Properties

Label 450.2.q.c.331.6
Level $450$
Weight $2$
Character 450.331
Analytic conductor $3.593$
Analytic rank $0$
Dimension $120$
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] = [450,2,Mod(31,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([10, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.q (of order \(15\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(15\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 331.6
Character \(\chi\) \(=\) 450.331
Dual form 450.2.q.c.121.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.978148 + 0.207912i) q^{2} +(-0.893432 + 1.48384i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-2.22939 + 0.172643i) q^{5} +(-1.18242 + 1.26566i) q^{6} +(-1.15080 + 1.99324i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.40356 - 2.65142i) q^{9} +O(q^{10})\) \(q+(0.978148 + 0.207912i) q^{2} +(-0.893432 + 1.48384i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-2.22939 + 0.172643i) q^{5} +(-1.18242 + 1.26566i) q^{6} +(-1.15080 + 1.99324i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.40356 - 2.65142i) q^{9} +(-2.21657 - 0.294647i) q^{10} +(-3.46535 - 0.736584i) q^{11} +(-1.41972 + 0.992164i) q^{12} +(-0.869609 + 0.184841i) q^{13} +(-1.54007 + 1.71042i) q^{14} +(1.73564 - 3.46231i) q^{15} +(0.669131 + 0.743145i) q^{16} +(0.116096 + 0.0843484i) q^{17} +(-0.821628 - 2.88530i) q^{18} +(-0.606848 - 0.440901i) q^{19} +(-2.10687 - 0.749059i) q^{20} +(-1.92949 - 3.48843i) q^{21} +(-3.23648 - 1.44097i) q^{22} +(-4.28489 + 4.75885i) q^{23} +(-1.59498 + 0.675305i) q^{24} +(4.94039 - 0.769777i) q^{25} -0.889036 q^{26} +(5.18826 + 0.286204i) q^{27} +(-1.86203 + 1.35285i) q^{28} +(-0.492657 - 4.68731i) q^{29} +(2.41756 - 3.02579i) q^{30} +(-0.751219 + 7.14737i) q^{31} +(0.500000 + 0.866025i) q^{32} +(4.18903 - 4.48394i) q^{33} +(0.0960217 + 0.106643i) q^{34} +(2.22147 - 4.64240i) q^{35} +(-0.203787 - 2.99307i) q^{36} +(-2.95432 + 9.09245i) q^{37} +(-0.501918 - 0.557437i) q^{38} +(0.502662 - 1.45550i) q^{39} +(-1.90509 - 1.17073i) q^{40} +(-7.03192 + 1.49468i) q^{41} +(-1.16204 - 3.81336i) q^{42} +(3.11939 - 5.40294i) q^{43} +(-2.86616 - 2.08239i) q^{44} +(3.58683 + 5.66874i) q^{45} +(-5.18068 + 3.76398i) q^{46} +(1.09544 + 10.4224i) q^{47} +(-1.70053 + 0.328933i) q^{48} +(0.851322 + 1.47453i) q^{49} +(4.99248 + 0.274209i) q^{50} +(-0.228883 + 0.0969078i) q^{51} +(-0.869609 - 0.184841i) q^{52} +(10.8364 - 7.87309i) q^{53} +(5.01538 + 1.35865i) q^{54} +(7.85280 + 1.04387i) q^{55} +(-2.10261 + 0.936144i) q^{56} +(1.19640 - 0.506550i) q^{57} +(0.492657 - 4.68731i) q^{58} +(-5.04821 + 1.07303i) q^{59} +(2.99383 - 2.45703i) q^{60} +(3.90745 + 0.830555i) q^{61} +(-2.22083 + 6.83500i) q^{62} +(6.90014 + 0.253615i) q^{63} +(0.309017 + 0.951057i) q^{64} +(1.90679 - 0.562215i) q^{65} +(5.02975 - 3.51501i) q^{66} +(-0.282276 + 2.68568i) q^{67} +(0.0717511 + 0.124277i) q^{68} +(-3.23312 - 10.6098i) q^{69} +(3.13813 - 4.07908i) q^{70} +(1.77752 - 1.29144i) q^{71} +(0.422961 - 2.97003i) q^{72} +(-1.47640 - 4.54388i) q^{73} +(-4.78019 + 8.27952i) q^{74} +(-3.27167 + 8.01849i) q^{75} +(-0.375053 - 0.649610i) q^{76} +(5.45612 - 6.05963i) q^{77} +(0.794293 - 1.31919i) q^{78} +(0.860832 + 8.19027i) q^{79} +(-1.62005 - 1.54124i) q^{80} +(-5.06004 + 7.44285i) q^{81} -7.18902 q^{82} +(-0.543418 + 0.241945i) q^{83} +(-0.343807 - 3.97163i) q^{84} +(-0.273385 - 0.168003i) q^{85} +(4.17455 - 4.63631i) q^{86} +(7.39538 + 3.45677i) q^{87} +(-2.37058 - 2.63279i) q^{88} +(-1.05446 - 3.24530i) q^{89} +(2.32986 + 6.29061i) q^{90} +(0.632312 - 1.94606i) q^{91} +(-5.85004 + 2.60461i) q^{92} +(-9.93439 - 7.50038i) q^{93} +(-1.09544 + 10.4224i) q^{94} +(1.42902 + 0.878173i) q^{95} +(-1.73176 - 0.0318147i) q^{96} +(1.68007 + 15.9848i) q^{97} +(0.526146 + 1.61931i) q^{98} +(2.91084 + 10.2219i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q - 15 q^{2} + 2 q^{3} + 15 q^{4} + 4 q^{5} + 4 q^{6} + 16 q^{7} + 30 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 120 q - 15 q^{2} + 2 q^{3} + 15 q^{4} + 4 q^{5} + 4 q^{6} + 16 q^{7} + 30 q^{8} - 10 q^{9} - 2 q^{10} + 2 q^{11} - 3 q^{12} - 6 q^{13} + 4 q^{14} + 19 q^{15} + 15 q^{16} + 12 q^{17} + 2 q^{18} + 18 q^{19} - q^{20} - 8 q^{21} - 2 q^{22} - 2 q^{24} - 2 q^{25} + 48 q^{26} + 2 q^{27} + 8 q^{28} - 5 q^{30} + 60 q^{32} - q^{33} + 6 q^{34} + 10 q^{35} + 2 q^{36} + 32 q^{37} - 6 q^{38} - 46 q^{39} + q^{40} - 4 q^{41} - 16 q^{42} + 40 q^{43} - 4 q^{44} - 38 q^{45} + 13 q^{47} + 6 q^{48} - 48 q^{49} - 3 q^{50} - 106 q^{51} - 6 q^{52} - 72 q^{53} + 15 q^{54} - 12 q^{55} + 4 q^{56} - 10 q^{57} + 18 q^{59} - 9 q^{60} + 34 q^{61} - 53 q^{63} - 30 q^{64} - 22 q^{65} + 13 q^{66} + 24 q^{68} - 5 q^{69} - 25 q^{70} - 22 q^{71} - 5 q^{72} + 32 q^{73} - 64 q^{74} - 147 q^{75} + 6 q^{76} + 10 q^{77} - 9 q^{78} + 14 q^{79} + 2 q^{80} + 22 q^{81} - 88 q^{82} - 52 q^{83} + 12 q^{84} - 3 q^{85} + 10 q^{86} + 25 q^{87} - 2 q^{88} - 94 q^{89} - 82 q^{90} + 104 q^{91} + 22 q^{93} - 13 q^{94} + 4 q^{95} - 2 q^{96} - 14 q^{97} + 54 q^{98} - 86 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.978148 + 0.207912i 0.691655 + 0.147016i
\(3\) −0.893432 + 1.48384i −0.515823 + 0.856695i
\(4\) 0.913545 + 0.406737i 0.456773 + 0.203368i
\(5\) −2.22939 + 0.172643i −0.997015 + 0.0772081i
\(6\) −1.18242 + 1.26566i −0.482719 + 0.516703i
\(7\) −1.15080 + 1.99324i −0.434961 + 0.753375i −0.997292 0.0735371i \(-0.976571\pi\)
0.562331 + 0.826912i \(0.309905\pi\)
\(8\) 0.809017 + 0.587785i 0.286031 + 0.207813i
\(9\) −1.40356 2.65142i −0.467853 0.883806i
\(10\) −2.21657 0.294647i −0.700941 0.0931755i
\(11\) −3.46535 0.736584i −1.04484 0.222088i −0.346648 0.937995i \(-0.612680\pi\)
−0.698196 + 0.715907i \(0.746013\pi\)
\(12\) −1.41972 + 0.992164i −0.409839 + 0.286413i
\(13\) −0.869609 + 0.184841i −0.241186 + 0.0512657i −0.326919 0.945053i \(-0.606010\pi\)
0.0857325 + 0.996318i \(0.472677\pi\)
\(14\) −1.54007 + 1.71042i −0.411601 + 0.457129i
\(15\) 1.73564 3.46231i 0.448139 0.893964i
\(16\) 0.669131 + 0.743145i 0.167283 + 0.185786i
\(17\) 0.116096 + 0.0843484i 0.0281573 + 0.0204575i 0.601775 0.798666i \(-0.294460\pi\)
−0.573618 + 0.819123i \(0.694460\pi\)
\(18\) −0.821628 2.88530i −0.193660 0.680071i
\(19\) −0.606848 0.440901i −0.139220 0.101150i 0.515995 0.856591i \(-0.327422\pi\)
−0.655216 + 0.755442i \(0.727422\pi\)
\(20\) −2.10687 0.749059i −0.471111 0.167495i
\(21\) −1.92949 3.48843i −0.421050 0.761237i
\(22\) −3.23648 1.44097i −0.690020 0.307217i
\(23\) −4.28489 + 4.75885i −0.893461 + 0.992289i −0.999998 0.00201952i \(-0.999357\pi\)
0.106537 + 0.994309i \(0.466024\pi\)
\(24\) −1.59498 + 0.675305i −0.325574 + 0.137846i
\(25\) 4.94039 0.769777i 0.988078 0.153955i
\(26\) −0.889036 −0.174354
\(27\) 5.18826 + 0.286204i 0.998482 + 0.0550799i
\(28\) −1.86203 + 1.35285i −0.351891 + 0.255664i
\(29\) −0.492657 4.68731i −0.0914840 0.870412i −0.939984 0.341217i \(-0.889161\pi\)
0.848500 0.529195i \(-0.177506\pi\)
\(30\) 2.41756 3.02579i 0.441385 0.552431i
\(31\) −0.751219 + 7.14737i −0.134923 + 1.28371i 0.692209 + 0.721697i \(0.256638\pi\)
−0.827132 + 0.562008i \(0.810029\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 4.18903 4.48394i 0.729216 0.780554i
\(34\) 0.0960217 + 0.106643i 0.0164676 + 0.0182891i
\(35\) 2.22147 4.64240i 0.375496 0.784709i
\(36\) −0.203787 2.99307i −0.0339644 0.498845i
\(37\) −2.95432 + 9.09245i −0.485687 + 1.49479i 0.345297 + 0.938493i \(0.387778\pi\)
−0.830984 + 0.556297i \(0.812222\pi\)
\(38\) −0.501918 0.557437i −0.0814219 0.0904282i
\(39\) 0.502662 1.45550i 0.0804903 0.233067i
\(40\) −1.90509 1.17073i −0.301222 0.185109i
\(41\) −7.03192 + 1.49468i −1.09820 + 0.233430i −0.721161 0.692767i \(-0.756391\pi\)
−0.377040 + 0.926197i \(0.623058\pi\)
\(42\) −1.16204 3.81336i −0.179307 0.588414i
\(43\) 3.11939 5.40294i 0.475702 0.823940i −0.523911 0.851773i \(-0.675527\pi\)
0.999613 + 0.0278332i \(0.00886072\pi\)
\(44\) −2.86616 2.08239i −0.432090 0.313932i
\(45\) 3.58683 + 5.66874i 0.534694 + 0.845046i
\(46\) −5.18068 + 3.76398i −0.763849 + 0.554969i
\(47\) 1.09544 + 10.4224i 0.159786 + 1.52026i 0.721199 + 0.692728i \(0.243591\pi\)
−0.561413 + 0.827536i \(0.689742\pi\)
