Properties

Label 324.2.p.a.263.31
Level $324$
Weight $2$
Character 324.263
Analytic conductor $2.587$
Analytic rank $0$
Dimension $936$
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] = [324,2,Mod(11,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([27, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("324.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 324.p (of order \(54\), degree \(18\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.58715302549\)
Analytic rank: \(0\)
Dimension: \(936\)
Relative dimension: \(52\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 263.31
Character \(\chi\) \(=\) 324.263
Dual form 324.2.p.a.239.31

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.403275 + 1.35550i) q^{2} +(-1.52566 + 0.819976i) q^{3} +(-1.67474 + 1.09328i) q^{4} +(1.81176 - 3.60751i) q^{5} +(-1.72673 - 1.73735i) q^{6} +(3.06406 - 0.917319i) q^{7} +(-2.15731 - 1.82921i) q^{8} +(1.65528 - 2.50201i) q^{9} +O(q^{10})\) \(q+(0.403275 + 1.35550i) q^{2} +(-1.52566 + 0.819976i) q^{3} +(-1.67474 + 1.09328i) q^{4} +(1.81176 - 3.60751i) q^{5} +(-1.72673 - 1.73735i) q^{6} +(3.06406 - 0.917319i) q^{7} +(-2.15731 - 1.82921i) q^{8} +(1.65528 - 2.50201i) q^{9} +(5.62061 + 1.00102i) q^{10} +(0.0562807 - 0.966303i) q^{11} +(1.65862 - 3.04121i) q^{12} +(1.00752 - 1.35334i) q^{13} +(2.47908 + 3.78339i) q^{14} +(0.193942 + 6.98944i) q^{15} +(1.60950 - 3.66190i) q^{16} +(1.25854 + 1.49987i) q^{17} +(4.05900 + 1.23473i) q^{18} +(-4.84027 + 5.76840i) q^{19} +(0.909779 + 8.02240i) q^{20} +(-3.92253 + 3.91197i) q^{21} +(1.33252 - 0.313397i) q^{22} +(1.64757 - 5.50326i) q^{23} +(4.79123 + 1.02181i) q^{24} +(-6.74588 - 9.06130i) q^{25} +(2.24075 + 0.819924i) q^{26} +(-0.473805 + 5.17451i) q^{27} +(-4.12861 + 4.88613i) q^{28} +(3.97620 + 1.71517i) q^{29} +(-9.39595 + 3.08155i) q^{30} +(3.44433 - 3.24956i) q^{31} +(5.61276 + 0.704916i) q^{32} +(0.706480 + 1.52040i) q^{33} +(-1.52553 + 2.31081i) q^{34} +(2.24210 - 12.7156i) q^{35} +(-0.0367738 + 5.99989i) q^{36} +(1.58111 + 8.96693i) q^{37} +(-9.77101 - 4.23471i) q^{38} +(-0.427432 + 2.89087i) q^{39} +(-10.5074 + 4.46843i) q^{40} +(-0.0921716 + 0.788578i) q^{41} +(-6.88452 - 3.73938i) q^{42} +(0.0145201 - 0.0220768i) q^{43} +(0.962180 + 1.67984i) q^{44} +(-6.02706 - 10.5045i) q^{45} +(8.12407 + 0.0139445i) q^{46} +(4.87410 - 5.16624i) q^{47} +(0.547122 + 6.90657i) q^{48} +(2.69856 - 1.77487i) q^{49} +(9.56210 - 12.7982i) q^{50} +(-3.14996 - 1.25632i) q^{51} +(-0.207766 + 3.36798i) q^{52} +(-3.07902 + 1.77767i) q^{53} +(-7.20510 + 1.44451i) q^{54} +(-3.38398 - 1.95374i) q^{55} +(-8.28809 - 3.62587i) q^{56} +(2.65465 - 12.7695i) q^{57} +(-0.721398 + 6.08141i) q^{58} +(-0.416173 - 7.14541i) q^{59} +(-7.96619 - 11.4935i) q^{60} +(0.919016 + 0.217811i) q^{61} +(5.79378 + 3.35831i) q^{62} +(2.77673 - 9.18472i) q^{63} +(1.30798 + 7.89235i) q^{64} +(-3.05679 - 6.08657i) q^{65} +(-1.77599 + 1.57077i) q^{66} +(-13.5355 + 5.83865i) q^{67} +(-3.74750 - 1.13596i) q^{68} +(1.99891 + 9.74707i) q^{69} +(18.1401 - 2.08872i) q^{70} +(3.54954 + 1.29193i) q^{71} +(-8.14765 + 2.36976i) q^{72} +(0.192945 - 0.0702261i) q^{73} +(-11.5170 + 5.75933i) q^{74} +(17.7220 + 8.29299i) q^{75} +(1.79973 - 14.9523i) q^{76} +(-0.713960 - 3.01244i) q^{77} +(-4.09094 + 0.586435i) q^{78} +(1.06783 + 9.13583i) q^{79} +(-10.2943 - 12.4408i) q^{80} +(-3.52010 - 8.28305i) q^{81} +(-1.10609 + 0.193076i) q^{82} +(-3.99227 + 0.466629i) q^{83} +(2.29235 - 10.8399i) q^{84} +(7.69098 - 1.82280i) q^{85} +(0.0357806 + 0.0107790i) q^{86} +(-7.47273 + 0.643629i) q^{87} +(-1.88899 + 1.98167i) q^{88} +(2.78775 + 7.65928i) q^{89} +(11.8082 - 12.4059i) q^{90} +(1.84566 - 5.07092i) q^{91} +(3.25733 + 11.0178i) q^{92} +(-2.59032 + 7.78199i) q^{93} +(8.96842 + 4.52340i) q^{94} +(12.0402 + 27.9123i) q^{95} +(-9.14118 + 3.52687i) q^{96} +(-15.2704 + 7.66910i) q^{97} +(3.49409 + 2.94213i) q^{98} +(-2.32454 - 1.74032i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{25}{54}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.403275 + 1.35550i 0.285158 + 0.958480i
\(3\) −1.52566 + 0.819976i −0.880840 + 0.473413i
\(4\) −1.67474 + 1.09328i −0.837369 + 0.546638i
\(5\) 1.81176 3.60751i 0.810244 1.61333i 0.0205817 0.999788i \(-0.493448\pi\)
0.789663 0.613541i \(-0.210256\pi\)
\(6\) −1.72673 1.73735i −0.704937 0.709270i
\(7\) 3.06406 0.917319i 1.15810 0.346714i 0.350572 0.936536i \(-0.385987\pi\)
0.807533 + 0.589822i \(0.200802\pi\)
\(8\) −2.15731 1.82921i −0.762724 0.646724i
\(9\) 1.65528 2.50201i 0.551760 0.834003i
\(10\) 5.62061 + 1.00102i 1.77739 + 0.316549i
\(11\) 0.0562807 0.966303i 0.0169693 0.291351i −0.979138 0.203198i \(-0.934866\pi\)
0.996107 0.0881532i \(-0.0280965\pi\)
\(12\) 1.65862 3.04121i 0.478803 0.877922i
\(13\) 1.00752 1.35334i 0.279436 0.375348i −0.640141 0.768257i \(-0.721124\pi\)
0.919577 + 0.392910i \(0.128531\pi\)
\(14\) 2.47908 + 3.78339i 0.662562 + 1.01115i
\(15\) 0.193942 + 6.98944i 0.0500756 + 1.80467i
\(16\) 1.60950 3.66190i 0.402375 0.915475i
\(17\) 1.25854 + 1.49987i 0.305241 + 0.363772i 0.896759 0.442520i \(-0.145915\pi\)
−0.591518 + 0.806292i \(0.701471\pi\)
\(18\) 4.05900 + 1.23473i 0.956715 + 0.291028i
\(19\) −4.84027 + 5.76840i −1.11043 + 1.32336i −0.169209 + 0.985580i \(0.554121\pi\)
−0.941224 + 0.337783i \(0.890323\pi\)
\(20\) 0.909779 + 8.02240i 0.203433 + 1.79386i
\(21\) −3.92253 + 3.91197i −0.855967 + 0.853662i
\(22\) 1.33252 0.313397i 0.284093 0.0668166i
\(23\) 1.64757 5.50326i 0.343542 1.14751i −0.595399 0.803430i \(-0.703006\pi\)
0.938941 0.344079i \(-0.111809\pi\)
\(24\) 4.79123 + 1.02181i 0.978006 + 0.208576i
\(25\) −6.74588 9.06130i −1.34918 1.81226i
\(26\) 2.24075 + 0.819924i 0.439447 + 0.160800i
\(27\) −0.473805 + 5.17451i −0.0911838 + 0.995834i
\(28\) −4.12861 + 4.88613i −0.780235 + 0.923391i
\(29\) 3.97620 + 1.71517i 0.738362 + 0.318498i 0.731836 0.681480i \(-0.238664\pi\)
0.00652562 + 0.999979i \(0.497923\pi\)
\(30\) −9.39595 + 3.08155i −1.71546 + 0.562612i
\(31\) 3.44433 3.24956i 0.618620 0.583638i −0.311793 0.950150i \(-0.600930\pi\)
0.930413 + 0.366512i \(0.119448\pi\)
\(32\) 5.61276 + 0.704916i 0.992205 + 0.124613i
\(33\) 0.706480 + 1.52040i 0.122982 + 0.264667i
\(34\) −1.52553 + 2.31081i −0.261626 + 0.396300i
\(35\) 2.24210 12.7156i 0.378984 2.14933i
\(36\) −0.0367738 + 5.99989i −0.00612897 + 0.999981i
\(37\) 1.58111 + 8.96693i 0.259933 + 1.47415i 0.783085 + 0.621915i \(0.213645\pi\)
−0.523152 + 0.852240i \(0.675244\pi\)
\(38\) −9.77101 4.23471i −1.58507 0.686960i
\(39\) −0.427432 + 2.89087i −0.0684439 + 0.462910i
\(40\) −10.5074 + 4.46843i −1.66137 + 0.706521i
\(41\) −0.0921716 + 0.788578i −0.0143948 + 0.123155i −0.998525 0.0542920i \(-0.982710\pi\)
0.984130 + 0.177447i \(0.0567839\pi\)
\(42\) −6.88452 3.73938i −1.06230 0.576998i
\(43\) 0.0145201 0.0220768i 0.00221430 0.00336668i −0.834379 0.551191i \(-0.814173\pi\)
0.836593 + 0.547825i \(0.184544\pi\)
\(44\) 0.962180 + 1.67984i 0.145054 + 0.253245i
\(45\) −6.02706 10.5045i −0.898462 1.56592i
\(46\) 8.12407 + 0.0139445i 1.19783 + 0.00205600i
\(47\) 4.87410 5.16624i 0.710960 0.753573i −0.266697 0.963780i \(-0.585932\pi\)
0.977657 + 0.210207i \(0.0674138\pi\)
\(48\) 0.547122 + 6.90657i 0.0789703 + 0.996877i
\(49\) 2.69856 1.77487i 0.385509 0.253553i
\(50\) 9.56210 12.7982i 1.35229 1.80994i
\(51\) −3.14996 1.25632i −0.441083 0.175920i
\(52\) −0.207766 + 3.36798i −0.0288120 + 0.467055i
\(53\) −3.07902 + 1.77767i −0.422936 + 0.244182i −0.696333 0.717719i \(-0.745186\pi\)
0.273397 + 0.961901i \(0.411853\pi\)
\(54\) −7.20510 + 1.44451i −0.980489 + 0.196573i
\(55\) −3.38398 1.95374i −0.456296 0.263443i
\(56\) −8.28809 3.62587i −1.10754 0.484527i
\(57\) 2.65465 12.7695i 0.351617 1.69137i
\(58\) −0.721398 + 6.08141i −0.0947242 + 0.798528i
\(59\) −0.416173 7.14541i −0.0541811 0.930253i −0.910423 0.413678i \(-0.864244\pi\)
0.856242 0.516575i \(-0.172793\pi\)
\(60\) −7.96619 11.4935i −1.02843 1.48380i
\(61\) 0.919016 + 0.217811i 0.117668 + 0.0278878i 0.289028 0.957321i \(-0.406668\pi\)
−0.171360 + 0.985208i \(0.554816\pi\)
\(62\) 5.79378 + 3.35831i 0.735811 + 0.426506i
