Properties

Label 315.2.bz.d.73.5
Level $315$
Weight $2$
Character 315.73
Analytic conductor $2.515$
Analytic rank $0$
Dimension $32$
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(73,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.73");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bz (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 73.5
Character \(\chi\) \(=\) 315.73
Dual form 315.2.bz.d.82.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.394487 + 0.105703i) q^{2} +(-1.58760 - 0.916603i) q^{4} +(2.18897 + 0.456535i) q^{5} +(-0.605712 - 2.57548i) q^{7} +(-1.10697 - 1.10697i) q^{8} +O(q^{10})\) \(q+(0.394487 + 0.105703i) q^{2} +(-1.58760 - 0.916603i) q^{4} +(2.18897 + 0.456535i) q^{5} +(-0.605712 - 2.57548i) q^{7} +(-1.10697 - 1.10697i) q^{8} +(0.815263 + 0.411477i) q^{10} +(0.463738 - 0.803218i) q^{11} +(4.08169 - 4.08169i) q^{13} +(0.0332893 - 1.08002i) q^{14} +(1.51353 + 2.62151i) q^{16} +(0.719705 - 0.192844i) q^{17} +(-1.21966 - 2.11252i) q^{19} +(-3.05675 - 2.73121i) q^{20} +(0.267841 - 0.267841i) q^{22} +(-1.34176 + 5.00751i) q^{23} +(4.58315 + 1.99868i) q^{25} +(2.04162 - 1.17873i) q^{26} +(-1.39907 + 4.64404i) q^{28} -8.08080i q^{29} +(-1.05279 - 0.607827i) q^{31} +(1.13033 + 4.21844i) q^{32} +0.304299 q^{34} +(-0.150086 - 5.91418i) q^{35} +(1.76271 + 0.472316i) q^{37} +(-0.257843 - 0.962282i) q^{38} +(-1.91775 - 2.92850i) q^{40} +6.97323i q^{41} +(-0.781574 - 0.781574i) q^{43} +(-1.47246 + 0.850128i) q^{44} +(-1.05861 + 1.83357i) q^{46} +(-2.70351 + 10.0896i) q^{47} +(-6.26622 + 3.12000i) q^{49} +(1.59673 + 1.27291i) q^{50} +(-10.2214 + 2.73882i) q^{52} +(6.42117 - 1.72055i) q^{53} +(1.38180 - 1.54650i) q^{55} +(-2.18048 + 3.52149i) q^{56} +(0.854162 - 3.18778i) q^{58} +(-5.91173 + 10.2394i) q^{59} +(-3.72841 + 2.15260i) q^{61} +(-0.351062 - 0.351062i) q^{62} -4.27052i q^{64} +(10.7981 - 7.07126i) q^{65} +(2.80929 + 10.4844i) q^{67} +(-1.31937 - 0.353523i) q^{68} +(0.565937 - 2.34893i) q^{70} -9.89994 q^{71} +(1.07879 + 4.02609i) q^{73} +(0.645441 + 0.372646i) q^{74} +4.47178i q^{76} +(-2.34957 - 0.707830i) q^{77} +(7.02976 - 4.05863i) q^{79} +(2.11626 + 6.42938i) q^{80} +(-0.737088 + 2.75085i) q^{82} +(5.91429 - 5.91429i) q^{83} +(1.66345 - 0.0935594i) q^{85} +(-0.225707 - 0.390935i) q^{86} +(-1.40248 + 0.375795i) q^{88} +(-7.78809 - 13.4894i) q^{89} +(-12.9847 - 8.04000i) q^{91} +(6.72008 - 6.72008i) q^{92} +(-2.13300 + 3.69446i) q^{94} +(-1.70536 - 5.18105i) q^{95} +(4.89426 + 4.89426i) q^{97} +(-2.80174 + 0.568446i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 12 q^{5} + 8 q^{7} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 12 q^{5} + 8 q^{7} + 24 q^{8} - 12 q^{10} + 8 q^{11} - 8 q^{22} + 8 q^{23} + 12 q^{25} - 24 q^{26} - 24 q^{28} + 24 q^{31} - 24 q^{32} - 44 q^{35} + 4 q^{37} - 12 q^{38} + 12 q^{40} + 40 q^{43} - 40 q^{46} + 60 q^{47} - 72 q^{50} - 108 q^{52} + 24 q^{53} + 48 q^{56} + 4 q^{58} - 24 q^{61} + 4 q^{65} + 8 q^{67} - 132 q^{68} + 4 q^{70} + 16 q^{71} + 36 q^{73} - 60 q^{77} + 12 q^{80} + 12 q^{82} - 72 q^{85} + 16 q^{86} - 32 q^{88} - 24 q^{91} + 56 q^{92} + 12 q^{95} + 72 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.394487 + 0.105703i 0.278945 + 0.0747430i 0.395579 0.918432i \(-0.370544\pi\)
−0.116634 + 0.993175i \(0.537211\pi\)
\(3\) 0 0
\(4\) −1.58760 0.916603i −0.793802 0.458302i
\(5\) 2.18897 + 0.456535i 0.978936 + 0.204169i
\(6\) 0 0
\(7\) −0.605712 2.57548i −0.228938 0.973441i
\(8\) −1.10697 1.10697i −0.391374 0.391374i
\(9\) 0 0
\(10\) 0.815263 + 0.411477i 0.257809 + 0.130120i
\(11\) 0.463738 0.803218i 0.139822 0.242179i −0.787607 0.616178i \(-0.788680\pi\)
0.927429 + 0.373999i \(0.122014\pi\)
\(12\) 0 0
\(13\) 4.08169 4.08169i 1.13206 1.13206i 0.142224 0.989835i \(-0.454575\pi\)
0.989835 0.142224i \(-0.0454252\pi\)
\(14\) 0.0332893 1.08002i 0.00889694 0.288648i
\(15\) 0 0
\(16\) 1.51353 + 2.62151i 0.378382 + 0.655378i
\(17\) 0.719705 0.192844i 0.174554 0.0467716i −0.170483 0.985361i \(-0.554533\pi\)
0.345037 + 0.938589i \(0.387866\pi\)
\(18\) 0 0
\(19\) −1.21966 2.11252i −0.279810 0.484644i 0.691528 0.722350i \(-0.256938\pi\)
−0.971337 + 0.237706i \(0.923605\pi\)
\(20\) −3.05675 2.73121i −0.683510 0.610717i
\(21\) 0 0
\(22\) 0.267841 0.267841i 0.0571039 0.0571039i
\(23\) −1.34176 + 5.00751i −0.279776 + 1.04414i 0.672797 + 0.739827i \(0.265093\pi\)
−0.952573 + 0.304311i \(0.901574\pi\)
\(24\) 0 0
\(25\) 4.58315 + 1.99868i 0.916630 + 0.399736i
\(26\) 2.04162 1.17873i 0.400395 0.231168i
\(27\) 0 0
\(28\) −1.39907 + 4.64404i −0.264398 + 0.877642i
\(29\) 8.08080i 1.50057i −0.661116 0.750284i \(-0.729917\pi\)
0.661116 0.750284i \(-0.270083\pi\)
\(30\) 0 0
\(31\) −1.05279 0.607827i −0.189086 0.109169i 0.402469 0.915434i \(-0.368152\pi\)
−0.591555 + 0.806265i \(0.701486\pi\)
\(32\) 1.13033 + 4.21844i 0.199816 + 0.745722i
\(33\) 0 0
\(34\) 0.304299 0.0521868
\(35\) −0.150086 5.91418i −0.0253692 0.999678i
\(36\) 0 0
\(37\) 1.76271 + 0.472316i 0.289787 + 0.0776483i 0.400784 0.916172i \(-0.368738\pi\)
−0.110997 + 0.993821i \(0.535404\pi\)
\(38\) −0.257843 0.962282i −0.0418276 0.156103i
\(39\) 0 0
\(40\) −1.91775 2.92850i −0.303224 0.463036i
\(41\) 6.97323i 1.08903i 0.838749 + 0.544517i \(0.183287\pi\)
−0.838749 + 0.544517i \(0.816713\pi\)
\(42\) 0 0
\(43\) −0.781574 0.781574i −0.119189 0.119189i 0.644997 0.764185i \(-0.276859\pi\)
−0.764185 + 0.644997i \(0.776859\pi\)
\(44\) −1.47246 + 0.850128i −0.221982 + 0.128162i
\(45\) 0 0
\(46\) −1.05861 + 1.83357i −0.156084 + 0.270345i
\(47\) −2.70351 + 10.0896i −0.394347 + 1.47172i 0.428542 + 0.903522i \(0.359027\pi\)
−0.822889 + 0.568202i \(0.807639\pi\)
\(48\) 0 0
\(49\) −6.26622 + 3.12000i −0.895175 + 0.445715i
\(50\) 1.59673 + 1.27291i 0.225812 + 0.180016i
\(51\) 0 0
\(52\) −10.2214 + 2.73882i −1.41745 + 0.379806i
\(53\) 6.42117 1.72055i 0.882016 0.236335i 0.210739 0.977542i \(-0.432413\pi\)
0.671277 + 0.741207i \(0.265746\pi\)
\(54\) 0 0
\(55\) 1.38180 1.54650i 0.186322 0.208531i
\(56\) −2.18048 + 3.52149i −0.291379 + 0.470580i
\(57\) 0 0
\(58\) 0.854162 3.18778i 0.112157 0.418575i
\(59\) −5.91173 + 10.2394i −0.769642 + 1.33306i 0.168115 + 0.985767i \(0.446232\pi\)
−0.937757 + 0.347292i \(0.887101\pi\)
\(60\) 0 0
\(61\) −3.72841 + 2.15260i −0.477374 + 0.275612i −0.719322 0.694677i \(-0.755547\pi\)
0.241947 + 0.970289i \(0.422214\pi\)
\(62\) −0.351062 0.351062i −0.0445849 0.0445849i
\(63\) 0 0
\(64\) 4.27052i 0.533815i