\(48\) −1.70053 + 0.328933i −0.245450 + 0.0474774i
\(49\) 0.851322 + 1.47453i 0.121617 + 0.210648i
\(50\) 4.99248 + 0.274209i 0.706043 + 0.0387791i
\(51\) −0.228883 + 0.0969078i −0.0320500 + 0.0135698i
\(52\) −0.869609 0.184841i −0.120593 0.0256328i
\(53\) 10.8364 7.87309i 1.48849 1.08145i 0.513797 0.857912i \(-0.328238\pi\)
0.974695 0.223541i \(-0.0717615\pi\)
\(54\) 5.01538 + 1.35865i 0.682507 + 0.184889i
\(55\) 7.85280 + 1.04387i 1.05887 + 0.140755i
\(56\) −2.10261 + 0.936144i −0.280974 + 0.125098i
\(57\) 1.19640 0.506550i 0.158467 0.0670942i
\(58\) 0.492657 4.68731i 0.0646890 0.615474i
\(59\) −5.04821 + 1.07303i −0.657221 + 0.139697i −0.524438 0.851449i \(-0.675725\pi\)
−0.132783 + 0.991145i \(0.542391\pi\)
\(60\) 2.99383 2.45703i 0.386502 0.317201i
\(61\) 3.90745 + 0.830555i 0.500298 + 0.106342i 0.451147 0.892450i \(-0.351015\pi\)
0.0491511 + 0.998791i \(0.484348\pi\)
\(62\) −2.22083 + 6.83500i −0.282045 + 0.868045i
\(63\) 6.90014 + 0.253615i 0.869335 + 0.0319525i
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) 1.90679 0.562215i 0.236508 0.0697342i
\(66\) 5.02975 3.51501i 0.619120 0.432668i
\(67\) −0.282276 + 2.68568i −0.0344855 + 0.328108i 0.963655 + 0.267150i \(0.0860820\pi\)
−0.998140 + 0.0609573i \(0.980585\pi\)
\(68\) 0.0717511 + 0.124277i 0.00870110 + 0.0150707i
\(69\) −3.23312 10.6098i −0.389222 1.27727i
\(70\) 3.13813 4.07908i 0.375078 0.487544i
\(71\) 1.77752 1.29144i 0.210952 0.153266i −0.477292 0.878745i \(-0.658382\pi\)
0.688244 + 0.725479i \(0.258382\pi\)
\(72\) 0.422961 2.97003i 0.0498464 0.350022i
\(73\) −1.47640 4.54388i −0.172799 0.531821i 0.826727 0.562603i \(-0.190200\pi\)
−0.999526 + 0.0307823i \(0.990200\pi\)
\(74\) −4.78019 + 8.27952i −0.555685 + 0.962475i
\(75\) −3.27167 + 8.01849i −0.377780 + 0.925895i
\(76\) −0.375053 0.649610i −0.0430215 0.0745154i
\(77\) 5.45612 6.05963i 0.621782 0.690559i
\(78\) 0.794293 1.31919i 0.0899360 0.149369i
\(79\) 0.860832 + 8.19027i 0.0968512 + 0.921478i 0.929785 + 0.368104i \(0.119993\pi\)
−0.832933 + 0.553373i \(0.813340\pi\)
\(80\) −1.62005 1.54124i −0.181128 0.172316i
\(81\) −5.06004 + 7.44285i −0.562227 + 0.826983i
\(82\) −7.18902 −0.793894
\(83\) −0.543418 + 0.241945i −0.0596479 + 0.0265569i −0.436344 0.899780i \(-0.643727\pi\)
0.376696 + 0.926337i \(0.377060\pi\)
\(84\) −0.343807 3.97163i −0.0375125 0.433341i
\(85\) −0.273385 0.168003i −0.0296528 0.0182225i
\(86\) 4.17455 4.63631i 0.450154 0.499946i
\(87\) 7.39538 + 3.45677i 0.792868 + 0.370605i
\(88\) −2.37058 2.63279i −0.252704 0.280657i
\(89\) −1.05446 3.24530i −0.111773 0.344001i 0.879487 0.475922i \(-0.157886\pi\)
−0.991260 + 0.131921i \(0.957886\pi\)
\(90\) 2.32986 + 6.29061i 0.245588 + 0.663088i
\(91\) 0.632312 1.94606i 0.0662843 0.204002i
\(92\) −5.85004 + 2.60461i −0.609909 + 0.271549i
\(93\) −9.93439 7.50038i −1.03015 0.777753i
\(94\) −1.09544 + 10.4224i −0.112986 + 1.07499i
\(95\) 1.42902 + 0.878173i 0.146614 + 0.0900987i
\(96\) −1.73176 0.0318147i −0.176747 0.00324708i
\(97\) 1.68007 + 15.9848i 0.170585 + 1.62301i 0.660215 + 0.751077i \(0.270465\pi\)
−0.489630 + 0.871931i \(0.662868\pi\)
\(98\) 0.526146 + 1.61931i 0.0531488 + 0.163575i
\(99\) 2.91084 + 10.2219i 0.292550 + 1.02734i
\(100\) 4.82637 + 1.30621i 0.482637 + 0.130621i
\(101\) −0.735105 + 1.27324i −0.0731457 + 0.126692i −0.900278 0.435315i \(-0.856637\pi\)
0.827133 + 0.562007i \(0.189970\pi\)
\(102\) −0.244030 + 0.0472026i −0.0241625 + 0.00467376i
\(103\) 9.35861 + 4.16672i 0.922131 + 0.410559i 0.812200 0.583380i \(-0.198270\pi\)
0.109932 + 0.993939i \(0.464937\pi\)
\(104\) −0.812175 0.361604i −0.0796403 0.0354582i
\(105\) 4.90385 + 7.44396i 0.478567 + 0.726457i
\(106\) 12.2365 5.44804i 1.18851 0.529160i
\(107\) 13.6869 1.32316 0.661579 0.749876i \(-0.269887\pi\)
0.661579 + 0.749876i \(0.269887\pi\)
\(108\) 4.62331 + 2.37172i 0.444878 + 0.228219i
\(109\) 4.02681 12.3932i 0.385698 1.18706i −0.550275 0.834984i \(-0.685477\pi\)
0.935973 0.352073i \(-0.114523\pi\)
\(110\) 7.46417 + 2.65374i 0.711680 + 0.253025i
\(111\) −10.8523 12.5072i −1.03005 1.18713i
\(112\) −2.25130 + 0.478529i −0.212728 + 0.0452168i
\(113\) −16.7556 + 3.56151i −1.57623 + 0.335038i −0.911260 0.411831i \(-0.864889\pi\)
−0.664971 + 0.746869i \(0.731556\pi\)
\(114\) 1.27558 0.246735i 0.119469 0.0231088i
\(115\) 8.73112 11.3491i 0.814181 1.05831i
\(116\) 1.45644 4.48246i 0.135227 0.416186i
\(117\) 1.71064 + 2.04626i 0.158149 + 0.189177i
\(118\) −5.16099 −0.475108
\(119\) −0.301730 + 0.134339i −0.0276595 + 0.0123148i
\(120\) 3.43925 1.78088i 0.313959 0.162572i
\(121\) 1.41712 + 0.630941i 0.128829 + 0.0573583i
\(122\) 3.64938 + 1.62481i 0.330400 + 0.147103i
\(123\) 4.06467 11.7696i 0.366499 1.06123i
\(124\) −3.59337 + 6.22390i −0.322694 + 0.558923i
\(125\) −10.8812 + 2.56906i −0.973242 + 0.229783i
\(126\) 6.69662 + 1.68269i 0.596582 + 0.149906i
\(127\) −1.01693 3.12979i −0.0902378 0.277724i 0.895746 0.444567i \(-0.146642\pi\)
−0.985983 + 0.166844i \(0.946642\pi\)
\(128\) 0.104528 + 0.994522i 0.00923910 + 0.0879041i
\(129\) 5.23013 + 9.45582i 0.460487 + 0.832539i
\(130\) 1.98201 0.153486i 0.173834 0.0134616i
\(131\) −0.750726 + 7.14268i −0.0655912 + 0.624059i 0.911509 + 0.411280i \(0.134918\pi\)
−0.977100 + 0.212779i \(0.931749\pi\)
\(132\) 5.65065 2.39245i 0.491826 0.208236i
\(133\) 1.57718 0.702207i 0.136759 0.0608890i
\(134\) −0.834491 + 2.56830i −0.0720891 + 0.221867i
\(135\) −11.6161 + 0.257655i −0.999754 + 0.0221754i
\(136\) 0.0443446 + 0.136479i 0.00380252 + 0.0117029i
\(137\) −7.99150 8.87546i −0.682760 0.758282i 0.297773 0.954637i \(-0.403756\pi\)
−0.980533 + 0.196355i \(0.937090\pi\)
\(138\) −0.956565 11.0502i −0.0814282 0.940651i
\(139\) 7.37639 8.19232i 0.625658 0.694863i −0.344100 0.938933i \(-0.611816\pi\)
0.969758 + 0.244070i \(0.0784826\pi\)
\(140\) 3.91764 3.33749i 0.331101 0.282069i
\(141\) −16.4439 7.68625i −1.38482 0.647299i
\(142\) 2.00718 0.893653i 0.168439 0.0749937i
\(143\) 3.14965 0.263387
\(144\) 1.03122 2.81719i 0.0859353 0.234766i
\(145\) 1.90756 + 10.3648i 0.158414 + 0.860751i
\(146\) −0.499408 4.75155i −0.0413313 0.393241i
\(147\) −2.94857 0.0541692i −0.243194 0.00446780i
\(148\) −6.39714 + 7.10474i −0.525841 + 0.584006i
\(149\) −11.9726 20.7371i −0.980832 1.69885i −0.659167 0.751997i \(-0.729091\pi\)
−0.321665 0.946854i \(-0.604242\pi\)
\(150\) −4.86732 + 7.16304i −0.397415 + 0.584860i
\(151\) 7.15112 12.3861i 0.581950 1.00797i −0.413298 0.910596i \(-0.635623\pi\)
0.995248 0.0973711i \(-0.0310434\pi\)
\(152\) −0.231795 0.713392i −0.0188011 0.0578638i
\(153\) 0.0606958 0.426206i 0.00490697 0.0344567i
\(154\) 6.59675 4.79282i 0.531582 0.386217i
\(155\) 0.440822 16.0640i 0.0354076 1.29029i
\(156\) 1.05121 1.12522i 0.0841642 0.0900895i
\(157\) 7.33368 + 12.7023i 0.585292 + 1.01376i 0.994839 + 0.101466i \(0.0323533\pi\)
−0.409547 + 0.912289i \(0.634313\pi\)
\(158\) −0.860832 + 8.19027i −0.0684841 + 0.651583i
\(159\) 2.00084 + 23.1135i 0.158677 + 1.83302i
\(160\) −1.26421 1.84439i −0.0999445 0.145812i
\(161\) −4.55450 14.0173i −0.358945 1.10472i
\(162\) −6.49692 + 6.22816i −0.510446 + 0.489331i
\(163\) 1.05549 3.24847i 0.0826726 0.254440i −0.901173 0.433460i \(-0.857293\pi\)
0.983845 + 0.179020i \(0.0572926\pi\)
\(164\) −7.03192 1.49468i −0.549101 0.116715i
\(165\) −8.56487 + 10.7197i −0.666774 + 0.834525i
\(166\) −0.581846 + 0.123675i −0.0451600 + 0.00959906i
\(167\) 1.17503 11.1797i 0.0909267 0.865110i −0.850064 0.526679i \(-0.823437\pi\)
0.940991 0.338431i \(-0.109896\pi\)
\(168\) 0.489454 3.95632i 0.0377622 0.305237i
\(169\) −11.1540 + 4.96610i −0.858003 + 0.382007i
\(170\) −0.232481 0.221171i −0.0178305 0.0169631i
\(171\) −0.317265 + 2.22784i −0.0242619 + 0.170367i
\(172\) 5.04727 3.66706i 0.384851 0.279611i
\(173\) −1.65590 0.351973i −0.125896 0.0267600i 0.144533 0.989500i \(-0.453832\pi\)
−0.270429 + 0.962740i \(0.587165\pi\)
\(174\) 6.51507 + 4.91882i 0.493906 + 0.372895i
\(175\) −4.15104 + 10.7333i −0.313789 + 0.811358i
\(176\) −1.77139 3.06813i −0.133523 0.231269i
\(177\) 2.91803 8.44941i 0.219332 0.635097i
\(178\) −0.356684 3.39362i −0.0267346 0.254363i
\(179\) −20.1768 + 14.6593i −1.50808 + 1.09569i −0.541066 + 0.840980i \(0.681979\pi\)
