Properties

Label 315.2.bf.a.289.2
Level $315$
Weight $2$
Character 315.289
Analytic conductor $2.515$
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] = [315,2,Mod(109,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, 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("315.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bf (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: \(2.51528766367\)
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 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 289.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 315.289
Dual form 315.2.bf.a.109.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +(-2.59808 - 0.500000i) q^{7} -3.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +(-2.59808 - 0.500000i) q^{7} -3.00000i q^{8} +(-0.133975 - 2.23205i) q^{10} -2.00000i q^{13} +(-2.00000 - 1.73205i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{17} +(3.00000 - 5.19615i) q^{19} +(-1.00000 + 2.00000i) q^{20} +(2.59808 + 1.50000i) q^{23} +(-1.96410 + 4.59808i) q^{25} +(1.00000 - 1.73205i) q^{26} +(0.866025 + 2.50000i) q^{28} +7.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(-4.33013 + 2.50000i) q^{32} -2.00000 q^{34} +(2.26795 + 5.46410i) q^{35} +(6.92820 + 4.00000i) q^{37} +(5.19615 - 3.00000i) q^{38} +(-5.59808 + 3.69615i) q^{40} -5.00000 q^{41} -7.00000i q^{43} +(1.50000 + 2.59808i) q^{46} +(6.50000 + 2.59808i) q^{49} +(-4.00000 + 3.00000i) q^{50} +(-1.73205 + 1.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(-1.50000 + 7.79423i) q^{56} +(6.06218 + 3.50000i) q^{58} +(-5.00000 - 8.66025i) q^{59} +(-3.50000 + 6.06218i) q^{61} -2.00000i q^{62} -7.00000 q^{64} +(-3.73205 + 2.46410i) q^{65} +(-4.33013 + 2.50000i) q^{67} +(1.73205 + 1.00000i) q^{68} +(-0.767949 + 5.86603i) q^{70} +2.00000 q^{71} +(5.19615 - 3.00000i) q^{73} +(4.00000 + 6.92820i) q^{74} -6.00000 q^{76} +(-1.00000 + 1.73205i) q^{79} +(-2.23205 + 0.133975i) q^{80} +(-4.33013 - 2.50000i) q^{82} -11.0000i q^{83} +(4.00000 + 2.00000i) q^{85} +(3.50000 - 6.06218i) q^{86} +(-4.50000 + 7.79423i) q^{89} +(-1.00000 + 5.19615i) q^{91} -3.00000i q^{92} +(-13.3923 + 0.803848i) q^{95} -16.0000i q^{97} +(4.33013 + 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{4} + 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{4} + 2 q^{5} - 4 q^{10} - 8 q^{14} + 2 q^{16} + 12 q^{19} - 4 q^{20} + 6 q^{25} + 4 q^{26} + 28 q^{29} - 4 q^{31} - 8 q^{34} + 16 q^{35} - 12 q^{40} - 20 q^{41} + 6 q^{46} + 26 q^{49} - 16 q^{50} - 6 q^{56} - 20 q^{59} - 14 q^{61} - 28 q^{64} - 8 q^{65} - 10 q^{70} + 8 q^{71} + 16 q^{74} - 24 q^{76} - 4 q^{79} - 2 q^{80} + 16 q^{85} + 14 q^{86} - 18 q^{89} - 4 q^{91} - 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i 0.773893 0.633316i \(-0.218307\pi\)
−0.161521 + 0.986869i \(0.551640\pi\)
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.23205 1.86603i −0.550990 0.834512i
\(6\) 0 0
\(7\) −2.59808 0.500000i −0.981981 0.188982i
\(8\) 3.00000i 1.06066i
\(9\) 0 0
\(10\) −0.133975 2.23205i −0.0423665 0.705836i
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 0 0
\(13\) 2.00000i 0.554700i −0.960769 0.277350i \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) −2.00000 1.73205i −0.534522 0.462910i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −1.73205 + 1.00000i −0.420084 + 0.242536i −0.695113 0.718900i \(-0.744646\pi\)
0.275029 + 0.961436i \(0.411312\pi\)
\(18\) 0 0
\(19\) 3.00000 5.19615i 0.688247 1.19208i −0.284157 0.958778i \(-0.591714\pi\)
0.972404 0.233301i \(-0.0749529\pi\)
\(20\) −1.00000 + 2.00000i −0.223607 + 0.447214i
\(21\) 0 0
\(22\) 0 0
\(23\) 2.59808 + 1.50000i 0.541736 + 0.312772i 0.745782 0.666190i \(-0.232076\pi\)
−0.204046 + 0.978961i \(0.565409\pi\)
\(24\) 0 0
\(25\) −1.96410 + 4.59808i −0.392820 + 0.919615i
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) 0 0
\(28\) 0.866025 + 2.50000i 0.163663 + 0.472456i
\(29\) 7.00000 1.29987 0.649934 0.759991i \(-0.274797\pi\)
0.649934 + 0.759991i \(0.274797\pi\)
\(30\) 0 0
\(31\) −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i \(-0.224149\pi\)
−0.941745 + 0.336327i \(0.890815\pi\)
\(32\) −4.33013 + 2.50000i −0.765466 + 0.441942i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) 2.26795 + 5.46410i 0.383353 + 0.923602i
\(36\) 0 0
\(37\) 6.92820 + 4.00000i 1.13899 + 0.657596i 0.946180 0.323640i \(-0.104907\pi\)
0.192809 + 0.981236i \(0.438240\pi\)
\(38\) 5.19615 3.00000i 0.842927 0.486664i
\(39\) 0 0
\(40\) −5.59808 + 3.69615i −0.885134 + 0.584413i
\(41\) −5.00000 −0.780869 −0.390434 0.920631i \(-0.627675\pi\)
−0.390434 + 0.920631i \(0.627675\pi\)
\(42\) 0 0
\(43\) 7.00000i 1.06749i −0.845645 0.533745i \(-0.820784\pi\)
0.845645 0.533745i \(-0.179216\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 1.50000 + 2.59808i 0.221163 + 0.383065i
\(47\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(48\) 0 0
\(49\) 6.50000 + 2.59808i 0.928571 + 0.371154i
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) 0 0
\(52\) −1.73205 + 1.00000i −0.240192 + 0.138675i
\(53\) 5.19615 3.00000i 0.713746 0.412082i −0.0987002 0.995117i \(-0.531468\pi\)
0.812447 + 0.583036i \(0.198135\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.50000 + 7.79423i −0.200446 + 1.04155i
\(57\) 0 0
\(58\) 6.06218 + 3.50000i 0.796003 + 0.459573i
\(59\) −5.00000 8.66025i −0.650945 1.12747i −0.982894 0.184172i \(-0.941040\pi\)
0.331949 0.943297i \(-0.392294\pi\)
\(60\) 0 0
\(61\) −3.50000 + 6.06218i −0.448129 + 0.776182i −0.998264 0.0588933i \(-0.981243\pi\)
0.550135 + 0.835076i \(0.314576\pi\)
\(62\) 2.00000i 0.254000i
\(63\) 0 0
\(64\) −7.00000 −0.875000
\(65\) −3.73205 + 2.46410i −0.462904 + 0.305634i
\(66\) 0 0
\(67\) −4.33013 + 2.50000i −0.529009 + 0.305424i −0.740613 0.671932i \(-0.765465\pi\)
0.211604 + 0.977356i \(0.432131\pi\)
\(68\) 1.73205 + 1.00000i 0.210042 + 0.121268i
\(69\) 0 0
