 0.760593 0.439129i
\(93\) 0 0
\(94\) −1.45436 + 0.839677i −0.150006 + 0.0866061i
\(95\) −5.02959 + 2.90383i −0.516025 + 0.297927i
\(96\) 0 0
\(97\) 13.4322 7.75510i 1.36384 0.787411i 0.373704 0.927548i \(-0.378088\pi\)
0.990132 + 0.140137i \(0.0447543\pi\)
\(98\) −0.692961 + 4.97918i −0.0699997 + 0.502973i
\(99\) 0 0
\(100\) 2.15556 + 3.73354i 0.215556 + 0.373354i
\(101\) 3.94618 0.392659 0.196330 0.980538i \(-0.437098\pi\)
0.196330 + 0.980538i \(0.437098\pi\)
\(102\) 0 0
\(103\) 4.15522i 0.409426i −0.978822 0.204713i \(-0.934374\pi\)
0.978822 0.204713i \(-0.0656261\pi\)
\(104\) 2.72853 4.72595i 0.267554 0.463417i
\(105\) 0 0
\(106\) 0.413271 + 0.715806i 0.0401404 + 0.0695253i
\(107\) −4.91092 + 2.83532i −0.474757 + 0.274101i −0.718229 0.695807i \(-0.755047\pi\)
0.243472 + 0.969908i \(0.421714\pi\)
\(108\) 0 0
\(109\) 5.99916 10.3908i 0.574615 0.995262i −0.421468 0.906843i \(-0.638485\pi\)
0.996083 0.0884193i \(-0.0281815\pi\)
\(110\) 0.935915 1.62105i 0.0892360 0.154561i
\(111\) 0 0
\(112\) −2.78473 + 1.36052i −0.263133 + 0.128557i
\(113\) −6.27800 3.62461i −0.590585 0.340974i 0.174744 0.984614i \(-0.444090\pi\)
−0.765329 + 0.643640i \(0.777424\pi\)
\(114\) 0 0
\(115\) 8.21572i 0.766120i
\(116\) 12.6074 + 7.27887i 1.17057 + 0.675826i
\(117\) 0 0
\(118\) 7.03164i 0.647315i
\(119\) 9.28205 4.53487i 0.850884 0.415711i
\(120\) 0 0
\(121\) 7.75798 0.705271
\(122\) 0.845770 + 1.46492i 0.0765724 + 0.132627i
\(123\) 0 0
\(124\) 3.63829 + 2.10057i 0.326728 + 0.188637i
\(125\) −11.4423 −1.02343
\(126\) 0 0
\(127\) −0.881336 −0.0782059 −0.0391030 0.999235i \(-0.512450\pi\)
−0.0391030 + 0.999235i \(0.512450\pi\)
\(128\) 8.97127 + 5.17956i 0.792956 + 0.457813i
\(129\) 0 0
\(130\) 1.13358 + 1.96343i 0.0994219 + 0.172204i
\(131\) 2.97441 0.259876 0.129938 0.991522i \(-0.458522\pi\)
0.129938 + 0.991522i \(0.458522\pi\)
\(132\) 0 0
\(133\) −10.5896 0.733352i −0.918233 0.0635897i
\(134\) 0.224646i 0.0194065i
\(135\) 0 0
\(136\) −8.46137 4.88517i −0.725556 0.418900i
\(137\) 11.8986i 1.01657i −0.861190 0.508283i \(-0.830280\pi\)
0.861190 0.508283i \(-0.169720\pi\)
\(138\) 0 0
\(139\) −10.4143 6.01268i −0.883327 0.509989i −0.0115731 0.999933i \(-0.503684\pi\)
−0.871754 + 0.489944i \(0.837017\pi\)
\(140\) 0.392717 5.67083i 0.0331907 0.479272i
\(141\) 0 0
\(142\) 0.699971 1.21239i 0.0587403 0.101741i
\(143\) 1.96338 3.40067i 0.164186 0.284378i
\(144\) 0 0
\(145\) −12.2957 + 7.09895i −1.02111 + 0.589536i
\(146\) 1.00693 + 1.74405i 0.0833338 + 0.144338i
\(147\) 0 0
\(148\) −0.611160 + 1.05856i −0.0502370 + 0.0870131i
\(149\) 7.07901i 0.579935i −0.957036 0.289968i \(-0.906355\pi\)
0.957036 0.289968i \(-0.0936446\pi\)
\(150\) 0 0
\(151\) 15.5819 1.26803 0.634017 0.773319i \(-0.281405\pi\)
0.634017 + 0.773319i \(0.281405\pi\)
\(152\) 5.01963 + 8.69425i 0.407146 + 0.705197i
\(153\) 0 0
\(154\) 3.07397 1.50183i 0.247708 0.121021i
\(155\) −3.54836 + 2.04865i −0.285011 + 0.164551i
\(156\) 0 0
\(157\) 1.80677 1.04314i 0.144196 0.0832517i −0.426166 0.904645i \(-0.640136\pi\)
0.570362 + 0.821393i \(0.306803\pi\)
\(158\) −7.73188 + 4.46400i −0.615115 + 0.355137i
\(159\) 0 0
\(160\) −7.32839 + 4.23105i −0.579360 + 0.334494i
\(161\) −8.38862 + 12.4547i −0.661116 + 0.981566i
\(162\) 0 0
\(163\) −5.58983 9.68188i −0.437830 0.758343i 0.559692 0.828700i \(-0.310919\pi\)
−0.997522 + 0.0703575i \(0.977586\pi\)
\(164\) −17.5323 −1.36904
\(165\) 0 0
\(166\) 5.18395i 0.402353i
\(167\) −0.960750 + 1.66407i −0.0743450 + 0.128769i −0.900801 0.434232i \(-0.857020\pi\)
0.826456 + 0.563001i \(0.190353\pi\)
\(168\) 0 0
\(169\) −4.12195 7.13943i −0.317073 0.549187i
\(170\) 3.51533 2.02958i 0.269613 0.155661i
\(171\) 0 0
\(172\) −5.59210 + 9.68580i −0.426393 + 0.738535i
\(173\) −7.61290 + 13.1859i −0.578798 + 1.00251i 0.416820 + 0.908989i \(0.363145\pi\)
−0.995618 + 0.0935182i \(0.970189\pi\)
\(174\) 0 0
\(175\) −6.37392 4.29304i −0.481823 0.324523i
\(176\) 1.82665 + 1.05462i 0.137689 + 0.0794948i
\(177\) 0 0
\(178\) 7.59818i 0.569508i
\(179\) 0.299401 + 0.172859i 0.0223783 + 0.0129201i 0.511147 0.859493i \(-0.329221\pi\)
−0.488769 + 0.872413i \(0.662554\pi\)
\(180\) 0 0
\(181\) 3.27661i 0.243548i −0.992558 0.121774i \(-0.961142\pi\)
0.992558 0.121774i \(-0.0388583\pi\)
\(182\) −0.286282 + 4.13391i −0.0212207 + 0.306426i
\(183\) 0 0
\(184\) 14.2019 1.04698
\(185\) −0.596053 1.03239i −0.0438227 0.0759031i
\(186\) 0 0
\(187\) −6.08857 3.51524i −0.445241 0.257060i
\(188\) 3.47073 0.253129
\(189\) 0 0
\(190\) −4.17087 −0.302587
\(191\) −6.40096 3.69560i −0.463158 0.267404i 0.250213 0.968191i \(-0.419499\pi\)
−0.713371 + 0.700787i \(0.752833\pi\)
\(192\) 0 0
\(193\) −6.51425 11.2830i −0.468906 0.812169i 0.530462 0.847708i \(-0.322018\pi\)
−0.999368 + 0.0355398i \(0.988685\pi\)
\(194\) 11.1389 0.799727
\(195\) 0 0
\(196\) 6.38551 8.19574i 0.456108 0.585410i
\(197\) 4.03035i 0.287151i 0.989639 + 0.143575i \(0.0458599\pi\)
−0.989639 + 0.143575i \(0.954140\pi\)
\(198\) 0 0
\(199\) 14.2096 + 8.20390i 1.00729 + 0.581559i 0.910397 0.413736i \(-0.135776\pi\)
0.0968925 + 0.995295i \(0.469110\pi\)
\(200\) 7.26808i 0.513931i
\(201\) 0 0
\(202\) 2.45433 + 1.41701i 0.172686 + 0.0997003i
\(203\) −25.8882 1.79281i −1.81699 0.125831i
\(204\) 0 0
\(205\) 8.54947 14.8081i 0.597121 1.03424i
