Properties

Label 630.2.bk.c.101.10
Level $630$
Weight $2$
Character 630.101
Analytic conductor $5.031$
Analytic rank $0$
Dimension $32$
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] = [630,2,Mod(101,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.bk (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: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.10
Character \(\chi\) \(=\) 630.101
Dual form 630.2.bk.c.131.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-1.61346 + 0.629881i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.629881 - 1.61346i) q^{6} +(-0.166511 + 2.64051i) q^{7} -1.00000i q^{8} +(2.20650 - 2.03258i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-1.61346 + 0.629881i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.629881 - 1.61346i) q^{6} +(-0.166511 + 2.64051i) q^{7} -1.00000i q^{8} +(2.20650 - 2.03258i) q^{9} +(0.866025 + 0.500000i) q^{10} +(4.91769 - 2.83923i) q^{11} +(1.61346 - 0.629881i) q^{12} +(1.57532 - 0.909513i) q^{13} +(-2.64051 - 0.166511i) q^{14} +(-0.261236 + 1.71224i) q^{15} +1.00000 q^{16} +(-2.85981 + 4.95334i) q^{17} +(2.03258 + 2.20650i) q^{18} +(1.07373 - 0.619917i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-1.39455 - 4.36523i) q^{21} +(2.83923 + 4.91769i) q^{22} +(3.01902 + 1.74303i) q^{23} +(0.629881 + 1.61346i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.909513 + 1.57532i) q^{26} +(-2.27981 + 4.66931i) q^{27} +(0.166511 - 2.64051i) q^{28} +(-2.25780 - 1.30354i) q^{29} +(-1.71224 - 0.261236i) q^{30} +8.91829i q^{31} +1.00000i q^{32} +(-6.14612 + 7.67855i) q^{33} +(-4.95334 - 2.85981i) q^{34} +(2.20349 + 1.46446i) q^{35} +(-2.20650 + 2.03258i) q^{36} +(-2.02715 - 3.51113i) q^{37} +(0.619917 + 1.07373i) q^{38} +(-1.96883 + 2.45973i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(6.21952 + 10.7725i) q^{41} +(4.36523 - 1.39455i) q^{42} +(-2.45956 + 4.26008i) q^{43} +(-4.91769 + 2.83923i) q^{44} +(-0.657012 - 2.92717i) q^{45} +(-1.74303 + 3.01902i) q^{46} +10.0448 q^{47} +(-1.61346 + 0.629881i) q^{48} +(-6.94455 - 0.879348i) q^{49} +(0.866025 - 0.500000i) q^{50} +(1.49417 - 9.79335i) q^{51} +(-1.57532 + 0.909513i) q^{52} +(0.844055 + 0.487315i) q^{53} +(-4.66931 - 2.27981i) q^{54} -5.67846i q^{55} +(2.64051 + 0.166511i) q^{56} +(-1.34194 + 1.67653i) q^{57} +(1.30354 - 2.25780i) q^{58} +11.3708 q^{59} +(0.261236 - 1.71224i) q^{60} -7.44834i q^{61} -8.91829 q^{62} +(4.99962 + 6.16472i) q^{63} -1.00000 q^{64} -1.81903i q^{65} +(-7.67855 - 6.14612i) q^{66} -0.0689019 q^{67} +(2.85981 - 4.95334i) q^{68} +(-5.96898 - 0.910688i) q^{69} +(-1.46446 + 2.20349i) q^{70} +6.62319i q^{71} +(-2.03258 - 2.20650i) q^{72} +(-7.47035 - 4.31301i) q^{73} +(3.51113 - 2.02715i) q^{74} +(1.35222 + 1.08236i) q^{75} +(-1.07373 + 0.619917i) q^{76} +(6.67816 + 13.4580i) q^{77} +(-2.45973 - 1.96883i) q^{78} -1.36666 q^{79} +(0.500000 - 0.866025i) q^{80} +(0.737278 - 8.96975i) q^{81} +(-10.7725 + 6.21952i) q^{82} +(-6.04923 + 10.4776i) q^{83} +(1.39455 + 4.36523i) q^{84} +(2.85981 + 4.95334i) q^{85} +(-4.26008 - 2.45956i) q^{86} +(4.46395 + 0.681066i) q^{87} +(-2.83923 - 4.91769i) q^{88} +(-7.88750 - 13.6615i) q^{89} +(2.92717 - 0.657012i) q^{90} +(2.13927 + 4.31109i) q^{91} +(-3.01902 - 1.74303i) q^{92} +(-5.61747 - 14.3893i) q^{93} +10.0448i q^{94} -1.23983i q^{95} +(-0.629881 - 1.61346i) q^{96} +(-1.67919 - 0.969482i) q^{97} +(0.879348 - 6.94455i) q^{98} +(5.07994 - 16.2603i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 32 q^{16} - 6 q^{17} + 8 q^{18} - 16 q^{20} + 18 q^{23} + 2 q^{24} - 16 q^{25} - 12 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} - 4 q^{30} + 20 q^{33} + 2 q^{35} + 2 q^{37} + 30 q^{39} + 6 q^{41} + 10 q^{42} - 28 q^{43} + 6 q^{44} + 6 q^{45} + 48 q^{47} - 2 q^{48} + 8 q^{49} + 34 q^{51} + 36 q^{53} - 46 q^{54} - 6 q^{56} + 18 q^{57} - 60 q^{59} - 2 q^{60} + 32 q^{63} - 32 q^{64} - 34 q^{66} - 8 q^{67} + 6 q^{68} - 28 q^{69} + 6 q^{70} - 8 q^{72} - 30 q^{73} - 18 q^{74} + 4 q^{75} - 6 q^{77} - 22 q^{78} - 8 q^{79} + 16 q^{80} + 20 q^{81} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 30 q^{86} - 22 q^{87} + 12 q^{89} + 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 2 q^{96} - 96 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.61346 + 0.629881i −0.931531 + 0.363662i
\(4\) −1.00000 −0.500000
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) −0.629881 1.61346i −0.257148 0.658692i
\(7\) −0.166511 + 2.64051i −0.0629353 + 0.998018i
\(8\) 1.00000i 0.353553i
\(9\) 2.20650 2.03258i 0.735500 0.677525i
\(10\) 0.866025 + 0.500000i 0.273861 + 0.158114i
\(11\) 4.91769 2.83923i 1.48274 0.856061i 0.482932 0.875658i \(-0.339572\pi\)
0.999808 + 0.0195971i \(0.00623836\pi\)
\(12\) 1.61346 0.629881i 0.465765 0.181831i
\(13\) 1.57532 0.909513i 0.436916 0.252254i −0.265373 0.964146i \(-0.585495\pi\)
0.702289 + 0.711892i \(0.252162\pi\)
\(14\) −2.64051 0.166511i −0.705705 0.0445020i
\(15\) −0.261236 + 1.71224i −0.0674509 + 0.442098i
\(16\) 1.00000 0.250000
\(17\) −2.85981 + 4.95334i −0.693606 + 1.20136i 0.277042 + 0.960858i \(0.410646\pi\)
−0.970648 + 0.240503i \(0.922688\pi\)
\(18\) 2.03258 + 2.20650i 0.479083 + 0.520077i
\(19\) 1.07373 0.619917i 0.246330 0.142219i −0.371753 0.928332i \(-0.621243\pi\)
0.618083 + 0.786113i \(0.287910\pi\)
\(20\) −0.500000 + 0.866025i −0.111803 + 0.193649i
\(21\) −1.39455 4.36523i −0.304315 0.952571i
\(22\) 2.83923 + 4.91769i 0.605326 + 1.04846i
\(23\) 3.01902 + 1.74303i 0.629510 + 0.363448i 0.780562 0.625078i \(-0.214933\pi\)
−0.151052 + 0.988526i \(0.548266\pi\)
\(24\) 0.629881 + 1.61346i 0.128574 + 0.329346i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0.909513 + 1.57532i 0.178370 + 0.308946i
\(27\) −2.27981 + 4.66931i −0.438751 + 0.898609i
\(28\) 0.166511 2.64051i 0.0314677 0.499009i
\(29\) −2.25780 1.30354i −0.419264 0.242062i 0.275499 0.961301i \(-0.411157\pi\)
−0.694762 + 0.719240i \(0.744490\pi\)
\(30\) −1.71224 0.261236i −0.312610 0.0476950i
\(31\) 8.91829i 1.60177i 0.598816 + 0.800886i \(0.295638\pi\)
−0.598816 + 0.800886i \(0.704362\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −6.14612 + 7.67855i −1.06990 + 1.33666i
\(34\) −4.95334 2.85981i −0.849490 0.490454i
\(35\) 2.20349 + 1.46446i 0.372458 + 0.247538i
\(36\) −2.20650 + 2.03258i −0.367750 + 0.338763i
\(37\) −2.02715 3.51113i −0.333262 0.577226i 0.649888 0.760030i \(-0.274816\pi\)
−0.983149 + 0.182804i \(0.941483\pi\)
\(38\) 0.619917 + 1.07373i 0.100564 + 0.174182i
\(39\) −1.96883 + 2.45973i −0.315266 + 0.393872i
\(40\) −0.866025 0.500000i −0.136931 0.0790569i
\(41\) 6.21952 + 10.7725i 0.971326 + 1.68239i 0.691563 + 0.722316i \(0.256923\pi\)
0.279763 + 0.960069i \(0.409744\pi\)
\(42\) 4.36523 1.39455i 0.673570 0.215183i
\(43\) −2.45956 + 4.26008i −0.375079 + 0.649656i −0.990339 0.138669i \(-0.955718\pi\)
0.615260 + 0.788324i \(0.289051\pi\)
\(44\) −4.91769 + 2.83923i −0.741370 + 0.428030i
\(45\) −0.657012 2.92717i −0.0979416 0.436357i
\(46\) −1.74303 + 3.01902i −0.256996 + 0.445131i
\(47\) 10.0448 1.46518 0.732590 0.680670i \(-0.238311\pi\)
0.732590 + 0.680670i \(0.238311\pi\)
\(48\) −1.61346 + 0.629881i −0.232883 + 0.0909155i
\(49\) −6.94455 0.879348i −0.992078 0.125621i
\(50\) 0.866025 0.500000i 0.122474 0.0707107i
\(51\) 1.49417 9.79335i 0.209226 1.37134i
\(52\) −1.57532 + 0.909513i −0.218458 + 0.126127i
\(53\) 0.844055 + 0.487315i 0.115940 + 0.0669379i 0.556848 0.830614i \(-0.312010\pi\)
−0.440909 + 0.897552i \(0.645344\pi\)
\(54\) −4.66931 2.27981i −0.635412 0.310244i
\(55\) 5.67846i 0.765684i
\(56\) 2.64051 + 0.166511i 0.352853 + 0.0222510i
\(57\) −1.34194 + 1.67653i −0.177745 + 0.222062i
