Properties

Label 175.2.k.a.149.1
Level $175$
Weight $2$
Character 175.149
Analytic conductor $1.397$
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] = [175,2,Mod(74,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.74");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.k (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: \(1.39738203537\)
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 149.1
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 175.149
Dual form 175.2.k.a.74.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.09077 - 1.20711i) q^{2} +(0.358719 - 0.207107i) q^{3} +(1.91421 + 3.31552i) q^{4} -1.00000 q^{6} +(0.358719 + 2.62132i) q^{7} -4.41421i q^{8} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})\) \(q+(-2.09077 - 1.20711i) q^{2} +(0.358719 - 0.207107i) q^{3} +(1.91421 + 3.31552i) q^{4} -1.00000 q^{6} +(0.358719 + 2.62132i) q^{7} -4.41421i q^{8} +(-1.41421 + 2.44949i) q^{9} +(0.414214 + 0.717439i) q^{11} +(1.37333 + 0.792893i) q^{12} +4.82843i q^{13} +(2.41421 - 5.91359i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(4.18154 - 2.41421i) q^{17} +(5.91359 - 3.41421i) q^{18} +(1.41421 - 2.44949i) q^{19} +(0.671573 + 0.866025i) q^{21} -2.00000i q^{22} +(0.358719 + 0.207107i) q^{23} +(-0.914214 - 1.58346i) q^{24} +(5.82843 - 10.0951i) q^{26} +2.41421i q^{27} +(-8.00436 + 6.20711i) q^{28} +1.00000 q^{29} +(3.00000 + 5.19615i) q^{31} +(-1.37333 + 0.792893i) q^{32} +(0.297173 + 0.171573i) q^{33} -11.6569 q^{34} -10.8284 q^{36} +(-5.91359 + 3.41421i) q^{38} +(1.00000 + 1.73205i) q^{39} -7.82843 q^{41} +(-0.358719 - 2.62132i) q^{42} -3.58579i q^{43} +(-1.58579 + 2.74666i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(-1.73205 - 1.00000i) q^{47} +1.24264i q^{48} +(-6.74264 + 1.88064i) q^{49} +(1.00000 - 1.73205i) q^{51} +(-16.0087 + 9.24264i) q^{52} +(1.01461 - 0.585786i) q^{53} +(2.91421 - 5.04757i) q^{54} +(11.5711 - 1.58346i) q^{56} -1.17157i q^{57} +(-2.09077 - 1.20711i) q^{58} +(2.24264 + 3.88437i) q^{59} +(-2.74264 + 4.75039i) q^{61} -14.4853i q^{62} +(-6.92820 - 2.82843i) q^{63} +9.82843 q^{64} +(-0.414214 - 0.717439i) q^{66} +(8.30153 - 4.79289i) q^{67} +(16.0087 + 9.24264i) q^{68} +0.171573 q^{69} +4.48528 q^{71} +(10.8126 + 6.24264i) q^{72} +(0.717439 - 0.414214i) q^{73} +10.8284 q^{76} +(-1.73205 + 1.34315i) q^{77} -4.82843i q^{78} +(7.41421 - 12.8418i) q^{79} +(-3.74264 - 6.48244i) q^{81} +(16.3674 + 9.44975i) q^{82} -13.7279i q^{83} +(-1.58579 + 3.88437i) q^{84} +(-4.32843 + 7.49706i) q^{86} +(0.358719 - 0.207107i) q^{87} +(3.16693 - 1.82843i) q^{88} +(-4.32843 + 7.49706i) q^{89} +(-12.6569 + 1.73205i) q^{91} +1.58579i q^{92} +(2.15232 + 1.24264i) q^{93} +(2.41421 + 4.18154i) q^{94} +(-0.328427 + 0.568852i) q^{96} +11.6569i q^{97} +(16.3674 + 4.20711i) q^{98} -2.34315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} - 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} - 8 q^{6} - 8 q^{11} + 8 q^{14} - 12 q^{16} + 28 q^{21} + 4 q^{24} + 24 q^{26} + 8 q^{29} + 24 q^{31} - 48 q^{34} - 64 q^{36} + 8 q^{39} - 40 q^{41} - 24 q^{44} - 4 q^{46} - 20 q^{49} + 8 q^{51} + 12 q^{54} + 36 q^{56} - 16 q^{59} + 12 q^{61} + 56 q^{64} + 8 q^{66} + 24 q^{69} - 32 q^{71} + 64 q^{76} + 48 q^{79} + 4 q^{81} - 24 q^{84} - 12 q^{86} - 12 q^{89} - 56 q^{91} + 8 q^{94} + 20 q^{96} - 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.09077 1.20711i −1.47840 0.853553i −0.478696 0.877981i \(-0.658890\pi\)
−0.999702 + 0.0244272i \(0.992224\pi\)
\(3\) 0.358719 0.207107i 0.207107 0.119573i −0.392859 0.919599i \(-0.628514\pi\)
0.599966 + 0.800025i \(0.295181\pi\)
\(4\) 1.91421 + 3.31552i 0.957107 + 1.65776i
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) 0.358719 + 2.62132i 0.135583 + 0.990766i
\(8\) 4.41421i 1.56066i
\(9\) −1.41421 + 2.44949i −0.471405 + 0.816497i
\(10\) 0 0
\(11\) 0.414214 + 0.717439i 0.124890 + 0.216316i 0.921690 0.387927i \(-0.126809\pi\)
−0.796800 + 0.604243i \(0.793476\pi\)
\(12\) 1.37333 + 0.792893i 0.396447 + 0.228889i
\(13\) 4.82843i 1.33916i 0.742738 + 0.669582i \(0.233527\pi\)
−0.742738 + 0.669582i \(0.766473\pi\)
\(14\) 2.41421 5.91359i 0.645226 1.58047i
\(15\) 0 0
\(16\) −1.50000 + 2.59808i −0.375000 + 0.649519i
\(17\) 4.18154 2.41421i 1.01417 0.585533i 0.101762 0.994809i \(-0.467552\pi\)
0.912411 + 0.409276i \(0.134219\pi\)
\(18\) 5.91359 3.41421i 1.39385 0.804738i
\(19\) 1.41421 2.44949i 0.324443 0.561951i −0.656957 0.753928i \(-0.728157\pi\)
0.981399 + 0.191977i \(0.0614899\pi\)
\(20\) 0 0
\(21\) 0.671573 + 0.866025i 0.146549 + 0.188982i
\(22\) 2.00000i 0.426401i
\(23\) 0.358719 + 0.207107i 0.0747982 + 0.0431847i 0.536933 0.843625i \(-0.319583\pi\)
−0.462134 + 0.886810i \(0.652916\pi\)
\(24\) −0.914214 1.58346i −0.186613 0.323223i
\(25\) 0 0
\(26\) 5.82843 10.0951i 1.14305 1.97982i
\(27\) 2.41421i 0.464616i
\(28\) −8.00436 + 6.20711i −1.51268 + 1.17303i
\(29\) 1.00000 0.185695 0.0928477 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) 0 0
\(31\) 3.00000 + 5.19615i 0.538816 + 0.933257i 0.998968 + 0.0454165i \(0.0144615\pi\)
−0.460152 + 0.887840i \(0.652205\pi\)
\(32\) −1.37333 + 0.792893i −0.242773 + 0.140165i
\(33\) 0.297173 + 0.171573i 0.0517312 + 0.0298670i
\(34\) −11.6569 −1.99913
\(35\) 0 0
\(36\) −10.8284 −1.80474
\(37\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) −5.91359 + 3.41421i −0.959311 + 0.553859i
\(39\) 1.00000 + 1.73205i 0.160128 + 0.277350i
\(40\) 0 0
\(41\) −7.82843 −1.22259 −0.611297 0.791401i \(-0.709352\pi\)
−0.611297 + 0.791401i \(0.709352\pi\)
\(42\) −0.358719 2.62132i −0.0553516 0.404479i
\(43\) 3.58579i 0.546827i −0.961897 0.273414i \(-0.911847\pi\)
0.961897 0.273414i \(-0.0881528\pi\)
\(44\) −1.58579 + 2.74666i −0.239066 + 0.414075i
\(45\) 0 0
\(46\) −0.500000 0.866025i −0.0737210 0.127688i
\(47\) −1.73205 1.00000i −0.252646 0.145865i 0.368329 0.929695i \(-0.379930\pi\)
−0.620975 + 0.783830i \(0.713263\pi\)
\(48\) 1.24264i 0.179360i
\(49\) −6.74264 + 1.88064i −0.963234 + 0.268662i
\(50\) 0 0
\(51\) 1.00000 1.73205i 0.140028 0.242536i
\(52\) −16.0087 + 9.24264i −2.22001 + 1.28172i
\(53\) 1.01461 0.585786i 0.139368 0.0804640i −0.428695 0.903449i \(-0.641026\pi\)
0.568063 + 0.822985i \(0.307693\pi\)
\(54\) 2.91421 5.04757i 0.396574 0.686887i
\(55\) 0 0
\(56\) 11.5711 1.58346i 1.54625 0.211599i
\(57\) 1.17157i 0.155179i
\(58\) −2.09077 1.20711i −0.274532 0.158501i
\(59\) 2.24264 + 3.88437i 0.291967 + 0.505702i 0.974275 0.225363i \(-0.0723569\pi\)
−0.682308 + 0.731065i \(0.739024\pi\)
\(60\) 0 0
\(61\) −2.74264 + 4.75039i −0.351159 + 0.608226i −0.986453 0.164045i \(-0.947546\pi\)
