Properties

Label 225.2.q.a.31.2
Level $225$
Weight $2$
Character 225.31
Analytic conductor $1.797$
Analytic rank $0$
Dimension $224$
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] = [225,2,Mod(16,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.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: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(28\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 31.2
Character \(\chi\) \(=\) 225.31
Dual form 225.2.q.a.196.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.66247 + 1.84635i) q^{2} +(1.70628 - 0.297695i) q^{3} +(-0.436178 - 4.14996i) q^{4} +(1.32553 + 1.80083i) q^{5} +(-2.28697 + 3.64530i) q^{6} +(-0.644527 - 1.11635i) q^{7} +(4.36740 + 3.17310i) q^{8} +(2.82275 - 1.01590i) q^{9} +O(q^{10})\) \(q+(-1.66247 + 1.84635i) q^{2} +(1.70628 - 0.297695i) q^{3} +(-0.436178 - 4.14996i) q^{4} +(1.32553 + 1.80083i) q^{5} +(-2.28697 + 3.64530i) q^{6} +(-0.644527 - 1.11635i) q^{7} +(4.36740 + 3.17310i) q^{8} +(2.82275 - 1.01590i) q^{9} +(-5.52861 - 0.546422i) q^{10} +(-0.343631 + 0.381641i) q^{11} +(-1.97966 - 6.95113i) q^{12} +(3.33655 + 3.70562i) q^{13} +(3.13269 + 0.665873i) q^{14} +(2.79781 + 2.67811i) q^{15} +(-4.95605 + 1.05344i) q^{16} +(5.60571 + 4.07278i) q^{17} +(-2.81702 + 6.90071i) q^{18} +(-4.21905 - 3.06532i) q^{19} +(6.89520 - 6.28636i) q^{20} +(-1.43207 - 1.71293i) q^{21} +(-0.133370 - 1.26893i) q^{22} +(-4.07593 - 0.866366i) q^{23} +(8.39660 + 4.11403i) q^{24} +(-1.48596 + 4.77409i) q^{25} -12.3888 q^{26} +(4.51397 - 2.57373i) q^{27} +(-4.35169 + 3.16169i) q^{28} +(-6.33037 - 2.81846i) q^{29} +(-9.59600 + 0.713494i) q^{30} +(-1.40416 + 0.625171i) q^{31} +(0.895838 - 1.55164i) q^{32} +(-0.472716 + 0.753482i) q^{33} +(-16.8391 + 3.57926i) q^{34} +(1.15602 - 2.64044i) q^{35} +(-5.44717 - 11.2712i) q^{36} +(2.27325 - 6.99635i) q^{37} +(12.6737 - 2.69388i) q^{38} +(6.79622 + 5.32953i) q^{39} +(0.0748925 + 12.0710i) q^{40} +(2.72638 + 3.02795i) q^{41} +(5.54346 + 0.203577i) q^{42} +(2.08364 + 3.60897i) q^{43} +(1.73368 + 1.25959i) q^{44} +(5.57110 + 3.73669i) q^{45} +(8.37572 - 6.08531i) q^{46} +(-7.35774 - 3.27588i) q^{47} +(-8.14279 + 3.27286i) q^{48} +(2.66917 - 4.62314i) q^{49} +(-6.34430 - 10.6804i) q^{50} +(10.7773 + 5.28050i) q^{51} +(13.9228 - 15.4629i) q^{52} +(2.21350 - 1.60820i) q^{53} +(-2.75230 + 12.6131i) q^{54} +(-1.14276 - 0.112945i) q^{55} +(0.727395 - 6.92070i) q^{56} +(-8.11140 - 3.97429i) q^{57} +(15.7279 - 7.00251i) q^{58} +(-2.04720 - 2.27364i) q^{59} +(9.89368 - 12.7789i) q^{60} +(4.90975 - 5.45283i) q^{61} +(1.18008 - 3.63190i) q^{62} +(-2.95344 - 2.49642i) q^{63} +(-1.75586 - 5.40400i) q^{64} +(-2.25049 + 10.9204i) q^{65} +(-0.605320 - 2.12544i) q^{66} +(-0.415400 + 0.184948i) q^{67} +(14.4568 - 25.0399i) q^{68} +(-7.21258 - 0.264873i) q^{69} +(2.95334 + 6.52406i) q^{70} +(1.33759 - 0.971819i) q^{71} +(15.5516 + 4.52004i) q^{72} +(-2.72548 - 8.38816i) q^{73} +(9.13854 + 15.8284i) q^{74} +(-1.11424 + 8.58828i) q^{75} +(-10.8807 + 18.8459i) q^{76} +(0.647525 + 0.137636i) q^{77} +(-21.1387 + 3.68808i) q^{78} +(-3.14525 - 1.40036i) q^{79} +(-8.46644 - 7.52863i) q^{80} +(6.93589 - 5.73528i) q^{81} -10.1232 q^{82} +(-1.53461 + 14.6009i) q^{83} +(-6.48396 + 6.69019i) q^{84} +(0.0961272 + 15.4935i) q^{85} +(-10.1274 - 2.15265i) q^{86} +(-11.6404 - 2.92455i) q^{87} +(-2.71176 + 0.576402i) q^{88} +(-2.98202 - 9.17771i) q^{89} +(-16.1610 + 4.07410i) q^{90} +(1.98628 - 6.11314i) q^{91} +(-1.81755 + 17.2928i) q^{92} +(-2.20977 + 1.48473i) q^{93} +(18.2804 - 8.13897i) q^{94} +(-0.0723487 - 11.6610i) q^{95} +(1.06663 - 2.91421i) q^{96} +(7.36689 + 3.27995i) q^{97} +(4.09855 + 12.6140i) q^{98} +(-0.582277 + 1.42637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.66247 + 1.84635i −1.17554 + 1.30557i −0.232614 + 0.972569i \(0.574728\pi\)
−0.942926 + 0.333001i \(0.891939\pi\)
\(3\) 1.70628 0.297695i 0.985119 0.171875i
\(4\) −0.436178 4.14996i −0.218089 2.07498i
\(5\) 1.32553 + 1.80083i 0.592793 + 0.805355i
\(6\) −2.28697 + 3.64530i −0.933653 + 1.48819i
\(7\) −0.644527 1.11635i −0.243608 0.421942i 0.718131 0.695908i \(-0.244998\pi\)
−0.961739 + 0.273966i \(0.911664\pi\)
\(8\) 4.36740 + 3.17310i 1.54411 + 1.12186i
\(9\) 2.82275 1.01590i 0.940918 0.338634i
\(10\) −5.52861 0.546422i −1.74830 0.172794i
\(11\) −0.343631 + 0.381641i −0.103609 + 0.115069i −0.792719 0.609588i \(-0.791335\pi\)
0.689110 + 0.724657i \(0.258002\pi\)
\(12\) −1.97966 6.95113i −0.571480 2.00662i
\(13\) 3.33655 + 3.70562i 0.925393 + 1.02775i 0.999535 + 0.0305051i \(0.00971158\pi\)
−0.0741418 + 0.997248i \(0.523622\pi\)
\(14\) 3.13269 + 0.665873i 0.837246 + 0.177962i
\(15\) 2.79781 + 2.67811i 0.722392 + 0.691484i
\(16\) −4.95605 + 1.05344i −1.23901 + 0.263360i
\(17\) 5.60571 + 4.07278i 1.35958 + 0.987795i 0.998471 + 0.0552732i \(0.0176030\pi\)
0.361113 + 0.932522i \(0.382397\pi\)
\(18\) −2.81702 + 6.90071i −0.663978 + 1.62651i
\(19\) −4.21905 3.06532i −0.967917 0.703233i −0.0129412 0.999916i \(-0.504119\pi\)
−0.954976 + 0.296683i \(0.904119\pi\)
\(20\) 6.89520 6.28636i 1.54181 1.40567i
\(21\) −1.43207 1.71293i −0.312504 0.373793i
\(22\) −0.133370 1.26893i −0.0284345 0.270537i
\(23\) −4.07593 0.866366i −0.849891 0.180650i −0.237679 0.971344i \(-0.576387\pi\)
−0.612212 + 0.790694i \(0.709720\pi\)
\(24\) 8.39660 + 4.11403i 1.71395 + 0.839773i
\(25\) −1.48596 + 4.77409i −0.297192 + 0.954818i
\(26\) −12.3888 −2.42964
\(27\) 4.51397 2.57373i 0.868714 0.495314i
\(28\) −4.35169 + 3.16169i −0.822392 + 0.597503i
\(29\) −6.33037 2.81846i −1.17552 0.523375i −0.276385 0.961047i \(-0.589137\pi\)
−0.899135 + 0.437672i \(0.855803\pi\)
\(30\) −9.59600 + 0.713494i −1.75198 + 0.130266i
\(31\) −1.40416 + 0.625171i −0.252194 + 0.112284i −0.528940 0.848659i \(-0.677410\pi\)
0.276746 + 0.960943i \(0.410744\pi\)
\(32\) 0.895838 1.55164i 0.158363 0.274293i
\(33\) −0.472716 + 0.753482i −0.0822894 + 0.131164i
\(34\) −16.8391 + 3.57926i −2.88788 + 0.613838i
\(35\) 1.15602 2.64044i 0.195403 0.446315i
\(36\) −5.44717 11.2712i −0.907862 1.87853i
\(37\) 2.27325 6.99635i 0.373720 1.15019i −0.570618 0.821216i \(-0.693296\pi\)
0.944338 0.328977i \(-0.106704\pi\)
\(38\) 12.6737 2.69388i 2.05595 0.437005i
\(39\) 6.79622 + 5.32953i 1.08827 + 0.853407i
\(40\) 0.0748925 + 12.0710i 0.0118416 + 1.90859i
\(41\) 2.72638 + 3.02795i 0.425789 + 0.472886i 0.917422 0.397916i \(-0.130267\pi\)
−0.491633 + 0.870802i \(0.663600\pi\)
\(42\) 5.54346 + 0.203577i 0.855374 + 0.0314126i
\(43\) 2.08364 + 3.60897i 0.317752 + 0.550362i 0.980019 0.198906i \(-0.0637387\pi\)
−0.662267 + 0.749268i \(0.730405\pi\)
\(44\) 1.73368 + 1.25959i 0.261362 + 0.189890i
\(45\) 5.57110 + 3.73669i 0.830490 + 0.557033i
\(46\) 8.37572 6.08531i 1.23493 0.897231i
\(47\) −7.35774 3.27588i −1.07324 0.477836i −0.207449 0.978246i \(-0.566516\pi\)
−0.865789 + 0.500410i \(0.833183\pi\)
\(48\) −8.14279 + 3.27286i −1.17531 + 0.472396i
\(49\) 2.66917 4.62314i 0.381310 0.660448i
\(50\) −6.34430 10.6804i −0.897220 1.51043i
\(51\) 10.7773 + 5.28050i 1.50913 + 0.739418i
\(52\) 13.9228 15.4629i 1.93075 2.14431i
\(53\) 2.21350 1.60820i 0.304047 0.220903i −0.425291 0.905057i \(-0.639828\pi\)
0.729338 + 0.684153i \(0.239828\pi\)
\(54\) −2.75230 + 12.6131i −0.374541 + 1.71643i
\(55\) −1.14276 0.112945i −0.154090 0.0152295i
\(56\) 0.727395 6.92070i 0.0972023 0.924818i
\(57\) −8.11140 3.97429i −1.07438 0.526408i
\(58\) 15.7279 7.00251i 2.06517 0.919475i
\(59\) −2.04720 2.27364i −0.266522 0.296003i 0.594997 0.803728i \(-0.297153\pi\)
−0.861519 + 0.507725i \(0.830487\pi\)
\(60\) 9.89368 12.7789i 1.27727 1.64975i
\(61\) 4.90975 5.45283i 0.628630 0.698164i −0.341739 0.939795i \(-0.611016\pi\)
0.970368 + 0.241631i \(0.0776824\pi\)
\(62\) 1.18008 3.63190i 0.149870 0.461251i
\(63\) −2.95344 2.49642i −0.372099 0.314519i
\(64\) −1.75586 5.40400i −0.219483 0.675499i
\(65\) −2.25049 + 10.9204i −0.279139 + 1.35451i
\(66\) −0.605320 2.12544i −0.0745098 0.261624i
