Properties

Label 315.2.bh.c.169.8
Level $315$
Weight $2$
Character 315.169
Analytic conductor $2.515$
Analytic rank $0$
Dimension $64$
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(169,315)]
 
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([4, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.169");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bh (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: \(64\)
Relative dimension: \(32\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 169.8
Character \(\chi\) \(=\) 315.169
Dual form 315.2.bh.c.274.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39315 - 0.804334i) q^{2} +(1.72917 + 0.0997919i) q^{3} +(0.293908 + 0.509063i) q^{4} +(-2.18712 + 0.465298i) q^{5} +(-2.32873 - 1.52986i) q^{6} +(0.866025 + 0.500000i) q^{7} +2.27174i q^{8} +(2.98008 + 0.345115i) q^{9} +O(q^{10})\) \(q+(-1.39315 - 0.804334i) q^{2} +(1.72917 + 0.0997919i) q^{3} +(0.293908 + 0.509063i) q^{4} +(-2.18712 + 0.465298i) q^{5} +(-2.32873 - 1.52986i) q^{6} +(0.866025 + 0.500000i) q^{7} +2.27174i q^{8} +(2.98008 + 0.345115i) q^{9} +(3.42124 + 1.11095i) q^{10} +(2.56920 - 4.44998i) q^{11} +(0.457417 + 0.909589i) q^{12} +(2.41638 - 1.39510i) q^{13} +(-0.804334 - 1.39315i) q^{14} +(-3.82834 + 0.586324i) q^{15} +(2.41505 - 4.18299i) q^{16} -5.02287i q^{17} +(-3.87411 - 2.87778i) q^{18} +3.95491 q^{19} +(-0.879678 - 0.976628i) q^{20} +(1.44761 + 0.951009i) q^{21} +(-7.15854 + 4.13299i) q^{22} +(-2.87747 + 1.66131i) q^{23} +(-0.226701 + 3.92823i) q^{24} +(4.56700 - 2.03533i) q^{25} -4.48850 q^{26} +(5.11864 + 0.894152i) q^{27} +0.587816i q^{28} +(-3.53526 + 6.12325i) q^{29} +(5.80505 + 2.26243i) q^{30} +(-1.26129 - 2.18461i) q^{31} +(-2.79429 + 1.61328i) q^{32} +(4.88666 - 7.43840i) q^{33} +(-4.04006 + 6.99760i) q^{34} +(-2.12675 - 0.690600i) q^{35} +(0.700185 + 1.61848i) q^{36} -0.847715i q^{37} +(-5.50977 - 3.18107i) q^{38} +(4.31756 - 2.17123i) q^{39} +(-1.05704 - 4.96856i) q^{40} +(-0.533089 - 0.923337i) q^{41} +(-1.25181 - 2.48926i) q^{42} +(-1.32058 - 0.762435i) q^{43} +3.02043 q^{44} +(-6.67838 + 0.631819i) q^{45} +5.34499 q^{46} +(6.74570 + 3.89463i) q^{47} +(4.59347 - 6.99212i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-7.99958 - 0.837880i) q^{50} +(0.501241 - 8.68541i) q^{51} +(1.42039 + 0.820060i) q^{52} -13.6197i q^{53} +(-6.41183 - 5.36279i) q^{54} +(-3.54858 + 10.9281i) q^{55} +(-1.13587 + 1.96738i) q^{56} +(6.83872 + 0.394668i) q^{57} +(9.85028 - 5.68706i) q^{58} +(6.59761 + 11.4274i) q^{59} +(-1.42366 - 1.77654i) q^{60} +(-2.62959 + 4.55458i) q^{61} +4.05798i q^{62} +(2.40827 + 1.78892i) q^{63} -4.46973 q^{64} +(-4.63578 + 4.17558i) q^{65} +(-12.7908 + 6.43229i) q^{66} +(-8.26580 + 4.77226i) q^{67} +(2.55696 - 1.47626i) q^{68} +(-5.14143 + 2.58554i) q^{69} +(2.40741 + 2.67273i) q^{70} +0.967909 q^{71} +(-0.784011 + 6.76996i) q^{72} +4.82868i q^{73} +(-0.681846 + 1.18099i) q^{74} +(8.10024 - 3.06368i) q^{75} +(1.16238 + 2.01330i) q^{76} +(4.44998 - 2.56920i) q^{77} +(-7.76139 - 0.447916i) q^{78} +(-3.00027 + 5.19662i) q^{79} +(-3.33567 + 10.2724i) q^{80} +(8.76179 + 2.05694i) q^{81} +1.71513i q^{82} +(2.17078 + 1.25330i) q^{83} +(-0.0586592 + 1.01644i) q^{84} +(2.33713 + 10.9856i) q^{85} +(1.22651 + 2.12437i) q^{86} +(-6.72413 + 10.2354i) q^{87} +(10.1092 + 5.83654i) q^{88} +7.34250 q^{89} +(9.81217 + 4.49144i) q^{90} +2.79019 q^{91} +(-1.69142 - 0.976544i) q^{92} +(-1.96298 - 3.90344i) q^{93} +(-6.26518 - 10.8516i) q^{94} +(-8.64986 + 1.84021i) q^{95} +(-4.99280 + 2.51080i) q^{96} +(-2.22850 - 1.28662i) q^{97} -1.60867i q^{98} +(9.19217 - 12.3746i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} - 6 q^{14} - 14 q^{15} - 46 q^{16} + 48 q^{19} - 2 q^{20} - 2 q^{21} - 12 q^{24} + 18 q^{25} - 12 q^{26} - 30 q^{29} - 4 q^{30} - 4 q^{31} + 34 q^{34} + 8 q^{35} - 42 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} + 68 q^{44} - 6 q^{45} - 24 q^{46} + 32 q^{49} - 58 q^{50} + 62 q^{51} + 54 q^{54} - 12 q^{55} + 18 q^{56} + 16 q^{59} - 66 q^{60} + 40 q^{61} - 100 q^{64} - 18 q^{65} - 146 q^{66} - 20 q^{69} - 4 q^{70} - 176 q^{71} - 20 q^{74} + 60 q^{75} - 22 q^{79} + 64 q^{80} - 58 q^{81} - 4 q^{84} - 14 q^{85} + 60 q^{86} - 200 q^{89} + 8 q^{90} - 16 q^{91} - 42 q^{94} + 68 q^{95} + 210 q^{96} + 90 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39315 0.804334i −0.985105 0.568750i −0.0812972 0.996690i \(-0.525906\pi\)
−0.903807 + 0.427940i \(0.859240\pi\)
\(3\) 1.72917 + 0.0997919i 0.998339 + 0.0576149i
\(4\) 0.293908 + 0.509063i 0.146954 + 0.254532i
\(5\) −2.18712 + 0.465298i −0.978110 + 0.208088i
\(6\) −2.32873 1.52986i −0.950700 0.624562i
\(7\) 0.866025 + 0.500000i 0.327327 + 0.188982i
\(8\) 2.27174i 0.803180i
\(9\) 2.98008 + 0.345115i 0.993361 + 0.115038i
\(10\) 3.42124 + 1.11095i 1.08189 + 0.351312i
\(11\) 2.56920 4.44998i 0.774642 1.34172i −0.160354 0.987060i \(-0.551264\pi\)
0.934996 0.354659i \(-0.115403\pi\)
\(12\) 0.457417 + 0.909589i 0.132045 + 0.262576i
\(13\) 2.41638 1.39510i 0.670183 0.386930i −0.125963 0.992035i \(-0.540202\pi\)
0.796146 + 0.605105i \(0.206869\pi\)
\(14\) −0.804334 1.39315i −0.214967 0.372335i
\(15\) −3.82834 + 0.586324i −0.988474 + 0.151388i
\(16\) 2.41505 4.18299i 0.603763 1.04575i
\(17\) 5.02287i 1.21822i −0.793084 0.609112i \(-0.791526\pi\)
0.793084 0.609112i \(-0.208474\pi\)
\(18\) −3.87411 2.87778i −0.913136 0.678299i
\(19\) 3.95491 0.907318 0.453659 0.891175i \(-0.350118\pi\)
0.453659 + 0.891175i \(0.350118\pi\)
\(20\) −0.879678 0.976628i −0.196702 0.218381i
\(21\) 1.44761 + 0.951009i 0.315895 + 0.207527i
\(22\) −7.15854 + 4.13299i −1.52621 + 0.881155i
\(23\) −2.87747 + 1.66131i −0.599994 + 0.346407i −0.769039 0.639201i \(-0.779265\pi\)
0.169045 + 0.985608i \(0.445932\pi\)
\(24\) −0.226701 + 3.92823i −0.0462751 + 0.801846i
\(25\) 4.56700 2.03533i 0.913399 0.407065i
\(26\) −4.48850 −0.880267
\(27\) 5.11864 + 0.894152i 0.985083 + 0.172080i
\(28\) 0.587816i 0.111087i
\(29\) −3.53526 + 6.12325i −0.656481 + 1.13706i 0.325039 + 0.945701i \(0.394622\pi\)
−0.981520 + 0.191358i \(0.938711\pi\)
\(30\) 5.80505 + 2.26243i 1.05985 + 0.413062i
\(31\) −1.26129 2.18461i −0.226534 0.392368i 0.730245 0.683186i \(-0.239406\pi\)
−0.956778 + 0.290818i \(0.906073\pi\)
\(32\) −2.79429 + 1.61328i −0.493965 + 0.285191i
\(33\) 4.88666 7.43840i 0.850658 1.29486i
\(34\) −4.04006 + 6.99760i −0.692865 + 1.20008i
\(35\) −2.12675 0.690600i −0.359487 0.116733i
\(36\) 0.700185 + 1.61848i 0.116697 + 0.269747i
\(37\) 0.847715i 0.139364i −0.997569 0.0696818i \(-0.977802\pi\)
0.997569 0.0696818i \(-0.0221984\pi\)
\(38\) −5.50977 3.18107i −0.893803 0.516037i
\(39\) 4.31756 2.17123i 0.691363 0.347675i
\(40\) −1.05704 4.96856i −0.167132 0.785599i
\(41\) −0.533089 0.923337i −0.0832545 0.144201i 0.821392 0.570365i \(-0.193198\pi\)
−0.904646 + 0.426164i \(0.859865\pi\)
\(42\) −1.25181 2.48926i −0.193158 0.384101i
\(43\) −1.32058 0.762435i −0.201386 0.116270i 0.395916 0.918287i \(-0.370427\pi\)
−0.597302 + 0.802017i \(0.703761\pi\)
\(44\) 3.02043 0.455347
\(45\) −6.67838 + 0.631819i −0.995555 + 0.0941860i
\(46\) 5.34499 0.788076
\(47\) 6.74570 + 3.89463i 0.983962 + 0.568091i 0.903464 0.428664i \(-0.141016\pi\)
0.0804981 + 0.996755i \(0.474349\pi\)
\(48\) 4.59347 6.99212i 0.663011 1.00923i
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) −7.99958 0.837880i −1.13131 0.118494i
\(51\) 0.501241 8.68541i 0.0701878 1.21620i
\(52\) 1.42039 + 0.820060i 0.196972 + 0.113722i
\(53\) 13.6197i 1.87081i −0.353581 0.935404i \(-0.615036\pi\)
0.353581 0.935404i \(-0.384964\pi\)
\(54\) −6.41183 5.36279i −0.872539 0.729783i
\(55\) −3.54858 + 10.9281i −0.478490 + 1.47354i
