Properties

Label 630.2.u.c.109.1
Level $630$
Weight $2$
Character 630.109
Analytic conductor $5.031$
Analytic rank $0$
Dimension $4$
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] = [630,2,Mod(109,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 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("630.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.u (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 109.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 630.109
Dual form 630.2.u.c.289.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-1.73205 - 2.00000i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-1.73205 - 2.00000i) q^{7} +1.00000i q^{8} +(-2.23205 - 0.133975i) q^{10} +(-2.50000 + 4.33013i) q^{11} +1.00000i q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(3.50000 + 6.06218i) q^{19} +(2.00000 - 1.00000i) q^{20} -5.00000i q^{22} +(-2.59808 + 1.50000i) q^{23} +(1.96410 + 4.59808i) q^{25} +(-0.500000 - 0.866025i) q^{26} +(-2.59808 + 0.500000i) q^{28} +(3.00000 - 5.19615i) q^{31} +(0.866025 + 0.500000i) q^{32} -2.00000 q^{34} +(-0.767949 - 5.86603i) q^{35} +(4.33013 - 2.50000i) q^{37} +(-6.06218 - 3.50000i) q^{38} +(-1.23205 + 1.86603i) q^{40} +9.00000 q^{41} +10.0000i q^{43} +(2.50000 + 4.33013i) q^{44} +(1.50000 - 2.59808i) q^{46} +(-11.2583 + 6.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-4.00000 - 3.00000i) q^{50} +(0.866025 + 0.500000i) q^{52} +(-0.866025 - 0.500000i) q^{53} +(-10.0000 + 5.00000i) q^{55} +(2.00000 - 1.73205i) q^{56} +(-2.00000 + 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} +6.00000i q^{62} -1.00000 q^{64} +(-1.23205 + 1.86603i) q^{65} +(5.19615 + 3.00000i) q^{67} +(1.73205 - 1.00000i) q^{68} +(3.59808 + 4.69615i) q^{70} +2.00000 q^{71} +(-3.46410 - 2.00000i) q^{73} +(-2.50000 + 4.33013i) q^{74} +7.00000 q^{76} +(12.9904 - 2.50000i) q^{77} +(-7.00000 - 12.1244i) q^{79} +(0.133975 - 2.23205i) q^{80} +(-7.79423 + 4.50000i) q^{82} +10.0000i q^{83} +(2.00000 + 4.00000i) q^{85} +(-5.00000 - 8.66025i) q^{86} +(-4.33013 - 2.50000i) q^{88} +(-5.00000 - 8.66025i) q^{89} +(2.00000 - 1.73205i) q^{91} +3.00000i q^{92} +(6.50000 - 11.2583i) q^{94} +(-0.937822 + 15.6244i) q^{95} -8.00000i q^{97} +(-2.59808 - 6.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} + 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} + 4 q^{5} - 2 q^{10} - 10 q^{11} + 10 q^{14} - 2 q^{16} + 14 q^{19} + 8 q^{20} - 6 q^{25} - 2 q^{26} + 12 q^{31} - 8 q^{34} - 10 q^{35} + 2 q^{40} + 36 q^{41} + 10 q^{44} + 6 q^{46} - 4 q^{49} - 16 q^{50} - 40 q^{55} + 8 q^{56} - 8 q^{59} + 4 q^{61} - 4 q^{64} + 2 q^{65} + 4 q^{70} + 8 q^{71} - 10 q^{74} + 28 q^{76} - 28 q^{79} + 4 q^{80} + 8 q^{85} - 20 q^{86} - 20 q^{89} + 8 q^{91} + 26 q^{94} - 28 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.86603 + 1.23205i 0.834512 + 0.550990i
\(6\) 0 0
\(7\) −1.73205 2.00000i −0.654654 0.755929i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −2.23205 0.133975i −0.705836 0.0423665i
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i 0.990338 + 0.138675i \(0.0442844\pi\)
−0.990338 + 0.138675i \(0.955716\pi\)
\(14\) 2.50000 + 0.866025i 0.668153 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.73205 + 1.00000i 0.420084 + 0.242536i 0.695113 0.718900i \(-0.255354\pi\)
−0.275029 + 0.961436i \(0.588688\pi\)
\(18\) 0 0
\(19\) 3.50000 + 6.06218i 0.802955 + 1.39076i 0.917663 + 0.397360i \(0.130073\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 2.00000 1.00000i 0.447214 0.223607i
\(21\) 0 0
\(22\) 5.00000i 1.06600i
\(23\) −2.59808 + 1.50000i −0.541736 + 0.312772i −0.745782 0.666190i \(-0.767924\pi\)
0.204046 + 0.978961i \(0.434591\pi\)
\(24\) 0 0
\(25\) 1.96410 + 4.59808i 0.392820 + 0.919615i
\(26\) −0.500000 0.866025i −0.0980581 0.169842i
\(27\) 0 0
\(28\) −2.59808 + 0.500000i −0.490990 + 0.0944911i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 3.00000 5.19615i 0.538816 0.933257i −0.460152 0.887840i \(-0.652205\pi\)
0.998968 0.0454165i \(-0.0144615\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) −0.767949 5.86603i −0.129807 0.991539i
\(36\) 0 0
\(37\) 4.33013 2.50000i 0.711868 0.410997i −0.0998840 0.994999i \(-0.531847\pi\)
0.811752 + 0.584002i \(0.198514\pi\)
\(38\) −6.06218 3.50000i −0.983415 0.567775i
\(39\) 0 0
\(40\) −1.23205 + 1.86603i −0.194804 + 0.295045i
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 0 0
\(43\) 10.0000i 1.52499i 0.646997 + 0.762493i \(0.276025\pi\)
−0.646997 + 0.762493i \(0.723975\pi\)
\(44\) 2.50000 + 4.33013i 0.376889 + 0.652791i
\(45\) 0 0
\(46\) 1.50000 2.59808i 0.221163 0.383065i
\(47\) −11.2583 + 6.50000i −1.64220 + 0.948122i −0.662145 + 0.749375i \(0.730354\pi\)
−0.980051 + 0.198747i \(0.936313\pi\)
\(48\) 0 0
\(49\) −1.00000 + 6.92820i −0.142857 + 0.989743i
\(50\) −4.00000 3.00000i −0.565685 0.424264i
\(51\) 0 0
\(52\) 0.866025 + 0.500000i 0.120096 + 0.0693375i
\(53\) −0.866025 0.500000i −0.118958 0.0686803i 0.439340 0.898321i \(-0.355212\pi\)
−0.558298 + 0.829640i \(0.688546\pi\)
\(54\) 0 0
\(55\) −10.0000 + 5.00000i −1.34840 + 0.674200i
\(56\) 2.00000 1.73205i 0.267261 0.231455i
\(57\) 0 0
\(58\) 0 0
\(59\) −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 6.00000i 0.762001i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −1.23205 + 1.86603i −0.152817 + 0.231452i
\(66\) 0 0
\(67\) 5.19615 + 3.00000i 0.634811 + 0.366508i 0.782613 0.622509i \(-0.213886\pi\)
−0.147802 + 0.989017i \(0.547220\pi\)
\(68\) 1.73205 1.00000i 0.210042 0.121268i
\(69\) 0 0
\(70\) 3.59808 + 4.69615i 0.430052 + 0.561298i
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 0 0
\(73\) −3.46410 2.00000i −0.405442 0.234082i 0.283387 0.959006i \(-0.408542\pi\)
−0.688830 + 0.724923i \(0.741875\pi\)
\(74\) −2.50000 + 4.33013i −0.290619 + 0.503367i
\(75\) 0 0
\(76\) 7.00000 0.802955
\(77\) 12.9904 2.50000i 1.48039 0.284901i
