Properties

Label 930.2.n.e.481.2
Level $930$
Weight $2$
Character 930.481
Analytic conductor $7.426$
Analytic rank $0$
Dimension $12$
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] = [930,2,Mod(481,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.481");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.n (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 16 x^{10} - 6 x^{9} + 161 x^{8} - 180 x^{7} + 1725 x^{6} - 2255 x^{5} + 17635 x^{4} - 18375 x^{3} + 60975 x^{2} + 2000 x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 481.2
Root \(-0.0163000 - 0.0118427i\) of defining polynomial
Character \(\chi\) \(=\) 930.481
Dual form 930.2.n.e.901.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 - 0.587785i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-0.302791 + 0.931895i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(0.809017 - 0.587785i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-0.302791 + 0.931895i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.809017 - 0.587785i) q^{10} +(0.197209 - 0.606947i) q^{11} +(-0.809017 + 0.587785i) q^{12} +(-5.66279 - 4.11426i) q^{13} +(0.302791 + 0.931895i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.21877 - 3.75099i) q^{17} +(0.809017 + 0.587785i) q^{18} +(5.17909 - 3.76283i) q^{19} +(0.309017 - 0.951057i) q^{20} +(0.792717 - 0.575943i) q^{21} +(-0.197209 - 0.606947i) q^{22} +(-0.319091 - 0.982061i) q^{23} +(-0.309017 + 0.951057i) q^{24} +1.00000 q^{25} -6.99959 q^{26} +(0.309017 - 0.951057i) q^{27} +(0.792717 + 0.575943i) q^{28} +(1.97201 - 1.43275i) q^{29} -1.00000 q^{30} +(0.409753 - 5.55267i) q^{31} -1.00000 q^{32} +(-0.516300 + 0.375114i) q^{33} +(-3.19078 - 2.31824i) q^{34} +(-0.302791 + 0.931895i) q^{35} +1.00000 q^{36} +1.93157 q^{37} +(1.97824 - 6.08839i) q^{38} +(2.16299 + 6.65701i) q^{39} +(-0.309017 - 0.951057i) q^{40} +(0.827931 - 0.601527i) q^{41} +(0.302791 - 0.931895i) q^{42} +(-4.17286 + 3.03176i) q^{43} +(-0.516300 - 0.375114i) q^{44} +(0.309017 + 0.951057i) q^{45} +(-0.835391 - 0.606947i) q^{46} +(-5.48188 - 3.98282i) q^{47} +(0.309017 + 0.951057i) q^{48} +(4.88637 + 3.55016i) q^{49} +(0.809017 - 0.587785i) q^{50} +(-1.21877 + 3.75099i) q^{51} +(-5.66279 + 4.11426i) q^{52} +(0.824351 + 2.53709i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(0.197209 - 0.606947i) q^{55} +0.979852 q^{56} -6.40171 q^{57} +(0.753241 - 2.31824i) q^{58} +(-4.13019 - 3.00076i) q^{59} +(-0.809017 + 0.587785i) q^{60} -8.93157 q^{61} +(-2.93228 - 4.73305i) q^{62} -0.979852 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-5.66279 - 4.11426i) q^{65} +(-0.197209 + 0.606947i) q^{66} +8.74062 q^{67} -3.94402 q^{68} +(-0.319091 + 0.982061i) q^{69} +(0.302791 + 0.931895i) q^{70} +(-3.07287 - 9.45733i) q^{71} +(0.809017 - 0.587785i) q^{72} +(-3.76611 + 11.5909i) q^{73} +(1.56267 - 1.13535i) q^{74} +(-0.809017 - 0.587785i) q^{75} +(-1.97824 - 6.08839i) q^{76} +(0.505898 + 0.367556i) q^{77} +(5.66279 + 4.11426i) q^{78} +(0.0759239 + 0.233670i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(0.316241 - 0.973291i) q^{82} +(12.0607 - 8.76258i) q^{83} +(-0.302791 - 0.931895i) q^{84} +(-1.21877 - 3.75099i) q^{85} +(-1.59389 + 4.90550i) q^{86} -2.43754 q^{87} -0.638182 q^{88} +(-4.06590 + 12.5136i) q^{89} +(0.809017 + 0.587785i) q^{90} +(5.54870 - 4.03136i) q^{91} -1.03260 q^{92} +(-3.59527 + 4.25135i) q^{93} -6.77598 q^{94} +(5.17909 - 3.76283i) q^{95} +(0.809017 + 0.587785i) q^{96} +(-3.54708 + 10.9168i) q^{97} +6.03989 q^{98} +0.638182 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} - 3 q^{12} - 5 q^{13} + q^{14} - 3 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{24} + 12 q^{25} + 10 q^{26} - 3 q^{27} + 4 q^{28} + q^{29} - 12 q^{30} - 6 q^{31} - 12 q^{32} - 5 q^{33} + 2 q^{34} - q^{35} + 12 q^{36} - 14 q^{37} - 3 q^{38} + 10 q^{39} + 3 q^{40} + 15 q^{41} + q^{42} + 10 q^{43} - 5 q^{44} - 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 3 q^{50} + 3 q^{51} - 5 q^{52} - 13 q^{53} + 3 q^{54} + 5 q^{55} + 6 q^{56} - 2 q^{57} + 4 q^{58} + 11 q^{59} - 3 q^{60} - 70 q^{61} - 19 q^{62} - 6 q^{63} - 3 q^{64} - 5 q^{65} - 5 q^{66} + 38 q^{67} - 2 q^{68} + q^{70} + 21 q^{71} + 3 q^{72} - 14 q^{73} - 11 q^{74} - 3 q^{75} + 3 q^{76} - 14 q^{77} + 5 q^{78} + 5 q^{79} - 3 q^{80} - 3 q^{81} - 15 q^{82} - q^{84} + 3 q^{85} + 10 q^{86} + 6 q^{87} + 3 q^{89} + 3 q^{90} + 16 q^{91} - 10 q^{92} - 11 q^{93} - 6 q^{94} - 2 q^{95} + 3 q^{96} - 35 q^{97} - 10 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 0.587785i 0.572061 0.415627i
\(3\) −0.809017 0.587785i −0.467086 0.339358i
\(4\) 0.309017 0.951057i 0.154508 0.475528i
\(5\) 1.00000 0.447214
\(6\) −1.00000 −0.408248
\(7\) −0.302791 + 0.931895i −0.114444 + 0.352223i −0.991831 0.127561i \(-0.959285\pi\)
0.877386 + 0.479784i \(0.159285\pi\)
\(8\) −0.309017 0.951057i −0.109254 0.336249i
\(9\) 0.309017 + 0.951057i 0.103006 + 0.317019i
\(10\) 0.809017 0.587785i 0.255834 0.185874i
\(11\) 0.197209 0.606947i 0.0594608 0.183001i −0.916914 0.399084i \(-0.869328\pi\)
0.976375 + 0.216083i \(0.0693281\pi\)
\(12\) −0.809017 + 0.587785i −0.233543 + 0.169679i
\(13\) −5.66279 4.11426i −1.57058 1.14109i −0.926603 0.376041i \(-0.877285\pi\)
−0.643973 0.765049i \(-0.722715\pi\)
\(14\) 0.302791 + 0.931895i 0.0809243 + 0.249059i
\(15\) −0.809017 0.587785i −0.208887 0.151765i
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) −1.21877 3.75099i −0.295595 0.909748i −0.983021 0.183493i \(-0.941259\pi\)
0.687426 0.726255i \(-0.258741\pi\)
\(18\) 0.809017 + 0.587785i 0.190687 + 0.138542i
\(19\) 5.17909 3.76283i 1.18816 0.863252i 0.195096 0.980784i \(-0.437498\pi\)
0.993069 + 0.117532i \(0.0374982\pi\)
\(20\) 0.309017 0.951057i 0.0690983 0.212663i
\(21\) 0.792717 0.575943i 0.172985 0.125681i
\(22\) −0.197209 0.606947i −0.0420451 0.129402i
\(23\) −0.319091 0.982061i −0.0665351 0.204774i 0.912262 0.409608i \(-0.134335\pi\)
−0.978797 + 0.204834i \(0.934335\pi\)
\(24\) −0.309017 + 0.951057i −0.0630778 + 0.194134i
\(25\) 1.00000 0.200000
\(26\) −6.99959 −1.37273
\(27\) 0.309017 0.951057i 0.0594703 0.183031i
\(28\) 0.792717 + 0.575943i 0.149809 + 0.108843i
\(29\) 1.97201 1.43275i 0.366193 0.266055i −0.389437 0.921053i \(-0.627331\pi\)
0.755631 + 0.654998i \(0.227331\pi\)
\(30\) −1.00000 −0.182574
\(31\) 0.409753 5.55267i 0.0735937 0.997288i
\(32\) −1.00000 −0.176777
\(33\) −0.516300 + 0.375114i −0.0898763 + 0.0652990i
\(34\) −3.19078 2.31824i −0.547214 0.397574i
\(35\) −0.302791 + 0.931895i −0.0511810 + 0.157519i
\(36\) 1.00000 0.166667
\(37\) 1.93157 0.317548 0.158774 0.987315i \(-0.449246\pi\)
0.158774 + 0.987315i \(0.449246\pi\)
\(38\) 1.97824 6.08839i 0.320912 0.987667i
\(39\) 2.16299 + 6.65701i 0.346356 + 1.06597i
\(40\) −0.309017 0.951057i −0.0488599 0.150375i
\(41\) 0.827931 0.601527i 0.129301 0.0939427i −0.521255 0.853401i \(-0.674536\pi\)
0.650556 + 0.759458i \(0.274536\pi\)
\(42\) 0.302791 0.931895i 0.0467217 0.143794i
\(43\) −4.17286 + 3.03176i −0.636356 + 0.462340i −0.858596 0.512652i \(-0.828663\pi\)
0.222240 + 0.974992i \(0.428663\pi\)
\(44\) −0.516300 0.375114i −0.0778352 0.0565506i
\(45\) 0.309017 + 0.951057i 0.0460655 + 0.141775i
\(46\) −0.835391 0.606947i −0.123172 0.0894895i
\(47\) −5.48188 3.98282i −0.799615 0.580954i 0.111186 0.993800i \(-0.464535\pi\)
−0.910801 + 0.412846i \(0.864535\pi\)
\(48\) 0.309017 + 0.951057i 0.0446028 + 0.137273i
\(49\) 4.88637 + 3.55016i 0.698053 + 0.507165i
\(50\) 0.809017 0.587785i 0.114412 0.0831254i
\(51\) −1.21877 + 3.75099i −0.170662 + 0.525243i
\(52\) −5.66279 + 4.11426i −0.785288 + 0.570545i
\(53\) 0.824351 + 2.53709i 0.113233 + 0.348496i 0.991574 0.129538i \(-0.0413494\pi\)