−0.967018 + 0.254707i \(0.918021\pi\)
\(180\) 0.971052 + 6.63755i 0.0723779 + 0.494734i
\(181\) 3.26734 + 2.37386i 0.242860 + 0.176448i 0.702556 0.711628i \(-0.252042\pi\)
−0.459697 + 0.888076i \(0.652042\pi\)
\(182\) 1.02310 1.77207i 0.0758374 0.131354i
\(183\) −4.72345 + 5.05599i −0.349168 + 0.373749i
\(184\) −6.26373 + 1.33140i −0.461768 + 0.0981519i
\(185\) 5.01659 20.7807i 0.368827 1.52783i
\(186\) −8.15788 9.40195i −0.598165 0.689384i
\(187\) −0.340183 0.377811i −0.0248766 0.0276283i
\(188\) −3.23844 + 9.96689i −0.236187 + 0.726910i
\(189\) −6.54112 + 10.0121i −0.475797 + 0.728274i
\(190\) 1.21521 + 1.15609i 0.0881607 + 0.0838718i
\(191\) 10.5467 + 11.7133i 0.763136 + 0.847548i 0.992043 0.125900i \(-0.0401819\pi\)
−0.228907 + 0.973448i \(0.573515\pi\)
\(192\) −1.68730 0.391172i −0.121770 0.0282304i
\(193\) −12.0957 20.9504i −0.870668 1.50804i −0.861307 0.508085i \(-0.830353\pi\)
−0.00936136 0.999956i \(-0.502980\pi\)
\(194\) −1.68007 + 15.9848i −0.120622 + 1.14764i
\(195\) −0.869349 + 3.33167i −0.0622553 + 0.238586i
\(196\) 0.177975 + 1.69332i 0.0127125 + 0.120951i
\(197\) −0.605381 + 0.439835i −0.0431316 + 0.0313369i −0.609142 0.793061i \(-0.708486\pi\)
0.566011 + 0.824398i \(0.308486\pi\)
\(198\) 0.721969 + 10.6038i 0.0513081 + 0.753577i
\(199\) −9.16144 −0.649437 −0.324719 0.945811i \(-0.605270\pi\)
−0.324719 + 0.945811i \(0.605270\pi\)
\(200\) 4.44932 + 2.28113i 0.314615 + 0.161300i
\(201\) −3.73292 2.81832i −0.263300 0.198789i
\(202\) −0.983763 + 1.09258i −0.0692173 + 0.0768736i
\(203\) 9.90990 + 4.41217i 0.695539 + 0.309674i
\(204\) −0.248511 0.00456548i −0.0173993 0.000319648i
\(205\) 15.4189 4.54624i 1.07690 0.317523i
\(206\) 8.28779 + 6.02143i 0.577438 + 0.419533i
\(207\) 18.6318 + 4.68170i 1.29500 + 0.325401i
\(208\) −0.719246 0.522563i −0.0498707 0.0362332i
\(209\) 1.77818 + 1.97487i 0.122999 + 0.136605i
\(210\) 3.24900 + 8.30086i 0.224202 + 0.572814i
\(211\) −4.66558 + 5.18166i −0.321192 + 0.356720i −0.882020 0.471213i \(-0.843816\pi\)
0.560828 + 0.827933i \(0.310483\pi\)
\(212\) 13.1018 2.78487i 0.899835 0.191266i
\(213\) 0.328202 + 3.79136i 0.0224880 + 0.259780i
\(214\) 13.3878 + 2.84566i 0.915169 + 0.194525i
\(215\) −6.02156 + 12.5838i −0.410667 + 0.858209i
\(216\) 4.02917 + 3.28113i 0.274150 + 0.223253i
\(217\) −13.3819 9.72255i −0.908425 0.660010i
\(218\) 6.51551 11.2852i 0.441286 0.764330i
\(219\) 8.06145 + 1.86891i 0.544742 + 0.126289i
\(220\) 6.74931 + 4.14764i 0.455039 + 0.279634i
\(221\) −0.116549 0.0518909i −0.00783993 0.00349056i
\(222\) −8.01472 14.4902i −0.537913 0.972520i
\(223\) −15.9201 3.38392i −1.06609 0.226604i −0.358718 0.933446i \(-0.616786\pi\)
−0.707372 + 0.706842i \(0.750119\pi\)
\(224\) −2.30160 −0.153782
\(225\) −8.97513 12.0186i −0.598342 0.801241i
\(226\) −17.1299 −1.13946
\(227\) 1.84405 + 0.391965i 0.122394 + 0.0260156i 0.268701 0.963224i \(-0.413406\pi\)
−0.146307 + 0.989239i \(0.546739\pi\)
\(228\) 1.29900 + 0.0238644i 0.0860284 + 0.00158046i
\(229\) −1.82367 0.811951i −0.120512 0.0536552i 0.345595 0.938384i \(-0.387677\pi\)
−0.466107 + 0.884729i \(0.654344\pi\)
\(230\) 10.8999 9.28580i 0.718721 0.612288i
\(231\) 4.11685 + 13.5099i 0.270869 + 0.888884i
\(232\) 2.35657 4.08169i 0.154716 0.267976i
\(233\) 4.06114 + 2.95059i 0.266054 + 0.193300i 0.712812 0.701355i \(-0.247421\pi\)
−0.446758 + 0.894655i \(0.647421\pi\)
\(234\) 1.24782 + 2.35721i 0.0815723 + 0.154095i
\(235\) −4.24151 23.0465i −0.276686 1.50339i
\(236\) −5.04821 1.07303i −0.328610 0.0698483i
\(237\) −12.9221 6.04011i −0.839384 0.392347i
\(238\) −0.323067 + 0.0686700i −0.0209413 + 0.00445121i
\(239\) −4.73247 + 5.25594i −0.306118 + 0.339978i −0.876501 0.481401i \(-0.840128\pi\)
0.570383 + 0.821379i \(0.306795\pi\)
\(240\) 3.73436 1.02691i 0.241052 0.0662865i
\(241\) 11.3882 + 12.6479i 0.733578 + 0.814720i 0.988337 0.152284i \(-0.0486629\pi\)
−0.254759 + 0.967005i \(0.581996\pi\)
\(242\) 1.25497 + 0.911789i 0.0806725 + 0.0586120i
\(243\) −6.52319 14.1580i −0.418463 0.908234i
\(244\) 3.23182 + 2.34805i 0.206896 + 0.150319i
\(245\) −2.15250 3.14034i −0.137518 0.200629i
\(246\) 6.42290 10.6673i 0.409509 0.680125i
\(247\) 0.609217 + 0.271241i 0.0387635 + 0.0172586i
\(248\) −4.80887 + 5.34079i −0.305363 + 0.339140i
\(249\) 0.126499 1.02251i 0.00801654 0.0647987i
\(250\) −11.1775 + 0.250593i −0.706929 + 0.0158489i
\(251\) −1.11517 −0.0703890 −0.0351945 0.999380i \(-0.511205\pi\)
−0.0351945 + 0.999380i \(0.511205\pi\)
\(252\) 6.20043 + 3.03823i 0.390591 + 0.191390i
\(253\) 18.3539 13.3349i 1.15390 0.838359i
\(254\) −0.343988 3.27282i −0.0215837 0.205355i
\(255\) 0.493540 0.255561i 0.0309067 0.0160038i
\(256\) −0.104528 + 0.994522i −0.00653303 + 0.0621576i
\(257\) 9.04620 + 15.6685i 0.564286 + 0.977373i 0.997116 + 0.0758967i \(0.0241819\pi\)
−0.432829 + 0.901476i \(0.642485\pi\)
\(258\) 3.14986 + 10.3366i 0.196102 + 0.643528i
\(259\) −14.7236 16.3523i −0.914883 1.01608i
\(260\) 1.97061 + 0.261952i 0.122212 + 0.0162456i
\(261\) −11.7366 + 7.88516i −0.726475 + 0.488079i
\(262\) −2.21937 + 6.83051i −0.137113 + 0.421990i
\(263\) 20.8403 + 23.1455i 1.28507 + 1.42721i 0.849973 + 0.526827i \(0.176618\pi\)
0.435095 + 0.900385i \(0.356715\pi\)
\(264\) 6.02459 1.16534i 0.370788 0.0717215i
\(265\) −22.7993 + 19.4230i −1.40055 + 1.19315i
\(266\) 1.68871 0.358947i 0.103542 0.0220085i
\(267\) 5.75760 + 1.33480i 0.352359 + 0.0816886i
\(268\) −1.35024 + 2.33868i −0.0824787 + 0.142857i
\(269\) 11.1148 + 8.07541i 0.677684 + 0.492366i 0.872589 0.488456i \(-0.162440\pi\)
−0.194904 + 0.980822i \(0.562440\pi\)
\(270\) −11.4158 2.16310i −0.694745 0.131642i
\(271\) −12.6541 + 9.19376i −0.768683 + 0.558481i −0.901561 0.432651i \(-0.857578\pi\)
0.132878 + 0.991132i \(0.457578\pi\)
\(272\) 0.0150001 + 0.142716i 0.000909512 + 0.00865343i
\(273\) 2.32271 + 2.67692i 0.140577 + 0.162014i
\(274\) −5.97156 10.3430i −0.360755 0.624846i
\(275\) −17.6872 0.971461i −1.06658 0.0585813i
\(276\) 1.36179 11.0076i 0.0819704 0.662577i
\(277\) −19.1121 4.06240i −1.14833 0.244086i −0.405843 0.913943i \(-0.633022\pi\)
−0.742490 + 0.669857i \(0.766355\pi\)
\(278\) 8.91848 6.47965i 0.534895 0.388624i
\(279\) 20.0051 8.03997i 1.19767 0.481340i
\(280\) 4.52594 2.45004i 0.270476 0.146418i
\(281\) 10.2046 4.54336i 0.608752 0.271034i −0.0791206 0.996865i \(-0.525211\pi\)
0.687873 + 0.725831i \(0.258545\pi\)
\(282\) −14.4865 10.9372i −0.862657 0.651298i
\(283\) −0.678361 + 6.45418i −0.0403244 + 0.383661i 0.955684 + 0.294396i \(0.0951185\pi\)
−0.996008 + 0.0892650i \(0.971548\pi\)
\(284\) 2.14912 0.456809i 0.127527 0.0271066i
\(285\) −2.57980 + 1.33585i −0.152814 + 0.0791289i
\(286\) 3.08083 + 0.654850i 0.182173 + 0.0387221i
\(287\) 5.11307 15.7364i 0.301815 0.928890i
\(288\) 1.59442 2.54123i 0.0939519 0.149743i
\(289\) −5.24693 16.1484i −0.308643 0.949904i
\(290\) −0.289095 + 10.5349i −0.0169762 + 0.618632i
\(291\) −25.2199 11.7884i −1.47841 0.691045i
\(292\) 0.499408 4.75155i 0.0292256 0.278063i
\(293\) 16.7482 + 29.0088i 0.978443 + 1.69471i 0.668070 + 0.744099i \(0.267121\pi\)
0.310373 + 0.950615i \(0.399546\pi\)
\(294\) −2.87287 0.666028i −0.167549 0.0388435i
\(295\) 11.0692 3.26374i 0.644473 0.190022i
\(296\) −7.73450 + 5.61945i −0.449559 + 0.326624i
\(297\) −17.7684 4.81339i −1.03102 0.279301i
\(298\) −7.39946 22.7732i −0.428639 1.31922i
\(299\) 2.84655 4.93036i 0.164620 0.285130i
\(300\) −6.25024 + 5.99454i −0.360858 + 0.346095i
\(301\) 7.17958 + 12.4354i 0.413824 + 0.716764i
\(302\) 9.57007 10.6286i 0.550695 0.611609i
\(303\) −1.23252 2.22833i −0.0708062 0.128014i
\(304\) −0.0784073 0.745996i −0.00449697 0.0427858i
\(305\) −8.85464 1.17704i −0.507015 0.0673971i
\(306\) 0.147983 0.404273i 0.00845961 0.0231108i
\(307\) −30.5763 −1.74508 −0.872540 0.488542i \(-0.837529\pi\)
−0.872540 + 0.488542i \(0.837529\pi\)
\(308\) 7.44908 3.31655i 0.424451 0.188978i
\(309\) −14.5440 + 10.1640i −0.827381 + 0.578210i
\(310\) 3.77108 15.6213i 0.214183 0.887231i
\(311\) 17.6292 19.5792i 0.999660 1.11024i 0.00575670 0.999983i \(-0.498168\pi\)
0.993904 0.110252i \(-0.0351658\pi\)
\(312\) 1.26218 0.882070i 0.0714572 0.0499374i
\(313\) 10.0530 + 11.1650i 0.568229 + 0.631082i 0.956943 0.290276i \(-0.0937473\pi\)
