Properties

Label 429.2.bd.b.175.1
Level $429$
Weight $2$
Character 429.175
Analytic conductor $3.426$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(76,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.bd (of order \(12\), 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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 175.1
Character \(\chi\) \(=\) 429.175
Dual form 429.2.bd.b.76.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.44393 + 0.654849i) q^{2} +(0.500000 - 0.866025i) q^{3} +(3.81192 - 2.20081i) q^{4} +(-0.748465 + 0.748465i) q^{5} +(-0.654849 + 2.44393i) q^{6} +(-0.270535 - 0.0724897i) q^{7} +(-4.29670 + 4.29670i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-2.44393 + 0.654849i) q^{2} +(0.500000 - 0.866025i) q^{3} +(3.81192 - 2.20081i) q^{4} +(-0.748465 + 0.748465i) q^{5} +(-0.654849 + 2.44393i) q^{6} +(-0.270535 - 0.0724897i) q^{7} +(-4.29670 + 4.29670i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.33906 - 2.31933i) q^{10} +(-2.59095 + 2.07050i) q^{11} -4.40162i q^{12} +(-2.42671 - 2.66666i) q^{13} +0.708639 q^{14} +(0.273957 + 1.02242i) q^{15} +(3.28552 - 5.69069i) q^{16} +(0.0934440 + 0.161850i) q^{17} +(1.78908 + 1.78908i) q^{18} +(-0.228087 + 0.851231i) q^{19} +(-1.20586 + 4.50032i) q^{20} +(-0.198045 + 0.198045i) q^{21} +(4.97623 - 6.75684i) q^{22} +(-1.93986 - 1.11998i) q^{23} +(1.57270 + 5.86940i) q^{24} +3.87960i q^{25} +(7.67697 + 4.92801i) q^{26} -1.00000 q^{27} +(-1.19079 + 0.319072i) q^{28} +(2.15228 + 1.24262i) q^{29} +(-1.33906 - 2.31933i) q^{30} +(-6.46328 + 6.46328i) q^{31} +(-1.15764 + 4.32037i) q^{32} +(0.497633 + 3.27908i) q^{33} +(-0.334358 - 0.334358i) q^{34} +(0.256742 - 0.148230i) q^{35} +(-3.81192 - 2.20081i) q^{36} +(4.61681 - 1.23707i) q^{37} -2.22971i q^{38} +(-3.52275 + 0.768259i) q^{39} -6.43185i q^{40} +(-11.4750 + 3.07471i) q^{41} +(0.354319 - 0.613699i) q^{42} +(-1.00862 - 1.74698i) q^{43} +(-5.31970 + 13.5948i) q^{44} +(1.02242 + 0.273957i) q^{45} +(5.47431 + 1.46684i) q^{46} +(-2.49262 - 2.49262i) q^{47} +(-3.28552 - 5.69069i) q^{48} +(-5.99424 - 3.46078i) q^{49} +(-2.54055 - 9.48148i) q^{50} +0.186888 q^{51} +(-15.1192 - 4.82437i) q^{52} -10.1750 q^{53} +(2.44393 - 0.654849i) q^{54} +(0.389537 - 3.48893i) q^{55} +(1.47387 - 0.850942i) q^{56} +(0.623145 + 0.623145i) q^{57} +(-6.07376 - 1.62746i) q^{58} +(-0.394865 + 1.47366i) q^{59} +(3.29446 + 3.29446i) q^{60} +(-6.06587 + 3.50213i) q^{61} +(11.5633 - 20.0283i) q^{62} +(0.0724897 + 0.270535i) q^{63} +1.82533i q^{64} +(3.81221 + 0.179598i) q^{65} +(-3.36348 - 7.68797i) q^{66} +(0.153377 + 0.572411i) q^{67} +(0.712401 + 0.411305i) q^{68} +(-1.93986 + 1.11998i) q^{69} +(-0.530391 + 0.530391i) q^{70} +(2.46664 + 0.660935i) q^{71} +(5.86940 + 1.57270i) q^{72} +(-3.86319 + 3.86319i) q^{73} +(-10.4731 + 6.04663i) q^{74} +(3.35983 + 1.93980i) q^{75} +(1.00395 + 3.74680i) q^{76} +(0.851033 - 0.372326i) q^{77} +(8.10627 - 4.18444i) q^{78} +9.45814i q^{79} +(1.80018 + 6.71838i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(26.0306 - 15.0288i) q^{82} +(-0.0514974 - 0.0514974i) q^{83} +(-0.319072 + 1.19079i) q^{84} +(-0.191078 - 0.0511993i) q^{85} +(3.60900 + 3.60900i) q^{86} +(2.15228 - 1.24262i) q^{87} +(2.23621 - 20.0289i) q^{88} +(12.9166 - 3.46100i) q^{89} -2.67813 q^{90} +(0.463204 + 0.897337i) q^{91} -9.85946 q^{92} +(2.36572 + 8.82900i) q^{93} +(7.72407 + 4.45949i) q^{94} +(-0.466402 - 0.807831i) q^{95} +(3.16273 + 3.16273i) q^{96} +(0.320398 + 0.0858504i) q^{97} +(16.9158 + 4.53258i) q^{98} +(3.08858 + 1.20858i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9} - 4 q^{11} - 24 q^{14} - 8 q^{15} + 4 q^{16} + 80 q^{20} - 10 q^{22} - 12 q^{23} + 40 q^{26} - 56 q^{27} - 12 q^{31} - 8 q^{33} - 16 q^{34} - 12 q^{37} - 12 q^{42} + 24 q^{44} - 4 q^{45} - 40 q^{47} - 4 q^{48} + 24 q^{49} - 88 q^{53} - 18 q^{55} + 72 q^{56} + 40 q^{58} + 8 q^{59} + 52 q^{60} - 20 q^{66} - 4 q^{67} - 12 q^{69} + 40 q^{70} - 24 q^{71} + 12 q^{75} - 4 q^{78} - 188 q^{80} - 28 q^{81} - 12 q^{82} + 32 q^{86} + 18 q^{88} - 16 q^{89} + 28 q^{91} - 96 q^{92} - 12 q^{93} - 28 q^{97} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.44393 + 0.654849i −1.72812 + 0.463048i −0.979749 0.200232i \(-0.935830\pi\)
−0.748371 + 0.663280i \(0.769164\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 3.81192 2.20081i 1.90596 1.10041i
\(5\) −0.748465 + 0.748465i −0.334724 + 0.334724i −0.854377 0.519654i \(-0.826061\pi\)
0.519654 + 0.854377i \(0.326061\pi\)
\(6\) −0.654849 + 2.44393i −0.267341 + 0.997730i
\(7\) −0.270535 0.0724897i −0.102253 0.0273985i 0.207330 0.978271i \(-0.433523\pi\)
−0.309583 + 0.950873i \(0.600189\pi\)
\(8\) −4.29670 + 4.29670i −1.51911 + 1.51911i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.33906 2.31933i 0.423449 0.733436i
\(11\) −2.59095 + 2.07050i −0.781201 + 0.624280i
\(12\) 4.40162i 1.27064i
\(13\) −2.42671 2.66666i −0.673048 0.739599i
\(14\) 0.708639 0.189392
\(15\) 0.273957 + 1.02242i 0.0707354 + 0.263988i
\(16\) 3.28552 5.69069i 0.821380 1.42267i
\(17\) 0.0934440 + 0.161850i 0.0226635 + 0.0392543i 0.877135 0.480244i \(-0.159452\pi\)
−0.854471 + 0.519499i \(0.826119\pi\)
\(18\) 1.78908 + 1.78908i 0.421690 + 0.421690i
\(19\) −0.228087 + 0.851231i −0.0523267 + 0.195286i −0.987141 0.159850i \(-0.948899\pi\)
0.934815 + 0.355136i \(0.115566\pi\)
\(20\) −1.20586 + 4.50032i −0.269638 + 1.00630i
\(21\) −0.198045 + 0.198045i −0.0432171 + 0.0432171i
\(22\) 4.97623 6.75684i 1.06094 1.44056i
\(23\) −1.93986 1.11998i −0.404489 0.233532i 0.283930 0.958845i \(-0.408362\pi\)
−0.688419 + 0.725313i \(0.741695\pi\)
\(24\) 1.57270 + 5.86940i 0.321026 + 1.19809i
\(25\) 3.87960i 0.775920i
\(26\) 7.67697 + 4.92801i 1.50558 + 0.966462i
\(27\) −1.00000 −0.192450
\(28\) −1.19079 + 0.319072i −0.225039 + 0.0602990i
\(29\) 2.15228 + 1.24262i 0.399669 + 0.230749i 0.686341 0.727280i \(-0.259216\pi\)
−0.286672 + 0.958029i \(0.592549\pi\)
\(30\) −1.33906 2.31933i −0.244479 0.423449i
\(31\) −6.46328 + 6.46328i −1.16084 + 1.16084i −0.176547 + 0.984292i \(0.556493\pi\)
−0.984292 + 0.176547i \(0.943507\pi\)
\(32\) −1.15764 + 4.32037i −0.204644 + 0.763740i
\(33\) 0.497633 + 3.27908i 0.0866267 + 0.570814i
\(34\) −0.334358 0.334358i −0.0573419 0.0573419i
\(35\) 0.256742 0.148230i 0.0433973 0.0250554i
\(36\) −3.81192 2.20081i −0.635320 0.366802i
\(37\) 4.61681 1.23707i 0.758999 0.203373i 0.141493 0.989939i \(-0.454810\pi\)
0.617506 + 0.786566i \(0.288143\pi\)
\(38\) 2.22971i 0.361707i
\(39\) −3.52275 + 0.768259i −0.564092 + 0.123020i
\(40\) 6.43185i 1.01697i
\(41\) −11.4750 + 3.07471i −1.79209 + 0.480189i −0.992699 0.120620i \(-0.961512\pi\)
−0.799392 + 0.600810i \(0.794845\pi\)
\(42\) 0.354319 0.613699i 0.0546727 0.0946958i
\(43\) −1.00862 1.74698i −0.153813 0.266412i 0.778813 0.627256i \(-0.215822\pi\)
−0.932626 + 0.360844i \(0.882489\pi\)
\(44\) −5.31970 + 13.5948i −0.801975 + 2.04949i
\(45\) 1.02242 + 0.273957i 0.152414 + 0.0408391i
\(46\) 5.47431 + 1.46684i 0.807143 + 0.216273i
\(47\) −2.49262 2.49262i −0.363585 0.363585i 0.501546 0.865131i \(-0.332765\pi\)
−0.865131 + 0.501546i \(0.832765\pi\)
\(48\) −3.28552 5.69069i −0.474224 0.821380i
\(49\) −5.99424 3.46078i −0.856320 0.494397i
\(50\) −2.54055 9.48148i −0.359289 1.34088i
\(51\) 0.186888 0.0261695
\(52\) −15.1192 4.82437i −2.09666 0.669020i
\(53\) −10.1750 −1.39765 −0.698824 0.715294i \(-0.746293\pi\)
−0.698824 + 0.715294i \(0.746293\pi\)
\(54\) 2.44393 0.654849i 0.332577 0.0891137i
\(55\) 0.389537 3.48893i 0.0525251 0.470448i
\(56\) 1.47387 0.850942i 0.196955 0.113712i
\(57\) 0.623145 + 0.623145i 0.0825375 + 0.0825375i
\(58\) −6.07376 1.62746i −0.797524 0.213696i
\(59\) −0.394865 + 1.47366i −0.0514071 + 0.191854i −0.986854 0.161613i \(-0.948330\pi\)
0.935447 + 0.353466i \(0.114997\pi\)
