Properties

Label 450.2.j.f.349.2
Level $450$
Weight $2$
Character 450.349
Analytic conductor $3.593$
Analytic rank $0$
Dimension $8$
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] = [450,2,Mod(49,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.j (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: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 349.2
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 450.349
Dual form 450.2.j.f.49.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(1.41421 - 1.00000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.72474 + 0.158919i) q^{6} +(3.85337 + 2.22474i) q^{7} -1.00000i q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(1.41421 - 1.00000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.72474 + 0.158919i) q^{6} +(3.85337 + 2.22474i) q^{7} -1.00000i q^{8} +(1.00000 - 2.82843i) q^{9} +(-2.44949 + 4.24264i) q^{11} +(1.57313 + 0.724745i) q^{12} +(3.85337 - 2.22474i) q^{13} +(-2.22474 - 3.85337i) q^{14} +(-0.500000 + 0.866025i) q^{16} +4.89898i q^{17} +(-2.28024 + 1.94949i) q^{18} -2.55051 q^{19} +(7.67423 - 0.707107i) q^{21} +(4.24264 - 2.44949i) q^{22} +(2.12132 - 1.22474i) q^{23} +(-1.00000 - 1.41421i) q^{24} -4.44949 q^{26} +(-1.41421 - 5.00000i) q^{27} +4.44949i q^{28} +(1.22474 - 2.12132i) q^{29} +(0.224745 + 0.389270i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.778539 + 8.44949i) q^{33} +(2.44949 - 4.24264i) q^{34} +(2.94949 - 0.548188i) q^{36} -3.34847i q^{37} +(2.20881 + 1.27526i) q^{38} +(3.22474 - 6.99964i) q^{39} +(-4.50000 - 7.79423i) q^{41} +(-6.99964 - 3.22474i) q^{42} +(-6.45145 - 3.72474i) q^{43} -4.89898 q^{44} -2.44949 q^{46} +(-0.953512 - 0.550510i) q^{47} +(0.158919 + 1.72474i) q^{48} +(6.39898 + 11.0834i) q^{49} +(4.89898 + 6.92820i) q^{51} +(3.85337 + 2.22474i) q^{52} -8.44949i q^{53} +(-1.27526 + 5.03723i) q^{54} +(2.22474 - 3.85337i) q^{56} +(-3.60697 + 2.55051i) q^{57} +(-2.12132 + 1.22474i) q^{58} +(-0.275255 - 0.476756i) q^{59} +(-4.00000 + 6.92820i) q^{61} -0.449490i q^{62} +(10.1459 - 8.67423i) q^{63} -1.00000 q^{64} +(3.55051 - 7.70674i) q^{66} +(12.4261 - 7.17423i) q^{67} +(-4.24264 + 2.44949i) q^{68} +(1.77526 - 3.85337i) q^{69} -1.34847 q^{71} +(-2.82843 - 1.00000i) q^{72} -1.00000i q^{73} +(-1.67423 + 2.89986i) q^{74} +(-1.27526 - 2.20881i) q^{76} +(-18.8776 + 10.8990i) q^{77} +(-6.29253 + 4.44949i) q^{78} +(-6.34847 + 10.9959i) q^{79} +(-7.00000 - 5.65685i) q^{81} +9.00000i q^{82} +(0.476756 + 0.275255i) q^{83} +(4.44949 + 6.29253i) q^{84} +(3.72474 + 6.45145i) q^{86} +(-0.389270 - 4.22474i) q^{87} +(4.24264 + 2.44949i) q^{88} +9.00000 q^{89} +19.7980 q^{91} +(2.12132 + 1.22474i) q^{92} +(0.707107 + 0.325765i) q^{93} +(0.550510 + 0.953512i) q^{94} +(0.724745 - 1.57313i) q^{96} +(-9.35131 - 5.39898i) q^{97} -12.7980i q^{98} +(9.55051 + 11.1708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} - 4 q^{6} + 8 q^{9} - 8 q^{14} - 4 q^{16} - 40 q^{19} + 32 q^{21} - 8 q^{24} - 16 q^{26} - 8 q^{31} + 4 q^{36} + 16 q^{39} - 36 q^{41} + 12 q^{49} - 20 q^{54} + 8 q^{56} - 12 q^{59} - 32 q^{61} - 8 q^{64} + 48 q^{66} + 24 q^{69} + 48 q^{71} + 16 q^{74} - 20 q^{76} + 8 q^{79} - 56 q^{81} + 16 q^{84} + 20 q^{86} + 72 q^{89} + 80 q^{91} + 24 q^{94} - 4 q^{96} + 96 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 1.41421 1.00000i 0.816497 0.577350i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) −1.72474 + 0.158919i −0.704124 + 0.0648783i
\(7\) 3.85337 + 2.22474i 1.45644 + 0.840875i 0.998834 0.0482818i \(-0.0153745\pi\)
0.457604 + 0.889156i \(0.348708\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000 2.82843i 0.333333 0.942809i
\(10\) 0 0
\(11\) −2.44949 + 4.24264i −0.738549 + 1.27920i 0.214600 + 0.976702i \(0.431155\pi\)
−0.953149 + 0.302502i \(0.902178\pi\)
\(12\) 1.57313 + 0.724745i 0.454124 + 0.209216i
\(13\) 3.85337 2.22474i 1.06873 0.617033i 0.140898 0.990024i \(-0.455001\pi\)
0.927835 + 0.372991i \(0.121668\pi\)
\(14\) −2.22474 3.85337i −0.594588 1.02986i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 4.89898i 1.18818i 0.804400 + 0.594089i \(0.202487\pi\)
−0.804400 + 0.594089i \(0.797513\pi\)
\(18\) −2.28024 + 1.94949i −0.537457 + 0.459499i
\(19\) −2.55051 −0.585127 −0.292564 0.956246i \(-0.594508\pi\)
−0.292564 + 0.956246i \(0.594508\pi\)
\(20\) 0 0
\(21\) 7.67423 0.707107i 1.67466 0.154303i
\(22\) 4.24264 2.44949i 0.904534 0.522233i
\(23\) 2.12132 1.22474i 0.442326 0.255377i −0.262258 0.964998i \(-0.584467\pi\)
0.704584 + 0.709621i \(0.251134\pi\)
\(24\) −1.00000 1.41421i −0.204124 0.288675i
\(25\) 0 0
\(26\) −4.44949 −0.872617
\(27\) −1.41421 5.00000i −0.272166 0.962250i
\(28\) 4.44949i 0.840875i
\(29\) 1.22474 2.12132i 0.227429 0.393919i −0.729616 0.683857i \(-0.760301\pi\)
0.957046 + 0.289938i \(0.0936346\pi\)
\(30\) 0 0
\(31\) 0.224745 + 0.389270i 0.0403654 + 0.0699149i 0.885502 0.464635i \(-0.153814\pi\)
−0.845137 + 0.534550i \(0.820481\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0.778539 + 8.44949i 0.135526 + 1.47087i
\(34\) 2.44949 4.24264i 0.420084 0.727607i
\(35\) 0 0
\(36\) 2.94949 0.548188i 0.491582 0.0913647i
\(37\) 3.34847i 0.550485i −0.961375 0.275242i \(-0.911242\pi\)
0.961375 0.275242i \(-0.0887581\pi\)
\(38\) 2.20881 + 1.27526i 0.358316 + 0.206874i
\(39\) 3.22474 6.99964i 0.516372 1.12084i
\(40\) 0 0
\(41\) −4.50000 7.79423i −0.702782 1.21725i −0.967486 0.252924i \(-0.918608\pi\)
0.264704 0.964330i \(-0.414726\pi\)
\(42\) −6.99964 3.22474i −1.08007 0.497589i
\(43\) −6.45145 3.72474i −0.983836 0.568018i −0.0804103 0.996762i \(-0.525623\pi\)
−0.903426 + 0.428744i \(0.858956\pi\)
\(44\) −4.89898 −0.738549
\(45\) 0 0
\(46\) −2.44949 −0.361158
\(47\) −0.953512 0.550510i −0.139084 0.0803002i 0.428843 0.903379i \(-0.358921\pi\)
−0.567927 + 0.823079i \(0.692255\pi\)
\(48\) 0.158919 + 1.72474i 0.0229379 + 0.248945i
\(49\) 6.39898 + 11.0834i 0.914140 + 1.58334i
\(50\) 0 0
\(51\) 4.89898 + 6.92820i 0.685994 + 0.970143i
\(52\) 3.85337 + 2.22474i 0.534366 + 0.308517i
\(53\) 8.44949i 1.16063i −0.814393 0.580313i \(-0.802930\pi\)
0.814393 0.580313i \(-0.197070\pi\)
\(54\) −1.27526 + 5.03723i −0.173540 + 0.685481i
\(55\) 0 0
\(56\) 2.22474 3.85337i 0.297294 0.514928i
\(57\) −3.60697 + 2.55051i −0.477754 + 0.337823i
\(58\) −2.12132 + 1.22474i −0.278543 + 0.160817i
\(59\) −0.275255 0.476756i −0.0358352 0.0620683i 0.847552 0.530713i \(-0.178076\pi\)
−0.883387 + 0.468645i \(0.844742\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) 0.449490i 0.0570853i
\(63\) 10.1459 8.67423i 1.27826 1.09285i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 3.55051 7.70674i 0.437038 0.948634i
\(67\) 12.4261 7.17423i 1.51809 0.876472i 0.518321 0.855186i \(-0.326557\pi\)
0.999773 0.0212861i \(-0.00677610\pi\)