−0.878341 + 0.478034i \(0.841349\pi\)
\(54\) −0.309017 0.951057i −0.0420519 0.129422i
\(55\) 0.197209 0.606947i 0.0265917 0.0818407i
\(56\) 0.979852 0.130938
\(57\) −6.40171 −0.847927
\(58\) 0.753241 2.31824i 0.0989054 0.304399i
\(59\) −4.13019 3.00076i −0.537705 0.390666i 0.285527 0.958371i \(-0.407831\pi\)
−0.823232 + 0.567705i \(0.807831\pi\)
\(60\) −0.809017 + 0.587785i −0.104444 + 0.0758827i
\(61\) −8.93157 −1.14357 −0.571785 0.820403i \(-0.693749\pi\)
−0.571785 + 0.820403i \(0.693749\pi\)
\(62\) −2.93228 4.73305i −0.372400 0.601098i
\(63\) −0.979852 −0.123450
\(64\) −0.809017 + 0.587785i −0.101127 + 0.0734732i
\(65\) −5.66279 4.11426i −0.702383 0.510311i
\(66\) −0.197209 + 0.606947i −0.0242748 + 0.0747100i
\(67\) 8.74062 1.06784 0.533918 0.845536i \(-0.320719\pi\)
0.533918 + 0.845536i \(0.320719\pi\)
\(68\) −3.94402 −0.478283
\(69\) −0.319091 + 0.982061i −0.0384140 + 0.118226i
\(70\) 0.302791 + 0.931895i 0.0361904 + 0.111383i
\(71\) −3.07287 9.45733i −0.364683 1.12238i −0.950179 0.311703i \(-0.899100\pi\)
0.585497 0.810675i \(-0.300900\pi\)
\(72\) 0.809017 0.587785i 0.0953436 0.0692712i
\(73\) −3.76611 + 11.5909i −0.440790 + 1.35661i 0.446246 + 0.894910i \(0.352761\pi\)
−0.887036 + 0.461700i \(0.847239\pi\)
\(74\) 1.56267 1.13535i 0.181657 0.131981i
\(75\) −0.809017 0.587785i −0.0934172 0.0678716i
\(76\) −1.97824 6.08839i −0.226919 0.698386i
\(77\) 0.505898 + 0.367556i 0.0576524 + 0.0418869i
\(78\) 5.66279 + 4.11426i 0.641185 + 0.465848i
\(79\) 0.0759239 + 0.233670i 0.00854211 + 0.0262899i 0.955237 0.295843i \(-0.0956004\pi\)
−0.946695 + 0.322132i \(0.895600\pi\)
\(80\) −0.809017 0.587785i −0.0904508 0.0657164i
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 0.316241 0.973291i 0.0349230 0.107482i
\(83\) 12.0607 8.76258i 1.32383 0.961818i 0.323952 0.946073i \(-0.394988\pi\)
0.999876 0.0157442i \(-0.00501175\pi\)
\(84\) −0.302791 0.931895i −0.0330372 0.101678i
\(85\) −1.21877 3.75099i −0.132194 0.406852i
\(86\) −1.59389 + 4.90550i −0.171874 + 0.528973i
\(87\) −2.43754 −0.261332
\(88\) −0.638182 −0.0680304
\(89\) −4.06590 + 12.5136i −0.430985 + 1.32643i 0.466161 + 0.884700i \(0.345637\pi\)
−0.897146 + 0.441735i \(0.854363\pi\)
\(90\) 0.809017 + 0.587785i 0.0852779 + 0.0619580i
\(91\) 5.54870 4.03136i 0.581662 0.422602i
\(92\) −1.03260 −0.107656
\(93\) −3.59527 + 4.25135i −0.372812 + 0.440845i
\(94\) −6.77598 −0.698889
\(95\) 5.17909 3.76283i 0.531363 0.386058i
\(96\) 0.809017 + 0.587785i 0.0825700 + 0.0599906i
\(97\) −3.54708 + 10.9168i −0.360152 + 1.10843i 0.592810 + 0.805342i \(0.298018\pi\)
−0.952962 + 0.303090i \(0.901982\pi\)
\(98\) 6.03989 0.610121
\(99\) 0.638182 0.0641397
\(100\) 0.309017 0.951057i 0.0309017 0.0951057i
\(101\) 2.01817 + 6.21129i 0.200816 + 0.618047i 0.999859 + 0.0167739i \(0.00533954\pi\)
−0.799044 + 0.601273i \(0.794660\pi\)
\(102\) 1.21877 + 3.75099i 0.120676 + 0.371403i
\(103\) 10.8739 7.90035i 1.07144 0.778444i 0.0952669 0.995452i \(-0.469630\pi\)
0.976170 + 0.217007i \(0.0696295\pi\)
\(104\) −2.16299 + 6.65701i −0.212099 + 0.652773i
\(105\) 0.792717 0.575943i 0.0773613 0.0562062i
\(106\) 2.15818 + 1.56801i 0.209621 + 0.152299i
\(107\) 2.99072 + 9.20449i 0.289124 + 0.889832i 0.985132 + 0.171798i \(0.0549577\pi\)
−0.696008 + 0.718034i \(0.745042\pi\)
\(108\) −0.809017 0.587785i −0.0778477 0.0565597i
\(109\) 13.0042 + 9.44807i 1.24557 + 0.904961i 0.997956 0.0638975i \(-0.0203531\pi\)
0.247615 + 0.968858i \(0.420353\pi\)
\(110\) −0.197209 0.606947i −0.0188031 0.0578701i
\(111\) −1.56267 1.13535i −0.148322 0.107762i
\(112\) 0.792717 0.575943i 0.0749047 0.0544215i
\(113\) 1.41598 4.35793i 0.133204 0.409960i −0.862102 0.506734i \(-0.830853\pi\)
0.995306 + 0.0967744i \(0.0308525\pi\)
\(114\) −5.17909 + 3.76283i −0.485066 + 0.352421i
\(115\) −0.319091 0.982061i −0.0297554 0.0915777i
\(116\) −0.753241 2.31824i −0.0699367 0.215243i
\(117\) 2.16299 6.65701i 0.199969 0.615441i
\(118\) −5.10520 −0.469971
\(119\) 3.86456 0.354263
\(120\) −0.309017 + 0.951057i −0.0282093 + 0.0868192i
\(121\) 8.56969 + 6.22625i 0.779063 + 0.566022i
\(122\) −7.22579 + 5.24984i −0.654192 + 0.475299i
\(123\) −1.02338 −0.0922750
\(124\) −5.15428 2.10557i −0.462868 0.189085i
\(125\) 1.00000 0.0894427
\(126\) −0.792717 + 0.575943i −0.0706208 + 0.0513090i
\(127\) −5.14188 3.73579i −0.456268 0.331498i 0.335797 0.941934i \(-0.390994\pi\)
−0.792066 + 0.610436i \(0.790994\pi\)
\(128\) −0.309017 + 0.951057i −0.0273135 + 0.0840623i
\(129\) 5.15794 0.454132
\(130\) −6.99959 −0.613905
\(131\) 5.75020 17.6973i 0.502397 1.54622i −0.302705 0.953084i \(-0.597890\pi\)
0.805102 0.593136i \(-0.202110\pi\)
\(132\) 0.197209 + 0.606947i 0.0171648 + 0.0528280i
\(133\) 1.93838 + 5.96572i 0.168079 + 0.517293i
\(134\) 7.07131 5.13761i 0.610868 0.443822i
\(135\) 0.309017 0.951057i 0.0265959 0.0818539i
\(136\) −3.19078 + 2.31824i −0.273607 + 0.198787i
\(137\) −8.99175 6.53289i −0.768217 0.558143i 0.133202 0.991089i \(-0.457474\pi\)
−0.901420 + 0.432946i \(0.857474\pi\)
\(138\) 0.319091 + 0.982061i 0.0271628 + 0.0835986i
\(139\) 8.97798 + 6.52288i 0.761502 + 0.553264i 0.899371 0.437187i \(-0.144025\pi\)
−0.137868 + 0.990451i \(0.544025\pi\)
\(140\) 0.792717 + 0.575943i 0.0669968 + 0.0486760i
\(141\) 2.09389 + 6.44434i 0.176338 + 0.542711i
\(142\) −8.04488 5.84495i −0.675112 0.490497i
\(143\) −3.61389 + 2.62565i −0.302209 + 0.219567i
\(144\) 0.309017 0.951057i 0.0257514 0.0792547i
\(145\) 1.97201 1.43275i 0.163767 0.118983i
\(146\) 3.76611 + 11.5909i 0.311685 + 0.959269i
\(147\) −1.86643 5.74428i −0.153940 0.473780i
\(148\) 0.596888 1.83703i 0.0490639 0.151003i
\(149\) 13.5520 1.11022 0.555110 0.831777i \(-0.312676\pi\)
0.555110 + 0.831777i \(0.312676\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 1.54597 4.75801i 0.125809 0.387201i −0.868238 0.496147i \(-0.834748\pi\)
0.994048 + 0.108946i \(0.0347476\pi\)
\(152\) −5.17909 3.76283i −0.420080 0.305206i
\(153\) 3.19078 2.31824i 0.257959 0.187418i
\(154\) 0.625324 0.0503900
\(155\) 0.409753 5.55267i 0.0329121 0.446001i
\(156\) 6.99959 0.560416
\(157\) 1.35410 0.983813i 0.108069 0.0785168i −0.532438 0.846469i \(-0.678724\pi\)
0.640507 + 0.767952i \(0.278724\pi\)
\(158\) 0.198771 + 0.144416i 0.0158134 + 0.0114891i
\(159\) 0.824351 2.53709i 0.0653753 0.201205i
\(160\) −1.00000 −0.0790569
\(161\) 1.01180 0.0797406
\(162\) −0.309017 + 0.951057i −0.0242787 + 0.0747221i
\(163\) 2.70006 + 8.30993i 0.211485 + 0.650884i 0.999385 + 0.0350799i \(0.0111686\pi\)
−0.787900 + 0.615804i \(0.788831\pi\)
\(164\) −0.316241 0.973291i −0.0246943 0.0760013i
\(165\) −0.516300 + 0.375114i −0.0401939 + 0.0292026i
\(166\) 4.60676 14.1781i 0.357554 1.10044i
\(167\) −1.52103 + 1.10509i −0.117701 + 0.0855146i −0.645078 0.764116i \(-0.723175\pi\)
0.527378 + 0.849631i \(0.323175\pi\)
\(168\) −0.792717 0.575943i −0.0611594 0.0444349i
\(169\) 11.1229 + 34.2326i 0.855604 + 2.63328i
\(170\) −3.19078 2.31824i −0.244722 0.177801i
\(171\) 5.17909 + 3.76283i 0.396055 + 0.287751i
\(172\) 1.59389 + 4.90550i 0.121533 + 0.374041i
\(173\) −11.1506 8.10136i −0.847762 0.615935i 0.0767660 0.997049i \(-0.475541\pi\)
−0.924528 + 0.381114i \(0.875541\pi\)
\(174\) −1.97201 + 1.43275i −0.149498 + 0.108616i
\(175\) −0.302791 + 0.931895i −0.0228888 + 0.0704446i
\(176\) −0.516300 + 0.375114i −0.0389176 + 0.0282753i
\(177\) 1.57759 + 4.85533i 0.118579 + 0.364949i
\(178\) 4.06590 + 12.5136i 0.304752 + 0.937931i
\(179\) −2.48546 + 7.64946i −0.185772 + 0.571748i −0.999961 0.00885262i \(-0.997182\pi\)
0.814189 + 0.580600i \(0.197182\pi\)
\(180\) 1.00000 0.0745356
\(181\) 2.35377 0.174954 0.0874770 0.996167i \(-0.472120\pi\)
0.0874770 + 0.996167i \(0.472120\pi\)