\(60\) 3.29446 + 3.29446i 0.425313 + 0.425313i
\(61\) −6.06587 + 3.50213i −0.776655 + 0.448402i −0.835244 0.549880i \(-0.814673\pi\)
0.0585885 + 0.998282i \(0.481340\pi\)
\(62\) 11.5633 20.0283i 1.46854 2.54359i
\(63\) 0.0724897 + 0.270535i 0.00913284 + 0.0340842i
\(64\) 1.82533i 0.228166i
\(65\) 3.81221 + 0.179598i 0.472846 + 0.0222764i
\(66\) −3.36348 7.68797i −0.414016 0.946323i
\(67\) 0.153377 + 0.572411i 0.0187380 + 0.0699311i 0.974662 0.223684i \(-0.0718083\pi\)
−0.955924 + 0.293615i \(0.905142\pi\)
\(68\) 0.712401 + 0.411305i 0.0863913 + 0.0498781i
\(69\) −1.93986 + 1.11998i −0.233532 + 0.134830i
\(70\) −0.530391 + 0.530391i −0.0633939 + 0.0633939i
\(71\) 2.46664 + 0.660935i 0.292737 + 0.0784386i 0.402199 0.915552i \(-0.368246\pi\)
−0.109462 + 0.993991i \(0.534913\pi\)
\(72\) 5.86940 + 1.57270i 0.691715 + 0.185345i
\(73\) −3.86319 + 3.86319i −0.452152 + 0.452152i −0.896068 0.443916i \(-0.853589\pi\)
0.443916 + 0.896068i \(0.353589\pi\)
\(74\) −10.4731 + 6.04663i −1.21747 + 0.702906i
\(75\) 3.35983 + 1.93980i 0.387960 + 0.223989i
\(76\) 1.00395 + 3.74680i 0.115161 + 0.429787i
\(77\) 0.851033 0.372326i 0.0969842 0.0424305i
\(78\) 8.10627 4.18444i 0.917854 0.473795i
\(79\) 9.45814i 1.06412i 0.846706 + 0.532062i \(0.178583\pi\)
−0.846706 + 0.532062i \(0.821417\pi\)
\(80\) 1.80018 + 6.71838i 0.201267 + 0.751137i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 26.0306 15.0288i 2.87460 1.65965i
\(83\) −0.0514974 0.0514974i −0.00565257 0.00565257i 0.704275 0.709927i \(-0.251272\pi\)
−0.709927 + 0.704275i \(0.751272\pi\)
\(84\) −0.319072 + 1.19079i −0.0348136 + 0.129926i
\(85\) −0.191078 0.0511993i −0.0207253 0.00555334i
\(86\) 3.60900 + 3.60900i 0.389168 + 0.389168i
\(87\) 2.15228 1.24262i 0.230749 0.133223i
\(88\) 2.23621 20.0289i 0.238380 2.13508i
\(89\) 12.9166 3.46100i 1.36916 0.366866i 0.501989 0.864874i \(-0.332602\pi\)
0.867172 + 0.498009i \(0.165935\pi\)
\(90\) −2.67813 −0.282299
\(91\) 0.463204 + 0.897337i 0.0485570 + 0.0940665i
\(92\) −9.85946 −1.02792
\(93\) 2.36572 + 8.82900i 0.245314 + 0.915525i
\(94\) 7.72407 + 4.45949i 0.796677 + 0.459962i
\(95\) −0.466402 0.807831i −0.0478518 0.0828818i
\(96\) 3.16273 + 3.16273i 0.322795 + 0.322795i
\(97\) 0.320398 + 0.0858504i 0.0325315 + 0.00871679i 0.275048 0.961430i \(-0.411306\pi\)
−0.242517 + 0.970147i \(0.577973\pi\)
\(98\) 16.9158 + 4.53258i 1.70875 + 0.457859i
\(99\) 3.08858 + 1.20858i 0.310414 + 0.121467i
\(100\) 8.53827 + 14.7887i 0.853827 + 1.47887i
\(101\) 5.60420 9.70675i 0.557638 0.965858i −0.440055 0.897971i \(-0.645041\pi\)
0.997693 0.0678870i \(-0.0216257\pi\)
\(102\) −0.456741 + 0.122383i −0.0452241 + 0.0121178i
\(103\) 5.68987i 0.560640i 0.959907 + 0.280320i \(0.0904406\pi\)
−0.959907 + 0.280320i \(0.909559\pi\)
\(104\) 21.8847 + 1.03101i 2.14597 + 0.101099i
\(105\) 0.296460i 0.0289315i
\(106\) 24.8671 6.66311i 2.41530 0.647178i
\(107\) 13.0485 + 7.53358i 1.26145 + 0.728299i 0.973355 0.229303i \(-0.0736445\pi\)
0.288096 + 0.957602i \(0.406978\pi\)
\(108\) −3.81192 + 2.20081i −0.366802 + 0.211773i
\(109\) −1.75786 1.75786i −0.168373 0.168373i 0.617891 0.786264i \(-0.287987\pi\)
−0.786264 + 0.617891i \(0.787987\pi\)
\(110\) 1.33272 + 8.78179i 0.127070 + 0.837311i
\(111\) 1.23707 4.61681i 0.117418 0.438208i
\(112\) −1.30136 + 1.30136i −0.122967 + 0.122967i
\(113\) −8.16542 14.1429i −0.768138 1.33045i −0.938572 0.345084i \(-0.887850\pi\)
0.170434 0.985369i \(-0.445483\pi\)
\(114\) −1.93099 1.11486i −0.180854 0.104416i
\(115\) 2.29018 0.613653i 0.213561 0.0572234i
\(116\) 10.9391 1.01567
\(117\) −1.09604 + 3.43492i −0.101329 + 0.317559i
\(118\) 3.86009i 0.355350i
\(119\) −0.0135474 0.0505597i −0.00124189 0.00463480i
\(120\) −5.57015 3.21593i −0.508483 0.293573i
\(121\) 2.42604 10.7291i 0.220549 0.975376i
\(122\) 12.5312 12.5312i 1.13452 1.13452i
\(123\) −3.07471 + 11.4750i −0.277237 + 1.03466i
\(124\) −10.4130 + 38.8619i −0.935117 + 3.48991i
\(125\) −6.64607 6.64607i −0.594442 0.594442i
\(126\) −0.354319 0.613699i −0.0315653 0.0546727i
\(127\) 2.63643 4.56642i 0.233945 0.405205i −0.725021 0.688727i \(-0.758170\pi\)
0.958966 + 0.283523i \(0.0915031\pi\)
\(128\) −3.51059 13.1017i −0.310295 1.15804i
\(129\) −2.01724 −0.177608
\(130\) −9.43438 + 2.05750i −0.827450 + 0.180454i
\(131\) 18.8707i 1.64874i 0.566049 + 0.824372i \(0.308471\pi\)
−0.566049 + 0.824372i \(0.691529\pi\)
\(132\) 9.11357 + 11.4044i 0.793235 + 0.992624i
\(133\) 0.123411 0.213754i 0.0107011 0.0185348i
\(134\) −0.749686 1.29849i −0.0647630 0.112173i
\(135\) 0.748465 0.748465i 0.0644176 0.0644176i
\(136\) −1.09692 0.293919i −0.0940601 0.0252033i
\(137\) 2.55530 9.53652i 0.218314 0.814760i −0.766659 0.642054i \(-0.778082\pi\)
0.984973 0.172706i \(-0.0552510\pi\)
\(138\) 4.00747 4.00747i 0.341139 0.341139i
\(139\) −11.7030 + 6.75670i −0.992632 + 0.573096i −0.906060 0.423149i \(-0.860925\pi\)
−0.0865718 + 0.996246i \(0.527591\pi\)
\(140\) 0.652453 1.13008i 0.0551423 0.0955093i
\(141\) −3.40498 + 0.912361i −0.286751 + 0.0768346i
\(142\) −6.46112 −0.542205
\(143\) 11.8088 + 1.88468i 0.987502 + 0.157605i
\(144\) −6.57104 −0.547587
\(145\) −2.54097 + 0.680850i −0.211016 + 0.0565415i
\(146\) 6.91156 11.9712i 0.572005 0.990741i
\(147\) −5.99424 + 3.46078i −0.494397 + 0.285440i
\(148\) 14.8763 14.8763i 1.22283 1.22283i
\(149\) −0.366939 + 1.36944i −0.0300608 + 0.112189i −0.979326 0.202288i \(-0.935162\pi\)
0.949265 + 0.314477i \(0.101829\pi\)
\(150\) −9.48148 2.54055i −0.774159 0.207435i
\(151\) 11.2855 11.2855i 0.918399 0.918399i −0.0785141 0.996913i \(-0.525018\pi\)
0.996913 + 0.0785141i \(0.0250176\pi\)
\(152\) −2.67746 4.63751i −0.217171 0.376151i
\(153\) 0.0934440 0.161850i 0.00755450 0.0130848i
\(154\) −1.83605 + 1.46724i −0.147953 + 0.118233i
\(155\) 9.67507i 0.777120i
\(156\) −11.7376 + 10.6815i −0.939764 + 0.855201i
\(157\) 5.52193 0.440698 0.220349 0.975421i \(-0.429280\pi\)
0.220349 + 0.975421i \(0.429280\pi\)
\(158\) −6.19365 23.1150i −0.492741 1.83893i
\(159\) −5.08752 + 8.81183i −0.403466 + 0.698824i
\(160\) −2.36719 4.10009i −0.187143 0.324141i
\(161\) 0.443614 + 0.443614i 0.0349617 + 0.0349617i
\(162\) 0.654849 2.44393i 0.0514498 0.192013i
\(163\) −1.09557 + 4.08871i −0.0858115 + 0.320253i −0.995467 0.0951115i \(-0.969679\pi\)
0.909655 + 0.415364i \(0.136346\pi\)
\(164\) −36.9748 + 36.9748i −2.88725 + 2.88725i
\(165\) −2.82674 2.08181i −0.220061 0.162069i
\(166\) 0.159579 + 0.0921330i 0.0123857 + 0.00715091i
\(167\) −6.12266 22.8501i −0.473785 1.76819i −0.625979 0.779840i \(-0.715300\pi\)
0.152193 0.988351i \(-0.451366\pi\)
\(168\) 1.70188i 0.131303i
\(169\) −1.22218 + 12.9424i −0.0940138 + 0.995571i
\(170\) 0.500510 0.0383873
\(171\) 0.851231 0.228087i 0.0650953 0.0174422i
\(172\) −7.68954 4.43956i −0.586322 0.338513i
\(173\) 5.52783 + 9.57449i 0.420273 + 0.727935i 0.995966 0.0897313i \(-0.0286008\pi\)
−0.575693 + 0.817666i \(0.695267\pi\)
\(174\) −4.44630 + 4.44630i −0.337073 + 0.337073i
\(175\) 0.281231 1.04957i 0.0212591 0.0793399i
\(176\) 3.26996 + 21.5470i 0.246483 + 1.62416i
\(177\) 1.07879 + 1.07879i 0.0810869 + 0.0810869i
\(178\) −29.3009 + 16.9169i −2.19620 + 1.26798i
\(179\) 4.12519 + 2.38168i 0.308331 + 0.178015i 0.646179 0.763185i \(-0.276366\pi\)
−0.337848 + 0.941201i \(0.609699\pi\)
\(180\) 4.50032 1.20586i 0.335434 0.0898792i
\(181\) 19.2838i 1.43335i −0.697406 0.716676i \(-0.745663\pi\)
0.697406 0.716676i \(-0.254337\pi\)
\(182\) −1.71966 1.88970i −0.127470 0.140074i
\(183\) 7.00426i 0.517770i
\(184\) 13.1472 3.52279i 0.969226 0.259703i
\(185\) −2.52962 + 4.38142i −0.185981 + 0.322129i
\(186\) −11.5633 20.0283i −0.847865 1.46854i
\(187\) −0.577219 0.225868i −0.0422104 0.0165171i
\(188\) −14.9874 4.01587i −1.09307 0.292887i
\(189\) 0.270535 + 0.0724897i 0.0196785 + 0.00527285i
