Properties

Label 165.2.m.d.136.2
Level $165$
Weight $2$
Character 165.136
Analytic conductor $1.318$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [165,2,Mod(16,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.m (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.31753163335\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 136.2
Root \(0.418926 + 1.28932i\) of defining polynomial
Character \(\chi\) \(=\) 165.136
Dual form 165.2.m.d.91.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.90578 + 1.38463i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.09676 + 3.37549i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(1.90578 - 1.38463i) q^{6} +(0.0598032 + 0.184055i) q^{7} +(-1.12773 + 3.47080i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(1.90578 + 1.38463i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.09676 + 3.37549i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(1.90578 - 1.38463i) q^{6} +(0.0598032 + 0.184055i) q^{7} +(-1.12773 + 3.47080i) q^{8} +(-0.809017 - 0.587785i) q^{9} -2.35567 q^{10} +(-1.96213 - 2.67395i) q^{11} +3.54920 q^{12} +(-0.787747 - 0.572331i) q^{13} +(-0.140877 + 0.433574i) q^{14} +(0.309017 + 0.951057i) q^{15} +(-1.21225 + 0.880754i) q^{16} +(2.16469 - 1.57274i) q^{17} +(-0.727943 - 2.24038i) q^{18} +(-1.71480 + 5.27760i) q^{19} +(-2.87136 - 2.08617i) q^{20} +0.193527 q^{21} +(-0.0369604 - 7.81280i) q^{22} -4.80040 q^{23} +(2.95244 + 2.14507i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-0.708805 - 2.18148i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.555687 + 0.403730i) q^{28} +(-3.12657 - 9.62260i) q^{29} +(-0.727943 + 2.24038i) q^{30} +(2.02685 + 1.47259i) q^{31} +3.76902 q^{32} +(-3.14941 + 1.03980i) q^{33} +6.30309 q^{34} +(-0.156567 - 0.113752i) q^{35} +(1.09676 - 3.37549i) q^{36} +(1.76516 + 5.43260i) q^{37} +(-10.5756 + 7.68359i) q^{38} +(-0.787747 + 0.572331i) q^{39} +(-1.12773 - 3.47080i) q^{40} +(-2.55823 + 7.87342i) q^{41} +(0.368820 + 0.267964i) q^{42} +5.11353 q^{43} +(6.87391 - 9.55586i) q^{44} +1.00000 q^{45} +(-9.14851 - 6.64678i) q^{46} +(-3.35354 + 10.3211i) q^{47} +(0.463040 + 1.42509i) q^{48} +(5.63282 - 4.09248i) q^{49} +(1.90578 - 1.38463i) q^{50} +(-0.826838 - 2.54475i) q^{51} +(1.06793 - 3.28674i) q^{52} +(7.51479 + 5.45981i) q^{53} -2.35567 q^{54} +(3.15911 + 1.00996i) q^{55} -0.706260 q^{56} +(4.48940 + 3.26174i) q^{57} +(7.36518 - 22.6677i) q^{58} +(-3.46656 - 10.6690i) q^{59} +(-2.87136 + 2.08617i) q^{60} +(-0.975693 + 0.708883i) q^{61} +(1.82374 + 5.61288i) q^{62} +(0.0598032 - 0.184055i) q^{63} +(9.60743 + 6.98021i) q^{64} +0.973708 q^{65} +(-7.44184 - 2.37914i) q^{66} +3.25922 q^{67} +(7.68293 + 5.58197i) q^{68} +(-1.48341 + 4.56545i) q^{69} +(-0.140877 - 0.433574i) q^{70} +(-4.84664 + 3.52129i) q^{71} +(2.95244 - 2.14507i) q^{72} +(1.02168 + 3.14442i) q^{73} +(-4.15814 + 12.7974i) q^{74} +(-0.809017 - 0.587785i) q^{75} -19.6952 q^{76} +(0.374813 - 0.521052i) q^{77} -2.29374 q^{78} +(-8.21389 - 5.96774i) q^{79} +(0.463040 - 1.42509i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-15.7772 + 11.4628i) q^{82} +(-6.72704 + 4.88748i) q^{83} +(0.212253 + 0.653249i) q^{84} +(-0.826838 + 2.54475i) q^{85} +(9.74527 + 7.08035i) q^{86} -10.1178 q^{87} +(11.4935 - 3.79468i) q^{88} +7.34270 q^{89} +(1.90578 + 1.38463i) q^{90} +(0.0582308 - 0.179216i) q^{91} +(-5.26490 - 16.2037i) q^{92} +(2.02685 - 1.47259i) q^{93} +(-20.6821 + 15.0264i) q^{94} +(-1.71480 - 5.27760i) q^{95} +(1.16469 - 3.58455i) q^{96} +(12.8248 + 9.31774i) q^{97} +16.4015 q^{98} +(0.0156899 + 3.31659i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 4 q^{6} + 3 q^{7} - q^{8} - 2 q^{9} - 6 q^{10} + 3 q^{11} + 2 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 12 q^{16} - q^{18} + 2 q^{19} - 3 q^{20} - 12 q^{21} + 9 q^{22} - 6 q^{23} + 4 q^{24} - 2 q^{25} + 2 q^{26} - 2 q^{27} - 11 q^{28} + 10 q^{29} - q^{30} + 19 q^{31} + 12 q^{32} - 2 q^{33} - 6 q^{34} + 3 q^{35} + 2 q^{36} - q^{37} - 20 q^{38} - 4 q^{39} - q^{40} - 9 q^{41} + q^{42} + 17 q^{44} + 8 q^{45} - 22 q^{46} - 19 q^{47} + 13 q^{48} + q^{49} + 4 q^{50} + 10 q^{51} - 2 q^{52} + 25 q^{53} - 6 q^{54} + 3 q^{55} - 16 q^{56} + 7 q^{57} - 12 q^{58} + 13 q^{59} - 3 q^{60} + 13 q^{61} + 35 q^{62} + 3 q^{63} + 39 q^{64} - 14 q^{65} - 11 q^{66} + 2 q^{67} + 19 q^{68} + 9 q^{69} - 4 q^{70} - 11 q^{71} + 4 q^{72} - 7 q^{73} - 43 q^{74} - 2 q^{75} - 38 q^{76} - 7 q^{77} - 8 q^{78} - 22 q^{79} + 13 q^{80} - 2 q^{81} - 35 q^{82} - 21 q^{83} + 4 q^{84} + 10 q^{85} + 20 q^{86} - 30 q^{87} + 59 q^{88} - 20 q^{89} + 4 q^{90} - 11 q^{91} - 28 q^{92} + 19 q^{93} - 35 q^{94} + 2 q^{95} - 8 q^{96} + 31 q^{97} + 22 q^{98} - 7 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.90578 + 1.38463i 1.34759 + 0.979082i 0.999128 + 0.0417590i \(0.0132962\pi\)
0.348463 + 0.937323i \(0.386704\pi\)
\(3\) 0.309017 0.951057i 0.178411 0.549093i
\(4\) 1.09676 + 3.37549i 0.548382 + 1.68775i
\(5\) −0.809017 + 0.587785i −0.361803 + 0.262866i
\(6\) 1.90578 1.38463i 0.778032 0.565273i
\(7\) 0.0598032 + 0.184055i 0.0226035 + 0.0695663i 0.961722 0.274027i \(-0.0883558\pi\)
−0.939119 + 0.343593i \(0.888356\pi\)
\(8\) −1.12773 + 3.47080i −0.398713 + 1.22711i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) −2.35567 −0.744930
\(11\) −1.96213 2.67395i −0.591606 0.806227i
\(12\) 3.54920 1.02457
\(13\) −0.787747 0.572331i −0.218482 0.158736i 0.473161 0.880976i \(-0.343113\pi\)
−0.691643 + 0.722240i \(0.743113\pi\)
\(14\) −0.140877 + 0.433574i −0.0376509 + 0.115878i
\(15\) 0.309017 + 0.951057i 0.0797878 + 0.245562i
\(16\) −1.21225 + 0.880754i −0.303063 + 0.220188i
\(17\) 2.16469 1.57274i 0.525015 0.381446i −0.293475 0.955967i \(-0.594812\pi\)
0.818490 + 0.574521i \(0.194812\pi\)
\(18\) −0.727943 2.24038i −0.171578 0.528062i
\(19\) −1.71480 + 5.27760i −0.393402 + 1.21077i 0.536798 + 0.843711i \(0.319634\pi\)
−0.930199 + 0.367055i \(0.880366\pi\)
\(20\) −2.87136 2.08617i −0.642057 0.466481i
\(21\) 0.193527 0.0422311
\(22\) −0.0369604 7.81280i −0.00787998 1.66569i
\(23\) −4.80040 −1.00095 −0.500476 0.865750i \(-0.666842\pi\)
−0.500476 + 0.865750i \(0.666842\pi\)
\(24\) 2.95244 + 2.14507i 0.602664 + 0.437861i
\(25\) 0.309017 0.951057i 0.0618034 0.190211i
\(26\) −0.708805 2.18148i −0.139008 0.427823i
\(27\) −0.809017 + 0.587785i −0.155695 + 0.113119i
\(28\) −0.555687 + 0.403730i −0.105015 + 0.0762978i
\(29\) −3.12657 9.62260i −0.580590 1.78687i −0.616303 0.787509i \(-0.711370\pi\)
0.0357132 0.999362i \(-0.488630\pi\)
\(30\) −0.727943 + 2.24038i −0.132904 + 0.409035i
\(31\) 2.02685 + 1.47259i 0.364033 + 0.264486i 0.754732 0.656033i \(-0.227767\pi\)
−0.390699 + 0.920518i \(0.627767\pi\)
\(32\) 3.76902 0.666275
\(33\) −3.14941 + 1.03980i −0.548243 + 0.181007i
\(34\) 6.30309 1.08097
\(35\) −0.156567 0.113752i −0.0264646 0.0192277i
\(36\) 1.09676 3.37549i 0.182794 0.562582i
\(37\) 1.76516 + 5.43260i 0.290190 + 0.893114i 0.984795 + 0.173722i \(0.0555794\pi\)
−0.694604 + 0.719392i \(0.744421\pi\)
\(38\) −10.5756 + 7.68359i −1.71558 + 1.24644i
\(39\) −0.787747 + 0.572331i −0.126140 + 0.0916464i
\(40\) −1.12773 3.47080i −0.178310 0.548781i
\(41\) −2.55823 + 7.87342i −0.399529 + 1.22962i 0.525850 + 0.850577i \(0.323747\pi\)
−0.925378 + 0.379045i \(0.876253\pi\)
\(42\) 0.368820 + 0.267964i 0.0569102 + 0.0413477i
\(43\) 5.11353 0.779807 0.389903 0.920856i \(-0.372508\pi\)
0.389903 + 0.920856i \(0.372508\pi\)
\(44\) 6.87391 9.55586i 1.03628 1.44060i
\(45\) 1.00000 0.149071
\(46\) −9.14851 6.64678i −1.34887 0.980014i
\(47\) −3.35354 + 10.3211i −0.489164 + 1.50549i 0.336693 + 0.941614i \(0.390692\pi\)
−0.825857 + 0.563879i \(0.809308\pi\)
\(48\) 0.463040 + 1.42509i 0.0668340 + 0.205694i
\(49\) 5.63282 4.09248i 0.804688 0.584640i
\(50\) 1.90578 1.38463i 0.269518 0.195816i