\(206\) 1.49207 2.58434i 0.103957 0.180060i
\(207\) 0 0
\(208\) −2.21245 + 1.27736i −0.153406 + 0.0885688i
\(209\) 3.61199 + 6.25615i 0.249847 + 0.432747i
\(210\) 0 0
\(211\) −6.00827 + 10.4066i −0.413627 + 0.716422i −0.995283 0.0970121i \(-0.969071\pi\)
0.581657 + 0.813434i \(0.302405\pi\)
\(212\) 1.70822i 0.117321i
\(213\) 0 0
\(214\) −4.07247 −0.278388
\(215\) −5.45387 9.44638i −0.371951 0.644238i
\(216\) 0 0
\(217\) −7.47092 0.517377i −0.507159 0.0351219i
\(218\) 7.46236 4.30839i 0.505415 0.291801i
\(219\) 0 0
\(220\) −3.35023 + 1.93426i −0.225873 + 0.130408i
\(221\) 7.37451 4.25767i 0.496063 0.286402i
\(222\) 0 0
\(223\) −22.7932 + 13.1597i −1.52635 + 0.881237i −0.526836 + 0.849967i \(0.676622\pi\)
−0.999511 + 0.0312693i \(0.990045\pi\)
\(224\) −15.4296 1.06853i −1.03093 0.0713944i
\(225\) 0 0
\(226\) −2.60307 4.50865i −0.173154 0.299911i
\(227\) −10.8082 −0.717366 −0.358683 0.933459i \(-0.616774\pi\)
−0.358683 + 0.933459i \(0.616774\pi\)
\(228\) 0 0
\(229\) 9.69691i 0.640790i 0.947284 + 0.320395i \(0.103816\pi\)
−0.947284 + 0.320395i \(0.896184\pi\)
\(230\) −2.95013 + 5.10977i −0.194526 + 0.336928i
\(231\) 0 0
\(232\) 12.2714 + 21.2547i 0.805657 + 1.39544i
\(233\) 1.92897 1.11369i 0.126371 0.0729605i −0.435482 0.900198i \(-0.643422\pi\)
0.561853 + 0.827237i \(0.310089\pi\)
\(234\) 0 0
\(235\) −1.69247 + 2.93144i −0.110404 + 0.191226i
\(236\) 7.26616 12.5854i 0.472986 0.819237i
\(237\) 0 0
\(238\) 7.40137 + 0.512561i 0.479760 + 0.0332244i
\(239\) 15.9697 + 9.22008i 1.03299 + 0.596398i 0.917840 0.396950i \(-0.129932\pi\)
0.115151 + 0.993348i \(0.463265\pi\)
\(240\) 0 0
\(241\) 6.47181i 0.416886i 0.978035 + 0.208443i \(0.0668396\pi\)
−0.978035 + 0.208443i \(0.933160\pi\)
\(242\) 4.82508 + 2.78576i 0.310168 + 0.179075i
\(243\) 0 0
\(244\) 3.49591i 0.223803i
\(245\) 3.80844 + 9.38990i 0.243312 + 0.599899i
\(246\) 0 0
\(247\) −8.74972 −0.556731
\(248\) 3.54133 + 6.13377i 0.224875 + 0.389495i
\(249\) 0 0
\(250\) −7.11654 4.10874i −0.450090 0.259859i
\(251\) −0.416679 −0.0263005 −0.0131503 0.999914i \(-0.504186\pi\)
−0.0131503 + 0.999914i \(0.504186\pi\)
\(252\) 0 0
\(253\) 10.2193 0.642481
\(254\) −0.548147 0.316473i −0.0343938 0.0198573i
\(255\) 0 0
\(256\) 5.57519 + 9.65652i 0.348449 + 0.603532i
\(257\) 21.1284 1.31795 0.658976 0.752164i \(-0.270990\pi\)
0.658976 + 0.752164i \(0.270990\pi\)
\(258\) 0 0
\(259\) 0.150531 2.17366i 0.00935353 0.135065i
\(260\) 4.68556i 0.290586i
\(261\) 0 0
\(262\) 1.84994 + 1.06806i 0.114290 + 0.0659851i
\(263\) 22.2456i 1.37172i −0.727732 0.685862i \(-0.759426\pi\)
0.727732 0.685862i \(-0.240574\pi\)
\(264\) 0 0
\(265\) 1.44279 + 0.832996i 0.0886299 + 0.0511705i
\(266\) −6.32286 4.25865i −0.387680 0.261115i
\(267\) 0 0
\(268\) 0.232138 0.402075i 0.0141801 0.0245607i
\(269\) 14.5164 25.1432i 0.885083 1.53301i 0.0394642 0.999221i \(-0.487435\pi\)
0.845619 0.533788i \(-0.179232\pi\)
\(270\) 0 0
\(271\) 20.8174 12.0189i 1.26456 0.730097i 0.290610 0.956842i \(-0.406142\pi\)
0.973954 + 0.226745i \(0.0728084\pi\)
\(272\) 2.28699 + 3.96118i 0.138669 + 0.240182i
\(273\) 0 0
\(274\) 4.27259 7.40034i 0.258117 0.447071i
\(275\) 5.22992i 0.315376i
\(276\) 0 0
\(277\) 8.06485 0.484570 0.242285 0.970205i \(-0.422103\pi\)
0.242285 + 0.970205i \(0.422103\pi\)
\(278\) −4.31811 7.47918i −0.258983 0.448572i
\(279\) 0 0
\(280\) 5.35358 7.94851i 0.319937 0.475014i
\(281\) 12.0876 6.97879i 0.721087 0.416320i −0.0940658 0.995566i \(-0.529986\pi\)
0.815153 + 0.579246i \(0.196653\pi\)
\(282\) 0 0
\(283\) 13.4559 7.76876i 0.799869 0.461805i −0.0435563 0.999051i \(-0.513869\pi\)
0.843425 + 0.537246i \(0.180535\pi\)
\(284\) −2.50564 + 1.44663i −0.148682 + 0.0858418i
\(285\) 0 0
\(286\) 2.44225 1.41003i 0.144413 0.0833769i
\(287\) 28.0804 13.7191i 1.65753 0.809810i
\(288\) 0 0
\(289\) 0.877036 + 1.51907i 0.0515904 + 0.0893571i
\(290\) −10.1965 −0.598757
\(291\) 0 0
\(292\) 4.16203i 0.243564i
\(293\) −6.73712 + 11.6690i −0.393587 + 0.681712i −0.992920 0.118788i \(-0.962099\pi\)
0.599333 + 0.800500i \(0.295433\pi\)
\(294\) 0 0
\(295\) 7.08655 + 12.2743i 0.412595 + 0.714635i
\(296\) −1.78462 + 1.03035i −0.103729 + 0.0598879i
\(297\) 0 0
\(298\) 2.54196 4.40280i 0.147252 0.255047i
\(299\) −6.18882 + 10.7194i −0.357909 + 0.619916i
\(300\) 0 0
\(301\) 1.37735 19.8889i 0.0793893 1.14638i
\(302\) 9.69114 + 5.59518i 0.557663 + 0.321967i
\(303\) 0 0
\(304\) 4.69987i 0.269556i
\(305\) 2.95271 + 1.70475i 0.169072 + 0.0976136i
\(306\) 0 0
\(307\) 8.62791i 0.492421i 0.969216 + 0.246210i \(0.0791854\pi\)
−0.969216 + 0.246210i \(0.920815\pi\)
\(308\) −7.05377 0.488489i −0.401926 0.0278342i
\(309\) 0 0
\(310\) −2.94254 −0.167125
\(311\) 8.12200 + 14.0677i 0.460556 + 0.797707i 0.998989 0.0449616i \(-0.0143165\pi\)
−0.538432 + 0.842669i \(0.680983\pi\)
\(312\) 0 0
\(313\) 5.86899 + 3.38846i 0.331735 + 0.191527i 0.656611 0.754229i \(-0.271989\pi\)
−0.324876 + 0.945757i \(0.605323\pi\)
\(314\) 1.49830 0.0845538
\(315\) 0 0
\(316\) 18.4515 1.03798
\(317\) −19.0245 10.9838i −1.06852 0.616911i −0.140744 0.990046i \(-0.544949\pi\)
−0.927777 + 0.373135i \(0.878283\pi\)
\(318\) 0 0
\(319\) 8.83017 + 15.2943i 0.494395 + 0.856316i
\(320\) −2.68578 −0.150140
\(321\) 0 0
\(322\) −9.68958 + 4.73398i −0.539979 + 0.263814i
\(323\) 15.6655i 0.871654i
\(324\) 0 0
