Properties

Label 630.2.cd.a.23.9
Level $630$
Weight $2$
Character 630.23
Analytic conductor $5.031$
Analytic rank $0$
Dimension $192$
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] = [630,2,Mod(23,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([10, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.23");
 
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.cd (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: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(48\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 23.9
Character \(\chi\) \(=\) 630.23
Dual form 630.2.cd.a.137.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(-0.853456 - 1.50719i) q^{3} +1.00000i q^{4} +(-2.22267 + 0.244427i) q^{5} +(-0.462258 + 1.66923i) q^{6} +(2.34249 - 1.22994i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.54323 + 2.57264i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(-0.853456 - 1.50719i) q^{3} +1.00000i q^{4} +(-2.22267 + 0.244427i) q^{5} +(-0.462258 + 1.66923i) q^{6} +(2.34249 - 1.22994i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.54323 + 2.57264i) q^{9} +(1.74450 + 1.39883i) q^{10} +(-4.18245 - 2.41474i) q^{11} +(1.50719 - 0.853456i) q^{12} +(-0.177591 + 0.0475855i) q^{13} +(-2.52609 - 0.786692i) q^{14} +(2.26535 + 3.14137i) q^{15} -1.00000 q^{16} +(-1.82699 + 6.81840i) q^{17} +(2.91035 - 0.727903i) q^{18} +(-1.09576 - 0.632638i) q^{19} +(-0.244427 - 2.22267i) q^{20} +(-3.85296 - 2.48087i) q^{21} +(1.24996 + 4.66492i) q^{22} +(-1.20545 - 0.322999i) q^{23} +(-1.66923 - 0.462258i) q^{24} +(4.88051 - 1.08656i) q^{25} +(0.159224 + 0.0919281i) q^{26} +(5.19452 + 0.130298i) q^{27} +(1.22994 + 2.34249i) q^{28} +(2.32602 + 4.02879i) q^{29} +(0.619441 - 3.82313i) q^{30} -5.64567 q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.0699256 + 8.36461i) q^{33} +(6.11321 - 3.52947i) q^{34} +(-4.90595 + 3.30631i) q^{35} +(-2.57264 - 1.54323i) q^{36} +(2.60690 + 9.72908i) q^{37} +(0.327478 + 1.22216i) q^{38} +(0.223287 + 0.227051i) q^{39} +(-1.39883 + 1.74450i) q^{40} +(4.51180 + 2.60489i) q^{41} +(0.970213 + 4.47869i) q^{42} +(-0.513956 + 1.91811i) q^{43} +(2.41474 - 4.18245i) q^{44} +(2.80126 - 6.09532i) q^{45} +(0.623987 + 1.08078i) q^{46} +(0.893226 + 0.893226i) q^{47} +(0.853456 + 1.50719i) q^{48} +(3.97450 - 5.76223i) q^{49} +(-4.21936 - 2.68273i) q^{50} +(11.8359 - 3.06560i) q^{51} +(-0.0475855 - 0.177591i) q^{52} +(2.52372 + 0.676229i) q^{53} +(-3.58094 - 3.76521i) q^{54} +(9.88643 + 4.34486i) q^{55} +(0.786692 - 2.52609i) q^{56} +(-0.0183198 + 2.19145i) q^{57} +(1.20404 - 4.49353i) q^{58} +1.35120 q^{59} +(-3.14137 + 2.26535i) q^{60} -11.6088 q^{61} +(3.99209 + 3.99209i) q^{62} +(-0.450805 + 7.92444i) q^{63} -1.00000i q^{64} +(0.383096 - 0.149175i) q^{65} +(5.96411 - 5.86523i) q^{66} +(8.89129 - 8.89129i) q^{67} +(-6.81840 - 1.82699i) q^{68} +(0.541978 + 2.09250i) q^{69} +(5.80694 + 1.13111i) q^{70} +1.54376i q^{71} +(0.727903 + 2.91035i) q^{72} +(-3.26694 + 12.1924i) q^{73} +(5.03614 - 8.72285i) q^{74} +(-5.80295 - 6.42851i) q^{75} +(0.632638 - 1.09576i) q^{76} +(-12.7673 - 0.512342i) q^{77} +(0.00266204 - 0.318437i) q^{78} +9.24893i q^{79} +(2.22267 - 0.244427i) q^{80} +(-4.23691 - 7.94031i) q^{81} +(-1.34839 - 5.03225i) q^{82} +(-9.37820 - 2.51288i) q^{83} +(2.48087 - 3.85296i) q^{84} +(2.39418 - 15.6016i) q^{85} +(1.71973 - 0.992886i) q^{86} +(4.08698 - 6.94414i) q^{87} +(-4.66492 + 1.24996i) q^{88} +(-4.15534 + 7.19726i) q^{89} +(-6.29083 + 2.32926i) q^{90} +(-0.357479 + 0.329895i) q^{91} +(0.322999 - 1.20545i) q^{92} +(4.81833 + 8.50908i) q^{93} -1.26321i q^{94} +(2.59015 + 1.13831i) q^{95} +(0.462258 - 1.66923i) q^{96} +(-9.63550 - 2.58182i) q^{97} +(-6.88491 + 1.26411i) q^{98} +(12.6667 - 7.03343i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) −0.853456 1.50719i −0.492743 0.870175i
\(4\) 1.00000i 0.500000i
\(5\) −2.22267 + 0.244427i −0.994008 + 0.109311i
\(6\) −0.462258 + 1.66923i −0.188716 + 0.681459i
\(7\) 2.34249 1.22994i 0.885377 0.464873i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −1.54323 + 2.57264i −0.514409 + 0.857545i
\(10\) 1.74450 + 1.39883i 0.551659 + 0.442348i
\(11\) −4.18245 2.41474i −1.26106 0.728071i −0.287777 0.957697i \(-0.592916\pi\)
−0.973279 + 0.229626i \(0.926250\pi\)
\(12\) 1.50719 0.853456i 0.435087 0.246372i
\(13\) −0.177591 + 0.0475855i −0.0492550 + 0.0131978i −0.283362 0.959013i \(-0.591450\pi\)
0.234107 + 0.972211i \(0.424783\pi\)
\(14\) −2.52609 0.786692i −0.675125 0.210252i
\(15\) 2.26535 + 3.14137i 0.584910 + 0.811098i
\(16\) −1.00000 −0.250000
\(17\) −1.82699 + 6.81840i −0.443109 + 1.65371i 0.277772 + 0.960647i \(0.410404\pi\)
−0.720881 + 0.693059i \(0.756263\pi\)
\(18\) 2.91035 0.727903i 0.685977 0.171568i
\(19\) −1.09576 0.632638i −0.251385 0.145137i 0.369013 0.929424i \(-0.379696\pi\)
−0.620398 + 0.784287i \(0.713029\pi\)
\(20\) −0.244427 2.22267i −0.0546556 0.497004i
\(21\) −3.85296 2.48087i −0.840784 0.541370i
\(22\) 1.24996 + 4.66492i 0.266492 + 0.994563i
\(23\) −1.20545 0.322999i −0.251354 0.0673500i 0.130942 0.991390i \(-0.458200\pi\)
−0.382296 + 0.924040i \(0.624866\pi\)
\(24\) −1.66923 0.462258i −0.340729 0.0943579i
\(25\) 4.88051 1.08656i 0.976102 0.217312i
\(26\) 0.159224 + 0.0919281i 0.0312264 + 0.0180286i
\(27\) 5.19452 + 0.130298i 0.999686 + 0.0250759i
\(28\) 1.22994 + 2.34249i 0.232436 + 0.442689i
\(29\) 2.32602 + 4.02879i 0.431931 + 0.748127i 0.997040 0.0768897i \(-0.0244989\pi\)
−0.565108 + 0.825017i \(0.691166\pi\)
\(30\) 0.619441 3.82313i 0.113094 0.698004i
\(31\) −5.64567 −1.01399 −0.506996 0.861948i \(-0.669244\pi\)
−0.506996 + 0.861948i \(0.669244\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) −0.0699256 + 8.36461i −0.0121725 + 1.45609i
\(34\) 6.11321 3.52947i 1.04841 0.605298i
\(35\) −4.90595 + 3.30631i −0.829256 + 0.558869i
\(36\) −2.57264 1.54323i −0.428773 0.257204i
\(37\) 2.60690 + 9.72908i 0.428572 + 1.59945i 0.755998 + 0.654574i \(0.227152\pi\)
−0.327426 + 0.944877i \(0.606181\pi\)
\(38\) 0.327478 + 1.22216i 0.0531239 + 0.198261i
\(39\) 0.223287 + 0.227051i 0.0357545 + 0.0363573i
\(40\) −1.39883 + 1.74450i −0.221174 + 0.275830i
\(41\) 4.51180 + 2.60489i 0.704624 + 0.406815i 0.809067 0.587716i \(-0.199973\pi\)
−0.104443 + 0.994531i \(0.533306\pi\)
\(42\) 0.970213 + 4.47869i 0.149707 + 0.691077i
\(43\) −0.513956 + 1.91811i −0.0783775 + 0.292509i −0.993978 0.109581i \(-0.965049\pi\)
0.915600 + 0.402089i \(0.131716\pi\)
\(44\) 2.41474 4.18245i 0.364036 0.630528i
\(45\) 2.80126 6.09532i 0.417587 0.908637i
\(46\) 0.623987 + 1.08078i 0.0920018 + 0.159352i
\(47\) 0.893226 + 0.893226i 0.130290 + 0.130290i 0.769245 0.638954i \(-0.220633\pi\)
−0.638954 + 0.769245i \(0.720633\pi\)
\(48\) 0.853456 + 1.50719i 0.123186 + 0.217544i
\(49\) 3.97450 5.76223i 0.567786 0.823176i
\(50\) −4.21936 2.68273i −0.596707 0.379395i
\(51\) 11.8359 3.06560i 1.65735 0.429270i
\(52\) −0.0475855 0.177591i −0.00659892 0.0246275i
\(53\) 2.52372 + 0.676229i 0.346660 + 0.0928872i 0.427948 0.903803i \(-0.359237\pi\)
−0.0812881 + 0.996691i \(0.525903\pi\)
\(54\) −3.58094 3.76521i −0.487305 0.512381i
\(55\) 9.88643 + 4.34486i 1.33309 + 0.585861i
\(56\) 0.786692 2.52609i 0.105126 0.337563i
\(57\) −0.0183198 + 2.19145i −0.00242652 + 0.290264i
\(58\) 1.20404 4.49353i 0.158098 0.590029i
\(59\) 1.35120 0.175911 0.0879557 0.996124i \(-0.471967\pi\)
0.0879557 + 0.996124i \(0.471967\pi\)
\(60\) −3.14137 + 2.26535i −0.405549 + 0.292455i
\(61\) −11.6088 −1.48636 −0.743178 0.669094i \(-0.766682\pi\)
−0.743178 + 0.669094i \(0.766682\pi\)
\(62\) 3.99209 + 3.99209i 0.506996 + 0.506996i
\(63\) −0.450805 + 7.92444i −0.0567961 + 0.998386i
\(64\) 1.00000i 0.125000i
\(65\) 0.383096 0.149175i 0.0475172 0.0185029i
\(66\) 5.96411 5.86523i 0.734132 0.721959i
\(67\) 8.89129 8.89129i 1.08624 1.08624i 0.0903319 0.995912i \(-0.471207\pi\)
0.995912 0.0903319i \(-0.0287928\pi\)
\(68\) −6.81840 1.82699i −0.826853 0.221555i