\(68\) −4.24264 + 2.44949i −0.514496 + 0.297044i
\(69\) 1.77526 3.85337i 0.213716 0.463891i
\(70\) 0 0
\(71\) −1.34847 −0.160034 −0.0800169 0.996794i \(-0.525497\pi\)
−0.0800169 + 0.996794i \(0.525497\pi\)
\(72\) −2.82843 1.00000i −0.333333 0.117851i
\(73\) 1.00000i 0.117041i −0.998286 0.0585206i \(-0.981362\pi\)
0.998286 0.0585206i \(-0.0186383\pi\)
\(74\) −1.67423 + 2.89986i −0.194626 + 0.337102i
\(75\) 0 0
\(76\) −1.27526 2.20881i −0.146282 0.253368i
\(77\) −18.8776 + 10.8990i −2.15130 + 1.24205i
\(78\) −6.29253 + 4.44949i −0.712489 + 0.503806i
\(79\) −6.34847 + 10.9959i −0.714259 + 1.23713i 0.248986 + 0.968507i \(0.419903\pi\)
−0.963245 + 0.268625i \(0.913431\pi\)
\(80\) 0 0
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) 9.00000i 0.993884i
\(83\) 0.476756 + 0.275255i 0.0523308 + 0.0302132i 0.525937 0.850523i \(-0.323715\pi\)
−0.473606 + 0.880737i \(0.657048\pi\)
\(84\) 4.44949 + 6.29253i 0.485479 + 0.686571i
\(85\) 0 0
\(86\) 3.72474 + 6.45145i 0.401650 + 0.695677i
\(87\) −0.389270 4.22474i −0.0417341 0.452940i
\(88\) 4.24264 + 2.44949i 0.452267 + 0.261116i
\(89\) 9.00000 0.953998 0.476999 0.878904i \(-0.341725\pi\)
0.476999 + 0.878904i \(0.341725\pi\)
\(90\) 0 0
\(91\) 19.7980 2.07539
\(92\) 2.12132 + 1.22474i 0.221163 + 0.127688i
\(93\) 0.707107 + 0.325765i 0.0733236 + 0.0337803i
\(94\) 0.550510 + 0.953512i 0.0567808 + 0.0983472i
\(95\) 0 0
\(96\) 0.724745 1.57313i 0.0739690 0.160557i
\(97\) −9.35131 5.39898i −0.949481 0.548183i −0.0565616 0.998399i \(-0.518014\pi\)
−0.892920 + 0.450216i \(0.851347\pi\)
\(98\) 12.7980i 1.29279i
\(99\) 9.55051 + 11.1708i 0.959862 + 1.12271i
\(100\) 0 0
\(101\) −1.77526 + 3.07483i −0.176644 + 0.305957i −0.940729 0.339159i \(-0.889858\pi\)
0.764085 + 0.645116i \(0.223191\pi\)
\(102\) −0.778539 8.44949i −0.0770869 0.836624i
\(103\) −10.9959 + 6.34847i −1.08346 + 0.625533i −0.931826 0.362904i \(-0.881785\pi\)
−0.151629 + 0.988437i \(0.548452\pi\)
\(104\) −2.22474 3.85337i −0.218154 0.377854i
\(105\) 0 0
\(106\) −4.22474 + 7.31747i −0.410343 + 0.710736i
\(107\) 15.2474i 1.47403i 0.675878 + 0.737013i \(0.263764\pi\)
−0.675878 + 0.737013i \(0.736236\pi\)
\(108\) 3.62302 3.72474i 0.348625 0.358414i
\(109\) −10.4495 −1.00088 −0.500440 0.865771i \(-0.666828\pi\)
−0.500440 + 0.865771i \(0.666828\pi\)
\(110\) 0 0
\(111\) −3.34847 4.73545i −0.317823 0.449469i
\(112\) −3.85337 + 2.22474i −0.364109 + 0.210219i
\(113\) −12.0369 + 6.94949i −1.13233 + 0.653753i −0.944521 0.328452i \(-0.893473\pi\)
−0.187813 + 0.982205i \(0.560140\pi\)
\(114\) 4.39898 0.405324i 0.412002 0.0379620i
\(115\) 0 0
\(116\) 2.44949 0.227429
\(117\) −2.43916 13.1237i −0.225500 1.21329i
\(118\) 0.550510i 0.0506786i
\(119\) −10.8990 + 18.8776i −0.999108 + 1.73051i
\(120\) 0 0
\(121\) −6.50000 11.2583i −0.590909 1.02348i
\(122\) 6.92820 4.00000i 0.627250 0.362143i
\(123\) −14.1582 6.52270i −1.27660 0.588132i
\(124\) −0.224745 + 0.389270i −0.0201827 + 0.0349574i
\(125\) 0 0
\(126\) −13.1237 + 2.43916i −1.16915 + 0.217297i
\(127\) 11.3485i 1.00701i 0.863991 + 0.503507i \(0.167957\pi\)
−0.863991 + 0.503507i \(0.832043\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −12.8485 + 1.18386i −1.13124 + 0.104233i
\(130\) 0 0
\(131\) −7.89898 13.6814i −0.690137 1.19535i −0.971793 0.235837i \(-0.924217\pi\)
0.281656 0.959516i \(-0.409116\pi\)
\(132\) −6.92820 + 4.89898i −0.603023 + 0.426401i
\(133\) −9.82806 5.67423i −0.852201 0.492019i
\(134\) −14.3485 −1.23952
\(135\) 0 0
\(136\) 4.89898 0.420084
\(137\) 2.59808 + 1.50000i 0.221969 + 0.128154i 0.606861 0.794808i \(-0.292428\pi\)
−0.384893 + 0.922961i \(0.625762\pi\)
\(138\) −3.46410 + 2.44949i −0.294884 + 0.208514i
\(139\) −2.00000 3.46410i −0.169638 0.293821i 0.768655 0.639664i \(-0.220926\pi\)
−0.938293 + 0.345843i \(0.887593\pi\)
\(140\) 0 0
\(141\) −1.89898 + 0.174973i −0.159923 + 0.0147354i
\(142\) 1.16781 + 0.674235i 0.0980003 + 0.0565805i
\(143\) 21.7980i 1.82284i
\(144\) 1.94949 + 2.28024i 0.162457 + 0.190020i
\(145\) 0 0
\(146\) −0.500000 + 0.866025i −0.0413803 + 0.0716728i
\(147\) 20.1329 + 9.27526i 1.66053 + 0.765010i
\(148\) 2.89986 1.67423i 0.238367 0.137621i
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) −10.0000 + 17.3205i −0.813788 + 1.40952i 0.0964061 + 0.995342i \(0.469265\pi\)
−0.910195 + 0.414181i \(0.864068\pi\)
\(152\) 2.55051i 0.206874i
\(153\) 13.8564 + 4.89898i 1.12022 + 0.396059i
\(154\) 21.7980 1.75653
\(155\) 0 0
\(156\) 7.67423 0.707107i 0.614431 0.0566139i
\(157\) 0.174973 0.101021i 0.0139643 0.00806231i −0.493002 0.870028i \(-0.664100\pi\)
0.506966 + 0.861966i \(0.330767\pi\)
\(158\) 10.9959 6.34847i 0.874785 0.505057i
\(159\) −8.44949 11.9494i −0.670088 0.947648i
\(160\) 0 0
\(161\) 10.8990 0.858960
\(162\) 3.23375 + 8.39898i 0.254067 + 0.659886i
\(163\) 2.55051i 0.199771i 0.994999 + 0.0998857i \(0.0318477\pi\)
−0.994999 + 0.0998857i \(0.968152\pi\)
\(164\) 4.50000 7.79423i 0.351391 0.608627i
\(165\) 0 0
\(166\) −0.275255 0.476756i −0.0213639 0.0370034i
\(167\) 16.9706 9.79796i 1.31322 0.758189i 0.330593 0.943773i \(-0.392751\pi\)
0.982628 + 0.185584i \(0.0594178\pi\)
\(168\) −0.707107 7.67423i −0.0545545 0.592080i
\(169\) 3.39898 5.88721i 0.261460 0.452862i
\(170\) 0 0
\(171\) −2.55051 + 7.21393i −0.195042 + 0.551663i
\(172\) 7.44949i 0.568018i
\(173\) 8.48528 + 4.89898i 0.645124 + 0.372463i 0.786586 0.617481i \(-0.211847\pi\)
−0.141462 + 0.989944i \(0.545180\pi\)
\(174\) −1.77526 + 3.85337i −0.134582 + 0.292123i
\(175\) 0 0
\(176\) −2.44949 4.24264i −0.184637 0.319801i
\(177\) −0.866025 0.398979i −0.0650945 0.0299891i
\(178\) −7.79423 4.50000i −0.584202 0.337289i
\(179\) 15.2474 1.13965 0.569824 0.821767i \(-0.307011\pi\)
0.569824 + 0.821767i \(0.307011\pi\)
\(180\) 0 0
\(181\) −1.79796 −0.133641 −0.0668206 0.997765i \(-0.521286\pi\)
−0.0668206 + 0.997765i \(0.521286\pi\)
\(182\) −17.1455 9.89898i −1.27091 0.733761i
\(183\) 1.27135 + 13.7980i 0.0939808 + 1.01997i
\(184\) −1.22474 2.12132i −0.0902894 0.156386i
\(185\) 0 0
\(186\) −0.449490 0.635674i −0.0329582 0.0466099i
\(187\) −20.7846 12.0000i −1.51992 0.877527i
\(188\) 1.10102i 0.0803002i
\(189\) 5.67423 22.4131i 0.412740 1.63031i
\(190\) 0 0
\(191\) 5.44949 9.43879i 0.394311 0.682967i −0.598702 0.800972i \(-0.704317\pi\)
0.993013 + 0.118005i \(0.0376499\pi\)
\(192\) −1.41421 + 1.00000i −0.102062 + 0.0721688i
\(193\) 17.3205 10.0000i 1.24676 0.719816i 0.276296 0.961073i \(-0.410893\pi\)
0.970461 + 0.241257i \(0.0775596\pi\)
\(194\) 5.39898 + 9.35131i 0.387624 + 0.671385i
\(195\) 0 0
\(196\) −6.39898 + 11.0834i −0.457070 + 0.791668i
\(197\) 24.2474i 1.72756i −0.503870 0.863780i \(-0.668091\pi\)
0.503870 0.863780i \(-0.331909\pi\)
\(198\) −2.68556 14.4495i −0.190855 1.02688i
