Properties

Label 315.2.bo.b.4.13
Level $315$
Weight $2$
Character 315.4
Analytic conductor $2.515$
Analytic rank $0$
Dimension $84$
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(4,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bo (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(84\)
Relative dimension: \(42\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 4.13
Character \(\chi\) \(=\) 315.4
Dual form 315.2.bo.b.79.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.17913 - 0.680771i) q^{2} +(0.973105 + 1.43285i) q^{3} +(-0.0731024 - 0.126617i) q^{4} +(-2.23088 - 0.152304i) q^{5} +(-0.171973 - 2.35198i) q^{6} +(2.52908 - 0.777026i) q^{7} +2.92215i q^{8} +(-1.10613 + 2.78863i) q^{9} +O(q^{10})\) \(q+(-1.17913 - 0.680771i) q^{2} +(0.973105 + 1.43285i) q^{3} +(-0.0731024 - 0.126617i) q^{4} +(-2.23088 - 0.152304i) q^{5} +(-0.171973 - 2.35198i) q^{6} +(2.52908 - 0.777026i) q^{7} +2.92215i q^{8} +(-1.10613 + 2.78863i) q^{9} +(2.52681 + 1.69830i) q^{10} +0.621221 q^{11} +(0.110287 - 0.227957i) q^{12} +(2.17808 + 1.25751i) q^{13} +(-3.51109 - 0.805508i) q^{14} +(-1.95265 - 3.34472i) q^{15} +(1.84311 - 3.19236i) q^{16} +(5.28156 + 3.04931i) q^{17} +(3.20269 - 2.53513i) q^{18} +(-0.100966 - 0.174878i) q^{19} +(0.143798 + 0.293601i) q^{20} +(3.57442 + 2.86767i) q^{21} +(-0.732500 - 0.422909i) q^{22} +4.00481i q^{23} +(-4.18701 + 2.84356i) q^{24} +(4.95361 + 0.679544i) q^{25} +(-1.71216 - 2.96554i) q^{26} +(-5.07208 + 1.12870i) q^{27} +(-0.283266 - 0.263422i) q^{28} +(-0.297732 - 0.515687i) q^{29} +(0.0254323 + 5.27317i) q^{30} +(3.51551 + 6.08904i) q^{31} +(0.714782 - 0.412680i) q^{32} +(0.604514 + 0.890119i) q^{33} +(-4.15176 - 7.19106i) q^{34} +(-5.76040 + 1.34826i) q^{35} +(0.433949 - 0.0638003i) q^{36} +(-5.67340 + 3.27554i) q^{37} +0.274938i q^{38} +(0.317666 + 4.34456i) q^{39} +(0.445056 - 6.51894i) q^{40} +(1.68428 - 2.91726i) q^{41} +(-2.26248 - 5.81471i) q^{42} +(7.13977 - 4.12215i) q^{43} +(-0.0454127 - 0.0786572i) q^{44} +(2.89237 - 6.05262i) q^{45} +(2.72636 - 4.72219i) q^{46} +(1.33585 + 0.771254i) q^{47} +(6.36771 - 0.465596i) q^{48} +(5.79246 - 3.93032i) q^{49} +(-5.37833 - 4.17354i) q^{50} +(0.770300 + 10.5350i) q^{51} -0.367709i q^{52} +(-2.16836 - 1.25190i) q^{53} +(6.74903 + 2.12204i) q^{54} +(-1.38587 - 0.0946147i) q^{55} +(2.27058 + 7.39033i) q^{56} +(0.152324 - 0.314844i) q^{57} +0.810750i q^{58} +(-6.88298 - 11.9217i) q^{59} +(-0.280756 + 0.491745i) q^{60} +(3.33132 - 5.77001i) q^{61} -9.57302i q^{62} +(-0.630658 + 7.91216i) q^{63} -8.49619 q^{64} +(-4.66750 - 3.13709i) q^{65} +(-0.106833 - 1.46110i) q^{66} +(-11.1570 + 6.44148i) q^{67} -0.891647i q^{68} +(-5.73830 + 3.89710i) q^{69} +(7.71011 + 2.33174i) q^{70} -8.76528 q^{71} +(-8.14879 - 3.23228i) q^{72} +(1.02561 + 0.592135i) q^{73} +8.91957 q^{74} +(3.84669 + 7.75906i) q^{75} +(-0.0147617 + 0.0255680i) q^{76} +(1.57112 - 0.482705i) q^{77} +(2.58308 - 5.33905i) q^{78} +(-7.80418 + 13.5172i) q^{79} +(-4.59795 + 6.84103i) q^{80} +(-6.55294 - 6.16920i) q^{81} +(-3.97197 + 2.29322i) q^{82} +(7.36846 - 4.25418i) q^{83} +(0.101797 - 0.662216i) q^{84} +(-11.3181 - 7.60704i) q^{85} -11.2250 q^{86} +(0.449179 - 0.928424i) q^{87} +1.81530i q^{88} +(-1.99854 - 3.46158i) q^{89} +(-7.53092 + 5.16778i) q^{90} +(6.48565 + 1.48793i) q^{91} +(0.507077 - 0.292761i) q^{92} +(-5.30374 + 10.9625i) q^{93} +(-1.05009 - 1.81882i) q^{94} +(0.198607 + 0.405508i) q^{95} +(1.28687 + 0.622597i) q^{96} +(-0.922012 + 0.532324i) q^{97} +(-9.50571 + 0.691014i) q^{98} +(-0.687154 + 1.73236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9} + 6 q^{10} - 24 q^{11} - 10 q^{14} + 4 q^{15} - 36 q^{16} + 8 q^{19} - 10 q^{20} - 14 q^{21} + 18 q^{24} + 10 q^{25} - 40 q^{26} - 10 q^{29} - 28 q^{30} - 6 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} + 4 q^{39} - 8 q^{40} - 30 q^{41} - 4 q^{44} - 30 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} + 14 q^{51} + 18 q^{54} - 54 q^{55} + 48 q^{56} + 42 q^{59} + 66 q^{60} + 22 q^{61} - 28 q^{64} + 8 q^{65} - 38 q^{66} - 32 q^{69} - 26 q^{70} - 4 q^{71} - 108 q^{74} + 6 q^{75} + 24 q^{76} + 24 q^{79} - 9 q^{80} - 106 q^{81} - 64 q^{84} + q^{85} - 92 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} - 8 q^{94} - 25 q^{95} + 54 q^{96} - 102 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.17913 0.680771i −0.833770 0.481378i 0.0213714 0.999772i \(-0.493197\pi\)
−0.855142 + 0.518394i \(0.826530\pi\)
\(3\) 0.973105 + 1.43285i 0.561822 + 0.827258i
\(4\) −0.0731024 0.126617i −0.0365512 0.0633085i
\(5\) −2.23088 0.152304i −0.997678 0.0681126i
\(6\) −0.171973 2.35198i −0.0702075 0.960192i
\(7\) 2.52908 0.777026i 0.955901 0.293688i
\(8\) 2.92215i 1.03313i
\(9\) −1.10613 + 2.78863i −0.368711 + 0.929544i
\(10\) 2.52681 + 1.69830i 0.799046 + 0.537050i
\(11\) 0.621221 0.187305 0.0936526 0.995605i \(-0.470146\pi\)
0.0936526 + 0.995605i \(0.470146\pi\)
\(12\) 0.110287 0.227957i 0.0318372 0.0658054i
\(13\) 2.17808 + 1.25751i 0.604090 + 0.348772i 0.770649 0.637260i \(-0.219932\pi\)
−0.166559 + 0.986032i \(0.553266\pi\)
\(14\) −3.51109 0.805508i −0.938377 0.215281i
\(15\) −1.95265 3.34472i −0.504171 0.863604i
\(16\) 1.84311 3.19236i 0.460777 0.798089i
\(17\) 5.28156 + 3.04931i 1.28097 + 0.739566i 0.977025 0.213124i \(-0.0683639\pi\)
0.303942 + 0.952691i \(0.401697\pi\)
\(18\) 3.20269 2.53513i 0.754882 0.597537i
\(19\) −0.100966 0.174878i −0.0231631 0.0401198i 0.854211 0.519926i \(-0.174040\pi\)
−0.877375 + 0.479806i \(0.840707\pi\)
\(20\) 0.143798 + 0.293601i 0.0321542 + 0.0656511i
\(21\) 3.57442 + 2.86767i 0.780003 + 0.625776i
\(22\) −0.732500 0.422909i −0.156170 0.0901646i
\(23\) 4.00481i 0.835060i 0.908663 + 0.417530i \(0.137104\pi\)
−0.908663 + 0.417530i \(0.862896\pi\)
\(24\) −4.18701 + 2.84356i −0.854669 + 0.580438i
\(25\) 4.95361 + 0.679544i 0.990721 + 0.135909i
\(26\) −1.71216 2.96554i −0.335782 0.581591i
\(27\) −5.07208 + 1.12870i −0.976123 + 0.217219i
\(28\) −0.283266 0.263422i −0.0535323 0.0497820i
\(29\) −0.297732 0.515687i −0.0552875 0.0957607i 0.837057 0.547116i \(-0.184274\pi\)
−0.892345 + 0.451355i \(0.850941\pi\)
\(30\) 0.0254323 + 5.27317i 0.00464327 + 0.962744i
\(31\) 3.51551 + 6.08904i 0.631404 + 1.09362i 0.987265 + 0.159085i \(0.0508543\pi\)
−0.355861 + 0.934539i \(0.615812\pi\)
\(32\) 0.714782 0.412680i 0.126357 0.0729521i
\(33\) 0.604514 + 0.890119i 0.105232 + 0.154950i
\(34\) −4.15176 7.19106i −0.712021 1.23326i
\(35\) −5.76040 + 1.34826i −0.973685 + 0.227897i
\(36\) 0.433949 0.0638003i 0.0723249 0.0106334i
\(37\) −5.67340 + 3.27554i −0.932702 + 0.538496i −0.887665 0.460490i \(-0.847674\pi\)
−0.0450367 + 0.998985i \(0.514340\pi\)
\(38\) 0.274938i 0.0446009i
\(39\) 0.317666 + 4.34456i 0.0508673 + 0.695686i
\(40\) 0.445056 6.51894i 0.0703695 1.03074i
\(41\) 1.68428 2.91726i 0.263040 0.455599i −0.704008 0.710192i \(-0.748608\pi\)
0.967048 + 0.254593i \(0.0819414\pi\)
\(42\) −2.26248 5.81471i −0.349108 0.897230i
\(43\) 7.13977 4.12215i 1.08880 0.628622i 0.155547 0.987829i \(-0.450286\pi\)
0.933258 + 0.359207i \(0.116953\pi\)
\(44\) −0.0454127 0.0786572i −0.00684623 0.0118580i
\(45\) 2.89237 6.05262i 0.431169 0.902271i
\(46\) 2.72636 4.72219i 0.401979 0.696249i
\(47\) 1.33585 + 0.771254i 0.194854 + 0.112499i 0.594253 0.804278i \(-0.297448\pi\)
−0.399399 + 0.916777i \(0.630781\pi\)
\(48\) 6.36771 0.465596i 0.919100 0.0672029i
\(49\) 5.79246 3.93032i 0.827495 0.561474i
\(50\) −5.37833 4.17354i −0.760611 0.590228i
\(51\) 0.770300 + 10.5350i 0.107864 + 1.47519i
\(52\) 0.367709i 0.0509921i
\(53\) −2.16836 1.25190i −0.297847 0.171962i 0.343628 0.939106i \(-0.388344\pi\)
−0.641475 + 0.767144i \(0.721677\pi\)
\(54\) 6.74903 + 2.12204i 0.918427 + 0.288773i
\(55\) −1.38587 0.0946147i −0.186870 0.0127578i
\(56\) 2.27058 + 7.39033i 0.303419 + 0.987575i
\(57\) 0.152324 0.314844i 0.0201758 0.0417021i
\(58\) 0.810750i 0.106457i