\(69\) 0.541978 + 2.09250i 0.0652465 + 0.251908i
\(70\) 5.80694 + 1.13111i 0.694062 + 0.135194i
\(71\) 1.54376i 0.183211i 0.995795 + 0.0916053i \(0.0291998\pi\)
−0.995795 + 0.0916053i \(0.970800\pi\)
\(72\) 0.727903 + 2.91035i 0.0857842 + 0.342988i
\(73\) −3.26694 + 12.1924i −0.382367 + 1.42701i 0.459910 + 0.887966i \(0.347882\pi\)
−0.842276 + 0.539046i \(0.818785\pi\)
\(74\) 5.03614 8.72285i 0.585440 1.01401i
\(75\) −5.80295 6.42851i −0.670067 0.742300i
\(76\) 0.632638 1.09576i 0.0725686 0.125693i
\(77\) −12.7673 0.512342i −1.45497 0.0583868i
\(78\) 0.00266204 0.318437i 0.000301416 0.0360559i
\(79\) 9.24893i 1.04059i 0.853988 + 0.520293i \(0.174177\pi\)
−0.853988 + 0.520293i \(0.825823\pi\)
\(80\) 2.22267 0.244427i 0.248502 0.0273278i
\(81\) −4.23691 7.94031i −0.470768 0.882257i
\(82\) −1.34839 5.03225i −0.148905 0.555720i
\(83\) −9.37820 2.51288i −1.02939 0.275825i −0.295681 0.955287i \(-0.595546\pi\)
−0.733710 + 0.679462i \(0.762213\pi\)
\(84\) 2.48087 3.85296i 0.270685 0.420392i
\(85\) 2.39418 15.6016i 0.259685 1.69223i
\(86\) 1.71973 0.992886i 0.185443 0.107066i
\(87\) 4.08698 6.94414i 0.438170 0.744490i
\(88\) −4.66492 + 1.24996i −0.497282 + 0.133246i
\(89\) −4.15534 + 7.19726i −0.440465 + 0.762908i −0.997724 0.0674311i \(-0.978520\pi\)
0.557259 + 0.830339i \(0.311853\pi\)
\(90\) −6.29083 + 2.32926i −0.663112 + 0.245525i
\(91\) −0.357479 + 0.329895i −0.0374739 + 0.0345824i
\(92\) 0.322999 1.20545i 0.0336750 0.125677i
\(93\) 4.81833 + 8.50908i 0.499638 + 0.882351i
\(94\) 1.26321i 0.130290i
\(95\) 2.59015 + 1.13831i 0.265744 + 0.116788i
\(96\) 0.462258 1.66923i 0.0471790 0.170365i
\(97\) −9.63550 2.58182i −0.978337 0.262144i −0.265993 0.963975i \(-0.585700\pi\)
−0.712344 + 0.701831i \(0.752366\pi\)
\(98\) −6.88491 + 1.26411i −0.695481 + 0.127695i
\(99\) 12.6667 7.03343i 1.27305 0.706887i
\(100\) 1.08656 + 4.88051i 0.108656 + 0.488051i
\(101\) −12.4479 7.18677i −1.23861 0.715110i −0.269798 0.962917i \(-0.586957\pi\)
−0.968810 + 0.247807i \(0.920290\pi\)
\(102\) −10.5369 6.20151i −1.04331 0.614041i
\(103\) −4.77148 + 17.8074i −0.470148 + 1.75462i 0.169083 + 0.985602i \(0.445920\pi\)
−0.639231 + 0.769015i \(0.720747\pi\)
\(104\) −0.0919281 + 0.159224i −0.00901429 + 0.0156132i
\(105\) 9.17024 + 4.57238i 0.894924 + 0.446219i
\(106\) −1.30637 2.26271i −0.126886 0.219773i
\(107\) −0.774365 + 0.207491i −0.0748607 + 0.0200589i −0.296055 0.955171i \(-0.595671\pi\)
0.221194 + 0.975230i \(0.429005\pi\)
\(108\) −0.130298 + 5.19452i −0.0125379 + 0.499843i
\(109\) 5.81142 3.35523i 0.556634 0.321373i −0.195160 0.980771i \(-0.562523\pi\)
0.751793 + 0.659399i \(0.229189\pi\)
\(110\) −3.91848 10.0630i −0.373612 0.959473i
\(111\) 12.4387 12.2324i 1.18063 1.16105i
\(112\) −2.34249 + 1.22994i −0.221344 + 0.116218i
\(113\) −1.44770 5.40288i −0.136188 0.508260i −0.999990 0.00442910i \(-0.998590\pi\)
0.863802 0.503831i \(-0.168076\pi\)
\(114\) 1.56254 1.53663i 0.146345 0.143919i
\(115\) 2.75827 + 0.423276i 0.257210 + 0.0394707i
\(116\) −4.02879 + 2.32602i −0.374064 + 0.215966i
\(117\) 0.151643 0.530313i 0.0140194 0.0490275i
\(118\) −0.955444 0.955444i −0.0879557 0.0879557i
\(119\) 4.10652 + 18.2191i 0.376444 + 1.67014i
\(120\) 3.82313 + 0.619441i 0.349002 + 0.0565470i
\(121\) 6.16192 + 10.6728i 0.560175 + 0.970251i
\(122\) 8.20867 + 8.20867i 0.743178 + 0.743178i
\(123\) 0.0754318 9.02328i 0.00680146 0.813602i
\(124\) 5.64567i 0.506996i
\(125\) −10.5822 + 3.60799i −0.946498 + 0.322709i
\(126\) 5.92219 5.28466i 0.527591 0.470795i
\(127\) −2.18708 + 2.18708i −0.194072 + 0.194072i −0.797453 0.603381i \(-0.793820\pi\)
0.603381 + 0.797453i \(0.293820\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 3.32959 0.862394i 0.293154 0.0759296i
\(130\) −0.376372 0.165407i −0.0330100 0.0145071i
\(131\) −13.7180 + 7.92011i −1.19855 + 0.691983i −0.960232 0.279204i \(-0.909929\pi\)
−0.238318 + 0.971187i \(0.576596\pi\)
\(132\) −8.36461 0.0699256i −0.728046 0.00608624i
\(133\) −3.34492 0.134229i −0.290041 0.0116391i
\(134\) −12.5742 −1.08624
\(135\) −11.5775 + 0.980072i −0.996436 + 0.0843511i
\(136\) 3.52947 + 6.11321i 0.302649 + 0.524204i
\(137\) 6.98457 1.87151i 0.596732 0.159894i 0.0522037 0.998636i \(-0.483375\pi\)
0.544528 + 0.838743i \(0.316709\pi\)
\(138\) 1.09639 1.86286i 0.0933307 0.158577i
\(139\) −13.1934 7.61723i −1.11905 0.646085i −0.177893 0.984050i \(-0.556928\pi\)
−0.941159 + 0.337965i \(0.890262\pi\)
\(140\) −3.30631 4.90595i −0.279434 0.414628i
\(141\) 0.583929 2.10859i 0.0491757 0.177575i
\(142\) 1.09160 1.09160i 0.0916053 0.0916053i
\(143\) 0.857673 + 0.229813i 0.0717222 + 0.0192179i
\(144\) 1.54323 2.57264i 0.128602 0.214386i
\(145\) −6.15472 8.38612i −0.511122 0.696429i
\(146\) 10.9314 6.31125i 0.904689 0.522323i
\(147\) −12.0768 1.07251i −0.996080 0.0884591i
\(148\) −9.72908 + 2.60690i −0.799725 + 0.214286i
\(149\) −9.44270 16.3552i −0.773576 1.33987i −0.935591 0.353085i \(-0.885133\pi\)
0.162015 0.986788i \(-0.448201\pi\)
\(150\) −0.442337 + 8.64895i −0.0361167 + 0.706184i
\(151\) −7.70459 + 13.3447i −0.626991 + 1.08598i 0.361162 + 0.932503i \(0.382380\pi\)
−0.988152 + 0.153477i \(0.950953\pi\)
\(152\) −1.22216 + 0.327478i −0.0991306 + 0.0265620i
\(153\) −14.7218 15.2225i −1.19019 1.23067i
\(154\) 8.66558 + 9.39014i 0.698292 + 0.756679i
\(155\) 12.5485 1.37996i 1.00792 0.110841i
\(156\) −0.227051 + 0.223287i −0.0181787 + 0.0178772i
\(157\) −6.60761 + 6.60761i −0.527345 + 0.527345i −0.919780 0.392435i \(-0.871633\pi\)
0.392435 + 0.919780i \(0.371633\pi\)
\(158\) 6.53998 6.53998i 0.520293 0.520293i
\(159\) −1.13468 4.38085i −0.0899861 0.347424i
\(160\) −1.74450 1.39883i −0.137915 0.110587i
\(161\) −3.22102 + 0.726007i −0.253852 + 0.0572173i
\(162\) −2.61870 + 8.61060i −0.205745 + 0.676512i
\(163\) −3.75065 + 1.00498i −0.293774 + 0.0787164i −0.402696 0.915334i \(-0.631927\pi\)
0.108922 + 0.994050i \(0.465260\pi\)
\(164\) −2.60489 + 4.51180i −0.203407 + 0.352312i
\(165\) −1.88912 18.6088i −0.147067 1.44870i
\(166\) 4.85451 + 8.40826i 0.376783 + 0.652608i
\(167\) 17.5223 4.69510i 1.35592 0.363318i 0.493603 0.869687i \(-0.335679\pi\)
0.862317 + 0.506369i \(0.169013\pi\)
\(168\) −4.47869 + 0.970213i −0.345539 + 0.0748535i
\(169\) −11.2291 + 6.48310i −0.863774 + 0.498700i
\(170\) −12.7249 + 9.33907i −0.975959 + 0.716274i
\(171\) 3.31856 1.84269i 0.253776 0.140914i
\(172\) −1.91811 0.513956i −0.146254 0.0391888i
\(173\) 13.9299 13.9299i 1.05907 1.05907i 0.0609304 0.998142i \(-0.480593\pi\)
0.998142 0.0609304i \(-0.0194068\pi\)
\(174\) −7.80018 + 2.02032i −0.591330 + 0.153160i
\(175\) 10.0961 8.54798i 0.763196 0.646167i
\(176\) 4.18245 + 2.41474i 0.315264 + 0.182018i
\(177\) −1.15319 2.03651i −0.0866791 0.153074i
\(178\) 8.02750 2.15096i 0.601686 0.161221i
\(179\) −6.59655 11.4256i −0.493049 0.853986i 0.506919 0.861994i \(-0.330784\pi\)
−0.999968 + 0.00800778i \(0.997451\pi\)
\(180\) 6.09532 + 2.80126i 0.454319 + 0.208793i
\(181\) −16.6832 −1.24005 −0.620027 0.784580i \(-0.712879\pi\)
−0.620027 + 0.784580i \(0.712879\pi\)
\(182\) 0.486046 + 0.0195046i 0.0360282 + 0.00144578i
\(183\) 9.90761 + 17.4967i 0.732392 + 1.29339i
\(184\) −1.08078 + 0.623987i −0.0796759 + 0.0460009i
\(185\) −8.17232 20.9873i −0.600841 1.54302i
\(186\) 2.60976 9.42391i 0.191357 0.690994i
\(187\) 24.1059 24.1059i 1.76280 1.76280i
\(188\) −0.893226 + 0.893226i −0.0651452 + 0.0651452i
\(189\) 12.3284 6.08372i 0.896756 0.442525i
\(190\) −1.02660 2.63642i −0.0744777 0.191266i
\(191\) 13.8102i 0.999269i −0.866236 0.499634i \(-0.833468\pi\)
0.866236 0.499634i \(-0.166532\pi\)
\(192\) −1.50719 + 0.853456i −0.108772 + 0.0615929i
\(193\) −2.67173 2.67173i −0.192316 0.192316i 0.604380 0.796696i \(-0.293421\pi\)
−0.796696 + 0.604380i \(0.793421\pi\)
\(194\) 4.98770 + 8.63895i 0.358096 + 0.620241i
\(195\) −0.551790 0.450082i −0.0395145 0.0322311i
\(196\) 5.76223 + 3.97450i 0.411588 + 0.283893i