\(56\) −1.13587 + 1.96738i −0.151787 + 0.262902i
\(57\) 6.83872 + 0.394668i 0.905810 + 0.0522750i
\(58\) 9.85028 5.68706i 1.29340 0.746748i
\(59\) 6.59761 + 11.4274i 0.858935 + 1.48772i 0.872946 + 0.487817i \(0.162207\pi\)
−0.0140106 + 0.999902i \(0.504460\pi\)
\(60\) −1.42366 1.77654i −0.183793 0.229351i
\(61\) −2.62959 + 4.55458i −0.336684 + 0.583154i −0.983807 0.179232i \(-0.942639\pi\)
0.647123 + 0.762386i \(0.275972\pi\)
\(62\) 4.05798i 0.515364i
\(63\) 2.40827 + 1.78892i 0.303414 + 0.225383i
\(64\) −4.46973 −0.558717
\(65\) −4.63578 + 4.17558i −0.574997 + 0.517917i
\(66\) −12.7908 + 6.43229i −1.57444 + 0.791760i
\(67\) −8.26580 + 4.77226i −1.00983 + 0.583024i −0.911141 0.412094i \(-0.864797\pi\)
−0.0986866 + 0.995119i \(0.531464\pi\)
\(68\) 2.55696 1.47626i 0.310077 0.179023i
\(69\) −5.14143 + 2.58554i −0.618956 + 0.311263i
\(70\) 2.40741 + 2.67273i 0.287740 + 0.319452i
\(71\) 0.967909 0.114870 0.0574349 0.998349i \(-0.481708\pi\)
0.0574349 + 0.998349i \(0.481708\pi\)
\(72\) −0.784011 + 6.76996i −0.0923965 + 0.797848i
\(73\) 4.82868i 0.565155i 0.959245 + 0.282577i \(0.0911894\pi\)
−0.959245 + 0.282577i \(0.908811\pi\)
\(74\) −0.681846 + 1.18099i −0.0792630 + 0.137288i
\(75\) 8.10024 3.06368i 0.935335 0.353764i
\(76\) 1.16238 + 2.01330i 0.133334 + 0.230941i
\(77\) 4.44998 2.56920i 0.507122 0.292787i
\(78\) −7.76139 0.447916i −0.878805 0.0507165i
\(79\) −3.00027 + 5.19662i −0.337556 + 0.584665i −0.983973 0.178320i \(-0.942934\pi\)
0.646416 + 0.762985i \(0.276267\pi\)
\(80\) −3.33567 + 10.2724i −0.372939 + 1.14849i
\(81\) 8.76179 + 2.05694i 0.973532 + 0.228549i
\(82\) 1.71513i 0.189404i
\(83\) 2.17078 + 1.25330i 0.238275 + 0.137568i 0.614383 0.789008i \(-0.289405\pi\)
−0.376109 + 0.926575i \(0.622738\pi\)
\(84\) −0.0586592 + 1.01644i −0.00640025 + 0.110902i
\(85\) 2.33713 + 10.9856i 0.253497 + 1.19156i
\(86\) 1.22651 + 2.12437i 0.132258 + 0.229077i
\(87\) −6.72413 + 10.2354i −0.720902 + 1.09735i
\(88\) 10.1092 + 5.83654i 1.07764 + 0.622177i
\(89\) 7.34250 0.778303 0.389152 0.921174i \(-0.372768\pi\)
0.389152 + 0.921174i \(0.372768\pi\)
\(90\) 9.81217 + 4.49144i 1.03429 + 0.473439i
\(91\) 2.79019 0.292492
\(92\) −1.69142 0.976544i −0.176343 0.101812i
\(93\) −1.96298 3.90344i −0.203551 0.404768i
\(94\) −6.26518 10.8516i −0.646204 1.11926i
\(95\) −8.64986 + 1.84021i −0.887457 + 0.188802i
\(96\) −4.99280 + 2.51080i −0.509576 + 0.256257i
\(97\) −2.22850 1.28662i −0.226270 0.130637i 0.382580 0.923922i \(-0.375036\pi\)
−0.608850 + 0.793285i \(0.708369\pi\)
\(98\) 1.60867i 0.162500i
\(99\) 9.19217 12.3746i 0.923848 1.24370i
\(100\) 2.37839 + 1.72669i 0.237839 + 0.172669i
\(101\) −2.50533 + 4.33935i −0.249289 + 0.431782i −0.963329 0.268324i \(-0.913530\pi\)
0.714039 + 0.700105i \(0.246864\pi\)
\(102\) −7.68428 + 11.6969i −0.760857 + 1.15817i
\(103\) −13.8168 + 7.97712i −1.36141 + 0.786009i −0.989811 0.142386i \(-0.954523\pi\)
−0.371596 + 0.928395i \(0.621189\pi\)
\(104\) 3.16929 + 5.48938i 0.310775 + 0.538278i
\(105\) −3.60861 1.40640i −0.352164 0.137251i
\(106\) −10.9548 + 18.9742i −1.06402 + 1.84294i
\(107\) 14.8227i 1.43296i −0.697606 0.716481i \(-0.745752\pi\)
0.697606 0.716481i \(-0.254248\pi\)
\(108\) 1.04923 + 2.86851i 0.100962 + 0.276023i
\(109\) −5.14661 −0.492956 −0.246478 0.969148i \(-0.579273\pi\)
−0.246478 + 0.969148i \(0.579273\pi\)
\(110\) 13.7335 12.3702i 1.30944 1.17945i
\(111\) 0.0845951 1.46585i 0.00802941 0.139132i
\(112\) 4.18299 2.41505i 0.395256 0.228201i
\(113\) −16.2597 + 9.38755i −1.52958 + 0.883106i −0.530206 + 0.847869i \(0.677885\pi\)
−0.999379 + 0.0352374i \(0.988781\pi\)
\(114\) −9.20990 6.05045i −0.862587 0.566676i
\(115\) 5.52037 4.97237i 0.514778 0.463676i
\(116\) −4.15616 −0.385890
\(117\) 7.68248 3.32358i 0.710246 0.307265i
\(118\) 21.2267i 1.95408i
\(119\) 2.51143 4.34993i 0.230223 0.398757i
\(120\) −1.33197 8.69699i −0.121592 0.793923i
\(121\) −7.70153 13.3394i −0.700139 1.21268i
\(122\) 7.32681 4.23014i 0.663338 0.382979i
\(123\) −0.829662 1.64981i −0.0748081 0.148758i
\(124\) 0.741404 1.28415i 0.0665800 0.115320i
\(125\) −9.04154 + 6.57652i −0.808700 + 0.588222i
\(126\) −1.91619 4.42929i −0.170708 0.394592i
\(127\) 10.0154i 0.888724i −0.895847 0.444362i \(-0.853430\pi\)
0.895847 0.444362i \(-0.146570\pi\)
\(128\) 11.8156 + 6.82173i 1.04436 + 0.602961i
\(129\) −2.20742 1.45017i −0.194353 0.127680i
\(130\) 9.81689 2.08849i 0.860998 0.183173i
\(131\) 7.33474 + 12.7041i 0.640840 + 1.10997i 0.985246 + 0.171146i \(0.0547470\pi\)
−0.344406 + 0.938821i \(0.611920\pi\)
\(132\) 5.22284 + 0.301414i 0.454590 + 0.0262347i
\(133\) 3.42505 + 1.97745i 0.296989 + 0.171467i
\(134\) 15.3540 1.32638
\(135\) −11.6111 + 0.426076i −0.999327 + 0.0366708i
\(136\) 11.4106 0.978453
\(137\) −6.19298 3.57552i −0.529102 0.305477i 0.211549 0.977367i \(-0.432149\pi\)
−0.740651 + 0.671890i \(0.765483\pi\)
\(138\) 9.24242 + 0.533387i 0.786767 + 0.0454049i
\(139\) −9.20239 15.9390i −0.780536 1.35193i −0.931630 0.363409i \(-0.881613\pi\)
0.151093 0.988519i \(-0.451721\pi\)
\(140\) −0.273510 1.28562i −0.0231158 0.108655i
\(141\) 11.2758 + 7.40767i 0.949597 + 0.623838i
\(142\) −1.34844 0.778523i −0.113159 0.0653322i
\(143\) 14.3371i 1.19893i
\(144\) 8.64067 11.6322i 0.720056 0.969350i
\(145\) 4.88290 15.0372i 0.405503 1.24877i
\(146\) 3.88388 6.72707i 0.321432 0.556736i
\(147\) 0.778165 + 1.54740i 0.0641819 + 0.127628i
\(148\) 0.431541 0.249150i 0.0354724 0.0204800i
\(149\) 3.50121 + 6.06427i 0.286830 + 0.496804i 0.973051 0.230589i \(-0.0740651\pi\)
−0.686221 + 0.727393i \(0.740732\pi\)
\(150\) −13.7491 2.24713i −1.12261 0.183478i
\(151\) −3.63064 + 6.28846i −0.295458 + 0.511747i −0.975091 0.221804i \(-0.928805\pi\)
0.679634 + 0.733552i \(0.262139\pi\)
\(152\) 8.98450i 0.728740i
\(153\) 1.73347 14.9686i 0.140142 1.21014i
\(154\) −8.26597 −0.666091
\(155\) 3.77508 + 4.19114i 0.303222 + 0.336640i
\(156\) 2.37426 + 1.55977i 0.190093 + 0.124881i
\(157\) −8.03571 + 4.63942i −0.641320 + 0.370266i −0.785123 0.619340i \(-0.787400\pi\)
0.143803 + 0.989606i \(0.454067\pi\)
\(158\) 8.35963 4.82644i 0.665057 0.383971i
\(159\) 1.35913 23.5508i 0.107786 1.86770i
\(160\) 5.36079 4.82862i 0.423807 0.381736i
\(161\) −3.32262 −0.261859
\(162\) −10.5520 9.91304i −0.829044 0.778842i
\(163\) 9.61624i 0.753202i 0.926376 + 0.376601i \(0.122907\pi\)
−0.926376 + 0.376601i \(0.877093\pi\)
\(164\) 0.313358 0.542752i 0.0244692 0.0423818i
\(165\) −7.22664 + 18.5424i −0.562593 + 1.44353i
\(166\) −2.01615 3.49207i −0.156484 0.271038i
\(167\) 20.1797 11.6508i 1.56155 0.901563i 0.564452 0.825466i \(-0.309088\pi\)
0.997100 0.0760968i \(-0.0242458\pi\)
\(168\) −2.16044 + 3.28859i −0.166682 + 0.253721i
\(169\) −2.60741 + 4.51616i −0.200570 + 0.347397i
\(170\) 5.58014 17.1844i 0.427977 1.31799i
\(171\) 11.7859 + 1.36490i 0.901294 + 0.104376i
\(172\) 0.896343i 0.0683455i
\(173\) 9.10571 + 5.25719i 0.692295 + 0.399696i 0.804471 0.593992i \(-0.202449\pi\)
−0.112176 + 0.993688i \(0.535782\pi\)
\(174\) 17.6004 8.85094i 1.33428 0.670988i
\(175\) 4.97280 + 0.520853i 0.375908 + 0.0393728i
\(176\) −12.4095 21.4939i −0.935400 1.62016i
\(177\) 10.2680 + 20.4183i 0.771794 + 1.53474i
\(178\) −10.2292 5.90582i −0.766710 0.442660i
\(179\) −23.5829 −1.76267 −0.881333 0.472496i \(-0.843353\pi\)
−0.881333 + 0.472496i \(0.843353\pi\)
\(180\) −2.28447 3.21402i −0.170274 0.239559i
\(181\) 13.9662 1.03810 0.519050 0.854744i \(-0.326286\pi\)
0.519050 + 0.854744i \(0.326286\pi\)
\(182\) −3.88715 2.24425i −0.288135 0.166355i
\(183\) −5.00153 + 7.61325i −0.369723 + 0.562788i
\(184\) −3.77406 6.53686i −0.278227 0.481904i
\(185\) 0.394440 + 1.85406i 0.0289998 + 0.136313i