\(325\) −5.48584 3.16725i −0.304299 0.175687i
\(326\) 8.02886i 0.444678i
\(327\) 0 0
\(328\) −25.5976 14.7788i −1.41339 0.816022i
\(329\) −5.55884 + 2.71585i −0.306469 + 0.149730i
\(330\) 0 0
\(331\) 7.30179 12.6471i 0.401342 0.695145i −0.592546 0.805537i \(-0.701877\pi\)
0.993888 + 0.110391i \(0.0352104\pi\)
\(332\) 5.35684 9.27833i 0.293995 0.509214i
\(333\) 0 0
\(334\) −1.19508 + 0.689978i −0.0653917 + 0.0377539i
\(335\) 0.226400 + 0.392137i 0.0123696 + 0.0214247i
\(336\) 0 0
\(337\) −16.2629 + 28.1681i −0.885894 + 1.53441i −0.0412090 + 0.999151i \(0.513121\pi\)
−0.844685 + 0.535263i \(0.820212\pi\)
\(338\) 5.92049i 0.322032i
\(339\) 0 0
\(340\) −8.38906 −0.454961
\(341\) 2.54825 + 4.41370i 0.137995 + 0.239015i
\(342\) 0 0
\(343\) −3.81408 + 18.1233i −0.205941 + 0.978564i
\(344\) −16.3292 + 9.42767i −0.880412 + 0.508306i
\(345\) 0 0
\(346\) −9.46969 + 5.46733i −0.509094 + 0.293925i
\(347\) −2.76005 + 1.59352i −0.148167 + 0.0855444i −0.572251 0.820079i \(-0.693930\pi\)
0.424084 + 0.905623i \(0.360596\pi\)
\(348\) 0 0
\(349\) −6.48224 + 3.74252i −0.346986 + 0.200333i −0.663357 0.748303i \(-0.730869\pi\)
0.316371 + 0.948636i \(0.397536\pi\)
\(350\) −2.42270 4.95883i −0.129499 0.265060i
\(351\) 0 0
\(352\) 5.26287 + 9.11556i 0.280512 + 0.485861i
\(353\) 11.3808 0.605739 0.302869 0.953032i \(-0.402055\pi\)
0.302869 + 0.953032i \(0.402055\pi\)
\(354\) 0 0
\(355\) 2.82175i 0.149763i
\(356\) −7.85159 + 13.5994i −0.416134 + 0.720764i
\(357\) 0 0
\(358\) 0.124142 + 0.215020i 0.00656109 + 0.0113641i
\(359\) 4.77569 2.75725i 0.252051 0.145522i −0.368652 0.929568i \(-0.620181\pi\)
0.620703 + 0.784046i \(0.286847\pi\)
\(360\) 0 0
\(361\) −1.45164 + 2.51432i −0.0764022 + 0.132332i
\(362\) 1.17657 2.03789i 0.0618394 0.107109i
\(363\) 0 0
\(364\) 4.78417 7.10311i 0.250759 0.372304i
\(365\) 3.51533 + 2.02958i 0.184001 + 0.106233i
\(366\) 0 0
\(367\) 21.1025i 1.10154i −0.834657 0.550770i \(-0.814334\pi\)
0.834657 0.550770i \(-0.185666\pi\)
\(368\) −5.75785 3.32430i −0.300149 0.173291i
\(369\) 0 0
\(370\) 0.856131i 0.0445081i
\(371\) 1.33668 + 2.73594i 0.0693970 + 0.142043i
\(372\) 0 0
\(373\) 15.3700 0.795826 0.397913 0.917423i \(-0.369735\pi\)
0.397913 + 0.917423i \(0.369735\pi\)
\(374\) −2.52453 4.37261i −0.130540 0.226102i
\(375\) 0 0
\(376\) 5.06735 + 2.92563i 0.261328 + 0.150878i
\(377\) −21.3903 −1.10166
\(378\) 0 0
\(379\) −32.3630 −1.66238 −0.831188 0.555991i \(-0.812339\pi\)
−0.831188 + 0.555991i \(0.812339\pi\)
\(380\) 7.46510 + 4.30998i 0.382951 + 0.221097i
\(381\) 0 0
\(382\) −2.65406 4.59696i −0.135793 0.235201i
\(383\) −19.8346 −1.01350 −0.506750 0.862093i \(-0.669153\pi\)
−0.506750 + 0.862093i \(0.669153\pi\)
\(384\) 0 0
\(385\) 3.85229 5.71954i 0.196331 0.291495i
\(386\) 9.35663i 0.476240i
\(387\) 0 0
\(388\) −19.9366 11.5104i −1.01213 0.584352i
\(389\) 5.10283i 0.258724i 0.991597 + 0.129362i \(0.0412928\pi\)
−0.991597 + 0.129362i \(0.958707\pi\)
\(390\) 0 0
\(391\) 19.1920 + 11.0805i 0.970581 + 0.560365i
\(392\) 16.2316 6.58335i 0.819818 0.332509i
\(393\) 0 0
\(394\) −1.44723 + 2.50668i −0.0729105 + 0.126285i
\(395\) −8.99772 + 15.5845i −0.452724 + 0.784141i
\(396\) 0 0
\(397\) −11.5288 + 6.65615i −0.578613 + 0.334062i −0.760582 0.649242i \(-0.775086\pi\)
0.181969 + 0.983304i \(0.441753\pi\)
\(398\) 5.89177 + 10.2048i 0.295328 + 0.511522i
\(399\) 0 0
\(400\) 1.70127 2.94669i 0.0850636 0.147334i
\(401\) 16.3678i 0.817371i −0.912675 0.408685i \(-0.865987\pi\)
0.912675 0.408685i \(-0.134013\pi\)
\(402\) 0 0
\(403\) −6.17290 −0.307494
\(404\) −2.92853 5.07237i −0.145700 0.252360i
\(405\) 0 0
\(406\) −15.4574 10.4110i −0.767137 0.516692i
\(407\) −1.28416 + 0.741412i −0.0636536 + 0.0367504i
\(408\) 0 0
\(409\) 3.75604 2.16855i 0.185724 0.107228i −0.404255 0.914646i \(-0.632469\pi\)
0.589979 + 0.807418i \(0.299136\pi\)
\(410\) 10.6347 6.13994i 0.525210 0.303230i
\(411\) 0 0
\(412\) −5.34107 + 3.08367i −0.263135 + 0.151921i
\(413\) −1.78968 + 25.8429i −0.0880644 + 1.27165i
\(414\) 0 0
\(415\) 5.22443 + 9.04898i 0.256457 + 0.444197i
\(416\) −12.7488 −0.625062
\(417\) 0 0
\(418\) 5.18802i 0.253754i
\(419\) 9.41294 16.3037i 0.459852 0.796487i −0.539100 0.842241i \(-0.681236\pi\)
0.998953 + 0.0457540i \(0.0145690\pi\)
\(420\) 0 0
\(421\) 0.913453 + 1.58215i 0.0445190 + 0.0771092i 0.887426 0.460950i \(-0.152491\pi\)
−0.842907 + 0.538059i \(0.819158\pi\)
\(422\) −7.47370 + 4.31494i −0.363814 + 0.210048i
\(423\) 0 0
\(424\) 1.43993 2.49404i 0.0699294 0.121121i
\(425\) −5.67066 + 9.82187i −0.275068 + 0.476431i
\(426\) 0 0
\(427\) 2.73555 + 5.59917i 0.132383 + 0.270963i
\(428\) 7.28897 + 4.20829i 0.352326 + 0.203415i
\(429\) 0 0
\(430\) 7.83357i 0.377768i
\(431\) 12.4526 + 7.18954i 0.599823 + 0.346308i 0.768972 0.639283i \(-0.220769\pi\)
−0.169149 + 0.985590i \(0.554102\pi\)
\(432\) 0 0
\(433\) 2.22130i 0.106749i −0.998575 0.0533745i \(-0.983002\pi\)
0.998575 0.0533745i \(-0.0169977\pi\)
\(434\) −4.46076 3.00446i −0.214123 0.144219i
\(435\) 0 0
\(436\) −17.8083 −0.852865
\(437\) −11.3855 19.7202i −0.544641 0.943347i
\(438\) 0 0
\(439\) 8.69907 + 5.02241i 0.415184 + 0.239706i 0.693015 0.720924i \(-0.256282\pi\)
−0.277831 + 0.960630i \(0.589615\pi\)
\(440\) −6.52190 −0.310919
\(441\) 0 0
\(442\) 6.11544 0.290882
\(443\) −12.0321 6.94672i −0.571661 0.330049i 0.186151 0.982521i \(-0.440398\pi\)