\(197\) 5.44571 + 5.44571i 0.387991 + 0.387991i 0.873970 0.485979i \(-0.161537\pi\)
−0.485979 + 0.873970i \(0.661537\pi\)
\(198\) −13.9301 3.98332i −0.989969 0.283083i
\(199\) 11.0581 6.38441i 0.783890 0.452579i −0.0539173 0.998545i \(-0.517171\pi\)
0.837807 + 0.545966i \(0.183837\pi\)
\(200\) 2.68273 4.21936i 0.189698 0.298354i
\(201\) −20.9892 5.81251i −1.48046 0.409983i
\(202\) 3.72015 + 13.8838i 0.261749 + 0.976859i
\(203\) 10.4038 + 6.57653i 0.730206 + 0.461582i
\(204\) 3.06560 + 11.8359i 0.214635 + 0.828676i
\(205\) −10.6649 4.68699i −0.744871 0.327354i
\(206\) 15.9657 9.21780i 1.11238 0.642234i
\(207\) 2.69124 2.60272i 0.187054 0.180902i
\(208\) 0.177591 0.0475855i 0.0123137 0.00329946i
\(209\) 3.05531 + 5.29196i 0.211340 + 0.366052i
\(210\) −3.25117 9.71750i −0.224352 0.670571i
\(211\) 4.03431 6.98763i 0.277734 0.481049i −0.693088 0.720853i \(-0.743750\pi\)
0.970821 + 0.239805i \(0.0770834\pi\)
\(212\) −0.676229 + 2.52372i −0.0464436 + 0.173330i
\(213\) 2.32673 1.31753i 0.159425 0.0902757i
\(214\) 0.694277 + 0.400841i 0.0474598 + 0.0274009i
\(215\) 0.673516 4.38895i 0.0459334 0.299324i
\(216\) 3.76521 3.58094i 0.256190 0.243652i
\(217\) −13.2249 + 6.94383i −0.897766 + 0.471378i
\(218\) −6.48180 1.73679i −0.439003 0.117631i
\(219\) 21.1644 5.48178i 1.43016 0.370424i
\(220\) −4.34486 + 9.88643i −0.292930 + 0.666543i
\(221\) 1.29783i 0.0873013i
\(222\) −17.4451 0.145836i −1.17084 0.00978785i
\(223\) 3.84121 14.3356i 0.257227 0.959983i −0.709611 0.704593i \(-0.751129\pi\)
0.966838 0.255390i \(-0.0822038\pi\)
\(224\) 2.52609 + 0.786692i 0.168781 + 0.0525631i
\(225\) −4.73640 + 14.2326i −0.315760 + 0.948839i
\(226\) −2.79673 + 4.84409i −0.186036 + 0.322224i
\(227\) 3.01823 0.808732i 0.200327 0.0536774i −0.157260 0.987557i \(-0.550266\pi\)
0.357587 + 0.933880i \(0.383600\pi\)
\(228\) −2.19145 0.0183198i −0.145132 0.00121326i
\(229\) 12.4975 7.21542i 0.825856 0.476808i −0.0265755 0.999647i \(-0.508460\pi\)
0.852432 + 0.522838i \(0.175127\pi\)
\(230\) −1.65109 2.24969i −0.108869 0.148340i
\(231\) 10.1241 + 19.6800i 0.666120 + 1.29485i
\(232\) 4.49353 + 1.20404i 0.295015 + 0.0790489i
\(233\) 3.89376 + 14.5317i 0.255089 + 0.952004i 0.968041 + 0.250792i \(0.0806909\pi\)
−0.712952 + 0.701213i \(0.752642\pi\)
\(234\) −0.482216 + 0.267760i −0.0315234 + 0.0175040i
\(235\) −2.20367 1.76702i −0.143752 0.115267i
\(236\) 1.35120i 0.0879557i
\(237\) 13.9399 7.89356i 0.905492 0.512742i
\(238\) 9.97911 15.7866i 0.646849 1.02329i
\(239\) −12.0443 + 20.8613i −0.779078 + 1.34940i 0.153396 + 0.988165i \(0.450979\pi\)
−0.932474 + 0.361238i \(0.882354\pi\)
\(240\) −2.26535 3.14137i −0.146228 0.202775i
\(241\) −4.75148 + 8.22980i −0.306070 + 0.530128i −0.977499 0.210940i \(-0.932347\pi\)
0.671429 + 0.741069i \(0.265681\pi\)
\(242\) 3.18965 11.9039i 0.205038 0.765213i
\(243\) −8.35152 + 13.1625i −0.535750 + 0.844376i
\(244\) 11.6088i 0.743178i
\(245\) −7.42556 + 13.7790i −0.474402 + 0.880309i
\(246\) −6.43376 + 6.32708i −0.410201 + 0.403400i
\(247\) 0.224702 + 0.0602088i 0.0142975 + 0.00383099i
\(248\) −3.99209 + 3.99209i −0.253498 + 0.253498i
\(249\) 4.21650 + 16.2793i 0.267210 + 1.03166i
\(250\) 10.0340 + 4.93149i 0.634604 + 0.311895i
\(251\) 27.1128i 1.71135i 0.517516 + 0.855674i \(0.326857\pi\)
−0.517516 + 0.855674i \(0.673143\pi\)
\(252\) −7.92444 0.450805i −0.499193 0.0283980i
\(253\) 4.26177 + 4.26177i 0.267935 + 0.267935i
\(254\) 3.09299 0.194072
\(255\) −25.5579 + 9.70681i −1.60050 + 0.607864i
\(256\) 1.00000 0.0625000
\(257\) −3.55961 + 13.2847i −0.222043 + 0.828674i 0.761525 + 0.648135i \(0.224451\pi\)
−0.983568 + 0.180539i \(0.942216\pi\)
\(258\) −2.96418 1.74457i −0.184542 0.108612i
\(259\) 18.0728 + 19.5839i 1.12299 + 1.21689i
\(260\) 0.149175 + 0.383096i 0.00925143 + 0.0237586i
\(261\) −13.9542 0.233322i −0.863742 0.0144423i
\(262\) 15.3005 + 4.09975i 0.945266 + 0.253283i
\(263\) −0.0411747 0.153666i −0.00253894 0.00947545i 0.964645 0.263554i \(-0.0848946\pi\)
−0.967184 + 0.254078i \(0.918228\pi\)
\(264\) 5.86523 + 5.96411i 0.360980 + 0.367066i
\(265\) −5.77468 0.886167i −0.354736 0.0544368i
\(266\) 2.27030 + 2.46013i 0.139201 + 0.150840i
\(267\) 14.3940 + 0.120330i 0.880899 + 0.00736405i
\(268\) 8.89129 + 8.89129i 0.543122 + 0.543122i
\(269\) 6.12973 + 10.6170i 0.373736 + 0.647330i 0.990137 0.140103i \(-0.0447433\pi\)
−0.616401 + 0.787432i \(0.711410\pi\)
\(270\) 8.87957 + 7.49354i 0.540394 + 0.456042i
\(271\) 13.7993 23.9011i 0.838249 1.45189i −0.0531090 0.998589i \(-0.516913\pi\)
0.891358 0.453301i \(-0.149754\pi\)
\(272\) 1.82699 6.81840i 0.110777 0.413426i
\(273\) 0.802305 + 0.257236i 0.0485577 + 0.0155686i
\(274\) −6.26219 3.61548i −0.378313 0.218419i
\(275\) −23.0362 7.24067i −1.38914 0.436629i
\(276\) −2.09250 + 0.541978i −0.125954 + 0.0326232i
\(277\) −1.06946 3.99129i −0.0642579 0.239814i 0.926326 0.376724i \(-0.122949\pi\)
−0.990583 + 0.136910i \(0.956283\pi\)
\(278\) 3.94297 + 14.7154i 0.236484 + 0.882568i
\(279\) 8.71255 14.5243i 0.521607 0.869545i
\(280\) −1.13111 + 5.80694i −0.0675968 + 0.347031i
\(281\) 17.9800 10.3808i 1.07260 0.619264i 0.143707 0.989620i \(-0.454098\pi\)
0.928890 + 0.370356i \(0.120764\pi\)
\(282\) −1.90390 + 1.07810i −0.113375 + 0.0641997i
\(283\) 6.22568 + 6.22568i 0.370078 + 0.370078i 0.867506 0.497427i \(-0.165722\pi\)
−0.497427 + 0.867506i \(0.665722\pi\)
\(284\) −1.54376 −0.0916053
\(285\) −0.494930 4.87534i −0.0293171 0.288790i
\(286\) −0.443964 0.768969i −0.0262522 0.0454701i
\(287\) 13.7727 + 0.552687i 0.812976 + 0.0326241i
\(288\) −2.91035 + 0.727903i −0.171494 + 0.0428921i
\(289\) −28.4303 16.4143i −1.67237 0.965544i
\(290\) −1.57784 + 10.2819i −0.0926537 + 0.603775i
\(291\) 4.33218 + 16.7260i 0.253957 + 0.980494i
\(292\) −12.1924 3.26694i −0.713506 0.191183i
\(293\) −4.99037 18.6243i −0.291541 1.08804i −0.943926 0.330157i \(-0.892898\pi\)
0.652385 0.757888i \(-0.273768\pi\)
\(294\) 7.78123 + 9.29798i 0.453810 + 0.542269i
\(295\) −3.00327 + 0.330270i −0.174857 + 0.0192291i
\(296\) 8.72285 + 5.03614i 0.507006 + 0.292720i
\(297\) −21.4112 13.0884i −1.24240 0.759464i
\(298\) −4.88790 + 18.2419i −0.283149 + 1.05673i
\(299\) 0.229448 0.0132693
\(300\) 6.42851 5.80295i 0.371150 0.335034i
\(301\) 1.15522 + 5.12528i 0.0665858 + 0.295416i
\(302\) 14.8841 3.98819i 0.856485 0.229495i
\(303\) −0.208113 + 24.8948i −0.0119558 + 1.43017i
\(304\) 1.09576 + 0.632638i 0.0628463 + 0.0362843i
\(305\) 25.8025 2.83751i 1.47745 0.162475i
\(306\) −0.354038 + 21.1738i −0.0202390 + 1.21043i
\(307\) −12.4832 + 12.4832i −0.712453 + 0.712453i −0.967048 0.254595i \(-0.918058\pi\)
0.254595 + 0.967048i \(0.418058\pi\)
\(308\) 0.512342 12.7673i 0.0291934 0.727485i
\(309\) 30.9114 8.00633i 1.75849 0.455464i
\(310\) −9.84888 7.89732i −0.559379 0.448538i
\(311\) 7.99239i 0.453207i 0.973987 + 0.226604i \(0.0727622\pi\)
−0.973987 + 0.226604i \(0.927238\pi\)
\(312\) 0.318437 + 0.00266204i 0.0180279 + 0.000150708i
\(313\) −4.27800 4.27800i −0.241807 0.241807i 0.575791 0.817597i \(-0.304694\pi\)
−0.817597 + 0.575791i \(0.804694\pi\)
\(314\) 9.34457 0.527345
\(315\) −0.934958 17.7236i −0.0526789 0.998612i
\(316\) −9.24893 −0.520293
\(317\) 13.4554 + 13.4554i 0.755730 + 0.755730i 0.975542 0.219813i \(-0.0705446\pi\)
−0.219813 + 0.975542i \(0.570545\pi\)
\(318\) −2.29539 + 3.90007i −0.128719 + 0.218705i
\(319\) 22.4669i 1.25791i
\(320\) 0.244427 + 2.22267i 0.0136639 + 0.124251i
\(321\) 0.973614 + 0.990029i 0.0543418 + 0.0552580i
\(322\) 2.79097 + 1.76424i 0.155535 + 0.0983174i
\(323\) 6.31552 6.31552i 0.351405 0.351405i
\(324\) 7.94031 4.23691i 0.441129 0.235384i
\(325\) −0.815032 + 0.425205i −0.0452098 + 0.0235861i
\(326\) 3.36274 + 1.94148i 0.186245 + 0.107529i
\(327\) −10.0168 5.89536i −0.553928 0.326014i
\(328\) 5.03225 1.34839i 0.277860 0.0744523i
\(329\) 3.19098 + 0.993759i 0.175925 + 0.0547877i
\(330\) −11.8226 + 14.4942i −0.650814 + 0.797882i
\(331\) −5.93048 −0.325969 −0.162984 0.986629i \(-0.552112\pi\)