\(78\) 0 0
\(79\) −7.00000 12.1244i −0.787562 1.36410i −0.927457 0.373930i \(-0.878010\pi\)
0.139895 0.990166i \(-0.455323\pi\)
\(80\) 0.133975 2.23205i 0.0149788 0.249551i
\(81\) 0 0
\(82\) −7.79423 + 4.50000i −0.860729 + 0.496942i
\(83\) 10.0000i 1.09764i 0.835940 + 0.548821i \(0.184923\pi\)
−0.835940 + 0.548821i \(0.815077\pi\)
\(84\) 0 0
\(85\) 2.00000 + 4.00000i 0.216930 + 0.433861i
\(86\) −5.00000 8.66025i −0.539164 0.933859i
\(87\) 0 0
\(88\) −4.33013 2.50000i −0.461593 0.266501i
\(89\) −5.00000 8.66025i −0.529999 0.917985i −0.999388 0.0349934i \(-0.988859\pi\)
0.469389 0.882992i \(-0.344474\pi\)
\(90\) 0 0
\(91\) 2.00000 1.73205i 0.209657 0.181568i
\(92\) 3.00000i 0.312772i
\(93\) 0 0
\(94\) 6.50000 11.2583i 0.670424 1.16121i
\(95\) −0.937822 + 15.6244i −0.0962185 + 1.60303i
\(96\) 0 0
\(97\) 8.00000i 0.812277i −0.913812 0.406138i \(-0.866875\pi\)
0.913812 0.406138i \(-0.133125\pi\)
\(98\) −2.59808 6.50000i −0.262445 0.656599i
\(99\) 0 0
\(100\) 4.96410 + 0.598076i 0.496410 + 0.0598076i
\(101\) 4.00000 6.92820i 0.398015 0.689382i −0.595466 0.803380i \(-0.703033\pi\)
0.993481 + 0.113998i \(0.0363659\pi\)
\(102\) 0 0
\(103\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 1.00000 0.0971286
\(107\) 10.3923 6.00000i 1.00466 0.580042i 0.0950377 0.995474i \(-0.469703\pi\)
0.909624 + 0.415432i \(0.136370\pi\)
\(108\) 0 0
\(109\) −9.00000 + 15.5885i −0.862044 + 1.49310i 0.00790932 + 0.999969i \(0.497482\pi\)
−0.869953 + 0.493135i \(0.835851\pi\)
\(110\) 6.16025 9.33013i 0.587357 0.889593i
\(111\) 0 0
\(112\) −0.866025 + 2.50000i −0.0818317 + 0.236228i
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 0 0
\(115\) −6.69615 0.401924i −0.624419 0.0374796i
\(116\) 0 0
\(117\) 0 0
\(118\) 4.00000i 0.368230i
\(119\) −1.00000 5.19615i −0.0916698 0.476331i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) −1.73205 1.00000i −0.156813 0.0905357i
\(123\) 0 0
\(124\) −3.00000 5.19615i −0.269408 0.466628i
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) 0 0
\(127\) 9.00000i 0.798621i −0.916816 0.399310i \(-0.869250\pi\)
0.916816 0.399310i \(-0.130750\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 0.133975 2.23205i 0.0117503 0.195764i
\(131\) −8.50000 14.7224i −0.742648 1.28630i −0.951285 0.308312i \(-0.900236\pi\)
0.208637 0.977993i \(-0.433097\pi\)
\(132\) 0 0
\(133\) 6.06218 17.5000i 0.525657 1.51744i
\(134\) −6.00000 −0.518321
\(135\) 0 0
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) 3.46410 + 2.00000i 0.295958 + 0.170872i 0.640626 0.767853i \(-0.278675\pi\)
−0.344668 + 0.938725i \(0.612008\pi\)
\(138\) 0 0
\(139\) 8.00000 0.678551 0.339276 0.940687i \(-0.389818\pi\)
0.339276 + 0.940687i \(0.389818\pi\)
\(140\) −5.46410 2.26795i −0.461801 0.191677i
\(141\) 0 0
\(142\) −1.73205 + 1.00000i −0.145350 + 0.0839181i
\(143\) −4.33013 2.50000i −0.362103 0.209061i
\(144\) 0 0
\(145\) 0 0
\(146\) 4.00000 0.331042
\(147\) 0 0
\(148\) 5.00000i 0.410997i
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0 0
\(151\) 11.0000 19.0526i 0.895167 1.55048i 0.0615699 0.998103i \(-0.480389\pi\)
0.833597 0.552372i \(-0.186277\pi\)
\(152\) −6.06218 + 3.50000i −0.491708 + 0.283887i
\(153\) 0 0
\(154\) −10.0000 + 8.66025i −0.805823 + 0.697863i
\(155\) 12.0000 6.00000i 0.963863 0.481932i
\(156\) 0 0
\(157\) 11.2583 + 6.50000i 0.898513 + 0.518756i 0.876717 0.481006i \(-0.159728\pi\)
0.0217953 + 0.999762i \(0.493062\pi\)
\(158\) 12.1244 + 7.00000i 0.964562 + 0.556890i
\(159\) 0 0
\(160\) 1.00000 + 2.00000i 0.0790569 + 0.158114i
\(161\) 7.50000 + 2.59808i 0.591083 + 0.204757i
\(162\) 0 0
\(163\) −10.3923 + 6.00000i −0.813988 + 0.469956i −0.848339 0.529454i \(-0.822397\pi\)
0.0343508 + 0.999410i \(0.489064\pi\)
\(164\) 4.50000 7.79423i 0.351391 0.608627i
\(165\) 0 0
\(166\) −5.00000 8.66025i −0.388075 0.672166i
\(167\) 19.0000i 1.47026i −0.677924 0.735132i \(-0.737120\pi\)
0.677924 0.735132i \(-0.262880\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) −3.73205 2.46410i −0.286235 0.188988i
\(171\) 0 0
\(172\) 8.66025 + 5.00000i 0.660338 + 0.381246i
\(173\) −6.06218 + 3.50000i −0.460899 + 0.266100i −0.712422 0.701751i \(-0.752402\pi\)
0.251523 + 0.967851i \(0.419068\pi\)
\(174\) 0 0
\(175\) 5.79423 11.8923i 0.438003 0.898974i
\(176\) 5.00000 0.376889
\(177\) 0 0
\(178\) 8.66025 + 5.00000i 0.649113 + 0.374766i
\(179\) 5.50000 9.52628i 0.411089 0.712028i −0.583920 0.811811i \(-0.698482\pi\)
0.995009 + 0.0997838i \(0.0318151\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) −0.866025 + 2.50000i −0.0641941 + 0.185312i
\(183\) 0 0
\(184\) −1.50000 2.59808i −0.110581 0.191533i
\(185\) 11.1603 + 0.669873i 0.820518 + 0.0492500i
\(186\) 0 0
\(187\) −8.66025 + 5.00000i −0.633300 + 0.365636i
\(188\) 13.0000i 0.948122i
\(189\) 0 0
\(190\) −7.00000 14.0000i −0.507833 1.01567i
\(191\) −8.00000 13.8564i −0.578860 1.00261i −0.995610 0.0935936i \(-0.970165\pi\)
0.416751 0.909021i \(-0.363169\pi\)
\(192\) 0 0
\(193\) 15.5885 + 9.00000i 1.12208 + 0.647834i 0.941932 0.335805i \(-0.109008\pi\)
0.180150 + 0.983639i \(0.442342\pi\)
\(194\) 4.00000 + 6.92820i 0.287183 + 0.497416i
\(195\) 0 0
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) 27.0000i 1.92367i −0.273629 0.961835i \(-0.588224\pi\)
0.273629 0.961835i \(-0.411776\pi\)
\(198\) 0 0
\(199\) −7.00000 + 12.1244i −0.496217 + 0.859473i −0.999990 0.00436292i \(-0.998611\pi\)
0.503774 + 0.863836i \(0.331945\pi\)
\(200\) −4.59808 + 1.96410i −0.325133 + 0.138883i
\(201\) 0 0
\(202\) 8.00000i 0.562878i
\(203\) 0 0
\(204\) 0 0
\(205\) 16.7942 + 11.0885i 1.17296 + 0.774451i
\(206\) 0 0
\(207\) 0 0
\(208\) 0.866025 0.500000i 0.0600481 0.0346688i
\(209\) −35.0000 −2.42100
\(210\) 0 0
\(211\) 19.0000 1.30801 0.654007 0.756489i \(-0.273087\pi\)
0.654007 + 0.756489i \(0.273087\pi\)
\(212\) −0.866025 + 0.500000i −0.0594789 + 0.0343401i
\(213\) 0 0
