Properties

Label 630.2.u.a.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 70)
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.a.289.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.133975 - 2.23205i) q^{5} +(-1.73205 - 2.00000i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.133975 - 2.23205i) q^{5} +(-1.73205 - 2.00000i) q^{7} +1.00000i q^{8} +(1.23205 + 1.86603i) q^{10} +(1.50000 - 2.59808i) q^{11} +5.00000i q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} +(-2.50000 - 4.33013i) q^{19} +(-2.00000 - 1.00000i) q^{20} +3.00000i q^{22} +(-6.06218 + 3.50000i) q^{23} +(-4.96410 + 0.598076i) q^{25} +(-2.50000 - 4.33013i) q^{26} +(-2.59808 + 0.500000i) q^{28} -4.00000 q^{29} +(1.00000 - 1.73205i) q^{31} +(0.866025 + 0.500000i) q^{32} +2.00000 q^{34} +(-4.23205 + 4.13397i) q^{35} +(0.866025 - 0.500000i) q^{37} +(4.33013 + 2.50000i) q^{38} +(2.23205 - 0.133975i) q^{40} -3.00000 q^{41} -2.00000i q^{43} +(-1.50000 - 2.59808i) q^{44} +(3.50000 - 6.06218i) q^{46} +(6.06218 - 3.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(4.00000 - 3.00000i) q^{50} +(4.33013 + 2.50000i) q^{52} +(-7.79423 - 4.50000i) q^{53} +(-6.00000 - 3.00000i) q^{55} +(2.00000 - 1.73205i) q^{56} +(3.46410 - 2.00000i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{61} +2.00000i q^{62} -1.00000 q^{64} +(11.1603 - 0.669873i) q^{65} +(-1.73205 - 1.00000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +(1.59808 - 5.69615i) q^{70} +6.00000 q^{71} +(-13.8564 - 8.00000i) q^{73} +(-0.500000 + 0.866025i) q^{74} -5.00000 q^{76} +(-7.79423 + 1.50000i) q^{77} +(7.00000 + 12.1244i) q^{79} +(-1.86603 + 1.23205i) q^{80} +(2.59808 - 1.50000i) q^{82} -6.00000i q^{83} +(-2.00000 + 4.00000i) q^{85} +(1.00000 + 1.73205i) q^{86} +(2.59808 + 1.50000i) q^{88} +(-1.00000 - 1.73205i) q^{89} +(10.0000 - 8.66025i) q^{91} +7.00000i q^{92} +(-3.50000 + 6.06218i) q^{94} +(-9.33013 + 6.16025i) q^{95} -12.0000i q^{97} +(-2.59808 - 6.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} - 4 q^{5} - 2 q^{10} + 6 q^{11} + 10 q^{14} - 2 q^{16} - 10 q^{19} - 8 q^{20} - 6 q^{25} - 10 q^{26} - 16 q^{29} + 4 q^{31} + 8 q^{34} - 10 q^{35} + 2 q^{40} - 12 q^{41} - 6 q^{44} + 14 q^{46} - 4 q^{49} + 16 q^{50} - 24 q^{55} + 8 q^{56} + 8 q^{59} - 12 q^{61} - 4 q^{64} + 10 q^{65} - 4 q^{70} + 24 q^{71} - 2 q^{74} - 20 q^{76} + 28 q^{79} - 4 q^{80} - 8 q^{85} + 4 q^{86} - 4 q^{89} + 40 q^{91} - 14 q^{94} - 20 q^{95}+O(q^{100}) \) 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
\(5\) −0.133975 2.23205i −0.0599153 0.998203i
\(6\) 0 0
\(7\) −1.73205 2.00000i −0.654654 0.755929i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.23205 + 1.86603i 0.389609 + 0.590089i
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0 0
\(13\) 5.00000i 1.38675i 0.720577 + 0.693375i \(0.243877\pi\)
−0.720577 + 0.693375i \(0.756123\pi\)
\(14\) 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 0.275029 0.961436i \(-0.411312\pi\)
−0.695113 + 0.718900i \(0.744646\pi\)
\(18\) 0 0
\(19\) −2.50000 4.33013i −0.573539 0.993399i −0.996199 0.0871106i \(-0.972237\pi\)
0.422659 0.906289i \(-0.361097\pi\)
\(20\) −2.00000 1.00000i −0.447214 0.223607i
\(21\) 0 0
\(22\) 3.00000i 0.639602i
\(23\) −6.06218 + 3.50000i −1.26405 + 0.729800i −0.973856 0.227167i \(-0.927054\pi\)
−0.290196 + 0.956967i \(0.593720\pi\)
\(24\) 0 0
\(25\) −4.96410 + 0.598076i −0.992820 + 0.119615i
\(26\) −2.50000 4.33013i −0.490290 0.849208i
\(27\) 0 0
\(28\) −2.59808 + 0.500000i −0.490990 + 0.0944911i
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) 1.00000 1.73205i 0.179605 0.311086i −0.762140 0.647412i \(-0.775851\pi\)
0.941745 + 0.336327i \(0.109185\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) −4.23205 + 4.13397i −0.715347 + 0.698769i
\(36\) 0 0
\(37\) 0.866025 0.500000i 0.142374 0.0821995i −0.427121 0.904194i \(-0.640472\pi\)
0.569495 + 0.821995i \(0.307139\pi\)
\(38\) 4.33013 + 2.50000i 0.702439 + 0.405554i
\(39\) 0 0
\(40\) 2.23205 0.133975i 0.352918 0.0211832i
\(41\) −3.00000 −0.468521 −0.234261 0.972174i \(-0.575267\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i −0.988304 0.152499i \(-0.951268\pi\)
0.988304 0.152499i \(-0.0487319\pi\)
\(44\) −1.50000 2.59808i −0.226134 0.391675i
\(45\) 0 0
\(46\) 3.50000 6.06218i 0.516047 0.893819i
\(47\) 6.06218 3.50000i 0.884260 0.510527i 0.0121990 0.999926i \(-0.496117\pi\)
0.872060 + 0.489398i \(0.162783\pi\)
\(48\) 0 0
\(49\) −1.00000 + 6.92820i −0.142857 + 0.989743i
\(50\) 4.00000 3.00000i 0.565685 0.424264i
\(51\) 0 0
\(52\) 4.33013 + 2.50000i 0.600481 + 0.346688i
\(53\) −7.79423 4.50000i −1.07062 0.618123i −0.142269 0.989828i \(-0.545440\pi\)
−0.928351 + 0.371706i \(0.878773\pi\)
\(54\) 0 0
\(55\) −6.00000 3.00000i −0.809040 0.404520i
\(56\) 2.00000 1.73205i 0.267261 0.231455i
\(57\) 0 0
\(58\) 3.46410 2.00000i 0.454859 0.262613i
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 0 0
\(61\) −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i \(-0.292159\pi\)
−0.991645 + 0.128994i \(0.958825\pi\)
\(62\) 2.00000i 0.254000i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 11.1603 0.669873i 1.38426 0.0830875i
\(66\) 0 0
\(67\) −1.73205 1.00000i −0.211604 0.122169i 0.390453 0.920623i \(-0.372318\pi\)
−0.602056 + 0.798454i \(0.705652\pi\)
\(68\) −1.73205 + 1.00000i −0.210042 + 0.121268i
\(69\) 0 0
\(70\) 1.59808 5.69615i 0.191007 0.680820i
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) −13.8564 8.00000i −1.62177 0.936329i −0.986447 0.164083i \(-0.947534\pi\)
−0.635323 0.772246i \(-0.719133\pi\)
\(74\) −0.500000 + 0.866025i −0.0581238 + 0.100673i
\(75\) 0 0
\(76\) −5.00000 −0.573539
\(77\) −7.79423 + 1.50000i −0.888235 + 0.170941i
\(78\) 0 0
\(79\) 7.00000 + 12.1244i 0.787562 + 1.36410i 0.927457 + 0.373930i \(0.121990\pi\)
−0.139895 + 0.990166i \(0.544677\pi\)
\(80\) −1.86603 + 1.23205i −0.208628 + 0.137747i
\(81\) 0 0
\(82\) 2.59808 1.50000i 0.286910 0.165647i