\(190\) 1.66886 + 1.66886i 0.121072 + 0.121072i
\(191\) −7.30126 12.6461i −0.528300 0.915043i −0.999456 0.0329927i \(-0.989496\pi\)
0.471155 0.882050i \(-0.343837\pi\)
\(192\) 1.58078 + 0.912664i 0.114083 + 0.0658659i
\(193\) −4.24728 15.8511i −0.305726 1.14098i −0.932319 0.361638i \(-0.882218\pi\)
0.626593 0.779347i \(-0.284449\pi\)
\(194\) −0.839250 −0.0602546
\(195\) 2.06164 3.21167i 0.147637 0.229992i
\(196\) −30.4661 −2.17615
\(197\) −4.04885 + 1.08489i −0.288469 + 0.0772950i −0.400152 0.916449i \(-0.631043\pi\)
0.111683 + 0.993744i \(0.464376\pi\)
\(198\) −8.33972 0.931123i −0.592678 0.0661720i
\(199\) 10.8005 6.23568i 0.765628 0.442036i −0.0656848 0.997840i \(-0.520923\pi\)
0.831313 + 0.555805i \(0.187590\pi\)
\(200\) −16.6695 16.6695i −1.17871 1.17871i
\(201\) 0.572411 + 0.153377i 0.0403748 + 0.0108184i
\(202\) −7.33981 + 27.3925i −0.516427 + 1.92733i
\(203\) −0.492191 0.492191i −0.0345451 0.0345451i
\(204\) 0.712401 0.411305i 0.0498781 0.0287971i
\(205\) 6.28730 10.8899i 0.439124 0.760586i
\(206\) −3.72601 13.9057i −0.259603 0.968853i
\(207\) 2.23996i 0.155688i
\(208\) −23.1481 + 5.04826i −1.60503 + 0.350034i
\(209\) −1.17152 2.67775i −0.0810354 0.185224i
\(210\) 0.194137 + 0.724528i 0.0133967 + 0.0499972i
\(211\) 20.4019 + 11.7790i 1.40452 + 0.810902i 0.994853 0.101331i \(-0.0323101\pi\)
0.409671 + 0.912233i \(0.365643\pi\)
\(212\) −38.7864 + 22.3933i −2.66386 + 1.53798i
\(213\) 1.80571 1.80571i 0.123725 0.123725i
\(214\) −36.8231 9.86672i −2.51718 0.674475i
\(215\) 2.06247 + 0.552636i 0.140659 + 0.0376895i
\(216\) 4.29670 4.29670i 0.292353 0.292353i
\(217\) 2.21706 1.28002i 0.150504 0.0868936i
\(218\) 5.44723 + 3.14496i 0.368933 + 0.213004i
\(219\) 1.41403 + 5.27721i 0.0955510 + 0.356601i
\(220\) −6.19360 14.1568i −0.417573 0.954452i
\(221\) 0.204837 0.641945i 0.0137788 0.0431819i
\(222\) 12.0933i 0.811646i
\(223\) −2.00040 7.46560i −0.133957 0.499933i 0.866043 0.499969i \(-0.166655\pi\)
−1.00000 3.56387e-5i \(0.999989\pi\)
\(224\) 0.626364 1.08489i 0.0418507 0.0724875i
\(225\) 3.35983 1.93980i 0.223989 0.129320i
\(226\) 29.2172 + 29.2172i 1.94350 + 1.94350i
\(227\) −1.03567 + 3.86518i −0.0687400 + 0.256541i −0.991741 0.128256i \(-0.959062\pi\)
0.923001 + 0.384797i \(0.125729\pi\)
\(228\) 3.74680 + 1.00395i 0.248138 + 0.0664883i
\(229\) 13.2463 + 13.2463i 0.875341 + 0.875341i 0.993048 0.117708i \(-0.0375545\pi\)
−0.117708 + 0.993048i \(0.537555\pi\)
\(230\) −5.19520 + 2.99945i −0.342561 + 0.197778i
\(231\) 0.103072 0.923179i 0.00678166 0.0607407i
\(232\) −14.5869 + 3.90855i −0.957677 + 0.256609i
\(233\) 18.6734 1.22334 0.611669 0.791114i \(-0.290498\pi\)
0.611669 + 0.791114i \(0.290498\pi\)
\(234\) 0.429299 9.11245i 0.0280641 0.595700i
\(235\) 3.73127 0.243401
\(236\) 1.73805 + 6.48648i 0.113137 + 0.422234i
\(237\) 8.19099 + 4.72907i 0.532062 + 0.307186i
\(238\) 0.0662180 + 0.114693i 0.00429228 + 0.00743444i
\(239\) 6.02314 + 6.02314i 0.389604 + 0.389604i 0.874546 0.484942i \(-0.161159\pi\)
−0.484942 + 0.874546i \(0.661159\pi\)
\(240\) 6.71838 + 1.80018i 0.433669 + 0.116201i
\(241\) −13.9338 3.73354i −0.897553 0.240499i −0.219588 0.975593i \(-0.570471\pi\)
−0.677965 + 0.735094i \(0.737138\pi\)
\(242\) 1.09689 + 27.8099i 0.0705108 + 1.78769i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −15.4151 + 26.6997i −0.986848 + 1.70927i
\(245\) 7.07675 1.89621i 0.452117 0.121144i
\(246\) 30.0575i 1.91640i
\(247\) 2.82345 1.45746i 0.179652 0.0927359i
\(248\) 55.5415i 3.52689i
\(249\) −0.0703468 + 0.0188494i −0.00445804 + 0.00119453i
\(250\) 20.5947 + 11.8904i 1.30252 + 0.752012i
\(251\) −20.2960 + 11.7179i −1.28107 + 0.739629i −0.977045 0.213034i \(-0.931665\pi\)
−0.304029 + 0.952663i \(0.598332\pi\)
\(252\) 0.871721 + 0.871721i 0.0549133 + 0.0549133i
\(253\) 7.34501 1.11468i 0.461777 0.0700792i
\(254\) −3.45292 + 12.8865i −0.216656 + 0.808570i
\(255\) −0.139879 + 0.139879i −0.00875956 + 0.00875956i
\(256\) 15.3340 + 26.5592i 0.958372 + 1.65995i
\(257\) 22.2621 + 12.8530i 1.38867 + 0.801750i 0.993166 0.116713i \(-0.0372359\pi\)
0.395506 + 0.918463i \(0.370569\pi\)
\(258\) 4.92999 1.32099i 0.306927 0.0822410i
\(259\) −1.33868 −0.0831818
\(260\) 14.9271 7.70534i 0.925738 0.477865i
\(261\) 2.48524i 0.153833i
\(262\) −12.3575 46.1188i −0.763448 2.84923i
\(263\) −19.9874 11.5397i −1.23248 0.711571i −0.264931 0.964267i \(-0.585349\pi\)
−0.967546 + 0.252697i \(0.918682\pi\)
\(264\) −16.2274 11.9510i −0.998727 0.735536i
\(265\) 7.61565 7.61565i 0.467826 0.467826i
\(266\) −0.161631 + 0.603216i −0.00991024 + 0.0369855i
\(267\) 3.46100 12.9166i 0.211810 0.790485i
\(268\) 1.84443 + 1.84443i 0.112666 + 0.112666i
\(269\) 10.6666 + 18.4751i 0.650355 + 1.12645i 0.983037 + 0.183409i \(0.0587132\pi\)
−0.332682 + 0.943039i \(0.607953\pi\)
\(270\) −1.33906 + 2.31933i −0.0814928 + 0.141150i
\(271\) 5.11203 + 19.0784i 0.310534 + 1.15893i 0.928076 + 0.372390i \(0.121462\pi\)
−0.617542 + 0.786538i \(0.711872\pi\)
\(272\) 1.22805 0.0744614
\(273\) 1.00872 + 0.0475220i 0.0610504 + 0.00287616i
\(274\) 24.9799i 1.50909i
\(275\) −8.03272 10.0519i −0.484391 0.606149i
\(276\) −4.92973 + 8.53854i −0.296735 + 0.513960i
\(277\) −14.4632 25.0511i −0.869012 1.50517i −0.863007 0.505192i \(-0.831422\pi\)
−0.00600516 0.999982i \(-0.501912\pi\)
\(278\) 24.1766 24.1766i 1.45002 1.45002i
\(279\) 8.82900 + 2.36572i 0.528579 + 0.141632i
\(280\) −0.466243 + 1.74004i −0.0278633 + 0.103987i
\(281\) 7.57512 7.57512i 0.451894 0.451894i −0.444089 0.895983i \(-0.646473\pi\)
0.895983 + 0.444089i \(0.146473\pi\)
\(282\) 7.72407 4.45949i 0.459962 0.265559i
\(283\) −6.39383 + 11.0744i −0.380074 + 0.658307i −0.991072 0.133325i \(-0.957435\pi\)
0.610999 + 0.791632i \(0.290768\pi\)
\(284\) 10.8572 2.90919i 0.644258 0.172628i
\(285\) −0.932803 −0.0552545
\(286\) −30.0941 + 3.12695i −1.77950 + 0.184900i
\(287\) 3.32727 0.196403
\(288\) 4.32037 1.15764i 0.254580 0.0682145i
\(289\) 8.48254 14.6922i 0.498973 0.864246i
\(290\) 5.76409 3.32790i 0.338479 0.195421i
\(291\) 0.234548 0.234548i 0.0137494 0.0137494i
\(292\) −6.22401 + 23.2283i −0.364232 + 1.35933i
\(293\) 9.11447 + 2.44222i 0.532473 + 0.142676i 0.515030 0.857172i \(-0.327781\pi\)
0.0174430 + 0.999848i \(0.494447\pi\)
\(294\) 12.3832 12.3832i 0.722204 0.722204i
\(295\) −0.807437 1.39852i −0.0470108 0.0814251i
\(296\) −14.5217 + 25.1524i −0.844058 + 1.46195i
\(297\) 2.59095 2.07050i 0.150342 0.120143i
\(298\) 3.58709i 0.207795i
\(299\) 1.72087 + 7.89082i 0.0995205 + 0.456338i
\(300\) 17.0765 0.985915
\(301\) 0.146229 + 0.545733i 0.00842849 + 0.0314555i
\(302\) −20.1906 + 34.9712i −1.16184 + 2.01237i
\(303\) −5.60420 9.70675i −0.321953 0.557638i
\(304\) 4.09471 + 4.09471i 0.234848 + 0.234848i
\(305\) 1.91887 7.16131i 0.109874 0.410055i
\(306\) −0.122383 + 0.456741i −0.00699619 + 0.0261101i
\(307\) −17.6330 + 17.6330i −1.00637 + 1.00637i −0.00638873 + 0.999980i \(0.502034\pi\)
−0.999980 + 0.00638873i \(0.997966\pi\)
\(308\) 2.42465 3.29224i 0.138157 0.187593i
\(309\) 4.92758 + 2.84494i 0.280320 + 0.161843i
\(310\) 6.33571 + 23.6452i 0.359844 + 1.34296i
\(311\) 5.23394i 0.296789i −0.988928 0.148395i \(-0.952589\pi\)
0.988928 0.148395i \(-0.0474106\pi\)
\(312\) 11.8352 18.4372i 0.670038 1.04380i
\(313\) −19.1637 −1.08320 −0.541599 0.840637i \(-0.682181\pi\)
−0.541599 + 0.840637i \(0.682181\pi\)
\(314\) −13.4952 + 3.61603i −0.761579 + 0.204064i
\(315\) −0.256742 0.148230i −0.0144658 0.00835181i
\(316\) 20.8156 + 36.0536i 1.17097 + 2.02818i
\(317\) −12.9300 + 12.9300i −0.726223 + 0.726223i −0.969865 0.243642i \(-0.921658\pi\)
0.243642 + 0.969865i \(0.421658\pi\)
\(318\) 6.66311 24.8671i 0.373649 1.39448i
\(319\) −8.14931 + 1.23674i −0.456274 + 0.0692441i
\(320\) −1.36619 1.36619i −0.0763726 0.0763726i
\(321\) 13.0485 7.53358i 0.728299 0.420484i