\(199\) −5.79796 −0.411006 −0.205503 0.978656i \(-0.565883\pi\)
−0.205503 + 0.978656i \(0.565883\pi\)
\(200\) 0 0
\(201\) 10.3990 22.5720i 0.733487 1.59211i
\(202\) 3.07483 1.77526i 0.216344 0.124907i
\(203\) 9.43879 5.44949i 0.662473 0.382479i
\(204\) −3.55051 + 7.70674i −0.248585 + 0.539580i
\(205\) 0 0
\(206\) 12.6969 0.884638
\(207\) −1.34278 7.22474i −0.0933298 0.502154i
\(208\) 4.44949i 0.308517i
\(209\) 6.24745 10.8209i 0.432145 0.748497i
\(210\) 0 0
\(211\) −0.724745 1.25529i −0.0498935 0.0864181i 0.840000 0.542586i \(-0.182555\pi\)
−0.889894 + 0.456168i \(0.849222\pi\)
\(212\) 7.31747 4.22474i 0.502566 0.290157i
\(213\) −1.90702 + 1.34847i −0.130667 + 0.0923956i
\(214\) 7.62372 13.2047i 0.521147 0.902653i
\(215\) 0 0
\(216\) −5.00000 + 1.41421i −0.340207 + 0.0962250i
\(217\) 2.00000i 0.135769i
\(218\) 9.04952 + 5.22474i 0.612911 + 0.353864i
\(219\) −1.00000 1.41421i −0.0675737 0.0955637i
\(220\) 0 0
\(221\) 10.8990 + 18.8776i 0.733145 + 1.26984i
\(222\) 0.532134 + 5.77526i 0.0357145 + 0.387610i
\(223\) 1.55708 + 0.898979i 0.104270 + 0.0602001i 0.551228 0.834355i \(-0.314159\pi\)
−0.446958 + 0.894555i \(0.647493\pi\)
\(224\) 4.44949 0.297294
\(225\) 0 0
\(226\) 13.8990 0.924546
\(227\) 24.5505 + 14.1742i 1.62947 + 0.940777i 0.984250 + 0.176783i \(0.0565692\pi\)
0.645224 + 0.763994i \(0.276764\pi\)
\(228\) −4.01229 1.84847i −0.265720 0.122418i
\(229\) −10.5732 18.3133i −0.698698 1.21018i −0.968918 0.247381i \(-0.920430\pi\)
0.270221 0.962798i \(-0.412903\pi\)
\(230\) 0 0
\(231\) −15.7980 + 34.2911i −1.03943 + 2.25619i
\(232\) −2.12132 1.22474i −0.139272 0.0804084i
\(233\) 5.69694i 0.373219i 0.982434 + 0.186609i \(0.0597499\pi\)
−0.982434 + 0.186609i \(0.940250\pi\)
\(234\) −4.44949 + 12.5851i −0.290872 + 0.822711i
\(235\) 0 0
\(236\) 0.275255 0.476756i 0.0179176 0.0310342i
\(237\) 2.01778 + 21.8990i 0.131069 + 1.42249i
\(238\) 18.8776 10.8990i 1.22365 0.706476i
\(239\) 4.77526 + 8.27098i 0.308886 + 0.535006i 0.978119 0.208047i \(-0.0667107\pi\)
−0.669233 + 0.743052i \(0.733377\pi\)
\(240\) 0 0
\(241\) 11.3990 19.7436i 0.734273 1.27180i −0.220769 0.975326i \(-0.570857\pi\)
0.955042 0.296472i \(-0.0958100\pi\)
\(242\) 13.0000i 0.835672i
\(243\) −15.5563 1.00000i −0.997940 0.0641500i
\(244\) −8.00000 −0.512148
\(245\) 0 0
\(246\) 9.00000 + 12.7279i 0.573819 + 0.811503i
\(247\) −9.82806 + 5.67423i −0.625345 + 0.361043i
\(248\) 0.389270 0.224745i 0.0247186 0.0142713i
\(249\) 0.949490 0.0874863i 0.0601715 0.00554422i
\(250\) 0 0
\(251\) −5.44949 −0.343969 −0.171984 0.985100i \(-0.555018\pi\)
−0.171984 + 0.985100i \(0.555018\pi\)
\(252\) 12.5851 + 4.44949i 0.792784 + 0.280292i
\(253\) 12.0000i 0.754434i
\(254\) 5.67423 9.82806i 0.356033 0.616667i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −5.88721 + 3.39898i −0.367234 + 0.212023i −0.672249 0.740325i \(-0.734672\pi\)
0.305016 + 0.952347i \(0.401338\pi\)
\(258\) 11.7190 + 5.39898i 0.729595 + 0.336126i
\(259\) 7.44949 12.9029i 0.462889 0.801747i
\(260\) 0 0
\(261\) −4.77526 5.58542i −0.295581 0.345729i
\(262\) 15.7980i 0.976001i
\(263\) −13.4671 7.77526i −0.830419 0.479443i 0.0235770 0.999722i \(-0.492495\pi\)
−0.853996 + 0.520279i \(0.825828\pi\)
\(264\) 8.44949 0.778539i 0.520030 0.0479158i
\(265\) 0 0
\(266\) 5.67423 + 9.82806i 0.347910 + 0.602597i
\(267\) 12.7279 9.00000i 0.778936 0.550791i
\(268\) 12.4261 + 7.17423i 0.759047 + 0.438236i
\(269\) −9.55051 −0.582305 −0.291152 0.956677i \(-0.594039\pi\)
−0.291152 + 0.956677i \(0.594039\pi\)
\(270\) 0 0
\(271\) 0.651531 0.0395777 0.0197888 0.999804i \(-0.493701\pi\)
0.0197888 + 0.999804i \(0.493701\pi\)
\(272\) −4.24264 2.44949i −0.257248 0.148522i
\(273\) 27.9985 19.7980i 1.69455 1.19823i
\(274\) −1.50000 2.59808i −0.0906183 0.156956i
\(275\) 0 0
\(276\) 4.22474 0.389270i 0.254300 0.0234313i
\(277\) −5.58542 3.22474i −0.335595 0.193756i 0.322727 0.946492i \(-0.395400\pi\)
−0.658323 + 0.752736i \(0.728734\pi\)
\(278\) 4.00000i 0.239904i
\(279\) 1.32577 0.246405i 0.0793715 0.0147519i
\(280\) 0 0
\(281\) −14.4495 + 25.0273i −0.861984 + 1.49300i 0.00802643 + 0.999968i \(0.497445\pi\)
−0.870011 + 0.493033i \(0.835888\pi\)
\(282\) 1.73205 + 0.797959i 0.103142 + 0.0475178i
\(283\) 9.74058 5.62372i 0.579017 0.334296i −0.181726 0.983349i \(-0.558168\pi\)
0.760743 + 0.649054i \(0.224835\pi\)
\(284\) −0.674235 1.16781i −0.0400085 0.0692967i
\(285\) 0 0
\(286\) 10.8990 18.8776i 0.644470 1.11626i
\(287\) 40.0454i 2.36381i
\(288\) −0.548188 2.94949i −0.0323023 0.173800i
\(289\) −7.00000 −0.411765
\(290\) 0 0
\(291\) −18.6237 + 1.71600i −1.09174 + 0.100594i
\(292\) 0.866025 0.500000i 0.0506803 0.0292603i
\(293\) −24.2880 + 14.0227i −1.41892 + 0.819215i −0.996204 0.0870462i \(-0.972257\pi\)
−0.422718 + 0.906261i \(0.638924\pi\)
\(294\) −12.7980 18.0990i −0.746392 1.05556i
\(295\) 0 0
\(296\) −3.34847 −0.194626
\(297\) 24.6773 + 6.24745i 1.43192 + 0.362514i
\(298\) 6.00000i 0.347571i
\(299\) 5.44949 9.43879i 0.315152 0.545859i
\(300\) 0 0
\(301\) −16.5732 28.7056i −0.955264 1.65457i
\(302\) 17.3205 10.0000i 0.996683 0.575435i
\(303\) 0.564242 + 6.12372i 0.0324149 + 0.351799i
\(304\) 1.27526 2.20881i 0.0731409 0.126684i
\(305\) 0 0
\(306\) −9.55051 11.1708i −0.545966 0.638595i
\(307\) 6.69694i 0.382214i 0.981569 + 0.191107i \(0.0612078\pi\)
−0.981569 + 0.191107i \(0.938792\pi\)
\(308\) −18.8776 10.8990i −1.07565 0.621027i
\(309\) −9.20204 + 19.9740i −0.523486 + 1.13628i
\(310\) 0 0
\(311\) 5.44949 + 9.43879i 0.309012 + 0.535225i 0.978147 0.207917i \(-0.0666683\pi\)
−0.669134 + 0.743141i \(0.733335\pi\)
\(312\) −6.99964 3.22474i −0.396276 0.182565i
\(313\) −3.37662 1.94949i −0.190858 0.110192i 0.401526 0.915847i \(-0.368480\pi\)
−0.592384 + 0.805656i \(0.701813\pi\)
\(314\) −0.202041 −0.0114018
\(315\) 0 0
\(316\) −12.6969 −0.714259
\(317\) −14.8492 8.57321i −0.834017 0.481520i 0.0212094 0.999775i \(-0.493248\pi\)
−0.855226 + 0.518255i \(0.826582\pi\)
\(318\) 1.34278 + 14.5732i 0.0752994 + 0.817225i
\(319\) 6.00000 + 10.3923i 0.335936 + 0.581857i
\(320\) 0 0
\(321\) 15.2474 + 21.5631i 0.851030 + 1.20354i
\(322\) −9.43879 5.44949i −0.526003 0.303688i
\(323\) 12.4949i 0.695235i
\(324\) 1.39898 8.89060i 0.0777211 0.493922i
\(325\) 0 0
\(326\) 1.27526 2.20881i 0.0706298 0.122334i
\(327\) −14.7778 + 10.4495i −0.817215 + 0.577858i
\(328\) −7.79423 + 4.50000i −0.430364 + 0.248471i
\(329\) −2.44949 4.24264i −0.135045 0.233904i
\(330\) 0 0
\(331\) 4.17423 7.22999i 0.229437 0.397396i −0.728205 0.685360i \(-0.759645\pi\)
0.957641 + 0.287964i \(0.0929783\pi\)
\(332\) 0.550510i 0.0302132i
\(333\) −9.47090 3.34847i −0.519002 0.183495i
\(334\) −19.5959 −1.07224
\(335\) 0 0
\(336\) −3.22474 + 6.99964i −0.175924 + 0.381861i
\(337\) 9.61377 5.55051i 0.523695 0.302356i −0.214750 0.976669i \(-0.568894\pi\)
