Properties

Label 666.2.be.c.125.2
Level $666$
Weight $2$
Character 666.125
Analytic conductor $5.318$
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] = [666,2,Mod(125,666)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(666, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("666.125");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 666.be (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.31803677462\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 125.2
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 666.125
Dual form 666.2.be.c.341.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.448288 - 1.67303i) q^{5} +(0.633975 + 1.09808i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.448288 - 1.67303i) q^{5} +(0.633975 + 1.09808i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.73205 q^{10} +2.44949 q^{11} +(0.366025 + 0.0980762i) q^{13} +(-0.896575 + 0.896575i) q^{14} +(0.500000 - 0.866025i) q^{16} +(6.24384 - 1.67303i) q^{17} +(-5.09808 - 1.36603i) q^{19} +(0.448288 + 1.67303i) q^{20} +(0.633975 + 2.36603i) q^{22} +(2.44949 + 2.44949i) q^{23} +(1.73205 + 1.00000i) q^{25} +0.378937i q^{26} +(-1.09808 - 0.633975i) q^{28} +(6.12372 - 6.12372i) q^{29} +(5.73205 + 5.73205i) q^{31} +(0.965926 + 0.258819i) q^{32} +(3.23205 + 5.59808i) q^{34} +(2.12132 - 0.568406i) q^{35} +(-4.69615 + 3.86603i) q^{37} -5.27792i q^{38} +(-1.50000 + 0.866025i) q^{40} +(2.89778 + 5.01910i) q^{41} +(0.267949 - 0.267949i) q^{43} +(-2.12132 + 1.22474i) q^{44} +(-1.73205 + 3.00000i) q^{46} -4.24264i q^{47} +(2.69615 - 4.66987i) q^{49} +(-0.517638 + 1.93185i) q^{50} +(-0.366025 + 0.0980762i) q^{52} +(-5.22715 - 3.01790i) q^{53} +(1.09808 - 4.09808i) q^{55} +(0.328169 - 1.22474i) q^{56} +(7.50000 + 4.33013i) q^{58} +(-5.79555 + 1.55291i) q^{59} +(-2.86603 + 10.6962i) q^{61} +(-4.05317 + 7.02030i) q^{62} +1.00000i q^{64} +(0.328169 - 0.568406i) q^{65} +(-3.63397 + 2.09808i) q^{67} +(-4.57081 + 4.57081i) q^{68} +(1.09808 + 1.90192i) q^{70} +(2.12132 - 1.22474i) q^{71} -6.39230i q^{73} +(-4.94975 - 3.53553i) q^{74} +(5.09808 - 1.36603i) q^{76} +(1.55291 + 2.68973i) q^{77} +(-3.36603 - 0.901924i) q^{79} +(-1.22474 - 1.22474i) q^{80} +(-4.09808 + 4.09808i) q^{82} +(-3.10583 - 1.79315i) q^{83} -11.1962i q^{85} +(0.328169 + 0.189469i) q^{86} +(-1.73205 - 1.73205i) q^{88} +(-1.10463 - 4.12252i) q^{89} +(0.124356 + 0.464102i) q^{91} +(-3.34607 - 0.896575i) q^{92} +(4.09808 - 1.09808i) q^{94} +(-4.57081 + 7.91688i) q^{95} +(0.366025 - 0.366025i) q^{97} +(5.20857 + 1.39563i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 12 q^{7} - 4 q^{13} + 4 q^{16} - 20 q^{19} + 12 q^{22} + 12 q^{28} + 32 q^{31} + 12 q^{34} + 4 q^{37} - 12 q^{40} + 16 q^{43} - 20 q^{49} + 4 q^{52} - 12 q^{55} + 60 q^{58} - 16 q^{61} - 36 q^{67} - 12 q^{70} + 20 q^{76} - 20 q^{79} - 12 q^{82} - 96 q^{91} + 12 q^{94} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/666\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\)
\(\chi(n)\) \(-1\) \(e\left(\frac{11}{12}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.258819 + 0.965926i 0.183013 + 0.683013i
\(3\) 0 0
\(4\) −0.866025 + 0.500000i −0.433013 + 0.250000i
\(5\) 0.448288 1.67303i 0.200480 0.748203i −0.790299 0.612721i \(-0.790075\pi\)
0.990780 0.135482i \(-0.0432583\pi\)
\(6\) 0 0
\(7\) 0.633975 + 1.09808i 0.239620 + 0.415034i 0.960605 0.277916i \(-0.0896439\pi\)
−0.720985 + 0.692950i \(0.756311\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0 0
\(10\) 1.73205 0.547723
\(11\) 2.44949 0.738549 0.369274 0.929320i \(-0.379606\pi\)
0.369274 + 0.929320i \(0.379606\pi\)
\(12\) 0 0
\(13\) 0.366025 + 0.0980762i 0.101517 + 0.0272014i 0.309220 0.950991i \(-0.399932\pi\)
−0.207703 + 0.978192i \(0.566599\pi\)
\(14\) −0.896575 + 0.896575i −0.239620 + 0.239620i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 6.24384 1.67303i 1.51435 0.405770i 0.596476 0.802631i \(-0.296567\pi\)
0.917879 + 0.396861i \(0.129901\pi\)
\(18\) 0 0
\(19\) −5.09808 1.36603i −1.16958 0.313388i −0.378793 0.925481i \(-0.623661\pi\)
−0.790785 + 0.612093i \(0.790328\pi\)
\(20\) 0.448288 + 1.67303i 0.100240 + 0.374101i
\(21\) 0 0
\(22\) 0.633975 + 2.36603i 0.135164 + 0.504438i
\(23\) 2.44949 + 2.44949i 0.510754 + 0.510754i 0.914757 0.404004i \(-0.132382\pi\)
−0.404004 + 0.914757i \(0.632382\pi\)
\(24\) 0 0
\(25\) 1.73205 + 1.00000i 0.346410 + 0.200000i
\(26\) 0.378937i 0.0743157i
\(27\) 0 0
\(28\) −1.09808 0.633975i −0.207517 0.119810i
\(29\) 6.12372 6.12372i 1.13715 1.13715i 0.148188 0.988959i \(-0.452656\pi\)
0.988959 0.148188i \(-0.0473440\pi\)
\(30\) 0 0
\(31\) 5.73205 + 5.73205i 1.02951 + 1.02951i 0.999551 + 0.0299555i \(0.00953655\pi\)
0.0299555 + 0.999551i \(0.490463\pi\)
\(32\) 0.965926 + 0.258819i 0.170753 + 0.0457532i
\(33\) 0 0
\(34\) 3.23205 + 5.59808i 0.554292 + 0.960062i
\(35\) 2.12132 0.568406i 0.358569 0.0960782i
\(36\) 0 0
\(37\) −4.69615 + 3.86603i −0.772043 + 0.635571i
\(38\) 5.27792i 0.856191i
\(39\) 0 0
\(40\) −1.50000 + 0.866025i −0.237171 + 0.136931i
\(41\) 2.89778 + 5.01910i 0.452557 + 0.783851i 0.998544 0.0539421i \(-0.0171786\pi\)
−0.545987 + 0.837793i \(0.683845\pi\)
\(42\) 0 0
\(43\) 0.267949 0.267949i 0.0408619 0.0408619i −0.686381 0.727242i \(-0.740802\pi\)
0.727242 + 0.686381i \(0.240802\pi\)
\(44\) −2.12132 + 1.22474i −0.319801 + 0.184637i
\(45\) 0 0
\(46\) −1.73205 + 3.00000i −0.255377 + 0.442326i
\(47\) 4.24264i 0.618853i −0.950923 0.309426i \(-0.899863\pi\)
0.950923 0.309426i \(-0.100137\pi\)
\(48\) 0 0
\(49\) 2.69615 4.66987i 0.385165 0.667125i
\(50\) −0.517638 + 1.93185i −0.0732051 + 0.273205i
\(51\) 0 0
\(52\) −0.366025 + 0.0980762i −0.0507586 + 0.0136007i
\(53\) −5.22715 3.01790i −0.718004 0.414540i 0.0960135 0.995380i \(-0.469391\pi\)
−0.814018 + 0.580840i \(0.802724\pi\)
\(54\) 0 0
\(55\) 1.09808 4.09808i 0.148065 0.552584i
\(56\) 0.328169 1.22474i 0.0438535 0.163663i
\(57\) 0 0
\(58\) 7.50000 + 4.33013i 0.984798 + 0.568574i
\(59\) −5.79555 + 1.55291i −0.754517 + 0.202172i −0.615521 0.788121i \(-0.711054\pi\)
−0.138996 + 0.990293i \(0.544388\pi\)
\(60\) 0 0
\(61\) −2.86603 + 10.6962i −0.366957 + 1.36950i 0.497792 + 0.867297i \(0.334144\pi\)
−0.864748 + 0.502205i \(0.832522\pi\)
