Properties

Label 572.2.n.b.157.7
Level $572$
Weight $2$
Character 572.157
Analytic conductor $4.567$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [572,2,Mod(53,572)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(572, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("572.53");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.n (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.56744299562\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 157.7
Character \(\chi\) \(=\) 572.157
Dual form 572.2.n.b.521.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965759 + 2.97230i) q^{3} +(1.96166 + 1.42523i) q^{5} +(-0.681960 + 2.09886i) q^{7} +(-5.47482 + 3.97769i) q^{9} +O(q^{10})\) \(q+(0.965759 + 2.97230i) q^{3} +(1.96166 + 1.42523i) q^{5} +(-0.681960 + 2.09886i) q^{7} +(-5.47482 + 3.97769i) q^{9} +(-0.402908 - 3.29206i) q^{11} +(0.809017 - 0.587785i) q^{13} +(-2.34171 + 7.20705i) q^{15} +(2.69648 + 1.95911i) q^{17} +(-0.295228 - 0.908620i) q^{19} -6.89704 q^{21} +2.75510 q^{23} +(0.271738 + 0.836325i) q^{25} +(-9.52508 - 6.92038i) q^{27} +(2.70254 - 8.31758i) q^{29} +(-4.33655 + 3.15069i) q^{31} +(9.39588 - 4.37690i) q^{33} +(-4.32912 + 3.14529i) q^{35} +(1.67674 - 5.16048i) q^{37} +(2.52839 + 1.83698i) q^{39} +(-2.06468 - 6.35442i) q^{41} +7.04857 q^{43} -16.4088 q^{45} +(3.50513 + 10.7877i) q^{47} +(1.72298 + 1.25182i) q^{49} +(-3.21891 + 9.90678i) q^{51} +(-4.17380 + 3.03244i) q^{53} +(3.90157 - 7.03213i) q^{55} +(2.41557 - 1.75501i) q^{57} +(-3.98434 + 12.2625i) q^{59} +(0.131388 + 0.0954591i) q^{61} +(-4.61500 - 14.2035i) q^{63} +2.42474 q^{65} -5.50821 q^{67} +(2.66076 + 8.18898i) q^{69} +(-9.78658 - 7.11036i) q^{71} +(0.190697 - 0.586905i) q^{73} +(-2.22337 + 1.61538i) q^{75} +(7.18434 + 1.39941i) q^{77} +(-7.20582 + 5.23534i) q^{79} +(5.09691 - 15.6867i) q^{81} +(1.45763 + 1.05903i) q^{83} +(2.49740 + 7.68619i) q^{85} +27.3323 q^{87} +6.18551 q^{89} +(0.681960 + 2.09886i) q^{91} +(-13.5529 - 9.84673i) q^{93} +(0.715852 - 2.20317i) q^{95} +(0.314159 - 0.228250i) q^{97} +(15.3007 + 16.4208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(353\) \(365\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\)

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 0
\(3\) 0.965759 + 2.97230i 0.557581 + 1.71606i 0.689028 + 0.724735i \(0.258038\pi\)
−0.131447 + 0.991323i \(0.541962\pi\)
\(4\) 0 0
\(5\) 1.96166 + 1.42523i 0.877279 + 0.637381i 0.932530 0.361092i \(-0.117596\pi\)
−0.0552511 + 0.998472i \(0.517596\pi\)
\(6\) 0 0
\(7\) −0.681960 + 2.09886i −0.257757 + 0.793294i 0.735517 + 0.677506i \(0.236939\pi\)
−0.993274 + 0.115788i \(0.963061\pi\)
\(8\) 0 0
\(9\) −5.47482 + 3.97769i −1.82494 + 1.32590i
\(10\) 0 0
\(11\) −0.402908 3.29206i −0.121481 0.992594i
\(12\) 0 0
\(13\) 0.809017 0.587785i 0.224381 0.163022i
\(14\) 0 0
\(15\) −2.34171 + 7.20705i −0.604628 + 1.86085i
\(16\) 0 0
\(17\) 2.69648 + 1.95911i 0.653993 + 0.475154i 0.864629 0.502411i \(-0.167554\pi\)
−0.210636 + 0.977565i \(0.567554\pi\)
\(18\) 0 0
\(19\) −0.295228 0.908620i −0.0677300 0.208452i 0.911463 0.411382i \(-0.134954\pi\)
−0.979193 + 0.202930i \(0.934954\pi\)
\(20\) 0 0
\(21\) −6.89704 −1.50506
\(22\) 0 0
\(23\) 2.75510 0.574478 0.287239 0.957859i \(-0.407263\pi\)
0.287239 + 0.957859i \(0.407263\pi\)
\(24\) 0 0
\(25\) 0.271738 + 0.836325i 0.0543477 + 0.167265i
\(26\) 0 0
\(27\) −9.52508 6.92038i −1.83310 1.33183i
\(28\) 0 0
\(29\) 2.70254 8.31758i 0.501850 1.54454i −0.304153 0.952623i \(-0.598373\pi\)
0.806003 0.591912i \(-0.201627\pi\)
\(30\) 0 0
\(31\) −4.33655 + 3.15069i −0.778868 + 0.565881i −0.904639 0.426179i \(-0.859859\pi\)
0.125771 + 0.992059i \(0.459859\pi\)
\(32\) 0 0
\(33\) 9.39588 4.37690i 1.63561 0.761920i
\(34\) 0 0
\(35\) −4.32912 + 3.14529i −0.731755 + 0.531651i
\(36\) 0 0
\(37\) 1.67674 5.16048i 0.275655 0.848378i −0.713391 0.700766i \(-0.752841\pi\)
0.989045 0.147611i \(-0.0471585\pi\)
\(38\) 0 0
\(39\) 2.52839 + 1.83698i 0.404866 + 0.294153i
\(40\) 0 0
\(41\) −2.06468 6.35442i −0.322448 0.992394i −0.972579 0.232572i \(-0.925286\pi\)
0.650131 0.759822i \(-0.274714\pi\)
\(42\) 0 0
\(43\) 7.04857 1.07490 0.537449 0.843297i \(-0.319388\pi\)
0.537449 + 0.843297i \(0.319388\pi\)
\(44\) 0 0
\(45\) −16.4088 −2.44608
\(46\) 0 0
\(47\) 3.50513 + 10.7877i 0.511276 + 1.57355i 0.789956 + 0.613163i \(0.210103\pi\)
−0.278680 + 0.960384i \(0.589897\pi\)
\(48\) 0 0
\(49\) 1.72298 + 1.25182i 0.246141 + 0.178832i
\(50\) 0 0
\(51\) −3.21891 + 9.90678i −0.450737 + 1.38723i
\(52\) 0 0
\(53\) −4.17380 + 3.03244i −0.573315 + 0.416538i −0.836308 0.548260i \(-0.815290\pi\)
0.262993 + 0.964798i \(0.415290\pi\)
\(54\) 0 0
\(55\) 3.90157 7.03213i 0.526087 0.948212i
\(56\) 0 0
\(57\) 2.41557 1.75501i 0.319950 0.232457i
\(58\) 0 0
\(59\) −3.98434 + 12.2625i −0.518717 + 1.59645i 0.257700 + 0.966225i \(0.417035\pi\)
−0.776416 + 0.630220i \(0.782965\pi\)
\(60\) 0 0
\(61\) 0.131388 + 0.0954591i 0.0168225 + 0.0122223i 0.596165 0.802862i \(-0.296691\pi\)
−0.579342 + 0.815084i \(0.696691\pi\)
\(62\) 0 0
\(63\) −4.61500 14.2035i −0.581435 1.78947i
\(64\) 0 0
\(65\) 2.42474 0.300752
\(66\) 0 0
\(67\) −5.50821 −0.672935 −0.336467 0.941695i \(-0.609232\pi\)
−0.336467 + 0.941695i \(0.609232\pi\)
\(68\) 0 0
\(69\) 2.66076 + 8.18898i 0.320318 + 0.985838i
\(70\) 0 0
\(71\) −9.78658 7.11036i −1.16145 0.843845i −0.171492 0.985186i \(-0.554859\pi\)