\(63\) 2.77673 9.18472i 0.349835 1.15717i
\(64\) 1.30798 + 7.89235i 0.163497 + 0.986544i
\(65\) −3.05679 6.08657i −0.379148 0.754946i
\(66\) −1.77599 + 1.57077i −0.218609 + 0.193348i
\(67\) −13.5355 + 5.83865i −1.65363 + 0.713304i −0.999087 0.0427247i \(-0.986396\pi\)
−0.654538 + 0.756029i \(0.727137\pi\)
\(68\) −3.74750 1.13596i −0.454451 0.137755i
\(69\) 1.99891 + 9.74707i 0.240641 + 1.17341i
\(70\) 18.1401 2.08872i 2.16816 0.249650i
\(71\) 3.54954 + 1.29193i 0.421253 + 0.153324i 0.543944 0.839121i \(-0.316930\pi\)
−0.122691 + 0.992445i \(0.539152\pi\)
\(72\) −8.14765 + 2.36976i −0.960210 + 0.279279i
\(73\) 0.192945 0.0702261i 0.0225824 0.00821934i −0.330704 0.943734i \(-0.607286\pi\)
0.353287 + 0.935515i \(0.385064\pi\)
\(74\) −11.5170 + 5.75933i −1.33883 + 0.669508i
\(75\) 17.7220 + 8.29299i 2.04636 + 0.957593i
\(76\) 1.79973 14.9523i 0.206443 1.71515i
\(77\) −0.713960 3.01244i −0.0813633 0.343299i
\(78\) −4.09094 + 0.586435i −0.463208 + 0.0664006i
\(79\) 1.06783 + 9.13583i 0.120140 + 1.02786i 0.910010 + 0.414587i \(0.136074\pi\)
−0.789870 + 0.613275i \(0.789852\pi\)
\(80\) −10.2943 12.4408i −1.15094 1.39092i
\(81\) −3.52010 8.28305i −0.391123 0.920339i
\(82\) −1.10609 + 0.193076i −0.122147 + 0.0213216i
\(83\) −3.99227 + 0.466629i −0.438209 + 0.0512192i −0.332337 0.943161i \(-0.607837\pi\)
−0.105871 + 0.994380i \(0.533763\pi\)
\(84\) 2.29235 10.8399i 0.250116 1.18273i
\(85\) 7.69098 1.82280i 0.834204 0.197710i
\(86\) 0.0357806 + 0.0107790i 0.00385832 + 0.00116233i
\(87\) −7.47273 + 0.643629i −0.801160 + 0.0690043i
\(88\) −1.88899 + 1.98167i −0.201367 + 0.211246i
\(89\) 2.78775 + 7.65928i 0.295501 + 0.811882i 0.995237 + 0.0974810i \(0.0310785\pi\)
−0.699736 + 0.714401i \(0.746699\pi\)
\(90\) 11.8082 12.4059i 1.24470 1.30769i
\(91\) 1.84566 5.07092i 0.193478 0.531577i
\(92\) 3.25733 + 11.0178i 0.339600 + 1.14868i
\(93\) −2.59032 + 7.78199i −0.268604 + 0.806955i
\(94\) 8.96842 + 4.52340i 0.925022 + 0.466553i
\(95\) 12.0402 + 27.9123i 1.23530 + 2.86374i
\(96\) −9.14118 + 3.52687i −0.932968 + 0.359959i
\(97\) −15.2704 + 7.66910i −1.55048 + 0.778679i −0.998477 0.0551653i \(-0.982431\pi\)
−0.552000 + 0.833844i \(0.686135\pi\)
\(98\) 3.49409 + 2.94213i 0.352957 + 0.297200i
\(99\) −2.32454 1.74032i −0.233625 0.174908i
\(100\) 21.2041 + 7.80019i 2.12041 + 0.780019i
\(101\) 1.26798 5.35004i 0.126169 0.532349i −0.872847 0.487994i \(-0.837729\pi\)
0.999016 0.0443547i \(-0.0141232\pi\)
\(102\) 0.432635 4.77640i 0.0428372 0.472934i
\(103\) 1.91726 0.111668i 0.188913 0.0110029i 0.0365726 0.999331i \(-0.488356\pi\)
0.152341 + 0.988328i \(0.451319\pi\)
\(104\) −4.64907 + 1.07660i −0.455879 + 0.105569i
\(105\) 7.00580 + 21.2381i 0.683696 + 2.07263i
\(106\) −3.65132 3.45671i −0.354648 0.335745i
\(107\) −3.87118 + 6.70507i −0.374241 + 0.648204i −0.990213 0.139564i \(-0.955430\pi\)
0.615972 + 0.787768i \(0.288763\pi\)
\(108\) −4.86366 9.18394i −0.468006 0.883725i
\(109\) −5.68637 9.84908i −0.544656 0.943371i −0.998629 0.0523557i \(-0.983327\pi\)
0.453973 0.891015i \(-0.350006\pi\)
\(110\) 1.28362 5.37487i 0.122388 0.512474i
\(111\) −9.76491 12.3840i −0.926844 1.17544i
\(112\) 1.57247 12.6967i 0.148584 1.19973i
\(113\) 4.31291 + 6.55746i 0.405725 + 0.616874i 0.979333 0.202255i \(-0.0648271\pi\)
−0.573608 + 0.819130i \(0.694457\pi\)
\(114\) 18.3796 1.55127i 1.72141 0.145289i
\(115\) −16.8681 15.9142i −1.57296 1.48401i
\(116\) −8.53424 + 1.47463i −0.792385 + 0.136916i
\(117\) −1.71833 4.76098i −0.158860 0.440152i
\(118\) 9.51774 3.44569i 0.876179 0.317201i
\(119\) 5.23210 + 3.44121i 0.479626 + 0.315455i
\(120\) 12.3668 15.4332i 1.12893 1.40885i
\(121\) 9.99505 + 1.16825i 0.908641 + 0.106205i
\(122\) 0.0753745 + 1.33356i 0.00682409 + 0.120735i
\(123\) −0.505993 1.27868i −0.0456238 0.115295i
\(124\) −2.21569 + 9.20777i −0.198975 + 0.826882i
\(125\) −25.0328 + 4.41396i −2.23900 + 0.394796i
\(126\) 13.5696 + 0.0598774i 1.20888 + 0.00533430i
\(127\) −1.87661 0.330898i −0.166523 0.0293624i 0.0897651 0.995963i \(-0.471388\pi\)
−0.256288 + 0.966601i \(0.582499\pi\)
\(128\) −10.1706 + 4.95574i −0.898960 + 0.438030i
\(129\) −0.00405035 + 0.0455878i −0.000356614 + 0.00401379i
\(130\) 7.01759 6.59803i 0.615484 0.578685i
\(131\) −12.3721 13.1136i −1.08095 1.14574i −0.988685 0.150010i \(-0.952069\pi\)
−0.0922691 0.995734i \(-0.529412\pi\)
\(132\) −2.84538 1.77389i −0.247659 0.154398i
\(133\) −9.53939 + 22.1148i −0.827170 + 1.91760i
\(134\) −13.3728 15.9927i −1.15523 1.38156i
\(135\) 17.8087 + 11.0842i 1.53273 + 0.953979i
\(136\) 0.0285162 5.53782i 0.00244525 0.474864i
\(137\) −4.05312 + 3.01744i −0.346281 + 0.257797i −0.756222 0.654315i \(-0.772957\pi\)
0.409940 + 0.912112i \(0.365549\pi\)
\(138\) −12.4060 + 6.64027i −1.05607 + 0.565257i
\(139\) 18.3126 + 5.48245i 1.55326 + 0.465015i 0.944547 0.328377i \(-0.106502\pi\)
0.608711 + 0.793392i \(0.291687\pi\)
\(140\) 10.1467 + 23.7465i 0.857553 + 2.00695i
\(141\) −3.20002 + 11.8786i −0.269490 + 1.00036i
\(142\) −0.319761 + 5.33240i −0.0268338 + 0.447485i
\(143\) −1.25103 1.04974i −0.104616 0.0877835i
\(144\) −6.49794 10.0884i −0.541495 0.840704i
\(145\) 13.3914 11.2367i 1.11210 0.933160i
\(146\) 0.173001 + 0.233215i 0.0143177 + 0.0193010i
\(147\) −2.66173 + 4.92061i −0.219536 + 0.405845i
\(148\) −12.4513 13.2887i −1.02349 1.09232i
\(149\) 16.6106 + 12.3661i 1.36079 + 1.01307i 0.996655 + 0.0817258i \(0.0260432\pi\)
0.364136 + 0.931346i \(0.381364\pi\)
\(150\) −4.09429 + 27.3664i −0.334298 + 2.23446i
\(151\) −10.6597 0.620856i −0.867473 0.0505245i −0.381366 0.924424i \(-0.624546\pi\)
−0.486107 + 0.873900i \(0.661583\pi\)
\(152\) 20.9936 3.59037i 1.70280 0.291218i
\(153\) 5.83592 0.666177i 0.471807 0.0538572i
\(154\) 3.79542 2.18261i 0.305844 0.175880i
\(155\) −5.48252 18.3129i −0.440367 1.47093i
\(156\) −2.44468 5.30876i −0.195731 0.425041i
\(157\) −6.67493 3.35227i −0.532717 0.267541i 0.162041 0.986784i \(-0.448192\pi\)
−0.694758 + 0.719243i \(0.744489\pi\)
\(158\) −11.9530 + 5.13169i −0.950926 + 0.408255i
\(159\) 3.23989 5.23685i 0.256940 0.415309i
\(160\) 12.7120 18.9710i 1.00497 1.49979i
\(161\) 18.3737i 1.44805i
\(162\) 9.80807 8.11183i 0.770594 0.637326i
\(163\) 20.8599i 1.63387i 0.576726 + 0.816937i \(0.304330\pi\)
−0.576726 + 0.816937i \(0.695670\pi\)
\(164\) −0.707770 1.42143i −0.0552676 0.110995i
\(165\) 6.76483 + 0.205964i 0.526642 + 0.0160343i
\(166\) −2.24250 5.22333i −0.174052 0.405409i
\(167\) −8.73061 4.38468i −0.675595 0.339297i 0.0777025 0.996977i \(-0.475242\pi\)
−0.753297 + 0.657680i \(0.771538\pi\)
\(168\) 15.6179 1.26420i 1.20495 0.0975349i
\(169\) 2.91202 + 9.72683i 0.224002 + 0.748218i
\(170\) 5.57237 + 9.69000i 0.427381 + 0.743189i
\(171\) 6.42061 + 21.6587i 0.490997 + 1.65628i
\(172\) −0.000181419 0.0528474i −1.38331e−5 0.00402957i
\(173\) 1.34614 + 0.0784035i 0.102345 + 0.00596091i 0.109241 0.994015i \(-0.465158\pi\)
−0.00689595 + 0.999976i \(0.502195\pi\)
\(174\) −3.88600 9.86969i −0.294597 0.748219i
\(175\) −28.9819 21.5762i −2.19082 1.63101i
\(176\) −3.44792 1.76136i −0.259897 0.132767i
\(177\) 6.49400 + 10.5602i 0.488119 + 0.793754i
\(178\) −9.25789 + 6.86758i −0.693908 + 0.514747i
\(179\) 1.65628 1.38978i 0.123796 0.103877i −0.578788 0.815478i \(-0.696474\pi\)
0.702584 + 0.711601i \(0.252030\pi\)
\(180\) 21.5781 + 11.0030i 1.60833 + 0.820117i
\(181\) 0.587591 + 0.493048i 0.0436753 + 0.0366479i 0.664364 0.747409i \(-0.268702\pi\)
−0.620689 + 0.784057i \(0.713147\pi\)
\(182\) 7.61792 + 0.456815i 0.564678 + 0.0338613i
\(183\) −1.58071 + 0.421266i −0.116849 + 0.0311409i
\(184\) −13.6209 + 8.85849i −1.00415 + 0.653057i
\(185\) 35.2129 + 10.5421i 2.58891 + 0.775067i
\(186\) −11.5931 0.372884i −0.850045 0.0273412i
\(187\) 1.52016 1.13172i 0.111165 0.0827594i
\(188\) −2.51471 + 13.9808i −0.183404 + 1.01966i
\(189\) 3.29490 + 16.2896i 0.239669 + 1.18490i
\(190\) −32.9795 + 27.5768i −2.39258 + 2.00063i
\(191\) −4.83014 + 11.1975i −0.349497 + 0.810224i 0.649269 + 0.760559i \(0.275075\pi\)
−0.998766 + 0.0496657i \(0.984184\pi\)
\(192\) −8.46706 10.9685i −0.611058 0.791586i