0.738445 + 0.674313i \(0.235560\pi\)
\(338\) −5.88721 + 3.39898i −0.320222 + 0.184880i
\(339\) −10.0732 + 21.8649i −0.547102 + 1.18754i
\(340\) 0 0
\(341\) −2.20204 −0.119247
\(342\) 5.81577 4.97219i 0.314481 0.268865i
\(343\) 25.7980i 1.39296i
\(344\) −3.72474 + 6.45145i −0.200825 + 0.347839i
\(345\) 0 0
\(346\) −4.89898 8.48528i −0.263371 0.456172i
\(347\) −10.3923 + 6.00000i −0.557888 + 0.322097i −0.752297 0.658824i \(-0.771054\pi\)
0.194409 + 0.980921i \(0.437721\pi\)
\(348\) 3.46410 2.44949i 0.185695 0.131306i
\(349\) 7.00000 12.1244i 0.374701 0.649002i −0.615581 0.788074i \(-0.711079\pi\)
0.990282 + 0.139072i \(0.0444119\pi\)
\(350\) 0 0
\(351\) −16.5732 16.1206i −0.884613 0.860454i
\(352\) 4.89898i 0.261116i
\(353\) 7.79423 + 4.50000i 0.414845 + 0.239511i 0.692869 0.721063i \(-0.256346\pi\)
−0.278024 + 0.960574i \(0.589680\pi\)
\(354\) 0.550510 + 0.778539i 0.0292593 + 0.0413789i
\(355\) 0 0
\(356\) 4.50000 + 7.79423i 0.238500 + 0.413093i
\(357\) 3.46410 + 37.5959i 0.183340 + 1.98979i
\(358\) −13.2047 7.62372i −0.697889 0.402926i
\(359\) 33.7980 1.78379 0.891894 0.452244i \(-0.149377\pi\)
0.891894 + 0.452244i \(0.149377\pi\)
\(360\) 0 0
\(361\) −12.4949 −0.657626
\(362\) 1.55708 + 0.898979i 0.0818382 + 0.0472493i
\(363\) −20.4507 9.42168i −1.07338 0.494510i
\(364\) 9.89898 + 17.1455i 0.518848 + 0.898670i
\(365\) 0 0
\(366\) 5.79796 12.5851i 0.303064 0.657831i
\(367\) 14.4600 + 8.34847i 0.754804 + 0.435787i 0.827427 0.561573i \(-0.189804\pi\)
−0.0726228 + 0.997359i \(0.523137\pi\)
\(368\) 2.44949i 0.127688i
\(369\) −26.5454 + 4.93369i −1.38190 + 0.256838i
\(370\) 0 0
\(371\) 18.7980 32.5590i 0.975941 1.69038i
\(372\) 0.0714323 + 0.775255i 0.00370359 + 0.0401951i
\(373\) 13.5065 7.79796i 0.699338 0.403763i −0.107763 0.994177i \(-0.534369\pi\)
0.807101 + 0.590414i \(0.201035\pi\)
\(374\) 12.0000 + 20.7846i 0.620505 + 1.07475i
\(375\) 0 0
\(376\) −0.550510 + 0.953512i −0.0283904 + 0.0491736i
\(377\) 10.8990i 0.561326i
\(378\) −16.1206 + 16.5732i −0.829154 + 0.852434i
\(379\) −0.898979 −0.0461775 −0.0230887 0.999733i \(-0.507350\pi\)
−0.0230887 + 0.999733i \(0.507350\pi\)
\(380\) 0 0
\(381\) 11.3485 + 16.0492i 0.581400 + 0.822223i
\(382\) −9.43879 + 5.44949i −0.482931 + 0.278820i
\(383\) 22.9059 13.2247i 1.17044 0.675753i 0.216655 0.976248i \(-0.430485\pi\)
0.953783 + 0.300495i \(0.0971520\pi\)
\(384\) 1.72474 0.158919i 0.0880155 0.00810978i
\(385\) 0 0
\(386\) −20.0000 −1.01797
\(387\) −16.9866 + 14.5227i −0.863478 + 0.738231i
\(388\) 10.7980i 0.548183i
\(389\) −6.79796 + 11.7744i −0.344670 + 0.596986i −0.985294 0.170869i \(-0.945343\pi\)
0.640624 + 0.767855i \(0.278676\pi\)
\(390\) 0 0
\(391\) 6.00000 + 10.3923i 0.303433 + 0.525561i
\(392\) 11.0834 6.39898i 0.559794 0.323197i
\(393\) −24.8523 11.4495i −1.25363 0.577550i
\(394\) −12.1237 + 20.9989i −0.610784 + 1.05791i
\(395\) 0 0
\(396\) −4.89898 + 13.8564i −0.246183 + 0.696311i
\(397\) 21.5959i 1.08387i −0.840421 0.541934i \(-0.817692\pi\)
0.840421 0.541934i \(-0.182308\pi\)
\(398\) 5.02118 + 2.89898i 0.251689 + 0.145313i
\(399\) −19.5732 + 1.80348i −0.979886 + 0.0902871i
\(400\) 0 0
\(401\) −4.65153 8.05669i −0.232286 0.402332i 0.726194 0.687490i \(-0.241287\pi\)
−0.958481 + 0.285158i \(0.907954\pi\)
\(402\) −20.2918 + 14.3485i −1.01206 + 0.715637i
\(403\) 1.73205 + 1.00000i 0.0862796 + 0.0498135i
\(404\) −3.55051 −0.176644
\(405\) 0 0
\(406\) −10.8990 −0.540907
\(407\) 14.2064 + 8.20204i 0.704183 + 0.406560i
\(408\) 6.92820 4.89898i 0.342997 0.242536i
\(409\) 4.94949 + 8.57277i 0.244737 + 0.423896i 0.962058 0.272847i \(-0.0879652\pi\)
−0.717321 + 0.696743i \(0.754632\pi\)
\(410\) 0 0
\(411\) 5.17423 0.476756i 0.255226 0.0235166i
\(412\) −10.9959 6.34847i −0.541728 0.312767i
\(413\) 2.44949i 0.120532i
\(414\) −2.44949 + 6.92820i −0.120386 + 0.340503i
\(415\) 0 0
\(416\) 2.22474 3.85337i 0.109077 0.188927i
\(417\) −6.29253 2.89898i −0.308146 0.141964i
\(418\) −10.8209 + 6.24745i −0.529267 + 0.305573i
\(419\) 4.07321 + 7.05501i 0.198990 + 0.344660i 0.948201 0.317671i \(-0.102901\pi\)
−0.749212 + 0.662331i \(0.769567\pi\)
\(420\) 0 0
\(421\) −9.02270 + 15.6278i −0.439740 + 0.761651i −0.997669 0.0682369i \(-0.978263\pi\)
0.557929 + 0.829888i \(0.311596\pi\)
\(422\) 1.44949i 0.0705601i
\(423\) −2.51059 + 2.14643i −0.122069 + 0.104363i
\(424\) −8.44949 −0.410343
\(425\) 0 0
\(426\) 2.32577 0.214297i 0.112684 0.0103827i
\(427\) −30.8270 + 17.7980i −1.49182 + 0.861304i
\(428\) −13.2047 + 7.62372i −0.638272 + 0.368507i
\(429\) 21.7980 + 30.8270i 1.05242 + 1.48834i
\(430\) 0 0
\(431\) 10.6515 0.513066 0.256533 0.966535i \(-0.417420\pi\)
0.256533 + 0.966535i \(0.417420\pi\)
\(432\) 5.03723 + 1.27526i 0.242354 + 0.0613557i
\(433\) 29.5959i 1.42229i −0.703046 0.711145i \(-0.748177\pi\)
0.703046 0.711145i \(-0.251823\pi\)
\(434\) 1.00000 1.73205i 0.0480015 0.0831411i
\(435\) 0 0
\(436\) −5.22474 9.04952i −0.250220 0.433394i
\(437\) −5.41045 + 3.12372i −0.258817 + 0.149428i
\(438\) 0.158919 + 1.72474i 0.00759343 + 0.0824115i
\(439\) −5.67423 + 9.82806i −0.270816 + 0.469068i −0.969071 0.246782i \(-0.920627\pi\)
0.698255 + 0.715849i \(0.253960\pi\)
\(440\) 0 0
\(441\) 37.7474 7.01569i 1.79750 0.334080i
\(442\) 21.7980i 1.03682i
\(443\) −24.0737 13.8990i −1.14378 0.660360i −0.196415 0.980521i \(-0.562930\pi\)
−0.947363 + 0.320161i \(0.896263\pi\)
\(444\) 2.42679 5.26758i 0.115170 0.249989i
\(445\) 0 0
\(446\) −0.898979 1.55708i −0.0425679 0.0737298i
\(447\) −9.43879 4.34847i −0.446440 0.205676i
\(448\) −3.85337 2.22474i −0.182055 0.105109i
\(449\) −10.5959 −0.500052 −0.250026 0.968239i \(-0.580439\pi\)
−0.250026 + 0.968239i \(0.580439\pi\)
\(450\) 0 0
\(451\) 44.0908 2.07616
\(452\) −12.0369 6.94949i −0.566167 0.326877i
\(453\) 3.17837 + 34.4949i 0.149333 + 1.62071i
\(454\) −14.1742 24.5505i −0.665230 1.15221i
\(455\) 0 0
\(456\) 2.55051 + 3.60697i 0.119439 + 0.168912i
\(457\) −13.5939 7.84847i −0.635898 0.367136i 0.147135 0.989116i \(-0.452995\pi\)
−0.783033 + 0.621981i \(0.786328\pi\)
\(458\) 21.1464i 0.988108i
\(459\) 24.4949 6.92820i 1.14332 0.323381i
\(460\) 0 0
\(461\) −9.67423 + 16.7563i −0.450574 + 0.780417i −0.998422 0.0561610i \(-0.982114\pi\)
0.547848 + 0.836578i \(0.315447\pi\)
\(462\) 30.8270 21.7980i 1.43420 1.01413i
\(463\) 8.09601 4.67423i 0.376254 0.217230i −0.299933 0.953960i \(-0.596964\pi\)
0.676187 + 0.736730i \(0.263631\pi\)
\(464\) 1.22474 + 2.12132i 0.0568574 + 0.0984798i
\(465\) 0 0
\(466\) 2.84847 4.93369i 0.131953 0.228549i
\(467\) 4.34847i 0.201223i −0.994926 0.100612i \(-0.967920\pi\)
0.994926 0.100612i \(-0.0320799\pi\)
\(468\) 10.1459 8.67423i 0.468994 0.400967i
\(469\) 63.8434 2.94801
\(470\) 0 0
\(471\) 0.146428 0.317837i 0.00674706 0.0146452i