\(58\) 1.30354 2.25780i 0.171164 0.296464i
\(59\) 11.3708 1.48035 0.740176 0.672413i \(-0.234742\pi\)
0.740176 + 0.672413i \(0.234742\pi\)
\(60\) 0.261236 1.71224i 0.0337255 0.221049i
\(61\) 7.44834i 0.953662i −0.878995 0.476831i \(-0.841785\pi\)
0.878995 0.476831i \(-0.158215\pi\)
\(62\) −8.91829 −1.13262
\(63\) 4.99962 + 6.16472i 0.629893 + 0.776682i
\(64\) −1.00000 −0.125000
\(65\) 1.81903i 0.225622i
\(66\) −7.67855 6.14612i −0.945164 0.756535i
\(67\) −0.0689019 −0.00841770 −0.00420885 0.999991i \(-0.501340\pi\)
−0.00420885 + 0.999991i \(0.501340\pi\)
\(68\) 2.85981 4.95334i 0.346803 0.600680i
\(69\) −5.96898 0.910688i −0.718580 0.109634i
\(70\) −1.46446 + 2.20349i −0.175036 + 0.263367i
\(71\) 6.62319i 0.786028i 0.919532 + 0.393014i \(0.128568\pi\)
−0.919532 + 0.393014i \(0.871432\pi\)
\(72\) −2.03258 2.20650i −0.239541 0.260038i
\(73\) −7.47035 4.31301i −0.874339 0.504800i −0.00555117 0.999985i \(-0.501767\pi\)
−0.868788 + 0.495185i \(0.835100\pi\)
\(74\) 3.51113 2.02715i 0.408160 0.235651i
\(75\) 1.35222 + 1.08236i 0.156141 + 0.124980i
\(76\) −1.07373 + 0.619917i −0.123165 + 0.0711094i
\(77\) 6.67816 + 13.4580i 0.761047 + 1.53368i
\(78\) −2.45973 1.96883i −0.278509 0.222927i
\(79\) −1.36666 −0.153761 −0.0768806 0.997040i \(-0.524496\pi\)
−0.0768806 + 0.997040i \(0.524496\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) 0.737278 8.96975i 0.0819197 0.996639i
\(82\) −10.7725 + 6.21952i −1.18963 + 0.686831i
\(83\) −6.04923 + 10.4776i −0.663989 + 1.15006i 0.315569 + 0.948903i \(0.397805\pi\)
−0.979558 + 0.201161i \(0.935529\pi\)
\(84\) 1.39455 + 4.36523i 0.152157 + 0.476286i
\(85\) 2.85981 + 4.95334i 0.310190 + 0.537265i
\(86\) −4.26008 2.45956i −0.459376 0.265221i
\(87\) 4.46395 + 0.681066i 0.478586 + 0.0730179i
\(88\) −2.83923 4.91769i −0.302663 0.524228i
\(89\) −7.88750 13.6615i −0.836073 1.44812i −0.893154 0.449752i \(-0.851513\pi\)
0.0570806 0.998370i \(-0.481821\pi\)
\(90\) 2.92717 0.657012i 0.308551 0.0692551i
\(91\) 2.13927 + 4.31109i 0.224256 + 0.451926i
\(92\) −3.01902 1.74303i −0.314755 0.181724i
\(93\) −5.61747 14.3893i −0.582504 1.49210i
\(94\) 10.0448i 1.03604i
\(95\) 1.23983i 0.127204i
\(96\) −0.629881 1.61346i −0.0642870 0.164673i
\(97\) −1.67919 0.969482i −0.170496 0.0984360i 0.412324 0.911037i \(-0.364717\pi\)
−0.582820 + 0.812601i \(0.698051\pi\)
\(98\) 0.879348 6.94455i 0.0888276 0.701505i
\(99\) 5.07994 16.2603i 0.510553 1.63423i
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) 2.75742 + 4.77599i 0.274373 + 0.475229i 0.969977 0.243197i \(-0.0781963\pi\)
−0.695603 + 0.718426i \(0.744863\pi\)
\(102\) 9.79335 + 1.49417i 0.969686 + 0.147945i
\(103\) 6.52554 + 3.76752i 0.642980 + 0.371225i 0.785762 0.618529i \(-0.212271\pi\)
−0.142781 + 0.989754i \(0.545605\pi\)
\(104\) −0.909513 1.57532i −0.0891851 0.154473i
\(105\) −4.47767 0.974903i −0.436976 0.0951408i
\(106\) −0.487315 + 0.844055i −0.0473322 + 0.0819818i
\(107\) 15.6906 9.05896i 1.51686 0.875762i 0.517061 0.855949i \(-0.327026\pi\)
0.999804 0.0198138i \(-0.00630733\pi\)
\(108\) 2.27981 4.66931i 0.219375 0.449304i
\(109\) −1.76968 + 3.06518i −0.169505 + 0.293591i −0.938246 0.345969i \(-0.887550\pi\)
0.768741 + 0.639560i \(0.220884\pi\)
\(110\) 5.67846 0.541420
\(111\) 5.48232 + 4.38820i 0.520359 + 0.416509i
\(112\) −0.166511 + 2.64051i −0.0157338 + 0.249504i
\(113\) 5.41190 3.12456i 0.509109 0.293934i −0.223358 0.974736i \(-0.571702\pi\)
0.732467 + 0.680802i \(0.238369\pi\)
\(114\) −1.67653 1.34194i −0.157022 0.125684i
\(115\) 3.01902 1.74303i 0.281526 0.162539i
\(116\) 2.25780 + 1.30354i 0.209632 + 0.121031i
\(117\) 1.62730 5.20880i 0.150444 0.481554i
\(118\) 11.3708i 1.04677i
\(119\) −12.6031 8.37614i −1.15533 0.767839i
\(120\) 1.71224 + 0.261236i 0.156305 + 0.0238475i
\(121\) 10.6225 18.3987i 0.965679 1.67261i
\(122\) 7.44834 0.674341
\(123\) −16.8203 13.4635i −1.51664 1.21396i
\(124\) 8.91829i 0.800886i
\(125\) −1.00000 −0.0894427
\(126\) −6.16472 + 4.99962i −0.549197 + 0.445402i
\(127\) 19.0703 1.69222 0.846110 0.533009i \(-0.178939\pi\)
0.846110 + 0.533009i \(0.178939\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 1.28505 8.42269i 0.113142 0.741576i
\(130\) 1.81903 0.159539
\(131\) −0.0646409 + 0.111961i −0.00564770 + 0.00978211i −0.868835 0.495101i \(-0.835131\pi\)
0.863188 + 0.504883i \(0.168464\pi\)
\(132\) 6.14612 7.67855i 0.534951 0.668332i
\(133\) 1.45811 + 2.93841i 0.126434 + 0.254792i
\(134\) 0.0689019i 0.00595221i
\(135\) 2.90383 + 4.30903i 0.249922 + 0.370862i
\(136\) 4.95334 + 2.85981i 0.424745 + 0.245227i
\(137\) 6.91408 3.99184i 0.590710 0.341046i −0.174668 0.984627i \(-0.555885\pi\)
0.765378 + 0.643581i \(0.222552\pi\)
\(138\) 0.910688 5.96898i 0.0775229 0.508113i
\(139\) −4.54379 + 2.62336i −0.385400 + 0.222511i −0.680165 0.733059i \(-0.738092\pi\)
0.294765 + 0.955570i \(0.404759\pi\)
\(140\) −2.20349 1.46446i −0.186229 0.123769i
\(141\) −16.2068 + 6.32701i −1.36486 + 0.532831i
\(142\) −6.62319 −0.555806
\(143\) 5.16464 8.94541i 0.431889 0.748053i
\(144\) 2.20650 2.03258i 0.183875 0.169381i
\(145\) −2.25780 + 1.30354i −0.187500 + 0.108253i
\(146\) 4.31301 7.47035i 0.356947 0.618251i
\(147\) 11.7586 2.95545i 0.969835 0.243761i
\(148\) 2.02715 + 3.51113i 0.166631 + 0.288613i
\(149\) 13.7747 + 7.95281i 1.12847 + 0.651520i 0.943549 0.331234i \(-0.107465\pi\)
0.184917 + 0.982754i \(0.440798\pi\)
\(150\) −1.08236 + 1.35222i −0.0883740 + 0.110409i
\(151\) −9.79120 16.9589i −0.796797 1.38009i −0.921692 0.387923i \(-0.873193\pi\)
0.124895 0.992170i \(-0.460141\pi\)
\(152\) −0.619917 1.07373i −0.0502819 0.0870909i
\(153\) 3.75786 + 16.7423i 0.303805 + 1.35354i
\(154\) −13.4580 + 6.67816i −1.08447 + 0.538141i
\(155\) 7.72347 + 4.45915i 0.620364 + 0.358167i
\(156\) 1.96883 2.45973i 0.157633 0.196936i
\(157\) 16.3621i 1.30584i 0.757426 + 0.652921i \(0.226457\pi\)
−0.757426 + 0.652921i \(0.773543\pi\)
\(158\) 1.36666i 0.108726i
\(159\) −1.66880 0.254609i −0.132344 0.0201918i
\(160\) 0.866025 + 0.500000i 0.0684653 + 0.0395285i
\(161\) −5.10520 + 7.68152i −0.402346 + 0.605389i
\(162\) 8.96975 + 0.737278i 0.704730 + 0.0579260i
\(163\) −6.59007 11.4143i −0.516174 0.894040i −0.999824 0.0187781i \(-0.994022\pi\)
0.483650 0.875262i \(-0.339311\pi\)
\(164\) −6.21952 10.7725i −0.485663 0.841193i
\(165\) 3.57676 + 9.16197i 0.278450 + 0.713258i
\(166\) −10.4776 6.04923i −0.813217 0.469511i
\(167\) −2.81257 4.87151i −0.217643 0.376969i 0.736444 0.676499i \(-0.236503\pi\)
−0.954087 + 0.299530i \(0.903170\pi\)
\(168\) −4.36523 + 1.39455i −0.336785 + 0.107592i
\(169\) −4.84557 + 8.39278i −0.372736 + 0.645598i
\(170\) −4.95334 + 2.85981i −0.379904 + 0.219337i
\(171\) 1.10915 3.55028i 0.0848190 0.271497i
\(172\) 2.45956 4.26008i 0.187539 0.324828i
\(173\) −7.96037 −0.605216 −0.302608 0.953115i \(-0.597857\pi\)
−0.302608 + 0.953115i \(0.597857\pi\)
\(174\) −0.681066 + 4.46395i −0.0516315 + 0.338411i
\(175\) 2.37000 1.17605i 0.179155 0.0889010i
\(176\) 4.91769 2.83923i 0.370685 0.214015i
\(177\) −18.3463 + 7.16226i −1.37899 + 0.538348i
\(178\) 13.6615 7.88750i 1.02398 0.591193i
\(179\) 5.99647 + 3.46206i 0.448197 + 0.258767i 0.707068 0.707145i \(-0.250017\pi\)
−0.258871 + 0.965912i \(0.583351\pi\)
\(180\) 0.657012 + 2.92717i 0.0489708 + 0.218179i
\(181\) 2.78183i 0.206772i −0.994641 0.103386i \(-0.967032\pi\)
0.994641 0.103386i \(-0.0329676\pi\)
\(182\) −4.31109 + 2.13927i −0.319560 + 0.158573i
\(183\) 4.69157 + 12.0176i 0.346811 + 0.888366i
\(184\) 1.74303 3.01902i 0.128498 0.222565i
\(185\) −4.05430 −0.298078
\(186\) 14.3893 5.61747i 1.05507 0.411893i
\(187\) 32.4787i 2.37508i
\(188\) −10.0448 −0.732590
\(189\) −11.9497 6.79736i −0.869215 0.494435i