\(83\) 6.00000i 0.658586i −0.944228 0.329293i \(-0.893190\pi\)
0.944228 0.329293i \(-0.106810\pi\)
\(84\) 0 0
\(85\) −2.00000 + 4.00000i −0.216930 + 0.433861i
\(86\) 1.00000 + 1.73205i 0.107833 + 0.186772i
\(87\) 0 0
\(88\) 2.59808 + 1.50000i 0.276956 + 0.159901i
\(89\) −1.00000 1.73205i −0.106000 0.183597i 0.808146 0.588982i \(-0.200471\pi\)
−0.914146 + 0.405385i \(0.867138\pi\)
\(90\) 0 0
\(91\) 10.0000 8.66025i 1.04828 0.907841i
\(92\) 7.00000i 0.729800i
\(93\) 0 0
\(94\) −3.50000 + 6.06218i −0.360997 + 0.625266i
\(95\) −9.33013 + 6.16025i −0.957251 + 0.632029i
\(96\) 0 0
\(97\) 12.0000i 1.21842i −0.793011 0.609208i \(-0.791488\pi\)
0.793011 0.609208i \(-0.208512\pi\)
\(98\) −2.59808 6.50000i −0.262445 0.656599i
\(99\) 0 0
\(100\) −1.96410 + 4.59808i −0.196410 + 0.459808i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) 6.92820 4.00000i 0.682656 0.394132i −0.118199 0.992990i \(-0.537712\pi\)
0.800855 + 0.598858i \(0.204379\pi\)
\(104\) −5.00000 −0.490290
\(105\) 0 0
\(106\) 9.00000 0.874157
\(107\) 13.8564 8.00000i 1.33955 0.773389i 0.352809 0.935695i \(-0.385227\pi\)
0.986740 + 0.162306i \(0.0518932\pi\)
\(108\) 0 0
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 6.69615 0.401924i 0.638453 0.0383219i
\(111\) 0 0
\(112\) −0.866025 + 2.50000i −0.0818317 + 0.236228i
\(113\) 14.0000i 1.31701i 0.752577 + 0.658505i \(0.228811\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 0 0
\(115\) 8.62436 + 13.0622i 0.804225 + 1.21805i
\(116\) −2.00000 + 3.46410i −0.185695 + 0.321634i
\(117\) 0 0
\(118\) 4.00000i 0.368230i
\(119\) 1.00000 + 5.19615i 0.0916698 + 0.476331i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 5.19615 + 3.00000i 0.470438 + 0.271607i
\(123\) 0 0
\(124\) −1.00000 1.73205i −0.0898027 0.155543i
\(125\) 2.00000 + 11.0000i 0.178885 + 0.983870i
\(126\) 0 0
\(127\) 7.00000i 0.621150i 0.950549 + 0.310575i \(0.100522\pi\)
−0.950549 + 0.310575i \(0.899478\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −9.33013 + 6.16025i −0.818306 + 0.540290i
\(131\) −0.500000 0.866025i −0.0436852 0.0756650i 0.843356 0.537355i \(-0.180577\pi\)
−0.887041 + 0.461690i \(0.847243\pi\)
\(132\) 0 0
\(133\) −4.33013 + 12.5000i −0.375470 + 1.08389i
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) 1.00000 1.73205i 0.0857493 0.148522i
\(137\) −6.92820 4.00000i −0.591916 0.341743i 0.173939 0.984757i \(-0.444351\pi\)
−0.765855 + 0.643013i \(0.777684\pi\)
\(138\) 0 0
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 1.46410 + 5.73205i 0.123739 + 0.484447i
\(141\) 0 0
\(142\) −5.19615 + 3.00000i −0.436051 + 0.251754i
\(143\) 12.9904 + 7.50000i 1.08631 + 0.627182i
\(144\) 0 0
\(145\) 0.535898 + 8.92820i 0.0445039 + 0.741447i
\(146\) 16.0000 1.32417
\(147\) 0 0
\(148\) 1.00000i 0.0821995i
\(149\) 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0 0
\(151\) 3.00000 5.19615i 0.244137 0.422857i −0.717752 0.696299i \(-0.754829\pi\)
0.961888 + 0.273442i \(0.0881622\pi\)
\(152\) 4.33013 2.50000i 0.351220 0.202777i
\(153\) 0 0
\(154\) 6.00000 5.19615i 0.483494 0.418718i
\(155\) −4.00000 2.00000i −0.321288 0.160644i
\(156\) 0 0
\(157\) 7.79423 + 4.50000i 0.622047 + 0.359139i 0.777666 0.628678i \(-0.216404\pi\)
−0.155618 + 0.987817i \(0.549737\pi\)
\(158\) −12.1244 7.00000i −0.964562 0.556890i
\(159\) 0 0
\(160\) 1.00000 2.00000i 0.0790569 0.158114i
\(161\) 17.5000 + 6.06218i 1.37919 + 0.477767i
\(162\) 0 0
\(163\) 10.3923 6.00000i 0.813988 0.469956i −0.0343508 0.999410i \(-0.510936\pi\)
0.848339 + 0.529454i \(0.177603\pi\)
\(164\) −1.50000 + 2.59808i −0.117130 + 0.202876i
\(165\) 0 0
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) 15.0000i 1.16073i −0.814355 0.580367i \(-0.802909\pi\)
0.814355 0.580367i \(-0.197091\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) −0.267949 4.46410i −0.0205508 0.342381i
\(171\) 0 0
\(172\) −1.73205 1.00000i −0.132068 0.0762493i
\(173\) 7.79423 4.50000i 0.592584 0.342129i −0.173534 0.984828i \(-0.555519\pi\)
0.766119 + 0.642699i \(0.222185\pi\)
\(174\) 0 0
\(175\) 9.79423 + 8.89230i 0.740374 + 0.672195i
\(176\) −3.00000 −0.226134
\(177\) 0 0
\(178\) 1.73205 + 1.00000i 0.129823 + 0.0749532i
\(179\) −6.50000 + 11.2583i −0.485833 + 0.841487i −0.999867 0.0162823i \(-0.994817\pi\)
0.514035 + 0.857769i \(0.328150\pi\)
\(180\) 0 0
\(181\) 26.0000 1.93256 0.966282 0.257485i \(-0.0828937\pi\)
0.966282 + 0.257485i \(0.0828937\pi\)
\(182\) −4.33013 + 12.5000i −0.320970 + 0.926562i
\(183\) 0 0
\(184\) −3.50000 6.06218i −0.258023 0.446910i
\(185\) −1.23205 1.86603i −0.0905822 0.137193i
\(186\) 0 0
\(187\) −5.19615 + 3.00000i −0.379980 + 0.219382i
\(188\) 7.00000i 0.510527i
\(189\) 0 0
\(190\) 5.00000 10.0000i 0.362738 0.725476i
\(191\) −10.0000 17.3205i −0.723575 1.25327i −0.959558 0.281511i \(-0.909164\pi\)
0.235983 0.971757i \(-0.424169\pi\)
\(192\) 0 0
\(193\) −8.66025 5.00000i −0.623379 0.359908i 0.154805 0.987945i \(-0.450525\pi\)
−0.778183 + 0.628037i \(0.783859\pi\)
\(194\) 6.00000 + 10.3923i 0.430775 + 0.746124i
\(195\) 0 0
\(196\) 5.50000 + 4.33013i 0.392857 + 0.309295i
\(197\) 5.00000i 0.356235i 0.984009 + 0.178118i \(0.0570008\pi\)
−0.984009 + 0.178118i \(0.942999\pi\)
\(198\) 0 0
\(199\) 9.00000 15.5885i 0.637993 1.10504i −0.347879 0.937539i \(-0.613098\pi\)
0.985873 0.167497i \(-0.0535685\pi\)
\(200\) −0.598076 4.96410i −0.0422904 0.351015i
\(201\) 0 0
\(202\) 0 0
\(203\) 6.92820 + 8.00000i 0.486265 + 0.561490i
\(204\) 0 0
\(205\) 0.401924 + 6.69615i 0.0280716 + 0.467680i
\(206\) −4.00000 + 6.92820i −0.278693 + 0.482711i
\(207\) 0 0
\(208\) 4.33013 2.50000i 0.300240 0.173344i
\(209\) −15.0000 −1.03757
\(210\) 0 0
\(211\) −9.00000 −0.619586 −0.309793 0.950804i \(-0.600260\pi\)
−0.309793 + 0.950804i \(0.600260\pi\)
\(212\) −7.79423 + 4.50000i −0.535310 + 0.309061i
\(213\) 0 0
\(214\) −8.00000 + 13.8564i −0.546869 + 0.947204i
\(215\) −4.46410 + 0.267949i −0.304449 + 0.0182740i
\(216\) 0 0