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) −12.3205 + 18.6603i −0.840252 + 1.27262i
\(216\) 0 0
\(217\) −15.5885 + 3.00000i −1.05821 + 0.203653i
\(218\) 18.0000i 1.21911i
\(219\) 0 0
\(220\) −0.669873 + 11.1603i −0.0451628 + 0.752424i
\(221\) −1.00000 + 1.73205i −0.0672673 + 0.116510i
\(222\) 0 0
\(223\) 16.0000i 1.07144i 0.844396 + 0.535720i \(0.179960\pi\)
−0.844396 + 0.535720i \(0.820040\pi\)
\(224\) −0.500000 2.59808i −0.0334077 0.173591i
\(225\) 0 0
\(226\) 3.00000 + 5.19615i 0.199557 + 0.345643i
\(227\) −12.1244 7.00000i −0.804722 0.464606i 0.0403978 0.999184i \(-0.487137\pi\)
−0.845120 + 0.534577i \(0.820471\pi\)
\(228\) 0 0
\(229\) −2.00000 3.46410i −0.132164 0.228914i 0.792347 0.610071i \(-0.208859\pi\)
−0.924510 + 0.381157i \(0.875526\pi\)
\(230\) 6.00000 3.00000i 0.395628 0.197814i
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(234\) 0 0
\(235\) −29.0167 1.74167i −1.89284 0.113614i
\(236\) 2.00000 + 3.46410i 0.130189 + 0.225494i
\(237\) 0 0
\(238\) 3.46410 + 4.00000i 0.224544 + 0.259281i
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) 12.1244 + 7.00000i 0.779383 + 0.449977i
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) −10.4019 + 11.6962i −0.664555 + 0.747240i
\(246\) 0 0
\(247\) −6.06218 + 3.50000i −0.385727 + 0.222700i
\(248\) 5.19615 + 3.00000i 0.329956 + 0.190500i
\(249\) 0 0
\(250\) −3.76795 10.5263i −0.238306 0.665740i
\(251\) 3.00000 0.189358 0.0946792 0.995508i \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) 0 0
\(253\) 15.0000i 0.943042i
\(254\) 4.50000 + 7.79423i 0.282355 + 0.489053i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −8.66025 + 5.00000i −0.540212 + 0.311891i −0.745165 0.666880i \(-0.767629\pi\)
0.204953 + 0.978772i \(0.434296\pi\)
\(258\) 0 0
\(259\) −12.5000 4.33013i −0.776712 0.269061i
\(260\) 1.00000 + 2.00000i 0.0620174 + 0.124035i
\(261\) 0 0
\(262\) 14.7224 + 8.50000i 0.909555 + 0.525132i
\(263\) 20.7846 + 12.0000i 1.28163 + 0.739952i 0.977147 0.212565i \(-0.0681817\pi\)
0.304487 + 0.952517i \(0.401515\pi\)
\(264\) 0 0
\(265\) −1.00000 2.00000i −0.0614295 0.122859i
\(266\) 3.50000 + 18.1865i 0.214599 + 1.11509i
\(267\) 0 0
\(268\) 5.19615 3.00000i 0.317406 0.183254i
\(269\) −7.00000 + 12.1244i −0.426798 + 0.739235i −0.996586 0.0825561i \(-0.973692\pi\)
0.569789 + 0.821791i \(0.307025\pi\)
\(270\) 0 0
\(271\) −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i \(-0.244792\pi\)
−0.961563 + 0.274586i \(0.911459\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) −4.00000 −0.241649
\(275\) −24.8205 2.99038i −1.49673 0.180327i
\(276\) 0 0
\(277\) 1.73205 + 1.00000i 0.104069 + 0.0600842i 0.551131 0.834419i \(-0.314196\pi\)
−0.447062 + 0.894503i \(0.647530\pi\)
\(278\) −6.92820 + 4.00000i −0.415526 + 0.239904i
\(279\) 0 0
\(280\) 5.86603 0.767949i 0.350562 0.0458937i
\(281\) 11.0000 0.656205 0.328102 0.944642i \(-0.393591\pi\)
0.328102 + 0.944642i \(0.393591\pi\)
\(282\) 0 0
\(283\) −22.5167 13.0000i −1.33848 0.772770i −0.351895 0.936039i \(-0.614463\pi\)
−0.986581 + 0.163270i \(0.947796\pi\)
\(284\) 1.00000 1.73205i 0.0593391 0.102778i
\(285\) 0 0
\(286\) 5.00000 0.295656
\(287\) −15.5885 18.0000i −0.920158 1.06251i
\(288\) 0 0
\(289\) −6.50000 11.2583i −0.382353 0.662255i
\(290\) 0 0
\(291\) 0 0
\(292\) −3.46410 + 2.00000i −0.202721 + 0.117041i
\(293\) 1.00000i 0.0584206i −0.999573 0.0292103i \(-0.990701\pi\)
0.999573 0.0292103i \(-0.00929925\pi\)
\(294\) 0 0
\(295\) −8.00000 + 4.00000i −0.465778 + 0.232889i
\(296\) 2.50000 + 4.33013i 0.145310 + 0.251684i
\(297\) 0 0
\(298\) −5.19615 3.00000i −0.301005 0.173785i
\(299\) −1.50000 2.59808i −0.0867472 0.150251i
\(300\) 0 0
\(301\) 20.0000 17.3205i 1.15278 0.998337i
\(302\) 22.0000i 1.26596i
\(303\) 0 0
\(304\) 3.50000 6.06218i 0.200739 0.347690i
\(305\) −0.267949 + 4.46410i −0.0153427 + 0.255614i
\(306\) 0 0
\(307\) 2.00000i 0.114146i −0.998370 0.0570730i \(-0.981823\pi\)
0.998370 0.0570730i \(-0.0181768\pi\)
\(308\) 4.33013 12.5000i 0.246732 0.712254i
\(309\) 0 0
\(310\) −7.39230 + 11.1962i −0.419855 + 0.635899i
\(311\) −13.0000 + 22.5167i −0.737162 + 1.27680i 0.216606 + 0.976259i \(0.430501\pi\)
−0.953768 + 0.300544i \(0.902832\pi\)
\(312\) 0 0
\(313\) −8.66025 + 5.00000i −0.489506 + 0.282617i −0.724370 0.689412i \(-0.757869\pi\)
0.234863 + 0.972028i \(0.424536\pi\)
\(314\) −13.0000 −0.733632
\(315\) 0 0
\(316\) −14.0000 −0.787562
\(317\) 1.73205 1.00000i 0.0972817 0.0561656i −0.450570 0.892741i \(-0.648779\pi\)
0.547852 + 0.836576i \(0.315446\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.86603 1.23205i −0.104314 0.0688737i
\(321\) 0 0
\(322\) −7.79423 + 1.50000i −0.434355 + 0.0835917i
\(323\) 14.0000i 0.778981i
\(324\) 0 0
\(325\) −4.59808 + 1.96410i −0.255055 + 0.108949i
\(326\) 6.00000 10.3923i 0.332309 0.575577i
\(327\) 0 0
\(328\) 9.00000i 0.496942i
\(329\) 32.5000 + 11.2583i 1.79178 + 0.620692i
\(330\) 0 0
\(331\) 7.50000 + 12.9904i 0.412237 + 0.714016i 0.995134 0.0985303i \(-0.0314141\pi\)
−0.582897 + 0.812546i \(0.698081\pi\)
\(332\) 8.66025 + 5.00000i 0.475293 + 0.274411i
\(333\) 0 0
\(334\) 9.50000 + 16.4545i 0.519817 + 0.900349i
\(335\) 6.00000 + 12.0000i 0.327815 + 0.655630i
\(336\) 0 0
\(337\) 14.0000i 0.762629i 0.924445 + 0.381314i \(0.124528\pi\)
−0.924445 + 0.381314i \(0.875472\pi\)
\(338\) −10.3923 + 6.00000i −0.565267 + 0.326357i
\(339\) 0 0
\(340\) 4.46410 + 0.267949i 0.242100 + 0.0145316i
\(341\) 15.0000 + 25.9808i 0.812296 + 1.40694i
\(342\) 0 0
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) −10.0000 −0.539164
\(345\) 0 0
\(346\) 3.50000 6.06218i 0.188161 0.325905i
\(347\) 13.8564 + 8.00000i 0.743851 + 0.429463i 0.823468 0.567363i \(-0.192036\pi\)
−0.0796169 + 0.996826i \(0.525370\pi\)
\(348\) 0 0
\(349\) 24.0000 1.28469 0.642345 0.766415i \(-0.277962\pi\)
0.642345 + 0.766415i \(0.277962\pi\)