−0.388714 + 0.921358i \(0.627081\pi\)
\(314\) 4.53247 + 13.9495i 0.255782 + 0.787216i
\(315\) −15.4269 + 0.625850i −0.869207 + 0.0352627i
\(316\) −2.54487 + 7.83232i −0.143160 + 0.440602i
\(317\) −11.5173 + 5.12782i −0.646874 + 0.288007i −0.703828 0.710370i \(-0.748528\pi\)
0.0569546 + 0.998377i \(0.481861\pi\)
\(318\) −2.84846 + 23.0244i −0.159733 + 1.29115i
\(319\) −1.74537 + 16.6061i −0.0977219 + 0.929762i
\(320\) −0.853113 2.06693i −0.0476905 0.115545i
\(321\) −12.2283 + 20.3091i −0.682515 + 1.13354i
\(322\) −1.54061 14.6579i −0.0858549 0.816855i
\(323\) −0.0332631 0.102373i −0.00185081 0.00569621i
\(324\) −7.64986 + 4.74128i −0.424992 + 0.263404i
\(325\) −4.15392 + 1.58259i −0.230418 + 0.0877864i
\(326\) 1.70782 2.95804i 0.0945876 0.163831i
\(327\) 14.7919 + 17.0476i 0.817994 + 0.942737i
\(328\) −6.56749 2.92404i −0.362629 0.161453i
\(329\) −22.0350 9.81062i −1.21483 0.540877i
\(330\) −10.6065 + 8.70469i −0.583866 + 0.479177i
\(331\) −3.10179 + 1.38100i −0.170490 + 0.0759068i −0.490207 0.871606i \(-0.663079\pi\)
0.319717 + 0.947513i \(0.396412\pi\)
\(332\) −0.594845 −0.0326464
\(333\) 28.2545 4.92867i 1.54833 0.270089i
\(334\) 3.47374 10.6911i 0.190075 0.584990i
\(335\) 0.165642 6.03616i 0.00904998 0.329791i
\(336\) 1.30132 3.76811i 0.0709931 0.205567i
\(337\) 10.0573 2.13775i 0.547857 0.116451i 0.0743361 0.997233i \(-0.476316\pi\)
0.473521 + 0.880783i \(0.342983\pi\)
\(338\) −11.9428 + 2.53852i −0.649603 + 0.138077i
\(339\) 9.68525 28.0445i 0.526031 1.52317i
\(340\) −0.181417 0.264674i −0.00983871 0.0143540i
\(341\) 7.86788 24.2148i 0.426069 1.31131i
\(342\) −0.773526 + 2.11319i −0.0418275 + 0.114268i
\(343\) −20.0300 −1.08152
\(344\) 5.69940 2.53754i 0.307291 0.136815i
\(345\) 9.03959 + 23.0952i 0.486675 + 1.24341i
\(346\) −1.54654 0.688562i −0.0831423 0.0370173i
\(347\) 13.5549 + 6.03504i 0.727666 + 0.323978i 0.736921 0.675979i \(-0.236279\pi\)
−0.00925453 + 0.999957i \(0.502946\pi\)
\(348\) 5.35002 + 6.16589i 0.286791 + 0.330526i
\(349\) 17.2110 29.8104i 0.921285 1.59571i 0.123856 0.992300i \(-0.460474\pi\)
0.797429 0.603413i \(-0.206193\pi\)
\(350\) −6.29190 + 9.63565i −0.336316 + 0.515047i
\(351\) −4.56466 + 0.710119i −0.243644 + 0.0379034i
\(352\) −1.09478 3.36938i −0.0583518 0.179588i
\(353\) −0.258350 2.45804i −0.0137506 0.130828i 0.985493 0.169716i \(-0.0542851\pi\)
−0.999244 + 0.0388880i \(0.987618\pi\)
\(354\) 4.61099 7.65808i 0.245071 0.407022i
\(355\) −3.73982 + 3.18600i −0.198489 + 0.169096i
\(356\) 0.356684 3.39362i 0.0189042 0.179862i
\(357\) 0.0702378 0.567741i 0.00371738 0.0300480i
\(358\) −22.7837 + 10.1440i −1.20416 + 0.536125i
\(359\) −2.58562 + 7.95772i −0.136464 + 0.419993i −0.995815 0.0913936i \(-0.970868\pi\)
0.859351 + 0.511386i \(0.170868\pi\)
\(360\) −0.430192 + 6.69440i −0.0226731 + 0.352826i
\(361\) −5.69745 17.5350i −0.299866 0.922892i
\(362\) 2.70239 + 3.00131i 0.142034 + 0.157745i
\(363\) −2.20231 + 1.53907i −0.115591 + 0.0807803i
\(364\) 1.36918 1.52063i 0.0717644 0.0797025i
\(365\) 4.07594 + 9.87521i 0.213344 + 0.516892i
\(366\) −5.67143 + 3.96344i −0.296450 + 0.207172i
\(367\) 9.13877 4.06884i 0.477040 0.212392i −0.154108 0.988054i \(-0.549251\pi\)
0.631149 + 0.775662i \(0.282584\pi\)
\(368\) −6.40367 −0.333814
\(369\) 13.8327 + 16.5467i 0.720104 + 0.861386i
\(370\) 9.22752 19.2836i 0.479716 1.00251i
\(371\) 3.22248 + 30.6599i 0.167303 + 1.59178i
\(372\) −6.02484 10.8926i −0.312373 0.564756i
\(373\) 11.0022 12.2191i 0.569670 0.632683i −0.387617 0.921820i \(-0.626702\pi\)
0.957288 + 0.289137i \(0.0933685\pi\)
\(374\) −0.254198 0.440283i −0.0131442 0.0227665i
\(375\) 5.90952 18.4412i 0.305166 0.952299i
\(376\) −5.23991 + 9.07578i −0.270227 + 0.468048i
\(377\) 1.29483 + 3.98507i 0.0666870 + 0.205241i
\(378\) −8.47982 + 8.43334i −0.436155 + 0.433764i
\(379\) 16.8249 12.2240i 0.864235 0.627904i −0.0647986 0.997898i \(-0.520641\pi\)
0.929034 + 0.369995i \(0.120641\pi\)
\(380\) 0.948290 + 1.38349i 0.0486463 + 0.0709714i
\(381\) 5.55266 + 1.28729i 0.284471 + 0.0659499i
\(382\) 7.88093 + 13.6502i 0.403224 + 0.698404i
\(383\) 0.272663 2.59422i 0.0139324 0.132558i −0.985345 0.170575i \(-0.945437\pi\)
0.999277 + 0.0380169i \(0.0121041\pi\)
\(384\) −1.56910 0.733434i −0.0800728 0.0374279i
\(385\) −11.1177 + 14.4513i −0.566609 + 0.736504i
\(386\) −7.47556 23.0074i −0.380496 1.17105i
\(387\) −18.7037 0.687456i −0.950762 0.0349453i
\(388\) −4.96677 + 15.2862i −0.252150 + 0.776037i
\(389\) 12.7447 + 2.70897i 0.646181 + 0.137350i 0.519333 0.854572i \(-0.326181\pi\)
0.126848 + 0.991922i \(0.459514\pi\)
\(390\) −1.54304 + 3.07812i −0.0781351 + 0.155866i
\(391\) −0.898859 + 0.191058i −0.0454572 + 0.00966224i
\(392\) −0.177975 + 1.69332i −0.00898909 + 0.0855254i
\(393\) −9.92787 7.49546i −0.500795 0.378096i
\(394\) −0.683599 + 0.304358i −0.0344392 + 0.0153333i
\(395\) −3.33312 18.1107i −0.167708 0.911249i
\(396\) −1.49845 + 10.5222i −0.0753001 + 0.528758i
\(397\) −12.7975 + 9.29795i −0.642290 + 0.466651i −0.860636 0.509220i \(-0.829934\pi\)
0.218346 + 0.975871i \(0.429934\pi\)
\(398\) −8.96124 1.90477i −0.449187 0.0954775i
\(399\) −0.367142 + 2.96766i −0.0183801 + 0.148569i
\(400\) 3.87782 + 3.15634i 0.193891 + 0.157817i
\(401\) 5.99557 + 10.3846i 0.299405 + 0.518584i 0.976000 0.217771i \(-0.0698786\pi\)
−0.676595 + 0.736355i \(0.736545\pi\)
\(402\) −3.06538 3.53285i −0.152887 0.176203i
\(403\) −0.667861 6.35427i −0.0332685 0.316529i
\(404\) −1.18942 + 0.864168i −0.0591761 + 0.0429940i
\(405\) 9.99587 17.4666i 0.496699 0.867923i
\(406\) 8.77601 + 6.37614i 0.435546 + 0.316443i
\(407\) 16.9351 29.3325i 0.839442 1.45396i
\(408\) −0.242131 0.0561341i −0.0119873 0.00277905i
\(409\) 14.1305 3.00354i 0.698710 0.148515i 0.155156 0.987890i \(-0.450412\pi\)
0.543554 + 0.839375i \(0.317078\pi\)
\(410\) 16.0271 1.24113i 0.791524 0.0612951i
\(411\) 20.3096 3.92849i 1.00180 0.193778i
\(412\) 6.85476 + 7.61298i 0.337710 + 0.375065i
\(413\) 3.67067 11.2971i 0.180622 0.555896i
\(414\) 17.2513 + 8.45317i 0.847854 + 0.415450i
\(415\) 1.16972 0.633208i 0.0574194 0.0310830i
\(416\) −0.594882 0.660683i −0.0291665 0.0323926i
\(417\) 5.56578 + 18.2647i 0.272557 + 0.894424i
\(418\) 1.32873 + 2.30142i 0.0649901 + 0.112566i
\(419\) 2.00650 19.0906i 0.0980239 0.932635i −0.829408 0.558643i \(-0.811322\pi\)
0.927432 0.373992i \(-0.122011\pi\)
\(420\) 1.45215 + 8.79497i 0.0708579 + 0.429151i
\(421\) 1.90411 + 18.1164i 0.0928006 + 0.882938i 0.937567 + 0.347804i \(0.113072\pi\)
−0.844767 + 0.535135i \(0.820261\pi\)
\(422\) −5.64096 + 4.09840i −0.274597 + 0.199507i
\(423\) 26.0966 17.5329i 1.26886 0.852480i
\(424\) 13.3945 0.650495
\(425\) 0.638487 + 0.327346i 0.0309712 + 0.0158786i
\(426\) −0.467238 + 3.77675i −0.0226378 + 0.182984i
\(427\) −6.15219 + 6.83270i −0.297725 + 0.330657i
\(428\) 12.5036 + 5.56694i 0.604382 + 0.269088i
\(429\) −2.81400 + 4.67358i −0.135861 + 0.225643i
\(430\) −8.50630 + 11.0569i −0.410210 + 0.533210i
\(431\) 8.53170 + 6.19864i 0.410957 + 0.298578i 0.773989 0.633199i \(-0.218258\pi\)
−0.363032 + 0.931777i \(0.618258\pi\)
\(432\) 3.25894 + 4.04714i 0.156796 + 0.194718i
\(433\) 11.1986 + 8.13629i 0.538172 + 0.391005i 0.823406 0.567453i \(-0.192071\pi\)
−0.285233 + 0.958458i \(0.592071\pi\)
\(434\) −11.0681 12.2924i −0.531285 0.590052i
\(435\) −17.0840 6.42975i −0.819115 0.308283i
\(436\) 8.71945 9.68393i 0.417586 0.463776i
\(437\) 4.69846 0.998688i 0.224758 0.0477737i
\(438\) 7.49672 + 3.50414i 0.358207 + 0.167434i
\(439\) −3.57536 0.759966i −0.170643 0.0362712i 0.121798 0.992555i \(-0.461134\pi\)
−0.292441 + 0.956284i \(0.594467\pi\)
\(440\) 5.73948 + 5.46027i 0.273619 + 0.260308i
\(441\) 2.71472 4.32681i 0.129273 0.206038i
\(442\) −0.103213 0.0749888i −0.00490936 0.00356686i
\(443\) −14.1183 + 24.4536i −0.670780 + 1.16182i 0.306904 + 0.951741i \(0.400707\pi\)
−0.977683 + 0.210084i \(0.932626\pi\)
\(444\) −4.82689 15.8399i −0.229074 0.751730i
\(445\) 2.91109 + 7.05301i 0.137999 + 0.334345i
\(446\) −14.8687 6.61995i −0.704052 0.313464i
\(447\) 41.4672 + 0.761808i 1.96133 + 0.0360323i
\(448\) −2.25130 0.478529i −0.106364 0.0226084i
\(449\) 35.6213 1.68107 0.840536 0.541755i \(-0.182240\pi\)