\(217\) −5.19615 + 1.00000i −0.352738 + 0.0678844i
\(218\) 2.00000i 0.135457i
\(219\) 0 0
\(220\) −5.59808 + 3.69615i −0.377422 + 0.249195i
\(221\) 5.00000 8.66025i 0.336336 0.582552i
\(222\) 0 0
\(223\) 8.00000i 0.535720i 0.963458 + 0.267860i \(0.0863164\pi\)
−0.963458 + 0.267860i \(0.913684\pi\)
\(224\) −0.500000 2.59808i −0.0334077 0.173591i
\(225\) 0 0
\(226\) −7.00000 12.1244i −0.465633 0.806500i
\(227\) −5.19615 3.00000i −0.344881 0.199117i 0.317547 0.948242i \(-0.397141\pi\)
−0.662428 + 0.749125i \(0.730474\pi\)
\(228\) 0 0
\(229\) 8.00000 + 13.8564i 0.528655 + 0.915657i 0.999442 + 0.0334101i \(0.0106368\pi\)
−0.470787 + 0.882247i \(0.656030\pi\)
\(230\) −14.0000 7.00000i −0.923133 0.461566i
\(231\) 0 0
\(232\) 4.00000i 0.262613i
\(233\) −6.92820 + 4.00000i −0.453882 + 0.262049i −0.709468 0.704737i \(-0.751065\pi\)
0.255586 + 0.966786i \(0.417731\pi\)
\(234\) 0 0
\(235\) −8.62436 13.0622i −0.562591 0.852083i
\(236\) −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
\(241\) 4.50000 7.79423i 0.289870 0.502070i −0.683908 0.729568i \(-0.739721\pi\)
0.973779 + 0.227498i \(0.0730544\pi\)
\(242\) −1.73205 1.00000i −0.111340 0.0642824i
\(243\) 0 0
\(244\) −6.00000 −0.384111
\(245\) 15.5981 + 1.30385i 0.996525 + 0.0832998i
\(246\) 0 0
\(247\) 21.6506 12.5000i 1.37760 0.795356i
\(248\) 1.73205 + 1.00000i 0.109985 + 0.0635001i
\(249\) 0 0
\(250\) −7.23205 8.52628i −0.457395 0.539249i
\(251\) −5.00000 −0.315597 −0.157799 0.987471i \(-0.550440\pi\)
−0.157799 + 0.987471i \(0.550440\pi\)
\(252\) 0 0
\(253\) 21.0000i 1.32026i
\(254\) −3.50000 6.06218i −0.219610 0.380375i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 5.19615 3.00000i 0.324127 0.187135i −0.329104 0.944294i \(-0.606747\pi\)
0.653231 + 0.757159i \(0.273413\pi\)
\(258\) 0 0
\(259\) −2.50000 0.866025i −0.155342 0.0538122i
\(260\) 5.00000 10.0000i 0.310087 0.620174i
\(261\) 0 0
\(262\) 0.866025 + 0.500000i 0.0535032 + 0.0308901i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) −9.00000 + 18.0000i −0.552866 + 1.10573i
\(266\) −2.50000 12.9904i −0.153285 0.796491i
\(267\) 0 0
\(268\) −1.73205 + 1.00000i −0.105802 + 0.0610847i
\(269\) 5.00000 8.66025i 0.304855 0.528025i −0.672374 0.740212i \(-0.734725\pi\)
0.977229 + 0.212187i \(0.0680585\pi\)
\(270\) 0 0
\(271\) −12.0000 20.7846i −0.728948 1.26258i −0.957328 0.289003i \(-0.906676\pi\)
0.228380 0.973572i \(-0.426657\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) 8.00000 0.483298
\(275\) −5.89230 + 13.7942i −0.355319 + 0.831823i
\(276\) 0 0
\(277\) 1.73205 + 1.00000i 0.104069 + 0.0600842i 0.551131 0.834419i \(-0.314196\pi\)
−0.447062 + 0.894503i \(0.647530\pi\)
\(278\) 13.8564 8.00000i 0.831052 0.479808i
\(279\) 0 0
\(280\) −4.13397 4.23205i −0.247052 0.252913i
\(281\) −9.00000 −0.536895 −0.268447 0.963294i \(-0.586511\pi\)
−0.268447 + 0.963294i \(0.586511\pi\)
\(282\) 0 0
\(283\) 12.1244 + 7.00000i 0.720718 + 0.416107i 0.815017 0.579437i \(-0.196728\pi\)
−0.0942988 + 0.995544i \(0.530061\pi\)
\(284\) 3.00000 5.19615i 0.178017 0.308335i
\(285\) 0 0
\(286\) −15.0000 −0.886969
\(287\) 5.19615 + 6.00000i 0.306719 + 0.354169i
\(288\) 0 0
\(289\) −6.50000 11.2583i −0.382353 0.662255i
\(290\) −4.92820 7.46410i −0.289394 0.438307i
\(291\) 0 0
\(292\) −13.8564 + 8.00000i −0.810885 + 0.468165i
\(293\) 9.00000i 0.525786i −0.964825 0.262893i \(-0.915323\pi\)
0.964825 0.262893i \(-0.0846766\pi\)
\(294\) 0 0
\(295\) −8.00000 4.00000i −0.465778 0.232889i
\(296\) 0.500000 + 0.866025i 0.0290619 + 0.0503367i
\(297\) 0 0
\(298\) −15.5885 9.00000i −0.903015 0.521356i
\(299\) −17.5000 30.3109i −1.01205 1.75292i
\(300\) 0 0
\(301\) −4.00000 + 3.46410i −0.230556 + 0.199667i
\(302\) 6.00000i 0.345261i
\(303\) 0 0
\(304\) −2.50000 + 4.33013i −0.143385 + 0.248350i
\(305\) −11.1962 + 7.39230i −0.641090 + 0.423282i
\(306\) 0 0
\(307\) 22.0000i 1.25561i −0.778372 0.627803i \(-0.783954\pi\)
0.778372 0.627803i \(-0.216046\pi\)
\(308\) −2.59808 + 7.50000i −0.148039 + 0.427352i
\(309\) 0 0
\(310\) 4.46410 0.267949i 0.253544 0.0152185i
\(311\) 3.00000 5.19615i 0.170114 0.294647i −0.768345 0.640036i \(-0.778920\pi\)
0.938460 + 0.345389i \(0.112253\pi\)
\(312\) 0 0
\(313\) 19.0526 11.0000i 1.07691 0.621757i 0.146852 0.989158i \(-0.453086\pi\)
0.930062 + 0.367402i \(0.119753\pi\)
\(314\) −9.00000 −0.507899
\(315\) 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
\(319\) −6.00000 + 10.3923i −0.335936 + 0.581857i
\(320\) 0.133975 + 2.23205i 0.00748941 + 0.124775i
\(321\) 0 0
\(322\) −18.1865 + 3.50000i −1.01350 + 0.195047i
\(323\) 10.0000i 0.556415i
\(324\) 0 0
\(325\) −2.99038 24.8205i −0.165876 1.37679i
\(326\) −6.00000 + 10.3923i −0.332309 + 0.575577i
\(327\) 0 0
\(328\) 3.00000i 0.165647i
\(329\) −17.5000 6.06218i −0.964806 0.334219i
\(330\) 0 0
\(331\) −2.50000 4.33013i −0.137412 0.238005i 0.789104 0.614260i \(-0.210545\pi\)
−0.926516 + 0.376254i \(0.877212\pi\)
\(332\) −5.19615 3.00000i −0.285176 0.164646i
\(333\) 0 0
\(334\) 7.50000 + 12.9904i 0.410382 + 0.710802i
\(335\) −2.00000 + 4.00000i −0.109272 + 0.218543i
\(336\) 0 0
\(337\) 10.0000i 0.544735i 0.962193 + 0.272367i \(0.0878066\pi\)
−0.962193 + 0.272367i \(0.912193\pi\)
\(338\) 10.3923 6.00000i 0.565267 0.326357i
\(339\) 0 0
\(340\) 2.46410 + 3.73205i 0.133635 + 0.202399i
\(341\) −3.00000 5.19615i −0.162459 0.281387i
\(342\) 0 0
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) 2.00000 0.107833
\(345\) 0 0
\(346\) −4.50000 + 7.79423i −0.241921 + 0.419020i
\(347\) −10.3923 6.00000i −0.557888 0.322097i 0.194409 0.980921i \(-0.437721\pi\)
−0.752297 + 0.658824i \(0.771054\pi\)
\(348\) 0 0
\(349\) 12.0000 0.642345 0.321173 0.947021i \(-0.395923\pi\)
0.321173 + 0.947021i \(0.395923\pi\)
\(350\) −12.9282 2.80385i −0.691042 0.149872i
\(351\) 0 0
\(352\) 2.59808 1.50000i 0.138478 0.0799503i
\(353\) −20.7846 12.0000i −1.10625 0.638696i −0.168397 0.985719i \(-0.553859\pi\)
−0.937856 + 0.347024i \(0.887192\pi\)