\(59\) −6.88298 11.9217i −0.896087 1.55207i −0.832453 0.554096i \(-0.813064\pi\)
−0.0636344 0.997973i \(-0.520269\pi\)
\(60\) −0.280756 + 0.491745i −0.0362454 + 0.0634841i
\(61\) 3.33132 5.77001i 0.426531 0.738774i −0.570031 0.821623i \(-0.693069\pi\)
0.996562 + 0.0828495i \(0.0264021\pi\)
\(62\) 9.57302i 1.21577i
\(63\) −0.630658 + 7.91216i −0.0794555 + 0.996838i
\(64\) −8.49619 −1.06202
\(65\) −4.66750 3.13709i −0.578932 0.389108i
\(66\) −0.106833 1.46110i −0.0131502 0.179849i
\(67\) −11.1570 + 6.44148i −1.36304 + 0.786952i −0.990028 0.140873i \(-0.955009\pi\)
−0.373014 + 0.927826i \(0.621676\pi\)
\(68\) 0.891647i 0.108128i
\(69\) −5.73830 + 3.89710i −0.690810 + 0.469156i
\(70\) 7.71011 + 2.33174i 0.921535 + 0.278696i
\(71\) −8.76528 −1.04025 −0.520124 0.854091i \(-0.674114\pi\)
−0.520124 + 0.854091i \(0.674114\pi\)
\(72\) −8.14879 3.23228i −0.960344 0.380928i
\(73\) 1.02561 + 0.592135i 0.120038 + 0.0693042i 0.558817 0.829291i \(-0.311255\pi\)
−0.438779 + 0.898595i \(0.644589\pi\)
\(74\) 8.91957 1.03688
\(75\) 3.84669 + 7.75906i 0.444178 + 0.895939i
\(76\) −0.0147617 + 0.0255680i −0.00169328 + 0.00293285i
\(77\) 1.57112 0.482705i 0.179045 0.0550093i
\(78\) 2.58308 5.33905i 0.292476 0.604529i
\(79\) −7.80418 + 13.5172i −0.878039 + 1.52081i −0.0245499 + 0.999699i \(0.507815\pi\)
−0.853489 + 0.521110i \(0.825518\pi\)
\(80\) −4.59795 + 6.84103i −0.514067 + 0.764851i
\(81\) −6.55294 6.16920i −0.728104 0.685467i
\(82\) −3.97197 + 2.29322i −0.438630 + 0.253243i
\(83\) 7.36846 4.25418i 0.808793 0.466957i −0.0377433 0.999287i \(-0.512017\pi\)
0.846537 + 0.532330i \(0.178684\pi\)
\(84\) 0.101797 0.662216i 0.0111069 0.0722537i
\(85\) −11.3181 7.60704i −1.22762 0.825099i
\(86\) −11.2250 −1.21042
\(87\) 0.449179 0.928424i 0.0481571 0.0995375i
\(88\) 1.81530i 0.193512i
\(89\) −1.99854 3.46158i −0.211845 0.366927i 0.740447 0.672115i \(-0.234614\pi\)
−0.952292 + 0.305188i \(0.901281\pi\)
\(90\) −7.53092 + 5.16778i −0.793829 + 0.544732i
\(91\) 6.48565 + 1.48793i 0.679881 + 0.155977i
\(92\) 0.507077 0.292761i 0.0528664 0.0305224i
\(93\) −5.30374 + 10.9625i −0.549972 + 1.13676i
\(94\) −1.05009 1.81882i −0.108309 0.187597i
\(95\) 0.198607 + 0.405508i 0.0203767 + 0.0416043i
\(96\) 1.28687 + 0.622597i 0.131340 + 0.0635435i
\(97\) −0.922012 + 0.532324i −0.0936162 + 0.0540493i −0.546077 0.837735i \(-0.683879\pi\)
0.452461 + 0.891784i \(0.350546\pi\)
\(98\) −9.50571 + 0.691014i −0.960221 + 0.0698029i
\(99\) −0.687154 + 1.73236i −0.0690616 + 0.174108i
\(100\) −0.276079 0.676887i −0.0276079 0.0676887i
\(101\) −10.9221 −1.08679 −0.543394 0.839478i \(-0.682861\pi\)
−0.543394 + 0.839478i \(0.682861\pi\)
\(102\) 6.26363 12.9465i 0.620192 1.28190i
\(103\) 11.3226i 1.11565i −0.829959 0.557824i \(-0.811636\pi\)
0.829959 0.557824i \(-0.188364\pi\)
\(104\) −3.67464 + 6.36466i −0.360328 + 0.624107i
\(105\) −7.53733 6.94181i −0.735568 0.677451i
\(106\) 1.70452 + 2.95231i 0.165557 + 0.286754i
\(107\) 14.3799 8.30225i 1.39016 0.802609i 0.396827 0.917893i \(-0.370111\pi\)
0.993333 + 0.115284i \(0.0367780\pi\)
\(108\) 0.513695 + 0.559701i 0.0494303 + 0.0538573i
\(109\) 2.59019 4.48634i 0.248095 0.429713i −0.714902 0.699224i \(-0.753529\pi\)
0.962997 + 0.269511i \(0.0868622\pi\)
\(110\) 1.56971 + 1.05502i 0.149666 + 0.100592i
\(111\) −10.2142 4.94171i −0.969487 0.469046i
\(112\) 2.18082 9.50586i 0.206068 0.898219i
\(113\) 5.18922 + 2.99600i 0.488160 + 0.281840i 0.723811 0.689998i \(-0.242389\pi\)
−0.235651 + 0.971838i \(0.575722\pi\)
\(114\) −0.393946 + 0.267544i −0.0368964 + 0.0250578i
\(115\) 0.609950 8.93423i 0.0568781 0.833121i
\(116\) −0.0435299 + 0.0753959i −0.00404165 + 0.00700034i
\(117\) −5.91599 + 4.68288i −0.546933 + 0.432932i
\(118\) 18.7429i 1.72543i
\(119\) 15.7269 + 3.60803i 1.44168 + 0.330748i
\(120\) 9.77377 5.70592i 0.892219 0.520877i
\(121\) −10.6141 −0.964917
\(122\) −7.85611 + 4.53572i −0.711258 + 0.410645i
\(123\) 5.81898 0.425473i 0.524680 0.0383636i
\(124\) 0.513984 0.890246i 0.0461571 0.0799465i
\(125\) −10.9474 2.27043i −0.979163 0.203074i
\(126\) 6.12999 8.90013i 0.546103 0.792886i
\(127\) 6.32526i 0.561276i 0.959814 + 0.280638i \(0.0905460\pi\)
−0.959814 + 0.280638i \(0.909454\pi\)
\(128\) 8.58854 + 4.95860i 0.759127 + 0.438282i
\(129\) 12.8542 + 6.21896i 1.13175 + 0.547549i
\(130\) 3.36794 + 6.87653i 0.295388 + 0.603111i
\(131\) 17.5276 1.53139 0.765695 0.643204i \(-0.222395\pi\)
0.765695 + 0.643204i \(0.222395\pi\)
\(132\) 0.0685128 0.141611i 0.00596327 0.0123257i
\(133\) −0.391235 0.363827i −0.0339244 0.0315478i
\(134\) 17.5407 1.51529
\(135\) 11.4871 1.74550i 0.988651 0.150229i
\(136\) −8.91053 + 15.4335i −0.764072 + 1.32341i
\(137\) 14.0633i 1.20151i 0.799433 + 0.600755i \(0.205133\pi\)
−0.799433 + 0.600755i \(0.794867\pi\)
\(138\) 9.41923 0.688717i 0.801818 0.0586275i
\(139\) 6.68525 11.5792i 0.567036 0.982135i −0.429821 0.902914i \(-0.641423\pi\)
0.996857 0.0792208i \(-0.0252432\pi\)
\(140\) 0.591811 + 0.630804i 0.0500172 + 0.0533126i
\(141\) 0.194830 + 2.66459i 0.0164076 + 0.224399i
\(142\) 10.3354 + 5.96715i 0.867328 + 0.500752i
\(143\) 1.35307 + 0.781194i 0.113149 + 0.0653268i
\(144\) 6.86358 + 8.67092i 0.571965 + 0.722577i
\(145\) 0.585662 + 1.19578i 0.0486366 + 0.0993041i
\(146\) −0.806216 1.39641i −0.0667229 0.115568i
\(147\) 11.2682 + 4.47513i 0.929389 + 0.369103i
\(148\) 0.829478 + 0.478900i 0.0681827 + 0.0393653i
\(149\) 20.9587 1.71700 0.858502 0.512810i \(-0.171396\pi\)
0.858502 + 0.512810i \(0.171396\pi\)
\(150\) 0.746390 11.7676i 0.0609425 0.960824i
\(151\) −5.24141 −0.426540 −0.213270 0.976993i \(-0.568411\pi\)
−0.213270 + 0.976993i \(0.568411\pi\)
\(152\) 0.511019 0.295037i 0.0414491 0.0239307i
\(153\) −14.3455 + 11.3554i −1.15977 + 0.918028i
\(154\) −2.18116 0.500398i −0.175763 0.0403233i
\(155\) −6.91527 14.1193i −0.555448 1.13409i
\(156\) 0.526873 0.357819i 0.0421836 0.0286485i
\(157\) −8.49494 + 4.90456i −0.677970 + 0.391426i −0.799090 0.601212i \(-0.794685\pi\)
0.121120 + 0.992638i \(0.461352\pi\)
\(158\) 18.4043 10.6257i 1.46417 0.845337i
\(159\) −0.316248 4.32517i −0.0250801 0.343008i
\(160\) −1.65744 + 0.811772i −0.131032 + 0.0641762i
\(161\) 3.11184 + 10.1285i 0.245247 + 0.798235i
\(162\) 3.52695 + 11.7353i 0.277103 + 0.922015i
\(163\) −1.19707 + 0.691129i −0.0937618 + 0.0541334i −0.546148 0.837689i \(-0.683906\pi\)
0.452386 + 0.891822i \(0.350573\pi\)
\(164\) −0.492499 −0.0384577
\(165\) −1.21303 2.07781i −0.0944339 0.161758i
\(166\) −11.5845 −0.899131
\(167\) −5.10891 2.94963i −0.395339 0.228249i 0.289132 0.957289i \(-0.406633\pi\)
−0.684471 + 0.729040i \(0.739967\pi\)
\(168\) −8.37974 + 10.4450i −0.646511 + 0.805848i
\(169\) −3.33732 5.78040i −0.256717 0.444646i
\(170\) 8.16683 + 16.6747i 0.626368 + 1.27889i
\(171\) 0.599352 0.0881182i 0.0458336 0.00673856i
\(172\) −1.04387 0.602678i −0.0795942 0.0459537i
\(173\) −15.8285 9.13861i −1.20342 0.694796i −0.242107 0.970250i \(-0.577839\pi\)
−0.961314 + 0.275454i \(0.911172\pi\)
\(174\) −1.16168 + 0.788944i −0.0880671 + 0.0598097i
\(175\) 13.0561 2.13046i 0.986947 0.161048i
\(176\) 1.14498 1.98316i 0.0863059 0.149486i
\(177\) 10.3841 21.4633i 0.780519 1.61328i
\(178\) 5.44220i 0.407910i
\(179\) 9.23806 16.0008i 0.690485 1.19596i −0.281194 0.959651i \(-0.590730\pi\)
0.971679 0.236305i \(-0.0759363\pi\)
\(180\) −0.977804 + 0.0762380i −0.0728812 + 0.00568245i
\(181\) 20.4831 1.52250 0.761248 0.648461i \(-0.224587\pi\)
0.761248 + 0.648461i \(0.224587\pi\)
\(182\) −6.63448 6.16970i −0.491781 0.457328i
\(183\) 11.5093 0.841539i 0.850791 0.0622083i
\(184\) −11.7026 −0.862730
\(185\) 13.1555 6.44324i 0.967214 0.473716i
\(186\) 13.7167 9.31555i 1.00576 0.683049i
\(187\) 3.28102 + 1.89430i 0.239932 + 0.138525i
\(188\) 0.225522i 0.0164479i
\(189\) −11.9507 + 6.79572i −0.869282 + 0.494316i
\(190\) 0.0418743 0.613353i 0.00303788 0.0444973i
\(191\) 2.91632 5.05121i 0.211017 0.365493i −0.741016 0.671488i \(-0.765656\pi\)