\(182\) 2.11941 6.52288i 0.157101 0.483508i
\(183\) 7.22579 + 5.24984i 0.534146 + 0.388080i
\(184\) −0.835391 + 0.606947i −0.0615858 + 0.0447447i
\(185\) 1.93157 0.142012
\(186\) −0.409753 + 5.55267i −0.0300445 + 0.407141i
\(187\) −2.51700 −0.184061
\(188\) −5.48188 + 3.98282i −0.399807 + 0.290477i
\(189\) 0.792717 + 0.575943i 0.0576617 + 0.0418937i
\(190\) 1.97824 6.08839i 0.143516 0.441698i
\(191\) −9.44364 −0.683317 −0.341659 0.939824i \(-0.610989\pi\)
−0.341659 + 0.939824i \(0.610989\pi\)
\(192\) 1.00000 0.0721688
\(193\) −5.46861 + 16.8307i −0.393639 + 1.21150i 0.536377 + 0.843979i \(0.319793\pi\)
−0.930016 + 0.367519i \(0.880207\pi\)
\(194\) 3.54708 + 10.9168i 0.254666 + 0.783780i
\(195\) 2.16299 + 6.65701i 0.154895 + 0.476718i
\(196\) 4.88637 3.55016i 0.349027 0.253583i
\(197\) 4.72540 14.5433i 0.336671 1.03617i −0.629223 0.777225i \(-0.716627\pi\)
0.965893 0.258941i \(-0.0833734\pi\)
\(198\) 0.516300 0.375114i 0.0366918 0.0266582i
\(199\) 21.6590 + 15.7361i 1.53536 + 1.11551i 0.953162 + 0.302461i \(0.0978081\pi\)
0.582200 + 0.813045i \(0.302192\pi\)
\(200\) −0.309017 0.951057i −0.0218508 0.0672499i
\(201\) −7.07131 5.13761i −0.498772 0.362379i
\(202\) 5.28364 + 3.83879i 0.371756 + 0.270096i
\(203\) 0.738065 + 2.27153i 0.0518020 + 0.159430i
\(204\) 3.19078 + 2.31824i 0.223399 + 0.162309i
\(205\) 0.827931 0.601527i 0.0578252 0.0420125i
\(206\) 4.15346 12.7830i 0.289385 0.890636i
\(207\) 0.835391 0.606947i 0.0580637 0.0421857i
\(208\) 2.16299 + 6.65701i 0.149977 + 0.461581i
\(209\) −1.26247 3.88550i −0.0873272 0.268766i
\(210\) 0.302791 0.931895i 0.0208946 0.0643068i
\(211\) −3.59124 −0.247231 −0.123616 0.992330i \(-0.539449\pi\)
−0.123616 + 0.992330i \(0.539449\pi\)
\(212\) 2.66766 0.183215
\(213\) −3.07287 + 9.45733i −0.210550 + 0.648005i
\(214\) 7.82981 + 5.68869i 0.535235 + 0.388871i
\(215\) −4.17286 + 3.03176i −0.284587 + 0.206765i
\(216\) −1.00000 −0.0680414
\(217\) 5.05043 + 2.06314i 0.342846 + 0.140055i
\(218\) 16.0740 1.08867
\(219\) 9.85980 7.16356i 0.666263 0.484069i
\(220\) −0.516300 0.375114i −0.0348089 0.0252902i
\(221\) −8.53089 + 26.2554i −0.573850 + 1.76613i
\(222\) −1.93157 −0.129638
\(223\) 0.357890 0.0239661 0.0119830 0.999928i \(-0.496186\pi\)
0.0119830 + 0.999928i \(0.496186\pi\)
\(224\) 0.302791 0.931895i 0.0202311 0.0622648i
\(225\) 0.309017 + 0.951057i 0.0206011 + 0.0634038i
\(226\) −1.41598 4.35793i −0.0941895 0.289885i
\(227\) 11.8878 8.63701i 0.789023 0.573259i −0.118651 0.992936i \(-0.537857\pi\)
0.907673 + 0.419678i \(0.137857\pi\)
\(228\) −1.97824 + 6.08839i −0.131012 + 0.403213i
\(229\) 3.83947 2.78954i 0.253719 0.184338i −0.453654 0.891178i \(-0.649880\pi\)
0.707374 + 0.706840i \(0.249880\pi\)
\(230\) −0.835391 0.606947i −0.0550840 0.0400209i
\(231\) −0.193236 0.594718i −0.0127140 0.0391296i
\(232\) −1.97201 1.43275i −0.129469 0.0940646i
\(233\) −6.78059 4.92639i −0.444211 0.322738i 0.343095 0.939301i \(-0.388525\pi\)
−0.787306 + 0.616562i \(0.788525\pi\)
\(234\) −2.16299 6.65701i −0.141399 0.435182i
\(235\) −5.48188 3.98282i −0.357599 0.259811i
\(236\) −4.13019 + 3.00076i −0.268853 + 0.195333i
\(237\) 0.0759239 0.233670i 0.00493179 0.0151785i
\(238\) 3.12649 2.27153i 0.202660 0.147241i
\(239\) −6.93759 21.3517i −0.448756 1.38113i −0.878312 0.478088i \(-0.841330\pi\)
0.429557 0.903040i \(-0.358670\pi\)
\(240\) 0.309017 + 0.951057i 0.0199470 + 0.0613904i
\(241\) 6.37005 19.6050i 0.410331 1.26287i −0.506030 0.862516i \(-0.668887\pi\)
0.916361 0.400353i \(-0.131113\pi\)
\(242\) 10.5927 0.680926
\(243\) 1.00000 0.0641500
\(244\) −2.76001 + 8.49443i −0.176691 + 0.543800i
\(245\) 4.88637 + 3.55016i 0.312179 + 0.226811i
\(246\) −0.827931 + 0.601527i −0.0527869 + 0.0383520i
\(247\) −44.8094 −2.85115
\(248\) −5.40752 + 1.32617i −0.343378 + 0.0842119i
\(249\) −14.9078 −0.944742
\(250\) 0.809017 0.587785i 0.0511667 0.0371748i
\(251\) 13.3163 + 9.67486i 0.840518 + 0.610672i 0.922515 0.385961i \(-0.126130\pi\)
−0.0819976 + 0.996633i \(0.526130\pi\)
\(252\) −0.302791 + 0.931895i −0.0190740 + 0.0587038i
\(253\) −0.658987 −0.0414301
\(254\) −6.35571 −0.398793
\(255\) −1.21877 + 3.75099i −0.0763223 + 0.234896i
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) −6.66380 20.5091i −0.415677 1.27932i −0.911644 0.410980i \(-0.865187\pi\)
0.495968 0.868341i \(-0.334813\pi\)
\(258\) 4.17286 3.03176i 0.259791 0.188749i
\(259\) −0.584862 + 1.80002i −0.0363415 + 0.111848i
\(260\) −5.66279 + 4.11426i −0.351191 + 0.255155i
\(261\) 1.97201 + 1.43275i 0.122064 + 0.0886850i
\(262\) −5.75020 17.6973i −0.355249 1.09334i
\(263\) 8.84843 + 6.42876i 0.545617 + 0.396414i 0.826167 0.563425i \(-0.190517\pi\)
−0.280550 + 0.959840i \(0.590517\pi\)
\(264\) 0.516300 + 0.375114i 0.0317761 + 0.0230867i
\(265\) 0.824351 + 2.53709i 0.0506395 + 0.155852i
\(266\) 5.07474 + 3.68702i 0.311152 + 0.226065i
\(267\) 10.6447 7.73381i 0.651443 0.473301i
\(268\) 2.70100 8.31282i 0.164990 0.507786i
\(269\) 14.6594 10.6507i 0.893800 0.649384i −0.0430660 0.999072i \(-0.513713\pi\)
0.936866 + 0.349689i \(0.113713\pi\)
\(270\) −0.309017 0.951057i −0.0188062 0.0578795i
\(271\) −1.11363 3.42739i −0.0676480 0.208199i 0.911518 0.411260i \(-0.134911\pi\)
−0.979166 + 0.203061i \(0.934911\pi\)
\(272\) −1.21877 + 3.75099i −0.0738988 + 0.227437i
\(273\) −6.85857 −0.415099
\(274\) −11.1144 −0.671447
\(275\) 0.197209 0.606947i 0.0118922 0.0366003i
\(276\) 0.835391 + 0.606947i 0.0502846 + 0.0365339i
\(277\) 2.62840 1.90964i 0.157925 0.114739i −0.506016 0.862524i \(-0.668882\pi\)
0.663941 + 0.747785i \(0.268882\pi\)
\(278\) 11.0974 0.665577
\(279\) 5.40752 1.32617i 0.323740 0.0793957i
\(280\) 0.979852 0.0585574
\(281\) −20.0327 + 14.5546i −1.19505 + 0.868253i −0.993789 0.111284i \(-0.964504\pi\)
−0.201260 + 0.979538i \(0.564504\pi\)
\(282\) 5.48188 + 3.98282i 0.326441 + 0.237173i
\(283\) −8.47201 + 26.0742i −0.503609 + 1.54995i 0.299488 + 0.954100i \(0.403184\pi\)
−0.803097 + 0.595848i \(0.796816\pi\)
\(284\) −9.94402 −0.590069
\(285\) −6.40171 −0.379204
\(286\) −1.38038 + 4.24838i −0.0816238 + 0.251212i
\(287\) 0.309870 + 0.953681i 0.0182910 + 0.0562940i
\(288\) −0.309017 0.951057i −0.0182090 0.0560415i
\(289\) 1.16879 0.849172i 0.0687521 0.0499513i
\(290\) 0.753241 2.31824i 0.0442318 0.136132i
\(291\) 9.28638 6.74695i 0.544377 0.395513i
\(292\) 9.85980 + 7.16356i 0.577001 + 0.419216i
\(293\) −2.16525 6.66394i −0.126495 0.389312i 0.867675 0.497131i \(-0.165613\pi\)
−0.994171 + 0.107819i \(0.965613\pi\)
\(294\) −4.88637 3.55016i −0.284979 0.207049i
\(295\) −4.13019 3.00076i −0.240469 0.174711i
\(296\) −0.596888 1.83703i −0.0346934 0.106775i
\(297\) −0.516300 0.375114i −0.0299588 0.0217663i
\(298\) 10.9638 7.96564i 0.635114 0.461437i
\(299\) −2.23351 + 6.87403i −0.129167 + 0.397535i
\(300\) −0.809017 + 0.587785i −0.0467086 + 0.0339358i
\(301\) −1.56178 4.80666i −0.0900194 0.277051i
\(302\) −1.54597 4.75801i −0.0889606 0.273793i
\(303\) 2.01817 6.21129i 0.115941 0.356829i
\(304\) −6.40171 −0.367163
\(305\) −8.93157 −0.511420
\(306\) 1.21877 3.75099i 0.0696724 0.214430i
\(307\) −2.35759 1.71289i −0.134555 0.0977597i 0.518472 0.855095i \(-0.326501\pi\)
−0.653027 + 0.757335i \(0.726501\pi\)
\(308\) 0.505898 0.367556i 0.0288262 0.0209435i
\(309\) −13.4409 −0.764625
\(310\) −2.93228 4.73305i −0.166542 0.268819i
\(311\) 24.8497 1.40910 0.704550 0.709655i \(-0.251149\pi\)
0.704550 + 0.709655i \(0.251149\pi\)
\(312\) 5.66279 4.11426i 0.320592 0.232924i
\(313\) −8.91612 6.47794i −0.503969 0.366155i 0.306562 0.951851i \(-0.400821\pi\)
−0.810531 + 0.585696i \(0.800821\pi\)
\(314\) 0.517221 1.59184i 0.0291885 0.0898329i
\(315\) −0.979852 −0.0552084
\(316\) 0.245695 0.0138214