\(350\) 0.928203 + 13.1962i 0.0496145 + 0.705364i
\(351\) 0 0
\(352\) −4.33013 + 2.50000i −0.230797 + 0.133250i
\(353\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(354\) 0 0
\(355\) 3.73205 + 2.46410i 0.198077 + 0.130781i
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) 11.0000i 0.581368i
\(359\) 14.0000 + 24.2487i 0.738892 + 1.27980i 0.952995 + 0.302987i \(0.0979839\pi\)
−0.214103 + 0.976811i \(0.568683\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) 1.73205 1.00000i 0.0910346 0.0525588i
\(363\) 0 0
\(364\) −0.500000 2.59808i −0.0262071 0.136176i
\(365\) −4.00000 8.00000i −0.209370 0.418739i
\(366\) 0 0
\(367\) −32.0429 18.5000i −1.67263 0.965692i −0.966159 0.257948i \(-0.916954\pi\)
−0.706469 0.707744i \(-0.749713\pi\)
\(368\) 2.59808 + 1.50000i 0.135434 + 0.0781929i
\(369\) 0 0
\(370\) −10.0000 + 5.00000i −0.519875 + 0.259938i
\(371\) 0.500000 + 2.59808i 0.0259587 + 0.134885i
\(372\) 0 0
\(373\) 5.19615 3.00000i 0.269047 0.155334i −0.359408 0.933181i \(-0.617021\pi\)
0.628454 + 0.777847i \(0.283688\pi\)
\(374\) 5.00000 8.66025i 0.258544 0.447811i
\(375\) 0 0
\(376\) −6.50000 11.2583i −0.335212 0.580604i
\(377\) 0 0
\(378\) 0 0
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) 13.0622 + 8.62436i 0.670076 + 0.442420i
\(381\) 0 0
\(382\) 13.8564 + 8.00000i 0.708955 + 0.409316i
\(383\) 7.79423 4.50000i 0.398266 0.229939i −0.287469 0.957790i \(-0.592814\pi\)
0.685736 + 0.727851i \(0.259481\pi\)
\(384\) 0 0
\(385\) 27.3205 + 11.3397i 1.39238 + 0.577927i
\(386\) −18.0000 −0.916176
\(387\) 0 0
\(388\) −6.92820 4.00000i −0.351726 0.203069i
\(389\) −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i \(-0.881939\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(390\) 0 0
\(391\) −6.00000 −0.303433
\(392\) −6.92820 1.00000i −0.349927 0.0505076i
\(393\) 0 0
\(394\) 13.5000 + 23.3827i 0.680120 + 1.17800i
\(395\) 1.87564 31.2487i 0.0943739 1.57229i
\(396\) 0 0
\(397\) 1.73205 1.00000i 0.0869291 0.0501886i −0.455905 0.890028i \(-0.650684\pi\)
0.542834 + 0.839840i \(0.317351\pi\)
\(398\) 14.0000i 0.701757i
\(399\) 0 0
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) −13.5000 23.3827i −0.674158 1.16768i −0.976714 0.214544i \(-0.931173\pi\)
0.302556 0.953131i \(-0.402160\pi\)
\(402\) 0 0
\(403\) 5.19615 + 3.00000i 0.258839 + 0.149441i
\(404\) −4.00000 6.92820i −0.199007 0.344691i
\(405\) 0 0
\(406\) 0 0
\(407\) 25.0000i 1.23920i
\(408\) 0 0
\(409\) 5.00000 8.66025i 0.247234 0.428222i −0.715523 0.698589i \(-0.753812\pi\)
0.962757 + 0.270367i \(0.0871450\pi\)
\(410\) −20.0885 1.20577i −0.992098 0.0595488i
\(411\) 0 0
\(412\) 0 0
\(413\) 10.3923 2.00000i 0.511372 0.0984136i
\(414\) 0 0
\(415\) −12.3205 + 18.6603i −0.604790 + 0.915996i
\(416\) −0.500000 + 0.866025i −0.0245145 + 0.0424604i
\(417\) 0 0
\(418\) 30.3109 17.5000i 1.48255 0.855953i
\(419\) 3.00000 0.146560 0.0732798 0.997311i \(-0.476653\pi\)
0.0732798 + 0.997311i \(0.476653\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) −16.4545 + 9.50000i −0.800992 + 0.462453i
\(423\) 0 0
\(424\) 0.500000 0.866025i 0.0242821 0.0420579i
\(425\) −1.19615 + 9.92820i −0.0580219 + 0.481589i
\(426\) 0 0
\(427\) 1.73205 5.00000i 0.0838198 0.241967i
\(428\) 12.0000i 0.580042i
\(429\) 0 0
\(430\) 1.33975 22.3205i 0.0646083 1.07639i
\(431\) 9.00000 15.5885i 0.433515 0.750870i −0.563658 0.826008i \(-0.690607\pi\)
0.997173 + 0.0751385i \(0.0239399\pi\)
\(432\) 0 0
\(433\) 4.00000i 0.192228i 0.995370 + 0.0961139i \(0.0306413\pi\)
−0.995370 + 0.0961139i \(0.969359\pi\)
\(434\) 12.0000 10.3923i 0.576018 0.498847i
\(435\) 0 0
\(436\) 9.00000 + 15.5885i 0.431022 + 0.746552i
\(437\) −18.1865 10.5000i −0.869980 0.502283i
\(438\) 0 0
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) −5.00000 10.0000i −0.238366 0.476731i
\(441\) 0 0
\(442\) 2.00000i 0.0951303i
\(443\) 5.19615 3.00000i 0.246877 0.142534i −0.371457 0.928450i \(-0.621142\pi\)
0.618333 + 0.785916i \(0.287808\pi\)
\(444\) 0 0
\(445\) 1.33975 22.3205i 0.0635100 1.05809i
\(446\) −8.00000 13.8564i −0.378811 0.656120i
\(447\) 0 0
\(448\) 1.73205 + 2.00000i 0.0818317 + 0.0944911i
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) 0 0
\(451\) −22.5000 + 38.9711i −1.05948 + 1.83508i
\(452\) −5.19615 3.00000i −0.244406 0.141108i
\(453\) 0 0
\(454\) 14.0000 0.657053
\(455\) 5.86603 0.767949i 0.275004 0.0360020i
\(456\) 0 0
\(457\) 32.9090 19.0000i 1.53942 0.888783i 0.540544 0.841316i \(-0.318219\pi\)
0.998873 0.0474665i \(-0.0151147\pi\)
\(458\) 3.46410 + 2.00000i 0.161867 + 0.0934539i
\(459\) 0 0
\(460\) −3.69615 + 5.59808i −0.172334 + 0.261012i
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) 15.0000i 0.697109i −0.937288 0.348555i \(-0.886673\pi\)
0.937288 0.348555i \(-0.113327\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.73205 1.00000i 0.0801498 0.0462745i −0.459390 0.888235i \(-0.651932\pi\)
0.539539 + 0.841960i \(0.318598\pi\)
\(468\) 0 0
\(469\) −3.00000 15.5885i −0.138527 0.719808i
\(470\) 26.0000 13.0000i 1.19929 0.599645i
\(471\) 0 0
\(472\) −3.46410 2.00000i −0.159448 0.0920575i
\(473\) −43.3013 25.0000i −1.99099 1.14950i
\(474\) 0 0
\(475\) −21.0000 + 28.0000i −0.963546 + 1.28473i
\(476\) −5.00000 1.73205i −0.229175 0.0793884i
\(477\) 0 0
\(478\) −17.3205 + 10.0000i −0.792222 + 0.457389i
\(479\) −4.00000 + 6.92820i −0.182765 + 0.316558i −0.942821 0.333300i \(-0.891838\pi\)
0.760056 + 0.649857i \(0.225171\pi\)
\(480\) 0 0
\(481\) 2.50000 + 4.33013i 0.113990 + 0.197437i
\(482\) 1.00000i 0.0455488i
\(483\) 0 0
\(484\) −14.0000 −0.636364
\(485\) 9.85641 14.9282i 0.447556 0.677855i
\(486\) 0 0
\(487\) 20.7846 + 12.0000i 0.941841 + 0.543772i 0.890537 0.454911i \(-0.150329\pi\)
0.0513038 + 0.998683i \(0.483662\pi\)
\(488\) −1.73205 + 1.00000i −0.0784063 + 0.0452679i
\(489\) 0 0
\(490\) 3.16025 15.3301i 0.142766 0.692545i