\(354\) 0 0
\(355\) −0.803848 13.3923i −0.0426638 0.710790i
\(356\) −2.00000 −0.106000
\(357\) 0 0
\(358\) 13.0000i 0.687071i
\(359\) −8.00000 13.8564i −0.422224 0.731313i 0.573933 0.818902i \(-0.305417\pi\)
−0.996157 + 0.0875892i \(0.972084\pi\)
\(360\) 0 0
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) −22.5167 + 13.0000i −1.18345 + 0.683265i
\(363\) 0 0
\(364\) −2.50000 12.9904i −0.131036 0.680881i
\(365\) −16.0000 + 32.0000i −0.837478 + 1.67496i
\(366\) 0 0
\(367\) −11.2583 6.50000i −0.587680 0.339297i 0.176500 0.984301i \(-0.443523\pi\)
−0.764180 + 0.645003i \(0.776856\pi\)
\(368\) 6.06218 + 3.50000i 0.316013 + 0.182450i
\(369\) 0 0
\(370\) 2.00000 + 1.00000i 0.103975 + 0.0519875i
\(371\) 4.50000 + 23.3827i 0.233628 + 1.21397i
\(372\) 0 0
\(373\) −22.5167 + 13.0000i −1.16587 + 0.673114i −0.952703 0.303902i \(-0.901711\pi\)
−0.213165 + 0.977016i \(0.568377\pi\)
\(374\) 3.00000 5.19615i 0.155126 0.268687i
\(375\) 0 0
\(376\) 3.50000 + 6.06218i 0.180499 + 0.312633i
\(377\) 20.0000i 1.03005i
\(378\) 0 0
\(379\) 29.0000 1.48963 0.744815 0.667271i \(-0.232538\pi\)
0.744815 + 0.667271i \(0.232538\pi\)
\(380\) 0.669873 + 11.1603i 0.0343638 + 0.572509i
\(381\) 0 0
\(382\) 17.3205 + 10.0000i 0.886194 + 0.511645i
\(383\) 18.1865 10.5000i 0.929288 0.536525i 0.0427020 0.999088i \(-0.486403\pi\)
0.886586 + 0.462563i \(0.153070\pi\)
\(384\) 0 0
\(385\) 4.39230 + 17.1962i 0.223853 + 0.876397i
\(386\) 10.0000 0.508987
\(387\) 0 0
\(388\) −10.3923 6.00000i −0.527589 0.304604i
\(389\) 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) 0 0
\(391\) 14.0000 0.708010
\(392\) −6.92820 1.00000i −0.349927 0.0505076i
\(393\) 0 0
\(394\) −2.50000 4.33013i −0.125948 0.218149i
\(395\) 26.1244 17.2487i 1.31446 0.867877i
\(396\) 0 0
\(397\) −12.1244 + 7.00000i −0.608504 + 0.351320i −0.772380 0.635161i \(-0.780934\pi\)
0.163876 + 0.986481i \(0.447600\pi\)
\(398\) 18.0000i 0.902258i
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) −7.50000 12.9904i −0.374532 0.648709i 0.615725 0.787961i \(-0.288863\pi\)
−0.990257 + 0.139253i \(0.955530\pi\)
\(402\) 0 0
\(403\) 8.66025 + 5.00000i 0.431398 + 0.249068i
\(404\) 0 0
\(405\) 0 0
\(406\) −10.0000 3.46410i −0.496292 0.171920i
\(407\) 3.00000i 0.148704i
\(408\) 0 0
\(409\) −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) −3.69615 5.59808i −0.182540 0.276469i
\(411\) 0 0
\(412\) 8.00000i 0.394132i
\(413\) −10.3923 + 2.00000i −0.511372 + 0.0984136i
\(414\) 0 0
\(415\) −13.3923 + 0.803848i −0.657402 + 0.0394593i
\(416\) −2.50000 + 4.33013i −0.122573 + 0.212302i
\(417\) 0 0
\(418\) 12.9904 7.50000i 0.635380 0.366837i
\(419\) 35.0000 1.70986 0.854931 0.518742i \(-0.173599\pi\)
0.854931 + 0.518742i \(0.173599\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 7.79423 4.50000i 0.379417 0.219057i
\(423\) 0 0
\(424\) 4.50000 7.79423i 0.218539 0.378521i
\(425\) 9.19615 + 3.92820i 0.446079 + 0.190546i
\(426\) 0 0
\(427\) −5.19615 + 15.0000i −0.251459 + 0.725901i
\(428\) 16.0000i 0.773389i
\(429\) 0 0
\(430\) 3.73205 2.46410i 0.179975 0.118830i
\(431\) 1.00000 1.73205i 0.0481683 0.0834300i −0.840936 0.541135i \(-0.817995\pi\)
0.889104 + 0.457705i \(0.151328\pi\)
\(432\) 0 0
\(433\) 28.0000i 1.34559i −0.739827 0.672797i \(-0.765093\pi\)
0.739827 0.672797i \(-0.234907\pi\)
\(434\) 4.00000 3.46410i 0.192006 0.166282i
\(435\) 0 0
\(436\) −1.00000 1.73205i −0.0478913 0.0829502i
\(437\) 30.3109 + 17.5000i 1.44997 + 0.837139i
\(438\) 0 0
\(439\) −14.0000 24.2487i −0.668184 1.15733i −0.978412 0.206666i \(-0.933739\pi\)
0.310228 0.950662i \(-0.399595\pi\)
\(440\) 3.00000 6.00000i 0.143019 0.286039i
\(441\) 0 0
\(442\) 10.0000i 0.475651i
\(443\) 25.9808 15.0000i 1.23438 0.712672i 0.266443 0.963851i \(-0.414152\pi\)
0.967941 + 0.251179i \(0.0808184\pi\)
\(444\) 0 0
\(445\) −3.73205 + 2.46410i −0.176916 + 0.116810i
\(446\) −4.00000 6.92820i −0.189405 0.328060i
\(447\) 0 0
\(448\) 1.73205 + 2.00000i 0.0818317 + 0.0944911i
\(449\) 5.00000 0.235965 0.117982 0.993016i \(-0.462357\pi\)
0.117982 + 0.993016i \(0.462357\pi\)
\(450\) 0 0
\(451\) −4.50000 + 7.79423i −0.211897 + 0.367016i
\(452\) 12.1244 + 7.00000i 0.570282 + 0.329252i
\(453\) 0 0
\(454\) 6.00000 0.281594
\(455\) −20.6699 21.1603i −0.969019 0.992008i
\(456\) 0 0
\(457\) −8.66025 + 5.00000i −0.405110 + 0.233890i −0.688686 0.725059i \(-0.741812\pi\)
0.283577 + 0.958950i \(0.408479\pi\)
\(458\) −13.8564 8.00000i −0.647467 0.373815i
\(459\) 0 0
\(460\) 15.6244 0.937822i 0.728489 0.0437262i
\(461\) 32.0000 1.49039 0.745194 0.666847i \(-0.232357\pi\)
0.745194 + 0.666847i \(0.232357\pi\)
\(462\) 0 0
\(463\) 17.0000i 0.790057i 0.918669 + 0.395029i \(0.129265\pi\)
−0.918669 + 0.395029i \(0.870735\pi\)
\(464\) 2.00000 + 3.46410i 0.0928477 + 0.160817i
\(465\) 0 0
\(466\) 4.00000 6.92820i 0.185296 0.320943i
\(467\) −29.4449 + 17.0000i −1.36255 + 0.786666i −0.989962 0.141332i \(-0.954861\pi\)
−0.372584 + 0.927999i \(0.621528\pi\)
\(468\) 0 0
\(469\) 1.00000 + 5.19615i 0.0461757 + 0.239936i
\(470\) 14.0000 + 7.00000i 0.645772 + 0.322886i
\(471\) 0 0
\(472\) 3.46410 + 2.00000i 0.159448 + 0.0920575i
\(473\) −5.19615 3.00000i −0.238919 0.137940i
\(474\) 0 0
\(475\) 15.0000 + 20.0000i 0.688247 + 0.917663i
\(476\) 5.00000 + 1.73205i 0.229175 + 0.0793884i
\(477\) 0 0
\(478\) −17.3205 + 10.0000i −0.792222 + 0.457389i
\(479\) −18.0000 + 31.1769i −0.822441 + 1.42451i 0.0814184 + 0.996680i \(0.474055\pi\)
−0.903859 + 0.427830i \(0.859278\pi\)
\(480\) 0 0
\(481\) 2.50000 + 4.33013i 0.113990 + 0.197437i
\(482\) 9.00000i 0.409939i
\(483\) 0 0
\(484\) 2.00000 0.0909091
\(485\) −26.7846 + 1.60770i −1.21623 + 0.0730017i
\(486\) 0 0
\(487\) 27.7128 + 16.0000i 1.25579 + 0.725029i 0.972253 0.233933i \(-0.0751596\pi\)
0.283535 + 0.958962i \(0.408493\pi\)
\(488\) 5.19615 3.00000i 0.235219 0.135804i
\(489\) 0 0
\(490\) −14.1603 + 6.66987i −0.639695 + 0.301314i