−0.757812 + 0.652472i \(0.773732\pi\)
\(444\) 0 0
\(445\) −7.65751 13.2632i −0.363001 0.628736i
\(446\) −18.9017 −0.895020
\(447\) 0 0
\(448\) −4.07153 2.74231i −0.192362 0.129562i
\(449\) 10.5630i 0.498498i 0.968439 + 0.249249i \(0.0801837\pi\)
−0.968439 + 0.249249i \(0.919816\pi\)
\(450\) 0 0
\(451\) −18.4194 10.6344i −0.867334 0.500755i
\(452\) 10.7595i 0.506086i
\(453\) 0 0
\(454\) −6.72217 3.88105i −0.315487 0.182147i
\(455\) 3.66646 + 7.50456i 0.171886 + 0.351819i
\(456\) 0 0
\(457\) −2.55654 + 4.42805i −0.119590 + 0.207135i −0.919605 0.392844i \(-0.871491\pi\)
0.800015 + 0.599979i \(0.204825\pi\)
\(458\) −3.48200 + 6.03100i −0.162703 + 0.281810i
\(459\) 0 0
\(460\) 10.5604 6.09704i 0.492380 0.284276i
\(461\) 4.16691 + 7.21730i 0.194072 + 0.336143i 0.946596 0.322422i \(-0.104497\pi\)
−0.752524 + 0.658565i \(0.771164\pi\)
\(462\) 0 0
\(463\) 10.0143 17.3452i 0.465403 0.806102i −0.533817 0.845600i \(-0.679243\pi\)
0.999220 + 0.0394986i \(0.0125761\pi\)
\(464\) 11.4897i 0.533395i
\(465\) 0 0
\(466\) 1.59963 0.0741016
\(467\) 10.3896 + 17.9953i 0.480773 + 0.832723i 0.999757 0.0220611i \(-0.00702284\pi\)
−0.518984 + 0.854784i \(0.673690\pi\)
\(468\) 0 0
\(469\) −0.0571765 + 0.825627i −0.00264016 + 0.0381239i
\(470\) −2.10526 + 1.21547i −0.0971085 + 0.0560656i
\(471\) 0 0
\(472\) 21.2175 12.2500i 0.976616 0.563850i
\(473\) −11.7501 + 6.78390i −0.540268 + 0.311924i
\(474\) 0 0
\(475\) 10.0922 5.82674i 0.463062 0.267349i
\(476\) −12.7174 8.56561i −0.582903 0.392604i
\(477\) 0 0
\(478\) 6.62156 + 11.4689i 0.302863 + 0.524574i
\(479\) 32.0617 1.46494 0.732468 0.680802i \(-0.238368\pi\)
0.732468 + 0.680802i \(0.238368\pi\)
\(480\) 0 0
\(481\) 1.79600i 0.0818907i
\(482\) −2.32392 + 4.02515i −0.105852 + 0.183340i
\(483\) 0 0
\(484\) −5.75734 9.97200i −0.261697 0.453273i
\(485\) 19.4438 11.2259i 0.882897 0.509741i
\(486\) 0 0
\(487\) 11.8375 20.5032i 0.536408 0.929087i −0.462685 0.886523i \(-0.653114\pi\)
0.999094 0.0425641i \(-0.0135527\pi\)
\(488\) 2.94686 5.10412i 0.133398 0.231052i
\(489\) 0 0
\(490\) −1.00310 + 7.20760i −0.0453152 + 0.325606i
\(491\) −15.4664 8.92951i −0.697987 0.402983i 0.108610 0.994084i \(-0.465360\pi\)
−0.806597 + 0.591101i \(0.798693\pi\)
\(492\) 0 0
\(493\) 38.2973i 1.72482i
\(494\) −5.44189 3.14188i −0.244842 0.141360i
\(495\) 0 0
\(496\) 3.31574i 0.148881i
\(497\) 2.88113 4.27764i 0.129236 0.191879i
\(498\) 0 0
\(499\) −23.1204 −1.03501 −0.517506 0.855680i \(-0.673139\pi\)
−0.517506 + 0.855680i \(0.673139\pi\)
\(500\) 8.49154 + 14.7078i 0.379753 + 0.657752i
\(501\) 0 0
\(502\) −0.259154 0.149622i −0.0115666 0.00667798i
\(503\) 13.9995 0.624206 0.312103 0.950048i \(-0.398967\pi\)
0.312103 + 0.950048i \(0.398967\pi\)
\(504\) 0 0
\(505\) 5.71228 0.254193
\(506\) 6.35589 + 3.66958i 0.282554 + 0.163133i
\(507\) 0 0
\(508\) 0.654056 + 1.13286i 0.0290190 + 0.0502624i
\(509\) 13.5834 0.602074 0.301037 0.953612i \(-0.402667\pi\)
0.301037 + 0.953612i \(0.402667\pi\)
\(510\) 0 0
\(511\) 3.25680 + 6.66606i 0.144072 + 0.294889i
\(512\) 12.7104i 0.561727i
\(513\) 0 0
\(514\) 13.1408 + 7.58684i 0.579616 + 0.334641i
\(515\) 6.01488i 0.265047i
\(516\) 0 0
\(517\) 3.64633 + 2.10521i 0.160365 + 0.0925870i
\(518\) 0.874148 1.29786i 0.0384079 0.0570246i
\(519\) 0 0
\(520\) 3.94968 6.84104i 0.173205 0.299999i
\(521\) −15.9477 + 27.6222i −0.698682 + 1.21015i 0.270242 + 0.962792i \(0.412896\pi\)
−0.968924 + 0.247360i \(0.920437\pi\)
\(522\) 0 0
\(523\) −1.20531 + 0.695886i −0.0527046 + 0.0304290i −0.526121 0.850410i \(-0.676354\pi\)
0.473416 + 0.880839i \(0.343021\pi\)
\(524\) −2.20737 3.82327i −0.0964293 0.167020i
\(525\) 0 0
\(526\) 7.98803 13.8357i 0.348295 0.603264i
\(527\) 11.0520i 0.481433i
\(528\) 0 0
\(529\) −9.21257 −0.400546
\(530\) 0.598230 + 1.03616i 0.0259854 + 0.0450081i
\(531\) 0 0
\(532\) 6.91608 + 14.1559i 0.299850 + 0.613738i
\(533\) 22.3096 12.8805i 0.966337 0.557915i
\(534\) 0 0
\(535\) −7.10880 + 4.10427i −0.307340 + 0.177443i
\(536\) 0.677855 0.391360i 0.0292789 0.0169042i
\(537\) 0 0
\(538\) 18.0570 10.4252i 0.778493 0.449463i
\(539\) 11.6798 4.73720i 0.503085 0.204046i
\(540\) 0 0
\(541\) 12.9736 + 22.4709i 0.557779 + 0.966101i 0.997682 + 0.0680555i \(0.0216795\pi\)
−0.439903 + 0.898045i \(0.644987\pi\)
\(542\) 17.2632 0.741516
\(543\) 0 0
\(544\) 22.8256i 0.978638i
\(545\) 8.68407 15.0413i 0.371985 0.644296i
\(546\) 0 0
\(547\) −9.32438 16.1503i −0.398682 0.690537i 0.594882 0.803813i \(-0.297199\pi\)
−0.993564 + 0.113276i \(0.963865\pi\)
\(548\) −15.2943 + 8.83017i −0.653340 + 0.377206i
\(549\) 0 0
\(550\) −1.87798 + 3.25275i −0.0800772 + 0.138698i
\(551\) 19.6757 34.0793i 0.838212 1.45183i
\(552\) 0 0
\(553\) −29.5526 + 14.4383i −1.25671 + 0.613981i
\(554\) 5.01594 + 2.89595i 0.213107 + 0.123037i
\(555\) 0 0
\(556\) 17.8485i 0.756944i
\(557\) −36.3567 20.9905i −1.54048 0.889398i −0.998808 0.0488092i \(-0.984457\pi\)
−0.541674 0.840589i \(-0.682209\pi\)
\(558\) 0 0
\(559\) 16.4334i 0.695058i
\(560\) −4.03104 + 1.96942i −0.170342 + 0.0832232i
\(561\) 0 0
\(562\) 10.0239 0.422831
\(563\) −19.3006 33.4295i −0.813422 1.40889i −0.910456 0.413606i \(-0.864269\pi\)
0.0970343 0.995281i \(-0.469064\pi\)
\(564\) 0 0
\(565\) −9.08771 5.24679i −0.382323 0.220734i
\(566\) 11.1585 0.469028