0.635294 + 0.772271i \(0.280879\pi\)
\(62\) 14.4853i 1.83963i
\(63\) −6.92820 2.82843i −0.872872 0.356348i
\(64\) 9.82843 1.22855
\(65\) 0 0
\(66\) −0.414214 0.717439i −0.0509862 0.0883106i
\(67\) 8.30153 4.79289i 1.01419 0.585545i 0.101777 0.994807i \(-0.467547\pi\)
0.912417 + 0.409262i \(0.134214\pi\)
\(68\) 16.0087 + 9.24264i 1.94134 + 1.12083i
\(69\) 0.171573 0.0206549
\(70\) 0 0
\(71\) 4.48528 0.532305 0.266152 0.963931i \(-0.414248\pi\)
0.266152 + 0.963931i \(0.414248\pi\)
\(72\) 10.8126 + 6.24264i 1.27427 + 0.735702i
\(73\) 0.717439 0.414214i 0.0839699 0.0484800i −0.457427 0.889247i \(-0.651229\pi\)
0.541397 + 0.840767i \(0.317896\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 10.8284 1.24211
\(77\) −1.73205 + 1.34315i −0.197386 + 0.153066i
\(78\) 4.82843i 0.546712i
\(79\) 7.41421 12.8418i 0.834164 1.44481i −0.0605449 0.998165i \(-0.519284\pi\)
0.894709 0.446649i \(-0.147383\pi\)
\(80\) 0 0
\(81\) −3.74264 6.48244i −0.415849 0.720272i
\(82\) 16.3674 + 9.44975i 1.80748 + 1.04355i
\(83\) 13.7279i 1.50684i −0.657542 0.753418i \(-0.728404\pi\)
0.657542 0.753418i \(-0.271596\pi\)
\(84\) −1.58579 + 3.88437i −0.173023 + 0.423819i
\(85\) 0 0
\(86\) −4.32843 + 7.49706i −0.466746 + 0.808428i
\(87\) 0.358719 0.207107i 0.0384588 0.0222042i
\(88\) 3.16693 1.82843i 0.337596 0.194911i
\(89\) −4.32843 + 7.49706i −0.458812 + 0.794686i −0.998898 0.0469234i \(-0.985058\pi\)
0.540086 + 0.841610i \(0.318392\pi\)
\(90\) 0 0
\(91\) −12.6569 + 1.73205i −1.32680 + 0.181568i
\(92\) 1.58579i 0.165330i
\(93\) 2.15232 + 1.24264i 0.223185 + 0.128856i
\(94\) 2.41421 + 4.18154i 0.249007 + 0.431293i
\(95\) 0 0
\(96\) −0.328427 + 0.568852i −0.0335200 + 0.0580583i
\(97\) 11.6569i 1.18357i 0.806094 + 0.591787i \(0.201577\pi\)
−0.806094 + 0.591787i \(0.798423\pi\)
\(98\) 16.3674 + 4.20711i 1.65336 + 0.424982i
\(99\) −2.34315 −0.235495
\(100\) 0 0
\(101\) 5.15685 + 8.93193i 0.513126 + 0.888761i 0.999884 + 0.0152237i \(0.00484604\pi\)
−0.486758 + 0.873537i \(0.661821\pi\)
\(102\) −4.18154 + 2.41421i −0.414034 + 0.239043i
\(103\) −2.09077 1.20711i −0.206010 0.118940i 0.393446 0.919348i \(-0.371283\pi\)
−0.599456 + 0.800408i \(0.704616\pi\)
\(104\) 21.3137 2.08998
\(105\) 0 0
\(106\) −2.82843 −0.274721
\(107\) −9.73641 5.62132i −0.941255 0.543434i −0.0509012 0.998704i \(-0.516209\pi\)
−0.890353 + 0.455270i \(0.849543\pi\)
\(108\) −8.00436 + 4.62132i −0.770220 + 0.444687i
\(109\) −6.74264 11.6786i −0.645828 1.11861i −0.984110 0.177562i \(-0.943179\pi\)
0.338282 0.941045i \(-0.390154\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −7.34847 3.00000i −0.694365 0.283473i
\(113\) 4.48528i 0.421940i 0.977493 + 0.210970i \(0.0676622\pi\)
−0.977493 + 0.210970i \(0.932338\pi\)
\(114\) −1.41421 + 2.44949i −0.132453 + 0.229416i
\(115\) 0 0
\(116\) 1.91421 + 3.31552i 0.177730 + 0.307838i
\(117\) −11.8272 6.82843i −1.09342 0.631288i
\(118\) 10.8284i 0.996838i
\(119\) 7.82843 + 10.0951i 0.717631 + 0.925419i
\(120\) 0 0
\(121\) 5.15685 8.93193i 0.468805 0.811994i
\(122\) 11.4685 6.62132i 1.03831 0.599466i
\(123\) −2.80821 + 1.62132i −0.253208 + 0.146190i
\(124\) −11.4853 + 19.8931i −1.03141 + 1.78645i
\(125\) 0 0
\(126\) 11.0711 + 14.2767i 0.986289 + 1.27187i
\(127\) 9.31371i 0.826458i −0.910627 0.413229i \(-0.864401\pi\)
0.910627 0.413229i \(-0.135599\pi\)
\(128\) −17.8023 10.2782i −1.57352 0.908471i
\(129\) −0.742641 1.28629i −0.0653859 0.113252i
\(130\) 0 0
\(131\) 9.65685 16.7262i 0.843723 1.46137i −0.0430021 0.999075i \(-0.513692\pi\)
0.886725 0.462297i \(-0.152974\pi\)
\(132\) 1.31371i 0.114344i
\(133\) 6.92820 + 2.82843i 0.600751 + 0.245256i
\(134\) −23.1421 −1.99918
\(135\) 0 0
\(136\) −10.6569 18.4582i −0.913818 1.58278i
\(137\) −8.36308 + 4.82843i −0.714506 + 0.412520i −0.812727 0.582644i \(-0.802018\pi\)
0.0982211 + 0.995165i \(0.468685\pi\)
\(138\) −0.358719 0.207107i −0.0305362 0.0176301i
\(139\) 16.1421 1.36916 0.684579 0.728939i \(-0.259986\pi\)
0.684579 + 0.728939i \(0.259986\pi\)
\(140\) 0 0
\(141\) −0.828427 −0.0697661
\(142\) −9.37769 5.41421i −0.786959 0.454351i
\(143\) −3.46410 + 2.00000i −0.289683 + 0.167248i
\(144\) −4.24264 7.34847i −0.353553 0.612372i
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) −2.02922 + 2.07107i −0.167368 + 0.170819i
\(148\) 0 0
\(149\) −1.08579 + 1.88064i −0.0889511 + 0.154068i −0.907068 0.420984i \(-0.861685\pi\)
0.818117 + 0.575052i \(0.195018\pi\)
\(150\) 0 0
\(151\) −5.82843 10.0951i −0.474311 0.821530i 0.525257 0.850944i \(-0.323969\pi\)
−0.999567 + 0.0294137i \(0.990636\pi\)
\(152\) −10.8126 6.24264i −0.877015 0.506345i
\(153\) 13.6569i 1.10409i
\(154\) 5.24264 0.717439i 0.422464 0.0578129i
\(155\) 0 0
\(156\) −3.82843 + 6.63103i −0.306519 + 0.530907i
\(157\) 14.9941 8.65685i 1.19666 0.690892i 0.236851 0.971546i \(-0.423885\pi\)
0.959809 + 0.280654i \(0.0905513\pi\)
\(158\) −31.0028 + 17.8995i −2.46645 + 1.42401i
\(159\) 0.242641 0.420266i 0.0192427 0.0333293i
\(160\) 0 0
\(161\) −0.414214 + 1.01461i −0.0326446 + 0.0799626i
\(162\) 18.0711i 1.41980i
\(163\) 10.6895 + 6.17157i 0.837265 + 0.483395i 0.856333 0.516423i \(-0.172737\pi\)
−0.0190689 + 0.999818i \(0.506070\pi\)
\(164\) −14.9853 25.9553i −1.17015 2.02677i
\(165\) 0 0
\(166\) −16.5711 + 28.7019i −1.28616 + 2.22770i
\(167\) 22.4142i 1.73446i 0.497904 + 0.867232i \(0.334103\pi\)
−0.497904 + 0.867232i \(0.665897\pi\)
\(168\) 3.82282 2.96447i 0.294937 0.228714i
\(169\) −10.3137 −0.793362
\(170\) 0 0
\(171\) 4.00000 + 6.92820i 0.305888 + 0.529813i
\(172\) 11.8887 6.86396i 0.906507 0.523372i
\(173\) 2.86976 + 1.65685i 0.218183 + 0.125968i 0.605109 0.796143i \(-0.293130\pi\)
−0.386925 + 0.922111i \(0.626463\pi\)
\(174\) −1.00000 −0.0758098
\(175\) 0 0
\(176\) −2.48528 −0.187335
\(177\) 1.60896 + 0.928932i 0.120937 + 0.0698228i
\(178\) 18.0995 10.4497i 1.35661 0.783242i
\(179\) −5.00000 8.66025i −0.373718 0.647298i 0.616417 0.787420i \(-0.288584\pi\)
−0.990134 + 0.140122i \(0.955250\pi\)
\(180\) 0 0
\(181\) 2.65685 0.197482 0.0987412 0.995113i \(-0.468518\pi\)
0.0987412 + 0.995113i \(0.468518\pi\)
\(182\) 28.5533 + 11.6569i 2.11651 + 0.864064i
\(183\) 2.27208i 0.167957i
\(184\) 0.914214 1.58346i 0.0673967 0.116735i
\(185\) 0 0
\(186\) −3.00000 5.19615i −0.219971 0.381000i
\(187\) 3.46410 + 2.00000i 0.253320 + 0.146254i
\(188\) 7.65685i 0.558433i
\(189\) −6.32843 + 0.866025i −0.460325 + 0.0629941i
\(190\) 0 0
\(191\) 6.41421 11.1097i 0.464116 0.803873i −0.535045 0.844824i \(-0.679705\pi\)
0.999161 + 0.0409507i \(0.0130387\pi\)
\(192\) 3.52565 2.03553i 0.254442 0.146902i