\(491\) −24.0000 −1.08310 −0.541552 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) 0 0
\(493\) 6.92820 + 4.00000i 0.312031 + 0.180151i
\(494\) −12.5000 + 21.6506i −0.562402 + 0.974108i
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) −10.3923 12.0000i −0.466159 0.538274i
\(498\) 0 0
\(499\) 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) 10.5263 + 3.76795i 0.470750 + 0.168508i
\(501\) 0 0
\(502\) 4.33013 2.50000i 0.193263 0.111580i
\(503\) 40.0000i 1.78351i 0.452517 + 0.891756i \(0.350526\pi\)
−0.452517 + 0.891756i \(0.649474\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −10.5000 18.1865i −0.466782 0.808490i
\(507\) 0 0
\(508\) 6.06218 + 3.50000i 0.268966 + 0.155287i
\(509\) 17.0000 + 29.4449i 0.753512 + 1.30512i 0.946111 + 0.323843i \(0.104975\pi\)
−0.192599 + 0.981278i \(0.561692\pi\)
\(510\) 0 0
\(511\) 8.00000 + 41.5692i 0.353899 + 1.83891i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −3.00000 + 5.19615i −0.132324 + 0.229192i
\(515\) −9.85641 14.9282i −0.434325 0.657815i
\(516\) 0 0
\(517\) 21.0000i 0.923579i
\(518\) 2.59808 0.500000i 0.114153 0.0219687i
\(519\) 0 0
\(520\) 0.669873 + 11.1603i 0.0293759 + 0.489410i
\(521\) −13.5000 + 23.3827i −0.591446 + 1.02441i 0.402592 + 0.915379i \(0.368109\pi\)
−0.994038 + 0.109035i \(0.965224\pi\)
\(522\) 0 0
\(523\) −13.8564 + 8.00000i −0.605898 + 0.349816i −0.771358 0.636401i \(-0.780422\pi\)
0.165460 + 0.986216i \(0.447089\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 0 0
\(526\) 0 0
\(527\) −3.46410 + 2.00000i −0.150899 + 0.0871214i
\(528\) 0 0
\(529\) 13.0000 22.5167i 0.565217 0.978985i
\(530\) −1.20577 20.0885i −0.0523754 0.872587i
\(531\) 0 0
\(532\) 8.66025 + 10.0000i 0.375470 + 0.433555i
\(533\) 15.0000i 0.649722i
\(534\) 0 0
\(535\) −19.7128 29.8564i −0.852259 1.29081i
\(536\) 1.00000 1.73205i 0.0431934 0.0748132i
\(537\) 0 0
\(538\) 10.0000i 0.431131i
\(539\) 16.5000 + 12.9904i 0.710705 + 0.559535i
\(540\) 0 0
\(541\) 8.00000 + 13.8564i 0.343947 + 0.595733i 0.985162 0.171628i \(-0.0549027\pi\)
−0.641215 + 0.767361i \(0.721569\pi\)
\(542\) 20.7846 + 12.0000i 0.892775 + 0.515444i
\(543\) 0 0
\(544\) −1.00000 1.73205i −0.0428746 0.0742611i
\(545\) −4.00000 2.00000i −0.171341 0.0856706i
\(546\) 0 0
\(547\) 26.0000i 1.11168i −0.831289 0.555840i \(-0.812397\pi\)
0.831289 0.555840i \(-0.187603\pi\)
\(548\) −6.92820 + 4.00000i −0.295958 + 0.170872i
\(549\) 0 0
\(550\) −1.79423 14.8923i −0.0765062 0.635010i
\(551\) 10.0000 + 17.3205i 0.426014 + 0.737878i
\(552\) 0 0
\(553\) 12.1244 35.0000i 0.515580 1.48835i
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) −8.00000 + 13.8564i −0.339276 + 0.587643i
\(557\) 19.9186 + 11.5000i 0.843978 + 0.487271i 0.858614 0.512622i \(-0.171326\pi\)
−0.0146368 + 0.999893i \(0.504659\pi\)
\(558\) 0 0
\(559\) 10.0000 0.422955
\(560\) 5.69615 + 1.59808i 0.240706 + 0.0675310i
\(561\) 0 0
\(562\) 7.79423 4.50000i 0.328780 0.189821i
\(563\) −1.73205 1.00000i −0.0729972 0.0421450i 0.463057 0.886328i \(-0.346752\pi\)
−0.536054 + 0.844183i \(0.680086\pi\)
\(564\) 0 0
\(565\) 31.2487 1.87564i 1.31464 0.0789090i
\(566\) −14.0000 −0.588464
\(567\) 0 0
\(568\) 6.00000i 0.251754i
\(569\) 7.50000 + 12.9904i 0.314416 + 0.544585i 0.979313 0.202350i \(-0.0648579\pi\)
−0.664897 + 0.746935i \(0.731525\pi\)
\(570\) 0 0
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) 12.9904 7.50000i 0.543155 0.313591i
\(573\) 0 0
\(574\) −7.50000 2.59808i −0.313044 0.108442i
\(575\) 28.0000 21.0000i 1.16768 0.875761i
\(576\) 0 0
\(577\) 3.46410 + 2.00000i 0.144212 + 0.0832611i 0.570370 0.821388i \(-0.306800\pi\)
−0.426158 + 0.904649i \(0.640133\pi\)
\(578\) 11.2583 + 6.50000i 0.468285 + 0.270364i
\(579\) 0 0
\(580\) 8.00000 + 4.00000i 0.332182 + 0.166091i
\(581\) −12.0000 + 10.3923i −0.497844 + 0.431145i
\(582\) 0 0
\(583\) −23.3827 + 13.5000i −0.968412 + 0.559113i
\(584\) 8.00000 13.8564i 0.331042 0.573382i
\(585\) 0 0
\(586\) 4.50000 + 7.79423i 0.185893 + 0.321977i
\(587\) 34.0000i 1.40333i −0.712507 0.701665i \(-0.752440\pi\)
0.712507 0.701665i \(-0.247560\pi\)
\(588\) 0 0
\(589\) −10.0000 −0.412043
\(590\) 8.92820 0.535898i 0.367568 0.0220626i
\(591\) 0 0
\(592\) −0.866025 0.500000i −0.0355934 0.0205499i
\(593\) −5.19615 + 3.00000i −0.213380 + 0.123195i −0.602881 0.797831i \(-0.705981\pi\)
0.389501 + 0.921026i \(0.372647\pi\)
\(594\) 0 0
\(595\) 11.4641 2.92820i 0.469982 0.120045i
\(596\) 18.0000 0.737309
\(597\) 0 0
\(598\) 30.3109 + 17.5000i 1.23950 + 0.715628i
\(599\) 6.00000 10.3923i 0.245153 0.424618i −0.717021 0.697051i \(-0.754495\pi\)
0.962175 + 0.272433i \(0.0878284\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 1.73205 5.00000i 0.0705931 0.203785i
\(603\) 0 0
\(604\) −3.00000 5.19615i −0.122068 0.211428i
\(605\) 3.73205 2.46410i 0.151729 0.100180i
\(606\) 0 0
\(607\) −11.2583 + 6.50000i −0.456962 + 0.263827i −0.710766 0.703429i \(-0.751651\pi\)
0.253804 + 0.967256i \(0.418318\pi\)
\(608\) 5.00000i 0.202777i
\(609\) 0 0
\(610\) 6.00000 12.0000i 0.242933 0.485866i
\(611\) 17.5000 + 30.3109i 0.707974 + 1.22625i
\(612\) 0 0
\(613\) −12.9904 7.50000i −0.524677 0.302922i 0.214169 0.976797i \(-0.431296\pi\)
−0.738846 + 0.673874i \(0.764629\pi\)
\(614\) 11.0000 + 19.0526i 0.443924 + 0.768899i
\(615\) 0 0
\(616\) −1.50000 7.79423i −0.0604367 0.314038i
\(617\) 14.0000i 0.563619i −0.959470 0.281809i \(-0.909065\pi\)
0.959470 0.281809i \(-0.0909346\pi\)
\(618\) 0 0
\(619\) 9.50000 16.4545i 0.381837 0.661361i −0.609488 0.792796i \(-0.708625\pi\)
0.991325 + 0.131434i \(0.0419582\pi\)
\(620\) −3.73205 + 2.46410i −0.149883 + 0.0989607i
\(621\) 0 0
\(622\) 6.00000i 0.240578i
\(623\) −1.73205 + 5.00000i −0.0693932 + 0.200321i
\(624\) 0 0
\(625\) 24.2846 5.93782i 0.971384 0.237513i
\(626\) −11.0000 + 19.0526i −0.439648 + 0.761493i
\(627\) 0 0
\(628\) 7.79423 4.50000i 0.311024 0.179570i
\(629\) −2.00000 −0.0797452
\(630\) 0 0
\(631\) −18.0000 −0.716569 −0.358284 0.933613i \(-0.616638\pi\)