\(491\) −24.0000 −1.08310 −0.541552 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 3.50000 6.06218i 0.157472 0.272750i
\(495\) 0 0
\(496\) −6.00000 −0.269408
\(497\) −3.46410 4.00000i −0.155386 0.179425i
\(498\) 0 0
\(499\) −14.0000 24.2487i −0.626726 1.08552i −0.988204 0.153141i \(-0.951061\pi\)
0.361478 0.932381i \(-0.382272\pi\)
\(500\) 8.52628 + 7.23205i 0.381307 + 0.323427i
\(501\) 0 0
\(502\) −2.59808 + 1.50000i −0.115958 + 0.0669483i
\(503\) 24.0000i 1.07011i −0.844818 0.535054i \(-0.820291\pi\)
0.844818 0.535054i \(-0.179709\pi\)
\(504\) 0 0
\(505\) 16.0000 8.00000i 0.711991 0.355995i
\(506\) 7.50000 + 12.9904i 0.333416 + 0.577493i
\(507\) 0 0
\(508\) −7.79423 4.50000i −0.345813 0.199655i
\(509\) −7.00000 12.1244i −0.310270 0.537403i 0.668151 0.744026i \(-0.267086\pi\)
−0.978421 + 0.206623i \(0.933753\pi\)
\(510\) 0 0
\(511\) 2.00000 + 10.3923i 0.0884748 + 0.459728i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 5.00000 8.66025i 0.220541 0.381987i
\(515\) 0 0
\(516\) 0 0
\(517\) 65.0000i 2.85870i
\(518\) 12.9904 2.50000i 0.570765 0.109844i
\(519\) 0 0
\(520\) −1.86603 1.23205i −0.0818306 0.0540290i
\(521\) −7.50000 + 12.9904i −0.328581 + 0.569119i −0.982231 0.187678i \(-0.939904\pi\)
0.653650 + 0.756797i \(0.273237\pi\)
\(522\) 0 0
\(523\) 10.3923 6.00000i 0.454424 0.262362i −0.255273 0.966869i \(-0.582165\pi\)
0.709697 + 0.704507i \(0.248832\pi\)
\(524\) −17.0000 −0.742648
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) 10.3923 6.00000i 0.452696 0.261364i
\(528\) 0 0
\(529\) −7.00000 + 12.1244i −0.304348 + 0.527146i
\(530\) 1.86603 + 1.23205i 0.0810550 + 0.0535169i
\(531\) 0 0
\(532\) −12.1244 14.0000i −0.525657 0.606977i
\(533\) 9.00000i 0.389833i
\(534\) 0 0
\(535\) 26.7846 + 1.60770i 1.15800 + 0.0695067i
\(536\) −3.00000 + 5.19615i −0.129580 + 0.224440i
\(537\) 0 0
\(538\) 14.0000i 0.603583i
\(539\) −27.5000 21.6506i −1.18451 0.932559i
\(540\) 0 0
\(541\) −2.00000 3.46410i −0.0859867 0.148933i 0.819825 0.572615i \(-0.194071\pi\)
−0.905811 + 0.423681i \(0.860738\pi\)
\(542\) 6.92820 + 4.00000i 0.297592 + 0.171815i
\(543\) 0 0
\(544\) 1.00000 + 1.73205i 0.0428746 + 0.0742611i
\(545\) −36.0000 + 18.0000i −1.54207 + 0.771035i
\(546\) 0 0
\(547\) 14.0000i 0.598597i 0.954160 + 0.299298i \(0.0967526\pi\)
−0.954160 + 0.299298i \(0.903247\pi\)
\(548\) 3.46410 2.00000i 0.147979 0.0854358i
\(549\) 0 0
\(550\) 22.9904 9.82051i 0.980313 0.418748i
\(551\) 0 0
\(552\) 0 0
\(553\) −12.1244 + 35.0000i −0.515580 + 1.48835i
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) 4.00000 6.92820i 0.169638 0.293821i
\(557\) 33.7750 + 19.5000i 1.43109 + 0.826242i 0.997204 0.0747252i \(-0.0238080\pi\)
0.433888 + 0.900967i \(0.357141\pi\)
\(558\) 0 0
\(559\) −10.0000 −0.422955
\(560\) −4.69615 + 3.59808i −0.198449 + 0.152046i
\(561\) 0 0
\(562\) −9.52628 + 5.50000i −0.401842 + 0.232003i
\(563\) 25.9808 + 15.0000i 1.09496 + 0.632175i 0.934892 0.354932i \(-0.115496\pi\)
0.160066 + 0.987106i \(0.448829\pi\)
\(564\) 0 0
\(565\) 7.39230 11.1962i 0.310997 0.471026i
\(566\) 26.0000 1.09286
\(567\) 0 0
\(568\) 2.00000i 0.0839181i
\(569\) 1.50000 + 2.59808i 0.0628833 + 0.108917i 0.895753 0.444552i \(-0.146637\pi\)
−0.832870 + 0.553469i \(0.813304\pi\)
\(570\) 0 0
\(571\) 4.00000 6.92820i 0.167395 0.289936i −0.770108 0.637913i \(-0.779798\pi\)
0.937503 + 0.347977i \(0.113131\pi\)
\(572\) −4.33013 + 2.50000i −0.181052 + 0.104530i
\(573\) 0 0
\(574\) 22.5000 + 7.79423i 0.939132 + 0.325325i
\(575\) −12.0000 9.00000i −0.500435 0.375326i
\(576\) 0 0
\(577\) 20.7846 + 12.0000i 0.865275 + 0.499567i 0.865775 0.500433i \(-0.166826\pi\)
−0.000500448 1.00000i \(0.500159\pi\)
\(578\) 11.2583 + 6.50000i 0.468285 + 0.270364i
\(579\) 0 0
\(580\) 0 0
\(581\) 20.0000 17.3205i 0.829740 0.718576i
\(582\) 0 0
\(583\) 4.33013 2.50000i 0.179336 0.103539i
\(584\) 2.00000 3.46410i 0.0827606 0.143346i
\(585\) 0 0
\(586\) 0.500000 + 0.866025i 0.0206548 + 0.0357752i
\(587\) 2.00000i 0.0825488i 0.999148 + 0.0412744i \(0.0131418\pi\)
−0.999148 + 0.0412744i \(0.986858\pi\)
\(588\) 0 0
\(589\) 42.0000 1.73058
\(590\) 4.92820 7.46410i 0.202891 0.307292i
\(591\) 0 0
\(592\) −4.33013 2.50000i −0.177967 0.102749i
\(593\) 29.4449 17.0000i 1.20916 0.698106i 0.246581 0.969122i \(-0.420693\pi\)
0.962575 + 0.271016i \(0.0873596\pi\)
\(594\) 0 0
\(595\) 4.53590 10.9282i 0.185954 0.448013i
\(596\) 6.00000 0.245770
\(597\) 0 0
\(598\) 2.59808 + 1.50000i 0.106243 + 0.0613396i
\(599\) 14.0000 24.2487i 0.572024 0.990775i −0.424333 0.905506i \(-0.639492\pi\)
0.996358 0.0852695i \(-0.0271751\pi\)
\(600\) 0 0
\(601\) −30.0000 −1.22373 −0.611863 0.790964i \(-0.709580\pi\)
−0.611863 + 0.790964i \(0.709580\pi\)
\(602\) −8.66025 + 25.0000i −0.352966 + 1.01892i
\(603\) 0 0
\(604\) −11.0000 19.0526i −0.447584 0.775238i
\(605\) 1.87564 31.2487i 0.0762558 1.27044i
\(606\) 0 0
\(607\) −11.2583 + 6.50000i −0.456962 + 0.263827i −0.710766 0.703429i \(-0.751651\pi\)
0.253804 + 0.967256i \(0.418318\pi\)
\(608\) 7.00000i 0.283887i
\(609\) 0 0
\(610\) −2.00000 4.00000i −0.0809776 0.161955i
\(611\) −6.50000 11.2583i −0.262962 0.455463i
\(612\) 0 0
\(613\) −16.4545 9.50000i −0.664590 0.383701i 0.129433 0.991588i \(-0.458684\pi\)
−0.794024 + 0.607887i \(0.792017\pi\)
\(614\) 1.00000 + 1.73205i 0.0403567 + 0.0698999i
\(615\) 0 0
\(616\) 2.50000 + 12.9904i 0.100728 + 0.523397i
\(617\) 30.0000i 1.20775i 0.797077 + 0.603877i \(0.206378\pi\)
−0.797077 + 0.603877i \(0.793622\pi\)
\(618\) 0 0
\(619\) 7.50000 12.9904i 0.301450 0.522127i −0.675014 0.737805i \(-0.735863\pi\)
0.976465 + 0.215677i \(0.0691959\pi\)
\(620\) 0.803848 13.3923i 0.0322833 0.537848i
\(621\) 0 0
\(622\) 26.0000i 1.04251i
\(623\) −8.66025 + 25.0000i −0.346966 + 1.00160i
\(624\) 0 0
\(625\) −17.2846 + 18.0622i −0.691384 + 0.722487i
\(626\) 5.00000 8.66025i 0.199840 0.346133i
\(627\) 0 0
\(628\) 11.2583 6.50000i 0.449256 0.259378i
\(629\) 10.0000 0.398726