−0.162984 + 0.986629i \(0.552112\pi\)
\(332\) 2.51288 9.37820i 0.137912 0.514696i
\(333\) −29.0524 8.30756i −1.59206 0.455252i
\(334\) −15.7101 9.07024i −0.859619 0.496301i
\(335\) −17.5891 + 21.9357i −0.960996 + 1.19847i
\(336\) 3.85296 + 2.48087i 0.210196 + 0.135343i
\(337\) 5.77250 + 21.5433i 0.314448 + 1.17354i 0.924502 + 0.381177i \(0.124481\pi\)
−0.610054 + 0.792360i \(0.708852\pi\)
\(338\) 12.5244 + 3.35590i 0.681237 + 0.182537i
\(339\) −6.90760 + 6.79307i −0.375169 + 0.368949i
\(340\) 15.6016 + 2.39418i 0.846116 + 0.129843i
\(341\) 23.6127 + 13.6328i 1.27870 + 0.738259i
\(342\) −3.64955 1.04359i −0.197345 0.0564311i
\(343\) 2.22304 18.3864i 0.120033 0.992770i
\(344\) 0.992886 + 1.71973i 0.0535328 + 0.0927216i
\(345\) −1.71610 4.51847i −0.0923918 0.243266i
\(346\) −19.6999 −1.05907
\(347\) 18.7185 + 18.7185i 1.00486 + 1.00486i 0.999988 + 0.00487336i \(0.00155125\pi\)
0.00487336 + 0.999988i \(0.498449\pi\)
\(348\) 6.94414 + 4.08698i 0.372245 + 0.219085i
\(349\) −3.94585 + 2.27814i −0.211217 + 0.121946i −0.601877 0.798589i \(-0.705580\pi\)
0.390660 + 0.920535i \(0.372247\pi\)
\(350\) −13.1834 1.09471i −0.704682 0.0585147i
\(351\) −0.928702 + 0.224044i −0.0495704 + 0.0119586i
\(352\) −1.24996 4.66492i −0.0666231 0.248641i
\(353\) 0.395422 + 1.47573i 0.0210462 + 0.0785454i 0.975650 0.219332i \(-0.0703879\pi\)
−0.954604 + 0.297878i \(0.903721\pi\)
\(354\) −0.624603 + 2.25546i −0.0331973 + 0.119876i
\(355\) −0.377337 3.43127i −0.0200270 0.182113i
\(356\) −7.19726 4.15534i −0.381454 0.220232i
\(357\) 23.9549 21.7385i 1.26783 1.15052i
\(358\) −3.41462 + 12.7435i −0.180468 + 0.673517i
\(359\) 0.774061 1.34071i 0.0408534 0.0707601i −0.844876 0.534963i \(-0.820326\pi\)
0.885729 + 0.464203i \(0.153659\pi\)
\(360\) −2.32926 6.29083i −0.122763 0.331556i
\(361\) −8.69954 15.0680i −0.457870 0.793055i
\(362\) 11.7968 + 11.7968i 0.620027 + 0.620027i
\(363\) 10.8269 18.3959i 0.568266 0.965535i
\(364\) −0.329895 0.357479i −0.0172912 0.0187370i
\(365\) 4.28118 27.8982i 0.224087 1.46026i
\(366\) 5.36626 19.3777i 0.280499 1.01289i
\(367\) −1.12596 4.20215i −0.0587748 0.219350i 0.930292 0.366820i \(-0.119554\pi\)
−0.989067 + 0.147470i \(0.952887\pi\)
\(368\) 1.20545 + 0.322999i 0.0628384 + 0.0168375i
\(369\) −13.6641 + 7.58728i −0.711327 + 0.394978i
\(370\) −9.06157 + 20.6190i −0.471089 + 1.07193i
\(371\) 6.74351 1.51996i 0.350105 0.0789125i
\(372\) −8.50908 + 4.81833i −0.441175 + 0.249819i
\(373\) −1.00941 + 3.76716i −0.0522652 + 0.195056i −0.987122 0.159968i \(-0.948861\pi\)
0.934857 + 0.355025i \(0.115527\pi\)
\(374\) −34.0909 −1.76280
\(375\) 14.4693 + 12.8701i 0.747194 + 0.664607i
\(376\) 1.26321 0.0651452
\(377\) −0.604793 0.604793i −0.0311484 0.0311484i
\(378\) −13.0193 4.41563i −0.669641 0.227115i
\(379\) 27.4556i 1.41030i 0.709058 + 0.705150i \(0.249120\pi\)
−0.709058 + 0.705150i \(0.750880\pi\)
\(380\) −1.13831 + 2.59015i −0.0583942 + 0.132872i
\(381\) 5.16291 + 1.42976i 0.264504 + 0.0732488i
\(382\) −9.76526 + 9.76526i −0.499634 + 0.499634i
\(383\) −21.9460 5.88041i −1.12139 0.300475i −0.349943 0.936771i \(-0.613799\pi\)
−0.771445 + 0.636296i \(0.780466\pi\)
\(384\) 1.66923 + 0.462258i 0.0851824 + 0.0235895i
\(385\) 28.5027 1.98191i 1.45263 0.101008i
\(386\) 3.77840i 0.192316i
\(387\) −4.14145 4.28230i −0.210522 0.217681i
\(388\) 2.58182 9.63550i 0.131072 0.489168i
\(389\) −7.40808 + 12.8312i −0.375605 + 0.650566i −0.990417 0.138107i \(-0.955898\pi\)
0.614813 + 0.788673i \(0.289232\pi\)
\(390\) 0.0719178 + 0.708431i 0.00364170 + 0.0358728i
\(391\) 4.40468 7.62913i 0.222754 0.385822i
\(392\) −1.26411 6.88491i −0.0638474 0.347741i
\(393\) 23.6448 + 13.9162i 1.19272 + 0.701978i
\(394\) 7.70140i 0.387991i
\(395\) −2.26069 20.5573i −0.113748 1.03435i
\(396\) 7.03343 + 12.6667i 0.353443 + 0.636526i
\(397\) −3.99241 14.8999i −0.200373 0.747804i −0.990810 0.135260i \(-0.956813\pi\)
0.790437 0.612544i \(-0.209854\pi\)
\(398\) −12.3337 3.30481i −0.618234 0.165655i
\(399\) 2.65243 + 5.15597i 0.132788 + 0.258121i
\(400\) −4.88051 + 1.08656i −0.244026 + 0.0543280i
\(401\) 3.42369 1.97667i 0.170971 0.0987101i −0.412073 0.911151i \(-0.635195\pi\)
0.583044 + 0.812441i \(0.301862\pi\)
\(402\) 10.7315 + 18.9516i 0.535239 + 0.945222i
\(403\) 1.00262 0.268652i 0.0499442 0.0133825i
\(404\) 7.18677 12.4479i 0.357555 0.619304i
\(405\) 11.3581 + 16.6131i 0.564387 + 0.825510i
\(406\) −2.70632 12.0069i −0.134312 0.595894i
\(407\) 12.5900 46.9864i 0.624061 2.32903i
\(408\) 6.20151 10.5369i 0.307021 0.521655i
\(409\) 18.7041i 0.924858i 0.886656 + 0.462429i \(0.153022\pi\)
−0.886656 + 0.462429i \(0.846978\pi\)
\(410\) 4.22704 + 10.8555i 0.208759 + 0.536113i
\(411\) −8.78173 8.92980i −0.433171 0.440474i
\(412\) −17.8074 4.77148i −0.877308 0.235074i
\(413\) 3.16517 1.66189i 0.155748 0.0817765i
\(414\) −3.74340 0.0625917i −0.183978 0.00307621i
\(415\) 21.4588 + 3.29302i 1.05337 + 0.161648i
\(416\) −0.159224 0.0919281i −0.00780660 0.00450714i
\(417\) −0.220578 + 26.3859i −0.0108018 + 1.29212i
\(418\) 1.58155 5.90241i 0.0773559 0.288696i
\(419\) −11.9221 + 20.6497i −0.582434 + 1.00881i 0.412756 + 0.910842i \(0.364566\pi\)
−0.995190 + 0.0979641i \(0.968767\pi\)
\(420\) −4.57238 + 9.17024i −0.223110 + 0.447462i
\(421\) −5.70308 9.87803i −0.277951 0.481426i 0.692924 0.721010i \(-0.256322\pi\)
−0.970875 + 0.239585i \(0.922989\pi\)
\(422\) −7.79369 + 2.08831i −0.379391 + 0.101658i
\(423\) −3.67639 + 0.919496i −0.178752 + 0.0447074i
\(424\) 2.26271 1.30637i 0.109887 0.0634431i
\(425\) −1.50801 + 35.2624i −0.0731494 + 1.71048i
\(426\) −2.57689 0.713615i −0.124850 0.0345747i
\(427\) −27.1935 + 14.2781i −1.31599 + 0.690967i
\(428\) −0.207491 0.774365i −0.0100294 0.0374304i
\(429\) −0.385615 1.48881i −0.0186177 0.0718804i
\(430\) −3.57970 + 2.62721i −0.172628 + 0.126695i
\(431\) −7.78274 + 4.49337i −0.374881 + 0.216438i −0.675589 0.737279i \(-0.736111\pi\)
0.300708 + 0.953716i \(0.402777\pi\)
\(432\) −5.19452 0.130298i −0.249921 0.00626897i
\(433\) −15.0264 15.0264i −0.722122 0.722122i 0.246915 0.969037i \(-0.420583\pi\)
−0.969037 + 0.246915i \(0.920583\pi\)
\(434\) 14.2615 + 4.44140i 0.684572 + 0.213194i
\(435\) −7.38666 + 16.4335i −0.354163 + 0.787926i
\(436\) 3.35523 + 5.81142i 0.160686 + 0.278317i
\(437\) 1.11654 + 1.11654i 0.0534115 + 0.0534115i
\(438\) −18.8417 11.0893i −0.900291 0.529867i
\(439\) 18.5053i 0.883212i −0.897209 0.441606i \(-0.854409\pi\)
0.897209 0.441606i \(-0.145591\pi\)
\(440\) 10.0630 3.91848i 0.479737 0.186806i
\(441\) 8.69057 + 19.1174i 0.413837 + 0.910351i
\(442\) −0.917703 + 0.917703i −0.0436507 + 0.0436507i
\(443\) 0.725427 0.725427i 0.0344661 0.0344661i −0.689664 0.724130i \(-0.742242\pi\)
0.724130 + 0.689664i \(0.242242\pi\)
\(444\) 12.2324 + 12.4387i 0.580525 + 0.590313i
\(445\) 7.47673 17.0128i 0.354431 0.806484i
\(446\) −12.8530 + 7.42066i −0.608605 + 0.351378i
\(447\) −16.5915 + 28.1904i −0.784750 + 1.33336i
\(448\) −1.22994 2.34249i −0.0581091 0.110672i
\(449\) 17.0741 0.805778 0.402889 0.915249i \(-0.368006\pi\)
0.402889 + 0.915249i \(0.368006\pi\)
\(450\) 13.4131 6.71481i 0.632300 0.316539i
\(451\) −12.5802 21.7896i −0.592380 1.02603i
\(452\) 5.40288 1.44770i 0.254130 0.0680939i
\(453\) 26.6886 + 0.223108i 1.25394 + 0.0104825i
\(454\) −2.70607 1.56235i −0.127002 0.0733247i
\(455\) 0.713921 0.820624i 0.0334691 0.0384715i
\(456\) 1.53663 + 1.56254i 0.0719594 + 0.0731727i
\(457\) −22.0678 + 22.0678i −1.03229 + 1.03229i −0.0328258 + 0.999461i \(0.510451\pi\)
−0.999461 + 0.0328258i \(0.989549\pi\)
\(458\) −13.9391 3.73498i −0.651332 0.174524i
\(459\) −10.3787 + 35.1803i −0.484438 + 1.64207i
\(460\) −0.423276 + 2.75827i −0.0197353 + 0.128605i
\(461\) 17.3949 10.0430i 0.810162 0.467748i −0.0368498 0.999321i \(-0.511732\pi\)
0.847012 + 0.531573i \(0.178399\pi\)
\(462\) 6.75701 21.0747i 0.314364 0.980484i
\(463\) 22.3258 5.98219i 1.03757 0.278016i 0.300464 0.953793i \(-0.402859\pi\)