\(322\) −1.37466 0.793661i −0.0766069 0.0442290i
\(323\) −0.159085 + 0.0426267i −0.00885172 + 0.00237181i
\(324\) 4.40162i 0.244535i
\(325\) 10.3456 9.41466i 0.573870 0.522231i
\(326\) 10.7100i 0.593170i
\(327\) −2.40128 + 0.643422i −0.132791 + 0.0355813i
\(328\) 36.0934 62.5156i 1.99293 3.45185i
\(329\) 0.493651 + 0.855029i 0.0272159 + 0.0471393i
\(330\) 8.27162 + 3.23672i 0.455338 + 0.178176i
\(331\) −19.3111 5.17440i −1.06144 0.284411i −0.314466 0.949269i \(-0.601825\pi\)
−0.746970 + 0.664858i \(0.768492\pi\)
\(332\) −0.309640 0.0829678i −0.0169937 0.00455345i
\(333\) −3.37974 3.37974i −0.185209 0.185209i
\(334\) 29.9267 + 51.8346i 1.63752 + 2.83626i
\(335\) −0.543227 0.313632i −0.0296796 0.0171356i
\(336\) 0.476333 + 1.77770i 0.0259861 + 0.0969813i
\(337\) −34.4099 −1.87443 −0.937214 0.348755i \(-0.886605\pi\)
−0.937214 + 0.348755i \(0.886605\pi\)
\(338\) −5.48841 32.4307i −0.298530 1.76400i
\(339\) −16.3308 −0.886969
\(340\) −0.841055 + 0.225360i −0.0456126 + 0.0122219i
\(341\) 3.36380 30.1283i 0.182160 1.63154i
\(342\) −1.93099 + 1.11486i −0.104416 + 0.0602845i
\(343\) 2.75710 + 2.75710i 0.148869 + 0.148869i
\(344\) 11.8400 + 3.17251i 0.638368 + 0.171050i
\(345\) 0.613653 2.29018i 0.0330380 0.123299i
\(346\) −19.7795 19.7795i −1.06335 1.06335i
\(347\) 4.21522 2.43366i 0.226285 0.130646i −0.382572 0.923926i \(-0.624962\pi\)
0.608857 + 0.793280i \(0.291628\pi\)
\(348\) 5.46956 9.47355i 0.293199 0.507835i
\(349\) −6.78712 25.3299i −0.363306 1.35588i −0.869702 0.493576i \(-0.835689\pi\)
0.506396 0.862301i \(-0.330977\pi\)
\(350\) 2.74924i 0.146953i
\(351\) 2.42671 + 2.66666i 0.129528 + 0.142336i
\(352\) −5.94594 13.5907i −0.316920 0.724389i
\(353\) 4.90537 + 18.3071i 0.261086 + 0.974388i 0.964602 + 0.263708i \(0.0849457\pi\)
−0.703516 + 0.710679i \(0.748388\pi\)
\(354\) −3.34294 1.93005i −0.177675 0.102581i
\(355\) −2.34088 + 1.35151i −0.124241 + 0.0717306i
\(356\) 41.6201 41.6201i 2.20586 2.20586i
\(357\) −0.0505597 0.0135474i −0.00267590 0.000717007i
\(358\) −11.6413 3.11928i −0.615263 0.164859i
\(359\) −8.76688 + 8.76688i −0.462698 + 0.462698i −0.899539 0.436841i \(-0.856097\pi\)
0.436841 + 0.899539i \(0.356097\pi\)
\(360\) −5.57015 + 3.21593i −0.293573 + 0.169494i
\(361\) 15.7819 + 9.11169i 0.830627 + 0.479563i
\(362\) 12.6280 + 47.1282i 0.663711 + 2.47700i
\(363\) −8.07868 7.46558i −0.424021 0.391841i
\(364\) 3.74057 + 2.40115i 0.196059 + 0.125854i
\(365\) 5.78292i 0.302692i
\(366\) −4.58674 17.1179i −0.239753 0.894769i
\(367\) −14.1338 + 24.4805i −0.737779 + 1.27787i 0.215714 + 0.976457i \(0.430792\pi\)
−0.953493 + 0.301414i \(0.902541\pi\)
\(368\) −12.7469 + 7.35944i −0.664479 + 0.383637i
\(369\) 8.40027 + 8.40027i 0.437301 + 0.437301i
\(370\) 3.31303 12.3644i 0.172236 0.642795i
\(371\) 2.75270 + 0.737584i 0.142913 + 0.0382935i
\(372\) 28.4489 + 28.4489i 1.47501 + 1.47501i
\(373\) 20.9884 12.1177i 1.08674 0.627429i 0.154033 0.988066i \(-0.450774\pi\)
0.932706 + 0.360637i \(0.117441\pi\)
\(374\) 1.55859 + 0.174016i 0.0805929 + 0.00899813i
\(375\) −9.07870 + 2.43263i −0.468822 + 0.125620i
\(376\) 21.4200 1.10465
\(377\) −1.90931 8.75490i −0.0983346 0.450900i
\(378\) −0.708639 −0.0364484
\(379\) −0.169900 0.634075i −0.00872717 0.0325703i 0.961425 0.275067i \(-0.0887002\pi\)
−0.970152 + 0.242497i \(0.922034\pi\)
\(380\) −3.55577 2.05292i −0.182407 0.105313i
\(381\) −2.63643 4.56642i −0.135068 0.233945i
\(382\) 26.1251 + 26.1251i 1.33668 + 1.33668i
\(383\) 36.0341 + 9.65531i 1.84126 + 0.493363i 0.998958 0.0456472i \(-0.0145350\pi\)
0.842299 + 0.539010i \(0.181202\pi\)
\(384\) −13.1017 3.51059i −0.668594 0.179149i
\(385\) −0.358295 + 0.915641i −0.0182604 + 0.0466654i
\(386\) 20.7601 + 35.9576i 1.05666 + 1.83019i
\(387\) −1.00862 + 1.74698i −0.0512709 + 0.0888039i
\(388\) 1.41027 0.377881i 0.0715957 0.0191840i
\(389\) 21.7449i 1.10251i 0.834337 + 0.551254i \(0.185850\pi\)
−0.834337 + 0.551254i \(0.814150\pi\)
\(390\) −2.93535 + 9.19916i −0.148637 + 0.465818i
\(391\) 0.418622i 0.0211706i
\(392\) 40.6254 10.8855i 2.05189 0.549803i
\(393\) 16.3425 + 9.43537i 0.824372 + 0.475951i
\(394\) 9.18468 5.30278i 0.462717 0.267150i
\(395\) −7.07908 7.07908i −0.356187 0.356187i
\(396\) 14.4333 2.19039i 0.725299 0.110071i
\(397\) 8.11490 30.2852i 0.407275 1.51997i −0.392546 0.919732i \(-0.628406\pi\)
0.799821 0.600239i \(-0.204928\pi\)
\(398\) −22.3123 + 22.3123i −1.11841 + 1.11841i
\(399\) −0.123411 0.213754i −0.00617827 0.0107011i
\(400\) 22.0776 + 12.7465i 1.10388 + 0.637325i
\(401\) −26.2470 + 7.03286i −1.31071 + 0.351204i −0.845491 0.533990i \(-0.820692\pi\)
−0.465221 + 0.885194i \(0.654025\pi\)
\(402\) −1.49937 −0.0747819
\(403\) 32.9199 + 1.55089i 1.63986 + 0.0772556i
\(404\) 49.3351i 2.45451i
\(405\) −0.273957 1.02242i −0.0136130 0.0508045i
\(406\) 1.52519 + 0.880570i 0.0756940 + 0.0437020i
\(407\) −9.40056 + 12.7643i −0.465969 + 0.632703i
\(408\) −0.803001 + 0.803001i −0.0397545 + 0.0397545i
\(409\) 6.00431 22.4084i 0.296894 1.10802i −0.642808 0.766028i \(-0.722231\pi\)
0.939702 0.341996i \(-0.111103\pi\)
\(410\) −8.23447 + 30.7315i −0.406672 + 1.51772i
\(411\) −6.98122 6.98122i −0.344358 0.344358i
\(412\) 12.5223 + 21.6893i 0.616931 + 1.06856i
\(413\) 0.213650 0.370052i 0.0105130 0.0182091i
\(414\) −1.46684 5.47431i −0.0720911 0.269048i
\(415\) 0.0770880 0.00378410
\(416\) 14.3302 7.39723i 0.702596 0.362679i
\(417\) 13.5134i 0.661754i
\(418\) 4.61663 + 5.77707i 0.225807 + 0.282566i
\(419\) −14.6051 + 25.2968i −0.713507 + 1.23583i 0.250026 + 0.968239i \(0.419561\pi\)
−0.963533 + 0.267591i \(0.913772\pi\)
\(420\) −0.652453 1.13008i −0.0318364 0.0551423i
\(421\) −0.263632 + 0.263632i −0.0128487 + 0.0128487i −0.713502 0.700653i \(-0.752892\pi\)
0.700653 + 0.713502i \(0.252892\pi\)
\(422\) −57.5743 15.4270i −2.80267 0.750974i
\(423\) −0.912361 + 3.40498i −0.0443605 + 0.165556i
\(424\) 43.7190 43.7190i 2.12318 2.12318i
\(425\) −0.627912 + 0.362525i −0.0304582 + 0.0175851i
\(426\) −3.23056 + 5.59549i −0.156521 + 0.271102i
\(427\) 1.89490 0.507737i 0.0917006 0.0245711i
\(428\) 66.3200 3.20570
\(429\) 7.53659 9.28439i 0.363870 0.448254i
\(430\) −5.40242 −0.260528
\(431\) −29.6837 + 7.95371i −1.42981 + 0.383117i −0.888954 0.457997i \(-0.848567\pi\)
−0.540858 + 0.841114i \(0.681900\pi\)
\(432\) −3.28552 + 5.69069i −0.158075 + 0.273793i
\(433\) −18.3422 + 10.5899i −0.881472 + 0.508918i −0.871144 0.491028i \(-0.836621\pi\)
−0.0103286 + 0.999947i \(0.503288\pi\)
\(434\) −4.58013 + 4.58013i −0.219853 + 0.219853i
\(435\) −0.680850 + 2.54097i −0.0326443 + 0.121830i
\(436\) −10.5696 2.83210i −0.506190 0.135633i
\(437\) 1.39582 1.39582i 0.0667711 0.0667711i
\(438\) −6.91156 11.9712i −0.330247 0.572005i
\(439\) 10.2325 17.7231i 0.488369 0.845879i −0.511542 0.859258i \(-0.670926\pi\)
0.999910 + 0.0133791i \(0.00425884\pi\)
\(440\) 13.3172 + 16.6646i 0.634871 + 0.794454i
\(441\) 6.92156i 0.329598i
\(442\) −0.0802307 + 1.70301i −0.00381619 + 0.0810038i
\(443\) −1.83504 −0.0871854 −0.0435927 0.999049i \(-0.513880\pi\)
−0.0435927 + 0.999049i \(0.513880\pi\)
\(444\) −5.44512 20.3215i −0.258414 0.964414i
\(445\) −7.07721 + 12.2581i −0.335492 + 0.581089i
\(446\) 9.77768 + 16.9354i 0.462987 + 0.801916i
\(447\) 1.00250 + 1.00250i 0.0474165 + 0.0474165i
\(448\) 0.132317 0.493815i 0.00625141 0.0233306i
\(449\) −6.31978 + 23.5857i −0.298249 + 1.11308i 0.640354 + 0.768080i \(0.278788\pi\)
−0.938603 + 0.345000i \(0.887879\pi\)
\(450\) −6.94092 + 6.94092i −0.327198 + 0.327198i
\(451\) 23.3649 31.7254i 1.10021 1.49389i
\(452\) −62.2518 35.9411i −2.92808 1.69053i
\(453\) −4.13077 15.4162i −0.194081 0.724318i
\(454\) 10.1244i 0.475164i
\(455\) −1.01832 0.324933i −0.0477394 0.0152331i
\(456\) −5.35493 −0.250768
\(457\) −15.4421 + 4.13770i −0.722352 + 0.193554i −0.601221 0.799083i \(-0.705319\pi\)