\(567\) 0 0
\(568\) −4.87773 −0.204665
\(569\) 30.4460 + 17.5780i 1.27636 + 0.736908i 0.976178 0.216973i \(-0.0696185\pi\)
0.300184 + 0.953881i \(0.402952\pi\)
\(570\) 0 0
\(571\) 17.6766 + 30.6167i 0.739742 + 1.28127i 0.952611 + 0.304190i \(0.0983857\pi\)
−0.212870 + 0.977081i \(0.568281\pi\)
\(572\) −5.82823 −0.243690
\(573\) 0 0
\(574\) 22.3909 + 1.55062i 0.934578 + 0.0647216i
\(575\) 16.4854i 0.687489i
\(576\) 0 0
\(577\) 23.2557 + 13.4267i 0.968147 + 0.558960i 0.898671 0.438624i \(-0.144534\pi\)
0.0694761 + 0.997584i \(0.477867\pi\)
\(578\) 1.25972i 0.0523973i
\(579\) 0 0
\(580\) 18.2498 + 10.5365i 0.757781 + 0.437505i
\(581\) −1.31941 + 19.0522i −0.0547383 + 0.790420i
\(582\) 0 0
\(583\) 1.03614 1.79464i 0.0429125 0.0743266i
\(584\) 3.50837 6.07667i 0.145177 0.251454i
\(585\) 0 0
\(586\) −8.38031 + 4.83837i −0.346187 + 0.199871i
\(587\) −15.6788 27.1565i −0.647134 1.12087i −0.983804 0.179246i \(-0.942634\pi\)
0.336671 0.941622i \(-0.390699\pi\)
\(588\) 0 0
\(589\) 5.67809 9.83474i 0.233962 0.405234i
\(590\) 10.1786i 0.419048i
\(591\) 0 0
\(592\) 0.964714 0.0396495
\(593\) 4.56131 + 7.90043i 0.187311 + 0.324432i 0.944353 0.328935i \(-0.106690\pi\)
−0.757042 + 0.653366i \(0.773356\pi\)
\(594\) 0 0
\(595\) 13.4362 6.56445i 0.550831 0.269116i
\(596\) −9.09927 + 5.25347i −0.372721 + 0.215190i
\(597\) 0 0
\(598\) −7.69828 + 4.44461i −0.314806 + 0.181753i
\(599\) −1.11316 + 0.642683i −0.0454825 + 0.0262593i −0.522569 0.852597i \(-0.675026\pi\)
0.477086 + 0.878856i \(0.341693\pi\)
\(600\) 0 0
\(601\) −16.7126 + 9.64903i −0.681721 + 0.393592i −0.800503 0.599328i \(-0.795434\pi\)
0.118782 + 0.992920i \(0.462101\pi\)
\(602\) 7.99843 11.8754i 0.325992 0.484003i
\(603\) 0 0
\(604\) −11.5636 20.0287i −0.470515 0.814956i
\(605\) 11.2300 0.456566
\(606\) 0 0
\(607\) 38.9502i 1.58094i −0.612501 0.790470i \(-0.709836\pi\)
0.612501 0.790470i \(-0.290164\pi\)
\(608\) 11.7269 20.3116i 0.475589 0.823744i
\(609\) 0 0
\(610\) 1.22429 + 2.12054i 0.0495702 + 0.0858581i
\(611\) −4.41645 + 2.54984i −0.178670 + 0.103155i
\(612\) 0 0
\(613\) −3.65018 + 6.32229i −0.147429 + 0.255355i −0.930277 0.366859i \(-0.880433\pi\)
0.782847 + 0.622214i \(0.213767\pi\)
\(614\) −3.09814 + 5.36613i −0.125031 + 0.216560i
\(615\) 0 0
\(616\) −9.88691 6.65915i −0.398355 0.268305i
\(617\) −38.3641 22.1495i −1.54448 0.891706i −0.998548 0.0538763i \(-0.982842\pi\)
−0.545932 0.837829i \(-0.683824\pi\)
\(618\) 0 0
\(619\) 0.471636i 0.0189566i −0.999955 0.00947832i \(-0.996983\pi\)
0.999955 0.00947832i \(-0.00301709\pi\)
\(620\) 5.26660 + 3.04068i 0.211512 + 0.122116i
\(621\) 0 0
\(622\) 11.6659i 0.467760i
\(623\) 1.93387 27.9251i 0.0774790 1.11880i
\(624\) 0 0
\(625\) −2.04026 −0.0816105
\(626\) 2.43348 + 4.21491i 0.0972614 + 0.168462i
\(627\) 0 0
\(628\) −2.68168 1.54827i −0.107011 0.0617826i
\(629\) −3.21558 −0.128213
\(630\) 0 0
\(631\) 10.2247 0.407038 0.203519 0.979071i \(-0.434762\pi\)
0.203519 + 0.979071i \(0.434762\pi\)
\(632\) 26.9397 + 15.5536i 1.07160 + 0.618691i
\(633\) 0 0
\(634\) −7.88819 13.6627i −0.313280 0.542617i
\(635\) −1.27578 −0.0506277
\(636\) 0 0
\(637\) −2.10431 + 15.1202i −0.0833757 + 0.599085i
\(638\) 12.6831i 0.502127i
\(639\) 0 0
\(640\) 12.9863 + 7.49767i 0.513330 + 0.296371i
\(641\) 50.1815i 1.98205i 0.133677 + 0.991025i \(0.457321\pi\)
−0.133677 + 0.991025i \(0.542679\pi\)
\(642\) 0 0
\(643\) 9.18633 + 5.30373i 0.362274 + 0.209159i 0.670078 0.742291i \(-0.266261\pi\)
−0.307804 + 0.951450i \(0.599594\pi\)
\(644\) 22.2344 + 1.53978i 0.876159 + 0.0606760i
\(645\) 0 0
\(646\) −5.62524 + 9.74320i −0.221322 + 0.383341i
\(647\) −14.9203 + 25.8427i −0.586577 + 1.01598i 0.408100 + 0.912937i \(0.366191\pi\)
−0.994677 + 0.103044i \(0.967142\pi\)
\(648\) 0 0
\(649\) 15.2676 8.81474i 0.599305 0.346009i
\(650\) −2.27461 3.93975i −0.0892177 0.154530i
\(651\) 0 0
\(652\) −8.29664 + 14.3702i −0.324921 + 0.562780i
\(653\) 35.2561i 1.37968i 0.723962 + 0.689839i \(0.242319\pi\)
−0.723962 + 0.689839i \(0.757681\pi\)
\(654\) 0 0
\(655\) 4.30561 0.168234
\(656\) 6.91868 + 11.9835i 0.270129 + 0.467877i
\(657\) 0 0
\(658\) −4.43254 0.306963i −0.172798 0.0119667i
\(659\) −29.3751 + 16.9597i −1.14429 + 0.660656i −0.947489 0.319787i \(-0.896389\pi\)
−0.196801 + 0.980443i \(0.563055\pi\)
\(660\) 0 0
\(661\) −13.6550 + 7.88371i −0.531117 + 0.306641i −0.741471 0.670985i \(-0.765872\pi\)
0.210354 + 0.977625i \(0.432538\pi\)
\(662\) 9.08270 5.24390i 0.353009 0.203810i
\(663\) 0 0
\(664\) 15.6423 9.03106i 0.607037 0.350473i
\(665\) −15.3289 1.06156i −0.594430 0.0411656i
\(666\) 0 0
\(667\) −27.8339 48.2097i −1.07773 1.86669i
\(668\) 2.85196 0.110346
\(669\) 0 0
\(670\) 0.325186i 0.0125630i
\(671\) 2.12048 3.67279i 0.0818604 0.141786i
\(672\) 0 0
\(673\) −7.35627 12.7414i −0.283563 0.491146i 0.688696 0.725050i \(-0.258183\pi\)
−0.972260 + 0.233904i \(0.924850\pi\)
\(674\) −20.2294 + 11.6794i −0.779207 + 0.449875i
\(675\) 0 0
\(676\) −6.11795 + 10.5966i −0.235306 + 0.407562i
\(677\) −1.99217 + 3.45054i −0.0765654 + 0.132615i −0.901766 0.432225i \(-0.857729\pi\)
0.825201 + 0.564840i \(0.191062\pi\)
\(678\) 0 0
\(679\) 40.9381 + 2.83505i 1.57106 + 0.108799i
\(680\) −12.2482 7.07152i −0.469698 0.271181i
\(681\) 0 0
\(682\) 3.66013i 0.140154i
\(683\) 19.2812 + 11.1320i 0.737774 + 0.425954i 0.821259 0.570555i \(-0.193272\pi\)