\(70\) −0.767949 + 5.86603i −0.0917875 + 0.701124i
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) 0 0
\(73\) 5.19615 3.00000i 0.608164 0.351123i −0.164083 0.986447i \(-0.552466\pi\)
0.772246 + 0.635323i \(0.219133\pi\)
\(74\) 4.00000 + 6.92820i 0.464991 + 0.805387i
\(75\) 0 0
\(76\) −6.00000 −0.688247
\(77\) 0 0
\(78\) 0 0
\(79\) −1.00000 + 1.73205i −0.112509 + 0.194871i −0.916781 0.399390i \(-0.869222\pi\)
0.804272 + 0.594261i \(0.202555\pi\)
\(80\) −2.23205 + 0.133975i −0.249551 + 0.0149788i
\(81\) 0 0
\(82\) −4.33013 2.50000i −0.478183 0.276079i
\(83\) 11.0000i 1.20741i −0.797209 0.603703i \(-0.793691\pi\)
0.797209 0.603703i \(-0.206309\pi\)
\(84\) 0 0
\(85\) 4.00000 + 2.00000i 0.433861 + 0.216930i
\(86\) 3.50000 6.06218i 0.377415 0.653701i
\(87\) 0 0
\(88\) 0 0
\(89\) −4.50000 + 7.79423i −0.476999 + 0.826187i −0.999653 0.0263586i \(-0.991609\pi\)
0.522654 + 0.852545i \(0.324942\pi\)
\(90\) 0 0
\(91\) −1.00000 + 5.19615i −0.104828 + 0.544705i
\(92\) 3.00000i 0.312772i
\(93\) 0 0
\(94\) 0 0
\(95\) −13.3923 + 0.803848i −1.37402 + 0.0824730i
\(96\) 0 0
\(97\) 16.0000i 1.62455i −0.583272 0.812277i \(-0.698228\pi\)
0.583272 0.812277i \(-0.301772\pi\)
\(98\) 4.33013 + 5.50000i 0.437409 + 0.555584i
\(99\) 0 0
\(100\) 4.96410 0.598076i 0.496410 0.0598076i
\(101\) 4.50000 + 7.79423i 0.447767 + 0.775555i 0.998240 0.0592978i \(-0.0188862\pi\)
−0.550474 + 0.834853i \(0.685553\pi\)
\(102\) 0 0
\(103\) 6.06218 + 3.50000i 0.597324 + 0.344865i 0.767988 0.640464i \(-0.221258\pi\)
−0.170664 + 0.985329i \(0.554591\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 9.52628 + 5.50000i 0.920940 + 0.531705i 0.883935 0.467610i \(-0.154885\pi\)
0.0370053 + 0.999315i \(0.488218\pi\)
\(108\) 0 0
\(109\) 2.50000 + 4.33013i 0.239457 + 0.414751i 0.960558 0.278078i \(-0.0896974\pi\)
−0.721102 + 0.692829i \(0.756364\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.73205 + 2.00000i −0.163663 + 0.188982i
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 0 0
\(115\) −0.401924 6.69615i −0.0374796 0.624419i
\(116\) −3.50000 6.06218i −0.324967 0.562859i
\(117\) 0 0
\(118\) 10.0000i 0.920575i
\(119\) 5.00000 1.73205i 0.458349 0.158777i
\(120\) 0 0
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) −6.06218 + 3.50000i −0.548844 + 0.316875i
\(123\) 0 0
\(124\) −1.00000 + 1.73205i −0.0898027 + 0.155543i
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 0 0
\(127\) 16.0000i 1.41977i 0.704317 + 0.709885i \(0.251253\pi\)
−0.704317 + 0.709885i \(0.748747\pi\)
\(128\) 2.59808 + 1.50000i 0.229640 + 0.132583i
\(129\) 0 0
\(130\) −4.46410 + 0.267949i −0.391528 + 0.0235007i
\(131\) 2.00000 3.46410i 0.174741 0.302660i −0.765331 0.643637i \(-0.777425\pi\)
0.940072 + 0.340977i \(0.110758\pi\)
\(132\) 0 0
\(133\) −10.3923 + 12.0000i −0.901127 + 1.04053i
\(134\) −5.00000 −0.431934
\(135\) 0 0
\(136\) 3.00000 + 5.19615i 0.257248 + 0.445566i
\(137\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(138\) 0 0
\(139\) −8.00000 −0.678551 −0.339276 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) 3.59808 4.69615i 0.304093 0.396897i
\(141\) 0 0
\(142\) 1.73205 + 1.00000i 0.145350 + 0.0839181i
\(143\) 0 0
\(144\) 0 0
\(145\) −8.62436 13.0622i −0.716214 1.08475i
\(146\) 6.00000 0.496564
\(147\) 0 0
\(148\) 8.00000i 0.657596i
\(149\) −0.500000 + 0.866025i −0.0409616 + 0.0709476i −0.885779 0.464107i \(-0.846375\pi\)
0.844818 + 0.535054i \(0.179709\pi\)
\(150\) 0 0
\(151\) −7.00000 12.1244i −0.569652 0.986666i −0.996600 0.0823900i \(-0.973745\pi\)
0.426948 0.904276i \(-0.359589\pi\)
\(152\) −15.5885 9.00000i −1.26439 0.729996i
\(153\) 0 0
\(154\) 0 0
\(155\) −2.00000 + 4.00000i −0.160644 + 0.321288i
\(156\) 0 0
\(157\) 10.3923 6.00000i 0.829396 0.478852i −0.0242497 0.999706i \(-0.507720\pi\)
0.853646 + 0.520854i \(0.174386\pi\)
\(158\) −1.73205 + 1.00000i −0.137795 + 0.0795557i
\(159\) 0 0
\(160\) 10.0000 + 5.00000i 0.790569 + 0.395285i
\(161\) −6.00000 5.19615i −0.472866 0.409514i
\(162\) 0 0
\(163\) −3.46410 2.00000i −0.271329 0.156652i 0.358162 0.933659i \(-0.383403\pi\)
−0.629492 + 0.777007i \(0.716737\pi\)
\(164\) 2.50000 + 4.33013i 0.195217 + 0.338126i
\(165\) 0 0
\(166\) 5.50000 9.52628i 0.426883 0.739383i
\(167\) 3.00000i 0.232147i 0.993241 + 0.116073i \(0.0370308\pi\)
−0.993241 + 0.116073i \(0.962969\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) 2.46410 + 3.73205i 0.188988 + 0.286235i
\(171\) 0 0
\(172\) −6.06218 + 3.50000i −0.462237 + 0.266872i
\(173\) 10.3923 + 6.00000i 0.790112 + 0.456172i 0.840002 0.542583i \(-0.182554\pi\)
−0.0498898 + 0.998755i \(0.515887\pi\)
\(174\) 0 0
\(175\) 7.40192 10.9641i 0.559533 0.828808i
\(176\) 0 0
\(177\) 0 0
\(178\) −7.79423 + 4.50000i −0.584202 + 0.337289i
\(179\) 1.00000 + 1.73205i 0.0747435 + 0.129460i 0.900975 0.433872i \(-0.142853\pi\)
−0.826231 + 0.563331i \(0.809520\pi\)
\(180\) 0 0
\(181\) −3.00000 −0.222988 −0.111494 0.993765i \(-0.535564\pi\)
−0.111494 + 0.993765i \(0.535564\pi\)
\(182\) −3.46410 + 4.00000i −0.256776 + 0.296500i
\(183\) 0 0
\(184\) 4.50000 7.79423i 0.331744 0.574598i
\(185\) −1.07180 17.8564i −0.0788001 1.31283i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) −12.0000 6.00000i −0.870572 0.435286i
\(191\) 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i \(-0.690384\pi\)
0.997225 + 0.0744412i \(0.0237173\pi\)
\(192\) 0 0
\(193\) 3.46410 2.00000i 0.249351 0.143963i −0.370116 0.928986i \(-0.620682\pi\)
0.619467 + 0.785022i \(0.287349\pi\)
\(194\) 8.00000 13.8564i 0.574367 0.994832i
\(195\) 0 0
\(196\) −1.00000 6.92820i −0.0714286 0.494872i
\(197\) 8.00000i 0.569976i 0.958531 + 0.284988i \(0.0919897\pi\)
−0.958531 + 0.284988i \(0.908010\pi\)
\(198\) 0 0
\(199\) −2.00000 3.46410i −0.141776 0.245564i 0.786389 0.617731i \(-0.211948\pi\)
−0.928166 + 0.372168i \(0.878615\pi\)
\(200\) 13.7942 + 5.89230i 0.975399 + 0.416649i
\(201\) 0 0
\(202\) 9.00000i 0.633238i