0.737106 + 0.675777i \(0.236192\pi\)
\(464\) −2.32602 4.02879i −0.107983 0.187032i
\(465\) −12.7894 17.7351i −0.593095 0.822448i
\(466\) 7.52217 13.0288i 0.348458 0.603546i
\(467\) −14.0144 + 3.75516i −0.648511 + 0.173768i −0.568056 0.822990i \(-0.692304\pi\)
−0.0804556 + 0.996758i \(0.525638\pi\)
\(468\) 0.530313 + 0.151643i 0.0245137 + 0.00700972i
\(469\) 9.89200 31.7635i 0.456770 1.46670i
\(470\) 0.308763 + 2.80770i 0.0142422 + 0.129510i
\(471\) 15.5982 + 4.31960i 0.718728 + 0.199037i
\(472\) 0.955444 0.955444i 0.0439779 0.0439779i
\(473\) 6.78133 6.78133i 0.311806 0.311806i
\(474\) −15.4386 4.27539i −0.709117 0.196375i
\(475\) −6.03528 1.89699i −0.276918 0.0870397i
\(476\) −18.2191 + 4.10652i −0.835072 + 0.188222i
\(477\) −5.63436 + 5.44904i −0.257980 + 0.249494i
\(478\) 23.2677 6.23456i 1.06424 0.285162i
\(479\) −0.447489 + 0.775073i −0.0204463 + 0.0354140i −0.876068 0.482188i \(-0.839842\pi\)
0.855621 + 0.517602i \(0.173175\pi\)
\(480\) −0.619441 + 3.82313i −0.0282735 + 0.174501i
\(481\) −0.925925 1.60375i −0.0422186 0.0731247i
\(482\) 9.17915 2.45955i 0.418099 0.112029i
\(483\) 3.84323 + 4.23507i 0.174873 + 0.192702i
\(484\) −10.6728 + 6.16192i −0.485126 + 0.280087i
\(485\) 22.0476 + 3.38336i 1.00113 + 0.153631i
\(486\) 15.2127 3.40189i 0.690063 0.154313i
\(487\) 6.99411 + 1.87407i 0.316933 + 0.0849220i 0.413779 0.910377i \(-0.364209\pi\)
−0.0968457 + 0.995299i \(0.530875\pi\)
\(488\) −8.20867 + 8.20867i −0.371589 + 0.371589i
\(489\) 4.71571 + 4.79522i 0.213252 + 0.216847i
\(490\) 14.9939 4.49257i 0.677355 0.202953i
\(491\) −20.8825 12.0565i −0.942416 0.544104i −0.0516990 0.998663i \(-0.516464\pi\)
−0.890717 + 0.454559i \(0.849797\pi\)
\(492\) 9.02328 + 0.0754318i 0.406801 + 0.00340073i
\(493\) −31.7195 + 8.49922i −1.42857 + 0.382785i
\(494\) −0.116314 0.201462i −0.00523323 0.00906423i
\(495\) −26.4347 + 18.7291i −1.18815 + 0.841809i
\(496\) 5.64567 0.253498
\(497\) 1.89873 + 3.61624i 0.0851696 + 0.162211i
\(498\) 8.52971 14.4927i 0.382226 0.649435i
\(499\) −0.649129 + 0.374775i −0.0290590 + 0.0167772i −0.514459 0.857515i \(-0.672007\pi\)
0.485400 + 0.874292i \(0.338674\pi\)
\(500\) −3.60799 10.5822i −0.161354 0.473249i
\(501\) −22.0309 22.4024i −0.984270 1.00087i
\(502\) 19.1717 19.1717i 0.855674 0.855674i
\(503\) 19.9246 19.9246i 0.888395 0.888395i −0.105974 0.994369i \(-0.533796\pi\)
0.994369 + 0.105974i \(0.0337960\pi\)
\(504\) 5.28466 + 5.92219i 0.235397 + 0.263795i
\(505\) 29.4241 + 12.9312i 1.30935 + 0.575432i
\(506\) 6.02706i 0.267935i
\(507\) 19.3547 + 11.3912i 0.859575 + 0.505903i
\(508\) −2.18708 2.18708i −0.0970359 0.0970359i
\(509\) 21.7037 + 37.5919i 0.962000 + 1.66623i 0.717467 + 0.696593i \(0.245302\pi\)
0.244534 + 0.969641i \(0.421365\pi\)
\(510\) 24.9359 + 11.2084i 1.10418 + 0.496316i
\(511\) 7.34312 + 32.5787i 0.324840 + 1.44120i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −5.60952 3.42903i −0.247667 0.151395i
\(514\) 11.9107 6.87665i 0.525358 0.303316i
\(515\) 6.25281 40.7463i 0.275532 1.79549i
\(516\) 0.862394 + 3.32959i 0.0379648 + 0.146577i
\(517\) −1.57897 5.89278i −0.0694428 0.259164i
\(518\) 1.06853 26.6273i 0.0469487 1.16994i
\(519\) −32.8836 9.10642i −1.44343 0.399728i
\(520\) 0.165407 0.376372i 0.00725357 0.0165050i
\(521\) 22.3396 12.8978i 0.978715 0.565062i 0.0768334 0.997044i \(-0.475519\pi\)
0.901882 + 0.431982i \(0.142186\pi\)
\(522\) 9.70211 + 10.0321i 0.424650 + 0.439092i
\(523\) 38.6748 10.3629i 1.69113 0.453137i 0.720450 0.693507i \(-0.243935\pi\)
0.970681 + 0.240370i \(0.0772687\pi\)
\(524\) −7.92011 13.7180i −0.345991 0.599275i
\(525\) −21.5000 7.92144i −0.938338 0.345720i
\(526\) −0.0795434 + 0.137773i −0.00346826 + 0.00600719i
\(527\) 10.3146 38.4945i 0.449309 1.67685i
\(528\) 0.0699256 8.36461i 0.00304312 0.364023i
\(529\) −18.5698 10.7213i −0.807383 0.466143i
\(530\) 3.45670 + 4.70993i 0.150150 + 0.204586i
\(531\) −2.08521 + 3.47615i −0.0904903 + 0.150852i
\(532\) 0.134229 3.34492i 0.00581956 0.145020i
\(533\) −0.925211 0.247909i −0.0400753 0.0107382i
\(534\) −10.0930 10.2632i −0.436767 0.444132i
\(535\) 1.67044 0.650459i 0.0722195 0.0281218i
\(536\) 12.5742i 0.543122i
\(537\) −11.5906 + 19.6934i −0.500171 + 0.849835i
\(538\) 3.17298 11.8417i 0.136797 0.510533i
\(539\) −30.5374 + 14.5029i −1.31534 + 0.624682i
\(540\) −0.980072 11.5775i −0.0421756 0.498218i
\(541\) 17.9564 31.1013i 0.772004 1.33715i −0.164459 0.986384i \(-0.552588\pi\)
0.936463 0.350766i \(-0.114079\pi\)
\(542\) −26.6582 + 7.14305i −1.14507 + 0.306820i
\(543\) 14.2384 + 25.1447i 0.611028 + 1.07906i
\(544\) −6.11321 + 3.52947i −0.262102 + 0.151325i
\(545\) −12.0968 + 8.87803i −0.518168 + 0.380293i
\(546\) −0.385422 0.749209i −0.0164945 0.0320632i
\(547\) −37.7501 10.1151i −1.61408 0.432491i −0.664823 0.747001i \(-0.731493\pi\)
−0.949254 + 0.314511i \(0.898160\pi\)
\(548\) 1.87151 + 6.98457i 0.0799469 + 0.298366i
\(549\) 17.9150 29.8652i 0.764594 1.27462i
\(550\) 11.1692 + 21.4090i 0.476255 + 0.912884i
\(551\) 5.88612i 0.250757i
\(552\) 1.86286 + 1.09639i 0.0792886 + 0.0466653i
\(553\) 11.3756 + 21.6655i 0.483740 + 0.921311i
\(554\) −2.06605 + 3.57850i −0.0877779 + 0.152036i
\(555\) −24.6571 + 30.2290i −1.04664 + 1.28315i
\(556\) 7.61723 13.1934i 0.323042 0.559526i
\(557\) 11.6604 43.5173i 0.494068 1.84389i −0.0411206 0.999154i \(-0.513093\pi\)
0.535189 0.844733i \(-0.320241\pi\)
\(558\) −16.4309 + 4.10950i −0.695576 + 0.173969i
\(559\) 0.365096i 0.0154419i
\(560\) 4.90595 3.30631i 0.207314 0.139717i
\(561\) −56.9055 15.7588i −2.40255 0.665337i
\(562\) −20.0541 5.37348i −0.845931 0.226666i
\(563\) −10.1373 + 10.1373i −0.427236 + 0.427236i −0.887686 0.460450i \(-0.847688\pi\)
0.460450 + 0.887686i \(0.347688\pi\)
\(564\) 2.10859 + 0.583929i 0.0887875 + 0.0245879i
\(565\) 4.53836 + 11.6549i 0.190930 + 0.490327i
\(566\) 8.80445i 0.370078i
\(567\) −19.6910 13.3890i −0.826945 0.562283i
\(568\) 1.09160 + 1.09160i 0.0458026 + 0.0458026i
\(569\) −39.8931 −1.67240 −0.836202 0.548421i \(-0.815229\pi\)
−0.836202 + 0.548421i \(0.815229\pi\)
\(570\) −3.09742 + 3.79735i −0.129736 + 0.159054i
\(571\) −24.8538 −1.04010 −0.520050 0.854136i \(-0.674087\pi\)
−0.520050 + 0.854136i \(0.674087\pi\)
\(572\) −0.229813 + 0.857673i −0.00960896 + 0.0358611i
\(573\) −20.8145 + 11.7864i −0.869538 + 0.492383i
\(574\) −9.34795 10.1296i −0.390176 0.422800i
\(575\) −6.23417 0.266607i −0.259983 0.0111183i
\(576\) 2.57264 + 1.54323i 0.107193 + 0.0643011i
\(577\) 16.8814 + 4.52337i 0.702783 + 0.188310i 0.592477 0.805587i \(-0.298150\pi\)
0.110306 + 0.993898i \(0.464817\pi\)
\(578\) 8.49664 + 31.7099i 0.353414 + 1.31896i
\(579\) −1.74660 + 6.30701i −0.0725860 + 0.262110i
\(580\) 8.38612 6.15472i 0.348215 0.255561i
\(581\) −25.0590 + 5.64821i −1.03962 + 0.234327i
\(582\) 8.76373 14.8904i 0.363268 0.617225i
\(583\) −8.92242 8.92242i −0.369529 0.369529i
\(584\) 6.31125 + 10.9314i 0.261161 + 0.452345i
\(585\) −0.207430 + 1.21578i −0.00857619 + 0.0502661i
\(586\) −9.64066 + 16.6981i −0.398252 + 0.689793i
\(587\) −0.503646 + 1.87963i −0.0207877 + 0.0775807i −0.975540 0.219820i \(-0.929453\pi\)
0.954753 + 0.297401i \(0.0961197\pi\)
\(588\) 1.07251 12.0768i 0.0442295 0.498040i
\(589\) 6.18631 + 3.57167i 0.254903 + 0.147168i
\(590\) 2.35717 + 1.89010i 0.0970432 + 0.0778141i
\(591\) 3.56003 12.8554i 0.146440 0.528800i
\(592\) −2.60690 9.72908i −0.107143 0.399863i
\(593\) −7.39416 27.5954i −0.303642 1.13321i −0.934108 0.356990i \(-0.883803\pi\)
0.630467 0.776216i \(-0.282864\pi\)
\(594\) 5.88511 + 24.3949i 0.241469 + 1.00093i
\(595\) −13.5807 39.4913i −0.556754 1.61899i
\(596\) 16.3552 9.44270i 0.669937 0.386788i
\(597\) −19.0601 11.2178i −0.780079 0.459116i
\(598\) −0.162244 0.162244i −0.00663465 0.00663465i
\(599\) −23.7866 −0.971893 −0.485947 0.873988i \(-0.661525\pi\)
−0.485947 + 0.873988i \(0.661525\pi\)
\(600\) −8.64895 0.442337i −0.353092 0.0180583i