\(472\) −0.476756 + 0.275255i −0.0219445 + 0.0126696i
\(473\) 31.6055 18.2474i 1.45322 0.839019i
\(474\) 9.20204 19.9740i 0.422664 0.917434i
\(475\) 0 0
\(476\) −21.7980 −0.999108
\(477\) −23.8988 8.44949i −1.09425 0.386876i
\(478\) 9.55051i 0.436830i
\(479\) −12.1237 + 20.9989i −0.553947 + 0.959465i 0.444038 + 0.896008i \(0.353546\pi\)
−0.997985 + 0.0634563i \(0.979788\pi\)
\(480\) 0 0
\(481\) −7.44949 12.9029i −0.339667 0.588321i
\(482\) −19.7436 + 11.3990i −0.899297 + 0.519209i
\(483\) 15.4135 10.8990i 0.701338 0.495921i
\(484\) 6.50000 11.2583i 0.295455 0.511742i
\(485\) 0 0
\(486\) 12.9722 + 8.64420i 0.588431 + 0.392109i
\(487\) 19.5505i 0.885918i 0.896542 + 0.442959i \(0.146071\pi\)
−0.896542 + 0.442959i \(0.853929\pi\)
\(488\) 6.92820 + 4.00000i 0.313625 + 0.181071i
\(489\) 2.55051 + 3.60697i 0.115338 + 0.163113i
\(490\) 0 0
\(491\) 1.37628 + 2.38378i 0.0621105 + 0.107578i 0.895409 0.445245i \(-0.146884\pi\)
−0.833298 + 0.552824i \(0.813550\pi\)
\(492\) −1.43027 15.5227i −0.0644814 0.699818i
\(493\) 10.3923 + 6.00000i 0.468046 + 0.270226i
\(494\) 11.3485 0.510592
\(495\) 0 0
\(496\) −0.449490 −0.0201827
\(497\) −5.19615 3.00000i −0.233079 0.134568i
\(498\) −0.866025 0.398979i −0.0388075 0.0178787i
\(499\) 3.17423 + 5.49794i 0.142098 + 0.246121i 0.928287 0.371866i \(-0.121282\pi\)
−0.786188 + 0.617987i \(0.787948\pi\)
\(500\) 0 0
\(501\) 14.2020 30.8270i 0.634500 1.37725i
\(502\) 4.71940 + 2.72474i 0.210637 + 0.121611i
\(503\) 26.4495i 1.17932i 0.807650 + 0.589662i \(0.200739\pi\)
−0.807650 + 0.589662i \(0.799261\pi\)
\(504\) −8.67423 10.1459i −0.386381 0.451934i
\(505\) 0 0
\(506\) 6.00000 10.3923i 0.266733 0.461994i
\(507\) −1.08032 11.7247i −0.0479788 0.520714i
\(508\) −9.82806 + 5.67423i −0.436050 + 0.251753i
\(509\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(510\) 0 0
\(511\) 2.22474 3.85337i 0.0984169 0.170463i
\(512\) 1.00000i 0.0441942i
\(513\) 3.60697 + 12.7526i 0.159251 + 0.563039i
\(514\) 6.79796 0.299845
\(515\) 0 0
\(516\) −7.44949 10.5352i −0.327945 0.463785i
\(517\) 4.67123 2.69694i 0.205441 0.118611i
\(518\) −12.9029 + 7.44949i −0.566921 + 0.327312i
\(519\) 16.8990 1.55708i 0.741783 0.0683481i
\(520\) 0 0
\(521\) 29.3939 1.28777 0.643885 0.765123i \(-0.277322\pi\)
0.643885 + 0.765123i \(0.277322\pi\)
\(522\) 1.34278 + 7.22474i 0.0587719 + 0.316218i
\(523\) 5.65153i 0.247124i −0.992337 0.123562i \(-0.960568\pi\)
0.992337 0.123562i \(-0.0394318\pi\)
\(524\) 7.89898 13.6814i 0.345069 0.597676i
\(525\) 0 0
\(526\) 7.77526 + 13.4671i 0.339017 + 0.587195i
\(527\) −1.90702 + 1.10102i −0.0830712 + 0.0479612i
\(528\) −7.70674 3.55051i −0.335393 0.154516i
\(529\) −8.50000 + 14.7224i −0.369565 + 0.640106i
\(530\) 0 0
\(531\) −1.62372 + 0.301783i −0.0704636 + 0.0130963i
\(532\) 11.3485i 0.492019i
\(533\) −34.6803 20.0227i −1.50217 0.867280i
\(534\) −15.5227 + 1.43027i −0.671733 + 0.0618937i
\(535\) 0 0
\(536\) −7.17423 12.4261i −0.309880 0.536727i
\(537\) 21.5631 15.2474i 0.930519 0.657976i
\(538\) 8.27098 + 4.77526i 0.356587 + 0.205876i
\(539\) −62.6969 −2.70055
\(540\) 0 0
\(541\) −18.2020 −0.782567 −0.391283 0.920270i \(-0.627969\pi\)
−0.391283 + 0.920270i \(0.627969\pi\)
\(542\) −0.564242 0.325765i −0.0242363 0.0139928i
\(543\) −2.54270 + 1.79796i −0.109118 + 0.0771578i
\(544\) 2.44949 + 4.24264i 0.105021 + 0.181902i
\(545\) 0 0
\(546\) −34.1464 + 3.14626i −1.46133 + 0.134648i
\(547\) 26.2825 + 15.1742i 1.12376 + 0.648803i 0.942358 0.334606i \(-0.108603\pi\)
0.181402 + 0.983409i \(0.441936\pi\)
\(548\) 3.00000i 0.128154i
\(549\) 15.5959 + 18.2419i 0.665618 + 0.778546i
\(550\) 0 0
\(551\) −3.12372 + 5.41045i −0.133075 + 0.230493i
\(552\) −3.85337 1.77526i −0.164010 0.0755599i
\(553\) −48.9260 + 28.2474i −2.08055 + 1.20120i
\(554\) 3.22474 + 5.58542i 0.137006 + 0.237302i
\(555\) 0 0
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) 17.3939i 0.737002i 0.929627 + 0.368501i \(0.120129\pi\)
−0.929627 + 0.368501i \(0.879871\pi\)
\(558\) −1.27135 0.449490i −0.0538205 0.0190284i
\(559\) −33.1464 −1.40194
\(560\) 0 0
\(561\) −41.3939 + 3.81405i −1.74765 + 0.161029i
\(562\) 25.0273 14.4495i 1.05571 0.609515i
\(563\) 25.9326 14.9722i 1.09293 0.631003i 0.158574 0.987347i \(-0.449310\pi\)
0.934355 + 0.356344i \(0.115977\pi\)
\(564\) −1.10102 1.55708i −0.0463613 0.0655648i
\(565\) 0 0
\(566\) −11.2474 −0.472766
\(567\) −14.3885 37.3712i −0.604262 1.56944i
\(568\) 1.34847i 0.0565805i
\(569\) 7.10102 12.2993i 0.297690 0.515615i −0.677917 0.735139i \(-0.737117\pi\)
0.975607 + 0.219524i \(0.0704504\pi\)
\(570\) 0 0
\(571\) 13.9722 + 24.2005i 0.584718 + 1.01276i 0.994911 + 0.100762i \(0.0321282\pi\)
−0.410192 + 0.911999i \(0.634538\pi\)
\(572\) −18.8776 + 10.8990i −0.789312 + 0.455709i
\(573\) −1.73205 18.7980i −0.0723575 0.785296i
\(574\) −20.0227 + 34.6803i −0.835732 + 1.44753i
\(575\) 0 0
\(576\) −1.00000 + 2.82843i −0.0416667 + 0.117851i
\(577\) 18.3939i 0.765747i 0.923801 + 0.382874i \(0.125066\pi\)
−0.923801 + 0.382874i \(0.874934\pi\)
\(578\) 6.06218 + 3.50000i 0.252153 + 0.145581i
\(579\) 14.4949 31.4626i 0.602387 1.30754i
\(580\) 0 0
\(581\) 1.22474 + 2.12132i 0.0508110 + 0.0880072i
\(582\) 16.9866 + 7.82577i 0.704118 + 0.324388i
\(583\) 35.8481 + 20.6969i 1.48468 + 0.857180i
\(584\) −1.00000 −0.0413803
\(585\) 0 0
\(586\) 28.0454 1.15855
\(587\) 2.33562 + 1.34847i 0.0964012 + 0.0556573i 0.547426 0.836854i \(-0.315608\pi\)
−0.451024 + 0.892512i \(0.648941\pi\)
\(588\) 2.03383 + 22.0732i 0.0838739 + 0.910284i
\(589\) −0.573214 0.992836i −0.0236189 0.0409091i
\(590\) 0 0
\(591\) −24.2474 34.2911i −0.997407 1.41055i
\(592\) 2.89986 + 1.67423i 0.119183 + 0.0688106i
\(593\) 1.89898i 0.0779817i 0.999240 + 0.0389909i \(0.0124143\pi\)
−0.999240 + 0.0389909i \(0.987586\pi\)
\(594\) −18.2474 17.7491i −0.748702 0.728254i
\(595\) 0 0
\(596\) 3.00000 5.19615i 0.122885 0.212843i
\(597\) −8.19955 + 5.79796i −0.335585 + 0.237295i
\(598\) −9.43879 + 5.44949i −0.385981 + 0.222846i
\(599\) −18.6742 32.3447i −0.763009 1.32157i −0.941293 0.337591i \(-0.890388\pi\)
0.178285 0.983979i \(-0.442945\pi\)
\(600\) 0 0
\(601\) −16.2474 + 28.1414i −0.662747 + 1.14791i 0.317144 + 0.948378i \(0.397276\pi\)
−0.979891 + 0.199534i \(0.936057\pi\)
\(602\) 33.1464i 1.35095i
\(603\) −7.86566 42.3207i −0.320314 1.72343i
\(604\) −20.0000 −0.813788
\(605\) 0 0
\(606\) 2.57321 5.58542i 0.104530 0.226892i
\(607\) 9.82806 5.67423i 0.398909 0.230310i −0.287104 0.957899i \(-0.592693\pi\)
0.686013 + 0.727589i \(0.259359\pi\)
\(608\) −2.20881 + 1.27526i −0.0895789 + 0.0517184i
\(609\) 7.89898 17.1455i 0.320083 0.694772i
\(610\) 0 0
\(611\) −4.89898 −0.198191
\(612\) 2.68556 + 14.4495i 0.108557 + 0.584086i
\(613\) 32.0454i 1.29430i −0.762362 0.647151i \(-0.775960\pi\)