\(317\) −7.36015 + 22.6522i −0.413387 + 1.27227i 0.500299 + 0.865853i \(0.333223\pi\)
−0.913686 + 0.406421i \(0.866777\pi\)
\(318\) −0.824351 2.53709i −0.0462273 0.142273i
\(319\) −0.480705 1.47946i −0.0269143 0.0828337i
\(320\) −0.809017 + 0.587785i −0.0452254 + 0.0328582i
\(321\) 2.99072 9.20449i 0.166926 0.513745i
\(322\) 0.818560 0.594718i 0.0456165 0.0331424i
\(323\) −20.4264 14.8407i −1.13656 0.825757i
\(324\) 0.309017 + 0.951057i 0.0171676 + 0.0528365i
\(325\) −5.66279 4.11426i −0.314115 0.228218i
\(326\) 7.06884 + 5.13582i 0.391507 + 0.284447i
\(327\) −4.96714 15.2873i −0.274684 0.845389i
\(328\) −0.827931 0.601527i −0.0457148 0.0332138i
\(329\) 5.37143 3.90257i 0.296137 0.215156i
\(330\) −0.197209 + 0.606947i −0.0108560 + 0.0334113i
\(331\) −11.8804 + 8.63159i −0.653004 + 0.474435i −0.864293 0.502989i \(-0.832234\pi\)
0.211289 + 0.977424i \(0.432234\pi\)
\(332\) −4.60676 14.1781i −0.252829 0.778127i
\(333\) 0.596888 + 1.83703i 0.0327092 + 0.100669i
\(334\) −0.580981 + 1.78808i −0.0317899 + 0.0978392i
\(335\) 8.74062 0.477551
\(336\) −0.979852 −0.0534553
\(337\) 0.212982 0.655491i 0.0116019 0.0357069i −0.945088 0.326816i \(-0.894024\pi\)
0.956690 + 0.291109i \(0.0940243\pi\)
\(338\) 29.1200 + 21.1569i 1.58392 + 1.15079i
\(339\) −3.70708 + 2.69335i −0.201341 + 0.146283i
\(340\) −3.94402 −0.213895
\(341\) −3.28937 1.34373i −0.178129 0.0727673i
\(342\) 6.40171 0.346165
\(343\) −10.3369 + 7.51023i −0.558142 + 0.405514i
\(344\) 4.17286 + 3.03176i 0.224986 + 0.163462i
\(345\) −0.319091 + 0.982061i −0.0171793 + 0.0528724i
\(346\) −13.7829 −0.740971
\(347\) −5.75848 −0.309132 −0.154566 0.987982i \(-0.549398\pi\)
−0.154566 + 0.987982i \(0.549398\pi\)
\(348\) −0.753241 + 2.31824i −0.0403780 + 0.124271i
\(349\) −3.85018 11.8496i −0.206095 0.634297i −0.999667 0.0258192i \(-0.991781\pi\)
0.793571 0.608477i \(-0.208219\pi\)
\(350\) 0.302791 + 0.931895i 0.0161849 + 0.0498119i
\(351\) −5.66279 + 4.11426i −0.302257 + 0.219603i
\(352\) −0.197209 + 0.606947i −0.0105113 + 0.0323504i
\(353\) 20.1464 14.6372i 1.07229 0.779062i 0.0959652 0.995385i \(-0.469406\pi\)
0.976322 + 0.216323i \(0.0694063\pi\)
\(354\) 4.13019 + 3.00076i 0.219517 + 0.159489i
\(355\) −3.07287 9.45733i −0.163091 0.501943i
\(356\) 10.6447 + 7.73381i 0.564166 + 0.409891i
\(357\) −3.12649 2.27153i −0.165472 0.120222i
\(358\) 2.48546 + 7.64946i 0.131361 + 0.404287i
\(359\) −0.737163 0.535580i −0.0389060 0.0282669i 0.568162 0.822917i \(-0.307655\pi\)
−0.607068 + 0.794650i \(0.707655\pi\)
\(360\) 0.809017 0.587785i 0.0426389 0.0309790i
\(361\) 6.79277 20.9060i 0.357514 1.10032i
\(362\) 1.90424 1.38351i 0.100084 0.0727156i
\(363\) −3.27333 10.0743i −0.171805 0.528763i
\(364\) −2.11941 6.52288i −0.111087 0.341892i
\(365\) −3.76611 + 11.5909i −0.197127 + 0.606695i
\(366\) 8.93157 0.466861
\(367\) 20.6237 1.07655 0.538274 0.842770i \(-0.319077\pi\)
0.538274 + 0.842770i \(0.319077\pi\)
\(368\) −0.319091 + 0.982061i −0.0166338 + 0.0511935i
\(369\) 0.827931 + 0.601527i 0.0431004 + 0.0313142i
\(370\) 1.56267 1.13535i 0.0812395 0.0590239i
\(371\) −2.61391 −0.135707
\(372\) 2.93228 + 4.73305i 0.152032 + 0.245397i
\(373\) 18.2982 0.947443 0.473722 0.880675i \(-0.342910\pi\)
0.473722 + 0.880675i \(0.342910\pi\)
\(374\) −2.03630 + 1.47946i −0.105294 + 0.0765009i
\(375\) −0.809017 0.587785i −0.0417775 0.0303531i
\(376\) −2.09389 + 6.44434i −0.107984 + 0.332341i
\(377\) −17.0618 −0.878727
\(378\) 0.979852 0.0503982
\(379\) −0.279156 + 0.859154i −0.0143393 + 0.0441318i −0.957970 0.286868i \(-0.907386\pi\)
0.943631 + 0.331000i \(0.107386\pi\)
\(380\) −1.97824 6.08839i −0.101481 0.312328i
\(381\) 1.96402 + 6.04464i 0.100620 + 0.309676i
\(382\) −7.64006 + 5.55083i −0.390900 + 0.284005i
\(383\) 2.03137 6.25190i 0.103798 0.319457i −0.885648 0.464356i \(-0.846286\pi\)
0.989446 + 0.144899i \(0.0462857\pi\)
\(384\) 0.809017 0.587785i 0.0412850 0.0299953i
\(385\) 0.505898 + 0.367556i 0.0257829 + 0.0187324i
\(386\) 5.46861 + 16.8307i 0.278345 + 0.856658i
\(387\) −4.17286 3.03176i −0.212119 0.154113i
\(388\) 9.28638 + 6.74695i 0.471445 + 0.342525i
\(389\) 4.23173 + 13.0239i 0.214557 + 0.660340i 0.999185 + 0.0403721i \(0.0128543\pi\)
−0.784627 + 0.619968i \(0.787146\pi\)
\(390\) 5.66279 + 4.11426i 0.286747 + 0.208334i
\(391\) −3.29480 + 2.39381i −0.166625 + 0.121060i
\(392\) 1.86643 5.74428i 0.0942689 0.290130i
\(393\) −15.0542 + 10.9375i −0.759385 + 0.551726i
\(394\) −4.72540 14.5433i −0.238062 0.732680i
\(395\) 0.0759239 + 0.233670i 0.00382015 + 0.0117572i
\(396\) 0.197209 0.606947i 0.00991013 0.0305002i
\(397\) −3.69480 −0.185437 −0.0927184 0.995692i \(-0.529556\pi\)
−0.0927184 + 0.995692i \(0.529556\pi\)
\(398\) 26.7719 1.34196
\(399\) 1.93838 5.96572i 0.0970403 0.298659i
\(400\) −0.809017 0.587785i −0.0404508 0.0293893i
\(401\) −14.4921 + 10.5292i −0.723703 + 0.525801i −0.887565 0.460682i \(-0.847605\pi\)
0.163862 + 0.986483i \(0.447605\pi\)
\(402\) −8.74062 −0.435942
\(403\) −25.1654 + 29.7578i −1.25358 + 1.48234i
\(404\) 6.53094 0.324926
\(405\) −0.809017 + 0.587785i −0.0402004 + 0.0292073i
\(406\) 1.93228 + 1.40388i 0.0958974 + 0.0696735i
\(407\) 0.380923 1.17236i 0.0188816 0.0581117i
\(408\) 3.94402 0.195258
\(409\) −20.2226 −0.999946 −0.499973 0.866041i \(-0.666657\pi\)
−0.499973 + 0.866041i \(0.666657\pi\)
\(410\) 0.316241 0.973291i 0.0156181 0.0480674i
\(411\) 3.43454 + 10.5704i 0.169414 + 0.521401i
\(412\) −4.15346 12.7830i −0.204626 0.629775i
\(413\) 4.04698 2.94030i 0.199139 0.144683i
\(414\) 0.319091 0.982061i 0.0156825 0.0482657i
\(415\) 12.0607 8.76258i 0.592034 0.430138i
\(416\) 5.66279 + 4.11426i 0.277641 + 0.201718i
\(417\) −3.42928 10.5542i −0.167933 0.516844i
\(418\) −3.30520 2.40137i −0.161663 0.117455i
\(419\) 2.30793 + 1.67681i 0.112750 + 0.0819176i 0.642731 0.766092i \(-0.277801\pi\)
−0.529981 + 0.848009i \(0.677801\pi\)
\(420\) −0.302791 0.931895i −0.0147747 0.0454718i
\(421\) 19.1149 + 13.8878i 0.931601 + 0.676848i 0.946384 0.323043i \(-0.104706\pi\)
−0.0147829 + 0.999891i \(0.504706\pi\)
\(422\) −2.90537 + 2.11088i −0.141431 + 0.102756i
\(423\) 2.09389 6.44434i 0.101809 0.313334i
\(424\) 2.15818 1.56801i 0.104810 0.0761493i
\(425\) −1.21877 3.75099i −0.0591190 0.181950i
\(426\) 3.07287 + 9.45733i 0.148881 + 0.458209i
\(427\) 2.70440 8.32328i 0.130875 0.402792i
\(428\) 9.67818 0.467812
\(429\) 4.46701 0.215669
\(430\) −1.59389 + 4.90550i −0.0768643 + 0.236564i
\(431\) −27.0843 19.6779i −1.30460 0.947851i −0.304616 0.952475i \(-0.598528\pi\)
−0.999989 + 0.00462440i \(0.998528\pi\)
\(432\) −0.809017 + 0.587785i −0.0389238 + 0.0282798i
\(433\) −0.904025 −0.0434447 −0.0217223 0.999764i \(-0.506915\pi\)
−0.0217223 + 0.999764i \(0.506915\pi\)
\(434\) 5.29857 1.29945i 0.254339 0.0623756i
\(435\) −2.43754 −0.116871
\(436\) 13.0042 9.44807i 0.622786 0.452480i
\(437\) −5.34793 3.88550i −0.255826 0.185869i
\(438\) 3.76611 11.5909i 0.179952 0.553834i
\(439\) −28.6944 −1.36951 −0.684755 0.728773i \(-0.740091\pi\)
−0.684755 + 0.728773i \(0.740091\pi\)
\(440\) −0.638182 −0.0304241
\(441\) −1.86643 + 5.74428i −0.0888776 + 0.273537i
\(442\) 8.53089 + 26.2554i 0.405773 + 1.24884i
\(443\) −10.1569 31.2598i −0.482571 1.48520i −0.835469 0.549538i \(-0.814804\pi\)
0.352898 0.935662i \(-0.385196\pi\)
\(444\) −1.56267 + 1.13535i −0.0741611 + 0.0538812i
\(445\) −4.06590 + 12.5136i −0.192742 + 0.593200i
\(446\) 0.289539 0.210362i 0.0137101 0.00996095i
\(447\) −10.9638 7.96564i −0.518568 0.376762i
\(448\) −0.302791 0.931895i −0.0143055 0.0440279i
\(449\) −22.9007 16.6383i −1.08075 0.785212i −0.102938 0.994688i \(-0.532824\pi\)
−0.977814 + 0.209476i \(0.932824\pi\)
\(450\) 0.809017 + 0.587785i 0.0381374 + 0.0277085i