\(67\) −0.415400 + 0.184948i −0.0507492 + 0.0225950i −0.431954 0.901895i \(-0.642176\pi\)
0.381205 + 0.924490i \(0.375509\pi\)
\(68\) 14.4568 25.0399i 1.75314 3.03654i
\(69\) −7.21258 0.264873i −0.868292 0.0318870i
\(70\) 2.95334 + 6.52406i 0.352991 + 0.779775i
\(71\) 1.33759 0.971819i 0.158743 0.115334i −0.505578 0.862781i \(-0.668721\pi\)
0.664321 + 0.747447i \(0.268721\pi\)
\(72\) 15.5516 + 4.52004i 1.83278 + 0.532692i
\(73\) −2.72548 8.38816i −0.318993 0.981760i −0.974079 0.226206i \(-0.927368\pi\)
0.655086 0.755554i \(-0.272632\pi\)
\(74\) 9.13854 + 15.8284i 1.06233 + 1.84002i
\(75\) −1.11424 + 8.58828i −0.128661 + 0.991689i
\(76\) −10.8807 + 18.8459i −1.24810 + 2.16178i
\(77\) 0.647525 + 0.137636i 0.0737923 + 0.0156850i
\(78\) −21.1387 + 3.68808i −2.39348 + 0.417593i
\(79\) −3.14525 1.40036i −0.353869 0.157553i 0.222101 0.975024i \(-0.428709\pi\)
−0.575969 + 0.817471i \(0.695375\pi\)
\(80\) −8.46644 7.52863i −0.946577 0.841727i
\(81\) 6.93589 5.73528i 0.770654 0.637253i
\(82\) −10.1232 −1.11792
\(83\) −1.53461 + 14.6009i −0.168446 + 1.60265i 0.504802 + 0.863235i \(0.331566\pi\)
−0.673247 + 0.739417i \(0.735101\pi\)
\(84\) −6.48396 + 6.69019i −0.707458 + 0.729960i
\(85\) 0.0961272 + 15.4935i 0.0104265 + 1.68051i
\(86\) −10.1274 2.15265i −1.09207 0.232126i
\(87\) −11.6404 2.92455i −1.24798 0.313545i
\(88\) −2.71176 + 0.576402i −0.289074 + 0.0614446i
\(89\) −2.98202 9.17771i −0.316093 0.972835i −0.975302 0.220875i \(-0.929109\pi\)
0.659209 0.751960i \(-0.270891\pi\)
\(90\) −16.1610 + 4.07410i −1.70352 + 0.429448i
\(91\) 1.98628 6.11314i 0.208219 0.640831i
\(92\) −1.81755 + 17.2928i −0.189493 + 1.80290i
\(93\) −2.20977 + 1.48473i −0.229142 + 0.153959i
\(94\) 18.2804 8.13897i 1.88548 0.839471i
\(95\) −0.0723487 11.6610i −0.00742282 1.19639i
\(96\) 1.06663 2.91421i 0.108863 0.297430i
\(97\) 7.36689 + 3.27995i 0.747994 + 0.333028i 0.745087 0.666967i \(-0.232408\pi\)
0.00290713 + 0.999996i \(0.499075\pi\)
\(98\) 4.09855 + 12.6140i 0.414016 + 1.27421i
\(99\) −0.582277 + 1.42637i −0.0585210 + 0.143356i
\(100\) 20.4604 + 4.08432i 2.04604 + 0.408432i
\(101\) −7.80298 13.5152i −0.776425 1.34481i −0.933990 0.357299i \(-0.883698\pi\)
0.157565 0.987509i \(-0.449636\pi\)
\(102\) −27.6666 + 11.1201i −2.73940 + 1.10106i
\(103\) −1.58857 15.1142i −0.156526 1.48925i −0.737512 0.675334i \(-0.764000\pi\)
0.580986 0.813913i \(-0.302667\pi\)
\(104\) 2.81376 + 26.7711i 0.275912 + 2.62512i
\(105\) 1.18645 4.84946i 0.115785 0.473258i
\(106\) −0.710555 + 6.76048i −0.0690152 + 0.656636i
\(107\) −10.6981 −1.03422 −0.517111 0.855919i \(-0.672992\pi\)
−0.517111 + 0.855919i \(0.672992\pi\)
\(108\) −12.6498 17.6102i −1.21722 1.69454i
\(109\) −4.10780 + 12.6425i −0.393456 + 1.21093i 0.536702 + 0.843772i \(0.319670\pi\)
−0.930158 + 0.367160i \(0.880330\pi\)
\(110\) 2.10834 1.92217i 0.201022 0.183272i
\(111\) 1.79601 12.6144i 0.170470 1.19731i
\(112\) 4.37032 + 4.85373i 0.412956 + 0.458635i
\(113\) −6.37245 7.07732i −0.599470 0.665778i 0.364681 0.931132i \(-0.381178\pi\)
−0.964151 + 0.265354i \(0.914511\pi\)
\(114\) 20.8229 8.36940i 1.95024 0.783866i
\(115\) −3.84258 8.48844i −0.358322 0.791551i
\(116\) −8.93533 + 27.5001i −0.829625 + 2.55332i
\(117\) 13.1828 + 7.07044i 1.21875 + 0.653662i
\(118\) 7.60135 0.699761
\(119\) 0.933637 8.88297i 0.0855864 0.814300i
\(120\) 3.72126 + 20.5741i 0.339703 + 1.87815i
\(121\) 1.12225 + 10.6775i 0.102022 + 0.970678i
\(122\) 1.90557 + 18.1303i 0.172522 + 1.64144i
\(123\) 5.55336 + 4.35489i 0.500730 + 0.392667i
\(124\) 3.20690 + 5.55451i 0.287988 + 0.498810i
\(125\) −10.5670 + 3.65222i −0.945140 + 0.326664i
\(126\) 9.51927 1.30290i 0.848044 0.116072i
\(127\) 4.08839 + 12.5828i 0.362786 + 1.11654i 0.951356 + 0.308094i \(0.0996913\pi\)
−0.588570 + 0.808447i \(0.700309\pi\)
\(128\) 16.1703 + 7.19949i 1.42927 + 0.636351i
\(129\) 4.62964 + 5.53761i 0.407617 + 0.487559i
\(130\) −16.4217 22.3101i −1.44027 1.95672i
\(131\) 9.15975 4.07819i 0.800291 0.356313i 0.0345024 0.999405i \(-0.489015\pi\)
0.765789 + 0.643092i \(0.222349\pi\)
\(132\) 3.33311 + 1.63310i 0.290110 + 0.142143i
\(133\) −0.702688 + 6.68563i −0.0609308 + 0.579718i
\(134\) 0.349108 1.07445i 0.0301584 0.0928179i
\(135\) 10.6182 + 4.71734i 0.913871 + 0.406004i
\(136\) 11.5590 + 35.5749i 0.991176 + 3.05053i
\(137\) −10.3384 + 2.19749i −0.883268 + 0.187744i −0.627148 0.778900i \(-0.715778\pi\)
−0.256121 + 0.966645i \(0.582444\pi\)
\(138\) 12.4797 12.8766i 1.06234 1.09613i
\(139\) −0.581824 0.123671i −0.0493497 0.0104896i 0.183171 0.983081i \(-0.441364\pi\)
−0.232520 + 0.972592i \(0.574697\pi\)
\(140\) −11.4619 3.64574i −0.968710 0.308122i
\(141\) −13.5296 3.39919i −1.13939 0.286263i
\(142\) −0.429381 + 4.08529i −0.0360329 + 0.342830i
\(143\) −2.56076 −0.214141
\(144\) −12.9195 + 8.00847i −1.07663 + 0.667372i
\(145\) −3.31550 15.1358i −0.275338 1.25696i
\(146\) 20.0185 + 8.91283i 1.65675 + 0.737631i
\(147\) 3.17805 8.68295i 0.262122 0.716158i
\(148\) −30.0261 6.38224i −2.46813 0.524617i
\(149\) −1.01642 + 1.76049i −0.0832683 + 0.144225i −0.904652 0.426151i \(-0.859869\pi\)
0.821384 + 0.570376i \(0.193203\pi\)
\(150\) −14.0046 16.3350i −1.14347 1.33375i
\(151\) −2.10363 3.64359i −0.171191 0.296511i 0.767646 0.640874i \(-0.221428\pi\)
−0.938836 + 0.344363i \(0.888095\pi\)
\(152\) −8.69971 26.7750i −0.705640 2.17174i
\(153\) 19.9611 + 5.80163i 1.61376 + 0.469034i
\(154\) −1.33061 + 0.966746i −0.107224 + 0.0779027i
\(155\) −2.98707 1.69996i −0.239927 0.136544i
\(156\) 19.1529 30.5287i 1.53346 2.44425i
\(157\) 0.279109 0.483431i 0.0222753 0.0385820i −0.854673 0.519167i \(-0.826242\pi\)
0.876948 + 0.480585i \(0.159576\pi\)
\(158\) 7.81443 3.47921i 0.621683 0.276791i
\(159\) 3.29808 3.40298i 0.261555 0.269874i
\(160\) 3.98169 0.443485i 0.314780 0.0350606i
\(161\) 1.65988 + 5.10858i 0.130817 + 0.402612i
\(162\) −0.941316 + 22.3408i −0.0739568 + 1.75526i
\(163\) −5.35439 + 16.4791i −0.419388 + 1.29074i 0.488879 + 0.872352i \(0.337406\pi\)
−0.908267 + 0.418392i \(0.862594\pi\)
\(164\) 11.3767 12.6351i 0.888369 0.986634i
\(165\) −1.98349 + 0.147479i −0.154414 + 0.0114812i
\(166\) −24.4071 27.1069i −1.89436 2.10390i
\(167\) −5.98923 + 2.66658i −0.463461 + 0.206346i −0.625164 0.780493i \(-0.714968\pi\)
0.161703 + 0.986839i \(0.448301\pi\)
\(168\) −0.819125 12.0252i −0.0631969 0.927762i
\(169\) −1.24014 + 11.7992i −0.0953956 + 0.907628i
\(170\) −28.7663 25.5799i −2.20627 1.96189i
\(171\) −15.0234 4.36651i −1.14887 0.333915i
\(172\) 14.0682 10.2212i 1.07269 0.779357i
\(173\) −0.719368 + 0.798939i −0.0546925 + 0.0607422i −0.769870 0.638200i \(-0.779679\pi\)
0.715178 + 0.698943i \(0.246346\pi\)
\(174\) 24.7515 16.6303i 1.87641 1.26074i
\(175\) 6.28731 1.41817i 0.475276 0.107204i
\(176\) 1.30102 2.25343i 0.0980678 0.169858i
\(177\) −4.16994 3.27002i −0.313432 0.245790i
\(178\) 21.9028 + 9.75176i 1.64168 + 0.730925i
\(179\) 15.2398 11.0724i 1.13908 0.827587i 0.152085 0.988367i \(-0.451401\pi\)
0.986990 + 0.160781i \(0.0514012\pi\)
\(180\) 13.0771 24.7497i 0.974711 1.84473i
\(181\) −11.6647 8.47488i −0.867029 0.629933i 0.0627594 0.998029i \(-0.480010\pi\)
−0.929788 + 0.368096i \(0.880010\pi\)
\(182\) 7.98490 + 13.8303i 0.591880 + 1.02517i
\(183\) 6.75411 10.7656i 0.499278 0.795820i
\(184\) −15.0521 16.7171i −1.10966 1.23240i
\(185\) 15.6125 5.18011i 1.14785 0.380849i
\(186\) 0.932334 6.54832i 0.0683621 0.480146i
\(187\) −3.48064 + 0.739832i −0.254529 + 0.0541019i
\(188\) −10.3855 + 31.9632i −0.757439 + 2.33116i
\(189\) −5.78256 3.38035i −0.420620 0.245884i
\(190\) 21.6505 + 19.2523i 1.57069 + 1.39671i
\(191\) 18.1108 3.84958i 1.31046 0.278546i 0.500857 0.865530i \(-0.333018\pi\)
0.809598 + 0.586984i \(0.199685\pi\)
\(192\) −4.60473 8.69799i −0.332318 0.627724i
\(193\) −2.70053 + 4.67746i −0.194388 + 0.336691i −0.946700 0.322117i \(-0.895606\pi\)
0.752311 + 0.658808i \(0.228939\pi\)
\(194\) −18.3031 + 8.14909i −1.31409 + 0.585070i