\(65\) 10.7981 7.07126i 1.33934 0.877081i
\(66\) 0 0
\(67\) 2.80929 + 10.4844i 0.343210 + 1.28088i 0.894690 + 0.446688i \(0.147397\pi\)
−0.551480 + 0.834188i \(0.685937\pi\)
\(68\) −1.31937 0.353523i −0.159997 0.0428710i
\(69\) 0 0
\(70\) 0.565937 2.34893i 0.0676424 0.280751i
\(71\) −9.89994 −1.17491 −0.587454 0.809258i \(-0.699870\pi\)
−0.587454 + 0.809258i \(0.699870\pi\)
\(72\) 0 0
\(73\) 1.07879 + 4.02609i 0.126262 + 0.471218i 0.999882 0.0153927i \(-0.00489983\pi\)
−0.873619 + 0.486610i \(0.838233\pi\)
\(74\) 0.645441 + 0.372646i 0.0750310 + 0.0433192i
\(75\) 0 0
\(76\) 4.47178i 0.512949i
\(77\) −2.34957 0.707830i −0.267758 0.0806648i
\(78\) 0 0
\(79\) 7.02976 4.05863i 0.790910 0.456632i −0.0493729 0.998780i \(-0.515722\pi\)
0.840283 + 0.542148i \(0.182389\pi\)
\(80\) 2.11626 + 6.42938i 0.236605 + 0.718826i
\(81\) 0 0
\(82\) −0.737088 + 2.75085i −0.0813978 + 0.303781i
\(83\) 5.91429 5.91429i 0.649177 0.649177i −0.303617 0.952794i \(-0.598194\pi\)
0.952794 + 0.303617i \(0.0981943\pi\)
\(84\) 0 0
\(85\) 1.66345 0.0935594i 0.180427 0.0101479i
\(86\) −0.225707 0.390935i −0.0243386 0.0421557i
\(87\) 0 0
\(88\) −1.40248 + 0.375795i −0.149505 + 0.0400598i
\(89\) −7.78809 13.4894i −0.825536 1.42987i −0.901509 0.432761i \(-0.857540\pi\)
0.0759727 0.997110i \(-0.475794\pi\)
\(90\) 0 0
\(91\) −12.9847 8.04000i −1.36116 0.842821i
\(92\) 6.72008 6.72008i 0.700617 0.700617i
\(93\) 0 0
\(94\) −2.13300 + 3.69446i −0.220002 + 0.381055i
\(95\) −1.70536 5.18105i −0.174966 0.531564i
\(96\) 0 0
\(97\) 4.89426 + 4.89426i 0.496936 + 0.496936i 0.910483 0.413547i \(-0.135710\pi\)
−0.413547 + 0.910483i \(0.635710\pi\)
\(98\) −2.80174 + 0.568446i −0.283018 + 0.0574217i
\(99\) 0 0
\(100\) −5.44423 7.37404i −0.544423 0.737404i
\(101\) −7.19322 4.15301i −0.715753 0.413240i 0.0974348 0.995242i \(-0.468936\pi\)
−0.813187 + 0.582002i \(0.802270\pi\)
\(102\) 0 0
\(103\) 2.53653 + 0.679662i 0.249932 + 0.0669691i 0.381610 0.924323i \(-0.375370\pi\)
−0.131678 + 0.991293i \(0.542036\pi\)
\(104\) −9.03664 −0.886116
\(105\) 0 0
\(106\) 2.71494 0.263698
\(107\) 0.851889 + 0.228263i 0.0823553 + 0.0220670i 0.299761 0.954014i \(-0.403093\pi\)
−0.217406 + 0.976081i \(0.569760\pi\)
\(108\) 0 0
\(109\) 10.7021 + 6.17883i 1.02507 + 0.591825i 0.915569 0.402162i \(-0.131741\pi\)
0.109502 + 0.993987i \(0.465074\pi\)
\(110\) 0.708574 0.464016i 0.0675599 0.0442422i
\(111\) 0 0
\(112\) 5.83489 5.48595i 0.551345 0.518374i
\(113\) 13.7439 + 13.7439i 1.29291 + 1.29291i 0.932976 + 0.359938i \(0.117202\pi\)
0.359938 + 0.932976i \(0.382798\pi\)
\(114\) 0 0
\(115\) −5.22317 + 10.3487i −0.487063 + 0.965022i
\(116\) −7.40689 + 12.8291i −0.687713 + 1.19115i
\(117\) 0 0
\(118\) −3.41444 + 3.41444i −0.314324 + 0.314324i
\(119\) −0.932601 1.73678i −0.0854914 0.159210i
\(120\) 0 0
\(121\) 5.06989 + 8.78131i 0.460899 + 0.798301i
\(122\) −1.69835 + 0.455071i −0.153761 + 0.0412002i
\(123\) 0 0
\(124\) 1.11427 + 1.92998i 0.100065 + 0.173317i
\(125\) 9.11990 + 6.46741i 0.815709 + 0.578463i
\(126\) 0 0
\(127\) 9.30227 9.30227i 0.825443 0.825443i −0.161440 0.986883i \(-0.551614\pi\)
0.986883 + 0.161440i \(0.0516138\pi\)
\(128\) 2.71206 10.1215i 0.239715 0.894627i
\(129\) 0 0
\(130\) 5.00718 1.64813i 0.439158 0.144551i
\(131\) 8.95081 5.16775i 0.782036 0.451509i −0.0551154 0.998480i \(-0.517553\pi\)
0.837151 + 0.546971i \(0.184219\pi\)
\(132\) 0 0
\(133\) −4.70198 + 4.42079i −0.407714 + 0.383332i
\(134\) 4.43292i 0.382946i
\(135\) 0 0
\(136\) −1.01017 0.583220i −0.0866211 0.0500107i
\(137\) −0.228594 0.853123i −0.0195301 0.0728872i 0.955473 0.295078i \(-0.0953458\pi\)
−0.975003 + 0.222191i \(0.928679\pi\)
\(138\) 0 0
\(139\) −18.6742 −1.58392 −0.791961 0.610572i \(-0.790940\pi\)
−0.791961 + 0.610572i \(0.790940\pi\)
\(140\) −5.18268 + 9.52694i −0.438016 + 0.805173i
\(141\) 0 0
\(142\) −3.90540 1.04645i −0.327734 0.0878161i
\(143\) −1.38565 5.17133i −0.115874 0.432448i
\(144\) 0 0
\(145\) 3.68917 17.6886i 0.306369 1.46896i
\(146\) 1.70227i 0.140881i
\(147\) 0 0
\(148\) −2.36555 2.36555i −0.194447 0.194447i
\(149\) −4.96877 + 2.86872i −0.407057 + 0.235015i −0.689524 0.724262i \(-0.742180\pi\)
0.282467 + 0.959277i \(0.408847\pi\)
\(150\) 0 0
\(151\) 9.44257 16.3550i 0.768425 1.33095i −0.169991 0.985446i \(-0.554374\pi\)
0.938417 0.345506i \(-0.112293\pi\)
\(152\) −0.988365 + 3.68863i −0.0801670 + 0.299187i
\(153\) 0 0
\(154\) −0.852055 0.527585i −0.0686605 0.0425140i
\(155\) −2.02702 1.81115i −0.162814 0.145475i
\(156\) 0 0
\(157\) 4.31024 1.15493i 0.343995 0.0921731i −0.0826855 0.996576i \(-0.526350\pi\)
0.426680 + 0.904403i \(0.359683\pi\)
\(158\) 3.20216 0.858016i 0.254750 0.0682601i
\(159\) 0 0
\(160\) 0.548385 + 9.75006i 0.0433536 + 0.770810i
\(161\) 13.7095 + 0.422564i 1.08046 + 0.0333027i
\(162\) 0 0
\(163\) 0.843763 3.14897i 0.0660886 0.246646i −0.924977 0.380024i \(-0.875916\pi\)
0.991065 + 0.133378i \(0.0425824\pi\)
\(164\) 6.39168 11.0707i 0.499107 0.864478i
\(165\) 0 0
\(166\) 2.95827 1.70796i 0.229606 0.132563i
\(167\) 2.23479 + 2.23479i 0.172933 + 0.172933i 0.788267 0.615334i \(-0.210979\pi\)
−0.615334 + 0.788267i \(0.710979\pi\)
\(168\) 0 0
\(169\) 20.3205i 1.56311i
\(170\) 0.666100 + 0.138923i 0.0510875 + 0.0106549i
\(171\) 0 0
\(172\) 0.524436 + 1.95722i 0.0399879 + 0.149237i
\(173\) −15.4919 4.15104i −1.17783 0.315598i −0.383763 0.923432i \(-0.625372\pi\)
−0.794064 + 0.607834i \(0.792039\pi\)
\(174\) 0 0
\(175\) 2.37149 13.0145i 0.179268 0.983800i
\(176\) 2.80753 0.211625
\(177\) 0 0
\(178\) −1.64644 6.14461i −0.123406 0.460558i
\(179\) 7.94393 + 4.58643i 0.593758 + 0.342806i 0.766582 0.642147i \(-0.221956\pi\)
−0.172824 + 0.984953i \(0.555289\pi\)
\(180\) 0 0
\(181\) 5.57424i 0.414330i −0.978306 0.207165i \(-0.933576\pi\)
0.978306 0.207165i \(-0.0664237\pi\)
\(182\) −4.27244 4.54419i −0.316694 0.336838i
\(183\) 0 0
\(184\) 7.02846 4.05788i 0.518145 0.299151i
\(185\) 3.64288 + 1.83862i 0.267830 + 0.135178i
\(186\) 0 0
\(187\) 0.178859 0.667509i 0.0130794 0.0488131i
\(188\) 13.5403 13.5403i 0.987527 0.987527i
\(189\) 0 0
\(190\) −0.125094 2.22412i −0.00907526 0.161355i
\(191\) 0.290017 + 0.502325i 0.0209849 + 0.0363469i 0.876327 0.481716i \(-0.159986\pi\)
−0.855342 + 0.518063i \(0.826653\pi\)
\(192\) 0 0
\(193\) −5.84505 + 1.56618i −0.420736 + 0.112736i −0.462974 0.886372i \(-0.653218\pi\)
0.0422384 + 0.999108i \(0.486551\pi\)
\(194\) 1.41339 + 2.44806i 0.101475 + 0.175760i
\(195\) 0 0