\(451\) −0.201820 0.621137i −0.00950331 0.0292482i
\(452\) −3.70708 2.69335i −0.174366 0.126685i
\(453\) −4.04740 + 2.94061i −0.190164 + 0.138162i
\(454\) 4.54075 13.9750i 0.213108 0.655878i
\(455\) 5.54870 4.03136i 0.260127 0.188993i
\(456\) 1.97824 + 6.08839i 0.0926394 + 0.285115i
\(457\) 9.07320 + 27.9245i 0.424427 + 1.30625i 0.903542 + 0.428499i \(0.140957\pi\)
−0.479116 + 0.877752i \(0.659043\pi\)
\(458\) 1.46655 4.51357i 0.0685272 0.210905i
\(459\) −3.94402 −0.184091
\(460\) −1.03260 −0.0481452
\(461\) −10.8555 + 33.4099i −0.505592 + 1.55605i 0.294180 + 0.955750i \(0.404953\pi\)
−0.799773 + 0.600303i \(0.795047\pi\)
\(462\) −0.505898 0.367556i −0.0235365 0.0171003i
\(463\) 14.6761 10.6628i 0.682056 0.495543i −0.191983 0.981398i \(-0.561492\pi\)
0.874039 + 0.485855i \(0.161492\pi\)
\(464\) −2.43754 −0.113160
\(465\) −3.59527 + 4.25135i −0.166727 + 0.197152i
\(466\) −8.38127 −0.388255
\(467\) 12.4867 9.07212i 0.577816 0.419808i −0.260120 0.965576i \(-0.583762\pi\)
0.837936 + 0.545769i \(0.183762\pi\)
\(468\) −5.66279 4.11426i −0.261763 0.190182i
\(469\) −2.64658 + 8.14534i −0.122208 + 0.376117i
\(470\) −6.77598 −0.312553
\(471\) −1.67376 −0.0771229
\(472\) −1.57759 + 4.85533i −0.0726146 + 0.223485i
\(473\) 1.01719 + 3.13060i 0.0467706 + 0.143945i
\(474\) −0.0759239 0.233670i −0.00348730 0.0107328i
\(475\) 5.17909 3.76283i 0.237633 0.172650i
\(476\) 1.19421 3.67541i 0.0547367 0.168462i
\(477\) −2.15818 + 1.56801i −0.0988163 + 0.0717942i
\(478\) −18.1629 13.1961i −0.830749 0.603575i
\(479\) 7.62482 + 23.4668i 0.348387 + 1.07222i 0.959746 + 0.280871i \(0.0906233\pi\)
−0.611359 + 0.791354i \(0.709377\pi\)
\(480\) 0.809017 + 0.587785i 0.0369264 + 0.0268286i
\(481\) −10.9381 7.94697i −0.498733 0.362351i
\(482\) −6.37005 19.6050i −0.290148 0.892984i
\(483\) −0.818560 0.594718i −0.0372458 0.0270606i
\(484\) 8.56969 6.22625i 0.389532 0.283011i
\(485\) −3.54708 + 10.9168i −0.161065 + 0.495706i
\(486\) 0.809017 0.587785i 0.0366978 0.0266625i
\(487\) −0.368282 1.13346i −0.0166885 0.0513618i 0.942365 0.334585i \(-0.108596\pi\)
−0.959054 + 0.283223i \(0.908596\pi\)
\(488\) 2.76001 + 8.49443i 0.124940 + 0.384525i
\(489\) 2.70006 8.30993i 0.122101 0.375788i
\(490\) 6.03989 0.272854
\(491\) 20.3648 0.919049 0.459525 0.888165i \(-0.348020\pi\)
0.459525 + 0.888165i \(0.348020\pi\)
\(492\) −0.316241 + 0.973291i −0.0142573 + 0.0438794i
\(493\) −7.77765 5.65079i −0.350288 0.254499i
\(494\) −36.2515 + 26.3383i −1.63103 + 1.18502i
\(495\) 0.638182 0.0286841
\(496\) −3.59527 + 4.25135i −0.161432 + 0.190891i
\(497\) 9.74367 0.437063
\(498\) −12.0607 + 8.76258i −0.540451 + 0.392660i
\(499\) 22.8881 + 16.6292i 1.02461 + 0.744425i 0.967223 0.253927i \(-0.0817224\pi\)
0.0573893 + 0.998352i \(0.481722\pi\)
\(500\) 0.309017 0.951057i 0.0138197 0.0425325i
\(501\) 1.88010 0.0839965
\(502\) 16.4599 0.734639
\(503\) −7.07307 + 21.7687i −0.315373 + 0.970617i 0.660228 + 0.751065i \(0.270460\pi\)
−0.975601 + 0.219552i \(0.929540\pi\)
\(504\) 0.302791 + 0.931895i 0.0134874 + 0.0415099i
\(505\) 2.01817 + 6.21129i 0.0898075 + 0.276399i
\(506\) −0.533131 + 0.387343i −0.0237006 + 0.0172195i
\(507\) 11.1229 34.2326i 0.493983 1.52032i
\(508\) −5.14188 + 3.73579i −0.228134 + 0.165749i
\(509\) 12.1129 + 8.80051i 0.536893 + 0.390076i 0.822930 0.568143i \(-0.192338\pi\)
−0.286037 + 0.958219i \(0.592338\pi\)
\(510\) 1.21877 + 3.75099i 0.0539680 + 0.166096i
\(511\) −9.66114 7.01923i −0.427384 0.310512i
\(512\) 0.809017 + 0.587785i 0.0357538 + 0.0259767i
\(513\) −1.97824 6.08839i −0.0873413 0.268809i
\(514\) −17.4461 12.6753i −0.769513 0.559084i
\(515\) 10.8739 7.90035i 0.479161 0.348131i
\(516\) 1.59389 4.90550i 0.0701672 0.215952i
\(517\) −3.49844 + 2.54176i −0.153861 + 0.111787i
\(518\) 0.584862 + 1.80002i 0.0256973 + 0.0790883i
\(519\) 4.25914 + 13.1083i 0.186955 + 0.575390i
\(520\) −2.16299 + 6.65701i −0.0948535 + 0.291929i
\(521\) −33.5284 −1.46890 −0.734452 0.678661i \(-0.762561\pi\)
−0.734452 + 0.678661i \(0.762561\pi\)
\(522\) 2.43754 0.106688
\(523\) 12.0001 36.9325i 0.524728 1.61495i −0.240125 0.970742i \(-0.577188\pi\)
0.764853 0.644205i \(-0.222812\pi\)
\(524\) −15.0542 10.9375i −0.657647 0.477808i
\(525\) 0.792717 0.575943i 0.0345970 0.0251362i
\(526\) 10.9373 0.476887
\(527\) −21.3274 + 5.23044i −0.929035 + 0.227842i
\(528\) 0.638182 0.0277733
\(529\) 17.7448 12.8923i 0.771512 0.560536i
\(530\) 2.15818 + 1.56801i 0.0937453 + 0.0681100i
\(531\) 1.57759 4.85533i 0.0684617 0.210703i
\(532\) 6.27273 0.271957
\(533\) −7.16324 −0.310274
\(534\) 4.06590 12.5136i 0.175949 0.541515i
\(535\) 2.99072 + 9.20449i 0.129300 + 0.397945i
\(536\) −2.70100 8.31282i −0.116665 0.359059i
\(537\) 6.50702 4.72763i 0.280799 0.204012i
\(538\) 5.59940 17.2332i 0.241407 0.742975i
\(539\) 3.11840 2.26565i 0.134319 0.0975883i
\(540\) −0.809017 0.587785i −0.0348145 0.0252942i
\(541\) −10.6491 32.7747i −0.457842 1.40909i −0.867766 0.496973i \(-0.834445\pi\)
0.409924 0.912120i \(-0.365555\pi\)
\(542\) −2.91551 2.11824i −0.125232 0.0909863i
\(543\) −1.90424 1.38351i −0.0817186 0.0593720i
\(544\) 1.21877 + 3.75099i 0.0522543 + 0.160822i
\(545\) 13.0042 + 9.44807i 0.557037 + 0.404711i
\(546\) −5.54870 + 4.03136i −0.237462 + 0.172526i
\(547\) −8.29020 + 25.5146i −0.354464 + 1.09093i 0.601856 + 0.798604i \(0.294428\pi\)
−0.956320 + 0.292322i \(0.905572\pi\)
\(548\) −8.99175 + 6.53289i −0.384109 + 0.279071i
\(549\) −2.76001 8.49443i −0.117794 0.362533i
\(550\) −0.197209 0.606947i −0.00840902 0.0258803i
\(551\) 4.82203 14.8407i 0.205425 0.632234i
\(552\) 1.03260 0.0439504
\(553\) −0.240745 −0.0102375
\(554\) 1.00396 3.08987i 0.0426541 0.131276i
\(555\) −1.56267 1.13535i −0.0663317 0.0481928i
\(556\) 8.97798 6.52288i 0.380751 0.276632i
\(557\) −3.99121 −0.169113 −0.0845566 0.996419i \(-0.526947\pi\)
−0.0845566 + 0.996419i \(0.526947\pi\)
\(558\) 3.59527 4.25135i 0.152200 0.179974i
\(559\) 36.1035 1.52702
\(560\) 0.792717 0.575943i 0.0334984 0.0243380i
\(561\) 2.03630 + 1.47946i 0.0859726 + 0.0624627i
\(562\) −7.65180 + 23.5498i −0.322772 + 0.993389i
\(563\) −34.4435 −1.45162 −0.725811 0.687894i \(-0.758535\pi\)
−0.725811 + 0.687894i \(0.758535\pi\)
\(564\) 6.77598 0.285320
\(565\) 1.41598 4.35793i 0.0595707 0.183340i
\(566\) 8.47201 + 26.0742i 0.356105 + 1.09598i
\(567\) −0.302791 0.931895i −0.0127160 0.0391359i
\(568\) −8.04488 + 5.84495i −0.337556 + 0.245249i
\(569\) 6.58102 20.2543i 0.275891 0.849104i −0.713092 0.701071i \(-0.752706\pi\)
0.988982 0.148033i \(-0.0472943\pi\)
\(570\) −5.17909 + 3.76283i −0.216928 + 0.157608i
\(571\) −18.7063 13.5910i −0.782836 0.568764i 0.122993 0.992408i \(-0.460751\pi\)
−0.905829 + 0.423644i \(0.860751\pi\)
\(572\) 1.38038 + 4.24838i 0.0577167 + 0.177634i
\(573\) 7.64006 + 5.55083i 0.319168 + 0.231889i
\(574\) 0.811250 + 0.589408i 0.0338609 + 0.0246014i
\(575\) −0.319091 0.982061i −0.0133070 0.0409548i
\(576\) −0.809017 0.587785i −0.0337090 0.0244911i
\(577\) 1.92827 1.40097i 0.0802750 0.0583232i −0.546924 0.837182i \(-0.684201\pi\)
0.627199 + 0.778859i \(0.284201\pi\)
\(578\) 0.446436 1.37399i 0.0185693 0.0571504i
\(579\) 14.3170 10.4019i 0.594995 0.432289i
\(580\) −0.753241 2.31824i −0.0312766 0.0962596i
\(581\) 4.51394 + 13.8925i 0.187270 + 0.576357i
\(582\) 3.54708 10.9168i 0.147031 0.452516i
\(583\) 1.70245 0.0705083
\(584\) 12.1874 0.504317
\(585\) 2.16299 6.65701i 0.0894288 0.275233i
\(586\) −5.66869 4.11854i −0.234171 0.170135i
\(587\) −19.2256 + 13.9682i −0.793527 + 0.576531i −0.909008 0.416779i \(-0.863159\pi\)
0.115481 + 0.993310i \(0.463159\pi\)
\(588\) −6.03989 −0.249081
\(589\) −18.7716 30.2996i −0.773470 1.24847i
\(590\) −5.10520 −0.210178