\(195\) −0.588990 + 19.3033i −0.0421785 + 1.38233i
\(196\) −20.3501 9.06044i −1.45358 0.647174i
\(197\) −12.6037 + 9.15716i −0.897980 + 0.652421i −0.937946 0.346780i \(-0.887275\pi\)
0.0399665 + 0.999201i \(0.487275\pi\)
\(198\) −1.66558 3.44639i −0.118367 0.244924i
\(199\) −17.1285 −1.21421 −0.607104 0.794623i \(-0.707669\pi\)
−0.607104 + 0.794623i \(0.707669\pi\)
\(200\) −21.6384 + 16.1352i −1.53007 + 1.14093i
\(201\) −0.653729 + 0.439235i −0.0461105 + 0.0309812i
\(202\) 37.9260 + 8.06141i 2.66846 + 0.567199i
\(203\) 0.933693 + 8.88350i 0.0655324 + 0.623499i
\(204\) 17.2130 47.0287i 1.20515 3.29267i
\(205\) −1.83893 + 8.92336i −0.128436 + 0.623235i
\(206\) 30.5471 + 22.1938i 2.12832 + 1.54631i
\(207\) −12.3855 + 1.69520i −0.860852 + 0.117825i
\(208\) −20.4398 14.8504i −1.41724 1.02969i
\(209\) 2.61965 0.556824i 0.181205 0.0385163i
\(210\) 6.98139 + 10.2527i 0.481762 + 0.707500i
\(211\) 14.1558 + 3.00892i 0.974529 + 0.207142i 0.667543 0.744572i \(-0.267346\pi\)
0.306986 + 0.951714i \(0.400680\pi\)
\(212\) −7.63944 8.48446i −0.524679 0.582715i
\(213\) 1.99300 2.05639i 0.136558 0.140901i
\(214\) 17.7852 19.7524i 1.21577 1.35025i
\(215\) −3.73721 + 8.53606i −0.254876 + 0.582154i
\(216\) 27.8810 + 3.08278i 1.89706 + 0.209757i
\(217\) 1.60293 + 1.16460i 0.108814 + 0.0790579i
\(218\) −16.5135 28.6022i −1.11843 1.93718i
\(219\) −7.14754 13.5012i −0.482986 0.912324i
\(220\) 0.0297293 + 4.79168i 0.00200435 + 0.323055i
\(221\) 3.61156 + 34.3617i 0.242939 + 2.31141i
\(222\) 20.3049 + 24.2871i 1.36278 + 1.63005i
\(223\) −12.4797 + 13.8601i −0.835699 + 0.928138i −0.998284 0.0585563i \(-0.981350\pi\)
0.162585 + 0.986695i \(0.448017\pi\)
\(224\) −2.30957 −0.154314
\(225\) 0.655497 + 14.9857i 0.0436998 + 0.999045i
\(226\) 23.6612 1.57392
\(227\) 11.3804 12.6392i 0.755341 0.838891i −0.235787 0.971805i \(-0.575767\pi\)
0.991128 + 0.132914i \(0.0424333\pi\)
\(228\) −12.9551 + 35.3955i −0.857974 + 2.34412i
\(229\) 2.27581 + 21.6529i 0.150390 + 1.43086i 0.766015 + 0.642823i \(0.222237\pi\)
−0.615626 + 0.788039i \(0.711097\pi\)
\(230\) 22.0608 + 7.01698i 1.45465 + 0.462686i
\(231\) 1.14583 + 0.0420792i 0.0753901 + 0.00276861i
\(232\) −18.7040 32.3962i −1.22798 2.12692i
\(233\) −7.60150 5.52281i −0.497991 0.361811i 0.310258 0.950652i \(-0.399584\pi\)
−0.808249 + 0.588841i \(0.799584\pi\)
\(234\) −34.9705 + 12.5858i −2.28609 + 0.822758i
\(235\) −3.85359 17.5923i −0.251380 1.14759i
\(236\) −8.54258 + 9.48750i −0.556075 + 0.617583i
\(237\) −5.78355 1.45307i −0.375682 0.0943869i
\(238\) 14.8490 + 16.4915i 0.962516 + 1.06898i
\(239\) −4.80649 1.02165i −0.310906 0.0660851i 0.0498163 0.998758i \(-0.484136\pi\)
−0.360722 + 0.932673i \(0.617470\pi\)
\(240\) −16.6873 10.3255i −1.07716 0.666508i
\(241\) 7.81201 1.66049i 0.503216 0.106962i 0.0506924 0.998714i \(-0.483857\pi\)
0.452524 + 0.891752i \(0.350524\pi\)
\(242\) −21.5801 15.6788i −1.38722 1.00787i
\(243\) 10.1272 11.8508i 0.649659 0.760226i
\(244\) −24.7706 17.9969i −1.58577 1.15213i
\(245\) 11.8635 1.32137i 0.757933 0.0844195i
\(246\) −17.2729 + 3.01362i −1.10128 + 0.192142i
\(247\) −2.71818 25.8618i −0.172954 1.64555i
\(248\) −8.11624 1.72516i −0.515382 0.109548i
\(249\) 1.72814 + 25.3699i 0.109516 + 1.60775i
\(250\) 10.8240 25.5821i 0.684568 1.61795i
\(251\) 21.5099 1.35769 0.678847 0.734279i \(-0.262480\pi\)
0.678847 + 0.734279i \(0.262480\pi\)
\(252\) −9.07179 + 13.3456i −0.571469 + 0.840691i
\(253\) 1.73126 1.25783i 0.108843 0.0790792i
\(254\) −30.0291 13.3698i −1.88419 0.838897i
\(255\) 4.77636 + 26.4076i 0.299107 + 1.65371i
\(256\) −29.7937 + 13.2650i −1.86211 + 0.829063i
\(257\) 4.80713 8.32619i 0.299860 0.519373i −0.676243 0.736678i \(-0.736393\pi\)
0.976104 + 0.217305i \(0.0697266\pi\)
\(258\) −17.9210 0.658127i −1.11571 0.0409732i
\(259\) −9.27556 + 1.97158i −0.576356 + 0.122508i
\(260\) 46.3010 + 4.57618i 2.87147 + 0.283803i
\(261\) −20.7324 1.52480i −1.28330 0.0943826i
\(262\) −7.69800 + 23.6920i −0.475584 + 1.46370i
\(263\) −9.44631 + 2.00788i −0.582484 + 0.123811i −0.489724 0.871878i \(-0.662902\pi\)
−0.0927605 + 0.995688i \(0.529569\pi\)
\(264\) −4.45541 + 1.79078i −0.274212 + 0.110215i
\(265\) 5.83014 + 1.85442i 0.358143 + 0.113916i
\(266\) −11.1759 12.4120i −0.685236 0.761031i
\(267\) −7.82031 14.7720i −0.478595 0.904030i
\(268\) 0.948715 + 1.64322i 0.0579520 + 0.100376i
\(269\) 14.7015 + 10.6812i 0.896364 + 0.651246i 0.937529 0.347906i \(-0.113107\pi\)
−0.0411659 + 0.999152i \(0.513107\pi\)
\(270\) −26.3623 + 11.7626i −1.60436 + 0.715849i
\(271\) −2.02436 + 1.47078i −0.122971 + 0.0893437i −0.647571 0.762005i \(-0.724215\pi\)
0.524600 + 0.851349i \(0.324215\pi\)
\(272\) −32.0726 14.2796i −1.94469 0.865831i
\(273\) 1.56929 11.0220i 0.0949775 0.667082i
\(274\) 13.1299 22.7416i 0.793204 1.37387i
\(275\) −1.31136 2.20763i −0.0790783 0.133125i
\(276\) 2.04676 + 30.0474i 0.123200 + 1.80864i
\(277\) 9.01502 10.0122i 0.541660 0.601574i −0.408722 0.912659i \(-0.634026\pi\)
0.950382 + 0.311084i \(0.100692\pi\)
\(278\) 1.19560 0.868656i 0.0717075 0.0520985i
\(279\) −3.32848 + 3.19119i −0.199271 + 0.191052i
\(280\) 13.4272 7.86366i 0.802427 0.469944i
\(281\) 0.0790201 0.751826i 0.00471394 0.0448502i −0.991912 0.126927i \(-0.959489\pi\)
0.996626 + 0.0820768i \(0.0261553\pi\)
\(282\) 28.7685 19.3293i 1.71314 1.15105i
\(283\) −3.82568 + 1.70330i −0.227413 + 0.101251i −0.517280 0.855816i \(-0.673055\pi\)
0.289867 + 0.957067i \(0.406389\pi\)
\(284\) −4.61644 5.12707i −0.273935 0.304236i
\(285\) −3.59486 19.8753i −0.212941 1.17731i
\(286\) 4.25717 4.72806i 0.251732 0.279576i
\(287\) 1.62304 4.99519i 0.0958049 0.294857i
\(288\) 0.952422 5.28998i 0.0561220 0.311715i
\(289\) 9.58309 + 29.4937i 0.563711 + 1.73492i
\(290\) 33.4581 + 19.0412i 1.96472 + 1.11814i
\(291\) 13.5464 + 3.40341i 0.794102 + 0.199511i
\(292\) −33.6217 + 14.9694i −1.96756 + 0.876016i
\(293\) −13.1006 + 22.6909i −0.765344 + 1.32561i 0.174721 + 0.984618i \(0.444098\pi\)
−0.940065 + 0.340997i \(0.889236\pi\)
\(294\) 10.7484 + 20.3029i 0.626860 + 1.18409i
\(295\) 1.38083 6.70042i 0.0803948 0.390114i
\(296\) 32.1283 23.3426i 1.86742 1.35676i
\(297\) −0.568900 + 2.60713i −0.0330109 + 0.151281i
\(298\) −1.56073 4.80343i −0.0904105 0.278255i
\(299\) −10.3891 17.9945i −0.600819 1.04065i
\(300\) 36.1270 + 0.878013i 2.08579 + 0.0506921i
\(301\) 2.68592 4.65215i 0.154814 0.268146i
\(302\) 10.2246 + 2.17330i 0.588358 + 0.125059i
\(303\) −17.3374 20.7377i −0.996010 1.19135i
\(304\) 24.1390 + 10.7474i 1.38447 + 0.616404i
\(305\) 16.3276 + 1.61375i 0.934917 + 0.0924029i
\(306\) −43.8965 + 27.2102i −2.50939 + 1.55551i
\(307\) 13.6647 0.779887 0.389944 0.920839i \(-0.372495\pi\)
0.389944 + 0.920839i \(0.372495\pi\)
\(308\) 0.288746 2.74724i 0.0164528 0.156538i
\(309\) −7.20996 25.3161i −0.410160 1.44018i
\(310\) 8.10464 2.68906i 0.460313 0.152729i
\(311\) −0.934468 0.198627i −0.0529888 0.0112631i 0.181341 0.983420i \(-0.441956\pi\)
−0.234330 + 0.972157i \(0.575290\pi\)
\(312\) 12.7707 + 44.8412i 0.722997 + 2.53864i
\(313\) 11.7240 2.49201i 0.662680 0.140857i 0.135720 0.990747i \(-0.456665\pi\)
0.526960 + 0.849890i \(0.323332\pi\)
\(314\) 0.428576 + 1.31902i 0.0241859 + 0.0744367i
\(315\) 0.580746 8.62771i 0.0327213 0.486116i
\(316\) −4.43953 + 13.6635i −0.249743 + 0.768631i
\(317\) −0.235992 + 2.24531i −0.0132546 + 0.126109i −0.999148 0.0412635i \(-0.986862\pi\)
0.985894 + 0.167373i \(0.0535284\pi\)
\(318\) 0.800161 + 11.7468i 0.0448708 + 0.658726i
\(319\) 3.25095 1.44742i 0.182018 0.0810398i
\(320\) 7.40422 10.3251i 0.413908 0.577193i
\(321\) −18.2539 + 3.18477i −1.01883 + 0.177756i
\(322\) −12.1917 5.42811i −0.679419 0.302497i
\(323\) −11.1664 34.3666i −0.621314 1.91221i
\(324\) −26.8265 26.2821i −1.49036 1.46011i
\(325\) −22.6489 + 10.4226i −1.25634 + 0.578141i
\(326\) −21.5248 37.2821i −1.19215 2.06486i
\(327\) −3.24542 + 22.7945i −0.179472 + 1.26054i
\(328\) 2.29919 + 21.8753i 0.126952 + 1.20786i
\(329\) 1.08523 + 10.3252i 0.0598304 + 0.569248i