\(190\) 1.23983 0.0899471
\(191\) 3.02993i 0.219238i 0.993974 + 0.109619i \(0.0349631\pi\)
−0.993974 + 0.109619i \(0.965037\pi\)
\(192\) 1.61346 0.629881i 0.116441 0.0454578i
\(193\) −3.52611 −0.253815 −0.126907 0.991915i \(-0.540505\pi\)
−0.126907 + 0.991915i \(0.540505\pi\)
\(194\) 0.969482 1.67919i 0.0696048 0.120559i
\(195\) 1.14577 + 2.93492i 0.0820503 + 0.210174i
\(196\) 6.94455 + 0.879348i 0.496039 + 0.0628106i
\(197\) 9.09265i 0.647825i −0.946087 0.323912i \(-0.895002\pi\)
0.946087 0.323912i \(-0.104998\pi\)
\(198\) 16.2603 + 5.07994i 1.15557 + 0.361015i
\(199\) −12.5241 7.23082i −0.887813 0.512579i −0.0145863 0.999894i \(-0.504643\pi\)
−0.873226 + 0.487315i \(0.837976\pi\)
\(200\) −0.866025 + 0.500000i −0.0612372 + 0.0353553i
\(201\) 0.111170 0.0434000i 0.00784135 0.00306120i
\(202\) −4.77599 + 2.75742i −0.336037 + 0.194011i
\(203\) 3.81796 5.74469i 0.267969 0.403198i
\(204\) −1.49417 + 9.79335i −0.104613 + 0.685672i
\(205\) 12.4390 0.868780
\(206\) −3.76752 + 6.52554i −0.262496 + 0.454656i
\(207\) 10.2043 2.29039i 0.709250 0.159193i
\(208\) 1.57532 0.909513i 0.109229 0.0630634i
\(209\) 3.52018 6.09713i 0.243496 0.421747i
\(210\) 0.974903 4.47767i 0.0672747 0.308989i
\(211\) −6.72807 11.6534i −0.463179 0.802250i 0.535938 0.844257i \(-0.319958\pi\)
−0.999117 + 0.0420072i \(0.986625\pi\)
\(212\) −0.844055 0.487315i −0.0579699 0.0334689i
\(213\) −4.17182 10.6862i −0.285849 0.732210i
\(214\) 9.05896 + 15.6906i 0.619257 + 1.07259i
\(215\) 2.45956 + 4.26008i 0.167740 + 0.290535i
\(216\) 4.66931 + 2.27981i 0.317706 + 0.155122i
\(217\) −23.5488 1.48500i −1.59860 0.100808i
\(218\) −3.06518 1.76968i −0.207600 0.119858i
\(219\) 14.7698 + 2.25343i 0.998050 + 0.152273i
\(220\) 5.67846i 0.382842i
\(221\) 10.4041i 0.699858i
\(222\) −4.38820 + 5.48232i −0.294516 + 0.367949i
\(223\) −9.11125 5.26038i −0.610135 0.352261i 0.162884 0.986645i \(-0.447921\pi\)
−0.773018 + 0.634384i \(0.781254\pi\)
\(224\) −2.64051 0.166511i −0.176426 0.0111255i
\(225\) −2.86351 0.894597i −0.190901 0.0596398i
\(226\) 3.12456 + 5.41190i 0.207843 + 0.359994i
\(227\) −14.5390 25.1823i −0.964987 1.67141i −0.709651 0.704554i \(-0.751147\pi\)
−0.255336 0.966852i \(-0.582186\pi\)
\(228\) 1.34194 1.67653i 0.0888723 0.111031i
\(229\) 7.36868 + 4.25431i 0.486936 + 0.281133i 0.723302 0.690531i \(-0.242623\pi\)
−0.236367 + 0.971664i \(0.575957\pi\)
\(230\) 1.74303 + 3.01902i 0.114932 + 0.199069i
\(231\) −19.2519 17.5074i −1.26668 1.15190i
\(232\) −1.30354 + 2.25780i −0.0855818 + 0.148232i
\(233\) −22.5702 + 13.0309i −1.47863 + 0.853685i −0.999708 0.0241753i \(-0.992304\pi\)
−0.478917 + 0.877860i \(0.658971\pi\)
\(234\) 5.20880 + 1.62730i 0.340510 + 0.106380i
\(235\) 5.02238 8.69903i 0.327624 0.567462i
\(236\) −11.3708 −0.740176
\(237\) 2.20505 0.860833i 0.143233 0.0559171i
\(238\) 8.37614 12.6031i 0.542944 0.816940i
\(239\) −13.6870 + 7.90222i −0.885341 + 0.511152i −0.872416 0.488764i \(-0.837448\pi\)
−0.0129256 + 0.999916i \(0.504114\pi\)
\(240\) −0.261236 + 1.71224i −0.0168627 + 0.110524i
\(241\) −4.20612 + 2.42841i −0.270940 + 0.156427i −0.629315 0.777150i \(-0.716664\pi\)
0.358375 + 0.933578i \(0.383331\pi\)
\(242\) 18.3987 + 10.6225i 1.18271 + 0.682838i
\(243\) 4.46031 + 14.9367i 0.286129 + 0.958191i
\(244\) 7.44834i 0.476831i
\(245\) −4.23381 + 5.57448i −0.270488 + 0.356141i
\(246\) 13.4635 16.8203i 0.858399 1.07243i
\(247\) 1.12765 1.95314i 0.0717504 0.124275i
\(248\) 8.91829 0.566312
\(249\) 3.16056 20.7154i 0.200292 1.31279i
\(250\) 1.00000i 0.0632456i
\(251\) −21.6259 −1.36502 −0.682508 0.730879i \(-0.739111\pi\)
−0.682508 + 0.730879i \(0.739111\pi\)
\(252\) −4.99962 6.16472i −0.314946 0.388341i
\(253\) 19.7955 1.24453
\(254\) 19.0703i 1.19658i
\(255\) −7.73420 6.19067i −0.484335 0.387675i
\(256\) 1.00000 0.0625000
\(257\) 2.44084 4.22766i 0.152255 0.263714i −0.779801 0.626028i \(-0.784680\pi\)
0.932056 + 0.362314i \(0.118013\pi\)
\(258\) 8.42269 + 1.28505i 0.524374 + 0.0800038i
\(259\) 9.60870 4.76806i 0.597056 0.296273i
\(260\) 1.81903i 0.112811i
\(261\) −7.63139 + 1.71289i −0.472371 + 0.106025i
\(262\) −0.111961 0.0646409i −0.00691699 0.00399353i
\(263\) −12.3336 + 7.12083i −0.760524 + 0.439089i −0.829484 0.558530i \(-0.811365\pi\)
0.0689596 + 0.997619i \(0.478032\pi\)
\(264\) 7.67855 + 6.14612i 0.472582 + 0.378267i
\(265\) 0.844055 0.487315i 0.0518499 0.0299355i
\(266\) −2.93841 + 1.45811i −0.180165 + 0.0894023i
\(267\) 21.3313 + 17.0742i 1.30545 + 1.04492i
\(268\) 0.0689019 0.00420885
\(269\) 11.3169 19.6014i 0.690003 1.19512i −0.281834 0.959463i \(-0.590943\pi\)
0.971836 0.235656i \(-0.0757240\pi\)
\(270\) −4.30903 + 2.90383i −0.262239 + 0.176722i
\(271\) 6.61815 3.82099i 0.402024 0.232109i −0.285333 0.958428i \(-0.592104\pi\)
0.687357 + 0.726320i \(0.258771\pi\)
\(272\) −2.85981 + 4.95334i −0.173402 + 0.300340i
\(273\) −6.16710 5.60829i −0.373250 0.339429i
\(274\) 3.99184 + 6.91408i 0.241156 + 0.417695i
\(275\) −4.91769 2.83923i −0.296548 0.171212i
\(276\) 5.96898 + 0.910688i 0.359290 + 0.0548170i
\(277\) 6.26276 + 10.8474i 0.376293 + 0.651758i 0.990520 0.137372i \(-0.0438654\pi\)
−0.614227 + 0.789129i \(0.710532\pi\)
\(278\) −2.62336 4.54379i −0.157339 0.272519i
\(279\) 18.1271 + 19.6782i 1.08524 + 1.17810i
\(280\) 1.46446 2.20349i 0.0875180 0.131684i
\(281\) 18.6742 + 10.7815i 1.11401 + 0.643172i 0.939864 0.341548i \(-0.110951\pi\)
0.174143 + 0.984720i \(0.444284\pi\)
\(282\) −6.32701 16.2068i −0.376768 0.965102i
\(283\) 27.4419i 1.63125i 0.578581 + 0.815625i \(0.303607\pi\)
−0.578581 + 0.815625i \(0.696393\pi\)
\(284\) 6.62319i 0.393014i
\(285\) 0.780949 + 2.00042i 0.0462594 + 0.118495i
\(286\) 8.94541 + 5.16464i 0.528953 + 0.305391i
\(287\) −29.4805 + 14.6289i −1.74018 + 0.863519i
\(288\) 2.03258 + 2.20650i 0.119771 + 0.130019i
\(289\) −7.85704 13.6088i −0.462179 0.800517i
\(290\) −1.30354 2.25780i −0.0765467 0.132583i
\(291\) 3.31997 + 0.506528i 0.194620 + 0.0296932i
\(292\) 7.47035 + 4.31301i 0.437169 + 0.252400i
\(293\) −11.5161 19.9464i −0.672776 1.16528i −0.977114 0.212718i \(-0.931768\pi\)
0.304337 0.952564i \(-0.401565\pi\)
\(294\) 2.95545 + 11.7586i 0.172365 + 0.685777i
\(295\) 5.68540 9.84741i 0.331017 0.573338i
\(296\) −3.51113 + 2.02715i −0.204080 + 0.117826i
\(297\) 2.04582 + 29.4352i 0.118710 + 1.70800i
\(298\) −7.95281 + 13.7747i −0.460694 + 0.797946i
\(299\) 6.34125 0.366724
\(300\) −1.35222 1.08236i −0.0780706 0.0624898i
\(301\) −10.8392 7.20383i −0.624762 0.415222i
\(302\) 16.9589 9.79120i 0.975873 0.563421i
\(303\) −7.45729 5.96902i −0.428410 0.342911i
\(304\) 1.07373 0.619917i 0.0615825 0.0355547i
\(305\) −6.45045 3.72417i −0.369352 0.213245i
\(306\) −16.7423 + 3.75786i −0.957095 + 0.214823i
\(307\) 14.6153i 0.834137i −0.908875 0.417069i \(-0.863057\pi\)
0.908875 0.417069i \(-0.136943\pi\)
\(308\) −6.67816 13.4580i −0.380523 0.766839i
\(309\) −12.9018 1.96843i −0.733957 0.111980i
\(310\) −4.45915 + 7.72347i −0.253262 + 0.438664i
\(311\) 4.33309 0.245707 0.122853 0.992425i \(-0.460796\pi\)
0.122853 + 0.992425i \(0.460796\pi\)
\(312\) 2.45973 + 1.96883i 0.139255 + 0.111463i
\(313\) 9.03514i 0.510697i −0.966849 0.255348i \(-0.917810\pi\)
0.966849 0.255348i \(-0.0821901\pi\)
\(314\) −16.3621 −0.923370
\(315\) 7.83862 1.24744i 0.441656 0.0702851i
\(316\) 1.36666 0.0768806
\(317\) 19.3816i 1.08858i −0.838897 0.544289i \(-0.816799\pi\)
0.838897 0.544289i \(-0.183201\pi\)
\(318\) 0.254609 1.66880i 0.0142778 0.0935816i
\(319\) −14.8042 −0.828879
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) −19.6100 + 24.4994i −1.09452 + 1.36743i
\(322\) −7.68152 5.10520i −0.428074 0.284501i
\(323\) 7.09139i 0.394575i