\(51\) −0.826838 2.54475i −0.115781 0.356336i
\(52\) 1.06793 3.28674i 0.148095 0.455789i
\(53\) 7.51479 + 5.45981i 1.03224 + 0.749963i 0.968755 0.248020i \(-0.0797800\pi\)
0.0634803 + 0.997983i \(0.479780\pi\)
\(54\) −2.35567 −0.320567
\(55\) 3.15911 + 1.00996i 0.425974 + 0.136183i
\(56\) −0.706260 −0.0943780
\(57\) 4.48940 + 3.26174i 0.594635 + 0.432028i
\(58\) 7.36518 22.6677i 0.967096 2.97642i
\(59\) −3.46656 10.6690i −0.451307 1.38898i −0.875416 0.483369i \(-0.839413\pi\)
0.424109 0.905611i \(-0.360587\pi\)
\(60\) −2.87136 + 2.08617i −0.370692 + 0.269323i
\(61\) −0.975693 + 0.708883i −0.124925 + 0.0907631i −0.648493 0.761221i \(-0.724600\pi\)
0.523568 + 0.851984i \(0.324600\pi\)
\(62\) 1.82374 + 5.61288i 0.231615 + 0.712836i
\(63\) 0.0598032 0.184055i 0.00753449 0.0231888i
\(64\) 9.60743 + 6.98021i 1.20093 + 0.872526i
\(65\) 0.973708 0.120774
\(66\) −7.44184 2.37914i −0.916027 0.292851i
\(67\) 3.25922 0.398176 0.199088 0.979982i \(-0.436202\pi\)
0.199088 + 0.979982i \(0.436202\pi\)
\(68\) 7.68293 + 5.58197i 0.931692 + 0.676914i
\(69\) −1.48341 + 4.56545i −0.178581 + 0.549616i
\(70\) −0.140877 0.433574i −0.0168380 0.0518220i
\(71\) −4.84664 + 3.52129i −0.575191 + 0.417901i −0.836987 0.547222i \(-0.815685\pi\)
0.261796 + 0.965123i \(0.415685\pi\)
\(72\) 2.95244 2.14507i 0.347948 0.252799i
\(73\) 1.02168 + 3.14442i 0.119579 + 0.368026i 0.992875 0.119165i \(-0.0380216\pi\)
−0.873296 + 0.487191i \(0.838022\pi\)
\(74\) −4.15814 + 12.7974i −0.483374 + 1.48767i
\(75\) −0.809017 0.587785i −0.0934172 0.0678716i
\(76\) −19.6952 −2.25920
\(77\) 0.374813 0.521052i 0.0427139 0.0593794i
\(78\) −2.29374 −0.259715
\(79\) −8.21389 5.96774i −0.924135 0.671423i 0.0204147 0.999792i \(-0.493501\pi\)
−0.944550 + 0.328368i \(0.893501\pi\)
\(80\) 0.463040 1.42509i 0.0517694 0.159330i
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) −15.7772 + 11.4628i −1.74230 + 1.26586i
\(83\) −6.72704 + 4.88748i −0.738388 + 0.536471i −0.892206 0.451629i \(-0.850843\pi\)
0.153818 + 0.988099i \(0.450843\pi\)
\(84\) 0.212253 + 0.653249i 0.0231588 + 0.0712753i
\(85\) −0.826838 + 2.54475i −0.0896832 + 0.276017i
\(86\) 9.74527 + 7.08035i 1.05086 + 0.763494i
\(87\) −10.1178 −1.08474
\(88\) 11.4935 3.79468i 1.22521 0.404514i
\(89\) 7.34270 0.778325 0.389163 0.921169i \(-0.372764\pi\)
0.389163 + 0.921169i \(0.372764\pi\)
\(90\) 1.90578 + 1.38463i 0.200887 + 0.145953i
\(91\) 0.0582308 0.179216i 0.00610425 0.0187869i
\(92\) −5.26490 16.2037i −0.548904 1.68935i
\(93\) 2.02685 1.47259i 0.210175 0.152701i
\(94\) −20.6821 + 15.0264i −2.13319 + 1.54986i
\(95\) −1.71480 5.27760i −0.175935 0.541471i
\(96\) 1.16469 3.58455i 0.118871 0.365847i
\(97\) 12.8248 + 9.31774i 1.30216 + 0.946074i 0.999974 0.00717602i \(-0.00228422\pi\)
0.302184 + 0.953250i \(0.402284\pi\)
\(98\) 16.4015 1.65680
\(99\) 0.0156899 + 3.31659i 0.00157690 + 0.333330i
\(100\) 3.54920 0.354920
\(101\) −10.6460 7.73475i −1.05931 0.769636i −0.0853519 0.996351i \(-0.527201\pi\)
−0.973961 + 0.226715i \(0.927201\pi\)
\(102\) 1.94776 5.99460i 0.192857 0.593553i
\(103\) 1.23525 + 3.80172i 0.121713 + 0.374595i 0.993288 0.115668i \(-0.0369009\pi\)
−0.871575 + 0.490263i \(0.836901\pi\)
\(104\) 2.87481 2.08867i 0.281899 0.204811i
\(105\) −0.156567 + 0.113752i −0.0152793 + 0.0111011i
\(106\) 6.76171 + 20.8104i 0.656755 + 2.02129i
\(107\) 1.51011 4.64764i 0.145988 0.449304i −0.851149 0.524924i \(-0.824094\pi\)
0.997137 + 0.0756201i \(0.0240936\pi\)
\(108\) −2.87136 2.08617i −0.276297 0.200742i
\(109\) −7.51977 −0.720263 −0.360131 0.932902i \(-0.617268\pi\)
−0.360131 + 0.932902i \(0.617268\pi\)
\(110\) 4.62215 + 6.29896i 0.440705 + 0.600583i
\(111\) 5.71217 0.542176
\(112\) −0.234604 0.170450i −0.0221680 0.0161060i
\(113\) 6.24947 19.2339i 0.587901 1.80937i 0.000604375 1.00000i \(-0.499808\pi\)
0.587296 0.809372i \(-0.300192\pi\)
\(114\) 4.03950 + 12.4323i 0.378334 + 1.16439i
\(115\) 3.88361 2.82160i 0.362148 0.263116i
\(116\) 29.0519 21.1074i 2.69740 1.95978i
\(117\) 0.300892 + 0.926052i 0.0278175 + 0.0856135i
\(118\) 8.16608 25.1326i 0.751748 2.31364i
\(119\) 0.418926 + 0.304368i 0.0384029 + 0.0279014i
\(120\) −3.64941 −0.333144
\(121\) −3.30005 + 10.4933i −0.300005 + 0.953938i
\(122\) −2.84100 −0.257212
\(123\) 6.69754 + 4.86604i 0.603896 + 0.438756i
\(124\) −2.74775 + 8.45670i −0.246755 + 0.759434i
\(125\) 0.309017 + 0.951057i 0.0276393 + 0.0850651i
\(126\) 0.368820 0.267964i 0.0328571 0.0238721i
\(127\) −5.74419 + 4.17340i −0.509715 + 0.370329i −0.812715 0.582661i \(-0.802012\pi\)
0.303001 + 0.952990i \(0.402012\pi\)
\(128\) 6.31526 + 19.4364i 0.558196 + 1.71795i
\(129\) 1.58017 4.86326i 0.139126 0.428186i
\(130\) 1.85567 + 1.34823i 0.162753 + 0.118247i
\(131\) −2.50024 −0.218447 −0.109223 0.994017i \(-0.534836\pi\)
−0.109223 + 0.994017i \(0.534836\pi\)
\(132\) −6.96401 9.49040i −0.606139 0.826033i
\(133\) −1.07392 −0.0931207
\(134\) 6.21135 + 4.51281i 0.536579 + 0.389847i
\(135\) 0.309017 0.951057i 0.0265959 0.0818539i
\(136\) 3.01748 + 9.28684i 0.258746 + 0.796340i
\(137\) 12.3734 8.98981i 1.05713 0.768052i 0.0835766 0.996501i \(-0.473366\pi\)
0.973556 + 0.228450i \(0.0733657\pi\)
\(138\) −9.14851 + 6.64678i −0.778773 + 0.565812i
\(139\) −6.07484 18.6964i −0.515261 1.58581i −0.782806 0.622266i \(-0.786212\pi\)
0.267544 0.963546i \(-0.413788\pi\)
\(140\) 0.212253 0.653249i 0.0179387 0.0552096i
\(141\) 8.77969 + 6.37882i 0.739383 + 0.537193i
\(142\) −14.1123 −1.18428
\(143\) 0.0152774 + 3.22939i 0.00127756 + 0.270055i
\(144\) 1.49843 0.124869
\(145\) 8.18547 + 5.94709i 0.679766 + 0.493879i
\(146\) −2.40675 + 7.40722i −0.199184 + 0.613026i
\(147\) −2.15155 6.62178i −0.177456 0.546155i
\(148\) −16.4017 + 11.9166i −1.34821 + 0.979535i
\(149\) 8.19771 5.95599i 0.671583 0.487933i −0.198972 0.980005i \(-0.563760\pi\)
0.870555 + 0.492072i \(0.163760\pi\)
\(150\) −0.727943 2.24038i −0.0594363 0.182926i
\(151\) 3.69682 11.3776i 0.300843 0.925899i −0.680353 0.732884i \(-0.738174\pi\)
0.981196 0.193015i \(-0.0618264\pi\)
\(152\) −16.3837 11.9034i −1.32889 0.965496i
\(153\) −2.67571 −0.216318
\(154\) 1.43578 0.474033i 0.115698 0.0381987i
\(155\) −2.50533 −0.201233
\(156\) −2.79587 2.03132i −0.223849 0.162636i
\(157\) −0.811494 + 2.49752i −0.0647643 + 0.199324i −0.978202 0.207654i \(-0.933417\pi\)
0.913438 + 0.406978i \(0.133417\pi\)
\(158\) −7.39076 22.7464i −0.587977 1.80961i
\(159\) 7.51479 5.45981i 0.595961 0.432991i
\(160\) −3.04920 + 2.21537i −0.241061 + 0.175141i
\(161\) −0.287079 0.883539i −0.0226250 0.0696326i
\(162\) −0.727943 + 2.24038i −0.0571926 + 0.176021i
\(163\) −19.1927 13.9443i −1.50329 1.09220i −0.969049 0.246868i \(-0.920598\pi\)
−0.534238 0.845334i \(-0.679402\pi\)
\(164\) −29.3825 −2.29438
\(165\) 1.93675 2.69240i 0.150776 0.209603i
\(166\) −19.5876 −1.52029
\(167\) −2.82488 2.05240i −0.218596 0.158819i 0.473098 0.881010i \(-0.343135\pi\)
−0.691694 + 0.722190i \(0.743135\pi\)
\(168\) −0.218246 + 0.671694i −0.0168381 + 0.0518223i
\(169\) −3.72424 11.4620i −0.286480 0.881695i
\(170\) −5.09931 + 3.70486i −0.391099 + 0.284150i
\(171\) 4.48940 3.26174i 0.343313 0.249431i
\(172\) 5.60834 + 17.2607i 0.427632 + 1.31612i
\(173\) −6.29145 + 19.3631i −0.478330 + 1.47215i 0.363083 + 0.931757i \(0.381724\pi\)
−0.841413 + 0.540392i \(0.818276\pi\)
\(174\) −19.2823 14.0094i −1.46179 1.06205i
\(175\) 0.193527 0.0146293
\(176\) 4.73370 + 1.51335i 0.356816 + 0.114073i
\(177\) −11.2180 −0.843197
\(178\) 13.9936 + 10.1669i 1.04886 + 0.762044i
\(179\) 1.19008 3.66268i 0.0889506 0.273762i −0.896679 0.442681i \(-0.854028\pi\)
0.985630 + 0.168919i \(0.0540276\pi\)
\(180\) 1.09676 + 3.37549i 0.0817479 + 0.251594i
\(181\) 14.2509 10.3539i 1.05926 0.769599i 0.0853107 0.996354i \(-0.472812\pi\)
0.973952 + 0.226755i \(0.0728117\pi\)
\(182\) 0.359123 0.260918i 0.0266200 0.0193406i