\(330\) 3.02518 3.90740i 0.166531 0.215095i
\(331\) −1.40101 + 13.3298i −0.0770067 + 0.732669i 0.886090 + 0.463513i \(0.153411\pi\)
−0.963097 + 0.269156i \(0.913255\pi\)
\(332\) 61.2623 3.36221
\(333\) −0.690766 22.0584i −0.0378538 1.20879i
\(334\) 5.03344 15.4913i 0.275418 0.847649i
\(335\) −0.883683 0.502910i −0.0482807 0.0274769i
\(336\) 8.90190 + 6.98078i 0.485639 + 0.380833i
\(337\) 8.05962 + 8.95111i 0.439035 + 0.487598i 0.921534 0.388299i \(-0.126937\pi\)
−0.482498 + 0.875897i \(0.660270\pi\)
\(338\) −19.7238 21.9054i −1.07283 1.19150i
\(339\) −12.9800 10.1788i −0.704979 0.552837i
\(340\) 64.2554 7.15685i 3.48474 0.388135i
\(341\) 0.243921 0.750712i 0.0132091 0.0406533i
\(342\) 33.0380 20.4794i 1.78649 1.10740i
\(343\) −15.9048 −0.858777
\(344\) −2.35154 + 22.3734i −0.126786 + 1.20629i
\(345\) −9.08347 13.3397i −0.489038 0.718186i
\(346\) −0.279201 2.65642i −0.0150099 0.142810i
\(347\) −0.0730635 0.695153i −0.00392226 0.0373178i 0.992386 0.123169i \(-0.0393057\pi\)
−0.996308 + 0.0858512i \(0.972639\pi\)
\(348\) −7.05948 + 49.5828i −0.378428 + 2.65792i
\(349\) 8.65614 + 14.9929i 0.463353 + 0.802551i 0.999126 0.0418117i \(-0.0133130\pi\)
−0.535773 + 0.844362i \(0.679980\pi\)
\(350\) −7.83399 + 13.9663i −0.418744 + 0.746528i
\(351\) 24.5983 + 8.13966i 1.31296 + 0.434463i
\(352\) 0.284330 + 0.875079i 0.0151549 + 0.0466419i
\(353\) −4.82374 2.14767i −0.256742 0.114309i 0.274330 0.961636i \(-0.411544\pi\)
−0.531072 + 0.847327i \(0.678211\pi\)
\(354\) 12.9700 2.26289i 0.689347 0.120271i
\(355\) 3.52310 + 1.12061i 0.186986 + 0.0594756i
\(356\) −36.7864 + 16.3784i −1.94968 + 0.868052i
\(357\) −1.05138 15.4347i −0.0556447 0.816893i
\(358\) −4.89212 + 46.5455i −0.258557 + 2.46000i
\(359\) 0.334961 1.03090i 0.0176786 0.0544091i −0.941828 0.336095i \(-0.890894\pi\)
0.959507 + 0.281686i \(0.0908937\pi\)
\(360\) 12.4743 + 33.9973i 0.657453 + 1.79181i
\(361\) 2.53289 + 7.79543i 0.133310 + 0.410286i
\(362\) 35.0398 7.44793i 1.84165 0.391455i
\(363\) 5.09349 + 17.8846i 0.267339 + 0.938698i
\(364\) −26.2356 5.57656i −1.37512 0.292291i
\(365\) 11.4929 16.0268i 0.601568 0.838884i
\(366\) 8.64874 + 30.3680i 0.452077 + 1.58736i
\(367\) −3.26474 + 31.0619i −0.170418 + 1.62142i 0.490833 + 0.871254i \(0.336692\pi\)
−0.661251 + 0.750165i \(0.729974\pi\)
\(368\) 21.1132 1.10060
\(369\) 10.7720 + 5.77743i 0.560768 + 0.300761i
\(370\) −16.3909 + 37.4379i −0.852121 + 1.94630i
\(371\) −3.22198 1.43452i −0.167277 0.0744764i
\(372\) 7.12540 + 8.52284i 0.369435 + 0.441889i
\(373\) 0.241813 + 0.0513989i 0.0125206 + 0.00266133i 0.214168 0.976797i \(-0.431296\pi\)
−0.201647 + 0.979458i \(0.564629\pi\)
\(374\) 4.42044 7.65643i 0.228576 0.395905i
\(375\) −16.9430 + 9.37744i −0.874930 + 0.484249i
\(376\) −21.7395 37.6539i −1.12113 1.94185i
\(377\) −10.6775 32.8619i −0.549917 1.69247i
\(378\) 15.8546 5.05696i 0.815474 0.260102i
\(379\) 18.0726 13.1305i 0.928325 0.674467i −0.0172574 0.999851i \(-0.505493\pi\)
0.945582 + 0.325384i \(0.105493\pi\)
\(380\) −48.3609 + 5.38650i −2.48086 + 0.276321i
\(381\) 10.7218 + 20.2526i 0.549292 + 1.03757i
\(382\) −23.0010 + 39.8388i −1.17683 + 2.03833i
\(383\) 24.2261 10.7861i 1.23789 0.551146i 0.319792 0.947488i \(-0.396387\pi\)
0.918103 + 0.396342i \(0.129720\pi\)
\(384\) 29.7343 + 7.47048i 1.51737 + 0.381227i
\(385\) 0.610453 + 1.34852i 0.0311116 + 0.0687270i
\(386\) −4.14671 12.7622i −0.211062 0.649581i
\(387\) 9.54796 + 8.07046i 0.485350 + 0.410245i
\(388\) 10.3984 32.0029i 0.527898 1.62470i
\(389\) −8.70282 + 9.66546i −0.441250 + 0.490058i −0.922213 0.386683i \(-0.873621\pi\)
0.480962 + 0.876741i \(0.340287\pi\)
\(390\) −34.6615 33.1785i −1.75515 1.68006i
\(391\) −19.3200 21.4570i −0.977052 1.08513i
\(392\) 26.3270 11.7215i 1.32971 0.592027i
\(393\) 14.4150 9.68533i 0.727141 0.488560i
\(394\) 4.04593 38.4945i 0.203831 1.93932i
\(395\) −1.64731 7.52027i −0.0828854 0.378386i
\(396\) 6.17337 + 1.79427i 0.310223 + 0.0901655i
\(397\) 24.8748 18.0726i 1.24843 0.907040i 0.250303 0.968168i \(-0.419470\pi\)
0.998130 + 0.0611280i \(0.0194698\pi\)
\(398\) 28.4755 31.6253i 1.42735 1.58523i
\(399\) 0.791302 + 11.6167i 0.0396147 + 0.581564i
\(400\) 2.33528 25.2260i 0.116764 1.26130i
\(401\) 5.05931 8.76298i 0.252650 0.437602i −0.711605 0.702580i \(-0.752031\pi\)
0.964255 + 0.264978i \(0.0853646\pi\)
\(402\) 0.275818 1.93723i 0.0137565 0.0966201i
\(403\) −7.00169 3.11735i −0.348779 0.155286i
\(404\) −52.6838 + 38.2771i −2.62112 + 1.90435i
\(405\) 19.5220 + 4.88808i 0.970054 + 0.242891i
\(406\) −17.9543 13.0446i −0.891058 0.647392i
\(407\) 1.88893 + 3.27173i 0.0936309 + 0.162173i
\(408\) 30.3133 + 57.2596i 1.50073 + 2.83477i
\(409\) −11.8509 13.1617i −0.585987 0.650804i 0.375121 0.926976i \(-0.377601\pi\)
−0.961108 + 0.276171i \(0.910934\pi\)
\(410\) −13.4185 18.2301i −0.662694 0.900321i
\(411\) −16.9860 + 6.82722i −0.837856 + 0.336762i
\(412\) −62.0304 + 13.1850i −3.05602 + 0.649577i
\(413\) −1.21871 + 3.75082i −0.0599690 + 0.184566i
\(414\) 17.4605 25.6862i 0.858138 1.26241i
\(415\) −28.3278 + 16.5902i −1.39056 + 0.814383i
\(416\) 8.73878 1.85749i 0.428454 0.0910707i
\(417\) −1.02957 0.0378097i −0.0504182 0.00185155i
\(418\) −3.32698 + 5.76250i −0.162728 + 0.281853i
\(419\) −12.2652 + 5.46080i −0.599193 + 0.266778i −0.683839 0.729633i \(-0.739691\pi\)
0.0846460 + 0.996411i \(0.473024\pi\)
\(420\) −20.6425 2.80848i −1.00725 0.137040i
\(421\) −29.7828 13.2601i −1.45152 0.646260i −0.478736 0.877959i \(-0.658905\pi\)
−0.972788 + 0.231699i \(0.925572\pi\)
\(422\) −29.0891 + 21.1345i −1.41604 + 1.02881i
\(423\) −24.0971 1.77226i −1.17164 0.0861704i
\(424\) 14.7702 0.717304
\(425\) −27.7737 + 20.7101i −1.34722 + 1.00459i
\(426\) 0.483529 + 7.09846i 0.0234271 + 0.343921i
\(427\) −9.25175 1.96652i −0.447724 0.0951666i
\(428\) 4.66626 + 44.3965i 0.225552 + 2.14599i
\(429\) −4.36936 + 0.762325i −0.210955 + 0.0368054i
\(430\) −9.54760 21.0911i −0.460426 1.01710i
\(431\) 7.24479 + 5.26365i 0.348969 + 0.253541i 0.748436 0.663206i \(-0.230805\pi\)
−0.399467 + 0.916747i \(0.630805\pi\)
\(432\) −19.6602 + 17.5107i −0.945902 + 0.842486i
\(433\) 22.5500 + 16.3836i 1.08369 + 0.787344i 0.978322 0.207090i \(-0.0663992\pi\)
0.105364 + 0.994434i \(0.466399\pi\)
\(434\) −4.81507 + 1.02347i −0.231131 + 0.0491284i
\(435\) −10.1630 24.8389i −0.487280 1.19094i
\(436\) 54.2576 + 11.5328i 2.59847 + 0.552321i
\(437\) 14.5409 + 16.1493i 0.695585 + 0.772525i
\(438\) 36.8105 + 9.24832i 1.75887 + 0.441902i
\(439\) −2.10414 + 2.33689i −0.100425 + 0.111533i −0.791262 0.611477i \(-0.790576\pi\)
0.690837 + 0.723011i \(0.257242\pi\)
\(440\) −4.63250 4.11937i −0.220846 0.196383i
\(441\) 2.83776 15.7616i 0.135132 0.750553i
\(442\) −69.4479 50.4568i −3.30330 2.39999i
\(443\) 9.86697 + 17.0901i 0.468794 + 0.811975i 0.999364 0.0356665i \(-0.0113554\pi\)
−0.530570 + 0.847641i \(0.678022\pi\)
\(444\) −53.1328 1.95124i −2.52157 0.0926016i
\(445\) 12.5747 17.5354i 0.596099 0.831257i
\(446\) −4.84360 46.0837i −0.229351 2.18213i
\(447\) −1.21020 + 3.30647i −0.0572406 + 0.156390i
\(448\) −4.90106 + 5.44318i −0.231554 + 0.257166i
\(449\) −13.7726 −0.649970 −0.324985 0.945719i \(-0.605359\pi\)
−0.324985 + 0.945719i \(0.605359\pi\)
\(450\) −28.7586 23.7029i −1.35569 1.11736i
\(451\) −2.09246 −0.0985300
\(452\) −26.5911 + 29.5324i −1.25074 + 1.38909i
\(453\) −4.67405 5.59073i −0.219606 0.262675i
\(454\) 4.41694 + 42.0244i 0.207297 + 1.97230i
\(455\) 13.6416 4.52618i 0.639527 0.212190i
\(456\) −22.8149 43.0956i −1.06840 2.01814i
\(457\) 8.03370 + 13.9148i 0.375801 + 0.650906i 0.990447 0.137897i \(-0.0440344\pi\)
−0.614646 + 0.788803i \(0.710701\pi\)
\(458\) −43.7623 31.7952i −2.04488 1.48569i
\(459\) 35.7862 + 3.95686i 1.67036 + 0.184690i
\(460\) −33.5506 + 19.6490i −1.56431 + 0.916140i
\(461\) 6.87074 7.63073i 0.320002 0.355399i −0.561585 0.827419i \(-0.689808\pi\)
0.881588 + 0.472020i \(0.156475\pi\)
\(462\) −1.98260 + 2.04565i −0.0922387 + 0.0951724i