\(193\) 6.03986 + 6.40188i 0.434759 + 0.460818i 0.907296 0.420493i \(-0.138143\pi\)
−0.472537 + 0.881311i \(0.656662\pi\)
\(194\) −16.5536 17.6062i −1.18848 1.26405i
\(195\) 9.65446 + 6.77954i 0.691371 + 0.485493i
\(196\) −2.57896 + 5.92271i −0.184211 + 0.423051i
\(197\) −11.4817 2.02454i −0.818039 0.144242i −0.251057 0.967972i \(-0.580778\pi\)
−0.566982 + 0.823730i \(0.691889\pi\)
\(198\) 1.42156 3.85273i 0.101026 0.273802i
\(199\) 10.2771 1.81213i 0.728525 0.128459i 0.202930 0.979193i \(-0.434954\pi\)
0.525595 + 0.850735i \(0.323843\pi\)
\(200\) −2.02205 + 31.8877i −0.142981 + 2.25480i
\(201\) 15.8630 20.0066i 1.11889 1.41116i
\(202\) 7.76331 0.438792i 0.546224 0.0308733i
\(203\) 13.7567 + 1.60792i 0.965528 + 0.112854i
\(204\) 6.64887 1.33977i 0.465514 0.0938026i
\(205\) 2.67781 + 1.76123i 0.187027 + 0.123009i
\(206\) 0.924548 + 2.55380i 0.0644163 + 0.177932i
\(207\) −11.0420 13.2317i −0.767474 0.919664i
\(208\) −3.33418 5.86763i −0.231184 0.406847i
\(209\) 5.30161 + 5.00181i 0.366720 + 0.345983i
\(210\) −25.9630 + 18.0611i −1.79161 + 1.24634i
\(211\) 11.3522 + 17.2602i 0.781517 + 1.18824i 0.978178 + 0.207768i \(0.0666199\pi\)
−0.196661 + 0.980472i \(0.563010\pi\)
\(212\) 3.21307 6.34335i 0.220674 0.435663i
\(213\) −6.47475 + 0.939497i −0.443642 + 0.0643733i
\(214\) −10.6498 2.54337i −0.728009 0.173862i
\(215\) −0.0533353 0.0923795i −0.00363744 0.00630023i
\(216\) 10.4874 10.2963i 0.713578 0.700576i
\(217\) 7.57275 13.1164i 0.514072 0.890398i
\(218\) 11.0572 11.6797i 0.748890 0.791052i
\(219\) −0.236784 + 0.265351i −0.0160004 + 0.0179308i
\(220\) 7.80327 0.427615i 0.526096 0.0288298i
\(221\) 3.29783 0.192077i 0.221836 0.0129205i
\(222\) 12.8485 18.2305i 0.862338 1.22355i
\(223\) 4.51801 19.0630i 0.302548 1.27655i −0.583178 0.812344i \(-0.698191\pi\)
0.885727 0.464207i \(-0.153661\pi\)
\(224\) 17.8445 2.98879i 1.19228 0.199697i
\(225\) −33.8378 + 1.87930i −2.25585 + 0.125287i
\(226\) −7.14933 + 8.49060i −0.475566 + 0.564786i
\(227\) 13.6713 6.86601i 0.907399 0.455713i 0.0670443 0.997750i \(-0.478643\pi\)
0.840355 + 0.542037i \(0.182347\pi\)
\(228\) 9.51477 + 24.2879i 0.630131 + 1.60850i
\(229\) −9.18809 21.3004i −0.607166 1.40757i −0.893335 0.449391i \(-0.851641\pi\)
0.286169 0.958179i \(-0.407618\pi\)
\(230\) 14.7692 29.2824i 0.973851 1.93083i
\(231\) 3.55939 + 4.01052i 0.234190 + 0.263873i
\(232\) −5.44050 10.9735i −0.357186 0.720443i
\(233\) 3.40302 9.34973i 0.222939 0.612521i −0.776915 0.629606i \(-0.783216\pi\)
0.999854 + 0.0170849i \(0.00543857\pi\)
\(234\) 5.76052 4.24917i 0.376577 0.277777i
\(235\) −9.80658 26.9434i −0.639711 1.75759i
\(236\) 8.50888 + 11.5117i 0.553881 + 0.749348i
\(237\) −9.12030 13.0626i −0.592427 0.848506i
\(238\) −2.55457 + 8.47984i −0.165588 + 0.549666i
\(239\) 6.34122 1.50290i 0.410179 0.0972143i −0.0203454 0.999793i \(-0.506477\pi\)
0.430525 + 0.902579i \(0.358328\pi\)
\(240\) 25.9068 + 10.5393i 1.67228 + 0.680309i
\(241\) 13.8009 1.61309i 0.888991 0.103908i 0.340677 0.940180i \(-0.389344\pi\)
0.548314 + 0.836272i \(0.315270\pi\)
\(242\) 2.44719 + 14.0194i 0.157311 + 0.901200i
\(243\) 12.1624 + 9.75071i 0.780217 + 0.625509i
\(244\) −1.77724 + 0.639962i −0.113776 + 0.0409693i
\(245\) −1.51372 12.9507i −0.0967083 0.827392i
\(246\) 1.52919 1.20153i 0.0974978 0.0766069i
\(247\) 2.92992 + 12.3623i 0.186426 + 0.786594i
\(248\) −13.3746 + 0.709899i −0.849289 + 0.0450787i
\(249\) 5.70822 3.98548i 0.361744 0.252570i
\(250\) −16.0782 32.1518i −1.01687 2.03346i
\(251\) 3.86228 1.40576i 0.243785 0.0887305i −0.217238 0.976119i \(-0.569705\pi\)
0.461023 + 0.887388i \(0.347483\pi\)
\(252\) 5.39113 + 18.4177i 0.339609 + 1.16021i
\(253\) −5.22509 1.90178i −0.328499 0.119564i
\(254\) −0.308261 2.67719i −0.0193420 0.167982i
\(255\) −10.2392 + 9.08738i −0.641202 + 0.569074i
\(256\) −10.8190 11.7876i −0.676189 0.736728i
\(257\) −18.7945 + 8.10715i −1.17237 + 0.505710i −0.891050 0.453905i \(-0.850031\pi\)
−0.281317 + 0.959615i \(0.590771\pi\)
\(258\) −0.0634275 + 0.0128942i −0.00394883 + 0.000802758i
\(259\) 13.0701 + 26.0248i 0.812140 + 1.61710i
\(260\) 11.7736 + 6.85150i 0.730169 + 0.424912i
\(261\) 10.8731 7.10942i 0.673027 0.440062i
\(262\) 12.7861 22.0587i 0.789930 1.36279i
\(263\) −4.12482 0.977599i −0.254347 0.0602814i 0.101464 0.994839i \(-0.467647\pi\)
−0.355811 + 0.934558i \(0.615795\pi\)
\(264\) 1.25703 4.57227i 0.0773651 0.281404i
\(265\) 0.834530 + 14.3283i 0.0512648 + 0.880182i
\(266\) −33.8235 4.01226i −2.07385 0.246008i
\(267\) −10.5336 9.39957i −0.644645 0.575244i
\(268\) 16.2852 24.5762i 0.994776 1.50123i
\(269\) −22.2825 12.8648i −1.35859 0.784383i −0.369156 0.929367i \(-0.620353\pi\)
−0.989434 + 0.144985i \(0.953687\pi\)
\(270\) −7.84283 + 28.6096i −0.477300 + 1.74112i
\(271\) 18.3768 10.6099i 1.11631 0.644503i 0.175855 0.984416i \(-0.443731\pi\)
0.940457 + 0.339914i \(0.110398\pi\)
\(272\) 7.51799 2.19461i 0.455845 0.133068i
\(273\) 1.34218 + 9.24990i 0.0812322 + 0.559829i
\(274\) −5.72464 4.27713i −0.345838 0.258391i
\(275\) −9.13562 + 6.00859i −0.550899 + 0.362332i
\(276\) −14.0039 14.1384i −0.842935 0.851034i
\(277\) −2.38601 + 2.52902i −0.143361 + 0.151954i −0.795075 0.606511i \(-0.792569\pi\)
0.651714 + 0.758465i \(0.274050\pi\)
\(278\) −0.0464017 + 27.0336i −0.00278299 + 1.62137i
\(279\) −2.42910 13.9967i −0.145426 0.837959i
\(280\) −28.0964 + 23.3302i −1.67908 + 1.39425i
\(281\) −11.0344 + 16.7769i −0.658254 + 1.00083i 0.339921 + 0.940454i \(0.389600\pi\)
−0.998176 + 0.0603734i \(0.980771\pi\)
\(282\) −17.3918 + 0.452713i −1.03567 + 0.0269587i
\(283\) 0.157022 1.34341i 0.00933398 0.0798573i −0.987768 0.155928i \(-0.950163\pi\)
0.997102 + 0.0760704i \(0.0242374\pi\)
\(284\) −7.35699 + 1.71699i −0.436557 + 0.101884i
\(285\) −41.2567 32.7120i −2.44383 1.93769i
\(286\) 0.918406 2.11910i 0.0543065 0.125305i
\(287\) 0.440959 + 2.50080i 0.0260290 + 0.147618i
\(288\) 11.0544 12.8764i 0.651386 0.758746i
\(289\) 2.28633 12.9664i 0.134490 0.762732i
\(290\) 20.6318 + 13.6205i 1.21154 + 0.799824i
\(291\) 17.0090 24.2218i 0.997086 1.41991i
\(292\) −0.246355 + 0.328552i −0.0144168 + 0.0192270i
\(293\) −22.4631 + 21.1928i −1.31231 + 1.23810i −0.360002 + 0.932952i \(0.617224\pi\)
−0.952305 + 0.305146i \(0.901295\pi\)
\(294\) −7.74327 1.62361i −0.451597 0.0946911i
\(295\) −26.5312 11.4444i −1.54470 0.666320i
\(296\) 12.9915 22.2366i 0.755113 1.29248i
\(297\) 4.97347 + 0.749064i 0.288590 + 0.0434651i
\(298\) −10.0636 + 27.5025i −0.582968 + 1.59318i
\(299\) −5.78780 7.77437i −0.334717 0.449603i
\(300\) −38.7462 + 5.48640i −2.23701 + 0.316757i
\(301\) 0.0242391 0.0809641i 0.00139712 0.00466670i
\(302\) −3.45722 14.6995i −0.198940 0.845863i
\(303\) 2.45239 + 9.20206i 0.140886 + 0.528645i
\(304\) 13.3329 + 27.0088i 0.764696 + 1.54906i
\(305\) 2.45079 2.92074i 0.140332 0.167241i
\(306\) 3.25648 + 7.64192i 0.186161 + 0.436859i
\(307\) 1.07337 + 1.27920i 0.0612606 + 0.0730075i 0.795805 0.605554i \(-0.207048\pi\)
−0.734544 + 0.678561i \(0.762604\pi\)
\(308\) 4.48912 + 4.26449i 0.255791 + 0.242992i
\(309\) −2.83352 + 1.74247i −0.161193 + 0.0991259i
\(310\) 22.6121 14.8167i 1.28428 0.841531i
\(311\) −7.90575 + 10.6193i −0.448294 + 0.602163i −0.967620 0.252413i \(-0.918776\pi\)
0.519326 + 0.854576i \(0.326183\pi\)
\(312\) 6.21012 5.45465i 0.351579 0.308809i
\(313\) −0.983307 + 16.8827i −0.0555798 + 0.954269i 0.849115 + 0.528208i \(0.177136\pi\)
−0.904695 + 0.426060i \(0.859901\pi\)
\(314\) 1.85216 10.3997i 0.104524 0.586890i
\(315\) −28.1032 26.6576i −1.58344 1.50199i
\(316\) −11.7763 14.1327i −0.662469 0.795027i
\(317\) 8.95998 2.68244i 0.503243 0.150661i −0.0251120 0.999685i \(-0.507994\pi\)
0.528355 + 0.849024i \(0.322809\pi\)
\(318\) 8.40509 + 2.27977i 0.471334 + 0.127843i
\(319\) 1.88115 3.74568i 0.105324 0.209718i
\(320\) 30.8415 + 9.58052i 1.72409 + 0.535567i
\(321\) 0.408100 13.4039i 0.0227779 0.748135i
\(322\) 24.9054 7.40963i 1.38792 0.412923i
\(323\) −14.7435 −0.820352
\(324\) 14.9509 + 10.0235i 0.830606 + 0.556861i
\(325\) −19.0596 −1.05724
\(326\) −28.2755 + 8.41228i −1.56604 + 0.465913i
\(327\) 16.7515 + 10.3637i 0.926359 + 0.573112i