−0.989961 + 0.141340i \(0.954859\pi\)
\(72\) 0 0
\(73\) 0.190697 0.586905i 0.0223194 0.0686921i −0.939276 0.343161i \(-0.888502\pi\)
0.961596 + 0.274469i \(0.0885022\pi\)
\(74\) 0 0
\(75\) −2.22337 + 1.61538i −0.256733 + 0.186528i
\(76\) 0 0
\(77\) 7.18434 + 1.39941i 0.818731 + 0.159477i
\(78\) 0 0
\(79\) −7.20582 + 5.23534i −0.810719 + 0.589022i −0.914039 0.405627i \(-0.867053\pi\)
0.103320 + 0.994648i \(0.467053\pi\)
\(80\) 0 0
\(81\) 5.09691 15.6867i 0.566323 1.74296i
\(82\) 0 0
\(83\) 1.45763 + 1.05903i 0.159995 + 0.116243i 0.664902 0.746930i \(-0.268473\pi\)
−0.504907 + 0.863174i \(0.668473\pi\)
\(84\) 0 0
\(85\) 2.49740 + 7.68619i 0.270881 + 0.833685i
\(86\) 0 0
\(87\) 27.3323 2.93033
\(88\) 0 0
\(89\) 6.18551 0.655663 0.327831 0.944736i \(-0.393682\pi\)
0.327831 + 0.944736i \(0.393682\pi\)
\(90\) 0 0
\(91\) 0.681960 + 2.09886i 0.0714889 + 0.220020i
\(92\) 0 0
\(93\) −13.5529 9.84673i −1.40537 1.02106i
\(94\) 0 0
\(95\) 0.715852 2.20317i 0.0734449 0.226040i
\(96\) 0 0
\(97\) 0.314159 0.228250i 0.0318980 0.0231753i −0.571722 0.820447i \(-0.693724\pi\)
0.603620 + 0.797272i \(0.293724\pi\)
\(98\) 0 0
\(99\) 15.3007 + 16.4208i 1.53777 + 1.65035i
\(100\) 0 0
\(101\) 13.5551 9.84837i 1.34878 0.979949i 0.349714 0.936857i \(-0.386279\pi\)
0.999071 0.0430927i \(-0.0137211\pi\)
\(102\) 0 0
\(103\) 5.13911 15.8166i 0.506372 1.55845i −0.292080 0.956394i \(-0.594347\pi\)
0.798452 0.602058i \(-0.205653\pi\)
\(104\) 0 0
\(105\) −13.5296 9.82985i −1.32036 0.959295i
\(106\) 0 0
\(107\) 5.13623 + 15.8077i 0.496538 + 1.52819i 0.814547 + 0.580098i \(0.196986\pi\)
−0.318009 + 0.948088i \(0.603014\pi\)
\(108\) 0 0
\(109\) 12.5350 1.20064 0.600318 0.799762i \(-0.295041\pi\)
0.600318 + 0.799762i \(0.295041\pi\)
\(110\) 0 0
\(111\) 16.9578 1.60957
\(112\) 0 0
\(113\) 2.48061 + 7.63452i 0.233356 + 0.718196i 0.997335 + 0.0729549i \(0.0232429\pi\)
−0.763979 + 0.645241i \(0.776757\pi\)
\(114\) 0 0
\(115\) 5.40456 + 3.92664i 0.503978 + 0.366161i
\(116\) 0 0
\(117\) −2.09120 + 6.43604i −0.193331 + 0.595012i
\(118\) 0 0
\(119\) −5.95078 + 4.32350i −0.545507 + 0.396334i
\(120\) 0 0
\(121\) −10.6753 + 2.65280i −0.970485 + 0.241163i
\(122\) 0 0
\(123\) 16.8933 12.2737i 1.52321 1.10668i
\(124\) 0 0
\(125\) 3.08753 9.50245i 0.276157 0.849925i
\(126\) 0 0
\(127\) 7.05492 + 5.12570i 0.626023 + 0.454832i 0.855020 0.518595i \(-0.173545\pi\)
−0.228997 + 0.973427i \(0.573545\pi\)
\(128\) 0 0
\(129\) 6.80722 + 20.9505i 0.599342 + 1.84459i
\(130\) 0 0
\(131\) −10.5956 −0.925745 −0.462872 0.886425i \(-0.653181\pi\)
−0.462872 + 0.886425i \(0.653181\pi\)
\(132\) 0 0
\(133\) 2.10840 0.182821
\(134\) 0 0
\(135\) −8.82183 27.1508i −0.759262 2.33677i
\(136\) 0 0
\(137\) −11.9916 8.71239i −1.02451 0.744350i −0.0573073 0.998357i \(-0.518251\pi\)
−0.967202 + 0.254007i \(0.918251\pi\)
\(138\) 0 0
\(139\) 7.13690 21.9651i 0.605344 1.86306i 0.110938 0.993827i \(-0.464615\pi\)
0.494407 0.869231i \(-0.335385\pi\)
\(140\) 0 0
\(141\) −28.6791 + 20.8366i −2.41522 + 1.75476i
\(142\) 0 0
\(143\) −2.26098 2.42651i −0.189073 0.202915i
\(144\) 0 0
\(145\) 17.1559 12.4645i 1.42472 1.03512i
\(146\) 0 0
\(147\) −2.05680 + 6.33018i −0.169642 + 0.522105i
\(148\) 0 0
\(149\) −6.66194 4.84019i −0.545768 0.396523i 0.280455 0.959867i \(-0.409515\pi\)
−0.826223 + 0.563344i \(0.809515\pi\)
\(150\) 0 0
\(151\) −3.74504 11.5260i −0.304767 0.937976i −0.979764 0.200156i \(-0.935855\pi\)
0.674997 0.737820i \(-0.264145\pi\)
\(152\) 0 0
\(153\) −22.5555 −1.82350
\(154\) 0 0
\(155\) −12.9973 −1.04397
\(156\) 0 0
\(157\) −2.66190 8.19248i −0.212442 0.653831i −0.999325 0.0367283i \(-0.988306\pi\)
0.786883 0.617102i \(-0.211694\pi\)
\(158\) 0 0
\(159\) −13.0442 9.47717i −1.03447 0.751589i
\(160\) 0 0
\(161\) −1.87887 + 5.78256i −0.148076 + 0.455730i
\(162\) 0 0
\(163\) 10.7881 7.83800i 0.844987 0.613919i −0.0787720 0.996893i \(-0.525100\pi\)
0.923759 + 0.382973i \(0.125100\pi\)
\(164\) 0 0
\(165\) 24.6696 + 4.80528i 1.92052 + 0.374091i
\(166\) 0 0
\(167\) 15.4795 11.2465i 1.19784 0.870280i 0.203768 0.979019i \(-0.434681\pi\)
0.994070 + 0.108739i \(0.0346812\pi\)
\(168\) 0 0
\(169\) 0.309017 0.951057i 0.0237705 0.0731582i
\(170\) 0 0
\(171\) 5.23053 + 3.80020i 0.399989 + 0.290609i
\(172\) 0 0
\(173\) 4.77097 + 14.6835i 0.362730 + 1.11637i 0.951390 + 0.307987i \(0.0996554\pi\)
−0.588661 + 0.808380i \(0.700345\pi\)
\(174\) 0 0
\(175\) −1.94064 −0.146699
\(176\) 0 0
\(177\) −40.2958 −3.02882
\(178\) 0 0
\(179\) 7.00828 + 21.5693i 0.523824 + 1.61216i 0.766631 + 0.642089i \(0.221932\pi\)
−0.242807 + 0.970075i \(0.578068\pi\)
\(180\) 0 0
\(181\) 4.99929 + 3.63220i 0.371595 + 0.269979i 0.757872 0.652403i \(-0.226239\pi\)
−0.386277 + 0.922383i \(0.626239\pi\)
\(182\) 0 0
\(183\) −0.156844 + 0.482715i −0.0115942 + 0.0356833i
\(184\) 0 0
\(185\) 10.6440 7.73335i 0.782566 0.568567i
\(186\) 0 0
\(187\) 5.36307 9.66632i 0.392187 0.706871i
\(188\) 0 0
\(189\) 21.0206 15.2724i 1.52902 1.11090i
\(190\) 0 0
\(191\) −2.13163 + 6.56049i −0.154240 + 0.474700i −0.998083 0.0618889i \(-0.980288\pi\)
0.843844 + 0.536589i \(0.180288\pi\)
\(192\) 0 0
\(193\) −9.87632 7.17557i −0.710913 0.516508i 0.172555 0.985000i \(-0.444798\pi\)
−0.883468 + 0.468491i \(0.844798\pi\)
\(194\) 0 0
\(195\) 2.34171 + 7.20705i 0.167694 + 0.516108i
\(196\) 0 0