\(601\) 8.26152 + 14.3094i 0.336994 + 0.583692i 0.983866 0.178908i \(-0.0572563\pi\)
−0.646871 + 0.762599i \(0.723923\pi\)
\(602\) 2.80726 4.44099i 0.114415 0.181001i
\(603\) 9.15278 + 36.5953i 0.372730 + 1.49028i
\(604\) −13.3447 7.70459i −0.542990 0.313495i
\(605\) −16.3046 22.2159i −0.662877 0.903204i
\(606\) 17.7505 17.4561i 0.721063 0.709108i
\(607\) 34.7241 + 9.30431i 1.40941 + 0.377650i 0.881714 0.471784i \(-0.156390\pi\)
0.527695 + 0.849434i \(0.323056\pi\)
\(608\) −0.327478 1.22216i −0.0132810 0.0495653i
\(609\) 1.03284 21.2933i 0.0418526 0.862848i
\(610\) −20.2516 16.2387i −0.819962 0.657487i
\(611\) −0.201134 0.116125i −0.00813700 0.00469790i
\(612\) 15.2225 14.7218i 0.615333 0.595094i
\(613\) −9.22756 + 34.4377i −0.372697 + 1.39093i 0.483982 + 0.875078i \(0.339190\pi\)
−0.856680 + 0.515848i \(0.827477\pi\)
\(614\) 17.6539 0.712453
\(615\) 2.03787 + 20.0742i 0.0821750 + 0.809470i
\(616\) −9.39014 + 8.66558i −0.378339 + 0.349146i
\(617\) 36.8494 9.87378i 1.48350 0.397503i 0.575965 0.817474i \(-0.304626\pi\)
0.907538 + 0.419971i \(0.137960\pi\)
\(618\) −27.5190 16.1963i −1.10697 0.651511i
\(619\) 21.6005 + 12.4711i 0.868198 + 0.501255i 0.866749 0.498744i \(-0.166205\pi\)
0.00144919 + 0.999999i \(0.499539\pi\)
\(620\) 1.37996 + 12.5485i 0.0554203 + 0.503958i
\(621\) −6.21964 1.83489i −0.249586 0.0736317i
\(622\) 5.65148 5.65148i 0.226604 0.226604i
\(623\) −0.881650 + 21.9703i −0.0353226 + 0.880221i
\(624\) −0.223287 0.227051i −0.00893862 0.00908933i
\(625\) 22.6388 10.6059i 0.905551 0.424238i
\(626\) 6.05000i 0.241807i
\(627\) 5.36839 9.12138i 0.214393 0.364273i
\(628\) −6.60761 6.60761i −0.263672 0.263672i
\(629\) −71.0996 −2.83492
\(630\) −11.8714 + 13.1936i −0.472966 + 0.525645i
\(631\) −42.7354 −1.70127 −0.850635 0.525757i \(-0.823782\pi\)
−0.850635 + 0.525757i \(0.823782\pi\)
\(632\) 6.53998 + 6.53998i 0.260146 + 0.260146i
\(633\) −13.9748 0.116825i −0.555448 0.00464337i
\(634\) 19.0288i 0.755730i
\(635\) 4.32657 5.39573i 0.171695 0.214123i
\(636\) 4.38085 1.13468i 0.173712 0.0449930i
\(637\) −0.431639 + 1.21245i −0.0171022 + 0.0480391i
\(638\) −15.8865 + 15.8865i −0.628953 + 0.628953i
\(639\) −3.97153 2.38237i −0.157111 0.0942451i
\(640\) 1.39883 1.74450i 0.0552935 0.0689574i
\(641\) 32.4056 + 18.7094i 1.27994 + 0.738975i 0.976838 0.213982i \(-0.0686434\pi\)
0.303105 + 0.952957i \(0.401977\pi\)
\(642\) 0.0116075 1.38851i 0.000458111 0.0547999i
\(643\) −19.9201 + 5.33756i −0.785571 + 0.210493i −0.629239 0.777212i \(-0.716633\pi\)
−0.156331 + 0.987705i \(0.549967\pi\)
\(644\) −0.726007 3.22102i −0.0286087 0.126926i
\(645\) −7.18978 + 2.73066i −0.283097 + 0.107520i
\(646\) −8.93150 −0.351405
\(647\) −7.39788 + 27.6093i −0.290841 + 1.08543i 0.653624 + 0.756819i \(0.273248\pi\)
−0.944465 + 0.328613i \(0.893419\pi\)
\(648\) −8.61060 2.61870i −0.338256 0.102872i
\(649\) −5.65133 3.26280i −0.221834 0.128076i
\(650\) 0.876980 + 0.275649i 0.0343980 + 0.0108119i
\(651\) 21.7525 + 14.0062i 0.852549 + 0.548945i
\(652\) −1.00498 3.75065i −0.0393582 0.146887i
\(653\) 17.1972 + 4.60797i 0.672978 + 0.180324i 0.579096 0.815259i \(-0.303406\pi\)
0.0938822 + 0.995583i \(0.470072\pi\)
\(654\) 2.91426 + 11.2516i 0.113957 + 0.439971i
\(655\) 28.5547 20.9568i 1.11573 0.818851i
\(656\) −4.51180 2.60489i −0.176156 0.101704i
\(657\) −26.3250 27.2203i −1.02703 1.06196i
\(658\) −1.55367 2.95906i −0.0605685 0.115356i
\(659\) −20.8707 36.1491i −0.813008 1.40817i −0.910750 0.412959i \(-0.864495\pi\)
0.0977417 0.995212i \(-0.468838\pi\)
\(660\) 18.6088 1.88912i 0.724348 0.0735337i
\(661\) 16.1816 0.629390 0.314695 0.949193i \(-0.398098\pi\)
0.314695 + 0.949193i \(0.398098\pi\)
\(662\) 4.19348 + 4.19348i 0.162984 + 0.162984i
\(663\) −1.95607 + 1.10764i −0.0759674 + 0.0430171i
\(664\) −8.40826 + 4.85451i −0.326304 + 0.188392i
\(665\) 7.46745 0.519242i 0.289575 0.0201353i
\(666\) 14.6688 + 26.4175i 0.568405 + 1.02366i
\(667\) −1.50261 5.60780i −0.0581812 0.217135i
\(668\) 4.69510 + 17.5223i 0.181659 + 0.677960i
\(669\) −24.8847 + 6.44538i −0.962100 + 0.249193i
\(670\) 27.9482 3.07347i 1.07973 0.118739i
\(671\) 48.5533 + 28.0322i 1.87438 + 1.08217i
\(672\) −0.970213 4.47869i −0.0374268 0.172769i
\(673\) 2.64718 9.87942i 0.102041 0.380824i −0.895951 0.444152i \(-0.853505\pi\)
0.997993 + 0.0633286i \(0.0201716\pi\)
\(674\) 11.1516 19.3152i 0.429544 0.743992i
\(675\) 25.4935 5.00824i 0.981245 0.192767i
\(676\) −6.48310 11.2291i −0.249350 0.431887i
\(677\) −4.92442 4.92442i −0.189261 0.189261i 0.606116 0.795377i \(-0.292727\pi\)
−0.795377 + 0.606116i \(0.792727\pi\)
\(678\) 9.68784 + 0.0809874i 0.372059 + 0.00311030i
\(679\) −25.7465 + 5.80317i −0.988061 + 0.222705i
\(680\) −9.33907 12.7249i −0.358137 0.487980i
\(681\) −3.79484 3.85882i −0.145418 0.147870i
\(682\) −7.05687 26.3366i −0.270221 1.00848i
\(683\) 7.78578 + 2.08619i 0.297915 + 0.0798260i 0.404680 0.914458i \(-0.367383\pi\)
−0.106766 + 0.994284i \(0.534049\pi\)
\(684\) 1.84269 + 3.31856i 0.0704571 + 0.126888i
\(685\) −15.0669 + 5.86696i −0.575678 + 0.224165i
\(686\) −14.5730 + 11.4292i −0.556401 + 0.436369i
\(687\) −21.5410 12.6780i −0.821842 0.483695i
\(688\) 0.513956 1.91811i 0.0195944 0.0731272i
\(689\) −0.480370 −0.0183006
\(690\) −1.98157 + 4.40851i −0.0754372 + 0.167829i
\(691\) 7.93478 0.301853 0.150927 0.988545i \(-0.451774\pi\)
0.150927 + 0.988545i \(0.451774\pi\)
\(692\) 13.9299 + 13.9299i 0.529536 + 0.529536i
\(693\) 21.0209 32.0550i 0.798519 1.21767i
\(694\) 26.4720i 1.00486i
\(695\) 31.1865 + 13.7057i 1.18297 + 0.519889i
\(696\) −2.02032 7.80018i −0.0765800 0.295665i
\(697\) −26.0042 + 26.0042i −0.984978 + 0.984978i
\(698\) 4.40102 + 1.17925i 0.166581 + 0.0446353i
\(699\) 18.5789 18.2708i 0.702717 0.691065i
\(700\) 8.54798 + 10.0961i 0.323083 + 0.381598i
\(701\) 31.3968i 1.18584i 0.805261 + 0.592920i \(0.202025\pi\)
−0.805261 + 0.592920i \(0.797975\pi\)
\(702\) 0.815114 + 0.498269i 0.0307645 + 0.0188059i
\(703\) 3.29845 12.3100i 0.124403 0.464280i
\(704\) −2.41474 + 4.18245i −0.0910089 + 0.157632i
\(705\) −0.782486 + 4.82942i −0.0294701 + 0.181886i
\(706\) 0.763896 1.32311i 0.0287496 0.0497958i
\(707\) −37.9982 1.52484i −1.42907 0.0573475i
\(708\) 2.03651 1.15319i 0.0765369 0.0433396i
\(709\) 21.1676i 0.794966i 0.917610 + 0.397483i \(0.130116\pi\)
−0.917610 + 0.397483i \(0.869884\pi\)
\(710\) −2.15945 + 2.69309i −0.0810429 + 0.101070i
\(711\) −23.7941 14.2732i −0.892350 0.535286i
\(712\) 2.15096 + 8.02750i 0.0806107 + 0.300843i
\(713\) 6.80557 + 1.82355i 0.254871 + 0.0682924i
\(714\) −32.3101 1.56721i −1.20918 0.0586512i
\(715\) −1.96250 0.301159i −0.0733932 0.0112627i
\(716\) 11.4256 6.59655i 0.426993 0.246525i
\(717\) 41.7211 + 0.348775i 1.55810 + 0.0130253i
\(718\) −1.49537 + 0.400683i −0.0558067 + 0.0149534i
\(719\) 4.31065 7.46626i 0.160760 0.278444i −0.774381 0.632719i \(-0.781939\pi\)
0.935141 + 0.354275i \(0.115272\pi\)
\(720\) −2.80126 + 6.09532i −0.104397 + 0.227159i
\(721\) 10.7249 + 47.5823i 0.399415 + 1.77206i
\(722\) −4.50321 + 16.8062i −0.167592 + 0.625463i
\(723\) 16.4590 + 0.137593i 0.612118 + 0.00511712i
\(724\) 16.6832i 0.620027i
\(725\) 15.7297 + 17.1352i 0.584186 + 0.636385i
\(726\) −20.6637 + 5.35208i −0.766900 + 0.198634i
\(727\) 25.0409 + 6.70968i 0.928714 + 0.248848i 0.691306 0.722562i \(-0.257036\pi\)
0.237408 + 0.971410i \(0.423702\pi\)
\(728\) −0.0195046 + 0.486046i −0.000722890 + 0.0180141i
\(729\) 26.9660 + 1.35367i 0.998742 + 0.0501360i
\(730\) −22.7542 + 16.6997i −0.842172 + 0.618085i
\(731\) −12.1395 7.00872i −0.448994 0.259227i
\(732\) −17.4967 + 9.90761i −0.646695 + 0.366196i
\(733\) 6.10111 22.7696i 0.225350 0.841016i −0.756915 0.653514i \(-0.773294\pi\)
0.982264 0.187502i \(-0.0600392\pi\)
\(734\) −2.17519 + 3.76754i −0.0802878 + 0.139063i
\(735\) 27.1049 0.568071i 0.999780 0.0209536i
\(736\) −0.623987 1.08078i −0.0230005 0.0398380i
\(737\) −58.6575 + 15.7172i −2.16068 + 0.578952i