\(328\) 1.64132 1.53261i 0.0906267 0.0846241i
\(329\) 10.1954 20.3008i 0.562092 1.11922i
\(330\) 2.44890 + 9.25276i 0.134808 + 0.509348i
\(331\) 3.22568 0.965706i 0.177299 0.0530800i −0.196923 0.980419i \(-0.563095\pi\)
0.374222 + 0.927339i \(0.377910\pi\)
\(332\) 6.17585 5.14613i 0.338944 0.282431i
\(333\) 25.0525 + 10.8868i 1.37287 + 0.596594i
\(334\) 2.42258 13.6025i 0.132557 0.744298i
\(335\) −3.46011 + 59.4078i −0.189046 + 3.24579i
\(336\) 8.01194 + 20.6602i 0.437087 + 1.12711i
\(337\) −2.48633 + 3.33972i −0.135439 + 0.181926i −0.864668 0.502343i \(-0.832471\pi\)
0.729229 + 0.684270i \(0.239879\pi\)
\(338\) −12.0103 + 7.86982i −0.653276 + 0.428062i
\(339\) −11.9570 6.46798i −0.649415 0.351292i
\(340\) −10.8876 + 11.4611i −0.590461 + 0.621563i
\(341\) −2.94621 3.51116i −0.159546 0.190140i
\(342\) −26.7690 + 17.4375i −1.44750 + 0.942914i
\(343\) −7.75093 + 9.23720i −0.418511 + 0.498762i
\(344\) −0.0717075 + 0.0210661i −0.00386621 + 0.00113581i
\(345\) 38.7843 + 10.4483i 2.08807 + 0.562516i
\(346\) 0.436588 + 1.85630i 0.0234711 + 0.0997954i
\(347\) −4.57793 + 15.2914i −0.245756 + 0.820883i 0.742732 + 0.669588i \(0.233530\pi\)
−0.988489 + 0.151295i \(0.951656\pi\)
\(348\) 11.8112 9.24766i 0.633147 0.495726i
\(349\) −3.49198 4.69055i −0.186922 0.251079i 0.698777 0.715339i \(-0.253728\pi\)
−0.885699 + 0.464260i \(0.846320\pi\)
\(350\) 17.5588 47.9860i 0.938557 2.56496i
\(351\) 6.52548 + 5.85464i 0.348304 + 0.312498i
\(352\) 0.997053 5.38395i 0.0531431 0.286966i
\(353\) −0.251081 0.108306i −0.0133637 0.00576453i 0.389387 0.921074i \(-0.372687\pi\)
−0.402751 + 0.915310i \(0.631946\pi\)
\(354\) −11.6955 + 13.0613i −0.621607 + 0.694198i
\(355\) 11.0916 10.4644i 0.588680 0.555391i
\(356\) −13.0425 9.77951i −0.691249 0.518313i
\(357\) −10.8041 0.959915i −0.571814 0.0508041i
\(358\) 2.55178 + 1.68461i 0.134866 + 0.0890345i
\(359\) −1.84727 + 10.4764i −0.0974953 + 0.552923i 0.896459 + 0.443127i \(0.146131\pi\)
−0.993954 + 0.109796i \(0.964980\pi\)
\(360\) −6.21267 + 33.6862i −0.327437 + 1.77542i
\(361\) −6.54700 37.1299i −0.344579 1.95420i
\(362\) −0.431363 + 0.995312i −0.0226719 + 0.0523124i
\(363\) −16.2070 + 6.41334i −0.850646 + 0.336613i
\(364\) 2.45291 + 10.5103i 0.128567 + 0.550888i
\(365\) 0.0962280 0.823283i 0.00503680 0.0430926i
\(366\) −1.20848 1.97276i −0.0631685 0.103118i
\(367\) −7.69073 + 11.6932i −0.401453 + 0.610380i −0.978479 0.206346i \(-0.933843\pi\)
0.577026 + 0.816726i \(0.304213\pi\)
\(368\) −17.5006 14.8907i −0.912284 0.776232i
\(369\) 1.82046 + 1.53593i 0.0947694 + 0.0799574i
\(370\) −0.0892246 + 51.9823i −0.00463857 + 2.70243i
\(371\) −7.80360 + 8.27133i −0.405143 + 0.429426i
\(372\) −4.16975 15.8647i −0.216192 0.822548i
\(373\) 22.3785 14.7185i 1.15871 0.762097i 0.183424 0.983034i \(-0.441282\pi\)
0.975288 + 0.220937i \(0.0709114\pi\)
\(374\) 2.14708 + 1.60418i 0.111023 + 0.0829501i
\(375\) 34.5722 27.2605i 1.78530 1.40773i
\(376\) −19.9651 + 2.22943i −1.02962 + 0.114974i
\(377\) 6.32730 3.65307i 0.325873 0.188143i
\(378\) −20.7518 + 11.0354i −1.06735 + 0.567601i
\(379\) 5.38448 + 3.10873i 0.276582 + 0.159685i 0.631875 0.775070i \(-0.282286\pi\)
−0.355293 + 0.934755i \(0.615619\pi\)
\(380\) −50.6800 33.5826i −2.59983 1.72275i
\(381\) 3.13441 1.03394i 0.160580 0.0529704i
\(382\) −17.1261 2.03155i −0.876246 0.103943i
\(383\) −0.0747727 1.28380i −0.00382071 0.0655990i 0.995859 0.0909129i \(-0.0289785\pi\)
−0.999680 + 0.0253139i \(0.991941\pi\)
\(384\) 11.4533 15.9004i 0.584471 0.811414i
\(385\) −12.1609 2.88219i −0.619778 0.146890i
\(386\) −6.24200 + 10.7687i −0.317709 + 0.548114i
\(387\) −0.0312015 0.0728728i −0.00158606 0.00370433i
\(388\) 17.1895 29.5385i 0.872667 1.49959i
\(389\) −1.32959 2.64744i −0.0674131 0.134230i 0.857402 0.514647i \(-0.172077\pi\)
−0.924815 + 0.380416i \(0.875781\pi\)
\(390\) −5.29624 + 15.8206i −0.268185 + 0.801108i
\(391\) 10.3277 4.45494i 0.522295 0.225296i
\(392\) −9.06825 1.10729i −0.458016 0.0559265i
\(393\) 29.6285 + 9.86215i 1.49456 + 0.497480i
\(394\) −1.88604 16.3799i −0.0950174 0.825207i
\(395\) 34.8923 + 12.6998i 1.75562 + 0.638994i
\(396\) 5.79564 + 0.373213i 0.291242 + 0.0187546i
\(397\) 5.74124 2.08964i 0.288145 0.104876i −0.193904 0.981020i \(-0.562115\pi\)
0.482049 + 0.876144i \(0.339893\pi\)
\(398\) 6.60084 + 13.1998i 0.330870 + 0.661646i
\(399\) −3.57973 41.5617i −0.179211 2.08069i
\(400\) −44.0391 + 10.1186i −2.20195 + 0.505931i
\(401\) −7.77020 32.7851i −0.388025 1.63721i −0.720040 0.693933i \(-0.755876\pi\)
0.332014 0.943274i \(-0.392272\pi\)
\(402\) 33.5160 + 13.4341i 1.67163 + 0.670033i
\(403\) −0.927508 7.93534i −0.0462025 0.395287i
\(404\) 3.72553 + 10.3462i 0.185352 + 0.514741i
\(405\) −36.2588 2.30808i −1.80171 0.114689i
\(406\) 3.36818 + 19.2955i 0.167160 + 0.957621i
\(407\) 8.75376 1.02317i 0.433908 0.0507165i
\(408\) 4.49737 + 8.47222i 0.222653 + 0.419437i
\(409\) −2.75688 + 0.653393i −0.136319 + 0.0323082i −0.298209 0.954501i \(-0.596389\pi\)
0.161890 + 0.986809i \(0.448241\pi\)
\(410\) −1.30744 + 4.34003i −0.0645698 + 0.214339i
\(411\) 3.70946 7.92704i 0.182974 0.391012i
\(412\) −3.08882 + 2.28311i −0.152175 + 0.112481i
\(413\) −7.82979 21.5122i −0.385279 1.05855i
\(414\) 13.4825 20.3034i 0.662628 0.997859i
\(415\) −5.54967 + 15.2476i −0.272423 + 0.748475i
\(416\) 6.60896 6.88573i 0.324031 0.337601i
\(417\) −32.4343 + 6.65158i −1.58832 + 0.325729i
\(418\) −4.64193 + 9.20342i −0.227044 + 0.450154i
\(419\) 1.30611 + 3.02791i 0.0638077 + 0.147923i 0.947136 0.320831i \(-0.103962\pi\)
−0.883329 + 0.468754i \(0.844703\pi\)
\(420\) −34.9520 27.9091i −1.70548 1.36182i
\(421\) −16.5865 + 8.33004i −0.808375 + 0.405981i −0.804457 0.594011i \(-0.797544\pi\)
−0.00391833 + 0.999992i \(0.501247\pi\)
\(422\) −18.8180 + 22.3485i −0.916048 + 1.08791i
\(423\) −4.85799 20.7466i −0.236204 1.00873i
\(424\) 9.89414 + 1.79718i 0.480502 + 0.0872790i
\(425\) 5.10080 21.5220i 0.247425 1.04397i
\(426\) −3.88459 8.39762i −0.188209 0.406866i
\(427\) 3.01572 0.175646i 0.145941 0.00850009i
\(428\) −0.847283 15.4615i −0.0409550 0.747360i
\(429\) 2.76940 + 0.575730i 0.133708 + 0.0277965i
\(430\) 0.103711 0.109550i 0.00500140 0.00528298i
\(431\) 9.52837 16.5036i 0.458965 0.794951i −0.539941 0.841703i \(-0.681554\pi\)
0.998907 + 0.0467514i \(0.0148869\pi\)
\(432\) 18.1859 + 10.0634i 0.874971 + 0.484175i
\(433\) 10.8493 + 18.7915i 0.521384 + 0.903063i 0.999691 + 0.0248706i \(0.00791738\pi\)
−0.478307 + 0.878193i \(0.658749\pi\)
\(434\) 20.8331 + 4.97532i 1.00002 + 0.238823i
\(435\) −11.2169 + 28.1241i −0.537809 + 1.34845i
\(436\) 20.2909 + 10.2779i 0.971760 + 0.492221i
\(437\) 23.7704 + 36.1411i 1.13709 + 1.72886i
\(438\) −0.455171 0.213950i −0.0217489 0.0102229i
\(439\) 16.8350 + 15.8830i 0.803492 + 0.758056i 0.973817 0.227332i \(-0.0730003\pi\)
−0.170325 + 0.985388i \(0.554482\pi\)
\(440\) 3.72649 + 10.4049i 0.177654 + 0.496032i
\(441\) 0.0261248 9.68973i 0.00124404 0.461416i
\(442\) 1.59029 + 4.39274i 0.0756426 + 0.208941i
\(443\) −4.76718 3.13542i −0.226496 0.148969i 0.431190 0.902261i \(-0.358094\pi\)
−0.657685 + 0.753293i \(0.728464\pi\)
\(444\) 29.8928 + 10.0643i 1.41865 + 0.477629i
\(445\) 32.6817 + 3.81994i 1.54926 + 0.181083i
\(446\) 27.6618 1.56348i 1.30982 0.0740329i
\(447\) −35.4820 5.24622i −1.67824 0.248138i
\(448\) 11.2475 + 22.9828i 0.531395 + 1.08583i
\(449\) 5.42615 0.956777i 0.256076 0.0451531i −0.0441363 0.999026i \(-0.514054\pi\)
0.300212 + 0.953872i \(0.402942\pi\)
\(450\) −16.1933 45.1091i −0.763360 2.12646i
\(451\) 0.756818 + 0.133447i 0.0356372 + 0.00628380i
\(452\) −14.3921 6.26684i −0.676948 0.294767i
\(453\) 16.7721 7.79347i 0.788024 0.366169i
\(454\) 14.8202 + 15.7626i 0.695544 + 0.739774i
\(455\) −14.9495 15.8455i −0.700844 0.742851i
\(456\) −29.0851 + 22.6919i −1.36203 + 1.06265i
\(457\) −1.99918 + 4.63462i −0.0935178 + 0.216799i −0.958554 0.284911i \(-0.908036\pi\)
0.865036 + 0.501709i \(0.167295\pi\)
\(458\) 25.1673 21.0443i 1.17599 0.983337i
\(459\) −8.35739 + 5.80168i −0.390089 + 0.270799i
\(460\) 45.6483 + 8.21070i 2.12836 + 0.382826i