0.840536 + 0.541755i \(0.182240\pi\)
\(450\) −6.28019 13.6220i −0.296051 0.642148i
\(451\) 25.4690 1.19929
\(452\) −16.7556 3.56151i −0.788116 0.167519i
\(453\) 11.9900 + 21.6773i 0.563337 + 1.01849i
\(454\) 1.72226 + 0.766799i 0.0808296 + 0.0359877i
\(455\) −1.07370 + 4.44769i −0.0503358 + 0.208511i
\(456\) 1.26565 + 0.293420i 0.0592696 + 0.0137407i
\(457\) −8.32562 + 14.4204i −0.389456 + 0.674557i −0.992376 0.123244i \(-0.960670\pi\)
0.602921 + 0.797801i \(0.294004\pi\)
\(458\) −1.61501 1.17337i −0.0754643 0.0548280i
\(459\) 0.578194 + 0.470849i 0.0269878 + 0.0219774i
\(460\) 12.5924 6.81666i 0.587123 0.317828i
\(461\) 28.2018 + 5.99448i 1.31349 + 0.279191i 0.810824 0.585290i \(-0.199019\pi\)
0.502666 + 0.864481i \(0.332353\pi\)
\(462\) 1.21803 + 14.0706i 0.0566679 + 0.654623i
\(463\) 37.5433 7.98008i 1.74479 0.370866i 0.778361 0.627816i \(-0.216051\pi\)
0.966424 + 0.256951i \(0.0827178\pi\)
\(464\) 3.15370 3.50254i 0.146407 0.162601i
\(465\) 23.4425 + 15.0062i 1.08712 + 0.695895i
\(466\) 3.35893 + 3.73047i 0.155599 + 0.172811i
\(467\) 31.7320 + 23.0546i 1.46838 + 1.06684i 0.981079 + 0.193607i \(0.0620185\pi\)
0.487301 + 0.873234i \(0.337981\pi\)
\(468\) 0.730457 + 2.56513i 0.0337654 + 0.118573i
\(469\) −5.02836 3.65332i −0.232188 0.168695i
\(470\) 0.642812 23.4248i 0.0296507 1.08050i
\(471\) −25.4003 0.466638i −1.17039 0.0215016i
\(472\) −4.71480 2.09916i −0.217016 0.0966218i
\(473\) −14.7895 + 16.4254i −0.680022 + 0.755240i
\(474\) −11.3840 8.59479i −0.522882 0.394772i
\(475\) −3.33746 1.71108i −0.153133 0.0785099i
\(476\) −0.330284 −0.0151386
\(477\) −36.0844 17.6814i −1.65219 0.809577i
\(478\) −5.72182 + 4.15715i −0.261710 + 0.190144i
\(479\) 2.96286 + 28.1897i 0.135377 + 1.28802i 0.825530 + 0.564358i \(0.190876\pi\)
−0.690153 + 0.723663i \(0.742457\pi\)
\(480\) 3.86626 0.228048i 0.176470 0.0104089i
\(481\) 0.888442 8.45296i 0.0405095 0.385422i
\(482\) 8.50969 + 14.7392i 0.387606 + 0.671353i
\(483\) 24.8686 + 5.76536i 1.13156 + 0.262333i
\(484\) 1.03797 + 1.15279i 0.0471806 + 0.0523994i
\(485\) −6.50518 35.3463i −0.295385 1.60499i
\(486\) −3.43704 15.2048i −0.155907 0.689705i
\(487\) −6.30450 + 19.4033i −0.285684 + 0.879246i 0.700508 + 0.713644i \(0.252957\pi\)
−0.986193 + 0.165602i \(0.947043\pi\)
\(488\) 2.67301 + 2.96868i 0.121001 + 0.134386i
\(489\) 3.87720 + 4.46847i 0.175333 + 0.202071i
\(490\) −1.45255 3.51925i −0.0656195 0.158983i
\(491\) 7.11796 1.51297i 0.321229 0.0682794i −0.0444750 0.999010i \(-0.514162\pi\)
0.365704 + 0.930731i \(0.380828\pi\)
\(492\) 8.50041 9.09885i 0.383228 0.410208i
\(493\) 0.338172 0.585732i 0.0152305 0.0263800i
\(494\) 0.539510 + 0.391977i 0.0242737 + 0.0176359i
\(495\) −8.25415 22.2862i −0.370996 1.00169i
\(496\) −5.81420 + 4.22426i −0.261065 + 0.189675i
\(497\) 0.528591 + 5.02921i 0.0237106 + 0.225591i
\(498\) 0.336326 0.973862i 0.0150711 0.0436398i
\(499\) −4.33253 7.50416i −0.193951 0.335932i 0.752605 0.658472i \(-0.228797\pi\)
−0.946556 + 0.322540i \(0.895463\pi\)
\(500\) −10.9854 2.07882i −0.491281 0.0929677i
\(501\) 15.5390 + 11.7318i 0.694233 + 0.524140i
\(502\) −1.09080 0.231857i −0.0486849 0.0103483i
\(503\) −29.0893 + 21.1346i −1.29703 + 0.942347i −0.999922 0.0124976i \(-0.996022\pi\)
−0.297107 + 0.954844i \(0.596022\pi\)
\(504\) 5.43326 + 4.26098i 0.242016 + 0.189799i
\(505\) 1.41902 2.96546i 0.0631457 0.131961i
\(506\) 20.7254 9.22752i 0.921354 0.410213i
\(507\) 2.59648 20.9877i 0.115314 0.932095i
\(508\) 0.343988 3.27282i 0.0152620 0.145208i
\(509\) 21.4275 4.55455i 0.949757 0.201877i 0.293113 0.956078i \(-0.405309\pi\)
0.656644 + 0.754201i \(0.271975\pi\)
\(510\) 0.535889 0.147363i 0.0237296 0.00652535i
\(511\) 10.7561 + 2.28628i 0.475821 + 0.101139i
\(512\) −0.309017 + 0.951057i −0.0136568 + 0.0420312i
\(513\) −3.02230 2.46119i −0.133438 0.108664i
\(514\) 5.59086 + 17.2069i 0.246602 + 0.758963i
\(515\) −21.5834 7.67357i −0.951077 0.338138i
\(516\) 0.931933 + 10.7656i 0.0410261 + 0.473930i
\(517\) 3.88089 36.9242i 0.170681 1.62392i
\(518\) −11.0021 19.0561i −0.483403 0.837279i
\(519\) 2.00171 2.14263i 0.0878651 0.0940509i
\(520\) 1.87309 + 0.665941i 0.0821403 + 0.0292034i
\(521\) 3.32879 2.41851i 0.145837 0.105957i −0.512474 0.858702i \(-0.671271\pi\)
0.658311 + 0.752746i \(0.271271\pi\)
\(522\) −13.1195 + 5.27269i −0.574225 + 0.230779i
\(523\) 2.75668 + 8.48418i 0.120541 + 0.370987i 0.993062 0.117589i \(-0.0375165\pi\)
−0.872521 + 0.488576i \(0.837516\pi\)
\(524\) −3.59101 + 6.21982i −0.156874 + 0.271714i
\(525\) −12.2178 15.7489i −0.533226 0.687339i
\(526\) 15.5727 + 26.9726i 0.679000 + 1.17606i
\(527\) −0.690083 + 0.766415i −0.0300605 + 0.0333855i
\(528\) 6.13522 + 0.112712i 0.267001 + 0.00490517i
\(529\) −1.88224 17.9083i −0.0818365 0.778622i
\(530\) −26.3394 + 14.2584i −1.14411 + 0.619343i
\(531\) 9.93052 + 11.8789i 0.430948 + 0.515498i
\(532\) 1.72644 0.0748507
\(533\) 5.83874 2.59958i 0.252904 0.112600i
\(534\) 5.35426 + 2.50271i 0.231702 + 0.108303i
\(535\) −30.5134 + 2.36293i −1.31921 + 0.102159i
\(536\) −1.80697 + 2.00684i −0.0780491 + 0.0866823i
\(537\) −3.72546 43.0362i −0.160765 1.85715i
\(538\) 9.19299 + 10.2098i 0.396338 + 0.440178i
\(539\) −1.86402 5.73685i −0.0802888 0.247104i
\(540\) −10.7166 4.48931i −0.461170 0.193189i
\(541\) −3.89555 + 11.9893i −0.167483 + 0.515458i −0.999211 0.0397248i \(-0.987352\pi\)
0.831728 + 0.555183i \(0.187352\pi\)
\(542\) −14.2891 + 6.36191i −0.613769 + 0.273268i
\(543\) −6.44158 + 2.72733i −0.276434 + 0.117041i
\(544\) −0.0150001 + 0.142716i −0.000643122 + 0.00611890i
\(545\) −6.83773 + 28.3246i −0.292896 + 1.21329i
\(546\) 1.71539 + 3.10134i 0.0734119 + 0.132725i
\(547\) −0.851270 8.09929i −0.0363977 0.346301i −0.997532 0.0702183i \(-0.977630\pi\)
0.961134 0.276082i \(-0.0890363\pi\)
\(548\) −3.69062 11.3586i −0.157656 0.485214i
\(549\) −3.28219 11.5260i −0.140081 0.491919i
\(550\) −17.0987 4.62761i −0.729092 0.197322i
\(551\) −1.76767 + 3.06170i −0.0753054 + 0.130433i
\(552\) 3.62064 10.4839i 0.154105 0.446224i
\(553\) −17.3158 7.70951i −0.736345 0.327842i
\(554\) −17.8498 7.94725i −0.758366 0.337646i
\(555\) 26.3532 + 26.0099i 1.11863 + 1.10406i
\(556\) 10.0708 4.48380i 0.427096 0.190156i
\(557\) −12.7630 −0.540787 −0.270394 0.962750i \(-0.587154\pi\)
−0.270394 + 0.962750i \(0.587154\pi\)
\(558\) 21.2395 3.70499i 0.899140 0.156845i
\(559\) −1.71396 + 5.27503i −0.0724929 + 0.223110i
\(560\) 4.93643 1.45550i 0.208602 0.0615061i
\(561\) 0.864541 0.167228i 0.0365010 0.00706038i
\(562\) 10.9262 2.32243i 0.460893 0.0979658i
\(563\) −43.5377 + 9.25422i −1.83489 + 0.390019i −0.989548 0.144201i \(-0.953939\pi\)
−0.845345 + 0.534220i \(0.820605\pi\)
\(564\) −11.8959 13.7101i −0.500910 0.577298i
\(565\) 36.7399 10.8327i 1.54566 0.455736i
\(566\) −2.00544 + 6.17210i −0.0842948 + 0.259433i
\(567\) −9.01231 18.6511i −0.378482 0.783273i
\(568\) 2.19713 0.0921895
\(569\) 13.2033 5.87848i 0.553510 0.246439i −0.110868 0.993835i \(-0.535363\pi\)
0.664378 + 0.747397i \(0.268696\pi\)
\(570\) −2.80116 + 0.770287i −0.117328 + 0.0322638i
\(571\) −28.1297 12.5242i −1.17719 0.524120i −0.277534 0.960716i \(-0.589517\pi\)
−0.899658 + 0.436596i \(0.856184\pi\)
\(572\) 2.87735 + 1.28108i 0.120308 + 0.0535646i
\(573\) −26.8035 + 5.18460i −1.11973 + 0.216590i
\(574\) 8.27312 14.3295i 0.345313 0.598100i
\(575\) −17.5058 + 26.8090i −0.730041 + 1.11801i
\(576\) 2.08793 2.15420i 0.0869969 0.0897583i
\(577\) 10.5165 + 32.3666i 0.437809 + 1.34744i 0.890181 + 0.455608i \(0.150578\pi\)
−0.452372 + 0.891829i \(0.649422\pi\)
\(578\) −1.77483 16.8864i −0.0738233 0.702381i
\(579\) 41.8937 + 0.769643i 1.74104 + 0.0319853i
\(580\) −2.47311 + 10.2446i −0.102690 + 0.425384i
\(581\) 0.143109 1.36159i 0.00593718 0.0564884i
\(582\) −22.2178 16.7743i −0.920958 0.695315i
\(583\) −43.3511 + 19.3011i −1.79542 + 0.799372i
\(584\) 1.47640 4.54388i 0.0610937 0.188027i
\(585\) −4.16696 4.26659i −0.172283 0.176402i
\(586\) 10.3510 + 31.8571i 0.427595 + 1.31600i
\(587\) −20.2995 22.5449i −0.837851 0.930528i 0.160552 0.987027i \(-0.448673\pi\)
−0.998403 + 0.0564997i \(0.982006\pi\)
\(588\) −2.67162 1.24878i −0.110176 0.0514987i
\(589\) 3.60716 4.00615i 0.148630 0.165071i