−0.0834856 + 0.996509i \(0.526605\pi\)
\(684\) 0 0
\(685\) 17.2238i 0.658088i
\(686\) −8.87993 + 9.90220i −0.339037 + 0.378068i
\(687\) 0 0
\(688\) 8.82711 0.336530
\(689\) 1.25498 + 2.17368i 0.0478107 + 0.0828106i
\(690\) 0 0
\(691\) −41.9003 24.1912i −1.59396 0.920275i −0.992618 0.121287i \(-0.961298\pi\)
−0.601346 0.798989i \(-0.705369\pi\)
\(692\) 22.5987 0.859073
\(693\) 0 0
\(694\) −2.28882 −0.0868824
\(695\) −15.0752 8.70365i −0.571834 0.330148i
\(696\) 0 0
\(697\) −23.0613 39.9433i −0.873507 1.51296i
\(698\) −5.37551 −0.203466
\(699\) 0 0
\(700\) −0.788014 + 11.3789i −0.0297841 + 0.430082i
\(701\) 23.3129i 0.880514i −0.897872 0.440257i \(-0.854887\pi\)
0.897872 0.440257i \(-0.145113\pi\)
\(702\) 0 0
\(703\) 2.86142 + 1.65204i 0.107920 + 0.0623079i
\(704\) 3.34076i 0.125910i
\(705\) 0 0
\(706\) 7.07830 + 4.08666i 0.266395 + 0.153803i
\(707\) 8.65957 + 5.83250i 0.325677 + 0.219354i
\(708\) 0 0
\(709\) −8.83884 + 15.3093i −0.331949 + 0.574953i −0.982894 0.184172i \(-0.941040\pi\)
0.650945 + 0.759125i \(0.274373\pi\)
\(710\) 1.01324 1.75499i 0.0380263 0.0658635i
\(711\) 0 0
\(712\) −22.9270 + 13.2369i −0.859227 + 0.496075i
\(713\) −8.03242 13.9126i −0.300817 0.521030i
\(714\) 0 0
\(715\) 2.84208 4.92263i 0.106288 0.184096i
\(716\) 0.513128i 0.0191765i
\(717\) 0 0
\(718\) 3.96033 0.147798
\(719\) −15.2102 26.3449i −0.567246 0.982498i −0.996837 0.0794749i \(-0.974676\pi\)
0.429591 0.903024i \(-0.358658\pi\)
\(720\) 0 0
\(721\) 6.14147 9.11830i 0.228720 0.339583i
\(722\) −1.80570 + 1.04252i −0.0672011 + 0.0387986i
\(723\) 0 0
\(724\) −4.21171 + 2.43163i −0.156527 + 0.0903708i
\(725\) 24.6722 14.2445i 0.916304 0.529028i
\(726\) 0 0
\(727\) 38.5219 22.2406i 1.42870 0.824859i 0.431680 0.902027i \(-0.357921\pi\)
0.997018 + 0.0771674i \(0.0245876\pi\)
\(728\) 12.9725 6.33792i 0.480795 0.234899i
\(729\) 0 0
\(730\) 1.45757 + 2.52459i 0.0539472 + 0.0934393i
\(731\) −29.4224 −1.08823
\(732\) 0 0
\(733\) 45.2954i 1.67302i 0.547949 + 0.836512i \(0.315409\pi\)
−0.547949 + 0.836512i \(0.684591\pi\)
\(734\) 7.57755 13.1247i 0.279692 0.484442i
\(735\) 0 0
\(736\) −16.5893 28.7335i −0.611489 1.05913i
\(737\) 0.487767 0.281612i 0.0179671 0.0103733i
\(738\) 0 0
\(739\) −10.3086 + 17.8550i −0.379208 + 0.656808i −0.990947 0.134252i \(-0.957137\pi\)
0.611739 + 0.791060i \(0.290470\pi\)
\(740\) −0.884684 + 1.53232i −0.0325216 + 0.0563291i
\(741\) 0 0
\(742\) −0.151081 + 2.18160i −0.00554634 + 0.0800890i
\(743\) −7.69885 4.44493i −0.282443 0.163069i 0.352086 0.935968i \(-0.385473\pi\)
−0.634529 + 0.772899i \(0.718806\pi\)
\(744\) 0 0
\(745\) 10.2472i 0.375429i
\(746\) 9.55935 + 5.51909i 0.349993 + 0.202068i
\(747\) 0 0
\(748\) 10.4349i 0.381538i
\(749\) −14.9673 1.03652i −0.546892 0.0378735i
\(750\) 0 0
\(751\) −25.0017 −0.912324 −0.456162 0.889897i \(-0.650776\pi\)
−0.456162 + 0.889897i \(0.650776\pi\)
\(752\) −1.36963 2.37227i −0.0499454 0.0865079i
\(753\) 0 0
\(754\) −13.3037 7.68089i −0.484492 0.279722i
\(755\) 22.5555 0.820878
\(756\) 0 0
\(757\) −27.1262 −0.985919 −0.492959 0.870052i \(-0.664085\pi\)
−0.492959 + 0.870052i \(0.664085\pi\)
\(758\) −20.1282 11.6210i −0.731089 0.422094i
\(759\) 0 0
\(760\) 7.26616 + 12.5854i 0.263571 + 0.456519i
\(761\) 3.16732 0.114815 0.0574075 0.998351i \(-0.481717\pi\)
0.0574075 + 0.998351i \(0.481717\pi\)
\(762\) 0 0
\(763\) 28.5225 13.9350i 1.03258 0.504483i
\(764\) 10.9703i 0.396891i
\(765\) 0 0
\(766\) −12.3361 7.12228i −0.445723 0.257338i
\(767\) 21.3529i 0.771009i
\(768\) 0 0
\(769\) 2.48873 + 1.43687i 0.0897460 + 0.0518149i 0.544201 0.838955i \(-0.316833\pi\)
−0.454455 + 0.890770i \(0.650166\pi\)
\(770\) 4.44973 2.17398i 0.160357 0.0783446i
\(771\) 0 0
\(772\) −9.66868 + 16.7467i −0.347984 + 0.602725i
\(773\) −6.15679 + 10.6639i −0.221444 + 0.383553i −0.955247 0.295810i \(-0.904410\pi\)
0.733802 + 0.679363i \(0.237744\pi\)
\(774\) 0 0
\(775\) 7.12002 4.11075i 0.255759 0.147662i
\(776\) −19.4053 33.6110i −0.696610 1.20656i
\(777\) 0 0
\(778\) −1.83234 + 3.17371i −0.0656926 + 0.113783i
\(779\) 47.3920i 1.69799i
\(780\) 0 0
\(781\) −3.50988 −0.125594
\(782\) 7.95765 + 13.7831i 0.284565 + 0.492881i
\(783\) 0 0
\(784\) −8.12174 1.13032i −0.290062 0.0403685i
\(785\) 2.61539 1.51000i 0.0933473 0.0538941i
\(786\) 0 0
\(787\) −3.30450 + 1.90785i −0.117793 + 0.0680076i −0.557739 0.830017i \(-0.688331\pi\)
0.439946 + 0.898024i \(0.354998\pi\)
\(788\) 5.18056 2.99100i 0.184550 0.106550i
\(789\) 0 0
\(790\) −11.1923 + 6.46186i −0.398203 + 0.229903i
\(791\) −8.41936 17.2329i −0.299358 0.612730i
\(792\) 0 0
\(793\) 2.56834 + 4.44849i 0.0912044 + 0.157971i
\(794\) −9.56045 −0.339288
\(795\) 0 0
\(796\) 24.3530i 0.863171i
\(797\) −24.5682 + 42.5535i −0.870252 + 1.50732i −0.00851609 + 0.999964i \(0.502711\pi\)
−0.861736 + 0.507357i \(0.830623\pi\)
\(798\) 0 0
\(799\) 4.56524 + 7.90724i 0.161507 + 0.279738i
\(800\) 14.7049 8.48988i 0.519897 0.300162i
\(801\) 0 0
\(802\) 5.87742 10.1800i 0.207539 0.359468i
\(803\) 2.52453 4.37261i 0.0890886 0.154306i
\(804\) 0 0
\(805\) −12.1429 + 18.0287i −0.427982 + 0.635430i
\(806\) −3.83924 2.21659i −0.135231 0.0780759i
\(807\) 0 0
\(808\) 9.87437i 0.347379i
\(809\) −39.4929 22.8012i −1.38850 0.801648i −0.395350 0.918531i \(-0.629377\pi\)