\(196\) 12.8081 + 0.790313i 0.914863 + 0.0564509i
\(197\) 6.05651 6.05651i 0.431508 0.431508i −0.457633 0.889141i \(-0.651303\pi\)
0.889141 + 0.457633i \(0.151303\pi\)
\(198\) 0 0
\(199\) −5.61335 + 9.72261i −0.397920 + 0.689218i −0.993469 0.114101i \(-0.963601\pi\)
0.595549 + 0.803319i \(0.296935\pi\)
\(200\) −2.86094 7.28590i −0.202299 0.515191i
\(201\) 0 0
\(202\) −2.39865 2.39865i −0.168769 0.168769i
\(203\) −20.8120 + 4.89464i −1.46071 + 0.343537i
\(204\) 0 0
\(205\) −3.18352 + 15.2642i −0.222347 + 1.06610i
\(206\) 0.928789 + 0.536237i 0.0647118 + 0.0373614i
\(207\) 0 0
\(208\) 16.8780 + 4.52244i 1.17028 + 0.313575i
\(209\) −2.26241 −0.156494
\(210\) 0 0
\(211\) −4.46617 −0.307464 −0.153732 0.988113i \(-0.549129\pi\)
−0.153732 + 0.988113i \(0.549129\pi\)
\(212\) −11.7713 3.15412i −0.808459 0.216626i
\(213\) 0 0
\(214\) 0.311932 + 0.180094i 0.0213232 + 0.0123110i
\(215\) −1.35402 2.06765i −0.0923436 0.141013i
\(216\) 0 0
\(217\) −0.927761 + 3.07960i −0.0629805 + 0.209057i
\(218\) 3.56871 + 3.56871i 0.241703 + 0.241703i
\(219\) 0 0
\(220\) −3.61129 + 1.18867i −0.243473 + 0.0801401i
\(221\) 2.15048 3.72475i 0.144657 0.250554i
\(222\) 0 0
\(223\) 3.05982 3.05982i 0.204900 0.204900i −0.597195 0.802096i \(-0.703718\pi\)
0.802096 + 0.597195i \(0.203718\pi\)
\(224\) 10.1799 5.46630i 0.680171 0.365233i
\(225\) 0 0
\(226\) 3.96902 + 6.87455i 0.264015 + 0.457288i
\(227\) −1.41031 + 0.377892i −0.0936057 + 0.0250816i −0.305318 0.952250i \(-0.598763\pi\)
0.211712 + 0.977332i \(0.432096\pi\)
\(228\) 0 0
\(229\) 7.79011 + 13.4929i 0.514785 + 0.891633i 0.999853 + 0.0171570i \(0.00546151\pi\)
−0.485068 + 0.874476i \(0.661205\pi\)
\(230\) −3.15436 + 3.53033i −0.207992 + 0.232783i
\(231\) 0 0
\(232\) −8.94522 + 8.94522i −0.587283 + 0.587283i
\(233\) −6.02142 + 22.4723i −0.394476 + 1.47221i 0.428194 + 0.903687i \(0.359150\pi\)
−0.822670 + 0.568519i \(0.807517\pi\)
\(234\) 0 0
\(235\) −10.5242 + 20.8516i −0.686520 + 1.36021i
\(236\) 18.7710 10.8374i 1.22189 0.705456i
\(237\) 0 0
\(238\) −0.184318 0.783716i −0.0119475 0.0508008i
\(239\) 1.48712i 0.0961937i −0.998843 0.0480968i \(-0.984684\pi\)
0.998843 0.0480968i \(-0.0153156\pi\)
\(240\) 0 0
\(241\) 1.28163 + 0.739950i 0.0825571 + 0.0476643i 0.540710 0.841209i \(-0.318156\pi\)
−0.458153 + 0.888873i \(0.651489\pi\)
\(242\) 1.07180 + 4.00002i 0.0688980 + 0.257131i
\(243\) 0 0
\(244\) 7.89232 0.505254
\(245\) −15.1409 + 3.96883i −0.967320 + 0.253560i
\(246\) 0 0
\(247\) −13.6009 3.64436i −0.865406 0.231885i
\(248\) 0.492558 + 1.83825i 0.0312775 + 0.116729i
\(249\) 0 0
\(250\) 2.91406 + 3.51531i 0.184302 + 0.222328i
\(251\) 18.3956i 1.16112i −0.814218 0.580559i \(-0.802834\pi\)
0.814218 0.580559i \(-0.197166\pi\)
\(252\) 0 0
\(253\) 3.39990 + 3.39990i 0.213750 + 0.213750i
\(254\) 4.65290 2.68635i 0.291949 0.168557i
\(255\) 0 0
\(256\) −2.13077 + 3.69060i −0.133173 + 0.230663i
\(257\) −2.53039 + 9.44356i −0.157842 + 0.589073i 0.841004 + 0.541030i \(0.181965\pi\)
−0.998845 + 0.0480436i \(0.984701\pi\)
\(258\) 0 0
\(259\) 0.148748 4.82591i 0.00924276 0.299868i
\(260\) −23.6247 + 1.32875i −1.46514 + 0.0824057i
\(261\) 0 0
\(262\) 4.07723 1.09249i 0.251892 0.0674943i
\(263\) −10.7348 + 2.87639i −0.661939 + 0.177366i −0.574121 0.818771i \(-0.694656\pi\)
−0.0878181 + 0.996137i \(0.527989\pi\)
\(264\) 0 0
\(265\) 14.8412 0.834733i 0.911689 0.0512772i
\(266\) −2.32216 + 1.24694i −0.142381 + 0.0764546i
\(267\) 0 0
\(268\) 5.15001 19.2201i 0.314587 1.17406i
\(269\) −4.23477 + 7.33484i −0.258199 + 0.447213i −0.965759 0.259439i \(-0.916462\pi\)
0.707561 + 0.706652i \(0.249796\pi\)
\(270\) 0 0
\(271\) −20.3136 + 11.7281i −1.23396 + 0.712429i −0.967854 0.251514i \(-0.919072\pi\)
−0.266110 + 0.963943i \(0.585738\pi\)
\(272\) 1.59484 + 1.59484i 0.0967013 + 0.0967013i
\(273\) 0 0
\(274\) 0.360709i 0.0217912i
\(275\) 3.73076 2.75441i 0.224973 0.166097i
\(276\) 0 0
\(277\) −1.89698 7.07963i −0.113979 0.425374i 0.885230 0.465154i \(-0.154001\pi\)
−0.999208 + 0.0397799i \(0.987334\pi\)
\(278\) −7.36672 1.97391i −0.441827 0.118387i
\(279\) 0 0
\(280\) −6.38069 + 6.71297i −0.381319 + 0.401177i
\(281\) −16.9863 −1.01332 −0.506658 0.862147i \(-0.669119\pi\)
−0.506658 + 0.862147i \(0.669119\pi\)
\(282\) 0 0
\(283\) −0.342140 1.27688i −0.0203381 0.0759029i 0.955011 0.296571i \(-0.0958430\pi\)
−0.975349 + 0.220668i \(0.929176\pi\)
\(284\) 15.7172 + 9.07432i 0.932643 + 0.538462i
\(285\) 0 0
\(286\) 2.18649i 0.129290i
\(287\) 17.9594 4.22377i 1.06011 0.249321i
\(288\) 0 0
\(289\) −14.2416 + 8.22242i −0.837744 + 0.483672i
\(290\) 3.32506 6.58798i 0.195254 0.386860i
\(291\) 0 0
\(292\) 1.97764 7.38065i 0.115733 0.431920i
\(293\) −2.80762 + 2.80762i −0.164023 + 0.164023i −0.784346 0.620323i \(-0.787001\pi\)
0.620323 + 0.784346i \(0.287001\pi\)
\(294\) 0 0
\(295\) −17.6152 + 19.7148i −1.02560 + 1.14784i
\(296\) −1.42843 2.47411i −0.0830257 0.143805i
\(297\) 0 0
\(298\) −2.26335 + 0.606462i −0.131112 + 0.0351314i
\(299\) 14.9625 + 25.9158i 0.865302 + 1.49875i
\(300\) 0 0
\(301\) −1.53952 + 2.48634i −0.0887365 + 0.143310i
\(302\) 5.45374 5.45374i 0.313828 0.313828i
\(303\) 0 0
\(304\) 3.69199 6.39471i 0.211750 0.366762i
\(305\) −9.14411 + 3.00982i −0.523590 + 0.172342i
\(306\) 0 0
\(307\) −9.39163 9.39163i −0.536009 0.536009i 0.386345 0.922354i \(-0.373737\pi\)
−0.922354 + 0.386345i \(0.873737\pi\)
\(308\) 3.08138 + 3.27737i 0.175578 + 0.186746i
\(309\) 0 0
\(310\) −0.608191 0.928736i −0.0345430 0.0527486i
\(311\) −1.04801 0.605067i −0.0594270 0.0343102i 0.469992 0.882671i \(-0.344257\pi\)
−0.529419 + 0.848360i \(0.677590\pi\)
\(312\) 0 0
\(313\) −26.4462 7.08623i −1.49483 0.400538i −0.583463 0.812140i \(-0.698303\pi\)
−0.911364 + 0.411602i \(0.864969\pi\)
\(314\) 1.82241 0.102845
\(315\) 0 0
\(316\) −14.8806 −0.837101
\(317\) 13.9458 + 3.73676i 0.783273 + 0.209877i 0.628227 0.778030i \(-0.283781\pi\)
0.155046 + 0.987907i \(0.450448\pi\)
\(318\) 0 0
\(319\) −6.49065 3.74738i −0.363406 0.209813i
\(320\) 1.94964 9.34802i 0.108988 0.522570i
\(321\) 0 0
\(322\) 5.36355 + 1.61582i 0.298899 + 0.0900463i
\(323\) −1.28518 1.28518i −0.0715095 0.0715095i
\(324\) 0 0
\(325\) 26.8650 10.5490i 1.49020 0.585155i
\(326\) 0.665708 1.15304i 0.0368702 0.0638610i
\(327\) 0 0
\(328\) 7.71917 7.71917i 0.426220 0.426220i
\(329\) 27.6232 + 0.851425i 1.52292 + 0.0469406i
\(330\) 0 0
\(331\) 3.39956 + 5.88820i 0.186856 + 0.323645i 0.944201 0.329371i \(-0.106837\pi\)