\(324\) −0.737278 + 8.96975i −0.0409599 + 0.498319i
\(325\) −1.57532 0.909513i −0.0873832 0.0504507i
\(326\) 11.4143 6.59007i 0.632182 0.364990i
\(327\) 0.924611 6.06024i 0.0511311 0.335132i
\(328\) 10.7725 6.21952i 0.594813 0.343416i
\(329\) −1.67257 + 26.5233i −0.0922116 + 1.46228i
\(330\) −9.16197 + 3.57676i −0.504350 + 0.196894i
\(331\) 8.35472 0.459217 0.229608 0.973283i \(-0.426255\pi\)
0.229608 + 0.973283i \(0.426255\pi\)
\(332\) 6.04923 10.4776i 0.331995 0.575032i
\(333\) −11.6095 3.62697i −0.636199 0.198756i
\(334\) 4.87151 2.81257i 0.266557 0.153897i
\(335\) −0.0344509 + 0.0596708i −0.00188226 + 0.00326016i
\(336\) −1.39455 4.36523i −0.0760787 0.238143i
\(337\) −16.8897 29.2538i −0.920039 1.59355i −0.799351 0.600864i \(-0.794823\pi\)
−0.120688 0.992690i \(-0.538510\pi\)
\(338\) −8.39278 4.84557i −0.456507 0.263564i
\(339\) −6.76378 + 8.45021i −0.367358 + 0.458952i
\(340\) −2.85981 4.95334i −0.155095 0.268632i
\(341\) 25.3211 + 43.8574i 1.37121 + 2.37501i
\(342\) 3.55028 + 1.10915i 0.191977 + 0.0599761i
\(343\) 3.47827 18.1907i 0.187809 0.982206i
\(344\) 4.26008 + 2.45956i 0.229688 + 0.132610i
\(345\) −3.77317 + 4.71394i −0.203141 + 0.253790i
\(346\) 7.96037i 0.427952i
\(347\) 11.3240i 0.607906i 0.952687 + 0.303953i \(0.0983066\pi\)
−0.952687 + 0.303953i \(0.901693\pi\)
\(348\) −4.46395 0.681066i −0.239293 0.0365090i
\(349\) −3.37360 1.94775i −0.180585 0.104261i 0.406983 0.913436i \(-0.366581\pi\)
−0.587567 + 0.809175i \(0.699914\pi\)
\(350\) 1.17605 + 2.37000i 0.0628625 + 0.126682i
\(351\) 0.655353 + 9.42919i 0.0349802 + 0.503293i
\(352\) 2.83923 + 4.91769i 0.151332 + 0.262114i
\(353\) −14.3522 24.8588i −0.763892 1.32310i −0.940830 0.338878i \(-0.889953\pi\)
0.176938 0.984222i \(-0.443381\pi\)
\(354\) −7.16226 18.3463i −0.380670 0.975096i
\(355\) 5.73585 + 3.31160i 0.304427 + 0.175761i
\(356\) 7.88750 + 13.6615i 0.418037 + 0.724061i
\(357\) 25.6106 + 5.57608i 1.35546 + 0.295117i
\(358\) −3.46206 + 5.99647i −0.182976 + 0.316923i
\(359\) −2.00897 + 1.15988i −0.106029 + 0.0612161i −0.552077 0.833793i \(-0.686165\pi\)
0.446048 + 0.895009i \(0.352831\pi\)
\(360\) −2.92717 + 0.657012i −0.154276 + 0.0346276i
\(361\) −8.73140 + 15.1232i −0.459548 + 0.795960i
\(362\) 2.78183 0.146210
\(363\) −5.54995 + 36.3764i −0.291297 + 1.90926i
\(364\) −2.13927 4.31109i −0.112128 0.225963i
\(365\) −7.47035 + 4.31301i −0.391016 + 0.225753i
\(366\) −12.0176 + 4.69157i −0.628170 + 0.245232i
\(367\) −11.4932 + 6.63561i −0.599941 + 0.346376i −0.769018 0.639227i \(-0.779255\pi\)
0.169077 + 0.985603i \(0.445921\pi\)
\(368\) 3.01902 + 1.74303i 0.157378 + 0.0908620i
\(369\) 35.6193 + 11.1279i 1.85427 + 0.579297i
\(370\) 4.05430i 0.210773i
\(371\) −1.42730 + 2.14759i −0.0741019 + 0.111497i
\(372\) 5.61747 + 14.3893i 0.291252 + 0.746050i
\(373\) 2.07132 3.58763i 0.107249 0.185760i −0.807406 0.589996i \(-0.799129\pi\)
0.914655 + 0.404236i \(0.132463\pi\)
\(374\) −32.4787 −1.67943
\(375\) 1.61346 0.629881i 0.0833187 0.0325269i
\(376\) 10.0448i 0.518019i
\(377\) −4.74236 −0.244244
\(378\) 6.79736 11.9497i 0.349618 0.614628i
\(379\) 6.21425 0.319204 0.159602 0.987181i \(-0.448979\pi\)
0.159602 + 0.987181i \(0.448979\pi\)
\(380\) 1.23983i 0.0636022i
\(381\) −30.7692 + 12.0121i −1.57635 + 0.615396i
\(382\) −3.02993 −0.155025
\(383\) 6.81820 11.8095i 0.348394 0.603435i −0.637571 0.770392i \(-0.720061\pi\)
0.985964 + 0.166957i \(0.0533940\pi\)
\(384\) 0.629881 + 1.61346i 0.0321435 + 0.0823365i
\(385\) 14.9940 + 0.945528i 0.764166 + 0.0481886i
\(386\) 3.52611i 0.179474i
\(387\) 3.23192 + 14.3991i 0.164288 + 0.731947i
\(388\) 1.67919 + 0.969482i 0.0852481 + 0.0492180i
\(389\) 25.3739 14.6496i 1.28651 0.742766i 0.308479 0.951231i \(-0.400180\pi\)
0.978030 + 0.208465i \(0.0668467\pi\)
\(390\) −2.93492 + 1.14577i −0.148616 + 0.0580184i
\(391\) −17.2677 + 9.96950i −0.873264 + 0.504179i
\(392\) −0.879348 + 6.94455i −0.0444138 + 0.350753i
\(393\) 0.0337731 0.221361i 0.00170363 0.0111662i
\(394\) 9.09265 0.458081
\(395\) −0.683330 + 1.18356i −0.0343820 + 0.0595514i
\(396\) −5.07994 + 16.2603i −0.255276 + 0.817113i
\(397\) 9.62007 5.55415i 0.482817 0.278755i −0.238772 0.971076i \(-0.576745\pi\)
0.721590 + 0.692321i \(0.243412\pi\)
\(398\) 7.23082 12.5241i 0.362448 0.627778i
\(399\) −4.20345 3.82257i −0.210436 0.191368i
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) −1.25249 0.723128i −0.0625466 0.0361113i 0.468401 0.883516i \(-0.344830\pi\)
−0.530947 + 0.847405i \(0.678164\pi\)
\(402\) 0.0434000 + 0.111170i 0.00216459 + 0.00554467i
\(403\) 8.11131 + 14.0492i 0.404053 + 0.699840i
\(404\) −2.75742 4.77599i −0.137187 0.237614i
\(405\) −7.39939 5.12338i −0.367679 0.254583i
\(406\) 5.74469 + 3.81796i 0.285104 + 0.189482i
\(407\) −19.9378 11.5111i −0.988281 0.570584i
\(408\) −9.79335 1.49417i −0.484843 0.0739726i
\(409\) 16.2396i 0.802996i −0.915860 0.401498i \(-0.868490\pi\)
0.915860 0.401498i \(-0.131510\pi\)
\(410\) 12.4390i 0.614320i
\(411\) −8.64119 + 10.7957i −0.426239 + 0.532514i
\(412\) −6.52554 3.76752i −0.321490 0.185612i
\(413\) −1.89337 + 30.0247i −0.0931665 + 1.47742i
\(414\) 2.29039 + 10.2043i 0.112567 + 0.501515i
\(415\) 6.04923 + 10.4776i 0.296945 + 0.514324i
\(416\) 0.909513 + 1.57532i 0.0445926 + 0.0772366i
\(417\) 5.67882 7.09474i 0.278093 0.347431i
\(418\) 6.09713 + 3.52018i 0.298220 + 0.172178i
\(419\) 4.24495 + 7.35247i 0.207379 + 0.359192i 0.950888 0.309534i \(-0.100173\pi\)
−0.743509 + 0.668726i \(0.766840\pi\)
\(420\) 4.47767 + 0.974903i 0.218488 + 0.0475704i
\(421\) 0.808166 1.39979i 0.0393876 0.0682214i −0.845660 0.533723i \(-0.820793\pi\)
0.885047 + 0.465501i \(0.154126\pi\)
\(422\) 11.6534 6.72807i 0.567277 0.327517i
\(423\) 22.1638 20.4167i 1.07764 0.992696i
\(424\) 0.487315 0.844055i 0.0236661 0.0409909i
\(425\) 5.71962 0.277442
\(426\) 10.6862 4.17182i 0.517750 0.202126i
\(427\) 19.6674 + 1.24023i 0.951772 + 0.0600191i
\(428\) −15.6906 + 9.05896i −0.758432 + 0.437881i
\(429\) −2.69838 + 17.6862i −0.130279 + 0.853896i
\(430\) −4.26008 + 2.45956i −0.205439 + 0.118610i
\(431\) 20.0356 + 11.5676i 0.965081 + 0.557190i 0.897733 0.440540i \(-0.145213\pi\)
0.0673476 + 0.997730i \(0.478546\pi\)
\(432\) −2.27981 + 4.66931i −0.109688 + 0.224652i
\(433\) 2.88532i 0.138660i 0.997594 + 0.0693299i \(0.0220861\pi\)
−0.997594 + 0.0693299i \(0.977914\pi\)
\(434\) 1.48500 23.5488i 0.0712821 1.13038i
\(435\) 2.82180 3.52536i 0.135295 0.169028i
\(436\) 1.76968 3.06518i 0.0847525 0.146796i
\(437\) 4.32215 0.206756
\(438\) −2.25343 + 14.7698i −0.107673 + 0.705728i
\(439\) 5.18281i 0.247362i −0.992322 0.123681i \(-0.960530\pi\)
0.992322 0.123681i \(-0.0394699\pi\)
\(440\) −5.67846 −0.270710
\(441\) −17.1105 + 12.1750i −0.814785 + 0.579764i
\(442\) −10.4041 −0.494875
\(443\) 18.7790i 0.892215i −0.894979 0.446108i \(-0.852810\pi\)
0.894979 0.446108i \(-0.147190\pi\)
\(444\) −5.48232 4.38820i −0.260179 0.208255i
\(445\) −15.7750 −0.747807
\(446\) 5.26038 9.11125i 0.249086 0.431430i
\(447\) −27.2342 4.15513i −1.28813 0.196531i
\(448\) 0.166511 2.64051i 0.00786692 0.124752i
\(449\) 23.1775i 1.09381i −0.837194 0.546907i \(-0.815805\pi\)
0.837194 0.546907i \(-0.184195\pi\)
\(450\) 0.894597 2.86351i 0.0421717 0.134987i
\(451\) 61.1714 + 35.3173i 2.88045 + 1.66303i
\(452\) −5.41190 + 3.12456i −0.254554 + 0.146967i
\(453\) 26.4798 + 21.1951i 1.24413 + 0.995834i
\(454\) 25.1823 14.5390i 1.18186 0.682349i
\(455\) 4.80315 + 0.302888i 0.225175 + 0.0141996i
\(456\) 1.67653 + 1.34194i 0.0785108 + 0.0628422i
\(457\) 19.7423 0.923506 0.461753 0.887008i \(-0.347221\pi\)
0.461753 + 0.887008i \(0.347221\pi\)
\(458\) −4.25431 + 7.36868i −0.198791 + 0.344316i