\(62\) −4.05317 + 7.02030i −0.514753 + 0.891579i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0.328169 0.568406i 0.0407044 0.0705021i
\(66\) 0 0
\(67\) −3.63397 + 2.09808i −0.443961 + 0.256321i −0.705276 0.708933i \(-0.749177\pi\)
0.261316 + 0.965253i \(0.415844\pi\)
\(68\) −4.57081 + 4.57081i −0.554292 + 0.554292i
\(69\) 0 0
\(70\) 1.09808 + 1.90192i 0.131245 + 0.227323i
\(71\) 2.12132 1.22474i 0.251754 0.145350i −0.368813 0.929504i \(-0.620236\pi\)
0.620567 + 0.784153i \(0.286902\pi\)
\(72\) 0 0
\(73\) 6.39230i 0.748163i −0.927396 0.374081i \(-0.877958\pi\)
0.927396 0.374081i \(-0.122042\pi\)
\(74\) −4.94975 3.53553i −0.575396 0.410997i
\(75\) 0 0
\(76\) 5.09808 1.36603i 0.584789 0.156694i
\(77\) 1.55291 + 2.68973i 0.176971 + 0.306523i
\(78\) 0 0
\(79\) −3.36603 0.901924i −0.378707 0.101474i 0.0644435 0.997921i \(-0.479473\pi\)
−0.443151 + 0.896447i \(0.646139\pi\)
\(80\) −1.22474 1.22474i −0.136931 0.136931i
\(81\) 0 0
\(82\) −4.09808 + 4.09808i −0.452557 + 0.452557i
\(83\) −3.10583 1.79315i −0.340909 0.196824i 0.319765 0.947497i \(-0.396396\pi\)
−0.660674 + 0.750673i \(0.729729\pi\)
\(84\) 0 0
\(85\) 11.1962i 1.21439i
\(86\) 0.328169 + 0.189469i 0.0353874 + 0.0204309i
\(87\) 0 0
\(88\) −1.73205 1.73205i −0.184637 0.184637i
\(89\) −1.10463 4.12252i −0.117090 0.436986i 0.882345 0.470604i \(-0.155964\pi\)
−0.999435 + 0.0336174i \(0.989297\pi\)
\(90\) 0 0
\(91\) 0.124356 + 0.464102i 0.0130360 + 0.0486511i
\(92\) −3.34607 0.896575i −0.348851 0.0934745i
\(93\) 0 0
\(94\) 4.09808 1.09808i 0.422684 0.113258i
\(95\) −4.57081 + 7.91688i −0.468955 + 0.812254i
\(96\) 0 0
\(97\) 0.366025 0.366025i 0.0371642 0.0371642i −0.688280 0.725445i \(-0.741634\pi\)
0.725445 + 0.688280i \(0.241634\pi\)
\(98\) 5.20857 + 1.39563i 0.526145 + 0.140980i
\(99\) 0 0
\(100\) −2.00000 −0.200000
\(101\) −2.20925 −0.219829 −0.109914 0.993941i \(-0.535058\pi\)
−0.109914 + 0.993941i \(0.535058\pi\)
\(102\) 0 0
\(103\) −3.73205 3.73205i −0.367730 0.367730i 0.498919 0.866649i \(-0.333731\pi\)
−0.866649 + 0.498919i \(0.833731\pi\)
\(104\) −0.189469 0.328169i −0.0185789 0.0321797i
\(105\) 0 0
\(106\) 1.56218 5.83013i 0.151732 0.566272i
\(107\) −9.46979 + 5.46739i −0.915479 + 0.528552i −0.882190 0.470894i \(-0.843932\pi\)
−0.0332891 + 0.999446i \(0.510598\pi\)
\(108\) 0 0
\(109\) −0.794229 2.96410i −0.0760733 0.283909i 0.917401 0.397964i \(-0.130283\pi\)
−0.993475 + 0.114054i \(0.963616\pi\)
\(110\) 4.24264 0.404520
\(111\) 0 0
\(112\) 1.26795 0.119810
\(113\) −2.03339 7.58871i −0.191285 0.713885i −0.993197 0.116444i \(-0.962851\pi\)
0.801912 0.597442i \(-0.203816\pi\)
\(114\) 0 0
\(115\) 5.19615 3.00000i 0.484544 0.279751i
\(116\) −2.24144 + 8.36516i −0.208112 + 0.776686i
\(117\) 0 0
\(118\) −3.00000 5.19615i −0.276172 0.478345i
\(119\) 5.79555 + 5.79555i 0.531278 + 0.531278i
\(120\) 0 0
\(121\) −5.00000 −0.454545
\(122\) −11.0735 −1.00255
\(123\) 0 0
\(124\) −7.83013 2.09808i −0.703166 0.188413i
\(125\) 8.57321 8.57321i 0.766812 0.766812i
\(126\) 0 0
\(127\) −1.19615 + 2.07180i −0.106141 + 0.183842i −0.914204 0.405254i \(-0.867183\pi\)
0.808063 + 0.589097i \(0.200516\pi\)
\(128\) −0.965926 + 0.258819i −0.0853766 + 0.0228766i
\(129\) 0 0
\(130\) 0.633975 + 0.169873i 0.0556033 + 0.0148988i
\(131\) 2.03339 + 7.58871i 0.177658 + 0.663028i 0.996084 + 0.0884160i \(0.0281805\pi\)
−0.818426 + 0.574612i \(0.805153\pi\)
\(132\) 0 0
\(133\) −1.73205 6.46410i −0.150188 0.560509i
\(134\) −2.96713 2.96713i −0.256321 0.256321i
\(135\) 0 0
\(136\) −5.59808 3.23205i −0.480031 0.277146i
\(137\) 16.0740i 1.37329i −0.726991 0.686647i \(-0.759082\pi\)
0.726991 0.686647i \(-0.240918\pi\)
\(138\) 0 0
\(139\) 0.339746 + 0.196152i 0.0288169 + 0.0166374i 0.514339 0.857587i \(-0.328037\pi\)
−0.485522 + 0.874224i \(0.661371\pi\)
\(140\) −1.55291 + 1.55291i −0.131245 + 0.131245i
\(141\) 0 0
\(142\) 1.73205 + 1.73205i 0.145350 + 0.145350i
\(143\) 0.896575 + 0.240237i 0.0749754 + 0.0200896i
\(144\) 0 0
\(145\) −7.50000 12.9904i −0.622841 1.07879i
\(146\) 6.17449 1.65445i 0.511005 0.136923i
\(147\) 0 0
\(148\) 2.13397 5.69615i 0.175412 0.468221i
\(149\) 15.5935i 1.27747i −0.769427 0.638735i \(-0.779458\pi\)
0.769427 0.638735i \(-0.220542\pi\)
\(150\) 0 0
\(151\) 15.0000 8.66025i 1.22068 0.704761i 0.255619 0.966778i \(-0.417721\pi\)
0.965064 + 0.262016i \(0.0843873\pi\)
\(152\) 2.63896 + 4.57081i 0.214048 + 0.370742i
\(153\) 0 0
\(154\) −2.19615 + 2.19615i −0.176971 + 0.176971i
\(155\) 12.1595 7.02030i 0.976676 0.563884i
\(156\) 0 0
\(157\) −3.06218 + 5.30385i −0.244388 + 0.423293i −0.961959 0.273192i \(-0.911921\pi\)
0.717571 + 0.696485i \(0.245254\pi\)
\(158\) 3.48477i 0.277233i
\(159\) 0 0
\(160\) 0.866025 1.50000i 0.0684653 0.118585i
\(161\) −1.13681 + 4.24264i −0.0895933 + 0.334367i
\(162\) 0 0
\(163\) −0.366025 + 0.0980762i −0.0286693 + 0.00768192i −0.273125 0.961978i \(-0.588057\pi\)
0.244456 + 0.969660i \(0.421391\pi\)
\(164\) −5.01910 2.89778i −0.391926 0.226278i
\(165\) 0 0
\(166\) 0.928203 3.46410i 0.0720425 0.268866i
\(167\) −6.45189 + 24.0788i −0.499263 + 1.86327i 0.00544916 + 0.999985i \(0.498265\pi\)
−0.504712 + 0.863288i \(0.668401\pi\)
\(168\) 0 0
\(169\) −11.1340 6.42820i −0.856460 0.494477i
\(170\) 10.8147 2.89778i 0.829446 0.222249i
\(171\) 0 0
\(172\) −0.0980762 + 0.366025i −0.00747824 + 0.0279092i
\(173\) −8.03699 + 13.9205i −0.611041 + 1.05835i 0.380024 + 0.924977i \(0.375916\pi\)
−0.991065 + 0.133378i \(0.957418\pi\)
\(174\) 0 0
\(175\) 2.53590i 0.191696i
\(176\) 1.22474 2.12132i 0.0923186 0.159901i
\(177\) 0 0
\(178\) 3.69615 2.13397i 0.277038 0.159948i
\(179\) −15.8338 + 15.8338i −1.18347 + 1.18347i −0.204631 + 0.978839i \(0.565599\pi\)
−0.978839 + 0.204631i \(0.934401\pi\)
\(180\) 0 0
\(181\) −8.59808 14.8923i −0.639090 1.10694i −0.985633 0.168902i \(-0.945978\pi\)
0.346543 0.938034i \(-0.387356\pi\)
\(182\) −0.416102 + 0.240237i −0.0308435 + 0.0178075i
\(183\) 0 0
\(184\) 3.46410i 0.255377i
\(185\) 4.36276 + 9.58991i 0.320756 + 0.705064i
\(186\) 0 0
\(187\) 15.2942 4.09808i 1.11842 0.299681i
\(188\) 2.12132 + 3.67423i 0.154713 + 0.267971i
\(189\) 0 0
\(190\) −8.83013 2.36603i −0.640605 0.171650i