\(193\) 1.73205 1.00000i 0.124676 0.0719816i −0.436365 0.899770i \(-0.643734\pi\)
0.561041 + 0.827788i \(0.310401\pi\)
\(194\) 14.0711 24.3718i 1.01024 1.74979i
\(195\) 0 0
\(196\) −19.1421 18.7554i −1.36730 1.33967i
\(197\) 12.3431i 0.879413i −0.898142 0.439706i \(-0.855083\pi\)
0.898142 0.439706i \(-0.144917\pi\)
\(198\) 4.89898 + 2.82843i 0.348155 + 0.201008i
\(199\) −4.82843 8.36308i −0.342278 0.592843i 0.642577 0.766221i \(-0.277865\pi\)
−0.984855 + 0.173378i \(0.944532\pi\)
\(200\) 0 0
\(201\) 1.98528 3.43861i 0.140031 0.242541i
\(202\) 24.8995i 1.75192i
\(203\) 0.358719 + 2.62132i 0.0251772 + 0.183981i
\(204\) 7.65685 0.536087
\(205\) 0 0
\(206\) 2.91421 + 5.04757i 0.203043 + 0.351681i
\(207\) −1.01461 + 0.585786i −0.0705204 + 0.0407150i
\(208\) −12.5446 7.24264i −0.869813 0.502187i
\(209\) 2.34315 0.162079
\(210\) 0 0
\(211\) 20.4853 1.41026 0.705132 0.709076i \(-0.250888\pi\)
0.705132 + 0.709076i \(0.250888\pi\)
\(212\) 3.88437 + 2.24264i 0.266779 + 0.154025i
\(213\) 1.60896 0.928932i 0.110244 0.0636494i
\(214\) 13.5711 + 23.5058i 0.927699 + 1.60682i
\(215\) 0 0
\(216\) 10.6569 0.725107
\(217\) −12.5446 + 9.72792i −0.851584 + 0.660374i
\(218\) 32.5563i 2.20499i
\(219\) 0.171573 0.297173i 0.0115938 0.0200811i
\(220\) 0 0
\(221\) 11.6569 + 20.1903i 0.784125 + 1.35814i
\(222\) 0 0
\(223\) 0.343146i 0.0229787i −0.999934 0.0114894i \(-0.996343\pi\)
0.999934 0.0114894i \(-0.00365726\pi\)
\(224\) −2.57107 3.31552i −0.171787 0.221527i
\(225\) 0 0
\(226\) 5.41421 9.37769i 0.360148 0.623795i
\(227\) −6.03668 + 3.48528i −0.400669 + 0.231326i −0.686773 0.726872i \(-0.740973\pi\)
0.286104 + 0.958199i \(0.407640\pi\)
\(228\) 3.88437 2.24264i 0.257249 0.148523i
\(229\) −5.82843 + 10.0951i −0.385153 + 0.667105i −0.991790 0.127874i \(-0.959185\pi\)
0.606637 + 0.794979i \(0.292518\pi\)
\(230\) 0 0
\(231\) −0.343146 + 0.840532i −0.0225773 + 0.0553029i
\(232\) 4.41421i 0.289807i
\(233\) −14.5738 8.41421i −0.954764 0.551233i −0.0602067 0.998186i \(-0.519176\pi\)
−0.894558 + 0.446952i \(0.852509\pi\)
\(234\) 16.4853 + 28.5533i 1.07768 + 1.86659i
\(235\) 0 0
\(236\) −8.58579 + 14.8710i −0.558887 + 0.968021i
\(237\) 6.14214i 0.398975i
\(238\) −4.18154 30.5563i −0.271049 1.98067i
\(239\) 21.3137 1.37867 0.689335 0.724443i \(-0.257903\pi\)
0.689335 + 0.724443i \(0.257903\pi\)
\(240\) 0 0
\(241\) −13.8284 23.9515i −0.890767 1.54285i −0.838957 0.544197i \(-0.816834\pi\)
−0.0518100 0.998657i \(-0.516499\pi\)
\(242\) −21.5636 + 12.4497i −1.38616 + 0.800300i
\(243\) −8.95743 5.17157i −0.574619 0.331757i
\(244\) −21.0000 −1.34439
\(245\) 0 0
\(246\) 7.82843 0.499122
\(247\) 11.8272 + 6.82843i 0.752546 + 0.434482i
\(248\) 22.9369 13.2426i 1.45650 0.840909i
\(249\) −2.84315 4.92447i −0.180177 0.312076i
\(250\) 0 0
\(251\) −9.31371 −0.587876 −0.293938 0.955824i \(-0.594966\pi\)
−0.293938 + 0.955824i \(0.594966\pi\)
\(252\) −3.88437 28.3848i −0.244692 1.78807i
\(253\) 0.343146i 0.0215734i
\(254\) −11.2426 + 19.4728i −0.705426 + 1.22183i
\(255\) 0 0
\(256\) 14.9853 + 25.9553i 0.936580 + 1.62220i
\(257\) −5.49333 3.17157i −0.342664 0.197837i 0.318785 0.947827i \(-0.396725\pi\)
−0.661450 + 0.749990i \(0.730058\pi\)
\(258\) 3.58579i 0.223241i
\(259\) 0 0
\(260\) 0 0
\(261\) −1.41421 + 2.44949i −0.0875376 + 0.151620i
\(262\) −40.3805 + 23.3137i −2.49472 + 1.44033i
\(263\) 25.1508 14.5208i 1.55086 0.895392i 0.552793 0.833319i \(-0.313562\pi\)
0.998072 0.0620729i \(-0.0197711\pi\)
\(264\) 0.757359 1.31178i 0.0466122 0.0807348i
\(265\) 0 0
\(266\) −11.0711 14.2767i −0.678811 0.875359i
\(267\) 3.58579i 0.219447i
\(268\) 31.7818 + 18.3492i 1.94138 + 1.12086i
\(269\) 10.2279 + 17.7153i 0.623607 + 1.08012i 0.988808 + 0.149191i \(0.0476669\pi\)
−0.365201 + 0.930929i \(0.619000\pi\)
\(270\) 0 0
\(271\) −8.24264 + 14.2767i −0.500705 + 0.867246i 0.499295 + 0.866432i \(0.333592\pi\)
−1.00000 0.000813982i \(0.999741\pi\)
\(272\) 14.4853i 0.878299i
\(273\) −4.18154 + 3.24264i −0.253078 + 0.196254i
\(274\) 23.3137 1.40843
\(275\) 0 0
\(276\) 0.328427 + 0.568852i 0.0197690 + 0.0342409i
\(277\) 13.9795 8.07107i 0.839947 0.484943i −0.0172994 0.999850i \(-0.505507\pi\)
0.857246 + 0.514907i \(0.172174\pi\)
\(278\) −33.7495 19.4853i −2.02416 1.16865i
\(279\) −16.9706 −1.01600
\(280\) 0 0
\(281\) −30.2843 −1.80661 −0.903304 0.429001i \(-0.858866\pi\)
−0.903304 + 0.429001i \(0.858866\pi\)
\(282\) 1.73205 + 1.00000i 0.103142 + 0.0595491i
\(283\) −12.1244 + 7.00000i −0.720718 + 0.416107i −0.815017 0.579437i \(-0.803272\pi\)
0.0942988 + 0.995544i \(0.469939\pi\)
\(284\) 8.58579 + 14.8710i 0.509473 + 0.882433i
\(285\) 0 0
\(286\) 9.65685 0.571022
\(287\) −2.80821 20.5208i −0.165763 1.21131i
\(288\) 4.48528i 0.264298i
\(289\) 3.15685 5.46783i 0.185697 0.321637i
\(290\) 0 0
\(291\) 2.41421 + 4.18154i 0.141524 + 0.245126i
\(292\) 2.74666 + 1.58579i 0.160736 + 0.0928011i
\(293\) 16.0000i 0.934730i 0.884064 + 0.467365i \(0.154797\pi\)
−0.884064 + 0.467365i \(0.845203\pi\)
\(294\) 6.74264 1.88064i 0.393239 0.109681i
\(295\) 0 0
\(296\) 0 0
\(297\) −1.73205 + 1.00000i −0.100504 + 0.0580259i
\(298\) 4.54026 2.62132i 0.263010 0.151849i
\(299\) −1.00000 + 1.73205i −0.0578315 + 0.100167i
\(300\) 0 0
\(301\) 9.39949 1.28629i 0.541778 0.0741406i
\(302\) 28.1421i 1.61940i
\(303\) 3.69973 + 2.13604i 0.212544 + 0.122712i
\(304\) 4.24264 + 7.34847i 0.243332 + 0.421464i
\(305\) 0 0
\(306\) 16.4853 28.5533i 0.942401 1.63229i
\(307\) 4.75736i 0.271517i −0.990742 0.135758i \(-0.956653\pi\)
0.990742 0.135758i \(-0.0433471\pi\)
\(308\) −7.76874 3.17157i −0.442665 0.180717i
\(309\) −1.00000 −0.0568880
\(310\) 0 0
\(311\) 6.58579 + 11.4069i 0.373446 + 0.646827i 0.990093 0.140413i \(-0.0448429\pi\)
−0.616647 + 0.787239i \(0.711510\pi\)
\(312\) 7.64564 4.41421i 0.432849 0.249906i
\(313\) −5.49333 3.17157i −0.310501 0.179268i 0.336650 0.941630i \(-0.390706\pi\)
−0.647151 + 0.762362i \(0.724040\pi\)
\(314\) −41.7990 −2.35885
\(315\) 0 0
\(316\) 56.7696 3.19354
\(317\) 11.9503 + 6.89949i 0.671194 + 0.387514i 0.796529 0.604600i \(-0.206667\pi\)
−0.125335 + 0.992115i \(0.540000\pi\)
\(318\) −1.01461 + 0.585786i −0.0568966 + 0.0328493i
\(319\) 0.414214 + 0.717439i 0.0231915 + 0.0401689i
\(320\) 0 0
\(321\) −4.65685 −0.259920
\(322\) 2.09077 1.62132i 0.116514 0.0903527i
\(323\) 13.6569i 0.759888i
\(324\) 14.3284 24.8176i 0.796024 1.37875i
\(325\) 0 0
\(326\) −14.8995 25.8067i −0.825207 1.42930i
\(327\) −4.83743 2.79289i −0.267511 0.154447i
\(328\) 34.5563i 1.90806i
\(329\) 2.00000 4.89898i 0.110264 0.270089i
\(330\) 0 0
\(331\) −11.4853 + 19.8931i −0.631288 + 1.09342i 0.356001 + 0.934486i \(0.384140\pi\)