−0.358284 + 0.933613i \(0.616638\pi\)
\(632\) −12.1244 + 7.00000i −0.482281 + 0.278445i
\(633\) 0 0
\(634\) −1.00000 + 1.73205i −0.0397151 + 0.0687885i
\(635\) 15.6244 0.937822i 0.620034 0.0372163i
\(636\) 0 0
\(637\) −34.6410 5.00000i −1.37253 0.198107i
\(638\) 12.0000i 0.475085i
\(639\) 0 0
\(640\) −1.23205 1.86603i −0.0487011 0.0737611i
\(641\) −2.50000 + 4.33013i −0.0987441 + 0.171030i −0.911165 0.412042i \(-0.864816\pi\)
0.812421 + 0.583071i \(0.198149\pi\)
\(642\) 0 0
\(643\) 14.0000i 0.552106i 0.961142 + 0.276053i \(0.0890266\pi\)
−0.961142 + 0.276053i \(0.910973\pi\)
\(644\) 14.0000 12.1244i 0.551677 0.477767i
\(645\) 0 0
\(646\) −5.00000 8.66025i −0.196722 0.340733i
\(647\) −23.3827 13.5000i −0.919268 0.530740i −0.0358667 0.999357i \(-0.511419\pi\)
−0.883402 + 0.468617i \(0.844753\pi\)
\(648\) 0 0
\(649\) −6.00000 10.3923i −0.235521 0.407934i
\(650\) 15.0000 + 20.0000i 0.588348 + 0.784465i
\(651\) 0 0
\(652\) 12.0000i 0.469956i
\(653\) 2.59808 1.50000i 0.101671 0.0586995i −0.448303 0.893882i \(-0.647971\pi\)
0.549973 + 0.835182i \(0.314638\pi\)
\(654\) 0 0
\(655\) −1.86603 + 1.23205i −0.0729116 + 0.0481402i
\(656\) 1.50000 + 2.59808i 0.0585652 + 0.101438i
\(657\) 0 0
\(658\) 18.1865 3.50000i 0.708985 0.136444i
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) −8.00000 + 13.8564i −0.311164 + 0.538952i −0.978615 0.205702i \(-0.934052\pi\)
0.667451 + 0.744654i \(0.267385\pi\)
\(662\) 4.33013 + 2.50000i 0.168295 + 0.0971653i
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 28.4808 + 7.99038i 1.10444 + 0.309854i
\(666\) 0 0
\(667\) 24.2487 14.0000i 0.938914 0.542082i
\(668\) −12.9904 7.50000i −0.502613 0.290184i
\(669\) 0 0
\(670\) −0.267949 4.46410i −0.0103518 0.172463i
\(671\) −18.0000 −0.694882
\(672\) 0 0
\(673\) 32.0000i 1.23351i −0.787155 0.616755i \(-0.788447\pi\)
0.787155 0.616755i \(-0.211553\pi\)
\(674\) −5.00000 8.66025i −0.192593 0.333581i
\(675\) 0 0
\(676\) −6.00000 + 10.3923i −0.230769 + 0.399704i
\(677\) 14.7224 8.50000i 0.565829 0.326682i −0.189653 0.981851i \(-0.560736\pi\)
0.755482 + 0.655170i \(0.227403\pi\)
\(678\) 0 0
\(679\) −24.0000 + 20.7846i −0.921035 + 0.797640i
\(680\) −4.00000 2.00000i −0.153393 0.0766965i
\(681\) 0 0
\(682\) 5.19615 + 3.00000i 0.198971 + 0.114876i
\(683\) 38.1051 + 22.0000i 1.45805 + 0.841807i 0.998916 0.0465592i \(-0.0148256\pi\)
0.459136 + 0.888366i \(0.348159\pi\)
\(684\) 0 0
\(685\) −8.00000 + 16.0000i −0.305664 + 0.611329i
\(686\) −8.50000 + 16.4545i −0.324532 + 0.628235i
\(687\) 0 0
\(688\) −1.73205 + 1.00000i −0.0660338 + 0.0381246i
\(689\) 22.5000 38.9711i 0.857182 1.48468i
\(690\) 0 0
\(691\) 22.0000 + 38.1051i 0.836919 + 1.44959i 0.892458 + 0.451130i \(0.148979\pi\)
−0.0555386 + 0.998457i \(0.517688\pi\)
\(692\) 9.00000i 0.342129i
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 2.14359 + 35.7128i 0.0813111 + 1.35466i
\(696\) 0 0
\(697\) 5.19615 + 3.00000i 0.196818 + 0.113633i
\(698\) −10.3923 + 6.00000i −0.393355 + 0.227103i
\(699\) 0 0
\(700\) 12.5981 4.03590i 0.476163 0.152543i
\(701\) −26.0000 −0.982006 −0.491003 0.871158i \(-0.663370\pi\)
−0.491003 + 0.871158i \(0.663370\pi\)
\(702\) 0 0
\(703\) −4.33013 2.50000i −0.163314 0.0942893i
\(704\) −1.50000 + 2.59808i −0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) 0 0
\(708\) 0 0
\(709\) 6.00000 + 10.3923i 0.225335 + 0.390291i 0.956420 0.291995i \(-0.0943191\pi\)
−0.731085 + 0.682286i \(0.760986\pi\)
\(710\) 7.39230 + 11.1962i 0.277428 + 0.420184i
\(711\) 0 0
\(712\) 1.73205 1.00000i 0.0649113 0.0374766i
\(713\) 14.0000i 0.524304i
\(714\) 0 0
\(715\) 15.0000 30.0000i 0.560968 1.12194i
\(716\) 6.50000 + 11.2583i 0.242916 + 0.420744i
\(717\) 0 0
\(718\) 13.8564 + 8.00000i 0.517116 + 0.298557i
\(719\) −13.0000 22.5167i −0.484818 0.839730i 0.515030 0.857172i \(-0.327781\pi\)
−0.999848 + 0.0174426i \(0.994448\pi\)
\(720\) 0 0
\(721\) −20.0000 6.92820i −0.744839 0.258020i
\(722\) 6.00000i 0.223297i
\(723\) 0 0
\(724\) 13.0000 22.5167i 0.483141 0.836825i
\(725\) 19.8564 2.39230i 0.737448 0.0888480i
\(726\) 0 0
\(727\) 29.0000i 1.07555i −0.843088 0.537775i \(-0.819265\pi\)
0.843088 0.537775i \(-0.180735\pi\)
\(728\) 8.66025 + 10.0000i 0.320970 + 0.370625i
\(729\) 0 0
\(730\) −2.14359 35.7128i −0.0793380 1.32179i
\(731\) −2.00000 + 3.46410i −0.0739727 + 0.128124i
\(732\) 0 0
\(733\) −35.5070 + 20.5000i −1.31148 + 0.757185i −0.982342 0.187096i \(-0.940092\pi\)
−0.329141 + 0.944281i \(0.606759\pi\)
\(734\) 13.0000 0.479839
\(735\) 0 0
\(736\) −7.00000 −0.258023
\(737\) −5.19615 + 3.00000i −0.191403 + 0.110506i
\(738\) 0 0
\(739\) −14.5000 + 25.1147i −0.533391 + 0.923861i 0.465848 + 0.884865i \(0.345749\pi\)
−0.999239 + 0.0389959i \(0.987584\pi\)
\(740\) −2.23205 + 0.133975i −0.0820518 + 0.00492500i
\(741\) 0 0
\(742\) −15.5885 18.0000i −0.572270 0.660801i
\(743\) 21.0000i 0.770415i −0.922830 0.385208i \(-0.874130\pi\)
0.922830 0.385208i \(-0.125870\pi\)
\(744\) 0 0
\(745\) 33.5885 22.1769i 1.23059 0.812499i
\(746\) 13.0000 22.5167i 0.475964 0.824394i
\(747\) 0 0
\(748\) 6.00000i 0.219382i
\(749\) −40.0000 13.8564i −1.46157 0.506302i
\(750\) 0 0
\(751\) −14.0000 24.2487i −0.510867 0.884848i −0.999921 0.0125942i \(-0.995991\pi\)
0.489053 0.872254i \(-0.337342\pi\)
\(752\) −6.06218 3.50000i −0.221065 0.127632i
\(753\) 0 0
\(754\) 10.0000 + 17.3205i 0.364179 + 0.630776i
\(755\) −12.0000 6.00000i −0.436725 0.218362i
\(756\) 0 0
\(757\) 42.0000i 1.52652i 0.646094 + 0.763258i \(0.276401\pi\)
−0.646094 + 0.763258i \(0.723599\pi\)
\(758\) −25.1147 + 14.5000i −0.912208 + 0.526664i
\(759\) 0 0
\(760\) −6.16025 9.33013i −0.223456 0.338439i
\(761\) 0.500000 + 0.866025i 0.0181250 + 0.0313934i 0.874946 0.484221i \(-0.160897\pi\)
−0.856821 + 0.515615i \(0.827564\pi\)
\(762\) 0 0
\(763\) −5.19615 + 1.00000i −0.188113 + 0.0362024i
\(764\) −20.0000 −0.723575
\(765\) 0 0
\(766\) −10.5000 + 18.1865i −0.379380 + 0.657106i