\(461\) 30.4564 22.6740i 1.41850 1.05603i 0.430325 0.902674i \(-0.358399\pi\)
0.988171 0.153357i \(-0.0490086\pi\)
\(462\) −4.00084 + 6.44208i −0.186136 + 0.299712i
\(463\) −9.00206 2.69504i −0.418361 0.125249i 0.0707020 0.997497i \(-0.477476\pi\)
−0.489063 + 0.872248i \(0.662661\pi\)
\(464\) 12.6805 11.7999i 0.588675 0.547796i
\(465\) 23.3806 + 23.4437i 1.08425 + 1.08718i
\(466\) 14.0459 + 0.842272i 0.650662 + 0.0390175i
\(467\) −17.7879 14.9258i −0.823127 0.690686i 0.130575 0.991438i \(-0.458318\pi\)
−0.953702 + 0.300753i \(0.902762\pi\)
\(468\) 8.08281 + 6.09478i 0.373628 + 0.281731i
\(469\) −36.1177 + 30.3063i −1.66776 + 1.39942i
\(470\) 32.5669 24.1584i 1.50220 1.11434i
\(471\) 12.9325 0.358848i 0.595896 0.0165349i
\(472\) −12.1726 + 16.1761i −0.560291 + 0.744567i
\(473\) −0.0205157 0.0152733i −0.000943311 0.000702269i
\(474\) 14.0283 17.6304i 0.644341 0.809789i
\(475\) 84.9211 + 4.94609i 3.89645 + 0.226942i
\(476\) −12.5246 0.0429955i −0.574063 0.00197070i
\(477\) −0.648881 + 10.6463i −0.0297102 + 0.487460i
\(478\) 4.59443 + 7.98942i 0.210144 + 0.365428i
\(479\) −4.10984 13.7278i −0.187783 0.627240i −0.999091 0.0426210i \(-0.986429\pi\)
0.811308 0.584619i \(-0.198756\pi\)
\(480\) −3.83842 + 39.3668i −0.175199 + 1.79684i
\(481\) 13.7283 + 6.89460i 0.625955 + 0.314367i
\(482\) 7.75208 + 18.0565i 0.353097 + 0.822450i
\(483\) 15.0660 + 28.0320i 0.685525 + 1.27550i
\(484\) −18.0163 + 8.97082i −0.818923 + 0.407765i
\(485\) 68.9829i 3.13235i
\(486\) −8.31227 + 20.4183i −0.377052 + 0.926192i
\(487\) 2.48820i 0.112751i −0.998410 0.0563756i \(-0.982046\pi\)
0.998410 0.0563756i \(-0.0179544\pi\)
\(488\) −1.58418 2.15096i −0.0717125 0.0973694i
\(489\) −17.1046 31.8251i −0.773498 1.43918i
\(490\) 16.9442 7.27456i 0.765462 0.328631i
\(491\) −12.7872 6.42199i −0.577080 0.289821i 0.136221 0.990679i \(-0.456504\pi\)
−0.713301 + 0.700858i \(0.752801\pi\)
\(492\) 2.24536 + 1.58827i 0.101228 + 0.0716046i
\(493\) 2.43168 + 8.12239i 0.109518 + 0.365814i
\(494\) −15.5755 + 8.95690i −0.700774 + 0.402990i
\(495\) −10.4897 + 5.23277i −0.471478 + 0.235196i
\(496\) −6.35592 17.8430i −0.285389 0.801173i
\(497\) 12.0611 + 0.702480i 0.541015 + 0.0315105i
\(498\) 7.70429 + 6.13023i 0.345238 + 0.274702i
\(499\) 2.30989 + 1.71965i 0.103405 + 0.0769821i 0.647619 0.761964i \(-0.275765\pi\)
−0.544214 + 0.838946i \(0.683172\pi\)
\(500\) 37.0977 34.7599i 1.65906 1.55451i
\(501\) 16.9153 0.469363i 0.755719 0.0209696i
\(502\) 3.46306 + 4.66840i 0.154564 + 0.208361i
\(503\) 13.3937 11.2386i 0.597194 0.501105i −0.293348 0.956006i \(-0.594770\pi\)
0.890542 + 0.454900i \(0.150325\pi\)
\(504\) −22.7911 + 14.7351i −1.01519 + 0.656352i
\(505\) −17.0031 14.2673i −0.756626 0.634885i
\(506\) 0.470703 7.84953i 0.0209253 0.348954i
\(507\) −12.4185 12.4521i −0.551526 0.553015i
\(508\) 3.50460 1.49749i 0.155492 0.0664403i
\(509\) 14.5920 + 4.36856i 0.646780 + 0.193633i 0.593358 0.804939i \(-0.297802\pi\)
0.0534220 + 0.998572i \(0.482987\pi\)
\(510\) −16.4471 10.2144i −0.728290 0.452303i
\(511\) 0.526773 0.392168i 0.0233031 0.0173485i
\(512\) 11.6151 19.4188i 0.513318 0.858198i
\(513\) −27.5553 27.7791i −1.21660 1.22648i
\(514\) −18.5686 22.2064i −0.819024 0.979484i
\(515\) 3.07077 7.11886i 0.135314 0.313694i
\(516\) −0.0430568 0.0807759i −0.00189547 0.00355596i
\(517\) −4.71783 5.00061i −0.207490 0.219927i
\(518\) −30.0057 + 28.2117i −1.31837 + 1.23955i
\(519\) −2.11804 + 0.984183i −0.0929715 + 0.0432008i
\(520\) −4.53917 + 18.7221i −0.199056 + 0.821020i
\(521\) −21.7399 3.83334i −0.952444 0.167942i −0.324227 0.945979i \(-0.605104\pi\)
−0.628218 + 0.778038i \(0.716215\pi\)
\(522\) 14.0216 + 11.8714i 0.613710 + 0.519596i
\(523\) 30.1746 5.32059i 1.31944 0.232653i 0.530796 0.847500i \(-0.321893\pi\)
0.788647 + 0.614847i \(0.210782\pi\)
\(524\) 35.0568 + 8.43583i 1.53146 + 0.368521i
\(525\) 61.9085 + 9.15352i 2.70191 + 0.399492i
\(526\) −0.338303 5.98541i −0.0147507 0.260976i
\(527\) 9.20875 + 1.07635i 0.401139 + 0.0468865i
\(528\) 6.70463 0.139979i 0.291781 0.00609182i
\(529\) −8.35518 5.49529i −0.363269 0.238926i
\(530\) −19.0854 + 6.90946i −0.829019 + 0.300128i
\(531\) −18.5668 10.7864i −0.805729 0.468089i
\(532\) −8.20157 47.4657i −0.355583 2.05790i
\(533\) 0.974347 + 0.919249i 0.0422036 + 0.0398171i
\(534\) 8.49315 18.0688i 0.367535 0.781915i
\(535\) 17.1750 + 26.1133i 0.742540 + 1.12898i
\(536\) 39.8804 + 12.1635i 1.72257 + 0.525384i
\(537\) −1.38733 + 3.47844i −0.0598676 + 0.150106i
\(538\) 8.45223 35.3920i 0.364402 1.52586i
\(539\) −1.56319 2.70752i −0.0673312 0.116621i
\(540\) −41.9430 + 0.906603i −1.80494 + 0.0390140i
\(541\) −8.40440 + 14.5568i −0.361333 + 0.625847i −0.988181 0.153295i \(-0.951012\pi\)
0.626847 + 0.779142i \(0.284345\pi\)
\(542\) 21.7925 + 20.6310i 0.936069 + 0.886177i
\(543\) −1.30075 0.270412i −0.0558206 0.0116045i
\(544\) 6.00660 + 9.30558i 0.257531 + 0.398973i
\(545\) −45.8331 + 2.66947i −1.96327 + 0.114348i
\(546\) −11.9969 + 5.54957i −0.513421 + 0.237499i
\(547\) 2.28592 9.64506i 0.0977389 0.412393i −0.902077 0.431575i \(-0.857958\pi\)
0.999816 + 0.0191821i \(0.00610622\pi\)
\(548\) 3.48903 9.48459i 0.149044 0.405162i
\(549\) 2.06619 1.93885i 0.0881830 0.0827481i
\(550\) −11.8288 9.96018i −0.504381 0.424704i
\(551\) −29.1396 + 14.6345i −1.24139 + 0.623450i
\(552\) 13.5172 24.6839i 0.575329 1.05062i
\(553\) 11.6524 + 27.0132i 0.495508 + 1.14872i
\(554\) −4.39029 2.21433i −0.186526 0.0940780i
\(555\) −62.3672 + 12.7902i −2.64734 + 0.542912i
\(556\) −36.6627 + 10.8391i −1.55485 + 0.459680i
\(557\) −4.83448 + 13.2826i −0.204843 + 0.562803i −0.998990 0.0449230i \(-0.985696\pi\)
0.794147 + 0.607726i \(0.207918\pi\)
\(558\) 17.9928 8.93715i 0.761698 0.378340i
\(559\) −0.0152480 0.0418935i −0.000644920 0.00177190i
\(560\) −42.9546 28.6761i −1.81516 1.21179i
\(561\) −1.39127 + 2.97311i −0.0587393 + 0.125525i
\(562\) −27.1909 8.19131i −1.14698 0.345530i
\(563\) −30.4102 + 7.20735i −1.28164 + 0.303754i −0.814361 0.580358i \(-0.802913\pi\)
−0.467276 + 0.884112i \(0.654764\pi\)
\(564\) −7.62734 23.3920i −0.321169 0.984981i
\(565\) 31.4701 3.67833i 1.32396 0.154748i
\(566\) 1.88431 0.328920i 0.0792033 0.0138256i
\(567\) −18.3840 22.1507i −0.772055 0.930241i
\(568\) −5.29426 9.27996i −0.222142 0.389378i
\(569\) −2.80513 23.9994i −0.117597 1.00611i −0.915221 0.402953i \(-0.867984\pi\)
0.797623 0.603156i \(-0.206090\pi\)
\(570\) 27.7032 69.1152i 1.16036 2.89492i
\(571\) 6.64849 + 28.0522i 0.278231 + 1.17395i 0.915181 + 0.403043i \(0.132047\pi\)
−0.636951 + 0.770905i \(0.719805\pi\)
\(572\) 3.24280 + 0.390317i 0.135588 + 0.0163200i
\(573\) −1.81255 21.0442i −0.0757203 0.879135i
\(574\) −3.21200 + 1.60623i −0.134066 + 0.0670427i
\(575\) −60.9810 + 22.1953i −2.54308 + 0.925606i
\(576\) 21.9118 + 9.79147i 0.912992 + 0.407978i
\(577\) 3.24649 + 1.18162i 0.135153 + 0.0491916i 0.408711 0.912664i \(-0.365978\pi\)
−0.273558 + 0.961855i \(0.588201\pi\)
\(578\) 18.4980 2.12993i 0.769414 0.0885932i
\(579\) −14.4642 4.81455i −0.601110 0.200086i
\(580\) −10.1423 + 33.4591i −0.421135 + 1.38931i
\(581\) −11.8045 + 5.09196i −0.489733 + 0.211250i
\(582\) 39.6919 + 13.2876i 1.64528 + 0.550788i
\(583\) 1.54448 + 3.07531i 0.0639659 + 0.127367i
\(584\) −0.544699 0.201437i −0.0225398 0.00833551i
\(585\) −20.2885 2.42685i −0.838826 0.100338i
\(586\) −37.7856 21.9021i −1.56091 0.904767i
\(587\) 36.7619 + 8.71273i 1.51733 + 0.359613i 0.903070 0.429494i \(-0.141308\pi\)
0.614256 + 0.789106i \(0.289456\pi\)
\(588\) −0.921866 11.1507i −0.0380171 0.459849i
\(589\) 2.07329 + 35.5970i 0.0854285 + 1.46675i
\(590\) 4.81352 40.5781i 0.198170 1.67058i
\(591\) 19.1773 6.32599i 0.788849 0.260216i
\(592\) 35.3808 + 8.64239i 1.45414 + 0.355200i
\(593\) 17.9786 + 10.3800i 0.738293 + 0.426254i 0.821449 0.570283i \(-0.193166\pi\)
−0.0831551 + 0.996537i \(0.526500\pi\)
\(594\) 0.990324 + 7.04360i 0.0406335 + 0.289003i
\(595\) 21.8935 12.6402i 0.897547 0.518199i
\(596\) −41.3379 2.55008i −1.69327 0.104455i
\(597\) −14.1935 + 11.1917i −0.580900 + 0.458045i
\(598\) 8.20405 10.9805i 0.335488 0.449028i
\(599\) 29.5693 19.4480i 1.20817 0.794624i 0.224475 0.974480i \(-0.427933\pi\)