\(186\) −0.404954 + 7.01696i −0.0296927 + 0.514508i
\(187\) −22.3516 12.9047i −1.63451 0.943687i
\(188\) 4.57866i 0.333933i
\(189\) 3.98580 + 3.33368i 0.289924 + 0.242489i
\(190\) 13.5307 + 4.39369i 0.981618 + 0.318752i
\(191\) 2.67604 4.63504i 0.193631 0.335380i −0.752820 0.658227i \(-0.771307\pi\)
0.946451 + 0.322847i \(0.104640\pi\)
\(192\) −7.72895 0.446043i −0.557789 0.0321904i
\(193\) 6.16954 3.56199i 0.444093 0.256397i −0.261239 0.965274i \(-0.584131\pi\)
0.705332 + 0.708877i \(0.250798\pi\)
\(194\) 2.06975 + 3.58492i 0.148600 + 0.257382i
\(195\) −8.43275 + 6.75770i −0.603882 + 0.483929i
\(196\) −0.293908 + 0.509063i −0.0209934 + 0.0363617i
\(197\) 13.5208i 0.963320i 0.876358 + 0.481660i \(0.159966\pi\)
−0.876358 + 0.481660i \(0.840034\pi\)
\(198\) −22.7594 + 9.84612i −1.61744 + 0.699733i
\(199\) −6.61711 −0.469074 −0.234537 0.972107i \(-0.575357\pi\)
−0.234537 + 0.972107i \(0.575357\pi\)
\(200\) 4.62373 + 10.3750i 0.326947 + 0.733624i
\(201\) −14.7692 + 7.42721i −1.04174 + 0.523875i
\(202\) 6.98058 4.03024i 0.491152 0.283567i
\(203\) −6.12325 + 3.53526i −0.429768 + 0.248127i
\(204\) 4.56874 2.29755i 0.319876 0.160860i
\(205\) 1.59556 + 1.77140i 0.111439 + 0.123720i
\(206\) 25.6651 1.78817
\(207\) −9.14845 + 3.95778i −0.635861 + 0.275085i
\(208\) 13.4769i 0.934457i
\(209\) 10.1609 17.5992i 0.702846 1.21736i
\(210\) 3.89611 + 4.86185i 0.268857 + 0.335500i
\(211\) −4.11043 7.11948i −0.282974 0.490125i 0.689142 0.724626i \(-0.257988\pi\)
−0.972116 + 0.234501i \(0.924654\pi\)
\(212\) 6.93328 4.00293i 0.476180 0.274923i
\(213\) 1.67368 + 0.0965895i 0.114679 + 0.00661820i
\(214\) −11.9224 + 20.6502i −0.814998 + 1.41162i
\(215\) 3.24302 + 1.05308i 0.221172 + 0.0718192i
\(216\) −2.03128 + 11.6282i −0.138211 + 0.791199i
\(217\) 2.52257i 0.171243i
\(218\) 7.17000 + 4.13960i 0.485613 + 0.280369i
\(219\) −0.481864 + 8.34963i −0.0325613 + 0.564216i
\(220\) −6.60604 + 1.40540i −0.445379 + 0.0947520i
\(221\) −7.00739 12.1371i −0.471368 0.816433i
\(222\) −1.29688 + 1.97410i −0.0870412 + 0.132493i
\(223\) −2.57291 1.48547i −0.172295 0.0994745i 0.411373 0.911467i \(-0.365049\pi\)
−0.583667 + 0.811993i \(0.698383\pi\)
\(224\) −3.22656 −0.215584
\(225\) 14.3124 4.48930i 0.954163 0.299287i
\(226\) 30.2029 2.00907
\(227\) 9.15036 + 5.28296i 0.607331 + 0.350643i 0.771920 0.635720i \(-0.219297\pi\)
−0.164589 + 0.986362i \(0.552630\pi\)
\(228\) 1.80904 + 3.59734i 0.119807 + 0.238239i
\(229\) 5.94717 + 10.3008i 0.393000 + 0.680696i 0.992844 0.119421i \(-0.0381039\pi\)
−0.599844 + 0.800117i \(0.704771\pi\)
\(230\) −11.6901 + 2.48702i −0.770825 + 0.163989i
\(231\) 7.95117 3.99851i 0.523148 0.263083i
\(232\) −13.9104 8.03118i −0.913263 0.527273i
\(233\) 18.9856i 1.24379i 0.783103 + 0.621893i \(0.213636\pi\)
−0.783103 + 0.621893i \(0.786364\pi\)
\(234\) −13.3761 1.54905i −0.874423 0.101264i
\(235\) −16.5658 5.37927i −1.08064 0.350905i
\(236\) −3.87818 + 6.71720i −0.252448 + 0.437252i
\(237\) −5.70656 + 8.68645i −0.370681 + 0.564245i
\(238\) −6.99760 + 4.04006i −0.453587 + 0.261878i
\(239\) −9.59908 16.6261i −0.620913 1.07545i −0.989316 0.145786i \(-0.953429\pi\)
0.368404 0.929666i \(-0.379904\pi\)
\(240\) −6.79306 + 17.4299i −0.438490 + 1.12510i
\(241\) 12.5787 21.7869i 0.810263 1.40342i −0.102418 0.994741i \(-0.532658\pi\)
0.912680 0.408674i \(-0.134009\pi\)
\(242\) 24.7784i 1.59282i
\(243\) 14.9454 + 4.43117i 0.958747 + 0.284260i
\(244\) −3.09143 −0.197908
\(245\) −1.49652 1.66145i −0.0956092 0.106146i
\(246\) −0.171156 + 2.96575i −0.0109125 + 0.189090i
\(247\) 9.55655 5.51748i 0.608069 0.351069i
\(248\) 4.96286 2.86531i 0.315142 0.181947i
\(249\) 3.62859 + 2.38381i 0.229953 + 0.151068i
\(250\) 17.8859 1.88965i 1.13121 0.119512i
\(251\) −29.8394 −1.88344 −0.941722 0.336391i \(-0.890794\pi\)
−0.941722 + 0.336391i \(0.890794\pi\)
\(252\) −0.202864 + 1.75174i −0.0127792 + 0.110349i
\(253\) 17.0729i 1.07336i
\(254\) −8.05574 + 13.9529i −0.505462 + 0.875486i
\(255\) 2.94503 + 19.2293i 0.184425 + 1.20418i
\(256\) −6.50416 11.2655i −0.406510 0.704096i
\(257\) 5.13224 2.96310i 0.320140 0.184833i −0.331315 0.943520i \(-0.607492\pi\)
0.651455 + 0.758687i \(0.274159\pi\)
\(258\) 1.90885 + 3.79580i 0.118840 + 0.236316i
\(259\) 0.423858 0.734143i 0.0263372 0.0456174i
\(260\) −3.48813 1.13267i −0.216325 0.0702451i
\(261\) −12.6486 + 17.0277i −0.782928 + 1.05399i
\(262\) 23.5984i 1.45791i
\(263\) −17.8685 10.3164i −1.10182 0.636136i −0.165121 0.986273i \(-0.552801\pi\)
−0.936698 + 0.350138i \(0.886135\pi\)
\(264\) 16.8981 + 11.1012i 1.04001 + 0.683232i
\(265\) 6.33722 + 29.7879i 0.389292 + 1.82986i
\(266\) −3.18107 5.50977i −0.195044 0.337826i
\(267\) 12.6965 + 0.732722i 0.777010 + 0.0448418i
\(268\) −4.85877 2.80521i −0.296796 0.171355i
\(269\) 27.8389 1.69737 0.848683 0.528902i \(-0.177396\pi\)
0.848683 + 0.528902i \(0.177396\pi\)
\(270\) 16.5187 + 8.74565i 1.00530 + 0.532243i
\(271\) −1.10302 −0.0670039 −0.0335020 0.999439i \(-0.510666\pi\)
−0.0335020 + 0.999439i \(0.510666\pi\)
\(272\) −21.0106 12.1305i −1.27396 0.735519i
\(273\) 4.82473 + 0.278439i 0.292006 + 0.0168519i
\(274\) 5.75183 + 9.96246i 0.347481 + 0.601854i
\(275\) 2.67635 25.5522i 0.161390 1.54085i
\(276\) −2.82731 1.85740i −0.170184 0.111803i
\(277\) 21.9744 + 12.6869i 1.32031 + 0.762283i 0.983778 0.179388i \(-0.0574119\pi\)
0.336534 + 0.941671i \(0.390745\pi\)
\(278\) 29.6072i 1.77572i
\(279\) −3.00479 6.94561i −0.179892 0.415823i
\(280\) 1.56886 4.83142i 0.0937575 0.288733i
\(281\) −7.19700 + 12.4656i −0.429337 + 0.743634i −0.996814 0.0797551i \(-0.974586\pi\)
0.567477 + 0.823389i \(0.307920\pi\)
\(282\) −9.75068 19.3895i −0.580644 1.15463i
\(283\) 7.06326 4.07798i 0.419867 0.242411i −0.275153 0.961400i \(-0.588729\pi\)
0.695021 + 0.718990i \(0.255395\pi\)
\(284\) 0.284476 + 0.492727i 0.0168806 + 0.0292380i
\(285\) −15.1407 + 2.31886i −0.896860 + 0.137357i
\(286\) −11.5318 + 19.9737i −0.681892 + 1.18107i
\(287\) 1.06618i 0.0629345i
\(288\) −8.88398 + 3.84337i −0.523493 + 0.226472i
\(289\) −8.22918 −0.484069
\(290\) −18.8976 + 17.0216i −1.10970 + 0.999543i
\(291\) −3.72507 2.44718i −0.218367 0.143456i
\(292\) −2.45811 + 1.41919i −0.143850 + 0.0830517i
\(293\) 1.79534 1.03654i 0.104885 0.0605552i −0.446640 0.894714i \(-0.647380\pi\)
0.551525 + 0.834159i \(0.314046\pi\)
\(294\) 0.160532 2.78167i 0.00936242 0.162230i
\(295\) −19.7469 21.9232i −1.14971 1.27642i
\(296\) 1.92579 0.111934
\(297\) 17.1297 20.4806i 0.993969 1.18840i
\(298\) 11.2646i 0.652539i
\(299\) −4.63537 + 8.02870i −0.268071 + 0.464312i
\(300\) 3.94033 + 3.22309i 0.227495 + 0.186085i
\(301\) −0.762435 1.32058i −0.0439460 0.0761168i
\(302\) 10.1160 5.84050i 0.582113 0.336083i
\(303\) −4.76518 + 7.25349i −0.273752 + 0.416702i
\(304\) 9.55130 16.5433i 0.547805 0.948826i
\(305\) 3.63199 11.1850i 0.207967 0.640449i
\(306\) −14.4547 + 19.4591i −0.826320 + 1.11240i
\(307\) 21.5818i 1.23174i 0.787849 + 0.615869i \(0.211195\pi\)
−0.787849 + 0.615869i \(0.788805\pi\)
\(308\) 2.61577 + 1.51021i 0.149047 + 0.0860524i
\(309\) −24.6876 + 12.4150i −1.40443 + 0.706266i
\(310\) −1.88817 8.87530i −0.107241 0.504083i
\(311\) −3.87305 6.70832i −0.219621 0.380394i 0.735071 0.677990i \(-0.237149\pi\)
−0.954692 + 0.297596i \(0.903815\pi\)
\(312\) 4.93246 + 9.80836i 0.279246 + 0.555289i
\(313\) −1.39842 0.807378i −0.0790434 0.0456357i 0.459957 0.887941i \(-0.347865\pi\)
−0.539001 + 0.842305i \(0.681198\pi\)
\(314\) 14.9266 0.842356
\(315\) −6.09956 2.79202i −0.343671 0.157313i
\(316\) −3.52721 −0.198421
\(317\) −11.0720 6.39243i −0.621867 0.359035i 0.155729 0.987800i \(-0.450227\pi\)
−0.777595 + 0.628765i \(0.783561\pi\)
\(318\) −20.8362 + 31.7166i −1.16844 + 1.77858i