\(203\) −18.1865 3.50000i −1.27644 0.245652i
\(204\) 0 0
\(205\) 6.16025 + 9.33013i 0.430251 + 0.651644i
\(206\) 3.50000 + 6.06218i 0.243857 + 0.422372i
\(207\) 0 0
\(208\) −1.73205 1.00000i −0.120096 0.0693375i
\(209\) 0 0
\(210\) 0 0
\(211\) −10.0000 −0.688428 −0.344214 0.938891i \(-0.611855\pi\)
−0.344214 + 0.938891i \(0.611855\pi\)
\(212\) −5.19615 3.00000i −0.356873 0.206041i
\(213\) 0 0
\(214\) 5.50000 + 9.52628i 0.375972 + 0.651203i
\(215\) −13.0622 + 8.62436i −0.890833 + 0.588176i
\(216\) 0 0
\(217\) 1.73205 + 5.00000i 0.117579 + 0.339422i
\(218\) 5.00000i 0.338643i
\(219\) 0 0
\(220\) 0 0
\(221\) 2.00000 + 3.46410i 0.134535 + 0.233021i
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 12.5000 4.33013i 0.835191 0.289319i
\(225\) 0 0
\(226\) 3.00000 5.19615i 0.199557 0.345643i
\(227\) 17.3205 10.0000i 1.14960 0.663723i 0.200812 0.979630i \(-0.435642\pi\)
0.948790 + 0.315906i \(0.102309\pi\)
\(228\) 0 0
\(229\) −11.0000 + 19.0526i −0.726900 + 1.25903i 0.231287 + 0.972886i \(0.425707\pi\)
−0.958187 + 0.286143i \(0.907627\pi\)
\(230\) 3.00000 6.00000i 0.197814 0.395628i
\(231\) 0 0
\(232\) 21.0000i 1.37872i
\(233\) −12.1244 7.00000i −0.794293 0.458585i 0.0471787 0.998886i \(-0.484977\pi\)
−0.841472 + 0.540301i \(0.818310\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −5.00000 + 8.66025i −0.325472 + 0.563735i
\(237\) 0 0
\(238\) 5.19615 + 1.00000i 0.336817 + 0.0648204i
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) 0 0
\(241\) 7.00000 + 12.1244i 0.450910 + 0.780998i 0.998443 0.0557856i \(-0.0177663\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 9.52628 5.50000i 0.612372 0.353553i
\(243\) 0 0
\(244\) 7.00000 0.448129
\(245\) −3.16025 15.3301i −0.201901 0.979406i
\(246\) 0 0
\(247\) −10.3923 6.00000i −0.661247 0.381771i
\(248\) −5.19615 + 3.00000i −0.329956 + 0.190500i
\(249\) 0 0
\(250\) 10.5263 + 3.76795i 0.665740 + 0.238306i
\(251\) −30.0000 −1.89358 −0.946792 0.321847i \(-0.895696\pi\)
−0.946792 + 0.321847i \(0.895696\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −8.00000 + 13.8564i −0.501965 + 0.869428i
\(255\) 0 0
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) 17.3205 + 10.0000i 1.08042 + 0.623783i 0.931011 0.364992i \(-0.118928\pi\)
0.149413 + 0.988775i \(0.452262\pi\)
\(258\) 0 0
\(259\) −16.0000 13.8564i −0.994192 0.860995i
\(260\) 4.00000 + 2.00000i 0.248069 + 0.124035i
\(261\) 0 0
\(262\) 3.46410 2.00000i 0.214013 0.123560i
\(263\) −7.79423 + 4.50000i −0.480613 + 0.277482i −0.720672 0.693276i \(-0.756167\pi\)
0.240059 + 0.970758i \(0.422833\pi\)
\(264\) 0 0
\(265\) −12.0000 6.00000i −0.737154 0.368577i
\(266\) −15.0000 + 5.19615i −0.919709 + 0.318597i
\(267\) 0 0
\(268\) 4.33013 + 2.50000i 0.264505 + 0.152712i
\(269\) 5.50000 + 9.52628i 0.335341 + 0.580828i 0.983550 0.180635i \(-0.0578152\pi\)
−0.648209 + 0.761462i \(0.724482\pi\)
\(270\) 0 0
\(271\) 1.00000 1.73205i 0.0607457 0.105215i −0.834053 0.551684i \(-0.813985\pi\)
0.894799 + 0.446469i \(0.147319\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 8.66025 5.00000i 0.520344 0.300421i −0.216731 0.976231i \(-0.569540\pi\)
0.737075 + 0.675810i \(0.236206\pi\)
\(278\) −6.92820 4.00000i −0.415526 0.239904i
\(279\) 0 0
\(280\) 16.3923 6.80385i 0.979628 0.406608i
\(281\) 14.0000 0.835170 0.417585 0.908638i \(-0.362877\pi\)
0.417585 + 0.908638i \(0.362877\pi\)
\(282\) 0 0
\(283\) −13.8564 + 8.00000i −0.823678 + 0.475551i −0.851683 0.524057i \(-0.824418\pi\)
0.0280052 + 0.999608i \(0.491084\pi\)
\(284\) −1.00000 1.73205i −0.0593391 0.102778i
\(285\) 0 0
\(286\) 0 0
\(287\) 12.9904 + 2.50000i 0.766798 + 0.147570i
\(288\) 0 0
\(289\) −6.50000 + 11.2583i −0.382353 + 0.662255i
\(290\) −0.937822 15.6244i −0.0550708 0.917494i
\(291\) 0 0
\(292\) −5.19615 3.00000i −0.304082 0.175562i
\(293\) 24.0000i 1.40209i 0.713115 + 0.701047i \(0.247284\pi\)
−0.713115 + 0.701047i \(0.752716\pi\)
\(294\) 0 0
\(295\) −10.0000 + 20.0000i −0.582223 + 1.16445i
\(296\) 12.0000 20.7846i 0.697486 1.20808i
\(297\) 0 0
\(298\) −0.866025 + 0.500000i −0.0501675 + 0.0289642i
\(299\) 3.00000 5.19615i 0.173494 0.300501i
\(300\) 0 0
\(301\) −3.50000 + 18.1865i −0.201737 + 1.04825i
\(302\) 14.0000i 0.805609i
\(303\) 0 0
\(304\) −3.00000 5.19615i −0.172062 0.298020i
\(305\) 15.6244 0.937822i 0.894648 0.0536995i
\(306\) 0 0
\(307\) 23.0000i 1.31268i 0.754466 + 0.656340i \(0.227896\pi\)
−0.754466 + 0.656340i \(0.772104\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −3.73205 + 2.46410i −0.211966 + 0.139952i
\(311\) 15.0000 + 25.9808i 0.850572 + 1.47323i 0.880693 + 0.473688i \(0.157077\pi\)
−0.0301210 + 0.999546i \(0.509589\pi\)
\(312\) 0 0
\(313\) 20.7846 + 12.0000i 1.17482 + 0.678280i 0.954810 0.297218i \(-0.0960589\pi\)
0.220006 + 0.975499i \(0.429392\pi\)
\(314\) 12.0000 0.677199
\(315\) 0 0
\(316\) 2.00000 0.112509
\(317\) −5.19615 3.00000i −0.291845 0.168497i 0.346929 0.937892i \(-0.387225\pi\)
−0.638774 + 0.769395i \(0.720558\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 8.62436 + 13.0622i 0.482116 + 0.730198i
\(321\) 0 0
\(322\) −2.59808 7.50000i −0.144785 0.417959i
\(323\) 12.0000i 0.667698i
\(324\) 0 0
\(325\) 9.19615 + 3.92820i 0.510111 + 0.217898i
\(326\) −2.00000 3.46410i −0.110770 0.191859i
\(327\) 0 0
\(328\) 15.0000i 0.828236i
\(329\) 0 0
\(330\) 0 0
\(331\) −3.00000 + 5.19615i −0.164895 + 0.285606i −0.936618 0.350352i \(-0.886062\pi\)
0.771723 + 0.635959i \(0.219395\pi\)
\(332\) −9.52628 + 5.50000i −0.522823 + 0.301852i
\(333\) 0 0
\(334\) −1.50000 + 2.59808i −0.0820763 + 0.142160i
\(335\) 10.0000 + 5.00000i 0.546358 + 0.273179i
\(336\) 0 0
\(337\) 18.0000i 0.980522i 0.871576 + 0.490261i \(0.163099\pi\)
−0.871576 + 0.490261i \(0.836901\pi\)
\(338\) 7.79423 + 4.50000i 0.423950 + 0.244768i
\(339\) 0 0
\(340\) −0.267949 4.46410i −0.0145316 0.242100i
\(341\) 0 0
\(342\) 0 0
\(343\) −15.5885 10.0000i −0.841698 0.539949i