\(590\) 11.5059 0.891007i 0.473689 0.0366822i
\(591\) −0.111778 1.29125i −0.00459794 0.0531149i
\(592\) −8.73383 + 3.88855i −0.358958 + 0.159819i
\(593\) −23.6814 −0.972480 −0.486240 0.873825i \(-0.661632\pi\)
−0.486240 + 0.873825i \(0.661632\pi\)
\(594\) −16.3793 8.40245i −0.672051 0.344757i
\(595\) 0.649482 0.351585i 0.0266262 0.0144136i
\(596\) −2.50295 23.8140i −0.102525 0.975459i
\(597\) 8.18512 13.5941i 0.334995 0.556370i
\(598\) 3.80942 4.23079i 0.155779 0.173010i
\(599\) −5.07144 8.78399i −0.207213 0.358904i 0.743622 0.668600i \(-0.233106\pi\)
−0.950836 + 0.309696i \(0.899773\pi\)
\(600\) −7.35999 + 4.56405i −0.300470 + 0.186327i
\(601\) 11.8068 20.4499i 0.481608 0.834169i −0.518170 0.855278i \(-0.673386\pi\)
0.999777 + 0.0211090i \(0.00671972\pi\)
\(602\) 4.43722 + 13.6564i 0.180848 + 0.556592i
\(603\) 7.51704 3.02108i 0.306118 0.123028i
\(604\) 11.5708 8.40665i 0.470807 0.342062i
\(605\) −3.26824 1.16196i −0.132873 0.0472404i
\(606\) −0.742287 2.43589i −0.0301534 0.0989513i
\(607\) −14.3412 24.8397i −0.582091 1.00821i −0.995231 0.0975436i \(-0.968901\pi\)
0.413140 0.910667i \(-0.364432\pi\)
\(608\) 0.0784073 0.745996i 0.00317984 0.0302541i
\(609\) −15.4008 + 10.7627i −0.624071 + 0.436128i
\(610\) −8.41642 2.99230i −0.340771 0.121155i
\(611\) −2.87909 8.86093i −0.116476 0.358475i
\(612\) 0.228802 0.364672i 0.00924878 0.0147410i
\(613\) −7.44761 + 22.9214i −0.300806 + 0.925786i 0.680403 + 0.732838i \(0.261805\pi\)
−0.981209 + 0.192948i \(0.938195\pi\)
\(614\) −29.9081 6.35717i −1.20699 0.256554i
\(615\) −7.02982 + 26.9409i −0.283470 + 1.08636i
\(616\) 7.97585 1.69532i 0.321356 0.0683064i
\(617\) −0.373831 + 3.55677i −0.0150499 + 0.143190i −0.999466 0.0326622i \(-0.989601\pi\)
0.984417 + 0.175852i \(0.0562681\pi\)
\(618\) −16.3394 + 6.91802i −0.657268 + 0.278283i
\(619\) −34.4407 + 15.3340i −1.38429 + 0.616325i −0.957607 0.288077i \(-0.906984\pi\)
−0.426681 + 0.904402i \(0.640317\pi\)
\(620\) 6.93653 14.4959i 0.278578 0.582169i
\(621\) −23.5931 + 23.4638i −0.946760 + 0.941571i
\(622\) 21.3147 15.4860i 0.854642 0.620934i
\(623\) 7.68215 + 1.63289i 0.307779 + 0.0654204i
\(624\) 1.41800 0.600371i 0.0567653 0.0240341i
\(625\) 23.8149 7.60599i 0.952596 0.304240i
\(626\) 7.51198 + 13.0111i 0.300239 + 0.520029i
\(627\) −4.51908 + 0.874124i −0.180474 + 0.0349092i
\(628\) 1.53316 + 14.5870i 0.0611796 + 0.582085i
\(629\) −1.10992 + 0.806403i −0.0442553 + 0.0321534i
\(630\) −15.2199 2.59526i −0.606376 0.103398i
\(631\) 34.6264 + 25.1576i 1.37846 + 1.00151i 0.997023 + 0.0771096i \(0.0245691\pi\)
0.381433 + 0.924397i \(0.375431\pi\)
\(632\) −4.11769 + 7.13205i −0.163793 + 0.283698i
\(633\) −3.52037 11.5524i −0.139922 0.459168i
\(634\) −12.3317 + 2.62119i −0.489755 + 0.104101i
\(635\) 2.80747 + 6.80196i 0.111411 + 0.269927i
\(636\) −7.57326 + 21.9291i −0.300299 + 0.869544i
\(637\) −1.01287 1.12491i −0.0401314 0.0445705i
\(638\) −5.15983 + 15.8803i −0.204280 + 0.628708i
\(639\) −5.91900 2.90032i −0.234152 0.114735i
\(640\) −0.404732 2.19913i −0.0159984 0.0869284i
\(641\) 17.6059 + 19.5534i 0.695392 + 0.772311i 0.982635 0.185547i \(-0.0594056\pi\)
−0.287244 + 0.957858i \(0.592739\pi\)
\(642\) −16.1835 + 17.3229i −0.638714 + 0.683680i
\(643\) −2.92305 5.06287i −0.115274 0.199660i 0.802615 0.596497i \(-0.203441\pi\)
−0.917889 + 0.396837i \(0.870108\pi\)
\(644\) 1.54061 14.6579i 0.0607086 0.577603i
\(645\) −13.2925 20.1778i −0.523392 0.794500i
\(646\) −0.0112516 0.107052i −0.000442689 0.00421191i
\(647\) −19.5758 + 14.2227i −0.769604 + 0.559150i −0.901841 0.432068i \(-0.857784\pi\)
0.132237 + 0.991218i \(0.457784\pi\)
\(648\) −8.46845 + 3.04717i −0.332672 + 0.119704i
\(649\) 18.2842 0.717718
\(650\) −4.39219 + 0.684360i −0.172276 + 0.0268428i
\(651\) 26.3826 11.1702i 1.03401 0.437796i
\(652\) 2.28551 2.53832i 0.0895076 0.0994083i
\(653\) 25.4457 + 11.3291i 0.995767 + 0.443344i 0.838906 0.544277i \(-0.183196\pi\)
0.156861 + 0.987621i \(0.449863\pi\)
\(654\) 10.9243 + 19.7505i 0.427172 + 0.772306i
\(655\) 0.440532 16.0535i 0.0172130 0.627260i
\(656\) −5.81604 4.22560i −0.227078 0.164982i
\(657\) −9.97552 + 10.2922i −0.389182 + 0.401535i
\(658\) −19.5137 14.1776i −0.760725 0.552699i
\(659\) −14.7305 16.3598i −0.573817 0.637288i 0.384456 0.923143i \(-0.374389\pi\)
−0.958273 + 0.285855i \(0.907722\pi\)
\(660\) −12.1845 + 6.30926i −0.474280 + 0.245588i
\(661\) −0.586056 + 0.650881i −0.0227949 + 0.0253164i −0.754434 0.656375i \(-0.772089\pi\)
0.731640 + 0.681692i \(0.238755\pi\)
\(662\) −3.32113 + 0.705928i −0.129079 + 0.0274367i
\(663\) 0.181126 0.126579i 0.00703436 0.00491592i
\(664\) −0.581846 0.123675i −0.0225800 0.00479953i
\(665\) −3.39493 + 1.83778i −0.131650 + 0.0712662i
\(666\) 28.6618 + 1.05347i 1.11062 + 0.0408210i
\(667\) 24.4172 + 17.7401i 0.945438 + 0.686901i
\(668\) 5.62063 9.73522i 0.217469 0.376667i
\(669\) 19.2447 20.5996i 0.744044 0.796426i
\(670\) 1.41701 5.86982i 0.0547439 0.226771i
\(671\) −12.9289 5.75633i −0.499116 0.222221i
\(672\) 2.05632 3.41520i 0.0793243 0.131744i
\(673\) −29.7380 6.32101i −1.14632 0.243657i −0.404679 0.914459i \(-0.632617\pi\)
−0.741637 + 0.670802i \(0.765950\pi\)
\(674\) 10.2820 0.396048
\(675\) 25.8524 2.57985i 0.995058 0.0992984i
\(676\) −12.2096 −0.469601
\(677\) −31.0581 6.60159i −1.19366 0.253720i −0.432105 0.901823i \(-0.642229\pi\)
−0.761552 + 0.648103i \(0.775563\pi\)
\(678\) 15.3044 25.4180i 0.587762 0.976173i
\(679\) −33.7949 15.0465i −1.29693 0.577431i
\(680\) −0.122424 0.296609i −0.00469473 0.0113744i
\(681\) −2.22914 + 2.38608i −0.0854210 + 0.0914348i
\(682\) 12.7305 22.0499i 0.487476 0.844333i
\(683\) −27.6138 20.0626i −1.05661 0.767674i −0.0831534 0.996537i \(-0.526499\pi\)
−0.973459 + 0.228863i \(0.926499\pi\)
\(684\) −1.19598 + 1.90619i −0.0457294 + 0.0728849i
\(685\) 19.3485 + 18.4072i 0.739268 + 0.703304i
\(686\) −19.5923 4.16447i −0.748037 0.159000i
\(687\) 2.83413 1.98061i 0.108129 0.0755651i
\(688\) 6.10244 1.29711i 0.232653 0.0494520i
\(689\) −7.96814 + 8.84952i −0.303562 + 0.337140i
\(690\) 4.04029 + 24.4700i 0.153811 + 0.931557i
\(691\) −23.3127 25.8914i −0.886857 0.984955i 0.113106 0.993583i \(-0.463920\pi\)
−0.999963 + 0.00862835i \(0.997253\pi\)
\(692\) −1.36958 0.995059i −0.0520637 0.0378265i
\(693\) −23.7246 5.96139i −0.901223 0.226455i
\(694\) 12.0040 + 8.72138i 0.455664 + 0.331059i
\(695\) −15.0305 + 19.5374i −0.570141 + 0.741095i
\(696\) 3.95115 + 7.14348i 0.149768 + 0.270773i
\(697\) −0.942450 0.419606i −0.0356978 0.0158937i
\(698\) 23.0329 25.5806i 0.871806 0.968239i
\(699\) −8.00655 + 3.38993i −0.302836 + 0.128219i
\(700\) −8.15777 + 8.11693i −0.308335 + 0.306791i
\(701\) 24.3828 0.920925 0.460462 0.887679i \(-0.347684\pi\)
0.460462 + 0.887679i \(0.347684\pi\)
\(702\) −4.61256 0.254446i −0.174090 0.00960343i
\(703\) 5.80169 4.21518i 0.218815 0.158978i
\(704\) −0.370320 3.52336i −0.0139570 0.132792i
\(705\) 37.9868 + 14.2968i 1.43067 + 0.538447i
\(706\) 0.258350 2.45804i 0.00972314 0.0925095i
\(707\) −1.69192 2.93049i −0.0636311 0.110212i
\(708\) 6.10243 6.53205i 0.229344 0.245490i
\(709\) 21.8201 + 24.2336i 0.819470 + 0.910114i 0.997262 0.0739544i \(-0.0235619\pi\)
−0.177792 + 0.984068i \(0.556895\pi\)
\(710\) −4.32051 + 2.33883i −0.162146 + 0.0877747i
\(711\) 20.5076 13.7780i 0.769095 0.516714i
\(712\) 1.05446 3.24530i 0.0395177 0.121623i
\(713\) −30.7944 34.2006i −1.15326 1.28082i
\(714\) 0.186743 0.540731i 0.00698868 0.0202364i
\(715\) −7.02181 + 0.543764i −0.262601 + 0.0203356i
\(716\) −24.3949 + 5.18529i −0.911680 + 0.193784i
\(717\) −3.57083 11.7180i −0.133355 0.437618i
\(718\) −4.18362 + 7.24625i −0.156131 + 0.270428i
\(719\) 15.2873 + 11.1069i 0.570121 + 0.414217i 0.835149 0.550024i \(-0.185381\pi\)
−0.265028 + 0.964241i \(0.585381\pi\)
\(720\) −1.81263 + 6.45867i −0.0675529 + 0.240700i
\(721\) −19.0752 + 13.8589i −0.710397 + 0.516133i
\(722\) −1.92723 18.3363i −0.0717240 0.682408i
\(723\) −28.9420 + 5.59824i −1.07636 + 0.208201i
\(724\) 2.01933 + 3.49758i 0.0750477 + 0.129986i
\(725\) −6.04210 22.7779i −0.224398 0.845951i
\(726\) −2.47418 + 1.04755i −0.0918254 + 0.0388783i
\(727\) −0.115132 0.0244722i −0.00427003 0.000907622i 0.205776 0.978599i \(-0.434028\pi\)