\(191\) −9.14162 9.14162i −0.661464 0.661464i 0.294261 0.955725i \(-0.404927\pi\)
−0.955725 + 0.294261i \(0.904927\pi\)
\(192\) 0 0
\(193\) −2.90192 + 2.90192i −0.208885 + 0.208885i −0.803793 0.594908i \(-0.797188\pi\)
0.594908 + 0.803793i \(0.297188\pi\)
\(194\) 0.448288 + 0.258819i 0.0321852 + 0.0185821i
\(195\) 0 0
\(196\) 5.39230i 0.385165i
\(197\) 9.67784 + 5.58750i 0.689518 + 0.398093i 0.803431 0.595397i \(-0.203005\pi\)
−0.113914 + 0.993491i \(0.536339\pi\)
\(198\) 0 0
\(199\) 19.5885 + 19.5885i 1.38859 + 1.38859i 0.828291 + 0.560297i \(0.189313\pi\)
0.560297 + 0.828291i \(0.310687\pi\)
\(200\) −0.517638 1.93185i −0.0366025 0.136603i
\(201\) 0 0
\(202\) −0.571797 2.13397i −0.0402315 0.150146i
\(203\) 10.6066 + 2.84203i 0.744438 + 0.199471i
\(204\) 0 0
\(205\) 9.69615 2.59808i 0.677209 0.181458i
\(206\) 2.63896 4.57081i 0.183865 0.318463i
\(207\) 0 0
\(208\) 0.267949 0.267949i 0.0185789 0.0185789i
\(209\) −12.4877 3.34607i −0.863791 0.231452i
\(210\) 0 0
\(211\) −17.8038 −1.22567 −0.612834 0.790212i \(-0.709970\pi\)
−0.612834 + 0.790212i \(0.709970\pi\)
\(212\) 6.03579 0.414540
\(213\) 0 0
\(214\) −7.73205 7.73205i −0.528552 0.528552i
\(215\) −0.328169 0.568406i −0.0223810 0.0387650i
\(216\) 0 0
\(217\) −2.66025 + 9.92820i −0.180590 + 0.673970i
\(218\) 2.65754 1.53433i 0.179991 0.103918i
\(219\) 0 0
\(220\) 1.09808 + 4.09808i 0.0740323 + 0.276292i
\(221\) 2.44949 0.164771
\(222\) 0 0
\(223\) 18.3923 1.23164 0.615820 0.787887i \(-0.288825\pi\)
0.615820 + 0.787887i \(0.288825\pi\)
\(224\) 0.328169 + 1.22474i 0.0219267 + 0.0818317i
\(225\) 0 0
\(226\) 6.80385 3.92820i 0.452585 0.261300i
\(227\) 5.22715 19.5080i 0.346938 1.29479i −0.543394 0.839478i \(-0.682861\pi\)
0.890332 0.455312i \(-0.150472\pi\)
\(228\) 0 0
\(229\) −0.500000 0.866025i −0.0330409 0.0572286i 0.849032 0.528341i \(-0.177186\pi\)
−0.882073 + 0.471113i \(0.843853\pi\)
\(230\) 4.24264 + 4.24264i 0.279751 + 0.279751i
\(231\) 0 0
\(232\) −8.66025 −0.568574
\(233\) −9.38186 −0.614626 −0.307313 0.951609i \(-0.599430\pi\)
−0.307313 + 0.951609i \(0.599430\pi\)
\(234\) 0 0
\(235\) −7.09808 1.90192i −0.463027 0.124068i
\(236\) 4.24264 4.24264i 0.276172 0.276172i
\(237\) 0 0
\(238\) −4.09808 + 7.09808i −0.265639 + 0.460100i
\(239\) −22.8541 + 6.12372i −1.47831 + 0.396111i −0.905770 0.423769i \(-0.860707\pi\)
−0.572535 + 0.819880i \(0.694040\pi\)
\(240\) 0 0
\(241\) −13.2942 3.56218i −0.856357 0.229460i −0.196178 0.980568i \(-0.562853\pi\)
−0.660179 + 0.751108i \(0.729520\pi\)
\(242\) −1.29410 4.82963i −0.0831876 0.310460i
\(243\) 0 0
\(244\) −2.86603 10.6962i −0.183478 0.684751i
\(245\) −6.60420 6.60420i −0.421927 0.421927i
\(246\) 0 0
\(247\) −1.73205 1.00000i −0.110208 0.0636285i
\(248\) 8.10634i 0.514753i
\(249\) 0 0
\(250\) 10.5000 + 6.06218i 0.664078 + 0.383406i
\(251\) −5.13922 + 5.13922i −0.324384 + 0.324384i −0.850446 0.526062i \(-0.823668\pi\)
0.526062 + 0.850446i \(0.323668\pi\)
\(252\) 0 0
\(253\) 6.00000 + 6.00000i 0.377217 + 0.377217i
\(254\) −2.31079 0.619174i −0.144992 0.0388504i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −5.91567 + 1.58510i −0.369010 + 0.0988758i −0.438558 0.898703i \(-0.644511\pi\)
0.0695487 + 0.997579i \(0.477844\pi\)
\(258\) 0 0
\(259\) −7.22243 2.70577i −0.448780 0.168128i
\(260\) 0.656339i 0.0407044i
\(261\) 0 0
\(262\) −6.80385 + 3.92820i −0.420343 + 0.242685i
\(263\) −2.20925 3.82654i −0.136228 0.235954i 0.789838 0.613316i \(-0.210165\pi\)
−0.926066 + 0.377361i \(0.876831\pi\)
\(264\) 0 0
\(265\) −7.39230 + 7.39230i −0.454106 + 0.454106i
\(266\) 5.79555 3.34607i 0.355348 0.205160i
\(267\) 0 0
\(268\) 2.09808 3.63397i 0.128160 0.221980i
\(269\) 4.24264i 0.258678i 0.991600 + 0.129339i \(0.0412856\pi\)
−0.991600 + 0.129339i \(0.958714\pi\)
\(270\) 0 0
\(271\) 13.5622 23.4904i 0.823844 1.42694i −0.0789562 0.996878i \(-0.525159\pi\)
0.902800 0.430061i \(-0.141508\pi\)
\(272\) 1.67303 6.24384i 0.101443 0.378589i
\(273\) 0 0
\(274\) 15.5263 4.16025i 0.937977 0.251330i
\(275\) 4.24264 + 2.44949i 0.255841 + 0.147710i
\(276\) 0 0
\(277\) −7.06218 + 26.3564i −0.424325 + 1.58360i 0.341067 + 0.940039i \(0.389212\pi\)
−0.765392 + 0.643564i \(0.777455\pi\)
\(278\) −0.101536 + 0.378937i −0.00608972 + 0.0227272i
\(279\) 0 0
\(280\) −1.90192 1.09808i −0.113662 0.0656226i
\(281\) 27.5450 7.38065i 1.64320 0.440293i 0.685499 0.728073i \(-0.259584\pi\)
0.957696 + 0.287780i \(0.0929173\pi\)
\(282\) 0 0
\(283\) −5.22243 + 19.4904i −0.310441 + 1.15858i 0.617718 + 0.786400i \(0.288057\pi\)
−0.928159 + 0.372183i \(0.878609\pi\)
\(284\) −1.22474 + 2.12132i −0.0726752 + 0.125877i
\(285\) 0 0
\(286\) 0.928203i 0.0548858i
\(287\) −3.67423 + 6.36396i −0.216883 + 0.375653i
\(288\) 0 0
\(289\) 21.4641 12.3923i 1.26259 0.728959i
\(290\) 10.6066 10.6066i 0.622841 0.622841i
\(291\) 0 0
\(292\) 3.19615 + 5.53590i 0.187041 + 0.323964i
\(293\) −10.2462 + 5.91567i −0.598592 + 0.345597i −0.768488 0.639865i \(-0.778990\pi\)
0.169895 + 0.985462i \(0.445657\pi\)
\(294\) 0 0
\(295\) 10.3923i 0.605063i
\(296\) 6.05437 + 0.586988i 0.351903 + 0.0341180i
\(297\) 0 0
\(298\) 15.0622 4.03590i 0.872529 0.233793i
\(299\) 0.656339 + 1.13681i 0.0379571 + 0.0657435i
\(300\) 0 0
\(301\) 0.464102 + 0.124356i 0.0267504 + 0.00716774i
\(302\) 12.2474 + 12.2474i 0.704761 + 0.704761i
\(303\) 0 0
\(304\) −3.73205 + 3.73205i −0.214048 + 0.214048i
\(305\) 16.6102 + 9.58991i 0.951098 + 0.549117i
\(306\) 0 0
\(307\) 33.1244i 1.89051i 0.326337 + 0.945253i \(0.394186\pi\)
−0.326337 + 0.945253i \(0.605814\pi\)
\(308\) −2.68973 1.55291i −0.153261 0.0884855i
\(309\) 0 0
\(310\) 9.92820 + 9.92820i 0.563884 + 0.563884i
\(311\) 0.744272 + 2.77766i 0.0422038 + 0.157507i 0.983812 0.179204i \(-0.0573522\pi\)
−0.941608 + 0.336711i \(0.890686\pi\)
\(312\) 0 0
\(313\) 4.52628 + 16.8923i 0.255840 + 0.954810i 0.967621 + 0.252408i \(0.0812224\pi\)
−0.711781 + 0.702402i \(0.752111\pi\)
\(314\) −5.91567 1.58510i −0.333841 0.0894524i
\(315\) 0 0
\(316\) 3.36603 0.901924i 0.189354 0.0507372i
\(317\) 7.70882 13.3521i 0.432971 0.749927i −0.564157 0.825668i \(-0.690799\pi\)
0.997128 + 0.0757404i \(0.0241320\pi\)
\(318\) 0 0
\(319\) 15.0000 15.0000i 0.839839 0.839839i
\(320\) 1.67303 + 0.448288i 0.0935254 + 0.0250600i