\(344\) −21.0000 −1.13224
\(345\) 0 0
\(346\) 6.00000 + 10.3923i 0.322562 + 0.558694i
\(347\) −12.9904 + 7.50000i −0.697360 + 0.402621i −0.806363 0.591420i \(-0.798567\pi\)
0.109003 + 0.994041i \(0.465234\pi\)
\(348\) 0 0
\(349\) 17.0000 0.909989 0.454995 0.890494i \(-0.349641\pi\)
0.454995 + 0.890494i \(0.349641\pi\)
\(350\) 11.8923 5.79423i 0.635670 0.309715i
\(351\) 0 0
\(352\) 0 0
\(353\) −22.5167 + 13.0000i −1.19844 + 0.691920i −0.960207 0.279288i \(-0.909902\pi\)
−0.238233 + 0.971208i \(0.576568\pi\)
\(354\) 0 0
\(355\) −2.46410 3.73205i −0.130781 0.198077i
\(356\) 9.00000 0.476999
\(357\) 0 0
\(358\) 2.00000i 0.105703i
\(359\) −5.00000 + 8.66025i −0.263890 + 0.457071i −0.967272 0.253741i \(-0.918339\pi\)
0.703382 + 0.710812i \(0.251672\pi\)
\(360\) 0 0
\(361\) −8.50000 14.7224i −0.447368 0.774865i
\(362\) −2.59808 1.50000i −0.136552 0.0788382i
\(363\) 0 0
\(364\) 5.00000 1.73205i 0.262071 0.0907841i
\(365\) −12.0000 6.00000i −0.628109 0.314054i
\(366\) 0 0
\(367\) 23.3827 13.5000i 1.22057 0.704694i 0.255528 0.966802i \(-0.417751\pi\)
0.965039 + 0.262108i \(0.0844175\pi\)
\(368\) 2.59808 1.50000i 0.135434 0.0781929i
\(369\) 0 0
\(370\) 8.00000 16.0000i 0.415900 0.831800i
\(371\) −15.0000 + 5.19615i −0.778761 + 0.269771i
\(372\) 0 0
\(373\) −20.7846 12.0000i −1.07619 0.621336i −0.146321 0.989237i \(-0.546743\pi\)
−0.929865 + 0.367901i \(0.880077\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 14.0000i 0.721037i
\(378\) 0 0
\(379\) 10.0000 0.513665 0.256833 0.966456i \(-0.417321\pi\)
0.256833 + 0.966456i \(0.417321\pi\)
\(380\) 7.39230 + 11.1962i 0.379217 + 0.574351i
\(381\) 0 0
\(382\) 10.3923 6.00000i 0.531717 0.306987i
\(383\) −4.33013 2.50000i −0.221259 0.127744i 0.385274 0.922802i \(-0.374107\pi\)
−0.606533 + 0.795058i \(0.707440\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 4.00000 0.203595
\(387\) 0 0
\(388\) −13.8564 + 8.00000i −0.703452 + 0.406138i
\(389\) −7.00000 12.1244i −0.354914 0.614729i 0.632189 0.774814i \(-0.282157\pi\)
−0.987103 + 0.160085i \(0.948823\pi\)
\(390\) 0 0
\(391\) −6.00000 −0.303433
\(392\) 7.79423 19.5000i 0.393668 0.984899i
\(393\) 0 0
\(394\) −4.00000 + 6.92820i −0.201517 + 0.349038i
\(395\) 4.46410 0.267949i 0.224613 0.0134820i
\(396\) 0 0
\(397\) 13.8564 + 8.00000i 0.695433 + 0.401508i 0.805644 0.592400i \(-0.201819\pi\)
−0.110211 + 0.993908i \(0.535153\pi\)
\(398\) 4.00000i 0.200502i
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) 1.50000 2.59808i 0.0749064 0.129742i −0.826139 0.563466i \(-0.809468\pi\)
0.901046 + 0.433724i \(0.142801\pi\)
\(402\) 0 0
\(403\) −3.46410 + 2.00000i −0.172559 + 0.0996271i
\(404\) 4.50000 7.79423i 0.223883 0.387777i
\(405\) 0 0
\(406\) −14.0000 12.1244i −0.694808 0.601722i
\(407\) 0 0
\(408\) 0 0
\(409\) −12.5000 21.6506i −0.618085 1.07056i −0.989835 0.142222i \(-0.954575\pi\)
0.371750 0.928333i \(-0.378758\pi\)
\(410\) 0.669873 + 11.1603i 0.0330827 + 0.551166i
\(411\) 0 0
\(412\) 7.00000i 0.344865i
\(413\) 8.66025 + 25.0000i 0.426143 + 1.23017i
\(414\) 0 0
\(415\) −20.5263 + 13.5526i −1.00760 + 0.665269i
\(416\) 5.00000 + 8.66025i 0.245145 + 0.424604i
\(417\) 0 0
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) 15.0000 0.731055 0.365528 0.930800i \(-0.380889\pi\)
0.365528 + 0.930800i \(0.380889\pi\)
\(422\) −8.66025 5.00000i −0.421575 0.243396i
\(423\) 0 0
\(424\) −9.00000 15.5885i −0.437079 0.757042i
\(425\) −1.19615 9.92820i −0.0580219 0.481589i
\(426\) 0 0
\(427\) 12.1244 14.0000i 0.586739 0.677507i
\(428\) 11.0000i 0.531705i
\(429\) 0 0
\(430\) −15.6244 + 0.937822i −0.753473 + 0.0452258i
\(431\) −16.0000 27.7128i −0.770693 1.33488i −0.937184 0.348836i \(-0.886577\pi\)
0.166491 0.986043i \(-0.446756\pi\)
\(432\) 0 0
\(433\) 2.00000i 0.0961139i 0.998845 + 0.0480569i \(0.0153029\pi\)
−0.998845 + 0.0480569i \(0.984697\pi\)
\(434\) −1.00000 + 5.19615i −0.0480015 + 0.249423i
\(435\) 0 0
\(436\) 2.50000 4.33013i 0.119728 0.207375i
\(437\) 15.5885 9.00000i 0.745697 0.430528i
\(438\) 0 0
\(439\) 12.0000 20.7846i 0.572729 0.991995i −0.423556 0.905870i \(-0.639218\pi\)
0.996284 0.0861252i \(-0.0274485\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 4.00000i 0.190261i
\(443\) −26.8468 15.5000i −1.27553 0.736427i −0.299506 0.954094i \(-0.596822\pi\)
−0.976023 + 0.217667i \(0.930155\pi\)
\(444\) 0 0
\(445\) 20.0885 1.20577i 0.952284 0.0571590i
\(446\) 0 0
\(447\) 0 0
\(448\) 18.1865 + 3.50000i 0.859233 + 0.165359i
\(449\) 31.0000 1.46298 0.731490 0.681852i \(-0.238825\pi\)
0.731490 + 0.681852i \(0.238825\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −5.19615 + 3.00000i −0.244406 + 0.141108i
\(453\) 0 0
\(454\) 20.0000 0.938647
\(455\) 10.9282 4.53590i 0.512322 0.212646i
\(456\) 0 0
\(457\) −27.7128 16.0000i −1.29635 0.748448i −0.316579 0.948566i \(-0.602534\pi\)
−0.979772 + 0.200118i \(0.935868\pi\)
\(458\) −19.0526 + 11.0000i −0.890268 + 0.513996i
\(459\) 0 0
\(460\) −5.59808 + 3.69615i −0.261012 + 0.172334i
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) 3.00000i 0.139422i −0.997567 0.0697109i \(-0.977792\pi\)
0.997567 0.0697109i \(-0.0222077\pi\)
\(464\) 3.50000 6.06218i 0.162483 0.281430i
\(465\) 0 0
\(466\) −7.00000 12.1244i −0.324269 0.561650i
\(467\) 2.59808 + 1.50000i 0.120225 + 0.0694117i 0.558906 0.829231i \(-0.311221\pi\)
−0.438682 + 0.898642i \(0.644554\pi\)
\(468\) 0 0
\(469\) 12.5000 4.33013i 0.577196 0.199947i
\(470\) 0 0
\(471\) 0 0
\(472\) −25.9808 + 15.0000i −1.19586 + 0.690431i
\(473\) 0 0
\(474\) 0 0
\(475\) 18.0000 + 24.0000i 0.825897 + 1.10120i
\(476\) −4.00000 3.46410i −0.183340 0.158777i
\(477\) 0 0
\(478\) −15.5885 9.00000i −0.712999 0.411650i
\(479\) −21.0000 36.3731i −0.959514 1.66193i −0.723681 0.690134i \(-0.757551\pi\)
−0.235833 0.971794i \(-0.575782\pi\)
\(480\) 0 0
\(481\) 8.00000 13.8564i 0.364769 0.631798i
\(482\) 14.0000i 0.637683i