−0.121131 + 0.992637i \(0.538652\pi\)
\(458\) −41.0474 23.6987i −1.91802 1.10737i
\(459\) −0.0934440 0.161850i −0.00436159 0.00755450i
\(460\) 7.37946 7.37946i 0.344069 0.344069i
\(461\) 9.07241 33.8587i 0.422544 1.57696i −0.346683 0.937982i \(-0.612692\pi\)
0.769228 0.638975i \(-0.220641\pi\)
\(462\) 0.352642 + 2.32368i 0.0164064 + 0.108107i
\(463\) −8.93284 8.93284i −0.415144 0.415144i 0.468382 0.883526i \(-0.344837\pi\)
−0.883526 + 0.468382i \(0.844837\pi\)
\(464\) 14.1428 8.16532i 0.656561 0.379066i
\(465\) −8.37886 4.83754i −0.388560 0.224335i
\(466\) −45.6366 + 12.2283i −2.11407 + 0.566465i
\(467\) 12.9587i 0.599658i 0.953993 + 0.299829i \(0.0969296\pi\)
−0.953993 + 0.299829i \(0.903070\pi\)
\(468\) 3.38159 + 15.5058i 0.156314 + 0.716757i
\(469\) 0.165976i 0.00766404i
\(470\) −9.11897 + 2.44342i −0.420627 + 0.112707i
\(471\) 2.76096 4.78213i 0.127219 0.220349i
\(472\) −4.63524 8.02848i −0.213354 0.369541i
\(473\) 6.23040 + 2.43799i 0.286474 + 0.112099i
\(474\) −23.1150 6.19365i −1.06171 0.284484i
\(475\) −3.30244 0.884886i −0.151526 0.0406013i
\(476\) −0.162914 0.162914i −0.00746716 0.00746716i
\(477\) 5.08752 + 8.81183i 0.232941 + 0.403466i
\(478\) −18.6644 10.7759i −0.853689 0.492877i
\(479\) −5.46407 20.3922i −0.249660 0.931742i −0.970984 0.239145i \(-0.923133\pi\)
0.721324 0.692597i \(-0.243534\pi\)
\(480\) −4.73438 −0.216094
\(481\) −14.5025 9.30946i −0.661257 0.424475i
\(482\) 36.4981 1.66244
\(483\) 0.605988 0.162374i 0.0275734 0.00738827i
\(484\) −14.3649 46.2378i −0.652952 2.10172i
\(485\) −0.304063 + 0.175551i −0.0138068 + 0.00797134i
\(486\) −1.78908 1.78908i −0.0811544 0.0811544i
\(487\) 27.0709 + 7.25362i 1.22670 + 0.328693i 0.813293 0.581855i \(-0.197673\pi\)
0.413405 + 0.910547i \(0.364339\pi\)
\(488\) 11.0156 41.1108i 0.498653 1.86100i
\(489\) 2.99315 + 2.99315i 0.135355 + 0.135355i
\(490\) −16.0534 + 9.26841i −0.725217 + 0.418704i
\(491\) −0.572806 + 0.992130i −0.0258504 + 0.0447742i −0.878661 0.477446i \(-0.841563\pi\)
0.852811 + 0.522220i \(0.174896\pi\)
\(492\) 13.5337 + 50.5085i 0.610147 + 2.27710i
\(493\) 0.464462i 0.0209183i
\(494\) −5.94589 + 5.41086i −0.267518 + 0.243446i
\(495\) −3.21627 + 1.40712i −0.144561 + 0.0632452i
\(496\) 15.5453 + 58.0157i 0.698003 + 2.60498i
\(497\) −0.619403 0.357612i −0.0277840 0.0160411i
\(498\) 0.159579 0.0921330i 0.00715091 0.00412858i
\(499\) −21.9819 + 21.9819i −0.984046 + 0.984046i −0.999875 0.0158290i \(-0.994961\pi\)
0.0158290 + 0.999875i \(0.494961\pi\)
\(500\) −39.9610 10.7075i −1.78711 0.478855i
\(501\) −22.8501 6.12266i −1.02087 0.273540i
\(502\) 41.9286 41.9286i 1.87137 1.87137i
\(503\) −25.6533 + 14.8109i −1.14382 + 0.660387i −0.947375 0.320127i \(-0.896274\pi\)
−0.196449 + 0.980514i \(0.562941\pi\)
\(504\) −1.47387 0.850942i −0.0656516 0.0379040i
\(505\) 3.07062 + 11.4597i 0.136641 + 0.509950i
\(506\) −17.2207 + 7.53407i −0.765555 + 0.334930i
\(507\) 10.5974 + 7.52965i 0.470646 + 0.334403i
\(508\) 23.2091i 1.02974i
\(509\) −2.18354 8.14910i −0.0967839 0.361202i 0.900500 0.434856i \(-0.143201\pi\)
−0.997284 + 0.0736536i \(0.976534\pi\)
\(510\) 0.250255 0.433454i 0.0110815 0.0191937i
\(511\) 1.32517 0.765087i 0.0586220 0.0338455i
\(512\) −35.6852 35.6852i −1.57708 1.57708i
\(513\) 0.228087 0.851231i 0.0100703 0.0375828i
\(514\) −62.8238 16.8336i −2.77104 0.742498i
\(515\) −4.25867 4.25867i −0.187659 0.187659i
\(516\) −7.68954 + 4.43956i −0.338513 + 0.195441i
\(517\) 11.6192 + 1.29728i 0.511012 + 0.0570541i
\(518\) 3.27165 0.876636i 0.143748 0.0385172i
\(519\) 11.0557 0.485290
\(520\) −17.1516 + 15.6082i −0.752147 + 0.684466i
\(521\) −40.3986 −1.76989 −0.884947 0.465692i \(-0.845805\pi\)
−0.884947 + 0.465692i \(0.845805\pi\)
\(522\) 1.62746 + 6.07376i 0.0712320 + 0.265841i
\(523\) −1.46121 0.843630i −0.0638942 0.0368893i 0.467713 0.883881i \(-0.345078\pi\)
−0.531607 + 0.846991i \(0.678412\pi\)
\(524\) 41.5309 + 71.9337i 1.81429 + 3.14244i
\(525\) −0.768337 0.768337i −0.0335330 0.0335330i
\(526\) 56.4046 + 15.1136i 2.45936 + 0.658983i
\(527\) −1.65003 0.442125i −0.0718766 0.0192593i
\(528\) 20.2952 + 7.94161i 0.883235 + 0.345614i
\(529\) −8.99129 15.5734i −0.390926 0.677103i
\(530\) −13.6250 + 23.5992i −0.591833 + 1.02508i
\(531\) 1.47366 0.394865i 0.0639512 0.0171357i
\(532\) 1.08642i 0.0471021i
\(533\) 36.0456 + 23.1385i 1.56131 + 1.00224i
\(534\) 33.8338i 1.46413i
\(535\) −15.4050 + 4.12776i −0.666016 + 0.178459i
\(536\) −3.11849 1.80046i −0.134698 0.0777681i
\(537\) 4.12519 2.38168i 0.178015 0.102777i
\(538\) −38.1669 38.1669i −1.64549 1.64549i
\(539\) 22.6963 3.44439i 0.977600 0.148360i
\(540\) 1.20586 4.50032i 0.0518918 0.193663i
\(541\) 14.9548 14.9548i 0.642958 0.642958i −0.308323 0.951282i \(-0.599768\pi\)
0.951282 + 0.308323i \(0.0997679\pi\)
\(542\) −24.9869 43.2786i −1.07328 1.85897i
\(543\) −16.7002 9.64189i −0.716676 0.413773i
\(544\) −0.807424 + 0.216349i −0.0346180 + 0.00927587i
\(545\) 2.63140 0.112717
\(546\) −2.49636 + 0.544418i −0.106834 + 0.0232990i
\(547\) 34.2479i 1.46434i 0.681124 + 0.732168i \(0.261491\pi\)
−0.681124 + 0.732168i \(0.738509\pi\)
\(548\) −11.2475 41.9762i −0.480469 1.79313i
\(549\) 6.06587 + 3.50213i 0.258885 + 0.149467i
\(550\) 26.2139 + 19.3058i 1.11776 + 0.823202i
\(551\) −1.54867 + 1.54867i −0.0659754 + 0.0659754i
\(552\) 3.52279 13.1472i 0.149940 0.559583i
\(553\) 0.685617 2.55876i 0.0291554 0.108809i
\(554\) 51.7519 + 51.7519i 2.19873 + 2.19873i
\(555\) 2.52962 + 4.38142i 0.107376 + 0.185981i
\(556\) −29.7405 + 51.5120i −1.26128 + 2.18460i
\(557\) 3.79872 + 14.1770i 0.160957 + 0.600700i 0.998521 + 0.0543610i \(0.0173122\pi\)
−0.837564 + 0.546339i \(0.816021\pi\)
\(558\) −23.1267 −0.979030
\(559\) −2.21098 + 6.92905i −0.0935145 + 0.293068i
\(560\) 1.94805i 0.0823202i
\(561\) −0.484217 + 0.386952i −0.0204437 + 0.0163371i
\(562\) −13.5525 + 23.4736i −0.571678 + 0.990175i
\(563\) 13.8604 + 24.0070i 0.584147 + 1.01177i 0.994981 + 0.100063i \(0.0319043\pi\)
−0.410834 + 0.911710i \(0.634762\pi\)
\(564\) −10.9716 + 10.9716i −0.461986 + 0.461986i
\(565\) 16.6970 + 4.47395i 0.702448 + 0.188220i
\(566\) 8.37399 31.2521i 0.351985 1.31363i
\(567\) 0.198045 0.198045i 0.00831713 0.00831713i
\(568\) −13.4383 + 7.75858i −0.563857 + 0.325543i
\(569\) 1.50257 2.60253i 0.0629911 0.109104i −0.832810 0.553559i \(-0.813269\pi\)
0.895801 + 0.444455i \(0.146603\pi\)
\(570\) 2.27971 0.610846i 0.0954864 0.0255855i
\(571\) 27.1145 1.13471 0.567354 0.823474i \(-0.307967\pi\)
0.567354 + 0.823474i \(0.307967\pi\)
\(572\) 49.1620 18.8047i 2.05557 0.786264i
\(573\) −14.6025 −0.610029
\(574\) −8.13162 + 2.17886i −0.339407 + 0.0909438i
\(575\) 4.34508 7.52589i 0.181202 0.313851i
\(576\) 1.58078 0.912664i 0.0658659 0.0380277i
\(577\) 15.0421 15.0421i 0.626211 0.626211i −0.320902 0.947113i \(-0.603986\pi\)
0.947113 + 0.320902i \(0.103986\pi\)
\(578\) −11.1096 + 41.4615i −0.462097 + 1.72457i
\(579\) −15.8511 4.24728i −0.658748 0.176511i
\(580\) −8.18754 + 8.18754i −0.339969 + 0.339969i
\(581\) 0.0101988 + 0.0176649i 0.000423119 + 0.000732863i
\(582\) −0.419625 + 0.726812i −0.0173940 + 0.0301273i
\(583\) 26.3630 21.0674i 1.09184 0.872524i
\(584\) 33.1979i 1.37374i
\(585\) −1.75057 3.39127i −0.0723771 0.140212i
\(586\) −23.8744 −0.986243
\(587\) 5.36505 + 20.0226i 0.221439 + 0.826422i 0.983800 + 0.179270i \(0.0573735\pi\)
−0.762361 + 0.647152i \(0.775960\pi\)
\(588\) −15.2330 + 26.3844i −0.628200 + 1.08807i
\(589\) −4.02756 6.97593i −0.165953 0.287438i
\(590\) 2.88914 + 2.88914i 0.118944 + 0.118944i
\(591\) −1.08489 + 4.04885i −0.0446263 + 0.166548i
\(592\) 8.12884 30.3372i 0.334093 1.24685i
\(593\) −5.93322 + 5.93322i −0.243648 + 0.243648i −0.818358 0.574709i \(-0.805115\pi\)
0.574709 + 0.818358i \(0.305115\pi\)