0.983693 + 0.179855i \(0.0575630\pi\)
\(600\) −23.0622 50.3078i −0.941509 2.05381i
\(601\) 12.7594 13.5242i 0.520467 0.551663i −0.412811 0.910817i \(-0.635453\pi\)
0.933279 + 0.359153i \(0.116935\pi\)
\(602\) 0.119522 0.000205152i 0.00487134 8.36136e-6i
\(603\) −7.79668 + 43.5306i −0.317505 + 1.77270i
\(604\) 18.5309 10.6142i 0.754014 0.431885i
\(605\) 22.3231 33.9407i 0.907565 1.37988i
\(606\) −11.4844 + 7.03517i −0.466521 + 0.285784i
\(607\) 2.66915 22.8360i 0.108337 0.926885i −0.824321 0.566123i \(-0.808443\pi\)
0.932658 0.360762i \(-0.117483\pi\)
\(608\) −31.2335 + 28.9647i −1.26669 + 1.17467i
\(609\) −22.3064 + 8.82699i −0.903903 + 0.357688i
\(610\) 4.94740 + 2.14418i 0.200314 + 0.0868153i
\(611\) −2.08090 11.8014i −0.0841843 0.477433i
\(612\) −9.04533 + 7.49594i −0.365636 + 0.303006i
\(613\) 1.70092 9.64638i 0.0686994 0.389613i −0.930998 0.365024i \(-0.881061\pi\)
0.999698 0.0245899i \(-0.00782798\pi\)
\(614\) −1.30108 + 1.97082i −0.0525073 + 0.0795358i
\(615\) −5.52960 0.491289i −0.222975 0.0198107i
\(616\) −3.97015 + 7.80474i −0.159962 + 0.314462i
\(617\) −15.0552 + 14.2039i −0.606100 + 0.571826i −0.926894 0.375323i \(-0.877532\pi\)
0.320794 + 0.947149i \(0.396050\pi\)
\(618\) −3.50460 3.13813i −0.140976 0.126234i
\(619\) 9.84716 + 4.24765i 0.395791 + 0.170727i 0.584667 0.811273i \(-0.301225\pi\)
−0.188876 + 0.982001i \(0.560484\pi\)
\(620\) 29.2028 + 24.6754i 1.17281 + 0.990989i
\(621\) 27.6960 + 11.1328i 1.11140 + 0.446745i
\(622\) −17.5826 6.43373i −0.704997 0.257969i
\(623\) 15.5678 + 20.9112i 0.623712 + 0.837790i
\(624\) 9.89814 + 6.21807i 0.396243 + 0.248922i
\(625\) −13.2305 + 44.1929i −0.529219 + 1.76771i
\(626\) −23.2810 + 5.47552i −0.930497 + 0.218846i
\(627\) −12.1898 3.28387i −0.486815 0.131145i
\(628\) 14.8437 1.68335i 0.592329 0.0671730i
\(629\) −11.4593 + 13.6567i −0.456914 + 0.544529i
\(630\) 24.8010 48.8442i 0.988094 1.94600i
\(631\) 27.0253 + 32.2075i 1.07586 + 1.28216i 0.957263 + 0.289220i \(0.0933958\pi\)
0.118599 + 0.992942i \(0.462160\pi\)
\(632\) 14.4077 21.6621i 0.573109 0.861672i
\(633\) −31.4725 17.0246i −1.25092 0.676669i
\(634\) 7.24938 + 11.0635i 0.287910 + 0.439386i
\(635\) −4.59370 + 6.17041i −0.182295 + 0.244865i
\(636\) 0.299348 + 12.3124i 0.0118699 + 0.488220i
\(637\) 0.316860 5.44028i 0.0125545 0.215552i
\(638\) 5.83588 + 1.03935i 0.231045 + 0.0411484i
\(639\) 9.10790 6.74249i 0.360303 0.266729i
\(640\) −0.548744 + 45.6691i −0.0216910 + 1.80523i
\(641\) −20.0381 + 5.99902i −0.791458 + 0.236947i −0.656919 0.753961i \(-0.728141\pi\)
−0.134539 + 0.990908i \(0.542955\pi\)
\(642\) 18.3336 4.85229i 0.723568 0.191505i
\(643\) 14.3563 28.5856i 0.566155 1.12731i −0.410373 0.911918i \(-0.634601\pi\)
0.976528 0.215390i \(-0.0691023\pi\)
\(644\) 20.0875 + 30.7711i 0.791557 + 1.21255i
\(645\) 0.157121 + 0.0972060i 0.00618661 + 0.00382748i
\(646\) −5.94570 19.9848i −0.233930 0.786291i
\(647\) −29.0957 −1.14387 −0.571935 0.820299i \(-0.693807\pi\)
−0.571935 + 0.820299i \(0.693807\pi\)
\(648\) −7.55748 + 24.3081i −0.296886 + 0.954913i
\(649\) −6.92805 −0.271950
\(650\) −7.68626 25.8352i −0.301480 1.01334i
\(651\) −0.798321 + 26.2206i −0.0312887 + 1.02767i
\(652\) −22.8056 34.9349i −0.893137 1.36816i
\(653\) −5.37024 + 10.6930i −0.210154 + 0.418451i −0.973871 0.227100i \(-0.927076\pi\)
0.763718 + 0.645550i \(0.223372\pi\)
\(654\) −7.29246 + 26.8860i −0.285158 + 1.05132i
\(655\) −69.7229 + 20.8737i −2.72430 + 0.815602i
\(656\) 2.73935 + 1.60674i 0.106953 + 0.0627326i
\(657\) 0.143671 0.598993i 0.00560513 0.0233689i
\(658\) 31.6291 + 5.63307i 1.23303 + 0.219600i
\(659\) 2.06748 35.4973i 0.0805377 1.38278i −0.679870 0.733333i \(-0.737964\pi\)
0.760408 0.649446i \(-0.224999\pi\)
\(660\) −11.5545 + 7.05089i −0.449758 + 0.274455i
\(661\) 10.0598 13.5127i 0.391282 0.525584i −0.562212 0.826993i \(-0.690050\pi\)
0.953495 + 0.301409i \(0.0974571\pi\)
\(662\) 2.60985 + 3.98295i 0.101435 + 0.154802i
\(663\) −4.87388 + 2.99719i −0.189286 + 0.116401i
\(664\) 9.46613 + 6.29604i 0.367357 + 0.244334i
\(665\) 62.4963 + 74.4802i 2.42350 + 2.88822i
\(666\) −4.65397 + 38.3490i −0.180338 + 1.48599i
\(667\) 15.9901 19.0562i 0.619138 0.737860i
\(668\) 19.4151 2.20177i 0.751195 0.0851891i
\(669\) 8.73824 + 32.7883i 0.337840 + 1.26767i
\(670\) −81.9224 + 19.2675i −3.16494 + 0.744369i
\(671\) 0.262194 0.875790i 0.0101219 0.0338095i
\(672\) −24.7738 + 19.1919i −0.955672 + 0.740344i
\(673\) −12.7412 17.1144i −0.491138 0.659713i 0.485592 0.874186i \(-0.338604\pi\)
−0.976730 + 0.214473i \(0.931197\pi\)
\(674\) −5.52966 2.02339i −0.212994 0.0779379i
\(675\) 50.0840 30.6133i 1.92773 1.17831i
\(676\) −15.5110 13.1063i −0.596576 0.504087i
\(677\) −14.3199 6.17700i −0.550358 0.237401i 0.102696 0.994713i \(-0.467253\pi\)
−0.653054 + 0.757312i \(0.726512\pi\)
\(678\) 3.94536 18.8160i 0.151521 0.722626i
\(679\) −39.7545 + 37.5064i −1.52564 + 1.43936i
\(680\) −19.9261 10.1361i −0.764131 0.388701i
\(681\) −15.2279 + 21.6854i −0.583533 + 0.830985i
\(682\) 3.57122 5.40954i 0.136749 0.207142i
\(683\) −3.02640 + 17.1636i −0.115802 + 0.656745i 0.870548 + 0.492083i \(0.163764\pi\)
−0.986350 + 0.164662i \(0.947347\pi\)
\(684\) −34.4318 29.2532i −1.31653 1.11852i
\(685\) 3.54216 + 20.0886i 0.135339 + 0.767544i
\(686\) −15.6467 6.78123i −0.597396 0.258908i
\(687\) 31.4837 + 24.9632i 1.20118 + 0.952404i
\(688\) −0.0574729 0.0887038i −0.00219113 0.00338180i
\(689\) −0.696389 + 5.95799i −0.0265303 + 0.226981i
\(690\) 1.47814 + 56.7854i 0.0562717 + 2.16178i
\(691\) 6.24641 9.49720i 0.237624 0.361290i −0.696913 0.717156i \(-0.745444\pi\)
0.934537 + 0.355866i \(0.115814\pi\)
\(692\) −2.34014 + 1.34039i −0.0889589 + 0.0509541i
\(693\) −8.71895 3.20008i −0.331205 0.121561i
\(694\) −22.5735 0.0387462i −0.856880 0.00147078i
\(695\) 52.9561 56.1302i 2.00874 2.12914i
\(696\) 17.2983 + 12.2807i 0.655691 + 0.465498i
\(697\) −1.29877 + 0.854212i −0.0491943 + 0.0323556i
\(698\) 4.94979 6.62495i 0.187352 0.250758i
\(699\) 2.47470 + 17.0549i 0.0936016 + 0.645076i
\(700\) 72.1258 + 4.44934i 2.72610 + 0.168169i
\(701\) 35.4139 20.4462i 1.33756 0.772243i 0.351118 0.936331i \(-0.385801\pi\)
0.986446 + 0.164088i \(0.0524681\pi\)
\(702\) −5.30438 + 11.2063i −0.200201 + 0.422954i
\(703\) −59.3779 34.2818i −2.23948 1.29296i
\(704\) 7.70002 0.819714i 0.290205 0.0308941i
\(705\) 37.0544 + 33.0653i 1.39555 + 1.24531i
\(706\) 0.0455533 0.384016i 0.00171442 0.0144526i
\(707\) −1.02252 17.5560i −0.0384558 0.660261i
\(708\) −22.4210 10.5859i −0.842632 0.397841i
\(709\) −41.3753 9.80613i −1.55388 0.368277i −0.638101 0.769953i \(-0.720280\pi\)
−0.915782 + 0.401676i \(0.868428\pi\)
\(710\) 18.6574 + 10.8146i 0.700198 + 0.405864i
\(711\) 24.6255 + 12.4506i 0.923528 + 0.466936i
\(712\) 7.99640 21.6228i 0.299678 0.810350i
\(713\) −12.2084 24.3089i −0.457208 0.910377i
\(714\) −3.05587 15.0320i −0.114363 0.562560i
\(715\) −6.05351 + 2.61123i −0.226388 + 0.0976544i
\(716\) −1.25442 + 4.13829i −0.0468798 + 0.154655i
\(717\) −8.44221 + 7.49256i −0.315280 + 0.279815i
\(718\) −14.9457 + 1.72090i −0.557768 + 0.0642234i
\(719\) 18.6042 + 6.77139i 0.693821 + 0.252530i 0.664770 0.747048i \(-0.268529\pi\)
0.0290505 + 0.999578i \(0.490752\pi\)
\(720\) −48.1669 + 5.16356i −1.79508 + 0.192434i
\(721\) 5.77216 2.10089i 0.214966 0.0782414i
\(722\) 47.6892 23.8480i 1.77481 0.887530i
\(723\) −19.7327 + 13.7774i −0.733868 + 0.512387i
\(724\) −1.52310 0.183327i −0.0566055 0.00681329i
\(725\) −11.2814 47.5998i −0.418980 1.76781i
\(726\) −15.2291 19.3822i −0.565206 0.719340i
\(727\) −2.43335 20.8187i −0.0902481 0.772122i −0.960263 0.279096i \(-0.909965\pi\)
0.870015 0.493025i \(-0.164109\pi\)
\(728\) −13.2574 + 7.56344i −0.491354 + 0.280320i
\(729\) −26.5510 4.90341i −0.983371 0.181608i
\(730\) 1.15476 0.201573i 0.0427397 0.00746054i
\(731\) 0.0513865 0.00600622i 0.00190060 0.000222148i
\(732\) 2.18671 2.43366i 0.0808231 0.0899506i
\(733\) 12.4313 2.94628i 0.459161 0.108823i 0.00547557 0.999985i \(-0.498257\pi\)
0.453686 + 0.891162i \(0.350109\pi\)
\(734\) −18.9516 5.70919i −0.699515 0.210730i