\(183\) 0.372682 + 1.14700i 0.0275494 + 0.0847884i
\(184\) 5.41356 16.6612i 0.399093 1.22828i
\(185\) −4.62125 3.35753i −0.339761 0.246851i
\(186\) 5.90173 0.432736
\(187\) −8.45285 2.70236i −0.618134 0.197616i
\(188\) −38.5170 −2.80914
\(189\) −0.156567 0.113752i −0.0113886 0.00827427i
\(190\) 4.03950 12.4323i 0.293056 0.901935i
\(191\) 0.128891 + 0.396685i 0.00932620 + 0.0287031i 0.955611 0.294630i \(-0.0951965\pi\)
−0.946285 + 0.323333i \(0.895196\pi\)
\(192\) 9.60743 6.98021i 0.693357 0.503753i
\(193\) −9.46269 + 6.87505i −0.681140 + 0.494877i −0.873736 0.486401i \(-0.838309\pi\)
0.192596 + 0.981278i \(0.438309\pi\)
\(194\) 11.5396 + 35.5151i 0.828493 + 2.54984i
\(195\) 0.300892 0.926052i 0.0215474 0.0663159i
\(196\) 19.9920 + 14.5250i 1.42800 + 1.03750i
\(197\) 21.5958 1.53864 0.769320 0.638863i \(-0.220595\pi\)
0.769320 + 0.638863i \(0.220595\pi\)
\(198\) −4.56235 + 6.34241i −0.324232 + 0.450736i
\(199\) 7.76028 0.550111 0.275056 0.961428i \(-0.411304\pi\)
0.275056 + 0.961428i \(0.411304\pi\)
\(200\) 2.95244 + 2.14507i 0.208769 + 0.151679i
\(201\) 1.00715 3.09970i 0.0710391 0.218636i
\(202\) −9.57911 29.4815i −0.673984 2.07431i
\(203\) 1.58411 1.15092i 0.111183 0.0807790i
\(204\) 7.68293 5.58197i 0.537912 0.390816i
\(205\) −2.55823 7.87342i −0.178675 0.549904i
\(206\) −2.90986 + 8.95561i −0.202739 + 0.623967i
\(207\) 3.88361 + 2.82160i 0.269929 + 0.196115i
\(208\) 1.45903 0.101166
\(209\) 17.4767 5.77008i 1.20889 0.399125i
\(210\) −0.455887 −0.0314592
\(211\) 10.1173 + 7.35065i 0.696504 + 0.506040i 0.878792 0.477205i \(-0.158350\pi\)
−0.182288 + 0.983245i \(0.558350\pi\)
\(212\) −10.1876 + 31.3542i −0.699687 + 2.15342i
\(213\) 1.85125 + 5.69757i 0.126846 + 0.390391i
\(214\) 9.31320 6.76644i 0.636637 0.462544i
\(215\) −4.13694 + 3.00566i −0.282137 + 0.204984i
\(216\) −1.12773 3.47080i −0.0767324 0.236158i
\(217\) −0.149826 + 0.461118i −0.0101709 + 0.0313027i
\(218\) −14.3310 10.4121i −0.970619 0.705196i
\(219\) 3.30624 0.223415
\(220\) 0.0556868 + 11.7712i 0.00375440 + 0.793617i
\(221\) −2.60536 −0.175255
\(222\) 10.8861 + 7.90925i 0.730631 + 0.530834i
\(223\) −1.66118 + 5.11257i −0.111241 + 0.342363i −0.991144 0.132789i \(-0.957607\pi\)
0.879904 + 0.475152i \(0.157607\pi\)
\(224\) 0.225399 + 0.693708i 0.0150601 + 0.0463503i
\(225\) −0.809017 + 0.587785i −0.0539345 + 0.0391857i
\(226\) 38.5419 28.0024i 2.56377 1.86269i
\(227\) −6.72202 20.6882i −0.446156 1.37313i −0.881211 0.472723i \(-0.843271\pi\)
0.435055 0.900404i \(-0.356729\pi\)
\(228\) −6.08616 + 18.7313i −0.403066 + 1.24051i
\(229\) −2.16068 1.56983i −0.142782 0.103737i 0.514101 0.857730i \(-0.328126\pi\)
−0.656883 + 0.753992i \(0.728126\pi\)
\(230\) 11.3082 0.745639
\(231\) −0.379726 0.517482i −0.0249842 0.0340478i
\(232\) 36.9240 2.42418
\(233\) 4.63323 + 3.36624i 0.303533 + 0.220530i 0.729117 0.684389i \(-0.239931\pi\)
−0.425584 + 0.904919i \(0.639931\pi\)
\(234\) −0.708805 + 2.18148i −0.0463360 + 0.142608i
\(235\) −3.35354 10.3211i −0.218761 0.673277i
\(236\) 32.2110 23.4027i 2.09676 1.52338i
\(237\) −8.21389 + 5.96774i −0.533550 + 0.387647i
\(238\) 0.376945 + 1.16012i 0.0244337 + 0.0751992i
\(239\) −7.53013 + 23.1754i −0.487084 + 1.49909i 0.341857 + 0.939752i \(0.388944\pi\)
−0.828940 + 0.559337i \(0.811056\pi\)
\(240\) −1.21225 0.880754i −0.0782506 0.0568524i
\(241\) −16.7082 −1.07627 −0.538135 0.842859i \(-0.680871\pi\)
−0.538135 + 0.842859i \(0.680871\pi\)
\(242\) −20.8185 + 15.4286i −1.33827 + 0.991788i
\(243\) 1.00000 0.0641500
\(244\) −3.46293 2.51597i −0.221691 0.161068i
\(245\) −2.15155 + 6.62178i −0.137457 + 0.423050i
\(246\) 6.02636 + 18.5472i 0.384227 + 1.18253i
\(247\) 4.37136 3.17598i 0.278143 0.202083i
\(248\) −7.39682 + 5.37410i −0.469698 + 0.341256i
\(249\) 2.56950 + 7.90811i 0.162835 + 0.501156i
\(250\) −0.727943 + 2.24038i −0.0460392 + 0.141694i
\(251\) 13.0239 + 9.46240i 0.822060 + 0.597262i 0.917302 0.398193i \(-0.130362\pi\)
−0.0952418 + 0.995454i \(0.530362\pi\)
\(252\) 0.686867 0.0432685
\(253\) 9.41903 + 12.8360i 0.592169 + 0.806995i
\(254\) −16.7258 −1.04947
\(255\) 2.16469 + 1.57274i 0.135558 + 0.0984888i
\(256\) −7.53728 + 23.1974i −0.471080 + 1.44984i
\(257\) 1.84445 + 5.67662i 0.115053 + 0.354098i 0.991958 0.126566i \(-0.0403956\pi\)
−0.876905 + 0.480664i \(0.840396\pi\)
\(258\) 9.74527 7.08035i 0.606714 0.440804i
\(259\) −0.894336 + 0.649773i −0.0555713 + 0.0403749i
\(260\) 1.06793 + 3.28674i 0.0662301 + 0.203835i
\(261\) −3.12657 + 9.62260i −0.193530 + 0.595624i
\(262\) −4.76490 3.46191i −0.294377 0.213877i
\(263\) −0.451149 −0.0278190 −0.0139095 0.999903i \(-0.504428\pi\)
−0.0139095 + 0.999903i \(0.504428\pi\)
\(264\) −0.0572591 12.1036i −0.00352405 0.744925i
\(265\) −9.28879 −0.570606
\(266\) −2.04666 1.48698i −0.125489 0.0911728i
\(267\) 2.26902 6.98333i 0.138862 0.427373i
\(268\) 3.57459 + 11.0015i 0.218353 + 0.672021i
\(269\) −11.9085 + 8.65203i −0.726074 + 0.527524i −0.888319 0.459227i \(-0.848127\pi\)
0.162245 + 0.986751i \(0.448127\pi\)
\(270\) 1.90578 1.38463i 0.115982 0.0842659i
\(271\) 1.36829 + 4.21115i 0.0831175 + 0.255809i 0.983975 0.178305i \(-0.0570614\pi\)
−0.900858 + 0.434114i \(0.857061\pi\)
\(272\) −1.23896 + 3.81312i −0.0751228 + 0.231204i
\(273\) −0.152450 0.110762i −0.00922671 0.00670360i
\(274\) 36.0286 2.17657
\(275\) −3.14941 + 1.03980i −0.189917 + 0.0627025i
\(276\) −17.0376 −1.02554
\(277\) 0.0746965 + 0.0542702i 0.00448808 + 0.00326078i 0.590027 0.807383i \(-0.299117\pi\)
−0.585539 + 0.810644i \(0.699117\pi\)
\(278\) 14.3104 44.0427i 0.858278 2.64151i
\(279\) −0.774188 2.38271i −0.0463494 0.142649i
\(280\) 0.571377 0.415129i 0.0341463 0.0248087i
\(281\) −4.19314 + 3.04650i −0.250142 + 0.181739i −0.705790 0.708421i \(-0.749408\pi\)
0.455648 + 0.890160i \(0.349408\pi\)
\(282\) 7.89985 + 24.3133i 0.470429 + 1.44783i
\(283\) 0.483496 1.48805i 0.0287408 0.0884552i −0.935657 0.352910i \(-0.885192\pi\)
0.964398 + 0.264455i \(0.0851921\pi\)
\(284\) −17.2017 12.4978i −1.02073 0.741607i
\(285\) −5.54920 −0.328706
\(286\) −4.44240 + 6.17566i −0.262684 + 0.365174i
\(287\) −1.60214 −0.0945710
\(288\) −3.04920 2.21537i −0.179676 0.130542i
\(289\) −3.04091 + 9.35897i −0.178877 + 0.550527i
\(290\) 7.36518 + 22.6677i 0.432498 + 1.33109i
\(291\) 12.8248 9.31774i 0.751802 0.546216i
\(292\) −9.49341 + 6.89736i −0.555560 + 0.403638i
\(293\) −7.15592 22.0236i −0.418053 1.28664i −0.909491 0.415723i \(-0.863529\pi\)
0.491438 0.870912i \(-0.336471\pi\)
\(294\) 5.06834 15.5987i 0.295592 0.909737i
\(295\) 9.07556 + 6.59378i 0.528400 + 0.383905i
\(296\) −20.8461 −1.21165
\(297\) 3.15911 + 1.00996i 0.183310 + 0.0586038i
\(298\) 23.8699 1.38274
\(299\) 3.78150 + 2.74742i 0.218690 + 0.158887i
\(300\) 1.09676 3.37549i 0.0633217 0.194884i
\(301\) 0.305805 + 0.941172i 0.0176263 + 0.0542483i
\(302\) 22.7991 16.5646i 1.31194 0.953183i
\(303\) −10.6460 + 7.73475i −0.611595 + 0.444350i
\(304\) −2.56950 7.90811i −0.147371 0.453561i
\(305\) 0.372682 1.14700i 0.0213397 0.0656768i
\(306\) −5.09931 3.70486i −0.291508 0.211793i
\(307\) −7.72480 −0.440878 −0.220439 0.975401i \(-0.570749\pi\)
−0.220439 + 0.975401i \(0.570749\pi\)
\(308\) 2.16989 + 0.693708i 0.123641 + 0.0395277i
\(309\) 3.99737 0.227402
\(310\) −4.77460 3.46895i −0.271179 0.197023i
\(311\) −5.90867 + 18.1850i −0.335050 + 1.03118i 0.631647 + 0.775256i \(0.282379\pi\)
−0.966697 + 0.255922i \(0.917621\pi\)
\(312\) −1.09808 3.37955i −0.0621666 0.191329i
\(313\) −2.34863 + 1.70638i −0.132752 + 0.0964503i −0.652180 0.758064i \(-0.726145\pi\)
0.519427 + 0.854515i \(0.326145\pi\)
\(314\) −5.00468 + 3.63611i −0.282430 + 0.205198i
\(315\) 0.0598032 + 0.184055i 0.00336953 + 0.0103703i
\(316\) 11.1354 34.2711i 0.626413 1.92790i
\(317\) −1.82962 1.32930i −0.102762 0.0746607i 0.535218 0.844714i \(-0.320230\pi\)
−0.637979 + 0.770053i \(0.720230\pi\)