0.952033 + 0.305995i \(0.0989890\pi\)
\(192\) −8.26768 12.1738i −0.596669 0.878568i
\(193\) −6.27202 + 3.62115i −0.451470 + 0.260656i −0.708451 0.705760i \(-0.750606\pi\)
0.256981 + 0.966416i \(0.417272\pi\)
\(194\) 1.44956 0.104073
\(195\) −0.0469783 9.74055i −0.00336418 0.697535i
\(196\) −0.921088 0.446109i −0.0657920 0.0318649i
\(197\) 15.2073i 1.08348i 0.840547 + 0.541739i \(0.182234\pi\)
−0.840547 + 0.541739i \(0.817766\pi\)
\(198\) 1.98958 1.57488i 0.141393 0.111922i
\(199\) −0.772275 + 1.33762i −0.0547451 + 0.0948213i −0.892099 0.451840i \(-0.850768\pi\)
0.837354 + 0.546661i \(0.184101\pi\)
\(200\) −1.98573 + 14.4752i −0.140412 + 1.02355i
\(201\) −20.0866 9.71806i −1.41680 0.685459i
\(202\) 12.8786 + 7.43544i 0.906132 + 0.523155i
\(203\) −1.15369 1.07287i −0.0809732 0.0753005i
\(204\) 1.27760 0.867666i 0.0894498 0.0607488i
\(205\) −4.20173 + 6.25151i −0.293461 + 0.436625i
\(206\) −7.70809 + 13.3508i −0.537048 + 0.930194i
\(207\) −11.1679 4.42985i −0.776225 0.307896i
\(208\) 8.02886 4.63547i 0.556702 0.321412i
\(209\) −0.0627221 0.108638i −0.00433858 0.00751464i
\(210\) 4.16171 + 13.3165i 0.287185 + 0.918925i
\(211\) −8.98538 + 15.5631i −0.618579 + 1.07141i 0.371166 + 0.928566i \(0.378958\pi\)
−0.989745 + 0.142844i \(0.954375\pi\)
\(212\) 0.366068i 0.0251416i
\(213\) −8.52954 12.5594i −0.584434 0.860553i
\(214\) −22.6077 −1.54543
\(215\) −16.5558 + 8.10858i −1.12909 + 0.553000i
\(216\) −3.29824 14.8214i −0.224417 1.00847i
\(217\) 13.6223 + 12.6680i 0.924744 + 0.859960i
\(218\) −6.10833 + 3.52665i −0.413709 + 0.238855i
\(219\) 0.149582 + 2.04575i 0.0101078 + 0.138239i
\(220\) 0.0893303 + 0.182391i 0.00602265 + 0.0122968i
\(221\) 7.66910 + 13.2833i 0.515880 + 0.893530i
\(222\) 8.67968 + 12.7804i 0.582542 + 0.857766i
\(223\) 24.1381 13.9362i 1.61641 0.933235i 0.628571 0.777752i \(-0.283640\pi\)
0.987839 0.155483i \(-0.0496934\pi\)
\(224\) 1.48708 1.59910i 0.0993595 0.106845i
\(225\) −7.37435 + 13.0621i −0.491623 + 0.870808i
\(226\) −4.07917 7.06533i −0.271342 0.469979i
\(227\) 12.4868i 0.828778i −0.910100 0.414389i \(-0.863995\pi\)
0.910100 0.414389i \(-0.136005\pi\)
\(228\) −0.0509998 + 0.00372901i −0.00337755 + 0.000246960i
\(229\) −16.5328 −1.09252 −0.546258 0.837617i \(-0.683948\pi\)
−0.546258 + 0.837617i \(0.683948\pi\)
\(230\) −6.80137 + 10.1194i −0.448469 + 0.667252i
\(231\) 2.22051 + 1.78146i 0.146099 + 0.117211i
\(232\) 1.50691 0.870017i 0.0989338 0.0571194i
\(233\) 10.0137 5.78138i 0.656016 0.378751i −0.134741 0.990881i \(-0.543020\pi\)
0.790757 + 0.612130i \(0.209687\pi\)
\(234\) 10.1637 1.49429i 0.664421 0.0976848i
\(235\) −2.86265 1.92403i −0.186739 0.125510i
\(236\) −1.00632 + 1.74300i −0.0655061 + 0.113460i
\(237\) −26.9625 + 1.97145i −1.75140 + 0.128059i
\(238\) −16.0878 14.9607i −1.04282 0.969760i
\(239\) −3.97892 + 6.89170i −0.257375 + 0.445787i −0.965538 0.260262i \(-0.916191\pi\)
0.708163 + 0.706049i \(0.249524\pi\)
\(240\) −14.2765 + 0.0688549i −0.921543 + 0.00444456i
\(241\) 1.61227 0.103855 0.0519277 0.998651i \(-0.483463\pi\)
0.0519277 + 0.998651i \(0.483463\pi\)
\(242\) 12.5154 + 7.22576i 0.804519 + 0.464489i
\(243\) 2.46286 15.3927i 0.157992 0.987440i
\(244\) −0.974108 −0.0623609
\(245\) −13.5209 + 7.88583i −0.863816 + 0.503807i
\(246\) −7.15098 3.45970i −0.455930 0.220583i
\(247\) 0.507864i 0.0323146i
\(248\) −17.7931 + 10.2728i −1.12986 + 0.652325i
\(249\) 13.2659 + 6.41815i 0.840692 + 0.406734i
\(250\) 11.3627 + 10.1298i 0.718642 + 0.640664i
\(251\) 14.8246 0.935719 0.467860 0.883803i \(-0.345025\pi\)
0.467860 + 0.883803i \(0.345025\pi\)
\(252\) 1.04792 0.498546i 0.0660125 0.0314054i
\(253\) 2.48787i 0.156411i
\(254\) 4.30605 7.45830i 0.270186 0.467975i
\(255\) −0.113916 23.6196i −0.00713371 1.47912i
\(256\) 1.74485 + 3.02217i 0.109053 + 0.188886i
\(257\) 22.5121i 1.40427i 0.712045 + 0.702133i \(0.247769\pi\)
−0.712045 + 0.702133i \(0.752231\pi\)
\(258\) −10.9231 16.0837i −0.680040 1.00133i
\(259\) −11.8033 + 12.6925i −0.733421 + 0.788672i
\(260\) −0.0560037 + 0.820313i −0.00347320 + 0.0508736i
\(261\) 1.76739 0.259847i 0.109399 0.0160841i
\(262\) −20.6673 11.9322i −1.27683 0.737177i
\(263\) 12.9951i 0.801312i 0.916229 + 0.400656i \(0.131218\pi\)
−0.916229 + 0.400656i \(0.868782\pi\)
\(264\) −2.60106 + 1.76648i −0.160084 + 0.108719i
\(265\) 4.64666 + 3.12309i 0.285442 + 0.191850i
\(266\) 0.213634 + 0.695340i 0.0130988 + 0.0426340i
\(267\) 3.01514 6.23210i 0.184524 0.381398i
\(268\) 1.63120 + 0.941775i 0.0996416 + 0.0575281i
\(269\) 3.97205 6.87979i 0.242180 0.419468i −0.719155 0.694850i \(-0.755471\pi\)
0.961335 + 0.275382i \(0.0888042\pi\)
\(270\) −14.7331 5.76191i −0.896625 0.350658i
\(271\) 2.85337 + 4.94217i 0.173330 + 0.300216i 0.939582 0.342324i \(-0.111214\pi\)
−0.766252 + 0.642540i \(0.777881\pi\)
\(272\) 19.4690 11.2404i 1.18048 0.681550i
\(273\) 4.17924 + 10.7409i 0.252939 + 0.650068i
\(274\) 9.57389 16.5825i 0.578380 1.00178i
\(275\) 3.07729 + 0.422147i 0.185567 + 0.0254564i
\(276\) 0.912922 + 0.441679i 0.0549515 + 0.0265860i
\(277\) 12.3722i 0.743371i −0.928359 0.371686i \(-0.878780\pi\)
0.928359 0.371686i \(-0.121220\pi\)
\(278\) −15.7656 + 9.10225i −0.945555 + 0.545917i
\(279\) −20.8687 + 3.06817i −1.24938 + 0.183686i
\(280\) −3.93981 16.8327i −0.235449 1.00595i
\(281\) −9.64532 16.7062i −0.575391 0.996607i −0.995999 0.0893643i \(-0.971516\pi\)
0.420608 0.907243i \(-0.361817\pi\)
\(282\) 1.58424 3.27453i 0.0943403 0.194995i
\(283\) −4.02201 + 2.32211i −0.239083 + 0.138035i −0.614755 0.788718i \(-0.710745\pi\)
0.375672 + 0.926753i \(0.377412\pi\)
\(284\) 0.640763 + 1.10983i 0.0380223 + 0.0658565i
\(285\) −0.387768 + 0.679177i −0.0229694 + 0.0402310i
\(286\) −1.06363 1.84226i −0.0628937 0.108935i
\(287\) 1.99289 8.68670i 0.117636 0.512760i
\(288\) 0.360167 + 2.44974i 0.0212231 + 0.144352i
\(289\) 10.0966 + 17.4878i 0.593917 + 1.02869i
\(290\) 0.123481 1.80868i 0.00725104 0.106209i
\(291\) −1.65996 0.803101i −0.0973084 0.0470786i
\(292\) 0.173146i 0.0101326i
\(293\) −26.2767 15.1708i −1.53510 0.886289i −0.999115 0.0420610i \(-0.986608\pi\)
−0.535983 0.844229i \(-0.680059\pi\)
\(294\) −10.2402 12.9478i −0.597219 0.755134i
\(295\) 13.5393 + 27.6441i 0.788291 + 1.60950i
\(296\) −9.57161 16.5785i −0.556339 0.963607i
\(297\) −3.15089 + 0.701176i −0.182833 + 0.0406863i
\(298\) −24.7130 14.2681i −1.43159 0.826527i
\(299\) −5.03610 + 8.72279i −0.291245 + 0.504452i
\(300\) 0.701226 1.05426i 0.0404853 0.0608678i
\(301\) 14.8540 15.9730i 0.856171 0.920669i
\(302\) 6.18030 + 3.56820i 0.355636 + 0.205327i
\(303\) −10.6283 15.6497i −0.610582 0.899054i
\(304\) −0.744363 −0.0426922
\(305\) −8.31055 + 12.3648i −0.475861 + 0.708006i
\(306\) 24.6456 3.62346i 1.40890 0.207139i
\(307\) 5.12962i 0.292763i 0.989228 + 0.146381i \(0.0467627\pi\)
−0.989228 + 0.146381i \(0.953237\pi\)
\(308\) −0.175971 0.163643i −0.0100269 0.00932444i
\(309\) 16.2236 11.0181i 0.922928 0.626796i
\(310\) −1.45801 + 21.3562i −0.0828096 + 1.21295i
\(311\) 4.14014 + 7.17094i 0.234766 + 0.406627i 0.959205 0.282713i \(-0.0912343\pi\)
−0.724439 + 0.689339i \(0.757901\pi\)
\(312\) −12.6954 + 0.928267i −0.718738 + 0.0525528i
\(313\) −17.5702 10.1441i −0.993125 0.573381i −0.0869183 0.996215i \(-0.527702\pi\)
−0.906207 + 0.422834i \(0.861035\pi\)
\(314\) 13.3555 0.753695
\(315\) 2.61198 17.5550i 0.147168 0.989111i
\(316\) 2.28202 0.128374
\(317\) −20.5664 11.8740i −1.15512 0.666911i −0.204993 0.978764i \(-0.565717\pi\)
−0.950130 + 0.311853i \(0.899050\pi\)
\(318\) −2.57155 + 5.31523i −0.144205 + 0.298063i
\(319\) −0.184958 0.320356i −0.0103556 0.0179365i
\(320\) 18.9539 + 1.29401i 1.05956 + 0.0723372i
\(321\) 25.8891 + 12.5253i 1.44499 + 0.699097i
\(322\) 3.22590 14.0612i 0.179773 0.783602i
\(323\) 1.23150i 0.0685228i
\(324\) −0.302090 + 1.28070i −0.0167828 + 0.0711498i
\(325\) 9.93481 + 7.70933i 0.551084 + 0.427637i