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) −29.8564 + 19.7128i −1.35571 + 0.895113i
\(486\) 0 0
\(487\) −10.3923 + 6.00000i −0.470920 + 0.271886i −0.716625 0.697459i \(-0.754314\pi\)
0.245705 + 0.969345i \(0.420981\pi\)
\(488\) 18.1865 + 10.5000i 0.823266 + 0.475313i
\(489\) 0 0
\(490\) 4.92820 14.8564i 0.222634 0.671144i
\(491\) 26.0000 1.17336 0.586682 0.809818i \(-0.300434\pi\)
0.586682 + 0.809818i \(0.300434\pi\)
\(492\) 0 0
\(493\) −12.1244 + 7.00000i −0.546054 + 0.315264i
\(494\) −6.00000 10.3923i −0.269953 0.467572i
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) −5.19615 1.00000i −0.233079 0.0448561i
\(498\) 0 0
\(499\) 8.00000 13.8564i 0.358129 0.620298i −0.629519 0.776985i \(-0.716748\pi\)
0.987648 + 0.156687i \(0.0500814\pi\)
\(500\) −7.23205 8.52628i −0.323427 0.381307i
\(501\) 0 0
\(502\) −25.9808 15.0000i −1.15958 0.669483i
\(503\) 15.0000i 0.668817i −0.942428 0.334408i \(-0.891463\pi\)
0.942428 0.334408i \(-0.108537\pi\)
\(504\) 0 0
\(505\) 9.00000 18.0000i 0.400495 0.800989i
\(506\) 0 0
\(507\) 0 0
\(508\) 13.8564 8.00000i 0.614779 0.354943i
\(509\) −13.5000 + 23.3827i −0.598377 + 1.03642i 0.394684 + 0.918817i \(0.370854\pi\)
−0.993061 + 0.117602i \(0.962479\pi\)
\(510\) 0 0
\(511\) −15.0000 + 5.19615i −0.663561 + 0.229864i
\(512\) 11.0000i 0.486136i
\(513\) 0 0
\(514\) 10.0000 + 17.3205i 0.441081 + 0.763975i
\(515\) −0.937822 15.6244i −0.0413254 0.688491i
\(516\) 0 0
\(517\) 0 0
\(518\) −6.92820 20.0000i −0.304408 0.878750i
\(519\) 0 0
\(520\) 7.39230 + 11.1962i 0.324174 + 0.490984i
\(521\) 7.00000 + 12.1244i 0.306676 + 0.531178i 0.977633 0.210318i \(-0.0674500\pi\)
−0.670957 + 0.741496i \(0.734117\pi\)
\(522\) 0 0
\(523\) 3.46410 + 2.00000i 0.151475 + 0.0874539i 0.573822 0.818980i \(-0.305460\pi\)
−0.422347 + 0.906434i \(0.638794\pi\)
\(524\) −4.00000 −0.174741
\(525\) 0 0
\(526\) −9.00000 −0.392419
\(527\) 3.46410 + 2.00000i 0.150899 + 0.0871214i
\(528\) 0 0
\(529\) −7.00000 12.1244i −0.304348 0.527146i
\(530\) −7.39230 11.1962i −0.321101 0.486330i
\(531\) 0 0
\(532\) 15.5885 + 3.00000i 0.675845 + 0.130066i
\(533\) 10.0000i 0.433148i
\(534\) 0 0
\(535\) −1.47372 24.5526i −0.0637145 1.06150i
\(536\) 7.50000 + 12.9904i 0.323951 + 0.561099i
\(537\) 0 0
\(538\) 11.0000i 0.474244i
\(539\) 0 0
\(540\) 0 0
\(541\) 1.50000 2.59808i 0.0644900 0.111700i −0.831978 0.554809i \(-0.812791\pi\)
0.896468 + 0.443109i \(0.146125\pi\)
\(542\) 1.73205 1.00000i 0.0743980 0.0429537i
\(543\) 0 0
\(544\) 5.00000 8.66025i 0.214373 0.371305i
\(545\) 5.00000 10.0000i 0.214176 0.428353i
\(546\) 0 0
\(547\) 17.0000i 0.726868i −0.931620 0.363434i \(-0.881604\pi\)
0.931620 0.363434i \(-0.118396\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 21.0000 36.3731i 0.894630 1.54954i
\(552\) 0 0
\(553\) 3.46410 4.00000i 0.147309 0.170097i
\(554\) 10.0000 0.424859
\(555\) 0 0
\(556\) 4.00000 + 6.92820i 0.169638 + 0.293821i
\(557\) 38.1051 22.0000i 1.61457 0.932170i 0.626272 0.779604i \(-0.284580\pi\)
0.988293 0.152566i \(-0.0487535\pi\)
\(558\) 0 0
\(559\) −14.0000 −0.592137
\(560\) 5.86603 + 0.767949i 0.247885 + 0.0324518i
\(561\) 0 0
\(562\) 12.1244 + 7.00000i 0.511435 + 0.295277i
\(563\) 28.5788 16.5000i 1.20445 0.695392i 0.242912 0.970048i \(-0.421897\pi\)
0.961542 + 0.274656i \(0.0885641\pi\)
\(564\) 0 0
\(565\) −11.1962 + 7.39230i −0.471026 + 0.310997i
\(566\) −16.0000 −0.672530
\(567\) 0 0
\(568\) 6.00000i 0.251754i
\(569\) 9.00000 15.5885i 0.377300 0.653502i −0.613369 0.789797i \(-0.710186\pi\)
0.990668 + 0.136295i \(0.0435194\pi\)
\(570\) 0 0
\(571\) 9.00000 + 15.5885i 0.376638 + 0.652357i 0.990571 0.137002i \(-0.0437466\pi\)
−0.613933 + 0.789359i \(0.710413\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 10.0000 + 8.66025i 0.417392 + 0.361472i
\(575\) −12.0000 + 9.00000i −0.500435 + 0.375326i
\(576\) 0 0
\(577\) −27.7128 + 16.0000i −1.15370 + 0.666089i −0.949786 0.312900i \(-0.898699\pi\)
−0.203913 + 0.978989i \(0.565366\pi\)
\(578\) −11.2583 + 6.50000i −0.468285 + 0.270364i
\(579\) 0 0
\(580\) −7.00000 + 14.0000i −0.290659 + 0.581318i
\(581\) −5.50000 + 28.5788i −0.228178 + 1.18565i
\(582\) 0 0
\(583\) 0 0
\(584\) −9.00000 15.5885i −0.372423 0.645055i
\(585\) 0 0
\(586\) −12.0000 + 20.7846i −0.495715 + 0.858604i
\(587\) 36.0000i 1.48588i 0.669359 + 0.742940i \(0.266569\pi\)
−0.669359 + 0.742940i \(0.733431\pi\)
\(588\) 0 0
\(589\) −12.0000 −0.494451
\(590\) −18.6603 + 12.3205i −0.768231 + 0.507227i
\(591\) 0 0
\(592\) 6.92820 4.00000i 0.284747 0.164399i
\(593\) −19.0526 11.0000i −0.782395 0.451716i 0.0548835 0.998493i \(-0.482521\pi\)
−0.837278 + 0.546777i \(0.815855\pi\)
\(594\) 0 0
\(595\) −9.39230 7.19615i −0.385047 0.295013i
\(596\) 1.00000 0.0409616
\(597\) 0 0
\(598\) 5.19615 3.00000i 0.212486 0.122679i
\(599\) 22.0000 + 38.1051i 0.898896 + 1.55693i 0.828908 + 0.559385i \(0.188963\pi\)
0.0699877 + 0.997548i \(0.477704\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) −12.1244 + 14.0000i −0.494152 + 0.570597i
\(603\) 0 0
\(604\) −7.00000 + 12.1244i −0.284826 + 0.493333i
\(605\) −24.5526 + 1.47372i −0.998203 + 0.0599153i
\(606\) 0 0
\(607\) 28.5788 + 16.5000i 1.15998 + 0.669714i 0.951299 0.308270i \(-0.0997499\pi\)
0.208680 + 0.977984i \(0.433083\pi\)
\(608\) 30.0000i 1.21666i
\(609\) 0 0
\(610\) 14.0000 + 7.00000i 0.566843 + 0.283422i
\(611\) 0 0
\(612\) 0 0
\(613\) 29.4449 17.0000i 1.18927 0.686624i 0.231127 0.972924i \(-0.425759\pi\)
0.958140 + 0.286300i \(0.0924254\pi\)
\(614\) −11.5000 + 19.9186i −0.464102 + 0.803849i
\(615\) 0 0
\(616\) 0 0
\(617\) 4.00000i 0.161034i 0.996753 + 0.0805170i \(0.0256571\pi\)
−0.996753 + 0.0805170i \(0.974343\pi\)
\(618\) 0 0
\(619\) 14.0000 + 24.2487i 0.562708 + 0.974638i 0.997259 + 0.0739910i \(0.0235736\pi\)
−0.434551 + 0.900647i \(0.643093\pi\)
\(620\) 4.46410 0.267949i 0.179283 0.0107611i
\(621\) 0 0
\(622\) 30.0000i 1.20289i
\(623\) 15.5885 18.0000i 0.624538 0.721155i