−0.987289 + 0.158937i \(0.949193\pi\)
\(332\) 45.5151 26.2782i 2.49797 1.44220i
\(333\) 0 0
\(334\) 27.0563 46.8630i 1.48046 2.56423i
\(335\) 0 0
\(336\) −3.25736 + 0.445759i −0.177704 + 0.0243182i
\(337\) 9.17157i 0.499607i 0.968296 + 0.249804i \(0.0803661\pi\)
−0.968296 + 0.249804i \(0.919634\pi\)
\(338\) 21.5636 + 12.4497i 1.17290 + 0.677177i
\(339\) 0.928932 + 1.60896i 0.0504527 + 0.0873866i
\(340\) 0 0
\(341\) −2.48528 + 4.30463i −0.134586 + 0.233109i
\(342\) 19.3137i 1.04437i
\(343\) −7.34847 17.0000i −0.396780 0.917914i
\(344\) −15.8284 −0.853412
\(345\) 0 0
\(346\) −4.00000 6.92820i −0.215041 0.372463i
\(347\) 6.86666 3.96447i 0.368621 0.212824i −0.304235 0.952597i \(-0.598401\pi\)
0.672856 + 0.739773i \(0.265067\pi\)
\(348\) 1.37333 + 0.792893i 0.0736183 + 0.0425035i
\(349\) 15.3431 0.821300 0.410650 0.911793i \(-0.365302\pi\)
0.410650 + 0.911793i \(0.365302\pi\)
\(350\) 0 0
\(351\) −11.6569 −0.622197
\(352\) −1.13770 0.656854i −0.0606399 0.0350104i
\(353\) 23.2341 13.4142i 1.23663 0.713967i 0.268223 0.963357i \(-0.413564\pi\)
0.968403 + 0.249390i \(0.0802302\pi\)
\(354\) −2.24264 3.88437i −0.119195 0.206452i
\(355\) 0 0
\(356\) −33.1421 −1.75653
\(357\) 4.89898 + 2.00000i 0.259281 + 0.105851i
\(358\) 24.1421i 1.27595i
\(359\) −5.00000 + 8.66025i −0.263890 + 0.457071i −0.967272 0.253741i \(-0.918339\pi\)
0.703382 + 0.710812i \(0.251672\pi\)
\(360\) 0 0
\(361\) 5.50000 + 9.52628i 0.289474 + 0.501383i
\(362\) −5.55487 3.20711i −0.291958 0.168562i
\(363\) 4.27208i 0.224226i
\(364\) −29.9706 38.6485i −1.57088 2.02573i
\(365\) 0 0
\(366\) 2.74264 4.75039i 0.143360 0.248307i
\(367\) −2.38794 + 1.37868i −0.124650 + 0.0719665i −0.561028 0.827797i \(-0.689594\pi\)
0.436379 + 0.899763i \(0.356261\pi\)
\(368\) −1.07616 + 0.621320i −0.0560986 + 0.0323886i
\(369\) 11.0711 19.1757i 0.576337 0.998245i
\(370\) 0 0
\(371\) 1.89949 + 2.44949i 0.0986169 + 0.127171i
\(372\) 9.51472i 0.493315i
\(373\) −18.1610 10.4853i −0.940343 0.542907i −0.0502752 0.998735i \(-0.516010\pi\)
−0.890068 + 0.455828i \(0.849343\pi\)
\(374\) −4.82843 8.36308i −0.249672 0.432445i
\(375\) 0 0
\(376\) −4.41421 + 7.64564i −0.227646 + 0.394294i
\(377\) 4.82843i 0.248677i
\(378\) 14.2767 + 5.82843i 0.734313 + 0.299782i
\(379\) −26.8284 −1.37808 −0.689042 0.724722i \(-0.741968\pi\)
−0.689042 + 0.724722i \(0.741968\pi\)
\(380\) 0 0
\(381\) −1.92893 3.34101i −0.0988222 0.171165i
\(382\) −26.8213 + 15.4853i −1.37230 + 0.792296i
\(383\) −2.51104 1.44975i −0.128308 0.0740786i 0.434472 0.900685i \(-0.356935\pi\)
−0.562780 + 0.826607i \(0.690268\pi\)
\(384\) −8.51472 −0.434515
\(385\) 0 0
\(386\) −4.82843 −0.245760
\(387\) 8.78335 + 5.07107i 0.446483 + 0.257777i
\(388\) −38.6485 + 22.3137i −1.96208 + 1.13281i
\(389\) 11.8284 + 20.4874i 0.599725 + 1.03875i 0.992861 + 0.119274i \(0.0380567\pi\)
−0.393136 + 0.919480i \(0.628610\pi\)
\(390\) 0 0
\(391\) 2.00000 0.101144
\(392\) 8.30153 + 29.7635i 0.419291 + 1.50328i
\(393\) 8.00000i 0.403547i
\(394\) −14.8995 + 25.8067i −0.750626 + 1.30012i
\(395\) 0 0
\(396\) −4.48528 7.76874i −0.225394 0.390394i
\(397\) 14.3998 + 8.31371i 0.722704 + 0.417253i 0.815747 0.578409i \(-0.196326\pi\)
−0.0930434 + 0.995662i \(0.529660\pi\)
\(398\) 23.3137i 1.16861i
\(399\) 3.07107 0.420266i 0.153746 0.0210396i
\(400\) 0 0
\(401\) −15.1569 + 26.2524i −0.756897 + 1.31098i 0.187528 + 0.982259i \(0.439952\pi\)
−0.944426 + 0.328725i \(0.893381\pi\)
\(402\) −8.30153 + 4.79289i −0.414043 + 0.239048i
\(403\) −25.0892 + 14.4853i −1.24978 + 0.721563i
\(404\) −19.7426 + 34.1953i −0.982233 + 1.70128i
\(405\) 0 0
\(406\) 2.41421 5.91359i 0.119815 0.293487i
\(407\) 0 0
\(408\) −7.64564 4.41421i −0.378516 0.218536i
\(409\) −7.39949 12.8163i −0.365881 0.633725i 0.623036 0.782193i \(-0.285899\pi\)
−0.988917 + 0.148468i \(0.952566\pi\)
\(410\) 0 0
\(411\) −2.00000 + 3.46410i −0.0986527 + 0.170872i
\(412\) 9.24264i 0.455352i
\(413\) −9.37769 + 7.27208i −0.461446 + 0.357836i
\(414\) 2.82843 0.139010
\(415\) 0 0
\(416\) −3.82843 6.63103i −0.187704 0.325113i
\(417\) 5.79050 3.34315i 0.283562 0.163715i
\(418\) −4.89898 2.82843i −0.239617 0.138343i
\(419\) 0.686292 0.0335275 0.0167638 0.999859i \(-0.494664\pi\)
0.0167638 + 0.999859i \(0.494664\pi\)
\(420\) 0 0
\(421\) 13.4853 0.657232 0.328616 0.944464i \(-0.393418\pi\)
0.328616 + 0.944464i \(0.393418\pi\)
\(422\) −42.8300 24.7279i −2.08493 1.20374i
\(423\) 4.89898 2.82843i 0.238197 0.137523i
\(424\) −2.58579 4.47871i −0.125577 0.217506i
\(425\) 0 0
\(426\) −4.48528 −0.217313
\(427\) −13.4361 5.48528i −0.650220 0.265451i
\(428\) 43.0416i 2.08050i
\(429\) −0.828427 + 1.43488i −0.0399968 + 0.0692766i
\(430\) 0 0
\(431\) −8.89949 15.4144i −0.428674 0.742484i 0.568082 0.822972i \(-0.307686\pi\)
−0.996756 + 0.0804875i \(0.974352\pi\)
\(432\) −6.27231 3.62132i −0.301777 0.174231i
\(433\) 7.79899i 0.374796i −0.982284 0.187398i \(-0.939995\pi\)
0.982284 0.187398i \(-0.0600053\pi\)
\(434\) 37.9706 5.19615i 1.82265 0.249423i
\(435\) 0 0
\(436\) 25.8137 44.7107i 1.23625 2.14125i
\(437\) 1.01461 0.585786i 0.0485355 0.0280220i
\(438\) −0.717439 + 0.414214i −0.0342806 + 0.0197919i
\(439\) −16.9706 + 29.3939i −0.809961 + 1.40289i 0.102930 + 0.994689i \(0.467178\pi\)
−0.912890 + 0.408205i \(0.866155\pi\)
\(440\) 0 0
\(441\) 4.92893 19.1757i 0.234711 0.913126i
\(442\) 56.2843i 2.67717i
\(443\) 26.1654 + 15.1066i 1.24316 + 0.717736i 0.969735 0.244158i \(-0.0785117\pi\)
0.273420 + 0.961895i \(0.411845\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −0.414214 + 0.717439i −0.0196136 + 0.0339717i
\(447\) 0.899495i 0.0425447i
\(448\) 3.52565 + 25.7635i 0.166571 + 1.21721i
\(449\) −3.82843 −0.180675 −0.0903373 0.995911i \(-0.528795\pi\)
−0.0903373 + 0.995911i \(0.528795\pi\)
\(450\) 0 0
\(451\) −3.24264 5.61642i −0.152690 0.264467i
\(452\) −14.8710 + 8.58579i −0.699474 + 0.403841i
\(453\) −4.18154 2.41421i −0.196466 0.113430i
\(454\) 16.8284 0.789797
\(455\) 0 0
\(456\) −5.17157 −0.242181
\(457\) −21.0308 12.1421i −0.983779 0.567985i −0.0803702 0.996765i \(-0.525610\pi\)
−0.903409 + 0.428780i \(0.858944\pi\)
\(458\) 24.3718 14.0711i 1.13882 0.657498i
\(459\) 5.82843 + 10.0951i 0.272048 + 0.471200i
\(460\) 0 0
\(461\) 41.3137 1.92417 0.962086 0.272748i \(-0.0879324\pi\)
0.962086 + 0.272748i \(0.0879324\pi\)
\(462\) 1.73205 1.34315i 0.0805823 0.0624888i
\(463\) 37.0416i 1.72147i 0.509053 + 0.860735i \(0.329996\pi\)
−0.509053 + 0.860735i \(0.670004\pi\)
\(464\) −1.50000 + 2.59808i −0.0696358 + 0.120613i
\(465\) 0 0
\(466\) 20.3137 + 35.1844i 0.941014 + 1.62988i