\(197\) −6.22791 −0.443720 −0.221860 0.975079i \(-0.571213\pi\)
−0.221860 + 0.975079i \(0.571213\pi\)
\(198\) 0 0
\(199\) 11.3142 0.802044 0.401022 0.916069i \(-0.368655\pi\)
0.401022 + 0.916069i \(0.368655\pi\)
\(200\) 0 0
\(201\) −5.31960 16.3720i −0.375216 1.15479i
\(202\) 0 0
\(203\) 15.6144 + 11.3445i 1.09592 + 0.796229i
\(204\) 0 0
\(205\) 5.00630 15.4078i 0.349655 1.07613i
\(206\) 0 0
\(207\) −15.0837 + 10.9589i −1.04839 + 0.761699i
\(208\) 0 0
\(209\) −2.87228 + 1.33800i −0.198680 + 0.0925514i
\(210\) 0 0
\(211\) −20.2684 + 14.7258i −1.39533 + 1.01377i −0.400075 + 0.916482i \(0.631016\pi\)
−0.995257 + 0.0972857i \(0.968984\pi\)
\(212\) 0 0
\(213\) 11.6827 35.9555i 0.800483 2.46363i
\(214\) 0 0
\(215\) 13.8269 + 10.0458i 0.942985 + 0.685119i
\(216\) 0 0
\(217\) −3.65549 11.2505i −0.248151 0.763731i
\(218\) 0 0
\(219\) 1.92863 0.130324
\(220\) 0 0
\(221\) 3.33303 0.224204
\(222\) 0 0
\(223\) −5.71554 17.5906i −0.382741 1.17796i −0.938106 0.346349i \(-0.887421\pi\)
0.555365 0.831607i \(-0.312579\pi\)
\(224\) 0 0
\(225\) −4.81436 3.49784i −0.320957 0.233189i
\(226\) 0 0
\(227\) −3.20541 + 9.86523i −0.212750 + 0.654778i 0.786555 + 0.617520i \(0.211862\pi\)
−0.999306 + 0.0372583i \(0.988138\pi\)
\(228\) 0 0
\(229\) −4.98350 + 3.62072i −0.329319 + 0.239264i −0.740142 0.672451i \(-0.765242\pi\)
0.410823 + 0.911715i \(0.365242\pi\)
\(230\) 0 0
\(231\) 2.77887 + 22.7055i 0.182836 + 1.49391i
\(232\) 0 0
\(233\) −15.8903 + 11.5449i −1.04100 + 0.756334i −0.970481 0.241176i \(-0.922467\pi\)
−0.0705235 + 0.997510i \(0.522467\pi\)
\(234\) 0 0
\(235\) −8.49904 + 26.1574i −0.554416 + 1.70632i
\(236\) 0 0
\(237\) −22.5201 16.3618i −1.46284 1.06281i
\(238\) 0 0
\(239\) −4.68203 14.4098i −0.302856 0.932094i −0.980469 0.196675i \(-0.936986\pi\)
0.677613 0.735419i \(-0.263014\pi\)
\(240\) 0 0
\(241\) −13.9436 −0.898184 −0.449092 0.893486i \(-0.648252\pi\)
−0.449092 + 0.893486i \(0.648252\pi\)
\(242\) 0 0
\(243\) 16.2270 1.04096
\(244\) 0 0
\(245\) 1.59577 + 4.91128i 0.101950 + 0.313770i
\(246\) 0 0
\(247\) −0.772918 0.561558i −0.0491796 0.0357311i
\(248\) 0 0
\(249\) −1.74003 + 5.35527i −0.110270 + 0.339377i
\(250\) 0 0
\(251\) −13.6026 + 9.88286i −0.858588 + 0.623801i −0.927500 0.373822i \(-0.878047\pi\)
0.0689126 + 0.997623i \(0.478047\pi\)
\(252\) 0 0
\(253\) −1.11005 9.06996i −0.0697884 0.570223i
\(254\) 0 0
\(255\) −20.4338 + 14.8460i −1.27961 + 0.929693i
\(256\) 0 0
\(257\) −4.06083 + 12.4980i −0.253308 + 0.779601i 0.740850 + 0.671670i \(0.234423\pi\)
−0.994158 + 0.107931i \(0.965577\pi\)
\(258\) 0 0
\(259\) 9.68765 + 7.03849i 0.601961 + 0.437350i
\(260\) 0 0
\(261\) 18.2888 + 56.2872i 1.13205 + 3.48409i
\(262\) 0 0
\(263\) −4.18888 −0.258297 −0.129149 0.991625i \(-0.541224\pi\)
−0.129149 + 0.991625i \(0.541224\pi\)
\(264\) 0 0
\(265\) −12.5095 −0.768451
\(266\) 0 0
\(267\) 5.97371 + 18.3852i 0.365585 + 1.12515i
\(268\) 0 0
\(269\) 13.3164 + 9.67490i 0.811913 + 0.589889i 0.914385 0.404847i \(-0.132675\pi\)
−0.102472 + 0.994736i \(0.532675\pi\)
\(270\) 0 0
\(271\) 6.23748 19.1970i 0.378900 1.16613i −0.561910 0.827198i \(-0.689933\pi\)
0.940810 0.338935i \(-0.110067\pi\)
\(272\) 0 0
\(273\) −5.57983 + 4.05398i −0.337706 + 0.245358i
\(274\) 0 0
\(275\) 2.64375 1.23154i 0.159424 0.0742647i
\(276\) 0 0
\(277\) 15.6947 11.4028i 0.943001 0.685130i −0.00614026 0.999981i \(-0.501955\pi\)
0.949141 + 0.314851i \(0.101955\pi\)
\(278\) 0 0
\(279\) 11.2094 34.4989i 0.671088 2.06540i
\(280\) 0 0
\(281\) 9.29974 + 6.75666i 0.554776 + 0.403069i 0.829543 0.558442i \(-0.188601\pi\)
−0.274767 + 0.961511i \(0.588601\pi\)
\(282\) 0 0
\(283\) −5.64458 17.3722i −0.335535 1.03267i −0.966458 0.256825i \(-0.917323\pi\)
0.630923 0.775846i \(-0.282677\pi\)
\(284\) 0 0
\(285\) 7.23981 0.428849
\(286\) 0 0
\(287\) 14.7451 0.870373
\(288\) 0 0
\(289\) −1.82038 5.60256i −0.107081 0.329562i
\(290\) 0 0
\(291\) 0.981829 + 0.713340i 0.0575558 + 0.0418168i
\(292\) 0 0
\(293\) 3.45808 10.6429i 0.202023 0.621763i −0.797799 0.602923i \(-0.794003\pi\)
0.999823 0.0188403i \(-0.00599740\pi\)
\(294\) 0 0
\(295\) −25.2928 + 18.3763i −1.47260 + 1.06991i
\(296\) 0 0
\(297\) −18.9446 + 34.1454i −1.09928 + 1.98132i
\(298\) 0 0
\(299\) 2.22892 1.61941i 0.128902 0.0936527i
\(300\) 0 0
\(301\) −4.80685 + 14.7940i −0.277062 + 0.852709i
\(302\) 0 0
\(303\) 42.3633 + 30.7787i 2.43371 + 1.76819i
\(304\) 0 0
\(305\) 0.121688 + 0.374516i 0.00696781 + 0.0214447i
\(306\) 0 0
\(307\) −31.7892 −1.81430 −0.907152 0.420804i \(-0.861748\pi\)
−0.907152 + 0.420804i \(0.861748\pi\)
\(308\) 0 0
\(309\) 51.9747 2.95674
\(310\) 0 0
\(311\) 2.28383 + 7.02890i 0.129504 + 0.398572i 0.994695 0.102871i \(-0.0328027\pi\)
−0.865191 + 0.501443i \(0.832803\pi\)
\(312\) 0 0
\(313\) 13.2730 + 9.64343i 0.750237 + 0.545079i 0.895900 0.444255i \(-0.146532\pi\)
−0.145663 + 0.989334i \(0.546532\pi\)
\(314\) 0 0
\(315\) 11.1902 34.4398i 0.630495 1.94046i
\(316\) 0 0
\(317\) 0.317566 0.230725i 0.0178363 0.0129588i −0.578831 0.815447i \(-0.696491\pi\)
0.596668 + 0.802488i \(0.296491\pi\)
\(318\) 0 0
\(319\) −28.4709 5.54572i −1.59406 0.310501i
\(320\) 0 0
\(321\) −42.0248 + 30.5328i −2.34560 + 1.70417i
\(322\) 0 0
\(323\) 0.984007 3.02846i 0.0547516 0.168508i
\(324\) 0 0
\(325\) 0.711420 + 0.516877i 0.0394625 + 0.0286712i
\(326\) 0 0
\(327\) 12.1058 + 37.2578i 0.669451 + 2.06036i
\(328\) 0 0