\(463\) 12.0593 + 13.3932i 0.560444 + 0.622436i 0.955061 0.296409i \(-0.0957893\pi\)
−0.394617 + 0.918846i \(0.629123\pi\)
\(464\) 34.3427 + 7.29977i 1.59432 + 0.338883i
\(465\) −5.60284 2.01137i −0.259826 0.0932751i
\(466\) 22.8343 4.85358i 1.05778 0.224838i
\(467\) 28.5731 + 20.7596i 1.32221 + 0.960639i 0.999902 + 0.0140027i \(0.00445734\pi\)
0.322304 + 0.946636i \(0.395543\pi\)
\(468\) 23.5920 57.7921i 1.09054 2.67144i
\(469\) 0.474203 + 0.344529i 0.0218967 + 0.0159089i
\(470\) 38.8881 + 22.1315i 1.79377 + 1.02085i
\(471\) 0.332322 0.907956i 0.0153126 0.0418364i
\(472\) −1.72643 16.4259i −0.0794653 0.756062i
\(473\) −2.09333 0.444951i −0.0962515 0.0204589i
\(474\) 12.2978 8.26281i 0.564858 0.379524i
\(475\) 20.9035 15.5872i 0.959117 0.715189i
\(476\) −37.2712 −1.70832
\(477\) 4.61439 6.78825i 0.211278 0.310813i
\(478\) 9.87695 7.17603i 0.451761 0.328224i
\(479\) −1.56127 0.695122i −0.0713362 0.0317609i 0.370758 0.928729i \(-0.379098\pi\)
−0.442095 + 0.896968i \(0.645764\pi\)
\(480\) 6.66184 1.94204i 0.304070 0.0886416i
\(481\) 33.5106 14.9199i 1.52795 0.680288i
\(482\) −9.92134 + 17.1843i −0.451905 + 0.782722i
\(483\) 4.35301 + 8.22250i 0.198069 + 0.374137i
\(484\) 43.8215 9.31455i 1.99189 0.423388i
\(485\) 3.85838 + 17.6142i 0.175200 + 0.799818i
\(486\) 5.04461 + 38.3998i 0.228828 + 1.74185i
\(487\) 10.1084 31.1106i 0.458057 1.40975i −0.409452 0.912332i \(-0.634280\pi\)
0.867509 0.497422i \(-0.165720\pi\)
\(488\) 38.7452 8.23555i 1.75391 0.372806i
\(489\) −4.23031 + 29.7119i −0.191301 + 1.34362i
\(490\) −17.2830 + 24.1010i −0.780766 + 1.08877i
\(491\) 27.6113 + 30.6655i 1.24608 + 1.38391i 0.894077 + 0.447914i \(0.147833\pi\)
0.352004 + 0.935999i \(0.385500\pi\)
\(492\) 15.6503 24.9457i 0.705572 1.12464i
\(493\) −24.0072 41.5817i −1.08123 1.87275i
\(494\) 52.2689 + 37.9756i 2.35169 + 1.70860i
\(495\) −3.34048 + 0.842115i −0.150143 + 0.0378503i
\(496\) 6.30049 4.57758i 0.282901 0.205539i
\(497\) −1.94701 0.866864i −0.0873353 0.0388842i
\(498\) −49.7149 38.9859i −2.22778 1.74700i
\(499\) 1.73929 3.01255i 0.0778615 0.134860i −0.824466 0.565912i \(-0.808524\pi\)
0.902327 + 0.431052i \(0.141857\pi\)
\(500\) 19.7656 + 42.2596i 0.883947 + 1.88990i
\(501\) −9.42546 + 6.33289i −0.421098 + 0.282933i
\(502\) −35.7595 + 39.7150i −1.59603 + 1.77257i
\(503\) 13.8073 10.0316i 0.615638 0.447287i −0.235757 0.971812i \(-0.575757\pi\)
0.851395 + 0.524525i \(0.175757\pi\)
\(504\) −4.97749 20.2744i −0.221715 0.903094i
\(505\) 13.9954 31.9665i 0.622788 1.42249i
\(506\) −0.555751 + 5.28762i −0.0247061 + 0.235063i
\(507\) 1.39653 + 20.5018i 0.0620222 + 0.910518i
\(508\) 50.4347 22.4550i 2.23768 0.996279i
\(509\) 5.21858 + 5.79582i 0.231309 + 0.256895i 0.847615 0.530612i \(-0.178038\pi\)
−0.616305 + 0.787507i \(0.711371\pi\)
\(510\) −56.6983 35.0828i −2.51064 1.55349i
\(511\) −7.60751 + 8.44899i −0.336536 + 0.373761i
\(512\) 14.0995 43.3938i 0.623115 1.91775i
\(513\) −26.9340 2.97807i −1.18916 0.131485i
\(514\) 7.38142 + 22.7177i 0.325580 + 1.00203i
\(515\) 25.1124 22.8950i 1.10658 1.00887i
\(516\) 20.9615 21.6282i 0.922778 0.952128i
\(517\) 3.77856 1.68232i 0.166181 0.0739884i
\(518\) 11.7801 20.4037i 0.517586 0.896486i
\(519\) −0.989600 + 1.57736i −0.0434386 + 0.0692386i
\(520\) −44.4804 + 40.5529i −1.95060 + 1.77836i
\(521\) −9.24944 + 6.72011i −0.405225 + 0.294413i −0.771666 0.636028i \(-0.780576\pi\)
0.366441 + 0.930441i \(0.380576\pi\)
\(522\) 37.2821 35.7444i 1.63180 1.56449i
\(523\) 6.03668 + 18.5790i 0.263966 + 0.812403i 0.991930 + 0.126788i \(0.0404667\pi\)
−0.727964 + 0.685615i \(0.759533\pi\)
\(524\) −20.9196 36.2338i −0.913876 1.58288i
\(525\) 10.3057 4.29149i 0.449778 0.187296i
\(526\) 11.9969 20.7793i 0.523090 0.906019i
\(527\) −10.4175 2.21430i −0.453793 0.0964566i
\(528\) 1.54906 4.23227i 0.0674141 0.184186i
\(529\) −5.14891 2.29244i −0.223866 0.0996714i
\(530\) −13.1163 + 7.68160i −0.569736 + 0.333668i
\(531\) −8.08853 4.33819i −0.351012 0.188261i
\(532\) 28.0516 1.21619
\(533\) −2.12372 + 20.2058i −0.0919884 + 0.875211i
\(534\) 40.2753 + 10.1188i 1.74288 + 0.437884i
\(535\) −14.1806 19.2654i −0.613079 0.832915i
\(536\) −2.40107 0.510364i −0.103711 0.0220444i
\(537\) 22.7071 23.4293i 0.979883 1.01105i
\(538\) −44.1620 + 9.38692i −1.90396 + 0.404699i
\(539\) 0.847169 + 2.60732i 0.0364902 + 0.112305i
\(540\) 14.9453 46.1228i 0.643144 1.98481i
\(541\) 2.36879 7.29039i 0.101842 0.313439i −0.887134 0.461512i \(-0.847307\pi\)
0.988976 + 0.148073i \(0.0473072\pi\)
\(542\) 0.649839 6.18281i 0.0279130 0.265574i
\(543\) −22.4261 10.9880i −0.962396 0.471539i
\(544\) 11.3413 5.04947i 0.486254 0.216494i
\(545\) −28.2120 + 9.36053i −1.20847 + 0.400961i
\(546\) 17.7416 + 21.2212i 0.759272 + 0.908182i
\(547\) −13.1622 5.86017i −0.562773 0.250563i 0.105575 0.994411i \(-0.466332\pi\)
−0.668348 + 0.743849i \(0.732998\pi\)
\(548\) 13.6289 + 41.9454i 0.582197 + 1.79182i
\(549\) 8.31949 20.3798i 0.355067 0.869790i
\(550\) 6.25616 + 1.24886i 0.266764 + 0.0532516i
\(551\) 18.0687 + 31.2959i 0.769751 + 1.33325i
\(552\) −30.6597 24.0430i −1.30496 1.02334i
\(553\) 0.463907 + 4.41378i 0.0197273 + 0.187693i
\(554\) 3.49890 + 33.2899i 0.148654 + 1.41435i
\(555\) 25.0971 13.4865i 1.06531 0.572468i
\(556\) −0.259449 + 2.46849i −0.0110031 + 0.104687i
\(557\) 11.9602 0.506771 0.253386 0.967365i \(-0.418456\pi\)
0.253386 + 0.967365i \(0.418456\pi\)
\(558\) −0.358586 11.4508i −0.0151802 0.484751i
\(559\) −6.42128 + 19.7627i −0.271591 + 0.835872i
\(560\) −2.94776 + 14.3039i −0.124566 + 0.604452i
\(561\) −5.71868 + 2.29853i −0.241443 + 0.0970439i
\(562\) 1.25677 + 1.39578i 0.0530136 + 0.0588776i
\(563\) −27.6349 30.6917i −1.16467 1.29350i −0.948367 0.317175i \(-0.897266\pi\)
−0.216306 0.976326i \(-0.569401\pi\)
\(564\) −8.20519 + 57.6298i −0.345501 + 2.42665i
\(565\) 4.29819 20.8569i 0.180826 0.877455i
\(566\) 3.21516 9.89523i 0.135143 0.415928i
\(567\) −10.8730 4.04636i −0.456621 0.169931i
\(568\) 8.92549 0.374505
\(569\) 1.53101 14.5666i 0.0641832 0.610662i −0.914400 0.404811i \(-0.867337\pi\)
0.978583 0.205851i \(-0.0659961\pi\)
\(570\) 42.6731 + 26.4046i 1.78738 + 1.10596i
\(571\) 2.44705 + 23.2822i 0.102406 + 0.974328i 0.918235 + 0.396035i \(0.129614\pi\)
−0.815829 + 0.578293i \(0.803719\pi\)
\(572\) 1.11695 + 10.6270i 0.0467019 + 0.444339i
\(573\) 29.7561 11.9600i 1.24308 0.499635i
\(574\) 6.52466 + 11.3010i 0.272334 + 0.471696i
\(575\) 10.1928 18.1715i 0.425069 0.757803i
\(576\) −10.4463 13.4704i −0.435262 0.561265i
\(577\) 0.219132 + 0.674419i 0.00912259 + 0.0280764i 0.955514 0.294945i \(-0.0953014\pi\)
−0.946392 + 0.323022i \(0.895301\pi\)
\(578\) −70.3874 31.3385i −2.92773 1.30351i
\(579\) −3.21539 + 8.78497i −0.133627 + 0.365091i
\(580\) −61.3670 + 20.3611i −2.54813 + 0.845450i
\(581\) 17.2888 7.69747i 0.717261 0.319345i
\(582\) −28.8043 + 19.3534i −1.19398 + 0.802222i
\(583\) −0.146871 + 1.39739i −0.00608279 + 0.0578739i
\(584\) 14.7132 45.2827i 0.608838 1.87381i
\(585\) 4.74151 + 33.1120i 0.196037 + 1.36901i
\(586\) −20.1161 61.9111i −0.830990 2.55752i
\(587\) 10.4158 2.21394i 0.429905 0.0913791i 0.0121230 0.999927i \(-0.496141\pi\)
0.417782 + 0.908547i \(0.362808\pi\)
\(588\) −37.4201 9.40148i −1.54318 0.387710i
\(589\) 7.84056 + 1.66656i 0.323065 + 0.0686695i
\(590\) 10.0758 + 13.6887i 0.414813 + 0.563555i
\(591\) −18.7794 + 19.3767i −0.772482 + 0.797052i
\(592\) −3.89611 + 37.0690i −0.160129 + 1.52353i
\(593\) −47.7160 −1.95946 −0.979730 0.200323i \(-0.935801\pi\)
−0.979730 + 0.200323i \(0.935801\pi\)
\(594\) −3.86791 5.38465i −0.158702 0.220935i
\(595\) 17.2343 10.0933i 0.706535 0.413784i
\(596\) 7.74930 + 3.45021i 0.317424 + 0.141326i
\(597\) −29.2260 + 5.09908i −1.19614 + 0.208691i
\(598\) 50.4958 + 10.7332i 2.06493 + 0.438914i
\(599\) 1.95259 3.38199i 0.0797808 0.138184i −0.823374 0.567498i \(-0.807911\pi\)
0.903155 + 0.429314i \(0.141245\pi\)
\(600\) −32.1178 + 33.9728i −1.31120 + 1.38693i