\(321\) 0 0
\(322\) −4.39230 −0.244774
\(323\) −34.1170 −1.89832
\(324\) 0 0
\(325\) 0.535898 + 0.535898i 0.0297263 + 0.0297263i
\(326\) −0.189469 0.328169i −0.0104937 0.0181756i
\(327\) 0 0
\(328\) 1.50000 5.59808i 0.0828236 0.309102i
\(329\) 4.65874 2.68973i 0.256845 0.148289i
\(330\) 0 0
\(331\) 5.85641 + 21.8564i 0.321897 + 1.20134i 0.917394 + 0.397979i \(0.130288\pi\)
−0.595497 + 0.803357i \(0.703045\pi\)
\(332\) 3.58630 0.196824
\(333\) 0 0
\(334\) −24.9282 −1.36401
\(335\) 1.88108 + 7.02030i 0.102775 + 0.383560i
\(336\) 0 0
\(337\) −31.2846 + 18.0622i −1.70418 + 0.983910i −0.762757 + 0.646685i \(0.776155\pi\)
−0.941424 + 0.337224i \(0.890512\pi\)
\(338\) 3.32748 12.4183i 0.180991 0.675468i
\(339\) 0 0
\(340\) 5.59808 + 9.69615i 0.303598 + 0.525848i
\(341\) 14.0406 + 14.0406i 0.760341 + 0.760341i
\(342\) 0 0
\(343\) 15.7128 0.848412
\(344\) −0.378937 −0.0204309
\(345\) 0 0
\(346\) −15.5263 4.16025i −0.834698 0.223657i
\(347\) 13.3843 13.3843i 0.718505 0.718505i −0.249794 0.968299i \(-0.580363\pi\)
0.968299 + 0.249794i \(0.0803630\pi\)
\(348\) 0 0
\(349\) −2.76795 + 4.79423i −0.148165 + 0.256629i −0.930549 0.366167i \(-0.880670\pi\)
0.782384 + 0.622796i \(0.214003\pi\)
\(350\) −2.44949 + 0.656339i −0.130931 + 0.0350828i
\(351\) 0 0
\(352\) 2.36603 + 0.633975i 0.126110 + 0.0337910i
\(353\) −6.48408 24.1989i −0.345113 1.28798i −0.892480 0.451086i \(-0.851037\pi\)
0.547368 0.836892i \(-0.315630\pi\)
\(354\) 0 0
\(355\) −1.09808 4.09808i −0.0582798 0.217503i
\(356\) 3.01790 + 3.01790i 0.159948 + 0.159948i
\(357\) 0 0
\(358\) −19.3923 11.1962i −1.02492 0.591735i
\(359\) 3.10583i 0.163919i 0.996636 + 0.0819597i \(0.0261179\pi\)
−0.996636 + 0.0819597i \(0.973882\pi\)
\(360\) 0 0
\(361\) 7.66987 + 4.42820i 0.403678 + 0.233063i
\(362\) 12.1595 12.1595i 0.639090 0.639090i
\(363\) 0 0
\(364\) −0.339746 0.339746i −0.0178075 0.0178075i
\(365\) −10.6945 2.86559i −0.559778 0.149992i
\(366\) 0 0
\(367\) 14.5885 + 25.2679i 0.761511 + 1.31898i 0.942071 + 0.335412i \(0.108876\pi\)
−0.180560 + 0.983564i \(0.557791\pi\)
\(368\) 3.34607 0.896575i 0.174426 0.0467372i
\(369\) 0 0
\(370\) −8.13397 + 6.69615i −0.422865 + 0.348116i
\(371\) 7.65308i 0.397328i
\(372\) 0 0
\(373\) −6.06218 + 3.50000i −0.313888 + 0.181223i −0.648665 0.761074i \(-0.724672\pi\)
0.334777 + 0.942297i \(0.391339\pi\)
\(374\) 7.91688 + 13.7124i 0.409372 + 0.709053i
\(375\) 0 0
\(376\) −3.00000 + 3.00000i −0.154713 + 0.154713i
\(377\) 2.84203 1.64085i 0.146372 0.0845079i
\(378\) 0 0
\(379\) −4.56218 + 7.90192i −0.234343 + 0.405895i −0.959082 0.283130i \(-0.908627\pi\)
0.724738 + 0.689024i \(0.241961\pi\)
\(380\) 9.14162i 0.468955i
\(381\) 0 0
\(382\) 6.46410 11.1962i 0.330732 0.572845i
\(383\) −4.81105 + 17.9551i −0.245833 + 0.917461i 0.727130 + 0.686500i \(0.240854\pi\)
−0.972963 + 0.230961i \(0.925813\pi\)
\(384\) 0 0
\(385\) 5.19615 1.39230i 0.264820 0.0709584i
\(386\) −3.55412 2.05197i −0.180900 0.104443i
\(387\) 0 0
\(388\) −0.133975 + 0.500000i −0.00680153 + 0.0253837i
\(389\) 0.536220 2.00120i 0.0271875 0.101465i −0.950999 0.309194i \(-0.899941\pi\)
0.978186 + 0.207729i \(0.0666073\pi\)
\(390\) 0 0
\(391\) 19.3923 + 11.1962i 0.980711 + 0.566214i
\(392\) −5.20857 + 1.39563i −0.263072 + 0.0704900i
\(393\) 0 0
\(394\) −2.89230 + 10.7942i −0.145712 + 0.543805i
\(395\) −3.01790 + 5.22715i −0.151847 + 0.263006i
\(396\) 0 0
\(397\) 7.58846i 0.380854i 0.981701 + 0.190427i \(0.0609872\pi\)
−0.981701 + 0.190427i \(0.939013\pi\)
\(398\) −13.8511 + 23.9909i −0.694294 + 1.20255i
\(399\) 0 0
\(400\) 1.73205 1.00000i 0.0866025 0.0500000i
\(401\) −12.0716 + 12.0716i −0.602826 + 0.602826i −0.941062 0.338235i \(-0.890170\pi\)
0.338235 + 0.941062i \(0.390170\pi\)
\(402\) 0 0
\(403\) 1.53590 + 2.66025i 0.0765085 + 0.132517i
\(404\) 1.91327 1.10463i 0.0951887 0.0549572i
\(405\) 0 0
\(406\) 10.9808i 0.544966i
\(407\) −11.5032 + 9.46979i −0.570191 + 0.469400i
\(408\) 0 0
\(409\) 27.2583 7.30385i 1.34784 0.361152i 0.488501 0.872563i \(-0.337544\pi\)
0.859336 + 0.511411i \(0.170877\pi\)
\(410\) 5.01910 + 8.69333i 0.247876 + 0.429333i
\(411\) 0 0
\(412\) 5.09808 + 1.36603i 0.251164 + 0.0672992i
\(413\) −5.37945 5.37945i −0.264706 0.264706i
\(414\) 0 0
\(415\) −4.39230 + 4.39230i −0.215610 + 0.215610i
\(416\) 0.328169 + 0.189469i 0.0160898 + 0.00928947i
\(417\) 0 0
\(418\) 12.9282i 0.632339i
\(419\) 17.5390 + 10.1261i 0.856835 + 0.494694i 0.862951 0.505288i \(-0.168614\pi\)
−0.00611634 + 0.999981i \(0.501947\pi\)
\(420\) 0 0
\(421\) −10.8301 10.8301i −0.527828 0.527828i 0.392096 0.919924i \(-0.371750\pi\)
−0.919924 + 0.392096i \(0.871750\pi\)
\(422\) −4.60797 17.1972i −0.224313 0.837146i
\(423\) 0 0
\(424\) 1.56218 + 5.83013i 0.0758661 + 0.283136i
\(425\) 12.4877 + 3.34607i 0.605742 + 0.162308i
\(426\) 0 0
\(427\) −13.5622 + 3.63397i −0.656320 + 0.175860i
\(428\) 5.46739 9.46979i 0.264276 0.457740i
\(429\) 0 0
\(430\) 0.464102 0.464102i 0.0223810 0.0223810i
\(431\) 19.5080 + 5.22715i 0.939667 + 0.251783i 0.695972 0.718069i \(-0.254974\pi\)
0.243695 + 0.969852i \(0.421640\pi\)
\(432\) 0 0
\(433\) 18.8038 0.903655 0.451828 0.892105i \(-0.350772\pi\)
0.451828 + 0.892105i \(0.350772\pi\)
\(434\) −10.2784 −0.493381
\(435\) 0 0
\(436\) 2.16987 + 2.16987i 0.103918 + 0.103918i
\(437\) −9.14162 15.8338i −0.437303 0.757431i
\(438\) 0 0
\(439\) 7.66025 28.5885i 0.365604 1.36445i −0.500996 0.865449i \(-0.667033\pi\)
0.866600 0.499003i \(-0.166300\pi\)
\(440\) −3.67423 + 2.12132i −0.175162 + 0.101130i
\(441\) 0 0
\(442\) 0.633975 + 2.36603i 0.0301551 + 0.112540i
\(443\) 23.6627 1.12425 0.562124 0.827053i \(-0.309984\pi\)
0.562124 + 0.827053i \(0.309984\pi\)
\(444\) 0 0
\(445\) −7.39230 −0.350429
\(446\) 4.76028 + 17.7656i 0.225406 + 0.841226i
\(447\) 0 0
\(448\) −1.09808 + 0.633975i −0.0518792 + 0.0299525i
\(449\) 4.00240 14.9372i 0.188885 0.704929i −0.804880 0.593437i \(-0.797771\pi\)
0.993765 0.111492i \(-0.0355628\pi\)
\(450\) 0 0
\(451\) 7.09808 + 12.2942i 0.334235 + 0.578913i
\(452\) 5.55532 + 5.55532i 0.261300 + 0.261300i
\(453\) 0 0
\(454\) 20.1962 0.947852
\(455\) 0.832204 0.0390143
\(456\) 0 0
\(457\) 0.669873 + 0.179492i 0.0313353 + 0.00839628i 0.274453 0.961601i \(-0.411503\pi\)