\(467\) 2.68512 + 1.55025i 0.124252 + 0.0717371i 0.560838 0.827926i \(-0.310479\pi\)
−0.436586 + 0.899663i \(0.643812\pi\)
\(468\) 52.2843i 2.41684i
\(469\) 15.5416 + 20.0417i 0.717646 + 0.925439i
\(470\) 0 0
\(471\) 3.58579 6.21076i 0.165224 0.286177i
\(472\) 17.1464 9.89949i 0.789228 0.455661i
\(473\) 2.57258 1.48528i 0.118287 0.0682933i
\(474\) −7.41421 + 12.8418i −0.340546 + 0.589843i
\(475\) 0 0
\(476\) −18.4853 + 45.2795i −0.847271 + 2.07538i
\(477\) 3.31371i 0.151724i
\(478\) −44.5621 25.7279i −2.03822 1.17677i
\(479\) −17.8284 30.8797i −0.814602 1.41093i −0.909614 0.415455i \(-0.863622\pi\)
0.0950120 0.995476i \(-0.469711\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 66.7696i 3.04127i
\(483\) 0.0615465 + 0.449747i 0.00280046 + 0.0204642i
\(484\) 39.4853 1.79479
\(485\) 0 0
\(486\) 12.4853 + 21.6251i 0.566344 + 0.980936i
\(487\) 3.76127 2.17157i 0.170440 0.0984034i −0.412353 0.911024i \(-0.635293\pi\)
0.582793 + 0.812621i \(0.301960\pi\)
\(488\) 20.9692 + 12.1066i 0.949233 + 0.548040i
\(489\) 5.11270 0.231204
\(490\) 0 0
\(491\) 9.31371 0.420322 0.210161 0.977667i \(-0.432601\pi\)
0.210161 + 0.977667i \(0.432601\pi\)
\(492\) −10.7510 6.20711i −0.484694 0.279838i
\(493\) 4.18154 2.41421i 0.188327 0.108731i
\(494\) −16.4853 28.5533i −0.741708 1.28468i
\(495\) 0 0
\(496\) −18.0000 −0.808224
\(497\) 1.60896 + 11.7574i 0.0721716 + 0.527390i
\(498\) 13.7279i 0.615163i
\(499\) −0.414214 + 0.717439i −0.0185427 + 0.0321170i −0.875148 0.483856i \(-0.839236\pi\)
0.856605 + 0.515973i \(0.172569\pi\)
\(500\) 0 0
\(501\) 4.64214 + 8.04041i 0.207395 + 0.359219i
\(502\) 19.4728 + 11.2426i 0.869115 + 0.501784i
\(503\) 15.8701i 0.707611i 0.935319 + 0.353805i \(0.115113\pi\)
−0.935319 + 0.353805i \(0.884887\pi\)
\(504\) −12.4853 + 30.5826i −0.556139 + 1.36226i
\(505\) 0 0
\(506\) 0.414214 0.717439i 0.0184140 0.0318941i
\(507\) −3.69973 + 2.13604i −0.164311 + 0.0948648i
\(508\) 30.8797 17.8284i 1.37007 0.791009i
\(509\) 6.67157 11.5555i 0.295712 0.512189i −0.679438 0.733733i \(-0.737776\pi\)
0.975150 + 0.221544i \(0.0711097\pi\)
\(510\) 0 0
\(511\) 1.34315 + 1.73205i 0.0594173 + 0.0766214i
\(512\) 31.2426i 1.38074i
\(513\) 5.91359 + 3.41421i 0.261091 + 0.150741i
\(514\) 7.65685 + 13.2621i 0.337729 + 0.584964i
\(515\) 0 0
\(516\) 2.84315 4.92447i 0.125163 0.216788i
\(517\) 1.65685i 0.0728684i
\(518\) 0 0
\(519\) 1.37258 0.0602497
\(520\) 0 0
\(521\) −7.48528 12.9649i −0.327936 0.568002i 0.654166 0.756351i \(-0.273020\pi\)
−0.982102 + 0.188349i \(0.939686\pi\)
\(522\) 5.91359 3.41421i 0.258831 0.149436i
\(523\) 30.8797 + 17.8284i 1.35028 + 0.779583i 0.988288 0.152600i \(-0.0487645\pi\)
0.361989 + 0.932182i \(0.382098\pi\)
\(524\) 73.9411 3.23013
\(525\) 0 0
\(526\) −70.1127 −3.05706
\(527\) 25.0892 + 14.4853i 1.09290 + 0.630989i
\(528\) −0.891519 + 0.514719i −0.0387984 + 0.0224003i
\(529\) −11.4142 19.7700i −0.496270 0.859565i
\(530\) 0 0
\(531\) −12.6863 −0.550538
\(532\) 3.88437 + 28.3848i 0.168409 + 1.23064i
\(533\) 37.7990i 1.63726i
\(534\) 4.32843 7.49706i 0.187309 0.324429i
\(535\) 0 0
\(536\) −21.1569 36.6447i −0.913837 1.58281i
\(537\) −3.58719 2.07107i −0.154799 0.0893732i
\(538\) 49.3848i 2.12913i
\(539\) −4.14214 4.05845i −0.178414 0.174810i
\(540\) 0 0
\(541\) −3.67157 + 6.35935i −0.157853 + 0.273410i −0.934094 0.357026i \(-0.883791\pi\)
0.776241 + 0.630436i \(0.217124\pi\)
\(542\) 34.4669 19.8995i 1.48048 0.854756i
\(543\) 0.953065 0.550253i 0.0408999 0.0236136i
\(544\) −3.82843 + 6.63103i −0.164142 + 0.284303i
\(545\) 0 0
\(546\) 12.6569 1.73205i 0.541663 0.0741249i
\(547\) 24.8995i 1.06463i 0.846548 + 0.532313i \(0.178677\pi\)
−0.846548 + 0.532313i \(0.821323\pi\)
\(548\) −32.0174 18.4853i −1.36772 0.789652i
\(549\) −7.75736 13.4361i −0.331076 0.573441i
\(550\) 0 0
\(551\) 1.41421 2.44949i 0.0602475 0.104352i
\(552\) 0.757359i 0.0322354i
\(553\) 36.3221 + 14.8284i 1.54457 + 0.630569i
\(554\) −38.9706 −1.65570
\(555\) 0 0
\(556\) 30.8995 + 53.5195i 1.31043 + 2.26973i
\(557\) 19.2987 11.1421i 0.817714 0.472107i −0.0319135 0.999491i \(-0.510160\pi\)
0.849628 + 0.527383i \(0.176827\pi\)
\(558\) 35.4815 + 20.4853i 1.50205 + 0.867211i
\(559\) 17.3137 0.732292
\(560\) 0 0
\(561\) 1.65685 0.0699524
\(562\) 63.3175 + 36.5563i 2.67089 + 1.54204i
\(563\) −36.1374 + 20.8640i −1.52301 + 0.879311i −0.523382 + 0.852098i \(0.675330\pi\)
−0.999630 + 0.0272129i \(0.991337\pi\)
\(564\) −1.58579 2.74666i −0.0667737 0.115655i
\(565\) 0 0
\(566\) 33.7990 1.42068
\(567\) 15.6500 12.1360i 0.657238 0.509666i
\(568\) 19.7990i 0.830747i
\(569\) 3.82843 6.63103i 0.160496 0.277987i −0.774551 0.632512i \(-0.782024\pi\)
0.935047 + 0.354525i \(0.115357\pi\)
\(570\) 0 0
\(571\) −4.58579 7.94282i −0.191909 0.332396i 0.753974 0.656905i \(-0.228135\pi\)
−0.945883 + 0.324508i \(0.894801\pi\)
\(572\) −13.2621 7.65685i −0.554515 0.320149i
\(573\) 5.31371i 0.221983i
\(574\) −18.8995 + 46.2941i −0.788850 + 1.93228i
\(575\) 0 0
\(576\) −13.8995 + 24.0746i −0.579146 + 1.00311i
\(577\) −38.0541 + 21.9706i −1.58421 + 0.914646i −0.589980 + 0.807418i \(0.700864\pi\)
−0.994234 + 0.107228i \(0.965802\pi\)
\(578\) −13.2005 + 7.62132i −0.549069 + 0.317005i
\(579\) 0.414214 0.717439i 0.0172141 0.0298157i
\(580\) 0 0
\(581\) 35.9853 4.92447i 1.49292 0.204302i
\(582\) 11.6569i 0.483192i
\(583\) 0.840532 + 0.485281i 0.0348113 + 0.0200983i
\(584\) −1.82843 3.16693i −0.0756609 0.131048i
\(585\) 0 0
\(586\) 19.3137 33.4523i 0.797842 1.38190i
\(587\) 34.2843i 1.41506i −0.706682 0.707532i \(-0.749809\pi\)
0.706682 0.707532i \(-0.250191\pi\)
\(588\) −10.7510 2.76346i −0.443365 0.113963i
\(589\) 16.9706 0.699260
\(590\) 0 0
\(591\) −2.55635 4.42773i −0.105154 0.182132i
\(592\) 0 0
\(593\) 3.63818 + 2.10051i 0.149402 + 0.0862574i 0.572838 0.819669i \(-0.305843\pi\)
−0.423435 + 0.905926i \(0.639176\pi\)
\(594\) 4.82843 0.198113
\(595\) 0 0
\(596\) −8.31371 −0.340543
\(597\) −3.46410 2.00000i −0.141776 0.0818546i
\(598\) 4.18154 2.41421i 0.170996 0.0987245i
\(599\) 3.17157 + 5.49333i 0.129587 + 0.224451i 0.923517 0.383558i \(-0.125302\pi\)
−0.793930 + 0.608010i \(0.791968\pi\)
\(600\) 0 0
\(601\) 19.6569 0.801820 0.400910 0.916117i \(-0.368694\pi\)
0.400910 + 0.916117i \(0.368694\pi\)
\(602\) −21.2049 8.65685i −0.864246 0.352827i
\(603\) 27.1127i 1.10411i
\(604\) 22.3137 38.6485i 0.907932 1.57258i
\(605\) 0 0
\(606\) −5.15685 8.93193i −0.209483 0.362835i
\(607\) −33.0936 19.1066i −1.34323 0.775513i −0.355948 0.934506i \(-0.615842\pi\)
−0.987280 + 0.158993i \(0.949175\pi\)
\(608\) 4.48528i 0.181902i
\(609\) 0.671573 + 0.866025i 0.0272135 + 0.0350931i
\(610\) 0 0