\(326\) 1.88200 0.104234
\(327\) 8.94878 0.654319i 0.494869 0.0361839i
\(328\) 8.52466 + 4.92171i 0.470695 + 0.271756i
\(329\) 3.97775 + 0.912569i 0.219301 + 0.0503116i
\(330\) 0.0157991 + 3.27580i 0.000869710 + 0.180327i
\(331\) 13.7078 23.7426i 0.753447 1.30501i −0.192696 0.981259i \(-0.561723\pi\)
0.946143 0.323750i \(-0.104944\pi\)
\(332\) −1.07730 0.621981i −0.0591247 0.0341357i
\(333\) −2.85874 19.4442i −0.156658 1.06554i
\(334\) 4.01605 + 6.95599i 0.219748 + 0.380615i
\(335\) 25.8709 12.6709i 1.41348 0.692284i
\(336\) 15.7427 6.12540i 0.858832 0.334168i
\(337\) −4.77272 2.75553i −0.259986 0.150103i 0.364342 0.931265i \(-0.381294\pi\)
−0.624328 + 0.781162i \(0.714627\pi\)
\(338\) 9.08779i 0.494311i
\(339\) 0.756832 + 10.3508i 0.0411055 + 0.562178i
\(340\) −0.135802 + 1.98915i −0.00736489 + 0.107877i
\(341\) 2.18391 + 3.78264i 0.118265 + 0.204841i
\(342\) −0.766702 0.304119i −0.0414585 0.0164448i
\(343\) 11.5956 14.4410i 0.626105 0.779739i
\(344\) 12.0455 + 20.8635i 0.649451 + 1.12488i
\(345\) 13.3950 7.81997i 0.721161 0.421013i
\(346\) 12.4426 + 21.5512i 0.668918 + 1.15860i
\(347\) −0.329422 + 0.190192i −0.0176843 + 0.0102100i −0.508816 0.860875i \(-0.669917\pi\)
0.491132 + 0.871085i \(0.336583\pi\)
\(348\) −0.150390 + 0.0109963i −0.00806177 + 0.000589462i
\(349\) 0.417229 + 0.722662i 0.0223338 + 0.0386832i 0.876976 0.480534i \(-0.159557\pi\)
−0.854643 + 0.519217i \(0.826224\pi\)
\(350\) −16.8452 6.37611i −0.900412 0.340817i
\(351\) −12.4668 3.91981i −0.665426 0.209224i
\(352\) 0.444038 0.256365i 0.0236673 0.0136643i
\(353\) 14.6935i 0.782056i 0.920379 + 0.391028i \(0.127880\pi\)
−0.920379 + 0.391028i \(0.872120\pi\)
\(354\) −26.8558 + 18.2388i −1.42737 + 0.969383i
\(355\) 19.5542 + 1.33499i 1.03783 + 0.0708540i
\(356\) −0.292196 + 0.506099i −0.0154864 + 0.0268232i
\(357\) 10.1341 + 26.0453i 0.536354 + 1.37846i
\(358\) −21.7857 + 12.5780i −1.15141 + 0.664768i
\(359\) −9.92659 17.1934i −0.523905 0.907430i −0.999613 0.0278269i \(-0.991141\pi\)
0.475708 0.879603i \(-0.342192\pi\)
\(360\) 17.6866 + 8.45192i 0.932168 + 0.445455i
\(361\) 9.47961 16.4192i 0.498927 0.864167i
\(362\) −24.1522 13.9443i −1.26941 0.732896i
\(363\) −10.3286 15.2084i −0.542112 0.798235i
\(364\) −0.285719 0.929964i −0.0149758 0.0487434i
\(365\) −2.19782 1.47718i −0.115039 0.0773193i
\(366\) −14.1438 6.84291i −0.739310 0.357684i
\(367\) 18.8839i 0.985734i 0.870105 + 0.492867i \(0.164051\pi\)
−0.870105 + 0.492867i \(0.835949\pi\)
\(368\) 12.7848 + 7.38129i 0.666452 + 0.384776i
\(369\) 6.27212 + 7.92371i 0.326514 + 0.412492i
\(370\) −19.8984 1.35849i −1.03447 0.0706245i
\(371\) −6.45670 1.48129i −0.335215 0.0769045i
\(372\) 1.77575 0.129840i 0.0920684 0.00673188i
\(373\) 5.41346i 0.280298i −0.990130 0.140149i \(-0.955242\pi\)
0.990130 0.140149i \(-0.0447582\pi\)
\(374\) −2.57916 4.46724i −0.133365 0.230996i
\(375\) −7.39975 17.8954i −0.382122 0.924112i
\(376\) −2.25372 + 3.90355i −0.116227 + 0.201310i
\(377\) 1.49761i 0.0771308i
\(378\) 18.7177 + 0.122621i 0.962735 + 0.00630696i
\(379\) −36.1233 −1.85553 −0.927765 0.373164i \(-0.878273\pi\)
−0.927765 + 0.373164i \(0.878273\pi\)
\(380\) 0.0368256 0.0547907i 0.00188911 0.00281070i
\(381\) −9.06316 + 6.15514i −0.464320 + 0.315337i
\(382\) −6.87743 + 3.97069i −0.351880 + 0.203158i
\(383\) 34.8120i 1.77881i −0.457119 0.889405i \(-0.651119\pi\)
0.457119 0.889405i \(-0.348881\pi\)
\(384\) 1.25261 + 17.1314i 0.0639222 + 0.874231i
\(385\) −3.57848 + 0.837567i −0.182376 + 0.0426863i
\(386\) 9.86069 0.501896
\(387\) 3.59761 + 24.4698i 0.182877 + 1.24387i
\(388\) 0.134803 + 0.0778283i 0.00684356 + 0.00395113i
\(389\) −27.8227 −1.41067 −0.705333 0.708876i \(-0.749203\pi\)
−0.705333 + 0.708876i \(0.749203\pi\)
\(390\) −6.57569 + 11.5173i −0.332973 + 0.583204i
\(391\) −12.2119 + 21.1516i −0.617583 + 1.06968i
\(392\) 11.4850 + 16.9264i 0.580078 + 0.854913i
\(393\) 17.0562 + 25.1144i 0.860369 + 1.26685i
\(394\) 10.3527 17.9314i 0.521562 0.903372i
\(395\) 19.4689 28.9667i 0.979586 1.45747i
\(396\) 0.269579 0.0396341i 0.0135468 0.00199169i
\(397\) 22.6589 13.0821i 1.13722 0.656572i 0.191476 0.981497i \(-0.438672\pi\)
0.945740 + 0.324925i \(0.105339\pi\)
\(398\) 1.82122 1.05148i 0.0912897 0.0527062i
\(399\) 0.140597 0.914624i 0.00703867 0.0457885i
\(400\) 11.2994 14.5612i 0.564969 0.728060i
\(401\) −11.7942 −0.588974 −0.294487 0.955656i \(-0.595149\pi\)
−0.294487 + 0.955656i \(0.595149\pi\)
\(402\) 17.0689 + 25.1332i 0.851321 + 1.25353i
\(403\) 17.6832i 0.880863i
\(404\) 0.798430 + 1.38292i 0.0397234 + 0.0688029i
\(405\) 13.6792 + 14.7608i 0.679724 + 0.733468i
\(406\) 0.629973 + 2.05045i 0.0312651 + 0.101762i
\(407\) −3.52444 + 2.03484i −0.174700 + 0.100863i
\(408\) −30.7848 + 2.25093i −1.52408 + 0.111438i
\(409\) −16.6197 28.7862i −0.821791 1.42338i −0.904347 0.426798i \(-0.859642\pi\)
0.0825559 0.996586i \(-0.473692\pi\)
\(410\) 9.21023 4.51093i 0.454861 0.222779i
\(411\) −20.1507 + 13.6851i −0.993959 + 0.675035i
\(412\) −1.43363 + 0.827708i −0.0706300 + 0.0407782i
\(413\) −26.6710 24.8026i −1.31240 1.22045i
\(414\) 10.1527 + 12.8262i 0.498979 + 0.630372i
\(415\) −17.0860 + 8.36830i −0.838721 + 0.410784i
\(416\) 2.07580 0.101775
\(417\) 23.0967 1.68879i 1.13105 0.0827005i
\(418\) 0.170798i 0.00835398i
\(419\) 7.56943 13.1106i 0.369791 0.640496i −0.619742 0.784806i \(-0.712763\pi\)
0.989533 + 0.144309i \(0.0460960\pi\)
\(420\) −0.327954 + 1.46182i −0.0160025 + 0.0713293i
\(421\) −0.116982 0.202619i −0.00570136 0.00987504i 0.863161 0.504929i \(-0.168481\pi\)
−0.868862 + 0.495054i \(0.835148\pi\)
\(422\) 21.1898 12.2340i 1.03151 0.595540i
\(423\) −3.62837 + 2.87209i −0.176417 + 0.139646i
\(424\) 3.65824 6.33626i 0.177660 0.307716i
\(425\) 24.0906 + 18.6941i 1.16857 + 0.906799i
\(426\) 1.50739 + 20.6158i 0.0730332 + 0.998837i
\(427\) 3.94171 17.1813i 0.190753 0.831462i
\(428\) −2.10241 1.21383i −0.101624 0.0586726i
\(429\) 0.197341 + 2.69893i 0.00952771 + 0.130306i
\(430\) 25.0415 + 1.70961i 1.20761 + 0.0824447i
\(431\) 0.544288 0.942735i 0.0262174 0.0454099i −0.852619 0.522533i \(-0.824987\pi\)
0.878836 + 0.477123i \(0.158320\pi\)
\(432\) −5.74517 + 18.2722i −0.276414 + 0.879122i
\(433\) 26.5259i 1.27476i 0.770552 + 0.637378i \(0.219981\pi\)
−0.770552 + 0.637378i \(0.780019\pi\)
\(434\) −7.43848 24.2109i −0.357059 1.16216i
\(435\) −1.14347 + 2.00279i −0.0548250 + 0.0960263i
\(436\) −0.757395 −0.0362727
\(437\) 0.700353 0.404349i 0.0335024 0.0193426i
\(438\) 1.21631 2.51404i 0.0581177 0.120125i
\(439\) 13.8382 23.9684i 0.660460 1.14395i −0.320035 0.947406i \(-0.603695\pi\)
0.980495 0.196545i \(-0.0629721\pi\)
\(440\) 0.276478 4.04971i 0.0131806 0.193062i
\(441\) 4.55297 + 20.5005i 0.216808 + 0.976214i
\(442\) 20.8836i 0.993332i
\(443\) 9.75448 + 5.63175i 0.463449 + 0.267573i 0.713494 0.700662i \(-0.247112\pi\)
−0.250044 + 0.968234i \(0.580445\pi\)
\(444\) 0.120977 + 1.65454i 0.00574131 + 0.0785210i
\(445\) 3.93129 + 8.02674i 0.186361 + 0.380504i
\(446\) −37.9493 −1.79695
\(447\) 20.3950 + 30.0307i 0.964651 + 1.42041i
\(448\) −21.4875 + 6.60176i −1.01519 + 0.311904i
\(449\) −7.28739 −0.343913 −0.171957 0.985105i \(-0.555009\pi\)
−0.171957 + 0.985105i \(0.555009\pi\)
\(450\) 17.5876 10.3817i 0.829088 0.489398i
\(451\) 1.04631 1.81226i 0.0492688 0.0853361i
\(452\) 0.876057i 0.0412063i
\(453\) −5.10044 7.51017i −0.239640 0.352858i
\(454\) −8.50064 + 14.7235i −0.398955 + 0.691010i
\(455\) −14.2421 4.30717i −0.667678 0.201923i
\(456\) 0.920020 + 0.445113i 0.0430839 + 0.0208443i
\(457\) −20.6044 11.8960i −0.963833 0.556469i −0.0664826 0.997788i \(-0.521178\pi\)
−0.897351 + 0.441318i \(0.854511\pi\)
\(458\) 19.4943 + 11.2550i 0.910908 + 0.525913i
\(459\) −30.2303 9.50503i −1.41103 0.443657i
\(460\) −1.17581 + 0.575883i −0.0548226 + 0.0268507i
\(461\) 6.23874 + 10.8058i 0.290567 + 0.503277i 0.973944 0.226789i \(-0.0728227\pi\)
−0.683377 + 0.730066i \(0.739489\pi\)