−0.757344 + 0.653016i \(0.773503\pi\)
\(332\) −14.8106 + 3.96849i −0.812837 + 0.217799i
\(333\) 0 0
\(334\) 0.645374 + 1.11782i 0.0353133 + 0.0611644i
\(335\) 1.36294 + 24.2326i 0.0744655 + 1.32397i
\(336\) 0 0
\(337\) 3.49179 3.49179i 0.190210 0.190210i −0.605577 0.795787i \(-0.707058\pi\)
0.795787 + 0.605577i \(0.207058\pi\)
\(338\) 2.14792 8.01616i 0.116832 0.436022i
\(339\) 0 0
\(340\) −2.72666 1.37619i −0.147874 0.0746343i
\(341\) −0.976434 + 0.563745i −0.0528769 + 0.0305285i
\(342\) 0 0
\(343\) 11.8310 + 14.2487i 0.638817 + 0.769359i
\(344\) 1.73036i 0.0932948i
\(345\) 0 0
\(346\) −5.67258 3.27507i −0.304960 0.176069i
\(347\) −3.21794 12.0095i −0.172748 0.644704i −0.996924 0.0783710i \(-0.975028\pi\)
0.824176 0.566333i \(-0.191639\pi\)
\(348\) 0 0
\(349\) 0.973873 0.0521302 0.0260651 0.999660i \(-0.491702\pi\)
0.0260651 + 0.999660i \(0.491702\pi\)
\(350\) 2.31119 4.88337i 0.123538 0.261027i
\(351\) 0 0
\(352\) 3.91250 + 1.04835i 0.208537 + 0.0558774i
\(353\) −0.562056 2.09762i −0.0299152 0.111645i 0.949354 0.314209i \(-0.101739\pi\)
−0.979269 + 0.202564i \(0.935073\pi\)
\(354\) 0 0
\(355\) −21.6706 4.51967i −1.15016 0.239879i
\(356\) 28.5544i 1.51338i
\(357\) 0 0
\(358\) 2.64899 + 2.64899i 0.140003 + 0.140003i
\(359\) −17.9132 + 10.3422i −0.945422 + 0.545840i −0.891656 0.452714i \(-0.850456\pi\)
−0.0537661 + 0.998554i \(0.517123\pi\)
\(360\) 0 0
\(361\) 6.52485 11.3014i 0.343413 0.594809i
\(362\) 0.589212 2.19897i 0.0309683 0.115575i
\(363\) 0 0
\(364\) 13.2450 + 24.6661i 0.694227 + 1.29286i
\(365\) 0.523379 + 9.30547i 0.0273949 + 0.487071i
\(366\) 0 0
\(367\) −6.63239 + 1.77714i −0.346208 + 0.0927662i −0.427733 0.903905i \(-0.640688\pi\)
0.0815249 + 0.996671i \(0.474021\pi\)
\(368\) −15.1580 + 4.06158i −0.790167 + 0.211725i
\(369\) 0 0
\(370\) 1.24272 + 1.11038i 0.0646061 + 0.0577257i
\(371\) −8.32063 15.4955i −0.431985 0.804484i
\(372\) 0 0
\(373\) −6.61420 + 24.6845i −0.342470 + 1.27812i 0.553070 + 0.833135i \(0.313456\pi\)
−0.895540 + 0.444981i \(0.853210\pi\)
\(374\) 0.141115 0.244418i 0.00729688 0.0126386i
\(375\) 0 0
\(376\) 14.1616 8.17623i 0.730331 0.421657i
\(377\) −32.9834 32.9834i −1.69873 1.69873i
\(378\) 0 0
\(379\) 36.6543i 1.88281i 0.337284 + 0.941403i \(0.390492\pi\)
−0.337284 + 0.941403i \(0.609508\pi\)
\(380\) −2.04153 + 9.78859i −0.104728 + 0.502144i
\(381\) 0 0
\(382\) 0.0613112 + 0.228816i 0.00313695 + 0.0117073i
\(383\) −13.9820 3.74645i −0.714445 0.191435i −0.116753 0.993161i \(-0.537249\pi\)
−0.597692 + 0.801726i \(0.703915\pi\)
\(384\) 0 0
\(385\) −4.81997 2.62208i −0.245649 0.133633i
\(386\) −2.47135 −0.125788
\(387\) 0 0
\(388\) −3.28405 12.2562i −0.166722 0.622216i
\(389\) 2.22749 + 1.28604i 0.112938 + 0.0652050i 0.555405 0.831580i \(-0.312563\pi\)
−0.442467 + 0.896785i \(0.645897\pi\)
\(390\) 0 0
\(391\) 3.86268i 0.195344i
\(392\) 10.3903 + 3.48278i 0.524789 + 0.175907i
\(393\) 0 0
\(394\) 3.02941 1.74903i 0.152619 0.0881148i
\(395\) 17.2408 5.67488i 0.867480 0.285534i
\(396\) 0 0
\(397\) −2.30188 + 8.59074i −0.115528 + 0.431157i −0.999326 0.0367123i \(-0.988311\pi\)
0.883798 + 0.467869i \(0.154978\pi\)
\(398\) −3.24210 + 3.24210i −0.162512 + 0.162512i
\(399\) 0 0
\(400\) 1.69718 + 15.0398i 0.0848588 + 0.751992i
\(401\) −15.9532 27.6318i −0.796665 1.37986i −0.921776 0.387722i \(-0.873262\pi\)
0.125111 0.992143i \(-0.460071\pi\)
\(402\) 0 0
\(403\) −6.77811 + 1.81619i −0.337642 + 0.0904709i
\(404\) 7.61333 + 13.1867i 0.378777 + 0.656061i
\(405\) 0 0
\(406\) −8.72744 0.269004i −0.433136 0.0133505i
\(407\) 1.19681 1.19681i 0.0593235 0.0593235i
\(408\) 0 0
\(409\) 16.4328 28.4625i 0.812550 1.40738i −0.0985239 0.995135i \(-0.531412\pi\)
0.911074 0.412243i \(-0.135255\pi\)
\(410\) −2.86932 + 5.68501i −0.141706 + 0.280763i
\(411\) 0 0
\(412\) −3.40403 3.40403i −0.167705 0.167705i
\(413\) 29.9523 + 9.02342i 1.47385 + 0.444013i
\(414\) 0 0
\(415\) 15.6463 10.2461i 0.768045 0.502961i
\(416\) 21.8320 + 12.6047i 1.07040 + 0.617998i
\(417\) 0 0
\(418\) −0.892494 0.239143i −0.0436533 0.0116969i
\(419\) −12.2544 −0.598669 −0.299334 0.954148i \(-0.596765\pi\)
−0.299334 + 0.954148i \(0.596765\pi\)
\(420\) 0 0
\(421\) 34.4993 1.68140 0.840698 0.541505i \(-0.182145\pi\)
0.840698 + 0.541505i \(0.182145\pi\)
\(422\) −1.76185 0.472085i −0.0857654 0.0229808i
\(423\) 0 0
\(424\) −9.01266 5.20346i −0.437693 0.252702i
\(425\) 3.68395 + 0.554625i 0.178698 + 0.0269032i
\(426\) 0 0
\(427\) 7.80233 + 8.29861i 0.377581 + 0.401598i
\(428\) −1.14324 1.14324i −0.0552604 0.0552604i
\(429\) 0 0
\(430\) −0.315589 0.958788i −0.0152190 0.0462369i
\(431\) 8.92167 15.4528i 0.429742 0.744334i −0.567109 0.823643i \(-0.691938\pi\)
0.996850 + 0.0793088i \(0.0252713\pi\)
\(432\) 0 0
\(433\) −2.49490 + 2.49490i −0.119897 + 0.119897i −0.764510 0.644612i \(-0.777019\pi\)
0.644612 + 0.764510i \(0.277019\pi\)
\(434\) −0.691512 + 1.11680i −0.0331936 + 0.0536080i
\(435\) 0 0
\(436\) −11.3271 19.6191i −0.542469 0.939583i
\(437\) 12.2149 3.27298i 0.584319 0.156568i
\(438\) 0 0
\(439\) 1.77922 + 3.08171i 0.0849177 + 0.147082i 0.905356 0.424653i \(-0.139604\pi\)
−0.820438 + 0.571735i \(0.806271\pi\)
\(440\) −3.24156 + 0.182319i −0.154535 + 0.00869171i
\(441\) 0 0
\(442\) 1.24205 1.24205i 0.0590785 0.0590785i
\(443\) 1.21891 4.54905i 0.0579124 0.216132i −0.930905 0.365260i \(-0.880980\pi\)
0.988818 + 0.149128i \(0.0476467\pi\)
\(444\) 0 0
\(445\) −10.8895 33.0833i −0.516212 1.56830i
\(446\) 1.53049 0.883629i 0.0724708 0.0418410i
\(447\) 0 0
\(448\) −10.9986 + 2.58671i −0.519637 + 0.122210i
\(449\) 34.4214i 1.62444i −0.583348 0.812222i \(-0.698258\pi\)
0.583348 0.812222i \(-0.301742\pi\)
\(450\) 0 0
\(451\) 5.60102 + 3.23375i 0.263742 + 0.152271i
\(452\) −9.22214 34.4175i −0.433773 1.61886i
\(453\) 0 0
\(454\) −0.596294 −0.0279855
\(455\) −24.7525 23.5272i −1.16041 1.10297i
\(456\) 0 0
\(457\) 1.18187 + 0.316680i 0.0552853 + 0.0148137i 0.286356 0.958123i \(-0.407556\pi\)
−0.231070 + 0.972937i \(0.574223\pi\)
\(458\) 1.64687 + 6.14620i 0.0769532 + 0.287193i
\(459\) 0 0
\(460\) 17.7780 11.6421i 0.828903 0.542815i
\(461\) 15.0355i 0.700272i 0.936699 + 0.350136i \(0.113865\pi\)
−0.936699 + 0.350136i \(0.886135\pi\)
\(462\) 0 0
\(463\) 25.5793 + 25.5793i 1.18877 + 1.18877i 0.977407 + 0.211366i \(0.0677913\pi\)
0.211366 + 0.977407i \(0.432209\pi\)
\(464\) 21.1839 12.2305i 0.983438 0.567788i
\(465\) 0 0
\(466\) −4.75075 + 8.22854i −0.220074 + 0.381180i