\(611\) 4.82843 8.36308i 0.195337 0.338334i
\(612\) −45.2795 + 26.1421i −1.83032 + 1.05673i
\(613\) −30.7057 + 17.7279i −1.24019 + 0.716024i −0.969133 0.246539i \(-0.920707\pi\)
−0.271057 + 0.962563i \(0.587373\pi\)
\(614\) −5.74264 + 9.94655i −0.231754 + 0.401410i
\(615\) 0 0
\(616\) 5.92893 + 7.64564i 0.238883 + 0.308052i
\(617\) 11.3137i 0.455473i 0.973723 + 0.227736i \(0.0731324\pi\)
−0.973723 + 0.227736i \(0.926868\pi\)
\(618\) 2.09077 + 1.20711i 0.0841031 + 0.0485570i
\(619\) 12.7574 + 22.0964i 0.512762 + 0.888129i 0.999890 + 0.0147990i \(0.00471084\pi\)
−0.487129 + 0.873330i \(0.661956\pi\)
\(620\) 0 0
\(621\) −0.500000 + 0.866025i −0.0200643 + 0.0347524i
\(622\) 31.7990i 1.27502i
\(623\) −21.2049 8.65685i −0.849555 0.346830i
\(624\) −6.00000 −0.240192
\(625\) 0 0
\(626\) 7.65685 + 13.2621i 0.306029 + 0.530059i
\(627\) 0.840532 0.485281i 0.0335676 0.0193803i
\(628\) 57.4039 + 33.1421i 2.29066 + 1.32252i
\(629\) 0 0
\(630\) 0 0
\(631\) −20.1421 −0.801846 −0.400923 0.916112i \(-0.631310\pi\)
−0.400923 + 0.916112i \(0.631310\pi\)
\(632\) −56.6864 32.7279i −2.25486 1.30185i
\(633\) 7.34847 4.24264i 0.292075 0.168630i
\(634\) −16.6569 28.8505i −0.661528 1.14580i
\(635\) 0 0
\(636\) 1.85786 0.0736691
\(637\) −9.08052 32.5563i −0.359783 1.28993i
\(638\) 2.00000i 0.0791808i
\(639\) −6.34315 + 10.9867i −0.250931 + 0.434625i
\(640\) 0 0
\(641\) −15.7426 27.2671i −0.621797 1.07698i −0.989151 0.146903i \(-0.953070\pi\)
0.367354 0.930081i \(-0.380264\pi\)
\(642\) 9.73641 + 5.62132i 0.384266 + 0.221856i
\(643\) 26.2843i 1.03655i −0.855214 0.518275i \(-0.826574\pi\)
0.855214 0.518275i \(-0.173426\pi\)
\(644\) −4.15685 + 0.568852i −0.163803 + 0.0224159i
\(645\) 0 0
\(646\) −16.4853 + 28.5533i −0.648605 + 1.12342i
\(647\) −26.8828 + 15.5208i −1.05687 + 0.610186i −0.924566 0.381022i \(-0.875572\pi\)
−0.132308 + 0.991209i \(0.542239\pi\)
\(648\) −28.6149 + 16.5208i −1.12410 + 0.648999i
\(649\) −1.85786 + 3.21792i −0.0729276 + 0.126314i
\(650\) 0 0
\(651\) −2.48528 + 6.08767i −0.0974059 + 0.238595i
\(652\) 47.2548i 1.85064i
\(653\) −16.6031 9.58579i −0.649728 0.375121i 0.138624 0.990345i \(-0.455732\pi\)
−0.788352 + 0.615224i \(0.789065\pi\)
\(654\) 6.74264 + 11.6786i 0.263658 + 0.456669i
\(655\) 0 0
\(656\) 11.7426 20.3389i 0.458473 0.794099i
\(657\) 2.34315i 0.0914148i
\(658\) −10.0951 + 7.82843i −0.393549 + 0.305184i
\(659\) −21.1716 −0.824727 −0.412364 0.911019i \(-0.635297\pi\)
−0.412364 + 0.911019i \(0.635297\pi\)
\(660\) 0 0
\(661\) −15.9142 27.5642i −0.618991 1.07212i −0.989670 0.143363i \(-0.954208\pi\)
0.370679 0.928761i \(-0.379125\pi\)
\(662\) 48.0262 27.7279i 1.86659 1.07768i
\(663\) 8.36308 + 4.82843i 0.324795 + 0.187521i
\(664\) −60.5980 −2.35166
\(665\) 0 0
\(666\) 0 0
\(667\) 0.358719 + 0.207107i 0.0138897 + 0.00801921i
\(668\) −74.3147 + 42.9056i −2.87532 + 1.66007i
\(669\) −0.0710678 0.123093i −0.00274764 0.00475905i
\(670\) 0 0
\(671\) −4.54416 −0.175425
\(672\) −1.60896 0.656854i −0.0620669 0.0253387i
\(673\) 29.6569i 1.14319i −0.820537 0.571594i \(-0.806325\pi\)
0.820537 0.571594i \(-0.193675\pi\)
\(674\) 11.0711 19.1757i 0.426442 0.738619i
\(675\) 0 0
\(676\) −19.7426 34.1953i −0.759332 1.31520i
\(677\) 24.3718 + 14.0711i 0.936685 + 0.540795i 0.888919 0.458064i \(-0.151457\pi\)
0.0477651 + 0.998859i \(0.484790\pi\)
\(678\) 4.48528i 0.172256i
\(679\) −30.5563 + 4.18154i −1.17265 + 0.160473i
\(680\) 0 0
\(681\) −1.44365 + 2.50048i −0.0553208 + 0.0958185i
\(682\) 10.3923 6.00000i 0.397942 0.229752i
\(683\) 30.1008 17.3787i 1.15177 0.664977i 0.202455 0.979292i \(-0.435108\pi\)
0.949319 + 0.314315i \(0.101775\pi\)
\(684\) −15.3137 + 26.5241i −0.585534 + 1.01418i
\(685\) 0 0
\(686\) −5.15685 + 44.4135i −0.196890 + 1.69571i
\(687\) 4.82843i 0.184216i
\(688\) 9.31615 + 5.37868i 0.355175 + 0.205060i
\(689\) 2.82843 + 4.89898i 0.107754 + 0.186636i
\(690\) 0 0
\(691\) −0.414214 + 0.717439i −0.0157574 + 0.0272927i −0.873797 0.486292i \(-0.838349\pi\)
0.858039 + 0.513584i \(0.171683\pi\)
\(692\) 12.6863i 0.482260i
\(693\) −0.840532 6.14214i −0.0319292 0.233320i
\(694\) −19.1421 −0.726626
\(695\) 0 0
\(696\) −0.914214 1.58346i −0.0346532 0.0600211i
\(697\) −32.7349 + 18.8995i −1.23992 + 0.715869i
\(698\) −32.0790 18.5208i −1.21421 0.701023i
\(699\) −6.97056 −0.263651
\(700\) 0 0
\(701\) −3.20101 −0.120900 −0.0604502 0.998171i \(-0.519254\pi\)
−0.0604502 + 0.998171i \(0.519254\pi\)
\(702\) 24.3718 + 14.0711i 0.919854 + 0.531078i
\(703\) 0 0
\(704\) 4.07107 + 7.05130i 0.153434 + 0.265756i
\(705\) 0 0
\(706\) −64.7696 −2.43763
\(707\) −21.5636 + 16.7218i −0.810982 + 0.628889i
\(708\) 7.11270i 0.267312i
\(709\) 7.84315 13.5847i 0.294556 0.510185i −0.680326 0.732910i \(-0.738162\pi\)
0.974881 + 0.222725i \(0.0714951\pi\)
\(710\) 0 0
\(711\) 20.9706 + 36.3221i 0.786458 + 1.36218i
\(712\) 33.0936 + 19.1066i 1.24024 + 0.716050i
\(713\) 2.48528i 0.0930745i
\(714\) −7.82843 10.0951i −0.292972 0.377801i
\(715\) 0 0
\(716\) 19.1421 33.1552i 0.715375 1.23907i
\(717\) 7.64564 4.41421i 0.285532 0.164852i
\(718\) 20.9077 12.0711i 0.780269 0.450488i
\(719\) 10.5563 18.2841i 0.393685 0.681883i −0.599247 0.800564i \(-0.704533\pi\)
0.992932 + 0.118681i \(0.0378666\pi\)
\(720\) 0 0
\(721\) 2.41421 5.91359i 0.0899100 0.220234i
\(722\) 26.5563i 0.988325i
\(723\) −9.92105 5.72792i −0.368968 0.213024i
\(724\) 5.08579 + 8.80884i 0.189012 + 0.327378i
\(725\) 0 0
\(726\) −5.15685 + 8.93193i −0.191389 + 0.331495i
\(727\) 37.5858i 1.39398i −0.717081 0.696990i \(-0.754522\pi\)
0.717081 0.696990i \(-0.245478\pi\)
\(728\) 7.64564 + 55.8701i 0.283366 + 2.07068i
\(729\) 18.1716 0.673021
\(730\) 0 0
\(731\) −8.65685 14.9941i −0.320185 0.554577i
\(732\) −7.53311 + 4.34924i −0.278432 + 0.160753i
\(733\) −19.0526 11.0000i −0.703722 0.406294i 0.105010 0.994471i \(-0.466513\pi\)
−0.808732 + 0.588177i \(0.799846\pi\)
\(734\) 6.65685 0.245709
\(735\) 0 0
\(736\) −0.656854 −0.0242120
\(737\) 6.87722 + 3.97056i 0.253326 + 0.146258i
\(738\) −46.2941 + 26.7279i −1.70411 + 0.983868i
\(739\) −10.5563 18.2841i −0.388322 0.672593i 0.603902 0.797058i \(-0.293612\pi\)
−0.992224 + 0.124466i \(0.960278\pi\)
\(740\) 0 0
\(741\) 5.65685 0.207810
\(742\) −1.01461 7.41421i −0.0372476 0.272184i
\(743\) 16.0711i 0.589590i 0.955560 + 0.294795i \(0.0952514\pi\)
−0.955560 + 0.294795i \(0.904749\pi\)
\(744\) 5.48528 9.50079i 0.201100 0.348316i
\(745\) 0 0
\(746\) 25.3137 + 43.8446i 0.926801 + 1.60527i
\(747\) 33.6264 + 19.4142i 1.23033 + 0.710329i
\(748\) 15.3137i 0.559925i
\(749\) 11.2426 27.5387i 0.410797 1.00624i
\(750\) 0 0