0.762362 0.647151i \(-0.224040\pi\)
\(614\) 3.34847 5.79972i 0.135133 0.234058i
\(615\) 0 0
\(616\) 10.8990 + 18.8776i 0.439132 + 0.760600i
\(617\) 12.4655 7.19694i 0.501841 0.289738i −0.227633 0.973747i \(-0.573099\pi\)
0.729473 + 0.684009i \(0.239765\pi\)
\(618\) 17.9562 12.6969i 0.722304 0.510746i
\(619\) 20.8712 36.1499i 0.838883 1.45299i −0.0519458 0.998650i \(-0.516542\pi\)
0.890829 0.454339i \(-0.150124\pi\)
\(620\) 0 0
\(621\) −9.12372 8.87455i −0.366122 0.356123i
\(622\) 10.8990i 0.437009i
\(623\) 34.6803 + 20.0227i 1.38944 + 0.802193i
\(624\) 4.44949 + 6.29253i 0.178122 + 0.251903i
\(625\) 0 0
\(626\) 1.94949 + 3.37662i 0.0779173 + 0.134957i
\(627\) −1.98567 21.5505i −0.0793001 0.860644i
\(628\) 0.174973 + 0.101021i 0.00698217 + 0.00403116i
\(629\) 16.4041 0.654074
\(630\) 0 0
\(631\) −25.7980 −1.02700 −0.513500 0.858089i \(-0.671651\pi\)
−0.513500 + 0.858089i \(0.671651\pi\)
\(632\) 10.9959 + 6.34847i 0.437392 + 0.252529i
\(633\) −2.28024 1.05051i −0.0906314 0.0417540i
\(634\) 8.57321 + 14.8492i 0.340486 + 0.589739i
\(635\) 0 0
\(636\) 6.12372 13.2922i 0.242821 0.527069i
\(637\) 49.3153 + 28.4722i 1.95394 + 1.12811i
\(638\) 12.0000i 0.475085i
\(639\) −1.34847 + 3.81405i −0.0533446 + 0.150881i
\(640\) 0 0
\(641\) −22.1969 + 38.4462i −0.876726 + 1.51853i −0.0218141 + 0.999762i \(0.506944\pi\)
−0.854912 + 0.518773i \(0.826389\pi\)
\(642\) −2.42310 26.2980i −0.0956323 1.03790i
\(643\) −28.0146 + 16.1742i −1.10479 + 0.637850i −0.937474 0.348054i \(-0.886843\pi\)
−0.167313 + 0.985904i \(0.553509\pi\)
\(644\) 5.44949 + 9.43879i 0.214740 + 0.371941i
\(645\) 0 0
\(646\) −6.24745 + 10.8209i −0.245803 + 0.425743i
\(647\) 0.247449i 0.00972821i 0.999988 + 0.00486411i \(0.00154830\pi\)
−0.999988 + 0.00486411i \(0.998452\pi\)
\(648\) −5.65685 + 7.00000i −0.222222 + 0.274986i
\(649\) 2.69694 0.105864
\(650\) 0 0
\(651\) 2.00000 + 2.82843i 0.0783862 + 0.110855i
\(652\) −2.20881 + 1.27526i −0.0865035 + 0.0499428i
\(653\) −5.41045 + 3.12372i −0.211727 + 0.122241i −0.602114 0.798410i \(-0.705675\pi\)
0.390387 + 0.920651i \(0.372341\pi\)
\(654\) 18.0227 1.66062i 0.704743 0.0649353i
\(655\) 0 0
\(656\) 9.00000 0.351391
\(657\) −2.82843 1.00000i −0.110347 0.0390137i
\(658\) 4.89898i 0.190982i
\(659\) 22.0732 38.2319i 0.859850 1.48930i −0.0122208 0.999925i \(-0.503890\pi\)
0.872071 0.489379i \(-0.162777\pi\)
\(660\) 0 0
\(661\) 25.6969 + 44.5084i 0.999495 + 1.73118i 0.527265 + 0.849701i \(0.323218\pi\)
0.472230 + 0.881475i \(0.343449\pi\)
\(662\) −7.22999 + 4.17423i −0.281001 + 0.162236i
\(663\) 34.2911 + 15.7980i 1.33175 + 0.613542i
\(664\) 0.275255 0.476756i 0.0106820 0.0185017i
\(665\) 0 0
\(666\) 6.52781 + 7.63531i 0.252947 + 0.295862i
\(667\) 6.00000i 0.232321i
\(668\) 16.9706 + 9.79796i 0.656611 + 0.379094i
\(669\) 3.10102 0.285729i 0.119892 0.0110469i
\(670\) 0 0
\(671\) −19.5959 33.9411i −0.756492 1.31028i
\(672\) 6.29253 4.44949i 0.242740 0.171643i
\(673\) 5.79972 + 3.34847i 0.223563 + 0.129074i 0.607599 0.794244i \(-0.292133\pi\)
−0.384036 + 0.923318i \(0.625466\pi\)
\(674\) −11.1010 −0.427595
\(675\) 0 0
\(676\) 6.79796 0.261460
\(677\) 32.7733 + 18.9217i 1.25958 + 0.727219i 0.972993 0.230835i \(-0.0741456\pi\)
0.286588 + 0.958054i \(0.407479\pi\)
\(678\) 19.6561 13.8990i 0.754889 0.533787i
\(679\) −24.0227 41.6085i −0.921907 1.59679i
\(680\) 0 0
\(681\) 48.8939 4.50510i 1.87362 0.172636i
\(682\) 1.90702 + 1.10102i 0.0730237 + 0.0421603i
\(683\) 11.9444i 0.457039i −0.973539 0.228520i \(-0.926611\pi\)
0.973539 0.228520i \(-0.0733885\pi\)
\(684\) −7.52270 + 1.39816i −0.287638 + 0.0534600i
\(685\) 0 0
\(686\) 12.8990 22.3417i 0.492485 0.853010i
\(687\) −33.2661 15.3258i −1.26918 0.584714i
\(688\) 6.45145 3.72474i 0.245959 0.142005i
\(689\) −18.7980 32.5590i −0.716145 1.24040i
\(690\) 0 0
\(691\) 2.52270 4.36945i 0.0959682 0.166222i −0.814044 0.580803i \(-0.802739\pi\)
0.910012 + 0.414581i \(0.136072\pi\)
\(692\) 9.79796i 0.372463i
\(693\) 11.9494 + 64.2929i 0.453920 + 2.44228i
\(694\) 12.0000 0.455514
\(695\) 0 0
\(696\) −4.22474 + 0.389270i −0.160139 + 0.0147552i
\(697\) 38.1838 22.0454i 1.44631 0.835029i
\(698\) −12.1244 + 7.00000i −0.458914 + 0.264954i
\(699\) 5.69694 + 8.05669i 0.215478 + 0.304732i
\(700\) 0 0
\(701\) 14.2020 0.536404 0.268202 0.963363i \(-0.413571\pi\)
0.268202 + 0.963363i \(0.413571\pi\)
\(702\) 6.29253 + 22.2474i 0.237496 + 0.839676i
\(703\) 8.54031i 0.322104i
\(704\) 2.44949 4.24264i 0.0923186 0.159901i
\(705\) 0 0
\(706\) −4.50000 7.79423i −0.169360 0.293340i
\(707\) −13.6814 + 7.89898i −0.514543 + 0.297072i
\(708\) −0.0874863 0.949490i −0.00328794 0.0356840i
\(709\) −0.224745 + 0.389270i −0.00844047 + 0.0146193i −0.870215 0.492673i \(-0.836020\pi\)
0.861774 + 0.507292i \(0.169353\pi\)
\(710\) 0 0
\(711\) 24.7526 + 28.9521i 0.928293 + 1.08579i
\(712\) 9.00000i 0.337289i
\(713\) 0.953512 + 0.550510i 0.0357093 + 0.0206168i
\(714\) 15.7980 34.2911i 0.591224 1.28331i
\(715\) 0 0
\(716\) 7.62372 + 13.2047i 0.284912 + 0.493482i
\(717\) 15.0242 + 6.92168i 0.561090 + 0.258495i
\(718\) −29.2699 16.8990i −1.09234 0.630664i
\(719\) −52.0454 −1.94097 −0.970483 0.241169i \(-0.922469\pi\)
−0.970483 + 0.241169i \(0.922469\pi\)
\(720\) 0 0
\(721\) −56.4949 −2.10398
\(722\) 10.8209 + 6.24745i 0.402712 + 0.232506i
\(723\) −3.62302 39.3207i −0.134742 1.46235i
\(724\) −0.898979 1.55708i −0.0334103 0.0578684i
\(725\) 0 0
\(726\) 13.0000 + 18.3848i 0.482475 + 0.682323i
\(727\) −13.8564 8.00000i −0.513906 0.296704i 0.220532 0.975380i \(-0.429221\pi\)
−0.734438 + 0.678676i \(0.762554\pi\)
\(728\) 19.7980i 0.733761i
\(729\) −23.0000 + 14.1421i −0.851852 + 0.523783i
\(730\) 0 0
\(731\) 18.2474 31.6055i 0.674906 1.16897i
\(732\) −11.3137 + 8.00000i −0.418167 + 0.295689i
\(733\) 22.5167 13.0000i 0.831672 0.480166i −0.0227529 0.999741i \(-0.507243\pi\)
0.854425 + 0.519575i \(0.173910\pi\)
\(734\) −8.34847 14.4600i −0.308148 0.533727i
\(735\) 0 0
\(736\) 1.22474 2.12132i 0.0451447 0.0781929i
\(737\) 70.2929i 2.58927i
\(738\) 25.4558 + 9.00000i 0.937043 + 0.331295i
\(739\) 41.0454 1.50988 0.754940 0.655794i \(-0.227666\pi\)
0.754940 + 0.655794i \(0.227666\pi\)
\(740\) 0 0
\(741\) −8.22474 + 17.8526i −0.302144 + 0.655833i
\(742\) −32.5590 + 18.7980i −1.19528 + 0.690095i
\(743\) 30.0091 17.3258i 1.10093 0.635621i 0.164463 0.986383i \(-0.447411\pi\)
0.936464 + 0.350763i \(0.114078\pi\)
\(744\) 0.325765 0.707107i 0.0119431 0.0259238i
\(745\) 0 0
\(746\) −15.5959 −0.571007
\(747\) 1.25529 1.07321i 0.0459288 0.0392669i
\(748\) 24.0000i 0.877527i
\(749\) −33.9217 + 58.7541i −1.23947 + 2.14683i
\(750\) 0 0
\(751\) 25.0227 + 43.3406i 0.913091 + 1.58152i 0.809672 + 0.586883i \(0.199645\pi\)
0.103420 + 0.994638i \(0.467022\pi\)