\(735\) 12.9287 + 18.5172i 0.476883 + 0.683018i
\(736\) 13.1267 29.7271i 0.483858 1.09576i
\(737\) 4.88011 + 13.4080i 0.179761 + 0.493890i
\(738\) −1.34780 + 3.08703i −0.0496133 + 0.113635i
\(739\) −14.9032 + 40.9463i −0.548225 + 1.50624i 0.287880 + 0.957666i \(0.407049\pi\)
−0.836105 + 0.548569i \(0.815173\pi\)
\(740\) −70.4978 + 20.8422i −2.59155 + 0.766176i
\(741\) −14.6068 16.4582i −0.536596 0.604607i
\(742\) −14.3588 7.24213i −0.527127 0.265867i
\(743\) −11.8045 27.3660i −0.433067 1.00396i −0.985387 0.170329i \(-0.945517\pi\)
0.552321 0.833632i \(-0.313742\pi\)
\(744\) 19.8230 12.0499i 0.726748 0.441772i
\(745\) 74.7053 37.5184i 2.73699 1.37457i
\(746\) 28.9756 + 24.3983i 1.06087 + 0.893285i
\(747\) −5.44081 + 10.7611i −0.199069 + 0.393728i
\(748\) −1.30859 + 3.55728i −0.0478469 + 0.130067i
\(749\) −5.71082 + 24.0958i −0.208669 + 0.880443i
\(750\) 50.8936 + 35.8690i 1.85837 + 1.30975i
\(751\) 9.74636 0.567661i 0.355650 0.0207142i 0.120610 0.992700i \(-0.461515\pi\)
0.235040 + 0.971986i \(0.424478\pi\)
\(752\) −11.0734 26.1635i −0.403806 0.954085i
\(753\) −4.73984 + 5.31168i −0.172730 + 0.193569i
\(754\) 7.50336 + 7.10344i 0.273256 + 0.258692i
\(755\) −21.5525 + 37.3301i −0.784378 + 1.35858i
\(756\) −23.3271 23.6786i −0.848400 0.861183i
\(757\) −4.76258 8.24903i −0.173099 0.299816i 0.766403 0.642360i \(-0.222045\pi\)
−0.939502 + 0.342544i \(0.888711\pi\)
\(758\) −2.04244 + 8.55231i −0.0741849 + 0.310634i
\(759\) 9.53113 1.38298i 0.345958 0.0501991i
\(760\) 25.0831 82.2395i 0.909858 2.98314i
\(761\) −5.27979 8.02752i −0.191392 0.290997i 0.727025 0.686611i \(-0.240902\pi\)
−0.918417 + 0.395613i \(0.870532\pi\)
\(762\) 2.66553 + 3.83171i 0.0965620 + 0.138808i
\(763\) −26.4581 24.9619i −0.957848 0.903683i
\(764\) −4.15275 24.0336i −0.150241 0.869505i
\(765\) 8.17006 22.2601i 0.295389 0.804817i
\(766\) 1.71003 0.619078i 0.0617859 0.0223682i
\(767\) −10.0894 6.63593i −0.364309 0.239610i
\(768\) 26.1718 + 9.11260i 0.944392 + 0.328823i
\(769\) −34.8737 4.07615i −1.25758 0.146990i −0.538922 0.842355i \(-0.681168\pi\)
−0.718656 + 0.695366i \(0.755242\pi\)
\(770\) −0.997397 17.6464i −0.0359437 0.635932i
\(771\) 22.0263 27.7798i 0.793259 1.00046i
\(772\) −17.1142 4.11824i −0.615954 0.148219i
\(773\) −23.2496 + 4.09954i −0.836231 + 0.147450i −0.575336 0.817917i \(-0.695129\pi\)
−0.260895 + 0.965367i \(0.584018\pi\)
\(774\) 0.0861959 0.0716812i 0.00309825 0.00257653i
\(775\) −52.6803 9.28896i −1.89233 0.333669i
\(776\) 46.9714 + 11.3882i 1.68618 + 0.408813i
\(777\) −41.2803 28.9878i −1.48092 1.03993i
\(778\) 3.05240 2.86990i 0.109434 0.102891i
\(779\) −4.10270 4.34861i −0.146995 0.155805i
\(780\) −23.5806 0.798975i −0.844321 0.0286079i
\(781\) 1.44817 3.35722i 0.0518194 0.120131i
\(782\) 10.2036 + 12.2026i 0.364878 + 0.436364i
\(783\) −10.7591 + 19.7622i −0.384498 + 0.706244i
\(784\) −2.15607 12.7385i −0.0770026 0.454947i
\(785\) −24.1868 + 18.0064i −0.863262 + 0.642675i
\(786\) −1.41969 + 44.1384i −0.0506385 + 1.57437i
\(787\) −25.5060 7.63601i −0.909192 0.272194i −0.202141 0.979356i \(-0.564790\pi\)
−0.707051 + 0.707162i \(0.749975\pi\)
\(788\) 21.4423 9.16212i 0.763849 0.326387i
\(789\) 7.09468 1.89077i 0.252577 0.0673130i
\(790\) −3.14328 + 52.4179i −0.111833 + 1.86494i
\(791\) 19.2303 + 16.1361i 0.683751 + 0.573735i
\(792\) 1.83135 + 8.00647i 0.0650741 + 0.284498i
\(793\) 1.22070 1.02429i 0.0433483 0.0363736i
\(794\) 5.14780 + 6.93953i 0.182689 + 0.246275i
\(795\) −13.0221 21.1759i −0.461846 0.751031i
\(796\) −15.2303 + 14.2706i −0.539824 + 0.505806i
\(797\) −32.3653 24.0951i −1.14644 0.853492i −0.155504 0.987835i \(-0.549700\pi\)
−0.990935 + 0.134343i \(0.957108\pi\)
\(798\) 54.8931 21.6131i 1.94320 0.765096i
\(799\) 13.8829 + 0.808589i 0.491143 + 0.0286058i
\(800\) −31.4756 55.6142i −1.11283 1.96626i
\(801\) 23.7781 + 5.70327i 0.840158 + 0.201515i
\(802\) 41.3065 23.7539i 1.45858 0.838778i
\(803\) −0.0570006 0.190395i −0.00201151 0.00671890i
\(804\) −4.69373 + 50.8485i −0.165535 + 1.79329i
\(805\) −66.2832 33.2887i −2.33618 1.17327i
\(806\) 10.3823 4.45736i 0.365700 0.157004i
\(807\) 44.5444 + 1.35621i 1.56804 + 0.0477410i
\(808\) −12.5218 + 9.22229i −0.440515 + 0.324439i
\(809\) 13.9541i 0.490601i −0.969447 0.245301i \(-0.921113\pi\)
0.969447 0.245301i \(-0.0788867\pi\)
\(810\) −11.4937 50.0794i −0.403847 1.75961i
\(811\) 35.1669i 1.23488i −0.786619 0.617439i \(-0.788170\pi\)
0.786619 0.617439i \(-0.211830\pi\)
\(812\) −24.7967 + 12.3470i −0.870194 + 0.433294i
\(813\) −19.3369 + 31.2556i −0.678176 + 1.09618i
\(814\) 4.91707 + 11.4531i 0.172343 + 0.401430i
\(815\) 75.2524 + 37.7932i 2.63598 + 1.32384i
\(816\) −9.67038 + 9.51280i −0.338531 + 0.333015i
\(817\) 0.0570665 + 0.190616i 0.00199651 + 0.00666879i
\(818\) −1.99745 3.47345i −0.0698393 0.121446i
\(819\) −9.63240 13.0116i −0.336583 0.454664i
\(820\) −6.41015 0.0220053i −0.223852 0.000768460i
\(821\) 16.8091 + 0.979021i 0.586643 + 0.0341681i 0.348900 0.937160i \(-0.386555\pi\)
0.237743 + 0.971328i \(0.423592\pi\)
\(822\) 12.2410 + 1.83138i 0.426954 + 0.0638766i
\(823\) −30.9530 23.0437i −1.07895 0.803252i −0.0975552 0.995230i \(-0.531102\pi\)
−0.981399 + 0.191978i \(0.938510\pi\)
\(824\) −4.34039 3.26617i −0.151205 0.113782i
\(825\) 9.01095 16.6581i 0.313721 0.579959i
\(826\) 26.0021 19.2886i 0.904729 0.671136i
\(827\) 39.1786 32.8748i 1.36237 1.14317i 0.387134 0.922024i \(-0.373465\pi\)
0.975241 0.221144i \(-0.0709792\pi\)
\(828\) 32.9584 + 10.0876i 1.14538 + 0.350568i
\(829\) 20.6037 + 17.2885i 0.715595 + 0.600455i 0.926163 0.377124i \(-0.123087\pi\)
−0.210568 + 0.977579i \(0.567531\pi\)
\(830\) −22.9061 1.37358i −0.795082 0.0476777i
\(831\) 1.56650 5.81490i 0.0543413 0.201716i
\(832\) 11.9988 + 6.18158i 0.415984 + 0.214308i
\(833\) 6.05832 + 1.81374i 0.209908 + 0.0628425i
\(834\) −22.0961 41.2822i −0.765127 1.42949i
\(835\) −31.6356 + 23.5518i −1.09479 + 0.815044i
\(836\) −14.3472 2.58061i −0.496207 0.0892522i
\(837\) 15.1829 + 19.3624i 0.524799 + 0.669262i
\(838\) −3.57759 + 2.99151i −0.123586 + 0.103340i
\(839\) 1.07224 2.48573i 0.0370179 0.0858170i −0.898704 0.438556i \(-0.855490\pi\)
0.935722 + 0.352739i \(0.114749\pi\)
\(840\) 23.7354 58.6323i 0.818948 2.02301i
\(841\) −7.03263 7.45415i −0.242504 0.257040i
\(842\) −17.9802 19.1236i −0.619640 0.659043i
\(843\) 3.07800 34.6438i 0.106012 1.19320i
\(844\) −37.8821 16.4952i −1.30396 0.567788i
\(845\) 40.3656 + 7.11754i 1.38862 + 0.244851i
\(846\) 26.1628 14.9516i 0.899496 0.514046i
\(847\) 31.6971 5.58905i 1.08912 0.192042i
\(848\) 1.55398 + 14.1362i 0.0533640 + 0.485440i
\(849\) 0.862000 + 2.17834i 0.0295838 + 0.0747604i
\(850\) 31.2299 1.76516i 1.07118 0.0605444i
\(851\) 51.9523 + 6.07236i 1.78090 + 0.208158i
\(852\) 9.81638 8.65210i 0.336304 0.296416i
\(853\) −14.3077 9.41034i −0.489887 0.322204i 0.280419 0.959878i \(-0.409527\pi\)
−0.770307 + 0.637674i \(0.779897\pi\)
\(854\) 1.45425 + 4.01696i 0.0497635 + 0.137458i
\(855\) 89.7667 + 16.0780i 3.06996 + 0.549855i
\(856\) 20.6163 7.38373i 0.704651 0.252371i
\(857\) −1.25551 1.18451i −0.0428874 0.0404622i 0.664500 0.747289i \(-0.268645\pi\)
−0.707387 + 0.706826i \(0.750126\pi\)
\(858\) 0.336432 + 3.98609i 0.0114856 + 0.136083i
\(859\) −28.4284 43.2232i −0.969963 1.47476i −0.877808 0.479013i \(-0.840995\pi\)
−0.0921558 0.995745i \(-0.529376\pi\)
\(860\) 0.190319 + 0.0964013i 0.00648982 + 0.00328726i
\(861\) −2.72335 3.45380i −0.0928115 0.117705i
\(862\) 26.2131 + 6.26017i 0.892823 + 0.213222i
\(863\) 16.4895 + 28.5607i 0.561310 + 0.972217i 0.997382 + 0.0723059i \(0.0230358\pi\)
−0.436072 + 0.899912i \(0.643631\pi\)
\(864\) −6.30695 + 28.7093i −0.214567 + 0.976709i
\(865\) 2.72172 4.71416i 0.0925413 0.160286i
\(866\) −21.0966 + 22.2843i −0.716892 + 0.757252i
\(867\) 7.14400 + 21.6571i 0.242623 + 0.735514i
\(868\) 1.65745 + 30.2456i 0.0562574 + 1.02660i
\(869\) 8.88808 0.517672i 0.301508 0.0175608i
\(870\) −42.6456 3.86273i −1.44582 0.130959i
\(871\) −5.73566 + 24.2006i −0.194345 + 0.820008i
\(872\) −5.74878 + 31.6491i −0.194678 + 1.07177i
\(873\) −6.08866 + 50.9013i −0.206070 + 1.72275i