\(624\) 0 0
\(625\) −17.2846 18.0622i −0.691384 0.722487i
\(626\) 12.0000 + 20.7846i 0.479616 + 0.830720i
\(627\) 0 0
\(628\) −10.3923 6.00000i −0.414698 0.239426i
\(629\) −16.0000 −0.637962
\(630\) 0 0
\(631\) 40.0000 1.59237 0.796187 0.605050i \(-0.206847\pi\)
0.796187 + 0.605050i \(0.206847\pi\)
\(632\) 5.19615 + 3.00000i 0.206692 + 0.119334i
\(633\) 0 0
\(634\) −3.00000 5.19615i −0.119145 0.206366i
\(635\) 29.8564 19.7128i 1.18482 0.782279i
\(636\) 0 0
\(637\) 5.19615 13.0000i 0.205879 0.515079i
\(638\) 0 0
\(639\) 0 0
\(640\) −0.401924 6.69615i −0.0158874 0.264689i
\(641\) −5.50000 9.52628i −0.217237 0.376265i 0.736725 0.676192i \(-0.236371\pi\)
−0.953962 + 0.299927i \(0.903038\pi\)
\(642\) 0 0
\(643\) 4.00000i 0.157745i 0.996885 + 0.0788723i \(0.0251319\pi\)
−0.996885 + 0.0788723i \(0.974868\pi\)
\(644\) −1.50000 + 7.79423i −0.0591083 + 0.307136i
\(645\) 0 0
\(646\) −6.00000 + 10.3923i −0.236067 + 0.408880i
\(647\) −40.7032 + 23.5000i −1.60021 + 0.923880i −0.608763 + 0.793352i \(0.708334\pi\)
−0.991445 + 0.130528i \(0.958333\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 6.00000 + 8.00000i 0.235339 + 0.313786i
\(651\) 0 0
\(652\) 4.00000i 0.156652i
\(653\) 22.5167 + 13.0000i 0.881145 + 0.508729i 0.871036 0.491220i \(-0.163449\pi\)
0.0101092 + 0.999949i \(0.496782\pi\)
\(654\) 0 0
\(655\) −8.92820 + 0.535898i −0.348854 + 0.0209393i
\(656\) −2.50000 + 4.33013i −0.0976086 + 0.169063i
\(657\) 0 0
\(658\) 0 0
\(659\) 6.00000 0.233727 0.116863 0.993148i \(-0.462716\pi\)
0.116863 + 0.993148i \(0.462716\pi\)
\(660\) 0 0
\(661\) 4.50000 + 7.79423i 0.175030 + 0.303160i 0.940172 0.340701i \(-0.110665\pi\)
−0.765142 + 0.643862i \(0.777331\pi\)
\(662\) −5.19615 + 3.00000i −0.201954 + 0.116598i
\(663\) 0 0
\(664\) −33.0000 −1.28065
\(665\) 35.1962 + 4.60770i 1.36485 + 0.178679i
\(666\) 0 0
\(667\) 18.1865 + 10.5000i 0.704185 + 0.406562i
\(668\) 2.59808 1.50000i 0.100523 0.0580367i
\(669\) 0 0
\(670\) 6.16025 + 9.33013i 0.237991 + 0.360454i
\(671\) 0 0
\(672\) 0 0
\(673\) 36.0000i 1.38770i 0.720121 + 0.693849i \(0.244086\pi\)
−0.720121 + 0.693849i \(0.755914\pi\)
\(674\) −9.00000 + 15.5885i −0.346667 + 0.600445i
\(675\) 0 0
\(676\) −4.50000 7.79423i −0.173077 0.299778i
\(677\) −12.1244 7.00000i −0.465977 0.269032i 0.248577 0.968612i \(-0.420037\pi\)
−0.714554 + 0.699580i \(0.753370\pi\)
\(678\) 0 0
\(679\) −8.00000 + 41.5692i −0.307012 + 1.59528i
\(680\) 6.00000 12.0000i 0.230089 0.460179i
\(681\) 0 0
\(682\) 0 0
\(683\) 30.3109 17.5000i 1.15981 0.669619i 0.208555 0.978011i \(-0.433124\pi\)
0.951259 + 0.308392i \(0.0997908\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) 0 0
\(688\) −6.06218 3.50000i −0.231118 0.133436i
\(689\) −6.00000 10.3923i −0.228582 0.395915i
\(690\) 0 0
\(691\) 10.0000 17.3205i 0.380418 0.658903i −0.610704 0.791859i \(-0.709113\pi\)
0.991122 + 0.132956i \(0.0424468\pi\)
\(692\) 12.0000i 0.456172i
\(693\) 0 0
\(694\) −15.0000 −0.569392
\(695\) 9.85641 + 14.9282i 0.373875 + 0.566259i
\(696\) 0 0
\(697\) 8.66025 5.00000i 0.328031 0.189389i
\(698\) 14.7224 + 8.50000i 0.557252 + 0.321730i
\(699\) 0 0
\(700\) −13.1962 0.928203i −0.498768 0.0350828i
\(701\) 1.00000 0.0377695 0.0188847 0.999822i \(-0.493988\pi\)
0.0188847 + 0.999822i \(0.493988\pi\)
\(702\) 0 0
\(703\) 41.5692 24.0000i 1.56781 0.905177i
\(704\) 0 0
\(705\) 0 0
\(706\) −26.0000 −0.978523
\(707\) −7.79423 22.5000i −0.293132 0.846200i
\(708\) 0 0
\(709\) −24.5000 + 42.4352i −0.920117 + 1.59369i −0.120885 + 0.992667i \(0.538573\pi\)
−0.799232 + 0.601023i \(0.794760\pi\)
\(710\) −0.267949 4.46410i −0.0100560 0.167535i
\(711\) 0 0
\(712\) 23.3827 + 13.5000i 0.876303 + 0.505934i
\(713\) 6.00000i 0.224702i
\(714\) 0 0
\(715\) 0 0
\(716\) 1.00000 1.73205i 0.0373718 0.0647298i
\(717\) 0 0
\(718\) −8.66025 + 5.00000i −0.323198 + 0.186598i
\(719\) −18.0000 + 31.1769i −0.671287 + 1.16270i 0.306253 + 0.951950i \(0.400925\pi\)
−0.977539 + 0.210752i \(0.932409\pi\)
\(720\) 0 0
\(721\) −14.0000 12.1244i −0.521387 0.451535i
\(722\) 17.0000i 0.632674i
\(723\) 0 0
\(724\) 1.50000 + 2.59808i 0.0557471 + 0.0965567i
\(725\) −13.7487 + 32.1865i −0.510614 + 1.19538i
\(726\) 0 0
\(727\) 47.0000i 1.74313i −0.490277 0.871567i \(-0.663104\pi\)
0.490277 0.871567i \(-0.336896\pi\)
\(728\) 15.5885 + 3.00000i 0.577747 + 0.111187i
\(729\) 0 0
\(730\) −7.39230 11.1962i −0.273601 0.414388i
\(731\) 7.00000 + 12.1244i 0.258904 + 0.448435i
\(732\) 0 0
\(733\) −13.8564 8.00000i −0.511798 0.295487i 0.221774 0.975098i \(-0.428815\pi\)
−0.733572 + 0.679611i \(0.762148\pi\)
\(734\) 27.0000 0.996588
\(735\) 0 0
\(736\) −15.0000 −0.552907
\(737\) 0 0
\(738\) 0 0
\(739\) 8.00000 + 13.8564i 0.294285 + 0.509716i 0.974818 0.223001i \(-0.0715853\pi\)
−0.680534 + 0.732717i \(0.738252\pi\)
\(740\) −14.9282 + 9.85641i −0.548772 + 0.362329i
\(741\) 0 0
\(742\) −15.5885 3.00000i −0.572270 0.110133i
\(743\) 49.0000i 1.79764i −0.438322 0.898818i \(-0.644427\pi\)
0.438322 0.898818i \(-0.355573\pi\)
\(744\) 0 0
\(745\) 2.23205 0.133975i 0.0817760 0.00490845i
\(746\) −12.0000 20.7846i −0.439351 0.760979i
\(747\) 0 0
\(748\) 0 0
\(749\) −22.0000 19.0526i −0.803863 0.696165i
\(750\) 0 0
\(751\) 6.00000 10.3923i 0.218943 0.379221i −0.735542 0.677479i \(-0.763072\pi\)
0.954485 + 0.298259i \(0.0964058\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 7.00000 12.1244i 0.254925 0.441543i
\(755\) −14.0000 + 28.0000i −0.509512 + 1.01902i
\(756\) 0 0
\(757\) 22.0000i 0.799604i 0.916602 + 0.399802i \(0.130921\pi\)
−0.916602 + 0.399802i \(0.869079\pi\)
\(758\) 8.66025 + 5.00000i 0.314555 + 0.181608i
\(759\) 0 0
\(760\) 2.41154 + 40.1769i 0.0874758 + 1.45737i
\(761\) 7.00000 12.1244i 0.253750 0.439508i −0.710805 0.703389i \(-0.751669\pi\)
0.964555 + 0.263881i \(0.0850027\pi\)
\(762\) 0 0
\(763\) −4.33013 12.5000i −0.156761 0.452530i