\(467\) 2.92500 10.9162i 0.135353 0.505144i −0.864643 0.502386i \(-0.832456\pi\)
0.999996 0.00275754i \(-0.000877754\pi\)
\(468\) 0 0
\(469\) 25.3008 13.5858i 1.16828 0.627335i
\(470\) −6.35572 + 7.11327i −0.293167 + 0.328111i
\(471\) 0 0
\(472\) 17.8789 4.79063i 0.822942 0.220507i
\(473\) −0.990220 + 0.265329i −0.0455303 + 0.0121998i
\(474\) 0 0
\(475\) −1.36765 12.1197i −0.0627522 0.556090i
\(476\) −0.111336 + 3.61214i −0.00510309 + 0.165562i
\(477\) 0 0
\(478\) 0.157192 0.586649i 0.00718981 0.0268327i
\(479\) −7.26651 + 12.5860i −0.332015 + 0.575067i −0.982907 0.184104i \(-0.941062\pi\)
0.650892 + 0.759171i \(0.274395\pi\)
\(480\) 0 0
\(481\) 9.12268 5.26698i 0.415959 0.240154i
\(482\) 0.427372 + 0.427372i 0.0194663 + 0.0194663i
\(483\) 0 0
\(484\) 18.5883i 0.844924i
\(485\) 8.47896 + 12.9478i 0.385010 + 0.587928i
\(486\) 0 0
\(487\) −9.99761 37.3116i −0.453035 1.69075i −0.693802 0.720166i \(-0.744066\pi\)
0.240767 0.970583i \(-0.422601\pi\)
\(488\) 6.51012 + 1.74438i 0.294699 + 0.0789644i
\(489\) 0 0
\(490\) −6.39243 0.0347821i −0.288781 0.00157130i
\(491\) 25.2637 1.14014 0.570068 0.821598i \(-0.306917\pi\)
0.570068 + 0.821598i \(0.306917\pi\)
\(492\) 0 0
\(493\) −1.55834 5.81579i −0.0701840 0.261930i
\(494\) −4.98018 2.87531i −0.224069 0.129366i
\(495\) 0 0
\(496\) 3.67985i 0.165230i
\(497\) 5.99652 + 25.4971i 0.268981 + 1.14370i
\(498\) 0 0
\(499\) 2.71355 1.56667i 0.121475 0.0701339i −0.438031 0.898960i \(-0.644324\pi\)
0.559506 + 0.828826i \(0.310991\pi\)
\(500\) −8.55073 18.6270i −0.382400 0.833026i
\(501\) 0 0
\(502\) 1.94446 7.25682i 0.0867854 0.323888i
\(503\) 23.8589 23.8589i 1.06382 1.06382i 0.0659958 0.997820i \(-0.478978\pi\)
0.997820 0.0659958i \(-0.0210224\pi\)
\(504\) 0 0
\(505\) −13.8497 12.3748i −0.616305 0.550670i
\(506\) 0.981839 + 1.70059i 0.0436480 + 0.0756006i
\(507\) 0 0
\(508\) −23.2948 + 6.24182i −1.03354 + 0.276936i
\(509\) 0.244582 + 0.423629i 0.0108409 + 0.0187770i 0.871395 0.490582i \(-0.163216\pi\)
−0.860554 + 0.509359i \(0.829882\pi\)
\(510\) 0 0
\(511\) 9.71568 5.21705i 0.429796 0.230789i
\(512\) −16.0496 + 16.0496i −0.709301 + 0.709301i
\(513\) 0 0
\(514\) −1.99642 + 3.45790i −0.0880582 + 0.152521i
\(515\) 5.24210 + 2.64577i 0.230995 + 0.116587i
\(516\) 0 0
\(517\) 6.85045 + 6.85045i 0.301282 + 0.301282i
\(518\) 0.568791 1.88804i 0.0249912 0.0829557i
\(519\) 0 0
\(520\) −19.7809 4.12554i −0.867450 0.180917i
\(521\) 7.19061 + 4.15150i 0.315026 + 0.181881i 0.649173 0.760640i \(-0.275115\pi\)
−0.334147 + 0.942521i \(0.608448\pi\)
\(522\) 0 0
\(523\) −15.8284 4.24121i −0.692128 0.185455i −0.104426 0.994533i \(-0.533301\pi\)
−0.587702 + 0.809078i \(0.699967\pi\)
\(524\) −18.9471 −0.827709
\(525\) 0 0
\(526\) −4.53880 −0.197901
\(527\) −0.874911 0.234432i −0.0381117 0.0102120i
\(528\) 0 0
\(529\) −3.35624 1.93773i −0.145924 0.0842490i
\(530\) 5.94291 + 1.23946i 0.258144 + 0.0538389i
\(531\) 0 0
\(532\) 11.5170 2.70861i 0.499325 0.117433i
\(533\) 28.4626 + 28.4626i 1.23285 + 1.23285i
\(534\) 0 0
\(535\) 1.76055 + 0.888578i 0.0761151 + 0.0384166i
\(536\) 8.49616 14.7158i 0.366978 0.635625i
\(537\) 0 0
\(538\) −2.44588 + 2.44588i −0.105449 + 0.105449i
\(539\) −0.399844 + 6.48001i −0.0172225 + 0.279114i
\(540\) 0 0
\(541\) −10.9266 18.9255i −0.469772 0.813670i 0.529630 0.848229i \(-0.322331\pi\)
−0.999403 + 0.0345590i \(0.988997\pi\)
\(542\) −9.25315 + 2.47937i −0.397457 + 0.106498i
\(543\) 0 0
\(544\) 1.62700 + 2.81806i 0.0697573 + 0.120823i
\(545\) 20.6056 + 18.4111i 0.882646 + 0.788646i
\(546\) 0 0
\(547\) −5.48357 + 5.48357i −0.234460 + 0.234460i −0.814552 0.580091i \(-0.803017\pi\)
0.580091 + 0.814552i \(0.303017\pi\)
\(548\) −0.419059 + 1.56395i −0.0179013 + 0.0668087i
\(549\) 0 0
\(550\) 1.76288 0.692228i 0.0751697 0.0295167i
\(551\) −17.0708 + 9.85585i −0.727242 + 0.419873i
\(552\) 0 0
\(553\) −14.7110 15.6467i −0.625573 0.665364i
\(554\) 2.99334i 0.127175i
\(555\) 0 0
\(556\) 29.6472 + 17.1168i 1.25732 + 0.725914i
\(557\) 6.84583 + 25.5490i 0.290067 + 1.08254i 0.945057 + 0.326907i \(0.106006\pi\)
−0.654990 + 0.755638i \(0.727327\pi\)
\(558\) 0 0
\(559\) −6.38029 −0.269858
\(560\) 15.2769 9.34473i 0.645567 0.394887i
\(561\) 0 0
\(562\) −6.70087 1.79549i −0.282659 0.0757383i
\(563\) −11.0066 41.0771i −0.463872 1.73119i −0.660602 0.750736i \(-0.729699\pi\)
0.196730 0.980458i \(-0.436968\pi\)
\(564\) 0 0
\(565\) 23.8103 + 36.3594i 1.00171 + 1.52965i
\(566\) 0.539880i 0.0226929i
\(567\) 0 0
\(568\) 10.9590 + 10.9590i 0.459828 + 0.459828i
\(569\) −17.6275 + 10.1772i −0.738982 + 0.426651i −0.821699 0.569922i \(-0.806974\pi\)
0.0827171 + 0.996573i \(0.473640\pi\)
\(570\) 0 0
\(571\) 5.57836 9.66200i 0.233447 0.404342i −0.725373 0.688356i \(-0.758333\pi\)
0.958820 + 0.284014i \(0.0916661\pi\)
\(572\) −2.54019 + 9.48011i −0.106211 + 0.396383i
\(573\) 0 0
\(574\) 7.53123 + 0.232134i 0.314348 + 0.00968907i
\(575\) −16.1579 + 20.2684i −0.673830 + 0.845252i
\(576\) 0 0
\(577\) −17.1708 + 4.60090i −0.714830 + 0.191538i −0.597864 0.801598i \(-0.703984\pi\)
−0.116966 + 0.993136i \(0.537317\pi\)
\(578\) −6.48728 + 1.73826i −0.269835 + 0.0723022i
\(579\) 0 0
\(580\) −22.0704 + 24.7010i −0.916423 + 1.02565i
\(581\) −18.8145 11.6498i −0.780557 0.483315i
\(582\) 0 0
\(583\) 1.59577 5.95548i 0.0660899 0.246651i
\(584\) 3.26258 5.65095i 0.135006 0.233838i
\(585\) 0 0
\(586\) −1.40434 + 0.810798i −0.0580129 + 0.0334938i
\(587\) −19.9795 19.9795i −0.824644 0.824644i 0.162126 0.986770i \(-0.448165\pi\)
−0.986770 + 0.162126i \(0.948165\pi\)
\(588\) 0 0
\(589\) 2.96537i 0.122186i
\(590\) −9.03290 + 5.91528i −0.371879 + 0.243528i
\(591\) 0 0
\(592\) 1.42973 + 5.33582i 0.0587615 + 0.219301i
\(593\) −22.5538 6.04327i −0.926172 0.248167i −0.235951 0.971765i \(-0.575820\pi\)
−0.690222 + 0.723598i \(0.742487\pi\)
\(594\) 0 0
\(595\) −1.24853 4.22752i −0.0511849 0.173311i
\(596\) 10.5179 0.430830
\(597\) 0 0
\(598\) 3.16314 + 11.8050i 0.129351 + 0.482743i
\(599\) −12.7696 7.37252i −0.521751 0.301233i 0.215900 0.976416i \(-0.430732\pi\)
−0.737651 + 0.675182i \(0.764065\pi\)
\(600\) 0 0
\(601\) 31.4686i 1.28363i 0.766859 + 0.641815i \(0.221818\pi\)
−0.766859 + 0.641815i \(0.778182\pi\)
\(602\) −0.870134 + 0.818098i −0.0354640 + 0.0333432i
\(603\) 0 0
\(604\) −29.9821 + 17.3102i −1.21995 + 0.704341i
\(605\) 7.08885 + 21.5366i 0.288203 + 0.875587i
\(606\) 0 0
\(607\) −5.58329 + 20.8371i −0.226619 + 0.845753i 0.755131 + 0.655574i \(0.227573\pi\)