\(318\) 21.8814 1.22705
\(319\) −19.5956 + 27.2411i −1.09714 + 1.52521i
\(320\) −11.8754 −0.663857
\(321\) −3.95352 2.87240i −0.220664 0.160322i
\(322\) 0.676265 2.08133i 0.0376868 0.115988i
\(323\) 4.58829 + 14.1213i 0.255299 + 0.785731i
\(324\) −2.87136 + 2.08617i −0.159520 + 0.115898i
\(325\) −0.787747 + 0.572331i −0.0436963 + 0.0317472i
\(326\) −17.2693 53.1496i −0.956460 2.94368i
\(327\) −2.32374 + 7.15172i −0.128503 + 0.395491i
\(328\) −24.4421 17.7582i −1.34959 0.980533i
\(329\) −2.10021 −0.115788
\(330\) 7.41899 2.44944i 0.408402 0.134837i
\(331\) 6.02336 0.331074 0.165537 0.986204i \(-0.447064\pi\)
0.165537 + 0.986204i \(0.447064\pi\)
\(332\) −23.8756 17.3466i −1.31034 0.952021i
\(333\) 1.76516 5.43260i 0.0967301 0.297705i
\(334\) −2.54179 7.82284i −0.139081 0.428047i
\(335\) −2.63676 + 1.91572i −0.144062 + 0.104667i
\(336\) −0.234604 + 0.170450i −0.0127987 + 0.00929879i
\(337\) −4.50076 13.8519i −0.245172 0.754562i −0.995608 0.0936187i \(-0.970157\pi\)
0.750436 0.660943i \(-0.229843\pi\)
\(338\) 8.77310 27.0008i 0.477193 1.46865i
\(339\) −16.3613 11.8872i −0.888625 0.645624i
\(340\) −9.49662 −0.515026
\(341\) −0.0393084 8.30913i −0.00212867 0.449965i
\(342\) 13.0721 0.706859
\(343\) 2.18607 + 1.58827i 0.118037 + 0.0857587i
\(344\) −5.76669 + 17.7480i −0.310919 + 0.956911i
\(345\) −1.48341 4.56545i −0.0798639 0.245796i
\(346\) −38.8009 + 28.1905i −2.08595 + 1.51553i
\(347\) −23.3281 + 16.9489i −1.25232 + 0.909863i −0.998354 0.0573506i \(-0.981735\pi\)
−0.253965 + 0.967213i \(0.581735\pi\)
\(348\) −11.0968 34.1525i −0.594853 1.83077i
\(349\) −0.504421 + 1.55245i −0.0270010 + 0.0831006i −0.963649 0.267172i \(-0.913911\pi\)
0.936648 + 0.350272i \(0.113911\pi\)
\(350\) 0.368820 + 0.267964i 0.0197143 + 0.0143233i
\(351\) 0.973708 0.0519727
\(352\) −7.39533 10.0782i −0.394172 0.537169i
\(353\) 24.9297 1.32687 0.663437 0.748232i \(-0.269097\pi\)
0.663437 + 0.748232i \(0.269097\pi\)
\(354\) −21.3791 15.5328i −1.13628 0.825559i
\(355\) 1.85125 5.69757i 0.0982543 0.302396i
\(356\) 8.05321 + 24.7852i 0.426819 + 1.31361i
\(357\) 0.418926 0.304368i 0.0221719 0.0161089i
\(358\) 7.33949 5.33245i 0.387904 0.281829i
\(359\) 8.78874 + 27.0489i 0.463852 + 1.42759i 0.860421 + 0.509584i \(0.170201\pi\)
−0.396569 + 0.918005i \(0.629799\pi\)
\(360\) −1.12773 + 3.47080i −0.0594366 + 0.182927i
\(361\) −9.54125 6.93213i −0.502171 0.364849i
\(362\) 41.4955 2.18095
\(363\) 8.95996 + 6.38115i 0.470276 + 0.334924i
\(364\) 0.668808 0.0350550
\(365\) −2.67480 1.94336i −0.140005 0.101720i
\(366\) −0.877916 + 2.70195i −0.0458894 + 0.141233i
\(367\) −3.22653 9.93023i −0.168423 0.518354i 0.830849 0.556498i \(-0.187855\pi\)
−0.999272 + 0.0381442i \(0.987855\pi\)
\(368\) 5.81930 4.22797i 0.303352 0.220398i
\(369\) 6.69754 4.86604i 0.348660 0.253316i
\(370\) −4.15814 12.7974i −0.216171 0.665307i
\(371\) −0.555499 + 1.70965i −0.0288401 + 0.0887606i
\(372\) 7.19370 + 5.22653i 0.372976 + 0.270983i
\(373\) −2.81747 −0.145883 −0.0729416 0.997336i \(-0.523239\pi\)
−0.0729416 + 0.997336i \(0.523239\pi\)
\(374\) −12.3675 16.8542i −0.639509 0.871508i
\(375\) 1.00000 0.0516398
\(376\) −32.0407 23.2789i −1.65237 1.20052i
\(377\) −3.04437 + 9.36960i −0.156793 + 0.482559i
\(378\) −0.140877 0.433574i −0.00724592 0.0223006i
\(379\) −7.22711 + 5.25080i −0.371231 + 0.269715i −0.757721 0.652578i \(-0.773687\pi\)
0.386490 + 0.922294i \(0.373687\pi\)
\(380\) 15.9338 11.5766i 0.817386 0.593865i
\(381\) 2.19409 + 6.75270i 0.112406 + 0.345951i
\(382\) −0.303625 + 0.934460i −0.0155348 + 0.0478111i
\(383\) 6.90317 + 5.01545i 0.352736 + 0.256278i 0.750016 0.661420i \(-0.230046\pi\)
−0.397280 + 0.917697i \(0.630046\pi\)
\(384\) 20.4366 1.04290
\(385\) 0.00303643 + 0.641850i 0.000154751 + 0.0327117i
\(386\) −27.5532 −1.40242
\(387\) −4.13694 3.00566i −0.210292 0.152786i
\(388\) −17.3862 + 53.5093i −0.882651 + 2.71652i
\(389\) 3.63890 + 11.1994i 0.184500 + 0.567832i 0.999939 0.0110104i \(-0.00350478\pi\)
−0.815440 + 0.578842i \(0.803505\pi\)
\(390\) 1.85567 1.34823i 0.0939657 0.0682701i
\(391\) −10.3914 + 7.54978i −0.525515 + 0.381809i
\(392\) 7.85188 + 24.1656i 0.396580 + 1.22055i
\(393\) −0.772616 + 2.37787i −0.0389733 + 0.119948i
\(394\) 41.1569 + 29.9023i 2.07346 + 1.50645i
\(395\) 10.1529 0.510849
\(396\) −11.1779 + 3.69047i −0.561711 + 0.185453i
\(397\) −1.41214 −0.0708735 −0.0354368 0.999372i \(-0.511282\pi\)
−0.0354368 + 0.999372i \(0.511282\pi\)
\(398\) 14.7894 + 10.7451i 0.741325 + 0.538604i
\(399\) −0.331860 + 1.02136i −0.0166138 + 0.0511319i
\(400\) 0.463040 + 1.42509i 0.0231520 + 0.0712545i
\(401\) −6.84361 + 4.97217i −0.341753 + 0.248298i −0.745401 0.666616i \(-0.767742\pi\)
0.403648 + 0.914914i \(0.367742\pi\)
\(402\) 6.21135 4.51281i 0.309794 0.225078i
\(403\) −0.753833 2.32006i −0.0375511 0.115570i
\(404\) 14.4325 44.4185i 0.718042 2.20991i
\(405\) −0.809017 0.587785i −0.0402004 0.0292073i
\(406\) 4.61257 0.228918
\(407\) 11.0630 15.3794i 0.548375 0.762331i
\(408\) 9.76476 0.483428
\(409\) −8.19172 5.95163i −0.405054 0.294289i 0.366542 0.930401i \(-0.380542\pi\)
−0.771597 + 0.636112i \(0.780542\pi\)
\(410\) 6.02636 18.5472i 0.297621 0.915982i
\(411\) −4.72622 14.5458i −0.233127 0.717493i
\(412\) −11.4779 + 8.33918i −0.565475 + 0.410842i
\(413\) 1.75637 1.27608i 0.0864252 0.0627915i
\(414\) 3.49442 + 10.7547i 0.171741 + 0.528566i
\(415\) 2.56950 7.90811i 0.126132 0.388194i
\(416\) −2.96903 2.15713i −0.145569 0.105762i
\(417\) −19.6586 −0.962686
\(418\) 41.2962 + 13.2023i 2.01987 + 0.645746i
\(419\) 32.8019 1.60248 0.801240 0.598343i \(-0.204174\pi\)
0.801240 + 0.598343i \(0.204174\pi\)
\(420\) −0.555687 0.403730i −0.0271147 0.0197000i
\(421\) −4.36619 + 13.4377i −0.212795 + 0.654915i 0.786508 + 0.617580i \(0.211887\pi\)
−0.999303 + 0.0373351i \(0.988113\pi\)
\(422\) 9.10342 + 28.0175i 0.443148 + 1.36387i
\(423\) 8.77969 6.37882i 0.426883 0.310149i
\(424\) −27.4246 + 19.9251i −1.33185 + 0.967649i
\(425\) −0.826838 2.54475i −0.0401076 0.123438i
\(426\) −4.36095 + 13.4216i −0.211289 + 0.650280i
\(427\) −0.188823 0.137188i −0.00913779 0.00663899i
\(428\) 17.3443 0.838368
\(429\) 3.07605 + 0.983406i 0.148513 + 0.0474793i
\(430\) −12.0458 −0.580901
\(431\) −15.4569 11.2301i −0.744531 0.540933i 0.149596 0.988747i \(-0.452203\pi\)
−0.894127 + 0.447814i \(0.852203\pi\)
\(432\) 0.463040 1.42509i 0.0222780 0.0685646i
\(433\) 4.67235 + 14.3800i 0.224539 + 0.691059i 0.998338 + 0.0576283i \(0.0183538\pi\)
−0.773799 + 0.633431i \(0.781646\pi\)
\(434\) −0.924015 + 0.671336i −0.0443541 + 0.0322252i
\(435\) 8.18547 5.94709i 0.392463 0.285141i
\(436\) −8.24740 25.3829i −0.394979 1.21562i
\(437\) 8.23171 25.3346i 0.393776 1.21192i
\(438\) 6.30096 + 4.57791i 0.301071 + 0.218741i
\(439\) 37.1642 1.77375 0.886876 0.462008i \(-0.152871\pi\)
0.886876 + 0.462008i \(0.152871\pi\)
\(440\) −7.06799 + 9.82567i −0.336953 + 0.468421i
\(441\) −6.96255 −0.331550
\(442\) −4.96524 3.60746i −0.236172 0.171589i
\(443\) −0.853040 + 2.62539i −0.0405291 + 0.124736i −0.969274 0.245984i \(-0.920889\pi\)
0.928745 + 0.370720i \(0.120889\pi\)
\(444\) 6.26490 + 19.2814i 0.297319 + 0.915054i
\(445\) −5.94037 + 4.31593i −0.281601 + 0.204595i
\(446\) −10.2449 + 7.44333i −0.485108 + 0.352452i
\(447\) −3.13125 9.63699i −0.148103 0.455814i
\(448\) −0.710189 + 2.18574i −0.0335533 + 0.103266i
\(449\) 14.4540 + 10.5015i 0.682127 + 0.495594i 0.874063 0.485813i \(-0.161476\pi\)
−0.191936 + 0.981408i \(0.561476\pi\)
\(450\) −2.35567 −0.111048
\(451\) 26.0728 8.60813i 1.22772 0.405341i
\(452\) 71.7780 3.37615
\(453\) −9.67840 7.03177i −0.454731 0.330381i
\(454\) 15.8349 48.7348i 0.743168 2.28724i
\(455\) 0.0582308 + 0.179216i 0.00272990 + 0.00840178i
\(456\) −16.3837 + 11.9034i −0.767236 + 0.557429i
\(457\) 17.1205 12.4388i 0.800864 0.581862i −0.110304 0.993898i \(-0.535182\pi\)