\(738\) 15.0270 + 4.29699i 0.553152 + 0.158174i
\(739\) 16.3520 9.44086i 0.601520 0.347287i −0.168120 0.985767i \(-0.553769\pi\)
0.769639 + 0.638479i \(0.220436\pi\)
\(740\) 20.9873 8.17232i 0.771509 0.300421i
\(741\) −0.101028 0.390054i −0.00371134 0.0143290i
\(742\) −5.84315 3.69360i −0.214509 0.135596i
\(743\) −4.80997 17.9511i −0.176461 0.658561i −0.996298 0.0859643i \(-0.972603\pi\)
0.819837 0.572596i \(-0.194064\pi\)
\(744\) 9.42391 + 2.60976i 0.345497 + 0.0956783i
\(745\) 24.9857 + 34.0442i 0.915404 + 1.24728i
\(746\) 3.37754 1.95003i 0.123661 0.0713955i
\(747\) 20.9374 20.2487i 0.766060 0.740863i
\(748\) 24.1059 + 24.1059i 0.881400 + 0.881400i
\(749\) −1.55874 + 1.43847i −0.0569552 + 0.0525604i
\(750\) −1.13087 19.3319i −0.0412935 0.705900i
\(751\) 13.5254 + 23.4267i 0.493549 + 0.854852i 0.999972 0.00743325i \(-0.00236610\pi\)
−0.506424 + 0.862285i \(0.669033\pi\)
\(752\) −0.893226 0.893226i −0.0325726 0.0325726i
\(753\) 40.8641 23.1396i 1.48917 0.843254i
\(754\) 0.855307i 0.0311484i
\(755\) 13.8629 31.5442i 0.504524 1.14801i
\(756\) 6.08372 + 12.3284i 0.221263 + 0.448378i
\(757\) −10.6629 + 10.6629i −0.387548 + 0.387548i −0.873812 0.486264i \(-0.838359\pi\)
0.486264 + 0.873812i \(0.338359\pi\)
\(758\) 19.4140 19.4140i 0.705150 0.705150i
\(759\) 2.78605 10.0605i 0.101127 0.365174i
\(760\) 2.63642 1.02660i 0.0956330 0.0372389i
\(761\) −18.1821 + 10.4975i −0.659102 + 0.380533i −0.791935 0.610606i \(-0.790926\pi\)
0.132832 + 0.991139i \(0.457593\pi\)
\(762\) −2.63973 4.66172i −0.0956275 0.168876i
\(763\) 9.48647 15.0073i 0.343433 0.543300i
\(764\) 13.8102 0.499634
\(765\) 36.4425 + 30.2362i 1.31758 + 1.09319i
\(766\) 11.3601 + 19.6762i 0.410457 + 0.710932i
\(767\) −0.239962 + 0.0642975i −0.00866451 + 0.00232165i
\(768\) −0.853456 1.50719i −0.0307964 0.0543859i
\(769\) −14.7777 8.53189i −0.532896 0.307668i 0.209299 0.977852i \(-0.432882\pi\)
−0.742195 + 0.670184i \(0.766215\pi\)
\(770\) −21.5559 18.7531i −0.776821 0.675813i
\(771\) 23.0604 5.97287i 0.830501 0.215108i
\(772\) 2.67173 2.67173i 0.0961578 0.0961578i
\(773\) 0.115893 + 0.0310535i 0.00416839 + 0.00111692i 0.260903 0.965365i \(-0.415980\pi\)
−0.256734 + 0.966482i \(0.582647\pi\)
\(774\) −0.0995958 + 5.95649i −0.00357990 + 0.214101i
\(775\) −27.5538 + 6.13437i −0.989761 + 0.220353i
\(776\) −8.63895 + 4.98770i −0.310120 + 0.179048i
\(777\) 14.0923 43.9531i 0.505559 1.57681i
\(778\) 14.3113 3.83470i 0.513085 0.137481i
\(779\) −3.29590 5.70867i −0.118088 0.204534i
\(780\) 0.450082 0.551790i 0.0161155 0.0197572i
\(781\) 3.72778 6.45670i 0.133390 0.231039i
\(782\) −8.50919 + 2.28003i −0.304288 + 0.0815337i
\(783\) 11.5576 + 21.2307i 0.413036 + 0.758723i
\(784\) −3.97450 + 5.76223i −0.141947 + 0.205794i
\(785\) 13.0714 16.3016i 0.466540 0.581829i
\(786\) −6.87919 26.5596i −0.245373 0.947350i
\(787\) −16.2043 + 16.2043i −0.577619 + 0.577619i −0.934247 0.356627i \(-0.883927\pi\)
0.356627 + 0.934247i \(0.383927\pi\)
\(788\) −5.44571 + 5.44571i −0.193996 + 0.193996i
\(789\) −0.196463 + 0.193205i −0.00699425 + 0.00687828i
\(790\) −12.9377 + 16.1348i −0.460301 + 0.574049i
\(791\) −10.0364 10.8756i −0.356854 0.386692i
\(792\) 3.98332 13.9301i 0.141541 0.494985i
\(793\) 2.06162 0.552411i 0.0732104 0.0196167i
\(794\) −7.71275 + 13.3589i −0.273715 + 0.474089i
\(795\) 3.59282 + 9.45983i 0.127424 + 0.335506i
\(796\) 6.38441 + 11.0581i 0.226289 + 0.391945i
\(797\) −22.5250 + 6.03554i −0.797875 + 0.213790i −0.634651 0.772799i \(-0.718856\pi\)
−0.163224 + 0.986589i \(0.552189\pi\)
\(798\) 1.77027 5.52137i 0.0626669 0.195455i
\(799\) −7.72228 + 4.45846i −0.273195 + 0.157729i
\(800\) 4.21936 + 2.68273i 0.149177 + 0.0948488i
\(801\) −12.1033 21.7972i −0.427649 0.770165i
\(802\) −3.81863 1.02320i −0.134841 0.0361304i
\(803\) 43.1053 43.1053i 1.52115 1.52115i
\(804\) 5.81251 20.9892i 0.204991 0.740230i
\(805\) 6.98181 2.40098i 0.246076 0.0846233i
\(806\) −0.898927 0.518996i −0.0316633 0.0182808i
\(807\) 10.7703 18.2998i 0.379134 0.644183i
\(808\) −13.8838 + 3.72015i −0.488429 + 0.130874i
\(809\) 2.79658 + 4.84381i 0.0983224 + 0.170299i 0.910990 0.412428i \(-0.135319\pi\)
−0.812668 + 0.582727i \(0.801986\pi\)
\(810\) 3.71584 19.7786i 0.130561 0.694949i
\(811\) 17.5649 0.616787 0.308393 0.951259i \(-0.400209\pi\)
0.308393 + 0.951259i \(0.400209\pi\)
\(812\) −6.57653 + 10.4038i −0.230791 + 0.365103i
\(813\) −47.8006 0.399598i −1.67644 0.0140145i
\(814\) −42.1268 + 24.3219i −1.47654 + 0.852483i
\(815\) 8.09080 3.15051i 0.283409 0.110357i
\(816\) −11.8359 + 3.06560i −0.414338 + 0.107317i
\(817\) 1.77664 1.77664i 0.0621569 0.0621569i
\(818\) 13.2258 13.2258i 0.462429 0.462429i
\(819\) −0.297029 1.42876i −0.0103790 0.0499251i
\(820\) 4.68699 10.6649i 0.163677 0.372436i
\(821\) 24.6658i 0.860842i 0.902628 + 0.430421i \(0.141635\pi\)
−0.902628 + 0.430421i \(0.858365\pi\)
\(822\) −0.104696 + 12.5239i −0.00365170 + 0.436823i
\(823\) 15.1451 + 15.1451i 0.527927 + 0.527927i 0.919954 0.392027i \(-0.128226\pi\)
−0.392027 + 0.919954i \(0.628226\pi\)
\(824\) 9.21780 + 15.9657i 0.321117 + 0.556191i
\(825\) 8.74738 + 40.8995i 0.304545 + 1.42394i
\(826\) −3.41325 1.06298i −0.118762 0.0369858i
\(827\) 12.6164 + 12.6164i 0.438716 + 0.438716i 0.891580 0.452864i \(-0.149598\pi\)
−0.452864 + 0.891580i \(0.649598\pi\)
\(828\) 2.60272 + 2.69124i 0.0904509 + 0.0935271i
\(829\) −10.9537 + 6.32413i −0.380438 + 0.219646i −0.678009 0.735054i \(-0.737157\pi\)
0.297571 + 0.954700i \(0.403824\pi\)
\(830\) −12.8452 17.5022i −0.445863 0.607511i
\(831\) −5.10289 + 5.01828i −0.177017 + 0.174082i
\(832\) 0.0475855 + 0.177591i 0.00164973 + 0.00615687i
\(833\) 32.0279 + 37.6273i 1.10970 + 1.30371i
\(834\) 18.8136 18.5017i 0.651463 0.640662i
\(835\) −37.7988 + 14.7186i −1.30808 + 0.509358i
\(836\) −5.29196 + 3.05531i −0.183026 + 0.105670i
\(837\) −29.3266 0.735620i −1.01367 0.0254268i
\(838\) 23.0318 6.17135i 0.795620 0.213186i
\(839\) 7.14105 + 12.3687i 0.246537 + 0.427014i 0.962562 0.271060i \(-0.0873741\pi\)
−0.716026 + 0.698074i \(0.754041\pi\)
\(840\) 9.71750 3.25117i 0.335286 0.112176i
\(841\) 3.67925 6.37264i 0.126871 0.219746i
\(842\) −2.95213 + 11.0175i −0.101737 + 0.379688i
\(843\) −30.9909 18.2397i −1.06738 0.628209i
\(844\) 6.98763 + 4.03431i 0.240524 + 0.138867i
\(845\) 23.3738 17.1545i 0.804084 0.590132i
\(846\) 3.24978 + 1.94942i 0.111730 + 0.0670225i
\(847\) 27.5611 + 17.4220i 0.947010 + 0.598628i
\(848\) −2.52372 0.676229i −0.0866649 0.0232218i
\(849\) 4.06992 14.6966i 0.139679 0.504387i
\(850\) 26.0006 23.8680i 0.891814 0.818665i
\(851\) 12.5699i 0.430892i
\(852\) 1.31753 + 2.32673i 0.0451379 + 0.0797126i
\(853\) −7.17000 + 26.7588i −0.245496 + 0.916203i 0.727638 + 0.685962i \(0.240618\pi\)
−0.973133 + 0.230242i \(0.926048\pi\)
\(854\) 29.3249 + 9.13256i 1.00348 + 0.312510i
\(855\) −6.92565 + 4.90684i −0.236852 + 0.167810i
\(856\) −0.400841 + 0.694277i −0.0137005 + 0.0237299i
\(857\) −50.9278 + 13.6461i −1.73966 + 0.466140i −0.982371 0.186940i \(-0.940143\pi\)
−0.757288 + 0.653081i \(0.773476\pi\)
\(858\) −0.780076 + 1.32542i −0.0266313 + 0.0452490i
\(859\) 4.49440 2.59484i 0.153347 0.0885348i −0.421363 0.906892i \(-0.638448\pi\)
0.574710 + 0.818357i \(0.305115\pi\)
\(860\) 4.38895 + 0.673516i 0.149662 + 0.0229667i
\(861\) −10.9214 21.2297i −0.372199 0.723506i
\(862\) 8.68052 + 2.32594i 0.295660 + 0.0792217i
\(863\) −7.67533 28.6447i −0.261271 0.975078i −0.964493 0.264108i \(-0.914923\pi\)
0.703222 0.710971i \(-0.251744\pi\)
\(864\) 3.58094 + 3.76521i 0.121826 + 0.128095i
\(865\) −27.5568 + 34.3665i −0.936958 + 1.16849i
\(866\) 21.2505i 0.722122i
\(867\) −0.475321 + 56.8586i −0.0161427 + 1.93102i
\(868\) −6.94383 13.2249i −0.235689 0.448883i
\(869\) 22.3337 38.6832i 0.757620 1.31224i
\(870\) 16.8434 6.39708i 0.571045 0.216881i
\(871\) −1.15592 + 2.00211i −0.0391668 + 0.0678390i
\(872\) 1.73679 6.48180i 0.0588153 0.219502i
\(873\) 21.5118 20.8043i 0.728065 0.704118i