\(329\) −25.0322 −1.38007
\(330\) 0 0
\(331\) 19.6115 1.07795 0.538974 0.842323i \(-0.318812\pi\)
0.538974 + 0.842323i \(0.318812\pi\)
\(332\) 0 0
\(333\) 11.3469 + 34.9223i 0.621808 + 1.91373i
\(334\) 0 0
\(335\) −10.8052 7.85044i −0.590352 0.428916i
\(336\) 0 0
\(337\) 6.26782 19.2904i 0.341430 1.05081i −0.622037 0.782988i \(-0.713695\pi\)
0.963467 0.267826i \(-0.0863052\pi\)
\(338\) 0 0
\(339\) −20.2964 + 14.7462i −1.10235 + 0.800904i
\(340\) 0 0
\(341\) 12.1195 + 13.0068i 0.656307 + 0.704355i
\(342\) 0 0
\(343\) −16.3002 + 11.8428i −0.880126 + 0.639449i
\(344\) 0 0
\(345\) −6.45166 + 19.8562i −0.347345 + 1.06902i
\(346\) 0 0
\(347\) −21.3532 15.5140i −1.14630 0.832836i −0.158316 0.987389i \(-0.550606\pi\)
−0.987985 + 0.154553i \(0.950606\pi\)
\(348\) 0 0
\(349\) 1.54209 + 4.74608i 0.0825464 + 0.254052i 0.983809 0.179222i \(-0.0573582\pi\)
−0.901262 + 0.433274i \(0.857358\pi\)
\(350\) 0 0
\(351\) −11.7736 −0.628431
\(352\) 0 0
\(353\) −8.76581 −0.466557 −0.233278 0.972410i \(-0.574945\pi\)
−0.233278 + 0.972410i \(0.574945\pi\)
\(354\) 0 0
\(355\) −9.06402 27.8962i −0.481068 1.48058i
\(356\) 0 0
\(357\) −18.5977 13.5121i −0.984297 0.715134i
\(358\) 0 0
\(359\) 0.678227 2.08737i 0.0357955 0.110167i −0.931562 0.363582i \(-0.881554\pi\)
0.967358 + 0.253415i \(0.0815537\pi\)
\(360\) 0 0
\(361\) 14.6329 10.6314i 0.770152 0.559548i
\(362\) 0 0
\(363\) −18.1947 29.1683i −0.954974 1.53094i
\(364\) 0 0
\(365\) 1.21056 0.879520i 0.0633634 0.0460362i
\(366\) 0 0
\(367\) 11.1831 34.4181i 0.583753 1.79661i −0.0204670 0.999791i \(-0.506515\pi\)
0.604220 0.796817i \(-0.293485\pi\)
\(368\) 0 0
\(369\) 36.5797 + 26.5767i 1.90426 + 1.38353i
\(370\) 0 0
\(371\) −3.51830 10.8282i −0.182661 0.562173i
\(372\) 0 0
\(373\) −17.6696 −0.914896 −0.457448 0.889236i \(-0.651236\pi\)
−0.457448 + 0.889236i \(0.651236\pi\)
\(374\) 0 0
\(375\) 31.2259 1.61250
\(376\) 0 0
\(377\) −2.70254 8.31758i −0.139188 0.428377i
\(378\) 0 0
\(379\) −14.5800 10.5930i −0.748926 0.544127i 0.146568 0.989201i \(-0.453177\pi\)
−0.895494 + 0.445074i \(0.853177\pi\)
\(380\) 0 0
\(381\) −8.42176 + 25.9195i −0.431460 + 1.32790i
\(382\) 0 0
\(383\) −4.38963 + 3.18925i −0.224300 + 0.162963i −0.694260 0.719724i \(-0.744268\pi\)
0.469960 + 0.882687i \(0.344268\pi\)
\(384\) 0 0
\(385\) 12.0987 + 12.9845i 0.616608 + 0.661749i
\(386\) 0 0
\(387\) −38.5897 + 28.0370i −1.96162 + 1.42520i
\(388\) 0 0
\(389\) 5.58539 17.1901i 0.283191 0.871571i −0.703745 0.710453i \(-0.748490\pi\)
0.986935 0.161118i \(-0.0515100\pi\)
\(390\) 0 0
\(391\) 7.42908 + 5.39754i 0.375705 + 0.272965i
\(392\) 0 0
\(393\) −10.2328 31.4934i −0.516178 1.58863i
\(394\) 0 0
\(395\) −21.5969 −1.08666
\(396\) 0 0
\(397\) −18.3394 −0.920426 −0.460213 0.887809i \(-0.652227\pi\)
−0.460213 + 0.887809i \(0.652227\pi\)
\(398\) 0 0
\(399\) 2.03620 + 6.26679i 0.101938 + 0.313732i
\(400\) 0 0
\(401\) 9.90405 + 7.19571i 0.494585 + 0.359337i 0.806945 0.590627i \(-0.201120\pi\)
−0.312360 + 0.949964i \(0.601120\pi\)
\(402\) 0 0
\(403\) −1.65642 + 5.09792i −0.0825119 + 0.253946i
\(404\) 0 0
\(405\) 32.3555 23.5076i 1.60776 1.16810i
\(406\) 0 0
\(407\) −17.6642 3.44074i −0.875581 0.170551i
\(408\) 0 0
\(409\) 14.5690 10.5850i 0.720392 0.523395i −0.166117 0.986106i \(-0.553123\pi\)
0.886509 + 0.462711i \(0.153123\pi\)
\(410\) 0 0
\(411\) 14.3149 44.0566i 0.706100 2.17315i
\(412\) 0 0
\(413\) −23.0201 16.7251i −1.13275 0.822989i
\(414\) 0 0
\(415\) 1.35001 + 4.15490i 0.0662693 + 0.203956i
\(416\) 0 0
\(417\) 72.1795 3.53464
\(418\) 0 0
\(419\) 10.9915 0.536969 0.268484 0.963284i \(-0.413477\pi\)
0.268484 + 0.963284i \(0.413477\pi\)
\(420\) 0 0
\(421\) −6.00857 18.4925i −0.292840 0.901267i −0.983939 0.178507i \(-0.942873\pi\)
0.691099 0.722760i \(-0.257127\pi\)
\(422\) 0 0
\(423\) −62.1001 45.1184i −3.01941 2.19373i
\(424\) 0 0
\(425\) −0.905713 + 2.78750i −0.0439336 + 0.135214i
\(426\) 0 0
\(427\) −0.289957 + 0.210666i −0.0140320 + 0.0101948i
\(428\) 0 0
\(429\) 5.02875 9.06374i 0.242790 0.437602i
\(430\) 0 0
\(431\) −16.5773 + 12.0441i −0.798500 + 0.580144i −0.910474 0.413567i \(-0.864283\pi\)
0.111974 + 0.993711i \(0.464283\pi\)
\(432\) 0 0
\(433\) −10.0531 + 30.9402i −0.483120 + 1.48689i 0.351566 + 0.936163i \(0.385649\pi\)
−0.834686 + 0.550727i \(0.814351\pi\)
\(434\) 0 0
\(435\) 53.6166 + 38.9548i 2.57072 + 1.86774i
\(436\) 0 0
\(437\) −0.813384 2.50334i −0.0389094 0.119751i
\(438\) 0 0
\(439\) −19.6025 −0.935576 −0.467788 0.883841i \(-0.654949\pi\)
−0.467788 + 0.883841i \(0.654949\pi\)
\(440\) 0 0
\(441\) −14.4124 −0.686304
\(442\) 0 0
\(443\) −6.27456 19.3111i −0.298113 0.917499i −0.982158 0.188059i \(-0.939781\pi\)
0.684044 0.729440i \(-0.260219\pi\)
\(444\) 0 0
\(445\) 12.1338 + 8.81575i 0.575199 + 0.417907i
\(446\) 0 0
\(447\) 7.95265 24.4757i 0.376147 1.15766i
\(448\) 0 0
\(449\) −17.1975 + 12.4948i −0.811602 + 0.589664i −0.914295 0.405049i \(-0.867254\pi\)
0.102692 + 0.994713i \(0.467254\pi\)
\(450\) 0 0
\(451\) −20.0873 + 9.35729i −0.945873 + 0.440618i
\(452\) 0 0
\(453\) 30.6420 22.2627i 1.43969 1.04599i
\(454\) 0 0
\(455\) −1.65358 + 5.08918i −0.0775209 + 0.238585i
\(456\) 0 0
\(457\) 23.4808 + 17.0598i 1.09838 + 0.798023i 0.980795 0.195039i \(-0.0624835\pi\)
0.117589 + 0.993062i \(0.462483\pi\)
\(458\) 0 0
\(459\) −12.1264 37.3213i −0.566014 1.74201i
\(460\) 0 0