\(459\) −16.6088 24.6460i −0.775234 1.15038i
\(460\) −3.01902 + 1.74303i −0.140763 + 0.0812694i
\(461\) 6.37073 11.0344i 0.296714 0.513924i −0.678668 0.734445i \(-0.737442\pi\)
0.975382 + 0.220521i \(0.0707758\pi\)
\(462\) 17.5074 19.2519i 0.814519 0.895677i
\(463\) 6.41119 + 11.1045i 0.297953 + 0.516070i 0.975668 0.219255i \(-0.0703627\pi\)
−0.677714 + 0.735325i \(0.737029\pi\)
\(464\) −2.25780 1.30354i −0.104816 0.0605155i
\(465\) −15.2702 2.32978i −0.708140 0.108041i
\(466\) −13.0309 22.5702i −0.603646 1.04555i
\(467\) −2.77900 4.81337i −0.128597 0.222736i 0.794536 0.607217i \(-0.207714\pi\)
−0.923133 + 0.384480i \(0.874381\pi\)
\(468\) −1.62730 + 5.20880i −0.0752218 + 0.240777i
\(469\) 0.0114729 0.181936i 0.000529771 0.00840101i
\(470\) 8.69903 + 5.02238i 0.401256 + 0.231665i
\(471\) −10.3062 26.3997i −0.474885 1.21643i
\(472\) 11.3708i 0.523384i
\(473\) 27.9330i 1.28436i
\(474\) 0.860833 + 2.20505i 0.0395394 + 0.101281i
\(475\) −1.07373 0.619917i −0.0492660 0.0284438i
\(476\) 12.6031 + 8.37614i 0.577664 + 0.383920i
\(477\) 2.85291 0.640344i 0.130626 0.0293193i
\(478\) −7.90222 13.6870i −0.361439 0.626031i
\(479\) 2.87590 + 4.98120i 0.131403 + 0.227597i 0.924218 0.381866i \(-0.124718\pi\)
−0.792815 + 0.609463i \(0.791385\pi\)
\(480\) −1.71224 0.261236i −0.0781526 0.0119238i
\(481\) −6.38683 3.68744i −0.291215 0.168133i
\(482\) −2.42841 4.20612i −0.110611 0.191584i
\(483\) 3.39858 15.6095i 0.154641 0.710256i
\(484\) −10.6225 + 18.3987i −0.482840 + 0.836303i
\(485\) −1.67919 + 0.969482i −0.0762482 + 0.0440219i
\(486\) −14.9367 + 4.46031i −0.677543 + 0.202324i
\(487\) −15.3840 + 26.6459i −0.697116 + 1.20744i 0.272346 + 0.962199i \(0.412200\pi\)
−0.969462 + 0.245241i \(0.921133\pi\)
\(488\) −7.44834 −0.337171
\(489\) 17.8225 + 14.2656i 0.805961 + 0.645113i
\(490\) −5.57448 4.23381i −0.251829 0.191264i
\(491\) −12.6416 + 7.29865i −0.570509 + 0.329383i −0.757353 0.653006i \(-0.773508\pi\)
0.186844 + 0.982390i \(0.440174\pi\)
\(492\) 16.8203 + 13.4635i 0.758320 + 0.606980i
\(493\) 12.9138 7.45578i 0.581608 0.335791i
\(494\) 1.95314 + 1.12765i 0.0878759 + 0.0507352i
\(495\) −11.5419 12.5295i −0.518770 0.563160i
\(496\) 8.91829i 0.400443i
\(497\) −17.4886 1.10284i −0.784470 0.0494689i
\(498\) 20.7154 + 3.16056i 0.928281 + 0.141628i
\(499\) 7.38881 12.7978i 0.330768 0.572908i −0.651894 0.758310i \(-0.726025\pi\)
0.982663 + 0.185402i \(0.0593588\pi\)
\(500\) 1.00000 0.0447214
\(501\) 7.60643 + 6.08840i 0.339830 + 0.272009i
\(502\) 21.6259i 0.965211i
\(503\) 12.4283 0.554152 0.277076 0.960848i \(-0.410635\pi\)
0.277076 + 0.960848i \(0.410635\pi\)
\(504\) 6.16472 4.99962i 0.274599 0.222701i
\(505\) 5.51484 0.245407
\(506\) 19.7955i 0.880018i
\(507\) 2.53168 16.5935i 0.112436 0.736945i
\(508\) −19.0703 −0.846110
\(509\) 13.0624 22.6248i 0.578982 1.00283i −0.416614 0.909083i \(-0.636783\pi\)
0.995596 0.0937432i \(-0.0298833\pi\)
\(510\) 6.19067 7.73420i 0.274127 0.342476i
\(511\) 12.6324 19.0074i 0.558826 0.840836i
\(512\) 1.00000i 0.0441942i
\(513\) 0.446684 + 6.42687i 0.0197216 + 0.283753i
\(514\) 4.22766 + 2.44084i 0.186474 + 0.107661i
\(515\) 6.52554 3.76752i 0.287550 0.166017i
\(516\) −1.28505 + 8.42269i −0.0565712 + 0.370788i
\(517\) 49.3971 28.5194i 2.17248 1.25428i
\(518\) 4.76806 + 9.60870i 0.209497 + 0.422182i
\(519\) 12.8437 5.01409i 0.563778 0.220094i
\(520\) −1.81903 −0.0797696
\(521\) −1.65977 + 2.87480i −0.0727157 + 0.125947i −0.900091 0.435703i \(-0.856500\pi\)
0.827375 + 0.561650i \(0.189833\pi\)
\(522\) −1.71289 7.63139i −0.0749710 0.334017i
\(523\) −26.8169 + 15.4828i −1.17262 + 0.677014i −0.954296 0.298862i \(-0.903393\pi\)
−0.218326 + 0.975876i \(0.570060\pi\)
\(524\) 0.0646409 0.111961i 0.00282385 0.00489105i
\(525\) −3.08313 + 3.39033i −0.134559 + 0.147966i
\(526\) −7.12083 12.3336i −0.310483 0.537772i
\(527\) −44.1753 25.5046i −1.92431 1.11100i
\(528\) −6.14612 + 7.67855i −0.267475 + 0.334166i
\(529\) −5.42366 9.39405i −0.235811 0.408437i
\(530\) 0.487315 + 0.844055i 0.0211676 + 0.0366634i
\(531\) 25.0897 23.1120i 1.08880 1.00298i
\(532\) −1.45811 2.93841i −0.0632170 0.127396i
\(533\) 19.5955 + 11.3135i 0.848775 + 0.490041i
\(534\) −17.0742 + 21.3313i −0.738871 + 0.923096i
\(535\) 18.1179i 0.783306i
\(536\) 0.0689019i 0.00297611i
\(537\) −11.8557 1.80883i −0.511613 0.0780569i
\(538\) 19.6014 + 11.3169i 0.845077 + 0.487906i
\(539\) −36.6478 + 15.3928i −1.57853 + 0.663016i
\(540\) −2.90383 4.30903i −0.124961 0.185431i
\(541\) −16.6857 28.9005i −0.717375 1.24253i −0.962036 0.272921i \(-0.912010\pi\)
0.244662 0.969608i \(-0.421323\pi\)
\(542\) 3.82099 + 6.61815i 0.164126 + 0.284274i
\(543\) 1.75222 + 4.48836i 0.0751950 + 0.192614i
\(544\) −4.95334 2.85981i −0.212373 0.122613i
\(545\) 1.76968 + 3.06518i 0.0758049 + 0.131298i
\(546\) 5.60829 6.16710i 0.240013 0.263927i
\(547\) 0.847928 1.46865i 0.0362548 0.0627951i −0.847329 0.531069i \(-0.821791\pi\)
0.883583 + 0.468274i \(0.155124\pi\)
\(548\) −6.91408 + 3.99184i −0.295355 + 0.170523i
\(549\) −15.1393 16.4348i −0.646130 0.701418i
\(550\) 2.83923 4.91769i 0.121065 0.209691i
\(551\) −3.23236 −0.137703
\(552\) −0.910688 + 5.96898i −0.0387614 + 0.254057i
\(553\) 0.227564 3.60867i 0.00967701 0.153456i
\(554\) −10.8474 + 6.26276i −0.460862 + 0.266079i
\(555\) 6.54145 2.55373i 0.277669 0.108400i
\(556\) 4.54379 2.62336i 0.192700 0.111255i
\(557\) −28.4998 16.4544i −1.20757 0.697194i −0.245346 0.969436i \(-0.578902\pi\)
−0.962229 + 0.272242i \(0.912235\pi\)
\(558\) −19.6782 + 18.1271i −0.833045 + 0.767381i
\(559\) 8.94800i 0.378460i
\(560\) 2.20349 + 1.46446i 0.0931144 + 0.0618846i
\(561\) −20.4577 52.4030i −0.863725 2.21246i
\(562\) −10.7815 + 18.6742i −0.454792 + 0.787722i
\(563\) 31.7973 1.34010 0.670048 0.742318i \(-0.266273\pi\)
0.670048 + 0.742318i \(0.266273\pi\)
\(564\) 16.2068 6.32701i 0.682430 0.266415i
\(565\) 6.24913i 0.262903i
\(566\) −27.4419 −1.15347
\(567\) 23.5619 + 3.44035i 0.989508 + 0.144481i
\(568\) 6.62319 0.277903
\(569\) 38.0755i 1.59621i 0.602519 + 0.798105i \(0.294164\pi\)
−0.602519 + 0.798105i \(0.705836\pi\)
\(570\) −2.00042 + 0.780949i −0.0837885 + 0.0327103i
\(571\) −1.98160 −0.0829274 −0.0414637 0.999140i \(-0.513202\pi\)
−0.0414637 + 0.999140i \(0.513202\pi\)
\(572\) −5.16464 + 8.94541i −0.215944 + 0.374027i
\(573\) −1.90850 4.88867i −0.0797286 0.204227i
\(574\) −14.6289 29.4805i −0.610600 1.23049i
\(575\) 3.48607i 0.145379i
\(576\) −2.20650 + 2.03258i −0.0919375 + 0.0846906i
\(577\) −5.04572 2.91315i −0.210056 0.121276i 0.391281 0.920271i \(-0.372032\pi\)
−0.601337 + 0.798995i \(0.705365\pi\)
\(578\) 13.6088 7.85704i 0.566051 0.326810i
\(579\) 5.68923 2.22103i 0.236436 0.0923028i
\(580\) 2.25780 1.30354i 0.0937502 0.0541267i
\(581\) −26.6588 17.7177i −1.10599 0.735053i
\(582\) −0.506528 + 3.31997i −0.0209963 + 0.137617i
\(583\) 5.53440 0.229212
\(584\) −4.31301 + 7.47035i −0.178474 + 0.309125i
\(585\) −3.69731 4.01368i −0.152865 0.165945i
\(586\) 19.9464 11.5161i 0.823979 0.475725i
\(587\) −0.0736389 + 0.127546i −0.00303940 + 0.00526440i −0.867541 0.497365i \(-0.834301\pi\)
0.864502 + 0.502630i \(0.167634\pi\)
\(588\) −11.7586 + 2.95545i −0.484918 + 0.121881i
\(589\) 5.52860 + 9.57582i 0.227802 + 0.394565i
\(590\) 9.84741 + 5.68540i 0.405411 + 0.234064i
\(591\) 5.72729 + 14.6706i 0.235589 + 0.603469i
\(592\) −2.02715 3.51113i −0.0833154 0.144306i
\(593\) −5.61919 9.73273i −0.230753 0.399675i 0.727277 0.686344i \(-0.240785\pi\)
−0.958030 + 0.286669i \(0.907452\pi\)
\(594\) −29.4352 + 2.04582i −1.20774 + 0.0839409i
\(595\) −13.5555 + 6.72656i −0.555722 + 0.275762i
\(596\) −13.7747 7.95281i −0.564233 0.325760i
\(597\) 24.7617 + 3.77790i 1.01343 + 0.154619i