\(591\) −12.3713 + 8.98824i −0.508885 + 0.369727i
\(592\) −1.56267 1.13535i −0.0642254 0.0466625i
\(593\) −9.25331 + 28.4787i −0.379988 + 1.16948i 0.560064 + 0.828450i \(0.310777\pi\)
−0.940051 + 0.341033i \(0.889223\pi\)
\(594\) −0.638182 −0.0261849
\(595\) 3.86456 0.158431
\(596\) 4.18778 12.8887i 0.171538 0.527941i
\(597\) −8.27298 25.4616i −0.338591 1.04207i
\(598\) 2.23351 + 6.87403i 0.0913349 + 0.281100i
\(599\) 14.1071 10.2494i 0.576400 0.418779i −0.261025 0.965332i \(-0.584060\pi\)
0.837424 + 0.546553i \(0.184060\pi\)
\(600\) −0.309017 + 0.951057i −0.0126156 + 0.0388267i
\(601\) 0.741681 0.538863i 0.0302538 0.0219807i −0.572556 0.819866i \(-0.694048\pi\)
0.602809 + 0.797885i \(0.294048\pi\)
\(602\) −4.08879 2.97068i −0.166647 0.121076i
\(603\) 2.70100 + 8.31282i 0.109993 + 0.338524i
\(604\) −4.04740 2.94061i −0.164686 0.119652i
\(605\) 8.56969 + 6.22625i 0.348408 + 0.253133i
\(606\) −2.01817 6.21129i −0.0819826 0.252317i
\(607\) −2.28505 1.66019i −0.0927475 0.0673850i 0.540445 0.841379i \(-0.318256\pi\)
−0.633193 + 0.773994i \(0.718256\pi\)
\(608\) −5.17909 + 3.76283i −0.210040 + 0.152603i
\(609\) 0.738065 2.27153i 0.0299079 0.0920470i
\(610\) −7.22579 + 5.24984i −0.292564 + 0.212560i
\(611\) 14.6564 + 45.1078i 0.592934 + 1.82486i
\(612\) −1.21877 3.75099i −0.0492658 0.151625i
\(613\) 12.8093 39.4229i 0.517361 1.59227i −0.261583 0.965181i \(-0.584244\pi\)
0.778944 0.627093i \(-0.215756\pi\)
\(614\) −2.91414 −0.117605
\(615\) −1.02338 −0.0412666
\(616\) 0.193236 0.594718i 0.00778569 0.0239619i
\(617\) 36.3494 + 26.4094i 1.46337 + 1.06320i 0.982469 + 0.186426i \(0.0596903\pi\)
0.480901 + 0.876775i \(0.340310\pi\)
\(618\) −10.8739 + 7.90035i −0.437412 + 0.317799i
\(619\) −43.1962 −1.73620 −0.868100 0.496389i \(-0.834659\pi\)
−0.868100 + 0.496389i \(0.834659\pi\)
\(620\) −5.15428 2.10557i −0.207001 0.0845616i
\(621\) −1.03260 −0.0414368
\(622\) 20.1039 14.6063i 0.806092 0.585660i
\(623\) −10.4302 7.57799i −0.417877 0.303606i
\(624\) 2.16299 6.65701i 0.0865890 0.266494i
\(625\) 1.00000 0.0400000
\(626\) −11.0209 −0.440485
\(627\) −1.26247 + 3.88550i −0.0504184 + 0.155172i
\(628\) −0.517221 1.59184i −0.0206394 0.0635214i
\(629\) −2.35414 7.24529i −0.0938656 0.288889i
\(630\) −0.792717 + 0.575943i −0.0315826 + 0.0229461i
\(631\) 1.64000 5.04740i 0.0652874 0.200934i −0.913091 0.407755i \(-0.866312\pi\)
0.978379 + 0.206821i \(0.0663118\pi\)
\(632\) 0.198771 0.144416i 0.00790670 0.00574456i
\(633\) 2.90537 + 2.11088i 0.115478 + 0.0838998i
\(634\) 7.36015 + 22.6522i 0.292309 + 0.899634i
\(635\) −5.14188 3.73579i −0.204049 0.148250i
\(636\) −2.15818 1.56801i −0.0855774 0.0621756i
\(637\) −13.0642 40.2076i −0.517624 1.59308i
\(638\) −1.25850 0.914355i −0.0498245 0.0361997i
\(639\) 8.04488 5.84495i 0.318251 0.231223i
\(640\) −0.309017 + 0.951057i −0.0122150 + 0.0375938i
\(641\) −31.9810 + 23.2356i −1.26318 + 0.917751i −0.998909 0.0466992i \(-0.985130\pi\)
−0.264266 + 0.964450i \(0.585130\pi\)
\(642\) −2.99072 9.20449i −0.118034 0.363272i
\(643\) −2.72004 8.37144i −0.107268 0.330137i 0.882988 0.469396i \(-0.155528\pi\)
−0.990256 + 0.139258i \(0.955528\pi\)
\(644\) 0.312662 0.962274i 0.0123206 0.0379189i
\(645\) 5.15794 0.203094
\(646\) −25.2485 −0.993388
\(647\) 10.0392 30.8975i 0.394681 1.21470i −0.534528 0.845151i \(-0.679511\pi\)
0.929209 0.369554i \(-0.120489\pi\)
\(648\) 0.809017 + 0.587785i 0.0317812 + 0.0230904i
\(649\) −2.63581 + 1.91503i −0.103465 + 0.0751715i
\(650\) −6.99959 −0.274547
\(651\) −2.87320 4.63769i −0.112610 0.181765i
\(652\) 8.73757 0.342190
\(653\) 1.77801 1.29180i 0.0695788 0.0505520i −0.552452 0.833545i \(-0.686308\pi\)
0.622031 + 0.782993i \(0.286308\pi\)
\(654\) −13.0042 9.44807i −0.508503 0.369449i
\(655\) 5.75020 17.6973i 0.224679 0.691491i
\(656\) −1.02338 −0.0399562
\(657\) −12.1874 −0.475475
\(658\) 2.05170 6.31450i 0.0799838 0.246165i
\(659\) 13.9322 + 42.8790i 0.542722 + 1.67033i 0.726345 + 0.687331i \(0.241218\pi\)
−0.183622 + 0.982997i \(0.558782\pi\)
\(660\) 0.197209 + 0.606947i 0.00767635 + 0.0236254i
\(661\) 3.68403 2.67660i 0.143292 0.104108i −0.513830 0.857892i \(-0.671774\pi\)
0.657122 + 0.753784i \(0.271774\pi\)
\(662\) −4.53789 + 13.9662i −0.176370 + 0.542812i
\(663\) 22.3342 16.2267i 0.867387 0.630194i
\(664\) −12.0607 8.76258i −0.468044 0.340054i
\(665\) 1.93838 + 5.96572i 0.0751671 + 0.231341i
\(666\) 1.56267 + 1.13535i 0.0605523 + 0.0439938i
\(667\) −2.03630 1.47946i −0.0788458 0.0572848i
\(668\) 0.580981 + 1.78808i 0.0224788 + 0.0691828i
\(669\) −0.289539 0.210362i −0.0111942 0.00813308i
\(670\) 7.07131 5.13761i 0.273189 0.198483i
\(671\) −1.76139 + 5.42099i −0.0679976 + 0.209275i
\(672\) −0.792717 + 0.575943i −0.0305797 + 0.0222175i
\(673\) −13.9706 42.9970i −0.538527 1.65741i −0.735903 0.677087i \(-0.763242\pi\)
0.197377 0.980328i \(-0.436758\pi\)
\(674\) −0.212982 0.655491i −0.00820376 0.0252486i
\(675\) 0.309017 0.951057i 0.0118941 0.0366062i
\(676\) 35.9943 1.38440
\(677\) −8.39375 −0.322598 −0.161299 0.986906i \(-0.551568\pi\)
−0.161299 + 0.986906i \(0.551568\pi\)
\(678\) −1.41598 + 4.35793i −0.0543803 + 0.167365i
\(679\) −9.09928 6.61101i −0.349198 0.253707i
\(680\) −3.19078 + 2.31824i −0.122361 + 0.0889003i
\(681\) −14.6942 −0.563081
\(682\) −3.45098 + 0.846338i −0.132145 + 0.0324080i
\(683\) 44.9622 1.72043 0.860215 0.509932i \(-0.170329\pi\)
0.860215 + 0.509932i \(0.170329\pi\)
\(684\) 5.17909 3.76283i 0.198027 0.143875i
\(685\) −8.99175 6.53289i −0.343557 0.249609i
\(686\) −3.94836 + 12.1518i −0.150749 + 0.463958i
\(687\) −4.74585 −0.181065
\(688\) 5.15794 0.196645
\(689\) 5.77013 17.7586i 0.219824 0.676550i
\(690\) 0.319091 + 0.982061i 0.0121476 + 0.0373864i
\(691\) −6.90265 21.2442i −0.262589 0.808167i −0.992239 0.124346i \(-0.960317\pi\)
0.729650 0.683821i \(-0.239683\pi\)
\(692\) −11.1506 + 8.10136i −0.423881 + 0.307968i
\(693\) −0.193236 + 0.594718i −0.00734042 + 0.0225915i
\(694\) −4.65871 + 3.38475i −0.176842 + 0.128483i
\(695\) 8.97798 + 6.52288i 0.340554 + 0.247427i
\(696\) 0.753241 + 2.31824i 0.0285515 + 0.0878726i
\(697\) −3.26538 2.37244i −0.123685 0.0898624i
\(698\) −10.0799 7.32348i −0.381530 0.277198i
\(699\) 2.58995 + 7.97106i 0.0979611 + 0.301493i
\(700\) 0.792717 + 0.575943i 0.0299619 + 0.0217686i
\(701\) −4.78463 + 3.47623i −0.180713 + 0.131296i −0.674464 0.738308i \(-0.735625\pi\)
0.493751 + 0.869603i \(0.335625\pi\)
\(702\) −2.16299 + 6.65701i −0.0816369 + 0.251253i
\(703\) 10.0038 7.26816i 0.377299 0.274124i
\(704\) 0.197209 + 0.606947i 0.00743260 + 0.0228752i
\(705\) 2.09389 + 6.44434i 0.0788606 + 0.242708i
\(706\) 7.69526 23.6836i 0.289615 0.891343i
\(707\) −6.39936 −0.240673
\(708\) 5.10520 0.191865
\(709\) −12.8558 + 39.5660i −0.482809 + 1.48593i 0.352320 + 0.935880i \(0.385393\pi\)
−0.835129 + 0.550054i \(0.814607\pi\)
\(710\) −8.04488 5.84495i −0.301919 0.219357i
\(711\) −0.198771 + 0.144416i −0.00745451 + 0.00541602i
\(712\) 13.1575 0.493100
\(713\) −5.58381 + 1.36940i −0.209115 + 0.0512846i
\(714\) −3.86456 −0.144627
\(715\) −3.61389 + 2.62565i −0.135152 + 0.0981936i
\(716\) 6.50702 + 4.72763i 0.243179 + 0.176680i
\(717\) −6.93759 + 21.3517i −0.259089 + 0.797394i
\(718\) −0.911184 −0.0340051
\(719\) −2.88043 −0.107422 −0.0537109 0.998557i \(-0.517105\pi\)
−0.0537109 + 0.998557i \(0.517105\pi\)
\(720\) 0.309017 0.951057i 0.0115164 0.0354438i
\(721\) 4.06978 + 12.5255i 0.151566 + 0.466473i
\(722\) −6.79277 20.9060i −0.252801 0.778041i
\(723\) −16.6770 + 12.1166i −0.620225 + 0.450620i
\(724\) 0.727353 2.23856i 0.0270319 0.0831956i
\(725\) 1.97201 1.43275i 0.0732386 0.0532110i
\(726\) −8.56969 6.22625i −0.318051 0.231078i