\(751\) 15.1716 26.2779i 0.553619 0.958895i −0.444391 0.895833i \(-0.646580\pi\)
0.998010 0.0630625i \(-0.0200868\pi\)
\(752\) 5.19615 3.00000i 0.189484 0.109399i
\(753\) −3.34101 + 1.92893i −0.121753 + 0.0702942i
\(754\) 5.82843 10.0951i 0.212259 0.367643i
\(755\) 0 0
\(756\) −14.9853 19.3242i −0.545009 0.702816i
\(757\) 31.4558i 1.14328i −0.820504 0.571641i \(-0.806307\pi\)
0.820504 0.571641i \(-0.193693\pi\)
\(758\) 56.0921 + 32.3848i 2.03736 + 1.17627i
\(759\) 0.0710678 + 0.123093i 0.00257960 + 0.00446800i
\(760\) 0 0
\(761\) −4.65685 + 8.06591i −0.168811 + 0.292389i −0.938002 0.346630i \(-0.887326\pi\)
0.769191 + 0.639019i \(0.220659\pi\)
\(762\) 9.31371i 0.337400i
\(763\) 28.1946 21.8640i 1.02071 0.791529i
\(764\) 49.1127 1.77684
\(765\) 0 0
\(766\) 3.50000 + 6.06218i 0.126460 + 0.219035i
\(767\) −18.7554 + 10.8284i −0.677218 + 0.390992i
\(768\) 10.7510 + 6.20711i 0.387944 + 0.223980i
\(769\) 0.627417 0.0226252 0.0113126 0.999936i \(-0.496399\pi\)
0.0113126 + 0.999936i \(0.496399\pi\)
\(770\) 0 0
\(771\) −2.62742 −0.0946241
\(772\) 6.63103 + 3.82843i 0.238656 + 0.137788i
\(773\) 32.1405 18.5563i 1.15601 0.667425i 0.205669 0.978622i \(-0.434063\pi\)
0.950346 + 0.311196i \(0.100730\pi\)
\(774\) −12.2426 21.2049i −0.440053 0.762194i
\(775\) 0 0
\(776\) 51.4558 1.84716
\(777\) 0 0
\(778\) 57.1127i 2.04759i
\(779\) −11.0711 + 19.1757i −0.396662 + 0.687039i
\(780\) 0 0
\(781\) 1.85786 + 3.21792i 0.0664796 + 0.115146i
\(782\) −4.18154 2.41421i −0.149532 0.0863321i
\(783\) 2.41421i 0.0862770i
\(784\) 5.22792 20.3389i 0.186712 0.726388i
\(785\) 0 0
\(786\) −9.65685 + 16.7262i −0.344449 + 0.596602i
\(787\) 2.21386 1.27817i 0.0789157 0.0455620i −0.460023 0.887907i \(-0.652159\pi\)
0.538939 + 0.842345i \(0.318825\pi\)
\(788\) 40.9239 23.6274i 1.45785 0.841692i
\(789\) 6.01472 10.4178i 0.214130 0.370883i
\(790\) 0 0
\(791\) −11.7574 + 1.60896i −0.418044 + 0.0572080i
\(792\) 10.3431i 0.367528i
\(793\) −22.9369 13.2426i −0.814514 0.470260i
\(794\) −20.0711 34.7641i −0.712296 1.23373i
\(795\) 0 0
\(796\) 18.4853 32.0174i 0.655193 1.13483i
\(797\) 8.00000i 0.283375i −0.989911 0.141687i \(-0.954747\pi\)
0.989911 0.141687i \(-0.0452527\pi\)
\(798\) −6.92820 2.82843i −0.245256 0.100125i
\(799\) −9.65685 −0.341635
\(800\) 0 0
\(801\) −12.2426 21.2049i −0.432572 0.749237i
\(802\) 63.3790 36.5919i 2.23799 1.29210i
\(803\) 0.594346 + 0.343146i 0.0209740 + 0.0121094i
\(804\) 15.2010 0.536098
\(805\) 0 0
\(806\) 69.9411 2.46357
\(807\) 7.33791 + 4.23654i 0.258307 + 0.149133i
\(808\) 39.4275 22.7635i 1.38705 0.800816i
\(809\) 17.8137 + 30.8542i 0.626297 + 1.08478i 0.988289 + 0.152596i \(0.0487634\pi\)
−0.361992 + 0.932181i \(0.617903\pi\)
\(810\) 0 0
\(811\) −20.6274 −0.724327 −0.362163 0.932115i \(-0.617962\pi\)
−0.362163 + 0.932115i \(0.617962\pi\)
\(812\) −8.00436 + 6.20711i −0.280898 + 0.217827i
\(813\) 6.82843i 0.239483i
\(814\) 0 0
\(815\) 0 0
\(816\) 3.00000 + 5.19615i 0.105021 + 0.181902i
\(817\) −8.78335 5.07107i −0.307290 0.177414i
\(818\) 35.7279i 1.24920i
\(819\) 13.6569 33.4523i 0.477209 1.16892i
\(820\) 0 0
\(821\) −23.9706 + 41.5182i −0.836578 + 1.44900i 0.0561604 + 0.998422i \(0.482114\pi\)
−0.892739 + 0.450575i \(0.851219\pi\)
\(822\) 8.36308 4.82843i 0.291696 0.168411i
\(823\) −1.79360 + 1.03553i −0.0625209 + 0.0360964i −0.530935 0.847413i \(-0.678159\pi\)
0.468414 + 0.883509i \(0.344826\pi\)
\(824\) −5.32843 + 9.22911i −0.185625 + 0.321511i
\(825\) 0 0
\(826\) 28.3848 3.88437i 0.987633 0.135154i
\(827\) 26.2132i 0.911522i −0.890102 0.455761i \(-0.849367\pi\)
0.890102 0.455761i \(-0.150633\pi\)
\(828\) −3.88437 2.24264i −0.134991 0.0779372i
\(829\) 14.6569 + 25.3864i 0.509054 + 0.881707i 0.999945 + 0.0104859i \(0.00333784\pi\)
−0.490891 + 0.871221i \(0.663329\pi\)
\(830\) 0 0
\(831\) 3.34315 5.79050i 0.115972 0.200870i
\(832\) 47.4558i 1.64524i
\(833\) −23.6544 + 24.1421i −0.819575 + 0.836475i
\(834\) −16.1421 −0.558956
\(835\) 0 0
\(836\) 4.48528 + 7.76874i 0.155127 + 0.268687i
\(837\) −12.5446 + 7.24264i −0.433606 + 0.250342i
\(838\) −1.43488 0.828427i −0.0495670 0.0286175i
\(839\) −15.1716 −0.523781 −0.261890 0.965098i \(-0.584346\pi\)
−0.261890 + 0.965098i \(0.584346\pi\)
\(840\) 0 0
\(841\) −28.0000 −0.965517
\(842\) −28.1946 16.2782i −0.971651 0.560983i
\(843\) −10.8636 + 6.27208i −0.374161 + 0.216022i
\(844\) 39.2132 + 67.9193i 1.34977 + 2.33788i
\(845\) 0 0
\(846\) −13.6569 −0.469532
\(847\) 25.2633 + 10.3137i 0.868058 + 0.354383i
\(848\) 3.51472i 0.120696i
\(849\) −2.89949 + 5.02207i −0.0995104 + 0.172357i
\(850\) 0 0
\(851\) 0 0
\(852\) 6.15978 + 3.55635i 0.211030 + 0.121839i
\(853\) 2.54416i 0.0871102i −0.999051 0.0435551i \(-0.986132\pi\)
0.999051 0.0435551i \(-0.0138684\pi\)
\(854\) 21.4706 + 27.6873i 0.734708 + 0.947441i
\(855\) 0 0
\(856\) −24.8137 + 42.9786i −0.848115 + 1.46898i
\(857\) 29.6910 17.1421i 1.01423 0.585564i 0.101800 0.994805i \(-0.467540\pi\)
0.912426 + 0.409241i \(0.134206\pi\)
\(858\) 3.46410 2.00000i 0.118262 0.0682789i
\(859\) 0.686292 1.18869i 0.0234160 0.0405576i −0.854080 0.520142i \(-0.825879\pi\)
0.877496 + 0.479584i \(0.159212\pi\)
\(860\) 0 0
\(861\) −5.25736 6.77962i −0.179170 0.231049i
\(862\) 42.9706i 1.46358i
\(863\) 12.6062 + 7.27817i 0.429119 + 0.247752i 0.698971 0.715150i \(-0.253642\pi\)
−0.269852 + 0.962902i \(0.586975\pi\)
\(864\) −1.91421 3.31552i −0.0651229 0.112796i
\(865\) 0 0
\(866\) −9.41421 + 16.3059i −0.319908 + 0.554097i
\(867\) 2.61522i 0.0888177i
\(868\) −56.2662 22.9706i −1.90980 0.779672i
\(869\) 12.2843 0.416715
\(870\) 0 0
\(871\) 23.1421 + 40.0834i 0.784141 + 1.35817i
\(872\) −51.5518 + 29.7635i −1.74576 + 1.00792i
\(873\) −28.5533 16.4853i −0.966384 0.557942i
\(874\) −2.82843 −0.0956730
\(875\) 0 0
\(876\) 1.31371 0.0443861
\(877\) −21.7992 12.5858i −0.736107 0.424992i 0.0845449 0.996420i \(-0.473056\pi\)
−0.820652 + 0.571428i \(0.806390\pi\)
\(878\) 70.9631 40.9706i 2.39489 1.38269i
\(879\) 3.31371 + 5.73951i 0.111769 + 0.193589i
\(880\) 0 0
\(881\) 1.82843 0.0616013 0.0308006 0.999526i \(-0.490194\pi\)
0.0308006 + 0.999526i \(0.490194\pi\)
\(882\) −33.4523 + 34.1421i −1.12640 + 1.14963i
\(883\) 18.2843i 0.615315i −0.951497 0.307657i \(-0.900455\pi\)
0.951497 0.307657i \(-0.0995450\pi\)
\(884\) −44.6274 + 77.2970i −1.50098 + 2.59978i
\(885\) 0 0
\(886\) −36.4706 63.1689i −1.22525 2.12220i
\(887\) −25.9192 14.9645i −0.870282 0.502458i −0.00284012 0.999996i \(-0.500904\pi\)
−0.867442 + 0.497538i \(0.834237\pi\)
\(888\) 0 0
\(889\) 24.4142 3.34101i 0.818826 0.112054i
\(890\) 0 0
\(891\) 3.10051 5.37023i 0.103871 0.179910i