−0.210046 + 0.977691i \(0.567361\pi\)
\(728\) 1.65541 1.20273i 0.0613537 0.0445761i
\(729\) 26.8362 + 2.96980i 0.993932 + 0.109993i
\(730\) 1.93370 + 10.5068i 0.0715693 + 0.388876i
\(731\) 0.817877 0.364142i 0.0302503 0.0134683i
\(732\) −6.37154 + 2.69767i −0.235499 + 0.0997089i
\(733\) −4.21537 + 40.1066i −0.155698 + 1.48137i 0.585822 + 0.810440i \(0.300772\pi\)
−0.741520 + 0.670931i \(0.765895\pi\)
\(734\) 9.78503 2.07987i 0.361172 0.0767695i
\(735\) 6.58287 0.388284i 0.242813 0.0143221i
\(736\) −6.26373 1.33140i −0.230884 0.0490760i
\(737\) 2.95641 9.09890i 0.108901 0.335162i
\(738\) 10.0902 + 19.0611i 0.371426 + 0.701649i
\(739\) 4.10221 + 12.6253i 0.150902 + 0.464430i 0.997723 0.0674492i \(-0.0214861\pi\)
−0.846820 + 0.531879i \(0.821486\pi\)
\(740\) 13.0352 16.9437i 0.479182 0.622862i
\(741\) −0.946771 + 0.661645i −0.0347805 + 0.0243061i
\(742\) −3.22248 + 30.6599i −0.118301 + 1.12556i
\(743\) 14.9471 + 25.8891i 0.548355 + 0.949779i 0.998387 + 0.0567670i \(0.0180792\pi\)
−0.450032 + 0.893012i \(0.648587\pi\)
\(744\) −3.62848 11.9072i −0.133027 0.436540i
\(745\) 30.2717 + 44.1642i 1.10907 + 1.61805i
\(746\) 13.3022 9.66464i 0.487030 0.353848i
\(747\) 1.40422 + 1.10124i 0.0513776 + 0.0402924i
\(748\) −0.157103 0.483513i −0.00574425 0.0176790i
\(749\) −15.7508 + 27.2812i −0.575522 + 0.996834i
\(750\) 9.61452 16.8096i 0.351073 0.613798i
\(751\) 0.305271 + 0.528746i 0.0111395 + 0.0192942i 0.871541 0.490322i \(-0.163121\pi\)
−0.860402 + 0.509616i \(0.829787\pi\)
\(752\) −7.01236 + 7.78802i −0.255715 + 0.284000i
\(753\) 0.996330 1.65474i 0.0363083 0.0603019i
\(754\) 0.437990 + 4.16719i 0.0159506 + 0.151760i
\(755\) −13.8043 + 28.8481i −0.502390 + 1.04989i
\(756\) −10.0479 + 6.48600i −0.365439 + 0.235894i
\(757\) −9.57801 −0.348119 −0.174059 0.984735i \(-0.555688\pi\)
−0.174059 + 0.984735i \(0.555688\pi\)
\(758\) 18.9987 8.45877i 0.690064 0.307236i
\(759\) 3.38889 + 39.1482i 0.123009 + 1.42099i
\(760\) 0.639925 + 1.55041i 0.0232125 + 0.0562394i
\(761\) −17.9122 + 19.8935i −0.649316 + 0.721138i −0.974469 0.224523i \(-0.927918\pi\)
0.325153 + 0.945661i \(0.394584\pi\)
\(762\) 5.16367 + 2.41362i 0.187060 + 0.0874363i
\(763\) 20.0687 + 22.2885i 0.726535 + 0.806899i
\(764\) 4.87068 + 14.9904i 0.176215 + 0.542334i
\(765\) −0.0617335 + 0.960660i −0.00223198 + 0.0347327i
\(766\) 0.806073 2.48084i 0.0291246 0.0896363i
\(767\) 4.19163 1.86623i 0.151351 0.0673858i
\(768\) −1.38232 1.04364i −0.0498802 0.0376591i
\(769\) 2.80115 26.6511i 0.101012 0.961064i −0.820220 0.572049i \(-0.806149\pi\)
0.921231 0.389015i \(-0.127185\pi\)
\(770\) −13.8793 + 11.8240i −0.500176 + 0.426106i
\(771\) −31.3317 0.575605i −1.12838 0.0207299i
\(772\) −2.52869 24.0589i −0.0910096 0.865899i
\(773\) −13.9242 42.8542i −0.500818 1.54136i −0.807689 0.589609i \(-0.799282\pi\)
0.306871 0.951751i \(-0.400718\pi\)
\(774\) −18.1520 4.56115i −0.652462 0.163947i
\(775\) 1.79057 + 35.8891i 0.0643190 + 1.28917i
\(776\) −8.03641 + 13.9195i −0.288490 + 0.499680i
\(777\) 37.4187 7.23789i 1.34239 0.259658i
\(778\) 11.9030 + 5.29954i 0.426742 + 0.189998i
\(779\) 4.92631 + 2.19334i 0.176503 + 0.0785844i
\(780\) −2.14930 + 2.69004i −0.0769573 + 0.0963187i
\(781\) −7.11097 + 3.16601i −0.254451 + 0.113289i
\(782\) −0.918940 −0.0328612
\(783\) −1.21451 24.4600i −0.0434029 0.874130i
\(784\) −0.526146 + 1.61931i −0.0187909 + 0.0578325i
\(785\) −18.5426 27.0523i −0.661815 0.965540i
\(786\) −8.15253 9.39578i −0.290791 0.335136i
\(787\) −12.6186 + 2.68216i −0.449804 + 0.0956088i −0.427243 0.904137i \(-0.640515\pi\)
−0.0225607 + 0.999745i \(0.507182\pi\)
\(788\) −0.731940 + 0.155579i −0.0260743 + 0.00554226i
\(789\) −52.9636 + 10.2447i −1.88555 + 0.364722i
\(790\) 0.505144 18.4080i 0.0179722 0.654926i
\(791\) 12.1833 37.4965i 0.433190 1.33322i
\(792\) −3.65339 + 9.98067i −0.129817 + 0.354648i
\(793\) −3.55148 −0.126117
\(794\) −14.4510 + 6.43401i −0.512848 + 0.228335i
\(795\) −8.45104 51.1837i −0.299727 1.81530i
\(796\) −8.36939 3.72629i −0.296645 0.132075i
\(797\) −28.6240 12.7442i −1.01392 0.451424i −0.168596 0.985685i \(-0.553923\pi\)
−0.845319 + 0.534261i \(0.820590\pi\)
\(798\) −0.976130 + 2.82648i −0.0345546 + 0.100056i
\(799\) −0.751938 + 1.30239i −0.0266016 + 0.0460754i
\(800\) 3.13684 + 3.89361i 0.110904 + 0.137660i
\(801\) −7.12466 + 7.35080i −0.251737 + 0.259728i
\(802\) 3.70547 + 11.4043i 0.130845 + 0.402698i
\(803\) 1.76929 + 16.8336i 0.0624368 + 0.594046i
\(804\) −2.26388 4.09298i −0.0798408 0.144348i
\(805\) 12.5738 + 30.4638i 0.443167 + 1.07371i
\(806\) 0.667861 6.35427i 0.0235244 0.223820i
\(807\) −21.9130 + 9.27782i −0.771373 + 0.326595i
\(808\) −1.34310 + 0.597988i −0.0472502 + 0.0210372i
\(809\) 12.4929 38.4491i 0.439226 1.35180i −0.449467 0.893297i \(-0.648386\pi\)
0.888693 0.458502i \(-0.151614\pi\)
\(810\) 13.4089 15.0067i 0.471142 0.527281i
\(811\) −16.6685 51.3005i −0.585311 1.80140i −0.598017 0.801483i \(-0.704045\pi\)
0.0127062 0.999919i \(-0.495955\pi\)
\(812\) 7.25855 + 8.06144i 0.254725 + 0.282901i
\(813\) −2.33647 26.9907i −0.0819435 0.946605i
\(814\) 22.6636 25.1705i 0.794359 0.882225i
\(815\) −1.79228 + 7.42435i −0.0627810 + 0.260064i
\(816\) −0.225169 0.105249i −0.00788250 0.00368446i
\(817\) −4.27515 + 1.90342i −0.149569 + 0.0665922i
\(818\) 14.4462 0.505100
\(819\) −6.04730 + 1.05488i −0.211310 + 0.0368606i
\(820\) 15.9350 + 2.11822i 0.556473 + 0.0739715i
\(821\) 5.46918 + 52.0358i 0.190876 + 1.81606i 0.501091 + 0.865394i \(0.332932\pi\)
−0.310216 + 0.950666i \(0.600401\pi\)
\(822\) 20.6826 + 0.379967i 0.721388 + 0.0132529i
\(823\) −3.54188 + 3.93366i −0.123462 + 0.137119i −0.801707 0.597718i \(-0.796074\pi\)
0.678244 + 0.734836i \(0.262741\pi\)
\(824\) 5.12214 + 8.87180i 0.178438 + 0.309064i
\(825\) 17.2438 25.3770i 0.600352 0.883515i
\(826\) 5.93926 10.2871i 0.206653 0.357934i
\(827\) 9.10911 + 28.0350i 0.316755 + 0.974871i 0.975026 + 0.222090i \(0.0712880\pi\)
−0.658271 + 0.752781i \(0.728712\pi\)
\(828\) 15.1168 + 11.8552i 0.525345 + 0.411996i
\(829\) −17.9280 + 13.0254i −0.622664 + 0.452392i −0.853851 0.520518i \(-0.825739\pi\)
0.231187 + 0.972909i \(0.425739\pi\)
\(830\) 1.27581 0.376172i 0.0442841 0.0130571i
\(831\) 23.1033 24.7298i 0.801444 0.857867i
\(832\) −0.444518 0.769928i −0.0154109 0.0266925i
\(833\) −0.0255398 + 0.242995i −0.000884901 + 0.00841927i
\(834\) 1.64672 + 19.0227i 0.0570211 + 0.658703i
\(835\) −0.689518 + 25.1268i −0.0238618 + 0.869548i
\(836\) 0.821198 + 2.52739i 0.0284017 + 0.0874115i
\(837\) −5.94313 + 36.8674i −0.205425 + 1.27433i
\(838\) 5.93180 18.2562i 0.204911 0.630651i
\(839\) −24.6945 5.24898i −0.852548 0.181215i −0.239144 0.970984i \(-0.576867\pi\)
−0.613404 + 0.789769i \(0.710200\pi\)
\(840\) −0.408156 + 8.90470i −0.0140827 + 0.307241i
\(841\) 6.63808 1.41097i 0.228899 0.0486541i
\(842\) −1.90411 + 18.1164i −0.0656199 + 0.624332i
\(843\) −2.37545 + 19.2011i −0.0818150 + 0.661321i
\(844\) −6.36979 + 2.83601i −0.219257 + 0.0976196i
\(845\) 24.0094 12.9970i 0.825948 0.447112i
\(846\) 29.1717 11.7240i 1.00294 0.403079i
\(847\) −2.88844 + 2.09857i −0.0992478 + 0.0721078i
\(848\) 13.1018 + 2.78487i 0.449918 + 0.0956330i
\(849\) −8.97090 6.77295i −0.307880 0.232447i
\(850\) 0.556476 + 0.452942i 0.0190870 + 0.0155358i
\(851\) −30.6107 53.0193i −1.04932 1.81748i
\(852\) −1.24226 + 3.59707i −0.0425591 + 0.123234i
\(853\) −3.53198 33.6045i −0.120933 1.15060i −0.871703 0.490034i \(-0.836984\pi\)
0.750771 0.660563i \(-0.229682\pi\)
\(854\) −7.43835 + 5.40428i −0.254535 + 0.184931i
\(855\) 0.322689 5.02150i 0.0110357 0.171732i
\(856\) 11.0729 + 8.04493i 0.378464 + 0.274970i
\(857\) 7.36964 12.7646i 0.251742 0.436030i −0.712263 0.701912i \(-0.752330\pi\)
0.964006 + 0.265882i \(0.0856632\pi\)
\(858\) −3.72420 + 3.98639i −0.127142 + 0.136093i
\(859\) −22.0644 + 4.68993i −0.752827 + 0.160018i −0.568314 0.822812i \(-0.692404\pi\)
−0.184513 + 0.982830i \(0.559071\pi\)
\(860\) −10.6193 + 9.04669i −0.362114 + 0.308490i
\(861\) 18.7821 + 21.6464i 0.640093 + 0.737706i
\(862\) 7.05649 + 7.83702i 0.240345 + 0.266930i
\(863\) −17.5309 + 53.9545i −0.596758 + 1.83663i −0.0509870 + 0.998699i \(0.516237\pi\)
−0.545771 + 0.837934i \(0.683763\pi\)