\(767\) 17.3205 + 10.0000i 0.625407 + 0.361079i
\(768\) 0 0
\(769\) 29.0000 1.04577 0.522883 0.852404i \(-0.324856\pi\)
0.522883 + 0.852404i \(0.324856\pi\)
\(770\) −12.4019 12.6962i −0.446934 0.457538i
\(771\) 0 0
\(772\) −8.66025 + 5.00000i −0.311689 + 0.179954i
\(773\) −38.9711 22.5000i −1.40169 0.809269i −0.407128 0.913371i \(-0.633470\pi\)
−0.994567 + 0.104102i \(0.966803\pi\)
\(774\) 0 0
\(775\) −3.92820 + 9.19615i −0.141105 + 0.330336i
\(776\) 12.0000 0.430775
\(777\) 0 0
\(778\) 6.00000i 0.215110i
\(779\) 7.50000 + 12.9904i 0.268715 + 0.465429i
\(780\) 0 0
\(781\) 9.00000 15.5885i 0.322045 0.557799i
\(782\) −12.1244 + 7.00000i −0.433566 + 0.250319i
\(783\) 0 0
\(784\) 6.50000 2.59808i 0.232143 0.0927884i
\(785\) 9.00000 18.0000i 0.321224 0.642448i
\(786\) 0 0
\(787\) −15.5885 9.00000i −0.555668 0.320815i 0.195737 0.980656i \(-0.437290\pi\)
−0.751405 + 0.659841i \(0.770624\pi\)
\(788\) 4.33013 + 2.50000i 0.154254 + 0.0890588i
\(789\) 0 0
\(790\) −14.0000 + 28.0000i −0.498098 + 0.996195i
\(791\) 28.0000 24.2487i 0.995565 0.862185i
\(792\) 0 0
\(793\) 25.9808 15.0000i 0.922604 0.532666i
\(794\) 7.00000 12.1244i 0.248421 0.430277i
\(795\) 0 0
\(796\) −9.00000 15.5885i −0.318997 0.552518i
\(797\) 2.00000i 0.0708436i 0.999372 + 0.0354218i \(0.0112775\pi\)
−0.999372 + 0.0354218i \(0.988723\pi\)
\(798\) 0 0
\(799\) −14.0000 −0.495284
\(800\) −4.59808 1.96410i −0.162567 0.0694415i
\(801\) 0 0
\(802\) 12.9904 + 7.50000i 0.458706 + 0.264834i
\(803\) −41.5692 + 24.0000i −1.46695 + 0.846942i
\(804\) 0 0
\(805\) 11.1865 39.8731i 0.394273 1.40534i
\(806\) −10.0000 −0.352235
\(807\) 0 0
\(808\) 0 0
\(809\) 2.50000 4.33013i 0.0878953 0.152239i −0.818726 0.574184i \(-0.805319\pi\)
0.906621 + 0.421945i \(0.138653\pi\)
\(810\) 0 0
\(811\) −33.0000 −1.15879 −0.579393 0.815048i \(-0.696710\pi\)
−0.579393 + 0.815048i \(0.696710\pi\)
\(812\) 10.3923 2.00000i 0.364698 0.0701862i
\(813\) 0 0
\(814\) 1.50000 + 2.59808i 0.0525750 + 0.0910625i
\(815\) −14.7846 22.3923i −0.517882 0.784368i
\(816\) 0 0
\(817\) −8.66025 + 5.00000i −0.302984 + 0.174928i
\(818\) 14.0000i 0.489499i
\(819\) 0 0
\(820\) 6.00000 + 3.00000i 0.209529 + 0.104765i
\(821\) −9.00000 15.5885i −0.314102 0.544041i 0.665144 0.746715i \(-0.268370\pi\)
−0.979246 + 0.202674i \(0.935037\pi\)
\(822\) 0 0
\(823\) −20.7846 12.0000i −0.724506 0.418294i 0.0919029 0.995768i \(-0.470705\pi\)
−0.816409 + 0.577474i \(0.804038\pi\)
\(824\) 4.00000 + 6.92820i 0.139347 + 0.241355i
\(825\) 0 0
\(826\) 8.00000 6.92820i 0.278356 0.241063i
\(827\) 22.0000i 0.765015i 0.923952 + 0.382507i \(0.124939\pi\)
−0.923952 + 0.382507i \(0.875061\pi\)
\(828\) 0 0
\(829\) −13.0000 + 22.5167i −0.451509 + 0.782036i −0.998480 0.0551154i \(-0.982447\pi\)
0.546971 + 0.837151i \(0.315781\pi\)
\(830\) 11.1962 7.39230i 0.388624 0.256591i
\(831\) 0 0
\(832\) 5.00000i 0.173344i
\(833\) 8.66025 11.0000i 0.300060 0.381127i
\(834\) 0 0
\(835\) −33.4808 + 2.00962i −1.15865 + 0.0695457i
\(836\) −7.50000 + 12.9904i −0.259393 + 0.449282i
\(837\) 0 0
\(838\) −30.3109 + 17.5000i −1.04707 + 0.604527i
\(839\) −34.0000 −1.17381 −0.586905 0.809656i \(-0.699654\pi\)
−0.586905 + 0.809656i \(0.699654\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) 17.3205 10.0000i 0.596904 0.344623i
\(843\) 0 0
\(844\) −4.50000 + 7.79423i −0.154896 + 0.268288i
\(845\) 1.60770 + 26.7846i 0.0553064 + 0.921419i
\(846\) 0 0
\(847\) 1.73205 5.00000i 0.0595140 0.171802i
\(848\) 9.00000i 0.309061i
\(849\) 0 0
\(850\) −9.92820 + 1.19615i −0.340535 + 0.0410277i
\(851\) −3.50000 + 6.06218i −0.119978 + 0.207809i
\(852\) 0 0
\(853\) 43.0000i 1.47229i 0.676823 + 0.736146i \(0.263356\pi\)
−0.676823 + 0.736146i \(0.736644\pi\)
\(854\) −3.00000 15.5885i −0.102658 0.533426i
\(855\) 0 0
\(856\) 8.00000 + 13.8564i 0.273434 + 0.473602i
\(857\) 6.92820 + 4.00000i 0.236663 + 0.136637i 0.613642 0.789584i \(-0.289704\pi\)
−0.376979 + 0.926222i \(0.623037\pi\)
\(858\) 0 0
\(859\) −6.00000 10.3923i −0.204717 0.354581i 0.745325 0.666701i \(-0.232294\pi\)
−0.950043 + 0.312120i \(0.898961\pi\)
\(860\) −2.00000 + 4.00000i −0.0681994 + 0.136399i
\(861\) 0 0
\(862\) 2.00000i 0.0681203i
\(863\) −9.52628 + 5.50000i −0.324278 + 0.187222i −0.653298 0.757101i \(-0.726615\pi\)
0.329020 + 0.944323i \(0.393282\pi\)
\(864\) 0 0
\(865\) −11.0885 16.7942i −0.377019 0.571021i
\(866\) 14.0000 + 24.2487i 0.475739 + 0.824005i
\(867\) 0 0
\(868\) −1.73205 + 5.00000i −0.0587896 + 0.169711i
\(869\) 42.0000 1.42475
\(870\) 0 0
\(871\) 5.00000 8.66025i 0.169419 0.293442i
\(872\) 1.73205 + 1.00000i 0.0586546 + 0.0338643i
\(873\) 0 0
\(874\) −35.0000 −1.18389
\(875\) 18.5359 23.0526i 0.626628 0.779319i
\(876\) 0 0
\(877\) 26.8468 15.5000i 0.906552 0.523398i 0.0272316 0.999629i \(-0.491331\pi\)
0.879320 + 0.476231i \(0.157998\pi\)
\(878\) 24.2487 + 14.0000i 0.818354 + 0.472477i
\(879\) 0 0
\(880\) 0.401924 + 6.69615i 0.0135488 + 0.225727i
\(881\) 15.0000 0.505363 0.252681 0.967550i \(-0.418688\pi\)
0.252681 + 0.967550i \(0.418688\pi\)
\(882\) 0 0
\(883\) 16.0000i 0.538443i −0.963078 0.269221i \(-0.913234\pi\)
0.963078 0.269221i \(-0.0867663\pi\)
\(884\) −5.00000 8.66025i −0.168168 0.291276i
\(885\) 0 0
\(886\) −15.0000 + 25.9808i −0.503935 + 0.872841i
\(887\) −31.1769 + 18.0000i −1.04682 + 0.604381i −0.921757 0.387768i \(-0.873246\pi\)
−0.125061 + 0.992149i \(0.539913\pi\)
\(888\) 0 0
\(889\) 14.0000 12.1244i 0.469545 0.406638i
\(890\) 2.00000 4.00000i 0.0670402 0.134080i
\(891\) 0 0
\(892\) 6.92820 + 4.00000i 0.231973 + 0.133930i
\(893\) −30.3109 17.5000i −1.01432 0.585615i
\(894\) 0 0
\(895\) 26.0000 + 13.0000i 0.869084 + 0.434542i
\(896\) −2.50000 0.866025i −0.0835191 0.0289319i
\(897\) 0 0
\(898\) −4.33013 + 2.50000i −0.144498 + 0.0834261i
\(899\) −4.00000 + 6.92820i −0.133407 + 0.231069i
\(900\) 0 0
\(901\) 9.00000 + 15.5885i 0.299833 + 0.519327i
\(902\) 9.00000i 0.299667i
\(903\) 0 0
\(904\) −14.0000 −0.465633
\(905\) −3.48334 58.0333i −0.115790 1.92909i