\(461\) −18.9485 −0.882520 −0.441260 0.897379i \(-0.645468\pi\)
−0.441260 + 0.897379i \(0.645468\pi\)
\(462\) 0 0
\(463\) 5.96519 0.277226 0.138613 0.990347i \(-0.455736\pi\)
0.138613 + 0.990347i \(0.455736\pi\)
\(464\) 0 0
\(465\) −12.5522 38.6318i −0.582095 1.79151i
\(466\) 0 0
\(467\) 19.8733 + 14.4388i 0.919626 + 0.668148i 0.943431 0.331569i \(-0.107578\pi\)
−0.0238047 + 0.999717i \(0.507578\pi\)
\(468\) 0 0
\(469\) 3.75638 11.5609i 0.173453 0.533835i
\(470\) 0 0
\(471\) 21.7797 15.8239i 1.00356 0.729127i
\(472\) 0 0
\(473\) −2.83993 23.2043i −0.130580 1.06694i
\(474\) 0 0
\(475\) 0.679676 0.493814i 0.0311857 0.0226577i
\(476\) 0 0
\(477\) 10.7887 33.2042i 0.493980 1.52031i
\(478\) 0 0
\(479\) −18.0192 13.0917i −0.823320 0.598177i 0.0943417 0.995540i \(-0.469925\pi\)
−0.917662 + 0.397363i \(0.869925\pi\)
\(480\) 0 0
\(481\) −1.67674 5.16048i −0.0764529 0.235298i
\(482\) 0 0
\(483\) −19.0020 −0.864623
\(484\) 0 0
\(485\) 0.941580 0.0427549
\(486\) 0 0
\(487\) −3.56403 10.9690i −0.161502 0.497051i 0.837260 0.546805i \(-0.184156\pi\)
−0.998761 + 0.0497542i \(0.984156\pi\)
\(488\) 0 0
\(489\) 33.7156 + 24.4958i 1.52467 + 1.10774i
\(490\) 0 0
\(491\) 3.44323 10.5972i 0.155391 0.478244i −0.842809 0.538212i \(-0.819100\pi\)
0.998200 + 0.0599680i \(0.0190999\pi\)
\(492\) 0 0
\(493\) 23.5824 17.1336i 1.06210 0.771659i
\(494\) 0 0
\(495\) 6.61125 + 54.0189i 0.297154 + 2.42797i
\(496\) 0 0
\(497\) 21.5977 15.6916i 0.968789 0.703867i
\(498\) 0 0
\(499\) −4.20731 + 12.9488i −0.188345 + 0.579666i −0.999990 0.00448468i \(-0.998572\pi\)
0.811645 + 0.584151i \(0.198572\pi\)
\(500\) 0 0
\(501\) 48.3774 + 35.1482i 2.16134 + 1.57031i
\(502\) 0 0
\(503\) 2.47585 + 7.61987i 0.110392 + 0.339753i 0.990958 0.134171i \(-0.0428371\pi\)
−0.880566 + 0.473924i \(0.842837\pi\)
\(504\) 0 0
\(505\) 40.6266 1.80786
\(506\) 0 0
\(507\) 3.12526 0.138798
\(508\) 0 0
\(509\) 0.285778 + 0.879533i 0.0126669 + 0.0389846i 0.957190 0.289460i \(-0.0934756\pi\)
−0.944523 + 0.328444i \(0.893476\pi\)
\(510\) 0 0
\(511\) 1.10178 + 0.800492i 0.0487400 + 0.0354117i
\(512\) 0 0
\(513\) −3.47591 + 10.6978i −0.153465 + 0.472318i
\(514\) 0 0
\(515\) 32.6233 23.7023i 1.43756 1.04445i
\(516\) 0 0
\(517\) 34.1015 15.8856i 1.49978 0.698646i
\(518\) 0 0
\(519\) −39.0362 + 28.3615i −1.71350 + 1.24493i
\(520\) 0 0
\(521\) −0.796725 + 2.45207i −0.0349051 + 0.107427i −0.966991 0.254810i \(-0.917987\pi\)
0.932086 + 0.362237i \(0.117987\pi\)
\(522\) 0 0
\(523\) −0.630466 0.458060i −0.0275683 0.0200296i 0.573916 0.818914i \(-0.305424\pi\)
−0.601484 + 0.798885i \(0.705424\pi\)
\(524\) 0 0
\(525\) −1.87419 5.76817i −0.0817964 0.251744i
\(526\) 0 0
\(527\) −17.8660 −0.778254
\(528\) 0 0
\(529\) −15.4094 −0.669975
\(530\) 0 0
\(531\) −26.9630 82.9836i −1.17010 3.60118i
\(532\) 0 0
\(533\) −5.40539 3.92725i −0.234134 0.170108i
\(534\) 0 0
\(535\) −12.4540 + 38.3295i −0.538434 + 1.65713i
\(536\) 0 0
\(537\) −57.3420 + 41.6614i −2.47449 + 1.79782i
\(538\) 0 0
\(539\) 3.42687 6.17654i 0.147606 0.266042i
\(540\) 0 0
\(541\) −28.3500 + 20.5975i −1.21886 + 0.885554i −0.996005 0.0892972i \(-0.971538\pi\)
−0.222856 + 0.974851i \(0.571538\pi\)
\(542\) 0 0
\(543\) −5.96787 + 18.3672i −0.256106 + 0.788213i
\(544\) 0 0
\(545\) 24.5894 + 17.8652i 1.05329 + 0.765262i
\(546\) 0 0
\(547\) 8.60928 + 26.4966i 0.368106 + 1.13291i 0.948013 + 0.318231i \(0.103089\pi\)
−0.579907 + 0.814683i \(0.696911\pi\)
\(548\) 0 0
\(549\) −1.09903 −0.0469056
\(550\) 0 0
\(551\) −8.35538 −0.355951
\(552\) 0 0
\(553\) −6.07414 18.6943i −0.258299 0.794962i
\(554\) 0 0
\(555\) 33.2654 + 24.1687i 1.41204 + 1.02591i
\(556\) 0 0
\(557\) 4.96360 15.2764i 0.210314 0.647281i −0.789139 0.614215i \(-0.789473\pi\)
0.999453 0.0330663i \(-0.0105273\pi\)
\(558\) 0 0
\(559\) 5.70241 4.14305i 0.241186 0.175232i
\(560\) 0 0
\(561\) 33.9106 + 6.60532i 1.43171 + 0.278877i
\(562\) 0 0
\(563\) 17.5731 12.7676i 0.740619 0.538091i −0.152286 0.988337i \(-0.548663\pi\)
0.892905 + 0.450245i \(0.148663\pi\)
\(564\) 0 0
\(565\) −6.01483 + 18.5117i −0.253046 + 0.778795i
\(566\) 0 0
\(567\) 29.4482 + 21.3954i 1.23671 + 0.898522i
\(568\) 0 0
\(569\) 10.2374 + 31.5074i 0.429173 + 1.32086i 0.898941 + 0.438069i \(0.144337\pi\)
−0.469768 + 0.882790i \(0.655663\pi\)
\(570\) 0 0
\(571\) −29.2494 −1.22405 −0.612026 0.790838i \(-0.709645\pi\)
−0.612026 + 0.790838i \(0.709645\pi\)
\(572\) 0 0
\(573\) −21.5584 −0.900615
\(574\) 0 0
\(575\) 0.748667 + 2.30416i 0.0312216 + 0.0960901i
\(576\) 0 0
\(577\) −17.1716 12.4759i −0.714863 0.519378i 0.169876 0.985465i \(-0.445663\pi\)
−0.884739 + 0.466087i \(0.845663\pi\)
\(578\) 0 0
\(579\) 11.7898 36.2852i 0.489967 1.50796i
\(580\) 0 0
\(581\) −3.21679 + 2.33714i −0.133455 + 0.0969608i
\(582\) 0 0
\(583\) 11.6646 + 12.5186i 0.483100 + 0.518468i
\(584\) 0 0
\(585\) −13.2750 + 9.64487i −0.548855 + 0.398766i
\(586\) 0 0
\(587\) 3.30781 10.1804i 0.136528 0.420190i −0.859297 0.511478i \(-0.829098\pi\)
0.995825 + 0.0912876i \(0.0290983\pi\)
\(588\) 0 0
\(589\) 4.14305 + 3.01010i 0.170711 + 0.124029i
\(590\) 0 0
\(591\) −6.01465 18.5112i −0.247410 0.761449i
\(592\) 0 0
\(593\) 12.8443 0.527450 0.263725 0.964598i \(-0.415049\pi\)
0.263725 + 0.964598i \(0.415049\pi\)
\(594\) 0 0
\(595\) −17.8354 −0.731178
\(596\) 0 0
\(597\) 10.9268 + 33.6292i 0.447204 + 1.37635i
\(598\) 0 0
\(599\) 29.0010 + 21.0704i 1.18495 + 0.860915i 0.992721 0.120436i \(-0.0384292\pi\)