−0.243117 + 0.969997i \(0.578170\pi\)
\(458\) 0.707107 0.707107i 0.0330409 0.0330409i
\(459\) 0 0
\(460\) −3.00000 + 5.19615i −0.139876 + 0.242272i
\(461\) 9.14162 2.44949i 0.425768 0.114084i −0.0395711 0.999217i \(-0.512599\pi\)
0.465339 + 0.885133i \(0.345932\pi\)
\(462\) 0 0
\(463\) −40.9545 10.9737i −1.90332 0.509992i −0.995979 0.0895888i \(-0.971445\pi\)
−0.907337 0.420403i \(-0.861889\pi\)
\(464\) −2.24144 8.36516i −0.104056 0.388343i
\(465\) 0 0
\(466\) −2.42820 9.06218i −0.112484 0.419797i
\(467\) −3.76217 3.76217i −0.174092 0.174092i 0.614682 0.788775i \(-0.289284\pi\)
−0.788775 + 0.614682i \(0.789284\pi\)
\(468\) 0 0
\(469\) −4.60770 2.66025i −0.212764 0.122839i
\(470\) 7.34847i 0.338960i
\(471\) 0 0
\(472\) 5.19615 + 3.00000i 0.239172 + 0.138086i
\(473\) 0.656339 0.656339i 0.0301785 0.0301785i
\(474\) 0 0
\(475\) −7.46410 7.46410i −0.342476 0.342476i
\(476\) −7.91688 2.12132i −0.362869 0.0972306i
\(477\) 0 0
\(478\) −11.8301 20.4904i −0.541097 0.937208i
\(479\) −2.68973 + 0.720710i −0.122897 + 0.0329301i −0.319743 0.947504i \(-0.603597\pi\)
0.196846 + 0.980434i \(0.436930\pi\)
\(480\) 0 0
\(481\) −2.09808 + 0.954483i −0.0956640 + 0.0435207i
\(482\) 13.7632i 0.626897i
\(483\) 0 0
\(484\) 4.33013 2.50000i 0.196824 0.113636i
\(485\) −0.448288 0.776457i −0.0203557 0.0352571i
\(486\) 0 0
\(487\) −9.26795 + 9.26795i −0.419971 + 0.419971i −0.885194 0.465223i \(-0.845974\pi\)
0.465223 + 0.885194i \(0.345974\pi\)
\(488\) 9.58991 5.53674i 0.434115 0.250636i
\(489\) 0 0
\(490\) 4.66987 8.08846i 0.210963 0.365399i
\(491\) 22.5259i 1.01658i −0.861186 0.508289i \(-0.830278\pi\)
0.861186 0.508289i \(-0.169722\pi\)
\(492\) 0 0
\(493\) 27.9904 48.4808i 1.26062 2.18346i
\(494\) 0.517638 1.93185i 0.0232896 0.0869181i
\(495\) 0 0
\(496\) 7.83013 2.09808i 0.351583 0.0942064i
\(497\) 2.68973 + 1.55291i 0.120651 + 0.0696577i
\(498\) 0 0
\(499\) 0.366025 1.36603i 0.0163855 0.0611517i −0.957249 0.289265i \(-0.906589\pi\)
0.973635 + 0.228113i \(0.0732557\pi\)
\(500\) −3.13801 + 11.7112i −0.140336 + 0.523742i
\(501\) 0 0
\(502\) −6.29423 3.63397i −0.280925 0.162192i
\(503\) −3.67423 + 0.984508i −0.163826 + 0.0438971i −0.339800 0.940498i \(-0.610359\pi\)
0.175974 + 0.984395i \(0.443693\pi\)
\(504\) 0 0
\(505\) −0.990381 + 3.69615i −0.0440714 + 0.164477i
\(506\) −4.24264 + 7.34847i −0.188608 + 0.326679i
\(507\) 0 0
\(508\) 2.39230i 0.106141i
\(509\) 3.46618 6.00361i 0.153636 0.266105i −0.778926 0.627116i \(-0.784235\pi\)
0.932561 + 0.361011i \(0.117568\pi\)
\(510\) 0 0
\(511\) 7.01924 4.05256i 0.310513 0.179275i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) −3.06218 5.30385i −0.135067 0.233943i
\(515\) −7.91688 + 4.57081i −0.348859 + 0.201414i
\(516\) 0 0
\(517\) 10.3923i 0.457053i
\(518\) 0.744272 7.67664i 0.0327014 0.337292i
\(519\) 0 0
\(520\) −0.633975 + 0.169873i −0.0278016 + 0.00744942i
\(521\) 13.9527 + 24.1667i 0.611277 + 1.05876i 0.991025 + 0.133674i \(0.0426774\pi\)
−0.379748 + 0.925090i \(0.623989\pi\)
\(522\) 0 0
\(523\) −31.5885 8.46410i −1.38127 0.370109i −0.509686 0.860361i \(-0.670238\pi\)
−0.871581 + 0.490251i \(0.836905\pi\)
\(524\) −5.55532 5.55532i −0.242685 0.242685i
\(525\) 0 0
\(526\) 3.12436 3.12436i 0.136228 0.136228i
\(527\) 45.3799 + 26.2001i 1.97678 + 1.14129i
\(528\) 0 0
\(529\) 11.0000i 0.478261i
\(530\) −9.05369 5.22715i −0.393267 0.227053i
\(531\) 0 0
\(532\) 4.73205 + 4.73205i 0.205160 + 0.205160i
\(533\) 0.568406 + 2.12132i 0.0246204 + 0.0918846i
\(534\) 0 0
\(535\) 4.90192 + 18.2942i 0.211929 + 0.790928i
\(536\) 4.05317 + 1.08604i 0.175070 + 0.0469100i
\(537\) 0 0
\(538\) −4.09808 + 1.09808i −0.176681 + 0.0473414i
\(539\) 6.60420 11.4388i 0.284463 0.492704i
\(540\) 0 0
\(541\) 19.4186 19.4186i 0.834870 0.834870i −0.153308 0.988178i \(-0.548993\pi\)
0.988178 + 0.153308i \(0.0489927\pi\)
\(542\) 26.2001 + 7.02030i 1.12539 + 0.301548i
\(543\) 0 0
\(544\) 6.46410 0.277146
\(545\) −5.31508 −0.227673
\(546\) 0 0
\(547\) −28.3205 28.3205i −1.21090 1.21090i −0.970732 0.240166i \(-0.922798\pi\)
−0.240166 0.970732i \(-0.577202\pi\)
\(548\) 8.03699 + 13.9205i 0.343323 + 0.594653i
\(549\) 0 0
\(550\) −1.26795 + 4.73205i −0.0540655 + 0.201775i
\(551\) −39.5844 + 22.8541i −1.68635 + 0.973615i
\(552\) 0 0
\(553\) −1.14359 4.26795i −0.0486305 0.181492i
\(554\) −27.2862 −1.15928
\(555\) 0 0
\(556\) −0.392305 −0.0166374
\(557\) −4.53862 16.9384i −0.192308 0.717702i −0.992947 0.118556i \(-0.962174\pi\)
0.800640 0.599146i \(-0.204493\pi\)
\(558\) 0 0
\(559\) 0.124356 0.0717968i 0.00525968 0.00303668i
\(560\) 0.568406 2.12132i 0.0240195 0.0896421i
\(561\) 0 0
\(562\) 14.2583 + 24.6962i 0.601451 + 1.04174i
\(563\) −28.7375 28.7375i −1.21114 1.21114i −0.970651 0.240492i \(-0.922691\pi\)
−0.240492 0.970651i \(-0.577309\pi\)
\(564\) 0 0
\(565\) −13.6077 −0.572480
\(566\) −20.1779 −0.848142
\(567\) 0 0
\(568\) −2.36603 0.633975i −0.0992762 0.0266010i
\(569\) 17.7148 17.7148i 0.742644 0.742644i −0.230442 0.973086i \(-0.574017\pi\)
0.973086 + 0.230442i \(0.0740171\pi\)
\(570\) 0 0
\(571\) 12.9282 22.3923i 0.541028 0.937089i −0.457817 0.889047i \(-0.651368\pi\)
0.998845 0.0480423i \(-0.0152982\pi\)
\(572\) −0.896575 + 0.240237i −0.0374877 + 0.0100448i
\(573\) 0 0
\(574\) −7.09808 1.90192i −0.296268 0.0793848i
\(575\) 1.79315 + 6.69213i 0.0747796 + 0.279081i
\(576\) 0 0
\(577\) −3.70577 13.8301i −0.154273 0.575756i −0.999166 0.0408207i \(-0.987003\pi\)
0.844893 0.534935i \(-0.179664\pi\)
\(578\) 17.5254 + 17.5254i 0.728959 + 0.728959i
\(579\) 0 0
\(580\) 12.9904 + 7.50000i 0.539396 + 0.311421i
\(581\) 4.54725i 0.188652i
\(582\) 0 0
\(583\) −12.8038 7.39230i −0.530281 0.306158i
\(584\) −4.52004 + 4.52004i −0.187041 + 0.187041i
\(585\) 0 0
\(586\) −8.36603 8.36603i −0.345597 0.345597i
\(587\) −12.4877 3.34607i −0.515422 0.138107i −0.00827376 0.999966i \(-0.502634\pi\)
−0.507148 + 0.861859i \(0.669300\pi\)
\(588\) 0 0
\(589\) −21.3923 37.0526i −0.881455 1.52672i
\(590\) −10.0382 + 2.68973i −0.413266 + 0.110734i
\(591\) 0 0
\(592\) 1.00000 + 6.00000i 0.0410997 + 0.246598i
\(593\) 21.1488i 0.868478i −0.900798 0.434239i \(-0.857017\pi\)
0.900798 0.434239i \(-0.142983\pi\)
\(594\) 0 0
\(595\) 12.2942 7.09808i 0.504014 0.290993i