\(727\) 0.277581 + 0.854307i 0.0102949 + 0.0316845i 0.956072 0.293132i \(-0.0946975\pi\)
−0.945777 + 0.324816i \(0.894698\pi\)
\(728\) −5.54870 4.03136i −0.205648 0.149412i
\(729\) −0.809017 0.587785i −0.0299636 0.0217698i
\(730\) 3.76611 + 11.5909i 0.139390 + 0.428998i
\(731\) 16.4579 + 11.9573i 0.608716 + 0.442258i
\(732\) 7.22579 5.24984i 0.267073 0.194040i
\(733\) 0.952102 2.93027i 0.0351667 0.108232i −0.931932 0.362632i \(-0.881878\pi\)
0.967099 + 0.254400i \(0.0818781\pi\)
\(734\) 16.6849 12.1223i 0.615851 0.447442i
\(735\) −1.86643 5.74428i −0.0688443 0.211881i
\(736\) 0.319091 + 0.982061i 0.0117618 + 0.0361992i
\(737\) 1.72373 5.30509i 0.0634944 0.195416i
\(738\) 1.02338 0.0376711
\(739\) −12.2372 −0.450153 −0.225077 0.974341i \(-0.572263\pi\)
−0.225077 + 0.974341i \(0.572263\pi\)
\(740\) 0.596888 1.83703i 0.0219420 0.0675306i
\(741\) 36.2515 + 26.3383i 1.33173 + 0.967561i
\(742\) −2.11470 + 1.53642i −0.0776330 + 0.0564037i
\(743\) −4.77574 −0.175205 −0.0876025 0.996156i \(-0.527921\pi\)
−0.0876025 + 0.996156i \(0.527921\pi\)
\(744\) 5.15428 + 2.10557i 0.188965 + 0.0771938i
\(745\) 13.5520 0.496505
\(746\) 14.8035 10.7554i 0.541996 0.393783i
\(747\) 12.0607 + 8.76258i 0.441276 + 0.320606i
\(748\) −0.777797 + 2.39381i −0.0284391 + 0.0875264i
\(749\) −9.48318 −0.346508
\(750\) −1.00000 −0.0365148
\(751\) 10.9925 33.8313i 0.401121 1.23452i −0.522971 0.852351i \(-0.675176\pi\)
0.924091 0.382172i \(-0.124824\pi\)
\(752\) 2.09389 + 6.44434i 0.0763564 + 0.235001i
\(753\) −5.08637 15.6543i −0.185358 0.570473i
\(754\) −13.8033 + 10.0287i −0.502686 + 0.365222i
\(755\) 1.54597 4.75801i 0.0562636 0.173162i
\(756\) 0.792717 0.575943i 0.0288308 0.0209468i
\(757\) 43.8291 + 31.8437i 1.59300 + 1.15738i 0.899500 + 0.436920i \(0.143931\pi\)
0.693496 + 0.720460i \(0.256069\pi\)
\(758\) 0.279156 + 0.859154i 0.0101394 + 0.0312059i
\(759\) 0.533131 + 0.387343i 0.0193514 + 0.0140596i
\(760\) −5.17909 3.76283i −0.187865 0.136492i
\(761\) 4.32086 + 13.2983i 0.156631 + 0.482061i 0.998323 0.0578977i \(-0.0184397\pi\)
−0.841691 + 0.539959i \(0.818440\pi\)
\(762\) 5.14188 + 3.73579i 0.186271 + 0.135334i
\(763\) −12.7421 + 9.25771i −0.461297 + 0.335152i
\(764\) −2.91824 + 8.98143i −0.105578 + 0.324937i
\(765\) 3.19078 2.31824i 0.115363 0.0838160i
\(766\) −2.03137 6.25190i −0.0733962 0.225890i
\(767\) 11.0425 + 33.9853i 0.398722 + 1.22714i
\(768\) 0.309017 0.951057i 0.0111507 0.0343183i
\(769\) 39.2991 1.41716 0.708581 0.705630i \(-0.249336\pi\)
0.708581 + 0.705630i \(0.249336\pi\)
\(770\) 0.625324 0.0225351
\(771\) −6.66380 + 20.5091i −0.239991 + 0.738616i
\(772\) 14.3170 + 10.4019i 0.515281 + 0.374373i
\(773\) 11.8276 8.59323i 0.425408 0.309077i −0.354402 0.935093i \(-0.615316\pi\)
0.779810 + 0.626016i \(0.215316\pi\)
\(774\) −5.15794 −0.185398
\(775\) 0.409753 5.55267i 0.0147187 0.199458i
\(776\) 11.4786 0.412058
\(777\) 1.53119 1.11247i 0.0549310 0.0399097i
\(778\) 11.0788 + 8.04924i 0.397195 + 0.288579i
\(779\) 2.02449 6.23073i 0.0725347 0.223239i
\(780\) 6.99959 0.250626
\(781\) −6.34609 −0.227081
\(782\) −1.25850 + 3.87327i −0.0450039 + 0.138508i
\(783\) −0.753241 2.31824i −0.0269186 0.0828470i
\(784\) −1.86643 5.74428i −0.0666582 0.205153i
\(785\) 1.35410 0.983813i 0.0483300 0.0351138i
\(786\) −5.75020 + 17.6973i −0.205103 + 0.631242i
\(787\) 14.4303 10.4842i 0.514384 0.373722i −0.300100 0.953908i \(-0.597020\pi\)
0.814484 + 0.580186i \(0.197020\pi\)
\(788\) −12.3713 8.98824i −0.440708 0.320193i
\(789\) −3.37980 10.4020i −0.120324 0.370319i
\(790\) 0.198771 + 0.144416i 0.00707197 + 0.00513809i
\(791\) 3.63239 + 2.63909i 0.129153 + 0.0938351i
\(792\) −0.197209 0.606947i −0.00700752 0.0215669i
\(793\) 50.5776 + 36.7468i 1.79606 + 1.30492i
\(794\) −2.98916 + 2.17175i −0.106081 + 0.0770726i
\(795\) 0.824351 2.53709i 0.0292367 0.0899814i
\(796\) 21.6590 15.7361i 0.767681 0.557753i
\(797\) 10.2174 + 31.4460i 0.361920 + 1.11387i 0.951888 + 0.306448i \(0.0991404\pi\)
−0.589968 + 0.807427i \(0.700860\pi\)
\(798\) −1.93838 5.96572i −0.0686179 0.211184i
\(799\) −8.25836 + 25.4166i −0.292160 + 0.899175i
\(800\) −1.00000 −0.0353553
\(801\) −13.1575 −0.464899
\(802\) −5.53550 + 17.0365i −0.195465 + 0.601581i
\(803\) 6.29234 + 4.57166i 0.222052 + 0.161330i
\(804\) −7.07131 + 5.13761i −0.249386 + 0.181189i
\(805\) 1.01180 0.0356611
\(806\) −2.86810 + 38.8664i −0.101025 + 1.36901i
\(807\) −18.1200 −0.637855
\(808\) 5.28364 3.83879i 0.185878 0.135048i
\(809\) −40.5983 29.4964i −1.42736 1.03704i −0.990500 0.137510i \(-0.956090\pi\)
−0.436861 0.899529i \(-0.643910\pi\)
\(810\) −0.309017 + 0.951057i −0.0108578 + 0.0334167i
\(811\) 51.8830 1.82186 0.910930 0.412561i \(-0.135366\pi\)
0.910930 + 0.412561i \(0.135366\pi\)
\(812\) 2.38843 0.0838174
\(813\) −1.11363 + 3.42739i −0.0390566 + 0.120204i
\(814\) −0.380923 1.17236i −0.0133513 0.0410912i
\(815\) 2.70006 + 8.30993i 0.0945789 + 0.291084i
\(816\) 3.19078 2.31824i 0.111700 0.0811545i
\(817\) −10.2036 + 31.4036i −0.356980 + 1.09867i
\(818\) −16.3605 + 11.8866i −0.572030 + 0.415604i
\(819\) 5.54870 + 4.03136i 0.193887 + 0.140867i
\(820\) −0.316241 0.973291i −0.0110436 0.0339888i
\(821\) −17.3634 12.6153i −0.605988 0.440276i 0.242011 0.970273i \(-0.422193\pi\)
−0.847999 + 0.529997i \(0.822193\pi\)
\(822\) 8.99175 + 6.53289i 0.313623 + 0.227861i
\(823\) 4.09944 + 12.6168i 0.142898 + 0.439793i 0.996735 0.0807469i \(-0.0257306\pi\)
−0.853837 + 0.520540i \(0.825731\pi\)
\(824\) −10.8739 7.90035i −0.378810 0.275222i
\(825\) −0.516300 + 0.375114i −0.0179753 + 0.0130598i
\(826\) 1.54581 4.75751i 0.0537855 0.165535i
\(827\) −2.31191 + 1.67970i −0.0803929 + 0.0584088i −0.627256 0.778813i \(-0.715822\pi\)
0.546863 + 0.837222i \(0.315822\pi\)
\(828\) −0.319091 0.982061i −0.0110892 0.0341290i
\(829\) −15.7715 48.5397i −0.547767 1.68585i −0.714319 0.699820i \(-0.753263\pi\)
0.166552 0.986033i \(-0.446737\pi\)
\(830\) 4.60676 14.1781i 0.159903 0.492131i
\(831\) −3.24888 −0.112702
\(832\) 6.99959 0.242667
\(833\) 7.36123 22.6555i 0.255052 0.784968i
\(834\) −8.97798 6.52288i −0.310882 0.225869i
\(835\) −1.52103 + 1.10509i −0.0526374 + 0.0382433i
\(836\) −4.08545 −0.141298
\(837\) −5.15428 2.10557i −0.178158 0.0727790i
\(838\) 2.85276 0.0985470
\(839\) 6.65926 4.83824i 0.229903 0.167035i −0.466870 0.884326i \(-0.654618\pi\)
0.696773 + 0.717291i \(0.254618\pi\)
\(840\) −0.792717 0.575943i −0.0273513 0.0198719i
\(841\) −7.12544 + 21.9298i −0.245705 + 0.756202i
\(842\) 23.6273 0.814250
\(843\) 24.7617 0.852839
\(844\) −1.10975 + 3.41547i −0.0381993 + 0.117565i
\(845\) 11.1229 + 34.2326i 0.382638 + 1.17764i
\(846\) −2.09389 6.44434i −0.0719895 0.221561i
\(847\) −8.39703 + 6.10080i −0.288525 + 0.209626i
\(848\) 0.824351 2.53709i 0.0283083 0.0871241i
\(849\) 22.1800 16.1147i 0.761216 0.553056i
\(850\) −3.19078 2.31824i −0.109443 0.0795149i
\(851\) −0.616346 1.89692i −0.0211281 0.0650255i
\(852\) 8.04488 + 5.84495i 0.275613 + 0.200245i
\(853\) −3.93766 2.86088i −0.134823 0.0979547i 0.518330 0.855181i \(-0.326554\pi\)
−0.653153 + 0.757226i \(0.726554\pi\)
\(854\) −2.70440 8.32328i −0.0925426 0.284817i
\(855\) 5.17909 + 3.76283i 0.177121 + 0.128686i
\(856\) 7.82981 5.68869i 0.267617 0.194435i
\(857\) 2.51469 7.73943i 0.0859003 0.264374i −0.898875 0.438205i \(-0.855615\pi\)
0.984776 + 0.173831i \(0.0556146\pi\)
\(858\) 3.61389 2.62565i 0.123376 0.0896380i
\(859\) 12.6809 + 39.0277i 0.432666 + 1.33161i 0.895460 + 0.445142i \(0.146847\pi\)
−0.462794 + 0.886466i \(0.653153\pi\)
\(860\) 1.59389 + 4.90550i 0.0543513 + 0.167276i
\(861\) 0.309870 0.953681i 0.0105603 0.0325014i
\(862\) −33.4780 −1.14027
\(863\) −11.6267 −0.395778 −0.197889 0.980224i \(-0.563409\pi\)