\(630\) 0 0
\(631\) 18.0000 0.716569 0.358284 0.933613i \(-0.383362\pi\)
0.358284 + 0.933613i \(0.383362\pi\)
\(632\) 12.1244 7.00000i 0.482281 0.278445i
\(633\) 0 0
\(634\) −1.00000 + 1.73205i −0.0397151 + 0.0687885i
\(635\) 11.0885 16.7942i 0.440032 0.666459i
\(636\) 0 0
\(637\) −6.92820 1.00000i −0.274505 0.0396214i
\(638\) 0 0
\(639\) 0 0
\(640\) 2.23205 + 0.133975i 0.0882296 + 0.00529581i
\(641\) −16.5000 + 28.5788i −0.651711 + 1.12880i 0.330997 + 0.943632i \(0.392615\pi\)
−0.982708 + 0.185164i \(0.940718\pi\)
\(642\) 0 0
\(643\) 38.0000i 1.49857i 0.662246 + 0.749287i \(0.269604\pi\)
−0.662246 + 0.749287i \(0.730396\pi\)
\(644\) 6.00000 5.19615i 0.236433 0.204757i
\(645\) 0 0
\(646\) −7.00000 12.1244i −0.275411 0.477026i
\(647\) 0.866025 + 0.500000i 0.0340470 + 0.0196570i 0.516927 0.856030i \(-0.327076\pi\)
−0.482880 + 0.875687i \(0.660409\pi\)
\(648\) 0 0
\(649\) −10.0000 17.3205i −0.392534 0.679889i
\(650\) 3.00000 4.00000i 0.117670 0.156893i
\(651\) 0 0
\(652\) 12.0000i 0.469956i
\(653\) −4.33013 + 2.50000i −0.169451 + 0.0978326i −0.582327 0.812955i \(-0.697858\pi\)
0.412876 + 0.910787i \(0.364524\pi\)
\(654\) 0 0
\(655\) 2.27757 37.9449i 0.0889920 1.48263i
\(656\) −4.50000 7.79423i −0.175695 0.304314i
\(657\) 0 0
\(658\) −33.7750 + 6.50000i −1.31669 + 0.253396i
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) −20.0000 + 34.6410i −0.777910 + 1.34738i 0.155235 + 0.987878i \(0.450387\pi\)
−0.933144 + 0.359502i \(0.882947\pi\)
\(662\) −12.9904 7.50000i −0.504885 0.291496i
\(663\) 0 0
\(664\) −10.0000 −0.388075
\(665\) 32.8731 25.1865i 1.27476 0.976692i
\(666\) 0 0
\(667\) 0 0
\(668\) −16.4545 9.50000i −0.636643 0.367566i
\(669\) 0 0
\(670\) −11.1962 7.39230i −0.432545 0.285590i
\(671\) −10.0000 −0.386046
\(672\) 0 0
\(673\) 36.0000i 1.38770i 0.720121 + 0.693849i \(0.244086\pi\)
−0.720121 + 0.693849i \(0.755914\pi\)
\(674\) −7.00000 12.1244i −0.269630 0.467013i
\(675\) 0 0
\(676\) 6.00000 10.3923i 0.230769 0.399704i
\(677\) 28.5788 16.5000i 1.09837 0.634147i 0.162581 0.986695i \(-0.448018\pi\)
0.935793 + 0.352549i \(0.114685\pi\)
\(678\) 0 0
\(679\) −16.0000 + 13.8564i −0.614024 + 0.531760i
\(680\) −4.00000 + 2.00000i −0.153393 + 0.0766965i
\(681\) 0 0
\(682\) −25.9808 15.0000i −0.994855 0.574380i
\(683\) −3.46410 2.00000i −0.132550 0.0765279i 0.432259 0.901750i \(-0.357717\pi\)
−0.564809 + 0.825222i \(0.691050\pi\)
\(684\) 0 0
\(685\) 4.00000 + 8.00000i 0.152832 + 0.305664i
\(686\) −8.50000 + 16.4545i −0.324532 + 0.628235i
\(687\) 0 0
\(688\) 8.66025 5.00000i 0.330169 0.190623i
\(689\) 0.500000 0.866025i 0.0190485 0.0329929i
\(690\) 0 0
\(691\) 10.0000 + 17.3205i 0.380418 + 0.658903i 0.991122 0.132956i \(-0.0424468\pi\)
−0.610704 + 0.791859i \(0.709113\pi\)
\(692\) 7.00000i 0.266100i
\(693\) 0 0
\(694\) −16.0000 −0.607352
\(695\) 14.9282 + 9.85641i 0.566259 + 0.373875i
\(696\) 0 0
\(697\) 15.5885 + 9.00000i 0.590455 + 0.340899i
\(698\) −20.7846 + 12.0000i −0.786709 + 0.454207i
\(699\) 0 0
\(700\) −7.40192 10.9641i −0.279766 0.414404i
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) 30.3109 + 17.5000i 1.14320 + 0.660025i
\(704\) 2.50000 4.33013i 0.0942223 0.163198i
\(705\) 0 0
\(706\) 0 0
\(707\) −20.7846 + 4.00000i −0.781686 + 0.150435i
\(708\) 0 0
\(709\) 8.00000 + 13.8564i 0.300446 + 0.520388i 0.976237 0.216705i \(-0.0695310\pi\)
−0.675791 + 0.737093i \(0.736198\pi\)
\(710\) −4.46410 0.267949i −0.167535 0.0100560i
\(711\) 0 0
\(712\) 8.66025 5.00000i 0.324557 0.187383i
\(713\) 18.0000i 0.674105i
\(714\) 0 0
\(715\) −5.00000 10.0000i −0.186989 0.373979i
\(716\) −5.50000 9.52628i −0.205545 0.356014i
\(717\) 0 0
\(718\) −24.2487 14.0000i −0.904954 0.522475i
\(719\) 1.00000 + 1.73205i 0.0372937 + 0.0645946i 0.884070 0.467355i \(-0.154793\pi\)
−0.846776 + 0.531949i \(0.821460\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 30.0000i 1.11648i
\(723\) 0 0
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) 0 0
\(726\) 0 0
\(727\) 53.0000i 1.96566i −0.184510 0.982831i \(-0.559070\pi\)
0.184510 0.982831i \(-0.440930\pi\)
\(728\) 1.73205 + 2.00000i 0.0641941 + 0.0741249i
\(729\) 0 0
\(730\) 7.46410 + 4.92820i 0.276259 + 0.182401i
\(731\) −10.0000 + 17.3205i −0.369863 + 0.640622i
\(732\) 0 0
\(733\) −18.1865 + 10.5000i −0.671735 + 0.387826i −0.796734 0.604331i \(-0.793441\pi\)
0.124999 + 0.992157i \(0.460107\pi\)
\(734\) 37.0000 1.36569
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) −25.9808 + 15.0000i −0.957014 + 0.552532i
\(738\) 0 0
\(739\) 23.5000 40.7032i 0.864461 1.49729i −0.00311943 0.999995i \(-0.500993\pi\)
0.867581 0.497296i \(-0.165674\pi\)
\(740\) 6.16025 9.33013i 0.226455 0.342982i
\(741\) 0 0
\(742\) −1.73205 2.00000i −0.0635856 0.0734223i
\(743\) 31.0000i 1.13728i 0.822587 + 0.568640i \(0.192530\pi\)
−0.822587 + 0.568640i \(0.807470\pi\)
\(744\) 0 0
\(745\) −0.803848 + 13.3923i −0.0294507 + 0.490656i
\(746\) −3.00000 + 5.19615i −0.109838 + 0.190245i
\(747\) 0 0
\(748\) 10.0000i 0.365636i
\(749\) −30.0000 10.3923i −1.09618 0.379727i
\(750\) 0 0
\(751\) −2.00000 3.46410i −0.0729810 0.126407i 0.827225 0.561870i \(-0.189918\pi\)
−0.900207 + 0.435463i \(0.856585\pi\)
\(752\) 11.2583 + 6.50000i 0.410549 + 0.237031i
\(753\) 0 0
\(754\) 0 0
\(755\) 44.0000 22.0000i 1.60132 0.800662i
\(756\) 0 0
\(757\) 26.0000i 0.944986i 0.881334 + 0.472493i \(0.156646\pi\)
−0.881334 + 0.472493i \(0.843354\pi\)
\(758\) −0.866025 + 0.500000i −0.0314555 + 0.0181608i
\(759\) 0 0
\(760\) −15.6244 0.937822i −0.566755 0.0340184i
\(761\) −1.50000 2.59808i −0.0543750 0.0941802i 0.837557 0.546350i \(-0.183983\pi\)
−0.891932 + 0.452170i \(0.850650\pi\)
\(762\) 0 0
\(763\) 46.7654 9.00000i 1.69302 0.325822i
\(764\) −16.0000 −0.578860
\(765\) 0 0
\(766\) −4.50000 + 7.79423i −0.162592 + 0.281617i
\(767\) −3.46410 2.00000i −0.125081 0.0722158i
\(768\) 0 0