\(319\) 18.1655 + 31.4636i 1.01708 + 1.76163i
\(320\) 9.77585 2.07976i 0.546487 0.116262i
\(321\) 1.47918 25.6310i 0.0825600 1.43058i
\(322\) 4.62890 + 2.67250i 0.257958 + 0.148932i
\(323\) 19.8650i 1.10532i
\(324\) 1.52805 + 5.06486i 0.0848914 + 0.281381i
\(325\) 8.19611 11.2895i 0.454639 0.626230i
\(326\) 7.73468 13.3969i 0.428384 0.741983i
\(327\) −8.89939 0.513590i −0.492137 0.0284016i
\(328\) 2.09758 1.21104i 0.115819 0.0668684i
\(329\) 3.89463 + 6.74570i 0.214718 + 0.371903i
\(330\) 24.9821 20.0197i 1.37522 1.10205i
\(331\) 5.62073 9.73540i 0.308943 0.535106i −0.669188 0.743093i \(-0.733358\pi\)
0.978132 + 0.207987i \(0.0666913\pi\)
\(332\) 1.47342i 0.0808646i
\(333\) 0.292559 2.52626i 0.0160321 0.138438i
\(334\) −37.4844 −2.05106
\(335\) 15.8578 14.2836i 0.866403 0.780395i
\(336\) 7.47412 3.75862i 0.407747 0.205049i
\(337\) 26.5384 15.3219i 1.44564 0.834639i 0.447420 0.894324i \(-0.352343\pi\)
0.998217 + 0.0596846i \(0.0190095\pi\)
\(338\) 7.26501 4.19446i 0.395165 0.228148i
\(339\) −29.0527 + 14.6101i −1.57792 + 0.793512i
\(340\) −4.90547 + 4.41851i −0.266037 + 0.239627i
\(341\) −12.9620 −0.701930
\(342\) −15.3217 11.3813i −0.828505 0.615433i
\(343\) 1.00000i 0.0539949i
\(344\) 1.73205 3.00000i 0.0933860 0.161749i
\(345\) 10.0419 8.04720i 0.540637 0.433246i
\(346\) −8.45707 14.6481i −0.454655 0.787486i
\(347\) 14.3293 8.27302i 0.769236 0.444119i −0.0633658 0.997990i \(-0.520183\pi\)
0.832602 + 0.553872i \(0.186850\pi\)
\(348\) −7.18673 0.414751i −0.385249 0.0222330i
\(349\) −7.08905 + 12.2786i −0.379468 + 0.657258i −0.990985 0.133973i \(-0.957226\pi\)
0.611517 + 0.791231i \(0.290560\pi\)
\(350\) −6.50890 4.72542i −0.347916 0.252584i
\(351\) 13.6160 4.98039i 0.726769 0.265834i
\(352\) 16.5794i 0.883682i
\(353\) 4.67333 + 2.69815i 0.248736 + 0.143608i 0.619185 0.785245i \(-0.287463\pi\)
−0.370449 + 0.928853i \(0.620796\pi\)
\(354\) 2.11826 36.7047i 0.112584 1.95083i
\(355\) −2.11693 + 0.450366i −0.112355 + 0.0239030i
\(356\) 2.15802 + 3.73780i 0.114375 + 0.198103i
\(357\) 4.77679 7.27116i 0.252815 0.384831i
\(358\) 32.8544 + 18.9685i 1.73641 + 1.00252i
\(359\) −7.90118 −0.417008 −0.208504 0.978021i \(-0.566859\pi\)
−0.208504 + 0.978021i \(0.566859\pi\)
\(360\) −1.43533 15.1715i −0.0756484 0.799610i
\(361\) −3.35872 −0.176775
\(362\) −19.4570 11.2335i −1.02264 0.590420i
\(363\) −11.9861 23.8348i −0.629108 1.25100i
\(364\) 0.820060 + 1.42039i 0.0429828 + 0.0744484i
\(365\) −2.24678 10.5609i −0.117602 0.552784i
\(366\) 13.0915 6.58349i 0.684302 0.344124i
\(367\) 9.46994 + 5.46747i 0.494327 + 0.285400i 0.726368 0.687306i \(-0.241207\pi\)
−0.232041 + 0.972706i \(0.574540\pi\)
\(368\) 16.0486i 0.836591i
\(369\) −1.26999 2.93560i −0.0661131 0.152821i
\(370\) 0.941767 2.90024i 0.0489601 0.150776i
\(371\) 6.80984 11.7950i 0.353549 0.612366i
\(372\) 1.41016 2.14653i 0.0731136 0.111292i
\(373\) −13.5989 + 7.85130i −0.704122 + 0.406525i −0.808881 0.587973i \(-0.799926\pi\)
0.104759 + 0.994498i \(0.466593\pi\)
\(374\) 20.7594 + 35.9564i 1.07344 + 1.85926i
\(375\) −16.2907 + 10.4697i −0.841247 + 0.540652i
\(376\) −8.84758 + 15.3245i −0.456279 + 0.790299i
\(377\) 19.7281i 1.01605i
\(378\) −2.87141 7.85022i −0.147690 0.403772i
\(379\) −19.3313 −0.992981 −0.496491 0.868042i \(-0.665378\pi\)
−0.496491 + 0.868042i \(0.665378\pi\)
\(380\) −3.47904 3.86247i −0.178471 0.198141i
\(381\) 0.999456 17.3184i 0.0512037 0.887247i
\(382\) −7.45624 + 4.30486i −0.381495 + 0.220256i
\(383\) −19.2876 + 11.1357i −0.985551 + 0.569008i −0.903941 0.427657i \(-0.859339\pi\)
−0.0816093 + 0.996664i \(0.526006\pi\)
\(384\) 19.7504 + 12.9750i 1.00788 + 0.662130i
\(385\) −8.53720 + 7.68971i −0.435096 + 0.391904i
\(386\) −11.4601 −0.583305
\(387\) −3.67230 2.72787i −0.186673 0.138665i
\(388\) 1.51260i 0.0767905i
\(389\) −17.1650 + 29.7307i −0.870301 + 1.50741i −0.00861633 + 0.999963i \(0.502743\pi\)
−0.861685 + 0.507443i \(0.830591\pi\)
\(390\) 17.1835 2.63172i 0.870121 0.133262i
\(391\) 8.34453 + 14.4532i 0.422001 + 0.730927i
\(392\) −1.96738 + 1.13587i −0.0993678 + 0.0573700i
\(393\) 11.4153 + 22.6996i 0.575824 + 1.14504i
\(394\) 10.8753 18.8365i 0.547888 0.948971i
\(395\) 4.14397 12.7616i 0.208506 0.642108i
\(396\) 9.00113 + 1.04239i 0.452324 + 0.0523823i
\(397\) 7.97072i 0.400039i 0.979792 + 0.200019i \(0.0641005\pi\)
−0.979792 + 0.200019i \(0.935899\pi\)
\(398\) 9.21861 + 5.32237i 0.462087 + 0.266786i
\(399\) 5.72517 + 3.76115i 0.286617 + 0.188293i
\(400\) 2.51577 24.0191i 0.125789 1.20096i
\(401\) 10.4149 + 18.0392i 0.520096 + 0.900832i 0.999727 + 0.0233622i \(0.00743709\pi\)
−0.479631 + 0.877470i \(0.659230\pi\)
\(402\) 26.5497 + 1.53220i 1.32418 + 0.0764193i
\(403\) −6.09549 3.51923i −0.303638 0.175305i
\(404\) −2.94534 −0.146536
\(405\) −20.1202 0.421937i −0.999780 0.0209662i
\(406\) 11.3741 0.564488
\(407\) −3.77231 2.17795i −0.186987 0.107957i
\(408\) 19.7310 + 1.13869i 0.976828 + 0.0563735i
\(409\) −8.72032 15.1040i −0.431192 0.746847i 0.565784 0.824553i \(-0.308574\pi\)
−0.996976 + 0.0777066i \(0.975240\pi\)
\(410\) −0.798046 3.75119i −0.0394127 0.185258i
\(411\) −10.3519 6.80070i −0.510623 0.335454i
\(412\) −8.12172 4.68907i −0.400128 0.231014i
\(413\) 13.1952i 0.649294i
\(414\) 15.9285 + 1.84464i 0.782844 + 0.0906590i
\(415\) −5.33093 1.73106i −0.261685 0.0849746i
\(416\) −4.50137 + 7.79660i −0.220698 + 0.382260i
\(417\) −14.3219 28.4796i −0.701348 1.39465i
\(418\) −28.3114 + 16.3456i −1.38475 + 0.799488i
\(419\) 2.45387 + 4.25022i 0.119879 + 0.207637i 0.919720 0.392576i \(-0.128416\pi\)
−0.799840 + 0.600213i \(0.795083\pi\)
\(420\) −0.344651 2.25036i −0.0168172 0.109806i
\(421\) −9.61276 + 16.6498i −0.468497 + 0.811461i −0.999352 0.0360017i \(-0.988538\pi\)
0.530854 + 0.847463i \(0.321871\pi\)
\(422\) 13.2247i 0.643766i
\(423\) 18.7587 + 13.9344i 0.912077 + 0.677513i
\(424\) 30.9403 1.50260
\(425\) −10.2232 22.9394i −0.495897 1.11272i
\(426\) −2.25400 1.48076i −0.109207 0.0717433i
\(427\) −4.55458 + 2.62959i −0.220412 + 0.127255i
\(428\) 7.54568 4.35650i 0.364734 0.210580i
\(429\) 1.43073 24.7914i 0.0690762 1.19694i
\(430\) −3.67098 4.07556i −0.177030 0.196541i
\(431\) 40.8153 1.96600 0.983001 0.183601i \(-0.0587753\pi\)
0.983001 + 0.183601i \(0.0587753\pi\)
\(432\) 16.1020 19.2518i 0.774709 0.926254i
\(433\) 33.9312i 1.63063i 0.579019 + 0.815314i \(0.303436\pi\)
−0.579019 + 0.815314i \(0.696564\pi\)
\(434\) −2.02899 + 3.51432i −0.0973947 + 0.168693i
\(435\) 9.94398 25.5147i 0.476777 1.22334i
\(436\) −1.51263 2.61995i −0.0724419 0.125473i
\(437\) −11.3801 + 6.57032i −0.544385 + 0.314301i
\(438\) 7.38721 11.2447i 0.352974 0.537292i
\(439\) 9.57454 16.5836i 0.456968 0.791492i −0.541831 0.840487i \(-0.682269\pi\)
0.998799 + 0.0489957i \(0.0156021\pi\)
\(440\) −24.8257 8.06143i −1.18352 0.384314i
\(441\) 1.19116 + 2.75339i 0.0567221 + 0.131114i
\(442\) 22.5451i 1.07236i
\(443\) −18.9074 10.9162i −0.898317 0.518644i −0.0216634 0.999765i \(-0.506896\pi\)
−0.876654 + 0.481122i \(0.840230\pi\)
\(444\) 0.771072 0.387760i 0.0365935 0.0184023i
\(445\) −16.0589 + 3.41645i −0.761266 + 0.161955i
\(446\) 2.38963 + 4.13896i 0.113152 + 0.195985i
\(447\) 5.44903 + 10.8356i 0.257730 + 0.512505i
\(448\) −3.87090 2.23487i −0.182883 0.105588i
\(449\) 33.8190 1.59601 0.798007 0.602648i \(-0.205887\pi\)
0.798007 + 0.602648i \(0.205887\pi\)
\(450\) −23.5503 5.25773i −1.11017 0.247852i
\(451\) −5.47844 −0.257970
\(452\) −9.55771 5.51815i −0.449557 0.259552i
\(453\) −6.90555 + 10.5115i −0.324451 + 0.493875i
\(454\) −8.49854 14.7199i −0.398856 0.690839i
\(455\) −6.10249 + 1.29827i −0.286089 + 0.0608639i
\(456\) −0.896581 + 15.5358i −0.0419862 + 0.727529i