0.192226 + 0.981351i \(0.438429\pi\)
\(600\) 0 0
\(601\) 11.5510 35.5502i 0.471174 1.45012i −0.379876 0.925038i \(-0.624033\pi\)
0.851049 0.525086i \(-0.175967\pi\)
\(602\) 0 0
\(603\) 30.1565 21.9100i 1.22807 0.892242i
\(604\) 0 0
\(605\) −24.7222 10.0109i −1.00510 0.407001i
\(606\) 0 0
\(607\) 0.599052 0.435237i 0.0243148 0.0176657i −0.575562 0.817758i \(-0.695216\pi\)
0.599876 + 0.800093i \(0.295216\pi\)
\(608\) 0 0
\(609\) −18.6396 + 57.3667i −0.755313 + 2.32462i
\(610\) 0 0
\(611\) 9.17656 + 6.66716i 0.371244 + 0.269725i
\(612\) 0 0
\(613\) 6.82410 + 21.0024i 0.275623 + 0.848279i 0.989054 + 0.147554i \(0.0471400\pi\)
−0.713431 + 0.700725i \(0.752860\pi\)
\(614\) 0 0
\(615\) 50.6315 2.04166
\(616\) 0 0
\(617\) −28.3874 −1.14283 −0.571416 0.820661i \(-0.693606\pi\)
−0.571416 + 0.820661i \(0.693606\pi\)
\(618\) 0 0
\(619\) 6.40162 + 19.7022i 0.257303 + 0.791897i 0.993367 + 0.114985i \(0.0366821\pi\)
−0.736064 + 0.676912i \(0.763318\pi\)
\(620\) 0 0
\(621\) −26.2425 19.0663i −1.05308 0.765105i
\(622\) 0 0
\(623\) −4.21827 + 12.9825i −0.169001 + 0.520133i
\(624\) 0 0
\(625\) 23.1569 16.8245i 0.926277 0.672980i
\(626\) 0 0
\(627\) −6.75087 7.24509i −0.269604 0.289341i
\(628\) 0 0
\(629\) 14.6312 10.6302i 0.583386 0.423855i
\(630\) 0 0
\(631\) 6.44876 19.8472i 0.256721 0.790106i −0.736765 0.676149i \(-0.763647\pi\)
0.993486 0.113957i \(-0.0363526\pi\)
\(632\) 0 0
\(633\) −63.3439 46.0221i −2.51769 1.82921i
\(634\) 0 0
\(635\) 6.53404 + 20.1097i 0.259296 + 0.798030i
\(636\) 0 0
\(637\) 2.12973 0.0843828
\(638\) 0 0
\(639\) 81.8626 3.23843
\(640\) 0 0
\(641\) −10.2076 31.4159i −0.403178 1.24085i −0.922407 0.386218i \(-0.873781\pi\)
0.519230 0.854635i \(-0.326219\pi\)
\(642\) 0 0
\(643\) 40.8252 + 29.6612i 1.60999 + 1.16973i 0.863537 + 0.504286i \(0.168244\pi\)
0.746452 + 0.665439i \(0.231756\pi\)
\(644\) 0 0
\(645\) −16.5057 + 50.7994i −0.649913 + 2.00023i
\(646\) 0 0
\(647\) −6.84701 + 4.97465i −0.269184 + 0.195573i −0.714186 0.699956i \(-0.753203\pi\)
0.445002 + 0.895530i \(0.353203\pi\)
\(648\) 0 0
\(649\) 41.9743 + 8.17601i 1.64764 + 0.320936i
\(650\) 0 0
\(651\) 29.9094 21.7304i 1.17224 0.851683i
\(652\) 0 0
\(653\) −2.63742 + 8.11714i −0.103210 + 0.317648i −0.989306 0.145853i \(-0.953407\pi\)
0.886096 + 0.463502i \(0.153407\pi\)
\(654\) 0 0
\(655\) −20.7850 15.1012i −0.812136 0.590052i
\(656\) 0 0
\(657\) 1.29050 + 3.97174i 0.0503470 + 0.154952i
\(658\) 0 0
\(659\) −9.20657 −0.358637 −0.179318 0.983791i \(-0.557389\pi\)
−0.179318 + 0.983791i \(0.557389\pi\)
\(660\) 0 0
\(661\) −1.95052 −0.0758666 −0.0379333 0.999280i \(-0.512077\pi\)
−0.0379333 + 0.999280i \(0.512077\pi\)
\(662\) 0 0
\(663\) 3.21891 + 9.90678i 0.125012 + 0.384747i
\(664\) 0 0
\(665\) 4.13595 + 3.00494i 0.160385 + 0.116527i
\(666\) 0 0
\(667\) 7.44578 22.9158i 0.288302 0.887302i
\(668\) 0 0
\(669\) 46.7648 33.9766i 1.80803 1.31361i
\(670\) 0 0
\(671\) 0.261320 0.470999i 0.0100881 0.0181827i
\(672\) 0 0
\(673\) −18.5975 + 13.5118i −0.716879 + 0.520843i −0.885386 0.464857i \(-0.846106\pi\)
0.168506 + 0.985701i \(0.446106\pi\)
\(674\) 0 0
\(675\) 3.19935 9.84659i 0.123143 0.378996i
\(676\) 0 0
\(677\) −26.3580 19.1502i −1.01302 0.736003i −0.0481804 0.998839i \(-0.515342\pi\)
−0.964841 + 0.262836i \(0.915342\pi\)
\(678\) 0 0
\(679\) 0.264820 + 0.815033i 0.0101629 + 0.0312781i
\(680\) 0 0
\(681\) −32.4181 −1.24226
\(682\) 0 0
\(683\) −11.2643 −0.431017 −0.215508 0.976502i \(-0.569141\pi\)
−0.215508 + 0.976502i \(0.569141\pi\)
\(684\) 0 0
\(685\) −11.1062 34.1814i −0.424347 1.30601i
\(686\) 0 0
\(687\) −15.5747 11.3157i −0.594213 0.431721i
\(688\) 0 0
\(689\) −1.59425 + 4.90660i −0.0607361 + 0.186926i
\(690\) 0 0
\(691\) 7.07433 5.13980i 0.269120 0.195527i −0.445038 0.895512i \(-0.646810\pi\)
0.714158 + 0.699985i \(0.246810\pi\)
\(692\) 0 0
\(693\) −44.8994 + 20.9156i −1.70559 + 0.794516i
\(694\) 0 0
\(695\) 45.3054 32.9163i 1.71853 1.24859i
\(696\) 0 0
\(697\) 6.88164 21.1795i 0.260661 0.802231i
\(698\) 0 0
\(699\) −49.6612 36.0810i −1.87836 1.36471i
\(700\) 0 0
\(701\) −3.97550 12.2353i −0.150153 0.462122i 0.847485 0.530820i \(-0.178116\pi\)
−0.997638 + 0.0686971i \(0.978116\pi\)
\(702\) 0 0
\(703\) −5.18394 −0.195516
\(704\) 0 0
\(705\) −85.9555 −3.23727
\(706\) 0 0
\(707\) 11.4263 + 35.1665i 0.429729 + 1.32257i
\(708\) 0 0
\(709\) 38.4486 + 27.9345i 1.44397 + 1.04910i 0.987195 + 0.159521i \(0.0509949\pi\)
0.456773 + 0.889583i \(0.349005\pi\)
\(710\) 0 0
\(711\) 18.6261 57.3251i 0.698531 2.14986i
\(712\) 0 0
\(713\) −11.9476 + 8.68047i −0.447443 + 0.325086i
\(714\) 0 0
\(715\) −0.976947 7.98239i −0.0365358 0.298525i
\(716\) 0 0
\(717\) 38.3086 27.8328i 1.43066 1.03944i
\(718\) 0 0
\(719\) 1.27223 3.91553i 0.0474462 0.146024i −0.924527 0.381117i \(-0.875539\pi\)
0.971973 + 0.235093i \(0.0755394\pi\)
\(720\) 0 0
\(721\) 29.6920 + 21.5725i 1.10579 + 0.803403i
\(722\) 0 0
\(723\) −13.4661 41.4445i −0.500810 1.54134i
\(724\) 0 0
\(725\) 7.69058 0.285621
\(726\) 0 0
\(727\) −32.9974 −1.22380 −0.611902 0.790933i \(-0.709596\pi\)
−0.611902 + 0.790933i \(0.709596\pi\)
\(728\) 0 0
\(729\) 0.380588 + 1.17133i 0.0140959 + 0.0433826i
\(730\) 0 0
\(731\) 19.0063 + 13.8089i 0.702975 + 0.510741i
\(732\) 0 0
\(733\) −10.8641 + 33.4362i −0.401274 + 1.23499i 0.522693 + 0.852521i \(0.324927\pi\)