\(864\) 2.34627 + 4.63627i 0.0798218 + 0.157729i
\(865\) 3.75242 + 0.498806i 0.127586 + 0.0169599i
\(866\) 9.26230 + 10.2868i 0.314746 + 0.349560i
\(867\) 28.6494 + 6.64187i 0.972984 + 0.225570i
\(868\) −8.27050 14.3249i −0.280719 0.486219i
\(869\) 3.04973 29.0163i 0.103455 0.984309i
\(870\) −15.3738 9.84120i −0.521222 0.333648i
\(871\) −0.250954 2.38766i −0.00850324 0.0809029i
\(872\) 10.5423 7.65944i 0.357008 0.259381i
\(873\) 40.0242 26.8901i 1.35462 0.910093i
\(874\) 4.80342 0.162478
\(875\) 7.40129 24.6453i 0.250209 0.833163i
\(876\) 6.60434 + 4.98622i 0.223140 + 0.168469i
\(877\) 5.59021 6.20856i 0.188768 0.209648i −0.641331 0.767265i \(-0.721617\pi\)
0.830099 + 0.557616i \(0.188284\pi\)
\(878\) −3.33922 1.48672i −0.112693 0.0501743i
\(879\) −58.0079 1.06568i −1.95656 0.0359446i
\(880\) 4.47881 + 6.53425i 0.150980 + 0.220270i
\(881\) −18.2764 13.2786i −0.615749 0.447368i 0.235685 0.971830i \(-0.424267\pi\)
−0.851434 + 0.524462i \(0.824267\pi\)
\(882\) 3.55499 3.66783i 0.119703 0.123502i
\(883\) 30.7392 + 22.3333i 1.03446 + 0.751576i 0.969196 0.246292i \(-0.0792123\pi\)
0.0652600 + 0.997868i \(0.479212\pi\)
\(884\) −0.0853668 0.0948094i −0.00287120 0.00318879i
\(885\) −5.04670 + 19.3408i −0.169643 + 0.650135i
\(886\) −18.8939 + 20.9839i −0.634754 + 0.704966i
\(887\) 20.9806 4.45957i 0.704460 0.149738i 0.158266 0.987396i \(-0.449410\pi\)
0.546194 + 0.837659i \(0.316076\pi\)
\(888\) −1.42811 16.4974i −0.0479241 0.553615i
\(889\) 7.40870 + 1.57477i 0.248480 + 0.0528160i
\(890\) 1.38107 + 7.50414i 0.0462937 + 0.251539i
\(891\) 23.0171 22.0650i 0.771102 0.739204i
\(892\) −13.1674 9.56666i −0.440876 0.320316i
\(893\) 3.93048 6.80779i 0.131528 0.227814i
\(894\) 40.4027 + 9.36668i 1.35127 + 0.313269i
\(895\) 42.4512 36.1647i 1.41899 1.20885i
\(896\) −2.10261 0.936144i −0.0702434 0.0312744i
\(897\) 4.77267 + 8.62876i 0.159355 + 0.288106i
\(898\) 34.8429 + 7.40608i 1.16272 + 0.247144i
\(899\) 33.8721 1.12970
\(900\) −3.31078 14.6301i −0.110359 0.487669i
\(901\) 1.92214 0.0640358
\(902\) 24.9125 + 5.29531i 0.829495 + 0.176315i
\(903\) −24.8666 0.456832i −0.827508 0.0152024i
\(904\) −15.6489 6.96736i −0.520476 0.231731i
\(905\) −7.69402 4.72819i −0.255758 0.157170i
\(906\) 7.22099 + 23.6964i 0.239901 + 0.787260i
\(907\) 2.41580 4.18429i 0.0802154 0.138937i −0.823127 0.567857i \(-0.807773\pi\)
0.903342 + 0.428920i \(0.141106\pi\)
\(908\) 1.52520 + 1.10812i 0.0506154 + 0.0367743i
\(909\) 4.40765 + 0.162004i 0.146193 + 0.00537332i
\(910\) −1.97496 + 4.12726i −0.0654694 + 0.136817i
\(911\) −29.2159 6.21004i −0.967967 0.205748i −0.303307 0.952893i \(-0.598091\pi\)
−0.664661 + 0.747145i \(0.731424\pi\)
\(912\) 1.17699 + 0.550153i 0.0389740 + 0.0182174i
\(913\) 2.06135 0.438153i 0.0682207 0.0145007i
\(914\) −11.1418 + 12.3743i −0.368540 + 0.409305i
\(915\) 9.65755 12.0873i 0.319269 0.399592i
\(916\) −1.33576 1.48351i −0.0441346 0.0490165i
\(917\) −13.3732 9.71617i −0.441621 0.320856i
\(918\) 0.467664 + 0.580773i 0.0154352 + 0.0191684i
\(919\) −15.7982 11.4780i −0.521134 0.378626i 0.295897 0.955220i \(-0.404381\pi\)
−0.817031 + 0.576594i \(0.804381\pi\)
\(920\) 13.7345 4.04960i 0.452812 0.133511i
\(921\) 27.3178 45.3703i 0.900153 1.49500i
\(922\) 26.3392 + 11.7270i 0.867436 + 0.386208i
\(923\) −1.30703 + 1.45161i −0.0430215 + 0.0477802i
\(924\) −1.73403 + 14.0164i −0.0570452 + 0.461104i
\(925\) −7.59632 + 47.1944i −0.249765 + 1.55174i
\(926\) 38.3821 1.26131
\(927\) −2.08765 30.6618i −0.0685673 1.00707i
\(928\) 3.81300 2.77031i 0.125168 0.0909399i
\(929\) 1.92126 + 18.2796i 0.0630346 + 0.599734i 0.979754 + 0.200203i \(0.0641603\pi\)
−0.916720 + 0.399531i \(0.869173\pi\)
\(930\) 19.8103 + 19.5522i 0.649606 + 0.641143i
\(931\) 0.133500 1.27017i 0.00437528 0.0416280i
\(932\) 2.50992 + 4.34731i 0.0822152 + 0.142401i
\(933\) 13.3019 + 43.6516i 0.435485 + 1.42909i
\(934\) 26.2452 + 29.1483i 0.858770 + 0.953760i
\(935\) 0.823628 + 0.783560i 0.0269355 + 0.0256252i
\(936\) 0.181174 + 2.66095i 0.00592185 + 0.0869758i
\(937\) 15.6629 48.2055i 0.511685 1.57480i −0.277549 0.960711i \(-0.589522\pi\)
0.789234 0.614092i \(-0.210478\pi\)
\(938\) −4.15891 4.61894i −0.135793 0.150814i
\(939\) −25.5487 + 4.94188i −0.833750 + 0.161272i
\(940\) 5.49904 22.7792i 0.179359 0.742976i
\(941\) 23.8456 5.06855i 0.777346 0.165230i 0.197880 0.980226i \(-0.436594\pi\)
0.579466 + 0.814996i \(0.303261\pi\)
\(942\) −24.7483 5.73747i −0.806342 0.186937i
\(943\) 23.0180 39.8684i 0.749570 1.29829i
\(944\) −4.17533 3.03355i −0.135895 0.0987338i
\(945\) 12.8542 23.4502i 0.418148 0.762835i
\(946\) −17.8813 + 12.9916i −0.581372 + 0.422392i
\(947\) 0.494368 + 4.70360i 0.0160648 + 0.152846i 0.999614 0.0277962i \(-0.00884895\pi\)
−0.983549 + 0.180643i \(0.942182\pi\)
\(948\) −9.34823 10.7738i −0.303616 0.349918i
\(949\) 2.12378 + 3.67850i 0.0689409 + 0.119409i
\(950\) −2.90877 2.36759i −0.0943731 0.0768147i
\(951\) 2.68103 21.6711i 0.0869384 0.702734i
\(952\) −0.323067 0.0686700i −0.0104707 0.00222561i
\(953\) 35.7864 26.0004i 1.15924 0.842234i 0.169555 0.985521i \(-0.445767\pi\)
0.989681 + 0.143286i \(0.0457670\pi\)
\(954\) −31.6197 24.7974i −1.02372 0.802846i
\(955\) −25.5351 24.2928i −0.826295 0.786098i
\(956\) −6.46111 + 2.87667i −0.208967 + 0.0930382i
\(957\) −23.0814 17.4262i −0.746115 0.563311i
\(958\) −2.96286 + 28.1897i −0.0957257 + 0.910769i
\(959\) 26.8876 5.71513i 0.868245 0.184551i
\(960\) 3.82919 + 0.580777i 0.123587 + 0.0187445i
\(961\) −20.1980 4.29322i −0.651549 0.138491i
\(962\) 2.62650 8.08352i 0.0846816 0.260623i
\(963\) −19.2103 36.2896i −0.619044 1.16942i
\(964\) 5.25928 + 16.1864i 0.169390 + 0.521329i
\(965\) 30.5830 + 44.6184i 0.984502 + 1.43632i
\(966\) 23.1264 + 10.8098i 0.744081 + 0.347801i
\(967\) 4.23947 40.3359i 0.136332 1.29711i −0.685788 0.727801i \(-0.740542\pi\)
0.822121 0.569313i \(-0.192791\pi\)
\(968\) 0.775614 + 1.34340i 0.0249292 + 0.0431786i
\(969\) 0.181624 + 0.0421065i 0.00583460 + 0.00135265i
\(970\) 0.985877 35.9264i 0.0316546 1.15353i
\(971\) −35.6294 + 25.8863i −1.14340 + 0.830731i −0.987590 0.157056i \(-0.949800\pi\)
−0.155813 + 0.987787i \(0.549800\pi\)
\(972\) −0.200671 15.5872i −0.00643652 0.499959i
\(973\) 7.84052 + 24.1307i 0.251356 + 0.773593i
\(974\) −10.2009 + 17.6685i −0.326858 + 0.566134i
\(975\) 1.36293 7.57769i 0.0436487 0.242680i
\(976\) 1.99737 + 3.45955i 0.0639344 + 0.110738i
\(977\) −10.5095 + 11.6720i −0.336230 + 0.373421i −0.887422 0.460957i \(-0.847506\pi\)
0.551193 + 0.834378i \(0.314173\pi\)
\(978\) 2.86343 + 5.17694i 0.0915624 + 0.165540i
\(979\) 1.26365 + 12.0228i 0.0403864 + 0.384251i
\(980\) −0.689115 3.74434i −0.0220130 0.119609i
\(981\) −38.5115 + 6.71790i −1.22958 + 0.214486i
\(982\) 7.27698 0.232218
\(983\) 35.4414 15.7795i 1.13041 0.503289i 0.245657 0.969357i \(-0.420996\pi\)
0.884749 + 0.466067i \(0.154330\pi\)
\(984\) 10.2064 7.13268i 0.325368 0.227382i
\(985\) 1.27370 1.08508i 0.0405834 0.0345735i
\(986\) 0.452563 0.502622i 0.0144125 0.0160067i
\(987\) 34.2442 23.9313i 1.09000 0.761742i
\(988\) 0.446224 + 0.495582i 0.0141963 + 0.0157666i
\(989\) 12.3455 + 37.9957i 0.392566 + 1.20819i
\(990\) −3.44022 23.5153i −0.109337 0.747366i
\(991\) 15.7730 48.5443i 0.501046 1.54206i −0.306273 0.951944i \(-0.599082\pi\)
0.807318 0.590116i \(-0.200918\pi\)
\(992\) −6.56541 + 2.92311i −0.208452 + 0.0928089i
\(993\) 0.722045 5.83639i 0.0229134 0.185212i
\(994\) −0.528591 + 5.02921i −0.0167659 + 0.159517i
\(995\) 20.4245 1.58166i 0.647499 0.0501419i
\(996\) 0.531453 0.882655i 0.0168397 0.0279680i
\(997\) 5.96746 + 56.7766i 0.188991 + 1.79813i 0.519646 + 0.854381i \(0.326064\pi\)
−0.330655 + 0.943752i \(0.607270\pi\)
\(998\) −2.67765 8.24096i −0.0847595 0.260863i
\(999\) −17.9301 + 46.3285i −0.567282 + 1.46577i
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 450.2.q.c.331.6 yes 120
9.4 even 3 inner 450.2.q.c.31.2 120
25.21 even 5 inner 450.2.q.c.421.2 yes 120
225.121 even 15 inner 450.2.q.c.121.6 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
450.2.q.c.31.2 120 9.4 even 3 inner
450.2.q.c.121.6 yes 120 225.121 even 15 inner
450.2.q.c.331.6 yes 120 1.1 even 1 trivial
450.2.q.c.421.2 yes 120 25.21 even 5 inner