\(598\) 6.34125i 0.259313i
\(599\) 20.7903i 0.849470i 0.905318 + 0.424735i \(0.139633\pi\)
−0.905318 + 0.424735i \(0.860367\pi\)
\(600\) 1.08236 1.35222i 0.0441870 0.0552043i
\(601\) 8.15985 + 4.71109i 0.332847 + 0.192169i 0.657104 0.753800i \(-0.271781\pi\)
−0.324257 + 0.945969i \(0.605114\pi\)
\(602\) 7.20383 10.8392i 0.293606 0.441773i
\(603\) −0.152032 + 0.140048i −0.00619122 + 0.00570320i
\(604\) 9.79120 + 16.9589i 0.398398 + 0.690046i
\(605\) −10.6225 18.3987i −0.431865 0.748012i
\(606\) 5.96902 7.45729i 0.242475 0.302932i
\(607\) −37.6028 21.7100i −1.52625 0.881182i −0.999515 0.0311539i \(-0.990082\pi\)
−0.526737 0.850028i \(-0.676585\pi\)
\(608\) 0.619917 + 1.07373i 0.0251410 + 0.0435454i
\(609\) −2.54166 + 11.6737i −0.102993 + 0.473042i
\(610\) 3.72417 6.45045i 0.150787 0.261171i
\(611\) 15.8238 9.13585i 0.640161 0.369597i
\(612\) −3.75786 16.7423i −0.151902 0.676768i
\(613\) 4.95622 8.58442i 0.200180 0.346722i −0.748406 0.663240i \(-0.769181\pi\)
0.948586 + 0.316519i \(0.102514\pi\)
\(614\) 14.6153 0.589824
\(615\) −20.0699 + 7.83512i −0.809296 + 0.315942i
\(616\) 13.4580 6.67816i 0.542237 0.269071i
\(617\) 32.9309 19.0126i 1.32575 0.765420i 0.341108 0.940024i \(-0.389198\pi\)
0.984639 + 0.174604i \(0.0558645\pi\)
\(618\) 1.96843 12.9018i 0.0791817 0.518986i
\(619\) −35.4802 + 20.4845i −1.42607 + 0.823341i −0.996808 0.0798398i \(-0.974559\pi\)
−0.429261 + 0.903181i \(0.641226\pi\)
\(620\) −7.72347 4.45915i −0.310182 0.179084i
\(621\) −15.0216 + 10.1230i −0.602795 + 0.406220i
\(622\) 4.33309i 0.173741i
\(623\) 37.3868 18.5522i 1.49787 0.743278i
\(624\) −1.96883 + 2.45973i −0.0788164 + 0.0984679i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 9.03514 0.361117
\(627\) −1.83920 + 12.0548i −0.0734504 + 0.481421i
\(628\) 16.3621i 0.652921i
\(629\) 23.1891 0.924609
\(630\) 1.24744 + 7.83862i 0.0496991 + 0.312298i
\(631\) 47.1379 1.87653 0.938265 0.345917i \(-0.112432\pi\)
0.938265 + 0.345917i \(0.112432\pi\)
\(632\) 1.36666i 0.0543628i
\(633\) 18.1957 + 14.5643i 0.723214 + 0.578880i
\(634\) 19.3816 0.769742
\(635\) 9.53517 16.5154i 0.378392 0.655394i
\(636\) 1.66880 + 0.254609i 0.0661722 + 0.0100959i
\(637\) −11.7397 + 4.93090i −0.465143 + 0.195369i
\(638\) 14.8042i 0.586106i
\(639\) 13.4621 + 14.6141i 0.532554 + 0.578123i
\(640\) −0.866025 0.500000i −0.0342327 0.0197642i
\(641\) −27.5136 + 15.8850i −1.08672 + 0.627418i −0.932701 0.360649i \(-0.882555\pi\)
−0.154019 + 0.988068i \(0.549222\pi\)
\(642\) −24.4994 19.6100i −0.966916 0.773946i
\(643\) −22.8044 + 13.1661i −0.899319 + 0.519222i −0.876979 0.480528i \(-0.840445\pi\)
−0.0223397 + 0.999750i \(0.507112\pi\)
\(644\) 5.10520 7.68152i 0.201173 0.302694i
\(645\) −6.65174 5.32423i −0.261912 0.209641i
\(646\) −7.09139 −0.279007
\(647\) 14.6898 25.4435i 0.577517 1.00029i −0.418247 0.908333i \(-0.637355\pi\)
0.995763 0.0919545i \(-0.0293114\pi\)
\(648\) −8.96975 0.737278i −0.352365 0.0289630i
\(649\) 55.9181 32.2843i 2.19498 1.26727i
\(650\) 0.909513 1.57532i 0.0356740 0.0617893i
\(651\) 38.9304 12.4370i 1.52580 0.487443i
\(652\) 6.59007 + 11.4143i 0.258087 + 0.447020i
\(653\) 16.0056 + 9.24086i 0.626349 + 0.361623i 0.779337 0.626605i \(-0.215556\pi\)
−0.152988 + 0.988228i \(0.548889\pi\)
\(654\) 6.06024 + 0.924611i 0.236974 + 0.0361552i
\(655\) 0.0646409 + 0.111961i 0.00252573 + 0.00437469i
\(656\) 6.21952 + 10.7725i 0.242831 + 0.420596i
\(657\) −25.2498 + 5.66740i −0.985090 + 0.221106i
\(658\) −26.5233 1.67257i −1.03399 0.0652034i
\(659\) −26.9328 15.5497i −1.04915 0.605729i −0.126741 0.991936i \(-0.540452\pi\)
−0.922412 + 0.386207i \(0.873785\pi\)
\(660\) −3.57676 9.16197i −0.139225 0.356629i
\(661\) 4.02105i 0.156401i −0.996938 0.0782003i \(-0.975083\pi\)
0.996938 0.0782003i \(-0.0249174\pi\)
\(662\) 8.35472i 0.324715i
\(663\) −6.55337 16.7867i −0.254512 0.651940i
\(664\) 10.4776 + 6.04923i 0.406609 + 0.234756i
\(665\) 3.27379 + 0.206446i 0.126952 + 0.00800565i
\(666\) 3.62697 11.6095i 0.140542 0.449860i
\(667\) −4.54424 7.87086i −0.175954 0.304761i
\(668\) 2.81257 + 4.87151i 0.108821 + 0.188484i
\(669\) 18.0140 + 2.74841i 0.696463 + 0.106260i
\(670\) −0.0596708 0.0344509i −0.00230528 0.00133096i
\(671\) −21.1476 36.6287i −0.816393 1.41403i
\(672\) 4.36523 1.39455i 0.168392 0.0537958i
\(673\) 3.92719 6.80209i 0.151382 0.262201i −0.780354 0.625338i \(-0.784961\pi\)
0.931736 + 0.363137i \(0.118294\pi\)
\(674\) 29.2538 16.8897i 1.12681 0.650566i
\(675\) 5.18365 0.360277i 0.199519 0.0138671i
\(676\) 4.84557 8.39278i 0.186368 0.322799i
\(677\) −33.9569 −1.30507 −0.652534 0.757760i \(-0.726294\pi\)
−0.652534 + 0.757760i \(0.726294\pi\)
\(678\) −8.45021 6.76378i −0.324528 0.259761i
\(679\) 2.83953 4.27249i 0.108971 0.163963i
\(680\) 4.95334 2.85981i 0.189952 0.109669i
\(681\) 39.3199 + 31.4727i 1.50674 + 1.20604i
\(682\) −43.8574 + 25.3211i −1.67939 + 0.969595i
\(683\) 5.22203 + 3.01494i 0.199815 + 0.115363i 0.596569 0.802562i \(-0.296530\pi\)
−0.396754 + 0.917925i \(0.629863\pi\)
\(684\) −1.10915 + 3.55028i −0.0424095 + 0.135748i
\(685\) 7.98369i 0.305041i
\(686\) 18.1907 + 3.47827i 0.694524 + 0.132801i
\(687\) −14.5688 2.22276i −0.555833 0.0848035i
\(688\) −2.45956 + 4.26008i −0.0937697 + 0.162414i
\(689\) 1.77288 0.0675413
\(690\) −4.71394 3.77317i −0.179457 0.143642i
\(691\) 17.6548i 0.671621i 0.941930 + 0.335811i \(0.109010\pi\)
−0.941930 + 0.335811i \(0.890990\pi\)
\(692\) 7.96037 0.302608
\(693\) 42.0897 + 16.1211i 1.59885 + 0.612391i
\(694\) −11.3240 −0.429854
\(695\) 5.24672i 0.199019i
\(696\) 0.681066 4.46395i 0.0258157 0.169206i
\(697\) −71.1466 −2.69487
\(698\) 1.94775 3.37360i 0.0737234 0.127693i
\(699\) 28.2082 35.2414i 1.06693 1.33295i
\(700\) −2.37000 + 1.17605i −0.0895776 + 0.0444505i
\(701\) 27.1258i 1.02453i 0.858828 + 0.512263i \(0.171193\pi\)
−0.858828 + 0.512263i \(0.828807\pi\)
\(702\) −9.42919 + 0.655353i −0.355882 + 0.0247347i
\(703\) −4.35322 2.51333i −0.164185 0.0947921i
\(704\) −4.91769 + 2.83923i −0.185343 + 0.107008i
\(705\) −2.62406 + 17.1990i −0.0988277 + 0.647753i
\(706\) 24.8588 14.3522i 0.935573 0.540153i
\(707\) −13.0702 + 6.48572i −0.491554 + 0.243921i
\(708\) 18.3463 7.16226i 0.689497 0.269174i
\(709\) 21.7165 0.815582 0.407791 0.913075i \(-0.366299\pi\)
0.407791 + 0.913075i \(0.366299\pi\)
\(710\) −3.31160 + 5.73585i −0.124282 + 0.215263i
\(711\) −3.01553 + 2.77784i −0.113091 + 0.104177i
\(712\) −13.6615 + 7.88750i −0.511988 + 0.295596i
\(713\) −15.5449 + 26.9245i −0.582161 + 1.00833i
\(714\) −5.57608 + 25.6106i −0.208679 + 0.958453i
\(715\) −5.16464 8.94541i −0.193146 0.334540i
\(716\) −5.99647 3.46206i −0.224098 0.129383i
\(717\) 17.1060 21.3711i 0.638836 0.798119i
\(718\) −1.15988 2.00897i −0.0432863 0.0749741i
\(719\) −13.2510 22.9514i −0.494178 0.855941i 0.505800 0.862651i \(-0.331198\pi\)
−0.999977 + 0.00670969i \(0.997864\pi\)
\(720\) −0.657012 2.92717i −0.0244854 0.109089i
\(721\) −11.0347 + 16.6034i −0.410955 + 0.618343i
\(722\) −15.1232 8.73140i −0.562829 0.324949i
\(723\) 5.25680 6.56749i 0.195503 0.244248i
\(724\) 2.78183i 0.103386i
\(725\) 2.60709i 0.0968248i
\(726\) −36.3764 5.54995i −1.35005 0.205978i
\(727\) 6.52916 + 3.76961i 0.242153 + 0.139807i 0.616166 0.787616i \(-0.288685\pi\)
−0.374013 + 0.927424i \(0.622018\pi\)
\(728\) 4.31109 2.13927i 0.159780 0.0792865i
\(729\) −16.6049 21.2903i −0.614996 0.788530i
\(730\) −4.31301 7.47035i −0.159632 0.276490i
\(731\) −14.0677 24.3660i −0.520314 0.901210i
\(732\) −4.69157 12.0176i −0.173405 0.444183i
\(733\) −18.3456 10.5918i −0.677610 0.391218i 0.121344 0.992611i \(-0.461280\pi\)
−0.798954 + 0.601392i \(0.794613\pi\)
\(734\) −6.63561 11.4932i −0.244925 0.424222i