0.911167 + 0.412036i \(0.135182\pi\)
\(458\) −1.94416 5.98350i −0.0908444 0.279590i
\(459\) −0.826838 + 2.54475i −0.0385935 + 0.118779i
\(460\) 13.7837 + 10.0144i 0.642668 + 0.466926i
\(461\) −34.3476 −1.59973 −0.799864 0.600181i \(-0.795095\pi\)
−0.799864 + 0.600181i \(0.795095\pi\)
\(462\) −0.00715284 1.51199i −0.000332780 0.0703441i
\(463\) 10.4516 0.485727 0.242864 0.970060i \(-0.421913\pi\)
0.242864 + 0.970060i \(0.421913\pi\)
\(464\) 12.2653 + 8.91129i 0.569404 + 0.413696i
\(465\) −0.774188 + 2.38271i −0.0359021 + 0.110495i
\(466\) 4.16892 + 12.8306i 0.193122 + 0.594367i
\(467\) −23.9820 + 17.4239i −1.10975 + 0.806284i −0.982625 0.185602i \(-0.940576\pi\)
−0.127129 + 0.991886i \(0.540576\pi\)
\(468\) −2.79587 + 2.03132i −0.129239 + 0.0938978i
\(469\) 0.194911 + 0.599875i 0.00900017 + 0.0276997i
\(470\) 7.89985 24.3133i 0.364393 1.12149i
\(471\) 2.12452 + 1.54355i 0.0978927 + 0.0711232i
\(472\) 40.9392 1.88438
\(473\) −10.0334 13.6734i −0.461338 0.628701i
\(474\) −23.9170 −1.09854
\(475\) 4.48940 + 3.26174i 0.205988 + 0.149659i
\(476\) −0.567928 + 1.74790i −0.0260309 + 0.0801150i
\(477\) −2.87039 8.83416i −0.131426 0.404488i
\(478\) −46.4401 + 33.7407i −2.12412 + 1.54326i
\(479\) 10.6941 7.76971i 0.488625 0.355007i −0.316030 0.948749i \(-0.602350\pi\)
0.804655 + 0.593742i \(0.202350\pi\)
\(480\) 1.16469 + 3.58455i 0.0531606 + 0.163612i
\(481\) 1.71875 5.28977i 0.0783682 0.241193i
\(482\) −31.8422 23.1347i −1.45037 1.05376i
\(483\) −0.929007 −0.0422713
\(484\) −39.0395 + 0.369380i −1.77452 + 0.0167900i
\(485\) −15.8523 −0.719816
\(486\) 1.90578 + 1.38463i 0.0864480 + 0.0628081i
\(487\) −13.1325 + 40.4176i −0.595089 + 1.83150i −0.0408075 + 0.999167i \(0.512993\pi\)
−0.554282 + 0.832329i \(0.687007\pi\)
\(488\) −1.36007 4.18586i −0.0615675 0.189485i
\(489\) −19.1927 + 13.9443i −0.867923 + 0.630583i
\(490\) −13.2691 + 9.64056i −0.599436 + 0.435516i
\(491\) −4.86568 14.9750i −0.219585 0.675813i −0.998796 0.0490515i \(-0.984380\pi\)
0.779211 0.626761i \(-0.215620\pi\)
\(492\) −9.07968 + 27.9444i −0.409343 + 1.25983i
\(493\) −21.9019 15.9127i −0.986412 0.716670i
\(494\) 12.7284 0.572679
\(495\) −1.96213 2.67395i −0.0881914 0.120185i
\(496\) −3.75405 −0.168562
\(497\) −0.937957 0.681466i −0.0420731 0.0305679i
\(498\) −6.05291 + 18.6289i −0.271237 + 0.834782i
\(499\) −10.3607 31.8869i −0.463808 1.42746i −0.860475 0.509493i \(-0.829833\pi\)
0.396666 0.917963i \(-0.370167\pi\)
\(500\) −2.87136 + 2.08617i −0.128411 + 0.0932963i
\(501\) −2.82488 + 2.05240i −0.126206 + 0.0916943i
\(502\) 11.7187 + 36.0665i 0.523032 + 1.60973i
\(503\) −7.05063 + 21.6996i −0.314372 + 0.967537i 0.661640 + 0.749821i \(0.269861\pi\)
−0.976012 + 0.217716i \(0.930139\pi\)
\(504\) 0.571377 + 0.415129i 0.0254511 + 0.0184913i
\(505\) 13.1591 0.585574
\(506\) 0.177425 + 37.5046i 0.00788749 + 1.66728i
\(507\) −12.0519 −0.535243
\(508\) −20.3873 14.8122i −0.904540 0.657187i
\(509\) 12.2731 37.7727i 0.543996 1.67425i −0.179370 0.983782i \(-0.557406\pi\)
0.723365 0.690465i \(-0.242594\pi\)
\(510\) 1.94776 + 5.99460i 0.0862484 + 0.265445i
\(511\) −0.517646 + 0.376092i −0.0228993 + 0.0166373i
\(512\) −13.4170 + 9.74805i −0.592955 + 0.430807i
\(513\) −1.71480 5.27760i −0.0757102 0.233012i
\(514\) −4.34491 + 13.3723i −0.191646 + 0.589826i
\(515\) −3.23394 2.34959i −0.142504 0.103535i
\(516\) 18.1490 0.798963
\(517\) 34.1784 11.2843i 1.50316 0.496281i
\(518\) −2.60410 −0.114418
\(519\) 16.4712 + 11.9670i 0.723007 + 0.525295i
\(520\) −1.09808 + 3.37955i −0.0481540 + 0.148203i
\(521\) 7.88005 + 24.2523i 0.345231 + 1.06251i 0.961460 + 0.274945i \(0.0886597\pi\)
−0.616229 + 0.787567i \(0.711340\pi\)
\(522\) −19.2823 + 14.0094i −0.843963 + 0.613175i
\(523\) 12.4835 9.06977i 0.545864 0.396593i −0.280394 0.959885i \(-0.590465\pi\)
0.826258 + 0.563291i \(0.190465\pi\)
\(524\) −2.74217 8.43953i −0.119792 0.368683i
\(525\) 0.0598032 0.184055i 0.00261002 0.00803283i
\(526\) −0.859791 0.624675i −0.0374887 0.0272371i
\(527\) 6.70351 0.292010
\(528\) 2.90208 4.03436i 0.126297 0.175573i
\(529\) 0.0438407 0.00190612
\(530\) −17.7024 12.8615i −0.768943 0.558669i
\(531\) −3.46656 + 10.6690i −0.150436 + 0.462993i
\(532\) −1.17784 3.62501i −0.0510657 0.157164i
\(533\) 6.52145 4.73811i 0.282475 0.205230i
\(534\) 13.9936 10.1669i 0.605561 0.439966i
\(535\) 1.51011 + 4.64764i 0.0652877 + 0.200935i
\(536\) −3.67552 + 11.3121i −0.158758 + 0.488607i
\(537\) −3.11567 2.26366i −0.134451 0.0976843i
\(538\) −34.6749 −1.49494
\(539\) −21.9955 7.03189i −0.947411 0.302885i
\(540\) 3.54920 0.152733
\(541\) −22.3294 16.2233i −0.960018 0.697494i −0.00686309 0.999976i \(-0.502185\pi\)
−0.953155 + 0.302483i \(0.902185\pi\)
\(542\) −3.22324 + 9.92010i −0.138450 + 0.426105i
\(543\) −5.44337 16.7530i −0.233597 0.718938i
\(544\) 8.15877 5.92769i 0.349804 0.254148i
\(545\) 6.08362 4.42001i 0.260594 0.189332i
\(546\) −0.137173 0.422175i −0.00587046 0.0180674i
\(547\) 9.50800 29.2626i 0.406533 1.25118i −0.513076 0.858343i \(-0.671494\pi\)
0.919608 0.392836i \(-0.128506\pi\)
\(548\) 43.9157 + 31.9067i 1.87599 + 1.36298i
\(549\) 1.20602 0.0514718
\(550\) −7.44184 2.37914i −0.317321 0.101447i
\(551\) 56.1457 2.39189
\(552\) −14.1729 10.2972i −0.603238 0.438278i
\(553\) 0.607177 1.86870i 0.0258198 0.0794652i
\(554\) 0.0672109 + 0.206854i 0.00285552 + 0.00878838i
\(555\) −4.62125 + 3.35753i −0.196161 + 0.142519i
\(556\) 56.4470 41.0112i 2.39389 1.73926i
\(557\) −4.30642 13.2538i −0.182469 0.561582i 0.817427 0.576033i \(-0.195400\pi\)
−0.999896 + 0.0144509i \(0.995400\pi\)
\(558\) 1.82374 5.61288i 0.0772049 0.237612i
\(559\) −4.02817 2.92664i −0.170373 0.123783i
\(560\) 0.289986 0.0122542
\(561\) −5.18217 + 7.20406i −0.218791 + 0.304156i
\(562\) −12.2095 −0.515026
\(563\) −4.72456 3.43259i −0.199117 0.144667i 0.483759 0.875201i \(-0.339271\pi\)
−0.682876 + 0.730534i \(0.739271\pi\)
\(564\) −11.9024 + 36.6318i −0.501181 + 1.54248i
\(565\) 6.24947 + 19.2339i 0.262917 + 0.809176i
\(566\) 2.98183 2.16643i 0.125336 0.0910618i
\(567\) −0.156567 + 0.113752i −0.00657518 + 0.00477715i
\(568\) −6.75599 20.7928i −0.283475 0.872447i
\(569\) −1.68536 + 5.18701i −0.0706540 + 0.217451i −0.980148 0.198266i \(-0.936469\pi\)
0.909494 + 0.415716i \(0.136469\pi\)
\(570\) −10.5756 7.68359i −0.442961 0.321830i
\(571\) 40.2894 1.68606 0.843030 0.537866i \(-0.180770\pi\)
0.843030 + 0.537866i \(0.180770\pi\)
\(572\) −10.8840 + 3.59344i −0.455084 + 0.150249i
\(573\) 0.417099 0.0174246
\(574\) −3.05332 2.21837i −0.127443 0.0925928i
\(575\) −1.48341 + 4.56545i −0.0618623 + 0.190392i
\(576\) −3.66971 11.2942i −0.152905 0.470592i
\(577\) 19.2737 14.0032i 0.802374 0.582959i −0.109236 0.994016i \(-0.534840\pi\)
0.911610 + 0.411057i \(0.134840\pi\)
\(578\) −18.7540 + 13.6256i −0.780065 + 0.566750i
\(579\) 3.61443 + 11.1241i 0.150210 + 0.462300i
\(580\) −11.0968 + 34.1525i −0.460771 + 1.41811i
\(581\) −1.30186 0.945860i −0.0540104 0.0392409i
\(582\) 37.3428 1.54791
\(583\) −0.145740 30.8071i −0.00603595 1.27590i
\(584\) −12.0658 −0.499287
\(585\) −0.787747 0.572331i −0.0325693 0.0236630i
\(586\) 16.8570 51.8805i 0.696357 2.14317i
\(587\) 6.05919 + 18.6483i 0.250090 + 0.769697i 0.994758 + 0.102262i \(0.0326079\pi\)
−0.744668 + 0.667435i \(0.767392\pi\)
\(588\) 19.9920 14.5250i 0.824457 0.599003i
\(589\) −11.2474 + 8.17172i −0.463441 + 0.336710i
\(590\) 8.16608 + 25.1326i 0.336192 + 1.03469i
\(591\) 6.67348 20.5389i 0.274510 0.844856i
\(592\) −6.92460 5.03102i −0.284599 0.206774i
\(593\) 3.31095 0.135964 0.0679822 0.997687i \(-0.478344\pi\)
0.0679822 + 0.997687i \(0.478344\pi\)
\(594\) 4.62215 + 6.29896i 0.189649 + 0.258450i
\(595\) −0.517822 −0.0212286
\(596\) 29.0953 + 21.1390i 1.19179 + 0.865887i
\(597\) 2.39806 7.38046i 0.0981460 0.302062i
\(598\) 3.40255 + 10.4720i 0.139140 + 0.428230i