\(457\) −10.2735 5.93139i −0.480573 0.277459i 0.240082 0.970753i \(-0.422826\pi\)
−0.720655 + 0.693294i \(0.756159\pi\)
\(458\) 19.1341i 0.894076i
\(459\) 4.49121 25.7102i 0.209631 1.20005i
\(460\) 4.15373 + 1.34880i 0.193669 + 0.0628883i
\(461\) −10.5461 + 18.2664i −0.491182 + 0.850753i −0.999948 0.0101519i \(-0.996769\pi\)
0.508766 + 0.860905i \(0.330102\pi\)
\(462\) −14.2933 0.824877i −0.664984 0.0383767i
\(463\) 7.80262 4.50485i 0.362619 0.209358i −0.307610 0.951512i \(-0.599529\pi\)
0.670229 + 0.742155i \(0.266196\pi\)
\(464\) 17.0757 + 29.5759i 0.792718 + 1.37303i
\(465\) 6.10953 + 7.62392i 0.283323 + 0.353551i
\(466\) 15.2707 26.4497i 0.707403 1.22526i
\(467\) 2.76614i 0.128002i −0.997950 0.0640008i \(-0.979614\pi\)
0.997950 0.0640008i \(-0.0203860\pi\)
\(468\) 3.94985 + 2.93404i 0.182582 + 0.135626i
\(469\) −9.54452 −0.440725
\(470\) 18.7519 + 20.8186i 0.864962 + 0.960290i
\(471\) −14.3581 + 7.22047i −0.661587 + 0.332701i
\(472\) −25.9600 + 14.9880i −1.19491 + 0.689880i
\(473\) −6.78564 + 3.91769i −0.312004 + 0.180136i
\(474\) 14.9369 7.51152i 0.686074 0.345016i
\(475\) 18.0620 8.04952i 0.828743 0.369338i
\(476\) 2.95252 0.135329
\(477\) 4.70036 40.5878i 0.215215 1.85839i
\(478\) 30.8835i 1.41258i
\(479\) 3.77488 6.53828i 0.172479 0.298742i −0.766807 0.641878i \(-0.778156\pi\)
0.939286 + 0.343136i \(0.111489\pi\)
\(480\) 9.75159 7.81456i 0.445097 0.356684i
\(481\) −1.18264 2.04840i −0.0539240 0.0933991i
\(482\) −35.0479 + 20.2349i −1.59639 + 0.921674i
\(483\) −5.74538 0.331570i −0.261424 0.0150870i
\(484\) 4.52708 7.84114i 0.205776 0.356415i
\(485\) 5.47266 + 1.77709i 0.248501 + 0.0806934i
\(486\) −17.2570 18.1944i −0.782794 0.825313i
\(487\) 6.91178i 0.313203i −0.987662 0.156601i \(-0.949946\pi\)
0.987662 0.156601i \(-0.0500538\pi\)
\(488\) −10.3468 5.97373i −0.468378 0.270418i
\(489\) −0.959623 + 16.6282i −0.0433957 + 0.751951i
\(490\) 0.748511 + 3.51835i 0.0338143 + 0.158943i
\(491\) 1.20549 + 2.08798i 0.0544032 + 0.0942290i 0.891944 0.452145i \(-0.149341\pi\)
−0.837541 + 0.546374i \(0.816008\pi\)
\(492\) 0.596013 0.907242i 0.0268703 0.0409016i
\(493\) 30.7562 + 17.7571i 1.38519 + 0.799741i
\(494\) −17.7516 −0.798682
\(495\) −14.3465 + 31.3419i −0.644827 + 1.40871i
\(496\) −12.1843 −0.547091
\(497\) 0.838234 + 0.483955i 0.0375999 + 0.0217083i
\(498\) −3.13779 6.23960i −0.140608 0.279603i
\(499\) 15.6623 + 27.1278i 0.701139 + 1.21441i 0.968067 + 0.250692i \(0.0806581\pi\)
−0.266928 + 0.963716i \(0.586009\pi\)
\(500\) −6.00524 2.66982i −0.268563 0.119398i
\(501\) 36.0569 18.1324i 1.61090 0.810096i
\(502\) 41.5707 + 24.0008i 1.85539 + 1.07121i
\(503\) 26.5245i 1.18267i −0.806427 0.591333i \(-0.798602\pi\)
0.806427 0.591333i \(-0.201398\pi\)
\(504\) −4.06396 + 5.47096i −0.181023 + 0.243696i
\(505\) 3.46036 10.6564i 0.153984 0.474204i
\(506\) 13.7323 23.7851i 0.610477 1.05738i
\(507\) −4.95934 + 7.54903i −0.220252 + 0.335264i
\(508\) 5.09848 2.94361i 0.226208 0.130601i
\(509\) 4.22519 + 7.31825i 0.187278 + 0.324376i 0.944342 0.328966i \(-0.106700\pi\)
−0.757064 + 0.653341i \(0.773367\pi\)
\(510\) 11.3639 29.1580i 0.503202 1.29114i
\(511\) −2.41434 + 4.18176i −0.106804 + 0.184990i
\(512\) 6.36081i 0.281111i
\(513\) 20.2437 + 3.53629i 0.893783 + 0.156131i
\(514\) −9.53329 −0.420495
\(515\) 26.5072 23.8758i 1.16805 1.05209i
\(516\) 0.0894477 1.54993i 0.00393772 0.0682320i
\(517\) 34.6621 20.0122i 1.52444 0.880134i
\(518\) −1.18099 + 0.681846i −0.0518898 + 0.0299586i
\(519\) 15.2207 + 9.99926i 0.668116 + 0.438919i
\(520\) −9.48583 10.5313i −0.415981 0.461827i
\(521\) −2.93428 −0.128553 −0.0642767 0.997932i \(-0.520474\pi\)
−0.0642767 + 0.997932i \(0.520474\pi\)
\(522\) 31.3173 13.5484i 1.37072 0.592999i
\(523\) 6.38846i 0.279348i −0.990198 0.139674i \(-0.955395\pi\)
0.990198 0.139674i \(-0.0446055\pi\)
\(524\) −4.31148 + 7.46770i −0.188348 + 0.326228i
\(525\) 8.54685 + 1.39689i 0.373015 + 0.0609653i
\(526\) 16.5957 + 28.7445i 0.723605 + 1.25332i
\(527\) −10.9730 + 6.33527i −0.477992 + 0.275969i
\(528\) −19.3132 38.4050i −0.840501 1.67136i
\(529\) −5.98010 + 10.3578i −0.260005 + 0.450341i
\(530\) 15.1308 46.5962i 0.657238 2.02401i
\(531\) 15.7177 + 36.3315i 0.682088 + 1.57665i
\(532\) 2.32476i 0.100791i
\(533\) −2.57629 1.48742i −0.111592 0.0644274i
\(534\) −17.0987 11.2330i −0.739932 0.486099i
\(535\) 6.89697 + 32.4190i 0.298182 + 1.40160i
\(536\) −10.8413 18.7777i −0.468274 0.811074i
\(537\) −40.7789 2.35338i −1.75974 0.101556i
\(538\) −38.7837 22.3918i −1.67208 0.965378i
\(539\) 5.13839 0.221326
\(540\) −3.62950 5.78558i −0.156189 0.248972i
\(541\) −14.9483 −0.642678 −0.321339 0.946964i \(-0.604133\pi\)
−0.321339 + 0.946964i \(0.604133\pi\)
\(542\) 1.53668 + 0.887200i 0.0660059 + 0.0381085i
\(543\) 24.1500 + 1.39371i 1.03638 + 0.0598100i
\(544\) 8.10330 + 14.0353i 0.347426 + 0.601760i
\(545\) 11.2563 2.39471i 0.482166 0.102578i
\(546\) −6.49761 4.26860i −0.278072 0.182679i
\(547\) 25.5542 + 14.7537i 1.09262 + 0.630824i 0.934273 0.356559i \(-0.116050\pi\)
0.158347 + 0.987384i \(0.449384\pi\)
\(548\) 4.20349i 0.179564i
\(549\) −9.40825 + 12.6655i −0.401534 + 0.540551i
\(550\) −24.2810 + 33.4453i −1.03535 + 1.42611i
\(551\) −13.9816 + 24.2169i −0.595637 + 1.03167i
\(552\) −5.87367 11.6800i −0.250000 0.497133i
\(553\) −5.19662 + 3.00027i −0.220983 + 0.127584i
\(554\) −20.4090 35.3495i −0.867097 1.50186i
\(555\) 0.497036 + 3.24535i 0.0210980 + 0.137757i
\(556\) 5.40931 9.36920i 0.229406 0.397342i
\(557\) 10.5465i 0.446868i −0.974719 0.223434i \(-0.928273\pi\)
0.974719 0.223434i \(-0.0717267\pi\)
\(558\) −1.40047 + 12.0931i −0.0592867 + 0.511943i
\(559\) −4.25468 −0.179954
\(560\) −8.02499 + 7.22835i −0.339118 + 0.305454i
\(561\) −37.3621 24.5450i −1.57743 1.03629i
\(562\) 20.0530 11.5776i 0.845884 0.488371i
\(563\) 4.86466 2.80861i 0.205021 0.118369i −0.393974 0.919121i \(-0.628900\pi\)
0.598995 + 0.800752i \(0.295567\pi\)
\(564\) −0.456913 + 7.91729i −0.0192395 + 0.333378i
\(565\) 31.1939 28.0973i 1.31234 1.18206i
\(566\) −13.1202 −0.551484
\(567\) 6.55946 + 6.16226i 0.275472 + 0.258791i
\(568\) 2.19884i 0.0922611i
\(569\) 15.4294 26.7245i 0.646834 1.12035i −0.337041 0.941490i \(-0.609426\pi\)
0.983875 0.178859i \(-0.0572406\pi\)
\(570\) 22.9584 + 8.94771i 0.961623 + 0.374778i
\(571\) −4.11966 7.13545i −0.172402 0.298609i 0.766857 0.641818i \(-0.221820\pi\)
−0.939259 + 0.343209i \(0.888486\pi\)
\(572\) 7.29850 4.21379i 0.305166 0.176187i
\(573\) 5.08988 7.74774i 0.212633 0.323666i
\(574\) −0.857564 + 1.48534i −0.0357940 + 0.0619971i
\(575\) −9.76009 + 13.4438i −0.407024 + 0.560645i
\(576\) −13.3202 1.54257i −0.555007 0.0642738i
\(577\) 7.25745i 0.302132i −0.988524 0.151066i \(-0.951729\pi\)
0.988524 0.151066i \(-0.0482705\pi\)
\(578\) 11.4645 + 6.61901i 0.476859 + 0.275315i
\(579\) 11.0237 5.54363i 0.458128 0.230385i
\(580\) 9.09003 1.93385i 0.377443 0.0802989i
\(581\) 1.25330 + 2.17078i 0.0519958 + 0.0900593i
\(582\) 3.22122 + 6.40549i 0.133524 + 0.265516i
\(583\) −60.6073 34.9916i −2.51010 1.44921i
\(584\) −10.9695 −0.453921
\(585\) −15.2561 + 10.8437i −0.630760 + 0.448332i
\(586\) −3.33489 −0.137763
\(587\) −6.79751 3.92455i −0.280563 0.161983i 0.353115 0.935580i \(-0.385122\pi\)
−0.633678 + 0.773597i \(0.718456\pi\)
\(588\) −0.559018 + 0.850929i −0.0230535 + 0.0350917i
\(589\) −4.98827 8.63993i −0.205538 0.356002i
\(590\) 9.87676 + 46.4254i 0.406620 + 1.91130i
\(591\) −1.34927 + 23.3799i −0.0555015 + 0.961720i
\(592\) −3.54599 2.04728i −0.145739 0.0841425i
\(593\) 9.64578i 0.396105i −0.980191 0.198052i \(-0.936538\pi\)
0.980191 0.198052i \(-0.0634616\pi\)
\(594\) −40.3375 + 14.7544i −1.65507 + 0.605382i
\(595\) −3.46879 + 10.6824i −0.142207 + 0.437935i