\(601\) −3.54162 6.13427i −0.144466 0.250222i 0.784708 0.619866i \(-0.212813\pi\)
−0.929174 + 0.369644i \(0.879480\pi\)
\(602\) 4.12427 + 12.6932i 0.168093 + 0.517336i
\(603\) −0.984683 + 0.944068i −0.0400994 + 0.0384454i
\(604\) −14.2032 + 10.3192i −0.577920 + 0.419883i
\(605\) −17.7407 + 16.1742i −0.721262 + 0.657575i
\(606\) 67.1120 + 2.46461i 2.72624 + 0.100118i
\(607\) 2.38982 4.13929i 0.0969997 0.168008i −0.813442 0.581646i \(-0.802409\pi\)
0.910441 + 0.413638i \(0.135742\pi\)
\(608\) −8.53586 + 3.80041i −0.346175 + 0.154127i
\(609\) 4.23772 + 14.8797i 0.171721 + 0.602958i
\(610\) −30.1237 + 27.4638i −1.21967 + 1.11198i
\(611\) −12.4103 38.1951i −0.502069 1.54521i
\(612\) 15.3699 85.3682i 0.621293 3.45081i
\(613\) 14.0778 43.3269i 0.568596 1.74996i −0.0884219 0.996083i \(-0.528182\pi\)
0.657018 0.753875i \(-0.271818\pi\)
\(614\) −22.7171 + 25.2299i −0.916789 + 1.01820i
\(615\) −0.481278 + 15.7732i −0.0194070 + 0.636035i
\(616\) 2.39127 + 2.65577i 0.0963469 + 0.107004i
\(617\) −17.7401 + 7.89839i −0.714189 + 0.317977i −0.731470 0.681873i \(-0.761166\pi\)
0.0172815 + 0.999851i \(0.494499\pi\)
\(618\) 58.7288 + 28.7750i 2.36242 + 1.15750i
\(619\) −2.85213 + 27.1362i −0.114637 + 1.09070i 0.774348 + 0.632760i \(0.218078\pi\)
−0.888985 + 0.457936i \(0.848589\pi\)
\(620\) −5.75189 + 13.1377i −0.231001 + 0.527623i
\(621\) −20.6284 + 6.57959i −0.827790 + 0.264030i
\(622\) 1.92026 1.39515i 0.0769953 0.0559404i
\(623\) −8.32357 + 9.24426i −0.333477 + 0.370363i
\(624\) −39.2968 19.2540i −1.57313 0.770776i
\(625\) −20.5838 14.1882i −0.823354 0.567529i
\(626\) −14.8896 + 25.7896i −0.595109 + 1.03076i
\(627\) 4.30408 1.72995i 0.171888 0.0690876i
\(628\) −2.12796 0.947428i −0.0849148 0.0378065i
\(629\) 41.2378 29.9610i 1.64426 1.19462i
\(630\) 14.9643 + 15.4155i 0.596194 + 0.614169i
\(631\) 12.6772 + 9.21053i 0.504672 + 0.366665i 0.810799 0.585325i \(-0.199033\pi\)
−0.306127 + 0.951991i \(0.599033\pi\)
\(632\) −9.29310 16.0961i −0.369660 0.640269i
\(633\) 25.0495 + 0.919914i 0.995629 + 0.0365633i
\(634\) −3.75332 4.16848i −0.149063 0.165551i
\(635\) −17.2401 + 24.0413i −0.684154 + 0.954050i
\(636\) −15.5608 12.2026i −0.617025 0.483865i
\(637\) 26.0374 5.53442i 1.03164 0.219282i
\(638\) −2.73215 + 8.40869i −0.108167 + 0.332903i
\(639\) 2.78843 4.10207i 0.110309 0.162275i
\(640\) 8.46913 + 38.6631i 0.334772 + 1.52829i
\(641\) −34.5500 + 7.34383i −1.36464 + 0.290064i −0.831295 0.555832i \(-0.812400\pi\)
−0.533348 + 0.845896i \(0.679067\pi\)
\(642\) 24.4662 38.9977i 0.965604 1.53911i
\(643\) 5.45444 9.44736i 0.215102 0.372567i −0.738202 0.674580i \(-0.764325\pi\)
0.953304 + 0.302012i \(0.0976583\pi\)
\(644\) 20.4764 9.11667i 0.806882 0.359247i
\(645\) −3.83557 + 15.6774i −0.151025 + 0.617298i
\(646\) 82.0167 + 36.5162i 3.22690 + 1.43671i
\(647\) −28.4306 + 20.6560i −1.11772 + 0.812072i −0.983862 0.178928i \(-0.942737\pi\)
−0.133860 + 0.991000i \(0.542737\pi\)
\(648\) 48.4904 3.03997i 1.90488 0.119421i
\(649\) 1.57119 0.0616748
\(650\) 18.4093 59.1451i 0.722070 2.31986i
\(651\) 3.08173 + 1.50994i 0.120783 + 0.0591791i
\(652\) 70.7231 + 15.0327i 2.76973 + 0.588724i
\(653\) 1.31892 + 12.5487i 0.0516135 + 0.491070i 0.989542 + 0.144242i \(0.0460744\pi\)
−0.937929 + 0.346828i \(0.887259\pi\)
\(654\) −36.6913 43.8872i −1.43474 1.71613i
\(655\) 19.4856 + 11.0894i 0.761365 + 0.433299i
\(656\) −16.7018 12.1346i −0.652097 0.473776i
\(657\) −16.2149 20.9089i −0.632604 0.815734i
\(658\) −20.8682 15.1616i −0.813527 0.591062i
\(659\) 17.4588 3.71099i 0.680099 0.144559i 0.145106 0.989416i \(-0.453648\pi\)
0.534993 + 0.844857i \(0.320314\pi\)
\(660\) 1.47719 + 8.16707i 0.0574994 + 0.317903i
\(661\) −35.8685 7.62409i −1.39512 0.296543i −0.551812 0.833968i \(-0.686063\pi\)
−0.843311 + 0.537426i \(0.819397\pi\)
\(662\) −22.2823 24.7470i −0.866027 0.961820i
\(663\) 16.3916 + 57.5553i 0.636598 + 2.23526i
\(664\) −53.0322 + 58.8983i −2.05805 + 2.28570i
\(665\) −12.9711 + 7.59656i −0.502998 + 0.294582i
\(666\) 41.8760 + 35.3959i 1.62266 + 1.37156i
\(667\) 23.3603 + 16.9723i 0.904516 + 0.657169i
\(668\) 13.6786 + 23.6920i 0.529240 + 0.916670i
\(669\) −17.1677 + 27.3642i −0.663740 + 1.05796i
\(670\) 2.39764 0.795521i 0.0926290 0.0307337i
\(671\) 0.393881 + 3.74752i 0.0152056 + 0.144672i
\(672\) −3.94076 + 0.687548i −0.152018 + 0.0265227i
\(673\) 13.9358 15.4773i 0.537186 0.596606i −0.412053 0.911160i \(-0.635188\pi\)
0.949240 + 0.314554i \(0.101855\pi\)
\(674\) −29.9258 −1.15270
\(675\) 5.57962 + 25.3746i 0.214760 + 0.976667i
\(676\) 49.5070 1.90411
\(677\) 4.62872 5.14071i 0.177896 0.197574i −0.647602 0.761979i \(-0.724228\pi\)
0.825498 + 0.564406i \(0.190895\pi\)
\(678\) 40.3726 7.04384i 1.55050 0.270517i
\(679\) −1.08657 10.3381i −0.0416989 0.396738i
\(680\) −48.7426 + 67.9713i −1.86919 + 2.60658i
\(681\) 15.6554 24.9538i 0.599917 0.956231i
\(682\) 0.980570 + 1.69840i 0.0375480 + 0.0650350i
\(683\) 25.6445 + 18.6318i 0.981258 + 0.712926i 0.957989 0.286803i \(-0.0925926\pi\)
0.0232689 + 0.999729i \(0.492593\pi\)
\(684\) −11.5680 + 64.2511i −0.442312 + 2.45670i
\(685\) −17.6611 15.7048i −0.674796 0.600050i
\(686\) 26.4411 29.3659i 1.00953 1.12119i
\(687\) 10.3291 + 36.2683i 0.394080 + 1.38372i
\(688\) −14.1285 15.6912i −0.538642 0.598223i
\(689\) 13.3448 + 2.83653i 0.508397 + 0.108063i
\(690\) 39.7308 + 5.40549i 1.51253 + 0.205784i
\(691\) 4.00894 0.852126i 0.152507 0.0324164i −0.131025 0.991379i \(-0.541827\pi\)
0.283533 + 0.958963i \(0.408494\pi\)
\(692\) 3.62934 + 2.63687i 0.137967 + 0.100239i
\(693\) 1.96763 0.269310i 0.0747440 0.0102302i
\(694\) 1.40496 + 1.02077i 0.0533317 + 0.0387478i
\(695\) −0.548514 1.21169i −0.0208063 0.0459622i
\(696\) −41.5584 49.7088i −1.57527 1.88421i
\(697\) 2.95109 + 28.0778i 0.111781 + 1.06352i
\(698\) −42.0727 8.94283i −1.59248 0.338491i
\(699\) −14.6144 7.16051i −0.552766 0.270835i
\(700\) −8.62773 25.4735i −0.326098 0.962808i
\(701\) 1.75231 0.0661838 0.0330919 0.999452i \(-0.489465\pi\)
0.0330919 + 0.999452i \(0.489465\pi\)
\(702\) −55.9226 + 31.8854i −2.11066 + 1.20344i
\(703\) −31.0370 + 22.5497i −1.17058 + 0.850479i
\(704\) 2.66575 + 1.18687i 0.100469 + 0.0447319i
\(705\) −11.8124 28.8701i −0.444882 1.08731i
\(706\) 11.9846 5.33591i 0.451048 0.200820i
\(707\) −10.0585 + 17.4218i −0.378287 + 0.655213i
\(708\) −11.7516 + 18.7314i −0.441653 + 0.703968i
\(709\) 24.9030 5.29330i 0.935253 0.198794i 0.285013 0.958524i \(-0.408002\pi\)
0.650239 + 0.759729i \(0.274669\pi\)
\(710\) −7.92606 + 4.64192i −0.297460 + 0.174208i
\(711\) −10.3009 0.757599i −0.386314 0.0284122i
\(712\) 16.0981 49.5449i 0.603303 1.85677i
\(713\) 6.26488 1.33164i 0.234621 0.0498703i
\(714\) 30.2459 + 23.7185i 1.13192 + 0.887642i
\(715\) −3.39435 4.61148i −0.126941 0.172460i
\(716\) −52.5971 58.4150i −1.96564 2.18307i
\(717\) −8.50534 0.312348i −0.317638 0.0116649i
\(718\) 1.34655 + 2.33230i 0.0502530 + 0.0870407i
\(719\) 9.49736 + 6.90024i 0.354192 + 0.257335i 0.750625 0.660728i \(-0.229752\pi\)
−0.396434 + 0.918063i \(0.629752\pi\)
\(720\) −31.5470 12.6504i −1.17569 0.471453i
\(721\) −15.8489 + 11.5149i −0.590244 + 0.428838i
\(722\) −18.6040 8.28303i −0.692369 0.308262i
\(723\) 12.8351 5.15886i 0.477344 0.191860i
\(724\) −30.0825 + 52.1045i −1.11801 + 1.93645i
\(725\) 22.8623 26.0336i 0.849083 0.966864i
\(726\) −41.4891 20.3281i −1.53980 0.754448i
\(727\) 13.6361 15.1445i 0.505737 0.561677i −0.435168 0.900349i \(-0.643311\pi\)
0.940905 + 0.338672i \(0.109978\pi\)
\(728\) 28.0725 20.3958i 1.04043 0.755920i
\(729\) 13.7518 23.2355i 0.509327 0.860573i
\(730\) 10.4846 + 47.8641i 0.388054 + 1.77153i
\(731\) −3.01828 + 28.7170i −0.111635 + 1.06214i
\(732\) −47.6230 23.3335i −1.76020 0.862432i
\(733\) −39.6552 + 17.6556i −1.46470 + 0.652125i −0.975490 0.220043i \(-0.929380\pi\)
−0.489207 + 0.872168i \(0.662714\pi\)
\(734\) −51.9238 57.6672i −1.91654 2.12854i
\(735\) 19.8491 5.78635i 0.732145 0.213433i
\(736\) −4.99566 + 5.54825i −0.184143 + 0.204511i