\(906\) 0 0
\(907\) 34.6410 + 20.0000i 1.15024 + 0.664089i 0.948945 0.315442i \(-0.102153\pi\)
0.201291 + 0.979531i \(0.435486\pi\)
\(908\) −5.19615 + 3.00000i −0.172440 + 0.0995585i
\(909\) 0 0
\(910\) 28.4808 + 7.99038i 0.944128 + 0.264879i
\(911\) −2.00000 −0.0662630 −0.0331315 0.999451i \(-0.510548\pi\)
−0.0331315 + 0.999451i \(0.510548\pi\)
\(912\) 0 0
\(913\) −15.5885 9.00000i −0.515903 0.297857i
\(914\) 5.00000 8.66025i 0.165385 0.286456i
\(915\) 0 0
\(916\) 16.0000 0.528655
\(917\) −0.866025 + 2.50000i −0.0285987 + 0.0825573i
\(918\) 0 0
\(919\) 10.0000 + 17.3205i 0.329870 + 0.571351i 0.982486 0.186338i \(-0.0596619\pi\)
−0.652616 + 0.757689i \(0.726329\pi\)
\(920\) −13.0622 + 8.62436i −0.430647 + 0.284337i
\(921\) 0 0
\(922\) −27.7128 + 16.0000i −0.912673 + 0.526932i
\(923\) 30.0000i 0.987462i
\(924\) 0 0
\(925\) −4.00000 + 3.00000i −0.131519 + 0.0986394i
\(926\) −8.50000 14.7224i −0.279327 0.483809i
\(927\) 0 0
\(928\) −3.46410 2.00000i −0.113715 0.0656532i
\(929\) −10.5000 18.1865i −0.344494 0.596681i 0.640768 0.767735i \(-0.278616\pi\)
−0.985262 + 0.171054i \(0.945283\pi\)
\(930\) 0 0
\(931\) 32.5000 12.9904i 1.06514 0.425743i
\(932\) 8.00000i 0.262049i
\(933\) 0 0
\(934\) 17.0000 29.4449i 0.556257 0.963465i
\(935\) 7.39230 + 11.1962i 0.241754 + 0.366153i
\(936\) 0 0
\(937\) 26.0000i 0.849383i −0.905338 0.424691i \(-0.860383\pi\)
0.905338 0.424691i \(-0.139617\pi\)
\(938\) −3.46410 4.00000i −0.113107 0.130605i
\(939\) 0 0
\(940\) −15.6244 + 0.937822i −0.509610 + 0.0305884i
\(941\) −14.0000 + 24.2487i −0.456387 + 0.790485i −0.998767 0.0496480i \(-0.984190\pi\)
0.542380 + 0.840133i \(0.317523\pi\)
\(942\) 0 0
\(943\) 18.1865 10.5000i 0.592235 0.341927i
\(944\) −4.00000 −0.130189
\(945\) 0 0
\(946\) 6.00000 0.195077
\(947\) 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
\(949\) 40.0000 69.2820i 1.29845 2.24899i
\(950\) −22.9904 9.82051i −0.745906 0.318619i
\(951\) 0 0
\(952\) −5.19615 + 1.00000i −0.168408 + 0.0324102i
\(953\) 24.0000i 0.777436i −0.921357 0.388718i \(-0.872918\pi\)
0.921357 0.388718i \(-0.127082\pi\)
\(954\) 0 0
\(955\) −37.3205 + 24.6410i −1.20766 + 0.797365i
\(956\) 10.0000 17.3205i 0.323423 0.560185i
\(957\) 0 0
\(958\) 36.0000i 1.16311i
\(959\) 4.00000 + 20.7846i 0.129167 + 0.671170i
\(960\) 0 0
\(961\) 13.5000 + 23.3827i 0.435484 + 0.754280i
\(962\) −4.33013 2.50000i −0.139609 0.0806032i
\(963\) 0 0
\(964\) −4.50000 7.79423i −0.144935 0.251035i
\(965\) −10.0000 + 20.0000i −0.321911 + 0.643823i
\(966\) 0 0
\(967\) 32.0000i 1.02905i 0.857475 + 0.514525i \(0.172032\pi\)
−0.857475 + 0.514525i \(0.827968\pi\)
\(968\) −1.73205 + 1.00000i −0.0556702 + 0.0321412i
\(969\) 0 0
\(970\) 22.3923 14.7846i 0.718974 0.474705i
\(971\) −16.5000 28.5788i −0.529510 0.917139i −0.999408 0.0344175i \(-0.989042\pi\)
0.469897 0.882721i \(-0.344291\pi\)
\(972\) 0 0
\(973\) 27.7128 + 32.0000i 0.888432 + 1.02587i
\(974\) −32.0000 −1.02535
\(975\) 0 0
\(976\) −3.00000 + 5.19615i −0.0960277 + 0.166325i
\(977\) 46.7654 + 27.0000i 1.49616 + 0.863807i 0.999990 0.00442082i \(-0.00140720\pi\)
0.496167 + 0.868227i \(0.334741\pi\)
\(978\) 0 0
\(979\) −6.00000 −0.191761
\(980\) 8.92820 12.8564i 0.285201 0.410683i
\(981\) 0 0
\(982\) 20.7846 12.0000i 0.663264 0.382935i
\(983\) 25.1147 + 14.5000i 0.801036 + 0.462478i 0.843833 0.536606i \(-0.180294\pi\)
−0.0427975 + 0.999084i \(0.513627\pi\)
\(984\) 0 0
\(985\) 11.1603 0.669873i 0.355595 0.0213439i
\(986\) −8.00000 −0.254772
\(987\) 0 0
\(988\) 25.0000i 0.795356i
\(989\) 7.00000 + 12.1244i 0.222587 + 0.385532i
\(990\) 0 0
\(991\) 4.00000 6.92820i 0.127064 0.220082i −0.795474 0.605988i \(-0.792778\pi\)
0.922538 + 0.385906i \(0.126111\pi\)
\(992\) 1.73205 1.00000i 0.0549927 0.0317500i
\(993\) 0 0
\(994\) 15.0000 + 5.19615i 0.475771 + 0.164812i
\(995\) −36.0000 18.0000i −1.14128 0.570638i
\(996\) 0 0
\(997\) 32.9090 + 19.0000i 1.04224 + 0.601736i 0.920466 0.390822i \(-0.127809\pi\)
0.121771 + 0.992558i \(0.461143\pi\)
\(998\) −3.46410 2.00000i −0.109654 0.0633089i
\(999\) 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.a.109.1 4
3.2 odd 2 70.2.i.b.39.2 yes 4
5.4 even 2 inner 630.2.u.a.109.2 4
7.2 even 3 inner 630.2.u.a.289.2 4
12.11 even 2 560.2.bw.d.529.1 4
15.2 even 4 350.2.e.j.151.1 2
15.8 even 4 350.2.e.c.151.1 2
15.14 odd 2 70.2.i.b.39.1 yes 4
21.2 odd 6 70.2.i.b.9.1 4
21.5 even 6 490.2.i.a.79.1 4
21.11 odd 6 490.2.c.a.99.2 2
21.17 even 6 490.2.c.d.99.2 2
21.20 even 2 490.2.i.a.459.2 4
35.9 even 6 inner 630.2.u.a.289.1 4
60.59 even 2 560.2.bw.d.529.2 4
84.23 even 6 560.2.bw.d.289.2 4
105.2 even 12 350.2.e.j.51.1 2
105.17 odd 12 2450.2.a.j.1.1 1
105.23 even 12 350.2.e.c.51.1 2
105.32 even 12 2450.2.a.k.1.1 1
105.38 odd 12 2450.2.a.bb.1.1 1
105.44 odd 6 70.2.i.b.9.2 yes 4
105.53 even 12 2450.2.a.ba.1.1 1
105.59 even 6 490.2.c.d.99.1 2
105.74 odd 6 490.2.c.a.99.1 2
105.89 even 6 490.2.i.a.79.2 4
105.104 even 2 490.2.i.a.459.1 4
420.359 even 6 560.2.bw.d.289.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.2.i.b.9.1 4 21.2 odd 6
70.2.i.b.9.2 yes 4 105.44 odd 6
70.2.i.b.39.1 yes 4 15.14 odd 2
70.2.i.b.39.2 yes 4 3.2 odd 2
350.2.e.c.51.1 2 105.23 even 12
350.2.e.c.151.1 2 15.8 even 4
350.2.e.j.51.1 2 105.2 even 12
350.2.e.j.151.1 2 15.2 even 4
490.2.c.a.99.1 2 105.74 odd 6
490.2.c.a.99.2 2 21.11 odd 6
490.2.c.d.99.1 2 105.59 even 6
490.2.c.d.99.2 2 21.17 even 6
490.2.i.a.79.1 4 21.5 even 6
490.2.i.a.79.2 4 105.89 even 6
490.2.i.a.459.1 4 105.104 even 2
490.2.i.a.459.2 4 21.20 even 2
560.2.bw.d.289.1 4 420.359 even 6
560.2.bw.d.289.2 4 84.23 even 6
560.2.bw.d.529.1 4 12.11 even 2
560.2.bw.d.529.2 4 60.59 even 2
630.2.u.a.109.1 4 1.1 even 1 trivial
630.2.u.a.109.2 4 5.4 even 2 inner
630.2.u.a.289.1 4 35.9 even 6 inner
630.2.u.a.289.2 4 7.2 even 3 inner
2450.2.a.j.1.1 1 105.17 odd 12
2450.2.a.k.1.1 1 105.32 even 12
2450.2.a.ba.1.1 1 105.53 even 12
2450.2.a.bb.1.1 1 105.38 odd 12