\(596\) −2.05807 + 3.56467i −0.0843016 + 0.146015i
\(597\) −11.4421 0.660333i −0.468295 0.0270256i
\(598\) 12.9155 7.45678i 0.528155 0.304931i
\(599\) −22.5812 39.1118i −0.922643 1.59806i −0.795309 0.606204i \(-0.792692\pi\)
−0.127333 0.991860i \(-0.540642\pi\)
\(600\) 6.95988 + 18.4016i 0.284136 + 0.751242i
\(601\) 6.56530 11.3714i 0.267804 0.463850i −0.700490 0.713662i \(-0.747035\pi\)
0.968294 + 0.249811i \(0.0803687\pi\)
\(602\) 2.45301i 0.0999773i
\(603\) −26.2797 + 11.3691i −1.07019 + 0.462985i
\(604\) −4.26830 −0.173675
\(605\) 23.0510 + 25.5915i 0.937157 + 1.04044i
\(606\) 12.4728 6.27238i 0.506674 0.254798i
\(607\) 18.9487 10.9400i 0.769105 0.444043i −0.0634504 0.997985i \(-0.520210\pi\)
0.832555 + 0.553942i \(0.186877\pi\)
\(608\) −11.0511 + 6.38038i −0.448183 + 0.258759i
\(609\) −10.9409 + 5.50203i −0.443350 + 0.222953i
\(610\) −14.0564 + 12.6610i −0.569125 + 0.512628i
\(611\) 21.7336 0.879246
\(612\) 8.12942 3.51693i 0.328613 0.142164i
\(613\) 7.96920i 0.321873i −0.986965 0.160937i \(-0.948549\pi\)
0.986965 0.160937i \(-0.0514515\pi\)
\(614\) 17.3590 30.0666i 0.700551 1.21339i
\(615\) 2.58222 + 3.22229i 0.104125 + 0.129935i
\(616\) 5.83654 + 10.1092i 0.235161 + 0.407310i
\(617\) −14.9784 + 8.64777i −0.603007 + 0.348146i −0.770223 0.637774i \(-0.779855\pi\)
0.167217 + 0.985920i \(0.446522\pi\)
\(618\) 44.3794 + 2.56117i 1.78520 + 0.103025i
\(619\) 7.76411 13.4478i 0.312066 0.540514i −0.666743 0.745287i \(-0.732312\pi\)
0.978809 + 0.204773i \(0.0656457\pi\)
\(620\) −1.02403 + 3.15356i −0.0411259 + 0.126650i
\(621\) −16.2142 + 5.93075i −0.650654 + 0.237993i
\(622\) 12.4609i 0.499637i
\(623\) 6.35879 + 3.67125i 0.254759 + 0.147085i
\(624\) 1.34489 23.3040i 0.0538386 0.932905i
\(625\) 16.7149 18.5907i 0.668596 0.743626i
\(626\) 1.29880 + 2.24960i 0.0519107 + 0.0899119i
\(627\) 19.3263 29.4182i 0.771817 1.17485i
\(628\) −4.72352 2.72712i −0.188489 0.108824i
\(629\) −4.25796 −0.169776
\(630\) 6.25187 + 8.79578i 0.249081 + 0.350432i
\(631\) 7.88432 0.313870 0.156935 0.987609i \(-0.449839\pi\)
0.156935 + 0.987609i \(0.449839\pi\)
\(632\) −11.8053 6.81582i −0.469591 0.271119i
\(633\) −6.39719 12.7210i −0.254265 0.505615i
\(634\) 10.2833 + 17.8112i 0.408402 + 0.707374i
\(635\) 4.66015 + 21.9049i 0.184932 + 0.869270i
\(636\) 12.3883 6.22988i 0.491229 0.247031i
\(637\) 2.41638 + 1.39510i 0.0957404 + 0.0552758i
\(638\) 58.4447i 2.31385i
\(639\) 2.88445 + 0.334040i 0.114107 + 0.0132144i
\(640\) −29.0162 9.42217i −1.14697 0.372444i
\(641\) −0.192272 + 0.333025i −0.00759428 + 0.0131537i −0.869798 0.493409i \(-0.835751\pi\)
0.862203 + 0.506562i \(0.169084\pi\)
\(642\) −22.6766 + 34.5180i −0.894974 + 1.36232i
\(643\) −15.0953 + 8.71526i −0.595299 + 0.343696i −0.767190 0.641420i \(-0.778346\pi\)
0.171891 + 0.985116i \(0.445012\pi\)
\(644\) −0.976544 1.69142i −0.0384812 0.0666514i
\(645\) 5.50266 + 2.14458i 0.216667 + 0.0844427i
\(646\) −15.9781 + 27.6748i −0.628649 + 1.08885i
\(647\) 38.8775i 1.52843i 0.644961 + 0.764215i \(0.276874\pi\)
−0.644961 + 0.764215i \(0.723126\pi\)
\(648\) −4.67283 + 19.9045i −0.183566 + 0.781922i
\(649\) 67.8022 2.66147
\(650\) −20.4990 + 9.13556i −0.804035 + 0.358326i
\(651\) 0.251732 4.36197i 0.00986616 0.170959i
\(652\) −4.89528 + 2.82629i −0.191714 + 0.110686i
\(653\) −23.1331 + 13.3559i −0.905269 + 0.522657i −0.878906 0.476995i \(-0.841726\pi\)
−0.0263633 + 0.999652i \(0.508393\pi\)
\(654\) 11.9851 + 7.87359i 0.468653 + 0.307882i
\(655\) −21.9532 24.3727i −0.857782 0.952319i
\(656\) −5.14975 −0.201064
\(657\) −1.66645 + 14.3899i −0.0650145 + 0.561403i
\(658\) 12.5304i 0.488484i
\(659\) −10.3342 + 17.8993i −0.402562 + 0.697258i −0.994034 0.109068i \(-0.965214\pi\)
0.591472 + 0.806325i \(0.298547\pi\)
\(660\) −11.5632 + 1.77095i −0.450098 + 0.0689342i
\(661\) 7.59618 + 13.1570i 0.295457 + 0.511747i 0.975091 0.221804i \(-0.0711947\pi\)
−0.679634 + 0.733551i \(0.737861\pi\)
\(662\) −15.6610 + 9.04190i −0.608683 + 0.351423i
\(663\) −10.9058 21.6865i −0.423546 0.842235i
\(664\) −2.84718 + 4.93145i −0.110492 + 0.191377i
\(665\) −8.41110 2.73126i −0.326168 0.105914i
\(666\) −2.43954 + 3.28414i −0.0945302 + 0.127258i
\(667\) 23.4926i 0.909638i
\(668\) 11.8619 + 6.84850i 0.458953 + 0.264976i
\(669\) −4.30077 2.82539i −0.166277 0.109236i
\(670\) −33.5810 + 7.14418i −1.29735 + 0.276004i
\(671\) 13.5119 + 23.4032i 0.521619 + 0.903471i
\(672\) −5.57929 0.321985i −0.215226 0.0124208i
\(673\) 34.6344 + 19.9962i 1.33506 + 0.770796i 0.986070 0.166332i \(-0.0531922\pi\)
0.348988 + 0.937127i \(0.386526\pi\)
\(674\) −49.2959 −1.89881
\(675\) 25.1967 6.33452i 0.969822 0.243816i
\(676\) −3.06535 −0.117898
\(677\) −23.0021 13.2803i −0.884043 0.510402i −0.0120534 0.999927i \(-0.503837\pi\)
−0.871989 + 0.489525i \(0.837170\pi\)
\(678\) 52.2261 + 3.01401i 2.00573 + 0.115752i
\(679\) −1.28662 2.22850i −0.0493761 0.0855220i
\(680\) −24.9564 + 5.30935i −0.957035 + 0.203604i
\(681\) 15.2954 + 10.0483i 0.586120 + 0.385051i
\(682\) 18.0579 + 10.4258i 0.691474 + 0.399223i
\(683\) 10.3626i 0.396512i 0.980150 + 0.198256i \(0.0635277\pi\)
−0.980150 + 0.198256i \(0.936472\pi\)
\(684\) 2.76916 + 6.40095i 0.105882 + 0.244746i
\(685\) 15.2085 + 4.93851i 0.581086 + 0.188691i
\(686\) 0.804334 1.39315i 0.0307096 0.0531906i
\(687\) 9.25576 + 18.4054i 0.353129 + 0.702208i
\(688\) −6.37852 + 3.68264i −0.243179 + 0.140399i
\(689\) −19.0008 32.9103i −0.723872 1.25378i
\(690\) −20.4625 + 3.13390i −0.778993 + 0.119306i
\(691\) −0.423942 + 0.734290i −0.0161275 + 0.0279337i −0.873977 0.485968i \(-0.838467\pi\)
0.857849 + 0.513902i \(0.171800\pi\)
\(692\) 6.18051i 0.234948i
\(693\) 14.1480 6.12066i 0.537437 0.232505i
\(694\) −26.6171 −1.01037
\(695\) 27.5431 + 30.5787i 1.04477 + 1.15991i
\(696\) −23.2521 15.2754i −0.881367 0.579014i
\(697\) −4.63780 + 2.67763i −0.175669 + 0.101423i
\(698\) 19.7522 11.4039i 0.747632 0.431645i
\(699\) −1.89460 + 32.8293i −0.0716605 + 1.24172i
\(700\) 1.19640 + 2.68455i 0.0452196 + 0.101467i
\(701\) −21.6568 −0.817968 −0.408984 0.912542i \(-0.634117\pi\)
−0.408984 + 0.912542i \(0.634117\pi\)
\(702\) −22.9750 4.01340i −0.867136 0.151476i
\(703\) 3.35263i 0.126447i
\(704\) −11.4836 + 19.8902i −0.432805 + 0.749641i
\(705\) −28.1084 10.9548i −1.05862 0.412583i
\(706\) −4.34043 7.51784i −0.163354 0.282938i
\(707\) −4.33935 + 2.50533i −0.163198 + 0.0942225i
\(708\) −7.37636 + 11.2282i −0.277221 + 0.421981i
\(709\) 1.22418 2.12035i 0.0459751 0.0796313i −0.842122 0.539287i \(-0.818694\pi\)
0.888097 + 0.459656i \(0.152027\pi\)
\(710\) 3.31145 + 1.07530i 0.124276 + 0.0403552i
\(711\) −10.7345 + 14.4509i −0.402574 + 0.541951i
\(712\) 16.6802i 0.625118i
\(713\) 7.25863 + 4.19077i 0.271838 + 0.156946i
\(714\) −12.5032 + 6.28767i −0.467921 + 0.235310i
\(715\) 6.67103 + 31.3570i 0.249482 + 1.17269i
\(716\) −6.93119 12.0052i −0.259031 0.448654i
\(717\) −14.9393 29.7073i −0.557919 1.10944i
\(718\) 11.0075 + 6.35519i 0.410797 + 0.237174i
\(719\) −36.6105 −1.36534 −0.682671 0.730726i \(-0.739182\pi\)
−0.682671 + 0.730726i \(0.739182\pi\)
\(720\) −13.4857 + 29.4615i −0.502584 + 1.09797i
\(721\) −15.9542 −0.594167
\(722\) 4.67920 + 2.70154i 0.174142 + 0.100541i
\(723\) 23.9248 36.4180i 0.889774 1.35440i
\(724\) 4.10478 + 7.10968i 0.152553 + 0.264229i
\(725\) −3.68270 + 35.1602i −0.136772 + 1.30582i
\(726\) −2.47269 + 42.8462i −0.0917700 + 1.59017i
\(727\) 3.87756 + 2.23871i 0.143811 + 0.0830292i 0.570179 0.821521i \(-0.306874\pi\)
−0.426368 + 0.904550i \(0.640207\pi\)
\(728\) 6.33859i 0.234924i
\(729\) 25.4010 + 9.15369i 0.940777 + 0.339025i
\(730\) −5.36441 + 16.5201i −0.198546 + 0.611436i
\(731\) −3.82961 + 6.63308i −0.141643 + 0.245333i