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) −2.50000 4.33013i −0.0903287 0.156454i
\(767\) −17.3205 + 10.0000i −0.625407 + 0.361079i
\(768\) 0 0
\(769\) 30.0000 1.08183 0.540914 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3.46410 2.00000i −0.124676 0.0719816i
\(773\) 15.5885 9.00000i 0.560678 0.323708i −0.192740 0.981250i \(-0.561737\pi\)
0.753418 + 0.657542i \(0.228404\pi\)
\(774\) 0 0
\(775\) 9.92820 1.19615i 0.356632 0.0429671i
\(776\) −48.0000 −1.72310
\(777\) 0 0
\(778\) 14.0000i 0.501924i
\(779\) −15.0000 + 25.9808i −0.537431 + 0.930857i
\(780\) 0 0
\(781\) 0 0
\(782\) −5.19615 3.00000i −0.185814 0.107280i
\(783\) 0 0
\(784\) 5.50000 4.33013i 0.196429 0.154647i
\(785\) −24.0000 12.0000i −0.856597 0.428298i
\(786\) 0 0
\(787\) −14.7224 + 8.50000i −0.524798 + 0.302992i −0.738896 0.673820i \(-0.764652\pi\)
0.214097 + 0.976812i \(0.431319\pi\)
\(788\) 6.92820 4.00000i 0.246807 0.142494i
\(789\) 0 0
\(790\) 4.00000 + 2.00000i 0.142314 + 0.0711568i
\(791\) −3.00000 + 15.5885i −0.106668 + 0.554262i
\(792\) 0 0
\(793\) 12.1244 + 7.00000i 0.430548 + 0.248577i
\(794\) 8.00000 + 13.8564i 0.283909 + 0.491745i
\(795\) 0 0
\(796\) −2.00000 + 3.46410i −0.0708881 + 0.122782i
\(797\) 40.0000i 1.41687i −0.705775 0.708436i \(-0.749401\pi\)
0.705775 0.708436i \(-0.250599\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −2.99038 24.8205i −0.105726 0.877537i
\(801\) 0 0
\(802\) 2.59808 1.50000i 0.0917413 0.0529668i
\(803\) 0 0
\(804\) 0 0
\(805\) −2.30385 + 17.5981i −0.0812000 + 0.620251i
\(806\) −4.00000 −0.140894
\(807\) 0 0
\(808\) 23.3827 13.5000i 0.822600 0.474928i
\(809\) −4.50000 7.79423i −0.158212 0.274030i 0.776012 0.630718i \(-0.217239\pi\)
−0.934224 + 0.356687i \(0.883906\pi\)
\(810\) 0 0
\(811\) −2.00000 −0.0702295 −0.0351147 0.999383i \(-0.511180\pi\)
−0.0351147 + 0.999383i \(0.511180\pi\)
\(812\) 6.06218 + 17.5000i 0.212741 + 0.614130i
\(813\) 0 0
\(814\) 0 0
\(815\) 0.535898 + 8.92820i 0.0187717 + 0.312741i
\(816\) 0 0
\(817\) −36.3731 21.0000i −1.27253 0.734697i
\(818\) 25.0000i 0.874105i
\(819\) 0 0
\(820\) 5.00000 10.0000i 0.174608 0.349215i
\(821\) 11.0000 19.0526i 0.383903 0.664939i −0.607714 0.794156i \(-0.707913\pi\)
0.991616 + 0.129217i \(0.0412465\pi\)
\(822\) 0 0
\(823\) −21.6506 + 12.5000i −0.754694 + 0.435723i −0.827387 0.561632i \(-0.810174\pi\)
0.0726937 + 0.997354i \(0.476840\pi\)
\(824\) 10.5000 18.1865i 0.365785 0.633558i
\(825\) 0 0
\(826\) −5.00000 + 25.9808i −0.173972 + 0.903986i
\(827\) 39.0000i 1.35616i 0.734987 + 0.678081i \(0.237188\pi\)
−0.734987 + 0.678081i \(0.762812\pi\)
\(828\) 0 0
\(829\) −15.0000 25.9808i −0.520972 0.902349i −0.999703 0.0243876i \(-0.992236\pi\)
0.478731 0.877962i \(-0.341097\pi\)
\(830\) −24.5526 + 1.47372i −0.852232 + 0.0511536i
\(831\) 0 0
\(832\) 14.0000i 0.485363i
\(833\) −13.8564 + 2.00000i −0.480096 + 0.0692959i
\(834\) 0 0
\(835\) 5.59808 3.69615i 0.193729 0.127911i
\(836\) 0 0
\(837\) 0 0
\(838\) 20.7846 + 12.0000i 0.717992 + 0.414533i
\(839\) 48.0000 1.65714 0.828572 0.559883i \(-0.189154\pi\)
0.828572 + 0.559883i \(0.189154\pi\)
\(840\) 0 0
\(841\) 20.0000 0.689655
\(842\) 12.9904 + 7.50000i 0.447678 + 0.258467i
\(843\) 0 0
\(844\) 5.00000 + 8.66025i 0.172107 + 0.298098i
\(845\) −11.0885 16.7942i −0.381455 0.577739i
\(846\) 0 0
\(847\) −19.0526 + 22.0000i −0.654654 + 0.755929i
\(848\) 6.00000i 0.206041i
\(849\) 0 0
\(850\) 3.92820 9.19615i 0.134736 0.315425i
\(851\) 12.0000 + 20.7846i 0.411355 + 0.712487i
\(852\) 0 0
\(853\) 6.00000i 0.205436i 0.994711 + 0.102718i \(0.0327539\pi\)
−0.994711 + 0.102718i \(0.967246\pi\)
\(854\) 17.5000 6.06218i 0.598838 0.207443i
\(855\) 0 0
\(856\) 16.5000 28.5788i 0.563958 0.976805i
\(857\) 10.3923 6.00000i 0.354994 0.204956i −0.311888 0.950119i \(-0.600962\pi\)
0.666883 + 0.745163i \(0.267628\pi\)
\(858\) 0 0
\(859\) −16.0000 + 27.7128i −0.545913 + 0.945549i 0.452636 + 0.891695i \(0.350484\pi\)
−0.998549 + 0.0538535i \(0.982850\pi\)
\(860\) 14.0000 + 7.00000i 0.477396 + 0.238698i
\(861\) 0 0
\(862\) 32.0000i 1.08992i
\(863\) 7.79423 + 4.50000i 0.265319 + 0.153182i 0.626758 0.779214i \(-0.284381\pi\)
−0.361440 + 0.932395i \(0.617715\pi\)
\(864\) 0 0
\(865\) −1.60770 26.7846i −0.0546633 0.910704i
\(866\) −1.00000 + 1.73205i −0.0339814 + 0.0588575i
\(867\) 0 0
\(868\) 3.46410 4.00000i 0.117579 0.135769i
\(869\) 0 0
\(870\) 0 0
\(871\) 5.00000 + 8.66025i 0.169419 + 0.293442i
\(872\) 12.9904 7.50000i 0.439910 0.253982i
\(873\) 0 0
\(874\) 18.0000 0.608859
\(875\) −29.5788 0.303848i −0.999947 0.0102719i
\(876\) 0 0
\(877\) 1.73205 + 1.00000i 0.0584872 + 0.0337676i 0.528958 0.848648i \(-0.322583\pi\)
−0.470471 + 0.882415i \(0.655916\pi\)
\(878\) 20.7846 12.0000i 0.701447 0.404980i
\(879\) 0 0
\(880\) 0 0
\(881\) 43.0000 1.44871 0.724353 0.689429i \(-0.242138\pi\)
0.724353 + 0.689429i \(0.242138\pi\)
\(882\) 0 0
\(883\) 36.0000i 1.21150i −0.795656 0.605748i \(-0.792874\pi\)
0.795656 0.605748i \(-0.207126\pi\)
\(884\) 2.00000 3.46410i 0.0672673 0.116510i
\(885\) 0 0
\(886\) −15.5000 26.8468i −0.520733 0.901935i
\(887\) 37.2391 + 21.5000i 1.25037 + 0.721899i 0.971182 0.238338i \(-0.0766027\pi\)
0.279184 + 0.960238i \(0.409936\pi\)
\(888\) 0 0
\(889\) 8.00000 41.5692i 0.268311 1.39419i
\(890\) 18.0000 + 9.00000i 0.603361 + 0.301681i
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 2.00000 4.00000i 0.0668526 0.133705i
\(896\) −6.00000 5.19615i −0.200446 0.173591i
\(897\) 0 0
\(898\) 26.8468 + 15.5000i 0.895889 + 0.517242i
\(899\) −7.00000 12.1244i −0.233463 0.404370i
\(900\) 0 0
\(901\) −6.00000 + 10.3923i −0.199889 + 0.346218i
\(902\) 0 0
\(903\) 0 0
\(904\) −18.0000 −0.598671
\(905\) 3.69615 + 5.59808i 0.122864 + 0.186086i
\(906\) 0 0
\(907\) −16.4545 + 9.50000i −0.546362 + 0.315442i −0.747653 0.664089i \(-0.768820\pi\)
0.201291 + 0.979531i \(0.435486\pi\)
\(908\) −17.3205 10.0000i −0.574801 0.331862i
\(909\) 0 0
\(910\) 11.7321 + 1.53590i 0.388914 + 0.0509145i