−0.981750 + 0.190178i \(0.939093\pi\)
\(608\) 7.53291 7.53291i 0.305500 0.305500i
\(609\) 0 0
\(610\) −3.92538 + 0.220780i −0.158934 + 0.00893912i
\(611\) 30.1479 + 52.2177i 1.21965 + 2.11250i
\(612\) 0 0
\(613\) 28.7726 7.70959i 1.16211 0.311388i 0.374304 0.927306i \(-0.377882\pi\)
0.787810 + 0.615918i \(0.211215\pi\)
\(614\) −2.71216 4.69760i −0.109454 0.189580i
\(615\) 0 0
\(616\) 1.81736 + 3.38445i 0.0732233 + 0.136363i
\(617\) 12.6484 12.6484i 0.509204 0.509204i −0.405078 0.914282i \(-0.632756\pi\)
0.914282 + 0.405078i \(0.132756\pi\)
\(618\) 0 0
\(619\) 9.98720 17.2983i 0.401419 0.695279i −0.592478 0.805587i \(-0.701850\pi\)
0.993897 + 0.110308i \(0.0351837\pi\)
\(620\) 1.55800 + 4.73336i 0.0625709 + 0.190096i
\(621\) 0 0
\(622\) −0.349468 0.349468i −0.0140124 0.0140124i
\(623\) −30.0243 + 28.2288i −1.20290 + 1.13096i
\(624\) 0 0
\(625\) 17.0106 + 18.3205i 0.680422 + 0.732820i
\(626\) −9.68366 5.59086i −0.387037 0.223456i
\(627\) 0 0
\(628\) −7.90156 2.11722i −0.315307 0.0844861i
\(629\) 1.35971 0.0542153
\(630\) 0 0
\(631\) −33.1850 −1.32107 −0.660536 0.750794i \(-0.729671\pi\)
−0.660536 + 0.750794i \(0.729671\pi\)
\(632\) −12.2745 3.28895i −0.488255 0.130828i
\(633\) 0 0
\(634\) 5.10645 + 2.94821i 0.202803 + 0.117088i
\(635\) 24.6092 16.1155i 0.976585 0.639526i
\(636\) 0 0
\(637\) −12.8419 + 38.3117i −0.508815 + 1.51797i
\(638\) −2.16437 2.16437i −0.0856883 0.0856883i
\(639\) 0 0
\(640\) 10.5575 20.9176i 0.417320 0.826840i
\(641\) 5.49850 9.52368i 0.217178 0.376163i −0.736766 0.676147i \(-0.763648\pi\)
0.953944 + 0.299985i \(0.0969816\pi\)
\(642\) 0 0
\(643\) 12.1848 12.1848i 0.480522 0.480522i −0.424777 0.905298i \(-0.639647\pi\)
0.905298 + 0.424777i \(0.139647\pi\)
\(644\) −21.3779 13.2370i −0.842407 0.521611i
\(645\) 0 0
\(646\) −0.371141 0.642836i −0.0146024 0.0252920i
\(647\) 32.4815 8.70340i 1.27698 0.342166i 0.444280 0.895888i \(-0.353460\pi\)
0.832702 + 0.553722i \(0.186793\pi\)
\(648\) 0 0
\(649\) 5.48299 + 9.49682i 0.215226 + 0.372783i
\(650\) 11.7130 1.32176i 0.459421 0.0518435i
\(651\) 0 0
\(652\) −4.22591 + 4.22591i −0.165500 + 0.165500i
\(653\) 12.7016 47.4030i 0.497052 1.85502i −0.0211667 0.999776i \(-0.506738\pi\)
0.518219 0.855248i \(-0.326595\pi\)
\(654\) 0 0
\(655\) 21.9523 7.22568i 0.857747 0.282331i
\(656\) −18.2804 + 10.5542i −0.713729 + 0.412072i
\(657\) 0 0
\(658\) 10.8070 + 3.25572i 0.421301 + 0.126921i
\(659\) 8.69642i 0.338764i 0.985550 + 0.169382i \(0.0541772\pi\)
−0.985550 + 0.169382i \(0.945823\pi\)
\(660\) 0 0
\(661\) −31.2860 18.0630i −1.21689 0.702569i −0.252635 0.967562i \(-0.581297\pi\)
−0.964250 + 0.264993i \(0.914630\pi\)
\(662\) 0.718684 + 2.68216i 0.0279324 + 0.104245i
\(663\) 0 0
\(664\) −13.0939 −0.508142
\(665\) −12.3107 + 7.53035i −0.477390 + 0.292015i
\(666\) 0 0
\(667\) 40.4647 + 10.8425i 1.56680 + 0.419823i
\(668\) −1.49954 5.59638i −0.0580191 0.216530i
\(669\) 0 0
\(670\) −2.02378 + 9.70352i −0.0781856 + 0.374880i
\(671\) 3.99297i 0.154147i
\(672\) 0 0
\(673\) −17.0769 17.0769i −0.658268 0.658268i 0.296702 0.954970i \(-0.404113\pi\)
−0.954970 + 0.296702i \(0.904113\pi\)
\(674\) 1.74656 1.00838i 0.0672750 0.0388412i
\(675\) 0 0
\(676\) −18.6258 + 32.2608i −0.716377 + 1.24080i
\(677\) 0.600353 2.24055i 0.0230734 0.0861113i −0.953429 0.301617i \(-0.902473\pi\)
0.976502 + 0.215506i \(0.0691401\pi\)
\(678\) 0 0
\(679\) 9.64056 15.5696i 0.369971 0.597506i
\(680\) −1.94496 1.73783i −0.0745858 0.0666426i
\(681\) 0 0
\(682\) −0.444780 + 0.119179i −0.0170315 + 0.00456358i
\(683\) −15.1994 + 4.07266i −0.581588 + 0.155836i −0.537606 0.843196i \(-0.680671\pi\)
−0.0439822 + 0.999032i \(0.514004\pi\)
\(684\) 0 0
\(685\) −0.110903 1.97182i −0.00423740 0.0753393i
\(686\) 3.16107 + 6.87152i 0.120690 + 0.262356i
\(687\) 0 0
\(688\) 0.865969 3.23184i 0.0330147 0.123213i
\(689\) 19.1865 33.2320i 0.730948 1.26604i
\(690\) 0 0
\(691\) 11.8944 6.86721i 0.452483 0.261241i −0.256395 0.966572i \(-0.582535\pi\)
0.708878 + 0.705331i \(0.249202\pi\)
\(692\) 20.7901 + 20.7901i 0.790322 + 0.790322i
\(693\) 0 0
\(694\) 5.07775i 0.192749i
\(695\) −40.8771 8.52541i −1.55056 0.323387i
\(696\) 0 0
\(697\) 1.34475 + 5.01866i 0.0509359 + 0.190095i
\(698\) 0.384181 + 0.102941i 0.0145415 + 0.00389637i
\(699\) 0 0
\(700\) −15.6941 + 18.4881i −0.593181 + 0.698784i
\(701\) −50.1869 −1.89553 −0.947766 0.318966i \(-0.896664\pi\)
−0.947766 + 0.318966i \(0.896664\pi\)
\(702\) 0 0
\(703\) −1.15213 4.29981i −0.0434535 0.162171i
\(704\) −3.43016 1.98040i −0.129279 0.0746392i
\(705\) 0 0
\(706\) 0.886896i 0.0333788i
\(707\) −6.33898 + 21.0416i −0.238402 + 0.791349i
\(708\) 0 0
\(709\) −22.2408 + 12.8408i −0.835272 + 0.482245i −0.855654 0.517547i \(-0.826845\pi\)
0.0203820 + 0.999792i \(0.493512\pi\)
\(710\) −8.07106 4.07360i −0.302901 0.152879i
\(711\) 0 0
\(712\) −6.31116 + 23.5536i −0.236521 + 0.882707i
\(713\) 4.45628 4.45628i 0.166889 0.166889i
\(714\) 0 0
\(715\) −0.672257 11.9525i −0.0251410 0.446997i
\(716\) −8.40788 14.5629i −0.314217 0.544240i
\(717\) 0 0
\(718\) −8.15972 + 2.18639i −0.304518 + 0.0815954i
\(719\) 20.2778 + 35.1222i 0.756235 + 1.30984i 0.944758 + 0.327769i \(0.106297\pi\)
−0.188522 + 0.982069i \(0.560370\pi\)
\(720\) 0 0
\(721\) 0.214048 6.94448i 0.00797158 0.258626i
\(722\) 3.76856 3.76856i 0.140251 0.140251i
\(723\) 0 0
\(724\) −5.10937 + 8.84968i −0.189888 + 0.328896i
\(725\) 16.1509 37.0355i 0.599831 1.37547i
\(726\) 0 0
\(727\) −19.3599 19.3599i −0.718020 0.718020i 0.250180 0.968199i \(-0.419510\pi\)
−0.968199 + 0.250180i \(0.919510\pi\)
\(728\) 5.47361 + 23.2737i 0.202865 + 0.862581i
\(729\) 0 0
\(730\) −0.777146 + 3.72621i −0.0287635 + 0.137913i
\(731\) −0.713225 0.411780i −0.0263796 0.0152302i
\(732\) 0 0
\(733\) 16.4569 + 4.40962i 0.607851 + 0.162873i 0.549599 0.835429i \(-0.314781\pi\)
0.0582520 + 0.998302i \(0.481447\pi\)
\(734\) −2.80424 −0.103507
\(735\) 0 0
\(736\) −22.6405 −0.834540
\(737\) 9.72405 + 2.60555i 0.358190 + 0.0959767i
\(738\) 0 0
\(739\) 1.49335 + 0.862189i 0.0549339 + 0.0317161i 0.527215 0.849732i \(-0.323236\pi\)
−0.472281 + 0.881448i \(0.656569\pi\)
\(740\) −4.09816 6.25808i −0.150651 0.230052i
\(741\) 0 0
\(742\) −1.64447 6.99228i −0.0603705 0.256695i
\(743\) 23.6008 + 23.6008i 0.865830 + 0.865830i 0.992008 0.126178i \(-0.0402710\pi\)
−0.126178 + 0.992008i \(0.540271\pi\)
\(744\) 0 0
\(745\) −12.1861 + 4.01111i −0.446465 + 0.146956i
\(746\) −5.21844 + 9.03859i −0.191060 + 0.330926i