\(596\) 7.79676 + 13.5044i 0.319368 + 0.553161i
\(597\) 0 0
\(598\) −0.928203 + 0.928203i −0.0379571 + 0.0379571i
\(599\) 14.4331 8.33298i 0.589722 0.340476i −0.175266 0.984521i \(-0.556078\pi\)
0.764988 + 0.644045i \(0.222745\pi\)
\(600\) 0 0
\(601\) −12.2321 + 21.1865i −0.498956 + 0.864217i −0.999999 0.00120537i \(-0.999616\pi\)
0.501044 + 0.865422i \(0.332950\pi\)
\(602\) 0.480473i 0.0195826i
\(603\) 0 0
\(604\) −8.66025 + 15.0000i −0.352381 + 0.610341i
\(605\) −2.24144 + 8.36516i −0.0911274 + 0.340092i
\(606\) 0 0
\(607\) −37.4904 + 10.0455i −1.52169 + 0.407735i −0.920297 0.391220i \(-0.872053\pi\)
−0.601391 + 0.798955i \(0.705386\pi\)
\(608\) −4.57081 2.63896i −0.185371 0.107024i
\(609\) 0 0
\(610\) −4.96410 + 18.5263i −0.200991 + 0.750107i
\(611\) 0.416102 1.55291i 0.0168337 0.0628242i
\(612\) 0 0
\(613\) 26.0885 + 15.0622i 1.05370 + 0.608356i 0.923684 0.383156i \(-0.125163\pi\)
0.130019 + 0.991511i \(0.458496\pi\)
\(614\) −31.9957 + 8.57321i −1.29124 + 0.345987i
\(615\) 0 0
\(616\) 0.803848 3.00000i 0.0323879 0.120873i
\(617\) −17.4746 + 30.2669i −0.703501 + 1.21850i 0.263729 + 0.964597i \(0.415048\pi\)
−0.967230 + 0.253902i \(0.918286\pi\)
\(618\) 0 0
\(619\) 44.1962i 1.77639i −0.459463 0.888197i \(-0.651958\pi\)
0.459463 0.888197i \(-0.348042\pi\)
\(620\) −7.02030 + 12.1595i −0.281942 + 0.488338i
\(621\) 0 0
\(622\) −2.49038 + 1.43782i −0.0998552 + 0.0576514i
\(623\) 3.82654 3.82654i 0.153307 0.153307i
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) −15.1452 + 8.74410i −0.605325 + 0.349485i
\(627\) 0 0
\(628\) 6.12436i 0.244388i
\(629\) −22.8541 + 31.9957i −0.911251 + 1.27575i
\(630\) 0 0
\(631\) 10.6603 2.85641i 0.424378 0.113712i −0.0403079 0.999187i \(-0.512834\pi\)
0.464686 + 0.885476i \(0.346167\pi\)
\(632\) 1.74238 + 3.01790i 0.0693083 + 0.120045i
\(633\) 0 0
\(634\) 14.8923 + 3.99038i 0.591449 + 0.158478i
\(635\) 2.92996 + 2.92996i 0.116272 + 0.116272i
\(636\) 0 0
\(637\) 1.44486 1.44486i 0.0572476 0.0572476i
\(638\) 18.3712 + 10.6066i 0.727322 + 0.419919i
\(639\) 0 0
\(640\) 1.73205i 0.0684653i
\(641\) −42.3299 24.4392i −1.67193 0.965288i −0.966557 0.256450i \(-0.917447\pi\)
−0.705371 0.708838i \(-0.749220\pi\)
\(642\) 0 0
\(643\) −13.3397 13.3397i −0.526068 0.526068i 0.393329 0.919398i \(-0.371323\pi\)
−0.919398 + 0.393329i \(0.871323\pi\)
\(644\) −1.13681 4.24264i −0.0447967 0.167183i
\(645\) 0 0
\(646\) −8.83013 32.9545i −0.347417 1.29658i
\(647\) 26.8565 + 7.19617i 1.05584 + 0.282910i 0.744662 0.667442i \(-0.232611\pi\)
0.311175 + 0.950353i \(0.399278\pi\)
\(648\) 0 0
\(649\) −14.1962 + 3.80385i −0.557248 + 0.149314i
\(650\) −0.378937 + 0.656339i −0.0148631 + 0.0257437i
\(651\) 0 0
\(652\) 0.267949 0.267949i 0.0104937 0.0104937i
\(653\) 13.5923 + 3.64205i 0.531908 + 0.142524i 0.514769 0.857329i \(-0.327878\pi\)
0.0171389 + 0.999853i \(0.494544\pi\)
\(654\) 0 0
\(655\) 13.6077 0.531697
\(656\) 5.79555 0.226278
\(657\) 0 0
\(658\) 3.80385 + 3.80385i 0.148289 + 0.148289i
\(659\) −17.8671 30.9468i −0.696005 1.20552i −0.969841 0.243739i \(-0.921626\pi\)
0.273836 0.961776i \(-0.411707\pi\)
\(660\) 0 0
\(661\) −7.55256 + 28.1865i −0.293760 + 1.09633i 0.648436 + 0.761269i \(0.275423\pi\)
−0.942197 + 0.335060i \(0.891243\pi\)
\(662\) −19.5959 + 11.3137i −0.761617 + 0.439720i
\(663\) 0 0
\(664\) 0.928203 + 3.46410i 0.0360213 + 0.134433i
\(665\) −11.5911 −0.449484
\(666\) 0 0
\(667\) 30.0000 1.16160
\(668\) −6.45189 24.0788i −0.249631 0.931637i
\(669\) 0 0
\(670\) −6.29423 + 3.63397i −0.243167 + 0.140393i
\(671\) −7.02030 + 26.2001i −0.271016 + 1.01144i
\(672\) 0 0
\(673\) 11.6603 + 20.1962i 0.449470 + 0.778504i 0.998352 0.0573955i \(-0.0182796\pi\)
−0.548882 + 0.835900i \(0.684946\pi\)
\(674\) −25.5438 25.5438i −0.983910 0.983910i
\(675\) 0 0
\(676\) 12.8564 0.494477
\(677\) 20.3166 0.780831 0.390416 0.920639i \(-0.372331\pi\)
0.390416 + 0.920639i \(0.372331\pi\)
\(678\) 0 0
\(679\) 0.633975 + 0.169873i 0.0243297 + 0.00651913i
\(680\) −7.91688 + 7.91688i −0.303598 + 0.303598i
\(681\) 0 0
\(682\) −9.92820 + 17.1962i −0.380171 + 0.658475i
\(683\) −14.3688 + 3.85010i −0.549806 + 0.147320i −0.523019 0.852321i \(-0.675194\pi\)
−0.0267869 + 0.999641i \(0.508528\pi\)
\(684\) 0 0
\(685\) −26.8923 7.20577i −1.02750 0.275318i
\(686\) 4.06678 + 15.1774i 0.155270 + 0.579476i
\(687\) 0 0
\(688\) −0.0980762 0.366025i −0.00373912 0.0139546i
\(689\) −1.61729 1.61729i −0.0616137 0.0616137i
\(690\) 0 0
\(691\) −19.5622 11.2942i −0.744180 0.429653i 0.0794069 0.996842i \(-0.474697\pi\)
−0.823587 + 0.567190i \(0.808031\pi\)
\(692\) 16.0740i 0.611041i
\(693\) 0 0
\(694\) 16.3923 + 9.46410i 0.622243 + 0.359252i
\(695\) 0.480473 0.480473i 0.0182254 0.0182254i
\(696\) 0 0
\(697\) 26.4904 + 26.4904i 1.00339 + 1.00339i
\(698\) −5.34727 1.43280i −0.202397 0.0542321i
\(699\) 0 0
\(700\) −1.26795 2.19615i −0.0479240 0.0830068i
\(701\) 15.8338 4.24264i 0.598033 0.160242i 0.0529108 0.998599i \(-0.483150\pi\)
0.545122 + 0.838357i \(0.316483\pi\)
\(702\) 0 0
\(703\) 29.2224 13.2942i 1.10214 0.501401i
\(704\) 2.44949i 0.0923186i
\(705\) 0 0
\(706\) 21.6962 12.5263i 0.816545 0.471433i
\(707\) −1.40061 2.42593i −0.0526754 0.0912364i
\(708\) 0 0
\(709\) −25.9282 + 25.9282i −0.973754 + 0.973754i −0.999664 0.0259102i \(-0.991752\pi\)
0.0259102 + 0.999664i \(0.491752\pi\)
\(710\) 3.67423 2.12132i 0.137892 0.0796117i
\(711\) 0 0
\(712\) −2.13397 + 3.69615i −0.0799741 + 0.138519i
\(713\) 28.0812i 1.05165i
\(714\) 0 0
\(715\) 0.803848 1.39230i 0.0300622 0.0520692i
\(716\) 5.79555 21.6293i 0.216590 0.808325i
\(717\) 0 0
\(718\) −3.00000 + 0.803848i −0.111959 + 0.0299993i
\(719\) 10.8704 + 6.27603i 0.405398 + 0.234056i 0.688810 0.724942i \(-0.258133\pi\)
−0.283413 + 0.958998i \(0.591467\pi\)
\(720\) 0 0
\(721\) 1.73205 6.46410i 0.0645049 0.240736i
\(722\) −2.29221 + 8.55463i −0.0853071 + 0.318370i
\(723\) 0 0
\(724\) 14.8923 + 8.59808i 0.553468 + 0.319545i
\(725\) 16.7303 4.48288i 0.621349 0.166490i
\(726\) 0 0
\(727\) −11.4641 + 42.7846i −0.425180 + 1.58679i 0.338350 + 0.941020i \(0.390131\pi\)
−0.763530 + 0.645773i \(0.776535\pi\)
\(728\) 0.240237 0.416102i 0.00890376 0.0154218i
\(729\) 0 0
\(730\) 11.0718i 0.409786i