−0.923967 + 0.382473i \(0.875073\pi\)
\(734\) 0 0
\(735\) −13.0567 + 9.48623i −0.481603 + 0.349905i
\(736\) 0 0
\(737\) 2.21930 + 18.1334i 0.0817490 + 0.667951i
\(738\) 0 0
\(739\) 7.61152 5.53009i 0.279994 0.203428i −0.438921 0.898526i \(-0.644639\pi\)
0.718915 + 0.695098i \(0.244639\pi\)
\(740\) 0 0
\(741\) 0.922666 2.83967i 0.0338950 0.104318i
\(742\) 0 0
\(743\) −38.2078 27.7596i −1.40171 1.01840i −0.994464 0.105082i \(-0.966490\pi\)
−0.407245 0.913319i \(-0.633510\pi\)
\(744\) 0 0
\(745\) −6.17008 18.9896i −0.226054 0.695724i
\(746\) 0 0
\(747\) −12.1927 −0.446109
\(748\) 0 0
\(749\) −36.6808 −1.34029
\(750\) 0 0
\(751\) −7.61945 23.4502i −0.278038 0.855712i −0.988400 0.151875i \(-0.951469\pi\)
0.710362 0.703836i \(-0.248531\pi\)
\(752\) 0 0
\(753\) −42.5116 30.8865i −1.54921 1.12557i
\(754\) 0 0
\(755\) 9.08074 27.9476i 0.330482 1.01712i
\(756\) 0 0
\(757\) −23.4016 + 17.0023i −0.850547 + 0.617959i −0.925297 0.379244i \(-0.876184\pi\)
0.0747496 + 0.997202i \(0.476184\pi\)
\(758\) 0 0
\(759\) 25.8866 12.0588i 0.939624 0.437707i
\(760\) 0 0
\(761\) 0.561785 0.408161i 0.0203647 0.0147958i −0.577556 0.816351i \(-0.695994\pi\)
0.597921 + 0.801555i \(0.295994\pi\)
\(762\) 0 0
\(763\) −8.54837 + 26.3092i −0.309472 + 0.952456i
\(764\) 0 0
\(765\) −44.2461 32.1467i −1.59972 1.16227i
\(766\) 0 0
\(767\) 3.98434 + 12.2625i 0.143866 + 0.442774i
\(768\) 0 0
\(769\) 2.04753 0.0738358 0.0369179 0.999318i \(-0.488246\pi\)
0.0369179 + 0.999318i \(0.488246\pi\)
\(770\) 0 0
\(771\) −41.0695 −1.47908
\(772\) 0 0
\(773\) 10.6341 + 32.7283i 0.382481 + 1.17716i 0.938291 + 0.345847i \(0.112408\pi\)
−0.555810 + 0.831310i \(0.687592\pi\)
\(774\) 0 0
\(775\) −3.81341 2.77060i −0.136982 0.0995230i
\(776\) 0 0
\(777\) −11.5646 + 35.5921i −0.414876 + 1.27686i
\(778\) 0 0
\(779\) −5.16420 + 3.75201i −0.185027 + 0.134430i
\(780\) 0 0
\(781\) −19.4647 + 35.0828i −0.696500 + 1.25536i
\(782\) 0 0
\(783\) −83.3027 + 60.5230i −2.97700 + 2.16291i
\(784\) 0 0
\(785\) 6.45441 19.8646i 0.230368 0.708999i
\(786\) 0 0
\(787\) −10.0833 7.32594i −0.359430 0.261141i 0.393384 0.919374i \(-0.371304\pi\)
−0.752814 + 0.658233i \(0.771304\pi\)
\(788\) 0 0
\(789\) −4.04544 12.4506i −0.144022 0.443253i
\(790\) 0 0
\(791\) −17.7155 −0.629889
\(792\) 0 0
\(793\) 0.162405 0.00576716
\(794\) 0 0
\(795\) −12.0811 37.1819i −0.428474 1.31871i
\(796\) 0 0
\(797\) −18.8870 13.7222i −0.669013 0.486066i 0.200682 0.979656i \(-0.435684\pi\)
−0.869695 + 0.493590i \(0.835684\pi\)
\(798\) 0 0
\(799\) −11.6827 + 35.9558i −0.413305 + 1.27202i
\(800\) 0 0
\(801\) −33.8646 + 24.6040i −1.19655 + 0.869341i
\(802\) 0 0
\(803\) −2.00896 0.391318i −0.0708947 0.0138093i
\(804\) 0 0
\(805\) −11.9272 + 8.66559i −0.420377 + 0.305422i
\(806\) 0 0
\(807\) −15.8963 + 48.9238i −0.559577 + 1.72220i
\(808\) 0 0
\(809\) 25.1435 + 18.2678i 0.883998 + 0.642262i 0.934306 0.356472i \(-0.116020\pi\)
−0.0503083 + 0.998734i \(0.516020\pi\)
\(810\) 0 0
\(811\) 6.61212 + 20.3500i 0.232183 + 0.714586i 0.997483 + 0.0709117i \(0.0225908\pi\)
−0.765300 + 0.643674i \(0.777409\pi\)
\(812\) 0 0
\(813\) 63.0831 2.21242
\(814\) 0 0
\(815\) 32.3334 1.13259
\(816\) 0 0
\(817\) −2.08094 6.40447i −0.0728028 0.224064i
\(818\) 0 0
\(819\) −12.0822 8.77825i −0.422187 0.306737i
\(820\) 0 0
\(821\) 11.2585 34.6501i 0.392925 1.20930i −0.537641 0.843174i \(-0.680684\pi\)
0.930566 0.366124i \(-0.119316\pi\)
\(822\) 0 0
\(823\) 19.5713 14.2194i 0.682212 0.495656i −0.191879 0.981419i \(-0.561458\pi\)
0.874091 + 0.485763i \(0.161458\pi\)
\(824\) 0 0
\(825\) 6.21373 + 6.66863i 0.216334 + 0.232172i
\(826\) 0 0
\(827\) −15.7822 + 11.4665i −0.548802 + 0.398728i −0.827343 0.561696i \(-0.810149\pi\)
0.278542 + 0.960424i \(0.410149\pi\)
\(828\) 0 0
\(829\) −7.35646 + 22.6408i −0.255500 + 0.786349i 0.738230 + 0.674549i \(0.235662\pi\)
−0.993731 + 0.111800i \(0.964338\pi\)
\(830\) 0 0
\(831\) 49.0499 + 35.6368i 1.70152 + 1.23623i
\(832\) 0 0
\(833\) 2.19354 + 6.75103i 0.0760017 + 0.233909i
\(834\) 0 0
\(835\) 46.3942 1.60554
\(836\) 0 0
\(837\) 63.1100 2.18140
\(838\) 0 0
\(839\) 3.11310 + 9.58112i 0.107476 + 0.330777i 0.990304 0.138920i \(-0.0443631\pi\)
−0.882828 + 0.469697i \(0.844363\pi\)
\(840\) 0 0
\(841\) −38.4169 27.9115i −1.32472 0.962465i
\(842\) 0 0
\(843\) −11.1015 + 34.1669i −0.382356 + 1.17677i
\(844\) 0 0
\(845\) 1.96166 1.42523i 0.0674830 0.0490293i
\(846\) 0 0
\(847\) 1.71231 24.2151i 0.0588357 0.832041i
\(848\) 0 0
\(849\) 46.1841 33.5547i 1.58504 1.15160i
\(850\) 0 0
\(851\) 4.61959 14.2176i 0.158358 0.487375i
\(852\) 0 0
\(853\) 41.6624 + 30.2695i 1.42649 + 1.03641i 0.990656 + 0.136384i \(0.0435480\pi\)
0.435838 + 0.900025i \(0.356452\pi\)
\(854\) 0 0
\(855\) 4.84435 + 14.9094i 0.165673 + 0.509890i
\(856\) 0 0
\(857\) −8.19131 −0.279810 −0.139905 0.990165i \(-0.544680\pi\)
−0.139905 + 0.990165i \(0.544680\pi\)
\(858\) 0 0
\(859\) 16.9106 0.576981 0.288491 0.957483i \(-0.406847\pi\)
0.288491 + 0.957483i \(0.406847\pi\)
\(860\) 0 0
\(861\) 14.2402 + 43.8267i 0.485304 + 1.49361i
\(862\) 0 0
\(863\) 15.1759 + 11.0259i 0.516593 + 0.375327i 0.815319 0.579012i \(-0.196562\pi\)
−0.298726 + 0.954339i \(0.596562\pi\)
\(864\) 0 0
\(865\) −11.5684 + 35.6037i −0.393336 + 1.21056i
\(866\) 0 0
\(867\) 14.8944 10.8214i 0.505842 0.367515i
\(868\) 0 0
\(869\) 20.1383 + 21.6127i 0.683146 + 0.733159i
\(870\) 0 0