\(874\) 1.57903i 0.0534115i
\(875\) −20.3510 + 21.4671i −0.687990 + 0.725720i
\(876\) 5.48178 + 21.1644i 0.185212 + 0.715079i
\(877\) 40.0178 + 10.7227i 1.35130 + 0.362081i 0.860616 0.509254i \(-0.170079\pi\)
0.490688 + 0.871335i \(0.336745\pi\)
\(878\) −13.0852 + 13.0852i −0.441606 + 0.441606i
\(879\) −23.8113 + 23.4165i −0.803134 + 0.789818i
\(880\) −9.88643 4.34486i −0.333271 0.146465i
\(881\) 25.8897i 0.872245i 0.899887 + 0.436123i \(0.143649\pi\)
−0.899887 + 0.436123i \(0.856351\pi\)
\(882\) 7.37287 19.6632i 0.248257 0.662094i
\(883\) −24.3887 24.3887i −0.820745 0.820745i 0.165470 0.986215i \(-0.447086\pi\)
−0.986215 + 0.165470i \(0.947086\pi\)
\(884\) 1.29783 0.0436507
\(885\) 3.06094 + 4.24462i 0.102892 + 0.142681i
\(886\) −1.02591 −0.0344661
\(887\) 7.09099 26.4639i 0.238092 0.888572i −0.738638 0.674102i \(-0.764531\pi\)
0.976731 0.214470i \(-0.0688025\pi\)
\(888\) 0.145836 17.4451i 0.00489393 0.585419i
\(889\) −2.43323 + 7.81317i −0.0816080 + 0.262045i
\(890\) −17.3167 + 6.74301i −0.580457 + 0.226026i
\(891\) −1.45312 + 43.4410i −0.0486814 + 1.45533i
\(892\) 14.3356 + 3.84121i 0.479992 + 0.128613i
\(893\) −0.413674 1.54385i −0.0138431 0.0516630i
\(894\) 31.6656 8.20168i 1.05906 0.274305i
\(895\) 17.4547 + 23.7828i 0.583445 + 0.794973i
\(896\) −0.786692 + 2.52609i −0.0262815 + 0.0843906i
\(897\) −0.195823 0.345820i −0.00653835 0.0115466i
\(898\) −12.0732 12.0732i −0.402889 0.402889i
\(899\) −13.1320 22.7452i −0.437975 0.758595i
\(900\) −14.2326 4.73640i −0.474420 0.157880i
\(901\) −9.22160 + 15.9723i −0.307216 + 0.532114i
\(902\) −6.51201 + 24.3032i −0.216826 + 0.809207i
\(903\) 6.73883 6.11534i 0.224254 0.203506i
\(904\) −4.84409 2.79673i −0.161112 0.0930180i
\(905\) 37.0813 4.07783i 1.23262 0.135552i
\(906\) −18.7139 19.0294i −0.621728 0.632210i
\(907\) −1.08172 4.03702i −0.0359178 0.134047i 0.945639 0.325219i \(-0.105438\pi\)
−0.981557 + 0.191172i \(0.938771\pi\)
\(908\) 0.808732 + 3.01823i 0.0268387 + 0.100163i
\(909\) 37.6988 20.9330i 1.25039 0.694303i
\(910\) −1.08509 + 0.0754505i −0.0359703 + 0.00250116i
\(911\) −21.5924 + 12.4664i −0.715389 + 0.413030i −0.813053 0.582190i \(-0.802196\pi\)
0.0976644 + 0.995219i \(0.468863\pi\)
\(912\) 0.0183198 2.19145i 0.000606630 0.0725661i
\(913\) 33.1559 + 33.1559i 1.09730 + 1.09730i
\(914\) 31.2085 1.03229
\(915\) −26.2980 36.4676i −0.869385 1.20558i
\(916\) 7.21542 + 12.4975i 0.238404 + 0.412928i
\(917\) −22.3931 + 35.4251i −0.739485 + 1.16984i
\(918\) 32.2151 17.5373i 1.06326 0.578818i
\(919\) 43.0102 + 24.8319i 1.41877 + 0.819130i 0.996191 0.0871944i \(-0.0277901\pi\)
0.422583 + 0.906324i \(0.361123\pi\)
\(920\) 2.24969 1.65109i 0.0741701 0.0544347i
\(921\) 29.4684 + 8.16065i 0.971015 + 0.268902i
\(922\) −19.4015 5.19862i −0.638955 0.171207i
\(923\) −0.0734605 0.274158i −0.00241798 0.00902403i
\(924\) −19.6800 + 10.1241i −0.647424 + 0.333060i
\(925\) 23.2942 + 44.6503i 0.765910 + 1.46809i
\(926\) −20.0168 11.5567i −0.657793 0.379777i
\(927\) −38.4485 39.7561i −1.26282 1.30576i
\(928\) −1.20404 + 4.49353i −0.0395245 + 0.147507i
\(929\) 8.08865 0.265380 0.132690 0.991158i \(-0.457639\pi\)
0.132690 + 0.991158i \(0.457639\pi\)
\(930\) −3.49716 + 21.5841i −0.114676 + 0.707771i
\(931\) −8.00052 + 3.79961i −0.262206 + 0.124527i
\(932\) −14.5317 + 3.89376i −0.476002 + 0.127544i
\(933\) 12.0460 6.82116i 0.394369 0.223315i
\(934\) 12.5650 + 7.25441i 0.411140 + 0.237372i
\(935\) −47.6874 + 59.4716i −1.55954 + 1.94493i
\(936\) −0.267760 0.482216i −0.00875200 0.0157617i
\(937\) 2.74794 2.74794i 0.0897713 0.0897713i −0.660795 0.750566i \(-0.729781\pi\)
0.750566 + 0.660795i \(0.229781\pi\)
\(938\) −29.4549 + 15.4655i −0.961736 + 0.504965i
\(939\) −2.79666 + 10.0988i −0.0912656 + 0.329563i
\(940\) 1.76702 2.20367i 0.0576337 0.0718759i
\(941\) 27.7840i 0.905733i 0.891578 + 0.452866i \(0.149599\pi\)
−0.891578 + 0.452866i \(0.850401\pi\)
\(942\) −7.97518 14.0840i −0.259845 0.458882i
\(943\) −4.59737 4.59737i −0.149711 0.149711i
\(944\) −1.35120 −0.0439779
\(945\) −25.9148 + 16.5355i −0.843009 + 0.537899i
\(946\) −9.59024 −0.311806
\(947\) −10.0669 10.0669i −0.327131 0.327131i 0.524364 0.851494i \(-0.324303\pi\)
−0.851494 + 0.524364i \(0.824303\pi\)
\(948\) 7.89356 + 13.9399i 0.256371 + 0.452746i
\(949\) 2.32072i 0.0753339i
\(950\) 2.92621 + 5.60896i 0.0949389 + 0.181979i
\(951\) 8.79620 31.7634i 0.285236 1.03000i
\(952\) 15.7866 + 9.97911i 0.511647 + 0.323425i
\(953\) −19.6325 + 19.6325i −0.635958 + 0.635958i −0.949556 0.313598i \(-0.898466\pi\)
0.313598 + 0.949556i \(0.398466\pi\)
\(954\) 7.83715 + 0.131042i 0.253737 + 0.00424263i
\(955\) 3.37558 + 30.6954i 0.109231 + 0.993281i
\(956\) −20.8613 12.0443i −0.674701 0.389539i
\(957\) −33.8619 + 19.1745i −1.09460 + 0.619825i
\(958\) 0.864482 0.231637i 0.0279301 0.00748386i
\(959\) 14.0594 12.9746i 0.454002 0.418971i
\(960\) 3.14137 2.26535i 0.101387 0.0731138i
\(961\) 0.873619 0.0281813
\(962\) −0.479294 + 1.78875i −0.0154531 + 0.0576716i
\(963\) 0.661223 2.31236i 0.0213076 0.0745149i
\(964\) −8.22980 4.75148i −0.265064 0.153035i
\(965\) 6.59142 + 5.28533i 0.212185 + 0.170141i
\(966\) 0.277072 5.71222i 0.00891465 0.183788i
\(967\) −5.98379 22.3318i −0.192426 0.718143i −0.992918 0.118800i \(-0.962095\pi\)
0.800492 0.599343i \(-0.204571\pi\)
\(968\) 11.9039 + 3.18965i 0.382606 + 0.102519i
\(969\) −14.9087 4.12865i −0.478936 0.132631i
\(970\) −13.1976 17.9824i −0.423749 0.577380i
\(971\) 8.03616 + 4.63968i 0.257893 + 0.148894i 0.623373 0.781925i \(-0.285762\pi\)
−0.365480 + 0.930819i \(0.619095\pi\)
\(972\) −13.1625 8.35152i −0.422188 0.267875i
\(973\) −40.2742 1.61617i −1.29113 0.0518120i
\(974\) −3.62042 6.27075i −0.116006 0.200928i
\(975\) 1.33646 + 0.865512i 0.0428009 + 0.0277186i
\(976\) 11.6088 0.371589
\(977\) −22.5542 22.5542i −0.721573 0.721573i 0.247353 0.968925i \(-0.420439\pi\)
−0.968925 + 0.247353i \(0.920439\pi\)
\(978\) 0.0562210 6.72525i 0.00179775 0.215050i
\(979\) 34.7590 20.0681i 1.11090 0.641379i
\(980\) −13.7790 7.42556i −0.440154 0.237201i
\(981\) −0.336561 + 20.1286i −0.0107456 + 0.642655i
\(982\) 6.24092 + 23.2914i 0.199156 + 0.743260i
\(983\) −9.18430 34.2763i −0.292934 1.09324i −0.942845 0.333233i \(-0.891860\pi\)
0.649911 0.760010i \(-0.274806\pi\)
\(984\) −6.32708 6.43376i −0.201700 0.205101i
\(985\) −13.4351 10.7729i −0.428078 0.343254i
\(986\) 28.4389 + 16.4192i 0.905680 + 0.522895i
\(987\) −1.22558 5.65754i −0.0390108 0.180081i
\(988\) −0.0602088 + 0.224702i −0.00191550 + 0.00714873i
\(989\) 1.23910 2.14618i 0.0394010 0.0682445i
\(990\) 31.9356 + 5.44872i 1.01498 + 0.173172i
\(991\) −21.7071 37.5978i −0.689548 1.19433i −0.971984 0.235046i \(-0.924476\pi\)
0.282436 0.959286i \(-0.408857\pi\)
\(992\) −3.99209 3.99209i −0.126749 0.126749i
\(993\) 5.06141 + 8.93835i 0.160619 + 0.283650i
\(994\) 1.21446 3.89967i 0.0385204 0.123690i
\(995\) −23.0180 + 16.8933i −0.729720 + 0.535555i
\(996\) −16.2793 + 4.21650i −0.515830 + 0.133605i
\(997\) 13.7761 + 51.4132i 0.436294 + 1.62827i 0.737950 + 0.674855i \(0.235794\pi\)
−0.301656 + 0.953417i \(0.597539\pi\)
\(998\) 0.724010 + 0.193998i 0.0229181 + 0.00614089i
\(999\) 12.2739 + 50.8776i 0.388329 + 1.60969i
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.cd.a.23.9 yes 192
5.2 odd 4 inner 630.2.cd.a.527.28 yes 192
7.4 even 3 630.2.bt.a.473.32 yes 192
9.2 odd 6 630.2.bt.a.443.45 yes 192
35.32 odd 12 630.2.bt.a.347.45 yes 192
45.2 even 12 630.2.bt.a.317.32 192
63.11 odd 6 inner 630.2.cd.a.263.28 yes 192
315.137 even 12 inner 630.2.cd.a.137.9 yes 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.bt.a.317.32 192 45.2 even 12
630.2.bt.a.347.45 yes 192 35.32 odd 12
630.2.bt.a.443.45 yes 192 9.2 odd 6
630.2.bt.a.473.32 yes 192 7.4 even 3
630.2.cd.a.23.9 yes 192 1.1 even 1 trivial
630.2.cd.a.137.9 yes 192 315.137 even 12 inner
630.2.cd.a.263.28 yes 192 63.11 odd 6 inner
630.2.cd.a.527.28 yes 192 5.2 odd 4 inner