\(599\) −25.9460 + 18.8509i −1.06012 + 0.770225i −0.974111 0.226069i \(-0.927413\pi\)
−0.0860126 + 0.996294i \(0.527413\pi\)
\(600\) 2.95244 2.14507i 0.120533 0.0875722i
\(601\) −9.05125 27.8569i −0.369208 1.13631i −0.947304 0.320337i \(-0.896204\pi\)
0.578095 0.815969i \(-0.303796\pi\)
\(602\) −0.720378 + 2.21710i −0.0293604 + 0.0903621i
\(603\) −2.63676 1.91572i −0.107377 0.0780141i
\(604\) 42.4596 1.72766
\(605\) −3.49802 10.4290i −0.142215 0.423999i
\(606\) −30.9986 −1.25923
\(607\) 31.6169 + 22.9710i 1.28329 + 0.932364i 0.999647 0.0265657i \(-0.00845712\pi\)
0.283642 + 0.958930i \(0.408457\pi\)
\(608\) −6.46311 + 19.8914i −0.262114 + 0.806703i
\(609\) −0.605076 1.86223i −0.0245189 0.0754615i
\(610\) 2.29842 1.66990i 0.0930601 0.0676121i
\(611\) 8.54886 6.21111i 0.345850 0.251275i
\(612\) −2.93462 9.03182i −0.118625 0.365090i
\(613\) −3.93452 + 12.1092i −0.158914 + 0.489086i −0.998536 0.0540840i \(-0.982776\pi\)
0.839623 + 0.543170i \(0.182776\pi\)
\(614\) −14.7218 10.6960i −0.594123 0.431655i
\(615\) −8.27861 −0.333826
\(616\) 1.38578 + 1.88851i 0.0558346 + 0.0760901i
\(617\) −8.97789 −0.361436 −0.180718 0.983535i \(-0.557842\pi\)
−0.180718 + 0.983535i \(0.557842\pi\)
\(618\) 7.61810 + 5.53487i 0.306445 + 0.222645i
\(619\) −6.86392 + 21.1250i −0.275884 + 0.849084i 0.713100 + 0.701062i \(0.247290\pi\)
−0.988984 + 0.148022i \(0.952710\pi\)
\(620\) −2.74775 8.45670i −0.110352 0.339629i
\(621\) 3.88361 2.82160i 0.155844 0.113227i
\(622\) −36.4402 + 26.4753i −1.46112 + 1.06156i
\(623\) 0.439117 + 1.35146i 0.0175928 + 0.0541452i
\(624\) 0.450866 1.38762i 0.0180491 0.0555493i
\(625\) −0.809017 0.587785i −0.0323607 0.0235114i
\(626\) −6.83868 −0.273329
\(627\) −0.0870666 18.4044i −0.00347711 0.735001i
\(628\) −9.32038 −0.371924
\(629\) 12.3651 + 8.98377i 0.493029 + 0.358206i
\(630\) −0.140877 + 0.433574i −0.00561266 + 0.0172740i
\(631\) 8.27153 + 25.4572i 0.329285 + 1.01343i 0.969469 + 0.245213i \(0.0788578\pi\)
−0.640185 + 0.768221i \(0.721142\pi\)
\(632\) 29.9759 21.7788i 1.19238 0.866313i
\(633\) 10.1173 7.35065i 0.402127 0.292162i
\(634\) −1.64627 5.06670i −0.0653817 0.201224i
\(635\) 2.19409 6.75270i 0.0870697 0.267973i
\(636\) 26.6715 + 19.3780i 1.05759 + 0.768386i
\(637\) −6.77949 −0.268613
\(638\) −75.0639 + 24.7829i −2.97181 + 0.981166i
\(639\) 5.99078 0.236992
\(640\) −16.5336 12.0123i −0.653547 0.474830i
\(641\) 4.65770 14.3349i 0.183968 0.566195i −0.815961 0.578107i \(-0.803792\pi\)
0.999929 + 0.0119117i \(0.00379170\pi\)
\(642\) −3.55733 10.9483i −0.140396 0.432096i
\(643\) 31.7840 23.0925i 1.25344 0.910678i 0.255024 0.966935i \(-0.417917\pi\)
0.998416 + 0.0562569i \(0.0179166\pi\)
\(644\) 2.66752 1.93807i 0.105115 0.0763705i
\(645\) 1.58017 + 4.86326i 0.0622191 + 0.191491i
\(646\) −10.8085 + 33.2652i −0.425256 + 1.30880i
\(647\) −19.2656 13.9973i −0.757408 0.550289i 0.140706 0.990051i \(-0.455063\pi\)
−0.898114 + 0.439762i \(0.855063\pi\)
\(648\) −3.64941 −0.143363
\(649\) −21.7265 + 30.2033i −0.852838 + 1.18559i
\(650\) −2.29374 −0.0899679
\(651\) 0.392251 + 0.284987i 0.0153735 + 0.0111695i
\(652\) 26.0190 80.0784i 1.01898 3.13611i
\(653\) 2.13331 + 6.56566i 0.0834829 + 0.256934i 0.984081 0.177718i \(-0.0568714\pi\)
−0.900599 + 0.434652i \(0.856871\pi\)
\(654\) −14.3310 + 10.4121i −0.560387 + 0.407145i
\(655\) 2.02273 1.46960i 0.0790348 0.0574221i
\(656\) −3.83332 11.7978i −0.149666 0.460625i
\(657\) 1.02168 3.14442i 0.0398596 0.122675i
\(658\) −4.00254 2.90802i −0.156035 0.113366i
\(659\) −20.3718 −0.793571 −0.396786 0.917911i \(-0.629874\pi\)
−0.396786 + 0.917911i \(0.629874\pi\)
\(660\) 11.2123 + 3.58455i 0.436439 + 0.139528i
\(661\) −19.7451 −0.767994 −0.383997 0.923334i \(-0.625453\pi\)
−0.383997 + 0.923334i \(0.625453\pi\)
\(662\) 11.4792 + 8.34013i 0.446152 + 0.324148i
\(663\) −0.805099 + 2.47784i −0.0312675 + 0.0962314i
\(664\) −9.37717 28.8600i −0.363905 1.11998i
\(665\) 0.868820 0.631235i 0.0336914 0.0244782i
\(666\) 10.8861 7.90925i 0.421830 0.306477i
\(667\) 15.0088 + 46.1923i 0.581143 + 1.78857i
\(668\) 3.82962 11.7864i 0.148172 0.456028i
\(669\) 4.34901 + 3.15974i 0.168143 + 0.122163i
\(670\) −7.67765 −0.296613
\(671\) 3.80996 + 1.21803i 0.147082 + 0.0470217i
\(672\) 0.729407 0.0281375
\(673\) −29.6207 21.5207i −1.14180 0.829563i −0.154427 0.988004i \(-0.549353\pi\)
−0.987368 + 0.158441i \(0.949353\pi\)
\(674\) 10.6023 32.6306i 0.408386 1.25688i
\(675\) 0.309017 + 0.951057i 0.0118941 + 0.0366062i
\(676\) 34.6054 25.1423i 1.33098 0.967011i
\(677\) −5.96357 + 4.33279i −0.229199 + 0.166523i −0.696458 0.717598i \(-0.745242\pi\)
0.467259 + 0.884120i \(0.345242\pi\)
\(678\) −14.7217 45.3088i −0.565384 1.74007i
\(679\) −0.948017 + 2.91770i −0.0363816 + 0.111971i
\(680\) −7.89985 5.73958i −0.302946 0.220103i
\(681\) −21.7529 −0.833573
\(682\) 11.4302 15.8898i 0.437684 0.608452i
\(683\) 24.5651 0.939959 0.469979 0.882677i \(-0.344261\pi\)
0.469979 + 0.882677i \(0.344261\pi\)
\(684\) 15.9338 + 11.5766i 0.609243 + 0.442641i
\(685\) −4.72622 + 14.5458i −0.180580 + 0.555767i
\(686\) 1.96700 + 6.05380i 0.0751004 + 0.231135i
\(687\) −2.16068 + 1.56983i −0.0824352 + 0.0598927i
\(688\) −6.19890 + 4.50376i −0.236331 + 0.171704i
\(689\) −2.79492 8.60189i −0.106478 0.327706i
\(690\) 3.49442 10.7547i 0.133030 0.409425i
\(691\) −24.1439 17.5416i −0.918479 0.667314i 0.0246662 0.999696i \(-0.492148\pi\)
−0.943145 + 0.332382i \(0.892148\pi\)
\(692\) −72.2602 −2.74692
\(693\) −0.609497 + 0.201230i −0.0231529 + 0.00764410i
\(694\) −67.9262 −2.57844
\(695\) 15.9041 + 11.5550i 0.603279 + 0.438308i
\(696\) 11.4102 35.1168i 0.432501 1.33110i
\(697\) 6.84507 + 21.0670i 0.259276 + 0.797968i
\(698\) −3.11088 + 2.26019i −0.117749 + 0.0855494i
\(699\) 4.63323 3.36624i 0.175245 0.127323i
\(700\) 0.212253 + 0.653249i 0.00802243 + 0.0246905i
\(701\) −4.45569 + 13.7132i −0.168289 + 0.517940i −0.999264 0.0383701i \(-0.987783\pi\)
0.830975 + 0.556310i \(0.187783\pi\)
\(702\) 1.85567 + 1.34823i 0.0700379 + 0.0508855i
\(703\) −31.6980 −1.19551
\(704\) −0.186325 39.3859i −0.00702238 1.48441i
\(705\) −10.8523 −0.408721
\(706\) 47.5106 + 34.5184i 1.78808 + 1.29912i
\(707\) 0.786958 2.42201i 0.0295966 0.0910890i
\(708\) −12.3035 37.8663i −0.462394 1.42310i
\(709\) 36.0084 26.1616i 1.35232 0.982520i 0.353430 0.935461i \(-0.385015\pi\)
0.998892 0.0470585i \(-0.0149847\pi\)
\(710\) 11.4171 8.29502i 0.428477 0.311307i
\(711\) 3.13743 + 9.65601i 0.117663 + 0.362129i
\(712\) −8.28059 + 25.4850i −0.310328 + 0.955093i
\(713\) −9.72970 7.06904i −0.364380 0.264738i
\(714\) 1.21982 0.0456506
\(715\) −1.91055 2.60365i −0.0714504 0.0973710i
\(716\) 13.6686 0.510819
\(717\) 19.7141 + 14.3232i 0.736238 + 0.534908i
\(718\) −20.7034 + 63.7185i −0.772644 + 2.37795i
\(719\) 1.11044 + 3.41758i 0.0414124 + 0.127454i 0.969625 0.244595i \(-0.0786551\pi\)
−0.928213 + 0.372050i \(0.878655\pi\)
\(720\) −1.21225 + 0.880754i −0.0451780 + 0.0328238i
\(721\) −0.625854 + 0.454710i −0.0233080 + 0.0169343i
\(722\) −8.58510 26.4222i −0.319504 0.983333i
\(723\) −5.16312 + 15.8904i −0.192018 + 0.590972i
\(724\) 50.5794 + 36.7481i 1.87977 + 1.36573i
\(725\) −10.1178 −0.375766
\(726\) 8.24018 + 24.5673i 0.305822 + 0.911778i
\(727\) −39.0846 −1.44957 −0.724784 0.688976i \(-0.758060\pi\)
−0.724784 + 0.688976i \(0.758060\pi\)
\(728\) 0.556354 + 0.404215i 0.0206199 + 0.0149812i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) −2.40675 7.40722i −0.0890779 0.274154i
\(731\) 11.0692 8.04226i 0.409410 0.297454i
\(732\) −3.46293 + 2.51597i −0.127994 + 0.0929928i
\(733\) 11.6519 + 35.8610i 0.430374 + 1.32455i 0.897753 + 0.440498i \(0.145198\pi\)
−0.467379 + 0.884057i \(0.654802\pi\)
\(734\) 7.60065 23.3924i 0.280545 0.863429i
\(735\) 5.63282 + 4.09248i 0.207770 + 0.150953i
\(736\) −18.0928 −0.666910