\(747\) 0 0
\(748\) −0.895797 + 0.895797i −0.0327536 + 0.0327536i
\(749\) 0.0718877 2.33229i 0.00262672 0.0852200i
\(750\) 0 0
\(751\) 3.70285 + 6.41353i 0.135119 + 0.234033i 0.925643 0.378398i \(-0.123525\pi\)
−0.790524 + 0.612431i \(0.790192\pi\)
\(752\) −30.5419 + 8.18368i −1.11375 + 0.298428i
\(753\) 0 0
\(754\) −9.52510 16.4980i −0.346884 0.600820i
\(755\) 28.1361 31.4897i 1.02398 1.14603i
\(756\) 0 0
\(757\) 13.1631 13.1631i 0.478421 0.478421i −0.426205 0.904626i \(-0.640150\pi\)
0.904626 + 0.426205i \(0.140150\pi\)
\(758\) −3.87446 + 14.4597i −0.140727 + 0.525199i
\(759\) 0 0
\(760\) −3.84749 + 7.62306i −0.139563 + 0.276517i
\(761\) −28.4617 + 16.4324i −1.03174 + 0.595674i −0.917482 0.397778i \(-0.869782\pi\)
−0.114255 + 0.993451i \(0.536448\pi\)
\(762\) 0 0
\(763\) 9.43111 31.3055i 0.341429 1.13334i
\(764\) 1.06332i 0.0384697i
\(765\) 0 0
\(766\) −5.11970 2.95586i −0.184982 0.106799i
\(767\) 17.6643 + 65.9241i 0.637821 + 2.38038i
\(768\) 0 0
\(769\) −14.4951 −0.522707 −0.261353 0.965243i \(-0.584169\pi\)
−0.261353 + 0.965243i \(0.584169\pi\)
\(770\) −1.62426 1.54386i −0.0585342 0.0556368i
\(771\) 0 0
\(772\) 10.7152 + 2.87112i 0.385648 + 0.103334i
\(773\) 7.39923 + 27.6143i 0.266132 + 0.993218i 0.961554 + 0.274616i \(0.0885509\pi\)
−0.695422 + 0.718602i \(0.744782\pi\)
\(774\) 0 0
\(775\) −3.61023 4.88994i −0.129683 0.175652i
\(776\) 10.8356i 0.388976i
\(777\) 0 0
\(778\) 0.742780 + 0.742780i 0.0266300 + 0.0266300i
\(779\) 14.7311 8.50498i 0.527795 0.304722i
\(780\) 0 0
\(781\) −4.59098 + 7.95181i −0.164278 + 0.284538i
\(782\) −0.408295 + 1.52378i −0.0146006 + 0.0544902i
\(783\) 0 0
\(784\) −17.6632 11.7048i −0.630830 0.418027i
\(785\) 9.96223 0.560318i 0.355567 0.0199986i
\(786\) 0 0
\(787\) 10.2518 2.74696i 0.365437 0.0979185i −0.0714277 0.997446i \(-0.522756\pi\)
0.436865 + 0.899527i \(0.356089\pi\)
\(788\) −15.1668 + 4.06392i −0.540293 + 0.144771i
\(789\) 0 0
\(790\) 7.40114 0.416271i 0.263321 0.0148103i
\(791\) 27.0723 43.7219i 0.962579 1.55457i
\(792\) 0 0
\(793\) −6.43199 + 24.0045i −0.228407 + 0.852425i
\(794\) −1.81613 + 3.14562i −0.0644519 + 0.111634i
\(795\) 0 0
\(796\) 17.8236 10.2904i 0.631739 0.364735i
\(797\) 8.79395 + 8.79395i 0.311498 + 0.311498i 0.845490 0.533992i \(-0.179309\pi\)
−0.533992 + 0.845490i \(0.679309\pi\)
\(798\) 0 0
\(799\) 7.78291i 0.275340i
\(800\) −3.25085 + 21.5929i −0.114935 + 0.763425i
\(801\) 0 0
\(802\) −3.37259 12.5867i −0.119090 0.444451i
\(803\) 3.73410 + 1.00055i 0.131773 + 0.0353086i
\(804\) 0 0
\(805\) 29.8167 + 7.18383i 1.05090 + 0.253197i
\(806\) −2.86586 −0.100946
\(807\) 0 0
\(808\) 3.36543 + 12.5600i 0.118396 + 0.441858i
\(809\) −41.4536 23.9333i −1.45743 0.841449i −0.458547 0.888670i \(-0.651630\pi\)
−0.998884 + 0.0472214i \(0.984963\pi\)
\(810\) 0 0
\(811\) 20.2287i 0.710327i 0.934804 + 0.355163i \(0.115575\pi\)
−0.934804 + 0.355163i \(0.884425\pi\)
\(812\) 37.5276 + 11.3056i 1.31696 + 0.396748i
\(813\) 0 0
\(814\) 0.598631 0.345620i 0.0209820 0.0121140i
\(815\) 3.28458 6.50778i 0.115054 0.227957i
\(816\) 0 0
\(817\) −0.697832 + 2.60434i −0.0244140 + 0.0911144i
\(818\) 9.49109 9.49109i 0.331848 0.331848i
\(819\) 0 0
\(820\) 19.0454 21.3154i 0.665092 0.744366i
\(821\) 7.84950 + 13.5957i 0.273949 + 0.474494i 0.969870 0.243625i \(-0.0783366\pi\)
−0.695920 + 0.718119i \(0.745003\pi\)
\(822\) 0 0
\(823\) 8.46662 2.26862i 0.295128 0.0790793i −0.108217 0.994127i \(-0.534514\pi\)
0.403345 + 0.915048i \(0.367847\pi\)
\(824\) −2.05551 3.56024i −0.0716069 0.124027i
\(825\) 0 0
\(826\) 10.8620 + 6.72566i 0.377937 + 0.234016i
\(827\) −12.7483 + 12.7483i −0.443302 + 0.443302i −0.893120 0.449818i \(-0.851489\pi\)
0.449818 + 0.893120i \(0.351489\pi\)
\(828\) 0 0
\(829\) −26.2262 + 45.4252i −0.910875 + 1.57768i −0.0980444 + 0.995182i \(0.531259\pi\)
−0.812831 + 0.582500i \(0.802075\pi\)
\(830\) 7.25529 2.38811i 0.251835 0.0828925i
\(831\) 0 0
\(832\) −17.4309 17.4309i −0.604309 0.604309i
\(833\) −3.90816 + 3.45389i −0.135410 + 0.119670i
\(834\) 0 0
\(835\) 3.87162 + 5.91214i 0.133983 + 0.204598i
\(836\) 3.59182 + 2.07374i 0.124226 + 0.0717217i
\(837\) 0 0
\(838\) −4.83422 1.29533i −0.166995 0.0447463i
\(839\) 1.48091 0.0511267 0.0255633 0.999673i \(-0.491862\pi\)
0.0255633 + 0.999673i \(0.491862\pi\)
\(840\) 0 0
\(841\) −36.2994 −1.25170
\(842\) 13.6096 + 3.64667i 0.469016 + 0.125673i
\(843\) 0 0
\(844\) 7.09050 + 4.09370i 0.244065 + 0.140911i
\(845\) 9.27700 44.4808i 0.319138 1.53019i
\(846\) 0 0
\(847\) 19.5452 18.3764i 0.671582 0.631420i
\(848\) 14.2291 + 14.2291i 0.488628 + 0.488628i
\(849\) 0 0
\(850\) 1.39465 + 0.608196i 0.0478360 + 0.0208609i
\(851\) −4.73025 + 8.19304i −0.162151 + 0.280854i
\(852\) 0 0
\(853\) 35.7294 35.7294i 1.22335 1.22335i 0.256918 0.966433i \(-0.417293\pi\)
0.966433 0.256918i \(-0.0827070\pi\)
\(854\) 2.20074 + 4.09842i 0.0753077 + 0.140245i
\(855\) 0 0
\(856\) −0.690337 1.19570i −0.0235952 0.0408681i
\(857\) −43.0261 + 11.5288i −1.46974 + 0.393816i −0.902843 0.429971i \(-0.858524\pi\)
−0.566899 + 0.823787i \(0.691857\pi\)
\(858\) 0 0
\(859\) −12.6056 21.8335i −0.430096 0.744948i 0.566785 0.823866i \(-0.308187\pi\)
−0.996881 + 0.0789174i \(0.974854\pi\)
\(860\) 0.254433 + 4.52372i 0.00867609 + 0.154258i
\(861\) 0 0
\(862\) 5.15289 5.15289i 0.175508 0.175508i
\(863\) 6.17854 23.0586i 0.210320 0.784924i −0.777442 0.628955i \(-0.783483\pi\)
0.987762 0.155970i \(-0.0498502\pi\)
\(864\) 0 0
\(865\) −32.0161 16.1591i −1.08858 0.549425i
\(866\) −1.24792 + 0.720489i −0.0424062 + 0.0244832i
\(867\) 0 0
\(868\) 4.29569 4.03880i 0.145805 0.137086i
\(869\) 7.52857i 0.255389i
\(870\) 0 0
\(871\) 54.2609 + 31.3275i 1.83856 + 1.06149i
\(872\) −5.00708 18.6867i −0.169561 0.632810i
\(873\) 0 0
\(874\) 5.16460 0.174695
\(875\) 11.1327 27.4055i 0.376353 0.926476i
\(876\) 0 0
\(877\) −46.3608 12.4223i −1.56549 0.419472i −0.631095 0.775706i \(-0.717394\pi\)
−0.934397 + 0.356234i \(0.884061\pi\)
\(878\) 0.376137 + 1.40376i 0.0126940 + 0.0473747i
\(879\) 0 0
\(880\) 6.14558 + 1.28173i 0.207167 + 0.0432072i
\(881\) 17.3873i 0.585793i −0.956144 0.292896i \(-0.905381\pi\)
0.956144 0.292896i \(-0.0946191\pi\)
\(882\) 0 0
\(883\) 11.2463 + 11.2463i 0.378469 + 0.378469i 0.870550 0.492080i \(-0.163763\pi\)
−0.492080 + 0.870550i \(0.663763\pi\)
\(884\) −6.82823 + 3.94228i −0.229658 + 0.132593i
\(885\) 0 0
\(886\) 0.961693 1.66570i 0.0323087 0.0559603i