\(735\) 3.31982 11.6610i 0.122453 0.430122i
\(736\) −1.74303 + 3.01902i −0.0642491 + 0.111283i
\(737\) −0.338838 + 0.195628i −0.0124813 + 0.00720606i
\(738\) −11.1279 + 35.6193i −0.409625 + 1.31117i
\(739\) −23.0621 + 39.9448i −0.848355 + 1.46939i 0.0343210 + 0.999411i \(0.489073\pi\)
−0.882676 + 0.469983i \(0.844260\pi\)
\(740\) 4.05430 0.149039
\(741\) −0.589164 + 3.86159i −0.0216435 + 0.141859i
\(742\) −2.14759 1.42730i −0.0788405 0.0523980i
\(743\) −33.6453 + 19.4252i −1.23433 + 0.712640i −0.967929 0.251223i \(-0.919167\pi\)
−0.266399 + 0.963863i \(0.585834\pi\)
\(744\) −14.3893 + 5.61747i −0.527537 + 0.205946i
\(745\) 13.7747 7.95281i 0.504665 0.291369i
\(746\) 3.58763 + 2.07132i 0.131352 + 0.0758364i
\(747\) 7.94883 + 35.4143i 0.290833 + 1.29574i
\(748\) 32.4787i 1.18754i
\(749\) 21.3076 + 42.9395i 0.778562 + 1.56897i
\(750\) 0.629881 + 1.61346i 0.0230000 + 0.0589152i
\(751\) 8.52796 14.7709i 0.311190 0.538996i −0.667431 0.744672i \(-0.732606\pi\)
0.978620 + 0.205676i \(0.0659392\pi\)
\(752\) 10.0448 0.366295
\(753\) 34.8925 13.6218i 1.27155 0.496404i
\(754\) 4.74236i 0.172707i
\(755\) −19.5824 −0.712677
\(756\) 11.9497 + 6.79736i 0.434607 + 0.247218i
\(757\) 3.74105 0.135971 0.0679854 0.997686i \(-0.478343\pi\)
0.0679854 + 0.997686i \(0.478343\pi\)
\(758\) 6.21425i 0.225712i
\(759\) −31.9393 + 12.4688i −1.15932 + 0.452590i
\(760\) −1.23983 −0.0449735
\(761\) 12.0610 20.8902i 0.437210 0.757271i −0.560263 0.828315i \(-0.689300\pi\)
0.997473 + 0.0710443i \(0.0226332\pi\)
\(762\) −12.0121 30.7692i −0.435151 1.11465i
\(763\) −7.79896 5.18325i −0.282341 0.187646i
\(764\) 3.02993i 0.109619i
\(765\) 16.3782 + 5.11676i 0.592155 + 0.184997i
\(766\) 11.8095 + 6.81820i 0.426693 + 0.246351i
\(767\) 17.9127 10.3419i 0.646790 0.373424i
\(768\) −1.61346 + 0.629881i −0.0582207 + 0.0227289i
\(769\) −11.7667 + 6.79354i −0.424320 + 0.244981i −0.696924 0.717145i \(-0.745448\pi\)
0.272604 + 0.962126i \(0.412115\pi\)
\(770\) −0.945528 + 14.9940i −0.0340745 + 0.540347i
\(771\) −1.27527 + 8.35859i −0.0459278 + 0.301027i
\(772\) 3.52611 0.126907
\(773\) 9.03034 15.6410i 0.324799 0.562568i −0.656673 0.754175i \(-0.728037\pi\)
0.981472 + 0.191608i \(0.0613701\pi\)
\(774\) −14.3991 + 3.23192i −0.517565 + 0.116169i
\(775\) 7.72347 4.45915i 0.277435 0.160177i
\(776\) −0.969482 + 1.67919i −0.0348024 + 0.0602795i
\(777\) −12.4999 + 13.7454i −0.448432 + 0.493114i
\(778\) 14.6496 + 25.3739i 0.525215 + 0.909699i
\(779\) 13.3561 + 7.71118i 0.478534 + 0.276282i
\(780\) −1.14577 2.93492i −0.0410252 0.105087i
\(781\) 18.8048 + 32.5708i 0.672888 + 1.16548i
\(782\) −9.96950 17.2677i −0.356509 0.617491i
\(783\) 11.2340 7.57054i 0.401471 0.270549i
\(784\) −6.94455 0.879348i −0.248020 0.0314053i
\(785\) 14.1700 + 8.18107i 0.505750 + 0.291995i
\(786\) 0.221361 + 0.0337731i 0.00789569 + 0.00120465i
\(787\) 33.3047i 1.18718i 0.804766 + 0.593592i \(0.202291\pi\)
−0.804766 + 0.593592i \(0.797709\pi\)
\(788\) 9.09265i 0.323912i
\(789\) 15.4145 19.2579i 0.548772 0.685599i
\(790\) −1.18356 0.683330i −0.0421092 0.0243118i
\(791\) 7.34929 + 14.8104i 0.261311 + 0.526599i
\(792\) −16.2603 5.07994i −0.577786 0.180508i
\(793\) −6.77436 11.7335i −0.240565 0.416670i
\(794\) 5.55415 + 9.62007i 0.197109 + 0.341403i
\(795\) −1.05490 + 1.31792i −0.0374133 + 0.0467417i
\(796\) 12.5241 + 7.23082i 0.443906 + 0.256289i
\(797\) −3.47393 6.01703i −0.123053 0.213134i 0.797917 0.602767i \(-0.205935\pi\)
−0.920970 + 0.389633i \(0.872602\pi\)
\(798\) 3.82257 4.20345i 0.135317 0.148800i
\(799\) −28.7261 + 49.7551i −1.01626 + 1.76021i
\(800\) 0.866025 0.500000i 0.0306186 0.0176777i
\(801\) −45.1719 14.1123i −1.59607 0.498632i
\(802\) 0.723128 1.25249i 0.0255345 0.0442271i
\(803\) −48.9825 −1.72856
\(804\) −0.111170 + 0.0434000i −0.00392067 + 0.00153060i
\(805\) 4.09979 + 8.26199i 0.144499 + 0.291197i
\(806\) −14.0492 + 8.11131i −0.494862 + 0.285709i
\(807\) −5.91276 + 38.7544i −0.208139 + 1.36422i
\(808\) 4.77599 2.75742i 0.168019 0.0970056i
\(809\) 4.12744 + 2.38298i 0.145113 + 0.0837810i 0.570799 0.821090i \(-0.306634\pi\)
−0.425686 + 0.904871i \(0.639967\pi\)
\(810\) 5.12338 7.39939i 0.180017 0.259988i
\(811\) 28.2422i 0.991716i −0.868404 0.495858i \(-0.834854\pi\)
0.868404 0.495858i \(-0.165146\pi\)
\(812\) −3.81796 + 5.74469i −0.133984 + 0.201599i
\(813\) −8.27134 + 10.3337i −0.290089 + 0.362417i
\(814\) 11.5111 19.9378i 0.403464 0.698820i
\(815\) −13.1801 −0.461680
\(816\) 1.49417 9.79335i 0.0523065 0.342836i
\(817\) 6.09889i 0.213373i
\(818\) 16.2396 0.567804
\(819\) 13.4829 + 5.16421i 0.471131 + 0.180452i
\(820\) −12.4390 −0.434390
\(821\) 37.1488i 1.29650i 0.761427 + 0.648250i \(0.224499\pi\)
−0.761427 + 0.648250i \(0.775501\pi\)
\(822\) −10.7957 8.64119i −0.376544 0.301396i
\(823\) −4.24631 −0.148017 −0.0740086 0.997258i \(-0.523579\pi\)
−0.0740086 + 0.997258i \(0.523579\pi\)
\(824\) 3.76752 6.52554i 0.131248 0.227328i
\(825\) 9.72287 + 1.48342i 0.338507 + 0.0516461i
\(826\) −30.0247 1.89337i −1.04469 0.0658787i
\(827\) 25.2354i 0.877519i −0.898604 0.438760i \(-0.855418\pi\)
0.898604 0.438760i \(-0.144582\pi\)
\(828\) −10.2043 + 2.29039i −0.354625 + 0.0795965i
\(829\) 3.50716 + 2.02486i 0.121809 + 0.0703262i 0.559666 0.828718i \(-0.310929\pi\)
−0.437858 + 0.899044i \(0.644263\pi\)
\(830\) −10.4776 + 6.04923i −0.363682 + 0.209972i
\(831\) −16.9373 13.5571i −0.587548 0.470289i
\(832\) −1.57532 + 0.909513i −0.0546145 + 0.0315317i
\(833\) 24.2158 31.8839i 0.839028 1.10471i
\(834\) 7.09474 + 5.67882i 0.245671 + 0.196641i
\(835\) −5.62513 −0.194666
\(836\) −3.52018 + 6.09713i −0.121748 + 0.210874i
\(837\) −41.6423 20.3321i −1.43937 0.702779i
\(838\) −7.35247 + 4.24495i −0.253987 + 0.146639i
\(839\) 23.7002 41.0500i 0.818222 1.41720i −0.0887683 0.996052i \(-0.528293\pi\)
0.906991 0.421151i \(-0.138374\pi\)
\(840\) −0.974903 + 4.47767i −0.0336373 + 0.154494i
\(841\) −11.1015 19.2284i −0.382812 0.663050i
\(842\) 1.39979 + 0.808166i 0.0482398 + 0.0278513i
\(843\) −36.9211 5.63306i −1.27163 0.194013i
\(844\) 6.72807 + 11.6534i 0.231590 + 0.401125i
\(845\) 4.84557 + 8.39278i 0.166693 + 0.288720i
\(846\) 20.4167 + 22.1638i 0.701942 + 0.762006i
\(847\) 46.8130 + 31.1123i 1.60851 + 1.06903i
\(848\) 0.844055 + 0.487315i 0.0289850 + 0.0167345i
\(849\) −17.2851 44.2763i −0.593224 1.51956i
\(850\) 5.71962i 0.196181i
\(851\) 14.1336i 0.484493i
\(852\) 4.17182 + 10.6862i 0.142924 + 0.366105i
\(853\) 15.0033 + 8.66216i 0.513703 + 0.296587i 0.734354 0.678766i \(-0.237485\pi\)
−0.220651 + 0.975353i \(0.570818\pi\)
\(854\) −1.24023 + 19.6674i −0.0424399 + 0.673004i
\(855\) −2.52006 2.73569i −0.0861841 0.0935588i
\(856\) −9.05896 15.6906i −0.309629 0.536293i
\(857\) 14.0937 + 24.4111i 0.481433 + 0.833866i 0.999773 0.0213087i \(-0.00678329\pi\)
−0.518340 + 0.855174i \(0.673450\pi\)
\(858\) −17.6862 2.69838i −0.603796 0.0921212i
\(859\) 42.5542 + 24.5687i 1.45193 + 0.838272i 0.998591 0.0530671i \(-0.0168997\pi\)
0.453338 + 0.891339i \(0.350233\pi\)
\(860\) −2.45956 4.26008i −0.0838702 0.145267i
\(861\) 38.3511 42.1724i 1.30700 1.43723i
\(862\) −11.5676 + 20.0356i −0.393993 + 0.682415i
\(863\) 20.4648 11.8154i 0.696631 0.402200i −0.109460 0.993991i \(-0.534912\pi\)
0.806092 + 0.591791i \(0.201579\pi\)
\(864\) −4.66931 2.27981i −0.158853 0.0775609i
\(865\) −3.98019 + 6.89389i −0.135330 + 0.234399i
\(866\) −2.88532 −0.0980473
\(867\) 21.2489 + 17.0082i 0.721651 + 0.577629i
\(868\) 23.5488 + 1.48500i 0.799299 + 0.0504040i
\(869\) −6.72081 + 3.88026i −0.227988 + 0.131629i
\(870\) 3.52536 + 2.82180i 0.119521 + 0.0956678i
\(871\) −0.108543 + 0.0626672i −0.00367783 + 0.00212340i
\(872\) 3.06518 + 1.76968i 0.103800 + 0.0599291i