\(737\) −6.39502 8.71499i −0.235564 0.321021i
\(738\) 19.5017 0.717868
\(739\) −12.0806 8.77706i −0.444392 0.322869i 0.342986 0.939341i \(-0.388562\pi\)
−0.787377 + 0.616471i \(0.788562\pi\)
\(740\) 6.26490 19.2814i 0.230302 0.708798i
\(741\) −1.66971 5.13885i −0.0613384 0.188780i
\(742\) −3.42589 + 2.48906i −0.125768 + 0.0913761i
\(743\) −10.8149 + 7.85749i −0.396760 + 0.288263i −0.768220 0.640186i \(-0.778857\pi\)
0.371460 + 0.928449i \(0.378857\pi\)
\(744\) 2.82533 + 8.69548i 0.103582 + 0.318792i
\(745\) −3.13125 + 9.63699i −0.114720 + 0.353072i
\(746\) −5.36949 3.90116i −0.196591 0.142832i
\(747\) 8.31508 0.304233
\(748\) −0.149001 31.4964i −0.00544803 1.15162i
\(749\) 0.945731 0.0345563
\(750\) 1.90578 + 1.38463i 0.0695893 + 0.0505596i
\(751\) 12.5045 38.4849i 0.456296 1.40434i −0.413310 0.910590i \(-0.635627\pi\)
0.869606 0.493745i \(-0.164373\pi\)
\(752\) −5.02504 15.4655i −0.183244 0.563968i
\(753\) 13.0239 9.46240i 0.474617 0.344829i
\(754\) −18.7753 + 13.6411i −0.683757 + 0.496779i
\(755\) 3.69682 + 11.3776i 0.134541 + 0.414075i
\(756\) 0.212253 0.653249i 0.00771958 0.0237584i
\(757\) 6.90704 + 5.01826i 0.251040 + 0.182392i 0.706188 0.708025i \(-0.250413\pi\)
−0.455147 + 0.890416i \(0.650413\pi\)
\(758\) −21.0437 −0.764341
\(759\) 15.1184 4.99148i 0.548765 0.181179i
\(760\) 20.2513 0.734593
\(761\) 17.2162 + 12.5083i 0.624089 + 0.453427i 0.854347 0.519703i \(-0.173957\pi\)
−0.230259 + 0.973129i \(0.573957\pi\)
\(762\) −5.16855 + 15.9072i −0.187237 + 0.576256i
\(763\) −0.449706 1.38405i −0.0162804 0.0501060i
\(764\) −1.19764 + 0.870139i −0.0433292 + 0.0314805i
\(765\) 2.16469 1.57274i 0.0782646 0.0568625i
\(766\) 6.21139 + 19.1167i 0.224427 + 0.690714i
\(767\) −3.37541 + 10.3885i −0.121879 + 0.375105i
\(768\) 19.7329 + 14.3368i 0.712048 + 0.517333i
\(769\) −24.4717 −0.882471 −0.441235 0.897391i \(-0.645460\pi\)
−0.441235 + 0.897391i \(0.645460\pi\)
\(770\) −0.882938 + 1.22743i −0.0318189 + 0.0442335i
\(771\) 5.96875 0.214959
\(772\) −33.5850 24.4009i −1.20875 0.878209i
\(773\) 4.21721 12.9792i 0.151682 0.466830i −0.846127 0.532981i \(-0.821072\pi\)
0.997810 + 0.0661505i \(0.0210717\pi\)
\(774\) −3.72236 11.4563i −0.133798 0.411787i
\(775\) 2.02685 1.47259i 0.0728066 0.0528971i
\(776\) −46.8029 + 34.0043i −1.68013 + 1.22068i
\(777\) 0.341606 + 1.05136i 0.0122550 + 0.0377172i
\(778\) −8.57207 + 26.3821i −0.307324 + 0.945845i
\(779\) −37.1660 27.0027i −1.33161 0.967471i
\(780\) 3.45589 0.123741
\(781\) 18.9255 + 6.05045i 0.677209 + 0.216502i
\(782\) −30.2574 −1.08200
\(783\) 8.18547 + 5.94709i 0.292525 + 0.212532i
\(784\) −3.22394 + 9.92225i −0.115141 + 0.354366i
\(785\) −0.811494 2.49752i −0.0289635 0.0891404i
\(786\) −4.76490 + 3.46191i −0.169958 + 0.123482i
\(787\) 6.03291 4.38317i 0.215050 0.156243i −0.475046 0.879961i \(-0.657568\pi\)
0.690096 + 0.723718i \(0.257568\pi\)
\(788\) 23.6855 + 72.8966i 0.843762 + 2.59683i
\(789\) −0.139413 + 0.429068i −0.00496322 + 0.0152752i
\(790\) 19.3493 + 14.0581i 0.688416 + 0.500163i
\(791\) 3.91383 0.139160
\(792\) −11.5289 3.68576i −0.409662 0.130968i
\(793\) 1.17431 0.0417011
\(794\) −2.69124 1.95530i −0.0955085 0.0693910i
\(795\) −2.87039 + 8.83416i −0.101802 + 0.313315i
\(796\) 8.51119 + 26.1947i 0.301671 + 0.928448i
\(797\) −9.73624 + 7.07379i −0.344875 + 0.250567i −0.746716 0.665143i \(-0.768371\pi\)
0.401841 + 0.915710i \(0.368371\pi\)
\(798\) −2.04666 + 1.48698i −0.0724509 + 0.0526386i
\(799\) 8.97309 + 27.6163i 0.317445 + 0.976996i
\(800\) 1.16469 3.58455i 0.0411781 0.126733i
\(801\) −5.94037 4.31593i −0.209893 0.152496i
\(802\) −19.9270 −0.703648
\(803\) 6.40334 8.90170i 0.225969 0.314134i
\(804\) 11.5676 0.407958
\(805\) 0.751583 + 0.546057i 0.0264898 + 0.0192460i
\(806\) 1.77579 5.46531i 0.0625494 0.192507i
\(807\) 4.54864 + 13.9993i 0.160120 + 0.492798i
\(808\) 38.8515 28.2273i 1.36679 0.993033i
\(809\) 40.4782 29.4091i 1.42314 1.03397i 0.431892 0.901925i \(-0.357846\pi\)
0.991244 0.132044i \(-0.0421539\pi\)
\(810\) −0.727943 2.24038i −0.0255773 0.0787189i
\(811\) −3.46678 + 10.6697i −0.121735 + 0.374663i −0.993292 0.115632i \(-0.963111\pi\)
0.871557 + 0.490294i \(0.163111\pi\)
\(812\) 5.62233 + 4.08486i 0.197305 + 0.143350i
\(813\) 4.42787 0.155292
\(814\) 42.3786 13.9916i 1.48537 0.490406i
\(815\) 23.7235 0.830997
\(816\) 3.24363 + 2.35664i 0.113550 + 0.0824988i
\(817\) −8.76867 + 26.9872i −0.306777 + 0.944163i
\(818\) −7.37080 22.6850i −0.257714 0.793163i
\(819\) −0.152450 + 0.110762i −0.00532704 + 0.00387032i
\(820\) 23.7709 17.2706i 0.830116 0.603114i
\(821\) 2.27969 + 7.01616i 0.0795617 + 0.244866i 0.982924 0.184013i \(-0.0589088\pi\)
−0.903362 + 0.428879i \(0.858909\pi\)
\(822\) 11.1334 34.2652i 0.388323 1.19514i
\(823\) −28.8318 20.9475i −1.00501 0.730184i −0.0418554 0.999124i \(-0.513327\pi\)
−0.963157 + 0.268939i \(0.913327\pi\)
\(824\) −14.5880 −0.508198
\(825\) 0.0156899 + 3.31659i 0.000546254 + 0.115469i
\(826\) 5.11414 0.177944
\(827\) 40.8789 + 29.7003i 1.42150 + 1.03278i 0.991522 + 0.129940i \(0.0414784\pi\)
0.429977 + 0.902840i \(0.358522\pi\)
\(828\) −5.26490 + 16.2037i −0.182968 + 0.563118i
\(829\) −1.89888 5.84416i −0.0659509 0.202976i 0.912651 0.408741i \(-0.134032\pi\)
−0.978602 + 0.205765i \(0.934032\pi\)
\(830\) 15.8467 11.5133i 0.550047 0.399633i
\(831\) 0.0746965 0.0542702i 0.00259119 0.00188261i
\(832\) −3.57323 10.9973i −0.123879 0.381262i
\(833\) 5.75690 17.7179i 0.199465 0.613890i
\(834\) −37.4650 27.2199i −1.29731 0.942548i
\(835\) 3.49175 0.120837
\(836\) 38.6447 + 52.6641i 1.33655 + 1.82143i
\(837\) −2.50533 −0.0865967
\(838\) 62.5133 + 45.4186i 2.15949 + 1.56896i
\(839\) −11.5953 + 35.6865i −0.400312 + 1.23204i 0.524434 + 0.851451i \(0.324277\pi\)
−0.924746 + 0.380584i \(0.875723\pi\)
\(840\) −0.218246 0.671694i −0.00753022 0.0231756i
\(841\) −59.3574 + 43.1257i −2.04681 + 1.48709i
\(842\) −26.9273 + 19.5638i −0.927976 + 0.674214i
\(843\) 1.60164 + 4.92934i 0.0551633 + 0.169775i
\(844\) −13.7158 + 42.2128i −0.472116 + 1.45302i
\(845\) 9.75019 + 7.08392i 0.335417 + 0.243694i
\(846\) 25.5645 0.878924
\(847\) −2.12870 + 0.0201412i −0.0731431 + 0.000692058i
\(848\) −13.9186 −0.477966
\(849\) −1.26581 0.919664i −0.0434424 0.0315628i
\(850\) 1.94776 5.99460i 0.0668077 0.205613i
\(851\) −8.47347 26.0787i −0.290467 0.893965i
\(852\) −17.2017 + 12.4978i −0.589321 + 0.428167i
\(853\) 21.8533 15.8774i 0.748244 0.543631i −0.147038 0.989131i \(-0.546974\pi\)
0.895282 + 0.445500i \(0.146974\pi\)
\(854\) −0.169901 0.522900i −0.00581388 0.0178933i
\(855\) −1.71480 + 5.27760i −0.0586448 + 0.180490i
\(856\) 14.4280 + 10.4826i 0.493140 + 0.358287i
\(857\) −2.51515 −0.0859159 −0.0429580 0.999077i \(-0.513678\pi\)
−0.0429580 + 0.999077i \(0.513678\pi\)
\(858\) 4.50063 + 6.13335i 0.153649 + 0.209389i
\(859\) 6.70885 0.228903 0.114451 0.993429i \(-0.463489\pi\)
0.114451 + 0.993429i \(0.463489\pi\)
\(860\) −14.6828 10.6677i −0.500680 0.363765i
\(861\) −0.495087 + 1.52372i −0.0168725 + 0.0519283i
\(862\) −13.9079 42.8041i −0.473705 1.45791i
\(863\) 2.67577 1.94406i 0.0910844 0.0661767i −0.541311 0.840822i \(-0.682072\pi\)
0.632395 + 0.774646i \(0.282072\pi\)
\(864\) −3.04920 + 2.21537i −0.103736 + 0.0753686i
\(865\) −6.29145 19.3631i −0.213916 0.658365i
\(866\) −11.0065 + 33.8746i −0.374017 + 1.15111i
\(867\) 7.96121 + 5.78416i 0.270377 + 0.196440i
\(868\) −1.72082 −0.0584086
\(869\) 0.159299 + 33.6731i 0.00540384 + 1.14228i
\(870\) 23.8342 0.808056
\(871\) −2.56744 1.86535i −0.0869942 0.0632050i
\(872\) 8.48027 26.0996i 0.287178 0.883844i
\(873\) −4.89863 15.0764i −0.165793 0.510260i
\(874\) 50.7669 36.8843i 1.71722 1.24763i
\(875\) −0.156567 + 0.113752i −0.00529292 + 0.00384553i
\(876\) 3.62616 + 11.1602i 0.122517 + 0.377067i
\(877\) 9.91956 30.5293i 0.334960 1.03090i −0.631782 0.775146i \(-0.717676\pi\)