\(737\) 0.0721606 0.222087i 0.00265807 0.00818069i
\(738\) −28.5753 + 10.2841i −1.05187 + 0.378565i
\(739\) −2.42742 7.47084i −0.0892942 0.274819i 0.896431 0.443184i \(-0.146151\pi\)
−0.985725 + 0.168365i \(0.946151\pi\)
\(740\) −28.3071 62.5317i −1.04059 2.29871i
\(741\) −12.3369 43.3182i −0.453208 1.59133i
\(742\) 8.00505 3.56408i 0.293875 0.130841i
\(743\) −16.6131 + 28.7747i −0.609475 + 1.05564i 0.381852 + 0.924223i \(0.375286\pi\)
−0.991327 + 0.131418i \(0.958047\pi\)
\(744\) −14.3621 0.527432i −0.526541 0.0193366i
\(745\) −4.51763 + 0.503179i −0.165513 + 0.0184351i
\(746\) −0.496906 + 0.361023i −0.0181930 + 0.0132180i
\(747\) 10.5012 + 42.7737i 0.384219 + 1.56501i
\(748\) 4.58845 + 14.1218i 0.167770 + 0.516344i
\(749\) 6.89519 + 11.9428i 0.251945 + 0.436381i
\(750\) 10.8530 46.8724i 0.396295 1.71154i
\(751\) −16.9328 + 29.3284i −0.617886 + 1.07021i 0.371985 + 0.928239i \(0.378677\pi\)
−0.989871 + 0.141971i \(0.954656\pi\)
\(752\) 39.9163 + 8.48447i 1.45560 + 0.309397i
\(753\) 36.7019 6.40341i 1.33749 0.233353i
\(754\) 78.4256 + 34.9173i 2.85609 + 1.27161i
\(755\) 3.77306 8.61794i 0.137316 0.313639i
\(756\) −11.5061 + 25.4718i −0.418472 + 0.926402i
\(757\) −9.25569 −0.336404 −0.168202 0.985753i \(-0.553796\pi\)
−0.168202 + 0.985753i \(0.553796\pi\)
\(758\) −5.80147 + 55.1973i −0.210719 + 2.00486i
\(759\) 2.57955 2.66160i 0.0936318 0.0966098i
\(760\) 36.6854 51.1576i 1.33072 1.85568i
\(761\) −15.0763 3.20457i −0.546517 0.116166i −0.0736245 0.997286i \(-0.523457\pi\)
−0.472892 + 0.881120i \(0.656790\pi\)
\(762\) −55.2180 13.8731i −2.00034 0.502568i
\(763\) 16.7611 3.56268i 0.606792 0.128978i
\(764\) −23.8752 73.4802i −0.863773 2.65842i
\(765\) 16.0112 + 43.6367i 0.578886 + 1.57769i
\(766\) −20.3600 + 62.6615i −0.735636 + 2.26405i
\(767\) 1.59467 15.1722i 0.0575801 0.547838i
\(768\) −46.8873 + 31.5032i −1.69190 + 1.13677i
\(769\) 15.5474 6.92217i 0.560655 0.249620i −0.106786 0.994282i \(-0.534056\pi\)
0.667441 + 0.744662i \(0.267389\pi\)
\(770\) −3.50471 1.11476i −0.126301 0.0401730i
\(771\) 5.72362 15.6378i 0.206131 0.563183i
\(772\) 20.5892 + 9.16689i 0.741020 + 0.329923i
\(773\) 8.95270 + 27.5536i 0.322006 + 0.991033i 0.972774 + 0.231756i \(0.0744471\pi\)
−0.650768 + 0.759277i \(0.725553\pi\)
\(774\) −30.7741 + 4.21205i −1.10615 + 0.151399i
\(775\) −0.898098 7.63255i −0.0322606 0.274169i
\(776\) 21.7665 + 37.7007i 0.781372 + 1.35338i
\(777\) −15.2397 + 6.12536i −0.546723 + 0.219746i
\(778\) −3.37773 32.1370i −0.121098 1.15217i
\(779\) −2.22109 21.1323i −0.0795790 0.757143i
\(780\) 80.3646 5.97537i 2.87751 0.213953i
\(781\) −0.0887529 + 0.844428i −0.00317583 + 0.0302160i
\(782\) 71.7360 2.56527
\(783\) −35.8290 + 3.57020i −1.28043 + 0.127589i
\(784\) −8.35834 + 25.7243i −0.298512 + 0.918726i
\(785\) 1.24054 0.138173i 0.0442768 0.00493161i
\(786\) −6.08191 + 42.7167i −0.216934 + 1.52366i
\(787\) 5.00153 + 5.55477i 0.178285 + 0.198006i 0.825663 0.564163i \(-0.190801\pi\)
−0.647378 + 0.762169i \(0.724134\pi\)
\(788\) 43.4993 + 48.3109i 1.54960 + 1.72100i
\(789\) −15.5203 + 6.23811i −0.552537 + 0.222083i
\(790\) 16.6237 + 9.46067i 0.591445 + 0.336595i
\(791\) −3.79358 + 11.6754i −0.134884 + 0.415130i
\(792\) −7.06906 + 4.38192i −0.251188 + 0.155705i
\(793\) 36.5877 1.29927
\(794\) −7.98508 + 75.9729i −0.283380 + 2.69618i
\(795\) 10.4999 + 1.42854i 0.372392 + 0.0506651i
\(796\) 7.47108 + 71.0826i 0.264805 + 2.51946i
\(797\) −1.65961 15.7902i −0.0587865 0.559317i −0.983786 0.179348i \(-0.942601\pi\)
0.924999 0.379969i \(-0.124065\pi\)
\(798\) −22.7641 17.8514i −0.805841 0.631932i
\(799\) −27.9034 48.3301i −0.987152 1.70980i
\(800\) 6.07647 + 6.58249i 0.214836 + 0.232726i
\(801\) −17.7411 22.8770i −0.626853 0.808318i
\(802\) 7.76865 + 23.9094i 0.274320 + 0.844271i
\(803\) 4.13782 + 1.84228i 0.146021 + 0.0650126i
\(804\) 2.10795 + 2.52136i 0.0743416 + 0.0889216i
\(805\) −6.99945 + 9.76070i −0.246698 + 0.344020i
\(806\) 17.3958 7.74511i 0.612741 0.272810i
\(807\) 28.2645 + 13.8486i 0.994957 + 0.487493i
\(808\) 8.80623 83.7857i 0.309802 2.94757i
\(809\) −0.927281 + 2.85388i −0.0326015 + 0.100337i −0.966033 0.258418i \(-0.916799\pi\)
0.933432 + 0.358755i \(0.116799\pi\)
\(810\) −41.4797 + 27.9182i −1.45745 + 0.980945i
\(811\) −11.0539 34.0205i −0.388156 1.19462i −0.934165 0.356841i \(-0.883854\pi\)
0.546009 0.837779i \(-0.316146\pi\)
\(812\) 36.4589 7.74958i 1.27946 0.271957i
\(813\) −3.01627 + 3.11220i −0.105785 + 0.109150i
\(814\) −9.18105 1.95149i −0.321796 0.0683998i
\(815\) −36.7734 + 12.2012i −1.28812 + 0.427388i
\(816\) −58.9757 14.8171i −2.06456 0.518704i
\(817\) 2.27167 21.6135i 0.0794755 0.756159i
\(818\) 44.0028 1.53852
\(819\) −0.603565 19.2737i −0.0210903 0.673479i
\(820\) 37.8337 + 3.73931i 1.32121 + 0.130582i
\(821\) −42.4446 18.8975i −1.48133 0.659529i −0.502566 0.864539i \(-0.667611\pi\)
−0.978760 + 0.205010i \(0.934277\pi\)
\(822\) 15.6331 42.7121i 0.545267 1.48976i
\(823\) −40.1400 8.53203i −1.39919 0.297408i −0.554289 0.832325i \(-0.687010\pi\)
−0.844905 + 0.534917i \(0.820343\pi\)
\(824\) 41.0210 71.0504i 1.42903 2.47516i
\(825\) −2.89475 3.37643i −0.100782 0.117552i
\(826\) −4.89927 8.48578i −0.170467 0.295258i
\(827\) 12.0368 + 37.0454i 0.418560 + 1.28820i 0.909028 + 0.416736i \(0.136826\pi\)
−0.490468 + 0.871459i \(0.663174\pi\)
\(828\) 12.4373 + 50.6599i 0.432227 + 1.76055i
\(829\) −4.44553 + 3.22987i −0.154400 + 0.112178i −0.662303 0.749236i \(-0.730421\pi\)
0.507903 + 0.861414i \(0.330421\pi\)
\(830\) 16.4625 79.8839i 0.571422 2.77281i
\(831\) 12.4015 19.7673i 0.430204 0.685720i
\(832\) 14.1666 24.5373i 0.491138 0.850677i
\(833\) 33.7916 15.0450i 1.17081 0.521279i
\(834\) 1.78143 1.83809i 0.0616860 0.0636479i
\(835\) −12.7409 7.25096i −0.440918 0.250930i
\(836\) −3.45343 10.6286i −0.119439 0.367596i
\(837\) −4.72930 + 6.43592i −0.163469 + 0.222458i
\(838\) 10.3078 31.7242i 0.356078 1.09590i
\(839\) 10.5199 11.6836i 0.363188 0.403362i −0.533660 0.845699i \(-0.679184\pi\)
0.896849 + 0.442337i \(0.145851\pi\)
\(840\) 20.5695 17.4148i 0.709715 0.600867i
\(841\) 12.7251 + 14.1326i 0.438795 + 0.487331i
\(842\) 73.9958 32.9450i 2.55006 1.13536i
\(843\) −0.0889851 1.30635i −0.00306481 0.0449930i
\(844\) 6.31241 60.0586i 0.217282 2.06730i
\(845\) −22.8921 + 13.4068i −0.787512 + 0.461209i
\(846\) 43.3328 41.5454i 1.48981 1.42836i
\(847\) 11.1965 8.13473i 0.384716 0.279512i
\(848\) −9.27606 + 10.3021i −0.318541 + 0.353776i
\(849\) −6.02059 + 4.04519i −0.206626 + 0.138830i
\(850\) 7.93454 85.7100i 0.272153 2.93983i
\(851\) −15.3270 + 26.5472i −0.525403 + 0.910025i
\(852\) −9.40323 7.37391i −0.322149 0.252626i
\(853\) 1.27176 + 0.566226i 0.0435444 + 0.0193872i 0.428393 0.903592i \(-0.359080\pi\)
−0.384849 + 0.922980i \(0.625746\pi\)
\(854\) 19.0116 13.8127i 0.650564 0.472662i
\(855\) −12.0506 32.8425i −0.412122 1.12319i
\(856\) −46.7227 33.9460i −1.59695 1.16025i
\(857\) −12.7340 22.0559i −0.434985 0.753415i 0.562310 0.826927i \(-0.309913\pi\)
−0.997294 + 0.0735113i \(0.976580\pi\)
\(858\) 5.85638 9.33472i 0.199934 0.318682i
\(859\) −4.28776 4.76204i −0.146297 0.162479i 0.665543 0.746360i \(-0.268200\pi\)
−0.811839 + 0.583881i \(0.801533\pi\)
\(860\) 37.0544 + 11.7860i 1.26354 + 0.401900i
\(861\) 1.28230 9.00635i 0.0437008 0.306936i
\(862\) −21.7628 + 4.62582i −0.741243 + 0.157556i
\(863\) −3.68829 + 11.3514i −0.125551 + 0.386406i −0.994001 0.109370i \(-0.965117\pi\)
0.868450 + 0.495777i \(0.165117\pi\)
\(864\) 0.0502928 9.30969i 0.00171100 0.316722i
\(865\) −2.39229 0.236443i −0.0813404 0.00803931i
\(866\) −67.7386 + 14.3983i −2.30185 + 0.489273i
\(867\) 25.1315 + 47.4716i 0.853512 + 1.61222i
\(868\) 4.13386 7.16006i 0.140312 0.243028i
\(869\) 1.61524 0.719151i 0.0547933 0.0243955i
\(870\) 62.7572 + 22.5293i 2.12767 + 0.763814i
\(871\) −2.07135 0.922224i −0.0701850 0.0312484i
\(872\) −58.0563 + 42.1804i −1.96603 + 1.42841i
\(873\) 24.1270 + 1.77446i 0.816576 + 0.0600565i