\(871\) −4.45623 + 3.23764i −0.150994 + 0.109703i
\(872\) 0 0
\(873\) −0.812057 + 2.49926i −0.0274840 + 0.0845870i
\(874\) 0 0
\(875\) 17.8387 + 12.9606i 0.603059 + 0.438148i
\(876\) 0 0
\(877\) 14.1163 + 43.4456i 0.476674 + 1.46705i 0.843686 + 0.536837i \(0.180381\pi\)
−0.367012 + 0.930216i \(0.619619\pi\)
\(878\) 0 0
\(879\) 34.9735 1.17963
\(880\) 0 0
\(881\) 31.8104 1.07172 0.535859 0.844307i \(-0.319988\pi\)
0.535859 + 0.844307i \(0.319988\pi\)
\(882\) 0 0
\(883\) −3.65717 11.2556i −0.123073 0.378781i 0.870472 0.492218i \(-0.163814\pi\)
−0.993545 + 0.113437i \(0.963814\pi\)
\(884\) 0 0
\(885\) −79.0465 57.4307i −2.65712 1.93051i
\(886\) 0 0
\(887\) 2.85106 8.77466i 0.0957292 0.294624i −0.891714 0.452600i \(-0.850497\pi\)
0.987443 + 0.157975i \(0.0504967\pi\)
\(888\) 0 0
\(889\) −15.5693 + 11.3118i −0.522177 + 0.379384i
\(890\) 0 0
\(891\) −53.6951 10.4591i −1.79885 0.350391i
\(892\) 0 0
\(893\) 8.76710 6.36967i 0.293380 0.213153i
\(894\) 0 0
\(895\) −16.9933 + 52.2999i −0.568022 + 1.74819i
\(896\) 0 0
\(897\) 6.96596 + 5.06107i 0.232587 + 0.168984i
\(898\) 0 0
\(899\) 14.4864 + 44.5845i 0.483148 + 1.48698i
\(900\) 0 0
\(901\) −17.1955 −0.572864
\(902\) 0 0
\(903\) −48.6143 −1.61778
\(904\) 0 0
\(905\) 4.63019 + 14.2502i 0.153913 + 0.473694i
\(906\) 0 0
\(907\) 25.4122 + 18.4630i 0.843798 + 0.613055i 0.923429 0.383769i \(-0.125374\pi\)
−0.0796308 + 0.996824i \(0.525374\pi\)
\(908\) 0 0
\(909\) −35.0381 + 107.836i −1.16214 + 3.57670i
\(910\) 0 0
\(911\) 17.0572 12.3928i 0.565132 0.410592i −0.268202 0.963363i \(-0.586429\pi\)
0.833334 + 0.552770i \(0.186429\pi\)
\(912\) 0 0
\(913\) 2.89910 5.22529i 0.0959461 0.172932i
\(914\) 0 0
\(915\) −0.995652 + 0.723384i −0.0329152 + 0.0239143i
\(916\) 0 0
\(917\) 7.22580 22.2387i 0.238617 0.734387i
\(918\) 0 0
\(919\) −6.97985 5.07116i −0.230244 0.167282i 0.466682 0.884425i \(-0.345449\pi\)
−0.696926 + 0.717143i \(0.745449\pi\)
\(920\) 0 0
\(921\) −30.7007 94.4869i −1.01162 3.11345i
\(922\) 0 0
\(923\) −12.0969 −0.398173
\(924\) 0 0
\(925\) 4.77147 0.156885
\(926\) 0 0
\(927\) 34.7777 + 107.035i 1.14225 + 3.51548i
\(928\) 0 0
\(929\) −36.9618 26.8543i −1.21268 0.881062i −0.217207 0.976126i \(-0.569695\pi\)
−0.995471 + 0.0950634i \(0.969695\pi\)
\(930\) 0 0
\(931\) 0.628755 1.93511i 0.0206066 0.0634207i
\(932\) 0 0
\(933\) −18.6864 + 13.5764i −0.611764 + 0.444473i
\(934\) 0 0
\(935\) 24.2972 11.3184i 0.794603 0.370152i
\(936\) 0 0
\(937\) 25.0413 18.1936i 0.818064 0.594358i −0.0980935 0.995177i \(-0.531274\pi\)
0.916157 + 0.400819i \(0.131274\pi\)
\(938\) 0 0
\(939\) −15.8446 + 48.7647i −0.517069 + 1.59138i
\(940\) 0 0
\(941\) −14.7496 10.7162i −0.480824 0.349339i 0.320821 0.947140i \(-0.396041\pi\)
−0.801645 + 0.597801i \(0.796041\pi\)
\(942\) 0 0
\(943\) −5.68839 17.5071i −0.185240 0.570109i
\(944\) 0 0
\(945\) 63.0018 2.04945
\(946\) 0 0
\(947\) 38.3499 1.24620 0.623102 0.782141i \(-0.285872\pi\)
0.623102 + 0.782141i \(0.285872\pi\)
\(948\) 0 0
\(949\) −0.190697 0.586905i −0.00619029 0.0190518i
\(950\) 0 0
\(951\) 0.992476 + 0.721076i 0.0321832 + 0.0233825i
\(952\) 0 0
\(953\) −8.23863 + 25.3559i −0.266876 + 0.821359i 0.724380 + 0.689401i \(0.242126\pi\)
−0.991255 + 0.131957i \(0.957874\pi\)
\(954\) 0 0
\(955\) −13.5317 + 9.83137i −0.437876 + 0.318136i
\(956\) 0 0
\(957\) −11.0124 89.9797i −0.355981 2.90863i
\(958\) 0 0
\(959\) 26.4639 19.2271i 0.854562 0.620876i
\(960\) 0 0
\(961\) −0.700685 + 2.15649i −0.0226028 + 0.0695641i
\(962\) 0 0
\(963\) −90.9980 66.1139i −2.93237 2.13049i
\(964\) 0 0
\(965\) −9.14713 28.1520i −0.294457 0.906244i
\(966\) 0 0
\(967\) −12.1213 −0.389796 −0.194898 0.980824i \(-0.562438\pi\)
−0.194898 + 0.980824i \(0.562438\pi\)
\(968\) 0 0
\(969\) 9.95180 0.319698
\(970\) 0 0
\(971\) 9.79043 + 30.1318i 0.314190 + 0.966977i 0.976087 + 0.217382i \(0.0697517\pi\)
−0.661897 + 0.749595i \(0.730248\pi\)
\(972\) 0 0
\(973\) 41.2346 + 29.9587i 1.32192 + 0.960432i
\(974\) 0 0
\(975\) −0.849253 + 2.61373i −0.0271979 + 0.0837064i
\(976\) 0 0
\(977\) −44.4034 + 32.2609i −1.42059 + 1.03212i −0.428916 + 0.903344i \(0.641104\pi\)
−0.991674 + 0.128775i \(0.958896\pi\)
\(978\) 0 0
\(979\) −2.49219 20.3631i −0.0796508 0.650807i
\(980\) 0 0
\(981\) −68.6269 + 49.8604i −2.19109 + 1.59192i
\(982\) 0 0
\(983\) −0.857177 + 2.63812i −0.0273397 + 0.0841430i −0.963795 0.266643i \(-0.914086\pi\)
0.936456 + 0.350786i \(0.114086\pi\)
\(984\) 0 0
\(985\) −12.2170 8.87618i −0.389266 0.282819i
\(986\) 0 0
\(987\) −24.1751 74.4032i −0.769501 2.36828i
\(988\) 0 0
\(989\) 19.4195 0.617505
\(990\) 0 0
\(991\) 14.7848 0.469655 0.234828 0.972037i \(-0.424547\pi\)
0.234828 + 0.972037i \(0.424547\pi\)
\(992\) 0 0
\(993\) 18.9400 + 58.2913i 0.601043 + 1.84982i
\(994\) 0 0
\(995\) 22.1946 + 16.1253i 0.703616 + 0.511207i
\(996\) 0 0
\(997\) 12.4241 38.2374i 0.393474 1.21099i −0.536669 0.843793i \(-0.680318\pi\)
0.930143 0.367196i \(-0.119682\pi\)
\(998\) 0 0
\(999\) −51.6836 + 37.5503i −1.63520 + 1.18804i
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 572.2.n.b.157.7 28
11.2 odd 10 6292.2.a.y.1.14 14
11.4 even 5 inner 572.2.n.b.521.7 yes 28
11.9 even 5 6292.2.a.z.1.14 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
572.2.n.b.157.7 28 1.1 even 1 trivial
572.2.n.b.521.7 yes 28 11.4 even 5 inner
6292.2.a.y.1.14 14 11.2 odd 10
6292.2.a.z.1.14 14 11.9 even 5