\(462\) −1.40550 3.61222i −0.0653899 0.168056i
\(463\) 2.21515 + 1.27892i 0.102947 + 0.0594364i 0.550590 0.834776i \(-0.314403\pi\)
−0.447643 + 0.894213i \(0.647736\pi\)
\(464\) −2.19501 −0.101901
\(465\) 13.5016 23.6481i 0.626122 1.09666i
\(466\) −15.7432 −0.729289
\(467\) −15.7910 + 9.11692i −0.730719 + 0.421881i −0.818685 0.574243i \(-0.805297\pi\)
0.0879663 + 0.996123i \(0.471963\pi\)
\(468\) 1.02541 + 0.406735i 0.0473994 + 0.0188013i
\(469\) −23.2117 + 24.9603i −1.07181 + 1.15256i
\(470\) 2.06561 + 4.21748i 0.0952797 + 0.194538i
\(471\) −15.2940 7.39935i −0.704709 0.340944i
\(472\) 34.8369 20.1131i 1.60350 0.925779i
\(473\) 4.43538 2.56077i 0.203939 0.117744i
\(474\) 33.1344 + 16.0307i 1.52191 + 0.736314i
\(475\) −0.381308 0.934887i −0.0174956 0.0428956i
\(476\) −0.692833 2.25504i −0.0317559 0.103360i
\(477\) 5.88959 4.66198i 0.269666 0.213457i
\(478\) 9.38333 5.41747i 0.429184 0.247789i
\(479\) 6.46962 0.295604 0.147802 0.989017i \(-0.452780\pi\)
0.147802 + 0.989017i \(0.452780\pi\)
\(480\) −2.77602 1.58493i −0.126707 0.0723419i
\(481\) −16.4762 −0.751248
\(482\) −1.90107 1.09759i −0.0865916 0.0499937i
\(483\) −11.4845 + 14.3149i −0.522561 + 0.651349i
\(484\) 0.775915 + 1.34392i 0.0352688 + 0.0610874i
\(485\) 2.13797 1.04712i 0.0970802 0.0475474i
\(486\) −13.3829 + 16.4733i −0.607061 + 0.747245i
\(487\) 10.1016 + 5.83216i 0.457747 + 0.264280i 0.711096 0.703095i \(-0.248199\pi\)
−0.253350 + 0.967375i \(0.581532\pi\)
\(488\) 16.8608 + 9.73459i 0.763253 + 0.440664i
\(489\) −2.15516 1.04268i −0.0974597 0.0471518i
\(490\) 21.3113 0.0938043i 0.962746 0.00423765i
\(491\) −6.24877 + 10.8232i −0.282003 + 0.488444i −0.971878 0.235485i \(-0.924332\pi\)
0.689875 + 0.723929i \(0.257666\pi\)
\(492\) −0.479254 0.705679i −0.0216064 0.0318145i
\(493\) 3.63151i 0.163555i
\(494\) −0.345739 + 0.598837i −0.0155555 + 0.0269430i
\(495\) 1.79680 3.76002i 0.0807602 0.169000i
\(496\) 25.9178 1.16375
\(497\) −22.1681 + 6.81085i −0.994374 + 0.305508i
\(498\) −11.2729 16.5989i −0.505152 0.743813i
\(499\) 38.3583 1.71715 0.858577 0.512684i \(-0.171349\pi\)
0.858577 + 0.512684i \(0.171349\pi\)
\(500\) 0.512804 + 1.55210i 0.0229333 + 0.0694120i
\(501\) −0.745119 10.1906i −0.0332895 0.455283i
\(502\) −17.4801 10.0921i −0.780175 0.450434i
\(503\) 7.04254i 0.314012i −0.987598 0.157006i \(-0.949816\pi\)
0.987598 0.157006i \(-0.0501841\pi\)
\(504\) −23.1205 1.84288i −1.02987 0.0820882i
\(505\) 24.3658 + 1.66348i 1.08426 + 0.0740240i
\(506\) 1.69367 2.93352i 0.0752928 0.130411i
\(507\) 5.03491 10.4068i 0.223608 0.462183i
\(508\) 0.800885 0.462391i 0.0355335 0.0205153i
\(509\) −30.3133 −1.34361 −0.671806 0.740727i \(-0.734481\pi\)
−0.671806 + 0.740727i \(0.734481\pi\)
\(510\) −15.9452 + 27.9281i −0.706065 + 1.23668i
\(511\) 3.05395 + 0.700631i 0.135099 + 0.0309941i
\(512\) 24.5858i 1.08655i
\(513\) 0.709493 + 0.773035i 0.0313249 + 0.0341303i
\(514\) 15.3256 26.5447i 0.675983 1.17084i
\(515\) −1.72448 + 25.2593i −0.0759897 + 1.11306i
\(516\) −0.152245 2.08218i −0.00670222 0.0916628i
\(517\) 0.829859 + 0.479119i 0.0364971 + 0.0210716i
\(518\) 22.5583 6.93074i 0.991154 0.304519i
\(519\) −2.30855 31.5728i −0.101334 1.38589i
\(520\) 9.16703 13.6391i 0.402001 0.598114i
\(521\) −4.69553 + 8.13289i −0.205715 + 0.356308i −0.950360 0.311152i \(-0.899285\pi\)
0.744645 + 0.667460i \(0.232619\pi\)
\(522\) −2.26088 0.896797i −0.0989561 0.0392518i
\(523\) 12.0758 6.97198i 0.528039 0.304864i −0.212178 0.977231i \(-0.568056\pi\)
0.740218 + 0.672367i \(0.234722\pi\)
\(524\) −1.28131 2.21929i −0.0559741 0.0969500i
\(525\) 15.7576 + 16.6343i 0.687717 + 0.725979i
\(526\) 8.84668 15.3229i 0.385734 0.668110i
\(527\) 42.8795i 1.86786i
\(528\) 3.95576 0.289238i 0.172152 0.0125875i
\(529\) 6.96151 0.302674
\(530\) −3.35291 6.84584i −0.145641 0.297364i
\(531\) 40.8586 6.00713i 1.77311 0.260687i
\(532\) −0.0174664 + 0.0761336i −0.000757267 + 0.00330081i
\(533\) 7.33699 4.23601i 0.317800 0.183482i
\(534\) −7.79787 + 5.29583i −0.337447 + 0.229173i
\(535\) −33.3443 + 16.3312i −1.44160 + 0.706058i
\(536\) −18.8230 32.6023i −0.813028 1.40821i
\(537\) 31.9164 2.33367i 1.37729 0.100705i
\(538\) −9.36711 + 5.40811i −0.403845 + 0.233160i
\(539\) 3.59840 2.44160i 0.154994 0.105167i
\(540\) −1.06074 1.32686i −0.0456471 0.0570990i
\(541\) −15.4984 26.8440i −0.666328 1.15411i −0.978923 0.204228i \(-0.934532\pi\)
0.312595 0.949886i \(-0.398802\pi\)
\(542\) 7.76995i 0.333748i
\(543\) 19.9322 + 29.3493i 0.855373 + 1.25950i
\(544\) 5.03355 0.215812
\(545\) −6.46167 + 9.61396i −0.276788 + 0.411817i
\(546\) 2.38422 15.5100i 0.102035 0.663767i
\(547\) −17.9331 + 10.3537i −0.766764 + 0.442691i −0.831719 0.555197i \(-0.812643\pi\)
0.0649551 + 0.997888i \(0.479310\pi\)
\(548\) 1.78065 1.02806i 0.0760658 0.0439166i
\(549\) 12.4055 + 15.6722i 0.529456 + 0.668874i
\(550\) −3.34113 2.59269i −0.142466 0.110553i
\(551\) −0.0601216 + 0.104134i −0.00256126 + 0.00443624i
\(552\) −11.3879 16.7682i −0.484701 0.713700i
\(553\) −9.23414 + 40.2502i −0.392675 + 1.71161i
\(554\) −8.42261 + 14.5884i −0.357842 + 0.619801i
\(555\) 22.0339 + 12.5800i 0.935288 + 0.533991i
\(556\) −1.95483 −0.0829033
\(557\) −0.264013 0.152428i −0.0111866 0.00645859i 0.494396 0.869237i \(-0.335389\pi\)
−0.505583 + 0.862778i \(0.668723\pi\)
\(558\) 26.6956 + 10.5890i 1.13012 + 0.448270i
\(559\) 20.7346 0.876982
\(560\) −6.31292 + 20.8742i −0.266769 + 0.882097i
\(561\) 0.478527 + 6.54456i 0.0202034 + 0.276312i
\(562\) 26.2650i 1.10792i
\(563\) 12.4984 7.21597i 0.526746 0.304117i −0.212945 0.977064i \(-0.568305\pi\)
0.739690 + 0.672948i \(0.234972\pi\)
\(564\) 0.323140 0.219456i 0.0136066 0.00924078i
\(565\) −11.1202 7.47403i −0.467830 0.314435i
\(566\) 6.32329 0.265788
\(567\) −21.3665 10.5106i −0.897309 0.441403i
\(568\) 25.6134i 1.07472i
\(569\) −0.101351 + 0.175545i −0.00424885 + 0.00735922i −0.868142 0.496316i \(-0.834686\pi\)
0.863893 + 0.503675i \(0.168019\pi\)
\(570\) 0.919593 0.536857i 0.0385175 0.0224865i
\(571\) 16.5797 + 28.7168i 0.693838 + 1.20176i 0.970571 + 0.240815i \(0.0774148\pi\)
−0.276733 + 0.960947i \(0.589252\pi\)
\(572\) 0.228429i 0.00955108i
\(573\) 10.0755 0.736704i 0.420911 0.0307763i
\(574\) −8.26352 + 8.88604i −0.344913 + 0.370896i
\(575\) −2.72144 + 19.8382i −0.113492 + 0.827312i
\(576\) 9.39792 23.6927i 0.391580 0.987198i
\(577\) 12.7694 + 7.37241i 0.531596 + 0.306917i 0.741666 0.670769i \(-0.234036\pi\)
−0.210070 + 0.977686i \(0.567369\pi\)
\(578\) 27.4939i 1.14359i
\(579\) −11.2919 5.46312i −0.469275 0.227039i
\(580\) 0.108593 0.161569i 0.00450907 0.00670879i
\(581\) 15.3298 16.4846i 0.635987 0.683898i
\(582\) 1.41058 + 2.07701i 0.0584703 + 0.0860948i
\(583\) −1.34703 0.777708i −0.0557883 0.0322094i
\(584\) −1.73031 + 2.99698i −0.0716005 + 0.124016i
\(585\) 13.9111 9.54589i 0.575151 0.394674i
\(586\) 20.6557 + 35.7768i 0.853280 + 1.47792i
\(587\) 9.38322 5.41741i 0.387287 0.223600i −0.293697 0.955899i \(-0.594886\pi\)
0.680984 + 0.732298i \(0.261552\pi\)
\(588\) −0.257107 1.75389i −0.0106029 0.0723293i
\(589\) 0.709892 1.22957i 0.0292506 0.0506635i
\(590\) 2.85463 41.8131i 0.117523 1.72142i
\(591\) −21.7899 + 14.7983i −0.896315 + 0.608722i
\(592\) 24.1487i 0.992505i
\(593\) −3.46118 + 1.99831i −0.142134 + 0.0820608i −0.569380 0.822074i \(-0.692817\pi\)
0.427247 + 0.904135i \(0.359484\pi\)
\(594\) 4.19264 + 1.31825i 0.172026 + 0.0540886i
\(595\) −34.5352 10.4443i −1.41580 0.428176i
\(596\) −1.53213 2.65373i −0.0627585 0.108701i
\(597\) −2.66812 + 0.195088i −0.109199 + 0.00798441i
\(598\) 11.8764 6.85686i 0.485664 0.280398i
\(599\) −1.16483 2.01754i −0.0475935 0.0824344i 0.841247 0.540651i \(-0.181822\pi\)
−0.888841 + 0.458216i \(0.848489\pi\)
\(600\) −22.6731 + 11.2406i −0.925626 + 0.458896i
\(601\) −9.73443 16.8605i −0.397076 0.687755i 0.596288 0.802771i \(-0.296642\pi\)
−0.993364 + 0.115015i \(0.963308\pi\)