\(752\) 0.953512 0.550510i 0.0347710 0.0200750i
\(753\) −7.70674 + 5.44949i −0.280849 + 0.198590i
\(754\) −5.44949 + 9.43879i −0.198459 + 0.343741i
\(755\) 0 0
\(756\) 22.2474 6.29253i 0.809132 0.228857i
\(757\) 6.04541i 0.219724i −0.993947 0.109862i \(-0.964959\pi\)
0.993947 0.109862i \(-0.0350409\pi\)
\(758\) 0.778539 + 0.449490i 0.0282778 + 0.0163262i
\(759\) 12.0000 + 16.9706i 0.435572 + 0.615992i
\(760\) 0 0
\(761\) −2.05051 3.55159i −0.0743309 0.128745i 0.826464 0.562989i \(-0.190349\pi\)
−0.900795 + 0.434244i \(0.857015\pi\)
\(762\) −1.80348 19.5732i −0.0653333 0.709063i
\(763\) −40.2658 23.2474i −1.45772 0.841614i
\(764\) 10.8990 0.394311
\(765\) 0 0
\(766\) −26.4495 −0.955659
\(767\) −2.12132 1.22474i −0.0765964 0.0442230i
\(768\) −1.57313 0.724745i −0.0567655 0.0261520i
\(769\) 25.0959 + 43.4674i 0.904982 + 1.56747i 0.820941 + 0.571012i \(0.193449\pi\)
0.0840405 + 0.996462i \(0.473217\pi\)
\(770\) 0 0
\(771\) −4.92679 + 10.6941i −0.177434 + 0.385138i
\(772\) 17.3205 + 10.0000i 0.623379 + 0.359908i
\(773\) 49.5959i 1.78384i −0.452192 0.891921i \(-0.649358\pi\)
0.452192 0.891921i \(-0.350642\pi\)
\(774\) 21.9722 4.08372i 0.789774 0.146786i
\(775\) 0 0
\(776\) −5.39898 + 9.35131i −0.193812 + 0.335692i
\(777\) −2.36773 25.6969i −0.0849417 0.921873i
\(778\) 11.7744 6.79796i 0.422133 0.243719i
\(779\) 11.4773 + 19.8793i 0.411217 + 0.712248i
\(780\) 0 0
\(781\) 3.30306 5.72107i 0.118193 0.204716i
\(782\) 12.0000i 0.429119i
\(783\) −12.3387 3.12372i −0.440947 0.111633i
\(784\) −12.7980 −0.457070
\(785\) 0 0
\(786\) 15.7980 + 22.3417i 0.563495 + 0.796902i
\(787\) −4.59259 + 2.65153i −0.163708 + 0.0945169i −0.579616 0.814890i \(-0.696797\pi\)
0.415908 + 0.909407i \(0.363464\pi\)
\(788\) 20.9989 12.1237i 0.748055 0.431890i
\(789\) −26.8207 + 2.47127i −0.954841 + 0.0879794i
\(790\) 0 0
\(791\) −61.8434 −2.19890
\(792\) 11.1708 9.55051i 0.396939 0.339363i
\(793\) 35.5959i 1.26405i
\(794\) −10.7980 + 18.7026i −0.383205 + 0.663731i
\(795\) 0 0
\(796\) −2.89898 5.02118i −0.102752 0.177971i
\(797\) 4.98186 2.87628i 0.176466 0.101883i −0.409165 0.912460i \(-0.634180\pi\)
0.585631 + 0.810577i \(0.300847\pi\)
\(798\) 17.8526 + 8.22474i 0.631977 + 0.291153i
\(799\) 2.69694 4.67123i 0.0954108 0.165256i
\(800\) 0 0
\(801\) 9.00000 25.4558i 0.317999 0.899438i
\(802\) 9.30306i 0.328503i
\(803\) 4.24264 + 2.44949i 0.149720 + 0.0864406i
\(804\) 24.7474 2.28024i 0.872775 0.0804178i
\(805\) 0 0
\(806\) −1.00000 1.73205i −0.0352235 0.0610089i
\(807\) −13.5065 + 9.55051i −0.475450 + 0.336194i
\(808\) 3.07483 + 1.77526i 0.108172 + 0.0624533i
\(809\) 35.6969 1.25504 0.627519 0.778601i \(-0.284071\pi\)
0.627519 + 0.778601i \(0.284071\pi\)
\(810\) 0 0
\(811\) −33.4495 −1.17457 −0.587285 0.809380i \(-0.699803\pi\)
−0.587285 + 0.809380i \(0.699803\pi\)
\(812\) 9.43879 + 5.44949i 0.331237 + 0.191240i
\(813\) 0.921404 0.651531i 0.0323150 0.0228502i
\(814\) −8.20204 14.2064i −0.287481 0.497932i
\(815\) 0 0
\(816\) −8.44949 + 0.778539i −0.295791 + 0.0272543i
\(817\) 16.4545 + 9.50000i 0.575669 + 0.332363i
\(818\) 9.89898i 0.346110i
\(819\) 19.7980 55.9971i 0.691797 1.95670i
\(820\) 0 0
\(821\) 25.5959 44.3334i 0.893304 1.54725i 0.0574136 0.998350i \(-0.481715\pi\)
0.835890 0.548897i \(-0.184952\pi\)
\(822\) −4.71940 2.17423i −0.164608 0.0758351i
\(823\) −23.2952 + 13.4495i −0.812020 + 0.468820i −0.847657 0.530545i \(-0.821987\pi\)
0.0356371 + 0.999365i \(0.488654\pi\)
\(824\) 6.34847 + 10.9959i 0.221159 + 0.383059i
\(825\) 0 0
\(826\) −1.22474 + 2.12132i −0.0426143 + 0.0738102i
\(827\) 17.9444i 0.623987i −0.950084 0.311994i \(-0.899003\pi\)
0.950084 0.311994i \(-0.100997\pi\)
\(828\) 5.58542 4.77526i 0.194107 0.165952i
\(829\) −26.7423 −0.928800 −0.464400 0.885626i \(-0.653730\pi\)
−0.464400 + 0.885626i \(0.653730\pi\)
\(830\) 0 0
\(831\) −11.1237 + 1.02494i −0.385878 + 0.0355549i
\(832\) −3.85337 + 2.22474i −0.133592 + 0.0771292i
\(833\) −54.2971 + 31.3485i −1.88128 + 1.08616i
\(834\) 4.00000 + 5.65685i 0.138509 + 0.195881i
\(835\) 0 0
\(836\) 12.4949 0.432145
\(837\) 1.62851 1.67423i 0.0562896 0.0578700i
\(838\) 8.14643i 0.281414i
\(839\) 11.3258 19.6168i 0.391009 0.677247i −0.601574 0.798817i \(-0.705460\pi\)
0.992583 + 0.121570i \(0.0387928\pi\)
\(840\) 0 0
\(841\) 11.5000 + 19.9186i 0.396552 + 0.686848i
\(842\) 15.6278 9.02270i 0.538569 0.310943i
\(843\) 4.59259 + 49.8434i 0.158177 + 1.71670i
\(844\) 0.724745 1.25529i 0.0249467 0.0432090i
\(845\) 0 0
\(846\) 3.24745 0.603566i 0.111650 0.0207510i
\(847\) 57.8434i 1.98752i
\(848\) 7.31747 + 4.22474i 0.251283 + 0.145078i
\(849\) 8.15153 17.6937i 0.279760 0.607247i
\(850\) 0 0
\(851\) −4.10102 7.10318i −0.140581 0.243494i
\(852\) −2.12132 0.977296i −0.0726752 0.0334816i
\(853\) 39.8372 + 23.0000i 1.36400 + 0.787505i 0.990153 0.139986i \(-0.0447058\pi\)
0.373845 + 0.927491i \(0.378039\pi\)
\(854\) 35.5959 1.21807
\(855\) 0 0
\(856\) 15.2474 0.521147
\(857\) −34.7285 20.0505i −1.18630 0.684912i −0.228839 0.973464i \(-0.573493\pi\)
−0.957464 + 0.288552i \(0.906826\pi\)
\(858\) −3.46410 37.5959i −0.118262 1.28350i
\(859\) −2.82577 4.89437i −0.0964139 0.166994i 0.813784 0.581168i \(-0.197404\pi\)
−0.910198 + 0.414174i \(0.864071\pi\)
\(860\) 0 0
\(861\) −40.0454 56.6328i −1.36474 1.93004i
\(862\) −9.22450 5.32577i −0.314188 0.181396i
\(863\) 19.8434i 0.675476i 0.941240 + 0.337738i \(0.109662\pi\)
−0.941240 + 0.337738i \(0.890338\pi\)
\(864\) −3.72474 3.62302i −0.126718 0.123258i
\(865\) 0 0
\(866\) −14.7980 + 25.6308i −0.502855 + 0.870971i
\(867\) −9.89949 + 7.00000i −0.336204 + 0.237732i
\(868\) −1.73205 + 1.00000i −0.0587896 + 0.0339422i
\(869\) −31.1010 53.8685i −1.05503 1.82737i
\(870\) 0 0
\(871\) 31.9217 55.2900i 1.08162 1.87343i
\(872\) 10.4495i 0.353864i
\(873\) −24.6219 + 21.0505i −0.833326 + 0.712452i
\(874\) 6.24745 0.211323
\(875\) 0 0
\(876\) 0.724745 1.57313i 0.0244869 0.0531512i
\(877\) 10.5673 6.10102i 0.356832 0.206017i −0.310858 0.950456i \(-0.600617\pi\)
0.667690 + 0.744439i \(0.267283\pi\)
\(878\) 9.82806 5.67423i 0.331681 0.191496i
\(879\) −20.3258 + 44.1191i −0.685571 + 1.48810i
\(880\) 0 0
\(881\) 9.30306 0.313428 0.156714 0.987644i \(-0.449910\pi\)
0.156714 + 0.987644i \(0.449910\pi\)
\(882\) −36.1981 12.7980i −1.21885 0.430930i
\(883\) 28.2020i 0.949074i 0.880235 + 0.474537i \(0.157385\pi\)
−0.880235 + 0.474537i \(0.842615\pi\)
\(884\) −10.8990 + 18.8776i −0.366572 + 0.634922i
\(885\) 0 0
\(886\) 13.8990 + 24.0737i 0.466945 + 0.808773i
\(887\) −47.1940 + 27.2474i −1.58462 + 0.914880i −0.590446 + 0.807077i \(0.701048\pi\)
−0.994172 + 0.107803i \(0.965619\pi\)
\(888\) −4.73545 + 3.34847i −0.158911 + 0.112367i
\(889\) −25.2474 + 43.7299i −0.846772 + 1.46665i
\(890\) 0 0
\(891\) 41.1464 15.8421i 1.37846 0.530730i