\(769\) −51.0000 −1.83911 −0.919554 0.392965i \(-0.871449\pi\)
−0.919554 + 0.392965i \(0.871449\pi\)
\(770\) −29.3301 + 3.83975i −1.05698 + 0.138375i
\(771\) 0 0
\(772\) 15.5885 9.00000i 0.561041 0.323917i
\(773\) −32.0429 18.5000i −1.15250 0.665399i −0.203008 0.979177i \(-0.565072\pi\)
−0.949496 + 0.313778i \(0.898405\pi\)
\(774\) 0 0
\(775\) 29.7846 + 3.58846i 1.06989 + 0.128901i
\(776\) 8.00000 0.287183
\(777\) 0 0
\(778\) 6.00000i 0.215110i
\(779\) 31.5000 + 54.5596i 1.12860 + 1.95480i
\(780\) 0 0
\(781\) −5.00000 + 8.66025i −0.178914 + 0.309888i
\(782\) 5.19615 3.00000i 0.185814 0.107280i
\(783\) 0 0
\(784\) 6.50000 2.59808i 0.232143 0.0927884i
\(785\) 13.0000 + 26.0000i 0.463990 + 0.927980i
\(786\) 0 0
\(787\) 32.9090 + 19.0000i 1.17308 + 0.677277i 0.954403 0.298521i \(-0.0964933\pi\)
0.218675 + 0.975798i \(0.429827\pi\)
\(788\) −23.3827 13.5000i −0.832974 0.480918i
\(789\) 0 0
\(790\) 14.0000 + 28.0000i 0.498098 + 0.996195i
\(791\) −12.0000 + 10.3923i −0.426671 + 0.369508i
\(792\) 0 0
\(793\) −1.73205 + 1.00000i −0.0615069 + 0.0355110i
\(794\) −1.00000 + 1.73205i −0.0354887 + 0.0614682i
\(795\) 0 0
\(796\) 7.00000 + 12.1244i 0.248108 + 0.429736i
\(797\) 30.0000i 1.06265i −0.847167 0.531327i \(-0.821693\pi\)
0.847167 0.531327i \(-0.178307\pi\)
\(798\) 0 0
\(799\) −26.0000 −0.919814
\(800\) −0.598076 + 4.96410i −0.0211452 + 0.175507i
\(801\) 0 0
\(802\) 23.3827 + 13.5000i 0.825671 + 0.476702i
\(803\) 17.3205 10.0000i 0.611227 0.352892i
\(804\) 0 0
\(805\) 10.7942 + 14.0885i 0.380447 + 0.496553i
\(806\) −6.00000 −0.211341
\(807\) 0 0
\(808\) 6.92820 + 4.00000i 0.243733 + 0.140720i
\(809\) 4.50000 7.79423i 0.158212 0.274030i −0.776012 0.630718i \(-0.782761\pi\)
0.934224 + 0.356687i \(0.116094\pi\)
\(810\) 0 0
\(811\) 11.0000 0.386262 0.193131 0.981173i \(-0.438136\pi\)
0.193131 + 0.981173i \(0.438136\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −12.5000 21.6506i −0.438125 0.758854i
\(815\) −26.7846 1.60770i −0.938224 0.0563151i
\(816\) 0 0
\(817\) −60.6218 + 35.0000i −2.12089 + 1.22449i
\(818\) 10.0000i 0.349642i
\(819\) 0 0
\(820\) 18.0000 9.00000i 0.628587 0.314294i
\(821\) 3.00000 + 5.19615i 0.104701 + 0.181347i 0.913616 0.406578i \(-0.133278\pi\)
−0.808915 + 0.587925i \(0.799945\pi\)
\(822\) 0 0
\(823\) 6.92820 + 4.00000i 0.241502 + 0.139431i 0.615867 0.787850i \(-0.288806\pi\)
−0.374365 + 0.927281i \(0.622139\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) −8.00000 + 6.92820i −0.278356 + 0.241063i
\(827\) 42.0000i 1.46048i −0.683189 0.730242i \(-0.739408\pi\)
0.683189 0.730242i \(-0.260592\pi\)
\(828\) 0 0
\(829\) 1.00000 1.73205i 0.0347314 0.0601566i −0.848137 0.529777i \(-0.822276\pi\)
0.882869 + 0.469620i \(0.155609\pi\)
\(830\) 1.33975 22.3205i 0.0465033 0.774756i
\(831\) 0 0
\(832\) 1.00000i 0.0346688i
\(833\) −8.66025 + 11.0000i −0.300060 + 0.381127i
\(834\) 0 0
\(835\) 23.4090 35.4545i 0.810101 1.22695i
\(836\) −17.5000 + 30.3109i −0.605250 + 1.04832i
\(837\) 0 0
\(838\) −2.59808 + 1.50000i −0.0897491 + 0.0518166i
\(839\) 2.00000 0.0690477 0.0345238 0.999404i \(-0.489009\pi\)
0.0345238 + 0.999404i \(0.489009\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 17.3205 10.0000i 0.596904 0.344623i
\(843\) 0 0
\(844\) 9.50000 16.4545i 0.327003 0.566387i
\(845\) 22.3923 + 14.7846i 0.770319 + 0.508606i
\(846\) 0 0
\(847\) −12.1244 + 35.0000i −0.416598 + 1.20261i
\(848\) 1.00000i 0.0343401i
\(849\) 0 0
\(850\) −3.92820 9.19615i −0.134736 0.315425i
\(851\) −7.50000 + 12.9904i −0.257097 + 0.445305i
\(852\) 0 0
\(853\) 49.0000i 1.67773i −0.544341 0.838864i \(-0.683220\pi\)
0.544341 0.838864i \(-0.316780\pi\)
\(854\) 1.00000 + 5.19615i 0.0342193 + 0.177809i
\(855\) 0 0
\(856\) 6.00000 + 10.3923i 0.205076 + 0.355202i
\(857\) 48.4974 + 28.0000i 1.65664 + 0.956462i 0.974249 + 0.225475i \(0.0723933\pi\)
0.682391 + 0.730987i \(0.260940\pi\)
\(858\) 0 0
\(859\) 18.0000 + 31.1769i 0.614152 + 1.06374i 0.990533 + 0.137277i \(0.0438352\pi\)
−0.376381 + 0.926465i \(0.622831\pi\)
\(860\) 10.0000 + 20.0000i 0.340997 + 0.681994i
\(861\) 0 0
\(862\) 18.0000i 0.613082i
\(863\) −12.9904 + 7.50000i −0.442198 + 0.255303i −0.704529 0.709675i \(-0.748842\pi\)
0.262332 + 0.964978i \(0.415509\pi\)
\(864\) 0 0
\(865\) −15.6244 0.937822i −0.531244 0.0318869i
\(866\) −2.00000 3.46410i −0.0679628 0.117715i
\(867\) 0 0
\(868\) −5.19615 + 15.0000i −0.176369 + 0.509133i
\(869\) 70.0000 2.37459
\(870\) 0 0
\(871\) −3.00000 + 5.19615i −0.101651 + 0.176065i
\(872\) −15.5885 9.00000i −0.527892 0.304778i
\(873\) 0 0
\(874\) 21.0000 0.710336
\(875\) 25.4641 15.0526i 0.860844 0.508869i
\(876\) 0 0
\(877\) 23.3827 13.5000i 0.789577 0.455863i −0.0502365 0.998737i \(-0.515998\pi\)
0.839814 + 0.542875i \(0.182664\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 9.33013 + 6.16025i 0.314519 + 0.207662i
\(881\) 3.00000 0.101073 0.0505363 0.998722i \(-0.483907\pi\)
0.0505363 + 0.998722i \(0.483907\pi\)
\(882\) 0 0
\(883\) 52.0000i 1.74994i −0.484178 0.874970i \(-0.660881\pi\)
0.484178 0.874970i \(-0.339119\pi\)
\(884\) 1.00000 + 1.73205i 0.0336336 + 0.0582552i
\(885\) 0 0
\(886\) −3.00000 + 5.19615i −0.100787 + 0.174568i
\(887\) −10.3923 + 6.00000i −0.348939 + 0.201460i −0.664218 0.747539i \(-0.731235\pi\)
0.315279 + 0.948999i \(0.397902\pi\)
\(888\) 0 0
\(889\) −18.0000 + 15.5885i −0.603701 + 0.522820i
\(890\) 10.0000 + 20.0000i 0.335201 + 0.670402i
\(891\) 0 0
\(892\) 13.8564 + 8.00000i 0.463947 + 0.267860i
\(893\) −78.8083 45.5000i −2.63722 1.52260i
\(894\) 0 0
\(895\) 22.0000 11.0000i 0.735379 0.367689i
\(896\) −2.50000 0.866025i −0.0835191 0.0289319i
\(897\) 0 0
\(898\) −7.79423 + 4.50000i −0.260097 + 0.150167i
\(899\) 0 0
\(900\) 0 0
\(901\) −1.00000 1.73205i −0.0333148 0.0577030i
\(902\) 45.0000i 1.49834i
\(903\) 0 0
\(904\) 6.00000 0.199557
\(905\) −3.73205 2.46410i −0.124058 0.0819095i
\(906\) 0 0