\(602\) −28.3888 + 8.72208i −1.15704 + 0.355485i
\(603\) −5.62182 38.2378i −0.228938 1.55717i
\(604\) 0.383159 + 0.663651i 0.0155905 + 0.0270036i
\(605\) 23.6787 + 1.61657i 0.962676 + 0.0657230i
\(606\) 1.87830 + 25.6885i 0.0763007 + 1.04353i
\(607\) 16.6627i 0.676318i −0.941089 0.338159i \(-0.890196\pi\)
0.941089 0.338159i \(-0.109804\pi\)
\(608\) −0.144337 0.0833331i −0.00585364 0.00337960i
\(609\) 0.414599 2.69708i 0.0168004 0.109291i
\(610\) 18.2168 8.92211i 0.737577 0.361246i
\(611\) 1.93972 + 3.35970i 0.0784728 + 0.135919i
\(612\) 2.48648 + 0.986281i 0.100510 + 0.0398680i
\(613\) −24.0303 13.8739i −0.970573 0.560361i −0.0711621 0.997465i \(-0.522671\pi\)
−0.899411 + 0.437104i \(0.856004\pi\)
\(614\) 3.49209 6.04848i 0.140929 0.244097i
\(615\) −13.0462 + 0.0629214i −0.526074 + 0.00253724i
\(616\) 1.41053 + 4.59103i 0.0568321 + 0.184978i
\(617\) −3.67819 2.12360i −0.148078 0.0854931i 0.424130 0.905601i \(-0.360580\pi\)
−0.572209 + 0.820108i \(0.693913\pi\)
\(618\) −26.6305 + 1.94717i −1.07124 + 0.0783268i
\(619\) 31.7725 1.27705 0.638523 0.769603i \(-0.279546\pi\)
0.638523 + 0.769603i \(0.279546\pi\)
\(620\) −1.28222 + 1.90775i −0.0514953 + 0.0766169i
\(621\) −4.52025 20.3127i −0.181391 0.815121i
\(622\) 11.2740i 0.452044i
\(623\) −7.74421 7.20168i −0.310265 0.288529i
\(624\) 14.4549 + 6.99338i 0.578658 + 0.279959i
\(625\) 24.0764 + 6.73239i 0.963058 + 0.269296i
\(626\) 13.8117 + 23.9225i 0.552026 + 0.956137i
\(627\) 0.0946269 0.195588i 0.00377903 0.00781102i
\(628\) 1.24200 + 0.717069i 0.0495612 + 0.0286142i
\(629\) −39.9526 −1.59301
\(630\) −15.0308 + 18.9214i −0.598841 + 0.753848i
\(631\) −11.3375 −0.451340 −0.225670 0.974204i \(-0.572457\pi\)
−0.225670 + 0.974204i \(0.572457\pi\)
\(632\) −39.4994 22.8050i −1.57120 0.907133i
\(633\) −31.0434 + 2.26984i −1.23386 + 0.0902179i
\(634\) 16.1670 + 28.0020i 0.642072 + 1.11210i
\(635\) 0.963364 14.1109i 0.0382299 0.559972i
\(636\) −0.524521 + 0.356222i −0.0207986 + 0.0141251i
\(637\) 17.5589 1.27643i 0.695707 0.0505742i
\(638\) 0.503655i 0.0199399i
\(639\) 9.69557 24.4431i 0.383551 0.966956i
\(640\) −18.4048 12.3701i −0.727512 0.488971i
\(641\) 13.0143 0.514036 0.257018 0.966407i \(-0.417260\pi\)
0.257018 + 0.966407i \(0.417260\pi\)
\(642\) −21.9997 32.3935i −0.868258 1.27847i
\(643\) 39.0292 + 22.5335i 1.53916 + 0.888635i 0.998888 + 0.0471444i \(0.0150121\pi\)
0.540272 + 0.841490i \(0.318321\pi\)
\(644\) 1.05495 1.13443i 0.0415710 0.0447027i
\(645\) −27.7289 15.8315i −1.09182 0.623363i
\(646\) −0.838372 + 1.45210i −0.0329853 + 0.0571322i
\(647\) 15.7349 + 9.08453i 0.618602 + 0.357150i 0.776324 0.630334i \(-0.217082\pi\)
−0.157723 + 0.987483i \(0.550415\pi\)
\(648\) 18.0273 19.1486i 0.708179 0.752230i
\(649\) −4.27585 7.40599i −0.167842 0.290711i
\(650\) −6.46614 15.8536i −0.253623 0.621830i
\(651\) −4.89543 + 31.8461i −0.191867 + 1.24815i
\(652\) 0.175017 + 0.101046i 0.00685421 + 0.00395728i
\(653\) 34.4395i 1.34772i 0.738859 + 0.673860i \(0.235365\pi\)
−0.738859 + 0.673860i \(0.764635\pi\)
\(654\) −10.9972 5.32054i −0.430025 0.208050i
\(655\) −39.1018 2.66952i −1.52783 0.104307i
\(656\) −6.20862 10.7536i −0.242406 0.419859i
\(657\) −2.78571 + 2.20506i −0.108681 + 0.0860277i
\(658\) −4.06903 3.78397i −0.158627 0.147515i
\(659\) 20.7037 + 35.8598i 0.806501 + 1.39690i 0.915273 + 0.402834i \(0.131975\pi\)
−0.108772 + 0.994067i \(0.534692\pi\)
\(660\) −0.174412 + 0.305483i −0.00678896 + 0.0118909i
\(661\) −15.5052 26.8558i −0.603083 1.04457i −0.992351 0.123447i \(-0.960605\pi\)
0.389268 0.921125i \(-0.372728\pi\)
\(662\) −32.3265 + 18.6637i −1.25640 + 0.725385i
\(663\) −11.5701 + 23.9147i −0.449347 + 0.928770i
\(664\) 12.4313 + 21.5317i 0.482430 + 0.835593i
\(665\) 0.817384 + 0.871239i 0.0316968 + 0.0337852i
\(666\) −9.86624 + 24.8734i −0.382309 + 0.963825i
\(667\) 2.06523 1.19236i 0.0799660 0.0461684i
\(668\) 0.862500i 0.0333711i
\(669\) 43.4574 + 21.0251i 1.68016 + 0.812876i
\(670\) −39.1311 2.67152i −1.51177 0.103210i
\(671\) 2.06948 3.58445i 0.0798916 0.138376i
\(672\) 3.73836 + 0.574666i 0.144210 + 0.0221682i
\(673\) 22.6091 13.0533i 0.871515 0.503169i 0.00366358 0.999993i \(-0.498834\pi\)
0.867851 + 0.496824i \(0.165501\pi\)
\(674\) 3.75177 + 6.49825i 0.144513 + 0.250303i
\(675\) −25.8921 + 2.14446i −0.996588 + 0.0825401i
\(676\) −0.487932 + 0.845122i −0.0187666 + 0.0325047i
\(677\) 12.7724 + 7.37415i 0.490883 + 0.283412i 0.724941 0.688811i \(-0.241867\pi\)
−0.234058 + 0.972223i \(0.575200\pi\)
\(678\) 6.15412 12.7202i 0.236348 0.488515i
\(679\) −1.91821 + 2.06272i −0.0736142 + 0.0791598i
\(680\) 22.2289 33.0731i 0.852438 1.26829i
\(681\) 17.8917 12.1510i 0.685613 0.465626i
\(682\) 5.94696i 0.227721i
\(683\) −8.69914 5.02245i −0.332863 0.192179i 0.324248 0.945972i \(-0.394889\pi\)
−0.657112 + 0.753793i \(0.728222\pi\)
\(684\) −0.0549713 0.0694465i −0.00210188 0.00265535i
\(685\) 2.14190 31.3735i 0.0818380 1.19872i
\(686\) −23.5037 + 9.13381i −0.897377 + 0.348730i
\(687\) −16.0881 23.6890i −0.613800 0.903793i
\(688\) 30.3902i 1.15862i
\(689\) −3.14857 5.45348i −0.119951 0.207761i
\(690\) −21.1180 + 0.101851i −0.803949 + 0.00387741i
\(691\) 17.5582 30.4117i 0.667946 1.15692i −0.310531 0.950563i \(-0.600507\pi\)
0.978478 0.206353i \(-0.0661597\pi\)
\(692\) 2.67222i 0.101582i
\(693\) −0.391778 + 4.91520i −0.0148824 + 0.186713i
\(694\) 0.517909 0.0196595
\(695\) −16.6775 + 24.8136i −0.632615 + 0.941232i
\(696\) 2.71299 + 1.31257i 0.102836 + 0.0497528i
\(697\) 17.7913 10.2718i 0.673892 0.389072i
\(698\) 1.13615i 0.0430039i
\(699\) 18.0282 + 8.72219i 0.681889 + 0.329904i
\(700\) −1.22418 1.49738i −0.0462698 0.0565956i
\(701\) −19.0065 −0.717865 −0.358933 0.933363i \(-0.616859\pi\)
−0.358933 + 0.933363i \(0.616859\pi\)
\(702\) 12.0314 + 13.1090i 0.454097 + 0.494766i
\(703\) 1.14564 + 0.661435i 0.0432086 + 0.0249465i
\(704\) −5.27801 −0.198923
\(705\) −0.0288125 5.97403i −0.00108514 0.224995i
\(706\) 10.0029 17.3255i 0.376464 0.652055i
\(707\) −27.6228 + 8.48674i −1.03886 + 0.319177i
\(708\) −3.47673 + 0.254212i −0.130663 + 0.00955387i
\(709\) −10.2642 + 17.7781i −0.385481 + 0.667672i −0.991836 0.127522i \(-0.959298\pi\)
0.606355 + 0.795194i \(0.292631\pi\)
\(710\) −22.1482 14.8861i −0.831206 0.558665i
\(711\) −29.0621 36.7149i −1.08992 1.37692i
\(712\) 10.1152 5.84004i 0.379085 0.218865i
\(713\) −24.3854 + 14.0789i −0.913242 + 0.527260i
\(714\) 5.78143 37.6098i 0.216365 1.40751i
\(715\) −2.89955 1.94883i −0.108437 0.0728819i
\(716\) −2.70130 −0.100952
\(717\) −13.7467 + 1.00513i −0.513380 + 0.0375374i
\(718\) 27.0309i 1.00878i
\(719\) 21.9283 + 37.9809i 0.817786 + 1.41645i 0.907310 + 0.420463i \(0.138132\pi\)
−0.0895237 + 0.995985i \(0.528534\pi\)
\(720\) −13.9912 20.3891i −0.521420 0.759857i
\(721\) −8.79794 28.6357i −0.327653 1.06645i
\(722\) −22.3554 + 12.9069i −0.831981 + 0.480345i
\(723\) 1.56891 + 2.31015i 0.0583483 + 0.0859152i
\(724\) −1.49736 2.59351i −0.0556490 0.0963870i
\(725\) −1.12442 2.75683i −0.0417598 0.102386i
\(726\) 1.82533 + 24.9641i 0.0677444 + 0.926505i
\(727\) −8.29739 + 4.79050i −0.307733 + 0.177670i −0.645912 0.763412i \(-0.723523\pi\)
0.338178 + 0.941082i \(0.390189\pi\)
\(728\) −4.34794 + 18.9520i −0.161145 + 0.702408i
\(729\) 24.4521 11.4498i 0.905631 0.424066i
\(730\) 1.58589 + 3.23800i 0.0586964 + 0.119844i
\(731\) 50.2788 1.85963
\(732\) −0.947909 1.39575i −0.0350357 0.0515885i
\(733\) 40.1522i 1.48306i 0.670922 + 0.741528i \(0.265899\pi\)
−0.670922 + 0.741528i \(0.734101\pi\)
\(734\) 12.8556 22.2666i 0.474510 0.821876i
\(735\) −24.4564 11.6997i −0.902090 0.431549i
\(736\) 1.65270 + 2.86257i 0.0609194 + 0.105516i
\(737\) −6.93095 + 4.00159i −0.255305 + 0.147400i
\(738\) −2.00141 13.6130i −0.0736729 0.501100i
\(739\) −1.19273 + 2.06588i −0.0438755 + 0.0759945i −0.887129 0.461521i \(-0.847304\pi\)
0.843254 + 0.537516i \(0.180637\pi\)
\(740\) −1.77752 1.19470i −0.0653431 0.0439180i