\(732\) −5.34561 0.308499i −0.197580 0.0114025i
\(733\) 40.6147 23.4489i 1.50014 0.866106i 0.500139 0.865945i \(-0.333282\pi\)
1.00000 0.000160408i \(-5.10595e-5\pi\)
\(734\) −8.79535 15.2340i −0.324642 0.562297i
\(735\) −2.42194 3.02228i −0.0893348 0.111479i
\(736\) 5.36032 9.28435i 0.197584 0.342226i
\(737\) 49.0435i 1.80654i
\(738\) −0.591916 + 5.11122i −0.0217887 + 0.188147i
\(739\) 8.33703 0.306683 0.153341 0.988173i \(-0.450997\pi\)
0.153341 + 0.988173i \(0.450997\pi\)
\(740\) −0.827903 + 0.745717i −0.0304343 + 0.0274131i
\(741\) 17.0755 8.58701i 0.627286 0.315452i
\(742\) −18.9742 + 10.9548i −0.696566 + 0.402163i
\(743\) 26.4585 15.2758i 0.970668 0.560415i 0.0712280 0.997460i \(-0.477308\pi\)
0.899440 + 0.437045i \(0.143975\pi\)
\(744\) 8.86759 4.45937i 0.325101 0.163488i
\(745\) −10.4793 11.6342i −0.383930 0.426244i
\(746\) 25.2603 0.924845
\(747\) 6.03659 + 4.48412i 0.220867 + 0.164065i
\(748\) 15.1712i 0.554714i
\(749\) 7.41134 12.8368i 0.270804 0.469047i
\(750\) 31.1164 1.48266i 1.13621 0.0541390i
\(751\) −11.5992 20.0904i −0.423260 0.733109i 0.572996 0.819558i \(-0.305781\pi\)
−0.996256 + 0.0864497i \(0.972448\pi\)
\(752\) 32.5825 18.8115i 1.18816 0.685984i
\(753\) −51.5975 2.97773i −1.88032 0.108514i
\(754\) 15.8680 27.4842i 0.577879 1.00092i
\(755\) 5.01465 15.4429i 0.182502 0.562026i
\(756\) −0.525597 + 3.00882i −0.0191158 + 0.109430i
\(757\) 7.34831i 0.267079i −0.991044 0.133539i \(-0.957366\pi\)
0.991044 0.133539i \(-0.0426343\pi\)
\(758\) 26.9313 + 15.5488i 0.978190 + 0.564759i
\(759\) −1.70374 + 29.5220i −0.0618418 + 1.07158i
\(760\) −4.18047 19.6502i −0.151642 0.712788i
\(761\) 4.42586 + 7.66582i 0.160437 + 0.277886i 0.935026 0.354580i \(-0.115376\pi\)
−0.774588 + 0.632466i \(0.782043\pi\)
\(762\) −15.3222 + 23.3232i −0.555063 + 0.844909i
\(763\) −4.45710 2.57331i −0.161358 0.0931600i
\(764\) 3.14604 0.113820
\(765\) 3.17354 + 33.5446i 0.114740 + 1.21281i
\(766\) 35.8273 1.29449
\(767\) 31.8846 + 18.4086i 1.15129 + 0.664696i
\(768\) −10.1226 20.1291i −0.365269 0.726348i
\(769\) −7.42151 12.8544i −0.267627 0.463543i 0.700622 0.713533i \(-0.252906\pi\)
−0.968248 + 0.249990i \(0.919573\pi\)
\(770\) 18.0787 3.84614i 0.651510 0.138605i
\(771\) 9.17022 4.61156i 0.330257 0.166081i
\(772\) 3.62656 + 2.09379i 0.130523 + 0.0753572i
\(773\) 13.6071i 0.489415i −0.969597 0.244707i \(-0.921308\pi\)
0.969597 0.244707i \(-0.0786919\pi\)
\(774\) 2.92194 + 6.75409i 0.105027 + 0.242771i
\(775\) −10.2067 7.40998i −0.366635 0.266174i
\(776\) 2.92287 5.06256i 0.104925 0.181735i
\(777\) 0.806185 1.22716i 0.0289217 0.0440242i
\(778\) 47.8269 27.6128i 1.71468 0.989968i
\(779\) −2.10832 3.65171i −0.0755383 0.130836i
\(780\) −5.91855 2.30667i −0.211918 0.0825919i
\(781\) 2.48675 4.30718i 0.0889829 0.154123i
\(782\) 26.8472i 0.960053i
\(783\) −23.5708 + 28.1817i −0.842353 + 1.00713i
\(784\) 4.83010 0.172504
\(785\) 15.4164 13.8860i 0.550233 0.495612i
\(786\) 2.35492 40.8056i 0.0839974 1.45549i
\(787\) −43.6762 + 25.2164i −1.55689 + 0.898869i −0.559335 + 0.828942i \(0.688944\pi\)
−0.997552 + 0.0699278i \(0.977723\pi\)
\(788\) −6.88296 + 3.97388i −0.245195 + 0.141564i
\(789\) −29.8683 19.6220i −1.06334 0.698560i
\(790\) −16.0378 + 14.4457i −0.570599 + 0.513956i
\(791\) −18.7751 −0.667566
\(792\) 28.1119 + 20.8822i 0.998913 + 0.742016i
\(793\) 14.6741i 0.521093i
\(794\) 6.41112 11.1044i 0.227522 0.394080i
\(795\) 7.98556 + 52.1409i 0.283218 + 1.84925i
\(796\) −1.94482 3.36853i −0.0689323 0.119394i
\(797\) 18.1215 10.4625i 0.641897 0.370599i −0.143448 0.989658i \(-0.545819\pi\)
0.785345 + 0.619058i \(0.212486\pi\)
\(798\) −4.95079 9.84479i −0.175256 0.348502i
\(799\) 19.5622 33.8828i 0.692062 1.19869i
\(800\) −9.47794 + 13.0551i −0.335096 + 0.461569i
\(801\) 21.8812 + 2.53401i 0.773136 + 0.0895347i
\(802\) 33.5083i 1.18322i
\(803\) 21.4875 + 12.4058i 0.758279 + 0.437792i
\(804\) −8.12171 5.33556i −0.286431 0.188171i
\(805\) 7.26697 1.54601i 0.256127 0.0544896i
\(806\) 5.66128 + 9.80563i 0.199410 + 0.345388i
\(807\) 48.1383 + 2.77809i 1.69455 + 0.0977935i
\(808\) −9.85787 5.69144i −0.346799 0.200224i
\(809\) −18.1877 −0.639445 −0.319722 0.947511i \(-0.603590\pi\)
−0.319722 + 0.947511i \(0.603590\pi\)
\(810\) 27.6910 + 16.7712i 0.972963 + 0.589279i
\(811\) −24.5937 −0.863600 −0.431800 0.901969i \(-0.642121\pi\)
−0.431800 + 0.901969i \(0.642121\pi\)
\(812\) −3.59934 2.07808i −0.126312 0.0729263i
\(813\) −1.90732 0.110073i −0.0668926 0.00386042i
\(814\) 3.50359 + 6.06840i 0.122801 + 0.212697i
\(815\) −4.47442 21.0319i −0.156732 0.736715i
\(816\) −35.1205 23.0724i −1.22946 0.807696i
\(817\) −5.22276 3.01536i −0.182721 0.105494i
\(818\) 28.0562i 0.980963i
\(819\) 8.31501 + 0.962938i 0.290550 + 0.0336478i
\(820\) −0.432811 + 1.33287i −0.0151144 + 0.0465458i
\(821\) 5.06771 8.77753i 0.176864 0.306338i −0.763941 0.645287i \(-0.776738\pi\)
0.940805 + 0.338949i \(0.110071\pi\)
\(822\) 8.95174 + 17.8008i 0.312228 + 0.620874i
\(823\) −17.4650 + 10.0834i −0.608793 + 0.351487i −0.772493 0.635024i \(-0.780990\pi\)
0.163700 + 0.986510i \(0.447657\pi\)
\(824\) −18.1219 31.3881i −0.631307 1.09346i
\(825\) 7.17777 43.9171i 0.249898 1.52900i
\(826\) 10.6134 18.3829i 0.369286 0.639622i
\(827\) 42.4406i 1.47581i 0.674907 + 0.737903i \(0.264184\pi\)
−0.674907 + 0.737903i \(0.735816\pi\)
\(828\) −4.70356 3.49392i −0.163460 0.121422i
\(829\) −37.3130 −1.29593 −0.647967 0.761668i \(-0.724381\pi\)
−0.647967 + 0.761668i \(0.724381\pi\)
\(830\) 6.03442 + 6.69948i 0.209458 + 0.232542i
\(831\) 36.7315 + 24.1307i 1.27420 + 0.837086i
\(832\) −10.8006 + 6.23571i −0.374442 + 0.216184i
\(833\) 4.34993 2.51143i 0.150716 0.0870160i
\(834\) −2.95456 + 51.1960i −0.102308 + 1.77277i
\(835\) −38.7144 + 34.8712i −1.33977 + 1.20677i
\(836\) 11.9455 0.413144
\(837\) −4.50270 12.3100i −0.155636 0.425497i
\(838\) 7.89491i 0.272725i
\(839\) 20.9567 36.2981i 0.723505 1.25315i −0.236081 0.971733i \(-0.575863\pi\)
0.959586 0.281415i \(-0.0908036\pi\)
\(840\) 3.19497 8.19780i 0.110237 0.282851i
\(841\) −10.4961 18.1798i −0.361935 0.626889i
\(842\) 26.7840 15.4638i 0.923038 0.532916i
\(843\) −13.6888 + 20.8369i −0.471469 + 0.717663i
\(844\) 2.41618 4.18494i 0.0831683 0.144052i
\(845\) 3.60135 11.0906i 0.123890 0.381529i
\(846\) −14.9257 34.5009i −0.513156 1.18617i
\(847\) 15.4031i 0.529256i
\(848\) −56.9711 32.8923i −1.95639 1.12952i
\(849\) 12.6206 6.34667i 0.433136 0.217817i
\(850\) −4.20856 + 40.1808i −0.144352 + 1.37819i
\(851\) 1.40832 + 2.43928i 0.0482765 + 0.0836173i
\(852\) 0.442739 + 0.880399i 0.0151680 + 0.0301620i
\(853\) 7.52505 + 4.34459i 0.257653 + 0.148756i 0.623263 0.782012i \(-0.285806\pi\)
−0.365611 + 0.930768i \(0.619140\pi\)
\(854\) 8.46027 0.289505
\(855\) −26.4124 + 2.49878i −0.903284 + 0.0854566i
\(856\) 33.6732 1.15093
\(857\) −33.2805 19.2145i −1.13684 0.656355i −0.191194 0.981552i \(-0.561236\pi\)
−0.945646 + 0.325197i \(0.894569\pi\)
\(858\) −21.9338 + 33.3872i −0.748806 + 1.13982i
\(859\) 6.59880 + 11.4295i 0.225148 + 0.389968i 0.956364 0.292178i \(-0.0943800\pi\)
−0.731216 + 0.682146i \(0.761047\pi\)
\(860\) 0.417067 + 1.96041i 0.0142219 + 0.0668494i
\(861\) 0.106396 1.84361i 0.00362596 0.0628300i
\(862\) −56.8617 32.8291i −1.93672 1.11816i
\(863\) 10.5429i 0.358885i −0.983768 0.179443i \(-0.942571\pi\)
0.983768 0.179443i \(-0.0574294\pi\)
\(864\) −15.7455 + 5.75930i −0.535672 + 0.195935i
\(865\) −22.3615 7.26123i −0.760312 0.246889i
\(866\) 27.2920 47.2711i 0.927420 1.60634i
\(867\) −14.2297 0.821205i −0.483265 0.0278896i
\(868\) 1.28415 0.741404i 0.0435869 0.0251649i
\(869\) 15.4165 + 26.7022i 0.522971 + 0.905812i
\(870\) −34.3758 + 27.5475i −1.16545 + 0.933947i