\(892\) 1.13770 0.656854i 0.0380932 0.0219931i
\(893\) −4.89898 + 2.82843i −0.163938 + 0.0946497i
\(894\) 1.08579 1.88064i 0.0363141 0.0628979i
\(895\) 0 0
\(896\) 20.5563 50.3526i 0.686739 1.68216i
\(897\) 0.828427i 0.0276604i
\(898\) 8.00436 + 4.62132i 0.267109 + 0.154215i
\(899\) 3.00000 + 5.19615i 0.100056 + 0.173301i
\(900\) 0 0
\(901\) 2.82843 4.89898i 0.0942286 0.163209i
\(902\) 15.6569i 0.521316i
\(903\) 3.10538 2.40812i 0.103341 0.0801371i
\(904\) 19.7990 0.658505
\(905\) 0 0
\(906\) 5.82843 + 10.0951i 0.193637 + 0.335388i
\(907\) −12.3090 + 7.10660i −0.408713 + 0.235971i −0.690237 0.723584i \(-0.742494\pi\)
0.281523 + 0.959554i \(0.409160\pi\)
\(908\) −23.1110 13.3431i −0.766966 0.442808i
\(909\) −29.1716 −0.967560
\(910\) 0 0
\(911\) −10.2010 −0.337975 −0.168987 0.985618i \(-0.554050\pi\)
−0.168987 + 0.985618i \(0.554050\pi\)
\(912\) 3.04384 + 1.75736i 0.100791 + 0.0581920i
\(913\) 9.84895 5.68629i 0.325953 0.188189i
\(914\) 29.3137 + 50.7728i 0.969611 + 1.67942i
\(915\) 0 0
\(916\) −44.6274 −1.47453
\(917\) 47.3087 + 19.3137i 1.56227 + 0.637795i
\(918\) 28.1421i 0.928829i
\(919\) −21.5563 + 37.3367i −0.711078 + 1.23162i 0.253374 + 0.967368i \(0.418460\pi\)
−0.964453 + 0.264256i \(0.914874\pi\)
\(920\) 0 0
\(921\) −0.985281 1.70656i −0.0324661 0.0562330i
\(922\) −86.3775 49.8701i −2.84469 1.64238i
\(923\) 21.6569i 0.712844i
\(924\) −3.44365 + 0.471253i −0.113288 + 0.0155031i
\(925\) 0 0
\(926\) 44.7132 77.4455i 1.46937 2.54502i
\(927\) 5.91359 3.41421i 0.194228 0.112137i
\(928\) −1.37333 + 0.792893i −0.0450818 + 0.0260280i
\(929\) 2.74264 4.75039i 0.0899831 0.155855i −0.817521 0.575899i \(-0.804652\pi\)
0.907504 + 0.420044i \(0.137985\pi\)
\(930\) 0 0
\(931\) −4.92893 + 19.1757i −0.161539 + 0.628457i
\(932\) 64.4264i 2.11036i
\(933\) 4.72490 + 2.72792i 0.154686 + 0.0893082i
\(934\) −3.74264 6.48244i −0.122463 0.212112i
\(935\) 0 0
\(936\) −30.1421 + 52.2077i −0.985227 + 1.70646i
\(937\) 34.6274i 1.13123i 0.824670 + 0.565614i \(0.191361\pi\)
−0.824670 + 0.565614i \(0.808639\pi\)
\(938\) −8.30153 60.6630i −0.271055 1.98072i
\(939\) −2.62742 −0.0857425
\(940\) 0 0
\(941\) 23.1421 + 40.0834i 0.754412 + 1.30668i 0.945666 + 0.325139i \(0.105411\pi\)
−0.191254 + 0.981541i \(0.561255\pi\)
\(942\) −14.9941 + 8.65685i −0.488535 + 0.282056i
\(943\) −2.80821 1.62132i −0.0914479 0.0527975i
\(944\) −13.4558 −0.437950
\(945\) 0 0
\(946\) −7.17157 −0.233168
\(947\) −28.7380 16.5919i −0.933859 0.539164i −0.0458290 0.998949i \(-0.514593\pi\)
−0.888030 + 0.459786i \(0.847926\pi\)
\(948\) 20.3643 11.7574i 0.661403 0.381861i
\(949\) 2.00000 + 3.46410i 0.0649227 + 0.112449i
\(950\) 0 0
\(951\) 5.71573 0.185345
\(952\) 44.5621 34.5563i 1.44426 1.11998i
\(953\) 13.6569i 0.442389i 0.975230 + 0.221194i \(0.0709955\pi\)
−0.975230 + 0.221194i \(0.929004\pi\)
\(954\) 4.00000 6.92820i 0.129505 0.224309i
\(955\) 0 0
\(956\) 40.7990 + 70.6659i 1.31953 + 2.28550i
\(957\) 0.297173 + 0.171573i 0.00960624 + 0.00554616i
\(958\) 86.0833i 2.78122i
\(959\) −15.6569 20.1903i −0.505586 0.651978i
\(960\) 0 0
\(961\) −2.50000 + 4.33013i −0.0806452 + 0.139682i
\(962\) 0 0
\(963\) 27.5387 15.8995i 0.887423 0.512354i
\(964\) 52.9411 91.6967i 1.70512 2.95335i
\(965\) 0 0
\(966\) 0.414214 1.01461i 0.0133271 0.0326446i
\(967\) 37.5269i 1.20678i 0.797445 + 0.603392i \(0.206185\pi\)
−0.797445 + 0.603392i \(0.793815\pi\)
\(968\) −39.4275 22.7635i −1.26725 0.731645i
\(969\) −2.82843 4.89898i −0.0908622 0.157378i
\(970\) 0 0
\(971\) 12.0000 20.7846i 0.385098 0.667010i −0.606685 0.794943i \(-0.707501\pi\)
0.991783 + 0.127933i \(0.0408342\pi\)
\(972\) 39.5980i 1.27011i
\(973\) 5.79050 + 42.3137i 0.185635 + 1.35652i
\(974\) −10.4853 −0.335970
\(975\) 0 0
\(976\) −8.22792 14.2512i −0.263369 0.456169i
\(977\) −1.13770 + 0.656854i −0.0363984 + 0.0210146i −0.518089 0.855327i \(-0.673356\pi\)
0.481690 + 0.876341i \(0.340023\pi\)
\(978\) −10.6895 6.17157i −0.341812 0.197345i
\(979\) −7.17157 −0.229204
\(980\) 0 0
\(981\) 38.1421 1.21778
\(982\) −19.4728 11.2426i −0.621403 0.358767i
\(983\) −24.4334 + 14.1066i −0.779303 + 0.449931i −0.836183 0.548450i \(-0.815218\pi\)
0.0568803 + 0.998381i \(0.481885\pi\)
\(984\) 7.15685 + 12.3960i 0.228152 + 0.395171i
\(985\) 0 0
\(986\) −11.6569 −0.371230
\(987\) −0.297173 2.17157i −0.00945912 0.0691219i
\(988\) 52.2843i 1.66338i
\(989\) 0.742641 1.28629i 0.0236146 0.0409017i
\(990\) 0 0
\(991\) 2.17157 + 3.76127i 0.0689823 + 0.119481i 0.898454 0.439069i \(-0.144691\pi\)
−0.829471 + 0.558549i \(0.811358\pi\)
\(992\) −8.23999 4.75736i −0.261620 0.151046i
\(993\) 9.51472i 0.301940i
\(994\) 10.8284 26.5241i 0.343457 0.841294i
\(995\) 0 0
\(996\) 10.8848 18.8530i 0.344897 0.597380i
\(997\) 28.9736 16.7279i 0.917603 0.529779i 0.0347337 0.999397i \(-0.488942\pi\)
0.882870 + 0.469618i \(0.155608\pi\)
\(998\) 1.73205 1.00000i 0.0548271 0.0316544i
\(999\) 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 175.2.k.a.149.1 8
5.2 odd 4 175.2.e.c.51.2 4
5.3 odd 4 35.2.e.a.16.1 yes 4
5.4 even 2 inner 175.2.k.a.149.4 8
7.2 even 3 1225.2.b.g.99.4 4
7.4 even 3 inner 175.2.k.a.74.4 8
7.5 odd 6 1225.2.b.h.99.4 4
15.8 even 4 315.2.j.e.226.2 4
20.3 even 4 560.2.q.k.401.1 4
35.2 odd 12 1225.2.a.k.1.1 2
35.3 even 12 245.2.e.e.116.1 4
35.4 even 6 inner 175.2.k.a.74.1 8
35.9 even 6 1225.2.b.g.99.1 4
35.12 even 12 1225.2.a.m.1.1 2
35.13 even 4 245.2.e.e.226.1 4
35.18 odd 12 35.2.e.a.11.1 4
35.19 odd 6 1225.2.b.h.99.1 4
35.23 odd 12 245.2.a.h.1.2 2
35.32 odd 12 175.2.e.c.151.2 4
35.33 even 12 245.2.a.g.1.2 2
105.23 even 12 2205.2.a.n.1.1 2
105.53 even 12 315.2.j.e.46.2 4
105.68 odd 12 2205.2.a.q.1.1 2
140.23 even 12 3920.2.a.bq.1.2 2
140.103 odd 12 3920.2.a.bv.1.1 2
140.123 even 12 560.2.q.k.81.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.2.e.a.11.1 4 35.18 odd 12
35.2.e.a.16.1 yes 4 5.3 odd 4
175.2.e.c.51.2 4 5.2 odd 4
175.2.e.c.151.2 4 35.32 odd 12
175.2.k.a.74.1 8 35.4 even 6 inner
175.2.k.a.74.4 8 7.4 even 3 inner
175.2.k.a.149.1 8 1.1 even 1 trivial
175.2.k.a.149.4 8 5.4 even 2 inner
245.2.a.g.1.2 2 35.33 even 12
245.2.a.h.1.2 2 35.23 odd 12
245.2.e.e.116.1 4 35.3 even 12
245.2.e.e.226.1 4 35.13 even 4
315.2.j.e.46.2 4 105.53 even 12
315.2.j.e.226.2 4 15.8 even 4
560.2.q.k.81.1 4 140.123 even 12
560.2.q.k.401.1 4 20.3 even 4
1225.2.a.k.1.1 2 35.2 odd 12
1225.2.a.m.1.1 2 35.12 even 12
1225.2.b.g.99.1 4 35.9 even 6
1225.2.b.g.99.4 4 7.2 even 3
1225.2.b.h.99.1 4 35.19 odd 6
1225.2.b.h.99.4 4 7.5 odd 6
2205.2.a.n.1.1 2 105.23 even 12
2205.2.a.q.1.1 2 105.68 odd 12
3920.2.a.bq.1.2 2 140.23 even 12
3920.2.a.bv.1.1 2 140.103 odd 12