\(731\) 1.22474 2.12132i 0.0452988 0.0784599i
\(732\) 0 0
\(733\) 6.00000 3.46410i 0.221615 0.127950i −0.385083 0.922882i \(-0.625827\pi\)
0.606698 + 0.794933i \(0.292494\pi\)
\(734\) −20.6312 + 20.6312i −0.761511 + 0.761511i
\(735\) 0 0
\(736\) 1.73205 + 3.00000i 0.0638442 + 0.110581i
\(737\) −8.90138 + 5.13922i −0.327887 + 0.189305i
\(738\) 0 0
\(739\) 28.3923i 1.04443i −0.852815 0.522214i \(-0.825106\pi\)
0.852815 0.522214i \(-0.174894\pi\)
\(740\) −8.57321 6.12372i −0.315158 0.225113i
\(741\) 0 0
\(742\) 7.39230 1.98076i 0.271380 0.0727161i
\(743\) 2.12132 + 3.67423i 0.0778237 + 0.134795i 0.902311 0.431086i \(-0.141870\pi\)
−0.824487 + 0.565881i \(0.808536\pi\)
\(744\) 0 0
\(745\) −26.0885 6.99038i −0.955807 0.256108i
\(746\) −4.94975 4.94975i −0.181223 0.181223i
\(747\) 0 0
\(748\) −11.1962 + 11.1962i −0.409372 + 0.409372i
\(749\) −12.0072 6.93237i −0.438734 0.253303i
\(750\) 0 0
\(751\) 50.5885i 1.84600i −0.384801 0.923000i \(-0.625730\pi\)
0.384801 0.923000i \(-0.374270\pi\)
\(752\) −3.67423 2.12132i −0.133986 0.0773566i
\(753\) 0 0
\(754\) 2.32051 + 2.32051i 0.0845079 + 0.0845079i
\(755\) −7.76457 28.9778i −0.282582 1.05461i
\(756\) 0 0
\(757\) 9.91858 + 37.0167i 0.360497 + 1.34539i 0.873424 + 0.486961i \(0.161895\pi\)
−0.512927 + 0.858432i \(0.671439\pi\)
\(758\) −8.81345 2.36156i −0.320119 0.0857756i
\(759\) 0 0
\(760\) 8.83013 2.36603i 0.320302 0.0858248i
\(761\) −0.776457 + 1.34486i −0.0281465 + 0.0487513i −0.879756 0.475426i \(-0.842294\pi\)
0.851609 + 0.524178i \(0.175627\pi\)
\(762\) 0 0
\(763\) 2.75129 2.75129i 0.0996033 0.0996033i
\(764\) 12.4877 + 3.34607i 0.451789 + 0.121056i
\(765\) 0 0
\(766\) −18.5885 −0.671628
\(767\) −2.27362 −0.0820958
\(768\) 0 0
\(769\) −27.1962 27.1962i −0.980718 0.980718i 0.0190993 0.999818i \(-0.493920\pi\)
−0.999818 + 0.0190993i \(0.993920\pi\)
\(770\) 2.68973 + 4.65874i 0.0969310 + 0.167889i
\(771\) 0 0
\(772\) 1.06218 3.96410i 0.0382286 0.142671i
\(773\) −14.0728 + 8.12493i −0.506163 + 0.292233i −0.731255 0.682104i \(-0.761065\pi\)
0.225092 + 0.974337i \(0.427732\pi\)
\(774\) 0 0
\(775\) 4.19615 + 15.6603i 0.150730 + 0.562533i
\(776\) −0.517638 −0.0185821
\(777\) 0 0
\(778\) 2.07180 0.0742775
\(779\) −7.91688 29.5462i −0.283651 1.05860i
\(780\) 0 0
\(781\) 5.19615 3.00000i 0.185933 0.107348i
\(782\) −5.79555 + 21.6293i −0.207249 + 0.773462i
\(783\) 0 0
\(784\) −2.69615 4.66987i −0.0962912 0.166781i
\(785\) 7.50077 + 7.50077i 0.267714 + 0.267714i
\(786\) 0 0
\(787\) 8.00000 0.285169 0.142585 0.989783i \(-0.454459\pi\)
0.142585 + 0.989783i \(0.454459\pi\)
\(788\) −11.1750 −0.398093
\(789\) 0 0
\(790\) −5.83013 1.56218i −0.207427 0.0555798i
\(791\) 7.04386 7.04386i 0.250451 0.250451i
\(792\) 0 0
\(793\) −2.09808 + 3.63397i −0.0745049 + 0.129046i
\(794\) −7.32989 + 1.96404i −0.260128 + 0.0697011i
\(795\) 0 0
\(796\) −26.7583 7.16987i −0.948424 0.254129i
\(797\) 3.52193 + 13.1440i 0.124753 + 0.465585i 0.999831 0.0183975i \(-0.00585643\pi\)
−0.875078 + 0.483983i \(0.839190\pi\)
\(798\) 0 0
\(799\) −7.09808 26.4904i −0.251112 0.937162i
\(800\) 1.41421 + 1.41421i 0.0500000 + 0.0500000i
\(801\) 0 0
\(802\) −14.7846 8.53590i −0.522063 0.301413i
\(803\) 15.6579i 0.552555i
\(804\) 0 0
\(805\) 6.58846 + 3.80385i 0.232213 + 0.134068i
\(806\) −2.17209 + 2.17209i −0.0765085 + 0.0765085i
\(807\) 0 0
\(808\) 1.56218 + 1.56218i 0.0549572 + 0.0549572i
\(809\) 6.69213 + 1.79315i 0.235283 + 0.0630438i 0.374534 0.927213i \(-0.377803\pi\)
−0.139251 + 0.990257i \(0.544469\pi\)
\(810\) 0 0
\(811\) −15.0000 25.9808i −0.526721 0.912308i −0.999515 0.0311349i \(-0.990088\pi\)
0.472794 0.881173i \(-0.343245\pi\)
\(812\) −10.6066 + 2.84203i −0.372219 + 0.0997357i
\(813\) 0 0
\(814\) −12.1244 8.66025i −0.424958 0.303542i
\(815\) 0.656339i 0.0229905i
\(816\) 0 0
\(817\) −1.73205 + 1.00000i −0.0605968 + 0.0349856i
\(818\) 14.1100 + 24.4392i 0.493343 + 0.854495i
\(819\) 0 0
\(820\) −7.09808 + 7.09808i −0.247876 + 0.247876i
\(821\) 44.6592 25.7840i 1.55862 0.899868i 0.561228 0.827661i \(-0.310329\pi\)
0.997390 0.0722070i \(-0.0230042\pi\)
\(822\) 0 0
\(823\) −16.0000 + 27.7128i −0.557725 + 0.966008i 0.439961 + 0.898017i \(0.354992\pi\)
−0.997686 + 0.0679910i \(0.978341\pi\)
\(824\) 5.27792i 0.183865i
\(825\) 0 0
\(826\) 3.80385 6.58846i 0.132353 0.229242i
\(827\) 10.7589 40.1528i 0.374124 1.39625i −0.480497 0.876996i \(-0.659544\pi\)
0.854621 0.519253i \(-0.173790\pi\)
\(828\) 0 0
\(829\) 46.4186 12.4378i 1.61218 0.431983i 0.663492 0.748184i \(-0.269074\pi\)
0.948692 + 0.316200i \(0.102407\pi\)
\(830\) −5.37945 3.10583i −0.186724 0.107805i
\(831\) 0 0
\(832\) −0.0980762 + 0.366025i −0.00340018 + 0.0126896i
\(833\) 9.02150 33.6687i 0.312577 1.16655i
\(834\) 0 0
\(835\) 37.3923 + 21.5885i 1.29401 + 0.747099i
\(836\) 12.4877 3.34607i 0.431896 0.115726i
\(837\) 0 0
\(838\) −5.24167 + 19.5622i −0.181070 + 0.675764i
\(839\) −12.9038 + 22.3500i −0.445488 + 0.771608i −0.998086 0.0618398i \(-0.980303\pi\)
0.552598 + 0.833448i \(0.313637\pi\)
\(840\) 0 0
\(841\) 46.0000i 1.58621i
\(842\) 7.65806 13.2641i 0.263914 0.457113i
\(843\) 0 0
\(844\) 15.4186 8.90192i 0.530730 0.306417i
\(845\) −15.7458 + 15.7458i −0.541673 + 0.541673i
\(846\) 0 0
\(847\) −3.16987 5.49038i −0.108918 0.188652i
\(848\) −5.22715 + 3.01790i −0.179501 + 0.103635i
\(849\) 0 0
\(850\) 12.9282i 0.443434i
\(851\) −20.9730 2.03339i −0.718944 0.0697036i
\(852\) 0 0
\(853\) 0.0358984 0.00961894i 0.00122914 0.000329346i −0.258204 0.966090i \(-0.583131\pi\)
0.259434 + 0.965761i \(0.416464\pi\)
\(854\) −7.02030 12.1595i −0.240230 0.416090i
\(855\) 0 0
\(856\) 10.5622 + 2.83013i 0.361008 + 0.0967318i
\(857\) 20.6448 + 20.6448i 0.705213 + 0.705213i 0.965525 0.260312i \(-0.0838253\pi\)
−0.260312 + 0.965525i \(0.583825\pi\)
\(858\) 0 0
\(859\) −29.0000 + 29.0000i −0.989467 + 0.989467i −0.999945 0.0104779i \(-0.996665\pi\)
0.0104779 + 0.999945i \(0.496665\pi\)
\(860\) 0.568406 + 0.328169i 0.0193825 + 0.0111905i
\(861\) 0 0
\(862\) 20.1962i 0.687884i
\(863\) 8.18067 + 4.72311i 0.278473 + 0.160777i 0.632732 0.774371i \(-0.281933\pi\)
−0.354259 + 0.935147i \(0.615267\pi\)
\(864\) 0 0
\(865\) 19.6865 + 19.6865i 0.669362 + 0.669362i