\(594\) −4.97623 + 6.75684i −0.204177 + 0.277237i
\(595\) 0.0479820 + 0.0277024i 0.00196707 + 0.00113569i
\(596\) 1.61513 + 6.02774i 0.0661582 + 0.246906i
\(597\) 12.4714i 0.510419i
\(598\) −9.37299 18.1577i −0.383290 0.742524i
\(599\) 23.2576 0.950280 0.475140 0.879910i \(-0.342397\pi\)
0.475140 + 0.879910i \(0.342397\pi\)
\(600\) −22.7709 + 6.10145i −0.929619 + 0.249091i
\(601\) 25.8836 + 14.9439i 1.05581 + 0.609574i 0.924271 0.381737i \(-0.124674\pi\)
0.131542 + 0.991311i \(0.458007\pi\)
\(602\) −0.714746 1.23798i −0.0291309 0.0504561i
\(603\) 0.419034 0.419034i 0.0170644 0.0170644i
\(604\) 18.1821 67.8565i 0.739819 2.76104i
\(605\) 6.21457 + 9.84618i 0.252658 + 0.400304i
\(606\) 20.0527 + 20.0527i 0.814586 + 0.814586i
\(607\) −5.04566 + 2.91311i −0.204797 + 0.118240i −0.598891 0.800830i \(-0.704392\pi\)
0.394094 + 0.919070i \(0.371058\pi\)
\(608\) −3.41359 1.97084i −0.138439 0.0799280i
\(609\) −0.672346 + 0.180155i −0.0272448 + 0.00730023i
\(610\) 18.7583i 0.759502i
\(611\) −0.598115 + 12.6958i −0.0241972 + 0.513618i
\(612\) 0.822610i 0.0332520i
\(613\) −21.5385 + 5.77123i −0.869933 + 0.233098i −0.666059 0.745899i \(-0.732020\pi\)
−0.203874 + 0.978997i \(0.565353\pi\)
\(614\) 31.5469 54.6408i 1.27313 2.20512i
\(615\) −6.28730 10.8899i −0.253529 0.439124i
\(616\) −2.05686 + 5.25641i −0.0828731 + 0.211787i
\(617\) 3.03997 + 0.814558i 0.122385 + 0.0327929i 0.319491 0.947589i \(-0.396488\pi\)
−0.197107 + 0.980382i \(0.563155\pi\)
\(618\) −13.9057 3.72601i −0.559368 0.149882i
\(619\) 6.76152 + 6.76152i 0.271769 + 0.271769i 0.829812 0.558043i \(-0.188448\pi\)
−0.558043 + 0.829812i \(0.688448\pi\)
\(620\) −21.2930 36.8806i −0.855148 1.48116i
\(621\) 1.93986 + 1.11998i 0.0778440 + 0.0449433i
\(622\) 3.42744 + 12.7914i 0.137428 + 0.512888i
\(623\) −3.74529 −0.150052
\(624\) −7.20215 + 22.5710i −0.288317 + 0.903564i
\(625\) −9.44931 −0.377973
\(626\) 46.8349 12.5494i 1.87190 0.501573i
\(627\) −2.90476 0.324314i −0.116005 0.0129519i
\(628\) 21.0491 12.1527i 0.839952 0.484947i
\(629\) 0.631632 + 0.631632i 0.0251848 + 0.0251848i
\(630\) 0.724528 + 0.194137i 0.0288659 + 0.00773459i
\(631\) 6.90782 25.7803i 0.274996 1.02630i −0.680848 0.732425i \(-0.738389\pi\)
0.955844 0.293874i \(-0.0949447\pi\)
\(632\) −40.6388 40.6388i −1.61652 1.61652i
\(633\) 20.4019 11.7790i 0.810902 0.468175i
\(634\) 23.1329 40.0673i 0.918725 1.59128i
\(635\) 1.44453 + 5.39108i 0.0573246 + 0.213938i
\(636\) 44.7867i 1.77591i
\(637\) 5.31755 + 24.3829i 0.210689 + 0.966087i
\(638\) 19.1065 8.35908i 0.756433 0.330939i
\(639\) −0.660935 2.46664i −0.0261462 0.0975789i
\(640\) 12.4337 + 7.17861i 0.491486 + 0.283760i
\(641\) 20.0459 11.5735i 0.791765 0.457126i −0.0488184 0.998808i \(-0.515546\pi\)
0.840584 + 0.541682i \(0.182212\pi\)
\(642\) −26.9564 + 26.9564i −1.06388 + 1.06388i
\(643\) −38.3344 10.2717i −1.51176 0.405075i −0.594740 0.803918i \(-0.702745\pi\)
−0.917019 + 0.398843i \(0.869412\pi\)
\(644\) 2.66733 + 0.714709i 0.105108 + 0.0281635i
\(645\) 1.50983 1.50983i 0.0594495 0.0594495i
\(646\) 0.360878 0.208353i 0.0141986 0.00819755i
\(647\) −23.0636 13.3158i −0.906725 0.523498i −0.0273491 0.999626i \(-0.508707\pi\)
−0.879376 + 0.476128i \(0.842040\pi\)
\(648\) −1.57270 5.86940i −0.0617815 0.230572i
\(649\) −2.02813 4.63574i −0.0796112 0.181969i
\(650\) −19.1187 + 29.7836i −0.749898 + 1.16821i
\(651\) 2.56005i 0.100336i
\(652\) 4.82228 + 17.9970i 0.188855 + 0.704816i
\(653\) 5.84447 10.1229i 0.228712 0.396140i −0.728715 0.684817i \(-0.759882\pi\)
0.957427 + 0.288677i \(0.0932153\pi\)
\(654\) 5.44723 3.14496i 0.213004 0.122978i
\(655\) −14.1241 14.1241i −0.551873 0.551873i
\(656\) −20.2041 + 75.4026i −0.788836 + 2.94398i
\(657\) 5.27721 + 1.41403i 0.205884 + 0.0551664i
\(658\) −1.76636 1.76636i −0.0688601 0.0688601i
\(659\) 4.96055 2.86397i 0.193235 0.111565i −0.400261 0.916401i \(-0.631080\pi\)
0.593496 + 0.804837i \(0.297747\pi\)
\(660\) −15.3570 1.71459i −0.597769 0.0667404i
\(661\) −39.2136 + 10.5073i −1.52523 + 0.408685i −0.921461 0.388471i \(-0.873003\pi\)
−0.603773 + 0.797156i \(0.706337\pi\)
\(662\) 50.5835 1.96598
\(663\) −0.453522 0.498367i −0.0176133 0.0193550i
\(664\) 0.442538 0.0171738
\(665\) 0.0676186 + 0.252356i 0.00262214 + 0.00978595i
\(666\) 10.4731 + 6.04663i 0.405823 + 0.234302i
\(667\) −2.78342 4.82103i −0.107775 0.186671i
\(668\) −73.6277 73.6277i −2.84874 2.84874i
\(669\) −7.46560 2.00040i −0.288637 0.0773400i
\(670\) 1.53299 + 0.410763i 0.0592246 + 0.0158692i
\(671\) 8.46519 21.6332i 0.326795 0.835142i
\(672\) −0.626364 1.08489i −0.0241625 0.0418507i
\(673\) −10.9897 + 19.0347i −0.423621 + 0.733733i −0.996291 0.0860532i \(-0.972574\pi\)
0.572670 + 0.819786i \(0.305908\pi\)
\(674\) 84.0955 22.5333i 3.23924 0.867951i
\(675\) 3.87960i 0.149326i
\(676\) 23.8250 + 52.0252i 0.916346 + 2.00097i
\(677\) 1.44089i 0.0553779i 0.999617 + 0.0276889i \(0.00881479\pi\)
−0.999617 + 0.0276889i \(0.991185\pi\)
\(678\) 39.9114 10.6942i 1.53279 0.410709i
\(679\) −0.0804557 0.0464511i −0.00308760 0.00178263i
\(680\) 1.04099 0.601018i 0.0399203 0.0230480i
\(681\) 2.82951 + 2.82951i 0.108427 + 0.108427i
\(682\) 11.5086 + 75.8342i 0.440686 + 2.90384i
\(683\) 2.49612 9.31565i 0.0955115 0.356454i −0.901585 0.432602i \(-0.857596\pi\)
0.997097 + 0.0761483i \(0.0242622\pi\)
\(684\) 2.74285 2.74285i 0.104875 0.104875i
\(685\) 5.22519 + 9.05030i 0.199644 + 0.345794i
\(686\) −8.54365 4.93268i −0.326198 0.188330i
\(687\) 18.0948 4.84849i 0.690360 0.184981i
\(688\) −13.2553 −0.505355
\(689\) 24.6918 + 27.1334i 0.940684 + 1.03370i
\(690\) 5.99890i 0.228374i
\(691\) 11.4054 + 42.5657i 0.433883 + 1.61927i 0.743725 + 0.668486i \(0.233057\pi\)
−0.309842 + 0.950788i \(0.600276\pi\)
\(692\) 42.1433 + 24.3314i 1.60205 + 0.924943i
\(693\) −0.747961 0.550853i −0.0284127 0.0209252i
\(694\) −8.70802 + 8.70802i −0.330552 + 0.330552i
\(695\) 3.70209 13.8164i 0.140428 0.524086i
\(696\) −3.90855 + 14.5869i −0.148153 + 0.552915i
\(697\) −1.56991 1.56991i −0.0594645 0.0594645i
\(698\) 33.1745 + 57.4599i 1.25567 + 2.17489i
\(699\) 9.33672 16.1717i 0.353147 0.611669i
\(700\) −1.23787 4.61980i −0.0467872 0.174612i
\(701\) −10.0232 −0.378569 −0.189285 0.981922i \(-0.560617\pi\)
−0.189285 + 0.981922i \(0.560617\pi\)
\(702\) −7.67697 4.92801i −0.289748 0.185996i
\(703\) 4.21213i 0.158864i
\(704\) −3.77935 4.72933i −0.142439 0.178243i
\(705\) 1.86564 3.23137i 0.0702639 0.121701i
\(706\) −23.9768 41.5290i −0.902377 1.56296i
\(707\) −2.21977 + 2.21977i −0.0834831 + 0.0834831i
\(708\) 6.48648 + 1.73805i 0.243777 + 0.0653198i
\(709\) 10.4860 39.1344i 0.393811 1.46972i −0.429985 0.902836i \(-0.641481\pi\)
0.823796 0.566886i \(-0.191852\pi\)
\(710\) 4.83592 4.83592i 0.181489 0.181489i
\(711\) 8.19099 4.72907i 0.307186 0.177354i
\(712\) −40.6280 + 70.3698i −1.52260 + 2.63722i
\(713\) 19.7766 5.29913i 0.740640 0.198454i
\(714\) 0.132436 0.00495629
\(715\) −10.2491 + 7.42786i −0.383294 + 0.277786i
\(716\) 20.9665 0.783556
\(717\) 8.22776 2.20462i 0.307271 0.0823331i
\(718\) 15.6847 27.1666i 0.585347 1.01385i
\(719\) 7.59445 4.38466i 0.283225 0.163520i −0.351657 0.936129i \(-0.614382\pi\)
0.634883 + 0.772609i \(0.281048\pi\)
\(720\) 4.91819 4.91819i 0.183290 0.183290i
\(721\) 0.412457 1.53931i 0.0153607 0.0573269i
\(722\) −44.5367 11.9336i −1.65748 0.444121i
\(723\) −10.2002 + 10.2002i −0.379351 + 0.379351i
\(724\) −42.4400 73.5082i −1.57727 2.73191i
\(725\) −4.82088 + 8.35001i −0.179043 + 0.310111i
\(726\) 24.6326 + 12.9550i 0.914200 + 0.480807i
\(727\) 9.35419i 0.346928i −0.984840 0.173464i \(-0.944504\pi\)
0.984840 0.173464i \(-0.0554960\pi\)
\(728\) −5.84584 1.86534i −0.216661 0.0691340i
\(729\) 1.00000 0.0370370
\(730\) 3.78694 + 14.1331i 0.140161 + 0.523088i
\(731\) 0.188499 0.326489i 0.00697187 0.0120756i