\(892\) 1.79796i 0.0602001i
\(893\) 2.43194 + 1.40408i 0.0813818 + 0.0469858i
\(894\) 6.00000 + 8.48528i 0.200670 + 0.283790i
\(895\) 0 0
\(896\) 2.22474 + 3.85337i 0.0743235 + 0.128732i
\(897\) −1.73205 18.7980i −0.0578315 0.627646i
\(898\) 9.17633 + 5.29796i 0.306218 + 0.176795i
\(899\) 1.10102 0.0367211
\(900\) 0 0
\(901\) 41.3939 1.37903
\(902\) −38.1838 22.0454i −1.27138 0.734032i
\(903\) −52.1437 24.0227i −1.73523 0.799426i
\(904\) 6.94949 + 12.0369i 0.231137 + 0.400340i
\(905\) 0 0
\(906\) 14.4949 31.4626i 0.481561 1.04528i
\(907\) 18.7508 + 10.8258i 0.622609 + 0.359464i 0.777884 0.628408i \(-0.216293\pi\)
−0.155275 + 0.987871i \(0.549626\pi\)
\(908\) 28.3485i 0.940777i
\(909\) 6.92168 + 8.09601i 0.229578 + 0.268528i
\(910\) 0 0
\(911\) −3.67423 + 6.36396i −0.121733 + 0.210847i −0.920451 0.390858i \(-0.872178\pi\)
0.798718 + 0.601705i \(0.205512\pi\)
\(912\) −0.405324 4.39898i −0.0134216 0.145665i
\(913\) −2.33562 + 1.34847i −0.0772976 + 0.0446278i
\(914\) 7.84847 + 13.5939i 0.259604 + 0.449648i
\(915\) 0 0
\(916\) 10.5732 18.3133i 0.349349 0.605090i
\(917\) 70.2929i 2.32127i
\(918\) −24.6773 6.24745i −0.814472 0.206197i
\(919\) 11.3485 0.374351 0.187176 0.982326i \(-0.440067\pi\)
0.187176 + 0.982326i \(0.440067\pi\)
\(920\) 0 0
\(921\) 6.69694 + 9.47090i 0.220672 + 0.312077i
\(922\) 16.7563 9.67423i 0.551838 0.318604i
\(923\) −5.19615 + 3.00000i −0.171033 + 0.0987462i
\(924\) −37.5959 + 3.46410i −1.23681 + 0.113961i
\(925\) 0 0
\(926\) −9.34847 −0.307210
\(927\) 6.96031 + 37.4495i 0.228607 + 1.23000i
\(928\) 2.44949i 0.0804084i
\(929\) 13.5959 23.5488i 0.446068 0.772612i −0.552058 0.833806i \(-0.686157\pi\)
0.998126 + 0.0611938i \(0.0194908\pi\)
\(930\) 0 0
\(931\) −16.3207 28.2682i −0.534888 0.926453i
\(932\) −4.93369 + 2.84847i −0.161609 + 0.0933047i
\(933\) 17.1455 + 7.89898i 0.561320 + 0.258601i
\(934\) −2.17423 + 3.76588i −0.0711431 + 0.123224i
\(935\) 0 0
\(936\) −13.1237 + 2.43916i −0.428962 + 0.0797264i
\(937\) 26.7980i 0.875451i −0.899109 0.437726i \(-0.855784\pi\)
0.899109 0.437726i \(-0.144216\pi\)
\(938\) −55.2900 31.9217i −1.80528 1.04228i
\(939\) −6.72474 + 0.619620i −0.219454 + 0.0202205i
\(940\) 0 0
\(941\) 14.8207 + 25.6701i 0.483140 + 0.836823i 0.999813 0.0193603i \(-0.00616295\pi\)
−0.516673 + 0.856183i \(0.672830\pi\)
\(942\) −0.285729 + 0.202041i −0.00930956 + 0.00658285i
\(943\) −19.0919 11.0227i −0.621717 0.358949i
\(944\) 0.550510 0.0179176
\(945\) 0 0
\(946\) −36.4949 −1.18655
\(947\) −7.05501 4.07321i −0.229257 0.132362i 0.380972 0.924587i \(-0.375589\pi\)
−0.610229 + 0.792225i \(0.708923\pi\)
\(948\) −17.9562 + 12.6969i −0.583190 + 0.412377i
\(949\) −2.22474 3.85337i −0.0722183 0.125086i
\(950\) 0 0
\(951\) −29.5732 + 2.72489i −0.958977 + 0.0883605i
\(952\) 18.8776 + 10.8990i 0.611826 + 0.353238i
\(953\) 21.7980i 0.706105i 0.935603 + 0.353053i \(0.114856\pi\)
−0.935603 + 0.353053i \(0.885144\pi\)
\(954\) 16.4722 + 19.2669i 0.533307 + 0.623787i
\(955\) 0 0
\(956\) −4.77526 + 8.27098i −0.154443 + 0.267503i
\(957\) 18.8776 + 8.69694i 0.610226 + 0.281132i
\(958\) 20.9989 12.1237i 0.678444 0.391700i
\(959\) 6.67423 + 11.5601i 0.215522 + 0.373296i
\(960\) 0 0
\(961\) 15.3990 26.6718i 0.496741 0.860381i
\(962\) 14.8990i 0.480362i
\(963\) 43.1263 + 15.2474i 1.38973 + 0.491342i
\(964\) 22.7980 0.734273
\(965\) 0 0
\(966\) −18.7980 + 1.73205i −0.604814 + 0.0557278i
\(967\) −27.7128 + 16.0000i −0.891184 + 0.514525i −0.874330 0.485333i \(-0.838699\pi\)
−0.0168544 + 0.999858i \(0.505365\pi\)
\(968\) −11.2583 + 6.50000i −0.361856 + 0.208918i
\(969\) −12.4949 17.6705i −0.401394 0.567657i
\(970\) 0 0
\(971\) 22.8434 0.733079 0.366539 0.930403i \(-0.380543\pi\)
0.366539 + 0.930403i \(0.380543\pi\)
\(972\) −6.91215 13.9722i −0.221707 0.448158i
\(973\) 17.7980i 0.570576i
\(974\) 9.77526 16.9312i 0.313219 0.542512i
\(975\) 0 0
\(976\) −4.00000 6.92820i −0.128037 0.221766i
\(977\) 7.79423 4.50000i 0.249359 0.143968i −0.370111 0.928987i \(-0.620681\pi\)
0.619471 + 0.785020i \(0.287347\pi\)
\(978\) −0.405324 4.39898i −0.0129608 0.140664i
\(979\) −22.0454 + 38.1838i −0.704574 + 1.22036i
\(980\) 0 0
\(981\) −10.4495 + 29.5556i −0.333627 + 0.943638i
\(982\) 2.75255i 0.0878374i
\(983\) 19.8311 + 11.4495i 0.632514 + 0.365182i 0.781725 0.623623i \(-0.214340\pi\)
−0.149211 + 0.988805i \(0.547673\pi\)
\(984\) −6.52270 + 14.1582i −0.207936 + 0.451347i
\(985\) 0 0
\(986\) −6.00000 10.3923i −0.191079 0.330958i
\(987\) −7.70674 3.55051i −0.245308 0.113014i
\(988\) −9.82806 5.67423i −0.312672 0.180521i
\(989\) −18.2474 −0.580235
\(990\) 0 0
\(991\) −16.0000 −0.508257 −0.254128 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) 0.389270 + 0.224745i 0.0123593 + 0.00713566i
\(993\) −1.32673 14.3990i −0.0421024 0.456938i
\(994\) 3.00000 + 5.19615i 0.0951542 + 0.164812i
\(995\) 0 0
\(996\) 0.550510 + 0.778539i 0.0174436 + 0.0246690i
\(997\) 31.2162 + 18.0227i 0.988628 + 0.570785i 0.904864 0.425701i \(-0.139972\pi\)
0.0837642 + 0.996486i \(0.473306\pi\)
\(998\) 6.34847i 0.200957i
\(999\) −16.7423 + 4.73545i −0.529704 + 0.149823i
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 450.2.j.f.349.2 8
3.2 odd 2 1350.2.j.g.1099.4 8
5.2 odd 4 450.2.e.m.151.1 yes 4
5.3 odd 4 450.2.e.l.151.2 4
5.4 even 2 inner 450.2.j.f.349.3 8
9.2 odd 6 4050.2.c.w.649.1 4
9.4 even 3 inner 450.2.j.f.49.3 8
9.5 odd 6 1350.2.j.g.199.1 8
9.7 even 3 4050.2.c.y.649.3 4
15.2 even 4 1350.2.e.k.451.1 4
15.8 even 4 1350.2.e.n.451.2 4
15.14 odd 2 1350.2.j.g.1099.1 8
45.2 even 12 4050.2.a.by.1.2 2
45.4 even 6 inner 450.2.j.f.49.2 8
45.7 odd 12 4050.2.a.br.1.2 2
45.13 odd 12 450.2.e.l.301.1 yes 4
45.14 odd 6 1350.2.j.g.199.4 8
45.22 odd 12 450.2.e.m.301.2 yes 4
45.23 even 12 1350.2.e.n.901.2 4
45.29 odd 6 4050.2.c.w.649.4 4
45.32 even 12 1350.2.e.k.901.1 4
45.34 even 6 4050.2.c.y.649.2 4
45.38 even 12 4050.2.a.bl.1.1 2
45.43 odd 12 4050.2.a.bu.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
450.2.e.l.151.2 4 5.3 odd 4
450.2.e.l.301.1 yes 4 45.13 odd 12
450.2.e.m.151.1 yes 4 5.2 odd 4
450.2.e.m.301.2 yes 4 45.22 odd 12
450.2.j.f.49.2 8 45.4 even 6 inner
450.2.j.f.49.3 8 9.4 even 3 inner
450.2.j.f.349.2 8 1.1 even 1 trivial
450.2.j.f.349.3 8 5.4 even 2 inner
1350.2.e.k.451.1 4 15.2 even 4
1350.2.e.k.901.1 4 45.32 even 12
1350.2.e.n.451.2 4 15.8 even 4
1350.2.e.n.901.2 4 45.23 even 12
1350.2.j.g.199.1 8 9.5 odd 6
1350.2.j.g.199.4 8 45.14 odd 6
1350.2.j.g.1099.1 8 15.14 odd 2
1350.2.j.g.1099.4 8 3.2 odd 2
4050.2.a.bl.1.1 2 45.38 even 12
4050.2.a.br.1.2 2 45.7 odd 12
4050.2.a.bu.1.1 2 45.43 odd 12
4050.2.a.by.1.2 2 45.2 even 12
4050.2.c.w.649.1 4 9.2 odd 6
4050.2.c.w.649.4 4 45.29 odd 6
4050.2.c.y.649.2 4 45.34 even 6
4050.2.c.y.649.3 4 9.7 even 3