\(887\) 5.00349 18.6733i 0.168001 0.626987i −0.829638 0.558302i \(-0.811453\pi\)
0.997638 0.0686850i \(-0.0218803\pi\)
\(888\) 0 0
\(889\) −29.5923 18.3233i −0.992495 0.614545i
\(890\) −0.798781 14.2020i −0.0267752 0.476052i
\(891\) 0 0
\(892\) −7.66241 + 2.05314i −0.256556 + 0.0687441i
\(893\) 24.6119 6.59473i 0.823605 0.220684i
\(894\) 0 0
\(895\) 15.2951 + 13.6662i 0.511260 + 0.456812i
\(896\) −27.7106 0.854119i −0.925746 0.0285341i
\(897\) 0 0
\(898\) 3.63843 13.5788i 0.121416 0.453130i
\(899\) −4.91173 + 8.50736i −0.163815 + 0.283736i
\(900\) 0 0
\(901\) 4.28955 2.47657i 0.142906 0.0825066i
\(902\) 1.86772 + 1.86772i 0.0621882 + 0.0621882i
\(903\) 0 0
\(904\) 30.4282i 1.01203i
\(905\) 2.54483 12.2018i 0.0845932 0.405602i
\(906\) 0 0
\(907\) 11.4540 + 42.7470i 0.380325 + 1.41939i 0.845406 + 0.534123i \(0.179358\pi\)
−0.465082 + 0.885268i \(0.653975\pi\)
\(908\) 2.58539 + 0.692754i 0.0857993 + 0.0229898i
\(909\) 0 0
\(910\) −7.27765 11.8976i −0.241252 0.394402i
\(911\) 16.2351 0.537894 0.268947 0.963155i \(-0.413324\pi\)
0.268947 + 0.963155i \(0.413324\pi\)
\(912\) 0 0
\(913\) −2.00778 7.49314i −0.0664479 0.247987i
\(914\) 0.432757 + 0.249852i 0.0143143 + 0.00826438i
\(915\) 0 0
\(916\) 28.5618i 0.943707i
\(917\) −18.7311 19.9225i −0.618555 0.657899i
\(918\) 0 0
\(919\) 37.3664 21.5735i 1.23260 0.711644i 0.265032 0.964240i \(-0.414618\pi\)
0.967572 + 0.252596i \(0.0812842\pi\)
\(920\) 17.2376 5.67384i 0.568308 0.187061i
\(921\) 0 0
\(922\) −1.58929 + 5.93131i −0.0523405 + 0.195337i
\(923\) −40.4085 + 40.4085i −1.33006 + 1.33006i
\(924\) 0 0
\(925\) 7.13475 + 5.68778i 0.234589 + 0.187013i
\(926\) 7.38693 + 12.7945i 0.242750 + 0.420455i
\(927\) 0 0
\(928\) 34.0884 9.13396i 1.11901 0.299837i
\(929\) −14.8286 25.6838i −0.486510 0.842659i 0.513370 0.858167i \(-0.328397\pi\)
−0.999880 + 0.0155078i \(0.995064\pi\)
\(930\) 0 0
\(931\) 14.2337 + 9.43215i 0.466492 + 0.309126i
\(932\) 30.1578 30.1578i 0.987851 0.987851i
\(933\) 0 0
\(934\) 2.30775 3.99714i 0.0755119 0.130791i
\(935\) 0.696257 1.37950i 0.0227700 0.0451145i
\(936\) 0 0
\(937\) 23.5836 + 23.5836i 0.770443 + 0.770443i 0.978184 0.207741i \(-0.0666111\pi\)
−0.207741 + 0.978184i \(0.566611\pi\)
\(938\) 11.4169 2.68508i 0.372776 0.0876709i
\(939\) 0 0
\(940\) 35.8208 23.4576i 1.16835 0.765103i
\(941\) 19.4488 + 11.2288i 0.634014 + 0.366048i 0.782305 0.622896i \(-0.214044\pi\)
−0.148291 + 0.988944i \(0.547377\pi\)
\(942\) 0 0
\(943\) −34.9185 9.35638i −1.13710 0.304686i
\(944\) −35.7903 −1.16488
\(945\) 0 0
\(946\) −0.418675 −0.0136123
\(947\) −2.88568 0.773216i −0.0937720 0.0251261i 0.211628 0.977350i \(-0.432123\pi\)
−0.305400 + 0.952224i \(0.598790\pi\)
\(948\) 0 0
\(949\) 20.8365 + 12.0300i 0.676382 + 0.390509i
\(950\) 0.741562 4.92563i 0.0240594 0.159809i
\(951\) 0 0
\(952\) −0.890203 + 2.95493i −0.0288516 + 0.0957698i
\(953\) −24.1870 24.1870i −0.783494 0.783494i 0.196924 0.980419i \(-0.436905\pi\)
−0.980419 + 0.196924i \(0.936905\pi\)
\(954\) 0 0
\(955\) 0.405510 + 1.23198i 0.0131220 + 0.0398658i
\(956\) −1.36310 + 2.36095i −0.0440857 + 0.0763587i
\(957\) 0 0
\(958\) −4.19691 + 4.19691i −0.135596 + 0.135596i
\(959\) −2.05874 + 1.10549i −0.0664802 + 0.0356980i
\(960\) 0 0
\(961\) −14.7611 25.5670i −0.476164 0.824741i
\(962\) 4.15552 1.11347i 0.133979 0.0358996i
\(963\) 0 0
\(964\) −1.35648 2.34949i −0.0436893 0.0756721i
\(965\) −13.5096 + 0.759839i −0.434890 + 0.0244601i
\(966\) 0 0
\(967\) 22.8071 22.8071i 0.733427 0.733427i −0.237870 0.971297i \(-0.576449\pi\)
0.971297 + 0.237870i \(0.0764493\pi\)
\(968\) 4.10844 15.3329i 0.132050 0.492818i
\(969\) 0 0
\(970\) 1.97623 + 6.00398i 0.0634530 + 0.192776i
\(971\) −3.42093 + 1.97508i −0.109783 + 0.0633832i −0.553886 0.832592i \(-0.686856\pi\)
0.444103 + 0.895976i \(0.353522\pi\)
\(972\) 0 0
\(973\) 11.3112 + 48.0950i 0.362619 + 1.54185i
\(974\) 15.7757i 0.505487i
\(975\) 0 0
\(976\) −11.2861 6.51605i −0.361260 0.208574i
\(977\) 4.82812 + 18.0188i 0.154465 + 0.576472i 0.999151 + 0.0412088i \(0.0131209\pi\)
−0.844685 + 0.535263i \(0.820212\pi\)
\(978\) 0 0
\(979\) −14.4465 −0.461713
\(980\) 27.6757 + 7.57731i 0.884067 + 0.242048i
\(981\) 0 0
\(982\) 9.96622 + 2.67044i 0.318035 + 0.0852172i
\(983\) −0.300042 1.11977i −0.00956985 0.0357152i 0.960976 0.276632i \(-0.0892184\pi\)
−0.970546 + 0.240917i \(0.922552\pi\)
\(984\) 0 0
\(985\) 16.0225 10.4925i 0.510519 0.334319i
\(986\) 2.45898i 0.0783098i
\(987\) 0 0
\(988\) 18.2525 + 18.2525i 0.580688 + 0.580688i
\(989\) 4.96242 2.86505i 0.157796 0.0911034i
\(990\) 0 0
\(991\) −6.38011 + 11.0507i −0.202671 + 0.351036i −0.949388 0.314105i \(-0.898295\pi\)
0.746717 + 0.665142i \(0.231629\pi\)
\(992\) 1.37409 5.12816i 0.0436273 0.162819i
\(993\) 0 0
\(994\) −0.329562 + 10.6921i −0.0104531 + 0.339134i
\(995\) −16.7262 + 18.7198i −0.530255 + 0.593457i
\(996\) 0 0
\(997\) −3.01416 + 0.807643i −0.0954595 + 0.0255783i −0.306233 0.951957i \(-0.599069\pi\)
0.210773 + 0.977535i \(0.432402\pi\)
\(998\) 1.23606 0.331203i 0.0391269 0.0104840i
\(999\) 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.bz.d.73.5 32
3.2 odd 2 105.2.u.a.73.4 yes 32
5.2 odd 4 inner 315.2.bz.d.262.4 32
7.5 odd 6 inner 315.2.bz.d.208.4 32
15.2 even 4 105.2.u.a.52.5 32
15.8 even 4 525.2.bc.e.157.4 32
15.14 odd 2 525.2.bc.e.493.5 32
21.2 odd 6 735.2.v.b.313.5 32
21.5 even 6 105.2.u.a.103.5 yes 32
21.11 odd 6 735.2.m.c.538.9 32
21.17 even 6 735.2.m.c.538.10 32
21.20 even 2 735.2.v.b.178.4 32
35.12 even 12 inner 315.2.bz.d.82.5 32
105.2 even 12 735.2.v.b.607.4 32
105.17 odd 12 735.2.m.c.97.9 32
105.32 even 12 735.2.m.c.97.10 32
105.47 odd 12 105.2.u.a.82.4 yes 32
105.62 odd 4 735.2.v.b.472.5 32
105.68 odd 12 525.2.bc.e.82.5 32
105.89 even 6 525.2.bc.e.418.4 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.u.a.52.5 32 15.2 even 4
105.2.u.a.73.4 yes 32 3.2 odd 2
105.2.u.a.82.4 yes 32 105.47 odd 12
105.2.u.a.103.5 yes 32 21.5 even 6
315.2.bz.d.73.5 32 1.1 even 1 trivial
315.2.bz.d.82.5 32 35.12 even 12 inner
315.2.bz.d.208.4 32 7.5 odd 6 inner
315.2.bz.d.262.4 32 5.2 odd 4 inner
525.2.bc.e.82.5 32 105.68 odd 12
525.2.bc.e.157.4 32 15.8 even 4
525.2.bc.e.418.4 32 105.89 even 6
525.2.bc.e.493.5 32 15.14 odd 2
735.2.m.c.97.9 32 105.17 odd 12
735.2.m.c.97.10 32 105.32 even 12
735.2.m.c.538.9 32 21.11 odd 6
735.2.m.c.538.10 32 21.17 even 6
735.2.v.b.178.4 32 21.20 even 2
735.2.v.b.313.5 32 21.2 odd 6
735.2.v.b.472.5 32 105.62 odd 4
735.2.v.b.607.4 32 105.2 even 12