\(911\) −24.0000 −0.795155 −0.397578 0.917568i \(-0.630149\pi\)
−0.397578 + 0.917568i \(0.630149\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −16.0000 27.7128i −0.529233 0.916658i
\(915\) 0 0
\(916\) 22.0000 0.726900
\(917\) −6.92820 + 8.00000i −0.228789 + 0.264183i
\(918\) 0 0
\(919\) 17.0000 29.4449i 0.560778 0.971296i −0.436650 0.899631i \(-0.643835\pi\)
0.997429 0.0716652i \(-0.0228313\pi\)
\(920\) −20.0885 + 1.20577i −0.662297 + 0.0397531i
\(921\) 0 0
\(922\) −15.5885 9.00000i −0.513378 0.296399i
\(923\) 4.00000i 0.131662i
\(924\) 0 0
\(925\) −32.0000 + 24.0000i −1.05215 + 0.789115i
\(926\) 1.50000 2.59808i 0.0492931 0.0853781i
\(927\) 0 0
\(928\) −30.3109 + 17.5000i −0.995004 + 0.574466i
\(929\) 14.5000 25.1147i 0.475730 0.823988i −0.523884 0.851790i \(-0.675517\pi\)
0.999613 + 0.0278019i \(0.00885076\pi\)
\(930\) 0 0
\(931\) 33.0000 25.9808i 1.08153 0.851485i
\(932\) 14.0000i 0.458585i
\(933\) 0 0
\(934\) 1.50000 + 2.59808i 0.0490815 + 0.0850117i
\(935\) 0 0
\(936\) 0 0
\(937\) 8.00000i 0.261349i −0.991425 0.130674i \(-0.958286\pi\)
0.991425 0.130674i \(-0.0417142\pi\)
\(938\) 12.9904 + 2.50000i 0.424151 + 0.0816279i
\(939\) 0 0
\(940\) 0 0
\(941\) −9.00000 15.5885i −0.293392 0.508169i 0.681218 0.732081i \(-0.261451\pi\)
−0.974609 + 0.223912i \(0.928117\pi\)
\(942\) 0 0
\(943\) −12.9904 7.50000i −0.423025 0.244234i
\(944\) −10.0000 −0.325472
\(945\) 0 0
\(946\) 0 0
\(947\) −49.3634 28.5000i −1.60410 0.926126i −0.990656 0.136385i \(-0.956452\pi\)
−0.613441 0.789741i \(-0.710215\pi\)
\(948\) 0 0
\(949\) −6.00000 10.3923i −0.194768 0.337348i
\(950\) 3.58846 + 29.7846i 0.116425 + 0.966340i
\(951\) 0 0
\(952\) −5.19615 15.0000i −0.168408 0.486153i
\(953\) 60.0000i 1.94359i 0.235826 + 0.971795i \(0.424220\pi\)
−0.235826 + 0.971795i \(0.575780\pi\)
\(954\) 0 0
\(955\) −26.7846 + 1.60770i −0.866730 + 0.0520238i
\(956\) 9.00000 + 15.5885i 0.291081 + 0.504167i
\(957\) 0 0
\(958\) 42.0000i 1.35696i
\(959\) 0 0
\(960\) 0 0
\(961\) 13.5000 23.3827i 0.435484 0.754280i
\(962\) 13.8564 8.00000i 0.446748 0.257930i
\(963\) 0 0
\(964\) 7.00000 12.1244i 0.225455 0.390499i
\(965\) −8.00000 4.00000i −0.257529 0.128765i
\(966\) 0 0
\(967\) 13.0000i 0.418052i −0.977910 0.209026i \(-0.932971\pi\)
0.977910 0.209026i \(-0.0670293\pi\)
\(968\) −28.5788 16.5000i −0.918559 0.530330i
\(969\) 0 0
\(970\) −35.7128 + 2.14359i −1.14667 + 0.0688266i
\(971\) −16.0000 + 27.7128i −0.513464 + 0.889346i 0.486414 + 0.873729i \(0.338305\pi\)
−0.999878 + 0.0156178i \(0.995028\pi\)
\(972\) 0 0
\(973\) 20.7846 + 4.00000i 0.666324 + 0.128234i
\(974\) −12.0000 −0.384505
\(975\) 0 0
\(976\) 3.50000 + 6.06218i 0.112032 + 0.194046i
\(977\) −51.9615 + 30.0000i −1.66240 + 0.959785i −0.690830 + 0.723017i \(0.742755\pi\)
−0.971566 + 0.236768i \(0.923912\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −11.6962 + 10.4019i −0.373620 + 0.332277i
\(981\) 0 0
\(982\) 22.5167 + 13.0000i 0.718536 + 0.414847i
\(983\) 2.59808 1.50000i 0.0828658 0.0478426i −0.457995 0.888955i \(-0.651432\pi\)
0.540860 + 0.841112i \(0.318099\pi\)
\(984\) 0 0
\(985\) 14.9282 9.85641i 0.475652 0.314051i
\(986\) −14.0000 −0.445851
\(987\) 0 0
\(988\) 12.0000i 0.381771i
\(989\) 10.5000 18.1865i 0.333881 0.578298i
\(990\) 0 0
\(991\) 25.0000 + 43.3013i 0.794151 + 1.37551i 0.923377 + 0.383895i \(0.125418\pi\)
−0.129226 + 0.991615i \(0.541249\pi\)
\(992\) 8.66025 + 5.00000i 0.274963 + 0.158750i
\(993\) 0 0
\(994\) −4.00000 3.46410i −0.126872 0.109875i
\(995\) −4.00000 + 8.00000i −0.126809 + 0.253617i
\(996\) 0 0
\(997\) −1.73205 + 1.00000i −0.0548546 + 0.0316703i −0.527176 0.849756i \(-0.676749\pi\)
0.472322 + 0.881426i \(0.343416\pi\)
\(998\) 13.8564 8.00000i 0.438617 0.253236i
\(999\) 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 315.2.bf.a.289.2 4
3.2 odd 2 35.2.j.a.9.1 yes 4
5.4 even 2 inner 315.2.bf.a.289.1 4
7.2 even 3 2205.2.d.d.1324.1 2
7.4 even 3 inner 315.2.bf.a.109.1 4
7.5 odd 6 2205.2.d.e.1324.1 2
12.11 even 2 560.2.bw.b.289.1 4
15.2 even 4 175.2.e.b.51.1 2
15.8 even 4 175.2.e.a.51.1 2
15.14 odd 2 35.2.j.a.9.2 yes 4
21.2 odd 6 245.2.b.c.99.2 2
21.5 even 6 245.2.b.b.99.2 2
21.11 odd 6 35.2.j.a.4.2 yes 4
21.17 even 6 245.2.j.c.214.2 4
21.20 even 2 245.2.j.c.79.1 4
35.4 even 6 inner 315.2.bf.a.109.2 4
35.9 even 6 2205.2.d.d.1324.2 2
35.19 odd 6 2205.2.d.e.1324.2 2
60.59 even 2 560.2.bw.b.289.2 4
84.11 even 6 560.2.bw.b.529.2 4
105.2 even 12 1225.2.a.d.1.1 1
105.23 even 12 1225.2.a.f.1.1 1
105.32 even 12 175.2.e.b.151.1 2
105.44 odd 6 245.2.b.c.99.1 2
105.47 odd 12 1225.2.a.b.1.1 1
105.53 even 12 175.2.e.a.151.1 2
105.59 even 6 245.2.j.c.214.1 4
105.68 odd 12 1225.2.a.g.1.1 1
105.74 odd 6 35.2.j.a.4.1 4
105.89 even 6 245.2.b.b.99.1 2
105.104 even 2 245.2.j.c.79.2 4
420.179 even 6 560.2.bw.b.529.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.2.j.a.4.1 4 105.74 odd 6
35.2.j.a.4.2 yes 4 21.11 odd 6
35.2.j.a.9.1 yes 4 3.2 odd 2
35.2.j.a.9.2 yes 4 15.14 odd 2
175.2.e.a.51.1 2 15.8 even 4
175.2.e.a.151.1 2 105.53 even 12
175.2.e.b.51.1 2 15.2 even 4
175.2.e.b.151.1 2 105.32 even 12
245.2.b.b.99.1 2 105.89 even 6
245.2.b.b.99.2 2 21.5 even 6
245.2.b.c.99.1 2 105.44 odd 6
245.2.b.c.99.2 2 21.2 odd 6
245.2.j.c.79.1 4 21.20 even 2
245.2.j.c.79.2 4 105.104 even 2
245.2.j.c.214.1 4 105.59 even 6
245.2.j.c.214.2 4 21.17 even 6
315.2.bf.a.109.1 4 7.4 even 3 inner
315.2.bf.a.109.2 4 35.4 even 6 inner
315.2.bf.a.289.1 4 5.4 even 2 inner
315.2.bf.a.289.2 4 1.1 even 1 trivial
560.2.bw.b.289.1 4 12.11 even 2
560.2.bw.b.289.2 4 60.59 even 2
560.2.bw.b.529.1 4 420.179 even 6
560.2.bw.b.529.2 4 84.11 even 6
1225.2.a.b.1.1 1 105.47 odd 12
1225.2.a.d.1.1 1 105.2 even 12
1225.2.a.f.1.1 1 105.23 even 12
1225.2.a.g.1.1 1 105.68 odd 12
2205.2.d.d.1324.1 2 7.2 even 3
2205.2.d.d.1324.2 2 35.9 even 6
2205.2.d.e.1324.1 2 7.5 odd 6
2205.2.d.e.1324.2 2 35.19 odd 6