\(866\) 4.86679 + 18.1631i 0.165380 + 0.617208i
\(867\) 0 0
\(868\) −2.66025 9.92820i −0.0902949 0.336985i
\(869\) −8.24504 2.20925i −0.279694 0.0749438i
\(870\) 0 0
\(871\) −1.53590 + 0.411543i −0.0520419 + 0.0139446i
\(872\) −1.53433 + 2.65754i −0.0519590 + 0.0899957i
\(873\) 0 0
\(874\) 12.9282 12.9282i 0.437303 0.437303i
\(875\) 14.8492 + 3.97884i 0.501996 + 0.134509i
\(876\) 0 0
\(877\) 55.7321 1.88194 0.940969 0.338493i \(-0.109917\pi\)
0.940969 + 0.338493i \(0.109917\pi\)
\(878\) 29.5969 0.998849
\(879\) 0 0
\(880\) −3.00000 3.00000i −0.101130 0.101130i
\(881\) −10.0060 17.3309i −0.337111 0.583893i 0.646777 0.762679i \(-0.276116\pi\)
−0.983888 + 0.178786i \(0.942783\pi\)
\(882\) 0 0
\(883\) −6.53590 + 24.3923i −0.219950 + 0.820866i 0.764414 + 0.644725i \(0.223028\pi\)
−0.984365 + 0.176141i \(0.943638\pi\)
\(884\) −2.12132 + 1.22474i −0.0713477 + 0.0411926i
\(885\) 0 0
\(886\) 6.12436 + 22.8564i 0.205752 + 0.767876i
\(887\) 31.1870 1.04716 0.523579 0.851977i \(-0.324597\pi\)
0.523579 + 0.851977i \(0.324597\pi\)
\(888\) 0 0
\(889\) −3.03332 −0.101734
\(890\) −1.91327 7.14042i −0.0641329 0.239347i
\(891\) 0 0
\(892\) −15.9282 + 9.19615i −0.533316 + 0.307910i
\(893\) −5.79555 + 21.6293i −0.193941 + 0.723797i
\(894\) 0 0
\(895\) 19.3923 + 33.5885i 0.648213 + 1.12274i
\(896\) −0.896575 0.896575i −0.0299525 0.0299525i
\(897\) 0 0
\(898\) 15.4641 0.516044
\(899\) 70.2030 2.34140
\(900\) 0 0
\(901\) −37.6865 10.0981i −1.25552 0.336416i
\(902\) −10.0382 + 10.0382i −0.334235 + 0.334235i
\(903\) 0 0
\(904\) −3.92820 + 6.80385i −0.130650 + 0.226293i
\(905\) −28.7697 + 7.70882i −0.956338 + 0.256250i
\(906\) 0 0
\(907\) 3.56218 + 0.954483i 0.118280 + 0.0316931i 0.317474 0.948267i \(-0.397166\pi\)
−0.199193 + 0.979960i \(0.563832\pi\)
\(908\) 5.22715 + 19.5080i 0.173469 + 0.647395i
\(909\) 0 0
\(910\) 0.215390 + 0.803848i 0.00714012 + 0.0266473i
\(911\) 12.7279 + 12.7279i 0.421695 + 0.421695i 0.885787 0.464092i \(-0.153619\pi\)
−0.464092 + 0.885787i \(0.653619\pi\)
\(912\) 0 0
\(913\) −7.60770 4.39230i −0.251778 0.145364i
\(914\) 0.693504i 0.0229391i
\(915\) 0 0
\(916\) 0.866025 + 0.500000i 0.0286143 + 0.0165205i
\(917\) −7.04386 + 7.04386i −0.232609 + 0.232609i
\(918\) 0 0
\(919\) −11.1244 11.1244i −0.366959 0.366959i 0.499408 0.866367i \(-0.333551\pi\)
−0.866367 + 0.499408i \(0.833551\pi\)
\(920\) −5.79555 1.55291i −0.191074 0.0511981i
\(921\) 0 0
\(922\) 4.73205 + 8.19615i 0.155842 + 0.269926i
\(923\) 0.896575 0.240237i 0.0295111 0.00790749i
\(924\) 0 0
\(925\) −12.0000 + 2.00000i −0.394558 + 0.0657596i
\(926\) 42.3992i 1.39332i
\(927\) 0 0
\(928\) 7.50000 4.33013i 0.246200 0.142143i
\(929\) 7.55652 + 13.0883i 0.247921 + 0.429412i 0.962949 0.269684i \(-0.0869192\pi\)
−0.715028 + 0.699096i \(0.753586\pi\)
\(930\) 0 0
\(931\) −20.1244 + 20.1244i −0.659549 + 0.659549i
\(932\) 8.12493 4.69093i 0.266141 0.153656i
\(933\) 0 0
\(934\) 2.66025 4.60770i 0.0870462 0.150768i
\(935\) 27.4249i 0.896889i
\(936\) 0 0
\(937\) 7.59808 13.1603i 0.248218 0.429927i −0.714813 0.699315i \(-0.753488\pi\)
0.963032 + 0.269389i \(0.0868216\pi\)
\(938\) 1.37705 5.13922i 0.0449622 0.167801i
\(939\) 0 0
\(940\) 7.09808 1.90192i 0.231514 0.0620339i
\(941\) −13.1998 7.62089i −0.430300 0.248434i 0.269174 0.963091i \(-0.413249\pi\)
−0.699475 + 0.714658i \(0.746583\pi\)
\(942\) 0 0
\(943\) −5.19615 + 19.3923i −0.169210 + 0.631500i
\(944\) −1.55291 + 5.79555i −0.0505431 + 0.188629i
\(945\) 0 0
\(946\) 0.803848 + 0.464102i 0.0261353 + 0.0150892i
\(947\) 27.6651 7.41284i 0.898995 0.240885i 0.220410 0.975407i \(-0.429260\pi\)
0.678585 + 0.734522i \(0.262594\pi\)
\(948\) 0 0
\(949\) 0.626933 2.33975i 0.0203511 0.0759514i
\(950\) 5.27792 9.14162i 0.171238 0.296593i
\(951\) 0 0
\(952\) 8.19615i 0.265639i
\(953\) −7.26054 + 12.5756i −0.235192 + 0.407364i −0.959328 0.282292i \(-0.908905\pi\)
0.724137 + 0.689657i \(0.242239\pi\)
\(954\) 0 0
\(955\) −19.3923 + 11.1962i −0.627520 + 0.362299i
\(956\) 16.7303 16.7303i 0.541097 0.541097i
\(957\) 0 0
\(958\) −1.39230 2.41154i −0.0449833 0.0779134i
\(959\) 17.6505 10.1905i 0.569963 0.329068i
\(960\) 0 0
\(961\) 34.7128i 1.11977i
\(962\) −1.46498 1.77955i −0.0472329 0.0573749i
\(963\) 0 0
\(964\) 13.2942 3.56218i 0.428178 0.114730i
\(965\) 3.55412 + 6.15591i 0.114411 + 0.198166i
\(966\) 0 0
\(967\) −12.2679 3.28719i −0.394511 0.105709i 0.0561095 0.998425i \(-0.482130\pi\)
−0.450620 + 0.892716i \(0.648797\pi\)
\(968\) 3.53553 + 3.53553i 0.113636 + 0.113636i
\(969\) 0 0
\(970\) 0.633975 0.633975i 0.0203557 0.0203557i
\(971\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(972\) 0 0
\(973\) 0.497423i 0.0159466i
\(974\) −11.3509 6.55343i −0.363705 0.209985i
\(975\) 0 0
\(976\) 7.83013 + 7.83013i 0.250636 + 0.250636i
\(977\) −13.5601 50.6071i −0.433827 1.61906i −0.743858 0.668338i \(-0.767006\pi\)
0.310031 0.950726i \(-0.399660\pi\)
\(978\) 0 0
\(979\) −2.70577 10.0981i −0.0864768 0.322736i
\(980\) 9.02150 + 2.41730i 0.288181 + 0.0772179i
\(981\) 0 0
\(982\) 21.7583 5.83013i 0.694336 0.186047i
\(983\) −12.1595 + 21.0609i −0.387828 + 0.671738i −0.992157 0.124997i \(-0.960108\pi\)
0.604329 + 0.796735i \(0.293441\pi\)
\(984\) 0 0
\(985\) 13.6865 13.6865i 0.436089 0.436089i
\(986\) 54.0733 + 14.4889i 1.72204 + 0.461420i
\(987\) 0 0
\(988\) 2.00000 0.0636285
\(989\) 1.31268 0.0417407
\(990\) 0 0
\(991\) 34.6603 + 34.6603i 1.10102 + 1.10102i 0.994288 + 0.106731i \(0.0340385\pi\)
0.106731 + 0.994288i \(0.465962\pi\)
\(992\) 4.05317 + 7.02030i 0.128688 + 0.222895i
\(993\) 0 0
\(994\) −0.803848 + 3.00000i −0.0254965 + 0.0951542i
\(995\) 41.5534 23.9909i 1.31733 0.760561i
\(996\) 0 0
\(997\) 8.04552 + 30.0263i 0.254804 + 0.950942i 0.968199 + 0.250180i \(0.0804898\pi\)
−0.713395 + 0.700762i \(0.752844\pi\)
\(998\) 1.41421 0.0447661
\(999\) 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 666.2.be.c.125.2 yes 8
3.2 odd 2 inner 666.2.be.c.125.1 8
37.8 odd 12 inner 666.2.be.c.341.1 yes 8
111.8 even 12 inner 666.2.be.c.341.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
666.2.be.c.125.1 8 3.2 odd 2 inner
666.2.be.c.125.2 yes 8 1.1 even 1 trivial
666.2.be.c.341.1 yes 8 37.8 odd 12 inner
666.2.be.c.341.2 yes 8 111.8 even 12 inner