\(741\) 0.727694 0.494205i 0.0267325 0.0181551i
\(742\) 6.60487 + 6.14216i 0.242473 + 0.225486i
\(743\) −0.855753 0.494069i −0.0313945 0.0181256i 0.484221 0.874946i \(-0.339103\pi\)
−0.515615 + 0.856820i \(0.672437\pi\)
\(744\) −32.0340 15.4983i −1.17442 0.568195i
\(745\) −46.7563 3.19210i −1.71302 0.116950i
\(746\) −3.68532 + 6.38317i −0.134929 + 0.233704i
\(747\) 3.71285 + 25.2536i 0.135846 + 0.923981i
\(748\) 0.553910i 0.0202530i
\(749\) 29.9169 32.1706i 1.09314 1.17549i
\(750\) −3.45737 + 26.1385i −0.126245 + 0.954442i
\(751\) −26.9996 −0.985230 −0.492615 0.870247i \(-0.663959\pi\)
−0.492615 + 0.870247i \(0.663959\pi\)
\(752\) 4.92423 2.84301i 0.179568 0.103674i
\(753\) 14.4259 + 21.2414i 0.525708 + 0.774081i
\(754\) −1.01953 + 1.76588i −0.0371291 + 0.0643094i
\(755\) 11.6929 + 0.798290i 0.425549 + 0.0290527i
\(756\) 1.73408 + 1.01637i 0.0630677 + 0.0369651i
\(757\) 40.0695i 1.45635i −0.685391 0.728175i \(-0.740369\pi\)
0.685391 0.728175i \(-0.259631\pi\)
\(758\) 42.5941 + 24.5917i 1.54709 + 0.893211i
\(759\) −3.56475 + 2.42096i −0.129392 + 0.0878753i
\(760\) −1.18496 + 0.580360i −0.0429828 + 0.0210519i
\(761\) 11.7722 0.426742 0.213371 0.976971i \(-0.431556\pi\)
0.213371 + 0.976971i \(0.431556\pi\)
\(762\) 14.8769 1.08777i 0.538932 0.0394058i
\(763\) 3.06478 13.3589i 0.110953 0.483626i
\(764\) −0.852759 −0.0308517
\(765\) 33.7325 23.1476i 1.21960 0.836902i
\(766\) −23.6990 + 41.0479i −0.856280 + 1.48312i
\(767\) 34.6218i 1.25012i
\(768\) −2.63240 + 5.44101i −0.0949887 + 0.196335i
\(769\) −16.4254 + 28.4496i −0.592314 + 1.02592i 0.401606 + 0.915813i \(0.368452\pi\)
−0.993920 + 0.110106i \(0.964881\pi\)
\(770\) 4.78969 + 1.44853i 0.172608 + 0.0522013i
\(771\) −32.2565 + 21.9066i −1.16169 + 0.788949i
\(772\) 0.916998 + 0.529429i 0.0330035 + 0.0190546i
\(773\) −3.24032 1.87080i −0.116546 0.0672879i 0.440594 0.897707i \(-0.354768\pi\)
−0.557140 + 0.830419i \(0.688101\pi\)
\(774\) 12.4163 31.3023i 0.446295 1.12514i
\(775\) 13.2767 + 32.5516i 0.476912 + 1.16929i
\(776\) −1.55553 2.69426i −0.0558402 0.0967181i
\(777\) −29.6723 4.56127i −1.06449 0.163635i
\(778\) 32.8066 + 18.9409i 1.17617 + 0.679063i
\(779\) −0.680219 −0.0243714
\(780\) −1.22988 + 0.718005i −0.0440369 + 0.0257087i
\(781\) −5.44518 −0.194844
\(782\) 28.7988 16.6270i 1.02984 0.594581i
\(783\) 2.09218 + 2.27956i 0.0747685 + 0.0814647i
\(784\) −1.87084 25.7356i −0.0668157 0.919128i
\(785\) 19.6981 9.64764i 0.703057 0.344339i
\(786\) −3.01426 41.2245i −0.107515 1.47043i
\(787\) −13.5507 + 7.82351i −0.483031 + 0.278878i −0.721679 0.692228i \(-0.756629\pi\)
0.238648 + 0.971106i \(0.423296\pi\)
\(788\) 1.92551 1.11169i 0.0685934 0.0396024i
\(789\) −18.6201 + 12.6456i −0.662892 + 0.450195i
\(790\) −42.6760 + 20.9016i −1.51834 + 0.743646i
\(791\) 15.4519 + 3.54495i 0.549406 + 0.126044i
\(792\) −5.06220 2.00796i −0.179878 0.0713499i
\(793\) 14.5117 8.37835i 0.515327 0.297524i
\(794\) −35.6237 −1.26424
\(795\) 0.0467686 + 9.69708i 0.00165871 + 0.343920i
\(796\) 0.225821 0.00800400
\(797\) 1.28952 + 0.744503i 0.0456771 + 0.0263717i 0.522665 0.852538i \(-0.324938\pi\)
−0.476988 + 0.878910i \(0.658271\pi\)
\(798\) −0.788432 + 0.982745i −0.0279102 + 0.0347888i
\(799\) 4.70358 + 8.14684i 0.166401 + 0.288215i
\(800\) 3.82118 1.55853i 0.135099 0.0551022i
\(801\) 11.8637 1.74423i 0.419184 0.0616294i
\(802\) 13.9069 + 8.02914i 0.491069 + 0.283519i
\(803\) 0.637129 + 0.367847i 0.0224838 + 0.0129810i
\(804\) 0.237906 + 3.25372i 0.00839030 + 0.114750i
\(805\) −5.39952 23.0693i −0.190308 0.813086i
\(806\) 12.0382 20.8508i 0.424028 0.734438i
\(807\) 13.7229 1.00340i 0.483070 0.0353212i
\(808\) 31.9159i 1.12280i
\(809\) −17.6030 + 30.4893i −0.618889 + 1.07195i 0.370800 + 0.928713i \(0.379083\pi\)
−0.989689 + 0.143234i \(0.954250\pi\)
\(810\) −6.08084 26.7172i −0.213659 0.938748i
\(811\) −26.5990 −0.934017 −0.467008 0.884253i \(-0.654668\pi\)
−0.467008 + 0.884253i \(0.654668\pi\)
\(812\) −0.0515058 + 0.224506i −0.00180750 + 0.00787861i
\(813\) −4.30478 + 8.89771i −0.150975 + 0.312056i
\(814\) 5.54103 0.194213
\(815\) 2.77578 1.35950i 0.0972312 0.0476213i
\(816\) 35.0512 + 16.9581i 1.22704 + 0.593651i
\(817\) −1.44175 0.832392i −0.0504403 0.0291217i
\(818\) 45.2568i 1.58237i
\(819\) −11.3233 + 16.4402i −0.395667 + 0.574468i
\(820\) 1.09870 + 0.0750098i 0.0383684 + 0.00261946i
\(821\) −10.8684 + 18.8247i −0.379311 + 0.656986i −0.990962 0.134142i \(-0.957172\pi\)
0.611651 + 0.791127i \(0.290506\pi\)
\(822\) 33.0766 2.41850i 1.15368 0.0843550i
\(823\) −18.5115 + 10.6876i −0.645270 + 0.372547i −0.786642 0.617410i \(-0.788182\pi\)
0.141372 + 0.989957i \(0.454849\pi\)
\(824\) 33.0863 1.15261
\(825\) 2.38965 + 4.82009i 0.0831968 + 0.167814i
\(826\) 14.5637 + 47.4023i 0.506737 + 1.64934i
\(827\) 15.4869i 0.538531i 0.963066 + 0.269265i \(0.0867809\pi\)
−0.963066 + 0.269265i \(0.913219\pi\)
\(828\) 0.255508 + 1.73788i 0.00887951 + 0.0603956i
\(829\) 19.1032 33.0877i 0.663481 1.14918i −0.316213 0.948688i \(-0.602411\pi\)
0.979695 0.200495i \(-0.0642552\pi\)
\(830\) 25.8435 + 1.76437i 0.897043 + 0.0612421i
\(831\) 17.7275 12.0394i 0.614960 0.417643i
\(832\) −18.5054 10.6841i −0.641558 0.370404i
\(833\) 42.5780 3.09519i 1.47524 0.107242i
\(834\) −28.3837 13.7323i −0.982848 0.475510i
\(835\) 10.9481 + 7.35837i 0.378875 + 0.254647i
\(836\) −0.00917027 + 0.0158834i −0.000317160 + 0.000549338i
\(837\) −24.7037 26.9161i −0.853884 0.930358i
\(838\) −17.8507 + 10.3061i −0.616641 + 0.356018i
\(839\) 3.17437 + 5.49817i 0.109591 + 0.189818i 0.915605 0.402079i \(-0.131712\pi\)
−0.806013 + 0.591897i \(0.798379\pi\)
\(840\) 20.2850 22.0252i 0.699898 0.759941i
\(841\) 14.3227 24.8077i 0.493887 0.855437i
\(842\) 0.318552i 0.0109780i
\(843\) 14.5516 30.0772i 0.501183 1.03591i
\(844\) 2.62741 0.0904392
\(845\) 6.56476 + 13.4036i 0.225834 + 0.461099i
\(846\) 6.23355 0.916472i 0.214314 0.0315089i
\(847\) −26.8438 + 8.24742i −0.922365 + 0.283385i
\(848\) −7.99303 + 4.61478i −0.274482 + 0.158472i
\(849\) −7.24107 3.50329i −0.248513 0.120233i
\(850\) −15.6796 38.4430i −0.537804 1.31858i
\(851\) −13.1179 22.7209i −0.449676 0.778862i
\(852\) −0.966699 + 1.99810i −0.0331186 + 0.0684539i
\(853\) 0.907008 0.523661i 0.0310554 0.0179298i −0.484392 0.874851i \(-0.660959\pi\)
0.515447 + 0.856921i \(0.327626\pi\)
\(854\) −16.3443 + 17.5756i −0.559291 + 0.601424i
\(855\) −1.35050 + 0.105297i −0.0461861 + 0.00360107i
\(856\) 24.2604 + 42.0202i 0.829203 + 1.43622i
\(857\) 22.6370i 0.773264i −0.922234 0.386632i \(-0.873638\pi\)
0.922234 0.386632i \(-0.126362\pi\)
\(858\) 1.60466 3.31673i 0.0547823 0.113231i
\(859\) −12.9486 −0.441802 −0.220901 0.975296i \(-0.570900\pi\)
−0.220901 + 0.975296i \(0.570900\pi\)
\(860\) 2.23695 + 1.50348i 0.0762793 + 0.0512684i
\(861\) 14.3861 5.59755i 0.490275 0.190764i
\(862\) −1.28357 + 0.741071i −0.0437187 + 0.0252410i
\(863\) 16.5213 9.53859i 0.562392 0.324697i −0.191713 0.981451i \(-0.561404\pi\)
0.754105 + 0.656754i \(0.228071\pi\)
\(864\) −3.15964 + 2.89992i −0.107493 + 0.0986574i
\(865\) 33.9196 + 22.7979i 1.15330 + 0.775150i
\(866\) 18.0581 31.2775i 0.613639 1.06285i
\(867\) −15.2324 + 31.4844i −0.517320 + 1.06927i
\(868\) 0.608161 2.65088i 0.0206423 0.0899767i
\(869\) −4.84813 + 8.39720i −0.164461 + 0.284855i
\(870\) 2.71173 1.58311i 0.0919364 0.0536723i
\(871\) −32.4010 −1.09787
\(872\) 13.1097 + 7.56891i 0.443952 + 0.256316i
\(873\) −0.464587 3.15997i −0.0157239 0.106949i
\(874\) −1.10108 −0.0372444
\(875\) −29.4510 + 2.76429i −0.995624 + 0.0934502i
\(876\) 0.248093 0.168489i 0.00838227 0.00569272i
\(877\) 32.9362i 1.11218i 0.831124 + 0.556088i \(0.187698\pi\)
−0.831124 + 0.556088i \(0.812302\pi\)
\(878\) −32.6340 + 18.8413i −1.10134 + 0.635861i
\(879\) −3.83237 52.4134i −0.129263 1.76786i
\(880\) −2.85635 + 4.24980i −0.0962874 + 0.143261i
\(881\) 5.91693 0.199347 0.0996733 0.995020i \(-0.468220\pi\)