\(907\) −13.8564 8.00000i −0.460094 0.265636i 0.251990 0.967730i \(-0.418915\pi\)
−0.712084 + 0.702094i \(0.752248\pi\)
\(908\) −12.1244 + 7.00000i −0.402361 + 0.232303i
\(909\) 0 0
\(910\) −4.69615 + 3.59808i −0.155676 + 0.119275i
\(911\) 6.00000 0.198789 0.0993944 0.995048i \(-0.468309\pi\)
0.0993944 + 0.995048i \(0.468309\pi\)
\(912\) 0 0
\(913\) −43.3013 25.0000i −1.43306 0.827379i
\(914\) −19.0000 + 32.9090i −0.628464 + 1.08853i
\(915\) 0 0
\(916\) −4.00000 −0.132164
\(917\) −14.7224 + 42.5000i −0.486178 + 1.40347i
\(918\) 0 0
\(919\) 28.0000 + 48.4974i 0.923635 + 1.59978i 0.793742 + 0.608254i \(0.208130\pi\)
0.129893 + 0.991528i \(0.458537\pi\)
\(920\) 0.401924 6.69615i 0.0132510 0.220766i
\(921\) 0 0
\(922\) −10.3923 + 6.00000i −0.342252 + 0.197599i
\(923\) 2.00000i 0.0658308i
\(924\) 0 0
\(925\) 20.0000 + 15.0000i 0.657596 + 0.493197i
\(926\) 7.50000 + 12.9904i 0.246465 + 0.426890i
\(927\) 0 0
\(928\) 0 0
\(929\) −16.5000 28.5788i −0.541347 0.937641i −0.998827 0.0484211i \(-0.984581\pi\)
0.457480 0.889220i \(-0.348752\pi\)
\(930\) 0 0
\(931\) −45.5000 + 18.1865i −1.49120 + 0.596040i
\(932\) 0 0
\(933\) 0 0
\(934\) −1.00000 + 1.73205i −0.0327210 + 0.0566744i
\(935\) −22.3205 1.33975i −0.729959 0.0438144i
\(936\) 0 0
\(937\) 34.0000i 1.11073i 0.831606 + 0.555366i \(0.187422\pi\)
−0.831606 + 0.555366i \(0.812578\pi\)
\(938\) 10.3923 + 12.0000i 0.339321 + 0.391814i
\(939\) 0 0
\(940\) −16.0167 + 24.2583i −0.522406 + 0.791219i
\(941\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(942\) 0 0
\(943\) −23.3827 + 13.5000i −0.761445 + 0.439620i
\(944\) 4.00000 0.130189
\(945\) 0 0
\(946\) 50.0000 1.62564
\(947\) 10.3923 6.00000i 0.337705 0.194974i −0.321552 0.946892i \(-0.604204\pi\)
0.659256 + 0.751918i \(0.270871\pi\)
\(948\) 0 0
\(949\) 2.00000 3.46410i 0.0649227 0.112449i
\(950\) 4.18653 34.7487i 0.135829 1.12740i
\(951\) 0 0
\(952\) 5.19615 1.00000i 0.168408 0.0324102i
\(953\) 24.0000i 0.777436i 0.921357 + 0.388718i \(0.127082\pi\)
−0.921357 + 0.388718i \(0.872918\pi\)
\(954\) 0 0
\(955\) 2.14359 35.7128i 0.0693651 1.15564i
\(956\) 10.0000 17.3205i 0.323423 0.560185i
\(957\) 0 0
\(958\) 8.00000i 0.258468i
\(959\) −2.00000 10.3923i −0.0645834 0.335585i
\(960\) 0 0
\(961\) −2.50000 4.33013i −0.0806452 0.139682i
\(962\) −4.33013 2.50000i −0.139609 0.0806032i
\(963\) 0 0
\(964\) −0.500000 0.866025i −0.0161039 0.0278928i
\(965\) 18.0000 + 36.0000i 0.579441 + 1.15888i
\(966\) 0 0
\(967\) 24.0000i 0.771788i 0.922543 + 0.385894i \(0.126107\pi\)
−0.922543 + 0.385894i \(0.873893\pi\)
\(968\) 12.1244 7.00000i 0.389692 0.224989i
\(969\) 0 0
\(970\) −1.07180 + 17.8564i −0.0344133 + 0.573335i
\(971\) 19.5000 + 33.7750i 0.625785 + 1.08389i 0.988389 + 0.151948i \(0.0485545\pi\)
−0.362604 + 0.931943i \(0.618112\pi\)
\(972\) 0 0
\(973\) −13.8564 16.0000i −0.444216 0.512936i
\(974\) −24.0000 −0.769010
\(975\) 0 0
\(976\) 1.00000 1.73205i 0.0320092 0.0554416i
\(977\) −36.3731 21.0000i −1.16368 0.671850i −0.211495 0.977379i \(-0.567833\pi\)
−0.952183 + 0.305530i \(0.901167\pi\)
\(978\) 0 0
\(979\) 50.0000 1.59801
\(980\) 4.92820 + 14.8564i 0.157426 + 0.474570i
\(981\) 0 0
\(982\) 20.7846 12.0000i 0.663264 0.382935i
\(983\) 28.5788 + 16.5000i 0.911523 + 0.526268i 0.880921 0.473263i \(-0.156924\pi\)
0.0306024 + 0.999532i \(0.490257\pi\)
\(984\) 0 0
\(985\) 33.2654 50.3827i 1.05992 1.60533i
\(986\) 0 0
\(987\) 0 0
\(988\) 7.00000i 0.222700i
\(989\) −15.0000 25.9808i −0.476972 0.826140i
\(990\) 0 0
\(991\) 18.0000 31.1769i 0.571789 0.990367i −0.424594 0.905384i \(-0.639583\pi\)
0.996382 0.0849833i \(-0.0270837\pi\)
\(992\) 5.19615 3.00000i 0.164978 0.0952501i
\(993\) 0 0
\(994\) 5.00000 + 1.73205i 0.158590 + 0.0549373i
\(995\) −28.0000 + 14.0000i −0.887660 + 0.443830i
\(996\) 0 0
\(997\) −8.66025 5.00000i −0.274273 0.158352i 0.356555 0.934274i \(-0.383951\pi\)
−0.630828 + 0.775923i \(0.717285\pi\)
\(998\) 24.2487 + 14.0000i 0.767580 + 0.443162i
\(999\) 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 630.2.u.c.109.1 4
3.2 odd 2 210.2.n.a.109.2 yes 4
5.4 even 2 inner 630.2.u.c.109.2 4
7.2 even 3 inner 630.2.u.c.289.2 4
12.11 even 2 1680.2.di.a.529.2 4
15.2 even 4 1050.2.i.o.151.1 2
15.8 even 4 1050.2.i.f.151.1 2
15.14 odd 2 210.2.n.a.109.1 yes 4
21.2 odd 6 210.2.n.a.79.1 4
21.5 even 6 1470.2.n.i.79.1 4
21.11 odd 6 1470.2.g.f.589.2 2
21.17 even 6 1470.2.g.a.589.2 2
21.20 even 2 1470.2.n.i.949.2 4
35.9 even 6 inner 630.2.u.c.289.1 4
60.59 even 2 1680.2.di.a.529.1 4
84.23 even 6 1680.2.di.a.289.1 4
105.2 even 12 1050.2.i.o.751.1 2
105.17 odd 12 7350.2.a.b.1.1 1
105.23 even 12 1050.2.i.f.751.1 2
105.32 even 12 7350.2.a.t.1.1 1
105.38 odd 12 7350.2.a.ch.1.1 1
105.44 odd 6 210.2.n.a.79.2 yes 4
105.53 even 12 7350.2.a.bn.1.1 1
105.59 even 6 1470.2.g.a.589.1 2
105.74 odd 6 1470.2.g.f.589.1 2
105.89 even 6 1470.2.n.i.79.2 4
105.104 even 2 1470.2.n.i.949.1 4
420.359 even 6 1680.2.di.a.289.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.n.a.79.1 4 21.2 odd 6
210.2.n.a.79.2 yes 4 105.44 odd 6
210.2.n.a.109.1 yes 4 15.14 odd 2
210.2.n.a.109.2 yes 4 3.2 odd 2
630.2.u.c.109.1 4 1.1 even 1 trivial
630.2.u.c.109.2 4 5.4 even 2 inner
630.2.u.c.289.1 4 35.9 even 6 inner
630.2.u.c.289.2 4 7.2 even 3 inner
1050.2.i.f.151.1 2 15.8 even 4
1050.2.i.f.751.1 2 105.23 even 12
1050.2.i.o.151.1 2 15.2 even 4
1050.2.i.o.751.1 2 105.2 even 12
1470.2.g.a.589.1 2 105.59 even 6
1470.2.g.a.589.2 2 21.17 even 6
1470.2.g.f.589.1 2 105.74 odd 6
1470.2.g.f.589.2 2 21.11 odd 6
1470.2.n.i.79.1 4 21.5 even 6
1470.2.n.i.79.2 4 105.89 even 6
1470.2.n.i.949.1 4 105.104 even 2
1470.2.n.i.949.2 4 21.20 even 2
1680.2.di.a.289.1 4 84.23 even 6
1680.2.di.a.289.2 4 420.359 even 6
1680.2.di.a.529.1 4 60.59 even 2
1680.2.di.a.529.2 4 12.11 even 2
7350.2.a.b.1.1 1 105.17 odd 12
7350.2.a.t.1.1 1 105.32 even 12
7350.2.a.bn.1.1 1 105.53 even 12
7350.2.a.ch.1.1 1 105.38 odd 12