\(732\) 15.4151 + 26.6997i 0.569757 + 0.986848i
\(733\) −0.419471 0.419471i −0.0154935 0.0154935i 0.699318 0.714811i \(-0.253487\pi\)
−0.714811 + 0.699318i \(0.753487\pi\)
\(734\) 18.5110 69.0841i 0.683255 2.54994i
\(735\) 1.89621 7.07675i 0.0699427 0.261030i
\(736\) 7.08438 7.08438i 0.261134 0.261134i
\(737\) −1.58257 1.16552i −0.0582947 0.0429325i
\(738\) −26.0306 15.0288i −0.958199 0.553216i
\(739\) 12.3624 + 46.1371i 0.454758 + 1.69718i 0.688797 + 0.724954i \(0.258139\pi\)
−0.234039 + 0.972227i \(0.575194\pi\)
\(740\) 22.2688i 0.818618i
\(741\) 0.149527 3.17391i 0.00549300 0.116596i
\(742\) −7.21042 −0.264703
\(743\) −16.5083 + 4.42338i −0.605630 + 0.162278i −0.548587 0.836094i \(-0.684834\pi\)
−0.0570430 + 0.998372i \(0.518167\pi\)
\(744\) −48.1004 27.7708i −1.76345 1.01813i
\(745\) −0.750333 1.29962i −0.0274901 0.0476142i
\(746\) −43.3590 + 43.3590i −1.58749 + 1.58749i
\(747\) −0.0188494 + 0.0703468i −0.000689662 + 0.00257385i
\(748\) −2.69740 + 0.409358i −0.0986269 + 0.0149676i
\(749\) −2.98398 2.98398i −0.109032 0.109032i
\(750\) 20.5947 11.8904i 0.752012 0.434174i
\(751\) 11.0208 + 6.36287i 0.402155 + 0.232184i 0.687413 0.726266i \(-0.258746\pi\)
−0.285258 + 0.958451i \(0.592079\pi\)
\(752\) −22.3742 + 5.99516i −0.815905 + 0.218621i
\(753\) 23.4358i 0.854049i
\(754\) 10.3994 + 20.1461i 0.378723 + 0.733676i
\(755\) 16.8936i 0.614820i
\(756\) 1.19079 0.319072i 0.0433087 0.0116045i
\(757\) 9.29878 16.1060i 0.337970 0.585381i −0.646081 0.763269i \(-0.723593\pi\)
0.984051 + 0.177888i \(0.0569264\pi\)
\(758\) 0.830447 + 1.43838i 0.0301632 + 0.0522442i
\(759\) 2.70716 6.91830i 0.0982639 0.251118i
\(760\) 5.47500 + 1.46702i 0.198599 + 0.0532144i
\(761\) −26.0492 6.97985i −0.944281 0.253019i −0.246347 0.969182i \(-0.579230\pi\)
−0.697934 + 0.716162i \(0.745897\pi\)
\(762\) 9.43356 + 9.43356i 0.341742 + 0.341742i
\(763\) 0.348137 + 0.602990i 0.0126034 + 0.0218297i
\(764\) −55.6636 32.1374i −2.01384 1.16269i
\(765\) 0.0511993 + 0.191078i 0.00185111 + 0.00690845i
\(766\) −94.3876 −3.41036
\(767\) 4.88797 2.52316i 0.176494 0.0911061i
\(768\) 30.6679 1.10663
\(769\) −19.0218 + 5.09687i −0.685943 + 0.183798i −0.584926 0.811087i \(-0.698876\pi\)
−0.101017 + 0.994885i \(0.532210\pi\)
\(770\) 0.276041 2.47239i 0.00994781 0.0890988i
\(771\) 22.2621 12.8530i 0.801750 0.462891i
\(772\) −51.0755 51.0755i −1.83825 1.83825i
\(773\) 31.1770 + 8.35386i 1.12136 + 0.300467i 0.771433 0.636310i \(-0.219540\pi\)
0.349926 + 0.936777i \(0.386207\pi\)
\(774\) 1.32099 4.92999i 0.0474818 0.177205i
\(775\) −25.0749 25.0749i −0.900719 0.900719i
\(776\) −1.74553 + 1.00778i −0.0626608 + 0.0361772i
\(777\) −0.669342 + 1.15933i −0.0240125 + 0.0415909i
\(778\) −14.2396 53.1429i −0.510514 1.90527i
\(779\) 10.4692i 0.375097i
\(780\) 0.790521 16.7799i 0.0283052 0.600817i
\(781\) −7.75942 + 3.39474i −0.277654 + 0.121473i
\(782\) 0.274134 + 1.02308i 0.00980301 + 0.0365853i
\(783\) −2.15228 1.24262i −0.0769164 0.0444077i
\(784\) −39.3884 + 22.7409i −1.40673 + 0.812175i
\(785\) −4.13297 + 4.13297i −0.147512 + 0.147512i
\(786\) −46.1188 12.3575i −1.64500 0.440777i
\(787\) 11.5604 + 3.09759i 0.412083 + 0.110417i 0.458904 0.888486i \(-0.348242\pi\)
−0.0468209 + 0.998903i \(0.514909\pi\)
\(788\) −13.0463 + 13.0463i −0.464754 + 0.464754i
\(789\) −19.9874 + 11.5397i −0.711571 + 0.410825i
\(790\) 21.9365 + 12.6651i 0.780466 + 0.450602i
\(791\) 1.18382 + 4.41806i 0.0420917 + 0.157088i
\(792\) −18.4636 + 8.07782i −0.656076 + 0.287033i
\(793\) 24.0591 + 7.67698i 0.854364 + 0.272617i
\(794\) 79.3290i 2.81528i
\(795\) −2.78752 10.4032i −0.0988632 0.368963i
\(796\) 27.4471 47.5398i 0.972837 1.68500i
\(797\) −23.3585 + 13.4861i −0.827402 + 0.477701i −0.852962 0.521973i \(-0.825196\pi\)
0.0255605 + 0.999673i \(0.491863\pi\)
\(798\) 0.441584 + 0.441584i 0.0156319 + 0.0156319i
\(799\) 0.170509 0.636349i 0.00603218 0.0225124i
\(800\) −16.7613 4.49118i −0.592601 0.158787i
\(801\) −9.45563 9.45563i −0.334098 0.334098i
\(802\) 59.5403 34.3756i 2.10244 1.21385i
\(803\) 2.01059 18.0081i 0.0709521 0.635491i
\(804\) 2.51954 0.675108i 0.0888572 0.0238092i
\(805\) −0.664059 −0.0234050
\(806\) −81.4695 + 17.7673i −2.86964 + 0.625825i
\(807\) 21.3332 0.750965
\(808\) 17.6275 + 65.7865i 0.620132 + 2.31436i
\(809\) −26.4470 15.2692i −0.929825 0.536835i −0.0430690 0.999072i \(-0.513714\pi\)
−0.886756 + 0.462237i \(0.847047\pi\)
\(810\) 1.33906 + 2.31933i 0.0470499 + 0.0814928i
\(811\) 29.0949 + 29.0949i 1.02166 + 1.02166i 0.999760 + 0.0219016i \(0.00697206\pi\)
0.0219016 + 0.999760i \(0.493028\pi\)
\(812\) −2.95941 0.792972i −0.103855 0.0278279i
\(813\) 19.0784 + 5.11203i 0.669107 + 0.179287i
\(814\) 14.6156 37.3510i 0.512278 1.30915i
\(815\) −2.24026 3.88025i −0.0784730 0.135919i
\(816\) 0.614024 1.06352i 0.0214951 0.0372307i
\(817\) 1.71713 0.460105i 0.0600749 0.0160970i
\(818\) 58.6965i 2.05227i
\(819\) 0.545515 0.849815i 0.0190618 0.0296949i
\(820\) 55.3487i 1.93286i
\(821\) −23.2267 + 6.22358i −0.810619 + 0.217205i −0.640241 0.768174i \(-0.721165\pi\)
−0.170378 + 0.985379i \(0.554499\pi\)
\(822\) 21.6333 + 12.4900i 0.754546 + 0.435638i
\(823\) −40.0236 + 23.1076i −1.39513 + 0.805481i −0.993878 0.110485i \(-0.964760\pi\)
−0.401256 + 0.915966i \(0.631426\pi\)
\(824\) −24.4477 24.4477i −0.851675 0.851675i
\(825\) −12.7215 + 1.93062i −0.442906 + 0.0672154i
\(826\) −0.279817 + 1.04429i −0.00973607 + 0.0363355i
\(827\) −7.35431 + 7.35431i −0.255734 + 0.255734i −0.823317 0.567582i \(-0.807879\pi\)
0.567582 + 0.823317i \(0.307879\pi\)
\(828\) 4.92973 + 8.53854i 0.171320 + 0.296735i
\(829\) −0.689949 0.398342i −0.0239629 0.0138350i 0.487971 0.872860i \(-0.337737\pi\)
−0.511934 + 0.859025i \(0.671071\pi\)
\(830\) −0.188398 + 0.0504810i −0.00653938 + 0.00175222i
\(831\) −28.9265 −1.00345
\(832\) 4.86754 4.42954i 0.168751 0.153567i
\(833\) 1.29356i 0.0448190i
\(834\) −8.84924 33.0258i −0.306424 1.14359i
\(835\) 21.6851 + 12.5199i 0.750442 + 0.433268i
\(836\) −10.3589 7.62909i −0.358272 0.263857i
\(837\) 6.46328 6.46328i 0.223404 0.223404i
\(838\) 19.1283 71.3878i 0.660776 2.46605i
\(839\) 6.15459 22.9692i 0.212480 0.792986i −0.774559 0.632502i \(-0.782028\pi\)
0.987038 0.160484i \(-0.0513054\pi\)
\(840\) 1.27380 + 1.27380i 0.0439503 + 0.0439503i
\(841\) −11.4118 19.7658i −0.393510 0.681579i
\(842\) 0.471660 0.816938i 0.0162545 0.0281536i
\(843\) −2.77269 10.3478i −0.0954964 0.356397i
\(844\) 103.694 3.56929
\(845\) −8.77219 10.6017i −0.301772 0.364710i
\(846\) 8.91899i 0.306641i
\(847\) −1.43408 + 2.72674i −0.0492756 + 0.0936920i
\(848\) −33.4303 + 57.9029i −1.14800 + 1.98839i
\(849\) 6.39383 + 11.0744i 0.219436 + 0.380074i
\(850\) 1.29717 1.29717i 0.0444927 0.0444927i
\(851\) −10.3415 2.77099i −0.354501 0.0949883i
\(852\) 2.90919 10.8572i 0.0996671 0.371963i
\(853\) −17.8786 + 17.8786i −0.612151 + 0.612151i −0.943506 0.331355i \(-0.892494\pi\)
0.331355 + 0.943506i \(0.392494\pi\)
\(854\) −4.29851 + 2.48175i −0.147092 + 0.0849236i
\(855\) −0.466402 + 0.807831i −0.0159506 + 0.0276273i
\(856\) −88.4352 + 23.6961i −3.02265 + 0.809918i
\(857\) −9.17853 −0.313533 −0.156766 0.987636i \(-0.550107\pi\)
−0.156766 + 0.987636i \(0.550107\pi\)
\(858\) −12.3390 + 27.6257i −0.421247 + 0.943127i
\(859\) −11.0895 −0.378367 −0.189184 0.981942i \(-0.560584\pi\)
−0.189184 + 0.981942i \(0.560584\pi\)
\(860\) 9.07820 2.43250i 0.309564 0.0829474i
\(861\) 1.66363 2.88150i 0.0566965 0.0982013i
\(862\) 67.3363 38.8766i 2.29348 1.32414i
\(863\) −11.7942 + 11.7942i −0.401479 + 0.401479i −0.878754 0.477275i \(-0.841624\pi\)
0.477275 + 0.878754i \(0.341624\pi\)
\(864\) 1.15764 4.32037i 0.0393837 0.146982i
\(865\) −11.3036 3.02878i −0.384332 0.102982i
\(866\) 37.8924 37.8924i 1.28764 1.28764i
\(867\) −8.48254 14.6922i −0.288082 0.498973i