−0.993146 + 0.116882i \(0.962710\pi\)
\(810\) 0 0
\(811\) 39.1391i 1.37436i 0.726488 + 0.687180i \(0.241151\pi\)
−0.726488 + 0.687180i \(0.758849\pi\)
\(812\) 16.9076 + 34.6068i 0.593341 + 1.21446i
\(813\) 0 0
\(814\) −1.06492 −0.0373253
\(815\) −8.09155 14.0150i −0.283435 0.490923i
\(816\) 0 0
\(817\) 26.1819 + 15.1161i 0.915988 + 0.528846i
\(818\) 3.11476 0.108905
\(819\) 0 0
\(820\) −25.3789 −0.886269
\(821\) −10.2976 5.94530i −0.359387 0.207492i 0.309425 0.950924i \(-0.399864\pi\)
−0.668812 + 0.743432i \(0.733197\pi\)
\(822\) 0 0
\(823\) −1.51195 2.61877i −0.0527031 0.0912844i 0.838470 0.544947i \(-0.183450\pi\)
−0.891173 + 0.453663i \(0.850117\pi\)
\(824\) −10.3975 −0.362213
\(825\) 0 0
\(826\) −10.3929 + 15.4304i −0.361614 + 0.536891i
\(827\) 15.2436i 0.530071i 0.964239 + 0.265035i \(0.0853836\pi\)
−0.964239 + 0.265035i \(0.914616\pi\)
\(828\) 0 0
\(829\) −29.7306 17.1649i −1.03259 0.596163i −0.114861 0.993382i \(-0.536642\pi\)
−0.917724 + 0.397218i \(0.869976\pi\)
\(830\) 7.50402i 0.260468i
\(831\) 0 0
\(832\) −3.50424 2.02317i −0.121488 0.0701409i
\(833\) 27.0713 + 3.76756i 0.937965 + 0.130538i
\(834\) 0 0
\(835\) −1.39073 + 2.40882i −0.0481283 + 0.0833606i
\(836\) 5.36105 9.28561i 0.185416 0.321150i
\(837\) 0 0
\(838\) 11.7088 6.76006i 0.404473 0.233522i
\(839\) 6.16024 + 10.6698i 0.212675 + 0.368364i 0.952551 0.304379i \(-0.0984491\pi\)
−0.739876 + 0.672744i \(0.765116\pi\)
\(840\) 0 0
\(841\) 33.6008 58.1983i 1.15865 2.00684i
\(842\) 1.31202i 0.0452153i
\(843\) 0 0
\(844\) 17.8354 0.613920
\(845\) −5.96672 10.3347i −0.205262 0.355523i
\(846\) 0 0
\(847\) 17.0243 + 11.4664i 0.584961 + 0.393990i
\(848\) −1.16758 + 0.674104i −0.0400949 + 0.0231488i
\(849\) 0 0
\(850\) −7.05374 + 4.07248i −0.241941 + 0.139685i
\(851\) 4.04786 2.33703i 0.138759 0.0801124i
\(852\) 0 0
\(853\) −3.92537 + 2.26631i −0.134402 + 0.0775971i −0.565693 0.824616i \(-0.691391\pi\)
0.431291 + 0.902213i \(0.358058\pi\)
\(854\) −0.309190 + 4.46470i −0.0105803 + 0.152779i
\(855\) 0 0
\(856\) 7.09472 + 12.2884i 0.242493 + 0.420010i
\(857\) 32.2614 1.10203 0.551014 0.834496i \(-0.314241\pi\)
0.551014 + 0.834496i \(0.314241\pi\)
\(858\) 0 0
\(859\) 17.6335i 0.601647i −0.953680 0.300824i \(-0.902738\pi\)
0.953680 0.300824i \(-0.0972615\pi\)
\(860\) −8.09483 + 14.0207i −0.276032 + 0.478101i
\(861\) 0 0
\(862\) 5.16329 + 8.94307i 0.175862 + 0.304602i
\(863\) 26.4091 15.2473i 0.898975 0.519023i 0.0221074 0.999756i \(-0.492962\pi\)
0.876867 + 0.480732i \(0.159629\pi\)
\(864\) 0 0
\(865\) −11.0200 + 19.0873i −0.374693 + 0.648987i
\(866\) 0.797632 1.38154i 0.0271046 0.0469466i
\(867\) 0 0
\(868\) 4.87927 + 9.98697i 0.165613 + 0.338980i
\(869\) 19.3851 + 11.1920i 0.657594 + 0.379662i
\(870\) 0 0
\(871\) 0.682180i 0.0231148i
\(872\) −26.0006 15.0115i −0.880492 0.508352i
\(873\) 0 0
\(874\) 16.3533i 0.553160i
\(875\) −25.1092 16.9119i −0.848846 0.571725i
\(876\) 0 0
\(877\) 8.80725 0.297400 0.148700 0.988882i \(-0.452491\pi\)
0.148700 + 0.988882i \(0.452491\pi\)
\(878\) 3.60693 + 6.24738i 0.121728 + 0.210839i
\(879\) 0 0
\(880\) 2.64417 + 1.52661i 0.0891348 + 0.0514620i
\(881\) 38.6776 1.30308 0.651540 0.758614i \(-0.274123\pi\)
0.651540 + 0.758614i \(0.274123\pi\)
\(882\) 0 0
\(883\) 37.4489 1.26026 0.630128 0.776491i \(-0.283002\pi\)
0.630128 + 0.776491i \(0.283002\pi\)
\(884\) −10.9455 6.31940i −0.368137 0.212544i
\(885\) 0 0
\(886\) −4.98890 8.64103i −0.167605 0.290301i
\(887\) −27.4050 −0.920171 −0.460086 0.887875i \(-0.652181\pi\)
−0.460086 + 0.887875i \(0.652181\pi\)
\(888\) 0 0
\(889\) −1.93402 1.30263i −0.0648650 0.0436887i
\(890\) 10.9987i 0.368679i
\(891\) 0 0
\(892\) 33.8305 + 19.5321i 1.13273 + 0.653982i
\(893\) 9.38179i 0.313950i
\(894\) 0 0
\(895\) 0.433397 + 0.250222i 0.0144869 + 0.00836400i
\(896\) 12.0313 + 24.6258i 0.401937 + 0.822690i
\(897\) 0 0
\(898\) −3.79299 + 6.56965i −0.126574 + 0.219232i
\(899\) 13.8811 24.0428i 0.462962 0.801873i
\(900\) 0 0
\(901\) 3.89177 2.24691i 0.129654 0.0748556i
\(902\) −7.63729 13.2282i −0.254294 0.440450i
\(903\) 0 0
\(904\) −9.06971 + 15.7092i −0.301654 + 0.522480i
\(905\) 4.74305i 0.157664i
\(906\) 0 0
\(907\) −23.6433 −0.785062 −0.392531 0.919739i \(-0.628400\pi\)
−0.392531 + 0.919739i \(0.628400\pi\)
\(908\) 8.02097 + 13.8927i 0.266185 + 0.461046i
\(909\) 0 0
\(910\) −0.414407 + 5.98403i −0.0137375 + 0.198369i
\(911\) 3.92249 2.26465i 0.129958 0.0750313i −0.433612 0.901100i \(-0.642761\pi\)
0.563570 + 0.826069i \(0.309428\pi\)
\(912\) 0 0
\(913\) 11.2557 6.49851i 0.372511 0.215069i
\(914\) −3.18008 + 1.83602i −0.105188 + 0.0607301i
\(915\) 0 0
\(916\) 12.4643 7.19626i 0.411832 0.237771i
\(917\) 6.52711 + 4.39622i 0.215544 + 0.145176i
\(918\) 0 0
\(919\) 16.9149 + 29.2975i 0.557971 + 0.966434i 0.997666 + 0.0682866i \(0.0217532\pi\)
−0.439695 + 0.898147i \(0.644913\pi\)
\(920\) 20.5579 0.677774
\(921\) 0 0
\(922\) 5.98508i 0.197108i
\(923\) 2.12559 3.68164i 0.0699648 0.121183i
\(924\) 0 0
\(925\) 1.19602 + 2.07157i 0.0393249 + 0.0681127i
\(926\) 12.4568 7.19192i 0.409355 0.236341i
\(927\) 0 0
\(928\) 28.6685 49.6554i 0.941091 1.63002i
\(929\) −16.4582 + 28.5064i −0.539976 + 0.935266i 0.458928 + 0.888473i \(0.348233\pi\)
−0.998905 + 0.0467929i \(0.985100\pi\)
\(930\) 0 0
\(931\) −22.1541 17.2608i −0.726071 0.565700i