\(871\) −13.3155 + 23.0632i −0.451180 + 0.781466i
\(872\) 11.6918i 0.395933i
\(873\) −6.19708 4.60334i −0.209739 0.155799i
\(874\) 21.1389 0.715035
\(875\) −11.1185 + 1.17467i −0.375873 + 0.0397109i
\(876\) −4.39212 + 2.20872i −0.148396 + 0.0746259i
\(877\) −0.289820 + 0.167328i −0.00978654 + 0.00565026i −0.504885 0.863186i \(-0.668465\pi\)
0.495099 + 0.868837i \(0.335132\pi\)
\(878\) −26.6775 + 15.4023i −0.900322 + 0.519801i
\(879\) 3.20789 1.61319i 0.108199 0.0544117i
\(880\) 37.1421 + 41.2355i 1.25206 + 1.39005i
\(881\) 36.2414 1.22100 0.610501 0.792015i \(-0.290968\pi\)
0.610501 + 0.792015i \(0.290968\pi\)
\(882\) 0.555176 4.79397i 0.0186937 0.161421i
\(883\) 42.7261i 1.43785i −0.695089 0.718924i \(-0.744635\pi\)
0.695089 0.718924i \(-0.255365\pi\)
\(884\) 4.11905 7.13441i 0.138539 0.239956i
\(885\) −31.9581 39.8796i −1.07426 1.34054i
\(886\) 17.5605 + 30.4157i 0.589958 + 1.02184i
\(887\) 42.5235 24.5509i 1.42780 0.824340i 0.430852 0.902423i \(-0.358213\pi\)
0.996947 + 0.0780826i \(0.0248798\pi\)
\(888\) 3.33002 + 0.192178i 0.111748 + 0.00644906i
\(889\) 5.00770 8.67360i 0.167953 0.290903i
\(890\) 25.1204 + 8.15713i 0.842039 + 0.273428i
\(891\) 31.6641 33.7051i 1.06079 1.12916i
\(892\) 1.74637i 0.0584727i
\(893\) 26.6786 + 15.4029i 0.892766 + 0.515439i
\(894\) 1.12411 19.4784i 0.0375960 0.651455i
\(895\) 51.5786 10.9731i 1.72408 0.366789i
\(896\) 6.82173 + 11.8156i 0.227898 + 0.394731i
\(897\) −8.81657 + 13.4205i −0.294377 + 0.448096i
\(898\) −47.1148 27.2017i −1.57224 0.907734i
\(899\) 17.8359 0.594860
\(900\) 6.49188 + 5.96650i 0.216396 + 0.198883i
\(901\) −68.4099 −2.27906
\(902\) 7.63228 + 4.40650i 0.254127 + 0.146720i
\(903\) −1.18660 2.35959i −0.0394876 0.0785223i
\(904\) −21.3260 36.9378i −0.709294 1.22853i
\(905\) −30.5458 + 6.49845i −1.01538 + 0.216016i
\(906\) 18.0752 9.08974i 0.600509 0.301986i
\(907\) −9.31713 5.37925i −0.309370 0.178615i 0.337274 0.941406i \(-0.390495\pi\)
−0.646645 + 0.762791i \(0.723828\pi\)
\(908\) 6.21082i 0.206113i
\(909\) −8.96366 + 12.0670i −0.297306 + 0.400238i
\(910\) 9.54592 + 3.09976i 0.316444 + 0.102756i
\(911\) −11.5054 + 19.9280i −0.381191 + 0.660243i −0.991233 0.132127i \(-0.957819\pi\)
0.610041 + 0.792369i \(0.291153\pi\)
\(912\) 18.1668 27.6532i 0.601561 0.915688i
\(913\) 11.1543 6.43996i 0.369155 0.213132i
\(914\) 9.54165 + 16.5266i 0.315610 + 0.546652i
\(915\) 7.39651 18.9783i 0.244521 0.627403i
\(916\) −3.49584 + 6.05497i −0.115506 + 0.200062i
\(917\) 14.6695i 0.484429i
\(918\) −26.9366 + 32.2058i −0.889039 + 1.06295i
\(919\) 15.3731 0.507110 0.253555 0.967321i \(-0.418400\pi\)
0.253555 + 0.967321i \(0.418400\pi\)
\(920\) 11.2959 + 12.5408i 0.372415 + 0.413459i
\(921\) −2.15369 + 37.3187i −0.0709664 + 1.22969i
\(922\) 29.3847 16.9652i 0.967732 0.558720i
\(923\) 2.33884 1.35033i 0.0769837 0.0444466i
\(924\) 4.37241 + 2.87245i 0.143842 + 0.0944968i
\(925\) −1.72538 3.87151i −0.0567301 0.127294i
\(926\) −14.4936 −0.476290
\(927\) −43.9281 + 19.0041i −1.44279 + 0.624176i
\(928\) 22.8135i 0.748889i
\(929\) −13.5022 + 23.3866i −0.442994 + 0.767288i −0.997910 0.0646182i \(-0.979417\pi\)
0.554916 + 0.831906i \(0.312750\pi\)
\(930\) −2.37929 15.5354i −0.0780201 0.509424i
\(931\) 1.97745 + 3.42505i 0.0648084 + 0.112251i
\(932\) −9.66485 + 5.58001i −0.316583 + 0.182779i
\(933\) −6.02774 11.9864i −0.197339 0.392416i
\(934\) −2.22490 + 3.85364i −0.0728010 + 0.126095i
\(935\) 54.8903 + 17.8240i 1.79510 + 0.582908i
\(936\) 7.55029 + 17.4526i 0.246789 + 0.570455i
\(937\) 7.70105i 0.251582i 0.992057 + 0.125791i \(0.0401469\pi\)
−0.992057 + 0.125791i \(0.959853\pi\)
\(938\) 13.2969 + 7.67699i 0.434160 + 0.250663i
\(939\) −2.33754 1.53565i −0.0762828 0.0501140i
\(940\) −2.13044 10.0141i −0.0694873 0.326623i
\(941\) −2.03358 3.52227i −0.0662929 0.114823i 0.830974 0.556311i \(-0.187784\pi\)
−0.897267 + 0.441489i \(0.854450\pi\)
\(942\) 25.8107 + 1.48955i 0.840957 + 0.0485322i
\(943\) 3.06790 + 1.77125i 0.0999045 + 0.0576799i
\(944\) 63.7342 2.07437
\(945\) −10.2686 5.43657i −0.334037 0.176852i
\(946\) 12.6045 0.409809
\(947\) −0.656686 0.379138i −0.0213394 0.0123203i 0.489292 0.872120i \(-0.337255\pi\)
−0.510632 + 0.859800i \(0.670588\pi\)
\(948\) −6.09916 0.351987i −0.198091 0.0114320i
\(949\) 6.73648 + 11.6679i 0.218676 + 0.378757i
\(950\) −31.6376 3.31374i −1.02646 0.107512i
\(951\) −18.5075 12.1585i −0.600148 0.394267i
\(952\) 9.88189 + 5.70531i 0.320274 + 0.184910i
\(953\) 36.3529i 1.17759i −0.808284 0.588793i \(-0.799603\pi\)
0.808284 0.588793i \(-0.200397\pi\)
\(954\) −39.1945 + 52.7642i −1.26897 + 1.70830i
\(955\) −3.69615 + 11.3825i −0.119605 + 0.368331i
\(956\) 5.64249 9.77308i 0.182491 0.316084i
\(957\) 28.2716 + 56.2189i 0.913890 + 1.81730i
\(958\) −10.5179 + 6.07253i −0.339819 + 0.196195i
\(959\) −3.57552 6.19298i −0.115460 0.199982i
\(960\) 17.1117 2.62071i 0.552277 0.0845832i
\(961\) 12.3183 21.3359i 0.397365 0.688256i
\(962\) 3.80497i 0.122677i
\(963\) 5.11553 44.1728i 0.164846 1.42345i
\(964\) 14.7879 0.476285
\(965\) −11.8362 + 10.6612i −0.381019 + 0.343195i
\(966\) 7.73748 + 5.08314i 0.248949 + 0.163547i
\(967\) −9.30540 + 5.37247i −0.299241 + 0.172767i −0.642102 0.766619i \(-0.721937\pi\)
0.342861 + 0.939386i \(0.388604\pi\)
\(968\) 30.3037 17.4959i 0.973998 0.562338i
\(969\) 1.98236 34.3500i 0.0636826 1.10348i
\(970\) −6.19486 6.87760i −0.198905 0.220826i
\(971\) −30.5229 −0.979528 −0.489764 0.871855i \(-0.662917\pi\)
−0.489764 + 0.871855i \(0.662917\pi\)
\(972\) 2.13682 + 8.91051i 0.0685387 + 0.285805i
\(973\) 18.4048i 0.590030i
\(974\) −5.55938 + 9.62914i −0.178134 + 0.308537i
\(975\) 15.2991 18.7036i 0.489964 0.598996i
\(976\) 12.7012 + 21.9991i 0.406555 + 0.704174i
\(977\) 13.6399 7.87497i 0.436378 0.251943i −0.265682 0.964061i \(-0.585597\pi\)
0.702060 + 0.712118i \(0.252264\pi\)
\(978\) 14.7115 22.3936i 0.470422 0.716069i
\(979\) 18.8643 32.6739i 0.602906 1.04426i
\(980\) 0.405946 1.25014i 0.0129675 0.0399342i
\(981\) −15.3373 1.77617i −0.489684 0.0567089i
\(982\) 3.87848i 0.123767i
\(983\) 18.0937 + 10.4464i 0.577099 + 0.333188i 0.759980 0.649947i \(-0.225209\pi\)
−0.182881 + 0.983135i \(0.558542\pi\)
\(984\) 3.74793 1.88477i 0.119480 0.0600844i
\(985\) −6.29122 29.5717i −0.200455 0.942233i
\(986\) −28.5653 49.4766i −0.909706 1.57566i
\(987\) 6.06133 + 12.0531i 0.192934 + 0.383656i
\(988\) 5.61749 + 3.24326i 0.178716 + 0.103182i
\(989\) 5.06656 0.161107
\(990\) 45.1962 32.1246i 1.43643 1.02099i
\(991\) −54.0076 −1.71561 −0.857803 0.513978i \(-0.828171\pi\)
−0.857803 + 0.513978i \(0.828171\pi\)
\(992\) 7.04879 + 4.06962i 0.223799 + 0.129211i
\(993\) 10.6907 16.2733i 0.339260 0.516417i
\(994\) −0.778523 1.34844i −0.0246932 0.0427700i
\(995\) 14.4724 3.07893i 0.458806 0.0976086i
\(996\) −0.147036 + 2.54780i −0.00465900 + 0.0807303i
\(997\) −20.2659 11.7005i −0.641827 0.370559i 0.143491 0.989652i \(-0.454167\pi\)
−0.785318 + 0.619093i \(0.787500\pi\)
\(998\) 50.3908i 1.59509i
\(999\) 0.757986 4.33915i 0.0239816 0.137285i
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.bh.c.169.8 64
3.2 odd 2 945.2.bh.c.694.25 64
5.4 even 2 inner 315.2.bh.c.169.25 yes 64
9.4 even 3 inner 315.2.bh.c.274.25 yes 64
9.5 odd 6 945.2.bh.c.64.8 64
15.14 odd 2 945.2.bh.c.694.8 64
45.4 even 6 inner 315.2.bh.c.274.8 yes 64
45.14 odd 6 945.2.bh.c.64.25 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.bh.c.169.8 64 1.1 even 1 trivial
315.2.bh.c.169.25 yes 64 5.4 even 2 inner
315.2.bh.c.274.8 yes 64 45.4 even 6 inner
315.2.bh.c.274.25 yes 64 9.4 even 3 inner
945.2.bh.c.64.8 64 9.5 odd 6
945.2.bh.c.64.25 64 45.14 odd 6
945.2.bh.c.694.8 64 15.14 odd 2
945.2.bh.c.694.25 64 3.2 odd 2