\(868\) 5.63418 9.75868i 0.191236 0.331231i
\(869\) −19.5831 24.5056i −0.664311 0.831294i
\(870\) 6.65580i 0.225653i
\(871\) 1.15423 1.79808i 0.0391094 0.0609256i
\(872\) 15.1060 0.511554
\(873\) −0.0858504 0.320398i −0.00290560 0.0108438i
\(874\) −2.49723 + 4.32534i −0.0844702 + 0.146307i
\(875\) 1.31622 + 2.27977i 0.0444965 + 0.0770701i
\(876\) 17.0043 + 17.0043i 0.574522 + 0.574522i
\(877\) −9.12001 + 34.0364i −0.307961 + 1.14933i 0.622405 + 0.782695i \(0.286155\pi\)
−0.930366 + 0.366631i \(0.880511\pi\)
\(878\) −13.4014 + 50.0148i −0.452276 + 1.68792i
\(879\) 6.67226 6.67226i 0.225050 0.225050i
\(880\) −18.5746 13.6797i −0.626149 0.461142i
\(881\) 2.68348 + 1.54931i 0.0904087 + 0.0521975i 0.544523 0.838746i \(-0.316711\pi\)
−0.454114 + 0.890944i \(0.650044\pi\)
\(882\) −4.53258 16.9158i −0.152620 0.569585i
\(883\) 39.7425i 1.33744i −0.743514 0.668720i \(-0.766842\pi\)
0.743514 0.668720i \(-0.233158\pi\)
\(884\) −0.631978 2.89785i −0.0212557 0.0974653i
\(885\) −1.61487 −0.0542834
\(886\) 4.48471 1.20168i 0.150667 0.0403711i
\(887\) −21.9346 12.6640i −0.736493 0.425214i 0.0843000 0.996440i \(-0.473135\pi\)
−0.820793 + 0.571226i \(0.806468\pi\)
\(888\) 14.5217 + 25.1524i 0.487317 + 0.844058i
\(889\) −1.04426 + 1.04426i −0.0350235 + 0.0350235i
\(890\) 9.26901 34.5924i 0.310698 1.15954i
\(891\) −0.497633 3.27908i −0.0166713 0.109853i
\(892\) −24.0557 24.0557i −0.805446 0.805446i
\(893\) 2.69033 1.55326i 0.0900283 0.0519779i
\(894\) −3.10652 1.79355i −0.103897 0.0599852i
\(895\) −4.87016 + 1.30496i −0.162792 + 0.0436199i
\(896\) 3.79895i 0.126914i
\(897\) 7.69409 + 2.45509i 0.256898 + 0.0819732i
\(898\) 61.7804i 2.06164i
\(899\) −21.9422 + 5.87940i −0.731814 + 0.196089i
\(900\) 8.53827 14.7887i 0.284609 0.492957i
\(901\) −0.950795 1.64683i −0.0316756 0.0548637i
\(902\) −36.3268 + 92.8351i −1.20955 + 3.09107i
\(903\) 0.545733 + 0.146229i 0.0181609 + 0.00486619i
\(904\) 95.8522 + 25.6835i 3.18800 + 0.854221i
\(905\) 14.4332 + 14.4332i 0.479777 + 0.479777i
\(906\) 20.1906 + 34.9712i 0.670789 + 1.16184i
\(907\) −0.445515 0.257218i −0.0147931 0.00854079i 0.492585 0.870264i \(-0.336052\pi\)
−0.507378 + 0.861723i \(0.669385\pi\)
\(908\) 4.55864 + 17.0131i 0.151284 + 0.564599i
\(909\) −11.2084 −0.371759
\(910\) 2.70148 + 0.127270i 0.0895531 + 0.00421896i
\(911\) 6.69235 0.221728 0.110864 0.993836i \(-0.464638\pi\)
0.110864 + 0.993836i \(0.464638\pi\)
\(912\) 5.59348 1.49877i 0.185219 0.0496291i
\(913\) 0.240053 + 0.0268017i 0.00794458 + 0.000887006i
\(914\) 35.0299 20.2245i 1.15869 0.668967i
\(915\) −5.24244 5.24244i −0.173310 0.173310i
\(916\) 79.6465 + 21.3412i 2.63159 + 0.705133i
\(917\) 1.36793 5.10520i 0.0451731 0.168588i
\(918\) 0.334358 + 0.334358i 0.0110354 + 0.0110354i
\(919\) 50.3854 29.0900i 1.66206 0.959591i 0.690331 0.723493i \(-0.257465\pi\)
0.971729 0.236098i \(-0.0758686\pi\)
\(920\) −7.20355 + 12.4769i −0.237494 + 0.411352i
\(921\) 6.45413 + 24.0871i 0.212671 + 0.793698i
\(922\) 88.6894i 2.92083i
\(923\) −4.22333 8.18160i −0.139013 0.269301i
\(924\) −1.63884 3.74593i −0.0539139 0.123232i
\(925\) 4.79934 + 17.9114i 0.157801 + 0.588923i
\(926\) 27.6809 + 15.9816i 0.909651 + 0.525187i
\(927\) 4.92758 2.84494i 0.161843 0.0934400i
\(928\) −7.86015 + 7.86015i −0.258022 + 0.258022i
\(929\) 9.28360 + 2.48753i 0.304585 + 0.0816133i 0.407874 0.913038i \(-0.366270\pi\)
−0.103289 + 0.994651i \(0.532937\pi\)
\(930\) 23.6452 + 6.33571i 0.775357 + 0.207756i
\(931\) 4.31313 4.31313i 0.141357 0.141357i
\(932\) 71.1816 41.0967i 2.33163 1.34617i
\(933\) −4.53272 2.61697i −0.148395 0.0856757i
\(934\) −8.48601 31.6702i −0.277671 1.03628i
\(935\) 0.601082 0.262973i 0.0196575 0.00860014i
\(936\) −10.0495 19.4682i −0.328477 0.636338i
\(937\) 38.3153i 1.25171i −0.779941 0.625853i \(-0.784751\pi\)
0.779941 0.625853i \(-0.215249\pi\)
\(938\) 0.108689 + 0.405633i 0.00354882 + 0.0132444i
\(939\) −9.58187 + 16.5963i −0.312693 + 0.541599i
\(940\) 14.2233 8.21182i 0.463913 0.267840i
\(941\) 35.8498 + 35.8498i 1.16867 + 1.16867i 0.982521 + 0.186150i \(0.0596011\pi\)
0.186150 + 0.982521i \(0.440399\pi\)
\(942\) −3.61603 + 13.4952i −0.117817 + 0.439698i
\(943\) 25.7035 + 6.88723i 0.837021 + 0.224279i
\(944\) 7.08878 + 7.08878i 0.230720 + 0.230720i
\(945\) −0.256742 + 0.148230i −0.00835181 + 0.00482192i
\(946\) −16.8232 1.87829i −0.546969 0.0610686i
\(947\) 31.9585 8.56326i 1.03851 0.278269i 0.301016 0.953619i \(-0.402674\pi\)
0.737497 + 0.675351i \(0.236008\pi\)
\(948\) 41.6312 1.35212
\(949\) 19.6767 + 0.926991i 0.638731 + 0.0300914i
\(950\) 8.65040 0.280656
\(951\) 4.73272 + 17.6628i 0.153469 + 0.572754i
\(952\) 0.275449 + 0.159031i 0.00892736 + 0.00515421i
\(953\) 24.8550 + 43.0502i 0.805133 + 1.39453i 0.916201 + 0.400719i \(0.131240\pi\)
−0.111068 + 0.993813i \(0.535427\pi\)
\(954\) −18.2040 18.2040i −0.589375 0.589375i
\(955\) 14.9299 + 4.00046i 0.483121 + 0.129452i
\(956\) 36.2155 + 9.70391i 1.17129 + 0.313847i
\(957\) −3.00361 + 7.67588i −0.0970929 + 0.248126i
\(958\) 26.7076 + 46.2589i 0.862883 + 1.49456i
\(959\) −1.38260 + 2.39473i −0.0446464 + 0.0773299i
\(960\) −1.86626 + 0.500062i −0.0602331 + 0.0161394i
\(961\) 52.5479i 1.69509i
\(962\) 41.5394 + 13.2547i 1.33928 + 0.427350i
\(963\) 15.0672i 0.485533i
\(964\) −61.3312 + 16.4336i −1.97534 + 0.529292i
\(965\) 15.0429 + 8.68502i 0.484248 + 0.279581i
\(966\) −1.37466 + 0.793661i −0.0442290 + 0.0255356i
\(967\) −12.3750 12.3750i −0.397954 0.397954i 0.479557 0.877511i \(-0.340797\pi\)
−0.877511 + 0.479557i \(0.840797\pi\)
\(968\) 35.6759 + 56.5238i 1.14667 + 1.81674i
\(969\) −0.0426267 + 0.159085i −0.00136937 + 0.00511054i
\(970\) 0.628149 0.628149i 0.0201686 0.0201686i
\(971\) −8.36478 14.4882i −0.268438 0.464949i 0.700020 0.714123i \(-0.253174\pi\)
−0.968459 + 0.249174i \(0.919841\pi\)
\(972\) 3.81192 + 2.20081i 0.122267 + 0.0705911i
\(973\) 3.65585 0.979582i 0.117201 0.0314040i
\(974\) −70.9093 −2.27208
\(975\) −2.98054 13.6669i −0.0954537 0.437690i
\(976\) 46.0253i 1.47323i
\(977\) −9.13756 34.1018i −0.292336 1.09101i −0.943310 0.331914i \(-0.892306\pi\)
0.650973 0.759101i \(-0.274361\pi\)
\(978\) −9.27510 5.35498i −0.296585 0.171233i
\(979\) −26.3003 + 35.7112i −0.840563 + 1.14134i
\(980\) 22.8028 22.8028i 0.728408 0.728408i
\(981\) −0.643422 + 2.40128i −0.0205429 + 0.0766671i
\(982\) 0.750204 2.79980i 0.0239400 0.0893451i
\(983\) 21.4490 + 21.4490i 0.684118 + 0.684118i 0.960925 0.276808i \(-0.0892765\pi\)
−0.276808 + 0.960925i \(0.589276\pi\)
\(984\) −36.0934 62.5156i −1.15062 1.99293i
\(985\) 2.21842 3.84242i 0.0706849 0.122430i
\(986\) −0.304153 1.13511i −0.00968619 0.0361494i
\(987\) 0.987303 0.0314262
\(988\) 7.55515 11.7696i 0.240361 0.374441i
\(989\) 4.51853i 0.143681i
\(990\) 6.93890 5.54507i 0.220533 0.176234i
\(991\) −9.56048 + 16.5592i −0.303699 + 0.526022i −0.976971 0.213373i \(-0.931555\pi\)
0.673272 + 0.739395i \(0.264888\pi\)
\(992\) −20.4416 35.4059i −0.649021 1.12414i
\(993\) −14.1367 + 14.1367i −0.448615 + 0.448615i
\(994\) 1.74796 + 0.468364i 0.0554419 + 0.0148556i
\(995\) −3.41662 + 12.7510i −0.108314 + 0.404233i
\(996\) −0.226672 + 0.226672i −0.00718238 + 0.00718238i
\(997\) −20.3493 + 11.7487i −0.644470 + 0.372085i −0.786334 0.617801i \(-0.788024\pi\)
0.141864 + 0.989886i \(0.454690\pi\)
\(998\) 39.3274 68.1171i 1.24489 2.15621i
\(999\) −4.61681 + 1.23707i −0.146069 + 0.0391392i
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 429.2.bd.b.175.1 yes 56
11.10 odd 2 inner 429.2.bd.b.175.14 yes 56
13.11 odd 12 inner 429.2.bd.b.76.14 yes 56
143.76 even 12 inner 429.2.bd.b.76.1 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.bd.b.76.1 56 143.76 even 12 inner
429.2.bd.b.76.14 yes 56 13.11 odd 12 inner
429.2.bd.b.175.1 yes 56 1.1 even 1 trivial
429.2.bd.b.175.14 yes 56 11.10 odd 2 inner