\(932\) −2.86305 1.65298i −0.0937824 0.0541453i
\(933\) 0 0
\(934\) 14.9229i 0.488293i
\(935\) −8.81350 5.08848i −0.288232 0.166411i
\(936\) 0 0
\(937\) 38.1057i 1.24486i −0.782676 0.622430i \(-0.786146\pi\)
0.782676 0.622430i \(-0.213854\pi\)
\(938\) −0.332030 + 0.492968i −0.0108412 + 0.0160960i
\(939\) 0 0
\(940\) 5.02404 0.163866
\(941\) 9.93855 + 17.2141i 0.323987 + 0.561163i 0.981307 0.192449i \(-0.0616431\pi\)
−0.657319 + 0.753612i \(0.728310\pi\)
\(942\) 0 0
\(943\) 58.0603 + 33.5211i 1.89070 + 1.09160i
\(944\) −11.4696 −0.373304
\(945\) 0 0
\(946\) −9.74394 −0.316803
\(947\) −17.9696 10.3747i −0.583933 0.337134i 0.178762 0.983892i \(-0.442791\pi\)
−0.762695 + 0.646759i \(0.776124\pi\)
\(948\) 0 0
\(949\) 3.05772 + 5.29613i 0.0992578 + 0.171919i
\(950\) 8.36914 0.271531
\(951\) 0 0
\(952\) −11.3474 23.2261i −0.367773 0.752763i
\(953\) 12.8345i 0.415751i 0.978155 + 0.207876i \(0.0666549\pi\)
−0.978155 + 0.207876i \(0.933345\pi\)
\(954\) 0 0
\(955\) −9.26571 5.34956i −0.299831 0.173108i
\(956\) 27.3696i 0.885195i
\(957\) 0 0
\(958\) 19.9408 + 11.5128i 0.644258 + 0.371962i
\(959\) 17.5863 26.1105i 0.567891 0.843153i
\(960\) 0 0
\(961\) −11.4941 + 19.9084i −0.370778 + 0.642207i
\(962\) 0.644915 1.11703i 0.0207929 0.0360143i
\(963\) 0 0
\(964\) 8.31878 4.80285i 0.267930 0.154689i
\(965\) −9.42969 16.3327i −0.303552 0.525768i
\(966\) 0 0
\(967\) −17.8941 + 30.9936i −0.575437 + 0.996685i 0.420557 + 0.907266i \(0.361835\pi\)
−0.995994 + 0.0894195i \(0.971499\pi\)
\(968\) 19.4125i 0.623941i
\(969\) 0 0
\(970\) 16.1241 0.517714
\(971\) −14.5129 25.1370i −0.465740 0.806686i 0.533494 0.845804i \(-0.320879\pi\)
−0.999235 + 0.0391177i \(0.987545\pi\)
\(972\) 0 0
\(973\) −13.9665 28.5868i −0.447744 0.916450i
\(974\) 14.7247 8.50130i 0.471809 0.272399i
\(975\) 0 0
\(976\) −2.38949 + 1.37957i −0.0764856 + 0.0441590i
\(977\) −7.73439 + 4.46545i −0.247445 + 0.142862i −0.618594 0.785711i \(-0.712297\pi\)
0.371149 + 0.928573i \(0.378964\pi\)
\(978\) 0 0
\(979\) −16.4977 + 9.52495i −0.527268 + 0.304419i
\(980\) 9.24334 11.8637i 0.295268 0.378973i
\(981\) 0 0
\(982\) −6.41288 11.1074i −0.204643 0.354452i
\(983\) 52.2693 1.66713 0.833566 0.552420i \(-0.186296\pi\)
0.833566 + 0.552420i \(0.186296\pi\)
\(984\) 0 0
\(985\) 5.83413i 0.185891i
\(986\) −13.7519 + 23.8190i −0.437950 + 0.758552i
\(987\) 0 0
\(988\) 6.49333 + 11.2468i 0.206580 + 0.357807i
\(989\) 37.0378 21.3838i 1.17773 0.679964i
\(990\) 0 0
\(991\) −21.9151 + 37.9581i −0.696158 + 1.20578i 0.273631 + 0.961835i \(0.411775\pi\)
−0.969789 + 0.243946i \(0.921558\pi\)
\(992\) 8.27329 14.3298i 0.262677 0.454970i
\(993\) 0 0
\(994\) 3.32795 1.62592i 0.105556 0.0515710i
\(995\) 20.5690 + 11.8755i 0.652082 + 0.376480i
\(996\) 0 0
\(997\) 44.9975i 1.42508i −0.701630 0.712542i \(-0.747544\pi\)
0.701630 0.712542i \(-0.252456\pi\)
\(998\) −14.3797 8.30215i −0.455183 0.262800i
\(999\) 0 0
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 189.2.s.b.17.4 10
3.2 odd 2 63.2.s.b.59.2 yes 10
4.3 odd 2 3024.2.df.b.17.4 10
7.2 even 3 1323.2.i.b.1097.2 10
7.3 odd 6 1323.2.o.c.881.2 10
7.4 even 3 1323.2.o.d.881.2 10
7.5 odd 6 189.2.i.b.152.2 10
7.6 odd 2 1323.2.s.b.962.4 10
9.2 odd 6 189.2.i.b.143.4 10
9.4 even 3 567.2.p.d.80.2 10
9.5 odd 6 567.2.p.c.80.4 10
9.7 even 3 63.2.i.b.38.2 yes 10
12.11 even 2 1008.2.df.b.689.2 10
21.2 odd 6 441.2.i.b.68.4 10
21.5 even 6 63.2.i.b.5.4 10
21.11 odd 6 441.2.o.c.293.4 10
21.17 even 6 441.2.o.d.293.4 10
21.20 even 2 441.2.s.b.374.2 10
28.19 even 6 3024.2.ca.b.2609.4 10
36.7 odd 6 1008.2.ca.b.353.3 10
36.11 even 6 3024.2.ca.b.2033.4 10
63.2 odd 6 1323.2.s.b.656.4 10
63.5 even 6 567.2.p.d.404.2 10
63.11 odd 6 1323.2.o.c.440.2 10
63.16 even 3 441.2.s.b.362.2 10
63.20 even 6 1323.2.i.b.521.4 10
63.25 even 3 441.2.o.d.146.4 10
63.34 odd 6 441.2.i.b.227.2 10
63.38 even 6 1323.2.o.d.440.2 10
63.40 odd 6 567.2.p.c.404.4 10
63.47 even 6 inner 189.2.s.b.89.4 10
63.52 odd 6 441.2.o.c.146.4 10
63.61 odd 6 63.2.s.b.47.2 yes 10
84.47 odd 6 1008.2.ca.b.257.3 10
252.47 odd 6 3024.2.df.b.1601.4 10
252.187 even 6 1008.2.df.b.929.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.i.b.5.4 10 21.5 even 6
63.2.i.b.38.2 yes 10 9.7 even 3
63.2.s.b.47.2 yes 10 63.61 odd 6
63.2.s.b.59.2 yes 10 3.2 odd 2
189.2.i.b.143.4 10 9.2 odd 6
189.2.i.b.152.2 10 7.5 odd 6
189.2.s.b.17.4 10 1.1 even 1 trivial
189.2.s.b.89.4 10 63.47 even 6 inner
441.2.i.b.68.4 10 21.2 odd 6
441.2.i.b.227.2 10 63.34 odd 6
441.2.o.c.146.4 10 63.52 odd 6
441.2.o.c.293.4 10 21.11 odd 6
441.2.o.d.146.4 10 63.25 even 3
441.2.o.d.293.4 10 21.17 even 6
441.2.s.b.362.2 10 63.16 even 3
441.2.s.b.374.2 10 21.20 even 2
567.2.p.c.80.4 10 9.5 odd 6
567.2.p.c.404.4 10 63.40 odd 6
567.2.p.d.80.2 10 9.4 even 3
567.2.p.d.404.2 10 63.5 even 6
1008.2.ca.b.257.3 10 84.47 odd 6
1008.2.ca.b.353.3 10 36.7 odd 6
1008.2.df.b.689.2 10 12.11 even 2
1008.2.df.b.929.2 10 252.187 even 6
1323.2.i.b.521.4 10 63.20 even 6
1323.2.i.b.1097.2 10 7.2 even 3
1323.2.o.c.440.2 10 63.11 odd 6
1323.2.o.c.881.2 10 7.3 odd 6
1323.2.o.d.440.2 10 63.38 even 6
1323.2.o.d.881.2 10 7.4 even 3
1323.2.s.b.656.4 10 63.2 odd 6
1323.2.s.b.962.4 10 7.6 odd 2
3024.2.ca.b.2033.4 10 36.11 even 6
3024.2.ca.b.2609.4 10 28.19 even 6
3024.2.df.b.17.4 10 4.3 odd 2
3024.2.df.b.1601.4 10 252.47 odd 6