\(874\) −39.4031 + 46.7954i −1.33283 + 1.58288i
\(875\) −72.6529 + 36.4877i −2.45612 + 1.23351i
\(876\) 0.106450 0.703264i 0.00359661 0.0237611i
\(877\) −12.2348 28.3634i −0.413139 0.957764i −0.990019 0.140935i \(-0.954989\pi\)
0.576880 0.816829i \(-0.304270\pi\)
\(878\) −14.7402 + 29.2251i −0.497459 + 0.986298i
\(879\) 16.8934 50.7522i 0.569801 1.71183i
\(880\) −12.6009 + 9.24726i −0.424777 + 0.311725i
\(881\) 19.4074 53.3214i 0.653852 1.79644i 0.0508468 0.998706i \(-0.483808\pi\)
0.603005 0.797737i \(-0.293970\pi\)
\(882\) 13.1449 3.87221i 0.442613 0.130384i
\(883\) −4.07229 11.1885i −0.137044 0.376524i 0.852119 0.523348i \(-0.175317\pi\)
−0.989163 + 0.146824i \(0.953095\pi\)
\(884\) −5.31302 + 3.92712i −0.178696 + 0.132083i
\(885\) 49.8617 4.29461i 1.67608 0.144362i
\(886\) 2.32757 7.72633i 0.0781962 0.259571i
\(887\) −24.5109 + 5.80918i −0.822994 + 0.195053i −0.620476 0.784225i \(-0.713061\pi\)
−0.202518 + 0.979279i \(0.564912\pi\)
\(888\) −1.58704 + 44.5782i −0.0532576 + 1.49595i
\(889\) −6.05359 + 0.707564i −0.203031 + 0.0237309i
\(890\) 8.00179 + 45.8404i 0.268221 + 1.53657i
\(891\) −8.20205 + 2.93531i −0.274779 + 0.0983366i
\(892\) 13.2746 + 36.8649i 0.444466 + 1.23433i
\(893\) 6.20904 + 53.1217i 0.207778 + 1.77765i
\(894\) −7.19778 50.2114i −0.240730 1.67932i
\(895\) −2.01288 8.49299i −0.0672830 0.283889i
\(896\) −26.6172 + 24.5143i −0.889219 + 0.818967i
\(897\) 15.2050 + 7.11518i 0.507681 + 0.237569i
\(898\) 3.48514 + 6.96928i 0.116301 + 0.232568i
\(899\) 19.2689 7.01330i 0.642653 0.233907i
\(900\) 54.6148 40.1413i 1.82049 1.33804i
\(901\) −6.54135 2.38086i −0.217924 0.0793178i
\(902\) 0.124318 + 1.07968i 0.00413935 + 0.0359494i
\(903\) 0.0294081 + 0.143399i 0.000978639 + 0.00477203i
\(904\) 2.69069 22.0357i 0.0894912 0.732897i
\(905\) 2.84325 1.22646i 0.0945129 0.0407689i
\(906\) 17.3278 + 19.5917i 0.575678 + 0.650889i
\(907\) −0.364041 0.724865i −0.0120878 0.0240688i 0.887508 0.460793i \(-0.152435\pi\)
−0.899595 + 0.436724i \(0.856139\pi\)
\(908\) −15.3895 + 26.4453i −0.510718 + 0.877618i
\(909\) −11.2870 12.0283i −0.374366 0.398954i
\(910\) 15.4498 26.6541i 0.512156 0.883575i
\(911\) −49.0765 11.6313i −1.62598 0.385364i −0.686270 0.727346i \(-0.740753\pi\)
−0.939706 + 0.341983i \(0.888901\pi\)
\(912\) −42.4881 30.2736i −1.40692 1.00246i
\(913\) 0.226218 + 3.88400i 0.00748671 + 0.128542i
\(914\) −7.08843 0.840855i −0.234465 0.0278130i
\(915\) −1.34414 + 6.46565i −0.0444359 + 0.213748i
\(916\) 38.6748 + 25.6275i 1.27785 + 0.846756i
\(917\) −49.9381 28.8318i −1.64910 0.952110i
\(918\) −11.2345 8.98873i −0.370793 0.296672i
\(919\) −29.7084 + 17.1522i −0.979990 + 0.565797i −0.902267 0.431178i \(-0.858098\pi\)
−0.0777229 + 0.996975i \(0.524765\pi\)
\(920\) 7.27924 + 65.1872i 0.239989 + 2.14916i
\(921\) −2.68651 1.07148i −0.0885236 0.0353064i
\(922\) 43.0168 + 32.1397i 1.41668 + 1.05846i
\(923\) 5.32465 3.50208i 0.175263 0.115272i
\(924\) −10.3456 2.82519i −0.340347 0.0929419i
\(925\) 70.5860 74.8168i 2.32085 2.45996i
\(926\) 0.0228099 13.2891i 0.000749581 0.436707i
\(927\) 2.89421 4.98184i 0.0950582 0.163625i
\(928\) 21.1084 + 12.4297i 0.692918 + 0.408025i
\(929\) −15.3762 + 23.3784i −0.504477 + 0.767020i −0.994505 0.104686i \(-0.966616\pi\)
0.490028 + 0.871707i \(0.336987\pi\)
\(930\) −22.3491 + 41.1466i −0.732855 + 1.34925i
\(931\) −2.82358 + 24.1572i −0.0925390 + 0.791722i
\(932\) 4.52265 + 19.3788i 0.148144 + 0.634773i
\(933\) 3.35395 22.6839i 0.109803 0.742638i
\(934\) 13.0585 30.1307i 0.427287 0.985906i
\(935\) −1.32852 7.53440i −0.0434472 0.246401i
\(936\) −5.00186 + 13.4141i −0.163491 + 0.438453i
\(937\) −4.12560 + 23.3974i −0.134778 + 0.764361i 0.840237 + 0.542220i \(0.182416\pi\)
−0.975014 + 0.222142i \(0.928695\pi\)
\(938\) −55.6454 36.7356i −1.81689 1.19946i
\(939\) −12.3432 26.5636i −0.402807 0.866871i
\(940\) 45.8800 + 34.4018i 1.49644 + 1.12206i
\(941\) 10.1458 9.57207i 0.330744 0.312040i −0.502899 0.864345i \(-0.667733\pi\)
0.833642 + 0.552305i \(0.186252\pi\)
\(942\) 5.70175 + 17.3852i 0.185773 + 0.566440i
\(943\) 4.18789 + 1.80648i 0.136377 + 0.0588271i
\(944\) −26.8356 9.97654i −0.873425 0.324709i
\(945\) 64.7346 + 17.6265i 2.10582 + 0.573390i
\(946\) 0.0124295 0.0339683i 0.000404118 0.00110440i
\(947\) 22.8468 + 30.6886i 0.742423 + 0.997247i 0.999524 + 0.0308623i \(0.00982533\pi\)
−0.257101 + 0.966385i \(0.582767\pi\)
\(948\) 29.5551 + 11.9054i 0.959906 + 0.386670i
\(949\) 0.0993563 0.331873i 0.00322524 0.0107731i
\(950\) 27.5421 + 117.105i 0.893585 + 3.79938i
\(951\) −11.4704 + 11.4395i −0.371952 + 0.370950i
\(952\) −4.99257 16.9944i −0.161810 0.550790i
\(953\) 38.1649 45.4831i 1.23628 1.47334i 0.408049 0.912960i \(-0.366209\pi\)
0.828233 0.560383i \(-0.189346\pi\)
\(954\) −14.6927 + 3.41382i −0.475693 + 0.110527i
\(955\) 31.6442 + 37.7120i 1.02398 + 1.22033i
\(956\) −8.97681 + 9.44966i −0.290331 + 0.305624i
\(957\) 0.201370 + 7.25714i 0.00650938 + 0.234590i
\(958\) 16.9506 11.1070i 0.547649 0.358849i
\(959\) −9.65104 + 12.9636i −0.311648 + 0.418616i
\(960\) −54.9095 + 10.6727i −1.77220 + 0.344459i
\(961\) −0.498705 + 8.56243i −0.0160872 + 0.276207i
\(962\) −3.80933 + 21.3890i −0.122818 + 0.689610i
\(963\) 10.3683 + 20.7845i 0.334113 + 0.669771i
\(964\) −21.3493 + 17.7896i −0.687614 + 0.572966i
\(965\) 34.0377 10.1902i 1.09571 0.328034i
\(966\) −31.9215 + 31.7264i −1.02706 + 1.02078i
\(967\) 5.29467 10.5425i 0.170265 0.339026i −0.792275 0.610164i \(-0.791104\pi\)
0.962540 + 0.271138i \(0.0874000\pi\)
\(968\) −19.4254 20.8033i −0.624357 0.668645i
\(969\) 22.4936 12.0893i 0.722599 0.388366i
\(970\) −93.5060 + 27.8191i −3.00230 + 0.893216i
\(971\) −55.5737 −1.78345 −0.891723 0.452581i \(-0.850503\pi\)
−0.891723 + 0.452581i \(0.850503\pi\)
\(972\) −31.0290 3.03306i −0.995257 0.0972856i
\(973\) 61.1401 1.96006
\(974\) 3.37275 1.00343i 0.108070 0.0321519i
\(975\) 29.0785 15.6284i 0.931256 0.500510i
\(976\) 2.27676 3.01478i 0.0728772 0.0965008i
\(977\) −7.54581 + 15.0249i −0.241412 + 0.480690i −0.981411 0.191917i \(-0.938529\pi\)
0.739999 + 0.672608i \(0.234826\pi\)
\(978\) 36.2410 36.0195i 1.15886 1.15178i
\(979\) 7.55808 2.26274i 0.241557 0.0723175i
\(980\) 16.6938 + 20.0342i 0.533264 + 0.639969i
\(981\) −34.0550 2.07562i −1.08729 0.0662695i
\(982\) 3.54821 19.9229i 0.113228 0.635765i
\(983\) −0.409906 + 7.03782i −0.0130740 + 0.224472i 0.985442 + 0.170012i \(0.0543807\pi\)
−0.998516 + 0.0544596i \(0.982656\pi\)
\(984\) −1.24739 + 3.68408i −0.0397655 + 0.117444i
\(985\) −28.1057 + 37.7525i −0.895522 + 1.20290i
\(986\) −10.0292 + 6.57169i −0.319396 + 0.209285i
\(987\) 1.09138 + 39.3321i 0.0347390 + 1.25195i
\(988\) −18.4222 17.5004i −0.586090 0.556762i
\(989\) −0.0975714 0.116281i −0.00310259 0.00369752i
\(990\) −11.3232 12.1085i −0.359876 0.384834i
\(991\) −21.3916 + 25.4935i −0.679527 + 0.809829i −0.990047 0.140738i \(-0.955052\pi\)
0.310520 + 0.950567i \(0.399497\pi\)
\(992\) 21.6229 15.8110i 0.686527 0.502001i
\(993\) −4.12944 + 4.11832i −0.131044 + 0.130691i
\(994\) 3.91174 + 16.6321i 0.124073 + 0.527538i
\(995\) 12.0824 40.3580i 0.383037 1.27943i
\(996\) −5.20255 + 12.9153i −0.164849 + 0.409237i
\(997\) 19.5656 + 26.2812i 0.619650 + 0.832335i 0.995541 0.0943293i \(-0.0300707\pi\)
−0.375891 + 0.926664i \(0.622663\pi\)
\(998\) −1.39946 + 3.82454i −0.0442991 + 0.121064i
\(999\) −47.1486 + 3.93289i −1.49171 + 0.124431i
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 324.2.p.a.263.31 yes 936
3.2 odd 2 972.2.p.a.467.22 936
4.3 odd 2 inner 324.2.p.a.263.26 yes 936
12.11 even 2 972.2.p.a.467.27 936
81.4 even 27 972.2.p.a.179.27 936
81.77 odd 54 inner 324.2.p.a.239.26 936
324.239 even 54 inner 324.2.p.a.239.31 yes 936
324.247 odd 54 972.2.p.a.179.22 936
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
324.2.p.a.239.26 936 81.77 odd 54 inner
324.2.p.a.239.31 yes 936 324.239 even 54 inner
324.2.p.a.263.26 yes 936 4.3 odd 2 inner
324.2.p.a.263.31 yes 936 1.1 even 1 trivial
972.2.p.a.179.22 936 324.247 odd 54
972.2.p.a.179.27 936 81.4 even 27
972.2.p.a.467.22 936 3.2 odd 2
972.2.p.a.467.27 936 12.11 even 2