0.966742 0.255754i \(-0.0823238\pi\)
\(878\) 70.8269 + 51.4587i 2.39029 + 1.73665i
\(879\) −23.1570 −0.781067
\(880\) −4.71917 + 1.55807i −0.159083 + 0.0525226i
\(881\) −35.2547 −1.18776 −0.593881 0.804553i \(-0.702405\pi\)
−0.593881 + 0.804553i \(0.702405\pi\)
\(882\) −13.2691 9.64056i −0.446793 0.324614i
\(883\) −0.140866 + 0.433541i −0.00474052 + 0.0145898i −0.953399 0.301713i \(-0.902442\pi\)
0.948658 + 0.316303i \(0.102442\pi\)
\(884\) −2.85746 8.79436i −0.0961068 0.295786i
\(885\) 9.07556 6.59378i 0.305072 0.221647i
\(886\) −5.26090 + 3.82226i −0.176743 + 0.128411i
\(887\) −0.556725 1.71342i −0.0186930 0.0575312i 0.941275 0.337641i \(-0.109629\pi\)
−0.959968 + 0.280110i \(0.909629\pi\)
\(888\) −6.44179 + 19.8258i −0.216172 + 0.665310i
\(889\) −1.11166 0.807666i −0.0372838 0.0270882i
\(890\) −17.2970 −0.579797
\(891\) 1.93675 2.69240i 0.0648835 0.0901987i
\(892\) −19.0794 −0.638824
\(893\) −48.7203 35.3973i −1.63036 1.18453i
\(894\) 7.37620 22.7016i 0.246697 0.759255i
\(895\) 1.19008 + 3.66268i 0.0397799 + 0.122430i
\(896\) −3.19970 + 2.32471i −0.106894 + 0.0776633i
\(897\) 3.78150 2.74742i 0.126261 0.0917337i
\(898\) 13.0055 + 40.0269i 0.434001 + 1.33572i
\(899\) 7.83308 24.1077i 0.261248 0.804038i
\(900\) −2.87136 2.08617i −0.0957121 0.0695389i
\(901\) 24.8541 0.828009
\(902\) 61.6080 + 19.6959i 2.05132 + 0.655803i
\(903\) 0.989607 0.0329321
\(904\) 59.7092 + 43.3813i 1.98590 + 1.44284i
\(905\) −5.44337 + 16.7530i −0.180944 + 0.556887i
\(906\) −8.70850 26.8020i −0.289321 0.890437i
\(907\) 28.5962 20.7764i 0.949522 0.689868i −0.00117159 0.999999i \(-0.500373\pi\)
0.950694 + 0.310131i \(0.100373\pi\)
\(908\) 62.4605 45.3802i 2.07282 1.50600i
\(909\) 4.06640 + 12.5151i 0.134874 + 0.415099i
\(910\) −0.137173 + 0.422175i −0.00454724 + 0.0139950i
\(911\) 1.33388 + 0.969123i 0.0441935 + 0.0321085i 0.609663 0.792661i \(-0.291305\pi\)
−0.565469 + 0.824769i \(0.691305\pi\)
\(912\) −8.31508 −0.275340
\(913\) 26.2682 + 8.39789i 0.869352 + 0.277930i
\(914\) 49.8511 1.64893
\(915\) −0.975693 0.708883i −0.0322554 0.0234349i
\(916\) 2.92918 9.01510i 0.0967829 0.297867i
\(917\) −0.149522 0.460182i −0.00493765 0.0151965i
\(918\) −5.09931 + 3.70486i −0.168302 + 0.122279i
\(919\) 0.258068 0.187498i 0.00851288 0.00618497i −0.583521 0.812098i \(-0.698325\pi\)
0.592034 + 0.805913i \(0.298325\pi\)
\(920\) 5.41356 + 16.6612i 0.178480 + 0.549304i
\(921\) −2.38710 + 7.34672i −0.0786575 + 0.242083i
\(922\) −65.4590 47.5588i −2.15578 1.56626i
\(923\) 5.83327 0.192005
\(924\) 1.33029 1.84932i 0.0437632 0.0608381i
\(925\) 5.71217 0.187815
\(926\) 19.9185 + 14.4716i 0.654561 + 0.475567i
\(927\) 1.23525 3.80172i 0.0405711 0.124865i
\(928\) −11.7841 36.2678i −0.386832 1.19055i
\(929\) −45.4270 + 33.0046i −1.49041 + 1.08285i −0.516400 + 0.856347i \(0.672728\pi\)
−0.974011 + 0.226500i \(0.927272\pi\)
\(930\) −4.77460 + 3.46895i −0.156565 + 0.113751i
\(931\) 11.9394 + 36.7456i 0.391297 + 1.20429i
\(932\) −6.28115 + 19.3314i −0.205746 + 0.633221i
\(933\) 15.4691 + 11.2390i 0.506436 + 0.367947i
\(934\) −69.8301 −2.28491
\(935\) 8.42690 2.78221i 0.275589 0.0909880i
\(936\) −3.55346 −0.116149
\(937\) −29.8061 21.6554i −0.973724 0.707452i −0.0174269 0.999848i \(-0.505547\pi\)
−0.956297 + 0.292396i \(0.905547\pi\)
\(938\) −0.459148 + 1.41311i −0.0149917 + 0.0461397i
\(939\) 0.897097 + 2.76098i 0.0292756 + 0.0901012i
\(940\) 31.1609 22.6397i 1.01636 0.738426i
\(941\) 12.3865 8.99929i 0.403787 0.293368i −0.367295 0.930105i \(-0.619716\pi\)
0.771082 + 0.636736i \(0.219716\pi\)
\(942\) 1.91162 + 5.88335i 0.0622838 + 0.191690i
\(943\) 12.2805 37.7956i 0.399909 1.23079i
\(944\) 13.5991 + 9.88030i 0.442612 + 0.321576i
\(945\) 0.193527 0.00629544
\(946\) −0.188998 39.9510i −0.00614486 1.29892i
\(947\) −22.6654 −0.736526 −0.368263 0.929722i \(-0.620047\pi\)
−0.368263 + 0.929722i \(0.620047\pi\)
\(948\) −29.1528 21.1807i −0.946838 0.687918i
\(949\) 0.994821 3.06174i 0.0322933 0.0993884i
\(950\) 4.03950 + 12.4323i 0.131059 + 0.403358i
\(951\) −1.82962 + 1.32930i −0.0593295 + 0.0431054i
\(952\) −1.52884 + 1.11076i −0.0495499 + 0.0360001i
\(953\) 12.1544 + 37.4074i 0.393719 + 1.21174i 0.929955 + 0.367675i \(0.119846\pi\)
−0.536235 + 0.844069i \(0.680154\pi\)
\(954\) 6.76171 20.8104i 0.218918 0.673762i
\(955\) −0.337440 0.245165i −0.0109193 0.00793334i
\(956\) −86.4870 −2.79719
\(957\) 19.8525 + 27.0545i 0.641740 + 0.874548i
\(958\) 31.1388 1.00605
\(959\) 2.39459 + 1.73977i 0.0773254 + 0.0561802i
\(960\) −3.66971 + 11.2942i −0.118439 + 0.364519i
\(961\) −7.63993 23.5133i −0.246449 0.758493i
\(962\) 10.5999 7.70130i 0.341756 0.248300i
\(963\) −3.95352 + 2.87240i −0.127400 + 0.0925618i
\(964\) −18.3249 56.3984i −0.590207 1.81647i
\(965\) 3.61443 11.1241i 0.116353 0.358096i
\(966\) −1.77048 1.28633i −0.0569644 0.0413871i
\(967\) 3.06103 0.0984360 0.0492180 0.998788i \(-0.484327\pi\)
0.0492180 + 0.998788i \(0.484327\pi\)
\(968\) −32.6986 23.2875i −1.05097 0.748487i
\(969\) 14.8480 0.476987
\(970\) −30.2110 21.9496i −0.970016 0.704758i
\(971\) 9.90043 30.4704i 0.317720 0.977841i −0.656900 0.753977i \(-0.728133\pi\)
0.974620 0.223864i \(-0.0718672\pi\)
\(972\) 1.09676 + 3.37549i 0.0351787 + 0.108269i
\(973\) 3.07788 2.23621i 0.0986724 0.0716897i
\(974\) −80.9911 + 58.8434i −2.59512 + 1.88547i
\(975\) 0.300892 + 0.926052i 0.00963627 + 0.0296574i
\(976\) 0.558436 1.71869i 0.0178751 0.0550139i
\(977\) 43.0366 + 31.2679i 1.37686 + 1.00035i 0.997166 + 0.0752388i \(0.0239719\pi\)
0.379697 + 0.925111i \(0.376028\pi\)
\(978\) −55.8848 −1.78700
\(979\) −14.4074 19.6340i −0.460462 0.627507i
\(980\) −24.7115 −0.789379
\(981\) 6.08362 + 4.42001i 0.194235 + 0.141120i
\(982\) 11.4619 35.2762i 0.365765 1.12571i
\(983\) −7.57104 23.3013i −0.241479 0.743195i −0.996196 0.0871446i \(-0.972226\pi\)
0.754717 0.656051i \(-0.227774\pi\)
\(984\) −24.4421 + 17.7582i −0.779185 + 0.566111i
\(985\) −17.4714 + 12.6937i −0.556685 + 0.404456i
\(986\) −19.7071 60.6521i −0.627601 1.93156i
\(987\) −0.649001 + 1.99742i −0.0206579 + 0.0635786i
\(988\) 15.5149 + 11.2722i 0.493593 + 0.358616i
\(989\) −24.5470 −0.780549
\(990\) −0.0369604 7.81280i −0.00117468 0.248307i
\(991\) −6.34819 −0.201657 −0.100828 0.994904i \(-0.532149\pi\)
−0.100828 + 0.994904i \(0.532149\pi\)
\(992\) 7.63924 + 5.55023i 0.242546 + 0.176220i
\(993\) 1.86132 5.72856i 0.0590673 0.181790i
\(994\) −0.843962 2.59745i −0.0267689 0.0823861i
\(995\) −6.27820 + 4.56138i −0.199032 + 0.144605i
\(996\) −23.8756 + 17.3466i −0.756528 + 0.549650i
\(997\) −8.01777 24.6761i −0.253925 0.781501i −0.994040 0.109020i \(-0.965229\pi\)
0.740114 0.672481i \(-0.234771\pi\)
\(998\) 24.4064 75.1152i 0.772572 2.37773i
\(999\) −4.62125 3.35753i −0.146210 0.106228i
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 165.2.m.d.136.2 yes 8
3.2 odd 2 495.2.n.a.136.1 8
5.2 odd 4 825.2.bx.f.499.1 16
5.3 odd 4 825.2.bx.f.499.4 16
5.4 even 2 825.2.n.g.301.1 8
11.3 even 5 inner 165.2.m.d.91.2 8
11.5 even 5 1815.2.a.p.1.1 4
11.6 odd 10 1815.2.a.w.1.4 4
33.5 odd 10 5445.2.a.bt.1.4 4
33.14 odd 10 495.2.n.a.91.1 8
33.17 even 10 5445.2.a.bf.1.1 4
55.3 odd 20 825.2.bx.f.124.1 16
55.14 even 10 825.2.n.g.751.1 8
55.39 odd 10 9075.2.a.cm.1.1 4
55.47 odd 20 825.2.bx.f.124.4 16
55.49 even 10 9075.2.a.di.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.m.d.91.2 8 11.3 even 5 inner
165.2.m.d.136.2 yes 8 1.1 even 1 trivial
495.2.n.a.91.1 8 33.14 odd 10
495.2.n.a.136.1 8 3.2 odd 2
825.2.n.g.301.1 8 5.4 even 2
825.2.n.g.751.1 8 55.14 even 10
825.2.bx.f.124.1 16 55.3 odd 20
825.2.bx.f.124.4 16 55.47 odd 20
825.2.bx.f.499.1 16 5.2 odd 4
825.2.bx.f.499.4 16 5.3 odd 4
1815.2.a.p.1.1 4 11.5 even 5
1815.2.a.w.1.4 4 11.6 odd 10
5445.2.a.bf.1.1 4 33.17 even 10
5445.2.a.bt.1.4 4 33.5 odd 10
9075.2.a.cm.1.1 4 55.39 odd 10
9075.2.a.di.1.4 4 55.49 even 10