0.0996733 + 0.995020i \(0.468220\pi\)
\(882\) 8.58760 27.2723i 0.289160 0.918305i
\(883\) 54.0403i 1.81860i 0.416141 + 0.909300i \(0.363382\pi\)
−0.416141 + 0.909300i \(0.636618\pi\)
\(884\) 1.12126 1.94208i 0.0377120 0.0653191i
\(885\) −26.4347 + 46.3004i −0.888591 + 1.55637i
\(886\) −7.66786 13.2811i −0.257607 0.446188i
\(887\) 15.3232i 0.514503i −0.966344 0.257252i \(-0.917183\pi\)
0.966344 0.257252i \(-0.0828169\pi\)
\(888\) 14.4404 29.8473i 0.484588 1.00161i
\(889\) 4.91489 + 15.9971i 0.164840 + 0.536524i
\(890\) 0.828871 12.1409i 0.0277838 0.406963i
\(891\) −4.07082 3.83244i −0.136378 0.128392i
\(892\) −3.52911 2.03753i −0.118163 0.0682217i
\(893\) 0.311481i 0.0104233i
\(894\) −3.60432 49.2945i −0.120547 1.64865i
\(895\) −23.0460 + 34.2888i −0.770341 + 1.14615i
\(896\) 25.5741 + 5.86716i 0.854369 + 0.196008i
\(897\) −17.3991 + 1.27219i −0.580940 + 0.0424773i
\(898\) 8.59278 + 4.96104i 0.286745 + 0.165552i
\(899\) 2.09336 3.62581i 0.0698175 0.120927i
\(900\) 2.19297 0.0211537i 0.0730990 0.000705123i
\(901\) −7.63487 13.2240i −0.254355 0.440555i
\(902\) −2.46747 + 1.42460i −0.0821578 + 0.0474338i
\(903\) 37.3415 + 5.74019i 1.24265 + 0.191022i
\(904\) −8.75474 + 15.1637i −0.291178 + 0.504335i
\(905\) −45.6952 3.11967i −1.51896 0.103701i
\(906\) 0.901378 + 12.3277i 0.0299463 + 0.409560i
\(907\) 41.5300i 1.37898i −0.724295 0.689491i \(-0.757834\pi\)
0.724295 0.689491i \(-0.242166\pi\)
\(908\) −1.58104 + 0.912814i −0.0524687 + 0.0302928i
\(909\) 12.0813 30.4577i 0.400711 1.01022i
\(910\) 13.8610 + 14.7743i 0.459489 + 0.489763i
\(911\) 8.99143 + 15.5736i 0.297899 + 0.515977i 0.975655 0.219310i \(-0.0703807\pi\)
−0.677756 + 0.735287i \(0.737047\pi\)
\(912\) −0.724344 1.06656i −0.0239854 0.0353174i
\(913\) 4.57744 2.64279i 0.151491 0.0874635i
\(914\) 16.1968 + 28.0538i 0.535744 + 0.927936i
\(915\) −25.8040 + 0.124451i −0.853053 + 0.00411424i
\(916\) 1.20858 + 2.09333i 0.0399328 + 0.0691656i
\(917\) 44.3285 13.6194i 1.46386 0.449751i
\(918\) 29.1747 + 31.7876i 0.962908 + 1.04915i
\(919\) 23.7506 + 41.1372i 0.783459 + 1.35699i 0.929915 + 0.367774i \(0.119880\pi\)
−0.146456 + 0.989217i \(0.546787\pi\)
\(920\) 26.1071 + 1.78236i 0.860726 + 0.0587628i
\(921\) −7.34999 + 4.99166i −0.242190 + 0.164481i
\(922\) 16.9886i 0.559490i
\(923\) −19.0915 11.0225i −0.628403 0.362809i
\(924\) 0.0632384 0.411383i 0.00208039 0.0135335i
\(925\) −30.3297 + 12.3704i −0.997234 + 0.406737i
\(926\) −1.74130 3.01602i −0.0572227 0.0991127i
\(927\) 31.5745 + 12.5243i 1.03704 + 0.411352i
\(928\) −0.425627 0.245736i −0.0139719 0.00806668i
\(929\) −4.54460 + 7.87148i −0.149104 + 0.258255i −0.930896 0.365283i \(-0.880972\pi\)
0.781793 + 0.623538i \(0.214305\pi\)
\(930\) −32.0191 + 18.6927i −1.04995 + 0.612958i
\(931\) −1.27217 0.616146i −0.0416936 0.0201934i
\(932\) −1.46404 0.845266i −0.0479563 0.0276876i
\(933\) −6.24610 + 12.9103i −0.204488 + 0.422664i
\(934\) 24.8261 0.812336
\(935\) −7.03103 4.72565i −0.229939 0.154545i
\(936\) −13.6841 17.2874i −0.447278 0.565056i
\(937\) 0.442145i 0.0144442i 0.999974 + 0.00722212i \(0.00229889\pi\)
−0.999974 + 0.00722212i \(0.997701\pi\)
\(938\) 44.3618 13.6296i 1.44846 0.445021i
\(939\) −2.56256 35.0468i −0.0836259 1.14371i
\(940\) −0.0343480 + 0.503111i −0.00112031 + 0.0164097i
\(941\) 19.4845 + 33.7481i 0.635175 + 1.10016i 0.986478 + 0.163894i \(0.0524053\pi\)
−0.351303 + 0.936262i \(0.614261\pi\)
\(942\) 12.9963 + 19.1365i 0.423443 + 0.623500i
\(943\) 11.6831 + 6.74522i 0.380453 + 0.219655i
\(944\) −50.7443 −1.65159
\(945\) 27.6954 13.3403i 0.900933 0.433959i
\(946\) −6.97318 −0.226718
\(947\) −6.56983 3.79309i −0.213491 0.123259i 0.389442 0.921051i \(-0.372668\pi\)
−0.602933 + 0.797792i \(0.706001\pi\)
\(948\) 2.22064 + 3.26979i 0.0721231 + 0.106198i
\(949\) 1.48924 + 2.57943i 0.0483426 + 0.0837319i
\(950\) −0.186833 + 1.36194i −0.00606166 + 0.0441871i
\(951\) −2.99955 41.0232i −0.0972669 1.33027i
\(952\) −10.5432 + 45.9562i −0.341707 + 1.48945i
\(953\) 22.6949i 0.735161i 0.929992 + 0.367581i \(0.119814\pi\)
−0.929992 + 0.367581i \(0.880186\pi\)
\(954\) −10.1183 + 1.48762i −0.327593 + 0.0481635i
\(955\) −7.27526 + 10.8245i −0.235422 + 0.350271i
\(956\) 1.16347 0.0376295
\(957\) 0.279040 0.576757i 0.00902008 0.0186439i
\(958\) −7.62852 4.40433i −0.246466 0.142297i
\(959\) 10.9276 + 35.5672i 0.352869 + 1.14852i
\(960\) 16.5900 + 28.4174i 0.535442 + 0.917168i
\(961\) −9.21759 + 15.9653i −0.297342 + 0.515011i
\(962\) 19.4275 + 11.2165i 0.626368 + 0.361634i
\(963\) 7.24581 + 49.2837i 0.233493 + 1.58815i
\(964\) −0.117861 0.204141i −0.00379604 0.00657493i
\(965\) 14.5436 7.12308i 0.468175 0.229300i
\(966\) 23.2868 9.06080i 0.749241 0.291527i
\(967\) 12.8032 + 7.39193i 0.411723 + 0.237708i 0.691530 0.722348i \(-0.256937\pi\)
−0.279807 + 0.960056i \(0.590270\pi\)
\(968\) 31.0159i 0.996889i
\(969\) 1.76456 1.19838i 0.0566860 0.0384976i
\(970\) −3.23379 0.220775i −0.103831 0.00708865i
\(971\) 10.2470 + 17.7483i 0.328841 + 0.569569i 0.982282 0.187408i \(-0.0600086\pi\)
−0.653441 + 0.756977i \(0.726675\pi\)
\(972\) −2.12901 + 0.813401i −0.0682882 + 0.0260898i
\(973\) 7.91018 34.4793i 0.253589 1.10536i
\(974\) −7.94072 13.7537i −0.254437 0.440698i
\(975\) −1.37873 + 21.7371i −0.0441546 + 0.696144i
\(976\) −12.2799 21.2695i −0.393071 0.680820i
\(977\) 22.0190 12.7127i 0.704449 0.406714i −0.104553 0.994519i \(-0.533341\pi\)
0.809002 + 0.587805i \(0.200008\pi\)
\(978\) 1.83138 + 2.69663i 0.0585612 + 0.0862287i
\(979\) −1.24154 2.15041i −0.0396797 0.0687273i
\(980\) 1.98689 + 1.13550i 0.0634688 + 0.0362722i
\(981\) 9.64565 + 12.1856i 0.307962 + 0.389055i
\(982\) 14.7362 8.50797i 0.470252 0.271500i
\(983\) 4.57328i 0.145865i 0.997337 + 0.0729325i \(0.0232358\pi\)
−0.997337 + 0.0729325i \(0.976764\pi\)
\(984\) 1.24330 + 17.0039i 0.0396348 + 0.542065i
\(985\) 2.31614 33.9257i 0.0737985 1.08096i
\(986\) −2.47223 + 4.28202i −0.0787318 + 0.136367i
\(987\) 2.56319 + 6.58756i 0.0815873 + 0.209684i
\(988\) −0.0643042 + 0.0371260i −0.00204579 + 0.00118114i
\(989\) 16.5084 + 28.5934i 0.524937 + 0.909218i
\(990\) −4.67837 + 3.21034i −0.148688 + 0.102031i
\(991\) 11.3064 19.5833i 0.359161 0.622085i −0.628660 0.777680i \(-0.716396\pi\)
0.987821 + 0.155595i \(0.0497296\pi\)
\(992\) 5.02564 + 2.90156i 0.159564 + 0.0921245i
\(993\) 47.3587 3.46278i 1.50288 0.109888i
\(994\) 30.7757 + 7.06050i 0.976145 + 0.223945i
\(995\) 1.92657 2.86644i 0.0610765 0.0908723i
\(996\) −0.157122 2.14887i −0.00497859 0.0680896i
\(997\) 26.2712i 0.832017i 0.909361 + 0.416008i \(0.136571\pi\)
−0.909361 + 0.416008i \(0.863429\pi\)
\(998\) −45.2294 26.1132i −1.43171 0.826600i
\(999\) 25.0789 23.0174i 0.793460 0.728239i
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.bo.b.4.13 yes 84
3.2 odd 2 945.2.bo.b.739.30 84
5.4 even 2 inner 315.2.bo.b.4.30 yes 84
7.2 even 3 315.2.r.b.184.30 yes 84
9.2 odd 6 945.2.r.b.424.13 84
9.7 even 3 315.2.r.b.214.30 yes 84
15.14 odd 2 945.2.bo.b.739.13 84
21.2 odd 6 945.2.r.b.604.13 84
35.9 even 6 315.2.r.b.184.13 84
45.29 odd 6 945.2.r.b.424.30 84
45.34 even 6 315.2.r.b.214.13 yes 84
63.2 odd 6 945.2.bo.b.289.13 84
63.16 even 3 inner 315.2.bo.b.79.30 yes 84
105.44 odd 6 945.2.r.b.604.30 84
315.79 even 6 inner 315.2.bo.b.79.13 yes 84
315.254 odd 6 945.2.bo.b.289.30 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.r.b.184.13 84 35.9 even 6
315.2.r.b.184.30 yes 84 7.2 even 3
315.2.r.b.214.13 yes 84 45.34 even 6
315.2.r.b.214.30 yes 84 9.7 even 3
315.2.bo.b.4.13 yes 84 1.1 even 1 trivial
315.2.bo.b.4.30 yes 84 5.4 even 2 inner
315.2.bo.b.79.13 yes 84 315.79 even 6 inner
315.2.bo.b.79.30 yes 84 63.16 even 3 inner
945.2.r.b.424.13 84 9.2 odd 6
945.2.r.b.424.30 84 45.29 odd 6
945.2.r.b.604.13 84 21.2 odd 6
945.2.r.b.604.30 84 105.44 odd 6
945.2.bo.b.289.13 84 63.2 odd 6
945.2.bo.b.289.30 84 315.254 odd 6
945.2.bo.b.739.13 84 15.14 odd 2
945.2.bo.b.739.30 84 3.2 odd 2