\(874\) −53.9910 −1.82627
\(875\) 10.8879 + 9.44254i 0.368077 + 0.319216i
\(876\) −52.9116 + 35.5509i −1.78772 + 1.20115i
\(877\) 0.819396 + 0.174168i 0.0276690 + 0.00588123i 0.221725 0.975109i \(-0.428831\pi\)
−0.194056 + 0.980990i \(0.562164\pi\)
\(878\) −0.816658 7.76998i −0.0275609 0.262224i
\(879\) −15.5982 + 42.6169i −0.526115 + 1.43743i
\(880\) 5.78256 0.644069i 0.194930 0.0217116i
\(881\) −8.77572 6.37593i −0.295661 0.214811i 0.430058 0.902801i \(-0.358493\pi\)
−0.725720 + 0.687991i \(0.758493\pi\)
\(882\) 24.3838 + 31.4426i 0.821046 + 1.05873i
\(883\) −29.2715 21.2670i −0.985064 0.715691i −0.0262292 0.999656i \(-0.508350\pi\)
−0.958835 + 0.283965i \(0.908350\pi\)
\(884\) 141.024 29.9756i 4.74316 1.00819i
\(885\) 0.361385 11.8438i 0.0121478 0.398126i
\(886\) −47.9579 10.1938i −1.61118 0.342466i
\(887\) −30.3562 33.7140i −1.01926 1.13201i −0.991196 0.132399i \(-0.957732\pi\)
−0.0280658 0.999606i \(-0.508935\pi\)
\(888\) 47.8708 49.3933i 1.60644 1.65753i
\(889\) 11.4117 12.6740i 0.382738 0.425073i
\(890\) 11.4715 + 52.3694i 0.384526 + 1.75543i
\(891\) −0.194570 + 4.61784i −0.00651833 + 0.154703i
\(892\) 62.9620 + 45.7446i 2.10812 + 1.53164i
\(893\) 21.0011 + 36.3750i 0.702775 + 1.21724i
\(894\) −4.09299 7.73135i −0.136890 0.258575i
\(895\) 40.1401 + 12.7675i 1.34174 + 0.426772i
\(896\) −2.38503 22.6920i −0.0796782 0.758088i
\(897\) −23.0836 27.6108i −0.770740 0.921898i
\(898\) 22.8965 25.4291i 0.764066 0.848581i
\(899\) 10.6509 0.355226
\(900\) 61.9040 9.25671i 2.06347 0.308557i
\(901\) 18.9581 0.631585
\(902\) 3.47864 3.86342i 0.115826 0.128638i
\(903\) 3.19800 8.73744i 0.106423 0.290764i
\(904\) −5.37397 51.1299i −0.178736 1.70055i
\(905\) −0.200027 32.2398i −0.00664912 1.07169i
\(906\) 18.0929 + 0.664440i 0.601097 + 0.0220746i
\(907\) −8.10153 14.0323i −0.269007 0.465933i 0.699599 0.714536i \(-0.253362\pi\)
−0.968606 + 0.248602i \(0.920029\pi\)
\(908\) −57.4159 41.7151i −1.90541 1.38436i
\(909\) −35.7560 30.2229i −1.18595 1.00243i
\(910\) −14.3217 + 32.7118i −0.474760 + 1.08439i
\(911\) −9.27545 + 10.3014i −0.307309 + 0.341302i −0.876941 0.480599i \(-0.840419\pi\)
0.569631 + 0.821900i \(0.307086\pi\)
\(912\) 44.3872 + 11.1519i 1.46981 + 0.369277i
\(913\) −5.04494 5.60298i −0.166963 0.185431i
\(914\) −39.0474 8.29977i −1.29157 0.274532i
\(915\) 28.3398 2.10716i 0.936886 0.0696606i
\(916\) 88.8658 18.8890i 2.93621 0.624111i
\(917\) −10.4564 7.59702i −0.345301 0.250876i
\(918\) −66.7991 + 59.4960i −2.20470 + 1.96366i
\(919\) 33.8071 + 24.5623i 1.11519 + 0.810236i 0.983474 0.181051i \(-0.0579500\pi\)
0.131720 + 0.991287i \(0.457950\pi\)
\(920\) 10.1526 49.2653i 0.334722 1.62423i
\(921\) 23.3158 4.06793i 0.768282 0.134043i
\(922\) 2.66667 + 25.3717i 0.0878221 + 0.835571i
\(923\) 8.06414 + 1.71409i 0.265434 + 0.0564198i
\(924\) −0.325159 4.77350i −0.0106969 0.157037i
\(925\) 30.0232 + 21.2490i 0.987157 + 0.698663i
\(926\) −44.7769 −1.47146
\(927\) −19.8387 41.0499i −0.651587 1.34825i
\(928\) −10.0442 + 7.29755i −0.329718 + 0.239554i
\(929\) −28.4644 12.6732i −0.933888 0.415794i −0.117353 0.993090i \(-0.537441\pi\)
−0.816535 + 0.577297i \(0.804108\pi\)
\(930\) 13.0282 7.00100i 0.427213 0.229572i
\(931\) −25.4328 + 11.3234i −0.833526 + 0.371110i
\(932\) −19.6038 + 33.9548i −0.642145 + 1.11223i
\(933\) −1.65359 0.0607261i −0.0541361 0.00198808i
\(934\) −85.8314 + 18.2440i −2.80849 + 0.596963i
\(935\) −5.94598 5.28736i −0.194454 0.172915i
\(936\) 35.1393 + 72.7098i 1.14857 + 2.37659i
\(937\) −11.2706 + 34.6872i −0.368193 + 1.13318i 0.579764 + 0.814784i \(0.303145\pi\)
−0.947957 + 0.318398i \(0.896855\pi\)
\(938\) −1.42447 + 0.302780i −0.0465106 + 0.00988613i
\(939\) 19.2625 7.74225i 0.628609 0.252659i
\(940\) −71.3264 + 23.6656i −2.32641 + 0.771887i
\(941\) 10.4003 + 11.5507i 0.339041 + 0.376543i 0.888421 0.459029i \(-0.151803\pi\)
−0.549380 + 0.835573i \(0.685136\pi\)
\(942\) 1.12394 + 2.12303i 0.0366198 + 0.0691720i
\(943\) −8.48922 14.7038i −0.276447 0.478820i
\(944\) 12.5412 + 9.11169i 0.408180 + 0.296560i
\(945\) −1.57752 14.8941i −0.0513166 0.484506i
\(946\) 4.30163 3.12532i 0.139858 0.101613i
\(947\) −14.8544 6.61361i −0.482704 0.214914i 0.150933 0.988544i \(-0.451772\pi\)
−0.633637 + 0.773630i \(0.718439\pi\)
\(948\) −3.50751 + 24.6353i −0.113919 + 0.800117i
\(949\) 21.9896 38.0871i 0.713813 1.23636i
\(950\) −5.97182 + 64.5084i −0.193751 + 2.09293i
\(951\) 0.265752 + 3.90138i 0.00861760 + 0.126511i
\(952\) 32.2641 35.8329i 1.04569 1.16135i
\(953\) 29.6469 21.5397i 0.960357 0.697741i 0.00712369 0.999975i \(-0.497732\pi\)
0.953234 + 0.302234i \(0.0977324\pi\)
\(954\) 4.86226 + 19.8050i 0.157421 + 0.641212i
\(955\) 30.9388 + 27.5118i 1.00116 + 0.890261i
\(956\) −2.14332 + 20.3924i −0.0693200 + 0.659536i
\(957\) 5.11613 3.43748i 0.165381 0.111118i
\(958\) 3.87900 1.72704i 0.125325 0.0557981i
\(959\) 9.11654 + 10.1249i 0.294389 + 0.326952i
\(960\) 9.55989 19.8217i 0.308544 0.639744i
\(961\) −19.1622 + 21.2818i −0.618136 + 0.686510i
\(962\) −28.1628 + 86.6762i −0.908006 + 2.79455i
\(963\) −30.1980 + 10.8682i −0.973118 + 0.350222i
\(964\) −10.2984 31.6953i −0.331690 1.02084i
\(965\) −12.0029 + 1.33690i −0.386388 + 0.0430363i
\(966\) −22.4184 5.63243i −0.721300 0.181220i
\(967\) −37.2631 + 16.5906i −1.19830 + 0.533517i −0.906191 0.422868i \(-0.861023\pi\)
−0.292108 + 0.956385i \(0.594357\pi\)
\(968\) −28.9793 + 50.1937i −0.931431 + 1.61329i
\(969\) −29.2837 55.3147i −0.940728 1.77696i
\(970\) −38.9364 22.1590i −1.25017 0.711482i
\(971\) 36.3301 26.3954i 1.16589 0.847068i 0.175378 0.984501i \(-0.443885\pi\)
0.990511 + 0.137433i \(0.0438852\pi\)
\(972\) −53.5974 36.8583i −1.71914 1.18223i
\(973\) 0.236941 + 0.729230i 0.00759599 + 0.0233780i
\(974\) 40.6362 + 70.3840i 1.30207 + 2.25525i
\(975\) −35.5426 + 24.5263i −1.13827 + 0.785470i
\(976\) −18.5888 + 32.1967i −0.595011 + 1.03059i
\(977\) 6.51932 + 1.38572i 0.208571 + 0.0443332i 0.311012 0.950406i \(-0.399332\pi\)
−0.102441 + 0.994739i \(0.532665\pi\)
\(978\) −47.8260 57.2056i −1.52931 1.82923i
\(979\) 4.52730 + 2.01568i 0.144693 + 0.0644215i
\(980\) −10.6583 48.6568i −0.340466 1.55429i
\(981\) 1.24822 + 39.8598i 0.0398528 + 1.27263i
\(982\) −102.522 −3.27161
\(983\) 3.26978 31.1098i 0.104290 0.992250i −0.809791 0.586718i \(-0.800420\pi\)
0.914081 0.405532i \(-0.132914\pi\)
\(984\) 10.4352 + 36.6409i 0.332663 + 1.16807i
\(985\) −33.1971 10.5591i −1.05775 0.336442i
\(986\) 116.686 + 24.8023i 3.71603 + 0.789867i
\(987\) 4.92547 + 17.2946i 0.156779 + 0.550494i
\(988\) −106.140 + 22.5607i −3.37676 + 0.717751i
\(989\) −5.36608 16.5151i −0.170632 0.525150i
\(990\) 3.99858 7.56769i 0.127083 0.240517i
\(991\) −1.60963 + 4.95394i −0.0511317 + 0.157367i −0.973362 0.229274i \(-0.926365\pi\)
0.922230 + 0.386641i \(0.126365\pi\)
\(992\) −0.287859 + 2.73880i −0.00913953 + 0.0869568i
\(993\) 1.57769 + 23.1613i 0.0500665 + 0.735002i
\(994\) 4.83737 2.15374i 0.153432 0.0683124i
\(995\) −22.7043 30.8455i −0.719774 0.977868i
\(996\) 104.530 18.2375i 3.31217 0.577878i
\(997\) −20.9597 9.33186i −0.663800 0.295543i 0.0470436 0.998893i \(-0.485020\pi\)
−0.710844 + 0.703350i \(0.751687\pi\)
\(998\) 2.67071 + 8.21961i 0.0845399 + 0.260187i
\(999\) −7.74532 37.4320i −0.245051 1.18430i
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 225.2.q.a.31.2 224
3.2 odd 2 675.2.r.a.631.27 224
9.2 odd 6 675.2.r.a.181.2 224
9.7 even 3 inner 225.2.q.a.106.27 yes 224
25.21 even 5 inner 225.2.q.a.121.27 yes 224
75.71 odd 10 675.2.r.a.496.2 224
225.146 odd 30 675.2.r.a.46.27 224
225.196 even 15 inner 225.2.q.a.196.2 yes 224
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
225.2.q.a.31.2 224 1.1 even 1 trivial
225.2.q.a.106.27 yes 224 9.7 even 3 inner
225.2.q.a.121.27 yes 224 25.21 even 5 inner
225.2.q.a.196.2 yes 224 225.196 even 15 inner
675.2.r.a.46.27 224 225.146 odd 30
675.2.r.a.181.2 224 9.2 odd 6
675.2.r.a.496.2 224 75.71 odd 10
675.2.r.a.631.27 224 3.2 odd 2