−0.197889 + 0.980224i \(0.563409\pi\)
\(864\) −0.309017 + 0.951057i −0.0105130 + 0.0323556i
\(865\) −11.1506 8.10136i −0.379131 0.275455i
\(866\) −0.731372 + 0.531373i −0.0248530 + 0.0180568i
\(867\) −1.44470 −0.0490645
\(868\) 3.52283 4.16570i 0.119573 0.141393i
\(869\) 0.156798 0.00531901
\(870\) −1.97201 + 1.43275i −0.0668574 + 0.0485748i
\(871\) −49.4963 35.9612i −1.67712 1.21850i
\(872\) 4.96714 15.2873i 0.168209 0.517693i
\(873\) −11.4786 −0.388492
\(874\) −6.61040 −0.223600
\(875\) −0.302791 + 0.931895i −0.0102362 + 0.0315038i
\(876\) −3.76611 11.5909i −0.127245 0.391620i
\(877\) 5.14874 + 15.8462i 0.173860 + 0.535087i 0.999580 0.0289940i \(-0.00923039\pi\)
−0.825719 + 0.564081i \(0.809230\pi\)
\(878\) −23.2143 + 16.8662i −0.783444 + 0.569205i
\(879\) −2.16525 + 6.66394i −0.0730319 + 0.224769i
\(880\) −0.516300 + 0.375114i −0.0174045 + 0.0126451i
\(881\) 24.6217 + 17.8887i 0.829526 + 0.602686i 0.919425 0.393265i \(-0.128655\pi\)
−0.0898994 + 0.995951i \(0.528655\pi\)
\(882\) 1.86643 + 5.74428i 0.0628459 + 0.193420i
\(883\) 8.54741 + 6.21006i 0.287643 + 0.208985i 0.722244 0.691638i \(-0.243111\pi\)
−0.434601 + 0.900623i \(0.643111\pi\)
\(884\) 22.3342 + 16.2267i 0.751179 + 0.545764i
\(885\) 1.57759 + 4.85533i 0.0530302 + 0.163210i
\(886\) −26.5912 19.3196i −0.893349 0.649056i
\(887\) 37.0235 26.8992i 1.24313 0.903185i 0.245325 0.969441i \(-0.421105\pi\)
0.997803 + 0.0662557i \(0.0211053\pi\)
\(888\) −0.596888 + 1.83703i −0.0200302 + 0.0616467i
\(889\) 5.03828 3.66053i 0.168979 0.122770i
\(890\) 4.06590 + 12.5136i 0.136289 + 0.419456i
\(891\) 0.197209 + 0.606947i 0.00660675 + 0.0203335i
\(892\) 0.110594 0.340374i 0.00370296 0.0113966i
\(893\) −43.3778 −1.45158
\(894\) −13.5520 −0.453245
\(895\) −2.48546 + 7.64946i −0.0830798 + 0.255693i
\(896\) −0.792717 0.575943i −0.0264828 0.0192409i
\(897\) 5.84740 4.24838i 0.195239 0.141849i
\(898\) −28.3068 −0.944611
\(899\) −7.14754 11.5370i −0.238384 0.384780i
\(900\) 1.00000 0.0333333
\(901\) 8.51191 6.18426i 0.283573 0.206028i
\(902\) −0.528371 0.383884i −0.0175928 0.0127819i
\(903\) −1.56178 + 4.80666i −0.0519727 + 0.159956i
\(904\) −4.58220 −0.152402
\(905\) 2.35377 0.0782418
\(906\) −1.54597 + 4.75801i −0.0513614 + 0.158074i
\(907\) 13.8311 + 42.5676i 0.459253 + 1.41344i 0.866069 + 0.499925i \(0.166639\pi\)
−0.406816 + 0.913510i \(0.633361\pi\)
\(908\) −4.54075 13.9750i −0.150690 0.463776i
\(909\) −5.28364 + 3.83879i −0.175247 + 0.127325i
\(910\) 2.11941 6.52288i 0.0702579 0.216232i
\(911\) 23.6796 17.2042i 0.784539 0.570001i −0.121799 0.992555i \(-0.538866\pi\)
0.906338 + 0.422554i \(0.138866\pi\)
\(912\) 5.17909 + 3.76283i 0.171497 + 0.124600i
\(913\) −2.93995 9.04824i −0.0972981 0.299453i
\(914\) 23.7540 + 17.2583i 0.785711 + 0.570853i
\(915\) 7.22579 + 5.24984i 0.238877 + 0.173555i
\(916\) −1.46655 4.51357i −0.0484561 0.149132i
\(917\) 14.7509 + 10.7172i 0.487118 + 0.353912i
\(918\) −3.19078 + 2.31824i −0.105311 + 0.0765132i
\(919\) −0.166982 + 0.513918i −0.00550823 + 0.0169526i −0.953773 0.300528i \(-0.902837\pi\)
0.948265 + 0.317481i \(0.102837\pi\)
\(920\) −0.835391 + 0.606947i −0.0275420 + 0.0200105i
\(921\) 0.900519 + 2.77151i 0.0296731 + 0.0913244i
\(922\) 10.8555 + 33.4099i 0.357508 + 1.10030i
\(923\) −21.5089 + 66.1974i −0.707973 + 2.17892i
\(924\) −0.625324 −0.0205716
\(925\) 1.93157 0.0635096
\(926\) 5.60577 17.2528i 0.184217 0.566962i
\(927\) 10.8739 + 7.90035i 0.357146 + 0.259481i
\(928\) −1.97201 + 1.43275i −0.0647344 + 0.0470323i
\(929\) −10.7530 −0.352794 −0.176397 0.984319i \(-0.556444\pi\)
−0.176397 + 0.984319i \(0.556444\pi\)
\(930\) −0.409753 + 5.55267i −0.0134363 + 0.182079i
\(931\) 38.6656 1.26721
\(932\) −6.78059 + 4.92639i −0.222106 + 0.161369i
\(933\) −20.1039 14.6063i −0.658171 0.478189i
\(934\) 4.76950 14.6790i 0.156063 0.480312i
\(935\) −2.51700 −0.0823148
\(936\) −6.99959 −0.228789
\(937\) 7.78738 23.9671i 0.254403 0.782971i −0.739544 0.673108i \(-0.764959\pi\)
0.993947 0.109863i \(-0.0350412\pi\)
\(938\) 2.64658 + 8.14534i 0.0864139 + 0.265955i
\(939\) 3.40566 + 10.4815i 0.111139 + 0.342052i
\(940\) −5.48188 + 3.98282i −0.178799 + 0.129905i
\(941\) 2.31264 7.11759i 0.0753901 0.232027i −0.906259 0.422723i \(-0.861074\pi\)
0.981649 + 0.190696i \(0.0610744\pi\)
\(942\) −1.35410 + 0.983813i −0.0441190 + 0.0320543i
\(943\) −0.854922 0.621137i −0.0278401 0.0202270i
\(944\) 1.57759 + 4.85533i 0.0513463 + 0.158028i
\(945\) 0.792717 + 0.575943i 0.0257871 + 0.0187354i
\(946\) 2.66305 + 1.93482i 0.0865831 + 0.0629063i
\(947\) 18.5469 + 57.0815i 0.602693 + 1.85490i 0.511933 + 0.859025i \(0.328930\pi\)
0.0907601 + 0.995873i \(0.471070\pi\)
\(948\) −0.198771 0.144416i −0.00645580 0.00469041i
\(949\) 69.0146 50.1420i 2.24031 1.62768i
\(950\) 1.97824 6.08839i 0.0641825 0.197533i
\(951\) 19.2691 13.9998i 0.624844 0.453976i
\(952\) −1.19421 3.67541i −0.0387047 0.119121i
\(953\) 4.15440 + 12.7859i 0.134574 + 0.414177i 0.995524 0.0945138i \(-0.0301296\pi\)
−0.860949 + 0.508691i \(0.830130\pi\)
\(954\) −0.824351 + 2.53709i −0.0266894 + 0.0821414i
\(955\) −9.44364 −0.305589
\(956\) −22.4505 −0.726102
\(957\) −0.480705 + 1.47946i −0.0155390 + 0.0478241i
\(958\) 19.9620 + 14.5033i 0.644944 + 0.468579i
\(959\) 8.81059 6.40127i 0.284509 0.206708i
\(960\) 1.00000 0.0322749
\(961\) −30.6642 4.55044i −0.989168 0.146788i
\(962\) −13.5202 −0.435909
\(963\) −7.82981 + 5.68869i −0.252312 + 0.183315i
\(964\) −16.6770 12.1166i −0.537131 0.390248i
\(965\) −5.46861 + 16.8307i −0.176041 + 0.541798i
\(966\) −1.01180 −0.0325540
\(967\) −22.3871 −0.719920 −0.359960 0.932968i \(-0.617210\pi\)
−0.359960 + 0.932968i \(0.617210\pi\)
\(968\) 3.27333 10.0743i 0.105209 0.323800i
\(969\) 7.80221 + 24.0127i 0.250643 + 0.771400i
\(970\) 3.54708 + 10.9168i 0.113890 + 0.350517i
\(971\) 10.8334 7.87089i 0.347659 0.252589i −0.400227 0.916416i \(-0.631069\pi\)
0.747886 + 0.663827i \(0.231069\pi\)
\(972\) 0.309017 0.951057i 0.00991172 0.0305052i
\(973\) −8.79709 + 6.39146i −0.282022 + 0.204901i
\(974\) −0.964176 0.700515i −0.0308942 0.0224459i
\(975\) 2.16299 + 6.65701i 0.0692712 + 0.213195i
\(976\) 7.22579 + 5.24984i 0.231292 + 0.168043i
\(977\) 40.2823 + 29.2668i 1.28875 + 0.936329i 0.999779 0.0210102i \(-0.00668823\pi\)
0.288967 + 0.957339i \(0.406688\pi\)
\(978\) −2.70006 8.30993i −0.0863384 0.265722i
\(979\) 6.79324 + 4.93558i 0.217113 + 0.157742i
\(980\) 4.88637 3.55016i 0.156089 0.113406i
\(981\) −4.96714 + 15.2873i −0.158589 + 0.488086i
\(982\) 16.4754 11.9701i 0.525753 0.381982i
\(983\) −1.74381 5.36690i −0.0556190 0.171178i 0.919388 0.393352i \(-0.128685\pi\)
−0.975007 + 0.222174i \(0.928685\pi\)
\(984\) 0.316241 + 0.973291i 0.0100814 + 0.0310274i
\(985\) 4.72540 14.5433i 0.150564 0.463387i
\(986\) −9.61371 −0.306163
\(987\) −6.63946 −0.211336
\(988\) −13.8469 + 42.6162i −0.440527 + 1.35580i
\(989\) 4.30890 + 3.13060i 0.137015 + 0.0995473i
\(990\) 0.516300 0.375114i 0.0164091 0.0119219i
\(991\) −36.9061 −1.17236 −0.586181 0.810180i \(-0.699369\pi\)
−0.586181 + 0.810180i \(0.699369\pi\)
\(992\) −0.409753 + 5.55267i −0.0130097 + 0.176297i
\(993\) 14.6849 0.466012
\(994\) 7.88279 5.72719i 0.250027 0.181655i
\(995\) 21.6590 + 15.7361i 0.686635 + 0.498869i
\(996\) −4.60676 + 14.1781i −0.145971 + 0.449252i
\(997\) 16.9472 0.536725 0.268362 0.963318i \(-0.413518\pi\)
0.268362 + 0.963318i \(0.413518\pi\)
\(998\) 28.2913 0.895544
\(999\) 0.596888 1.83703i 0.0188847 0.0581211i
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 930.2.n.e.481.2 12
31.2 even 5 inner 930.2.n.e.901.2 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.n.e.481.2 12 1.1 even 1 trivial
930.2.n.e.901.2 yes 12 31.2 even 5 inner