\(873\) −5.67568 + 1.27392i −0.192093 + 0.0431157i
\(874\) 4.32215i 0.146199i
\(875\) 0.166511 2.64051i 0.00562911 0.0892654i
\(876\) −14.7698 2.25343i −0.499025 0.0761363i
\(877\) −9.45337 + 16.3737i −0.319218 + 0.552901i −0.980325 0.197390i \(-0.936753\pi\)
0.661107 + 0.750291i \(0.270087\pi\)
\(878\) 5.18281 0.174911
\(879\) 31.1446 + 24.9290i 1.05048 + 0.840833i
\(880\) 5.67846i 0.191421i
\(881\) −17.7505 −0.598030 −0.299015 0.954248i \(-0.596658\pi\)
−0.299015 + 0.954248i \(0.596658\pi\)
\(882\) −12.1750 17.1105i −0.409955 0.576140i
\(883\) −45.1444 −1.51923 −0.759614 0.650374i \(-0.774612\pi\)
−0.759614 + 0.650374i \(0.774612\pi\)
\(884\) 10.4041i 0.349929i
\(885\) −2.97047 + 19.4695i −0.0998512 + 0.654461i
\(886\) 18.7790 0.630892
\(887\) −13.7214 + 23.7661i −0.460718 + 0.797988i −0.998997 0.0447794i \(-0.985742\pi\)
0.538279 + 0.842767i \(0.319075\pi\)
\(888\) 4.38820 5.48232i 0.147258 0.183975i
\(889\) −3.17543 + 50.3554i −0.106500 + 1.68886i
\(890\) 15.7750i 0.528779i
\(891\) −21.8415 46.2038i −0.731718 1.54788i
\(892\) 9.11125 + 5.26038i 0.305067 + 0.176131i
\(893\) 10.7854 6.22693i 0.360918 0.208376i
\(894\) 4.15513 27.2342i 0.138968 0.910848i
\(895\) 5.99647 3.46206i 0.200440 0.115724i
\(896\) 2.64051 + 0.166511i 0.0882131 + 0.00556275i
\(897\) −10.2314 + 3.99424i −0.341615 + 0.133364i
\(898\) 23.1775 0.773443
\(899\) 11.6254 20.1358i 0.387728 0.671565i
\(900\) 2.86351 + 0.894597i 0.0954504 + 0.0298199i
\(901\) −4.82767 + 2.78726i −0.160833 + 0.0928571i
\(902\) −35.3173 + 61.1714i −1.17594 + 2.03678i
\(903\) 22.0262 + 4.79566i 0.732986 + 0.159589i
\(904\) −3.12456 5.41190i −0.103921 0.179997i
\(905\) −2.40913 1.39091i −0.0800823 0.0462355i
\(906\) −21.1951 + 26.4798i −0.704161 + 0.879732i
\(907\) 17.0394 + 29.5132i 0.565785 + 0.979969i 0.996976 + 0.0777079i \(0.0247602\pi\)
−0.431191 + 0.902261i \(0.641907\pi\)
\(908\) 14.5390 + 25.1823i 0.482493 + 0.835703i
\(909\) 15.7918 + 4.93356i 0.523781 + 0.163636i
\(910\) −0.302888 + 4.80315i −0.0100407 + 0.159223i
\(911\) 50.8899 + 29.3813i 1.68606 + 0.973447i 0.957487 + 0.288477i \(0.0931490\pi\)
0.728572 + 0.684969i \(0.240184\pi\)
\(912\) −1.34194 + 1.67653i −0.0444361 + 0.0555155i
\(913\) 68.7007i 2.27366i
\(914\) 19.7423i 0.653018i
\(915\) 12.7533 + 1.94578i 0.421612 + 0.0643254i
\(916\) −7.36868 4.25431i −0.243468 0.140566i
\(917\) −0.284871 0.189328i −0.00940728 0.00625215i
\(918\) 24.6460 16.6088i 0.813440 0.548173i
\(919\) 25.0699 + 43.4223i 0.826979 + 1.43237i 0.900397 + 0.435068i \(0.143276\pi\)
−0.0734186 + 0.997301i \(0.523391\pi\)
\(920\) −1.74303 3.01902i −0.0574662 0.0995343i
\(921\) 9.20588 + 23.5811i 0.303344 + 0.777025i
\(922\) 11.0344 + 6.37073i 0.363399 + 0.209809i
\(923\) 6.02388 + 10.4337i 0.198278 + 0.343428i
\(924\) 19.2519 + 17.5074i 0.633339 + 0.575952i
\(925\) −2.02715 + 3.51113i −0.0666523 + 0.115445i
\(926\) −11.1045 + 6.41119i −0.364917 + 0.210685i
\(927\) 22.0564 4.95061i 0.724426 0.162599i
\(928\) 1.30354 2.25780i 0.0427909 0.0741160i
\(929\) 9.13789 0.299804 0.149902 0.988701i \(-0.452104\pi\)
0.149902 + 0.988701i \(0.452104\pi\)
\(930\) 2.32978 15.2702i 0.0763966 0.500731i
\(931\) −8.00168 + 3.36087i −0.262245 + 0.110148i
\(932\) 22.5702 13.0309i 0.739313 0.426842i
\(933\) −6.99126 + 2.72933i −0.228883 + 0.0893542i
\(934\) 4.81337 2.77900i 0.157498 0.0909316i
\(935\) 28.1273 + 16.2393i 0.919863 + 0.531083i
\(936\) −5.20880 1.62730i −0.170255 0.0531898i
\(937\) 12.3801i 0.404439i −0.979340 0.202219i \(-0.935185\pi\)
0.979340 0.202219i \(-0.0648154\pi\)
\(938\) 0.181936 + 0.0114729i 0.00594041 + 0.000374605i
\(939\) 5.69107 + 14.5778i 0.185721 + 0.475730i
\(940\) −5.02238 + 8.69903i −0.163812 + 0.283731i
\(941\) 28.2064 0.919502 0.459751 0.888048i \(-0.347939\pi\)
0.459751 + 0.888048i \(0.347939\pi\)
\(942\) 26.3997 10.3062i 0.860147 0.335795i
\(943\) 43.3634i 1.41211i
\(944\) 11.3708 0.370088
\(945\) −11.8615 + 6.95009i −0.385856 + 0.226086i
\(946\) −27.9330 −0.908180
\(947\) 7.08925i 0.230370i −0.993344 0.115185i \(-0.963254\pi\)
0.993344 0.115185i \(-0.0367460\pi\)
\(948\) −2.20505 + 0.860833i −0.0716166 + 0.0279586i
\(949\) −15.6910 −0.509350
\(950\) 0.619917 1.07373i 0.0201128 0.0348363i
\(951\) 12.2081 + 31.2714i 0.395875 + 1.01404i
\(952\) −8.37614 + 12.6031i −0.271472 + 0.408470i
\(953\) 27.1147i 0.878331i −0.898406 0.439165i \(-0.855274\pi\)
0.898406 0.439165i \(-0.144726\pi\)
\(954\) 0.640344 + 2.85291i 0.0207319 + 0.0923664i
\(955\) 2.62400 + 1.51497i 0.0849105 + 0.0490231i
\(956\) 13.6870 7.90222i 0.442671 0.255576i
\(957\) 23.8860 9.32492i 0.772126 0.301432i
\(958\) −4.98120 + 2.87590i −0.160935 + 0.0929160i
\(959\) 9.38922 + 18.9214i 0.303194 + 0.611002i
\(960\) 0.261236 1.71224i 0.00843136 0.0552622i
\(961\) −48.5359 −1.56568
\(962\) 3.68744 6.38683i 0.118888 0.205920i
\(963\) 16.2082 51.8808i 0.522303 1.67184i
\(964\) 4.20612 2.42841i 0.135470 0.0782137i
\(965\) −1.76305 + 3.05370i −0.0567547 + 0.0983020i
\(966\) 15.6095 + 3.39858i 0.502227 + 0.109347i
\(967\) −12.5108 21.6694i −0.402321 0.696840i 0.591685 0.806170i \(-0.298463\pi\)
−0.994006 + 0.109329i \(0.965130\pi\)
\(968\) −18.3987 10.6225i −0.591355 0.341419i
\(969\) −4.46673 11.4417i −0.143492 0.367559i
\(970\) −0.969482 1.67919i −0.0311282 0.0539156i
\(971\) −21.1676 36.6634i −0.679302 1.17659i −0.975191 0.221363i \(-0.928949\pi\)
0.295890 0.955222i \(-0.404384\pi\)
\(972\) −4.46031 14.9367i −0.143065 0.479096i
\(973\) −6.17041 12.4347i −0.197814 0.398639i
\(974\) −26.6459 15.3840i −0.853789 0.492935i
\(975\) 3.11460 + 0.475196i 0.0997472 + 0.0152184i
\(976\) 7.44834i 0.238416i
\(977\) 18.4350i 0.589787i −0.955530 0.294894i \(-0.904716\pi\)
0.955530 0.294894i \(-0.0952842\pi\)
\(978\) −14.2656 + 17.8225i −0.456164 + 0.569900i
\(979\) −77.5766 44.7889i −2.47936 1.43146i
\(980\) 4.23381 5.57448i 0.135244 0.178070i
\(981\) 2.32541 + 10.3603i 0.0742445 + 0.330780i
\(982\) −7.29865 12.6416i −0.232909 0.403411i
\(983\) 28.4754 + 49.3208i 0.908224 + 1.57309i 0.816530 + 0.577302i \(0.195895\pi\)
0.0916934 + 0.995787i \(0.470772\pi\)
\(984\) −13.4635 + 16.8203i −0.429200 + 0.536213i
\(985\) −7.87447 4.54633i −0.250901 0.144858i
\(986\) 7.45578 + 12.9138i 0.237440 + 0.411259i
\(987\) −14.0079 43.8477i −0.445876 1.39569i
\(988\) −1.12765 + 1.95314i −0.0358752 + 0.0621377i
\(989\) −14.8509 + 8.57419i −0.472232 + 0.272643i
\(990\) 12.5295 11.5419i 0.398214 0.366826i
\(991\) 20.5669 35.6229i 0.653328 1.13160i −0.328982 0.944336i \(-0.606706\pi\)
0.982310 0.187261i \(-0.0599611\pi\)
\(992\) −8.91829 −0.283156
\(993\) −13.4800 + 5.26248i −0.427775 + 0.167000i
\(994\) 1.10284 17.4886i 0.0349798 0.554704i
\(995\) −12.5241 + 7.23082i −0.397042 + 0.229232i
\(996\) −3.16056 + 20.7154i −0.100146 + 0.656394i
\(997\) −0.0787174 + 0.0454475i −0.00249300 + 0.00143934i −0.501246 0.865305i \(-0.667125\pi\)
0.498753 + 0.866744i \(0.333791\pi\)
\(998\) 12.7978 + 7.38881i 0.405107 + 0.233889i
\(999\) 21.0161 1.46067i 0.664919 0.0462136i
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 630.2.bk.c.101.10 yes 32
3.2 odd 2 1890.2.bk.c.521.16 32
7.5 odd 6 630.2.t.c.551.12 yes 32
9.4 even 3 1890.2.t.c.1151.8 32
9.5 odd 6 630.2.t.c.311.12 32
21.5 even 6 1890.2.t.c.1601.8 32
63.5 even 6 inner 630.2.bk.c.131.2 yes 32
63.40 odd 6 1890.2.bk.c.341.16 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.t.c.311.12 32 9.5 odd 6
630.2.t.c.551.12 yes 32 7.5 odd 6
630.2.bk.c.101.10 yes 32 1.1 even 1 trivial
630.2.bk.c.131.2 yes 32 63.5 even 6 inner
1890.2.t.c.1151.8 32 9.4 even 3
1890.2.t.c.1601.8 32 21.5 even 6
1890.2.bk.c.341.16 32 63.40 odd 6
1890.2.bk.c.521.16 32 3.2 odd 2